%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : CAT002-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 12:07:39 PM UTC 2026
% Result : Satisfiable 9.72s 1.92s
% Output : Saturation 0.81s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : codomain(domain(X)) = domain(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : domain(codomain(X)) = codomain(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : compose(domain(X),X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : compose(X,codomain(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( domain(compose(X,Y)) = domain(X)
| codomain(X) != domain(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( codomain(compose(X,Y)) = codomain(Y)
| codomain(X) != domain(Y) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
codomain(a) = domain(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
! [X,Y,Z] :
( X = Z
| compose(Z,a) != Y
| codomain(Z) != domain(b)
| compose(X,a) != Y
| codomain(X) != domain(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
! [X,Y,Z] :
( X = Z
| compose(Z,b) != Y
| codomain(Z) != domain(b)
| compose(X,b) != Y
| codomain(X) != domain(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
codomain(h) = domain(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
codomain(g) = domain(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0] : codomain(domain(X0)) = domain(X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0] : domain(codomain(X0)) = codomain(X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0] : compose(domain(X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0] : compose(X0,codomain(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X0,X1] :
( domain(compose(X0,X1)) = domain(X0)
| codomain(X0) != domain(X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0,X1] :
( codomain(compose(X0,X1)) = codomain(X1)
| codomain(X0) != domain(X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,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(f22,plain,
codomain(a) = domain(b),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
! [X,Z] :
( X = Z
| ! [Y] :
( compose(Z,a) != Y
| codomain(Z) != domain(b)
| compose(X,a) != Y
| codomain(X) != domain(a) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f24,plain,
! [X0,X1,X2] :
( X0 = X2
| compose(X2,a) != X1
| codomain(X2) != domain(b)
| compose(X0,a) != X1
| codomain(X0) != domain(a) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X,Z] :
( X = Z
| ! [Y] :
( compose(Z,b) != Y
| codomain(Z) != domain(b)
| compose(X,b) != Y
| codomain(X) != domain(a) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0,X1,X2] :
( X0 = X2
| compose(X2,b) != X1
| codomain(X2) != domain(b)
| compose(X0,b) != X1
| codomain(X0) != domain(a) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
codomain(h) = domain(compose(a,b)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
codomain(g) = domain(compose(a,b)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f30,plain,
h != g,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f31,plain,
! [X0,X1] :
( X0 = X1
| compose(X1,a) != compose(X0,a)
| codomain(X1) != domain(b)
| codomain(X0) != domain(a) ),
inference(destructive_equality_resolution,[status(thm)],[f24]) ).
fof(f32,plain,
! [X0,X1] :
( X0 = X1
| compose(X1,b) != compose(X0,b)
| codomain(X1) != domain(b)
| codomain(X0) != domain(a) ),
inference(destructive_equality_resolution,[status(thm)],[f26]) ).
fof(f33,plain,
codomain(g) = codomain(h),
inference(forward_demodulation,[status(thm)],[f27,f28]) ).
fof(f34,plain,
! [X0] : domain(domain(X0)) = codomain(domain(X0)),
inference(paramodulation,[status(thm)],[f15,f16]) ).
fof(f35,plain,
! [X0] : codomain(codomain(X0)) = domain(codomain(X0)),
inference(paramodulation,[status(thm)],[f16,f15]) ).
fof(f36,plain,
! [X0] : compose(codomain(X0),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f37,plain,
! [X0] : domain(domain(X0)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f15,f34]) ).
fof(f38,plain,
! [X0] : codomain(codomain(X0)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f16,f35]) ).
fof(f42,plain,
! [X0] : compose(domain(X0),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f37,f17]) ).
fof(f50,plain,
compose(a,domain(b)) = a,
inference(paramodulation,[status(thm)],[f22,f18]) ).
fof(f55,plain,
compose(g,codomain(h)) = g,
inference(paramodulation,[status(thm)],[f33,f18]) ).
fof(f60,plain,
domain(compose(a,b)) = domain(a),
inference(resolution,[status(thm)],[f19,f22]) ).
fof(f63,plain,
! [X0] :
( domain(compose(g,X0)) = domain(g)
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f33,f19]) ).
fof(f64,plain,
! [X0] :
( domain(compose(a,X0)) = domain(a)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f22,f19]) ).
fof(f65,plain,
! [X0,X1] :
( domain(compose(codomain(X0),X1)) = domain(codomain(X0))
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f19]) ).
fof(f66,plain,
! [X0,X1] :
( domain(compose(domain(X0),X1)) = domain(domain(X0))
| domain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f15,f19]) ).
fof(f67,plain,
! [X0,X1] :
( domain(compose(X0,domain(X1))) = domain(X0)
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f37,f19]) ).
fof(f68,plain,
! [X0,X1] :
( domain(compose(X0,codomain(X1))) = domain(X0)
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f16,f19]) ).
fof(f69,plain,
codomain(h) = domain(a),
inference(backward_demodulation,[status(thm)],[f60,f27]) ).
fof(f71,plain,
! [X0,X1] :
( domain(compose(codomain(X0),X1)) = codomain(X0)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f16,f65]) ).
fof(f72,plain,
! [X0,X1] :
( domain(compose(domain(X0),X1)) = domain(X0)
| domain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f37,f66]) ).
fof(f73,plain,
compose(g,domain(a)) = g,
inference(backward_demodulation,[status(thm)],[f69,f55]) ).
fof(f74,plain,
codomain(g) = domain(a),
inference(backward_demodulation,[status(thm)],[f69,f33]) ).
fof(f75,plain,
! [X0] :
( domain(compose(g,X0)) = domain(g)
| domain(a) != domain(X0) ),
inference(backward_demodulation,[status(thm)],[f69,f63]) ).
fof(f76,plain,
domain(compose(h,a)) = domain(h),
inference(resolution,[status(thm)],[f69,f19]) ).
fof(f77,plain,
! [X0] :
( domain(compose(h,X0)) = domain(h)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f69,f19]) ).
fof(f78,plain,
compose(h,domain(a)) = h,
inference(paramodulation,[status(thm)],[f69,f18]) ).
fof(f83,plain,
domain(compose(g,a)) = domain(g),
inference(resolution,[status(thm)],[f74,f19]) ).
fof(f118,plain,
codomain(compose(g,a)) = codomain(a),
inference(resolution,[status(thm)],[f20,f74]) ).
fof(f119,plain,
codomain(compose(h,a)) = codomain(a),
inference(resolution,[status(thm)],[f20,f69]) ).
fof(f120,plain,
codomain(compose(a,b)) = codomain(b),
inference(resolution,[status(thm)],[f20,f22]) ).
fof(f123,plain,
! [X0] :
( codomain(compose(g,X0)) = codomain(X0)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f74,f20]) ).
fof(f124,plain,
! [X0] :
( codomain(compose(h,X0)) = codomain(X0)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f69,f20]) ).
fof(f125,plain,
! [X0] :
( codomain(compose(a,X0)) = codomain(X0)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f126,plain,
! [X0,X1] :
( codomain(compose(codomain(X0),X1)) = codomain(X1)
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f20]) ).
fof(f127,plain,
! [X0,X1] :
( codomain(compose(domain(X0),X1)) = codomain(X1)
| domain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f15,f20]) ).
fof(f128,plain,
! [X0,X1] :
( codomain(compose(X0,domain(X1))) = codomain(domain(X1))
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f37,f20]) ).
fof(f129,plain,
! [X0,X1] :
( codomain(compose(X0,codomain(X1))) = codomain(codomain(X1))
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f16,f20]) ).
fof(f130,plain,
codomain(compose(g,a)) = domain(b),
inference(forward_demodulation,[status(thm)],[f22,f118]) ).
fof(f131,plain,
codomain(compose(h,a)) = domain(b),
inference(forward_demodulation,[status(thm)],[f22,f119]) ).
fof(f133,plain,
! [X0,X1] :
( codomain(compose(X0,domain(X1))) = domain(X1)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f15,f128]) ).
fof(f134,plain,
! [X0,X1] :
( codomain(compose(X0,codomain(X1))) = codomain(X1)
| codomain(X0) != codomain(X1) ),
inference(forward_demodulation,[status(thm)],[f38,f129]) ).
fof(f147,plain,
! [X0] :
( codomain(compose(X0,compose(a,b))) = codomain(compose(a,b))
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f20]) ).
fof(f148,plain,
! [X0] :
( domain(compose(X0,compose(a,b))) = domain(X0)
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f19]) ).
fof(f151,plain,
compose(domain(a),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f60,f17]) ).
fof(f156,plain,
! [X0] :
( codomain(compose(X0,compose(a,b))) = codomain(b)
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f120,f147]) ).
fof(f161,plain,
! [X0] :
( codomain(compose(X0,compose(h,a))) = codomain(compose(h,a))
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f20]) ).
fof(f162,plain,
! [X0] :
( domain(compose(X0,compose(h,a))) = domain(X0)
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f19]) ).
fof(f165,plain,
compose(domain(h),compose(h,a)) = compose(h,a),
inference(paramodulation,[status(thm)],[f76,f17]) ).
fof(f170,plain,
! [X0] :
( codomain(compose(X0,compose(h,a))) = domain(b)
| codomain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f131,f161]) ).
fof(f175,plain,
! [X0] :
( codomain(compose(X0,compose(g,a))) = codomain(compose(g,a))
| codomain(X0) != domain(g) ),
inference(paramodulation,[status(thm)],[f83,f20]) ).
fof(f176,plain,
! [X0] :
( domain(compose(X0,compose(g,a))) = domain(X0)
| codomain(X0) != domain(g) ),
inference(paramodulation,[status(thm)],[f83,f19]) ).
fof(f179,plain,
compose(domain(g),compose(g,a)) = compose(g,a),
inference(paramodulation,[status(thm)],[f83,f17]) ).
fof(f184,plain,
! [X0] :
( codomain(compose(X0,compose(g,a))) = domain(b)
| codomain(X0) != domain(g) ),
inference(forward_demodulation,[status(thm)],[f130,f175]) ).
fof(f188,plain,
domain(compose(compose(g,a),b)) = domain(compose(g,a)),
inference(resolution,[status(thm)],[f130,f19]) ).
fof(f189,plain,
! [X0] :
( codomain(compose(compose(g,a),X0)) = codomain(X0)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f130,f20]) ).
fof(f192,plain,
! [X0] :
( domain(compose(compose(g,a),X0)) = domain(compose(g,a))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f130,f19]) ).
fof(f193,plain,
compose(compose(g,a),domain(b)) = compose(g,a),
inference(paramodulation,[status(thm)],[f130,f18]) ).
fof(f196,plain,
domain(compose(compose(g,a),b)) = domain(g),
inference(forward_demodulation,[status(thm)],[f83,f188]) ).
fof(f201,plain,
! [X0] :
( domain(compose(compose(g,a),X0)) = domain(g)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f83,f192]) ).
fof(f204,plain,
! [X0] :
( compose(compose(g,a),compose(b,X0)) = compose(compose(compose(g,a),b),X0)
| codomain(b) != domain(X0) ),
inference(resolution,[status(thm)],[f21,f130]) ).
fof(f205,plain,
! [X0] :
( compose(g,compose(a,X0)) = compose(compose(g,a),X0)
| codomain(a) != domain(X0) ),
inference(resolution,[status(thm)],[f21,f74]) ).
fof(f206,plain,
! [X0] :
( compose(h,compose(a,X0)) = compose(compose(h,a),X0)
| codomain(a) != domain(X0) ),
inference(resolution,[status(thm)],[f21,f69]) ).
fof(f207,plain,
! [X0] :
( compose(a,compose(b,X0)) = compose(compose(a,b),X0)
| codomain(b) != domain(X0) ),
inference(resolution,[status(thm)],[f21,f22]) ).
fof(f208,plain,
! [X0,X1] :
( compose(domain(X0),compose(X0,X1)) = compose(compose(domain(X0),X0),X1)
| codomain(X0) != domain(X1) ),
inference(resolution,[status(thm)],[f21,f15]) ).
fof(f209,plain,
! [X0,X1] :
( compose(X0,compose(codomain(X0),X1)) = compose(compose(X0,codomain(X0)),X1)
| codomain(codomain(X0)) != domain(X1) ),
inference(resolution,[status(thm)],[f21,f16]) ).
fof(f210,plain,
! [X0,X1] :
( compose(compose(g,a),compose(X0,X1)) = compose(compose(compose(g,a),X0),X1)
| codomain(X0) != domain(X1)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f130,f21]) ).
fof(f211,plain,
! [X0,X1] :
( compose(g,compose(X0,X1)) = compose(compose(g,X0),X1)
| codomain(X0) != domain(X1)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f74,f21]) ).
fof(f212,plain,
! [X0,X1] :
( compose(h,compose(X0,X1)) = compose(compose(h,X0),X1)
| codomain(X0) != domain(X1)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f69,f21]) ).
fof(f213,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)],[f22,f21]) ).
fof(f214,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)],[f38,f21]) ).
fof(f215,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)],[f15,f21]) ).
fof(f216,plain,
! [X0,X1] :
( compose(X0,compose(compose(g,a),X1)) = compose(compose(X0,compose(g,a)),X1)
| codomain(compose(g,a)) != domain(X1)
| codomain(X0) != domain(g) ),
inference(paramodulation,[status(thm)],[f83,f21]) ).
fof(f217,plain,
! [X0,X1] :
( compose(X0,compose(compose(h,a),X1)) = compose(compose(X0,compose(h,a)),X1)
| codomain(compose(h,a)) != domain(X1)
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f21]) ).
fof(f218,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)],[f60,f21]) ).
fof(f219,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)],[f37,f21]) ).
fof(f220,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)],[f16,f21]) ).
fof(f221,plain,
! [X0] :
( compose(g,compose(a,X0)) = compose(compose(g,a),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f22,f205]) ).
fof(f222,plain,
! [X0] :
( compose(h,compose(a,X0)) = compose(compose(h,a),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f22,f206]) ).
fof(f223,plain,
! [X0,X1] :
( compose(domain(X0),compose(X0,X1)) = compose(X0,X1)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f17,f208]) ).
fof(f224,plain,
! [X0,X1] :
( compose(X0,compose(codomain(X0),X1)) = compose(compose(X0,codomain(X0)),X1)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f38,f209]) ).
fof(f225,plain,
! [X0,X1] :
( compose(X0,compose(codomain(X0),X1)) = compose(X0,X1)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f18,f224]) ).
fof(f226,plain,
! [X0,X1] :
( compose(X0,compose(compose(g,a),X1)) = compose(compose(X0,compose(g,a)),X1)
| domain(b) != domain(X1)
| codomain(X0) != domain(g) ),
inference(forward_demodulation,[status(thm)],[f130,f216]) ).
fof(f227,plain,
! [X0,X1] :
( compose(X0,compose(compose(h,a),X1)) = compose(compose(X0,compose(h,a)),X1)
| domain(b) != domain(X1)
| codomain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f131,f217]) ).
fof(f228,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)],[f120,f218]) ).
fof(f229,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)],[f15,f219]) ).
fof(f230,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)],[f38,f220]) ).
fof(f231,plain,
! [X0] :
( compose(compose(h,a),compose(b,X0)) = compose(compose(compose(h,a),b),X0)
| codomain(b) != domain(X0) ),
inference(resolution,[status(thm)],[f131,f21]) ).
fof(f233,plain,
domain(compose(compose(h,a),b)) = domain(compose(h,a)),
inference(resolution,[status(thm)],[f131,f19]) ).
fof(f234,plain,
! [X0,X1] :
( compose(compose(h,a),compose(X0,X1)) = compose(compose(compose(h,a),X0),X1)
| codomain(X0) != domain(X1)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f131,f21]) ).
fof(f235,plain,
! [X0] :
( codomain(compose(compose(h,a),X0)) = codomain(X0)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f131,f20]) ).
fof(f238,plain,
! [X0] :
( domain(compose(compose(h,a),X0)) = domain(compose(h,a))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f131,f19]) ).
fof(f239,plain,
compose(compose(h,a),domain(b)) = compose(h,a),
inference(paramodulation,[status(thm)],[f131,f18]) ).
fof(f242,plain,
domain(compose(compose(h,a),b)) = domain(h),
inference(forward_demodulation,[status(thm)],[f76,f233]) ).
fof(f247,plain,
! [X0] :
( domain(compose(compose(h,a),X0)) = domain(h)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f76,f238]) ).
fof(f250,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)],[f120,f21]) ).
fof(f251,plain,
! [X0] :
( codomain(compose(compose(a,b),X0)) = codomain(X0)
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f120,f20]) ).
fof(f254,plain,
! [X0] :
( domain(compose(compose(a,b),X0)) = domain(compose(a,b))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f120,f19]) ).
fof(f255,plain,
compose(compose(a,b),codomain(b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f120,f18]) ).
fof(f262,plain,
! [X0] :
( domain(compose(compose(a,b),X0)) = domain(a)
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f60,f254]) ).
fof(f311,plain,
! [X0] :
( X0 = domain(a)
| a != compose(X0,a)
| codomain(domain(a)) != domain(b)
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f17,f31]) ).
fof(f312,plain,
! [X0] :
( domain(a) = X0
| compose(X0,a) != a
| codomain(X0) != domain(b)
| codomain(domain(a)) != domain(a) ),
inference(paramodulation,[status(thm)],[f17,f31]) ).
fof(f314,definition,
! [X0] :
( sQ0_spl
<=> ( X0 = domain(a)
| a != compose(X0,a)
| codomain(X0) != domain(a) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f315,plain,
! [X0] :
( ~ sQ0_spl
| X0 = domain(a)
| a != compose(X0,a)
| codomain(X0) != domain(a) ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,definition,
( sQ1_spl
<=> codomain(domain(a)) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f319,plain,
( sQ1_spl
| codomain(domain(a)) != domain(b) ),
inference(component_clause,[status(thm)],[f317]) ).
fof(f320,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f311,f314,f317]) ).
fof(f321,definition,
( sQ2_spl
<=> codomain(domain(a)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f323,plain,
( sQ2_spl
| codomain(domain(a)) != domain(a) ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f324,definition,
! [X0] :
( sQ3_spl
<=> ( domain(a) = X0
| compose(X0,a) != a
| codomain(X0) != domain(b) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f325,plain,
! [X0] :
( ~ sQ3_spl
| domain(a) = X0
| compose(X0,a) != a
| codomain(X0) != domain(b) ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f327,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f312,f321,f324]) ).
fof(f328,plain,
( sQ2_spl
| domain(a) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f15,f323]) ).
fof(f329,plain,
( sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f328]) ).
fof(f330,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f329]) ).
fof(f366,plain,
! [X0] :
( domain(compose(codomain(X0),compose(g,a))) = codomain(X0)
| codomain(X0) != domain(g) ),
inference(paramodulation,[status(thm)],[f83,f71]) ).
fof(f367,plain,
! [X0] :
( domain(compose(codomain(X0),compose(h,a))) = codomain(X0)
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f71]) ).
fof(f368,plain,
! [X0] :
( domain(compose(codomain(X0),compose(a,b))) = codomain(X0)
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f71]) ).
fof(f369,plain,
! [X0,X1] :
( domain(compose(codomain(X0),domain(X1))) = codomain(X0)
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f37,f71]) ).
fof(f370,plain,
! [X0,X1] :
( domain(compose(codomain(X0),codomain(X1))) = codomain(X0)
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f16,f71]) ).
fof(f425,plain,
! [X0] :
( domain(compose(domain(X0),compose(g,a))) = domain(X0)
| domain(X0) != domain(g) ),
inference(paramodulation,[status(thm)],[f83,f72]) ).
fof(f426,plain,
! [X0] :
( domain(compose(domain(X0),compose(h,a))) = domain(X0)
| domain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f72]) ).
fof(f427,plain,
! [X0] :
( domain(compose(domain(X0),compose(a,b))) = domain(X0)
| domain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f72]) ).
fof(f428,plain,
! [X0,X1] :
( domain(compose(domain(X0),domain(X1))) = domain(X0)
| domain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f37,f72]) ).
fof(f429,plain,
! [X0,X1] :
( domain(compose(domain(X0),codomain(X1))) = domain(X0)
| domain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f16,f72]) ).
fof(f472,plain,
! [X0] :
( domain(compose(compose(a,b),domain(X0))) = domain(compose(a,b))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f120,f67]) ).
fof(f473,plain,
! [X0] :
( domain(compose(compose(h,a),domain(X0))) = domain(compose(h,a))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f131,f67]) ).
fof(f474,plain,
! [X0] :
( domain(compose(compose(g,a),domain(X0))) = domain(compose(g,a))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f130,f67]) ).
fof(f475,plain,
! [X0] :
( domain(compose(g,domain(X0))) = domain(g)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f74,f67]) ).
fof(f476,plain,
! [X0] :
( domain(compose(h,domain(X0))) = domain(h)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f69,f67]) ).
fof(f477,plain,
! [X0] :
( domain(compose(a,domain(X0))) = domain(a)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f22,f67]) ).
fof(f490,plain,
! [X0] :
( domain(compose(compose(a,b),domain(X0))) = domain(a)
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f60,f472]) ).
fof(f491,plain,
! [X0] :
( domain(compose(compose(h,a),domain(X0))) = domain(h)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f76,f473]) ).
fof(f492,plain,
! [X0] :
( domain(compose(compose(g,a),domain(X0))) = domain(g)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f83,f474]) ).
fof(f512,plain,
! [X0] :
( domain(compose(compose(a,b),codomain(X0))) = domain(compose(a,b))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f120,f68]) ).
fof(f513,plain,
! [X0] :
( domain(compose(compose(h,a),codomain(X0))) = domain(compose(h,a))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f131,f68]) ).
fof(f514,plain,
! [X0] :
( domain(compose(compose(g,a),codomain(X0))) = domain(compose(g,a))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f130,f68]) ).
fof(f515,plain,
! [X0] :
( domain(compose(g,codomain(X0))) = domain(g)
| domain(a) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f74,f68]) ).
fof(f516,plain,
! [X0] :
( domain(compose(h,codomain(X0))) = domain(h)
| domain(a) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f69,f68]) ).
fof(f517,plain,
! [X0] :
( domain(compose(a,codomain(X0))) = domain(a)
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f22,f68]) ).
fof(f537,plain,
! [X0] :
( domain(compose(compose(a,b),codomain(X0))) = domain(a)
| codomain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f60,f512]) ).
fof(f538,plain,
! [X0] :
( domain(compose(compose(h,a),codomain(X0))) = domain(h)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f76,f513]) ).
fof(f539,plain,
! [X0] :
( domain(compose(compose(g,a),codomain(X0))) = domain(g)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f83,f514]) ).
fof(f552,plain,
! [X0] :
( X0 = domain(b)
| b != compose(X0,b)
| codomain(domain(b)) != domain(b)
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f17,f32]) ).
fof(f553,plain,
! [X0] :
( domain(b) = X0
| compose(X0,b) != b
| codomain(X0) != domain(b)
| codomain(domain(b)) != domain(a) ),
inference(paramodulation,[status(thm)],[f17,f32]) ).
fof(f555,definition,
! [X0] :
( sQ4_spl
<=> ( X0 = domain(b)
| b != compose(X0,b)
| codomain(X0) != domain(a) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f556,plain,
! [X0] :
( ~ sQ4_spl
| X0 = domain(b)
| b != compose(X0,b)
| codomain(X0) != domain(a) ),
inference(component_clause,[status(thm)],[f555]) ).
fof(f558,definition,
( sQ5_spl
<=> codomain(domain(b)) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f560,plain,
( sQ5_spl
| codomain(domain(b)) != domain(b) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f561,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f552,f555,f558]) ).
fof(f562,definition,
( sQ6_spl
<=> codomain(domain(b)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f564,plain,
( sQ6_spl
| codomain(domain(b)) != domain(a) ),
inference(component_clause,[status(thm)],[f562]) ).
fof(f565,definition,
! [X0] :
( sQ7_spl
<=> ( domain(b) = X0
| compose(X0,b) != b
| codomain(X0) != domain(b) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f568,plain,
( sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f553,f562,f565]) ).
fof(f569,plain,
( sQ6_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f15,f564]) ).
fof(f570,plain,
codomain(compose(g,compose(a,b))) = codomain(compose(a,b)),
inference(resolution,[status(thm)],[f123,f60]) ).
fof(f572,plain,
( codomain(compose(g,compose(compose(h,a),b))) = codomain(compose(compose(h,a),b))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f242,f123]) ).
fof(f573,plain,
( codomain(compose(g,compose(compose(g,a),b))) = codomain(compose(compose(g,a),b))
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f196,f123]) ).
fof(f574,plain,
( codomain(compose(g,compose(g,a))) = codomain(compose(g,a))
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f83,f123]) ).
fof(f575,plain,
( codomain(compose(g,compose(h,a))) = codomain(compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f123]) ).
fof(f576,plain,
( codomain(compose(g,compose(a,b))) = codomain(compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f123]) ).
fof(f577,plain,
! [X0] :
( codomain(compose(g,domain(X0))) = codomain(domain(X0))
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f123]) ).
fof(f578,plain,
! [X0] :
( codomain(compose(g,codomain(X0))) = codomain(codomain(X0))
| domain(a) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f123]) ).
fof(f580,plain,
codomain(compose(h,compose(a,b))) = codomain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f29,f570]) ).
fof(f581,plain,
codomain(compose(h,compose(a,b))) = codomain(b),
inference(forward_demodulation,[status(thm)],[f120,f580]) ).
fof(f584,definition,
( sQ8_spl
<=> domain(a) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f586,plain,
( sQ8_spl
| domain(a) != domain(h) ),
inference(component_clause,[status(thm)],[f584]) ).
fof(f587,definition,
( sQ9_spl
<=> codomain(compose(g,compose(compose(h,a),b))) = codomain(compose(compose(h,a),b)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f590,plain,
( sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f572,f584,f587]) ).
fof(f591,definition,
( sQ10_spl
<=> domain(a) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f593,plain,
( sQ10_spl
| domain(a) != domain(g) ),
inference(component_clause,[status(thm)],[f591]) ).
fof(f594,definition,
( sQ11_spl
<=> codomain(compose(g,compose(compose(g,a),b))) = codomain(compose(compose(g,a),b)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f597,plain,
( sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f573,f591,f594]) ).
fof(f598,definition,
( sQ12_spl
<=> codomain(compose(g,compose(g,a))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( sQ12_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f574,f591,f598]) ).
fof(f602,definition,
( sQ13_spl
<=> codomain(compose(g,compose(h,a))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f605,plain,
( sQ13_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f575,f584,f602]) ).
fof(f606,definition,
( sQ14_spl
<=> domain(a) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f608,plain,
( sQ14_spl
| domain(a) != domain(a) ),
inference(component_clause,[status(thm)],[f606]) ).
fof(f609,definition,
( sQ15_spl
<=> codomain(compose(g,compose(a,b))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f612,plain,
( sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f576,f606,f609]) ).
fof(f613,plain,
! [X0] :
( codomain(compose(g,domain(X0))) = domain(X0)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f577]) ).
fof(f614,plain,
! [X0] :
( codomain(compose(g,codomain(X0))) = codomain(X0)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f38,f578]) ).
fof(f616,plain,
( sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f608]) ).
fof(f617,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f616]) ).
fof(f623,plain,
! [X0] :
( domain(compose(compose(h,compose(a,b)),codomain(X0))) = domain(compose(h,compose(a,b)))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f581,f68]) ).
fof(f624,plain,
! [X0] :
( domain(compose(compose(h,compose(a,b)),domain(X0))) = domain(compose(h,compose(a,b)))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f581,f67]) ).
fof(f626,plain,
! [X0,X1] :
( compose(compose(h,compose(a,b)),compose(X0,X1)) = compose(compose(compose(h,compose(a,b)),X0),X1)
| codomain(X0) != domain(X1)
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f581,f21]) ).
fof(f627,plain,
! [X0] :
( codomain(compose(compose(h,compose(a,b)),X0)) = codomain(X0)
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f581,f20]) ).
fof(f630,plain,
! [X0] :
( domain(compose(compose(h,compose(a,b)),X0)) = domain(compose(h,compose(a,b)))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f581,f19]) ).
fof(f631,plain,
compose(compose(h,compose(a,b)),codomain(b)) = compose(h,compose(a,b)),
inference(paramodulation,[status(thm)],[f581,f18]) ).
fof(f647,plain,
( codomain(compose(h,compose(compose(h,a),b))) = codomain(compose(compose(h,a),b))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f242,f124]) ).
fof(f648,plain,
( codomain(compose(h,compose(compose(g,a),b))) = codomain(compose(compose(g,a),b))
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f196,f124]) ).
fof(f649,plain,
( codomain(compose(h,compose(g,a))) = codomain(compose(g,a))
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f83,f124]) ).
fof(f650,plain,
( codomain(compose(h,compose(h,a))) = codomain(compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f124]) ).
fof(f651,plain,
( codomain(compose(h,compose(a,b))) = codomain(compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f124]) ).
fof(f652,plain,
! [X0] :
( codomain(compose(h,domain(X0))) = codomain(domain(X0))
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f124]) ).
fof(f653,plain,
! [X0] :
( codomain(compose(h,codomain(X0))) = codomain(codomain(X0))
| domain(a) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f124]) ).
fof(f658,definition,
( sQ16_spl
<=> codomain(compose(h,compose(compose(h,a),b))) = codomain(compose(compose(h,a),b)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f661,plain,
( sQ16_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f647,f584,f658]) ).
fof(f662,definition,
( sQ17_spl
<=> codomain(compose(h,compose(compose(g,a),b))) = codomain(compose(compose(g,a),b)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f665,plain,
( sQ17_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f648,f591,f662]) ).
fof(f666,definition,
( sQ18_spl
<=> codomain(compose(h,compose(g,a))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f669,plain,
( sQ18_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f649,f591,f666]) ).
fof(f670,definition,
( sQ19_spl
<=> codomain(compose(h,compose(h,a))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f673,plain,
( sQ19_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f650,f584,f670]) ).
fof(f674,definition,
( sQ20_spl
<=> codomain(compose(h,compose(a,b))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f677,plain,
( sQ20_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f651,f606,f674]) ).
fof(f678,plain,
! [X0] :
( codomain(compose(h,domain(X0))) = domain(X0)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f652]) ).
fof(f679,plain,
! [X0] :
( codomain(compose(h,codomain(X0))) = codomain(X0)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f38,f653]) ).
fof(f683,plain,
( codomain(compose(a,compose(compose(h,a),b))) = codomain(compose(compose(h,a),b))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f242,f125]) ).
fof(f684,plain,
( codomain(compose(a,compose(compose(g,a),b))) = codomain(compose(compose(g,a),b))
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f196,f125]) ).
fof(f685,plain,
( codomain(compose(a,compose(g,a))) = codomain(compose(g,a))
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f83,f125]) ).
fof(f686,plain,
( codomain(compose(a,compose(h,a))) = codomain(compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f125]) ).
fof(f687,plain,
( codomain(compose(a,compose(a,b))) = codomain(compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f125]) ).
fof(f688,plain,
! [X0] :
( codomain(compose(a,domain(X0))) = codomain(domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f125]) ).
fof(f689,plain,
! [X0] :
( codomain(compose(a,codomain(X0))) = codomain(codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f125]) ).
fof(f693,definition,
( sQ21_spl
<=> domain(b) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f695,plain,
( sQ21_spl
| domain(b) != domain(h) ),
inference(component_clause,[status(thm)],[f693]) ).
fof(f696,definition,
( sQ22_spl
<=> codomain(compose(a,compose(compose(h,a),b))) = codomain(compose(compose(h,a),b)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f699,plain,
( sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f683,f693,f696]) ).
fof(f700,definition,
( sQ23_spl
<=> domain(b) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f702,plain,
( sQ23_spl
| domain(b) != domain(g) ),
inference(component_clause,[status(thm)],[f700]) ).
fof(f703,definition,
( sQ24_spl
<=> codomain(compose(a,compose(compose(g,a),b))) = codomain(compose(compose(g,a),b)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f706,plain,
( sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f684,f700,f703]) ).
fof(f707,definition,
( sQ25_spl
<=> codomain(compose(a,compose(g,a))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f710,plain,
( sQ25_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f685,f700,f707]) ).
fof(f711,definition,
( sQ26_spl
<=> codomain(compose(a,compose(h,a))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f714,plain,
( sQ26_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f686,f693,f711]) ).
fof(f715,definition,
( sQ27_spl
<=> domain(b) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f717,plain,
( sQ27_spl
| domain(b) != domain(a) ),
inference(component_clause,[status(thm)],[f715]) ).
fof(f718,definition,
( sQ28_spl
<=> codomain(compose(a,compose(a,b))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f721,plain,
( sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f687,f715,f718]) ).
fof(f722,plain,
! [X0] :
( codomain(compose(a,domain(X0))) = domain(X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f688]) ).
fof(f723,plain,
! [X0] :
( codomain(compose(a,codomain(X0))) = codomain(X0)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f38,f689]) ).
fof(f744,plain,
! [X0] :
( codomain(compose(codomain(X0),compose(g,a))) = codomain(compose(g,a))
| codomain(X0) != domain(g) ),
inference(paramodulation,[status(thm)],[f83,f126]) ).
fof(f745,plain,
! [X0] :
( codomain(compose(codomain(X0),compose(h,a))) = codomain(compose(h,a))
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f126]) ).
fof(f746,plain,
! [X0] :
( codomain(compose(codomain(X0),compose(a,b))) = codomain(compose(a,b))
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f126]) ).
fof(f747,plain,
! [X0,X1] :
( codomain(compose(codomain(X0),domain(X1))) = codomain(domain(X1))
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f37,f126]) ).
fof(f748,plain,
! [X0,X1] :
( codomain(compose(codomain(X0),codomain(X1))) = codomain(codomain(X1))
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f16,f126]) ).
fof(f768,plain,
! [X0] :
( codomain(compose(codomain(X0),compose(g,a))) = domain(b)
| codomain(X0) != domain(g) ),
inference(forward_demodulation,[status(thm)],[f130,f744]) ).
fof(f769,plain,
! [X0] :
( codomain(compose(codomain(X0),compose(h,a))) = domain(b)
| codomain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f131,f745]) ).
fof(f770,plain,
! [X0] :
( codomain(compose(codomain(X0),compose(a,b))) = codomain(b)
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f120,f746]) ).
fof(f771,plain,
! [X0,X1] :
( codomain(compose(codomain(X0),domain(X1))) = domain(X1)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f15,f747]) ).
fof(f772,plain,
! [X0,X1] :
( codomain(compose(codomain(X0),codomain(X1))) = codomain(X1)
| codomain(X0) != codomain(X1) ),
inference(forward_demodulation,[status(thm)],[f38,f748]) ).
fof(f774,plain,
( domain(compose(a,compose(compose(h,a),b))) = domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f242,f64]) ).
fof(f775,plain,
( domain(compose(a,compose(compose(g,a),b))) = domain(a)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f196,f64]) ).
fof(f776,plain,
( domain(compose(a,compose(g,a))) = domain(a)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f83,f64]) ).
fof(f777,plain,
( domain(compose(a,compose(h,a))) = domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f64]) ).
fof(f778,plain,
( domain(compose(a,compose(a,b))) = domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f64]) ).
fof(f782,definition,
( sQ29_spl
<=> domain(compose(a,compose(compose(h,a),b))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f785,plain,
( sQ29_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f774,f693,f782]) ).
fof(f786,definition,
( sQ30_spl
<=> domain(compose(a,compose(compose(g,a),b))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f789,plain,
( sQ30_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f775,f700,f786]) ).
fof(f790,definition,
( sQ31_spl
<=> domain(compose(a,compose(g,a))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f793,plain,
( sQ31_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f776,f700,f790]) ).
fof(f794,definition,
( sQ32_spl
<=> domain(compose(a,compose(h,a))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f797,plain,
( sQ32_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f777,f693,f794]) ).
fof(f798,definition,
( sQ33_spl
<=> domain(compose(a,compose(a,b))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f801,plain,
( sQ33_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f778,f715,f798]) ).
fof(f823,plain,
! [X0] :
( codomain(compose(domain(X0),compose(g,a))) = codomain(compose(g,a))
| domain(X0) != domain(g) ),
inference(paramodulation,[status(thm)],[f83,f127]) ).
fof(f824,plain,
! [X0] :
( codomain(compose(domain(X0),compose(h,a))) = codomain(compose(h,a))
| domain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f127]) ).
fof(f825,plain,
! [X0] :
( codomain(compose(domain(X0),compose(a,b))) = codomain(compose(a,b))
| domain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f127]) ).
fof(f826,plain,
! [X0,X1] :
( codomain(compose(domain(X0),domain(X1))) = codomain(domain(X1))
| domain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f37,f127]) ).
fof(f827,plain,
! [X0,X1] :
( codomain(compose(domain(X0),codomain(X1))) = codomain(codomain(X1))
| domain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f16,f127]) ).
fof(f844,plain,
! [X0] :
( codomain(compose(domain(X0),compose(g,a))) = domain(b)
| domain(X0) != domain(g) ),
inference(forward_demodulation,[status(thm)],[f130,f823]) ).
fof(f845,plain,
! [X0] :
( codomain(compose(domain(X0),compose(h,a))) = domain(b)
| domain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f131,f824]) ).
fof(f846,plain,
! [X0] :
( codomain(compose(domain(X0),compose(a,b))) = codomain(b)
| domain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f120,f825]) ).
fof(f847,plain,
! [X0,X1] :
( codomain(compose(domain(X0),domain(X1))) = domain(X1)
| domain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f15,f826]) ).
fof(f848,plain,
! [X0,X1] :
( codomain(compose(domain(X0),codomain(X1))) = codomain(X1)
| domain(X0) != codomain(X1) ),
inference(forward_demodulation,[status(thm)],[f38,f827]) ).
fof(f858,plain,
! [X0] :
( codomain(compose(compose(a,b),domain(X0))) = domain(X0)
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f120,f133]) ).
fof(f859,plain,
! [X0] :
( codomain(compose(compose(h,compose(a,b)),domain(X0))) = domain(X0)
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f581,f133]) ).
fof(f860,plain,
! [X0] :
( codomain(compose(compose(h,a),domain(X0))) = domain(X0)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f131,f133]) ).
fof(f861,plain,
! [X0] :
( codomain(compose(compose(g,a),domain(X0))) = domain(X0)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f130,f133]) ).
fof(f908,plain,
! [X0] :
( codomain(compose(compose(a,b),codomain(X0))) = codomain(X0)
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f120,f134]) ).
fof(f909,plain,
! [X0] :
( codomain(compose(compose(h,compose(a,b)),codomain(X0))) = codomain(X0)
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f581,f134]) ).
fof(f910,plain,
! [X0] :
( codomain(compose(compose(h,a),codomain(X0))) = codomain(X0)
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f131,f134]) ).
fof(f911,plain,
! [X0] :
( codomain(compose(compose(g,a),codomain(X0))) = codomain(X0)
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f130,f134]) ).
fof(f966,plain,
domain(compose(g,compose(a,b))) = domain(g),
inference(resolution,[status(thm)],[f75,f60]) ).
fof(f968,plain,
( domain(compose(g,compose(compose(h,a),b))) = domain(g)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f242,f75]) ).
fof(f969,plain,
( domain(compose(g,compose(compose(g,a),b))) = domain(g)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f196,f75]) ).
fof(f970,plain,
( domain(compose(g,compose(g,a))) = domain(g)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f83,f75]) ).
fof(f971,plain,
( domain(compose(g,compose(h,a))) = domain(g)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f75]) ).
fof(f972,plain,
( domain(compose(g,compose(a,b))) = domain(g)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f75]) ).
fof(f976,plain,
! [X0] :
( domain(compose(compose(h,compose(a,b)),X0)) = domain(g)
| codomain(b) != domain(X0) ),
inference(backward_demodulation,[status(thm)],[f979,f630]) ).
fof(f977,plain,
! [X0] :
( domain(compose(compose(h,compose(a,b)),domain(X0))) = domain(g)
| codomain(b) != domain(X0) ),
inference(backward_demodulation,[status(thm)],[f979,f624]) ).
fof(f978,plain,
! [X0] :
( domain(compose(compose(h,compose(a,b)),codomain(X0))) = domain(g)
| codomain(b) != codomain(X0) ),
inference(backward_demodulation,[status(thm)],[f979,f623]) ).
fof(f979,plain,
domain(compose(h,compose(a,b))) = domain(g),
inference(forward_demodulation,[status(thm)],[f29,f966]) ).
fof(f980,definition,
( sQ34_spl
<=> domain(compose(g,compose(compose(h,a),b))) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f983,plain,
( sQ34_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f968,f584,f980]) ).
fof(f984,definition,
( sQ35_spl
<=> domain(compose(g,compose(compose(g,a),b))) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f987,plain,
( sQ35_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f969,f591,f984]) ).
fof(f988,definition,
( sQ36_spl
<=> domain(compose(g,compose(g,a))) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f991,plain,
( sQ36_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f970,f591,f988]) ).
fof(f992,definition,
( sQ37_spl
<=> domain(compose(g,compose(h,a))) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f995,plain,
( sQ37_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f971,f584,f992]) ).
fof(f996,definition,
( sQ38_spl
<=> domain(compose(g,compose(a,b))) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f999,plain,
( sQ38_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f972,f606,f996]) ).
fof(f1005,plain,
( domain(compose(g,compose(h,compose(a,b)))) = domain(g)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f979,f75]) ).
fof(f1007,plain,
! [X0] :
( codomain(compose(domain(X0),compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b)))
| domain(X0) != domain(g) ),
inference(paramodulation,[status(thm)],[f979,f127]) ).
fof(f1009,plain,
( domain(compose(a,compose(h,compose(a,b)))) = domain(a)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f979,f64]) ).
fof(f1010,plain,
! [X0] :
( codomain(compose(codomain(X0),compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b)))
| codomain(X0) != domain(g) ),
inference(paramodulation,[status(thm)],[f979,f126]) ).
fof(f1011,plain,
( codomain(compose(a,compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b)))
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f979,f125]) ).
fof(f1012,plain,
( codomain(compose(h,compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b)))
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f979,f124]) ).
fof(f1013,plain,
( codomain(compose(g,compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b)))
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f979,f123]) ).
fof(f1015,plain,
! [X0] :
( domain(compose(domain(X0),compose(h,compose(a,b)))) = domain(X0)
| domain(X0) != domain(g) ),
inference(paramodulation,[status(thm)],[f979,f72]) ).
fof(f1017,plain,
! [X0] :
( domain(compose(codomain(X0),compose(h,compose(a,b)))) = codomain(X0)
| codomain(X0) != domain(g) ),
inference(paramodulation,[status(thm)],[f979,f71]) ).
fof(f1018,plain,
! [X0,X1] :
( compose(X0,compose(compose(h,compose(a,b)),X1)) = compose(compose(X0,compose(h,compose(a,b))),X1)
| codomain(compose(h,compose(a,b))) != domain(X1)
| codomain(X0) != domain(g) ),
inference(paramodulation,[status(thm)],[f979,f21]) ).
fof(f1021,plain,
! [X0] :
( codomain(compose(X0,compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b)))
| codomain(X0) != domain(g) ),
inference(paramodulation,[status(thm)],[f979,f20]) ).
fof(f1022,plain,
! [X0] :
( domain(compose(X0,compose(h,compose(a,b)))) = domain(X0)
| codomain(X0) != domain(g) ),
inference(paramodulation,[status(thm)],[f979,f19]) ).
fof(f1025,plain,
compose(domain(g),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(paramodulation,[status(thm)],[f979,f17]) ).
fof(f1030,definition,
( sQ39_spl
<=> domain(compose(g,compose(h,compose(a,b)))) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f1033,plain,
( sQ39_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1005,f591,f1030]) ).
fof(f1036,plain,
! [X0] :
( codomain(compose(domain(X0),compose(h,compose(a,b)))) = codomain(b)
| domain(X0) != domain(g) ),
inference(forward_demodulation,[status(thm)],[f581,f1007]) ).
fof(f1038,definition,
( sQ40_spl
<=> domain(compose(a,compose(h,compose(a,b)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1041,plain,
( sQ40_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1009,f700,f1038]) ).
fof(f1042,plain,
! [X0] :
( codomain(compose(codomain(X0),compose(h,compose(a,b)))) = codomain(b)
| codomain(X0) != domain(g) ),
inference(forward_demodulation,[status(thm)],[f581,f1010]) ).
fof(f1043,definition,
( sQ41_spl
<=> codomain(compose(a,compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1046,plain,
( sQ41_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1011,f700,f1043]) ).
fof(f1047,definition,
( sQ42_spl
<=> codomain(compose(h,compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1050,plain,
( sQ42_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1012,f591,f1047]) ).
fof(f1051,definition,
( sQ43_spl
<=> codomain(compose(g,compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1054,plain,
( sQ43_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1013,f591,f1051]) ).
fof(f1058,plain,
! [X0,X1] :
( compose(X0,compose(compose(h,compose(a,b)),X1)) = compose(compose(X0,compose(h,compose(a,b))),X1)
| codomain(b) != domain(X1)
| codomain(X0) != domain(g) ),
inference(forward_demodulation,[status(thm)],[f581,f1018]) ).
fof(f1063,plain,
! [X0] :
( codomain(compose(X0,compose(h,compose(a,b)))) = codomain(b)
| codomain(X0) != domain(g) ),
inference(forward_demodulation,[status(thm)],[f581,f1021]) ).
fof(f1068,plain,
domain(compose(h,compose(a,b))) = domain(h),
inference(resolution,[status(thm)],[f77,f60]) ).
fof(f1070,plain,
( domain(compose(h,compose(compose(h,a),b))) = domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f242,f77]) ).
fof(f1071,plain,
( domain(compose(h,compose(compose(g,a),b))) = domain(h)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f196,f77]) ).
fof(f1072,plain,
( domain(compose(h,compose(g,a))) = domain(h)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f83,f77]) ).
fof(f1073,plain,
( domain(compose(h,compose(h,compose(a,b)))) = domain(h)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f979,f77]) ).
fof(f1074,plain,
( domain(compose(h,compose(h,a))) = domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f77]) ).
fof(f1075,plain,
( domain(compose(h,compose(a,b))) = domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f77]) ).
fof(f1079,plain,
domain(h) = domain(g),
inference(backward_demodulation,[status(thm)],[f1068,f979]) ).
fof(f1080,definition,
( sQ44_spl
<=> domain(compose(h,compose(compose(h,a),b))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f1083,plain,
( sQ44_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1070,f584,f1080]) ).
fof(f1084,definition,
( sQ45_spl
<=> domain(compose(h,compose(compose(g,a),b))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f1087,plain,
( sQ45_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1071,f591,f1084]) ).
fof(f1088,definition,
( sQ46_spl
<=> domain(compose(h,compose(g,a))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1091,plain,
( sQ46_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1072,f591,f1088]) ).
fof(f1092,definition,
( sQ47_spl
<=> domain(compose(h,compose(h,compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1095,plain,
( sQ47_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1073,f591,f1092]) ).
fof(f1096,definition,
( sQ48_spl
<=> domain(compose(h,compose(h,a))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1099,plain,
( sQ48_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1074,f584,f1096]) ).
fof(f1100,definition,
( sQ49_spl
<=> domain(compose(h,compose(a,b))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f1103,plain,
( sQ49_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1075,f606,f1100]) ).
fof(f1104,plain,
! [X0] :
( domain(compose(g,X0)) = domain(h)
| domain(a) != domain(X0) ),
inference(backward_demodulation,[status(thm)],[f1079,f75]) ).
fof(f1105,plain,
( sQ23_spl
| domain(b) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f702]) ).
fof(f1106,plain,
( sQ10_spl
| domain(a) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f593]) ).
fof(f1107,plain,
domain(compose(compose(g,a),b)) = domain(h),
inference(backward_demodulation,[status(thm)],[f1079,f196]) ).
fof(f1108,plain,
domain(compose(g,a)) = domain(h),
inference(backward_demodulation,[status(thm)],[f1079,f83]) ).
fof(f1109,plain,
compose(domain(h),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(backward_demodulation,[status(thm)],[f1079,f1025]) ).
fof(f1110,plain,
! [X0] :
( domain(compose(X0,compose(h,compose(a,b)))) = domain(X0)
| codomain(X0) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f1022]) ).
fof(f1111,plain,
! [X0] :
( codomain(compose(X0,compose(h,compose(a,b)))) = codomain(b)
| codomain(X0) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f1063]) ).
fof(f1112,plain,
! [X0,X1] :
( compose(X0,compose(compose(h,compose(a,b)),X1)) = compose(compose(X0,compose(h,compose(a,b))),X1)
| codomain(b) != domain(X1)
| codomain(X0) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f1058]) ).
fof(f1113,plain,
! [X0] :
( domain(compose(codomain(X0),compose(h,compose(a,b)))) = codomain(X0)
| codomain(X0) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f1017]) ).
fof(f1114,plain,
! [X0] :
( domain(compose(domain(X0),compose(h,compose(a,b)))) = domain(X0)
| domain(X0) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f1015]) ).
fof(f1115,plain,
! [X0] :
( codomain(compose(codomain(X0),compose(h,compose(a,b)))) = codomain(b)
| codomain(X0) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f1042]) ).
fof(f1116,plain,
! [X0] :
( codomain(compose(domain(X0),compose(h,compose(a,b)))) = codomain(b)
| domain(X0) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f1036]) ).
fof(f1117,plain,
! [X0] :
( domain(compose(compose(h,compose(a,b)),codomain(X0))) = domain(h)
| codomain(b) != codomain(X0) ),
inference(backward_demodulation,[status(thm)],[f1079,f978]) ).
fof(f1118,plain,
! [X0] :
( domain(compose(compose(h,compose(a,b)),domain(X0))) = domain(h)
| codomain(b) != domain(X0) ),
inference(backward_demodulation,[status(thm)],[f1079,f977]) ).
fof(f1119,plain,
! [X0] :
( domain(compose(compose(h,compose(a,b)),X0)) = domain(h)
| codomain(b) != domain(X0) ),
inference(backward_demodulation,[status(thm)],[f1079,f976]) ).
fof(f1120,plain,
! [X0] :
( codomain(compose(domain(X0),compose(g,a))) = domain(b)
| domain(X0) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f844]) ).
fof(f1122,plain,
! [X0] :
( codomain(compose(codomain(X0),compose(g,a))) = domain(b)
| codomain(X0) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f768]) ).
fof(f1124,plain,
! [X0] :
( domain(compose(g,codomain(X0))) = domain(h)
| domain(a) != codomain(X0) ),
inference(backward_demodulation,[status(thm)],[f1079,f515]) ).
fof(f1125,plain,
! [X0] :
( domain(compose(compose(g,a),codomain(X0))) = domain(h)
| domain(b) != codomain(X0) ),
inference(backward_demodulation,[status(thm)],[f1079,f539]) ).
fof(f1127,plain,
! [X0] :
( domain(compose(g,domain(X0))) = domain(h)
| domain(a) != domain(X0) ),
inference(backward_demodulation,[status(thm)],[f1079,f475]) ).
fof(f1128,plain,
! [X0] :
( domain(compose(compose(g,a),domain(X0))) = domain(h)
| domain(b) != domain(X0) ),
inference(backward_demodulation,[status(thm)],[f1079,f492]) ).
fof(f1130,plain,
! [X0] :
( domain(compose(domain(X0),compose(g,a))) = domain(X0)
| domain(X0) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f425]) ).
fof(f1132,plain,
! [X0] :
( domain(compose(codomain(X0),compose(g,a))) = codomain(X0)
| codomain(X0) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f366]) ).
fof(f1139,plain,
! [X0,X1] :
( compose(X0,compose(compose(g,a),X1)) = compose(compose(X0,compose(g,a)),X1)
| domain(b) != domain(X1)
| codomain(X0) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f226]) ).
fof(f1140,plain,
! [X0] :
( domain(compose(compose(g,a),X0)) = domain(h)
| domain(b) != domain(X0) ),
inference(backward_demodulation,[status(thm)],[f1079,f201]) ).
fof(f1141,plain,
compose(domain(h),compose(g,a)) = compose(g,a),
inference(backward_demodulation,[status(thm)],[f1079,f179]) ).
fof(f1142,plain,
! [X0] :
( domain(compose(X0,compose(g,a))) = domain(X0)
| codomain(X0) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f176]) ).
fof(f1143,plain,
! [X0] :
( codomain(compose(X0,compose(g,a))) = domain(b)
| codomain(X0) != domain(h) ),
inference(backward_demodulation,[status(thm)],[f1079,f184]) ).
fof(f1148,plain,
! [X0] :
( codomain(compose(domain(X0),g)) = codomain(g)
| domain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f127]) ).
fof(f1150,plain,
! [X0] :
( domain(compose(domain(X0),g)) = domain(X0)
| domain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f72]) ).
fof(f1156,plain,
compose(domain(h),g) = g,
inference(paramodulation,[status(thm)],[f1079,f17]) ).
fof(f1161,plain,
! [X0] :
( codomain(compose(domain(X0),g)) = domain(a)
| domain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f74,f1148]) ).
fof(f1177,plain,
( domain(compose(h,compose(g,a))) = domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f77]) ).
fof(f1181,plain,
( domain(compose(a,compose(g,a))) = domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f64]) ).
fof(f1183,plain,
( codomain(compose(a,compose(g,a))) = codomain(compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f125]) ).
fof(f1184,plain,
( codomain(compose(h,compose(g,a))) = codomain(compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f124]) ).
fof(f1185,plain,
( codomain(compose(g,compose(g,a))) = codomain(compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f123]) ).
fof(f1202,plain,
( sQ46_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1177,f584,f1088]) ).
fof(f1207,plain,
( sQ31_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1181,f693,f790]) ).
fof(f1209,plain,
( sQ25_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1183,f693,f707]) ).
fof(f1210,plain,
( sQ18_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1184,f584,f666]) ).
fof(f1211,plain,
( sQ12_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1185,f584,f598]) ).
fof(f1227,plain,
( domain(compose(h,compose(h,compose(a,b)))) = domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f77]) ).
fof(f1231,plain,
( domain(compose(a,compose(h,compose(a,b)))) = domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f64]) ).
fof(f1233,plain,
( codomain(compose(a,compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f125]) ).
fof(f1234,plain,
( codomain(compose(h,compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f124]) ).
fof(f1235,plain,
( codomain(compose(g,compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f123]) ).
fof(f1252,plain,
( sQ47_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1227,f584,f1092]) ).
fof(f1257,plain,
( sQ40_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1231,f693,f1038]) ).
fof(f1259,plain,
( sQ41_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1233,f693,f1043]) ).
fof(f1260,plain,
( sQ42_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1234,f584,f1047]) ).
fof(f1261,plain,
( sQ43_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1235,f584,f1051]) ).
fof(f1277,plain,
( domain(compose(h,compose(compose(g,a),b))) = domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1107,f77]) ).
fof(f1281,plain,
( domain(compose(a,compose(compose(g,a),b))) = domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1107,f64]) ).
fof(f1283,plain,
( codomain(compose(a,compose(compose(g,a),b))) = codomain(compose(compose(g,a),b))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1107,f125]) ).
fof(f1284,plain,
( codomain(compose(h,compose(compose(g,a),b))) = codomain(compose(compose(g,a),b))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1107,f124]) ).
fof(f1285,plain,
( codomain(compose(g,compose(compose(g,a),b))) = codomain(compose(compose(g,a),b))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1107,f123]) ).
fof(f1302,plain,
( sQ45_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1277,f584,f1084]) ).
fof(f1307,plain,
( sQ30_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1281,f693,f786]) ).
fof(f1309,plain,
( sQ24_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1283,f693,f703]) ).
fof(f1310,plain,
( sQ17_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1284,f584,f662]) ).
fof(f1311,plain,
( sQ11_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1285,f584,f594]) ).
fof(f1324,plain,
( compose(g,compose(a,compose(g,a))) = compose(compose(g,a),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f221]) ).
fof(f1325,plain,
( compose(g,compose(a,compose(compose(g,a),b))) = compose(compose(g,a),compose(compose(g,a),b))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1107,f221]) ).
fof(f1326,plain,
( compose(g,compose(a,compose(compose(h,a),b))) = compose(compose(g,a),compose(compose(h,a),b))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f242,f221]) ).
fof(f1327,plain,
( compose(g,compose(a,compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f221]) ).
fof(f1328,plain,
( compose(g,compose(a,compose(h,a))) = compose(compose(g,a),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f221]) ).
fof(f1329,plain,
( compose(g,compose(a,compose(a,b))) = compose(compose(g,a),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f221]) ).
fof(f1330,plain,
! [X0] :
( compose(g,compose(a,domain(X0))) = compose(compose(g,a),domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f221]) ).
fof(f1331,plain,
! [X0] :
( compose(g,compose(a,codomain(X0))) = compose(compose(g,a),codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f221]) ).
fof(f1332,plain,
compose(g,compose(a,b)) = compose(compose(g,a),b),
inference(equality_resolution,[status(thm)],[f221]) ).
fof(f1334,definition,
( sQ50_spl
<=> compose(g,compose(a,compose(g,a))) = compose(compose(g,a),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f1337,plain,
( sQ50_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1324,f693,f1334]) ).
fof(f1338,definition,
( sQ51_spl
<=> compose(g,compose(a,compose(compose(g,a),b))) = compose(compose(g,a),compose(compose(g,a),b)) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1341,plain,
( sQ51_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1325,f693,f1338]) ).
fof(f1342,definition,
( sQ52_spl
<=> compose(g,compose(a,compose(compose(h,a),b))) = compose(compose(g,a),compose(compose(h,a),b)) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1345,plain,
( sQ52_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1326,f693,f1342]) ).
fof(f1346,definition,
( sQ53_spl
<=> compose(g,compose(a,compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1349,plain,
( sQ53_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1327,f693,f1346]) ).
fof(f1350,definition,
( sQ54_spl
<=> compose(g,compose(a,compose(h,a))) = compose(compose(g,a),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f1353,plain,
( sQ54_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1328,f693,f1350]) ).
fof(f1354,definition,
( sQ55_spl
<=> compose(g,compose(a,compose(a,b))) = compose(compose(g,a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1357,plain,
( sQ55_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1329,f715,f1354]) ).
fof(f1376,plain,
! [X0] :
( compose(compose(g,a),compose(b,X0)) = compose(compose(h,compose(a,b)),X0)
| codomain(b) != domain(X0) ),
inference(backward_demodulation,[status(thm)],[f1377,f204]) ).
fof(f1377,plain,
compose(h,compose(a,b)) = compose(compose(g,a),b),
inference(forward_demodulation,[status(thm)],[f29,f1332]) ).
fof(f1383,plain,
( compose(h,compose(a,compose(g,a))) = compose(compose(h,a),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f222]) ).
fof(f1384,plain,
( compose(h,compose(a,compose(compose(h,a),b))) = compose(compose(h,a),compose(compose(h,a),b))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f242,f222]) ).
fof(f1385,plain,
( compose(h,compose(a,compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f222]) ).
fof(f1386,plain,
( compose(h,compose(a,compose(h,a))) = compose(compose(h,a),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f222]) ).
fof(f1387,plain,
( compose(h,compose(a,compose(a,b))) = compose(compose(h,a),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f222]) ).
fof(f1388,plain,
! [X0] :
( compose(h,compose(a,domain(X0))) = compose(compose(h,a),domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f222]) ).
fof(f1389,plain,
! [X0] :
( compose(h,compose(a,codomain(X0))) = compose(compose(h,a),codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f222]) ).
fof(f1390,plain,
compose(h,compose(a,b)) = compose(compose(h,a),b),
inference(equality_resolution,[status(thm)],[f222]) ).
fof(f1392,definition,
( sQ56_spl
<=> compose(h,compose(a,compose(g,a))) = compose(compose(h,a),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f1395,plain,
( sQ56_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1383,f693,f1392]) ).
fof(f1396,definition,
( sQ57_spl
<=> compose(h,compose(a,compose(compose(h,a),b))) = compose(compose(h,a),compose(compose(h,a),b)) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1399,plain,
( sQ57_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1384,f693,f1396]) ).
fof(f1400,definition,
( sQ58_spl
<=> compose(h,compose(a,compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f1403,plain,
( sQ58_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1385,f693,f1400]) ).
fof(f1404,definition,
( sQ59_spl
<=> compose(h,compose(a,compose(h,a))) = compose(compose(h,a),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1407,plain,
( sQ59_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1386,f693,f1404]) ).
fof(f1408,definition,
( sQ60_spl
<=> compose(h,compose(a,compose(a,b))) = compose(compose(h,a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1411,plain,
( sQ60_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1387,f715,f1408]) ).
fof(f1430,plain,
! [X0] :
( compose(compose(h,a),compose(b,X0)) = compose(compose(h,compose(a,b)),X0)
| codomain(b) != domain(X0) ),
inference(backward_demodulation,[status(thm)],[f1390,f231]) ).
fof(f1437,plain,
( domain(compose(g,compose(g,a))) = domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1104]) ).
fof(f1438,plain,
( domain(compose(g,compose(h,compose(a,b)))) = domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1104]) ).
fof(f1439,plain,
( domain(compose(g,compose(h,a))) = domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1104]) ).
fof(f1440,plain,
( domain(compose(g,compose(a,b))) = domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1104]) ).
fof(f1446,definition,
( sQ61_spl
<=> domain(compose(g,compose(g,a))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1449,plain,
( sQ61_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1437,f584,f1446]) ).
fof(f1450,definition,
( sQ62_spl
<=> domain(compose(g,compose(h,compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1453,plain,
( sQ62_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1438,f584,f1450]) ).
fof(f1454,definition,
( sQ63_spl
<=> domain(compose(g,compose(h,a))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1457,plain,
( sQ63_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1439,f584,f1454]) ).
fof(f1458,definition,
( sQ64_spl
<=> domain(compose(g,compose(a,b))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1461,plain,
( sQ64_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1440,f606,f1458]) ).
fof(f1470,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)],[f120,f223]) ).
fof(f1471,plain,
! [X0] :
( compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0)
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f581,f223]) ).
fof(f1472,plain,
! [X0] :
( compose(domain(compose(h,a)),compose(compose(h,a),X0)) = compose(compose(h,a),X0)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f131,f223]) ).
fof(f1473,plain,
! [X0] :
( compose(domain(compose(g,a)),compose(compose(g,a),X0)) = compose(compose(g,a),X0)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f130,f223]) ).
fof(f1474,plain,
! [X0] :
( compose(domain(g),compose(g,X0)) = compose(g,X0)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f74,f223]) ).
fof(f1475,plain,
! [X0] :
( compose(domain(h),compose(h,X0)) = compose(h,X0)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f69,f223]) ).
fof(f1476,plain,
! [X0] :
( compose(domain(a),compose(a,X0)) = compose(a,X0)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f22,f223]) ).
fof(f1477,plain,
! [X0,X1] :
( compose(domain(codomain(X0)),compose(codomain(X0),X1)) = compose(codomain(X0),X1)
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f223]) ).
fof(f1478,plain,
! [X0,X1] :
( compose(domain(domain(X0)),compose(domain(X0),X1)) = compose(domain(X0),X1)
| domain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f15,f223]) ).
fof(f1479,plain,
! [X0] :
( compose(domain(X0),compose(X0,compose(g,a))) = compose(X0,compose(g,a))
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f223]) ).
fof(f1480,plain,
! [X0] :
( compose(domain(X0),compose(X0,compose(h,compose(a,b)))) = compose(X0,compose(h,compose(a,b)))
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f223]) ).
fof(f1481,plain,
! [X0] :
( compose(domain(X0),compose(X0,compose(h,a))) = compose(X0,compose(h,a))
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f223]) ).
fof(f1482,plain,
! [X0] :
( compose(domain(X0),compose(X0,compose(a,b))) = compose(X0,compose(a,b))
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f223]) ).
fof(f1483,plain,
! [X0,X1] :
( compose(domain(X0),compose(X0,domain(X1))) = compose(X0,domain(X1))
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f37,f223]) ).
fof(f1484,plain,
! [X0,X1] :
( compose(domain(X0),compose(X0,codomain(X1))) = compose(X0,codomain(X1))
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f16,f223]) ).
fof(f1495,plain,
! [X0] :
( compose(domain(a),compose(compose(a,b),X0)) = compose(compose(a,b),X0)
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f60,f1470]) ).
fof(f1496,plain,
! [X0] :
( compose(domain(h),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0)
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f1068,f1471]) ).
fof(f1497,plain,
! [X0] :
( compose(domain(h),compose(compose(h,a),X0)) = compose(compose(h,a),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f76,f1472]) ).
fof(f1498,plain,
! [X0] :
( compose(domain(h),compose(compose(g,a),X0)) = compose(compose(g,a),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f1108,f1473]) ).
fof(f1499,plain,
! [X0] :
( compose(domain(h),compose(g,X0)) = compose(g,X0)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f1079,f1474]) ).
fof(f1500,plain,
! [X0,X1] :
( compose(codomain(X0),compose(codomain(X0),X1)) = compose(codomain(X0),X1)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f16,f1477]) ).
fof(f1501,plain,
! [X0,X1] :
( compose(domain(X0),compose(domain(X0),X1)) = compose(domain(X0),X1)
| domain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f37,f1478]) ).
fof(f1509,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)],[f120,f225]) ).
fof(f1510,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(h,compose(a,b)),X0)
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f581,f225]) ).
fof(f1511,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(h,a)),X0)) = compose(compose(h,a),X0)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f131,f225]) ).
fof(f1512,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(g,a)),X0)) = compose(compose(g,a),X0)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f130,f225]) ).
fof(f1513,plain,
! [X0] :
( compose(g,compose(codomain(g),X0)) = compose(g,X0)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f74,f225]) ).
fof(f1514,plain,
! [X0] :
( compose(h,compose(codomain(h),X0)) = compose(h,X0)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f69,f225]) ).
fof(f1515,plain,
! [X0] :
( compose(a,compose(codomain(a),X0)) = compose(a,X0)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f22,f225]) ).
fof(f1518,plain,
! [X0] :
( compose(X0,compose(codomain(X0),compose(g,a))) = compose(X0,compose(g,a))
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f225]) ).
fof(f1519,plain,
! [X0] :
( compose(X0,compose(codomain(X0),compose(h,compose(a,b)))) = compose(X0,compose(h,compose(a,b)))
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f225]) ).
fof(f1520,plain,
! [X0] :
( compose(X0,compose(codomain(X0),compose(h,a))) = compose(X0,compose(h,a))
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f225]) ).
fof(f1521,plain,
! [X0] :
( compose(X0,compose(codomain(X0),compose(a,b))) = compose(X0,compose(a,b))
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f225]) ).
fof(f1522,plain,
! [X0,X1] :
( compose(X0,compose(codomain(X0),domain(X1))) = compose(X0,domain(X1))
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f37,f225]) ).
fof(f1523,plain,
! [X0,X1] :
( compose(X0,compose(codomain(X0),codomain(X1))) = compose(X0,codomain(X1))
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f16,f225]) ).
fof(f1530,plain,
! [X0] :
( compose(compose(a,b),compose(codomain(b),X0)) = compose(compose(a,b),X0)
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f120,f1509]) ).
fof(f1531,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(codomain(b),X0)) = compose(compose(h,compose(a,b)),X0)
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f581,f1510]) ).
fof(f1532,plain,
! [X0] :
( compose(compose(h,a),compose(domain(b),X0)) = compose(compose(h,a),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f131,f1511]) ).
fof(f1533,plain,
! [X0] :
( compose(compose(g,a),compose(domain(b),X0)) = compose(compose(g,a),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f130,f1512]) ).
fof(f1534,plain,
! [X0] :
( compose(g,compose(domain(a),X0)) = compose(g,X0)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f74,f1513]) ).
fof(f1535,plain,
! [X0] :
( compose(h,compose(domain(a),X0)) = compose(h,X0)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f69,f1514]) ).
fof(f1536,plain,
! [X0] :
( compose(a,compose(domain(b),X0)) = compose(a,X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f22,f1515]) ).
fof(f1539,plain,
( ~ sQ0_spl
| domain(a) = domain(a)
| codomain(domain(a)) != domain(a) ),
inference(resolution,[status(thm)],[f315,f17]) ).
fof(f1541,plain,
( ~ sQ0_spl
| sQ14_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1539,f321,f606,f314]) ).
fof(f1546,plain,
( sQ1_spl
| domain(a) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f319]) ).
fof(f1548,plain,
( compose(a,compose(b,compose(g,a))) = compose(compose(a,b),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f207]) ).
fof(f1549,plain,
( compose(a,compose(b,compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f207]) ).
fof(f1550,plain,
( compose(a,compose(b,compose(h,a))) = compose(compose(a,b),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f207]) ).
fof(f1551,plain,
( compose(a,compose(b,compose(a,b))) = compose(compose(a,b),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f207]) ).
fof(f1552,plain,
! [X0] :
( compose(a,compose(b,domain(X0))) = compose(compose(a,b),domain(X0))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f207]) ).
fof(f1553,plain,
! [X0] :
( compose(a,compose(b,codomain(X0))) = compose(compose(a,b),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f207]) ).
fof(f1555,definition,
( sQ66_spl
<=> codomain(b) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1557,plain,
( sQ66_spl
| codomain(b) != domain(h) ),
inference(component_clause,[status(thm)],[f1555]) ).
fof(f1558,definition,
( sQ67_spl
<=> compose(a,compose(b,compose(g,a))) = compose(compose(a,b),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1561,plain,
( sQ67_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f1548,f1555,f1558]) ).
fof(f1562,definition,
( sQ68_spl
<=> compose(a,compose(b,compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1565,plain,
( sQ68_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f1549,f1555,f1562]) ).
fof(f1566,definition,
( sQ69_spl
<=> compose(a,compose(b,compose(h,a))) = compose(compose(a,b),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1569,plain,
( sQ69_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f1550,f1555,f1566]) ).
fof(f1570,definition,
( sQ70_spl
<=> codomain(b) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1572,plain,
( sQ70_spl
| codomain(b) != domain(a) ),
inference(component_clause,[status(thm)],[f1570]) ).
fof(f1573,definition,
( sQ71_spl
<=> compose(a,compose(b,compose(a,b))) = compose(compose(a,b),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1576,plain,
( sQ71_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f1551,f1570,f1573]) ).
fof(f1577,plain,
( ~ sQ3_spl
| domain(a) = domain(a)
| codomain(domain(a)) != domain(b) ),
inference(resolution,[status(thm)],[f325,f17]) ).
fof(f1579,plain,
( ~ sQ3_spl
| sQ14_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1577,f317,f606,f324]) ).
fof(f1714,plain,
( compose(g,compose(compose(h,a),b)) = compose(compose(g,compose(h,a)),b)
| domain(a) != domain(compose(h,a)) ),
inference(resolution,[status(thm)],[f211,f131]) ).
fof(f1715,plain,
( compose(g,compose(compose(g,a),b)) = compose(compose(g,compose(g,a)),b)
| domain(a) != domain(compose(g,a)) ),
inference(resolution,[status(thm)],[f211,f130]) ).
fof(f1716,plain,
( compose(g,compose(g,a)) = compose(compose(g,g),a)
| domain(a) != domain(g) ),
inference(resolution,[status(thm)],[f211,f74]) ).
fof(f1717,plain,
( compose(g,compose(h,a)) = compose(compose(g,h),a)
| domain(a) != domain(h) ),
inference(resolution,[status(thm)],[f211,f69]) ).
fof(f1718,plain,
( compose(g,compose(a,b)) = compose(compose(g,a),b)
| domain(a) != domain(a) ),
inference(resolution,[status(thm)],[f211,f22]) ).
fof(f1719,plain,
! [X0] :
( compose(g,compose(domain(X0),X0)) = compose(compose(g,domain(X0)),X0)
| domain(a) != domain(domain(X0)) ),
inference(resolution,[status(thm)],[f211,f15]) ).
fof(f1720,plain,
! [X0] :
( compose(g,compose(X0,codomain(X0))) = compose(compose(g,X0),codomain(X0))
| domain(a) != domain(X0) ),
inference(resolution,[status(thm)],[f211,f16]) ).
fof(f1721,plain,
! [X0] :
( compose(g,compose(compose(a,b),X0)) = compose(compose(g,compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f211]) ).
fof(f1722,plain,
! [X0] :
( compose(g,compose(compose(h,compose(a,b)),X0)) = compose(compose(g,compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f211]) ).
fof(f1723,plain,
! [X0] :
( compose(g,compose(compose(h,a),X0)) = compose(compose(g,compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f211]) ).
fof(f1724,plain,
! [X0] :
( compose(g,compose(compose(g,a),X0)) = compose(compose(g,compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f211]) ).
fof(f1725,plain,
! [X0] :
( compose(g,compose(g,X0)) = compose(compose(g,g),X0)
| domain(a) != domain(X0)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f211]) ).
fof(f1726,plain,
! [X0] :
( compose(g,compose(h,X0)) = compose(compose(g,h),X0)
| domain(a) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f211]) ).
fof(f1727,plain,
! [X0] :
( compose(g,compose(a,X0)) = compose(compose(g,a),X0)
| domain(b) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f211]) ).
fof(f1728,plain,
! [X0,X1] :
( compose(g,compose(codomain(X0),X1)) = compose(compose(g,codomain(X0)),X1)
| codomain(X0) != domain(X1)
| domain(a) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f211]) ).
fof(f1729,plain,
! [X0,X1] :
( compose(g,compose(domain(X0),X1)) = compose(compose(g,domain(X0)),X1)
| domain(X0) != domain(X1)
| domain(a) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f211]) ).
fof(f1730,plain,
! [X0] :
( compose(g,compose(X0,compose(g,a))) = compose(compose(g,X0),compose(g,a))
| codomain(X0) != domain(h)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f1108,f211]) ).
fof(f1731,plain,
! [X0] :
( compose(g,compose(X0,compose(h,compose(a,b)))) = compose(compose(g,X0),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f1068,f211]) ).
fof(f1732,plain,
! [X0] :
( compose(g,compose(X0,compose(h,a))) = compose(compose(g,X0),compose(h,a))
| codomain(X0) != domain(h)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f76,f211]) ).
fof(f1733,plain,
! [X0] :
( compose(g,compose(X0,compose(a,b))) = compose(compose(g,X0),compose(a,b))
| codomain(X0) != domain(a)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f60,f211]) ).
fof(f1734,plain,
! [X0,X1] :
( compose(g,compose(X0,domain(X1))) = compose(compose(g,X0),domain(X1))
| codomain(X0) != domain(X1)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f211]) ).
fof(f1735,plain,
! [X0,X1] :
( compose(g,compose(X0,codomain(X1))) = compose(compose(g,X0),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f16,f211]) ).
fof(f1736,definition,
( sQ72_spl
<=> domain(a) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1738,plain,
( sQ72_spl
| domain(a) != domain(compose(h,a)) ),
inference(component_clause,[status(thm)],[f1736]) ).
fof(f1739,definition,
( sQ73_spl
<=> compose(g,compose(compose(h,a),b)) = compose(compose(g,compose(h,a)),b) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1742,plain,
( sQ73_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f1714,f1736,f1739]) ).
fof(f1743,definition,
( sQ74_spl
<=> domain(a) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1745,plain,
( sQ74_spl
| domain(a) != domain(compose(g,a)) ),
inference(component_clause,[status(thm)],[f1743]) ).
fof(f1746,definition,
( sQ75_spl
<=> compose(g,compose(compose(g,a),b)) = compose(compose(g,compose(g,a)),b) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1749,plain,
( sQ75_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f1715,f1743,f1746]) ).
fof(f1750,definition,
( sQ76_spl
<=> compose(g,compose(g,a)) = compose(compose(g,g),a) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1753,plain,
( sQ76_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1716,f591,f1750]) ).
fof(f1754,definition,
( sQ77_spl
<=> compose(g,compose(h,a)) = compose(compose(g,h),a) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1757,plain,
( sQ77_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1717,f584,f1754]) ).
fof(f1758,definition,
( sQ78_spl
<=> compose(g,compose(a,b)) = compose(compose(g,a),b) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1761,plain,
( sQ78_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1718,f606,f1758]) ).
fof(f1762,plain,
! [X0] :
( compose(g,compose(domain(X0),X0)) = compose(compose(g,domain(X0)),X0)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f1719]) ).
fof(f1763,plain,
! [X0] :
( compose(g,X0) = compose(compose(g,domain(X0)),X0)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f17,f1762]) ).
fof(f1764,plain,
! [X0] :
( compose(g,X0) = compose(compose(g,X0),codomain(X0))
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f18,f1720]) ).
fof(f1765,definition,
( sQ79_spl
<=> domain(a) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1767,plain,
( sQ79_spl
| domain(a) != domain(compose(a,b)) ),
inference(component_clause,[status(thm)],[f1765]) ).
fof(f1768,definition,
! [X0] :
( sQ80_spl
<=> ( compose(g,compose(compose(a,b),X0)) = compose(compose(g,compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1769,plain,
! [X0] :
( ~ sQ80_spl
| compose(g,compose(compose(a,b),X0)) = compose(compose(g,compose(a,b)),X0)
| codomain(b) != domain(X0) ),
inference(component_clause,[status(thm)],[f1768]) ).
fof(f1771,plain,
( sQ80_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f1721,f1765,f1768]) ).
fof(f1772,definition,
( sQ81_spl
<=> domain(a) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1774,plain,
( sQ81_spl
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(component_clause,[status(thm)],[f1772]) ).
fof(f1775,definition,
! [X0] :
( sQ82_spl
<=> ( compose(g,compose(compose(h,compose(a,b)),X0)) = compose(compose(g,compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1778,plain,
( sQ82_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f1722,f1772,f1775]) ).
fof(f1779,definition,
! [X0] :
( sQ83_spl
<=> ( compose(g,compose(compose(h,a),X0)) = compose(compose(g,compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1782,plain,
( sQ83_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f1723,f1736,f1779]) ).
fof(f1783,definition,
! [X0] :
( sQ84_spl
<=> ( compose(g,compose(compose(g,a),X0)) = compose(compose(g,compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1786,plain,
( sQ84_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f1724,f1743,f1783]) ).
fof(f1787,definition,
! [X0] :
( sQ85_spl
<=> ( compose(g,compose(g,X0)) = compose(compose(g,g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1790,plain,
( sQ85_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1725,f591,f1787]) ).
fof(f1791,definition,
! [X0] :
( sQ86_spl
<=> ( compose(g,compose(h,X0)) = compose(compose(g,h),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1794,plain,
( sQ86_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1726,f584,f1791]) ).
fof(f1795,definition,
! [X0] :
( sQ87_spl
<=> ( compose(g,compose(a,X0)) = compose(compose(g,a),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1798,plain,
( sQ87_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1727,f606,f1795]) ).
fof(f1799,plain,
! [X0,X1] :
( compose(g,compose(codomain(X0),X1)) = compose(compose(g,codomain(X0)),X1)
| codomain(X0) != domain(X1)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f1728]) ).
fof(f1800,plain,
! [X0,X1] :
( compose(g,compose(domain(X0),X1)) = compose(compose(g,domain(X0)),X1)
| domain(X0) != domain(X1)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f1729]) ).
fof(f1801,plain,
( sQ74_spl
| domain(a) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f1108,f1745]) ).
fof(f1802,plain,
( sQ72_spl
| domain(a) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f76,f1738]) ).
fof(f1804,plain,
( sQ81_spl
| domain(a) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f1068,f1774]) ).
fof(f1805,plain,
( sQ79_spl
| domain(a) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f60,f1767]) ).
fof(f1806,plain,
( sQ79_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1805]) ).
fof(f1807,plain,
sQ79_spl,
inference(contradiction_clause,[status(thm)],[f1806]) ).
fof(f1808,plain,
! [X0] :
( ~ sQ80_spl
| compose(g,compose(compose(a,b),X0)) = compose(compose(h,compose(a,b)),X0)
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f29,f1769]) ).
fof(f1941,definition,
( sQ88_spl
<=> domain(b) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1943,plain,
( sQ88_spl
| domain(b) != domain(b) ),
inference(component_clause,[status(thm)],[f1941]) ).
fof(f1949,plain,
( sQ5_spl
| domain(b) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f560]) ).
fof(f1950,plain,
( sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1949]) ).
fof(f1951,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f1950]) ).
fof(f1954,plain,
( codomain(compose(g,domain(compose(g,a)))) = domain(compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f613]) ).
fof(f1955,plain,
( codomain(compose(g,domain(compose(h,compose(a,b))))) = domain(compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f613]) ).
fof(f1956,plain,
( codomain(compose(g,domain(compose(h,a)))) = domain(compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f613]) ).
fof(f1957,plain,
( codomain(compose(g,domain(compose(a,b)))) = domain(compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f613]) ).
fof(f1967,definition,
( sQ90_spl
<=> codomain(compose(g,domain(compose(g,a)))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1970,plain,
( sQ90_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1954,f584,f1967]) ).
fof(f1971,definition,
( sQ91_spl
<=> codomain(compose(g,domain(compose(h,compose(a,b))))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1974,plain,
( sQ91_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1955,f584,f1971]) ).
fof(f1975,definition,
( sQ92_spl
<=> codomain(compose(g,domain(compose(h,a)))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1978,plain,
( sQ92_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1956,f584,f1975]) ).
fof(f1979,definition,
( sQ93_spl
<=> codomain(compose(g,domain(compose(a,b)))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1982,plain,
( sQ93_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1957,f606,f1979]) ).
fof(f1994,plain,
( codomain(compose(g,codomain(compose(a,b)))) = codomain(compose(a,b))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f614]) ).
fof(f1995,plain,
( codomain(compose(g,codomain(compose(h,compose(a,b))))) = codomain(compose(h,compose(a,b)))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f614]) ).
fof(f1996,plain,
( codomain(compose(g,codomain(compose(h,a)))) = codomain(compose(h,a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f614]) ).
fof(f1997,plain,
( codomain(compose(g,codomain(compose(g,a)))) = codomain(compose(g,a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f614]) ).
fof(f1998,plain,
( codomain(compose(g,codomain(g))) = codomain(g)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f614]) ).
fof(f1999,plain,
( codomain(compose(g,codomain(h))) = codomain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f614]) ).
fof(f2000,plain,
( codomain(compose(g,codomain(a))) = codomain(a)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f614]) ).
fof(f2009,definition,
( sQ94_spl
<=> codomain(compose(g,codomain(compose(a,b)))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f2012,plain,
( sQ94_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f1994,f1570,f2009]) ).
fof(f2013,definition,
( sQ95_spl
<=> codomain(compose(g,codomain(compose(h,compose(a,b))))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f2016,plain,
( sQ95_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f1995,f1570,f2013]) ).
fof(f2017,definition,
( sQ96_spl
<=> codomain(compose(g,codomain(compose(h,a)))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f2020,plain,
( sQ96_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1996,f715,f2017]) ).
fof(f2021,definition,
( sQ97_spl
<=> codomain(compose(g,codomain(compose(g,a)))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f2024,plain,
( sQ97_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1997,f715,f2021]) ).
fof(f2025,definition,
( sQ98_spl
<=> codomain(compose(g,codomain(g))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f2028,plain,
( sQ98_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1998,f606,f2025]) ).
fof(f2029,definition,
( sQ99_spl
<=> codomain(compose(g,codomain(h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f2032,plain,
( sQ99_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1999,f606,f2029]) ).
fof(f2033,definition,
( sQ100_spl
<=> codomain(compose(g,codomain(a))) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f2036,plain,
( sQ100_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2000,f715,f2033]) ).
fof(f2044,plain,
( compose(h,compose(compose(h,a),b)) = compose(compose(h,compose(h,a)),b)
| domain(a) != domain(compose(h,a)) ),
inference(resolution,[status(thm)],[f212,f131]) ).
fof(f2045,plain,
( compose(h,compose(compose(g,a),b)) = compose(compose(h,compose(g,a)),b)
| domain(a) != domain(compose(g,a)) ),
inference(resolution,[status(thm)],[f212,f130]) ).
fof(f2046,plain,
( compose(h,compose(g,a)) = compose(compose(h,g),a)
| domain(a) != domain(g) ),
inference(resolution,[status(thm)],[f212,f74]) ).
fof(f2047,plain,
( compose(h,compose(h,a)) = compose(compose(h,h),a)
| domain(a) != domain(h) ),
inference(resolution,[status(thm)],[f212,f69]) ).
fof(f2048,plain,
( compose(h,compose(a,b)) = compose(compose(h,a),b)
| domain(a) != domain(a) ),
inference(resolution,[status(thm)],[f212,f22]) ).
fof(f2049,plain,
! [X0] :
( compose(h,compose(domain(X0),X0)) = compose(compose(h,domain(X0)),X0)
| domain(a) != domain(domain(X0)) ),
inference(resolution,[status(thm)],[f212,f15]) ).
fof(f2050,plain,
! [X0] :
( compose(h,compose(X0,codomain(X0))) = compose(compose(h,X0),codomain(X0))
| domain(a) != domain(X0) ),
inference(resolution,[status(thm)],[f212,f16]) ).
fof(f2051,plain,
! [X0] :
( compose(h,compose(compose(a,b),X0)) = compose(compose(h,compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f212]) ).
fof(f2052,plain,
! [X0] :
( compose(h,compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f212]) ).
fof(f2053,plain,
! [X0] :
( compose(h,compose(compose(h,a),X0)) = compose(compose(h,compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f212]) ).
fof(f2054,plain,
! [X0] :
( compose(h,compose(compose(g,a),X0)) = compose(compose(h,compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f212]) ).
fof(f2055,plain,
! [X0] :
( compose(h,compose(g,X0)) = compose(compose(h,g),X0)
| domain(a) != domain(X0)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f212]) ).
fof(f2056,plain,
! [X0] :
( compose(h,compose(h,X0)) = compose(compose(h,h),X0)
| domain(a) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f212]) ).
fof(f2057,plain,
! [X0] :
( compose(h,compose(a,X0)) = compose(compose(h,a),X0)
| domain(b) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f212]) ).
fof(f2058,plain,
! [X0,X1] :
( compose(h,compose(codomain(X0),X1)) = compose(compose(h,codomain(X0)),X1)
| codomain(X0) != domain(X1)
| domain(a) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f212]) ).
fof(f2059,plain,
! [X0,X1] :
( compose(h,compose(domain(X0),X1)) = compose(compose(h,domain(X0)),X1)
| domain(X0) != domain(X1)
| domain(a) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f212]) ).
fof(f2060,plain,
! [X0] :
( compose(h,compose(X0,compose(g,a))) = compose(compose(h,X0),compose(g,a))
| codomain(X0) != domain(h)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f1108,f212]) ).
fof(f2061,plain,
! [X0] :
( compose(h,compose(X0,compose(h,compose(a,b)))) = compose(compose(h,X0),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f1068,f212]) ).
fof(f2062,plain,
! [X0] :
( compose(h,compose(X0,compose(h,a))) = compose(compose(h,X0),compose(h,a))
| codomain(X0) != domain(h)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f76,f212]) ).
fof(f2063,plain,
! [X0] :
( compose(h,compose(X0,compose(a,b))) = compose(compose(h,X0),compose(a,b))
| codomain(X0) != domain(a)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f60,f212]) ).
fof(f2064,plain,
! [X0,X1] :
( compose(h,compose(X0,domain(X1))) = compose(compose(h,X0),domain(X1))
| codomain(X0) != domain(X1)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f212]) ).
fof(f2065,plain,
! [X0,X1] :
( compose(h,compose(X0,codomain(X1))) = compose(compose(h,X0),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f16,f212]) ).
fof(f2066,definition,
( sQ101_spl
<=> compose(h,compose(compose(h,a),b)) = compose(compose(h,compose(h,a)),b) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f2069,plain,
( sQ101_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f2044,f1736,f2066]) ).
fof(f2070,definition,
( sQ102_spl
<=> compose(h,compose(compose(g,a),b)) = compose(compose(h,compose(g,a)),b) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f2073,plain,
( sQ102_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f2045,f1743,f2070]) ).
fof(f2074,definition,
( sQ103_spl
<=> compose(h,compose(g,a)) = compose(compose(h,g),a) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f2077,plain,
( sQ103_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2046,f591,f2074]) ).
fof(f2078,definition,
( sQ104_spl
<=> compose(h,compose(h,a)) = compose(compose(h,h),a) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f2081,plain,
( sQ104_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2047,f584,f2078]) ).
fof(f2082,definition,
( sQ105_spl
<=> compose(h,compose(a,b)) = compose(compose(h,a),b) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f2085,plain,
( sQ105_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f2048,f606,f2082]) ).
fof(f2086,plain,
! [X0] :
( compose(h,compose(domain(X0),X0)) = compose(compose(h,domain(X0)),X0)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f2049]) ).
fof(f2087,plain,
! [X0] :
( compose(h,X0) = compose(compose(h,domain(X0)),X0)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f17,f2086]) ).
fof(f2088,plain,
! [X0] :
( compose(h,X0) = compose(compose(h,X0),codomain(X0))
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f18,f2050]) ).
fof(f2089,definition,
! [X0] :
( sQ106_spl
<=> ( compose(h,compose(compose(a,b),X0)) = compose(compose(h,compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f2090,plain,
! [X0] :
( ~ sQ106_spl
| compose(h,compose(compose(a,b),X0)) = compose(compose(h,compose(a,b)),X0)
| codomain(b) != domain(X0) ),
inference(component_clause,[status(thm)],[f2089]) ).
fof(f2092,plain,
( sQ106_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f2051,f1765,f2089]) ).
fof(f2093,definition,
! [X0] :
( sQ107_spl
<=> ( compose(h,compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f2096,plain,
( sQ107_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f2052,f1772,f2093]) ).
fof(f2097,definition,
! [X0] :
( sQ108_spl
<=> ( compose(h,compose(compose(h,a),X0)) = compose(compose(h,compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f2100,plain,
( sQ108_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f2053,f1736,f2097]) ).
fof(f2101,definition,
! [X0] :
( sQ109_spl
<=> ( compose(h,compose(compose(g,a),X0)) = compose(compose(h,compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f2104,plain,
( sQ109_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f2054,f1743,f2101]) ).
fof(f2105,definition,
! [X0] :
( sQ110_spl
<=> ( compose(h,compose(g,X0)) = compose(compose(h,g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f2108,plain,
( sQ110_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2055,f591,f2105]) ).
fof(f2109,definition,
! [X0] :
( sQ111_spl
<=> ( compose(h,compose(h,X0)) = compose(compose(h,h),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f2112,plain,
( sQ111_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2056,f584,f2109]) ).
fof(f2113,definition,
! [X0] :
( sQ112_spl
<=> ( compose(h,compose(a,X0)) = compose(compose(h,a),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f2116,plain,
( sQ112_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f2057,f606,f2113]) ).
fof(f2117,plain,
! [X0,X1] :
( compose(h,compose(codomain(X0),X1)) = compose(compose(h,codomain(X0)),X1)
| codomain(X0) != domain(X1)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f2058]) ).
fof(f2118,plain,
! [X0,X1] :
( compose(h,compose(domain(X0),X1)) = compose(compose(h,domain(X0)),X1)
| domain(X0) != domain(X1)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f2059]) ).
fof(f2121,plain,
( codomain(compose(h,domain(compose(g,a)))) = domain(compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f678]) ).
fof(f2122,plain,
( codomain(compose(h,domain(compose(h,compose(a,b))))) = domain(compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f678]) ).
fof(f2123,plain,
( codomain(compose(h,domain(compose(h,a)))) = domain(compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f678]) ).
fof(f2124,plain,
( codomain(compose(h,domain(compose(a,b)))) = domain(compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f678]) ).
fof(f2134,definition,
( sQ113_spl
<=> codomain(compose(h,domain(compose(g,a)))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f2137,plain,
( sQ113_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2121,f584,f2134]) ).
fof(f2138,definition,
( sQ114_spl
<=> codomain(compose(h,domain(compose(h,compose(a,b))))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f2141,plain,
( sQ114_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2122,f584,f2138]) ).
fof(f2142,definition,
( sQ115_spl
<=> codomain(compose(h,domain(compose(h,a)))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f2145,plain,
( sQ115_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2123,f584,f2142]) ).
fof(f2146,definition,
( sQ116_spl
<=> codomain(compose(h,domain(compose(a,b)))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f2149,plain,
( sQ116_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f2124,f606,f2146]) ).
fof(f2161,plain,
( codomain(compose(h,codomain(compose(a,b)))) = codomain(compose(a,b))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f679]) ).
fof(f2162,plain,
( codomain(compose(h,codomain(compose(h,compose(a,b))))) = codomain(compose(h,compose(a,b)))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f679]) ).
fof(f2163,plain,
( codomain(compose(h,codomain(compose(h,a)))) = codomain(compose(h,a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f679]) ).
fof(f2164,plain,
( codomain(compose(h,codomain(compose(g,a)))) = codomain(compose(g,a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f679]) ).
fof(f2165,plain,
( codomain(compose(h,codomain(g))) = codomain(g)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f679]) ).
fof(f2166,plain,
( codomain(compose(h,codomain(h))) = codomain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f679]) ).
fof(f2167,plain,
( codomain(compose(h,codomain(a))) = codomain(a)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f679]) ).
fof(f2176,definition,
( sQ117_spl
<=> codomain(compose(h,codomain(compose(a,b)))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f2179,plain,
( sQ117_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f2161,f1570,f2176]) ).
fof(f2180,definition,
( sQ118_spl
<=> codomain(compose(h,codomain(compose(h,compose(a,b))))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f2183,plain,
( sQ118_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f2162,f1570,f2180]) ).
fof(f2184,definition,
( sQ119_spl
<=> codomain(compose(h,codomain(compose(h,a)))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f2187,plain,
( sQ119_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2163,f715,f2184]) ).
fof(f2188,definition,
( sQ120_spl
<=> codomain(compose(h,codomain(compose(g,a)))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f2191,plain,
( sQ120_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2164,f715,f2188]) ).
fof(f2192,definition,
( sQ121_spl
<=> codomain(compose(h,codomain(g))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f2195,plain,
( sQ121_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f2165,f606,f2192]) ).
fof(f2196,definition,
( sQ122_spl
<=> codomain(compose(h,codomain(h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f2199,plain,
( sQ122_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f2166,f606,f2196]) ).
fof(f2200,definition,
( sQ123_spl
<=> codomain(compose(h,codomain(a))) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f2203,plain,
( sQ123_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2167,f715,f2200]) ).
fof(f2212,plain,
( codomain(compose(a,domain(compose(g,a)))) = domain(compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f722]) ).
fof(f2213,plain,
( codomain(compose(a,domain(compose(h,compose(a,b))))) = domain(compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f722]) ).
fof(f2214,plain,
( codomain(compose(a,domain(compose(h,a)))) = domain(compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f722]) ).
fof(f2215,plain,
( codomain(compose(a,domain(compose(a,b)))) = domain(compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f722]) ).
fof(f2222,definition,
( sQ124_spl
<=> codomain(compose(a,domain(compose(g,a)))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f2225,plain,
( sQ124_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2212,f693,f2222]) ).
fof(f2226,definition,
( sQ125_spl
<=> codomain(compose(a,domain(compose(h,compose(a,b))))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f2229,plain,
( sQ125_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2213,f693,f2226]) ).
fof(f2230,definition,
( sQ126_spl
<=> codomain(compose(a,domain(compose(h,a)))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f2233,plain,
( sQ126_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2214,f693,f2230]) ).
fof(f2234,definition,
( sQ127_spl
<=> codomain(compose(a,domain(compose(a,b)))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f2237,plain,
( sQ127_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2215,f715,f2234]) ).
fof(f2247,plain,
( codomain(compose(a,codomain(compose(a,b)))) = codomain(compose(a,b))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f723]) ).
fof(f2248,plain,
( codomain(compose(a,codomain(compose(h,compose(a,b))))) = codomain(compose(h,compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f723]) ).
fof(f2249,plain,
( codomain(compose(a,codomain(compose(h,a)))) = codomain(compose(h,a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f723]) ).
fof(f2250,plain,
( codomain(compose(a,codomain(compose(g,a)))) = codomain(compose(g,a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f723]) ).
fof(f2251,plain,
( codomain(compose(a,codomain(g))) = codomain(g)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f723]) ).
fof(f2252,plain,
( codomain(compose(a,codomain(h))) = codomain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f723]) ).
fof(f2253,plain,
( codomain(compose(a,codomain(a))) = codomain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f723]) ).
fof(f2265,definition,
( sQ128_spl
<=> domain(b) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f2267,plain,
( sQ128_spl
| domain(b) != codomain(b) ),
inference(component_clause,[status(thm)],[f2265]) ).
fof(f2268,definition,
( sQ129_spl
<=> codomain(compose(a,codomain(compose(a,b)))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f2271,plain,
( sQ129_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f2247,f2265,f2268]) ).
fof(f2272,definition,
( sQ130_spl
<=> codomain(compose(a,codomain(compose(h,compose(a,b))))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f2275,plain,
( sQ130_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f2248,f2265,f2272]) ).
fof(f2276,definition,
( sQ131_spl
<=> codomain(compose(a,codomain(compose(h,a)))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f2279,plain,
( sQ131_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f2249,f1941,f2276]) ).
fof(f2280,definition,
( sQ132_spl
<=> codomain(compose(a,codomain(compose(g,a)))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f2283,plain,
( sQ132_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f2250,f1941,f2280]) ).
fof(f2284,definition,
( sQ133_spl
<=> codomain(compose(a,codomain(g))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f2287,plain,
( sQ133_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2251,f715,f2284]) ).
fof(f2288,definition,
( sQ134_spl
<=> codomain(compose(a,codomain(h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f2291,plain,
( sQ134_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2252,f715,f2288]) ).
fof(f2292,definition,
( sQ135_spl
<=> codomain(compose(a,codomain(a))) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f2295,plain,
( sQ135_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f2253,f1941,f2292]) ).
fof(f2300,plain,
( sQ88_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1943]) ).
fof(f2301,plain,
sQ88_spl,
inference(contradiction_clause,[status(thm)],[f2300]) ).
fof(f2308,plain,
( compose(a,compose(compose(h,a),b)) = compose(compose(a,compose(h,a)),b)
| domain(b) != domain(compose(h,a)) ),
inference(resolution,[status(thm)],[f213,f131]) ).
fof(f2309,plain,
( compose(a,compose(compose(g,a),b)) = compose(compose(a,compose(g,a)),b)
| domain(b) != domain(compose(g,a)) ),
inference(resolution,[status(thm)],[f213,f130]) ).
fof(f2310,plain,
( compose(a,compose(g,a)) = compose(compose(a,g),a)
| domain(b) != domain(g) ),
inference(resolution,[status(thm)],[f213,f74]) ).
fof(f2311,plain,
( compose(a,compose(h,a)) = compose(compose(a,h),a)
| domain(b) != domain(h) ),
inference(resolution,[status(thm)],[f213,f69]) ).
fof(f2312,plain,
( compose(a,compose(a,b)) = compose(compose(a,a),b)
| domain(b) != domain(a) ),
inference(resolution,[status(thm)],[f213,f22]) ).
fof(f2313,plain,
! [X0] :
( compose(a,compose(domain(X0),X0)) = compose(compose(a,domain(X0)),X0)
| domain(b) != domain(domain(X0)) ),
inference(resolution,[status(thm)],[f213,f15]) ).
fof(f2314,plain,
! [X0] :
( compose(a,compose(X0,codomain(X0))) = compose(compose(a,X0),codomain(X0))
| domain(b) != domain(X0) ),
inference(resolution,[status(thm)],[f213,f16]) ).
fof(f2315,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)],[f120,f213]) ).
fof(f2316,plain,
! [X0] :
( compose(a,compose(compose(h,compose(a,b)),X0)) = compose(compose(a,compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f213]) ).
fof(f2317,plain,
! [X0] :
( compose(a,compose(compose(h,a),X0)) = compose(compose(a,compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f213]) ).
fof(f2318,plain,
! [X0] :
( compose(a,compose(compose(g,a),X0)) = compose(compose(a,compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f213]) ).
fof(f2319,plain,
! [X0] :
( compose(a,compose(g,X0)) = compose(compose(a,g),X0)
| domain(a) != domain(X0)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f213]) ).
fof(f2320,plain,
! [X0] :
( compose(a,compose(h,X0)) = compose(compose(a,h),X0)
| domain(a) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f213]) ).
fof(f2321,plain,
! [X0] :
( compose(a,compose(a,X0)) = compose(compose(a,a),X0)
| domain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f213]) ).
fof(f2322,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)],[f38,f213]) ).
fof(f2323,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)],[f15,f213]) ).
fof(f2324,plain,
! [X0] :
( compose(a,compose(X0,compose(g,a))) = compose(compose(a,X0),compose(g,a))
| codomain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f1108,f213]) ).
fof(f2325,plain,
! [X0] :
( compose(a,compose(X0,compose(h,compose(a,b)))) = compose(compose(a,X0),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f1068,f213]) ).
fof(f2326,plain,
! [X0] :
( compose(a,compose(X0,compose(h,a))) = compose(compose(a,X0),compose(h,a))
| codomain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f76,f213]) ).
fof(f2327,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)],[f60,f213]) ).
fof(f2328,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)],[f37,f213]) ).
fof(f2329,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)],[f16,f213]) ).
fof(f2330,definition,
( sQ136_spl
<=> domain(b) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f2332,plain,
( sQ136_spl
| domain(b) != domain(compose(h,a)) ),
inference(component_clause,[status(thm)],[f2330]) ).
fof(f2333,definition,
( sQ137_spl
<=> compose(a,compose(compose(h,a),b)) = compose(compose(a,compose(h,a)),b) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f2336,plain,
( sQ137_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f2308,f2330,f2333]) ).
fof(f2337,definition,
( sQ138_spl
<=> domain(b) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f2339,plain,
( sQ138_spl
| domain(b) != domain(compose(g,a)) ),
inference(component_clause,[status(thm)],[f2337]) ).
fof(f2340,definition,
( sQ139_spl
<=> compose(a,compose(compose(g,a),b)) = compose(compose(a,compose(g,a)),b) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f2343,plain,
( sQ139_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f2309,f2337,f2340]) ).
fof(f2344,definition,
( sQ140_spl
<=> compose(a,compose(g,a)) = compose(compose(a,g),a) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f2347,plain,
( sQ140_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f2310,f700,f2344]) ).
fof(f2348,definition,
( sQ141_spl
<=> compose(a,compose(h,a)) = compose(compose(a,h),a) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f2351,plain,
( sQ141_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2311,f693,f2348]) ).
fof(f2352,definition,
( sQ142_spl
<=> compose(a,compose(a,b)) = compose(compose(a,a),b) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f2355,plain,
( sQ142_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2312,f715,f2352]) ).
fof(f2356,plain,
! [X0] :
( compose(a,compose(domain(X0),X0)) = compose(compose(a,domain(X0)),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f2313]) ).
fof(f2357,plain,
! [X0] :
( compose(a,X0) = compose(compose(a,domain(X0)),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f17,f2356]) ).
fof(f2358,plain,
! [X0] :
( compose(a,X0) = compose(compose(a,X0),codomain(X0))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f18,f2314]) ).
fof(f2359,definition,
( sQ143_spl
<=> domain(b) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f2361,plain,
( sQ143_spl
| domain(b) != domain(compose(a,b)) ),
inference(component_clause,[status(thm)],[f2359]) ).
fof(f2362,definition,
! [X0] :
( sQ144_spl
<=> ( compose(a,compose(compose(a,b),X0)) = compose(compose(a,compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f2365,plain,
( sQ144_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f2315,f2359,f2362]) ).
fof(f2366,definition,
( sQ145_spl
<=> domain(b) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f2368,plain,
( sQ145_spl
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(component_clause,[status(thm)],[f2366]) ).
fof(f2369,definition,
! [X0] :
( sQ146_spl
<=> ( compose(a,compose(compose(h,compose(a,b)),X0)) = compose(compose(a,compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f2372,plain,
( sQ146_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f2316,f2366,f2369]) ).
fof(f2373,definition,
! [X0] :
( sQ147_spl
<=> ( compose(a,compose(compose(h,a),X0)) = compose(compose(a,compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f2376,plain,
( sQ147_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f2317,f2330,f2373]) ).
fof(f2377,definition,
! [X0] :
( sQ148_spl
<=> ( compose(a,compose(compose(g,a),X0)) = compose(compose(a,compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f2380,plain,
( sQ148_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f2318,f2337,f2377]) ).
fof(f2381,definition,
! [X0] :
( sQ149_spl
<=> ( compose(a,compose(g,X0)) = compose(compose(a,g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f2384,plain,
( sQ149_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f2319,f700,f2381]) ).
fof(f2385,definition,
! [X0] :
( sQ150_spl
<=> ( compose(a,compose(h,X0)) = compose(compose(a,h),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f2388,plain,
( sQ150_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2320,f693,f2385]) ).
fof(f2389,definition,
! [X0] :
( sQ151_spl
<=> ( compose(a,compose(a,X0)) = compose(compose(a,a),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f2392,plain,
( sQ151_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2321,f715,f2389]) ).
fof(f2393,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)],[f16,f2322]) ).
fof(f2394,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)],[f37,f2323]) ).
fof(f2395,plain,
( sQ138_spl
| domain(b) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f1108,f2339]) ).
fof(f2396,plain,
( sQ136_spl
| domain(b) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f76,f2332]) ).
fof(f2397,plain,
( sQ145_spl
| domain(b) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f1068,f2368]) ).
fof(f2398,plain,
( sQ143_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f60,f2361]) ).
fof(f2667,plain,
( domain(compose(domain(g),g)) = domain(g)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f1150]) ).
fof(f2668,plain,
( domain(compose(domain(compose(g,a)),g)) = domain(compose(g,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1150]) ).
fof(f2669,plain,
( domain(compose(domain(compose(h,compose(a,b))),g)) = domain(compose(h,compose(a,b)))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1150]) ).
fof(f2670,plain,
( domain(compose(domain(compose(h,a)),g)) = domain(compose(h,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1150]) ).
fof(f2671,plain,
( domain(compose(domain(compose(a,b)),g)) = domain(compose(a,b))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f1150]) ).
fof(f2673,plain,
! [X0] :
( domain(compose(domain(codomain(X0)),g)) = domain(codomain(X0))
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f16,f1150]) ).
fof(f2687,definition,
( sQ152_spl
<=> domain(h) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f2689,plain,
( sQ152_spl
| domain(h) != domain(h) ),
inference(component_clause,[status(thm)],[f2687]) ).
fof(f2690,definition,
( sQ153_spl
<=> domain(compose(domain(g),g)) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f2693,plain,
( sQ153_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f2667,f2687,f2690]) ).
fof(f2694,definition,
( sQ154_spl
<=> domain(compose(domain(compose(g,a)),g)) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f2697,plain,
( sQ154_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f2668,f2687,f2694]) ).
fof(f2698,definition,
( sQ155_spl
<=> domain(compose(domain(compose(h,compose(a,b))),g)) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f2701,plain,
( sQ155_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f2669,f2687,f2698]) ).
fof(f2702,definition,
( sQ156_spl
<=> domain(compose(domain(compose(h,a)),g)) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f2705,plain,
( sQ156_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f2670,f2687,f2702]) ).
fof(f2706,definition,
( sQ157_spl
<=> domain(compose(domain(compose(a,b)),g)) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f2709,plain,
( sQ157_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2671,f584,f2706]) ).
fof(f2712,plain,
! [X0] :
( domain(compose(codomain(X0),g)) = domain(codomain(X0))
| codomain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f16,f2673]) ).
fof(f2713,plain,
! [X0] :
( domain(compose(codomain(X0),g)) = codomain(X0)
| codomain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f16,f2712]) ).
fof(f2715,plain,
( sQ152_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2689]) ).
fof(f2716,plain,
sQ152_spl,
inference(contradiction_clause,[status(thm)],[f2715]) ).
fof(f2745,plain,
! [X0,X1] :
( compose(domain(X0),compose(g,X1)) = compose(compose(domain(X0),g),X1)
| codomain(g) != domain(X1)
| domain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f215]) ).
fof(f2746,plain,
! [X0,X1] :
( compose(domain(X0),compose(compose(g,a),X1)) = compose(compose(domain(X0),compose(g,a)),X1)
| codomain(compose(g,a)) != domain(X1)
| domain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f215]) ).
fof(f2747,plain,
! [X0,X1] :
( compose(domain(X0),compose(compose(h,compose(a,b)),X1)) = compose(compose(domain(X0),compose(h,compose(a,b))),X1)
| codomain(compose(h,compose(a,b))) != domain(X1)
| domain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f215]) ).
fof(f2748,plain,
! [X0,X1] :
( compose(domain(X0),compose(compose(h,a),X1)) = compose(compose(domain(X0),compose(h,a)),X1)
| codomain(compose(h,a)) != domain(X1)
| domain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f215]) ).
fof(f2749,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)],[f60,f215]) ).
fof(f2750,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)],[f37,f215]) ).
fof(f2751,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)],[f16,f215]) ).
fof(f2802,plain,
! [X0,X1] :
( compose(domain(X0),compose(g,X1)) = compose(compose(domain(X0),g),X1)
| domain(a) != domain(X1)
| domain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f74,f2745]) ).
fof(f2803,plain,
! [X0,X1] :
( compose(domain(X0),compose(compose(g,a),X1)) = compose(compose(domain(X0),compose(g,a)),X1)
| domain(b) != domain(X1)
| domain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f130,f2746]) ).
fof(f2804,plain,
! [X0,X1] :
( compose(domain(X0),compose(compose(h,compose(a,b)),X1)) = compose(compose(domain(X0),compose(h,compose(a,b))),X1)
| codomain(b) != domain(X1)
| domain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f581,f2747]) ).
fof(f2805,plain,
! [X0,X1] :
( compose(domain(X0),compose(compose(h,a),X1)) = compose(compose(domain(X0),compose(h,a)),X1)
| domain(b) != domain(X1)
| domain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f131,f2748]) ).
fof(f2806,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)],[f120,f2749]) ).
fof(f2807,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)],[f15,f2750]) ).
fof(f2808,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)],[f38,f2751]) ).
fof(f2810,plain,
( ~ sQ4_spl
| domain(b) = domain(b)
| codomain(domain(b)) != domain(a) ),
inference(resolution,[status(thm)],[f556,f17]) ).
fof(f2812,plain,
( ~ sQ4_spl
| sQ88_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f2810,f562,f1941,f555]) ).
fof(f2815,plain,
( domain(compose(codomain(compose(a,b)),g)) = codomain(compose(a,b))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f2713]) ).
fof(f2816,plain,
( domain(compose(codomain(compose(h,compose(a,b))),g)) = codomain(compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f2713]) ).
fof(f2817,plain,
( domain(compose(codomain(compose(h,a)),g)) = codomain(compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f2713]) ).
fof(f2818,plain,
( domain(compose(codomain(compose(g,a)),g)) = codomain(compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f2713]) ).
fof(f2819,plain,
( domain(compose(codomain(g),g)) = codomain(g)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f2713]) ).
fof(f2820,plain,
( domain(compose(codomain(h),g)) = codomain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f2713]) ).
fof(f2821,plain,
( domain(compose(codomain(a),g)) = codomain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f2713]) ).
fof(f2827,definition,
( sQ158_spl
<=> domain(compose(codomain(compose(a,b)),g)) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f2830,plain,
( sQ158_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f2815,f1555,f2827]) ).
fof(f2831,definition,
( sQ159_spl
<=> domain(compose(codomain(compose(h,compose(a,b))),g)) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f2834,plain,
( sQ159_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f2816,f1555,f2831]) ).
fof(f2835,definition,
( sQ160_spl
<=> domain(compose(codomain(compose(h,a)),g)) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f2838,plain,
( sQ160_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2817,f693,f2835]) ).
fof(f2839,definition,
( sQ161_spl
<=> domain(compose(codomain(compose(g,a)),g)) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f2842,plain,
( sQ161_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2818,f693,f2839]) ).
fof(f2843,definition,
( sQ162_spl
<=> domain(compose(codomain(g),g)) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f2846,plain,
( sQ162_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2819,f584,f2843]) ).
fof(f2847,definition,
( sQ163_spl
<=> domain(compose(codomain(h),g)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f2850,plain,
( sQ163_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2820,f584,f2847]) ).
fof(f2851,definition,
( sQ164_spl
<=> domain(compose(codomain(a),g)) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f2854,plain,
( sQ164_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2821,f693,f2851]) ).
fof(f2861,plain,
( domain(compose(h,domain(compose(g,a)))) = domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f476]) ).
fof(f2862,plain,
( domain(compose(h,domain(compose(h,compose(a,b))))) = domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f476]) ).
fof(f2863,plain,
( domain(compose(h,domain(compose(h,a)))) = domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f476]) ).
fof(f2864,plain,
( domain(compose(h,domain(compose(a,b)))) = domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f476]) ).
fof(f2870,definition,
( sQ165_spl
<=> domain(compose(h,domain(compose(g,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f2873,plain,
( sQ165_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2861,f584,f2870]) ).
fof(f2874,definition,
( sQ166_spl
<=> domain(compose(h,domain(compose(h,compose(a,b))))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f2877,plain,
( sQ166_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2862,f584,f2874]) ).
fof(f2878,definition,
( sQ167_spl
<=> domain(compose(h,domain(compose(h,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f2881,plain,
( sQ167_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2863,f584,f2878]) ).
fof(f2882,definition,
( sQ168_spl
<=> domain(compose(h,domain(compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f2885,plain,
( sQ168_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f2864,f606,f2882]) ).
fof(f2890,plain,
( domain(compose(a,domain(compose(g,a)))) = domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f477]) ).
fof(f2891,plain,
( domain(compose(a,domain(compose(h,compose(a,b))))) = domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f477]) ).
fof(f2892,plain,
( domain(compose(a,domain(compose(h,a)))) = domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f477]) ).
fof(f2893,plain,
( domain(compose(a,domain(compose(a,b)))) = domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f477]) ).
fof(f2898,definition,
( sQ169_spl
<=> domain(compose(a,domain(compose(g,a)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f2901,plain,
( sQ169_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2890,f693,f2898]) ).
fof(f2902,definition,
( sQ170_spl
<=> domain(compose(a,domain(compose(h,compose(a,b))))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f2905,plain,
( sQ170_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2891,f693,f2902]) ).
fof(f2906,definition,
( sQ171_spl
<=> domain(compose(a,domain(compose(h,a)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f2909,plain,
( sQ171_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2892,f693,f2906]) ).
fof(f2910,definition,
( sQ172_spl
<=> domain(compose(a,domain(compose(a,b)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f2913,plain,
( sQ172_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2893,f715,f2910]) ).
fof(f2919,plain,
( domain(compose(h,codomain(compose(a,b)))) = domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f516]) ).
fof(f2920,plain,
( domain(compose(h,codomain(compose(h,compose(a,b))))) = domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f516]) ).
fof(f2921,plain,
( domain(compose(h,codomain(compose(h,a)))) = domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f516]) ).
fof(f2922,plain,
( domain(compose(h,codomain(compose(g,a)))) = domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f516]) ).
fof(f2923,plain,
( domain(compose(h,codomain(g))) = domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f516]) ).
fof(f2924,plain,
( domain(compose(h,codomain(h))) = domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f516]) ).
fof(f2925,plain,
( domain(compose(h,codomain(a))) = domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f516]) ).
fof(f2930,definition,
( sQ173_spl
<=> domain(compose(h,codomain(compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f2933,plain,
( sQ173_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f2919,f1570,f2930]) ).
fof(f2934,definition,
( sQ174_spl
<=> domain(compose(h,codomain(compose(h,compose(a,b))))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f2937,plain,
( sQ174_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f2920,f1570,f2934]) ).
fof(f2938,definition,
( sQ175_spl
<=> domain(compose(h,codomain(compose(h,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f2941,plain,
( sQ175_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2921,f715,f2938]) ).
fof(f2942,definition,
( sQ176_spl
<=> domain(compose(h,codomain(compose(g,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f2945,plain,
( sQ176_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2922,f715,f2942]) ).
fof(f2946,definition,
( sQ177_spl
<=> domain(compose(h,codomain(g))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f2949,plain,
( sQ177_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f2923,f606,f2946]) ).
fof(f2950,definition,
( sQ178_spl
<=> domain(compose(h,codomain(h))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f2953,plain,
( sQ178_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f2924,f606,f2950]) ).
fof(f2954,definition,
( sQ179_spl
<=> domain(compose(h,codomain(a))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f2957,plain,
( sQ179_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2925,f715,f2954]) ).
fof(f2967,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)],[f120,f230]) ).
fof(f2968,plain,
! [X0,X1] :
( compose(compose(h,compose(a,b)),compose(codomain(X0),X1)) = compose(compose(compose(h,compose(a,b)),codomain(X0)),X1)
| codomain(X0) != domain(X1)
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f581,f230]) ).
fof(f2969,plain,
! [X0,X1] :
( compose(compose(h,a),compose(codomain(X0),X1)) = compose(compose(compose(h,a),codomain(X0)),X1)
| codomain(X0) != domain(X1)
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f131,f230]) ).
fof(f2970,plain,
! [X0,X1] :
( compose(compose(g,a),compose(codomain(X0),X1)) = compose(compose(compose(g,a),codomain(X0)),X1)
| codomain(X0) != domain(X1)
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f130,f230]) ).
fof(f2974,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)],[f38,f230]) ).
fof(f3033,plain,
( domain(compose(a,codomain(compose(a,b)))) = domain(a)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f517]) ).
fof(f3034,plain,
( domain(compose(a,codomain(compose(h,compose(a,b))))) = domain(a)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f517]) ).
fof(f3035,plain,
( domain(compose(a,codomain(compose(h,a)))) = domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f517]) ).
fof(f3036,plain,
( domain(compose(a,codomain(compose(g,a)))) = domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f517]) ).
fof(f3037,plain,
( domain(compose(a,codomain(g))) = domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f517]) ).
fof(f3038,plain,
( domain(compose(a,codomain(h))) = domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f517]) ).
fof(f3039,plain,
( domain(compose(a,codomain(a))) = domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f517]) ).
fof(f3045,definition,
( sQ180_spl
<=> domain(compose(a,codomain(compose(a,b)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f3048,plain,
( sQ180_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f3033,f2265,f3045]) ).
fof(f3049,definition,
( sQ181_spl
<=> domain(compose(a,codomain(compose(h,compose(a,b))))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f3052,plain,
( sQ181_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f3034,f2265,f3049]) ).
fof(f3053,definition,
( sQ182_spl
<=> domain(compose(a,codomain(compose(h,a)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f3056,plain,
( sQ182_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f3035,f1941,f3053]) ).
fof(f3057,definition,
( sQ183_spl
<=> domain(compose(a,codomain(compose(g,a)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f3060,plain,
( sQ183_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f3036,f1941,f3057]) ).
fof(f3061,definition,
( sQ184_spl
<=> domain(compose(a,codomain(g))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f3064,plain,
( sQ184_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3037,f715,f3061]) ).
fof(f3065,definition,
( sQ185_spl
<=> domain(compose(a,codomain(h))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f3068,plain,
( sQ185_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3038,f715,f3065]) ).
fof(f3069,definition,
( sQ186_spl
<=> domain(compose(a,codomain(a))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f3072,plain,
( sQ186_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f3039,f1941,f3069]) ).
fof(f3080,plain,
( domain(compose(g,codomain(compose(a,b)))) = domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f1124]) ).
fof(f3081,plain,
( domain(compose(g,codomain(compose(h,compose(a,b))))) = domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f1124]) ).
fof(f3082,plain,
( domain(compose(g,codomain(compose(h,a)))) = domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f1124]) ).
fof(f3083,plain,
( domain(compose(g,codomain(compose(g,a)))) = domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f1124]) ).
fof(f3084,plain,
( domain(compose(g,codomain(g))) = domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f1124]) ).
fof(f3085,plain,
( domain(compose(g,codomain(h))) = domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f1124]) ).
fof(f3086,plain,
( domain(compose(g,codomain(a))) = domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f1124]) ).
fof(f3094,definition,
( sQ187_spl
<=> domain(compose(g,codomain(compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f3097,plain,
( sQ187_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f3080,f1570,f3094]) ).
fof(f3098,definition,
( sQ188_spl
<=> domain(compose(g,codomain(compose(h,compose(a,b))))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f3101,plain,
( sQ188_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f3081,f1570,f3098]) ).
fof(f3102,definition,
( sQ189_spl
<=> domain(compose(g,codomain(compose(h,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f3105,plain,
( sQ189_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3082,f715,f3102]) ).
fof(f3106,definition,
( sQ190_spl
<=> domain(compose(g,codomain(compose(g,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f3109,plain,
( sQ190_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3083,f715,f3106]) ).
fof(f3110,definition,
( sQ191_spl
<=> domain(compose(g,codomain(g))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f3113,plain,
( sQ191_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f3084,f606,f3110]) ).
fof(f3114,definition,
( sQ192_spl
<=> domain(compose(g,codomain(h))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f3117,plain,
( sQ192_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f3085,f606,f3114]) ).
fof(f3118,definition,
( sQ193_spl
<=> domain(compose(g,codomain(a))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f3121,plain,
( sQ193_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3086,f715,f3118]) ).
fof(f3129,plain,
( domain(compose(g,domain(compose(g,a)))) = domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1127]) ).
fof(f3130,plain,
( domain(compose(g,domain(compose(h,compose(a,b))))) = domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1127]) ).
fof(f3131,plain,
( domain(compose(g,domain(compose(h,a)))) = domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1127]) ).
fof(f3132,plain,
( domain(compose(g,domain(compose(a,b)))) = domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1127]) ).
fof(f3140,definition,
( sQ194_spl
<=> domain(compose(g,domain(compose(g,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f3143,plain,
( sQ194_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3129,f584,f3140]) ).
fof(f3144,definition,
( sQ195_spl
<=> domain(compose(g,domain(compose(h,compose(a,b))))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f3147,plain,
( sQ195_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3130,f584,f3144]) ).
fof(f3148,definition,
( sQ196_spl
<=> domain(compose(g,domain(compose(h,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f3151,plain,
( sQ196_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3131,f584,f3148]) ).
fof(f3152,definition,
( sQ197_spl
<=> domain(compose(g,domain(compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f3155,plain,
( sQ197_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f3132,f606,f3152]) ).
fof(f3166,plain,
( codomain(compose(domain(g),g)) = domain(a)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f1161]) ).
fof(f3167,plain,
( codomain(compose(domain(compose(g,a)),g)) = domain(a)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1161]) ).
fof(f3168,plain,
( codomain(compose(domain(compose(h,compose(a,b))),g)) = domain(a)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1161]) ).
fof(f3169,plain,
( codomain(compose(domain(compose(h,a)),g)) = domain(a)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1161]) ).
fof(f3170,plain,
( codomain(compose(domain(compose(a,b)),g)) = domain(a)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f1161]) ).
fof(f3172,plain,
! [X0] :
( codomain(compose(domain(codomain(X0)),g)) = domain(a)
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f16,f1161]) ).
fof(f3183,definition,
( sQ198_spl
<=> codomain(compose(domain(g),g)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f3186,plain,
( sQ198_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f3166,f2687,f3183]) ).
fof(f3187,definition,
( sQ199_spl
<=> codomain(compose(domain(compose(g,a)),g)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f3190,plain,
( sQ199_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f3167,f2687,f3187]) ).
fof(f3191,definition,
( sQ200_spl
<=> codomain(compose(domain(compose(h,compose(a,b))),g)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f3194,plain,
( sQ200_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f3168,f2687,f3191]) ).
fof(f3195,definition,
( sQ201_spl
<=> codomain(compose(domain(compose(h,a)),g)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f3198,plain,
( sQ201_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f3169,f2687,f3195]) ).
fof(f3199,definition,
( sQ202_spl
<=> codomain(compose(domain(compose(a,b)),g)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f3202,plain,
( sQ202_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3170,f584,f3199]) ).
fof(f3204,plain,
! [X0] :
( codomain(compose(codomain(X0),g)) = domain(a)
| codomain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f16,f3172]) ).
fof(f3213,plain,
( ~ sQ4_spl
| compose(g,a) = domain(b)
| b != compose(h,compose(a,b))
| codomain(compose(g,a)) != domain(a) ),
inference(paramodulation,[status(thm)],[f1377,f556]) ).
fof(f3214,plain,
! [X0] :
( compose(g,a) = X0
| compose(X0,b) != compose(h,compose(a,b))
| codomain(X0) != domain(b)
| codomain(compose(g,a)) != domain(a) ),
inference(paramodulation,[status(thm)],[f1377,f32]) ).
fof(f3215,plain,
! [X0] :
( X0 = compose(g,a)
| compose(h,compose(a,b)) != compose(X0,b)
| codomain(compose(g,a)) != domain(b)
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f1377,f32]) ).
fof(f3216,definition,
( sQ203_spl
<=> codomain(compose(g,a)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f3218,plain,
( sQ203_spl
| codomain(compose(g,a)) != domain(a) ),
inference(component_clause,[status(thm)],[f3216]) ).
fof(f3219,definition,
( sQ204_spl
<=> b = compose(h,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f3222,definition,
( sQ205_spl
<=> compose(g,a) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f3225,plain,
( ~ sQ4_spl
| sQ205_spl
| ~ sQ204_spl
| ~ sQ203_spl ),
inference(split_clause,[status(thm)],[f3213,f3216,f3219,f3222,f555]) ).
fof(f3226,definition,
! [X0] :
( sQ206_spl
<=> ( compose(g,a) = X0
| compose(X0,b) != compose(h,compose(a,b))
| codomain(X0) != domain(b) ) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f3229,plain,
( sQ206_spl
| ~ sQ203_spl ),
inference(split_clause,[status(thm)],[f3214,f3216,f3226]) ).
fof(f3230,definition,
! [X0] :
( sQ207_spl
<=> ( X0 = compose(g,a)
| compose(h,compose(a,b)) != compose(X0,b)
| codomain(X0) != domain(a) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f3231,plain,
! [X0] :
( ~ sQ207_spl
| X0 = compose(g,a)
| compose(h,compose(a,b)) != compose(X0,b)
| codomain(X0) != domain(a) ),
inference(component_clause,[status(thm)],[f3230]) ).
fof(f3233,definition,
( sQ208_spl
<=> codomain(compose(g,a)) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f3235,plain,
( sQ208_spl
| codomain(compose(g,a)) != domain(b) ),
inference(component_clause,[status(thm)],[f3233]) ).
fof(f3236,plain,
( ~ sQ208_spl
| sQ207_spl ),
inference(split_clause,[status(thm)],[f3215,f3230,f3233]) ).
fof(f3237,plain,
( sQ203_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f130,f3218]) ).
fof(f3241,plain,
( codomain(compose(compose(a,b),compose(a,b))) = codomain(b)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f120,f156]) ).
fof(f3242,plain,
( codomain(compose(compose(h,compose(a,b)),compose(a,b))) = codomain(b)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f581,f156]) ).
fof(f3243,plain,
( codomain(compose(compose(h,a),compose(a,b))) = codomain(b)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f131,f156]) ).
fof(f3244,plain,
( codomain(compose(compose(g,a),compose(a,b))) = codomain(b)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f130,f156]) ).
fof(f3245,plain,
( codomain(compose(g,compose(a,b))) = codomain(b)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f156]) ).
fof(f3246,plain,
( codomain(compose(h,compose(a,b))) = codomain(b)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f156]) ).
fof(f3247,plain,
( codomain(compose(a,compose(a,b))) = codomain(b)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f156]) ).
fof(f3252,definition,
( sQ209_spl
<=> codomain(compose(compose(a,b),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f3255,plain,
( sQ209_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f3241,f1570,f3252]) ).
fof(f3256,definition,
( sQ210_spl
<=> codomain(compose(compose(h,compose(a,b)),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f3259,plain,
( sQ210_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f3242,f1570,f3256]) ).
fof(f3260,definition,
( sQ211_spl
<=> codomain(compose(compose(h,a),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f3263,plain,
( sQ211_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3243,f715,f3260]) ).
fof(f3264,definition,
( sQ212_spl
<=> codomain(compose(compose(g,a),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f3267,plain,
( sQ212_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3244,f715,f3264]) ).
fof(f3268,definition,
( sQ213_spl
<=> codomain(compose(g,compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f3271,plain,
( sQ213_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f3245,f606,f3268]) ).
fof(f3272,definition,
( sQ214_spl
<=> codomain(compose(h,compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f3275,plain,
( sQ214_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f3246,f606,f3272]) ).
fof(f3276,definition,
( sQ215_spl
<=> codomain(compose(a,compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f3279,plain,
( sQ215_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3247,f715,f3276]) ).
fof(f3281,plain,
( ~ sQ4_spl
| compose(h,a) = domain(b)
| b != compose(h,compose(a,b))
| codomain(compose(h,a)) != domain(a) ),
inference(paramodulation,[status(thm)],[f1390,f556]) ).
fof(f3282,plain,
! [X0] :
( compose(h,a) = X0
| compose(X0,b) != compose(h,compose(a,b))
| codomain(X0) != domain(b)
| codomain(compose(h,a)) != domain(a) ),
inference(paramodulation,[status(thm)],[f1390,f32]) ).
fof(f3283,plain,
! [X0] :
( X0 = compose(h,a)
| compose(h,compose(a,b)) != compose(X0,b)
| codomain(compose(h,a)) != domain(b)
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f1390,f32]) ).
fof(f3284,definition,
( sQ216_spl
<=> codomain(compose(h,a)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f3286,plain,
( sQ216_spl
| codomain(compose(h,a)) != domain(a) ),
inference(component_clause,[status(thm)],[f3284]) ).
fof(f3287,definition,
( sQ217_spl
<=> compose(h,a) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f3290,plain,
( ~ sQ4_spl
| sQ217_spl
| ~ sQ204_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f3281,f3284,f3219,f3287,f555]) ).
fof(f3291,definition,
! [X0] :
( sQ218_spl
<=> ( compose(h,a) = X0
| compose(X0,b) != compose(h,compose(a,b))
| codomain(X0) != domain(b) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f3294,plain,
( sQ218_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f3282,f3284,f3291]) ).
fof(f3295,definition,
! [X0] :
( sQ219_spl
<=> ( X0 = compose(h,a)
| compose(h,compose(a,b)) != compose(X0,b)
| codomain(X0) != domain(a) ) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f3296,plain,
! [X0] :
( ~ sQ219_spl
| X0 = compose(h,a)
| compose(h,compose(a,b)) != compose(X0,b)
| codomain(X0) != domain(a) ),
inference(component_clause,[status(thm)],[f3295]) ).
fof(f3298,definition,
( sQ220_spl
<=> codomain(compose(h,a)) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f3300,plain,
( sQ220_spl
| codomain(compose(h,a)) != domain(b) ),
inference(component_clause,[status(thm)],[f3298]) ).
fof(f3301,plain,
( ~ sQ220_spl
| sQ219_spl ),
inference(split_clause,[status(thm)],[f3283,f3295,f3298]) ).
fof(f3302,plain,
( sQ216_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f131,f3286]) ).
fof(f3304,plain,
( codomain(compose(codomain(compose(a,b)),g)) = domain(a)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f3204]) ).
fof(f3305,plain,
( codomain(compose(codomain(compose(h,compose(a,b))),g)) = domain(a)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f3204]) ).
fof(f3306,plain,
( codomain(compose(codomain(compose(h,a)),g)) = domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f3204]) ).
fof(f3307,plain,
( codomain(compose(codomain(compose(g,a)),g)) = domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f3204]) ).
fof(f3308,plain,
( codomain(compose(codomain(g),g)) = domain(a)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f3204]) ).
fof(f3309,plain,
( codomain(compose(codomain(h),g)) = domain(a)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f3204]) ).
fof(f3310,plain,
( codomain(compose(codomain(a),g)) = domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f3204]) ).
fof(f3315,definition,
( sQ221_spl
<=> codomain(compose(codomain(compose(a,b)),g)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f3318,plain,
( sQ221_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3304,f1555,f3315]) ).
fof(f3319,definition,
( sQ222_spl
<=> codomain(compose(codomain(compose(h,compose(a,b))),g)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f3322,plain,
( sQ222_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3305,f1555,f3319]) ).
fof(f3323,definition,
( sQ223_spl
<=> codomain(compose(codomain(compose(h,a)),g)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f3326,plain,
( sQ223_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3306,f693,f3323]) ).
fof(f3327,definition,
( sQ224_spl
<=> codomain(compose(codomain(compose(g,a)),g)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f3330,plain,
( sQ224_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3307,f693,f3327]) ).
fof(f3331,definition,
( sQ225_spl
<=> codomain(compose(codomain(g),g)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f3334,plain,
( sQ225_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3308,f584,f3331]) ).
fof(f3335,definition,
( sQ226_spl
<=> codomain(compose(codomain(h),g)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f3338,plain,
( sQ226_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3309,f584,f3335]) ).
fof(f3339,definition,
( sQ227_spl
<=> codomain(compose(codomain(a),g)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f3342,plain,
( sQ227_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3310,f693,f3339]) ).
fof(f3348,plain,
( domain(compose(compose(a,b),compose(a,b))) = domain(compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f120,f148]) ).
fof(f3349,plain,
( domain(compose(compose(h,compose(a,b)),compose(a,b))) = domain(compose(h,compose(a,b)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f581,f148]) ).
fof(f3350,plain,
( domain(compose(compose(h,a),compose(a,b))) = domain(compose(h,a))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f131,f148]) ).
fof(f3351,plain,
( domain(compose(compose(g,a),compose(a,b))) = domain(compose(g,a))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f130,f148]) ).
fof(f3361,definition,
( sQ228_spl
<=> domain(compose(compose(a,b),compose(a,b))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f3364,plain,
( sQ228_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f3348,f1570,f3361]) ).
fof(f3365,definition,
( sQ229_spl
<=> domain(compose(compose(h,compose(a,b)),compose(a,b))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f3368,plain,
( sQ229_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f3349,f1570,f3365]) ).
fof(f3369,definition,
( sQ230_spl
<=> domain(compose(compose(h,a),compose(a,b))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f3372,plain,
( sQ230_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3350,f715,f3369]) ).
fof(f3373,definition,
( sQ231_spl
<=> domain(compose(compose(g,a),compose(a,b))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f3376,plain,
( sQ231_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3351,f715,f3373]) ).
fof(f3383,plain,
( domain(compose(compose(a,b),compose(h,a))) = domain(compose(a,b))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f162]) ).
fof(f3384,plain,
( domain(compose(compose(h,compose(a,b)),compose(h,a))) = domain(compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f162]) ).
fof(f3385,plain,
( domain(compose(compose(h,a),compose(h,a))) = domain(compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f162]) ).
fof(f3386,plain,
( domain(compose(compose(g,a),compose(h,a))) = domain(compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f162]) ).
fof(f3394,definition,
( sQ232_spl
<=> domain(compose(compose(a,b),compose(h,a))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f3397,plain,
( sQ232_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3383,f1555,f3394]) ).
fof(f3398,definition,
( sQ233_spl
<=> domain(compose(compose(h,compose(a,b)),compose(h,a))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f3401,plain,
( sQ233_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3384,f1555,f3398]) ).
fof(f3402,definition,
( sQ234_spl
<=> domain(compose(compose(h,a),compose(h,a))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f3405,plain,
( sQ234_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3385,f693,f3402]) ).
fof(f3406,definition,
( sQ235_spl
<=> domain(compose(compose(g,a),compose(h,a))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f3409,plain,
( sQ235_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3386,f693,f3406]) ).
fof(f3416,plain,
( codomain(compose(compose(g,a),compose(g,a))) = codomain(compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f189]) ).
fof(f3417,plain,
( codomain(compose(compose(g,a),compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f189]) ).
fof(f3418,plain,
( codomain(compose(compose(g,a),compose(h,a))) = codomain(compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f189]) ).
fof(f3419,plain,
( codomain(compose(compose(g,a),compose(a,b))) = codomain(compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f189]) ).
fof(f3425,definition,
( sQ236_spl
<=> codomain(compose(compose(g,a),compose(g,a))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f3428,plain,
( sQ236_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3416,f693,f3425]) ).
fof(f3429,definition,
( sQ237_spl
<=> codomain(compose(compose(g,a),compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f3432,plain,
( sQ237_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3417,f693,f3429]) ).
fof(f3433,definition,
( sQ238_spl
<=> codomain(compose(compose(g,a),compose(h,a))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f3436,plain,
( sQ238_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3418,f693,f3433]) ).
fof(f3437,definition,
( sQ239_spl
<=> codomain(compose(compose(g,a),compose(a,b))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f3440,plain,
( sQ239_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3419,f715,f3437]) ).
fof(f3445,plain,
( codomain(compose(compose(a,b),compose(h,a))) = domain(b)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f170]) ).
fof(f3446,plain,
( codomain(compose(compose(h,compose(a,b)),compose(h,a))) = domain(b)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f170]) ).
fof(f3447,plain,
( codomain(compose(compose(h,a),compose(h,a))) = domain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f170]) ).
fof(f3448,plain,
( codomain(compose(compose(g,a),compose(h,a))) = domain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f170]) ).
fof(f3449,plain,
( codomain(compose(g,compose(h,a))) = domain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f170]) ).
fof(f3450,plain,
( codomain(compose(h,compose(h,a))) = domain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f170]) ).
fof(f3451,plain,
( codomain(compose(a,compose(h,a))) = domain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f170]) ).
fof(f3455,definition,
( sQ240_spl
<=> codomain(compose(compose(a,b),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f3458,plain,
( sQ240_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3445,f1555,f3455]) ).
fof(f3459,definition,
( sQ241_spl
<=> codomain(compose(compose(h,compose(a,b)),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f3462,plain,
( sQ241_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3446,f1555,f3459]) ).
fof(f3463,definition,
( sQ242_spl
<=> codomain(compose(compose(h,a),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f3466,plain,
( sQ242_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3447,f693,f3463]) ).
fof(f3467,definition,
( sQ243_spl
<=> codomain(compose(compose(g,a),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f3470,plain,
( sQ243_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3448,f693,f3467]) ).
fof(f3471,definition,
( sQ244_spl
<=> codomain(compose(g,compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f3474,plain,
( sQ244_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3449,f584,f3471]) ).
fof(f3475,definition,
( sQ245_spl
<=> codomain(compose(h,compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f3478,plain,
( sQ245_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3450,f584,f3475]) ).
fof(f3479,definition,
( sQ246_spl
<=> codomain(compose(a,compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f3482,plain,
( sQ246_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3451,f693,f3479]) ).
fof(f3484,plain,
( codomain(compose(compose(h,a),compose(g,a))) = codomain(compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f235]) ).
fof(f3485,plain,
( codomain(compose(compose(h,a),compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f235]) ).
fof(f3486,plain,
( codomain(compose(compose(h,a),compose(h,a))) = codomain(compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f235]) ).
fof(f3487,plain,
( codomain(compose(compose(h,a),compose(a,b))) = codomain(compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f235]) ).
fof(f3493,definition,
( sQ247_spl
<=> codomain(compose(compose(h,a),compose(g,a))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f3496,plain,
( sQ247_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3484,f693,f3493]) ).
fof(f3497,definition,
( sQ248_spl
<=> codomain(compose(compose(h,a),compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f3500,plain,
( sQ248_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3485,f693,f3497]) ).
fof(f3501,definition,
( sQ249_spl
<=> codomain(compose(compose(h,a),compose(h,a))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f3504,plain,
( sQ249_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3486,f693,f3501]) ).
fof(f3505,definition,
( sQ250_spl
<=> codomain(compose(compose(h,a),compose(a,b))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f3508,plain,
( sQ250_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3487,f715,f3505]) ).
fof(f3513,plain,
( codomain(compose(compose(a,b),compose(g,a))) = codomain(compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f251]) ).
fof(f3514,plain,
( codomain(compose(compose(a,b),compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f251]) ).
fof(f3515,plain,
( codomain(compose(compose(a,b),compose(h,a))) = codomain(compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f251]) ).
fof(f3516,plain,
( codomain(compose(compose(a,b),compose(a,b))) = codomain(compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f251]) ).
fof(f3521,definition,
( sQ251_spl
<=> codomain(compose(compose(a,b),compose(g,a))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f3524,plain,
( sQ251_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3513,f1555,f3521]) ).
fof(f3525,definition,
( sQ252_spl
<=> codomain(compose(compose(a,b),compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f3528,plain,
( sQ252_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3514,f1555,f3525]) ).
fof(f3529,definition,
( sQ253_spl
<=> codomain(compose(compose(a,b),compose(h,a))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f3532,plain,
( sQ253_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3515,f1555,f3529]) ).
fof(f3533,definition,
( sQ254_spl
<=> codomain(compose(compose(a,b),compose(a,b))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f3536,plain,
( sQ254_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f3516,f1570,f3533]) ).
fof(f3540,plain,
( domain(compose(compose(a,b),compose(g,a))) = domain(compose(a,b))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1142]) ).
fof(f3541,plain,
( domain(compose(compose(h,compose(a,b)),compose(g,a))) = domain(compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1142]) ).
fof(f3542,plain,
( domain(compose(compose(h,a),compose(g,a))) = domain(compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1142]) ).
fof(f3543,plain,
( domain(compose(compose(g,a),compose(g,a))) = domain(compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1142]) ).
fof(f3544,plain,
( domain(compose(g,compose(g,a))) = domain(g)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1142]) ).
fof(f3551,definition,
( sQ255_spl
<=> domain(compose(compose(a,b),compose(g,a))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f3554,plain,
( sQ255_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3540,f1555,f3551]) ).
fof(f3555,definition,
( sQ256_spl
<=> domain(compose(compose(h,compose(a,b)),compose(g,a))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f3558,plain,
( sQ256_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3541,f1555,f3555]) ).
fof(f3559,definition,
( sQ257_spl
<=> domain(compose(compose(h,a),compose(g,a))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f3562,plain,
( sQ257_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3542,f693,f3559]) ).
fof(f3563,definition,
( sQ258_spl
<=> domain(compose(compose(g,a),compose(g,a))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f3566,plain,
( sQ258_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3543,f693,f3563]) ).
fof(f3567,plain,
( sQ36_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3544,f584,f988]) ).
fof(f3573,plain,
( domain(compose(compose(h,a),compose(g,a))) = domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f247]) ).
fof(f3574,plain,
( domain(compose(compose(h,a),compose(h,compose(a,b)))) = domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f247]) ).
fof(f3575,plain,
( domain(compose(compose(h,a),compose(h,a))) = domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f247]) ).
fof(f3576,plain,
( domain(compose(compose(h,a),compose(a,b))) = domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f247]) ).
fof(f3581,definition,
( sQ259_spl
<=> domain(compose(compose(h,a),compose(g,a))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f3584,plain,
( sQ259_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3573,f693,f3581]) ).
fof(f3585,definition,
( sQ260_spl
<=> domain(compose(compose(h,a),compose(h,compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f3588,plain,
( sQ260_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3574,f693,f3585]) ).
fof(f3589,definition,
( sQ261_spl
<=> domain(compose(compose(h,a),compose(h,a))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f3592,plain,
( sQ261_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3575,f693,f3589]) ).
fof(f3593,definition,
( sQ262_spl
<=> domain(compose(compose(h,a),compose(a,b))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f3596,plain,
( sQ262_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3576,f715,f3593]) ).
fof(f3599,plain,
( domain(compose(compose(a,b),compose(g,a))) = domain(a)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f262]) ).
fof(f3600,plain,
( domain(compose(compose(a,b),compose(h,compose(a,b)))) = domain(a)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f262]) ).
fof(f3601,plain,
( domain(compose(compose(a,b),compose(h,a))) = domain(a)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f262]) ).
fof(f3602,plain,
( domain(compose(compose(a,b),compose(a,b))) = domain(a)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f262]) ).
fof(f3606,definition,
( sQ263_spl
<=> domain(compose(compose(a,b),compose(g,a))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f3609,plain,
( sQ263_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3599,f1555,f3606]) ).
fof(f3610,definition,
( sQ264_spl
<=> domain(compose(compose(a,b),compose(h,compose(a,b)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f3613,plain,
( sQ264_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3600,f1555,f3610]) ).
fof(f3614,definition,
( sQ265_spl
<=> domain(compose(compose(a,b),compose(h,a))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f3617,plain,
( sQ265_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3601,f1555,f3614]) ).
fof(f3618,definition,
( sQ266_spl
<=> domain(compose(compose(a,b),compose(a,b))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f3621,plain,
( sQ266_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f3602,f1570,f3618]) ).
fof(f3622,plain,
( compose(compose(g,a),compose(compose(h,a),b)) = compose(compose(compose(g,a),compose(h,a)),b)
| domain(b) != domain(compose(h,a)) ),
inference(resolution,[status(thm)],[f210,f131]) ).
fof(f3623,plain,
( compose(compose(g,a),compose(compose(g,a),b)) = compose(compose(compose(g,a),compose(g,a)),b)
| domain(b) != domain(compose(g,a)) ),
inference(resolution,[status(thm)],[f210,f130]) ).
fof(f3624,plain,
( compose(compose(g,a),compose(g,a)) = compose(compose(compose(g,a),g),a)
| domain(b) != domain(g) ),
inference(resolution,[status(thm)],[f210,f74]) ).
fof(f3625,plain,
( compose(compose(g,a),compose(h,a)) = compose(compose(compose(g,a),h),a)
| domain(b) != domain(h) ),
inference(resolution,[status(thm)],[f210,f69]) ).
fof(f3626,plain,
( compose(compose(g,a),compose(a,b)) = compose(compose(compose(g,a),a),b)
| domain(b) != domain(a) ),
inference(resolution,[status(thm)],[f210,f22]) ).
fof(f3627,plain,
! [X0] :
( compose(compose(g,a),compose(domain(X0),X0)) = compose(compose(compose(g,a),domain(X0)),X0)
| domain(b) != domain(domain(X0)) ),
inference(resolution,[status(thm)],[f210,f15]) ).
fof(f3628,plain,
! [X0] :
( compose(compose(g,a),compose(X0,codomain(X0))) = compose(compose(compose(g,a),X0),codomain(X0))
| domain(b) != domain(X0) ),
inference(resolution,[status(thm)],[f210,f16]) ).
fof(f3629,plain,
! [X0] :
( compose(compose(g,a),compose(compose(a,b),X0)) = compose(compose(compose(g,a),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f210]) ).
fof(f3630,plain,
! [X0] :
( compose(compose(g,a),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(g,a),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f210]) ).
fof(f3631,plain,
! [X0] :
( compose(compose(g,a),compose(compose(h,a),X0)) = compose(compose(compose(g,a),compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f210]) ).
fof(f3632,plain,
! [X0] :
( compose(compose(g,a),compose(compose(g,a),X0)) = compose(compose(compose(g,a),compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f210]) ).
fof(f3633,plain,
! [X0] :
( compose(compose(g,a),compose(g,X0)) = compose(compose(compose(g,a),g),X0)
| domain(a) != domain(X0)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f210]) ).
fof(f3634,plain,
! [X0] :
( compose(compose(g,a),compose(h,X0)) = compose(compose(compose(g,a),h),X0)
| domain(a) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f210]) ).
fof(f3635,plain,
! [X0] :
( compose(compose(g,a),compose(a,X0)) = compose(compose(compose(g,a),a),X0)
| domain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f210]) ).
fof(f3637,plain,
! [X0,X1] :
( compose(compose(g,a),compose(domain(X0),X1)) = compose(compose(compose(g,a),domain(X0)),X1)
| domain(X0) != domain(X1)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f210]) ).
fof(f3638,plain,
! [X0] :
( compose(compose(g,a),compose(X0,compose(g,a))) = compose(compose(compose(g,a),X0),compose(g,a))
| codomain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f1108,f210]) ).
fof(f3639,plain,
! [X0] :
( compose(compose(g,a),compose(X0,compose(h,compose(a,b)))) = compose(compose(compose(g,a),X0),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f1068,f210]) ).
fof(f3640,plain,
! [X0] :
( compose(compose(g,a),compose(X0,compose(h,a))) = compose(compose(compose(g,a),X0),compose(h,a))
| codomain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f76,f210]) ).
fof(f3641,plain,
! [X0] :
( compose(compose(g,a),compose(X0,compose(a,b))) = compose(compose(compose(g,a),X0),compose(a,b))
| codomain(X0) != domain(a)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f60,f210]) ).
fof(f3642,plain,
! [X0,X1] :
( compose(compose(g,a),compose(X0,domain(X1))) = compose(compose(compose(g,a),X0),domain(X1))
| codomain(X0) != domain(X1)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f210]) ).
fof(f3643,plain,
! [X0,X1] :
( compose(compose(g,a),compose(X0,codomain(X1))) = compose(compose(compose(g,a),X0),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f16,f210]) ).
fof(f3644,definition,
( sQ267_spl
<=> compose(compose(g,a),compose(compose(h,a),b)) = compose(compose(compose(g,a),compose(h,a)),b) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f3647,plain,
( sQ267_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f3622,f2330,f3644]) ).
fof(f3648,definition,
( sQ268_spl
<=> compose(compose(g,a),compose(compose(g,a),b)) = compose(compose(compose(g,a),compose(g,a)),b) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f3651,plain,
( sQ268_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f3623,f2337,f3648]) ).
fof(f3652,definition,
( sQ269_spl
<=> compose(compose(g,a),compose(g,a)) = compose(compose(compose(g,a),g),a) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f3655,plain,
( sQ269_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f3624,f700,f3652]) ).
fof(f3656,definition,
( sQ270_spl
<=> compose(compose(g,a),compose(h,a)) = compose(compose(compose(g,a),h),a) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f3659,plain,
( sQ270_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3625,f693,f3656]) ).
fof(f3660,definition,
( sQ271_spl
<=> compose(compose(g,a),compose(a,b)) = compose(compose(compose(g,a),a),b) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f3663,plain,
( sQ271_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3626,f715,f3660]) ).
fof(f3664,plain,
! [X0] :
( compose(compose(g,a),compose(domain(X0),X0)) = compose(compose(compose(g,a),domain(X0)),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f3627]) ).
fof(f3665,plain,
! [X0] :
( compose(compose(g,a),X0) = compose(compose(compose(g,a),domain(X0)),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f17,f3664]) ).
fof(f3666,plain,
! [X0] :
( compose(compose(g,a),X0) = compose(compose(compose(g,a),X0),codomain(X0))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f18,f3628]) ).
fof(f3667,definition,
! [X0] :
( sQ272_spl
<=> ( compose(compose(g,a),compose(compose(a,b),X0)) = compose(compose(compose(g,a),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f3670,plain,
( sQ272_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f3629,f2359,f3667]) ).
fof(f3671,definition,
! [X0] :
( sQ273_spl
<=> ( compose(compose(g,a),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(g,a),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f3674,plain,
( sQ273_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f3630,f2366,f3671]) ).
fof(f3675,definition,
! [X0] :
( sQ274_spl
<=> ( compose(compose(g,a),compose(compose(h,a),X0)) = compose(compose(compose(g,a),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f3678,plain,
( sQ274_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f3631,f2330,f3675]) ).
fof(f3679,definition,
! [X0] :
( sQ275_spl
<=> ( compose(compose(g,a),compose(compose(g,a),X0)) = compose(compose(compose(g,a),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f3682,plain,
( sQ275_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f3632,f2337,f3679]) ).
fof(f3683,definition,
! [X0] :
( sQ276_spl
<=> ( compose(compose(g,a),compose(g,X0)) = compose(compose(compose(g,a),g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f3686,plain,
( sQ276_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f3633,f700,f3683]) ).
fof(f3687,definition,
! [X0] :
( sQ277_spl
<=> ( compose(compose(g,a),compose(h,X0)) = compose(compose(compose(g,a),h),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f3690,plain,
( sQ277_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3634,f693,f3687]) ).
fof(f3691,definition,
! [X0] :
( sQ278_spl
<=> ( compose(compose(g,a),compose(a,X0)) = compose(compose(compose(g,a),a),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f3694,plain,
( sQ278_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3635,f715,f3691]) ).
fof(f3696,plain,
! [X0,X1] :
( compose(compose(g,a),compose(domain(X0),X1)) = compose(compose(compose(g,a),domain(X0)),X1)
| domain(X0) != domain(X1)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f3637]) ).
fof(f3698,plain,
( domain(compose(compose(g,a),compose(g,a))) = domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1140]) ).
fof(f3699,plain,
( domain(compose(compose(g,a),compose(h,compose(a,b)))) = domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1140]) ).
fof(f3700,plain,
( domain(compose(compose(g,a),compose(h,a))) = domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1140]) ).
fof(f3701,plain,
( domain(compose(compose(g,a),compose(a,b))) = domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1140]) ).
fof(f3706,definition,
( sQ279_spl
<=> domain(compose(compose(g,a),compose(g,a))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f3709,plain,
( sQ279_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3698,f693,f3706]) ).
fof(f3710,definition,
( sQ280_spl
<=> domain(compose(compose(g,a),compose(h,compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f3713,plain,
( sQ280_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3699,f693,f3710]) ).
fof(f3714,definition,
( sQ281_spl
<=> domain(compose(compose(g,a),compose(h,a))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f3717,plain,
( sQ281_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3700,f693,f3714]) ).
fof(f3718,definition,
( sQ282_spl
<=> domain(compose(compose(g,a),compose(a,b))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f3721,plain,
( sQ282_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3701,f715,f3718]) ).
fof(f3724,plain,
( codomain(compose(compose(a,b),compose(g,a))) = domain(b)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1143]) ).
fof(f3725,plain,
( codomain(compose(compose(h,compose(a,b)),compose(g,a))) = domain(b)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1143]) ).
fof(f3726,plain,
( codomain(compose(compose(h,a),compose(g,a))) = domain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1143]) ).
fof(f3727,plain,
( codomain(compose(compose(g,a),compose(g,a))) = domain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1143]) ).
fof(f3728,plain,
( codomain(compose(g,compose(g,a))) = domain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1143]) ).
fof(f3729,plain,
( codomain(compose(h,compose(g,a))) = domain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1143]) ).
fof(f3730,plain,
( codomain(compose(a,compose(g,a))) = domain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f1143]) ).
fof(f3734,definition,
( sQ283_spl
<=> codomain(compose(compose(a,b),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f3737,plain,
( sQ283_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3724,f1555,f3734]) ).
fof(f3738,definition,
( sQ284_spl
<=> codomain(compose(compose(h,compose(a,b)),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f3741,plain,
( sQ284_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3725,f1555,f3738]) ).
fof(f3742,definition,
( sQ285_spl
<=> codomain(compose(compose(h,a),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f3745,plain,
( sQ285_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3726,f693,f3742]) ).
fof(f3746,definition,
( sQ286_spl
<=> codomain(compose(compose(g,a),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f3749,plain,
( sQ286_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3727,f693,f3746]) ).
fof(f3750,definition,
( sQ287_spl
<=> codomain(compose(g,compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f3753,plain,
( sQ287_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3728,f584,f3750]) ).
fof(f3754,definition,
( sQ288_spl
<=> codomain(compose(h,compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f3757,plain,
( sQ288_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3729,f584,f3754]) ).
fof(f3758,definition,
( sQ289_spl
<=> codomain(compose(a,compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f3761,plain,
( sQ289_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3730,f693,f3758]) ).
fof(f3764,plain,
( compose(g,compose(g,a)) = compose(compose(g,domain(compose(g,a))),compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1763]) ).
fof(f3765,plain,
( compose(g,compose(h,compose(a,b))) = compose(compose(g,domain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1763]) ).
fof(f3766,plain,
( compose(g,compose(h,a)) = compose(compose(g,domain(compose(h,a))),compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1763]) ).
fof(f3767,plain,
( compose(g,compose(a,b)) = compose(compose(g,domain(compose(a,b))),compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1763]) ).
fof(f3768,plain,
! [X0] :
( compose(g,domain(X0)) = compose(compose(g,domain(domain(X0))),domain(X0))
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f1763]) ).
fof(f3769,plain,
! [X0] :
( compose(g,codomain(X0)) = compose(compose(g,domain(codomain(X0))),codomain(X0))
| domain(a) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f1763]) ).
fof(f3777,definition,
( sQ290_spl
<=> compose(g,compose(g,a)) = compose(compose(g,domain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f3780,plain,
( sQ290_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3764,f584,f3777]) ).
fof(f3781,definition,
( sQ291_spl
<=> compose(g,compose(h,compose(a,b))) = compose(compose(g,domain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f3784,plain,
( sQ291_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3765,f584,f3781]) ).
fof(f3785,definition,
( sQ292_spl
<=> compose(g,compose(h,a)) = compose(compose(g,domain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f3788,plain,
( sQ292_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3766,f584,f3785]) ).
fof(f3789,definition,
( sQ293_spl
<=> compose(g,compose(a,b)) = compose(compose(g,domain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f3792,plain,
( sQ293_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f3767,f606,f3789]) ).
fof(f3793,plain,
! [X0] :
( compose(g,domain(X0)) = compose(compose(g,domain(X0)),domain(X0))
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f3768]) ).
fof(f3794,plain,
! [X0] :
( compose(g,codomain(X0)) = compose(compose(g,codomain(X0)),codomain(X0))
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f3769]) ).
fof(f3800,plain,
( compose(g,compose(g,a)) = compose(compose(g,compose(g,a)),codomain(compose(g,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1764]) ).
fof(f3801,plain,
( compose(g,compose(h,compose(a,b))) = compose(compose(g,compose(h,compose(a,b))),codomain(compose(h,compose(a,b))))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1764]) ).
fof(f3802,plain,
( compose(g,compose(h,a)) = compose(compose(g,compose(h,a)),codomain(compose(h,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1764]) ).
fof(f3803,plain,
( compose(g,compose(a,b)) = compose(compose(g,compose(a,b)),codomain(compose(a,b)))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1764]) ).
fof(f3813,definition,
( sQ294_spl
<=> compose(g,compose(g,a)) = compose(compose(g,compose(g,a)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f3816,plain,
( sQ294_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3800,f584,f3813]) ).
fof(f3817,definition,
( sQ295_spl
<=> compose(g,compose(h,compose(a,b))) = compose(compose(g,compose(h,compose(a,b))),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f3820,plain,
( sQ295_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3801,f584,f3817]) ).
fof(f3821,definition,
( sQ296_spl
<=> compose(g,compose(h,a)) = compose(compose(g,compose(h,a)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f3824,plain,
( sQ296_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3802,f584,f3821]) ).
fof(f3825,definition,
( sQ297_spl
<=> compose(g,compose(a,b)) = compose(compose(g,compose(a,b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f3828,plain,
( sQ297_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f3803,f606,f3825]) ).
fof(f3837,plain,
( compose(h,compose(g,a)) = compose(compose(h,domain(compose(g,a))),compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f2087]) ).
fof(f3838,plain,
( compose(h,compose(h,compose(a,b))) = compose(compose(h,domain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f2087]) ).
fof(f3839,plain,
( compose(h,compose(h,a)) = compose(compose(h,domain(compose(h,a))),compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f2087]) ).
fof(f3840,plain,
( compose(h,compose(a,b)) = compose(compose(h,domain(compose(a,b))),compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f2087]) ).
fof(f3841,plain,
! [X0] :
( compose(h,domain(X0)) = compose(compose(h,domain(domain(X0))),domain(X0))
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f2087]) ).
fof(f3842,plain,
! [X0] :
( compose(h,codomain(X0)) = compose(compose(h,domain(codomain(X0))),codomain(X0))
| domain(a) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f2087]) ).
fof(f3848,definition,
( sQ298_spl
<=> compose(h,compose(g,a)) = compose(compose(h,domain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f3851,plain,
( sQ298_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3837,f584,f3848]) ).
fof(f3852,definition,
( sQ299_spl
<=> compose(h,compose(h,compose(a,b))) = compose(compose(h,domain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f3855,plain,
( sQ299_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3838,f584,f3852]) ).
fof(f3856,definition,
( sQ300_spl
<=> compose(h,compose(h,a)) = compose(compose(h,domain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f3859,plain,
( sQ300_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3839,f584,f3856]) ).
fof(f3860,definition,
( sQ301_spl
<=> compose(h,compose(a,b)) = compose(compose(h,domain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f3863,plain,
( sQ301_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f3840,f606,f3860]) ).
fof(f3864,plain,
! [X0] :
( compose(h,domain(X0)) = compose(compose(h,domain(X0)),domain(X0))
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f3841]) ).
fof(f3865,plain,
! [X0] :
( compose(h,codomain(X0)) = compose(compose(h,codomain(X0)),codomain(X0))
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f3842]) ).
fof(f3883,plain,
! [X0,X1] :
( compose(codomain(X0),compose(compose(g,a),X1)) = compose(compose(codomain(X0),compose(g,a)),X1)
| codomain(compose(g,a)) != domain(X1)
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f214]) ).
fof(f3884,plain,
! [X0,X1] :
( compose(codomain(X0),compose(compose(h,compose(a,b)),X1)) = compose(compose(codomain(X0),compose(h,compose(a,b))),X1)
| codomain(compose(h,compose(a,b))) != domain(X1)
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f214]) ).
fof(f3885,plain,
! [X0,X1] :
( compose(codomain(X0),compose(compose(h,a),X1)) = compose(compose(codomain(X0),compose(h,a)),X1)
| codomain(compose(h,a)) != domain(X1)
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f214]) ).
fof(f3886,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)],[f60,f214]) ).
fof(f3887,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)],[f37,f214]) ).
fof(f3929,plain,
! [X0,X1] :
( compose(codomain(X0),compose(compose(g,a),X1)) = compose(compose(codomain(X0),compose(g,a)),X1)
| domain(b) != domain(X1)
| codomain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f130,f3883]) ).
fof(f3930,plain,
! [X0,X1] :
( compose(codomain(X0),compose(compose(h,compose(a,b)),X1)) = compose(compose(codomain(X0),compose(h,compose(a,b))),X1)
| codomain(b) != domain(X1)
| codomain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f581,f3884]) ).
fof(f3931,plain,
! [X0,X1] :
( compose(codomain(X0),compose(compose(h,a),X1)) = compose(compose(codomain(X0),compose(h,a)),X1)
| domain(b) != domain(X1)
| codomain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f131,f3885]) ).
fof(f3932,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)],[f120,f3886]) ).
fof(f3933,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)],[f15,f3887]) ).
fof(f3937,plain,
( compose(h,compose(g,a)) = compose(compose(h,compose(g,a)),codomain(compose(g,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f2088]) ).
fof(f3938,plain,
( compose(h,compose(h,compose(a,b))) = compose(compose(h,compose(h,compose(a,b))),codomain(compose(h,compose(a,b))))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f2088]) ).
fof(f3939,plain,
( compose(h,compose(h,a)) = compose(compose(h,compose(h,a)),codomain(compose(h,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f2088]) ).
fof(f3940,plain,
( compose(h,compose(a,b)) = compose(compose(h,compose(a,b)),codomain(compose(a,b)))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f2088]) ).
fof(f3948,definition,
( sQ302_spl
<=> compose(h,compose(g,a)) = compose(compose(h,compose(g,a)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f3951,plain,
( sQ302_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3937,f584,f3948]) ).
fof(f3952,definition,
( sQ303_spl
<=> compose(h,compose(h,compose(a,b))) = compose(compose(h,compose(h,compose(a,b))),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f3955,plain,
( sQ303_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3938,f584,f3952]) ).
fof(f3956,definition,
( sQ304_spl
<=> compose(h,compose(h,a)) = compose(compose(h,compose(h,a)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f3959,plain,
( sQ304_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3939,f584,f3956]) ).
fof(f3960,definition,
( sQ305_spl
<=> compose(h,compose(a,b)) = compose(compose(h,compose(a,b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f3963,plain,
( sQ305_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f3940,f606,f3960]) ).
fof(f3969,plain,
( compose(a,compose(g,a)) = compose(compose(a,domain(compose(g,a))),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f2357]) ).
fof(f3970,plain,
( compose(a,compose(h,compose(a,b))) = compose(compose(a,domain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f2357]) ).
fof(f3971,plain,
( compose(a,compose(h,a)) = compose(compose(a,domain(compose(h,a))),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f2357]) ).
fof(f3972,plain,
( compose(a,compose(a,b)) = compose(compose(a,domain(compose(a,b))),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f2357]) ).
fof(f3973,plain,
! [X0] :
( compose(a,domain(X0)) = compose(compose(a,domain(domain(X0))),domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f2357]) ).
fof(f3974,plain,
! [X0] :
( compose(a,codomain(X0)) = compose(compose(a,domain(codomain(X0))),codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f2357]) ).
fof(f3979,definition,
( sQ306_spl
<=> compose(a,compose(g,a)) = compose(compose(a,domain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f3982,plain,
( sQ306_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3969,f693,f3979]) ).
fof(f3983,definition,
( sQ307_spl
<=> compose(a,compose(h,compose(a,b))) = compose(compose(a,domain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f3986,plain,
( sQ307_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3970,f693,f3983]) ).
fof(f3987,definition,
( sQ308_spl
<=> compose(a,compose(h,a)) = compose(compose(a,domain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ308_spl])],[split_symbol_definition]) ).
fof(f3990,plain,
( sQ308_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3971,f693,f3987]) ).
fof(f3991,definition,
( sQ309_spl
<=> compose(a,compose(a,b)) = compose(compose(a,domain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ309_spl])],[split_symbol_definition]) ).
fof(f3994,plain,
( sQ309_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f3972,f715,f3991]) ).
fof(f3995,plain,
! [X0] :
( compose(a,domain(X0)) = compose(compose(a,domain(X0)),domain(X0))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f3973]) ).
fof(f3996,plain,
! [X0] :
( compose(a,codomain(X0)) = compose(compose(a,codomain(X0)),codomain(X0))
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f3974]) ).
fof(f3998,plain,
( compose(a,compose(g,a)) = compose(compose(a,compose(g,a)),codomain(compose(g,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f2358]) ).
fof(f3999,plain,
( compose(a,compose(h,compose(a,b))) = compose(compose(a,compose(h,compose(a,b))),codomain(compose(h,compose(a,b))))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f2358]) ).
fof(f4000,plain,
( compose(a,compose(h,a)) = compose(compose(a,compose(h,a)),codomain(compose(h,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f2358]) ).
fof(f4001,plain,
( compose(a,compose(a,b)) = compose(compose(a,compose(a,b)),codomain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f2358]) ).
fof(f4008,definition,
( sQ310_spl
<=> compose(a,compose(g,a)) = compose(compose(a,compose(g,a)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f4011,plain,
( sQ310_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3998,f693,f4008]) ).
fof(f4012,definition,
( sQ311_spl
<=> compose(a,compose(h,compose(a,b))) = compose(compose(a,compose(h,compose(a,b))),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f4015,plain,
( sQ311_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3999,f693,f4012]) ).
fof(f4016,definition,
( sQ312_spl
<=> compose(a,compose(h,a)) = compose(compose(a,compose(h,a)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f4019,plain,
( sQ312_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4000,f693,f4016]) ).
fof(f4020,definition,
( sQ313_spl
<=> compose(a,compose(a,b)) = compose(compose(a,compose(a,b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f4023,plain,
( sQ313_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4001,f715,f4020]) ).
fof(f4027,plain,
( domain(compose(codomain(compose(a,b)),compose(h,a))) = codomain(compose(a,b))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f367]) ).
fof(f4028,plain,
( domain(compose(codomain(compose(h,compose(a,b))),compose(h,a))) = codomain(compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f367]) ).
fof(f4029,plain,
( domain(compose(codomain(compose(h,a)),compose(h,a))) = codomain(compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f367]) ).
fof(f4030,plain,
( domain(compose(codomain(compose(g,a)),compose(h,a))) = codomain(compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f367]) ).
fof(f4031,plain,
( domain(compose(codomain(g),compose(h,a))) = codomain(g)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f367]) ).
fof(f4032,plain,
( domain(compose(codomain(h),compose(h,a))) = codomain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f367]) ).
fof(f4033,plain,
( domain(compose(codomain(a),compose(h,a))) = codomain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f367]) ).
fof(f4039,definition,
( sQ314_spl
<=> domain(compose(codomain(compose(a,b)),compose(h,a))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition]) ).
fof(f4042,plain,
( sQ314_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f4027,f1555,f4039]) ).
fof(f4043,definition,
( sQ315_spl
<=> domain(compose(codomain(compose(h,compose(a,b))),compose(h,a))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition]) ).
fof(f4046,plain,
( sQ315_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f4028,f1555,f4043]) ).
fof(f4047,definition,
( sQ316_spl
<=> domain(compose(codomain(compose(h,a)),compose(h,a))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ316_spl])],[split_symbol_definition]) ).
fof(f4050,plain,
( sQ316_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4029,f693,f4047]) ).
fof(f4051,definition,
( sQ317_spl
<=> domain(compose(codomain(compose(g,a)),compose(h,a))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f4054,plain,
( sQ317_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4030,f693,f4051]) ).
fof(f4055,definition,
( sQ318_spl
<=> domain(compose(codomain(g),compose(h,a))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f4058,plain,
( sQ318_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4031,f584,f4055]) ).
fof(f4059,definition,
( sQ319_spl
<=> domain(compose(codomain(h),compose(h,a))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition]) ).
fof(f4062,plain,
( sQ319_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4032,f584,f4059]) ).
fof(f4063,definition,
( sQ320_spl
<=> domain(compose(codomain(a),compose(h,a))) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f4066,plain,
( sQ320_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4033,f693,f4063]) ).
fof(f4074,plain,
( domain(compose(codomain(compose(a,b)),compose(a,b))) = codomain(compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f120,f368]) ).
fof(f4075,plain,
( domain(compose(codomain(compose(h,compose(a,b))),compose(a,b))) = codomain(compose(h,compose(a,b)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f581,f368]) ).
fof(f4076,plain,
( domain(compose(codomain(compose(h,a)),compose(a,b))) = codomain(compose(h,a))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f131,f368]) ).
fof(f4077,plain,
( domain(compose(codomain(compose(g,a)),compose(a,b))) = codomain(compose(g,a))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f130,f368]) ).
fof(f4078,plain,
( domain(compose(codomain(g),compose(a,b))) = codomain(g)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f368]) ).
fof(f4079,plain,
( domain(compose(codomain(h),compose(a,b))) = codomain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f368]) ).
fof(f4080,plain,
( domain(compose(codomain(a),compose(a,b))) = codomain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f368]) ).
fof(f4092,definition,
( sQ321_spl
<=> domain(compose(codomain(compose(a,b)),compose(a,b))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ321_spl])],[split_symbol_definition]) ).
fof(f4095,plain,
( sQ321_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f4074,f1570,f4092]) ).
fof(f4096,definition,
( sQ322_spl
<=> domain(compose(codomain(compose(h,compose(a,b))),compose(a,b))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f4099,plain,
( sQ322_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f4075,f1570,f4096]) ).
fof(f4100,definition,
( sQ323_spl
<=> domain(compose(codomain(compose(h,a)),compose(a,b))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f4103,plain,
( sQ323_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4076,f715,f4100]) ).
fof(f4104,definition,
( sQ324_spl
<=> domain(compose(codomain(compose(g,a)),compose(a,b))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ324_spl])],[split_symbol_definition]) ).
fof(f4107,plain,
( sQ324_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4077,f715,f4104]) ).
fof(f4108,definition,
( sQ325_spl
<=> domain(compose(codomain(g),compose(a,b))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ325_spl])],[split_symbol_definition]) ).
fof(f4111,plain,
( sQ325_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f4078,f606,f4108]) ).
fof(f4112,definition,
( sQ326_spl
<=> domain(compose(codomain(h),compose(a,b))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ326_spl])],[split_symbol_definition]) ).
fof(f4115,plain,
( sQ326_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f4079,f606,f4112]) ).
fof(f4116,definition,
( sQ327_spl
<=> domain(compose(codomain(a),compose(a,b))) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f4119,plain,
( sQ327_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4080,f715,f4116]) ).
fof(f4131,plain,
! [X0] :
( compose(compose(a,b),compose(compose(h,a),X0)) = compose(compose(compose(a,b),compose(h,a)),X0)
| domain(b) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f227]) ).
fof(f4132,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(compose(h,a),X0)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),X0)
| domain(b) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f227]) ).
fof(f4133,plain,
! [X0] :
( compose(compose(h,a),compose(compose(h,a),X0)) = compose(compose(compose(h,a),compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f227]) ).
fof(f4134,plain,
! [X0] :
( compose(compose(g,a),compose(compose(h,a),X0)) = compose(compose(compose(g,a),compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f227]) ).
fof(f4135,plain,
! [X0] :
( compose(g,compose(compose(h,a),X0)) = compose(compose(g,compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f227]) ).
fof(f4136,plain,
! [X0] :
( compose(h,compose(compose(h,a),X0)) = compose(compose(h,compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f227]) ).
fof(f4137,plain,
! [X0] :
( compose(a,compose(compose(h,a),X0)) = compose(compose(a,compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f227]) ).
fof(f4141,definition,
! [X0] :
( sQ328_spl
<=> ( compose(compose(a,b),compose(compose(h,a),X0)) = compose(compose(compose(a,b),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f4144,plain,
( sQ328_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f4131,f1555,f4141]) ).
fof(f4145,definition,
! [X0] :
( sQ329_spl
<=> ( compose(compose(h,compose(a,b)),compose(compose(h,a),X0)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f4148,plain,
( sQ329_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f4132,f1555,f4145]) ).
fof(f4149,definition,
! [X0] :
( sQ330_spl
<=> ( compose(compose(h,a),compose(compose(h,a),X0)) = compose(compose(compose(h,a),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f4152,plain,
( sQ330_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4133,f693,f4149]) ).
fof(f4153,plain,
( sQ274_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4134,f693,f3675]) ).
fof(f4154,plain,
( sQ83_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4135,f584,f1779]) ).
fof(f4155,plain,
( sQ108_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4136,f584,f2097]) ).
fof(f4156,plain,
( sQ147_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4137,f693,f2373]) ).
fof(f4162,plain,
( domain(compose(domain(g),compose(h,a))) = domain(g)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f426]) ).
fof(f4163,plain,
( domain(compose(domain(compose(g,a)),compose(h,a))) = domain(compose(g,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f426]) ).
fof(f4164,plain,
( domain(compose(domain(compose(h,compose(a,b))),compose(h,a))) = domain(compose(h,compose(a,b)))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f426]) ).
fof(f4165,plain,
( domain(compose(domain(compose(h,a)),compose(h,a))) = domain(compose(h,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f426]) ).
fof(f4166,plain,
( domain(compose(domain(compose(a,b)),compose(h,a))) = domain(compose(a,b))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f426]) ).
fof(f4182,definition,
( sQ331_spl
<=> domain(compose(domain(g),compose(h,a))) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f4185,plain,
( sQ331_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f4162,f2687,f4182]) ).
fof(f4186,definition,
( sQ332_spl
<=> domain(compose(domain(compose(g,a)),compose(h,a))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f4189,plain,
( sQ332_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f4163,f2687,f4186]) ).
fof(f4190,definition,
( sQ333_spl
<=> domain(compose(domain(compose(h,compose(a,b))),compose(h,a))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f4193,plain,
( sQ333_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f4164,f2687,f4190]) ).
fof(f4194,definition,
( sQ334_spl
<=> domain(compose(domain(compose(h,a)),compose(h,a))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f4197,plain,
( sQ334_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f4165,f2687,f4194]) ).
fof(f4198,definition,
( sQ335_spl
<=> domain(compose(domain(compose(a,b)),compose(h,a))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f4201,plain,
( sQ335_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4166,f584,f4198]) ).
fof(f4218,plain,
( domain(compose(domain(compose(g,a)),compose(a,b))) = domain(compose(g,a))
| domain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f1108,f427]) ).
fof(f4219,plain,
( domain(compose(domain(compose(h,compose(a,b))),compose(a,b))) = domain(compose(h,compose(a,b)))
| domain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f1068,f427]) ).
fof(f4220,plain,
( domain(compose(domain(compose(h,a)),compose(a,b))) = domain(compose(h,a))
| domain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f76,f427]) ).
fof(f4221,plain,
( domain(compose(domain(compose(a,b)),compose(a,b))) = domain(compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f427]) ).
fof(f4228,definition,
( sQ336_spl
<=> domain(compose(domain(compose(g,a)),compose(a,b))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f4231,plain,
( sQ336_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4218,f584,f4228]) ).
fof(f4232,definition,
( sQ337_spl
<=> domain(compose(domain(compose(h,compose(a,b))),compose(a,b))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f4235,plain,
( sQ337_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4219,f584,f4232]) ).
fof(f4236,definition,
( sQ338_spl
<=> domain(compose(domain(compose(h,a)),compose(a,b))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f4239,plain,
( sQ338_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4220,f584,f4236]) ).
fof(f4240,definition,
( sQ339_spl
<=> domain(compose(domain(compose(a,b)),compose(a,b))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f4243,plain,
( sQ339_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f4221,f606,f4240]) ).
fof(f4250,plain,
( codomain(compose(compose(a,b),domain(compose(g,a)))) = domain(compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f858]) ).
fof(f4251,plain,
( codomain(compose(compose(a,b),domain(compose(h,compose(a,b))))) = domain(compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f858]) ).
fof(f4252,plain,
( codomain(compose(compose(a,b),domain(compose(h,a)))) = domain(compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f858]) ).
fof(f4253,plain,
( codomain(compose(compose(a,b),domain(compose(a,b)))) = domain(compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f858]) ).
fof(f4259,definition,
( sQ340_spl
<=> codomain(compose(compose(a,b),domain(compose(g,a)))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f4262,plain,
( sQ340_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f4250,f1555,f4259]) ).
fof(f4263,definition,
( sQ341_spl
<=> codomain(compose(compose(a,b),domain(compose(h,compose(a,b))))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ341_spl])],[split_symbol_definition]) ).
fof(f4266,plain,
( sQ341_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f4251,f1555,f4263]) ).
fof(f4267,definition,
( sQ342_spl
<=> codomain(compose(compose(a,b),domain(compose(h,a)))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ342_spl])],[split_symbol_definition]) ).
fof(f4270,plain,
( sQ342_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f4252,f1555,f4267]) ).
fof(f4271,definition,
( sQ343_spl
<=> codomain(compose(compose(a,b),domain(compose(a,b)))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ343_spl])],[split_symbol_definition]) ).
fof(f4274,plain,
( sQ343_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f4253,f1570,f4271]) ).
fof(f4280,plain,
( codomain(compose(compose(h,a),domain(compose(g,a)))) = domain(compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f860]) ).
fof(f4281,plain,
( codomain(compose(compose(h,a),domain(compose(h,compose(a,b))))) = domain(compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f860]) ).
fof(f4282,plain,
( codomain(compose(compose(h,a),domain(compose(h,a)))) = domain(compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f860]) ).
fof(f4283,plain,
( codomain(compose(compose(h,a),domain(compose(a,b)))) = domain(compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f860]) ).
fof(f4290,definition,
( sQ344_spl
<=> codomain(compose(compose(h,a),domain(compose(g,a)))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ344_spl])],[split_symbol_definition]) ).
fof(f4293,plain,
( sQ344_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4280,f693,f4290]) ).
fof(f4294,definition,
( sQ345_spl
<=> codomain(compose(compose(h,a),domain(compose(h,compose(a,b))))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f4297,plain,
( sQ345_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4281,f693,f4294]) ).
fof(f4298,definition,
( sQ346_spl
<=> codomain(compose(compose(h,a),domain(compose(h,a)))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f4301,plain,
( sQ346_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4282,f693,f4298]) ).
fof(f4302,definition,
( sQ347_spl
<=> codomain(compose(compose(h,a),domain(compose(a,b)))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f4305,plain,
( sQ347_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4283,f715,f4302]) ).
fof(f4312,plain,
( codomain(compose(compose(g,a),domain(compose(g,a)))) = domain(compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f861]) ).
fof(f4313,plain,
( codomain(compose(compose(g,a),domain(compose(h,compose(a,b))))) = domain(compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f861]) ).
fof(f4314,plain,
( codomain(compose(compose(g,a),domain(compose(h,a)))) = domain(compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f861]) ).
fof(f4315,plain,
( codomain(compose(compose(g,a),domain(compose(a,b)))) = domain(compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f861]) ).
fof(f4322,definition,
( sQ348_spl
<=> codomain(compose(compose(g,a),domain(compose(g,a)))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f4325,plain,
( sQ348_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4312,f693,f4322]) ).
fof(f4326,definition,
( sQ349_spl
<=> codomain(compose(compose(g,a),domain(compose(h,compose(a,b))))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ349_spl])],[split_symbol_definition]) ).
fof(f4329,plain,
( sQ349_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4313,f693,f4326]) ).
fof(f4330,definition,
( sQ350_spl
<=> codomain(compose(compose(g,a),domain(compose(h,a)))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f4333,plain,
( sQ350_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4314,f693,f4330]) ).
fof(f4334,definition,
( sQ351_spl
<=> codomain(compose(compose(g,a),domain(compose(a,b)))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f4337,plain,
( sQ351_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4315,f715,f4334]) ).
fof(f4343,plain,
! [X0] :
( compose(g,compose(compose(a,b),X0)) = compose(compose(g,compose(a,b)),X0)
| codomain(b) != domain(X0) ),
inference(resolution,[status(thm)],[f228,f74]) ).
fof(f4344,plain,
! [X0] :
( compose(h,compose(compose(a,b),X0)) = compose(compose(h,compose(a,b)),X0)
| codomain(b) != domain(X0) ),
inference(resolution,[status(thm)],[f228,f69]) ).
fof(f4346,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)],[f120,f228]) ).
fof(f4347,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(compose(a,b),X0)) = compose(compose(compose(h,compose(a,b)),compose(a,b)),X0)
| codomain(b) != domain(X0)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f581,f228]) ).
fof(f4348,plain,
! [X0] :
( compose(compose(h,a),compose(compose(a,b),X0)) = compose(compose(compose(h,a),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f131,f228]) ).
fof(f4349,plain,
! [X0] :
( compose(compose(g,a),compose(compose(a,b),X0)) = compose(compose(compose(g,a),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f130,f228]) ).
fof(f4350,plain,
! [X0] :
( compose(g,compose(compose(a,b),X0)) = compose(compose(g,compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f228]) ).
fof(f4351,plain,
! [X0] :
( compose(h,compose(compose(a,b),X0)) = compose(compose(h,compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f228]) ).
fof(f4352,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)],[f22,f228]) ).
fof(f4355,plain,
! [X0] :
( compose(g,compose(compose(a,b),X0)) = compose(compose(h,compose(a,b)),X0)
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f29,f4343]) ).
fof(f4357,definition,
! [X0] :
( sQ352_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,[sQ352_spl])],[split_symbol_definition]) ).
fof(f4360,plain,
( sQ352_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f4346,f1570,f4357]) ).
fof(f4361,definition,
! [X0] :
( sQ353_spl
<=> ( compose(compose(h,compose(a,b)),compose(compose(a,b),X0)) = compose(compose(compose(h,compose(a,b)),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ353_spl])],[split_symbol_definition]) ).
fof(f4364,plain,
( sQ353_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f4347,f1570,f4361]) ).
fof(f4365,definition,
! [X0] :
( sQ354_spl
<=> ( compose(compose(h,a),compose(compose(a,b),X0)) = compose(compose(compose(h,a),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f4368,plain,
( sQ354_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4348,f715,f4365]) ).
fof(f4369,plain,
( sQ272_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4349,f715,f3667]) ).
fof(f4370,plain,
( sQ80_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f4350,f606,f1768]) ).
fof(f4371,plain,
( sQ106_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f4351,f606,f2089]) ).
fof(f4372,plain,
( sQ144_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4352,f715,f2362]) ).
fof(f4376,plain,
( codomain(compose(compose(a,b),codomain(compose(a,b)))) = codomain(compose(a,b))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f908]) ).
fof(f4377,plain,
( codomain(compose(compose(a,b),codomain(compose(h,compose(a,b))))) = codomain(compose(h,compose(a,b)))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f908]) ).
fof(f4378,plain,
( codomain(compose(compose(a,b),codomain(compose(h,a)))) = codomain(compose(h,a))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f908]) ).
fof(f4379,plain,
( codomain(compose(compose(a,b),codomain(compose(g,a)))) = codomain(compose(g,a))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f908]) ).
fof(f4389,definition,
( sQ355_spl
<=> codomain(b) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f4391,plain,
( sQ355_spl
| codomain(b) != codomain(b) ),
inference(component_clause,[status(thm)],[f4389]) ).
fof(f4392,definition,
( sQ356_spl
<=> codomain(compose(compose(a,b),codomain(compose(a,b)))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ356_spl])],[split_symbol_definition]) ).
fof(f4395,plain,
( sQ356_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f4376,f4389,f4392]) ).
fof(f4396,definition,
( sQ357_spl
<=> codomain(compose(compose(a,b),codomain(compose(h,compose(a,b))))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f4399,plain,
( sQ357_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f4377,f4389,f4396]) ).
fof(f4400,definition,
( sQ358_spl
<=> codomain(compose(compose(a,b),codomain(compose(h,a)))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f4403,plain,
( sQ358_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f4378,f2265,f4400]) ).
fof(f4404,definition,
( sQ359_spl
<=> codomain(compose(compose(a,b),codomain(compose(g,a)))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f4407,plain,
( sQ359_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f4379,f2265,f4404]) ).
fof(f4413,plain,
( sQ355_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f4391]) ).
fof(f4414,plain,
sQ355_spl,
inference(contradiction_clause,[status(thm)],[f4413]) ).
fof(f4422,plain,
( codomain(compose(compose(h,a),codomain(compose(a,b)))) = codomain(compose(a,b))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f910]) ).
fof(f4423,plain,
( codomain(compose(compose(h,a),codomain(compose(h,compose(a,b))))) = codomain(compose(h,compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f910]) ).
fof(f4424,plain,
( codomain(compose(compose(h,a),codomain(compose(h,a)))) = codomain(compose(h,a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f910]) ).
fof(f4425,plain,
( codomain(compose(compose(h,a),codomain(compose(g,a)))) = codomain(compose(g,a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f910]) ).
fof(f4426,plain,
( codomain(compose(compose(h,a),codomain(g))) = codomain(g)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f910]) ).
fof(f4427,plain,
( codomain(compose(compose(h,a),codomain(h))) = codomain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f910]) ).
fof(f4428,plain,
( codomain(compose(compose(h,a),codomain(a))) = codomain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f910]) ).
fof(f4440,definition,
( sQ360_spl
<=> codomain(compose(compose(h,a),codomain(compose(a,b)))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ360_spl])],[split_symbol_definition]) ).
fof(f4443,plain,
( sQ360_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f4422,f2265,f4440]) ).
fof(f4444,definition,
( sQ361_spl
<=> codomain(compose(compose(h,a),codomain(compose(h,compose(a,b))))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f4447,plain,
( sQ361_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f4423,f2265,f4444]) ).
fof(f4448,definition,
( sQ362_spl
<=> codomain(compose(compose(h,a),codomain(compose(h,a)))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f4451,plain,
( sQ362_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f4424,f1941,f4448]) ).
fof(f4452,definition,
( sQ363_spl
<=> codomain(compose(compose(h,a),codomain(compose(g,a)))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f4455,plain,
( sQ363_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f4425,f1941,f4452]) ).
fof(f4456,definition,
( sQ364_spl
<=> codomain(compose(compose(h,a),codomain(g))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f4459,plain,
( sQ364_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4426,f715,f4456]) ).
fof(f4460,definition,
( sQ365_spl
<=> codomain(compose(compose(h,a),codomain(h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f4463,plain,
( sQ365_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4427,f715,f4460]) ).
fof(f4464,definition,
( sQ366_spl
<=> codomain(compose(compose(h,a),codomain(a))) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f4467,plain,
( sQ366_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f4428,f1941,f4464]) ).
fof(f4482,plain,
( codomain(compose(compose(g,a),codomain(compose(a,b)))) = codomain(compose(a,b))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f911]) ).
fof(f4483,plain,
( codomain(compose(compose(g,a),codomain(compose(h,compose(a,b))))) = codomain(compose(h,compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f911]) ).
fof(f4484,plain,
( codomain(compose(compose(g,a),codomain(compose(h,a)))) = codomain(compose(h,a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f911]) ).
fof(f4485,plain,
( codomain(compose(compose(g,a),codomain(compose(g,a)))) = codomain(compose(g,a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f911]) ).
fof(f4486,plain,
( codomain(compose(compose(g,a),codomain(g))) = codomain(g)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f911]) ).
fof(f4487,plain,
( codomain(compose(compose(g,a),codomain(h))) = codomain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f911]) ).
fof(f4488,plain,
( codomain(compose(compose(g,a),codomain(a))) = codomain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f911]) ).
fof(f4500,definition,
( sQ367_spl
<=> codomain(compose(compose(g,a),codomain(compose(a,b)))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f4503,plain,
( sQ367_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f4482,f2265,f4500]) ).
fof(f4504,definition,
( sQ368_spl
<=> codomain(compose(compose(g,a),codomain(compose(h,compose(a,b))))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ368_spl])],[split_symbol_definition]) ).
fof(f4507,plain,
( sQ368_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f4483,f2265,f4504]) ).
fof(f4508,definition,
( sQ369_spl
<=> codomain(compose(compose(g,a),codomain(compose(h,a)))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f4511,plain,
( sQ369_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f4484,f1941,f4508]) ).
fof(f4512,definition,
( sQ370_spl
<=> codomain(compose(compose(g,a),codomain(compose(g,a)))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition]) ).
fof(f4515,plain,
( sQ370_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f4485,f1941,f4512]) ).
fof(f4516,definition,
( sQ371_spl
<=> codomain(compose(compose(g,a),codomain(g))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f4519,plain,
( sQ371_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4486,f715,f4516]) ).
fof(f4520,definition,
( sQ372_spl
<=> codomain(compose(compose(g,a),codomain(h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ372_spl])],[split_symbol_definition]) ).
fof(f4523,plain,
( sQ372_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4487,f715,f4520]) ).
fof(f4524,definition,
( sQ373_spl
<=> codomain(compose(compose(g,a),codomain(a))) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f4527,plain,
( sQ373_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f4488,f1941,f4524]) ).
fof(f4543,plain,
( domain(compose(domain(g),compose(g,a))) = domain(g)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f1130]) ).
fof(f4544,plain,
( domain(compose(domain(compose(g,a)),compose(g,a))) = domain(compose(g,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1130]) ).
fof(f4545,plain,
( domain(compose(domain(compose(h,compose(a,b))),compose(g,a))) = domain(compose(h,compose(a,b)))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1130]) ).
fof(f4546,plain,
( domain(compose(domain(compose(h,a)),compose(g,a))) = domain(compose(h,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1130]) ).
fof(f4547,plain,
( domain(compose(domain(compose(a,b)),compose(g,a))) = domain(compose(a,b))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f1130]) ).
fof(f4563,definition,
( sQ374_spl
<=> domain(compose(domain(g),compose(g,a))) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f4566,plain,
( sQ374_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f4543,f2687,f4563]) ).
fof(f4567,definition,
( sQ375_spl
<=> domain(compose(domain(compose(g,a)),compose(g,a))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f4570,plain,
( sQ375_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f4544,f2687,f4567]) ).
fof(f4571,definition,
( sQ376_spl
<=> domain(compose(domain(compose(h,compose(a,b))),compose(g,a))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f4574,plain,
( sQ376_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f4545,f2687,f4571]) ).
fof(f4575,definition,
( sQ377_spl
<=> domain(compose(domain(compose(h,a)),compose(g,a))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f4578,plain,
( sQ377_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f4546,f2687,f4575]) ).
fof(f4579,definition,
( sQ378_spl
<=> domain(compose(domain(compose(a,b)),compose(g,a))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f4582,plain,
( sQ378_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4547,f584,f4579]) ).
fof(f4598,plain,
( domain(compose(codomain(compose(a,b)),compose(g,a))) = codomain(compose(a,b))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1132]) ).
fof(f4599,plain,
( domain(compose(codomain(compose(h,compose(a,b))),compose(g,a))) = codomain(compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1132]) ).
fof(f4600,plain,
( domain(compose(codomain(compose(h,a)),compose(g,a))) = codomain(compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1132]) ).
fof(f4601,plain,
( domain(compose(codomain(compose(g,a)),compose(g,a))) = codomain(compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1132]) ).
fof(f4602,plain,
( domain(compose(codomain(g),compose(g,a))) = codomain(g)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1132]) ).
fof(f4603,plain,
( domain(compose(codomain(h),compose(g,a))) = codomain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1132]) ).
fof(f4604,plain,
( domain(compose(codomain(a),compose(g,a))) = codomain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f1132]) ).
fof(f4610,definition,
( sQ379_spl
<=> domain(compose(codomain(compose(a,b)),compose(g,a))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ379_spl])],[split_symbol_definition]) ).
fof(f4613,plain,
( sQ379_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f4598,f1555,f4610]) ).
fof(f4614,definition,
( sQ380_spl
<=> domain(compose(codomain(compose(h,compose(a,b))),compose(g,a))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ380_spl])],[split_symbol_definition]) ).
fof(f4617,plain,
( sQ380_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f4599,f1555,f4614]) ).
fof(f4618,definition,
( sQ381_spl
<=> domain(compose(codomain(compose(h,a)),compose(g,a))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f4621,plain,
( sQ381_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4600,f693,f4618]) ).
fof(f4622,definition,
( sQ382_spl
<=> domain(compose(codomain(compose(g,a)),compose(g,a))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ382_spl])],[split_symbol_definition]) ).
fof(f4625,plain,
( sQ382_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4601,f693,f4622]) ).
fof(f4626,definition,
( sQ383_spl
<=> domain(compose(codomain(g),compose(g,a))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ383_spl])],[split_symbol_definition]) ).
fof(f4629,plain,
( sQ383_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4602,f584,f4626]) ).
fof(f4630,definition,
( sQ384_spl
<=> domain(compose(codomain(h),compose(g,a))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ384_spl])],[split_symbol_definition]) ).
fof(f4633,plain,
( sQ384_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4603,f584,f4630]) ).
fof(f4634,definition,
( sQ385_spl
<=> domain(compose(codomain(a),compose(g,a))) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ385_spl])],[split_symbol_definition]) ).
fof(f4637,plain,
( sQ385_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4604,f693,f4634]) ).
fof(f4649,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)],[f120,f229]) ).
fof(f4650,plain,
! [X0,X1] :
( compose(compose(h,compose(a,b)),compose(domain(X0),X1)) = compose(compose(compose(h,compose(a,b)),domain(X0)),X1)
| domain(X0) != domain(X1)
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f581,f229]) ).
fof(f4651,plain,
! [X0,X1] :
( compose(compose(h,a),compose(domain(X0),X1)) = compose(compose(compose(h,a),domain(X0)),X1)
| domain(X0) != domain(X1)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f131,f229]) ).
fof(f4694,plain,
( compose(domain(h),compose(g,compose(g,a))) = compose(g,compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1499]) ).
fof(f4695,plain,
( compose(domain(h),compose(g,compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1499]) ).
fof(f4696,plain,
( compose(domain(h),compose(g,compose(h,a))) = compose(g,compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1499]) ).
fof(f4697,plain,
( compose(domain(h),compose(g,compose(a,b))) = compose(g,compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1499]) ).
fof(f4698,plain,
! [X0] :
( compose(domain(h),compose(g,domain(X0))) = compose(g,domain(X0))
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f1499]) ).
fof(f4699,plain,
! [X0] :
( compose(domain(h),compose(g,codomain(X0))) = compose(g,codomain(X0))
| domain(a) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f1499]) ).
fof(f4705,definition,
( sQ386_spl
<=> compose(domain(h),compose(g,compose(g,a))) = compose(g,compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f4708,plain,
( sQ386_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4694,f584,f4705]) ).
fof(f4709,definition,
( sQ387_spl
<=> compose(domain(h),compose(g,compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f4712,plain,
( sQ387_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4695,f584,f4709]) ).
fof(f4713,definition,
( sQ388_spl
<=> compose(domain(h),compose(g,compose(h,a))) = compose(g,compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ388_spl])],[split_symbol_definition]) ).
fof(f4716,plain,
( sQ388_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4696,f584,f4713]) ).
fof(f4717,definition,
( sQ389_spl
<=> compose(domain(h),compose(g,compose(a,b))) = compose(g,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f4720,plain,
( sQ389_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f4697,f606,f4717]) ).
fof(f4725,plain,
( compose(domain(h),compose(h,compose(g,a))) = compose(h,compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1475]) ).
fof(f4726,plain,
( compose(domain(h),compose(h,compose(h,compose(a,b)))) = compose(h,compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1475]) ).
fof(f4727,plain,
( compose(domain(h),compose(h,compose(h,a))) = compose(h,compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1475]) ).
fof(f4728,plain,
( compose(domain(h),compose(h,compose(a,b))) = compose(h,compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1475]) ).
fof(f4729,plain,
! [X0] :
( compose(domain(h),compose(h,domain(X0))) = compose(h,domain(X0))
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f1475]) ).
fof(f4730,plain,
! [X0] :
( compose(domain(h),compose(h,codomain(X0))) = compose(h,codomain(X0))
| domain(a) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f1475]) ).
fof(f4734,definition,
( sQ390_spl
<=> compose(domain(h),compose(h,compose(g,a))) = compose(h,compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f4737,plain,
( sQ390_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4725,f584,f4734]) ).
fof(f4738,definition,
( sQ391_spl
<=> compose(domain(h),compose(h,compose(h,compose(a,b)))) = compose(h,compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f4741,plain,
( sQ391_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4726,f584,f4738]) ).
fof(f4742,definition,
( sQ392_spl
<=> compose(domain(h),compose(h,compose(h,a))) = compose(h,compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f4745,plain,
( sQ392_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4727,f584,f4742]) ).
fof(f4746,definition,
( sQ393_spl
<=> compose(domain(h),compose(h,compose(a,b))) = compose(h,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f4749,plain,
( sQ393_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f4728,f606,f4746]) ).
fof(f4751,plain,
( compose(domain(a),compose(a,compose(g,a))) = compose(a,compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1476]) ).
fof(f4752,plain,
( compose(domain(a),compose(a,compose(h,compose(a,b)))) = compose(a,compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1476]) ).
fof(f4753,plain,
( compose(domain(a),compose(a,compose(h,a))) = compose(a,compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1476]) ).
fof(f4754,plain,
( compose(domain(a),compose(a,compose(a,b))) = compose(a,compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1476]) ).
fof(f4755,plain,
! [X0] :
( compose(domain(a),compose(a,domain(X0))) = compose(a,domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f1476]) ).
fof(f4756,plain,
! [X0] :
( compose(domain(a),compose(a,codomain(X0))) = compose(a,codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f1476]) ).
fof(f4760,definition,
( sQ394_spl
<=> compose(domain(a),compose(a,compose(g,a))) = compose(a,compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ394_spl])],[split_symbol_definition]) ).
fof(f4763,plain,
( sQ394_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4751,f693,f4760]) ).
fof(f4764,definition,
( sQ395_spl
<=> compose(domain(a),compose(a,compose(h,compose(a,b)))) = compose(a,compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition]) ).
fof(f4767,plain,
( sQ395_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4752,f693,f4764]) ).
fof(f4768,definition,
( sQ396_spl
<=> compose(domain(a),compose(a,compose(h,a))) = compose(a,compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ396_spl])],[split_symbol_definition]) ).
fof(f4771,plain,
( sQ396_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4753,f693,f4768]) ).
fof(f4772,definition,
( sQ397_spl
<=> compose(domain(a),compose(a,compose(a,b))) = compose(a,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ397_spl])],[split_symbol_definition]) ).
fof(f4775,plain,
( sQ397_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4754,f715,f4772]) ).
fof(f4792,plain,
! [X0] :
( compose(codomain(X0),compose(codomain(X0),compose(g,a))) = compose(codomain(X0),compose(g,a))
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1500]) ).
fof(f4793,plain,
! [X0] :
( compose(codomain(X0),compose(codomain(X0),compose(h,compose(a,b)))) = compose(codomain(X0),compose(h,compose(a,b)))
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1500]) ).
fof(f4794,plain,
! [X0] :
( compose(codomain(X0),compose(codomain(X0),compose(h,a))) = compose(codomain(X0),compose(h,a))
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1500]) ).
fof(f4795,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)],[f60,f1500]) ).
fof(f4796,plain,
! [X0,X1] :
( compose(codomain(X0),compose(codomain(X0),domain(X1))) = compose(codomain(X0),domain(X1))
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f37,f1500]) ).
fof(f4797,plain,
! [X0,X1] :
( compose(codomain(X0),compose(codomain(X0),codomain(X1))) = compose(codomain(X0),codomain(X1))
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f16,f1500]) ).
fof(f4874,plain,
! [X0] :
( compose(domain(X0),compose(domain(X0),g)) = compose(domain(X0),g)
| domain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f1501]) ).
fof(f4875,plain,
! [X0] :
( compose(domain(X0),compose(domain(X0),compose(g,a))) = compose(domain(X0),compose(g,a))
| domain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1501]) ).
fof(f4876,plain,
! [X0] :
( compose(domain(X0),compose(domain(X0),compose(h,compose(a,b)))) = compose(domain(X0),compose(h,compose(a,b)))
| domain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1501]) ).
fof(f4877,plain,
! [X0] :
( compose(domain(X0),compose(domain(X0),compose(h,a))) = compose(domain(X0),compose(h,a))
| domain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1501]) ).
fof(f4878,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)],[f60,f1501]) ).
fof(f4879,plain,
! [X0,X1] :
( compose(domain(X0),compose(domain(X0),domain(X1))) = compose(domain(X0),domain(X1))
| domain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f37,f1501]) ).
fof(f4880,plain,
! [X0,X1] :
( compose(domain(X0),compose(domain(X0),codomain(X1))) = compose(domain(X0),codomain(X1))
| domain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f16,f1501]) ).
fof(f4933,plain,
( compose(compose(h,a),compose(compose(h,a),b)) = compose(compose(compose(h,a),compose(h,a)),b)
| domain(b) != domain(compose(h,a)) ),
inference(resolution,[status(thm)],[f234,f131]) ).
fof(f4934,plain,
( compose(compose(h,a),compose(compose(g,a),b)) = compose(compose(compose(h,a),compose(g,a)),b)
| domain(b) != domain(compose(g,a)) ),
inference(resolution,[status(thm)],[f234,f130]) ).
fof(f4935,plain,
( compose(compose(h,a),compose(g,a)) = compose(compose(compose(h,a),g),a)
| domain(b) != domain(g) ),
inference(resolution,[status(thm)],[f234,f74]) ).
fof(f4936,plain,
( compose(compose(h,a),compose(h,a)) = compose(compose(compose(h,a),h),a)
| domain(b) != domain(h) ),
inference(resolution,[status(thm)],[f234,f69]) ).
fof(f4937,plain,
( compose(compose(h,a),compose(a,b)) = compose(compose(compose(h,a),a),b)
| domain(b) != domain(a) ),
inference(resolution,[status(thm)],[f234,f22]) ).
fof(f4938,plain,
! [X0] :
( compose(compose(h,a),compose(domain(X0),X0)) = compose(compose(compose(h,a),domain(X0)),X0)
| domain(b) != domain(domain(X0)) ),
inference(resolution,[status(thm)],[f234,f15]) ).
fof(f4939,plain,
! [X0] :
( compose(compose(h,a),compose(X0,codomain(X0))) = compose(compose(compose(h,a),X0),codomain(X0))
| domain(b) != domain(X0) ),
inference(resolution,[status(thm)],[f234,f16]) ).
fof(f4940,plain,
! [X0] :
( compose(compose(h,a),compose(compose(a,b),X0)) = compose(compose(compose(h,a),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f234]) ).
fof(f4941,plain,
! [X0] :
( compose(compose(h,a),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(h,a),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f234]) ).
fof(f4942,plain,
! [X0] :
( compose(compose(h,a),compose(compose(h,a),X0)) = compose(compose(compose(h,a),compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f234]) ).
fof(f4943,plain,
! [X0] :
( compose(compose(h,a),compose(compose(g,a),X0)) = compose(compose(compose(h,a),compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f234]) ).
fof(f4944,plain,
! [X0] :
( compose(compose(h,a),compose(g,X0)) = compose(compose(compose(h,a),g),X0)
| domain(a) != domain(X0)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f234]) ).
fof(f4945,plain,
! [X0] :
( compose(compose(h,a),compose(h,X0)) = compose(compose(compose(h,a),h),X0)
| domain(a) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f234]) ).
fof(f4946,plain,
! [X0] :
( compose(compose(h,a),compose(a,X0)) = compose(compose(compose(h,a),a),X0)
| domain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f234]) ).
fof(f4949,plain,
! [X0] :
( compose(compose(h,a),compose(X0,compose(g,a))) = compose(compose(compose(h,a),X0),compose(g,a))
| codomain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f1108,f234]) ).
fof(f4950,plain,
! [X0] :
( compose(compose(h,a),compose(X0,compose(h,compose(a,b)))) = compose(compose(compose(h,a),X0),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f1068,f234]) ).
fof(f4951,plain,
! [X0] :
( compose(compose(h,a),compose(X0,compose(h,a))) = compose(compose(compose(h,a),X0),compose(h,a))
| codomain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f76,f234]) ).
fof(f4952,plain,
! [X0] :
( compose(compose(h,a),compose(X0,compose(a,b))) = compose(compose(compose(h,a),X0),compose(a,b))
| codomain(X0) != domain(a)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f60,f234]) ).
fof(f4953,plain,
! [X0,X1] :
( compose(compose(h,a),compose(X0,domain(X1))) = compose(compose(compose(h,a),X0),domain(X1))
| codomain(X0) != domain(X1)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f234]) ).
fof(f4954,plain,
! [X0,X1] :
( compose(compose(h,a),compose(X0,codomain(X1))) = compose(compose(compose(h,a),X0),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f16,f234]) ).
fof(f4955,definition,
( sQ398_spl
<=> compose(compose(h,a),compose(compose(h,a),b)) = compose(compose(compose(h,a),compose(h,a)),b) ),
introduced(definition,[new_symbols(definition,[sQ398_spl])],[split_symbol_definition]) ).
fof(f4958,plain,
( sQ398_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f4933,f2330,f4955]) ).
fof(f4959,definition,
( sQ399_spl
<=> compose(compose(h,a),compose(compose(g,a),b)) = compose(compose(compose(h,a),compose(g,a)),b) ),
introduced(definition,[new_symbols(definition,[sQ399_spl])],[split_symbol_definition]) ).
fof(f4962,plain,
( sQ399_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f4934,f2337,f4959]) ).
fof(f4963,definition,
( sQ400_spl
<=> compose(compose(h,a),compose(g,a)) = compose(compose(compose(h,a),g),a) ),
introduced(definition,[new_symbols(definition,[sQ400_spl])],[split_symbol_definition]) ).
fof(f4966,plain,
( sQ400_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f4935,f700,f4963]) ).
fof(f4967,definition,
( sQ401_spl
<=> compose(compose(h,a),compose(h,a)) = compose(compose(compose(h,a),h),a) ),
introduced(definition,[new_symbols(definition,[sQ401_spl])],[split_symbol_definition]) ).
fof(f4970,plain,
( sQ401_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4936,f693,f4967]) ).
fof(f4971,definition,
( sQ402_spl
<=> compose(compose(h,a),compose(a,b)) = compose(compose(compose(h,a),a),b) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f4974,plain,
( sQ402_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4937,f715,f4971]) ).
fof(f4975,plain,
! [X0] :
( compose(compose(h,a),compose(domain(X0),X0)) = compose(compose(compose(h,a),domain(X0)),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f4938]) ).
fof(f4976,plain,
! [X0] :
( compose(compose(h,a),X0) = compose(compose(compose(h,a),domain(X0)),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f17,f4975]) ).
fof(f4977,plain,
! [X0] :
( compose(compose(h,a),X0) = compose(compose(compose(h,a),X0),codomain(X0))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f18,f4939]) ).
fof(f4978,plain,
( sQ354_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f4940,f2359,f4365]) ).
fof(f4979,definition,
! [X0] :
( sQ403_spl
<=> ( compose(compose(h,a),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(h,a),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ403_spl])],[split_symbol_definition]) ).
fof(f4982,plain,
( sQ403_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f4941,f2366,f4979]) ).
fof(f4983,plain,
( sQ330_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f4942,f2330,f4149]) ).
fof(f4984,definition,
! [X0] :
( sQ404_spl
<=> ( compose(compose(h,a),compose(compose(g,a),X0)) = compose(compose(compose(h,a),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition]) ).
fof(f4987,plain,
( sQ404_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f4943,f2337,f4984]) ).
fof(f4988,definition,
! [X0] :
( sQ405_spl
<=> ( compose(compose(h,a),compose(g,X0)) = compose(compose(compose(h,a),g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ405_spl])],[split_symbol_definition]) ).
fof(f4991,plain,
( sQ405_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f4944,f700,f4988]) ).
fof(f4992,definition,
! [X0] :
( sQ406_spl
<=> ( compose(compose(h,a),compose(h,X0)) = compose(compose(compose(h,a),h),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition]) ).
fof(f4995,plain,
( sQ406_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4945,f693,f4992]) ).
fof(f4996,definition,
! [X0] :
( sQ407_spl
<=> ( compose(compose(h,a),compose(a,X0)) = compose(compose(compose(h,a),a),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition]) ).
fof(f4999,plain,
( sQ407_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f4946,f715,f4996]) ).
fof(f5009,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)],[f120,f1483]) ).
fof(f5010,plain,
! [X0] :
( compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f581,f1483]) ).
fof(f5011,plain,
! [X0] :
( compose(domain(compose(h,a)),compose(compose(h,a),domain(X0))) = compose(compose(h,a),domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f131,f1483]) ).
fof(f5012,plain,
! [X0] :
( compose(domain(compose(g,a)),compose(compose(g,a),domain(X0))) = compose(compose(g,a),domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f130,f1483]) ).
fof(f5042,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)],[f60,f5009]) ).
fof(f5043,plain,
! [X0] :
( compose(domain(h),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f1068,f5010]) ).
fof(f5044,plain,
! [X0] :
( compose(domain(h),compose(compose(h,a),domain(X0))) = compose(compose(h,a),domain(X0))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f76,f5011]) ).
fof(f5045,plain,
! [X0] :
( compose(domain(h),compose(compose(g,a),domain(X0))) = compose(compose(g,a),domain(X0))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f1108,f5012]) ).
fof(f5067,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)],[f120,f1484]) ).
fof(f5068,plain,
! [X0] :
( compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f581,f1484]) ).
fof(f5069,plain,
! [X0] :
( compose(domain(compose(h,a)),compose(compose(h,a),codomain(X0))) = compose(compose(h,a),codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f131,f1484]) ).
fof(f5070,plain,
! [X0] :
( compose(domain(compose(g,a)),compose(compose(g,a),codomain(X0))) = compose(compose(g,a),codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f130,f1484]) ).
fof(f5105,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)],[f60,f5067]) ).
fof(f5106,plain,
! [X0] :
( compose(domain(h),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f1068,f5068]) ).
fof(f5107,plain,
! [X0] :
( compose(domain(h),compose(compose(h,a),codomain(X0))) = compose(compose(h,a),codomain(X0))
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f76,f5069]) ).
fof(f5108,plain,
! [X0] :
( compose(domain(h),compose(compose(g,a),codomain(X0))) = compose(compose(g,a),codomain(X0))
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f1108,f5070]) ).
fof(f5134,plain,
( compose(g,compose(domain(a),compose(g,a))) = compose(g,compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1534]) ).
fof(f5135,plain,
( compose(g,compose(domain(a),compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1534]) ).
fof(f5136,plain,
( compose(g,compose(domain(a),compose(h,a))) = compose(g,compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1534]) ).
fof(f5137,plain,
( compose(g,compose(domain(a),compose(a,b))) = compose(g,compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1534]) ).
fof(f5138,plain,
! [X0] :
( compose(g,compose(domain(a),domain(X0))) = compose(g,domain(X0))
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f1534]) ).
fof(f5139,plain,
! [X0] :
( compose(g,compose(domain(a),codomain(X0))) = compose(g,codomain(X0))
| domain(a) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f1534]) ).
fof(f5141,definition,
( sQ408_spl
<=> compose(g,compose(domain(a),compose(g,a))) = compose(g,compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ408_spl])],[split_symbol_definition]) ).
fof(f5144,plain,
( sQ408_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5134,f584,f5141]) ).
fof(f5145,definition,
( sQ409_spl
<=> compose(g,compose(domain(a),compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ409_spl])],[split_symbol_definition]) ).
fof(f5148,plain,
( sQ409_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5135,f584,f5145]) ).
fof(f5149,definition,
( sQ410_spl
<=> compose(g,compose(domain(a),compose(h,a))) = compose(g,compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition]) ).
fof(f5152,plain,
( sQ410_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5136,f584,f5149]) ).
fof(f5153,definition,
( sQ411_spl
<=> compose(g,compose(domain(a),compose(a,b))) = compose(g,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ411_spl])],[split_symbol_definition]) ).
fof(f5156,plain,
( sQ411_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f5137,f606,f5153]) ).
fof(f5159,plain,
( compose(h,compose(domain(a),compose(g,a))) = compose(h,compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1535]) ).
fof(f5160,plain,
( compose(h,compose(domain(a),compose(h,compose(a,b)))) = compose(h,compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1535]) ).
fof(f5161,plain,
( compose(h,compose(domain(a),compose(h,a))) = compose(h,compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1535]) ).
fof(f5162,plain,
( compose(h,compose(domain(a),compose(a,b))) = compose(h,compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1535]) ).
fof(f5163,plain,
! [X0] :
( compose(h,compose(domain(a),domain(X0))) = compose(h,domain(X0))
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f1535]) ).
fof(f5164,plain,
! [X0] :
( compose(h,compose(domain(a),codomain(X0))) = compose(h,codomain(X0))
| domain(a) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f1535]) ).
fof(f5166,definition,
( sQ412_spl
<=> compose(h,compose(domain(a),compose(g,a))) = compose(h,compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ412_spl])],[split_symbol_definition]) ).
fof(f5169,plain,
( sQ412_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5159,f584,f5166]) ).
fof(f5170,definition,
( sQ413_spl
<=> compose(h,compose(domain(a),compose(h,compose(a,b)))) = compose(h,compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ413_spl])],[split_symbol_definition]) ).
fof(f5173,plain,
( sQ413_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5160,f584,f5170]) ).
fof(f5174,definition,
( sQ414_spl
<=> compose(h,compose(domain(a),compose(h,a))) = compose(h,compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f5177,plain,
( sQ414_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5161,f584,f5174]) ).
fof(f5178,definition,
( sQ415_spl
<=> compose(h,compose(domain(a),compose(a,b))) = compose(h,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f5181,plain,
( sQ415_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f5162,f606,f5178]) ).
fof(f5183,plain,
( compose(a,compose(domain(b),compose(g,a))) = compose(a,compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1536]) ).
fof(f5184,plain,
( compose(a,compose(domain(b),compose(h,compose(a,b)))) = compose(a,compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1536]) ).
fof(f5185,plain,
( compose(a,compose(domain(b),compose(h,a))) = compose(a,compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1536]) ).
fof(f5186,plain,
( compose(a,compose(domain(b),compose(a,b))) = compose(a,compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1536]) ).
fof(f5187,plain,
! [X0] :
( compose(a,compose(domain(b),domain(X0))) = compose(a,domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f1536]) ).
fof(f5188,plain,
! [X0] :
( compose(a,compose(domain(b),codomain(X0))) = compose(a,codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f1536]) ).
fof(f5190,definition,
( sQ416_spl
<=> compose(a,compose(domain(b),compose(g,a))) = compose(a,compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f5193,plain,
( sQ416_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5183,f693,f5190]) ).
fof(f5194,definition,
( sQ417_spl
<=> compose(a,compose(domain(b),compose(h,compose(a,b)))) = compose(a,compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ417_spl])],[split_symbol_definition]) ).
fof(f5197,plain,
( sQ417_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5184,f693,f5194]) ).
fof(f5198,definition,
( sQ418_spl
<=> compose(a,compose(domain(b),compose(h,a))) = compose(a,compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ418_spl])],[split_symbol_definition]) ).
fof(f5201,plain,
( sQ418_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5185,f693,f5198]) ).
fof(f5202,definition,
( sQ419_spl
<=> compose(a,compose(domain(b),compose(a,b))) = compose(a,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f5205,plain,
( sQ419_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f5186,f715,f5202]) ).
fof(f5207,plain,
! [X0] :
( compose(compose(a,b),compose(compose(g,a),X0)) = compose(compose(compose(a,b),compose(g,a)),X0)
| codomain(compose(g,a)) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f250]) ).
fof(f5208,plain,
! [X0] :
( compose(compose(a,b),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(a,b),compose(h,compose(a,b))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f250]) ).
fof(f5209,plain,
! [X0] :
( compose(compose(a,b),compose(compose(h,a),X0)) = compose(compose(compose(a,b),compose(h,a)),X0)
| codomain(compose(h,a)) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f250]) ).
fof(f5210,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)],[f60,f250]) ).
fof(f5215,definition,
! [X0] :
( sQ420_spl
<=> ( compose(compose(a,b),compose(compose(g,a),X0)) = compose(compose(compose(a,b),compose(g,a)),X0)
| codomain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f5218,plain,
( sQ420_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5207,f1555,f5215]) ).
fof(f5219,definition,
! [X0] :
( sQ421_spl
<=> ( compose(compose(a,b),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(a,b),compose(h,compose(a,b))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ421_spl])],[split_symbol_definition]) ).
fof(f5222,plain,
( sQ421_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5208,f1555,f5219]) ).
fof(f5223,definition,
! [X0] :
( sQ422_spl
<=> ( compose(compose(a,b),compose(compose(h,a),X0)) = compose(compose(compose(a,b),compose(h,a)),X0)
| codomain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ422_spl])],[split_symbol_definition]) ).
fof(f5226,plain,
( sQ422_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5209,f1555,f5223]) ).
fof(f5227,definition,
! [X0] :
( sQ423_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,[sQ423_spl])],[split_symbol_definition]) ).
fof(f5230,plain,
( sQ423_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f5210,f1570,f5227]) ).
fof(f5240,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)],[f120,f1522]) ).
fof(f5241,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f581,f1522]) ).
fof(f5242,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(h,a)),domain(X0))) = compose(compose(h,a),domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f131,f1522]) ).
fof(f5243,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(g,a)),domain(X0))) = compose(compose(g,a),domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f130,f1522]) ).
fof(f5265,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)],[f120,f5240]) ).
fof(f5266,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(codomain(b),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f581,f5241]) ).
fof(f5267,plain,
! [X0] :
( compose(compose(h,a),compose(domain(b),domain(X0))) = compose(compose(h,a),domain(X0))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f131,f5242]) ).
fof(f5268,plain,
! [X0] :
( compose(compose(g,a),compose(domain(b),domain(X0))) = compose(compose(g,a),domain(X0))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f130,f5243]) ).
fof(f5292,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)],[f120,f1523]) ).
fof(f5293,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f581,f1523]) ).
fof(f5294,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(h,a)),codomain(X0))) = compose(compose(h,a),codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f131,f1523]) ).
fof(f5295,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(g,a)),codomain(X0))) = compose(compose(g,a),codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f130,f1523]) ).
fof(f5325,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)],[f120,f5292]) ).
fof(f5326,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(codomain(b),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f581,f5293]) ).
fof(f5327,plain,
! [X0] :
( compose(compose(h,a),compose(domain(b),codomain(X0))) = compose(compose(h,a),codomain(X0))
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f131,f5294]) ).
fof(f5328,plain,
! [X0] :
( compose(compose(g,a),compose(domain(b),codomain(X0))) = compose(compose(g,a),codomain(X0))
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f130,f5295]) ).
fof(f5353,plain,
( domain(compose(compose(a,b),domain(compose(g,a)))) = domain(a)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f490]) ).
fof(f5354,plain,
( domain(compose(compose(a,b),domain(compose(h,compose(a,b))))) = domain(a)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f490]) ).
fof(f5355,plain,
( domain(compose(compose(a,b),domain(compose(h,a)))) = domain(a)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f490]) ).
fof(f5356,plain,
( domain(compose(compose(a,b),domain(compose(a,b)))) = domain(a)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f490]) ).
fof(f5361,definition,
( sQ424_spl
<=> domain(compose(compose(a,b),domain(compose(g,a)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ424_spl])],[split_symbol_definition]) ).
fof(f5364,plain,
( sQ424_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5353,f1555,f5361]) ).
fof(f5365,definition,
( sQ425_spl
<=> domain(compose(compose(a,b),domain(compose(h,compose(a,b))))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ425_spl])],[split_symbol_definition]) ).
fof(f5368,plain,
( sQ425_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5354,f1555,f5365]) ).
fof(f5369,definition,
( sQ426_spl
<=> domain(compose(compose(a,b),domain(compose(h,a)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f5372,plain,
( sQ426_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5355,f1555,f5369]) ).
fof(f5373,definition,
( sQ427_spl
<=> domain(compose(compose(a,b),domain(compose(a,b)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition]) ).
fof(f5376,plain,
( sQ427_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f5356,f1570,f5373]) ).
fof(f5380,plain,
( domain(compose(compose(h,a),domain(compose(g,a)))) = domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f491]) ).
fof(f5381,plain,
( domain(compose(compose(h,a),domain(compose(h,compose(a,b))))) = domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f491]) ).
fof(f5382,plain,
( domain(compose(compose(h,a),domain(compose(h,a)))) = domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f491]) ).
fof(f5383,plain,
( domain(compose(compose(h,a),domain(compose(a,b)))) = domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f491]) ).
fof(f5389,definition,
( sQ428_spl
<=> domain(compose(compose(h,a),domain(compose(g,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition]) ).
fof(f5392,plain,
( sQ428_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5380,f693,f5389]) ).
fof(f5393,definition,
( sQ429_spl
<=> domain(compose(compose(h,a),domain(compose(h,compose(a,b))))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ429_spl])],[split_symbol_definition]) ).
fof(f5396,plain,
( sQ429_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5381,f693,f5393]) ).
fof(f5397,definition,
( sQ430_spl
<=> domain(compose(compose(h,a),domain(compose(h,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ430_spl])],[split_symbol_definition]) ).
fof(f5400,plain,
( sQ430_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5382,f693,f5397]) ).
fof(f5401,definition,
( sQ431_spl
<=> domain(compose(compose(h,a),domain(compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ431_spl])],[split_symbol_definition]) ).
fof(f5404,plain,
( sQ431_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f5383,f715,f5401]) ).
fof(f5411,plain,
( domain(compose(compose(a,b),codomain(compose(a,b)))) = domain(a)
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f537]) ).
fof(f5412,plain,
( domain(compose(compose(a,b),codomain(compose(h,compose(a,b))))) = domain(a)
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f537]) ).
fof(f5413,plain,
( domain(compose(compose(a,b),codomain(compose(h,a)))) = domain(a)
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f537]) ).
fof(f5414,plain,
( domain(compose(compose(a,b),codomain(compose(g,a)))) = domain(a)
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f537]) ).
fof(f5423,definition,
( sQ432_spl
<=> domain(compose(compose(a,b),codomain(compose(a,b)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ432_spl])],[split_symbol_definition]) ).
fof(f5426,plain,
( sQ432_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f5411,f4389,f5423]) ).
fof(f5427,definition,
( sQ433_spl
<=> domain(compose(compose(a,b),codomain(compose(h,compose(a,b))))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ433_spl])],[split_symbol_definition]) ).
fof(f5430,plain,
( sQ433_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f5412,f4389,f5427]) ).
fof(f5431,definition,
( sQ434_spl
<=> domain(compose(compose(a,b),codomain(compose(h,a)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ434_spl])],[split_symbol_definition]) ).
fof(f5434,plain,
( sQ434_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f5413,f2265,f5431]) ).
fof(f5435,definition,
( sQ435_spl
<=> domain(compose(compose(a,b),codomain(compose(g,a)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ435_spl])],[split_symbol_definition]) ).
fof(f5438,plain,
( sQ435_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f5414,f2265,f5435]) ).
fof(f5449,plain,
( domain(compose(compose(h,a),codomain(compose(a,b)))) = domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f538]) ).
fof(f5450,plain,
( domain(compose(compose(h,a),codomain(compose(h,compose(a,b))))) = domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f538]) ).
fof(f5451,plain,
( domain(compose(compose(h,a),codomain(compose(h,a)))) = domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f538]) ).
fof(f5452,plain,
( domain(compose(compose(h,a),codomain(compose(g,a)))) = domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f538]) ).
fof(f5453,plain,
( domain(compose(compose(h,a),codomain(g))) = domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f538]) ).
fof(f5454,plain,
( domain(compose(compose(h,a),codomain(h))) = domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f538]) ).
fof(f5455,plain,
( domain(compose(compose(h,a),codomain(a))) = domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f538]) ).
fof(f5465,definition,
( sQ436_spl
<=> domain(compose(compose(h,a),codomain(compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ436_spl])],[split_symbol_definition]) ).
fof(f5468,plain,
( sQ436_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f5449,f2265,f5465]) ).
fof(f5469,definition,
( sQ437_spl
<=> domain(compose(compose(h,a),codomain(compose(h,compose(a,b))))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ437_spl])],[split_symbol_definition]) ).
fof(f5472,plain,
( sQ437_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f5450,f2265,f5469]) ).
fof(f5473,definition,
( sQ438_spl
<=> domain(compose(compose(h,a),codomain(compose(h,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ438_spl])],[split_symbol_definition]) ).
fof(f5476,plain,
( sQ438_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f5451,f1941,f5473]) ).
fof(f5477,definition,
( sQ439_spl
<=> domain(compose(compose(h,a),codomain(compose(g,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ439_spl])],[split_symbol_definition]) ).
fof(f5480,plain,
( sQ439_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f5452,f1941,f5477]) ).
fof(f5481,definition,
( sQ440_spl
<=> domain(compose(compose(h,a),codomain(g))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ440_spl])],[split_symbol_definition]) ).
fof(f5484,plain,
( sQ440_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f5453,f715,f5481]) ).
fof(f5485,definition,
( sQ441_spl
<=> domain(compose(compose(h,a),codomain(h))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f5488,plain,
( sQ441_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f5454,f715,f5485]) ).
fof(f5489,definition,
( sQ442_spl
<=> domain(compose(compose(h,a),codomain(a))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ442_spl])],[split_symbol_definition]) ).
fof(f5492,plain,
( sQ442_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f5455,f1941,f5489]) ).
fof(f5501,plain,
( codomain(compose(codomain(compose(a,b)),compose(h,a))) = domain(b)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f769]) ).
fof(f5502,plain,
( codomain(compose(codomain(compose(h,compose(a,b))),compose(h,a))) = domain(b)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f769]) ).
fof(f5503,plain,
( codomain(compose(codomain(compose(h,a)),compose(h,a))) = domain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f769]) ).
fof(f5504,plain,
( codomain(compose(codomain(compose(g,a)),compose(h,a))) = domain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f769]) ).
fof(f5505,plain,
( codomain(compose(codomain(g),compose(h,a))) = domain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f769]) ).
fof(f5506,plain,
( codomain(compose(codomain(h),compose(h,a))) = domain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f769]) ).
fof(f5507,plain,
( codomain(compose(codomain(a),compose(h,a))) = domain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f769]) ).
fof(f5512,definition,
( sQ443_spl
<=> codomain(compose(codomain(compose(a,b)),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ443_spl])],[split_symbol_definition]) ).
fof(f5515,plain,
( sQ443_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5501,f1555,f5512]) ).
fof(f5516,definition,
( sQ444_spl
<=> codomain(compose(codomain(compose(h,compose(a,b))),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ444_spl])],[split_symbol_definition]) ).
fof(f5519,plain,
( sQ444_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5502,f1555,f5516]) ).
fof(f5520,definition,
( sQ445_spl
<=> codomain(compose(codomain(compose(h,a)),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ445_spl])],[split_symbol_definition]) ).
fof(f5523,plain,
( sQ445_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5503,f693,f5520]) ).
fof(f5524,definition,
( sQ446_spl
<=> codomain(compose(codomain(compose(g,a)),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ446_spl])],[split_symbol_definition]) ).
fof(f5527,plain,
( sQ446_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5504,f693,f5524]) ).
fof(f5528,definition,
( sQ447_spl
<=> codomain(compose(codomain(g),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ447_spl])],[split_symbol_definition]) ).
fof(f5531,plain,
( sQ447_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5505,f584,f5528]) ).
fof(f5532,definition,
( sQ448_spl
<=> codomain(compose(codomain(h),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f5535,plain,
( sQ448_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5506,f584,f5532]) ).
fof(f5536,definition,
( sQ449_spl
<=> codomain(compose(codomain(a),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f5539,plain,
( sQ449_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5507,f693,f5536]) ).
fof(f5545,plain,
( codomain(compose(codomain(compose(a,b)),compose(a,b))) = codomain(b)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f120,f770]) ).
fof(f5546,plain,
( codomain(compose(codomain(compose(h,compose(a,b))),compose(a,b))) = codomain(b)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f581,f770]) ).
fof(f5547,plain,
( codomain(compose(codomain(compose(h,a)),compose(a,b))) = codomain(b)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f131,f770]) ).
fof(f5548,plain,
( codomain(compose(codomain(compose(g,a)),compose(a,b))) = codomain(b)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f130,f770]) ).
fof(f5549,plain,
( codomain(compose(codomain(g),compose(a,b))) = codomain(b)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f770]) ).
fof(f5550,plain,
( codomain(compose(codomain(h),compose(a,b))) = codomain(b)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f770]) ).
fof(f5551,plain,
( codomain(compose(codomain(a),compose(a,b))) = codomain(b)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f770]) ).
fof(f5560,definition,
( sQ450_spl
<=> codomain(compose(codomain(compose(a,b)),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ450_spl])],[split_symbol_definition]) ).
fof(f5563,plain,
( sQ450_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f5545,f1570,f5560]) ).
fof(f5564,definition,
( sQ451_spl
<=> codomain(compose(codomain(compose(h,compose(a,b))),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f5567,plain,
( sQ451_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f5546,f1570,f5564]) ).
fof(f5568,definition,
( sQ452_spl
<=> codomain(compose(codomain(compose(h,a)),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ452_spl])],[split_symbol_definition]) ).
fof(f5571,plain,
( sQ452_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f5547,f715,f5568]) ).
fof(f5572,definition,
( sQ453_spl
<=> codomain(compose(codomain(compose(g,a)),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f5575,plain,
( sQ453_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f5548,f715,f5572]) ).
fof(f5576,definition,
( sQ454_spl
<=> codomain(compose(codomain(g),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ454_spl])],[split_symbol_definition]) ).
fof(f5579,plain,
( sQ454_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f5549,f606,f5576]) ).
fof(f5580,definition,
( sQ455_spl
<=> codomain(compose(codomain(h),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ455_spl])],[split_symbol_definition]) ).
fof(f5583,plain,
( sQ455_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f5550,f606,f5580]) ).
fof(f5584,definition,
( sQ456_spl
<=> codomain(compose(codomain(a),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ456_spl])],[split_symbol_definition]) ).
fof(f5587,plain,
( sQ456_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f5551,f715,f5584]) ).
fof(f5599,plain,
( codomain(compose(domain(g),compose(h,a))) = domain(b)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f845]) ).
fof(f5600,plain,
( codomain(compose(domain(compose(g,a)),compose(h,a))) = domain(b)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f845]) ).
fof(f5601,plain,
( codomain(compose(domain(compose(h,compose(a,b))),compose(h,a))) = domain(b)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f845]) ).
fof(f5602,plain,
( codomain(compose(domain(compose(h,a)),compose(h,a))) = domain(b)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f845]) ).
fof(f5603,plain,
( codomain(compose(domain(compose(a,b)),compose(h,a))) = domain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f845]) ).
fof(f5616,definition,
( sQ457_spl
<=> codomain(compose(domain(g),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ457_spl])],[split_symbol_definition]) ).
fof(f5619,plain,
( sQ457_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f5599,f2687,f5616]) ).
fof(f5620,definition,
( sQ458_spl
<=> codomain(compose(domain(compose(g,a)),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ458_spl])],[split_symbol_definition]) ).
fof(f5623,plain,
( sQ458_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f5600,f2687,f5620]) ).
fof(f5624,definition,
( sQ459_spl
<=> codomain(compose(domain(compose(h,compose(a,b))),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ459_spl])],[split_symbol_definition]) ).
fof(f5627,plain,
( sQ459_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f5601,f2687,f5624]) ).
fof(f5628,definition,
( sQ460_spl
<=> codomain(compose(domain(compose(h,a)),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ460_spl])],[split_symbol_definition]) ).
fof(f5631,plain,
( sQ460_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f5602,f2687,f5628]) ).
fof(f5632,definition,
( sQ461_spl
<=> codomain(compose(domain(compose(a,b)),compose(h,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ461_spl])],[split_symbol_definition]) ).
fof(f5635,plain,
( sQ461_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5603,f584,f5632]) ).
fof(f5648,plain,
( codomain(compose(domain(compose(g,a)),compose(a,b))) = codomain(b)
| domain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f1108,f846]) ).
fof(f5649,plain,
( codomain(compose(domain(compose(h,compose(a,b))),compose(a,b))) = codomain(b)
| domain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f1068,f846]) ).
fof(f5650,plain,
( codomain(compose(domain(compose(h,a)),compose(a,b))) = codomain(b)
| domain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f76,f846]) ).
fof(f5651,plain,
( codomain(compose(domain(compose(a,b)),compose(a,b))) = codomain(b)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f846]) ).
fof(f5658,definition,
( sQ462_spl
<=> codomain(compose(domain(compose(g,a)),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ462_spl])],[split_symbol_definition]) ).
fof(f5661,plain,
( sQ462_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5648,f584,f5658]) ).
fof(f5662,definition,
( sQ463_spl
<=> codomain(compose(domain(compose(h,compose(a,b))),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ463_spl])],[split_symbol_definition]) ).
fof(f5665,plain,
( sQ463_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5649,f584,f5662]) ).
fof(f5666,definition,
( sQ464_spl
<=> codomain(compose(domain(compose(h,a)),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ464_spl])],[split_symbol_definition]) ).
fof(f5669,plain,
( sQ464_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5650,f584,f5666]) ).
fof(f5670,definition,
( sQ465_spl
<=> codomain(compose(domain(compose(a,b)),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ465_spl])],[split_symbol_definition]) ).
fof(f5673,plain,
( sQ465_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f5651,f606,f5670]) ).
fof(f5683,plain,
( codomain(compose(domain(g),compose(g,a))) = domain(b)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f1120]) ).
fof(f5684,plain,
( codomain(compose(domain(compose(g,a)),compose(g,a))) = domain(b)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1120]) ).
fof(f5685,plain,
( codomain(compose(domain(compose(h,compose(a,b))),compose(g,a))) = domain(b)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1120]) ).
fof(f5686,plain,
( codomain(compose(domain(compose(h,a)),compose(g,a))) = domain(b)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1120]) ).
fof(f5687,plain,
( codomain(compose(domain(compose(a,b)),compose(g,a))) = domain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f1120]) ).
fof(f5700,definition,
( sQ466_spl
<=> codomain(compose(domain(g),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ466_spl])],[split_symbol_definition]) ).
fof(f5703,plain,
( sQ466_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f5683,f2687,f5700]) ).
fof(f5704,definition,
( sQ467_spl
<=> codomain(compose(domain(compose(g,a)),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ467_spl])],[split_symbol_definition]) ).
fof(f5707,plain,
( sQ467_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f5684,f2687,f5704]) ).
fof(f5708,definition,
( sQ468_spl
<=> codomain(compose(domain(compose(h,compose(a,b))),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ468_spl])],[split_symbol_definition]) ).
fof(f5711,plain,
( sQ468_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f5685,f2687,f5708]) ).
fof(f5712,definition,
( sQ469_spl
<=> codomain(compose(domain(compose(h,a)),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ469_spl])],[split_symbol_definition]) ).
fof(f5715,plain,
( sQ469_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f5686,f2687,f5712]) ).
fof(f5716,definition,
( sQ470_spl
<=> codomain(compose(domain(compose(a,b)),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ470_spl])],[split_symbol_definition]) ).
fof(f5719,plain,
( sQ470_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5687,f584,f5716]) ).
fof(f5734,plain,
( domain(compose(compose(g,a),codomain(compose(a,b)))) = domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f1125]) ).
fof(f5735,plain,
( domain(compose(compose(g,a),codomain(compose(h,compose(a,b))))) = domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f1125]) ).
fof(f5736,plain,
( domain(compose(compose(g,a),codomain(compose(h,a)))) = domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f1125]) ).
fof(f5737,plain,
( domain(compose(compose(g,a),codomain(compose(g,a)))) = domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f1125]) ).
fof(f5738,plain,
( domain(compose(compose(g,a),codomain(g))) = domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f1125]) ).
fof(f5739,plain,
( domain(compose(compose(g,a),codomain(h))) = domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f1125]) ).
fof(f5740,plain,
( domain(compose(compose(g,a),codomain(a))) = domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f1125]) ).
fof(f5750,definition,
( sQ471_spl
<=> domain(compose(compose(g,a),codomain(compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ471_spl])],[split_symbol_definition]) ).
fof(f5753,plain,
( sQ471_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f5734,f2265,f5750]) ).
fof(f5754,definition,
( sQ472_spl
<=> domain(compose(compose(g,a),codomain(compose(h,compose(a,b))))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ472_spl])],[split_symbol_definition]) ).
fof(f5757,plain,
( sQ472_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f5735,f2265,f5754]) ).
fof(f5758,definition,
( sQ473_spl
<=> domain(compose(compose(g,a),codomain(compose(h,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ473_spl])],[split_symbol_definition]) ).
fof(f5761,plain,
( sQ473_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f5736,f1941,f5758]) ).
fof(f5762,definition,
( sQ474_spl
<=> domain(compose(compose(g,a),codomain(compose(g,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ474_spl])],[split_symbol_definition]) ).
fof(f5765,plain,
( sQ474_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f5737,f1941,f5762]) ).
fof(f5766,definition,
( sQ475_spl
<=> domain(compose(compose(g,a),codomain(g))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ475_spl])],[split_symbol_definition]) ).
fof(f5769,plain,
( sQ475_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f5738,f715,f5766]) ).
fof(f5770,definition,
( sQ476_spl
<=> domain(compose(compose(g,a),codomain(h))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ476_spl])],[split_symbol_definition]) ).
fof(f5773,plain,
( sQ476_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f5739,f715,f5770]) ).
fof(f5774,definition,
( sQ477_spl
<=> domain(compose(compose(g,a),codomain(a))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ477_spl])],[split_symbol_definition]) ).
fof(f5777,plain,
( sQ477_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f5740,f1941,f5774]) ).
fof(f5786,plain,
( codomain(compose(codomain(compose(a,b)),compose(g,a))) = domain(b)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1122]) ).
fof(f5787,plain,
( codomain(compose(codomain(compose(h,compose(a,b))),compose(g,a))) = domain(b)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1122]) ).
fof(f5788,plain,
( codomain(compose(codomain(compose(h,a)),compose(g,a))) = domain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1122]) ).
fof(f5789,plain,
( codomain(compose(codomain(compose(g,a)),compose(g,a))) = domain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1122]) ).
fof(f5790,plain,
( codomain(compose(codomain(g),compose(g,a))) = domain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1122]) ).
fof(f5791,plain,
( codomain(compose(codomain(h),compose(g,a))) = domain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1122]) ).
fof(f5792,plain,
( codomain(compose(codomain(a),compose(g,a))) = domain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f1122]) ).
fof(f5797,definition,
( sQ478_spl
<=> codomain(compose(codomain(compose(a,b)),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ478_spl])],[split_symbol_definition]) ).
fof(f5800,plain,
( sQ478_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5786,f1555,f5797]) ).
fof(f5801,definition,
( sQ479_spl
<=> codomain(compose(codomain(compose(h,compose(a,b))),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ479_spl])],[split_symbol_definition]) ).
fof(f5804,plain,
( sQ479_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5787,f1555,f5801]) ).
fof(f5805,definition,
( sQ480_spl
<=> codomain(compose(codomain(compose(h,a)),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ480_spl])],[split_symbol_definition]) ).
fof(f5808,plain,
( sQ480_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5788,f693,f5805]) ).
fof(f5809,definition,
( sQ481_spl
<=> codomain(compose(codomain(compose(g,a)),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ481_spl])],[split_symbol_definition]) ).
fof(f5812,plain,
( sQ481_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5789,f693,f5809]) ).
fof(f5813,definition,
( sQ482_spl
<=> codomain(compose(codomain(g),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ482_spl])],[split_symbol_definition]) ).
fof(f5816,plain,
( sQ482_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5790,f584,f5813]) ).
fof(f5817,definition,
( sQ483_spl
<=> codomain(compose(codomain(h),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ483_spl])],[split_symbol_definition]) ).
fof(f5820,plain,
( sQ483_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5791,f584,f5817]) ).
fof(f5821,definition,
( sQ484_spl
<=> codomain(compose(codomain(a),compose(g,a))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ484_spl])],[split_symbol_definition]) ).
fof(f5824,plain,
( sQ484_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5792,f693,f5821]) ).
fof(f5828,plain,
( domain(compose(compose(g,a),domain(compose(g,a)))) = domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1128]) ).
fof(f5829,plain,
( domain(compose(compose(g,a),domain(compose(h,compose(a,b))))) = domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1128]) ).
fof(f5830,plain,
( domain(compose(compose(g,a),domain(compose(h,a)))) = domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1128]) ).
fof(f5831,plain,
( domain(compose(compose(g,a),domain(compose(a,b)))) = domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1128]) ).
fof(f5837,definition,
( sQ485_spl
<=> domain(compose(compose(g,a),domain(compose(g,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ485_spl])],[split_symbol_definition]) ).
fof(f5840,plain,
( sQ485_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5828,f693,f5837]) ).
fof(f5841,definition,
( sQ486_spl
<=> domain(compose(compose(g,a),domain(compose(h,compose(a,b))))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ486_spl])],[split_symbol_definition]) ).
fof(f5844,plain,
( sQ486_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5829,f693,f5841]) ).
fof(f5845,definition,
( sQ487_spl
<=> domain(compose(compose(g,a),domain(compose(h,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ487_spl])],[split_symbol_definition]) ).
fof(f5848,plain,
( sQ487_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5830,f693,f5845]) ).
fof(f5849,definition,
( sQ488_spl
<=> domain(compose(compose(g,a),domain(compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ488_spl])],[split_symbol_definition]) ).
fof(f5852,plain,
( sQ488_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f5831,f715,f5849]) ).
fof(f5857,plain,
( codomain(compose(compose(h,compose(a,b)),compose(g,a))) = codomain(compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f627]) ).
fof(f5858,plain,
( codomain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f627]) ).
fof(f5859,plain,
( codomain(compose(compose(h,compose(a,b)),compose(h,a))) = codomain(compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f627]) ).
fof(f5860,plain,
( codomain(compose(compose(h,compose(a,b)),compose(a,b))) = codomain(compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f627]) ).
fof(f5865,definition,
( sQ489_spl
<=> codomain(compose(compose(h,compose(a,b)),compose(g,a))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ489_spl])],[split_symbol_definition]) ).
fof(f5868,plain,
( sQ489_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5857,f1555,f5865]) ).
fof(f5869,definition,
( sQ490_spl
<=> codomain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ490_spl])],[split_symbol_definition]) ).
fof(f5872,plain,
( sQ490_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5858,f1555,f5869]) ).
fof(f5873,definition,
( sQ491_spl
<=> codomain(compose(compose(h,compose(a,b)),compose(h,a))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ491_spl])],[split_symbol_definition]) ).
fof(f5876,plain,
( sQ491_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5859,f1555,f5873]) ).
fof(f5877,definition,
( sQ492_spl
<=> codomain(compose(compose(h,compose(a,b)),compose(a,b))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ492_spl])],[split_symbol_definition]) ).
fof(f5880,plain,
( sQ492_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f5860,f1570,f5877]) ).
fof(f5884,plain,
( domain(compose(compose(a,b),compose(h,compose(a,b)))) = domain(compose(a,b))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1110]) ).
fof(f5885,plain,
( domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = domain(compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1110]) ).
fof(f5886,plain,
( domain(compose(compose(h,a),compose(h,compose(a,b)))) = domain(compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1110]) ).
fof(f5887,plain,
( domain(compose(compose(g,a),compose(h,compose(a,b)))) = domain(compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1110]) ).
fof(f5888,plain,
( domain(compose(g,compose(h,compose(a,b)))) = domain(g)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1110]) ).
fof(f5895,definition,
( sQ493_spl
<=> domain(compose(compose(a,b),compose(h,compose(a,b)))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ493_spl])],[split_symbol_definition]) ).
fof(f5898,plain,
( sQ493_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5884,f1555,f5895]) ).
fof(f5899,definition,
( sQ494_spl
<=> domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ494_spl])],[split_symbol_definition]) ).
fof(f5902,plain,
( sQ494_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5885,f1555,f5899]) ).
fof(f5903,definition,
( sQ495_spl
<=> domain(compose(compose(h,a),compose(h,compose(a,b)))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ495_spl])],[split_symbol_definition]) ).
fof(f5906,plain,
( sQ495_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5886,f693,f5903]) ).
fof(f5907,definition,
( sQ496_spl
<=> domain(compose(compose(g,a),compose(h,compose(a,b)))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ496_spl])],[split_symbol_definition]) ).
fof(f5910,plain,
( sQ496_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5887,f693,f5907]) ).
fof(f5911,plain,
( sQ39_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5888,f584,f1030]) ).
fof(f5917,plain,
! [X0] :
( compose(compose(a,b),compose(compose(g,a),X0)) = compose(compose(compose(a,b),compose(g,a)),X0)
| domain(b) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1139]) ).
fof(f5918,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(compose(g,a),X0)) = compose(compose(compose(h,compose(a,b)),compose(g,a)),X0)
| domain(b) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1139]) ).
fof(f5919,plain,
! [X0] :
( compose(compose(h,a),compose(compose(g,a),X0)) = compose(compose(compose(h,a),compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1139]) ).
fof(f5920,plain,
! [X0] :
( compose(compose(g,a),compose(compose(g,a),X0)) = compose(compose(compose(g,a),compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1139]) ).
fof(f5921,plain,
! [X0] :
( compose(g,compose(compose(g,a),X0)) = compose(compose(g,compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1139]) ).
fof(f5922,plain,
! [X0] :
( compose(h,compose(compose(g,a),X0)) = compose(compose(h,compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1139]) ).
fof(f5923,plain,
! [X0] :
( compose(a,compose(compose(g,a),X0)) = compose(compose(a,compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f1139]) ).
fof(f5927,definition,
! [X0] :
( sQ497_spl
<=> ( compose(compose(a,b),compose(compose(g,a),X0)) = compose(compose(compose(a,b),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ497_spl])],[split_symbol_definition]) ).
fof(f5930,plain,
( sQ497_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5917,f1555,f5927]) ).
fof(f5931,definition,
! [X0] :
( sQ498_spl
<=> ( compose(compose(h,compose(a,b)),compose(compose(g,a),X0)) = compose(compose(compose(h,compose(a,b)),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ498_spl])],[split_symbol_definition]) ).
fof(f5934,plain,
( sQ498_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5918,f1555,f5931]) ).
fof(f5935,plain,
( sQ404_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5919,f693,f4984]) ).
fof(f5936,plain,
( sQ275_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5920,f693,f3679]) ).
fof(f5937,plain,
( sQ84_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5921,f584,f1783]) ).
fof(f5938,plain,
( sQ109_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5922,f584,f2101]) ).
fof(f5939,plain,
( sQ148_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5923,f693,f2377]) ).
fof(f5941,plain,
( codomain(compose(compose(a,b),compose(h,compose(a,b)))) = codomain(b)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1111]) ).
fof(f5942,plain,
( codomain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = codomain(b)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1111]) ).
fof(f5943,plain,
( codomain(compose(compose(h,a),compose(h,compose(a,b)))) = codomain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1111]) ).
fof(f5944,plain,
( codomain(compose(compose(g,a),compose(h,compose(a,b)))) = codomain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1111]) ).
fof(f5945,plain,
( codomain(compose(g,compose(h,compose(a,b)))) = codomain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1111]) ).
fof(f5946,plain,
( codomain(compose(h,compose(h,compose(a,b)))) = codomain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1111]) ).
fof(f5947,plain,
( codomain(compose(a,compose(h,compose(a,b)))) = codomain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f1111]) ).
fof(f5951,definition,
( sQ499_spl
<=> codomain(compose(compose(a,b),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ499_spl])],[split_symbol_definition]) ).
fof(f5954,plain,
( sQ499_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5941,f1555,f5951]) ).
fof(f5955,definition,
( sQ500_spl
<=> codomain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ500_spl])],[split_symbol_definition]) ).
fof(f5958,plain,
( sQ500_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5942,f1555,f5955]) ).
fof(f5959,definition,
( sQ501_spl
<=> codomain(compose(compose(h,a),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ501_spl])],[split_symbol_definition]) ).
fof(f5962,plain,
( sQ501_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5943,f693,f5959]) ).
fof(f5963,definition,
( sQ502_spl
<=> codomain(compose(compose(g,a),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ502_spl])],[split_symbol_definition]) ).
fof(f5966,plain,
( sQ502_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5944,f693,f5963]) ).
fof(f5967,definition,
( sQ503_spl
<=> codomain(compose(g,compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ503_spl])],[split_symbol_definition]) ).
fof(f5970,plain,
( sQ503_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5945,f584,f5967]) ).
fof(f5971,definition,
( sQ504_spl
<=> codomain(compose(h,compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ504_spl])],[split_symbol_definition]) ).
fof(f5974,plain,
( sQ504_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5946,f584,f5971]) ).
fof(f5975,definition,
( sQ505_spl
<=> codomain(compose(a,compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ505_spl])],[split_symbol_definition]) ).
fof(f5978,plain,
( sQ505_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5947,f693,f5975]) ).
fof(f5980,plain,
( domain(compose(compose(h,compose(a,b)),compose(g,a))) = domain(h)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1119]) ).
fof(f5981,plain,
( domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = domain(h)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1119]) ).
fof(f5982,plain,
( domain(compose(compose(h,compose(a,b)),compose(h,a))) = domain(h)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1119]) ).
fof(f5983,plain,
( domain(compose(compose(h,compose(a,b)),compose(a,b))) = domain(h)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1119]) ).
fof(f5987,definition,
( sQ506_spl
<=> domain(compose(compose(h,compose(a,b)),compose(g,a))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ506_spl])],[split_symbol_definition]) ).
fof(f5990,plain,
( sQ506_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5980,f1555,f5987]) ).
fof(f5991,definition,
( sQ507_spl
<=> domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ507_spl])],[split_symbol_definition]) ).
fof(f5994,plain,
( sQ507_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5981,f1555,f5991]) ).
fof(f5995,definition,
( sQ508_spl
<=> domain(compose(compose(h,compose(a,b)),compose(h,a))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ508_spl])],[split_symbol_definition]) ).
fof(f5998,plain,
( sQ508_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f5982,f1555,f5995]) ).
fof(f5999,definition,
( sQ509_spl
<=> domain(compose(compose(h,compose(a,b)),compose(a,b))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ509_spl])],[split_symbol_definition]) ).
fof(f6002,plain,
( sQ509_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f5983,f1570,f5999]) ).
fof(f6005,plain,
( compose(g,domain(compose(g,a))) = compose(compose(g,domain(compose(g,a))),domain(compose(g,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f3793]) ).
fof(f6006,plain,
( compose(g,domain(compose(h,compose(a,b)))) = compose(compose(g,domain(compose(h,compose(a,b)))),domain(compose(h,compose(a,b))))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f3793]) ).
fof(f6007,plain,
( compose(g,domain(compose(h,a))) = compose(compose(g,domain(compose(h,a))),domain(compose(h,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f3793]) ).
fof(f6008,plain,
( compose(g,domain(compose(a,b))) = compose(compose(g,domain(compose(a,b))),domain(compose(a,b)))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f3793]) ).
fof(f6022,definition,
( sQ510_spl
<=> compose(g,domain(compose(g,a))) = compose(compose(g,domain(compose(g,a))),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition]) ).
fof(f6025,plain,
( sQ510_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6005,f584,f6022]) ).
fof(f6026,definition,
( sQ511_spl
<=> compose(g,domain(compose(h,compose(a,b)))) = compose(compose(g,domain(compose(h,compose(a,b)))),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ511_spl])],[split_symbol_definition]) ).
fof(f6029,plain,
( sQ511_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6006,f584,f6026]) ).
fof(f6030,definition,
( sQ512_spl
<=> compose(g,domain(compose(h,a))) = compose(compose(g,domain(compose(h,a))),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ512_spl])],[split_symbol_definition]) ).
fof(f6033,plain,
( sQ512_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6007,f584,f6030]) ).
fof(f6034,definition,
( sQ513_spl
<=> compose(g,domain(compose(a,b))) = compose(compose(g,domain(compose(a,b))),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ513_spl])],[split_symbol_definition]) ).
fof(f6037,plain,
( sQ513_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f6008,f606,f6034]) ).
fof(f6054,plain,
( compose(g,codomain(compose(a,b))) = compose(compose(g,codomain(compose(a,b))),codomain(compose(a,b)))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f3794]) ).
fof(f6055,plain,
( compose(g,codomain(compose(h,compose(a,b)))) = compose(compose(g,codomain(compose(h,compose(a,b)))),codomain(compose(h,compose(a,b))))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f3794]) ).
fof(f6056,plain,
( compose(g,codomain(compose(h,a))) = compose(compose(g,codomain(compose(h,a))),codomain(compose(h,a)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f3794]) ).
fof(f6057,plain,
( compose(g,codomain(compose(g,a))) = compose(compose(g,codomain(compose(g,a))),codomain(compose(g,a)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f3794]) ).
fof(f6058,plain,
( compose(g,codomain(g)) = compose(compose(g,codomain(g)),codomain(g))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f3794]) ).
fof(f6059,plain,
( compose(g,codomain(h)) = compose(compose(g,codomain(h)),codomain(h))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f3794]) ).
fof(f6060,plain,
( compose(g,codomain(a)) = compose(compose(g,codomain(a)),codomain(a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f3794]) ).
fof(f6075,definition,
( sQ514_spl
<=> compose(g,codomain(compose(a,b))) = compose(compose(g,codomain(compose(a,b))),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ514_spl])],[split_symbol_definition]) ).
fof(f6078,plain,
( sQ514_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f6054,f1570,f6075]) ).
fof(f6079,definition,
( sQ515_spl
<=> compose(g,codomain(compose(h,compose(a,b)))) = compose(compose(g,codomain(compose(h,compose(a,b)))),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ515_spl])],[split_symbol_definition]) ).
fof(f6082,plain,
( sQ515_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f6055,f1570,f6079]) ).
fof(f6083,definition,
( sQ516_spl
<=> compose(g,codomain(compose(h,a))) = compose(compose(g,codomain(compose(h,a))),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ516_spl])],[split_symbol_definition]) ).
fof(f6086,plain,
( sQ516_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6056,f715,f6083]) ).
fof(f6087,definition,
( sQ517_spl
<=> compose(g,codomain(compose(g,a))) = compose(compose(g,codomain(compose(g,a))),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ517_spl])],[split_symbol_definition]) ).
fof(f6090,plain,
( sQ517_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6057,f715,f6087]) ).
fof(f6091,definition,
( sQ518_spl
<=> compose(g,codomain(g)) = compose(compose(g,codomain(g)),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ518_spl])],[split_symbol_definition]) ).
fof(f6094,plain,
( sQ518_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f6058,f606,f6091]) ).
fof(f6095,definition,
( sQ519_spl
<=> compose(g,codomain(h)) = compose(compose(g,codomain(h)),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ519_spl])],[split_symbol_definition]) ).
fof(f6098,plain,
( sQ519_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f6059,f606,f6095]) ).
fof(f6099,definition,
( sQ520_spl
<=> compose(g,codomain(a)) = compose(compose(g,codomain(a)),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ520_spl])],[split_symbol_definition]) ).
fof(f6102,plain,
( sQ520_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6060,f715,f6099]) ).
fof(f6117,plain,
( compose(g,compose(a,domain(compose(g,a)))) = compose(compose(g,a),domain(compose(g,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1330]) ).
fof(f6118,plain,
( compose(g,compose(a,domain(compose(h,compose(a,b))))) = compose(compose(g,a),domain(compose(h,compose(a,b))))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1330]) ).
fof(f6119,plain,
( compose(g,compose(a,domain(compose(h,a)))) = compose(compose(g,a),domain(compose(h,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1330]) ).
fof(f6120,plain,
( compose(g,compose(a,domain(compose(a,b)))) = compose(compose(g,a),domain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1330]) ).
fof(f6127,definition,
( sQ521_spl
<=> compose(g,compose(a,domain(compose(g,a)))) = compose(compose(g,a),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ521_spl])],[split_symbol_definition]) ).
fof(f6130,plain,
( sQ521_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6117,f693,f6127]) ).
fof(f6131,definition,
( sQ522_spl
<=> compose(g,compose(a,domain(compose(h,compose(a,b))))) = compose(compose(g,a),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ522_spl])],[split_symbol_definition]) ).
fof(f6134,plain,
( sQ522_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6118,f693,f6131]) ).
fof(f6135,definition,
( sQ523_spl
<=> compose(g,compose(a,domain(compose(h,a)))) = compose(compose(g,a),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ523_spl])],[split_symbol_definition]) ).
fof(f6138,plain,
( sQ523_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6119,f693,f6135]) ).
fof(f6139,definition,
( sQ524_spl
<=> compose(g,compose(a,domain(compose(a,b)))) = compose(compose(g,a),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ524_spl])],[split_symbol_definition]) ).
fof(f6142,plain,
( sQ524_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6120,f715,f6139]) ).
fof(f6150,plain,
( compose(h,domain(compose(g,a))) = compose(compose(h,domain(compose(g,a))),domain(compose(g,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f3864]) ).
fof(f6151,plain,
( compose(h,domain(compose(h,compose(a,b)))) = compose(compose(h,domain(compose(h,compose(a,b)))),domain(compose(h,compose(a,b))))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f3864]) ).
fof(f6152,plain,
( compose(h,domain(compose(h,a))) = compose(compose(h,domain(compose(h,a))),domain(compose(h,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f3864]) ).
fof(f6153,plain,
( compose(h,domain(compose(a,b))) = compose(compose(h,domain(compose(a,b))),domain(compose(a,b)))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f3864]) ).
fof(f6167,definition,
( sQ525_spl
<=> compose(h,domain(compose(g,a))) = compose(compose(h,domain(compose(g,a))),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ525_spl])],[split_symbol_definition]) ).
fof(f6170,plain,
( sQ525_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6150,f584,f6167]) ).
fof(f6171,definition,
( sQ526_spl
<=> compose(h,domain(compose(h,compose(a,b)))) = compose(compose(h,domain(compose(h,compose(a,b)))),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ526_spl])],[split_symbol_definition]) ).
fof(f6174,plain,
( sQ526_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6151,f584,f6171]) ).
fof(f6175,definition,
( sQ527_spl
<=> compose(h,domain(compose(h,a))) = compose(compose(h,domain(compose(h,a))),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ527_spl])],[split_symbol_definition]) ).
fof(f6178,plain,
( sQ527_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6152,f584,f6175]) ).
fof(f6179,definition,
( sQ528_spl
<=> compose(h,domain(compose(a,b))) = compose(compose(h,domain(compose(a,b))),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ528_spl])],[split_symbol_definition]) ).
fof(f6182,plain,
( sQ528_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f6153,f606,f6179]) ).
fof(f6199,plain,
( compose(h,codomain(compose(a,b))) = compose(compose(h,codomain(compose(a,b))),codomain(compose(a,b)))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f3865]) ).
fof(f6200,plain,
( compose(h,codomain(compose(h,compose(a,b)))) = compose(compose(h,codomain(compose(h,compose(a,b)))),codomain(compose(h,compose(a,b))))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f3865]) ).
fof(f6201,plain,
( compose(h,codomain(compose(h,a))) = compose(compose(h,codomain(compose(h,a))),codomain(compose(h,a)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f3865]) ).
fof(f6202,plain,
( compose(h,codomain(compose(g,a))) = compose(compose(h,codomain(compose(g,a))),codomain(compose(g,a)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f3865]) ).
fof(f6203,plain,
( compose(h,codomain(g)) = compose(compose(h,codomain(g)),codomain(g))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f3865]) ).
fof(f6204,plain,
( compose(h,codomain(h)) = compose(compose(h,codomain(h)),codomain(h))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f3865]) ).
fof(f6205,plain,
( compose(h,codomain(a)) = compose(compose(h,codomain(a)),codomain(a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f3865]) ).
fof(f6220,definition,
( sQ529_spl
<=> compose(h,codomain(compose(a,b))) = compose(compose(h,codomain(compose(a,b))),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ529_spl])],[split_symbol_definition]) ).
fof(f6223,plain,
( sQ529_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f6199,f1570,f6220]) ).
fof(f6224,definition,
( sQ530_spl
<=> compose(h,codomain(compose(h,compose(a,b)))) = compose(compose(h,codomain(compose(h,compose(a,b)))),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ530_spl])],[split_symbol_definition]) ).
fof(f6227,plain,
( sQ530_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f6200,f1570,f6224]) ).
fof(f6228,definition,
( sQ531_spl
<=> compose(h,codomain(compose(h,a))) = compose(compose(h,codomain(compose(h,a))),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ531_spl])],[split_symbol_definition]) ).
fof(f6231,plain,
( sQ531_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6201,f715,f6228]) ).
fof(f6232,definition,
( sQ532_spl
<=> compose(h,codomain(compose(g,a))) = compose(compose(h,codomain(compose(g,a))),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ532_spl])],[split_symbol_definition]) ).
fof(f6235,plain,
( sQ532_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6202,f715,f6232]) ).
fof(f6236,definition,
( sQ533_spl
<=> compose(h,codomain(g)) = compose(compose(h,codomain(g)),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ533_spl])],[split_symbol_definition]) ).
fof(f6239,plain,
( sQ533_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f6203,f606,f6236]) ).
fof(f6240,definition,
( sQ534_spl
<=> compose(h,codomain(h)) = compose(compose(h,codomain(h)),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ534_spl])],[split_symbol_definition]) ).
fof(f6243,plain,
( sQ534_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f6204,f606,f6240]) ).
fof(f6244,definition,
( sQ535_spl
<=> compose(h,codomain(a)) = compose(compose(h,codomain(a)),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ535_spl])],[split_symbol_definition]) ).
fof(f6247,plain,
( sQ535_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6205,f715,f6244]) ).
fof(f6262,plain,
( compose(a,domain(compose(g,a))) = compose(compose(a,domain(compose(g,a))),domain(compose(g,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f3995]) ).
fof(f6263,plain,
( compose(a,domain(compose(h,compose(a,b)))) = compose(compose(a,domain(compose(h,compose(a,b)))),domain(compose(h,compose(a,b))))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f3995]) ).
fof(f6264,plain,
( compose(a,domain(compose(h,a))) = compose(compose(a,domain(compose(h,a))),domain(compose(h,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f3995]) ).
fof(f6265,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)],[f60,f3995]) ).
fof(f6274,definition,
( sQ536_spl
<=> compose(a,domain(compose(g,a))) = compose(compose(a,domain(compose(g,a))),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ536_spl])],[split_symbol_definition]) ).
fof(f6277,plain,
( sQ536_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6262,f693,f6274]) ).
fof(f6278,definition,
( sQ537_spl
<=> compose(a,domain(compose(h,compose(a,b)))) = compose(compose(a,domain(compose(h,compose(a,b)))),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ537_spl])],[split_symbol_definition]) ).
fof(f6281,plain,
( sQ537_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6263,f693,f6278]) ).
fof(f6282,definition,
( sQ538_spl
<=> compose(a,domain(compose(h,a))) = compose(compose(a,domain(compose(h,a))),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ538_spl])],[split_symbol_definition]) ).
fof(f6285,plain,
( sQ538_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6264,f693,f6282]) ).
fof(f6286,definition,
( sQ539_spl
<=> compose(a,domain(compose(a,b))) = compose(compose(a,domain(compose(a,b))),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ539_spl])],[split_symbol_definition]) ).
fof(f6289,plain,
( sQ539_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6265,f715,f6286]) ).
fof(f6302,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)],[f120,f3996]) ).
fof(f6303,plain,
( compose(a,codomain(compose(h,compose(a,b)))) = compose(compose(a,codomain(compose(h,compose(a,b)))),codomain(compose(h,compose(a,b))))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f3996]) ).
fof(f6304,plain,
( compose(a,codomain(compose(h,a))) = compose(compose(a,codomain(compose(h,a))),codomain(compose(h,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f3996]) ).
fof(f6305,plain,
( compose(a,codomain(compose(g,a))) = compose(compose(a,codomain(compose(g,a))),codomain(compose(g,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f3996]) ).
fof(f6306,plain,
( compose(a,codomain(g)) = compose(compose(a,codomain(g)),codomain(g))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f3996]) ).
fof(f6307,plain,
( compose(a,codomain(h)) = compose(compose(a,codomain(h)),codomain(h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f3996]) ).
fof(f6308,plain,
( compose(a,codomain(a)) = compose(compose(a,codomain(a)),codomain(a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f3996]) ).
fof(f6328,definition,
( sQ540_spl
<=> compose(a,codomain(compose(a,b))) = compose(compose(a,codomain(compose(a,b))),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ540_spl])],[split_symbol_definition]) ).
fof(f6331,plain,
( sQ540_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f6302,f2265,f6328]) ).
fof(f6332,definition,
( sQ541_spl
<=> compose(a,codomain(compose(h,compose(a,b)))) = compose(compose(a,codomain(compose(h,compose(a,b)))),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ541_spl])],[split_symbol_definition]) ).
fof(f6335,plain,
( sQ541_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f6303,f2265,f6332]) ).
fof(f6336,definition,
( sQ542_spl
<=> compose(a,codomain(compose(h,a))) = compose(compose(a,codomain(compose(h,a))),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ542_spl])],[split_symbol_definition]) ).
fof(f6339,plain,
( sQ542_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f6304,f1941,f6336]) ).
fof(f6340,definition,
( sQ543_spl
<=> compose(a,codomain(compose(g,a))) = compose(compose(a,codomain(compose(g,a))),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ543_spl])],[split_symbol_definition]) ).
fof(f6343,plain,
( sQ543_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f6305,f1941,f6340]) ).
fof(f6344,definition,
( sQ544_spl
<=> compose(a,codomain(g)) = compose(compose(a,codomain(g)),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ544_spl])],[split_symbol_definition]) ).
fof(f6347,plain,
( sQ544_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6306,f715,f6344]) ).
fof(f6348,definition,
( sQ545_spl
<=> compose(a,codomain(h)) = compose(compose(a,codomain(h)),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ545_spl])],[split_symbol_definition]) ).
fof(f6351,plain,
( sQ545_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6307,f715,f6348]) ).
fof(f6352,definition,
( sQ546_spl
<=> compose(a,codomain(a)) = compose(compose(a,codomain(a)),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ546_spl])],[split_symbol_definition]) ).
fof(f6355,plain,
( sQ546_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f6308,f1941,f6352]) ).
fof(f6379,plain,
( compose(domain(g),compose(domain(g),g)) = compose(domain(g),g)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f4874]) ).
fof(f6380,plain,
( compose(domain(compose(g,a)),compose(domain(compose(g,a)),g)) = compose(domain(compose(g,a)),g)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f4874]) ).
fof(f6381,plain,
( compose(domain(compose(h,compose(a,b))),compose(domain(compose(h,compose(a,b))),g)) = compose(domain(compose(h,compose(a,b))),g)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f4874]) ).
fof(f6382,plain,
( compose(domain(compose(h,a)),compose(domain(compose(h,a)),g)) = compose(domain(compose(h,a)),g)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f4874]) ).
fof(f6383,plain,
( compose(domain(compose(a,b)),compose(domain(compose(a,b)),g)) = compose(domain(compose(a,b)),g)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f4874]) ).
fof(f6385,plain,
! [X0] :
( compose(domain(codomain(X0)),compose(domain(codomain(X0)),g)) = compose(domain(codomain(X0)),g)
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f16,f4874]) ).
fof(f6410,definition,
( sQ547_spl
<=> compose(domain(g),compose(domain(g),g)) = compose(domain(g),g) ),
introduced(definition,[new_symbols(definition,[sQ547_spl])],[split_symbol_definition]) ).
fof(f6413,plain,
( sQ547_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f6379,f2687,f6410]) ).
fof(f6414,definition,
( sQ548_spl
<=> compose(domain(compose(g,a)),compose(domain(compose(g,a)),g)) = compose(domain(compose(g,a)),g) ),
introduced(definition,[new_symbols(definition,[sQ548_spl])],[split_symbol_definition]) ).
fof(f6417,plain,
( sQ548_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f6380,f2687,f6414]) ).
fof(f6418,definition,
( sQ549_spl
<=> compose(domain(compose(h,compose(a,b))),compose(domain(compose(h,compose(a,b))),g)) = compose(domain(compose(h,compose(a,b))),g) ),
introduced(definition,[new_symbols(definition,[sQ549_spl])],[split_symbol_definition]) ).
fof(f6421,plain,
( sQ549_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f6381,f2687,f6418]) ).
fof(f6422,definition,
( sQ550_spl
<=> compose(domain(compose(h,a)),compose(domain(compose(h,a)),g)) = compose(domain(compose(h,a)),g) ),
introduced(definition,[new_symbols(definition,[sQ550_spl])],[split_symbol_definition]) ).
fof(f6425,plain,
( sQ550_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f6382,f2687,f6422]) ).
fof(f6426,definition,
( sQ551_spl
<=> compose(domain(compose(a,b)),compose(domain(compose(a,b)),g)) = compose(domain(compose(a,b)),g) ),
introduced(definition,[new_symbols(definition,[sQ551_spl])],[split_symbol_definition]) ).
fof(f6429,plain,
( sQ551_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6383,f584,f6426]) ).
fof(f6433,plain,
! [X0] :
( compose(codomain(X0),compose(domain(codomain(X0)),g)) = compose(domain(codomain(X0)),g)
| codomain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f16,f6385]) ).
fof(f6434,plain,
! [X0] :
( compose(codomain(X0),compose(codomain(X0),g)) = compose(domain(codomain(X0)),g)
| codomain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f16,f6433]) ).
fof(f6435,plain,
! [X0] :
( compose(codomain(X0),compose(codomain(X0),g)) = compose(codomain(X0),g)
| codomain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f16,f6434]) ).
fof(f6458,plain,
( compose(g,compose(a,codomain(compose(a,b)))) = compose(compose(g,a),codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f1331]) ).
fof(f6459,plain,
( compose(g,compose(a,codomain(compose(h,compose(a,b))))) = compose(compose(g,a),codomain(compose(h,compose(a,b))))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f1331]) ).
fof(f6460,plain,
( compose(g,compose(a,codomain(compose(h,a)))) = compose(compose(g,a),codomain(compose(h,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f1331]) ).
fof(f6461,plain,
( compose(g,compose(a,codomain(compose(g,a)))) = compose(compose(g,a),codomain(compose(g,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f1331]) ).
fof(f6462,plain,
( compose(g,compose(a,codomain(g))) = compose(compose(g,a),codomain(g))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f1331]) ).
fof(f6463,plain,
( compose(g,compose(a,codomain(h))) = compose(compose(g,a),codomain(h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f1331]) ).
fof(f6464,plain,
( compose(g,compose(a,codomain(a))) = compose(compose(g,a),codomain(a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f1331]) ).
fof(f6477,definition,
( sQ552_spl
<=> compose(g,compose(a,codomain(compose(a,b)))) = compose(compose(g,a),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ552_spl])],[split_symbol_definition]) ).
fof(f6480,plain,
( sQ552_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f6458,f2265,f6477]) ).
fof(f6481,definition,
( sQ553_spl
<=> compose(g,compose(a,codomain(compose(h,compose(a,b))))) = compose(compose(g,a),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ553_spl])],[split_symbol_definition]) ).
fof(f6484,plain,
( sQ553_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f6459,f2265,f6481]) ).
fof(f6485,definition,
( sQ554_spl
<=> compose(g,compose(a,codomain(compose(h,a)))) = compose(compose(g,a),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ554_spl])],[split_symbol_definition]) ).
fof(f6488,plain,
( sQ554_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f6460,f1941,f6485]) ).
fof(f6489,definition,
( sQ555_spl
<=> compose(g,compose(a,codomain(compose(g,a)))) = compose(compose(g,a),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ555_spl])],[split_symbol_definition]) ).
fof(f6492,plain,
( sQ555_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f6461,f1941,f6489]) ).
fof(f6493,definition,
( sQ556_spl
<=> compose(g,compose(a,codomain(g))) = compose(compose(g,a),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ556_spl])],[split_symbol_definition]) ).
fof(f6496,plain,
( sQ556_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6462,f715,f6493]) ).
fof(f6497,definition,
( sQ557_spl
<=> compose(g,compose(a,codomain(h))) = compose(compose(g,a),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ557_spl])],[split_symbol_definition]) ).
fof(f6500,plain,
( sQ557_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6463,f715,f6497]) ).
fof(f6501,definition,
( sQ558_spl
<=> compose(g,compose(a,codomain(a))) = compose(compose(g,a),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ558_spl])],[split_symbol_definition]) ).
fof(f6504,plain,
( sQ558_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f6464,f1941,f6501]) ).
fof(f6517,plain,
( compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),g)) = compose(codomain(compose(a,b)),g)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f6435]) ).
fof(f6518,plain,
( compose(codomain(compose(h,compose(a,b))),compose(codomain(compose(h,compose(a,b))),g)) = compose(codomain(compose(h,compose(a,b))),g)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f6435]) ).
fof(f6519,plain,
( compose(codomain(compose(h,a)),compose(codomain(compose(h,a)),g)) = compose(codomain(compose(h,a)),g)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f6435]) ).
fof(f6520,plain,
( compose(codomain(compose(g,a)),compose(codomain(compose(g,a)),g)) = compose(codomain(compose(g,a)),g)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f6435]) ).
fof(f6521,plain,
( compose(codomain(g),compose(codomain(g),g)) = compose(codomain(g),g)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f6435]) ).
fof(f6522,plain,
( compose(codomain(h),compose(codomain(h),g)) = compose(codomain(h),g)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f6435]) ).
fof(f6523,plain,
( compose(codomain(a),compose(codomain(a),g)) = compose(codomain(a),g)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f6435]) ).
fof(f6531,definition,
( sQ559_spl
<=> compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),g)) = compose(codomain(compose(a,b)),g) ),
introduced(definition,[new_symbols(definition,[sQ559_spl])],[split_symbol_definition]) ).
fof(f6534,plain,
( sQ559_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f6517,f1555,f6531]) ).
fof(f6535,definition,
( sQ560_spl
<=> compose(codomain(compose(h,compose(a,b))),compose(codomain(compose(h,compose(a,b))),g)) = compose(codomain(compose(h,compose(a,b))),g) ),
introduced(definition,[new_symbols(definition,[sQ560_spl])],[split_symbol_definition]) ).
fof(f6538,plain,
( sQ560_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f6518,f1555,f6535]) ).
fof(f6539,definition,
( sQ561_spl
<=> compose(codomain(compose(h,a)),compose(codomain(compose(h,a)),g)) = compose(codomain(compose(h,a)),g) ),
introduced(definition,[new_symbols(definition,[sQ561_spl])],[split_symbol_definition]) ).
fof(f6542,plain,
( sQ561_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6519,f693,f6539]) ).
fof(f6543,definition,
( sQ562_spl
<=> compose(codomain(compose(g,a)),compose(codomain(compose(g,a)),g)) = compose(codomain(compose(g,a)),g) ),
introduced(definition,[new_symbols(definition,[sQ562_spl])],[split_symbol_definition]) ).
fof(f6546,plain,
( sQ562_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6520,f693,f6543]) ).
fof(f6547,definition,
( sQ563_spl
<=> compose(codomain(g),compose(codomain(g),g)) = compose(codomain(g),g) ),
introduced(definition,[new_symbols(definition,[sQ563_spl])],[split_symbol_definition]) ).
fof(f6550,plain,
( sQ563_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6521,f584,f6547]) ).
fof(f6551,definition,
( sQ564_spl
<=> compose(codomain(h),compose(codomain(h),g)) = compose(codomain(h),g) ),
introduced(definition,[new_symbols(definition,[sQ564_spl])],[split_symbol_definition]) ).
fof(f6554,plain,
( sQ564_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6522,f584,f6551]) ).
fof(f6555,definition,
( sQ565_spl
<=> compose(codomain(a),compose(codomain(a),g)) = compose(codomain(a),g) ),
introduced(definition,[new_symbols(definition,[sQ565_spl])],[split_symbol_definition]) ).
fof(f6558,plain,
( sQ565_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6523,f693,f6555]) ).
fof(f6566,plain,
( codomain(compose(compose(h,compose(a,b)),domain(compose(g,a)))) = domain(compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f859]) ).
fof(f6567,plain,
( codomain(compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b))))) = domain(compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f859]) ).
fof(f6568,plain,
( codomain(compose(compose(h,compose(a,b)),domain(compose(h,a)))) = domain(compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f859]) ).
fof(f6569,plain,
( codomain(compose(compose(h,compose(a,b)),domain(compose(a,b)))) = domain(compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f859]) ).
fof(f6575,definition,
( sQ566_spl
<=> codomain(compose(compose(h,compose(a,b)),domain(compose(g,a)))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ566_spl])],[split_symbol_definition]) ).
fof(f6578,plain,
( sQ566_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f6566,f1555,f6575]) ).
fof(f6579,definition,
( sQ567_spl
<=> codomain(compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b))))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ567_spl])],[split_symbol_definition]) ).
fof(f6582,plain,
( sQ567_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f6567,f1555,f6579]) ).
fof(f6583,definition,
( sQ568_spl
<=> codomain(compose(compose(h,compose(a,b)),domain(compose(h,a)))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ568_spl])],[split_symbol_definition]) ).
fof(f6586,plain,
( sQ568_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f6568,f1555,f6583]) ).
fof(f6587,definition,
( sQ569_spl
<=> codomain(compose(compose(h,compose(a,b)),domain(compose(a,b)))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ569_spl])],[split_symbol_definition]) ).
fof(f6590,plain,
( sQ569_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f6569,f1570,f6587]) ).
fof(f6598,plain,
( codomain(compose(compose(h,compose(a,b)),codomain(compose(a,b)))) = codomain(compose(a,b))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f909]) ).
fof(f6599,plain,
( codomain(compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b))))) = codomain(compose(h,compose(a,b)))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f909]) ).
fof(f6600,plain,
( codomain(compose(compose(h,compose(a,b)),codomain(compose(h,a)))) = codomain(compose(h,a))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f909]) ).
fof(f6601,plain,
( codomain(compose(compose(h,compose(a,b)),codomain(compose(g,a)))) = codomain(compose(g,a))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f909]) ).
fof(f6611,definition,
( sQ570_spl
<=> codomain(compose(compose(h,compose(a,b)),codomain(compose(a,b)))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ570_spl])],[split_symbol_definition]) ).
fof(f6614,plain,
( sQ570_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f6598,f4389,f6611]) ).
fof(f6615,definition,
( sQ571_spl
<=> codomain(compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b))))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ571_spl])],[split_symbol_definition]) ).
fof(f6618,plain,
( sQ571_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f6599,f4389,f6615]) ).
fof(f6619,definition,
( sQ572_spl
<=> codomain(compose(compose(h,compose(a,b)),codomain(compose(h,a)))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ572_spl])],[split_symbol_definition]) ).
fof(f6622,plain,
( sQ572_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f6600,f2265,f6619]) ).
fof(f6623,definition,
( sQ573_spl
<=> codomain(compose(compose(h,compose(a,b)),codomain(compose(g,a)))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ573_spl])],[split_symbol_definition]) ).
fof(f6626,plain,
( sQ573_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f6601,f2265,f6623]) ).
fof(f6636,plain,
( domain(compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = codomain(compose(a,b))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1113]) ).
fof(f6637,plain,
( domain(compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1113]) ).
fof(f6638,plain,
( domain(compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = codomain(compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1113]) ).
fof(f6639,plain,
( domain(compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = codomain(compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1113]) ).
fof(f6640,plain,
( domain(compose(codomain(g),compose(h,compose(a,b)))) = codomain(g)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1113]) ).
fof(f6641,plain,
( domain(compose(codomain(h),compose(h,compose(a,b)))) = codomain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1113]) ).
fof(f6642,plain,
( domain(compose(codomain(a),compose(h,compose(a,b)))) = codomain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f1113]) ).
fof(f6648,definition,
( sQ574_spl
<=> domain(compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ574_spl])],[split_symbol_definition]) ).
fof(f6651,plain,
( sQ574_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f6636,f1555,f6648]) ).
fof(f6652,definition,
( sQ575_spl
<=> domain(compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ575_spl])],[split_symbol_definition]) ).
fof(f6655,plain,
( sQ575_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f6637,f1555,f6652]) ).
fof(f6656,definition,
( sQ576_spl
<=> domain(compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = codomain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ576_spl])],[split_symbol_definition]) ).
fof(f6659,plain,
( sQ576_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6638,f693,f6656]) ).
fof(f6660,definition,
( sQ577_spl
<=> domain(compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = codomain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ577_spl])],[split_symbol_definition]) ).
fof(f6663,plain,
( sQ577_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6639,f693,f6660]) ).
fof(f6664,definition,
( sQ578_spl
<=> domain(compose(codomain(g),compose(h,compose(a,b)))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ578_spl])],[split_symbol_definition]) ).
fof(f6667,plain,
( sQ578_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6640,f584,f6664]) ).
fof(f6668,definition,
( sQ579_spl
<=> domain(compose(codomain(h),compose(h,compose(a,b)))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ579_spl])],[split_symbol_definition]) ).
fof(f6671,plain,
( sQ579_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6641,f584,f6668]) ).
fof(f6672,definition,
( sQ580_spl
<=> domain(compose(codomain(a),compose(h,compose(a,b)))) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ580_spl])],[split_symbol_definition]) ).
fof(f6675,plain,
( sQ580_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6642,f693,f6672]) ).
fof(f6685,plain,
( domain(compose(domain(g),compose(h,compose(a,b)))) = domain(g)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f1114]) ).
fof(f6686,plain,
( domain(compose(domain(compose(g,a)),compose(h,compose(a,b)))) = domain(compose(g,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1114]) ).
fof(f6687,plain,
( domain(compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = domain(compose(h,compose(a,b)))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1114]) ).
fof(f6688,plain,
( domain(compose(domain(compose(h,a)),compose(h,compose(a,b)))) = domain(compose(h,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1114]) ).
fof(f6689,plain,
( domain(compose(domain(compose(a,b)),compose(h,compose(a,b)))) = domain(compose(a,b))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f1114]) ).
fof(f6705,definition,
( sQ581_spl
<=> domain(compose(domain(g),compose(h,compose(a,b)))) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ581_spl])],[split_symbol_definition]) ).
fof(f6708,plain,
( sQ581_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f6685,f2687,f6705]) ).
fof(f6709,definition,
( sQ582_spl
<=> domain(compose(domain(compose(g,a)),compose(h,compose(a,b)))) = domain(compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ582_spl])],[split_symbol_definition]) ).
fof(f6712,plain,
( sQ582_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f6686,f2687,f6709]) ).
fof(f6713,definition,
( sQ583_spl
<=> domain(compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ583_spl])],[split_symbol_definition]) ).
fof(f6716,plain,
( sQ583_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f6687,f2687,f6713]) ).
fof(f6717,definition,
( sQ584_spl
<=> domain(compose(domain(compose(h,a)),compose(h,compose(a,b)))) = domain(compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ584_spl])],[split_symbol_definition]) ).
fof(f6720,plain,
( sQ584_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f6688,f2687,f6717]) ).
fof(f6721,definition,
( sQ585_spl
<=> domain(compose(domain(compose(a,b)),compose(h,compose(a,b)))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ585_spl])],[split_symbol_definition]) ).
fof(f6724,plain,
( sQ585_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6689,f584,f6721]) ).
fof(f6740,plain,
( compose(compose(g,a),compose(b,compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1376]) ).
fof(f6741,plain,
( compose(compose(g,a),compose(b,compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1376]) ).
fof(f6742,plain,
( compose(compose(g,a),compose(b,compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1376]) ).
fof(f6743,plain,
( compose(compose(g,a),compose(b,compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1376]) ).
fof(f6744,plain,
! [X0] :
( compose(compose(g,a),compose(b,domain(X0))) = compose(compose(h,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f1376]) ).
fof(f6745,plain,
! [X0] :
( compose(compose(g,a),compose(b,codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f1376]) ).
fof(f6748,definition,
( sQ586_spl
<=> compose(compose(g,a),compose(b,compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ586_spl])],[split_symbol_definition]) ).
fof(f6751,plain,
( sQ586_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f6740,f1555,f6748]) ).
fof(f6752,definition,
( sQ587_spl
<=> compose(compose(g,a),compose(b,compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ587_spl])],[split_symbol_definition]) ).
fof(f6755,plain,
( sQ587_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f6741,f1555,f6752]) ).
fof(f6756,definition,
( sQ588_spl
<=> compose(compose(g,a),compose(b,compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ588_spl])],[split_symbol_definition]) ).
fof(f6759,plain,
( sQ588_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f6742,f1555,f6756]) ).
fof(f6760,definition,
( sQ589_spl
<=> compose(compose(g,a),compose(b,compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ589_spl])],[split_symbol_definition]) ).
fof(f6763,plain,
( sQ589_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f6743,f1570,f6760]) ).
fof(f6766,plain,
( compose(domain(h),compose(g,domain(compose(g,a)))) = compose(g,domain(compose(g,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f4698]) ).
fof(f6767,plain,
( compose(domain(h),compose(g,domain(compose(h,compose(a,b))))) = compose(g,domain(compose(h,compose(a,b))))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f4698]) ).
fof(f6768,plain,
( compose(domain(h),compose(g,domain(compose(h,a)))) = compose(g,domain(compose(h,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f4698]) ).
fof(f6769,plain,
( compose(domain(h),compose(g,domain(compose(a,b)))) = compose(g,domain(compose(a,b)))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f4698]) ).
fof(f6781,definition,
( sQ590_spl
<=> compose(domain(h),compose(g,domain(compose(g,a)))) = compose(g,domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ590_spl])],[split_symbol_definition]) ).
fof(f6784,plain,
( sQ590_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6766,f584,f6781]) ).
fof(f6785,definition,
( sQ591_spl
<=> compose(domain(h),compose(g,domain(compose(h,compose(a,b))))) = compose(g,domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ591_spl])],[split_symbol_definition]) ).
fof(f6788,plain,
( sQ591_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6767,f584,f6785]) ).
fof(f6789,definition,
( sQ592_spl
<=> compose(domain(h),compose(g,domain(compose(h,a)))) = compose(g,domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ592_spl])],[split_symbol_definition]) ).
fof(f6792,plain,
( sQ592_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6768,f584,f6789]) ).
fof(f6793,definition,
( sQ593_spl
<=> compose(domain(h),compose(g,domain(compose(a,b)))) = compose(g,domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ593_spl])],[split_symbol_definition]) ).
fof(f6796,plain,
( sQ593_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f6769,f606,f6793]) ).
fof(f6810,plain,
( compose(domain(h),compose(g,codomain(compose(a,b)))) = compose(g,codomain(compose(a,b)))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f4699]) ).
fof(f6811,plain,
( compose(domain(h),compose(g,codomain(compose(h,compose(a,b))))) = compose(g,codomain(compose(h,compose(a,b))))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f4699]) ).
fof(f6812,plain,
( compose(domain(h),compose(g,codomain(compose(h,a)))) = compose(g,codomain(compose(h,a)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f4699]) ).
fof(f6813,plain,
( compose(domain(h),compose(g,codomain(compose(g,a)))) = compose(g,codomain(compose(g,a)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f4699]) ).
fof(f6814,plain,
( compose(domain(h),compose(g,codomain(g))) = compose(g,codomain(g))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f4699]) ).
fof(f6815,plain,
( compose(domain(h),compose(g,codomain(h))) = compose(g,codomain(h))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f4699]) ).
fof(f6816,plain,
( compose(domain(h),compose(g,codomain(a))) = compose(g,codomain(a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f4699]) ).
fof(f6829,definition,
( sQ594_spl
<=> compose(domain(h),compose(g,codomain(compose(a,b)))) = compose(g,codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ594_spl])],[split_symbol_definition]) ).
fof(f6832,plain,
( sQ594_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f6810,f1570,f6829]) ).
fof(f6833,definition,
( sQ595_spl
<=> compose(domain(h),compose(g,codomain(compose(h,compose(a,b))))) = compose(g,codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ595_spl])],[split_symbol_definition]) ).
fof(f6836,plain,
( sQ595_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f6811,f1570,f6833]) ).
fof(f6837,definition,
( sQ596_spl
<=> compose(domain(h),compose(g,codomain(compose(h,a)))) = compose(g,codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ596_spl])],[split_symbol_definition]) ).
fof(f6840,plain,
( sQ596_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6812,f715,f6837]) ).
fof(f6841,definition,
( sQ597_spl
<=> compose(domain(h),compose(g,codomain(compose(g,a)))) = compose(g,codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ597_spl])],[split_symbol_definition]) ).
fof(f6844,plain,
( sQ597_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6813,f715,f6841]) ).
fof(f6845,definition,
( sQ598_spl
<=> compose(domain(h),compose(g,codomain(g))) = compose(g,codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ598_spl])],[split_symbol_definition]) ).
fof(f6848,plain,
( sQ598_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f6814,f606,f6845]) ).
fof(f6849,definition,
( sQ599_spl
<=> compose(domain(h),compose(g,codomain(h))) = compose(g,codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ599_spl])],[split_symbol_definition]) ).
fof(f6852,plain,
( sQ599_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f6815,f606,f6849]) ).
fof(f6853,definition,
( sQ600_spl
<=> compose(domain(h),compose(g,codomain(a))) = compose(g,codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ600_spl])],[split_symbol_definition]) ).
fof(f6856,plain,
( sQ600_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6816,f715,f6853]) ).
fof(f6869,plain,
( compose(domain(h),compose(h,domain(compose(g,a)))) = compose(h,domain(compose(g,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f4729]) ).
fof(f6870,plain,
( compose(domain(h),compose(h,domain(compose(h,compose(a,b))))) = compose(h,domain(compose(h,compose(a,b))))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f4729]) ).
fof(f6871,plain,
( compose(domain(h),compose(h,domain(compose(h,a)))) = compose(h,domain(compose(h,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f4729]) ).
fof(f6872,plain,
( compose(domain(h),compose(h,domain(compose(a,b)))) = compose(h,domain(compose(a,b)))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f4729]) ).
fof(f6884,definition,
( sQ601_spl
<=> compose(domain(h),compose(h,domain(compose(g,a)))) = compose(h,domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ601_spl])],[split_symbol_definition]) ).
fof(f6887,plain,
( sQ601_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6869,f584,f6884]) ).
fof(f6888,definition,
( sQ602_spl
<=> compose(domain(h),compose(h,domain(compose(h,compose(a,b))))) = compose(h,domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ602_spl])],[split_symbol_definition]) ).
fof(f6891,plain,
( sQ602_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6870,f584,f6888]) ).
fof(f6892,definition,
( sQ603_spl
<=> compose(domain(h),compose(h,domain(compose(h,a)))) = compose(h,domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ603_spl])],[split_symbol_definition]) ).
fof(f6895,plain,
( sQ603_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6871,f584,f6892]) ).
fof(f6896,definition,
( sQ604_spl
<=> compose(domain(h),compose(h,domain(compose(a,b)))) = compose(h,domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ604_spl])],[split_symbol_definition]) ).
fof(f6899,plain,
( sQ604_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f6872,f606,f6896]) ).
fof(f6913,plain,
( compose(domain(h),compose(h,codomain(compose(a,b)))) = compose(h,codomain(compose(a,b)))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f4730]) ).
fof(f6914,plain,
( compose(domain(h),compose(h,codomain(compose(h,compose(a,b))))) = compose(h,codomain(compose(h,compose(a,b))))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f4730]) ).
fof(f6915,plain,
( compose(domain(h),compose(h,codomain(compose(h,a)))) = compose(h,codomain(compose(h,a)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f4730]) ).
fof(f6916,plain,
( compose(domain(h),compose(h,codomain(compose(g,a)))) = compose(h,codomain(compose(g,a)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f4730]) ).
fof(f6917,plain,
( compose(domain(h),compose(h,codomain(g))) = compose(h,codomain(g))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f4730]) ).
fof(f6918,plain,
( compose(domain(h),compose(h,codomain(h))) = compose(h,codomain(h))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f4730]) ).
fof(f6919,plain,
( compose(domain(h),compose(h,codomain(a))) = compose(h,codomain(a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f4730]) ).
fof(f6932,definition,
( sQ605_spl
<=> compose(domain(h),compose(h,codomain(compose(a,b)))) = compose(h,codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ605_spl])],[split_symbol_definition]) ).
fof(f6935,plain,
( sQ605_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f6913,f1570,f6932]) ).
fof(f6936,definition,
( sQ606_spl
<=> compose(domain(h),compose(h,codomain(compose(h,compose(a,b))))) = compose(h,codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ606_spl])],[split_symbol_definition]) ).
fof(f6939,plain,
( sQ606_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f6914,f1570,f6936]) ).
fof(f6940,definition,
( sQ607_spl
<=> compose(domain(h),compose(h,codomain(compose(h,a)))) = compose(h,codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ607_spl])],[split_symbol_definition]) ).
fof(f6943,plain,
( sQ607_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6915,f715,f6940]) ).
fof(f6944,definition,
( sQ608_spl
<=> compose(domain(h),compose(h,codomain(compose(g,a)))) = compose(h,codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ608_spl])],[split_symbol_definition]) ).
fof(f6947,plain,
( sQ608_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6916,f715,f6944]) ).
fof(f6948,definition,
( sQ609_spl
<=> compose(domain(h),compose(h,codomain(g))) = compose(h,codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ609_spl])],[split_symbol_definition]) ).
fof(f6951,plain,
( sQ609_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f6917,f606,f6948]) ).
fof(f6952,definition,
( sQ610_spl
<=> compose(domain(h),compose(h,codomain(h))) = compose(h,codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ610_spl])],[split_symbol_definition]) ).
fof(f6955,plain,
( sQ610_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f6918,f606,f6952]) ).
fof(f6956,definition,
( sQ611_spl
<=> compose(domain(h),compose(h,codomain(a))) = compose(h,codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ611_spl])],[split_symbol_definition]) ).
fof(f6959,plain,
( sQ611_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6919,f715,f6956]) ).
fof(f6971,plain,
( compose(domain(a),compose(a,domain(compose(g,a)))) = compose(a,domain(compose(g,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f4755]) ).
fof(f6972,plain,
( compose(domain(a),compose(a,domain(compose(h,compose(a,b))))) = compose(a,domain(compose(h,compose(a,b))))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f4755]) ).
fof(f6973,plain,
( compose(domain(a),compose(a,domain(compose(h,a)))) = compose(a,domain(compose(h,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f4755]) ).
fof(f6974,plain,
( compose(domain(a),compose(a,domain(compose(a,b)))) = compose(a,domain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f4755]) ).
fof(f6982,definition,
( sQ612_spl
<=> compose(domain(a),compose(a,domain(compose(g,a)))) = compose(a,domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ612_spl])],[split_symbol_definition]) ).
fof(f6985,plain,
( sQ612_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6971,f693,f6982]) ).
fof(f6986,definition,
( sQ613_spl
<=> compose(domain(a),compose(a,domain(compose(h,compose(a,b))))) = compose(a,domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ613_spl])],[split_symbol_definition]) ).
fof(f6989,plain,
( sQ613_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6972,f693,f6986]) ).
fof(f6990,definition,
( sQ614_spl
<=> compose(domain(a),compose(a,domain(compose(h,a)))) = compose(a,domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ614_spl])],[split_symbol_definition]) ).
fof(f6993,plain,
( sQ614_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6973,f693,f6990]) ).
fof(f6994,definition,
( sQ615_spl
<=> compose(domain(a),compose(a,domain(compose(a,b)))) = compose(a,domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ615_spl])],[split_symbol_definition]) ).
fof(f6997,plain,
( sQ615_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6974,f715,f6994]) ).
fof(f7005,plain,
( compose(h,compose(a,domain(compose(g,a)))) = compose(compose(h,a),domain(compose(g,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1388]) ).
fof(f7006,plain,
( compose(h,compose(a,domain(compose(h,compose(a,b))))) = compose(compose(h,a),domain(compose(h,compose(a,b))))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1388]) ).
fof(f7007,plain,
( compose(h,compose(a,domain(compose(h,a)))) = compose(compose(h,a),domain(compose(h,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1388]) ).
fof(f7008,plain,
( compose(h,compose(a,domain(compose(a,b)))) = compose(compose(h,a),domain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1388]) ).
fof(f7015,definition,
( sQ616_spl
<=> compose(h,compose(a,domain(compose(g,a)))) = compose(compose(h,a),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ616_spl])],[split_symbol_definition]) ).
fof(f7018,plain,
( sQ616_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f7005,f693,f7015]) ).
fof(f7019,definition,
( sQ617_spl
<=> compose(h,compose(a,domain(compose(h,compose(a,b))))) = compose(compose(h,a),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ617_spl])],[split_symbol_definition]) ).
fof(f7022,plain,
( sQ617_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f7006,f693,f7019]) ).
fof(f7023,definition,
( sQ618_spl
<=> compose(h,compose(a,domain(compose(h,a)))) = compose(compose(h,a),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ618_spl])],[split_symbol_definition]) ).
fof(f7026,plain,
( sQ618_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f7007,f693,f7023]) ).
fof(f7027,definition,
( sQ619_spl
<=> compose(h,compose(a,domain(compose(a,b)))) = compose(compose(h,a),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ619_spl])],[split_symbol_definition]) ).
fof(f7030,plain,
( sQ619_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7008,f715,f7027]) ).
fof(f7040,plain,
( compose(domain(a),compose(a,codomain(compose(a,b)))) = compose(a,codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f4756]) ).
fof(f7041,plain,
( compose(domain(a),compose(a,codomain(compose(h,compose(a,b))))) = compose(a,codomain(compose(h,compose(a,b))))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f4756]) ).
fof(f7042,plain,
( compose(domain(a),compose(a,codomain(compose(h,a)))) = compose(a,codomain(compose(h,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f4756]) ).
fof(f7043,plain,
( compose(domain(a),compose(a,codomain(compose(g,a)))) = compose(a,codomain(compose(g,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f4756]) ).
fof(f7044,plain,
( compose(domain(a),compose(a,codomain(g))) = compose(a,codomain(g))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f4756]) ).
fof(f7045,plain,
( compose(domain(a),compose(a,codomain(h))) = compose(a,codomain(h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f4756]) ).
fof(f7046,plain,
( compose(domain(a),compose(a,codomain(a))) = compose(a,codomain(a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f4756]) ).
fof(f7063,definition,
( sQ620_spl
<=> compose(domain(a),compose(a,codomain(compose(a,b)))) = compose(a,codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ620_spl])],[split_symbol_definition]) ).
fof(f7066,plain,
( sQ620_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f7040,f2265,f7063]) ).
fof(f7067,definition,
( sQ621_spl
<=> compose(domain(a),compose(a,codomain(compose(h,compose(a,b))))) = compose(a,codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ621_spl])],[split_symbol_definition]) ).
fof(f7070,plain,
( sQ621_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f7041,f2265,f7067]) ).
fof(f7071,definition,
( sQ622_spl
<=> compose(domain(a),compose(a,codomain(compose(h,a)))) = compose(a,codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ622_spl])],[split_symbol_definition]) ).
fof(f7074,plain,
( sQ622_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f7042,f1941,f7071]) ).
fof(f7075,definition,
( sQ623_spl
<=> compose(domain(a),compose(a,codomain(compose(g,a)))) = compose(a,codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ623_spl])],[split_symbol_definition]) ).
fof(f7078,plain,
( sQ623_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f7043,f1941,f7075]) ).
fof(f7079,definition,
( sQ624_spl
<=> compose(domain(a),compose(a,codomain(g))) = compose(a,codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ624_spl])],[split_symbol_definition]) ).
fof(f7082,plain,
( sQ624_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7044,f715,f7079]) ).
fof(f7083,definition,
( sQ625_spl
<=> compose(domain(a),compose(a,codomain(h))) = compose(a,codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ625_spl])],[split_symbol_definition]) ).
fof(f7086,plain,
( sQ625_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7045,f715,f7083]) ).
fof(f7087,definition,
( sQ626_spl
<=> compose(domain(a),compose(a,codomain(a))) = compose(a,codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ626_spl])],[split_symbol_definition]) ).
fof(f7090,plain,
( sQ626_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f7046,f1941,f7087]) ).
fof(f7496,plain,
( compose(h,compose(a,codomain(compose(a,b)))) = compose(compose(h,a),codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f1389]) ).
fof(f7497,plain,
( compose(h,compose(a,codomain(compose(h,compose(a,b))))) = compose(compose(h,a),codomain(compose(h,compose(a,b))))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f1389]) ).
fof(f7498,plain,
( compose(h,compose(a,codomain(compose(h,a)))) = compose(compose(h,a),codomain(compose(h,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f1389]) ).
fof(f7499,plain,
( compose(h,compose(a,codomain(compose(g,a)))) = compose(compose(h,a),codomain(compose(g,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f1389]) ).
fof(f7500,plain,
( compose(h,compose(a,codomain(g))) = compose(compose(h,a),codomain(g))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f1389]) ).
fof(f7501,plain,
( compose(h,compose(a,codomain(h))) = compose(compose(h,a),codomain(h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f1389]) ).
fof(f7502,plain,
( compose(h,compose(a,codomain(a))) = compose(compose(h,a),codomain(a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f1389]) ).
fof(f7515,definition,
( sQ627_spl
<=> compose(h,compose(a,codomain(compose(a,b)))) = compose(compose(h,a),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ627_spl])],[split_symbol_definition]) ).
fof(f7518,plain,
( sQ627_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f7496,f2265,f7515]) ).
fof(f7519,definition,
( sQ628_spl
<=> compose(h,compose(a,codomain(compose(h,compose(a,b))))) = compose(compose(h,a),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ628_spl])],[split_symbol_definition]) ).
fof(f7522,plain,
( sQ628_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f7497,f2265,f7519]) ).
fof(f7523,definition,
( sQ629_spl
<=> compose(h,compose(a,codomain(compose(h,a)))) = compose(compose(h,a),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ629_spl])],[split_symbol_definition]) ).
fof(f7526,plain,
( sQ629_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f7498,f1941,f7523]) ).
fof(f7527,definition,
( sQ630_spl
<=> compose(h,compose(a,codomain(compose(g,a)))) = compose(compose(h,a),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ630_spl])],[split_symbol_definition]) ).
fof(f7530,plain,
( sQ630_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f7499,f1941,f7527]) ).
fof(f7531,definition,
( sQ631_spl
<=> compose(h,compose(a,codomain(g))) = compose(compose(h,a),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ631_spl])],[split_symbol_definition]) ).
fof(f7534,plain,
( sQ631_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7500,f715,f7531]) ).
fof(f7535,definition,
( sQ632_spl
<=> compose(h,compose(a,codomain(h))) = compose(compose(h,a),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ632_spl])],[split_symbol_definition]) ).
fof(f7538,plain,
( sQ632_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7501,f715,f7535]) ).
fof(f7539,definition,
( sQ633_spl
<=> compose(h,compose(a,codomain(a))) = compose(compose(h,a),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ633_spl])],[split_symbol_definition]) ).
fof(f7542,plain,
( sQ633_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f7502,f1941,f7539]) ).
fof(f7556,plain,
( compose(g,compose(domain(a),domain(compose(g,a)))) = compose(g,domain(compose(g,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f5138]) ).
fof(f7557,plain,
( compose(g,compose(domain(a),domain(compose(h,compose(a,b))))) = compose(g,domain(compose(h,compose(a,b))))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f5138]) ).
fof(f7558,plain,
( compose(g,compose(domain(a),domain(compose(h,a)))) = compose(g,domain(compose(h,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f5138]) ).
fof(f7559,plain,
( compose(g,compose(domain(a),domain(compose(a,b)))) = compose(g,domain(compose(a,b)))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f5138]) ).
fof(f7571,definition,
( sQ634_spl
<=> compose(g,compose(domain(a),domain(compose(g,a)))) = compose(g,domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ634_spl])],[split_symbol_definition]) ).
fof(f7574,plain,
( sQ634_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f7556,f584,f7571]) ).
fof(f7575,definition,
( sQ635_spl
<=> compose(g,compose(domain(a),domain(compose(h,compose(a,b))))) = compose(g,domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ635_spl])],[split_symbol_definition]) ).
fof(f7578,plain,
( sQ635_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f7557,f584,f7575]) ).
fof(f7579,definition,
( sQ636_spl
<=> compose(g,compose(domain(a),domain(compose(h,a)))) = compose(g,domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ636_spl])],[split_symbol_definition]) ).
fof(f7582,plain,
( sQ636_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f7558,f584,f7579]) ).
fof(f7583,definition,
( sQ637_spl
<=> compose(g,compose(domain(a),domain(compose(a,b)))) = compose(g,domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ637_spl])],[split_symbol_definition]) ).
fof(f7586,plain,
( sQ637_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f7559,f606,f7583]) ).
fof(f7598,plain,
( compose(g,compose(domain(a),codomain(compose(a,b)))) = compose(g,codomain(compose(a,b)))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f5139]) ).
fof(f7599,plain,
( compose(g,compose(domain(a),codomain(compose(h,compose(a,b))))) = compose(g,codomain(compose(h,compose(a,b))))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f5139]) ).
fof(f7600,plain,
( compose(g,compose(domain(a),codomain(compose(h,a)))) = compose(g,codomain(compose(h,a)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f5139]) ).
fof(f7601,plain,
( compose(g,compose(domain(a),codomain(compose(g,a)))) = compose(g,codomain(compose(g,a)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f5139]) ).
fof(f7602,plain,
( compose(g,compose(domain(a),codomain(g))) = compose(g,codomain(g))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f5139]) ).
fof(f7603,plain,
( compose(g,compose(domain(a),codomain(h))) = compose(g,codomain(h))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f5139]) ).
fof(f7604,plain,
( compose(g,compose(domain(a),codomain(a))) = compose(g,codomain(a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f5139]) ).
fof(f7617,definition,
( sQ638_spl
<=> compose(g,compose(domain(a),codomain(compose(a,b)))) = compose(g,codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ638_spl])],[split_symbol_definition]) ).
fof(f7620,plain,
( sQ638_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f7598,f1570,f7617]) ).
fof(f7621,definition,
( sQ639_spl
<=> compose(g,compose(domain(a),codomain(compose(h,compose(a,b))))) = compose(g,codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ639_spl])],[split_symbol_definition]) ).
fof(f7624,plain,
( sQ639_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f7599,f1570,f7621]) ).
fof(f7625,definition,
( sQ640_spl
<=> compose(g,compose(domain(a),codomain(compose(h,a)))) = compose(g,codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ640_spl])],[split_symbol_definition]) ).
fof(f7628,plain,
( sQ640_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7600,f715,f7625]) ).
fof(f7629,definition,
( sQ641_spl
<=> compose(g,compose(domain(a),codomain(compose(g,a)))) = compose(g,codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ641_spl])],[split_symbol_definition]) ).
fof(f7632,plain,
( sQ641_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7601,f715,f7629]) ).
fof(f7633,definition,
( sQ642_spl
<=> compose(g,compose(domain(a),codomain(g))) = compose(g,codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ642_spl])],[split_symbol_definition]) ).
fof(f7636,plain,
( sQ642_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f7602,f606,f7633]) ).
fof(f7637,definition,
( sQ643_spl
<=> compose(g,compose(domain(a),codomain(h))) = compose(g,codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ643_spl])],[split_symbol_definition]) ).
fof(f7640,plain,
( sQ643_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f7603,f606,f7637]) ).
fof(f7641,definition,
( sQ644_spl
<=> compose(g,compose(domain(a),codomain(a))) = compose(g,codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ644_spl])],[split_symbol_definition]) ).
fof(f7644,plain,
( sQ644_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7604,f715,f7641]) ).
fof(f7658,plain,
( compose(h,compose(domain(a),domain(compose(g,a)))) = compose(h,domain(compose(g,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f5163]) ).
fof(f7659,plain,
( compose(h,compose(domain(a),domain(compose(h,compose(a,b))))) = compose(h,domain(compose(h,compose(a,b))))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f5163]) ).
fof(f7660,plain,
( compose(h,compose(domain(a),domain(compose(h,a)))) = compose(h,domain(compose(h,a)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f5163]) ).
fof(f7661,plain,
( compose(h,compose(domain(a),domain(compose(a,b)))) = compose(h,domain(compose(a,b)))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f5163]) ).
fof(f7673,definition,
( sQ645_spl
<=> compose(h,compose(domain(a),domain(compose(g,a)))) = compose(h,domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ645_spl])],[split_symbol_definition]) ).
fof(f7676,plain,
( sQ645_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f7658,f584,f7673]) ).
fof(f7677,definition,
( sQ646_spl
<=> compose(h,compose(domain(a),domain(compose(h,compose(a,b))))) = compose(h,domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ646_spl])],[split_symbol_definition]) ).
fof(f7680,plain,
( sQ646_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f7659,f584,f7677]) ).
fof(f7681,definition,
( sQ647_spl
<=> compose(h,compose(domain(a),domain(compose(h,a)))) = compose(h,domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ647_spl])],[split_symbol_definition]) ).
fof(f7684,plain,
( sQ647_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f7660,f584,f7681]) ).
fof(f7685,definition,
( sQ648_spl
<=> compose(h,compose(domain(a),domain(compose(a,b)))) = compose(h,domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ648_spl])],[split_symbol_definition]) ).
fof(f7688,plain,
( sQ648_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f7661,f606,f7685]) ).
fof(f7700,plain,
( compose(h,compose(domain(a),codomain(compose(a,b)))) = compose(h,codomain(compose(a,b)))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f5164]) ).
fof(f7701,plain,
( compose(h,compose(domain(a),codomain(compose(h,compose(a,b))))) = compose(h,codomain(compose(h,compose(a,b))))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f5164]) ).
fof(f7702,plain,
( compose(h,compose(domain(a),codomain(compose(h,a)))) = compose(h,codomain(compose(h,a)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f5164]) ).
fof(f7703,plain,
( compose(h,compose(domain(a),codomain(compose(g,a)))) = compose(h,codomain(compose(g,a)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f5164]) ).
fof(f7704,plain,
( compose(h,compose(domain(a),codomain(g))) = compose(h,codomain(g))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f5164]) ).
fof(f7705,plain,
( compose(h,compose(domain(a),codomain(h))) = compose(h,codomain(h))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f5164]) ).
fof(f7706,plain,
( compose(h,compose(domain(a),codomain(a))) = compose(h,codomain(a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f5164]) ).
fof(f7719,definition,
( sQ649_spl
<=> compose(h,compose(domain(a),codomain(compose(a,b)))) = compose(h,codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ649_spl])],[split_symbol_definition]) ).
fof(f7722,plain,
( sQ649_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f7700,f1570,f7719]) ).
fof(f7723,definition,
( sQ650_spl
<=> compose(h,compose(domain(a),codomain(compose(h,compose(a,b))))) = compose(h,codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ650_spl])],[split_symbol_definition]) ).
fof(f7726,plain,
( sQ650_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f7701,f1570,f7723]) ).
fof(f7727,definition,
( sQ651_spl
<=> compose(h,compose(domain(a),codomain(compose(h,a)))) = compose(h,codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ651_spl])],[split_symbol_definition]) ).
fof(f7730,plain,
( sQ651_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7702,f715,f7727]) ).
fof(f7731,definition,
( sQ652_spl
<=> compose(h,compose(domain(a),codomain(compose(g,a)))) = compose(h,codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ652_spl])],[split_symbol_definition]) ).
fof(f7734,plain,
( sQ652_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7703,f715,f7731]) ).
fof(f7735,definition,
( sQ653_spl
<=> compose(h,compose(domain(a),codomain(g))) = compose(h,codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ653_spl])],[split_symbol_definition]) ).
fof(f7738,plain,
( sQ653_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f7704,f606,f7735]) ).
fof(f7739,definition,
( sQ654_spl
<=> compose(h,compose(domain(a),codomain(h))) = compose(h,codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ654_spl])],[split_symbol_definition]) ).
fof(f7742,plain,
( sQ654_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f7705,f606,f7739]) ).
fof(f7743,definition,
( sQ655_spl
<=> compose(h,compose(domain(a),codomain(a))) = compose(h,codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ655_spl])],[split_symbol_definition]) ).
fof(f7746,plain,
( sQ655_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7706,f715,f7743]) ).
fof(f7759,plain,
( compose(a,compose(domain(b),domain(compose(g,a)))) = compose(a,domain(compose(g,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f5187]) ).
fof(f7760,plain,
( compose(a,compose(domain(b),domain(compose(h,compose(a,b))))) = compose(a,domain(compose(h,compose(a,b))))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f5187]) ).
fof(f7761,plain,
( compose(a,compose(domain(b),domain(compose(h,a)))) = compose(a,domain(compose(h,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f5187]) ).
fof(f7762,plain,
( compose(a,compose(domain(b),domain(compose(a,b)))) = compose(a,domain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f5187]) ).
fof(f7770,definition,
( sQ656_spl
<=> compose(a,compose(domain(b),domain(compose(g,a)))) = compose(a,domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ656_spl])],[split_symbol_definition]) ).
fof(f7773,plain,
( sQ656_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f7759,f693,f7770]) ).
fof(f7774,definition,
( sQ657_spl
<=> compose(a,compose(domain(b),domain(compose(h,compose(a,b))))) = compose(a,domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ657_spl])],[split_symbol_definition]) ).
fof(f7777,plain,
( sQ657_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f7760,f693,f7774]) ).
fof(f7778,definition,
( sQ658_spl
<=> compose(a,compose(domain(b),domain(compose(h,a)))) = compose(a,domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ658_spl])],[split_symbol_definition]) ).
fof(f7781,plain,
( sQ658_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f7761,f693,f7778]) ).
fof(f7782,definition,
( sQ659_spl
<=> compose(a,compose(domain(b),domain(compose(a,b)))) = compose(a,domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ659_spl])],[split_symbol_definition]) ).
fof(f7785,plain,
( sQ659_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7762,f715,f7782]) ).
fof(f7791,plain,
( compose(compose(h,a),compose(b,compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1430]) ).
fof(f7792,plain,
( compose(compose(h,a),compose(b,compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1430]) ).
fof(f7793,plain,
( compose(compose(h,a),compose(b,compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1430]) ).
fof(f7794,plain,
( compose(compose(h,a),compose(b,compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1430]) ).
fof(f7795,plain,
! [X0] :
( compose(compose(h,a),compose(b,domain(X0))) = compose(compose(h,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f1430]) ).
fof(f7796,plain,
! [X0] :
( compose(compose(h,a),compose(b,codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f1430]) ).
fof(f7799,definition,
( sQ660_spl
<=> compose(compose(h,a),compose(b,compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ660_spl])],[split_symbol_definition]) ).
fof(f7802,plain,
( sQ660_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f7791,f1555,f7799]) ).
fof(f7803,definition,
( sQ661_spl
<=> compose(compose(h,a),compose(b,compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ661_spl])],[split_symbol_definition]) ).
fof(f7806,plain,
( sQ661_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f7792,f1555,f7803]) ).
fof(f7807,definition,
( sQ662_spl
<=> compose(compose(h,a),compose(b,compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ662_spl])],[split_symbol_definition]) ).
fof(f7810,plain,
( sQ662_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f7793,f1555,f7807]) ).
fof(f7811,definition,
( sQ663_spl
<=> compose(compose(h,a),compose(b,compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ663_spl])],[split_symbol_definition]) ).
fof(f7814,plain,
( sQ663_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f7794,f1570,f7811]) ).
fof(f7819,plain,
( compose(a,compose(domain(b),codomain(compose(a,b)))) = compose(a,codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f5188]) ).
fof(f7820,plain,
( compose(a,compose(domain(b),codomain(compose(h,compose(a,b))))) = compose(a,codomain(compose(h,compose(a,b))))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f5188]) ).
fof(f7821,plain,
( compose(a,compose(domain(b),codomain(compose(h,a)))) = compose(a,codomain(compose(h,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f5188]) ).
fof(f7822,plain,
( compose(a,compose(domain(b),codomain(compose(g,a)))) = compose(a,codomain(compose(g,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f5188]) ).
fof(f7823,plain,
( compose(a,compose(domain(b),codomain(g))) = compose(a,codomain(g))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f5188]) ).
fof(f7824,plain,
( compose(a,compose(domain(b),codomain(h))) = compose(a,codomain(h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f5188]) ).
fof(f7825,plain,
( compose(a,compose(domain(b),codomain(a))) = compose(a,codomain(a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f5188]) ).
fof(f7842,definition,
( sQ664_spl
<=> compose(a,compose(domain(b),codomain(compose(a,b)))) = compose(a,codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ664_spl])],[split_symbol_definition]) ).
fof(f7845,plain,
( sQ664_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f7819,f2265,f7842]) ).
fof(f7846,definition,
( sQ665_spl
<=> compose(a,compose(domain(b),codomain(compose(h,compose(a,b))))) = compose(a,codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ665_spl])],[split_symbol_definition]) ).
fof(f7849,plain,
( sQ665_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f7820,f2265,f7846]) ).
fof(f7850,definition,
( sQ666_spl
<=> compose(a,compose(domain(b),codomain(compose(h,a)))) = compose(a,codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ666_spl])],[split_symbol_definition]) ).
fof(f7853,plain,
( sQ666_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f7821,f1941,f7850]) ).
fof(f7854,definition,
( sQ667_spl
<=> compose(a,compose(domain(b),codomain(compose(g,a)))) = compose(a,codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ667_spl])],[split_symbol_definition]) ).
fof(f7857,plain,
( sQ667_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f7822,f1941,f7854]) ).
fof(f7858,definition,
( sQ668_spl
<=> compose(a,compose(domain(b),codomain(g))) = compose(a,codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ668_spl])],[split_symbol_definition]) ).
fof(f7861,plain,
( sQ668_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7823,f715,f7858]) ).
fof(f7862,definition,
( sQ669_spl
<=> compose(a,compose(domain(b),codomain(h))) = compose(a,codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ669_spl])],[split_symbol_definition]) ).
fof(f7865,plain,
( sQ669_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7824,f715,f7862]) ).
fof(f7866,definition,
( sQ670_spl
<=> compose(a,compose(domain(b),codomain(a))) = compose(a,codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ670_spl])],[split_symbol_definition]) ).
fof(f7869,plain,
( sQ670_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f7825,f1941,f7866]) ).
fof(f7886,plain,
( codomain(compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = codomain(b)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1115]) ).
fof(f7887,plain,
( codomain(compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = codomain(b)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1115]) ).
fof(f7888,plain,
( codomain(compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = codomain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1115]) ).
fof(f7889,plain,
( codomain(compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = codomain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1115]) ).
fof(f7890,plain,
( codomain(compose(codomain(g),compose(h,compose(a,b)))) = codomain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1115]) ).
fof(f7891,plain,
( codomain(compose(codomain(h),compose(h,compose(a,b)))) = codomain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1115]) ).
fof(f7892,plain,
( codomain(compose(codomain(a),compose(h,compose(a,b)))) = codomain(b)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f1115]) ).
fof(f7897,definition,
( sQ671_spl
<=> codomain(compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ671_spl])],[split_symbol_definition]) ).
fof(f7900,plain,
( sQ671_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f7886,f1555,f7897]) ).
fof(f7901,definition,
( sQ672_spl
<=> codomain(compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ672_spl])],[split_symbol_definition]) ).
fof(f7904,plain,
( sQ672_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f7887,f1555,f7901]) ).
fof(f7905,definition,
( sQ673_spl
<=> codomain(compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ673_spl])],[split_symbol_definition]) ).
fof(f7908,plain,
( sQ673_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f7888,f693,f7905]) ).
fof(f7909,definition,
( sQ674_spl
<=> codomain(compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ674_spl])],[split_symbol_definition]) ).
fof(f7912,plain,
( sQ674_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f7889,f693,f7909]) ).
fof(f7913,definition,
( sQ675_spl
<=> codomain(compose(codomain(g),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ675_spl])],[split_symbol_definition]) ).
fof(f7916,plain,
( sQ675_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f7890,f584,f7913]) ).
fof(f7917,definition,
( sQ676_spl
<=> codomain(compose(codomain(h),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ676_spl])],[split_symbol_definition]) ).
fof(f7920,plain,
( sQ676_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f7891,f584,f7917]) ).
fof(f7921,definition,
( sQ677_spl
<=> codomain(compose(codomain(a),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ677_spl])],[split_symbol_definition]) ).
fof(f7924,plain,
( sQ677_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f7892,f693,f7921]) ).
fof(f7932,plain,
( codomain(compose(domain(g),compose(h,compose(a,b)))) = codomain(b)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f1116]) ).
fof(f7933,plain,
( codomain(compose(domain(compose(g,a)),compose(h,compose(a,b)))) = codomain(b)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1116]) ).
fof(f7934,plain,
( codomain(compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = codomain(b)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1116]) ).
fof(f7935,plain,
( codomain(compose(domain(compose(h,a)),compose(h,compose(a,b)))) = codomain(b)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1116]) ).
fof(f7936,plain,
( codomain(compose(domain(compose(a,b)),compose(h,compose(a,b)))) = codomain(b)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f1116]) ).
fof(f7949,definition,
( sQ678_spl
<=> codomain(compose(domain(g),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ678_spl])],[split_symbol_definition]) ).
fof(f7952,plain,
( sQ678_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f7932,f2687,f7949]) ).
fof(f7953,definition,
( sQ679_spl
<=> codomain(compose(domain(compose(g,a)),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ679_spl])],[split_symbol_definition]) ).
fof(f7956,plain,
( sQ679_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f7933,f2687,f7953]) ).
fof(f7957,definition,
( sQ680_spl
<=> codomain(compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ680_spl])],[split_symbol_definition]) ).
fof(f7960,plain,
( sQ680_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f7934,f2687,f7957]) ).
fof(f7961,definition,
( sQ681_spl
<=> codomain(compose(domain(compose(h,a)),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ681_spl])],[split_symbol_definition]) ).
fof(f7964,plain,
( sQ681_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f7935,f2687,f7961]) ).
fof(f7965,definition,
( sQ682_spl
<=> codomain(compose(domain(compose(a,b)),compose(h,compose(a,b)))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ682_spl])],[split_symbol_definition]) ).
fof(f7968,plain,
( sQ682_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f7936,f584,f7965]) ).
fof(f7982,plain,
( domain(compose(compose(h,compose(a,b)),codomain(compose(a,b)))) = domain(h)
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f1117]) ).
fof(f7983,plain,
( domain(compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b))))) = domain(h)
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f1117]) ).
fof(f7984,plain,
( domain(compose(compose(h,compose(a,b)),codomain(compose(h,a)))) = domain(h)
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f1117]) ).
fof(f7985,plain,
( domain(compose(compose(h,compose(a,b)),codomain(compose(g,a)))) = domain(h)
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f1117]) ).
fof(f7994,definition,
( sQ683_spl
<=> domain(compose(compose(h,compose(a,b)),codomain(compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ683_spl])],[split_symbol_definition]) ).
fof(f7997,plain,
( sQ683_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f7982,f4389,f7994]) ).
fof(f7998,definition,
( sQ684_spl
<=> domain(compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b))))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ684_spl])],[split_symbol_definition]) ).
fof(f8001,plain,
( sQ684_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f7983,f4389,f7998]) ).
fof(f8002,definition,
( sQ685_spl
<=> domain(compose(compose(h,compose(a,b)),codomain(compose(h,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ685_spl])],[split_symbol_definition]) ).
fof(f8005,plain,
( sQ685_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f7984,f2265,f8002]) ).
fof(f8006,definition,
( sQ686_spl
<=> domain(compose(compose(h,compose(a,b)),codomain(compose(g,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ686_spl])],[split_symbol_definition]) ).
fof(f8009,plain,
( sQ686_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f7985,f2265,f8006]) ).
fof(f8017,plain,
( domain(compose(compose(h,compose(a,b)),domain(compose(g,a)))) = domain(h)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1118]) ).
fof(f8018,plain,
( domain(compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b))))) = domain(h)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1118]) ).
fof(f8019,plain,
( domain(compose(compose(h,compose(a,b)),domain(compose(h,a)))) = domain(h)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1118]) ).
fof(f8020,plain,
( domain(compose(compose(h,compose(a,b)),domain(compose(a,b)))) = domain(h)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1118]) ).
fof(f8025,definition,
( sQ687_spl
<=> domain(compose(compose(h,compose(a,b)),domain(compose(g,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ687_spl])],[split_symbol_definition]) ).
fof(f8028,plain,
( sQ687_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8017,f1555,f8025]) ).
fof(f8029,definition,
( sQ688_spl
<=> domain(compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b))))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ688_spl])],[split_symbol_definition]) ).
fof(f8032,plain,
( sQ688_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8018,f1555,f8029]) ).
fof(f8033,definition,
( sQ689_spl
<=> domain(compose(compose(h,compose(a,b)),domain(compose(h,a)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ689_spl])],[split_symbol_definition]) ).
fof(f8036,plain,
( sQ689_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8019,f1555,f8033]) ).
fof(f8037,definition,
( sQ690_spl
<=> domain(compose(compose(h,compose(a,b)),domain(compose(a,b)))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ690_spl])],[split_symbol_definition]) ).
fof(f8040,plain,
( sQ690_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f8020,f1570,f8037]) ).
fof(f8044,plain,
( compose(domain(a),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1495]) ).
fof(f8045,plain,
( compose(domain(a),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1495]) ).
fof(f8046,plain,
( compose(domain(a),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1495]) ).
fof(f8047,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)],[f60,f1495]) ).
fof(f8052,definition,
( sQ691_spl
<=> compose(domain(a),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ691_spl])],[split_symbol_definition]) ).
fof(f8055,plain,
( sQ691_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8044,f1555,f8052]) ).
fof(f8056,definition,
( sQ692_spl
<=> compose(domain(a),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ692_spl])],[split_symbol_definition]) ).
fof(f8059,plain,
( sQ692_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8045,f1555,f8056]) ).
fof(f8060,definition,
( sQ693_spl
<=> compose(domain(a),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ693_spl])],[split_symbol_definition]) ).
fof(f8063,plain,
( sQ693_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8046,f1555,f8060]) ).
fof(f8064,definition,
( sQ694_spl
<=> compose(domain(a),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ694_spl])],[split_symbol_definition]) ).
fof(f8067,plain,
( sQ694_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f8047,f1570,f8064]) ).
fof(f8069,plain,
( compose(a,compose(b,domain(compose(g,a)))) = compose(compose(a,b),domain(compose(g,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1552]) ).
fof(f8070,plain,
( compose(a,compose(b,domain(compose(h,compose(a,b))))) = compose(compose(a,b),domain(compose(h,compose(a,b))))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1552]) ).
fof(f8071,plain,
( compose(a,compose(b,domain(compose(h,a)))) = compose(compose(a,b),domain(compose(h,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1552]) ).
fof(f8072,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)],[f60,f1552]) ).
fof(f8078,definition,
( sQ695_spl
<=> compose(a,compose(b,domain(compose(g,a)))) = compose(compose(a,b),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ695_spl])],[split_symbol_definition]) ).
fof(f8081,plain,
( sQ695_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8069,f1555,f8078]) ).
fof(f8082,definition,
( sQ696_spl
<=> compose(a,compose(b,domain(compose(h,compose(a,b))))) = compose(compose(a,b),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ696_spl])],[split_symbol_definition]) ).
fof(f8085,plain,
( sQ696_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8070,f1555,f8082]) ).
fof(f8086,definition,
( sQ697_spl
<=> compose(a,compose(b,domain(compose(h,a)))) = compose(compose(a,b),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ697_spl])],[split_symbol_definition]) ).
fof(f8089,plain,
( sQ697_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8071,f1555,f8086]) ).
fof(f8090,definition,
( sQ698_spl
<=> compose(a,compose(b,domain(compose(a,b)))) = compose(compose(a,b),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ698_spl])],[split_symbol_definition]) ).
fof(f8093,plain,
( sQ698_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f8072,f1570,f8090]) ).
fof(f8101,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)],[f120,f1553]) ).
fof(f8102,plain,
( compose(a,compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(a,b),codomain(compose(h,compose(a,b))))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f1553]) ).
fof(f8103,plain,
( compose(a,compose(b,codomain(compose(h,a)))) = compose(compose(a,b),codomain(compose(h,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f1553]) ).
fof(f8104,plain,
( compose(a,compose(b,codomain(compose(g,a)))) = compose(compose(a,b),codomain(compose(g,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f1553]) ).
fof(f8116,definition,
( sQ699_spl
<=> compose(a,compose(b,codomain(compose(a,b)))) = compose(compose(a,b),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ699_spl])],[split_symbol_definition]) ).
fof(f8119,plain,
( sQ699_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f8101,f4389,f8116]) ).
fof(f8120,definition,
( sQ700_spl
<=> compose(a,compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(a,b),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ700_spl])],[split_symbol_definition]) ).
fof(f8123,plain,
( sQ700_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f8102,f4389,f8120]) ).
fof(f8124,definition,
( sQ701_spl
<=> compose(a,compose(b,codomain(compose(h,a)))) = compose(compose(a,b),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ701_spl])],[split_symbol_definition]) ).
fof(f8127,plain,
( sQ701_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f8103,f2265,f8124]) ).
fof(f8128,definition,
( sQ702_spl
<=> compose(a,compose(b,codomain(compose(g,a)))) = compose(compose(a,b),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ702_spl])],[split_symbol_definition]) ).
fof(f8131,plain,
( sQ702_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f8104,f2265,f8128]) ).
fof(f8142,plain,
( ~ sQ207_spl
| compose(h,a) = compose(g,a)
| codomain(compose(h,a)) != domain(a) ),
inference(resolution,[status(thm)],[f3231,f1390]) ).
fof(f8143,plain,
( ~ sQ207_spl
| compose(g,a) = compose(g,a)
| codomain(compose(g,a)) != domain(a) ),
inference(resolution,[status(thm)],[f3231,f1377]) ).
fof(f8146,definition,
( sQ703_spl
<=> compose(h,a) = compose(g,a) ),
introduced(definition,[new_symbols(definition,[sQ703_spl])],[split_symbol_definition]) ).
fof(f8149,plain,
( ~ sQ207_spl
| sQ703_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f8142,f3284,f8146,f3230]) ).
fof(f8150,definition,
( sQ704_spl
<=> compose(g,a) = compose(g,a) ),
introduced(definition,[new_symbols(definition,[sQ704_spl])],[split_symbol_definition]) ).
fof(f8153,plain,
( ~ sQ207_spl
| sQ704_spl
| ~ sQ203_spl ),
inference(split_clause,[status(thm)],[f8143,f3216,f8150,f3230]) ).
fof(f8159,plain,
( ~ sQ219_spl
| compose(h,a) = compose(h,a)
| codomain(compose(h,a)) != domain(a) ),
inference(resolution,[status(thm)],[f3296,f1390]) ).
fof(f8160,plain,
( ~ sQ219_spl
| compose(g,a) = compose(h,a)
| codomain(compose(g,a)) != domain(a) ),
inference(resolution,[status(thm)],[f3296,f1377]) ).
fof(f8163,definition,
( sQ706_spl
<=> compose(h,a) = compose(h,a) ),
introduced(definition,[new_symbols(definition,[sQ706_spl])],[split_symbol_definition]) ).
fof(f8166,plain,
( ~ sQ219_spl
| sQ706_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f8159,f3284,f8163,f3295]) ).
fof(f8167,plain,
( ~ sQ219_spl
| sQ703_spl
| ~ sQ203_spl ),
inference(split_clause,[status(thm)],[f8160,f3216,f8146,f3295]) ).
fof(f8171,plain,
( compose(domain(compose(a,b)),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1479]) ).
fof(f8172,plain,
( compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1479]) ).
fof(f8173,plain,
( compose(domain(compose(h,a)),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1479]) ).
fof(f8174,plain,
( compose(domain(compose(g,a)),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1479]) ).
fof(f8175,plain,
( compose(domain(g),compose(g,compose(g,a))) = compose(g,compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1479]) ).
fof(f8181,definition,
( sQ707_spl
<=> compose(domain(compose(a,b)),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ707_spl])],[split_symbol_definition]) ).
fof(f8184,plain,
( sQ707_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8171,f1555,f8181]) ).
fof(f8185,definition,
( sQ708_spl
<=> compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ708_spl])],[split_symbol_definition]) ).
fof(f8188,plain,
( sQ708_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8172,f1555,f8185]) ).
fof(f8189,definition,
( sQ709_spl
<=> compose(domain(compose(h,a)),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ709_spl])],[split_symbol_definition]) ).
fof(f8192,plain,
( sQ709_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8173,f693,f8189]) ).
fof(f8193,definition,
( sQ710_spl
<=> compose(domain(compose(g,a)),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ710_spl])],[split_symbol_definition]) ).
fof(f8196,plain,
( sQ710_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8174,f693,f8193]) ).
fof(f8197,definition,
( sQ711_spl
<=> compose(domain(g),compose(g,compose(g,a))) = compose(g,compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ711_spl])],[split_symbol_definition]) ).
fof(f8200,plain,
( sQ711_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f8175,f584,f8197]) ).
fof(f8206,plain,
( compose(domain(h),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1497]) ).
fof(f8207,plain,
( compose(domain(h),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1497]) ).
fof(f8208,plain,
( compose(domain(h),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1497]) ).
fof(f8209,plain,
( compose(domain(h),compose(compose(h,a),compose(a,b))) = compose(compose(h,a),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1497]) ).
fof(f8215,definition,
( sQ712_spl
<=> compose(domain(h),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ712_spl])],[split_symbol_definition]) ).
fof(f8218,plain,
( sQ712_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8206,f693,f8215]) ).
fof(f8219,definition,
( sQ713_spl
<=> compose(domain(h),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ713_spl])],[split_symbol_definition]) ).
fof(f8222,plain,
( sQ713_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8207,f693,f8219]) ).
fof(f8223,definition,
( sQ714_spl
<=> compose(domain(h),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ714_spl])],[split_symbol_definition]) ).
fof(f8226,plain,
( sQ714_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8208,f693,f8223]) ).
fof(f8227,definition,
( sQ715_spl
<=> compose(domain(h),compose(compose(h,a),compose(a,b))) = compose(compose(h,a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ715_spl])],[split_symbol_definition]) ).
fof(f8230,plain,
( sQ715_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8209,f715,f8227]) ).
fof(f8234,plain,
( compose(domain(compose(a,b)),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1481]) ).
fof(f8235,plain,
( compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1481]) ).
fof(f8236,plain,
( compose(domain(compose(h,a)),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1481]) ).
fof(f8237,plain,
( compose(domain(compose(g,a)),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1481]) ).
fof(f8238,plain,
( compose(domain(g),compose(g,compose(h,a))) = compose(g,compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1481]) ).
fof(f8244,definition,
( sQ716_spl
<=> compose(domain(compose(a,b)),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ716_spl])],[split_symbol_definition]) ).
fof(f8247,plain,
( sQ716_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8234,f1555,f8244]) ).
fof(f8248,definition,
( sQ717_spl
<=> compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ717_spl])],[split_symbol_definition]) ).
fof(f8251,plain,
( sQ717_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8235,f1555,f8248]) ).
fof(f8252,definition,
( sQ718_spl
<=> compose(domain(compose(h,a)),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ718_spl])],[split_symbol_definition]) ).
fof(f8255,plain,
( sQ718_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8236,f693,f8252]) ).
fof(f8256,definition,
( sQ719_spl
<=> compose(domain(compose(g,a)),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ719_spl])],[split_symbol_definition]) ).
fof(f8259,plain,
( sQ719_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8237,f693,f8256]) ).
fof(f8260,definition,
( sQ720_spl
<=> compose(domain(g),compose(g,compose(h,a))) = compose(g,compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ720_spl])],[split_symbol_definition]) ).
fof(f8263,plain,
( sQ720_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f8238,f584,f8260]) ).
fof(f8271,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)],[f120,f1482]) ).
fof(f8272,plain,
( compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f581,f1482]) ).
fof(f8273,plain,
( compose(domain(compose(h,a)),compose(compose(h,a),compose(a,b))) = compose(compose(h,a),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f131,f1482]) ).
fof(f8274,plain,
( compose(domain(compose(g,a)),compose(compose(g,a),compose(a,b))) = compose(compose(g,a),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f130,f1482]) ).
fof(f8275,plain,
( compose(domain(g),compose(g,compose(a,b))) = compose(g,compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f1482]) ).
fof(f8284,definition,
( sQ721_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,[sQ721_spl])],[split_symbol_definition]) ).
fof(f8287,plain,
( sQ721_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f8271,f1570,f8284]) ).
fof(f8288,definition,
( sQ722_spl
<=> compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ722_spl])],[split_symbol_definition]) ).
fof(f8291,plain,
( sQ722_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f8272,f1570,f8288]) ).
fof(f8292,definition,
( sQ723_spl
<=> compose(domain(compose(h,a)),compose(compose(h,a),compose(a,b))) = compose(compose(h,a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ723_spl])],[split_symbol_definition]) ).
fof(f8295,plain,
( sQ723_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8273,f715,f8292]) ).
fof(f8296,definition,
( sQ724_spl
<=> compose(domain(compose(g,a)),compose(compose(g,a),compose(a,b))) = compose(compose(g,a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ724_spl])],[split_symbol_definition]) ).
fof(f8299,plain,
( sQ724_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8274,f715,f8296]) ).
fof(f8300,definition,
( sQ725_spl
<=> compose(domain(g),compose(g,compose(a,b))) = compose(g,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ725_spl])],[split_symbol_definition]) ).
fof(f8303,plain,
( sQ725_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8275,f606,f8300]) ).
fof(f8312,plain,
( compose(compose(a,b),compose(codomain(compose(a,b)),compose(g,a))) = compose(compose(a,b),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1518]) ).
fof(f8313,plain,
( compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1518]) ).
fof(f8314,plain,
( compose(compose(h,a),compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(h,a),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1518]) ).
fof(f8315,plain,
( compose(compose(g,a),compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(g,a),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1518]) ).
fof(f8316,plain,
( compose(g,compose(codomain(g),compose(g,a))) = compose(g,compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1518]) ).
fof(f8317,plain,
( compose(h,compose(codomain(h),compose(g,a))) = compose(h,compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1518]) ).
fof(f8318,plain,
( compose(a,compose(codomain(a),compose(g,a))) = compose(a,compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f1518]) ).
fof(f8322,definition,
( sQ726_spl
<=> compose(compose(a,b),compose(codomain(compose(a,b)),compose(g,a))) = compose(compose(a,b),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ726_spl])],[split_symbol_definition]) ).
fof(f8325,plain,
( sQ726_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8312,f1555,f8322]) ).
fof(f8326,definition,
( sQ727_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ727_spl])],[split_symbol_definition]) ).
fof(f8329,plain,
( sQ727_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8313,f1555,f8326]) ).
fof(f8330,definition,
( sQ728_spl
<=> compose(compose(h,a),compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(h,a),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ728_spl])],[split_symbol_definition]) ).
fof(f8333,plain,
( sQ728_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8314,f693,f8330]) ).
fof(f8334,definition,
( sQ729_spl
<=> compose(compose(g,a),compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(g,a),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ729_spl])],[split_symbol_definition]) ).
fof(f8337,plain,
( sQ729_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8315,f693,f8334]) ).
fof(f8338,definition,
( sQ730_spl
<=> compose(g,compose(codomain(g),compose(g,a))) = compose(g,compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ730_spl])],[split_symbol_definition]) ).
fof(f8341,plain,
( sQ730_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f8316,f584,f8338]) ).
fof(f8342,definition,
( sQ731_spl
<=> compose(h,compose(codomain(h),compose(g,a))) = compose(h,compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ731_spl])],[split_symbol_definition]) ).
fof(f8345,plain,
( sQ731_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f8317,f584,f8342]) ).
fof(f8346,definition,
( sQ732_spl
<=> compose(a,compose(codomain(a),compose(g,a))) = compose(a,compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ732_spl])],[split_symbol_definition]) ).
fof(f8349,plain,
( sQ732_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8318,f693,f8346]) ).
fof(f8353,plain,
( compose(compose(a,b),compose(codomain(compose(a,b)),compose(h,a))) = compose(compose(a,b),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1520]) ).
fof(f8354,plain,
( compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1520]) ).
fof(f8355,plain,
( compose(compose(h,a),compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(h,a),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1520]) ).
fof(f8356,plain,
( compose(compose(g,a),compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(g,a),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1520]) ).
fof(f8357,plain,
( compose(g,compose(codomain(g),compose(h,a))) = compose(g,compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1520]) ).
fof(f8358,plain,
( compose(h,compose(codomain(h),compose(h,a))) = compose(h,compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1520]) ).
fof(f8359,plain,
( compose(a,compose(codomain(a),compose(h,a))) = compose(a,compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f1520]) ).
fof(f8363,definition,
( sQ733_spl
<=> compose(compose(a,b),compose(codomain(compose(a,b)),compose(h,a))) = compose(compose(a,b),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ733_spl])],[split_symbol_definition]) ).
fof(f8366,plain,
( sQ733_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8353,f1555,f8363]) ).
fof(f8367,definition,
( sQ734_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ734_spl])],[split_symbol_definition]) ).
fof(f8370,plain,
( sQ734_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8354,f1555,f8367]) ).
fof(f8371,definition,
( sQ735_spl
<=> compose(compose(h,a),compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(h,a),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ735_spl])],[split_symbol_definition]) ).
fof(f8374,plain,
( sQ735_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8355,f693,f8371]) ).
fof(f8375,definition,
( sQ736_spl
<=> compose(compose(g,a),compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(g,a),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ736_spl])],[split_symbol_definition]) ).
fof(f8378,plain,
( sQ736_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8356,f693,f8375]) ).
fof(f8379,definition,
( sQ737_spl
<=> compose(g,compose(codomain(g),compose(h,a))) = compose(g,compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ737_spl])],[split_symbol_definition]) ).
fof(f8382,plain,
( sQ737_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f8357,f584,f8379]) ).
fof(f8383,definition,
( sQ738_spl
<=> compose(h,compose(codomain(h),compose(h,a))) = compose(h,compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ738_spl])],[split_symbol_definition]) ).
fof(f8386,plain,
( sQ738_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f8358,f584,f8383]) ).
fof(f8387,definition,
( sQ739_spl
<=> compose(a,compose(codomain(a),compose(h,a))) = compose(a,compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ739_spl])],[split_symbol_definition]) ).
fof(f8390,plain,
( sQ739_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8359,f693,f8387]) ).
fof(f8396,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)],[f120,f1521]) ).
fof(f8397,plain,
( compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f581,f1521]) ).
fof(f8398,plain,
( compose(compose(h,a),compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(h,a),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f131,f1521]) ).
fof(f8399,plain,
( compose(compose(g,a),compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(g,a),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f130,f1521]) ).
fof(f8400,plain,
( compose(g,compose(codomain(g),compose(a,b))) = compose(g,compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f1521]) ).
fof(f8401,plain,
( compose(h,compose(codomain(h),compose(a,b))) = compose(h,compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f1521]) ).
fof(f8402,plain,
( compose(a,compose(codomain(a),compose(a,b))) = compose(a,compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f1521]) ).
fof(f8408,definition,
( sQ740_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,[sQ740_spl])],[split_symbol_definition]) ).
fof(f8411,plain,
( sQ740_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f8396,f1570,f8408]) ).
fof(f8412,definition,
( sQ741_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ741_spl])],[split_symbol_definition]) ).
fof(f8415,plain,
( sQ741_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f8397,f1570,f8412]) ).
fof(f8416,definition,
( sQ742_spl
<=> compose(compose(h,a),compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(h,a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ742_spl])],[split_symbol_definition]) ).
fof(f8419,plain,
( sQ742_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8398,f715,f8416]) ).
fof(f8420,definition,
( sQ743_spl
<=> compose(compose(g,a),compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(g,a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ743_spl])],[split_symbol_definition]) ).
fof(f8423,plain,
( sQ743_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8399,f715,f8420]) ).
fof(f8424,definition,
( sQ744_spl
<=> compose(g,compose(codomain(g),compose(a,b))) = compose(g,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ744_spl])],[split_symbol_definition]) ).
fof(f8427,plain,
( sQ744_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8400,f606,f8424]) ).
fof(f8428,definition,
( sQ745_spl
<=> compose(h,compose(codomain(h),compose(a,b))) = compose(h,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ745_spl])],[split_symbol_definition]) ).
fof(f8431,plain,
( sQ745_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8401,f606,f8428]) ).
fof(f8432,definition,
( sQ746_spl
<=> compose(a,compose(codomain(a),compose(a,b))) = compose(a,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ746_spl])],[split_symbol_definition]) ).
fof(f8435,plain,
( sQ746_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8402,f715,f8432]) ).
fof(f8441,plain,
( compose(domain(h),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1498]) ).
fof(f8442,plain,
( compose(domain(h),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1498]) ).
fof(f8443,plain,
( compose(domain(h),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1498]) ).
fof(f8444,plain,
( compose(domain(h),compose(compose(g,a),compose(a,b))) = compose(compose(g,a),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1498]) ).
fof(f8450,definition,
( sQ747_spl
<=> compose(domain(h),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ747_spl])],[split_symbol_definition]) ).
fof(f8453,plain,
( sQ747_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8441,f693,f8450]) ).
fof(f8454,definition,
( sQ748_spl
<=> compose(domain(h),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ748_spl])],[split_symbol_definition]) ).
fof(f8457,plain,
( sQ748_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8442,f693,f8454]) ).
fof(f8458,definition,
( sQ749_spl
<=> compose(domain(h),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ749_spl])],[split_symbol_definition]) ).
fof(f8461,plain,
( sQ749_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8443,f693,f8458]) ).
fof(f8462,definition,
( sQ750_spl
<=> compose(domain(h),compose(compose(g,a),compose(a,b))) = compose(compose(g,a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ750_spl])],[split_symbol_definition]) ).
fof(f8465,plain,
( sQ750_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8444,f715,f8462]) ).
fof(f8469,plain,
( compose(compose(g,a),compose(g,a)) = compose(compose(compose(g,a),domain(compose(g,a))),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f3665]) ).
fof(f8470,plain,
( compose(compose(g,a),compose(h,compose(a,b))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f3665]) ).
fof(f8471,plain,
( compose(compose(g,a),compose(h,a)) = compose(compose(compose(g,a),domain(compose(h,a))),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f3665]) ).
fof(f8472,plain,
( compose(compose(g,a),compose(a,b)) = compose(compose(compose(g,a),domain(compose(a,b))),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f3665]) ).
fof(f8473,plain,
! [X0] :
( compose(compose(g,a),domain(X0)) = compose(compose(compose(g,a),domain(domain(X0))),domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f3665]) ).
fof(f8474,plain,
! [X0] :
( compose(compose(g,a),codomain(X0)) = compose(compose(compose(g,a),domain(codomain(X0))),codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f3665]) ).
fof(f8479,definition,
( sQ751_spl
<=> compose(compose(g,a),compose(g,a)) = compose(compose(compose(g,a),domain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ751_spl])],[split_symbol_definition]) ).
fof(f8482,plain,
( sQ751_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8469,f693,f8479]) ).
fof(f8483,definition,
( sQ752_spl
<=> compose(compose(g,a),compose(h,compose(a,b))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ752_spl])],[split_symbol_definition]) ).
fof(f8486,plain,
( sQ752_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8470,f693,f8483]) ).
fof(f8487,definition,
( sQ753_spl
<=> compose(compose(g,a),compose(h,a)) = compose(compose(compose(g,a),domain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ753_spl])],[split_symbol_definition]) ).
fof(f8490,plain,
( sQ753_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8471,f693,f8487]) ).
fof(f8491,definition,
( sQ754_spl
<=> compose(compose(g,a),compose(a,b)) = compose(compose(compose(g,a),domain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ754_spl])],[split_symbol_definition]) ).
fof(f8494,plain,
( sQ754_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8472,f715,f8491]) ).
fof(f8495,plain,
! [X0] :
( compose(compose(g,a),domain(X0)) = compose(compose(compose(g,a),domain(X0)),domain(X0))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f8473]) ).
fof(f8496,plain,
! [X0] :
( compose(compose(g,a),codomain(X0)) = compose(compose(compose(g,a),codomain(X0)),codomain(X0))
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f8474]) ).
fof(f8500,plain,
( compose(compose(g,a),compose(g,a)) = compose(compose(compose(g,a),compose(g,a)),codomain(compose(g,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f3666]) ).
fof(f8501,plain,
( compose(compose(g,a),compose(h,compose(a,b))) = compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(compose(h,compose(a,b))))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f3666]) ).
fof(f8502,plain,
( compose(compose(g,a),compose(h,a)) = compose(compose(compose(g,a),compose(h,a)),codomain(compose(h,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f3666]) ).
fof(f8503,plain,
( compose(compose(g,a),compose(a,b)) = compose(compose(compose(g,a),compose(a,b)),codomain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f3666]) ).
fof(f8510,definition,
( sQ755_spl
<=> compose(compose(g,a),compose(g,a)) = compose(compose(compose(g,a),compose(g,a)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ755_spl])],[split_symbol_definition]) ).
fof(f8513,plain,
( sQ755_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8500,f693,f8510]) ).
fof(f8514,definition,
( sQ756_spl
<=> compose(compose(g,a),compose(h,compose(a,b))) = compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ756_spl])],[split_symbol_definition]) ).
fof(f8517,plain,
( sQ756_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8501,f693,f8514]) ).
fof(f8518,definition,
( sQ757_spl
<=> compose(compose(g,a),compose(h,a)) = compose(compose(compose(g,a),compose(h,a)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ757_spl])],[split_symbol_definition]) ).
fof(f8521,plain,
( sQ757_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8502,f693,f8518]) ).
fof(f8522,definition,
( sQ758_spl
<=> compose(compose(g,a),compose(a,b)) = compose(compose(compose(g,a),compose(a,b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ758_spl])],[split_symbol_definition]) ).
fof(f8525,plain,
( sQ758_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8503,f715,f8522]) ).
fof(f8531,plain,
( compose(compose(h,a),compose(g,a)) = compose(compose(compose(h,a),domain(compose(g,a))),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f4976]) ).
fof(f8532,plain,
( compose(compose(h,a),compose(h,compose(a,b))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f4976]) ).
fof(f8533,plain,
( compose(compose(h,a),compose(h,a)) = compose(compose(compose(h,a),domain(compose(h,a))),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f4976]) ).
fof(f8534,plain,
( compose(compose(h,a),compose(a,b)) = compose(compose(compose(h,a),domain(compose(a,b))),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f4976]) ).
fof(f8535,plain,
! [X0] :
( compose(compose(h,a),domain(X0)) = compose(compose(compose(h,a),domain(domain(X0))),domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f4976]) ).
fof(f8536,plain,
! [X0] :
( compose(compose(h,a),codomain(X0)) = compose(compose(compose(h,a),domain(codomain(X0))),codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f4976]) ).
fof(f8541,definition,
( sQ759_spl
<=> compose(compose(h,a),compose(g,a)) = compose(compose(compose(h,a),domain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ759_spl])],[split_symbol_definition]) ).
fof(f8544,plain,
( sQ759_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8531,f693,f8541]) ).
fof(f8545,definition,
( sQ760_spl
<=> compose(compose(h,a),compose(h,compose(a,b))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ760_spl])],[split_symbol_definition]) ).
fof(f8548,plain,
( sQ760_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8532,f693,f8545]) ).
fof(f8549,definition,
( sQ761_spl
<=> compose(compose(h,a),compose(h,a)) = compose(compose(compose(h,a),domain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ761_spl])],[split_symbol_definition]) ).
fof(f8552,plain,
( sQ761_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8533,f693,f8549]) ).
fof(f8553,definition,
( sQ762_spl
<=> compose(compose(h,a),compose(a,b)) = compose(compose(compose(h,a),domain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ762_spl])],[split_symbol_definition]) ).
fof(f8556,plain,
( sQ762_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8534,f715,f8553]) ).
fof(f8557,plain,
! [X0] :
( compose(compose(h,a),domain(X0)) = compose(compose(compose(h,a),domain(X0)),domain(X0))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f8535]) ).
fof(f8558,plain,
! [X0] :
( compose(compose(h,a),codomain(X0)) = compose(compose(compose(h,a),codomain(X0)),codomain(X0))
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f8536]) ).
fof(f8562,plain,
( compose(compose(h,a),compose(g,a)) = compose(compose(compose(h,a),compose(g,a)),codomain(compose(g,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f4977]) ).
fof(f8563,plain,
( compose(compose(h,a),compose(h,compose(a,b))) = compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(compose(h,compose(a,b))))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f4977]) ).
fof(f8564,plain,
( compose(compose(h,a),compose(h,a)) = compose(compose(compose(h,a),compose(h,a)),codomain(compose(h,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f4977]) ).
fof(f8565,plain,
( compose(compose(h,a),compose(a,b)) = compose(compose(compose(h,a),compose(a,b)),codomain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f4977]) ).
fof(f8572,definition,
( sQ763_spl
<=> compose(compose(h,a),compose(g,a)) = compose(compose(compose(h,a),compose(g,a)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ763_spl])],[split_symbol_definition]) ).
fof(f8575,plain,
( sQ763_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8562,f693,f8572]) ).
fof(f8576,definition,
( sQ764_spl
<=> compose(compose(h,a),compose(h,compose(a,b))) = compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ764_spl])],[split_symbol_definition]) ).
fof(f8579,plain,
( sQ764_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8563,f693,f8576]) ).
fof(f8580,definition,
( sQ765_spl
<=> compose(compose(h,a),compose(h,a)) = compose(compose(compose(h,a),compose(h,a)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ765_spl])],[split_symbol_definition]) ).
fof(f8583,plain,
( sQ765_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8564,f693,f8580]) ).
fof(f8584,definition,
( sQ766_spl
<=> compose(compose(h,a),compose(a,b)) = compose(compose(compose(h,a),compose(a,b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ766_spl])],[split_symbol_definition]) ).
fof(f8587,plain,
( sQ766_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8565,f715,f8584]) ).
fof(f8593,plain,
( compose(compose(a,b),compose(codomain(b),compose(g,a))) = compose(compose(a,b),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1530]) ).
fof(f8594,plain,
( compose(compose(a,b),compose(codomain(b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1530]) ).
fof(f8595,plain,
( compose(compose(a,b),compose(codomain(b),compose(h,a))) = compose(compose(a,b),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1530]) ).
fof(f8596,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)],[f60,f1530]) ).
fof(f8599,definition,
( sQ767_spl
<=> compose(compose(a,b),compose(codomain(b),compose(g,a))) = compose(compose(a,b),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ767_spl])],[split_symbol_definition]) ).
fof(f8602,plain,
( sQ767_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8593,f1555,f8599]) ).
fof(f8603,definition,
( sQ768_spl
<=> compose(compose(a,b),compose(codomain(b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ768_spl])],[split_symbol_definition]) ).
fof(f8606,plain,
( sQ768_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8594,f1555,f8603]) ).
fof(f8607,definition,
( sQ769_spl
<=> compose(compose(a,b),compose(codomain(b),compose(h,a))) = compose(compose(a,b),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ769_spl])],[split_symbol_definition]) ).
fof(f8610,plain,
( sQ769_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f8595,f1555,f8607]) ).
fof(f8611,definition,
( sQ770_spl
<=> compose(compose(a,b),compose(codomain(b),compose(a,b))) = compose(compose(a,b),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ770_spl])],[split_symbol_definition]) ).
fof(f8614,plain,
( sQ770_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f8596,f1570,f8611]) ).
fof(f8616,plain,
( compose(compose(h,a),compose(domain(b),compose(g,a))) = compose(compose(h,a),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1532]) ).
fof(f8617,plain,
( compose(compose(h,a),compose(domain(b),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1532]) ).
fof(f8618,plain,
( compose(compose(h,a),compose(domain(b),compose(h,a))) = compose(compose(h,a),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1532]) ).
fof(f8619,plain,
( compose(compose(h,a),compose(domain(b),compose(a,b))) = compose(compose(h,a),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1532]) ).
fof(f8623,definition,
( sQ771_spl
<=> compose(compose(h,a),compose(domain(b),compose(g,a))) = compose(compose(h,a),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ771_spl])],[split_symbol_definition]) ).
fof(f8626,plain,
( sQ771_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8616,f693,f8623]) ).
fof(f8627,definition,
( sQ772_spl
<=> compose(compose(h,a),compose(domain(b),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ772_spl])],[split_symbol_definition]) ).
fof(f8630,plain,
( sQ772_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8617,f693,f8627]) ).
fof(f8631,definition,
( sQ773_spl
<=> compose(compose(h,a),compose(domain(b),compose(h,a))) = compose(compose(h,a),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ773_spl])],[split_symbol_definition]) ).
fof(f8634,plain,
( sQ773_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8618,f693,f8631]) ).
fof(f8635,definition,
( sQ774_spl
<=> compose(compose(h,a),compose(domain(b),compose(a,b))) = compose(compose(h,a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ774_spl])],[split_symbol_definition]) ).
fof(f8638,plain,
( sQ774_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8619,f715,f8635]) ).
fof(f8640,plain,
( compose(compose(g,a),compose(domain(b),compose(g,a))) = compose(compose(g,a),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1533]) ).
fof(f8641,plain,
( compose(compose(g,a),compose(domain(b),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1533]) ).
fof(f8642,plain,
( compose(compose(g,a),compose(domain(b),compose(h,a))) = compose(compose(g,a),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1533]) ).
fof(f8643,plain,
( compose(compose(g,a),compose(domain(b),compose(a,b))) = compose(compose(g,a),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1533]) ).
fof(f8647,definition,
( sQ775_spl
<=> compose(compose(g,a),compose(domain(b),compose(g,a))) = compose(compose(g,a),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ775_spl])],[split_symbol_definition]) ).
fof(f8650,plain,
( sQ775_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8640,f693,f8647]) ).
fof(f8651,definition,
( sQ776_spl
<=> compose(compose(g,a),compose(domain(b),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ776_spl])],[split_symbol_definition]) ).
fof(f8654,plain,
( sQ776_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8641,f693,f8651]) ).
fof(f8655,definition,
( sQ777_spl
<=> compose(compose(g,a),compose(domain(b),compose(h,a))) = compose(compose(g,a),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ777_spl])],[split_symbol_definition]) ).
fof(f8658,plain,
( sQ777_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8642,f693,f8655]) ).
fof(f8659,definition,
( sQ778_spl
<=> compose(compose(g,a),compose(domain(b),compose(a,b))) = compose(compose(g,a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ778_spl])],[split_symbol_definition]) ).
fof(f8662,plain,
( sQ778_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8643,f715,f8659]) ).
fof(f8666,plain,
! [X0] :
( compose(g,compose(codomain(compose(a,b)),X0)) = compose(compose(g,codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f1799]) ).
fof(f8667,plain,
! [X0] :
( compose(g,compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(g,codomain(compose(h,compose(a,b)))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f1799]) ).
fof(f8668,plain,
! [X0] :
( compose(g,compose(codomain(compose(h,a)),X0)) = compose(compose(g,codomain(compose(h,a))),X0)
| codomain(compose(h,a)) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f1799]) ).
fof(f8669,plain,
! [X0] :
( compose(g,compose(codomain(compose(g,a)),X0)) = compose(compose(g,codomain(compose(g,a))),X0)
| codomain(compose(g,a)) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f1799]) ).
fof(f8670,plain,
! [X0] :
( compose(g,compose(codomain(g),X0)) = compose(compose(g,codomain(g)),X0)
| codomain(g) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f1799]) ).
fof(f8671,plain,
! [X0] :
( compose(g,compose(codomain(h),X0)) = compose(compose(g,codomain(h)),X0)
| codomain(h) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f1799]) ).
fof(f8672,plain,
! [X0] :
( compose(g,compose(codomain(a),X0)) = compose(compose(g,codomain(a)),X0)
| codomain(a) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f1799]) ).
fof(f8686,definition,
! [X0] :
( sQ779_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,[sQ779_spl])],[split_symbol_definition]) ).
fof(f8689,plain,
( sQ779_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f8666,f1570,f8686]) ).
fof(f8690,definition,
! [X0] :
( sQ780_spl
<=> ( compose(g,compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(g,codomain(compose(h,compose(a,b)))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ780_spl])],[split_symbol_definition]) ).
fof(f8693,plain,
( sQ780_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f8667,f1570,f8690]) ).
fof(f8694,definition,
! [X0] :
( sQ781_spl
<=> ( compose(g,compose(codomain(compose(h,a)),X0)) = compose(compose(g,codomain(compose(h,a))),X0)
| codomain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ781_spl])],[split_symbol_definition]) ).
fof(f8697,plain,
( sQ781_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8668,f715,f8694]) ).
fof(f8698,definition,
! [X0] :
( sQ782_spl
<=> ( compose(g,compose(codomain(compose(g,a)),X0)) = compose(compose(g,codomain(compose(g,a))),X0)
| codomain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ782_spl])],[split_symbol_definition]) ).
fof(f8701,plain,
( sQ782_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8669,f715,f8698]) ).
fof(f8702,definition,
! [X0] :
( sQ783_spl
<=> ( compose(g,compose(codomain(g),X0)) = compose(compose(g,codomain(g)),X0)
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ783_spl])],[split_symbol_definition]) ).
fof(f8705,plain,
( sQ783_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8670,f606,f8702]) ).
fof(f8706,definition,
! [X0] :
( sQ784_spl
<=> ( compose(g,compose(codomain(h),X0)) = compose(compose(g,codomain(h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ784_spl])],[split_symbol_definition]) ).
fof(f8709,plain,
( sQ784_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8671,f606,f8706]) ).
fof(f8710,definition,
! [X0] :
( sQ785_spl
<=> ( compose(g,compose(codomain(a),X0)) = compose(compose(g,codomain(a)),X0)
| codomain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ785_spl])],[split_symbol_definition]) ).
fof(f8713,plain,
( sQ785_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8672,f715,f8710]) ).
fof(f8729,plain,
! [X0] :
( compose(g,compose(domain(compose(g,a)),X0)) = compose(compose(g,domain(compose(g,a))),X0)
| domain(compose(g,a)) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1800]) ).
fof(f8730,plain,
! [X0] :
( compose(g,compose(domain(compose(h,compose(a,b))),X0)) = compose(compose(g,domain(compose(h,compose(a,b)))),X0)
| domain(compose(h,compose(a,b))) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1800]) ).
fof(f8731,plain,
! [X0] :
( compose(g,compose(domain(compose(h,a)),X0)) = compose(compose(g,domain(compose(h,a))),X0)
| domain(compose(h,a)) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1800]) ).
fof(f8732,plain,
! [X0] :
( compose(g,compose(domain(compose(a,b)),X0)) = compose(compose(g,domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1800]) ).
fof(f8744,definition,
! [X0] :
( sQ786_spl
<=> ( compose(g,compose(domain(compose(g,a)),X0)) = compose(compose(g,domain(compose(g,a))),X0)
| domain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ786_spl])],[split_symbol_definition]) ).
fof(f8747,plain,
( sQ786_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f8729,f584,f8744]) ).
fof(f8748,definition,
! [X0] :
( sQ787_spl
<=> ( compose(g,compose(domain(compose(h,compose(a,b))),X0)) = compose(compose(g,domain(compose(h,compose(a,b)))),X0)
| domain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ787_spl])],[split_symbol_definition]) ).
fof(f8751,plain,
( sQ787_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f8730,f584,f8748]) ).
fof(f8752,definition,
! [X0] :
( sQ788_spl
<=> ( compose(g,compose(domain(compose(h,a)),X0)) = compose(compose(g,domain(compose(h,a))),X0)
| domain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ788_spl])],[split_symbol_definition]) ).
fof(f8755,plain,
( sQ788_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f8731,f584,f8752]) ).
fof(f8756,definition,
! [X0] :
( sQ789_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,[sQ789_spl])],[split_symbol_definition]) ).
fof(f8759,plain,
( sQ789_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8732,f606,f8756]) ).
fof(f8771,plain,
( compose(g,compose(compose(h,a),domain(b))) = compose(compose(g,compose(h,a)),domain(b))
| domain(a) != domain(compose(h,a)) ),
inference(resolution,[status(thm)],[f1734,f131]) ).
fof(f8772,plain,
( compose(g,compose(compose(g,a),domain(b))) = compose(compose(g,compose(g,a)),domain(b))
| domain(a) != domain(compose(g,a)) ),
inference(resolution,[status(thm)],[f1734,f130]) ).
fof(f8773,plain,
( compose(g,compose(g,domain(a))) = compose(compose(g,g),domain(a))
| domain(a) != domain(g) ),
inference(resolution,[status(thm)],[f1734,f74]) ).
fof(f8774,plain,
( compose(g,compose(h,domain(a))) = compose(compose(g,h),domain(a))
| domain(a) != domain(h) ),
inference(resolution,[status(thm)],[f1734,f69]) ).
fof(f8775,plain,
( compose(g,compose(a,domain(b))) = compose(compose(g,a),domain(b))
| domain(a) != domain(a) ),
inference(resolution,[status(thm)],[f1734,f22]) ).
fof(f8778,plain,
! [X0] :
( compose(g,compose(compose(a,b),domain(X0))) = compose(compose(g,compose(a,b)),domain(X0))
| codomain(b) != domain(X0)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f1734]) ).
fof(f8779,plain,
! [X0] :
( compose(g,compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(g,compose(h,compose(a,b))),domain(X0))
| codomain(b) != domain(X0)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f1734]) ).
fof(f8780,plain,
! [X0] :
( compose(g,compose(compose(h,a),domain(X0))) = compose(compose(g,compose(h,a)),domain(X0))
| domain(b) != domain(X0)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f1734]) ).
fof(f8781,plain,
! [X0] :
( compose(g,compose(compose(g,a),domain(X0))) = compose(compose(g,compose(g,a)),domain(X0))
| domain(b) != domain(X0)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f1734]) ).
fof(f8782,plain,
! [X0] :
( compose(g,compose(g,domain(X0))) = compose(compose(g,g),domain(X0))
| domain(a) != domain(X0)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f1734]) ).
fof(f8783,plain,
! [X0] :
( compose(g,compose(h,domain(X0))) = compose(compose(g,h),domain(X0))
| domain(a) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1734]) ).
fof(f8784,plain,
! [X0] :
( compose(g,compose(a,domain(X0))) = compose(compose(g,a),domain(X0))
| domain(b) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f1734]) ).
fof(f8785,plain,
! [X0,X1] :
( compose(g,compose(codomain(X0),domain(X1))) = compose(compose(g,codomain(X0)),domain(X1))
| codomain(X0) != domain(X1)
| domain(a) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f1734]) ).
fof(f8786,plain,
! [X0,X1] :
( compose(g,compose(domain(X0),domain(X1))) = compose(compose(g,domain(X0)),domain(X1))
| domain(X0) != domain(X1)
| domain(a) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f1734]) ).
fof(f8793,definition,
( sQ790_spl
<=> compose(g,compose(compose(h,a),domain(b))) = compose(compose(g,compose(h,a)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ790_spl])],[split_symbol_definition]) ).
fof(f8796,plain,
( sQ790_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f8771,f1736,f8793]) ).
fof(f8797,definition,
( sQ791_spl
<=> compose(g,compose(compose(g,a),domain(b))) = compose(compose(g,compose(g,a)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ791_spl])],[split_symbol_definition]) ).
fof(f8800,plain,
( sQ791_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f8772,f1743,f8797]) ).
fof(f8801,definition,
( sQ792_spl
<=> compose(g,compose(g,domain(a))) = compose(compose(g,g),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ792_spl])],[split_symbol_definition]) ).
fof(f8804,plain,
( sQ792_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f8773,f591,f8801]) ).
fof(f8805,definition,
( sQ793_spl
<=> compose(g,compose(h,domain(a))) = compose(compose(g,h),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ793_spl])],[split_symbol_definition]) ).
fof(f8808,plain,
( sQ793_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f8774,f584,f8805]) ).
fof(f8809,definition,
( sQ794_spl
<=> compose(g,compose(a,domain(b))) = compose(compose(g,a),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ794_spl])],[split_symbol_definition]) ).
fof(f8812,plain,
( sQ794_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8775,f606,f8809]) ).
fof(f8818,definition,
! [X0] :
( sQ795_spl
<=> ( compose(g,compose(compose(a,b),domain(X0))) = compose(compose(g,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ795_spl])],[split_symbol_definition]) ).
fof(f8819,plain,
! [X0] :
( ~ sQ795_spl
| compose(g,compose(compose(a,b),domain(X0))) = compose(compose(g,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ),
inference(component_clause,[status(thm)],[f8818]) ).
fof(f8821,plain,
( sQ795_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f8778,f1765,f8818]) ).
fof(f8822,definition,
! [X0] :
( sQ796_spl
<=> ( compose(g,compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(g,compose(h,compose(a,b))),domain(X0))
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ796_spl])],[split_symbol_definition]) ).
fof(f8825,plain,
( sQ796_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f8779,f1772,f8822]) ).
fof(f8826,definition,
! [X0] :
( sQ797_spl
<=> ( compose(g,compose(compose(h,a),domain(X0))) = compose(compose(g,compose(h,a)),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ797_spl])],[split_symbol_definition]) ).
fof(f8829,plain,
( sQ797_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f8780,f1736,f8826]) ).
fof(f8830,definition,
! [X0] :
( sQ798_spl
<=> ( compose(g,compose(compose(g,a),domain(X0))) = compose(compose(g,compose(g,a)),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ798_spl])],[split_symbol_definition]) ).
fof(f8833,plain,
( sQ798_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f8781,f1743,f8830]) ).
fof(f8834,definition,
! [X0] :
( sQ799_spl
<=> ( compose(g,compose(g,domain(X0))) = compose(compose(g,g),domain(X0))
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ799_spl])],[split_symbol_definition]) ).
fof(f8837,plain,
( sQ799_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f8782,f591,f8834]) ).
fof(f8838,definition,
! [X0] :
( sQ800_spl
<=> ( compose(g,compose(h,domain(X0))) = compose(compose(g,h),domain(X0))
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ800_spl])],[split_symbol_definition]) ).
fof(f8841,plain,
( sQ800_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f8783,f584,f8838]) ).
fof(f8842,definition,
! [X0] :
( sQ801_spl
<=> ( compose(g,compose(a,domain(X0))) = compose(compose(g,a),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ801_spl])],[split_symbol_definition]) ).
fof(f8845,plain,
( sQ801_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8784,f606,f8842]) ).
fof(f8846,plain,
! [X0,X1] :
( compose(g,compose(codomain(X0),domain(X1))) = compose(compose(g,codomain(X0)),domain(X1))
| codomain(X0) != domain(X1)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f8785]) ).
fof(f8847,plain,
! [X0,X1] :
( compose(g,compose(domain(X0),domain(X1))) = compose(compose(g,domain(X0)),domain(X1))
| domain(X0) != domain(X1)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f8786]) ).
fof(f8861,plain,
! [X0] :
( ~ sQ795_spl
| compose(g,compose(compose(a,b),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f29,f8819]) ).
fof(f8862,plain,
( compose(g,compose(compose(a,b),codomain(b))) = compose(compose(g,compose(a,b)),codomain(b))
| domain(a) != domain(compose(a,b)) ),
inference(resolution,[status(thm)],[f1735,f120]) ).
fof(f8863,plain,
( compose(g,compose(compose(h,compose(a,b)),codomain(b))) = compose(compose(g,compose(h,compose(a,b))),codomain(b))
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(resolution,[status(thm)],[f1735,f581]) ).
fof(f8865,plain,
( compose(g,compose(b,codomain(compose(a,b)))) = compose(compose(g,b),codomain(compose(a,b)))
| domain(a) != domain(b) ),
inference(resolution,[status(thm)],[f1735,f120]) ).
fof(f8866,plain,
( compose(g,compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(g,b),codomain(compose(h,compose(a,b))))
| domain(a) != domain(b) ),
inference(resolution,[status(thm)],[f1735,f581]) ).
fof(f8868,plain,
! [X0] :
( compose(g,compose(compose(a,b),codomain(X0))) = compose(compose(g,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f1735]) ).
fof(f8869,plain,
! [X0] :
( compose(g,compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(g,compose(h,compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f1735]) ).
fof(f8870,plain,
! [X0] :
( compose(g,compose(compose(h,a),codomain(X0))) = compose(compose(g,compose(h,a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f1735]) ).
fof(f8871,plain,
! [X0] :
( compose(g,compose(compose(g,a),codomain(X0))) = compose(compose(g,compose(g,a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f1735]) ).
fof(f8872,plain,
! [X0] :
( compose(g,compose(g,codomain(X0))) = compose(compose(g,g),codomain(X0))
| domain(a) != codomain(X0)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f1735]) ).
fof(f8873,plain,
! [X0] :
( compose(g,compose(h,codomain(X0))) = compose(compose(g,h),codomain(X0))
| domain(a) != codomain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1735]) ).
fof(f8874,plain,
! [X0] :
( compose(g,compose(a,codomain(X0))) = compose(compose(g,a),codomain(X0))
| domain(b) != codomain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f1735]) ).
fof(f8875,plain,
! [X0,X1] :
( compose(g,compose(codomain(X0),codomain(X1))) = compose(compose(g,codomain(X0)),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(a) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f1735]) ).
fof(f8876,plain,
! [X0,X1] :
( compose(g,compose(domain(X0),codomain(X1))) = compose(compose(g,domain(X0)),codomain(X1))
| domain(X0) != codomain(X1)
| domain(a) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f1735]) ).
fof(f8887,definition,
( sQ802_spl
<=> compose(g,compose(compose(a,b),codomain(b))) = compose(compose(g,compose(a,b)),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ802_spl])],[split_symbol_definition]) ).
fof(f8890,plain,
( sQ802_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f8862,f1765,f8887]) ).
fof(f8891,definition,
( sQ803_spl
<=> compose(g,compose(compose(h,compose(a,b)),codomain(b))) = compose(compose(g,compose(h,compose(a,b))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ803_spl])],[split_symbol_definition]) ).
fof(f8894,plain,
( sQ803_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f8863,f1772,f8891]) ).
fof(f8897,definition,
( sQ804_spl
<=> compose(g,compose(b,codomain(compose(a,b)))) = compose(compose(g,b),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ804_spl])],[split_symbol_definition]) ).
fof(f8900,plain,
( sQ804_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8865,f715,f8897]) ).
fof(f8901,definition,
( sQ805_spl
<=> compose(g,compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(g,b),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ805_spl])],[split_symbol_definition]) ).
fof(f8904,plain,
( sQ805_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8866,f715,f8901]) ).
fof(f8908,definition,
! [X0] :
( sQ806_spl
<=> ( compose(g,compose(compose(a,b),codomain(X0))) = compose(compose(g,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ806_spl])],[split_symbol_definition]) ).
fof(f8909,plain,
! [X0] :
( ~ sQ806_spl
| compose(g,compose(compose(a,b),codomain(X0))) = compose(compose(g,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(component_clause,[status(thm)],[f8908]) ).
fof(f8911,plain,
( sQ806_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f8868,f1765,f8908]) ).
fof(f8912,definition,
! [X0] :
( sQ807_spl
<=> ( compose(g,compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(g,compose(h,compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ807_spl])],[split_symbol_definition]) ).
fof(f8915,plain,
( sQ807_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f8869,f1772,f8912]) ).
fof(f8916,definition,
! [X0] :
( sQ808_spl
<=> ( compose(g,compose(compose(h,a),codomain(X0))) = compose(compose(g,compose(h,a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ808_spl])],[split_symbol_definition]) ).
fof(f8919,plain,
( sQ808_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f8870,f1736,f8916]) ).
fof(f8920,definition,
! [X0] :
( sQ809_spl
<=> ( compose(g,compose(compose(g,a),codomain(X0))) = compose(compose(g,compose(g,a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ809_spl])],[split_symbol_definition]) ).
fof(f8923,plain,
( sQ809_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f8871,f1743,f8920]) ).
fof(f8924,definition,
! [X0] :
( sQ810_spl
<=> ( compose(g,compose(g,codomain(X0))) = compose(compose(g,g),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ810_spl])],[split_symbol_definition]) ).
fof(f8927,plain,
( sQ810_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f8872,f591,f8924]) ).
fof(f8928,definition,
! [X0] :
( sQ811_spl
<=> ( compose(g,compose(h,codomain(X0))) = compose(compose(g,h),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ811_spl])],[split_symbol_definition]) ).
fof(f8931,plain,
( sQ811_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f8873,f584,f8928]) ).
fof(f8932,definition,
! [X0] :
( sQ812_spl
<=> ( compose(g,compose(a,codomain(X0))) = compose(compose(g,a),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ812_spl])],[split_symbol_definition]) ).
fof(f8935,plain,
( sQ812_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8874,f606,f8932]) ).
fof(f8936,plain,
! [X0,X1] :
( compose(g,compose(codomain(X0),codomain(X1))) = compose(compose(g,codomain(X0)),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f8875]) ).
fof(f8937,plain,
! [X0,X1] :
( compose(g,compose(domain(X0),codomain(X1))) = compose(compose(g,domain(X0)),codomain(X1))
| domain(X0) != codomain(X1)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f8876]) ).
fof(f8960,plain,
! [X0] :
( ~ sQ806_spl
| compose(g,compose(compose(a,b),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f29,f8909]) ).
fof(f8961,plain,
( compose(g,compose(domain(h),compose(g,a))) = compose(compose(g,domain(h)),compose(g,a))
| domain(a) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f1730,f15]) ).
fof(f8962,plain,
( compose(g,compose(compose(a,b),compose(g,a))) = compose(compose(g,compose(a,b)),compose(g,a))
| codomain(b) != domain(h)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f1730]) ).
fof(f8963,plain,
( compose(g,compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(g,compose(h,compose(a,b))),compose(g,a))
| codomain(b) != domain(h)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f1730]) ).
fof(f8964,plain,
( compose(g,compose(compose(h,a),compose(g,a))) = compose(compose(g,compose(h,a)),compose(g,a))
| domain(b) != domain(h)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f1730]) ).
fof(f8965,plain,
( compose(g,compose(compose(g,a),compose(g,a))) = compose(compose(g,compose(g,a)),compose(g,a))
| domain(b) != domain(h)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f1730]) ).
fof(f8966,plain,
( compose(g,compose(g,compose(g,a))) = compose(compose(g,g),compose(g,a))
| domain(a) != domain(h)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f1730]) ).
fof(f8967,plain,
( compose(g,compose(h,compose(g,a))) = compose(compose(g,h),compose(g,a))
| domain(a) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1730]) ).
fof(f8968,plain,
( compose(g,compose(a,compose(g,a))) = compose(compose(g,a),compose(g,a))
| domain(b) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f1730]) ).
fof(f8969,plain,
! [X0] :
( compose(g,compose(codomain(X0),compose(g,a))) = compose(compose(g,codomain(X0)),compose(g,a))
| codomain(X0) != domain(h)
| domain(a) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f1730]) ).
fof(f8970,plain,
! [X0] :
( compose(g,compose(domain(X0),compose(g,a))) = compose(compose(g,domain(X0)),compose(g,a))
| domain(X0) != domain(h)
| domain(a) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f1730]) ).
fof(f8971,definition,
( sQ813_spl
<=> domain(a) = domain(domain(h)) ),
introduced(definition,[new_symbols(definition,[sQ813_spl])],[split_symbol_definition]) ).
fof(f8973,plain,
( sQ813_spl
| domain(a) != domain(domain(h)) ),
inference(component_clause,[status(thm)],[f8971]) ).
fof(f8974,definition,
( sQ814_spl
<=> compose(g,compose(domain(h),compose(g,a))) = compose(compose(g,domain(h)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ814_spl])],[split_symbol_definition]) ).
fof(f8977,plain,
( sQ814_spl
| ~ sQ813_spl ),
inference(split_clause,[status(thm)],[f8961,f8971,f8974]) ).
fof(f8978,definition,
( sQ815_spl
<=> compose(g,compose(compose(a,b),compose(g,a))) = compose(compose(g,compose(a,b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ815_spl])],[split_symbol_definition]) ).
fof(f8981,plain,
( sQ815_spl
| ~ sQ66_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f8962,f1765,f1555,f8978]) ).
fof(f8982,definition,
( sQ816_spl
<=> compose(g,compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(g,compose(h,compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ816_spl])],[split_symbol_definition]) ).
fof(f8985,plain,
( sQ816_spl
| ~ sQ66_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f8963,f1772,f1555,f8982]) ).
fof(f8986,definition,
( sQ817_spl
<=> compose(g,compose(compose(h,a),compose(g,a))) = compose(compose(g,compose(h,a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ817_spl])],[split_symbol_definition]) ).
fof(f8989,plain,
( sQ817_spl
| ~ sQ21_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f8964,f1736,f693,f8986]) ).
fof(f8990,definition,
( sQ818_spl
<=> compose(g,compose(compose(g,a),compose(g,a))) = compose(compose(g,compose(g,a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ818_spl])],[split_symbol_definition]) ).
fof(f8993,plain,
( sQ818_spl
| ~ sQ21_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f8965,f1743,f693,f8990]) ).
fof(f8994,definition,
( sQ819_spl
<=> compose(g,compose(g,compose(g,a))) = compose(compose(g,g),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ819_spl])],[split_symbol_definition]) ).
fof(f8997,plain,
( sQ819_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f8966,f591,f584,f8994]) ).
fof(f8998,definition,
( sQ820_spl
<=> compose(g,compose(h,compose(g,a))) = compose(compose(g,h),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ820_spl])],[split_symbol_definition]) ).
fof(f9001,plain,
( sQ820_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f8967,f584,f8998]) ).
fof(f9002,plain,
( sQ50_spl
| ~ sQ21_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8968,f606,f693,f1334]) ).
fof(f9003,plain,
! [X0] :
( compose(g,compose(codomain(X0),compose(g,a))) = compose(compose(g,codomain(X0)),compose(g,a))
| codomain(X0) != domain(h)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f8969]) ).
fof(f9004,plain,
! [X0] :
( compose(g,compose(domain(X0),compose(g,a))) = compose(compose(g,domain(X0)),compose(g,a))
| domain(X0) != domain(h)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f8970]) ).
fof(f9005,plain,
( sQ813_spl
| domain(a) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f37,f8973]) ).
fof(f9007,plain,
( ~ sQ80_spl
| compose(g,compose(compose(a,b),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1808]) ).
fof(f9008,plain,
( ~ sQ80_spl
| compose(g,compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1808]) ).
fof(f9009,plain,
( ~ sQ80_spl
| compose(g,compose(compose(a,b),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1808]) ).
fof(f9010,plain,
( ~ sQ80_spl
| compose(g,compose(compose(a,b),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1808]) ).
fof(f9011,plain,
! [X0] :
( ~ sQ80_spl
| compose(g,compose(compose(a,b),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f1808]) ).
fof(f9012,plain,
! [X0] :
( ~ sQ80_spl
| compose(g,compose(compose(a,b),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f1808]) ).
fof(f9015,definition,
( sQ821_spl
<=> compose(g,compose(compose(a,b),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ821_spl])],[split_symbol_definition]) ).
fof(f9018,plain,
( ~ sQ80_spl
| sQ821_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f9007,f1555,f9015,f1768]) ).
fof(f9019,definition,
( sQ822_spl
<=> compose(g,compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ822_spl])],[split_symbol_definition]) ).
fof(f9022,plain,
( ~ sQ80_spl
| sQ822_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f9008,f1555,f9019,f1768]) ).
fof(f9023,definition,
( sQ823_spl
<=> compose(g,compose(compose(a,b),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ823_spl])],[split_symbol_definition]) ).
fof(f9026,plain,
( ~ sQ80_spl
| sQ823_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f9009,f1555,f9023,f1768]) ).
fof(f9027,definition,
( sQ824_spl
<=> compose(g,compose(compose(a,b),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ824_spl])],[split_symbol_definition]) ).
fof(f9030,plain,
( ~ sQ80_spl
| sQ824_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f9010,f1570,f9027,f1768]) ).
fof(f9034,plain,
! [X0] :
( compose(h,compose(codomain(compose(a,b)),X0)) = compose(compose(h,codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f2117]) ).
fof(f9035,plain,
! [X0] :
( compose(h,compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(h,codomain(compose(h,compose(a,b)))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f2117]) ).
fof(f9036,plain,
! [X0] :
( compose(h,compose(codomain(compose(h,a)),X0)) = compose(compose(h,codomain(compose(h,a))),X0)
| codomain(compose(h,a)) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f2117]) ).
fof(f9037,plain,
! [X0] :
( compose(h,compose(codomain(compose(g,a)),X0)) = compose(compose(h,codomain(compose(g,a))),X0)
| codomain(compose(g,a)) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f2117]) ).
fof(f9038,plain,
! [X0] :
( compose(h,compose(codomain(g),X0)) = compose(compose(h,codomain(g)),X0)
| codomain(g) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f2117]) ).
fof(f9039,plain,
! [X0] :
( compose(h,compose(codomain(h),X0)) = compose(compose(h,codomain(h)),X0)
| codomain(h) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f2117]) ).
fof(f9040,plain,
! [X0] :
( compose(h,compose(codomain(a),X0)) = compose(compose(h,codomain(a)),X0)
| codomain(a) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f2117]) ).
fof(f9054,definition,
! [X0] :
( sQ825_spl
<=> ( compose(h,compose(codomain(compose(a,b)),X0)) = compose(compose(h,codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ825_spl])],[split_symbol_definition]) ).
fof(f9057,plain,
( sQ825_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f9034,f1570,f9054]) ).
fof(f9058,definition,
! [X0] :
( sQ826_spl
<=> ( compose(h,compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(h,codomain(compose(h,compose(a,b)))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ826_spl])],[split_symbol_definition]) ).
fof(f9061,plain,
( sQ826_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f9035,f1570,f9058]) ).
fof(f9062,definition,
! [X0] :
( sQ827_spl
<=> ( compose(h,compose(codomain(compose(h,a)),X0)) = compose(compose(h,codomain(compose(h,a))),X0)
| codomain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ827_spl])],[split_symbol_definition]) ).
fof(f9065,plain,
( sQ827_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f9036,f715,f9062]) ).
fof(f9066,definition,
! [X0] :
( sQ828_spl
<=> ( compose(h,compose(codomain(compose(g,a)),X0)) = compose(compose(h,codomain(compose(g,a))),X0)
| codomain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ828_spl])],[split_symbol_definition]) ).
fof(f9069,plain,
( sQ828_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f9037,f715,f9066]) ).
fof(f9070,definition,
! [X0] :
( sQ829_spl
<=> ( compose(h,compose(codomain(g),X0)) = compose(compose(h,codomain(g)),X0)
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ829_spl])],[split_symbol_definition]) ).
fof(f9073,plain,
( sQ829_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9038,f606,f9070]) ).
fof(f9074,definition,
! [X0] :
( sQ830_spl
<=> ( compose(h,compose(codomain(h),X0)) = compose(compose(h,codomain(h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ830_spl])],[split_symbol_definition]) ).
fof(f9077,plain,
( sQ830_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9039,f606,f9074]) ).
fof(f9078,definition,
! [X0] :
( sQ831_spl
<=> ( compose(h,compose(codomain(a),X0)) = compose(compose(h,codomain(a)),X0)
| codomain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ831_spl])],[split_symbol_definition]) ).
fof(f9081,plain,
( sQ831_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f9040,f715,f9078]) ).
fof(f9097,plain,
! [X0] :
( compose(h,compose(domain(compose(g,a)),X0)) = compose(compose(h,domain(compose(g,a))),X0)
| domain(compose(g,a)) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f2118]) ).
fof(f9098,plain,
! [X0] :
( compose(h,compose(domain(compose(h,compose(a,b))),X0)) = compose(compose(h,domain(compose(h,compose(a,b)))),X0)
| domain(compose(h,compose(a,b))) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f2118]) ).
fof(f9099,plain,
! [X0] :
( compose(h,compose(domain(compose(h,a)),X0)) = compose(compose(h,domain(compose(h,a))),X0)
| domain(compose(h,a)) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f2118]) ).
fof(f9100,plain,
! [X0] :
( compose(h,compose(domain(compose(a,b)),X0)) = compose(compose(h,domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f2118]) ).
fof(f9112,definition,
! [X0] :
( sQ832_spl
<=> ( compose(h,compose(domain(compose(g,a)),X0)) = compose(compose(h,domain(compose(g,a))),X0)
| domain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ832_spl])],[split_symbol_definition]) ).
fof(f9115,plain,
( sQ832_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f9097,f584,f9112]) ).
fof(f9116,definition,
! [X0] :
( sQ833_spl
<=> ( compose(h,compose(domain(compose(h,compose(a,b))),X0)) = compose(compose(h,domain(compose(h,compose(a,b)))),X0)
| domain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ833_spl])],[split_symbol_definition]) ).
fof(f9119,plain,
( sQ833_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f9098,f584,f9116]) ).
fof(f9120,definition,
! [X0] :
( sQ834_spl
<=> ( compose(h,compose(domain(compose(h,a)),X0)) = compose(compose(h,domain(compose(h,a))),X0)
| domain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ834_spl])],[split_symbol_definition]) ).
fof(f9123,plain,
( sQ834_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f9099,f584,f9120]) ).
fof(f9124,definition,
! [X0] :
( sQ835_spl
<=> ( compose(h,compose(domain(compose(a,b)),X0)) = compose(compose(h,domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ835_spl])],[split_symbol_definition]) ).
fof(f9127,plain,
( sQ835_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9100,f606,f9124]) ).
fof(f9139,plain,
( compose(h,compose(compose(h,a),domain(b))) = compose(compose(h,compose(h,a)),domain(b))
| domain(a) != domain(compose(h,a)) ),
inference(resolution,[status(thm)],[f2064,f131]) ).
fof(f9140,plain,
( compose(h,compose(compose(g,a),domain(b))) = compose(compose(h,compose(g,a)),domain(b))
| domain(a) != domain(compose(g,a)) ),
inference(resolution,[status(thm)],[f2064,f130]) ).
fof(f9141,plain,
( compose(h,compose(g,domain(a))) = compose(compose(h,g),domain(a))
| domain(a) != domain(g) ),
inference(resolution,[status(thm)],[f2064,f74]) ).
fof(f9142,plain,
( compose(h,compose(h,domain(a))) = compose(compose(h,h),domain(a))
| domain(a) != domain(h) ),
inference(resolution,[status(thm)],[f2064,f69]) ).
fof(f9143,plain,
( compose(h,compose(a,domain(b))) = compose(compose(h,a),domain(b))
| domain(a) != domain(a) ),
inference(resolution,[status(thm)],[f2064,f22]) ).
fof(f9146,plain,
! [X0] :
( compose(h,compose(compose(a,b),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0))
| codomain(b) != domain(X0)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f2064]) ).
fof(f9147,plain,
! [X0] :
( compose(h,compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(h,compose(a,b))),domain(X0))
| codomain(b) != domain(X0)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f2064]) ).
fof(f9148,plain,
! [X0] :
( compose(h,compose(compose(h,a),domain(X0))) = compose(compose(h,compose(h,a)),domain(X0))
| domain(b) != domain(X0)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f2064]) ).
fof(f9149,plain,
! [X0] :
( compose(h,compose(compose(g,a),domain(X0))) = compose(compose(h,compose(g,a)),domain(X0))
| domain(b) != domain(X0)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f2064]) ).
fof(f9150,plain,
! [X0] :
( compose(h,compose(g,domain(X0))) = compose(compose(h,g),domain(X0))
| domain(a) != domain(X0)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f2064]) ).
fof(f9151,plain,
! [X0] :
( compose(h,compose(h,domain(X0))) = compose(compose(h,h),domain(X0))
| domain(a) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f2064]) ).
fof(f9152,plain,
! [X0] :
( compose(h,compose(a,domain(X0))) = compose(compose(h,a),domain(X0))
| domain(b) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f2064]) ).
fof(f9153,plain,
! [X0,X1] :
( compose(h,compose(codomain(X0),domain(X1))) = compose(compose(h,codomain(X0)),domain(X1))
| codomain(X0) != domain(X1)
| domain(a) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f2064]) ).
fof(f9154,plain,
! [X0,X1] :
( compose(h,compose(domain(X0),domain(X1))) = compose(compose(h,domain(X0)),domain(X1))
| domain(X0) != domain(X1)
| domain(a) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f2064]) ).
fof(f9161,definition,
( sQ836_spl
<=> compose(h,compose(compose(h,a),domain(b))) = compose(compose(h,compose(h,a)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ836_spl])],[split_symbol_definition]) ).
fof(f9164,plain,
( sQ836_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f9139,f1736,f9161]) ).
fof(f9165,definition,
( sQ837_spl
<=> compose(h,compose(compose(g,a),domain(b))) = compose(compose(h,compose(g,a)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ837_spl])],[split_symbol_definition]) ).
fof(f9168,plain,
( sQ837_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f9140,f1743,f9165]) ).
fof(f9169,definition,
( sQ838_spl
<=> compose(h,compose(g,domain(a))) = compose(compose(h,g),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ838_spl])],[split_symbol_definition]) ).
fof(f9172,plain,
( sQ838_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f9141,f591,f9169]) ).
fof(f9173,definition,
( sQ839_spl
<=> compose(h,compose(h,domain(a))) = compose(compose(h,h),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ839_spl])],[split_symbol_definition]) ).
fof(f9176,plain,
( sQ839_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f9142,f584,f9173]) ).
fof(f9177,definition,
( sQ840_spl
<=> compose(h,compose(a,domain(b))) = compose(compose(h,a),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ840_spl])],[split_symbol_definition]) ).
fof(f9180,plain,
( sQ840_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9143,f606,f9177]) ).
fof(f9186,definition,
! [X0] :
( sQ841_spl
<=> ( compose(h,compose(compose(a,b),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ841_spl])],[split_symbol_definition]) ).
fof(f9187,plain,
! [X0] :
( ~ sQ841_spl
| compose(h,compose(compose(a,b),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ),
inference(component_clause,[status(thm)],[f9186]) ).
fof(f9189,plain,
( sQ841_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f9146,f1765,f9186]) ).
fof(f9190,definition,
! [X0] :
( sQ842_spl
<=> ( compose(h,compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(h,compose(a,b))),domain(X0))
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ842_spl])],[split_symbol_definition]) ).
fof(f9193,plain,
( sQ842_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f9147,f1772,f9190]) ).
fof(f9194,definition,
! [X0] :
( sQ843_spl
<=> ( compose(h,compose(compose(h,a),domain(X0))) = compose(compose(h,compose(h,a)),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ843_spl])],[split_symbol_definition]) ).
fof(f9197,plain,
( sQ843_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f9148,f1736,f9194]) ).
fof(f9198,definition,
! [X0] :
( sQ844_spl
<=> ( compose(h,compose(compose(g,a),domain(X0))) = compose(compose(h,compose(g,a)),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ844_spl])],[split_symbol_definition]) ).
fof(f9201,plain,
( sQ844_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f9149,f1743,f9198]) ).
fof(f9202,definition,
! [X0] :
( sQ845_spl
<=> ( compose(h,compose(g,domain(X0))) = compose(compose(h,g),domain(X0))
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ845_spl])],[split_symbol_definition]) ).
fof(f9205,plain,
( sQ845_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f9150,f591,f9202]) ).
fof(f9206,definition,
! [X0] :
( sQ846_spl
<=> ( compose(h,compose(h,domain(X0))) = compose(compose(h,h),domain(X0))
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ846_spl])],[split_symbol_definition]) ).
fof(f9209,plain,
( sQ846_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f9151,f584,f9206]) ).
fof(f9210,definition,
! [X0] :
( sQ847_spl
<=> ( compose(h,compose(a,domain(X0))) = compose(compose(h,a),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ847_spl])],[split_symbol_definition]) ).
fof(f9213,plain,
( sQ847_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9152,f606,f9210]) ).
fof(f9214,plain,
! [X0,X1] :
( compose(h,compose(codomain(X0),domain(X1))) = compose(compose(h,codomain(X0)),domain(X1))
| codomain(X0) != domain(X1)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f9153]) ).
fof(f9215,plain,
! [X0,X1] :
( compose(h,compose(domain(X0),domain(X1))) = compose(compose(h,domain(X0)),domain(X1))
| domain(X0) != domain(X1)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f9154]) ).
fof(f9229,plain,
( compose(h,compose(compose(a,b),codomain(b))) = compose(compose(h,compose(a,b)),codomain(b))
| domain(a) != domain(compose(a,b)) ),
inference(resolution,[status(thm)],[f2065,f120]) ).
fof(f9230,plain,
( compose(h,compose(compose(h,compose(a,b)),codomain(b))) = compose(compose(h,compose(h,compose(a,b))),codomain(b))
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(resolution,[status(thm)],[f2065,f581]) ).
fof(f9232,plain,
( compose(h,compose(b,codomain(compose(a,b)))) = compose(compose(h,b),codomain(compose(a,b)))
| domain(a) != domain(b) ),
inference(resolution,[status(thm)],[f2065,f120]) ).
fof(f9233,plain,
( compose(h,compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(h,b),codomain(compose(h,compose(a,b))))
| domain(a) != domain(b) ),
inference(resolution,[status(thm)],[f2065,f581]) ).
fof(f9235,plain,
! [X0] :
( compose(h,compose(compose(a,b),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f2065]) ).
fof(f9236,plain,
! [X0] :
( compose(h,compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(h,compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f2065]) ).
fof(f9237,plain,
! [X0] :
( compose(h,compose(compose(h,a),codomain(X0))) = compose(compose(h,compose(h,a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f2065]) ).
fof(f9238,plain,
! [X0] :
( compose(h,compose(compose(g,a),codomain(X0))) = compose(compose(h,compose(g,a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f2065]) ).
fof(f9239,plain,
! [X0] :
( compose(h,compose(g,codomain(X0))) = compose(compose(h,g),codomain(X0))
| domain(a) != codomain(X0)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f2065]) ).
fof(f9240,plain,
! [X0] :
( compose(h,compose(h,codomain(X0))) = compose(compose(h,h),codomain(X0))
| domain(a) != codomain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f2065]) ).
fof(f9241,plain,
! [X0] :
( compose(h,compose(a,codomain(X0))) = compose(compose(h,a),codomain(X0))
| domain(b) != codomain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f2065]) ).
fof(f9242,plain,
! [X0,X1] :
( compose(h,compose(codomain(X0),codomain(X1))) = compose(compose(h,codomain(X0)),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(a) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f2065]) ).
fof(f9243,plain,
! [X0,X1] :
( compose(h,compose(domain(X0),codomain(X1))) = compose(compose(h,domain(X0)),codomain(X1))
| domain(X0) != codomain(X1)
| domain(a) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f2065]) ).
fof(f9254,definition,
( sQ848_spl
<=> compose(h,compose(compose(a,b),codomain(b))) = compose(compose(h,compose(a,b)),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ848_spl])],[split_symbol_definition]) ).
fof(f9257,plain,
( sQ848_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f9229,f1765,f9254]) ).
fof(f9258,definition,
( sQ849_spl
<=> compose(h,compose(compose(h,compose(a,b)),codomain(b))) = compose(compose(h,compose(h,compose(a,b))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ849_spl])],[split_symbol_definition]) ).
fof(f9261,plain,
( sQ849_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f9230,f1772,f9258]) ).
fof(f9264,definition,
( sQ850_spl
<=> compose(h,compose(b,codomain(compose(a,b)))) = compose(compose(h,b),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ850_spl])],[split_symbol_definition]) ).
fof(f9267,plain,
( sQ850_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f9232,f715,f9264]) ).
fof(f9268,definition,
( sQ851_spl
<=> compose(h,compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(h,b),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ851_spl])],[split_symbol_definition]) ).
fof(f9271,plain,
( sQ851_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f9233,f715,f9268]) ).
fof(f9275,definition,
! [X0] :
( sQ852_spl
<=> ( compose(h,compose(compose(a,b),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ852_spl])],[split_symbol_definition]) ).
fof(f9276,plain,
! [X0] :
( ~ sQ852_spl
| compose(h,compose(compose(a,b),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(component_clause,[status(thm)],[f9275]) ).
fof(f9278,plain,
( sQ852_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f9235,f1765,f9275]) ).
fof(f9279,definition,
! [X0] :
( sQ853_spl
<=> ( compose(h,compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(h,compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ853_spl])],[split_symbol_definition]) ).
fof(f9282,plain,
( sQ853_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f9236,f1772,f9279]) ).
fof(f9283,definition,
! [X0] :
( sQ854_spl
<=> ( compose(h,compose(compose(h,a),codomain(X0))) = compose(compose(h,compose(h,a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ854_spl])],[split_symbol_definition]) ).
fof(f9286,plain,
( sQ854_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f9237,f1736,f9283]) ).
fof(f9287,definition,
! [X0] :
( sQ855_spl
<=> ( compose(h,compose(compose(g,a),codomain(X0))) = compose(compose(h,compose(g,a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ855_spl])],[split_symbol_definition]) ).
fof(f9290,plain,
( sQ855_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f9238,f1743,f9287]) ).
fof(f9291,definition,
! [X0] :
( sQ856_spl
<=> ( compose(h,compose(g,codomain(X0))) = compose(compose(h,g),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ856_spl])],[split_symbol_definition]) ).
fof(f9294,plain,
( sQ856_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f9239,f591,f9291]) ).
fof(f9295,definition,
! [X0] :
( sQ857_spl
<=> ( compose(h,compose(h,codomain(X0))) = compose(compose(h,h),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ857_spl])],[split_symbol_definition]) ).
fof(f9298,plain,
( sQ857_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f9240,f584,f9295]) ).
fof(f9299,definition,
! [X0] :
( sQ858_spl
<=> ( compose(h,compose(a,codomain(X0))) = compose(compose(h,a),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ858_spl])],[split_symbol_definition]) ).
fof(f9302,plain,
( sQ858_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9241,f606,f9299]) ).
fof(f9303,plain,
! [X0,X1] :
( compose(h,compose(codomain(X0),codomain(X1))) = compose(compose(h,codomain(X0)),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f9242]) ).
fof(f9304,plain,
! [X0,X1] :
( compose(h,compose(domain(X0),codomain(X1))) = compose(compose(h,domain(X0)),codomain(X1))
| domain(X0) != codomain(X1)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f9243]) ).
fof(f9325,plain,
( compose(g,compose(domain(h),compose(h,a))) = compose(compose(g,domain(h)),compose(h,a))
| domain(a) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f1732,f15]) ).
fof(f9326,plain,
( compose(g,compose(compose(a,b),compose(h,a))) = compose(compose(g,compose(a,b)),compose(h,a))
| codomain(b) != domain(h)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f1732]) ).
fof(f9327,plain,
( compose(g,compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(g,compose(h,compose(a,b))),compose(h,a))
| codomain(b) != domain(h)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f1732]) ).
fof(f9328,plain,
( compose(g,compose(compose(h,a),compose(h,a))) = compose(compose(g,compose(h,a)),compose(h,a))
| domain(b) != domain(h)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f1732]) ).
fof(f9329,plain,
( compose(g,compose(compose(g,a),compose(h,a))) = compose(compose(g,compose(g,a)),compose(h,a))
| domain(b) != domain(h)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f1732]) ).
fof(f9330,plain,
( compose(g,compose(g,compose(h,a))) = compose(compose(g,g),compose(h,a))
| domain(a) != domain(h)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f1732]) ).
fof(f9331,plain,
( compose(g,compose(h,compose(h,a))) = compose(compose(g,h),compose(h,a))
| domain(a) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1732]) ).
fof(f9332,plain,
( compose(g,compose(a,compose(h,a))) = compose(compose(g,a),compose(h,a))
| domain(b) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f1732]) ).
fof(f9333,plain,
! [X0] :
( compose(g,compose(codomain(X0),compose(h,a))) = compose(compose(g,codomain(X0)),compose(h,a))
| codomain(X0) != domain(h)
| domain(a) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f1732]) ).
fof(f9334,plain,
! [X0] :
( compose(g,compose(domain(X0),compose(h,a))) = compose(compose(g,domain(X0)),compose(h,a))
| domain(X0) != domain(h)
| domain(a) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f1732]) ).
fof(f9335,definition,
( sQ859_spl
<=> compose(g,compose(domain(h),compose(h,a))) = compose(compose(g,domain(h)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ859_spl])],[split_symbol_definition]) ).
fof(f9338,plain,
( sQ859_spl
| ~ sQ813_spl ),
inference(split_clause,[status(thm)],[f9325,f8971,f9335]) ).
fof(f9339,definition,
( sQ860_spl
<=> compose(g,compose(compose(a,b),compose(h,a))) = compose(compose(g,compose(a,b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ860_spl])],[split_symbol_definition]) ).
fof(f9342,plain,
( sQ860_spl
| ~ sQ66_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f9326,f1765,f1555,f9339]) ).
fof(f9343,definition,
( sQ861_spl
<=> compose(g,compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(g,compose(h,compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ861_spl])],[split_symbol_definition]) ).
fof(f9346,plain,
( sQ861_spl
| ~ sQ66_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f9327,f1772,f1555,f9343]) ).
fof(f9347,definition,
( sQ862_spl
<=> compose(g,compose(compose(h,a),compose(h,a))) = compose(compose(g,compose(h,a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ862_spl])],[split_symbol_definition]) ).
fof(f9350,plain,
( sQ862_spl
| ~ sQ21_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f9328,f1736,f693,f9347]) ).
fof(f9351,definition,
( sQ863_spl
<=> compose(g,compose(compose(g,a),compose(h,a))) = compose(compose(g,compose(g,a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ863_spl])],[split_symbol_definition]) ).
fof(f9354,plain,
( sQ863_spl
| ~ sQ21_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f9329,f1743,f693,f9351]) ).
fof(f9355,definition,
( sQ864_spl
<=> compose(g,compose(g,compose(h,a))) = compose(compose(g,g),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ864_spl])],[split_symbol_definition]) ).
fof(f9358,plain,
( sQ864_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f9330,f591,f584,f9355]) ).
fof(f9359,definition,
( sQ865_spl
<=> compose(g,compose(h,compose(h,a))) = compose(compose(g,h),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ865_spl])],[split_symbol_definition]) ).
fof(f9362,plain,
( sQ865_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f9331,f584,f9359]) ).
fof(f9363,plain,
( sQ54_spl
| ~ sQ21_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9332,f606,f693,f1350]) ).
fof(f9364,plain,
! [X0] :
( compose(g,compose(codomain(X0),compose(h,a))) = compose(compose(g,codomain(X0)),compose(h,a))
| codomain(X0) != domain(h)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f9333]) ).
fof(f9365,plain,
! [X0] :
( compose(g,compose(domain(X0),compose(h,a))) = compose(compose(g,domain(X0)),compose(h,a))
| domain(X0) != domain(h)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f9334]) ).
fof(f9367,plain,
( ~ sQ106_spl
| compose(h,compose(compose(a,b),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f2090]) ).
fof(f9368,plain,
( ~ sQ106_spl
| compose(h,compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f2090]) ).
fof(f9369,plain,
( ~ sQ106_spl
| compose(h,compose(compose(a,b),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f2090]) ).
fof(f9370,plain,
( ~ sQ106_spl
| compose(h,compose(compose(a,b),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f2090]) ).
fof(f9371,plain,
! [X0] :
( ~ sQ106_spl
| compose(h,compose(compose(a,b),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f37,f2090]) ).
fof(f9372,plain,
! [X0] :
( ~ sQ106_spl
| compose(h,compose(compose(a,b),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f2090]) ).
fof(f9374,definition,
( sQ866_spl
<=> compose(h,compose(compose(a,b),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ866_spl])],[split_symbol_definition]) ).
fof(f9377,plain,
( ~ sQ106_spl
| sQ866_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f9367,f1555,f9374,f2089]) ).
fof(f9378,definition,
( sQ867_spl
<=> compose(h,compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ867_spl])],[split_symbol_definition]) ).
fof(f9381,plain,
( ~ sQ106_spl
| sQ867_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f9368,f1555,f9378,f2089]) ).
fof(f9382,definition,
( sQ868_spl
<=> compose(h,compose(compose(a,b),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ868_spl])],[split_symbol_definition]) ).
fof(f9385,plain,
( ~ sQ106_spl
| sQ868_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f9369,f1555,f9382,f2089]) ).
fof(f9386,definition,
( sQ869_spl
<=> compose(h,compose(compose(a,b),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ869_spl])],[split_symbol_definition]) ).
fof(f9389,plain,
( ~ sQ106_spl
| sQ869_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f9370,f1570,f9386,f2089]) ).
fof(f9394,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)],[f120,f2393]) ).
fof(f9395,plain,
! [X0] :
( compose(a,compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(a,codomain(compose(h,compose(a,b)))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f2393]) ).
fof(f9396,plain,
! [X0] :
( compose(a,compose(codomain(compose(h,a)),X0)) = compose(compose(a,codomain(compose(h,a))),X0)
| codomain(compose(h,a)) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f2393]) ).
fof(f9397,plain,
! [X0] :
( compose(a,compose(codomain(compose(g,a)),X0)) = compose(compose(a,codomain(compose(g,a))),X0)
| codomain(compose(g,a)) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f2393]) ).
fof(f9398,plain,
! [X0] :
( compose(a,compose(codomain(g),X0)) = compose(compose(a,codomain(g)),X0)
| codomain(g) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f2393]) ).
fof(f9399,plain,
! [X0] :
( compose(a,compose(codomain(h),X0)) = compose(compose(a,codomain(h)),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f2393]) ).
fof(f9400,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)],[f22,f2393]) ).
fof(f9418,definition,
! [X0] :
( sQ870_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,[sQ870_spl])],[split_symbol_definition]) ).
fof(f9421,plain,
( sQ870_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f9394,f2265,f9418]) ).
fof(f9422,definition,
! [X0] :
( sQ871_spl
<=> ( compose(a,compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(a,codomain(compose(h,compose(a,b)))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ871_spl])],[split_symbol_definition]) ).
fof(f9425,plain,
( sQ871_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f9395,f2265,f9422]) ).
fof(f9426,definition,
! [X0] :
( sQ872_spl
<=> ( compose(a,compose(codomain(compose(h,a)),X0)) = compose(compose(a,codomain(compose(h,a))),X0)
| codomain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ872_spl])],[split_symbol_definition]) ).
fof(f9429,plain,
( sQ872_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f9396,f1941,f9426]) ).
fof(f9430,definition,
! [X0] :
( sQ873_spl
<=> ( compose(a,compose(codomain(compose(g,a)),X0)) = compose(compose(a,codomain(compose(g,a))),X0)
| codomain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ873_spl])],[split_symbol_definition]) ).
fof(f9433,plain,
( sQ873_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f9397,f1941,f9430]) ).
fof(f9434,definition,
! [X0] :
( sQ874_spl
<=> ( compose(a,compose(codomain(g),X0)) = compose(compose(a,codomain(g)),X0)
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ874_spl])],[split_symbol_definition]) ).
fof(f9437,plain,
( sQ874_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f9398,f715,f9434]) ).
fof(f9438,definition,
! [X0] :
( sQ875_spl
<=> ( compose(a,compose(codomain(h),X0)) = compose(compose(a,codomain(h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ875_spl])],[split_symbol_definition]) ).
fof(f9441,plain,
( sQ875_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f9399,f715,f9438]) ).
fof(f9442,definition,
! [X0] :
( sQ876_spl
<=> ( compose(a,compose(codomain(a),X0)) = compose(compose(a,codomain(a)),X0)
| codomain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ876_spl])],[split_symbol_definition]) ).
fof(f9445,plain,
( sQ876_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f9400,f1941,f9442]) ).
fof(f9464,plain,
! [X0] :
( compose(a,compose(domain(compose(g,a)),X0)) = compose(compose(a,domain(compose(g,a))),X0)
| domain(compose(g,a)) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f2394]) ).
fof(f9465,plain,
! [X0] :
( compose(a,compose(domain(compose(h,compose(a,b))),X0)) = compose(compose(a,domain(compose(h,compose(a,b)))),X0)
| domain(compose(h,compose(a,b))) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f2394]) ).
fof(f9466,plain,
! [X0] :
( compose(a,compose(domain(compose(h,a)),X0)) = compose(compose(a,domain(compose(h,a))),X0)
| domain(compose(h,a)) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f2394]) ).
fof(f9467,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)],[f60,f2394]) ).
fof(f9475,definition,
! [X0] :
( sQ877_spl
<=> ( compose(a,compose(domain(compose(g,a)),X0)) = compose(compose(a,domain(compose(g,a))),X0)
| domain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ877_spl])],[split_symbol_definition]) ).
fof(f9478,plain,
( sQ877_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f9464,f693,f9475]) ).
fof(f9479,definition,
! [X0] :
( sQ878_spl
<=> ( compose(a,compose(domain(compose(h,compose(a,b))),X0)) = compose(compose(a,domain(compose(h,compose(a,b)))),X0)
| domain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ878_spl])],[split_symbol_definition]) ).
fof(f9482,plain,
( sQ878_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f9465,f693,f9479]) ).
fof(f9483,definition,
! [X0] :
( sQ879_spl
<=> ( compose(a,compose(domain(compose(h,a)),X0)) = compose(compose(a,domain(compose(h,a))),X0)
| domain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ879_spl])],[split_symbol_definition]) ).
fof(f9486,plain,
( sQ879_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f9466,f693,f9483]) ).
fof(f9487,definition,
! [X0] :
( sQ880_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,[sQ880_spl])],[split_symbol_definition]) ).
fof(f9490,plain,
( sQ880_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f9467,f715,f9487]) ).
fof(f9498,plain,
( compose(a,compose(compose(h,a),domain(b))) = compose(compose(a,compose(h,a)),domain(b))
| domain(b) != domain(compose(h,a)) ),
inference(resolution,[status(thm)],[f2328,f131]) ).
fof(f9499,plain,
( compose(a,compose(compose(g,a),domain(b))) = compose(compose(a,compose(g,a)),domain(b))
| domain(b) != domain(compose(g,a)) ),
inference(resolution,[status(thm)],[f2328,f130]) ).
fof(f9500,plain,
( compose(a,compose(g,domain(a))) = compose(compose(a,g),domain(a))
| domain(b) != domain(g) ),
inference(resolution,[status(thm)],[f2328,f74]) ).
fof(f9501,plain,
( compose(a,compose(h,domain(a))) = compose(compose(a,h),domain(a))
| domain(b) != domain(h) ),
inference(resolution,[status(thm)],[f2328,f69]) ).
fof(f9502,plain,
( compose(a,compose(a,domain(b))) = compose(compose(a,a),domain(b))
| domain(b) != domain(a) ),
inference(resolution,[status(thm)],[f2328,f22]) ).
fof(f9505,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)],[f120,f2328]) ).
fof(f9506,plain,
! [X0] :
( compose(a,compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(a,compose(h,compose(a,b))),domain(X0))
| codomain(b) != domain(X0)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f2328]) ).
fof(f9507,plain,
! [X0] :
( compose(a,compose(compose(h,a),domain(X0))) = compose(compose(a,compose(h,a)),domain(X0))
| domain(b) != domain(X0)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f2328]) ).
fof(f9508,plain,
! [X0] :
( compose(a,compose(compose(g,a),domain(X0))) = compose(compose(a,compose(g,a)),domain(X0))
| domain(b) != domain(X0)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f2328]) ).
fof(f9509,plain,
! [X0] :
( compose(a,compose(g,domain(X0))) = compose(compose(a,g),domain(X0))
| domain(a) != domain(X0)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f2328]) ).
fof(f9510,plain,
! [X0] :
( compose(a,compose(h,domain(X0))) = compose(compose(a,h),domain(X0))
| domain(a) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f2328]) ).
fof(f9511,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)],[f22,f2328]) ).
fof(f9512,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)],[f38,f2328]) ).
fof(f9513,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)],[f15,f2328]) ).
fof(f9520,definition,
( sQ881_spl
<=> compose(a,compose(compose(h,a),domain(b))) = compose(compose(a,compose(h,a)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ881_spl])],[split_symbol_definition]) ).
fof(f9523,plain,
( sQ881_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f9498,f2330,f9520]) ).
fof(f9524,definition,
( sQ882_spl
<=> compose(a,compose(compose(g,a),domain(b))) = compose(compose(a,compose(g,a)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ882_spl])],[split_symbol_definition]) ).
fof(f9527,plain,
( sQ882_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f9499,f2337,f9524]) ).
fof(f9528,definition,
( sQ883_spl
<=> compose(a,compose(g,domain(a))) = compose(compose(a,g),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ883_spl])],[split_symbol_definition]) ).
fof(f9531,plain,
( sQ883_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f9500,f700,f9528]) ).
fof(f9532,definition,
( sQ884_spl
<=> compose(a,compose(h,domain(a))) = compose(compose(a,h),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ884_spl])],[split_symbol_definition]) ).
fof(f9535,plain,
( sQ884_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f9501,f693,f9532]) ).
fof(f9536,definition,
( sQ885_spl
<=> compose(a,compose(a,domain(b))) = compose(compose(a,a),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ885_spl])],[split_symbol_definition]) ).
fof(f9539,plain,
( sQ885_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f9502,f715,f9536]) ).
fof(f9545,definition,
! [X0] :
( sQ886_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,[sQ886_spl])],[split_symbol_definition]) ).
fof(f9548,plain,
( sQ886_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f9505,f2359,f9545]) ).
fof(f9549,definition,
! [X0] :
( sQ887_spl
<=> ( compose(a,compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(a,compose(h,compose(a,b))),domain(X0))
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ887_spl])],[split_symbol_definition]) ).
fof(f9552,plain,
( sQ887_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f9506,f2366,f9549]) ).
fof(f9553,definition,
! [X0] :
( sQ888_spl
<=> ( compose(a,compose(compose(h,a),domain(X0))) = compose(compose(a,compose(h,a)),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ888_spl])],[split_symbol_definition]) ).
fof(f9556,plain,
( sQ888_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f9507,f2330,f9553]) ).
fof(f9557,definition,
! [X0] :
( sQ889_spl
<=> ( compose(a,compose(compose(g,a),domain(X0))) = compose(compose(a,compose(g,a)),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ889_spl])],[split_symbol_definition]) ).
fof(f9560,plain,
( sQ889_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f9508,f2337,f9557]) ).
fof(f9561,definition,
! [X0] :
( sQ890_spl
<=> ( compose(a,compose(g,domain(X0))) = compose(compose(a,g),domain(X0))
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ890_spl])],[split_symbol_definition]) ).
fof(f9564,plain,
( sQ890_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f9509,f700,f9561]) ).
fof(f9565,definition,
! [X0] :
( sQ891_spl
<=> ( compose(a,compose(h,domain(X0))) = compose(compose(a,h),domain(X0))
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ891_spl])],[split_symbol_definition]) ).
fof(f9568,plain,
( sQ891_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f9510,f693,f9565]) ).
fof(f9569,definition,
! [X0] :
( sQ892_spl
<=> ( compose(a,compose(a,domain(X0))) = compose(compose(a,a),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ892_spl])],[split_symbol_definition]) ).
fof(f9572,plain,
( sQ892_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f9511,f715,f9569]) ).
fof(f9573,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)],[f16,f9512]) ).
fof(f9574,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)],[f37,f9513]) ).
fof(f9587,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)],[f2329,f120]) ).
fof(f9588,plain,
( compose(a,compose(compose(h,compose(a,b)),codomain(b))) = compose(compose(a,compose(h,compose(a,b))),codomain(b))
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(resolution,[status(thm)],[f2329,f581]) ).
fof(f9590,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)],[f2329,f120]) ).
fof(f9591,plain,
( compose(a,compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(a,b),codomain(compose(h,compose(a,b))))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f2329,f581]) ).
fof(f9593,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)],[f120,f2329]) ).
fof(f9594,plain,
! [X0] :
( compose(a,compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(a,compose(h,compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f2329]) ).
fof(f9595,plain,
! [X0] :
( compose(a,compose(compose(h,a),codomain(X0))) = compose(compose(a,compose(h,a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f2329]) ).
fof(f9596,plain,
! [X0] :
( compose(a,compose(compose(g,a),codomain(X0))) = compose(compose(a,compose(g,a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f2329]) ).
fof(f9597,plain,
! [X0] :
( compose(a,compose(g,codomain(X0))) = compose(compose(a,g),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f2329]) ).
fof(f9598,plain,
! [X0] :
( compose(a,compose(h,codomain(X0))) = compose(compose(a,h),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f2329]) ).
fof(f9599,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)],[f22,f2329]) ).
fof(f9600,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)],[f38,f2329]) ).
fof(f9601,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)],[f15,f2329]) ).
fof(f9612,definition,
( sQ893_spl
<=> compose(a,compose(compose(a,b),codomain(b))) = compose(compose(a,compose(a,b)),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ893_spl])],[split_symbol_definition]) ).
fof(f9615,plain,
( sQ893_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f9587,f2359,f9612]) ).
fof(f9616,definition,
( sQ894_spl
<=> compose(a,compose(compose(h,compose(a,b)),codomain(b))) = compose(compose(a,compose(h,compose(a,b))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ894_spl])],[split_symbol_definition]) ).
fof(f9619,plain,
( sQ894_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f9588,f2366,f9616]) ).
fof(f9622,plain,
( sQ699_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f9590,f1941,f8116]) ).
fof(f9623,plain,
( sQ700_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f9591,f1941,f8120]) ).
fof(f9627,definition,
! [X0] :
( sQ895_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,[sQ895_spl])],[split_symbol_definition]) ).
fof(f9630,plain,
( sQ895_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f9593,f2359,f9627]) ).
fof(f9631,definition,
! [X0] :
( sQ896_spl
<=> ( compose(a,compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(a,compose(h,compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ896_spl])],[split_symbol_definition]) ).
fof(f9634,plain,
( sQ896_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f9594,f2366,f9631]) ).
fof(f9635,definition,
! [X0] :
( sQ897_spl
<=> ( compose(a,compose(compose(h,a),codomain(X0))) = compose(compose(a,compose(h,a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ897_spl])],[split_symbol_definition]) ).
fof(f9638,plain,
( sQ897_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f9595,f2330,f9635]) ).
fof(f9639,definition,
! [X0] :
( sQ898_spl
<=> ( compose(a,compose(compose(g,a),codomain(X0))) = compose(compose(a,compose(g,a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ898_spl])],[split_symbol_definition]) ).
fof(f9642,plain,
( sQ898_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f9596,f2337,f9639]) ).
fof(f9643,definition,
! [X0] :
( sQ899_spl
<=> ( compose(a,compose(g,codomain(X0))) = compose(compose(a,g),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ899_spl])],[split_symbol_definition]) ).
fof(f9646,plain,
( sQ899_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f9597,f700,f9643]) ).
fof(f9647,definition,
! [X0] :
( sQ900_spl
<=> ( compose(a,compose(h,codomain(X0))) = compose(compose(a,h),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ900_spl])],[split_symbol_definition]) ).
fof(f9650,plain,
( sQ900_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f9598,f693,f9647]) ).
fof(f9651,definition,
! [X0] :
( sQ901_spl
<=> ( compose(a,compose(a,codomain(X0))) = compose(compose(a,a),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ901_spl])],[split_symbol_definition]) ).
fof(f9654,plain,
( sQ901_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f9599,f715,f9651]) ).
fof(f9655,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)],[f16,f9600]) ).
fof(f9656,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)],[f37,f9601]) ).
fof(f9676,plain,
( compose(g,compose(g,compose(a,b))) = compose(compose(g,g),compose(a,b))
| domain(a) != domain(g) ),
inference(resolution,[status(thm)],[f1733,f74]) ).
fof(f9677,plain,
( compose(g,compose(h,compose(a,b))) = compose(compose(g,h),compose(a,b))
| domain(a) != domain(h) ),
inference(resolution,[status(thm)],[f1733,f69]) ).
fof(f9678,plain,
( compose(g,compose(domain(a),compose(a,b))) = compose(compose(g,domain(a)),compose(a,b))
| domain(a) != domain(domain(a)) ),
inference(resolution,[status(thm)],[f1733,f15]) ).
fof(f9679,plain,
( compose(g,compose(compose(a,b),compose(a,b))) = compose(compose(g,compose(a,b)),compose(a,b))
| codomain(b) != domain(a)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f1733]) ).
fof(f9680,plain,
( compose(g,compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(g,compose(h,compose(a,b))),compose(a,b))
| codomain(b) != domain(a)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f1733]) ).
fof(f9681,plain,
( compose(g,compose(compose(h,a),compose(a,b))) = compose(compose(g,compose(h,a)),compose(a,b))
| domain(b) != domain(a)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f1733]) ).
fof(f9682,plain,
( compose(g,compose(compose(g,a),compose(a,b))) = compose(compose(g,compose(g,a)),compose(a,b))
| domain(b) != domain(a)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f1733]) ).
fof(f9685,plain,
( compose(g,compose(a,compose(a,b))) = compose(compose(g,a),compose(a,b))
| domain(b) != domain(a)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f1733]) ).
fof(f9686,plain,
! [X0] :
( compose(g,compose(codomain(X0),compose(a,b))) = compose(compose(g,codomain(X0)),compose(a,b))
| codomain(X0) != domain(a)
| domain(a) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f1733]) ).
fof(f9687,plain,
! [X0] :
( compose(g,compose(domain(X0),compose(a,b))) = compose(compose(g,domain(X0)),compose(a,b))
| domain(X0) != domain(a)
| domain(a) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f1733]) ).
fof(f9688,definition,
( sQ902_spl
<=> compose(g,compose(g,compose(a,b))) = compose(compose(g,g),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ902_spl])],[split_symbol_definition]) ).
fof(f9691,plain,
( sQ902_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f9676,f591,f9688]) ).
fof(f9692,definition,
( sQ903_spl
<=> compose(g,compose(h,compose(a,b))) = compose(compose(g,h),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ903_spl])],[split_symbol_definition]) ).
fof(f9695,plain,
( sQ903_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f9677,f584,f9692]) ).
fof(f9696,definition,
( sQ904_spl
<=> domain(a) = domain(domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ904_spl])],[split_symbol_definition]) ).
fof(f9698,plain,
( sQ904_spl
| domain(a) != domain(domain(a)) ),
inference(component_clause,[status(thm)],[f9696]) ).
fof(f9699,definition,
( sQ905_spl
<=> compose(g,compose(domain(a),compose(a,b))) = compose(compose(g,domain(a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ905_spl])],[split_symbol_definition]) ).
fof(f9702,plain,
( sQ905_spl
| ~ sQ904_spl ),
inference(split_clause,[status(thm)],[f9678,f9696,f9699]) ).
fof(f9703,definition,
( sQ906_spl
<=> compose(g,compose(compose(a,b),compose(a,b))) = compose(compose(g,compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ906_spl])],[split_symbol_definition]) ).
fof(f9706,plain,
( sQ906_spl
| ~ sQ70_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f9679,f1765,f1570,f9703]) ).
fof(f9707,definition,
( sQ907_spl
<=> compose(g,compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(g,compose(h,compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ907_spl])],[split_symbol_definition]) ).
fof(f9710,plain,
( sQ907_spl
| ~ sQ70_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f9680,f1772,f1570,f9707]) ).
fof(f9711,definition,
( sQ908_spl
<=> compose(g,compose(compose(h,a),compose(a,b))) = compose(compose(g,compose(h,a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ908_spl])],[split_symbol_definition]) ).
fof(f9714,plain,
( sQ908_spl
| ~ sQ27_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f9681,f1736,f715,f9711]) ).
fof(f9715,definition,
( sQ909_spl
<=> compose(g,compose(compose(g,a),compose(a,b))) = compose(compose(g,compose(g,a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ909_spl])],[split_symbol_definition]) ).
fof(f9718,plain,
( sQ909_spl
| ~ sQ27_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f9682,f1743,f715,f9715]) ).
fof(f9721,plain,
( sQ55_spl
| ~ sQ27_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9685,f606,f715,f1354]) ).
fof(f9722,plain,
! [X0] :
( compose(g,compose(codomain(X0),compose(a,b))) = compose(compose(g,codomain(X0)),compose(a,b))
| codomain(X0) != domain(a)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f9686]) ).
fof(f9723,plain,
! [X0] :
( compose(g,compose(codomain(X0),compose(a,b))) = compose(compose(g,codomain(X0)),compose(a,b))
| domain(a) != codomain(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f9722]) ).
fof(f9724,plain,
! [X0] :
( compose(g,compose(domain(X0),compose(a,b))) = compose(compose(g,domain(X0)),compose(a,b))
| domain(X0) != domain(a)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f9687]) ).
fof(f9725,plain,
! [X0] :
( compose(g,compose(domain(X0),compose(a,b))) = compose(compose(g,domain(X0)),compose(a,b))
| domain(a) != domain(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f9724]) ).
fof(f9726,plain,
( sQ904_spl
| domain(a) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f37,f9698]) ).
fof(f9727,plain,
( sQ904_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f9726]) ).
fof(f9728,plain,
sQ904_spl,
inference(contradiction_clause,[status(thm)],[f9727]) ).
fof(f9737,plain,
! [X0] :
( compose(domain(g),compose(g,X0)) = compose(compose(domain(g),g),X0)
| domain(a) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f2802]) ).
fof(f9738,plain,
! [X0] :
( compose(domain(compose(g,a)),compose(g,X0)) = compose(compose(domain(compose(g,a)),g),X0)
| domain(a) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f2802]) ).
fof(f9739,plain,
! [X0] :
( compose(domain(compose(h,compose(a,b))),compose(g,X0)) = compose(compose(domain(compose(h,compose(a,b))),g),X0)
| domain(a) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f2802]) ).
fof(f9740,plain,
! [X0] :
( compose(domain(compose(h,a)),compose(g,X0)) = compose(compose(domain(compose(h,a)),g),X0)
| domain(a) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f2802]) ).
fof(f9741,plain,
! [X0] :
( compose(domain(compose(a,b)),compose(g,X0)) = compose(compose(domain(compose(a,b)),g),X0)
| domain(a) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f2802]) ).
fof(f9743,plain,
! [X0,X1] :
( compose(domain(codomain(X0)),compose(g,X1)) = compose(compose(domain(codomain(X0)),g),X1)
| domain(a) != domain(X1)
| codomain(X0) != domain(h) ),
inference(paramodulation,[status(thm)],[f16,f2802]) ).
fof(f9759,definition,
! [X0] :
( sQ910_spl
<=> ( compose(domain(g),compose(g,X0)) = compose(compose(domain(g),g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ910_spl])],[split_symbol_definition]) ).
fof(f9762,plain,
( sQ910_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f9737,f2687,f9759]) ).
fof(f9763,definition,
! [X0] :
( sQ911_spl
<=> ( compose(domain(compose(g,a)),compose(g,X0)) = compose(compose(domain(compose(g,a)),g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ911_spl])],[split_symbol_definition]) ).
fof(f9766,plain,
( sQ911_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f9738,f2687,f9763]) ).
fof(f9767,definition,
! [X0] :
( sQ912_spl
<=> ( compose(domain(compose(h,compose(a,b))),compose(g,X0)) = compose(compose(domain(compose(h,compose(a,b))),g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ912_spl])],[split_symbol_definition]) ).
fof(f9770,plain,
( sQ912_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f9739,f2687,f9767]) ).
fof(f9771,definition,
! [X0] :
( sQ913_spl
<=> ( compose(domain(compose(h,a)),compose(g,X0)) = compose(compose(domain(compose(h,a)),g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ913_spl])],[split_symbol_definition]) ).
fof(f9774,plain,
( sQ913_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f9740,f2687,f9771]) ).
fof(f9775,definition,
! [X0] :
( sQ914_spl
<=> ( compose(domain(compose(a,b)),compose(g,X0)) = compose(compose(domain(compose(a,b)),g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ914_spl])],[split_symbol_definition]) ).
fof(f9778,plain,
( sQ914_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f9741,f584,f9775]) ).
fof(f9781,plain,
! [X0,X1] :
( compose(codomain(X0),compose(g,X1)) = compose(compose(domain(codomain(X0)),g),X1)
| domain(a) != domain(X1)
| codomain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f16,f9743]) ).
fof(f9782,plain,
! [X0,X1] :
( compose(codomain(X0),compose(g,X1)) = compose(compose(codomain(X0),g),X1)
| domain(a) != domain(X1)
| codomain(X0) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f16,f9781]) ).
fof(f10156,plain,
( compose(h,compose(domain(h),compose(g,a))) = compose(compose(h,domain(h)),compose(g,a))
| domain(a) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f2060,f15]) ).
fof(f10157,plain,
( compose(h,compose(compose(a,b),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a))
| codomain(b) != domain(h)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f2060]) ).
fof(f10158,plain,
( compose(h,compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(h,compose(a,b))),compose(g,a))
| codomain(b) != domain(h)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f2060]) ).
fof(f10159,plain,
( compose(h,compose(compose(h,a),compose(g,a))) = compose(compose(h,compose(h,a)),compose(g,a))
| domain(b) != domain(h)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f2060]) ).
fof(f10160,plain,
( compose(h,compose(compose(g,a),compose(g,a))) = compose(compose(h,compose(g,a)),compose(g,a))
| domain(b) != domain(h)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f2060]) ).
fof(f10161,plain,
( compose(h,compose(g,compose(g,a))) = compose(compose(h,g),compose(g,a))
| domain(a) != domain(h)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f2060]) ).
fof(f10162,plain,
( compose(h,compose(h,compose(g,a))) = compose(compose(h,h),compose(g,a))
| domain(a) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f2060]) ).
fof(f10163,plain,
( compose(h,compose(a,compose(g,a))) = compose(compose(h,a),compose(g,a))
| domain(b) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f2060]) ).
fof(f10164,plain,
! [X0] :
( compose(h,compose(codomain(X0),compose(g,a))) = compose(compose(h,codomain(X0)),compose(g,a))
| codomain(X0) != domain(h)
| domain(a) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f2060]) ).
fof(f10165,plain,
! [X0] :
( compose(h,compose(domain(X0),compose(g,a))) = compose(compose(h,domain(X0)),compose(g,a))
| domain(X0) != domain(h)
| domain(a) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f2060]) ).
fof(f10166,definition,
( sQ915_spl
<=> compose(h,compose(domain(h),compose(g,a))) = compose(compose(h,domain(h)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ915_spl])],[split_symbol_definition]) ).
fof(f10169,plain,
( sQ915_spl
| ~ sQ813_spl ),
inference(split_clause,[status(thm)],[f10156,f8971,f10166]) ).
fof(f10170,plain,
( sQ866_spl
| ~ sQ66_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f10157,f1765,f1555,f9374]) ).
fof(f10171,definition,
( sQ916_spl
<=> compose(h,compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(h,compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ916_spl])],[split_symbol_definition]) ).
fof(f10174,plain,
( sQ916_spl
| ~ sQ66_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f10158,f1772,f1555,f10171]) ).
fof(f10175,definition,
( sQ917_spl
<=> compose(h,compose(compose(h,a),compose(g,a))) = compose(compose(h,compose(h,a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ917_spl])],[split_symbol_definition]) ).
fof(f10178,plain,
( sQ917_spl
| ~ sQ21_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f10159,f1736,f693,f10175]) ).
fof(f10179,definition,
( sQ918_spl
<=> compose(h,compose(compose(g,a),compose(g,a))) = compose(compose(h,compose(g,a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ918_spl])],[split_symbol_definition]) ).
fof(f10182,plain,
( sQ918_spl
| ~ sQ21_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f10160,f1743,f693,f10179]) ).
fof(f10183,definition,
( sQ919_spl
<=> compose(h,compose(g,compose(g,a))) = compose(compose(h,g),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ919_spl])],[split_symbol_definition]) ).
fof(f10186,plain,
( sQ919_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f10161,f591,f584,f10183]) ).
fof(f10187,definition,
( sQ920_spl
<=> compose(h,compose(h,compose(g,a))) = compose(compose(h,h),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ920_spl])],[split_symbol_definition]) ).
fof(f10190,plain,
( sQ920_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f10162,f584,f10187]) ).
fof(f10191,plain,
( sQ56_spl
| ~ sQ21_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f10163,f606,f693,f1392]) ).
fof(f10192,plain,
! [X0] :
( compose(h,compose(codomain(X0),compose(g,a))) = compose(compose(h,codomain(X0)),compose(g,a))
| codomain(X0) != domain(h)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f10164]) ).
fof(f10193,plain,
! [X0] :
( compose(h,compose(domain(X0),compose(g,a))) = compose(compose(h,domain(X0)),compose(g,a))
| domain(X0) != domain(h)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f10165]) ).
fof(f10195,plain,
( compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),compose(g,a))) = compose(codomain(compose(a,b)),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f4792]) ).
fof(f10196,plain,
( compose(codomain(compose(h,compose(a,b))),compose(codomain(compose(h,compose(a,b))),compose(g,a))) = compose(codomain(compose(h,compose(a,b))),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f4792]) ).
fof(f10197,plain,
( compose(codomain(compose(h,a)),compose(codomain(compose(h,a)),compose(g,a))) = compose(codomain(compose(h,a)),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f4792]) ).
fof(f10198,plain,
( compose(codomain(compose(g,a)),compose(codomain(compose(g,a)),compose(g,a))) = compose(codomain(compose(g,a)),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f4792]) ).
fof(f10199,plain,
( compose(codomain(g),compose(codomain(g),compose(g,a))) = compose(codomain(g),compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f4792]) ).
fof(f10200,plain,
( compose(codomain(h),compose(codomain(h),compose(g,a))) = compose(codomain(h),compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f4792]) ).
fof(f10201,plain,
( compose(codomain(a),compose(codomain(a),compose(g,a))) = compose(codomain(a),compose(g,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f4792]) ).
fof(f10209,definition,
( sQ921_spl
<=> compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),compose(g,a))) = compose(codomain(compose(a,b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ921_spl])],[split_symbol_definition]) ).
fof(f10212,plain,
( sQ921_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f10195,f1555,f10209]) ).
fof(f10213,definition,
( sQ922_spl
<=> compose(codomain(compose(h,compose(a,b))),compose(codomain(compose(h,compose(a,b))),compose(g,a))) = compose(codomain(compose(h,compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ922_spl])],[split_symbol_definition]) ).
fof(f10216,plain,
( sQ922_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f10196,f1555,f10213]) ).
fof(f10217,definition,
( sQ923_spl
<=> compose(codomain(compose(h,a)),compose(codomain(compose(h,a)),compose(g,a))) = compose(codomain(compose(h,a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ923_spl])],[split_symbol_definition]) ).
fof(f10220,plain,
( sQ923_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10197,f693,f10217]) ).
fof(f10221,definition,
( sQ924_spl
<=> compose(codomain(compose(g,a)),compose(codomain(compose(g,a)),compose(g,a))) = compose(codomain(compose(g,a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ924_spl])],[split_symbol_definition]) ).
fof(f10224,plain,
( sQ924_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10198,f693,f10221]) ).
fof(f10225,definition,
( sQ925_spl
<=> compose(codomain(g),compose(codomain(g),compose(g,a))) = compose(codomain(g),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ925_spl])],[split_symbol_definition]) ).
fof(f10228,plain,
( sQ925_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f10199,f584,f10225]) ).
fof(f10229,definition,
( sQ926_spl
<=> compose(codomain(h),compose(codomain(h),compose(g,a))) = compose(codomain(h),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ926_spl])],[split_symbol_definition]) ).
fof(f10232,plain,
( sQ926_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f10200,f584,f10229]) ).
fof(f10233,definition,
( sQ927_spl
<=> compose(codomain(a),compose(codomain(a),compose(g,a))) = compose(codomain(a),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ927_spl])],[split_symbol_definition]) ).
fof(f10236,plain,
( sQ927_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10201,f693,f10233]) ).
fof(f10244,plain,
( compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),compose(h,a))) = compose(codomain(compose(a,b)),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f4794]) ).
fof(f10245,plain,
( compose(codomain(compose(h,compose(a,b))),compose(codomain(compose(h,compose(a,b))),compose(h,a))) = compose(codomain(compose(h,compose(a,b))),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f4794]) ).
fof(f10246,plain,
( compose(codomain(compose(h,a)),compose(codomain(compose(h,a)),compose(h,a))) = compose(codomain(compose(h,a)),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f4794]) ).
fof(f10247,plain,
( compose(codomain(compose(g,a)),compose(codomain(compose(g,a)),compose(h,a))) = compose(codomain(compose(g,a)),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f4794]) ).
fof(f10248,plain,
( compose(codomain(g),compose(codomain(g),compose(h,a))) = compose(codomain(g),compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f4794]) ).
fof(f10249,plain,
( compose(codomain(h),compose(codomain(h),compose(h,a))) = compose(codomain(h),compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f4794]) ).
fof(f10250,plain,
( compose(codomain(a),compose(codomain(a),compose(h,a))) = compose(codomain(a),compose(h,a))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f4794]) ).
fof(f10258,definition,
( sQ928_spl
<=> compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),compose(h,a))) = compose(codomain(compose(a,b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ928_spl])],[split_symbol_definition]) ).
fof(f10261,plain,
( sQ928_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f10244,f1555,f10258]) ).
fof(f10262,definition,
( sQ929_spl
<=> compose(codomain(compose(h,compose(a,b))),compose(codomain(compose(h,compose(a,b))),compose(h,a))) = compose(codomain(compose(h,compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ929_spl])],[split_symbol_definition]) ).
fof(f10265,plain,
( sQ929_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f10245,f1555,f10262]) ).
fof(f10266,definition,
( sQ930_spl
<=> compose(codomain(compose(h,a)),compose(codomain(compose(h,a)),compose(h,a))) = compose(codomain(compose(h,a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ930_spl])],[split_symbol_definition]) ).
fof(f10269,plain,
( sQ930_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10246,f693,f10266]) ).
fof(f10270,definition,
( sQ931_spl
<=> compose(codomain(compose(g,a)),compose(codomain(compose(g,a)),compose(h,a))) = compose(codomain(compose(g,a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ931_spl])],[split_symbol_definition]) ).
fof(f10273,plain,
( sQ931_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10247,f693,f10270]) ).
fof(f10274,definition,
( sQ932_spl
<=> compose(codomain(g),compose(codomain(g),compose(h,a))) = compose(codomain(g),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ932_spl])],[split_symbol_definition]) ).
fof(f10277,plain,
( sQ932_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f10248,f584,f10274]) ).
fof(f10278,definition,
( sQ933_spl
<=> compose(codomain(h),compose(codomain(h),compose(h,a))) = compose(codomain(h),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ933_spl])],[split_symbol_definition]) ).
fof(f10281,plain,
( sQ933_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f10249,f584,f10278]) ).
fof(f10282,definition,
( sQ934_spl
<=> compose(codomain(a),compose(codomain(a),compose(h,a))) = compose(codomain(a),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ934_spl])],[split_symbol_definition]) ).
fof(f10285,plain,
( sQ934_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10250,f693,f10282]) ).
fof(f10295,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)],[f120,f4795]) ).
fof(f10296,plain,
( compose(codomain(compose(h,compose(a,b))),compose(codomain(compose(h,compose(a,b))),compose(a,b))) = compose(codomain(compose(h,compose(a,b))),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f581,f4795]) ).
fof(f10297,plain,
( compose(codomain(compose(h,a)),compose(codomain(compose(h,a)),compose(a,b))) = compose(codomain(compose(h,a)),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f131,f4795]) ).
fof(f10298,plain,
( compose(codomain(compose(g,a)),compose(codomain(compose(g,a)),compose(a,b))) = compose(codomain(compose(g,a)),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f130,f4795]) ).
fof(f10299,plain,
( compose(codomain(g),compose(codomain(g),compose(a,b))) = compose(codomain(g),compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f4795]) ).
fof(f10300,plain,
( compose(codomain(h),compose(codomain(h),compose(a,b))) = compose(codomain(h),compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f4795]) ).
fof(f10301,plain,
( compose(codomain(a),compose(codomain(a),compose(a,b))) = compose(codomain(a),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f4795]) ).
fof(f10319,definition,
( sQ935_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,[sQ935_spl])],[split_symbol_definition]) ).
fof(f10322,plain,
( sQ935_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f10295,f1570,f10319]) ).
fof(f10323,definition,
( sQ936_spl
<=> compose(codomain(compose(h,compose(a,b))),compose(codomain(compose(h,compose(a,b))),compose(a,b))) = compose(codomain(compose(h,compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ936_spl])],[split_symbol_definition]) ).
fof(f10326,plain,
( sQ936_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f10296,f1570,f10323]) ).
fof(f10327,definition,
( sQ937_spl
<=> compose(codomain(compose(h,a)),compose(codomain(compose(h,a)),compose(a,b))) = compose(codomain(compose(h,a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ937_spl])],[split_symbol_definition]) ).
fof(f10330,plain,
( sQ937_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f10297,f715,f10327]) ).
fof(f10331,definition,
( sQ938_spl
<=> compose(codomain(compose(g,a)),compose(codomain(compose(g,a)),compose(a,b))) = compose(codomain(compose(g,a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ938_spl])],[split_symbol_definition]) ).
fof(f10334,plain,
( sQ938_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f10298,f715,f10331]) ).
fof(f10335,definition,
( sQ939_spl
<=> compose(codomain(g),compose(codomain(g),compose(a,b))) = compose(codomain(g),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ939_spl])],[split_symbol_definition]) ).
fof(f10338,plain,
( sQ939_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f10299,f606,f10335]) ).
fof(f10339,definition,
( sQ940_spl
<=> compose(codomain(h),compose(codomain(h),compose(a,b))) = compose(codomain(h),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ940_spl])],[split_symbol_definition]) ).
fof(f10342,plain,
( sQ940_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f10300,f606,f10339]) ).
fof(f10343,definition,
( sQ941_spl
<=> compose(codomain(a),compose(codomain(a),compose(a,b))) = compose(codomain(a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ941_spl])],[split_symbol_definition]) ).
fof(f10346,plain,
( sQ941_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f10301,f715,f10343]) ).
fof(f10368,plain,
( compose(domain(g),compose(domain(g),compose(g,a))) = compose(domain(g),compose(g,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f4875]) ).
fof(f10369,plain,
( compose(domain(compose(g,a)),compose(domain(compose(g,a)),compose(g,a))) = compose(domain(compose(g,a)),compose(g,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f4875]) ).
fof(f10370,plain,
( compose(domain(compose(h,compose(a,b))),compose(domain(compose(h,compose(a,b))),compose(g,a))) = compose(domain(compose(h,compose(a,b))),compose(g,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f4875]) ).
fof(f10371,plain,
( compose(domain(compose(h,a)),compose(domain(compose(h,a)),compose(g,a))) = compose(domain(compose(h,a)),compose(g,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f4875]) ).
fof(f10372,plain,
( compose(domain(compose(a,b)),compose(domain(compose(a,b)),compose(g,a))) = compose(domain(compose(a,b)),compose(g,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f4875]) ).
fof(f10399,definition,
( sQ942_spl
<=> compose(domain(g),compose(domain(g),compose(g,a))) = compose(domain(g),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ942_spl])],[split_symbol_definition]) ).
fof(f10402,plain,
( sQ942_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f10368,f2687,f10399]) ).
fof(f10403,definition,
( sQ943_spl
<=> compose(domain(compose(g,a)),compose(domain(compose(g,a)),compose(g,a))) = compose(domain(compose(g,a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ943_spl])],[split_symbol_definition]) ).
fof(f10406,plain,
( sQ943_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f10369,f2687,f10403]) ).
fof(f10407,definition,
( sQ944_spl
<=> compose(domain(compose(h,compose(a,b))),compose(domain(compose(h,compose(a,b))),compose(g,a))) = compose(domain(compose(h,compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ944_spl])],[split_symbol_definition]) ).
fof(f10410,plain,
( sQ944_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f10370,f2687,f10407]) ).
fof(f10411,definition,
( sQ945_spl
<=> compose(domain(compose(h,a)),compose(domain(compose(h,a)),compose(g,a))) = compose(domain(compose(h,a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ945_spl])],[split_symbol_definition]) ).
fof(f10414,plain,
( sQ945_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f10371,f2687,f10411]) ).
fof(f10415,definition,
( sQ946_spl
<=> compose(domain(compose(a,b)),compose(domain(compose(a,b)),compose(g,a))) = compose(domain(compose(a,b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ946_spl])],[split_symbol_definition]) ).
fof(f10418,plain,
( sQ946_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f10372,f584,f10415]) ).
fof(f10448,plain,
( compose(domain(g),compose(domain(g),compose(h,a))) = compose(domain(g),compose(h,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f4877]) ).
fof(f10449,plain,
( compose(domain(compose(g,a)),compose(domain(compose(g,a)),compose(h,a))) = compose(domain(compose(g,a)),compose(h,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f4877]) ).
fof(f10450,plain,
( compose(domain(compose(h,compose(a,b))),compose(domain(compose(h,compose(a,b))),compose(h,a))) = compose(domain(compose(h,compose(a,b))),compose(h,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f4877]) ).
fof(f10451,plain,
( compose(domain(compose(h,a)),compose(domain(compose(h,a)),compose(h,a))) = compose(domain(compose(h,a)),compose(h,a))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f4877]) ).
fof(f10452,plain,
( compose(domain(compose(a,b)),compose(domain(compose(a,b)),compose(h,a))) = compose(domain(compose(a,b)),compose(h,a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f4877]) ).
fof(f10479,definition,
( sQ947_spl
<=> compose(domain(g),compose(domain(g),compose(h,a))) = compose(domain(g),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ947_spl])],[split_symbol_definition]) ).
fof(f10482,plain,
( sQ947_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f10448,f2687,f10479]) ).
fof(f10483,definition,
( sQ948_spl
<=> compose(domain(compose(g,a)),compose(domain(compose(g,a)),compose(h,a))) = compose(domain(compose(g,a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ948_spl])],[split_symbol_definition]) ).
fof(f10486,plain,
( sQ948_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f10449,f2687,f10483]) ).
fof(f10487,definition,
( sQ949_spl
<=> compose(domain(compose(h,compose(a,b))),compose(domain(compose(h,compose(a,b))),compose(h,a))) = compose(domain(compose(h,compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ949_spl])],[split_symbol_definition]) ).
fof(f10490,plain,
( sQ949_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f10450,f2687,f10487]) ).
fof(f10491,definition,
( sQ950_spl
<=> compose(domain(compose(h,a)),compose(domain(compose(h,a)),compose(h,a))) = compose(domain(compose(h,a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ950_spl])],[split_symbol_definition]) ).
fof(f10494,plain,
( sQ950_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f10451,f2687,f10491]) ).
fof(f10495,definition,
( sQ951_spl
<=> compose(domain(compose(a,b)),compose(domain(compose(a,b)),compose(h,a))) = compose(domain(compose(a,b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ951_spl])],[split_symbol_definition]) ).
fof(f10498,plain,
( sQ951_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f10452,f584,f10495]) ).
fof(f10523,plain,
( compose(h,compose(domain(h),compose(h,a))) = compose(compose(h,domain(h)),compose(h,a))
| domain(a) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f2062,f15]) ).
fof(f10524,plain,
( compose(h,compose(compose(a,b),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a))
| codomain(b) != domain(h)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f2062]) ).
fof(f10525,plain,
( compose(h,compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(h,compose(a,b))),compose(h,a))
| codomain(b) != domain(h)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f2062]) ).
fof(f10526,plain,
( compose(h,compose(compose(h,a),compose(h,a))) = compose(compose(h,compose(h,a)),compose(h,a))
| domain(b) != domain(h)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f2062]) ).
fof(f10527,plain,
( compose(h,compose(compose(g,a),compose(h,a))) = compose(compose(h,compose(g,a)),compose(h,a))
| domain(b) != domain(h)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f2062]) ).
fof(f10528,plain,
( compose(h,compose(g,compose(h,a))) = compose(compose(h,g),compose(h,a))
| domain(a) != domain(h)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f2062]) ).
fof(f10529,plain,
( compose(h,compose(h,compose(h,a))) = compose(compose(h,h),compose(h,a))
| domain(a) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f2062]) ).
fof(f10530,plain,
( compose(h,compose(a,compose(h,a))) = compose(compose(h,a),compose(h,a))
| domain(b) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f2062]) ).
fof(f10531,plain,
! [X0] :
( compose(h,compose(codomain(X0),compose(h,a))) = compose(compose(h,codomain(X0)),compose(h,a))
| codomain(X0) != domain(h)
| domain(a) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f2062]) ).
fof(f10532,plain,
! [X0] :
( compose(h,compose(domain(X0),compose(h,a))) = compose(compose(h,domain(X0)),compose(h,a))
| domain(X0) != domain(h)
| domain(a) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f2062]) ).
fof(f10533,definition,
( sQ952_spl
<=> compose(h,compose(domain(h),compose(h,a))) = compose(compose(h,domain(h)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ952_spl])],[split_symbol_definition]) ).
fof(f10536,plain,
( sQ952_spl
| ~ sQ813_spl ),
inference(split_clause,[status(thm)],[f10523,f8971,f10533]) ).
fof(f10537,plain,
( sQ868_spl
| ~ sQ66_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f10524,f1765,f1555,f9382]) ).
fof(f10538,definition,
( sQ953_spl
<=> compose(h,compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(h,compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ953_spl])],[split_symbol_definition]) ).
fof(f10541,plain,
( sQ953_spl
| ~ sQ66_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f10525,f1772,f1555,f10538]) ).
fof(f10542,definition,
( sQ954_spl
<=> compose(h,compose(compose(h,a),compose(h,a))) = compose(compose(h,compose(h,a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ954_spl])],[split_symbol_definition]) ).
fof(f10545,plain,
( sQ954_spl
| ~ sQ21_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f10526,f1736,f693,f10542]) ).
fof(f10546,definition,
( sQ955_spl
<=> compose(h,compose(compose(g,a),compose(h,a))) = compose(compose(h,compose(g,a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ955_spl])],[split_symbol_definition]) ).
fof(f10549,plain,
( sQ955_spl
| ~ sQ21_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f10527,f1743,f693,f10546]) ).
fof(f10550,definition,
( sQ956_spl
<=> compose(h,compose(g,compose(h,a))) = compose(compose(h,g),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ956_spl])],[split_symbol_definition]) ).
fof(f10553,plain,
( sQ956_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f10528,f591,f584,f10550]) ).
fof(f10554,definition,
( sQ957_spl
<=> compose(h,compose(h,compose(h,a))) = compose(compose(h,h),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ957_spl])],[split_symbol_definition]) ).
fof(f10557,plain,
( sQ957_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f10529,f584,f10554]) ).
fof(f10558,plain,
( sQ59_spl
| ~ sQ21_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f10530,f606,f693,f1404]) ).
fof(f10559,plain,
! [X0] :
( compose(h,compose(codomain(X0),compose(h,a))) = compose(compose(h,codomain(X0)),compose(h,a))
| codomain(X0) != domain(h)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f10531]) ).
fof(f10560,plain,
! [X0] :
( compose(h,compose(domain(X0),compose(h,a))) = compose(compose(h,domain(X0)),compose(h,a))
| domain(X0) != domain(h)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f10532]) ).
fof(f10563,plain,
( compose(domain(compose(g,a)),compose(domain(compose(g,a)),compose(a,b))) = compose(domain(compose(g,a)),compose(a,b))
| domain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f1108,f4878]) ).
fof(f10564,plain,
( compose(domain(compose(h,compose(a,b))),compose(domain(compose(h,compose(a,b))),compose(a,b))) = compose(domain(compose(h,compose(a,b))),compose(a,b))
| domain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f1068,f4878]) ).
fof(f10565,plain,
( compose(domain(compose(h,a)),compose(domain(compose(h,a)),compose(a,b))) = compose(domain(compose(h,a)),compose(a,b))
| domain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f76,f4878]) ).
fof(f10566,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)],[f60,f4878]) ).
fof(f10578,definition,
( sQ958_spl
<=> compose(domain(compose(g,a)),compose(domain(compose(g,a)),compose(a,b))) = compose(domain(compose(g,a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ958_spl])],[split_symbol_definition]) ).
fof(f10581,plain,
( sQ958_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f10563,f584,f10578]) ).
fof(f10582,definition,
( sQ959_spl
<=> compose(domain(compose(h,compose(a,b))),compose(domain(compose(h,compose(a,b))),compose(a,b))) = compose(domain(compose(h,compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ959_spl])],[split_symbol_definition]) ).
fof(f10585,plain,
( sQ959_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f10564,f584,f10582]) ).
fof(f10586,definition,
( sQ960_spl
<=> compose(domain(compose(h,a)),compose(domain(compose(h,a)),compose(a,b))) = compose(domain(compose(h,a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ960_spl])],[split_symbol_definition]) ).
fof(f10589,plain,
( sQ960_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f10565,f584,f10586]) ).
fof(f10590,definition,
( sQ961_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,[sQ961_spl])],[split_symbol_definition]) ).
fof(f10593,plain,
( sQ961_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f10566,f606,f10590]) ).
fof(f10604,plain,
( compose(compose(g,a),domain(compose(g,a))) = compose(compose(compose(g,a),domain(compose(g,a))),domain(compose(g,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f8495]) ).
fof(f10605,plain,
( compose(compose(g,a),domain(compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),domain(compose(h,compose(a,b))))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f8495]) ).
fof(f10606,plain,
( compose(compose(g,a),domain(compose(h,a))) = compose(compose(compose(g,a),domain(compose(h,a))),domain(compose(h,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f8495]) ).
fof(f10607,plain,
( compose(compose(g,a),domain(compose(a,b))) = compose(compose(compose(g,a),domain(compose(a,b))),domain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f8495]) ).
fof(f10616,definition,
( sQ962_spl
<=> compose(compose(g,a),domain(compose(g,a))) = compose(compose(compose(g,a),domain(compose(g,a))),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ962_spl])],[split_symbol_definition]) ).
fof(f10619,plain,
( sQ962_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10604,f693,f10616]) ).
fof(f10620,definition,
( sQ963_spl
<=> compose(compose(g,a),domain(compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ963_spl])],[split_symbol_definition]) ).
fof(f10623,plain,
( sQ963_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10605,f693,f10620]) ).
fof(f10624,definition,
( sQ964_spl
<=> compose(compose(g,a),domain(compose(h,a))) = compose(compose(compose(g,a),domain(compose(h,a))),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ964_spl])],[split_symbol_definition]) ).
fof(f10627,plain,
( sQ964_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10606,f693,f10624]) ).
fof(f10628,definition,
( sQ965_spl
<=> compose(compose(g,a),domain(compose(a,b))) = compose(compose(compose(g,a),domain(compose(a,b))),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ965_spl])],[split_symbol_definition]) ).
fof(f10631,plain,
( sQ965_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f10607,f715,f10628]) ).
fof(f10644,plain,
( compose(compose(g,a),codomain(compose(a,b))) = compose(compose(compose(g,a),codomain(compose(a,b))),codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f8496]) ).
fof(f10645,plain,
( compose(compose(g,a),codomain(compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),codomain(compose(h,compose(a,b))))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f8496]) ).
fof(f10646,plain,
( compose(compose(g,a),codomain(compose(h,a))) = compose(compose(compose(g,a),codomain(compose(h,a))),codomain(compose(h,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f8496]) ).
fof(f10647,plain,
( compose(compose(g,a),codomain(compose(g,a))) = compose(compose(compose(g,a),codomain(compose(g,a))),codomain(compose(g,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f8496]) ).
fof(f10648,plain,
( compose(compose(g,a),codomain(g)) = compose(compose(compose(g,a),codomain(g)),codomain(g))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f8496]) ).
fof(f10649,plain,
( compose(compose(g,a),codomain(h)) = compose(compose(compose(g,a),codomain(h)),codomain(h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f8496]) ).
fof(f10650,plain,
( compose(compose(g,a),codomain(a)) = compose(compose(compose(g,a),codomain(a)),codomain(a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f8496]) ).
fof(f10670,definition,
( sQ966_spl
<=> compose(compose(g,a),codomain(compose(a,b))) = compose(compose(compose(g,a),codomain(compose(a,b))),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ966_spl])],[split_symbol_definition]) ).
fof(f10673,plain,
( sQ966_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f10644,f2265,f10670]) ).
fof(f10674,definition,
( sQ967_spl
<=> compose(compose(g,a),codomain(compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ967_spl])],[split_symbol_definition]) ).
fof(f10677,plain,
( sQ967_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f10645,f2265,f10674]) ).
fof(f10678,definition,
( sQ968_spl
<=> compose(compose(g,a),codomain(compose(h,a))) = compose(compose(compose(g,a),codomain(compose(h,a))),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ968_spl])],[split_symbol_definition]) ).
fof(f10681,plain,
( sQ968_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f10646,f1941,f10678]) ).
fof(f10682,definition,
( sQ969_spl
<=> compose(compose(g,a),codomain(compose(g,a))) = compose(compose(compose(g,a),codomain(compose(g,a))),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ969_spl])],[split_symbol_definition]) ).
fof(f10685,plain,
( sQ969_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f10647,f1941,f10682]) ).
fof(f10686,definition,
( sQ970_spl
<=> compose(compose(g,a),codomain(g)) = compose(compose(compose(g,a),codomain(g)),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ970_spl])],[split_symbol_definition]) ).
fof(f10689,plain,
( sQ970_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f10648,f715,f10686]) ).
fof(f10690,definition,
( sQ971_spl
<=> compose(compose(g,a),codomain(h)) = compose(compose(compose(g,a),codomain(h)),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ971_spl])],[split_symbol_definition]) ).
fof(f10693,plain,
( sQ971_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f10649,f715,f10690]) ).
fof(f10694,definition,
( sQ972_spl
<=> compose(compose(g,a),codomain(a)) = compose(compose(compose(g,a),codomain(a)),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ972_spl])],[split_symbol_definition]) ).
fof(f10697,plain,
( sQ972_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f10650,f1941,f10694]) ).
fof(f10717,plain,
( compose(compose(h,a),domain(compose(g,a))) = compose(compose(compose(h,a),domain(compose(g,a))),domain(compose(g,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f8557]) ).
fof(f10718,plain,
( compose(compose(h,a),domain(compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),domain(compose(h,compose(a,b))))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f8557]) ).
fof(f10719,plain,
( compose(compose(h,a),domain(compose(h,a))) = compose(compose(compose(h,a),domain(compose(h,a))),domain(compose(h,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f8557]) ).
fof(f10720,plain,
( compose(compose(h,a),domain(compose(a,b))) = compose(compose(compose(h,a),domain(compose(a,b))),domain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f8557]) ).
fof(f10729,definition,
( sQ973_spl
<=> compose(compose(h,a),domain(compose(g,a))) = compose(compose(compose(h,a),domain(compose(g,a))),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ973_spl])],[split_symbol_definition]) ).
fof(f10732,plain,
( sQ973_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10717,f693,f10729]) ).
fof(f10733,definition,
( sQ974_spl
<=> compose(compose(h,a),domain(compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ974_spl])],[split_symbol_definition]) ).
fof(f10736,plain,
( sQ974_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10718,f693,f10733]) ).
fof(f10737,definition,
( sQ975_spl
<=> compose(compose(h,a),domain(compose(h,a))) = compose(compose(compose(h,a),domain(compose(h,a))),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ975_spl])],[split_symbol_definition]) ).
fof(f10740,plain,
( sQ975_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10719,f693,f10737]) ).
fof(f10741,definition,
( sQ976_spl
<=> compose(compose(h,a),domain(compose(a,b))) = compose(compose(compose(h,a),domain(compose(a,b))),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ976_spl])],[split_symbol_definition]) ).
fof(f10744,plain,
( sQ976_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f10720,f715,f10741]) ).
fof(f10757,plain,
( compose(compose(h,a),codomain(compose(a,b))) = compose(compose(compose(h,a),codomain(compose(a,b))),codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f8558]) ).
fof(f10758,plain,
( compose(compose(h,a),codomain(compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),codomain(compose(h,compose(a,b))))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f8558]) ).
fof(f10759,plain,
( compose(compose(h,a),codomain(compose(h,a))) = compose(compose(compose(h,a),codomain(compose(h,a))),codomain(compose(h,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f8558]) ).
fof(f10760,plain,
( compose(compose(h,a),codomain(compose(g,a))) = compose(compose(compose(h,a),codomain(compose(g,a))),codomain(compose(g,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f8558]) ).
fof(f10761,plain,
( compose(compose(h,a),codomain(g)) = compose(compose(compose(h,a),codomain(g)),codomain(g))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f8558]) ).
fof(f10762,plain,
( compose(compose(h,a),codomain(h)) = compose(compose(compose(h,a),codomain(h)),codomain(h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f8558]) ).
fof(f10763,plain,
( compose(compose(h,a),codomain(a)) = compose(compose(compose(h,a),codomain(a)),codomain(a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f8558]) ).
fof(f10783,definition,
( sQ977_spl
<=> compose(compose(h,a),codomain(compose(a,b))) = compose(compose(compose(h,a),codomain(compose(a,b))),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ977_spl])],[split_symbol_definition]) ).
fof(f10786,plain,
( sQ977_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f10757,f2265,f10783]) ).
fof(f10787,definition,
( sQ978_spl
<=> compose(compose(h,a),codomain(compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ978_spl])],[split_symbol_definition]) ).
fof(f10790,plain,
( sQ978_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f10758,f2265,f10787]) ).
fof(f10791,definition,
( sQ979_spl
<=> compose(compose(h,a),codomain(compose(h,a))) = compose(compose(compose(h,a),codomain(compose(h,a))),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ979_spl])],[split_symbol_definition]) ).
fof(f10794,plain,
( sQ979_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f10759,f1941,f10791]) ).
fof(f10795,definition,
( sQ980_spl
<=> compose(compose(h,a),codomain(compose(g,a))) = compose(compose(compose(h,a),codomain(compose(g,a))),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ980_spl])],[split_symbol_definition]) ).
fof(f10798,plain,
( sQ980_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f10760,f1941,f10795]) ).
fof(f10799,definition,
( sQ981_spl
<=> compose(compose(h,a),codomain(g)) = compose(compose(compose(h,a),codomain(g)),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ981_spl])],[split_symbol_definition]) ).
fof(f10802,plain,
( sQ981_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f10761,f715,f10799]) ).
fof(f10803,definition,
( sQ982_spl
<=> compose(compose(h,a),codomain(h)) = compose(compose(compose(h,a),codomain(h)),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ982_spl])],[split_symbol_definition]) ).
fof(f10806,plain,
( sQ982_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f10762,f715,f10803]) ).
fof(f10807,definition,
( sQ983_spl
<=> compose(compose(h,a),codomain(a)) = compose(compose(compose(h,a),codomain(a)),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ983_spl])],[split_symbol_definition]) ).
fof(f10810,plain,
( sQ983_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f10763,f1941,f10807]) ).
fof(f10829,plain,
( compose(h,compose(g,compose(a,b))) = compose(compose(h,g),compose(a,b))
| domain(a) != domain(g) ),
inference(resolution,[status(thm)],[f2063,f74]) ).
fof(f10830,plain,
( compose(h,compose(h,compose(a,b))) = compose(compose(h,h),compose(a,b))
| domain(a) != domain(h) ),
inference(resolution,[status(thm)],[f2063,f69]) ).
fof(f10831,plain,
( compose(h,compose(domain(a),compose(a,b))) = compose(compose(h,domain(a)),compose(a,b))
| domain(a) != domain(domain(a)) ),
inference(resolution,[status(thm)],[f2063,f15]) ).
fof(f10832,plain,
( compose(h,compose(compose(a,b),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b))
| codomain(b) != domain(a)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f2063]) ).
fof(f10833,plain,
( compose(h,compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(h,compose(a,b))),compose(a,b))
| codomain(b) != domain(a)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f2063]) ).
fof(f10834,plain,
( compose(h,compose(compose(h,a),compose(a,b))) = compose(compose(h,compose(h,a)),compose(a,b))
| domain(b) != domain(a)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f2063]) ).
fof(f10835,plain,
( compose(h,compose(compose(g,a),compose(a,b))) = compose(compose(h,compose(g,a)),compose(a,b))
| domain(b) != domain(a)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f2063]) ).
fof(f10838,plain,
( compose(h,compose(a,compose(a,b))) = compose(compose(h,a),compose(a,b))
| domain(b) != domain(a)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f2063]) ).
fof(f10839,plain,
! [X0] :
( compose(h,compose(codomain(X0),compose(a,b))) = compose(compose(h,codomain(X0)),compose(a,b))
| codomain(X0) != domain(a)
| domain(a) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f2063]) ).
fof(f10840,plain,
! [X0] :
( compose(h,compose(domain(X0),compose(a,b))) = compose(compose(h,domain(X0)),compose(a,b))
| domain(X0) != domain(a)
| domain(a) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f2063]) ).
fof(f10841,definition,
( sQ984_spl
<=> compose(h,compose(g,compose(a,b))) = compose(compose(h,g),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ984_spl])],[split_symbol_definition]) ).
fof(f10844,plain,
( sQ984_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f10829,f591,f10841]) ).
fof(f10845,definition,
( sQ985_spl
<=> compose(h,compose(h,compose(a,b))) = compose(compose(h,h),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ985_spl])],[split_symbol_definition]) ).
fof(f10848,plain,
( sQ985_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f10830,f584,f10845]) ).
fof(f10849,definition,
( sQ986_spl
<=> compose(h,compose(domain(a),compose(a,b))) = compose(compose(h,domain(a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ986_spl])],[split_symbol_definition]) ).
fof(f10852,plain,
( sQ986_spl
| ~ sQ904_spl ),
inference(split_clause,[status(thm)],[f10831,f9696,f10849]) ).
fof(f10853,plain,
( sQ869_spl
| ~ sQ70_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f10832,f1765,f1570,f9386]) ).
fof(f10854,definition,
( sQ987_spl
<=> compose(h,compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(h,compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ987_spl])],[split_symbol_definition]) ).
fof(f10857,plain,
( sQ987_spl
| ~ sQ70_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f10833,f1772,f1570,f10854]) ).
fof(f10858,definition,
( sQ988_spl
<=> compose(h,compose(compose(h,a),compose(a,b))) = compose(compose(h,compose(h,a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ988_spl])],[split_symbol_definition]) ).
fof(f10861,plain,
( sQ988_spl
| ~ sQ27_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f10834,f1736,f715,f10858]) ).
fof(f10862,definition,
( sQ989_spl
<=> compose(h,compose(compose(g,a),compose(a,b))) = compose(compose(h,compose(g,a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ989_spl])],[split_symbol_definition]) ).
fof(f10865,plain,
( sQ989_spl
| ~ sQ27_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f10835,f1743,f715,f10862]) ).
fof(f10868,plain,
( sQ60_spl
| ~ sQ27_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f10838,f606,f715,f1408]) ).
fof(f10869,plain,
! [X0] :
( compose(h,compose(codomain(X0),compose(a,b))) = compose(compose(h,codomain(X0)),compose(a,b))
| codomain(X0) != domain(a)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f10839]) ).
fof(f10870,plain,
! [X0] :
( compose(h,compose(codomain(X0),compose(a,b))) = compose(compose(h,codomain(X0)),compose(a,b))
| domain(a) != codomain(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f10869]) ).
fof(f10871,plain,
! [X0] :
( compose(h,compose(domain(X0),compose(a,b))) = compose(compose(h,domain(X0)),compose(a,b))
| domain(X0) != domain(a)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f10840]) ).
fof(f10872,plain,
! [X0] :
( compose(h,compose(domain(X0),compose(a,b))) = compose(compose(h,domain(X0)),compose(a,b))
| domain(a) != domain(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f10871]) ).
fof(f10875,plain,
! [X0] :
( compose(codomain(compose(a,b)),compose(g,X0)) = compose(compose(codomain(compose(a,b)),g),X0)
| domain(a) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f9782]) ).
fof(f10876,plain,
! [X0] :
( compose(codomain(compose(h,compose(a,b))),compose(g,X0)) = compose(compose(codomain(compose(h,compose(a,b))),g),X0)
| domain(a) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f9782]) ).
fof(f10877,plain,
! [X0] :
( compose(codomain(compose(h,a)),compose(g,X0)) = compose(compose(codomain(compose(h,a)),g),X0)
| domain(a) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f9782]) ).
fof(f10878,plain,
! [X0] :
( compose(codomain(compose(g,a)),compose(g,X0)) = compose(compose(codomain(compose(g,a)),g),X0)
| domain(a) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f9782]) ).
fof(f10879,plain,
! [X0] :
( compose(codomain(g),compose(g,X0)) = compose(compose(codomain(g),g),X0)
| domain(a) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f9782]) ).
fof(f10880,plain,
! [X0] :
( compose(codomain(h),compose(g,X0)) = compose(compose(codomain(h),g),X0)
| domain(a) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f9782]) ).
fof(f10881,plain,
! [X0] :
( compose(codomain(a),compose(g,X0)) = compose(compose(codomain(a),g),X0)
| domain(a) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f9782]) ).
fof(f10887,definition,
! [X0] :
( sQ990_spl
<=> ( compose(codomain(compose(a,b)),compose(g,X0)) = compose(compose(codomain(compose(a,b)),g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ990_spl])],[split_symbol_definition]) ).
fof(f10890,plain,
( sQ990_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f10875,f1555,f10887]) ).
fof(f10891,definition,
! [X0] :
( sQ991_spl
<=> ( compose(codomain(compose(h,compose(a,b))),compose(g,X0)) = compose(compose(codomain(compose(h,compose(a,b))),g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ991_spl])],[split_symbol_definition]) ).
fof(f10894,plain,
( sQ991_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f10876,f1555,f10891]) ).
fof(f10895,definition,
! [X0] :
( sQ992_spl
<=> ( compose(codomain(compose(h,a)),compose(g,X0)) = compose(compose(codomain(compose(h,a)),g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ992_spl])],[split_symbol_definition]) ).
fof(f10898,plain,
( sQ992_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10877,f693,f10895]) ).
fof(f10899,definition,
! [X0] :
( sQ993_spl
<=> ( compose(codomain(compose(g,a)),compose(g,X0)) = compose(compose(codomain(compose(g,a)),g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ993_spl])],[split_symbol_definition]) ).
fof(f10902,plain,
( sQ993_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10878,f693,f10899]) ).
fof(f10903,definition,
! [X0] :
( sQ994_spl
<=> ( compose(codomain(g),compose(g,X0)) = compose(compose(codomain(g),g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ994_spl])],[split_symbol_definition]) ).
fof(f10906,plain,
( sQ994_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f10879,f584,f10903]) ).
fof(f10907,definition,
! [X0] :
( sQ995_spl
<=> ( compose(codomain(h),compose(g,X0)) = compose(compose(codomain(h),g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ995_spl])],[split_symbol_definition]) ).
fof(f10910,plain,
( sQ995_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f10880,f584,f10907]) ).
fof(f10911,definition,
! [X0] :
( sQ996_spl
<=> ( compose(codomain(a),compose(g,X0)) = compose(compose(codomain(a),g),X0)
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ996_spl])],[split_symbol_definition]) ).
fof(f10914,plain,
( sQ996_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10881,f693,f10911]) ).
fof(f10920,plain,
( compose(domain(a),compose(compose(a,b),domain(compose(g,a)))) = compose(compose(a,b),domain(compose(g,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f5042]) ).
fof(f10921,plain,
( compose(domain(a),compose(compose(a,b),domain(compose(h,compose(a,b))))) = compose(compose(a,b),domain(compose(h,compose(a,b))))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f5042]) ).
fof(f10922,plain,
( compose(domain(a),compose(compose(a,b),domain(compose(h,a)))) = compose(compose(a,b),domain(compose(h,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f5042]) ).
fof(f10923,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)],[f60,f5042]) ).
fof(f10930,definition,
( sQ997_spl
<=> compose(domain(a),compose(compose(a,b),domain(compose(g,a)))) = compose(compose(a,b),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ997_spl])],[split_symbol_definition]) ).
fof(f10933,plain,
( sQ997_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f10920,f1555,f10930]) ).
fof(f10934,definition,
( sQ998_spl
<=> compose(domain(a),compose(compose(a,b),domain(compose(h,compose(a,b))))) = compose(compose(a,b),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ998_spl])],[split_symbol_definition]) ).
fof(f10937,plain,
( sQ998_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f10921,f1555,f10934]) ).
fof(f10938,definition,
( sQ999_spl
<=> compose(domain(a),compose(compose(a,b),domain(compose(h,a)))) = compose(compose(a,b),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ999_spl])],[split_symbol_definition]) ).
fof(f10941,plain,
( sQ999_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f10922,f1555,f10938]) ).
fof(f10942,definition,
( sQ1000_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,[sQ1000_spl])],[split_symbol_definition]) ).
fof(f10945,plain,
( sQ1000_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f10923,f1570,f10942]) ).
fof(f10951,plain,
( compose(domain(h),compose(compose(h,a),domain(compose(g,a)))) = compose(compose(h,a),domain(compose(g,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f5044]) ).
fof(f10952,plain,
( compose(domain(h),compose(compose(h,a),domain(compose(h,compose(a,b))))) = compose(compose(h,a),domain(compose(h,compose(a,b))))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f5044]) ).
fof(f10953,plain,
( compose(domain(h),compose(compose(h,a),domain(compose(h,a)))) = compose(compose(h,a),domain(compose(h,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f5044]) ).
fof(f10954,plain,
( compose(domain(h),compose(compose(h,a),domain(compose(a,b)))) = compose(compose(h,a),domain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f5044]) ).
fof(f10962,definition,
( sQ1001_spl
<=> compose(domain(h),compose(compose(h,a),domain(compose(g,a)))) = compose(compose(h,a),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1001_spl])],[split_symbol_definition]) ).
fof(f10965,plain,
( sQ1001_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10951,f693,f10962]) ).
fof(f10966,definition,
( sQ1002_spl
<=> compose(domain(h),compose(compose(h,a),domain(compose(h,compose(a,b))))) = compose(compose(h,a),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1002_spl])],[split_symbol_definition]) ).
fof(f10969,plain,
( sQ1002_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10952,f693,f10966]) ).
fof(f10970,definition,
( sQ1003_spl
<=> compose(domain(h),compose(compose(h,a),domain(compose(h,a)))) = compose(compose(h,a),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1003_spl])],[split_symbol_definition]) ).
fof(f10973,plain,
( sQ1003_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10953,f693,f10970]) ).
fof(f10974,definition,
( sQ1004_spl
<=> compose(domain(h),compose(compose(h,a),domain(compose(a,b)))) = compose(compose(h,a),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1004_spl])],[split_symbol_definition]) ).
fof(f10977,plain,
( sQ1004_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f10954,f715,f10974]) ).
fof(f10985,plain,
( compose(domain(h),compose(compose(g,a),domain(compose(g,a)))) = compose(compose(g,a),domain(compose(g,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f5045]) ).
fof(f10986,plain,
( compose(domain(h),compose(compose(g,a),domain(compose(h,compose(a,b))))) = compose(compose(g,a),domain(compose(h,compose(a,b))))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f5045]) ).
fof(f10987,plain,
( compose(domain(h),compose(compose(g,a),domain(compose(h,a)))) = compose(compose(g,a),domain(compose(h,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f5045]) ).
fof(f10988,plain,
( compose(domain(h),compose(compose(g,a),domain(compose(a,b)))) = compose(compose(g,a),domain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f5045]) ).
fof(f10996,definition,
( sQ1005_spl
<=> compose(domain(h),compose(compose(g,a),domain(compose(g,a)))) = compose(compose(g,a),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1005_spl])],[split_symbol_definition]) ).
fof(f10999,plain,
( sQ1005_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10985,f693,f10996]) ).
fof(f11000,definition,
( sQ1006_spl
<=> compose(domain(h),compose(compose(g,a),domain(compose(h,compose(a,b))))) = compose(compose(g,a),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1006_spl])],[split_symbol_definition]) ).
fof(f11003,plain,
( sQ1006_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10986,f693,f11000]) ).
fof(f11004,definition,
( sQ1007_spl
<=> compose(domain(h),compose(compose(g,a),domain(compose(h,a)))) = compose(compose(g,a),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1007_spl])],[split_symbol_definition]) ).
fof(f11007,plain,
( sQ1007_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10987,f693,f11004]) ).
fof(f11008,definition,
( sQ1008_spl
<=> compose(domain(h),compose(compose(g,a),domain(compose(a,b)))) = compose(compose(g,a),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1008_spl])],[split_symbol_definition]) ).
fof(f11011,plain,
( sQ1008_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f10988,f715,f11008]) ).
fof(f11021,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)],[f120,f5105]) ).
fof(f11022,plain,
( compose(domain(a),compose(compose(a,b),codomain(compose(h,compose(a,b))))) = compose(compose(a,b),codomain(compose(h,compose(a,b))))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f5105]) ).
fof(f11023,plain,
( compose(domain(a),compose(compose(a,b),codomain(compose(h,a)))) = compose(compose(a,b),codomain(compose(h,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f5105]) ).
fof(f11024,plain,
( compose(domain(a),compose(compose(a,b),codomain(compose(g,a)))) = compose(compose(a,b),codomain(compose(g,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f5105]) ).
fof(f11038,definition,
( sQ1009_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,[sQ1009_spl])],[split_symbol_definition]) ).
fof(f11041,plain,
( sQ1009_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f11021,f4389,f11038]) ).
fof(f11042,definition,
( sQ1010_spl
<=> compose(domain(a),compose(compose(a,b),codomain(compose(h,compose(a,b))))) = compose(compose(a,b),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1010_spl])],[split_symbol_definition]) ).
fof(f11045,plain,
( sQ1010_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f11022,f4389,f11042]) ).
fof(f11046,definition,
( sQ1011_spl
<=> compose(domain(a),compose(compose(a,b),codomain(compose(h,a)))) = compose(compose(a,b),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1011_spl])],[split_symbol_definition]) ).
fof(f11049,plain,
( sQ1011_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11023,f2265,f11046]) ).
fof(f11050,definition,
( sQ1012_spl
<=> compose(domain(a),compose(compose(a,b),codomain(compose(g,a)))) = compose(compose(a,b),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1012_spl])],[split_symbol_definition]) ).
fof(f11053,plain,
( sQ1012_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11024,f2265,f11050]) ).
fof(f11066,plain,
( compose(a,compose(domain(h),compose(g,a))) = compose(compose(a,domain(h)),compose(g,a))
| domain(b) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f2324,f15]) ).
fof(f11067,plain,
( compose(a,compose(compose(a,b),compose(g,a))) = compose(compose(a,compose(a,b)),compose(g,a))
| codomain(b) != domain(h)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f2324]) ).
fof(f11068,plain,
( compose(a,compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(a,compose(h,compose(a,b))),compose(g,a))
| codomain(b) != domain(h)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f2324]) ).
fof(f11069,plain,
( compose(a,compose(compose(h,a),compose(g,a))) = compose(compose(a,compose(h,a)),compose(g,a))
| domain(b) != domain(h)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f2324]) ).
fof(f11070,plain,
( compose(a,compose(compose(g,a),compose(g,a))) = compose(compose(a,compose(g,a)),compose(g,a))
| domain(b) != domain(h)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f2324]) ).
fof(f11071,plain,
( compose(a,compose(g,compose(g,a))) = compose(compose(a,g),compose(g,a))
| domain(a) != domain(h)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f2324]) ).
fof(f11072,plain,
( compose(a,compose(h,compose(g,a))) = compose(compose(a,h),compose(g,a))
| domain(a) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f2324]) ).
fof(f11073,plain,
( compose(a,compose(a,compose(g,a))) = compose(compose(a,a),compose(g,a))
| domain(b) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f2324]) ).
fof(f11074,plain,
! [X0] :
( compose(a,compose(codomain(X0),compose(g,a))) = compose(compose(a,codomain(X0)),compose(g,a))
| codomain(X0) != domain(h)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f2324]) ).
fof(f11075,plain,
! [X0] :
( compose(a,compose(domain(X0),compose(g,a))) = compose(compose(a,domain(X0)),compose(g,a))
| domain(X0) != domain(h)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f2324]) ).
fof(f11076,definition,
( sQ1013_spl
<=> domain(b) = domain(domain(h)) ),
introduced(definition,[new_symbols(definition,[sQ1013_spl])],[split_symbol_definition]) ).
fof(f11078,plain,
( sQ1013_spl
| domain(b) != domain(domain(h)) ),
inference(component_clause,[status(thm)],[f11076]) ).
fof(f11079,definition,
( sQ1014_spl
<=> compose(a,compose(domain(h),compose(g,a))) = compose(compose(a,domain(h)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1014_spl])],[split_symbol_definition]) ).
fof(f11082,plain,
( sQ1014_spl
| ~ sQ1013_spl ),
inference(split_clause,[status(thm)],[f11066,f11076,f11079]) ).
fof(f11083,definition,
( sQ1015_spl
<=> compose(a,compose(compose(a,b),compose(g,a))) = compose(compose(a,compose(a,b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1015_spl])],[split_symbol_definition]) ).
fof(f11086,plain,
( sQ1015_spl
| ~ sQ66_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f11067,f2359,f1555,f11083]) ).
fof(f11087,definition,
( sQ1016_spl
<=> compose(a,compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(a,compose(h,compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1016_spl])],[split_symbol_definition]) ).
fof(f11090,plain,
( sQ1016_spl
| ~ sQ66_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f11068,f2366,f1555,f11087]) ).
fof(f11091,definition,
( sQ1017_spl
<=> compose(a,compose(compose(h,a),compose(g,a))) = compose(compose(a,compose(h,a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1017_spl])],[split_symbol_definition]) ).
fof(f11094,plain,
( sQ1017_spl
| ~ sQ21_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f11069,f2330,f693,f11091]) ).
fof(f11095,definition,
( sQ1018_spl
<=> compose(a,compose(compose(g,a),compose(g,a))) = compose(compose(a,compose(g,a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1018_spl])],[split_symbol_definition]) ).
fof(f11098,plain,
( sQ1018_spl
| ~ sQ21_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f11070,f2337,f693,f11095]) ).
fof(f11099,definition,
( sQ1019_spl
<=> compose(a,compose(g,compose(g,a))) = compose(compose(a,g),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1019_spl])],[split_symbol_definition]) ).
fof(f11102,plain,
( sQ1019_spl
| ~ sQ8_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f11071,f700,f584,f11099]) ).
fof(f11103,definition,
( sQ1020_spl
<=> compose(a,compose(h,compose(g,a))) = compose(compose(a,h),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1020_spl])],[split_symbol_definition]) ).
fof(f11106,plain,
( sQ1020_spl
| ~ sQ8_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f11072,f693,f584,f11103]) ).
fof(f11107,definition,
( sQ1021_spl
<=> compose(a,compose(a,compose(g,a))) = compose(compose(a,a),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1021_spl])],[split_symbol_definition]) ).
fof(f11110,plain,
( sQ1021_spl
| ~ sQ21_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11073,f715,f693,f11107]) ).
fof(f11111,plain,
! [X0] :
( compose(a,compose(codomain(X0),compose(g,a))) = compose(compose(a,codomain(X0)),compose(g,a))
| codomain(X0) != domain(h)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f11074]) ).
fof(f11112,plain,
! [X0] :
( compose(a,compose(domain(X0),compose(g,a))) = compose(compose(a,domain(X0)),compose(g,a))
| domain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f11075]) ).
fof(f11113,plain,
( sQ1013_spl
| domain(b) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f37,f11078]) ).
fof(f11118,plain,
( compose(domain(h),compose(compose(h,a),codomain(compose(a,b)))) = compose(compose(h,a),codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f5107]) ).
fof(f11119,plain,
( compose(domain(h),compose(compose(h,a),codomain(compose(h,compose(a,b))))) = compose(compose(h,a),codomain(compose(h,compose(a,b))))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f5107]) ).
fof(f11120,plain,
( compose(domain(h),compose(compose(h,a),codomain(compose(h,a)))) = compose(compose(h,a),codomain(compose(h,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f5107]) ).
fof(f11121,plain,
( compose(domain(h),compose(compose(h,a),codomain(compose(g,a)))) = compose(compose(h,a),codomain(compose(g,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f5107]) ).
fof(f11122,plain,
( compose(domain(h),compose(compose(h,a),codomain(g))) = compose(compose(h,a),codomain(g))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f5107]) ).
fof(f11123,plain,
( compose(domain(h),compose(compose(h,a),codomain(h))) = compose(compose(h,a),codomain(h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f5107]) ).
fof(f11124,plain,
( compose(domain(h),compose(compose(h,a),codomain(a))) = compose(compose(h,a),codomain(a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f5107]) ).
fof(f11141,definition,
( sQ1022_spl
<=> compose(domain(h),compose(compose(h,a),codomain(compose(a,b)))) = compose(compose(h,a),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1022_spl])],[split_symbol_definition]) ).
fof(f11144,plain,
( sQ1022_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11118,f2265,f11141]) ).
fof(f11145,definition,
( sQ1023_spl
<=> compose(domain(h),compose(compose(h,a),codomain(compose(h,compose(a,b))))) = compose(compose(h,a),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1023_spl])],[split_symbol_definition]) ).
fof(f11148,plain,
( sQ1023_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11119,f2265,f11145]) ).
fof(f11149,definition,
( sQ1024_spl
<=> compose(domain(h),compose(compose(h,a),codomain(compose(h,a)))) = compose(compose(h,a),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1024_spl])],[split_symbol_definition]) ).
fof(f11152,plain,
( sQ1024_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f11120,f1941,f11149]) ).
fof(f11153,definition,
( sQ1025_spl
<=> compose(domain(h),compose(compose(h,a),codomain(compose(g,a)))) = compose(compose(h,a),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1025_spl])],[split_symbol_definition]) ).
fof(f11156,plain,
( sQ1025_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f11121,f1941,f11153]) ).
fof(f11157,definition,
( sQ1026_spl
<=> compose(domain(h),compose(compose(h,a),codomain(g))) = compose(compose(h,a),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ1026_spl])],[split_symbol_definition]) ).
fof(f11160,plain,
( sQ1026_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11122,f715,f11157]) ).
fof(f11161,definition,
( sQ1027_spl
<=> compose(domain(h),compose(compose(h,a),codomain(h))) = compose(compose(h,a),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ1027_spl])],[split_symbol_definition]) ).
fof(f11164,plain,
( sQ1027_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11123,f715,f11161]) ).
fof(f11165,definition,
( sQ1028_spl
<=> compose(domain(h),compose(compose(h,a),codomain(a))) = compose(compose(h,a),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1028_spl])],[split_symbol_definition]) ).
fof(f11168,plain,
( sQ1028_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f11124,f1941,f11165]) ).
fof(f11187,plain,
( compose(domain(h),compose(compose(g,a),codomain(compose(a,b)))) = compose(compose(g,a),codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f5108]) ).
fof(f11188,plain,
( compose(domain(h),compose(compose(g,a),codomain(compose(h,compose(a,b))))) = compose(compose(g,a),codomain(compose(h,compose(a,b))))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f5108]) ).
fof(f11189,plain,
( compose(domain(h),compose(compose(g,a),codomain(compose(h,a)))) = compose(compose(g,a),codomain(compose(h,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f5108]) ).
fof(f11190,plain,
( compose(domain(h),compose(compose(g,a),codomain(compose(g,a)))) = compose(compose(g,a),codomain(compose(g,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f5108]) ).
fof(f11191,plain,
( compose(domain(h),compose(compose(g,a),codomain(g))) = compose(compose(g,a),codomain(g))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f5108]) ).
fof(f11192,plain,
( compose(domain(h),compose(compose(g,a),codomain(h))) = compose(compose(g,a),codomain(h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f5108]) ).
fof(f11193,plain,
( compose(domain(h),compose(compose(g,a),codomain(a))) = compose(compose(g,a),codomain(a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f5108]) ).
fof(f11210,definition,
( sQ1029_spl
<=> compose(domain(h),compose(compose(g,a),codomain(compose(a,b)))) = compose(compose(g,a),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1029_spl])],[split_symbol_definition]) ).
fof(f11213,plain,
( sQ1029_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11187,f2265,f11210]) ).
fof(f11214,definition,
( sQ1030_spl
<=> compose(domain(h),compose(compose(g,a),codomain(compose(h,compose(a,b))))) = compose(compose(g,a),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1030_spl])],[split_symbol_definition]) ).
fof(f11217,plain,
( sQ1030_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11188,f2265,f11214]) ).
fof(f11218,definition,
( sQ1031_spl
<=> compose(domain(h),compose(compose(g,a),codomain(compose(h,a)))) = compose(compose(g,a),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1031_spl])],[split_symbol_definition]) ).
fof(f11221,plain,
( sQ1031_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f11189,f1941,f11218]) ).
fof(f11222,definition,
( sQ1032_spl
<=> compose(domain(h),compose(compose(g,a),codomain(compose(g,a)))) = compose(compose(g,a),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1032_spl])],[split_symbol_definition]) ).
fof(f11225,plain,
( sQ1032_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f11190,f1941,f11222]) ).
fof(f11226,definition,
( sQ1033_spl
<=> compose(domain(h),compose(compose(g,a),codomain(g))) = compose(compose(g,a),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ1033_spl])],[split_symbol_definition]) ).
fof(f11229,plain,
( sQ1033_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11191,f715,f11226]) ).
fof(f11230,definition,
( sQ1034_spl
<=> compose(domain(h),compose(compose(g,a),codomain(h))) = compose(compose(g,a),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ1034_spl])],[split_symbol_definition]) ).
fof(f11233,plain,
( sQ1034_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11192,f715,f11230]) ).
fof(f11234,definition,
( sQ1035_spl
<=> compose(domain(h),compose(compose(g,a),codomain(a))) = compose(compose(g,a),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1035_spl])],[split_symbol_definition]) ).
fof(f11237,plain,
( sQ1035_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f11193,f1941,f11234]) ).
fof(f11253,plain,
( compose(compose(a,b),compose(codomain(b),domain(compose(g,a)))) = compose(compose(a,b),domain(compose(g,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f5265]) ).
fof(f11254,plain,
( compose(compose(a,b),compose(codomain(b),domain(compose(h,compose(a,b))))) = compose(compose(a,b),domain(compose(h,compose(a,b))))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f5265]) ).
fof(f11255,plain,
( compose(compose(a,b),compose(codomain(b),domain(compose(h,a)))) = compose(compose(a,b),domain(compose(h,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f5265]) ).
fof(f11256,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)],[f60,f5265]) ).
fof(f11263,definition,
( sQ1036_spl
<=> compose(compose(a,b),compose(codomain(b),domain(compose(g,a)))) = compose(compose(a,b),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1036_spl])],[split_symbol_definition]) ).
fof(f11266,plain,
( sQ1036_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f11253,f1555,f11263]) ).
fof(f11267,definition,
( sQ1037_spl
<=> compose(compose(a,b),compose(codomain(b),domain(compose(h,compose(a,b))))) = compose(compose(a,b),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1037_spl])],[split_symbol_definition]) ).
fof(f11270,plain,
( sQ1037_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f11254,f1555,f11267]) ).
fof(f11271,definition,
( sQ1038_spl
<=> compose(compose(a,b),compose(codomain(b),domain(compose(h,a)))) = compose(compose(a,b),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1038_spl])],[split_symbol_definition]) ).
fof(f11274,plain,
( sQ1038_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f11255,f1555,f11271]) ).
fof(f11275,definition,
( sQ1039_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,[sQ1039_spl])],[split_symbol_definition]) ).
fof(f11278,plain,
( sQ1039_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f11256,f1570,f11275]) ).
fof(f11284,plain,
( compose(compose(h,a),compose(domain(b),domain(compose(g,a)))) = compose(compose(h,a),domain(compose(g,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f5267]) ).
fof(f11285,plain,
( compose(compose(h,a),compose(domain(b),domain(compose(h,compose(a,b))))) = compose(compose(h,a),domain(compose(h,compose(a,b))))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f5267]) ).
fof(f11286,plain,
( compose(compose(h,a),compose(domain(b),domain(compose(h,a)))) = compose(compose(h,a),domain(compose(h,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f5267]) ).
fof(f11287,plain,
( compose(compose(h,a),compose(domain(b),domain(compose(a,b)))) = compose(compose(h,a),domain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f5267]) ).
fof(f11295,definition,
( sQ1040_spl
<=> compose(compose(h,a),compose(domain(b),domain(compose(g,a)))) = compose(compose(h,a),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1040_spl])],[split_symbol_definition]) ).
fof(f11298,plain,
( sQ1040_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f11284,f693,f11295]) ).
fof(f11299,definition,
( sQ1041_spl
<=> compose(compose(h,a),compose(domain(b),domain(compose(h,compose(a,b))))) = compose(compose(h,a),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1041_spl])],[split_symbol_definition]) ).
fof(f11302,plain,
( sQ1041_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f11285,f693,f11299]) ).
fof(f11303,definition,
( sQ1042_spl
<=> compose(compose(h,a),compose(domain(b),domain(compose(h,a)))) = compose(compose(h,a),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1042_spl])],[split_symbol_definition]) ).
fof(f11306,plain,
( sQ1042_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f11286,f693,f11303]) ).
fof(f11307,definition,
( sQ1043_spl
<=> compose(compose(h,a),compose(domain(b),domain(compose(a,b)))) = compose(compose(h,a),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1043_spl])],[split_symbol_definition]) ).
fof(f11310,plain,
( sQ1043_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11287,f715,f11307]) ).
fof(f11316,plain,
( compose(compose(g,a),compose(domain(b),domain(compose(g,a)))) = compose(compose(g,a),domain(compose(g,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f5268]) ).
fof(f11317,plain,
( compose(compose(g,a),compose(domain(b),domain(compose(h,compose(a,b))))) = compose(compose(g,a),domain(compose(h,compose(a,b))))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f5268]) ).
fof(f11318,plain,
( compose(compose(g,a),compose(domain(b),domain(compose(h,a)))) = compose(compose(g,a),domain(compose(h,a)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f5268]) ).
fof(f11319,plain,
( compose(compose(g,a),compose(domain(b),domain(compose(a,b)))) = compose(compose(g,a),domain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f5268]) ).
fof(f11327,definition,
( sQ1044_spl
<=> compose(compose(g,a),compose(domain(b),domain(compose(g,a)))) = compose(compose(g,a),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1044_spl])],[split_symbol_definition]) ).
fof(f11330,plain,
( sQ1044_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f11316,f693,f11327]) ).
fof(f11331,definition,
( sQ1045_spl
<=> compose(compose(g,a),compose(domain(b),domain(compose(h,compose(a,b))))) = compose(compose(g,a),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1045_spl])],[split_symbol_definition]) ).
fof(f11334,plain,
( sQ1045_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f11317,f693,f11331]) ).
fof(f11335,definition,
( sQ1046_spl
<=> compose(compose(g,a),compose(domain(b),domain(compose(h,a)))) = compose(compose(g,a),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1046_spl])],[split_symbol_definition]) ).
fof(f11338,plain,
( sQ1046_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f11318,f693,f11335]) ).
fof(f11339,definition,
( sQ1047_spl
<=> compose(compose(g,a),compose(domain(b),domain(compose(a,b)))) = compose(compose(g,a),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1047_spl])],[split_symbol_definition]) ).
fof(f11342,plain,
( sQ1047_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11319,f715,f11339]) ).
fof(f11347,plain,
( compose(a,compose(domain(h),compose(h,a))) = compose(compose(a,domain(h)),compose(h,a))
| domain(b) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f2326,f15]) ).
fof(f11348,plain,
( compose(a,compose(compose(a,b),compose(h,a))) = compose(compose(a,compose(a,b)),compose(h,a))
| codomain(b) != domain(h)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f2326]) ).
fof(f11349,plain,
( compose(a,compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(a,compose(h,compose(a,b))),compose(h,a))
| codomain(b) != domain(h)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f2326]) ).
fof(f11350,plain,
( compose(a,compose(compose(h,a),compose(h,a))) = compose(compose(a,compose(h,a)),compose(h,a))
| domain(b) != domain(h)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f2326]) ).
fof(f11351,plain,
( compose(a,compose(compose(g,a),compose(h,a))) = compose(compose(a,compose(g,a)),compose(h,a))
| domain(b) != domain(h)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f2326]) ).
fof(f11352,plain,
( compose(a,compose(g,compose(h,a))) = compose(compose(a,g),compose(h,a))
| domain(a) != domain(h)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f2326]) ).
fof(f11353,plain,
( compose(a,compose(h,compose(h,a))) = compose(compose(a,h),compose(h,a))
| domain(a) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f2326]) ).
fof(f11354,plain,
( compose(a,compose(a,compose(h,a))) = compose(compose(a,a),compose(h,a))
| domain(b) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f2326]) ).
fof(f11355,plain,
! [X0] :
( compose(a,compose(codomain(X0),compose(h,a))) = compose(compose(a,codomain(X0)),compose(h,a))
| codomain(X0) != domain(h)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f2326]) ).
fof(f11356,plain,
! [X0] :
( compose(a,compose(domain(X0),compose(h,a))) = compose(compose(a,domain(X0)),compose(h,a))
| domain(X0) != domain(h)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f2326]) ).
fof(f11357,definition,
( sQ1048_spl
<=> compose(a,compose(domain(h),compose(h,a))) = compose(compose(a,domain(h)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1048_spl])],[split_symbol_definition]) ).
fof(f11360,plain,
( sQ1048_spl
| ~ sQ1013_spl ),
inference(split_clause,[status(thm)],[f11347,f11076,f11357]) ).
fof(f11361,definition,
( sQ1049_spl
<=> compose(a,compose(compose(a,b),compose(h,a))) = compose(compose(a,compose(a,b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1049_spl])],[split_symbol_definition]) ).
fof(f11364,plain,
( sQ1049_spl
| ~ sQ66_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f11348,f2359,f1555,f11361]) ).
fof(f11365,definition,
( sQ1050_spl
<=> compose(a,compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(a,compose(h,compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1050_spl])],[split_symbol_definition]) ).
fof(f11368,plain,
( sQ1050_spl
| ~ sQ66_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f11349,f2366,f1555,f11365]) ).
fof(f11369,definition,
( sQ1051_spl
<=> compose(a,compose(compose(h,a),compose(h,a))) = compose(compose(a,compose(h,a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1051_spl])],[split_symbol_definition]) ).
fof(f11372,plain,
( sQ1051_spl
| ~ sQ21_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f11350,f2330,f693,f11369]) ).
fof(f11373,definition,
( sQ1052_spl
<=> compose(a,compose(compose(g,a),compose(h,a))) = compose(compose(a,compose(g,a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1052_spl])],[split_symbol_definition]) ).
fof(f11376,plain,
( sQ1052_spl
| ~ sQ21_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f11351,f2337,f693,f11373]) ).
fof(f11377,definition,
( sQ1053_spl
<=> compose(a,compose(g,compose(h,a))) = compose(compose(a,g),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1053_spl])],[split_symbol_definition]) ).
fof(f11380,plain,
( sQ1053_spl
| ~ sQ8_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f11352,f700,f584,f11377]) ).
fof(f11381,definition,
( sQ1054_spl
<=> compose(a,compose(h,compose(h,a))) = compose(compose(a,h),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1054_spl])],[split_symbol_definition]) ).
fof(f11384,plain,
( sQ1054_spl
| ~ sQ8_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f11353,f693,f584,f11381]) ).
fof(f11385,definition,
( sQ1055_spl
<=> compose(a,compose(a,compose(h,a))) = compose(compose(a,a),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1055_spl])],[split_symbol_definition]) ).
fof(f11388,plain,
( sQ1055_spl
| ~ sQ21_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11354,f715,f693,f11385]) ).
fof(f11389,plain,
! [X0] :
( compose(a,compose(codomain(X0),compose(h,a))) = compose(compose(a,codomain(X0)),compose(h,a))
| codomain(X0) != domain(h)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f11355]) ).
fof(f11390,plain,
! [X0] :
( compose(a,compose(domain(X0),compose(h,a))) = compose(compose(a,domain(X0)),compose(h,a))
| domain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f11356]) ).
fof(f11394,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)],[f120,f5325]) ).
fof(f11395,plain,
( compose(compose(a,b),compose(codomain(b),codomain(compose(h,compose(a,b))))) = compose(compose(a,b),codomain(compose(h,compose(a,b))))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f5325]) ).
fof(f11396,plain,
( compose(compose(a,b),compose(codomain(b),codomain(compose(h,a)))) = compose(compose(a,b),codomain(compose(h,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f5325]) ).
fof(f11397,plain,
( compose(compose(a,b),compose(codomain(b),codomain(compose(g,a)))) = compose(compose(a,b),codomain(compose(g,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f5325]) ).
fof(f11411,definition,
( sQ1056_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,[sQ1056_spl])],[split_symbol_definition]) ).
fof(f11414,plain,
( sQ1056_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f11394,f4389,f11411]) ).
fof(f11415,definition,
( sQ1057_spl
<=> compose(compose(a,b),compose(codomain(b),codomain(compose(h,compose(a,b))))) = compose(compose(a,b),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1057_spl])],[split_symbol_definition]) ).
fof(f11418,plain,
( sQ1057_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f11395,f4389,f11415]) ).
fof(f11419,definition,
( sQ1058_spl
<=> compose(compose(a,b),compose(codomain(b),codomain(compose(h,a)))) = compose(compose(a,b),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1058_spl])],[split_symbol_definition]) ).
fof(f11422,plain,
( sQ1058_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11396,f2265,f11419]) ).
fof(f11423,definition,
( sQ1059_spl
<=> compose(compose(a,b),compose(codomain(b),codomain(compose(g,a)))) = compose(compose(a,b),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1059_spl])],[split_symbol_definition]) ).
fof(f11426,plain,
( sQ1059_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11397,f2265,f11423]) ).
fof(f11442,plain,
( compose(compose(h,a),compose(domain(b),codomain(compose(a,b)))) = compose(compose(h,a),codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f5327]) ).
fof(f11443,plain,
( compose(compose(h,a),compose(domain(b),codomain(compose(h,compose(a,b))))) = compose(compose(h,a),codomain(compose(h,compose(a,b))))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f5327]) ).
fof(f11444,plain,
( compose(compose(h,a),compose(domain(b),codomain(compose(h,a)))) = compose(compose(h,a),codomain(compose(h,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f5327]) ).
fof(f11445,plain,
( compose(compose(h,a),compose(domain(b),codomain(compose(g,a)))) = compose(compose(h,a),codomain(compose(g,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f5327]) ).
fof(f11446,plain,
( compose(compose(h,a),compose(domain(b),codomain(g))) = compose(compose(h,a),codomain(g))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f5327]) ).
fof(f11447,plain,
( compose(compose(h,a),compose(domain(b),codomain(h))) = compose(compose(h,a),codomain(h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f5327]) ).
fof(f11448,plain,
( compose(compose(h,a),compose(domain(b),codomain(a))) = compose(compose(h,a),codomain(a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f5327]) ).
fof(f11465,definition,
( sQ1060_spl
<=> compose(compose(h,a),compose(domain(b),codomain(compose(a,b)))) = compose(compose(h,a),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1060_spl])],[split_symbol_definition]) ).
fof(f11468,plain,
( sQ1060_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11442,f2265,f11465]) ).
fof(f11469,definition,
( sQ1061_spl
<=> compose(compose(h,a),compose(domain(b),codomain(compose(h,compose(a,b))))) = compose(compose(h,a),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1061_spl])],[split_symbol_definition]) ).
fof(f11472,plain,
( sQ1061_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11443,f2265,f11469]) ).
fof(f11473,definition,
( sQ1062_spl
<=> compose(compose(h,a),compose(domain(b),codomain(compose(h,a)))) = compose(compose(h,a),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1062_spl])],[split_symbol_definition]) ).
fof(f11476,plain,
( sQ1062_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f11444,f1941,f11473]) ).
fof(f11477,definition,
( sQ1063_spl
<=> compose(compose(h,a),compose(domain(b),codomain(compose(g,a)))) = compose(compose(h,a),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1063_spl])],[split_symbol_definition]) ).
fof(f11480,plain,
( sQ1063_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f11445,f1941,f11477]) ).
fof(f11481,definition,
( sQ1064_spl
<=> compose(compose(h,a),compose(domain(b),codomain(g))) = compose(compose(h,a),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ1064_spl])],[split_symbol_definition]) ).
fof(f11484,plain,
( sQ1064_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11446,f715,f11481]) ).
fof(f11485,definition,
( sQ1065_spl
<=> compose(compose(h,a),compose(domain(b),codomain(h))) = compose(compose(h,a),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ1065_spl])],[split_symbol_definition]) ).
fof(f11488,plain,
( sQ1065_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11447,f715,f11485]) ).
fof(f11489,definition,
( sQ1066_spl
<=> compose(compose(h,a),compose(domain(b),codomain(a))) = compose(compose(h,a),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1066_spl])],[split_symbol_definition]) ).
fof(f11492,plain,
( sQ1066_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f11448,f1941,f11489]) ).
fof(f11512,plain,
( compose(compose(g,a),compose(domain(b),codomain(compose(a,b)))) = compose(compose(g,a),codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f5328]) ).
fof(f11513,plain,
( compose(compose(g,a),compose(domain(b),codomain(compose(h,compose(a,b))))) = compose(compose(g,a),codomain(compose(h,compose(a,b))))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f5328]) ).
fof(f11514,plain,
( compose(compose(g,a),compose(domain(b),codomain(compose(h,a)))) = compose(compose(g,a),codomain(compose(h,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f5328]) ).
fof(f11515,plain,
( compose(compose(g,a),compose(domain(b),codomain(compose(g,a)))) = compose(compose(g,a),codomain(compose(g,a)))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f5328]) ).
fof(f11516,plain,
( compose(compose(g,a),compose(domain(b),codomain(g))) = compose(compose(g,a),codomain(g))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f5328]) ).
fof(f11517,plain,
( compose(compose(g,a),compose(domain(b),codomain(h))) = compose(compose(g,a),codomain(h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f5328]) ).
fof(f11518,plain,
( compose(compose(g,a),compose(domain(b),codomain(a))) = compose(compose(g,a),codomain(a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f5328]) ).
fof(f11535,definition,
( sQ1067_spl
<=> compose(compose(g,a),compose(domain(b),codomain(compose(a,b)))) = compose(compose(g,a),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1067_spl])],[split_symbol_definition]) ).
fof(f11538,plain,
( sQ1067_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11512,f2265,f11535]) ).
fof(f11539,definition,
( sQ1068_spl
<=> compose(compose(g,a),compose(domain(b),codomain(compose(h,compose(a,b))))) = compose(compose(g,a),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1068_spl])],[split_symbol_definition]) ).
fof(f11542,plain,
( sQ1068_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11513,f2265,f11539]) ).
fof(f11543,definition,
( sQ1069_spl
<=> compose(compose(g,a),compose(domain(b),codomain(compose(h,a)))) = compose(compose(g,a),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1069_spl])],[split_symbol_definition]) ).
fof(f11546,plain,
( sQ1069_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f11514,f1941,f11543]) ).
fof(f11547,definition,
( sQ1070_spl
<=> compose(compose(g,a),compose(domain(b),codomain(compose(g,a)))) = compose(compose(g,a),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1070_spl])],[split_symbol_definition]) ).
fof(f11550,plain,
( sQ1070_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f11515,f1941,f11547]) ).
fof(f11551,definition,
( sQ1071_spl
<=> compose(compose(g,a),compose(domain(b),codomain(g))) = compose(compose(g,a),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ1071_spl])],[split_symbol_definition]) ).
fof(f11554,plain,
( sQ1071_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11516,f715,f11551]) ).
fof(f11555,definition,
( sQ1072_spl
<=> compose(compose(g,a),compose(domain(b),codomain(h))) = compose(compose(g,a),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ1072_spl])],[split_symbol_definition]) ).
fof(f11558,plain,
( sQ1072_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11517,f715,f11555]) ).
fof(f11559,definition,
( sQ1073_spl
<=> compose(compose(g,a),compose(domain(b),codomain(a))) = compose(compose(g,a),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1073_spl])],[split_symbol_definition]) ).
fof(f11562,plain,
( sQ1073_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f11518,f1941,f11559]) ).
fof(f11579,plain,
( compose(compose(g,a),compose(b,domain(compose(g,a)))) = compose(compose(h,compose(a,b)),domain(compose(g,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f6744]) ).
fof(f11580,plain,
( compose(compose(g,a),compose(b,domain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b))))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f6744]) ).
fof(f11581,plain,
( compose(compose(g,a),compose(b,domain(compose(h,a)))) = compose(compose(h,compose(a,b)),domain(compose(h,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f6744]) ).
fof(f11582,plain,
( compose(compose(g,a),compose(b,domain(compose(a,b)))) = compose(compose(h,compose(a,b)),domain(compose(a,b)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f6744]) ).
fof(f11589,definition,
( sQ1074_spl
<=> compose(compose(g,a),compose(b,domain(compose(g,a)))) = compose(compose(h,compose(a,b)),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1074_spl])],[split_symbol_definition]) ).
fof(f11592,plain,
( sQ1074_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f11579,f1555,f11589]) ).
fof(f11593,definition,
( sQ1075_spl
<=> compose(compose(g,a),compose(b,domain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1075_spl])],[split_symbol_definition]) ).
fof(f11596,plain,
( sQ1075_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f11580,f1555,f11593]) ).
fof(f11597,definition,
( sQ1076_spl
<=> compose(compose(g,a),compose(b,domain(compose(h,a)))) = compose(compose(h,compose(a,b)),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1076_spl])],[split_symbol_definition]) ).
fof(f11600,plain,
( sQ1076_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f11581,f1555,f11597]) ).
fof(f11601,definition,
( sQ1077_spl
<=> compose(compose(g,a),compose(b,domain(compose(a,b)))) = compose(compose(h,compose(a,b)),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1077_spl])],[split_symbol_definition]) ).
fof(f11604,plain,
( sQ1077_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f11582,f1570,f11601]) ).
fof(f11612,plain,
( compose(compose(g,a),compose(b,codomain(compose(a,b)))) = compose(compose(h,compose(a,b)),codomain(compose(a,b)))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f6745]) ).
fof(f11613,plain,
( compose(compose(g,a),compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b))))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f6745]) ).
fof(f11614,plain,
( compose(compose(g,a),compose(b,codomain(compose(h,a)))) = compose(compose(h,compose(a,b)),codomain(compose(h,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f6745]) ).
fof(f11615,plain,
( compose(compose(g,a),compose(b,codomain(compose(g,a)))) = compose(compose(h,compose(a,b)),codomain(compose(g,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f6745]) ).
fof(f11630,definition,
( sQ1078_spl
<=> compose(compose(g,a),compose(b,codomain(compose(a,b)))) = compose(compose(h,compose(a,b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1078_spl])],[split_symbol_definition]) ).
fof(f11633,plain,
( sQ1078_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f11612,f4389,f11630]) ).
fof(f11634,definition,
( sQ1079_spl
<=> compose(compose(g,a),compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1079_spl])],[split_symbol_definition]) ).
fof(f11637,plain,
( sQ1079_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f11613,f4389,f11634]) ).
fof(f11638,definition,
( sQ1080_spl
<=> compose(compose(g,a),compose(b,codomain(compose(h,a)))) = compose(compose(h,compose(a,b)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1080_spl])],[split_symbol_definition]) ).
fof(f11641,plain,
( sQ1080_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11614,f2265,f11638]) ).
fof(f11642,definition,
( sQ1081_spl
<=> compose(compose(g,a),compose(b,codomain(compose(g,a)))) = compose(compose(h,compose(a,b)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1081_spl])],[split_symbol_definition]) ).
fof(f11645,plain,
( sQ1081_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11615,f2265,f11642]) ).
fof(f11659,plain,
( compose(a,compose(g,compose(a,b))) = compose(compose(a,g),compose(a,b))
| domain(b) != domain(g) ),
inference(resolution,[status(thm)],[f2327,f74]) ).
fof(f11660,plain,
( compose(a,compose(h,compose(a,b))) = compose(compose(a,h),compose(a,b))
| domain(b) != domain(h) ),
inference(resolution,[status(thm)],[f2327,f69]) ).
fof(f11661,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)],[f2327,f15]) ).
fof(f11662,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)],[f120,f2327]) ).
fof(f11663,plain,
( compose(a,compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(a,compose(h,compose(a,b))),compose(a,b))
| codomain(b) != domain(a)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f2327]) ).
fof(f11664,plain,
( compose(a,compose(compose(h,a),compose(a,b))) = compose(compose(a,compose(h,a)),compose(a,b))
| domain(b) != domain(a)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f2327]) ).
fof(f11665,plain,
( compose(a,compose(compose(g,a),compose(a,b))) = compose(compose(a,compose(g,a)),compose(a,b))
| domain(b) != domain(a)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f2327]) ).
fof(f11668,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)],[f22,f2327]) ).
fof(f11669,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)],[f38,f2327]) ).
fof(f11670,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)],[f15,f2327]) ).
fof(f11671,definition,
( sQ1082_spl
<=> compose(a,compose(g,compose(a,b))) = compose(compose(a,g),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1082_spl])],[split_symbol_definition]) ).
fof(f11674,plain,
( sQ1082_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f11659,f700,f11671]) ).
fof(f11675,definition,
( sQ1083_spl
<=> compose(a,compose(h,compose(a,b))) = compose(compose(a,h),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1083_spl])],[split_symbol_definition]) ).
fof(f11678,plain,
( sQ1083_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f11660,f693,f11675]) ).
fof(f11679,definition,
( sQ1084_spl
<=> domain(b) = domain(domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1084_spl])],[split_symbol_definition]) ).
fof(f11681,plain,
( sQ1084_spl
| domain(b) != domain(domain(a)) ),
inference(component_clause,[status(thm)],[f11679]) ).
fof(f11682,definition,
( sQ1085_spl
<=> compose(a,compose(domain(a),compose(a,b))) = compose(compose(a,domain(a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1085_spl])],[split_symbol_definition]) ).
fof(f11685,plain,
( sQ1085_spl
| ~ sQ1084_spl ),
inference(split_clause,[status(thm)],[f11661,f11679,f11682]) ).
fof(f11686,definition,
( sQ1086_spl
<=> compose(a,compose(compose(a,b),compose(a,b))) = compose(compose(a,compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1086_spl])],[split_symbol_definition]) ).
fof(f11689,plain,
( sQ1086_spl
| ~ sQ70_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f11662,f2359,f1570,f11686]) ).
fof(f11690,definition,
( sQ1087_spl
<=> compose(a,compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(a,compose(h,compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1087_spl])],[split_symbol_definition]) ).
fof(f11693,plain,
( sQ1087_spl
| ~ sQ70_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f11663,f2366,f1570,f11690]) ).
fof(f11694,definition,
( sQ1088_spl
<=> compose(a,compose(compose(h,a),compose(a,b))) = compose(compose(a,compose(h,a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1088_spl])],[split_symbol_definition]) ).
fof(f11697,plain,
( sQ1088_spl
| ~ sQ27_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f11664,f2330,f715,f11694]) ).
fof(f11698,definition,
( sQ1089_spl
<=> compose(a,compose(compose(g,a),compose(a,b))) = compose(compose(a,compose(g,a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1089_spl])],[split_symbol_definition]) ).
fof(f11701,plain,
( sQ1089_spl
| ~ sQ27_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f11665,f2337,f715,f11698]) ).
fof(f11704,definition,
( sQ1090_spl
<=> compose(a,compose(a,compose(a,b))) = compose(compose(a,a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1090_spl])],[split_symbol_definition]) ).
fof(f11707,plain,
( sQ1090_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11668,f715,f11704]) ).
fof(f11708,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)],[f16,f11669]) ).
fof(f11709,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)],[f37,f11670]) ).
fof(f11710,plain,
( sQ1084_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f37,f11681]) ).
fof(f11712,plain,
( compose(compose(h,a),compose(b,domain(compose(g,a)))) = compose(compose(h,compose(a,b)),domain(compose(g,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f7795]) ).
fof(f11713,plain,
( compose(compose(h,a),compose(b,domain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b))))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f7795]) ).
fof(f11714,plain,
( compose(compose(h,a),compose(b,domain(compose(h,a)))) = compose(compose(h,compose(a,b)),domain(compose(h,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f7795]) ).
fof(f11715,plain,
( compose(compose(h,a),compose(b,domain(compose(a,b)))) = compose(compose(h,compose(a,b)),domain(compose(a,b)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f7795]) ).
fof(f11722,definition,
( sQ1091_spl
<=> compose(compose(h,a),compose(b,domain(compose(g,a)))) = compose(compose(h,compose(a,b)),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1091_spl])],[split_symbol_definition]) ).
fof(f11725,plain,
( sQ1091_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f11712,f1555,f11722]) ).
fof(f11726,definition,
( sQ1092_spl
<=> compose(compose(h,a),compose(b,domain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1092_spl])],[split_symbol_definition]) ).
fof(f11729,plain,
( sQ1092_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f11713,f1555,f11726]) ).
fof(f11730,definition,
( sQ1093_spl
<=> compose(compose(h,a),compose(b,domain(compose(h,a)))) = compose(compose(h,compose(a,b)),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1093_spl])],[split_symbol_definition]) ).
fof(f11733,plain,
( sQ1093_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f11714,f1555,f11730]) ).
fof(f11734,definition,
( sQ1094_spl
<=> compose(compose(h,a),compose(b,domain(compose(a,b)))) = compose(compose(h,compose(a,b)),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1094_spl])],[split_symbol_definition]) ).
fof(f11737,plain,
( sQ1094_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f11715,f1570,f11734]) ).
fof(f11745,plain,
( compose(compose(h,a),compose(b,codomain(compose(a,b)))) = compose(compose(h,compose(a,b)),codomain(compose(a,b)))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f7796]) ).
fof(f11746,plain,
( compose(compose(h,a),compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b))))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f7796]) ).
fof(f11747,plain,
( compose(compose(h,a),compose(b,codomain(compose(h,a)))) = compose(compose(h,compose(a,b)),codomain(compose(h,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f7796]) ).
fof(f11748,plain,
( compose(compose(h,a),compose(b,codomain(compose(g,a)))) = compose(compose(h,compose(a,b)),codomain(compose(g,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f7796]) ).
fof(f11763,definition,
( sQ1095_spl
<=> compose(compose(h,a),compose(b,codomain(compose(a,b)))) = compose(compose(h,compose(a,b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1095_spl])],[split_symbol_definition]) ).
fof(f11766,plain,
( sQ1095_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f11745,f4389,f11763]) ).
fof(f11767,definition,
( sQ1096_spl
<=> compose(compose(h,a),compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1096_spl])],[split_symbol_definition]) ).
fof(f11770,plain,
( sQ1096_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f11746,f4389,f11767]) ).
fof(f11771,definition,
( sQ1097_spl
<=> compose(compose(h,a),compose(b,codomain(compose(h,a)))) = compose(compose(h,compose(a,b)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1097_spl])],[split_symbol_definition]) ).
fof(f11774,plain,
( sQ1097_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11747,f2265,f11771]) ).
fof(f11775,definition,
( sQ1098_spl
<=> compose(compose(h,a),compose(b,codomain(compose(g,a)))) = compose(compose(h,compose(a,b)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1098_spl])],[split_symbol_definition]) ).
fof(f11778,plain,
( sQ1098_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f11748,f2265,f11775]) ).
fof(f11795,plain,
! [X0] :
( compose(g,compose(codomain(compose(a,b)),domain(X0))) = compose(compose(g,codomain(compose(a,b))),domain(X0))
| codomain(compose(a,b)) != domain(X0)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f8846]) ).
fof(f11796,plain,
! [X0] :
( compose(g,compose(codomain(compose(h,compose(a,b))),domain(X0))) = compose(compose(g,codomain(compose(h,compose(a,b)))),domain(X0))
| codomain(compose(h,compose(a,b))) != domain(X0)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f8846]) ).
fof(f11797,plain,
! [X0] :
( compose(g,compose(codomain(compose(h,a)),domain(X0))) = compose(compose(g,codomain(compose(h,a))),domain(X0))
| codomain(compose(h,a)) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f8846]) ).
fof(f11798,plain,
! [X0] :
( compose(g,compose(codomain(compose(g,a)),domain(X0))) = compose(compose(g,codomain(compose(g,a))),domain(X0))
| codomain(compose(g,a)) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f8846]) ).
fof(f11799,plain,
! [X0] :
( compose(g,compose(codomain(g),domain(X0))) = compose(compose(g,codomain(g)),domain(X0))
| codomain(g) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f8846]) ).
fof(f11800,plain,
! [X0] :
( compose(g,compose(codomain(h),domain(X0))) = compose(compose(g,codomain(h)),domain(X0))
| codomain(h) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f8846]) ).
fof(f11801,plain,
! [X0] :
( compose(g,compose(codomain(a),domain(X0))) = compose(compose(g,codomain(a)),domain(X0))
| codomain(a) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f8846]) ).
fof(f11815,definition,
! [X0] :
( sQ1099_spl
<=> ( compose(g,compose(codomain(compose(a,b)),domain(X0))) = compose(compose(g,codomain(compose(a,b))),domain(X0))
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1099_spl])],[split_symbol_definition]) ).
fof(f11818,plain,
( sQ1099_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f11795,f1570,f11815]) ).
fof(f11819,definition,
! [X0] :
( sQ1100_spl
<=> ( compose(g,compose(codomain(compose(h,compose(a,b))),domain(X0))) = compose(compose(g,codomain(compose(h,compose(a,b)))),domain(X0))
| codomain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1100_spl])],[split_symbol_definition]) ).
fof(f11822,plain,
( sQ1100_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f11796,f1570,f11819]) ).
fof(f11823,definition,
! [X0] :
( sQ1101_spl
<=> ( compose(g,compose(codomain(compose(h,a)),domain(X0))) = compose(compose(g,codomain(compose(h,a))),domain(X0))
| codomain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1101_spl])],[split_symbol_definition]) ).
fof(f11826,plain,
( sQ1101_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11797,f715,f11823]) ).
fof(f11827,definition,
! [X0] :
( sQ1102_spl
<=> ( compose(g,compose(codomain(compose(g,a)),domain(X0))) = compose(compose(g,codomain(compose(g,a))),domain(X0))
| codomain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1102_spl])],[split_symbol_definition]) ).
fof(f11830,plain,
( sQ1102_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11798,f715,f11827]) ).
fof(f11831,definition,
! [X0] :
( sQ1103_spl
<=> ( compose(g,compose(codomain(g),domain(X0))) = compose(compose(g,codomain(g)),domain(X0))
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1103_spl])],[split_symbol_definition]) ).
fof(f11834,plain,
( sQ1103_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f11799,f606,f11831]) ).
fof(f11835,definition,
! [X0] :
( sQ1104_spl
<=> ( compose(g,compose(codomain(h),domain(X0))) = compose(compose(g,codomain(h)),domain(X0))
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1104_spl])],[split_symbol_definition]) ).
fof(f11838,plain,
( sQ1104_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f11800,f606,f11835]) ).
fof(f11839,definition,
! [X0] :
( sQ1105_spl
<=> ( compose(g,compose(codomain(a),domain(X0))) = compose(compose(g,codomain(a)),domain(X0))
| codomain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1105_spl])],[split_symbol_definition]) ).
fof(f11842,plain,
( sQ1105_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f11801,f715,f11839]) ).
fof(f11858,plain,
! [X0] :
( compose(g,compose(domain(compose(g,a)),domain(X0))) = compose(compose(g,domain(compose(g,a))),domain(X0))
| domain(compose(g,a)) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f8847]) ).
fof(f11859,plain,
! [X0] :
( compose(g,compose(domain(compose(h,compose(a,b))),domain(X0))) = compose(compose(g,domain(compose(h,compose(a,b)))),domain(X0))
| domain(compose(h,compose(a,b))) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f8847]) ).
fof(f11860,plain,
! [X0] :
( compose(g,compose(domain(compose(h,a)),domain(X0))) = compose(compose(g,domain(compose(h,a))),domain(X0))
| domain(compose(h,a)) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f8847]) ).
fof(f11861,plain,
! [X0] :
( compose(g,compose(domain(compose(a,b)),domain(X0))) = compose(compose(g,domain(compose(a,b))),domain(X0))
| domain(compose(a,b)) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f8847]) ).
fof(f11873,definition,
! [X0] :
( sQ1106_spl
<=> ( compose(g,compose(domain(compose(g,a)),domain(X0))) = compose(compose(g,domain(compose(g,a))),domain(X0))
| domain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1106_spl])],[split_symbol_definition]) ).
fof(f11876,plain,
( sQ1106_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f11858,f584,f11873]) ).
fof(f11877,definition,
! [X0] :
( sQ1107_spl
<=> ( compose(g,compose(domain(compose(h,compose(a,b))),domain(X0))) = compose(compose(g,domain(compose(h,compose(a,b)))),domain(X0))
| domain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1107_spl])],[split_symbol_definition]) ).
fof(f11880,plain,
( sQ1107_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f11859,f584,f11877]) ).
fof(f11881,definition,
! [X0] :
( sQ1108_spl
<=> ( compose(g,compose(domain(compose(h,a)),domain(X0))) = compose(compose(g,domain(compose(h,a))),domain(X0))
| domain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1108_spl])],[split_symbol_definition]) ).
fof(f11884,plain,
( sQ1108_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f11860,f584,f11881]) ).
fof(f11885,definition,
! [X0] :
( sQ1109_spl
<=> ( compose(g,compose(domain(compose(a,b)),domain(X0))) = compose(compose(g,domain(compose(a,b))),domain(X0))
| domain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1109_spl])],[split_symbol_definition]) ).
fof(f11888,plain,
( sQ1109_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f11861,f606,f11885]) ).
fof(f11901,plain,
( ~ sQ795_spl
| compose(g,compose(compose(a,b),domain(compose(g,a)))) = compose(compose(h,compose(a,b)),domain(compose(g,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f8861]) ).
fof(f11902,plain,
( ~ sQ795_spl
| compose(g,compose(compose(a,b),domain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b))))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f8861]) ).
fof(f11903,plain,
( ~ sQ795_spl
| compose(g,compose(compose(a,b),domain(compose(h,a)))) = compose(compose(h,compose(a,b)),domain(compose(h,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f8861]) ).
fof(f11904,plain,
( ~ sQ795_spl
| compose(g,compose(compose(a,b),domain(compose(a,b)))) = compose(compose(h,compose(a,b)),domain(compose(a,b)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f8861]) ).
fof(f11906,plain,
! [X0] :
( ~ sQ795_spl
| compose(g,compose(compose(a,b),domain(codomain(X0)))) = compose(compose(h,compose(a,b)),domain(codomain(X0)))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f8861]) ).
fof(f11911,definition,
( sQ1110_spl
<=> compose(g,compose(compose(a,b),domain(compose(g,a)))) = compose(compose(h,compose(a,b)),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1110_spl])],[split_symbol_definition]) ).
fof(f11914,plain,
( ~ sQ795_spl
| sQ1110_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f11901,f1555,f11911,f8818]) ).
fof(f11915,definition,
( sQ1111_spl
<=> compose(g,compose(compose(a,b),domain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1111_spl])],[split_symbol_definition]) ).
fof(f11918,plain,
( ~ sQ795_spl
| sQ1111_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f11902,f1555,f11915,f8818]) ).
fof(f11919,definition,
( sQ1112_spl
<=> compose(g,compose(compose(a,b),domain(compose(h,a)))) = compose(compose(h,compose(a,b)),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1112_spl])],[split_symbol_definition]) ).
fof(f11922,plain,
( ~ sQ795_spl
| sQ1112_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f11903,f1555,f11919,f8818]) ).
fof(f11923,definition,
( sQ1113_spl
<=> compose(g,compose(compose(a,b),domain(compose(a,b)))) = compose(compose(h,compose(a,b)),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1113_spl])],[split_symbol_definition]) ).
fof(f11926,plain,
( ~ sQ795_spl
| sQ1113_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f11904,f1570,f11923,f8818]) ).
fof(f11929,plain,
! [X0] :
( ~ sQ795_spl
| compose(g,compose(compose(a,b),codomain(X0))) = compose(compose(h,compose(a,b)),domain(codomain(X0)))
| codomain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f11906]) ).
fof(f11930,plain,
! [X0] :
( ~ sQ795_spl
| compose(g,compose(compose(a,b),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f11929]) ).
fof(f11936,plain,
! [X0] :
( compose(domain(g),compose(compose(g,a),X0)) = compose(compose(domain(g),compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f2803]) ).
fof(f11937,plain,
! [X0] :
( compose(domain(compose(g,a)),compose(compose(g,a),X0)) = compose(compose(domain(compose(g,a)),compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f2803]) ).
fof(f11938,plain,
! [X0] :
( compose(domain(compose(h,compose(a,b))),compose(compose(g,a),X0)) = compose(compose(domain(compose(h,compose(a,b))),compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f2803]) ).
fof(f11939,plain,
! [X0] :
( compose(domain(compose(h,a)),compose(compose(g,a),X0)) = compose(compose(domain(compose(h,a)),compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f2803]) ).
fof(f11940,plain,
! [X0] :
( compose(domain(compose(a,b)),compose(compose(g,a),X0)) = compose(compose(domain(compose(a,b)),compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f2803]) ).
fof(f11958,definition,
! [X0] :
( sQ1114_spl
<=> ( compose(domain(g),compose(compose(g,a),X0)) = compose(compose(domain(g),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1114_spl])],[split_symbol_definition]) ).
fof(f11961,plain,
( sQ1114_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f11936,f2687,f11958]) ).
fof(f11962,definition,
! [X0] :
( sQ1115_spl
<=> ( compose(domain(compose(g,a)),compose(compose(g,a),X0)) = compose(compose(domain(compose(g,a)),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1115_spl])],[split_symbol_definition]) ).
fof(f11965,plain,
( sQ1115_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f11937,f2687,f11962]) ).
fof(f11966,definition,
! [X0] :
( sQ1116_spl
<=> ( compose(domain(compose(h,compose(a,b))),compose(compose(g,a),X0)) = compose(compose(domain(compose(h,compose(a,b))),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1116_spl])],[split_symbol_definition]) ).
fof(f11969,plain,
( sQ1116_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f11938,f2687,f11966]) ).
fof(f11970,definition,
! [X0] :
( sQ1117_spl
<=> ( compose(domain(compose(h,a)),compose(compose(g,a),X0)) = compose(compose(domain(compose(h,a)),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1117_spl])],[split_symbol_definition]) ).
fof(f11973,plain,
( sQ1117_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f11939,f2687,f11970]) ).
fof(f11974,definition,
! [X0] :
( sQ1118_spl
<=> ( compose(domain(compose(a,b)),compose(compose(g,a),X0)) = compose(compose(domain(compose(a,b)),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1118_spl])],[split_symbol_definition]) ).
fof(f11977,plain,
( sQ1118_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f11940,f584,f11974]) ).
fof(f11994,plain,
( compose(g,compose(codomain(compose(a,b)),codomain(b))) = compose(compose(g,codomain(compose(a,b))),codomain(b))
| domain(a) != codomain(compose(a,b)) ),
inference(resolution,[status(thm)],[f8936,f120]) ).
fof(f11995,plain,
( compose(g,compose(codomain(compose(h,compose(a,b))),codomain(b))) = compose(compose(g,codomain(compose(h,compose(a,b)))),codomain(b))
| domain(a) != codomain(compose(h,compose(a,b))) ),
inference(resolution,[status(thm)],[f8936,f581]) ).
fof(f11997,plain,
( compose(g,compose(codomain(b),codomain(compose(a,b)))) = compose(compose(g,codomain(b)),codomain(compose(a,b)))
| domain(a) != codomain(b) ),
inference(resolution,[status(thm)],[f8936,f120]) ).
fof(f11998,plain,
( compose(g,compose(codomain(b),codomain(compose(h,compose(a,b))))) = compose(compose(g,codomain(b)),codomain(compose(h,compose(a,b))))
| domain(a) != codomain(b) ),
inference(resolution,[status(thm)],[f8936,f581]) ).
fof(f12000,plain,
! [X0] :
( compose(g,compose(codomain(compose(a,b)),codomain(X0))) = compose(compose(g,codomain(compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(a) != codomain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f8936]) ).
fof(f12001,plain,
! [X0] :
( compose(g,compose(codomain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(g,codomain(compose(h,compose(a,b)))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(a) != codomain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f8936]) ).
fof(f12002,plain,
! [X0] :
( compose(g,compose(codomain(compose(h,a)),codomain(X0))) = compose(compose(g,codomain(compose(h,a))),codomain(X0))
| domain(b) != codomain(X0)
| domain(a) != codomain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f8936]) ).
fof(f12003,plain,
! [X0] :
( compose(g,compose(codomain(compose(g,a)),codomain(X0))) = compose(compose(g,codomain(compose(g,a))),codomain(X0))
| domain(b) != codomain(X0)
| domain(a) != codomain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f8936]) ).
fof(f12004,plain,
! [X0] :
( compose(g,compose(codomain(g),codomain(X0))) = compose(compose(g,codomain(g)),codomain(X0))
| domain(a) != codomain(X0)
| domain(a) != codomain(g) ),
inference(paramodulation,[status(thm)],[f74,f8936]) ).
fof(f12005,plain,
! [X0] :
( compose(g,compose(codomain(h),codomain(X0))) = compose(compose(g,codomain(h)),codomain(X0))
| domain(a) != codomain(X0)
| domain(a) != codomain(h) ),
inference(paramodulation,[status(thm)],[f69,f8936]) ).
fof(f12006,plain,
! [X0] :
( compose(g,compose(codomain(a),codomain(X0))) = compose(compose(g,codomain(a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(a) != codomain(a) ),
inference(paramodulation,[status(thm)],[f22,f8936]) ).
fof(f12013,plain,
! [X0] :
( compose(g,compose(codomain(X0),codomain(g))) = compose(compose(g,codomain(X0)),codomain(g))
| codomain(X0) != domain(a)
| domain(a) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f74,f8936]) ).
fof(f12019,definition,
( sQ1119_spl
<=> domain(a) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1119_spl])],[split_symbol_definition]) ).
fof(f12021,plain,
( sQ1119_spl
| domain(a) != codomain(compose(a,b)) ),
inference(component_clause,[status(thm)],[f12019]) ).
fof(f12022,definition,
( sQ1120_spl
<=> compose(g,compose(codomain(compose(a,b)),codomain(b))) = compose(compose(g,codomain(compose(a,b))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1120_spl])],[split_symbol_definition]) ).
fof(f12025,plain,
( sQ1120_spl
| ~ sQ1119_spl ),
inference(split_clause,[status(thm)],[f11994,f12019,f12022]) ).
fof(f12026,definition,
( sQ1121_spl
<=> domain(a) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1121_spl])],[split_symbol_definition]) ).
fof(f12028,plain,
( sQ1121_spl
| domain(a) != codomain(compose(h,compose(a,b))) ),
inference(component_clause,[status(thm)],[f12026]) ).
fof(f12029,definition,
( sQ1122_spl
<=> compose(g,compose(codomain(compose(h,compose(a,b))),codomain(b))) = compose(compose(g,codomain(compose(h,compose(a,b)))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1122_spl])],[split_symbol_definition]) ).
fof(f12032,plain,
( sQ1122_spl
| ~ sQ1121_spl ),
inference(split_clause,[status(thm)],[f11995,f12026,f12029]) ).
fof(f12037,definition,
( sQ1123_spl
<=> compose(g,compose(codomain(b),codomain(compose(a,b)))) = compose(compose(g,codomain(b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1123_spl])],[split_symbol_definition]) ).
fof(f12040,plain,
( sQ1123_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f11997,f1570,f12037]) ).
fof(f12041,definition,
( sQ1124_spl
<=> compose(g,compose(codomain(b),codomain(compose(h,compose(a,b))))) = compose(compose(g,codomain(b)),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1124_spl])],[split_symbol_definition]) ).
fof(f12044,plain,
( sQ1124_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f11998,f1570,f12041]) ).
fof(f12047,definition,
! [X0] :
( sQ1125_spl
<=> ( compose(g,compose(codomain(compose(a,b)),codomain(X0))) = compose(compose(g,codomain(compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1125_spl])],[split_symbol_definition]) ).
fof(f12050,plain,
( sQ1125_spl
| ~ sQ1119_spl ),
inference(split_clause,[status(thm)],[f12000,f12019,f12047]) ).
fof(f12051,definition,
! [X0] :
( sQ1126_spl
<=> ( compose(g,compose(codomain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(g,codomain(compose(h,compose(a,b)))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1126_spl])],[split_symbol_definition]) ).
fof(f12054,plain,
( sQ1126_spl
| ~ sQ1121_spl ),
inference(split_clause,[status(thm)],[f12001,f12026,f12051]) ).
fof(f12055,definition,
! [X0] :
( sQ1127_spl
<=> ( compose(g,compose(codomain(compose(h,a)),codomain(X0))) = compose(compose(g,codomain(compose(h,a))),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1127_spl])],[split_symbol_definition]) ).
fof(f12058,plain,
( sQ1127_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f12002,f3284,f12055]) ).
fof(f12059,definition,
! [X0] :
( sQ1128_spl
<=> ( compose(g,compose(codomain(compose(g,a)),codomain(X0))) = compose(compose(g,codomain(compose(g,a))),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1128_spl])],[split_symbol_definition]) ).
fof(f12062,plain,
( sQ1128_spl
| ~ sQ203_spl ),
inference(split_clause,[status(thm)],[f12003,f3216,f12059]) ).
fof(f12063,definition,
( sQ1129_spl
<=> domain(a) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ1129_spl])],[split_symbol_definition]) ).
fof(f12065,plain,
( sQ1129_spl
| domain(a) != codomain(g) ),
inference(component_clause,[status(thm)],[f12063]) ).
fof(f12066,definition,
! [X0] :
( sQ1130_spl
<=> ( compose(g,compose(codomain(g),codomain(X0))) = compose(compose(g,codomain(g)),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1130_spl])],[split_symbol_definition]) ).
fof(f12069,plain,
( sQ1130_spl
| ~ sQ1129_spl ),
inference(split_clause,[status(thm)],[f12004,f12063,f12066]) ).
fof(f12070,definition,
( sQ1131_spl
<=> domain(a) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ1131_spl])],[split_symbol_definition]) ).
fof(f12072,plain,
( sQ1131_spl
| domain(a) != codomain(h) ),
inference(component_clause,[status(thm)],[f12070]) ).
fof(f12073,definition,
! [X0] :
( sQ1132_spl
<=> ( compose(g,compose(codomain(h),codomain(X0))) = compose(compose(g,codomain(h)),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1132_spl])],[split_symbol_definition]) ).
fof(f12076,plain,
( sQ1132_spl
| ~ sQ1131_spl ),
inference(split_clause,[status(thm)],[f12005,f12070,f12073]) ).
fof(f12077,definition,
( sQ1133_spl
<=> domain(a) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ1133_spl])],[split_symbol_definition]) ).
fof(f12079,plain,
( sQ1133_spl
| domain(a) != codomain(a) ),
inference(component_clause,[status(thm)],[f12077]) ).
fof(f12080,definition,
! [X0] :
( sQ1134_spl
<=> ( compose(g,compose(codomain(a),codomain(X0))) = compose(compose(g,codomain(a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1134_spl])],[split_symbol_definition]) ).
fof(f12083,plain,
( sQ1134_spl
| ~ sQ1133_spl ),
inference(split_clause,[status(thm)],[f12006,f12077,f12080]) ).
fof(f12098,plain,
! [X0] :
( compose(g,compose(codomain(X0),domain(a))) = compose(compose(g,codomain(X0)),codomain(g))
| codomain(X0) != domain(a)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f74,f12013]) ).
fof(f12099,plain,
! [X0] :
( compose(g,compose(codomain(X0),domain(a))) = compose(compose(g,codomain(X0)),domain(a))
| codomain(X0) != domain(a)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f74,f12098]) ).
fof(f12100,plain,
! [X0] :
( compose(g,compose(codomain(X0),domain(a))) = compose(compose(g,codomain(X0)),domain(a))
| domain(a) != codomain(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f12099]) ).
fof(f12111,plain,
( sQ1121_spl
| domain(a) != codomain(b) ),
inference(forward_demodulation,[status(thm)],[f581,f12028]) ).
fof(f12112,plain,
( sQ1119_spl
| domain(a) != codomain(b) ),
inference(forward_demodulation,[status(thm)],[f120,f12021]) ).
fof(f12113,plain,
( sQ1133_spl
| domain(a) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f22,f12079]) ).
fof(f12114,plain,
( sQ1131_spl
| domain(a) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f69,f12072]) ).
fof(f12115,plain,
( sQ1131_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f12114]) ).
fof(f12116,plain,
sQ1131_spl,
inference(contradiction_clause,[status(thm)],[f12115]) ).
fof(f12117,plain,
( sQ1129_spl
| domain(a) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f74,f12065]) ).
fof(f12118,plain,
( sQ1129_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f12117]) ).
fof(f12119,plain,
sQ1129_spl,
inference(contradiction_clause,[status(thm)],[f12118]) ).
fof(f12128,plain,
( compose(g,compose(codomain(compose(a,b)),domain(a))) = compose(compose(g,codomain(compose(a,b))),domain(a))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f12100]) ).
fof(f12129,plain,
( compose(g,compose(codomain(compose(h,compose(a,b))),domain(a))) = compose(compose(g,codomain(compose(h,compose(a,b)))),domain(a))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f12100]) ).
fof(f12130,plain,
( compose(g,compose(codomain(compose(h,a)),domain(a))) = compose(compose(g,codomain(compose(h,a))),domain(a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f12100]) ).
fof(f12131,plain,
( compose(g,compose(codomain(compose(g,a)),domain(a))) = compose(compose(g,codomain(compose(g,a))),domain(a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f12100]) ).
fof(f12132,plain,
( compose(g,compose(codomain(g),domain(a))) = compose(compose(g,codomain(g)),domain(a))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f12100]) ).
fof(f12133,plain,
( compose(g,compose(codomain(h),domain(a))) = compose(compose(g,codomain(h)),domain(a))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f12100]) ).
fof(f12134,plain,
( compose(g,compose(codomain(a),domain(a))) = compose(compose(g,codomain(a)),domain(a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f12100]) ).
fof(f12136,plain,
! [X0] :
( compose(g,compose(codomain(domain(X0)),domain(a))) = compose(compose(g,codomain(domain(X0))),domain(a))
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f15,f12100]) ).
fof(f12151,definition,
( sQ1135_spl
<=> compose(g,compose(codomain(compose(a,b)),domain(a))) = compose(compose(g,codomain(compose(a,b))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1135_spl])],[split_symbol_definition]) ).
fof(f12154,plain,
( sQ1135_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f12128,f1570,f12151]) ).
fof(f12155,definition,
( sQ1136_spl
<=> compose(g,compose(codomain(compose(h,compose(a,b))),domain(a))) = compose(compose(g,codomain(compose(h,compose(a,b)))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1136_spl])],[split_symbol_definition]) ).
fof(f12158,plain,
( sQ1136_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f12129,f1570,f12155]) ).
fof(f12159,definition,
( sQ1137_spl
<=> compose(g,compose(codomain(compose(h,a)),domain(a))) = compose(compose(g,codomain(compose(h,a))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1137_spl])],[split_symbol_definition]) ).
fof(f12162,plain,
( sQ1137_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12130,f715,f12159]) ).
fof(f12163,definition,
( sQ1138_spl
<=> compose(g,compose(codomain(compose(g,a)),domain(a))) = compose(compose(g,codomain(compose(g,a))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1138_spl])],[split_symbol_definition]) ).
fof(f12166,plain,
( sQ1138_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12131,f715,f12163]) ).
fof(f12167,definition,
( sQ1139_spl
<=> compose(g,compose(codomain(g),domain(a))) = compose(compose(g,codomain(g)),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1139_spl])],[split_symbol_definition]) ).
fof(f12170,plain,
( sQ1139_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12132,f606,f12167]) ).
fof(f12171,definition,
( sQ1140_spl
<=> compose(g,compose(codomain(h),domain(a))) = compose(compose(g,codomain(h)),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1140_spl])],[split_symbol_definition]) ).
fof(f12174,plain,
( sQ1140_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12133,f606,f12171]) ).
fof(f12175,definition,
( sQ1141_spl
<=> compose(g,compose(codomain(a),domain(a))) = compose(compose(g,codomain(a)),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1141_spl])],[split_symbol_definition]) ).
fof(f12178,plain,
( sQ1141_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12134,f715,f12175]) ).
fof(f12181,plain,
! [X0] :
( compose(g,compose(domain(X0),domain(a))) = compose(compose(g,codomain(domain(X0))),domain(a))
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f12136]) ).
fof(f12182,plain,
! [X0] :
( compose(g,compose(domain(X0),domain(a))) = compose(compose(g,domain(X0)),domain(a))
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f12181]) ).
fof(f12194,plain,
( compose(g,compose(domain(compose(g,a)),domain(a))) = compose(compose(g,domain(compose(g,a))),domain(a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f12182]) ).
fof(f12195,plain,
( compose(g,compose(domain(compose(h,compose(a,b))),domain(a))) = compose(compose(g,domain(compose(h,compose(a,b)))),domain(a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f12182]) ).
fof(f12196,plain,
( compose(g,compose(domain(compose(h,a)),domain(a))) = compose(compose(g,domain(compose(h,a))),domain(a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f12182]) ).
fof(f12197,plain,
( compose(g,compose(domain(compose(a,b)),domain(a))) = compose(compose(g,domain(compose(a,b))),domain(a))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f12182]) ).
fof(f12210,definition,
( sQ1142_spl
<=> compose(g,compose(domain(compose(g,a)),domain(a))) = compose(compose(g,domain(compose(g,a))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1142_spl])],[split_symbol_definition]) ).
fof(f12213,plain,
( sQ1142_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f12194,f584,f12210]) ).
fof(f12214,definition,
( sQ1143_spl
<=> compose(g,compose(domain(compose(h,compose(a,b))),domain(a))) = compose(compose(g,domain(compose(h,compose(a,b)))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1143_spl])],[split_symbol_definition]) ).
fof(f12217,plain,
( sQ1143_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f12195,f584,f12214]) ).
fof(f12218,definition,
( sQ1144_spl
<=> compose(g,compose(domain(compose(h,a)),domain(a))) = compose(compose(g,domain(compose(h,a))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1144_spl])],[split_symbol_definition]) ).
fof(f12221,plain,
( sQ1144_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f12196,f584,f12218]) ).
fof(f12222,definition,
( sQ1145_spl
<=> compose(g,compose(domain(compose(a,b)),domain(a))) = compose(compose(g,domain(compose(a,b))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1145_spl])],[split_symbol_definition]) ).
fof(f12225,plain,
( sQ1145_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12197,f606,f12222]) ).
fof(f12239,plain,
( compose(g,compose(domain(b),codomain(compose(h,a)))) = compose(compose(g,domain(b)),codomain(compose(h,a)))
| domain(a) != domain(b) ),
inference(resolution,[status(thm)],[f8937,f131]) ).
fof(f12240,plain,
( compose(g,compose(domain(b),codomain(compose(g,a)))) = compose(compose(g,domain(b)),codomain(compose(g,a)))
| domain(a) != domain(b) ),
inference(resolution,[status(thm)],[f8937,f130]) ).
fof(f12241,plain,
( compose(g,compose(domain(a),codomain(g))) = compose(compose(g,domain(a)),codomain(g))
| domain(a) != domain(a) ),
inference(resolution,[status(thm)],[f8937,f74]) ).
fof(f12242,plain,
( compose(g,compose(domain(a),codomain(h))) = compose(compose(g,domain(a)),codomain(h))
| domain(a) != domain(a) ),
inference(resolution,[status(thm)],[f8937,f69]) ).
fof(f12243,plain,
( compose(g,compose(domain(b),codomain(a))) = compose(compose(g,domain(b)),codomain(a))
| domain(a) != domain(b) ),
inference(resolution,[status(thm)],[f8937,f22]) ).
fof(f12245,plain,
! [X0] :
( compose(g,compose(domain(compose(g,a)),codomain(X0))) = compose(compose(g,domain(compose(g,a))),codomain(X0))
| domain(h) != codomain(X0)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f1108,f8937]) ).
fof(f12246,plain,
! [X0] :
( compose(g,compose(domain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(g,domain(compose(h,compose(a,b)))),codomain(X0))
| domain(h) != codomain(X0)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f1068,f8937]) ).
fof(f12247,plain,
! [X0] :
( compose(g,compose(domain(compose(h,a)),codomain(X0))) = compose(compose(g,domain(compose(h,a))),codomain(X0))
| domain(h) != codomain(X0)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f76,f8937]) ).
fof(f12248,plain,
! [X0] :
( compose(g,compose(domain(compose(a,b)),codomain(X0))) = compose(compose(g,domain(compose(a,b))),codomain(X0))
| domain(a) != codomain(X0)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f60,f8937]) ).
fof(f12263,definition,
( sQ1146_spl
<=> compose(g,compose(domain(b),codomain(compose(h,a)))) = compose(compose(g,domain(b)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1146_spl])],[split_symbol_definition]) ).
fof(f12266,plain,
( sQ1146_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12239,f715,f12263]) ).
fof(f12267,definition,
( sQ1147_spl
<=> compose(g,compose(domain(b),codomain(compose(g,a)))) = compose(compose(g,domain(b)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1147_spl])],[split_symbol_definition]) ).
fof(f12270,plain,
( sQ1147_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12240,f715,f12267]) ).
fof(f12271,definition,
( sQ1148_spl
<=> compose(g,compose(domain(a),codomain(g))) = compose(compose(g,domain(a)),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ1148_spl])],[split_symbol_definition]) ).
fof(f12274,plain,
( sQ1148_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12241,f606,f12271]) ).
fof(f12275,definition,
( sQ1149_spl
<=> compose(g,compose(domain(a),codomain(h))) = compose(compose(g,domain(a)),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ1149_spl])],[split_symbol_definition]) ).
fof(f12278,plain,
( sQ1149_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12242,f606,f12275]) ).
fof(f12279,definition,
( sQ1150_spl
<=> compose(g,compose(domain(b),codomain(a))) = compose(compose(g,domain(b)),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1150_spl])],[split_symbol_definition]) ).
fof(f12282,plain,
( sQ1150_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12243,f715,f12279]) ).
fof(f12285,definition,
! [X0] :
( sQ1151_spl
<=> ( compose(g,compose(domain(compose(g,a)),codomain(X0))) = compose(compose(g,domain(compose(g,a))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1151_spl])],[split_symbol_definition]) ).
fof(f12288,plain,
( sQ1151_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f12245,f1743,f12285]) ).
fof(f12289,definition,
! [X0] :
( sQ1152_spl
<=> ( compose(g,compose(domain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(g,domain(compose(h,compose(a,b)))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1152_spl])],[split_symbol_definition]) ).
fof(f12292,plain,
( sQ1152_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f12246,f1772,f12289]) ).
fof(f12293,definition,
! [X0] :
( sQ1153_spl
<=> ( compose(g,compose(domain(compose(h,a)),codomain(X0))) = compose(compose(g,domain(compose(h,a))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1153_spl])],[split_symbol_definition]) ).
fof(f12296,plain,
( sQ1153_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f12247,f1736,f12293]) ).
fof(f12297,definition,
! [X0] :
( sQ1154_spl
<=> ( compose(g,compose(domain(compose(a,b)),codomain(X0))) = compose(compose(g,domain(compose(a,b))),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1154_spl])],[split_symbol_definition]) ).
fof(f12300,plain,
( sQ1154_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f12248,f1765,f12297]) ).
fof(f12342,plain,
( ~ sQ806_spl
| compose(g,compose(compose(a,b),codomain(compose(a,b)))) = compose(compose(h,compose(a,b)),codomain(compose(a,b)))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f8960]) ).
fof(f12343,plain,
( ~ sQ806_spl
| compose(g,compose(compose(a,b),codomain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b))))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f8960]) ).
fof(f12344,plain,
( ~ sQ806_spl
| compose(g,compose(compose(a,b),codomain(compose(h,a)))) = compose(compose(h,compose(a,b)),codomain(compose(h,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f8960]) ).
fof(f12345,plain,
( ~ sQ806_spl
| compose(g,compose(compose(a,b),codomain(compose(g,a)))) = compose(compose(h,compose(a,b)),codomain(compose(g,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f8960]) ).
fof(f12347,plain,
! [X0] :
( ~ sQ806_spl
| compose(g,compose(compose(a,b),codomain(domain(X0)))) = compose(compose(h,compose(a,b)),codomain(domain(X0)))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f15,f8960]) ).
fof(f12359,definition,
( sQ1155_spl
<=> compose(g,compose(compose(a,b),codomain(compose(a,b)))) = compose(compose(h,compose(a,b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1155_spl])],[split_symbol_definition]) ).
fof(f12362,plain,
( ~ sQ806_spl
| sQ1155_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f12342,f4389,f12359,f8908]) ).
fof(f12363,definition,
( sQ1156_spl
<=> compose(g,compose(compose(a,b),codomain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1156_spl])],[split_symbol_definition]) ).
fof(f12366,plain,
( ~ sQ806_spl
| sQ1156_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f12343,f4389,f12363,f8908]) ).
fof(f12367,definition,
( sQ1157_spl
<=> compose(g,compose(compose(a,b),codomain(compose(h,a)))) = compose(compose(h,compose(a,b)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1157_spl])],[split_symbol_definition]) ).
fof(f12370,plain,
( ~ sQ806_spl
| sQ1157_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f12344,f2265,f12367,f8908]) ).
fof(f12371,definition,
( sQ1158_spl
<=> compose(g,compose(compose(a,b),codomain(compose(g,a)))) = compose(compose(h,compose(a,b)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1158_spl])],[split_symbol_definition]) ).
fof(f12374,plain,
( ~ sQ806_spl
| sQ1158_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f12345,f2265,f12371,f8908]) ).
fof(f12377,plain,
! [X0] :
( ~ sQ806_spl
| compose(g,compose(compose(a,b),domain(X0))) = compose(compose(h,compose(a,b)),codomain(domain(X0)))
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f12347]) ).
fof(f12378,plain,
! [X0] :
( ~ sQ806_spl
| compose(g,compose(compose(a,b),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f12377]) ).
fof(f12392,plain,
! [X0] :
( compose(domain(g),compose(compose(h,a),X0)) = compose(compose(domain(g),compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f2805]) ).
fof(f12393,plain,
! [X0] :
( compose(domain(compose(g,a)),compose(compose(h,a),X0)) = compose(compose(domain(compose(g,a)),compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f2805]) ).
fof(f12394,plain,
! [X0] :
( compose(domain(compose(h,compose(a,b))),compose(compose(h,a),X0)) = compose(compose(domain(compose(h,compose(a,b))),compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f2805]) ).
fof(f12395,plain,
! [X0] :
( compose(domain(compose(h,a)),compose(compose(h,a),X0)) = compose(compose(domain(compose(h,a)),compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f2805]) ).
fof(f12396,plain,
! [X0] :
( compose(domain(compose(a,b)),compose(compose(h,a),X0)) = compose(compose(domain(compose(a,b)),compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f2805]) ).
fof(f12414,definition,
! [X0] :
( sQ1159_spl
<=> ( compose(domain(g),compose(compose(h,a),X0)) = compose(compose(domain(g),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1159_spl])],[split_symbol_definition]) ).
fof(f12417,plain,
( sQ1159_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f12392,f2687,f12414]) ).
fof(f12418,definition,
! [X0] :
( sQ1160_spl
<=> ( compose(domain(compose(g,a)),compose(compose(h,a),X0)) = compose(compose(domain(compose(g,a)),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1160_spl])],[split_symbol_definition]) ).
fof(f12421,plain,
( sQ1160_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f12393,f2687,f12418]) ).
fof(f12422,definition,
! [X0] :
( sQ1161_spl
<=> ( compose(domain(compose(h,compose(a,b))),compose(compose(h,a),X0)) = compose(compose(domain(compose(h,compose(a,b))),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1161_spl])],[split_symbol_definition]) ).
fof(f12425,plain,
( sQ1161_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f12394,f2687,f12422]) ).
fof(f12426,definition,
! [X0] :
( sQ1162_spl
<=> ( compose(domain(compose(h,a)),compose(compose(h,a),X0)) = compose(compose(domain(compose(h,a)),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1162_spl])],[split_symbol_definition]) ).
fof(f12429,plain,
( sQ1162_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f12395,f2687,f12426]) ).
fof(f12430,definition,
! [X0] :
( sQ1163_spl
<=> ( compose(domain(compose(a,b)),compose(compose(h,a),X0)) = compose(compose(domain(compose(a,b)),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1163_spl])],[split_symbol_definition]) ).
fof(f12433,plain,
( sQ1163_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f12396,f584,f12430]) ).
fof(f12453,plain,
! [X0] :
( compose(h,compose(codomain(compose(a,b)),domain(X0))) = compose(compose(h,codomain(compose(a,b))),domain(X0))
| codomain(compose(a,b)) != domain(X0)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f9214]) ).
fof(f12454,plain,
! [X0] :
( compose(h,compose(codomain(compose(h,compose(a,b))),domain(X0))) = compose(compose(h,codomain(compose(h,compose(a,b)))),domain(X0))
| codomain(compose(h,compose(a,b))) != domain(X0)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f9214]) ).
fof(f12455,plain,
! [X0] :
( compose(h,compose(codomain(compose(h,a)),domain(X0))) = compose(compose(h,codomain(compose(h,a))),domain(X0))
| codomain(compose(h,a)) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f9214]) ).
fof(f12456,plain,
! [X0] :
( compose(h,compose(codomain(compose(g,a)),domain(X0))) = compose(compose(h,codomain(compose(g,a))),domain(X0))
| codomain(compose(g,a)) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f9214]) ).
fof(f12457,plain,
! [X0] :
( compose(h,compose(codomain(g),domain(X0))) = compose(compose(h,codomain(g)),domain(X0))
| codomain(g) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f9214]) ).
fof(f12458,plain,
! [X0] :
( compose(h,compose(codomain(h),domain(X0))) = compose(compose(h,codomain(h)),domain(X0))
| codomain(h) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f9214]) ).
fof(f12459,plain,
! [X0] :
( compose(h,compose(codomain(a),domain(X0))) = compose(compose(h,codomain(a)),domain(X0))
| codomain(a) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f9214]) ).
fof(f12473,definition,
! [X0] :
( sQ1164_spl
<=> ( compose(h,compose(codomain(compose(a,b)),domain(X0))) = compose(compose(h,codomain(compose(a,b))),domain(X0))
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1164_spl])],[split_symbol_definition]) ).
fof(f12476,plain,
( sQ1164_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f12453,f1570,f12473]) ).
fof(f12477,definition,
! [X0] :
( sQ1165_spl
<=> ( compose(h,compose(codomain(compose(h,compose(a,b))),domain(X0))) = compose(compose(h,codomain(compose(h,compose(a,b)))),domain(X0))
| codomain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1165_spl])],[split_symbol_definition]) ).
fof(f12480,plain,
( sQ1165_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f12454,f1570,f12477]) ).
fof(f12481,definition,
! [X0] :
( sQ1166_spl
<=> ( compose(h,compose(codomain(compose(h,a)),domain(X0))) = compose(compose(h,codomain(compose(h,a))),domain(X0))
| codomain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1166_spl])],[split_symbol_definition]) ).
fof(f12484,plain,
( sQ1166_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12455,f715,f12481]) ).
fof(f12485,definition,
! [X0] :
( sQ1167_spl
<=> ( compose(h,compose(codomain(compose(g,a)),domain(X0))) = compose(compose(h,codomain(compose(g,a))),domain(X0))
| codomain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1167_spl])],[split_symbol_definition]) ).
fof(f12488,plain,
( sQ1167_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12456,f715,f12485]) ).
fof(f12489,definition,
! [X0] :
( sQ1168_spl
<=> ( compose(h,compose(codomain(g),domain(X0))) = compose(compose(h,codomain(g)),domain(X0))
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1168_spl])],[split_symbol_definition]) ).
fof(f12492,plain,
( sQ1168_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12457,f606,f12489]) ).
fof(f12493,definition,
! [X0] :
( sQ1169_spl
<=> ( compose(h,compose(codomain(h),domain(X0))) = compose(compose(h,codomain(h)),domain(X0))
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1169_spl])],[split_symbol_definition]) ).
fof(f12496,plain,
( sQ1169_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12458,f606,f12493]) ).
fof(f12497,definition,
! [X0] :
( sQ1170_spl
<=> ( compose(h,compose(codomain(a),domain(X0))) = compose(compose(h,codomain(a)),domain(X0))
| codomain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1170_spl])],[split_symbol_definition]) ).
fof(f12500,plain,
( sQ1170_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12459,f715,f12497]) ).
fof(f12516,plain,
! [X0] :
( compose(h,compose(domain(compose(g,a)),domain(X0))) = compose(compose(h,domain(compose(g,a))),domain(X0))
| domain(compose(g,a)) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f9215]) ).
fof(f12517,plain,
! [X0] :
( compose(h,compose(domain(compose(h,compose(a,b))),domain(X0))) = compose(compose(h,domain(compose(h,compose(a,b)))),domain(X0))
| domain(compose(h,compose(a,b))) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f9215]) ).
fof(f12518,plain,
! [X0] :
( compose(h,compose(domain(compose(h,a)),domain(X0))) = compose(compose(h,domain(compose(h,a))),domain(X0))
| domain(compose(h,a)) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f9215]) ).
fof(f12519,plain,
! [X0] :
( compose(h,compose(domain(compose(a,b)),domain(X0))) = compose(compose(h,domain(compose(a,b))),domain(X0))
| domain(compose(a,b)) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f9215]) ).
fof(f12531,definition,
! [X0] :
( sQ1171_spl
<=> ( compose(h,compose(domain(compose(g,a)),domain(X0))) = compose(compose(h,domain(compose(g,a))),domain(X0))
| domain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1171_spl])],[split_symbol_definition]) ).
fof(f12534,plain,
( sQ1171_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f12516,f584,f12531]) ).
fof(f12535,definition,
! [X0] :
( sQ1172_spl
<=> ( compose(h,compose(domain(compose(h,compose(a,b))),domain(X0))) = compose(compose(h,domain(compose(h,compose(a,b)))),domain(X0))
| domain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1172_spl])],[split_symbol_definition]) ).
fof(f12538,plain,
( sQ1172_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f12517,f584,f12535]) ).
fof(f12539,definition,
! [X0] :
( sQ1173_spl
<=> ( compose(h,compose(domain(compose(h,a)),domain(X0))) = compose(compose(h,domain(compose(h,a))),domain(X0))
| domain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1173_spl])],[split_symbol_definition]) ).
fof(f12542,plain,
( sQ1173_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f12518,f584,f12539]) ).
fof(f12543,definition,
! [X0] :
( sQ1174_spl
<=> ( compose(h,compose(domain(compose(a,b)),domain(X0))) = compose(compose(h,domain(compose(a,b))),domain(X0))
| domain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1174_spl])],[split_symbol_definition]) ).
fof(f12546,plain,
( sQ1174_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12519,f606,f12543]) ).
fof(f12559,plain,
( ~ sQ841_spl
| compose(h,compose(compose(a,b),domain(compose(g,a)))) = compose(compose(h,compose(a,b)),domain(compose(g,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f9187]) ).
fof(f12560,plain,
( ~ sQ841_spl
| compose(h,compose(compose(a,b),domain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b))))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f9187]) ).
fof(f12561,plain,
( ~ sQ841_spl
| compose(h,compose(compose(a,b),domain(compose(h,a)))) = compose(compose(h,compose(a,b)),domain(compose(h,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f9187]) ).
fof(f12562,plain,
( ~ sQ841_spl
| compose(h,compose(compose(a,b),domain(compose(a,b)))) = compose(compose(h,compose(a,b)),domain(compose(a,b)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f9187]) ).
fof(f12564,plain,
! [X0] :
( ~ sQ841_spl
| compose(h,compose(compose(a,b),domain(codomain(X0)))) = compose(compose(h,compose(a,b)),domain(codomain(X0)))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f16,f9187]) ).
fof(f12568,definition,
( sQ1175_spl
<=> compose(h,compose(compose(a,b),domain(compose(g,a)))) = compose(compose(h,compose(a,b)),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1175_spl])],[split_symbol_definition]) ).
fof(f12571,plain,
( ~ sQ841_spl
| sQ1175_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f12559,f1555,f12568,f9186]) ).
fof(f12572,definition,
( sQ1176_spl
<=> compose(h,compose(compose(a,b),domain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1176_spl])],[split_symbol_definition]) ).
fof(f12575,plain,
( ~ sQ841_spl
| sQ1176_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f12560,f1555,f12572,f9186]) ).
fof(f12576,definition,
( sQ1177_spl
<=> compose(h,compose(compose(a,b),domain(compose(h,a)))) = compose(compose(h,compose(a,b)),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1177_spl])],[split_symbol_definition]) ).
fof(f12579,plain,
( ~ sQ841_spl
| sQ1177_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f12561,f1555,f12576,f9186]) ).
fof(f12580,definition,
( sQ1178_spl
<=> compose(h,compose(compose(a,b),domain(compose(a,b)))) = compose(compose(h,compose(a,b)),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1178_spl])],[split_symbol_definition]) ).
fof(f12583,plain,
( ~ sQ841_spl
| sQ1178_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f12562,f1570,f12580,f9186]) ).
fof(f12586,plain,
! [X0] :
( ~ sQ841_spl
| compose(h,compose(compose(a,b),codomain(X0))) = compose(compose(h,compose(a,b)),domain(codomain(X0)))
| codomain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f12564]) ).
fof(f12587,plain,
! [X0] :
( ~ sQ841_spl
| compose(h,compose(compose(a,b),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f12586]) ).
fof(f12588,plain,
( compose(h,compose(codomain(compose(a,b)),codomain(b))) = compose(compose(h,codomain(compose(a,b))),codomain(b))
| domain(a) != codomain(compose(a,b)) ),
inference(resolution,[status(thm)],[f9303,f120]) ).
fof(f12589,plain,
( compose(h,compose(codomain(compose(h,compose(a,b))),codomain(b))) = compose(compose(h,codomain(compose(h,compose(a,b)))),codomain(b))
| domain(a) != codomain(compose(h,compose(a,b))) ),
inference(resolution,[status(thm)],[f9303,f581]) ).
fof(f12591,plain,
( compose(h,compose(codomain(b),codomain(compose(a,b)))) = compose(compose(h,codomain(b)),codomain(compose(a,b)))
| domain(a) != codomain(b) ),
inference(resolution,[status(thm)],[f9303,f120]) ).
fof(f12592,plain,
( compose(h,compose(codomain(b),codomain(compose(h,compose(a,b))))) = compose(compose(h,codomain(b)),codomain(compose(h,compose(a,b))))
| domain(a) != codomain(b) ),
inference(resolution,[status(thm)],[f9303,f581]) ).
fof(f12594,plain,
! [X0] :
( compose(h,compose(codomain(compose(a,b)),codomain(X0))) = compose(compose(h,codomain(compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(a) != codomain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f9303]) ).
fof(f12595,plain,
! [X0] :
( compose(h,compose(codomain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(h,codomain(compose(h,compose(a,b)))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(a) != codomain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f9303]) ).
fof(f12596,plain,
! [X0] :
( compose(h,compose(codomain(compose(h,a)),codomain(X0))) = compose(compose(h,codomain(compose(h,a))),codomain(X0))
| domain(b) != codomain(X0)
| domain(a) != codomain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f9303]) ).
fof(f12597,plain,
! [X0] :
( compose(h,compose(codomain(compose(g,a)),codomain(X0))) = compose(compose(h,codomain(compose(g,a))),codomain(X0))
| domain(b) != codomain(X0)
| domain(a) != codomain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f9303]) ).
fof(f12598,plain,
! [X0] :
( compose(h,compose(codomain(g),codomain(X0))) = compose(compose(h,codomain(g)),codomain(X0))
| domain(a) != codomain(X0)
| domain(a) != codomain(g) ),
inference(paramodulation,[status(thm)],[f74,f9303]) ).
fof(f12599,plain,
! [X0] :
( compose(h,compose(codomain(h),codomain(X0))) = compose(compose(h,codomain(h)),codomain(X0))
| domain(a) != codomain(X0)
| domain(a) != codomain(h) ),
inference(paramodulation,[status(thm)],[f69,f9303]) ).
fof(f12600,plain,
! [X0] :
( compose(h,compose(codomain(a),codomain(X0))) = compose(compose(h,codomain(a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(a) != codomain(a) ),
inference(paramodulation,[status(thm)],[f22,f9303]) ).
fof(f12607,plain,
! [X0] :
( compose(h,compose(codomain(X0),codomain(g))) = compose(compose(h,codomain(X0)),codomain(g))
| codomain(X0) != domain(a)
| domain(a) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f74,f9303]) ).
fof(f12613,definition,
( sQ1179_spl
<=> compose(h,compose(codomain(compose(a,b)),codomain(b))) = compose(compose(h,codomain(compose(a,b))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1179_spl])],[split_symbol_definition]) ).
fof(f12616,plain,
( sQ1179_spl
| ~ sQ1119_spl ),
inference(split_clause,[status(thm)],[f12588,f12019,f12613]) ).
fof(f12617,definition,
( sQ1180_spl
<=> compose(h,compose(codomain(compose(h,compose(a,b))),codomain(b))) = compose(compose(h,codomain(compose(h,compose(a,b)))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1180_spl])],[split_symbol_definition]) ).
fof(f12620,plain,
( sQ1180_spl
| ~ sQ1121_spl ),
inference(split_clause,[status(thm)],[f12589,f12026,f12617]) ).
fof(f12625,definition,
( sQ1181_spl
<=> compose(h,compose(codomain(b),codomain(compose(a,b)))) = compose(compose(h,codomain(b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1181_spl])],[split_symbol_definition]) ).
fof(f12628,plain,
( sQ1181_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f12591,f1570,f12625]) ).
fof(f12629,definition,
( sQ1182_spl
<=> compose(h,compose(codomain(b),codomain(compose(h,compose(a,b))))) = compose(compose(h,codomain(b)),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1182_spl])],[split_symbol_definition]) ).
fof(f12632,plain,
( sQ1182_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f12592,f1570,f12629]) ).
fof(f12635,definition,
! [X0] :
( sQ1183_spl
<=> ( compose(h,compose(codomain(compose(a,b)),codomain(X0))) = compose(compose(h,codomain(compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1183_spl])],[split_symbol_definition]) ).
fof(f12638,plain,
( sQ1183_spl
| ~ sQ1119_spl ),
inference(split_clause,[status(thm)],[f12594,f12019,f12635]) ).
fof(f12639,definition,
! [X0] :
( sQ1184_spl
<=> ( compose(h,compose(codomain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(h,codomain(compose(h,compose(a,b)))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1184_spl])],[split_symbol_definition]) ).
fof(f12642,plain,
( sQ1184_spl
| ~ sQ1121_spl ),
inference(split_clause,[status(thm)],[f12595,f12026,f12639]) ).
fof(f12643,definition,
! [X0] :
( sQ1185_spl
<=> ( compose(h,compose(codomain(compose(h,a)),codomain(X0))) = compose(compose(h,codomain(compose(h,a))),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1185_spl])],[split_symbol_definition]) ).
fof(f12646,plain,
( sQ1185_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f12596,f3284,f12643]) ).
fof(f12647,definition,
! [X0] :
( sQ1186_spl
<=> ( compose(h,compose(codomain(compose(g,a)),codomain(X0))) = compose(compose(h,codomain(compose(g,a))),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1186_spl])],[split_symbol_definition]) ).
fof(f12650,plain,
( sQ1186_spl
| ~ sQ203_spl ),
inference(split_clause,[status(thm)],[f12597,f3216,f12647]) ).
fof(f12651,definition,
! [X0] :
( sQ1187_spl
<=> ( compose(h,compose(codomain(g),codomain(X0))) = compose(compose(h,codomain(g)),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1187_spl])],[split_symbol_definition]) ).
fof(f12654,plain,
( sQ1187_spl
| ~ sQ1129_spl ),
inference(split_clause,[status(thm)],[f12598,f12063,f12651]) ).
fof(f12655,definition,
! [X0] :
( sQ1188_spl
<=> ( compose(h,compose(codomain(h),codomain(X0))) = compose(compose(h,codomain(h)),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1188_spl])],[split_symbol_definition]) ).
fof(f12658,plain,
( sQ1188_spl
| ~ sQ1131_spl ),
inference(split_clause,[status(thm)],[f12599,f12070,f12655]) ).
fof(f12659,definition,
! [X0] :
( sQ1189_spl
<=> ( compose(h,compose(codomain(a),codomain(X0))) = compose(compose(h,codomain(a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1189_spl])],[split_symbol_definition]) ).
fof(f12662,plain,
( sQ1189_spl
| ~ sQ1133_spl ),
inference(split_clause,[status(thm)],[f12600,f12077,f12659]) ).
fof(f12677,plain,
! [X0] :
( compose(h,compose(codomain(X0),domain(a))) = compose(compose(h,codomain(X0)),codomain(g))
| codomain(X0) != domain(a)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f74,f12607]) ).
fof(f12678,plain,
! [X0] :
( compose(h,compose(codomain(X0),domain(a))) = compose(compose(h,codomain(X0)),domain(a))
| codomain(X0) != domain(a)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f74,f12677]) ).
fof(f12679,plain,
! [X0] :
( compose(h,compose(codomain(X0),domain(a))) = compose(compose(h,codomain(X0)),domain(a))
| domain(a) != codomain(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f12678]) ).
fof(f12698,plain,
( compose(h,compose(codomain(compose(a,b)),domain(a))) = compose(compose(h,codomain(compose(a,b))),domain(a))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f12679]) ).
fof(f12699,plain,
( compose(h,compose(codomain(compose(h,compose(a,b))),domain(a))) = compose(compose(h,codomain(compose(h,compose(a,b)))),domain(a))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f12679]) ).
fof(f12700,plain,
( compose(h,compose(codomain(compose(h,a)),domain(a))) = compose(compose(h,codomain(compose(h,a))),domain(a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f12679]) ).
fof(f12701,plain,
( compose(h,compose(codomain(compose(g,a)),domain(a))) = compose(compose(h,codomain(compose(g,a))),domain(a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f12679]) ).
fof(f12702,plain,
( compose(h,compose(codomain(g),domain(a))) = compose(compose(h,codomain(g)),domain(a))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f12679]) ).
fof(f12703,plain,
( compose(h,compose(codomain(h),domain(a))) = compose(compose(h,codomain(h)),domain(a))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f12679]) ).
fof(f12704,plain,
( compose(h,compose(codomain(a),domain(a))) = compose(compose(h,codomain(a)),domain(a))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f12679]) ).
fof(f12706,plain,
! [X0] :
( compose(h,compose(codomain(domain(X0)),domain(a))) = compose(compose(h,codomain(domain(X0))),domain(a))
| domain(a) != domain(X0) ),
inference(paramodulation,[status(thm)],[f15,f12679]) ).
fof(f12721,definition,
( sQ1190_spl
<=> compose(h,compose(codomain(compose(a,b)),domain(a))) = compose(compose(h,codomain(compose(a,b))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1190_spl])],[split_symbol_definition]) ).
fof(f12724,plain,
( sQ1190_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f12698,f1570,f12721]) ).
fof(f12725,definition,
( sQ1191_spl
<=> compose(h,compose(codomain(compose(h,compose(a,b))),domain(a))) = compose(compose(h,codomain(compose(h,compose(a,b)))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1191_spl])],[split_symbol_definition]) ).
fof(f12728,plain,
( sQ1191_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f12699,f1570,f12725]) ).
fof(f12729,definition,
( sQ1192_spl
<=> compose(h,compose(codomain(compose(h,a)),domain(a))) = compose(compose(h,codomain(compose(h,a))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1192_spl])],[split_symbol_definition]) ).
fof(f12732,plain,
( sQ1192_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12700,f715,f12729]) ).
fof(f12733,definition,
( sQ1193_spl
<=> compose(h,compose(codomain(compose(g,a)),domain(a))) = compose(compose(h,codomain(compose(g,a))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1193_spl])],[split_symbol_definition]) ).
fof(f12736,plain,
( sQ1193_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12701,f715,f12733]) ).
fof(f12737,definition,
( sQ1194_spl
<=> compose(h,compose(codomain(g),domain(a))) = compose(compose(h,codomain(g)),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1194_spl])],[split_symbol_definition]) ).
fof(f12740,plain,
( sQ1194_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12702,f606,f12737]) ).
fof(f12741,definition,
( sQ1195_spl
<=> compose(h,compose(codomain(h),domain(a))) = compose(compose(h,codomain(h)),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1195_spl])],[split_symbol_definition]) ).
fof(f12744,plain,
( sQ1195_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12703,f606,f12741]) ).
fof(f12745,definition,
( sQ1196_spl
<=> compose(h,compose(codomain(a),domain(a))) = compose(compose(h,codomain(a)),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1196_spl])],[split_symbol_definition]) ).
fof(f12748,plain,
( sQ1196_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12704,f715,f12745]) ).
fof(f12751,plain,
! [X0] :
( compose(h,compose(domain(X0),domain(a))) = compose(compose(h,codomain(domain(X0))),domain(a))
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f12706]) ).
fof(f12752,plain,
! [X0] :
( compose(h,compose(domain(X0),domain(a))) = compose(compose(h,domain(X0)),domain(a))
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f12751]) ).
fof(f12764,plain,
! [X0] :
( compose(domain(compose(g,a)),compose(compose(a,b),X0)) = compose(compose(domain(compose(g,a)),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f1108,f2806]) ).
fof(f12765,plain,
! [X0] :
( compose(domain(compose(h,compose(a,b))),compose(compose(a,b),X0)) = compose(compose(domain(compose(h,compose(a,b))),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f1068,f2806]) ).
fof(f12766,plain,
! [X0] :
( compose(domain(compose(h,a)),compose(compose(a,b),X0)) = compose(compose(domain(compose(h,a)),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f76,f2806]) ).
fof(f12767,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)],[f60,f2806]) ).
fof(f12776,definition,
! [X0] :
( sQ1197_spl
<=> ( compose(domain(compose(g,a)),compose(compose(a,b),X0)) = compose(compose(domain(compose(g,a)),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1197_spl])],[split_symbol_definition]) ).
fof(f12779,plain,
( sQ1197_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f12764,f584,f12776]) ).
fof(f12780,definition,
! [X0] :
( sQ1198_spl
<=> ( compose(domain(compose(h,compose(a,b))),compose(compose(a,b),X0)) = compose(compose(domain(compose(h,compose(a,b))),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1198_spl])],[split_symbol_definition]) ).
fof(f12783,plain,
( sQ1198_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f12765,f584,f12780]) ).
fof(f12784,definition,
! [X0] :
( sQ1199_spl
<=> ( compose(domain(compose(h,a)),compose(compose(a,b),X0)) = compose(compose(domain(compose(h,a)),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1199_spl])],[split_symbol_definition]) ).
fof(f12787,plain,
( sQ1199_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f12766,f584,f12784]) ).
fof(f12788,definition,
! [X0] :
( sQ1200_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,[sQ1200_spl])],[split_symbol_definition]) ).
fof(f12791,plain,
( sQ1200_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12767,f606,f12788]) ).
fof(f12801,plain,
( compose(h,compose(domain(compose(g,a)),domain(a))) = compose(compose(h,domain(compose(g,a))),domain(a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f12752]) ).
fof(f12802,plain,
( compose(h,compose(domain(compose(h,compose(a,b))),domain(a))) = compose(compose(h,domain(compose(h,compose(a,b)))),domain(a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f12752]) ).
fof(f12803,plain,
( compose(h,compose(domain(compose(h,a)),domain(a))) = compose(compose(h,domain(compose(h,a))),domain(a))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f12752]) ).
fof(f12804,plain,
( compose(h,compose(domain(compose(a,b)),domain(a))) = compose(compose(h,domain(compose(a,b))),domain(a))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f12752]) ).
fof(f12817,definition,
( sQ1201_spl
<=> compose(h,compose(domain(compose(g,a)),domain(a))) = compose(compose(h,domain(compose(g,a))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1201_spl])],[split_symbol_definition]) ).
fof(f12820,plain,
( sQ1201_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f12801,f584,f12817]) ).
fof(f12821,definition,
( sQ1202_spl
<=> compose(h,compose(domain(compose(h,compose(a,b))),domain(a))) = compose(compose(h,domain(compose(h,compose(a,b)))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1202_spl])],[split_symbol_definition]) ).
fof(f12824,plain,
( sQ1202_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f12802,f584,f12821]) ).
fof(f12825,definition,
( sQ1203_spl
<=> compose(h,compose(domain(compose(h,a)),domain(a))) = compose(compose(h,domain(compose(h,a))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1203_spl])],[split_symbol_definition]) ).
fof(f12828,plain,
( sQ1203_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f12803,f584,f12825]) ).
fof(f12829,definition,
( sQ1204_spl
<=> compose(h,compose(domain(compose(a,b)),domain(a))) = compose(compose(h,domain(compose(a,b))),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1204_spl])],[split_symbol_definition]) ).
fof(f12832,plain,
( sQ1204_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12804,f606,f12829]) ).
fof(f12846,plain,
( compose(h,compose(domain(b),codomain(compose(h,a)))) = compose(compose(h,domain(b)),codomain(compose(h,a)))
| domain(a) != domain(b) ),
inference(resolution,[status(thm)],[f9304,f131]) ).
fof(f12847,plain,
( compose(h,compose(domain(b),codomain(compose(g,a)))) = compose(compose(h,domain(b)),codomain(compose(g,a)))
| domain(a) != domain(b) ),
inference(resolution,[status(thm)],[f9304,f130]) ).
fof(f12848,plain,
( compose(h,compose(domain(a),codomain(g))) = compose(compose(h,domain(a)),codomain(g))
| domain(a) != domain(a) ),
inference(resolution,[status(thm)],[f9304,f74]) ).
fof(f12849,plain,
( compose(h,compose(domain(a),codomain(h))) = compose(compose(h,domain(a)),codomain(h))
| domain(a) != domain(a) ),
inference(resolution,[status(thm)],[f9304,f69]) ).
fof(f12850,plain,
( compose(h,compose(domain(b),codomain(a))) = compose(compose(h,domain(b)),codomain(a))
| domain(a) != domain(b) ),
inference(resolution,[status(thm)],[f9304,f22]) ).
fof(f12852,plain,
! [X0] :
( compose(h,compose(domain(compose(g,a)),codomain(X0))) = compose(compose(h,domain(compose(g,a))),codomain(X0))
| domain(h) != codomain(X0)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f1108,f9304]) ).
fof(f12853,plain,
! [X0] :
( compose(h,compose(domain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(h,domain(compose(h,compose(a,b)))),codomain(X0))
| domain(h) != codomain(X0)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f1068,f9304]) ).
fof(f12854,plain,
! [X0] :
( compose(h,compose(domain(compose(h,a)),codomain(X0))) = compose(compose(h,domain(compose(h,a))),codomain(X0))
| domain(h) != codomain(X0)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f76,f9304]) ).
fof(f12855,plain,
! [X0] :
( compose(h,compose(domain(compose(a,b)),codomain(X0))) = compose(compose(h,domain(compose(a,b))),codomain(X0))
| domain(a) != codomain(X0)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f60,f9304]) ).
fof(f12870,definition,
( sQ1205_spl
<=> compose(h,compose(domain(b),codomain(compose(h,a)))) = compose(compose(h,domain(b)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1205_spl])],[split_symbol_definition]) ).
fof(f12873,plain,
( sQ1205_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12846,f715,f12870]) ).
fof(f12874,definition,
( sQ1206_spl
<=> compose(h,compose(domain(b),codomain(compose(g,a)))) = compose(compose(h,domain(b)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1206_spl])],[split_symbol_definition]) ).
fof(f12877,plain,
( sQ1206_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12847,f715,f12874]) ).
fof(f12878,definition,
( sQ1207_spl
<=> compose(h,compose(domain(a),codomain(g))) = compose(compose(h,domain(a)),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ1207_spl])],[split_symbol_definition]) ).
fof(f12881,plain,
( sQ1207_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12848,f606,f12878]) ).
fof(f12882,definition,
( sQ1208_spl
<=> compose(h,compose(domain(a),codomain(h))) = compose(compose(h,domain(a)),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ1208_spl])],[split_symbol_definition]) ).
fof(f12885,plain,
( sQ1208_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12849,f606,f12882]) ).
fof(f12886,definition,
( sQ1209_spl
<=> compose(h,compose(domain(b),codomain(a))) = compose(compose(h,domain(b)),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1209_spl])],[split_symbol_definition]) ).
fof(f12889,plain,
( sQ1209_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12850,f715,f12886]) ).
fof(f12892,definition,
! [X0] :
( sQ1210_spl
<=> ( compose(h,compose(domain(compose(g,a)),codomain(X0))) = compose(compose(h,domain(compose(g,a))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1210_spl])],[split_symbol_definition]) ).
fof(f12895,plain,
( sQ1210_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f12852,f1743,f12892]) ).
fof(f12896,definition,
! [X0] :
( sQ1211_spl
<=> ( compose(h,compose(domain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(h,domain(compose(h,compose(a,b)))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1211_spl])],[split_symbol_definition]) ).
fof(f12899,plain,
( sQ1211_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f12853,f1772,f12896]) ).
fof(f12900,definition,
! [X0] :
( sQ1212_spl
<=> ( compose(h,compose(domain(compose(h,a)),codomain(X0))) = compose(compose(h,domain(compose(h,a))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1212_spl])],[split_symbol_definition]) ).
fof(f12903,plain,
( sQ1212_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f12854,f1736,f12900]) ).
fof(f12904,definition,
! [X0] :
( sQ1213_spl
<=> ( compose(h,compose(domain(compose(a,b)),codomain(X0))) = compose(compose(h,domain(compose(a,b))),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1213_spl])],[split_symbol_definition]) ).
fof(f12907,plain,
( sQ1213_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f12855,f1765,f12904]) ).
fof(f12949,plain,
( ~ sQ852_spl
| compose(h,compose(compose(a,b),codomain(compose(a,b)))) = compose(compose(h,compose(a,b)),codomain(compose(a,b)))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f9276]) ).
fof(f12950,plain,
( ~ sQ852_spl
| compose(h,compose(compose(a,b),codomain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b))))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f9276]) ).
fof(f12951,plain,
( ~ sQ852_spl
| compose(h,compose(compose(a,b),codomain(compose(h,a)))) = compose(compose(h,compose(a,b)),codomain(compose(h,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f9276]) ).
fof(f12952,plain,
( ~ sQ852_spl
| compose(h,compose(compose(a,b),codomain(compose(g,a)))) = compose(compose(h,compose(a,b)),codomain(compose(g,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f9276]) ).
fof(f12954,plain,
! [X0] :
( ~ sQ852_spl
| compose(h,compose(compose(a,b),codomain(domain(X0)))) = compose(compose(h,compose(a,b)),codomain(domain(X0)))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f15,f9276]) ).
fof(f12963,definition,
( sQ1214_spl
<=> compose(h,compose(compose(a,b),codomain(compose(a,b)))) = compose(compose(h,compose(a,b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1214_spl])],[split_symbol_definition]) ).
fof(f12966,plain,
( ~ sQ852_spl
| sQ1214_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f12949,f4389,f12963,f9275]) ).
fof(f12967,definition,
( sQ1215_spl
<=> compose(h,compose(compose(a,b),codomain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1215_spl])],[split_symbol_definition]) ).
fof(f12970,plain,
( ~ sQ852_spl
| sQ1215_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f12950,f4389,f12967,f9275]) ).
fof(f12971,definition,
( sQ1216_spl
<=> compose(h,compose(compose(a,b),codomain(compose(h,a)))) = compose(compose(h,compose(a,b)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1216_spl])],[split_symbol_definition]) ).
fof(f12974,plain,
( ~ sQ852_spl
| sQ1216_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f12951,f2265,f12971,f9275]) ).
fof(f12975,definition,
( sQ1217_spl
<=> compose(h,compose(compose(a,b),codomain(compose(g,a)))) = compose(compose(h,compose(a,b)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1217_spl])],[split_symbol_definition]) ).
fof(f12978,plain,
( ~ sQ852_spl
| sQ1217_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f12952,f2265,f12975,f9275]) ).
fof(f12981,plain,
! [X0] :
( ~ sQ852_spl
| compose(h,compose(compose(a,b),domain(X0))) = compose(compose(h,compose(a,b)),codomain(domain(X0)))
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f12954]) ).
fof(f12982,plain,
! [X0] :
( ~ sQ852_spl
| compose(h,compose(compose(a,b),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f12981]) ).
fof(f12992,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)],[f120,f9573]) ).
fof(f12993,plain,
! [X0] :
( compose(a,compose(codomain(compose(h,compose(a,b))),domain(X0))) = compose(compose(a,codomain(compose(h,compose(a,b)))),domain(X0))
| codomain(compose(h,compose(a,b))) != domain(X0)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f9573]) ).
fof(f12994,plain,
! [X0] :
( compose(a,compose(codomain(compose(h,a)),domain(X0))) = compose(compose(a,codomain(compose(h,a))),domain(X0))
| codomain(compose(h,a)) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f9573]) ).
fof(f12995,plain,
! [X0] :
( compose(a,compose(codomain(compose(g,a)),domain(X0))) = compose(compose(a,codomain(compose(g,a))),domain(X0))
| codomain(compose(g,a)) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f9573]) ).
fof(f12996,plain,
! [X0] :
( compose(a,compose(codomain(g),domain(X0))) = compose(compose(a,codomain(g)),domain(X0))
| codomain(g) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f9573]) ).
fof(f12997,plain,
! [X0] :
( compose(a,compose(codomain(h),domain(X0))) = compose(compose(a,codomain(h)),domain(X0))
| codomain(h) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f9573]) ).
fof(f12998,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)],[f22,f9573]) ).
fof(f13016,definition,
! [X0] :
( sQ1218_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,[sQ1218_spl])],[split_symbol_definition]) ).
fof(f13019,plain,
( sQ1218_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f12992,f2265,f13016]) ).
fof(f13020,definition,
! [X0] :
( sQ1219_spl
<=> ( compose(a,compose(codomain(compose(h,compose(a,b))),domain(X0))) = compose(compose(a,codomain(compose(h,compose(a,b)))),domain(X0))
| codomain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1219_spl])],[split_symbol_definition]) ).
fof(f13023,plain,
( sQ1219_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f12993,f2265,f13020]) ).
fof(f13024,definition,
! [X0] :
( sQ1220_spl
<=> ( compose(a,compose(codomain(compose(h,a)),domain(X0))) = compose(compose(a,codomain(compose(h,a))),domain(X0))
| codomain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1220_spl])],[split_symbol_definition]) ).
fof(f13027,plain,
( sQ1220_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f12994,f1941,f13024]) ).
fof(f13028,definition,
! [X0] :
( sQ1221_spl
<=> ( compose(a,compose(codomain(compose(g,a)),domain(X0))) = compose(compose(a,codomain(compose(g,a))),domain(X0))
| codomain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1221_spl])],[split_symbol_definition]) ).
fof(f13031,plain,
( sQ1221_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f12995,f1941,f13028]) ).
fof(f13032,definition,
! [X0] :
( sQ1222_spl
<=> ( compose(a,compose(codomain(g),domain(X0))) = compose(compose(a,codomain(g)),domain(X0))
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1222_spl])],[split_symbol_definition]) ).
fof(f13035,plain,
( sQ1222_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12996,f715,f13032]) ).
fof(f13036,definition,
! [X0] :
( sQ1223_spl
<=> ( compose(a,compose(codomain(h),domain(X0))) = compose(compose(a,codomain(h)),domain(X0))
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1223_spl])],[split_symbol_definition]) ).
fof(f13039,plain,
( sQ1223_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f12997,f715,f13036]) ).
fof(f13040,definition,
! [X0] :
( sQ1224_spl
<=> ( compose(a,compose(codomain(a),domain(X0))) = compose(compose(a,codomain(a)),domain(X0))
| codomain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1224_spl])],[split_symbol_definition]) ).
fof(f13043,plain,
( sQ1224_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f12998,f1941,f13040]) ).
fof(f13062,plain,
! [X0] :
( compose(a,compose(domain(compose(g,a)),domain(X0))) = compose(compose(a,domain(compose(g,a))),domain(X0))
| domain(compose(g,a)) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f9574]) ).
fof(f13063,plain,
! [X0] :
( compose(a,compose(domain(compose(h,compose(a,b))),domain(X0))) = compose(compose(a,domain(compose(h,compose(a,b)))),domain(X0))
| domain(compose(h,compose(a,b))) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f9574]) ).
fof(f13064,plain,
! [X0] :
( compose(a,compose(domain(compose(h,a)),domain(X0))) = compose(compose(a,domain(compose(h,a))),domain(X0))
| domain(compose(h,a)) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f9574]) ).
fof(f13065,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)],[f60,f9574]) ).
fof(f13073,definition,
! [X0] :
( sQ1225_spl
<=> ( compose(a,compose(domain(compose(g,a)),domain(X0))) = compose(compose(a,domain(compose(g,a))),domain(X0))
| domain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1225_spl])],[split_symbol_definition]) ).
fof(f13076,plain,
( sQ1225_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f13062,f693,f13073]) ).
fof(f13077,definition,
! [X0] :
( sQ1226_spl
<=> ( compose(a,compose(domain(compose(h,compose(a,b))),domain(X0))) = compose(compose(a,domain(compose(h,compose(a,b)))),domain(X0))
| domain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1226_spl])],[split_symbol_definition]) ).
fof(f13080,plain,
( sQ1226_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f13063,f693,f13077]) ).
fof(f13081,definition,
! [X0] :
( sQ1227_spl
<=> ( compose(a,compose(domain(compose(h,a)),domain(X0))) = compose(compose(a,domain(compose(h,a))),domain(X0))
| domain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1227_spl])],[split_symbol_definition]) ).
fof(f13084,plain,
( sQ1227_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f13064,f693,f13081]) ).
fof(f13085,definition,
! [X0] :
( sQ1228_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,[sQ1228_spl])],[split_symbol_definition]) ).
fof(f13088,plain,
( sQ1228_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13065,f715,f13085]) ).
fof(f13099,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)],[f120,f2967]) ).
fof(f13100,plain,
! [X0] :
( compose(compose(a,b),compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(compose(a,b),codomain(compose(h,compose(a,b)))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0)
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f2967]) ).
fof(f13101,plain,
! [X0] :
( compose(compose(a,b),compose(codomain(compose(h,a)),X0)) = compose(compose(compose(a,b),codomain(compose(h,a))),X0)
| codomain(compose(h,a)) != domain(X0)
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f2967]) ).
fof(f13102,plain,
! [X0] :
( compose(compose(a,b),compose(codomain(compose(g,a)),X0)) = compose(compose(compose(a,b),codomain(compose(g,a))),X0)
| codomain(compose(g,a)) != domain(X0)
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f2967]) ).
fof(f13117,definition,
! [X0] :
( sQ1229_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,[sQ1229_spl])],[split_symbol_definition]) ).
fof(f13120,plain,
( sQ1229_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f13099,f4389,f13117]) ).
fof(f13121,definition,
! [X0] :
( sQ1230_spl
<=> ( compose(compose(a,b),compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(compose(a,b),codomain(compose(h,compose(a,b)))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1230_spl])],[split_symbol_definition]) ).
fof(f13124,plain,
( sQ1230_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f13100,f4389,f13121]) ).
fof(f13125,definition,
! [X0] :
( sQ1231_spl
<=> ( compose(compose(a,b),compose(codomain(compose(h,a)),X0)) = compose(compose(compose(a,b),codomain(compose(h,a))),X0)
| codomain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1231_spl])],[split_symbol_definition]) ).
fof(f13128,plain,
( sQ1231_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f13101,f2265,f13125]) ).
fof(f13129,definition,
! [X0] :
( sQ1232_spl
<=> ( compose(compose(a,b),compose(codomain(compose(g,a)),X0)) = compose(compose(compose(a,b),codomain(compose(g,a))),X0)
| codomain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1232_spl])],[split_symbol_definition]) ).
fof(f13132,plain,
( sQ1232_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f13102,f2265,f13129]) ).
fof(f13147,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)],[f9655,f120]) ).
fof(f13148,plain,
( compose(a,compose(codomain(compose(h,compose(a,b))),codomain(b))) = compose(compose(a,codomain(compose(h,compose(a,b)))),codomain(b))
| domain(b) != codomain(compose(h,compose(a,b))) ),
inference(resolution,[status(thm)],[f9655,f581]) ).
fof(f13150,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)],[f9655,f120]) ).
fof(f13151,plain,
( compose(a,compose(codomain(b),codomain(compose(h,compose(a,b))))) = compose(compose(a,codomain(b)),codomain(compose(h,compose(a,b))))
| domain(b) != codomain(b) ),
inference(resolution,[status(thm)],[f9655,f581]) ).
fof(f13153,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)],[f120,f9655]) ).
fof(f13154,plain,
! [X0] :
( compose(a,compose(codomain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(a,codomain(compose(h,compose(a,b)))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(b) != codomain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f9655]) ).
fof(f13155,plain,
! [X0] :
( compose(a,compose(codomain(compose(h,a)),codomain(X0))) = compose(compose(a,codomain(compose(h,a))),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != codomain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f9655]) ).
fof(f13156,plain,
! [X0] :
( compose(a,compose(codomain(compose(g,a)),codomain(X0))) = compose(compose(a,codomain(compose(g,a))),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != codomain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f9655]) ).
fof(f13157,plain,
! [X0] :
( compose(a,compose(codomain(g),codomain(X0))) = compose(compose(a,codomain(g)),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != codomain(g) ),
inference(paramodulation,[status(thm)],[f74,f9655]) ).
fof(f13158,plain,
! [X0] :
( compose(a,compose(codomain(h),codomain(X0))) = compose(compose(a,codomain(h)),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f69,f9655]) ).
fof(f13159,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)],[f22,f9655]) ).
fof(f13164,plain,
! [X0] :
( compose(a,compose(codomain(X0),codomain(compose(h,a)))) = compose(compose(a,codomain(X0)),codomain(compose(h,a)))
| codomain(X0) != domain(b)
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f131,f9655]) ).
fof(f13172,definition,
( sQ1233_spl
<=> domain(b) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1233_spl])],[split_symbol_definition]) ).
fof(f13174,plain,
( sQ1233_spl
| domain(b) != codomain(compose(a,b)) ),
inference(component_clause,[status(thm)],[f13172]) ).
fof(f13175,definition,
( sQ1234_spl
<=> compose(a,compose(codomain(compose(a,b)),codomain(b))) = compose(compose(a,codomain(compose(a,b))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1234_spl])],[split_symbol_definition]) ).
fof(f13178,plain,
( sQ1234_spl
| ~ sQ1233_spl ),
inference(split_clause,[status(thm)],[f13147,f13172,f13175]) ).
fof(f13179,definition,
( sQ1235_spl
<=> domain(b) = codomain(compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1235_spl])],[split_symbol_definition]) ).
fof(f13181,plain,
( sQ1235_spl
| domain(b) != codomain(compose(h,compose(a,b))) ),
inference(component_clause,[status(thm)],[f13179]) ).
fof(f13182,definition,
( sQ1236_spl
<=> compose(a,compose(codomain(compose(h,compose(a,b))),codomain(b))) = compose(compose(a,codomain(compose(h,compose(a,b)))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1236_spl])],[split_symbol_definition]) ).
fof(f13185,plain,
( sQ1236_spl
| ~ sQ1235_spl ),
inference(split_clause,[status(thm)],[f13148,f13179,f13182]) ).
fof(f13190,definition,
( sQ1237_spl
<=> compose(a,compose(codomain(b),codomain(compose(a,b)))) = compose(compose(a,codomain(b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1237_spl])],[split_symbol_definition]) ).
fof(f13193,plain,
( sQ1237_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f13150,f2265,f13190]) ).
fof(f13194,definition,
( sQ1238_spl
<=> compose(a,compose(codomain(b),codomain(compose(h,compose(a,b))))) = compose(compose(a,codomain(b)),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1238_spl])],[split_symbol_definition]) ).
fof(f13197,plain,
( sQ1238_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f13151,f2265,f13194]) ).
fof(f13200,definition,
! [X0] :
( sQ1239_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,[sQ1239_spl])],[split_symbol_definition]) ).
fof(f13203,plain,
( sQ1239_spl
| ~ sQ1233_spl ),
inference(split_clause,[status(thm)],[f13153,f13172,f13200]) ).
fof(f13204,definition,
! [X0] :
( sQ1240_spl
<=> ( compose(a,compose(codomain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(a,codomain(compose(h,compose(a,b)))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1240_spl])],[split_symbol_definition]) ).
fof(f13207,plain,
( sQ1240_spl
| ~ sQ1235_spl ),
inference(split_clause,[status(thm)],[f13154,f13179,f13204]) ).
fof(f13208,definition,
! [X0] :
( sQ1241_spl
<=> ( compose(a,compose(codomain(compose(h,a)),codomain(X0))) = compose(compose(a,codomain(compose(h,a))),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1241_spl])],[split_symbol_definition]) ).
fof(f13211,plain,
( sQ1241_spl
| ~ sQ220_spl ),
inference(split_clause,[status(thm)],[f13155,f3298,f13208]) ).
fof(f13212,definition,
! [X0] :
( sQ1242_spl
<=> ( compose(a,compose(codomain(compose(g,a)),codomain(X0))) = compose(compose(a,codomain(compose(g,a))),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1242_spl])],[split_symbol_definition]) ).
fof(f13215,plain,
( sQ1242_spl
| ~ sQ208_spl ),
inference(split_clause,[status(thm)],[f13156,f3233,f13212]) ).
fof(f13216,definition,
( sQ1243_spl
<=> domain(b) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ1243_spl])],[split_symbol_definition]) ).
fof(f13218,plain,
( sQ1243_spl
| domain(b) != codomain(g) ),
inference(component_clause,[status(thm)],[f13216]) ).
fof(f13219,definition,
! [X0] :
( sQ1244_spl
<=> ( compose(a,compose(codomain(g),codomain(X0))) = compose(compose(a,codomain(g)),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1244_spl])],[split_symbol_definition]) ).
fof(f13222,plain,
( sQ1244_spl
| ~ sQ1243_spl ),
inference(split_clause,[status(thm)],[f13157,f13216,f13219]) ).
fof(f13223,definition,
( sQ1245_spl
<=> domain(b) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ1245_spl])],[split_symbol_definition]) ).
fof(f13225,plain,
( sQ1245_spl
| domain(b) != codomain(h) ),
inference(component_clause,[status(thm)],[f13223]) ).
fof(f13226,definition,
! [X0] :
( sQ1246_spl
<=> ( compose(a,compose(codomain(h),codomain(X0))) = compose(compose(a,codomain(h)),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1246_spl])],[split_symbol_definition]) ).
fof(f13229,plain,
( sQ1246_spl
| ~ sQ1245_spl ),
inference(split_clause,[status(thm)],[f13158,f13223,f13226]) ).
fof(f13230,definition,
( sQ1247_spl
<=> domain(b) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ1247_spl])],[split_symbol_definition]) ).
fof(f13232,plain,
( sQ1247_spl
| domain(b) != codomain(a) ),
inference(component_clause,[status(thm)],[f13230]) ).
fof(f13233,definition,
! [X0] :
( sQ1248_spl
<=> ( compose(a,compose(codomain(a),codomain(X0))) = compose(compose(a,codomain(a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1248_spl])],[split_symbol_definition]) ).
fof(f13236,plain,
( sQ1248_spl
| ~ sQ1247_spl ),
inference(split_clause,[status(thm)],[f13159,f13230,f13233]) ).
fof(f13247,plain,
! [X0] :
( compose(a,compose(codomain(X0),domain(b))) = compose(compose(a,codomain(X0)),codomain(compose(h,a)))
| codomain(X0) != domain(b)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f131,f13164]) ).
fof(f13248,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)],[f131,f13247]) ).
fof(f13249,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)],[f13248]) ).
fof(f13265,plain,
( sQ208_spl
| domain(b) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f130,f3235]) ).
fof(f13266,plain,
( sQ208_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f13265]) ).
fof(f13267,plain,
sQ208_spl,
inference(contradiction_clause,[status(thm)],[f13266]) ).
fof(f13268,plain,
( sQ220_spl
| domain(b) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f131,f3300]) ).
fof(f13269,plain,
( sQ220_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f13268]) ).
fof(f13270,plain,
sQ220_spl,
inference(contradiction_clause,[status(thm)],[f13269]) ).
fof(f13271,plain,
( sQ1235_spl
| domain(b) != codomain(b) ),
inference(forward_demodulation,[status(thm)],[f581,f13181]) ).
fof(f13272,plain,
( sQ1233_spl
| domain(b) != codomain(b) ),
inference(forward_demodulation,[status(thm)],[f120,f13174]) ).
fof(f13273,plain,
( sQ1247_spl
| domain(b) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f22,f13232]) ).
fof(f13274,plain,
( sQ1247_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f13273]) ).
fof(f13275,plain,
sQ1247_spl,
inference(contradiction_clause,[status(thm)],[f13274]) ).
fof(f13276,plain,
( sQ1245_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f69,f13225]) ).
fof(f13277,plain,
( sQ1243_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f74,f13218]) ).
fof(f13306,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)],[f120,f13249]) ).
fof(f13307,plain,
( compose(a,compose(codomain(compose(h,compose(a,b))),domain(b))) = compose(compose(a,codomain(compose(h,compose(a,b)))),domain(b))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f13249]) ).
fof(f13308,plain,
( compose(a,compose(codomain(compose(h,a)),domain(b))) = compose(compose(a,codomain(compose(h,a))),domain(b))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f13249]) ).
fof(f13309,plain,
( compose(a,compose(codomain(compose(g,a)),domain(b))) = compose(compose(a,codomain(compose(g,a))),domain(b))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f13249]) ).
fof(f13310,plain,
( compose(a,compose(codomain(g),domain(b))) = compose(compose(a,codomain(g)),domain(b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f13249]) ).
fof(f13311,plain,
( compose(a,compose(codomain(h),domain(b))) = compose(compose(a,codomain(h)),domain(b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f13249]) ).
fof(f13312,plain,
( compose(a,compose(codomain(a),domain(b))) = compose(compose(a,codomain(a)),domain(b))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f13249]) ).
fof(f13314,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)],[f15,f13249]) ).
fof(f13334,definition,
( sQ1249_spl
<=> compose(a,compose(codomain(compose(a,b)),domain(b))) = compose(compose(a,codomain(compose(a,b))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1249_spl])],[split_symbol_definition]) ).
fof(f13337,plain,
( sQ1249_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f13306,f2265,f13334]) ).
fof(f13338,definition,
( sQ1250_spl
<=> compose(a,compose(codomain(compose(h,compose(a,b))),domain(b))) = compose(compose(a,codomain(compose(h,compose(a,b)))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1250_spl])],[split_symbol_definition]) ).
fof(f13341,plain,
( sQ1250_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f13307,f2265,f13338]) ).
fof(f13342,definition,
( sQ1251_spl
<=> compose(a,compose(codomain(compose(h,a)),domain(b))) = compose(compose(a,codomain(compose(h,a))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1251_spl])],[split_symbol_definition]) ).
fof(f13345,plain,
( sQ1251_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13308,f1941,f13342]) ).
fof(f13346,definition,
( sQ1252_spl
<=> compose(a,compose(codomain(compose(g,a)),domain(b))) = compose(compose(a,codomain(compose(g,a))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1252_spl])],[split_symbol_definition]) ).
fof(f13349,plain,
( sQ1252_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13309,f1941,f13346]) ).
fof(f13350,definition,
( sQ1253_spl
<=> compose(a,compose(codomain(g),domain(b))) = compose(compose(a,codomain(g)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1253_spl])],[split_symbol_definition]) ).
fof(f13353,plain,
( sQ1253_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13310,f715,f13350]) ).
fof(f13354,definition,
( sQ1254_spl
<=> compose(a,compose(codomain(h),domain(b))) = compose(compose(a,codomain(h)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1254_spl])],[split_symbol_definition]) ).
fof(f13357,plain,
( sQ1254_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13311,f715,f13354]) ).
fof(f13358,definition,
( sQ1255_spl
<=> compose(a,compose(codomain(a),domain(b))) = compose(compose(a,codomain(a)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1255_spl])],[split_symbol_definition]) ).
fof(f13361,plain,
( sQ1255_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13312,f1941,f13358]) ).
fof(f13364,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)],[f15,f13314]) ).
fof(f13365,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)],[f15,f13364]) ).
fof(f13381,plain,
( compose(a,compose(domain(compose(g,a)),domain(b))) = compose(compose(a,domain(compose(g,a))),domain(b))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f13365]) ).
fof(f13382,plain,
( compose(a,compose(domain(compose(h,compose(a,b))),domain(b))) = compose(compose(a,domain(compose(h,compose(a,b)))),domain(b))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f13365]) ).
fof(f13383,plain,
( compose(a,compose(domain(compose(h,a)),domain(b))) = compose(compose(a,domain(compose(h,a))),domain(b))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f13365]) ).
fof(f13384,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)],[f60,f13365]) ).
fof(f13392,definition,
( sQ1256_spl
<=> compose(a,compose(domain(compose(g,a)),domain(b))) = compose(compose(a,domain(compose(g,a))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1256_spl])],[split_symbol_definition]) ).
fof(f13395,plain,
( sQ1256_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f13381,f693,f13392]) ).
fof(f13396,definition,
( sQ1257_spl
<=> compose(a,compose(domain(compose(h,compose(a,b))),domain(b))) = compose(compose(a,domain(compose(h,compose(a,b)))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1257_spl])],[split_symbol_definition]) ).
fof(f13399,plain,
( sQ1257_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f13382,f693,f13396]) ).
fof(f13400,definition,
( sQ1258_spl
<=> compose(a,compose(domain(compose(h,a)),domain(b))) = compose(compose(a,domain(compose(h,a))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1258_spl])],[split_symbol_definition]) ).
fof(f13403,plain,
( sQ1258_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f13383,f693,f13400]) ).
fof(f13404,definition,
( sQ1259_spl
<=> compose(a,compose(domain(compose(a,b)),domain(b))) = compose(compose(a,domain(compose(a,b))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1259_spl])],[split_symbol_definition]) ).
fof(f13407,plain,
( sQ1259_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13384,f715,f13404]) ).
fof(f13419,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(a,b)),X0)) = compose(compose(compose(h,a),codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f2969]) ).
fof(f13420,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f2969]) ).
fof(f13421,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(h,a)),X0)) = compose(compose(compose(h,a),codomain(compose(h,a))),X0)
| codomain(compose(h,a)) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f2969]) ).
fof(f13422,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(g,a)),X0)) = compose(compose(compose(h,a),codomain(compose(g,a))),X0)
| codomain(compose(g,a)) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f2969]) ).
fof(f13423,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(g),X0)) = compose(compose(compose(h,a),codomain(g)),X0)
| codomain(g) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f2969]) ).
fof(f13424,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(h),X0)) = compose(compose(compose(h,a),codomain(h)),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f2969]) ).
fof(f13425,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(a),X0)) = compose(compose(compose(h,a),codomain(a)),X0)
| codomain(a) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f2969]) ).
fof(f13443,definition,
! [X0] :
( sQ1260_spl
<=> ( compose(compose(h,a),compose(codomain(compose(a,b)),X0)) = compose(compose(compose(h,a),codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1260_spl])],[split_symbol_definition]) ).
fof(f13446,plain,
( sQ1260_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f13419,f2265,f13443]) ).
fof(f13447,definition,
! [X0] :
( sQ1261_spl
<=> ( compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1261_spl])],[split_symbol_definition]) ).
fof(f13450,plain,
( sQ1261_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f13420,f2265,f13447]) ).
fof(f13451,definition,
! [X0] :
( sQ1262_spl
<=> ( compose(compose(h,a),compose(codomain(compose(h,a)),X0)) = compose(compose(compose(h,a),codomain(compose(h,a))),X0)
| codomain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1262_spl])],[split_symbol_definition]) ).
fof(f13454,plain,
( sQ1262_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13421,f1941,f13451]) ).
fof(f13455,definition,
! [X0] :
( sQ1263_spl
<=> ( compose(compose(h,a),compose(codomain(compose(g,a)),X0)) = compose(compose(compose(h,a),codomain(compose(g,a))),X0)
| codomain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1263_spl])],[split_symbol_definition]) ).
fof(f13458,plain,
( sQ1263_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13422,f1941,f13455]) ).
fof(f13459,definition,
! [X0] :
( sQ1264_spl
<=> ( compose(compose(h,a),compose(codomain(g),X0)) = compose(compose(compose(h,a),codomain(g)),X0)
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1264_spl])],[split_symbol_definition]) ).
fof(f13462,plain,
( sQ1264_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13423,f715,f13459]) ).
fof(f13463,definition,
! [X0] :
( sQ1265_spl
<=> ( compose(compose(h,a),compose(codomain(h),X0)) = compose(compose(compose(h,a),codomain(h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1265_spl])],[split_symbol_definition]) ).
fof(f13466,plain,
( sQ1265_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13424,f715,f13463]) ).
fof(f13467,definition,
! [X0] :
( sQ1266_spl
<=> ( compose(compose(h,a),compose(codomain(a),X0)) = compose(compose(compose(h,a),codomain(a)),X0)
| codomain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1266_spl])],[split_symbol_definition]) ).
fof(f13470,plain,
( sQ1266_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13425,f1941,f13467]) ).
fof(f13489,plain,
( compose(a,compose(domain(b),codomain(compose(h,a)))) = compose(compose(a,domain(b)),codomain(compose(h,a)))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f9656,f131]) ).
fof(f13490,plain,
( compose(a,compose(domain(b),codomain(compose(g,a)))) = compose(compose(a,domain(b)),codomain(compose(g,a)))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f9656,f130]) ).
fof(f13491,plain,
( compose(a,compose(domain(a),codomain(g))) = compose(compose(a,domain(a)),codomain(g))
| domain(b) != domain(a) ),
inference(resolution,[status(thm)],[f9656,f74]) ).
fof(f13492,plain,
( compose(a,compose(domain(a),codomain(h))) = compose(compose(a,domain(a)),codomain(h))
| domain(b) != domain(a) ),
inference(resolution,[status(thm)],[f9656,f69]) ).
fof(f13493,plain,
( compose(a,compose(domain(b),codomain(a))) = compose(compose(a,domain(b)),codomain(a))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f9656,f22]) ).
fof(f13495,plain,
! [X0] :
( compose(a,compose(domain(compose(g,a)),codomain(X0))) = compose(compose(a,domain(compose(g,a))),codomain(X0))
| domain(h) != codomain(X0)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f1108,f9656]) ).
fof(f13496,plain,
! [X0] :
( compose(a,compose(domain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(a,domain(compose(h,compose(a,b)))),codomain(X0))
| domain(h) != codomain(X0)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f1068,f9656]) ).
fof(f13497,plain,
! [X0] :
( compose(a,compose(domain(compose(h,a)),codomain(X0))) = compose(compose(a,domain(compose(h,a))),codomain(X0))
| domain(h) != codomain(X0)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f76,f9656]) ).
fof(f13498,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)],[f60,f9656]) ).
fof(f13513,definition,
( sQ1267_spl
<=> compose(a,compose(domain(b),codomain(compose(h,a)))) = compose(compose(a,domain(b)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1267_spl])],[split_symbol_definition]) ).
fof(f13516,plain,
( sQ1267_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13489,f1941,f13513]) ).
fof(f13517,definition,
( sQ1268_spl
<=> compose(a,compose(domain(b),codomain(compose(g,a)))) = compose(compose(a,domain(b)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1268_spl])],[split_symbol_definition]) ).
fof(f13520,plain,
( sQ1268_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13490,f1941,f13517]) ).
fof(f13521,definition,
( sQ1269_spl
<=> compose(a,compose(domain(a),codomain(g))) = compose(compose(a,domain(a)),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ1269_spl])],[split_symbol_definition]) ).
fof(f13524,plain,
( sQ1269_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13491,f715,f13521]) ).
fof(f13525,definition,
( sQ1270_spl
<=> compose(a,compose(domain(a),codomain(h))) = compose(compose(a,domain(a)),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ1270_spl])],[split_symbol_definition]) ).
fof(f13528,plain,
( sQ1270_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13492,f715,f13525]) ).
fof(f13529,definition,
( sQ1271_spl
<=> compose(a,compose(domain(b),codomain(a))) = compose(compose(a,domain(b)),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1271_spl])],[split_symbol_definition]) ).
fof(f13532,plain,
( sQ1271_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13493,f1941,f13529]) ).
fof(f13535,definition,
! [X0] :
( sQ1272_spl
<=> ( compose(a,compose(domain(compose(g,a)),codomain(X0))) = compose(compose(a,domain(compose(g,a))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1272_spl])],[split_symbol_definition]) ).
fof(f13538,plain,
( sQ1272_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f13495,f2337,f13535]) ).
fof(f13539,definition,
! [X0] :
( sQ1273_spl
<=> ( compose(a,compose(domain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(a,domain(compose(h,compose(a,b)))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1273_spl])],[split_symbol_definition]) ).
fof(f13542,plain,
( sQ1273_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f13496,f2366,f13539]) ).
fof(f13543,definition,
! [X0] :
( sQ1274_spl
<=> ( compose(a,compose(domain(compose(h,a)),codomain(X0))) = compose(compose(a,domain(compose(h,a))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1274_spl])],[split_symbol_definition]) ).
fof(f13546,plain,
( sQ1274_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f13497,f2330,f13543]) ).
fof(f13547,definition,
! [X0] :
( sQ1275_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,[sQ1275_spl])],[split_symbol_definition]) ).
fof(f13550,plain,
( sQ1275_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f13498,f2359,f13547]) ).
fof(f13595,plain,
( compose(g,compose(codomain(compose(a,b)),compose(a,b))) = compose(compose(g,codomain(compose(a,b))),compose(a,b))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f9723]) ).
fof(f13596,plain,
( compose(g,compose(codomain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(g,codomain(compose(h,compose(a,b)))),compose(a,b))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f9723]) ).
fof(f13597,plain,
( compose(g,compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(g,codomain(compose(h,a))),compose(a,b))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f9723]) ).
fof(f13598,plain,
( compose(g,compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(g,codomain(compose(g,a))),compose(a,b))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f9723]) ).
fof(f13599,plain,
( compose(g,compose(codomain(g),compose(a,b))) = compose(compose(g,codomain(g)),compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f9723]) ).
fof(f13600,plain,
( compose(g,compose(codomain(h),compose(a,b))) = compose(compose(g,codomain(h)),compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f9723]) ).
fof(f13601,plain,
( compose(g,compose(codomain(a),compose(a,b))) = compose(compose(g,codomain(a)),compose(a,b))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f9723]) ).
fof(f13618,definition,
( sQ1276_spl
<=> compose(g,compose(codomain(compose(a,b)),compose(a,b))) = compose(compose(g,codomain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1276_spl])],[split_symbol_definition]) ).
fof(f13621,plain,
( sQ1276_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f13595,f1570,f13618]) ).
fof(f13622,definition,
( sQ1277_spl
<=> compose(g,compose(codomain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(g,codomain(compose(h,compose(a,b)))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1277_spl])],[split_symbol_definition]) ).
fof(f13625,plain,
( sQ1277_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f13596,f1570,f13622]) ).
fof(f13626,definition,
( sQ1278_spl
<=> compose(g,compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(g,codomain(compose(h,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1278_spl])],[split_symbol_definition]) ).
fof(f13629,plain,
( sQ1278_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13597,f715,f13626]) ).
fof(f13630,definition,
( sQ1279_spl
<=> compose(g,compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(g,codomain(compose(g,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1279_spl])],[split_symbol_definition]) ).
fof(f13633,plain,
( sQ1279_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13598,f715,f13630]) ).
fof(f13634,definition,
( sQ1280_spl
<=> compose(g,compose(codomain(g),compose(a,b))) = compose(compose(g,codomain(g)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1280_spl])],[split_symbol_definition]) ).
fof(f13637,plain,
( sQ1280_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13599,f606,f13634]) ).
fof(f13638,definition,
( sQ1281_spl
<=> compose(g,compose(codomain(h),compose(a,b))) = compose(compose(g,codomain(h)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1281_spl])],[split_symbol_definition]) ).
fof(f13641,plain,
( sQ1281_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13600,f606,f13638]) ).
fof(f13642,definition,
( sQ1282_spl
<=> compose(g,compose(codomain(a),compose(a,b))) = compose(compose(g,codomain(a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1282_spl])],[split_symbol_definition]) ).
fof(f13645,plain,
( sQ1282_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13601,f715,f13642]) ).
fof(f13661,plain,
( compose(g,compose(domain(compose(g,a)),compose(a,b))) = compose(compose(g,domain(compose(g,a))),compose(a,b))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f9725]) ).
fof(f13662,plain,
( compose(g,compose(domain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(g,domain(compose(h,compose(a,b)))),compose(a,b))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f9725]) ).
fof(f13663,plain,
( compose(g,compose(domain(compose(h,a)),compose(a,b))) = compose(compose(g,domain(compose(h,a))),compose(a,b))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f9725]) ).
fof(f13664,plain,
( compose(g,compose(domain(compose(a,b)),compose(a,b))) = compose(compose(g,domain(compose(a,b))),compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f9725]) ).
fof(f13677,definition,
( sQ1283_spl
<=> compose(g,compose(domain(compose(g,a)),compose(a,b))) = compose(compose(g,domain(compose(g,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1283_spl])],[split_symbol_definition]) ).
fof(f13680,plain,
( sQ1283_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f13661,f584,f13677]) ).
fof(f13681,definition,
( sQ1284_spl
<=> compose(g,compose(domain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(g,domain(compose(h,compose(a,b)))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1284_spl])],[split_symbol_definition]) ).
fof(f13684,plain,
( sQ1284_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f13662,f584,f13681]) ).
fof(f13685,definition,
( sQ1285_spl
<=> compose(g,compose(domain(compose(h,a)),compose(a,b))) = compose(compose(g,domain(compose(h,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1285_spl])],[split_symbol_definition]) ).
fof(f13688,plain,
( sQ1285_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f13663,f584,f13685]) ).
fof(f13689,definition,
( sQ1286_spl
<=> compose(g,compose(domain(compose(a,b)),compose(a,b))) = compose(compose(g,domain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1286_spl])],[split_symbol_definition]) ).
fof(f13692,plain,
( sQ1286_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13664,f606,f13689]) ).
fof(f13707,plain,
( compose(h,compose(codomain(compose(a,b)),compose(a,b))) = compose(compose(h,codomain(compose(a,b))),compose(a,b))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f10870]) ).
fof(f13708,plain,
( compose(h,compose(codomain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(h,codomain(compose(h,compose(a,b)))),compose(a,b))
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f10870]) ).
fof(f13709,plain,
( compose(h,compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(h,codomain(compose(h,a))),compose(a,b))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f10870]) ).
fof(f13710,plain,
( compose(h,compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(h,codomain(compose(g,a))),compose(a,b))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f10870]) ).
fof(f13711,plain,
( compose(h,compose(codomain(g),compose(a,b))) = compose(compose(h,codomain(g)),compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f10870]) ).
fof(f13712,plain,
( compose(h,compose(codomain(h),compose(a,b))) = compose(compose(h,codomain(h)),compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f10870]) ).
fof(f13713,plain,
( compose(h,compose(codomain(a),compose(a,b))) = compose(compose(h,codomain(a)),compose(a,b))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f10870]) ).
fof(f13724,definition,
( sQ1287_spl
<=> compose(h,compose(codomain(compose(a,b)),compose(a,b))) = compose(compose(h,codomain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1287_spl])],[split_symbol_definition]) ).
fof(f13727,plain,
( sQ1287_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f13707,f1570,f13724]) ).
fof(f13728,definition,
( sQ1288_spl
<=> compose(h,compose(codomain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(h,codomain(compose(h,compose(a,b)))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1288_spl])],[split_symbol_definition]) ).
fof(f13731,plain,
( sQ1288_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f13708,f1570,f13728]) ).
fof(f13732,definition,
( sQ1289_spl
<=> compose(h,compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(h,codomain(compose(h,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1289_spl])],[split_symbol_definition]) ).
fof(f13735,plain,
( sQ1289_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13709,f715,f13732]) ).
fof(f13736,definition,
( sQ1290_spl
<=> compose(h,compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(h,codomain(compose(g,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1290_spl])],[split_symbol_definition]) ).
fof(f13739,plain,
( sQ1290_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13710,f715,f13736]) ).
fof(f13740,definition,
( sQ1291_spl
<=> compose(h,compose(codomain(g),compose(a,b))) = compose(compose(h,codomain(g)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1291_spl])],[split_symbol_definition]) ).
fof(f13743,plain,
( sQ1291_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13711,f606,f13740]) ).
fof(f13744,definition,
( sQ1292_spl
<=> compose(h,compose(codomain(h),compose(a,b))) = compose(compose(h,codomain(h)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1292_spl])],[split_symbol_definition]) ).
fof(f13747,plain,
( sQ1292_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13712,f606,f13744]) ).
fof(f13748,definition,
( sQ1293_spl
<=> compose(h,compose(codomain(a),compose(a,b))) = compose(compose(h,codomain(a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1293_spl])],[split_symbol_definition]) ).
fof(f13751,plain,
( sQ1293_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13713,f715,f13748]) ).
fof(f13763,plain,
( compose(h,compose(domain(compose(g,a)),compose(a,b))) = compose(compose(h,domain(compose(g,a))),compose(a,b))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f10872]) ).
fof(f13764,plain,
( compose(h,compose(domain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(h,domain(compose(h,compose(a,b)))),compose(a,b))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f10872]) ).
fof(f13765,plain,
( compose(h,compose(domain(compose(h,a)),compose(a,b))) = compose(compose(h,domain(compose(h,a))),compose(a,b))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f10872]) ).
fof(f13766,plain,
( compose(h,compose(domain(compose(a,b)),compose(a,b))) = compose(compose(h,domain(compose(a,b))),compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f10872]) ).
fof(f13775,definition,
( sQ1294_spl
<=> compose(h,compose(domain(compose(g,a)),compose(a,b))) = compose(compose(h,domain(compose(g,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1294_spl])],[split_symbol_definition]) ).
fof(f13778,plain,
( sQ1294_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f13763,f584,f13775]) ).
fof(f13779,definition,
( sQ1295_spl
<=> compose(h,compose(domain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(h,domain(compose(h,compose(a,b)))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1295_spl])],[split_symbol_definition]) ).
fof(f13782,plain,
( sQ1295_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f13764,f584,f13779]) ).
fof(f13783,definition,
( sQ1296_spl
<=> compose(h,compose(domain(compose(h,a)),compose(a,b))) = compose(compose(h,domain(compose(h,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1296_spl])],[split_symbol_definition]) ).
fof(f13786,plain,
( sQ1296_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f13765,f584,f13783]) ).
fof(f13787,definition,
( sQ1297_spl
<=> compose(h,compose(domain(compose(a,b)),compose(a,b))) = compose(compose(h,domain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1297_spl])],[split_symbol_definition]) ).
fof(f13790,plain,
( sQ1297_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13766,f606,f13787]) ).
fof(f13802,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(a,b)),X0)) = compose(compose(compose(g,a),codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f2970]) ).
fof(f13803,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f2970]) ).
fof(f13804,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(h,a)),X0)) = compose(compose(compose(g,a),codomain(compose(h,a))),X0)
| codomain(compose(h,a)) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f2970]) ).
fof(f13805,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(g,a)),X0)) = compose(compose(compose(g,a),codomain(compose(g,a))),X0)
| codomain(compose(g,a)) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f2970]) ).
fof(f13806,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(g),X0)) = compose(compose(compose(g,a),codomain(g)),X0)
| codomain(g) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f2970]) ).
fof(f13807,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(h),X0)) = compose(compose(compose(g,a),codomain(h)),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f2970]) ).
fof(f13808,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(a),X0)) = compose(compose(compose(g,a),codomain(a)),X0)
| codomain(a) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f2970]) ).
fof(f13826,definition,
! [X0] :
( sQ1298_spl
<=> ( compose(compose(g,a),compose(codomain(compose(a,b)),X0)) = compose(compose(compose(g,a),codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1298_spl])],[split_symbol_definition]) ).
fof(f13829,plain,
( sQ1298_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f13802,f2265,f13826]) ).
fof(f13830,definition,
! [X0] :
( sQ1299_spl
<=> ( compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1299_spl])],[split_symbol_definition]) ).
fof(f13833,plain,
( sQ1299_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f13803,f2265,f13830]) ).
fof(f13834,definition,
! [X0] :
( sQ1300_spl
<=> ( compose(compose(g,a),compose(codomain(compose(h,a)),X0)) = compose(compose(compose(g,a),codomain(compose(h,a))),X0)
| codomain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1300_spl])],[split_symbol_definition]) ).
fof(f13837,plain,
( sQ1300_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13804,f1941,f13834]) ).
fof(f13838,definition,
! [X0] :
( sQ1301_spl
<=> ( compose(compose(g,a),compose(codomain(compose(g,a)),X0)) = compose(compose(compose(g,a),codomain(compose(g,a))),X0)
| codomain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1301_spl])],[split_symbol_definition]) ).
fof(f13841,plain,
( sQ1301_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13805,f1941,f13838]) ).
fof(f13842,definition,
! [X0] :
( sQ1302_spl
<=> ( compose(compose(g,a),compose(codomain(g),X0)) = compose(compose(compose(g,a),codomain(g)),X0)
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1302_spl])],[split_symbol_definition]) ).
fof(f13845,plain,
( sQ1302_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13806,f715,f13842]) ).
fof(f13846,definition,
! [X0] :
( sQ1303_spl
<=> ( compose(compose(g,a),compose(codomain(h),X0)) = compose(compose(compose(g,a),codomain(h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1303_spl])],[split_symbol_definition]) ).
fof(f13849,plain,
( sQ1303_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13807,f715,f13846]) ).
fof(f13850,definition,
! [X0] :
( sQ1304_spl
<=> ( compose(compose(g,a),compose(codomain(a),X0)) = compose(compose(compose(g,a),codomain(a)),X0)
| codomain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1304_spl])],[split_symbol_definition]) ).
fof(f13853,plain,
( sQ1304_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13808,f1941,f13850]) ).
fof(f13872,plain,
( compose(domain(compose(a,b)),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1480]) ).
fof(f13873,plain,
( compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1480]) ).
fof(f13874,plain,
( compose(domain(compose(h,a)),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1480]) ).
fof(f13875,plain,
( compose(domain(compose(g,a)),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1480]) ).
fof(f13876,plain,
( compose(domain(g),compose(g,compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1480]) ).
fof(f13882,definition,
( sQ1305_spl
<=> compose(domain(compose(a,b)),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1305_spl])],[split_symbol_definition]) ).
fof(f13885,plain,
( sQ1305_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f13872,f1555,f13882]) ).
fof(f13886,definition,
( sQ1306_spl
<=> compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1306_spl])],[split_symbol_definition]) ).
fof(f13889,plain,
( sQ1306_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f13873,f1555,f13886]) ).
fof(f13890,definition,
( sQ1307_spl
<=> compose(domain(compose(h,a)),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1307_spl])],[split_symbol_definition]) ).
fof(f13893,plain,
( sQ1307_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f13874,f693,f13890]) ).
fof(f13894,definition,
( sQ1308_spl
<=> compose(domain(compose(g,a)),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1308_spl])],[split_symbol_definition]) ).
fof(f13897,plain,
( sQ1308_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f13875,f693,f13894]) ).
fof(f13898,definition,
( sQ1309_spl
<=> compose(domain(g),compose(g,compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1309_spl])],[split_symbol_definition]) ).
fof(f13901,plain,
( sQ1309_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f13876,f584,f13898]) ).
fof(f13907,plain,
( compose(compose(a,b),compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1519]) ).
fof(f13908,plain,
( compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1519]) ).
fof(f13909,plain,
( compose(compose(h,a),compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1519]) ).
fof(f13910,plain,
( compose(compose(g,a),compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1519]) ).
fof(f13911,plain,
( compose(g,compose(codomain(g),compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1519]) ).
fof(f13912,plain,
( compose(h,compose(codomain(h),compose(h,compose(a,b)))) = compose(h,compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1519]) ).
fof(f13913,plain,
( compose(a,compose(codomain(a),compose(h,compose(a,b)))) = compose(a,compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f1519]) ).
fof(f13917,definition,
( sQ1310_spl
<=> compose(compose(a,b),compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1310_spl])],[split_symbol_definition]) ).
fof(f13920,plain,
( sQ1310_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f13907,f1555,f13917]) ).
fof(f13921,definition,
( sQ1311_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1311_spl])],[split_symbol_definition]) ).
fof(f13924,plain,
( sQ1311_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f13908,f1555,f13921]) ).
fof(f13925,definition,
( sQ1312_spl
<=> compose(compose(h,a),compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1312_spl])],[split_symbol_definition]) ).
fof(f13928,plain,
( sQ1312_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f13909,f693,f13925]) ).
fof(f13929,definition,
( sQ1313_spl
<=> compose(compose(g,a),compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1313_spl])],[split_symbol_definition]) ).
fof(f13932,plain,
( sQ1313_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f13910,f693,f13929]) ).
fof(f13933,definition,
( sQ1314_spl
<=> compose(g,compose(codomain(g),compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1314_spl])],[split_symbol_definition]) ).
fof(f13936,plain,
( sQ1314_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f13911,f584,f13933]) ).
fof(f13937,definition,
( sQ1315_spl
<=> compose(h,compose(codomain(h),compose(h,compose(a,b)))) = compose(h,compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1315_spl])],[split_symbol_definition]) ).
fof(f13940,plain,
( sQ1315_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f13912,f584,f13937]) ).
fof(f13941,definition,
( sQ1316_spl
<=> compose(a,compose(codomain(a),compose(h,compose(a,b)))) = compose(a,compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1316_spl])],[split_symbol_definition]) ).
fof(f13944,plain,
( sQ1316_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f13913,f693,f13941]) ).
fof(f13948,plain,
( compose(domain(h),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1496]) ).
fof(f13949,plain,
( compose(domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1496]) ).
fof(f13950,plain,
( compose(domain(h),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1496]) ).
fof(f13951,plain,
( compose(domain(h),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1496]) ).
fof(f13956,definition,
( sQ1317_spl
<=> compose(domain(h),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1317_spl])],[split_symbol_definition]) ).
fof(f13959,plain,
( sQ1317_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f13948,f1555,f13956]) ).
fof(f13960,definition,
( sQ1318_spl
<=> compose(domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1318_spl])],[split_symbol_definition]) ).
fof(f13963,plain,
( sQ1318_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f13949,f1555,f13960]) ).
fof(f13964,definition,
( sQ1319_spl
<=> compose(domain(h),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1319_spl])],[split_symbol_definition]) ).
fof(f13967,plain,
( sQ1319_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f13950,f1555,f13964]) ).
fof(f13968,definition,
( sQ1320_spl
<=> compose(domain(h),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1320_spl])],[split_symbol_definition]) ).
fof(f13971,plain,
( sQ1320_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f13951,f1570,f13968]) ).
fof(f13973,plain,
( compose(compose(h,compose(a,b)),compose(codomain(b),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f1531]) ).
fof(f13974,plain,
( compose(compose(h,compose(a,b)),compose(codomain(b),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f1531]) ).
fof(f13975,plain,
( compose(compose(h,compose(a,b)),compose(codomain(b),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f1531]) ).
fof(f13976,plain,
( compose(compose(h,compose(a,b)),compose(codomain(b),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f1531]) ).
fof(f13979,definition,
( sQ1321_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(b),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1321_spl])],[split_symbol_definition]) ).
fof(f13982,plain,
( sQ1321_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f13973,f1555,f13979]) ).
fof(f13983,definition,
( sQ1322_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(b),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1322_spl])],[split_symbol_definition]) ).
fof(f13986,plain,
( sQ1322_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f13974,f1555,f13983]) ).
fof(f13987,definition,
( sQ1323_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(b),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1323_spl])],[split_symbol_definition]) ).
fof(f13990,plain,
( sQ1323_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f13975,f1555,f13987]) ).
fof(f13991,definition,
( sQ1324_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(b),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1324_spl])],[split_symbol_definition]) ).
fof(f13994,plain,
( sQ1324_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f13976,f1570,f13991]) ).
fof(f13996,plain,
! [X0] :
( compose(compose(g,a),compose(domain(compose(g,a)),X0)) = compose(compose(compose(g,a),domain(compose(g,a))),X0)
| domain(compose(g,a)) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f3696]) ).
fof(f13997,plain,
! [X0] :
( compose(compose(g,a),compose(domain(compose(h,compose(a,b))),X0)) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),X0)
| domain(compose(h,compose(a,b))) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f3696]) ).
fof(f13998,plain,
! [X0] :
( compose(compose(g,a),compose(domain(compose(h,a)),X0)) = compose(compose(compose(g,a),domain(compose(h,a))),X0)
| domain(compose(h,a)) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f3696]) ).
fof(f13999,plain,
! [X0] :
( compose(compose(g,a),compose(domain(compose(a,b)),X0)) = compose(compose(compose(g,a),domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f3696]) ).
fof(f14007,definition,
! [X0] :
( sQ1325_spl
<=> ( compose(compose(g,a),compose(domain(compose(g,a)),X0)) = compose(compose(compose(g,a),domain(compose(g,a))),X0)
| domain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1325_spl])],[split_symbol_definition]) ).
fof(f14010,plain,
( sQ1325_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f13996,f693,f14007]) ).
fof(f14011,definition,
! [X0] :
( sQ1326_spl
<=> ( compose(compose(g,a),compose(domain(compose(h,compose(a,b))),X0)) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),X0)
| domain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1326_spl])],[split_symbol_definition]) ).
fof(f14014,plain,
( sQ1326_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f13997,f693,f14011]) ).
fof(f14015,definition,
! [X0] :
( sQ1327_spl
<=> ( compose(compose(g,a),compose(domain(compose(h,a)),X0)) = compose(compose(compose(g,a),domain(compose(h,a))),X0)
| domain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1327_spl])],[split_symbol_definition]) ).
fof(f14018,plain,
( sQ1327_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f13998,f693,f14015]) ).
fof(f14019,definition,
! [X0] :
( sQ1328_spl
<=> ( compose(compose(g,a),compose(domain(compose(a,b)),X0)) = compose(compose(compose(g,a),domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1328_spl])],[split_symbol_definition]) ).
fof(f14022,plain,
( sQ1328_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f13999,f715,f14019]) ).
fof(f14031,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(compose(g,a),X0)) = compose(compose(compose(h,compose(a,b)),compose(g,a)),X0)
| codomain(compose(g,a)) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f626]) ).
fof(f14032,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f626]) ).
fof(f14033,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(compose(h,a),X0)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),X0)
| codomain(compose(h,a)) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f626]) ).
fof(f14034,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(compose(a,b),X0)) = compose(compose(compose(h,compose(a,b)),compose(a,b)),X0)
| codomain(compose(a,b)) != domain(X0)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f626]) ).
fof(f14039,definition,
! [X0] :
( sQ1329_spl
<=> ( compose(compose(h,compose(a,b)),compose(compose(g,a),X0)) = compose(compose(compose(h,compose(a,b)),compose(g,a)),X0)
| codomain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1329_spl])],[split_symbol_definition]) ).
fof(f14042,plain,
( sQ1329_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14031,f1555,f14039]) ).
fof(f14043,definition,
! [X0] :
( sQ1330_spl
<=> ( compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1330_spl])],[split_symbol_definition]) ).
fof(f14046,plain,
( sQ1330_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14032,f1555,f14043]) ).
fof(f14047,definition,
! [X0] :
( sQ1331_spl
<=> ( compose(compose(h,compose(a,b)),compose(compose(h,a),X0)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),X0)
| codomain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1331_spl])],[split_symbol_definition]) ).
fof(f14050,plain,
( sQ1331_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14033,f1555,f14047]) ).
fof(f14051,definition,
! [X0] :
( sQ1332_spl
<=> ( compose(compose(h,compose(a,b)),compose(compose(a,b),X0)) = compose(compose(compose(h,compose(a,b)),compose(a,b)),X0)
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1332_spl])],[split_symbol_definition]) ).
fof(f14054,plain,
( sQ1332_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f14034,f1570,f14051]) ).
fof(f14057,plain,
( compose(compose(g,a),compose(compose(h,a),domain(b))) = compose(compose(compose(g,a),compose(h,a)),domain(b))
| domain(b) != domain(compose(h,a)) ),
inference(resolution,[status(thm)],[f3642,f131]) ).
fof(f14058,plain,
( compose(compose(g,a),compose(compose(g,a),domain(b))) = compose(compose(compose(g,a),compose(g,a)),domain(b))
| domain(b) != domain(compose(g,a)) ),
inference(resolution,[status(thm)],[f3642,f130]) ).
fof(f14059,plain,
( compose(compose(g,a),compose(g,domain(a))) = compose(compose(compose(g,a),g),domain(a))
| domain(b) != domain(g) ),
inference(resolution,[status(thm)],[f3642,f74]) ).
fof(f14060,plain,
( compose(compose(g,a),compose(h,domain(a))) = compose(compose(compose(g,a),h),domain(a))
| domain(b) != domain(h) ),
inference(resolution,[status(thm)],[f3642,f69]) ).
fof(f14061,plain,
( compose(compose(g,a),compose(a,domain(b))) = compose(compose(compose(g,a),a),domain(b))
| domain(b) != domain(a) ),
inference(resolution,[status(thm)],[f3642,f22]) ).
fof(f14064,plain,
! [X0] :
( compose(compose(g,a),compose(compose(a,b),domain(X0))) = compose(compose(compose(g,a),compose(a,b)),domain(X0))
| codomain(b) != domain(X0)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f3642]) ).
fof(f14065,plain,
! [X0] :
( compose(compose(g,a),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(compose(g,a),compose(h,compose(a,b))),domain(X0))
| codomain(b) != domain(X0)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f3642]) ).
fof(f14066,plain,
! [X0] :
( compose(compose(g,a),compose(compose(h,a),domain(X0))) = compose(compose(compose(g,a),compose(h,a)),domain(X0))
| domain(b) != domain(X0)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f3642]) ).
fof(f14067,plain,
! [X0] :
( compose(compose(g,a),compose(compose(g,a),domain(X0))) = compose(compose(compose(g,a),compose(g,a)),domain(X0))
| domain(b) != domain(X0)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f3642]) ).
fof(f14068,plain,
! [X0] :
( compose(compose(g,a),compose(g,domain(X0))) = compose(compose(compose(g,a),g),domain(X0))
| domain(a) != domain(X0)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f3642]) ).
fof(f14069,plain,
! [X0] :
( compose(compose(g,a),compose(h,domain(X0))) = compose(compose(compose(g,a),h),domain(X0))
| domain(a) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f3642]) ).
fof(f14070,plain,
! [X0] :
( compose(compose(g,a),compose(a,domain(X0))) = compose(compose(compose(g,a),a),domain(X0))
| domain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f3642]) ).
fof(f14071,plain,
! [X0,X1] :
( compose(compose(g,a),compose(codomain(X0),domain(X1))) = compose(compose(compose(g,a),codomain(X0)),domain(X1))
| codomain(X0) != domain(X1)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f3642]) ).
fof(f14072,plain,
! [X0,X1] :
( compose(compose(g,a),compose(domain(X0),domain(X1))) = compose(compose(compose(g,a),domain(X0)),domain(X1))
| domain(X0) != domain(X1)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f3642]) ).
fof(f14079,definition,
( sQ1333_spl
<=> compose(compose(g,a),compose(compose(h,a),domain(b))) = compose(compose(compose(g,a),compose(h,a)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1333_spl])],[split_symbol_definition]) ).
fof(f14082,plain,
( sQ1333_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f14057,f2330,f14079]) ).
fof(f14083,definition,
( sQ1334_spl
<=> compose(compose(g,a),compose(compose(g,a),domain(b))) = compose(compose(compose(g,a),compose(g,a)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1334_spl])],[split_symbol_definition]) ).
fof(f14086,plain,
( sQ1334_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f14058,f2337,f14083]) ).
fof(f14087,definition,
( sQ1335_spl
<=> compose(compose(g,a),compose(g,domain(a))) = compose(compose(compose(g,a),g),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1335_spl])],[split_symbol_definition]) ).
fof(f14090,plain,
( sQ1335_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f14059,f700,f14087]) ).
fof(f14091,definition,
( sQ1336_spl
<=> compose(compose(g,a),compose(h,domain(a))) = compose(compose(compose(g,a),h),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1336_spl])],[split_symbol_definition]) ).
fof(f14094,plain,
( sQ1336_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14060,f693,f14091]) ).
fof(f14095,definition,
( sQ1337_spl
<=> compose(compose(g,a),compose(a,domain(b))) = compose(compose(compose(g,a),a),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1337_spl])],[split_symbol_definition]) ).
fof(f14098,plain,
( sQ1337_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f14061,f715,f14095]) ).
fof(f14104,definition,
! [X0] :
( sQ1338_spl
<=> ( compose(compose(g,a),compose(compose(a,b),domain(X0))) = compose(compose(compose(g,a),compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1338_spl])],[split_symbol_definition]) ).
fof(f14107,plain,
( sQ1338_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f14064,f2359,f14104]) ).
fof(f14108,definition,
! [X0] :
( sQ1339_spl
<=> ( compose(compose(g,a),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(compose(g,a),compose(h,compose(a,b))),domain(X0))
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1339_spl])],[split_symbol_definition]) ).
fof(f14111,plain,
( sQ1339_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f14065,f2366,f14108]) ).
fof(f14112,definition,
! [X0] :
( sQ1340_spl
<=> ( compose(compose(g,a),compose(compose(h,a),domain(X0))) = compose(compose(compose(g,a),compose(h,a)),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1340_spl])],[split_symbol_definition]) ).
fof(f14115,plain,
( sQ1340_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f14066,f2330,f14112]) ).
fof(f14116,definition,
! [X0] :
( sQ1341_spl
<=> ( compose(compose(g,a),compose(compose(g,a),domain(X0))) = compose(compose(compose(g,a),compose(g,a)),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1341_spl])],[split_symbol_definition]) ).
fof(f14119,plain,
( sQ1341_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f14067,f2337,f14116]) ).
fof(f14120,definition,
! [X0] :
( sQ1342_spl
<=> ( compose(compose(g,a),compose(g,domain(X0))) = compose(compose(compose(g,a),g),domain(X0))
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1342_spl])],[split_symbol_definition]) ).
fof(f14123,plain,
( sQ1342_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f14068,f700,f14120]) ).
fof(f14124,definition,
! [X0] :
( sQ1343_spl
<=> ( compose(compose(g,a),compose(h,domain(X0))) = compose(compose(compose(g,a),h),domain(X0))
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1343_spl])],[split_symbol_definition]) ).
fof(f14127,plain,
( sQ1343_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14069,f693,f14124]) ).
fof(f14128,definition,
! [X0] :
( sQ1344_spl
<=> ( compose(compose(g,a),compose(a,domain(X0))) = compose(compose(compose(g,a),a),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1344_spl])],[split_symbol_definition]) ).
fof(f14131,plain,
( sQ1344_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f14070,f715,f14128]) ).
fof(f14132,plain,
! [X0,X1] :
( compose(compose(g,a),compose(codomain(X0),domain(X1))) = compose(compose(compose(g,a),codomain(X0)),domain(X1))
| codomain(X0) != domain(X1)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f14071]) ).
fof(f14133,plain,
! [X0,X1] :
( compose(compose(g,a),compose(domain(X0),domain(X1))) = compose(compose(compose(g,a),domain(X0)),domain(X1))
| domain(X0) != domain(X1)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f14072]) ).
fof(f14146,plain,
( compose(compose(g,a),compose(compose(a,b),codomain(b))) = compose(compose(compose(g,a),compose(a,b)),codomain(b))
| domain(b) != domain(compose(a,b)) ),
inference(resolution,[status(thm)],[f3643,f120]) ).
fof(f14147,plain,
( compose(compose(g,a),compose(compose(h,compose(a,b)),codomain(b))) = compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(b))
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(resolution,[status(thm)],[f3643,f581]) ).
fof(f14149,plain,
( compose(compose(g,a),compose(b,codomain(compose(a,b)))) = compose(compose(compose(g,a),b),codomain(compose(a,b)))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f3643,f120]) ).
fof(f14150,plain,
( compose(compose(g,a),compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(compose(g,a),b),codomain(compose(h,compose(a,b))))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f3643,f581]) ).
fof(f14152,plain,
! [X0] :
( compose(compose(g,a),compose(compose(a,b),codomain(X0))) = compose(compose(compose(g,a),compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f3643]) ).
fof(f14153,plain,
! [X0] :
( compose(compose(g,a),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f3643]) ).
fof(f14154,plain,
! [X0] :
( compose(compose(g,a),compose(compose(h,a),codomain(X0))) = compose(compose(compose(g,a),compose(h,a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f3643]) ).
fof(f14155,plain,
! [X0] :
( compose(compose(g,a),compose(compose(g,a),codomain(X0))) = compose(compose(compose(g,a),compose(g,a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f3643]) ).
fof(f14156,plain,
! [X0] :
( compose(compose(g,a),compose(g,codomain(X0))) = compose(compose(compose(g,a),g),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f3643]) ).
fof(f14157,plain,
! [X0] :
( compose(compose(g,a),compose(h,codomain(X0))) = compose(compose(compose(g,a),h),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f3643]) ).
fof(f14158,plain,
! [X0] :
( compose(compose(g,a),compose(a,codomain(X0))) = compose(compose(compose(g,a),a),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f3643]) ).
fof(f14159,plain,
! [X0,X1] :
( compose(compose(g,a),compose(codomain(X0),codomain(X1))) = compose(compose(compose(g,a),codomain(X0)),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f3643]) ).
fof(f14160,plain,
! [X0,X1] :
( compose(compose(g,a),compose(domain(X0),codomain(X1))) = compose(compose(compose(g,a),domain(X0)),codomain(X1))
| domain(X0) != codomain(X1)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f3643]) ).
fof(f14171,definition,
( sQ1345_spl
<=> compose(compose(g,a),compose(compose(a,b),codomain(b))) = compose(compose(compose(g,a),compose(a,b)),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1345_spl])],[split_symbol_definition]) ).
fof(f14174,plain,
( sQ1345_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f14146,f2359,f14171]) ).
fof(f14175,definition,
( sQ1346_spl
<=> compose(compose(g,a),compose(compose(h,compose(a,b)),codomain(b))) = compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1346_spl])],[split_symbol_definition]) ).
fof(f14178,plain,
( sQ1346_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f14147,f2366,f14175]) ).
fof(f14181,definition,
( sQ1347_spl
<=> compose(compose(g,a),compose(b,codomain(compose(a,b)))) = compose(compose(compose(g,a),b),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1347_spl])],[split_symbol_definition]) ).
fof(f14184,plain,
( sQ1347_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f14149,f1941,f14181]) ).
fof(f14185,definition,
( sQ1348_spl
<=> compose(compose(g,a),compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(compose(g,a),b),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1348_spl])],[split_symbol_definition]) ).
fof(f14188,plain,
( sQ1348_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f14150,f1941,f14185]) ).
fof(f14192,definition,
! [X0] :
( sQ1349_spl
<=> ( compose(compose(g,a),compose(compose(a,b),codomain(X0))) = compose(compose(compose(g,a),compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1349_spl])],[split_symbol_definition]) ).
fof(f14195,plain,
( sQ1349_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f14152,f2359,f14192]) ).
fof(f14196,definition,
! [X0] :
( sQ1350_spl
<=> ( compose(compose(g,a),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1350_spl])],[split_symbol_definition]) ).
fof(f14199,plain,
( sQ1350_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f14153,f2366,f14196]) ).
fof(f14200,definition,
! [X0] :
( sQ1351_spl
<=> ( compose(compose(g,a),compose(compose(h,a),codomain(X0))) = compose(compose(compose(g,a),compose(h,a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1351_spl])],[split_symbol_definition]) ).
fof(f14203,plain,
( sQ1351_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f14154,f2330,f14200]) ).
fof(f14204,definition,
! [X0] :
( sQ1352_spl
<=> ( compose(compose(g,a),compose(compose(g,a),codomain(X0))) = compose(compose(compose(g,a),compose(g,a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1352_spl])],[split_symbol_definition]) ).
fof(f14207,plain,
( sQ1352_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f14155,f2337,f14204]) ).
fof(f14208,definition,
! [X0] :
( sQ1353_spl
<=> ( compose(compose(g,a),compose(g,codomain(X0))) = compose(compose(compose(g,a),g),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1353_spl])],[split_symbol_definition]) ).
fof(f14211,plain,
( sQ1353_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f14156,f700,f14208]) ).
fof(f14212,definition,
! [X0] :
( sQ1354_spl
<=> ( compose(compose(g,a),compose(h,codomain(X0))) = compose(compose(compose(g,a),h),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1354_spl])],[split_symbol_definition]) ).
fof(f14215,plain,
( sQ1354_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14157,f693,f14212]) ).
fof(f14216,definition,
! [X0] :
( sQ1355_spl
<=> ( compose(compose(g,a),compose(a,codomain(X0))) = compose(compose(compose(g,a),a),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1355_spl])],[split_symbol_definition]) ).
fof(f14219,plain,
( sQ1355_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f14158,f715,f14216]) ).
fof(f14220,plain,
! [X0,X1] :
( compose(compose(g,a),compose(codomain(X0),codomain(X1))) = compose(compose(compose(g,a),codomain(X0)),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f14159]) ).
fof(f14221,plain,
! [X0,X1] :
( compose(compose(g,a),compose(domain(X0),codomain(X1))) = compose(compose(compose(g,a),domain(X0)),codomain(X1))
| domain(X0) != codomain(X1)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f14160]) ).
fof(f14251,plain,
! [X0] :
( compose(compose(a,b),compose(domain(compose(g,a)),X0)) = compose(compose(compose(a,b),domain(compose(g,a))),X0)
| domain(compose(g,a)) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f4649]) ).
fof(f14252,plain,
! [X0] :
( compose(compose(a,b),compose(domain(compose(h,compose(a,b))),X0)) = compose(compose(compose(a,b),domain(compose(h,compose(a,b)))),X0)
| domain(compose(h,compose(a,b))) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f4649]) ).
fof(f14253,plain,
! [X0] :
( compose(compose(a,b),compose(domain(compose(h,a)),X0)) = compose(compose(compose(a,b),domain(compose(h,a))),X0)
| domain(compose(h,a)) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f4649]) ).
fof(f14254,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)],[f60,f4649]) ).
fof(f14261,definition,
! [X0] :
( sQ1356_spl
<=> ( compose(compose(a,b),compose(domain(compose(g,a)),X0)) = compose(compose(compose(a,b),domain(compose(g,a))),X0)
| domain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1356_spl])],[split_symbol_definition]) ).
fof(f14264,plain,
( sQ1356_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14251,f1555,f14261]) ).
fof(f14265,definition,
! [X0] :
( sQ1357_spl
<=> ( compose(compose(a,b),compose(domain(compose(h,compose(a,b))),X0)) = compose(compose(compose(a,b),domain(compose(h,compose(a,b)))),X0)
| domain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1357_spl])],[split_symbol_definition]) ).
fof(f14268,plain,
( sQ1357_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14252,f1555,f14265]) ).
fof(f14269,definition,
! [X0] :
( sQ1358_spl
<=> ( compose(compose(a,b),compose(domain(compose(h,a)),X0)) = compose(compose(compose(a,b),domain(compose(h,a))),X0)
| domain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1358_spl])],[split_symbol_definition]) ).
fof(f14272,plain,
( sQ1358_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14253,f1555,f14269]) ).
fof(f14273,definition,
! [X0] :
( sQ1359_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,[sQ1359_spl])],[split_symbol_definition]) ).
fof(f14276,plain,
( sQ1359_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f14254,f1570,f14273]) ).
fof(f14284,plain,
! [X0] :
( compose(compose(h,a),compose(domain(compose(g,a)),X0)) = compose(compose(compose(h,a),domain(compose(g,a))),X0)
| domain(compose(g,a)) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f4651]) ).
fof(f14285,plain,
! [X0] :
( compose(compose(h,a),compose(domain(compose(h,compose(a,b))),X0)) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),X0)
| domain(compose(h,compose(a,b))) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f4651]) ).
fof(f14286,plain,
! [X0] :
( compose(compose(h,a),compose(domain(compose(h,a)),X0)) = compose(compose(compose(h,a),domain(compose(h,a))),X0)
| domain(compose(h,a)) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f4651]) ).
fof(f14287,plain,
! [X0] :
( compose(compose(h,a),compose(domain(compose(a,b)),X0)) = compose(compose(compose(h,a),domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f4651]) ).
fof(f14295,definition,
! [X0] :
( sQ1360_spl
<=> ( compose(compose(h,a),compose(domain(compose(g,a)),X0)) = compose(compose(compose(h,a),domain(compose(g,a))),X0)
| domain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1360_spl])],[split_symbol_definition]) ).
fof(f14298,plain,
( sQ1360_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14284,f693,f14295]) ).
fof(f14299,definition,
! [X0] :
( sQ1361_spl
<=> ( compose(compose(h,a),compose(domain(compose(h,compose(a,b))),X0)) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),X0)
| domain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1361_spl])],[split_symbol_definition]) ).
fof(f14302,plain,
( sQ1361_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14285,f693,f14299]) ).
fof(f14303,definition,
! [X0] :
( sQ1362_spl
<=> ( compose(compose(h,a),compose(domain(compose(h,a)),X0)) = compose(compose(compose(h,a),domain(compose(h,a))),X0)
| domain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1362_spl])],[split_symbol_definition]) ).
fof(f14306,plain,
( sQ1362_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14286,f693,f14303]) ).
fof(f14307,definition,
! [X0] :
( sQ1363_spl
<=> ( compose(compose(h,a),compose(domain(compose(a,b)),X0)) = compose(compose(compose(h,a),domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1363_spl])],[split_symbol_definition]) ).
fof(f14310,plain,
( sQ1363_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f14287,f715,f14307]) ).
fof(f14318,plain,
( compose(compose(h,a),compose(compose(h,a),domain(b))) = compose(compose(compose(h,a),compose(h,a)),domain(b))
| domain(b) != domain(compose(h,a)) ),
inference(resolution,[status(thm)],[f4953,f131]) ).
fof(f14319,plain,
( compose(compose(h,a),compose(compose(g,a),domain(b))) = compose(compose(compose(h,a),compose(g,a)),domain(b))
| domain(b) != domain(compose(g,a)) ),
inference(resolution,[status(thm)],[f4953,f130]) ).
fof(f14320,plain,
( compose(compose(h,a),compose(g,domain(a))) = compose(compose(compose(h,a),g),domain(a))
| domain(b) != domain(g) ),
inference(resolution,[status(thm)],[f4953,f74]) ).
fof(f14321,plain,
( compose(compose(h,a),compose(h,domain(a))) = compose(compose(compose(h,a),h),domain(a))
| domain(b) != domain(h) ),
inference(resolution,[status(thm)],[f4953,f69]) ).
fof(f14322,plain,
( compose(compose(h,a),compose(a,domain(b))) = compose(compose(compose(h,a),a),domain(b))
| domain(b) != domain(a) ),
inference(resolution,[status(thm)],[f4953,f22]) ).
fof(f14325,plain,
! [X0] :
( compose(compose(h,a),compose(compose(a,b),domain(X0))) = compose(compose(compose(h,a),compose(a,b)),domain(X0))
| codomain(b) != domain(X0)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f4953]) ).
fof(f14326,plain,
! [X0] :
( compose(compose(h,a),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(compose(h,a),compose(h,compose(a,b))),domain(X0))
| codomain(b) != domain(X0)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f4953]) ).
fof(f14327,plain,
! [X0] :
( compose(compose(h,a),compose(compose(h,a),domain(X0))) = compose(compose(compose(h,a),compose(h,a)),domain(X0))
| domain(b) != domain(X0)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f4953]) ).
fof(f14328,plain,
! [X0] :
( compose(compose(h,a),compose(compose(g,a),domain(X0))) = compose(compose(compose(h,a),compose(g,a)),domain(X0))
| domain(b) != domain(X0)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f4953]) ).
fof(f14329,plain,
! [X0] :
( compose(compose(h,a),compose(g,domain(X0))) = compose(compose(compose(h,a),g),domain(X0))
| domain(a) != domain(X0)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f4953]) ).
fof(f14330,plain,
! [X0] :
( compose(compose(h,a),compose(h,domain(X0))) = compose(compose(compose(h,a),h),domain(X0))
| domain(a) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f4953]) ).
fof(f14331,plain,
! [X0] :
( compose(compose(h,a),compose(a,domain(X0))) = compose(compose(compose(h,a),a),domain(X0))
| domain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f4953]) ).
fof(f14332,plain,
! [X0,X1] :
( compose(compose(h,a),compose(codomain(X0),domain(X1))) = compose(compose(compose(h,a),codomain(X0)),domain(X1))
| codomain(X0) != domain(X1)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f4953]) ).
fof(f14333,plain,
! [X0,X1] :
( compose(compose(h,a),compose(domain(X0),domain(X1))) = compose(compose(compose(h,a),domain(X0)),domain(X1))
| domain(X0) != domain(X1)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f4953]) ).
fof(f14340,definition,
( sQ1364_spl
<=> compose(compose(h,a),compose(compose(h,a),domain(b))) = compose(compose(compose(h,a),compose(h,a)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1364_spl])],[split_symbol_definition]) ).
fof(f14343,plain,
( sQ1364_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f14318,f2330,f14340]) ).
fof(f14344,definition,
( sQ1365_spl
<=> compose(compose(h,a),compose(compose(g,a),domain(b))) = compose(compose(compose(h,a),compose(g,a)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1365_spl])],[split_symbol_definition]) ).
fof(f14347,plain,
( sQ1365_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f14319,f2337,f14344]) ).
fof(f14348,definition,
( sQ1366_spl
<=> compose(compose(h,a),compose(g,domain(a))) = compose(compose(compose(h,a),g),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1366_spl])],[split_symbol_definition]) ).
fof(f14351,plain,
( sQ1366_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f14320,f700,f14348]) ).
fof(f14352,definition,
( sQ1367_spl
<=> compose(compose(h,a),compose(h,domain(a))) = compose(compose(compose(h,a),h),domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1367_spl])],[split_symbol_definition]) ).
fof(f14355,plain,
( sQ1367_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14321,f693,f14352]) ).
fof(f14356,definition,
( sQ1368_spl
<=> compose(compose(h,a),compose(a,domain(b))) = compose(compose(compose(h,a),a),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1368_spl])],[split_symbol_definition]) ).
fof(f14359,plain,
( sQ1368_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f14322,f715,f14356]) ).
fof(f14365,definition,
! [X0] :
( sQ1369_spl
<=> ( compose(compose(h,a),compose(compose(a,b),domain(X0))) = compose(compose(compose(h,a),compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1369_spl])],[split_symbol_definition]) ).
fof(f14368,plain,
( sQ1369_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f14325,f2359,f14365]) ).
fof(f14369,definition,
! [X0] :
( sQ1370_spl
<=> ( compose(compose(h,a),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(compose(h,a),compose(h,compose(a,b))),domain(X0))
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1370_spl])],[split_symbol_definition]) ).
fof(f14372,plain,
( sQ1370_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f14326,f2366,f14369]) ).
fof(f14373,definition,
! [X0] :
( sQ1371_spl
<=> ( compose(compose(h,a),compose(compose(h,a),domain(X0))) = compose(compose(compose(h,a),compose(h,a)),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1371_spl])],[split_symbol_definition]) ).
fof(f14376,plain,
( sQ1371_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f14327,f2330,f14373]) ).
fof(f14377,definition,
! [X0] :
( sQ1372_spl
<=> ( compose(compose(h,a),compose(compose(g,a),domain(X0))) = compose(compose(compose(h,a),compose(g,a)),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1372_spl])],[split_symbol_definition]) ).
fof(f14380,plain,
( sQ1372_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f14328,f2337,f14377]) ).
fof(f14381,definition,
! [X0] :
( sQ1373_spl
<=> ( compose(compose(h,a),compose(g,domain(X0))) = compose(compose(compose(h,a),g),domain(X0))
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1373_spl])],[split_symbol_definition]) ).
fof(f14384,plain,
( sQ1373_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f14329,f700,f14381]) ).
fof(f14385,definition,
! [X0] :
( sQ1374_spl
<=> ( compose(compose(h,a),compose(h,domain(X0))) = compose(compose(compose(h,a),h),domain(X0))
| domain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1374_spl])],[split_symbol_definition]) ).
fof(f14388,plain,
( sQ1374_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14330,f693,f14385]) ).
fof(f14389,definition,
! [X0] :
( sQ1375_spl
<=> ( compose(compose(h,a),compose(a,domain(X0))) = compose(compose(compose(h,a),a),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1375_spl])],[split_symbol_definition]) ).
fof(f14392,plain,
( sQ1375_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f14331,f715,f14389]) ).
fof(f14393,plain,
! [X0,X1] :
( compose(compose(h,a),compose(codomain(X0),domain(X1))) = compose(compose(compose(h,a),codomain(X0)),domain(X1))
| codomain(X0) != domain(X1)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f14332]) ).
fof(f14394,plain,
! [X0,X1] :
( compose(compose(h,a),compose(domain(X0),domain(X1))) = compose(compose(compose(h,a),domain(X0)),domain(X1))
| domain(X0) != domain(X1)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f14333]) ).
fof(f14408,plain,
! [X0] :
( compose(compose(a,b),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(a,b),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f1112]) ).
fof(f14409,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f1112]) ).
fof(f14410,plain,
! [X0] :
( compose(compose(h,a),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(h,a),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f1112]) ).
fof(f14411,plain,
! [X0] :
( compose(compose(g,a),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(g,a),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f1112]) ).
fof(f14412,plain,
! [X0] :
( compose(g,compose(compose(h,compose(a,b)),X0)) = compose(compose(g,compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f1112]) ).
fof(f14413,plain,
! [X0] :
( compose(h,compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1112]) ).
fof(f14414,plain,
! [X0] :
( compose(a,compose(compose(h,compose(a,b)),X0)) = compose(compose(a,compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f1112]) ).
fof(f14418,definition,
! [X0] :
( sQ1376_spl
<=> ( compose(compose(a,b),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(a,b),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1376_spl])],[split_symbol_definition]) ).
fof(f14421,plain,
( sQ1376_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14408,f1555,f14418]) ).
fof(f14422,definition,
! [X0] :
( sQ1377_spl
<=> ( compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1377_spl])],[split_symbol_definition]) ).
fof(f14425,plain,
( sQ1377_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14409,f1555,f14422]) ).
fof(f14426,plain,
( sQ403_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14410,f693,f4979]) ).
fof(f14427,plain,
( sQ273_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14411,f693,f3671]) ).
fof(f14428,plain,
( sQ82_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f14412,f584,f1775]) ).
fof(f14429,plain,
( sQ107_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f14413,f584,f2093]) ).
fof(f14430,plain,
( sQ146_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14414,f693,f2369]) ).
fof(f14431,plain,
( compose(compose(h,a),compose(compose(a,b),codomain(b))) = compose(compose(compose(h,a),compose(a,b)),codomain(b))
| domain(b) != domain(compose(a,b)) ),
inference(resolution,[status(thm)],[f4954,f120]) ).
fof(f14432,plain,
( compose(compose(h,a),compose(compose(h,compose(a,b)),codomain(b))) = compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(b))
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(resolution,[status(thm)],[f4954,f581]) ).
fof(f14434,plain,
( compose(compose(h,a),compose(b,codomain(compose(a,b)))) = compose(compose(compose(h,a),b),codomain(compose(a,b)))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f4954,f120]) ).
fof(f14435,plain,
( compose(compose(h,a),compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(compose(h,a),b),codomain(compose(h,compose(a,b))))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f4954,f581]) ).
fof(f14437,plain,
! [X0] :
( compose(compose(h,a),compose(compose(a,b),codomain(X0))) = compose(compose(compose(h,a),compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f4954]) ).
fof(f14438,plain,
! [X0] :
( compose(compose(h,a),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f4954]) ).
fof(f14439,plain,
! [X0] :
( compose(compose(h,a),compose(compose(h,a),codomain(X0))) = compose(compose(compose(h,a),compose(h,a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f4954]) ).
fof(f14440,plain,
! [X0] :
( compose(compose(h,a),compose(compose(g,a),codomain(X0))) = compose(compose(compose(h,a),compose(g,a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f4954]) ).
fof(f14441,plain,
! [X0] :
( compose(compose(h,a),compose(g,codomain(X0))) = compose(compose(compose(h,a),g),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f4954]) ).
fof(f14442,plain,
! [X0] :
( compose(compose(h,a),compose(h,codomain(X0))) = compose(compose(compose(h,a),h),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f4954]) ).
fof(f14443,plain,
! [X0] :
( compose(compose(h,a),compose(a,codomain(X0))) = compose(compose(compose(h,a),a),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f4954]) ).
fof(f14444,plain,
! [X0,X1] :
( compose(compose(h,a),compose(codomain(X0),codomain(X1))) = compose(compose(compose(h,a),codomain(X0)),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f4954]) ).
fof(f14445,plain,
! [X0,X1] :
( compose(compose(h,a),compose(domain(X0),codomain(X1))) = compose(compose(compose(h,a),domain(X0)),codomain(X1))
| domain(X0) != codomain(X1)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f4954]) ).
fof(f14456,definition,
( sQ1378_spl
<=> compose(compose(h,a),compose(compose(a,b),codomain(b))) = compose(compose(compose(h,a),compose(a,b)),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1378_spl])],[split_symbol_definition]) ).
fof(f14459,plain,
( sQ1378_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f14431,f2359,f14456]) ).
fof(f14460,definition,
( sQ1379_spl
<=> compose(compose(h,a),compose(compose(h,compose(a,b)),codomain(b))) = compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1379_spl])],[split_symbol_definition]) ).
fof(f14463,plain,
( sQ1379_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f14432,f2366,f14460]) ).
fof(f14466,definition,
( sQ1380_spl
<=> compose(compose(h,a),compose(b,codomain(compose(a,b)))) = compose(compose(compose(h,a),b),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1380_spl])],[split_symbol_definition]) ).
fof(f14469,plain,
( sQ1380_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f14434,f1941,f14466]) ).
fof(f14470,definition,
( sQ1381_spl
<=> compose(compose(h,a),compose(b,codomain(compose(h,compose(a,b))))) = compose(compose(compose(h,a),b),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1381_spl])],[split_symbol_definition]) ).
fof(f14473,plain,
( sQ1381_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f14435,f1941,f14470]) ).
fof(f14477,definition,
! [X0] :
( sQ1382_spl
<=> ( compose(compose(h,a),compose(compose(a,b),codomain(X0))) = compose(compose(compose(h,a),compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1382_spl])],[split_symbol_definition]) ).
fof(f14480,plain,
( sQ1382_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f14437,f2359,f14477]) ).
fof(f14481,definition,
! [X0] :
( sQ1383_spl
<=> ( compose(compose(h,a),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1383_spl])],[split_symbol_definition]) ).
fof(f14484,plain,
( sQ1383_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f14438,f2366,f14481]) ).
fof(f14485,definition,
! [X0] :
( sQ1384_spl
<=> ( compose(compose(h,a),compose(compose(h,a),codomain(X0))) = compose(compose(compose(h,a),compose(h,a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1384_spl])],[split_symbol_definition]) ).
fof(f14488,plain,
( sQ1384_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f14439,f2330,f14485]) ).
fof(f14489,definition,
! [X0] :
( sQ1385_spl
<=> ( compose(compose(h,a),compose(compose(g,a),codomain(X0))) = compose(compose(compose(h,a),compose(g,a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1385_spl])],[split_symbol_definition]) ).
fof(f14492,plain,
( sQ1385_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f14440,f2337,f14489]) ).
fof(f14493,definition,
! [X0] :
( sQ1386_spl
<=> ( compose(compose(h,a),compose(g,codomain(X0))) = compose(compose(compose(h,a),g),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1386_spl])],[split_symbol_definition]) ).
fof(f14496,plain,
( sQ1386_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f14441,f700,f14493]) ).
fof(f14497,definition,
! [X0] :
( sQ1387_spl
<=> ( compose(compose(h,a),compose(h,codomain(X0))) = compose(compose(compose(h,a),h),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1387_spl])],[split_symbol_definition]) ).
fof(f14500,plain,
( sQ1387_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14442,f693,f14497]) ).
fof(f14501,definition,
! [X0] :
( sQ1388_spl
<=> ( compose(compose(h,a),compose(a,codomain(X0))) = compose(compose(compose(h,a),a),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1388_spl])],[split_symbol_definition]) ).
fof(f14504,plain,
( sQ1388_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f14443,f715,f14501]) ).
fof(f14505,plain,
! [X0,X1] :
( compose(compose(h,a),compose(codomain(X0),codomain(X1))) = compose(compose(compose(h,a),codomain(X0)),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f14444]) ).
fof(f14506,plain,
! [X0,X1] :
( compose(compose(h,a),compose(domain(X0),codomain(X1))) = compose(compose(compose(h,a),domain(X0)),codomain(X1))
| domain(X0) != codomain(X1)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f14445]) ).
fof(f14536,plain,
! [X0] :
( compose(codomain(compose(a,b)),compose(compose(g,a),X0)) = compose(compose(codomain(compose(a,b)),compose(g,a)),X0)
| domain(b) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f3929]) ).
fof(f14537,plain,
! [X0] :
( compose(codomain(compose(h,compose(a,b))),compose(compose(g,a),X0)) = compose(compose(codomain(compose(h,compose(a,b))),compose(g,a)),X0)
| domain(b) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f3929]) ).
fof(f14538,plain,
! [X0] :
( compose(codomain(compose(h,a)),compose(compose(g,a),X0)) = compose(compose(codomain(compose(h,a)),compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f3929]) ).
fof(f14539,plain,
! [X0] :
( compose(codomain(compose(g,a)),compose(compose(g,a),X0)) = compose(compose(codomain(compose(g,a)),compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f3929]) ).
fof(f14540,plain,
! [X0] :
( compose(codomain(g),compose(compose(g,a),X0)) = compose(compose(codomain(g),compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f3929]) ).
fof(f14541,plain,
! [X0] :
( compose(codomain(h),compose(compose(g,a),X0)) = compose(compose(codomain(h),compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f3929]) ).
fof(f14542,plain,
! [X0] :
( compose(codomain(a),compose(compose(g,a),X0)) = compose(compose(codomain(a),compose(g,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f3929]) ).
fof(f14548,definition,
! [X0] :
( sQ1389_spl
<=> ( compose(codomain(compose(a,b)),compose(compose(g,a),X0)) = compose(compose(codomain(compose(a,b)),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1389_spl])],[split_symbol_definition]) ).
fof(f14551,plain,
( sQ1389_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14536,f1555,f14548]) ).
fof(f14552,definition,
! [X0] :
( sQ1390_spl
<=> ( compose(codomain(compose(h,compose(a,b))),compose(compose(g,a),X0)) = compose(compose(codomain(compose(h,compose(a,b))),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1390_spl])],[split_symbol_definition]) ).
fof(f14555,plain,
( sQ1390_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14537,f1555,f14552]) ).
fof(f14556,definition,
! [X0] :
( sQ1391_spl
<=> ( compose(codomain(compose(h,a)),compose(compose(g,a),X0)) = compose(compose(codomain(compose(h,a)),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1391_spl])],[split_symbol_definition]) ).
fof(f14559,plain,
( sQ1391_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14538,f693,f14556]) ).
fof(f14560,definition,
! [X0] :
( sQ1392_spl
<=> ( compose(codomain(compose(g,a)),compose(compose(g,a),X0)) = compose(compose(codomain(compose(g,a)),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1392_spl])],[split_symbol_definition]) ).
fof(f14563,plain,
( sQ1392_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14539,f693,f14560]) ).
fof(f14564,definition,
! [X0] :
( sQ1393_spl
<=> ( compose(codomain(g),compose(compose(g,a),X0)) = compose(compose(codomain(g),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1393_spl])],[split_symbol_definition]) ).
fof(f14567,plain,
( sQ1393_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f14540,f584,f14564]) ).
fof(f14568,definition,
! [X0] :
( sQ1394_spl
<=> ( compose(codomain(h),compose(compose(g,a),X0)) = compose(compose(codomain(h),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1394_spl])],[split_symbol_definition]) ).
fof(f14571,plain,
( sQ1394_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f14541,f584,f14568]) ).
fof(f14572,definition,
! [X0] :
( sQ1395_spl
<=> ( compose(codomain(a),compose(compose(g,a),X0)) = compose(compose(codomain(a),compose(g,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1395_spl])],[split_symbol_definition]) ).
fof(f14575,plain,
( sQ1395_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14542,f693,f14572]) ).
fof(f14581,plain,
! [X0] :
( compose(codomain(compose(a,b)),compose(compose(h,a),X0)) = compose(compose(codomain(compose(a,b)),compose(h,a)),X0)
| domain(b) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f3931]) ).
fof(f14582,plain,
! [X0] :
( compose(codomain(compose(h,compose(a,b))),compose(compose(h,a),X0)) = compose(compose(codomain(compose(h,compose(a,b))),compose(h,a)),X0)
| domain(b) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f3931]) ).
fof(f14583,plain,
! [X0] :
( compose(codomain(compose(h,a)),compose(compose(h,a),X0)) = compose(compose(codomain(compose(h,a)),compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f3931]) ).
fof(f14584,plain,
! [X0] :
( compose(codomain(compose(g,a)),compose(compose(h,a),X0)) = compose(compose(codomain(compose(g,a)),compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f3931]) ).
fof(f14585,plain,
! [X0] :
( compose(codomain(g),compose(compose(h,a),X0)) = compose(compose(codomain(g),compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f3931]) ).
fof(f14586,plain,
! [X0] :
( compose(codomain(h),compose(compose(h,a),X0)) = compose(compose(codomain(h),compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f3931]) ).
fof(f14587,plain,
! [X0] :
( compose(codomain(a),compose(compose(h,a),X0)) = compose(compose(codomain(a),compose(h,a)),X0)
| domain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f3931]) ).
fof(f14593,definition,
! [X0] :
( sQ1396_spl
<=> ( compose(codomain(compose(a,b)),compose(compose(h,a),X0)) = compose(compose(codomain(compose(a,b)),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1396_spl])],[split_symbol_definition]) ).
fof(f14596,plain,
( sQ1396_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14581,f1555,f14593]) ).
fof(f14597,definition,
! [X0] :
( sQ1397_spl
<=> ( compose(codomain(compose(h,compose(a,b))),compose(compose(h,a),X0)) = compose(compose(codomain(compose(h,compose(a,b))),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1397_spl])],[split_symbol_definition]) ).
fof(f14600,plain,
( sQ1397_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14582,f1555,f14597]) ).
fof(f14601,definition,
! [X0] :
( sQ1398_spl
<=> ( compose(codomain(compose(h,a)),compose(compose(h,a),X0)) = compose(compose(codomain(compose(h,a)),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1398_spl])],[split_symbol_definition]) ).
fof(f14604,plain,
( sQ1398_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14583,f693,f14601]) ).
fof(f14605,definition,
! [X0] :
( sQ1399_spl
<=> ( compose(codomain(compose(g,a)),compose(compose(h,a),X0)) = compose(compose(codomain(compose(g,a)),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1399_spl])],[split_symbol_definition]) ).
fof(f14608,plain,
( sQ1399_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14584,f693,f14605]) ).
fof(f14609,definition,
! [X0] :
( sQ1400_spl
<=> ( compose(codomain(g),compose(compose(h,a),X0)) = compose(compose(codomain(g),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1400_spl])],[split_symbol_definition]) ).
fof(f14612,plain,
( sQ1400_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f14585,f584,f14609]) ).
fof(f14613,definition,
! [X0] :
( sQ1401_spl
<=> ( compose(codomain(h),compose(compose(h,a),X0)) = compose(compose(codomain(h),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1401_spl])],[split_symbol_definition]) ).
fof(f14616,plain,
( sQ1401_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f14586,f584,f14613]) ).
fof(f14617,definition,
! [X0] :
( sQ1402_spl
<=> ( compose(codomain(a),compose(compose(h,a),X0)) = compose(compose(codomain(a),compose(h,a)),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1402_spl])],[split_symbol_definition]) ).
fof(f14620,plain,
( sQ1402_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14587,f693,f14617]) ).
fof(f14628,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)],[f120,f3932]) ).
fof(f14629,plain,
! [X0] :
( compose(codomain(compose(h,compose(a,b))),compose(compose(a,b),X0)) = compose(compose(codomain(compose(h,compose(a,b))),compose(a,b)),X0)
| codomain(b) != domain(X0)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f581,f3932]) ).
fof(f14630,plain,
! [X0] :
( compose(codomain(compose(h,a)),compose(compose(a,b),X0)) = compose(compose(codomain(compose(h,a)),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f131,f3932]) ).
fof(f14631,plain,
! [X0] :
( compose(codomain(compose(g,a)),compose(compose(a,b),X0)) = compose(compose(codomain(compose(g,a)),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f130,f3932]) ).
fof(f14632,plain,
! [X0] :
( compose(codomain(g),compose(compose(a,b),X0)) = compose(compose(codomain(g),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f3932]) ).
fof(f14633,plain,
! [X0] :
( compose(codomain(h),compose(compose(a,b),X0)) = compose(compose(codomain(h),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f3932]) ).
fof(f14634,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)],[f22,f3932]) ).
fof(f14646,definition,
! [X0] :
( sQ1403_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,[sQ1403_spl])],[split_symbol_definition]) ).
fof(f14649,plain,
( sQ1403_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f14628,f1570,f14646]) ).
fof(f14650,definition,
! [X0] :
( sQ1404_spl
<=> ( compose(codomain(compose(h,compose(a,b))),compose(compose(a,b),X0)) = compose(compose(codomain(compose(h,compose(a,b))),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1404_spl])],[split_symbol_definition]) ).
fof(f14653,plain,
( sQ1404_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f14629,f1570,f14650]) ).
fof(f14654,definition,
! [X0] :
( sQ1405_spl
<=> ( compose(codomain(compose(h,a)),compose(compose(a,b),X0)) = compose(compose(codomain(compose(h,a)),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1405_spl])],[split_symbol_definition]) ).
fof(f14657,plain,
( sQ1405_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f14630,f715,f14654]) ).
fof(f14658,definition,
! [X0] :
( sQ1406_spl
<=> ( compose(codomain(compose(g,a)),compose(compose(a,b),X0)) = compose(compose(codomain(compose(g,a)),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1406_spl])],[split_symbol_definition]) ).
fof(f14661,plain,
( sQ1406_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f14631,f715,f14658]) ).
fof(f14662,definition,
! [X0] :
( sQ1407_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,[sQ1407_spl])],[split_symbol_definition]) ).
fof(f14665,plain,
( sQ1407_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f14632,f606,f14662]) ).
fof(f14666,definition,
! [X0] :
( sQ1408_spl
<=> ( compose(codomain(h),compose(compose(a,b),X0)) = compose(compose(codomain(h),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1408_spl])],[split_symbol_definition]) ).
fof(f14669,plain,
( sQ1408_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f14633,f606,f14666]) ).
fof(f14670,definition,
! [X0] :
( sQ1409_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,[sQ1409_spl])],[split_symbol_definition]) ).
fof(f14673,plain,
( sQ1409_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f14634,f715,f14670]) ).
fof(f14685,plain,
( compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = compose(codomain(compose(a,b)),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f4793]) ).
fof(f14686,plain,
( compose(codomain(compose(h,compose(a,b))),compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f4793]) ).
fof(f14687,plain,
( compose(codomain(compose(h,a)),compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(codomain(compose(h,a)),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f4793]) ).
fof(f14688,plain,
( compose(codomain(compose(g,a)),compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(codomain(compose(g,a)),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f4793]) ).
fof(f14689,plain,
( compose(codomain(g),compose(codomain(g),compose(h,compose(a,b)))) = compose(codomain(g),compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f4793]) ).
fof(f14690,plain,
( compose(codomain(h),compose(codomain(h),compose(h,compose(a,b)))) = compose(codomain(h),compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f4793]) ).
fof(f14691,plain,
( compose(codomain(a),compose(codomain(a),compose(h,compose(a,b)))) = compose(codomain(a),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f4793]) ).
fof(f14699,definition,
( sQ1410_spl
<=> compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = compose(codomain(compose(a,b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1410_spl])],[split_symbol_definition]) ).
fof(f14702,plain,
( sQ1410_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14685,f1555,f14699]) ).
fof(f14703,definition,
( sQ1411_spl
<=> compose(codomain(compose(h,compose(a,b))),compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1411_spl])],[split_symbol_definition]) ).
fof(f14706,plain,
( sQ1411_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14686,f1555,f14703]) ).
fof(f14707,definition,
( sQ1412_spl
<=> compose(codomain(compose(h,a)),compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(codomain(compose(h,a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1412_spl])],[split_symbol_definition]) ).
fof(f14710,plain,
( sQ1412_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14687,f693,f14707]) ).
fof(f14711,definition,
( sQ1413_spl
<=> compose(codomain(compose(g,a)),compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(codomain(compose(g,a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1413_spl])],[split_symbol_definition]) ).
fof(f14714,plain,
( sQ1413_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14688,f693,f14711]) ).
fof(f14715,definition,
( sQ1414_spl
<=> compose(codomain(g),compose(codomain(g),compose(h,compose(a,b)))) = compose(codomain(g),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1414_spl])],[split_symbol_definition]) ).
fof(f14718,plain,
( sQ1414_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f14689,f584,f14715]) ).
fof(f14719,definition,
( sQ1415_spl
<=> compose(codomain(h),compose(codomain(h),compose(h,compose(a,b)))) = compose(codomain(h),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1415_spl])],[split_symbol_definition]) ).
fof(f14722,plain,
( sQ1415_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f14690,f584,f14719]) ).
fof(f14723,definition,
( sQ1416_spl
<=> compose(codomain(a),compose(codomain(a),compose(h,compose(a,b)))) = compose(codomain(a),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1416_spl])],[split_symbol_definition]) ).
fof(f14726,plain,
( sQ1416_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f14691,f693,f14723]) ).
fof(f14733,plain,
( compose(g,compose(domain(h),compose(h,compose(a,b)))) = compose(compose(g,domain(h)),compose(h,compose(a,b)))
| domain(a) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f1731,f15]) ).
fof(f14734,plain,
( compose(g,compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(g,compose(a,b)),compose(h,compose(a,b)))
| codomain(b) != domain(h)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f1731]) ).
fof(f14735,plain,
( compose(g,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(g,compose(h,compose(a,b))),compose(h,compose(a,b)))
| codomain(b) != domain(h)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f1731]) ).
fof(f14736,plain,
( compose(g,compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(g,compose(h,a)),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f1731]) ).
fof(f14737,plain,
( compose(g,compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,compose(g,a)),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f1731]) ).
fof(f14738,plain,
( compose(g,compose(g,compose(h,compose(a,b)))) = compose(compose(g,g),compose(h,compose(a,b)))
| domain(a) != domain(h)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f1731]) ).
fof(f14739,plain,
( compose(g,compose(h,compose(h,compose(a,b)))) = compose(compose(g,h),compose(h,compose(a,b)))
| domain(a) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f1731]) ).
fof(f14740,plain,
( compose(g,compose(a,compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f1731]) ).
fof(f14741,plain,
! [X0] :
( compose(g,compose(codomain(X0),compose(h,compose(a,b)))) = compose(compose(g,codomain(X0)),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(a) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f1731]) ).
fof(f14742,plain,
! [X0] :
( compose(g,compose(domain(X0),compose(h,compose(a,b)))) = compose(compose(g,domain(X0)),compose(h,compose(a,b)))
| domain(X0) != domain(h)
| domain(a) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f1731]) ).
fof(f14743,definition,
( sQ1417_spl
<=> compose(g,compose(domain(h),compose(h,compose(a,b)))) = compose(compose(g,domain(h)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1417_spl])],[split_symbol_definition]) ).
fof(f14746,plain,
( sQ1417_spl
| ~ sQ813_spl ),
inference(split_clause,[status(thm)],[f14733,f8971,f14743]) ).
fof(f14747,definition,
( sQ1418_spl
<=> compose(g,compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(g,compose(a,b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1418_spl])],[split_symbol_definition]) ).
fof(f14750,plain,
( sQ1418_spl
| ~ sQ66_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f14734,f1765,f1555,f14747]) ).
fof(f14751,definition,
( sQ1419_spl
<=> compose(g,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(g,compose(h,compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1419_spl])],[split_symbol_definition]) ).
fof(f14754,plain,
( sQ1419_spl
| ~ sQ66_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f14735,f1772,f1555,f14751]) ).
fof(f14755,definition,
( sQ1420_spl
<=> compose(g,compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(g,compose(h,a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1420_spl])],[split_symbol_definition]) ).
fof(f14758,plain,
( sQ1420_spl
| ~ sQ21_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f14736,f1736,f693,f14755]) ).
fof(f14759,definition,
( sQ1421_spl
<=> compose(g,compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,compose(g,a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1421_spl])],[split_symbol_definition]) ).
fof(f14762,plain,
( sQ1421_spl
| ~ sQ21_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f14737,f1743,f693,f14759]) ).
fof(f14763,definition,
( sQ1422_spl
<=> compose(g,compose(g,compose(h,compose(a,b)))) = compose(compose(g,g),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1422_spl])],[split_symbol_definition]) ).
fof(f14766,plain,
( sQ1422_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f14738,f591,f584,f14763]) ).
fof(f14767,definition,
( sQ1423_spl
<=> compose(g,compose(h,compose(h,compose(a,b)))) = compose(compose(g,h),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1423_spl])],[split_symbol_definition]) ).
fof(f14770,plain,
( sQ1423_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f14739,f584,f14767]) ).
fof(f14771,plain,
( sQ53_spl
| ~ sQ21_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f14740,f606,f693,f1346]) ).
fof(f14772,plain,
! [X0] :
( compose(g,compose(codomain(X0),compose(h,compose(a,b)))) = compose(compose(g,codomain(X0)),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f14741]) ).
fof(f14773,plain,
! [X0] :
( compose(g,compose(domain(X0),compose(h,compose(a,b)))) = compose(compose(g,domain(X0)),compose(h,compose(a,b)))
| domain(X0) != domain(h)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f14742]) ).
fof(f14779,plain,
( compose(domain(g),compose(domain(g),compose(h,compose(a,b)))) = compose(domain(g),compose(h,compose(a,b)))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f4876]) ).
fof(f14780,plain,
( compose(domain(compose(g,a)),compose(domain(compose(g,a)),compose(h,compose(a,b)))) = compose(domain(compose(g,a)),compose(h,compose(a,b)))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f4876]) ).
fof(f14781,plain,
( compose(domain(compose(h,compose(a,b))),compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f4876]) ).
fof(f14782,plain,
( compose(domain(compose(h,a)),compose(domain(compose(h,a)),compose(h,compose(a,b)))) = compose(domain(compose(h,a)),compose(h,compose(a,b)))
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f4876]) ).
fof(f14783,plain,
( compose(domain(compose(a,b)),compose(domain(compose(a,b)),compose(h,compose(a,b)))) = compose(domain(compose(a,b)),compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f4876]) ).
fof(f14810,definition,
( sQ1424_spl
<=> compose(domain(g),compose(domain(g),compose(h,compose(a,b)))) = compose(domain(g),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1424_spl])],[split_symbol_definition]) ).
fof(f14813,plain,
( sQ1424_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f14779,f2687,f14810]) ).
fof(f14814,definition,
( sQ1425_spl
<=> compose(domain(compose(g,a)),compose(domain(compose(g,a)),compose(h,compose(a,b)))) = compose(domain(compose(g,a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1425_spl])],[split_symbol_definition]) ).
fof(f14817,plain,
( sQ1425_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f14780,f2687,f14814]) ).
fof(f14818,definition,
( sQ1426_spl
<=> compose(domain(compose(h,compose(a,b))),compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1426_spl])],[split_symbol_definition]) ).
fof(f14821,plain,
( sQ1426_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f14781,f2687,f14818]) ).
fof(f14822,definition,
( sQ1427_spl
<=> compose(domain(compose(h,a)),compose(domain(compose(h,a)),compose(h,compose(a,b)))) = compose(domain(compose(h,a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1427_spl])],[split_symbol_definition]) ).
fof(f14825,plain,
( sQ1427_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f14782,f2687,f14822]) ).
fof(f14826,definition,
( sQ1428_spl
<=> compose(domain(compose(a,b)),compose(domain(compose(a,b)),compose(h,compose(a,b)))) = compose(domain(compose(a,b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1428_spl])],[split_symbol_definition]) ).
fof(f14829,plain,
( sQ1428_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f14783,f584,f14826]) ).
fof(f14855,plain,
( compose(domain(h),compose(compose(h,compose(a,b)),domain(compose(g,a)))) = compose(compose(h,compose(a,b)),domain(compose(g,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f5043]) ).
fof(f14856,plain,
( compose(domain(h),compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b))))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f5043]) ).
fof(f14857,plain,
( compose(domain(h),compose(compose(h,compose(a,b)),domain(compose(h,a)))) = compose(compose(h,compose(a,b)),domain(compose(h,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f5043]) ).
fof(f14858,plain,
( compose(domain(h),compose(compose(h,compose(a,b)),domain(compose(a,b)))) = compose(compose(h,compose(a,b)),domain(compose(a,b)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f5043]) ).
fof(f14865,definition,
( sQ1429_spl
<=> compose(domain(h),compose(compose(h,compose(a,b)),domain(compose(g,a)))) = compose(compose(h,compose(a,b)),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1429_spl])],[split_symbol_definition]) ).
fof(f14868,plain,
( sQ1429_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14855,f1555,f14865]) ).
fof(f14869,definition,
( sQ1430_spl
<=> compose(domain(h),compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1430_spl])],[split_symbol_definition]) ).
fof(f14872,plain,
( sQ1430_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14856,f1555,f14869]) ).
fof(f14873,definition,
( sQ1431_spl
<=> compose(domain(h),compose(compose(h,compose(a,b)),domain(compose(h,a)))) = compose(compose(h,compose(a,b)),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1431_spl])],[split_symbol_definition]) ).
fof(f14876,plain,
( sQ1431_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14857,f1555,f14873]) ).
fof(f14877,definition,
( sQ1432_spl
<=> compose(domain(h),compose(compose(h,compose(a,b)),domain(compose(a,b)))) = compose(compose(h,compose(a,b)),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1432_spl])],[split_symbol_definition]) ).
fof(f14880,plain,
( sQ1432_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f14858,f1570,f14877]) ).
fof(f14888,plain,
( compose(domain(h),compose(compose(h,compose(a,b)),codomain(compose(a,b)))) = compose(compose(h,compose(a,b)),codomain(compose(a,b)))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f5106]) ).
fof(f14889,plain,
( compose(domain(h),compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b))))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f5106]) ).
fof(f14890,plain,
( compose(domain(h),compose(compose(h,compose(a,b)),codomain(compose(h,a)))) = compose(compose(h,compose(a,b)),codomain(compose(h,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f5106]) ).
fof(f14891,plain,
( compose(domain(h),compose(compose(h,compose(a,b)),codomain(compose(g,a)))) = compose(compose(h,compose(a,b)),codomain(compose(g,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f5106]) ).
fof(f14905,definition,
( sQ1433_spl
<=> compose(domain(h),compose(compose(h,compose(a,b)),codomain(compose(a,b)))) = compose(compose(h,compose(a,b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1433_spl])],[split_symbol_definition]) ).
fof(f14908,plain,
( sQ1433_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f14888,f4389,f14905]) ).
fof(f14909,definition,
( sQ1434_spl
<=> compose(domain(h),compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1434_spl])],[split_symbol_definition]) ).
fof(f14912,plain,
( sQ1434_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f14889,f4389,f14909]) ).
fof(f14913,definition,
( sQ1435_spl
<=> compose(domain(h),compose(compose(h,compose(a,b)),codomain(compose(h,a)))) = compose(compose(h,compose(a,b)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1435_spl])],[split_symbol_definition]) ).
fof(f14916,plain,
( sQ1435_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f14890,f2265,f14913]) ).
fof(f14917,definition,
( sQ1436_spl
<=> compose(domain(h),compose(compose(h,compose(a,b)),codomain(compose(g,a)))) = compose(compose(h,compose(a,b)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1436_spl])],[split_symbol_definition]) ).
fof(f14920,plain,
( sQ1436_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f14891,f2265,f14917]) ).
fof(f14934,plain,
( compose(compose(h,compose(a,b)),compose(codomain(b),domain(compose(g,a)))) = compose(compose(h,compose(a,b)),domain(compose(g,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f5266]) ).
fof(f14935,plain,
( compose(compose(h,compose(a,b)),compose(codomain(b),domain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b))))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f5266]) ).
fof(f14936,plain,
( compose(compose(h,compose(a,b)),compose(codomain(b),domain(compose(h,a)))) = compose(compose(h,compose(a,b)),domain(compose(h,a)))
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f5266]) ).
fof(f14937,plain,
( compose(compose(h,compose(a,b)),compose(codomain(b),domain(compose(a,b)))) = compose(compose(h,compose(a,b)),domain(compose(a,b)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f5266]) ).
fof(f14944,definition,
( sQ1437_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(b),domain(compose(g,a)))) = compose(compose(h,compose(a,b)),domain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1437_spl])],[split_symbol_definition]) ).
fof(f14947,plain,
( sQ1437_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14934,f1555,f14944]) ).
fof(f14948,definition,
( sQ1438_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(b),domain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1438_spl])],[split_symbol_definition]) ).
fof(f14951,plain,
( sQ1438_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14935,f1555,f14948]) ).
fof(f14952,definition,
( sQ1439_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(b),domain(compose(h,a)))) = compose(compose(h,compose(a,b)),domain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1439_spl])],[split_symbol_definition]) ).
fof(f14955,plain,
( sQ1439_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f14936,f1555,f14952]) ).
fof(f14956,definition,
( sQ1440_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(b),domain(compose(a,b)))) = compose(compose(h,compose(a,b)),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1440_spl])],[split_symbol_definition]) ).
fof(f14959,plain,
( sQ1440_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f14937,f1570,f14956]) ).
fof(f14967,plain,
( compose(compose(h,compose(a,b)),compose(codomain(b),codomain(compose(a,b)))) = compose(compose(h,compose(a,b)),codomain(compose(a,b)))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f5326]) ).
fof(f14968,plain,
( compose(compose(h,compose(a,b)),compose(codomain(b),codomain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b))))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f5326]) ).
fof(f14969,plain,
( compose(compose(h,compose(a,b)),compose(codomain(b),codomain(compose(h,a)))) = compose(compose(h,compose(a,b)),codomain(compose(h,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f5326]) ).
fof(f14970,plain,
( compose(compose(h,compose(a,b)),compose(codomain(b),codomain(compose(g,a)))) = compose(compose(h,compose(a,b)),codomain(compose(g,a)))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f5326]) ).
fof(f14984,definition,
( sQ1441_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(b),codomain(compose(a,b)))) = compose(compose(h,compose(a,b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1441_spl])],[split_symbol_definition]) ).
fof(f14987,plain,
( sQ1441_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f14967,f4389,f14984]) ).
fof(f14988,definition,
( sQ1442_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(b),codomain(compose(h,compose(a,b))))) = compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1442_spl])],[split_symbol_definition]) ).
fof(f14991,plain,
( sQ1442_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f14968,f4389,f14988]) ).
fof(f14992,definition,
( sQ1443_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(b),codomain(compose(h,a)))) = compose(compose(h,compose(a,b)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1443_spl])],[split_symbol_definition]) ).
fof(f14995,plain,
( sQ1443_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f14969,f2265,f14992]) ).
fof(f14996,definition,
( sQ1444_spl
<=> compose(compose(h,compose(a,b)),compose(codomain(b),codomain(compose(g,a)))) = compose(compose(h,compose(a,b)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1444_spl])],[split_symbol_definition]) ).
fof(f14999,plain,
( sQ1444_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f14970,f2265,f14996]) ).
fof(f15011,plain,
( compose(h,compose(domain(h),compose(h,compose(a,b)))) = compose(compose(h,domain(h)),compose(h,compose(a,b)))
| domain(a) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f2061,f15]) ).
fof(f15012,plain,
( compose(h,compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b)))
| codomain(b) != domain(h)
| domain(a) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f2061]) ).
fof(f15013,plain,
( compose(h,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(h,compose(a,b))),compose(h,compose(a,b)))
| codomain(b) != domain(h)
| domain(a) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f2061]) ).
fof(f15014,plain,
( compose(h,compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,compose(h,a)),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(a) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f2061]) ).
fof(f15015,plain,
( compose(h,compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(h,compose(g,a)),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(a) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f2061]) ).
fof(f15016,plain,
( compose(h,compose(g,compose(h,compose(a,b)))) = compose(compose(h,g),compose(h,compose(a,b)))
| domain(a) != domain(h)
| domain(a) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f2061]) ).
fof(f15017,plain,
( compose(h,compose(h,compose(h,compose(a,b)))) = compose(compose(h,h),compose(h,compose(a,b)))
| domain(a) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f2061]) ).
fof(f15018,plain,
( compose(h,compose(a,compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f2061]) ).
fof(f15019,plain,
! [X0] :
( compose(h,compose(codomain(X0),compose(h,compose(a,b)))) = compose(compose(h,codomain(X0)),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(a) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f2061]) ).
fof(f15020,plain,
! [X0] :
( compose(h,compose(domain(X0),compose(h,compose(a,b)))) = compose(compose(h,domain(X0)),compose(h,compose(a,b)))
| domain(X0) != domain(h)
| domain(a) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f2061]) ).
fof(f15021,definition,
( sQ1445_spl
<=> compose(h,compose(domain(h),compose(h,compose(a,b)))) = compose(compose(h,domain(h)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1445_spl])],[split_symbol_definition]) ).
fof(f15024,plain,
( sQ1445_spl
| ~ sQ813_spl ),
inference(split_clause,[status(thm)],[f15011,f8971,f15021]) ).
fof(f15025,plain,
( sQ867_spl
| ~ sQ66_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f15012,f1765,f1555,f9378]) ).
fof(f15026,definition,
( sQ1446_spl
<=> compose(h,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(h,compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1446_spl])],[split_symbol_definition]) ).
fof(f15029,plain,
( sQ1446_spl
| ~ sQ66_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f15013,f1772,f1555,f15026]) ).
fof(f15030,definition,
( sQ1447_spl
<=> compose(h,compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,compose(h,a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1447_spl])],[split_symbol_definition]) ).
fof(f15033,plain,
( sQ1447_spl
| ~ sQ21_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f15014,f1736,f693,f15030]) ).
fof(f15034,definition,
( sQ1448_spl
<=> compose(h,compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(h,compose(g,a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1448_spl])],[split_symbol_definition]) ).
fof(f15037,plain,
( sQ1448_spl
| ~ sQ21_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f15015,f1743,f693,f15034]) ).
fof(f15038,definition,
( sQ1449_spl
<=> compose(h,compose(g,compose(h,compose(a,b)))) = compose(compose(h,g),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1449_spl])],[split_symbol_definition]) ).
fof(f15041,plain,
( sQ1449_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f15016,f591,f584,f15038]) ).
fof(f15042,definition,
( sQ1450_spl
<=> compose(h,compose(h,compose(h,compose(a,b)))) = compose(compose(h,h),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1450_spl])],[split_symbol_definition]) ).
fof(f15045,plain,
( sQ1450_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15017,f584,f15042]) ).
fof(f15046,plain,
( sQ58_spl
| ~ sQ21_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15018,f606,f693,f1400]) ).
fof(f15047,plain,
! [X0] :
( compose(h,compose(codomain(X0),compose(h,compose(a,b)))) = compose(compose(h,codomain(X0)),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(a) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f15019]) ).
fof(f15048,plain,
! [X0] :
( compose(h,compose(domain(X0),compose(h,compose(a,b)))) = compose(compose(h,domain(X0)),compose(h,compose(a,b)))
| domain(X0) != domain(h)
| domain(a) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f15020]) ).
fof(f15049,plain,
( compose(g,compose(codomain(g),compose(g,a))) = compose(compose(g,codomain(g)),compose(g,a))
| codomain(g) != domain(h) ),
inference(resolution,[status(thm)],[f9003,f74]) ).
fof(f15050,plain,
( compose(g,compose(codomain(h),compose(g,a))) = compose(compose(g,codomain(h)),compose(g,a))
| codomain(h) != domain(h) ),
inference(resolution,[status(thm)],[f9003,f69]) ).
fof(f15051,plain,
( compose(g,compose(codomain(domain(a)),compose(g,a))) = compose(compose(g,codomain(domain(a))),compose(g,a))
| codomain(domain(a)) != domain(h) ),
inference(resolution,[status(thm)],[f9003,f15]) ).
fof(f15052,plain,
( compose(g,compose(codomain(compose(a,b)),compose(g,a))) = compose(compose(g,codomain(compose(a,b))),compose(g,a))
| codomain(compose(a,b)) != domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f9003]) ).
fof(f15053,plain,
( compose(g,compose(codomain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(g,codomain(compose(h,compose(a,b)))),compose(g,a))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f9003]) ).
fof(f15054,plain,
( compose(g,compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(g,codomain(compose(h,a))),compose(g,a))
| codomain(compose(h,a)) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f9003]) ).
fof(f15055,plain,
( compose(g,compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(g,codomain(compose(g,a))),compose(g,a))
| codomain(compose(g,a)) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f9003]) ).
fof(f15056,plain,
( compose(g,compose(codomain(g),compose(g,a))) = compose(compose(g,codomain(g)),compose(g,a))
| codomain(g) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f9003]) ).
fof(f15057,plain,
( compose(g,compose(codomain(h),compose(g,a))) = compose(compose(g,codomain(h)),compose(g,a))
| codomain(h) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f9003]) ).
fof(f15058,plain,
( compose(g,compose(codomain(a),compose(g,a))) = compose(compose(g,codomain(a)),compose(g,a))
| codomain(a) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f9003]) ).
fof(f15061,definition,
( sQ1451_spl
<=> codomain(g) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ1451_spl])],[split_symbol_definition]) ).
fof(f15063,plain,
( sQ1451_spl
| codomain(g) != domain(h) ),
inference(component_clause,[status(thm)],[f15061]) ).
fof(f15064,definition,
( sQ1452_spl
<=> compose(g,compose(codomain(g),compose(g,a))) = compose(compose(g,codomain(g)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1452_spl])],[split_symbol_definition]) ).
fof(f15067,plain,
( sQ1452_spl
| ~ sQ1451_spl ),
inference(split_clause,[status(thm)],[f15049,f15061,f15064]) ).
fof(f15068,definition,
( sQ1453_spl
<=> codomain(h) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ1453_spl])],[split_symbol_definition]) ).
fof(f15070,plain,
( sQ1453_spl
| codomain(h) != domain(h) ),
inference(component_clause,[status(thm)],[f15068]) ).
fof(f15071,definition,
( sQ1454_spl
<=> compose(g,compose(codomain(h),compose(g,a))) = compose(compose(g,codomain(h)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1454_spl])],[split_symbol_definition]) ).
fof(f15074,plain,
( sQ1454_spl
| ~ sQ1453_spl ),
inference(split_clause,[status(thm)],[f15050,f15068,f15071]) ).
fof(f15075,definition,
( sQ1455_spl
<=> codomain(domain(a)) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ1455_spl])],[split_symbol_definition]) ).
fof(f15077,plain,
( sQ1455_spl
| codomain(domain(a)) != domain(h) ),
inference(component_clause,[status(thm)],[f15075]) ).
fof(f15078,definition,
( sQ1456_spl
<=> compose(g,compose(codomain(domain(a)),compose(g,a))) = compose(compose(g,codomain(domain(a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1456_spl])],[split_symbol_definition]) ).
fof(f15081,plain,
( sQ1456_spl
| ~ sQ1455_spl ),
inference(split_clause,[status(thm)],[f15051,f15075,f15078]) ).
fof(f15082,definition,
( sQ1457_spl
<=> codomain(compose(a,b)) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ1457_spl])],[split_symbol_definition]) ).
fof(f15085,definition,
( sQ1458_spl
<=> compose(g,compose(codomain(compose(a,b)),compose(g,a))) = compose(compose(g,codomain(compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1458_spl])],[split_symbol_definition]) ).
fof(f15088,plain,
( sQ1458_spl
| ~ sQ1457_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f15052,f1570,f15082,f15085]) ).
fof(f15089,definition,
( sQ1459_spl
<=> codomain(compose(h,compose(a,b))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ1459_spl])],[split_symbol_definition]) ).
fof(f15092,definition,
( sQ1460_spl
<=> compose(g,compose(codomain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(g,codomain(compose(h,compose(a,b)))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1460_spl])],[split_symbol_definition]) ).
fof(f15095,plain,
( sQ1460_spl
| ~ sQ1459_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f15053,f1570,f15089,f15092]) ).
fof(f15096,definition,
( sQ1461_spl
<=> codomain(compose(h,a)) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ1461_spl])],[split_symbol_definition]) ).
fof(f15098,plain,
( sQ1461_spl
| codomain(compose(h,a)) != domain(h) ),
inference(component_clause,[status(thm)],[f15096]) ).
fof(f15099,definition,
( sQ1462_spl
<=> compose(g,compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(g,codomain(compose(h,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1462_spl])],[split_symbol_definition]) ).
fof(f15102,plain,
( sQ1462_spl
| ~ sQ1461_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15054,f715,f15096,f15099]) ).
fof(f15103,definition,
( sQ1463_spl
<=> codomain(compose(g,a)) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ1463_spl])],[split_symbol_definition]) ).
fof(f15105,plain,
( sQ1463_spl
| codomain(compose(g,a)) != domain(h) ),
inference(component_clause,[status(thm)],[f15103]) ).
fof(f15106,definition,
( sQ1464_spl
<=> compose(g,compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(g,codomain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1464_spl])],[split_symbol_definition]) ).
fof(f15109,plain,
( sQ1464_spl
| ~ sQ1463_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15055,f715,f15103,f15106]) ).
fof(f15110,plain,
( sQ1452_spl
| ~ sQ1451_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15056,f606,f15061,f15064]) ).
fof(f15111,plain,
( sQ1454_spl
| ~ sQ1453_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15057,f606,f15068,f15071]) ).
fof(f15112,definition,
( sQ1465_spl
<=> codomain(a) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ1465_spl])],[split_symbol_definition]) ).
fof(f15114,plain,
( sQ1465_spl
| codomain(a) != domain(h) ),
inference(component_clause,[status(thm)],[f15112]) ).
fof(f15115,definition,
( sQ1466_spl
<=> compose(g,compose(codomain(a),compose(g,a))) = compose(compose(g,codomain(a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1466_spl])],[split_symbol_definition]) ).
fof(f15118,plain,
( sQ1466_spl
| ~ sQ1465_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15058,f715,f15112,f15115]) ).
fof(f15125,plain,
( sQ1451_spl
| domain(a) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f74,f15063]) ).
fof(f15126,plain,
( sQ1453_spl
| domain(a) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f69,f15070]) ).
fof(f15127,plain,
( sQ1455_spl
| domain(a) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f15,f15077]) ).
fof(f15128,plain,
( compose(g,compose(domain(compose(a,b)),compose(g,a))) = compose(compose(g,domain(compose(a,b))),compose(g,a))
| domain(compose(a,b)) != domain(h) ),
inference(resolution,[status(thm)],[f9004,f60]) ).
fof(f15129,plain,
( compose(g,compose(domain(domain(a)),compose(g,a))) = compose(compose(g,domain(domain(a))),compose(g,a))
| domain(domain(a)) != domain(h) ),
inference(resolution,[status(thm)],[f9004,f37]) ).
fof(f15130,plain,
( compose(g,compose(domain(compose(g,a)),compose(g,a))) = compose(compose(g,domain(compose(g,a))),compose(g,a))
| domain(compose(g,a)) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f9004]) ).
fof(f15131,plain,
( compose(g,compose(domain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(g,domain(compose(h,compose(a,b)))),compose(g,a))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f9004]) ).
fof(f15132,plain,
( compose(g,compose(domain(compose(h,a)),compose(g,a))) = compose(compose(g,domain(compose(h,a))),compose(g,a))
| domain(compose(h,a)) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f9004]) ).
fof(f15133,plain,
( compose(g,compose(domain(compose(a,b)),compose(g,a))) = compose(compose(g,domain(compose(a,b))),compose(g,a))
| domain(compose(a,b)) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f9004]) ).
fof(f15136,plain,
( compose(g,compose(domain(a),compose(g,a))) = compose(compose(g,domain(a)),compose(g,a))
| domain(a) != domain(h) ),
inference(equality_resolution,[status(thm)],[f9004]) ).
fof(f15137,definition,
( sQ1467_spl
<=> domain(compose(a,b)) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ1467_spl])],[split_symbol_definition]) ).
fof(f15139,plain,
( sQ1467_spl
| domain(compose(a,b)) != domain(h) ),
inference(component_clause,[status(thm)],[f15137]) ).
fof(f15140,definition,
( sQ1468_spl
<=> compose(g,compose(domain(compose(a,b)),compose(g,a))) = compose(compose(g,domain(compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1468_spl])],[split_symbol_definition]) ).
fof(f15143,plain,
( sQ1468_spl
| ~ sQ1467_spl ),
inference(split_clause,[status(thm)],[f15128,f15137,f15140]) ).
fof(f15144,definition,
( sQ1469_spl
<=> domain(domain(a)) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ1469_spl])],[split_symbol_definition]) ).
fof(f15146,plain,
( sQ1469_spl
| domain(domain(a)) != domain(h) ),
inference(component_clause,[status(thm)],[f15144]) ).
fof(f15147,definition,
( sQ1470_spl
<=> compose(g,compose(domain(domain(a)),compose(g,a))) = compose(compose(g,domain(domain(a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1470_spl])],[split_symbol_definition]) ).
fof(f15150,plain,
( sQ1470_spl
| ~ sQ1469_spl ),
inference(split_clause,[status(thm)],[f15129,f15144,f15147]) ).
fof(f15151,definition,
( sQ1471_spl
<=> domain(compose(g,a)) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ1471_spl])],[split_symbol_definition]) ).
fof(f15154,definition,
( sQ1472_spl
<=> compose(g,compose(domain(compose(g,a)),compose(g,a))) = compose(compose(g,domain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1472_spl])],[split_symbol_definition]) ).
fof(f15157,plain,
( sQ1472_spl
| ~ sQ1471_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15130,f584,f15151,f15154]) ).
fof(f15158,definition,
( sQ1473_spl
<=> compose(g,compose(domain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(g,domain(compose(h,compose(a,b)))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1473_spl])],[split_symbol_definition]) ).
fof(f15161,plain,
( sQ1473_spl
| ~ sQ49_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15131,f584,f1100,f15158]) ).
fof(f15162,definition,
( sQ1474_spl
<=> domain(compose(h,a)) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ1474_spl])],[split_symbol_definition]) ).
fof(f15165,definition,
( sQ1475_spl
<=> compose(g,compose(domain(compose(h,a)),compose(g,a))) = compose(compose(g,domain(compose(h,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1475_spl])],[split_symbol_definition]) ).
fof(f15168,plain,
( sQ1475_spl
| ~ sQ1474_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15132,f584,f15162,f15165]) ).
fof(f15169,plain,
( sQ1468_spl
| ~ sQ1467_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15133,f606,f15137,f15140]) ).
fof(f15176,definition,
( sQ1476_spl
<=> compose(g,compose(domain(a),compose(g,a))) = compose(compose(g,domain(a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1476_spl])],[split_symbol_definition]) ).
fof(f15179,plain,
( sQ1476_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15136,f584,f15176]) ).
fof(f15180,plain,
( sQ1467_spl
| domain(a) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f60,f15139]) ).
fof(f15181,plain,
( sQ1469_spl
| domain(a) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f37,f15146]) ).
fof(f15182,plain,
( compose(g,compose(codomain(g),compose(h,a))) = compose(compose(g,codomain(g)),compose(h,a))
| codomain(g) != domain(h) ),
inference(resolution,[status(thm)],[f9364,f74]) ).
fof(f15183,plain,
( compose(g,compose(codomain(h),compose(h,a))) = compose(compose(g,codomain(h)),compose(h,a))
| codomain(h) != domain(h) ),
inference(resolution,[status(thm)],[f9364,f69]) ).
fof(f15184,plain,
( compose(g,compose(codomain(domain(a)),compose(h,a))) = compose(compose(g,codomain(domain(a))),compose(h,a))
| codomain(domain(a)) != domain(h) ),
inference(resolution,[status(thm)],[f9364,f15]) ).
fof(f15185,plain,
( compose(g,compose(codomain(compose(a,b)),compose(h,a))) = compose(compose(g,codomain(compose(a,b))),compose(h,a))
| codomain(compose(a,b)) != domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f9364]) ).
fof(f15186,plain,
( compose(g,compose(codomain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(g,codomain(compose(h,compose(a,b)))),compose(h,a))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f9364]) ).
fof(f15187,plain,
( compose(g,compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(g,codomain(compose(h,a))),compose(h,a))
| codomain(compose(h,a)) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f9364]) ).
fof(f15188,plain,
( compose(g,compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(g,codomain(compose(g,a))),compose(h,a))
| codomain(compose(g,a)) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f9364]) ).
fof(f15189,plain,
( compose(g,compose(codomain(g),compose(h,a))) = compose(compose(g,codomain(g)),compose(h,a))
| codomain(g) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f9364]) ).
fof(f15190,plain,
( compose(g,compose(codomain(h),compose(h,a))) = compose(compose(g,codomain(h)),compose(h,a))
| codomain(h) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f9364]) ).
fof(f15191,plain,
( compose(g,compose(codomain(a),compose(h,a))) = compose(compose(g,codomain(a)),compose(h,a))
| codomain(a) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f9364]) ).
fof(f15194,definition,
( sQ1477_spl
<=> compose(g,compose(codomain(g),compose(h,a))) = compose(compose(g,codomain(g)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1477_spl])],[split_symbol_definition]) ).
fof(f15197,plain,
( sQ1477_spl
| ~ sQ1451_spl ),
inference(split_clause,[status(thm)],[f15182,f15061,f15194]) ).
fof(f15198,definition,
( sQ1478_spl
<=> compose(g,compose(codomain(h),compose(h,a))) = compose(compose(g,codomain(h)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1478_spl])],[split_symbol_definition]) ).
fof(f15201,plain,
( sQ1478_spl
| ~ sQ1453_spl ),
inference(split_clause,[status(thm)],[f15183,f15068,f15198]) ).
fof(f15202,definition,
( sQ1479_spl
<=> compose(g,compose(codomain(domain(a)),compose(h,a))) = compose(compose(g,codomain(domain(a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1479_spl])],[split_symbol_definition]) ).
fof(f15205,plain,
( sQ1479_spl
| ~ sQ1455_spl ),
inference(split_clause,[status(thm)],[f15184,f15075,f15202]) ).
fof(f15206,definition,
( sQ1480_spl
<=> compose(g,compose(codomain(compose(a,b)),compose(h,a))) = compose(compose(g,codomain(compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1480_spl])],[split_symbol_definition]) ).
fof(f15209,plain,
( sQ1480_spl
| ~ sQ1457_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f15185,f1570,f15082,f15206]) ).
fof(f15210,definition,
( sQ1481_spl
<=> compose(g,compose(codomain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(g,codomain(compose(h,compose(a,b)))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1481_spl])],[split_symbol_definition]) ).
fof(f15213,plain,
( sQ1481_spl
| ~ sQ1459_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f15186,f1570,f15089,f15210]) ).
fof(f15214,definition,
( sQ1482_spl
<=> compose(g,compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(g,codomain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1482_spl])],[split_symbol_definition]) ).
fof(f15217,plain,
( sQ1482_spl
| ~ sQ1461_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15187,f715,f15096,f15214]) ).
fof(f15218,definition,
( sQ1483_spl
<=> compose(g,compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(g,codomain(compose(g,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1483_spl])],[split_symbol_definition]) ).
fof(f15221,plain,
( sQ1483_spl
| ~ sQ1463_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15188,f715,f15103,f15218]) ).
fof(f15222,plain,
( sQ1477_spl
| ~ sQ1451_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15189,f606,f15061,f15194]) ).
fof(f15223,plain,
( sQ1478_spl
| ~ sQ1453_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15190,f606,f15068,f15198]) ).
fof(f15224,definition,
( sQ1484_spl
<=> compose(g,compose(codomain(a),compose(h,a))) = compose(compose(g,codomain(a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1484_spl])],[split_symbol_definition]) ).
fof(f15227,plain,
( sQ1484_spl
| ~ sQ1465_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15191,f715,f15112,f15224]) ).
fof(f15234,plain,
( compose(g,compose(domain(compose(a,b)),compose(h,a))) = compose(compose(g,domain(compose(a,b))),compose(h,a))
| domain(compose(a,b)) != domain(h) ),
inference(resolution,[status(thm)],[f9365,f60]) ).
fof(f15235,plain,
( compose(g,compose(domain(domain(a)),compose(h,a))) = compose(compose(g,domain(domain(a))),compose(h,a))
| domain(domain(a)) != domain(h) ),
inference(resolution,[status(thm)],[f9365,f37]) ).
fof(f15236,plain,
( compose(g,compose(domain(compose(g,a)),compose(h,a))) = compose(compose(g,domain(compose(g,a))),compose(h,a))
| domain(compose(g,a)) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f9365]) ).
fof(f15237,plain,
( compose(g,compose(domain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(g,domain(compose(h,compose(a,b)))),compose(h,a))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f9365]) ).
fof(f15238,plain,
( compose(g,compose(domain(compose(h,a)),compose(h,a))) = compose(compose(g,domain(compose(h,a))),compose(h,a))
| domain(compose(h,a)) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f9365]) ).
fof(f15239,plain,
( compose(g,compose(domain(compose(a,b)),compose(h,a))) = compose(compose(g,domain(compose(a,b))),compose(h,a))
| domain(compose(a,b)) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f9365]) ).
fof(f15242,plain,
( compose(g,compose(domain(a),compose(h,a))) = compose(compose(g,domain(a)),compose(h,a))
| domain(a) != domain(h) ),
inference(equality_resolution,[status(thm)],[f9365]) ).
fof(f15243,definition,
( sQ1485_spl
<=> compose(g,compose(domain(compose(a,b)),compose(h,a))) = compose(compose(g,domain(compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1485_spl])],[split_symbol_definition]) ).
fof(f15246,plain,
( sQ1485_spl
| ~ sQ1467_spl ),
inference(split_clause,[status(thm)],[f15234,f15137,f15243]) ).
fof(f15247,definition,
( sQ1486_spl
<=> compose(g,compose(domain(domain(a)),compose(h,a))) = compose(compose(g,domain(domain(a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1486_spl])],[split_symbol_definition]) ).
fof(f15250,plain,
( sQ1486_spl
| ~ sQ1469_spl ),
inference(split_clause,[status(thm)],[f15235,f15144,f15247]) ).
fof(f15251,definition,
( sQ1487_spl
<=> compose(g,compose(domain(compose(g,a)),compose(h,a))) = compose(compose(g,domain(compose(g,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1487_spl])],[split_symbol_definition]) ).
fof(f15254,plain,
( sQ1487_spl
| ~ sQ1471_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15236,f584,f15151,f15251]) ).
fof(f15255,definition,
( sQ1488_spl
<=> compose(g,compose(domain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(g,domain(compose(h,compose(a,b)))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1488_spl])],[split_symbol_definition]) ).
fof(f15258,plain,
( sQ1488_spl
| ~ sQ49_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15237,f584,f1100,f15255]) ).
fof(f15259,definition,
( sQ1489_spl
<=> compose(g,compose(domain(compose(h,a)),compose(h,a))) = compose(compose(g,domain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1489_spl])],[split_symbol_definition]) ).
fof(f15262,plain,
( sQ1489_spl
| ~ sQ1474_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15238,f584,f15162,f15259]) ).
fof(f15263,plain,
( sQ1485_spl
| ~ sQ1467_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15239,f606,f15137,f15243]) ).
fof(f15270,definition,
( sQ1490_spl
<=> compose(g,compose(domain(a),compose(h,a))) = compose(compose(g,domain(a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1490_spl])],[split_symbol_definition]) ).
fof(f15273,plain,
( sQ1490_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15242,f584,f15270]) ).
fof(f15274,plain,
( compose(h,compose(codomain(g),compose(g,a))) = compose(compose(h,codomain(g)),compose(g,a))
| codomain(g) != domain(h) ),
inference(resolution,[status(thm)],[f10192,f74]) ).
fof(f15275,plain,
( compose(h,compose(codomain(h),compose(g,a))) = compose(compose(h,codomain(h)),compose(g,a))
| codomain(h) != domain(h) ),
inference(resolution,[status(thm)],[f10192,f69]) ).
fof(f15276,plain,
( compose(h,compose(codomain(domain(a)),compose(g,a))) = compose(compose(h,codomain(domain(a))),compose(g,a))
| codomain(domain(a)) != domain(h) ),
inference(resolution,[status(thm)],[f10192,f15]) ).
fof(f15277,plain,
( compose(h,compose(codomain(compose(a,b)),compose(g,a))) = compose(compose(h,codomain(compose(a,b))),compose(g,a))
| codomain(compose(a,b)) != domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f10192]) ).
fof(f15278,plain,
( compose(h,compose(codomain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(h,codomain(compose(h,compose(a,b)))),compose(g,a))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f10192]) ).
fof(f15279,plain,
( compose(h,compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(h,codomain(compose(h,a))),compose(g,a))
| codomain(compose(h,a)) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f10192]) ).
fof(f15280,plain,
( compose(h,compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(h,codomain(compose(g,a))),compose(g,a))
| codomain(compose(g,a)) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f10192]) ).
fof(f15281,plain,
( compose(h,compose(codomain(g),compose(g,a))) = compose(compose(h,codomain(g)),compose(g,a))
| codomain(g) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f10192]) ).
fof(f15282,plain,
( compose(h,compose(codomain(h),compose(g,a))) = compose(compose(h,codomain(h)),compose(g,a))
| codomain(h) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f10192]) ).
fof(f15283,plain,
( compose(h,compose(codomain(a),compose(g,a))) = compose(compose(h,codomain(a)),compose(g,a))
| codomain(a) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f10192]) ).
fof(f15286,definition,
( sQ1491_spl
<=> compose(h,compose(codomain(g),compose(g,a))) = compose(compose(h,codomain(g)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1491_spl])],[split_symbol_definition]) ).
fof(f15289,plain,
( sQ1491_spl
| ~ sQ1451_spl ),
inference(split_clause,[status(thm)],[f15274,f15061,f15286]) ).
fof(f15290,definition,
( sQ1492_spl
<=> compose(h,compose(codomain(h),compose(g,a))) = compose(compose(h,codomain(h)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1492_spl])],[split_symbol_definition]) ).
fof(f15293,plain,
( sQ1492_spl
| ~ sQ1453_spl ),
inference(split_clause,[status(thm)],[f15275,f15068,f15290]) ).
fof(f15294,definition,
( sQ1493_spl
<=> compose(h,compose(codomain(domain(a)),compose(g,a))) = compose(compose(h,codomain(domain(a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1493_spl])],[split_symbol_definition]) ).
fof(f15297,plain,
( sQ1493_spl
| ~ sQ1455_spl ),
inference(split_clause,[status(thm)],[f15276,f15075,f15294]) ).
fof(f15298,definition,
( sQ1494_spl
<=> compose(h,compose(codomain(compose(a,b)),compose(g,a))) = compose(compose(h,codomain(compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1494_spl])],[split_symbol_definition]) ).
fof(f15301,plain,
( sQ1494_spl
| ~ sQ1457_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f15277,f1570,f15082,f15298]) ).
fof(f15302,definition,
( sQ1495_spl
<=> compose(h,compose(codomain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(h,codomain(compose(h,compose(a,b)))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1495_spl])],[split_symbol_definition]) ).
fof(f15305,plain,
( sQ1495_spl
| ~ sQ1459_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f15278,f1570,f15089,f15302]) ).
fof(f15306,definition,
( sQ1496_spl
<=> compose(h,compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(h,codomain(compose(h,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1496_spl])],[split_symbol_definition]) ).
fof(f15309,plain,
( sQ1496_spl
| ~ sQ1461_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15279,f715,f15096,f15306]) ).
fof(f15310,definition,
( sQ1497_spl
<=> compose(h,compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(h,codomain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1497_spl])],[split_symbol_definition]) ).
fof(f15313,plain,
( sQ1497_spl
| ~ sQ1463_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15280,f715,f15103,f15310]) ).
fof(f15314,plain,
( sQ1491_spl
| ~ sQ1451_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15281,f606,f15061,f15286]) ).
fof(f15315,plain,
( sQ1492_spl
| ~ sQ1453_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15282,f606,f15068,f15290]) ).
fof(f15316,definition,
( sQ1498_spl
<=> compose(h,compose(codomain(a),compose(g,a))) = compose(compose(h,codomain(a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1498_spl])],[split_symbol_definition]) ).
fof(f15319,plain,
( sQ1498_spl
| ~ sQ1465_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15283,f715,f15112,f15316]) ).
fof(f15326,plain,
( compose(a,compose(domain(h),compose(h,compose(a,b)))) = compose(compose(a,domain(h)),compose(h,compose(a,b)))
| domain(b) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f2325,f15]) ).
fof(f15327,plain,
( compose(a,compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,compose(a,b)),compose(h,compose(a,b)))
| codomain(b) != domain(h)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f2325]) ).
fof(f15328,plain,
( compose(a,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(a,compose(h,compose(a,b))),compose(h,compose(a,b)))
| codomain(b) != domain(h)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f2325]) ).
fof(f15329,plain,
( compose(a,compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(a,compose(h,a)),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f2325]) ).
fof(f15330,plain,
( compose(a,compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(a,compose(g,a)),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f2325]) ).
fof(f15331,plain,
( compose(a,compose(g,compose(h,compose(a,b)))) = compose(compose(a,g),compose(h,compose(a,b)))
| domain(a) != domain(h)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f2325]) ).
fof(f15332,plain,
( compose(a,compose(h,compose(h,compose(a,b)))) = compose(compose(a,h),compose(h,compose(a,b)))
| domain(a) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f2325]) ).
fof(f15333,plain,
( compose(a,compose(a,compose(h,compose(a,b)))) = compose(compose(a,a),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f2325]) ).
fof(f15334,plain,
! [X0] :
( compose(a,compose(codomain(X0),compose(h,compose(a,b)))) = compose(compose(a,codomain(X0)),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f2325]) ).
fof(f15335,plain,
! [X0] :
( compose(a,compose(domain(X0),compose(h,compose(a,b)))) = compose(compose(a,domain(X0)),compose(h,compose(a,b)))
| domain(X0) != domain(h)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f2325]) ).
fof(f15336,definition,
( sQ1499_spl
<=> compose(a,compose(domain(h),compose(h,compose(a,b)))) = compose(compose(a,domain(h)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1499_spl])],[split_symbol_definition]) ).
fof(f15339,plain,
( sQ1499_spl
| ~ sQ1013_spl ),
inference(split_clause,[status(thm)],[f15326,f11076,f15336]) ).
fof(f15340,definition,
( sQ1500_spl
<=> compose(a,compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,compose(a,b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1500_spl])],[split_symbol_definition]) ).
fof(f15343,plain,
( sQ1500_spl
| ~ sQ66_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f15327,f2359,f1555,f15340]) ).
fof(f15344,definition,
( sQ1501_spl
<=> compose(a,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(a,compose(h,compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1501_spl])],[split_symbol_definition]) ).
fof(f15347,plain,
( sQ1501_spl
| ~ sQ66_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f15328,f2366,f1555,f15344]) ).
fof(f15348,definition,
( sQ1502_spl
<=> compose(a,compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(a,compose(h,a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1502_spl])],[split_symbol_definition]) ).
fof(f15351,plain,
( sQ1502_spl
| ~ sQ21_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f15329,f2330,f693,f15348]) ).
fof(f15352,definition,
( sQ1503_spl
<=> compose(a,compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(a,compose(g,a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1503_spl])],[split_symbol_definition]) ).
fof(f15355,plain,
( sQ1503_spl
| ~ sQ21_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f15330,f2337,f693,f15352]) ).
fof(f15356,definition,
( sQ1504_spl
<=> compose(a,compose(g,compose(h,compose(a,b)))) = compose(compose(a,g),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1504_spl])],[split_symbol_definition]) ).
fof(f15359,plain,
( sQ1504_spl
| ~ sQ8_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f15331,f700,f584,f15356]) ).
fof(f15360,definition,
( sQ1505_spl
<=> compose(a,compose(h,compose(h,compose(a,b)))) = compose(compose(a,h),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1505_spl])],[split_symbol_definition]) ).
fof(f15363,plain,
( sQ1505_spl
| ~ sQ8_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15332,f693,f584,f15360]) ).
fof(f15364,definition,
( sQ1506_spl
<=> compose(a,compose(a,compose(h,compose(a,b)))) = compose(compose(a,a),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1506_spl])],[split_symbol_definition]) ).
fof(f15367,plain,
( sQ1506_spl
| ~ sQ21_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15333,f715,f693,f15364]) ).
fof(f15368,plain,
! [X0] :
( compose(a,compose(codomain(X0),compose(h,compose(a,b)))) = compose(compose(a,codomain(X0)),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f15334]) ).
fof(f15369,plain,
! [X0] :
( compose(a,compose(domain(X0),compose(h,compose(a,b)))) = compose(compose(a,domain(X0)),compose(h,compose(a,b)))
| domain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f15335]) ).
fof(f15370,plain,
( compose(h,compose(domain(compose(a,b)),compose(g,a))) = compose(compose(h,domain(compose(a,b))),compose(g,a))
| domain(compose(a,b)) != domain(h) ),
inference(resolution,[status(thm)],[f10193,f60]) ).
fof(f15371,plain,
( compose(h,compose(domain(domain(a)),compose(g,a))) = compose(compose(h,domain(domain(a))),compose(g,a))
| domain(domain(a)) != domain(h) ),
inference(resolution,[status(thm)],[f10193,f37]) ).
fof(f15372,plain,
( compose(h,compose(domain(compose(g,a)),compose(g,a))) = compose(compose(h,domain(compose(g,a))),compose(g,a))
| domain(compose(g,a)) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f10193]) ).
fof(f15373,plain,
( compose(h,compose(domain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(h,domain(compose(h,compose(a,b)))),compose(g,a))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f10193]) ).
fof(f15374,plain,
( compose(h,compose(domain(compose(h,a)),compose(g,a))) = compose(compose(h,domain(compose(h,a))),compose(g,a))
| domain(compose(h,a)) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f10193]) ).
fof(f15375,plain,
( compose(h,compose(domain(compose(a,b)),compose(g,a))) = compose(compose(h,domain(compose(a,b))),compose(g,a))
| domain(compose(a,b)) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f10193]) ).
fof(f15378,plain,
( compose(h,compose(domain(a),compose(g,a))) = compose(compose(h,domain(a)),compose(g,a))
| domain(a) != domain(h) ),
inference(equality_resolution,[status(thm)],[f10193]) ).
fof(f15379,definition,
( sQ1507_spl
<=> compose(h,compose(domain(compose(a,b)),compose(g,a))) = compose(compose(h,domain(compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1507_spl])],[split_symbol_definition]) ).
fof(f15382,plain,
( sQ1507_spl
| ~ sQ1467_spl ),
inference(split_clause,[status(thm)],[f15370,f15137,f15379]) ).
fof(f15383,definition,
( sQ1508_spl
<=> compose(h,compose(domain(domain(a)),compose(g,a))) = compose(compose(h,domain(domain(a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1508_spl])],[split_symbol_definition]) ).
fof(f15386,plain,
( sQ1508_spl
| ~ sQ1469_spl ),
inference(split_clause,[status(thm)],[f15371,f15144,f15383]) ).
fof(f15387,definition,
( sQ1509_spl
<=> compose(h,compose(domain(compose(g,a)),compose(g,a))) = compose(compose(h,domain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1509_spl])],[split_symbol_definition]) ).
fof(f15390,plain,
( sQ1509_spl
| ~ sQ1471_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15372,f584,f15151,f15387]) ).
fof(f15391,definition,
( sQ1510_spl
<=> compose(h,compose(domain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(h,domain(compose(h,compose(a,b)))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1510_spl])],[split_symbol_definition]) ).
fof(f15394,plain,
( sQ1510_spl
| ~ sQ49_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15373,f584,f1100,f15391]) ).
fof(f15395,definition,
( sQ1511_spl
<=> compose(h,compose(domain(compose(h,a)),compose(g,a))) = compose(compose(h,domain(compose(h,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1511_spl])],[split_symbol_definition]) ).
fof(f15398,plain,
( sQ1511_spl
| ~ sQ1474_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15374,f584,f15162,f15395]) ).
fof(f15399,plain,
( sQ1507_spl
| ~ sQ1467_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15375,f606,f15137,f15379]) ).
fof(f15406,definition,
( sQ1512_spl
<=> compose(h,compose(domain(a),compose(g,a))) = compose(compose(h,domain(a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1512_spl])],[split_symbol_definition]) ).
fof(f15409,plain,
( sQ1512_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15378,f584,f15406]) ).
fof(f15410,plain,
( compose(h,compose(codomain(g),compose(h,a))) = compose(compose(h,codomain(g)),compose(h,a))
| codomain(g) != domain(h) ),
inference(resolution,[status(thm)],[f10559,f74]) ).
fof(f15411,plain,
( compose(h,compose(codomain(h),compose(h,a))) = compose(compose(h,codomain(h)),compose(h,a))
| codomain(h) != domain(h) ),
inference(resolution,[status(thm)],[f10559,f69]) ).
fof(f15412,plain,
( compose(h,compose(codomain(domain(a)),compose(h,a))) = compose(compose(h,codomain(domain(a))),compose(h,a))
| codomain(domain(a)) != domain(h) ),
inference(resolution,[status(thm)],[f10559,f15]) ).
fof(f15413,plain,
( compose(h,compose(codomain(compose(a,b)),compose(h,a))) = compose(compose(h,codomain(compose(a,b))),compose(h,a))
| codomain(compose(a,b)) != domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f10559]) ).
fof(f15414,plain,
( compose(h,compose(codomain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(h,codomain(compose(h,compose(a,b)))),compose(h,a))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f10559]) ).
fof(f15415,plain,
( compose(h,compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(h,codomain(compose(h,a))),compose(h,a))
| codomain(compose(h,a)) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f10559]) ).
fof(f15416,plain,
( compose(h,compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(h,codomain(compose(g,a))),compose(h,a))
| codomain(compose(g,a)) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f10559]) ).
fof(f15417,plain,
( compose(h,compose(codomain(g),compose(h,a))) = compose(compose(h,codomain(g)),compose(h,a))
| codomain(g) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f10559]) ).
fof(f15418,plain,
( compose(h,compose(codomain(h),compose(h,a))) = compose(compose(h,codomain(h)),compose(h,a))
| codomain(h) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f10559]) ).
fof(f15419,plain,
( compose(h,compose(codomain(a),compose(h,a))) = compose(compose(h,codomain(a)),compose(h,a))
| codomain(a) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f10559]) ).
fof(f15422,definition,
( sQ1513_spl
<=> compose(h,compose(codomain(g),compose(h,a))) = compose(compose(h,codomain(g)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1513_spl])],[split_symbol_definition]) ).
fof(f15425,plain,
( sQ1513_spl
| ~ sQ1451_spl ),
inference(split_clause,[status(thm)],[f15410,f15061,f15422]) ).
fof(f15426,definition,
( sQ1514_spl
<=> compose(h,compose(codomain(h),compose(h,a))) = compose(compose(h,codomain(h)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1514_spl])],[split_symbol_definition]) ).
fof(f15429,plain,
( sQ1514_spl
| ~ sQ1453_spl ),
inference(split_clause,[status(thm)],[f15411,f15068,f15426]) ).
fof(f15430,definition,
( sQ1515_spl
<=> compose(h,compose(codomain(domain(a)),compose(h,a))) = compose(compose(h,codomain(domain(a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1515_spl])],[split_symbol_definition]) ).
fof(f15433,plain,
( sQ1515_spl
| ~ sQ1455_spl ),
inference(split_clause,[status(thm)],[f15412,f15075,f15430]) ).
fof(f15434,definition,
( sQ1516_spl
<=> compose(h,compose(codomain(compose(a,b)),compose(h,a))) = compose(compose(h,codomain(compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1516_spl])],[split_symbol_definition]) ).
fof(f15437,plain,
( sQ1516_spl
| ~ sQ1457_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f15413,f1570,f15082,f15434]) ).
fof(f15438,definition,
( sQ1517_spl
<=> compose(h,compose(codomain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(h,codomain(compose(h,compose(a,b)))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1517_spl])],[split_symbol_definition]) ).
fof(f15441,plain,
( sQ1517_spl
| ~ sQ1459_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f15414,f1570,f15089,f15438]) ).
fof(f15442,definition,
( sQ1518_spl
<=> compose(h,compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(h,codomain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1518_spl])],[split_symbol_definition]) ).
fof(f15445,plain,
( sQ1518_spl
| ~ sQ1461_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15415,f715,f15096,f15442]) ).
fof(f15446,definition,
( sQ1519_spl
<=> compose(h,compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(h,codomain(compose(g,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1519_spl])],[split_symbol_definition]) ).
fof(f15449,plain,
( sQ1519_spl
| ~ sQ1463_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15416,f715,f15103,f15446]) ).
fof(f15450,plain,
( sQ1513_spl
| ~ sQ1451_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15417,f606,f15061,f15422]) ).
fof(f15451,plain,
( sQ1514_spl
| ~ sQ1453_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15418,f606,f15068,f15426]) ).
fof(f15452,definition,
( sQ1520_spl
<=> compose(h,compose(codomain(a),compose(h,a))) = compose(compose(h,codomain(a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1520_spl])],[split_symbol_definition]) ).
fof(f15455,plain,
( sQ1520_spl
| ~ sQ1465_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15419,f715,f15112,f15452]) ).
fof(f15462,plain,
( compose(h,compose(domain(compose(a,b)),compose(h,a))) = compose(compose(h,domain(compose(a,b))),compose(h,a))
| domain(compose(a,b)) != domain(h) ),
inference(resolution,[status(thm)],[f10560,f60]) ).
fof(f15463,plain,
( compose(h,compose(domain(domain(a)),compose(h,a))) = compose(compose(h,domain(domain(a))),compose(h,a))
| domain(domain(a)) != domain(h) ),
inference(resolution,[status(thm)],[f10560,f37]) ).
fof(f15464,plain,
( compose(h,compose(domain(compose(g,a)),compose(h,a))) = compose(compose(h,domain(compose(g,a))),compose(h,a))
| domain(compose(g,a)) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f10560]) ).
fof(f15465,plain,
( compose(h,compose(domain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(h,domain(compose(h,compose(a,b)))),compose(h,a))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f10560]) ).
fof(f15466,plain,
( compose(h,compose(domain(compose(h,a)),compose(h,a))) = compose(compose(h,domain(compose(h,a))),compose(h,a))
| domain(compose(h,a)) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f10560]) ).
fof(f15467,plain,
( compose(h,compose(domain(compose(a,b)),compose(h,a))) = compose(compose(h,domain(compose(a,b))),compose(h,a))
| domain(compose(a,b)) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f10560]) ).
fof(f15470,plain,
( compose(h,compose(domain(a),compose(h,a))) = compose(compose(h,domain(a)),compose(h,a))
| domain(a) != domain(h) ),
inference(equality_resolution,[status(thm)],[f10560]) ).
fof(f15471,definition,
( sQ1521_spl
<=> compose(h,compose(domain(compose(a,b)),compose(h,a))) = compose(compose(h,domain(compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1521_spl])],[split_symbol_definition]) ).
fof(f15474,plain,
( sQ1521_spl
| ~ sQ1467_spl ),
inference(split_clause,[status(thm)],[f15462,f15137,f15471]) ).
fof(f15475,definition,
( sQ1522_spl
<=> compose(h,compose(domain(domain(a)),compose(h,a))) = compose(compose(h,domain(domain(a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1522_spl])],[split_symbol_definition]) ).
fof(f15478,plain,
( sQ1522_spl
| ~ sQ1469_spl ),
inference(split_clause,[status(thm)],[f15463,f15144,f15475]) ).
fof(f15479,definition,
( sQ1523_spl
<=> compose(h,compose(domain(compose(g,a)),compose(h,a))) = compose(compose(h,domain(compose(g,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1523_spl])],[split_symbol_definition]) ).
fof(f15482,plain,
( sQ1523_spl
| ~ sQ1471_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15464,f584,f15151,f15479]) ).
fof(f15483,definition,
( sQ1524_spl
<=> compose(h,compose(domain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(h,domain(compose(h,compose(a,b)))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1524_spl])],[split_symbol_definition]) ).
fof(f15486,plain,
( sQ1524_spl
| ~ sQ49_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15465,f584,f1100,f15483]) ).
fof(f15487,definition,
( sQ1525_spl
<=> compose(h,compose(domain(compose(h,a)),compose(h,a))) = compose(compose(h,domain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1525_spl])],[split_symbol_definition]) ).
fof(f15490,plain,
( sQ1525_spl
| ~ sQ1474_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15466,f584,f15162,f15487]) ).
fof(f15491,plain,
( sQ1521_spl
| ~ sQ1467_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15467,f606,f15137,f15471]) ).
fof(f15498,definition,
( sQ1526_spl
<=> compose(h,compose(domain(a),compose(h,a))) = compose(compose(h,domain(a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1526_spl])],[split_symbol_definition]) ).
fof(f15501,plain,
( sQ1526_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15470,f584,f15498]) ).
fof(f15502,plain,
( compose(a,compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(a,codomain(compose(h,a))),compose(g,a))
| codomain(compose(h,a)) != domain(h) ),
inference(resolution,[status(thm)],[f11111,f131]) ).
fof(f15503,plain,
( compose(a,compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(a,codomain(compose(g,a))),compose(g,a))
| codomain(compose(g,a)) != domain(h) ),
inference(resolution,[status(thm)],[f11111,f130]) ).
fof(f15504,plain,
( compose(a,compose(codomain(a),compose(g,a))) = compose(compose(a,codomain(a)),compose(g,a))
| codomain(a) != domain(h) ),
inference(resolution,[status(thm)],[f11111,f22]) ).
fof(f15505,plain,
( compose(a,compose(codomain(domain(b)),compose(g,a))) = compose(compose(a,codomain(domain(b))),compose(g,a))
| codomain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f11111,f15]) ).
fof(f15506,plain,
( compose(a,compose(codomain(compose(a,b)),compose(g,a))) = compose(compose(a,codomain(compose(a,b))),compose(g,a))
| codomain(compose(a,b)) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f11111]) ).
fof(f15507,plain,
( compose(a,compose(codomain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(a,codomain(compose(h,compose(a,b)))),compose(g,a))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f11111]) ).
fof(f15508,plain,
( compose(a,compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(a,codomain(compose(h,a))),compose(g,a))
| codomain(compose(h,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f11111]) ).
fof(f15509,plain,
( compose(a,compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(a,codomain(compose(g,a))),compose(g,a))
| codomain(compose(g,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f11111]) ).
fof(f15510,plain,
( compose(a,compose(codomain(g),compose(g,a))) = compose(compose(a,codomain(g)),compose(g,a))
| codomain(g) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f11111]) ).
fof(f15511,plain,
( compose(a,compose(codomain(h),compose(g,a))) = compose(compose(a,codomain(h)),compose(g,a))
| codomain(h) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f11111]) ).
fof(f15512,plain,
( compose(a,compose(codomain(a),compose(g,a))) = compose(compose(a,codomain(a)),compose(g,a))
| codomain(a) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f11111]) ).
fof(f15515,definition,
( sQ1527_spl
<=> compose(a,compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(a,codomain(compose(h,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1527_spl])],[split_symbol_definition]) ).
fof(f15518,plain,
( sQ1527_spl
| ~ sQ1461_spl ),
inference(split_clause,[status(thm)],[f15502,f15096,f15515]) ).
fof(f15519,definition,
( sQ1528_spl
<=> compose(a,compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(a,codomain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1528_spl])],[split_symbol_definition]) ).
fof(f15522,plain,
( sQ1528_spl
| ~ sQ1463_spl ),
inference(split_clause,[status(thm)],[f15503,f15103,f15519]) ).
fof(f15523,definition,
( sQ1529_spl
<=> compose(a,compose(codomain(a),compose(g,a))) = compose(compose(a,codomain(a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1529_spl])],[split_symbol_definition]) ).
fof(f15526,plain,
( sQ1529_spl
| ~ sQ1465_spl ),
inference(split_clause,[status(thm)],[f15504,f15112,f15523]) ).
fof(f15527,definition,
( sQ1530_spl
<=> codomain(domain(b)) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ1530_spl])],[split_symbol_definition]) ).
fof(f15529,plain,
( sQ1530_spl
| codomain(domain(b)) != domain(h) ),
inference(component_clause,[status(thm)],[f15527]) ).
fof(f15530,definition,
( sQ1531_spl
<=> compose(a,compose(codomain(domain(b)),compose(g,a))) = compose(compose(a,codomain(domain(b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1531_spl])],[split_symbol_definition]) ).
fof(f15533,plain,
( sQ1531_spl
| ~ sQ1530_spl ),
inference(split_clause,[status(thm)],[f15505,f15527,f15530]) ).
fof(f15534,definition,
( sQ1532_spl
<=> compose(a,compose(codomain(compose(a,b)),compose(g,a))) = compose(compose(a,codomain(compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1532_spl])],[split_symbol_definition]) ).
fof(f15537,plain,
( sQ1532_spl
| ~ sQ1457_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f15506,f2265,f15082,f15534]) ).
fof(f15538,definition,
( sQ1533_spl
<=> compose(a,compose(codomain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(a,codomain(compose(h,compose(a,b)))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1533_spl])],[split_symbol_definition]) ).
fof(f15541,plain,
( sQ1533_spl
| ~ sQ1459_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f15507,f2265,f15089,f15538]) ).
fof(f15542,plain,
( sQ1527_spl
| ~ sQ1461_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15508,f1941,f15096,f15515]) ).
fof(f15543,plain,
( sQ1528_spl
| ~ sQ1463_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15509,f1941,f15103,f15519]) ).
fof(f15544,definition,
( sQ1534_spl
<=> compose(a,compose(codomain(g),compose(g,a))) = compose(compose(a,codomain(g)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1534_spl])],[split_symbol_definition]) ).
fof(f15547,plain,
( sQ1534_spl
| ~ sQ1451_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15510,f715,f15061,f15544]) ).
fof(f15548,definition,
( sQ1535_spl
<=> compose(a,compose(codomain(h),compose(g,a))) = compose(compose(a,codomain(h)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1535_spl])],[split_symbol_definition]) ).
fof(f15551,plain,
( sQ1535_spl
| ~ sQ1453_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15511,f715,f15068,f15548]) ).
fof(f15552,plain,
( sQ1529_spl
| ~ sQ1465_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15512,f1941,f15112,f15523]) ).
fof(f15559,plain,
( sQ1461_spl
| domain(b) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f131,f15098]) ).
fof(f15560,plain,
( sQ1463_spl
| domain(b) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f130,f15105]) ).
fof(f15561,plain,
( sQ1465_spl
| domain(b) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f22,f15114]) ).
fof(f15562,plain,
( sQ1530_spl
| domain(b) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f15,f15529]) ).
fof(f15563,plain,
( compose(a,compose(domain(domain(b)),compose(g,a))) = compose(compose(a,domain(domain(b))),compose(g,a))
| domain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f11112,f37]) ).
fof(f15564,plain,
( compose(a,compose(domain(compose(g,a)),compose(g,a))) = compose(compose(a,domain(compose(g,a))),compose(g,a))
| domain(compose(g,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f11112]) ).
fof(f15565,plain,
( compose(a,compose(domain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(a,domain(compose(h,compose(a,b)))),compose(g,a))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f11112]) ).
fof(f15566,plain,
( compose(a,compose(domain(compose(h,a)),compose(g,a))) = compose(compose(a,domain(compose(h,a))),compose(g,a))
| domain(compose(h,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f11112]) ).
fof(f15567,plain,
( compose(a,compose(domain(compose(a,b)),compose(g,a))) = compose(compose(a,domain(compose(a,b))),compose(g,a))
| domain(compose(a,b)) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f11112]) ).
fof(f15570,plain,
( compose(a,compose(domain(b),compose(g,a))) = compose(compose(a,domain(b)),compose(g,a))
| domain(b) != domain(h) ),
inference(equality_resolution,[status(thm)],[f11112]) ).
fof(f15571,definition,
( sQ1536_spl
<=> domain(domain(b)) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ1536_spl])],[split_symbol_definition]) ).
fof(f15573,plain,
( sQ1536_spl
| domain(domain(b)) != domain(h) ),
inference(component_clause,[status(thm)],[f15571]) ).
fof(f15574,definition,
( sQ1537_spl
<=> compose(a,compose(domain(domain(b)),compose(g,a))) = compose(compose(a,domain(domain(b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1537_spl])],[split_symbol_definition]) ).
fof(f15577,plain,
( sQ1537_spl
| ~ sQ1536_spl ),
inference(split_clause,[status(thm)],[f15563,f15571,f15574]) ).
fof(f15578,definition,
( sQ1538_spl
<=> compose(a,compose(domain(compose(g,a)),compose(g,a))) = compose(compose(a,domain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1538_spl])],[split_symbol_definition]) ).
fof(f15581,plain,
( sQ1538_spl
| ~ sQ1471_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15564,f693,f15151,f15578]) ).
fof(f15582,definition,
( sQ1539_spl
<=> compose(a,compose(domain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(a,domain(compose(h,compose(a,b)))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1539_spl])],[split_symbol_definition]) ).
fof(f15585,plain,
( sQ1539_spl
| ~ sQ49_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15565,f693,f1100,f15582]) ).
fof(f15586,definition,
( sQ1540_spl
<=> compose(a,compose(domain(compose(h,a)),compose(g,a))) = compose(compose(a,domain(compose(h,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1540_spl])],[split_symbol_definition]) ).
fof(f15589,plain,
( sQ1540_spl
| ~ sQ1474_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15566,f693,f15162,f15586]) ).
fof(f15590,definition,
( sQ1541_spl
<=> compose(a,compose(domain(compose(a,b)),compose(g,a))) = compose(compose(a,domain(compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1541_spl])],[split_symbol_definition]) ).
fof(f15593,plain,
( sQ1541_spl
| ~ sQ1467_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15567,f715,f15137,f15590]) ).
fof(f15600,definition,
( sQ1542_spl
<=> compose(a,compose(domain(b),compose(g,a))) = compose(compose(a,domain(b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1542_spl])],[split_symbol_definition]) ).
fof(f15603,plain,
( sQ1542_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15570,f693,f15600]) ).
fof(f15604,plain,
( sQ1536_spl
| domain(b) != domain(h) ),
inference(forward_demodulation,[status(thm)],[f37,f15573]) ).
fof(f15610,plain,
! [X0] :
( compose(domain(g),compose(compose(h,compose(a,b)),X0)) = compose(compose(domain(g),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1079,f2804]) ).
fof(f15611,plain,
! [X0] :
( compose(domain(compose(g,a)),compose(compose(h,compose(a,b)),X0)) = compose(compose(domain(compose(g,a)),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f2804]) ).
fof(f15612,plain,
! [X0] :
( compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),X0)) = compose(compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f2804]) ).
fof(f15613,plain,
! [X0] :
( compose(domain(compose(h,a)),compose(compose(h,compose(a,b)),X0)) = compose(compose(domain(compose(h,a)),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(h) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f2804]) ).
fof(f15614,plain,
! [X0] :
( compose(domain(compose(a,b)),compose(compose(h,compose(a,b)),X0)) = compose(compose(domain(compose(a,b)),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f60,f2804]) ).
fof(f15632,definition,
! [X0] :
( sQ1543_spl
<=> ( compose(domain(g),compose(compose(h,compose(a,b)),X0)) = compose(compose(domain(g),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1543_spl])],[split_symbol_definition]) ).
fof(f15635,plain,
( sQ1543_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f15610,f2687,f15632]) ).
fof(f15636,definition,
! [X0] :
( sQ1544_spl
<=> ( compose(domain(compose(g,a)),compose(compose(h,compose(a,b)),X0)) = compose(compose(domain(compose(g,a)),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1544_spl])],[split_symbol_definition]) ).
fof(f15639,plain,
( sQ1544_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f15611,f2687,f15636]) ).
fof(f15640,definition,
! [X0] :
( sQ1545_spl
<=> ( compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),X0)) = compose(compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1545_spl])],[split_symbol_definition]) ).
fof(f15643,plain,
( sQ1545_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f15612,f2687,f15640]) ).
fof(f15644,definition,
! [X0] :
( sQ1546_spl
<=> ( compose(domain(compose(h,a)),compose(compose(h,compose(a,b)),X0)) = compose(compose(domain(compose(h,a)),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1546_spl])],[split_symbol_definition]) ).
fof(f15647,plain,
( sQ1546_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f15613,f2687,f15644]) ).
fof(f15648,definition,
! [X0] :
( sQ1547_spl
<=> ( compose(domain(compose(a,b)),compose(compose(h,compose(a,b)),X0)) = compose(compose(domain(compose(a,b)),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1547_spl])],[split_symbol_definition]) ).
fof(f15651,plain,
( sQ1547_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f15614,f584,f15648]) ).
fof(f15668,plain,
( compose(a,compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(a,codomain(compose(h,a))),compose(h,a))
| codomain(compose(h,a)) != domain(h) ),
inference(resolution,[status(thm)],[f11389,f131]) ).
fof(f15669,plain,
( compose(a,compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(a,codomain(compose(g,a))),compose(h,a))
| codomain(compose(g,a)) != domain(h) ),
inference(resolution,[status(thm)],[f11389,f130]) ).
fof(f15670,plain,
( compose(a,compose(codomain(a),compose(h,a))) = compose(compose(a,codomain(a)),compose(h,a))
| codomain(a) != domain(h) ),
inference(resolution,[status(thm)],[f11389,f22]) ).
fof(f15671,plain,
( compose(a,compose(codomain(domain(b)),compose(h,a))) = compose(compose(a,codomain(domain(b))),compose(h,a))
| codomain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f11389,f15]) ).
fof(f15672,plain,
( compose(a,compose(codomain(compose(a,b)),compose(h,a))) = compose(compose(a,codomain(compose(a,b))),compose(h,a))
| codomain(compose(a,b)) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f11389]) ).
fof(f15673,plain,
( compose(a,compose(codomain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(a,codomain(compose(h,compose(a,b)))),compose(h,a))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f11389]) ).
fof(f15674,plain,
( compose(a,compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(a,codomain(compose(h,a))),compose(h,a))
| codomain(compose(h,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f11389]) ).
fof(f15675,plain,
( compose(a,compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(a,codomain(compose(g,a))),compose(h,a))
| codomain(compose(g,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f11389]) ).
fof(f15676,plain,
( compose(a,compose(codomain(g),compose(h,a))) = compose(compose(a,codomain(g)),compose(h,a))
| codomain(g) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f11389]) ).
fof(f15677,plain,
( compose(a,compose(codomain(h),compose(h,a))) = compose(compose(a,codomain(h)),compose(h,a))
| codomain(h) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f11389]) ).
fof(f15678,plain,
( compose(a,compose(codomain(a),compose(h,a))) = compose(compose(a,codomain(a)),compose(h,a))
| codomain(a) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f11389]) ).
fof(f15681,definition,
( sQ1548_spl
<=> compose(a,compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(a,codomain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1548_spl])],[split_symbol_definition]) ).
fof(f15684,plain,
( sQ1548_spl
| ~ sQ1461_spl ),
inference(split_clause,[status(thm)],[f15668,f15096,f15681]) ).
fof(f15685,definition,
( sQ1549_spl
<=> compose(a,compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(a,codomain(compose(g,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1549_spl])],[split_symbol_definition]) ).
fof(f15688,plain,
( sQ1549_spl
| ~ sQ1463_spl ),
inference(split_clause,[status(thm)],[f15669,f15103,f15685]) ).
fof(f15689,definition,
( sQ1550_spl
<=> compose(a,compose(codomain(a),compose(h,a))) = compose(compose(a,codomain(a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1550_spl])],[split_symbol_definition]) ).
fof(f15692,plain,
( sQ1550_spl
| ~ sQ1465_spl ),
inference(split_clause,[status(thm)],[f15670,f15112,f15689]) ).
fof(f15693,definition,
( sQ1551_spl
<=> compose(a,compose(codomain(domain(b)),compose(h,a))) = compose(compose(a,codomain(domain(b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1551_spl])],[split_symbol_definition]) ).
fof(f15696,plain,
( sQ1551_spl
| ~ sQ1530_spl ),
inference(split_clause,[status(thm)],[f15671,f15527,f15693]) ).
fof(f15697,definition,
( sQ1552_spl
<=> compose(a,compose(codomain(compose(a,b)),compose(h,a))) = compose(compose(a,codomain(compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1552_spl])],[split_symbol_definition]) ).
fof(f15700,plain,
( sQ1552_spl
| ~ sQ1457_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f15672,f2265,f15082,f15697]) ).
fof(f15701,definition,
( sQ1553_spl
<=> compose(a,compose(codomain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(a,codomain(compose(h,compose(a,b)))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1553_spl])],[split_symbol_definition]) ).
fof(f15704,plain,
( sQ1553_spl
| ~ sQ1459_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f15673,f2265,f15089,f15701]) ).
fof(f15705,plain,
( sQ1548_spl
| ~ sQ1461_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15674,f1941,f15096,f15681]) ).
fof(f15706,plain,
( sQ1549_spl
| ~ sQ1463_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15675,f1941,f15103,f15685]) ).
fof(f15707,definition,
( sQ1554_spl
<=> compose(a,compose(codomain(g),compose(h,a))) = compose(compose(a,codomain(g)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1554_spl])],[split_symbol_definition]) ).
fof(f15710,plain,
( sQ1554_spl
| ~ sQ1451_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15676,f715,f15061,f15707]) ).
fof(f15711,definition,
( sQ1555_spl
<=> compose(a,compose(codomain(h),compose(h,a))) = compose(compose(a,codomain(h)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1555_spl])],[split_symbol_definition]) ).
fof(f15714,plain,
( sQ1555_spl
| ~ sQ1453_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15677,f715,f15068,f15711]) ).
fof(f15715,plain,
( sQ1550_spl
| ~ sQ1465_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15678,f1941,f15112,f15689]) ).
fof(f15722,plain,
( compose(a,compose(domain(domain(b)),compose(h,a))) = compose(compose(a,domain(domain(b))),compose(h,a))
| domain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f11390,f37]) ).
fof(f15723,plain,
( compose(a,compose(domain(compose(g,a)),compose(h,a))) = compose(compose(a,domain(compose(g,a))),compose(h,a))
| domain(compose(g,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f11390]) ).
fof(f15724,plain,
( compose(a,compose(domain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(a,domain(compose(h,compose(a,b)))),compose(h,a))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f11390]) ).
fof(f15725,plain,
( compose(a,compose(domain(compose(h,a)),compose(h,a))) = compose(compose(a,domain(compose(h,a))),compose(h,a))
| domain(compose(h,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f11390]) ).
fof(f15726,plain,
( compose(a,compose(domain(compose(a,b)),compose(h,a))) = compose(compose(a,domain(compose(a,b))),compose(h,a))
| domain(compose(a,b)) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f11390]) ).
fof(f15729,plain,
( compose(a,compose(domain(b),compose(h,a))) = compose(compose(a,domain(b)),compose(h,a))
| domain(b) != domain(h) ),
inference(equality_resolution,[status(thm)],[f11390]) ).
fof(f15730,definition,
( sQ1556_spl
<=> compose(a,compose(domain(domain(b)),compose(h,a))) = compose(compose(a,domain(domain(b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1556_spl])],[split_symbol_definition]) ).
fof(f15733,plain,
( sQ1556_spl
| ~ sQ1536_spl ),
inference(split_clause,[status(thm)],[f15722,f15571,f15730]) ).
fof(f15734,definition,
( sQ1557_spl
<=> compose(a,compose(domain(compose(g,a)),compose(h,a))) = compose(compose(a,domain(compose(g,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1557_spl])],[split_symbol_definition]) ).
fof(f15737,plain,
( sQ1557_spl
| ~ sQ1471_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15723,f693,f15151,f15734]) ).
fof(f15738,definition,
( sQ1558_spl
<=> compose(a,compose(domain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(a,domain(compose(h,compose(a,b)))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1558_spl])],[split_symbol_definition]) ).
fof(f15741,plain,
( sQ1558_spl
| ~ sQ49_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15724,f693,f1100,f15738]) ).
fof(f15742,definition,
( sQ1559_spl
<=> compose(a,compose(domain(compose(h,a)),compose(h,a))) = compose(compose(a,domain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1559_spl])],[split_symbol_definition]) ).
fof(f15745,plain,
( sQ1559_spl
| ~ sQ1474_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15725,f693,f15162,f15742]) ).
fof(f15746,definition,
( sQ1560_spl
<=> compose(a,compose(domain(compose(a,b)),compose(h,a))) = compose(compose(a,domain(compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1560_spl])],[split_symbol_definition]) ).
fof(f15749,plain,
( sQ1560_spl
| ~ sQ1467_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15726,f715,f15137,f15746]) ).
fof(f15756,definition,
( sQ1561_spl
<=> compose(a,compose(domain(b),compose(h,a))) = compose(compose(a,domain(b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1561_spl])],[split_symbol_definition]) ).
fof(f15759,plain,
( sQ1561_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15729,f693,f15756]) ).
fof(f15760,plain,
( compose(a,compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(a,codomain(compose(h,a))),compose(a,b))
| codomain(compose(h,a)) != domain(a) ),
inference(resolution,[status(thm)],[f11708,f131]) ).
fof(f15761,plain,
( compose(a,compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(a,codomain(compose(g,a))),compose(a,b))
| codomain(compose(g,a)) != domain(a) ),
inference(resolution,[status(thm)],[f11708,f130]) ).
fof(f15762,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)],[f11708,f22]) ).
fof(f15763,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)],[f11708,f15]) ).
fof(f15764,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)],[f120,f11708]) ).
fof(f15765,plain,
( compose(a,compose(codomain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(a,codomain(compose(h,compose(a,b)))),compose(a,b))
| codomain(compose(h,compose(a,b))) != domain(a)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f11708]) ).
fof(f15766,plain,
( compose(a,compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(a,codomain(compose(h,a))),compose(a,b))
| codomain(compose(h,a)) != domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f11708]) ).
fof(f15767,plain,
( compose(a,compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(a,codomain(compose(g,a))),compose(a,b))
| codomain(compose(g,a)) != domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f11708]) ).
fof(f15768,plain,
( compose(a,compose(codomain(g),compose(a,b))) = compose(compose(a,codomain(g)),compose(a,b))
| codomain(g) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f11708]) ).
fof(f15769,plain,
( compose(a,compose(codomain(h),compose(a,b))) = compose(compose(a,codomain(h)),compose(a,b))
| codomain(h) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f11708]) ).
fof(f15770,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)],[f22,f11708]) ).
fof(f15773,definition,
( sQ1562_spl
<=> compose(a,compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(a,codomain(compose(h,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1562_spl])],[split_symbol_definition]) ).
fof(f15776,plain,
( sQ1562_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f15760,f3284,f15773]) ).
fof(f15777,definition,
( sQ1563_spl
<=> compose(a,compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(a,codomain(compose(g,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1563_spl])],[split_symbol_definition]) ).
fof(f15780,plain,
( sQ1563_spl
| ~ sQ203_spl ),
inference(split_clause,[status(thm)],[f15761,f3216,f15777]) ).
fof(f15781,definition,
( sQ1564_spl
<=> compose(a,compose(codomain(a),compose(a,b))) = compose(compose(a,codomain(a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1564_spl])],[split_symbol_definition]) ).
fof(f15784,plain,
( sQ1564_spl
| ~ sQ1133_spl ),
inference(split_clause,[status(thm)],[f15762,f12077,f15781]) ).
fof(f15785,definition,
( sQ1565_spl
<=> compose(a,compose(codomain(domain(b)),compose(a,b))) = compose(compose(a,codomain(domain(b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1565_spl])],[split_symbol_definition]) ).
fof(f15788,plain,
( sQ1565_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f15763,f562,f15785]) ).
fof(f15789,definition,
( sQ1566_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,[sQ1566_spl])],[split_symbol_definition]) ).
fof(f15792,plain,
( sQ1566_spl
| ~ sQ1119_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f15764,f2265,f12019,f15789]) ).
fof(f15793,definition,
( sQ1567_spl
<=> compose(a,compose(codomain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(a,codomain(compose(h,compose(a,b)))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1567_spl])],[split_symbol_definition]) ).
fof(f15796,plain,
( sQ1567_spl
| ~ sQ1121_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f15765,f2265,f12026,f15793]) ).
fof(f15797,plain,
( sQ1562_spl
| ~ sQ216_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15766,f1941,f3284,f15773]) ).
fof(f15798,plain,
( sQ1563_spl
| ~ sQ203_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15767,f1941,f3216,f15777]) ).
fof(f15799,definition,
( sQ1568_spl
<=> compose(a,compose(codomain(g),compose(a,b))) = compose(compose(a,codomain(g)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1568_spl])],[split_symbol_definition]) ).
fof(f15802,plain,
( sQ1568_spl
| ~ sQ1129_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15768,f715,f12063,f15799]) ).
fof(f15803,definition,
( sQ1569_spl
<=> compose(a,compose(codomain(h),compose(a,b))) = compose(compose(a,codomain(h)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1569_spl])],[split_symbol_definition]) ).
fof(f15806,plain,
( sQ1569_spl
| ~ sQ1131_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15769,f715,f12070,f15803]) ).
fof(f15807,plain,
( sQ1564_spl
| ~ sQ1133_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15770,f1941,f12077,f15781]) ).
fof(f15814,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)],[f11709,f37]) ).
fof(f15815,plain,
( compose(a,compose(domain(compose(g,a)),compose(a,b))) = compose(compose(a,domain(compose(g,a))),compose(a,b))
| domain(compose(g,a)) != domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f11709]) ).
fof(f15816,plain,
( compose(a,compose(domain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(a,domain(compose(h,compose(a,b)))),compose(a,b))
| domain(compose(h,compose(a,b))) != domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f11709]) ).
fof(f15817,plain,
( compose(a,compose(domain(compose(h,a)),compose(a,b))) = compose(compose(a,domain(compose(h,a))),compose(a,b))
| domain(compose(h,a)) != domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f11709]) ).
fof(f15818,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)],[f60,f11709]) ).
fof(f15821,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)],[f11709]) ).
fof(f15822,definition,
( sQ1570_spl
<=> domain(domain(b)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ1570_spl])],[split_symbol_definition]) ).
fof(f15824,plain,
( sQ1570_spl
| domain(domain(b)) != domain(a) ),
inference(component_clause,[status(thm)],[f15822]) ).
fof(f15825,definition,
( sQ1571_spl
<=> compose(a,compose(domain(domain(b)),compose(a,b))) = compose(compose(a,domain(domain(b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1571_spl])],[split_symbol_definition]) ).
fof(f15828,plain,
( sQ1571_spl
| ~ sQ1570_spl ),
inference(split_clause,[status(thm)],[f15814,f15822,f15825]) ).
fof(f15829,definition,
( sQ1572_spl
<=> compose(a,compose(domain(compose(g,a)),compose(a,b))) = compose(compose(a,domain(compose(g,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1572_spl])],[split_symbol_definition]) ).
fof(f15832,plain,
( sQ1572_spl
| ~ sQ74_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15815,f693,f1743,f15829]) ).
fof(f15833,definition,
( sQ1573_spl
<=> compose(a,compose(domain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(a,domain(compose(h,compose(a,b)))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1573_spl])],[split_symbol_definition]) ).
fof(f15836,plain,
( sQ1573_spl
| ~ sQ81_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15816,f693,f1772,f15833]) ).
fof(f15837,definition,
( sQ1574_spl
<=> compose(a,compose(domain(compose(h,a)),compose(a,b))) = compose(compose(a,domain(compose(h,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1574_spl])],[split_symbol_definition]) ).
fof(f15840,plain,
( sQ1574_spl
| ~ sQ72_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15817,f693,f1736,f15837]) ).
fof(f15841,definition,
( sQ1575_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,[sQ1575_spl])],[split_symbol_definition]) ).
fof(f15844,plain,
( sQ1575_spl
| ~ sQ79_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15818,f715,f1765,f15841]) ).
fof(f15851,definition,
( sQ1576_spl
<=> compose(a,compose(domain(b),compose(a,b))) = compose(compose(a,domain(b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1576_spl])],[split_symbol_definition]) ).
fof(f15854,plain,
( sQ1576_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15821,f715,f15851]) ).
fof(f15855,plain,
( sQ1570_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f37,f15824]) ).
fof(f15860,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(a,b)),domain(X0))) = compose(compose(compose(g,a),codomain(compose(a,b))),domain(X0))
| codomain(compose(a,b)) != domain(X0)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f14132]) ).
fof(f15861,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),domain(X0))
| codomain(compose(h,compose(a,b))) != domain(X0)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f14132]) ).
fof(f15862,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(h,a)),domain(X0))) = compose(compose(compose(g,a),codomain(compose(h,a))),domain(X0))
| codomain(compose(h,a)) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f14132]) ).
fof(f15863,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(g,a)),domain(X0))) = compose(compose(compose(g,a),codomain(compose(g,a))),domain(X0))
| codomain(compose(g,a)) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f14132]) ).
fof(f15864,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(g),domain(X0))) = compose(compose(compose(g,a),codomain(g)),domain(X0))
| codomain(g) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f14132]) ).
fof(f15865,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(h),domain(X0))) = compose(compose(compose(g,a),codomain(h)),domain(X0))
| codomain(h) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f14132]) ).
fof(f15866,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(a),domain(X0))) = compose(compose(compose(g,a),codomain(a)),domain(X0))
| codomain(a) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f14132]) ).
fof(f15884,definition,
! [X0] :
( sQ1577_spl
<=> ( compose(compose(g,a),compose(codomain(compose(a,b)),domain(X0))) = compose(compose(compose(g,a),codomain(compose(a,b))),domain(X0))
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1577_spl])],[split_symbol_definition]) ).
fof(f15887,plain,
( sQ1577_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f15860,f2265,f15884]) ).
fof(f15888,definition,
! [X0] :
( sQ1578_spl
<=> ( compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),domain(X0))
| codomain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1578_spl])],[split_symbol_definition]) ).
fof(f15891,plain,
( sQ1578_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f15861,f2265,f15888]) ).
fof(f15892,definition,
! [X0] :
( sQ1579_spl
<=> ( compose(compose(g,a),compose(codomain(compose(h,a)),domain(X0))) = compose(compose(compose(g,a),codomain(compose(h,a))),domain(X0))
| codomain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1579_spl])],[split_symbol_definition]) ).
fof(f15895,plain,
( sQ1579_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15862,f1941,f15892]) ).
fof(f15896,definition,
! [X0] :
( sQ1580_spl
<=> ( compose(compose(g,a),compose(codomain(compose(g,a)),domain(X0))) = compose(compose(compose(g,a),codomain(compose(g,a))),domain(X0))
| codomain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1580_spl])],[split_symbol_definition]) ).
fof(f15899,plain,
( sQ1580_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15863,f1941,f15896]) ).
fof(f15900,definition,
! [X0] :
( sQ1581_spl
<=> ( compose(compose(g,a),compose(codomain(g),domain(X0))) = compose(compose(compose(g,a),codomain(g)),domain(X0))
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1581_spl])],[split_symbol_definition]) ).
fof(f15903,plain,
( sQ1581_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15864,f715,f15900]) ).
fof(f15904,definition,
! [X0] :
( sQ1582_spl
<=> ( compose(compose(g,a),compose(codomain(h),domain(X0))) = compose(compose(compose(g,a),codomain(h)),domain(X0))
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1582_spl])],[split_symbol_definition]) ).
fof(f15907,plain,
( sQ1582_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15865,f715,f15904]) ).
fof(f15908,definition,
! [X0] :
( sQ1583_spl
<=> ( compose(compose(g,a),compose(codomain(a),domain(X0))) = compose(compose(compose(g,a),codomain(a)),domain(X0))
| codomain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1583_spl])],[split_symbol_definition]) ).
fof(f15911,plain,
( sQ1583_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15866,f1941,f15908]) ).
fof(f15932,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(codomain(compose(a,b)),X0)) = compose(compose(compose(h,compose(a,b)),codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0)
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f2968]) ).
fof(f15933,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b)))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0)
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f2968]) ).
fof(f15934,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(codomain(compose(h,a)),X0)) = compose(compose(compose(h,compose(a,b)),codomain(compose(h,a))),X0)
| codomain(compose(h,a)) != domain(X0)
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f2968]) ).
fof(f15935,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(codomain(compose(g,a)),X0)) = compose(compose(compose(h,compose(a,b)),codomain(compose(g,a))),X0)
| codomain(compose(g,a)) != domain(X0)
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f2968]) ).
fof(f15950,definition,
! [X0] :
( sQ1584_spl
<=> ( compose(compose(h,compose(a,b)),compose(codomain(compose(a,b)),X0)) = compose(compose(compose(h,compose(a,b)),codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1584_spl])],[split_symbol_definition]) ).
fof(f15953,plain,
( sQ1584_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f15932,f4389,f15950]) ).
fof(f15954,definition,
! [X0] :
( sQ1585_spl
<=> ( compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),X0)) = compose(compose(compose(h,compose(a,b)),codomain(compose(h,compose(a,b)))),X0)
| codomain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1585_spl])],[split_symbol_definition]) ).
fof(f15957,plain,
( sQ1585_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f15933,f4389,f15954]) ).
fof(f15958,definition,
! [X0] :
( sQ1586_spl
<=> ( compose(compose(h,compose(a,b)),compose(codomain(compose(h,a)),X0)) = compose(compose(compose(h,compose(a,b)),codomain(compose(h,a))),X0)
| codomain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1586_spl])],[split_symbol_definition]) ).
fof(f15961,plain,
( sQ1586_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f15934,f2265,f15958]) ).
fof(f15962,definition,
! [X0] :
( sQ1587_spl
<=> ( compose(compose(h,compose(a,b)),compose(codomain(compose(g,a)),X0)) = compose(compose(compose(h,compose(a,b)),codomain(compose(g,a))),X0)
| codomain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1587_spl])],[split_symbol_definition]) ).
fof(f15965,plain,
( sQ1587_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f15935,f2265,f15962]) ).
fof(f15981,plain,
! [X0] :
( compose(compose(g,a),compose(domain(compose(g,a)),domain(X0))) = compose(compose(compose(g,a),domain(compose(g,a))),domain(X0))
| domain(compose(g,a)) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f14133]) ).
fof(f15982,plain,
! [X0] :
( compose(compose(g,a),compose(domain(compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),domain(X0))
| domain(compose(h,compose(a,b))) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f14133]) ).
fof(f15983,plain,
! [X0] :
( compose(compose(g,a),compose(domain(compose(h,a)),domain(X0))) = compose(compose(compose(g,a),domain(compose(h,a))),domain(X0))
| domain(compose(h,a)) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f14133]) ).
fof(f15984,plain,
! [X0] :
( compose(compose(g,a),compose(domain(compose(a,b)),domain(X0))) = compose(compose(compose(g,a),domain(compose(a,b))),domain(X0))
| domain(compose(a,b)) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f14133]) ).
fof(f15992,definition,
! [X0] :
( sQ1588_spl
<=> ( compose(compose(g,a),compose(domain(compose(g,a)),domain(X0))) = compose(compose(compose(g,a),domain(compose(g,a))),domain(X0))
| domain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1588_spl])],[split_symbol_definition]) ).
fof(f15995,plain,
( sQ1588_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15981,f693,f15992]) ).
fof(f15996,definition,
! [X0] :
( sQ1589_spl
<=> ( compose(compose(g,a),compose(domain(compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),domain(X0))
| domain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1589_spl])],[split_symbol_definition]) ).
fof(f15999,plain,
( sQ1589_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15982,f693,f15996]) ).
fof(f16000,definition,
! [X0] :
( sQ1590_spl
<=> ( compose(compose(g,a),compose(domain(compose(h,a)),domain(X0))) = compose(compose(compose(g,a),domain(compose(h,a))),domain(X0))
| domain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1590_spl])],[split_symbol_definition]) ).
fof(f16003,plain,
( sQ1590_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f15983,f693,f16000]) ).
fof(f16004,definition,
! [X0] :
( sQ1591_spl
<=> ( compose(compose(g,a),compose(domain(compose(a,b)),domain(X0))) = compose(compose(compose(g,a),domain(compose(a,b))),domain(X0))
| domain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1591_spl])],[split_symbol_definition]) ).
fof(f16007,plain,
( sQ1591_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f15984,f715,f16004]) ).
fof(f16015,plain,
( compose(compose(g,a),compose(codomain(compose(a,b)),codomain(b))) = compose(compose(compose(g,a),codomain(compose(a,b))),codomain(b))
| domain(b) != codomain(compose(a,b)) ),
inference(resolution,[status(thm)],[f14220,f120]) ).
fof(f16016,plain,
( compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),codomain(b))
| domain(b) != codomain(compose(h,compose(a,b))) ),
inference(resolution,[status(thm)],[f14220,f581]) ).
fof(f16018,plain,
( compose(compose(g,a),compose(codomain(b),codomain(compose(a,b)))) = compose(compose(compose(g,a),codomain(b)),codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(resolution,[status(thm)],[f14220,f120]) ).
fof(f16019,plain,
( compose(compose(g,a),compose(codomain(b),codomain(compose(h,compose(a,b))))) = compose(compose(compose(g,a),codomain(b)),codomain(compose(h,compose(a,b))))
| domain(b) != codomain(b) ),
inference(resolution,[status(thm)],[f14220,f581]) ).
fof(f16021,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(a,b)),codomain(X0))) = compose(compose(compose(g,a),codomain(compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(b) != codomain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f14220]) ).
fof(f16022,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(b) != codomain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f14220]) ).
fof(f16023,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(h,a)),codomain(X0))) = compose(compose(compose(g,a),codomain(compose(h,a))),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != codomain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f14220]) ).
fof(f16024,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(compose(g,a)),codomain(X0))) = compose(compose(compose(g,a),codomain(compose(g,a))),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != codomain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f14220]) ).
fof(f16025,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(g),codomain(X0))) = compose(compose(compose(g,a),codomain(g)),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != codomain(g) ),
inference(paramodulation,[status(thm)],[f74,f14220]) ).
fof(f16026,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(h),codomain(X0))) = compose(compose(compose(g,a),codomain(h)),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f69,f14220]) ).
fof(f16027,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(a),codomain(X0))) = compose(compose(compose(g,a),codomain(a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != codomain(a) ),
inference(paramodulation,[status(thm)],[f22,f14220]) ).
fof(f16032,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(X0),codomain(compose(h,a)))) = compose(compose(compose(g,a),codomain(X0)),codomain(compose(h,a)))
| codomain(X0) != domain(b)
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f131,f14220]) ).
fof(f16040,definition,
( sQ1592_spl
<=> compose(compose(g,a),compose(codomain(compose(a,b)),codomain(b))) = compose(compose(compose(g,a),codomain(compose(a,b))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1592_spl])],[split_symbol_definition]) ).
fof(f16043,plain,
( sQ1592_spl
| ~ sQ1233_spl ),
inference(split_clause,[status(thm)],[f16015,f13172,f16040]) ).
fof(f16044,definition,
( sQ1593_spl
<=> compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1593_spl])],[split_symbol_definition]) ).
fof(f16047,plain,
( sQ1593_spl
| ~ sQ1235_spl ),
inference(split_clause,[status(thm)],[f16016,f13179,f16044]) ).
fof(f16052,definition,
( sQ1594_spl
<=> compose(compose(g,a),compose(codomain(b),codomain(compose(a,b)))) = compose(compose(compose(g,a),codomain(b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1594_spl])],[split_symbol_definition]) ).
fof(f16055,plain,
( sQ1594_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f16018,f2265,f16052]) ).
fof(f16056,definition,
( sQ1595_spl
<=> compose(compose(g,a),compose(codomain(b),codomain(compose(h,compose(a,b))))) = compose(compose(compose(g,a),codomain(b)),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1595_spl])],[split_symbol_definition]) ).
fof(f16059,plain,
( sQ1595_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f16019,f2265,f16056]) ).
fof(f16062,definition,
! [X0] :
( sQ1596_spl
<=> ( compose(compose(g,a),compose(codomain(compose(a,b)),codomain(X0))) = compose(compose(compose(g,a),codomain(compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1596_spl])],[split_symbol_definition]) ).
fof(f16065,plain,
( sQ1596_spl
| ~ sQ1233_spl ),
inference(split_clause,[status(thm)],[f16021,f13172,f16062]) ).
fof(f16066,definition,
! [X0] :
( sQ1597_spl
<=> ( compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1597_spl])],[split_symbol_definition]) ).
fof(f16069,plain,
( sQ1597_spl
| ~ sQ1235_spl ),
inference(split_clause,[status(thm)],[f16022,f13179,f16066]) ).
fof(f16070,definition,
! [X0] :
( sQ1598_spl
<=> ( compose(compose(g,a),compose(codomain(compose(h,a)),codomain(X0))) = compose(compose(compose(g,a),codomain(compose(h,a))),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1598_spl])],[split_symbol_definition]) ).
fof(f16073,plain,
( sQ1598_spl
| ~ sQ220_spl ),
inference(split_clause,[status(thm)],[f16023,f3298,f16070]) ).
fof(f16074,definition,
! [X0] :
( sQ1599_spl
<=> ( compose(compose(g,a),compose(codomain(compose(g,a)),codomain(X0))) = compose(compose(compose(g,a),codomain(compose(g,a))),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1599_spl])],[split_symbol_definition]) ).
fof(f16077,plain,
( sQ1599_spl
| ~ sQ208_spl ),
inference(split_clause,[status(thm)],[f16024,f3233,f16074]) ).
fof(f16078,definition,
! [X0] :
( sQ1600_spl
<=> ( compose(compose(g,a),compose(codomain(g),codomain(X0))) = compose(compose(compose(g,a),codomain(g)),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1600_spl])],[split_symbol_definition]) ).
fof(f16081,plain,
( sQ1600_spl
| ~ sQ1243_spl ),
inference(split_clause,[status(thm)],[f16025,f13216,f16078]) ).
fof(f16082,definition,
! [X0] :
( sQ1601_spl
<=> ( compose(compose(g,a),compose(codomain(h),codomain(X0))) = compose(compose(compose(g,a),codomain(h)),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1601_spl])],[split_symbol_definition]) ).
fof(f16085,plain,
( sQ1601_spl
| ~ sQ1245_spl ),
inference(split_clause,[status(thm)],[f16026,f13223,f16082]) ).
fof(f16086,definition,
! [X0] :
( sQ1602_spl
<=> ( compose(compose(g,a),compose(codomain(a),codomain(X0))) = compose(compose(compose(g,a),codomain(a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1602_spl])],[split_symbol_definition]) ).
fof(f16089,plain,
( sQ1602_spl
| ~ sQ1247_spl ),
inference(split_clause,[status(thm)],[f16027,f13230,f16086]) ).
fof(f16100,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(X0),domain(b))) = compose(compose(compose(g,a),codomain(X0)),codomain(compose(h,a)))
| codomain(X0) != domain(b)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f131,f16032]) ).
fof(f16101,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(X0),domain(b))) = compose(compose(compose(g,a),codomain(X0)),domain(b))
| codomain(X0) != domain(b)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f131,f16100]) ).
fof(f16102,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(X0),domain(b))) = compose(compose(compose(g,a),codomain(X0)),domain(b))
| domain(b) != codomain(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f16101]) ).
fof(f16130,plain,
( compose(compose(g,a),compose(codomain(compose(a,b)),domain(b))) = compose(compose(compose(g,a),codomain(compose(a,b))),domain(b))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f16102]) ).
fof(f16131,plain,
( compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),domain(b))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),domain(b))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f16102]) ).
fof(f16132,plain,
( compose(compose(g,a),compose(codomain(compose(h,a)),domain(b))) = compose(compose(compose(g,a),codomain(compose(h,a))),domain(b))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f16102]) ).
fof(f16133,plain,
( compose(compose(g,a),compose(codomain(compose(g,a)),domain(b))) = compose(compose(compose(g,a),codomain(compose(g,a))),domain(b))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f16102]) ).
fof(f16134,plain,
( compose(compose(g,a),compose(codomain(g),domain(b))) = compose(compose(compose(g,a),codomain(g)),domain(b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f16102]) ).
fof(f16135,plain,
( compose(compose(g,a),compose(codomain(h),domain(b))) = compose(compose(compose(g,a),codomain(h)),domain(b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f16102]) ).
fof(f16136,plain,
( compose(compose(g,a),compose(codomain(a),domain(b))) = compose(compose(compose(g,a),codomain(a)),domain(b))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f16102]) ).
fof(f16138,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(domain(X0)),domain(b))) = compose(compose(compose(g,a),codomain(domain(X0))),domain(b))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f15,f16102]) ).
fof(f16158,definition,
( sQ1603_spl
<=> compose(compose(g,a),compose(codomain(compose(a,b)),domain(b))) = compose(compose(compose(g,a),codomain(compose(a,b))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1603_spl])],[split_symbol_definition]) ).
fof(f16161,plain,
( sQ1603_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f16130,f2265,f16158]) ).
fof(f16162,definition,
( sQ1604_spl
<=> compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),domain(b))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1604_spl])],[split_symbol_definition]) ).
fof(f16165,plain,
( sQ1604_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f16131,f2265,f16162]) ).
fof(f16166,definition,
( sQ1605_spl
<=> compose(compose(g,a),compose(codomain(compose(h,a)),domain(b))) = compose(compose(compose(g,a),codomain(compose(h,a))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1605_spl])],[split_symbol_definition]) ).
fof(f16169,plain,
( sQ1605_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16132,f1941,f16166]) ).
fof(f16170,definition,
( sQ1606_spl
<=> compose(compose(g,a),compose(codomain(compose(g,a)),domain(b))) = compose(compose(compose(g,a),codomain(compose(g,a))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1606_spl])],[split_symbol_definition]) ).
fof(f16173,plain,
( sQ1606_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16133,f1941,f16170]) ).
fof(f16174,definition,
( sQ1607_spl
<=> compose(compose(g,a),compose(codomain(g),domain(b))) = compose(compose(compose(g,a),codomain(g)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1607_spl])],[split_symbol_definition]) ).
fof(f16177,plain,
( sQ1607_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16134,f715,f16174]) ).
fof(f16178,definition,
( sQ1608_spl
<=> compose(compose(g,a),compose(codomain(h),domain(b))) = compose(compose(compose(g,a),codomain(h)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1608_spl])],[split_symbol_definition]) ).
fof(f16181,plain,
( sQ1608_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16135,f715,f16178]) ).
fof(f16182,definition,
( sQ1609_spl
<=> compose(compose(g,a),compose(codomain(a),domain(b))) = compose(compose(compose(g,a),codomain(a)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1609_spl])],[split_symbol_definition]) ).
fof(f16185,plain,
( sQ1609_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16136,f1941,f16182]) ).
fof(f16188,plain,
! [X0] :
( compose(compose(g,a),compose(domain(X0),domain(b))) = compose(compose(compose(g,a),codomain(domain(X0))),domain(b))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f16138]) ).
fof(f16189,plain,
! [X0] :
( compose(compose(g,a),compose(domain(X0),domain(b))) = compose(compose(compose(g,a),domain(X0)),domain(b))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f16188]) ).
fof(f16205,plain,
( compose(compose(g,a),compose(domain(compose(g,a)),domain(b))) = compose(compose(compose(g,a),domain(compose(g,a))),domain(b))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f16189]) ).
fof(f16206,plain,
( compose(compose(g,a),compose(domain(compose(h,compose(a,b))),domain(b))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),domain(b))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f16189]) ).
fof(f16207,plain,
( compose(compose(g,a),compose(domain(compose(h,a)),domain(b))) = compose(compose(compose(g,a),domain(compose(h,a))),domain(b))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f16189]) ).
fof(f16208,plain,
( compose(compose(g,a),compose(domain(compose(a,b)),domain(b))) = compose(compose(compose(g,a),domain(compose(a,b))),domain(b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f16189]) ).
fof(f16216,definition,
( sQ1610_spl
<=> compose(compose(g,a),compose(domain(compose(g,a)),domain(b))) = compose(compose(compose(g,a),domain(compose(g,a))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1610_spl])],[split_symbol_definition]) ).
fof(f16219,plain,
( sQ1610_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f16205,f693,f16216]) ).
fof(f16220,definition,
( sQ1611_spl
<=> compose(compose(g,a),compose(domain(compose(h,compose(a,b))),domain(b))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1611_spl])],[split_symbol_definition]) ).
fof(f16223,plain,
( sQ1611_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f16206,f693,f16220]) ).
fof(f16224,definition,
( sQ1612_spl
<=> compose(compose(g,a),compose(domain(compose(h,a)),domain(b))) = compose(compose(compose(g,a),domain(compose(h,a))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1612_spl])],[split_symbol_definition]) ).
fof(f16227,plain,
( sQ1612_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f16207,f693,f16224]) ).
fof(f16228,definition,
( sQ1613_spl
<=> compose(compose(g,a),compose(domain(compose(a,b)),domain(b))) = compose(compose(compose(g,a),domain(compose(a,b))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1613_spl])],[split_symbol_definition]) ).
fof(f16231,plain,
( sQ1613_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16208,f715,f16228]) ).
fof(f16240,plain,
( compose(compose(g,a),compose(domain(b),codomain(compose(h,a)))) = compose(compose(compose(g,a),domain(b)),codomain(compose(h,a)))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f14221,f131]) ).
fof(f16241,plain,
( compose(compose(g,a),compose(domain(b),codomain(compose(g,a)))) = compose(compose(compose(g,a),domain(b)),codomain(compose(g,a)))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f14221,f130]) ).
fof(f16242,plain,
( compose(compose(g,a),compose(domain(a),codomain(g))) = compose(compose(compose(g,a),domain(a)),codomain(g))
| domain(b) != domain(a) ),
inference(resolution,[status(thm)],[f14221,f74]) ).
fof(f16243,plain,
( compose(compose(g,a),compose(domain(a),codomain(h))) = compose(compose(compose(g,a),domain(a)),codomain(h))
| domain(b) != domain(a) ),
inference(resolution,[status(thm)],[f14221,f69]) ).
fof(f16244,plain,
( compose(compose(g,a),compose(domain(b),codomain(a))) = compose(compose(compose(g,a),domain(b)),codomain(a))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f14221,f22]) ).
fof(f16246,plain,
! [X0] :
( compose(compose(g,a),compose(domain(compose(g,a)),codomain(X0))) = compose(compose(compose(g,a),domain(compose(g,a))),codomain(X0))
| domain(h) != codomain(X0)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f1108,f14221]) ).
fof(f16247,plain,
! [X0] :
( compose(compose(g,a),compose(domain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),codomain(X0))
| domain(h) != codomain(X0)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f1068,f14221]) ).
fof(f16248,plain,
! [X0] :
( compose(compose(g,a),compose(domain(compose(h,a)),codomain(X0))) = compose(compose(compose(g,a),domain(compose(h,a))),codomain(X0))
| domain(h) != codomain(X0)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f76,f14221]) ).
fof(f16249,plain,
! [X0] :
( compose(compose(g,a),compose(domain(compose(a,b)),codomain(X0))) = compose(compose(compose(g,a),domain(compose(a,b))),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f60,f14221]) ).
fof(f16264,definition,
( sQ1614_spl
<=> compose(compose(g,a),compose(domain(b),codomain(compose(h,a)))) = compose(compose(compose(g,a),domain(b)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1614_spl])],[split_symbol_definition]) ).
fof(f16267,plain,
( sQ1614_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16240,f1941,f16264]) ).
fof(f16268,definition,
( sQ1615_spl
<=> compose(compose(g,a),compose(domain(b),codomain(compose(g,a)))) = compose(compose(compose(g,a),domain(b)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1615_spl])],[split_symbol_definition]) ).
fof(f16271,plain,
( sQ1615_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16241,f1941,f16268]) ).
fof(f16272,definition,
( sQ1616_spl
<=> compose(compose(g,a),compose(domain(a),codomain(g))) = compose(compose(compose(g,a),domain(a)),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ1616_spl])],[split_symbol_definition]) ).
fof(f16275,plain,
( sQ1616_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16242,f715,f16272]) ).
fof(f16276,definition,
( sQ1617_spl
<=> compose(compose(g,a),compose(domain(a),codomain(h))) = compose(compose(compose(g,a),domain(a)),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ1617_spl])],[split_symbol_definition]) ).
fof(f16279,plain,
( sQ1617_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16243,f715,f16276]) ).
fof(f16280,definition,
( sQ1618_spl
<=> compose(compose(g,a),compose(domain(b),codomain(a))) = compose(compose(compose(g,a),domain(b)),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1618_spl])],[split_symbol_definition]) ).
fof(f16283,plain,
( sQ1618_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16244,f1941,f16280]) ).
fof(f16286,definition,
! [X0] :
( sQ1619_spl
<=> ( compose(compose(g,a),compose(domain(compose(g,a)),codomain(X0))) = compose(compose(compose(g,a),domain(compose(g,a))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1619_spl])],[split_symbol_definition]) ).
fof(f16289,plain,
( sQ1619_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f16246,f2337,f16286]) ).
fof(f16290,definition,
! [X0] :
( sQ1620_spl
<=> ( compose(compose(g,a),compose(domain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1620_spl])],[split_symbol_definition]) ).
fof(f16293,plain,
( sQ1620_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f16247,f2366,f16290]) ).
fof(f16294,definition,
! [X0] :
( sQ1621_spl
<=> ( compose(compose(g,a),compose(domain(compose(h,a)),codomain(X0))) = compose(compose(compose(g,a),domain(compose(h,a))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1621_spl])],[split_symbol_definition]) ).
fof(f16297,plain,
( sQ1621_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f16248,f2330,f16294]) ).
fof(f16298,definition,
! [X0] :
( sQ1622_spl
<=> ( compose(compose(g,a),compose(domain(compose(a,b)),codomain(X0))) = compose(compose(compose(g,a),domain(compose(a,b))),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1622_spl])],[split_symbol_definition]) ).
fof(f16301,plain,
( sQ1622_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f16249,f2359,f16298]) ).
fof(f16343,plain,
( compose(compose(g,a),compose(domain(h),compose(g,a))) = compose(compose(compose(g,a),domain(h)),compose(g,a))
| domain(b) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f3638,f15]) ).
fof(f16344,plain,
( compose(compose(g,a),compose(compose(a,b),compose(g,a))) = compose(compose(compose(g,a),compose(a,b)),compose(g,a))
| codomain(b) != domain(h)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f3638]) ).
fof(f16345,plain,
( compose(compose(g,a),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(g,a))
| codomain(b) != domain(h)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f3638]) ).
fof(f16346,plain,
( compose(compose(g,a),compose(compose(h,a),compose(g,a))) = compose(compose(compose(g,a),compose(h,a)),compose(g,a))
| domain(b) != domain(h)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f3638]) ).
fof(f16347,plain,
( compose(compose(g,a),compose(compose(g,a),compose(g,a))) = compose(compose(compose(g,a),compose(g,a)),compose(g,a))
| domain(b) != domain(h)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f3638]) ).
fof(f16348,plain,
( compose(compose(g,a),compose(g,compose(g,a))) = compose(compose(compose(g,a),g),compose(g,a))
| domain(a) != domain(h)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f3638]) ).
fof(f16349,plain,
( compose(compose(g,a),compose(h,compose(g,a))) = compose(compose(compose(g,a),h),compose(g,a))
| domain(a) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f3638]) ).
fof(f16350,plain,
( compose(compose(g,a),compose(a,compose(g,a))) = compose(compose(compose(g,a),a),compose(g,a))
| domain(b) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f3638]) ).
fof(f16351,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(X0),compose(g,a))) = compose(compose(compose(g,a),codomain(X0)),compose(g,a))
| codomain(X0) != domain(h)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f3638]) ).
fof(f16352,plain,
! [X0] :
( compose(compose(g,a),compose(domain(X0),compose(g,a))) = compose(compose(compose(g,a),domain(X0)),compose(g,a))
| domain(X0) != domain(h)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f3638]) ).
fof(f16353,definition,
( sQ1623_spl
<=> compose(compose(g,a),compose(domain(h),compose(g,a))) = compose(compose(compose(g,a),domain(h)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1623_spl])],[split_symbol_definition]) ).
fof(f16356,plain,
( sQ1623_spl
| ~ sQ1013_spl ),
inference(split_clause,[status(thm)],[f16343,f11076,f16353]) ).
fof(f16357,definition,
( sQ1624_spl
<=> compose(compose(g,a),compose(compose(a,b),compose(g,a))) = compose(compose(compose(g,a),compose(a,b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1624_spl])],[split_symbol_definition]) ).
fof(f16360,plain,
( sQ1624_spl
| ~ sQ66_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f16344,f2359,f1555,f16357]) ).
fof(f16361,definition,
( sQ1625_spl
<=> compose(compose(g,a),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1625_spl])],[split_symbol_definition]) ).
fof(f16364,plain,
( sQ1625_spl
| ~ sQ66_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f16345,f2366,f1555,f16361]) ).
fof(f16365,definition,
( sQ1626_spl
<=> compose(compose(g,a),compose(compose(h,a),compose(g,a))) = compose(compose(compose(g,a),compose(h,a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1626_spl])],[split_symbol_definition]) ).
fof(f16368,plain,
( sQ1626_spl
| ~ sQ21_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f16346,f2330,f693,f16365]) ).
fof(f16369,definition,
( sQ1627_spl
<=> compose(compose(g,a),compose(compose(g,a),compose(g,a))) = compose(compose(compose(g,a),compose(g,a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1627_spl])],[split_symbol_definition]) ).
fof(f16372,plain,
( sQ1627_spl
| ~ sQ21_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f16347,f2337,f693,f16369]) ).
fof(f16373,definition,
( sQ1628_spl
<=> compose(compose(g,a),compose(g,compose(g,a))) = compose(compose(compose(g,a),g),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1628_spl])],[split_symbol_definition]) ).
fof(f16376,plain,
( sQ1628_spl
| ~ sQ8_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f16348,f700,f584,f16373]) ).
fof(f16377,definition,
( sQ1629_spl
<=> compose(compose(g,a),compose(h,compose(g,a))) = compose(compose(compose(g,a),h),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1629_spl])],[split_symbol_definition]) ).
fof(f16380,plain,
( sQ1629_spl
| ~ sQ8_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f16349,f693,f584,f16377]) ).
fof(f16381,definition,
( sQ1630_spl
<=> compose(compose(g,a),compose(a,compose(g,a))) = compose(compose(compose(g,a),a),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1630_spl])],[split_symbol_definition]) ).
fof(f16384,plain,
( sQ1630_spl
| ~ sQ21_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16350,f715,f693,f16381]) ).
fof(f16385,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(X0),compose(g,a))) = compose(compose(compose(g,a),codomain(X0)),compose(g,a))
| codomain(X0) != domain(h)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f16351]) ).
fof(f16386,plain,
! [X0] :
( compose(compose(g,a),compose(domain(X0),compose(g,a))) = compose(compose(compose(g,a),domain(X0)),compose(g,a))
| domain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f16352]) ).
fof(f16391,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(a,b)),domain(X0))) = compose(compose(compose(h,a),codomain(compose(a,b))),domain(X0))
| codomain(compose(a,b)) != domain(X0)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f14393]) ).
fof(f16392,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),domain(X0))
| codomain(compose(h,compose(a,b))) != domain(X0)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f14393]) ).
fof(f16393,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(h,a)),domain(X0))) = compose(compose(compose(h,a),codomain(compose(h,a))),domain(X0))
| codomain(compose(h,a)) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f14393]) ).
fof(f16394,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(g,a)),domain(X0))) = compose(compose(compose(h,a),codomain(compose(g,a))),domain(X0))
| codomain(compose(g,a)) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f14393]) ).
fof(f16395,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(g),domain(X0))) = compose(compose(compose(h,a),codomain(g)),domain(X0))
| codomain(g) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f14393]) ).
fof(f16396,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(h),domain(X0))) = compose(compose(compose(h,a),codomain(h)),domain(X0))
| codomain(h) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f14393]) ).
fof(f16397,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(a),domain(X0))) = compose(compose(compose(h,a),codomain(a)),domain(X0))
| codomain(a) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f14393]) ).
fof(f16415,definition,
! [X0] :
( sQ1631_spl
<=> ( compose(compose(h,a),compose(codomain(compose(a,b)),domain(X0))) = compose(compose(compose(h,a),codomain(compose(a,b))),domain(X0))
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1631_spl])],[split_symbol_definition]) ).
fof(f16418,plain,
( sQ1631_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f16391,f2265,f16415]) ).
fof(f16419,definition,
! [X0] :
( sQ1632_spl
<=> ( compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),domain(X0))
| codomain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1632_spl])],[split_symbol_definition]) ).
fof(f16422,plain,
( sQ1632_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f16392,f2265,f16419]) ).
fof(f16423,definition,
! [X0] :
( sQ1633_spl
<=> ( compose(compose(h,a),compose(codomain(compose(h,a)),domain(X0))) = compose(compose(compose(h,a),codomain(compose(h,a))),domain(X0))
| codomain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1633_spl])],[split_symbol_definition]) ).
fof(f16426,plain,
( sQ1633_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16393,f1941,f16423]) ).
fof(f16427,definition,
! [X0] :
( sQ1634_spl
<=> ( compose(compose(h,a),compose(codomain(compose(g,a)),domain(X0))) = compose(compose(compose(h,a),codomain(compose(g,a))),domain(X0))
| codomain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1634_spl])],[split_symbol_definition]) ).
fof(f16430,plain,
( sQ1634_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16394,f1941,f16427]) ).
fof(f16431,definition,
! [X0] :
( sQ1635_spl
<=> ( compose(compose(h,a),compose(codomain(g),domain(X0))) = compose(compose(compose(h,a),codomain(g)),domain(X0))
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1635_spl])],[split_symbol_definition]) ).
fof(f16434,plain,
( sQ1635_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16395,f715,f16431]) ).
fof(f16435,definition,
! [X0] :
( sQ1636_spl
<=> ( compose(compose(h,a),compose(codomain(h),domain(X0))) = compose(compose(compose(h,a),codomain(h)),domain(X0))
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1636_spl])],[split_symbol_definition]) ).
fof(f16438,plain,
( sQ1636_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16396,f715,f16435]) ).
fof(f16439,definition,
! [X0] :
( sQ1637_spl
<=> ( compose(compose(h,a),compose(codomain(a),domain(X0))) = compose(compose(compose(h,a),codomain(a)),domain(X0))
| codomain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1637_spl])],[split_symbol_definition]) ).
fof(f16442,plain,
( sQ1637_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16397,f1941,f16439]) ).
fof(f16461,plain,
! [X0] :
( compose(compose(h,a),compose(domain(compose(g,a)),domain(X0))) = compose(compose(compose(h,a),domain(compose(g,a))),domain(X0))
| domain(compose(g,a)) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f14394]) ).
fof(f16462,plain,
! [X0] :
( compose(compose(h,a),compose(domain(compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),domain(X0))
| domain(compose(h,compose(a,b))) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f14394]) ).
fof(f16463,plain,
! [X0] :
( compose(compose(h,a),compose(domain(compose(h,a)),domain(X0))) = compose(compose(compose(h,a),domain(compose(h,a))),domain(X0))
| domain(compose(h,a)) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f14394]) ).
fof(f16464,plain,
! [X0] :
( compose(compose(h,a),compose(domain(compose(a,b)),domain(X0))) = compose(compose(compose(h,a),domain(compose(a,b))),domain(X0))
| domain(compose(a,b)) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f14394]) ).
fof(f16472,definition,
! [X0] :
( sQ1638_spl
<=> ( compose(compose(h,a),compose(domain(compose(g,a)),domain(X0))) = compose(compose(compose(h,a),domain(compose(g,a))),domain(X0))
| domain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1638_spl])],[split_symbol_definition]) ).
fof(f16475,plain,
( sQ1638_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f16461,f693,f16472]) ).
fof(f16476,definition,
! [X0] :
( sQ1639_spl
<=> ( compose(compose(h,a),compose(domain(compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),domain(X0))
| domain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1639_spl])],[split_symbol_definition]) ).
fof(f16479,plain,
( sQ1639_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f16462,f693,f16476]) ).
fof(f16480,definition,
! [X0] :
( sQ1640_spl
<=> ( compose(compose(h,a),compose(domain(compose(h,a)),domain(X0))) = compose(compose(compose(h,a),domain(compose(h,a))),domain(X0))
| domain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1640_spl])],[split_symbol_definition]) ).
fof(f16483,plain,
( sQ1640_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f16463,f693,f16480]) ).
fof(f16484,definition,
! [X0] :
( sQ1641_spl
<=> ( compose(compose(h,a),compose(domain(compose(a,b)),domain(X0))) = compose(compose(compose(h,a),domain(compose(a,b))),domain(X0))
| domain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1641_spl])],[split_symbol_definition]) ).
fof(f16487,plain,
( sQ1641_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16464,f715,f16484]) ).
fof(f16495,plain,
( compose(compose(h,a),compose(codomain(compose(a,b)),codomain(b))) = compose(compose(compose(h,a),codomain(compose(a,b))),codomain(b))
| domain(b) != codomain(compose(a,b)) ),
inference(resolution,[status(thm)],[f14505,f120]) ).
fof(f16496,plain,
( compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),codomain(b))
| domain(b) != codomain(compose(h,compose(a,b))) ),
inference(resolution,[status(thm)],[f14505,f581]) ).
fof(f16498,plain,
( compose(compose(h,a),compose(codomain(b),codomain(compose(a,b)))) = compose(compose(compose(h,a),codomain(b)),codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(resolution,[status(thm)],[f14505,f120]) ).
fof(f16499,plain,
( compose(compose(h,a),compose(codomain(b),codomain(compose(h,compose(a,b))))) = compose(compose(compose(h,a),codomain(b)),codomain(compose(h,compose(a,b))))
| domain(b) != codomain(b) ),
inference(resolution,[status(thm)],[f14505,f581]) ).
fof(f16501,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(a,b)),codomain(X0))) = compose(compose(compose(h,a),codomain(compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(b) != codomain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f14505]) ).
fof(f16502,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(b) != codomain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f14505]) ).
fof(f16503,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(h,a)),codomain(X0))) = compose(compose(compose(h,a),codomain(compose(h,a))),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != codomain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f14505]) ).
fof(f16504,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(compose(g,a)),codomain(X0))) = compose(compose(compose(h,a),codomain(compose(g,a))),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != codomain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f14505]) ).
fof(f16505,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(g),codomain(X0))) = compose(compose(compose(h,a),codomain(g)),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != codomain(g) ),
inference(paramodulation,[status(thm)],[f74,f14505]) ).
fof(f16506,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(h),codomain(X0))) = compose(compose(compose(h,a),codomain(h)),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f69,f14505]) ).
fof(f16507,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(a),codomain(X0))) = compose(compose(compose(h,a),codomain(a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != codomain(a) ),
inference(paramodulation,[status(thm)],[f22,f14505]) ).
fof(f16512,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(X0),codomain(compose(h,a)))) = compose(compose(compose(h,a),codomain(X0)),codomain(compose(h,a)))
| codomain(X0) != domain(b)
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f131,f14505]) ).
fof(f16520,definition,
( sQ1642_spl
<=> compose(compose(h,a),compose(codomain(compose(a,b)),codomain(b))) = compose(compose(compose(h,a),codomain(compose(a,b))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1642_spl])],[split_symbol_definition]) ).
fof(f16523,plain,
( sQ1642_spl
| ~ sQ1233_spl ),
inference(split_clause,[status(thm)],[f16495,f13172,f16520]) ).
fof(f16524,definition,
( sQ1643_spl
<=> compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1643_spl])],[split_symbol_definition]) ).
fof(f16527,plain,
( sQ1643_spl
| ~ sQ1235_spl ),
inference(split_clause,[status(thm)],[f16496,f13179,f16524]) ).
fof(f16532,definition,
( sQ1644_spl
<=> compose(compose(h,a),compose(codomain(b),codomain(compose(a,b)))) = compose(compose(compose(h,a),codomain(b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1644_spl])],[split_symbol_definition]) ).
fof(f16535,plain,
( sQ1644_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f16498,f2265,f16532]) ).
fof(f16536,definition,
( sQ1645_spl
<=> compose(compose(h,a),compose(codomain(b),codomain(compose(h,compose(a,b))))) = compose(compose(compose(h,a),codomain(b)),codomain(compose(h,compose(a,b)))) ),
introduced(definition,[new_symbols(definition,[sQ1645_spl])],[split_symbol_definition]) ).
fof(f16539,plain,
( sQ1645_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f16499,f2265,f16536]) ).
fof(f16542,definition,
! [X0] :
( sQ1646_spl
<=> ( compose(compose(h,a),compose(codomain(compose(a,b)),codomain(X0))) = compose(compose(compose(h,a),codomain(compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1646_spl])],[split_symbol_definition]) ).
fof(f16545,plain,
( sQ1646_spl
| ~ sQ1233_spl ),
inference(split_clause,[status(thm)],[f16501,f13172,f16542]) ).
fof(f16546,definition,
! [X0] :
( sQ1647_spl
<=> ( compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1647_spl])],[split_symbol_definition]) ).
fof(f16549,plain,
( sQ1647_spl
| ~ sQ1235_spl ),
inference(split_clause,[status(thm)],[f16502,f13179,f16546]) ).
fof(f16550,definition,
! [X0] :
( sQ1648_spl
<=> ( compose(compose(h,a),compose(codomain(compose(h,a)),codomain(X0))) = compose(compose(compose(h,a),codomain(compose(h,a))),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1648_spl])],[split_symbol_definition]) ).
fof(f16553,plain,
( sQ1648_spl
| ~ sQ220_spl ),
inference(split_clause,[status(thm)],[f16503,f3298,f16550]) ).
fof(f16554,definition,
! [X0] :
( sQ1649_spl
<=> ( compose(compose(h,a),compose(codomain(compose(g,a)),codomain(X0))) = compose(compose(compose(h,a),codomain(compose(g,a))),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1649_spl])],[split_symbol_definition]) ).
fof(f16557,plain,
( sQ1649_spl
| ~ sQ208_spl ),
inference(split_clause,[status(thm)],[f16504,f3233,f16554]) ).
fof(f16558,definition,
! [X0] :
( sQ1650_spl
<=> ( compose(compose(h,a),compose(codomain(g),codomain(X0))) = compose(compose(compose(h,a),codomain(g)),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1650_spl])],[split_symbol_definition]) ).
fof(f16561,plain,
( sQ1650_spl
| ~ sQ1243_spl ),
inference(split_clause,[status(thm)],[f16505,f13216,f16558]) ).
fof(f16562,definition,
! [X0] :
( sQ1651_spl
<=> ( compose(compose(h,a),compose(codomain(h),codomain(X0))) = compose(compose(compose(h,a),codomain(h)),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1651_spl])],[split_symbol_definition]) ).
fof(f16565,plain,
( sQ1651_spl
| ~ sQ1245_spl ),
inference(split_clause,[status(thm)],[f16506,f13223,f16562]) ).
fof(f16566,definition,
! [X0] :
( sQ1652_spl
<=> ( compose(compose(h,a),compose(codomain(a),codomain(X0))) = compose(compose(compose(h,a),codomain(a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1652_spl])],[split_symbol_definition]) ).
fof(f16569,plain,
( sQ1652_spl
| ~ sQ1247_spl ),
inference(split_clause,[status(thm)],[f16507,f13230,f16566]) ).
fof(f16580,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(X0),domain(b))) = compose(compose(compose(h,a),codomain(X0)),codomain(compose(h,a)))
| codomain(X0) != domain(b)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f131,f16512]) ).
fof(f16581,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(X0),domain(b))) = compose(compose(compose(h,a),codomain(X0)),domain(b))
| codomain(X0) != domain(b)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f131,f16580]) ).
fof(f16582,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(X0),domain(b))) = compose(compose(compose(h,a),codomain(X0)),domain(b))
| domain(b) != codomain(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f16581]) ).
fof(f16610,plain,
( compose(compose(h,a),compose(codomain(compose(a,b)),domain(b))) = compose(compose(compose(h,a),codomain(compose(a,b))),domain(b))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f16582]) ).
fof(f16611,plain,
( compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),domain(b))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),domain(b))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f16582]) ).
fof(f16612,plain,
( compose(compose(h,a),compose(codomain(compose(h,a)),domain(b))) = compose(compose(compose(h,a),codomain(compose(h,a))),domain(b))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f16582]) ).
fof(f16613,plain,
( compose(compose(h,a),compose(codomain(compose(g,a)),domain(b))) = compose(compose(compose(h,a),codomain(compose(g,a))),domain(b))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f16582]) ).
fof(f16614,plain,
( compose(compose(h,a),compose(codomain(g),domain(b))) = compose(compose(compose(h,a),codomain(g)),domain(b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f16582]) ).
fof(f16615,plain,
( compose(compose(h,a),compose(codomain(h),domain(b))) = compose(compose(compose(h,a),codomain(h)),domain(b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f16582]) ).
fof(f16616,plain,
( compose(compose(h,a),compose(codomain(a),domain(b))) = compose(compose(compose(h,a),codomain(a)),domain(b))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f16582]) ).
fof(f16618,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(domain(X0)),domain(b))) = compose(compose(compose(h,a),codomain(domain(X0))),domain(b))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f15,f16582]) ).
fof(f16638,definition,
( sQ1653_spl
<=> compose(compose(h,a),compose(codomain(compose(a,b)),domain(b))) = compose(compose(compose(h,a),codomain(compose(a,b))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1653_spl])],[split_symbol_definition]) ).
fof(f16641,plain,
( sQ1653_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f16610,f2265,f16638]) ).
fof(f16642,definition,
( sQ1654_spl
<=> compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),domain(b))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1654_spl])],[split_symbol_definition]) ).
fof(f16645,plain,
( sQ1654_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f16611,f2265,f16642]) ).
fof(f16646,definition,
( sQ1655_spl
<=> compose(compose(h,a),compose(codomain(compose(h,a)),domain(b))) = compose(compose(compose(h,a),codomain(compose(h,a))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1655_spl])],[split_symbol_definition]) ).
fof(f16649,plain,
( sQ1655_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16612,f1941,f16646]) ).
fof(f16650,definition,
( sQ1656_spl
<=> compose(compose(h,a),compose(codomain(compose(g,a)),domain(b))) = compose(compose(compose(h,a),codomain(compose(g,a))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1656_spl])],[split_symbol_definition]) ).
fof(f16653,plain,
( sQ1656_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16613,f1941,f16650]) ).
fof(f16654,definition,
( sQ1657_spl
<=> compose(compose(h,a),compose(codomain(g),domain(b))) = compose(compose(compose(h,a),codomain(g)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1657_spl])],[split_symbol_definition]) ).
fof(f16657,plain,
( sQ1657_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16614,f715,f16654]) ).
fof(f16658,definition,
( sQ1658_spl
<=> compose(compose(h,a),compose(codomain(h),domain(b))) = compose(compose(compose(h,a),codomain(h)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1658_spl])],[split_symbol_definition]) ).
fof(f16661,plain,
( sQ1658_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16615,f715,f16658]) ).
fof(f16662,definition,
( sQ1659_spl
<=> compose(compose(h,a),compose(codomain(a),domain(b))) = compose(compose(compose(h,a),codomain(a)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1659_spl])],[split_symbol_definition]) ).
fof(f16665,plain,
( sQ1659_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16616,f1941,f16662]) ).
fof(f16668,plain,
! [X0] :
( compose(compose(h,a),compose(domain(X0),domain(b))) = compose(compose(compose(h,a),codomain(domain(X0))),domain(b))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f16618]) ).
fof(f16669,plain,
! [X0] :
( compose(compose(h,a),compose(domain(X0),domain(b))) = compose(compose(compose(h,a),domain(X0)),domain(b))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f16668]) ).
fof(f16685,plain,
( compose(compose(h,a),compose(domain(compose(g,a)),domain(b))) = compose(compose(compose(h,a),domain(compose(g,a))),domain(b))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f16669]) ).
fof(f16686,plain,
( compose(compose(h,a),compose(domain(compose(h,compose(a,b))),domain(b))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),domain(b))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f16669]) ).
fof(f16687,plain,
( compose(compose(h,a),compose(domain(compose(h,a)),domain(b))) = compose(compose(compose(h,a),domain(compose(h,a))),domain(b))
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f16669]) ).
fof(f16688,plain,
( compose(compose(h,a),compose(domain(compose(a,b)),domain(b))) = compose(compose(compose(h,a),domain(compose(a,b))),domain(b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f16669]) ).
fof(f16696,definition,
( sQ1660_spl
<=> compose(compose(h,a),compose(domain(compose(g,a)),domain(b))) = compose(compose(compose(h,a),domain(compose(g,a))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1660_spl])],[split_symbol_definition]) ).
fof(f16699,plain,
( sQ1660_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f16685,f693,f16696]) ).
fof(f16700,definition,
( sQ1661_spl
<=> compose(compose(h,a),compose(domain(compose(h,compose(a,b))),domain(b))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1661_spl])],[split_symbol_definition]) ).
fof(f16703,plain,
( sQ1661_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f16686,f693,f16700]) ).
fof(f16704,definition,
( sQ1662_spl
<=> compose(compose(h,a),compose(domain(compose(h,a)),domain(b))) = compose(compose(compose(h,a),domain(compose(h,a))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1662_spl])],[split_symbol_definition]) ).
fof(f16707,plain,
( sQ1662_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f16687,f693,f16704]) ).
fof(f16708,definition,
( sQ1663_spl
<=> compose(compose(h,a),compose(domain(compose(a,b)),domain(b))) = compose(compose(compose(h,a),domain(compose(a,b))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ1663_spl])],[split_symbol_definition]) ).
fof(f16711,plain,
( sQ1663_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16688,f715,f16708]) ).
fof(f16719,plain,
( compose(compose(g,a),compose(domain(h),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(h)),compose(h,compose(a,b)))
| domain(b) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f3639,f15]) ).
fof(f16720,plain,
( compose(compose(g,a),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(a,b)),compose(h,compose(a,b)))
| codomain(b) != domain(h)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f3639]) ).
fof(f16721,plain,
( compose(compose(g,a),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b)))
| codomain(b) != domain(h)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f3639]) ).
fof(f16722,plain,
( compose(compose(g,a),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(h,a)),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f3639]) ).
fof(f16723,plain,
( compose(compose(g,a),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(g,a)),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f3639]) ).
fof(f16724,plain,
( compose(compose(g,a),compose(g,compose(h,compose(a,b)))) = compose(compose(compose(g,a),g),compose(h,compose(a,b)))
| domain(a) != domain(h)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f3639]) ).
fof(f16725,plain,
( compose(compose(g,a),compose(h,compose(h,compose(a,b)))) = compose(compose(compose(g,a),h),compose(h,compose(a,b)))
| domain(a) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f3639]) ).
fof(f16726,plain,
( compose(compose(g,a),compose(a,compose(h,compose(a,b)))) = compose(compose(compose(g,a),a),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f3639]) ).
fof(f16727,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(X0),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(X0)),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f3639]) ).
fof(f16728,plain,
! [X0] :
( compose(compose(g,a),compose(domain(X0),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(X0)),compose(h,compose(a,b)))
| domain(X0) != domain(h)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f3639]) ).
fof(f16729,definition,
( sQ1664_spl
<=> compose(compose(g,a),compose(domain(h),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(h)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1664_spl])],[split_symbol_definition]) ).
fof(f16732,plain,
( sQ1664_spl
| ~ sQ1013_spl ),
inference(split_clause,[status(thm)],[f16719,f11076,f16729]) ).
fof(f16733,definition,
( sQ1665_spl
<=> compose(compose(g,a),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(a,b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1665_spl])],[split_symbol_definition]) ).
fof(f16736,plain,
( sQ1665_spl
| ~ sQ66_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f16720,f2359,f1555,f16733]) ).
fof(f16737,definition,
( sQ1666_spl
<=> compose(compose(g,a),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1666_spl])],[split_symbol_definition]) ).
fof(f16740,plain,
( sQ1666_spl
| ~ sQ66_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f16721,f2366,f1555,f16737]) ).
fof(f16741,definition,
( sQ1667_spl
<=> compose(compose(g,a),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(h,a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1667_spl])],[split_symbol_definition]) ).
fof(f16744,plain,
( sQ1667_spl
| ~ sQ21_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f16722,f2330,f693,f16741]) ).
fof(f16745,definition,
( sQ1668_spl
<=> compose(compose(g,a),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(g,a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1668_spl])],[split_symbol_definition]) ).
fof(f16748,plain,
( sQ1668_spl
| ~ sQ21_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f16723,f2337,f693,f16745]) ).
fof(f16749,definition,
( sQ1669_spl
<=> compose(compose(g,a),compose(g,compose(h,compose(a,b)))) = compose(compose(compose(g,a),g),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1669_spl])],[split_symbol_definition]) ).
fof(f16752,plain,
( sQ1669_spl
| ~ sQ8_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f16724,f700,f584,f16749]) ).
fof(f16753,definition,
( sQ1670_spl
<=> compose(compose(g,a),compose(h,compose(h,compose(a,b)))) = compose(compose(compose(g,a),h),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1670_spl])],[split_symbol_definition]) ).
fof(f16756,plain,
( sQ1670_spl
| ~ sQ8_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f16725,f693,f584,f16753]) ).
fof(f16757,definition,
( sQ1671_spl
<=> compose(compose(g,a),compose(a,compose(h,compose(a,b)))) = compose(compose(compose(g,a),a),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1671_spl])],[split_symbol_definition]) ).
fof(f16760,plain,
( sQ1671_spl
| ~ sQ21_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16726,f715,f693,f16757]) ).
fof(f16761,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(X0),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(X0)),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f16727]) ).
fof(f16762,plain,
! [X0] :
( compose(compose(g,a),compose(domain(X0),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(X0)),compose(h,compose(a,b)))
| domain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f16728]) ).
fof(f16764,plain,
( compose(compose(h,a),compose(domain(b),codomain(compose(h,a)))) = compose(compose(compose(h,a),domain(b)),codomain(compose(h,a)))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f14506,f131]) ).
fof(f16765,plain,
( compose(compose(h,a),compose(domain(b),codomain(compose(g,a)))) = compose(compose(compose(h,a),domain(b)),codomain(compose(g,a)))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f14506,f130]) ).
fof(f16766,plain,
( compose(compose(h,a),compose(domain(a),codomain(g))) = compose(compose(compose(h,a),domain(a)),codomain(g))
| domain(b) != domain(a) ),
inference(resolution,[status(thm)],[f14506,f74]) ).
fof(f16767,plain,
( compose(compose(h,a),compose(domain(a),codomain(h))) = compose(compose(compose(h,a),domain(a)),codomain(h))
| domain(b) != domain(a) ),
inference(resolution,[status(thm)],[f14506,f69]) ).
fof(f16768,plain,
( compose(compose(h,a),compose(domain(b),codomain(a))) = compose(compose(compose(h,a),domain(b)),codomain(a))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f14506,f22]) ).
fof(f16770,plain,
! [X0] :
( compose(compose(h,a),compose(domain(compose(g,a)),codomain(X0))) = compose(compose(compose(h,a),domain(compose(g,a))),codomain(X0))
| domain(h) != codomain(X0)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f1108,f14506]) ).
fof(f16771,plain,
! [X0] :
( compose(compose(h,a),compose(domain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),codomain(X0))
| domain(h) != codomain(X0)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f1068,f14506]) ).
fof(f16772,plain,
! [X0] :
( compose(compose(h,a),compose(domain(compose(h,a)),codomain(X0))) = compose(compose(compose(h,a),domain(compose(h,a))),codomain(X0))
| domain(h) != codomain(X0)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f76,f14506]) ).
fof(f16773,plain,
! [X0] :
( compose(compose(h,a),compose(domain(compose(a,b)),codomain(X0))) = compose(compose(compose(h,a),domain(compose(a,b))),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f60,f14506]) ).
fof(f16788,definition,
( sQ1672_spl
<=> compose(compose(h,a),compose(domain(b),codomain(compose(h,a)))) = compose(compose(compose(h,a),domain(b)),codomain(compose(h,a))) ),
introduced(definition,[new_symbols(definition,[sQ1672_spl])],[split_symbol_definition]) ).
fof(f16791,plain,
( sQ1672_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16764,f1941,f16788]) ).
fof(f16792,definition,
( sQ1673_spl
<=> compose(compose(h,a),compose(domain(b),codomain(compose(g,a)))) = compose(compose(compose(h,a),domain(b)),codomain(compose(g,a))) ),
introduced(definition,[new_symbols(definition,[sQ1673_spl])],[split_symbol_definition]) ).
fof(f16795,plain,
( sQ1673_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16765,f1941,f16792]) ).
fof(f16796,definition,
( sQ1674_spl
<=> compose(compose(h,a),compose(domain(a),codomain(g))) = compose(compose(compose(h,a),domain(a)),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ1674_spl])],[split_symbol_definition]) ).
fof(f16799,plain,
( sQ1674_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16766,f715,f16796]) ).
fof(f16800,definition,
( sQ1675_spl
<=> compose(compose(h,a),compose(domain(a),codomain(h))) = compose(compose(compose(h,a),domain(a)),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ1675_spl])],[split_symbol_definition]) ).
fof(f16803,plain,
( sQ1675_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16767,f715,f16800]) ).
fof(f16804,definition,
( sQ1676_spl
<=> compose(compose(h,a),compose(domain(b),codomain(a))) = compose(compose(compose(h,a),domain(b)),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1676_spl])],[split_symbol_definition]) ).
fof(f16807,plain,
( sQ1676_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f16768,f1941,f16804]) ).
fof(f16810,definition,
! [X0] :
( sQ1677_spl
<=> ( compose(compose(h,a),compose(domain(compose(g,a)),codomain(X0))) = compose(compose(compose(h,a),domain(compose(g,a))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1677_spl])],[split_symbol_definition]) ).
fof(f16813,plain,
( sQ1677_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f16770,f2337,f16810]) ).
fof(f16814,definition,
! [X0] :
( sQ1678_spl
<=> ( compose(compose(h,a),compose(domain(compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1678_spl])],[split_symbol_definition]) ).
fof(f16817,plain,
( sQ1678_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f16771,f2366,f16814]) ).
fof(f16818,definition,
! [X0] :
( sQ1679_spl
<=> ( compose(compose(h,a),compose(domain(compose(h,a)),codomain(X0))) = compose(compose(compose(h,a),domain(compose(h,a))),codomain(X0))
| domain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1679_spl])],[split_symbol_definition]) ).
fof(f16821,plain,
( sQ1679_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f16772,f2330,f16818]) ).
fof(f16822,definition,
! [X0] :
( sQ1680_spl
<=> ( compose(compose(h,a),compose(domain(compose(a,b)),codomain(X0))) = compose(compose(compose(h,a),domain(compose(a,b))),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1680_spl])],[split_symbol_definition]) ).
fof(f16825,plain,
( sQ1680_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f16773,f2359,f16822]) ).
fof(f16867,plain,
( compose(compose(g,a),compose(domain(h),compose(h,a))) = compose(compose(compose(g,a),domain(h)),compose(h,a))
| domain(b) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f3640,f15]) ).
fof(f16868,plain,
( compose(compose(g,a),compose(compose(a,b),compose(h,a))) = compose(compose(compose(g,a),compose(a,b)),compose(h,a))
| codomain(b) != domain(h)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f3640]) ).
fof(f16869,plain,
( compose(compose(g,a),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,a))
| codomain(b) != domain(h)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f3640]) ).
fof(f16870,plain,
( compose(compose(g,a),compose(compose(h,a),compose(h,a))) = compose(compose(compose(g,a),compose(h,a)),compose(h,a))
| domain(b) != domain(h)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f3640]) ).
fof(f16871,plain,
( compose(compose(g,a),compose(compose(g,a),compose(h,a))) = compose(compose(compose(g,a),compose(g,a)),compose(h,a))
| domain(b) != domain(h)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f3640]) ).
fof(f16872,plain,
( compose(compose(g,a),compose(g,compose(h,a))) = compose(compose(compose(g,a),g),compose(h,a))
| domain(a) != domain(h)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f3640]) ).
fof(f16873,plain,
( compose(compose(g,a),compose(h,compose(h,a))) = compose(compose(compose(g,a),h),compose(h,a))
| domain(a) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f3640]) ).
fof(f16874,plain,
( compose(compose(g,a),compose(a,compose(h,a))) = compose(compose(compose(g,a),a),compose(h,a))
| domain(b) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f3640]) ).
fof(f16875,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(X0),compose(h,a))) = compose(compose(compose(g,a),codomain(X0)),compose(h,a))
| codomain(X0) != domain(h)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f3640]) ).
fof(f16876,plain,
! [X0] :
( compose(compose(g,a),compose(domain(X0),compose(h,a))) = compose(compose(compose(g,a),domain(X0)),compose(h,a))
| domain(X0) != domain(h)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f3640]) ).
fof(f16877,definition,
( sQ1681_spl
<=> compose(compose(g,a),compose(domain(h),compose(h,a))) = compose(compose(compose(g,a),domain(h)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1681_spl])],[split_symbol_definition]) ).
fof(f16880,plain,
( sQ1681_spl
| ~ sQ1013_spl ),
inference(split_clause,[status(thm)],[f16867,f11076,f16877]) ).
fof(f16881,definition,
( sQ1682_spl
<=> compose(compose(g,a),compose(compose(a,b),compose(h,a))) = compose(compose(compose(g,a),compose(a,b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1682_spl])],[split_symbol_definition]) ).
fof(f16884,plain,
( sQ1682_spl
| ~ sQ66_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f16868,f2359,f1555,f16881]) ).
fof(f16885,definition,
( sQ1683_spl
<=> compose(compose(g,a),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1683_spl])],[split_symbol_definition]) ).
fof(f16888,plain,
( sQ1683_spl
| ~ sQ66_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f16869,f2366,f1555,f16885]) ).
fof(f16889,definition,
( sQ1684_spl
<=> compose(compose(g,a),compose(compose(h,a),compose(h,a))) = compose(compose(compose(g,a),compose(h,a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1684_spl])],[split_symbol_definition]) ).
fof(f16892,plain,
( sQ1684_spl
| ~ sQ21_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f16870,f2330,f693,f16889]) ).
fof(f16893,definition,
( sQ1685_spl
<=> compose(compose(g,a),compose(compose(g,a),compose(h,a))) = compose(compose(compose(g,a),compose(g,a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1685_spl])],[split_symbol_definition]) ).
fof(f16896,plain,
( sQ1685_spl
| ~ sQ21_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f16871,f2337,f693,f16893]) ).
fof(f16897,definition,
( sQ1686_spl
<=> compose(compose(g,a),compose(g,compose(h,a))) = compose(compose(compose(g,a),g),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1686_spl])],[split_symbol_definition]) ).
fof(f16900,plain,
( sQ1686_spl
| ~ sQ8_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f16872,f700,f584,f16897]) ).
fof(f16901,definition,
( sQ1687_spl
<=> compose(compose(g,a),compose(h,compose(h,a))) = compose(compose(compose(g,a),h),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1687_spl])],[split_symbol_definition]) ).
fof(f16904,plain,
( sQ1687_spl
| ~ sQ8_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f16873,f693,f584,f16901]) ).
fof(f16905,definition,
( sQ1688_spl
<=> compose(compose(g,a),compose(a,compose(h,a))) = compose(compose(compose(g,a),a),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1688_spl])],[split_symbol_definition]) ).
fof(f16908,plain,
( sQ1688_spl
| ~ sQ21_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16874,f715,f693,f16905]) ).
fof(f16909,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(X0),compose(h,a))) = compose(compose(compose(g,a),codomain(X0)),compose(h,a))
| codomain(X0) != domain(h)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f16875]) ).
fof(f16910,plain,
! [X0] :
( compose(compose(g,a),compose(domain(X0),compose(h,a))) = compose(compose(compose(g,a),domain(X0)),compose(h,a))
| domain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f16876]) ).
fof(f16911,plain,
( compose(compose(g,a),compose(g,compose(a,b))) = compose(compose(compose(g,a),g),compose(a,b))
| domain(b) != domain(g) ),
inference(resolution,[status(thm)],[f3641,f74]) ).
fof(f16912,plain,
( compose(compose(g,a),compose(h,compose(a,b))) = compose(compose(compose(g,a),h),compose(a,b))
| domain(b) != domain(h) ),
inference(resolution,[status(thm)],[f3641,f69]) ).
fof(f16913,plain,
( compose(compose(g,a),compose(domain(a),compose(a,b))) = compose(compose(compose(g,a),domain(a)),compose(a,b))
| domain(b) != domain(domain(a)) ),
inference(resolution,[status(thm)],[f3641,f15]) ).
fof(f16914,plain,
( compose(compose(g,a),compose(compose(a,b),compose(a,b))) = compose(compose(compose(g,a),compose(a,b)),compose(a,b))
| codomain(b) != domain(a)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f3641]) ).
fof(f16915,plain,
( compose(compose(g,a),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(a,b))
| codomain(b) != domain(a)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f3641]) ).
fof(f16916,plain,
( compose(compose(g,a),compose(compose(h,a),compose(a,b))) = compose(compose(compose(g,a),compose(h,a)),compose(a,b))
| domain(b) != domain(a)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f3641]) ).
fof(f16917,plain,
( compose(compose(g,a),compose(compose(g,a),compose(a,b))) = compose(compose(compose(g,a),compose(g,a)),compose(a,b))
| domain(b) != domain(a)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f3641]) ).
fof(f16920,plain,
( compose(compose(g,a),compose(a,compose(a,b))) = compose(compose(compose(g,a),a),compose(a,b))
| domain(b) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f3641]) ).
fof(f16921,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(X0),compose(a,b))) = compose(compose(compose(g,a),codomain(X0)),compose(a,b))
| codomain(X0) != domain(a)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f3641]) ).
fof(f16922,plain,
! [X0] :
( compose(compose(g,a),compose(domain(X0),compose(a,b))) = compose(compose(compose(g,a),domain(X0)),compose(a,b))
| domain(X0) != domain(a)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f3641]) ).
fof(f16923,definition,
( sQ1689_spl
<=> compose(compose(g,a),compose(g,compose(a,b))) = compose(compose(compose(g,a),g),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1689_spl])],[split_symbol_definition]) ).
fof(f16926,plain,
( sQ1689_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f16911,f700,f16923]) ).
fof(f16927,definition,
( sQ1690_spl
<=> compose(compose(g,a),compose(h,compose(a,b))) = compose(compose(compose(g,a),h),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1690_spl])],[split_symbol_definition]) ).
fof(f16930,plain,
( sQ1690_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f16912,f693,f16927]) ).
fof(f16931,definition,
( sQ1691_spl
<=> compose(compose(g,a),compose(domain(a),compose(a,b))) = compose(compose(compose(g,a),domain(a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1691_spl])],[split_symbol_definition]) ).
fof(f16934,plain,
( sQ1691_spl
| ~ sQ1084_spl ),
inference(split_clause,[status(thm)],[f16913,f11679,f16931]) ).
fof(f16935,definition,
( sQ1692_spl
<=> compose(compose(g,a),compose(compose(a,b),compose(a,b))) = compose(compose(compose(g,a),compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1692_spl])],[split_symbol_definition]) ).
fof(f16938,plain,
( sQ1692_spl
| ~ sQ70_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f16914,f2359,f1570,f16935]) ).
fof(f16939,definition,
( sQ1693_spl
<=> compose(compose(g,a),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1693_spl])],[split_symbol_definition]) ).
fof(f16942,plain,
( sQ1693_spl
| ~ sQ70_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f16915,f2366,f1570,f16939]) ).
fof(f16943,definition,
( sQ1694_spl
<=> compose(compose(g,a),compose(compose(h,a),compose(a,b))) = compose(compose(compose(g,a),compose(h,a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1694_spl])],[split_symbol_definition]) ).
fof(f16946,plain,
( sQ1694_spl
| ~ sQ27_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f16916,f2330,f715,f16943]) ).
fof(f16947,definition,
( sQ1695_spl
<=> compose(compose(g,a),compose(compose(g,a),compose(a,b))) = compose(compose(compose(g,a),compose(g,a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1695_spl])],[split_symbol_definition]) ).
fof(f16950,plain,
( sQ1695_spl
| ~ sQ27_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f16917,f2337,f715,f16947]) ).
fof(f16953,definition,
( sQ1696_spl
<=> compose(compose(g,a),compose(a,compose(a,b))) = compose(compose(compose(g,a),a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1696_spl])],[split_symbol_definition]) ).
fof(f16956,plain,
( sQ1696_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16920,f715,f16953]) ).
fof(f16957,plain,
! [X0] :
( compose(compose(g,a),compose(codomain(X0),compose(a,b))) = compose(compose(compose(g,a),codomain(X0)),compose(a,b))
| codomain(X0) != domain(a)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f16921]) ).
fof(f16958,plain,
! [X0] :
( compose(compose(g,a),compose(domain(X0),compose(a,b))) = compose(compose(compose(g,a),domain(X0)),compose(a,b))
| domain(X0) != domain(a)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f16922]) ).
fof(f16959,plain,
( compose(compose(h,a),compose(domain(h),compose(g,a))) = compose(compose(compose(h,a),domain(h)),compose(g,a))
| domain(b) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f4949,f15]) ).
fof(f16960,plain,
( compose(compose(h,a),compose(compose(a,b),compose(g,a))) = compose(compose(compose(h,a),compose(a,b)),compose(g,a))
| codomain(b) != domain(h)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f4949]) ).
fof(f16961,plain,
( compose(compose(h,a),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(g,a))
| codomain(b) != domain(h)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f4949]) ).
fof(f16962,plain,
( compose(compose(h,a),compose(compose(h,a),compose(g,a))) = compose(compose(compose(h,a),compose(h,a)),compose(g,a))
| domain(b) != domain(h)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f4949]) ).
fof(f16963,plain,
( compose(compose(h,a),compose(compose(g,a),compose(g,a))) = compose(compose(compose(h,a),compose(g,a)),compose(g,a))
| domain(b) != domain(h)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f4949]) ).
fof(f16964,plain,
( compose(compose(h,a),compose(g,compose(g,a))) = compose(compose(compose(h,a),g),compose(g,a))
| domain(a) != domain(h)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f4949]) ).
fof(f16965,plain,
( compose(compose(h,a),compose(h,compose(g,a))) = compose(compose(compose(h,a),h),compose(g,a))
| domain(a) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f4949]) ).
fof(f16966,plain,
( compose(compose(h,a),compose(a,compose(g,a))) = compose(compose(compose(h,a),a),compose(g,a))
| domain(b) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f4949]) ).
fof(f16967,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(X0),compose(g,a))) = compose(compose(compose(h,a),codomain(X0)),compose(g,a))
| codomain(X0) != domain(h)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f4949]) ).
fof(f16968,plain,
! [X0] :
( compose(compose(h,a),compose(domain(X0),compose(g,a))) = compose(compose(compose(h,a),domain(X0)),compose(g,a))
| domain(X0) != domain(h)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f4949]) ).
fof(f16969,definition,
( sQ1697_spl
<=> compose(compose(h,a),compose(domain(h),compose(g,a))) = compose(compose(compose(h,a),domain(h)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1697_spl])],[split_symbol_definition]) ).
fof(f16972,plain,
( sQ1697_spl
| ~ sQ1013_spl ),
inference(split_clause,[status(thm)],[f16959,f11076,f16969]) ).
fof(f16973,definition,
( sQ1698_spl
<=> compose(compose(h,a),compose(compose(a,b),compose(g,a))) = compose(compose(compose(h,a),compose(a,b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1698_spl])],[split_symbol_definition]) ).
fof(f16976,plain,
( sQ1698_spl
| ~ sQ66_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f16960,f2359,f1555,f16973]) ).
fof(f16977,definition,
( sQ1699_spl
<=> compose(compose(h,a),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1699_spl])],[split_symbol_definition]) ).
fof(f16980,plain,
( sQ1699_spl
| ~ sQ66_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f16961,f2366,f1555,f16977]) ).
fof(f16981,definition,
( sQ1700_spl
<=> compose(compose(h,a),compose(compose(h,a),compose(g,a))) = compose(compose(compose(h,a),compose(h,a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1700_spl])],[split_symbol_definition]) ).
fof(f16984,plain,
( sQ1700_spl
| ~ sQ21_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f16962,f2330,f693,f16981]) ).
fof(f16985,definition,
( sQ1701_spl
<=> compose(compose(h,a),compose(compose(g,a),compose(g,a))) = compose(compose(compose(h,a),compose(g,a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1701_spl])],[split_symbol_definition]) ).
fof(f16988,plain,
( sQ1701_spl
| ~ sQ21_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f16963,f2337,f693,f16985]) ).
fof(f16989,definition,
( sQ1702_spl
<=> compose(compose(h,a),compose(g,compose(g,a))) = compose(compose(compose(h,a),g),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1702_spl])],[split_symbol_definition]) ).
fof(f16992,plain,
( sQ1702_spl
| ~ sQ8_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f16964,f700,f584,f16989]) ).
fof(f16993,definition,
( sQ1703_spl
<=> compose(compose(h,a),compose(h,compose(g,a))) = compose(compose(compose(h,a),h),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1703_spl])],[split_symbol_definition]) ).
fof(f16996,plain,
( sQ1703_spl
| ~ sQ8_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f16965,f693,f584,f16993]) ).
fof(f16997,definition,
( sQ1704_spl
<=> compose(compose(h,a),compose(a,compose(g,a))) = compose(compose(compose(h,a),a),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1704_spl])],[split_symbol_definition]) ).
fof(f17000,plain,
( sQ1704_spl
| ~ sQ21_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f16966,f715,f693,f16997]) ).
fof(f17001,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(X0),compose(g,a))) = compose(compose(compose(h,a),codomain(X0)),compose(g,a))
| codomain(X0) != domain(h)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f16967]) ).
fof(f17002,plain,
! [X0] :
( compose(compose(h,a),compose(domain(X0),compose(g,a))) = compose(compose(compose(h,a),domain(X0)),compose(g,a))
| domain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f16968]) ).
fof(f17003,plain,
( compose(compose(h,a),compose(domain(h),compose(h,a))) = compose(compose(compose(h,a),domain(h)),compose(h,a))
| domain(b) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f4951,f15]) ).
fof(f17004,plain,
( compose(compose(h,a),compose(compose(a,b),compose(h,a))) = compose(compose(compose(h,a),compose(a,b)),compose(h,a))
| codomain(b) != domain(h)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f4951]) ).
fof(f17005,plain,
( compose(compose(h,a),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,a))
| codomain(b) != domain(h)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f4951]) ).
fof(f17006,plain,
( compose(compose(h,a),compose(compose(h,a),compose(h,a))) = compose(compose(compose(h,a),compose(h,a)),compose(h,a))
| domain(b) != domain(h)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f4951]) ).
fof(f17007,plain,
( compose(compose(h,a),compose(compose(g,a),compose(h,a))) = compose(compose(compose(h,a),compose(g,a)),compose(h,a))
| domain(b) != domain(h)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f4951]) ).
fof(f17008,plain,
( compose(compose(h,a),compose(g,compose(h,a))) = compose(compose(compose(h,a),g),compose(h,a))
| domain(a) != domain(h)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f4951]) ).
fof(f17009,plain,
( compose(compose(h,a),compose(h,compose(h,a))) = compose(compose(compose(h,a),h),compose(h,a))
| domain(a) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f4951]) ).
fof(f17010,plain,
( compose(compose(h,a),compose(a,compose(h,a))) = compose(compose(compose(h,a),a),compose(h,a))
| domain(b) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f4951]) ).
fof(f17011,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(X0),compose(h,a))) = compose(compose(compose(h,a),codomain(X0)),compose(h,a))
| codomain(X0) != domain(h)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f4951]) ).
fof(f17012,plain,
! [X0] :
( compose(compose(h,a),compose(domain(X0),compose(h,a))) = compose(compose(compose(h,a),domain(X0)),compose(h,a))
| domain(X0) != domain(h)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f4951]) ).
fof(f17013,definition,
( sQ1705_spl
<=> compose(compose(h,a),compose(domain(h),compose(h,a))) = compose(compose(compose(h,a),domain(h)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1705_spl])],[split_symbol_definition]) ).
fof(f17016,plain,
( sQ1705_spl
| ~ sQ1013_spl ),
inference(split_clause,[status(thm)],[f17003,f11076,f17013]) ).
fof(f17017,definition,
( sQ1706_spl
<=> compose(compose(h,a),compose(compose(a,b),compose(h,a))) = compose(compose(compose(h,a),compose(a,b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1706_spl])],[split_symbol_definition]) ).
fof(f17020,plain,
( sQ1706_spl
| ~ sQ66_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f17004,f2359,f1555,f17017]) ).
fof(f17021,definition,
( sQ1707_spl
<=> compose(compose(h,a),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1707_spl])],[split_symbol_definition]) ).
fof(f17024,plain,
( sQ1707_spl
| ~ sQ66_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f17005,f2366,f1555,f17021]) ).
fof(f17025,definition,
( sQ1708_spl
<=> compose(compose(h,a),compose(compose(h,a),compose(h,a))) = compose(compose(compose(h,a),compose(h,a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1708_spl])],[split_symbol_definition]) ).
fof(f17028,plain,
( sQ1708_spl
| ~ sQ21_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f17006,f2330,f693,f17025]) ).
fof(f17029,definition,
( sQ1709_spl
<=> compose(compose(h,a),compose(compose(g,a),compose(h,a))) = compose(compose(compose(h,a),compose(g,a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1709_spl])],[split_symbol_definition]) ).
fof(f17032,plain,
( sQ1709_spl
| ~ sQ21_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f17007,f2337,f693,f17029]) ).
fof(f17033,definition,
( sQ1710_spl
<=> compose(compose(h,a),compose(g,compose(h,a))) = compose(compose(compose(h,a),g),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1710_spl])],[split_symbol_definition]) ).
fof(f17036,plain,
( sQ1710_spl
| ~ sQ8_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f17008,f700,f584,f17033]) ).
fof(f17037,definition,
( sQ1711_spl
<=> compose(compose(h,a),compose(h,compose(h,a))) = compose(compose(compose(h,a),h),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1711_spl])],[split_symbol_definition]) ).
fof(f17040,plain,
( sQ1711_spl
| ~ sQ8_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17009,f693,f584,f17037]) ).
fof(f17041,definition,
( sQ1712_spl
<=> compose(compose(h,a),compose(a,compose(h,a))) = compose(compose(compose(h,a),a),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1712_spl])],[split_symbol_definition]) ).
fof(f17044,plain,
( sQ1712_spl
| ~ sQ21_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17010,f715,f693,f17041]) ).
fof(f17045,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(X0),compose(h,a))) = compose(compose(compose(h,a),codomain(X0)),compose(h,a))
| codomain(X0) != domain(h)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f17011]) ).
fof(f17046,plain,
! [X0] :
( compose(compose(h,a),compose(domain(X0),compose(h,a))) = compose(compose(compose(h,a),domain(X0)),compose(h,a))
| domain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f17012]) ).
fof(f17048,plain,
! [X0] :
( compose(codomain(compose(a,b)),compose(compose(h,compose(a,b)),X0)) = compose(compose(codomain(compose(a,b)),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f120,f3930]) ).
fof(f17049,plain,
! [X0] :
( compose(codomain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),X0)) = compose(compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f581,f3930]) ).
fof(f17050,plain,
! [X0] :
( compose(codomain(compose(h,a)),compose(compose(h,compose(a,b)),X0)) = compose(compose(codomain(compose(h,a)),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f131,f3930]) ).
fof(f17051,plain,
! [X0] :
( compose(codomain(compose(g,a)),compose(compose(h,compose(a,b)),X0)) = compose(compose(codomain(compose(g,a)),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f130,f3930]) ).
fof(f17052,plain,
! [X0] :
( compose(codomain(g),compose(compose(h,compose(a,b)),X0)) = compose(compose(codomain(g),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f74,f3930]) ).
fof(f17053,plain,
! [X0] :
( compose(codomain(h),compose(compose(h,compose(a,b)),X0)) = compose(compose(codomain(h),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f3930]) ).
fof(f17054,plain,
! [X0] :
( compose(codomain(a),compose(compose(h,compose(a,b)),X0)) = compose(compose(codomain(a),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f22,f3930]) ).
fof(f17060,definition,
! [X0] :
( sQ1713_spl
<=> ( compose(codomain(compose(a,b)),compose(compose(h,compose(a,b)),X0)) = compose(compose(codomain(compose(a,b)),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1713_spl])],[split_symbol_definition]) ).
fof(f17063,plain,
( sQ1713_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f17048,f1555,f17060]) ).
fof(f17064,definition,
! [X0] :
( sQ1714_spl
<=> ( compose(codomain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),X0)) = compose(compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1714_spl])],[split_symbol_definition]) ).
fof(f17067,plain,
( sQ1714_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f17049,f1555,f17064]) ).
fof(f17068,definition,
! [X0] :
( sQ1715_spl
<=> ( compose(codomain(compose(h,a)),compose(compose(h,compose(a,b)),X0)) = compose(compose(codomain(compose(h,a)),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1715_spl])],[split_symbol_definition]) ).
fof(f17071,plain,
( sQ1715_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17050,f693,f17068]) ).
fof(f17072,definition,
! [X0] :
( sQ1716_spl
<=> ( compose(codomain(compose(g,a)),compose(compose(h,compose(a,b)),X0)) = compose(compose(codomain(compose(g,a)),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1716_spl])],[split_symbol_definition]) ).
fof(f17075,plain,
( sQ1716_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17051,f693,f17072]) ).
fof(f17076,definition,
! [X0] :
( sQ1717_spl
<=> ( compose(codomain(g),compose(compose(h,compose(a,b)),X0)) = compose(compose(codomain(g),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1717_spl])],[split_symbol_definition]) ).
fof(f17079,plain,
( sQ1717_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f17052,f584,f17076]) ).
fof(f17080,definition,
! [X0] :
( sQ1718_spl
<=> ( compose(codomain(h),compose(compose(h,compose(a,b)),X0)) = compose(compose(codomain(h),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1718_spl])],[split_symbol_definition]) ).
fof(f17083,plain,
( sQ1718_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f17053,f584,f17080]) ).
fof(f17084,definition,
! [X0] :
( sQ1719_spl
<=> ( compose(codomain(a),compose(compose(h,compose(a,b)),X0)) = compose(compose(codomain(a),compose(h,compose(a,b))),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1719_spl])],[split_symbol_definition]) ).
fof(f17087,plain,
( sQ1719_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17054,f693,f17084]) ).
fof(f17092,plain,
( compose(compose(h,a),compose(g,compose(a,b))) = compose(compose(compose(h,a),g),compose(a,b))
| domain(b) != domain(g) ),
inference(resolution,[status(thm)],[f4952,f74]) ).
fof(f17093,plain,
( compose(compose(h,a),compose(h,compose(a,b))) = compose(compose(compose(h,a),h),compose(a,b))
| domain(b) != domain(h) ),
inference(resolution,[status(thm)],[f4952,f69]) ).
fof(f17094,plain,
( compose(compose(h,a),compose(domain(a),compose(a,b))) = compose(compose(compose(h,a),domain(a)),compose(a,b))
| domain(b) != domain(domain(a)) ),
inference(resolution,[status(thm)],[f4952,f15]) ).
fof(f17095,plain,
( compose(compose(h,a),compose(compose(a,b),compose(a,b))) = compose(compose(compose(h,a),compose(a,b)),compose(a,b))
| codomain(b) != domain(a)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f4952]) ).
fof(f17096,plain,
( compose(compose(h,a),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(a,b))
| codomain(b) != domain(a)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f4952]) ).
fof(f17097,plain,
( compose(compose(h,a),compose(compose(h,a),compose(a,b))) = compose(compose(compose(h,a),compose(h,a)),compose(a,b))
| domain(b) != domain(a)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f4952]) ).
fof(f17098,plain,
( compose(compose(h,a),compose(compose(g,a),compose(a,b))) = compose(compose(compose(h,a),compose(g,a)),compose(a,b))
| domain(b) != domain(a)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f4952]) ).
fof(f17101,plain,
( compose(compose(h,a),compose(a,compose(a,b))) = compose(compose(compose(h,a),a),compose(a,b))
| domain(b) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f4952]) ).
fof(f17102,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(X0),compose(a,b))) = compose(compose(compose(h,a),codomain(X0)),compose(a,b))
| codomain(X0) != domain(a)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f4952]) ).
fof(f17103,plain,
! [X0] :
( compose(compose(h,a),compose(domain(X0),compose(a,b))) = compose(compose(compose(h,a),domain(X0)),compose(a,b))
| domain(X0) != domain(a)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f4952]) ).
fof(f17104,definition,
( sQ1720_spl
<=> compose(compose(h,a),compose(g,compose(a,b))) = compose(compose(compose(h,a),g),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1720_spl])],[split_symbol_definition]) ).
fof(f17107,plain,
( sQ1720_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f17092,f700,f17104]) ).
fof(f17108,definition,
( sQ1721_spl
<=> compose(compose(h,a),compose(h,compose(a,b))) = compose(compose(compose(h,a),h),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1721_spl])],[split_symbol_definition]) ).
fof(f17111,plain,
( sQ1721_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17093,f693,f17108]) ).
fof(f17112,definition,
( sQ1722_spl
<=> compose(compose(h,a),compose(domain(a),compose(a,b))) = compose(compose(compose(h,a),domain(a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1722_spl])],[split_symbol_definition]) ).
fof(f17115,plain,
( sQ1722_spl
| ~ sQ1084_spl ),
inference(split_clause,[status(thm)],[f17094,f11679,f17112]) ).
fof(f17116,definition,
( sQ1723_spl
<=> compose(compose(h,a),compose(compose(a,b),compose(a,b))) = compose(compose(compose(h,a),compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1723_spl])],[split_symbol_definition]) ).
fof(f17119,plain,
( sQ1723_spl
| ~ sQ70_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f17095,f2359,f1570,f17116]) ).
fof(f17120,definition,
( sQ1724_spl
<=> compose(compose(h,a),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1724_spl])],[split_symbol_definition]) ).
fof(f17123,plain,
( sQ1724_spl
| ~ sQ70_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f17096,f2366,f1570,f17120]) ).
fof(f17124,definition,
( sQ1725_spl
<=> compose(compose(h,a),compose(compose(h,a),compose(a,b))) = compose(compose(compose(h,a),compose(h,a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1725_spl])],[split_symbol_definition]) ).
fof(f17127,plain,
( sQ1725_spl
| ~ sQ27_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f17097,f2330,f715,f17124]) ).
fof(f17128,definition,
( sQ1726_spl
<=> compose(compose(h,a),compose(compose(g,a),compose(a,b))) = compose(compose(compose(h,a),compose(g,a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1726_spl])],[split_symbol_definition]) ).
fof(f17131,plain,
( sQ1726_spl
| ~ sQ27_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f17098,f2337,f715,f17128]) ).
fof(f17134,definition,
( sQ1727_spl
<=> compose(compose(h,a),compose(a,compose(a,b))) = compose(compose(compose(h,a),a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1727_spl])],[split_symbol_definition]) ).
fof(f17137,plain,
( sQ1727_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17101,f715,f17134]) ).
fof(f17138,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(X0),compose(a,b))) = compose(compose(compose(h,a),codomain(X0)),compose(a,b))
| codomain(X0) != domain(a)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f17102]) ).
fof(f17139,plain,
! [X0] :
( compose(compose(h,a),compose(domain(X0),compose(a,b))) = compose(compose(compose(h,a),domain(X0)),compose(a,b))
| domain(X0) != domain(a)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f17103]) ).
fof(f17141,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(domain(compose(g,a)),X0)) = compose(compose(compose(h,compose(a,b)),domain(compose(g,a))),X0)
| domain(compose(g,a)) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f4650]) ).
fof(f17142,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(domain(compose(h,compose(a,b))),X0)) = compose(compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b)))),X0)
| domain(compose(h,compose(a,b))) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f4650]) ).
fof(f17143,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(domain(compose(h,a)),X0)) = compose(compose(compose(h,compose(a,b)),domain(compose(h,a))),X0)
| domain(compose(h,a)) != domain(X0)
| codomain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f4650]) ).
fof(f17144,plain,
! [X0] :
( compose(compose(h,compose(a,b)),compose(domain(compose(a,b)),X0)) = compose(compose(compose(h,compose(a,b)),domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f4650]) ).
fof(f17151,definition,
! [X0] :
( sQ1728_spl
<=> ( compose(compose(h,compose(a,b)),compose(domain(compose(g,a)),X0)) = compose(compose(compose(h,compose(a,b)),domain(compose(g,a))),X0)
| domain(compose(g,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1728_spl])],[split_symbol_definition]) ).
fof(f17154,plain,
( sQ1728_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f17141,f1555,f17151]) ).
fof(f17155,definition,
! [X0] :
( sQ1729_spl
<=> ( compose(compose(h,compose(a,b)),compose(domain(compose(h,compose(a,b))),X0)) = compose(compose(compose(h,compose(a,b)),domain(compose(h,compose(a,b)))),X0)
| domain(compose(h,compose(a,b))) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1729_spl])],[split_symbol_definition]) ).
fof(f17158,plain,
( sQ1729_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f17142,f1555,f17155]) ).
fof(f17159,definition,
! [X0] :
( sQ1730_spl
<=> ( compose(compose(h,compose(a,b)),compose(domain(compose(h,a)),X0)) = compose(compose(compose(h,compose(a,b)),domain(compose(h,a))),X0)
| domain(compose(h,a)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1730_spl])],[split_symbol_definition]) ).
fof(f17162,plain,
( sQ1730_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f17143,f1555,f17159]) ).
fof(f17163,definition,
! [X0] :
( sQ1731_spl
<=> ( compose(compose(h,compose(a,b)),compose(domain(compose(a,b)),X0)) = compose(compose(compose(h,compose(a,b)),domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1731_spl])],[split_symbol_definition]) ).
fof(f17166,plain,
( sQ1731_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f17144,f1570,f17163]) ).
fof(f17173,plain,
( compose(g,compose(codomain(g),compose(h,compose(a,b)))) = compose(compose(g,codomain(g)),compose(h,compose(a,b)))
| codomain(g) != domain(h) ),
inference(resolution,[status(thm)],[f14772,f74]) ).
fof(f17174,plain,
( compose(g,compose(codomain(h),compose(h,compose(a,b)))) = compose(compose(g,codomain(h)),compose(h,compose(a,b)))
| codomain(h) != domain(h) ),
inference(resolution,[status(thm)],[f14772,f69]) ).
fof(f17175,plain,
( compose(g,compose(codomain(domain(a)),compose(h,compose(a,b)))) = compose(compose(g,codomain(domain(a))),compose(h,compose(a,b)))
| codomain(domain(a)) != domain(h) ),
inference(resolution,[status(thm)],[f14772,f15]) ).
fof(f17176,plain,
( compose(g,compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(g,codomain(compose(a,b))),compose(h,compose(a,b)))
| codomain(compose(a,b)) != domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f14772]) ).
fof(f17177,plain,
( compose(g,compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(g,codomain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f14772]) ).
fof(f17178,plain,
( compose(g,compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(g,codomain(compose(h,a))),compose(h,compose(a,b)))
| codomain(compose(h,a)) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f14772]) ).
fof(f17179,plain,
( compose(g,compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(g,codomain(compose(g,a))),compose(h,compose(a,b)))
| codomain(compose(g,a)) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f14772]) ).
fof(f17180,plain,
( compose(g,compose(codomain(g),compose(h,compose(a,b)))) = compose(compose(g,codomain(g)),compose(h,compose(a,b)))
| codomain(g) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f14772]) ).
fof(f17181,plain,
( compose(g,compose(codomain(h),compose(h,compose(a,b)))) = compose(compose(g,codomain(h)),compose(h,compose(a,b)))
| codomain(h) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f14772]) ).
fof(f17182,plain,
( compose(g,compose(codomain(a),compose(h,compose(a,b)))) = compose(compose(g,codomain(a)),compose(h,compose(a,b)))
| codomain(a) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f14772]) ).
fof(f17185,definition,
( sQ1732_spl
<=> compose(g,compose(codomain(g),compose(h,compose(a,b)))) = compose(compose(g,codomain(g)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1732_spl])],[split_symbol_definition]) ).
fof(f17188,plain,
( sQ1732_spl
| ~ sQ1451_spl ),
inference(split_clause,[status(thm)],[f17173,f15061,f17185]) ).
fof(f17189,definition,
( sQ1733_spl
<=> compose(g,compose(codomain(h),compose(h,compose(a,b)))) = compose(compose(g,codomain(h)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1733_spl])],[split_symbol_definition]) ).
fof(f17192,plain,
( sQ1733_spl
| ~ sQ1453_spl ),
inference(split_clause,[status(thm)],[f17174,f15068,f17189]) ).
fof(f17193,definition,
( sQ1734_spl
<=> compose(g,compose(codomain(domain(a)),compose(h,compose(a,b)))) = compose(compose(g,codomain(domain(a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1734_spl])],[split_symbol_definition]) ).
fof(f17196,plain,
( sQ1734_spl
| ~ sQ1455_spl ),
inference(split_clause,[status(thm)],[f17175,f15075,f17193]) ).
fof(f17197,definition,
( sQ1735_spl
<=> compose(g,compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(g,codomain(compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1735_spl])],[split_symbol_definition]) ).
fof(f17200,plain,
( sQ1735_spl
| ~ sQ1457_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f17176,f1570,f15082,f17197]) ).
fof(f17201,definition,
( sQ1736_spl
<=> compose(g,compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(g,codomain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1736_spl])],[split_symbol_definition]) ).
fof(f17204,plain,
( sQ1736_spl
| ~ sQ1459_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f17177,f1570,f15089,f17201]) ).
fof(f17205,definition,
( sQ1737_spl
<=> compose(g,compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(g,codomain(compose(h,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1737_spl])],[split_symbol_definition]) ).
fof(f17208,plain,
( sQ1737_spl
| ~ sQ1461_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17178,f715,f15096,f17205]) ).
fof(f17209,definition,
( sQ1738_spl
<=> compose(g,compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(g,codomain(compose(g,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1738_spl])],[split_symbol_definition]) ).
fof(f17212,plain,
( sQ1738_spl
| ~ sQ1463_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17179,f715,f15103,f17209]) ).
fof(f17213,plain,
( sQ1732_spl
| ~ sQ1451_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f17180,f606,f15061,f17185]) ).
fof(f17214,plain,
( sQ1733_spl
| ~ sQ1453_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f17181,f606,f15068,f17189]) ).
fof(f17215,definition,
( sQ1739_spl
<=> compose(g,compose(codomain(a),compose(h,compose(a,b)))) = compose(compose(g,codomain(a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1739_spl])],[split_symbol_definition]) ).
fof(f17218,plain,
( sQ1739_spl
| ~ sQ1465_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17182,f715,f15112,f17215]) ).
fof(f17225,plain,
( compose(g,compose(domain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(g,domain(compose(a,b))),compose(h,compose(a,b)))
| domain(compose(a,b)) != domain(h) ),
inference(resolution,[status(thm)],[f14773,f60]) ).
fof(f17226,plain,
( compose(g,compose(domain(domain(a)),compose(h,compose(a,b)))) = compose(compose(g,domain(domain(a))),compose(h,compose(a,b)))
| domain(domain(a)) != domain(h) ),
inference(resolution,[status(thm)],[f14773,f37]) ).
fof(f17227,plain,
( compose(g,compose(domain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(g,domain(compose(g,a))),compose(h,compose(a,b)))
| domain(compose(g,a)) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f14773]) ).
fof(f17228,plain,
( compose(g,compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(g,domain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f14773]) ).
fof(f17229,plain,
( compose(g,compose(domain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(g,domain(compose(h,a))),compose(h,compose(a,b)))
| domain(compose(h,a)) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f14773]) ).
fof(f17230,plain,
( compose(g,compose(domain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(g,domain(compose(a,b))),compose(h,compose(a,b)))
| domain(compose(a,b)) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f14773]) ).
fof(f17233,plain,
( compose(g,compose(domain(a),compose(h,compose(a,b)))) = compose(compose(g,domain(a)),compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(equality_resolution,[status(thm)],[f14773]) ).
fof(f17234,definition,
( sQ1740_spl
<=> compose(g,compose(domain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(g,domain(compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1740_spl])],[split_symbol_definition]) ).
fof(f17237,plain,
( sQ1740_spl
| ~ sQ1467_spl ),
inference(split_clause,[status(thm)],[f17225,f15137,f17234]) ).
fof(f17238,definition,
( sQ1741_spl
<=> compose(g,compose(domain(domain(a)),compose(h,compose(a,b)))) = compose(compose(g,domain(domain(a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1741_spl])],[split_symbol_definition]) ).
fof(f17241,plain,
( sQ1741_spl
| ~ sQ1469_spl ),
inference(split_clause,[status(thm)],[f17226,f15144,f17238]) ).
fof(f17242,definition,
( sQ1742_spl
<=> compose(g,compose(domain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(g,domain(compose(g,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1742_spl])],[split_symbol_definition]) ).
fof(f17245,plain,
( sQ1742_spl
| ~ sQ1471_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f17227,f584,f15151,f17242]) ).
fof(f17246,definition,
( sQ1743_spl
<=> compose(g,compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(g,domain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1743_spl])],[split_symbol_definition]) ).
fof(f17249,plain,
( sQ1743_spl
| ~ sQ49_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f17228,f584,f1100,f17246]) ).
fof(f17250,definition,
( sQ1744_spl
<=> compose(g,compose(domain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(g,domain(compose(h,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1744_spl])],[split_symbol_definition]) ).
fof(f17253,plain,
( sQ1744_spl
| ~ sQ1474_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f17229,f584,f15162,f17250]) ).
fof(f17254,plain,
( sQ1740_spl
| ~ sQ1467_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f17230,f606,f15137,f17234]) ).
fof(f17261,definition,
( sQ1745_spl
<=> compose(g,compose(domain(a),compose(h,compose(a,b)))) = compose(compose(g,domain(a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1745_spl])],[split_symbol_definition]) ).
fof(f17264,plain,
( sQ1745_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f17233,f584,f17261]) ).
fof(f17265,plain,
( compose(h,compose(codomain(g),compose(h,compose(a,b)))) = compose(compose(h,codomain(g)),compose(h,compose(a,b)))
| codomain(g) != domain(h) ),
inference(resolution,[status(thm)],[f15047,f74]) ).
fof(f17266,plain,
( compose(h,compose(codomain(h),compose(h,compose(a,b)))) = compose(compose(h,codomain(h)),compose(h,compose(a,b)))
| codomain(h) != domain(h) ),
inference(resolution,[status(thm)],[f15047,f69]) ).
fof(f17267,plain,
( compose(h,compose(codomain(domain(a)),compose(h,compose(a,b)))) = compose(compose(h,codomain(domain(a))),compose(h,compose(a,b)))
| codomain(domain(a)) != domain(h) ),
inference(resolution,[status(thm)],[f15047,f15]) ).
fof(f17268,plain,
( compose(h,compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,codomain(compose(a,b))),compose(h,compose(a,b)))
| codomain(compose(a,b)) != domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f15047]) ).
fof(f17269,plain,
( compose(h,compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(h,codomain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(a) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f15047]) ).
fof(f17270,plain,
( compose(h,compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(h,codomain(compose(h,a))),compose(h,compose(a,b)))
| codomain(compose(h,a)) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f15047]) ).
fof(f17271,plain,
( compose(h,compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(h,codomain(compose(g,a))),compose(h,compose(a,b)))
| codomain(compose(g,a)) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f15047]) ).
fof(f17272,plain,
( compose(h,compose(codomain(g),compose(h,compose(a,b)))) = compose(compose(h,codomain(g)),compose(h,compose(a,b)))
| codomain(g) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f15047]) ).
fof(f17273,plain,
( compose(h,compose(codomain(h),compose(h,compose(a,b)))) = compose(compose(h,codomain(h)),compose(h,compose(a,b)))
| codomain(h) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f15047]) ).
fof(f17274,plain,
( compose(h,compose(codomain(a),compose(h,compose(a,b)))) = compose(compose(h,codomain(a)),compose(h,compose(a,b)))
| codomain(a) != domain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f15047]) ).
fof(f17277,definition,
( sQ1746_spl
<=> compose(h,compose(codomain(g),compose(h,compose(a,b)))) = compose(compose(h,codomain(g)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1746_spl])],[split_symbol_definition]) ).
fof(f17280,plain,
( sQ1746_spl
| ~ sQ1451_spl ),
inference(split_clause,[status(thm)],[f17265,f15061,f17277]) ).
fof(f17281,definition,
( sQ1747_spl
<=> compose(h,compose(codomain(h),compose(h,compose(a,b)))) = compose(compose(h,codomain(h)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1747_spl])],[split_symbol_definition]) ).
fof(f17284,plain,
( sQ1747_spl
| ~ sQ1453_spl ),
inference(split_clause,[status(thm)],[f17266,f15068,f17281]) ).
fof(f17285,definition,
( sQ1748_spl
<=> compose(h,compose(codomain(domain(a)),compose(h,compose(a,b)))) = compose(compose(h,codomain(domain(a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1748_spl])],[split_symbol_definition]) ).
fof(f17288,plain,
( sQ1748_spl
| ~ sQ1455_spl ),
inference(split_clause,[status(thm)],[f17267,f15075,f17285]) ).
fof(f17289,definition,
( sQ1749_spl
<=> compose(h,compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,codomain(compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1749_spl])],[split_symbol_definition]) ).
fof(f17292,plain,
( sQ1749_spl
| ~ sQ1457_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f17268,f1570,f15082,f17289]) ).
fof(f17293,definition,
( sQ1750_spl
<=> compose(h,compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(h,codomain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1750_spl])],[split_symbol_definition]) ).
fof(f17296,plain,
( sQ1750_spl
| ~ sQ1459_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f17269,f1570,f15089,f17293]) ).
fof(f17297,definition,
( sQ1751_spl
<=> compose(h,compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(h,codomain(compose(h,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1751_spl])],[split_symbol_definition]) ).
fof(f17300,plain,
( sQ1751_spl
| ~ sQ1461_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17270,f715,f15096,f17297]) ).
fof(f17301,definition,
( sQ1752_spl
<=> compose(h,compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(h,codomain(compose(g,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1752_spl])],[split_symbol_definition]) ).
fof(f17304,plain,
( sQ1752_spl
| ~ sQ1463_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17271,f715,f15103,f17301]) ).
fof(f17305,plain,
( sQ1746_spl
| ~ sQ1451_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f17272,f606,f15061,f17277]) ).
fof(f17306,plain,
( sQ1747_spl
| ~ sQ1453_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f17273,f606,f15068,f17281]) ).
fof(f17307,definition,
( sQ1753_spl
<=> compose(h,compose(codomain(a),compose(h,compose(a,b)))) = compose(compose(h,codomain(a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1753_spl])],[split_symbol_definition]) ).
fof(f17310,plain,
( sQ1753_spl
| ~ sQ1465_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17274,f715,f15112,f17307]) ).
fof(f17317,plain,
( compose(compose(h,a),compose(domain(h),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(h)),compose(h,compose(a,b)))
| domain(b) != domain(domain(h)) ),
inference(resolution,[status(thm)],[f4950,f15]) ).
fof(f17318,plain,
( compose(compose(h,a),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(a,b)),compose(h,compose(a,b)))
| codomain(b) != domain(h)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f120,f4950]) ).
fof(f17319,plain,
( compose(compose(h,a),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b)))
| codomain(b) != domain(h)
| domain(b) != domain(compose(h,compose(a,b))) ),
inference(paramodulation,[status(thm)],[f581,f4950]) ).
fof(f17320,plain,
( compose(compose(h,a),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(h,a)),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(b) != domain(compose(h,a)) ),
inference(paramodulation,[status(thm)],[f131,f4950]) ).
fof(f17321,plain,
( compose(compose(h,a),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(g,a)),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(b) != domain(compose(g,a)) ),
inference(paramodulation,[status(thm)],[f130,f4950]) ).
fof(f17322,plain,
( compose(compose(h,a),compose(g,compose(h,compose(a,b)))) = compose(compose(compose(h,a),g),compose(h,compose(a,b)))
| domain(a) != domain(h)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f74,f4950]) ).
fof(f17323,plain,
( compose(compose(h,a),compose(h,compose(h,compose(a,b)))) = compose(compose(compose(h,a),h),compose(h,compose(a,b)))
| domain(a) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f69,f4950]) ).
fof(f17324,plain,
( compose(compose(h,a),compose(a,compose(h,compose(a,b)))) = compose(compose(compose(h,a),a),compose(h,compose(a,b)))
| domain(b) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f22,f4950]) ).
fof(f17325,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(X0),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(X0)),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f38,f4950]) ).
fof(f17326,plain,
! [X0] :
( compose(compose(h,a),compose(domain(X0),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(X0)),compose(h,compose(a,b)))
| domain(X0) != domain(h)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f15,f4950]) ).
fof(f17327,definition,
( sQ1754_spl
<=> compose(compose(h,a),compose(domain(h),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(h)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1754_spl])],[split_symbol_definition]) ).
fof(f17330,plain,
( sQ1754_spl
| ~ sQ1013_spl ),
inference(split_clause,[status(thm)],[f17317,f11076,f17327]) ).
fof(f17331,definition,
( sQ1755_spl
<=> compose(compose(h,a),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(a,b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1755_spl])],[split_symbol_definition]) ).
fof(f17334,plain,
( sQ1755_spl
| ~ sQ66_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f17318,f2359,f1555,f17331]) ).
fof(f17335,definition,
( sQ1756_spl
<=> compose(compose(h,a),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1756_spl])],[split_symbol_definition]) ).
fof(f17338,plain,
( sQ1756_spl
| ~ sQ66_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f17319,f2366,f1555,f17335]) ).
fof(f17339,definition,
( sQ1757_spl
<=> compose(compose(h,a),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(h,a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1757_spl])],[split_symbol_definition]) ).
fof(f17342,plain,
( sQ1757_spl
| ~ sQ21_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f17320,f2330,f693,f17339]) ).
fof(f17343,definition,
( sQ1758_spl
<=> compose(compose(h,a),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(g,a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1758_spl])],[split_symbol_definition]) ).
fof(f17346,plain,
( sQ1758_spl
| ~ sQ21_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f17321,f2337,f693,f17343]) ).
fof(f17347,definition,
( sQ1759_spl
<=> compose(compose(h,a),compose(g,compose(h,compose(a,b)))) = compose(compose(compose(h,a),g),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1759_spl])],[split_symbol_definition]) ).
fof(f17350,plain,
( sQ1759_spl
| ~ sQ8_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f17322,f700,f584,f17347]) ).
fof(f17351,definition,
( sQ1760_spl
<=> compose(compose(h,a),compose(h,compose(h,compose(a,b)))) = compose(compose(compose(h,a),h),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1760_spl])],[split_symbol_definition]) ).
fof(f17354,plain,
( sQ1760_spl
| ~ sQ8_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17323,f693,f584,f17351]) ).
fof(f17355,definition,
( sQ1761_spl
<=> compose(compose(h,a),compose(a,compose(h,compose(a,b)))) = compose(compose(compose(h,a),a),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1761_spl])],[split_symbol_definition]) ).
fof(f17358,plain,
( sQ1761_spl
| ~ sQ21_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17324,f715,f693,f17355]) ).
fof(f17359,plain,
! [X0] :
( compose(compose(h,a),compose(codomain(X0),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(X0)),compose(h,compose(a,b)))
| codomain(X0) != domain(h)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f17325]) ).
fof(f17360,plain,
! [X0] :
( compose(compose(h,a),compose(domain(X0),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(X0)),compose(h,compose(a,b)))
| domain(X0) != domain(h)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f37,f17326]) ).
fof(f17361,plain,
( compose(h,compose(domain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,domain(compose(a,b))),compose(h,compose(a,b)))
| domain(compose(a,b)) != domain(h) ),
inference(resolution,[status(thm)],[f15048,f60]) ).
fof(f17362,plain,
( compose(h,compose(domain(domain(a)),compose(h,compose(a,b)))) = compose(compose(h,domain(domain(a))),compose(h,compose(a,b)))
| domain(domain(a)) != domain(h) ),
inference(resolution,[status(thm)],[f15048,f37]) ).
fof(f17363,plain,
( compose(h,compose(domain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(h,domain(compose(g,a))),compose(h,compose(a,b)))
| domain(compose(g,a)) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f15048]) ).
fof(f17364,plain,
( compose(h,compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(h,domain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f15048]) ).
fof(f17365,plain,
( compose(h,compose(domain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(h,domain(compose(h,a))),compose(h,compose(a,b)))
| domain(compose(h,a)) != domain(h)
| domain(a) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f15048]) ).
fof(f17366,plain,
( compose(h,compose(domain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,domain(compose(a,b))),compose(h,compose(a,b)))
| domain(compose(a,b)) != domain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f15048]) ).
fof(f17369,plain,
( compose(h,compose(domain(a),compose(h,compose(a,b)))) = compose(compose(h,domain(a)),compose(h,compose(a,b)))
| domain(a) != domain(h) ),
inference(equality_resolution,[status(thm)],[f15048]) ).
fof(f17370,definition,
( sQ1762_spl
<=> compose(h,compose(domain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,domain(compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1762_spl])],[split_symbol_definition]) ).
fof(f17373,plain,
( sQ1762_spl
| ~ sQ1467_spl ),
inference(split_clause,[status(thm)],[f17361,f15137,f17370]) ).
fof(f17374,definition,
( sQ1763_spl
<=> compose(h,compose(domain(domain(a)),compose(h,compose(a,b)))) = compose(compose(h,domain(domain(a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1763_spl])],[split_symbol_definition]) ).
fof(f17377,plain,
( sQ1763_spl
| ~ sQ1469_spl ),
inference(split_clause,[status(thm)],[f17362,f15144,f17374]) ).
fof(f17378,definition,
( sQ1764_spl
<=> compose(h,compose(domain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(h,domain(compose(g,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1764_spl])],[split_symbol_definition]) ).
fof(f17381,plain,
( sQ1764_spl
| ~ sQ1471_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f17363,f584,f15151,f17378]) ).
fof(f17382,definition,
( sQ1765_spl
<=> compose(h,compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(h,domain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1765_spl])],[split_symbol_definition]) ).
fof(f17385,plain,
( sQ1765_spl
| ~ sQ49_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f17364,f584,f1100,f17382]) ).
fof(f17386,definition,
( sQ1766_spl
<=> compose(h,compose(domain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(h,domain(compose(h,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1766_spl])],[split_symbol_definition]) ).
fof(f17389,plain,
( sQ1766_spl
| ~ sQ1474_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f17365,f584,f15162,f17386]) ).
fof(f17390,plain,
( sQ1762_spl
| ~ sQ1467_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f17366,f606,f15137,f17370]) ).
fof(f17397,definition,
( sQ1767_spl
<=> compose(h,compose(domain(a),compose(h,compose(a,b)))) = compose(compose(h,domain(a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1767_spl])],[split_symbol_definition]) ).
fof(f17400,plain,
( sQ1767_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f17369,f584,f17397]) ).
fof(f17401,plain,
( compose(a,compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(a,codomain(compose(h,a))),compose(h,compose(a,b)))
| codomain(compose(h,a)) != domain(h) ),
inference(resolution,[status(thm)],[f15368,f131]) ).
fof(f17402,plain,
( compose(a,compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(a,codomain(compose(g,a))),compose(h,compose(a,b)))
| codomain(compose(g,a)) != domain(h) ),
inference(resolution,[status(thm)],[f15368,f130]) ).
fof(f17403,plain,
( compose(a,compose(codomain(a),compose(h,compose(a,b)))) = compose(compose(a,codomain(a)),compose(h,compose(a,b)))
| codomain(a) != domain(h) ),
inference(resolution,[status(thm)],[f15368,f22]) ).
fof(f17404,plain,
( compose(a,compose(codomain(domain(b)),compose(h,compose(a,b)))) = compose(compose(a,codomain(domain(b))),compose(h,compose(a,b)))
| codomain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f15368,f15]) ).
fof(f17405,plain,
( compose(a,compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(a,codomain(compose(a,b))),compose(h,compose(a,b)))
| codomain(compose(a,b)) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f15368]) ).
fof(f17406,plain,
( compose(a,compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(a,codomain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f15368]) ).
fof(f17407,plain,
( compose(a,compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(a,codomain(compose(h,a))),compose(h,compose(a,b)))
| codomain(compose(h,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f15368]) ).
fof(f17408,plain,
( compose(a,compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(a,codomain(compose(g,a))),compose(h,compose(a,b)))
| codomain(compose(g,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f15368]) ).
fof(f17409,plain,
( compose(a,compose(codomain(g),compose(h,compose(a,b)))) = compose(compose(a,codomain(g)),compose(h,compose(a,b)))
| codomain(g) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f15368]) ).
fof(f17410,plain,
( compose(a,compose(codomain(h),compose(h,compose(a,b)))) = compose(compose(a,codomain(h)),compose(h,compose(a,b)))
| codomain(h) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f15368]) ).
fof(f17411,plain,
( compose(a,compose(codomain(a),compose(h,compose(a,b)))) = compose(compose(a,codomain(a)),compose(h,compose(a,b)))
| codomain(a) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f15368]) ).
fof(f17414,definition,
( sQ1768_spl
<=> compose(a,compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(a,codomain(compose(h,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1768_spl])],[split_symbol_definition]) ).
fof(f17417,plain,
( sQ1768_spl
| ~ sQ1461_spl ),
inference(split_clause,[status(thm)],[f17401,f15096,f17414]) ).
fof(f17418,definition,
( sQ1769_spl
<=> compose(a,compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(a,codomain(compose(g,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1769_spl])],[split_symbol_definition]) ).
fof(f17421,plain,
( sQ1769_spl
| ~ sQ1463_spl ),
inference(split_clause,[status(thm)],[f17402,f15103,f17418]) ).
fof(f17422,definition,
( sQ1770_spl
<=> compose(a,compose(codomain(a),compose(h,compose(a,b)))) = compose(compose(a,codomain(a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1770_spl])],[split_symbol_definition]) ).
fof(f17425,plain,
( sQ1770_spl
| ~ sQ1465_spl ),
inference(split_clause,[status(thm)],[f17403,f15112,f17422]) ).
fof(f17426,definition,
( sQ1771_spl
<=> compose(a,compose(codomain(domain(b)),compose(h,compose(a,b)))) = compose(compose(a,codomain(domain(b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1771_spl])],[split_symbol_definition]) ).
fof(f17429,plain,
( sQ1771_spl
| ~ sQ1530_spl ),
inference(split_clause,[status(thm)],[f17404,f15527,f17426]) ).
fof(f17430,definition,
( sQ1772_spl
<=> compose(a,compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(a,codomain(compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1772_spl])],[split_symbol_definition]) ).
fof(f17433,plain,
( sQ1772_spl
| ~ sQ1457_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f17405,f2265,f15082,f17430]) ).
fof(f17434,definition,
( sQ1773_spl
<=> compose(a,compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(a,codomain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1773_spl])],[split_symbol_definition]) ).
fof(f17437,plain,
( sQ1773_spl
| ~ sQ1459_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f17406,f2265,f15089,f17434]) ).
fof(f17438,plain,
( sQ1768_spl
| ~ sQ1461_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17407,f1941,f15096,f17414]) ).
fof(f17439,plain,
( sQ1769_spl
| ~ sQ1463_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17408,f1941,f15103,f17418]) ).
fof(f17440,definition,
( sQ1774_spl
<=> compose(a,compose(codomain(g),compose(h,compose(a,b)))) = compose(compose(a,codomain(g)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1774_spl])],[split_symbol_definition]) ).
fof(f17443,plain,
( sQ1774_spl
| ~ sQ1451_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17409,f715,f15061,f17440]) ).
fof(f17444,definition,
( sQ1775_spl
<=> compose(a,compose(codomain(h),compose(h,compose(a,b)))) = compose(compose(a,codomain(h)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1775_spl])],[split_symbol_definition]) ).
fof(f17447,plain,
( sQ1775_spl
| ~ sQ1453_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17410,f715,f15068,f17444]) ).
fof(f17448,plain,
( sQ1770_spl
| ~ sQ1465_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17411,f1941,f15112,f17422]) ).
fof(f17455,plain,
( compose(a,compose(domain(domain(b)),compose(h,compose(a,b)))) = compose(compose(a,domain(domain(b))),compose(h,compose(a,b)))
| domain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f15369,f37]) ).
fof(f17456,plain,
( compose(a,compose(domain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(a,domain(compose(g,a))),compose(h,compose(a,b)))
| domain(compose(g,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f15369]) ).
fof(f17457,plain,
( compose(a,compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(a,domain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f15369]) ).
fof(f17458,plain,
( compose(a,compose(domain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(a,domain(compose(h,a))),compose(h,compose(a,b)))
| domain(compose(h,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f15369]) ).
fof(f17459,plain,
( compose(a,compose(domain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(a,domain(compose(a,b))),compose(h,compose(a,b)))
| domain(compose(a,b)) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f15369]) ).
fof(f17462,plain,
( compose(a,compose(domain(b),compose(h,compose(a,b)))) = compose(compose(a,domain(b)),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(equality_resolution,[status(thm)],[f15369]) ).
fof(f17463,definition,
( sQ1776_spl
<=> compose(a,compose(domain(domain(b)),compose(h,compose(a,b)))) = compose(compose(a,domain(domain(b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1776_spl])],[split_symbol_definition]) ).
fof(f17466,plain,
( sQ1776_spl
| ~ sQ1536_spl ),
inference(split_clause,[status(thm)],[f17455,f15571,f17463]) ).
fof(f17467,definition,
( sQ1777_spl
<=> compose(a,compose(domain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(a,domain(compose(g,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1777_spl])],[split_symbol_definition]) ).
fof(f17470,plain,
( sQ1777_spl
| ~ sQ1471_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17456,f693,f15151,f17467]) ).
fof(f17471,definition,
( sQ1778_spl
<=> compose(a,compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(a,domain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1778_spl])],[split_symbol_definition]) ).
fof(f17474,plain,
( sQ1778_spl
| ~ sQ49_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17457,f693,f1100,f17471]) ).
fof(f17475,definition,
( sQ1779_spl
<=> compose(a,compose(domain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(a,domain(compose(h,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1779_spl])],[split_symbol_definition]) ).
fof(f17478,plain,
( sQ1779_spl
| ~ sQ1474_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17458,f693,f15162,f17475]) ).
fof(f17479,definition,
( sQ1780_spl
<=> compose(a,compose(domain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(a,domain(compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1780_spl])],[split_symbol_definition]) ).
fof(f17482,plain,
( sQ1780_spl
| ~ sQ1467_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17459,f715,f15137,f17479]) ).
fof(f17489,definition,
( sQ1781_spl
<=> compose(a,compose(domain(b),compose(h,compose(a,b)))) = compose(compose(a,domain(b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1781_spl])],[split_symbol_definition]) ).
fof(f17492,plain,
( sQ1781_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17462,f693,f17489]) ).
fof(f17493,plain,
( compose(compose(g,a),compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(compose(g,a),codomain(compose(h,a))),compose(g,a))
| codomain(compose(h,a)) != domain(h) ),
inference(resolution,[status(thm)],[f16385,f131]) ).
fof(f17494,plain,
( compose(compose(g,a),compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(compose(g,a),codomain(compose(g,a))),compose(g,a))
| codomain(compose(g,a)) != domain(h) ),
inference(resolution,[status(thm)],[f16385,f130]) ).
fof(f17495,plain,
( compose(compose(g,a),compose(codomain(a),compose(g,a))) = compose(compose(compose(g,a),codomain(a)),compose(g,a))
| codomain(a) != domain(h) ),
inference(resolution,[status(thm)],[f16385,f22]) ).
fof(f17496,plain,
( compose(compose(g,a),compose(codomain(domain(b)),compose(g,a))) = compose(compose(compose(g,a),codomain(domain(b))),compose(g,a))
| codomain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f16385,f15]) ).
fof(f17497,plain,
( compose(compose(g,a),compose(codomain(compose(a,b)),compose(g,a))) = compose(compose(compose(g,a),codomain(compose(a,b))),compose(g,a))
| codomain(compose(a,b)) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f16385]) ).
fof(f17498,plain,
( compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),compose(g,a))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f16385]) ).
fof(f17499,plain,
( compose(compose(g,a),compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(compose(g,a),codomain(compose(h,a))),compose(g,a))
| codomain(compose(h,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f16385]) ).
fof(f17500,plain,
( compose(compose(g,a),compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(compose(g,a),codomain(compose(g,a))),compose(g,a))
| codomain(compose(g,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f16385]) ).
fof(f17501,plain,
( compose(compose(g,a),compose(codomain(g),compose(g,a))) = compose(compose(compose(g,a),codomain(g)),compose(g,a))
| codomain(g) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f16385]) ).
fof(f17502,plain,
( compose(compose(g,a),compose(codomain(h),compose(g,a))) = compose(compose(compose(g,a),codomain(h)),compose(g,a))
| codomain(h) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f16385]) ).
fof(f17503,plain,
( compose(compose(g,a),compose(codomain(a),compose(g,a))) = compose(compose(compose(g,a),codomain(a)),compose(g,a))
| codomain(a) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f16385]) ).
fof(f17506,definition,
( sQ1782_spl
<=> compose(compose(g,a),compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(compose(g,a),codomain(compose(h,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1782_spl])],[split_symbol_definition]) ).
fof(f17509,plain,
( sQ1782_spl
| ~ sQ1461_spl ),
inference(split_clause,[status(thm)],[f17493,f15096,f17506]) ).
fof(f17510,definition,
( sQ1783_spl
<=> compose(compose(g,a),compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(compose(g,a),codomain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1783_spl])],[split_symbol_definition]) ).
fof(f17513,plain,
( sQ1783_spl
| ~ sQ1463_spl ),
inference(split_clause,[status(thm)],[f17494,f15103,f17510]) ).
fof(f17514,definition,
( sQ1784_spl
<=> compose(compose(g,a),compose(codomain(a),compose(g,a))) = compose(compose(compose(g,a),codomain(a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1784_spl])],[split_symbol_definition]) ).
fof(f17517,plain,
( sQ1784_spl
| ~ sQ1465_spl ),
inference(split_clause,[status(thm)],[f17495,f15112,f17514]) ).
fof(f17518,definition,
( sQ1785_spl
<=> compose(compose(g,a),compose(codomain(domain(b)),compose(g,a))) = compose(compose(compose(g,a),codomain(domain(b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1785_spl])],[split_symbol_definition]) ).
fof(f17521,plain,
( sQ1785_spl
| ~ sQ1530_spl ),
inference(split_clause,[status(thm)],[f17496,f15527,f17518]) ).
fof(f17522,definition,
( sQ1786_spl
<=> compose(compose(g,a),compose(codomain(compose(a,b)),compose(g,a))) = compose(compose(compose(g,a),codomain(compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1786_spl])],[split_symbol_definition]) ).
fof(f17525,plain,
( sQ1786_spl
| ~ sQ1457_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f17497,f2265,f15082,f17522]) ).
fof(f17526,definition,
( sQ1787_spl
<=> compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1787_spl])],[split_symbol_definition]) ).
fof(f17529,plain,
( sQ1787_spl
| ~ sQ1459_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f17498,f2265,f15089,f17526]) ).
fof(f17530,plain,
( sQ1782_spl
| ~ sQ1461_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17499,f1941,f15096,f17506]) ).
fof(f17531,plain,
( sQ1783_spl
| ~ sQ1463_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17500,f1941,f15103,f17510]) ).
fof(f17532,definition,
( sQ1788_spl
<=> compose(compose(g,a),compose(codomain(g),compose(g,a))) = compose(compose(compose(g,a),codomain(g)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1788_spl])],[split_symbol_definition]) ).
fof(f17535,plain,
( sQ1788_spl
| ~ sQ1451_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17501,f715,f15061,f17532]) ).
fof(f17536,definition,
( sQ1789_spl
<=> compose(compose(g,a),compose(codomain(h),compose(g,a))) = compose(compose(compose(g,a),codomain(h)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1789_spl])],[split_symbol_definition]) ).
fof(f17539,plain,
( sQ1789_spl
| ~ sQ1453_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17502,f715,f15068,f17536]) ).
fof(f17540,plain,
( sQ1784_spl
| ~ sQ1465_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17503,f1941,f15112,f17514]) ).
fof(f17547,plain,
( compose(compose(g,a),compose(domain(domain(b)),compose(g,a))) = compose(compose(compose(g,a),domain(domain(b))),compose(g,a))
| domain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f16386,f37]) ).
fof(f17548,plain,
( compose(compose(g,a),compose(domain(compose(g,a)),compose(g,a))) = compose(compose(compose(g,a),domain(compose(g,a))),compose(g,a))
| domain(compose(g,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f16386]) ).
fof(f17549,plain,
( compose(compose(g,a),compose(domain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),compose(g,a))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f16386]) ).
fof(f17550,plain,
( compose(compose(g,a),compose(domain(compose(h,a)),compose(g,a))) = compose(compose(compose(g,a),domain(compose(h,a))),compose(g,a))
| domain(compose(h,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f16386]) ).
fof(f17551,plain,
( compose(compose(g,a),compose(domain(compose(a,b)),compose(g,a))) = compose(compose(compose(g,a),domain(compose(a,b))),compose(g,a))
| domain(compose(a,b)) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f16386]) ).
fof(f17554,plain,
( compose(compose(g,a),compose(domain(b),compose(g,a))) = compose(compose(compose(g,a),domain(b)),compose(g,a))
| domain(b) != domain(h) ),
inference(equality_resolution,[status(thm)],[f16386]) ).
fof(f17555,definition,
( sQ1790_spl
<=> compose(compose(g,a),compose(domain(domain(b)),compose(g,a))) = compose(compose(compose(g,a),domain(domain(b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1790_spl])],[split_symbol_definition]) ).
fof(f17558,plain,
( sQ1790_spl
| ~ sQ1536_spl ),
inference(split_clause,[status(thm)],[f17547,f15571,f17555]) ).
fof(f17559,definition,
( sQ1791_spl
<=> compose(compose(g,a),compose(domain(compose(g,a)),compose(g,a))) = compose(compose(compose(g,a),domain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1791_spl])],[split_symbol_definition]) ).
fof(f17562,plain,
( sQ1791_spl
| ~ sQ1471_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17548,f693,f15151,f17559]) ).
fof(f17563,definition,
( sQ1792_spl
<=> compose(compose(g,a),compose(domain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1792_spl])],[split_symbol_definition]) ).
fof(f17566,plain,
( sQ1792_spl
| ~ sQ49_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17549,f693,f1100,f17563]) ).
fof(f17567,definition,
( sQ1793_spl
<=> compose(compose(g,a),compose(domain(compose(h,a)),compose(g,a))) = compose(compose(compose(g,a),domain(compose(h,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1793_spl])],[split_symbol_definition]) ).
fof(f17570,plain,
( sQ1793_spl
| ~ sQ1474_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17550,f693,f15162,f17567]) ).
fof(f17571,definition,
( sQ1794_spl
<=> compose(compose(g,a),compose(domain(compose(a,b)),compose(g,a))) = compose(compose(compose(g,a),domain(compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1794_spl])],[split_symbol_definition]) ).
fof(f17574,plain,
( sQ1794_spl
| ~ sQ1467_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17551,f715,f15137,f17571]) ).
fof(f17581,definition,
( sQ1795_spl
<=> compose(compose(g,a),compose(domain(b),compose(g,a))) = compose(compose(compose(g,a),domain(b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1795_spl])],[split_symbol_definition]) ).
fof(f17584,plain,
( sQ1795_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17554,f693,f17581]) ).
fof(f17585,plain,
( compose(compose(g,a),compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(compose(h,a))),compose(h,compose(a,b)))
| codomain(compose(h,a)) != domain(h) ),
inference(resolution,[status(thm)],[f16761,f131]) ).
fof(f17586,plain,
( compose(compose(g,a),compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(compose(g,a))),compose(h,compose(a,b)))
| codomain(compose(g,a)) != domain(h) ),
inference(resolution,[status(thm)],[f16761,f130]) ).
fof(f17587,plain,
( compose(compose(g,a),compose(codomain(a),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(a)),compose(h,compose(a,b)))
| codomain(a) != domain(h) ),
inference(resolution,[status(thm)],[f16761,f22]) ).
fof(f17588,plain,
( compose(compose(g,a),compose(codomain(domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(domain(b))),compose(h,compose(a,b)))
| codomain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f16761,f15]) ).
fof(f17589,plain,
( compose(compose(g,a),compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(compose(a,b))),compose(h,compose(a,b)))
| codomain(compose(a,b)) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f16761]) ).
fof(f17590,plain,
( compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f16761]) ).
fof(f17591,plain,
( compose(compose(g,a),compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(compose(h,a))),compose(h,compose(a,b)))
| codomain(compose(h,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f16761]) ).
fof(f17592,plain,
( compose(compose(g,a),compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(compose(g,a))),compose(h,compose(a,b)))
| codomain(compose(g,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f16761]) ).
fof(f17593,plain,
( compose(compose(g,a),compose(codomain(g),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(g)),compose(h,compose(a,b)))
| codomain(g) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f16761]) ).
fof(f17594,plain,
( compose(compose(g,a),compose(codomain(h),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(h)),compose(h,compose(a,b)))
| codomain(h) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f16761]) ).
fof(f17595,plain,
( compose(compose(g,a),compose(codomain(a),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(a)),compose(h,compose(a,b)))
| codomain(a) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f16761]) ).
fof(f17598,definition,
( sQ1796_spl
<=> compose(compose(g,a),compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(compose(h,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1796_spl])],[split_symbol_definition]) ).
fof(f17601,plain,
( sQ1796_spl
| ~ sQ1461_spl ),
inference(split_clause,[status(thm)],[f17585,f15096,f17598]) ).
fof(f17602,definition,
( sQ1797_spl
<=> compose(compose(g,a),compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(compose(g,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1797_spl])],[split_symbol_definition]) ).
fof(f17605,plain,
( sQ1797_spl
| ~ sQ1463_spl ),
inference(split_clause,[status(thm)],[f17586,f15103,f17602]) ).
fof(f17606,definition,
( sQ1798_spl
<=> compose(compose(g,a),compose(codomain(a),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1798_spl])],[split_symbol_definition]) ).
fof(f17609,plain,
( sQ1798_spl
| ~ sQ1465_spl ),
inference(split_clause,[status(thm)],[f17587,f15112,f17606]) ).
fof(f17610,definition,
( sQ1799_spl
<=> compose(compose(g,a),compose(codomain(domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(domain(b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1799_spl])],[split_symbol_definition]) ).
fof(f17613,plain,
( sQ1799_spl
| ~ sQ1530_spl ),
inference(split_clause,[status(thm)],[f17588,f15527,f17610]) ).
fof(f17614,definition,
( sQ1800_spl
<=> compose(compose(g,a),compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1800_spl])],[split_symbol_definition]) ).
fof(f17617,plain,
( sQ1800_spl
| ~ sQ1457_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f17589,f2265,f15082,f17614]) ).
fof(f17618,definition,
( sQ1801_spl
<=> compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1801_spl])],[split_symbol_definition]) ).
fof(f17621,plain,
( sQ1801_spl
| ~ sQ1459_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f17590,f2265,f15089,f17618]) ).
fof(f17622,plain,
( sQ1796_spl
| ~ sQ1461_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17591,f1941,f15096,f17598]) ).
fof(f17623,plain,
( sQ1797_spl
| ~ sQ1463_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17592,f1941,f15103,f17602]) ).
fof(f17624,definition,
( sQ1802_spl
<=> compose(compose(g,a),compose(codomain(g),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(g)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1802_spl])],[split_symbol_definition]) ).
fof(f17627,plain,
( sQ1802_spl
| ~ sQ1451_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17593,f715,f15061,f17624]) ).
fof(f17628,definition,
( sQ1803_spl
<=> compose(compose(g,a),compose(codomain(h),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(h)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1803_spl])],[split_symbol_definition]) ).
fof(f17631,plain,
( sQ1803_spl
| ~ sQ1453_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17594,f715,f15068,f17628]) ).
fof(f17632,plain,
( sQ1798_spl
| ~ sQ1465_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17595,f1941,f15112,f17606]) ).
fof(f17639,plain,
( compose(compose(g,a),compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(compose(g,a),codomain(compose(h,a))),compose(h,a))
| codomain(compose(h,a)) != domain(h) ),
inference(resolution,[status(thm)],[f16909,f131]) ).
fof(f17640,plain,
( compose(compose(g,a),compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(compose(g,a),codomain(compose(g,a))),compose(h,a))
| codomain(compose(g,a)) != domain(h) ),
inference(resolution,[status(thm)],[f16909,f130]) ).
fof(f17641,plain,
( compose(compose(g,a),compose(codomain(a),compose(h,a))) = compose(compose(compose(g,a),codomain(a)),compose(h,a))
| codomain(a) != domain(h) ),
inference(resolution,[status(thm)],[f16909,f22]) ).
fof(f17642,plain,
( compose(compose(g,a),compose(codomain(domain(b)),compose(h,a))) = compose(compose(compose(g,a),codomain(domain(b))),compose(h,a))
| codomain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f16909,f15]) ).
fof(f17643,plain,
( compose(compose(g,a),compose(codomain(compose(a,b)),compose(h,a))) = compose(compose(compose(g,a),codomain(compose(a,b))),compose(h,a))
| codomain(compose(a,b)) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f16909]) ).
fof(f17644,plain,
( compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),compose(h,a))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f16909]) ).
fof(f17645,plain,
( compose(compose(g,a),compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(compose(g,a),codomain(compose(h,a))),compose(h,a))
| codomain(compose(h,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f16909]) ).
fof(f17646,plain,
( compose(compose(g,a),compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(compose(g,a),codomain(compose(g,a))),compose(h,a))
| codomain(compose(g,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f16909]) ).
fof(f17647,plain,
( compose(compose(g,a),compose(codomain(g),compose(h,a))) = compose(compose(compose(g,a),codomain(g)),compose(h,a))
| codomain(g) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f16909]) ).
fof(f17648,plain,
( compose(compose(g,a),compose(codomain(h),compose(h,a))) = compose(compose(compose(g,a),codomain(h)),compose(h,a))
| codomain(h) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f16909]) ).
fof(f17649,plain,
( compose(compose(g,a),compose(codomain(a),compose(h,a))) = compose(compose(compose(g,a),codomain(a)),compose(h,a))
| codomain(a) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f16909]) ).
fof(f17652,definition,
( sQ1804_spl
<=> compose(compose(g,a),compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(compose(g,a),codomain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1804_spl])],[split_symbol_definition]) ).
fof(f17655,plain,
( sQ1804_spl
| ~ sQ1461_spl ),
inference(split_clause,[status(thm)],[f17639,f15096,f17652]) ).
fof(f17656,definition,
( sQ1805_spl
<=> compose(compose(g,a),compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(compose(g,a),codomain(compose(g,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1805_spl])],[split_symbol_definition]) ).
fof(f17659,plain,
( sQ1805_spl
| ~ sQ1463_spl ),
inference(split_clause,[status(thm)],[f17640,f15103,f17656]) ).
fof(f17660,definition,
( sQ1806_spl
<=> compose(compose(g,a),compose(codomain(a),compose(h,a))) = compose(compose(compose(g,a),codomain(a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1806_spl])],[split_symbol_definition]) ).
fof(f17663,plain,
( sQ1806_spl
| ~ sQ1465_spl ),
inference(split_clause,[status(thm)],[f17641,f15112,f17660]) ).
fof(f17664,definition,
( sQ1807_spl
<=> compose(compose(g,a),compose(codomain(domain(b)),compose(h,a))) = compose(compose(compose(g,a),codomain(domain(b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1807_spl])],[split_symbol_definition]) ).
fof(f17667,plain,
( sQ1807_spl
| ~ sQ1530_spl ),
inference(split_clause,[status(thm)],[f17642,f15527,f17664]) ).
fof(f17668,definition,
( sQ1808_spl
<=> compose(compose(g,a),compose(codomain(compose(a,b)),compose(h,a))) = compose(compose(compose(g,a),codomain(compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1808_spl])],[split_symbol_definition]) ).
fof(f17671,plain,
( sQ1808_spl
| ~ sQ1457_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f17643,f2265,f15082,f17668]) ).
fof(f17672,definition,
( sQ1809_spl
<=> compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1809_spl])],[split_symbol_definition]) ).
fof(f17675,plain,
( sQ1809_spl
| ~ sQ1459_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f17644,f2265,f15089,f17672]) ).
fof(f17676,plain,
( sQ1804_spl
| ~ sQ1461_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17645,f1941,f15096,f17652]) ).
fof(f17677,plain,
( sQ1805_spl
| ~ sQ1463_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17646,f1941,f15103,f17656]) ).
fof(f17678,definition,
( sQ1810_spl
<=> compose(compose(g,a),compose(codomain(g),compose(h,a))) = compose(compose(compose(g,a),codomain(g)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1810_spl])],[split_symbol_definition]) ).
fof(f17681,plain,
( sQ1810_spl
| ~ sQ1451_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17647,f715,f15061,f17678]) ).
fof(f17682,definition,
( sQ1811_spl
<=> compose(compose(g,a),compose(codomain(h),compose(h,a))) = compose(compose(compose(g,a),codomain(h)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1811_spl])],[split_symbol_definition]) ).
fof(f17685,plain,
( sQ1811_spl
| ~ sQ1453_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17648,f715,f15068,f17682]) ).
fof(f17686,plain,
( sQ1806_spl
| ~ sQ1465_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17649,f1941,f15112,f17660]) ).
fof(f17693,plain,
( compose(compose(g,a),compose(domain(domain(b)),compose(h,a))) = compose(compose(compose(g,a),domain(domain(b))),compose(h,a))
| domain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f16910,f37]) ).
fof(f17694,plain,
( compose(compose(g,a),compose(domain(compose(g,a)),compose(h,a))) = compose(compose(compose(g,a),domain(compose(g,a))),compose(h,a))
| domain(compose(g,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f16910]) ).
fof(f17695,plain,
( compose(compose(g,a),compose(domain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),compose(h,a))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f16910]) ).
fof(f17696,plain,
( compose(compose(g,a),compose(domain(compose(h,a)),compose(h,a))) = compose(compose(compose(g,a),domain(compose(h,a))),compose(h,a))
| domain(compose(h,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f16910]) ).
fof(f17697,plain,
( compose(compose(g,a),compose(domain(compose(a,b)),compose(h,a))) = compose(compose(compose(g,a),domain(compose(a,b))),compose(h,a))
| domain(compose(a,b)) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f16910]) ).
fof(f17700,plain,
( compose(compose(g,a),compose(domain(b),compose(h,a))) = compose(compose(compose(g,a),domain(b)),compose(h,a))
| domain(b) != domain(h) ),
inference(equality_resolution,[status(thm)],[f16910]) ).
fof(f17701,definition,
( sQ1812_spl
<=> compose(compose(g,a),compose(domain(domain(b)),compose(h,a))) = compose(compose(compose(g,a),domain(domain(b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1812_spl])],[split_symbol_definition]) ).
fof(f17704,plain,
( sQ1812_spl
| ~ sQ1536_spl ),
inference(split_clause,[status(thm)],[f17693,f15571,f17701]) ).
fof(f17705,definition,
( sQ1813_spl
<=> compose(compose(g,a),compose(domain(compose(g,a)),compose(h,a))) = compose(compose(compose(g,a),domain(compose(g,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1813_spl])],[split_symbol_definition]) ).
fof(f17708,plain,
( sQ1813_spl
| ~ sQ1471_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17694,f693,f15151,f17705]) ).
fof(f17709,definition,
( sQ1814_spl
<=> compose(compose(g,a),compose(domain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1814_spl])],[split_symbol_definition]) ).
fof(f17712,plain,
( sQ1814_spl
| ~ sQ49_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17695,f693,f1100,f17709]) ).
fof(f17713,definition,
( sQ1815_spl
<=> compose(compose(g,a),compose(domain(compose(h,a)),compose(h,a))) = compose(compose(compose(g,a),domain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1815_spl])],[split_symbol_definition]) ).
fof(f17716,plain,
( sQ1815_spl
| ~ sQ1474_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17696,f693,f15162,f17713]) ).
fof(f17717,definition,
( sQ1816_spl
<=> compose(compose(g,a),compose(domain(compose(a,b)),compose(h,a))) = compose(compose(compose(g,a),domain(compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1816_spl])],[split_symbol_definition]) ).
fof(f17720,plain,
( sQ1816_spl
| ~ sQ1467_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17697,f715,f15137,f17717]) ).
fof(f17727,definition,
( sQ1817_spl
<=> compose(compose(g,a),compose(domain(b),compose(h,a))) = compose(compose(compose(g,a),domain(b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1817_spl])],[split_symbol_definition]) ).
fof(f17730,plain,
( sQ1817_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17700,f693,f17727]) ).
fof(f17731,plain,
( compose(compose(g,a),compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(compose(g,a),codomain(compose(h,a))),compose(a,b))
| codomain(compose(h,a)) != domain(a) ),
inference(resolution,[status(thm)],[f16957,f131]) ).
fof(f17732,plain,
( compose(compose(g,a),compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(compose(g,a),codomain(compose(g,a))),compose(a,b))
| codomain(compose(g,a)) != domain(a) ),
inference(resolution,[status(thm)],[f16957,f130]) ).
fof(f17733,plain,
( compose(compose(g,a),compose(codomain(a),compose(a,b))) = compose(compose(compose(g,a),codomain(a)),compose(a,b))
| codomain(a) != domain(a) ),
inference(resolution,[status(thm)],[f16957,f22]) ).
fof(f17734,plain,
( compose(compose(g,a),compose(codomain(domain(b)),compose(a,b))) = compose(compose(compose(g,a),codomain(domain(b))),compose(a,b))
| codomain(domain(b)) != domain(a) ),
inference(resolution,[status(thm)],[f16957,f15]) ).
fof(f17735,plain,
( compose(compose(g,a),compose(codomain(compose(a,b)),compose(a,b))) = compose(compose(compose(g,a),codomain(compose(a,b))),compose(a,b))
| codomain(compose(a,b)) != domain(a)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f16957]) ).
fof(f17736,plain,
( compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),compose(a,b))
| codomain(compose(h,compose(a,b))) != domain(a)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f16957]) ).
fof(f17737,plain,
( compose(compose(g,a),compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(compose(g,a),codomain(compose(h,a))),compose(a,b))
| codomain(compose(h,a)) != domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f16957]) ).
fof(f17738,plain,
( compose(compose(g,a),compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(compose(g,a),codomain(compose(g,a))),compose(a,b))
| codomain(compose(g,a)) != domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f16957]) ).
fof(f17739,plain,
( compose(compose(g,a),compose(codomain(g),compose(a,b))) = compose(compose(compose(g,a),codomain(g)),compose(a,b))
| codomain(g) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f16957]) ).
fof(f17740,plain,
( compose(compose(g,a),compose(codomain(h),compose(a,b))) = compose(compose(compose(g,a),codomain(h)),compose(a,b))
| codomain(h) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f16957]) ).
fof(f17741,plain,
( compose(compose(g,a),compose(codomain(a),compose(a,b))) = compose(compose(compose(g,a),codomain(a)),compose(a,b))
| codomain(a) != domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f16957]) ).
fof(f17744,definition,
( sQ1818_spl
<=> compose(compose(g,a),compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(compose(g,a),codomain(compose(h,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1818_spl])],[split_symbol_definition]) ).
fof(f17747,plain,
( sQ1818_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f17731,f3284,f17744]) ).
fof(f17748,definition,
( sQ1819_spl
<=> compose(compose(g,a),compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(compose(g,a),codomain(compose(g,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1819_spl])],[split_symbol_definition]) ).
fof(f17751,plain,
( sQ1819_spl
| ~ sQ203_spl ),
inference(split_clause,[status(thm)],[f17732,f3216,f17748]) ).
fof(f17752,definition,
( sQ1820_spl
<=> compose(compose(g,a),compose(codomain(a),compose(a,b))) = compose(compose(compose(g,a),codomain(a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1820_spl])],[split_symbol_definition]) ).
fof(f17755,plain,
( sQ1820_spl
| ~ sQ1133_spl ),
inference(split_clause,[status(thm)],[f17733,f12077,f17752]) ).
fof(f17756,definition,
( sQ1821_spl
<=> compose(compose(g,a),compose(codomain(domain(b)),compose(a,b))) = compose(compose(compose(g,a),codomain(domain(b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1821_spl])],[split_symbol_definition]) ).
fof(f17759,plain,
( sQ1821_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f17734,f562,f17756]) ).
fof(f17760,definition,
( sQ1822_spl
<=> compose(compose(g,a),compose(codomain(compose(a,b)),compose(a,b))) = compose(compose(compose(g,a),codomain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1822_spl])],[split_symbol_definition]) ).
fof(f17763,plain,
( sQ1822_spl
| ~ sQ1119_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f17735,f2265,f12019,f17760]) ).
fof(f17764,definition,
( sQ1823_spl
<=> compose(compose(g,a),compose(codomain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(g,a),codomain(compose(h,compose(a,b)))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1823_spl])],[split_symbol_definition]) ).
fof(f17767,plain,
( sQ1823_spl
| ~ sQ1121_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f17736,f2265,f12026,f17764]) ).
fof(f17768,plain,
( sQ1818_spl
| ~ sQ216_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17737,f1941,f3284,f17744]) ).
fof(f17769,plain,
( sQ1819_spl
| ~ sQ203_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17738,f1941,f3216,f17748]) ).
fof(f17770,definition,
( sQ1824_spl
<=> compose(compose(g,a),compose(codomain(g),compose(a,b))) = compose(compose(compose(g,a),codomain(g)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1824_spl])],[split_symbol_definition]) ).
fof(f17773,plain,
( sQ1824_spl
| ~ sQ1129_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17739,f715,f12063,f17770]) ).
fof(f17774,definition,
( sQ1825_spl
<=> compose(compose(g,a),compose(codomain(h),compose(a,b))) = compose(compose(compose(g,a),codomain(h)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1825_spl])],[split_symbol_definition]) ).
fof(f17777,plain,
( sQ1825_spl
| ~ sQ1131_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17740,f715,f12070,f17774]) ).
fof(f17778,plain,
( sQ1820_spl
| ~ sQ1133_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17741,f1941,f12077,f17752]) ).
fof(f17785,plain,
( compose(compose(g,a),compose(domain(domain(b)),compose(a,b))) = compose(compose(compose(g,a),domain(domain(b))),compose(a,b))
| domain(domain(b)) != domain(a) ),
inference(resolution,[status(thm)],[f16958,f37]) ).
fof(f17786,plain,
( compose(compose(g,a),compose(domain(compose(g,a)),compose(a,b))) = compose(compose(compose(g,a),domain(compose(g,a))),compose(a,b))
| domain(compose(g,a)) != domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f16958]) ).
fof(f17787,plain,
( compose(compose(g,a),compose(domain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),compose(a,b))
| domain(compose(h,compose(a,b))) != domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f16958]) ).
fof(f17788,plain,
( compose(compose(g,a),compose(domain(compose(h,a)),compose(a,b))) = compose(compose(compose(g,a),domain(compose(h,a))),compose(a,b))
| domain(compose(h,a)) != domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f16958]) ).
fof(f17789,plain,
( compose(compose(g,a),compose(domain(compose(a,b)),compose(a,b))) = compose(compose(compose(g,a),domain(compose(a,b))),compose(a,b))
| domain(compose(a,b)) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f16958]) ).
fof(f17792,plain,
( compose(compose(g,a),compose(domain(b),compose(a,b))) = compose(compose(compose(g,a),domain(b)),compose(a,b))
| domain(b) != domain(a) ),
inference(equality_resolution,[status(thm)],[f16958]) ).
fof(f17793,definition,
( sQ1826_spl
<=> compose(compose(g,a),compose(domain(domain(b)),compose(a,b))) = compose(compose(compose(g,a),domain(domain(b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1826_spl])],[split_symbol_definition]) ).
fof(f17796,plain,
( sQ1826_spl
| ~ sQ1570_spl ),
inference(split_clause,[status(thm)],[f17785,f15822,f17793]) ).
fof(f17797,definition,
( sQ1827_spl
<=> compose(compose(g,a),compose(domain(compose(g,a)),compose(a,b))) = compose(compose(compose(g,a),domain(compose(g,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1827_spl])],[split_symbol_definition]) ).
fof(f17800,plain,
( sQ1827_spl
| ~ sQ74_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17786,f693,f1743,f17797]) ).
fof(f17801,definition,
( sQ1828_spl
<=> compose(compose(g,a),compose(domain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1828_spl])],[split_symbol_definition]) ).
fof(f17804,plain,
( sQ1828_spl
| ~ sQ81_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17787,f693,f1772,f17801]) ).
fof(f17805,definition,
( sQ1829_spl
<=> compose(compose(g,a),compose(domain(compose(h,a)),compose(a,b))) = compose(compose(compose(g,a),domain(compose(h,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1829_spl])],[split_symbol_definition]) ).
fof(f17808,plain,
( sQ1829_spl
| ~ sQ72_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17788,f693,f1736,f17805]) ).
fof(f17809,definition,
( sQ1830_spl
<=> compose(compose(g,a),compose(domain(compose(a,b)),compose(a,b))) = compose(compose(compose(g,a),domain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1830_spl])],[split_symbol_definition]) ).
fof(f17812,plain,
( sQ1830_spl
| ~ sQ79_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17789,f715,f1765,f17809]) ).
fof(f17819,definition,
( sQ1831_spl
<=> compose(compose(g,a),compose(domain(b),compose(a,b))) = compose(compose(compose(g,a),domain(b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1831_spl])],[split_symbol_definition]) ).
fof(f17822,plain,
( sQ1831_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17792,f715,f17819]) ).
fof(f17823,plain,
( compose(compose(h,a),compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(compose(h,a),codomain(compose(h,a))),compose(g,a))
| codomain(compose(h,a)) != domain(h) ),
inference(resolution,[status(thm)],[f17001,f131]) ).
fof(f17824,plain,
( compose(compose(h,a),compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(compose(h,a),codomain(compose(g,a))),compose(g,a))
| codomain(compose(g,a)) != domain(h) ),
inference(resolution,[status(thm)],[f17001,f130]) ).
fof(f17825,plain,
( compose(compose(h,a),compose(codomain(a),compose(g,a))) = compose(compose(compose(h,a),codomain(a)),compose(g,a))
| codomain(a) != domain(h) ),
inference(resolution,[status(thm)],[f17001,f22]) ).
fof(f17826,plain,
( compose(compose(h,a),compose(codomain(domain(b)),compose(g,a))) = compose(compose(compose(h,a),codomain(domain(b))),compose(g,a))
| codomain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f17001,f15]) ).
fof(f17827,plain,
( compose(compose(h,a),compose(codomain(compose(a,b)),compose(g,a))) = compose(compose(compose(h,a),codomain(compose(a,b))),compose(g,a))
| codomain(compose(a,b)) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f17001]) ).
fof(f17828,plain,
( compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),compose(g,a))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f17001]) ).
fof(f17829,plain,
( compose(compose(h,a),compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(compose(h,a),codomain(compose(h,a))),compose(g,a))
| codomain(compose(h,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f17001]) ).
fof(f17830,plain,
( compose(compose(h,a),compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(compose(h,a),codomain(compose(g,a))),compose(g,a))
| codomain(compose(g,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f17001]) ).
fof(f17831,plain,
( compose(compose(h,a),compose(codomain(g),compose(g,a))) = compose(compose(compose(h,a),codomain(g)),compose(g,a))
| codomain(g) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f17001]) ).
fof(f17832,plain,
( compose(compose(h,a),compose(codomain(h),compose(g,a))) = compose(compose(compose(h,a),codomain(h)),compose(g,a))
| codomain(h) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f17001]) ).
fof(f17833,plain,
( compose(compose(h,a),compose(codomain(a),compose(g,a))) = compose(compose(compose(h,a),codomain(a)),compose(g,a))
| codomain(a) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f17001]) ).
fof(f17836,definition,
( sQ1832_spl
<=> compose(compose(h,a),compose(codomain(compose(h,a)),compose(g,a))) = compose(compose(compose(h,a),codomain(compose(h,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1832_spl])],[split_symbol_definition]) ).
fof(f17839,plain,
( sQ1832_spl
| ~ sQ1461_spl ),
inference(split_clause,[status(thm)],[f17823,f15096,f17836]) ).
fof(f17840,definition,
( sQ1833_spl
<=> compose(compose(h,a),compose(codomain(compose(g,a)),compose(g,a))) = compose(compose(compose(h,a),codomain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1833_spl])],[split_symbol_definition]) ).
fof(f17843,plain,
( sQ1833_spl
| ~ sQ1463_spl ),
inference(split_clause,[status(thm)],[f17824,f15103,f17840]) ).
fof(f17844,definition,
( sQ1834_spl
<=> compose(compose(h,a),compose(codomain(a),compose(g,a))) = compose(compose(compose(h,a),codomain(a)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1834_spl])],[split_symbol_definition]) ).
fof(f17847,plain,
( sQ1834_spl
| ~ sQ1465_spl ),
inference(split_clause,[status(thm)],[f17825,f15112,f17844]) ).
fof(f17848,definition,
( sQ1835_spl
<=> compose(compose(h,a),compose(codomain(domain(b)),compose(g,a))) = compose(compose(compose(h,a),codomain(domain(b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1835_spl])],[split_symbol_definition]) ).
fof(f17851,plain,
( sQ1835_spl
| ~ sQ1530_spl ),
inference(split_clause,[status(thm)],[f17826,f15527,f17848]) ).
fof(f17852,definition,
( sQ1836_spl
<=> compose(compose(h,a),compose(codomain(compose(a,b)),compose(g,a))) = compose(compose(compose(h,a),codomain(compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1836_spl])],[split_symbol_definition]) ).
fof(f17855,plain,
( sQ1836_spl
| ~ sQ1457_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f17827,f2265,f15082,f17852]) ).
fof(f17856,definition,
( sQ1837_spl
<=> compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1837_spl])],[split_symbol_definition]) ).
fof(f17859,plain,
( sQ1837_spl
| ~ sQ1459_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f17828,f2265,f15089,f17856]) ).
fof(f17860,plain,
( sQ1832_spl
| ~ sQ1461_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17829,f1941,f15096,f17836]) ).
fof(f17861,plain,
( sQ1833_spl
| ~ sQ1463_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17830,f1941,f15103,f17840]) ).
fof(f17862,definition,
( sQ1838_spl
<=> compose(compose(h,a),compose(codomain(g),compose(g,a))) = compose(compose(compose(h,a),codomain(g)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1838_spl])],[split_symbol_definition]) ).
fof(f17865,plain,
( sQ1838_spl
| ~ sQ1451_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17831,f715,f15061,f17862]) ).
fof(f17866,definition,
( sQ1839_spl
<=> compose(compose(h,a),compose(codomain(h),compose(g,a))) = compose(compose(compose(h,a),codomain(h)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1839_spl])],[split_symbol_definition]) ).
fof(f17869,plain,
( sQ1839_spl
| ~ sQ1453_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17832,f715,f15068,f17866]) ).
fof(f17870,plain,
( sQ1834_spl
| ~ sQ1465_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17833,f1941,f15112,f17844]) ).
fof(f17877,plain,
( compose(compose(g,a),compose(domain(domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(domain(b))),compose(h,compose(a,b)))
| domain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f16762,f37]) ).
fof(f17878,plain,
( compose(compose(g,a),compose(domain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(compose(g,a))),compose(h,compose(a,b)))
| domain(compose(g,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f16762]) ).
fof(f17879,plain,
( compose(compose(g,a),compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f16762]) ).
fof(f17880,plain,
( compose(compose(g,a),compose(domain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(compose(h,a))),compose(h,compose(a,b)))
| domain(compose(h,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f16762]) ).
fof(f17881,plain,
( compose(compose(g,a),compose(domain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(compose(a,b))),compose(h,compose(a,b)))
| domain(compose(a,b)) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f16762]) ).
fof(f17884,plain,
( compose(compose(g,a),compose(domain(b),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(b)),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(equality_resolution,[status(thm)],[f16762]) ).
fof(f17885,definition,
( sQ1840_spl
<=> compose(compose(g,a),compose(domain(domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(domain(b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1840_spl])],[split_symbol_definition]) ).
fof(f17888,plain,
( sQ1840_spl
| ~ sQ1536_spl ),
inference(split_clause,[status(thm)],[f17877,f15571,f17885]) ).
fof(f17889,definition,
( sQ1841_spl
<=> compose(compose(g,a),compose(domain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(compose(g,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1841_spl])],[split_symbol_definition]) ).
fof(f17892,plain,
( sQ1841_spl
| ~ sQ1471_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17878,f693,f15151,f17889]) ).
fof(f17893,definition,
( sQ1842_spl
<=> compose(compose(g,a),compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1842_spl])],[split_symbol_definition]) ).
fof(f17896,plain,
( sQ1842_spl
| ~ sQ49_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17879,f693,f1100,f17893]) ).
fof(f17897,definition,
( sQ1843_spl
<=> compose(compose(g,a),compose(domain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(compose(h,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1843_spl])],[split_symbol_definition]) ).
fof(f17900,plain,
( sQ1843_spl
| ~ sQ1474_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17880,f693,f15162,f17897]) ).
fof(f17901,definition,
( sQ1844_spl
<=> compose(compose(g,a),compose(domain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1844_spl])],[split_symbol_definition]) ).
fof(f17904,plain,
( sQ1844_spl
| ~ sQ1467_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17881,f715,f15137,f17901]) ).
fof(f17911,definition,
( sQ1845_spl
<=> compose(compose(g,a),compose(domain(b),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1845_spl])],[split_symbol_definition]) ).
fof(f17914,plain,
( sQ1845_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17884,f693,f17911]) ).
fof(f17915,plain,
( compose(compose(h,a),compose(domain(domain(b)),compose(g,a))) = compose(compose(compose(h,a),domain(domain(b))),compose(g,a))
| domain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f17002,f37]) ).
fof(f17916,plain,
( compose(compose(h,a),compose(domain(compose(g,a)),compose(g,a))) = compose(compose(compose(h,a),domain(compose(g,a))),compose(g,a))
| domain(compose(g,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f17002]) ).
fof(f17917,plain,
( compose(compose(h,a),compose(domain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),compose(g,a))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f17002]) ).
fof(f17918,plain,
( compose(compose(h,a),compose(domain(compose(h,a)),compose(g,a))) = compose(compose(compose(h,a),domain(compose(h,a))),compose(g,a))
| domain(compose(h,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f17002]) ).
fof(f17919,plain,
( compose(compose(h,a),compose(domain(compose(a,b)),compose(g,a))) = compose(compose(compose(h,a),domain(compose(a,b))),compose(g,a))
| domain(compose(a,b)) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f17002]) ).
fof(f17922,plain,
( compose(compose(h,a),compose(domain(b),compose(g,a))) = compose(compose(compose(h,a),domain(b)),compose(g,a))
| domain(b) != domain(h) ),
inference(equality_resolution,[status(thm)],[f17002]) ).
fof(f17923,definition,
( sQ1846_spl
<=> compose(compose(h,a),compose(domain(domain(b)),compose(g,a))) = compose(compose(compose(h,a),domain(domain(b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1846_spl])],[split_symbol_definition]) ).
fof(f17926,plain,
( sQ1846_spl
| ~ sQ1536_spl ),
inference(split_clause,[status(thm)],[f17915,f15571,f17923]) ).
fof(f17927,definition,
( sQ1847_spl
<=> compose(compose(h,a),compose(domain(compose(g,a)),compose(g,a))) = compose(compose(compose(h,a),domain(compose(g,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1847_spl])],[split_symbol_definition]) ).
fof(f17930,plain,
( sQ1847_spl
| ~ sQ1471_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17916,f693,f15151,f17927]) ).
fof(f17931,definition,
( sQ1848_spl
<=> compose(compose(h,a),compose(domain(compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1848_spl])],[split_symbol_definition]) ).
fof(f17934,plain,
( sQ1848_spl
| ~ sQ49_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17917,f693,f1100,f17931]) ).
fof(f17935,definition,
( sQ1849_spl
<=> compose(compose(h,a),compose(domain(compose(h,a)),compose(g,a))) = compose(compose(compose(h,a),domain(compose(h,a))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1849_spl])],[split_symbol_definition]) ).
fof(f17938,plain,
( sQ1849_spl
| ~ sQ1474_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17918,f693,f15162,f17935]) ).
fof(f17939,definition,
( sQ1850_spl
<=> compose(compose(h,a),compose(domain(compose(a,b)),compose(g,a))) = compose(compose(compose(h,a),domain(compose(a,b))),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1850_spl])],[split_symbol_definition]) ).
fof(f17942,plain,
( sQ1850_spl
| ~ sQ1467_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17919,f715,f15137,f17939]) ).
fof(f17949,definition,
( sQ1851_spl
<=> compose(compose(h,a),compose(domain(b),compose(g,a))) = compose(compose(compose(h,a),domain(b)),compose(g,a)) ),
introduced(definition,[new_symbols(definition,[sQ1851_spl])],[split_symbol_definition]) ).
fof(f17952,plain,
( sQ1851_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f17922,f693,f17949]) ).
fof(f17953,plain,
( compose(compose(h,a),compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(compose(h,a),codomain(compose(h,a))),compose(h,a))
| codomain(compose(h,a)) != domain(h) ),
inference(resolution,[status(thm)],[f17045,f131]) ).
fof(f17954,plain,
( compose(compose(h,a),compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(compose(h,a),codomain(compose(g,a))),compose(h,a))
| codomain(compose(g,a)) != domain(h) ),
inference(resolution,[status(thm)],[f17045,f130]) ).
fof(f17955,plain,
( compose(compose(h,a),compose(codomain(a),compose(h,a))) = compose(compose(compose(h,a),codomain(a)),compose(h,a))
| codomain(a) != domain(h) ),
inference(resolution,[status(thm)],[f17045,f22]) ).
fof(f17956,plain,
( compose(compose(h,a),compose(codomain(domain(b)),compose(h,a))) = compose(compose(compose(h,a),codomain(domain(b))),compose(h,a))
| codomain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f17045,f15]) ).
fof(f17957,plain,
( compose(compose(h,a),compose(codomain(compose(a,b)),compose(h,a))) = compose(compose(compose(h,a),codomain(compose(a,b))),compose(h,a))
| codomain(compose(a,b)) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f17045]) ).
fof(f17958,plain,
( compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),compose(h,a))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f17045]) ).
fof(f17959,plain,
( compose(compose(h,a),compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(compose(h,a),codomain(compose(h,a))),compose(h,a))
| codomain(compose(h,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f17045]) ).
fof(f17960,plain,
( compose(compose(h,a),compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(compose(h,a),codomain(compose(g,a))),compose(h,a))
| codomain(compose(g,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f17045]) ).
fof(f17961,plain,
( compose(compose(h,a),compose(codomain(g),compose(h,a))) = compose(compose(compose(h,a),codomain(g)),compose(h,a))
| codomain(g) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f17045]) ).
fof(f17962,plain,
( compose(compose(h,a),compose(codomain(h),compose(h,a))) = compose(compose(compose(h,a),codomain(h)),compose(h,a))
| codomain(h) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f17045]) ).
fof(f17963,plain,
( compose(compose(h,a),compose(codomain(a),compose(h,a))) = compose(compose(compose(h,a),codomain(a)),compose(h,a))
| codomain(a) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f17045]) ).
fof(f17966,definition,
( sQ1852_spl
<=> compose(compose(h,a),compose(codomain(compose(h,a)),compose(h,a))) = compose(compose(compose(h,a),codomain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1852_spl])],[split_symbol_definition]) ).
fof(f17969,plain,
( sQ1852_spl
| ~ sQ1461_spl ),
inference(split_clause,[status(thm)],[f17953,f15096,f17966]) ).
fof(f17970,definition,
( sQ1853_spl
<=> compose(compose(h,a),compose(codomain(compose(g,a)),compose(h,a))) = compose(compose(compose(h,a),codomain(compose(g,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1853_spl])],[split_symbol_definition]) ).
fof(f17973,plain,
( sQ1853_spl
| ~ sQ1463_spl ),
inference(split_clause,[status(thm)],[f17954,f15103,f17970]) ).
fof(f17974,definition,
( sQ1854_spl
<=> compose(compose(h,a),compose(codomain(a),compose(h,a))) = compose(compose(compose(h,a),codomain(a)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1854_spl])],[split_symbol_definition]) ).
fof(f17977,plain,
( sQ1854_spl
| ~ sQ1465_spl ),
inference(split_clause,[status(thm)],[f17955,f15112,f17974]) ).
fof(f17978,definition,
( sQ1855_spl
<=> compose(compose(h,a),compose(codomain(domain(b)),compose(h,a))) = compose(compose(compose(h,a),codomain(domain(b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1855_spl])],[split_symbol_definition]) ).
fof(f17981,plain,
( sQ1855_spl
| ~ sQ1530_spl ),
inference(split_clause,[status(thm)],[f17956,f15527,f17978]) ).
fof(f17982,definition,
( sQ1856_spl
<=> compose(compose(h,a),compose(codomain(compose(a,b)),compose(h,a))) = compose(compose(compose(h,a),codomain(compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1856_spl])],[split_symbol_definition]) ).
fof(f17985,plain,
( sQ1856_spl
| ~ sQ1457_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f17957,f2265,f15082,f17982]) ).
fof(f17986,definition,
( sQ1857_spl
<=> compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1857_spl])],[split_symbol_definition]) ).
fof(f17989,plain,
( sQ1857_spl
| ~ sQ1459_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f17958,f2265,f15089,f17986]) ).
fof(f17990,plain,
( sQ1852_spl
| ~ sQ1461_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17959,f1941,f15096,f17966]) ).
fof(f17991,plain,
( sQ1853_spl
| ~ sQ1463_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17960,f1941,f15103,f17970]) ).
fof(f17992,definition,
( sQ1858_spl
<=> compose(compose(h,a),compose(codomain(g),compose(h,a))) = compose(compose(compose(h,a),codomain(g)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1858_spl])],[split_symbol_definition]) ).
fof(f17995,plain,
( sQ1858_spl
| ~ sQ1451_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17961,f715,f15061,f17992]) ).
fof(f17996,definition,
( sQ1859_spl
<=> compose(compose(h,a),compose(codomain(h),compose(h,a))) = compose(compose(compose(h,a),codomain(h)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1859_spl])],[split_symbol_definition]) ).
fof(f17999,plain,
( sQ1859_spl
| ~ sQ1453_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f17962,f715,f15068,f17996]) ).
fof(f18000,plain,
( sQ1854_spl
| ~ sQ1465_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f17963,f1941,f15112,f17974]) ).
fof(f18007,plain,
( compose(compose(h,a),compose(domain(domain(b)),compose(h,a))) = compose(compose(compose(h,a),domain(domain(b))),compose(h,a))
| domain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f17046,f37]) ).
fof(f18008,plain,
( compose(compose(h,a),compose(domain(compose(g,a)),compose(h,a))) = compose(compose(compose(h,a),domain(compose(g,a))),compose(h,a))
| domain(compose(g,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f17046]) ).
fof(f18009,plain,
( compose(compose(h,a),compose(domain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),compose(h,a))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f17046]) ).
fof(f18010,plain,
( compose(compose(h,a),compose(domain(compose(h,a)),compose(h,a))) = compose(compose(compose(h,a),domain(compose(h,a))),compose(h,a))
| domain(compose(h,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f17046]) ).
fof(f18011,plain,
( compose(compose(h,a),compose(domain(compose(a,b)),compose(h,a))) = compose(compose(compose(h,a),domain(compose(a,b))),compose(h,a))
| domain(compose(a,b)) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f17046]) ).
fof(f18014,plain,
( compose(compose(h,a),compose(domain(b),compose(h,a))) = compose(compose(compose(h,a),domain(b)),compose(h,a))
| domain(b) != domain(h) ),
inference(equality_resolution,[status(thm)],[f17046]) ).
fof(f18015,definition,
( sQ1860_spl
<=> compose(compose(h,a),compose(domain(domain(b)),compose(h,a))) = compose(compose(compose(h,a),domain(domain(b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1860_spl])],[split_symbol_definition]) ).
fof(f18018,plain,
( sQ1860_spl
| ~ sQ1536_spl ),
inference(split_clause,[status(thm)],[f18007,f15571,f18015]) ).
fof(f18019,definition,
( sQ1861_spl
<=> compose(compose(h,a),compose(domain(compose(g,a)),compose(h,a))) = compose(compose(compose(h,a),domain(compose(g,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1861_spl])],[split_symbol_definition]) ).
fof(f18022,plain,
( sQ1861_spl
| ~ sQ1471_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f18008,f693,f15151,f18019]) ).
fof(f18023,definition,
( sQ1862_spl
<=> compose(compose(h,a),compose(domain(compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1862_spl])],[split_symbol_definition]) ).
fof(f18026,plain,
( sQ1862_spl
| ~ sQ49_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f18009,f693,f1100,f18023]) ).
fof(f18027,definition,
( sQ1863_spl
<=> compose(compose(h,a),compose(domain(compose(h,a)),compose(h,a))) = compose(compose(compose(h,a),domain(compose(h,a))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1863_spl])],[split_symbol_definition]) ).
fof(f18030,plain,
( sQ1863_spl
| ~ sQ1474_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f18010,f693,f15162,f18027]) ).
fof(f18031,definition,
( sQ1864_spl
<=> compose(compose(h,a),compose(domain(compose(a,b)),compose(h,a))) = compose(compose(compose(h,a),domain(compose(a,b))),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1864_spl])],[split_symbol_definition]) ).
fof(f18034,plain,
( sQ1864_spl
| ~ sQ1467_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f18011,f715,f15137,f18031]) ).
fof(f18041,definition,
( sQ1865_spl
<=> compose(compose(h,a),compose(domain(b),compose(h,a))) = compose(compose(compose(h,a),domain(b)),compose(h,a)) ),
introduced(definition,[new_symbols(definition,[sQ1865_spl])],[split_symbol_definition]) ).
fof(f18044,plain,
( sQ1865_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f18014,f693,f18041]) ).
fof(f18045,plain,
( compose(compose(h,a),compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(compose(h,a),codomain(compose(h,a))),compose(a,b))
| codomain(compose(h,a)) != domain(a) ),
inference(resolution,[status(thm)],[f17138,f131]) ).
fof(f18046,plain,
( compose(compose(h,a),compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(compose(h,a),codomain(compose(g,a))),compose(a,b))
| codomain(compose(g,a)) != domain(a) ),
inference(resolution,[status(thm)],[f17138,f130]) ).
fof(f18047,plain,
( compose(compose(h,a),compose(codomain(a),compose(a,b))) = compose(compose(compose(h,a),codomain(a)),compose(a,b))
| codomain(a) != domain(a) ),
inference(resolution,[status(thm)],[f17138,f22]) ).
fof(f18048,plain,
( compose(compose(h,a),compose(codomain(domain(b)),compose(a,b))) = compose(compose(compose(h,a),codomain(domain(b))),compose(a,b))
| codomain(domain(b)) != domain(a) ),
inference(resolution,[status(thm)],[f17138,f15]) ).
fof(f18049,plain,
( compose(compose(h,a),compose(codomain(compose(a,b)),compose(a,b))) = compose(compose(compose(h,a),codomain(compose(a,b))),compose(a,b))
| codomain(compose(a,b)) != domain(a)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f17138]) ).
fof(f18050,plain,
( compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),compose(a,b))
| codomain(compose(h,compose(a,b))) != domain(a)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f17138]) ).
fof(f18051,plain,
( compose(compose(h,a),compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(compose(h,a),codomain(compose(h,a))),compose(a,b))
| codomain(compose(h,a)) != domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f17138]) ).
fof(f18052,plain,
( compose(compose(h,a),compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(compose(h,a),codomain(compose(g,a))),compose(a,b))
| codomain(compose(g,a)) != domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f17138]) ).
fof(f18053,plain,
( compose(compose(h,a),compose(codomain(g),compose(a,b))) = compose(compose(compose(h,a),codomain(g)),compose(a,b))
| codomain(g) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f17138]) ).
fof(f18054,plain,
( compose(compose(h,a),compose(codomain(h),compose(a,b))) = compose(compose(compose(h,a),codomain(h)),compose(a,b))
| codomain(h) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f17138]) ).
fof(f18055,plain,
( compose(compose(h,a),compose(codomain(a),compose(a,b))) = compose(compose(compose(h,a),codomain(a)),compose(a,b))
| codomain(a) != domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f17138]) ).
fof(f18058,definition,
( sQ1866_spl
<=> compose(compose(h,a),compose(codomain(compose(h,a)),compose(a,b))) = compose(compose(compose(h,a),codomain(compose(h,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1866_spl])],[split_symbol_definition]) ).
fof(f18061,plain,
( sQ1866_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f18045,f3284,f18058]) ).
fof(f18062,definition,
( sQ1867_spl
<=> compose(compose(h,a),compose(codomain(compose(g,a)),compose(a,b))) = compose(compose(compose(h,a),codomain(compose(g,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1867_spl])],[split_symbol_definition]) ).
fof(f18065,plain,
( sQ1867_spl
| ~ sQ203_spl ),
inference(split_clause,[status(thm)],[f18046,f3216,f18062]) ).
fof(f18066,definition,
( sQ1868_spl
<=> compose(compose(h,a),compose(codomain(a),compose(a,b))) = compose(compose(compose(h,a),codomain(a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1868_spl])],[split_symbol_definition]) ).
fof(f18069,plain,
( sQ1868_spl
| ~ sQ1133_spl ),
inference(split_clause,[status(thm)],[f18047,f12077,f18066]) ).
fof(f18070,definition,
( sQ1869_spl
<=> compose(compose(h,a),compose(codomain(domain(b)),compose(a,b))) = compose(compose(compose(h,a),codomain(domain(b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1869_spl])],[split_symbol_definition]) ).
fof(f18073,plain,
( sQ1869_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f18048,f562,f18070]) ).
fof(f18074,definition,
( sQ1870_spl
<=> compose(compose(h,a),compose(codomain(compose(a,b)),compose(a,b))) = compose(compose(compose(h,a),codomain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1870_spl])],[split_symbol_definition]) ).
fof(f18077,plain,
( sQ1870_spl
| ~ sQ1119_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f18049,f2265,f12019,f18074]) ).
fof(f18078,definition,
( sQ1871_spl
<=> compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1871_spl])],[split_symbol_definition]) ).
fof(f18081,plain,
( sQ1871_spl
| ~ sQ1121_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f18050,f2265,f12026,f18078]) ).
fof(f18082,plain,
( sQ1866_spl
| ~ sQ216_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f18051,f1941,f3284,f18058]) ).
fof(f18083,plain,
( sQ1867_spl
| ~ sQ203_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f18052,f1941,f3216,f18062]) ).
fof(f18084,definition,
( sQ1872_spl
<=> compose(compose(h,a),compose(codomain(g),compose(a,b))) = compose(compose(compose(h,a),codomain(g)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1872_spl])],[split_symbol_definition]) ).
fof(f18087,plain,
( sQ1872_spl
| ~ sQ1129_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f18053,f715,f12063,f18084]) ).
fof(f18088,definition,
( sQ1873_spl
<=> compose(compose(h,a),compose(codomain(h),compose(a,b))) = compose(compose(compose(h,a),codomain(h)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1873_spl])],[split_symbol_definition]) ).
fof(f18091,plain,
( sQ1873_spl
| ~ sQ1131_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f18054,f715,f12070,f18088]) ).
fof(f18092,plain,
( sQ1868_spl
| ~ sQ1133_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f18055,f1941,f12077,f18066]) ).
fof(f18099,plain,
( compose(compose(h,a),compose(domain(domain(b)),compose(a,b))) = compose(compose(compose(h,a),domain(domain(b))),compose(a,b))
| domain(domain(b)) != domain(a) ),
inference(resolution,[status(thm)],[f17139,f37]) ).
fof(f18100,plain,
( compose(compose(h,a),compose(domain(compose(g,a)),compose(a,b))) = compose(compose(compose(h,a),domain(compose(g,a))),compose(a,b))
| domain(compose(g,a)) != domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f17139]) ).
fof(f18101,plain,
( compose(compose(h,a),compose(domain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),compose(a,b))
| domain(compose(h,compose(a,b))) != domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f17139]) ).
fof(f18102,plain,
( compose(compose(h,a),compose(domain(compose(h,a)),compose(a,b))) = compose(compose(compose(h,a),domain(compose(h,a))),compose(a,b))
| domain(compose(h,a)) != domain(a)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f17139]) ).
fof(f18103,plain,
( compose(compose(h,a),compose(domain(compose(a,b)),compose(a,b))) = compose(compose(compose(h,a),domain(compose(a,b))),compose(a,b))
| domain(compose(a,b)) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f17139]) ).
fof(f18106,plain,
( compose(compose(h,a),compose(domain(b),compose(a,b))) = compose(compose(compose(h,a),domain(b)),compose(a,b))
| domain(b) != domain(a) ),
inference(equality_resolution,[status(thm)],[f17139]) ).
fof(f18107,definition,
( sQ1874_spl
<=> compose(compose(h,a),compose(domain(domain(b)),compose(a,b))) = compose(compose(compose(h,a),domain(domain(b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1874_spl])],[split_symbol_definition]) ).
fof(f18110,plain,
( sQ1874_spl
| ~ sQ1570_spl ),
inference(split_clause,[status(thm)],[f18099,f15822,f18107]) ).
fof(f18111,definition,
( sQ1875_spl
<=> compose(compose(h,a),compose(domain(compose(g,a)),compose(a,b))) = compose(compose(compose(h,a),domain(compose(g,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1875_spl])],[split_symbol_definition]) ).
fof(f18114,plain,
( sQ1875_spl
| ~ sQ74_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f18100,f693,f1743,f18111]) ).
fof(f18115,definition,
( sQ1876_spl
<=> compose(compose(h,a),compose(domain(compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1876_spl])],[split_symbol_definition]) ).
fof(f18118,plain,
( sQ1876_spl
| ~ sQ81_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f18101,f693,f1772,f18115]) ).
fof(f18119,definition,
( sQ1877_spl
<=> compose(compose(h,a),compose(domain(compose(h,a)),compose(a,b))) = compose(compose(compose(h,a),domain(compose(h,a))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1877_spl])],[split_symbol_definition]) ).
fof(f18122,plain,
( sQ1877_spl
| ~ sQ72_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f18102,f693,f1736,f18119]) ).
fof(f18123,definition,
( sQ1878_spl
<=> compose(compose(h,a),compose(domain(compose(a,b)),compose(a,b))) = compose(compose(compose(h,a),domain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1878_spl])],[split_symbol_definition]) ).
fof(f18126,plain,
( sQ1878_spl
| ~ sQ79_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f18103,f715,f1765,f18123]) ).
fof(f18133,definition,
( sQ1879_spl
<=> compose(compose(h,a),compose(domain(b),compose(a,b))) = compose(compose(compose(h,a),domain(b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ1879_spl])],[split_symbol_definition]) ).
fof(f18136,plain,
( sQ1879_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f18106,f715,f18133]) ).
fof(f18137,plain,
( compose(compose(h,a),compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(compose(h,a))),compose(h,compose(a,b)))
| codomain(compose(h,a)) != domain(h) ),
inference(resolution,[status(thm)],[f17359,f131]) ).
fof(f18138,plain,
( compose(compose(h,a),compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(compose(g,a))),compose(h,compose(a,b)))
| codomain(compose(g,a)) != domain(h) ),
inference(resolution,[status(thm)],[f17359,f130]) ).
fof(f18139,plain,
( compose(compose(h,a),compose(codomain(a),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(a)),compose(h,compose(a,b)))
| codomain(a) != domain(h) ),
inference(resolution,[status(thm)],[f17359,f22]) ).
fof(f18140,plain,
( compose(compose(h,a),compose(codomain(domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(domain(b))),compose(h,compose(a,b)))
| codomain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f17359,f15]) ).
fof(f18141,plain,
( compose(compose(h,a),compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(compose(a,b))),compose(h,compose(a,b)))
| codomain(compose(a,b)) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f120,f17359]) ).
fof(f18142,plain,
( compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| codomain(compose(h,compose(a,b))) != domain(h)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f581,f17359]) ).
fof(f18143,plain,
( compose(compose(h,a),compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(compose(h,a))),compose(h,compose(a,b)))
| codomain(compose(h,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f131,f17359]) ).
fof(f18144,plain,
( compose(compose(h,a),compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(compose(g,a))),compose(h,compose(a,b)))
| codomain(compose(g,a)) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f130,f17359]) ).
fof(f18145,plain,
( compose(compose(h,a),compose(codomain(g),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(g)),compose(h,compose(a,b)))
| codomain(g) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f74,f17359]) ).
fof(f18146,plain,
( compose(compose(h,a),compose(codomain(h),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(h)),compose(h,compose(a,b)))
| codomain(h) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f69,f17359]) ).
fof(f18147,plain,
( compose(compose(h,a),compose(codomain(a),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(a)),compose(h,compose(a,b)))
| codomain(a) != domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f22,f17359]) ).
fof(f18150,definition,
( sQ1880_spl
<=> compose(compose(h,a),compose(codomain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(compose(h,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1880_spl])],[split_symbol_definition]) ).
fof(f18153,plain,
( sQ1880_spl
| ~ sQ1461_spl ),
inference(split_clause,[status(thm)],[f18137,f15096,f18150]) ).
fof(f18154,definition,
( sQ1881_spl
<=> compose(compose(h,a),compose(codomain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(compose(g,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1881_spl])],[split_symbol_definition]) ).
fof(f18157,plain,
( sQ1881_spl
| ~ sQ1463_spl ),
inference(split_clause,[status(thm)],[f18138,f15103,f18154]) ).
fof(f18158,definition,
( sQ1882_spl
<=> compose(compose(h,a),compose(codomain(a),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(a)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1882_spl])],[split_symbol_definition]) ).
fof(f18161,plain,
( sQ1882_spl
| ~ sQ1465_spl ),
inference(split_clause,[status(thm)],[f18139,f15112,f18158]) ).
fof(f18162,definition,
( sQ1883_spl
<=> compose(compose(h,a),compose(codomain(domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(domain(b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1883_spl])],[split_symbol_definition]) ).
fof(f18165,plain,
( sQ1883_spl
| ~ sQ1530_spl ),
inference(split_clause,[status(thm)],[f18140,f15527,f18162]) ).
fof(f18166,definition,
( sQ1884_spl
<=> compose(compose(h,a),compose(codomain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1884_spl])],[split_symbol_definition]) ).
fof(f18169,plain,
( sQ1884_spl
| ~ sQ1457_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f18141,f2265,f15082,f18166]) ).
fof(f18170,definition,
( sQ1885_spl
<=> compose(compose(h,a),compose(codomain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1885_spl])],[split_symbol_definition]) ).
fof(f18173,plain,
( sQ1885_spl
| ~ sQ1459_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f18142,f2265,f15089,f18170]) ).
fof(f18174,plain,
( sQ1880_spl
| ~ sQ1461_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f18143,f1941,f15096,f18150]) ).
fof(f18175,plain,
( sQ1881_spl
| ~ sQ1463_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f18144,f1941,f15103,f18154]) ).
fof(f18176,definition,
( sQ1886_spl
<=> compose(compose(h,a),compose(codomain(g),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(g)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1886_spl])],[split_symbol_definition]) ).
fof(f18179,plain,
( sQ1886_spl
| ~ sQ1451_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f18145,f715,f15061,f18176]) ).
fof(f18180,definition,
( sQ1887_spl
<=> compose(compose(h,a),compose(codomain(h),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(h)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1887_spl])],[split_symbol_definition]) ).
fof(f18183,plain,
( sQ1887_spl
| ~ sQ1453_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f18146,f715,f15068,f18180]) ).
fof(f18184,plain,
( sQ1882_spl
| ~ sQ1465_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f18147,f1941,f15112,f18158]) ).
fof(f18191,plain,
( compose(compose(h,a),compose(domain(domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(domain(b))),compose(h,compose(a,b)))
| domain(domain(b)) != domain(h) ),
inference(resolution,[status(thm)],[f17360,f37]) ).
fof(f18192,plain,
( compose(compose(h,a),compose(domain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(compose(g,a))),compose(h,compose(a,b)))
| domain(compose(g,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1108,f17360]) ).
fof(f18193,plain,
( compose(compose(h,a),compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),compose(h,compose(a,b)))
| domain(compose(h,compose(a,b))) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f1068,f17360]) ).
fof(f18194,plain,
( compose(compose(h,a),compose(domain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(compose(h,a))),compose(h,compose(a,b)))
| domain(compose(h,a)) != domain(h)
| domain(b) != domain(h) ),
inference(paramodulation,[status(thm)],[f76,f17360]) ).
fof(f18195,plain,
( compose(compose(h,a),compose(domain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(compose(a,b))),compose(h,compose(a,b)))
| domain(compose(a,b)) != domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f60,f17360]) ).
fof(f18198,plain,
( compose(compose(h,a),compose(domain(b),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(b)),compose(h,compose(a,b)))
| domain(b) != domain(h) ),
inference(equality_resolution,[status(thm)],[f17360]) ).
fof(f18199,definition,
( sQ1888_spl
<=> compose(compose(h,a),compose(domain(domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(domain(b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1888_spl])],[split_symbol_definition]) ).
fof(f18202,plain,
( sQ1888_spl
| ~ sQ1536_spl ),
inference(split_clause,[status(thm)],[f18191,f15571,f18199]) ).
fof(f18203,definition,
( sQ1889_spl
<=> compose(compose(h,a),compose(domain(compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(compose(g,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1889_spl])],[split_symbol_definition]) ).
fof(f18206,plain,
( sQ1889_spl
| ~ sQ1471_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f18192,f693,f15151,f18203]) ).
fof(f18207,definition,
( sQ1890_spl
<=> compose(compose(h,a),compose(domain(compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(compose(h,compose(a,b)))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1890_spl])],[split_symbol_definition]) ).
fof(f18210,plain,
( sQ1890_spl
| ~ sQ49_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f18193,f693,f1100,f18207]) ).
fof(f18211,definition,
( sQ1891_spl
<=> compose(compose(h,a),compose(domain(compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(compose(h,a))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1891_spl])],[split_symbol_definition]) ).
fof(f18214,plain,
( sQ1891_spl
| ~ sQ1474_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f18194,f693,f15162,f18211]) ).
fof(f18215,definition,
( sQ1892_spl
<=> compose(compose(h,a),compose(domain(compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(compose(a,b))),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1892_spl])],[split_symbol_definition]) ).
fof(f18218,plain,
( sQ1892_spl
| ~ sQ1467_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f18195,f715,f15137,f18215]) ).
fof(f18225,definition,
( sQ1893_spl
<=> compose(compose(h,a),compose(domain(b),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(b)),compose(h,compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1893_spl])],[split_symbol_definition]) ).
fof(f18228,plain,
( sQ1893_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f18198,f693,f18225]) ).
fof(model,axiom,
( ~ sQ1_spl
| sQ2_spl
| sQ3_spl
| sQ4_spl
| sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sQ14_spl
| sQ15_spl
| sQ20_spl
| ~ sQ21_spl
| ~ sQ23_spl
| ~ sQ27_spl
| sQ38_spl
| sQ49_spl
| sQ64_spl
| ~ sQ66_spl
| ~ sQ70_spl
| ~ sQ72_spl
| ~ sQ74_spl
| sQ78_spl
| sQ79_spl
| sQ80_spl
| ~ sQ81_spl
| sQ87_spl
| sQ88_spl
| sQ93_spl
| sQ98_spl
| sQ99_spl
| sQ105_spl
| sQ106_spl
| sQ112_spl
| sQ116_spl
| sQ121_spl
| sQ122_spl
| ~ sQ128_spl
| sQ131_spl
| sQ132_spl
| sQ135_spl
| ~ sQ136_spl
| ~ sQ138_spl
| ~ sQ143_spl
| ~ sQ145_spl
| sQ152_spl
| sQ153_spl
| sQ154_spl
| sQ155_spl
| sQ156_spl
| sQ168_spl
| sQ177_spl
| sQ178_spl
| sQ182_spl
| sQ183_spl
| sQ186_spl
| sQ191_spl
| sQ192_spl
| sQ197_spl
| sQ198_spl
| sQ199_spl
| sQ200_spl
| sQ201_spl
| ~ sQ203_spl
| sQ207_spl
| sQ208_spl
| sQ213_spl
| sQ214_spl
| ~ sQ216_spl
| sQ219_spl
| sQ220_spl
| sQ293_spl
| sQ297_spl
| sQ301_spl
| sQ305_spl
| sQ325_spl
| sQ326_spl
| sQ331_spl
| sQ332_spl
| sQ333_spl
| sQ334_spl
| sQ339_spl
| sQ355_spl
| sQ356_spl
| sQ357_spl
| sQ362_spl
| sQ363_spl
| sQ366_spl
| sQ369_spl
| sQ370_spl
| sQ373_spl
| sQ374_spl
| sQ375_spl
| sQ376_spl
| sQ377_spl
| sQ389_spl
| sQ393_spl
| sQ411_spl
| sQ415_spl
| sQ432_spl
| sQ433_spl
| sQ438_spl
| sQ439_spl
| sQ442_spl
| sQ454_spl
| sQ455_spl
| sQ457_spl
| sQ458_spl
| sQ459_spl
| sQ460_spl
| sQ465_spl
| sQ466_spl
| sQ467_spl
| sQ468_spl
| sQ469_spl
| sQ473_spl
| sQ474_spl
| sQ477_spl
| sQ513_spl
| sQ518_spl
| sQ519_spl
| sQ528_spl
| sQ533_spl
| sQ534_spl
| sQ542_spl
| sQ543_spl
| sQ546_spl
| sQ547_spl
| sQ548_spl
| sQ549_spl
| sQ550_spl
| sQ554_spl
| sQ555_spl
| sQ558_spl
| sQ570_spl
| sQ571_spl
| sQ581_spl
| sQ582_spl
| sQ583_spl
| sQ584_spl
| sQ593_spl
| sQ598_spl
| sQ599_spl
| sQ604_spl
| sQ609_spl
| sQ610_spl
| sQ622_spl
| sQ623_spl
| sQ626_spl
| sQ629_spl
| sQ630_spl
| sQ633_spl
| sQ637_spl
| sQ642_spl
| sQ643_spl
| sQ648_spl
| sQ653_spl
| sQ654_spl
| sQ666_spl
| sQ667_spl
| sQ670_spl
| sQ678_spl
| sQ679_spl
| sQ680_spl
| sQ681_spl
| sQ683_spl
| sQ684_spl
| sQ699_spl
| sQ700_spl
| sQ725_spl
| sQ744_spl
| sQ745_spl
| sQ783_spl
| sQ784_spl
| sQ789_spl
| sQ794_spl
| sQ795_spl
| sQ801_spl
| sQ802_spl
| sQ806_spl
| sQ812_spl
| ~ sQ813_spl
| sQ829_spl
| sQ830_spl
| sQ835_spl
| sQ840_spl
| sQ841_spl
| sQ847_spl
| sQ848_spl
| sQ852_spl
| sQ858_spl
| sQ872_spl
| sQ873_spl
| sQ876_spl
| sQ904_spl
| sQ905_spl
| sQ910_spl
| sQ911_spl
| sQ912_spl
| sQ913_spl
| sQ939_spl
| sQ940_spl
| sQ942_spl
| sQ943_spl
| sQ944_spl
| sQ945_spl
| sQ947_spl
| sQ948_spl
| sQ949_spl
| sQ950_spl
| sQ961_spl
| sQ968_spl
| sQ969_spl
| sQ972_spl
| sQ979_spl
| sQ980_spl
| sQ983_spl
| sQ986_spl
| sQ1009_spl
| sQ1010_spl
| ~ sQ1013_spl
| sQ1024_spl
| sQ1025_spl
| sQ1028_spl
| sQ1031_spl
| sQ1032_spl
| sQ1035_spl
| sQ1056_spl
| sQ1057_spl
| sQ1062_spl
| sQ1063_spl
| sQ1066_spl
| sQ1069_spl
| sQ1070_spl
| sQ1073_spl
| sQ1078_spl
| sQ1079_spl
| ~ sQ1084_spl
| sQ1095_spl
| sQ1096_spl
| sQ1103_spl
| sQ1104_spl
| sQ1109_spl
| sQ1114_spl
| sQ1115_spl
| sQ1116_spl
| sQ1117_spl
| ~ sQ1119_spl
| ~ sQ1121_spl
| sQ1129_spl
| sQ1130_spl
| sQ1131_spl
| sQ1132_spl
| ~ sQ1133_spl
| sQ1139_spl
| sQ1140_spl
| sQ1145_spl
| sQ1148_spl
| sQ1149_spl
| sQ1154_spl
| sQ1155_spl
| sQ1156_spl
| sQ1159_spl
| sQ1160_spl
| sQ1161_spl
| sQ1162_spl
| sQ1168_spl
| sQ1169_spl
| sQ1174_spl
| sQ1187_spl
| sQ1188_spl
| sQ1194_spl
| sQ1195_spl
| sQ1200_spl
| sQ1204_spl
| sQ1207_spl
| sQ1208_spl
| sQ1213_spl
| sQ1214_spl
| sQ1215_spl
| sQ1220_spl
| sQ1221_spl
| sQ1224_spl
| sQ1229_spl
| sQ1230_spl
| ~ sQ1233_spl
| ~ sQ1235_spl
| sQ1241_spl
| sQ1242_spl
| ~ sQ1243_spl
| ~ sQ1245_spl
| sQ1247_spl
| sQ1248_spl
| sQ1251_spl
| sQ1252_spl
| sQ1255_spl
| sQ1262_spl
| sQ1263_spl
| sQ1266_spl
| sQ1267_spl
| sQ1268_spl
| sQ1271_spl
| sQ1280_spl
| sQ1281_spl
| sQ1286_spl
| sQ1291_spl
| sQ1292_spl
| sQ1297_spl
| sQ1300_spl
| sQ1301_spl
| sQ1304_spl
| sQ1347_spl
| sQ1348_spl
| sQ1380_spl
| sQ1381_spl
| sQ1407_spl
| sQ1408_spl
| sQ1424_spl
| sQ1425_spl
| sQ1426_spl
| sQ1427_spl
| sQ1433_spl
| sQ1434_spl
| sQ1441_spl
| sQ1442_spl
| ~ sQ1451_spl
| ~ sQ1453_spl
| ~ sQ1455_spl
| ~ sQ1461_spl
| ~ sQ1463_spl
| ~ sQ1465_spl
| ~ sQ1467_spl
| ~ sQ1469_spl
| ~ sQ1530_spl
| ~ sQ1536_spl
| sQ1543_spl
| sQ1544_spl
| sQ1545_spl
| sQ1546_spl
| ~ sQ1570_spl
| sQ1579_spl
| sQ1580_spl
| sQ1583_spl
| sQ1584_spl
| sQ1585_spl
| sQ1598_spl
| sQ1599_spl
| sQ1602_spl
| sQ1605_spl
| sQ1606_spl
| sQ1609_spl
| sQ1614_spl
| sQ1615_spl
| sQ1618_spl
| sQ1633_spl
| sQ1634_spl
| sQ1637_spl
| sQ1648_spl
| sQ1649_spl
| sQ1652_spl
| sQ1655_spl
| sQ1656_spl
| sQ1659_spl
| sQ1672_spl
| sQ1673_spl
| sQ1676_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT002-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n017.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Mon Sep 21 13:50:29 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.58 % Drodi V4.1.1
% 9.72/1.92 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 9.72/1.92 % SZS output start Saturation for theBenchmark
% See solution above
% 0.81/2.04 % Elapsed time: 1.454931 seconds
% 0.81/2.04 % CPU time: 10.584149 seconds
% 0.81/2.04 % Total memory used: 168.460 MB
% 0.81/2.04 % Net memory used: 157.918 MB
%------------------------------------------------------------------------------