%------------------------------------------------------------------------------
% File : iProver-SAT---3.9.4
% Problem : CAT002-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p SAT
% Computer : n011.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 : Fri Sep 25 01:01:19 PM UTC 2026
% Result : Satisfiable 9.95s 5.79s
% Output : Saturation 39.33s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X0] : codomain(domain(X0)) = domain(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_domain_is_domain) ).
fof(f3,plain,
! [X0] : domain(X0) = codomain(domain(X0)),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X0] : domain(codomain(X0)) = codomain(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of_codomain_is_codomain) ).
fof(f5,plain,
! [X0] : codomain(X0) = domain(codomain(X0)),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0] : compose(domain(X0),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_composition) ).
fof(f7,axiom,
! [X0] : compose(X0,codomain(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_composition) ).
fof(f8,axiom,
! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(X0,X1)),domain(X0)) = domain(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_domain1) ).
fof(f9,plain,
! [X0,X1] : domain(X0) = ifeq(codomain(X0),domain(X1),domain(compose(X0,X1)),domain(X0)),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(X0,X1)),codomain(X1)) = codomain(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_domain2) ).
fof(f11,plain,
! [X0,X1] : codomain(X1) = ifeq(codomain(X0),domain(X1),codomain(compose(X0,X1)),codomain(X1)),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X2,X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(X0,X1)),compose(compose(X2,X0),X1)),compose(compose(X2,X0),X1)) = compose(compose(X2,X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_property) ).
fof(f13,plain,
! [X2,X0,X1] : compose(compose(X2,X0),X1) = ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(X0,X1)),compose(compose(X2,X0),X1)),compose(compose(X2,X0),X1)),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
codomain(a) = domain(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
fof(f15,axiom,
! [X2,X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,a),X2,ifeq(compose(X0,a),X2,X0,X1),X1),X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monomorphism1) ).
fof(f16,axiom,
! [X2,X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,b),X2,ifeq(compose(X0,b),X2,X0,X1),X1),X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monomorphism2) ).
fof(f17,axiom,
codomain(h) = domain(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_h_equals_domain_of_ab) ).
fof(f18,axiom,
codomain(g) = domain(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_g_equals_domain_of_ab) ).
fof(f19,plain,
domain(compose(a,b)) = codomain(g),
inference(reorient_equations,[],[f18]) ).
fof(f20,axiom,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_ab_equals_g_ab) ).
fof(f21,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_h_equals_g) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_65,plain,
! [X0: $i] : codomain(domain(X0)) = domain(X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_66,plain,
! [X0: $i] : domain(codomain(X0)) = codomain(X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_67,plain,
! [X0: $i] : compose(domain(X0),X0) = X0,
inference(cnf_transformation,[],[f6]) ).
tcf(c_68,plain,
! [X0: $i] : compose(X0,codomain(X0)) = X0,
inference(cnf_transformation,[],[f7]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),domain(compose(X0,X1)),domain(X0)) = domain(X0),
inference(cnf_transformation,[],[f9]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),codomain(compose(X0,X1)),codomain(X1)) = codomain(X1),
inference(cnf_transformation,[],[f11]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(X0,X1)),compose(compose(X2,X0),X1)),compose(compose(X2,X0),X1)) = compose(compose(X2,X0),X1),
inference(cnf_transformation,[],[f13]) ).
tcf(c_72,plain,
domain(b) = codomain(a),
inference(cnf_transformation,[],[f14]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,a),X2,ifeq(compose(X0,a),X2,X0,X1),X1),X1),X1) = X1,
inference(cnf_transformation,[],[f15]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,b),X2,ifeq(compose(X0,b),X2,X0,X1),X1),X1),X1) = X1,
inference(cnf_transformation,[],[f16]) ).
tcf(c_75,plain,
domain(compose(a,b)) = codomain(h),
inference(cnf_transformation,[],[f17]) ).
tcf(c_76,plain,
domain(compose(a,b)) = codomain(g),
inference(cnf_transformation,[],[f19]) ).
tcf(c_77,plain,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_78,negated_conjecture,
h != g,
inference(cnf_transformation,[],[f21]) ).
tcf(c_100,plain,
! [X0: $i] : domain(domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_66]) ).
tcf(c_102,plain,
! [X0: $i] : codomain(codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_66,c_65]) ).
tcf(c_103,plain,
! [X0: $i] : compose(codomain(X0),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_66,c_67]) ).
tcf(c_104,plain,
! [X0: $i] : compose(domain(X0),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_68]) ).
tcf(c_105,plain,
compose(a,domain(b)) = a,
inference(superposition,[status(thm)],[c_72,c_68]) ).
tcf(c_121,plain,
compose(codomain(h),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_75,c_67]) ).
tcf(c_123,plain,
codomain(h) = codomain(g),
inference(light_normalisation,[status(thm)],[c_76,c_75]) ).
tcf(c_126,plain,
compose(g,codomain(h)) = g,
inference(superposition,[status(thm)],[c_123,c_68]) ).
tcf(c_136,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),domain(compose(a,X0)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_72,c_69]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),domain(compose(X0,codomain(X1))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_66,c_69]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),domain(compose(X0,domain(X1))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_100,c_69]) ).
tcf(c_142,plain,
ifeq(codomain(a),domain(b),codomain(h),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_75,c_69]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(X1),domain(compose(codomain(X0),X1)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_66,c_69]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),domain(compose(domain(X0),X1)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_100,c_69]) ).
tcf(c_154,plain,
ifeq(domain(b),domain(b),codomain(h),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_142,c_72]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),domain(compose(domain(X0),X1)),domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_153,c_65]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),domain(compose(codomain(X0),X1)),codomain(X0)) = codomain(X0),
inference(light_normalisation,[status(thm)],[c_151,c_102]) ).
tcf(c_167,plain,
domain(a) = codomain(h),
inference(demodulation,[status(thm)],[c_154,c_64]) ).
tcf(c_168,plain,
compose(domain(a),compose(a,b)) = compose(a,b),
inference(demodulation,[status(thm)],[c_121,c_167]) ).
tcf(c_169,plain,
compose(g,domain(a)) = g,
inference(demodulation,[status(thm)],[c_126,c_167]) ).
tcf(c_170,plain,
domain(a) = codomain(g),
inference(demodulation,[status(thm)],[c_123,c_167]) ).
tcf(c_171,plain,
domain(compose(a,b)) = domain(a),
inference(demodulation,[status(thm)],[c_75,c_167]) ).
tcf(c_172,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),domain(compose(h,X0)),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_167,c_69]) ).
tcf(c_175,plain,
compose(h,domain(a)) = h,
inference(superposition,[status(thm)],[c_167,c_68]) ).
tcf(c_177,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),domain(compose(g,X0)),domain(g)) = domain(g),
inference(superposition,[status(thm)],[c_170,c_69]) ).
tcf(c_191,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),domain(compose(X0,compose(a,b))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_171,c_69]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),codomain(compose(domain(X0),X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_65,c_70]) ).
tcf(c_199,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),codomain(compose(a,X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_72,c_70]) ).
tcf(c_200,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),codomain(compose(h,X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_167,c_70]) ).
tcf(c_201,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),codomain(compose(g,X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_170,c_70]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),codomain(compose(codomain(X0),X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_70]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(domain(X1)),codomain(compose(X0,domain(X1))),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_70]) ).
tcf(c_216,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),codomain(compose(X0,a)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_72,c_70]) ).
tcf(c_217,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),codomain(compose(X0,h)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_167,c_70]) ).
tcf(c_218,plain,
! [X0: $i] : ifeq(codomain(X0),domain(g),codomain(compose(X0,g)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_170,c_70]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,a),X2,ifeq(compose(domain(X0),a),X2,domain(X0),X1),X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_65,c_73]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(a,a),X1,a,X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_72,c_73]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(h,a),X1,h,X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_167,c_73]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(g,a),X1,g,X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_170,c_73]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,a),X2,ifeq(compose(codomain(X0),a),X2,codomain(X0),X1),X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_102,c_73]) ).
tcf(c_234,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),a),X2,ifeq(compose(X0,a),X2,X0,domain(X1)),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_73]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(a,a),X1,ifeq(compose(X0,a),X1,X0,a),a),a),a) = a,
inference(superposition,[status(thm)],[c_72,c_73]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X1,ifeq(compose(X0,a),X1,X0,h),h),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_73]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X1,ifeq(compose(X0,a),X1,X0,g),g),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_73]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),a),X2,ifeq(compose(X0,a),X2,X0,codomain(X1)),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_73]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X0,a),compose(X1,a),X0,X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_64,c_73]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(a)),domain(b),ifeq(a,X1,ifeq(compose(X0,a),X1,X0,domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_67,c_73]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,a),compose(X0,a),X0,X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_64,c_73]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(a)),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(a,X1,domain(a),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_67,c_73]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,b),X2,ifeq(compose(domain(X0),b),X2,domain(X0),X1),X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_65,c_74]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(a,b),X1,a,X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_72,c_74]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(h,b),X1,h,X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_167,c_74]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(g,b),X1,g,X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_170,c_74]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,b),X2,ifeq(compose(codomain(X0),b),X2,codomain(X0),X1),X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_102,c_74]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),b),X2,ifeq(compose(X0,b),X2,X0,domain(X1)),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_74]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(a,b),X1,ifeq(compose(X0,b),X1,X0,a),a),a),a) = a,
inference(superposition,[status(thm)],[c_72,c_74]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X1,ifeq(compose(X0,b),X1,X0,h),h),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_74]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X1,ifeq(compose(X0,b),X1,X0,g),g),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_74]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),b),X2,ifeq(compose(X0,b),X2,X0,codomain(X1)),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_74]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X0,b),compose(X1,b),X0,X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_64,c_74]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(b)),domain(b),ifeq(b,X1,ifeq(compose(X0,b),X1,X0,domain(b)),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_67,c_74]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,b),compose(X0,b),X0,X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_64,c_74]) ).
tcf(c_256,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(b)),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(b,X1,domain(b),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_67,c_74]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(a,X0)),compose(compose(X1,a),X0)),compose(compose(X1,a),X0)) = compose(compose(X1,a),X0),
inference(superposition,[status(thm)],[c_72,c_71]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(h,X0)),compose(compose(X1,h),X0)),compose(compose(X1,h),X0)) = compose(compose(X1,h),X0),
inference(superposition,[status(thm)],[c_167,c_71]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(X0,codomain(X1))),compose(compose(X2,X0),codomain(X1))),compose(compose(X2,X0),codomain(X1))) = compose(compose(X2,X0),codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_71]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,compose(a,b))),compose(compose(X1,X0),compose(a,b))),compose(compose(X1,X0),compose(a,b))) = compose(compose(X1,X0),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_71]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(X0,domain(X1))),compose(compose(X2,X0),domain(X1))),compose(compose(X2,X0),domain(X1))) = compose(compose(X2,X0),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_71]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(X0,X1)),compose(compose(domain(X2),X0),X1)),compose(compose(domain(X2),X0),X1)) = compose(compose(domain(X2),X0),X1),
inference(superposition,[status(thm)],[c_65,c_71]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(a,compose(X0,X1)),compose(compose(a,X0),X1)),compose(compose(a,X0),X1)) = compose(compose(a,X0),X1),
inference(superposition,[status(thm)],[c_72,c_71]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),domain(X0),compose(h,compose(X0,X1)),compose(compose(h,X0),X1)),compose(compose(h,X0),X1)) = compose(compose(h,X0),X1),
inference(superposition,[status(thm)],[c_167,c_71]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),domain(X0),compose(g,compose(X0,X1)),compose(compose(g,X0),X1)),compose(compose(g,X0),X1)) = compose(compose(g,X0),X1),
inference(superposition,[status(thm)],[c_170,c_71]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(X0,X1)),compose(compose(codomain(X2),X0),X1)),compose(compose(codomain(X2),X0),X1)) = compose(compose(codomain(X2),X0),X1),
inference(superposition,[status(thm)],[c_102,c_71]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(codomain(X2),codomain(X0),compose(X2,compose(codomain(X0),X1)),compose(compose(X2,codomain(X0)),X1)),compose(compose(X2,codomain(X0)),X1)) = compose(compose(X2,codomain(X0)),X1),
inference(superposition,[status(thm)],[c_66,c_71]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(domain(X0),X1)),compose(compose(X2,domain(X0)),X1)),compose(compose(X2,domain(X0)),X1)) = compose(compose(X2,domain(X0)),X1),
inference(superposition,[status(thm)],[c_100,c_71]) ).
tcf(c_274,plain,
ifeq(codomain(a),domain(b),ifeq(codomain(g),domain(a),compose(h,compose(a,b)),compose(compose(g,a),b)),compose(compose(g,a),b)) = compose(compose(g,a),b),
inference(superposition,[status(thm)],[c_77,c_71]) ).
tcf(c_276,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X0),ifeq(codomain(X1),domain(domain(X0)),compose(X1,X0),compose(compose(X1,domain(X0)),X0)),compose(compose(X1,domain(X0)),X0)) = compose(compose(X1,domain(X0)),X0),
inference(superposition,[status(thm)],[c_67,c_71]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(codomain(X0)),ifeq(codomain(X1),domain(X0),compose(X1,X0),compose(compose(X1,X0),codomain(X0))),compose(compose(X1,X0),codomain(X0))) = compose(compose(X1,X0),codomain(X0)),
inference(superposition,[status(thm)],[c_68,c_71]) ).
tcf(c_278,plain,
! [X0: $i] : ifeq(codomain(g),domain(compose(a,b)),ifeq(codomain(X0),domain(g),compose(X0,compose(h,compose(a,b))),compose(compose(X0,g),compose(a,b))),compose(compose(X0,g),compose(a,b))) = compose(compose(X0,g),compose(a,b)),
inference(superposition,[status(thm)],[c_77,c_71]) ).
tcf(c_283,plain,
! [X0: $i] : ifeq(codomain(g),domain(domain(a)),ifeq(codomain(X0),domain(g),compose(X0,g),compose(compose(X0,g),domain(a))),compose(compose(X0,g),domain(a))) = compose(compose(X0,g),domain(a)),
inference(superposition,[status(thm)],[c_169,c_71]) ).
tcf(c_284,plain,
! [X0: $i] : ifeq(codomain(h),domain(domain(a)),ifeq(codomain(X0),domain(h),compose(X0,h),compose(compose(X0,h),domain(a))),compose(compose(X0,h),domain(a))) = compose(compose(X0,h),domain(a)),
inference(superposition,[status(thm)],[c_175,c_71]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(codomain(compose(X1,X0))),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,codomain(compose(X1,X0)))),compose(X1,X0)),compose(X1,X0)) = compose(X1,X0),
inference(superposition,[status(thm)],[c_68,c_71]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(domain(X0)),domain(X0),compose(domain(X0),compose(X0,X1)),compose(X0,X1)),compose(X0,X1)) = compose(X0,X1),
inference(superposition,[status(thm)],[c_67,c_71]) ).
tcf(c_297,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(codomain(X0),domain(codomain(X0)),compose(X0,compose(codomain(X0),X1)),compose(X0,X1)),compose(X0,X1)) = compose(X0,X1),
inference(superposition,[status(thm)],[c_68,c_71]) ).
tcf(c_303,plain,
! [X0: $i] : ifeq(codomain(domain(a)),domain(X0),ifeq(codomain(g),domain(domain(a)),compose(g,compose(domain(a),X0)),compose(g,X0)),compose(g,X0)) = compose(g,X0),
inference(superposition,[status(thm)],[c_169,c_71]) ).
tcf(c_304,plain,
! [X0: $i] : ifeq(codomain(domain(a)),domain(X0),ifeq(codomain(h),domain(domain(a)),compose(h,compose(domain(a),X0)),compose(h,X0)),compose(h,X0)) = compose(h,X0),
inference(superposition,[status(thm)],[c_175,c_71]) ).
tcf(c_305,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(X0),domain(X0),compose(domain(X0),compose(X0,X1)),compose(X0,X1)),compose(X0,X1)) = compose(X0,X1),
inference(light_normalisation,[status(thm)],[c_296,c_65]) ).
tcf(c_306,plain,
! [X0: $i] : ifeq(codomain(domain(a)),domain(X0),ifeq(domain(a),domain(domain(a)),compose(h,compose(domain(a),X0)),compose(h,X0)),compose(h,X0)) = compose(h,X0),
inference(light_normalisation,[status(thm)],[c_304,c_167]) ).
tcf(c_307,plain,
! [X0: $i] : ifeq(codomain(domain(a)),domain(X0),ifeq(domain(a),domain(domain(a)),compose(g,compose(domain(a),X0)),compose(g,X0)),compose(g,X0)) = compose(g,X0),
inference(light_normalisation,[status(thm)],[c_303,c_170]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X0),codomain(X0),compose(X0,compose(codomain(X0),X1)),compose(X0,X1)),compose(X0,X1)) = compose(X0,X1),
inference(light_normalisation,[status(thm)],[c_297,c_66,c_102]) ).
tcf(c_310,plain,
ifeq(domain(b),domain(b),ifeq(domain(a),domain(a),compose(h,compose(a,b)),compose(compose(g,a),b)),compose(compose(g,a),b)) = compose(compose(g,a),b),
inference(light_normalisation,[status(thm)],[c_274,c_72,c_170]) ).
tcf(c_313,plain,
! [X0: $i] : ifeq(domain(a),domain(domain(a)),ifeq(codomain(X0),domain(h),compose(X0,h),compose(compose(X0,h),domain(a))),compose(compose(X0,h),domain(a))) = compose(compose(X0,h),domain(a)),
inference(light_normalisation,[status(thm)],[c_284,c_167]) ).
tcf(c_314,plain,
! [X0: $i] : ifeq(domain(a),domain(domain(a)),ifeq(codomain(X0),domain(g),compose(X0,g),compose(compose(X0,g),domain(a))),compose(compose(X0,g),domain(a))) = compose(compose(X0,g),domain(a)),
inference(light_normalisation,[status(thm)],[c_283,c_170]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X0),ifeq(codomain(X1),domain(X0),compose(X1,X0),compose(compose(X1,X0),codomain(X0))),compose(compose(X1,X0),codomain(X0))) = compose(compose(X1,X0),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_277,c_66]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X0),ifeq(codomain(X1),domain(X0),compose(X1,X0),compose(compose(X1,domain(X0)),X0)),compose(compose(X1,domain(X0)),X0)) = compose(compose(X1,domain(X0)),X0),
inference(light_normalisation,[status(thm)],[c_276,c_65,c_100]) ).
tcf(c_319,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(domain(X0),X1)),compose(compose(X2,domain(X0)),X1)),compose(compose(X2,domain(X0)),X1)) = compose(compose(X2,domain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_272,c_65]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),codomain(X0),compose(X2,compose(codomain(X0),X1)),compose(compose(X2,codomain(X0)),X1)),compose(compose(X2,codomain(X0)),X1)) = compose(compose(X2,codomain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_270,c_102]) ).
tcf(c_326,plain,
! [X0: $i] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(g),compose(X0,compose(h,compose(a,b))),compose(compose(X0,g),compose(a,b))),compose(compose(X0,g),compose(a,b))) = compose(compose(X0,g),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_278,c_170,c_171]) ).
tcf(c_332,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),domain(compose(a,codomain(X0))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_66,c_136]) ).
tcf(c_333,plain,
ifeq(domain(b),domain(a),domain(compose(a,compose(a,b))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_171,c_136]) ).
tcf(c_334,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),domain(compose(a,domain(X0))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_100,c_136]) ).
tcf(c_342,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),domain(compose(h,codomain(X0))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_66,c_172]) ).
tcf(c_343,plain,
ifeq(domain(a),domain(a),domain(compose(h,compose(a,b))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_171,c_172]) ).
tcf(c_344,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),domain(compose(h,domain(X0))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_100,c_172]) ).
tcf(c_347,plain,
domain(compose(h,a)) = domain(h),
inference(superposition,[status(thm)],[c_172,c_64]) ).
tcf(c_349,plain,
ifeq(domain(a),domain(h),domain(compose(h,compose(h,a))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_347,c_172]) ).
tcf(c_350,plain,
ifeq(domain(b),domain(h),domain(compose(a,compose(h,a))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_347,c_136]) ).
tcf(c_355,plain,
compose(domain(h),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_347,c_67]) ).
tcf(c_357,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,compose(h,a))),compose(compose(X1,X0),compose(h,a))),compose(compose(X1,X0),compose(h,a))) = compose(compose(X1,X0),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_71]) ).
tcf(c_359,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),domain(compose(X0,compose(h,a))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_347,c_69]) ).
tcf(c_363,plain,
! [X0: $i] : ifeq(codomain(domain(h)),domain(compose(h,a)),ifeq(codomain(X0),domain(domain(h)),compose(X0,compose(h,a)),compose(compose(X0,domain(h)),compose(h,a))),compose(compose(X0,domain(h)),compose(h,a))) = compose(compose(X0,domain(h)),compose(h,a)),
inference(superposition,[status(thm)],[c_355,c_71]) ).
tcf(c_367,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(codomain(domain(h)),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),X0)),compose(compose(h,a),X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
inference(superposition,[status(thm)],[c_355,c_71]) ).
tcf(c_371,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(codomain(domain(h)),domain(h),compose(domain(h),compose(compose(h,a),X0)),compose(compose(h,a),X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
inference(light_normalisation,[status(thm)],[c_367,c_347]) ).
tcf(c_372,plain,
! [X0: $i] : ifeq(codomain(domain(h)),domain(h),ifeq(codomain(X0),domain(domain(h)),compose(X0,compose(h,a)),compose(compose(X0,domain(h)),compose(h,a))),compose(compose(X0,domain(h)),compose(h,a))) = compose(compose(X0,domain(h)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_363,c_347]) ).
tcf(c_375,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),domain(compose(g,codomain(X0))),domain(g)) = domain(g),
inference(superposition,[status(thm)],[c_66,c_177]) ).
tcf(c_376,plain,
ifeq(domain(a),domain(a),domain(compose(g,compose(a,b))),domain(g)) = domain(g),
inference(superposition,[status(thm)],[c_171,c_177]) ).
tcf(c_377,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),domain(compose(g,domain(X0))),domain(g)) = domain(g),
inference(superposition,[status(thm)],[c_100,c_177]) ).
tcf(c_378,plain,
ifeq(domain(a),domain(h),domain(compose(g,compose(h,a))),domain(g)) = domain(g),
inference(superposition,[status(thm)],[c_347,c_177]) ).
tcf(c_382,plain,
domain(compose(g,a)) = domain(g),
inference(superposition,[status(thm)],[c_177,c_64]) ).
tcf(c_384,plain,
ifeq(domain(a),domain(a),domain(compose(h,compose(a,b))),domain(g)) = domain(g),
inference(light_normalisation,[status(thm)],[c_376,c_77]) ).
tcf(c_393,plain,
compose(domain(g),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_382,c_67]) ).
tcf(c_397,plain,
! [X0: $i] : ifeq(codomain(X0),domain(g),domain(compose(X0,compose(g,a))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_382,c_69]) ).
tcf(c_420,plain,
! [X0: $i] : ifeq(domain(b),domain(domain(X0)),codomain(compose(a,domain(X0))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_199]) ).
tcf(c_421,plain,
ifeq(domain(b),domain(a),codomain(compose(a,a)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_72,c_199]) ).
tcf(c_422,plain,
ifeq(domain(b),domain(h),codomain(compose(a,h)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_167,c_199]) ).
tcf(c_423,plain,
ifeq(domain(b),domain(g),codomain(compose(a,g)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_170,c_199]) ).
tcf(c_424,plain,
! [X0: $i] : ifeq(domain(b),domain(codomain(X0)),codomain(compose(a,codomain(X0))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_199]) ).
tcf(c_425,plain,
codomain(compose(a,b)) = codomain(b),
inference(superposition,[status(thm)],[c_199,c_64]) ).
tcf(c_428,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),codomain(compose(a,codomain(X0))),codomain(X0)) = codomain(X0),
inference(light_normalisation,[status(thm)],[c_424,c_66]) ).
tcf(c_429,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),codomain(compose(a,domain(X0))),domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_420,c_100]) ).
tcf(c_434,plain,
ifeq(domain(b),domain(compose(a,b)),codomain(compose(a,compose(a,b))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_425,c_199]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(compose(a,b)),compose(X1,compose(compose(a,b),X0)),compose(compose(X1,compose(a,b)),X0)),compose(compose(X1,compose(a,b)),X0)) = compose(compose(X1,compose(a,b)),X0),
inference(superposition,[status(thm)],[c_425,c_71]) ).
tcf(c_436,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(compose(a,b),b),X1,compose(a,b),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_425,c_74]) ).
tcf(c_437,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(compose(a,b),a),X1,compose(a,b),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_425,c_73]) ).
tcf(c_438,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),codomain(compose(compose(a,b),X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_425,c_70]) ).
tcf(c_439,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),domain(compose(compose(a,b),X0)),domain(compose(a,b))) = domain(compose(a,b)),
inference(superposition,[status(thm)],[c_425,c_69]) ).
tcf(c_442,plain,
compose(compose(a,b),codomain(b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_68]) ).
tcf(c_445,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X1,ifeq(compose(X0,b),X1,X0,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_74]) ).
tcf(c_446,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X1,ifeq(compose(X0,a),X1,X0,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_73]) ).
tcf(c_447,plain,
! [X0: $i] : ifeq(codomain(X0),domain(compose(a,b)),codomain(compose(X0,compose(a,b))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_425,c_70]) ).
tcf(c_448,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,X1)),compose(compose(compose(a,b),X0),X1)),compose(compose(compose(a,b),X0),X1)) = compose(compose(compose(a,b),X0),X1),
inference(superposition,[status(thm)],[c_425,c_71]) ).
tcf(c_451,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),codomain(compose(X0,compose(a,b))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_447,c_171]) ).
tcf(c_452,plain,
ifeq(domain(b),domain(a),codomain(compose(a,compose(a,b))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_434,c_171]) ).
tcf(c_453,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),domain(compose(compose(a,b),X0)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_439,c_171]) ).
tcf(c_454,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,b),X0)),compose(compose(X1,compose(a,b)),X0)),compose(compose(X1,compose(a,b)),X0)) = compose(compose(X1,compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_435,c_171]) ).
tcf(c_478,plain,
! [X0: $i] : ifeq(domain(a),domain(domain(X0)),codomain(compose(h,domain(X0))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_200]) ).
tcf(c_480,plain,
ifeq(domain(a),domain(h),codomain(compose(h,h)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_167,c_200]) ).
tcf(c_481,plain,
ifeq(domain(a),domain(g),codomain(compose(h,g)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_170,c_200]) ).
tcf(c_482,plain,
! [X0: $i] : ifeq(domain(a),domain(codomain(X0)),codomain(compose(h,codomain(X0))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_200]) ).
tcf(c_483,plain,
ifeq(domain(a),domain(compose(a,b)),codomain(compose(h,compose(a,b))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_425,c_200]) ).
tcf(c_484,plain,
codomain(compose(h,a)) = codomain(a),
inference(superposition,[status(thm)],[c_200,c_64]) ).
tcf(c_485,plain,
codomain(compose(h,a)) = domain(b),
inference(light_normalisation,[status(thm)],[c_484,c_72]) ).
tcf(c_488,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),codomain(compose(h,codomain(X0))),codomain(X0)) = codomain(X0),
inference(light_normalisation,[status(thm)],[c_482,c_66]) ).
tcf(c_489,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),codomain(compose(h,domain(X0))),domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_478,c_100]) ).
tcf(c_492,plain,
ifeq(domain(a),domain(a),codomain(compose(h,compose(a,b))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_483,c_171]) ).
tcf(c_497,plain,
ifeq(domain(a),domain(compose(h,a)),codomain(compose(h,compose(h,a))),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_200]) ).
tcf(c_498,plain,
ifeq(domain(b),domain(compose(h,a)),codomain(compose(a,compose(h,a))),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_199]) ).
tcf(c_499,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(compose(h,a)),compose(X1,compose(compose(h,a),X0)),compose(compose(X1,compose(h,a)),X0)),compose(compose(X1,compose(h,a)),X0)) = compose(compose(X1,compose(h,a)),X0),
inference(superposition,[status(thm)],[c_485,c_71]) ).
tcf(c_501,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(compose(h,a),a),X1,compose(h,a),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_485,c_73]) ).
tcf(c_502,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),codomain(compose(compose(h,a),X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_485,c_70]) ).
tcf(c_503,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),domain(compose(compose(h,a),X0)),domain(compose(h,a))) = domain(compose(h,a)),
inference(superposition,[status(thm)],[c_485,c_69]) ).
tcf(c_506,plain,
compose(compose(h,a),domain(b)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_68]) ).
tcf(c_510,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X1,ifeq(compose(X0,a),X1,X0,compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_73]) ).
tcf(c_511,plain,
! [X0: $i] : ifeq(codomain(X0),domain(compose(h,a)),codomain(compose(X0,compose(h,a))),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_70]) ).
tcf(c_512,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,X1)),compose(compose(compose(h,a),X0),X1)),compose(compose(compose(h,a),X0),X1)) = compose(compose(compose(h,a),X0),X1),
inference(superposition,[status(thm)],[c_485,c_71]) ).
tcf(c_516,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),codomain(compose(X0,compose(h,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_511,c_347]) ).
tcf(c_517,plain,
ifeq(domain(b),domain(h),codomain(compose(a,compose(h,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_498,c_347]) ).
tcf(c_518,plain,
ifeq(domain(a),domain(h),codomain(compose(h,compose(h,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_497,c_347]) ).
tcf(c_519,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),domain(compose(compose(h,a),X0)),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_503,c_347]) ).
tcf(c_520,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(h,a),X0)),compose(compose(X1,compose(h,a)),X0)),compose(compose(X1,compose(h,a)),X0)) = compose(compose(X1,compose(h,a)),X0),
inference(light_normalisation,[status(thm)],[c_499,c_347]) ).
tcf(c_543,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(domain(b)),ifeq(codomain(X0),domain(compose(h,a)),compose(X0,compose(h,a)),compose(compose(X0,compose(h,a)),domain(b))),compose(compose(X0,compose(h,a)),domain(b))) = compose(compose(X0,compose(h,a)),domain(b)),
inference(superposition,[status(thm)],[c_506,c_71]) ).
tcf(c_546,plain,
! [X0: $i] : ifeq(codomain(domain(b)),domain(X0),ifeq(codomain(compose(h,a)),domain(domain(b)),compose(compose(h,a),compose(domain(b),X0)),compose(compose(h,a),X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
inference(superposition,[status(thm)],[c_506,c_71]) ).
tcf(c_551,plain,
! [X0: $i] : ifeq(codomain(domain(b)),domain(X0),ifeq(domain(b),domain(domain(b)),compose(compose(h,a),compose(domain(b),X0)),compose(compose(h,a),X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
inference(light_normalisation,[status(thm)],[c_546,c_485]) ).
tcf(c_552,plain,
! [X0: $i] : ifeq(domain(b),domain(domain(b)),ifeq(codomain(X0),domain(h),compose(X0,compose(h,a)),compose(compose(X0,compose(h,a)),domain(b))),compose(compose(X0,compose(h,a)),domain(b))) = compose(compose(X0,compose(h,a)),domain(b)),
inference(light_normalisation,[status(thm)],[c_543,c_347,c_485]) ).
tcf(c_563,plain,
! [X0: $i] : ifeq(domain(a),domain(domain(X0)),codomain(compose(g,domain(X0))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_201]) ).
tcf(c_565,plain,
ifeq(domain(a),domain(h),codomain(compose(g,h)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_167,c_201]) ).
tcf(c_566,plain,
ifeq(domain(a),domain(g),codomain(compose(g,g)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_170,c_201]) ).
tcf(c_567,plain,
! [X0: $i] : ifeq(domain(a),domain(codomain(X0)),codomain(compose(g,codomain(X0))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_201]) ).
tcf(c_569,plain,
ifeq(domain(a),domain(compose(h,a)),codomain(compose(g,compose(h,a))),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_201]) ).
tcf(c_570,plain,
codomain(compose(g,a)) = codomain(a),
inference(superposition,[status(thm)],[c_201,c_64]) ).
tcf(c_571,plain,
codomain(compose(g,a)) = domain(b),
inference(light_normalisation,[status(thm)],[c_570,c_72]) ).
tcf(c_574,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),codomain(compose(g,codomain(X0))),codomain(X0)) = codomain(X0),
inference(light_normalisation,[status(thm)],[c_567,c_66]) ).
tcf(c_575,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),codomain(compose(g,domain(X0))),domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_563,c_100]) ).
tcf(c_578,plain,
ifeq(domain(a),domain(h),codomain(compose(g,compose(h,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_569,c_347]) ).
tcf(c_588,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(compose(g,a),a),X1,compose(g,a),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_571,c_73]) ).
tcf(c_589,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),codomain(compose(compose(g,a),X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_571,c_70]) ).
tcf(c_593,plain,
compose(compose(g,a),domain(b)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_68]) ).
tcf(c_597,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),X1,ifeq(compose(X0,a),X1,X0,compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_73]) ).
tcf(c_599,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,X1)),compose(compose(compose(g,a),X0),X1)),compose(compose(compose(g,a),X0),X1)) = compose(compose(compose(g,a),X0),X1),
inference(superposition,[status(thm)],[c_571,c_71]) ).
tcf(c_608,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(domain(b)),ifeq(codomain(X0),domain(compose(g,a)),compose(X0,compose(g,a)),compose(compose(X0,compose(g,a)),domain(b))),compose(compose(X0,compose(g,a)),domain(b))) = compose(compose(X0,compose(g,a)),domain(b)),
inference(superposition,[status(thm)],[c_593,c_71]) ).
tcf(c_611,plain,
! [X0: $i] : ifeq(codomain(domain(b)),domain(X0),ifeq(codomain(compose(g,a)),domain(domain(b)),compose(compose(g,a),compose(domain(b),X0)),compose(compose(g,a),X0)),compose(compose(g,a),X0)) = compose(compose(g,a),X0),
inference(superposition,[status(thm)],[c_593,c_71]) ).
tcf(c_616,plain,
! [X0: $i] : ifeq(codomain(domain(b)),domain(X0),ifeq(domain(b),domain(domain(b)),compose(compose(g,a),compose(domain(b),X0)),compose(compose(g,a),X0)),compose(compose(g,a),X0)) = compose(compose(g,a),X0),
inference(light_normalisation,[status(thm)],[c_611,c_571]) ).
tcf(c_617,plain,
! [X0: $i] : ifeq(domain(b),domain(domain(b)),ifeq(codomain(X0),domain(g),compose(X0,compose(g,a)),compose(compose(X0,compose(g,a)),domain(b))),compose(compose(X0,compose(g,a)),domain(b))) = compose(compose(X0,compose(g,a)),domain(b)),
inference(light_normalisation,[status(thm)],[c_608,c_382,c_571]) ).
tcf(c_619,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),codomain(compose(domain(X0),a)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_65,c_216]) ).
tcf(c_623,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),codomain(compose(codomain(X0),a)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_102,c_216]) ).
tcf(c_624,plain,
ifeq(codomain(b),domain(a),codomain(compose(compose(a,b),a)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_425,c_216]) ).
tcf(c_625,plain,
ifeq(domain(b),domain(a),codomain(compose(compose(h,a),a)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_216]) ).
tcf(c_626,plain,
ifeq(domain(b),domain(a),codomain(compose(compose(g,a),a)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_571,c_216]) ).
tcf(c_634,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),h)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_65,c_217]) ).
tcf(c_638,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),h)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_102,c_217]) ).
tcf(c_639,plain,
ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),h)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_425,c_217]) ).
tcf(c_640,plain,
ifeq(domain(b),domain(h),codomain(compose(compose(h,a),h)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_485,c_217]) ).
tcf(c_641,plain,
ifeq(domain(b),domain(h),codomain(compose(compose(g,a),h)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_571,c_217]) ).
tcf(c_645,plain,
! [X0: $i] : ifeq(domain(X0),domain(g),codomain(compose(domain(X0),g)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_65,c_218]) ).
tcf(c_649,plain,
! [X0: $i] : ifeq(codomain(X0),domain(g),codomain(compose(codomain(X0),g)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_102,c_218]) ).
tcf(c_689,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),codomain(X1),domain(compose(codomain(X0),codomain(X1))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_66,c_139]) ).
tcf(c_690,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(X0),domain(compose(compose(a,b),codomain(X0))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_171,c_139]) ).
tcf(c_691,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(X1),domain(compose(domain(X0),codomain(X1))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_100,c_139]) ).
tcf(c_693,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),codomain(X0),domain(compose(compose(h,a),codomain(X0))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_347,c_139]) ).
tcf(c_697,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(X1),domain(compose(domain(X0),codomain(X1))),domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_691,c_65]) ).
tcf(c_698,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),domain(compose(codomain(X0),codomain(X1))),codomain(X0)) = codomain(X0),
inference(light_normalisation,[status(thm)],[c_689,c_102]) ).
tcf(c_701,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),domain(compose(compose(h,a),codomain(X0))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_693,c_485]) ).
tcf(c_703,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),domain(compose(compose(a,b),codomain(X0))),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_690,c_425]) ).
tcf(c_735,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(X1),domain(compose(codomain(X0),domain(X1))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_66,c_141]) ).
tcf(c_736,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),domain(compose(compose(a,b),domain(X0))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_171,c_141]) ).
tcf(c_737,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),domain(compose(domain(X0),domain(X1))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_100,c_141]) ).
tcf(c_739,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(X0),domain(compose(compose(h,a),domain(X0))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_347,c_141]) ).
tcf(c_741,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),domain(compose(domain(X0),domain(X1))),domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_737,c_65]) ).
tcf(c_742,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),domain(compose(codomain(X0),domain(X1))),codomain(X0)) = codomain(X0),
inference(light_normalisation,[status(thm)],[c_735,c_102]) ).
tcf(c_745,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),domain(compose(compose(h,a),domain(X0))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_739,c_485]) ).
tcf(c_747,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),domain(compose(compose(a,b),domain(X0))),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_736,c_425]) ).
tcf(c_762,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),domain(compose(domain(X0),compose(a,b))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_171,c_159]) ).
tcf(c_765,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),domain(compose(domain(X0),compose(h,a))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_347,c_159]) ).
tcf(c_799,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),domain(compose(codomain(X0),compose(a,b))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_171,c_160]) ).
tcf(c_802,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),domain(compose(codomain(X0),compose(h,a))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_347,c_160]) ).
tcf(c_853,plain,
! [X0: $i] : ifeq(domain(X0),domain(compose(a,b)),codomain(compose(domain(X0),compose(a,b))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_425,c_198]) ).
tcf(c_854,plain,
! [X0: $i] : ifeq(domain(X0),domain(compose(h,a)),codomain(compose(domain(X0),compose(h,a))),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_198]) ).
tcf(c_860,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),compose(h,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_854,c_347]) ).
tcf(c_861,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),codomain(compose(domain(X0),compose(a,b))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_853,c_171]) ).
tcf(c_898,plain,
! [X0: $i] : ifeq(codomain(X0),domain(compose(a,b)),codomain(compose(codomain(X0),compose(a,b))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_425,c_202]) ).
tcf(c_899,plain,
! [X0: $i] : ifeq(codomain(X0),domain(compose(h,a)),codomain(compose(codomain(X0),compose(h,a))),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_202]) ).
tcf(c_903,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),compose(h,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_899,c_347]) ).
tcf(c_904,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),codomain(compose(codomain(X0),compose(a,b))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_898,c_171]) ).
tcf(c_1260,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(h,a),X1,h,X0),X0),X0) = X0,
inference(demodulation,[status(thm)],[c_231,c_64]) ).
tcf(c_1261,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(h,a),X1,h,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_1260]) ).
tcf(c_1262,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(a,a),X0,ifeq(compose(h,a),X0,h,a),a),a) = a,
inference(superposition,[status(thm)],[c_72,c_1260]) ).
tcf(c_1263,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(compose(h,a),X0,h,h),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_1260]) ).
tcf(c_1264,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(compose(h,a),X0,h,g),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_1260]) ).
tcf(c_1265,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(compose(h,a),X1,h,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_1260]) ).
tcf(c_1266,plain,
! [X0: $i] : ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(compose(h,a),X0,h,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_1260]) ).
tcf(c_1267,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X0,ifeq(compose(h,a),X0,h,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_1260]) ).
tcf(c_1268,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),X0,ifeq(compose(h,a),X0,h,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_1260]) ).
tcf(c_1269,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(h,a),compose(X0,a),h,X0),X0) = X0,
inference(superposition,[status(thm)],[c_64,c_1260]) ).
tcf(c_1270,plain,
! [X0: $i] : ifeq(codomain(domain(a)),domain(b),ifeq(a,X0,ifeq(compose(h,a),X0,h,domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_67,c_1260]) ).
tcf(c_1271,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(h,a),h,X0),X0) = X0,
inference(superposition,[status(thm)],[c_64,c_1260]) ).
tcf(c_1287,plain,
ifeq(codomain(compose(a,b)),domain(a),domain(compose(compose(a,b),compose(a,b))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_171,c_191]) ).
tcf(c_1290,plain,
ifeq(codomain(compose(h,a)),domain(a),domain(compose(compose(h,a),compose(a,b))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_347,c_191]) ).
tcf(c_1297,plain,
ifeq(domain(b),domain(a),domain(compose(compose(h,a),compose(a,b))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_1290,c_485]) ).
tcf(c_1299,plain,
ifeq(codomain(b),domain(a),domain(compose(compose(a,b),compose(a,b))),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_1287,c_425]) ).
tcf(c_1305,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),codomain(compose(X0,domain(X1))),domain(X1)) = domain(X1),
inference(demodulation,[status(thm)],[c_215,c_100]) ).
tcf(c_1306,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),codomain(compose(domain(X0),domain(X1))),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_1305]) ).
tcf(c_1310,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),codomain(compose(codomain(X0),domain(X1))),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_102,c_1305]) ).
tcf(c_1311,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),codomain(compose(compose(a,b),domain(X0))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_425,c_1305]) ).
tcf(c_1312,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),codomain(compose(compose(h,a),domain(X0))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_485,c_1305]) ).
tcf(c_1313,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),codomain(compose(compose(g,a),domain(X0))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_571,c_1305]) ).
tcf(c_1331,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),codomain(compose(X0,codomain(X1))),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_66,c_1305]) ).
tcf(c_1345,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(X1),codomain(compose(domain(X0),codomain(X1))),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_65,c_1331]) ).
tcf(c_1349,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),codomain(compose(codomain(X0),codomain(X1))),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_1331]) ).
tcf(c_1350,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),codomain(compose(compose(a,b),codomain(X0))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_425,c_1331]) ).
tcf(c_1351,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),codomain(compose(compose(h,a),codomain(X0))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_485,c_1331]) ).
tcf(c_1352,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),codomain(compose(compose(g,a),codomain(X0))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_571,c_1331]) ).
tcf(c_1392,plain,
domain(compose(h,compose(a,b))) = domain(h),
inference(demodulation,[status(thm)],[c_343,c_64]) ).
tcf(c_1411,plain,
ifeq(domain(a),domain(h),domain(compose(h,compose(h,compose(a,b)))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_1392,c_172]) ).
tcf(c_1412,plain,
ifeq(domain(b),domain(h),domain(compose(a,compose(h,compose(a,b)))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_1392,c_136]) ).
tcf(c_1417,plain,
compose(domain(h),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_1392,c_67]) ).
tcf(c_1422,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),domain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_1392,c_160]) ).
tcf(c_1423,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),domain(compose(domain(X0),compose(h,compose(a,b)))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_1392,c_159]) ).
tcf(c_1425,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,compose(h,compose(a,b)))),compose(compose(X1,X0),compose(h,compose(a,b)))),compose(compose(X1,X0),compose(h,compose(a,b)))) = compose(compose(X1,X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_71]) ).
tcf(c_1427,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),domain(compose(X0,compose(h,compose(a,b)))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_1392,c_69]) ).
tcf(c_1436,plain,
! [X0: $i] : ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),ifeq(codomain(X0),domain(domain(h)),compose(X0,compose(h,compose(a,b))),compose(compose(X0,domain(h)),compose(h,compose(a,b)))),compose(compose(X0,domain(h)),compose(h,compose(a,b)))) = compose(compose(X0,domain(h)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1417,c_71]) ).
tcf(c_1449,plain,
! [X0: $i] : ifeq(codomain(domain(h)),domain(h),ifeq(codomain(X0),domain(domain(h)),compose(X0,compose(h,compose(a,b))),compose(compose(X0,domain(h)),compose(h,compose(a,b)))),compose(compose(X0,domain(h)),compose(h,compose(a,b)))) = compose(compose(X0,domain(h)),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_1436,c_1392]) ).
tcf(c_1462,plain,
ifeq(codomain(compose(a,b)),domain(h),domain(compose(compose(a,b),compose(h,a))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_171,c_359]) ).
tcf(c_1466,plain,
ifeq(codomain(compose(h,a)),domain(h),domain(compose(compose(h,a),compose(h,a))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_347,c_359]) ).
tcf(c_1472,plain,
ifeq(domain(b),domain(h),domain(compose(compose(h,a),compose(h,a))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_1466,c_485]) ).
tcf(c_1474,plain,
ifeq(codomain(b),domain(h),domain(compose(compose(a,b),compose(h,a))),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_1462,c_425]) ).
tcf(c_1479,plain,
ifeq(domain(a),domain(a),domain(h),domain(g)) = domain(g),
inference(light_normalisation,[status(thm)],[c_384,c_1392]) ).
tcf(c_1480,plain,
domain(h) = domain(g),
inference(demodulation,[status(thm)],[c_1479,c_64]) ).
tcf(c_1481,plain,
ifeq(domain(a),domain(h),domain(compose(g,compose(h,a))),domain(h)) = domain(h),
inference(demodulation,[status(thm)],[c_378,c_1480]) ).
tcf(c_1482,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),g)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_649,c_1480]) ).
tcf(c_1483,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),g)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_645,c_1480]) ).
tcf(c_1484,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),domain(compose(g,domain(X0))),domain(h)) = domain(h),
inference(demodulation,[status(thm)],[c_377,c_1480]) ).
tcf(c_1485,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),domain(compose(g,codomain(X0))),domain(h)) = domain(h),
inference(demodulation,[status(thm)],[c_375,c_1480]) ).
tcf(c_1486,plain,
ifeq(domain(a),domain(h),codomain(compose(g,g)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_566,c_1480]) ).
tcf(c_1487,plain,
ifeq(domain(a),domain(h),codomain(compose(h,g)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_481,c_1480]) ).
tcf(c_1488,plain,
ifeq(domain(b),domain(h),codomain(compose(a,g)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_423,c_1480]) ).
tcf(c_1489,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),codomain(compose(X0,g)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_218,c_1480]) ).
tcf(c_1490,plain,
compose(domain(h),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_393,c_1480]) ).
tcf(c_1491,plain,
domain(compose(g,a)) = domain(h),
inference(demodulation,[status(thm)],[c_382,c_1480]) ).
tcf(c_1492,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),domain(compose(g,X0)),domain(h)) = domain(h),
inference(demodulation,[status(thm)],[c_177,c_1480]) ).
tcf(c_1509,plain,
ifeq(domain(a),domain(h),domain(compose(h,g)),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_1480,c_172]) ).
tcf(c_1510,plain,
ifeq(domain(b),domain(h),domain(compose(a,g)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_1480,c_136]) ).
tcf(c_1511,plain,
! [X0: $i,X1: $i] : ifeq(codomain(g),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(g,X0)),compose(compose(X1,g),X0)),compose(compose(X1,g),X0)) = compose(compose(X1,g),X0),
inference(superposition,[status(thm)],[c_1480,c_71]) ).
tcf(c_1515,plain,
compose(domain(h),g) = g,
inference(superposition,[status(thm)],[c_1480,c_67]) ).
tcf(c_1520,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),domain(compose(codomain(X0),g)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_1480,c_160]) ).
tcf(c_1521,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),domain(compose(domain(X0),g)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_1480,c_159]) ).
tcf(c_1523,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,g)),compose(compose(X1,X0),g)),compose(compose(X1,X0),g)) = compose(compose(X1,X0),g),
inference(superposition,[status(thm)],[c_1480,c_71]) ).
tcf(c_1525,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),domain(compose(X0,g)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_1480,c_69]) ).
tcf(c_1537,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(g,X0)),compose(compose(X1,g),X0)),compose(compose(X1,g),X0)) = compose(compose(X1,g),X0),
inference(light_normalisation,[status(thm)],[c_1511,c_170]) ).
tcf(c_1546,plain,
! [X0: $i] : ifeq(codomain(domain(h)),domain(g),ifeq(codomain(X0),domain(domain(h)),compose(X0,g),compose(compose(X0,domain(h)),g)),compose(compose(X0,domain(h)),g)) = compose(compose(X0,domain(h)),g),
inference(superposition,[status(thm)],[c_1515,c_71]) ).
tcf(c_1557,plain,
! [X0: $i] : ifeq(codomain(domain(h)),domain(h),ifeq(codomain(X0),domain(domain(h)),compose(X0,g),compose(compose(X0,domain(h)),g)),compose(compose(X0,domain(h)),g)) = compose(compose(X0,domain(h)),g),
inference(light_normalisation,[status(thm)],[c_1546,c_1480]) ).
tcf(c_1559,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(g,a),X1,g,X0),X0),X0) = X0,
inference(demodulation,[status(thm)],[c_232,c_64]) ).
tcf(c_1560,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(g,a),X1,g,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_1559]) ).
tcf(c_1561,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(a,a),X0,ifeq(compose(g,a),X0,g,a),a),a) = a,
inference(superposition,[status(thm)],[c_72,c_1559]) ).
tcf(c_1562,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(compose(g,a),X0,g,h),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_1559]) ).
tcf(c_1563,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(compose(g,a),X0,g,g),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_1559]) ).
tcf(c_1564,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(compose(g,a),X1,g,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_1559]) ).
tcf(c_1565,plain,
! [X0: $i] : ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(compose(g,a),X0,g,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_1559]) ).
tcf(c_1566,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X0,ifeq(compose(g,a),X0,g,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_1559]) ).
tcf(c_1567,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),X0,ifeq(compose(g,a),X0,g,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_1559]) ).
tcf(c_1568,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(g,a),compose(X0,a),g,X0),X0) = X0,
inference(superposition,[status(thm)],[c_64,c_1559]) ).
tcf(c_1569,plain,
! [X0: $i] : ifeq(codomain(domain(a)),domain(b),ifeq(a,X0,ifeq(compose(g,a),X0,g,domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_67,c_1559]) ).
tcf(c_1570,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(g,a),g,X0),X0) = X0,
inference(superposition,[status(thm)],[c_64,c_1559]) ).
tcf(c_1581,plain,
ifeq(domain(b),domain(h),domain(compose(compose(g,a),g)),domain(compose(g,a))) = domain(compose(g,a)),
inference(superposition,[status(thm)],[c_571,c_1525]) ).
tcf(c_1585,plain,
ifeq(codomain(compose(a,b)),domain(h),domain(compose(compose(a,b),g)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_171,c_1525]) ).
tcf(c_1587,plain,
ifeq(codomain(g),domain(h),domain(compose(g,g)),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_1480,c_1525]) ).
tcf(c_1589,plain,
ifeq(codomain(compose(h,a)),domain(h),domain(compose(compose(h,a),g)),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_347,c_1525]) ).
tcf(c_1590,plain,
ifeq(domain(a),domain(h),domain(compose(g,g)),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_1587,c_170]) ).
tcf(c_1598,plain,
ifeq(domain(b),domain(h),domain(compose(compose(h,a),g)),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_1589,c_485]) ).
tcf(c_1599,plain,
ifeq(codomain(b),domain(h),domain(compose(compose(a,b),g)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_1585,c_425]) ).
tcf(c_1600,plain,
ifeq(domain(b),domain(h),domain(compose(compose(g,a),g)),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_1581,c_1491]) ).
tcf(c_1612,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),domain(compose(X0,compose(g,a))),domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_397,c_1480]) ).
tcf(c_1614,plain,
ifeq(domain(b),domain(h),domain(compose(a,compose(g,a))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_72,c_1612]) ).
tcf(c_1615,plain,
ifeq(domain(a),domain(h),domain(compose(h,compose(g,a))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_167,c_1612]) ).
tcf(c_1620,plain,
ifeq(domain(b),domain(h),domain(compose(compose(g,a),compose(g,a))),domain(compose(g,a))) = domain(compose(g,a)),
inference(superposition,[status(thm)],[c_571,c_1612]) ).
tcf(c_1622,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),domain(h),domain(compose(codomain(X0),compose(g,a))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_66,c_1612]) ).
tcf(c_1623,plain,
ifeq(codomain(compose(a,b)),domain(h),domain(compose(compose(a,b),compose(g,a))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_171,c_1612]) ).
tcf(c_1624,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),domain(h),domain(compose(domain(X0),compose(g,a))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_100,c_1612]) ).
tcf(c_1625,plain,
ifeq(codomain(g),domain(h),domain(compose(g,compose(g,a))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_1480,c_1612]) ).
tcf(c_1627,plain,
ifeq(codomain(compose(h,a)),domain(h),domain(compose(compose(h,a),compose(g,a))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_347,c_1612]) ).
tcf(c_1628,plain,
ifeq(domain(a),domain(h),domain(compose(g,compose(g,a))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_1625,c_170]) ).
tcf(c_1630,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),domain(compose(domain(X0),compose(g,a))),domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_1624,c_65]) ).
tcf(c_1631,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),domain(compose(codomain(X0),compose(g,a))),codomain(X0)) = codomain(X0),
inference(light_normalisation,[status(thm)],[c_1622,c_102]) ).
tcf(c_1634,plain,
ifeq(domain(b),domain(h),domain(compose(compose(h,a),compose(g,a))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_1627,c_485]) ).
tcf(c_1635,plain,
ifeq(codomain(b),domain(h),domain(compose(compose(a,b),compose(g,a))),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_1623,c_425]) ).
tcf(c_1636,plain,
ifeq(domain(b),domain(h),domain(compose(compose(g,a),compose(g,a))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_1620,c_1491]) ).
tcf(c_1644,plain,
ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),g)),codomain(g)) = codomain(g),
inference(superposition,[status(thm)],[c_1480,c_438]) ).
tcf(c_1654,plain,
ifeq(codomain(b),domain(compose(a,b)),codomain(compose(compose(a,b),compose(a,b))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_425,c_438]) ).
tcf(c_1655,plain,
ifeq(codomain(b),domain(compose(h,a)),codomain(compose(compose(a,b),compose(h,a))),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_438]) ).
tcf(c_1656,plain,
ifeq(codomain(b),domain(compose(g,a)),codomain(compose(compose(a,b),compose(g,a))),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_571,c_438]) ).
tcf(c_1657,plain,
ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),g)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_1644,c_170]) ).
tcf(c_1663,plain,
ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),compose(g,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_1656,c_1491]) ).
tcf(c_1664,plain,
ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),compose(h,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_1655,c_347]) ).
tcf(c_1665,plain,
ifeq(codomain(b),domain(a),codomain(compose(compose(a,b),compose(a,b))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_1654,c_171]) ).
tcf(c_1676,plain,
ifeq(domain(b),domain(a),codomain(compose(compose(h,a),compose(a,b))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_485,c_451]) ).
tcf(c_1677,plain,
ifeq(domain(b),domain(a),codomain(compose(compose(g,a),compose(a,b))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_571,c_451]) ).
tcf(c_1688,plain,
ifeq(codomain(compose(g,a)),domain(h),domain(compose(compose(g,a),compose(h,a))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_1491,c_359]) ).
tcf(c_1689,plain,
ifeq(codomain(compose(g,a)),domain(a),domain(compose(compose(g,a),compose(a,b))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_1491,c_191]) ).
tcf(c_1699,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),domain(compose(compose(g,a),domain(X0))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_1491,c_141]) ).
tcf(c_1700,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),codomain(X0),domain(compose(compose(g,a),codomain(X0))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_1491,c_139]) ).
tcf(c_1701,plain,
ifeq(domain(a),domain(h),codomain(compose(g,compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_201]) ).
tcf(c_1702,plain,
ifeq(domain(a),domain(h),codomain(compose(h,compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_200]) ).
tcf(c_1703,plain,
ifeq(domain(b),domain(h),codomain(compose(a,compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_199]) ).
tcf(c_1706,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(g,a),X0)),compose(compose(X1,compose(g,a)),X0)),compose(compose(X1,compose(g,a)),X0)) = compose(compose(X1,compose(g,a)),X0),
inference(superposition,[status(thm)],[c_1491,c_71]) ).
tcf(c_1707,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),domain(compose(compose(g,a),X0)),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_1491,c_69]) ).
tcf(c_1713,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_202]) ).
tcf(c_1714,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_198]) ).
tcf(c_1718,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,compose(g,a))),compose(compose(X1,X0),compose(g,a))),compose(compose(X1,X0),compose(g,a))) = compose(compose(X1,X0),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_71]) ).
tcf(c_1719,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),codomain(compose(X0,compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_70]) ).
tcf(c_1723,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),domain(compose(compose(g,a),X0)),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_1707,c_571]) ).
tcf(c_1725,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),domain(compose(compose(g,a),codomain(X0))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_1700,c_571]) ).
tcf(c_1726,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),domain(compose(compose(g,a),domain(X0))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_1699,c_571]) ).
tcf(c_1727,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),codomain(compose(X0,compose(g,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_1719,c_571]) ).
tcf(c_1728,plain,
ifeq(domain(b),domain(h),codomain(compose(a,compose(g,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_1703,c_571]) ).
tcf(c_1729,plain,
ifeq(domain(a),domain(h),codomain(compose(h,compose(g,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_1702,c_571]) ).
tcf(c_1730,plain,
ifeq(domain(a),domain(h),codomain(compose(g,compose(g,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_1701,c_571]) ).
tcf(c_1731,plain,
ifeq(domain(b),domain(a),domain(compose(compose(g,a),compose(a,b))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_1689,c_571]) ).
tcf(c_1732,plain,
ifeq(domain(b),domain(h),domain(compose(compose(g,a),compose(h,a))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_1688,c_571]) ).
tcf(c_1734,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),compose(g,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_1714,c_571]) ).
tcf(c_1735,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),compose(g,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_1713,c_571]) ).
tcf(c_1737,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(g,a),X0)),compose(compose(X1,compose(g,a)),X0)),compose(compose(X1,compose(g,a)),X0)) = compose(compose(X1,compose(g,a)),X0),
inference(light_normalisation,[status(thm)],[c_1706,c_571]) ).
tcf(c_1744,plain,
! [X0: $i] : ifeq(codomain(domain(h)),domain(compose(g,a)),ifeq(codomain(X0),domain(domain(h)),compose(X0,compose(g,a)),compose(compose(X0,domain(h)),compose(g,a))),compose(compose(X0,domain(h)),compose(g,a))) = compose(compose(X0,domain(h)),compose(g,a)),
inference(superposition,[status(thm)],[c_1490,c_71]) ).
tcf(c_1759,plain,
! [X0: $i] : ifeq(codomain(domain(h)),domain(h),ifeq(codomain(X0),domain(domain(h)),compose(X0,compose(g,a)),compose(compose(X0,domain(h)),compose(g,a))),compose(compose(X0,domain(h)),compose(g,a))) = compose(compose(X0,domain(h)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_1744,c_1491]) ).
tcf(c_1767,plain,
ifeq(domain(b),domain(h),codomain(compose(compose(h,a),g)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_485,c_1489]) ).
tcf(c_1768,plain,
ifeq(domain(b),domain(h),codomain(compose(compose(g,a),g)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_571,c_1489]) ).
tcf(c_1779,plain,
ifeq(domain(a),domain(h),domain(compose(g,compose(h,compose(a,b)))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_1392,c_1492]) ).
tcf(c_1792,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),h),h),h),h) = h,
inference(superposition,[status(thm)],[c_65,c_236]) ).
tcf(c_1793,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(compose(a,a),X0,a,h),h),h),h) = h,
inference(superposition,[status(thm)],[c_72,c_236]) ).
tcf(c_1796,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),h),h),h),h) = h,
inference(superposition,[status(thm)],[c_102,c_236]) ).
tcf(c_1797,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),h),h),h),h) = h,
inference(superposition,[status(thm)],[c_425,c_236]) ).
tcf(c_1798,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),h),h),h),h) = h,
inference(superposition,[status(thm)],[c_485,c_236]) ).
tcf(c_1799,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),h),h),h),h) = h,
inference(superposition,[status(thm)],[c_571,c_236]) ).
tcf(c_1800,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(X0,a),compose(h,a),X0,h),h),h) = h,
inference(superposition,[status(thm)],[c_64,c_236]) ).
tcf(c_1801,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(X0,a),X0,h),h),h) = h,
inference(superposition,[status(thm)],[c_64,c_236]) ).
tcf(c_1810,plain,
ifeq(codomain(b),domain(h),domain(compose(compose(a,b),compose(h,compose(a,b)))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_1392,c_453]) ).
tcf(c_1834,plain,
ifeq(domain(b),domain(compose(h,a)),codomain(compose(compose(h,a),compose(h,a))),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_502]) ).
tcf(c_1835,plain,
ifeq(domain(b),domain(compose(g,a)),codomain(compose(compose(h,a),compose(g,a))),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_571,c_502]) ).
tcf(c_1843,plain,
ifeq(domain(b),domain(h),codomain(compose(compose(h,a),compose(g,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_1835,c_1491]) ).
tcf(c_1844,plain,
ifeq(domain(b),domain(h),codomain(compose(compose(h,a),compose(h,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_1834,c_347]) ).
tcf(c_2068,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_65,c_237]) ).
tcf(c_2069,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(compose(a,a),X0,a,g),g),g),g) = g,
inference(superposition,[status(thm)],[c_72,c_237]) ).
tcf(c_2072,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_102,c_237]) ).
tcf(c_2073,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_425,c_237]) ).
tcf(c_2074,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_485,c_237]) ).
tcf(c_2075,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_571,c_237]) ).
tcf(c_2077,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(X0,a),compose(g,a),X0,g),g),g) = g,
inference(superposition,[status(thm)],[c_64,c_237]) ).
tcf(c_2078,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(X0,a),X0,g),g),g) = g,
inference(superposition,[status(thm)],[c_64,c_237]) ).
tcf(c_2090,plain,
ifeq(domain(b),domain(h),codomain(compose(compose(g,a),compose(h,a))),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_571,c_516]) ).
tcf(c_2104,plain,
ifeq(domain(b),domain(h),domain(compose(compose(h,a),compose(h,compose(a,b)))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_1392,c_519]) ).
tcf(c_2217,plain,
codomain(compose(h,compose(a,b))) = codomain(b),
inference(demodulation,[status(thm)],[c_492,c_64]) ).
tcf(c_2218,plain,
ifeq(codomain(b),domain(h),codomain(compose(compose(h,compose(a,b)),compose(h,a))),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_2217,c_516]) ).
tcf(c_2219,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_2217,c_237]) ).
tcf(c_2223,plain,
ifeq(domain(b),domain(compose(h,compose(a,b))),codomain(compose(compose(h,a),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_2217,c_502]) ).
tcf(c_2224,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),h),h),h),h) = h,
inference(superposition,[status(thm)],[c_2217,c_236]) ).
tcf(c_2225,plain,
ifeq(codomain(b),domain(h),codomain(compose(compose(h,compose(a,b)),g)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_2217,c_1489]) ).
tcf(c_2226,plain,
ifeq(codomain(b),domain(a),codomain(compose(compose(h,compose(a,b)),compose(a,b))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_2217,c_451]) ).
tcf(c_2227,plain,
ifeq(codomain(b),domain(compose(h,compose(a,b))),codomain(compose(compose(a,b),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_2217,c_438]) ).
tcf(c_2228,plain,
ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),compose(g,a))),domain(compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_1612]) ).
tcf(c_2229,plain,
ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),g)),domain(compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_1525]) ).
tcf(c_2230,plain,
! [X0: $i] : ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(compose(g,a),X0,g,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_1559]) ).
tcf(c_2231,plain,
ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),compose(h,a))),domain(compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_359]) ).
tcf(c_2232,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),codomain(compose(compose(h,compose(a,b)),codomain(X0))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_2217,c_1331]) ).
tcf(c_2233,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),codomain(compose(compose(h,compose(a,b)),domain(X0))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_2217,c_1305]) ).
tcf(c_2234,plain,
ifeq(codomain(b),domain(a),domain(compose(compose(h,compose(a,b)),compose(a,b))),domain(compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_191]) ).
tcf(c_2235,plain,
! [X0: $i] : ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(compose(h,a),X0,h,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_1260]) ).
tcf(c_2245,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),domain(compose(compose(h,compose(a,b)),domain(X0))),domain(compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_141]) ).
tcf(c_2246,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),domain(compose(compose(h,compose(a,b)),codomain(X0))),domain(compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_139]) ).
tcf(c_2247,plain,
ifeq(codomain(b),domain(h),codomain(compose(compose(h,compose(a,b)),h)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_2217,c_217]) ).
tcf(c_2248,plain,
ifeq(codomain(b),domain(a),codomain(compose(compose(h,compose(a,b)),a)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_2217,c_216]) ).
tcf(c_2249,plain,
ifeq(domain(a),domain(compose(h,compose(a,b))),codomain(compose(g,compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_2217,c_201]) ).
tcf(c_2250,plain,
ifeq(domain(a),domain(compose(h,compose(a,b))),codomain(compose(h,compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_2217,c_200]) ).
tcf(c_2251,plain,
ifeq(domain(b),domain(compose(h,compose(a,b))),codomain(compose(a,compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_2217,c_199]) ).
tcf(c_2252,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(compose(h,compose(a,b))),compose(X1,compose(compose(h,compose(a,b)),X0)),compose(compose(X1,compose(h,compose(a,b))),X0)),compose(compose(X1,compose(h,compose(a,b))),X0)) = compose(compose(X1,compose(h,compose(a,b))),X0),
inference(superposition,[status(thm)],[c_2217,c_71]) ).
tcf(c_2253,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(compose(h,compose(a,b)),b),X1,compose(h,compose(a,b)),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_2217,c_74]) ).
tcf(c_2254,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(compose(h,compose(a,b)),a),X1,compose(h,compose(a,b)),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_2217,c_73]) ).
tcf(c_2255,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),codomain(compose(compose(h,compose(a,b)),X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_2217,c_70]) ).
tcf(c_2256,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),domain(compose(compose(h,compose(a,b)),X0)),domain(compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_69]) ).
tcf(c_2259,plain,
compose(compose(h,compose(a,b)),codomain(b)) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_68]) ).
tcf(c_2263,plain,
! [X0: $i] : ifeq(codomain(X0),domain(compose(h,compose(a,b))),codomain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_2217,c_202]) ).
tcf(c_2264,plain,
! [X0: $i] : ifeq(domain(X0),domain(compose(h,compose(a,b))),codomain(compose(domain(X0),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_2217,c_198]) ).
tcf(c_2266,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X1,ifeq(compose(X0,b),X1,X0,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_74]) ).
tcf(c_2267,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X1,ifeq(compose(X0,a),X1,X0,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_73]) ).
tcf(c_2268,plain,
! [X0: $i] : ifeq(codomain(X0),domain(compose(h,compose(a,b))),codomain(compose(X0,compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_2217,c_70]) ).
tcf(c_2269,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,X1)),compose(compose(compose(h,compose(a,b)),X0),X1)),compose(compose(compose(h,compose(a,b)),X0),X1)) = compose(compose(compose(h,compose(a,b)),X0),X1),
inference(superposition,[status(thm)],[c_2217,c_71]) ).
tcf(c_2275,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),codomain(compose(X0,compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_2268,c_1392]) ).
tcf(c_2276,plain,
ifeq(domain(b),domain(h),codomain(compose(a,compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_2251,c_1392]) ).
tcf(c_2277,plain,
ifeq(domain(a),domain(h),codomain(compose(h,compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_2250,c_1392]) ).
tcf(c_2278,plain,
ifeq(domain(a),domain(h),codomain(compose(g,compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_2249,c_1392]) ).
tcf(c_2279,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_2264,c_1392]) ).
tcf(c_2280,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_2263,c_1392]) ).
tcf(c_2281,plain,
ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_2227,c_1392]) ).
tcf(c_2282,plain,
ifeq(domain(b),domain(h),codomain(compose(compose(h,a),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_2223,c_1392]) ).
tcf(c_2283,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),domain(compose(compose(h,compose(a,b)),X0)),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_2256,c_1392]) ).
tcf(c_2284,plain,
ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),g)),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_2229,c_1392]) ).
tcf(c_2285,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),domain(compose(compose(h,compose(a,b)),codomain(X0))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_2246,c_1392]) ).
tcf(c_2286,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),domain(compose(compose(h,compose(a,b)),domain(X0))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_2245,c_1392]) ).
tcf(c_2287,plain,
ifeq(codomain(b),domain(a),domain(compose(compose(h,compose(a,b)),compose(a,b))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_2234,c_1392]) ).
tcf(c_2288,plain,
ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),compose(h,a))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_2231,c_1392]) ).
tcf(c_2289,plain,
ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),compose(g,a))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_2228,c_1392]) ).
tcf(c_2290,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(h,compose(a,b)),X0)),compose(compose(X1,compose(h,compose(a,b))),X0)),compose(compose(X1,compose(h,compose(a,b))),X0)) = compose(compose(X1,compose(h,compose(a,b))),X0),
inference(light_normalisation,[status(thm)],[c_2252,c_1392]) ).
tcf(c_2323,plain,
ifeq(domain(b),domain(compose(h,compose(a,b))),codomain(compose(compose(g,a),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_2217,c_589]) ).
tcf(c_2325,plain,
ifeq(domain(b),domain(compose(g,a)),codomain(compose(compose(g,a),compose(g,a))),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_571,c_589]) ).
tcf(c_2334,plain,
ifeq(domain(b),domain(h),codomain(compose(compose(g,a),compose(g,a))),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_2325,c_1491]) ).
tcf(c_2342,plain,
ifeq(domain(b),domain(h),codomain(compose(compose(g,a),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_2323,c_1392]) ).
tcf(c_2415,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(h,b),X1,h,X0),X0),X0) = X0,
inference(demodulation,[status(thm)],[c_245,c_64]) ).
tcf(c_2416,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(h,b),X1,h,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_2415]) ).
tcf(c_2417,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(a,b),X0,ifeq(compose(h,b),X0,h,a),a),a) = a,
inference(superposition,[status(thm)],[c_72,c_2415]) ).
tcf(c_2418,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(h,b),X0,h,h),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_2415]) ).
tcf(c_2419,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(h,b),X0,h,g),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_2415]) ).
tcf(c_2420,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(h,b),X1,h,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_2415]) ).
tcf(c_2421,plain,
! [X0: $i] : ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(h,b),X0,h,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_2415]) ).
tcf(c_2422,plain,
! [X0: $i] : ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(h,b),X0,h,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_2415]) ).
tcf(c_2427,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(h,b),compose(X0,b),h,X0),X0) = X0,
inference(superposition,[status(thm)],[c_64,c_2415]) ).
tcf(c_2428,plain,
! [X0: $i] : ifeq(codomain(domain(b)),domain(b),ifeq(b,X0,ifeq(compose(h,b),X0,h,domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_67,c_2415]) ).
tcf(c_2429,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(h,b),h,X0),X0) = X0,
inference(superposition,[status(thm)],[c_64,c_2415]) ).
tcf(c_2579,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(g,b),X1,g,X0),X0),X0) = X0,
inference(demodulation,[status(thm)],[c_246,c_64]) ).
tcf(c_2580,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(g,b),X1,g,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_2579]) ).
tcf(c_2581,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(a,b),X0,ifeq(compose(g,b),X0,g,a),a),a) = a,
inference(superposition,[status(thm)],[c_72,c_2579]) ).
tcf(c_2582,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(g,b),X0,g,h),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_2579]) ).
tcf(c_2583,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(g,b),X0,g,g),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_2579]) ).
tcf(c_2584,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(g,b),X1,g,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_2579]) ).
tcf(c_2585,plain,
! [X0: $i] : ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(g,b),X0,g,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_2579]) ).
tcf(c_2586,plain,
! [X0: $i] : ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(g,b),X0,g,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_2579]) ).
tcf(c_2591,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(g,b),compose(X0,b),g,X0),X0) = X0,
inference(superposition,[status(thm)],[c_64,c_2579]) ).
tcf(c_2592,plain,
! [X0: $i] : ifeq(codomain(domain(b)),domain(b),ifeq(b,X0,ifeq(compose(g,b),X0,g,domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_67,c_2579]) ).
tcf(c_2593,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(g,b),g,X0),X0) = X0,
inference(superposition,[status(thm)],[c_64,c_2579]) ).
tcf(c_2703,plain,
ifeq(domain(b),domain(h),domain(compose(compose(g,a),compose(h,compose(a,b)))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_1392,c_1723]) ).
tcf(c_3016,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X1,ifeq(compose(domain(X0),b),X1,domain(X0),h),h),h),h) = h,
inference(superposition,[status(thm)],[c_65,c_250]) ).
tcf(c_3017,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(a,b),X0,a,h),h),h),h) = h,
inference(superposition,[status(thm)],[c_72,c_250]) ).
tcf(c_3020,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),h),h),h),h) = h,
inference(superposition,[status(thm)],[c_102,c_250]) ).
tcf(c_3021,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),h),h),h),h) = h,
inference(superposition,[status(thm)],[c_425,c_250]) ).
tcf(c_3022,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),h),h),h),h) = h,
inference(superposition,[status(thm)],[c_2217,c_250]) ).
tcf(c_3027,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(X0,b),compose(h,b),X0,h),h),h) = h,
inference(superposition,[status(thm)],[c_64,c_250]) ).
tcf(c_3028,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(X0,b),X0,h),h),h) = h,
inference(superposition,[status(thm)],[c_64,c_250]) ).
tcf(c_3039,plain,
ifeq(codomain(b),domain(h),codomain(compose(compose(h,compose(a,b)),compose(g,a))),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_2217,c_1727]) ).
tcf(c_3055,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X1,ifeq(compose(domain(X0),b),X1,domain(X0),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_65,c_251]) ).
tcf(c_3056,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(a,b),X0,a,g),g),g),g) = g,
inference(superposition,[status(thm)],[c_72,c_251]) ).
tcf(c_3059,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_102,c_251]) ).
tcf(c_3060,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_425,c_251]) ).
tcf(c_3061,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_2217,c_251]) ).
tcf(c_3066,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(X0,b),compose(g,b),X0,g),g),g) = g,
inference(superposition,[status(thm)],[c_64,c_251]) ).
tcf(c_3067,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(X0,b),X0,g),g),g) = g,
inference(superposition,[status(thm)],[c_64,c_251]) ).
tcf(c_3073,plain,
! [X0: $i] : ifeq(domain(X0),domain(b),ifeq(compose(h,a),compose(domain(X0),a),h,domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_1269]) ).
tcf(c_3074,plain,
ifeq(domain(b),domain(b),ifeq(compose(h,a),compose(a,a),h,a),a) = a,
inference(superposition,[status(thm)],[c_72,c_1269]) ).
tcf(c_3076,plain,
ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(g,a),h,g),g) = g,
inference(superposition,[status(thm)],[c_170,c_1269]) ).
tcf(c_3077,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(h,a),compose(codomain(X0),a),h,codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_1269]) ).
tcf(c_3078,plain,
ifeq(codomain(b),domain(b),ifeq(compose(h,a),compose(compose(a,b),a),h,compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_1269]) ).
tcf(c_3079,plain,
ifeq(codomain(b),domain(b),ifeq(compose(h,a),compose(compose(h,compose(a,b)),a),h,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_1269]) ).
tcf(c_3080,plain,
ifeq(domain(b),domain(b),ifeq(compose(h,a),compose(compose(h,a),a),h,compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_1269]) ).
tcf(c_3081,plain,
ifeq(domain(b),domain(b),ifeq(compose(h,a),compose(compose(g,a),a),h,compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_1269]) ).
tcf(c_3084,plain,
ifeq(codomain(h),domain(b),h,h) = h,
inference(superposition,[status(thm)],[c_64,c_1269]) ).
tcf(c_3085,plain,
ifeq(codomain(domain(a)),domain(b),ifeq(compose(h,a),a,h,domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_67,c_1269]) ).
tcf(c_3086,plain,
ifeq(domain(a),domain(b),h,h) = h,
inference(light_normalisation,[status(thm)],[c_3084,c_167]) ).
tcf(c_3088,plain,
! [X0: $i] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),compose(h,a),h,domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_1271]) ).
tcf(c_3089,plain,
ifeq(domain(b),domain(b),ifeq(compose(a,a),compose(h,a),h,a),a) = a,
inference(superposition,[status(thm)],[c_72,c_1271]) ).
tcf(c_3091,plain,
ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(h,a),h,g),g) = g,
inference(superposition,[status(thm)],[c_170,c_1271]) ).
tcf(c_3092,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),compose(h,a),h,codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_1271]) ).
tcf(c_3093,plain,
ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(h,a),h,compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_1271]) ).
tcf(c_3094,plain,
ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(h,a),h,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_1271]) ).
tcf(c_3095,plain,
ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),compose(h,a),h,compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_1271]) ).
tcf(c_3096,plain,
ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),compose(h,a),h,compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_1271]) ).
tcf(c_3100,plain,
ifeq(codomain(domain(a)),domain(b),ifeq(a,compose(h,a),h,domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_67,c_1271]) ).
tcf(c_3314,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),codomain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(h,codomain(X0))),compose(compose(X1,h),codomain(X0))),compose(compose(X1,h),codomain(X0))) = compose(compose(X1,h),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_259]) ).
tcf(c_3315,plain,
! [X0: $i] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,h),compose(a,b))),compose(compose(X0,h),compose(a,b))) = compose(compose(X0,h),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_259]) ).
tcf(c_3316,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(h,domain(X0))),compose(compose(X1,h),domain(X0))),compose(compose(X1,h),domain(X0))) = compose(compose(X1,h),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_259]) ).
tcf(c_3317,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(h,g)),compose(compose(X0,h),g)),compose(compose(X0,h),g)) = compose(compose(X0,h),g),
inference(superposition,[status(thm)],[c_1480,c_259]) ).
tcf(c_3318,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(h,compose(a,b)))),compose(compose(X0,h),compose(h,compose(a,b)))),compose(compose(X0,h),compose(h,compose(a,b)))) = compose(compose(X0,h),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_259]) ).
tcf(c_3319,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(g,a))),compose(compose(X0,h),compose(g,a))),compose(compose(X0,h),compose(g,a))) = compose(compose(X0,h),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_259]) ).
tcf(c_3320,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(h,a))),compose(compose(X0,h),compose(h,a))),compose(compose(X0,h),compose(h,a))) = compose(compose(X0,h),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_259]) ).
tcf(c_3323,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(h,X0)),compose(compose(domain(X1),h),X0)),compose(compose(domain(X1),h),X0)) = compose(compose(domain(X1),h),X0),
inference(superposition,[status(thm)],[c_65,c_259]) ).
tcf(c_3324,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(h,X0)),compose(compose(a,h),X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(superposition,[status(thm)],[c_72,c_259]) ).
tcf(c_3325,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(h,X0)),compose(compose(h,h),X0)),compose(compose(h,h),X0)) = compose(compose(h,h),X0),
inference(superposition,[status(thm)],[c_167,c_259]) ).
tcf(c_3326,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(h,X0)),compose(compose(g,h),X0)),compose(compose(g,h),X0)) = compose(compose(g,h),X0),
inference(superposition,[status(thm)],[c_170,c_259]) ).
tcf(c_3327,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(h,X0)),compose(compose(codomain(X1),h),X0)),compose(compose(codomain(X1),h),X0)) = compose(compose(codomain(X1),h),X0),
inference(superposition,[status(thm)],[c_102,c_259]) ).
tcf(c_3328,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,X0)),compose(compose(compose(a,b),h),X0)),compose(compose(compose(a,b),h),X0)) = compose(compose(compose(a,b),h),X0),
inference(superposition,[status(thm)],[c_425,c_259]) ).
tcf(c_3329,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,X0)),compose(compose(compose(h,compose(a,b)),h),X0)),compose(compose(compose(h,compose(a,b)),h),X0)) = compose(compose(compose(h,compose(a,b)),h),X0),
inference(superposition,[status(thm)],[c_2217,c_259]) ).
tcf(c_3330,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,X0)),compose(compose(compose(h,a),h),X0)),compose(compose(compose(h,a),h),X0)) = compose(compose(compose(h,a),h),X0),
inference(superposition,[status(thm)],[c_485,c_259]) ).
tcf(c_3331,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,X0)),compose(compose(compose(g,a),h),X0)),compose(compose(compose(g,a),h),X0)) = compose(compose(compose(g,a),h),X0),
inference(superposition,[status(thm)],[c_571,c_259]) ).
tcf(c_3343,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,a)),compose(compose(X0,h),a)) = compose(compose(X0,h),a),
inference(superposition,[status(thm)],[c_259,c_64]) ).
tcf(c_3375,plain,
! [X0: $i] : ifeq(domain(X0),domain(b),ifeq(compose(g,a),compose(domain(X0),a),g,domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_1568]) ).
tcf(c_3376,plain,
ifeq(domain(b),domain(b),ifeq(compose(g,a),compose(a,a),g,a),a) = a,
inference(superposition,[status(thm)],[c_72,c_1568]) ).
tcf(c_3377,plain,
ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(h,a),g,h),h) = h,
inference(superposition,[status(thm)],[c_167,c_1568]) ).
tcf(c_3379,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(g,a),compose(codomain(X0),a),g,codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_1568]) ).
tcf(c_3380,plain,
ifeq(codomain(b),domain(b),ifeq(compose(g,a),compose(compose(a,b),a),g,compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_1568]) ).
tcf(c_3381,plain,
ifeq(codomain(b),domain(b),ifeq(compose(g,a),compose(compose(h,compose(a,b)),a),g,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_1568]) ).
tcf(c_3382,plain,
ifeq(domain(b),domain(b),ifeq(compose(g,a),compose(compose(h,a),a),g,compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_1568]) ).
tcf(c_3383,plain,
ifeq(domain(b),domain(b),ifeq(compose(g,a),compose(compose(g,a),a),g,compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_1568]) ).
tcf(c_3386,plain,
ifeq(codomain(g),domain(b),g,g) = g,
inference(superposition,[status(thm)],[c_64,c_1568]) ).
tcf(c_3387,plain,
ifeq(codomain(domain(a)),domain(b),ifeq(compose(g,a),a,g,domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_67,c_1568]) ).
tcf(c_3388,plain,
ifeq(domain(a),domain(b),g,g) = g,
inference(light_normalisation,[status(thm)],[c_3386,c_170]) ).
tcf(c_3390,plain,
! [X0: $i] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),compose(g,a),g,domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_1570]) ).
tcf(c_3391,plain,
ifeq(domain(b),domain(b),ifeq(compose(a,a),compose(g,a),g,a),a) = a,
inference(superposition,[status(thm)],[c_72,c_1570]) ).
tcf(c_3392,plain,
ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(g,a),g,h),h) = h,
inference(superposition,[status(thm)],[c_167,c_1570]) ).
tcf(c_3394,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),compose(g,a),g,codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_1570]) ).
tcf(c_3395,plain,
ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(g,a),g,compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_1570]) ).
tcf(c_3396,plain,
ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(g,a),g,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_1570]) ).
tcf(c_3397,plain,
ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),compose(g,a),g,compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_1570]) ).
tcf(c_3398,plain,
ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),compose(g,a),g,compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_1570]) ).
tcf(c_3402,plain,
ifeq(codomain(domain(a)),domain(b),ifeq(a,compose(g,a),g,domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_67,c_1570]) ).
tcf(c_3642,plain,
! [X0: $i] : ifeq(domain(X0),domain(b),ifeq(compose(h,b),compose(domain(X0),b),h,domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_2427]) ).
tcf(c_3643,plain,
ifeq(domain(b),domain(b),ifeq(compose(h,b),compose(a,b),h,a),a) = a,
inference(superposition,[status(thm)],[c_72,c_2427]) ).
tcf(c_3645,plain,
ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(g,b),h,g),g) = g,
inference(superposition,[status(thm)],[c_170,c_2427]) ).
tcf(c_3646,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(h,b),compose(codomain(X0),b),h,codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_2427]) ).
tcf(c_3647,plain,
ifeq(codomain(b),domain(b),ifeq(compose(h,b),compose(compose(a,b),b),h,compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_2427]) ).
tcf(c_3648,plain,
ifeq(codomain(b),domain(b),ifeq(compose(h,b),compose(compose(h,compose(a,b)),b),h,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_2427]) ).
tcf(c_3654,plain,
ifeq(codomain(domain(b)),domain(b),ifeq(compose(h,b),b,h,domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_67,c_2427]) ).
tcf(c_3656,plain,
! [X0: $i] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(h,b),h,domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_2429]) ).
tcf(c_3657,plain,
ifeq(domain(b),domain(b),ifeq(compose(a,b),compose(h,b),h,a),a) = a,
inference(superposition,[status(thm)],[c_72,c_2429]) ).
tcf(c_3659,plain,
ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(h,b),h,g),g) = g,
inference(superposition,[status(thm)],[c_170,c_2429]) ).
tcf(c_3660,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(h,b),h,codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_2429]) ).
tcf(c_3661,plain,
ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(h,b),h,compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_2429]) ).
tcf(c_3662,plain,
ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(h,b),h,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_2429]) ).
tcf(c_3668,plain,
ifeq(codomain(domain(b)),domain(b),ifeq(b,compose(h,b),h,domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_67,c_2429]) ).
tcf(c_3670,plain,
! [X0: $i] : ifeq(domain(X0),domain(b),ifeq(compose(g,b),compose(domain(X0),b),g,domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_2591]) ).
tcf(c_3671,plain,
ifeq(domain(b),domain(b),ifeq(compose(g,b),compose(a,b),g,a),a) = a,
inference(superposition,[status(thm)],[c_72,c_2591]) ).
tcf(c_3672,plain,
ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(h,b),g,h),h) = h,
inference(superposition,[status(thm)],[c_167,c_2591]) ).
tcf(c_3674,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(g,b),compose(codomain(X0),b),g,codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_2591]) ).
tcf(c_3675,plain,
ifeq(codomain(b),domain(b),ifeq(compose(g,b),compose(compose(a,b),b),g,compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_2591]) ).
tcf(c_3676,plain,
ifeq(codomain(b),domain(b),ifeq(compose(g,b),compose(compose(h,compose(a,b)),b),g,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_2591]) ).
tcf(c_3682,plain,
ifeq(codomain(domain(b)),domain(b),ifeq(compose(g,b),b,g,domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_67,c_2591]) ).
tcf(c_3684,plain,
! [X0: $i] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(g,b),g,domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_2593]) ).
tcf(c_3685,plain,
ifeq(domain(b),domain(b),ifeq(compose(a,b),compose(g,b),g,a),a) = a,
inference(superposition,[status(thm)],[c_72,c_2593]) ).
tcf(c_3686,plain,
ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(g,b),g,h),h) = h,
inference(superposition,[status(thm)],[c_167,c_2593]) ).
tcf(c_3688,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(g,b),g,codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_2593]) ).
tcf(c_3689,plain,
ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(g,b),g,compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_2593]) ).
tcf(c_3690,plain,
ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(g,b),g,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_2593]) ).
tcf(c_3696,plain,
ifeq(codomain(domain(b)),domain(b),ifeq(b,compose(g,b),g,domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_67,c_2593]) ).
tcf(c_3979,plain,
ifeq(compose(h,a),compose(a,a),h,a) = a,
inference(demodulation,[status(thm)],[c_3074,c_64]) ).
tcf(c_3998,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(domain(a),domain(X0),compose(h,compose(X0,codomain(X1))),compose(compose(h,X0),codomain(X1))),compose(compose(h,X0),codomain(X1))) = compose(compose(h,X0),codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_267]) ).
tcf(c_3999,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(X0),compose(h,compose(X0,compose(a,b))),compose(compose(h,X0),compose(a,b))),compose(compose(h,X0),compose(a,b))) = compose(compose(h,X0),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_267]) ).
tcf(c_4000,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),domain(X0),compose(h,compose(X0,domain(X1))),compose(compose(h,X0),domain(X1))),compose(compose(h,X0),domain(X1))) = compose(compose(h,X0),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_267]) ).
tcf(c_4001,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(X0,g)),compose(compose(h,X0),g)),compose(compose(h,X0),g)) = compose(compose(h,X0),g),
inference(superposition,[status(thm)],[c_1480,c_267]) ).
tcf(c_4002,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(X0,compose(h,compose(a,b)))),compose(compose(h,X0),compose(h,compose(a,b)))),compose(compose(h,X0),compose(h,compose(a,b)))) = compose(compose(h,X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_267]) ).
tcf(c_4003,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(X0,compose(g,a))),compose(compose(h,X0),compose(g,a))),compose(compose(h,X0),compose(g,a))) = compose(compose(h,X0),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_267]) ).
tcf(c_4004,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(X0,compose(h,a))),compose(compose(h,X0),compose(h,a))),compose(compose(h,X0),compose(h,a))) = compose(compose(h,X0),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_267]) ).
tcf(c_4007,plain,
! [X0: $i] : ifeq(codomain(a),domain(X0),compose(h,compose(a,X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
inference(superposition,[status(thm)],[c_64,c_267]) ).
tcf(c_4008,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),X1)),compose(compose(h,codomain(X0)),X1)),compose(compose(h,codomain(X0)),X1)) = compose(compose(h,codomain(X0)),X1),
inference(superposition,[status(thm)],[c_66,c_267]) ).
tcf(c_4009,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(domain(a),domain(a),compose(h,compose(compose(a,b),X0)),compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
inference(superposition,[status(thm)],[c_171,c_267]) ).
tcf(c_4010,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),X1)),compose(compose(h,domain(X0)),X1)),compose(compose(h,domain(X0)),X1)) = compose(compose(h,domain(X0)),X1),
inference(superposition,[status(thm)],[c_100,c_267]) ).
tcf(c_4011,plain,
! [X0: $i] : ifeq(codomain(g),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(g,X0)),compose(compose(h,g),X0)),compose(compose(h,g),X0)) = compose(compose(h,g),X0),
inference(superposition,[status(thm)],[c_1480,c_267]) ).
tcf(c_4012,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(h,compose(a,b))),X0)),compose(compose(h,compose(h,compose(a,b))),X0)) = compose(compose(h,compose(h,compose(a,b))),X0),
inference(superposition,[status(thm)],[c_1392,c_267]) ).
tcf(c_4013,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),X0)),compose(compose(h,compose(g,a)),X0)),compose(compose(h,compose(g,a)),X0)) = compose(compose(h,compose(g,a)),X0),
inference(superposition,[status(thm)],[c_1491,c_267]) ).
tcf(c_4014,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),X0)),compose(compose(h,compose(h,a)),X0)),compose(compose(h,compose(h,a)),X0)) = compose(compose(h,compose(h,a)),X0),
inference(superposition,[status(thm)],[c_347,c_267]) ).
tcf(c_4048,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(h,compose(a,X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
inference(light_normalisation,[status(thm)],[c_4007,c_72]) ).
tcf(c_4051,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(g,X0)),compose(compose(h,g),X0)),compose(compose(h,g),X0)) = compose(compose(h,g),X0),
inference(light_normalisation,[status(thm)],[c_4011,c_170]) ).
tcf(c_4059,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),X1)),compose(compose(h,domain(X0)),X1)),compose(compose(h,domain(X0)),X1)) = compose(compose(h,domain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_4010,c_65]) ).
tcf(c_4060,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),X1)),compose(compose(h,codomain(X0)),X1)),compose(compose(h,codomain(X0)),X1)) = compose(compose(h,codomain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_4008,c_102]) ).
tcf(c_4067,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),X0)),compose(compose(h,compose(h,a)),X0)),compose(compose(h,compose(h,a)),X0)) = compose(compose(h,compose(h,a)),X0),
inference(light_normalisation,[status(thm)],[c_4014,c_485]) ).
tcf(c_4068,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),X0)),compose(compose(h,compose(g,a)),X0)),compose(compose(h,compose(g,a)),X0)) = compose(compose(h,compose(g,a)),X0),
inference(light_normalisation,[status(thm)],[c_4013,c_571]) ).
tcf(c_4069,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(a),compose(h,compose(compose(a,b),X0)),compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_4009,c_425]) ).
tcf(c_4081,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(h,compose(a,b))),X0)),compose(compose(h,compose(h,compose(a,b))),X0)) = compose(compose(h,compose(h,compose(a,b))),X0),
inference(light_normalisation,[status(thm)],[c_4012,c_2217]) ).
tcf(c_4119,plain,
ifeq(compose(a,a),compose(h,a),h,a) = a,
inference(demodulation,[status(thm)],[c_3089,c_64]) ).
tcf(c_4121,plain,
ifeq(compose(g,a),compose(a,a),g,a) = a,
inference(demodulation,[status(thm)],[c_3376,c_64]) ).
tcf(c_4126,plain,
ifeq(compose(a,a),compose(g,a),g,a) = a,
inference(demodulation,[status(thm)],[c_3391,c_64]) ).
tcf(c_4128,plain,
ifeq(compose(h,b),compose(a,b),h,a) = a,
inference(demodulation,[status(thm)],[c_3643,c_64]) ).
tcf(c_4134,plain,
ifeq(compose(a,b),compose(h,b),h,a) = a,
inference(demodulation,[status(thm)],[c_3657,c_64]) ).
tcf(c_4148,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(domain(a),domain(X0),compose(g,compose(X0,codomain(X1))),compose(compose(g,X0),codomain(X1))),compose(compose(g,X0),codomain(X1))) = compose(compose(g,X0),codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_268]) ).
tcf(c_4149,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(X0),compose(g,compose(X0,compose(a,b))),compose(compose(g,X0),compose(a,b))),compose(compose(g,X0),compose(a,b))) = compose(compose(g,X0),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_268]) ).
tcf(c_4150,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),domain(X0),compose(g,compose(X0,domain(X1))),compose(compose(g,X0),domain(X1))),compose(compose(g,X0),domain(X1))) = compose(compose(g,X0),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_268]) ).
tcf(c_4151,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(X0,g)),compose(compose(g,X0),g)),compose(compose(g,X0),g)) = compose(compose(g,X0),g),
inference(superposition,[status(thm)],[c_1480,c_268]) ).
tcf(c_4152,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(X0,compose(h,compose(a,b)))),compose(compose(g,X0),compose(h,compose(a,b)))),compose(compose(g,X0),compose(h,compose(a,b)))) = compose(compose(g,X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_268]) ).
tcf(c_4153,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(X0,compose(g,a))),compose(compose(g,X0),compose(g,a))),compose(compose(g,X0),compose(g,a))) = compose(compose(g,X0),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_268]) ).
tcf(c_4154,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(X0,compose(h,a))),compose(compose(g,X0),compose(h,a))),compose(compose(g,X0),compose(h,a))) = compose(compose(g,X0),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_268]) ).
tcf(c_4157,plain,
! [X0: $i] : ifeq(codomain(a),domain(X0),compose(g,compose(a,X0)),compose(compose(g,a),X0)) = compose(compose(g,a),X0),
inference(superposition,[status(thm)],[c_64,c_268]) ).
tcf(c_4158,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),X1)),compose(compose(g,codomain(X0)),X1)),compose(compose(g,codomain(X0)),X1)) = compose(compose(g,codomain(X0)),X1),
inference(superposition,[status(thm)],[c_66,c_268]) ).
tcf(c_4159,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(domain(a),domain(a),compose(g,compose(compose(a,b),X0)),compose(compose(g,compose(a,b)),X0)),compose(compose(g,compose(a,b)),X0)) = compose(compose(g,compose(a,b)),X0),
inference(superposition,[status(thm)],[c_171,c_268]) ).
tcf(c_4160,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),X1)),compose(compose(g,domain(X0)),X1)),compose(compose(g,domain(X0)),X1)) = compose(compose(g,domain(X0)),X1),
inference(superposition,[status(thm)],[c_100,c_268]) ).
tcf(c_4161,plain,
! [X0: $i] : ifeq(codomain(g),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(g,X0)),compose(compose(g,g),X0)),compose(compose(g,g),X0)) = compose(compose(g,g),X0),
inference(superposition,[status(thm)],[c_1480,c_268]) ).
tcf(c_4162,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),X0)),compose(compose(g,compose(h,compose(a,b))),X0)),compose(compose(g,compose(h,compose(a,b))),X0)) = compose(compose(g,compose(h,compose(a,b))),X0),
inference(superposition,[status(thm)],[c_1392,c_268]) ).
tcf(c_4163,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),X0)),compose(compose(g,compose(g,a)),X0)),compose(compose(g,compose(g,a)),X0)) = compose(compose(g,compose(g,a)),X0),
inference(superposition,[status(thm)],[c_1491,c_268]) ).
tcf(c_4164,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),X0)),compose(compose(g,compose(h,a)),X0)),compose(compose(g,compose(h,a)),X0)) = compose(compose(g,compose(h,a)),X0),
inference(superposition,[status(thm)],[c_347,c_268]) ).
tcf(c_4199,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(g,compose(a,X0)),compose(compose(g,a),X0)) = compose(compose(g,a),X0),
inference(light_normalisation,[status(thm)],[c_4157,c_72]) ).
tcf(c_4203,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(g,X0)),compose(compose(g,g),X0)),compose(compose(g,g),X0)) = compose(compose(g,g),X0),
inference(light_normalisation,[status(thm)],[c_4161,c_170]) ).
tcf(c_4211,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),X1)),compose(compose(g,domain(X0)),X1)),compose(compose(g,domain(X0)),X1)) = compose(compose(g,domain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_4160,c_65]) ).
tcf(c_4212,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),X1)),compose(compose(g,codomain(X0)),X1)),compose(compose(g,codomain(X0)),X1)) = compose(compose(g,codomain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_4158,c_102]) ).
tcf(c_4218,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),X0)),compose(compose(g,compose(h,a)),X0)),compose(compose(g,compose(h,a)),X0)) = compose(compose(g,compose(h,a)),X0),
inference(light_normalisation,[status(thm)],[c_4164,c_485]) ).
tcf(c_4219,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),X0)),compose(compose(g,compose(g,a)),X0)),compose(compose(g,compose(g,a)),X0)) = compose(compose(g,compose(g,a)),X0),
inference(light_normalisation,[status(thm)],[c_4163,c_571]) ).
tcf(c_4220,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(a),compose(g,compose(compose(a,b),X0)),compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_4159,c_77,c_425]) ).
tcf(c_4233,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),X0)),compose(compose(g,compose(h,compose(a,b))),X0)),compose(compose(g,compose(h,compose(a,b))),X0)) = compose(compose(g,compose(h,compose(a,b))),X0),
inference(light_normalisation,[status(thm)],[c_4162,c_2217]) ).
tcf(c_4243,plain,
ifeq(compose(g,b),compose(a,b),g,a) = a,
inference(demodulation,[status(thm)],[c_3671,c_64]) ).
tcf(c_4248,plain,
ifeq(compose(a,b),compose(g,b),g,a) = a,
inference(demodulation,[status(thm)],[c_3685,c_64]) ).
tcf(c_4261,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),compose(h,compose(domain(a),X0)),compose(h,X0)) = compose(h,X0),
inference(demodulation,[status(thm)],[c_306,c_64,c_65,c_100]) ).
tcf(c_4263,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),compose(h,compose(domain(a),codomain(X0))),compose(h,codomain(X0))) = compose(h,codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_4261]) ).
tcf(c_4265,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),compose(h,compose(domain(a),domain(X0))),compose(h,domain(X0))) = compose(h,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_4261]) ).
tcf(c_4266,plain,
ifeq(domain(a),domain(h),compose(h,compose(domain(a),g)),compose(h,g)) = compose(h,g),
inference(superposition,[status(thm)],[c_1480,c_4261]) ).
tcf(c_4267,plain,
ifeq(domain(a),domain(h),compose(h,compose(domain(a),compose(h,compose(a,b)))),compose(h,compose(h,compose(a,b)))) = compose(h,compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_4261]) ).
tcf(c_4268,plain,
ifeq(domain(a),domain(h),compose(h,compose(domain(a),compose(g,a))),compose(h,compose(g,a))) = compose(h,compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_4261]) ).
tcf(c_4269,plain,
ifeq(domain(a),domain(h),compose(h,compose(domain(a),compose(h,a))),compose(h,compose(h,a))) = compose(h,compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_4261]) ).
tcf(c_4302,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),domain(h)) = domain(h),
inference(superposition,[status(thm)],[c_1392,c_1427]) ).
tcf(c_4321,plain,
ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),domain(h)) = domain(h),
inference(light_normalisation,[status(thm)],[c_4302,c_2217]) ).
tcf(c_4416,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),compose(g,compose(domain(a),X0)),compose(g,X0)) = compose(g,X0),
inference(demodulation,[status(thm)],[c_307,c_64,c_65,c_100]) ).
tcf(c_4418,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),compose(g,compose(domain(a),codomain(X0))),compose(g,codomain(X0))) = compose(g,codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_4416]) ).
tcf(c_4420,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),compose(g,compose(domain(a),domain(X0))),compose(g,domain(X0))) = compose(g,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_4416]) ).
tcf(c_4421,plain,
ifeq(domain(a),domain(h),compose(g,compose(domain(a),g)),compose(g,g)) = compose(g,g),
inference(superposition,[status(thm)],[c_1480,c_4416]) ).
tcf(c_4422,plain,
ifeq(domain(a),domain(h),compose(g,compose(domain(a),compose(h,compose(a,b)))),compose(g,compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_4416]) ).
tcf(c_4423,plain,
ifeq(domain(a),domain(h),compose(g,compose(domain(a),compose(g,a))),compose(g,compose(g,a))) = compose(g,compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_4416]) ).
tcf(c_4424,plain,
ifeq(domain(a),domain(h),compose(g,compose(domain(a),compose(h,a))),compose(g,compose(h,a))) = compose(g,compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_4416]) ).
tcf(c_4489,plain,
ifeq(codomain(b),domain(compose(h,compose(a,b))),codomain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_2217,c_2255]) ).
tcf(c_4509,plain,
ifeq(codomain(b),domain(h),codomain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_4489,c_1392]) ).
tcf(c_4514,plain,
compose(compose(g,a),b) = compose(h,compose(a,b)),
inference(demodulation,[status(thm)],[c_310,c_64]) ).
tcf(c_4526,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(compose(g,a)),domain(b),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(X0,b),X1,X0,compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_4514,c_74]) ).
tcf(c_4527,plain,
ifeq(codomain(compose(g,a)),domain(b),ifeq(compose(h,compose(a,b)),compose(g,b),g,compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_4514,c_2593]) ).
tcf(c_4528,plain,
ifeq(codomain(compose(g,a)),domain(b),ifeq(compose(g,b),compose(h,compose(a,b)),g,compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_4514,c_2591]) ).
tcf(c_4529,plain,
ifeq(codomain(compose(g,a)),domain(b),ifeq(compose(h,compose(a,b)),compose(h,b),h,compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_4514,c_2429]) ).
tcf(c_4530,plain,
ifeq(codomain(compose(g,a)),domain(b),ifeq(compose(h,b),compose(h,compose(a,b)),h,compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_4514,c_2427]) ).
tcf(c_4531,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_4514,c_251]) ).
tcf(c_4532,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),h),h),h),h) = h,
inference(superposition,[status(thm)],[c_4514,c_250]) ).
tcf(c_4533,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(g,b),X0,g,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_4514,c_2579]) ).
tcf(c_4534,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,b),X0,h,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_4514,c_2415]) ).
tcf(c_4535,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(g,a)),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(h,compose(a,b)),X1,compose(g,a),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_4514,c_74]) ).
tcf(c_4543,plain,
ifeq(domain(b),domain(b),ifeq(compose(h,b),compose(h,compose(a,b)),h,compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_4530,c_571]) ).
tcf(c_4544,plain,
ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(h,b),h,compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_4529,c_571]) ).
tcf(c_4545,plain,
ifeq(domain(b),domain(b),ifeq(compose(g,b),compose(h,compose(a,b)),g,compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_4528,c_571]) ).
tcf(c_4546,plain,
ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(g,b),g,compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_4527,c_571]) ).
tcf(c_4549,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(h,compose(a,b)),X1,compose(g,a),X0),X0),X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_4535,c_571]) ).
tcf(c_4550,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,b),X0,h,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_4534,c_571]) ).
tcf(c_4551,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(g,b),X0,g,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_4533,c_571]) ).
tcf(c_4552,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),h),h),h),h) = h,
inference(light_normalisation,[status(thm)],[c_4532,c_571]) ).
tcf(c_4553,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),g),g),g),g) = g,
inference(light_normalisation,[status(thm)],[c_4531,c_571]) ).
tcf(c_4554,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(X0,b),X1,X0,compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_4526,c_571]) ).
tcf(c_4568,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,h),compose(compose(X0,h),domain(a))) = compose(compose(X0,h),domain(a)),
inference(demodulation,[status(thm)],[c_313,c_64,c_100]) ).
tcf(c_4569,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),h),compose(compose(domain(X0),h),domain(a))) = compose(compose(domain(X0),h),domain(a)),
inference(superposition,[status(thm)],[c_65,c_4568]) ).
tcf(c_4570,plain,
ifeq(domain(b),domain(h),compose(a,h),compose(compose(a,h),domain(a))) = compose(compose(a,h),domain(a)),
inference(superposition,[status(thm)],[c_72,c_4568]) ).
tcf(c_4571,plain,
ifeq(domain(a),domain(h),compose(h,h),compose(compose(h,h),domain(a))) = compose(compose(h,h),domain(a)),
inference(superposition,[status(thm)],[c_167,c_4568]) ).
tcf(c_4572,plain,
ifeq(domain(a),domain(h),compose(g,h),compose(compose(g,h),domain(a))) = compose(compose(g,h),domain(a)),
inference(superposition,[status(thm)],[c_170,c_4568]) ).
tcf(c_4573,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),h),compose(compose(codomain(X0),h),domain(a))) = compose(compose(codomain(X0),h),domain(a)),
inference(superposition,[status(thm)],[c_102,c_4568]) ).
tcf(c_4574,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),h),compose(compose(compose(a,b),h),domain(a))) = compose(compose(compose(a,b),h),domain(a)),
inference(superposition,[status(thm)],[c_425,c_4568]) ).
tcf(c_4575,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),h),compose(compose(compose(h,compose(a,b)),h),domain(a))) = compose(compose(compose(h,compose(a,b)),h),domain(a)),
inference(superposition,[status(thm)],[c_2217,c_4568]) ).
tcf(c_4576,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),h),compose(compose(compose(h,a),h),domain(a))) = compose(compose(compose(h,a),h),domain(a)),
inference(superposition,[status(thm)],[c_485,c_4568]) ).
tcf(c_4577,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),h),compose(compose(compose(g,a),h),domain(a))) = compose(compose(compose(g,a),h),domain(a)),
inference(superposition,[status(thm)],[c_571,c_4568]) ).
tcf(c_4615,plain,
! [X0: $i] : ifeq(domain(a),domain(domain(a)),ifeq(codomain(X0),domain(h),compose(X0,g),compose(compose(X0,g),domain(a))),compose(compose(X0,g),domain(a))) = compose(compose(X0,g),domain(a)),
inference(light_normalisation,[status(thm)],[c_314,c_1480]) ).
tcf(c_4616,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,g),compose(compose(X0,g),domain(a))) = compose(compose(X0,g),domain(a)),
inference(demodulation,[status(thm)],[c_4615,c_64,c_100]) ).
tcf(c_4617,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),g),compose(compose(domain(X0),g),domain(a))) = compose(compose(domain(X0),g),domain(a)),
inference(superposition,[status(thm)],[c_65,c_4616]) ).
tcf(c_4618,plain,
ifeq(domain(b),domain(h),compose(a,g),compose(compose(a,g),domain(a))) = compose(compose(a,g),domain(a)),
inference(superposition,[status(thm)],[c_72,c_4616]) ).
tcf(c_4619,plain,
ifeq(domain(a),domain(h),compose(h,g),compose(compose(h,g),domain(a))) = compose(compose(h,g),domain(a)),
inference(superposition,[status(thm)],[c_167,c_4616]) ).
tcf(c_4620,plain,
ifeq(domain(a),domain(h),compose(g,g),compose(compose(g,g),domain(a))) = compose(compose(g,g),domain(a)),
inference(superposition,[status(thm)],[c_170,c_4616]) ).
tcf(c_4621,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),g),compose(compose(codomain(X0),g),domain(a))) = compose(compose(codomain(X0),g),domain(a)),
inference(superposition,[status(thm)],[c_102,c_4616]) ).
tcf(c_4622,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),g),compose(compose(compose(a,b),g),domain(a))) = compose(compose(compose(a,b),g),domain(a)),
inference(superposition,[status(thm)],[c_425,c_4616]) ).
tcf(c_4623,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),g),compose(compose(compose(h,compose(a,b)),g),domain(a))) = compose(compose(compose(h,compose(a,b)),g),domain(a)),
inference(superposition,[status(thm)],[c_2217,c_4616]) ).
tcf(c_4624,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),g),compose(compose(compose(h,a),g),domain(a))) = compose(compose(compose(h,a),g),domain(a)),
inference(superposition,[status(thm)],[c_485,c_4616]) ).
tcf(c_4625,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),g),compose(compose(compose(g,a),g),domain(a))) = compose(compose(compose(g,a),g),domain(a)),
inference(superposition,[status(thm)],[c_571,c_4616]) ).
tcf(c_4633,plain,
ifeq(domain(a),domain(b),ifeq(compose(h,a),a,h,domain(a)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_3085,c_65]) ).
tcf(c_4634,plain,
ifeq(domain(a),domain(b),ifeq(a,compose(h,a),h,domain(a)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_3100,c_65]) ).
tcf(c_4635,plain,
ifeq(domain(a),domain(b),ifeq(compose(g,a),a,g,domain(a)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_3387,c_65]) ).
tcf(c_4636,plain,
ifeq(domain(a),domain(b),ifeq(a,compose(g,a),g,domain(a)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_3402,c_65]) ).
tcf(c_4647,plain,
! [X0: $i] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,g),compose(a,b))),compose(compose(X0,g),compose(a,b))) = compose(compose(X0,g),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_326,c_1480]) ).
tcf(c_4648,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,g),compose(a,b))) = compose(compose(X0,g),compose(a,b)),
inference(demodulation,[status(thm)],[c_4647,c_64]) ).
tcf(c_4649,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),g),compose(a,b))) = compose(compose(domain(X0),g),compose(a,b)),
inference(superposition,[status(thm)],[c_65,c_4648]) ).
tcf(c_4650,plain,
ifeq(domain(b),domain(h),compose(a,compose(h,compose(a,b))),compose(compose(a,g),compose(a,b))) = compose(compose(a,g),compose(a,b)),
inference(superposition,[status(thm)],[c_72,c_4648]) ).
tcf(c_4651,plain,
ifeq(domain(a),domain(h),compose(h,compose(h,compose(a,b))),compose(compose(h,g),compose(a,b))) = compose(compose(h,g),compose(a,b)),
inference(superposition,[status(thm)],[c_167,c_4648]) ).
tcf(c_4652,plain,
ifeq(domain(a),domain(h),compose(g,compose(h,compose(a,b))),compose(compose(g,g),compose(a,b))) = compose(compose(g,g),compose(a,b)),
inference(superposition,[status(thm)],[c_170,c_4648]) ).
tcf(c_4653,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),g),compose(a,b))) = compose(compose(codomain(X0),g),compose(a,b)),
inference(superposition,[status(thm)],[c_102,c_4648]) ).
tcf(c_4654,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),g),compose(a,b))) = compose(compose(compose(a,b),g),compose(a,b)),
inference(superposition,[status(thm)],[c_425,c_4648]) ).
tcf(c_4655,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),g),compose(a,b))) = compose(compose(compose(h,compose(a,b)),g),compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_4648]) ).
tcf(c_4656,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(compose(h,a),g),compose(a,b))) = compose(compose(compose(h,a),g),compose(a,b)),
inference(superposition,[status(thm)],[c_485,c_4648]) ).
tcf(c_4657,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),g),compose(a,b))) = compose(compose(compose(g,a),g),compose(a,b)),
inference(superposition,[status(thm)],[c_571,c_4648]) ).
tcf(c_4667,plain,
ifeq(compose(h,b),b,h,domain(b)) = domain(b),
inference(demodulation,[status(thm)],[c_3654,c_64,c_65]) ).
tcf(c_4671,plain,
ifeq(b,compose(h,b),h,domain(b)) = domain(b),
inference(demodulation,[status(thm)],[c_3668,c_64,c_65]) ).
tcf(c_4672,plain,
ifeq(compose(g,b),b,g,domain(b)) = domain(b),
inference(demodulation,[status(thm)],[c_3682,c_64,c_65]) ).
tcf(c_4676,plain,
ifeq(b,compose(g,b),g,domain(b)) = domain(b),
inference(demodulation,[status(thm)],[c_3696,c_64,c_65]) ).
tcf(c_5164,plain,
! [X0: $i] : ifeq(compose(a,a),X0,ifeq(compose(h,a),X0,h,a),a) = a,
inference(demodulation,[status(thm)],[c_1262,c_64]) ).
tcf(c_5173,plain,
! [X0: $i] : ifeq(compose(a,a),X0,ifeq(compose(g,a),X0,g,a),a) = a,
inference(demodulation,[status(thm)],[c_1561,c_64]) ).
tcf(c_5183,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(a,compose(h,a))),compose(compose(X0,a),compose(h,a))),compose(compose(X0,a),compose(h,a))) = compose(compose(X0,a),compose(h,a)),
inference(superposition,[status(thm)],[c_72,c_357]) ).
tcf(c_5192,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,compose(h,a))),compose(compose(domain(X1),X0),compose(h,a))),compose(compose(domain(X1),X0),compose(h,a))) = compose(compose(domain(X1),X0),compose(h,a)),
inference(superposition,[status(thm)],[c_65,c_357]) ).
tcf(c_5193,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(X0,compose(h,a))),compose(compose(a,X0),compose(h,a))),compose(compose(a,X0),compose(h,a))) = compose(compose(a,X0),compose(h,a)),
inference(superposition,[status(thm)],[c_72,c_357]) ).
tcf(c_5196,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,compose(h,a))),compose(compose(codomain(X1),X0),compose(h,a))),compose(compose(codomain(X1),X0),compose(h,a))) = compose(compose(codomain(X1),X0),compose(h,a)),
inference(superposition,[status(thm)],[c_102,c_357]) ).
tcf(c_5197,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,compose(h,a))),compose(compose(compose(a,b),X0),compose(h,a))),compose(compose(compose(a,b),X0),compose(h,a))) = compose(compose(compose(a,b),X0),compose(h,a)),
inference(superposition,[status(thm)],[c_425,c_357]) ).
tcf(c_5198,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,compose(h,a))),compose(compose(compose(h,compose(a,b)),X0),compose(h,a))),compose(compose(compose(h,compose(a,b)),X0),compose(h,a))) = compose(compose(compose(h,compose(a,b)),X0),compose(h,a)),
inference(superposition,[status(thm)],[c_2217,c_357]) ).
tcf(c_5199,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,compose(h,a))),compose(compose(compose(h,a),X0),compose(h,a))),compose(compose(compose(h,a),X0),compose(h,a))) = compose(compose(compose(h,a),X0),compose(h,a)),
inference(superposition,[status(thm)],[c_485,c_357]) ).
tcf(c_5200,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,compose(h,a))),compose(compose(compose(g,a),X0),compose(h,a))),compose(compose(compose(g,a),X0),compose(h,a))) = compose(compose(compose(g,a),X0),compose(h,a)),
inference(superposition,[status(thm)],[c_571,c_357]) ).
tcf(c_5202,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(h),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),compose(h,a))),compose(compose(X1,codomain(X0)),compose(h,a))),compose(compose(X1,codomain(X0)),compose(h,a))) = compose(compose(X1,codomain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_66,c_357]) ).
tcf(c_5203,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(h,a))),compose(compose(X0,compose(a,b)),compose(h,a))),compose(compose(X0,compose(a,b)),compose(h,a))) = compose(compose(X0,compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_171,c_357]) ).
tcf(c_5204,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),compose(h,a))),compose(compose(X1,domain(X0)),compose(h,a))),compose(compose(X1,domain(X0)),compose(h,a))) = compose(compose(X1,domain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_100,c_357]) ).
tcf(c_5205,plain,
! [X0: $i] : ifeq(codomain(g),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(g,compose(h,a))),compose(compose(X0,g),compose(h,a))),compose(compose(X0,g),compose(h,a))) = compose(compose(X0,g),compose(h,a)),
inference(superposition,[status(thm)],[c_1480,c_357]) ).
tcf(c_5206,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(X0,compose(h,compose(a,b))),compose(h,a))),compose(compose(X0,compose(h,compose(a,b))),compose(h,a))) = compose(compose(X0,compose(h,compose(a,b))),compose(h,a)),
inference(superposition,[status(thm)],[c_1392,c_357]) ).
tcf(c_5207,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),compose(h,a))),compose(compose(X0,compose(g,a)),compose(h,a))),compose(compose(X0,compose(g,a)),compose(h,a))) = compose(compose(X0,compose(g,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_1491,c_357]) ).
tcf(c_5208,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),compose(h,a))),compose(compose(X0,compose(h,a)),compose(h,a))),compose(compose(X0,compose(h,a)),compose(h,a))) = compose(compose(X0,compose(h,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_357]) ).
tcf(c_5259,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(g,compose(h,a))),compose(compose(X0,g),compose(h,a))),compose(compose(X0,g),compose(h,a))) = compose(compose(X0,g),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_5205,c_170]) ).
tcf(c_5263,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),compose(h,a))),compose(compose(X1,domain(X0)),compose(h,a))),compose(compose(X1,domain(X0)),compose(h,a))) = compose(compose(X1,domain(X0)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_5204,c_65]) ).
tcf(c_5264,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),compose(h,a))),compose(compose(X1,codomain(X0)),compose(h,a))),compose(compose(X1,codomain(X0)),compose(h,a))) = compose(compose(X1,codomain(X0)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_5202,c_102]) ).
tcf(c_5274,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),compose(h,a))),compose(compose(X0,compose(h,a)),compose(h,a))),compose(compose(X0,compose(h,a)),compose(h,a))) = compose(compose(X0,compose(h,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_5208,c_485]) ).
tcf(c_5275,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),compose(h,a))),compose(compose(X0,compose(g,a)),compose(h,a))),compose(compose(X0,compose(g,a)),compose(h,a))) = compose(compose(X0,compose(g,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_5207,c_571]) ).
tcf(c_5276,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(h,a))),compose(compose(X0,compose(a,b)),compose(h,a))),compose(compose(X0,compose(a,b)),compose(h,a))) = compose(compose(X0,compose(a,b)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_5203,c_425]) ).
tcf(c_5287,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(X0,compose(h,compose(a,b))),compose(h,a))),compose(compose(X0,compose(h,compose(a,b))),compose(h,a))) = compose(compose(X0,compose(h,compose(a,b))),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_5206,c_2217]) ).
tcf(c_5291,plain,
! [X0: $i] : ifeq(compose(a,b),X0,ifeq(compose(h,b),X0,h,a),a) = a,
inference(demodulation,[status(thm)],[c_2417,c_64]) ).
tcf(c_5299,plain,
! [X0: $i] : ifeq(compose(a,b),X0,ifeq(compose(g,b),X0,g,a),a) = a,
inference(demodulation,[status(thm)],[c_2581,c_64]) ).
tcf(c_5341,plain,
ifeq(compose(h,a),compose(domain(b),a),h,domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_3073,c_64]) ).
tcf(c_5388,plain,
ifeq(compose(domain(b),a),compose(h,a),h,domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_3088,c_64]) ).
tcf(c_5392,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,a)),compose(compose(domain(X0),h),a)) = compose(compose(domain(X0),h),a),
inference(superposition,[status(thm)],[c_65,c_3343]) ).
tcf(c_5393,plain,
ifeq(domain(b),domain(h),compose(a,compose(h,a)),compose(compose(a,h),a)) = compose(compose(a,h),a),
inference(superposition,[status(thm)],[c_72,c_3343]) ).
tcf(c_5394,plain,
ifeq(domain(a),domain(h),compose(h,compose(h,a)),compose(compose(h,h),a)) = compose(compose(h,h),a),
inference(superposition,[status(thm)],[c_167,c_3343]) ).
tcf(c_5395,plain,
ifeq(domain(a),domain(h),compose(g,compose(h,a)),compose(compose(g,h),a)) = compose(compose(g,h),a),
inference(superposition,[status(thm)],[c_170,c_3343]) ).
tcf(c_5396,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,a)),compose(compose(codomain(X0),h),a)) = compose(compose(codomain(X0),h),a),
inference(superposition,[status(thm)],[c_102,c_3343]) ).
tcf(c_5397,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,a)),compose(compose(compose(a,b),h),a)) = compose(compose(compose(a,b),h),a),
inference(superposition,[status(thm)],[c_425,c_3343]) ).
tcf(c_5398,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(compose(h,compose(a,b)),h),a)) = compose(compose(compose(h,compose(a,b)),h),a),
inference(superposition,[status(thm)],[c_2217,c_3343]) ).
tcf(c_5399,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,a)),compose(compose(compose(h,a),h),a)) = compose(compose(compose(h,a),h),a),
inference(superposition,[status(thm)],[c_485,c_3343]) ).
tcf(c_5400,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,a)),compose(compose(compose(g,a),h),a)) = compose(compose(compose(g,a),h),a),
inference(superposition,[status(thm)],[c_571,c_3343]) ).
tcf(c_5411,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(domain(h)),domain(h),compose(domain(h),compose(compose(h,a),X0)),compose(compose(h,a),X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
inference(light_normalisation,[status(thm)],[c_371,c_485]) ).
tcf(c_5412,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(domain(h),compose(compose(h,a),X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
inference(demodulation,[status(thm)],[c_5411,c_64,c_65]) ).
tcf(c_5414,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),compose(domain(h),compose(compose(h,a),codomain(X0))),compose(compose(h,a),codomain(X0))) = compose(compose(h,a),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_5412]) ).
tcf(c_5415,plain,
ifeq(domain(b),domain(a),compose(domain(h),compose(compose(h,a),compose(a,b))),compose(compose(h,a),compose(a,b))) = compose(compose(h,a),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_5412]) ).
tcf(c_5416,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(domain(h),compose(compose(h,a),domain(X0))),compose(compose(h,a),domain(X0))) = compose(compose(h,a),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_5412]) ).
tcf(c_5417,plain,
ifeq(domain(b),domain(h),compose(domain(h),compose(compose(h,a),g)),compose(compose(h,a),g)) = compose(compose(h,a),g),
inference(superposition,[status(thm)],[c_1480,c_5412]) ).
tcf(c_5418,plain,
ifeq(domain(b),domain(h),compose(domain(h),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_5412]) ).
tcf(c_5419,plain,
ifeq(domain(b),domain(h),compose(domain(h),compose(compose(h,a),compose(g,a))),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_5412]) ).
tcf(c_5420,plain,
ifeq(domain(b),domain(h),compose(domain(h),compose(compose(h,a),compose(h,a))),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_5412]) ).
tcf(c_5465,plain,
ifeq(compose(g,a),compose(domain(b),a),g,domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_3375,c_64]) ).
tcf(c_5506,plain,
ifeq(compose(domain(b),a),compose(g,a),g,domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_3390,c_64]) ).
tcf(c_5516,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,a)),compose(compose(X0,domain(h)),compose(h,a))) = compose(compose(X0,domain(h)),compose(h,a)),
inference(demodulation,[status(thm)],[c_372,c_64,c_65,c_100]) ).
tcf(c_5517,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,a)),compose(compose(domain(X0),domain(h)),compose(h,a))) = compose(compose(domain(X0),domain(h)),compose(h,a)),
inference(superposition,[status(thm)],[c_65,c_5516]) ).
tcf(c_5518,plain,
ifeq(domain(b),domain(h),compose(a,compose(h,a)),compose(compose(a,domain(h)),compose(h,a))) = compose(compose(a,domain(h)),compose(h,a)),
inference(superposition,[status(thm)],[c_72,c_5516]) ).
tcf(c_5519,plain,
ifeq(domain(a),domain(h),compose(h,compose(h,a)),compose(compose(h,domain(h)),compose(h,a))) = compose(compose(h,domain(h)),compose(h,a)),
inference(superposition,[status(thm)],[c_167,c_5516]) ).
tcf(c_5520,plain,
ifeq(domain(a),domain(h),compose(g,compose(h,a)),compose(compose(g,domain(h)),compose(h,a))) = compose(compose(g,domain(h)),compose(h,a)),
inference(superposition,[status(thm)],[c_170,c_5516]) ).
tcf(c_5521,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,a)),compose(compose(codomain(X0),domain(h)),compose(h,a))) = compose(compose(codomain(X0),domain(h)),compose(h,a)),
inference(superposition,[status(thm)],[c_102,c_5516]) ).
tcf(c_5522,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,a)),compose(compose(compose(a,b),domain(h)),compose(h,a))) = compose(compose(compose(a,b),domain(h)),compose(h,a)),
inference(superposition,[status(thm)],[c_425,c_5516]) ).
tcf(c_5523,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a)),
inference(superposition,[status(thm)],[c_2217,c_5516]) ).
tcf(c_5524,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,a)),compose(compose(compose(h,a),domain(h)),compose(h,a))) = compose(compose(compose(h,a),domain(h)),compose(h,a)),
inference(superposition,[status(thm)],[c_485,c_5516]) ).
tcf(c_5525,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,a)),compose(compose(compose(g,a),domain(h)),compose(h,a))) = compose(compose(compose(g,a),domain(h)),compose(h,a)),
inference(superposition,[status(thm)],[c_571,c_5516]) ).
tcf(c_6062,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),compose(h,compose(a,codomain(X0))),compose(compose(h,a),codomain(X0))) = compose(compose(h,a),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_4048]) ).
tcf(c_6063,plain,
ifeq(domain(b),domain(a),compose(h,compose(a,compose(a,b))),compose(compose(h,a),compose(a,b))) = compose(compose(h,a),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_4048]) ).
tcf(c_6064,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(h,compose(a,domain(X0))),compose(compose(h,a),domain(X0))) = compose(compose(h,a),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_4048]) ).
tcf(c_6065,plain,
ifeq(domain(b),domain(h),compose(h,compose(a,g)),compose(compose(h,a),g)) = compose(compose(h,a),g),
inference(superposition,[status(thm)],[c_1480,c_4048]) ).
tcf(c_6066,plain,
ifeq(domain(b),domain(h),compose(h,compose(a,compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_4048]) ).
tcf(c_6067,plain,
ifeq(domain(b),domain(h),compose(h,compose(a,compose(g,a))),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_4048]) ).
tcf(c_6068,plain,
ifeq(domain(b),domain(h),compose(h,compose(a,compose(h,a))),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_4048]) ).
tcf(c_6074,plain,
compose(compose(h,a),b) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_4048,c_64]) ).
tcf(c_6124,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(compose(h,a)),domain(b),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(X0,b),X1,X0,compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_6074,c_74]) ).
tcf(c_6125,plain,
ifeq(codomain(compose(h,a)),domain(b),ifeq(compose(h,compose(a,b)),compose(g,b),g,compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_6074,c_2593]) ).
tcf(c_6126,plain,
ifeq(codomain(compose(h,a)),domain(b),ifeq(compose(g,b),compose(h,compose(a,b)),g,compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_6074,c_2591]) ).
tcf(c_6127,plain,
ifeq(codomain(compose(h,a)),domain(b),ifeq(compose(h,compose(a,b)),compose(h,b),h,compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_6074,c_2429]) ).
tcf(c_6128,plain,
ifeq(codomain(compose(h,a)),domain(b),ifeq(compose(h,b),compose(h,compose(a,b)),h,compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_6074,c_2427]) ).
tcf(c_6129,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_6074,c_251]) ).
tcf(c_6130,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),h),h),h),h) = h,
inference(superposition,[status(thm)],[c_6074,c_250]) ).
tcf(c_6131,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(g,b),X0,g,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_6074,c_2579]) ).
tcf(c_6132,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,b),X0,h,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_6074,c_2415]) ).
tcf(c_6133,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(h,a)),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(h,compose(a,b)),X1,compose(h,a),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_6074,c_74]) ).
tcf(c_6143,plain,
ifeq(domain(b),domain(b),ifeq(compose(h,b),compose(h,compose(a,b)),h,compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_6128,c_485]) ).
tcf(c_6144,plain,
ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(h,b),h,compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_6127,c_485]) ).
tcf(c_6145,plain,
ifeq(domain(b),domain(b),ifeq(compose(g,b),compose(h,compose(a,b)),g,compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_6126,c_485]) ).
tcf(c_6146,plain,
ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(g,b),g,compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_6125,c_485]) ).
tcf(c_6149,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(h,compose(a,b)),X1,compose(h,a),X0),X0),X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_6133,c_485]) ).
tcf(c_6150,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,b),X0,h,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_6132,c_485]) ).
tcf(c_6151,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(g,b),X0,g,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_6131,c_485]) ).
tcf(c_6152,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),h),h),h),h) = h,
inference(light_normalisation,[status(thm)],[c_6130,c_485]) ).
tcf(c_6153,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),g),g),g),g) = g,
inference(light_normalisation,[status(thm)],[c_6129,c_485]) ).
tcf(c_6154,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(X0,b),X1,X0,compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_6124,c_485]) ).
tcf(c_6162,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),compose(g,compose(a,codomain(X0))),compose(compose(g,a),codomain(X0))) = compose(compose(g,a),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_4199]) ).
tcf(c_6163,plain,
ifeq(domain(b),domain(a),compose(g,compose(a,compose(a,b))),compose(compose(g,a),compose(a,b))) = compose(compose(g,a),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_4199]) ).
tcf(c_6164,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(g,compose(a,domain(X0))),compose(compose(g,a),domain(X0))) = compose(compose(g,a),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_4199]) ).
tcf(c_6165,plain,
ifeq(domain(b),domain(h),compose(g,compose(a,g)),compose(compose(g,a),g)) = compose(compose(g,a),g),
inference(superposition,[status(thm)],[c_1480,c_4199]) ).
tcf(c_6166,plain,
ifeq(domain(b),domain(h),compose(g,compose(a,compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_4199]) ).
tcf(c_6167,plain,
ifeq(domain(b),domain(h),compose(g,compose(a,compose(g,a))),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_4199]) ).
tcf(c_6168,plain,
ifeq(domain(b),domain(h),compose(g,compose(a,compose(h,a))),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_4199]) ).
tcf(c_6321,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(domain(X0),a),compose(X1,a),domain(X0),X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_65,c_239]) ).
tcf(c_6322,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(a,a),compose(X0,a),a,X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_72,c_239]) ).
tcf(c_6325,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X0),a),compose(X1,a),codomain(X0),X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_102,c_239]) ).
tcf(c_6326,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(a,b),a),compose(X0,a),compose(a,b),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_425,c_239]) ).
tcf(c_6327,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(X0,a),compose(h,compose(a,b)),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_2217,c_239]) ).
tcf(c_6328,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,a),a),compose(X0,a),compose(h,a),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_485,c_239]) ).
tcf(c_6329,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(g,a),a),compose(X0,a),compose(g,a),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_571,c_239]) ).
tcf(c_6334,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(X0,a),compose(domain(X1),a),X0,domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_239]) ).
tcf(c_6335,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(X0,a),compose(a,a),X0,a),a),a) = a,
inference(superposition,[status(thm)],[c_72,c_239]) ).
tcf(c_6338,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X0,a),compose(codomain(X1),a),X0,codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_239]) ).
tcf(c_6339,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(X0,a),compose(compose(a,b),a),X0,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_239]) ).
tcf(c_6340,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(X0,a),compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_239]) ).
tcf(c_6343,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X0),domain(b),X0,X0),X0) = X0,
inference(superposition,[status(thm)],[c_64,c_239]) ).
tcf(c_6348,plain,
! [X0: $i] : ifeq(codomain(domain(a)),domain(a),ifeq(codomain(X0),domain(b),ifeq(a,compose(X0,a),domain(a),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_67,c_239]) ).
tcf(c_6349,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(a)),domain(b),ifeq(compose(X0,a),a,X0,domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_67,c_239]) ).
tcf(c_6364,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(X0),domain(b),domain(X0),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6343]) ).
tcf(c_6365,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),a,a),a) = a,
inference(superposition,[status(thm)],[c_72,c_6343]) ).
tcf(c_6368,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X0),domain(b),codomain(X0),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6343]) ).
tcf(c_6369,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),compose(a,b),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6343]) ).
tcf(c_6370,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6343]) ).
tcf(c_6371,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),compose(h,a),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_6343]) ).
tcf(c_6372,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),compose(g,a),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_6343]) ).
tcf(c_6375,plain,
ifeq(domain(b),domain(a),a,a) = a,
inference(demodulation,[status(thm)],[c_6365,c_64]) ).
tcf(c_6385,plain,
ifeq(domain(b),domain(a),domain(b),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_64,c_6364]) ).
tcf(c_6414,plain,
ifeq(domain(a),domain(b),domain(a),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_6364,c_64]) ).
tcf(c_6471,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,a),compose(domain(X0),a),domain(X0),X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_65,c_241]) ).
tcf(c_6472,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(a,a),a,X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_72,c_241]) ).
tcf(c_6475,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,a),compose(codomain(X0),a),codomain(X0),X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_102,c_241]) ).
tcf(c_6476,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(compose(a,b),a),compose(a,b),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_425,c_241]) ).
tcf(c_6477,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_2217,c_241]) ).
tcf(c_6478,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(compose(h,a),a),compose(h,a),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_485,c_241]) ).
tcf(c_6479,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(compose(g,a),a),compose(g,a),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_571,c_241]) ).
tcf(c_6484,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),a),compose(X0,a),X0,domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_241]) ).
tcf(c_6485,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(a,a),compose(X0,a),X0,a),a),a) = a,
inference(superposition,[status(thm)],[c_72,c_241]) ).
tcf(c_6488,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),a),compose(X0,a),X0,codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_241]) ).
tcf(c_6489,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(X0,a),X0,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_241]) ).
tcf(c_6490,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(X0,a),X0,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_241]) ).
tcf(c_6498,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(a)),domain(b),ifeq(a,compose(X0,a),X0,domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_67,c_241]) ).
tcf(c_6499,plain,
! [X0: $i] : ifeq(codomain(domain(a)),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),a,domain(a),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_67,c_241]) ).
tcf(c_6503,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(domain(X0),b),compose(X1,b),domain(X0),X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_65,c_253]) ).
tcf(c_6504,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(a,b),compose(X0,b),a,X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_72,c_253]) ).
tcf(c_6507,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X0),b),compose(X1,b),codomain(X0),X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_102,c_253]) ).
tcf(c_6508,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(a,b),b),compose(X0,b),compose(a,b),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_425,c_253]) ).
tcf(c_6509,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(X0,b),compose(h,compose(a,b)),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_2217,c_253]) ).
tcf(c_6510,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,a),b),compose(X0,b),compose(h,a),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_485,c_253]) ).
tcf(c_6511,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(g,a),b),compose(X0,b),compose(g,a),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_571,c_253]) ).
tcf(c_6516,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(X0,b),compose(domain(X1),b),X0,domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_253]) ).
tcf(c_6517,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(X0,b),compose(a,b),X0,a),a),a) = a,
inference(superposition,[status(thm)],[c_72,c_253]) ).
tcf(c_6520,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X0,b),compose(codomain(X1),b),X0,codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_253]) ).
tcf(c_6521,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(X0,b),compose(compose(a,b),b),X0,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_253]) ).
tcf(c_6522,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(X0,b),compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_253]) ).
tcf(c_6523,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(X0,b),compose(compose(h,a),b),X0,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_253]) ).
tcf(c_6524,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(X0,b),compose(compose(g,a),b),X0,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_253]) ).
tcf(c_6528,plain,
! [X0: $i] : ifeq(codomain(domain(b)),domain(a),ifeq(codomain(X0),domain(b),ifeq(b,compose(X0,b),domain(b),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_67,c_253]) ).
tcf(c_6531,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(b)),domain(b),ifeq(compose(X0,b),b,X0,domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_67,c_253]) ).
tcf(c_6536,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(h,compose(a,b)),compose(X0,b),compose(g,a),X0),X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_6511,c_4514]) ).
tcf(c_6537,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(h,compose(a,b)),compose(X0,b),compose(h,a),X0),X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_6510,c_6074]) ).
tcf(c_6540,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(X0,b),compose(h,compose(a,b)),X0,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_6524,c_4514]) ).
tcf(c_6541,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(X0,b),compose(h,compose(a,b)),X0,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_6523,c_6074]) ).
tcf(c_6544,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,b),compose(domain(X0),b),domain(X0),X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_65,c_255]) ).
tcf(c_6545,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(a,b),a,X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_72,c_255]) ).
tcf(c_6548,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,b),compose(codomain(X0),b),codomain(X0),X1),X1),X1) = X1,
inference(superposition,[status(thm)],[c_102,c_255]) ).
tcf(c_6549,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(compose(a,b),b),compose(a,b),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_425,c_255]) ).
tcf(c_6550,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_2217,c_255]) ).
tcf(c_6551,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(compose(h,a),b),compose(h,a),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_485,c_255]) ).
tcf(c_6552,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(compose(g,a),b),compose(g,a),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_571,c_255]) ).
tcf(c_6557,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),b),compose(X0,b),X0,domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_255]) ).
tcf(c_6558,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(a,b),compose(X0,b),X0,a),a),a) = a,
inference(superposition,[status(thm)],[c_72,c_255]) ).
tcf(c_6561,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),b),compose(X0,b),X0,codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_255]) ).
tcf(c_6562,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(X0,b),X0,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_255]) ).
tcf(c_6563,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(X0,b),X0,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_255]) ).
tcf(c_6564,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),compose(X0,b),X0,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_255]) ).
tcf(c_6565,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),compose(X0,b),X0,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_255]) ).
tcf(c_6569,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(b)),domain(b),ifeq(b,compose(X0,b),X0,domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_67,c_255]) ).
tcf(c_6572,plain,
! [X0: $i] : ifeq(codomain(domain(b)),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),b,domain(b),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_67,c_255]) ).
tcf(c_6577,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(h,compose(a,b)),compose(g,a),X0),X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_6552,c_4514]) ).
tcf(c_6578,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(h,compose(a,b)),compose(h,a),X0),X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_6551,c_6074]) ).
tcf(c_6581,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(X0,b),X0,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_6565,c_4514]) ).
tcf(c_6582,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(X0,b),X0,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_6564,c_6074]) ).
tcf(c_6586,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(domain(X0),a),compose(h,a),domain(X0),h),h),h) = h,
inference(superposition,[status(thm)],[c_65,c_1800]) ).
tcf(c_6587,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(a,a),compose(h,a),a,h),h),h) = h,
inference(superposition,[status(thm)],[c_72,c_1800]) ).
tcf(c_6590,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(codomain(X0),a),compose(h,a),codomain(X0),h),h),h) = h,
inference(superposition,[status(thm)],[c_102,c_1800]) ).
tcf(c_6591,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(a,b),a),compose(h,a),compose(a,b),h),h),h) = h,
inference(superposition,[status(thm)],[c_425,c_1800]) ).
tcf(c_6592,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(h,a),compose(h,compose(a,b)),h),h),h) = h,
inference(superposition,[status(thm)],[c_2217,c_1800]) ).
tcf(c_6593,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,a),a),compose(h,a),compose(h,a),h),h),h) = h,
inference(superposition,[status(thm)],[c_485,c_1800]) ).
tcf(c_6594,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(g,a),a),compose(h,a),compose(g,a),h),h),h) = h,
inference(superposition,[status(thm)],[c_571,c_1800]) ).
tcf(c_6614,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(domain(X0),a),domain(X0),h),h),h) = h,
inference(superposition,[status(thm)],[c_65,c_1801]) ).
tcf(c_6615,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(a,a),a,h),h),h) = h,
inference(superposition,[status(thm)],[c_72,c_1801]) ).
tcf(c_6618,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(codomain(X0),a),codomain(X0),h),h),h) = h,
inference(superposition,[status(thm)],[c_102,c_1801]) ).
tcf(c_6619,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(compose(a,b),a),compose(a,b),h),h),h) = h,
inference(superposition,[status(thm)],[c_425,c_1801]) ).
tcf(c_6620,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),h),h),h) = h,
inference(superposition,[status(thm)],[c_2217,c_1801]) ).
tcf(c_6621,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(compose(h,a),a),compose(h,a),h),h),h) = h,
inference(superposition,[status(thm)],[c_485,c_1801]) ).
tcf(c_6622,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(compose(g,a),a),compose(g,a),h),h),h) = h,
inference(superposition,[status(thm)],[c_571,c_1801]) ).
tcf(c_6628,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(domain(X0),a),compose(g,a),domain(X0),g),g),g) = g,
inference(superposition,[status(thm)],[c_65,c_2077]) ).
tcf(c_6629,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(a,a),compose(g,a),a,g),g),g) = g,
inference(superposition,[status(thm)],[c_72,c_2077]) ).
tcf(c_6632,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(codomain(X0),a),compose(g,a),codomain(X0),g),g),g) = g,
inference(superposition,[status(thm)],[c_102,c_2077]) ).
tcf(c_6633,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(a,b),a),compose(g,a),compose(a,b),g),g),g) = g,
inference(superposition,[status(thm)],[c_425,c_2077]) ).
tcf(c_6634,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(g,a),compose(h,compose(a,b)),g),g),g) = g,
inference(superposition,[status(thm)],[c_2217,c_2077]) ).
tcf(c_6635,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,a),a),compose(g,a),compose(h,a),g),g),g) = g,
inference(superposition,[status(thm)],[c_485,c_2077]) ).
tcf(c_6636,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(g,a),a),compose(g,a),compose(g,a),g),g),g) = g,
inference(superposition,[status(thm)],[c_571,c_2077]) ).
tcf(c_6643,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(domain(X0),a),domain(X0),g),g),g) = g,
inference(superposition,[status(thm)],[c_65,c_2078]) ).
tcf(c_6644,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(a,a),a,g),g),g) = g,
inference(superposition,[status(thm)],[c_72,c_2078]) ).
tcf(c_6647,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(codomain(X0),a),codomain(X0),g),g),g) = g,
inference(superposition,[status(thm)],[c_102,c_2078]) ).
tcf(c_6648,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(compose(a,b),a),compose(a,b),g),g),g) = g,
inference(superposition,[status(thm)],[c_425,c_2078]) ).
tcf(c_6649,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),g),g),g) = g,
inference(superposition,[status(thm)],[c_2217,c_2078]) ).
tcf(c_6650,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(compose(h,a),a),compose(h,a),g),g),g) = g,
inference(superposition,[status(thm)],[c_485,c_2078]) ).
tcf(c_6651,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(compose(g,a),a),compose(g,a),g),g),g) = g,
inference(superposition,[status(thm)],[c_571,c_2078]) ).
tcf(c_6657,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(domain(X0),b),compose(h,b),domain(X0),h),h),h) = h,
inference(superposition,[status(thm)],[c_65,c_3027]) ).
tcf(c_6658,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(a,b),compose(h,b),a,h),h),h) = h,
inference(superposition,[status(thm)],[c_72,c_3027]) ).
tcf(c_6661,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(codomain(X0),b),compose(h,b),codomain(X0),h),h),h) = h,
inference(superposition,[status(thm)],[c_102,c_3027]) ).
tcf(c_6662,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(a,b),b),compose(h,b),compose(a,b),h),h),h) = h,
inference(superposition,[status(thm)],[c_425,c_3027]) ).
tcf(c_6663,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(h,b),compose(h,compose(a,b)),h),h),h) = h,
inference(superposition,[status(thm)],[c_2217,c_3027]) ).
tcf(c_6664,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,a),b),compose(h,b),compose(h,a),h),h),h) = h,
inference(superposition,[status(thm)],[c_485,c_3027]) ).
tcf(c_6665,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(g,a),b),compose(h,b),compose(g,a),h),h),h) = h,
inference(superposition,[status(thm)],[c_571,c_3027]) ).
tcf(c_6672,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,compose(a,b)),compose(h,b),compose(g,a),h),h),h) = h,
inference(light_normalisation,[status(thm)],[c_6665,c_4514]) ).
tcf(c_6673,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,compose(a,b)),compose(h,b),compose(h,a),h),h),h) = h,
inference(light_normalisation,[status(thm)],[c_6664,c_6074]) ).
tcf(c_6767,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(domain(X0),b),domain(X0),h),h),h) = h,
inference(superposition,[status(thm)],[c_65,c_3028]) ).
tcf(c_6768,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(a,b),a,h),h),h) = h,
inference(superposition,[status(thm)],[c_72,c_3028]) ).
tcf(c_6771,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(codomain(X0),b),codomain(X0),h),h),h) = h,
inference(superposition,[status(thm)],[c_102,c_3028]) ).
tcf(c_6772,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(compose(a,b),b),compose(a,b),h),h),h) = h,
inference(superposition,[status(thm)],[c_425,c_3028]) ).
tcf(c_6773,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),h),h),h) = h,
inference(superposition,[status(thm)],[c_2217,c_3028]) ).
tcf(c_6774,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(compose(h,a),b),compose(h,a),h),h),h) = h,
inference(superposition,[status(thm)],[c_485,c_3028]) ).
tcf(c_6775,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(compose(g,a),b),compose(g,a),h),h),h) = h,
inference(superposition,[status(thm)],[c_571,c_3028]) ).
tcf(c_6782,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(h,compose(a,b)),compose(g,a),h),h),h) = h,
inference(light_normalisation,[status(thm)],[c_6775,c_4514]) ).
tcf(c_6783,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(h,compose(a,b)),compose(h,a),h),h),h) = h,
inference(light_normalisation,[status(thm)],[c_6774,c_6074]) ).
tcf(c_6787,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(domain(X0),b),compose(g,b),domain(X0),g),g),g) = g,
inference(superposition,[status(thm)],[c_65,c_3066]) ).
tcf(c_6788,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(a,b),compose(g,b),a,g),g),g) = g,
inference(superposition,[status(thm)],[c_72,c_3066]) ).
tcf(c_6791,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(codomain(X0),b),compose(g,b),codomain(X0),g),g),g) = g,
inference(superposition,[status(thm)],[c_102,c_3066]) ).
tcf(c_6792,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(a,b),b),compose(g,b),compose(a,b),g),g),g) = g,
inference(superposition,[status(thm)],[c_425,c_3066]) ).
tcf(c_6793,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(g,b),compose(h,compose(a,b)),g),g),g) = g,
inference(superposition,[status(thm)],[c_2217,c_3066]) ).
tcf(c_6794,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,a),b),compose(g,b),compose(h,a),g),g),g) = g,
inference(superposition,[status(thm)],[c_485,c_3066]) ).
tcf(c_6795,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(g,a),b),compose(g,b),compose(g,a),g),g),g) = g,
inference(superposition,[status(thm)],[c_571,c_3066]) ).
tcf(c_6802,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,compose(a,b)),compose(g,b),compose(g,a),g),g),g) = g,
inference(light_normalisation,[status(thm)],[c_6795,c_4514]) ).
tcf(c_6803,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,compose(a,b)),compose(g,b),compose(h,a),g),g),g) = g,
inference(light_normalisation,[status(thm)],[c_6794,c_6074]) ).
tcf(c_6807,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(domain(X0),b),domain(X0),g),g),g) = g,
inference(superposition,[status(thm)],[c_65,c_3067]) ).
tcf(c_6808,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(a,b),a,g),g),g) = g,
inference(superposition,[status(thm)],[c_72,c_3067]) ).
tcf(c_6811,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(codomain(X0),b),codomain(X0),g),g),g) = g,
inference(superposition,[status(thm)],[c_102,c_3067]) ).
tcf(c_6812,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(compose(a,b),b),compose(a,b),g),g),g) = g,
inference(superposition,[status(thm)],[c_425,c_3067]) ).
tcf(c_6813,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),g),g),g) = g,
inference(superposition,[status(thm)],[c_2217,c_3067]) ).
tcf(c_6814,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(compose(h,a),b),compose(h,a),g),g),g) = g,
inference(superposition,[status(thm)],[c_485,c_3067]) ).
tcf(c_6815,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(compose(g,a),b),compose(g,a),g),g),g) = g,
inference(superposition,[status(thm)],[c_571,c_3067]) ).
tcf(c_6822,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(h,compose(a,b)),compose(g,a),g),g),g) = g,
inference(light_normalisation,[status(thm)],[c_6815,c_4514]) ).
tcf(c_6823,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(h,compose(a,b)),compose(h,a),g),g),g) = g,
inference(light_normalisation,[status(thm)],[c_6814,c_6074]) ).
tcf(c_6830,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(compose(h,a),a),X1,compose(h,a),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_501]) ).
tcf(c_6834,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(compose(compose(h,a),a),X1,compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_501]) ).
tcf(c_6835,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_501]) ).
tcf(c_6836,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_501]) ).
tcf(c_6846,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(a,a),compose(domain(X0),a),a,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6322]) ).
tcf(c_6850,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(a,a),compose(codomain(X0),a),a,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6322]) ).
tcf(c_6851,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(a,a),compose(compose(a,b),a),a,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6322]) ).
tcf(c_6852,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(a,a),compose(compose(h,compose(a,b)),a),a,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6322]) ).
tcf(c_6859,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,a),compose(a,a),X0,a),a) = a,
inference(demodulation,[status(thm)],[c_6335,c_64]) ).
tcf(c_6860,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),a),compose(a,a),domain(X0),a),a) = a,
inference(superposition,[status(thm)],[c_65,c_6859]) ).
tcf(c_6864,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),a),compose(a,a),codomain(X0),a),a) = a,
inference(superposition,[status(thm)],[c_102,c_6859]) ).
tcf(c_6865,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),a),compose(a,a),compose(a,b),a),a) = a,
inference(superposition,[status(thm)],[c_425,c_6859]) ).
tcf(c_6866,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),a),compose(a,a),compose(h,compose(a,b)),a),a) = a,
inference(superposition,[status(thm)],[c_2217,c_6859]) ).
tcf(c_6867,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),compose(a,a),compose(h,a),a),a) = a,
inference(superposition,[status(thm)],[c_485,c_6859]) ).
tcf(c_6868,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),compose(a,a),compose(g,a),a),a) = a,
inference(superposition,[status(thm)],[c_571,c_6859]) ).
tcf(c_6872,plain,
ifeq(codomain(domain(a)),domain(a),ifeq(a,compose(a,a),domain(a),a),a) = a,
inference(superposition,[status(thm)],[c_67,c_6859]) ).
tcf(c_6895,plain,
ifeq(a,compose(a,a),domain(a),a) = a,
inference(demodulation,[status(thm)],[c_6872,c_64,c_65]) ).
tcf(c_6951,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(a,compose(X0,a),domain(a),X0),X0) = X0,
inference(demodulation,[status(thm)],[c_6348,c_64,c_65]) ).
tcf(c_6952,plain,
! [X0: $i] : ifeq(domain(X0),domain(b),ifeq(a,compose(domain(X0),a),domain(a),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6951]) ).
tcf(c_6954,plain,
ifeq(domain(a),domain(b),ifeq(a,compose(h,a),domain(a),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_6951]) ).
tcf(c_6955,plain,
ifeq(domain(a),domain(b),ifeq(a,compose(g,a),domain(a),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_6951]) ).
tcf(c_6956,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(a,compose(codomain(X0),a),domain(a),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6951]) ).
tcf(c_6957,plain,
ifeq(codomain(b),domain(b),ifeq(a,compose(compose(a,b),a),domain(a),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6951]) ).
tcf(c_6958,plain,
ifeq(codomain(b),domain(b),ifeq(a,compose(compose(h,compose(a,b)),a),domain(a),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6951]) ).
tcf(c_6959,plain,
ifeq(domain(b),domain(b),ifeq(a,compose(compose(h,a),a),domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_6951]) ).
tcf(c_6960,plain,
ifeq(domain(b),domain(b),ifeq(a,compose(compose(g,a),a),domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_6951]) ).
tcf(c_6997,plain,
ifeq(a,compose(domain(b),a),domain(a),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_6952,c_64]) ).
tcf(c_7000,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),compose(a,a),a,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6472]) ).
tcf(c_7004,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),compose(a,a),a,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6472]) ).
tcf(c_7005,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(a,a),a,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6472]) ).
tcf(c_7006,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(a,a),a,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6472]) ).
tcf(c_7049,plain,
ifeq(domain(b),domain(a),compose(h,a),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_6371,c_64]) ).
tcf(c_7050,plain,
ifeq(domain(b),domain(a),compose(g,a),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_6372,c_64]) ).
tcf(c_7051,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(a,a),compose(X0,a),X0,a),a) = a,
inference(demodulation,[status(thm)],[c_6485,c_64]) ).
tcf(c_7052,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(a,a),compose(domain(X0),a),domain(X0),a),a) = a,
inference(superposition,[status(thm)],[c_65,c_7051]) ).
tcf(c_7056,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(a,a),compose(codomain(X0),a),codomain(X0),a),a) = a,
inference(superposition,[status(thm)],[c_102,c_7051]) ).
tcf(c_7057,plain,
ifeq(codomain(b),domain(a),ifeq(compose(a,a),compose(compose(a,b),a),compose(a,b),a),a) = a,
inference(superposition,[status(thm)],[c_425,c_7051]) ).
tcf(c_7058,plain,
ifeq(codomain(b),domain(a),ifeq(compose(a,a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),a),a) = a,
inference(superposition,[status(thm)],[c_2217,c_7051]) ).
tcf(c_7059,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,a),compose(compose(h,a),a),compose(h,a),a),a) = a,
inference(superposition,[status(thm)],[c_485,c_7051]) ).
tcf(c_7060,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,a),compose(compose(g,a),a),compose(g,a),a),a) = a,
inference(superposition,[status(thm)],[c_571,c_7051]) ).
tcf(c_7064,plain,
ifeq(codomain(domain(a)),domain(a),ifeq(compose(a,a),a,domain(a),a),a) = a,
inference(superposition,[status(thm)],[c_67,c_7051]) ).
tcf(c_7069,plain,
ifeq(compose(a,a),a,domain(a),a) = a,
inference(demodulation,[status(thm)],[c_7064,c_64,c_65]) ).
tcf(c_7125,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(h,a),a),X1,ifeq(compose(X0,a),X1,X0,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_510,c_64]) ).
tcf(c_7126,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(compose(compose(h,a),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_65,c_7125]) ).
tcf(c_7127,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),X0,ifeq(compose(a,a),X0,a,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_72,c_7125]) ).
tcf(c_7130,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(h,a),a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_102,c_7125]) ).
tcf(c_7131,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(compose(h,a),a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_425,c_7125]) ).
tcf(c_7132,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(compose(h,a),a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_2217,c_7125]) ).
tcf(c_7133,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_7125]) ).
tcf(c_7134,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_571,c_7125]) ).
tcf(c_7135,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,a),compose(compose(h,a),a),X0,compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_64,c_7125]) ).
tcf(c_7136,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(h,a),a),compose(X0,a),X0,compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_64,c_7125]) ).
tcf(c_7144,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),a,domain(a),X0),X0) = X0,
inference(demodulation,[status(thm)],[c_6499,c_64,c_65]) ).
tcf(c_7145,plain,
! [X0: $i] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),a,domain(a),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_7144]) ).
tcf(c_7147,plain,
ifeq(domain(a),domain(b),ifeq(compose(h,a),a,domain(a),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_7144]) ).
tcf(c_7148,plain,
ifeq(domain(a),domain(b),ifeq(compose(g,a),a,domain(a),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_7144]) ).
tcf(c_7149,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),a,domain(a),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_7144]) ).
tcf(c_7150,plain,
ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),a,domain(a),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_7144]) ).
tcf(c_7151,plain,
ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),a,domain(a),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_7144]) ).
tcf(c_7152,plain,
ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),a,domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_7144]) ).
tcf(c_7153,plain,
ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),a,domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_7144]) ).
tcf(c_7188,plain,
ifeq(compose(domain(b),a),a,domain(a),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_7145,c_64]) ).
tcf(c_7192,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(a,b),compose(domain(X0),b),a,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6504]) ).
tcf(c_7196,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(a,b),compose(codomain(X0),b),a,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6504]) ).
tcf(c_7197,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(a,b),compose(compose(a,b),b),a,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6504]) ).
tcf(c_7198,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(a,b),compose(compose(h,compose(a,b)),b),a,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6504]) ).
tcf(c_7250,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,b),compose(a,b),X0,a),a) = a,
inference(demodulation,[status(thm)],[c_6517,c_64]) ).
tcf(c_7251,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),b),compose(a,b),domain(X0),a),a) = a,
inference(superposition,[status(thm)],[c_65,c_7250]) ).
tcf(c_7255,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),b),compose(a,b),codomain(X0),a),a) = a,
inference(superposition,[status(thm)],[c_102,c_7250]) ).
tcf(c_7256,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),b),compose(a,b),compose(a,b),a),a) = a,
inference(superposition,[status(thm)],[c_425,c_7250]) ).
tcf(c_7257,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),b),compose(a,b),compose(h,compose(a,b)),a),a) = a,
inference(superposition,[status(thm)],[c_2217,c_7250]) ).
tcf(c_7258,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),b),compose(a,b),compose(h,a),a),a) = a,
inference(superposition,[status(thm)],[c_485,c_7250]) ).
tcf(c_7259,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),b),compose(a,b),compose(g,a),a),a) = a,
inference(superposition,[status(thm)],[c_571,c_7250]) ).
tcf(c_7263,plain,
ifeq(codomain(domain(b)),domain(a),ifeq(b,compose(a,b),domain(b),a),a) = a,
inference(superposition,[status(thm)],[c_67,c_7250]) ).
tcf(c_7268,plain,
ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(a,b),compose(g,a),a),a) = a,
inference(light_normalisation,[status(thm)],[c_7259,c_4514]) ).
tcf(c_7269,plain,
ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(a,b),compose(h,a),a),a) = a,
inference(light_normalisation,[status(thm)],[c_7258,c_6074]) ).
tcf(c_7277,plain,
ifeq(domain(b),domain(a),ifeq(b,compose(a,b),domain(b),a),a) = a,
inference(demodulation,[status(thm)],[c_7263,c_65]) ).
tcf(c_7302,plain,
ifeq(compose(domain(a),b),compose(a,b),domain(a),a) = a,
inference(superposition,[status(thm)],[c_7251,c_64]) ).
tcf(c_7340,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,X0)),compose(compose(compose(h,a),a),X0)),compose(compose(compose(h,a),a),X0)) = compose(compose(compose(h,a),a),X0),
inference(superposition,[status(thm)],[c_72,c_512]) ).
tcf(c_7348,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,codomain(X1))),compose(compose(compose(h,a),X0),codomain(X1))),compose(compose(compose(h,a),X0),codomain(X1))) = compose(compose(compose(h,a),X0),codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_512]) ).
tcf(c_7349,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,compose(a,b))),compose(compose(compose(h,a),X0),compose(a,b))),compose(compose(compose(h,a),X0),compose(a,b))) = compose(compose(compose(h,a),X0),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_512]) ).
tcf(c_7350,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,domain(X1))),compose(compose(compose(h,a),X0),domain(X1))),compose(compose(compose(h,a),X0),domain(X1))) = compose(compose(compose(h,a),X0),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_512]) ).
tcf(c_7351,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,g)),compose(compose(compose(h,a),X0),g)),compose(compose(compose(h,a),X0),g)) = compose(compose(compose(h,a),X0),g),
inference(superposition,[status(thm)],[c_1480,c_512]) ).
tcf(c_7352,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,compose(h,compose(a,b)))),compose(compose(compose(h,a),X0),compose(h,compose(a,b)))),compose(compose(compose(h,a),X0),compose(h,compose(a,b)))) = compose(compose(compose(h,a),X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_512]) ).
tcf(c_7353,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,compose(g,a))),compose(compose(compose(h,a),X0),compose(g,a))),compose(compose(compose(h,a),X0),compose(g,a))) = compose(compose(compose(h,a),X0),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_512]) ).
tcf(c_7355,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(h,a),compose(b,X0)),compose(compose(compose(h,a),b),X0)) = compose(compose(compose(h,a),b),X0),
inference(superposition,[status(thm)],[c_64,c_512]) ).
tcf(c_7356,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),X1)),compose(compose(compose(h,a),codomain(X0)),X1)),compose(compose(compose(h,a),codomain(X0)),X1)) = compose(compose(compose(h,a),codomain(X0)),X1),
inference(superposition,[status(thm)],[c_66,c_512]) ).
tcf(c_7357,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),X0)),compose(compose(compose(h,a),compose(a,b)),X0)),compose(compose(compose(h,a),compose(a,b)),X0)) = compose(compose(compose(h,a),compose(a,b)),X0),
inference(superposition,[status(thm)],[c_171,c_512]) ).
tcf(c_7358,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),X1)),compose(compose(compose(h,a),domain(X0)),X1)),compose(compose(compose(h,a),domain(X0)),X1)) = compose(compose(compose(h,a),domain(X0)),X1),
inference(superposition,[status(thm)],[c_100,c_512]) ).
tcf(c_7359,plain,
! [X0: $i] : ifeq(codomain(g),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,X0)),compose(compose(compose(h,a),g),X0)),compose(compose(compose(h,a),g),X0)) = compose(compose(compose(h,a),g),X0),
inference(superposition,[status(thm)],[c_1480,c_512]) ).
tcf(c_7360,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),X0)),compose(compose(compose(h,a),compose(h,compose(a,b))),X0)),compose(compose(compose(h,a),compose(h,compose(a,b))),X0)) = compose(compose(compose(h,a),compose(h,compose(a,b))),X0),
inference(superposition,[status(thm)],[c_1392,c_512]) ).
tcf(c_7361,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),X0)),compose(compose(compose(h,a),compose(g,a)),X0)),compose(compose(compose(h,a),compose(g,a)),X0)) = compose(compose(compose(h,a),compose(g,a)),X0),
inference(superposition,[status(thm)],[c_1491,c_512]) ).
tcf(c_7362,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),X0)),compose(compose(compose(h,a),compose(h,a)),X0)),compose(compose(compose(h,a),compose(h,a)),X0)) = compose(compose(compose(h,a),compose(h,a)),X0),
inference(superposition,[status(thm)],[c_347,c_512]) ).
tcf(c_7390,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(h,a),compose(b,X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_7355,c_6074]) ).
tcf(c_7391,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,X0)),compose(compose(compose(h,a),g),X0)),compose(compose(compose(h,a),g),X0)) = compose(compose(compose(h,a),g),X0),
inference(light_normalisation,[status(thm)],[c_7359,c_170]) ).
tcf(c_7400,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),X1)),compose(compose(compose(h,a),domain(X0)),X1)),compose(compose(compose(h,a),domain(X0)),X1)) = compose(compose(compose(h,a),domain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_7358,c_65]) ).
tcf(c_7401,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),X1)),compose(compose(compose(h,a),codomain(X0)),X1)),compose(compose(compose(h,a),codomain(X0)),X1)) = compose(compose(compose(h,a),codomain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_7356,c_102]) ).
tcf(c_7407,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),X0)),compose(compose(compose(h,a),compose(h,a)),X0)),compose(compose(compose(h,a),compose(h,a)),X0)) = compose(compose(compose(h,a),compose(h,a)),X0),
inference(light_normalisation,[status(thm)],[c_7362,c_485]) ).
tcf(c_7408,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),X0)),compose(compose(compose(h,a),compose(g,a)),X0)),compose(compose(compose(h,a),compose(g,a)),X0)) = compose(compose(compose(h,a),compose(g,a)),X0),
inference(light_normalisation,[status(thm)],[c_7361,c_571]) ).
tcf(c_7409,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),X0)),compose(compose(compose(h,a),compose(a,b)),X0)),compose(compose(compose(h,a),compose(a,b)),X0)) = compose(compose(compose(h,a),compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_7357,c_425]) ).
tcf(c_7421,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),X0)),compose(compose(compose(h,a),compose(h,compose(a,b))),X0)),compose(compose(compose(h,a),compose(h,compose(a,b))),X0)) = compose(compose(compose(h,a),compose(h,compose(a,b))),X0),
inference(light_normalisation,[status(thm)],[c_7360,c_2217]) ).
tcf(c_7433,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(b,compose(X0,b),domain(b),X0),X0),X0) = X0,
inference(demodulation,[status(thm)],[c_6528,c_65]) ).
tcf(c_7434,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(b,compose(domain(X0),b),domain(b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_7433]) ).
tcf(c_7436,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(b,compose(h,b),domain(b),h),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_7433]) ).
tcf(c_7437,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(b,compose(g,b),domain(b),g),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_7433]) ).
tcf(c_7438,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(b,compose(codomain(X0),b),domain(b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_7433]) ).
tcf(c_7439,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(b,compose(compose(a,b),b),domain(b),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_7433]) ).
tcf(c_7440,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(b,compose(compose(h,compose(a,b)),b),domain(b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_7433]) ).
tcf(c_7441,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(b,compose(compose(h,a),b),domain(b),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_7433]) ).
tcf(c_7442,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(b,compose(compose(g,a),b),domain(b),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_7433]) ).
tcf(c_7446,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(b,compose(h,compose(a,b)),domain(b),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_7442,c_4514]) ).
tcf(c_7447,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(b,compose(h,compose(a,b)),domain(b),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_7441,c_6074]) ).
tcf(c_7450,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(a,b),a,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6545]) ).
tcf(c_7454,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(a,b),a,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6545]) ).
tcf(c_7455,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(a,b),a,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6545]) ).
tcf(c_7456,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(a,b),a,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6545]) ).
tcf(c_7467,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),compose(X0,b),X0,a),a) = a,
inference(demodulation,[status(thm)],[c_6558,c_64]) ).
tcf(c_7468,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(a,b),compose(domain(X0),b),domain(X0),a),a) = a,
inference(superposition,[status(thm)],[c_65,c_7467]) ).
tcf(c_7472,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),compose(codomain(X0),b),codomain(X0),a),a) = a,
inference(superposition,[status(thm)],[c_102,c_7467]) ).
tcf(c_7473,plain,
ifeq(codomain(b),domain(a),ifeq(compose(a,b),compose(compose(a,b),b),compose(a,b),a),a) = a,
inference(superposition,[status(thm)],[c_425,c_7467]) ).
tcf(c_7474,plain,
ifeq(codomain(b),domain(a),ifeq(compose(a,b),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),a),a) = a,
inference(superposition,[status(thm)],[c_2217,c_7467]) ).
tcf(c_7475,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(compose(h,a),b),compose(h,a),a),a) = a,
inference(superposition,[status(thm)],[c_485,c_7467]) ).
tcf(c_7476,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(compose(g,a),b),compose(g,a),a),a) = a,
inference(superposition,[status(thm)],[c_571,c_7467]) ).
tcf(c_7480,plain,
ifeq(codomain(domain(b)),domain(a),ifeq(compose(a,b),b,domain(b),a),a) = a,
inference(superposition,[status(thm)],[c_67,c_7467]) ).
tcf(c_7485,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(h,compose(a,b)),compose(g,a),a),a) = a,
inference(light_normalisation,[status(thm)],[c_7476,c_4514]) ).
tcf(c_7486,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(h,compose(a,b)),compose(h,a),a),a) = a,
inference(light_normalisation,[status(thm)],[c_7475,c_6074]) ).
tcf(c_7491,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,b),b,domain(b),a),a) = a,
inference(demodulation,[status(thm)],[c_7480,c_65]) ).
tcf(c_7516,plain,
ifeq(compose(a,b),compose(domain(a),b),domain(a),a) = a,
inference(superposition,[status(thm)],[c_7468,c_64]) ).
tcf(c_7550,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),b,domain(b),X0),X0),X0) = X0,
inference(demodulation,[status(thm)],[c_6572,c_65]) ).
tcf(c_7551,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),b,domain(b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_7550]) ).
tcf(c_7553,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),b,domain(b),h),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_7550]) ).
tcf(c_7554,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),b,domain(b),g),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_7550]) ).
tcf(c_7555,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),b,domain(b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_7550]) ).
tcf(c_7556,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),b,domain(b),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_7550]) ).
tcf(c_7557,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),b,domain(b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_7550]) ).
tcf(c_7558,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),b,domain(b),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_7550]) ).
tcf(c_7559,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),b,domain(b),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_7550]) ).
tcf(c_7563,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),b,domain(b),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_7559,c_4514]) ).
tcf(c_7564,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),b,domain(b),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_7558,c_6074]) ).
tcf(c_7579,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(h,a),codomain(X0))),compose(compose(X1,compose(h,a)),codomain(X0))),compose(compose(X1,compose(h,a)),codomain(X0))) = compose(compose(X1,compose(h,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_520]) ).
tcf(c_7580,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),compose(a,b))),compose(compose(X0,compose(h,a)),compose(a,b))),compose(compose(X0,compose(h,a)),compose(a,b))) = compose(compose(X0,compose(h,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_520]) ).
tcf(c_7581,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(h,a),domain(X0))),compose(compose(X1,compose(h,a)),domain(X0))),compose(compose(X1,compose(h,a)),domain(X0))) = compose(compose(X1,compose(h,a)),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_520]) ).
tcf(c_7582,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),g)),compose(compose(X0,compose(h,a)),g)),compose(compose(X0,compose(h,a)),g)) = compose(compose(X0,compose(h,a)),g),
inference(superposition,[status(thm)],[c_1480,c_520]) ).
tcf(c_7583,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(X0,compose(h,a)),compose(h,compose(a,b)))),compose(compose(X0,compose(h,a)),compose(h,compose(a,b)))) = compose(compose(X0,compose(h,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_520]) ).
tcf(c_7584,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),compose(g,a))),compose(compose(X0,compose(h,a)),compose(g,a))),compose(compose(X0,compose(h,a)),compose(g,a))) = compose(compose(X0,compose(h,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_520]) ).
tcf(c_7586,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,a),X0)),compose(compose(domain(X1),compose(h,a)),X0)),compose(compose(domain(X1),compose(h,a)),X0)) = compose(compose(domain(X1),compose(h,a)),X0),
inference(superposition,[status(thm)],[c_65,c_520]) ).
tcf(c_7587,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),X0)),compose(compose(a,compose(h,a)),X0)),compose(compose(a,compose(h,a)),X0)) = compose(compose(a,compose(h,a)),X0),
inference(superposition,[status(thm)],[c_72,c_520]) ).
tcf(c_7590,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,a),X0)),compose(compose(codomain(X1),compose(h,a)),X0)),compose(compose(codomain(X1),compose(h,a)),X0)) = compose(compose(codomain(X1),compose(h,a)),X0),
inference(superposition,[status(thm)],[c_102,c_520]) ).
tcf(c_7591,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),X0)),compose(compose(compose(a,b),compose(h,a)),X0)),compose(compose(compose(a,b),compose(h,a)),X0)) = compose(compose(compose(a,b),compose(h,a)),X0),
inference(superposition,[status(thm)],[c_425,c_520]) ).
tcf(c_7592,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),X0)),compose(compose(compose(h,compose(a,b)),compose(h,a)),X0)),compose(compose(compose(h,compose(a,b)),compose(h,a)),X0)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),X0),
inference(superposition,[status(thm)],[c_2217,c_520]) ).
tcf(c_7594,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),X0)),compose(compose(compose(g,a),compose(h,a)),X0)),compose(compose(compose(g,a),compose(h,a)),X0)) = compose(compose(compose(g,a),compose(h,a)),X0),
inference(superposition,[status(thm)],[c_571,c_520]) ).
tcf(c_7605,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),b)),compose(compose(X0,compose(h,a)),b)) = compose(compose(X0,compose(h,a)),b),
inference(superposition,[status(thm)],[c_520,c_64]) ).
tcf(c_7606,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(h,a)),b)) = compose(compose(X0,compose(h,a)),b),
inference(light_normalisation,[status(thm)],[c_7605,c_6074]) ).
tcf(c_7614,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(h,a),X0,h,domain(a)),domain(a)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_1270,c_65]) ).
tcf(c_7620,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(g,a),X0,g,domain(a)),domain(a)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_1569,c_65]) ).
tcf(c_7625,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(b),X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
inference(demodulation,[status(thm)],[c_551,c_64,c_65,c_100]) ).
tcf(c_7627,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(domain(b),codomain(X0))),compose(compose(h,a),codomain(X0))) = compose(compose(h,a),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_7625]) ).
tcf(c_7628,plain,
ifeq(domain(b),domain(a),compose(compose(h,a),compose(domain(b),compose(a,b))),compose(compose(h,a),compose(a,b))) = compose(compose(h,a),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_7625]) ).
tcf(c_7629,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(b),domain(X0))),compose(compose(h,a),domain(X0))) = compose(compose(h,a),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_7625]) ).
tcf(c_7630,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(domain(b),g)),compose(compose(h,a),g)) = compose(compose(h,a),g),
inference(superposition,[status(thm)],[c_1480,c_7625]) ).
tcf(c_7631,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_7625]) ).
tcf(c_7632,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(domain(b),compose(g,a))),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_7625]) ).
tcf(c_7633,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(domain(b),compose(h,a))),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_7625]) ).
tcf(c_7646,plain,
! [X0: $i] : ifeq(b,X0,ifeq(compose(h,b),X0,h,domain(b)),domain(b)) = domain(b),
inference(demodulation,[status(thm)],[c_2428,c_64,c_65]) ).
tcf(c_7652,plain,
! [X0: $i] : ifeq(b,X0,ifeq(compose(g,b),X0,g,domain(b)),domain(b)) = domain(b),
inference(demodulation,[status(thm)],[c_2592,c_64,c_65]) ).
tcf(c_7718,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,a)),compose(compose(X0,compose(h,a)),domain(b))) = compose(compose(X0,compose(h,a)),domain(b)),
inference(demodulation,[status(thm)],[c_552,c_64,c_100]) ).
tcf(c_7719,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,a)),compose(compose(domain(X0),compose(h,a)),domain(b))) = compose(compose(domain(X0),compose(h,a)),domain(b)),
inference(superposition,[status(thm)],[c_65,c_7718]) ).
tcf(c_7720,plain,
ifeq(domain(b),domain(h),compose(a,compose(h,a)),compose(compose(a,compose(h,a)),domain(b))) = compose(compose(a,compose(h,a)),domain(b)),
inference(superposition,[status(thm)],[c_72,c_7718]) ).
tcf(c_7721,plain,
ifeq(domain(a),domain(h),compose(h,compose(h,a)),compose(compose(h,compose(h,a)),domain(b))) = compose(compose(h,compose(h,a)),domain(b)),
inference(superposition,[status(thm)],[c_167,c_7718]) ).
tcf(c_7722,plain,
ifeq(domain(a),domain(h),compose(g,compose(h,a)),compose(compose(g,compose(h,a)),domain(b))) = compose(compose(g,compose(h,a)),domain(b)),
inference(superposition,[status(thm)],[c_170,c_7718]) ).
tcf(c_7723,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,a)),compose(compose(codomain(X0),compose(h,a)),domain(b))) = compose(compose(codomain(X0),compose(h,a)),domain(b)),
inference(superposition,[status(thm)],[c_102,c_7718]) ).
tcf(c_7724,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,a)),compose(compose(compose(a,b),compose(h,a)),domain(b))) = compose(compose(compose(a,b),compose(h,a)),domain(b)),
inference(superposition,[status(thm)],[c_425,c_7718]) ).
tcf(c_7725,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b)),
inference(superposition,[status(thm)],[c_2217,c_7718]) ).
tcf(c_7726,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,a)),compose(compose(compose(h,a),compose(h,a)),domain(b))) = compose(compose(compose(h,a),compose(h,a)),domain(b)),
inference(superposition,[status(thm)],[c_485,c_7718]) ).
tcf(c_7727,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,a)),compose(compose(compose(g,a),compose(h,a)),domain(b))) = compose(compose(compose(g,a),compose(h,a)),domain(b)),
inference(superposition,[status(thm)],[c_571,c_7718]) ).
tcf(c_7975,plain,
ifeq(a,compose(compose(h,a),a),domain(a),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_6959,c_64]) ).
tcf(c_7978,plain,
ifeq(a,compose(compose(g,a),a),domain(a),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_6960,c_64]) ).
tcf(c_7994,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X0),a),compose(domain(X1),a),domain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_6321]) ).
tcf(c_7998,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(domain(X0),a),compose(codomain(X1),a),domain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_6321]) ).
tcf(c_7999,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(domain(X0),a),compose(compose(a,b),a),domain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6321]) ).
tcf(c_8000,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(domain(X0),a),compose(compose(h,compose(a,b)),a),domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6321]) ).
tcf(c_8024,plain,
ifeq(compose(compose(h,a),a),a,domain(a),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_7152,c_64]) ).
tcf(c_8026,plain,
ifeq(compose(compose(g,a),a),a,domain(a),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_7153,c_64]) ).
tcf(c_8029,plain,
ifeq(compose(h,a),compose(compose(h,a),a),h,compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_3080,c_64]) ).
tcf(c_8039,plain,
ifeq(compose(h,a),compose(compose(g,a),a),h,compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_3081,c_64]) ).
tcf(c_8048,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(compose(g,a),a),X1,compose(g,a),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_588]) ).
tcf(c_8052,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(compose(compose(g,a),a),X1,compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_588]) ).
tcf(c_8053,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_588]) ).
tcf(c_8054,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_588]) ).
tcf(c_8069,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),a),compose(domain(X0),a),domain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_6471]) ).
tcf(c_8073,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),a),compose(domain(X0),a),domain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_6471]) ).
tcf(c_8074,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(domain(X0),a),domain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6471]) ).
tcf(c_8075,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(domain(X0),a),domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6471]) ).
tcf(c_8148,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X0),b),compose(domain(X1),b),domain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_6503]) ).
tcf(c_8152,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(domain(X0),b),compose(codomain(X1),b),domain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_6503]) ).
tcf(c_8153,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(domain(X0),b),compose(compose(a,b),b),domain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6503]) ).
tcf(c_8154,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(domain(X0),b),compose(compose(h,compose(a,b)),b),domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6503]) ).
tcf(c_8177,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(domain(a),b),compose(X0,b),domain(a),X0),X0) = X0,
inference(superposition,[status(thm)],[c_6503,c_64]) ).
tcf(c_8184,plain,
! [X0: $i] : ifeq(domain(X0),domain(b),ifeq(compose(domain(a),b),compose(domain(X0),b),domain(a),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_8177]) ).
tcf(c_8186,plain,
ifeq(domain(a),domain(b),ifeq(compose(domain(a),b),compose(h,b),domain(a),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_8177]) ).
tcf(c_8187,plain,
ifeq(domain(a),domain(b),ifeq(compose(domain(a),b),compose(g,b),domain(a),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_8177]) ).
tcf(c_8188,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(domain(a),b),compose(codomain(X0),b),domain(a),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_8177]) ).
tcf(c_8189,plain,
ifeq(codomain(b),domain(b),ifeq(compose(domain(a),b),compose(compose(a,b),b),domain(a),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_8177]) ).
tcf(c_8190,plain,
ifeq(codomain(b),domain(b),ifeq(compose(domain(a),b),compose(compose(h,compose(a,b)),b),domain(a),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_8177]) ).
tcf(c_8191,plain,
ifeq(domain(b),domain(b),ifeq(compose(domain(a),b),compose(compose(h,a),b),domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_8177]) ).
tcf(c_8192,plain,
ifeq(domain(b),domain(b),ifeq(compose(domain(a),b),compose(compose(g,a),b),domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_8177]) ).
tcf(c_8195,plain,
ifeq(codomain(domain(b)),domain(b),ifeq(compose(domain(a),b),b,domain(a),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_67,c_8177]) ).
tcf(c_8202,plain,
ifeq(domain(b),domain(b),ifeq(compose(domain(a),b),compose(h,compose(a,b)),domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_8192,c_4514]) ).
tcf(c_8203,plain,
ifeq(domain(b),domain(b),ifeq(compose(domain(a),b),compose(h,compose(a,b)),domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_8191,c_6074]) ).
tcf(c_8208,plain,
ifeq(compose(domain(a),b),b,domain(a),domain(b)) = domain(b),
inference(demodulation,[status(thm)],[c_8195,c_64,c_65]) ).
tcf(c_8281,plain,
ifeq(compose(compose(h,a),a),compose(h,a),h,compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_3095,c_64]) ).
tcf(c_8284,plain,
ifeq(compose(compose(g,a),a),compose(h,a),h,compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_3096,c_64]) ).
tcf(c_8299,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),b),compose(domain(X0),b),domain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_6544]) ).
tcf(c_8303,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),b),compose(domain(X0),b),domain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_6544]) ).
tcf(c_8304,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(domain(X0),b),domain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6544]) ).
tcf(c_8305,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(domain(X0),b),domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6544]) ).
tcf(c_8328,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(domain(a),b),domain(a),X0),X0) = X0,
inference(superposition,[status(thm)],[c_6544,c_64]) ).
tcf(c_8334,plain,
! [X0: $i] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(domain(a),b),domain(a),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_8328]) ).
tcf(c_8336,plain,
ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(domain(a),b),domain(a),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_8328]) ).
tcf(c_8337,plain,
ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(domain(a),b),domain(a),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_8328]) ).
tcf(c_8338,plain,
! [X0: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(domain(a),b),domain(a),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_8328]) ).
tcf(c_8339,plain,
ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(domain(a),b),domain(a),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_8328]) ).
tcf(c_8340,plain,
ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(domain(a),b),domain(a),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_8328]) ).
tcf(c_8341,plain,
ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),compose(domain(a),b),domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_8328]) ).
tcf(c_8342,plain,
ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),compose(domain(a),b),domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_8328]) ).
tcf(c_8345,plain,
ifeq(codomain(domain(b)),domain(b),ifeq(b,compose(domain(a),b),domain(a),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_67,c_8328]) ).
tcf(c_8353,plain,
ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(domain(a),b),domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_8342,c_4514]) ).
tcf(c_8354,plain,
ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(domain(a),b),domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_8341,c_6074]) ).
tcf(c_8357,plain,
ifeq(b,compose(domain(a),b),domain(a),domain(b)) = domain(b),
inference(demodulation,[status(thm)],[c_8345,c_64,c_65]) ).
tcf(c_8430,plain,
ifeq(compose(g,a),compose(compose(h,a),a),g,compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_3382,c_64]) ).
tcf(c_8439,plain,
ifeq(compose(g,a),compose(compose(g,a),a),g,compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_3383,c_64]) ).
tcf(c_8446,plain,
ifeq(compose(compose(h,a),a),compose(g,a),g,compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_3397,c_64]) ).
tcf(c_8449,plain,
ifeq(compose(compose(g,a),a),compose(g,a),g,compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_3398,c_64]) ).
tcf(c_8453,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(g,a),a),X1,ifeq(compose(X0,a),X1,X0,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_597,c_64]) ).
tcf(c_8454,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(compose(compose(g,a),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_65,c_8453]) ).
tcf(c_8455,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),X0,ifeq(compose(a,a),X0,a,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_72,c_8453]) ).
tcf(c_8458,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(g,a),a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_102,c_8453]) ).
tcf(c_8459,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(compose(g,a),a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_425,c_8453]) ).
tcf(c_8460,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(compose(g,a),a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_2217,c_8453]) ).
tcf(c_8461,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_485,c_8453]) ).
tcf(c_8462,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_8453]) ).
tcf(c_8463,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,a),compose(compose(g,a),a),X0,compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_64,c_8453]) ).
tcf(c_8464,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(g,a),a),compose(X0,a),X0,compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_64,c_8453]) ).
tcf(c_8530,plain,
ifeq(compose(h,b),compose(h,compose(a,b)),h,compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_4543,c_64]) ).
tcf(c_8537,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,X0)),compose(compose(compose(g,a),a),X0)),compose(compose(compose(g,a),a),X0)) = compose(compose(compose(g,a),a),X0),
inference(superposition,[status(thm)],[c_72,c_599]) ).
tcf(c_8545,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,codomain(X1))),compose(compose(compose(g,a),X0),codomain(X1))),compose(compose(compose(g,a),X0),codomain(X1))) = compose(compose(compose(g,a),X0),codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_599]) ).
tcf(c_8546,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,compose(a,b))),compose(compose(compose(g,a),X0),compose(a,b))),compose(compose(compose(g,a),X0),compose(a,b))) = compose(compose(compose(g,a),X0),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_599]) ).
tcf(c_8547,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,domain(X1))),compose(compose(compose(g,a),X0),domain(X1))),compose(compose(compose(g,a),X0),domain(X1))) = compose(compose(compose(g,a),X0),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_599]) ).
tcf(c_8548,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,g)),compose(compose(compose(g,a),X0),g)),compose(compose(compose(g,a),X0),g)) = compose(compose(compose(g,a),X0),g),
inference(superposition,[status(thm)],[c_1480,c_599]) ).
tcf(c_8549,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,compose(h,compose(a,b)))),compose(compose(compose(g,a),X0),compose(h,compose(a,b)))),compose(compose(compose(g,a),X0),compose(h,compose(a,b)))) = compose(compose(compose(g,a),X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_599]) ).
tcf(c_8550,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,compose(g,a))),compose(compose(compose(g,a),X0),compose(g,a))),compose(compose(compose(g,a),X0),compose(g,a))) = compose(compose(compose(g,a),X0),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_599]) ).
tcf(c_8552,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(g,a),compose(b,X0)),compose(compose(compose(g,a),b),X0)) = compose(compose(compose(g,a),b),X0),
inference(superposition,[status(thm)],[c_64,c_599]) ).
tcf(c_8553,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),X1)),compose(compose(compose(g,a),codomain(X0)),X1)),compose(compose(compose(g,a),codomain(X0)),X1)) = compose(compose(compose(g,a),codomain(X0)),X1),
inference(superposition,[status(thm)],[c_66,c_599]) ).
tcf(c_8554,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),X0)),compose(compose(compose(g,a),compose(a,b)),X0)),compose(compose(compose(g,a),compose(a,b)),X0)) = compose(compose(compose(g,a),compose(a,b)),X0),
inference(superposition,[status(thm)],[c_171,c_599]) ).
tcf(c_8555,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),X1)),compose(compose(compose(g,a),domain(X0)),X1)),compose(compose(compose(g,a),domain(X0)),X1)) = compose(compose(compose(g,a),domain(X0)),X1),
inference(superposition,[status(thm)],[c_100,c_599]) ).
tcf(c_8556,plain,
! [X0: $i] : ifeq(codomain(g),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,X0)),compose(compose(compose(g,a),g),X0)),compose(compose(compose(g,a),g),X0)) = compose(compose(compose(g,a),g),X0),
inference(superposition,[status(thm)],[c_1480,c_599]) ).
tcf(c_8557,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),X0)),compose(compose(compose(g,a),compose(h,compose(a,b))),X0)),compose(compose(compose(g,a),compose(h,compose(a,b))),X0)) = compose(compose(compose(g,a),compose(h,compose(a,b))),X0),
inference(superposition,[status(thm)],[c_1392,c_599]) ).
tcf(c_8558,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),X0)),compose(compose(compose(g,a),compose(g,a)),X0)),compose(compose(compose(g,a),compose(g,a)),X0)) = compose(compose(compose(g,a),compose(g,a)),X0),
inference(superposition,[status(thm)],[c_1491,c_599]) ).
tcf(c_8587,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(g,a),compose(b,X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_8552,c_4514]) ).
tcf(c_8588,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,X0)),compose(compose(compose(g,a),g),X0)),compose(compose(compose(g,a),g),X0)) = compose(compose(compose(g,a),g),X0),
inference(light_normalisation,[status(thm)],[c_8556,c_170]) ).
tcf(c_8597,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),X1)),compose(compose(compose(g,a),domain(X0)),X1)),compose(compose(compose(g,a),domain(X0)),X1)) = compose(compose(compose(g,a),domain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_8555,c_65]) ).
tcf(c_8598,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),X1)),compose(compose(compose(g,a),codomain(X0)),X1)),compose(compose(compose(g,a),codomain(X0)),X1)) = compose(compose(compose(g,a),codomain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_8553,c_102]) ).
tcf(c_8605,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),X0)),compose(compose(compose(g,a),compose(g,a)),X0)),compose(compose(compose(g,a),compose(g,a)),X0)) = compose(compose(compose(g,a),compose(g,a)),X0),
inference(light_normalisation,[status(thm)],[c_8558,c_571]) ).
tcf(c_8606,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),X0)),compose(compose(compose(g,a),compose(a,b)),X0)),compose(compose(compose(g,a),compose(a,b)),X0)) = compose(compose(compose(g,a),compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_8554,c_425]) ).
tcf(c_8618,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),X0)),compose(compose(compose(g,a),compose(h,compose(a,b))),X0)),compose(compose(compose(g,a),compose(h,compose(a,b))),X0)) = compose(compose(compose(g,a),compose(h,compose(a,b))),X0),
inference(light_normalisation,[status(thm)],[c_8557,c_2217]) ).
tcf(c_8674,plain,
ifeq(compose(h,compose(a,b)),compose(h,b),h,compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_4544,c_64]) ).
tcf(c_8675,plain,
ifeq(compose(g,b),compose(h,compose(a,b)),g,compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_4545,c_64]) ).
tcf(c_8679,plain,
ifeq(compose(h,compose(a,b)),compose(g,b),g,compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_4546,c_64]) ).
tcf(c_8680,plain,
ifeq(compose(h,b),compose(h,compose(a,b)),h,compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_6143,c_64]) ).
tcf(c_8685,plain,
ifeq(compose(h,compose(a,b)),compose(h,b),h,compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_6144,c_64]) ).
tcf(c_8686,plain,
ifeq(compose(g,b),compose(h,compose(a,b)),g,compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_6145,c_64]) ).
tcf(c_8690,plain,
ifeq(compose(h,compose(a,b)),compose(g,b),g,compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_6146,c_64]) ).
tcf(c_8701,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(codomain(X0),a),compose(domain(X1),a),codomain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_6325]) ).
tcf(c_8705,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X0),a),compose(codomain(X1),a),codomain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_6325]) ).
tcf(c_8706,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(codomain(X0),a),compose(compose(a,b),a),codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6325]) ).
tcf(c_8707,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(codomain(X0),a),compose(compose(h,compose(a,b)),a),codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6325]) ).
tcf(c_8741,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),a),compose(codomain(X0),a),codomain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_6475]) ).
tcf(c_8745,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),a),compose(codomain(X0),a),codomain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_6475]) ).
tcf(c_8746,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(codomain(X0),a),codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6475]) ).
tcf(c_8747,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(codomain(X0),a),codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6475]) ).
tcf(c_8780,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(codomain(X0),b),compose(domain(X1),b),codomain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_6507]) ).
tcf(c_8784,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X0),b),compose(codomain(X1),b),codomain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_6507]) ).
tcf(c_8785,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(codomain(X0),b),compose(compose(a,b),b),codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6507]) ).
tcf(c_8786,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(codomain(X0),b),compose(compose(h,compose(a,b)),b),codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6507]) ).
tcf(c_8826,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),b),compose(codomain(X0),b),codomain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_6548]) ).
tcf(c_8830,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),b),compose(codomain(X0),b),codomain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_6548]) ).
tcf(c_8831,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(codomain(X0),b),codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6548]) ).
tcf(c_8832,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(codomain(X0),b),codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6548]) ).
tcf(c_9197,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),a),compose(compose(h,a),a),domain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_65,c_7135]) ).
tcf(c_9198,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,a),compose(compose(h,a),a),a,compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_72,c_7135]) ).
tcf(c_9201,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),a),compose(compose(h,a),a),codomain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_102,c_7135]) ).
tcf(c_9202,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),a),compose(compose(h,a),a),compose(a,b),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_425,c_7135]) ).
tcf(c_9203,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),a),compose(compose(h,a),a),compose(h,compose(a,b)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_2217,c_7135]) ).
tcf(c_9205,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),compose(compose(h,a),a),compose(g,a),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_571,c_7135]) ).
tcf(c_9217,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(compose(h,a),a),compose(domain(X0),a),domain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_65,c_7136]) ).
tcf(c_9218,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),compose(a,a),a,compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_72,c_7136]) ).
tcf(c_9221,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(h,a),a),compose(codomain(X0),a),codomain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_102,c_7136]) ).
tcf(c_9222,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(h,a),a),compose(compose(a,b),a),compose(a,b),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_425,c_7136]) ).
tcf(c_9223,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(h,a),a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_2217,c_7136]) ).
tcf(c_9225,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),compose(compose(g,a),a),compose(g,a),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_571,c_7136]) ).
tcf(c_9234,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(b),X0)),compose(compose(g,a),X0)) = compose(compose(g,a),X0),
inference(demodulation,[status(thm)],[c_616,c_64,c_65,c_100]) ).
tcf(c_9236,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(domain(b),codomain(X0))),compose(compose(g,a),codomain(X0))) = compose(compose(g,a),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_9234]) ).
tcf(c_9237,plain,
ifeq(domain(b),domain(a),compose(compose(g,a),compose(domain(b),compose(a,b))),compose(compose(g,a),compose(a,b))) = compose(compose(g,a),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_9234]) ).
tcf(c_9238,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(b),domain(X0))),compose(compose(g,a),domain(X0))) = compose(compose(g,a),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_9234]) ).
tcf(c_9239,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(domain(b),g)),compose(compose(g,a),g)) = compose(compose(g,a),g),
inference(superposition,[status(thm)],[c_1480,c_9234]) ).
tcf(c_9240,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_9234]) ).
tcf(c_9241,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(domain(b),compose(g,a))),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_9234]) ).
tcf(c_9242,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(domain(b),compose(h,a))),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_9234]) ).
tcf(c_9260,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),a),compose(compose(g,a),a),domain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_65,c_8463]) ).
tcf(c_9261,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,a),compose(compose(g,a),a),a,compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_72,c_8463]) ).
tcf(c_9264,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),a),compose(compose(g,a),a),codomain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_102,c_8463]) ).
tcf(c_9265,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),a),compose(compose(g,a),a),compose(a,b),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_425,c_8463]) ).
tcf(c_9266,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),a),compose(compose(g,a),a),compose(h,compose(a,b)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_2217,c_8463]) ).
tcf(c_9267,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),compose(compose(g,a),a),compose(h,a),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_485,c_8463]) ).
tcf(c_9280,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(compose(g,a),a),compose(domain(X0),a),domain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_65,c_8464]) ).
tcf(c_9281,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),compose(a,a),a,compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_72,c_8464]) ).
tcf(c_9284,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(g,a),a),compose(codomain(X0),a),codomain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_102,c_8464]) ).
tcf(c_9285,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(g,a),a),compose(compose(a,b),a),compose(a,b),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_425,c_8464]) ).
tcf(c_9286,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(g,a),a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_2217,c_8464]) ).
tcf(c_9287,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),compose(compose(h,a),a),compose(h,a),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_485,c_8464]) ).
tcf(c_9298,plain,
! [X0: $i] : ifeq(domain(b),domain(domain(b)),ifeq(codomain(X0),domain(h),compose(X0,compose(g,a)),compose(compose(X0,compose(g,a)),domain(b))),compose(compose(X0,compose(g,a)),domain(b))) = compose(compose(X0,compose(g,a)),domain(b)),
inference(light_normalisation,[status(thm)],[c_617,c_1480]) ).
tcf(c_9299,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(g,a)),compose(compose(X0,compose(g,a)),domain(b))) = compose(compose(X0,compose(g,a)),domain(b)),
inference(demodulation,[status(thm)],[c_9298,c_64,c_100]) ).
tcf(c_9300,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(g,a)),compose(compose(domain(X0),compose(g,a)),domain(b))) = compose(compose(domain(X0),compose(g,a)),domain(b)),
inference(superposition,[status(thm)],[c_65,c_9299]) ).
tcf(c_9301,plain,
ifeq(domain(b),domain(h),compose(a,compose(g,a)),compose(compose(a,compose(g,a)),domain(b))) = compose(compose(a,compose(g,a)),domain(b)),
inference(superposition,[status(thm)],[c_72,c_9299]) ).
tcf(c_9302,plain,
ifeq(domain(a),domain(h),compose(h,compose(g,a)),compose(compose(h,compose(g,a)),domain(b))) = compose(compose(h,compose(g,a)),domain(b)),
inference(superposition,[status(thm)],[c_167,c_9299]) ).
tcf(c_9303,plain,
ifeq(domain(a),domain(h),compose(g,compose(g,a)),compose(compose(g,compose(g,a)),domain(b))) = compose(compose(g,compose(g,a)),domain(b)),
inference(superposition,[status(thm)],[c_170,c_9299]) ).
tcf(c_9304,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,a)),compose(compose(codomain(X0),compose(g,a)),domain(b))) = compose(compose(codomain(X0),compose(g,a)),domain(b)),
inference(superposition,[status(thm)],[c_102,c_9299]) ).
tcf(c_9305,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,a)),compose(compose(compose(a,b),compose(g,a)),domain(b))) = compose(compose(compose(a,b),compose(g,a)),domain(b)),
inference(superposition,[status(thm)],[c_425,c_9299]) ).
tcf(c_9306,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b)),
inference(superposition,[status(thm)],[c_2217,c_9299]) ).
tcf(c_9307,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,a)),compose(compose(compose(h,a),compose(g,a)),domain(b))) = compose(compose(compose(h,a),compose(g,a)),domain(b)),
inference(superposition,[status(thm)],[c_485,c_9299]) ).
tcf(c_9308,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,a)),compose(compose(compose(g,a),compose(g,a)),domain(b))) = compose(compose(compose(g,a),compose(g,a)),domain(b)),
inference(superposition,[status(thm)],[c_571,c_9299]) ).
tcf(c_9319,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),compose(domain(X0),compose(X0,X1)),compose(X0,X1)) = compose(X0,X1),
inference(demodulation,[status(thm)],[c_305,c_64]) ).
tcf(c_9321,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(domain(a),compose(a,X0)),compose(a,X0)) = compose(a,X0),
inference(superposition,[status(thm)],[c_72,c_9319]) ).
tcf(c_9322,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),compose(domain(h),compose(h,X0)),compose(h,X0)) = compose(h,X0),
inference(superposition,[status(thm)],[c_167,c_9319]) ).
tcf(c_9329,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),compose(domain(X0),compose(X0,codomain(X1))),compose(X0,codomain(X1))) = compose(X0,codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_9319]) ).
tcf(c_9330,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(domain(X0),compose(X0,compose(a,b))),compose(X0,compose(a,b))) = compose(X0,compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_9319]) ).
tcf(c_9331,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),compose(domain(X0),compose(X0,domain(X1))),compose(X0,domain(X1))) = compose(X0,domain(X1)),
inference(superposition,[status(thm)],[c_100,c_9319]) ).
tcf(c_9332,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(domain(X0),compose(X0,g)),compose(X0,g)) = compose(X0,g),
inference(superposition,[status(thm)],[c_1480,c_9319]) ).
tcf(c_9333,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(domain(X0),compose(X0,compose(h,compose(a,b)))),compose(X0,compose(h,compose(a,b)))) = compose(X0,compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_9319]) ).
tcf(c_9334,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(domain(X0),compose(X0,compose(g,a))),compose(X0,compose(g,a))) = compose(X0,compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_9319]) ).
tcf(c_9335,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(domain(X0),compose(X0,compose(h,a))),compose(X0,compose(h,a))) = compose(X0,compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_9319]) ).
tcf(c_9339,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(X1),compose(codomain(X0),compose(codomain(X0),X1)),compose(codomain(X0),X1)) = compose(codomain(X0),X1),
inference(superposition,[status(thm)],[c_66,c_9319]) ).
tcf(c_9340,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),compose(domain(a),compose(compose(a,b),X0)),compose(compose(a,b),X0)) = compose(compose(a,b),X0),
inference(superposition,[status(thm)],[c_171,c_9319]) ).
tcf(c_9341,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),compose(domain(X0),compose(domain(X0),X1)),compose(domain(X0),X1)) = compose(domain(X0),X1),
inference(superposition,[status(thm)],[c_100,c_9319]) ).
tcf(c_9342,plain,
! [X0: $i] : ifeq(codomain(g),domain(X0),compose(domain(h),compose(g,X0)),compose(g,X0)) = compose(g,X0),
inference(superposition,[status(thm)],[c_1480,c_9319]) ).
tcf(c_9343,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),compose(domain(h),compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
inference(superposition,[status(thm)],[c_1392,c_9319]) ).
tcf(c_9344,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),compose(domain(h),compose(compose(g,a),X0)),compose(compose(g,a),X0)) = compose(compose(g,a),X0),
inference(superposition,[status(thm)],[c_1491,c_9319]) ).
tcf(c_9393,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),compose(domain(h),compose(g,X0)),compose(g,X0)) = compose(g,X0),
inference(light_normalisation,[status(thm)],[c_9342,c_170]) ).
tcf(c_9398,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),compose(domain(X0),compose(domain(X0),X1)),compose(domain(X0),X1)) = compose(domain(X0),X1),
inference(light_normalisation,[status(thm)],[c_9341,c_65]) ).
tcf(c_9399,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),compose(codomain(X0),compose(codomain(X0),X1)),compose(codomain(X0),X1)) = compose(codomain(X0),X1),
inference(light_normalisation,[status(thm)],[c_9339,c_102]) ).
tcf(c_9408,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(domain(h),compose(compose(g,a),X0)),compose(compose(g,a),X0)) = compose(compose(g,a),X0),
inference(light_normalisation,[status(thm)],[c_9344,c_571]) ).
tcf(c_9409,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(domain(a),compose(compose(a,b),X0)),compose(compose(a,b),X0)) = compose(compose(a,b),X0),
inference(light_normalisation,[status(thm)],[c_9340,c_425]) ).
tcf(c_9417,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(domain(h),compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_9343,c_2217]) ).
tcf(c_9431,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),compose(domain(a),compose(a,codomain(X0))),compose(a,codomain(X0))) = compose(a,codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_9321]) ).
tcf(c_9432,plain,
ifeq(domain(b),domain(a),compose(domain(a),compose(a,compose(a,b))),compose(a,compose(a,b))) = compose(a,compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_9321]) ).
tcf(c_9433,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(domain(a),compose(a,domain(X0))),compose(a,domain(X0))) = compose(a,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_9321]) ).
tcf(c_9434,plain,
ifeq(domain(b),domain(h),compose(domain(a),compose(a,g)),compose(a,g)) = compose(a,g),
inference(superposition,[status(thm)],[c_1480,c_9321]) ).
tcf(c_9435,plain,
ifeq(domain(b),domain(h),compose(domain(a),compose(a,compose(h,compose(a,b)))),compose(a,compose(h,compose(a,b)))) = compose(a,compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_9321]) ).
tcf(c_9436,plain,
ifeq(domain(b),domain(h),compose(domain(a),compose(a,compose(g,a))),compose(a,compose(g,a))) = compose(a,compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_9321]) ).
tcf(c_9437,plain,
ifeq(domain(b),domain(h),compose(domain(a),compose(a,compose(h,a))),compose(a,compose(h,a))) = compose(a,compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_9321]) ).
tcf(c_9447,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),compose(domain(h),compose(h,codomain(X0))),compose(h,codomain(X0))) = compose(h,codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_9322]) ).
tcf(c_9449,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),compose(domain(h),compose(h,domain(X0))),compose(h,domain(X0))) = compose(h,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_9322]) ).
tcf(c_9450,plain,
ifeq(domain(a),domain(h),compose(domain(h),compose(h,g)),compose(h,g)) = compose(h,g),
inference(superposition,[status(thm)],[c_1480,c_9322]) ).
tcf(c_9451,plain,
ifeq(domain(a),domain(h),compose(domain(h),compose(h,compose(h,compose(a,b)))),compose(h,compose(h,compose(a,b)))) = compose(h,compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_9322]) ).
tcf(c_9452,plain,
ifeq(domain(a),domain(h),compose(domain(h),compose(h,compose(g,a))),compose(h,compose(g,a))) = compose(h,compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_9322]) ).
tcf(c_9453,plain,
ifeq(domain(a),domain(h),compose(domain(h),compose(h,compose(h,a))),compose(h,compose(h,a))) = compose(h,compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_9322]) ).
tcf(c_9504,plain,
! [X0: $i] : ifeq(compose(domain(b),a),X0,ifeq(compose(h,a),X0,h,domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_1261,c_64]) ).
tcf(c_9533,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),codomain(X1),compose(codomain(X0),compose(codomain(X0),codomain(X1))),compose(codomain(X0),codomain(X1))) = compose(codomain(X0),codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_9329]) ).
tcf(c_9534,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(X0),compose(domain(a),compose(compose(a,b),codomain(X0))),compose(compose(a,b),codomain(X0))) = compose(compose(a,b),codomain(X0)),
inference(superposition,[status(thm)],[c_171,c_9329]) ).
tcf(c_9535,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(X1),compose(domain(X0),compose(domain(X0),codomain(X1))),compose(domain(X0),codomain(X1))) = compose(domain(X0),codomain(X1)),
inference(superposition,[status(thm)],[c_100,c_9329]) ).
tcf(c_9536,plain,
! [X0: $i] : ifeq(codomain(g),codomain(X0),compose(domain(h),compose(g,codomain(X0))),compose(g,codomain(X0))) = compose(g,codomain(X0)),
inference(superposition,[status(thm)],[c_1480,c_9329]) ).
tcf(c_9537,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),codomain(X0),compose(domain(h),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_1392,c_9329]) ).
tcf(c_9538,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),codomain(X0),compose(domain(h),compose(compose(g,a),codomain(X0))),compose(compose(g,a),codomain(X0))) = compose(compose(g,a),codomain(X0)),
inference(superposition,[status(thm)],[c_1491,c_9329]) ).
tcf(c_9573,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),compose(domain(h),compose(g,codomain(X0))),compose(g,codomain(X0))) = compose(g,codomain(X0)),
inference(light_normalisation,[status(thm)],[c_9536,c_170]) ).
tcf(c_9576,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(X1),compose(domain(X0),compose(domain(X0),codomain(X1))),compose(domain(X0),codomain(X1))) = compose(domain(X0),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_9535,c_65]) ).
tcf(c_9577,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),compose(codomain(X0),compose(codomain(X0),codomain(X1))),compose(codomain(X0),codomain(X1))) = compose(codomain(X0),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_9533,c_102]) ).
tcf(c_9581,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),compose(domain(h),compose(compose(g,a),codomain(X0))),compose(compose(g,a),codomain(X0))) = compose(compose(g,a),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_9538,c_571]) ).
tcf(c_9582,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),compose(domain(a),compose(compose(a,b),codomain(X0))),compose(compose(a,b),codomain(X0))) = compose(compose(a,b),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_9534,c_425]) ).
tcf(c_9587,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),compose(domain(h),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_9537,c_2217]) ).
tcf(c_9643,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(codomain(X0),compose(a,b))),compose(codomain(X0),compose(a,b))) = compose(codomain(X0),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_9399]) ).
tcf(c_9644,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),compose(codomain(X0),compose(codomain(X0),domain(X1))),compose(codomain(X0),domain(X1))) = compose(codomain(X0),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_9399]) ).
tcf(c_9645,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(codomain(X0),g)),compose(codomain(X0),g)) = compose(codomain(X0),g),
inference(superposition,[status(thm)],[c_1480,c_9399]) ).
tcf(c_9646,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(codomain(X0),compose(h,compose(a,b)))),compose(codomain(X0),compose(h,compose(a,b)))) = compose(codomain(X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_9399]) ).
tcf(c_9647,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(codomain(X0),compose(g,a))),compose(codomain(X0),compose(g,a))) = compose(codomain(X0),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_9399]) ).
tcf(c_9648,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(codomain(X0),compose(h,a))),compose(codomain(X0),compose(h,a))) = compose(codomain(X0),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_9399]) ).
tcf(c_9725,plain,
ifeq(codomain(compose(a,b)),domain(h),compose(domain(a),compose(compose(a,b),g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
inference(superposition,[status(thm)],[c_171,c_9332]) ).
tcf(c_9726,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),domain(h),compose(domain(X0),compose(domain(X0),g)),compose(domain(X0),g)) = compose(domain(X0),g),
inference(superposition,[status(thm)],[c_100,c_9332]) ).
tcf(c_9727,plain,
ifeq(codomain(g),domain(h),compose(domain(h),compose(g,g)),compose(g,g)) = compose(g,g),
inference(superposition,[status(thm)],[c_1480,c_9332]) ).
tcf(c_9728,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
inference(superposition,[status(thm)],[c_1392,c_9332]) ).
tcf(c_9729,plain,
ifeq(codomain(compose(g,a)),domain(h),compose(domain(h),compose(compose(g,a),g)),compose(compose(g,a),g)) = compose(compose(g,a),g),
inference(superposition,[status(thm)],[c_1491,c_9332]) ).
tcf(c_9736,plain,
ifeq(domain(a),domain(h),compose(domain(h),compose(g,g)),compose(g,g)) = compose(g,g),
inference(light_normalisation,[status(thm)],[c_9727,c_170]) ).
tcf(c_9738,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(domain(X0),g)),compose(domain(X0),g)) = compose(domain(X0),g),
inference(light_normalisation,[status(thm)],[c_9726,c_65]) ).
tcf(c_9743,plain,
ifeq(domain(b),domain(h),compose(domain(h),compose(compose(g,a),g)),compose(compose(g,a),g)) = compose(compose(g,a),g),
inference(light_normalisation,[status(thm)],[c_9729,c_571]) ).
tcf(c_9744,plain,
ifeq(codomain(b),domain(h),compose(domain(a),compose(compose(a,b),g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
inference(light_normalisation,[status(thm)],[c_9725,c_425]) ).
tcf(c_9748,plain,
ifeq(codomain(b),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
inference(light_normalisation,[status(thm)],[c_9728,c_2217]) ).
tcf(c_9754,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),compose(domain(h),compose(g,domain(X0))),compose(g,domain(X0))) = compose(g,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_9393]) ).
tcf(c_9756,plain,
ifeq(domain(a),domain(h),compose(domain(h),compose(g,compose(h,compose(a,b)))),compose(g,compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_9393]) ).
tcf(c_9757,plain,
ifeq(domain(a),domain(h),compose(domain(h),compose(g,compose(g,a))),compose(g,compose(g,a))) = compose(g,compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_9393]) ).
tcf(c_9758,plain,
ifeq(domain(a),domain(h),compose(domain(h),compose(g,compose(h,a))),compose(g,compose(h,a))) = compose(g,compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_9393]) ).
tcf(c_9789,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),compose(domain(a),compose(compose(a,b),domain(X0))),compose(compose(a,b),domain(X0))) = compose(compose(a,b),domain(X0)),
inference(superposition,[status(thm)],[c_171,c_9331]) ).
tcf(c_9790,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),compose(domain(X0),compose(domain(X0),domain(X1))),compose(domain(X0),domain(X1))) = compose(domain(X0),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_9331]) ).
tcf(c_9792,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),compose(domain(h),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_1392,c_9331]) ).
tcf(c_9793,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),compose(domain(h),compose(compose(g,a),domain(X0))),compose(compose(g,a),domain(X0))) = compose(compose(g,a),domain(X0)),
inference(superposition,[status(thm)],[c_1491,c_9331]) ).
tcf(c_9832,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),compose(domain(X0),compose(domain(X0),domain(X1))),compose(domain(X0),domain(X1))) = compose(domain(X0),domain(X1)),
inference(light_normalisation,[status(thm)],[c_9790,c_65]) ).
tcf(c_9837,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(domain(h),compose(compose(g,a),domain(X0))),compose(compose(g,a),domain(X0))) = compose(compose(g,a),domain(X0)),
inference(light_normalisation,[status(thm)],[c_9793,c_571]) ).
tcf(c_9838,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(domain(a),compose(compose(a,b),domain(X0))),compose(compose(a,b),domain(X0))) = compose(compose(a,b),domain(X0)),
inference(light_normalisation,[status(thm)],[c_9789,c_425]) ).
tcf(c_9842,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(domain(h),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_9792,c_2217]) ).
tcf(c_9854,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(domain(X0),compose(a,b))),compose(domain(X0),compose(a,b))) = compose(domain(X0),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_9398]) ).
tcf(c_9857,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(domain(X0),compose(h,compose(a,b)))),compose(domain(X0),compose(h,compose(a,b)))) = compose(domain(X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_9398]) ).
tcf(c_9858,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(domain(X0),compose(g,a))),compose(domain(X0),compose(g,a))) = compose(domain(X0),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_9398]) ).
tcf(c_9859,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(domain(X0),compose(h,a))),compose(domain(X0),compose(h,a))) = compose(domain(X0),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_9398]) ).
tcf(c_10060,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),compose(X0,compose(codomain(X0),X1)),compose(X0,X1)) = compose(X0,X1),
inference(demodulation,[status(thm)],[c_309,c_64]) ).
tcf(c_10070,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),compose(X0,compose(codomain(X0),codomain(X1))),compose(X0,codomain(X1))) = compose(X0,codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_10060]) ).
tcf(c_10071,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(X0,compose(codomain(X0),compose(a,b))),compose(X0,compose(a,b))) = compose(X0,compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_10060]) ).
tcf(c_10072,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),compose(X0,compose(codomain(X0),domain(X1))),compose(X0,domain(X1))) = compose(X0,domain(X1)),
inference(superposition,[status(thm)],[c_100,c_10060]) ).
tcf(c_10073,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(codomain(X0),g)),compose(X0,g)) = compose(X0,g),
inference(superposition,[status(thm)],[c_1480,c_10060]) ).
tcf(c_10074,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(codomain(X0),compose(h,compose(a,b)))),compose(X0,compose(h,compose(a,b)))) = compose(X0,compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_10060]) ).
tcf(c_10075,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(codomain(X0),compose(g,a))),compose(X0,compose(g,a))) = compose(X0,compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_10060]) ).
tcf(c_10076,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(codomain(X0),compose(h,a))),compose(X0,compose(h,a))) = compose(X0,compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_10060]) ).
tcf(c_10080,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(a,compose(domain(b),X0)),compose(a,X0)) = compose(a,X0),
inference(superposition,[status(thm)],[c_72,c_10060]) ).
tcf(c_10084,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(codomain(b),X0)),compose(compose(a,b),X0)) = compose(compose(a,b),X0),
inference(superposition,[status(thm)],[c_425,c_10060]) ).
tcf(c_10085,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(codomain(b),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
inference(superposition,[status(thm)],[c_2217,c_10060]) ).
tcf(c_10130,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),compose(a,compose(domain(b),codomain(X0))),compose(a,codomain(X0))) = compose(a,codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_10080]) ).
tcf(c_10131,plain,
ifeq(domain(b),domain(a),compose(a,compose(domain(b),compose(a,b))),compose(a,compose(a,b))) = compose(a,compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_10080]) ).
tcf(c_10132,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(a,compose(domain(b),domain(X0))),compose(a,domain(X0))) = compose(a,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_10080]) ).
tcf(c_10133,plain,
ifeq(domain(b),domain(h),compose(a,compose(domain(b),g)),compose(a,g)) = compose(a,g),
inference(superposition,[status(thm)],[c_1480,c_10080]) ).
tcf(c_10134,plain,
ifeq(domain(b),domain(h),compose(a,compose(domain(b),compose(h,compose(a,b)))),compose(a,compose(h,compose(a,b)))) = compose(a,compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_10080]) ).
tcf(c_10135,plain,
ifeq(domain(b),domain(h),compose(a,compose(domain(b),compose(g,a))),compose(a,compose(g,a))) = compose(a,compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_10080]) ).
tcf(c_10136,plain,
ifeq(domain(b),domain(h),compose(a,compose(domain(b),compose(h,a))),compose(a,compose(h,a))) = compose(a,compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_10080]) ).
tcf(c_10161,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(codomain(b),g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
inference(superposition,[status(thm)],[c_425,c_10073]) ).
tcf(c_10162,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(codomain(b),g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
inference(superposition,[status(thm)],[c_2217,c_10073]) ).
tcf(c_10285,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(b),codomain(X0))),compose(compose(a,b),codomain(X0))) = compose(compose(a,b),codomain(X0)),
inference(superposition,[status(thm)],[c_425,c_10070]) ).
tcf(c_10286,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_2217,c_10070]) ).
tcf(c_10479,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(codomain(b),domain(X0))),compose(compose(a,b),domain(X0))) = compose(compose(a,b),domain(X0)),
inference(superposition,[status(thm)],[c_425,c_10072]) ).
tcf(c_10480,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(codomain(b),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_2217,c_10072]) ).
tcf(c_10540,plain,
! [X0: $i] : ifeq(compose(compose(h,a),a),X0,ifeq(compose(h,a),X0,h,compose(h,a)),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_1267,c_64]) ).
tcf(c_10591,plain,
! [X0: $i] : ifeq(compose(domain(b),a),X0,ifeq(compose(g,a),X0,g,domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_1560,c_64]) ).
tcf(c_10604,plain,
! [X0: $i] : ifeq(compose(compose(g,a),a),X0,ifeq(compose(h,a),X0,h,compose(g,a)),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_1268,c_64]) ).
tcf(c_10714,plain,
ifeq(codomain(compose(a,b)),domain(a),compose(domain(a),compose(compose(a,b),compose(a,b))),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_9330]) ).
tcf(c_10717,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(a),compose(domain(h),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_1392,c_9330]) ).
tcf(c_10718,plain,
ifeq(codomain(compose(g,a)),domain(a),compose(domain(h),compose(compose(g,a),compose(a,b))),compose(compose(g,a),compose(a,b))) = compose(compose(g,a),compose(a,b)),
inference(superposition,[status(thm)],[c_1491,c_9330]) ).
tcf(c_10736,plain,
ifeq(domain(b),domain(a),compose(domain(h),compose(compose(g,a),compose(a,b))),compose(compose(g,a),compose(a,b))) = compose(compose(g,a),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_10718,c_571]) ).
tcf(c_10737,plain,
ifeq(codomain(b),domain(a),compose(domain(a),compose(compose(a,b),compose(a,b))),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_10714,c_425]) ).
tcf(c_10741,plain,
ifeq(codomain(b),domain(a),compose(domain(h),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_10717,c_2217]) ).
tcf(c_10754,plain,
ifeq(codomain(compose(a,b)),domain(h),compose(domain(a),compose(compose(a,b),compose(g,a))),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a)),
inference(superposition,[status(thm)],[c_171,c_9334]) ).
tcf(c_10757,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_1392,c_9334]) ).
tcf(c_10758,plain,
ifeq(codomain(compose(g,a)),domain(h),compose(domain(h),compose(compose(g,a),compose(g,a))),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_9334]) ).
tcf(c_10772,plain,
ifeq(domain(b),domain(h),compose(domain(h),compose(compose(g,a),compose(g,a))),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_10758,c_571]) ).
tcf(c_10773,plain,
ifeq(codomain(b),domain(h),compose(domain(a),compose(compose(a,b),compose(g,a))),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_10754,c_425]) ).
tcf(c_10777,plain,
ifeq(codomain(b),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_10757,c_2217]) ).
tcf(c_10790,plain,
ifeq(codomain(compose(a,b)),domain(h),compose(domain(a),compose(compose(a,b),compose(h,a))),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a)),
inference(superposition,[status(thm)],[c_171,c_9335]) ).
tcf(c_10793,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_1392,c_9335]) ).
tcf(c_10794,plain,
ifeq(codomain(compose(g,a)),domain(h),compose(domain(h),compose(compose(g,a),compose(h,a))),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)),
inference(superposition,[status(thm)],[c_1491,c_9335]) ).
tcf(c_10808,plain,
ifeq(domain(b),domain(h),compose(domain(h),compose(compose(g,a),compose(h,a))),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_10794,c_571]) ).
tcf(c_10809,plain,
ifeq(codomain(b),domain(h),compose(domain(a),compose(compose(a,b),compose(h,a))),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_10790,c_425]) ).
tcf(c_10813,plain,
ifeq(codomain(b),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_10793,c_2217]) ).
tcf(c_10821,plain,
ifeq(domain(b),domain(h),compose(domain(h),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_9408]) ).
tcf(c_10838,plain,
ifeq(codomain(b),domain(h),compose(domain(a),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_9409]) ).
tcf(c_10849,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(X0,a),a,X0,domain(a)),domain(a)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_6349,c_65]) ).
tcf(c_10850,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(domain(X0),a),a,domain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_65,c_10849]) ).
tcf(c_10851,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(a,a),a,a,domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_72,c_10849]) ).
tcf(c_10854,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(codomain(X0),a),a,codomain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_102,c_10849]) ).
tcf(c_10855,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(a,b),a),a,compose(a,b),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_425,c_10849]) ).
tcf(c_10856,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,compose(a,b)),a),a,compose(h,compose(a,b)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_2217,c_10849]) ).
tcf(c_10857,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,a),a),a,compose(h,a),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_485,c_10849]) ).
tcf(c_10858,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(g,a),a),a,compose(g,a),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_571,c_10849]) ).
tcf(c_10868,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(X0,a),X0,domain(a)),domain(a)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_6498,c_65]) ).
tcf(c_10869,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(domain(X0),a),domain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_65,c_10868]) ).
tcf(c_10870,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(a,a),a,domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_72,c_10868]) ).
tcf(c_10873,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(codomain(X0),a),codomain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_102,c_10868]) ).
tcf(c_10874,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(compose(a,b),a),compose(a,b),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_425,c_10868]) ).
tcf(c_10875,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_2217,c_10868]) ).
tcf(c_10876,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(compose(h,a),a),compose(h,a),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_485,c_10868]) ).
tcf(c_10877,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(compose(g,a),a),compose(g,a),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_571,c_10868]) ).
tcf(c_11066,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,b),b,X0,domain(b)),domain(b)) = domain(b),
inference(demodulation,[status(thm)],[c_6531,c_64,c_65]) ).
tcf(c_11067,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),b),b,domain(X0),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_65,c_11066]) ).
tcf(c_11068,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,b),b,a,domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_72,c_11066]) ).
tcf(c_11071,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),b),b,codomain(X0),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_102,c_11066]) ).
tcf(c_11072,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),b),b,compose(a,b),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_425,c_11066]) ).
tcf(c_11073,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),b),b,compose(h,compose(a,b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_2217,c_11066]) ).
tcf(c_11074,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),b),b,compose(h,a),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_11066]) ).
tcf(c_11075,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),b),b,compose(g,a),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_571,c_11066]) ).
tcf(c_11084,plain,
ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),b,compose(g,a),domain(b)),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_11075,c_4514]) ).
tcf(c_11085,plain,
ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),b,compose(h,a),domain(b)),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_11074,c_6074]) ).
tcf(c_11158,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(codomain(b),compose(a,b))),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)),
inference(superposition,[status(thm)],[c_425,c_10071]) ).
tcf(c_11159,plain,
ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(codomain(b),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_10071]) ).
tcf(c_11182,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(codomain(b),compose(g,a))),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a)),
inference(superposition,[status(thm)],[c_425,c_10075]) ).
tcf(c_11183,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(codomain(b),compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_2217,c_10075]) ).
tcf(c_11204,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(codomain(b),compose(h,a))),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a)),
inference(superposition,[status(thm)],[c_425,c_10076]) ).
tcf(c_11205,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(codomain(b),compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_2217,c_10076]) ).
tcf(c_11216,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_10084]) ).
tcf(c_11228,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(b,compose(X0,b),X0,domain(b)),domain(b)) = domain(b),
inference(demodulation,[status(thm)],[c_6569,c_64,c_65]) ).
tcf(c_11229,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(b,compose(domain(X0),b),domain(X0),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_65,c_11228]) ).
tcf(c_11230,plain,
ifeq(domain(b),domain(a),ifeq(b,compose(a,b),a,domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_72,c_11228]) ).
tcf(c_11233,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(b,compose(codomain(X0),b),codomain(X0),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_102,c_11228]) ).
tcf(c_11234,plain,
ifeq(codomain(b),domain(a),ifeq(b,compose(compose(a,b),b),compose(a,b),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_425,c_11228]) ).
tcf(c_11235,plain,
ifeq(codomain(b),domain(a),ifeq(b,compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_2217,c_11228]) ).
tcf(c_11236,plain,
ifeq(domain(b),domain(a),ifeq(b,compose(compose(h,a),b),compose(h,a),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_11228]) ).
tcf(c_11237,plain,
ifeq(domain(b),domain(a),ifeq(b,compose(compose(g,a),b),compose(g,a),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_571,c_11228]) ).
tcf(c_11246,plain,
ifeq(domain(b),domain(a),ifeq(b,compose(h,compose(a,b)),compose(g,a),domain(b)),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_11237,c_4514]) ).
tcf(c_11247,plain,
ifeq(domain(b),domain(a),ifeq(b,compose(h,compose(a,b)),compose(h,a),domain(b)),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_11236,c_6074]) ).
tcf(c_11457,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(a,a),X1,a,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_230]) ).
tcf(c_11461,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(compose(a,a),X1,a,codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_230]) ).
tcf(c_11462,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(compose(a,a),X0,a,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_230]) ).
tcf(c_11463,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(compose(a,a),X0,a,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_230]) ).
tcf(c_11470,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(a,a),X1,ifeq(compose(X0,a),X1,X0,a),a),a) = a,
inference(demodulation,[status(thm)],[c_235,c_64]) ).
tcf(c_11471,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(compose(a,a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),a),a),a) = a,
inference(superposition,[status(thm)],[c_65,c_11470]) ).
tcf(c_11472,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(a,a),X0,ifeq(compose(a,a),X0,a,a),a),a) = a,
inference(superposition,[status(thm)],[c_72,c_11470]) ).
tcf(c_11475,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(a,a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),a),a),a) = a,
inference(superposition,[status(thm)],[c_102,c_11470]) ).
tcf(c_11476,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(a,a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),a),a),a) = a,
inference(superposition,[status(thm)],[c_425,c_11470]) ).
tcf(c_11477,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(a,a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),a),a),a) = a,
inference(superposition,[status(thm)],[c_2217,c_11470]) ).
tcf(c_11478,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(a,a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),a),a),a) = a,
inference(superposition,[status(thm)],[c_485,c_11470]) ).
tcf(c_11479,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(a,a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),a),a),a) = a,
inference(superposition,[status(thm)],[c_571,c_11470]) ).
tcf(c_11486,plain,
! [X0: $i] : ifeq(codomain(domain(a)),domain(a),ifeq(compose(a,a),X0,ifeq(a,X0,domain(a),a),a),a) = a,
inference(superposition,[status(thm)],[c_67,c_11470]) ).
tcf(c_11495,plain,
! [X0: $i] : ifeq(compose(a,a),X0,ifeq(a,X0,domain(a),a),a) = a,
inference(demodulation,[status(thm)],[c_11486,c_64,c_65]) ).
tcf(c_11532,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(a,X1,domain(a),X0),X0),X0) = X0,
inference(demodulation,[status(thm)],[c_242,c_64,c_65]) ).
tcf(c_11533,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(a,X1,domain(a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_11532]) ).
tcf(c_11535,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(a,X0,domain(a),h),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_11532]) ).
tcf(c_11536,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(a,X0,domain(a),g),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_11532]) ).
tcf(c_11537,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(a,X1,domain(a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_11532]) ).
tcf(c_11538,plain,
! [X0: $i] : ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(a,X0,domain(a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_11532]) ).
tcf(c_11539,plain,
! [X0: $i] : ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(a,X0,domain(a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_11532]) ).
tcf(c_11540,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X0,ifeq(a,X0,domain(a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_11532]) ).
tcf(c_11541,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),X0,ifeq(a,X0,domain(a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_11532]) ).
tcf(c_11544,plain,
! [X0: $i] : ifeq(codomain(domain(a)),domain(b),ifeq(a,X0,ifeq(a,X0,domain(a),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_67,c_11532]) ).
tcf(c_11552,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(a,X0,domain(a),domain(a)),domain(a)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_11544,c_65]) ).
tcf(c_11596,plain,
! [X0: $i] : ifeq(compose(domain(b),a),X0,ifeq(a,X0,domain(a),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_11533,c_64]) ).
tcf(c_11699,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(a,b),X1,a,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_244]) ).
tcf(c_11703,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(a,b),X1,a,codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_244]) ).
tcf(c_11704,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(a,b),X0,a,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_244]) ).
tcf(c_11705,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(a,b),X0,a,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_244]) ).
tcf(c_11718,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(X0,b),X1,X0,a),a),a) = a,
inference(demodulation,[status(thm)],[c_249,c_64]) ).
tcf(c_11719,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(domain(X0),b),X1,domain(X0),a),a),a) = a,
inference(superposition,[status(thm)],[c_65,c_11718]) ).
tcf(c_11720,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(a,b),X0,a,a),a),a) = a,
inference(superposition,[status(thm)],[c_72,c_11718]) ).
tcf(c_11723,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),a),a),a) = a,
inference(superposition,[status(thm)],[c_102,c_11718]) ).
tcf(c_11724,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),a),a),a) = a,
inference(superposition,[status(thm)],[c_425,c_11718]) ).
tcf(c_11725,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),a),a),a) = a,
inference(superposition,[status(thm)],[c_2217,c_11718]) ).
tcf(c_11726,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(compose(h,a),b),X0,compose(h,a),a),a),a) = a,
inference(superposition,[status(thm)],[c_485,c_11718]) ).
tcf(c_11727,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(compose(g,a),b),X0,compose(g,a),a),a),a) = a,
inference(superposition,[status(thm)],[c_571,c_11718]) ).
tcf(c_11735,plain,
! [X0: $i] : ifeq(codomain(domain(b)),domain(a),ifeq(compose(a,b),X0,ifeq(b,X0,domain(b),a),a),a) = a,
inference(superposition,[status(thm)],[c_67,c_11718]) ).
tcf(c_11742,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),a),a),a) = a,
inference(light_normalisation,[status(thm)],[c_11727,c_4514]) ).
tcf(c_11743,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),a),a),a) = a,
inference(light_normalisation,[status(thm)],[c_11726,c_6074]) ).
tcf(c_11752,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(b,X0,domain(b),a),a),a) = a,
inference(demodulation,[status(thm)],[c_11735,c_65]) ).
tcf(c_11782,plain,
! [X0: $i] : ifeq(compose(a,b),X0,ifeq(compose(domain(a),b),X0,domain(a),a),a) = a,
inference(superposition,[status(thm)],[c_11719,c_64]) ).
tcf(c_11832,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(b,X1,domain(b),X0),X0),X0),X0) = X0,
inference(demodulation,[status(thm)],[c_256,c_65]) ).
tcf(c_11833,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(b,X1,domain(b),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_11832]) ).
tcf(c_11835,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(b,X0,domain(b),h),h),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_11832]) ).
tcf(c_11836,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(b,X0,domain(b),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_11832]) ).
tcf(c_11837,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(b,X1,domain(b),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_11832]) ).
tcf(c_11838,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(b,X0,domain(b),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_11832]) ).
tcf(c_11839,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(b,X0,domain(b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_11832]) ).
tcf(c_11840,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),X0,ifeq(b,X0,domain(b),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_11832]) ).
tcf(c_11841,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),X0,ifeq(b,X0,domain(b),compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_11832]) ).
tcf(c_11843,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(domain(b)),domain(b),ifeq(b,X0,ifeq(b,X0,domain(b),domain(b)),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_67,c_11832]) ).
tcf(c_11847,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(b,X0,domain(b),compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_11841,c_4514]) ).
tcf(c_11848,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(b,X0,domain(b),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_11840,c_6074]) ).
tcf(c_11866,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(a,compose(h,compose(a,b)))),compose(compose(X0,a),compose(h,compose(a,b)))),compose(compose(X0,a),compose(h,compose(a,b)))) = compose(compose(X0,a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_72,c_1425]) ).
tcf(c_11874,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,compose(h,compose(a,b)))),compose(compose(domain(X1),X0),compose(h,compose(a,b)))),compose(compose(domain(X1),X0),compose(h,compose(a,b)))) = compose(compose(domain(X1),X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_65,c_1425]) ).
tcf(c_11875,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(X0,compose(h,compose(a,b)))),compose(compose(a,X0),compose(h,compose(a,b)))),compose(compose(a,X0),compose(h,compose(a,b)))) = compose(compose(a,X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_72,c_1425]) ).
tcf(c_11878,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,compose(h,compose(a,b)))),compose(compose(codomain(X1),X0),compose(h,compose(a,b)))),compose(compose(codomain(X1),X0),compose(h,compose(a,b)))) = compose(compose(codomain(X1),X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_102,c_1425]) ).
tcf(c_11879,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,compose(h,compose(a,b)))),compose(compose(compose(a,b),X0),compose(h,compose(a,b)))),compose(compose(compose(a,b),X0),compose(h,compose(a,b)))) = compose(compose(compose(a,b),X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_425,c_1425]) ).
tcf(c_11880,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),X0),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),X0),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_1425]) ).
tcf(c_11883,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(h),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(X1,codomain(X0)),compose(h,compose(a,b)))),compose(compose(X1,codomain(X0)),compose(h,compose(a,b)))) = compose(compose(X1,codomain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_66,c_1425]) ).
tcf(c_11884,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(X0,compose(a,b)),compose(h,compose(a,b)))),compose(compose(X0,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(X0,compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_171,c_1425]) ).
tcf(c_11885,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),compose(h,compose(a,b)))),compose(compose(X1,domain(X0)),compose(h,compose(a,b)))),compose(compose(X1,domain(X0)),compose(h,compose(a,b)))) = compose(compose(X1,domain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_100,c_1425]) ).
tcf(c_11886,plain,
! [X0: $i] : ifeq(codomain(g),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(g,compose(h,compose(a,b)))),compose(compose(X0,g),compose(h,compose(a,b)))),compose(compose(X0,g),compose(h,compose(a,b)))) = compose(compose(X0,g),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1480,c_1425]) ).
tcf(c_11887,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(X0,compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(X0,compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(X0,compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_1425]) ).
tcf(c_11888,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(X0,compose(g,a)),compose(h,compose(a,b)))),compose(compose(X0,compose(g,a)),compose(h,compose(a,b)))) = compose(compose(X0,compose(g,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1491,c_1425]) ).
tcf(c_11937,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(g,compose(h,compose(a,b)))),compose(compose(X0,g),compose(h,compose(a,b)))),compose(compose(X0,g),compose(h,compose(a,b)))) = compose(compose(X0,g),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_11886,c_170]) ).
tcf(c_11941,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),compose(h,compose(a,b)))),compose(compose(X1,domain(X0)),compose(h,compose(a,b)))),compose(compose(X1,domain(X0)),compose(h,compose(a,b)))) = compose(compose(X1,domain(X0)),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_11885,c_65]) ).
tcf(c_11942,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(X1,codomain(X0)),compose(h,compose(a,b)))),compose(compose(X1,codomain(X0)),compose(h,compose(a,b)))) = compose(compose(X1,codomain(X0)),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_11883,c_102]) ).
tcf(c_11954,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(X0,compose(g,a)),compose(h,compose(a,b)))),compose(compose(X0,compose(g,a)),compose(h,compose(a,b)))) = compose(compose(X0,compose(g,a)),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_11888,c_571]) ).
tcf(c_11955,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(X0,compose(a,b)),compose(h,compose(a,b)))),compose(compose(X0,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(X0,compose(a,b)),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_11884,c_425]) ).
tcf(c_11962,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(X0,compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(X0,compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(X0,compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_11887,c_2217]) ).
tcf(c_12020,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),compose(compose(h,a),compose(b,codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_7390]) ).
tcf(c_12021,plain,
ifeq(codomain(b),domain(a),compose(compose(h,a),compose(b,compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_7390]) ).
tcf(c_12022,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(h,a),compose(b,domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_7390]) ).
tcf(c_12023,plain,
ifeq(codomain(b),domain(h),compose(compose(h,a),compose(b,g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
inference(superposition,[status(thm)],[c_1480,c_7390]) ).
tcf(c_12024,plain,
ifeq(codomain(b),domain(h),compose(compose(h,a),compose(b,compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_7390]) ).
tcf(c_12025,plain,
ifeq(codomain(b),domain(h),compose(compose(h,a),compose(b,compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_7390]) ).
tcf(c_12026,plain,
ifeq(codomain(b),domain(h),compose(compose(h,a),compose(b,compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_7390]) ).
tcf(c_12143,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(h,a)),b)) = compose(compose(domain(X0),compose(h,a)),b),
inference(superposition,[status(thm)],[c_65,c_7606]) ).
tcf(c_12144,plain,
ifeq(domain(b),domain(h),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(h,a)),b)) = compose(compose(a,compose(h,a)),b),
inference(superposition,[status(thm)],[c_72,c_7606]) ).
tcf(c_12145,plain,
ifeq(domain(a),domain(h),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(h,a)),b)) = compose(compose(h,compose(h,a)),b),
inference(superposition,[status(thm)],[c_167,c_7606]) ).
tcf(c_12146,plain,
ifeq(domain(a),domain(h),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(h,a)),b)) = compose(compose(g,compose(h,a)),b),
inference(superposition,[status(thm)],[c_170,c_7606]) ).
tcf(c_12147,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(h,a)),b)) = compose(compose(codomain(X0),compose(h,a)),b),
inference(superposition,[status(thm)],[c_102,c_7606]) ).
tcf(c_12148,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),compose(h,a)),b)) = compose(compose(compose(a,b),compose(h,a)),b),
inference(superposition,[status(thm)],[c_425,c_7606]) ).
tcf(c_12149,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,a)),b)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),b),
inference(superposition,[status(thm)],[c_2217,c_7606]) ).
tcf(c_12150,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(compose(h,a),compose(h,a)),b)) = compose(compose(compose(h,a),compose(h,a)),b),
inference(superposition,[status(thm)],[c_485,c_7606]) ).
tcf(c_12151,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),compose(h,a)),b)) = compose(compose(compose(g,a),compose(h,a)),b),
inference(superposition,[status(thm)],[c_571,c_7606]) ).
tcf(c_12164,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(compose(a,b),a),compose(domain(X0),a),compose(a,b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6326]) ).
tcf(c_12168,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(a,b),a),compose(codomain(X0),a),compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6326]) ).
tcf(c_12170,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(compose(h,compose(a,b)),a),compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6326]) ).
tcf(c_12180,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(compose(h,a),a),compose(domain(X0),a),compose(h,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6328]) ).
tcf(c_12184,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,a),a),compose(codomain(X0),a),compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6328]) ).
tcf(c_12185,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,a),a),compose(compose(a,b),a),compose(h,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6328]) ).
tcf(c_12186,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,a),a),compose(compose(h,compose(a,b)),a),compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6328]) ).
tcf(c_12197,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(compose(g,a),a),compose(domain(X0),a),compose(g,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6329]) ).
tcf(c_12201,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(g,a),a),compose(codomain(X0),a),compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6329]) ).
tcf(c_12202,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(g,a),a),compose(compose(a,b),a),compose(g,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6329]) ).
tcf(c_12203,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(g,a),a),compose(compose(h,compose(a,b)),a),compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6329]) ).
tcf(c_12214,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),compose(compose(a,b),a),compose(a,b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6476]) ).
tcf(c_12218,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),compose(compose(a,b),a),compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6476]) ).
tcf(c_12220,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(compose(a,b),a),compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6476]) ).
tcf(c_12232,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),compose(compose(h,a),a),compose(h,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6478]) ).
tcf(c_12236,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),compose(compose(h,a),a),compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6478]) ).
tcf(c_12237,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(compose(h,a),a),compose(h,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6478]) ).
tcf(c_12238,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(compose(h,a),a),compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6478]) ).
tcf(c_12244,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),compose(compose(g,a),a),compose(g,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6479]) ).
tcf(c_12248,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),compose(compose(g,a),a),compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6479]) ).
tcf(c_12249,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(compose(g,a),a),compose(g,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6479]) ).
tcf(c_12250,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(compose(g,a),a),compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6479]) ).
tcf(c_12256,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(compose(a,b),b),compose(domain(X0),b),compose(a,b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6508]) ).
tcf(c_12260,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(a,b),b),compose(codomain(X0),b),compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6508]) ).
tcf(c_12262,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(compose(h,compose(a,b)),b),compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6508]) ).
tcf(c_12274,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(h,compose(a,b)),compose(domain(X0),b),compose(g,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6536]) ).
tcf(c_12278,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(h,compose(a,b)),compose(codomain(X0),b),compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6536]) ).
tcf(c_12279,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(compose(a,b),b),compose(g,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6536]) ).
tcf(c_12280,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),b),compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6536]) ).
tcf(c_12297,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,domain(h)),compose(h,compose(a,b)))) = compose(compose(X0,domain(h)),compose(h,compose(a,b))),
inference(demodulation,[status(thm)],[c_1449,c_64,c_65,c_100]) ).
tcf(c_12298,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),domain(h)),compose(h,compose(a,b)))) = compose(compose(domain(X0),domain(h)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_65,c_12297]) ).
tcf(c_12299,plain,
ifeq(domain(b),domain(h),compose(a,compose(h,compose(a,b))),compose(compose(a,domain(h)),compose(h,compose(a,b)))) = compose(compose(a,domain(h)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_72,c_12297]) ).
tcf(c_12300,plain,
ifeq(domain(a),domain(h),compose(h,compose(h,compose(a,b))),compose(compose(h,domain(h)),compose(h,compose(a,b)))) = compose(compose(h,domain(h)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_167,c_12297]) ).
tcf(c_12301,plain,
ifeq(domain(a),domain(h),compose(g,compose(h,compose(a,b))),compose(compose(g,domain(h)),compose(h,compose(a,b)))) = compose(compose(g,domain(h)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_170,c_12297]) ).
tcf(c_12302,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b)))) = compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_102,c_12297]) ).
tcf(c_12303,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),domain(h)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),domain(h)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_425,c_12297]) ).
tcf(c_12304,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_12297]) ).
tcf(c_12305,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(compose(h,a),domain(h)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(h)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_485,c_12297]) ).
tcf(c_12306,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),domain(h)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(h)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_571,c_12297]) ).
tcf(c_12348,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),compose(compose(g,a),compose(b,codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_8587]) ).
tcf(c_12349,plain,
ifeq(codomain(b),domain(a),compose(compose(g,a),compose(b,compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_8587]) ).
tcf(c_12350,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(g,a),compose(b,domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_8587]) ).
tcf(c_12351,plain,
ifeq(codomain(b),domain(h),compose(compose(g,a),compose(b,g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
inference(superposition,[status(thm)],[c_1480,c_8587]) ).
tcf(c_12352,plain,
ifeq(codomain(b),domain(h),compose(compose(g,a),compose(b,compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_8587]) ).
tcf(c_12353,plain,
ifeq(codomain(b),domain(h),compose(compose(g,a),compose(b,compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_8587]) ).
tcf(c_12354,plain,
ifeq(codomain(b),domain(h),compose(compose(g,a),compose(b,compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_8587]) ).
tcf(c_12364,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(h,compose(a,b)),compose(domain(X0),b),compose(h,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6537]) ).
tcf(c_12368,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(h,compose(a,b)),compose(codomain(X0),b),compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6537]) ).
tcf(c_12369,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(compose(a,b),b),compose(h,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6537]) ).
tcf(c_12370,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),b),compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6537]) ).
tcf(c_12381,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(compose(a,b),b),compose(a,b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6549]) ).
tcf(c_12385,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(compose(a,b),b),compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6549]) ).
tcf(c_12387,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(compose(a,b),b),compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6549]) ).
tcf(c_12402,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(h,compose(a,b)),compose(g,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6577]) ).
tcf(c_12406,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(h,compose(a,b)),compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6577]) ).
tcf(c_12407,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(h,compose(a,b)),compose(g,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6577]) ).
tcf(c_12408,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6577]) ).
tcf(c_12420,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(h,compose(a,b)),compose(h,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6578]) ).
tcf(c_12424,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(h,compose(a,b)),compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6578]) ).
tcf(c_12425,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(h,compose(a,b)),compose(h,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6578]) ).
tcf(c_12426,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6578]) ).
tcf(c_12442,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(a,g)),compose(compose(X0,a),g)),compose(compose(X0,a),g)) = compose(compose(X0,a),g),
inference(superposition,[status(thm)],[c_72,c_1523]) ).
tcf(c_12450,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,g)),compose(compose(domain(X1),X0),g)),compose(compose(domain(X1),X0),g)) = compose(compose(domain(X1),X0),g),
inference(superposition,[status(thm)],[c_65,c_1523]) ).
tcf(c_12451,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(X0,g)),compose(compose(a,X0),g)),compose(compose(a,X0),g)) = compose(compose(a,X0),g),
inference(superposition,[status(thm)],[c_72,c_1523]) ).
tcf(c_12454,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,g)),compose(compose(codomain(X1),X0),g)),compose(compose(codomain(X1),X0),g)) = compose(compose(codomain(X1),X0),g),
inference(superposition,[status(thm)],[c_102,c_1523]) ).
tcf(c_12455,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,g)),compose(compose(compose(a,b),X0),g)),compose(compose(compose(a,b),X0),g)) = compose(compose(compose(a,b),X0),g),
inference(superposition,[status(thm)],[c_425,c_1523]) ).
tcf(c_12456,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,g)),compose(compose(compose(h,compose(a,b)),X0),g)),compose(compose(compose(h,compose(a,b)),X0),g)) = compose(compose(compose(h,compose(a,b)),X0),g),
inference(superposition,[status(thm)],[c_2217,c_1523]) ).
tcf(c_12459,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(h),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),g)),compose(compose(X1,codomain(X0)),g)),compose(compose(X1,codomain(X0)),g)) = compose(compose(X1,codomain(X0)),g),
inference(superposition,[status(thm)],[c_66,c_1523]) ).
tcf(c_12460,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),g)),compose(compose(X0,compose(a,b)),g)),compose(compose(X0,compose(a,b)),g)) = compose(compose(X0,compose(a,b)),g),
inference(superposition,[status(thm)],[c_171,c_1523]) ).
tcf(c_12461,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),g)),compose(compose(X1,domain(X0)),g)),compose(compose(X1,domain(X0)),g)) = compose(compose(X1,domain(X0)),g),
inference(superposition,[status(thm)],[c_100,c_1523]) ).
tcf(c_12462,plain,
! [X0: $i] : ifeq(codomain(g),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(g,g)),compose(compose(X0,g),g)),compose(compose(X0,g),g)) = compose(compose(X0,g),g),
inference(superposition,[status(thm)],[c_1480,c_1523]) ).
tcf(c_12463,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),g)),compose(compose(X0,compose(h,compose(a,b))),g)),compose(compose(X0,compose(h,compose(a,b))),g)) = compose(compose(X0,compose(h,compose(a,b))),g),
inference(superposition,[status(thm)],[c_1392,c_1523]) ).
tcf(c_12464,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),g)),compose(compose(X0,compose(g,a)),g)),compose(compose(X0,compose(g,a)),g)) = compose(compose(X0,compose(g,a)),g),
inference(superposition,[status(thm)],[c_1491,c_1523]) ).
tcf(c_12513,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(g,g)),compose(compose(X0,g),g)),compose(compose(X0,g),g)) = compose(compose(X0,g),g),
inference(light_normalisation,[status(thm)],[c_12462,c_170]) ).
tcf(c_12518,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),g)),compose(compose(X1,domain(X0)),g)),compose(compose(X1,domain(X0)),g)) = compose(compose(X1,domain(X0)),g),
inference(light_normalisation,[status(thm)],[c_12461,c_65]) ).
tcf(c_12519,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),g)),compose(compose(X1,codomain(X0)),g)),compose(compose(X1,codomain(X0)),g)) = compose(compose(X1,codomain(X0)),g),
inference(light_normalisation,[status(thm)],[c_12459,c_102]) ).
tcf(c_12531,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),g)),compose(compose(X0,compose(g,a)),g)),compose(compose(X0,compose(g,a)),g)) = compose(compose(X0,compose(g,a)),g),
inference(light_normalisation,[status(thm)],[c_12464,c_571]) ).
tcf(c_12532,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),g)),compose(compose(X0,compose(a,b)),g)),compose(compose(X0,compose(a,b)),g)) = compose(compose(X0,compose(a,b)),g),
inference(light_normalisation,[status(thm)],[c_12460,c_425]) ).
tcf(c_12539,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),g)),compose(compose(X0,compose(h,compose(a,b))),g)),compose(compose(X0,compose(h,compose(a,b))),g)) = compose(compose(X0,compose(h,compose(a,b))),g),
inference(light_normalisation,[status(thm)],[c_12463,c_2217]) ).
tcf(c_12577,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),codomain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(g,codomain(X0))),compose(compose(X1,g),codomain(X0))),compose(compose(X1,g),codomain(X0))) = compose(compose(X1,g),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_1537]) ).
tcf(c_12579,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(g,domain(X0))),compose(compose(X1,g),domain(X0))),compose(compose(X1,g),domain(X0))) = compose(compose(X1,g),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_1537]) ).
tcf(c_12582,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(g,compose(g,a))),compose(compose(X0,g),compose(g,a))),compose(compose(X0,g),compose(g,a))) = compose(compose(X0,g),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_1537]) ).
tcf(c_12584,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(g,X0)),compose(compose(domain(X1),g),X0)),compose(compose(domain(X1),g),X0)) = compose(compose(domain(X1),g),X0),
inference(superposition,[status(thm)],[c_65,c_1537]) ).
tcf(c_12585,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(g,X0)),compose(compose(a,g),X0)),compose(compose(a,g),X0)) = compose(compose(a,g),X0),
inference(superposition,[status(thm)],[c_72,c_1537]) ).
tcf(c_12588,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(g,X0)),compose(compose(codomain(X1),g),X0)),compose(compose(codomain(X1),g),X0)) = compose(compose(codomain(X1),g),X0),
inference(superposition,[status(thm)],[c_102,c_1537]) ).
tcf(c_12589,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,X0)),compose(compose(compose(a,b),g),X0)),compose(compose(compose(a,b),g),X0)) = compose(compose(compose(a,b),g),X0),
inference(superposition,[status(thm)],[c_425,c_1537]) ).
tcf(c_12590,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,X0)),compose(compose(compose(h,compose(a,b)),g),X0)),compose(compose(compose(h,compose(a,b)),g),X0)) = compose(compose(compose(h,compose(a,b)),g),X0),
inference(superposition,[status(thm)],[c_2217,c_1537]) ).
tcf(c_12604,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(g,a)),compose(compose(X0,g),a)) = compose(compose(X0,g),a),
inference(superposition,[status(thm)],[c_1537,c_64]) ).
tcf(c_12611,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(g,a)),compose(compose(domain(X0),g),a)) = compose(compose(domain(X0),g),a),
inference(superposition,[status(thm)],[c_65,c_12604]) ).
tcf(c_12612,plain,
ifeq(domain(b),domain(h),compose(a,compose(g,a)),compose(compose(a,g),a)) = compose(compose(a,g),a),
inference(superposition,[status(thm)],[c_72,c_12604]) ).
tcf(c_12613,plain,
ifeq(domain(a),domain(h),compose(h,compose(g,a)),compose(compose(h,g),a)) = compose(compose(h,g),a),
inference(superposition,[status(thm)],[c_167,c_12604]) ).
tcf(c_12614,plain,
ifeq(domain(a),domain(h),compose(g,compose(g,a)),compose(compose(g,g),a)) = compose(compose(g,g),a),
inference(superposition,[status(thm)],[c_170,c_12604]) ).
tcf(c_12615,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,a)),compose(compose(codomain(X0),g),a)) = compose(compose(codomain(X0),g),a),
inference(superposition,[status(thm)],[c_102,c_12604]) ).
tcf(c_12616,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,a)),compose(compose(compose(a,b),g),a)) = compose(compose(compose(a,b),g),a),
inference(superposition,[status(thm)],[c_425,c_12604]) ).
tcf(c_12617,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(compose(h,compose(a,b)),g),a)) = compose(compose(compose(h,compose(a,b)),g),a),
inference(superposition,[status(thm)],[c_2217,c_12604]) ).
tcf(c_12618,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,a)),compose(compose(compose(h,a),g),a)) = compose(compose(compose(h,a),g),a),
inference(superposition,[status(thm)],[c_485,c_12604]) ).
tcf(c_12619,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,a)),compose(compose(compose(g,a),g),a)) = compose(compose(compose(g,a),g),a),
inference(superposition,[status(thm)],[c_571,c_12604]) ).
tcf(c_12816,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,g),compose(compose(X0,domain(h)),g)) = compose(compose(X0,domain(h)),g),
inference(demodulation,[status(thm)],[c_1557,c_64,c_65,c_100]) ).
tcf(c_12817,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),g),compose(compose(domain(X0),domain(h)),g)) = compose(compose(domain(X0),domain(h)),g),
inference(superposition,[status(thm)],[c_65,c_12816]) ).
tcf(c_12818,plain,
ifeq(domain(b),domain(h),compose(a,g),compose(compose(a,domain(h)),g)) = compose(compose(a,domain(h)),g),
inference(superposition,[status(thm)],[c_72,c_12816]) ).
tcf(c_12819,plain,
ifeq(domain(a),domain(h),compose(h,g),compose(compose(h,domain(h)),g)) = compose(compose(h,domain(h)),g),
inference(superposition,[status(thm)],[c_167,c_12816]) ).
tcf(c_12820,plain,
ifeq(domain(a),domain(h),compose(g,g),compose(compose(g,domain(h)),g)) = compose(compose(g,domain(h)),g),
inference(superposition,[status(thm)],[c_170,c_12816]) ).
tcf(c_12821,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),g),compose(compose(codomain(X0),domain(h)),g)) = compose(compose(codomain(X0),domain(h)),g),
inference(superposition,[status(thm)],[c_102,c_12816]) ).
tcf(c_12822,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),g),compose(compose(compose(a,b),domain(h)),g)) = compose(compose(compose(a,b),domain(h)),g),
inference(superposition,[status(thm)],[c_425,c_12816]) ).
tcf(c_12823,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),g),compose(compose(compose(h,compose(a,b)),domain(h)),g)) = compose(compose(compose(h,compose(a,b)),domain(h)),g),
inference(superposition,[status(thm)],[c_2217,c_12816]) ).
tcf(c_12824,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),g),compose(compose(compose(h,a),domain(h)),g)) = compose(compose(compose(h,a),domain(h)),g),
inference(superposition,[status(thm)],[c_485,c_12816]) ).
tcf(c_12825,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),g),compose(compose(compose(g,a),domain(h)),g)) = compose(compose(compose(g,a),domain(h)),g),
inference(superposition,[status(thm)],[c_571,c_12816]) ).
tcf(c_12921,plain,
ifeq(compose(domain(a),b),compose(h,compose(a,b)),domain(a),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_8202,c_64]) ).
tcf(c_12986,plain,
ifeq(compose(domain(a),b),compose(h,compose(a,b)),domain(a),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_8203,c_64]) ).
tcf(c_12989,plain,
ifeq(compose(h,compose(a,b)),compose(domain(a),b),domain(a),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_8353,c_64]) ).
tcf(c_12990,plain,
ifeq(compose(h,compose(a,b)),compose(domain(a),b),domain(a),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_8354,c_64]) ).
tcf(c_13158,plain,
! [X0: $i] : ifeq(compose(compose(h,a),a),X0,ifeq(compose(g,a),X0,g,compose(h,a)),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_1566,c_64]) ).
tcf(c_13561,plain,
! [X0: $i] : ifeq(compose(compose(g,a),a),X0,ifeq(compose(g,a),X0,g,compose(g,a)),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_1567,c_64]) ).
tcf(c_13696,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(a,compose(g,a))),compose(compose(X0,a),compose(g,a))),compose(compose(X0,a),compose(g,a))) = compose(compose(X0,a),compose(g,a)),
inference(superposition,[status(thm)],[c_72,c_1718]) ).
tcf(c_13704,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,compose(g,a))),compose(compose(domain(X1),X0),compose(g,a))),compose(compose(domain(X1),X0),compose(g,a))) = compose(compose(domain(X1),X0),compose(g,a)),
inference(superposition,[status(thm)],[c_65,c_1718]) ).
tcf(c_13705,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(X0,compose(g,a))),compose(compose(a,X0),compose(g,a))),compose(compose(a,X0),compose(g,a))) = compose(compose(a,X0),compose(g,a)),
inference(superposition,[status(thm)],[c_72,c_1718]) ).
tcf(c_13708,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,compose(g,a))),compose(compose(codomain(X1),X0),compose(g,a))),compose(compose(codomain(X1),X0),compose(g,a))) = compose(compose(codomain(X1),X0),compose(g,a)),
inference(superposition,[status(thm)],[c_102,c_1718]) ).
tcf(c_13709,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,compose(g,a))),compose(compose(compose(a,b),X0),compose(g,a))),compose(compose(compose(a,b),X0),compose(g,a))) = compose(compose(compose(a,b),X0),compose(g,a)),
inference(superposition,[status(thm)],[c_425,c_1718]) ).
tcf(c_13710,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,compose(g,a))),compose(compose(compose(h,compose(a,b)),X0),compose(g,a))),compose(compose(compose(h,compose(a,b)),X0),compose(g,a))) = compose(compose(compose(h,compose(a,b)),X0),compose(g,a)),
inference(superposition,[status(thm)],[c_2217,c_1718]) ).
tcf(c_13713,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(h),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),compose(g,a))),compose(compose(X1,codomain(X0)),compose(g,a))),compose(compose(X1,codomain(X0)),compose(g,a))) = compose(compose(X1,codomain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_66,c_1718]) ).
tcf(c_13714,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(g,a))),compose(compose(X0,compose(a,b)),compose(g,a))),compose(compose(X0,compose(a,b)),compose(g,a))) = compose(compose(X0,compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_171,c_1718]) ).
tcf(c_13715,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),compose(g,a))),compose(compose(X1,domain(X0)),compose(g,a))),compose(compose(X1,domain(X0)),compose(g,a))) = compose(compose(X1,domain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_100,c_1718]) ).
tcf(c_13717,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(X0,compose(h,compose(a,b))),compose(g,a))),compose(compose(X0,compose(h,compose(a,b))),compose(g,a))) = compose(compose(X0,compose(h,compose(a,b))),compose(g,a)),
inference(superposition,[status(thm)],[c_1392,c_1718]) ).
tcf(c_13718,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),compose(g,a))),compose(compose(X0,compose(g,a)),compose(g,a))),compose(compose(X0,compose(g,a)),compose(g,a))) = compose(compose(X0,compose(g,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_1718]) ).
tcf(c_13771,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),compose(g,a))),compose(compose(X1,domain(X0)),compose(g,a))),compose(compose(X1,domain(X0)),compose(g,a))) = compose(compose(X1,domain(X0)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_13715,c_65]) ).
tcf(c_13772,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),compose(g,a))),compose(compose(X1,codomain(X0)),compose(g,a))),compose(compose(X1,codomain(X0)),compose(g,a))) = compose(compose(X1,codomain(X0)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_13713,c_102]) ).
tcf(c_13784,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),compose(g,a))),compose(compose(X0,compose(g,a)),compose(g,a))),compose(compose(X0,compose(g,a)),compose(g,a))) = compose(compose(X0,compose(g,a)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_13718,c_571]) ).
tcf(c_13785,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(g,a))),compose(compose(X0,compose(a,b)),compose(g,a))),compose(compose(X0,compose(a,b)),compose(g,a))) = compose(compose(X0,compose(a,b)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_13714,c_425]) ).
tcf(c_13793,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(X0,compose(h,compose(a,b))),compose(g,a))),compose(compose(X0,compose(h,compose(a,b))),compose(g,a))) = compose(compose(X0,compose(h,compose(a,b))),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_13717,c_2217]) ).
tcf(c_13803,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(domain(X0),a),compose(h,compose(a,b)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_2217,c_6334]) ).
tcf(c_13806,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,a),compose(domain(b),a),X0,domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_64,c_6334]) ).
tcf(c_13858,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),a),compose(domain(b),a),domain(X0),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_65,c_13806]) ).
tcf(c_13859,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,a),compose(domain(b),a),a,domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_72,c_13806]) ).
tcf(c_13862,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),a),compose(domain(b),a),codomain(X0),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_102,c_13806]) ).
tcf(c_13863,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),a),compose(domain(b),a),compose(a,b),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_425,c_13806]) ).
tcf(c_13864,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),a),compose(domain(b),a),compose(h,compose(a,b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_2217,c_13806]) ).
tcf(c_13865,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),compose(domain(b),a),compose(h,a),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_13806]) ).
tcf(c_13866,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),compose(domain(b),a),compose(g,a),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_571,c_13806]) ).
tcf(c_13931,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(g,a),codomain(X0))),compose(compose(X1,compose(g,a)),codomain(X0))),compose(compose(X1,compose(g,a)),codomain(X0))) = compose(compose(X1,compose(g,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_1737]) ).
tcf(c_13932,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),compose(a,b))),compose(compose(X0,compose(g,a)),compose(a,b))),compose(compose(X0,compose(g,a)),compose(a,b))) = compose(compose(X0,compose(g,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_1737]) ).
tcf(c_13933,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(g,a),domain(X0))),compose(compose(X1,compose(g,a)),domain(X0))),compose(compose(X1,compose(g,a)),domain(X0))) = compose(compose(X1,compose(g,a)),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_1737]) ).
tcf(c_13938,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(g,a),X0)),compose(compose(domain(X1),compose(g,a)),X0)),compose(compose(domain(X1),compose(g,a)),X0)) = compose(compose(domain(X1),compose(g,a)),X0),
inference(superposition,[status(thm)],[c_65,c_1737]) ).
tcf(c_13939,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),X0)),compose(compose(a,compose(g,a)),X0)),compose(compose(a,compose(g,a)),X0)) = compose(compose(a,compose(g,a)),X0),
inference(superposition,[status(thm)],[c_72,c_1737]) ).
tcf(c_13942,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(g,a),X0)),compose(compose(codomain(X1),compose(g,a)),X0)),compose(compose(codomain(X1),compose(g,a)),X0)) = compose(compose(codomain(X1),compose(g,a)),X0),
inference(superposition,[status(thm)],[c_102,c_1737]) ).
tcf(c_13943,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),X0)),compose(compose(compose(a,b),compose(g,a)),X0)),compose(compose(compose(a,b),compose(g,a)),X0)) = compose(compose(compose(a,b),compose(g,a)),X0),
inference(superposition,[status(thm)],[c_425,c_1737]) ).
tcf(c_13944,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),X0)),compose(compose(compose(h,compose(a,b)),compose(g,a)),X0)),compose(compose(compose(h,compose(a,b)),compose(g,a)),X0)) = compose(compose(compose(h,compose(a,b)),compose(g,a)),X0),
inference(superposition,[status(thm)],[c_2217,c_1737]) ).
tcf(c_13957,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),b)),compose(compose(X0,compose(g,a)),b)) = compose(compose(X0,compose(g,a)),b),
inference(superposition,[status(thm)],[c_1737,c_64]) ).
tcf(c_13958,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(g,a)),b)) = compose(compose(X0,compose(g,a)),b),
inference(light_normalisation,[status(thm)],[c_13957,c_4514]) ).
tcf(c_13972,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(g,a)),b)) = compose(compose(domain(X0),compose(g,a)),b),
inference(superposition,[status(thm)],[c_65,c_13958]) ).
tcf(c_13973,plain,
ifeq(domain(b),domain(h),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(g,a)),b)) = compose(compose(a,compose(g,a)),b),
inference(superposition,[status(thm)],[c_72,c_13958]) ).
tcf(c_13974,plain,
ifeq(domain(a),domain(h),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(g,a)),b)) = compose(compose(h,compose(g,a)),b),
inference(superposition,[status(thm)],[c_167,c_13958]) ).
tcf(c_13975,plain,
ifeq(domain(a),domain(h),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(g,a)),b)) = compose(compose(g,compose(g,a)),b),
inference(superposition,[status(thm)],[c_170,c_13958]) ).
tcf(c_13976,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(g,a)),b)) = compose(compose(codomain(X0),compose(g,a)),b),
inference(superposition,[status(thm)],[c_102,c_13958]) ).
tcf(c_13977,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),compose(g,a)),b)) = compose(compose(compose(a,b),compose(g,a)),b),
inference(superposition,[status(thm)],[c_425,c_13958]) ).
tcf(c_13978,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(g,a)),b)) = compose(compose(compose(h,compose(a,b)),compose(g,a)),b),
inference(superposition,[status(thm)],[c_2217,c_13958]) ).
tcf(c_13979,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(compose(h,a),compose(g,a)),b)) = compose(compose(compose(h,a),compose(g,a)),b),
inference(superposition,[status(thm)],[c_485,c_13958]) ).
tcf(c_13980,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),compose(g,a)),b)) = compose(compose(compose(g,a),compose(g,a)),b),
inference(superposition,[status(thm)],[c_571,c_13958]) ).
tcf(c_13996,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_2217,c_6484]) ).
tcf(c_13999,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(domain(b),a),compose(X0,a),X0,domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_64,c_6484]) ).
tcf(c_14046,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(domain(b),a),compose(domain(X0),a),domain(X0),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_65,c_13999]) ).
tcf(c_14047,plain,
ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),compose(a,a),a,domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_72,c_13999]) ).
tcf(c_14050,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(domain(b),a),compose(codomain(X0),a),codomain(X0),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_102,c_13999]) ).
tcf(c_14051,plain,
ifeq(codomain(b),domain(a),ifeq(compose(domain(b),a),compose(compose(a,b),a),compose(a,b),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_425,c_13999]) ).
tcf(c_14052,plain,
ifeq(codomain(b),domain(a),ifeq(compose(domain(b),a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_2217,c_13999]) ).
tcf(c_14053,plain,
ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),compose(compose(h,a),a),compose(h,a),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_13999]) ).
tcf(c_14054,plain,
ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),compose(compose(g,a),a),compose(g,a),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_571,c_13999]) ).
tcf(c_14125,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(domain(X0),b),compose(h,compose(a,b)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_2217,c_6516]) ).
tcf(c_14188,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_2217,c_6557]) ).
tcf(c_14245,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(g,a)),compose(compose(X0,domain(h)),compose(g,a))) = compose(compose(X0,domain(h)),compose(g,a)),
inference(demodulation,[status(thm)],[c_1759,c_64,c_65,c_100]) ).
tcf(c_14246,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(g,a)),compose(compose(domain(X0),domain(h)),compose(g,a))) = compose(compose(domain(X0),domain(h)),compose(g,a)),
inference(superposition,[status(thm)],[c_65,c_14245]) ).
tcf(c_14247,plain,
ifeq(domain(b),domain(h),compose(a,compose(g,a)),compose(compose(a,domain(h)),compose(g,a))) = compose(compose(a,domain(h)),compose(g,a)),
inference(superposition,[status(thm)],[c_72,c_14245]) ).
tcf(c_14248,plain,
ifeq(domain(a),domain(h),compose(h,compose(g,a)),compose(compose(h,domain(h)),compose(g,a))) = compose(compose(h,domain(h)),compose(g,a)),
inference(superposition,[status(thm)],[c_167,c_14245]) ).
tcf(c_14249,plain,
ifeq(domain(a),domain(h),compose(g,compose(g,a)),compose(compose(g,domain(h)),compose(g,a))) = compose(compose(g,domain(h)),compose(g,a)),
inference(superposition,[status(thm)],[c_170,c_14245]) ).
tcf(c_14250,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,a)),compose(compose(codomain(X0),domain(h)),compose(g,a))) = compose(compose(codomain(X0),domain(h)),compose(g,a)),
inference(superposition,[status(thm)],[c_102,c_14245]) ).
tcf(c_14251,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,a)),compose(compose(compose(a,b),domain(h)),compose(g,a))) = compose(compose(compose(a,b),domain(h)),compose(g,a)),
inference(superposition,[status(thm)],[c_425,c_14245]) ).
tcf(c_14252,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a)),
inference(superposition,[status(thm)],[c_2217,c_14245]) ).
tcf(c_14253,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,a)),compose(compose(compose(h,a),domain(h)),compose(g,a))) = compose(compose(compose(h,a),domain(h)),compose(g,a)),
inference(superposition,[status(thm)],[c_485,c_14245]) ).
tcf(c_14254,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,a)),compose(compose(compose(g,a),domain(h)),compose(g,a))) = compose(compose(compose(g,a),domain(h)),compose(g,a)),
inference(superposition,[status(thm)],[c_571,c_14245]) ).
tcf(c_14457,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(codomain(X0),a),compose(h,compose(a,b)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_2217,c_6338]) ).
tcf(c_14523,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_2217,c_6488]) ).
tcf(c_14585,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(codomain(X0),b),compose(h,compose(a,b)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_2217,c_6520]) ).
tcf(c_14653,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_2217,c_6561]) ).
tcf(c_14949,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),a),X2,ifeq(compose(domain(X0),a),X2,domain(X0),domain(X1)),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_229]) ).
tcf(c_14953,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),a),X2,ifeq(compose(domain(X0),a),X2,domain(X0),codomain(X1)),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_229]) ).
tcf(c_14954,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_229]) ).
tcf(c_14955,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_229]) ).
tcf(c_14992,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),a),X2,ifeq(compose(codomain(X0),a),X2,codomain(X0),domain(X1)),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_233]) ).
tcf(c_14996,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),a),X2,ifeq(compose(codomain(X0),a),X2,codomain(X0),codomain(X1)),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_233]) ).
tcf(c_14997,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_233]) ).
tcf(c_14998,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_233]) ).
tcf(c_15031,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),b),X2,ifeq(compose(domain(X0),b),X2,domain(X0),domain(X1)),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_243]) ).
tcf(c_15035,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),b),X2,ifeq(compose(domain(X0),b),X2,domain(X0),codomain(X1)),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_243]) ).
tcf(c_15036,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X1,ifeq(compose(domain(X0),b),X1,domain(X0),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_243]) ).
tcf(c_15037,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X1,ifeq(compose(domain(X0),b),X1,domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_243]) ).
tcf(c_15065,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(domain(a),b),X1,domain(a),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_243,c_64]) ).
tcf(c_15077,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(domain(a),b),X1,domain(a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_15065]) ).
tcf(c_15079,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(domain(a),b),X0,domain(a),h),h),h) = h,
inference(superposition,[status(thm)],[c_167,c_15065]) ).
tcf(c_15080,plain,
! [X0: $i] : ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(domain(a),b),X0,domain(a),g),g),g) = g,
inference(superposition,[status(thm)],[c_170,c_15065]) ).
tcf(c_15081,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(domain(a),b),X1,domain(a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_15065]) ).
tcf(c_15082,plain,
! [X0: $i] : ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_15065]) ).
tcf(c_15083,plain,
! [X0: $i] : ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_15065]) ).
tcf(c_15084,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_15065]) ).
tcf(c_15085,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_15065]) ).
tcf(c_15088,plain,
! [X0: $i] : ifeq(codomain(domain(b)),domain(b),ifeq(b,X0,ifeq(compose(domain(a),b),X0,domain(a),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_67,c_15065]) ).
tcf(c_15099,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_15085,c_4514]) ).
tcf(c_15100,plain,
! [X0: $i] : ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_15084,c_6074]) ).
tcf(c_15115,plain,
! [X0: $i] : ifeq(b,X0,ifeq(compose(domain(a),b),X0,domain(a),domain(b)),domain(b)) = domain(b),
inference(demodulation,[status(thm)],[c_15088,c_64,c_65]) ).
tcf(c_15222,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),b),X2,ifeq(compose(codomain(X0),b),X2,codomain(X0),domain(X1)),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
inference(superposition,[status(thm)],[c_65,c_247]) ).
tcf(c_15226,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),b),X2,ifeq(compose(codomain(X0),b),X2,codomain(X0),codomain(X1)),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_102,c_247]) ).
tcf(c_15227,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_247]) ).
tcf(c_15228,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_247]) ).
tcf(c_16859,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_9333]) ).
tcf(c_16879,plain,
ifeq(codomain(b),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_16859,c_2217]) ).
tcf(c_16898,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(b,X0,ifeq(b,X0,domain(b),domain(b)),domain(b)),domain(b)) = domain(b),
inference(demodulation,[status(thm)],[c_11843,c_64,c_65]) ).
tcf(c_16986,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_10074]) ).
tcf(c_17013,plain,
! [X0: $i] : ifeq(compose(compose(h,a),a),X0,ifeq(a,X0,domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_11540,c_64]) ).
tcf(c_17020,plain,
! [X0: $i] : ifeq(compose(compose(g,a),a),X0,ifeq(a,X0,domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_11541,c_64]) ).
tcf(c_17262,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(a,X1,ifeq(compose(X0,a),X1,X0,domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_240,c_65]) ).
tcf(c_17263,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(a,X1,ifeq(compose(domain(X0),a),X1,domain(X0),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_65,c_17262]) ).
tcf(c_17264,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(a,a),X0,a,domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_72,c_17262]) ).
tcf(c_17267,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(a,X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_102,c_17262]) ).
tcf(c_17268,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_425,c_17262]) ).
tcf(c_17269,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_2217,c_17262]) ).
tcf(c_17270,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_485,c_17262]) ).
tcf(c_17271,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_571,c_17262]) ).
tcf(c_17284,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(b,X1,ifeq(compose(X0,b),X1,X0,domain(b)),domain(b)),domain(b)) = domain(b),
inference(demodulation,[status(thm)],[c_254,c_64,c_65]) ).
tcf(c_17285,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(b,X1,ifeq(compose(domain(X0),b),X1,domain(X0),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_65,c_17284]) ).
tcf(c_17286,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(b,X0,ifeq(compose(a,b),X0,a,domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_72,c_17284]) ).
tcf(c_17289,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(b,X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_102,c_17284]) ).
tcf(c_17290,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(b,X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_425,c_17284]) ).
tcf(c_17291,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(b,X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_2217,c_17284]) ).
tcf(c_17292,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(b,X0,ifeq(compose(compose(h,a),b),X0,compose(h,a),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_17284]) ).
tcf(c_17293,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(b,X0,ifeq(compose(compose(g,a),b),X0,compose(g,a),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_571,c_17284]) ).
tcf(c_17309,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(b,X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),domain(b)),domain(b)),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_17293,c_4514]) ).
tcf(c_17310,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(b,X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),domain(b)),domain(b)),domain(b)) = domain(b),
inference(light_normalisation,[status(thm)],[c_17292,c_6074]) ).
tcf(c_17390,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(a,codomain(X0))),compose(compose(X1,a),codomain(X0))),compose(compose(X1,a),codomain(X0))) = compose(compose(X1,a),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_258]) ).
tcf(c_17391,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(a,compose(a,b))),compose(compose(X0,a),compose(a,b))),compose(compose(X0,a),compose(a,b))) = compose(compose(X0,a),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_258]) ).
tcf(c_17392,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(a,domain(X0))),compose(compose(X1,a),domain(X0))),compose(compose(X1,a),domain(X0))) = compose(compose(X1,a),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_258]) ).
tcf(c_17397,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(a,X0)),compose(compose(domain(X1),a),X0)),compose(compose(domain(X1),a),X0)) = compose(compose(domain(X1),a),X0),
inference(superposition,[status(thm)],[c_65,c_258]) ).
tcf(c_17398,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(a),compose(a,compose(a,X0)),compose(compose(a,a),X0)),compose(compose(a,a),X0)) = compose(compose(a,a),X0),
inference(superposition,[status(thm)],[c_72,c_258]) ).
tcf(c_17401,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(a,X0)),compose(compose(codomain(X1),a),X0)),compose(compose(codomain(X1),a),X0)) = compose(compose(codomain(X1),a),X0),
inference(superposition,[status(thm)],[c_102,c_258]) ).
tcf(c_17402,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,X0)),compose(compose(compose(a,b),a),X0)),compose(compose(compose(a,b),a),X0)) = compose(compose(compose(a,b),a),X0),
inference(superposition,[status(thm)],[c_425,c_258]) ).
tcf(c_17403,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,X0)),compose(compose(compose(h,compose(a,b)),a),X0)),compose(compose(compose(h,compose(a,b)),a),X0)) = compose(compose(compose(h,compose(a,b)),a),X0),
inference(superposition,[status(thm)],[c_2217,c_258]) ).
tcf(c_17423,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,b)),compose(compose(X0,a),b)) = compose(compose(X0,a),b),
inference(superposition,[status(thm)],[c_258,c_64]) ).
tcf(c_17431,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),a),b)) = compose(compose(domain(X0),a),b),
inference(superposition,[status(thm)],[c_65,c_17423]) ).
tcf(c_17432,plain,
ifeq(domain(b),domain(a),compose(a,compose(a,b)),compose(compose(a,a),b)) = compose(compose(a,a),b),
inference(superposition,[status(thm)],[c_72,c_17423]) ).
tcf(c_17435,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),a),b)) = compose(compose(codomain(X0),a),b),
inference(superposition,[status(thm)],[c_102,c_17423]) ).
tcf(c_17436,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,b)),compose(compose(compose(a,b),a),b)) = compose(compose(compose(a,b),a),b),
inference(superposition,[status(thm)],[c_425,c_17423]) ).
tcf(c_17437,plain,
ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,b)),compose(compose(compose(h,compose(a,b)),a),b)) = compose(compose(compose(h,compose(a,b)),a),b),
inference(superposition,[status(thm)],[c_2217,c_17423]) ).
tcf(c_17438,plain,
ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,b)),compose(compose(compose(h,a),a),b)) = compose(compose(compose(h,a),a),b),
inference(superposition,[status(thm)],[c_485,c_17423]) ).
tcf(c_17439,plain,
ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,b)),compose(compose(compose(g,a),a),b)) = compose(compose(compose(g,a),a),b),
inference(superposition,[status(thm)],[c_571,c_17423]) ).
tcf(c_17529,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(domain(b),domain(X0),compose(a,compose(X0,codomain(X1))),compose(compose(a,X0),codomain(X1))),compose(compose(a,X0),codomain(X1))) = compose(compose(a,X0),codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_266]) ).
tcf(c_17530,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(X0),compose(a,compose(X0,compose(a,b))),compose(compose(a,X0),compose(a,b))),compose(compose(a,X0),compose(a,b))) = compose(compose(a,X0),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_266]) ).
tcf(c_17531,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(a,compose(X0,domain(X1))),compose(compose(a,X0),domain(X1))),compose(compose(a,X0),domain(X1))) = compose(compose(a,X0),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_266]) ).
tcf(c_17536,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(a,compose(b,X0)),compose(compose(a,b),X0)) = compose(compose(a,b),X0),
inference(superposition,[status(thm)],[c_64,c_266]) ).
tcf(c_17539,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),X1)),compose(compose(a,codomain(X0)),X1)),compose(compose(a,codomain(X0)),X1)) = compose(compose(a,codomain(X0)),X1),
inference(superposition,[status(thm)],[c_66,c_266]) ).
tcf(c_17540,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),X0)),compose(compose(a,compose(a,b)),X0)),compose(compose(a,compose(a,b)),X0)) = compose(compose(a,compose(a,b)),X0),
inference(superposition,[status(thm)],[c_171,c_266]) ).
tcf(c_17541,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),X1)),compose(compose(a,domain(X0)),X1)),compose(compose(a,domain(X0)),X1)) = compose(compose(a,domain(X0)),X1),
inference(superposition,[status(thm)],[c_100,c_266]) ).
tcf(c_17543,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),X0)),compose(compose(a,compose(h,compose(a,b))),X0)),compose(compose(a,compose(h,compose(a,b))),X0)) = compose(compose(a,compose(h,compose(a,b))),X0),
inference(superposition,[status(thm)],[c_1392,c_266]) ).
tcf(c_17584,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),X1)),compose(compose(a,domain(X0)),X1)),compose(compose(a,domain(X0)),X1)) = compose(compose(a,domain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_17541,c_65]) ).
tcf(c_17585,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),X1)),compose(compose(a,codomain(X0)),X1)),compose(compose(a,codomain(X0)),X1)) = compose(compose(a,codomain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_17539,c_102]) ).
tcf(c_17593,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),X0)),compose(compose(a,compose(a,b)),X0)),compose(compose(a,compose(a,b)),X0)) = compose(compose(a,compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_17540,c_425]) ).
tcf(c_17605,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),X0)),compose(compose(a,compose(h,compose(a,b))),X0)),compose(compose(a,compose(h,compose(a,b))),X0)) = compose(compose(a,compose(h,compose(a,b))),X0),
inference(light_normalisation,[status(thm)],[c_17543,c_2217]) ).
tcf(c_17610,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),compose(a,compose(b,codomain(X0))),compose(compose(a,b),codomain(X0))) = compose(compose(a,b),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_17536]) ).
tcf(c_17611,plain,
ifeq(codomain(b),domain(a),compose(a,compose(b,compose(a,b))),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_17536]) ).
tcf(c_17612,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(a,compose(b,domain(X0))),compose(compose(a,b),domain(X0))) = compose(compose(a,b),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_17536]) ).
tcf(c_17613,plain,
ifeq(codomain(b),domain(h),compose(a,compose(b,g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
inference(superposition,[status(thm)],[c_1480,c_17536]) ).
tcf(c_17614,plain,
ifeq(codomain(b),domain(h),compose(a,compose(b,compose(h,compose(a,b)))),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17536]) ).
tcf(c_17615,plain,
ifeq(codomain(b),domain(h),compose(a,compose(b,compose(g,a))),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17536]) ).
tcf(c_17616,plain,
ifeq(codomain(b),domain(h),compose(a,compose(b,compose(h,a))),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17536]) ).
tcf(c_17660,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(compose(X1,X0)),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,codomain(compose(X1,X0)))),compose(X1,X0)),compose(X1,X0)) = compose(X1,X0),
inference(demodulation,[status(thm)],[c_295,c_66]) ).
tcf(c_17662,plain,
! [X0: $i] : ifeq(domain(b),codomain(compose(X0,a)),ifeq(codomain(X0),domain(a),compose(X0,compose(a,codomain(compose(X0,a)))),compose(X0,a)),compose(X0,a)) = compose(X0,a),
inference(superposition,[status(thm)],[c_72,c_17660]) ).
tcf(c_17663,plain,
! [X0: $i] : ifeq(domain(a),codomain(compose(X0,h)),ifeq(codomain(X0),domain(h),compose(X0,compose(h,codomain(compose(X0,h)))),compose(X0,h)),compose(X0,h)) = compose(X0,h),
inference(superposition,[status(thm)],[c_167,c_17660]) ).
tcf(c_17693,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(compose(domain(X1),X0)),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,codomain(compose(domain(X1),X0)))),compose(domain(X1),X0)),compose(domain(X1),X0)) = compose(domain(X1),X0),
inference(superposition,[status(thm)],[c_65,c_17660]) ).
tcf(c_17694,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(a,X0)),ifeq(domain(b),domain(X0),compose(a,compose(X0,codomain(compose(a,X0)))),compose(a,X0)),compose(a,X0)) = compose(a,X0),
inference(superposition,[status(thm)],[c_72,c_17660]) ).
tcf(c_17695,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(h,X0)),ifeq(domain(a),domain(X0),compose(h,compose(X0,codomain(compose(h,X0)))),compose(h,X0)),compose(h,X0)) = compose(h,X0),
inference(superposition,[status(thm)],[c_167,c_17660]) ).
tcf(c_17696,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(g,X0)),ifeq(domain(a),domain(X0),compose(g,compose(X0,codomain(compose(g,X0)))),compose(g,X0)),compose(g,X0)) = compose(g,X0),
inference(superposition,[status(thm)],[c_170,c_17660]) ).
tcf(c_17697,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(compose(codomain(X1),X0)),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,codomain(compose(codomain(X1),X0)))),compose(codomain(X1),X0)),compose(codomain(X1),X0)) = compose(codomain(X1),X0),
inference(superposition,[status(thm)],[c_102,c_17660]) ).
tcf(c_17698,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(compose(a,b),X0)),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,codomain(compose(compose(a,b),X0)))),compose(compose(a,b),X0)),compose(compose(a,b),X0)) = compose(compose(a,b),X0),
inference(superposition,[status(thm)],[c_425,c_17660]) ).
tcf(c_17699,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(compose(h,compose(a,b)),X0)),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,codomain(compose(compose(h,compose(a,b)),X0)))),compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
inference(superposition,[status(thm)],[c_2217,c_17660]) ).
tcf(c_17700,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(compose(h,a),X0)),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,codomain(compose(compose(h,a),X0)))),compose(compose(h,a),X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
inference(superposition,[status(thm)],[c_485,c_17660]) ).
tcf(c_17701,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(compose(g,a),X0)),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,codomain(compose(compose(g,a),X0)))),compose(compose(g,a),X0)),compose(compose(g,a),X0)) = compose(compose(g,a),X0),
inference(superposition,[status(thm)],[c_571,c_17660]) ).
tcf(c_17702,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),codomain(compose(X1,codomain(X0))),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),codomain(compose(X1,codomain(X0))))),compose(X1,codomain(X0))),compose(X1,codomain(X0))) = compose(X1,codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_17660]) ).
tcf(c_17703,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(compose(X0,compose(a,b))),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),codomain(compose(X0,compose(a,b))))),compose(X0,compose(a,b))),compose(X0,compose(a,b))) = compose(X0,compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_17660]) ).
tcf(c_17704,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(compose(X1,domain(X0))),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),codomain(compose(X1,domain(X0))))),compose(X1,domain(X0))),compose(X1,domain(X0))) = compose(X1,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_17660]) ).
tcf(c_17705,plain,
! [X0: $i] : ifeq(codomain(g),codomain(compose(X0,g)),ifeq(codomain(X0),domain(h),compose(X0,compose(g,codomain(compose(X0,g)))),compose(X0,g)),compose(X0,g)) = compose(X0,g),
inference(superposition,[status(thm)],[c_1480,c_17660]) ).
tcf(c_17706,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),codomain(compose(X0,compose(h,compose(a,b)))),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),codomain(compose(X0,compose(h,compose(a,b)))))),compose(X0,compose(h,compose(a,b)))),compose(X0,compose(h,compose(a,b)))) = compose(X0,compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17660]) ).
tcf(c_17707,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),codomain(compose(X0,compose(g,a))),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),codomain(compose(X0,compose(g,a))))),compose(X0,compose(g,a))),compose(X0,compose(g,a))) = compose(X0,compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17660]) ).
tcf(c_17708,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),codomain(compose(X0,compose(h,a))),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),codomain(compose(X0,compose(h,a))))),compose(X0,compose(h,a))),compose(X0,compose(h,a))) = compose(X0,compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17660]) ).
tcf(c_17781,plain,
! [X0: $i] : ifeq(domain(a),codomain(compose(X0,g)),ifeq(codomain(X0),domain(h),compose(X0,compose(g,codomain(compose(X0,g)))),compose(X0,g)),compose(X0,g)) = compose(X0,g),
inference(light_normalisation,[status(thm)],[c_17705,c_170]) ).
tcf(c_17786,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(compose(X1,domain(X0))),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),codomain(compose(X1,domain(X0))))),compose(X1,domain(X0))),compose(X1,domain(X0))) = compose(X1,domain(X0)),
inference(light_normalisation,[status(thm)],[c_17704,c_65]) ).
tcf(c_17787,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(compose(X1,codomain(X0))),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),codomain(compose(X1,codomain(X0))))),compose(X1,codomain(X0))),compose(X1,codomain(X0))) = compose(X1,codomain(X0)),
inference(light_normalisation,[status(thm)],[c_17702,c_102]) ).
tcf(c_17796,plain,
! [X0: $i] : ifeq(domain(b),codomain(compose(X0,compose(h,a))),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),codomain(compose(X0,compose(h,a))))),compose(X0,compose(h,a))),compose(X0,compose(h,a))) = compose(X0,compose(h,a)),
inference(light_normalisation,[status(thm)],[c_17708,c_485]) ).
tcf(c_17797,plain,
! [X0: $i] : ifeq(domain(b),codomain(compose(X0,compose(g,a))),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),codomain(compose(X0,compose(g,a))))),compose(X0,compose(g,a))),compose(X0,compose(g,a))) = compose(X0,compose(g,a)),
inference(light_normalisation,[status(thm)],[c_17707,c_571]) ).
tcf(c_17798,plain,
! [X0: $i] : ifeq(codomain(b),codomain(compose(X0,compose(a,b))),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),codomain(compose(X0,compose(a,b))))),compose(X0,compose(a,b))),compose(X0,compose(a,b))) = compose(X0,compose(a,b)),
inference(light_normalisation,[status(thm)],[c_17703,c_425]) ).
tcf(c_17805,plain,
! [X0: $i] : ifeq(codomain(b),codomain(compose(X0,compose(h,compose(a,b)))),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),codomain(compose(X0,compose(h,compose(a,b)))))),compose(X0,compose(h,compose(a,b)))),compose(X0,compose(h,compose(a,b)))) = compose(X0,compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_17706,c_2217]) ).
tcf(c_17849,plain,
! [X0: $i] : ifeq(domain(b),codomain(compose(domain(X0),a)),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,codomain(compose(domain(X0),a)))),compose(domain(X0),a)),compose(domain(X0),a)) = compose(domain(X0),a),
inference(superposition,[status(thm)],[c_65,c_17662]) ).
tcf(c_17850,plain,
ifeq(domain(b),codomain(compose(a,a)),ifeq(domain(b),domain(a),compose(a,compose(a,codomain(compose(a,a)))),compose(a,a)),compose(a,a)) = compose(a,a),
inference(superposition,[status(thm)],[c_72,c_17662]) ).
tcf(c_17853,plain,
! [X0: $i] : ifeq(domain(b),codomain(compose(codomain(X0),a)),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,codomain(compose(codomain(X0),a)))),compose(codomain(X0),a)),compose(codomain(X0),a)) = compose(codomain(X0),a),
inference(superposition,[status(thm)],[c_102,c_17662]) ).
tcf(c_17854,plain,
ifeq(domain(b),codomain(compose(compose(a,b),a)),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,codomain(compose(compose(a,b),a)))),compose(compose(a,b),a)),compose(compose(a,b),a)) = compose(compose(a,b),a),
inference(superposition,[status(thm)],[c_425,c_17662]) ).
tcf(c_17855,plain,
ifeq(domain(b),codomain(compose(compose(h,compose(a,b)),a)),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,codomain(compose(compose(h,compose(a,b)),a)))),compose(compose(h,compose(a,b)),a)),compose(compose(h,compose(a,b)),a)) = compose(compose(h,compose(a,b)),a),
inference(superposition,[status(thm)],[c_2217,c_17662]) ).
tcf(c_17856,plain,
ifeq(domain(b),codomain(compose(compose(h,a),a)),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,codomain(compose(compose(h,a),a)))),compose(compose(h,a),a)),compose(compose(h,a),a)) = compose(compose(h,a),a),
inference(superposition,[status(thm)],[c_485,c_17662]) ).
tcf(c_17857,plain,
ifeq(domain(b),codomain(compose(compose(g,a),a)),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,codomain(compose(compose(g,a),a)))),compose(compose(g,a),a)),compose(compose(g,a),a)) = compose(compose(g,a),a),
inference(superposition,[status(thm)],[c_571,c_17662]) ).
tcf(c_17871,plain,
ifeq(domain(a),codomain(compose(a,h)),ifeq(domain(b),domain(h),compose(a,compose(h,codomain(compose(a,h)))),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_167,c_17694]) ).
tcf(c_17882,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),codomain(compose(a,codomain(X0))),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),codomain(compose(a,codomain(X0))))),compose(a,codomain(X0))),compose(a,codomain(X0))) = compose(a,codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_17694]) ).
tcf(c_17883,plain,
ifeq(codomain(compose(a,b)),codomain(compose(a,compose(a,b))),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),codomain(compose(a,compose(a,b))))),compose(a,compose(a,b))),compose(a,compose(a,b))) = compose(a,compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_17694]) ).
tcf(c_17884,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(compose(a,domain(X0))),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),codomain(compose(a,domain(X0))))),compose(a,domain(X0))),compose(a,domain(X0))) = compose(a,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_17694]) ).
tcf(c_17885,plain,
ifeq(codomain(g),codomain(compose(a,g)),ifeq(domain(b),domain(h),compose(a,compose(g,codomain(compose(a,g)))),compose(a,g)),compose(a,g)) = compose(a,g),
inference(superposition,[status(thm)],[c_1480,c_17694]) ).
tcf(c_17886,plain,
ifeq(codomain(compose(h,compose(a,b))),codomain(compose(a,compose(h,compose(a,b)))),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),codomain(compose(a,compose(h,compose(a,b)))))),compose(a,compose(h,compose(a,b)))),compose(a,compose(h,compose(a,b)))) = compose(a,compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17694]) ).
tcf(c_17887,plain,
ifeq(codomain(compose(g,a)),codomain(compose(a,compose(g,a))),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),codomain(compose(a,compose(g,a))))),compose(a,compose(g,a))),compose(a,compose(g,a))) = compose(a,compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17694]) ).
tcf(c_17888,plain,
ifeq(codomain(compose(h,a)),codomain(compose(a,compose(h,a))),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),codomain(compose(a,compose(h,a))))),compose(a,compose(h,a))),compose(a,compose(h,a))) = compose(a,compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17694]) ).
tcf(c_17898,plain,
ifeq(domain(a),codomain(compose(a,g)),ifeq(domain(b),domain(h),compose(a,compose(g,codomain(compose(a,g)))),compose(a,g)),compose(a,g)) = compose(a,g),
inference(light_normalisation,[status(thm)],[c_17885,c_170]) ).
tcf(c_17900,plain,
! [X0: $i] : ifeq(domain(X0),codomain(compose(a,domain(X0))),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),codomain(compose(a,domain(X0))))),compose(a,domain(X0))),compose(a,domain(X0))) = compose(a,domain(X0)),
inference(light_normalisation,[status(thm)],[c_17884,c_65]) ).
tcf(c_17901,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(a,codomain(X0))),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),codomain(compose(a,codomain(X0))))),compose(a,codomain(X0))),compose(a,codomain(X0))) = compose(a,codomain(X0)),
inference(light_normalisation,[status(thm)],[c_17882,c_102]) ).
tcf(c_17904,plain,
ifeq(domain(b),codomain(compose(a,compose(h,a))),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),codomain(compose(a,compose(h,a))))),compose(a,compose(h,a))),compose(a,compose(h,a))) = compose(a,compose(h,a)),
inference(light_normalisation,[status(thm)],[c_17888,c_485]) ).
tcf(c_17905,plain,
ifeq(domain(b),codomain(compose(a,compose(g,a))),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),codomain(compose(a,compose(g,a))))),compose(a,compose(g,a))),compose(a,compose(g,a))) = compose(a,compose(g,a)),
inference(light_normalisation,[status(thm)],[c_17887,c_571]) ).
tcf(c_17906,plain,
ifeq(codomain(b),codomain(compose(a,compose(a,b))),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),codomain(compose(a,compose(a,b))))),compose(a,compose(a,b))),compose(a,compose(a,b))) = compose(a,compose(a,b)),
inference(light_normalisation,[status(thm)],[c_17883,c_425]) ).
tcf(c_17910,plain,
ifeq(codomain(b),codomain(compose(a,compose(h,compose(a,b)))),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),codomain(compose(a,compose(h,compose(a,b)))))),compose(a,compose(h,compose(a,b)))),compose(a,compose(h,compose(a,b)))) = compose(a,compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_17886,c_2217]) ).
tcf(c_17914,plain,
! [X0: $i] : ifeq(domain(a),codomain(compose(domain(X0),h)),ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,codomain(compose(domain(X0),h)))),compose(domain(X0),h)),compose(domain(X0),h)) = compose(domain(X0),h),
inference(superposition,[status(thm)],[c_65,c_17663]) ).
tcf(c_17916,plain,
ifeq(domain(a),codomain(compose(h,h)),ifeq(domain(a),domain(h),compose(h,compose(h,codomain(compose(h,h)))),compose(h,h)),compose(h,h)) = compose(h,h),
inference(superposition,[status(thm)],[c_167,c_17663]) ).
tcf(c_17917,plain,
ifeq(domain(a),codomain(compose(g,h)),ifeq(domain(a),domain(h),compose(g,compose(h,codomain(compose(g,h)))),compose(g,h)),compose(g,h)) = compose(g,h),
inference(superposition,[status(thm)],[c_170,c_17663]) ).
tcf(c_17918,plain,
! [X0: $i] : ifeq(domain(a),codomain(compose(codomain(X0),h)),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,codomain(compose(codomain(X0),h)))),compose(codomain(X0),h)),compose(codomain(X0),h)) = compose(codomain(X0),h),
inference(superposition,[status(thm)],[c_102,c_17663]) ).
tcf(c_17919,plain,
ifeq(domain(a),codomain(compose(compose(a,b),h)),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,codomain(compose(compose(a,b),h)))),compose(compose(a,b),h)),compose(compose(a,b),h)) = compose(compose(a,b),h),
inference(superposition,[status(thm)],[c_425,c_17663]) ).
tcf(c_17920,plain,
ifeq(domain(a),codomain(compose(compose(h,compose(a,b)),h)),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,codomain(compose(compose(h,compose(a,b)),h)))),compose(compose(h,compose(a,b)),h)),compose(compose(h,compose(a,b)),h)) = compose(compose(h,compose(a,b)),h),
inference(superposition,[status(thm)],[c_2217,c_17663]) ).
tcf(c_17921,plain,
ifeq(domain(a),codomain(compose(compose(h,a),h)),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,codomain(compose(compose(h,a),h)))),compose(compose(h,a),h)),compose(compose(h,a),h)) = compose(compose(h,a),h),
inference(superposition,[status(thm)],[c_485,c_17663]) ).
tcf(c_17922,plain,
ifeq(domain(a),codomain(compose(compose(g,a),h)),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,codomain(compose(compose(g,a),h)))),compose(compose(g,a),h)),compose(compose(g,a),h)) = compose(compose(g,a),h),
inference(superposition,[status(thm)],[c_571,c_17663]) ).
tcf(c_17930,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(compose(a,b),b),X1,compose(a,b),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_436]) ).
tcf(c_17934,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(compose(a,b),b),X1,compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_436]) ).
tcf(c_17935,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_436]) ).
tcf(c_17936,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_436]) ).
tcf(c_17949,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(compose(a,b),a),X1,compose(a,b),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_437]) ).
tcf(c_17953,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(compose(compose(a,b),a),X1,compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_437]) ).
tcf(c_17954,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_437]) ).
tcf(c_17955,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_437]) ).
tcf(c_17973,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(domain(b),domain(h),compose(a,compose(h,codomain(X0))),compose(compose(a,h),codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(a,h),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_3324]) ).
tcf(c_17975,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(h,domain(X0))),compose(compose(a,h),domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(a,h),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_3324]) ).
tcf(c_17976,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(h,g)),compose(compose(a,h),g)),compose(compose(a,h),g)) = compose(compose(a,h),g),
inference(superposition,[status(thm)],[c_1480,c_3324]) ).
tcf(c_17977,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(h,compose(h,compose(a,b)))),compose(compose(a,h),compose(h,compose(a,b)))),compose(compose(a,h),compose(h,compose(a,b)))) = compose(compose(a,h),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_3324]) ).
tcf(c_17978,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(h,compose(g,a))),compose(compose(a,h),compose(g,a))),compose(compose(a,h),compose(g,a))) = compose(compose(a,h),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_3324]) ).
tcf(c_17979,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(h,compose(h,a))),compose(compose(a,h),compose(h,a))),compose(compose(a,h),compose(h,a))) = compose(compose(a,h),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_3324]) ).
tcf(c_18003,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),codomain(compose(h,codomain(X0))),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),codomain(compose(h,codomain(X0))))),compose(h,codomain(X0))),compose(h,codomain(X0))) = compose(h,codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_17695]) ).
tcf(c_18005,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(compose(h,domain(X0))),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),codomain(compose(h,domain(X0))))),compose(h,domain(X0))),compose(h,domain(X0))) = compose(h,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_17695]) ).
tcf(c_18006,plain,
ifeq(codomain(g),codomain(compose(h,g)),ifeq(domain(a),domain(h),compose(h,compose(g,codomain(compose(h,g)))),compose(h,g)),compose(h,g)) = compose(h,g),
inference(superposition,[status(thm)],[c_1480,c_17695]) ).
tcf(c_18007,plain,
ifeq(codomain(compose(h,compose(a,b))),codomain(compose(h,compose(h,compose(a,b)))),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),codomain(compose(h,compose(h,compose(a,b)))))),compose(h,compose(h,compose(a,b)))),compose(h,compose(h,compose(a,b)))) = compose(h,compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17695]) ).
tcf(c_18008,plain,
ifeq(codomain(compose(g,a)),codomain(compose(h,compose(g,a))),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),codomain(compose(h,compose(g,a))))),compose(h,compose(g,a))),compose(h,compose(g,a))) = compose(h,compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17695]) ).
tcf(c_18009,plain,
ifeq(codomain(compose(h,a)),codomain(compose(h,compose(h,a))),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),codomain(compose(h,compose(h,a))))),compose(h,compose(h,a))),compose(h,compose(h,a))) = compose(h,compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17695]) ).
tcf(c_18022,plain,
ifeq(domain(a),codomain(compose(h,g)),ifeq(domain(a),domain(h),compose(h,compose(g,codomain(compose(h,g)))),compose(h,g)),compose(h,g)) = compose(h,g),
inference(light_normalisation,[status(thm)],[c_18006,c_170]) ).
tcf(c_18024,plain,
! [X0: $i] : ifeq(domain(X0),codomain(compose(h,domain(X0))),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),codomain(compose(h,domain(X0))))),compose(h,domain(X0))),compose(h,domain(X0))) = compose(h,domain(X0)),
inference(light_normalisation,[status(thm)],[c_18005,c_65]) ).
tcf(c_18025,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(h,codomain(X0))),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),codomain(compose(h,codomain(X0))))),compose(h,codomain(X0))),compose(h,codomain(X0))) = compose(h,codomain(X0)),
inference(light_normalisation,[status(thm)],[c_18003,c_102]) ).
tcf(c_18029,plain,
ifeq(domain(b),codomain(compose(h,compose(h,a))),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),codomain(compose(h,compose(h,a))))),compose(h,compose(h,a))),compose(h,compose(h,a))) = compose(h,compose(h,a)),
inference(light_normalisation,[status(thm)],[c_18009,c_485]) ).
tcf(c_18030,plain,
ifeq(domain(b),codomain(compose(h,compose(g,a))),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),codomain(compose(h,compose(g,a))))),compose(h,compose(g,a))),compose(h,compose(g,a))) = compose(h,compose(g,a)),
inference(light_normalisation,[status(thm)],[c_18008,c_571]) ).
tcf(c_18035,plain,
ifeq(codomain(b),codomain(compose(h,compose(h,compose(a,b)))),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),codomain(compose(h,compose(h,compose(a,b)))))),compose(h,compose(h,compose(a,b)))),compose(h,compose(h,compose(a,b)))) = compose(h,compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_18007,c_2217]) ).
tcf(c_18052,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),codomain(compose(g,codomain(X0))),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),codomain(compose(g,codomain(X0))))),compose(g,codomain(X0))),compose(g,codomain(X0))) = compose(g,codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_17696]) ).
tcf(c_18054,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(compose(g,domain(X0))),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),codomain(compose(g,domain(X0))))),compose(g,domain(X0))),compose(g,domain(X0))) = compose(g,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_17696]) ).
tcf(c_18055,plain,
ifeq(codomain(g),codomain(compose(g,g)),ifeq(domain(a),domain(h),compose(g,compose(g,codomain(compose(g,g)))),compose(g,g)),compose(g,g)) = compose(g,g),
inference(superposition,[status(thm)],[c_1480,c_17696]) ).
tcf(c_18056,plain,
ifeq(codomain(compose(h,compose(a,b))),codomain(compose(g,compose(h,compose(a,b)))),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),codomain(compose(g,compose(h,compose(a,b)))))),compose(g,compose(h,compose(a,b)))),compose(g,compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17696]) ).
tcf(c_18057,plain,
ifeq(codomain(compose(g,a)),codomain(compose(g,compose(g,a))),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),codomain(compose(g,compose(g,a))))),compose(g,compose(g,a))),compose(g,compose(g,a))) = compose(g,compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17696]) ).
tcf(c_18058,plain,
ifeq(codomain(compose(h,a)),codomain(compose(g,compose(h,a))),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),codomain(compose(g,compose(h,a))))),compose(g,compose(h,a))),compose(g,compose(h,a))) = compose(g,compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17696]) ).
tcf(c_18073,plain,
ifeq(domain(a),codomain(compose(g,g)),ifeq(domain(a),domain(h),compose(g,compose(g,codomain(compose(g,g)))),compose(g,g)),compose(g,g)) = compose(g,g),
inference(light_normalisation,[status(thm)],[c_18055,c_170]) ).
tcf(c_18075,plain,
! [X0: $i] : ifeq(domain(X0),codomain(compose(g,domain(X0))),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),codomain(compose(g,domain(X0))))),compose(g,domain(X0))),compose(g,domain(X0))) = compose(g,domain(X0)),
inference(light_normalisation,[status(thm)],[c_18054,c_65]) ).
tcf(c_18076,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(g,codomain(X0))),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),codomain(compose(g,codomain(X0))))),compose(g,codomain(X0))),compose(g,codomain(X0))) = compose(g,codomain(X0)),
inference(light_normalisation,[status(thm)],[c_18052,c_102]) ).
tcf(c_18079,plain,
ifeq(domain(b),codomain(compose(g,compose(h,a))),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),codomain(compose(g,compose(h,a))))),compose(g,compose(h,a))),compose(g,compose(h,a))) = compose(g,compose(h,a)),
inference(light_normalisation,[status(thm)],[c_18058,c_485]) ).
tcf(c_18080,plain,
ifeq(domain(b),codomain(compose(g,compose(g,a))),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),codomain(compose(g,compose(g,a))))),compose(g,compose(g,a))),compose(g,compose(g,a))) = compose(g,compose(g,a)),
inference(light_normalisation,[status(thm)],[c_18057,c_571]) ).
tcf(c_18086,plain,
ifeq(codomain(b),codomain(compose(g,compose(h,compose(a,b)))),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),codomain(compose(g,compose(h,compose(a,b)))))),compose(g,compose(h,compose(a,b)))),compose(g,compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_18056,c_2217]) ).
tcf(c_18091,plain,
! [X0: $i] : ifeq(domain(a),codomain(compose(domain(X0),g)),ifeq(domain(X0),domain(h),compose(domain(X0),compose(g,codomain(compose(domain(X0),g)))),compose(domain(X0),g)),compose(domain(X0),g)) = compose(domain(X0),g),
inference(superposition,[status(thm)],[c_65,c_17781]) ).
tcf(c_18095,plain,
! [X0: $i] : ifeq(domain(a),codomain(compose(codomain(X0),g)),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,codomain(compose(codomain(X0),g)))),compose(codomain(X0),g)),compose(codomain(X0),g)) = compose(codomain(X0),g),
inference(superposition,[status(thm)],[c_102,c_17781]) ).
tcf(c_18096,plain,
ifeq(domain(a),codomain(compose(compose(a,b),g)),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,codomain(compose(compose(a,b),g)))),compose(compose(a,b),g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
inference(superposition,[status(thm)],[c_425,c_17781]) ).
tcf(c_18097,plain,
ifeq(domain(a),codomain(compose(compose(h,compose(a,b)),g)),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,codomain(compose(compose(h,compose(a,b)),g)))),compose(compose(h,compose(a,b)),g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
inference(superposition,[status(thm)],[c_2217,c_17781]) ).
tcf(c_18098,plain,
ifeq(domain(a),codomain(compose(compose(h,a),g)),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,codomain(compose(compose(h,a),g)))),compose(compose(h,a),g)),compose(compose(h,a),g)) = compose(compose(h,a),g),
inference(superposition,[status(thm)],[c_485,c_17781]) ).
tcf(c_18099,plain,
ifeq(domain(a),codomain(compose(compose(g,a),g)),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,codomain(compose(compose(g,a),g)))),compose(compose(g,a),g)),compose(compose(g,a),g)) = compose(compose(g,a),g),
inference(superposition,[status(thm)],[c_571,c_17781]) ).
tcf(c_18158,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(h,compose(a,b)),X1,compose(g,a),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_4549]) ).
tcf(c_18162,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(h,compose(a,b)),X1,compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_4549]) ).
tcf(c_18163,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_4549]) ).
tcf(c_18164,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_4549]) ).
tcf(c_18177,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(h,compose(a,b)),X1,compose(h,a),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_6149]) ).
tcf(c_18181,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(h,compose(a,b)),X1,compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_6149]) ).
tcf(c_18182,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6149]) ).
tcf(c_18183,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_6149]) ).
tcf(c_18196,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,g)),compose(compose(domain(X0),h),g)),compose(compose(domain(X0),h),g)) = compose(compose(domain(X0),h),g),
inference(superposition,[status(thm)],[c_65,c_3317]) ).
tcf(c_18198,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(h,g)),compose(compose(h,h),g)),compose(compose(h,h),g)) = compose(compose(h,h),g),
inference(superposition,[status(thm)],[c_167,c_3317]) ).
tcf(c_18199,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(h,g)),compose(compose(g,h),g)),compose(compose(g,h),g)) = compose(compose(g,h),g),
inference(superposition,[status(thm)],[c_170,c_3317]) ).
tcf(c_18200,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,g)),compose(compose(codomain(X0),h),g)),compose(compose(codomain(X0),h),g)) = compose(compose(codomain(X0),h),g),
inference(superposition,[status(thm)],[c_102,c_3317]) ).
tcf(c_18201,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,g)),compose(compose(compose(a,b),h),g)),compose(compose(compose(a,b),h),g)) = compose(compose(compose(a,b),h),g),
inference(superposition,[status(thm)],[c_425,c_3317]) ).
tcf(c_18202,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,g)),compose(compose(compose(h,compose(a,b)),h),g)),compose(compose(compose(h,compose(a,b)),h),g)) = compose(compose(compose(h,compose(a,b)),h),g),
inference(superposition,[status(thm)],[c_2217,c_3317]) ).
tcf(c_18203,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,g)),compose(compose(compose(h,a),h),g)),compose(compose(compose(h,a),h),g)) = compose(compose(compose(h,a),h),g),
inference(superposition,[status(thm)],[c_485,c_3317]) ).
tcf(c_18204,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,g)),compose(compose(compose(g,a),h),g)),compose(compose(compose(g,a),h),g)) = compose(compose(compose(g,a),h),g),
inference(superposition,[status(thm)],[c_571,c_3317]) ).
tcf(c_18213,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(domain(a),domain(h),compose(h,compose(h,codomain(X0))),compose(compose(h,h),codomain(X0))),compose(compose(h,h),codomain(X0))) = compose(compose(h,h),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_3325]) ).
tcf(c_18215,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(h,domain(X0))),compose(compose(h,h),domain(X0))),compose(compose(h,h),domain(X0))) = compose(compose(h,h),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_3325]) ).
tcf(c_18217,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(h,compose(h,compose(a,b)))),compose(compose(h,h),compose(h,compose(a,b)))),compose(compose(h,h),compose(h,compose(a,b)))) = compose(compose(h,h),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_3325]) ).
tcf(c_18218,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(h,compose(g,a))),compose(compose(h,h),compose(g,a))),compose(compose(h,h),compose(g,a))) = compose(compose(h,h),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_3325]) ).
tcf(c_18219,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(h,compose(h,a))),compose(compose(h,h),compose(h,a))),compose(compose(h,h),compose(h,a))) = compose(compose(h,h),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_3325]) ).
tcf(c_18232,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(domain(a),domain(h),compose(g,compose(h,codomain(X0))),compose(compose(g,h),codomain(X0))),compose(compose(g,h),codomain(X0))) = compose(compose(g,h),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_3326]) ).
tcf(c_18234,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(h,domain(X0))),compose(compose(g,h),domain(X0))),compose(compose(g,h),domain(X0))) = compose(compose(g,h),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_3326]) ).
tcf(c_18236,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(h,compose(h,compose(a,b)))),compose(compose(g,h),compose(h,compose(a,b)))),compose(compose(g,h),compose(h,compose(a,b)))) = compose(compose(g,h),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_3326]) ).
tcf(c_18237,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(h,compose(g,a))),compose(compose(g,h),compose(g,a))),compose(compose(g,h),compose(g,a))) = compose(compose(g,h),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_3326]) ).
tcf(c_18238,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(h,compose(h,a))),compose(compose(g,h),compose(h,a))),compose(compose(g,h),compose(h,a))) = compose(compose(g,h),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_3326]) ).
tcf(c_18257,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),domain(h),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),g)),compose(compose(h,codomain(X0)),g)),compose(compose(h,codomain(X0)),g)) = compose(compose(h,codomain(X0)),g),
inference(superposition,[status(thm)],[c_66,c_4001]) ).
tcf(c_18259,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),g)),compose(compose(h,domain(X0)),g)),compose(compose(h,domain(X0)),g)) = compose(compose(h,domain(X0)),g),
inference(superposition,[status(thm)],[c_100,c_4001]) ).
tcf(c_18260,plain,
ifeq(codomain(g),domain(h),ifeq(domain(a),domain(h),compose(h,compose(g,g)),compose(compose(h,g),g)),compose(compose(h,g),g)) = compose(compose(h,g),g),
inference(superposition,[status(thm)],[c_1480,c_4001]) ).
tcf(c_18261,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),g)),compose(compose(h,compose(h,compose(a,b))),g)),compose(compose(h,compose(h,compose(a,b))),g)) = compose(compose(h,compose(h,compose(a,b))),g),
inference(superposition,[status(thm)],[c_1392,c_4001]) ).
tcf(c_18262,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),g)),compose(compose(h,compose(g,a)),g)),compose(compose(h,compose(g,a)),g)) = compose(compose(h,compose(g,a)),g),
inference(superposition,[status(thm)],[c_1491,c_4001]) ).
tcf(c_18263,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),g)),compose(compose(h,compose(h,a)),g)),compose(compose(h,compose(h,a)),g)) = compose(compose(h,compose(h,a)),g),
inference(superposition,[status(thm)],[c_347,c_4001]) ).
tcf(c_18272,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(g,g)),compose(compose(h,g),g)),compose(compose(h,g),g)) = compose(compose(h,g),g),
inference(light_normalisation,[status(thm)],[c_18260,c_170]) ).
tcf(c_18275,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),g)),compose(compose(h,domain(X0)),g)),compose(compose(h,domain(X0)),g)) = compose(compose(h,domain(X0)),g),
inference(light_normalisation,[status(thm)],[c_18259,c_65]) ).
tcf(c_18276,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),g)),compose(compose(h,codomain(X0)),g)),compose(compose(h,codomain(X0)),g)) = compose(compose(h,codomain(X0)),g),
inference(light_normalisation,[status(thm)],[c_18257,c_102]) ).
tcf(c_18279,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),g)),compose(compose(h,compose(h,a)),g)),compose(compose(h,compose(h,a)),g)) = compose(compose(h,compose(h,a)),g),
inference(light_normalisation,[status(thm)],[c_18263,c_485]) ).
tcf(c_18280,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),g)),compose(compose(h,compose(g,a)),g)),compose(compose(h,compose(g,a)),g)) = compose(compose(h,compose(g,a)),g),
inference(light_normalisation,[status(thm)],[c_18262,c_571]) ).
tcf(c_18285,plain,
ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),g)),compose(compose(h,compose(h,compose(a,b))),g)),compose(compose(h,compose(h,compose(a,b))),g)) = compose(compose(h,compose(h,compose(a,b))),g),
inference(light_normalisation,[status(thm)],[c_18261,c_2217]) ).
tcf(c_18292,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(domain(a),domain(h),compose(h,compose(g,codomain(X0))),compose(compose(h,g),codomain(X0))),compose(compose(h,g),codomain(X0))) = compose(compose(h,g),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_4051]) ).
tcf(c_18294,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(g,domain(X0))),compose(compose(h,g),domain(X0))),compose(compose(h,g),domain(X0))) = compose(compose(h,g),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_4051]) ).
tcf(c_18296,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(g,compose(h,compose(a,b)))),compose(compose(h,g),compose(h,compose(a,b)))),compose(compose(h,g),compose(h,compose(a,b)))) = compose(compose(h,g),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_4051]) ).
tcf(c_18297,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(g,compose(g,a))),compose(compose(h,g),compose(g,a))),compose(compose(h,g),compose(g,a))) = compose(compose(h,g),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_4051]) ).
tcf(c_18298,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(g,compose(h,a))),compose(compose(h,g),compose(h,a))),compose(compose(h,g),compose(h,a))) = compose(compose(h,g),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_4051]) ).
tcf(c_18326,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),domain(h),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),g)),compose(compose(g,codomain(X0)),g)),compose(compose(g,codomain(X0)),g)) = compose(compose(g,codomain(X0)),g),
inference(superposition,[status(thm)],[c_66,c_4151]) ).
tcf(c_18328,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),g)),compose(compose(g,domain(X0)),g)),compose(compose(g,domain(X0)),g)) = compose(compose(g,domain(X0)),g),
inference(superposition,[status(thm)],[c_100,c_4151]) ).
tcf(c_18329,plain,
ifeq(codomain(g),domain(h),ifeq(domain(a),domain(h),compose(g,compose(g,g)),compose(compose(g,g),g)),compose(compose(g,g),g)) = compose(compose(g,g),g),
inference(superposition,[status(thm)],[c_1480,c_4151]) ).
tcf(c_18330,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),g)),compose(compose(g,compose(h,compose(a,b))),g)),compose(compose(g,compose(h,compose(a,b))),g)) = compose(compose(g,compose(h,compose(a,b))),g),
inference(superposition,[status(thm)],[c_1392,c_4151]) ).
tcf(c_18331,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),g)),compose(compose(g,compose(g,a)),g)),compose(compose(g,compose(g,a)),g)) = compose(compose(g,compose(g,a)),g),
inference(superposition,[status(thm)],[c_1491,c_4151]) ).
tcf(c_18332,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),g)),compose(compose(g,compose(h,a)),g)),compose(compose(g,compose(h,a)),g)) = compose(compose(g,compose(h,a)),g),
inference(superposition,[status(thm)],[c_347,c_4151]) ).
tcf(c_18343,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(g,g)),compose(compose(g,g),g)),compose(compose(g,g),g)) = compose(compose(g,g),g),
inference(light_normalisation,[status(thm)],[c_18329,c_170]) ).
tcf(c_18346,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),g)),compose(compose(g,domain(X0)),g)),compose(compose(g,domain(X0)),g)) = compose(compose(g,domain(X0)),g),
inference(light_normalisation,[status(thm)],[c_18328,c_65]) ).
tcf(c_18347,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),g)),compose(compose(g,codomain(X0)),g)),compose(compose(g,codomain(X0)),g)) = compose(compose(g,codomain(X0)),g),
inference(light_normalisation,[status(thm)],[c_18326,c_102]) ).
tcf(c_18350,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),g)),compose(compose(g,compose(h,a)),g)),compose(compose(g,compose(h,a)),g)) = compose(compose(g,compose(h,a)),g),
inference(light_normalisation,[status(thm)],[c_18332,c_485]) ).
tcf(c_18351,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),g)),compose(compose(g,compose(g,a)),g)),compose(compose(g,compose(g,a)),g)) = compose(compose(g,compose(g,a)),g),
inference(light_normalisation,[status(thm)],[c_18331,c_571]) ).
tcf(c_18357,plain,
ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),g)),compose(compose(g,compose(h,compose(a,b))),g)),compose(compose(g,compose(h,compose(a,b))),g)) = compose(compose(g,compose(h,compose(a,b))),g),
inference(light_normalisation,[status(thm)],[c_18330,c_2217]) ).
tcf(c_18361,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(domain(a),domain(h),compose(g,compose(g,codomain(X0))),compose(compose(g,g),codomain(X0))),compose(compose(g,g),codomain(X0))) = compose(compose(g,g),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_4203]) ).
tcf(c_18363,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(g,domain(X0))),compose(compose(g,g),domain(X0))),compose(compose(g,g),domain(X0))) = compose(compose(g,g),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_4203]) ).
tcf(c_18365,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(g,compose(h,compose(a,b)))),compose(compose(g,g),compose(h,compose(a,b)))),compose(compose(g,g),compose(h,compose(a,b)))) = compose(compose(g,g),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_4203]) ).
tcf(c_18366,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(g,compose(g,a))),compose(compose(g,g),compose(g,a))),compose(compose(g,g),compose(g,a))) = compose(compose(g,g),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_4203]) ).
tcf(c_18367,plain,
ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(g,compose(h,a))),compose(compose(g,g),compose(h,a))),compose(compose(g,g),compose(h,a))) = compose(compose(g,g),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_4203]) ).
tcf(c_18388,plain,
! [X0: $i] : ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,b),X0,h,compose(g,a)),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_4550,c_64]) ).
tcf(c_18394,plain,
! [X0: $i] : ifeq(compose(h,compose(a,b)),X0,ifeq(compose(g,b),X0,g,compose(g,a)),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_4551,c_64]) ).
tcf(c_18406,plain,
! [X0: $i] : ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,b),X0,h,compose(h,a)),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_6150,c_64]) ).
tcf(c_18412,plain,
! [X0: $i] : ifeq(compose(h,compose(a,b)),X0,ifeq(compose(g,b),X0,g,compose(h,a)),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_6151,c_64]) ).
tcf(c_18429,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(compose(a,b),a),compose(h,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6327]) ).
tcf(c_18442,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6477]) ).
tcf(c_18468,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(compose(a,b),b),compose(h,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6509]) ).
tcf(c_18486,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_6550]) ).
tcf(c_18505,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,g)),compose(compose(domain(X0),a),g)),compose(compose(domain(X0),a),g)) = compose(compose(domain(X0),a),g),
inference(superposition,[status(thm)],[c_65,c_12442]) ).
tcf(c_18506,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(a,g)),compose(compose(a,a),g)),compose(compose(a,a),g)) = compose(compose(a,a),g),
inference(superposition,[status(thm)],[c_72,c_12442]) ).
tcf(c_18509,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,g)),compose(compose(codomain(X0),a),g)),compose(compose(codomain(X0),a),g)) = compose(compose(codomain(X0),a),g),
inference(superposition,[status(thm)],[c_102,c_12442]) ).
tcf(c_18510,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,g)),compose(compose(compose(a,b),a),g)),compose(compose(compose(a,b),a),g)) = compose(compose(compose(a,b),a),g),
inference(superposition,[status(thm)],[c_425,c_12442]) ).
tcf(c_18511,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,g)),compose(compose(compose(h,compose(a,b)),a),g)),compose(compose(compose(h,compose(a,b)),a),g)) = compose(compose(compose(h,compose(a,b)),a),g),
inference(superposition,[status(thm)],[c_2217,c_12442]) ).
tcf(c_18512,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,g)),compose(compose(compose(h,a),a),g)),compose(compose(compose(h,a),a),g)) = compose(compose(compose(h,a),a),g),
inference(superposition,[status(thm)],[c_485,c_12442]) ).
tcf(c_18513,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,g)),compose(compose(compose(g,a),a),g)),compose(compose(compose(g,a),a),g)) = compose(compose(compose(g,a),a),g),
inference(superposition,[status(thm)],[c_571,c_12442]) ).
tcf(c_18528,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),domain(h),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),g)),compose(compose(a,codomain(X0)),g)),compose(compose(a,codomain(X0)),g)) = compose(compose(a,codomain(X0)),g),
inference(superposition,[status(thm)],[c_66,c_12451]) ).
tcf(c_18529,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),g)),compose(compose(a,compose(a,b)),g)),compose(compose(a,compose(a,b)),g)) = compose(compose(a,compose(a,b)),g),
inference(superposition,[status(thm)],[c_171,c_12451]) ).
tcf(c_18530,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),g)),compose(compose(a,domain(X0)),g)),compose(compose(a,domain(X0)),g)) = compose(compose(a,domain(X0)),g),
inference(superposition,[status(thm)],[c_100,c_12451]) ).
tcf(c_18531,plain,
ifeq(codomain(g),domain(h),ifeq(domain(b),domain(h),compose(a,compose(g,g)),compose(compose(a,g),g)),compose(compose(a,g),g)) = compose(compose(a,g),g),
inference(superposition,[status(thm)],[c_1480,c_12451]) ).
tcf(c_18532,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),g)),compose(compose(a,compose(h,compose(a,b))),g)),compose(compose(a,compose(h,compose(a,b))),g)) = compose(compose(a,compose(h,compose(a,b))),g),
inference(superposition,[status(thm)],[c_1392,c_12451]) ).
tcf(c_18533,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),g)),compose(compose(a,compose(g,a)),g)),compose(compose(a,compose(g,a)),g)) = compose(compose(a,compose(g,a)),g),
inference(superposition,[status(thm)],[c_1491,c_12451]) ).
tcf(c_18534,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),g)),compose(compose(a,compose(h,a)),g)),compose(compose(a,compose(h,a)),g)) = compose(compose(a,compose(h,a)),g),
inference(superposition,[status(thm)],[c_347,c_12451]) ).
tcf(c_18542,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(g,g)),compose(compose(a,g),g)),compose(compose(a,g),g)) = compose(compose(a,g),g),
inference(light_normalisation,[status(thm)],[c_18531,c_170]) ).
tcf(c_18545,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),g)),compose(compose(a,domain(X0)),g)),compose(compose(a,domain(X0)),g)) = compose(compose(a,domain(X0)),g),
inference(light_normalisation,[status(thm)],[c_18530,c_65]) ).
tcf(c_18546,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),g)),compose(compose(a,codomain(X0)),g)),compose(compose(a,codomain(X0)),g)) = compose(compose(a,codomain(X0)),g),
inference(light_normalisation,[status(thm)],[c_18528,c_102]) ).
tcf(c_18549,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),g)),compose(compose(a,compose(h,a)),g)),compose(compose(a,compose(h,a)),g)) = compose(compose(a,compose(h,a)),g),
inference(light_normalisation,[status(thm)],[c_18534,c_485]) ).
tcf(c_18550,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),g)),compose(compose(a,compose(g,a)),g)),compose(compose(a,compose(g,a)),g)) = compose(compose(a,compose(g,a)),g),
inference(light_normalisation,[status(thm)],[c_18533,c_571]) ).
tcf(c_18551,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),g)),compose(compose(a,compose(a,b)),g)),compose(compose(a,compose(a,b)),g)) = compose(compose(a,compose(a,b)),g),
inference(light_normalisation,[status(thm)],[c_18529,c_425]) ).
tcf(c_18555,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),g)),compose(compose(a,compose(h,compose(a,b))),g)),compose(compose(a,compose(h,compose(a,b))),g)) = compose(compose(a,compose(h,compose(a,b))),g),
inference(light_normalisation,[status(thm)],[c_18532,c_2217]) ).
tcf(c_18559,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(domain(b),domain(h),compose(a,compose(g,codomain(X0))),compose(compose(a,g),codomain(X0))),compose(compose(a,g),codomain(X0))) = compose(compose(a,g),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_12585]) ).
tcf(c_18561,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(g,domain(X0))),compose(compose(a,g),domain(X0))),compose(compose(a,g),domain(X0))) = compose(compose(a,g),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_12585]) ).
tcf(c_18563,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(g,compose(h,compose(a,b)))),compose(compose(a,g),compose(h,compose(a,b)))),compose(compose(a,g),compose(h,compose(a,b)))) = compose(compose(a,g),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_12585]) ).
tcf(c_18564,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(g,compose(g,a))),compose(compose(a,g),compose(g,a))),compose(compose(a,g),compose(g,a))) = compose(compose(a,g),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_12585]) ).
tcf(c_18565,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(g,compose(h,a))),compose(compose(a,g),compose(h,a))),compose(compose(a,g),compose(h,a))) = compose(compose(a,g),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_12585]) ).
tcf(c_18588,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(g,g)),compose(compose(domain(X0),g),g)),compose(compose(domain(X0),g),g)) = compose(compose(domain(X0),g),g),
inference(superposition,[status(thm)],[c_65,c_12513]) ).
tcf(c_18592,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,g)),compose(compose(codomain(X0),g),g)),compose(compose(codomain(X0),g),g)) = compose(compose(codomain(X0),g),g),
inference(superposition,[status(thm)],[c_102,c_12513]) ).
tcf(c_18593,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,g)),compose(compose(compose(a,b),g),g)),compose(compose(compose(a,b),g),g)) = compose(compose(compose(a,b),g),g),
inference(superposition,[status(thm)],[c_425,c_12513]) ).
tcf(c_18594,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,g)),compose(compose(compose(h,compose(a,b)),g),g)),compose(compose(compose(h,compose(a,b)),g),g)) = compose(compose(compose(h,compose(a,b)),g),g),
inference(superposition,[status(thm)],[c_2217,c_12513]) ).
tcf(c_18595,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,g)),compose(compose(compose(h,a),g),g)),compose(compose(compose(h,a),g),g)) = compose(compose(compose(h,a),g),g),
inference(superposition,[status(thm)],[c_485,c_12513]) ).
tcf(c_18596,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,g)),compose(compose(compose(g,a),g),g)),compose(compose(compose(g,a),g),g)) = compose(compose(compose(g,a),g),g),
inference(superposition,[status(thm)],[c_571,c_12513]) ).
tcf(c_18610,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(a),compose(a,compose(a,codomain(X0))),compose(compose(a,a),codomain(X0))),compose(compose(a,a),codomain(X0))) = compose(compose(a,a),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_17398]) ).
tcf(c_18611,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(a),compose(a,compose(a,compose(a,b))),compose(compose(a,a),compose(a,b))),compose(compose(a,a),compose(a,b))) = compose(compose(a,a),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_17398]) ).
tcf(c_18612,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(a),compose(a,compose(a,domain(X0))),compose(compose(a,a),domain(X0))),compose(compose(a,a),domain(X0))) = compose(compose(a,a),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_17398]) ).
tcf(c_18614,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(a,compose(h,compose(a,b)))),compose(compose(a,a),compose(h,compose(a,b)))),compose(compose(a,a),compose(h,compose(a,b)))) = compose(compose(a,a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17398]) ).
tcf(c_18615,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(a,compose(g,a))),compose(compose(a,a),compose(g,a))),compose(compose(a,a),compose(g,a))) = compose(compose(a,a),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17398]) ).
tcf(c_18616,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(a,compose(h,a))),compose(compose(a,a),compose(h,a))),compose(compose(a,a),compose(h,a))) = compose(compose(a,a),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17398]) ).
tcf(c_18639,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),compose(X0,X1),compose(compose(X0,X1),codomain(X1))) = compose(compose(X0,X1),codomain(X1)),
inference(demodulation,[status(thm)],[c_316,c_64]) ).
tcf(c_18640,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),compose(domain(X0),X1),compose(compose(domain(X0),X1),codomain(X1))) = compose(compose(domain(X0),X1),codomain(X1)),
inference(superposition,[status(thm)],[c_65,c_18639]) ).
tcf(c_18641,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(a,X0),compose(compose(a,X0),codomain(X0))) = compose(compose(a,X0),codomain(X0)),
inference(superposition,[status(thm)],[c_72,c_18639]) ).
tcf(c_18642,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),compose(h,X0),compose(compose(h,X0),codomain(X0))) = compose(compose(h,X0),codomain(X0)),
inference(superposition,[status(thm)],[c_167,c_18639]) ).
tcf(c_18643,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),compose(g,X0),compose(compose(g,X0),codomain(X0))) = compose(compose(g,X0),codomain(X0)),
inference(superposition,[status(thm)],[c_170,c_18639]) ).
tcf(c_18644,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),compose(codomain(X0),X1),compose(compose(codomain(X0),X1),codomain(X1))) = compose(compose(codomain(X0),X1),codomain(X1)),
inference(superposition,[status(thm)],[c_102,c_18639]) ).
tcf(c_18645,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(a,b),X0),compose(compose(compose(a,b),X0),codomain(X0))) = compose(compose(compose(a,b),X0),codomain(X0)),
inference(superposition,[status(thm)],[c_425,c_18639]) ).
tcf(c_18646,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),X0),compose(compose(compose(h,compose(a,b)),X0),codomain(X0))) = compose(compose(compose(h,compose(a,b)),X0),codomain(X0)),
inference(superposition,[status(thm)],[c_2217,c_18639]) ).
tcf(c_18647,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(compose(h,a),X0),compose(compose(compose(h,a),X0),codomain(X0))) = compose(compose(compose(h,a),X0),codomain(X0)),
inference(superposition,[status(thm)],[c_485,c_18639]) ).
tcf(c_18648,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(compose(g,a),X0),compose(compose(compose(g,a),X0),codomain(X0))) = compose(compose(compose(g,a),X0),codomain(X0)),
inference(superposition,[status(thm)],[c_571,c_18639]) ).
tcf(c_18695,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(domain(X1)),compose(X0,domain(X1)),compose(compose(X0,domain(X1)),domain(X1))) = compose(compose(X0,domain(X1)),domain(X1)),
inference(superposition,[status(thm)],[c_65,c_18639]) ).
tcf(c_18696,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(X0,a),compose(compose(X0,a),domain(b))) = compose(compose(X0,a),domain(b)),
inference(superposition,[status(thm)],[c_72,c_18639]) ).
tcf(c_18700,plain,
! [X0: $i] : ifeq(codomain(X0),domain(compose(a,b)),compose(X0,compose(a,b)),compose(compose(X0,compose(a,b)),codomain(b))) = compose(compose(X0,compose(a,b)),codomain(b)),
inference(superposition,[status(thm)],[c_425,c_18639]) ).
tcf(c_18701,plain,
! [X0: $i] : ifeq(codomain(X0),domain(compose(h,compose(a,b))),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(h,compose(a,b))),codomain(b))) = compose(compose(X0,compose(h,compose(a,b))),codomain(b)),
inference(superposition,[status(thm)],[c_2217,c_18639]) ).
tcf(c_18722,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,b)),compose(compose(X0,compose(a,b)),codomain(b))) = compose(compose(X0,compose(a,b)),codomain(b)),
inference(light_normalisation,[status(thm)],[c_18700,c_171]) ).
tcf(c_18730,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(h,compose(a,b))),codomain(b))) = compose(compose(X0,compose(h,compose(a,b))),codomain(b)),
inference(light_normalisation,[status(thm)],[c_18701,c_1392]) ).
tcf(c_18747,plain,
! [X0: $i] : ifeq(domain(b),domain(domain(X0)),compose(a,domain(X0)),compose(compose(a,domain(X0)),domain(X0))) = compose(compose(a,domain(X0)),domain(X0)),
inference(superposition,[status(thm)],[c_65,c_18641]) ).
tcf(c_18748,plain,
ifeq(domain(b),domain(a),compose(a,a),compose(compose(a,a),domain(b))) = compose(compose(a,a),domain(b)),
inference(superposition,[status(thm)],[c_72,c_18641]) ).
tcf(c_18751,plain,
! [X0: $i] : ifeq(domain(b),domain(codomain(X0)),compose(a,codomain(X0)),compose(compose(a,codomain(X0)),codomain(X0))) = compose(compose(a,codomain(X0)),codomain(X0)),
inference(superposition,[status(thm)],[c_102,c_18641]) ).
tcf(c_18752,plain,
ifeq(domain(b),domain(compose(a,b)),compose(a,compose(a,b)),compose(compose(a,compose(a,b)),codomain(b))) = compose(compose(a,compose(a,b)),codomain(b)),
inference(superposition,[status(thm)],[c_425,c_18641]) ).
tcf(c_18753,plain,
ifeq(domain(b),domain(compose(h,compose(a,b))),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(h,compose(a,b))),codomain(b))) = compose(compose(a,compose(h,compose(a,b))),codomain(b)),
inference(superposition,[status(thm)],[c_2217,c_18641]) ).
tcf(c_18760,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),compose(a,codomain(X0)),compose(compose(a,codomain(X0)),codomain(X0))) = compose(compose(a,codomain(X0)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_18751,c_66]) ).
tcf(c_18761,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(a,domain(X0)),compose(compose(a,domain(X0)),domain(X0))) = compose(compose(a,domain(X0)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_18747,c_100]) ).
tcf(c_18766,plain,
ifeq(domain(b),domain(a),compose(a,compose(a,b)),compose(compose(a,compose(a,b)),codomain(b))) = compose(compose(a,compose(a,b)),codomain(b)),
inference(light_normalisation,[status(thm)],[c_18752,c_171]) ).
tcf(c_18770,plain,
ifeq(domain(b),domain(h),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(h,compose(a,b))),codomain(b))) = compose(compose(a,compose(h,compose(a,b))),codomain(b)),
inference(light_normalisation,[status(thm)],[c_18753,c_1392]) ).
tcf(c_18773,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),compose(domain(X0),a),compose(compose(domain(X0),a),domain(b))) = compose(compose(domain(X0),a),domain(b)),
inference(superposition,[status(thm)],[c_65,c_18696]) ).
tcf(c_18777,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(codomain(X0),a),compose(compose(codomain(X0),a),domain(b))) = compose(compose(codomain(X0),a),domain(b)),
inference(superposition,[status(thm)],[c_102,c_18696]) ).
tcf(c_18778,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),a),compose(compose(compose(a,b),a),domain(b))) = compose(compose(compose(a,b),a),domain(b)),
inference(superposition,[status(thm)],[c_425,c_18696]) ).
tcf(c_18779,plain,
ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),a),compose(compose(compose(h,compose(a,b)),a),domain(b))) = compose(compose(compose(h,compose(a,b)),a),domain(b)),
inference(superposition,[status(thm)],[c_2217,c_18696]) ).
tcf(c_18780,plain,
ifeq(domain(b),domain(a),compose(compose(h,a),a),compose(compose(compose(h,a),a),domain(b))) = compose(compose(compose(h,a),a),domain(b)),
inference(superposition,[status(thm)],[c_485,c_18696]) ).
tcf(c_18781,plain,
ifeq(domain(b),domain(a),compose(compose(g,a),a),compose(compose(compose(g,a),a),domain(b))) = compose(compose(compose(g,a),a),domain(b)),
inference(superposition,[status(thm)],[c_571,c_18696]) ).
tcf(c_18802,plain,
! [X0: $i] : ifeq(domain(a),domain(domain(X0)),compose(h,domain(X0)),compose(compose(h,domain(X0)),domain(X0))) = compose(compose(h,domain(X0)),domain(X0)),
inference(superposition,[status(thm)],[c_65,c_18642]) ).
tcf(c_18806,plain,
! [X0: $i] : ifeq(domain(a),domain(codomain(X0)),compose(h,codomain(X0)),compose(compose(h,codomain(X0)),codomain(X0))) = compose(compose(h,codomain(X0)),codomain(X0)),
inference(superposition,[status(thm)],[c_102,c_18642]) ).
tcf(c_18808,plain,
ifeq(domain(a),domain(compose(h,compose(a,b))),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(h,compose(a,b))),codomain(b))) = compose(compose(h,compose(h,compose(a,b))),codomain(b)),
inference(superposition,[status(thm)],[c_2217,c_18642]) ).
tcf(c_18816,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),compose(h,codomain(X0)),compose(compose(h,codomain(X0)),codomain(X0))) = compose(compose(h,codomain(X0)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_18806,c_66]) ).
tcf(c_18817,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),compose(h,domain(X0)),compose(compose(h,domain(X0)),domain(X0))) = compose(compose(h,domain(X0)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_18802,c_100]) ).
tcf(c_18826,plain,
ifeq(domain(a),domain(h),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(h,compose(a,b))),codomain(b))) = compose(compose(h,compose(h,compose(a,b))),codomain(b)),
inference(light_normalisation,[status(thm)],[c_18808,c_1392]) ).
tcf(c_18843,plain,
! [X0: $i] : ifeq(domain(a),domain(domain(X0)),compose(g,domain(X0)),compose(compose(g,domain(X0)),domain(X0))) = compose(compose(g,domain(X0)),domain(X0)),
inference(superposition,[status(thm)],[c_65,c_18643]) ).
tcf(c_18847,plain,
! [X0: $i] : ifeq(domain(a),domain(codomain(X0)),compose(g,codomain(X0)),compose(compose(g,codomain(X0)),codomain(X0))) = compose(compose(g,codomain(X0)),codomain(X0)),
inference(superposition,[status(thm)],[c_102,c_18643]) ).
tcf(c_18849,plain,
ifeq(domain(a),domain(compose(h,compose(a,b))),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(h,compose(a,b))),codomain(b))) = compose(compose(g,compose(h,compose(a,b))),codomain(b)),
inference(superposition,[status(thm)],[c_2217,c_18643]) ).
tcf(c_18857,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),compose(g,codomain(X0)),compose(compose(g,codomain(X0)),codomain(X0))) = compose(compose(g,codomain(X0)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_18847,c_66]) ).
tcf(c_18858,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),compose(g,domain(X0)),compose(compose(g,domain(X0)),domain(X0))) = compose(compose(g,domain(X0)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_18843,c_100]) ).
tcf(c_18868,plain,
ifeq(domain(a),domain(h),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(h,compose(a,b))),codomain(b))) = compose(compose(g,compose(h,compose(a,b))),codomain(b)),
inference(light_normalisation,[status(thm)],[c_18849,c_1392]) ).
tcf(c_18921,plain,
! [X0: $i] : ifeq(domain(X0),domain(compose(a,b)),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),compose(a,b)),codomain(b))) = compose(compose(domain(X0),compose(a,b)),codomain(b)),
inference(superposition,[status(thm)],[c_425,c_18640]) ).
tcf(c_18922,plain,
! [X0: $i] : ifeq(domain(X0),domain(compose(h,compose(a,b))),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b))) = compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b)),
inference(superposition,[status(thm)],[c_2217,c_18640]) ).
tcf(c_18938,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),compose(a,b)),codomain(b))) = compose(compose(domain(X0),compose(a,b)),codomain(b)),
inference(light_normalisation,[status(thm)],[c_18921,c_171]) ).
tcf(c_18943,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b))) = compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b)),
inference(light_normalisation,[status(thm)],[c_18922,c_1392]) ).
tcf(c_18989,plain,
! [X0: $i] : ifeq(codomain(X0),domain(compose(a,b)),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),compose(a,b)),codomain(b))) = compose(compose(codomain(X0),compose(a,b)),codomain(b)),
inference(superposition,[status(thm)],[c_425,c_18644]) ).
tcf(c_18990,plain,
! [X0: $i] : ifeq(codomain(X0),domain(compose(h,compose(a,b))),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b))) = compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b)),
inference(superposition,[status(thm)],[c_2217,c_18644]) ).
tcf(c_18999,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),compose(a,b)),codomain(b))) = compose(compose(codomain(X0),compose(a,b)),codomain(b)),
inference(light_normalisation,[status(thm)],[c_18989,c_171]) ).
tcf(c_19003,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b))) = compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b)),
inference(light_normalisation,[status(thm)],[c_18990,c_1392]) ).
tcf(c_19326,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),compose(X0,domain(X1)),compose(compose(X0,domain(X1)),domain(X1))) = compose(compose(X0,domain(X1)),domain(X1)),
inference(demodulation,[status(thm)],[c_18695,c_100]) ).
tcf(c_19327,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),compose(domain(X0),domain(X1)),compose(compose(domain(X0),domain(X1)),domain(X1))) = compose(compose(domain(X0),domain(X1)),domain(X1)),
inference(superposition,[status(thm)],[c_65,c_19326]) ).
tcf(c_19331,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),compose(codomain(X0),domain(X1)),compose(compose(codomain(X0),domain(X1)),domain(X1))) = compose(compose(codomain(X0),domain(X1)),domain(X1)),
inference(superposition,[status(thm)],[c_102,c_19326]) ).
tcf(c_19332,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(a,b),domain(X0)),compose(compose(compose(a,b),domain(X0)),domain(X0))) = compose(compose(compose(a,b),domain(X0)),domain(X0)),
inference(superposition,[status(thm)],[c_425,c_19326]) ).
tcf(c_19333,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),domain(X0)),compose(compose(compose(h,compose(a,b)),domain(X0)),domain(X0))) = compose(compose(compose(h,compose(a,b)),domain(X0)),domain(X0)),
inference(superposition,[status(thm)],[c_2217,c_19326]) ).
tcf(c_19334,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(compose(h,a),domain(X0)),compose(compose(compose(h,a),domain(X0)),domain(X0))) = compose(compose(compose(h,a),domain(X0)),domain(X0)),
inference(superposition,[status(thm)],[c_485,c_19326]) ).
tcf(c_19335,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(compose(g,a),domain(X0)),compose(compose(compose(g,a),domain(X0)),domain(X0))) = compose(compose(compose(g,a),domain(X0)),domain(X0)),
inference(superposition,[status(thm)],[c_571,c_19326]) ).
tcf(c_19371,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),compose(X0,codomain(X1)),compose(compose(X0,codomain(X1)),codomain(X1))) = compose(compose(X0,codomain(X1)),codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_19326]) ).
tcf(c_19382,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(X1),compose(domain(X0),codomain(X1)),compose(compose(domain(X0),codomain(X1)),codomain(X1))) = compose(compose(domain(X0),codomain(X1)),codomain(X1)),
inference(superposition,[status(thm)],[c_65,c_19371]) ).
tcf(c_19386,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),compose(codomain(X0),codomain(X1)),compose(compose(codomain(X0),codomain(X1)),codomain(X1))) = compose(compose(codomain(X0),codomain(X1)),codomain(X1)),
inference(superposition,[status(thm)],[c_102,c_19371]) ).
tcf(c_19387,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),compose(compose(a,b),codomain(X0)),compose(compose(compose(a,b),codomain(X0)),codomain(X0))) = compose(compose(compose(a,b),codomain(X0)),codomain(X0)),
inference(superposition,[status(thm)],[c_425,c_19371]) ).
tcf(c_19388,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),codomain(X0)),compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(X0)),
inference(superposition,[status(thm)],[c_2217,c_19371]) ).
tcf(c_19389,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),compose(compose(h,a),codomain(X0)),compose(compose(compose(h,a),codomain(X0)),codomain(X0))) = compose(compose(compose(h,a),codomain(X0)),codomain(X0)),
inference(superposition,[status(thm)],[c_485,c_19371]) ).
tcf(c_19390,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),compose(compose(g,a),codomain(X0)),compose(compose(compose(g,a),codomain(X0)),codomain(X0))) = compose(compose(compose(g,a),codomain(X0)),codomain(X0)),
inference(superposition,[status(thm)],[c_571,c_19371]) ).
tcf(c_19463,plain,
ifeq(codomain(b),domain(compose(a,b)),compose(compose(a,b),compose(a,b)),compose(compose(compose(a,b),compose(a,b)),codomain(b))) = compose(compose(compose(a,b),compose(a,b)),codomain(b)),
inference(superposition,[status(thm)],[c_425,c_18645]) ).
tcf(c_19464,plain,
ifeq(codomain(b),domain(compose(h,compose(a,b))),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(b)),
inference(superposition,[status(thm)],[c_2217,c_18645]) ).
tcf(c_19476,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,b)),compose(compose(compose(a,b),compose(a,b)),codomain(b))) = compose(compose(compose(a,b),compose(a,b)),codomain(b)),
inference(light_normalisation,[status(thm)],[c_19463,c_171]) ).
tcf(c_19480,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(b)),
inference(light_normalisation,[status(thm)],[c_19464,c_1392]) ).
tcf(c_19502,plain,
ifeq(domain(b),domain(compose(a,b)),compose(compose(h,a),compose(a,b)),compose(compose(compose(h,a),compose(a,b)),codomain(b))) = compose(compose(compose(h,a),compose(a,b)),codomain(b)),
inference(superposition,[status(thm)],[c_425,c_18647]) ).
tcf(c_19503,plain,
ifeq(domain(b),domain(compose(h,compose(a,b))),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(b)),
inference(superposition,[status(thm)],[c_2217,c_18647]) ).
tcf(c_19517,plain,
ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,b)),compose(compose(compose(h,a),compose(a,b)),codomain(b))) = compose(compose(compose(h,a),compose(a,b)),codomain(b)),
inference(light_normalisation,[status(thm)],[c_19502,c_171]) ).
tcf(c_19521,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(b)),
inference(light_normalisation,[status(thm)],[c_19503,c_1392]) ).
tcf(c_19543,plain,
ifeq(domain(b),domain(compose(a,b)),compose(compose(g,a),compose(a,b)),compose(compose(compose(g,a),compose(a,b)),codomain(b))) = compose(compose(compose(g,a),compose(a,b)),codomain(b)),
inference(superposition,[status(thm)],[c_425,c_18648]) ).
tcf(c_19544,plain,
ifeq(domain(b),domain(compose(h,compose(a,b))),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(b)),
inference(superposition,[status(thm)],[c_2217,c_18648]) ).
tcf(c_19557,plain,
ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,b)),compose(compose(compose(g,a),compose(a,b)),codomain(b))) = compose(compose(compose(g,a),compose(a,b)),codomain(b)),
inference(light_normalisation,[status(thm)],[c_19543,c_171]) ).
tcf(c_19561,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(b)),
inference(light_normalisation,[status(thm)],[c_19544,c_1392]) ).
tcf(c_19697,plain,
ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,b)),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b)),
inference(superposition,[status(thm)],[c_2217,c_18722]) ).
tcf(c_19846,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(compose(h,compose(a,b)),b),X1,compose(h,compose(a,b)),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_2253]) ).
tcf(c_19850,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(compose(h,compose(a,b)),b),X1,compose(h,compose(a,b)),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_2253]) ).
tcf(c_19851,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_2253]) ).
tcf(c_19852,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_2253]) ).
tcf(c_19865,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),compose(X0,X1),compose(compose(X0,domain(X1)),X1)) = compose(compose(X0,domain(X1)),X1),
inference(demodulation,[status(thm)],[c_318,c_64]) ).
tcf(c_19866,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),compose(domain(X0),X1),compose(compose(domain(X0),domain(X1)),X1)) = compose(compose(domain(X0),domain(X1)),X1),
inference(superposition,[status(thm)],[c_65,c_19865]) ).
tcf(c_19867,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(a,X0),compose(compose(a,domain(X0)),X0)) = compose(compose(a,domain(X0)),X0),
inference(superposition,[status(thm)],[c_72,c_19865]) ).
tcf(c_19868,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),compose(h,X0),compose(compose(h,domain(X0)),X0)) = compose(compose(h,domain(X0)),X0),
inference(superposition,[status(thm)],[c_167,c_19865]) ).
tcf(c_19869,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),compose(g,X0),compose(compose(g,domain(X0)),X0)) = compose(compose(g,domain(X0)),X0),
inference(superposition,[status(thm)],[c_170,c_19865]) ).
tcf(c_19870,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),compose(codomain(X0),X1),compose(compose(codomain(X0),domain(X1)),X1)) = compose(compose(codomain(X0),domain(X1)),X1),
inference(superposition,[status(thm)],[c_102,c_19865]) ).
tcf(c_19871,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(a,b),X0),compose(compose(compose(a,b),domain(X0)),X0)) = compose(compose(compose(a,b),domain(X0)),X0),
inference(superposition,[status(thm)],[c_425,c_19865]) ).
tcf(c_19872,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),X0),compose(compose(compose(h,compose(a,b)),domain(X0)),X0)) = compose(compose(compose(h,compose(a,b)),domain(X0)),X0),
inference(superposition,[status(thm)],[c_2217,c_19865]) ).
tcf(c_19873,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(compose(h,a),X0),compose(compose(compose(h,a),domain(X0)),X0)) = compose(compose(compose(h,a),domain(X0)),X0),
inference(superposition,[status(thm)],[c_485,c_19865]) ).
tcf(c_19874,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),compose(compose(g,a),X0),compose(compose(compose(g,a),domain(X0)),X0)) = compose(compose(compose(g,a),domain(X0)),X0),
inference(superposition,[status(thm)],[c_571,c_19865]) ).
tcf(c_19909,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,b)),compose(compose(X0,domain(a)),compose(a,b))) = compose(compose(X0,domain(a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_19865]) ).
tcf(c_19951,plain,
ifeq(domain(b),domain(a),compose(a,compose(a,b)),compose(compose(a,domain(a)),compose(a,b))) = compose(compose(a,domain(a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_19867]) ).
tcf(c_20001,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),domain(a)),compose(a,b))) = compose(compose(domain(X0),domain(a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_19866]) ).
tcf(c_20105,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),domain(a)),compose(a,b))) = compose(compose(codomain(X0),domain(a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_19870]) ).
tcf(c_20124,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,b)),compose(compose(compose(a,b),domain(a)),compose(a,b))) = compose(compose(compose(a,b),domain(a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_19871]) ).
tcf(c_20145,plain,
ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,b)),compose(compose(compose(h,a),domain(a)),compose(a,b))) = compose(compose(compose(h,a),domain(a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_19873]) ).
tcf(c_20169,plain,
ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,b)),compose(compose(compose(g,a),domain(a)),compose(a,b))) = compose(compose(compose(g,a),domain(a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_19874]) ).
tcf(c_20186,plain,
ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,b)),compose(compose(compose(h,compose(a,b)),domain(a)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),domain(a)),compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_19909]) ).
tcf(c_20202,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(compose(h,compose(a,b)),a),X1,compose(h,compose(a,b)),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_2254]) ).
tcf(c_20206,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(compose(compose(h,compose(a,b)),a),X1,compose(h,compose(a,b)),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_102,c_2254]) ).
tcf(c_20207,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_425,c_2254]) ).
tcf(c_20208,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_2254]) ).
tcf(c_20677,plain,
ifeq(domain(b),domain(a),ifeq(b,compose(h,compose(a,b)),domain(b),compose(g,a)),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_7446,c_64]) ).
tcf(c_20849,plain,
ifeq(domain(b),domain(a),ifeq(b,compose(h,compose(a,b)),domain(b),compose(h,a)),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_7447,c_64]) ).
tcf(c_20850,plain,
ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),b,domain(b),compose(g,a)),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_7563,c_64]) ).
tcf(c_20851,plain,
ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),b,domain(b),compose(h,a)),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_7564,c_64]) ).
tcf(c_21187,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,codomain(X1))),compose(compose(compose(h,compose(a,b)),X0),codomain(X1))),compose(compose(compose(h,compose(a,b)),X0),codomain(X1))) = compose(compose(compose(h,compose(a,b)),X0),codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_2269]) ).
tcf(c_21188,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,compose(a,b))),compose(compose(compose(h,compose(a,b)),X0),compose(a,b))),compose(compose(compose(h,compose(a,b)),X0),compose(a,b))) = compose(compose(compose(h,compose(a,b)),X0),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_2269]) ).
tcf(c_21189,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,domain(X1))),compose(compose(compose(h,compose(a,b)),X0),domain(X1))),compose(compose(compose(h,compose(a,b)),X0),domain(X1))) = compose(compose(compose(h,compose(a,b)),X0),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_2269]) ).
tcf(c_21194,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),X1)),compose(compose(compose(h,compose(a,b)),codomain(X0)),X1)),compose(compose(compose(h,compose(a,b)),codomain(X0)),X1)) = compose(compose(compose(h,compose(a,b)),codomain(X0)),X1),
inference(superposition,[status(thm)],[c_66,c_2269]) ).
tcf(c_21195,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),X0)),compose(compose(compose(h,compose(a,b)),compose(a,b)),X0)),compose(compose(compose(h,compose(a,b)),compose(a,b)),X0)) = compose(compose(compose(h,compose(a,b)),compose(a,b)),X0),
inference(superposition,[status(thm)],[c_171,c_2269]) ).
tcf(c_21196,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),X1)),compose(compose(compose(h,compose(a,b)),domain(X0)),X1)),compose(compose(compose(h,compose(a,b)),domain(X0)),X1)) = compose(compose(compose(h,compose(a,b)),domain(X0)),X1),
inference(superposition,[status(thm)],[c_100,c_2269]) ).
tcf(c_21198,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),X0)),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),X0)),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),X0)) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),X0),
inference(superposition,[status(thm)],[c_1392,c_2269]) ).
tcf(c_21234,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),X1)),compose(compose(compose(h,compose(a,b)),domain(X0)),X1)),compose(compose(compose(h,compose(a,b)),domain(X0)),X1)) = compose(compose(compose(h,compose(a,b)),domain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_21196,c_65]) ).
tcf(c_21235,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),X1)),compose(compose(compose(h,compose(a,b)),codomain(X0)),X1)),compose(compose(compose(h,compose(a,b)),codomain(X0)),X1)) = compose(compose(compose(h,compose(a,b)),codomain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_21194,c_102]) ).
tcf(c_21244,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),X0)),compose(compose(compose(h,compose(a,b)),compose(a,b)),X0)),compose(compose(compose(h,compose(a,b)),compose(a,b)),X0)) = compose(compose(compose(h,compose(a,b)),compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_21195,c_425]) ).
tcf(c_21256,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),X0)),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),X0)),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),X0)) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),X0),
inference(light_normalisation,[status(thm)],[c_21198,c_2217]) ).
tcf(c_21597,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(X1,compose(h,compose(a,b))),codomain(X0))),compose(compose(X1,compose(h,compose(a,b))),codomain(X0))) = compose(compose(X1,compose(h,compose(a,b))),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_2290]) ).
tcf(c_21598,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(X0,compose(h,compose(a,b))),compose(a,b))),compose(compose(X0,compose(h,compose(a,b))),compose(a,b))) = compose(compose(X0,compose(h,compose(a,b))),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_2290]) ).
tcf(c_21599,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(h,compose(a,b)),domain(X0))),compose(compose(X1,compose(h,compose(a,b))),domain(X0))),compose(compose(X1,compose(h,compose(a,b))),domain(X0))) = compose(compose(X1,compose(h,compose(a,b))),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_2290]) ).
tcf(c_21604,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,compose(a,b)),X0)),compose(compose(domain(X1),compose(h,compose(a,b))),X0)),compose(compose(domain(X1),compose(h,compose(a,b))),X0)) = compose(compose(domain(X1),compose(h,compose(a,b))),X0),
inference(superposition,[status(thm)],[c_65,c_2290]) ).
tcf(c_21608,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,compose(a,b)),X0)),compose(compose(codomain(X1),compose(h,compose(a,b))),X0)),compose(compose(codomain(X1),compose(h,compose(a,b))),X0)) = compose(compose(codomain(X1),compose(h,compose(a,b))),X0),
inference(superposition,[status(thm)],[c_102,c_2290]) ).
tcf(c_21609,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),X0)),compose(compose(compose(a,b),compose(h,compose(a,b))),X0)),compose(compose(compose(a,b),compose(h,compose(a,b))),X0)) = compose(compose(compose(a,b),compose(h,compose(a,b))),X0),
inference(superposition,[status(thm)],[c_425,c_2290]) ).
tcf(c_21911,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(domain(b),a),X1,ifeq(compose(X0,a),X1,X0,domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_64,c_234]) ).
tcf(c_21971,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(compose(domain(b),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_65,c_21911]) ).
tcf(c_21972,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),X0,ifeq(compose(a,a),X0,a,domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_72,c_21911]) ).
tcf(c_21975,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(domain(b),a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_102,c_21911]) ).
tcf(c_21976,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(domain(b),a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_425,c_21911]) ).
tcf(c_21977,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(domain(b),a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_2217,c_21911]) ).
tcf(c_21978,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_485,c_21911]) ).
tcf(c_21979,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),domain(b)),domain(b)),domain(b)) = domain(b),
inference(superposition,[status(thm)],[c_571,c_21911]) ).
tcf(c_22555,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,b),compose(h,compose(a,b)),X0,compose(g,a)),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_6540,c_64]) ).
tcf(c_22556,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),b),compose(h,compose(a,b)),domain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_65,c_22555]) ).
tcf(c_22557,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(h,compose(a,b)),a,compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_72,c_22555]) ).
tcf(c_22560,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),b),compose(h,compose(a,b)),codomain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_102,c_22555]) ).
tcf(c_22561,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),b),compose(h,compose(a,b)),compose(a,b),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_425,c_22555]) ).
tcf(c_22562,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),compose(h,compose(a,b)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_2217,c_22555]) ).
tcf(c_22563,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),b),compose(h,compose(a,b)),compose(h,a),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_485,c_22555]) ).
tcf(c_22574,plain,
ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(h,compose(a,b)),compose(h,a),compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_22563,c_6074]) ).
tcf(c_22634,plain,
ifeq(domain(b),domain(a),compose(h,a),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_22574,c_64]) ).
tcf(c_22636,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,b),compose(h,compose(a,b)),X0,compose(h,a)),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_6541,c_64]) ).
tcf(c_22637,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),b),compose(h,compose(a,b)),domain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_65,c_22636]) ).
tcf(c_22638,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(h,compose(a,b)),a,compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_72,c_22636]) ).
tcf(c_22641,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),b),compose(h,compose(a,b)),codomain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_102,c_22636]) ).
tcf(c_22642,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),b),compose(h,compose(a,b)),compose(a,b),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_425,c_22636]) ).
tcf(c_22643,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),compose(h,compose(a,b)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_2217,c_22636]) ).
tcf(c_22645,plain,
ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),b),compose(h,compose(a,b)),compose(g,a),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_571,c_22636]) ).
tcf(c_22654,plain,
ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(h,compose(a,b)),compose(g,a),compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_22645,c_4514]) ).
tcf(c_22713,plain,
ifeq(domain(b),domain(a),compose(g,a),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_22654,c_64]) ).
tcf(c_22738,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),compose(X0,b),X0,compose(g,a)),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_6581,c_64]) ).
tcf(c_22739,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(h,compose(a,b)),compose(domain(X0),b),domain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_65,c_22738]) ).
tcf(c_22740,plain,
ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(a,b),a,compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_72,c_22738]) ).
tcf(c_22743,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),compose(codomain(X0),b),codomain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_102,c_22738]) ).
tcf(c_22744,plain,
ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(compose(a,b),b),compose(a,b),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_425,c_22738]) ).
tcf(c_22745,plain,
ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_2217,c_22738]) ).
tcf(c_22816,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),compose(X0,b),X0,compose(h,a)),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_6582,c_64]) ).
tcf(c_22817,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(h,compose(a,b)),compose(domain(X0),b),domain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_65,c_22816]) ).
tcf(c_22818,plain,
ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(a,b),a,compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_72,c_22816]) ).
tcf(c_22821,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),compose(codomain(X0),b),codomain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_102,c_22816]) ).
tcf(c_22822,plain,
ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(compose(a,b),b),compose(a,b),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_425,c_22816]) ).
tcf(c_22823,plain,
ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_2217,c_22816]) ).
tcf(c_22913,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),codomain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(X0,codomain(X1))),compose(compose(domain(X2),X0),codomain(X1))),compose(compose(domain(X2),X0),codomain(X1))) = compose(compose(domain(X2),X0),codomain(X1)),
inference(superposition,[status(thm)],[c_65,c_262]) ).
tcf(c_22917,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(X0,codomain(X1))),compose(compose(codomain(X2),X0),codomain(X1))),compose(compose(codomain(X2),X0),codomain(X1))) = compose(compose(codomain(X2),X0),codomain(X1)),
inference(superposition,[status(thm)],[c_102,c_262]) ).
tcf(c_22918,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,codomain(X1))),compose(compose(compose(a,b),X0),codomain(X1))),compose(compose(compose(a,b),X0),codomain(X1))) = compose(compose(compose(a,b),X0),codomain(X1)),
inference(superposition,[status(thm)],[c_425,c_262]) ).
tcf(c_22922,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(codomain(X0)),codomain(X1),ifeq(codomain(X2),codomain(X0),compose(X2,compose(codomain(X0),codomain(X1))),compose(compose(X2,codomain(X0)),codomain(X1))),compose(compose(X2,codomain(X0)),codomain(X1))) = compose(compose(X2,codomain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_262]) ).
tcf(c_22923,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,b)),codomain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,b),codomain(X0))),compose(compose(X1,compose(a,b)),codomain(X0))),compose(compose(X1,compose(a,b)),codomain(X0))) = compose(compose(X1,compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_171,c_262]) ).
tcf(c_22924,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(domain(X0)),codomain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(domain(X0),codomain(X1))),compose(compose(X2,domain(X0)),codomain(X1))),compose(compose(X2,domain(X0)),codomain(X1))) = compose(compose(X2,domain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_100,c_262]) ).
tcf(c_23018,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),codomain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(domain(X0),codomain(X1))),compose(compose(X2,domain(X0)),codomain(X1))),compose(compose(X2,domain(X0)),codomain(X1))) = compose(compose(X2,domain(X0)),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_22924,c_65]) ).
tcf(c_23019,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(X2),codomain(X0),compose(X2,compose(codomain(X0),codomain(X1))),compose(compose(X2,codomain(X0)),codomain(X1))),compose(compose(X2,codomain(X0)),codomain(X1))) = compose(compose(X2,codomain(X0)),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_22922,c_102]) ).
tcf(c_23034,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,b),codomain(X0))),compose(compose(X1,compose(a,b)),codomain(X0))),compose(compose(X1,compose(a,b)),codomain(X0))) = compose(compose(X1,compose(a,b)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_22923,c_425]) ).
tcf(c_23100,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(X0,domain(X1))),compose(compose(domain(X2),X0),domain(X1))),compose(compose(domain(X2),X0),domain(X1))) = compose(compose(domain(X2),X0),domain(X1)),
inference(superposition,[status(thm)],[c_65,c_264]) ).
tcf(c_23104,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(X0,domain(X1))),compose(compose(codomain(X2),X0),domain(X1))),compose(compose(codomain(X2),X0),domain(X1))) = compose(compose(codomain(X2),X0),domain(X1)),
inference(superposition,[status(thm)],[c_102,c_264]) ).
tcf(c_23105,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,domain(X1))),compose(compose(compose(a,b),X0),domain(X1))),compose(compose(compose(a,b),X0),domain(X1))) = compose(compose(compose(a,b),X0),domain(X1)),
inference(superposition,[status(thm)],[c_425,c_264]) ).
tcf(c_23109,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(codomain(X2),codomain(X0),compose(X2,compose(codomain(X0),domain(X1))),compose(compose(X2,codomain(X0)),domain(X1))),compose(compose(X2,codomain(X0)),domain(X1))) = compose(compose(X2,codomain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_66,c_264]) ).
tcf(c_23110,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,b),domain(X0))),compose(compose(X1,compose(a,b)),domain(X0))),compose(compose(X1,compose(a,b)),domain(X0))) = compose(compose(X1,compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_171,c_264]) ).
tcf(c_23111,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(domain(X0),domain(X1))),compose(compose(X2,domain(X0)),domain(X1))),compose(compose(X2,domain(X0)),domain(X1))) = compose(compose(X2,domain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_264]) ).
tcf(c_23201,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(domain(X0),domain(X1))),compose(compose(X2,domain(X0)),domain(X1))),compose(compose(X2,domain(X0)),domain(X1))) = compose(compose(X2,domain(X0)),domain(X1)),
inference(light_normalisation,[status(thm)],[c_23111,c_65]) ).
tcf(c_23202,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),codomain(X0),compose(X2,compose(codomain(X0),domain(X1))),compose(compose(X2,codomain(X0)),domain(X1))),compose(compose(X2,codomain(X0)),domain(X1))) = compose(compose(X2,codomain(X0)),domain(X1)),
inference(light_normalisation,[status(thm)],[c_23109,c_102]) ).
tcf(c_23218,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,b),domain(X0))),compose(compose(X1,compose(a,b)),domain(X0))),compose(compose(X1,compose(a,b)),domain(X0))) = compose(compose(X1,compose(a,b)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_23110,c_425]) ).
tcf(c_23240,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,compose(a,b))),compose(compose(domain(X1),X0),compose(a,b))),compose(compose(domain(X1),X0),compose(a,b))) = compose(compose(domain(X1),X0),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_265]) ).
tcf(c_23256,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(domain(X2),codomain(X0),compose(domain(X2),compose(codomain(X0),X1)),compose(compose(domain(X2),codomain(X0)),X1)),compose(compose(domain(X2),codomain(X0)),X1)) = compose(compose(domain(X2),codomain(X0)),X1),
inference(superposition,[status(thm)],[c_66,c_265]) ).
tcf(c_23257,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,b),X0)),compose(compose(domain(X1),compose(a,b)),X0)),compose(compose(domain(X1),compose(a,b)),X0)) = compose(compose(domain(X1),compose(a,b)),X0),
inference(superposition,[status(thm)],[c_171,c_265]) ).
tcf(c_23258,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(domain(X0),X1)),compose(compose(domain(X2),domain(X0)),X1)),compose(compose(domain(X2),domain(X0)),X1)) = compose(compose(domain(X2),domain(X0)),X1),
inference(superposition,[status(thm)],[c_100,c_265]) ).
tcf(c_23263,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(compose(X0,X1)),domain(X0),compose(X0,X1),compose(compose(domain(compose(X0,X1)),X0),X1)),compose(compose(domain(compose(X0,X1)),X0),X1)) = compose(compose(domain(compose(X0,X1)),X0),X1),
inference(superposition,[status(thm)],[c_67,c_265]) ).
tcf(c_23346,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(domain(X0),X1)),compose(compose(domain(X2),domain(X0)),X1)),compose(compose(domain(X2),domain(X0)),X1)) = compose(compose(domain(X2),domain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_23258,c_65]) ).
tcf(c_23347,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(X2),codomain(X0),compose(domain(X2),compose(codomain(X0),X1)),compose(compose(domain(X2),codomain(X0)),X1)),compose(compose(domain(X2),codomain(X0)),X1)) = compose(compose(domain(X2),codomain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_23256,c_102]) ).
tcf(c_23356,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,b),X0)),compose(compose(domain(X1),compose(a,b)),X0)),compose(compose(domain(X1),compose(a,b)),X0)) = compose(compose(domain(X1),compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_23257,c_425]) ).
tcf(c_23394,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,compose(a,b))),compose(compose(codomain(X1),X0),compose(a,b))),compose(compose(codomain(X1),X0),compose(a,b))) = compose(compose(codomain(X1),X0),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_269]) ).
tcf(c_23411,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(codomain(X2),codomain(X0),compose(codomain(X2),compose(codomain(X0),X1)),compose(compose(codomain(X2),codomain(X0)),X1)),compose(compose(codomain(X2),codomain(X0)),X1)) = compose(compose(codomain(X2),codomain(X0)),X1),
inference(superposition,[status(thm)],[c_66,c_269]) ).
tcf(c_23412,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,b),X0)),compose(compose(codomain(X1),compose(a,b)),X0)),compose(compose(codomain(X1),compose(a,b)),X0)) = compose(compose(codomain(X1),compose(a,b)),X0),
inference(superposition,[status(thm)],[c_171,c_269]) ).
tcf(c_23413,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(domain(X0),X1)),compose(compose(codomain(X2),domain(X0)),X1)),compose(compose(codomain(X2),domain(X0)),X1)) = compose(compose(codomain(X2),domain(X0)),X1),
inference(superposition,[status(thm)],[c_100,c_269]) ).
tcf(c_23482,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(domain(X0),X1)),compose(compose(codomain(X2),domain(X0)),X1)),compose(compose(codomain(X2),domain(X0)),X1)) = compose(compose(codomain(X2),domain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_23413,c_65]) ).
tcf(c_23483,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),codomain(X0),compose(codomain(X2),compose(codomain(X0),X1)),compose(compose(codomain(X2),codomain(X0)),X1)),compose(compose(codomain(X2),codomain(X0)),X1)) = compose(compose(codomain(X2),codomain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_23411,c_102]) ).
tcf(c_23491,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,b),X0)),compose(compose(codomain(X1),compose(a,b)),X0)),compose(compose(codomain(X1),compose(a,b)),X0)) = compose(compose(codomain(X1),compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_23412,c_425]) ).
tcf(c_23554,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),compose(a,b))),compose(compose(X1,domain(X0)),compose(a,b))),compose(compose(X1,domain(X0)),compose(a,b))) = compose(compose(X1,domain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_319]) ).
tcf(c_23565,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),X1)),compose(compose(compose(a,b),domain(X0)),X1)),compose(compose(compose(a,b),domain(X0)),X1)) = compose(compose(compose(a,b),domain(X0)),X1),
inference(superposition,[status(thm)],[c_425,c_319]) ).
tcf(c_23649,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),compose(a,b))),compose(compose(X1,codomain(X0)),compose(a,b))),compose(compose(X1,codomain(X0)),compose(a,b))) = compose(compose(X1,codomain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_320]) ).
tcf(c_23661,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),X1)),compose(compose(compose(a,b),codomain(X0)),X1)),compose(compose(compose(a,b),codomain(X0)),X1)) = compose(compose(compose(a,b),codomain(X0)),X1),
inference(superposition,[status(thm)],[c_425,c_320]) ).
tcf(c_23772,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),codomain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(h,codomain(X0))),compose(compose(domain(X1),h),codomain(X0))),compose(compose(domain(X1),h),codomain(X0))) = compose(compose(domain(X1),h),codomain(X0)),
inference(superposition,[status(thm)],[c_65,c_3314]) ).
tcf(c_23776,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),codomain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(h,codomain(X0))),compose(compose(codomain(X1),h),codomain(X0))),compose(compose(codomain(X1),h),codomain(X0))) = compose(compose(codomain(X1),h),codomain(X0)),
inference(superposition,[status(thm)],[c_102,c_3314]) ).
tcf(c_23777,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,codomain(X0))),compose(compose(compose(a,b),h),codomain(X0))),compose(compose(compose(a,b),h),codomain(X0))) = compose(compose(compose(a,b),h),codomain(X0)),
inference(superposition,[status(thm)],[c_425,c_3314]) ).
tcf(c_23778,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,codomain(X0))),compose(compose(compose(h,compose(a,b)),h),codomain(X0))),compose(compose(compose(h,compose(a,b)),h),codomain(X0))) = compose(compose(compose(h,compose(a,b)),h),codomain(X0)),
inference(superposition,[status(thm)],[c_2217,c_3314]) ).
tcf(c_23779,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,codomain(X0))),compose(compose(compose(h,a),h),codomain(X0))),compose(compose(compose(h,a),h),codomain(X0))) = compose(compose(compose(h,a),h),codomain(X0)),
inference(superposition,[status(thm)],[c_485,c_3314]) ).
tcf(c_23780,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,codomain(X0))),compose(compose(compose(g,a),h),codomain(X0))),compose(compose(compose(g,a),h),codomain(X0))) = compose(compose(compose(g,a),h),codomain(X0)),
inference(superposition,[status(thm)],[c_571,c_3314]) ).
tcf(c_23821,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(h,domain(X0))),compose(compose(domain(X1),h),domain(X0))),compose(compose(domain(X1),h),domain(X0))) = compose(compose(domain(X1),h),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_3323]) ).
tcf(c_23823,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(h,compose(a,b)))),compose(compose(domain(X0),h),compose(h,compose(a,b)))),compose(compose(domain(X0),h),compose(h,compose(a,b)))) = compose(compose(domain(X0),h),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_3323]) ).
tcf(c_23824,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(g,a))),compose(compose(domain(X0),h),compose(g,a))),compose(compose(domain(X0),h),compose(g,a))) = compose(compose(domain(X0),h),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_3323]) ).
tcf(c_23825,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(h,a))),compose(compose(domain(X0),h),compose(h,a))),compose(compose(domain(X0),h),compose(h,a))) = compose(compose(domain(X0),h),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_3323]) ).
tcf(c_23835,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(compose(h,X0)),domain(h),compose(h,X0),compose(compose(domain(compose(h,X0)),h),X0)),compose(compose(domain(compose(h,X0)),h),X0)) = compose(compose(domain(compose(h,X0)),h),X0),
inference(superposition,[status(thm)],[c_67,c_3323]) ).
tcf(c_24065,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),codomain(X1),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),codomain(X1))),compose(compose(h,codomain(X0)),codomain(X1))),compose(compose(h,codomain(X0)),codomain(X1))) = compose(compose(h,codomain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_3998]) ).
tcf(c_24067,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(X1),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),codomain(X1))),compose(compose(h,domain(X0)),codomain(X1))),compose(compose(h,domain(X0)),codomain(X1))) = compose(compose(h,domain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_100,c_3998]) ).
tcf(c_24069,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),codomain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(h,compose(h,compose(a,b))),codomain(X0))),compose(compose(h,compose(h,compose(a,b))),codomain(X0))) = compose(compose(h,compose(h,compose(a,b))),codomain(X0)),
inference(superposition,[status(thm)],[c_1392,c_3998]) ).
tcf(c_24070,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),codomain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),codomain(X0))),compose(compose(h,compose(g,a)),codomain(X0))),compose(compose(h,compose(g,a)),codomain(X0))) = compose(compose(h,compose(g,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_1491,c_3998]) ).
tcf(c_24071,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),codomain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),codomain(X0))),compose(compose(h,compose(h,a)),codomain(X0))),compose(compose(h,compose(h,a)),codomain(X0))) = compose(compose(h,compose(h,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_347,c_3998]) ).
tcf(c_24119,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(X1),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),codomain(X1))),compose(compose(h,domain(X0)),codomain(X1))),compose(compose(h,domain(X0)),codomain(X1))) = compose(compose(h,domain(X0)),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_24067,c_65]) ).
tcf(c_24120,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),codomain(X1))),compose(compose(h,codomain(X0)),codomain(X1))),compose(compose(h,codomain(X0)),codomain(X1))) = compose(compose(h,codomain(X0)),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_24065,c_102]) ).
tcf(c_24125,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),codomain(X0))),compose(compose(h,compose(h,a)),codomain(X0))),compose(compose(h,compose(h,a)),codomain(X0))) = compose(compose(h,compose(h,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_24071,c_485]) ).
tcf(c_24126,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),codomain(X0))),compose(compose(h,compose(g,a)),codomain(X0))),compose(compose(h,compose(g,a)),codomain(X0))) = compose(compose(h,compose(g,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_24070,c_571]) ).
tcf(c_24131,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(h,compose(h,compose(a,b))),codomain(X0))),compose(compose(h,compose(h,compose(a,b))),codomain(X0))) = compose(compose(h,compose(h,compose(a,b))),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_24069,c_2217]) ).
tcf(c_24145,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),compose(a,b))),compose(compose(h,codomain(X0)),compose(a,b))),compose(compose(h,codomain(X0)),compose(a,b))) = compose(compose(h,codomain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_4060]) ).
tcf(c_24146,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),domain(X1))),compose(compose(h,codomain(X0)),domain(X1))),compose(compose(h,codomain(X0)),domain(X1))) = compose(compose(h,codomain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_4060]) ).
tcf(c_24148,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(h,codomain(X0)),compose(h,compose(a,b)))),compose(compose(h,codomain(X0)),compose(h,compose(a,b)))) = compose(compose(h,codomain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_4060]) ).
tcf(c_24149,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),compose(g,a))),compose(compose(h,codomain(X0)),compose(g,a))),compose(compose(h,codomain(X0)),compose(g,a))) = compose(compose(h,codomain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_4060]) ).
tcf(c_24150,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),compose(h,a))),compose(compose(h,codomain(X0)),compose(h,a))),compose(compose(h,codomain(X0)),compose(h,a))) = compose(compose(h,codomain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_4060]) ).
tcf(c_24356,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),codomain(X1),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),codomain(X1))),compose(compose(g,codomain(X0)),codomain(X1))),compose(compose(g,codomain(X0)),codomain(X1))) = compose(compose(g,codomain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_4148]) ).
tcf(c_24358,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(X1),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),codomain(X1))),compose(compose(g,domain(X0)),codomain(X1))),compose(compose(g,domain(X0)),codomain(X1))) = compose(compose(g,domain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_100,c_4148]) ).
tcf(c_24360,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),codomain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(g,compose(h,compose(a,b))),codomain(X0))),compose(compose(g,compose(h,compose(a,b))),codomain(X0))) = compose(compose(g,compose(h,compose(a,b))),codomain(X0)),
inference(superposition,[status(thm)],[c_1392,c_4148]) ).
tcf(c_24361,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),codomain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),codomain(X0))),compose(compose(g,compose(g,a)),codomain(X0))),compose(compose(g,compose(g,a)),codomain(X0))) = compose(compose(g,compose(g,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_1491,c_4148]) ).
tcf(c_24362,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),codomain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),codomain(X0))),compose(compose(g,compose(h,a)),codomain(X0))),compose(compose(g,compose(h,a)),codomain(X0))) = compose(compose(g,compose(h,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_347,c_4148]) ).
tcf(c_24410,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(X1),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),codomain(X1))),compose(compose(g,domain(X0)),codomain(X1))),compose(compose(g,domain(X0)),codomain(X1))) = compose(compose(g,domain(X0)),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_24358,c_65]) ).
tcf(c_24411,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),codomain(X1))),compose(compose(g,codomain(X0)),codomain(X1))),compose(compose(g,codomain(X0)),codomain(X1))) = compose(compose(g,codomain(X0)),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_24356,c_102]) ).
tcf(c_24416,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),codomain(X0))),compose(compose(g,compose(h,a)),codomain(X0))),compose(compose(g,compose(h,a)),codomain(X0))) = compose(compose(g,compose(h,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_24362,c_485]) ).
tcf(c_24417,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),codomain(X0))),compose(compose(g,compose(g,a)),codomain(X0))),compose(compose(g,compose(g,a)),codomain(X0))) = compose(compose(g,compose(g,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_24361,c_571]) ).
tcf(c_24423,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(g,compose(h,compose(a,b))),codomain(X0))),compose(compose(g,compose(h,compose(a,b))),codomain(X0))) = compose(compose(g,compose(h,compose(a,b))),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_24360,c_2217]) ).
tcf(c_24437,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),compose(a,b))),compose(compose(g,codomain(X0)),compose(a,b))),compose(compose(g,codomain(X0)),compose(a,b))) = compose(compose(g,codomain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_4212]) ).
tcf(c_24438,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),domain(X1))),compose(compose(g,codomain(X0)),domain(X1))),compose(compose(g,codomain(X0)),domain(X1))) = compose(compose(g,codomain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_4212]) ).
tcf(c_24440,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(g,codomain(X0)),compose(h,compose(a,b)))),compose(compose(g,codomain(X0)),compose(h,compose(a,b)))) = compose(compose(g,codomain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_4212]) ).
tcf(c_24441,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),compose(g,a))),compose(compose(g,codomain(X0)),compose(g,a))),compose(compose(g,codomain(X0)),compose(g,a))) = compose(compose(g,codomain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_4212]) ).
tcf(c_24442,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),compose(h,a))),compose(compose(g,codomain(X0)),compose(h,a))),compose(compose(g,codomain(X0)),compose(h,a))) = compose(compose(g,codomain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_4212]) ).
tcf(c_24517,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(h),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),g)),compose(compose(domain(X1),codomain(X0)),g)),compose(compose(domain(X1),codomain(X0)),g)) = compose(compose(domain(X1),codomain(X0)),g),
inference(superposition,[status(thm)],[c_66,c_12450]) ).
tcf(c_24518,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),g)),compose(compose(domain(X0),compose(a,b)),g)),compose(compose(domain(X0),compose(a,b)),g)) = compose(compose(domain(X0),compose(a,b)),g),
inference(superposition,[status(thm)],[c_171,c_12450]) ).
tcf(c_24519,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),g)),compose(compose(domain(X1),domain(X0)),g)),compose(compose(domain(X1),domain(X0)),g)) = compose(compose(domain(X1),domain(X0)),g),
inference(superposition,[status(thm)],[c_100,c_12450]) ).
tcf(c_24521,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),g)),compose(compose(domain(X0),compose(h,compose(a,b))),g)),compose(compose(domain(X0),compose(h,compose(a,b))),g)) = compose(compose(domain(X0),compose(h,compose(a,b))),g),
inference(superposition,[status(thm)],[c_1392,c_12450]) ).
tcf(c_24522,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),g)),compose(compose(domain(X0),compose(g,a)),g)),compose(compose(domain(X0),compose(g,a)),g)) = compose(compose(domain(X0),compose(g,a)),g),
inference(superposition,[status(thm)],[c_1491,c_12450]) ).
tcf(c_24523,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),g)),compose(compose(domain(X0),compose(h,a)),g)),compose(compose(domain(X0),compose(h,a)),g)) = compose(compose(domain(X0),compose(h,a)),g),
inference(superposition,[status(thm)],[c_347,c_12450]) ).
tcf(c_24524,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(compose(X0,g)),domain(X0),compose(X0,g),compose(compose(domain(compose(X0,g)),X0),g)),compose(compose(domain(compose(X0,g)),X0),g)) = compose(compose(domain(compose(X0,g)),X0),g),
inference(superposition,[status(thm)],[c_67,c_12450]) ).
tcf(c_24574,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),g)),compose(compose(domain(X1),domain(X0)),g)),compose(compose(domain(X1),domain(X0)),g)) = compose(compose(domain(X1),domain(X0)),g),
inference(light_normalisation,[status(thm)],[c_24519,c_65]) ).
tcf(c_24575,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),g)),compose(compose(domain(X1),codomain(X0)),g)),compose(compose(domain(X1),codomain(X0)),g)) = compose(compose(domain(X1),codomain(X0)),g),
inference(light_normalisation,[status(thm)],[c_24517,c_102]) ).
tcf(c_24578,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),g)),compose(compose(domain(X0),compose(h,a)),g)),compose(compose(domain(X0),compose(h,a)),g)) = compose(compose(domain(X0),compose(h,a)),g),
inference(light_normalisation,[status(thm)],[c_24523,c_485]) ).
tcf(c_24579,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),g)),compose(compose(domain(X0),compose(g,a)),g)),compose(compose(domain(X0),compose(g,a)),g)) = compose(compose(domain(X0),compose(g,a)),g),
inference(light_normalisation,[status(thm)],[c_24522,c_571]) ).
tcf(c_24580,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),g)),compose(compose(domain(X0),compose(a,b)),g)),compose(compose(domain(X0),compose(a,b)),g)) = compose(compose(domain(X0),compose(a,b)),g),
inference(light_normalisation,[status(thm)],[c_24518,c_425]) ).
tcf(c_24585,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),g)),compose(compose(domain(X0),compose(h,compose(a,b))),g)),compose(compose(domain(X0),compose(h,compose(a,b))),g)) = compose(compose(domain(X0),compose(h,compose(a,b))),g),
inference(light_normalisation,[status(thm)],[c_24521,c_2217]) ).
tcf(c_24602,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),g)),compose(compose(codomain(X1),codomain(X0)),g)),compose(compose(codomain(X1),codomain(X0)),g)) = compose(compose(codomain(X1),codomain(X0)),g),
inference(superposition,[status(thm)],[c_102,c_12519]) ).
tcf(c_24603,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),g)),compose(compose(compose(a,b),codomain(X0)),g)),compose(compose(compose(a,b),codomain(X0)),g)) = compose(compose(compose(a,b),codomain(X0)),g),
inference(superposition,[status(thm)],[c_425,c_12519]) ).
tcf(c_24604,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),g)),compose(compose(compose(h,compose(a,b)),codomain(X0)),g)),compose(compose(compose(h,compose(a,b)),codomain(X0)),g)) = compose(compose(compose(h,compose(a,b)),codomain(X0)),g),
inference(superposition,[status(thm)],[c_2217,c_12519]) ).
tcf(c_24605,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),g)),compose(compose(compose(h,a),codomain(X0)),g)),compose(compose(compose(h,a),codomain(X0)),g)) = compose(compose(compose(h,a),codomain(X0)),g),
inference(superposition,[status(thm)],[c_485,c_12519]) ).
tcf(c_24606,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),g)),compose(compose(compose(g,a),codomain(X0)),g)),compose(compose(compose(g,a),codomain(X0)),g)) = compose(compose(compose(g,a),codomain(X0)),g),
inference(superposition,[status(thm)],[c_571,c_12519]) ).
tcf(c_24669,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),codomain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(g,codomain(X0))),compose(compose(domain(X1),g),codomain(X0))),compose(compose(domain(X1),g),codomain(X0))) = compose(compose(domain(X1),g),codomain(X0)),
inference(superposition,[status(thm)],[c_65,c_12577]) ).
tcf(c_24673,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),codomain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(g,codomain(X0))),compose(compose(codomain(X1),g),codomain(X0))),compose(compose(codomain(X1),g),codomain(X0))) = compose(compose(codomain(X1),g),codomain(X0)),
inference(superposition,[status(thm)],[c_102,c_12577]) ).
tcf(c_24674,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,codomain(X0))),compose(compose(compose(a,b),g),codomain(X0))),compose(compose(compose(a,b),g),codomain(X0))) = compose(compose(compose(a,b),g),codomain(X0)),
inference(superposition,[status(thm)],[c_425,c_12577]) ).
tcf(c_24675,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,codomain(X0))),compose(compose(compose(h,compose(a,b)),g),codomain(X0))),compose(compose(compose(h,compose(a,b)),g),codomain(X0))) = compose(compose(compose(h,compose(a,b)),g),codomain(X0)),
inference(superposition,[status(thm)],[c_2217,c_12577]) ).
tcf(c_24676,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,codomain(X0))),compose(compose(compose(h,a),g),codomain(X0))),compose(compose(compose(h,a),g),codomain(X0))) = compose(compose(compose(h,a),g),codomain(X0)),
inference(superposition,[status(thm)],[c_485,c_12577]) ).
tcf(c_24677,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,codomain(X0))),compose(compose(compose(g,a),g),codomain(X0))),compose(compose(compose(g,a),g),codomain(X0))) = compose(compose(compose(g,a),g),codomain(X0)),
inference(superposition,[status(thm)],[c_571,c_12577]) ).
tcf(c_24720,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(g,domain(X0))),compose(compose(domain(X1),g),domain(X0))),compose(compose(domain(X1),g),domain(X0))) = compose(compose(domain(X1),g),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_12584]) ).
tcf(c_24722,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(g,compose(h,compose(a,b)))),compose(compose(domain(X0),g),compose(h,compose(a,b)))),compose(compose(domain(X0),g),compose(h,compose(a,b)))) = compose(compose(domain(X0),g),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_12584]) ).
tcf(c_24723,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(g,compose(g,a))),compose(compose(domain(X0),g),compose(g,a))),compose(compose(domain(X0),g),compose(g,a))) = compose(compose(domain(X0),g),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_12584]) ).
tcf(c_24724,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(g,compose(h,a))),compose(compose(domain(X0),g),compose(h,a))),compose(compose(domain(X0),g),compose(h,a))) = compose(compose(domain(X0),g),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_12584]) ).
tcf(c_24734,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(compose(g,X0)),domain(h),compose(g,X0),compose(compose(domain(compose(g,X0)),g),X0)),compose(compose(domain(compose(g,X0)),g),X0)) = compose(compose(domain(compose(g,X0)),g),X0),
inference(superposition,[status(thm)],[c_67,c_12584]) ).
tcf(c_24778,plain,
! [X0: $i] : ifeq(compose(h,compose(a,b)),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_15099,c_64]) ).
tcf(c_24784,plain,
! [X0: $i] : ifeq(compose(h,compose(a,b)),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_15100,c_64]) ).
tcf(c_24810,plain,
ifeq(codomain(b),domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b)),
inference(superposition,[status(thm)],[c_2217,c_18646]) ).
tcf(c_24826,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b)),
inference(light_normalisation,[status(thm)],[c_24810,c_1392]) ).
tcf(c_25175,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(a,codomain(X0))),compose(compose(domain(X1),a),codomain(X0))),compose(compose(domain(X1),a),codomain(X0))) = compose(compose(domain(X1),a),codomain(X0)),
inference(superposition,[status(thm)],[c_65,c_17390]) ).
tcf(c_25179,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(a,codomain(X0))),compose(compose(codomain(X1),a),codomain(X0))),compose(compose(codomain(X1),a),codomain(X0))) = compose(compose(codomain(X1),a),codomain(X0)),
inference(superposition,[status(thm)],[c_102,c_17390]) ).
tcf(c_25180,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,codomain(X0))),compose(compose(compose(a,b),a),codomain(X0))),compose(compose(compose(a,b),a),codomain(X0))) = compose(compose(compose(a,b),a),codomain(X0)),
inference(superposition,[status(thm)],[c_425,c_17390]) ).
tcf(c_25181,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,codomain(X0))),compose(compose(compose(h,compose(a,b)),a),codomain(X0))),compose(compose(compose(h,compose(a,b)),a),codomain(X0))) = compose(compose(compose(h,compose(a,b)),a),codomain(X0)),
inference(superposition,[status(thm)],[c_2217,c_17390]) ).
tcf(c_25182,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,codomain(X0))),compose(compose(compose(h,a),a),codomain(X0))),compose(compose(compose(h,a),a),codomain(X0))) = compose(compose(compose(h,a),a),codomain(X0)),
inference(superposition,[status(thm)],[c_485,c_17390]) ).
tcf(c_25183,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,codomain(X0))),compose(compose(compose(g,a),a),codomain(X0))),compose(compose(compose(g,a),a),codomain(X0))) = compose(compose(compose(g,a),a),codomain(X0)),
inference(superposition,[status(thm)],[c_571,c_17390]) ).
tcf(c_25227,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,compose(a,b))),compose(compose(domain(X0),a),compose(a,b))),compose(compose(domain(X0),a),compose(a,b))) = compose(compose(domain(X0),a),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_17397]) ).
tcf(c_25228,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(a,domain(X0))),compose(compose(domain(X1),a),domain(X0))),compose(compose(domain(X1),a),domain(X0))) = compose(compose(domain(X1),a),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_17397]) ).
tcf(c_25230,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,compose(h,compose(a,b)))),compose(compose(domain(X0),a),compose(h,compose(a,b)))),compose(compose(domain(X0),a),compose(h,compose(a,b)))) = compose(compose(domain(X0),a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17397]) ).
tcf(c_25231,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,compose(g,a))),compose(compose(domain(X0),a),compose(g,a))),compose(compose(domain(X0),a),compose(g,a))) = compose(compose(domain(X0),a),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17397]) ).
tcf(c_25232,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,compose(h,a))),compose(compose(domain(X0),a),compose(h,a))),compose(compose(domain(X0),a),compose(h,a))) = compose(compose(domain(X0),a),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17397]) ).
tcf(c_25242,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(compose(a,X0)),domain(a),compose(a,X0),compose(compose(domain(compose(a,X0)),a),X0)),compose(compose(domain(compose(a,X0)),a),X0)) = compose(compose(domain(compose(a,X0)),a),X0),
inference(superposition,[status(thm)],[c_67,c_17397]) ).
tcf(c_25297,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),codomain(X1),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),codomain(X1))),compose(compose(a,codomain(X0)),codomain(X1))),compose(compose(a,codomain(X0)),codomain(X1))) = compose(compose(a,codomain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_17529]) ).
tcf(c_25298,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(X0),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),codomain(X0))),compose(compose(a,compose(a,b)),codomain(X0))),compose(compose(a,compose(a,b)),codomain(X0))) = compose(compose(a,compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_171,c_17529]) ).
tcf(c_25299,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(X1),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),codomain(X1))),compose(compose(a,domain(X0)),codomain(X1))),compose(compose(a,domain(X0)),codomain(X1))) = compose(compose(a,domain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_100,c_17529]) ).
tcf(c_25301,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),codomain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(a,compose(h,compose(a,b))),codomain(X0))),compose(compose(a,compose(h,compose(a,b))),codomain(X0))) = compose(compose(a,compose(h,compose(a,b))),codomain(X0)),
inference(superposition,[status(thm)],[c_1392,c_17529]) ).
tcf(c_25302,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),codomain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),codomain(X0))),compose(compose(a,compose(g,a)),codomain(X0))),compose(compose(a,compose(g,a)),codomain(X0))) = compose(compose(a,compose(g,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_1491,c_17529]) ).
tcf(c_25303,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),codomain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),codomain(X0))),compose(compose(a,compose(h,a)),codomain(X0))),compose(compose(a,compose(h,a)),codomain(X0))) = compose(compose(a,compose(h,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_347,c_17529]) ).
tcf(c_25350,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(X1),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),codomain(X1))),compose(compose(a,domain(X0)),codomain(X1))),compose(compose(a,domain(X0)),codomain(X1))) = compose(compose(a,domain(X0)),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_25299,c_65]) ).
tcf(c_25351,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),codomain(X1))),compose(compose(a,codomain(X0)),codomain(X1))),compose(compose(a,codomain(X0)),codomain(X1))) = compose(compose(a,codomain(X0)),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_25297,c_102]) ).
tcf(c_25356,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),codomain(X0))),compose(compose(a,compose(h,a)),codomain(X0))),compose(compose(a,compose(h,a)),codomain(X0))) = compose(compose(a,compose(h,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_25303,c_485]) ).
tcf(c_25357,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),codomain(X0))),compose(compose(a,compose(g,a)),codomain(X0))),compose(compose(a,compose(g,a)),codomain(X0))) = compose(compose(a,compose(g,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_25302,c_571]) ).
tcf(c_25358,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),codomain(X0))),compose(compose(a,compose(a,b)),codomain(X0))),compose(compose(a,compose(a,b)),codomain(X0))) = compose(compose(a,compose(a,b)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_25298,c_425]) ).
tcf(c_25362,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(a,compose(h,compose(a,b))),codomain(X0))),compose(compose(a,compose(h,compose(a,b))),codomain(X0))) = compose(compose(a,compose(h,compose(a,b))),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_25301,c_2217]) ).
tcf(c_25394,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),compose(a,b))),compose(compose(a,codomain(X0)),compose(a,b))),compose(compose(a,codomain(X0)),compose(a,b))) = compose(compose(a,codomain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_17585]) ).
tcf(c_25395,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),domain(X1))),compose(compose(a,codomain(X0)),domain(X1))),compose(compose(a,codomain(X0)),domain(X1))) = compose(compose(a,codomain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_17585]) ).
tcf(c_25397,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(a,codomain(X0)),compose(h,compose(a,b)))),compose(compose(a,codomain(X0)),compose(h,compose(a,b)))) = compose(compose(a,codomain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17585]) ).
tcf(c_25398,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),compose(g,a))),compose(compose(a,codomain(X0)),compose(g,a))),compose(compose(a,codomain(X0)),compose(g,a))) = compose(compose(a,codomain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17585]) ).
tcf(c_25399,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),compose(h,a))),compose(compose(a,codomain(X0)),compose(h,a))),compose(compose(a,codomain(X0)),compose(h,a))) = compose(compose(a,codomain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17585]) ).
tcf(c_25515,plain,
ifeq(domain(a),domain(h),ifeq(domain(compose(h,g)),domain(h),compose(h,g),compose(compose(domain(compose(h,g)),h),g)),compose(compose(domain(compose(h,g)),h),g)) = compose(compose(domain(compose(h,g)),h),g),
inference(superposition,[status(thm)],[c_67,c_18196]) ).
tcf(c_25566,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(h,domain(X0))),compose(compose(codomain(X1),h),domain(X0))),compose(compose(codomain(X1),h),domain(X0))) = compose(compose(codomain(X1),h),domain(X0)),
inference(superposition,[status(thm)],[c_102,c_3316]) ).
tcf(c_25567,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,domain(X0))),compose(compose(compose(a,b),h),domain(X0))),compose(compose(compose(a,b),h),domain(X0))) = compose(compose(compose(a,b),h),domain(X0)),
inference(superposition,[status(thm)],[c_425,c_3316]) ).
tcf(c_25568,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,domain(X0))),compose(compose(compose(h,compose(a,b)),h),domain(X0))),compose(compose(compose(h,compose(a,b)),h),domain(X0))) = compose(compose(compose(h,compose(a,b)),h),domain(X0)),
inference(superposition,[status(thm)],[c_2217,c_3316]) ).
tcf(c_25569,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,domain(X0))),compose(compose(compose(h,a),h),domain(X0))),compose(compose(compose(h,a),h),domain(X0))) = compose(compose(compose(h,a),h),domain(X0)),
inference(superposition,[status(thm)],[c_485,c_3316]) ).
tcf(c_25570,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,domain(X0))),compose(compose(compose(g,a),h),domain(X0))),compose(compose(compose(g,a),h),domain(X0))) = compose(compose(compose(g,a),h),domain(X0)),
inference(superposition,[status(thm)],[c_571,c_3316]) ).
tcf(c_25742,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(h,compose(a,b)))),compose(compose(codomain(X0),h),compose(h,compose(a,b)))),compose(compose(codomain(X0),h),compose(h,compose(a,b)))) = compose(compose(codomain(X0),h),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_3327]) ).
tcf(c_25743,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(g,a))),compose(compose(codomain(X0),h),compose(g,a))),compose(compose(codomain(X0),h),compose(g,a))) = compose(compose(codomain(X0),h),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_3327]) ).
tcf(c_25744,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(h,a))),compose(compose(codomain(X0),h),compose(h,a))),compose(compose(codomain(X0),h),compose(h,a))) = compose(compose(codomain(X0),h),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_3327]) ).
tcf(c_25809,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),domain(X1))),compose(compose(h,domain(X0)),domain(X1))),compose(compose(h,domain(X0)),domain(X1))) = compose(compose(h,domain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_4000]) ).
tcf(c_25811,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(h,compose(a,b))),domain(X0))),compose(compose(h,compose(h,compose(a,b))),domain(X0))) = compose(compose(h,compose(h,compose(a,b))),domain(X0)),
inference(superposition,[status(thm)],[c_1392,c_4000]) ).
tcf(c_25812,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),domain(X0))),compose(compose(h,compose(g,a)),domain(X0))),compose(compose(h,compose(g,a)),domain(X0))) = compose(compose(h,compose(g,a)),domain(X0)),
inference(superposition,[status(thm)],[c_1491,c_4000]) ).
tcf(c_25813,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),domain(X0))),compose(compose(h,compose(h,a)),domain(X0))),compose(compose(h,compose(h,a)),domain(X0))) = compose(compose(h,compose(h,a)),domain(X0)),
inference(superposition,[status(thm)],[c_347,c_4000]) ).
tcf(c_25856,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),domain(X1))),compose(compose(h,domain(X0)),domain(X1))),compose(compose(h,domain(X0)),domain(X1))) = compose(compose(h,domain(X0)),domain(X1)),
inference(light_normalisation,[status(thm)],[c_25809,c_65]) ).
tcf(c_25863,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),domain(X0))),compose(compose(h,compose(h,a)),domain(X0))),compose(compose(h,compose(h,a)),domain(X0))) = compose(compose(h,compose(h,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_25813,c_485]) ).
tcf(c_25864,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),domain(X0))),compose(compose(h,compose(g,a)),domain(X0))),compose(compose(h,compose(g,a)),domain(X0))) = compose(compose(h,compose(g,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_25812,c_571]) ).
tcf(c_25869,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(h,compose(a,b))),domain(X0))),compose(compose(h,compose(h,compose(a,b))),domain(X0))) = compose(compose(h,compose(h,compose(a,b))),domain(X0)),
inference(light_normalisation,[status(thm)],[c_25811,c_2217]) ).
tcf(c_25881,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),compose(a,b))),compose(compose(h,domain(X0)),compose(a,b))),compose(compose(h,domain(X0)),compose(a,b))) = compose(compose(h,domain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_4059]) ).
tcf(c_25884,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),compose(h,compose(a,b)))),compose(compose(h,domain(X0)),compose(h,compose(a,b)))),compose(compose(h,domain(X0)),compose(h,compose(a,b)))) = compose(compose(h,domain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_4059]) ).
tcf(c_25885,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),compose(g,a))),compose(compose(h,domain(X0)),compose(g,a))),compose(compose(h,domain(X0)),compose(g,a))) = compose(compose(h,domain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_4059]) ).
tcf(c_25886,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),compose(h,a))),compose(compose(h,domain(X0)),compose(h,a))),compose(compose(h,domain(X0)),compose(h,a))) = compose(compose(h,domain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_4059]) ).
tcf(c_25958,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),domain(X1))),compose(compose(g,domain(X0)),domain(X1))),compose(compose(g,domain(X0)),domain(X1))) = compose(compose(g,domain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_4150]) ).
tcf(c_25960,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),domain(X0))),compose(compose(g,compose(h,compose(a,b))),domain(X0))),compose(compose(g,compose(h,compose(a,b))),domain(X0))) = compose(compose(g,compose(h,compose(a,b))),domain(X0)),
inference(superposition,[status(thm)],[c_1392,c_4150]) ).
tcf(c_25961,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),domain(X0))),compose(compose(g,compose(g,a)),domain(X0))),compose(compose(g,compose(g,a)),domain(X0))) = compose(compose(g,compose(g,a)),domain(X0)),
inference(superposition,[status(thm)],[c_1491,c_4150]) ).
tcf(c_25962,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),domain(X0))),compose(compose(g,compose(h,a)),domain(X0))),compose(compose(g,compose(h,a)),domain(X0))) = compose(compose(g,compose(h,a)),domain(X0)),
inference(superposition,[status(thm)],[c_347,c_4150]) ).
tcf(c_26007,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),domain(X1))),compose(compose(g,domain(X0)),domain(X1))),compose(compose(g,domain(X0)),domain(X1))) = compose(compose(g,domain(X0)),domain(X1)),
inference(light_normalisation,[status(thm)],[c_25958,c_65]) ).
tcf(c_26014,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),domain(X0))),compose(compose(g,compose(h,a)),domain(X0))),compose(compose(g,compose(h,a)),domain(X0))) = compose(compose(g,compose(h,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_25962,c_485]) ).
tcf(c_26015,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),domain(X0))),compose(compose(g,compose(g,a)),domain(X0))),compose(compose(g,compose(g,a)),domain(X0))) = compose(compose(g,compose(g,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_25961,c_571]) ).
tcf(c_26021,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),domain(X0))),compose(compose(g,compose(h,compose(a,b))),domain(X0))),compose(compose(g,compose(h,compose(a,b))),domain(X0))) = compose(compose(g,compose(h,compose(a,b))),domain(X0)),
inference(light_normalisation,[status(thm)],[c_25960,c_2217]) ).
tcf(c_26033,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),compose(a,b))),compose(compose(g,domain(X0)),compose(a,b))),compose(compose(g,domain(X0)),compose(a,b))) = compose(compose(g,domain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_4211]) ).
tcf(c_26036,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),compose(h,compose(a,b)))),compose(compose(g,domain(X0)),compose(h,compose(a,b)))),compose(compose(g,domain(X0)),compose(h,compose(a,b)))) = compose(compose(g,domain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_4211]) ).
tcf(c_26037,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),compose(g,a))),compose(compose(g,domain(X0)),compose(g,a))),compose(compose(g,domain(X0)),compose(g,a))) = compose(compose(g,domain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_4211]) ).
tcf(c_26038,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),compose(h,a))),compose(compose(g,domain(X0)),compose(h,a))),compose(compose(g,domain(X0)),compose(h,a))) = compose(compose(g,domain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_4211]) ).
tcf(c_26357,plain,
ifeq(domain(b),domain(h),ifeq(domain(compose(a,g)),domain(a),compose(a,g),compose(compose(domain(compose(a,g)),a),g)),compose(compose(domain(compose(a,g)),a),g)) = compose(compose(domain(compose(a,g)),a),g),
inference(superposition,[status(thm)],[c_67,c_18505]) ).
tcf(c_26583,plain,
ifeq(domain(a),domain(h),ifeq(domain(compose(g,g)),domain(h),compose(g,g),compose(compose(domain(compose(g,g)),g),g)),compose(compose(domain(compose(g,g)),g),g)) = compose(compose(domain(compose(g,g)),g),g),
inference(superposition,[status(thm)],[c_67,c_18588]) ).
tcf(c_26664,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),g)),compose(compose(codomain(X0),compose(a,b)),g)),compose(compose(codomain(X0),compose(a,b)),g)) = compose(compose(codomain(X0),compose(a,b)),g),
inference(superposition,[status(thm)],[c_171,c_12454]) ).
tcf(c_26665,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),g)),compose(compose(codomain(X1),domain(X0)),g)),compose(compose(codomain(X1),domain(X0)),g)) = compose(compose(codomain(X1),domain(X0)),g),
inference(superposition,[status(thm)],[c_100,c_12454]) ).
tcf(c_26667,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),g)),compose(compose(codomain(X0),compose(h,compose(a,b))),g)),compose(compose(codomain(X0),compose(h,compose(a,b))),g)) = compose(compose(codomain(X0),compose(h,compose(a,b))),g),
inference(superposition,[status(thm)],[c_1392,c_12454]) ).
tcf(c_26668,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),g)),compose(compose(codomain(X0),compose(g,a)),g)),compose(compose(codomain(X0),compose(g,a)),g)) = compose(compose(codomain(X0),compose(g,a)),g),
inference(superposition,[status(thm)],[c_1491,c_12454]) ).
tcf(c_26669,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),g)),compose(compose(codomain(X0),compose(h,a)),g)),compose(compose(codomain(X0),compose(h,a)),g)) = compose(compose(codomain(X0),compose(h,a)),g),
inference(superposition,[status(thm)],[c_347,c_12454]) ).
tcf(c_26708,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),g)),compose(compose(codomain(X1),domain(X0)),g)),compose(compose(codomain(X1),domain(X0)),g)) = compose(compose(codomain(X1),domain(X0)),g),
inference(light_normalisation,[status(thm)],[c_26665,c_65]) ).
tcf(c_26712,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),g)),compose(compose(codomain(X0),compose(h,a)),g)),compose(compose(codomain(X0),compose(h,a)),g)) = compose(compose(codomain(X0),compose(h,a)),g),
inference(light_normalisation,[status(thm)],[c_26669,c_485]) ).
tcf(c_26713,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),g)),compose(compose(codomain(X0),compose(g,a)),g)),compose(compose(codomain(X0),compose(g,a)),g)) = compose(compose(codomain(X0),compose(g,a)),g),
inference(light_normalisation,[status(thm)],[c_26668,c_571]) ).
tcf(c_26714,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),g)),compose(compose(codomain(X0),compose(a,b)),g)),compose(compose(codomain(X0),compose(a,b)),g)) = compose(compose(codomain(X0),compose(a,b)),g),
inference(light_normalisation,[status(thm)],[c_26664,c_425]) ).
tcf(c_26718,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),g)),compose(compose(codomain(X0),compose(h,compose(a,b))),g)),compose(compose(codomain(X0),compose(h,compose(a,b))),g)) = compose(compose(codomain(X0),compose(h,compose(a,b))),g),
inference(light_normalisation,[status(thm)],[c_26667,c_2217]) ).
tcf(c_26734,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),g)),compose(compose(compose(a,b),domain(X0)),g)),compose(compose(compose(a,b),domain(X0)),g)) = compose(compose(compose(a,b),domain(X0)),g),
inference(superposition,[status(thm)],[c_425,c_12518]) ).
tcf(c_26735,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),g)),compose(compose(compose(h,compose(a,b)),domain(X0)),g)),compose(compose(compose(h,compose(a,b)),domain(X0)),g)) = compose(compose(compose(h,compose(a,b)),domain(X0)),g),
inference(superposition,[status(thm)],[c_2217,c_12518]) ).
tcf(c_26736,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),g)),compose(compose(compose(h,a),domain(X0)),g)),compose(compose(compose(h,a),domain(X0)),g)) = compose(compose(compose(h,a),domain(X0)),g),
inference(superposition,[status(thm)],[c_485,c_12518]) ).
tcf(c_26737,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),g)),compose(compose(compose(g,a),domain(X0)),g)),compose(compose(compose(g,a),domain(X0)),g)) = compose(compose(compose(g,a),domain(X0)),g),
inference(superposition,[status(thm)],[c_571,c_12518]) ).
tcf(c_26795,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,h),compose(a,b))) = compose(compose(X0,h),compose(a,b)),
inference(demodulation,[status(thm)],[c_3315,c_64]) ).
tcf(c_26796,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),h),compose(a,b))) = compose(compose(domain(X0),h),compose(a,b)),
inference(superposition,[status(thm)],[c_65,c_26795]) ).
tcf(c_26797,plain,
ifeq(domain(b),domain(h),compose(a,compose(h,compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(superposition,[status(thm)],[c_72,c_26795]) ).
tcf(c_26798,plain,
ifeq(domain(a),domain(h),compose(h,compose(h,compose(a,b))),compose(compose(h,h),compose(a,b))) = compose(compose(h,h),compose(a,b)),
inference(superposition,[status(thm)],[c_167,c_26795]) ).
tcf(c_26799,plain,
ifeq(domain(a),domain(h),compose(g,compose(h,compose(a,b))),compose(compose(g,h),compose(a,b))) = compose(compose(g,h),compose(a,b)),
inference(superposition,[status(thm)],[c_170,c_26795]) ).
tcf(c_26800,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),h),compose(a,b))) = compose(compose(codomain(X0),h),compose(a,b)),
inference(superposition,[status(thm)],[c_102,c_26795]) ).
tcf(c_26801,plain,
ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),h),compose(a,b))) = compose(compose(compose(a,b),h),compose(a,b)),
inference(superposition,[status(thm)],[c_425,c_26795]) ).
tcf(c_26802,plain,
ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),h),compose(a,b))) = compose(compose(compose(h,compose(a,b)),h),compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_26795]) ).
tcf(c_26803,plain,
ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(compose(h,a),h),compose(a,b))) = compose(compose(compose(h,a),h),compose(a,b)),
inference(superposition,[status(thm)],[c_485,c_26795]) ).
tcf(c_26804,plain,
ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),h),compose(a,b))) = compose(compose(compose(g,a),h),compose(a,b)),
inference(superposition,[status(thm)],[c_571,c_26795]) ).
tcf(c_26951,plain,
! [X0: $i,X1: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(g,domain(X0))),compose(compose(codomain(X1),g),domain(X0))),compose(compose(codomain(X1),g),domain(X0))) = compose(compose(codomain(X1),g),domain(X0)),
inference(superposition,[status(thm)],[c_102,c_12579]) ).
tcf(c_26952,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,domain(X0))),compose(compose(compose(a,b),g),domain(X0))),compose(compose(compose(a,b),g),domain(X0))) = compose(compose(compose(a,b),g),domain(X0)),
inference(superposition,[status(thm)],[c_425,c_12579]) ).
tcf(c_26953,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,domain(X0))),compose(compose(compose(h,compose(a,b)),g),domain(X0))),compose(compose(compose(h,compose(a,b)),g),domain(X0))) = compose(compose(compose(h,compose(a,b)),g),domain(X0)),
inference(superposition,[status(thm)],[c_2217,c_12579]) ).
tcf(c_26954,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,domain(X0))),compose(compose(compose(h,a),g),domain(X0))),compose(compose(compose(h,a),g),domain(X0))) = compose(compose(compose(h,a),g),domain(X0)),
inference(superposition,[status(thm)],[c_485,c_12579]) ).
tcf(c_26955,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,domain(X0))),compose(compose(compose(g,a),g),domain(X0))),compose(compose(compose(g,a),g),domain(X0))) = compose(compose(compose(g,a),g),domain(X0)),
inference(superposition,[status(thm)],[c_571,c_12579]) ).
tcf(c_26993,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,compose(h,compose(a,b)))),compose(compose(codomain(X0),g),compose(h,compose(a,b)))),compose(compose(codomain(X0),g),compose(h,compose(a,b)))) = compose(compose(codomain(X0),g),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_12588]) ).
tcf(c_26994,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,compose(g,a))),compose(compose(codomain(X0),g),compose(g,a))),compose(compose(codomain(X0),g),compose(g,a))) = compose(compose(codomain(X0),g),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_12588]) ).
tcf(c_26995,plain,
! [X0: $i] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,compose(h,a))),compose(compose(codomain(X0),g),compose(h,a))),compose(compose(codomain(X0),g),compose(h,a))) = compose(compose(codomain(X0),g),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_12588]) ).
tcf(c_27131,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(h,compose(a,b)))),compose(compose(compose(a,b),h),compose(h,compose(a,b)))),compose(compose(compose(a,b),h),compose(h,compose(a,b)))) = compose(compose(compose(a,b),h),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_425,c_3318]) ).
tcf(c_27132,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),h),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),h),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),h),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_3318]) ).
tcf(c_27133,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(h,compose(a,b)))),compose(compose(compose(h,a),h),compose(h,compose(a,b)))),compose(compose(compose(h,a),h),compose(h,compose(a,b)))) = compose(compose(compose(h,a),h),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_485,c_3318]) ).
tcf(c_27134,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(h,compose(a,b)))),compose(compose(compose(g,a),h),compose(h,compose(a,b)))),compose(compose(compose(g,a),h),compose(h,compose(a,b)))) = compose(compose(compose(g,a),h),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_571,c_3318]) ).
tcf(c_27410,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(a,domain(X0))),compose(compose(codomain(X1),a),domain(X0))),compose(compose(codomain(X1),a),domain(X0))) = compose(compose(codomain(X1),a),domain(X0)),
inference(superposition,[status(thm)],[c_102,c_17392]) ).
tcf(c_27411,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,domain(X0))),compose(compose(compose(a,b),a),domain(X0))),compose(compose(compose(a,b),a),domain(X0))) = compose(compose(compose(a,b),a),domain(X0)),
inference(superposition,[status(thm)],[c_425,c_17392]) ).
tcf(c_27412,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,domain(X0))),compose(compose(compose(h,compose(a,b)),a),domain(X0))),compose(compose(compose(h,compose(a,b)),a),domain(X0))) = compose(compose(compose(h,compose(a,b)),a),domain(X0)),
inference(superposition,[status(thm)],[c_2217,c_17392]) ).
tcf(c_27413,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,domain(X0))),compose(compose(compose(h,a),a),domain(X0))),compose(compose(compose(h,a),a),domain(X0))) = compose(compose(compose(h,a),a),domain(X0)),
inference(superposition,[status(thm)],[c_485,c_17392]) ).
tcf(c_27414,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,domain(X0))),compose(compose(compose(g,a),a),domain(X0))),compose(compose(compose(g,a),a),domain(X0))) = compose(compose(compose(g,a),a),domain(X0)),
inference(superposition,[status(thm)],[c_571,c_17392]) ).
tcf(c_27451,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,compose(a,b))),compose(compose(codomain(X0),a),compose(a,b))),compose(compose(codomain(X0),a),compose(a,b))) = compose(compose(codomain(X0),a),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_17401]) ).
tcf(c_27454,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,compose(h,compose(a,b)))),compose(compose(codomain(X0),a),compose(h,compose(a,b)))),compose(compose(codomain(X0),a),compose(h,compose(a,b)))) = compose(compose(codomain(X0),a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17401]) ).
tcf(c_27455,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,compose(g,a))),compose(compose(codomain(X0),a),compose(g,a))),compose(compose(codomain(X0),a),compose(g,a))) = compose(compose(codomain(X0),a),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17401]) ).
tcf(c_27456,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,compose(h,a))),compose(compose(codomain(X0),a),compose(h,a))),compose(compose(codomain(X0),a),compose(h,a))) = compose(compose(codomain(X0),a),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17401]) ).
tcf(c_27526,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),domain(X0))),compose(compose(a,compose(a,b)),domain(X0))),compose(compose(a,compose(a,b)),domain(X0))) = compose(compose(a,compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_171,c_17531]) ).
tcf(c_27527,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),domain(X1))),compose(compose(a,domain(X0)),domain(X1))),compose(compose(a,domain(X0)),domain(X1))) = compose(compose(a,domain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_17531]) ).
tcf(c_27529,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),domain(X0))),compose(compose(a,compose(h,compose(a,b))),domain(X0))),compose(compose(a,compose(h,compose(a,b))),domain(X0))) = compose(compose(a,compose(h,compose(a,b))),domain(X0)),
inference(superposition,[status(thm)],[c_1392,c_17531]) ).
tcf(c_27530,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),domain(X0))),compose(compose(a,compose(g,a)),domain(X0))),compose(compose(a,compose(g,a)),domain(X0))) = compose(compose(a,compose(g,a)),domain(X0)),
inference(superposition,[status(thm)],[c_1491,c_17531]) ).
tcf(c_27531,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),domain(X0))),compose(compose(a,compose(h,a)),domain(X0))),compose(compose(a,compose(h,a)),domain(X0))) = compose(compose(a,compose(h,a)),domain(X0)),
inference(superposition,[status(thm)],[c_347,c_17531]) ).
tcf(c_27571,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),domain(X1))),compose(compose(a,domain(X0)),domain(X1))),compose(compose(a,domain(X0)),domain(X1))) = compose(compose(a,domain(X0)),domain(X1)),
inference(light_normalisation,[status(thm)],[c_27527,c_65]) ).
tcf(c_27578,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),domain(X0))),compose(compose(a,compose(h,a)),domain(X0))),compose(compose(a,compose(h,a)),domain(X0))) = compose(compose(a,compose(h,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_27531,c_485]) ).
tcf(c_27579,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),domain(X0))),compose(compose(a,compose(g,a)),domain(X0))),compose(compose(a,compose(g,a)),domain(X0))) = compose(compose(a,compose(g,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_27530,c_571]) ).
tcf(c_27580,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),domain(X0))),compose(compose(a,compose(a,b)),domain(X0))),compose(compose(a,compose(a,b)),domain(X0))) = compose(compose(a,compose(a,b)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_27526,c_425]) ).
tcf(c_27584,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),domain(X0))),compose(compose(a,compose(h,compose(a,b))),domain(X0))),compose(compose(a,compose(h,compose(a,b))),domain(X0))) = compose(compose(a,compose(h,compose(a,b))),domain(X0)),
inference(light_normalisation,[status(thm)],[c_27529,c_2217]) ).
tcf(c_27596,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),compose(a,b))),compose(compose(a,domain(X0)),compose(a,b))),compose(compose(a,domain(X0)),compose(a,b))) = compose(compose(a,domain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_17584]) ).
tcf(c_27599,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),compose(h,compose(a,b)))),compose(compose(a,domain(X0)),compose(h,compose(a,b)))),compose(compose(a,domain(X0)),compose(h,compose(a,b)))) = compose(compose(a,domain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17584]) ).
tcf(c_27600,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),compose(g,a))),compose(compose(a,domain(X0)),compose(g,a))),compose(compose(a,domain(X0)),compose(g,a))) = compose(compose(a,domain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17584]) ).
tcf(c_27601,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),compose(h,a))),compose(compose(a,domain(X0)),compose(h,a))),compose(compose(a,domain(X0)),compose(h,a))) = compose(compose(a,domain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17584]) ).
tcf(c_27798,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(g,a))),compose(compose(compose(a,b),h),compose(g,a))),compose(compose(compose(a,b),h),compose(g,a))) = compose(compose(compose(a,b),h),compose(g,a)),
inference(superposition,[status(thm)],[c_425,c_3319]) ).
tcf(c_27799,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(g,a))),compose(compose(compose(h,compose(a,b)),h),compose(g,a))),compose(compose(compose(h,compose(a,b)),h),compose(g,a))) = compose(compose(compose(h,compose(a,b)),h),compose(g,a)),
inference(superposition,[status(thm)],[c_2217,c_3319]) ).
tcf(c_27800,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(g,a))),compose(compose(compose(h,a),h),compose(g,a))),compose(compose(compose(h,a),h),compose(g,a))) = compose(compose(compose(h,a),h),compose(g,a)),
inference(superposition,[status(thm)],[c_485,c_3319]) ).
tcf(c_27801,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(g,a))),compose(compose(compose(g,a),h),compose(g,a))),compose(compose(compose(g,a),h),compose(g,a))) = compose(compose(compose(g,a),h),compose(g,a)),
inference(superposition,[status(thm)],[c_571,c_3319]) ).
tcf(c_28167,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(h,a))),compose(compose(compose(a,b),h),compose(h,a))),compose(compose(compose(a,b),h),compose(h,a))) = compose(compose(compose(a,b),h),compose(h,a)),
inference(superposition,[status(thm)],[c_425,c_3320]) ).
tcf(c_28168,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(h,a))),compose(compose(compose(h,compose(a,b)),h),compose(h,a))),compose(compose(compose(h,compose(a,b)),h),compose(h,a))) = compose(compose(compose(h,compose(a,b)),h),compose(h,a)),
inference(superposition,[status(thm)],[c_2217,c_3320]) ).
tcf(c_28169,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(h,a))),compose(compose(compose(h,a),h),compose(h,a))),compose(compose(compose(h,a),h),compose(h,a))) = compose(compose(compose(h,a),h),compose(h,a)),
inference(superposition,[status(thm)],[c_485,c_3320]) ).
tcf(c_28170,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(h,a))),compose(compose(compose(g,a),h),compose(h,a))),compose(compose(compose(g,a),h),compose(h,a))) = compose(compose(compose(g,a),h),compose(h,a)),
inference(superposition,[status(thm)],[c_571,c_3320]) ).
tcf(c_28251,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),codomain(compose(domain(X1),codomain(X0))),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),codomain(compose(domain(X1),codomain(X0))))),compose(domain(X1),codomain(X0))),compose(domain(X1),codomain(X0))) = compose(domain(X1),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_17693]) ).
tcf(c_28252,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(compose(domain(X0),compose(a,b))),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),codomain(compose(domain(X0),compose(a,b))))),compose(domain(X0),compose(a,b))),compose(domain(X0),compose(a,b))) = compose(domain(X0),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_17693]) ).
tcf(c_28253,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(compose(domain(X1),domain(X0))),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),codomain(compose(domain(X1),domain(X0))))),compose(domain(X1),domain(X0))),compose(domain(X1),domain(X0))) = compose(domain(X1),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_17693]) ).
tcf(c_28255,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),codomain(compose(domain(X0),compose(h,compose(a,b)))),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),codomain(compose(domain(X0),compose(h,compose(a,b)))))),compose(domain(X0),compose(h,compose(a,b)))),compose(domain(X0),compose(h,compose(a,b)))) = compose(domain(X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17693]) ).
tcf(c_28256,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),codomain(compose(domain(X0),compose(g,a))),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),codomain(compose(domain(X0),compose(g,a))))),compose(domain(X0),compose(g,a))),compose(domain(X0),compose(g,a))) = compose(domain(X0),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17693]) ).
tcf(c_28257,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),codomain(compose(domain(X0),compose(h,a))),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),codomain(compose(domain(X0),compose(h,a))))),compose(domain(X0),compose(h,a))),compose(domain(X0),compose(h,a))) = compose(domain(X0),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17693]) ).
tcf(c_28320,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(compose(domain(X1),domain(X0))),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),codomain(compose(domain(X1),domain(X0))))),compose(domain(X1),domain(X0))),compose(domain(X1),domain(X0))) = compose(domain(X1),domain(X0)),
inference(light_normalisation,[status(thm)],[c_28253,c_65]) ).
tcf(c_28321,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(compose(domain(X1),codomain(X0))),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),codomain(compose(domain(X1),codomain(X0))))),compose(domain(X1),codomain(X0))),compose(domain(X1),codomain(X0))) = compose(domain(X1),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_28251,c_102]) ).
tcf(c_28324,plain,
! [X0: $i] : ifeq(domain(b),codomain(compose(domain(X0),compose(h,a))),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),codomain(compose(domain(X0),compose(h,a))))),compose(domain(X0),compose(h,a))),compose(domain(X0),compose(h,a))) = compose(domain(X0),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_28257,c_485]) ).
tcf(c_28325,plain,
! [X0: $i] : ifeq(domain(b),codomain(compose(domain(X0),compose(g,a))),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),codomain(compose(domain(X0),compose(g,a))))),compose(domain(X0),compose(g,a))),compose(domain(X0),compose(g,a))) = compose(domain(X0),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_28256,c_571]) ).
tcf(c_28326,plain,
! [X0: $i] : ifeq(codomain(b),codomain(compose(domain(X0),compose(a,b))),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),codomain(compose(domain(X0),compose(a,b))))),compose(domain(X0),compose(a,b))),compose(domain(X0),compose(a,b))) = compose(domain(X0),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_28252,c_425]) ).
tcf(c_28331,plain,
! [X0: $i] : ifeq(codomain(b),codomain(compose(domain(X0),compose(h,compose(a,b)))),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),codomain(compose(domain(X0),compose(h,compose(a,b)))))),compose(domain(X0),compose(h,compose(a,b)))),compose(domain(X0),compose(h,compose(a,b)))) = compose(domain(X0),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_28255,c_2217]) ).
tcf(c_28364,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(compose(codomain(X1),codomain(X0))),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),codomain(compose(codomain(X1),codomain(X0))))),compose(codomain(X1),codomain(X0))),compose(codomain(X1),codomain(X0))) = compose(codomain(X1),codomain(X0)),
inference(superposition,[status(thm)],[c_102,c_17787]) ).
tcf(c_28365,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(compose(a,b),codomain(X0))),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),codomain(compose(compose(a,b),codomain(X0))))),compose(compose(a,b),codomain(X0))),compose(compose(a,b),codomain(X0))) = compose(compose(a,b),codomain(X0)),
inference(superposition,[status(thm)],[c_425,c_17787]) ).
tcf(c_28366,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(compose(h,compose(a,b)),codomain(X0))),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),codomain(compose(compose(h,compose(a,b)),codomain(X0))))),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_2217,c_17787]) ).
tcf(c_28367,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(compose(h,a),codomain(X0))),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),codomain(compose(compose(h,a),codomain(X0))))),compose(compose(h,a),codomain(X0))),compose(compose(h,a),codomain(X0))) = compose(compose(h,a),codomain(X0)),
inference(superposition,[status(thm)],[c_485,c_17787]) ).
tcf(c_28368,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(compose(g,a),codomain(X0))),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),codomain(compose(compose(g,a),codomain(X0))))),compose(compose(g,a),codomain(X0))),compose(compose(g,a),codomain(X0))) = compose(compose(g,a),codomain(X0)),
inference(superposition,[status(thm)],[c_571,c_17787]) ).
tcf(c_29337,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(compose(codomain(X0),compose(a,b))),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),codomain(compose(codomain(X0),compose(a,b))))),compose(codomain(X0),compose(a,b))),compose(codomain(X0),compose(a,b))) = compose(codomain(X0),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_17697]) ).
tcf(c_29338,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(compose(codomain(X1),domain(X0))),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),codomain(compose(codomain(X1),domain(X0))))),compose(codomain(X1),domain(X0))),compose(codomain(X1),domain(X0))) = compose(codomain(X1),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_17697]) ).
tcf(c_29340,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),codomain(compose(codomain(X0),compose(h,compose(a,b)))),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),codomain(compose(codomain(X0),compose(h,compose(a,b)))))),compose(codomain(X0),compose(h,compose(a,b)))),compose(codomain(X0),compose(h,compose(a,b)))) = compose(codomain(X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17697]) ).
tcf(c_29341,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),codomain(compose(codomain(X0),compose(g,a))),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),codomain(compose(codomain(X0),compose(g,a))))),compose(codomain(X0),compose(g,a))),compose(codomain(X0),compose(g,a))) = compose(codomain(X0),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17697]) ).
tcf(c_29342,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),codomain(compose(codomain(X0),compose(h,a))),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),codomain(compose(codomain(X0),compose(h,a))))),compose(codomain(X0),compose(h,a))),compose(codomain(X0),compose(h,a))) = compose(codomain(X0),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17697]) ).
tcf(c_29389,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(compose(codomain(X1),domain(X0))),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),codomain(compose(codomain(X1),domain(X0))))),compose(codomain(X1),domain(X0))),compose(codomain(X1),domain(X0))) = compose(codomain(X1),domain(X0)),
inference(light_normalisation,[status(thm)],[c_29338,c_65]) ).
tcf(c_29393,plain,
! [X0: $i] : ifeq(domain(b),codomain(compose(codomain(X0),compose(h,a))),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),codomain(compose(codomain(X0),compose(h,a))))),compose(codomain(X0),compose(h,a))),compose(codomain(X0),compose(h,a))) = compose(codomain(X0),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_29342,c_485]) ).
tcf(c_29394,plain,
! [X0: $i] : ifeq(domain(b),codomain(compose(codomain(X0),compose(g,a))),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),codomain(compose(codomain(X0),compose(g,a))))),compose(codomain(X0),compose(g,a))),compose(codomain(X0),compose(g,a))) = compose(codomain(X0),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_29341,c_571]) ).
tcf(c_29395,plain,
! [X0: $i] : ifeq(codomain(b),codomain(compose(codomain(X0),compose(a,b))),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),codomain(compose(codomain(X0),compose(a,b))))),compose(codomain(X0),compose(a,b))),compose(codomain(X0),compose(a,b))) = compose(codomain(X0),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_29337,c_425]) ).
tcf(c_29399,plain,
! [X0: $i] : ifeq(codomain(b),codomain(compose(codomain(X0),compose(h,compose(a,b)))),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),codomain(compose(codomain(X0),compose(h,compose(a,b)))))),compose(codomain(X0),compose(h,compose(a,b)))),compose(codomain(X0),compose(h,compose(a,b)))) = compose(codomain(X0),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_29340,c_2217]) ).
tcf(c_29428,plain,
! [X0: $i] : ifeq(domain(X0),codomain(compose(compose(a,b),domain(X0))),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),codomain(compose(compose(a,b),domain(X0))))),compose(compose(a,b),domain(X0))),compose(compose(a,b),domain(X0))) = compose(compose(a,b),domain(X0)),
inference(superposition,[status(thm)],[c_425,c_17786]) ).
tcf(c_29429,plain,
! [X0: $i] : ifeq(domain(X0),codomain(compose(compose(h,compose(a,b)),domain(X0))),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),codomain(compose(compose(h,compose(a,b)),domain(X0))))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_2217,c_17786]) ).
tcf(c_29430,plain,
! [X0: $i] : ifeq(domain(X0),codomain(compose(compose(h,a),domain(X0))),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),codomain(compose(compose(h,a),domain(X0))))),compose(compose(h,a),domain(X0))),compose(compose(h,a),domain(X0))) = compose(compose(h,a),domain(X0)),
inference(superposition,[status(thm)],[c_485,c_17786]) ).
tcf(c_29431,plain,
! [X0: $i] : ifeq(domain(X0),codomain(compose(compose(g,a),domain(X0))),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),codomain(compose(compose(g,a),domain(X0))))),compose(compose(g,a),domain(X0))),compose(compose(g,a),domain(X0))) = compose(compose(g,a),domain(X0)),
inference(superposition,[status(thm)],[c_571,c_17786]) ).
tcf(c_30341,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(a),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(h,compose(h,compose(a,b))),compose(a,b))),compose(compose(h,compose(h,compose(a,b))),compose(a,b))) = compose(compose(h,compose(h,compose(a,b))),compose(a,b)),
inference(superposition,[status(thm)],[c_1392,c_3999]) ).
tcf(c_30342,plain,
ifeq(codomain(compose(g,a)),domain(a),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),compose(a,b))),compose(compose(h,compose(g,a)),compose(a,b))),compose(compose(h,compose(g,a)),compose(a,b))) = compose(compose(h,compose(g,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_1491,c_3999]) ).
tcf(c_30343,plain,
ifeq(codomain(compose(h,a)),domain(a),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),compose(a,b))),compose(compose(h,compose(h,a)),compose(a,b))),compose(compose(h,compose(h,a)),compose(a,b))) = compose(compose(h,compose(h,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_347,c_3999]) ).
tcf(c_30363,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),compose(a,b))),compose(compose(h,compose(h,a)),compose(a,b))),compose(compose(h,compose(h,a)),compose(a,b))) = compose(compose(h,compose(h,a)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_30343,c_485]) ).
tcf(c_30364,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),compose(a,b))),compose(compose(h,compose(g,a)),compose(a,b))),compose(compose(h,compose(g,a)),compose(a,b))) = compose(compose(h,compose(g,a)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_30342,c_571]) ).
tcf(c_30370,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(h,compose(h,compose(a,b))),compose(a,b))),compose(compose(h,compose(h,compose(a,b))),compose(a,b))) = compose(compose(h,compose(h,compose(a,b))),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_30341,c_2217]) ).
tcf(c_30623,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(h,compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(h,compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_4002]) ).
tcf(c_30624,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(h,compose(g,a)),compose(h,compose(a,b)))),compose(compose(h,compose(g,a)),compose(h,compose(a,b)))) = compose(compose(h,compose(g,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1491,c_4002]) ).
tcf(c_30625,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,compose(h,a)),compose(h,compose(a,b)))),compose(compose(h,compose(h,a)),compose(h,compose(a,b)))) = compose(compose(h,compose(h,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_347,c_4002]) ).
tcf(c_30640,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,compose(h,a)),compose(h,compose(a,b)))),compose(compose(h,compose(h,a)),compose(h,compose(a,b)))) = compose(compose(h,compose(h,a)),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_30625,c_485]) ).
tcf(c_30641,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(h,compose(g,a)),compose(h,compose(a,b)))),compose(compose(h,compose(g,a)),compose(h,compose(a,b)))) = compose(compose(h,compose(g,a)),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_30624,c_571]) ).
tcf(c_30646,plain,
ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(h,compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(h,compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_30623,c_2217]) ).
tcf(c_30664,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(b,X0,domain(b),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_11847,c_64]) ).
tcf(c_30668,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(b,X0,domain(b),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_11848,c_64]) ).
tcf(c_30687,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(h,compose(h,compose(a,b))),compose(g,a))),compose(compose(h,compose(h,compose(a,b))),compose(g,a))) = compose(compose(h,compose(h,compose(a,b))),compose(g,a)),
inference(superposition,[status(thm)],[c_1392,c_4003]) ).
tcf(c_30688,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),compose(g,a))),compose(compose(h,compose(g,a)),compose(g,a))),compose(compose(h,compose(g,a)),compose(g,a))) = compose(compose(h,compose(g,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_4003]) ).
tcf(c_30689,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),compose(g,a))),compose(compose(h,compose(h,a)),compose(g,a))),compose(compose(h,compose(h,a)),compose(g,a))) = compose(compose(h,compose(h,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_347,c_4003]) ).
tcf(c_30704,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),compose(g,a))),compose(compose(h,compose(h,a)),compose(g,a))),compose(compose(h,compose(h,a)),compose(g,a))) = compose(compose(h,compose(h,a)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_30689,c_485]) ).
tcf(c_30705,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),compose(g,a))),compose(compose(h,compose(g,a)),compose(g,a))),compose(compose(h,compose(g,a)),compose(g,a))) = compose(compose(h,compose(g,a)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_30688,c_571]) ).
tcf(c_30711,plain,
ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(h,compose(h,compose(a,b))),compose(g,a))),compose(compose(h,compose(h,compose(a,b))),compose(g,a))) = compose(compose(h,compose(h,compose(a,b))),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_30687,c_2217]) ).
tcf(c_30729,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,compose(a,b))),compose(compose(compose(a,b),X0),compose(a,b))),compose(compose(compose(a,b),X0),compose(a,b))) = compose(compose(compose(a,b),X0),compose(a,b)),
inference(superposition,[status(thm)],[c_425,c_263]) ).
tcf(c_30734,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(a,b))),compose(compose(X0,compose(a,b)),compose(a,b))),compose(compose(X0,compose(a,b)),compose(a,b))) = compose(compose(X0,compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_263]) ).
tcf(c_30810,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(a,b))),compose(compose(X0,compose(a,b)),compose(a,b))),compose(compose(X0,compose(a,b)),compose(a,b))) = compose(compose(X0,compose(a,b)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_30734,c_425]) ).
tcf(c_30893,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),X0)),compose(compose(compose(a,b),compose(a,b)),X0)),compose(compose(compose(a,b),compose(a,b)),X0)) = compose(compose(compose(a,b),compose(a,b)),X0),
inference(superposition,[status(thm)],[c_171,c_448]) ).
tcf(c_30945,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),X0)),compose(compose(compose(a,b),compose(a,b)),X0)),compose(compose(compose(a,b),compose(a,b)),X0)) = compose(compose(compose(a,b),compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_30893,c_425]) ).
tcf(c_30976,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(h,compose(h,compose(a,b))),compose(h,a))),compose(compose(h,compose(h,compose(a,b))),compose(h,a))) = compose(compose(h,compose(h,compose(a,b))),compose(h,a)),
inference(superposition,[status(thm)],[c_1392,c_4004]) ).
tcf(c_30977,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),compose(h,a))),compose(compose(h,compose(g,a)),compose(h,a))),compose(compose(h,compose(g,a)),compose(h,a))) = compose(compose(h,compose(g,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_1491,c_4004]) ).
tcf(c_30978,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),compose(h,a))),compose(compose(h,compose(h,a)),compose(h,a))),compose(compose(h,compose(h,a)),compose(h,a))) = compose(compose(h,compose(h,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_4004]) ).
tcf(c_30993,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),compose(h,a))),compose(compose(h,compose(h,a)),compose(h,a))),compose(compose(h,compose(h,a)),compose(h,a))) = compose(compose(h,compose(h,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_30978,c_485]) ).
tcf(c_30994,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),compose(h,a))),compose(compose(h,compose(g,a)),compose(h,a))),compose(compose(h,compose(g,a)),compose(h,a))) = compose(compose(h,compose(g,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_30977,c_571]) ).
tcf(c_31000,plain,
ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(h,compose(h,compose(a,b))),compose(h,a))),compose(compose(h,compose(h,compose(a,b))),compose(h,a))) = compose(compose(h,compose(h,compose(a,b))),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_30976,c_2217]) ).
tcf(c_31038,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(X0,b),X1,X0,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(demodulation,[status(thm)],[c_4554,c_64]) ).
tcf(c_31039,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(domain(X0),b),X1,domain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_65,c_31038]) ).
tcf(c_31040,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(a,b),X0,a,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_72,c_31038]) ).
tcf(c_31043,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_102,c_31038]) ).
tcf(c_31044,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_425,c_31038]) ).
tcf(c_31045,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_2217,c_31038]) ).
tcf(c_31046,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(compose(h,a),b),X0,compose(h,a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_485,c_31038]) ).
tcf(c_31047,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(compose(g,a),b),X0,compose(g,a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(superposition,[status(thm)],[c_571,c_31038]) ).
tcf(c_31063,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_31047,c_4514]) ).
tcf(c_31064,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
inference(light_normalisation,[status(thm)],[c_31046,c_6074]) ).
tcf(c_31151,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,compose(h,a))),compose(compose(compose(a,b),a),compose(h,a))),compose(compose(compose(a,b),a),compose(h,a))) = compose(compose(compose(a,b),a),compose(h,a)),
inference(superposition,[status(thm)],[c_425,c_5183]) ).
tcf(c_31152,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,compose(h,a))),compose(compose(compose(h,compose(a,b)),a),compose(h,a))),compose(compose(compose(h,compose(a,b)),a),compose(h,a))) = compose(compose(compose(h,compose(a,b)),a),compose(h,a)),
inference(superposition,[status(thm)],[c_2217,c_5183]) ).
tcf(c_31153,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,compose(h,a))),compose(compose(compose(h,a),a),compose(h,a))),compose(compose(compose(h,a),a),compose(h,a))) = compose(compose(compose(h,a),a),compose(h,a)),
inference(superposition,[status(thm)],[c_485,c_5183]) ).
tcf(c_31154,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,compose(h,a))),compose(compose(compose(g,a),a),compose(h,a))),compose(compose(compose(g,a),a),compose(h,a))) = compose(compose(compose(g,a),a),compose(h,a)),
inference(superposition,[status(thm)],[c_571,c_5183]) ).
tcf(c_31170,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),compose(h,a))),compose(compose(a,compose(a,b)),compose(h,a))),compose(compose(a,compose(a,b)),compose(h,a))) = compose(compose(a,compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_171,c_5193]) ).
tcf(c_31173,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(a,compose(h,compose(a,b))),compose(h,a))),compose(compose(a,compose(h,compose(a,b))),compose(h,a))) = compose(compose(a,compose(h,compose(a,b))),compose(h,a)),
inference(superposition,[status(thm)],[c_1392,c_5193]) ).
tcf(c_31174,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),compose(h,a))),compose(compose(a,compose(g,a)),compose(h,a))),compose(compose(a,compose(g,a)),compose(h,a))) = compose(compose(a,compose(g,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_1491,c_5193]) ).
tcf(c_31175,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),compose(h,a))),compose(compose(a,compose(h,a)),compose(h,a))),compose(compose(a,compose(h,a)),compose(h,a))) = compose(compose(a,compose(h,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_5193]) ).
tcf(c_31189,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),compose(h,a))),compose(compose(a,compose(h,a)),compose(h,a))),compose(compose(a,compose(h,a)),compose(h,a))) = compose(compose(a,compose(h,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_31175,c_485]) ).
tcf(c_31190,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),compose(h,a))),compose(compose(a,compose(g,a)),compose(h,a))),compose(compose(a,compose(g,a)),compose(h,a))) = compose(compose(a,compose(g,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_31174,c_571]) ).
tcf(c_31191,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),compose(h,a))),compose(compose(a,compose(a,b)),compose(h,a))),compose(compose(a,compose(a,b)),compose(h,a))) = compose(compose(a,compose(a,b)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_31170,c_425]) ).
tcf(c_31196,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(a,compose(h,compose(a,b))),compose(h,a))),compose(compose(a,compose(h,compose(a,b))),compose(h,a))) = compose(compose(a,compose(h,compose(a,b))),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_31173,c_2217]) ).
tcf(c_31233,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(h,compose(compose(a,b),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
inference(demodulation,[status(thm)],[c_4069,c_64]) ).
tcf(c_31234,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),compose(h,compose(compose(a,b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_31233]) ).
tcf(c_31235,plain,
ifeq(codomain(b),domain(a),compose(h,compose(compose(a,b),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_31233]) ).
tcf(c_31236,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(h,compose(compose(a,b),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_31233]) ).
tcf(c_31237,plain,
ifeq(codomain(b),domain(h),compose(h,compose(compose(a,b),g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
inference(superposition,[status(thm)],[c_1480,c_31233]) ).
tcf(c_31238,plain,
ifeq(codomain(b),domain(h),compose(h,compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_31233]) ).
tcf(c_31239,plain,
ifeq(codomain(b),domain(h),compose(h,compose(compose(a,b),compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_31233]) ).
tcf(c_31240,plain,
ifeq(codomain(b),domain(h),compose(h,compose(compose(a,b),compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_31233]) ).
tcf(c_31313,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(X0,b),X1,X0,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(demodulation,[status(thm)],[c_6154,c_64]) ).
tcf(c_31314,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(domain(X0),b),X1,domain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_65,c_31313]) ).
tcf(c_31315,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(a,b),X0,a,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_72,c_31313]) ).
tcf(c_31318,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_102,c_31313]) ).
tcf(c_31319,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_425,c_31313]) ).
tcf(c_31320,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_2217,c_31313]) ).
tcf(c_31321,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(compose(h,a),b),X0,compose(h,a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_485,c_31313]) ).
tcf(c_31322,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(compose(g,a),b),X0,compose(g,a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(superposition,[status(thm)],[c_571,c_31313]) ).
tcf(c_31338,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_31322,c_4514]) ).
tcf(c_31339,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
inference(light_normalisation,[status(thm)],[c_31321,c_6074]) ).
tcf(c_31431,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(a),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(g,compose(h,compose(a,b))),compose(a,b))),compose(compose(g,compose(h,compose(a,b))),compose(a,b))) = compose(compose(g,compose(h,compose(a,b))),compose(a,b)),
inference(superposition,[status(thm)],[c_1392,c_4149]) ).
tcf(c_31432,plain,
ifeq(codomain(compose(g,a)),domain(a),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),compose(a,b))),compose(compose(g,compose(g,a)),compose(a,b))),compose(compose(g,compose(g,a)),compose(a,b))) = compose(compose(g,compose(g,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_1491,c_4149]) ).
tcf(c_31433,plain,
ifeq(codomain(compose(h,a)),domain(a),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),compose(a,b))),compose(compose(g,compose(h,a)),compose(a,b))),compose(compose(g,compose(h,a)),compose(a,b))) = compose(compose(g,compose(h,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_347,c_4149]) ).
tcf(c_31455,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),compose(a,b))),compose(compose(g,compose(h,a)),compose(a,b))),compose(compose(g,compose(h,a)),compose(a,b))) = compose(compose(g,compose(h,a)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_31433,c_485]) ).
tcf(c_31456,plain,
ifeq(domain(b),domain(a),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),compose(a,b))),compose(compose(g,compose(g,a)),compose(a,b))),compose(compose(g,compose(g,a)),compose(a,b))) = compose(compose(g,compose(g,a)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_31432,c_571]) ).
tcf(c_31463,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(g,compose(h,compose(a,b))),compose(a,b))),compose(compose(g,compose(h,compose(a,b))),compose(a,b))) = compose(compose(g,compose(h,compose(a,b))),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_31431,c_2217]) ).
tcf(c_31480,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(g,compose(h,compose(a,b))),compose(g,a))),compose(compose(g,compose(h,compose(a,b))),compose(g,a))) = compose(compose(g,compose(h,compose(a,b))),compose(g,a)),
inference(superposition,[status(thm)],[c_1392,c_4153]) ).
tcf(c_31481,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),compose(g,a))),compose(compose(g,compose(g,a)),compose(g,a))),compose(compose(g,compose(g,a)),compose(g,a))) = compose(compose(g,compose(g,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_4153]) ).
tcf(c_31482,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),compose(g,a))),compose(compose(g,compose(h,a)),compose(g,a))),compose(compose(g,compose(h,a)),compose(g,a))) = compose(compose(g,compose(h,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_347,c_4153]) ).
tcf(c_31499,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),compose(g,a))),compose(compose(g,compose(h,a)),compose(g,a))),compose(compose(g,compose(h,a)),compose(g,a))) = compose(compose(g,compose(h,a)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_31482,c_485]) ).
tcf(c_31500,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),compose(g,a))),compose(compose(g,compose(g,a)),compose(g,a))),compose(compose(g,compose(g,a)),compose(g,a))) = compose(compose(g,compose(g,a)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_31481,c_571]) ).
tcf(c_31507,plain,
ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(g,compose(h,compose(a,b))),compose(g,a))),compose(compose(g,compose(h,compose(a,b))),compose(g,a))) = compose(compose(g,compose(h,compose(a,b))),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_31480,c_2217]) ).
tcf(c_31524,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(g,compose(h,compose(a,b))),compose(h,a))),compose(compose(g,compose(h,compose(a,b))),compose(h,a))) = compose(compose(g,compose(h,compose(a,b))),compose(h,a)),
inference(superposition,[status(thm)],[c_1392,c_4154]) ).
tcf(c_31525,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),compose(h,a))),compose(compose(g,compose(g,a)),compose(h,a))),compose(compose(g,compose(g,a)),compose(h,a))) = compose(compose(g,compose(g,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_1491,c_4154]) ).
tcf(c_31526,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),compose(h,a))),compose(compose(g,compose(h,a)),compose(h,a))),compose(compose(g,compose(h,a)),compose(h,a))) = compose(compose(g,compose(h,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_4154]) ).
tcf(c_31543,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),compose(h,a))),compose(compose(g,compose(h,a)),compose(h,a))),compose(compose(g,compose(h,a)),compose(h,a))) = compose(compose(g,compose(h,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_31526,c_485]) ).
tcf(c_31544,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),compose(h,a))),compose(compose(g,compose(g,a)),compose(h,a))),compose(compose(g,compose(g,a)),compose(h,a))) = compose(compose(g,compose(g,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_31525,c_571]) ).
tcf(c_31551,plain,
ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(g,compose(h,compose(a,b))),compose(h,a))),compose(compose(g,compose(h,compose(a,b))),compose(h,a))) = compose(compose(g,compose(h,compose(a,b))),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_31524,c_2217]) ).
tcf(c_31566,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(g,compose(h,a)),compose(h,compose(a,b)))),compose(compose(g,compose(h,a)),compose(h,compose(a,b)))) = compose(compose(g,compose(h,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_4218]) ).
tcf(c_31583,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,compose(a,b))),compose(compose(compose(h,a),a),compose(a,b))),compose(compose(compose(h,a),a),compose(a,b))) = compose(compose(compose(h,a),a),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_7340]) ).
tcf(c_31586,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,compose(h,compose(a,b)))),compose(compose(compose(h,a),a),compose(h,compose(a,b)))),compose(compose(compose(h,a),a),compose(h,compose(a,b)))) = compose(compose(compose(h,a),a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_7340]) ).
tcf(c_31587,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,compose(g,a))),compose(compose(compose(h,a),a),compose(g,a))),compose(compose(compose(h,a),a),compose(g,a))) = compose(compose(compose(h,a),a),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_7340]) ).
tcf(c_31599,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),compose(a,b))),compose(compose(a,compose(h,a)),compose(a,b))),compose(compose(a,compose(h,a)),compose(a,b))) = compose(compose(a,compose(h,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_7587]) ).
tcf(c_31602,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(a,compose(h,a)),compose(h,compose(a,b)))),compose(compose(a,compose(h,a)),compose(h,compose(a,b)))) = compose(compose(a,compose(h,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_7587]) ).
tcf(c_31603,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),compose(g,a))),compose(compose(a,compose(h,a)),compose(g,a))),compose(compose(a,compose(h,a)),compose(g,a))) = compose(compose(a,compose(h,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_7587]) ).
tcf(c_31621,plain,
ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(g,compose(g,a)),compose(h,compose(a,b)))),compose(compose(g,compose(g,a)),compose(h,compose(a,b)))) = compose(compose(g,compose(g,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_4219]) ).
tcf(c_31633,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(g,compose(compose(a,b),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
inference(demodulation,[status(thm)],[c_4220,c_64]) ).
tcf(c_31634,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),compose(g,compose(compose(a,b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_31633]) ).
tcf(c_31635,plain,
ifeq(codomain(b),domain(a),compose(g,compose(compose(a,b),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_31633]) ).
tcf(c_31636,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(g,compose(compose(a,b),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_31633]) ).
tcf(c_31637,plain,
ifeq(codomain(b),domain(h),compose(g,compose(compose(a,b),g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
inference(superposition,[status(thm)],[c_1480,c_31633]) ).
tcf(c_31638,plain,
ifeq(codomain(b),domain(h),compose(g,compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_31633]) ).
tcf(c_31639,plain,
ifeq(codomain(b),domain(h),compose(g,compose(compose(a,b),compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_31633]) ).
tcf(c_31640,plain,
ifeq(codomain(b),domain(h),compose(g,compose(compose(a,b),compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_31633]) ).
tcf(c_31713,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,compose(a,b))),compose(compose(compose(g,a),a),compose(a,b))),compose(compose(compose(g,a),a),compose(a,b))) = compose(compose(compose(g,a),a),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_8537]) ).
tcf(c_31716,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,compose(h,compose(a,b)))),compose(compose(compose(g,a),a),compose(h,compose(a,b)))),compose(compose(compose(g,a),a),compose(h,compose(a,b)))) = compose(compose(compose(g,a),a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_8537]) ).
tcf(c_31717,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,compose(g,a))),compose(compose(compose(g,a),a),compose(g,a))),compose(compose(compose(g,a),a),compose(g,a))) = compose(compose(compose(g,a),a),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_8537]) ).
tcf(c_31732,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,compose(g,a))),compose(compose(compose(a,b),a),compose(g,a))),compose(compose(compose(a,b),a),compose(g,a))) = compose(compose(compose(a,b),a),compose(g,a)),
inference(superposition,[status(thm)],[c_425,c_13696]) ).
tcf(c_31733,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,compose(g,a))),compose(compose(compose(h,compose(a,b)),a),compose(g,a))),compose(compose(compose(h,compose(a,b)),a),compose(g,a))) = compose(compose(compose(h,compose(a,b)),a),compose(g,a)),
inference(superposition,[status(thm)],[c_2217,c_13696]) ).
tcf(c_31756,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,compose(h,a))),compose(compose(compose(a,b),g),compose(h,a))),compose(compose(compose(a,b),g),compose(h,a))) = compose(compose(compose(a,b),g),compose(h,a)),
inference(superposition,[status(thm)],[c_425,c_5259]) ).
tcf(c_31757,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,compose(h,a))),compose(compose(compose(h,compose(a,b)),g),compose(h,a))),compose(compose(compose(h,compose(a,b)),g),compose(h,a))) = compose(compose(compose(h,compose(a,b)),g),compose(h,a)),
inference(superposition,[status(thm)],[c_2217,c_5259]) ).
tcf(c_31758,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,compose(h,a))),compose(compose(compose(h,a),g),compose(h,a))),compose(compose(compose(h,a),g),compose(h,a))) = compose(compose(compose(h,a),g),compose(h,a)),
inference(superposition,[status(thm)],[c_485,c_5259]) ).
tcf(c_31759,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,compose(h,a))),compose(compose(compose(g,a),g),compose(h,a))),compose(compose(compose(g,a),g),compose(h,a))) = compose(compose(compose(g,a),g),compose(h,a)),
inference(superposition,[status(thm)],[c_571,c_5259]) ).
tcf(c_31782,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),compose(g,a))),compose(compose(a,compose(a,b)),compose(g,a))),compose(compose(a,compose(a,b)),compose(g,a))) = compose(compose(a,compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_171,c_13705]) ).
tcf(c_31785,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(a,compose(h,compose(a,b))),compose(g,a))),compose(compose(a,compose(h,compose(a,b))),compose(g,a))) = compose(compose(a,compose(h,compose(a,b))),compose(g,a)),
inference(superposition,[status(thm)],[c_1392,c_13705]) ).
tcf(c_31786,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),compose(g,a))),compose(compose(a,compose(g,a)),compose(g,a))),compose(compose(a,compose(g,a)),compose(g,a))) = compose(compose(a,compose(g,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_13705]) ).
tcf(c_31802,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),compose(g,a))),compose(compose(a,compose(g,a)),compose(g,a))),compose(compose(a,compose(g,a)),compose(g,a))) = compose(compose(a,compose(g,a)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_31786,c_571]) ).
tcf(c_31803,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),compose(g,a))),compose(compose(a,compose(a,b)),compose(g,a))),compose(compose(a,compose(a,b)),compose(g,a))) = compose(compose(a,compose(a,b)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_31782,c_425]) ).
tcf(c_31808,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(a,compose(h,compose(a,b))),compose(g,a))),compose(compose(a,compose(h,compose(a,b))),compose(g,a))) = compose(compose(a,compose(h,compose(a,b))),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_31785,c_2217]) ).
tcf(c_31813,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),compose(a,b))),compose(compose(a,compose(g,a)),compose(a,b))),compose(compose(a,compose(g,a)),compose(a,b))) = compose(compose(a,compose(g,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_13939]) ).
tcf(c_31816,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(a,compose(g,a)),compose(h,compose(a,b)))),compose(compose(a,compose(g,a)),compose(h,compose(a,b)))) = compose(compose(a,compose(g,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_13939]) ).
tcf(c_31846,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),g)),compose(compose(compose(h,a),compose(a,b)),g)),compose(compose(compose(h,a),compose(a,b)),g)) = compose(compose(compose(h,a),compose(a,b)),g),
inference(superposition,[status(thm)],[c_171,c_7351]) ).
tcf(c_31849,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),g)),compose(compose(compose(h,a),compose(h,compose(a,b))),g)),compose(compose(compose(h,a),compose(h,compose(a,b))),g)) = compose(compose(compose(h,a),compose(h,compose(a,b))),g),
inference(superposition,[status(thm)],[c_1392,c_7351]) ).
tcf(c_31850,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),g)),compose(compose(compose(h,a),compose(g,a)),g)),compose(compose(compose(h,a),compose(g,a)),g)) = compose(compose(compose(h,a),compose(g,a)),g),
inference(superposition,[status(thm)],[c_1491,c_7351]) ).
tcf(c_31851,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),g)),compose(compose(compose(h,a),compose(h,a)),g)),compose(compose(compose(h,a),compose(h,a)),g)) = compose(compose(compose(h,a),compose(h,a)),g),
inference(superposition,[status(thm)],[c_347,c_7351]) ).
tcf(c_31869,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),g)),compose(compose(compose(h,a),compose(h,a)),g)),compose(compose(compose(h,a),compose(h,a)),g)) = compose(compose(compose(h,a),compose(h,a)),g),
inference(light_normalisation,[status(thm)],[c_31851,c_485]) ).
tcf(c_31870,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),g)),compose(compose(compose(h,a),compose(g,a)),g)),compose(compose(compose(h,a),compose(g,a)),g)) = compose(compose(compose(h,a),compose(g,a)),g),
inference(light_normalisation,[status(thm)],[c_31850,c_571]) ).
tcf(c_31871,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),g)),compose(compose(compose(h,a),compose(a,b)),g)),compose(compose(compose(h,a),compose(a,b)),g)) = compose(compose(compose(h,a),compose(a,b)),g),
inference(light_normalisation,[status(thm)],[c_31846,c_425]) ).
tcf(c_31875,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),g)),compose(compose(compose(h,a),compose(h,compose(a,b))),g)),compose(compose(compose(h,a),compose(h,compose(a,b))),g)) = compose(compose(compose(h,a),compose(h,compose(a,b))),g),
inference(light_normalisation,[status(thm)],[c_31849,c_2217]) ).
tcf(c_31883,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,compose(h,compose(a,b)))),compose(compose(compose(h,a),g),compose(h,compose(a,b)))),compose(compose(compose(h,a),g),compose(h,compose(a,b)))) = compose(compose(compose(h,a),g),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_7391]) ).
tcf(c_31884,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,compose(g,a))),compose(compose(compose(h,a),g),compose(g,a))),compose(compose(compose(h,a),g),compose(g,a))) = compose(compose(compose(h,a),g),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_7391]) ).
tcf(c_31903,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),g)),compose(compose(compose(a,b),compose(h,a)),g)),compose(compose(compose(a,b),compose(h,a)),g)) = compose(compose(compose(a,b),compose(h,a)),g),
inference(superposition,[status(thm)],[c_425,c_7582]) ).
tcf(c_31904,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),g)),compose(compose(compose(h,compose(a,b)),compose(h,a)),g)),compose(compose(compose(h,compose(a,b)),compose(h,a)),g)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),g),
inference(superposition,[status(thm)],[c_2217,c_7582]) ).
tcf(c_31906,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),g)),compose(compose(compose(g,a),compose(h,a)),g)),compose(compose(compose(g,a),compose(h,a)),g)) = compose(compose(compose(g,a),compose(h,a)),g),
inference(superposition,[status(thm)],[c_571,c_7582]) ).
tcf(c_31928,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),g)),compose(compose(compose(g,a),compose(a,b)),g)),compose(compose(compose(g,a),compose(a,b)),g)) = compose(compose(compose(g,a),compose(a,b)),g),
inference(superposition,[status(thm)],[c_171,c_8548]) ).
tcf(c_31931,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),g)),compose(compose(compose(g,a),compose(h,compose(a,b))),g)),compose(compose(compose(g,a),compose(h,compose(a,b))),g)) = compose(compose(compose(g,a),compose(h,compose(a,b))),g),
inference(superposition,[status(thm)],[c_1392,c_8548]) ).
tcf(c_31932,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),g)),compose(compose(compose(g,a),compose(g,a)),g)),compose(compose(compose(g,a),compose(g,a)),g)) = compose(compose(compose(g,a),compose(g,a)),g),
inference(superposition,[status(thm)],[c_1491,c_8548]) ).
tcf(c_31952,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),g)),compose(compose(compose(g,a),compose(g,a)),g)),compose(compose(compose(g,a),compose(g,a)),g)) = compose(compose(compose(g,a),compose(g,a)),g),
inference(light_normalisation,[status(thm)],[c_31932,c_571]) ).
tcf(c_31953,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),g)),compose(compose(compose(g,a),compose(a,b)),g)),compose(compose(compose(g,a),compose(a,b)),g)) = compose(compose(compose(g,a),compose(a,b)),g),
inference(light_normalisation,[status(thm)],[c_31928,c_425]) ).
tcf(c_31957,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),g)),compose(compose(compose(g,a),compose(h,compose(a,b))),g)),compose(compose(compose(g,a),compose(h,compose(a,b))),g)) = compose(compose(compose(g,a),compose(h,compose(a,b))),g),
inference(light_normalisation,[status(thm)],[c_31931,c_2217]) ).
tcf(c_31965,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,compose(h,compose(a,b)))),compose(compose(compose(g,a),g),compose(h,compose(a,b)))),compose(compose(compose(g,a),g),compose(h,compose(a,b)))) = compose(compose(compose(g,a),g),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_8588]) ).
tcf(c_31966,plain,
ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,compose(g,a))),compose(compose(compose(g,a),g),compose(g,a))),compose(compose(compose(g,a),g),compose(g,a))) = compose(compose(compose(g,a),g),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_8588]) ).
tcf(c_32013,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(codomain(X0)),codomain(X1),ifeq(domain(X2),codomain(X0),compose(domain(X2),compose(codomain(X0),codomain(X1))),compose(compose(domain(X2),codomain(X0)),codomain(X1))),compose(compose(domain(X2),codomain(X0)),codomain(X1))) = compose(compose(domain(X2),codomain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_66,c_22913]) ).
tcf(c_32014,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,b)),codomain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,b),codomain(X0))),compose(compose(domain(X1),compose(a,b)),codomain(X0))),compose(compose(domain(X1),compose(a,b)),codomain(X0))) = compose(compose(domain(X1),compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_171,c_22913]) ).
tcf(c_32015,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(domain(X0)),codomain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(domain(X0),codomain(X1))),compose(compose(domain(X2),domain(X0)),codomain(X1))),compose(compose(domain(X2),domain(X0)),codomain(X1))) = compose(compose(domain(X2),domain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_100,c_22913]) ).
tcf(c_32017,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(h,compose(a,b))),codomain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(domain(X1),compose(h,compose(a,b))),codomain(X0))),compose(compose(domain(X1),compose(h,compose(a,b))),codomain(X0))) = compose(compose(domain(X1),compose(h,compose(a,b))),codomain(X0)),
inference(superposition,[status(thm)],[c_1392,c_22913]) ).
tcf(c_32018,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(g,a)),codomain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(g,a),codomain(X0))),compose(compose(domain(X1),compose(g,a)),codomain(X0))),compose(compose(domain(X1),compose(g,a)),codomain(X0))) = compose(compose(domain(X1),compose(g,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_1491,c_22913]) ).
tcf(c_32019,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(h,a)),codomain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,a),codomain(X0))),compose(compose(domain(X1),compose(h,a)),codomain(X0))),compose(compose(domain(X1),compose(h,a)),codomain(X0))) = compose(compose(domain(X1),compose(h,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_347,c_22913]) ).
tcf(c_32020,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(domain(compose(X0,codomain(X1))),domain(X0),compose(X0,codomain(X1)),compose(compose(domain(compose(X0,codomain(X1))),X0),codomain(X1))),compose(compose(domain(compose(X0,codomain(X1))),X0),codomain(X1))) = compose(compose(domain(compose(X0,codomain(X1))),X0),codomain(X1)),
inference(superposition,[status(thm)],[c_67,c_22913]) ).
tcf(c_32103,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),codomain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(domain(X0),codomain(X1))),compose(compose(domain(X2),domain(X0)),codomain(X1))),compose(compose(domain(X2),domain(X0)),codomain(X1))) = compose(compose(domain(X2),domain(X0)),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_32015,c_65]) ).
tcf(c_32104,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),codomain(X1),ifeq(domain(X2),codomain(X0),compose(domain(X2),compose(codomain(X0),codomain(X1))),compose(compose(domain(X2),codomain(X0)),codomain(X1))),compose(compose(domain(X2),codomain(X0)),codomain(X1))) = compose(compose(domain(X2),codomain(X0)),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_32013,c_102]) ).
tcf(c_32109,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,a),codomain(X0))),compose(compose(domain(X1),compose(h,a)),codomain(X0))),compose(compose(domain(X1),compose(h,a)),codomain(X0))) = compose(compose(domain(X1),compose(h,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_32019,c_485]) ).
tcf(c_32110,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(g,a),codomain(X0))),compose(compose(domain(X1),compose(g,a)),codomain(X0))),compose(compose(domain(X1),compose(g,a)),codomain(X0))) = compose(compose(domain(X1),compose(g,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_32018,c_571]) ).
tcf(c_32111,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),codomain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,b),codomain(X0))),compose(compose(domain(X1),compose(a,b)),codomain(X0))),compose(compose(domain(X1),compose(a,b)),codomain(X0))) = compose(compose(domain(X1),compose(a,b)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_32014,c_425]) ).
tcf(c_32116,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),codomain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(domain(X1),compose(h,compose(a,b))),codomain(X0))),compose(compose(domain(X1),compose(h,compose(a,b))),codomain(X0))) = compose(compose(domain(X1),compose(h,compose(a,b))),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_32017,c_2217]) ).
tcf(c_32151,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(X2),codomain(X0),compose(codomain(X2),compose(codomain(X0),codomain(X1))),compose(compose(codomain(X2),codomain(X0)),codomain(X1))),compose(compose(codomain(X2),codomain(X0)),codomain(X1))) = compose(compose(codomain(X2),codomain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_102,c_23019]) ).
tcf(c_32152,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),codomain(X1))),compose(compose(compose(a,b),codomain(X0)),codomain(X1))),compose(compose(compose(a,b),codomain(X0)),codomain(X1))) = compose(compose(compose(a,b),codomain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_425,c_23019]) ).
tcf(c_32153,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),codomain(X1))),compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(X1))),compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(X1))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_2217,c_23019]) ).
tcf(c_32154,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),codomain(X1))),compose(compose(compose(h,a),codomain(X0)),codomain(X1))),compose(compose(compose(h,a),codomain(X0)),codomain(X1))) = compose(compose(compose(h,a),codomain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_485,c_23019]) ).
tcf(c_32155,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),codomain(X1))),compose(compose(compose(g,a),codomain(X0)),codomain(X1))),compose(compose(compose(g,a),codomain(X0)),codomain(X1))) = compose(compose(compose(g,a),codomain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_571,c_23019]) ).
tcf(c_32279,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(domain(X2),codomain(X0),compose(domain(X2),compose(codomain(X0),domain(X1))),compose(compose(domain(X2),codomain(X0)),domain(X1))),compose(compose(domain(X2),codomain(X0)),domain(X1))) = compose(compose(domain(X2),codomain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_66,c_23100]) ).
tcf(c_32280,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,b),domain(X0))),compose(compose(domain(X1),compose(a,b)),domain(X0))),compose(compose(domain(X1),compose(a,b)),domain(X0))) = compose(compose(domain(X1),compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_171,c_23100]) ).
tcf(c_32281,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(domain(X0),domain(X1))),compose(compose(domain(X2),domain(X0)),domain(X1))),compose(compose(domain(X2),domain(X0)),domain(X1))) = compose(compose(domain(X2),domain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_23100]) ).
tcf(c_32283,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(domain(X1),compose(h,compose(a,b))),domain(X0))),compose(compose(domain(X1),compose(h,compose(a,b))),domain(X0))) = compose(compose(domain(X1),compose(h,compose(a,b))),domain(X0)),
inference(superposition,[status(thm)],[c_1392,c_23100]) ).
tcf(c_32284,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(g,a),domain(X0))),compose(compose(domain(X1),compose(g,a)),domain(X0))),compose(compose(domain(X1),compose(g,a)),domain(X0))) = compose(compose(domain(X1),compose(g,a)),domain(X0)),
inference(superposition,[status(thm)],[c_1491,c_23100]) ).
tcf(c_32285,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,a),domain(X0))),compose(compose(domain(X1),compose(h,a)),domain(X0))),compose(compose(domain(X1),compose(h,a)),domain(X0))) = compose(compose(domain(X1),compose(h,a)),domain(X0)),
inference(superposition,[status(thm)],[c_347,c_23100]) ).
tcf(c_32286,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(compose(X0,domain(X1))),domain(X0),compose(X0,domain(X1)),compose(compose(domain(compose(X0,domain(X1))),X0),domain(X1))),compose(compose(domain(compose(X0,domain(X1))),X0),domain(X1))) = compose(compose(domain(compose(X0,domain(X1))),X0),domain(X1)),
inference(superposition,[status(thm)],[c_67,c_23100]) ).
tcf(c_32365,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(domain(X0),domain(X1))),compose(compose(domain(X2),domain(X0)),domain(X1))),compose(compose(domain(X2),domain(X0)),domain(X1))) = compose(compose(domain(X2),domain(X0)),domain(X1)),
inference(light_normalisation,[status(thm)],[c_32281,c_65]) ).
tcf(c_32366,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(X2),codomain(X0),compose(domain(X2),compose(codomain(X0),domain(X1))),compose(compose(domain(X2),codomain(X0)),domain(X1))),compose(compose(domain(X2),codomain(X0)),domain(X1))) = compose(compose(domain(X2),codomain(X0)),domain(X1)),
inference(light_normalisation,[status(thm)],[c_32279,c_102]) ).
tcf(c_32372,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,a),domain(X0))),compose(compose(domain(X1),compose(h,a)),domain(X0))),compose(compose(domain(X1),compose(h,a)),domain(X0))) = compose(compose(domain(X1),compose(h,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_32285,c_485]) ).
tcf(c_32373,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(g,a),domain(X0))),compose(compose(domain(X1),compose(g,a)),domain(X0))),compose(compose(domain(X1),compose(g,a)),domain(X0))) = compose(compose(domain(X1),compose(g,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_32284,c_571]) ).
tcf(c_32374,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,b),domain(X0))),compose(compose(domain(X1),compose(a,b)),domain(X0))),compose(compose(domain(X1),compose(a,b)),domain(X0))) = compose(compose(domain(X1),compose(a,b)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_32280,c_425]) ).
tcf(c_32379,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(domain(X1),compose(h,compose(a,b))),domain(X0))),compose(compose(domain(X1),compose(h,compose(a,b))),domain(X0))) = compose(compose(domain(X1),compose(h,compose(a,b))),domain(X0)),
inference(light_normalisation,[status(thm)],[c_32283,c_2217]) ).
tcf(c_32403,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),codomain(X0),compose(codomain(X2),compose(codomain(X0),domain(X1))),compose(compose(codomain(X2),codomain(X0)),domain(X1))),compose(compose(codomain(X2),codomain(X0)),domain(X1))) = compose(compose(codomain(X2),codomain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_102,c_23202]) ).
tcf(c_32404,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),domain(X1))),compose(compose(compose(a,b),codomain(X0)),domain(X1))),compose(compose(compose(a,b),codomain(X0)),domain(X1))) = compose(compose(compose(a,b),codomain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_425,c_23202]) ).
tcf(c_32405,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),domain(X1))),compose(compose(compose(h,compose(a,b)),codomain(X0)),domain(X1))),compose(compose(compose(h,compose(a,b)),codomain(X0)),domain(X1))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_2217,c_23202]) ).
tcf(c_32406,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),domain(X1))),compose(compose(compose(h,a),codomain(X0)),domain(X1))),compose(compose(compose(h,a),codomain(X0)),domain(X1))) = compose(compose(compose(h,a),codomain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_485,c_23202]) ).
tcf(c_32407,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),domain(X1))),compose(compose(compose(g,a),codomain(X0)),domain(X1))),compose(compose(compose(g,a),codomain(X0)),domain(X1))) = compose(compose(compose(g,a),codomain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_571,c_23202]) ).
tcf(c_32498,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),compose(a,b))),compose(compose(domain(X1),codomain(X0)),compose(a,b))),compose(compose(domain(X1),codomain(X0)),compose(a,b))) = compose(compose(domain(X1),codomain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_23347]) ).
tcf(c_32501,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(domain(X1),codomain(X0)),compose(h,compose(a,b)))),compose(compose(domain(X1),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(domain(X1),codomain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_23347]) ).
tcf(c_32502,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),compose(g,a))),compose(compose(domain(X1),codomain(X0)),compose(g,a))),compose(compose(domain(X1),codomain(X0)),compose(g,a))) = compose(compose(domain(X1),codomain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_23347]) ).
tcf(c_32503,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),compose(h,a))),compose(compose(domain(X1),codomain(X0)),compose(h,a))),compose(compose(domain(X1),codomain(X0)),compose(h,a))) = compose(compose(domain(X1),codomain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_23347]) ).
tcf(c_32520,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(compose(codomain(X0),X1)),codomain(X0),compose(codomain(X0),X1),compose(compose(domain(compose(codomain(X0),X1)),codomain(X0)),X1)),compose(compose(domain(compose(codomain(X0),X1)),codomain(X0)),X1)) = compose(compose(domain(compose(codomain(X0),X1)),codomain(X0)),X1),
inference(superposition,[status(thm)],[c_67,c_23347]) ).
tcf(c_32592,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),compose(a,b))),compose(compose(codomain(X1),codomain(X0)),compose(a,b))),compose(compose(codomain(X1),codomain(X0)),compose(a,b))) = compose(compose(codomain(X1),codomain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_23483]) ).
tcf(c_32595,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(codomain(X1),codomain(X0)),compose(h,compose(a,b)))),compose(compose(codomain(X1),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(codomain(X1),codomain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_23483]) ).
tcf(c_32596,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),compose(g,a))),compose(compose(codomain(X1),codomain(X0)),compose(g,a))),compose(compose(codomain(X1),codomain(X0)),compose(g,a))) = compose(compose(codomain(X1),codomain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_23483]) ).
tcf(c_32597,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),compose(h,a))),compose(compose(codomain(X1),codomain(X0)),compose(h,a))),compose(compose(codomain(X1),codomain(X0)),compose(h,a))) = compose(compose(codomain(X1),codomain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_23483]) ).
tcf(c_32699,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),g)),compose(compose(compose(a,b),compose(a,b)),g)),compose(compose(compose(a,b),compose(a,b)),g)) = compose(compose(compose(a,b),compose(a,b)),g),
inference(superposition,[status(thm)],[c_171,c_12455]) ).
tcf(c_32702,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),g)),compose(compose(compose(a,b),compose(h,compose(a,b))),g)),compose(compose(compose(a,b),compose(h,compose(a,b))),g)) = compose(compose(compose(a,b),compose(h,compose(a,b))),g),
inference(superposition,[status(thm)],[c_1392,c_12455]) ).
tcf(c_32703,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),g)),compose(compose(compose(a,b),compose(g,a)),g)),compose(compose(compose(a,b),compose(g,a)),g)) = compose(compose(compose(a,b),compose(g,a)),g),
inference(superposition,[status(thm)],[c_1491,c_12455]) ).
tcf(c_32720,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),g)),compose(compose(compose(a,b),compose(g,a)),g)),compose(compose(compose(a,b),compose(g,a)),g)) = compose(compose(compose(a,b),compose(g,a)),g),
inference(light_normalisation,[status(thm)],[c_32703,c_571]) ).
tcf(c_32721,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),g)),compose(compose(compose(a,b),compose(a,b)),g)),compose(compose(compose(a,b),compose(a,b)),g)) = compose(compose(compose(a,b),compose(a,b)),g),
inference(light_normalisation,[status(thm)],[c_32699,c_425]) ).
tcf(c_32725,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),g)),compose(compose(compose(a,b),compose(h,compose(a,b))),g)),compose(compose(compose(a,b),compose(h,compose(a,b))),g)) = compose(compose(compose(a,b),compose(h,compose(a,b))),g),
inference(light_normalisation,[status(thm)],[c_32702,c_2217]) ).
tcf(c_32734,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),g)),compose(compose(compose(h,compose(a,b)),compose(g,a)),g)),compose(compose(compose(h,compose(a,b)),compose(g,a)),g)) = compose(compose(compose(h,compose(a,b)),compose(g,a)),g),
inference(superposition,[status(thm)],[c_2217,c_12531]) ).
tcf(c_32750,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),g)),compose(compose(compose(h,compose(a,b)),compose(a,b)),g)),compose(compose(compose(h,compose(a,b)),compose(a,b)),g)) = compose(compose(compose(h,compose(a,b)),compose(a,b)),g),
inference(superposition,[status(thm)],[c_2217,c_12532]) ).
tcf(c_32783,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(domain(compose(h,codomain(X0))),domain(h),compose(h,codomain(X0)),compose(compose(domain(compose(h,codomain(X0))),h),codomain(X0))),compose(compose(domain(compose(h,codomain(X0))),h),codomain(X0))) = compose(compose(domain(compose(h,codomain(X0))),h),codomain(X0)),
inference(superposition,[status(thm)],[c_67,c_23772]) ).
tcf(c_32948,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,compose(g,a))),compose(compose(compose(a,b),g),compose(g,a))),compose(compose(compose(a,b),g),compose(g,a))) = compose(compose(compose(a,b),g),compose(g,a)),
inference(superposition,[status(thm)],[c_425,c_12582]) ).
tcf(c_32949,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,compose(g,a))),compose(compose(compose(h,compose(a,b)),g),compose(g,a))),compose(compose(compose(h,compose(a,b)),g),compose(g,a))) = compose(compose(compose(h,compose(a,b)),g),compose(g,a)),
inference(superposition,[status(thm)],[c_2217,c_12582]) ).
tcf(c_32964,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,compose(h,compose(a,b)))),compose(compose(compose(a,b),g),compose(h,compose(a,b)))),compose(compose(compose(a,b),g),compose(h,compose(a,b)))) = compose(compose(compose(a,b),g),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_12589]) ).
tcf(c_32984,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,compose(a,b))),compose(compose(compose(a,b),a),compose(a,b))),compose(compose(compose(a,b),a),compose(a,b))) = compose(compose(compose(a,b),a),compose(a,b)),
inference(superposition,[status(thm)],[c_425,c_17391]) ).
tcf(c_32985,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,compose(a,b))),compose(compose(compose(h,compose(a,b)),a),compose(a,b))),compose(compose(compose(h,compose(a,b)),a),compose(a,b))) = compose(compose(compose(h,compose(a,b)),a),compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_17391]) ).
tcf(c_32997,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,compose(h,compose(a,b)))),compose(compose(compose(a,b),a),compose(h,compose(a,b)))),compose(compose(compose(a,b),a),compose(h,compose(a,b)))) = compose(compose(compose(a,b),a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17402]) ).
tcf(c_33021,plain,
ifeq(codomain(compose(a,b)),domain(a),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),compose(a,b))),compose(compose(a,compose(a,b)),compose(a,b))),compose(compose(a,compose(a,b)),compose(a,b))) = compose(compose(a,compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_17530]) ).
tcf(c_33024,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(a),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(a,compose(h,compose(a,b))),compose(a,b))),compose(compose(a,compose(h,compose(a,b))),compose(a,b))) = compose(compose(a,compose(h,compose(a,b))),compose(a,b)),
inference(superposition,[status(thm)],[c_1392,c_17530]) ).
tcf(c_33045,plain,
ifeq(codomain(b),domain(a),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),compose(a,b))),compose(compose(a,compose(a,b)),compose(a,b))),compose(compose(a,compose(a,b)),compose(a,b))) = compose(compose(a,compose(a,b)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_33021,c_425]) ).
tcf(c_33050,plain,
ifeq(codomain(b),domain(a),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(a,compose(h,compose(a,b))),compose(a,b))),compose(compose(a,compose(h,compose(a,b))),compose(a,b))) = compose(compose(a,compose(h,compose(a,b))),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_33024,c_2217]) ).
tcf(c_33057,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(a,compose(a,b)),compose(h,compose(a,b)))),compose(compose(a,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(a,compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17593]) ).
tcf(c_33199,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(compose(codomain(X0),g)),codomain(X0),compose(codomain(X0),g),compose(compose(domain(compose(codomain(X0),g)),codomain(X0)),g)),compose(compose(domain(compose(codomain(X0),g)),codomain(X0)),g)) = compose(compose(domain(compose(codomain(X0),g)),codomain(X0)),g),
inference(superposition,[status(thm)],[c_67,c_24575]) ).
tcf(c_33272,plain,
! [X0: $i] : ifeq(domain(a),codomain(X0),ifeq(domain(compose(g,codomain(X0))),domain(h),compose(g,codomain(X0)),compose(compose(domain(compose(g,codomain(X0))),g),codomain(X0))),compose(compose(domain(compose(g,codomain(X0))),g),codomain(X0))) = compose(compose(domain(compose(g,codomain(X0))),g),codomain(X0)),
inference(superposition,[status(thm)],[c_67,c_24669]) ).
tcf(c_33354,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(compose(a,codomain(X0))),domain(a),compose(a,codomain(X0)),compose(compose(domain(compose(a,codomain(X0))),a),codomain(X0))),compose(compose(domain(compose(a,codomain(X0))),a),codomain(X0))) = compose(compose(domain(compose(a,codomain(X0))),a),codomain(X0)),
inference(superposition,[status(thm)],[c_67,c_25175]) ).
tcf(c_33549,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,b)),codomain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,b),codomain(X0))),compose(compose(codomain(X1),compose(a,b)),codomain(X0))),compose(compose(codomain(X1),compose(a,b)),codomain(X0))) = compose(compose(codomain(X1),compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_171,c_22917]) ).
tcf(c_33550,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(domain(X0)),codomain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(domain(X0),codomain(X1))),compose(compose(codomain(X2),domain(X0)),codomain(X1))),compose(compose(codomain(X2),domain(X0)),codomain(X1))) = compose(compose(codomain(X2),domain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_100,c_22917]) ).
tcf(c_33552,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(h,compose(a,b))),codomain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(codomain(X1),compose(h,compose(a,b))),codomain(X0))),compose(compose(codomain(X1),compose(h,compose(a,b))),codomain(X0))) = compose(compose(codomain(X1),compose(h,compose(a,b))),codomain(X0)),
inference(superposition,[status(thm)],[c_1392,c_22917]) ).
tcf(c_33553,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(g,a)),codomain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(g,a),codomain(X0))),compose(compose(codomain(X1),compose(g,a)),codomain(X0))),compose(compose(codomain(X1),compose(g,a)),codomain(X0))) = compose(compose(codomain(X1),compose(g,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_1491,c_22917]) ).
tcf(c_33554,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(h,a)),codomain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,a),codomain(X0))),compose(compose(codomain(X1),compose(h,a)),codomain(X0))),compose(compose(codomain(X1),compose(h,a)),codomain(X0))) = compose(compose(codomain(X1),compose(h,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_347,c_22917]) ).
tcf(c_33626,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),codomain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(domain(X0),codomain(X1))),compose(compose(codomain(X2),domain(X0)),codomain(X1))),compose(compose(codomain(X2),domain(X0)),codomain(X1))) = compose(compose(codomain(X2),domain(X0)),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_33550,c_65]) ).
tcf(c_33632,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,a),codomain(X0))),compose(compose(codomain(X1),compose(h,a)),codomain(X0))),compose(compose(codomain(X1),compose(h,a)),codomain(X0))) = compose(compose(codomain(X1),compose(h,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_33554,c_485]) ).
tcf(c_33633,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(g,a),codomain(X0))),compose(compose(codomain(X1),compose(g,a)),codomain(X0))),compose(compose(codomain(X1),compose(g,a)),codomain(X0))) = compose(compose(codomain(X1),compose(g,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_33553,c_571]) ).
tcf(c_33634,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,b),codomain(X0))),compose(compose(codomain(X1),compose(a,b)),codomain(X0))),compose(compose(codomain(X1),compose(a,b)),codomain(X0))) = compose(compose(codomain(X1),compose(a,b)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_33549,c_425]) ).
tcf(c_33638,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(codomain(X1),compose(h,compose(a,b))),codomain(X0))),compose(compose(codomain(X1),compose(h,compose(a,b))),codomain(X0))) = compose(compose(codomain(X1),compose(h,compose(a,b))),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_33552,c_2217]) ).
tcf(c_33664,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(X1),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),codomain(X1))),compose(compose(compose(a,b),domain(X0)),codomain(X1))),compose(compose(compose(a,b),domain(X0)),codomain(X1))) = compose(compose(compose(a,b),domain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_425,c_23018]) ).
tcf(c_33665,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(X1),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),codomain(X1))),compose(compose(compose(h,compose(a,b)),domain(X0)),codomain(X1))),compose(compose(compose(h,compose(a,b)),domain(X0)),codomain(X1))) = compose(compose(compose(h,compose(a,b)),domain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_2217,c_23018]) ).
tcf(c_33666,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(X1),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),codomain(X1))),compose(compose(compose(h,a),domain(X0)),codomain(X1))),compose(compose(compose(h,a),domain(X0)),codomain(X1))) = compose(compose(compose(h,a),domain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_485,c_23018]) ).
tcf(c_33667,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(X1),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),codomain(X1))),compose(compose(compose(g,a),domain(X0)),codomain(X1))),compose(compose(compose(g,a),domain(X0)),codomain(X1))) = compose(compose(compose(g,a),domain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_571,c_23018]) ).
tcf(c_33770,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(compose(X0,compose(a,b))),domain(X0),compose(X0,compose(a,b)),compose(compose(domain(compose(X0,compose(a,b))),X0),compose(a,b))),compose(compose(domain(compose(X0,compose(a,b))),X0),compose(a,b))) = compose(compose(domain(compose(X0,compose(a,b))),X0),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_23263]) ).
tcf(c_33773,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(compose(X0,compose(h,compose(a,b)))),domain(X0),compose(X0,compose(h,compose(a,b))),compose(compose(domain(compose(X0,compose(h,compose(a,b)))),X0),compose(h,compose(a,b)))),compose(compose(domain(compose(X0,compose(h,compose(a,b)))),X0),compose(h,compose(a,b)))) = compose(compose(domain(compose(X0,compose(h,compose(a,b)))),X0),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_23263]) ).
tcf(c_33774,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(compose(X0,compose(g,a))),domain(X0),compose(X0,compose(g,a)),compose(compose(domain(compose(X0,compose(g,a))),X0),compose(g,a))),compose(compose(domain(compose(X0,compose(g,a))),X0),compose(g,a))) = compose(compose(domain(compose(X0,compose(g,a))),X0),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_23263]) ).
tcf(c_33775,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(compose(X0,compose(h,a))),domain(X0),compose(X0,compose(h,a)),compose(compose(domain(compose(X0,compose(h,a))),X0),compose(h,a))),compose(compose(domain(compose(X0,compose(h,a))),X0),compose(h,a))) = compose(compose(domain(compose(X0,compose(h,a))),X0),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_23263]) ).
tcf(c_33800,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(domain(compose(compose(a,b),X0)),domain(a),compose(compose(a,b),X0),compose(compose(domain(compose(compose(a,b),X0)),compose(a,b)),X0)),compose(compose(domain(compose(compose(a,b),X0)),compose(a,b)),X0)) = compose(compose(domain(compose(compose(a,b),X0)),compose(a,b)),X0),
inference(superposition,[status(thm)],[c_171,c_23263]) ).
tcf(c_33801,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(domain(compose(domain(X0),X1)),domain(X0),compose(domain(X0),X1),compose(compose(domain(compose(domain(X0),X1)),domain(X0)),X1)),compose(compose(domain(compose(domain(X0),X1)),domain(X0)),X1)) = compose(compose(domain(compose(domain(X0),X1)),domain(X0)),X1),
inference(superposition,[status(thm)],[c_100,c_23263]) ).
tcf(c_33803,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(domain(compose(compose(h,compose(a,b)),X0)),domain(h),compose(compose(h,compose(a,b)),X0),compose(compose(domain(compose(compose(h,compose(a,b)),X0)),compose(h,compose(a,b))),X0)),compose(compose(domain(compose(compose(h,compose(a,b)),X0)),compose(h,compose(a,b))),X0)) = compose(compose(domain(compose(compose(h,compose(a,b)),X0)),compose(h,compose(a,b))),X0),
inference(superposition,[status(thm)],[c_1392,c_23263]) ).
tcf(c_33804,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(domain(compose(compose(g,a),X0)),domain(h),compose(compose(g,a),X0),compose(compose(domain(compose(compose(g,a),X0)),compose(g,a)),X0)),compose(compose(domain(compose(compose(g,a),X0)),compose(g,a)),X0)) = compose(compose(domain(compose(compose(g,a),X0)),compose(g,a)),X0),
inference(superposition,[status(thm)],[c_1491,c_23263]) ).
tcf(c_33805,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(domain(compose(compose(h,a),X0)),domain(h),compose(compose(h,a),X0),compose(compose(domain(compose(compose(h,a),X0)),compose(h,a)),X0)),compose(compose(domain(compose(compose(h,a),X0)),compose(h,a)),X0)) = compose(compose(domain(compose(compose(h,a),X0)),compose(h,a)),X0),
inference(superposition,[status(thm)],[c_347,c_23263]) ).
tcf(c_33881,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(domain(compose(domain(X0),X1)),domain(X0),compose(domain(X0),X1),compose(compose(domain(compose(domain(X0),X1)),domain(X0)),X1)),compose(compose(domain(compose(domain(X0),X1)),domain(X0)),X1)) = compose(compose(domain(compose(domain(X0),X1)),domain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_33801,c_65]) ).
tcf(c_33892,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(compose(compose(h,a),X0)),domain(h),compose(compose(h,a),X0),compose(compose(domain(compose(compose(h,a),X0)),compose(h,a)),X0)),compose(compose(domain(compose(compose(h,a),X0)),compose(h,a)),X0)) = compose(compose(domain(compose(compose(h,a),X0)),compose(h,a)),X0),
inference(light_normalisation,[status(thm)],[c_33805,c_485]) ).
tcf(c_33893,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(compose(compose(g,a),X0)),domain(h),compose(compose(g,a),X0),compose(compose(domain(compose(compose(g,a),X0)),compose(g,a)),X0)),compose(compose(domain(compose(compose(g,a),X0)),compose(g,a)),X0)) = compose(compose(domain(compose(compose(g,a),X0)),compose(g,a)),X0),
inference(light_normalisation,[status(thm)],[c_33804,c_571]) ).
tcf(c_33894,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(compose(compose(a,b),X0)),domain(a),compose(compose(a,b),X0),compose(compose(domain(compose(compose(a,b),X0)),compose(a,b)),X0)),compose(compose(domain(compose(compose(a,b),X0)),compose(a,b)),X0)) = compose(compose(domain(compose(compose(a,b),X0)),compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_33800,c_425]) ).
tcf(c_33902,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(compose(compose(h,compose(a,b)),X0)),domain(h),compose(compose(h,compose(a,b)),X0),compose(compose(domain(compose(compose(h,compose(a,b)),X0)),compose(h,compose(a,b))),X0)),compose(compose(domain(compose(compose(h,compose(a,b)),X0)),compose(h,compose(a,b))),X0)) = compose(compose(domain(compose(compose(h,compose(a,b)),X0)),compose(h,compose(a,b))),X0),
inference(light_normalisation,[status(thm)],[c_33803,c_2217]) ).
tcf(c_33912,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(compose(h,domain(X0))),domain(h),compose(h,domain(X0)),compose(compose(domain(compose(h,domain(X0))),h),domain(X0))),compose(compose(domain(compose(h,domain(X0))),h),domain(X0))) = compose(compose(domain(compose(h,domain(X0))),h),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_23835]) ).
tcf(c_33914,plain,
ifeq(domain(a),domain(h),ifeq(domain(compose(h,compose(h,compose(a,b)))),domain(h),compose(h,compose(h,compose(a,b))),compose(compose(domain(compose(h,compose(h,compose(a,b)))),h),compose(h,compose(a,b)))),compose(compose(domain(compose(h,compose(h,compose(a,b)))),h),compose(h,compose(a,b)))) = compose(compose(domain(compose(h,compose(h,compose(a,b)))),h),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_23835]) ).
tcf(c_33915,plain,
ifeq(domain(a),domain(h),ifeq(domain(compose(h,compose(g,a))),domain(h),compose(h,compose(g,a)),compose(compose(domain(compose(h,compose(g,a))),h),compose(g,a))),compose(compose(domain(compose(h,compose(g,a))),h),compose(g,a))) = compose(compose(domain(compose(h,compose(g,a))),h),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_23835]) ).
tcf(c_33916,plain,
ifeq(domain(a),domain(h),ifeq(domain(compose(h,compose(h,a))),domain(h),compose(h,compose(h,a)),compose(compose(domain(compose(h,compose(h,a))),h),compose(h,a))),compose(compose(domain(compose(h,compose(h,a))),h),compose(h,a))) = compose(compose(domain(compose(h,compose(h,a))),h),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_23835]) ).
tcf(c_33947,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(domain(compose(compose(a,b),g)),domain(a),compose(compose(a,b),g),compose(compose(domain(compose(compose(a,b),g)),compose(a,b)),g)),compose(compose(domain(compose(compose(a,b),g)),compose(a,b)),g)) = compose(compose(domain(compose(compose(a,b),g)),compose(a,b)),g),
inference(superposition,[status(thm)],[c_171,c_24524]) ).
tcf(c_33948,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),domain(h),ifeq(domain(compose(domain(X0),g)),domain(X0),compose(domain(X0),g),compose(compose(domain(compose(domain(X0),g)),domain(X0)),g)),compose(compose(domain(compose(domain(X0),g)),domain(X0)),g)) = compose(compose(domain(compose(domain(X0),g)),domain(X0)),g),
inference(superposition,[status(thm)],[c_100,c_24524]) ).
tcf(c_33950,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(compose(compose(h,compose(a,b)),g)),domain(h),compose(compose(h,compose(a,b)),g),compose(compose(domain(compose(compose(h,compose(a,b)),g)),compose(h,compose(a,b))),g)),compose(compose(domain(compose(compose(h,compose(a,b)),g)),compose(h,compose(a,b))),g)) = compose(compose(domain(compose(compose(h,compose(a,b)),g)),compose(h,compose(a,b))),g),
inference(superposition,[status(thm)],[c_1392,c_24524]) ).
tcf(c_33951,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(compose(compose(g,a),g)),domain(h),compose(compose(g,a),g),compose(compose(domain(compose(compose(g,a),g)),compose(g,a)),g)),compose(compose(domain(compose(compose(g,a),g)),compose(g,a)),g)) = compose(compose(domain(compose(compose(g,a),g)),compose(g,a)),g),
inference(superposition,[status(thm)],[c_1491,c_24524]) ).
tcf(c_33952,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(compose(compose(h,a),g)),domain(h),compose(compose(h,a),g),compose(compose(domain(compose(compose(h,a),g)),compose(h,a)),g)),compose(compose(domain(compose(compose(h,a),g)),compose(h,a)),g)) = compose(compose(domain(compose(compose(h,a),g)),compose(h,a)),g),
inference(superposition,[status(thm)],[c_347,c_24524]) ).
tcf(c_33963,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(compose(domain(X0),g)),domain(X0),compose(domain(X0),g),compose(compose(domain(compose(domain(X0),g)),domain(X0)),g)),compose(compose(domain(compose(domain(X0),g)),domain(X0)),g)) = compose(compose(domain(compose(domain(X0),g)),domain(X0)),g),
inference(light_normalisation,[status(thm)],[c_33948,c_65]) ).
tcf(c_33967,plain,
ifeq(domain(b),domain(h),ifeq(domain(compose(compose(h,a),g)),domain(h),compose(compose(h,a),g),compose(compose(domain(compose(compose(h,a),g)),compose(h,a)),g)),compose(compose(domain(compose(compose(h,a),g)),compose(h,a)),g)) = compose(compose(domain(compose(compose(h,a),g)),compose(h,a)),g),
inference(light_normalisation,[status(thm)],[c_33952,c_485]) ).
tcf(c_33968,plain,
ifeq(domain(b),domain(h),ifeq(domain(compose(compose(g,a),g)),domain(h),compose(compose(g,a),g),compose(compose(domain(compose(compose(g,a),g)),compose(g,a)),g)),compose(compose(domain(compose(compose(g,a),g)),compose(g,a)),g)) = compose(compose(domain(compose(compose(g,a),g)),compose(g,a)),g),
inference(light_normalisation,[status(thm)],[c_33951,c_571]) ).
tcf(c_33969,plain,
ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(a,b),g)),domain(a),compose(compose(a,b),g),compose(compose(domain(compose(compose(a,b),g)),compose(a,b)),g)),compose(compose(domain(compose(compose(a,b),g)),compose(a,b)),g)) = compose(compose(domain(compose(compose(a,b),g)),compose(a,b)),g),
inference(light_normalisation,[status(thm)],[c_33947,c_425]) ).
tcf(c_33973,plain,
ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(h,compose(a,b)),g)),domain(h),compose(compose(h,compose(a,b)),g),compose(compose(domain(compose(compose(h,compose(a,b)),g)),compose(h,compose(a,b))),g)),compose(compose(domain(compose(compose(h,compose(a,b)),g)),compose(h,compose(a,b))),g)) = compose(compose(domain(compose(compose(h,compose(a,b)),g)),compose(h,compose(a,b))),g),
inference(light_normalisation,[status(thm)],[c_33950,c_2217]) ).
tcf(c_33979,plain,
! [X0: $i] : ifeq(domain(a),domain(X0),ifeq(domain(compose(g,domain(X0))),domain(h),compose(g,domain(X0)),compose(compose(domain(compose(g,domain(X0))),g),domain(X0))),compose(compose(domain(compose(g,domain(X0))),g),domain(X0))) = compose(compose(domain(compose(g,domain(X0))),g),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_24734]) ).
tcf(c_33981,plain,
ifeq(domain(a),domain(h),ifeq(domain(compose(g,compose(h,compose(a,b)))),domain(h),compose(g,compose(h,compose(a,b))),compose(compose(domain(compose(g,compose(h,compose(a,b)))),g),compose(h,compose(a,b)))),compose(compose(domain(compose(g,compose(h,compose(a,b)))),g),compose(h,compose(a,b)))) = compose(compose(domain(compose(g,compose(h,compose(a,b)))),g),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_24734]) ).
tcf(c_33982,plain,
ifeq(domain(a),domain(h),ifeq(domain(compose(g,compose(g,a))),domain(h),compose(g,compose(g,a)),compose(compose(domain(compose(g,compose(g,a))),g),compose(g,a))),compose(compose(domain(compose(g,compose(g,a))),g),compose(g,a))) = compose(compose(domain(compose(g,compose(g,a))),g),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_24734]) ).
tcf(c_33983,plain,
ifeq(domain(a),domain(h),ifeq(domain(compose(g,compose(h,a))),domain(h),compose(g,compose(h,a)),compose(compose(domain(compose(g,compose(h,a))),g),compose(h,a))),compose(compose(domain(compose(g,compose(h,a))),g),compose(h,a))) = compose(compose(domain(compose(g,compose(h,a))),g),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_24734]) ).
tcf(c_34007,plain,
ifeq(domain(b),domain(a),ifeq(domain(compose(a,compose(a,b))),domain(a),compose(a,compose(a,b)),compose(compose(domain(compose(a,compose(a,b))),a),compose(a,b))),compose(compose(domain(compose(a,compose(a,b))),a),compose(a,b))) = compose(compose(domain(compose(a,compose(a,b))),a),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_25242]) ).
tcf(c_34008,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(compose(a,domain(X0))),domain(a),compose(a,domain(X0)),compose(compose(domain(compose(a,domain(X0))),a),domain(X0))),compose(compose(domain(compose(a,domain(X0))),a),domain(X0))) = compose(compose(domain(compose(a,domain(X0))),a),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_25242]) ).
tcf(c_34010,plain,
ifeq(domain(b),domain(h),ifeq(domain(compose(a,compose(h,compose(a,b)))),domain(a),compose(a,compose(h,compose(a,b))),compose(compose(domain(compose(a,compose(h,compose(a,b)))),a),compose(h,compose(a,b)))),compose(compose(domain(compose(a,compose(h,compose(a,b)))),a),compose(h,compose(a,b)))) = compose(compose(domain(compose(a,compose(h,compose(a,b)))),a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_25242]) ).
tcf(c_34011,plain,
ifeq(domain(b),domain(h),ifeq(domain(compose(a,compose(g,a))),domain(a),compose(a,compose(g,a)),compose(compose(domain(compose(a,compose(g,a))),a),compose(g,a))),compose(compose(domain(compose(a,compose(g,a))),a),compose(g,a))) = compose(compose(domain(compose(a,compose(g,a))),a),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_25242]) ).
tcf(c_34012,plain,
ifeq(domain(b),domain(h),ifeq(domain(compose(a,compose(h,a))),domain(a),compose(a,compose(h,a)),compose(compose(domain(compose(a,compose(h,a))),a),compose(h,a))),compose(compose(domain(compose(a,compose(h,a))),a),compose(h,a))) = compose(compose(domain(compose(a,compose(h,a))),a),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_25242]) ).
tcf(c_34059,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,b),domain(X0))),compose(compose(codomain(X1),compose(a,b)),domain(X0))),compose(compose(codomain(X1),compose(a,b)),domain(X0))) = compose(compose(codomain(X1),compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_171,c_23104]) ).
tcf(c_34060,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(domain(X0),domain(X1))),compose(compose(codomain(X2),domain(X0)),domain(X1))),compose(compose(codomain(X2),domain(X0)),domain(X1))) = compose(compose(codomain(X2),domain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_23104]) ).
tcf(c_34062,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(codomain(X1),compose(h,compose(a,b))),domain(X0))),compose(compose(codomain(X1),compose(h,compose(a,b))),domain(X0))) = compose(compose(codomain(X1),compose(h,compose(a,b))),domain(X0)),
inference(superposition,[status(thm)],[c_1392,c_23104]) ).
tcf(c_34063,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(g,a),domain(X0))),compose(compose(codomain(X1),compose(g,a)),domain(X0))),compose(compose(codomain(X1),compose(g,a)),domain(X0))) = compose(compose(codomain(X1),compose(g,a)),domain(X0)),
inference(superposition,[status(thm)],[c_1491,c_23104]) ).
tcf(c_34064,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,a),domain(X0))),compose(compose(codomain(X1),compose(h,a)),domain(X0))),compose(compose(codomain(X1),compose(h,a)),domain(X0))) = compose(compose(codomain(X1),compose(h,a)),domain(X0)),
inference(superposition,[status(thm)],[c_347,c_23104]) ).
tcf(c_34132,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(domain(X0),domain(X1))),compose(compose(codomain(X2),domain(X0)),domain(X1))),compose(compose(codomain(X2),domain(X0)),domain(X1))) = compose(compose(codomain(X2),domain(X0)),domain(X1)),
inference(light_normalisation,[status(thm)],[c_34060,c_65]) ).
tcf(c_34139,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,a),domain(X0))),compose(compose(codomain(X1),compose(h,a)),domain(X0))),compose(compose(codomain(X1),compose(h,a)),domain(X0))) = compose(compose(codomain(X1),compose(h,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_34064,c_485]) ).
tcf(c_34140,plain,
! [X0: $i,X1: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(g,a),domain(X0))),compose(compose(codomain(X1),compose(g,a)),domain(X0))),compose(compose(codomain(X1),compose(g,a)),domain(X0))) = compose(compose(codomain(X1),compose(g,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_34063,c_571]) ).
tcf(c_34141,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,b),domain(X0))),compose(compose(codomain(X1),compose(a,b)),domain(X0))),compose(compose(codomain(X1),compose(a,b)),domain(X0))) = compose(compose(codomain(X1),compose(a,b)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_34059,c_425]) ).
tcf(c_34145,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(codomain(X1),compose(h,compose(a,b))),domain(X0))),compose(compose(codomain(X1),compose(h,compose(a,b))),domain(X0))) = compose(compose(codomain(X1),compose(h,compose(a,b))),domain(X0)),
inference(light_normalisation,[status(thm)],[c_34062,c_2217]) ).
tcf(c_34168,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),domain(X1))),compose(compose(compose(a,b),domain(X0)),domain(X1))),compose(compose(compose(a,b),domain(X0)),domain(X1))) = compose(compose(compose(a,b),domain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_425,c_23201]) ).
tcf(c_34169,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),domain(X1))),compose(compose(compose(h,compose(a,b)),domain(X0)),domain(X1))),compose(compose(compose(h,compose(a,b)),domain(X0)),domain(X1))) = compose(compose(compose(h,compose(a,b)),domain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_2217,c_23201]) ).
tcf(c_34170,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),domain(X1))),compose(compose(compose(h,a),domain(X0)),domain(X1))),compose(compose(compose(h,a),domain(X0)),domain(X1))) = compose(compose(compose(h,a),domain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_485,c_23201]) ).
tcf(c_34171,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),domain(X1))),compose(compose(compose(g,a),domain(X0)),domain(X1))),compose(compose(compose(g,a),domain(X0)),domain(X1))) = compose(compose(compose(g,a),domain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_571,c_23201]) ).
tcf(c_34266,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),compose(a,b))),compose(compose(domain(X1),domain(X0)),compose(a,b))),compose(compose(domain(X1),domain(X0)),compose(a,b))) = compose(compose(domain(X1),domain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_23346]) ).
tcf(c_34269,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),compose(h,compose(a,b)))),compose(compose(domain(X1),domain(X0)),compose(h,compose(a,b)))),compose(compose(domain(X1),domain(X0)),compose(h,compose(a,b)))) = compose(compose(domain(X1),domain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_23346]) ).
tcf(c_34270,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),compose(g,a))),compose(compose(domain(X1),domain(X0)),compose(g,a))),compose(compose(domain(X1),domain(X0)),compose(g,a))) = compose(compose(domain(X1),domain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_23346]) ).
tcf(c_34271,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),compose(h,a))),compose(compose(domain(X1),domain(X0)),compose(h,a))),compose(compose(domain(X1),domain(X0)),compose(h,a))) = compose(compose(domain(X1),domain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_23346]) ).
tcf(c_34366,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),compose(a,b))),compose(compose(codomain(X1),domain(X0)),compose(a,b))),compose(compose(codomain(X1),domain(X0)),compose(a,b))) = compose(compose(codomain(X1),domain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_23482]) ).
tcf(c_34369,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),compose(h,compose(a,b)))),compose(compose(codomain(X1),domain(X0)),compose(h,compose(a,b)))),compose(compose(codomain(X1),domain(X0)),compose(h,compose(a,b)))) = compose(compose(codomain(X1),domain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_23482]) ).
tcf(c_34370,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),compose(g,a))),compose(compose(codomain(X1),domain(X0)),compose(g,a))),compose(compose(codomain(X1),domain(X0)),compose(g,a))) = compose(compose(codomain(X1),domain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_23482]) ).
tcf(c_34371,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),compose(h,a))),compose(compose(codomain(X1),domain(X0)),compose(h,a))),compose(compose(codomain(X1),domain(X0)),compose(h,a))) = compose(compose(codomain(X1),domain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_23482]) ).
tcf(c_35108,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(g,compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(g,compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(g,compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_4152]) ).
tcf(c_35134,plain,
ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(g,compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(g,compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(g,compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_35108,c_2217]) ).
tcf(c_36372,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),compose(h,a))),compose(compose(domain(X0),compose(a,b)),compose(h,a))),compose(compose(domain(X0),compose(a,b)),compose(h,a))) = compose(compose(domain(X0),compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_171,c_5192]) ).
tcf(c_36375,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,a))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,a))) = compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,a)),
inference(superposition,[status(thm)],[c_1392,c_5192]) ).
tcf(c_36376,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),compose(h,a))),compose(compose(domain(X0),compose(g,a)),compose(h,a))),compose(compose(domain(X0),compose(g,a)),compose(h,a))) = compose(compose(domain(X0),compose(g,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_1491,c_5192]) ).
tcf(c_36377,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),compose(h,a))),compose(compose(domain(X0),compose(h,a)),compose(h,a))),compose(compose(domain(X0),compose(h,a)),compose(h,a))) = compose(compose(domain(X0),compose(h,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_5192]) ).
tcf(c_36431,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),compose(h,a))),compose(compose(domain(X0),compose(h,a)),compose(h,a))),compose(compose(domain(X0),compose(h,a)),compose(h,a))) = compose(compose(domain(X0),compose(h,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_36377,c_485]) ).
tcf(c_36432,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),compose(h,a))),compose(compose(domain(X0),compose(g,a)),compose(h,a))),compose(compose(domain(X0),compose(g,a)),compose(h,a))) = compose(compose(domain(X0),compose(g,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_36376,c_571]) ).
tcf(c_36433,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),compose(h,a))),compose(compose(domain(X0),compose(a,b)),compose(h,a))),compose(compose(domain(X0),compose(a,b)),compose(h,a))) = compose(compose(domain(X0),compose(a,b)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_36372,c_425]) ).
tcf(c_36439,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,a))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,a))) = compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_36375,c_2217]) ).
tcf(c_36457,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),compose(h,a))),compose(compose(compose(a,b),codomain(X0)),compose(h,a))),compose(compose(compose(a,b),codomain(X0)),compose(h,a))) = compose(compose(compose(a,b),codomain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_425,c_5264]) ).
tcf(c_36458,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),compose(h,a))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(h,a))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_2217,c_5264]) ).
tcf(c_36459,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),compose(h,a))),compose(compose(compose(h,a),codomain(X0)),compose(h,a))),compose(compose(compose(h,a),codomain(X0)),compose(h,a))) = compose(compose(compose(h,a),codomain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_485,c_5264]) ).
tcf(c_36460,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),compose(h,a))),compose(compose(compose(g,a),codomain(X0)),compose(h,a))),compose(compose(compose(g,a),codomain(X0)),compose(h,a))) = compose(compose(compose(g,a),codomain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_571,c_5264]) ).
tcf(c_36535,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),codomain(X0))),compose(compose(compose(h,a),compose(a,b)),codomain(X0))),compose(compose(compose(h,a),compose(a,b)),codomain(X0))) = compose(compose(compose(h,a),compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_171,c_7348]) ).
tcf(c_36538,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),codomain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(X0))),compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(X0)),
inference(superposition,[status(thm)],[c_1392,c_7348]) ).
tcf(c_36539,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),codomain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),codomain(X0))),compose(compose(compose(h,a),compose(g,a)),codomain(X0))),compose(compose(compose(h,a),compose(g,a)),codomain(X0))) = compose(compose(compose(h,a),compose(g,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_1491,c_7348]) ).
tcf(c_36540,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),codomain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),codomain(X0))),compose(compose(compose(h,a),compose(h,a)),codomain(X0))),compose(compose(compose(h,a),compose(h,a)),codomain(X0))) = compose(compose(compose(h,a),compose(h,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_347,c_7348]) ).
tcf(c_36594,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),codomain(X0))),compose(compose(compose(h,a),compose(h,a)),codomain(X0))),compose(compose(compose(h,a),compose(h,a)),codomain(X0))) = compose(compose(compose(h,a),compose(h,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_36540,c_485]) ).
tcf(c_36595,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),codomain(X0))),compose(compose(compose(h,a),compose(g,a)),codomain(X0))),compose(compose(compose(h,a),compose(g,a)),codomain(X0))) = compose(compose(compose(h,a),compose(g,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_36539,c_571]) ).
tcf(c_36596,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),codomain(X0))),compose(compose(compose(h,a),compose(a,b)),codomain(X0))),compose(compose(compose(h,a),compose(a,b)),codomain(X0))) = compose(compose(compose(h,a),compose(a,b)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_36535,c_425]) ).
tcf(c_36600,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(X0))),compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_36538,c_2217]) ).
tcf(c_36623,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),compose(a,b))),compose(compose(compose(h,a),codomain(X0)),compose(a,b))),compose(compose(compose(h,a),codomain(X0)),compose(a,b))) = compose(compose(compose(h,a),codomain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_7401]) ).
tcf(c_36626,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(compose(h,a),codomain(X0)),compose(h,compose(a,b)))),compose(compose(compose(h,a),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_7401]) ).
tcf(c_36627,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),compose(g,a))),compose(compose(compose(h,a),codomain(X0)),compose(g,a))),compose(compose(compose(h,a),codomain(X0)),compose(g,a))) = compose(compose(compose(h,a),codomain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_7401]) ).
tcf(c_36690,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),codomain(X0))),compose(compose(compose(a,b),compose(h,a)),codomain(X0))),compose(compose(compose(a,b),compose(h,a)),codomain(X0))) = compose(compose(compose(a,b),compose(h,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_425,c_7579]) ).
tcf(c_36691,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,a)),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,a)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_2217,c_7579]) ).
tcf(c_36693,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),codomain(X0))),compose(compose(compose(g,a),compose(h,a)),codomain(X0))),compose(compose(compose(g,a),compose(h,a)),codomain(X0))) = compose(compose(compose(g,a),compose(h,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_571,c_7579]) ).
tcf(c_36735,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),compose(a,b))),compose(compose(domain(X0),compose(h,a)),compose(a,b))),compose(compose(domain(X0),compose(h,a)),compose(a,b))) = compose(compose(domain(X0),compose(h,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_7586]) ).
tcf(c_36738,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(h,a)),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(domain(X0),compose(h,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_7586]) ).
tcf(c_36739,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),compose(g,a))),compose(compose(domain(X0),compose(h,a)),compose(g,a))),compose(compose(domain(X0),compose(h,a)),compose(g,a))) = compose(compose(domain(X0),compose(h,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_7586]) ).
tcf(c_36822,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),codomain(X0))),compose(compose(compose(g,a),compose(a,b)),codomain(X0))),compose(compose(compose(g,a),compose(a,b)),codomain(X0))) = compose(compose(compose(g,a),compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_171,c_8545]) ).
tcf(c_36825,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),codomain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(X0))),compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(X0)),
inference(superposition,[status(thm)],[c_1392,c_8545]) ).
tcf(c_36826,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),codomain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),codomain(X0))),compose(compose(compose(g,a),compose(g,a)),codomain(X0))),compose(compose(compose(g,a),compose(g,a)),codomain(X0))) = compose(compose(compose(g,a),compose(g,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_1491,c_8545]) ).
tcf(c_36882,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),codomain(X0))),compose(compose(compose(g,a),compose(g,a)),codomain(X0))),compose(compose(compose(g,a),compose(g,a)),codomain(X0))) = compose(compose(compose(g,a),compose(g,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_36826,c_571]) ).
tcf(c_36883,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),codomain(X0))),compose(compose(compose(g,a),compose(a,b)),codomain(X0))),compose(compose(compose(g,a),compose(a,b)),codomain(X0))) = compose(compose(compose(g,a),compose(a,b)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_36822,c_425]) ).
tcf(c_36887,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(X0))),compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_36825,c_2217]) ).
tcf(c_36902,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),compose(a,b))),compose(compose(compose(g,a),codomain(X0)),compose(a,b))),compose(compose(compose(g,a),codomain(X0)),compose(a,b))) = compose(compose(compose(g,a),codomain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_8598]) ).
tcf(c_36905,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(compose(g,a),codomain(X0)),compose(h,compose(a,b)))),compose(compose(compose(g,a),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_8598]) ).
tcf(c_36906,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),compose(g,a))),compose(compose(compose(g,a),codomain(X0)),compose(g,a))),compose(compose(compose(g,a),codomain(X0)),compose(g,a))) = compose(compose(compose(g,a),codomain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_8598]) ).
tcf(c_37013,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),compose(g,a))),compose(compose(domain(X0),compose(a,b)),compose(g,a))),compose(compose(domain(X0),compose(a,b)),compose(g,a))) = compose(compose(domain(X0),compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_171,c_13704]) ).
tcf(c_37016,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(g,a))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(g,a))) = compose(compose(domain(X0),compose(h,compose(a,b))),compose(g,a)),
inference(superposition,[status(thm)],[c_1392,c_13704]) ).
tcf(c_37017,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),compose(g,a))),compose(compose(domain(X0),compose(g,a)),compose(g,a))),compose(compose(domain(X0),compose(g,a)),compose(g,a))) = compose(compose(domain(X0),compose(g,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_13704]) ).
tcf(c_37073,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),compose(g,a))),compose(compose(domain(X0),compose(g,a)),compose(g,a))),compose(compose(domain(X0),compose(g,a)),compose(g,a))) = compose(compose(domain(X0),compose(g,a)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_37017,c_571]) ).
tcf(c_37074,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),compose(g,a))),compose(compose(domain(X0),compose(a,b)),compose(g,a))),compose(compose(domain(X0),compose(a,b)),compose(g,a))) = compose(compose(domain(X0),compose(a,b)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_37013,c_425]) ).
tcf(c_37080,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(g,a))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(g,a))) = compose(compose(domain(X0),compose(h,compose(a,b))),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_37016,c_2217]) ).
tcf(c_37098,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),compose(g,a))),compose(compose(compose(a,b),codomain(X0)),compose(g,a))),compose(compose(compose(a,b),codomain(X0)),compose(g,a))) = compose(compose(compose(a,b),codomain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_425,c_13772]) ).
tcf(c_37099,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),compose(g,a))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(g,a))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_2217,c_13772]) ).
tcf(c_37169,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),codomain(X0))),compose(compose(compose(a,b),compose(g,a)),codomain(X0))),compose(compose(compose(a,b),compose(g,a)),codomain(X0))) = compose(compose(compose(a,b),compose(g,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_425,c_13931]) ).
tcf(c_37170,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(g,a)),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(g,a)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_2217,c_13931]) ).
tcf(c_37214,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),compose(a,b))),compose(compose(domain(X0),compose(g,a)),compose(a,b))),compose(compose(domain(X0),compose(g,a)),compose(a,b))) = compose(compose(domain(X0),compose(g,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_13938]) ).
tcf(c_37217,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(g,a)),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(domain(X0),compose(g,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_13938]) ).
tcf(c_37512,plain,
ifeq(codomain(compose(a,b)),codomain(compose(compose(a,b),compose(a,b))),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),codomain(compose(compose(a,b),compose(a,b))))),compose(compose(a,b),compose(a,b))),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_17698]) ).
tcf(c_37515,plain,
ifeq(codomain(compose(h,compose(a,b))),codomain(compose(compose(a,b),compose(h,compose(a,b)))),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),codomain(compose(compose(a,b),compose(h,compose(a,b)))))),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17698]) ).
tcf(c_37516,plain,
ifeq(codomain(compose(g,a)),codomain(compose(compose(a,b),compose(g,a))),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),codomain(compose(compose(a,b),compose(g,a))))),compose(compose(a,b),compose(g,a))),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17698]) ).
tcf(c_37517,plain,
ifeq(codomain(compose(h,a)),codomain(compose(compose(a,b),compose(h,a))),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),codomain(compose(compose(a,b),compose(h,a))))),compose(compose(a,b),compose(h,a))),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17698]) ).
tcf(c_37532,plain,
ifeq(domain(b),codomain(compose(compose(a,b),compose(h,a))),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),codomain(compose(compose(a,b),compose(h,a))))),compose(compose(a,b),compose(h,a))),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_37517,c_485]) ).
tcf(c_37533,plain,
ifeq(domain(b),codomain(compose(compose(a,b),compose(g,a))),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),codomain(compose(compose(a,b),compose(g,a))))),compose(compose(a,b),compose(g,a))),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_37516,c_571]) ).
tcf(c_37534,plain,
ifeq(codomain(b),codomain(compose(compose(a,b),compose(a,b))),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),codomain(compose(compose(a,b),compose(a,b))))),compose(compose(a,b),compose(a,b))),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_37512,c_425]) ).
tcf(c_37538,plain,
ifeq(codomain(b),codomain(compose(compose(a,b),compose(h,compose(a,b)))),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),codomain(compose(compose(a,b),compose(h,compose(a,b)))))),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_37515,c_2217]) ).
tcf(c_37555,plain,
ifeq(codomain(compose(a,b)),codomain(compose(compose(h,a),compose(a,b))),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),codomain(compose(compose(h,a),compose(a,b))))),compose(compose(h,a),compose(a,b))),compose(compose(h,a),compose(a,b))) = compose(compose(h,a),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_17700]) ).
tcf(c_37558,plain,
ifeq(codomain(compose(h,compose(a,b))),codomain(compose(compose(h,a),compose(h,compose(a,b)))),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),codomain(compose(compose(h,a),compose(h,compose(a,b)))))),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17700]) ).
tcf(c_37559,plain,
ifeq(codomain(compose(g,a)),codomain(compose(compose(h,a),compose(g,a))),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),codomain(compose(compose(h,a),compose(g,a))))),compose(compose(h,a),compose(g,a))),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17700]) ).
tcf(c_37560,plain,
ifeq(codomain(compose(h,a)),codomain(compose(compose(h,a),compose(h,a))),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),codomain(compose(compose(h,a),compose(h,a))))),compose(compose(h,a),compose(h,a))),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17700]) ).
tcf(c_37580,plain,
ifeq(domain(b),codomain(compose(compose(h,a),compose(h,a))),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),codomain(compose(compose(h,a),compose(h,a))))),compose(compose(h,a),compose(h,a))),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_37560,c_485]) ).
tcf(c_37581,plain,
ifeq(domain(b),codomain(compose(compose(h,a),compose(g,a))),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),codomain(compose(compose(h,a),compose(g,a))))),compose(compose(h,a),compose(g,a))),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_37559,c_571]) ).
tcf(c_37582,plain,
ifeq(codomain(b),codomain(compose(compose(h,a),compose(a,b))),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),codomain(compose(compose(h,a),compose(a,b))))),compose(compose(h,a),compose(a,b))),compose(compose(h,a),compose(a,b))) = compose(compose(h,a),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_37555,c_425]) ).
tcf(c_37586,plain,
ifeq(codomain(b),codomain(compose(compose(h,a),compose(h,compose(a,b)))),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),codomain(compose(compose(h,a),compose(h,compose(a,b)))))),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_37558,c_2217]) ).
tcf(c_37603,plain,
ifeq(codomain(compose(a,b)),codomain(compose(compose(g,a),compose(a,b))),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),codomain(compose(compose(g,a),compose(a,b))))),compose(compose(g,a),compose(a,b))),compose(compose(g,a),compose(a,b))) = compose(compose(g,a),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_17701]) ).
tcf(c_37606,plain,
ifeq(codomain(compose(h,compose(a,b))),codomain(compose(compose(g,a),compose(h,compose(a,b)))),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),codomain(compose(compose(g,a),compose(h,compose(a,b)))))),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17701]) ).
tcf(c_37607,plain,
ifeq(codomain(compose(g,a)),codomain(compose(compose(g,a),compose(g,a))),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),codomain(compose(compose(g,a),compose(g,a))))),compose(compose(g,a),compose(g,a))),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_17701]) ).
tcf(c_37608,plain,
ifeq(codomain(compose(h,a)),codomain(compose(compose(g,a),compose(h,a))),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),codomain(compose(compose(g,a),compose(h,a))))),compose(compose(g,a),compose(h,a))),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_17701]) ).
tcf(c_37628,plain,
ifeq(domain(b),codomain(compose(compose(g,a),compose(h,a))),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),codomain(compose(compose(g,a),compose(h,a))))),compose(compose(g,a),compose(h,a))),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_37608,c_485]) ).
tcf(c_37629,plain,
ifeq(domain(b),codomain(compose(compose(g,a),compose(g,a))),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),codomain(compose(compose(g,a),compose(g,a))))),compose(compose(g,a),compose(g,a))),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_37607,c_571]) ).
tcf(c_37630,plain,
ifeq(codomain(b),codomain(compose(compose(g,a),compose(a,b))),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),codomain(compose(compose(g,a),compose(a,b))))),compose(compose(g,a),compose(a,b))),compose(compose(g,a),compose(a,b))) = compose(compose(g,a),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_37603,c_425]) ).
tcf(c_37634,plain,
ifeq(codomain(b),codomain(compose(compose(g,a),compose(h,compose(a,b)))),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),codomain(compose(compose(g,a),compose(h,compose(a,b)))))),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_37606,c_2217]) ).
tcf(c_37645,plain,
ifeq(domain(b),codomain(compose(compose(h,compose(a,b)),compose(h,a))),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),codomain(compose(compose(h,compose(a,b)),compose(h,a))))),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_2217,c_17796]) ).
tcf(c_37665,plain,
ifeq(domain(b),codomain(compose(compose(h,compose(a,b)),compose(g,a))),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),codomain(compose(compose(h,compose(a,b)),compose(g,a))))),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_2217,c_17797]) ).
tcf(c_37687,plain,
ifeq(codomain(b),codomain(compose(compose(h,compose(a,b)),compose(a,b))),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),codomain(compose(compose(h,compose(a,b)),compose(a,b))))),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_17798]) ).
tcf(c_37744,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(domain(compose(codomain(X0),codomain(X1))),codomain(X0),compose(codomain(X0),codomain(X1)),compose(compose(domain(compose(codomain(X0),codomain(X1))),codomain(X0)),codomain(X1))),compose(compose(domain(compose(codomain(X0),codomain(X1))),codomain(X0)),codomain(X1))) = compose(compose(domain(compose(codomain(X0),codomain(X1))),codomain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_67,c_32104]) ).
tcf(c_38207,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(domain(compose(codomain(X0),domain(X1))),codomain(X0),compose(codomain(X0),domain(X1)),compose(compose(domain(compose(codomain(X0),domain(X1))),codomain(X0)),domain(X1))),compose(compose(domain(compose(codomain(X0),domain(X1))),codomain(X0)),domain(X1))) = compose(compose(domain(compose(codomain(X0),domain(X1))),codomain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_67,c_32366]) ).
tcf(c_38306,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),compose(h,a))),compose(compose(codomain(X0),compose(a,b)),compose(h,a))),compose(compose(codomain(X0),compose(a,b)),compose(h,a))) = compose(compose(codomain(X0),compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_171,c_5196]) ).
tcf(c_38309,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,a))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,a))) = compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,a)),
inference(superposition,[status(thm)],[c_1392,c_5196]) ).
tcf(c_38310,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),compose(h,a))),compose(compose(codomain(X0),compose(g,a)),compose(h,a))),compose(compose(codomain(X0),compose(g,a)),compose(h,a))) = compose(compose(codomain(X0),compose(g,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_1491,c_5196]) ).
tcf(c_38311,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),compose(h,a))),compose(compose(codomain(X0),compose(h,a)),compose(h,a))),compose(compose(codomain(X0),compose(h,a)),compose(h,a))) = compose(compose(codomain(X0),compose(h,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_5196]) ).
tcf(c_38353,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),compose(h,a))),compose(compose(codomain(X0),compose(h,a)),compose(h,a))),compose(compose(codomain(X0),compose(h,a)),compose(h,a))) = compose(compose(codomain(X0),compose(h,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_38311,c_485]) ).
tcf(c_38354,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),compose(h,a))),compose(compose(codomain(X0),compose(g,a)),compose(h,a))),compose(compose(codomain(X0),compose(g,a)),compose(h,a))) = compose(compose(codomain(X0),compose(g,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_38310,c_571]) ).
tcf(c_38355,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),compose(h,a))),compose(compose(codomain(X0),compose(a,b)),compose(h,a))),compose(compose(codomain(X0),compose(a,b)),compose(h,a))) = compose(compose(codomain(X0),compose(a,b)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_38306,c_425]) ).
tcf(c_38360,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,a))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,a))) = compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_38309,c_2217]) ).
tcf(c_38376,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),compose(h,a))),compose(compose(compose(a,b),domain(X0)),compose(h,a))),compose(compose(compose(a,b),domain(X0)),compose(h,a))) = compose(compose(compose(a,b),domain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_425,c_5263]) ).
tcf(c_38377,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),compose(h,a))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(h,a))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),domain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_2217,c_5263]) ).
tcf(c_38378,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),compose(h,a))),compose(compose(compose(h,a),domain(X0)),compose(h,a))),compose(compose(compose(h,a),domain(X0)),compose(h,a))) = compose(compose(compose(h,a),domain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_485,c_5263]) ).
tcf(c_38379,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),compose(h,a))),compose(compose(compose(g,a),domain(X0)),compose(h,a))),compose(compose(compose(g,a),domain(X0)),compose(h,a))) = compose(compose(compose(g,a),domain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_571,c_5263]) ).
tcf(c_38387,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(domain(compose(domain(X0),compose(h,a)))),domain(X0),compose(domain(X0),compose(h,a)),compose(compose(domain(compose(domain(X0),compose(h,a))),domain(X0)),compose(h,a))),compose(compose(domain(compose(domain(X0),compose(h,a))),domain(X0)),compose(h,a))) = compose(compose(domain(compose(domain(X0),compose(h,a))),domain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_67,c_5263]) ).
tcf(c_38532,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),a),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_11866]) ).
tcf(c_38558,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),domain(X0))),compose(compose(compose(h,a),compose(a,b)),domain(X0))),compose(compose(compose(h,a),compose(a,b)),domain(X0))) = compose(compose(compose(h,a),compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_171,c_7350]) ).
tcf(c_38561,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(h,a),compose(h,compose(a,b))),domain(X0))),compose(compose(compose(h,a),compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(h,a),compose(h,compose(a,b))),domain(X0)),
inference(superposition,[status(thm)],[c_1392,c_7350]) ).
tcf(c_38562,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),domain(X0))),compose(compose(compose(h,a),compose(g,a)),domain(X0))),compose(compose(compose(h,a),compose(g,a)),domain(X0))) = compose(compose(compose(h,a),compose(g,a)),domain(X0)),
inference(superposition,[status(thm)],[c_1491,c_7350]) ).
tcf(c_38563,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),domain(X0))),compose(compose(compose(h,a),compose(h,a)),domain(X0))),compose(compose(compose(h,a),compose(h,a)),domain(X0))) = compose(compose(compose(h,a),compose(h,a)),domain(X0)),
inference(superposition,[status(thm)],[c_347,c_7350]) ).
tcf(c_38613,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),domain(X0))),compose(compose(compose(h,a),compose(h,a)),domain(X0))),compose(compose(compose(h,a),compose(h,a)),domain(X0))) = compose(compose(compose(h,a),compose(h,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_38563,c_485]) ).
tcf(c_38614,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),domain(X0))),compose(compose(compose(h,a),compose(g,a)),domain(X0))),compose(compose(compose(h,a),compose(g,a)),domain(X0))) = compose(compose(compose(h,a),compose(g,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_38562,c_571]) ).
tcf(c_38615,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),domain(X0))),compose(compose(compose(h,a),compose(a,b)),domain(X0))),compose(compose(compose(h,a),compose(a,b)),domain(X0))) = compose(compose(compose(h,a),compose(a,b)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_38558,c_425]) ).
tcf(c_38619,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(h,a),compose(h,compose(a,b))),domain(X0))),compose(compose(compose(h,a),compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(h,a),compose(h,compose(a,b))),domain(X0)),
inference(light_normalisation,[status(thm)],[c_38561,c_2217]) ).
tcf(c_38631,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),compose(a,b))),compose(compose(compose(h,a),domain(X0)),compose(a,b))),compose(compose(compose(h,a),domain(X0)),compose(a,b))) = compose(compose(compose(h,a),domain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_7400]) ).
tcf(c_38634,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),compose(h,compose(a,b)))),compose(compose(compose(h,a),domain(X0)),compose(h,compose(a,b)))),compose(compose(compose(h,a),domain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_7400]) ).
tcf(c_38635,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),compose(g,a))),compose(compose(compose(h,a),domain(X0)),compose(g,a))),compose(compose(compose(h,a),domain(X0)),compose(g,a))) = compose(compose(compose(h,a),domain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_7400]) ).
tcf(c_38702,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),domain(X0))),compose(compose(compose(a,b),compose(h,a)),domain(X0))),compose(compose(compose(a,b),compose(h,a)),domain(X0))) = compose(compose(compose(a,b),compose(h,a)),domain(X0)),
inference(superposition,[status(thm)],[c_425,c_7581]) ).
tcf(c_38703,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(X0))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(X0)),
inference(superposition,[status(thm)],[c_2217,c_7581]) ).
tcf(c_38705,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),domain(X0))),compose(compose(compose(g,a),compose(h,a)),domain(X0))),compose(compose(compose(g,a),compose(h,a)),domain(X0))) = compose(compose(compose(g,a),compose(h,a)),domain(X0)),
inference(superposition,[status(thm)],[c_571,c_7581]) ).
tcf(c_38740,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),compose(a,b))),compose(compose(codomain(X0),compose(h,a)),compose(a,b))),compose(compose(codomain(X0),compose(h,a)),compose(a,b))) = compose(compose(codomain(X0),compose(h,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_7590]) ).
tcf(c_38743,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(h,a)),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(codomain(X0),compose(h,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_7590]) ).
tcf(c_38744,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),compose(g,a))),compose(compose(codomain(X0),compose(h,a)),compose(g,a))),compose(compose(codomain(X0),compose(h,a)),compose(g,a))) = compose(compose(codomain(X0),compose(h,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_7590]) ).
tcf(c_38808,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),compose(h,a))),compose(compose(compose(a,b),compose(a,b)),compose(h,a))),compose(compose(compose(a,b),compose(a,b)),compose(h,a))) = compose(compose(compose(a,b),compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_171,c_5197]) ).
tcf(c_38811,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,a))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,a)),
inference(superposition,[status(thm)],[c_1392,c_5197]) ).
tcf(c_38812,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),compose(h,a))),compose(compose(compose(a,b),compose(g,a)),compose(h,a))),compose(compose(compose(a,b),compose(g,a)),compose(h,a))) = compose(compose(compose(a,b),compose(g,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_1491,c_5197]) ).
tcf(c_38813,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),compose(h,a))),compose(compose(compose(a,b),compose(h,a)),compose(h,a))),compose(compose(compose(a,b),compose(h,a)),compose(h,a))) = compose(compose(compose(a,b),compose(h,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_5197]) ).
tcf(c_38827,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),compose(h,a))),compose(compose(compose(a,b),compose(h,a)),compose(h,a))),compose(compose(compose(a,b),compose(h,a)),compose(h,a))) = compose(compose(compose(a,b),compose(h,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_38813,c_485]) ).
tcf(c_38828,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),compose(h,a))),compose(compose(compose(a,b),compose(g,a)),compose(h,a))),compose(compose(compose(a,b),compose(g,a)),compose(h,a))) = compose(compose(compose(a,b),compose(g,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_38812,c_571]) ).
tcf(c_38829,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),compose(h,a))),compose(compose(compose(a,b),compose(a,b)),compose(h,a))),compose(compose(compose(a,b),compose(a,b)),compose(h,a))) = compose(compose(compose(a,b),compose(a,b)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_38808,c_425]) ).
tcf(c_38834,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,a))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_38811,c_2217]) ).
tcf(c_38851,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(a,compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(a,compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(a,compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_11875]) ).
tcf(c_38873,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(a,compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(a,compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(a,compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_38851,c_2217]) ).
tcf(c_38895,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),domain(X0))),compose(compose(compose(g,a),compose(a,b)),domain(X0))),compose(compose(compose(g,a),compose(a,b)),domain(X0))) = compose(compose(compose(g,a),compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_171,c_8547]) ).
tcf(c_38898,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(g,a),compose(h,compose(a,b))),domain(X0))),compose(compose(compose(g,a),compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(g,a),compose(h,compose(a,b))),domain(X0)),
inference(superposition,[status(thm)],[c_1392,c_8547]) ).
tcf(c_38899,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),domain(X0))),compose(compose(compose(g,a),compose(g,a)),domain(X0))),compose(compose(compose(g,a),compose(g,a)),domain(X0))) = compose(compose(compose(g,a),compose(g,a)),domain(X0)),
inference(superposition,[status(thm)],[c_1491,c_8547]) ).
tcf(c_38951,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),domain(X0))),compose(compose(compose(g,a),compose(g,a)),domain(X0))),compose(compose(compose(g,a),compose(g,a)),domain(X0))) = compose(compose(compose(g,a),compose(g,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_38899,c_571]) ).
tcf(c_38952,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),domain(X0))),compose(compose(compose(g,a),compose(a,b)),domain(X0))),compose(compose(compose(g,a),compose(a,b)),domain(X0))) = compose(compose(compose(g,a),compose(a,b)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_38895,c_425]) ).
tcf(c_38956,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(g,a),compose(h,compose(a,b))),domain(X0))),compose(compose(compose(g,a),compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(g,a),compose(h,compose(a,b))),domain(X0)),
inference(light_normalisation,[status(thm)],[c_38898,c_2217]) ).
tcf(c_38968,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),compose(a,b))),compose(compose(compose(g,a),domain(X0)),compose(a,b))),compose(compose(compose(g,a),domain(X0)),compose(a,b))) = compose(compose(compose(g,a),domain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_8597]) ).
tcf(c_38971,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),compose(h,compose(a,b)))),compose(compose(compose(g,a),domain(X0)),compose(h,compose(a,b)))),compose(compose(compose(g,a),domain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_8597]) ).
tcf(c_38972,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),compose(g,a))),compose(compose(compose(g,a),domain(X0)),compose(g,a))),compose(compose(compose(g,a),domain(X0)),compose(g,a))) = compose(compose(compose(g,a),domain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_8597]) ).
tcf(c_39045,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),compose(g,a))),compose(compose(codomain(X0),compose(a,b)),compose(g,a))),compose(compose(codomain(X0),compose(a,b)),compose(g,a))) = compose(compose(codomain(X0),compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_171,c_13708]) ).
tcf(c_39048,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(g,a))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(g,a))) = compose(compose(codomain(X0),compose(h,compose(a,b))),compose(g,a)),
inference(superposition,[status(thm)],[c_1392,c_13708]) ).
tcf(c_39049,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),compose(g,a))),compose(compose(codomain(X0),compose(g,a)),compose(g,a))),compose(compose(codomain(X0),compose(g,a)),compose(g,a))) = compose(compose(codomain(X0),compose(g,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_13708]) ).
tcf(c_39093,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),compose(g,a))),compose(compose(codomain(X0),compose(g,a)),compose(g,a))),compose(compose(codomain(X0),compose(g,a)),compose(g,a))) = compose(compose(codomain(X0),compose(g,a)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_39049,c_571]) ).
tcf(c_39094,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),compose(g,a))),compose(compose(codomain(X0),compose(a,b)),compose(g,a))),compose(compose(codomain(X0),compose(a,b)),compose(g,a))) = compose(compose(codomain(X0),compose(a,b)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_39045,c_425]) ).
tcf(c_39099,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(g,a))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(g,a))) = compose(compose(codomain(X0),compose(h,compose(a,b))),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_39048,c_2217]) ).
tcf(c_39115,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),compose(g,a))),compose(compose(compose(a,b),domain(X0)),compose(g,a))),compose(compose(compose(a,b),domain(X0)),compose(g,a))) = compose(compose(compose(a,b),domain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_425,c_13771]) ).
tcf(c_39116,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),compose(g,a))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(g,a))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),domain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_2217,c_13771]) ).
tcf(c_39126,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(domain(compose(domain(X0),compose(g,a)))),domain(X0),compose(domain(X0),compose(g,a)),compose(compose(domain(compose(domain(X0),compose(g,a))),domain(X0)),compose(g,a))),compose(compose(domain(compose(domain(X0),compose(g,a))),domain(X0)),compose(g,a))) = compose(compose(domain(compose(domain(X0),compose(g,a))),domain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_67,c_13771]) ).
tcf(c_39186,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_171,c_5198]) ).
tcf(c_39189,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,a)),
inference(superposition,[status(thm)],[c_1392,c_5198]) ).
tcf(c_39190,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_1491,c_5198]) ).
tcf(c_39191,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_5198]) ).
tcf(c_39205,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_39191,c_485]) ).
tcf(c_39206,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_39190,c_571]) ).
tcf(c_39207,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_39186,c_425]) ).
tcf(c_39212,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_39189,c_2217]) ).
tcf(c_39249,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(X0),ifeq(domain(compose(compose(a,b),codomain(X0))),domain(a),compose(compose(a,b),codomain(X0)),compose(compose(domain(compose(compose(a,b),codomain(X0))),compose(a,b)),codomain(X0))),compose(compose(domain(compose(compose(a,b),codomain(X0))),compose(a,b)),codomain(X0))) = compose(compose(domain(compose(compose(a,b),codomain(X0))),compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_171,c_32020]) ).
tcf(c_39250,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(X1),ifeq(domain(compose(domain(X0),codomain(X1))),domain(X0),compose(domain(X0),codomain(X1)),compose(compose(domain(compose(domain(X0),codomain(X1))),domain(X0)),codomain(X1))),compose(compose(domain(compose(domain(X0),codomain(X1))),domain(X0)),codomain(X1))) = compose(compose(domain(compose(domain(X0),codomain(X1))),domain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_100,c_32020]) ).
tcf(c_39252,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),codomain(X0),ifeq(domain(compose(compose(h,compose(a,b)),codomain(X0))),domain(h),compose(compose(h,compose(a,b)),codomain(X0)),compose(compose(domain(compose(compose(h,compose(a,b)),codomain(X0))),compose(h,compose(a,b))),codomain(X0))),compose(compose(domain(compose(compose(h,compose(a,b)),codomain(X0))),compose(h,compose(a,b))),codomain(X0))) = compose(compose(domain(compose(compose(h,compose(a,b)),codomain(X0))),compose(h,compose(a,b))),codomain(X0)),
inference(superposition,[status(thm)],[c_1392,c_32020]) ).
tcf(c_39253,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),codomain(X0),ifeq(domain(compose(compose(g,a),codomain(X0))),domain(h),compose(compose(g,a),codomain(X0)),compose(compose(domain(compose(compose(g,a),codomain(X0))),compose(g,a)),codomain(X0))),compose(compose(domain(compose(compose(g,a),codomain(X0))),compose(g,a)),codomain(X0))) = compose(compose(domain(compose(compose(g,a),codomain(X0))),compose(g,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_1491,c_32020]) ).
tcf(c_39254,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),codomain(X0),ifeq(domain(compose(compose(h,a),codomain(X0))),domain(h),compose(compose(h,a),codomain(X0)),compose(compose(domain(compose(compose(h,a),codomain(X0))),compose(h,a)),codomain(X0))),compose(compose(domain(compose(compose(h,a),codomain(X0))),compose(h,a)),codomain(X0))) = compose(compose(domain(compose(compose(h,a),codomain(X0))),compose(h,a)),codomain(X0)),
inference(superposition,[status(thm)],[c_347,c_32020]) ).
tcf(c_39323,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(X1),ifeq(domain(compose(domain(X0),codomain(X1))),domain(X0),compose(domain(X0),codomain(X1)),compose(compose(domain(compose(domain(X0),codomain(X1))),domain(X0)),codomain(X1))),compose(compose(domain(compose(domain(X0),codomain(X1))),domain(X0)),codomain(X1))) = compose(compose(domain(compose(domain(X0),codomain(X1))),domain(X0)),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_39250,c_65]) ).
tcf(c_39327,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(compose(compose(h,a),codomain(X0))),domain(h),compose(compose(h,a),codomain(X0)),compose(compose(domain(compose(compose(h,a),codomain(X0))),compose(h,a)),codomain(X0))),compose(compose(domain(compose(compose(h,a),codomain(X0))),compose(h,a)),codomain(X0))) = compose(compose(domain(compose(compose(h,a),codomain(X0))),compose(h,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_39254,c_485]) ).
tcf(c_39328,plain,
! [X0: $i] : ifeq(domain(b),codomain(X0),ifeq(domain(compose(compose(g,a),codomain(X0))),domain(h),compose(compose(g,a),codomain(X0)),compose(compose(domain(compose(compose(g,a),codomain(X0))),compose(g,a)),codomain(X0))),compose(compose(domain(compose(compose(g,a),codomain(X0))),compose(g,a)),codomain(X0))) = compose(compose(domain(compose(compose(g,a),codomain(X0))),compose(g,a)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_39253,c_571]) ).
tcf(c_39329,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(domain(compose(compose(a,b),codomain(X0))),domain(a),compose(compose(a,b),codomain(X0)),compose(compose(domain(compose(compose(a,b),codomain(X0))),compose(a,b)),codomain(X0))),compose(compose(domain(compose(compose(a,b),codomain(X0))),compose(a,b)),codomain(X0))) = compose(compose(domain(compose(compose(a,b),codomain(X0))),compose(a,b)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_39249,c_425]) ).
tcf(c_39334,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(domain(compose(compose(h,compose(a,b)),codomain(X0))),domain(h),compose(compose(h,compose(a,b)),codomain(X0)),compose(compose(domain(compose(compose(h,compose(a,b)),codomain(X0))),compose(h,compose(a,b))),codomain(X0))),compose(compose(domain(compose(compose(h,compose(a,b)),codomain(X0))),compose(h,compose(a,b))),codomain(X0))) = compose(compose(domain(compose(compose(h,compose(a,b)),codomain(X0))),compose(h,compose(a,b))),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_39252,c_2217]) ).
tcf(c_39368,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(domain(compose(compose(a,b),domain(X0))),domain(a),compose(compose(a,b),domain(X0)),compose(compose(domain(compose(compose(a,b),domain(X0))),compose(a,b)),domain(X0))),compose(compose(domain(compose(compose(a,b),domain(X0))),compose(a,b)),domain(X0))) = compose(compose(domain(compose(compose(a,b),domain(X0))),compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_171,c_32286]) ).
tcf(c_39369,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(domain(compose(domain(X0),domain(X1))),domain(X0),compose(domain(X0),domain(X1)),compose(compose(domain(compose(domain(X0),domain(X1))),domain(X0)),domain(X1))),compose(compose(domain(compose(domain(X0),domain(X1))),domain(X0)),domain(X1))) = compose(compose(domain(compose(domain(X0),domain(X1))),domain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_32286]) ).
tcf(c_39371,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(domain(compose(compose(h,compose(a,b)),domain(X0))),domain(h),compose(compose(h,compose(a,b)),domain(X0)),compose(compose(domain(compose(compose(h,compose(a,b)),domain(X0))),compose(h,compose(a,b))),domain(X0))),compose(compose(domain(compose(compose(h,compose(a,b)),domain(X0))),compose(h,compose(a,b))),domain(X0))) = compose(compose(domain(compose(compose(h,compose(a,b)),domain(X0))),compose(h,compose(a,b))),domain(X0)),
inference(superposition,[status(thm)],[c_1392,c_32286]) ).
tcf(c_39372,plain,
! [X0: $i] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(domain(compose(compose(g,a),domain(X0))),domain(h),compose(compose(g,a),domain(X0)),compose(compose(domain(compose(compose(g,a),domain(X0))),compose(g,a)),domain(X0))),compose(compose(domain(compose(compose(g,a),domain(X0))),compose(g,a)),domain(X0))) = compose(compose(domain(compose(compose(g,a),domain(X0))),compose(g,a)),domain(X0)),
inference(superposition,[status(thm)],[c_1491,c_32286]) ).
tcf(c_39373,plain,
! [X0: $i] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(domain(compose(compose(h,a),domain(X0))),domain(h),compose(compose(h,a),domain(X0)),compose(compose(domain(compose(compose(h,a),domain(X0))),compose(h,a)),domain(X0))),compose(compose(domain(compose(compose(h,a),domain(X0))),compose(h,a)),domain(X0))) = compose(compose(domain(compose(compose(h,a),domain(X0))),compose(h,a)),domain(X0)),
inference(superposition,[status(thm)],[c_347,c_32286]) ).
tcf(c_39439,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(domain(compose(domain(X0),domain(X1))),domain(X0),compose(domain(X0),domain(X1)),compose(compose(domain(compose(domain(X0),domain(X1))),domain(X0)),domain(X1))),compose(compose(domain(compose(domain(X0),domain(X1))),domain(X0)),domain(X1))) = compose(compose(domain(compose(domain(X0),domain(X1))),domain(X0)),domain(X1)),
inference(light_normalisation,[status(thm)],[c_39369,c_65]) ).
tcf(c_39443,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(compose(compose(h,a),domain(X0))),domain(h),compose(compose(h,a),domain(X0)),compose(compose(domain(compose(compose(h,a),domain(X0))),compose(h,a)),domain(X0))),compose(compose(domain(compose(compose(h,a),domain(X0))),compose(h,a)),domain(X0))) = compose(compose(domain(compose(compose(h,a),domain(X0))),compose(h,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_39373,c_485]) ).
tcf(c_39444,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(domain(compose(compose(g,a),domain(X0))),domain(h),compose(compose(g,a),domain(X0)),compose(compose(domain(compose(compose(g,a),domain(X0))),compose(g,a)),domain(X0))),compose(compose(domain(compose(compose(g,a),domain(X0))),compose(g,a)),domain(X0))) = compose(compose(domain(compose(compose(g,a),domain(X0))),compose(g,a)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_39372,c_571]) ).
tcf(c_39445,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(compose(compose(a,b),domain(X0))),domain(a),compose(compose(a,b),domain(X0)),compose(compose(domain(compose(compose(a,b),domain(X0))),compose(a,b)),domain(X0))),compose(compose(domain(compose(compose(a,b),domain(X0))),compose(a,b)),domain(X0))) = compose(compose(domain(compose(compose(a,b),domain(X0))),compose(a,b)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_39368,c_425]) ).
tcf(c_39449,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(compose(compose(h,compose(a,b)),domain(X0))),domain(h),compose(compose(h,compose(a,b)),domain(X0)),compose(compose(domain(compose(compose(h,compose(a,b)),domain(X0))),compose(h,compose(a,b))),domain(X0))),compose(compose(domain(compose(compose(h,compose(a,b)),domain(X0))),compose(h,compose(a,b))),domain(X0))) = compose(compose(domain(compose(compose(h,compose(a,b)),domain(X0))),compose(h,compose(a,b))),domain(X0)),
inference(light_normalisation,[status(thm)],[c_39371,c_2217]) ).
tcf(c_39465,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),domain(X0))),compose(compose(compose(a,b),compose(g,a)),domain(X0))),compose(compose(compose(a,b),compose(g,a)),domain(X0))) = compose(compose(compose(a,b),compose(g,a)),domain(X0)),
inference(superposition,[status(thm)],[c_425,c_13933]) ).
tcf(c_39466,plain,
! [X0: $i] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(X0))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(X0)),
inference(superposition,[status(thm)],[c_2217,c_13933]) ).
tcf(c_39503,plain,
! [X0: $i] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),compose(a,b))),compose(compose(codomain(X0),compose(g,a)),compose(a,b))),compose(compose(codomain(X0),compose(g,a)),compose(a,b))) = compose(compose(codomain(X0),compose(g,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_13942]) ).
tcf(c_39506,plain,
! [X0: $i] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(g,a)),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(codomain(X0),compose(g,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_13942]) ).
tcf(c_39580,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),compose(h,a))),compose(compose(compose(h,a),compose(a,b)),compose(h,a))),compose(compose(compose(h,a),compose(a,b)),compose(h,a))) = compose(compose(compose(h,a),compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_171,c_5199]) ).
tcf(c_39583,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,a)),
inference(superposition,[status(thm)],[c_1392,c_5199]) ).
tcf(c_39584,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),compose(h,a))),compose(compose(compose(h,a),compose(g,a)),compose(h,a))),compose(compose(compose(h,a),compose(g,a)),compose(h,a))) = compose(compose(compose(h,a),compose(g,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_1491,c_5199]) ).
tcf(c_39585,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),compose(h,a))),compose(compose(compose(h,a),compose(h,a)),compose(h,a))),compose(compose(compose(h,a),compose(h,a)),compose(h,a))) = compose(compose(compose(h,a),compose(h,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_5199]) ).
tcf(c_39602,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),compose(h,a))),compose(compose(compose(h,a),compose(h,a)),compose(h,a))),compose(compose(compose(h,a),compose(h,a)),compose(h,a))) = compose(compose(compose(h,a),compose(h,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_39585,c_485]) ).
tcf(c_39603,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),compose(h,a))),compose(compose(compose(h,a),compose(g,a)),compose(h,a))),compose(compose(compose(h,a),compose(g,a)),compose(h,a))) = compose(compose(compose(h,a),compose(g,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_39584,c_571]) ).
tcf(c_39604,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),compose(h,a))),compose(compose(compose(h,a),compose(a,b)),compose(h,a))),compose(compose(compose(h,a),compose(a,b)),compose(h,a))) = compose(compose(compose(h,a),compose(a,b)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_39580,c_425]) ).
tcf(c_39609,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_39583,c_2217]) ).
tcf(c_39622,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(compose(codomain(X0),compose(a,b))),codomain(X0),compose(codomain(X0),compose(a,b)),compose(compose(domain(compose(codomain(X0),compose(a,b))),codomain(X0)),compose(a,b))),compose(compose(domain(compose(codomain(X0),compose(a,b))),codomain(X0)),compose(a,b))) = compose(compose(domain(compose(codomain(X0),compose(a,b))),codomain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_32520]) ).
tcf(c_39625,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(X0),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(domain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(X0)),compose(h,compose(a,b)))),compose(compose(domain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(domain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_32520]) ).
tcf(c_39626,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(compose(codomain(X0),compose(g,a))),codomain(X0),compose(codomain(X0),compose(g,a)),compose(compose(domain(compose(codomain(X0),compose(g,a))),codomain(X0)),compose(g,a))),compose(compose(domain(compose(codomain(X0),compose(g,a))),codomain(X0)),compose(g,a))) = compose(compose(domain(compose(codomain(X0),compose(g,a))),codomain(X0)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_32520]) ).
tcf(c_39627,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(domain(compose(codomain(X0),compose(h,a))),codomain(X0),compose(codomain(X0),compose(h,a)),compose(compose(domain(compose(codomain(X0),compose(h,a))),codomain(X0)),compose(h,a))),compose(compose(domain(compose(codomain(X0),compose(h,a))),codomain(X0)),compose(h,a))) = compose(compose(domain(compose(codomain(X0),compose(h,a))),codomain(X0)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_32520]) ).
tcf(c_39950,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),codomain(X0))),compose(compose(compose(a,b),compose(a,b)),codomain(X0))),compose(compose(compose(a,b),compose(a,b)),codomain(X0))) = compose(compose(compose(a,b),compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_171,c_22918]) ).
tcf(c_39953,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(X0))),compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(X0)),
inference(superposition,[status(thm)],[c_1392,c_22918]) ).
tcf(c_40009,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),codomain(X0))),compose(compose(compose(a,b),compose(a,b)),codomain(X0))),compose(compose(compose(a,b),compose(a,b)),codomain(X0))) = compose(compose(compose(a,b),compose(a,b)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_39950,c_425]) ).
tcf(c_40013,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(X0))),compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_39953,c_2217]) ).
tcf(c_40029,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),compose(h,a))),compose(compose(compose(g,a),compose(a,b)),compose(h,a))),compose(compose(compose(g,a),compose(a,b)),compose(h,a))) = compose(compose(compose(g,a),compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_171,c_5200]) ).
tcf(c_40032,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,a))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,a)),
inference(superposition,[status(thm)],[c_1392,c_5200]) ).
tcf(c_40033,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),compose(h,a))),compose(compose(compose(g,a),compose(g,a)),compose(h,a))),compose(compose(compose(g,a),compose(g,a)),compose(h,a))) = compose(compose(compose(g,a),compose(g,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_1491,c_5200]) ).
tcf(c_40034,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),compose(h,a))),compose(compose(compose(g,a),compose(h,a)),compose(h,a))),compose(compose(compose(g,a),compose(h,a)),compose(h,a))) = compose(compose(compose(g,a),compose(h,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_347,c_5200]) ).
tcf(c_40051,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),compose(h,a))),compose(compose(compose(g,a),compose(h,a)),compose(h,a))),compose(compose(compose(g,a),compose(h,a)),compose(h,a))) = compose(compose(compose(g,a),compose(h,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_40034,c_485]) ).
tcf(c_40052,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),compose(h,a))),compose(compose(compose(g,a),compose(g,a)),compose(h,a))),compose(compose(compose(g,a),compose(g,a)),compose(h,a))) = compose(compose(compose(g,a),compose(g,a)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_40033,c_571]) ).
tcf(c_40053,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),compose(h,a))),compose(compose(compose(g,a),compose(a,b)),compose(h,a))),compose(compose(compose(g,a),compose(a,b)),compose(h,a))) = compose(compose(compose(g,a),compose(a,b)),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_40029,c_425]) ).
tcf(c_40058,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,a))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,a)),
inference(light_normalisation,[status(thm)],[c_40032,c_2217]) ).
tcf(c_40151,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_2217,c_23034]) ).
tcf(c_40219,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),domain(X0))),compose(compose(compose(a,b),compose(a,b)),domain(X0))),compose(compose(compose(a,b),compose(a,b)),domain(X0))) = compose(compose(compose(a,b),compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_171,c_23105]) ).
tcf(c_40222,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(a,b),compose(h,compose(a,b))),domain(X0))),compose(compose(compose(a,b),compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(a,b),compose(h,compose(a,b))),domain(X0)),
inference(superposition,[status(thm)],[c_1392,c_23105]) ).
tcf(c_40273,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),domain(X0))),compose(compose(compose(a,b),compose(a,b)),domain(X0))),compose(compose(compose(a,b),compose(a,b)),domain(X0))) = compose(compose(compose(a,b),compose(a,b)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_40219,c_425]) ).
tcf(c_40277,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(a,b),compose(h,compose(a,b))),domain(X0))),compose(compose(compose(a,b),compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(a,b),compose(h,compose(a,b))),domain(X0)),
inference(light_normalisation,[status(thm)],[c_40222,c_2217]) ).
tcf(c_40295,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(a,b)),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(a,b)),domain(X0))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_2217,c_23218]) ).
tcf(c_40349,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),compose(a,b))),compose(compose(domain(X0),compose(a,b)),compose(a,b))),compose(compose(domain(X0),compose(a,b)),compose(a,b))) = compose(compose(domain(X0),compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_23240]) ).
tcf(c_40352,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(a),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(a,b))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(a,b))) = compose(compose(domain(X0),compose(h,compose(a,b))),compose(a,b)),
inference(superposition,[status(thm)],[c_1392,c_23240]) ).
tcf(c_40415,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),compose(a,b))),compose(compose(domain(X0),compose(a,b)),compose(a,b))),compose(compose(domain(X0),compose(a,b)),compose(a,b))) = compose(compose(domain(X0),compose(a,b)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_40349,c_425]) ).
tcf(c_40421,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(a,b))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(a,b))) = compose(compose(domain(X0),compose(h,compose(a,b))),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_40352,c_2217]) ).
tcf(c_40432,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(domain(X0),compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_23356]) ).
tcf(c_40498,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),compose(a,b))),compose(compose(codomain(X0),compose(a,b)),compose(a,b))),compose(compose(codomain(X0),compose(a,b)),compose(a,b))) = compose(compose(codomain(X0),compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_23394]) ).
tcf(c_40501,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(a),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(a,b))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(a,b))) = compose(compose(codomain(X0),compose(h,compose(a,b))),compose(a,b)),
inference(superposition,[status(thm)],[c_1392,c_23394]) ).
tcf(c_40550,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),compose(a,b))),compose(compose(codomain(X0),compose(a,b)),compose(a,b))),compose(compose(codomain(X0),compose(a,b)),compose(a,b))) = compose(compose(codomain(X0),compose(a,b)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_40498,c_425]) ).
tcf(c_40555,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(a,b))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(a,b))) = compose(compose(codomain(X0),compose(h,compose(a,b))),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_40501,c_2217]) ).
tcf(c_40568,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(a,b)),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(codomain(X0),compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_23491]) ).
tcf(c_40628,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),compose(a,b))),compose(compose(compose(a,b),domain(X0)),compose(a,b))),compose(compose(compose(a,b),domain(X0)),compose(a,b))) = compose(compose(compose(a,b),domain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_425,c_23554]) ).
tcf(c_40629,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),compose(a,b))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(a,b))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),domain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_23554]) ).
tcf(c_40639,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(domain(compose(domain(X0),compose(a,b)))),domain(X0),compose(domain(X0),compose(a,b)),compose(compose(domain(compose(domain(X0),compose(a,b))),domain(X0)),compose(a,b))),compose(compose(domain(compose(domain(X0),compose(a,b))),domain(X0)),compose(a,b))) = compose(compose(domain(compose(domain(X0),compose(a,b))),domain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_67,c_23554]) ).
tcf(c_40705,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),compose(h,compose(a,b)))),compose(compose(compose(a,b),domain(X0)),compose(h,compose(a,b)))),compose(compose(compose(a,b),domain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),domain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_23565]) ).
tcf(c_40772,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),compose(a,b))),compose(compose(compose(a,b),codomain(X0)),compose(a,b))),compose(compose(compose(a,b),codomain(X0)),compose(a,b))) = compose(compose(compose(a,b),codomain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_425,c_23649]) ).
tcf(c_40773,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),compose(a,b))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(a,b))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_23649]) ).
tcf(c_40843,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(compose(a,b),codomain(X0)),compose(h,compose(a,b)))),compose(compose(compose(a,b),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),codomain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_23661]) ).
tcf(c_42676,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_11874]) ).
tcf(c_42739,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_42676,c_2217]) ).
tcf(c_43107,plain,
ifeq(domain(b),domain(h),ifeq(codomain(domain(compose(compose(h,a),compose(h,a)))),domain(h),compose(compose(h,a),compose(h,a)),compose(compose(domain(compose(compose(h,a),compose(h,a))),compose(h,a)),compose(h,a))),compose(compose(domain(compose(compose(h,a),compose(h,a))),compose(h,a)),compose(h,a))) = compose(compose(domain(compose(compose(h,a),compose(h,a))),compose(h,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_67,c_5274]) ).
tcf(c_43130,plain,
! [X0: $i] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_11942]) ).
tcf(c_43210,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(X0)),
inference(superposition,[status(thm)],[c_1392,c_21187]) ).
tcf(c_43270,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_43210,c_2217]) ).
tcf(c_43842,plain,
ifeq(domain(b),domain(h),ifeq(codomain(domain(compose(compose(g,a),compose(h,a)))),domain(h),compose(compose(g,a),compose(h,a)),compose(compose(domain(compose(compose(g,a),compose(h,a))),compose(g,a)),compose(h,a))),compose(compose(domain(compose(compose(g,a),compose(h,a))),compose(g,a)),compose(h,a))) = compose(compose(domain(compose(compose(g,a),compose(h,a))),compose(g,a)),compose(h,a)),
inference(superposition,[status(thm)],[c_67,c_5275]) ).
tcf(c_44401,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(domain(compose(compose(a,b),compose(h,a)))),domain(a),compose(compose(a,b),compose(h,a)),compose(compose(domain(compose(compose(a,b),compose(h,a))),compose(a,b)),compose(h,a))),compose(compose(domain(compose(compose(a,b),compose(h,a))),compose(a,b)),compose(h,a))) = compose(compose(domain(compose(compose(a,b),compose(h,a))),compose(a,b)),compose(h,a)),
inference(superposition,[status(thm)],[c_67,c_5276]) ).
tcf(c_45505,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(domain(compose(compose(h,compose(a,b)),compose(h,a)))),domain(h),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,a))),compose(h,compose(a,b))),compose(h,a))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,a))),compose(h,compose(a,b))),compose(h,a))) = compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,a))),compose(h,compose(a,b))),compose(h,a)),
inference(superposition,[status(thm)],[c_67,c_5287]) ).
tcf(c_45531,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(compose(domain(X0),compose(h,a))),domain(X0),compose(domain(X0),compose(h,a)),compose(compose(domain(compose(domain(X0),compose(h,a))),domain(X0)),compose(h,a))),compose(compose(domain(compose(domain(X0),compose(h,a))),domain(X0)),compose(h,a))) = compose(compose(domain(compose(domain(X0),compose(h,a))),domain(X0)),compose(h,a)),
inference(demodulation,[status(thm)],[c_38387,c_65]) ).
tcf(c_45632,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(compose(domain(X0),compose(g,a))),domain(X0),compose(domain(X0),compose(g,a)),compose(compose(domain(compose(domain(X0),compose(g,a))),domain(X0)),compose(g,a))),compose(compose(domain(compose(domain(X0),compose(g,a))),domain(X0)),compose(g,a))) = compose(compose(domain(compose(domain(X0),compose(g,a))),domain(X0)),compose(g,a)),
inference(demodulation,[status(thm)],[c_39126,c_65]) ).
tcf(c_45910,plain,
ifeq(codomain(compose(a,b)),domain(a),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),compose(a,b))),compose(compose(compose(h,a),compose(a,b)),compose(a,b))),compose(compose(compose(h,a),compose(a,b)),compose(a,b))) = compose(compose(compose(h,a),compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_7349]) ).
tcf(c_45913,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(a),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(a,b))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(a,b)),
inference(superposition,[status(thm)],[c_1392,c_7349]) ).
tcf(c_45914,plain,
ifeq(codomain(compose(g,a)),domain(a),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),compose(a,b))),compose(compose(compose(h,a),compose(g,a)),compose(a,b))),compose(compose(compose(h,a),compose(g,a)),compose(a,b))) = compose(compose(compose(h,a),compose(g,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_1491,c_7349]) ).
tcf(c_45915,plain,
ifeq(codomain(compose(h,a)),domain(a),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),compose(a,b))),compose(compose(compose(h,a),compose(h,a)),compose(a,b))),compose(compose(compose(h,a),compose(h,a)),compose(a,b))) = compose(compose(compose(h,a),compose(h,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_347,c_7349]) ).
tcf(c_45935,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),compose(a,b))),compose(compose(compose(h,a),compose(h,a)),compose(a,b))),compose(compose(compose(h,a),compose(h,a)),compose(a,b))) = compose(compose(compose(h,a),compose(h,a)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_45915,c_485]) ).
tcf(c_45936,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),compose(a,b))),compose(compose(compose(h,a),compose(g,a)),compose(a,b))),compose(compose(compose(h,a),compose(g,a)),compose(a,b))) = compose(compose(compose(h,a),compose(g,a)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_45914,c_571]) ).
tcf(c_45937,plain,
ifeq(codomain(b),domain(a),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),compose(a,b))),compose(compose(compose(h,a),compose(a,b)),compose(a,b))),compose(compose(compose(h,a),compose(a,b)),compose(a,b))) = compose(compose(compose(h,a),compose(a,b)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_45910,c_425]) ).
tcf(c_45942,plain,
ifeq(codomain(b),domain(a),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(a,b))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_45913,c_2217]) ).
tcf(c_45946,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(compose(domain(X0),compose(a,b))),domain(X0),compose(domain(X0),compose(a,b)),compose(compose(domain(compose(domain(X0),compose(a,b))),domain(X0)),compose(a,b))),compose(compose(domain(compose(domain(X0),compose(a,b))),domain(X0)),compose(a,b))) = compose(compose(domain(compose(domain(X0),compose(a,b))),domain(X0)),compose(a,b)),
inference(demodulation,[status(thm)],[c_40639,c_65]) ).
tcf(c_46041,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_171,c_7352]) ).
tcf(c_46044,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_7352]) ).
tcf(c_46045,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(g,a)),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(g,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1491,c_7352]) ).
tcf(c_46046,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(h,a)),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(h,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_347,c_7352]) ).
tcf(c_46063,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(h,a)),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(h,a)),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_46046,c_485]) ).
tcf(c_46064,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(g,a)),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(g,a)),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_46045,c_571]) ).
tcf(c_46065,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(a,b)),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_46041,c_425]) ).
tcf(c_46069,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_46044,c_2217]) ).
tcf(c_46073,plain,
ifeq(domain(b),domain(h),ifeq(domain(compose(compose(h,a),compose(h,a))),domain(h),compose(compose(h,a),compose(h,a)),compose(compose(domain(compose(compose(h,a),compose(h,a))),compose(h,a)),compose(h,a))),compose(compose(domain(compose(compose(h,a),compose(h,a))),compose(h,a)),compose(h,a))) = compose(compose(domain(compose(compose(h,a),compose(h,a))),compose(h,a)),compose(h,a)),
inference(demodulation,[status(thm)],[c_43107,c_65]) ).
tcf(c_46086,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),compose(g,a))),compose(compose(compose(h,a),compose(a,b)),compose(g,a))),compose(compose(compose(h,a),compose(a,b)),compose(g,a))) = compose(compose(compose(h,a),compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_171,c_7353]) ).
tcf(c_46089,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(g,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(g,a)),
inference(superposition,[status(thm)],[c_1392,c_7353]) ).
tcf(c_46090,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),compose(g,a))),compose(compose(compose(h,a),compose(g,a)),compose(g,a))),compose(compose(compose(h,a),compose(g,a)),compose(g,a))) = compose(compose(compose(h,a),compose(g,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_7353]) ).
tcf(c_46091,plain,
ifeq(codomain(compose(h,a)),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),compose(g,a))),compose(compose(compose(h,a),compose(h,a)),compose(g,a))),compose(compose(compose(h,a),compose(h,a)),compose(g,a))) = compose(compose(compose(h,a),compose(h,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_347,c_7353]) ).
tcf(c_46108,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),compose(g,a))),compose(compose(compose(h,a),compose(h,a)),compose(g,a))),compose(compose(compose(h,a),compose(h,a)),compose(g,a))) = compose(compose(compose(h,a),compose(h,a)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_46091,c_485]) ).
tcf(c_46109,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),compose(g,a))),compose(compose(compose(h,a),compose(g,a)),compose(g,a))),compose(compose(compose(h,a),compose(g,a)),compose(g,a))) = compose(compose(compose(h,a),compose(g,a)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_46090,c_571]) ).
tcf(c_46110,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),compose(g,a))),compose(compose(compose(h,a),compose(a,b)),compose(g,a))),compose(compose(compose(h,a),compose(a,b)),compose(g,a))) = compose(compose(compose(h,a),compose(a,b)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_46086,c_425]) ).
tcf(c_46115,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(g,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_46089,c_2217]) ).
tcf(c_46172,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),compose(a,b))),compose(compose(compose(a,b),compose(h,a)),compose(a,b))),compose(compose(compose(a,b),compose(h,a)),compose(a,b))) = compose(compose(compose(a,b),compose(h,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_425,c_7580]) ).
tcf(c_46173,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_7580]) ).
tcf(c_46175,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),compose(a,b))),compose(compose(compose(g,a),compose(h,a)),compose(a,b))),compose(compose(compose(g,a),compose(h,a)),compose(a,b))) = compose(compose(compose(g,a),compose(h,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_571,c_7580]) ).
tcf(c_46176,plain,
ifeq(domain(b),domain(a),ifeq(codomain(domain(compose(compose(h,a),compose(a,b)))),domain(h),compose(compose(h,a),compose(a,b)),compose(compose(domain(compose(compose(h,a),compose(a,b))),compose(h,a)),compose(a,b))),compose(compose(domain(compose(compose(h,a),compose(a,b))),compose(h,a)),compose(a,b))) = compose(compose(domain(compose(compose(h,a),compose(a,b))),compose(h,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_67,c_7580]) ).
tcf(c_46188,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),compose(g,a))),compose(compose(compose(a,b),compose(h,a)),compose(g,a))),compose(compose(compose(a,b),compose(h,a)),compose(g,a))) = compose(compose(compose(a,b),compose(h,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_425,c_7584]) ).
tcf(c_46189,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_2217,c_7584]) ).
tcf(c_46191,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),compose(g,a))),compose(compose(compose(g,a),compose(h,a)),compose(g,a))),compose(compose(compose(g,a),compose(h,a)),compose(g,a))) = compose(compose(compose(g,a),compose(h,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_571,c_7584]) ).
tcf(c_46192,plain,
ifeq(domain(b),domain(h),ifeq(codomain(domain(compose(compose(h,a),compose(g,a)))),domain(h),compose(compose(h,a),compose(g,a)),compose(compose(domain(compose(compose(h,a),compose(g,a))),compose(h,a)),compose(g,a))),compose(compose(domain(compose(compose(h,a),compose(g,a))),compose(h,a)),compose(g,a))) = compose(compose(domain(compose(compose(h,a),compose(g,a))),compose(h,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_67,c_7584]) ).
tcf(c_46204,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(h,a)),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),compose(h,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_7591]) ).
tcf(c_46223,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(h,a)),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(h,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_7594]) ).
tcf(c_46248,plain,
ifeq(codomain(compose(a,b)),domain(a),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),compose(a,b))),compose(compose(compose(g,a),compose(a,b)),compose(a,b))),compose(compose(compose(g,a),compose(a,b)),compose(a,b))) = compose(compose(compose(g,a),compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_8546]) ).
tcf(c_46251,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(a),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(a,b))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(a,b)),
inference(superposition,[status(thm)],[c_1392,c_8546]) ).
tcf(c_46252,plain,
ifeq(codomain(compose(g,a)),domain(a),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),compose(a,b))),compose(compose(compose(g,a),compose(g,a)),compose(a,b))),compose(compose(compose(g,a),compose(g,a)),compose(a,b))) = compose(compose(compose(g,a),compose(g,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_1491,c_8546]) ).
tcf(c_46274,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),compose(a,b))),compose(compose(compose(g,a),compose(g,a)),compose(a,b))),compose(compose(compose(g,a),compose(g,a)),compose(a,b))) = compose(compose(compose(g,a),compose(g,a)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_46252,c_571]) ).
tcf(c_46275,plain,
ifeq(codomain(b),domain(a),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),compose(a,b))),compose(compose(compose(g,a),compose(a,b)),compose(a,b))),compose(compose(compose(g,a),compose(a,b)),compose(a,b))) = compose(compose(compose(g,a),compose(a,b)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_46248,c_425]) ).
tcf(c_46280,plain,
ifeq(codomain(b),domain(a),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(a,b))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_46251,c_2217]) ).
tcf(c_46294,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),compose(g,a))),compose(compose(compose(g,a),compose(a,b)),compose(g,a))),compose(compose(compose(g,a),compose(a,b)),compose(g,a))) = compose(compose(compose(g,a),compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_171,c_8550]) ).
tcf(c_46297,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(g,a))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(g,a)),
inference(superposition,[status(thm)],[c_1392,c_8550]) ).
tcf(c_46298,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),compose(g,a))),compose(compose(compose(g,a),compose(g,a)),compose(g,a))),compose(compose(compose(g,a),compose(g,a)),compose(g,a))) = compose(compose(compose(g,a),compose(g,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_8550]) ).
tcf(c_46317,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),compose(g,a))),compose(compose(compose(g,a),compose(g,a)),compose(g,a))),compose(compose(compose(g,a),compose(g,a)),compose(g,a))) = compose(compose(compose(g,a),compose(g,a)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_46298,c_571]) ).
tcf(c_46318,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),compose(g,a))),compose(compose(compose(g,a),compose(a,b)),compose(g,a))),compose(compose(compose(g,a),compose(a,b)),compose(g,a))) = compose(compose(compose(g,a),compose(a,b)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_46294,c_425]) ).
tcf(c_46323,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(g,a))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_46297,c_2217]) ).
tcf(c_46331,plain,
ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(g,a)),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(g,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_8605]) ).
tcf(c_46347,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_8606]) ).
tcf(c_46364,plain,
ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),g),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),g),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),g),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_11937]) ).
tcf(c_46373,plain,
ifeq(domain(b),domain(h),ifeq(domain(compose(compose(g,a),compose(h,a))),domain(h),compose(compose(g,a),compose(h,a)),compose(compose(domain(compose(compose(g,a),compose(h,a))),compose(g,a)),compose(h,a))),compose(compose(domain(compose(compose(g,a),compose(h,a))),compose(g,a)),compose(h,a))) = compose(compose(domain(compose(compose(g,a),compose(h,a))),compose(g,a)),compose(h,a)),
inference(demodulation,[status(thm)],[c_43842,c_65]) ).
tcf(c_46388,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),g)),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),g)),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),g)) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),g),
inference(superposition,[status(thm)],[c_1392,c_12456]) ).
tcf(c_46411,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),g)),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),g)),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),g)) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),g),
inference(light_normalisation,[status(thm)],[c_46388,c_2217]) ).
tcf(c_46429,plain,
ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(a,b),compose(h,a))),domain(a),compose(compose(a,b),compose(h,a)),compose(compose(domain(compose(compose(a,b),compose(h,a))),compose(a,b)),compose(h,a))),compose(compose(domain(compose(compose(a,b),compose(h,a))),compose(a,b)),compose(h,a))) = compose(compose(domain(compose(compose(a,b),compose(h,a))),compose(a,b)),compose(h,a)),
inference(demodulation,[status(thm)],[c_44401,c_65]) ).
tcf(c_46430,plain,
ifeq(domain(b),domain(a),ifeq(domain(compose(compose(h,a),compose(a,b))),domain(h),compose(compose(h,a),compose(a,b)),compose(compose(domain(compose(compose(h,a),compose(a,b))),compose(h,a)),compose(a,b))),compose(compose(domain(compose(compose(h,a),compose(a,b))),compose(h,a)),compose(a,b))) = compose(compose(domain(compose(compose(h,a),compose(a,b))),compose(h,a)),compose(a,b)),
inference(demodulation,[status(thm)],[c_46176,c_65]) ).
tcf(c_46431,plain,
ifeq(domain(b),domain(h),ifeq(domain(compose(compose(h,a),compose(g,a))),domain(h),compose(compose(h,a),compose(g,a)),compose(compose(domain(compose(compose(h,a),compose(g,a))),compose(h,a)),compose(g,a))),compose(compose(domain(compose(compose(h,a),compose(g,a))),compose(h,a)),compose(g,a))) = compose(compose(domain(compose(compose(h,a),compose(g,a))),compose(h,a)),compose(g,a)),
inference(demodulation,[status(thm)],[c_46192,c_65]) ).
tcf(c_46463,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),compose(g,a))),compose(compose(compose(a,b),compose(a,b)),compose(g,a))),compose(compose(compose(a,b),compose(a,b)),compose(g,a))) = compose(compose(compose(a,b),compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_171,c_13709]) ).
tcf(c_46466,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(g,a))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(a,b),compose(h,compose(a,b))),compose(g,a)),
inference(superposition,[status(thm)],[c_1392,c_13709]) ).
tcf(c_46467,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),compose(g,a))),compose(compose(compose(a,b),compose(g,a)),compose(g,a))),compose(compose(compose(a,b),compose(g,a)),compose(g,a))) = compose(compose(compose(a,b),compose(g,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_1491,c_13709]) ).
tcf(c_46483,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),compose(g,a))),compose(compose(compose(a,b),compose(g,a)),compose(g,a))),compose(compose(compose(a,b),compose(g,a)),compose(g,a))) = compose(compose(compose(a,b),compose(g,a)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_46467,c_571]) ).
tcf(c_46484,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),compose(g,a))),compose(compose(compose(a,b),compose(a,b)),compose(g,a))),compose(compose(compose(a,b),compose(a,b)),compose(g,a))) = compose(compose(compose(a,b),compose(a,b)),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_46463,c_425]) ).
tcf(c_46489,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(g,a))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(a,b),compose(h,compose(a,b))),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_46466,c_2217]) ).
tcf(c_46498,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_2217,c_13784]) ).
tcf(c_46501,plain,
ifeq(domain(b),domain(h),ifeq(codomain(domain(compose(compose(g,a),compose(g,a)))),domain(h),compose(compose(g,a),compose(g,a)),compose(compose(domain(compose(compose(g,a),compose(g,a))),compose(g,a)),compose(g,a))),compose(compose(domain(compose(compose(g,a),compose(g,a))),compose(g,a)),compose(g,a))) = compose(compose(domain(compose(compose(g,a),compose(g,a))),compose(g,a)),compose(g,a)),
inference(superposition,[status(thm)],[c_67,c_13784]) ).
tcf(c_46514,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_2217,c_13785]) ).
tcf(c_46517,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(domain(compose(compose(a,b),compose(g,a)))),domain(a),compose(compose(a,b),compose(g,a)),compose(compose(domain(compose(compose(a,b),compose(g,a))),compose(a,b)),compose(g,a))),compose(compose(domain(compose(compose(a,b),compose(g,a))),compose(a,b)),compose(g,a))) = compose(compose(domain(compose(compose(a,b),compose(g,a))),compose(a,b)),compose(g,a)),
inference(superposition,[status(thm)],[c_67,c_13785]) ).
tcf(c_46533,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),compose(a,b))),compose(compose(compose(a,b),compose(g,a)),compose(a,b))),compose(compose(compose(a,b),compose(g,a)),compose(a,b))) = compose(compose(compose(a,b),compose(g,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_425,c_13932]) ).
tcf(c_46534,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_13932]) ).
tcf(c_46537,plain,
ifeq(domain(b),domain(a),ifeq(codomain(domain(compose(compose(g,a),compose(a,b)))),domain(h),compose(compose(g,a),compose(a,b)),compose(compose(domain(compose(compose(g,a),compose(a,b))),compose(g,a)),compose(a,b))),compose(compose(domain(compose(compose(g,a),compose(a,b))),compose(g,a)),compose(a,b))) = compose(compose(domain(compose(compose(g,a),compose(a,b))),compose(g,a)),compose(a,b)),
inference(superposition,[status(thm)],[c_67,c_13932]) ).
tcf(c_46549,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(g,a)),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),compose(g,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_13943]) ).
tcf(c_46594,plain,
ifeq(domain(b),domain(h),ifeq(domain(compose(compose(g,a),compose(g,a))),domain(h),compose(compose(g,a),compose(g,a)),compose(compose(domain(compose(compose(g,a),compose(g,a))),compose(g,a)),compose(g,a))),compose(compose(domain(compose(compose(g,a),compose(g,a))),compose(g,a)),compose(g,a))) = compose(compose(domain(compose(compose(g,a),compose(g,a))),compose(g,a)),compose(g,a)),
inference(demodulation,[status(thm)],[c_46501,c_65]) ).
tcf(c_46595,plain,
ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(a,b),compose(g,a))),domain(a),compose(compose(a,b),compose(g,a)),compose(compose(domain(compose(compose(a,b),compose(g,a))),compose(a,b)),compose(g,a))),compose(compose(domain(compose(compose(a,b),compose(g,a))),compose(a,b)),compose(g,a))) = compose(compose(domain(compose(compose(a,b),compose(g,a))),compose(a,b)),compose(g,a)),
inference(demodulation,[status(thm)],[c_46517,c_65]) ).
tcf(c_46596,plain,
ifeq(domain(b),domain(a),ifeq(domain(compose(compose(g,a),compose(a,b))),domain(h),compose(compose(g,a),compose(a,b)),compose(compose(domain(compose(compose(g,a),compose(a,b))),compose(g,a)),compose(a,b))),compose(compose(domain(compose(compose(g,a),compose(a,b))),compose(g,a)),compose(a,b))) = compose(compose(domain(compose(compose(g,a),compose(a,b))),compose(g,a)),compose(a,b)),
inference(demodulation,[status(thm)],[c_46537,c_65]) ).
tcf(c_46612,plain,
ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(h,compose(a,b)),compose(h,a))),domain(h),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,a))),compose(h,compose(a,b))),compose(h,a))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,a))),compose(h,compose(a,b))),compose(h,a))) = compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,a))),compose(h,compose(a,b))),compose(h,a)),
inference(demodulation,[status(thm)],[c_45505,c_65]) ).
tcf(c_46625,plain,
ifeq(codomain(compose(a,b)),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),compose(a,b))),compose(compose(compose(a,b),compose(a,b)),compose(a,b))),compose(compose(compose(a,b),compose(a,b)),compose(a,b))) = compose(compose(compose(a,b),compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_171,c_30729]) ).
tcf(c_46628,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(a),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(a,b))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(a,b),compose(h,compose(a,b))),compose(a,b)),
inference(superposition,[status(thm)],[c_1392,c_30729]) ).
tcf(c_46649,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),compose(a,b))),compose(compose(compose(a,b),compose(a,b)),compose(a,b))),compose(compose(compose(a,b),compose(a,b)),compose(a,b))) = compose(compose(compose(a,b),compose(a,b)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_46625,c_425]) ).
tcf(c_46654,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(a,b))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(a,b),compose(h,compose(a,b))),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_46628,c_2217]) ).
tcf(c_46663,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_2217,c_30810]) ).
tcf(c_46666,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(domain(compose(compose(a,b),compose(a,b)))),domain(a),compose(compose(a,b),compose(a,b)),compose(compose(domain(compose(compose(a,b),compose(a,b))),compose(a,b)),compose(a,b))),compose(compose(domain(compose(compose(a,b),compose(a,b))),compose(a,b)),compose(a,b))) = compose(compose(domain(compose(compose(a,b),compose(a,b))),compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_67,c_30810]) ).
tcf(c_46681,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_30945]) ).
tcf(c_46703,plain,
ifeq(codomain(b),domain(a),ifeq(domain(compose(compose(a,b),compose(a,b))),domain(a),compose(compose(a,b),compose(a,b)),compose(compose(domain(compose(compose(a,b),compose(a,b))),compose(a,b)),compose(a,b))),compose(compose(domain(compose(compose(a,b),compose(a,b))),compose(a,b)),compose(a,b))) = compose(compose(domain(compose(compose(a,b),compose(a,b))),compose(a,b)),compose(a,b)),
inference(demodulation,[status(thm)],[c_46666,c_65]) ).
tcf(c_47306,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_7583]) ).
tcf(c_47309,plain,
ifeq(domain(b),domain(h),ifeq(codomain(domain(compose(compose(h,a),compose(h,compose(a,b))))),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(domain(compose(compose(h,a),compose(h,compose(a,b)))),compose(h,a)),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(h,a),compose(h,compose(a,b)))),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(h,a),compose(h,compose(a,b)))),compose(h,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_67,c_7583]) ).
tcf(c_47315,plain,
ifeq(domain(b),domain(h),ifeq(domain(compose(compose(h,a),compose(h,compose(a,b)))),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(domain(compose(compose(h,a),compose(h,compose(a,b)))),compose(h,a)),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(h,a),compose(h,compose(a,b)))),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(h,a),compose(h,compose(a,b)))),compose(h,a)),compose(h,compose(a,b))),
inference(demodulation,[status(thm)],[c_47309,c_65]) ).
tcf(c_49621,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_8549]) ).
tcf(c_49646,plain,
ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_49621,c_2217]) ).
tcf(c_50387,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(domain(compose(domain(X0),compose(h,compose(a,b)))),domain(X0),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(compose(domain(X0),compose(h,compose(a,b)))),domain(X0)),compose(h,compose(a,b)))),compose(compose(domain(compose(domain(X0),compose(h,compose(a,b)))),domain(X0)),compose(h,compose(a,b)))) = compose(compose(domain(compose(domain(X0),compose(h,compose(a,b)))),domain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_33881]) ).
tcf(c_50773,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_11878]) ).
tcf(c_50823,plain,
! [X0: $i] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_50773,c_2217]) ).
tcf(c_50841,plain,
! [X0: $i] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),domain(X0)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_2217,c_11941]) ).
tcf(c_50923,plain,
! [X0: $i] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),domain(X0)),
inference(superposition,[status(thm)],[c_1392,c_21189]) ).
tcf(c_50978,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),domain(X0)),
inference(light_normalisation,[status(thm)],[c_50923,c_2217]) ).
tcf(c_51420,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_11879]) ).
tcf(c_51442,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_51420,c_2217]) ).
tcf(c_51945,plain,
ifeq(codomain(compose(a,b)),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_171,c_11880]) ).
tcf(c_51948,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_11880]) ).
tcf(c_51949,plain,
ifeq(codomain(compose(g,a)),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1491,c_11880]) ).
tcf(c_51965,plain,
ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_51949,c_571]) ).
tcf(c_51966,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_51945,c_425]) ).
tcf(c_51970,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_51948,c_2217]) ).
tcf(c_54584,plain,
ifeq(domain(b),domain(h),ifeq(codomain(domain(compose(compose(g,a),compose(h,compose(a,b))))),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(domain(compose(compose(g,a),compose(h,compose(a,b)))),compose(g,a)),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(g,a),compose(h,compose(a,b)))),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(g,a),compose(h,compose(a,b)))),compose(g,a)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_67,c_11954]) ).
tcf(c_54590,plain,
ifeq(domain(b),domain(h),ifeq(domain(compose(compose(g,a),compose(h,compose(a,b)))),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(domain(compose(compose(g,a),compose(h,compose(a,b)))),compose(g,a)),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(g,a),compose(h,compose(a,b)))),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(g,a),compose(h,compose(a,b)))),compose(g,a)),compose(h,compose(a,b))),
inference(demodulation,[status(thm)],[c_54584,c_65]) ).
tcf(c_54629,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(domain(compose(compose(a,b),compose(h,compose(a,b))))),domain(a),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(domain(compose(compose(a,b),compose(h,compose(a,b)))),compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(a,b),compose(h,compose(a,b)))),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(a,b),compose(h,compose(a,b)))),compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_67,c_11955]) ).
tcf(c_54640,plain,
ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(a,b),compose(h,compose(a,b)))),domain(a),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(domain(compose(compose(a,b),compose(h,compose(a,b)))),compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(a,b),compose(h,compose(a,b)))),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(a,b),compose(h,compose(a,b)))),compose(a,b)),compose(h,compose(a,b))),
inference(demodulation,[status(thm)],[c_54629,c_65]) ).
tcf(c_54746,plain,
ifeq(codomain(compose(h,compose(a,b))),codomain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),codomain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_1392,c_17699]) ).
tcf(c_54769,plain,
ifeq(codomain(b),codomain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),codomain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
inference(light_normalisation,[status(thm)],[c_54746,c_2217]) ).
tcf(c_54807,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(g,a)),
inference(superposition,[status(thm)],[c_1392,c_13710]) ).
tcf(c_54830,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(g,a)),
inference(light_normalisation,[status(thm)],[c_54807,c_2217]) ).
tcf(c_54842,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(domain(compose(compose(h,compose(a,b)),compose(g,a)))),domain(h),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(domain(compose(compose(h,compose(a,b)),compose(g,a))),compose(h,compose(a,b))),compose(g,a))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(g,a))),compose(h,compose(a,b))),compose(g,a))) = compose(compose(domain(compose(compose(h,compose(a,b)),compose(g,a))),compose(h,compose(a,b))),compose(g,a)),
inference(superposition,[status(thm)],[c_67,c_13793]) ).
tcf(c_54894,plain,
ifeq(codomain(compose(h,compose(a,b))),domain(a),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(a,b)),
inference(superposition,[status(thm)],[c_1392,c_21188]) ).
tcf(c_54920,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_54894,c_2217]) ).
tcf(c_54922,plain,
ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(h,compose(a,b)),compose(g,a))),domain(h),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(domain(compose(compose(h,compose(a,b)),compose(g,a))),compose(h,compose(a,b))),compose(g,a))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(g,a))),compose(h,compose(a,b))),compose(g,a))) = compose(compose(domain(compose(compose(h,compose(a,b)),compose(g,a))),compose(h,compose(a,b))),compose(g,a)),
inference(demodulation,[status(thm)],[c_54842,c_65]) ).
tcf(c_54947,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(domain(compose(compose(h,compose(a,b)),compose(a,b)))),domain(h),compose(compose(h,compose(a,b)),compose(a,b)),compose(compose(domain(compose(compose(h,compose(a,b)),compose(a,b))),compose(h,compose(a,b))),compose(a,b))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(a,b))),compose(h,compose(a,b))),compose(a,b))) = compose(compose(domain(compose(compose(h,compose(a,b)),compose(a,b))),compose(h,compose(a,b))),compose(a,b)),
inference(superposition,[status(thm)],[c_67,c_21598]) ).
tcf(c_54977,plain,
ifeq(codomain(b),domain(h),ifeq(codomain(domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b))))),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(superposition,[status(thm)],[c_67,c_11962]) ).
tcf(c_54983,plain,
ifeq(codomain(b),domain(a),ifeq(domain(compose(compose(h,compose(a,b)),compose(a,b))),domain(h),compose(compose(h,compose(a,b)),compose(a,b)),compose(compose(domain(compose(compose(h,compose(a,b)),compose(a,b))),compose(h,compose(a,b))),compose(a,b))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(a,b))),compose(h,compose(a,b))),compose(a,b))) = compose(compose(domain(compose(compose(h,compose(a,b)),compose(a,b))),compose(h,compose(a,b))),compose(a,b)),
inference(demodulation,[status(thm)],[c_54947,c_65]) ).
tcf(c_54984,plain,
ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(h,compose(a,b))),compose(h,compose(a,b))),
inference(demodulation,[status(thm)],[c_54977,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT002-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p SAT
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 06:50:14 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p SAT
% 0.11/0.41 Running model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fnt_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 9.95/5.79 % SZS status Started for theBenchmark.p
% 9.95/5.79 % SZS status Satisfiable for theBenchmark.p
% 9.95/5.79
% 9.95/5.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 9.95/5.79
% 9.95/5.79 ------ iProver source info
% 9.95/5.79
% 9.95/5.79 git: date: 2026-07-19 20:42:38 +0200
% 9.95/5.79 git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 9.95/5.79 git: non_committed_changes: false
% 9.95/5.79
% 9.95/5.79 ------ Parsing...successful
% 9.95/5.79
% 9.95/5.79
% 9.95/5.79 ------ Clausification by vclausify_rel & Parsing by iProver...------ preprocesses with Option_UEQ
% 9.95/5.79
% 9.95/5.79 ------ Proving...
% 9.95/5.79 ------ Problem Properties
% 9.95/5.79
% 9.95/5.79
% 9.95/5.79 clauses 15
% 9.95/5.79 conjectures 1
% 9.95/5.79 EPR 1
% 9.95/5.79 Horn 15
% 9.95/5.79 unary 15
% 9.95/5.79 binary 0
% 9.95/5.79 lits 15
% 9.95/5.79 lits eq 15
% 9.95/5.79 fd_pure 0
% 9.95/5.79 fd_pseudo 0
% 9.95/5.79 fd_cond 0
% 9.95/5.79 fd_pseudo_cond 0
% 9.95/5.79 AC symbols 0
% 9.95/5.79
% 9.95/5.79 ------ Schedule UEQ
% 9.95/5.79
% 9.95/5.79 ------ Option_UEQ Time Limit: 10.
% 9.95/5.79
% 9.95/5.79
% 9.95/5.79 ------
% 9.95/5.79 Current options:
% 9.95/5.79 ------
% 9.95/5.79
% 9.95/5.79 ------ Input Options
% 9.95/5.79
% 9.95/5.79 --out_options all
% 9.95/5.79 --tptp_safe_out true
% 9.95/5.79 --problem_path ""
% 9.95/5.79 --include_path ""
% 9.95/5.79 --clausifier res/vclausify_rel
% 9.95/5.79 --clausifier_options --mode clausify -t 101.67 -updr off
% 9.95/5.79 --stdin false
% 9.95/5.79 --proof_out true
% 9.95/5.79 --proof_dot_file ""
% 9.95/5.79 --proof_reduce_dot []
% 9.95/5.79 --suppress_sat_res false
% 9.95/5.79 --suppress_unsat_res true
% 9.95/5.79 --stats_out none
% 9.95/5.79 --stats_mem false
% 9.95/5.79 --theory_stats_out false
% 9.95/5.79
% 9.95/5.79 ------ General Options
% 9.95/5.79
% 9.95/5.79 --fof false
% 9.95/5.79 --time_out_real 305.
% 9.95/5.79 --time_out_virtual -1.
% 9.95/5.79 --rnd_seed 13
% 9.95/5.79 --symbol_type_check false
% 9.95/5.79 --clausify_out false
% 9.95/5.79 --sig_cnt_out false
% 9.95/5.79 --trig_cnt_out false
% 9.95/5.79 --trig_cnt_out_tolerance 1.
% 9.95/5.79 --trig_cnt_out_sk_spl false
% 9.95/5.79 --abstr_cl_out false
% 9.95/5.79
% 9.95/5.79 ------ Interactive Mode
% 9.95/5.79
% 9.95/5.79 --interactive_mode false
% 9.95/5.79 --external_ip_address ""
% 9.95/5.79 --external_port 0
% 9.95/5.79
% 9.95/5.79 ------ Global Options
% 9.95/5.79
% 9.95/5.79 --schedule default
% 9.95/5.79 --add_important_lit false
% 9.95/5.79 --prop_solver_per_cl 500
% 9.95/5.79 --subs_bck_mult 8
% 9.95/5.79 --min_unsat_core false
% 9.95/5.79 --soft_assumptions false
% 9.95/5.79 --soft_lemma_size 3
% 9.95/5.79 --prop_impl_unit_size 0
% 9.95/5.79 --prop_impl_unit []
% 9.95/5.79 --share_sel_clauses true
% 9.95/5.79 --reset_solvers false
% 9.95/5.79 --bc_imp_inh [conj_cone]
% 9.95/5.79 --conj_cone_tolerance 3.
% 9.95/5.79 --extra_neg_conj none
% 9.95/5.79 --large_theory_mode true
% 9.95/5.79 --prolific_symb_bound 200
% 9.95/5.79 --lt_threshold 2000
% 9.95/5.79 --clause_weak_htbl true
% 9.95/5.79 --gc_record_bc_elim false
% 9.95/5.79
% 9.95/5.79 ------ Preprocessing Options
% 9.95/5.79
% 9.95/5.79 --preprocessing_flag false
% 9.95/5.79 --time_out_prep_mult 0.1
% 9.95/5.79 --splitting_mode input
% 9.95/5.79 --splitting_grd true
% 9.95/5.79 --splitting_cvd false
% 9.95/5.79 --splitting_cvd_svl false
% 9.95/5.79 --splitting_nvd 32
% 9.95/5.79 --sub_typing false
% 9.95/5.79 --prep_eq_flat_conj true
% 9.95/5.79 --prep_ineq_split false
% 9.95/5.79 --prep_eq_flat_all_gr false
% 9.95/5.79 --prep_gs_sim true
% 9.95/5.79 --prep_unflatten true
% 9.95/5.79 --prep_res_sim true
% 9.95/5.79 --prep_sup_sim_all true
% 9.95/5.79 --prep_sup_sim_sup false
% 9.95/5.79 --prep_upred true
% 9.95/5.79 --prep_well_definedness true
% 9.95/5.79 --prep_sem_filter exhaustive
% 9.95/5.79 --prep_sem_filter_out false
% 9.95/5.79 --pred_elim true
% 9.95/5.79 --res_sim_input true
% 9.95/5.79 --eq_ax_congr_red true
% 9.95/5.79 --pure_diseq_elim true
% 9.95/5.79 --brand_transform false
% 9.95/5.79 --non_eq_to_eq false
% 9.95/5.79 --prep_eq_proxy false
% 9.95/5.79 --prep_def_merge true
% 9.95/5.79 --prep_def_merge_prop_impl false
% 9.95/5.79 --prep_def_merge_mbd true
% 9.95/5.79 --prep_def_merge_tr_red false
% 9.95/5.79 --prep_def_merge_tr_cl false
% 9.95/5.79 --smt_preprocessing false
% 9.95/5.79 --smt_ac_axioms fast
% 9.95/5.79 --preprocessed_out false
% 9.95/5.79 --preprocessed_stats false
% 9.95/5.79
% 9.95/5.79 ------ Abstraction refinement Options
% 9.95/5.79
% 9.95/5.79 --abstr_ref []
% 9.95/5.79 --abstr_ref_prep false
% 9.95/5.79 --abstr_ref_until_sat false
% 9.95/5.79 --abstr_ref_sig_restrict funpre
% 9.95/5.79 --abstr_ref_af_restrict_to_split_sk false
% 9.95/5.79 --abstr_ref_under []
% 9.95/5.79
% 9.95/5.79 ------ SAT Options
% 9.95/5.79
% 9.95/5.79 --sat_mode false
% 9.95/5.79 --sat_fm_restart_options ""
% 9.95/5.79 --sat_gr_def false
% 9.95/5.79 --sat_epr_types true
% 9.95/5.79 --sat_non_cyclic_types false
% 9.95/5.79 --sat_finite_models false
% 9.95/5.79 --sat_fm_lemmas false
% 9.95/5.79 --sat_fm_prep false
% 9.95/5.79 --sat_fm_uc_incr true
% 9.95/5.79 --sat_out_model pos
% 9.95/5.79 --sat_out_clauses false
% 9.95/5.79
% 9.95/5.79 ------ QBF Options
% 9.95/5.79
% 9.95/5.79 --qbf_mode false
% 9.95/5.79 --qbf_elim_univ false
% 9.95/5.79 --qbf_dom_inst none
% 9.95/5.79 --qbf_dom_pre_inst false
% 9.95/5.79 --qbf_sk_in false
% 9.95/5.79 --qbf_pred_elim true
% 9.95/5.79 --qbf_split 512
% 9.95/5.79
% 9.95/5.79 ------ BMC1 Options
% 9.95/5.79
% 9.95/5.79 --bmc1_incremental false
% 9.95/5.79 --bmc1_axioms reachable_all
% 9.95/5.79 --bmc1_min_bound 0
% 9.95/5.79 --bmc1_max_bound -1
% 9.95/5.79 --bmc1_max_bound_default -1
% 9.95/5.79 --bmc1_symbol_reachability true
% 9.95/5.79 --bmc1_property_lemmas false
% 9.95/5.79 --bmc1_k_induction false
% 9.95/5.79 --bmc1_non_equiv_states false
% 9.95/5.79 --bmc1_deadlock false
% 9.95/5.79 --bmc1_ucm false
% 9.95/5.79 --bmc1_add_unsat_core none
% 9.95/5.79 --bmc1_unsat_core_children false
% 9.95/5.79 --bmc1_unsat_core_extrapolate_axioms false
% 9.95/5.79 --bmc1_out_stat full
% 9.95/5.79 --bmc1_ground_init false
% 9.95/5.79 --bmc1_pre_inst_next_state false
% 9.95/5.79 --bmc1_pre_inst_state false
% 9.95/5.79 --bmc1_pre_inst_reach_state false
% 9.95/5.79 --bmc1_out_unsat_core false
% 9.95/5.79 --bmc1_aig_witness_out false
% 9.95/5.79 --bmc1_verbose false
% 9.95/5.79 --bmc1_dump_clauses_tptp false
% 9.95/5.79 --bmc1_dump_unsat_core_tptp false
% 9.95/5.79 --bmc1_dump_file -
% 9.95/5.79 --bmc1_ucm_expand_uc_limit 128
% 9.95/5.79 --bmc1_ucm_n_expand_iterations 6
% 9.95/5.79 --bmc1_ucm_extend_mode 1
% 9.95/5.79 --bmc1_ucm_init_mode 2
% 9.95/5.79 --bmc1_ucm_cone_mode none
% 9.95/5.79 --bmc1_ucm_reduced_relation_type 0
% 9.95/5.79 --bmc1_ucm_relax_model 4
% 9.95/5.79 --bmc1_ucm_full_tr_after_sat true
% 9.95/5.79 --bmc1_ucm_expand_neg_assumptions false
% 9.95/5.79 --bmc1_ucm_layered_model none
% 9.95/5.79 --bmc1_ucm_max_lemma_size 10
% 9.95/5.79
% 9.95/5.79 ------ AIG Options
% 9.95/5.79
% 9.95/5.79 --aig_mode false
% 9.95/5.79
% 9.95/5.79 ------ Instantiation Options
% 9.95/5.79
% 9.95/5.79 --instantiation_flag true
% 9.95/5.79 --inst_sos_flag false
% 9.95/5.79 --inst_sos_phase true
% 9.95/5.79 --inst_sos_sth_lit_sel [+prop;+non_prol_conj_symb;-eq;+ground;-num_var;-num_symb]
% 9.95/5.79 --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 9.95/5.79 --inst_lit_sel_side num_symb
% 9.95/5.79 --inst_solver_per_active 1400
% 9.95/5.79 --inst_solver_calls_frac 1.
% 9.95/5.79 --inst_to_smt_solver true
% 9.95/5.79 --inst_passive_queue_type priority_queues
% 9.95/5.79 --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 9.95/5.79 --inst_passive_queues_freq [25;2]
% 9.95/5.79 --inst_dismatching true
% 9.95/5.79 --inst_eager_unprocessed_to_passive true
% 9.95/5.79 --inst_unprocessed_bound 1000
% 9.95/5.79 --inst_prop_sim_given true
% 9.95/5.79 --inst_prop_sim_new false
% 9.95/5.79 --inst_subs_new false
% 9.95/5.79 --inst_eq_res_simp false
% 9.95/5.79 --inst_subs_given false
% 9.95/5.79 --inst_orphan_elimination true
% 9.95/5.79 --inst_learning_loop_flag true
% 9.95/5.79 --inst_learning_start 3000
% 9.95/5.79 --inst_learning_factor 2
% 9.95/5.79 --inst_start_prop_sim_after_learn 3
% 9.95/5.79 --inst_sel_renew solver
% 9.95/5.79 --inst_lit_activity_flag true
% 9.95/5.79 --inst_restr_to_given false
% 9.95/5.79 --inst_activity_threshold 500
% 9.95/5.79
% 9.95/5.79 ------ Resolution Options
% 9.95/5.79
% 9.95/5.79 --resolution_flag false
% 9.95/5.79 --res_lit_sel adaptive
% 9.95/5.79 --res_lit_sel_side none
% 9.95/5.79 --res_ordering kbo
% 9.95/5.79 --res_to_prop_solver active
% 9.95/5.79 --res_prop_simpl_new false
% 9.95/5.79 --res_prop_simpl_given true
% 9.95/5.79 --res_to_smt_solver true
% 9.95/5.79 --res_passive_queue_type priority_queues
% 9.95/5.79 --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 9.95/5.79 --res_passive_queues_freq [15;5]
% 9.95/5.79 --res_forward_subs full
% 9.95/5.79 --res_backward_subs full
% 9.95/5.79 --res_forward_subs_resolution true
% 9.95/5.79 --res_backward_subs_resolution true
% 9.95/5.79 --res_orphan_elimination true
% 9.95/5.79 --res_time_limit 300.
% 9.95/5.79
% 9.95/5.79 ------ Superposition Options
% 9.95/5.79
% 9.95/5.79 --superposition_flag true
% 9.95/5.79 --sup_passive_queue_type priority_queues
% 9.95/5.79 --sup_passive_queues [[-conj_dist;-num_symb];[+score;+min_def_symb;-max_atom_input_occur;+conj_non_prolific_symb];[+age;-num_symb];[+score;-num_symb]]
% 9.95/5.79 --sup_passive_queues_freq [8;1;4;4]
% 9.95/5.79 --twee_lhs_weight 4
% 9.95/5.79 --sup_set_join false
% 9.95/5.79 --sup_set_join_goals true
% 9.95/5.79 --sup_set_join_limit 1000
% 9.95/5.79 --demod_completeness_check fast
% 9.95/5.79 --demod_use_ground true
% 9.95/5.79 --sup_unprocessed_bound 0
% 9.95/5.79 --sup_to_prop_solver none
% 9.95/5.79 --sup_prop_simpl_new false
% 9.95/5.79 --sup_prop_simpl_given true
% 9.95/5.79 --sup_fun_splitting false
% 9.95/5.79 --sup_iter_deepening 0
% 9.95/5.79 --sup_restarts_mult 12
% 9.95/5.79 --sup_score sim_d_gen
% 9.95/5.79 --sup_share_score_frac 0.2
% 9.95/5.79 --sup_share_max_num_cl 500
% 9.95/5.79 --sup_ordering kbo
% 9.95/5.79 --sup_symb_ordering invfreq
% 9.95/5.79 --sup_term_weight default
% 9.95/5.79
% 9.95/5.79 ------ Superposition Simplification Setup
% 9.95/5.79
% 9.95/5.79 --sup_indices_passive [LightNormIndex;FwDemodIndex]
% 9.95/5.79 --sup_full_triv [SMTSimplify;PropSubs]
% 9.95/5.79 --sup_full_fw [ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability]
% 9.95/5.79 --sup_full_bw [BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes]
% 9.95/5.79 --sup_immed_triv []
% 9.95/5.79 --sup_immed_fw_main [ACNormalisation;FwLightNorm;FwUnitSubsAndRes]
% 9.95/5.79 --sup_immed_fw_immed [ACNormalisation;FwUnitSubsAndRes]
% 9.95/5.79 --sup_immed_bw_main [BwUnitSubsAndRes;BwDemod]
% 9.95/5.79 --sup_immed_bw_immed [BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes]
% 9.95/5.79 --sup_input_triv [Unflattening;SMTSimplify]
% 9.95/5.79 --sup_input_fw [FwACDemod;ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability]
% 9.95/5.79 --sup_input_bw [BwACDemod;BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes]
% 9.95/5.79 --sup_full_fixpoint true
% 9.95/5.79 --sup_main_fixpoint true
% 9.95/5.79 --sup_immed_fixpoint false
% 9.95/5.79 --sup_input_fixpoint true
% 9.95/5.79 --sup_cache_sim none
% 9.95/5.79 --sup_smt_interval 500
% 9.95/5.79 --sup_bw_gjoin_interval 0
% 9.95/5.79
% 9.95/5.79 ------ Combination Options
% 9.95/5.79
% 9.95/5.79 --comb_mode clause_based
% 9.95/5.79 --comb_inst_mult 1
% 9.95/5.79 --comb_res_mult 0
% 9.95/5.79 --comb_sup_mult 8
% 9.95/5.79 --comb_sup_deep_mult 0
% 9.95/5.79
% 9.95/5.79 ------ Debug Options
% 9.95/5.79
% 9.95/5.79 --dbg_backtrace false
% 9.95/5.79 --dbg_dump_prop_clauses false
% 9.95/5.79 --dbg_dump_prop_clauses_file -
% 9.95/5.79 --dbg_out_stat false
% 9.95/5.79 --dbg_just_parse false
% 9.95/5.79
% 9.95/5.79
% 9.95/5.79
% 9.95/5.79
% 9.95/5.79 ------ Proving...
% 9.95/5.79
% 9.95/5.79
% 9.95/5.79 % SZS status Satisfiable for theBenchmark.p
% 9.95/5.79
% 9.95/5.79 % SZS output start Saturation for theBenchmark.p
% See solution above
% 39.33/5.86
% 39.33/5.86
%------------------------------------------------------------------------------