%------------------------------------------------------------------------------
% File : iProver-SAT---3.9.4
% Problem : CAT001-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p SAT
% Computer : n026.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 01:01:18 PM UTC 2026
% Result : Satisfiable 10.29s 2.21s
% Output : Saturation 12.32s
% 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,
! [X2,X0,X1] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(codomain(X1),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X2,ifeq(compose(X1,compose(a,b)),X2,X1,X0),X0),X0),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c1) ).
fof(f15,axiom,
codomain(a) = domain(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
fof(f16,axiom,
codomain(a) = domain(h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_h) ).
fof(f17,axiom,
codomain(a) = domain(g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_g) ).
fof(f18,axiom,
compose(a,h) = compose(a,g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ah_equals_ag) ).
fof(f19,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_h_equals_g) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
! [X0: $i] : codomain(domain(X0)) = domain(X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_65,plain,
! [X0: $i] : domain(codomain(X0)) = codomain(X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_66,plain,
! [X0: $i] : compose(domain(X0),X0) = X0,
inference(cnf_transformation,[],[f6]) ).
tcf(c_67,plain,
! [X0: $i] : compose(X0,codomain(X0)) = X0,
inference(cnf_transformation,[],[f7]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),domain(compose(X0,X1)),domain(X0)) = domain(X0),
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),codomain(compose(X0,X1)),codomain(X1)) = codomain(X1),
inference(cnf_transformation,[],[f11]) ).
tcf(c_70,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_71,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(codomain(X1),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X2,ifeq(compose(X1,compose(a,b)),X2,X1,X0),X0),X0),X0) = X0,
inference(cnf_transformation,[],[f14]) ).
tcf(c_72,plain,
domain(b) = codomain(a),
inference(cnf_transformation,[],[f15]) ).
tcf(c_73,plain,
domain(h) = codomain(a),
inference(cnf_transformation,[],[f16]) ).
tcf(c_74,plain,
domain(g) = codomain(a),
inference(cnf_transformation,[],[f17]) ).
tcf(c_75,plain,
compose(a,h) = compose(a,g),
inference(cnf_transformation,[],[f18]) ).
tcf(c_76,negated_conjecture,
h != g,
inference(cnf_transformation,[],[f19]) ).
tcf(c_100,plain,
! [X0: $i] : domain(domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_65]) ).
tcf(c_101,plain,
! [X0: $i] : codomain(codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_65,c_64]) ).
tcf(c_103,plain,
! [X0: $i] : compose(codomain(X0),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_65,c_66]) ).
tcf(c_104,plain,
compose(codomain(a),b) = b,
inference(superposition,[status(thm)],[c_72,c_66]) ).
tcf(c_105,plain,
compose(codomain(a),h) = h,
inference(superposition,[status(thm)],[c_73,c_66]) ).
tcf(c_106,plain,
compose(codomain(a),g) = g,
inference(superposition,[status(thm)],[c_74,c_66]) ).
tcf(c_108,plain,
! [X0: $i] : compose(domain(X0),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_67]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),domain(compose(X0,codomain(X1))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_65,c_68]) ).
tcf(c_120,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),domain(compose(X0,b)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_72,c_68]) ).
tcf(c_121,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),domain(compose(X0,h)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_73,c_68]) ).
tcf(c_122,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),domain(compose(X0,g)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_74,c_68]) ).
tcf(c_123,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_68]) ).
tcf(c_130,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_65,c_68]) ).
tcf(c_131,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),domain(compose(b,X0)),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_72,c_68]) ).
tcf(c_132,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),domain(compose(h,X0)),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_73,c_68]) ).
tcf(c_133,plain,
! [X0: $i] : ifeq(codomain(g),domain(X0),domain(compose(g,X0)),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_74,c_68]) ).
tcf(c_134,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_68]) ).
tcf(c_141,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_134,c_64]) ).
tcf(c_142,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_130,c_101]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),codomain(compose(domain(X0),X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_64,c_69]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),codomain(compose(codomain(X0),X1)),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_101,c_69]) ).
tcf(c_176,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),codomain(compose(X0,b)),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_72,c_69]) ).
tcf(c_177,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),codomain(compose(X0,h)),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_73,c_69]) ).
tcf(c_178,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),codomain(compose(X0,g)),codomain(g)) = codomain(g),
inference(superposition,[status(thm)],[c_74,c_69]) ).
tcf(c_188,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_64,c_69]) ).
tcf(c_235,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_65,c_70]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,b)),compose(compose(X1,X0),b)),compose(compose(X1,X0),b)) = compose(compose(X1,X0),b),
inference(superposition,[status(thm)],[c_72,c_70]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,h)),compose(compose(X1,X0),h)),compose(compose(X1,X0),h)) = compose(compose(X1,X0),h),
inference(superposition,[status(thm)],[c_73,c_70]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),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_74,c_70]) ).
tcf(c_239,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_70]) ).
tcf(c_240,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_64,c_70]) ).
tcf(c_241,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_101,c_70]) ).
tcf(c_242,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_65,c_70]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),codomain(a),compose(X1,compose(b,X0)),compose(compose(X1,b),X0)),compose(compose(X1,b),X0)) = compose(compose(X1,b),X0),
inference(superposition,[status(thm)],[c_72,c_70]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),codomain(a),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_73,c_70]) ).
tcf(c_246,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_70]) ).
tcf(c_248,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_66,c_70]) ).
tcf(c_249,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_67,c_70]) ).
tcf(c_265,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_67,c_70]) ).
tcf(c_266,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_66,c_70]) ).
tcf(c_267,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_67,c_70]) ).
tcf(c_268,plain,
! [X0: $i] : ifeq(codomain(g),domain(X0),ifeq(codomain(a),domain(g),compose(a,compose(g,X0)),compose(compose(a,h),X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(superposition,[status(thm)],[c_75,c_70]) ).
tcf(c_277,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_266,c_64]) ).
tcf(c_278,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_267,c_65,c_101]) ).
tcf(c_279,plain,
! [X0: $i] : ifeq(codomain(g),domain(X0),ifeq(codomain(a),codomain(a),compose(a,compose(g,X0)),compose(compose(a,h),X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(light_normalisation,[status(thm)],[c_268,c_74]) ).
tcf(c_283,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_249,c_65]) ).
tcf(c_287,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_248,c_64,c_100]) ).
tcf(c_288,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_246,c_64]) ).
tcf(c_289,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_242,c_101]) ).
tcf(c_363,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),codomain(a),domain(compose(codomain(X0),b)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_65,c_120]) ).
tcf(c_364,plain,
ifeq(codomain(b),codomain(a),domain(compose(b,b)),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_72,c_120]) ).
tcf(c_365,plain,
ifeq(codomain(h),codomain(a),domain(compose(h,b)),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_73,c_120]) ).
tcf(c_367,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(a),domain(compose(domain(X0),b)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_100,c_120]) ).
tcf(c_368,plain,
domain(compose(a,b)) = domain(a),
inference(superposition,[status(thm)],[c_120,c_63]) ).
tcf(c_371,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),domain(compose(domain(X0),b)),domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_367,c_64]) ).
tcf(c_372,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),domain(compose(codomain(X0),b)),codomain(X0)) = codomain(X0),
inference(light_normalisation,[status(thm)],[c_363,c_101]) ).
tcf(c_385,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(X0,compose(a,b)),X2,ifeq(compose(X1,compose(a,b)),X2,X1,X0),X0),X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_71,c_368]) ).
tcf(c_386,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(domain(X0),compose(a,b)),X2,ifeq(compose(X1,compose(a,b)),X2,X1,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_385]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X2,ifeq(compose(X1,compose(a,b)),X2,X1,codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_385]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(X0,compose(a,b)),X2,ifeq(compose(domain(X1),compose(a,b)),X2,domain(X1),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_64,c_385]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(X0,compose(a,b)),X2,ifeq(compose(codomain(X1),compose(a,b)),X2,codomain(X1),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_101,c_385]) ).
tcf(c_390,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(X1,compose(a,b)),compose(X0,compose(a,b)),X1,X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_63,c_385]) ).
tcf(c_391,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(compose(a,b))),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(X0,compose(a,b)),X1,X0,domain(compose(a,b))),domain(compose(a,b))),domain(compose(a,b))),domain(compose(a,b))) = domain(compose(a,b)),
inference(superposition,[status(thm)],[c_66,c_385]) ).
tcf(c_392,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(X0,compose(a,b)),compose(X1,compose(a,b)),X1,X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_63,c_385]) ).
tcf(c_393,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(compose(a,b))),domain(a),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(a,b),X1,domain(compose(a,b)),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_66,c_385]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(a)),domain(a),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(a,b),X1,domain(a),X0),X0),X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_393,c_368]) ).
tcf(c_395,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(a)),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(X0,compose(a,b)),X1,X0,domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_391,c_368]) ).
tcf(c_432,plain,
compose(domain(a),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_368,c_66]) ).
tcf(c_434,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_368,c_70]) ).
tcf(c_436,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),domain(compose(X0,compose(a,b))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_368,c_68]) ).
tcf(c_500,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),codomain(a),domain(compose(codomain(X0),h)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_65,c_121]) ).
tcf(c_502,plain,
ifeq(codomain(b),codomain(a),domain(compose(b,h)),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_72,c_121]) ).
tcf(c_503,plain,
ifeq(codomain(h),codomain(a),domain(compose(h,h)),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_73,c_121]) ).
tcf(c_505,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(a),domain(compose(domain(X0),h)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_100,c_121]) ).
tcf(c_506,plain,
domain(compose(a,h)) = domain(a),
inference(superposition,[status(thm)],[c_121,c_63]) ).
tcf(c_509,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),domain(compose(domain(X0),h)),domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_505,c_64]) ).
tcf(c_510,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),domain(compose(codomain(X0),h)),codomain(X0)) = codomain(X0),
inference(light_normalisation,[status(thm)],[c_500,c_101]) ).
tcf(c_541,plain,
compose(domain(a),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_506,c_66]) ).
tcf(c_543,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,compose(a,h))),compose(compose(X1,X0),compose(a,h))),compose(compose(X1,X0),compose(a,h))) = compose(compose(X1,X0),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_70]) ).
tcf(c_545,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),domain(compose(X0,compose(a,h))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_506,c_68]) ).
tcf(c_596,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),codomain(a),domain(compose(codomain(X0),g)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_65,c_122]) ).
tcf(c_598,plain,
ifeq(codomain(b),codomain(a),domain(compose(b,g)),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_72,c_122]) ).
tcf(c_599,plain,
ifeq(codomain(h),codomain(a),domain(compose(h,g)),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_73,c_122]) ).
tcf(c_601,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(a),domain(compose(domain(X0),g)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_100,c_122]) ).
tcf(c_608,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),domain(compose(domain(X0),g)),domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_601,c_64]) ).
tcf(c_609,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),domain(compose(codomain(X0),g)),codomain(X0)) = codomain(X0),
inference(light_normalisation,[status(thm)],[c_596,c_101]) ).
tcf(c_614,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),domain(compose(b,codomain(X0))),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_65,c_131]) ).
tcf(c_615,plain,
ifeq(codomain(b),domain(a),domain(compose(b,compose(a,b))),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_368,c_131]) ).
tcf(c_619,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),domain(compose(b,domain(X0))),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_100,c_131]) ).
tcf(c_620,plain,
ifeq(codomain(b),domain(a),domain(compose(b,compose(a,h))),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_506,c_131]) ).
tcf(c_625,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),domain(compose(h,codomain(X0))),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_65,c_132]) ).
tcf(c_626,plain,
ifeq(codomain(h),domain(a),domain(compose(h,compose(a,b))),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_368,c_132]) ).
tcf(c_630,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),domain(compose(h,domain(X0))),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_100,c_132]) ).
tcf(c_631,plain,
ifeq(codomain(h),domain(a),domain(compose(h,compose(a,h))),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_506,c_132]) ).
tcf(c_678,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),codomain(compose(domain(X0),b)),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_64,c_176]) ).
tcf(c_679,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),codomain(compose(codomain(X0),b)),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_101,c_176]) ).
tcf(c_682,plain,
codomain(compose(a,b)) = codomain(b),
inference(superposition,[status(thm)],[c_176,c_63]) ).
tcf(c_698,plain,
ifeq(codomain(b),codomain(a),codomain(compose(compose(a,b),b)),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_682,c_176]) ).
tcf(c_699,plain,
ifeq(codomain(b),codomain(a),domain(compose(compose(a,b),g)),domain(compose(a,b))) = domain(compose(a,b)),
inference(superposition,[status(thm)],[c_682,c_122]) ).
tcf(c_700,plain,
ifeq(codomain(b),codomain(a),domain(compose(compose(a,b),h)),domain(compose(a,b))) = domain(compose(a,b)),
inference(superposition,[status(thm)],[c_682,c_121]) ).
tcf(c_701,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_385]) ).
tcf(c_702,plain,
ifeq(codomain(b),codomain(a),domain(compose(compose(a,b),b)),domain(compose(a,b))) = domain(compose(a,b)),
inference(superposition,[status(thm)],[c_682,c_120]) ).
tcf(c_703,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_682,c_70]) ).
tcf(c_704,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),codomain(compose(compose(a,b),X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_682,c_69]) ).
tcf(c_706,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_682,c_68]) ).
tcf(c_708,plain,
compose(compose(a,b),codomain(b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_67]) ).
tcf(c_711,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(compose(a,b),compose(a,b)),X1,compose(a,b),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_682,c_385]) ).
tcf(c_712,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_682,c_69]) ).
tcf(c_713,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_682,c_70]) ).
tcf(c_716,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),codomain(compose(X0,compose(a,b))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_712,c_368]) ).
tcf(c_717,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),domain(compose(compose(a,b),X0)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_706,c_368]) ).
tcf(c_718,plain,
ifeq(codomain(b),codomain(a),domain(compose(compose(a,b),b)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_702,c_368]) ).
tcf(c_719,plain,
ifeq(codomain(b),codomain(a),domain(compose(compose(a,b),h)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_700,c_368]) ).
tcf(c_720,plain,
ifeq(codomain(b),codomain(a),domain(compose(compose(a,b),g)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_699,c_368]) ).
tcf(c_721,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_703,c_368]) ).
tcf(c_836,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),codomain(compose(domain(X0),h)),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_64,c_177]) ).
tcf(c_837,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),codomain(compose(codomain(X0),h)),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_101,c_177]) ).
tcf(c_838,plain,
ifeq(codomain(b),codomain(a),codomain(compose(compose(a,b),h)),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_682,c_177]) ).
tcf(c_841,plain,
codomain(compose(a,h)) = codomain(h),
inference(superposition,[status(thm)],[c_177,c_63]) ).
tcf(c_845,plain,
ifeq(codomain(h),codomain(a),codomain(compose(compose(a,h),h)),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_841,c_177]) ).
tcf(c_846,plain,
ifeq(codomain(h),codomain(a),codomain(compose(compose(a,h),b)),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_841,c_176]) ).
tcf(c_847,plain,
ifeq(codomain(h),codomain(a),domain(compose(compose(a,h),g)),domain(compose(a,h))) = domain(compose(a,h)),
inference(superposition,[status(thm)],[c_841,c_122]) ).
tcf(c_848,plain,
ifeq(codomain(h),codomain(a),domain(compose(compose(a,h),h)),domain(compose(a,h))) = domain(compose(a,h)),
inference(superposition,[status(thm)],[c_841,c_121]) ).
tcf(c_849,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_385]) ).
tcf(c_850,plain,
ifeq(codomain(h),codomain(a),domain(compose(compose(a,h),b)),domain(compose(a,h))) = domain(compose(a,h)),
inference(superposition,[status(thm)],[c_841,c_120]) ).
tcf(c_851,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(compose(a,h)),compose(X1,compose(compose(a,h),X0)),compose(compose(X1,compose(a,h)),X0)),compose(compose(X1,compose(a,h)),X0)) = compose(compose(X1,compose(a,h)),X0),
inference(superposition,[status(thm)],[c_841,c_70]) ).
tcf(c_852,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),codomain(compose(compose(a,h),X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_841,c_69]) ).
tcf(c_854,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),domain(compose(compose(a,h),X0)),domain(compose(a,h))) = domain(compose(a,h)),
inference(superposition,[status(thm)],[c_841,c_68]) ).
tcf(c_856,plain,
compose(compose(a,h),codomain(h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_67]) ).
tcf(c_859,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(compose(a,h),compose(a,b)),X1,compose(a,h),X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_841,c_385]) ).
tcf(c_860,plain,
! [X0: $i] : ifeq(codomain(X0),domain(compose(a,h)),codomain(compose(X0,compose(a,h))),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_841,c_69]) ).
tcf(c_861,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,X1)),compose(compose(compose(a,h),X0),X1)),compose(compose(compose(a,h),X0),X1)) = compose(compose(compose(a,h),X0),X1),
inference(superposition,[status(thm)],[c_841,c_70]) ).
tcf(c_864,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),codomain(compose(X0,compose(a,h))),codomain(h)) = codomain(h),
inference(light_normalisation,[status(thm)],[c_860,c_506]) ).
tcf(c_865,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),domain(compose(compose(a,h),X0)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_854,c_506]) ).
tcf(c_866,plain,
ifeq(codomain(h),codomain(a),domain(compose(compose(a,h),b)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_850,c_506]) ).
tcf(c_867,plain,
ifeq(codomain(h),codomain(a),domain(compose(compose(a,h),h)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_848,c_506]) ).
tcf(c_868,plain,
ifeq(codomain(h),codomain(a),domain(compose(compose(a,h),g)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_847,c_506]) ).
tcf(c_869,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,h),X0)),compose(compose(X1,compose(a,h)),X0)),compose(compose(X1,compose(a,h)),X0)) = compose(compose(X1,compose(a,h)),X0),
inference(light_normalisation,[status(thm)],[c_851,c_506]) ).
tcf(c_959,plain,
codomain(compose(a,g)) = codomain(g),
inference(superposition,[status(thm)],[c_178,c_63]) ).
tcf(c_960,plain,
codomain(h) = codomain(g),
inference(light_normalisation,[status(thm)],[c_959,c_75,c_841]) ).
tcf(c_962,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),codomain(compose(X0,g)),codomain(h)) = codomain(h),
inference(demodulation,[status(thm)],[c_178,c_960]) ).
tcf(c_963,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),domain(compose(g,X0)),codomain(a)) = codomain(a),
inference(demodulation,[status(thm)],[c_133,c_960]) ).
tcf(c_975,plain,
ifeq(codomain(h),codomain(a),codomain(compose(g,h)),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_960,c_177]) ).
tcf(c_976,plain,
ifeq(codomain(h),codomain(a),codomain(compose(g,b)),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_960,c_176]) ).
tcf(c_977,plain,
ifeq(codomain(h),codomain(a),domain(compose(g,g)),domain(g)) = domain(g),
inference(superposition,[status(thm)],[c_960,c_122]) ).
tcf(c_978,plain,
ifeq(codomain(h),codomain(a),domain(compose(g,h)),domain(g)) = domain(g),
inference(superposition,[status(thm)],[c_960,c_121]) ).
tcf(c_979,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(g,compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,g),g),g),g) = g,
inference(superposition,[status(thm)],[c_960,c_385]) ).
tcf(c_980,plain,
ifeq(codomain(h),codomain(a),domain(compose(g,b)),domain(g)) = domain(g),
inference(superposition,[status(thm)],[c_960,c_120]) ).
tcf(c_981,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(g),compose(X1,compose(g,X0)),compose(compose(X1,g),X0)),compose(compose(X1,g),X0)) = compose(compose(X1,g),X0),
inference(superposition,[status(thm)],[c_960,c_70]) ).
tcf(c_982,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),codomain(compose(g,X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_960,c_69]) ).
tcf(c_986,plain,
compose(g,codomain(h)) = g,
inference(superposition,[status(thm)],[c_960,c_67]) ).
tcf(c_988,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(g,compose(a,b)),X1,g,X0),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_960,c_385]) ).
tcf(c_990,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(X0,X1)),compose(compose(g,X0),X1)),compose(compose(g,X0),X1)) = compose(compose(g,X0),X1),
inference(superposition,[status(thm)],[c_960,c_70]) ).
tcf(c_993,plain,
ifeq(codomain(h),codomain(a),domain(compose(g,b)),codomain(a)) = codomain(a),
inference(light_normalisation,[status(thm)],[c_980,c_74]) ).
tcf(c_994,plain,
ifeq(codomain(h),codomain(a),domain(compose(g,h)),codomain(a)) = codomain(a),
inference(light_normalisation,[status(thm)],[c_978,c_74]) ).
tcf(c_995,plain,
ifeq(codomain(h),codomain(a),domain(compose(g,g)),codomain(a)) = codomain(a),
inference(light_normalisation,[status(thm)],[c_977,c_74]) ).
tcf(c_996,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),codomain(a),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_981,c_74]) ).
tcf(c_1090,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),codomain(compose(domain(X0),g)),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_64,c_962]) ).
tcf(c_1091,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),codomain(compose(codomain(X0),g)),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_101,c_962]) ).
tcf(c_1092,plain,
ifeq(codomain(h),codomain(a),codomain(compose(g,g)),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_960,c_962]) ).
tcf(c_1093,plain,
ifeq(codomain(h),codomain(a),codomain(compose(compose(a,h),g)),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_841,c_962]) ).
tcf(c_1094,plain,
ifeq(codomain(b),codomain(a),codomain(compose(compose(a,b),g)),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_682,c_962]) ).
tcf(c_1105,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),domain(compose(g,codomain(X0))),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_65,c_963]) ).
tcf(c_1106,plain,
ifeq(codomain(h),domain(a),domain(compose(g,compose(a,b))),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_368,c_963]) ).
tcf(c_1110,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),domain(compose(g,domain(X0))),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_100,c_963]) ).
tcf(c_1111,plain,
ifeq(codomain(h),domain(a),domain(compose(g,compose(a,h))),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[c_506,c_963]) ).
tcf(c_1164,plain,
! [X0: $i] : ifeq(codomain(h),domain(domain(X0)),codomain(compose(g,domain(X0))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_982]) ).
tcf(c_1165,plain,
! [X0: $i] : ifeq(codomain(h),domain(codomain(X0)),codomain(compose(g,codomain(X0))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_982]) ).
tcf(c_1167,plain,
ifeq(codomain(h),domain(compose(a,h)),codomain(compose(g,compose(a,h))),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_841,c_982]) ).
tcf(c_1168,plain,
ifeq(codomain(h),domain(compose(a,b)),codomain(compose(g,compose(a,b))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_682,c_982]) ).
tcf(c_1173,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),codomain(compose(g,codomain(X0))),codomain(X0)) = codomain(X0),
inference(light_normalisation,[status(thm)],[c_1165,c_65]) ).
tcf(c_1174,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),codomain(compose(g,domain(X0))),domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_1164,c_100]) ).
tcf(c_1177,plain,
ifeq(codomain(h),domain(a),codomain(compose(g,compose(a,b))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_1168,c_368]) ).
tcf(c_1178,plain,
ifeq(codomain(h),domain(a),codomain(compose(g,compose(a,h))),codomain(h)) = codomain(h),
inference(light_normalisation,[status(thm)],[c_1167,c_506]) ).
tcf(c_1205,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_65,c_119]) ).
tcf(c_1206,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_368,c_119]) ).
tcf(c_1210,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_119]) ).
tcf(c_1211,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(X0),domain(compose(compose(a,h),codomain(X0))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_506,c_119]) ).
tcf(c_1217,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_1210,c_64]) ).
tcf(c_1218,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_1205,c_101]) ).
tcf(c_1221,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),domain(compose(compose(a,h),codomain(X0))),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_1211,c_841]) ).
tcf(c_1222,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_1206,c_682]) ).
tcf(c_1253,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_65,c_123]) ).
tcf(c_1254,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_368,c_123]) ).
tcf(c_1258,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_123]) ).
tcf(c_1259,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(X0),domain(compose(compose(a,h),domain(X0))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_506,c_123]) ).
tcf(c_1262,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_1258,c_64]) ).
tcf(c_1263,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_1253,c_101]) ).
tcf(c_1266,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),domain(compose(compose(a,h),domain(X0))),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_1259,c_841]) ).
tcf(c_1267,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_1254,c_682]) ).
tcf(c_1284,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),domain(compose(domain(X0),compose(a,b))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_368,c_141]) ).
tcf(c_1289,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),domain(compose(domain(X0),compose(a,h))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_506,c_141]) ).
tcf(c_1323,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),domain(compose(codomain(X0),compose(a,b))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_368,c_142]) ).
tcf(c_1328,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),domain(compose(codomain(X0),compose(a,h))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_506,c_142]) ).
tcf(c_1381,plain,
! [X0: $i] : ifeq(domain(X0),domain(compose(a,h)),codomain(compose(domain(X0),compose(a,h))),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_841,c_173]) ).
tcf(c_1382,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_682,c_173]) ).
tcf(c_1387,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_1382,c_368]) ).
tcf(c_1388,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),codomain(compose(domain(X0),compose(a,h))),codomain(h)) = codomain(h),
inference(light_normalisation,[status(thm)],[c_1381,c_506]) ).
tcf(c_1425,plain,
! [X0: $i] : ifeq(codomain(X0),domain(compose(a,h)),codomain(compose(codomain(X0),compose(a,h))),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_841,c_174]) ).
tcf(c_1426,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_682,c_174]) ).
tcf(c_1430,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_1426,c_368]) ).
tcf(c_1431,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),codomain(compose(codomain(X0),compose(a,h))),codomain(h)) = codomain(h),
inference(light_normalisation,[status(thm)],[c_1425,c_506]) ).
tcf(c_1848,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),codomain(compose(X0,domain(X1))),domain(X1)) = domain(X1),
inference(demodulation,[status(thm)],[c_188,c_100]) ).
tcf(c_1849,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_64,c_1848]) ).
tcf(c_1850,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_101,c_1848]) ).
tcf(c_1852,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),codomain(compose(compose(a,h),domain(X0))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_841,c_1848]) ).
tcf(c_1853,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),codomain(compose(compose(a,b),domain(X0))),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_682,c_1848]) ).
tcf(c_1870,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),codomain(compose(X0,codomain(X1))),codomain(X1)) = codomain(X1),
inference(superposition,[status(thm)],[c_65,c_1848]) ).
tcf(c_1885,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_64,c_1870]) ).
tcf(c_1886,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_101,c_1870]) ).
tcf(c_1888,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),codomain(compose(compose(a,h),codomain(X0))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_841,c_1870]) ).
tcf(c_1889,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),codomain(compose(compose(a,b),codomain(X0))),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_682,c_1870]) ).
tcf(c_1930,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_368,c_436]) ).
tcf(c_1935,plain,
ifeq(codomain(compose(a,h)),domain(a),domain(compose(compose(a,h),compose(a,b))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_506,c_436]) ).
tcf(c_1942,plain,
ifeq(codomain(h),domain(a),domain(compose(compose(a,h),compose(a,b))),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_1935,c_841]) ).
tcf(c_1943,plain,
ifeq(codomain(b),domain(a),domain(compose(compose(a,b),compose(a,b))),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_1930,c_682]) ).
tcf(c_1955,plain,
ifeq(codomain(compose(a,b)),domain(a),domain(compose(compose(a,b),compose(a,h))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_368,c_545]) ).
tcf(c_1960,plain,
ifeq(codomain(compose(a,h)),domain(a),domain(compose(compose(a,h),compose(a,h))),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_506,c_545]) ).
tcf(c_1967,plain,
ifeq(codomain(h),domain(a),domain(compose(compose(a,h),compose(a,h))),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_1960,c_841]) ).
tcf(c_1968,plain,
ifeq(codomain(b),domain(a),domain(compose(compose(a,b),compose(a,h))),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_1955,c_682]) ).
tcf(c_1984,plain,
ifeq(codomain(b),domain(compose(a,h)),codomain(compose(compose(a,b),compose(a,h))),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_841,c_704]) ).
tcf(c_1985,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_682,c_704]) ).
tcf(c_1992,plain,
ifeq(codomain(b),domain(a),codomain(compose(compose(a,b),compose(a,b))),codomain(b)) = codomain(b),
inference(light_normalisation,[status(thm)],[c_1985,c_368]) ).
tcf(c_1993,plain,
ifeq(codomain(b),domain(a),codomain(compose(compose(a,b),compose(a,h))),codomain(h)) = codomain(h),
inference(light_normalisation,[status(thm)],[c_1984,c_506]) ).
tcf(c_2000,plain,
ifeq(codomain(h),domain(a),codomain(compose(compose(a,h),compose(a,b))),codomain(b)) = codomain(b),
inference(superposition,[status(thm)],[c_841,c_716]) ).
tcf(c_2031,plain,
ifeq(codomain(h),domain(compose(a,h)),codomain(compose(compose(a,h),compose(a,h))),codomain(h)) = codomain(h),
inference(superposition,[status(thm)],[c_841,c_852]) ).
tcf(c_2040,plain,
ifeq(codomain(h),domain(a),codomain(compose(compose(a,h),compose(a,h))),codomain(h)) = codomain(h),
inference(light_normalisation,[status(thm)],[c_2031,c_506]) ).
tcf(c_2650,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_277,c_63]) ).
tcf(c_2656,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_65,c_2650]) ).
tcf(c_2657,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_368,c_2650]) ).
tcf(c_2658,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(domain(X0),compose(X0,b)),compose(X0,b)) = compose(X0,b),
inference(superposition,[status(thm)],[c_72,c_2650]) ).
tcf(c_2659,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(domain(X0),compose(X0,h)),compose(X0,h)) = compose(X0,h),
inference(superposition,[status(thm)],[c_73,c_2650]) ).
tcf(c_2660,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(domain(X0),compose(X0,g)),compose(X0,g)) = compose(X0,g),
inference(superposition,[status(thm)],[c_74,c_2650]) ).
tcf(c_2661,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_2650]) ).
tcf(c_2662,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(domain(X0),compose(X0,compose(a,h))),compose(X0,compose(a,h))) = compose(X0,compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_2650]) ).
tcf(c_2665,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_65,c_2650]) ).
tcf(c_2666,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_368,c_2650]) ).
tcf(c_2667,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(codomain(a),compose(b,X0)),compose(b,X0)) = compose(b,X0),
inference(superposition,[status(thm)],[c_72,c_2650]) ).
tcf(c_2668,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(codomain(a),compose(h,X0)),compose(h,X0)) = compose(h,X0),
inference(superposition,[status(thm)],[c_73,c_2650]) ).
tcf(c_2669,plain,
! [X0: $i] : ifeq(codomain(g),domain(X0),compose(codomain(a),compose(g,X0)),compose(g,X0)) = compose(g,X0),
inference(superposition,[status(thm)],[c_74,c_2650]) ).
tcf(c_2670,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_2650]) ).
tcf(c_2671,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(X0),compose(domain(a),compose(compose(a,h),X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(superposition,[status(thm)],[c_506,c_2650]) ).
tcf(c_2709,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(codomain(a),compose(g,X0)),compose(g,X0)) = compose(g,X0),
inference(light_normalisation,[status(thm)],[c_2669,c_960]) ).
tcf(c_2713,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_2670,c_64]) ).
tcf(c_2714,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_2665,c_101]) ).
tcf(c_2719,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(domain(a),compose(compose(a,h),X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(light_normalisation,[status(thm)],[c_2671,c_841]) ).
tcf(c_2720,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_2666,c_682]) ).
tcf(c_2744,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),codomain(a),compose(codomain(X0),compose(codomain(X0),b)),compose(codomain(X0),b)) = compose(codomain(X0),b),
inference(superposition,[status(thm)],[c_65,c_2658]) ).
tcf(c_2745,plain,
ifeq(codomain(compose(a,b)),codomain(a),compose(domain(a),compose(compose(a,b),b)),compose(compose(a,b),b)) = compose(compose(a,b),b),
inference(superposition,[status(thm)],[c_368,c_2658]) ).
tcf(c_2746,plain,
ifeq(codomain(b),codomain(a),compose(codomain(a),compose(b,b)),compose(b,b)) = compose(b,b),
inference(superposition,[status(thm)],[c_72,c_2658]) ).
tcf(c_2747,plain,
ifeq(codomain(h),codomain(a),compose(codomain(a),compose(h,b)),compose(h,b)) = compose(h,b),
inference(superposition,[status(thm)],[c_73,c_2658]) ).
tcf(c_2748,plain,
ifeq(codomain(g),codomain(a),compose(codomain(a),compose(g,b)),compose(g,b)) = compose(g,b),
inference(superposition,[status(thm)],[c_74,c_2658]) ).
tcf(c_2749,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(a),compose(domain(X0),compose(domain(X0),b)),compose(domain(X0),b)) = compose(domain(X0),b),
inference(superposition,[status(thm)],[c_100,c_2658]) ).
tcf(c_2750,plain,
ifeq(codomain(compose(a,h)),codomain(a),compose(domain(a),compose(compose(a,h),b)),compose(compose(a,h),b)) = compose(compose(a,h),b),
inference(superposition,[status(thm)],[c_506,c_2658]) ).
tcf(c_2757,plain,
ifeq(codomain(h),codomain(a),compose(codomain(a),compose(g,b)),compose(g,b)) = compose(g,b),
inference(light_normalisation,[status(thm)],[c_2748,c_960]) ).
tcf(c_2759,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),compose(domain(X0),compose(domain(X0),b)),compose(domain(X0),b)) = compose(domain(X0),b),
inference(light_normalisation,[status(thm)],[c_2749,c_64]) ).
tcf(c_2760,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(codomain(X0),b)),compose(codomain(X0),b)) = compose(codomain(X0),b),
inference(light_normalisation,[status(thm)],[c_2744,c_101]) ).
tcf(c_2763,plain,
ifeq(codomain(h),codomain(a),compose(domain(a),compose(compose(a,h),b)),compose(compose(a,h),b)) = compose(compose(a,h),b),
inference(light_normalisation,[status(thm)],[c_2750,c_841]) ).
tcf(c_2764,plain,
ifeq(codomain(b),codomain(a),compose(domain(a),compose(compose(a,b),b)),compose(compose(a,b),b)) = compose(compose(a,b),b),
inference(light_normalisation,[status(thm)],[c_2745,c_682]) ).
tcf(c_2776,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),codomain(a),compose(codomain(X0),compose(codomain(X0),h)),compose(codomain(X0),h)) = compose(codomain(X0),h),
inference(superposition,[status(thm)],[c_65,c_2659]) ).
tcf(c_2777,plain,
ifeq(codomain(compose(a,b)),codomain(a),compose(domain(a),compose(compose(a,b),h)),compose(compose(a,b),h)) = compose(compose(a,b),h),
inference(superposition,[status(thm)],[c_368,c_2659]) ).
tcf(c_2778,plain,
ifeq(codomain(b),codomain(a),compose(codomain(a),compose(b,h)),compose(b,h)) = compose(b,h),
inference(superposition,[status(thm)],[c_72,c_2659]) ).
tcf(c_2779,plain,
ifeq(codomain(h),codomain(a),compose(codomain(a),compose(h,h)),compose(h,h)) = compose(h,h),
inference(superposition,[status(thm)],[c_73,c_2659]) ).
tcf(c_2780,plain,
ifeq(codomain(g),codomain(a),compose(codomain(a),compose(g,h)),compose(g,h)) = compose(g,h),
inference(superposition,[status(thm)],[c_74,c_2659]) ).
tcf(c_2781,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(a),compose(domain(X0),compose(domain(X0),h)),compose(domain(X0),h)) = compose(domain(X0),h),
inference(superposition,[status(thm)],[c_100,c_2659]) ).
tcf(c_2782,plain,
ifeq(codomain(compose(a,h)),codomain(a),compose(domain(a),compose(compose(a,h),h)),compose(compose(a,h),h)) = compose(compose(a,h),h),
inference(superposition,[status(thm)],[c_506,c_2659]) ).
tcf(c_2789,plain,
ifeq(codomain(h),codomain(a),compose(codomain(a),compose(g,h)),compose(g,h)) = compose(g,h),
inference(light_normalisation,[status(thm)],[c_2780,c_960]) ).
tcf(c_2791,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),compose(domain(X0),compose(domain(X0),h)),compose(domain(X0),h)) = compose(domain(X0),h),
inference(light_normalisation,[status(thm)],[c_2781,c_64]) ).
tcf(c_2792,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(codomain(X0),h)),compose(codomain(X0),h)) = compose(codomain(X0),h),
inference(light_normalisation,[status(thm)],[c_2776,c_101]) ).
tcf(c_2795,plain,
ifeq(codomain(h),codomain(a),compose(domain(a),compose(compose(a,h),h)),compose(compose(a,h),h)) = compose(compose(a,h),h),
inference(light_normalisation,[status(thm)],[c_2782,c_841]) ).
tcf(c_2796,plain,
ifeq(codomain(b),codomain(a),compose(domain(a),compose(compose(a,b),h)),compose(compose(a,b),h)) = compose(compose(a,b),h),
inference(light_normalisation,[status(thm)],[c_2777,c_682]) ).
tcf(c_2807,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),codomain(a),compose(codomain(X0),compose(codomain(X0),g)),compose(codomain(X0),g)) = compose(codomain(X0),g),
inference(superposition,[status(thm)],[c_65,c_2660]) ).
tcf(c_2808,plain,
ifeq(codomain(compose(a,b)),codomain(a),compose(domain(a),compose(compose(a,b),g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
inference(superposition,[status(thm)],[c_368,c_2660]) ).
tcf(c_2809,plain,
ifeq(codomain(b),codomain(a),compose(codomain(a),compose(b,g)),compose(b,g)) = compose(b,g),
inference(superposition,[status(thm)],[c_72,c_2660]) ).
tcf(c_2810,plain,
ifeq(codomain(h),codomain(a),compose(codomain(a),compose(h,g)),compose(h,g)) = compose(h,g),
inference(superposition,[status(thm)],[c_73,c_2660]) ).
tcf(c_2811,plain,
ifeq(codomain(g),codomain(a),compose(codomain(a),compose(g,g)),compose(g,g)) = compose(g,g),
inference(superposition,[status(thm)],[c_74,c_2660]) ).
tcf(c_2812,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(a),compose(domain(X0),compose(domain(X0),g)),compose(domain(X0),g)) = compose(domain(X0),g),
inference(superposition,[status(thm)],[c_100,c_2660]) ).
tcf(c_2813,plain,
ifeq(codomain(compose(a,h)),codomain(a),compose(domain(a),compose(compose(a,h),g)),compose(compose(a,h),g)) = compose(compose(a,h),g),
inference(superposition,[status(thm)],[c_506,c_2660]) ).
tcf(c_2824,plain,
ifeq(codomain(h),codomain(a),compose(codomain(a),compose(g,g)),compose(g,g)) = compose(g,g),
inference(light_normalisation,[status(thm)],[c_2811,c_960]) ).
tcf(c_2826,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),compose(domain(X0),compose(domain(X0),g)),compose(domain(X0),g)) = compose(domain(X0),g),
inference(light_normalisation,[status(thm)],[c_2812,c_64]) ).
tcf(c_2827,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(codomain(X0),g)),compose(codomain(X0),g)) = compose(codomain(X0),g),
inference(light_normalisation,[status(thm)],[c_2807,c_101]) ).
tcf(c_2830,plain,
ifeq(codomain(h),codomain(a),compose(domain(a),compose(compose(a,h),g)),compose(compose(a,h),g)) = compose(compose(a,h),g),
inference(light_normalisation,[status(thm)],[c_2813,c_841]) ).
tcf(c_2831,plain,
ifeq(codomain(b),codomain(a),compose(domain(a),compose(compose(a,b),g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
inference(light_normalisation,[status(thm)],[c_2808,c_682]) ).
tcf(c_2836,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),compose(codomain(a),compose(b,codomain(X0))),compose(b,codomain(X0))) = compose(b,codomain(X0)),
inference(superposition,[status(thm)],[c_65,c_2667]) ).
tcf(c_2837,plain,
ifeq(codomain(b),domain(a),compose(codomain(a),compose(b,compose(a,b))),compose(b,compose(a,b))) = compose(b,compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_2667]) ).
tcf(c_2841,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),compose(codomain(a),compose(b,domain(X0))),compose(b,domain(X0))) = compose(b,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_2667]) ).
tcf(c_2842,plain,
ifeq(codomain(b),domain(a),compose(codomain(a),compose(b,compose(a,h))),compose(b,compose(a,h))) = compose(b,compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_2667]) ).
tcf(c_2848,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),compose(codomain(a),compose(h,codomain(X0))),compose(h,codomain(X0))) = compose(h,codomain(X0)),
inference(superposition,[status(thm)],[c_65,c_2668]) ).
tcf(c_2849,plain,
ifeq(codomain(h),domain(a),compose(codomain(a),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_2668]) ).
tcf(c_2853,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(codomain(a),compose(h,domain(X0))),compose(h,domain(X0))) = compose(h,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_2668]) ).
tcf(c_2854,plain,
ifeq(codomain(h),domain(a),compose(codomain(a),compose(h,compose(a,h))),compose(h,compose(a,h))) = compose(h,compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_2668]) ).
tcf(c_2866,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),compose(codomain(a),compose(g,codomain(X0))),compose(g,codomain(X0))) = compose(g,codomain(X0)),
inference(superposition,[status(thm)],[c_65,c_2709]) ).
tcf(c_2867,plain,
ifeq(codomain(h),domain(a),compose(codomain(a),compose(g,compose(a,b))),compose(g,compose(a,b))) = compose(g,compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_2709]) ).
tcf(c_2871,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(codomain(a),compose(g,domain(X0))),compose(g,domain(X0))) = compose(g,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_2709]) ).
tcf(c_2872,plain,
ifeq(codomain(h),domain(a),compose(codomain(a),compose(g,compose(a,h))),compose(g,compose(a,h))) = compose(g,compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_2709]) ).
tcf(c_2898,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_65,c_2656]) ).
tcf(c_2899,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_368,c_2656]) ).
tcf(c_2903,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_2656]) ).
tcf(c_2904,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(X0),compose(domain(a),compose(compose(a,h),codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(a,h),codomain(X0)),
inference(superposition,[status(thm)],[c_506,c_2656]) ).
tcf(c_2937,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_2903,c_64]) ).
tcf(c_2938,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_2898,c_101]) ).
tcf(c_2941,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),compose(domain(a),compose(compose(a,h),codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(a,h),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_2904,c_841]) ).
tcf(c_2942,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_2899,c_682]) ).
tcf(c_2967,plain,
! [X0: $i,X1: $i] : ifeq(codomain(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_65,c_2661]) ).
tcf(c_2968,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_368,c_2661]) ).
tcf(c_2972,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_2661]) ).
tcf(c_2973,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(X0),compose(domain(a),compose(compose(a,h),domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(a,h),domain(X0)),
inference(superposition,[status(thm)],[c_506,c_2661]) ).
tcf(c_2996,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_2972,c_64]) ).
tcf(c_2997,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(light_normalisation,[status(thm)],[c_2967,c_101]) ).
tcf(c_3000,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(domain(a),compose(compose(a,h),domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(a,h),domain(X0)),
inference(light_normalisation,[status(thm)],[c_2973,c_841]) ).
tcf(c_3001,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_2968,c_682]) ).
tcf(c_3020,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_368,c_2714]) ).
tcf(c_3025,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(codomain(X0),compose(a,h))),compose(codomain(X0),compose(a,h))) = compose(codomain(X0),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_2714]) ).
tcf(c_3092,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_368,c_2713]) ).
tcf(c_3097,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(domain(X0),compose(a,h))),compose(domain(X0),compose(a,h))) = compose(domain(X0),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_2713]) ).
tcf(c_3490,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_368,c_2657]) ).
tcf(c_3495,plain,
ifeq(codomain(compose(a,h)),domain(a),compose(domain(a),compose(compose(a,h),compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(superposition,[status(thm)],[c_506,c_2657]) ).
tcf(c_3507,plain,
ifeq(codomain(h),domain(a),compose(domain(a),compose(compose(a,h),compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_3495,c_841]) ).
tcf(c_3508,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_3490,c_682]) ).
tcf(c_3558,plain,
ifeq(codomain(compose(a,b)),domain(a),compose(domain(a),compose(compose(a,b),compose(a,h))),compose(compose(a,b),compose(a,h))) = compose(compose(a,b),compose(a,h)),
inference(superposition,[status(thm)],[c_368,c_2662]) ).
tcf(c_3563,plain,
ifeq(codomain(compose(a,h)),domain(a),compose(domain(a),compose(compose(a,h),compose(a,h))),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_2662]) ).
tcf(c_3575,plain,
ifeq(codomain(h),domain(a),compose(domain(a),compose(compose(a,h),compose(a,h))),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_3563,c_841]) ).
tcf(c_3576,plain,
ifeq(codomain(b),domain(a),compose(domain(a),compose(compose(a,b),compose(a,h))),compose(compose(a,b),compose(a,h))) = compose(compose(a,b),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_3558,c_682]) ).
tcf(c_3598,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_278,c_63]) ).
tcf(c_3604,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_65,c_3598]) ).
tcf(c_3605,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_368,c_3598]) ).
tcf(c_3606,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(X0,compose(codomain(X0),b)),compose(X0,b)) = compose(X0,b),
inference(superposition,[status(thm)],[c_72,c_3598]) ).
tcf(c_3607,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(X0,compose(codomain(X0),h)),compose(X0,h)) = compose(X0,h),
inference(superposition,[status(thm)],[c_73,c_3598]) ).
tcf(c_3608,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(X0,compose(codomain(X0),g)),compose(X0,g)) = compose(X0,g),
inference(superposition,[status(thm)],[c_74,c_3598]) ).
tcf(c_3609,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_3598]) ).
tcf(c_3610,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(X0,compose(codomain(X0),compose(a,h))),compose(X0,compose(a,h))) = compose(X0,compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_3598]) ).
tcf(c_3618,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(g,compose(codomain(h),X0)),compose(g,X0)) = compose(g,X0),
inference(superposition,[status(thm)],[c_960,c_3598]) ).
tcf(c_3619,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(codomain(h),X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(superposition,[status(thm)],[c_841,c_3598]) ).
tcf(c_3620,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_682,c_3598]) ).
tcf(c_3714,plain,
ifeq(codomain(h),codomain(a),compose(g,compose(codomain(h),b)),compose(g,b)) = compose(g,b),
inference(superposition,[status(thm)],[c_960,c_3606]) ).
tcf(c_3715,plain,
ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(codomain(h),b)),compose(compose(a,h),b)) = compose(compose(a,h),b),
inference(superposition,[status(thm)],[c_841,c_3606]) ).
tcf(c_3716,plain,
ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(codomain(b),b)),compose(compose(a,b),b)) = compose(compose(a,b),b),
inference(superposition,[status(thm)],[c_682,c_3606]) ).
tcf(c_3731,plain,
ifeq(codomain(h),codomain(a),compose(g,compose(codomain(h),h)),compose(g,h)) = compose(g,h),
inference(superposition,[status(thm)],[c_960,c_3607]) ).
tcf(c_3732,plain,
ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(codomain(h),h)),compose(compose(a,h),h)) = compose(compose(a,h),h),
inference(superposition,[status(thm)],[c_841,c_3607]) ).
tcf(c_3733,plain,
ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(codomain(b),h)),compose(compose(a,b),h)) = compose(compose(a,b),h),
inference(superposition,[status(thm)],[c_682,c_3607]) ).
tcf(c_3748,plain,
ifeq(codomain(h),codomain(a),compose(g,compose(codomain(h),g)),compose(g,g)) = compose(g,g),
inference(superposition,[status(thm)],[c_960,c_3608]) ).
tcf(c_3749,plain,
ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(codomain(h),g)),compose(compose(a,h),g)) = compose(compose(a,h),g),
inference(superposition,[status(thm)],[c_841,c_3608]) ).
tcf(c_3750,plain,
ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(codomain(b),g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
inference(superposition,[status(thm)],[c_682,c_3608]) ).
tcf(c_3759,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(h),codomain(X0))),compose(g,codomain(X0))) = compose(g,codomain(X0)),
inference(superposition,[status(thm)],[c_65,c_3618]) ).
tcf(c_3760,plain,
ifeq(codomain(h),domain(a),compose(g,compose(codomain(h),compose(a,b))),compose(g,compose(a,b))) = compose(g,compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_3618]) ).
tcf(c_3764,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(g,compose(codomain(h),domain(X0))),compose(g,domain(X0))) = compose(g,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_3618]) ).
tcf(c_3765,plain,
ifeq(codomain(h),domain(a),compose(g,compose(codomain(h),compose(a,h))),compose(g,compose(a,h))) = compose(g,compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_3618]) ).
tcf(c_3818,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(h),codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(a,h),codomain(X0)),
inference(superposition,[status(thm)],[c_841,c_3604]) ).
tcf(c_3819,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_682,c_3604]) ).
tcf(c_3895,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(codomain(h),domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(a,h),domain(X0)),
inference(superposition,[status(thm)],[c_841,c_3609]) ).
tcf(c_3896,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_682,c_3609]) ).
tcf(c_3938,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(X1,compose(a,b)),compose(domain(X0),compose(a,b)),X1,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_390]) ).
tcf(c_3939,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(X1,compose(a,b)),compose(codomain(X0),compose(a,b)),X1,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_390]) ).
tcf(c_3940,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(g,compose(a,b)),X0,g),g),g) = g,
inference(superposition,[status(thm)],[c_960,c_390]) ).
tcf(c_3941,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(compose(a,h),compose(a,b)),X0,compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_390]) ).
tcf(c_3942,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(compose(a,b),compose(a,b)),X0,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_390]) ).
tcf(c_3943,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(domain(X1),compose(a,b)),compose(X0,compose(a,b)),domain(X1),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_64,c_390]) ).
tcf(c_3944,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(codomain(X1),compose(a,b)),compose(X0,compose(a,b)),codomain(X1),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_101,c_390]) ).
tcf(c_3945,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(X0,compose(a,b)),g,X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_960,c_390]) ).
tcf(c_3946,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(X0,compose(a,b)),compose(a,h),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_841,c_390]) ).
tcf(c_3947,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(X0,compose(a,b)),compose(a,b),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_682,c_390]) ).
tcf(c_3948,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X0),domain(a),X0,X0),X0) = X0,
inference(superposition,[status(thm)],[c_63,c_390]) ).
tcf(c_3982,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(X0),domain(a),domain(X0),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_3948]) ).
tcf(c_3983,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X0),domain(a),codomain(X0),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_3948]) ).
tcf(c_3984,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),g,g),g) = g,
inference(superposition,[status(thm)],[c_960,c_3948]) ).
tcf(c_3985,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),compose(a,h),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_3948]) ).
tcf(c_3986,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(a),compose(a,b),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_3948]) ).
tcf(c_4071,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(X1,compose(a,b)),X1,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_392]) ).
tcf(c_4072,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(X1,compose(a,b)),X1,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_392]) ).
tcf(c_4073,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(g,compose(a,b)),compose(X0,compose(a,b)),X0,g),g),g) = g,
inference(superposition,[status(thm)],[c_960,c_392]) ).
tcf(c_4074,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(X0,compose(a,b)),X0,compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_392]) ).
tcf(c_4075,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(X0,compose(a,b)),X0,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_392]) ).
tcf(c_4076,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(X0,compose(a,b)),compose(domain(X1),compose(a,b)),domain(X1),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_64,c_392]) ).
tcf(c_4077,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(X0,compose(a,b)),compose(codomain(X1),compose(a,b)),codomain(X1),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_101,c_392]) ).
tcf(c_4078,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(X0,compose(a,b)),compose(g,compose(a,b)),g,X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_960,c_392]) ).
tcf(c_4079,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(X0,compose(a,b)),compose(compose(a,h),compose(a,b)),compose(a,h),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_841,c_392]) ).
tcf(c_4080,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(X0,compose(a,b)),compose(compose(a,b),compose(a,b)),compose(a,b),X0),X0),X0) = X0,
inference(superposition,[status(thm)],[c_682,c_392]) ).
tcf(c_4145,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(domain(X1),compose(a,b)),compose(domain(X0),compose(a,b)),domain(X1),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_3943]) ).
tcf(c_4146,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(domain(X1),compose(a,b)),compose(codomain(X0),compose(a,b)),domain(X1),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_3943]) ).
tcf(c_4147,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(g,compose(a,b)),domain(X0),g),g),g) = g,
inference(superposition,[status(thm)],[c_960,c_3943]) ).
tcf(c_4148,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(compose(a,h),compose(a,b)),domain(X0),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_3943]) ).
tcf(c_4149,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(compose(a,b),compose(a,b)),domain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_3943]) ).
tcf(c_4150,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(domain(a),compose(a,b)),compose(X0,compose(a,b)),domain(a),X0),X0) = X0,
inference(superposition,[status(thm)],[c_63,c_3943]) ).
tcf(c_4178,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),compose(X0,compose(a,b)),domain(a),X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_4150,c_432]) ).
tcf(c_4189,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(a,b),compose(domain(X0),compose(a,b)),domain(a),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_4178]) ).
tcf(c_4190,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),compose(codomain(X0),compose(a,b)),domain(a),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_4178]) ).
tcf(c_4191,plain,
ifeq(codomain(h),domain(a),ifeq(compose(a,b),compose(g,compose(a,b)),domain(a),g),g) = g,
inference(superposition,[status(thm)],[c_960,c_4178]) ).
tcf(c_4192,plain,
ifeq(codomain(h),domain(a),ifeq(compose(a,b),compose(compose(a,h),compose(a,b)),domain(a),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_4178]) ).
tcf(c_4193,plain,
ifeq(codomain(b),domain(a),ifeq(compose(a,b),compose(compose(a,b),compose(a,b)),domain(a),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_4178]) ).
tcf(c_4243,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(domain(X1),compose(a,b)),domain(X1),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_4076]) ).
tcf(c_4244,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(domain(X1),compose(a,b)),domain(X1),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_4076]) ).
tcf(c_4245,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(g,compose(a,b)),compose(domain(X0),compose(a,b)),domain(X0),g),g),g) = g,
inference(superposition,[status(thm)],[c_960,c_4076]) ).
tcf(c_4246,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(domain(X0),compose(a,b)),domain(X0),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_4076]) ).
tcf(c_4247,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(domain(X0),compose(a,b)),domain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_4076]) ).
tcf(c_4248,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(domain(a),compose(a,b)),domain(a),X0),X0) = X0,
inference(superposition,[status(thm)],[c_63,c_4076]) ).
tcf(c_4275,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(a,b),domain(a),X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_4248,c_432]) ).
tcf(c_4333,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(a,b),domain(a),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_4275]) ).
tcf(c_4334,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(a,b),domain(a),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_4275]) ).
tcf(c_4335,plain,
ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(a,b),domain(a),g),g) = g,
inference(superposition,[status(thm)],[c_960,c_4275]) ).
tcf(c_4336,plain,
ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(a,b),domain(a),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_4275]) ).
tcf(c_4337,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(a,b),domain(a),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_4275]) ).
tcf(c_4495,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(codomain(h),compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(superposition,[status(thm)],[c_841,c_3605]) ).
tcf(c_4496,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_682,c_3605]) ).
tcf(c_4508,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(codomain(h),compose(a,h))),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h)),
inference(superposition,[status(thm)],[c_841,c_3610]) ).
tcf(c_4509,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(codomain(b),compose(a,h))),compose(compose(a,b),compose(a,h))) = compose(compose(a,b),compose(a,h)),
inference(superposition,[status(thm)],[c_682,c_3610]) ).
tcf(c_4547,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,b)),compose(compose(domain(X1),X0),b)),compose(compose(domain(X1),X0),b)) = compose(compose(domain(X1),X0),b),
inference(superposition,[status(thm)],[c_64,c_236]) ).
tcf(c_4548,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,b)),compose(compose(codomain(X1),X0),b)),compose(compose(codomain(X1),X0),b)) = compose(compose(codomain(X1),X0),b),
inference(superposition,[status(thm)],[c_101,c_236]) ).
tcf(c_4549,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(h),domain(X0),compose(g,compose(X0,b)),compose(compose(g,X0),b)),compose(compose(g,X0),b)) = compose(compose(g,X0),b),
inference(superposition,[status(thm)],[c_960,c_236]) ).
tcf(c_4550,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,b)),compose(compose(compose(a,h),X0),b)),compose(compose(compose(a,h),X0),b)) = compose(compose(compose(a,h),X0),b),
inference(superposition,[status(thm)],[c_841,c_236]) ).
tcf(c_4551,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,b)),compose(compose(compose(a,b),X0),b)),compose(compose(compose(a,b),X0),b)) = compose(compose(compose(a,b),X0),b),
inference(superposition,[status(thm)],[c_682,c_236]) ).
tcf(c_4552,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),codomain(a),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),b)),compose(compose(X1,codomain(X0)),b)),compose(compose(X1,codomain(X0)),b)) = compose(compose(X1,codomain(X0)),b),
inference(superposition,[status(thm)],[c_65,c_236]) ).
tcf(c_4553,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),b)),compose(compose(X0,compose(a,b)),b)),compose(compose(X0,compose(a,b)),b)) = compose(compose(X0,compose(a,b)),b),
inference(superposition,[status(thm)],[c_368,c_236]) ).
tcf(c_4554,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(codomain(X0),codomain(a),compose(X0,compose(b,b)),compose(compose(X0,b),b)),compose(compose(X0,b),b)) = compose(compose(X0,b),b),
inference(superposition,[status(thm)],[c_72,c_236]) ).
tcf(c_4555,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),codomain(a),compose(X0,compose(h,b)),compose(compose(X0,h),b)),compose(compose(X0,h),b)) = compose(compose(X0,h),b),
inference(superposition,[status(thm)],[c_73,c_236]) ).
tcf(c_4556,plain,
! [X0: $i] : ifeq(codomain(g),codomain(a),ifeq(codomain(X0),codomain(a),compose(X0,compose(g,b)),compose(compose(X0,g),b)),compose(compose(X0,g),b)) = compose(compose(X0,g),b),
inference(superposition,[status(thm)],[c_74,c_236]) ).
tcf(c_4557,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(a),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),b)),compose(compose(X1,domain(X0)),b)),compose(compose(X1,domain(X0)),b)) = compose(compose(X1,domain(X0)),b),
inference(superposition,[status(thm)],[c_100,c_236]) ).
tcf(c_4558,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),b)),compose(compose(X0,compose(a,h)),b)),compose(compose(X0,compose(a,h)),b)) = compose(compose(X0,compose(a,h)),b),
inference(superposition,[status(thm)],[c_506,c_236]) ).
tcf(c_4589,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_236,c_63]) ).
tcf(c_4597,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),codomain(a),compose(X0,compose(g,b)),compose(compose(X0,g),b)),compose(compose(X0,g),b)) = compose(compose(X0,g),b),
inference(light_normalisation,[status(thm)],[c_4556,c_960]) ).
tcf(c_4602,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(a),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),b)),compose(compose(X1,domain(X0)),b)),compose(compose(X1,domain(X0)),b)) = compose(compose(X1,domain(X0)),b),
inference(light_normalisation,[status(thm)],[c_4557,c_64]) ).
tcf(c_4603,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),b)),compose(compose(X1,codomain(X0)),b)),compose(compose(X1,codomain(X0)),b)) = compose(compose(X1,codomain(X0)),b),
inference(light_normalisation,[status(thm)],[c_4552,c_101]) ).
tcf(c_4610,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),b)),compose(compose(X0,compose(a,h)),b)),compose(compose(X0,compose(a,h)),b)) = compose(compose(X0,compose(a,h)),b),
inference(light_normalisation,[status(thm)],[c_4558,c_841]) ).
tcf(c_4611,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),b)),compose(compose(X0,compose(a,b)),b)),compose(compose(X0,compose(a,b)),b)) = compose(compose(X0,compose(a,b)),b),
inference(light_normalisation,[status(thm)],[c_4553,c_682]) ).
tcf(c_4691,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_64,c_4589]) ).
tcf(c_4692,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_101,c_4589]) ).
tcf(c_4693,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,b)),compose(compose(g,a),b)) = compose(compose(g,a),b),
inference(superposition,[status(thm)],[c_960,c_4589]) ).
tcf(c_4694,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),a),b)) = compose(compose(compose(a,h),a),b),
inference(superposition,[status(thm)],[c_841,c_4589]) ).
tcf(c_4695,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_682,c_4589]) ).
tcf(c_4753,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,h)),compose(compose(domain(X1),X0),h)),compose(compose(domain(X1),X0),h)) = compose(compose(domain(X1),X0),h),
inference(superposition,[status(thm)],[c_64,c_237]) ).
tcf(c_4754,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,h)),compose(compose(codomain(X1),X0),h)),compose(compose(codomain(X1),X0),h)) = compose(compose(codomain(X1),X0),h),
inference(superposition,[status(thm)],[c_101,c_237]) ).
tcf(c_4755,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(h),domain(X0),compose(g,compose(X0,h)),compose(compose(g,X0),h)),compose(compose(g,X0),h)) = compose(compose(g,X0),h),
inference(superposition,[status(thm)],[c_960,c_237]) ).
tcf(c_4756,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,h)),compose(compose(compose(a,h),X0),h)),compose(compose(compose(a,h),X0),h)) = compose(compose(compose(a,h),X0),h),
inference(superposition,[status(thm)],[c_841,c_237]) ).
tcf(c_4757,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,h)),compose(compose(compose(a,b),X0),h)),compose(compose(compose(a,b),X0),h)) = compose(compose(compose(a,b),X0),h),
inference(superposition,[status(thm)],[c_682,c_237]) ).
tcf(c_4758,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),codomain(a),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),h)),compose(compose(X1,codomain(X0)),h)),compose(compose(X1,codomain(X0)),h)) = compose(compose(X1,codomain(X0)),h),
inference(superposition,[status(thm)],[c_65,c_237]) ).
tcf(c_4759,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),h)),compose(compose(X0,compose(a,b)),h)),compose(compose(X0,compose(a,b)),h)) = compose(compose(X0,compose(a,b)),h),
inference(superposition,[status(thm)],[c_368,c_237]) ).
tcf(c_4760,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(codomain(X0),codomain(a),compose(X0,compose(b,h)),compose(compose(X0,b),h)),compose(compose(X0,b),h)) = compose(compose(X0,b),h),
inference(superposition,[status(thm)],[c_72,c_237]) ).
tcf(c_4761,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),codomain(a),compose(X0,compose(h,h)),compose(compose(X0,h),h)),compose(compose(X0,h),h)) = compose(compose(X0,h),h),
inference(superposition,[status(thm)],[c_73,c_237]) ).
tcf(c_4762,plain,
! [X0: $i] : ifeq(codomain(g),codomain(a),ifeq(codomain(X0),codomain(a),compose(X0,compose(g,h)),compose(compose(X0,g),h)),compose(compose(X0,g),h)) = compose(compose(X0,g),h),
inference(superposition,[status(thm)],[c_74,c_237]) ).
tcf(c_4763,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(a),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),h)),compose(compose(X1,domain(X0)),h)),compose(compose(X1,domain(X0)),h)) = compose(compose(X1,domain(X0)),h),
inference(superposition,[status(thm)],[c_100,c_237]) ).
tcf(c_4764,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),h)),compose(compose(X0,compose(a,h)),h)),compose(compose(X0,compose(a,h)),h)) = compose(compose(X0,compose(a,h)),h),
inference(superposition,[status(thm)],[c_506,c_237]) ).
tcf(c_4795,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,h)),compose(compose(X0,a),h)) = compose(compose(X0,a),h),
inference(superposition,[status(thm)],[c_237,c_63]) ).
tcf(c_4803,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),codomain(a),compose(X0,compose(g,h)),compose(compose(X0,g),h)),compose(compose(X0,g),h)) = compose(compose(X0,g),h),
inference(light_normalisation,[status(thm)],[c_4762,c_960]) ).
tcf(c_4808,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(a),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),h)),compose(compose(X1,domain(X0)),h)),compose(compose(X1,domain(X0)),h)) = compose(compose(X1,domain(X0)),h),
inference(light_normalisation,[status(thm)],[c_4763,c_64]) ).
tcf(c_4809,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),h)),compose(compose(X1,codomain(X0)),h)),compose(compose(X1,codomain(X0)),h)) = compose(compose(X1,codomain(X0)),h),
inference(light_normalisation,[status(thm)],[c_4758,c_101]) ).
tcf(c_4816,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),h)),compose(compose(X0,compose(a,h)),h)),compose(compose(X0,compose(a,h)),h)) = compose(compose(X0,compose(a,h)),h),
inference(light_normalisation,[status(thm)],[c_4764,c_841]) ).
tcf(c_4817,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),h)),compose(compose(X0,compose(a,b)),h)),compose(compose(X0,compose(a,b)),h)) = compose(compose(X0,compose(a,b)),h),
inference(light_normalisation,[status(thm)],[c_4759,c_682]) ).
tcf(c_4878,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),a),h)) = compose(compose(domain(X0),a),h),
inference(superposition,[status(thm)],[c_64,c_4795]) ).
tcf(c_4879,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),a),h)) = compose(compose(codomain(X0),a),h),
inference(superposition,[status(thm)],[c_101,c_4795]) ).
tcf(c_4880,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,h)),compose(compose(g,a),h)) = compose(compose(g,a),h),
inference(superposition,[status(thm)],[c_960,c_4795]) ).
tcf(c_4881,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),a),h)) = compose(compose(compose(a,h),a),h),
inference(superposition,[status(thm)],[c_841,c_4795]) ).
tcf(c_4882,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(compose(a,b),a),h)) = compose(compose(compose(a,b),a),h),
inference(superposition,[status(thm)],[c_682,c_4795]) ).
tcf(c_5003,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),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_64,c_238]) ).
tcf(c_5004,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),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_101,c_238]) ).
tcf(c_5005,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(h),domain(X0),compose(g,compose(X0,g)),compose(compose(g,X0),g)),compose(compose(g,X0),g)) = compose(compose(g,X0),g),
inference(superposition,[status(thm)],[c_960,c_238]) ).
tcf(c_5006,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,g)),compose(compose(compose(a,h),X0),g)),compose(compose(compose(a,h),X0),g)) = compose(compose(compose(a,h),X0),g),
inference(superposition,[status(thm)],[c_841,c_238]) ).
tcf(c_5007,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),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_682,c_238]) ).
tcf(c_5008,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),codomain(a),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_65,c_238]) ).
tcf(c_5009,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(a),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_368,c_238]) ).
tcf(c_5010,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(codomain(X0),codomain(a),compose(X0,compose(b,g)),compose(compose(X0,b),g)),compose(compose(X0,b),g)) = compose(compose(X0,b),g),
inference(superposition,[status(thm)],[c_72,c_238]) ).
tcf(c_5011,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),codomain(a),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_73,c_238]) ).
tcf(c_5012,plain,
! [X0: $i] : ifeq(codomain(g),codomain(a),ifeq(codomain(X0),codomain(a),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_74,c_238]) ).
tcf(c_5013,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(a),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_238]) ).
tcf(c_5014,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),g)),compose(compose(X0,compose(a,h)),g)),compose(compose(X0,compose(a,h)),g)) = compose(compose(X0,compose(a,h)),g),
inference(superposition,[status(thm)],[c_506,c_238]) ).
tcf(c_5045,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,g)),compose(compose(X0,a),g)) = compose(compose(X0,a),g),
inference(superposition,[status(thm)],[c_238,c_63]) ).
tcf(c_5046,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,h)),compose(compose(X0,a),g)) = compose(compose(X0,a),g),
inference(light_normalisation,[status(thm)],[c_5045,c_75]) ).
tcf(c_5054,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),codomain(a),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_5012,c_960]) ).
tcf(c_5059,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(a),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_5013,c_64]) ).
tcf(c_5060,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),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_5008,c_101]) ).
tcf(c_5067,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),g)),compose(compose(X0,compose(a,h)),g)),compose(compose(X0,compose(a,h)),g)) = compose(compose(X0,compose(a,h)),g),
inference(light_normalisation,[status(thm)],[c_5014,c_841]) ).
tcf(c_5068,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),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_5009,c_682]) ).
tcf(c_5125,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),a),g)) = compose(compose(domain(X0),a),g),
inference(superposition,[status(thm)],[c_64,c_5046]) ).
tcf(c_5126,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),a),g)) = compose(compose(codomain(X0),a),g),
inference(superposition,[status(thm)],[c_101,c_5046]) ).
tcf(c_5127,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,h)),compose(compose(g,a),g)) = compose(compose(g,a),g),
inference(superposition,[status(thm)],[c_960,c_5046]) ).
tcf(c_5128,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),a),g)) = compose(compose(compose(a,h),a),g),
inference(superposition,[status(thm)],[c_841,c_5046]) ).
tcf(c_5129,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(compose(a,b),a),g)) = compose(compose(compose(a,b),a),g),
inference(superposition,[status(thm)],[c_682,c_5046]) ).
tcf(c_5252,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(X1),codomain(a),compose(X1,compose(b,codomain(X0))),compose(compose(X1,b),codomain(X0))),compose(compose(X1,b),codomain(X0))) = compose(compose(X1,b),codomain(X0)),
inference(superposition,[status(thm)],[c_65,c_243]) ).
tcf(c_5253,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),codomain(a),compose(X0,compose(b,compose(a,b))),compose(compose(X0,b),compose(a,b))),compose(compose(X0,b),compose(a,b))) = compose(compose(X0,b),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_243]) ).
tcf(c_5257,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),codomain(a),compose(X1,compose(b,domain(X0))),compose(compose(X1,b),domain(X0))),compose(compose(X1,b),domain(X0))) = compose(compose(X1,b),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_243]) ).
tcf(c_5258,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),codomain(a),compose(X0,compose(b,compose(a,h))),compose(compose(X0,b),compose(a,h))),compose(compose(X0,b),compose(a,h))) = compose(compose(X0,b),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_243]) ).
tcf(c_5259,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_63,c_243]) ).
tcf(c_5260,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(X1),codomain(a),compose(domain(X1),compose(b,X0)),compose(compose(domain(X1),b),X0)),compose(compose(domain(X1),b),X0)) = compose(compose(domain(X1),b),X0),
inference(superposition,[status(thm)],[c_64,c_243]) ).
tcf(c_5261,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),codomain(a),compose(codomain(X1),compose(b,X0)),compose(compose(codomain(X1),b),X0)),compose(compose(codomain(X1),b),X0)) = compose(compose(codomain(X1),b),X0),
inference(superposition,[status(thm)],[c_101,c_243]) ).
tcf(c_5262,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),codomain(a),compose(g,compose(b,X0)),compose(compose(g,b),X0)),compose(compose(g,b),X0)) = compose(compose(g,b),X0),
inference(superposition,[status(thm)],[c_960,c_243]) ).
tcf(c_5263,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(b,X0)),compose(compose(compose(a,h),b),X0)),compose(compose(compose(a,h),b),X0)) = compose(compose(compose(a,h),b),X0),
inference(superposition,[status(thm)],[c_841,c_243]) ).
tcf(c_5264,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(b,X0)),compose(compose(compose(a,b),b),X0)),compose(compose(compose(a,b),b),X0)) = compose(compose(compose(a,b),b),X0),
inference(superposition,[status(thm)],[c_682,c_243]) ).
tcf(c_5289,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_65,c_5259]) ).
tcf(c_5290,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_368,c_5259]) ).
tcf(c_5291,plain,
ifeq(codomain(b),codomain(a),compose(a,compose(b,b)),compose(compose(a,b),b)) = compose(compose(a,b),b),
inference(superposition,[status(thm)],[c_72,c_5259]) ).
tcf(c_5292,plain,
ifeq(codomain(b),codomain(a),compose(a,compose(b,h)),compose(compose(a,b),h)) = compose(compose(a,b),h),
inference(superposition,[status(thm)],[c_73,c_5259]) ).
tcf(c_5293,plain,
ifeq(codomain(b),codomain(a),compose(a,compose(b,g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
inference(superposition,[status(thm)],[c_74,c_5259]) ).
tcf(c_5294,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_5259]) ).
tcf(c_5295,plain,
ifeq(codomain(b),domain(a),compose(a,compose(b,compose(a,h))),compose(compose(a,b),compose(a,h))) = compose(compose(a,b),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5259]) ).
tcf(c_5336,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(X1),codomain(a),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_65,c_244]) ).
tcf(c_5337,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),codomain(a),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_368,c_244]) ).
tcf(c_5341,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),codomain(a),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_244]) ).
tcf(c_5342,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),codomain(a),compose(X0,compose(h,compose(a,h))),compose(compose(X0,h),compose(a,h))),compose(compose(X0,h),compose(a,h))) = compose(compose(X0,h),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_244]) ).
tcf(c_5343,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(a,compose(h,X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(superposition,[status(thm)],[c_63,c_244]) ).
tcf(c_5344,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(domain(X1),codomain(a),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_64,c_244]) ).
tcf(c_5345,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),codomain(a),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_101,c_244]) ).
tcf(c_5346,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),codomain(a),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_960,c_244]) ).
tcf(c_5347,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(h,X0)),compose(compose(compose(a,h),h),X0)),compose(compose(compose(a,h),h),X0)) = compose(compose(compose(a,h),h),X0),
inference(superposition,[status(thm)],[c_841,c_244]) ).
tcf(c_5348,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(b),codomain(a),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_682,c_244]) ).
tcf(c_5405,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),compose(a,compose(h,codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(a,h),codomain(X0)),
inference(superposition,[status(thm)],[c_65,c_5343]) ).
tcf(c_5406,plain,
ifeq(codomain(h),domain(a),compose(a,compose(h,compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_5343]) ).
tcf(c_5407,plain,
ifeq(codomain(h),codomain(a),compose(a,compose(h,b)),compose(compose(a,h),b)) = compose(compose(a,h),b),
inference(superposition,[status(thm)],[c_72,c_5343]) ).
tcf(c_5408,plain,
ifeq(codomain(h),codomain(a),compose(a,compose(h,h)),compose(compose(a,h),h)) = compose(compose(a,h),h),
inference(superposition,[status(thm)],[c_73,c_5343]) ).
tcf(c_5409,plain,
ifeq(codomain(h),codomain(a),compose(a,compose(h,g)),compose(compose(a,h),g)) = compose(compose(a,h),g),
inference(superposition,[status(thm)],[c_74,c_5343]) ).
tcf(c_5410,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(a,compose(h,domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(a,h),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_5343]) ).
tcf(c_5411,plain,
ifeq(codomain(h),domain(a),compose(a,compose(h,compose(a,h))),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5343]) ).
tcf(c_5507,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_265,c_65]) ).
tcf(c_5528,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_64,c_5507]) ).
tcf(c_5529,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_101,c_5507]) ).
tcf(c_5530,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(g,X0)),ifeq(codomain(h),domain(X0),compose(g,compose(X0,codomain(compose(g,X0)))),compose(g,X0)),compose(g,X0)) = compose(g,X0),
inference(superposition,[status(thm)],[c_960,c_5507]) ).
tcf(c_5531,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(compose(a,h),X0)),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,codomain(compose(compose(a,h),X0)))),compose(compose(a,h),X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(superposition,[status(thm)],[c_841,c_5507]) ).
tcf(c_5532,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_682,c_5507]) ).
tcf(c_5533,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_65,c_5507]) ).
tcf(c_5534,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_368,c_5507]) ).
tcf(c_5535,plain,
! [X0: $i] : ifeq(codomain(b),codomain(compose(X0,b)),ifeq(codomain(X0),codomain(a),compose(X0,compose(b,codomain(compose(X0,b)))),compose(X0,b)),compose(X0,b)) = compose(X0,b),
inference(superposition,[status(thm)],[c_72,c_5507]) ).
tcf(c_5536,plain,
! [X0: $i] : ifeq(codomain(h),codomain(compose(X0,h)),ifeq(codomain(X0),codomain(a),compose(X0,compose(h,codomain(compose(X0,h)))),compose(X0,h)),compose(X0,h)) = compose(X0,h),
inference(superposition,[status(thm)],[c_73,c_5507]) ).
tcf(c_5537,plain,
! [X0: $i] : ifeq(codomain(g),codomain(compose(X0,g)),ifeq(codomain(X0),codomain(a),compose(X0,compose(g,codomain(compose(X0,g)))),compose(X0,g)),compose(X0,g)) = compose(X0,g),
inference(superposition,[status(thm)],[c_74,c_5507]) ).
tcf(c_5538,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_5507]) ).
tcf(c_5539,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(compose(X0,compose(a,h))),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),codomain(compose(X0,compose(a,h))))),compose(X0,compose(a,h))),compose(X0,compose(a,h))) = compose(X0,compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5507]) ).
tcf(c_5592,plain,
! [X0: $i] : ifeq(codomain(h),codomain(compose(X0,g)),ifeq(codomain(X0),codomain(a),compose(X0,compose(g,codomain(compose(X0,g)))),compose(X0,g)),compose(X0,g)) = compose(X0,g),
inference(light_normalisation,[status(thm)],[c_5537,c_960]) ).
tcf(c_5596,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_5538,c_64]) ).
tcf(c_5597,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_5533,c_101]) ).
tcf(c_5602,plain,
! [X0: $i] : ifeq(codomain(h),codomain(compose(X0,compose(a,h))),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),codomain(compose(X0,compose(a,h))))),compose(X0,compose(a,h))),compose(X0,compose(a,h))) = compose(X0,compose(a,h)),
inference(light_normalisation,[status(thm)],[c_5539,c_841]) ).
tcf(c_5603,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_5534,c_682]) ).
tcf(c_5706,plain,
! [X0: $i] : ifeq(codomain(b),codomain(compose(domain(X0),b)),ifeq(domain(X0),codomain(a),compose(domain(X0),compose(b,codomain(compose(domain(X0),b)))),compose(domain(X0),b)),compose(domain(X0),b)) = compose(domain(X0),b),
inference(superposition,[status(thm)],[c_64,c_5535]) ).
tcf(c_5707,plain,
! [X0: $i] : ifeq(codomain(b),codomain(compose(codomain(X0),b)),ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(b,codomain(compose(codomain(X0),b)))),compose(codomain(X0),b)),compose(codomain(X0),b)) = compose(codomain(X0),b),
inference(superposition,[status(thm)],[c_101,c_5535]) ).
tcf(c_5708,plain,
ifeq(codomain(b),codomain(compose(g,b)),ifeq(codomain(h),codomain(a),compose(g,compose(b,codomain(compose(g,b)))),compose(g,b)),compose(g,b)) = compose(g,b),
inference(superposition,[status(thm)],[c_960,c_5535]) ).
tcf(c_5709,plain,
ifeq(codomain(b),codomain(compose(compose(a,h),b)),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(b,codomain(compose(compose(a,h),b)))),compose(compose(a,h),b)),compose(compose(a,h),b)) = compose(compose(a,h),b),
inference(superposition,[status(thm)],[c_841,c_5535]) ).
tcf(c_5710,plain,
ifeq(codomain(b),codomain(compose(compose(a,b),b)),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(b,codomain(compose(compose(a,b),b)))),compose(compose(a,b),b)),compose(compose(a,b),b)) = compose(compose(a,b),b),
inference(superposition,[status(thm)],[c_682,c_5535]) ).
tcf(c_5725,plain,
! [X0: $i] : ifeq(codomain(h),codomain(compose(domain(X0),h)),ifeq(domain(X0),codomain(a),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_64,c_5536]) ).
tcf(c_5726,plain,
! [X0: $i] : ifeq(codomain(h),codomain(compose(codomain(X0),h)),ifeq(codomain(X0),codomain(a),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_101,c_5536]) ).
tcf(c_5727,plain,
ifeq(codomain(h),codomain(compose(g,h)),ifeq(codomain(h),codomain(a),compose(g,compose(h,codomain(compose(g,h)))),compose(g,h)),compose(g,h)) = compose(g,h),
inference(superposition,[status(thm)],[c_960,c_5536]) ).
tcf(c_5728,plain,
ifeq(codomain(h),codomain(compose(compose(a,h),h)),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(h,codomain(compose(compose(a,h),h)))),compose(compose(a,h),h)),compose(compose(a,h),h)) = compose(compose(a,h),h),
inference(superposition,[status(thm)],[c_841,c_5536]) ).
tcf(c_5729,plain,
ifeq(codomain(h),codomain(compose(compose(a,b),h)),ifeq(codomain(b),codomain(a),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_682,c_5536]) ).
tcf(c_5744,plain,
! [X0: $i] : ifeq(codomain(h),codomain(compose(domain(X0),g)),ifeq(domain(X0),codomain(a),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_64,c_5592]) ).
tcf(c_5745,plain,
! [X0: $i] : ifeq(codomain(h),codomain(compose(codomain(X0),g)),ifeq(codomain(X0),codomain(a),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_101,c_5592]) ).
tcf(c_5746,plain,
ifeq(codomain(h),codomain(compose(g,g)),ifeq(codomain(h),codomain(a),compose(g,compose(g,codomain(compose(g,g)))),compose(g,g)),compose(g,g)) = compose(g,g),
inference(superposition,[status(thm)],[c_960,c_5592]) ).
tcf(c_5747,plain,
ifeq(codomain(h),codomain(compose(compose(a,h),g)),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(g,codomain(compose(compose(a,h),g)))),compose(compose(a,h),g)),compose(compose(a,h),g)) = compose(compose(a,h),g),
inference(superposition,[status(thm)],[c_841,c_5592]) ).
tcf(c_5748,plain,
ifeq(codomain(h),codomain(compose(compose(a,b),g)),ifeq(codomain(b),codomain(a),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_682,c_5592]) ).
tcf(c_5773,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(a),codomain(a),compose(a,compose(g,X0)),compose(compose(a,h),X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(light_normalisation,[status(thm)],[c_279,c_960]) ).
tcf(c_5774,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(a,compose(g,X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(demodulation,[status(thm)],[c_5773,c_63]) ).
tcf(c_5775,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),compose(a,compose(g,codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(a,h),codomain(X0)),
inference(superposition,[status(thm)],[c_65,c_5774]) ).
tcf(c_5776,plain,
ifeq(codomain(h),domain(a),compose(a,compose(g,compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_5774]) ).
tcf(c_5777,plain,
ifeq(codomain(h),codomain(a),compose(a,compose(g,b)),compose(compose(a,h),b)) = compose(compose(a,h),b),
inference(superposition,[status(thm)],[c_72,c_5774]) ).
tcf(c_5778,plain,
ifeq(codomain(h),codomain(a),compose(a,compose(g,h)),compose(compose(a,h),h)) = compose(compose(a,h),h),
inference(superposition,[status(thm)],[c_73,c_5774]) ).
tcf(c_5779,plain,
ifeq(codomain(h),codomain(a),compose(a,compose(g,g)),compose(compose(a,h),g)) = compose(compose(a,h),g),
inference(superposition,[status(thm)],[c_74,c_5774]) ).
tcf(c_5780,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(a,compose(g,domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(a,h),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_5774]) ).
tcf(c_5781,plain,
ifeq(codomain(h),domain(a),compose(a,compose(g,compose(a,h))),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5774]) ).
tcf(c_5840,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(a,b),X1,domain(a),X0),X0),X0) = X0,
inference(demodulation,[status(thm)],[c_394,c_63,c_64]) ).
tcf(c_5841,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),compose(a,b)),X1,ifeq(compose(a,b),X1,domain(a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_5840]) ).
tcf(c_5842,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X1,ifeq(compose(a,b),X1,domain(a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_5840]) ).
tcf(c_5843,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),X0,ifeq(compose(a,b),X0,domain(a),g),g),g) = g,
inference(superposition,[status(thm)],[c_960,c_5840]) ).
tcf(c_5844,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X0,ifeq(compose(a,b),X0,domain(a),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_5840]) ).
tcf(c_5845,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X0,ifeq(compose(a,b),X0,domain(a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_5840]) ).
tcf(c_5947,plain,
! [X0: $i] : ifeq(compose(domain(a),compose(a,b)),X0,ifeq(compose(a,b),X0,domain(a),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_5841,c_63]) ).
tcf(c_5948,plain,
! [X0: $i] : ifeq(compose(a,b),X0,ifeq(compose(a,b),X0,domain(a),domain(a)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_5947,c_432]) ).
tcf(c_6002,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(X0,codomain(X1))),compose(compose(g,X0),codomain(X1))),compose(compose(g,X0),codomain(X1))) = compose(compose(g,X0),codomain(X1)),
inference(superposition,[status(thm)],[c_65,c_990]) ).
tcf(c_6003,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(g,compose(X0,compose(a,b))),compose(compose(g,X0),compose(a,b))),compose(compose(g,X0),compose(a,b))) = compose(compose(g,X0),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_990]) ).
tcf(c_6007,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(X0,domain(X1))),compose(compose(g,X0),domain(X1))),compose(compose(g,X0),domain(X1))) = compose(compose(g,X0),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_990]) ).
tcf(c_6008,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(g,compose(X0,compose(a,h))),compose(compose(g,X0),compose(a,h))),compose(compose(g,X0),compose(a,h))) = compose(compose(g,X0),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_990]) ).
tcf(c_6011,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),X1)),compose(compose(g,codomain(X0)),X1)),compose(compose(g,codomain(X0)),X1)) = compose(compose(g,codomain(X0)),X1),
inference(superposition,[status(thm)],[c_65,c_990]) ).
tcf(c_6012,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),X0)),compose(compose(g,compose(a,b)),X0)),compose(compose(g,compose(a,b)),X0)) = compose(compose(g,compose(a,b)),X0),
inference(superposition,[status(thm)],[c_368,c_990]) ).
tcf(c_6015,plain,
! [X0: $i] : ifeq(codomain(g),domain(X0),ifeq(codomain(h),codomain(a),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_74,c_990]) ).
tcf(c_6016,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),X1)),compose(compose(g,domain(X0)),X1)),compose(compose(g,domain(X0)),X1)) = compose(compose(g,domain(X0)),X1),
inference(superposition,[status(thm)],[c_100,c_990]) ).
tcf(c_6017,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),X0)),compose(compose(g,compose(a,h)),X0)),compose(compose(g,compose(a,h)),X0)) = compose(compose(g,compose(a,h)),X0),
inference(superposition,[status(thm)],[c_506,c_990]) ).
tcf(c_6041,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),codomain(a),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_6015,c_960]) ).
tcf(c_6049,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),X1)),compose(compose(g,domain(X0)),X1)),compose(compose(g,domain(X0)),X1)) = compose(compose(g,domain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_6016,c_64]) ).
tcf(c_6050,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),X1)),compose(compose(g,codomain(X0)),X1)),compose(compose(g,codomain(X0)),X1)) = compose(compose(g,codomain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_6011,c_101]) ).
tcf(c_6055,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),X0)),compose(compose(g,compose(a,h)),X0)),compose(compose(g,compose(a,h)),X0)) = compose(compose(g,compose(a,h)),X0),
inference(light_normalisation,[status(thm)],[c_6017,c_841]) ).
tcf(c_6056,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),X0)),compose(compose(g,compose(a,b)),X0)),compose(compose(g,compose(a,b)),X0)) = compose(compose(g,compose(a,b)),X0),
inference(light_normalisation,[status(thm)],[c_6012,c_682]) ).
tcf(c_6150,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(X1),codomain(a),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_65,c_996]) ).
tcf(c_6151,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),codomain(a),compose(X0,compose(g,compose(a,b))),compose(compose(X0,g),compose(a,b))),compose(compose(X0,g),compose(a,b))) = compose(compose(X0,g),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_996]) ).
tcf(c_6155,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),codomain(a),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_996]) ).
tcf(c_6156,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),codomain(a),compose(X0,compose(g,compose(a,h))),compose(compose(X0,g),compose(a,h))),compose(compose(X0,g),compose(a,h))) = compose(compose(X0,g),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_996]) ).
tcf(c_6158,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(domain(X1),codomain(a),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_64,c_996]) ).
tcf(c_6159,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),codomain(a),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_101,c_996]) ).
tcf(c_6161,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(g,X0)),compose(compose(compose(a,h),g),X0)),compose(compose(compose(a,h),g),X0)) = compose(compose(compose(a,h),g),X0),
inference(superposition,[status(thm)],[c_841,c_996]) ).
tcf(c_6162,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(b),codomain(a),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_682,c_996]) ).
tcf(c_6269,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(domain(X0),codomain(a),compose(domain(X0),compose(b,b)),compose(compose(domain(X0),b),b)),compose(compose(domain(X0),b),b)) = compose(compose(domain(X0),b),b),
inference(superposition,[status(thm)],[c_64,c_4554]) ).
tcf(c_6270,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(b,b)),compose(compose(codomain(X0),b),b)),compose(compose(codomain(X0),b),b)) = compose(compose(codomain(X0),b),b),
inference(superposition,[status(thm)],[c_101,c_4554]) ).
tcf(c_6271,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(h),codomain(a),compose(g,compose(b,b)),compose(compose(g,b),b)),compose(compose(g,b),b)) = compose(compose(g,b),b),
inference(superposition,[status(thm)],[c_960,c_4554]) ).
tcf(c_6272,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(b,b)),compose(compose(compose(a,h),b),b)),compose(compose(compose(a,h),b),b)) = compose(compose(compose(a,h),b),b),
inference(superposition,[status(thm)],[c_841,c_4554]) ).
tcf(c_6273,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(b,b)),compose(compose(compose(a,b),b),b)),compose(compose(compose(a,b),b),b)) = compose(compose(compose(a,b),b),b),
inference(superposition,[status(thm)],[c_682,c_4554]) ).
tcf(c_6406,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(domain(X0),codomain(a),compose(domain(X0),compose(h,b)),compose(compose(domain(X0),h),b)),compose(compose(domain(X0),h),b)) = compose(compose(domain(X0),h),b),
inference(superposition,[status(thm)],[c_64,c_4555]) ).
tcf(c_6407,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(h,b)),compose(compose(codomain(X0),h),b)),compose(compose(codomain(X0),h),b)) = compose(compose(codomain(X0),h),b),
inference(superposition,[status(thm)],[c_101,c_4555]) ).
tcf(c_6408,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),codomain(a),compose(g,compose(h,b)),compose(compose(g,h),b)),compose(compose(g,h),b)) = compose(compose(g,h),b),
inference(superposition,[status(thm)],[c_960,c_4555]) ).
tcf(c_6409,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(h,b)),compose(compose(compose(a,h),h),b)),compose(compose(compose(a,h),h),b)) = compose(compose(compose(a,h),h),b),
inference(superposition,[status(thm)],[c_841,c_4555]) ).
tcf(c_6410,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(h,b)),compose(compose(compose(a,b),h),b)),compose(compose(compose(a,b),h),b)) = compose(compose(compose(a,b),h),b),
inference(superposition,[status(thm)],[c_682,c_4555]) ).
tcf(c_6444,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(g,compose(a,b)),codomain(X0),g),g),g) = g,
inference(superposition,[status(thm)],[c_101,c_3940]) ).
tcf(c_6446,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(g,compose(a,b)),compose(a,h),g),g),g) = g,
inference(superposition,[status(thm)],[c_841,c_3940]) ).
tcf(c_6447,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(g,compose(a,b)),compose(a,b),g),g),g) = g,
inference(superposition,[status(thm)],[c_682,c_3940]) ).
tcf(c_6454,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(domain(X0),compose(a,b)),g,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_3945]) ).
tcf(c_6455,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(codomain(X0),compose(a,b)),g,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_3945]) ).
tcf(c_6457,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(compose(a,h),compose(a,b)),g,compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_3945]) ).
tcf(c_6458,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(compose(a,b),compose(a,b)),g,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_3945]) ).
tcf(c_6491,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(g,compose(a,b)),compose(codomain(X0),compose(a,b)),codomain(X0),g),g),g) = g,
inference(superposition,[status(thm)],[c_101,c_4073]) ).
tcf(c_6493,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(compose(a,h),compose(a,b)),compose(a,h),g),g),g) = g,
inference(superposition,[status(thm)],[c_841,c_4073]) ).
tcf(c_6494,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(g,compose(a,b)),compose(compose(a,b),compose(a,b)),compose(a,b),g),g),g) = g,
inference(superposition,[status(thm)],[c_682,c_4073]) ).
tcf(c_6501,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(domain(X0),codomain(a),compose(domain(X0),compose(g,b)),compose(compose(domain(X0),g),b)),compose(compose(domain(X0),g),b)) = compose(compose(domain(X0),g),b),
inference(superposition,[status(thm)],[c_64,c_4597]) ).
tcf(c_6502,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(g,b)),compose(compose(codomain(X0),g),b)),compose(compose(codomain(X0),g),b)) = compose(compose(codomain(X0),g),b),
inference(superposition,[status(thm)],[c_101,c_4597]) ).
tcf(c_6503,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),codomain(a),compose(g,compose(g,b)),compose(compose(g,g),b)),compose(compose(g,g),b)) = compose(compose(g,g),b),
inference(superposition,[status(thm)],[c_960,c_4597]) ).
tcf(c_6504,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(g,b)),compose(compose(compose(a,h),g),b)),compose(compose(compose(a,h),g),b)) = compose(compose(compose(a,h),g),b),
inference(superposition,[status(thm)],[c_841,c_4597]) ).
tcf(c_6505,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(g,b)),compose(compose(compose(a,b),g),b)),compose(compose(compose(a,b),g),b)) = compose(compose(compose(a,b),g),b),
inference(superposition,[status(thm)],[c_682,c_4597]) ).
tcf(c_6517,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(g,compose(a,b)),g,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_4078]) ).
tcf(c_6518,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(g,compose(a,b)),g,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_4078]) ).
tcf(c_6520,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(g,compose(a,b)),g,compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_4078]) ).
tcf(c_6521,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(g,compose(a,b)),g,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_4078]) ).
tcf(c_6529,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(domain(X0),codomain(a),compose(domain(X0),compose(b,h)),compose(compose(domain(X0),b),h)),compose(compose(domain(X0),b),h)) = compose(compose(domain(X0),b),h),
inference(superposition,[status(thm)],[c_64,c_4760]) ).
tcf(c_6530,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(b,h)),compose(compose(codomain(X0),b),h)),compose(compose(codomain(X0),b),h)) = compose(compose(codomain(X0),b),h),
inference(superposition,[status(thm)],[c_101,c_4760]) ).
tcf(c_6531,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(h),codomain(a),compose(g,compose(b,h)),compose(compose(g,b),h)),compose(compose(g,b),h)) = compose(compose(g,b),h),
inference(superposition,[status(thm)],[c_960,c_4760]) ).
tcf(c_6532,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(b,h)),compose(compose(compose(a,h),b),h)),compose(compose(compose(a,h),b),h)) = compose(compose(compose(a,h),b),h),
inference(superposition,[status(thm)],[c_841,c_4760]) ).
tcf(c_6533,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(b,h)),compose(compose(compose(a,b),b),h)),compose(compose(compose(a,b),b),h)) = compose(compose(compose(a,b),b),h),
inference(superposition,[status(thm)],[c_682,c_4760]) ).
tcf(c_6567,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(domain(X0),codomain(a),compose(domain(X0),compose(h,h)),compose(compose(domain(X0),h),h)),compose(compose(domain(X0),h),h)) = compose(compose(domain(X0),h),h),
inference(superposition,[status(thm)],[c_64,c_4761]) ).
tcf(c_6568,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(h,h)),compose(compose(codomain(X0),h),h)),compose(compose(codomain(X0),h),h)) = compose(compose(codomain(X0),h),h),
inference(superposition,[status(thm)],[c_101,c_4761]) ).
tcf(c_6569,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),codomain(a),compose(g,compose(h,h)),compose(compose(g,h),h)),compose(compose(g,h),h)) = compose(compose(g,h),h),
inference(superposition,[status(thm)],[c_960,c_4761]) ).
tcf(c_6570,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(h,h)),compose(compose(compose(a,h),h),h)),compose(compose(compose(a,h),h),h)) = compose(compose(compose(a,h),h),h),
inference(superposition,[status(thm)],[c_841,c_4761]) ).
tcf(c_6571,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(h,h)),compose(compose(compose(a,b),h),h)),compose(compose(compose(a,b),h),h)) = compose(compose(compose(a,b),h),h),
inference(superposition,[status(thm)],[c_682,c_4761]) ).
tcf(c_6581,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(domain(X0),codomain(a),compose(domain(X0),compose(g,h)),compose(compose(domain(X0),g),h)),compose(compose(domain(X0),g),h)) = compose(compose(domain(X0),g),h),
inference(superposition,[status(thm)],[c_64,c_4803]) ).
tcf(c_6582,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(g,h)),compose(compose(codomain(X0),g),h)),compose(compose(codomain(X0),g),h)) = compose(compose(codomain(X0),g),h),
inference(superposition,[status(thm)],[c_101,c_4803]) ).
tcf(c_6583,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),codomain(a),compose(g,compose(g,h)),compose(compose(g,g),h)),compose(compose(g,g),h)) = compose(compose(g,g),h),
inference(superposition,[status(thm)],[c_960,c_4803]) ).
tcf(c_6584,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(g,h)),compose(compose(compose(a,h),g),h)),compose(compose(compose(a,h),g),h)) = compose(compose(compose(a,h),g),h),
inference(superposition,[status(thm)],[c_841,c_4803]) ).
tcf(c_6585,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(g,h)),compose(compose(compose(a,b),g),h)),compose(compose(compose(a,b),g),h)) = compose(compose(compose(a,b),g),h),
inference(superposition,[status(thm)],[c_682,c_4803]) ).
tcf(c_6598,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(domain(X0),codomain(a),compose(domain(X0),compose(b,g)),compose(compose(domain(X0),b),g)),compose(compose(domain(X0),b),g)) = compose(compose(domain(X0),b),g),
inference(superposition,[status(thm)],[c_64,c_5010]) ).
tcf(c_6599,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(b,g)),compose(compose(codomain(X0),b),g)),compose(compose(codomain(X0),b),g)) = compose(compose(codomain(X0),b),g),
inference(superposition,[status(thm)],[c_101,c_5010]) ).
tcf(c_6600,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(h),codomain(a),compose(g,compose(b,g)),compose(compose(g,b),g)),compose(compose(g,b),g)) = compose(compose(g,b),g),
inference(superposition,[status(thm)],[c_960,c_5010]) ).
tcf(c_6601,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(b,g)),compose(compose(compose(a,h),b),g)),compose(compose(compose(a,h),b),g)) = compose(compose(compose(a,h),b),g),
inference(superposition,[status(thm)],[c_841,c_5010]) ).
tcf(c_6602,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(b,g)),compose(compose(compose(a,b),b),g)),compose(compose(compose(a,b),b),g)) = compose(compose(compose(a,b),b),g),
inference(superposition,[status(thm)],[c_682,c_5010]) ).
tcf(c_6620,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(domain(X0),codomain(a),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_64,c_5011]) ).
tcf(c_6621,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),codomain(a),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_101,c_5011]) ).
tcf(c_6622,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),codomain(a),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_960,c_5011]) ).
tcf(c_6623,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(h,g)),compose(compose(compose(a,h),h),g)),compose(compose(compose(a,h),h),g)) = compose(compose(compose(a,h),h),g),
inference(superposition,[status(thm)],[c_841,c_5011]) ).
tcf(c_6624,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(b),codomain(a),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_682,c_5011]) ).
tcf(c_6658,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(domain(X0),codomain(a),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_64,c_5054]) ).
tcf(c_6659,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),codomain(a),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_101,c_5054]) ).
tcf(c_6660,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),codomain(a),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_960,c_5054]) ).
tcf(c_6661,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(g,g)),compose(compose(compose(a,h),g),g)),compose(compose(compose(a,h),g),g)) = compose(compose(compose(a,h),g),g),
inference(superposition,[status(thm)],[c_841,c_5054]) ).
tcf(c_6662,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(b),codomain(a),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_682,c_5054]) ).
tcf(c_6675,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),codomain(a),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_65,c_6041]) ).
tcf(c_6676,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),codomain(a),compose(g,compose(g,compose(a,b))),compose(compose(g,g),compose(a,b))),compose(compose(g,g),compose(a,b))) = compose(compose(g,g),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_6041]) ).
tcf(c_6680,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),codomain(a),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_6041]) ).
tcf(c_6681,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),codomain(a),compose(g,compose(g,compose(a,h))),compose(compose(g,g),compose(a,h))),compose(compose(g,g),compose(a,h))) = compose(compose(g,g),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_6041]) ).
tcf(c_6699,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_283,c_63]) ).
tcf(c_6700,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_64,c_6699]) ).
tcf(c_6701,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_101,c_6699]) ).
tcf(c_6702,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(g,X0),compose(compose(g,X0),codomain(X0))) = compose(compose(g,X0),codomain(X0)),
inference(superposition,[status(thm)],[c_960,c_6699]) ).
tcf(c_6703,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(compose(a,h),X0),compose(compose(compose(a,h),X0),codomain(X0))) = compose(compose(compose(a,h),X0),codomain(X0)),
inference(superposition,[status(thm)],[c_841,c_6699]) ).
tcf(c_6704,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_682,c_6699]) ).
tcf(c_6707,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(X0,b),compose(compose(X0,b),codomain(b))) = compose(compose(X0,b),codomain(b)),
inference(superposition,[status(thm)],[c_72,c_6699]) ).
tcf(c_6708,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(X0,h),compose(compose(X0,h),codomain(h))) = compose(compose(X0,h),codomain(h)),
inference(superposition,[status(thm)],[c_73,c_6699]) ).
tcf(c_6740,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_64,c_6699]) ).
tcf(c_6742,plain,
! [X0: $i] : ifeq(codomain(X0),domain(g),compose(X0,g),compose(compose(X0,g),codomain(h))) = compose(compose(X0,g),codomain(h)),
inference(superposition,[status(thm)],[c_960,c_6699]) ).
tcf(c_6743,plain,
! [X0: $i] : ifeq(codomain(X0),domain(compose(a,h)),compose(X0,compose(a,h)),compose(compose(X0,compose(a,h)),codomain(h))) = compose(compose(X0,compose(a,h)),codomain(h)),
inference(superposition,[status(thm)],[c_841,c_6699]) ).
tcf(c_6744,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_682,c_6699]) ).
tcf(c_6751,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(X0,g),compose(compose(X0,g),codomain(h))) = compose(compose(X0,g),codomain(h)),
inference(light_normalisation,[status(thm)],[c_6742,c_74]) ).
tcf(c_6760,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_6744,c_368]) ).
tcf(c_6761,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,h)),compose(compose(X0,compose(a,h)),codomain(h))) = compose(compose(X0,compose(a,h)),codomain(h)),
inference(light_normalisation,[status(thm)],[c_6743,c_506]) ).
tcf(c_6811,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),compose(domain(X0),b),compose(compose(domain(X0),b),codomain(b))) = compose(compose(domain(X0),b),codomain(b)),
inference(superposition,[status(thm)],[c_64,c_6707]) ).
tcf(c_6812,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(codomain(X0),b),compose(compose(codomain(X0),b),codomain(b))) = compose(compose(codomain(X0),b),codomain(b)),
inference(superposition,[status(thm)],[c_101,c_6707]) ).
tcf(c_6813,plain,
ifeq(codomain(h),codomain(a),compose(g,b),compose(compose(g,b),codomain(b))) = compose(compose(g,b),codomain(b)),
inference(superposition,[status(thm)],[c_960,c_6707]) ).
tcf(c_6814,plain,
ifeq(codomain(h),codomain(a),compose(compose(a,h),b),compose(compose(compose(a,h),b),codomain(b))) = compose(compose(compose(a,h),b),codomain(b)),
inference(superposition,[status(thm)],[c_841,c_6707]) ).
tcf(c_6815,plain,
ifeq(codomain(b),codomain(a),compose(compose(a,b),b),compose(compose(compose(a,b),b),codomain(b))) = compose(compose(compose(a,b),b),codomain(b)),
inference(superposition,[status(thm)],[c_682,c_6707]) ).
tcf(c_6826,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),compose(domain(X0),h),compose(compose(domain(X0),h),codomain(h))) = compose(compose(domain(X0),h),codomain(h)),
inference(superposition,[status(thm)],[c_64,c_6708]) ).
tcf(c_6827,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(codomain(X0),h),compose(compose(codomain(X0),h),codomain(h))) = compose(compose(codomain(X0),h),codomain(h)),
inference(superposition,[status(thm)],[c_101,c_6708]) ).
tcf(c_6828,plain,
ifeq(codomain(h),codomain(a),compose(g,h),compose(compose(g,h),codomain(h))) = compose(compose(g,h),codomain(h)),
inference(superposition,[status(thm)],[c_960,c_6708]) ).
tcf(c_6829,plain,
ifeq(codomain(h),codomain(a),compose(compose(a,h),h),compose(compose(compose(a,h),h),codomain(h))) = compose(compose(compose(a,h),h),codomain(h)),
inference(superposition,[status(thm)],[c_841,c_6708]) ).
tcf(c_6830,plain,
ifeq(codomain(b),codomain(a),compose(compose(a,b),h),compose(compose(compose(a,b),h),codomain(h))) = compose(compose(compose(a,b),h),codomain(h)),
inference(superposition,[status(thm)],[c_682,c_6708]) ).
tcf(c_6859,plain,
! [X0: $i] : ifeq(codomain(h),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_64,c_6702]) ).
tcf(c_6860,plain,
! [X0: $i] : ifeq(codomain(h),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_101,c_6702]) ).
tcf(c_6861,plain,
ifeq(codomain(h),domain(g),compose(g,g),compose(compose(g,g),codomain(h))) = compose(compose(g,g),codomain(h)),
inference(superposition,[status(thm)],[c_960,c_6702]) ).
tcf(c_6862,plain,
ifeq(codomain(h),domain(compose(a,h)),compose(g,compose(a,h)),compose(compose(g,compose(a,h)),codomain(h))) = compose(compose(g,compose(a,h)),codomain(h)),
inference(superposition,[status(thm)],[c_841,c_6702]) ).
tcf(c_6863,plain,
ifeq(codomain(h),domain(compose(a,b)),compose(g,compose(a,b)),compose(compose(g,compose(a,b)),codomain(b))) = compose(compose(g,compose(a,b)),codomain(b)),
inference(superposition,[status(thm)],[c_682,c_6702]) ).
tcf(c_6865,plain,
ifeq(codomain(h),codomain(a),compose(g,g),compose(compose(g,g),codomain(h))) = compose(compose(g,g),codomain(h)),
inference(light_normalisation,[status(thm)],[c_6861,c_74]) ).
tcf(c_6867,plain,
! [X0: $i] : ifeq(codomain(h),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_6860,c_65]) ).
tcf(c_6868,plain,
! [X0: $i] : ifeq(codomain(h),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_6859,c_100]) ).
tcf(c_6871,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,b)),compose(compose(g,compose(a,b)),codomain(b))) = compose(compose(g,compose(a,b)),codomain(b)),
inference(light_normalisation,[status(thm)],[c_6863,c_368]) ).
tcf(c_6872,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,h)),compose(compose(g,compose(a,h)),codomain(h))) = compose(compose(g,compose(a,h)),codomain(h)),
inference(light_normalisation,[status(thm)],[c_6862,c_506]) ).
tcf(c_6878,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),compose(domain(X0),g),compose(compose(domain(X0),g),codomain(h))) = compose(compose(domain(X0),g),codomain(h)),
inference(superposition,[status(thm)],[c_64,c_6751]) ).
tcf(c_6879,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(codomain(X0),g),compose(compose(codomain(X0),g),codomain(h))) = compose(compose(codomain(X0),g),codomain(h)),
inference(superposition,[status(thm)],[c_101,c_6751]) ).
tcf(c_6881,plain,
ifeq(codomain(h),codomain(a),compose(compose(a,h),g),compose(compose(compose(a,h),g),codomain(h))) = compose(compose(compose(a,h),g),codomain(h)),
inference(superposition,[status(thm)],[c_841,c_6751]) ).
tcf(c_6882,plain,
ifeq(codomain(b),codomain(a),compose(compose(a,b),g),compose(compose(compose(a,b),g),codomain(h))) = compose(compose(compose(a,b),g),codomain(h)),
inference(superposition,[status(thm)],[c_682,c_6751]) ).
tcf(c_6963,plain,
! [X0: $i] : ifeq(domain(X0),domain(compose(a,h)),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),compose(a,h)),codomain(h))) = compose(compose(domain(X0),compose(a,h)),codomain(h)),
inference(superposition,[status(thm)],[c_841,c_6700]) ).
tcf(c_6964,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_682,c_6700]) ).
tcf(c_6974,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_6964,c_368]) ).
tcf(c_6975,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),compose(a,h)),codomain(h))) = compose(compose(domain(X0),compose(a,h)),codomain(h)),
inference(light_normalisation,[status(thm)],[c_6963,c_506]) ).
tcf(c_7093,plain,
! [X0: $i] : ifeq(codomain(X0),domain(compose(a,h)),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),compose(a,h)),codomain(h))) = compose(compose(codomain(X0),compose(a,h)),codomain(h)),
inference(superposition,[status(thm)],[c_841,c_6701]) ).
tcf(c_7094,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_682,c_6701]) ).
tcf(c_7102,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_7094,c_368]) ).
tcf(c_7103,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),compose(a,h)),codomain(h))) = compose(compose(codomain(X0),compose(a,h)),codomain(h)),
inference(light_normalisation,[status(thm)],[c_7093,c_506]) ).
tcf(c_7254,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_6740,c_100]) ).
tcf(c_7255,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_64,c_7254]) ).
tcf(c_7256,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_101,c_7254]) ).
tcf(c_7258,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(compose(a,h),domain(X0)),compose(compose(compose(a,h),domain(X0)),domain(X0))) = compose(compose(compose(a,h),domain(X0)),domain(X0)),
inference(superposition,[status(thm)],[c_841,c_7254]) ).
tcf(c_7259,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_682,c_7254]) ).
tcf(c_7285,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_65,c_7254]) ).
tcf(c_7300,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_64,c_7285]) ).
tcf(c_7301,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_101,c_7285]) ).
tcf(c_7303,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),compose(compose(a,h),codomain(X0)),compose(compose(compose(a,h),codomain(X0)),codomain(X0))) = compose(compose(compose(a,h),codomain(X0)),codomain(X0)),
inference(superposition,[status(thm)],[c_841,c_7285]) ).
tcf(c_7304,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_682,c_7285]) ).
tcf(c_7429,plain,
ifeq(codomain(h),domain(compose(a,h)),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),compose(a,h)),codomain(h))) = compose(compose(compose(a,h),compose(a,h)),codomain(h)),
inference(superposition,[status(thm)],[c_841,c_6703]) ).
tcf(c_7430,plain,
ifeq(codomain(h),domain(compose(a,b)),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),compose(a,b)),codomain(b))) = compose(compose(compose(a,h),compose(a,b)),codomain(b)),
inference(superposition,[status(thm)],[c_682,c_6703]) ).
tcf(c_7438,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),compose(a,b)),codomain(b))) = compose(compose(compose(a,h),compose(a,b)),codomain(b)),
inference(light_normalisation,[status(thm)],[c_7430,c_368]) ).
tcf(c_7439,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),compose(a,h)),codomain(h))) = compose(compose(compose(a,h),compose(a,h)),codomain(h)),
inference(light_normalisation,[status(thm)],[c_7429,c_506]) ).
tcf(c_7456,plain,
ifeq(codomain(b),domain(compose(a,h)),compose(compose(a,b),compose(a,h)),compose(compose(compose(a,b),compose(a,h)),codomain(h))) = compose(compose(compose(a,b),compose(a,h)),codomain(h)),
inference(superposition,[status(thm)],[c_841,c_6704]) ).
tcf(c_7457,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_682,c_6704]) ).
tcf(c_7465,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_7457,c_368]) ).
tcf(c_7466,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(compose(a,b),compose(a,h)),codomain(h))) = compose(compose(compose(a,b),compose(a,h)),codomain(h)),
inference(light_normalisation,[status(thm)],[c_7456,c_506]) ).
tcf(c_7635,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_287,c_63]) ).
tcf(c_7636,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_64,c_7635]) ).
tcf(c_7637,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_101,c_7635]) ).
tcf(c_7638,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(g,X0),compose(compose(g,domain(X0)),X0)) = compose(compose(g,domain(X0)),X0),
inference(superposition,[status(thm)],[c_960,c_7635]) ).
tcf(c_7639,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),compose(compose(a,h),X0),compose(compose(compose(a,h),domain(X0)),X0)) = compose(compose(compose(a,h),domain(X0)),X0),
inference(superposition,[status(thm)],[c_841,c_7635]) ).
tcf(c_7640,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_682,c_7635]) ).
tcf(c_7664,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_368,c_7635]) ).
tcf(c_7665,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(X0,b),compose(compose(X0,codomain(a)),b)) = compose(compose(X0,codomain(a)),b),
inference(superposition,[status(thm)],[c_72,c_7635]) ).
tcf(c_7666,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(X0,h),compose(compose(X0,codomain(a)),h)) = compose(compose(X0,codomain(a)),h),
inference(superposition,[status(thm)],[c_73,c_7635]) ).
tcf(c_7667,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(X0,g),compose(compose(X0,codomain(a)),g)) = compose(compose(X0,codomain(a)),g),
inference(superposition,[status(thm)],[c_74,c_7635]) ).
tcf(c_7669,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,h)),compose(compose(X0,domain(a)),compose(a,h))) = compose(compose(X0,domain(a)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_7635]) ).
tcf(c_7711,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,b)),compose(compose(g,domain(a)),compose(a,b))) = compose(compose(g,domain(a)),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_7638]) ).
tcf(c_7712,plain,
ifeq(codomain(h),codomain(a),compose(g,b),compose(compose(g,codomain(a)),b)) = compose(compose(g,codomain(a)),b),
inference(superposition,[status(thm)],[c_72,c_7638]) ).
tcf(c_7713,plain,
ifeq(codomain(h),codomain(a),compose(g,h),compose(compose(g,codomain(a)),h)) = compose(compose(g,codomain(a)),h),
inference(superposition,[status(thm)],[c_73,c_7638]) ).
tcf(c_7714,plain,
ifeq(codomain(h),codomain(a),compose(g,g),compose(compose(g,codomain(a)),g)) = compose(compose(g,codomain(a)),g),
inference(superposition,[status(thm)],[c_74,c_7638]) ).
tcf(c_7716,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,h)),compose(compose(g,domain(a)),compose(a,h))) = compose(compose(g,domain(a)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_7638]) ).
tcf(c_7724,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),compose(domain(X0),b),compose(compose(domain(X0),codomain(a)),b)) = compose(compose(domain(X0),codomain(a)),b),
inference(superposition,[status(thm)],[c_64,c_7665]) ).
tcf(c_7725,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(codomain(X0),b),compose(compose(codomain(X0),codomain(a)),b)) = compose(compose(codomain(X0),codomain(a)),b),
inference(superposition,[status(thm)],[c_101,c_7665]) ).
tcf(c_7727,plain,
ifeq(codomain(h),codomain(a),compose(compose(a,h),b),compose(compose(compose(a,h),codomain(a)),b)) = compose(compose(compose(a,h),codomain(a)),b),
inference(superposition,[status(thm)],[c_841,c_7665]) ).
tcf(c_7728,plain,
ifeq(codomain(b),codomain(a),compose(compose(a,b),b),compose(compose(compose(a,b),codomain(a)),b)) = compose(compose(compose(a,b),codomain(a)),b),
inference(superposition,[status(thm)],[c_682,c_7665]) ).
tcf(c_7790,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),compose(domain(X0),h),compose(compose(domain(X0),codomain(a)),h)) = compose(compose(domain(X0),codomain(a)),h),
inference(superposition,[status(thm)],[c_64,c_7666]) ).
tcf(c_7791,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(codomain(X0),h),compose(compose(codomain(X0),codomain(a)),h)) = compose(compose(codomain(X0),codomain(a)),h),
inference(superposition,[status(thm)],[c_101,c_7666]) ).
tcf(c_7793,plain,
ifeq(codomain(h),codomain(a),compose(compose(a,h),h),compose(compose(compose(a,h),codomain(a)),h)) = compose(compose(compose(a,h),codomain(a)),h),
inference(superposition,[status(thm)],[c_841,c_7666]) ).
tcf(c_7794,plain,
ifeq(codomain(b),codomain(a),compose(compose(a,b),h),compose(compose(compose(a,b),codomain(a)),h)) = compose(compose(compose(a,b),codomain(a)),h),
inference(superposition,[status(thm)],[c_682,c_7666]) ).
tcf(c_7831,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),compose(domain(X0),g),compose(compose(domain(X0),codomain(a)),g)) = compose(compose(domain(X0),codomain(a)),g),
inference(superposition,[status(thm)],[c_64,c_7667]) ).
tcf(c_7832,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),compose(codomain(X0),g),compose(compose(codomain(X0),codomain(a)),g)) = compose(compose(codomain(X0),codomain(a)),g),
inference(superposition,[status(thm)],[c_101,c_7667]) ).
tcf(c_7834,plain,
ifeq(codomain(h),codomain(a),compose(compose(a,h),g),compose(compose(compose(a,h),codomain(a)),g)) = compose(compose(compose(a,h),codomain(a)),g),
inference(superposition,[status(thm)],[c_841,c_7667]) ).
tcf(c_7835,plain,
ifeq(codomain(b),codomain(a),compose(compose(a,b),g),compose(compose(compose(a,b),codomain(a)),g)) = compose(compose(compose(a,b),codomain(a)),g),
inference(superposition,[status(thm)],[c_682,c_7667]) ).
tcf(c_7907,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_368,c_7636]) ).
tcf(c_7912,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),domain(a)),compose(a,h))) = compose(compose(domain(X0),domain(a)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_7636]) ).
tcf(c_8030,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_368,c_7637]) ).
tcf(c_8035,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),domain(a)),compose(a,h))) = compose(compose(codomain(X0),domain(a)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_7637]) ).
tcf(c_8052,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(codomain(X1),compose(a,b)),compose(domain(X0),compose(a,b)),codomain(X1),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_101,c_3938]) ).
tcf(c_8054,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(domain(X0),compose(a,b)),compose(a,h),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_841,c_3938]) ).
tcf(c_8055,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(domain(X0),compose(a,b)),compose(a,b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_682,c_3938]) ).
tcf(c_8089,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(domain(a),compose(a,b)),X0,domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_3938,c_63]) ).
tcf(c_8091,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(a,b),X0,domain(a)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_8089,c_432]) ).
tcf(c_8549,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(a,b),domain(X0),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_64,c_8091]) ).
tcf(c_8550,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(a,b),codomain(X0),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_101,c_8091]) ).
tcf(c_8551,plain,
ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(a,b),g,domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_960,c_8091]) ).
tcf(c_8552,plain,
ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(a,b),compose(a,h),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_841,c_8091]) ).
tcf(c_8553,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(a,b),compose(a,b),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_682,c_8091]) ).
tcf(c_8657,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(codomain(X1),compose(a,b)),codomain(X1),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_101,c_4071]) ).
tcf(c_8659,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(compose(a,h),compose(a,b)),compose(a,h),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_841,c_4071]) ).
tcf(c_8660,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(compose(a,b),compose(a,b)),compose(a,b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_682,c_4071]) ).
tcf(c_8694,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(domain(a),compose(a,b)),compose(X0,compose(a,b)),X0,domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_4071,c_63]) ).
tcf(c_8695,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),compose(X0,compose(a,b)),X0,domain(a)),domain(a)) = domain(a),
inference(light_normalisation,[status(thm)],[c_8694,c_432]) ).
tcf(c_8704,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(compose(a,b),compose(domain(X0),compose(a,b)),domain(X0),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_64,c_8695]) ).
tcf(c_8705,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),compose(codomain(X0),compose(a,b)),codomain(X0),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_101,c_8695]) ).
tcf(c_8706,plain,
ifeq(codomain(h),domain(a),ifeq(compose(a,b),compose(g,compose(a,b)),g,domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_960,c_8695]) ).
tcf(c_8707,plain,
ifeq(codomain(h),domain(a),ifeq(compose(a,b),compose(compose(a,h),compose(a,b)),compose(a,h),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_841,c_8695]) ).
tcf(c_8708,plain,
ifeq(codomain(b),domain(a),ifeq(compose(a,b),compose(compose(a,b),compose(a,b)),compose(a,b),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_682,c_8695]) ).
tcf(c_8864,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),domain(a)),compose(a,b))) = compose(compose(compose(a,h),domain(a)),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_7639]) ).
tcf(c_8869,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),domain(a)),compose(a,h))) = compose(compose(compose(a,h),domain(a)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_7639]) ).
tcf(c_8881,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_368,c_7640]) ).
tcf(c_8886,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(compose(a,b),domain(a)),compose(a,h))) = compose(compose(compose(a,b),domain(a)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_7640]) ).
tcf(c_8954,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(domain(X0),compose(a,b)),X2,ifeq(compose(domain(X1),compose(a,b)),X2,domain(X1),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_388]) ).
tcf(c_8955,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X2,ifeq(compose(domain(X1),compose(a,b)),X2,domain(X1),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_388]) ).
tcf(c_8956,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(g,compose(a,b)),X1,ifeq(compose(domain(X0),compose(a,b)),X1,domain(X0),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_960,c_388]) ).
tcf(c_8957,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X1,ifeq(compose(domain(X0),compose(a,b)),X1,domain(X0),compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_388]) ).
tcf(c_8958,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X1,ifeq(compose(domain(X0),compose(a,b)),X1,domain(X0),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_388]) ).
tcf(c_9009,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(codomain(X1),compose(a,b)),compose(codomain(X0),compose(a,b)),codomain(X1),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_3944]) ).
tcf(c_9011,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(compose(a,h),compose(a,b)),codomain(X0),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_3944]) ).
tcf(c_9012,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(compose(a,b),compose(a,b)),codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_3944]) ).
tcf(c_9038,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(codomain(X1),compose(a,b)),codomain(X1),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_4077]) ).
tcf(c_9040,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(codomain(X0),compose(a,b)),codomain(X0),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_4077]) ).
tcf(c_9041,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(codomain(X0),compose(a,b)),codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_4077]) ).
tcf(c_9326,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),codomain(compose(g,codomain(X0))),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),codomain(compose(g,codomain(X0))))),compose(g,codomain(X0))),compose(g,codomain(X0))) = compose(g,codomain(X0)),
inference(superposition,[status(thm)],[c_65,c_5530]) ).
tcf(c_9327,plain,
ifeq(codomain(compose(a,b)),codomain(compose(g,compose(a,b))),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),codomain(compose(g,compose(a,b))))),compose(g,compose(a,b))),compose(g,compose(a,b))) = compose(g,compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_5530]) ).
tcf(c_9331,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(compose(g,domain(X0))),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),codomain(compose(g,domain(X0))))),compose(g,domain(X0))),compose(g,domain(X0))) = compose(g,domain(X0)),
inference(superposition,[status(thm)],[c_100,c_5530]) ).
tcf(c_9332,plain,
ifeq(codomain(compose(a,h)),codomain(compose(g,compose(a,h))),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),codomain(compose(g,compose(a,h))))),compose(g,compose(a,h))),compose(g,compose(a,h))) = compose(g,compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5530]) ).
tcf(c_9343,plain,
! [X0: $i] : ifeq(domain(X0),codomain(compose(g,domain(X0))),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),codomain(compose(g,domain(X0))))),compose(g,domain(X0))),compose(g,domain(X0))) = compose(g,domain(X0)),
inference(light_normalisation,[status(thm)],[c_9331,c_64]) ).
tcf(c_9344,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(g,codomain(X0))),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),codomain(compose(g,codomain(X0))))),compose(g,codomain(X0))),compose(g,codomain(X0))) = compose(g,codomain(X0)),
inference(light_normalisation,[status(thm)],[c_9326,c_101]) ).
tcf(c_9347,plain,
ifeq(codomain(h),codomain(compose(g,compose(a,h))),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),codomain(compose(g,compose(a,h))))),compose(g,compose(a,h))),compose(g,compose(a,h))) = compose(g,compose(a,h)),
inference(light_normalisation,[status(thm)],[c_9332,c_841]) ).
tcf(c_9348,plain,
ifeq(codomain(b),codomain(compose(g,compose(a,b))),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),codomain(compose(g,compose(a,b))))),compose(g,compose(a,b))),compose(g,compose(a,b))) = compose(g,compose(a,b)),
inference(light_normalisation,[status(thm)],[c_9327,c_682]) ).
tcf(c_9364,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_64,c_235]) ).
tcf(c_9365,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_101,c_235]) ).
tcf(c_9367,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,codomain(X1))),compose(compose(compose(a,h),X0),codomain(X1))),compose(compose(compose(a,h),X0),codomain(X1))) = compose(compose(compose(a,h),X0),codomain(X1)),
inference(superposition,[status(thm)],[c_841,c_235]) ).
tcf(c_9368,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_682,c_235]) ).
tcf(c_9369,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_65,c_235]) ).
tcf(c_9370,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_368,c_235]) ).
tcf(c_9374,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_235]) ).
tcf(c_9375,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,h)),codomain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,h),codomain(X0))),compose(compose(X1,compose(a,h)),codomain(X0))),compose(compose(X1,compose(a,h)),codomain(X0))) = compose(compose(X1,compose(a,h)),codomain(X0)),
inference(superposition,[status(thm)],[c_506,c_235]) ).
tcf(c_9444,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_9374,c_64]) ).
tcf(c_9445,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_9369,c_101]) ).
tcf(c_9455,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,h),codomain(X0))),compose(compose(X1,compose(a,h)),codomain(X0))),compose(compose(X1,compose(a,h)),codomain(X0))) = compose(compose(X1,compose(a,h)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_9375,c_841]) ).
tcf(c_9456,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_9370,c_682]) ).
tcf(c_9518,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_64,c_239]) ).
tcf(c_9519,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_101,c_239]) ).
tcf(c_9521,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,domain(X1))),compose(compose(compose(a,h),X0),domain(X1))),compose(compose(compose(a,h),X0),domain(X1))) = compose(compose(compose(a,h),X0),domain(X1)),
inference(superposition,[status(thm)],[c_841,c_239]) ).
tcf(c_9522,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_682,c_239]) ).
tcf(c_9523,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_65,c_239]) ).
tcf(c_9524,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_368,c_239]) ).
tcf(c_9528,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_239]) ).
tcf(c_9529,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,h),domain(X0))),compose(compose(X1,compose(a,h)),domain(X0))),compose(compose(X1,compose(a,h)),domain(X0))) = compose(compose(X1,compose(a,h)),domain(X0)),
inference(superposition,[status(thm)],[c_506,c_239]) ).
tcf(c_9592,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_9528,c_64]) ).
tcf(c_9593,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_9523,c_101]) ).
tcf(c_9601,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,h),domain(X0))),compose(compose(X1,compose(a,h)),domain(X0))),compose(compose(X1,compose(a,h)),domain(X0))) = compose(compose(X1,compose(a,h)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_9529,c_841]) ).
tcf(c_9602,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_9524,c_682]) ).
tcf(c_9981,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(g,compose(a,b)),X1,ifeq(compose(codomain(X0),compose(a,b)),X1,codomain(X0),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_101,c_979]) ).
tcf(c_9982,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),X0,ifeq(compose(g,compose(a,b)),X0,g,g),g),g),g) = g,
inference(superposition,[status(thm)],[c_960,c_979]) ).
tcf(c_9983,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),X0,ifeq(compose(compose(a,h),compose(a,b)),X0,compose(a,h),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_841,c_979]) ).
tcf(c_9984,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(g,compose(a,b)),X0,ifeq(compose(compose(a,b),compose(a,b)),X0,compose(a,b),g),g),g),g) = g,
inference(superposition,[status(thm)],[c_682,c_979]) ).
tcf(c_9995,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(domain(X0),compose(a,b)),X1,ifeq(compose(g,compose(a,b)),X1,g,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_988]) ).
tcf(c_9996,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X1,ifeq(compose(g,compose(a,b)),X1,g,codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_988]) ).
tcf(c_9998,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X0,ifeq(compose(g,compose(a,b)),X0,g,compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_988]) ).
tcf(c_9999,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X0,ifeq(compose(g,compose(a,b)),X0,g,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_988]) ).
tcf(c_10016,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_368,c_240]) ).
tcf(c_10021,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,compose(a,h))),compose(compose(domain(X1),X0),compose(a,h))),compose(compose(domain(X1),X0),compose(a,h))) = compose(compose(domain(X1),X0),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_240]) ).
tcf(c_10032,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_65,c_240]) ).
tcf(c_10033,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_368,c_240]) ).
tcf(c_10037,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_240]) ).
tcf(c_10038,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,h),X0)),compose(compose(domain(X1),compose(a,h)),X0)),compose(compose(domain(X1),compose(a,h)),X0)) = compose(compose(domain(X1),compose(a,h)),X0),
inference(superposition,[status(thm)],[c_506,c_240]) ).
tcf(c_10039,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_66,c_240]) ).
tcf(c_10106,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_10037,c_64]) ).
tcf(c_10107,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_10032,c_101]) ).
tcf(c_10112,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,h),X0)),compose(compose(domain(X1),compose(a,h)),X0)),compose(compose(domain(X1),compose(a,h)),X0)) = compose(compose(domain(X1),compose(a,h)),X0),
inference(light_normalisation,[status(thm)],[c_10038,c_841]) ).
tcf(c_10113,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_10033,c_682]) ).
tcf(c_10195,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(codomain(X0),compose(a,b)),compose(a,h),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_3946]) ).
tcf(c_10198,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(compose(a,b),compose(a,b)),compose(a,h),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_3946]) ).
tcf(c_10244,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_368,c_241]) ).
tcf(c_10249,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,compose(a,h))),compose(compose(codomain(X1),X0),compose(a,h))),compose(compose(codomain(X1),X0),compose(a,h))) = compose(compose(codomain(X1),X0),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_241]) ).
tcf(c_10257,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_65,c_241]) ).
tcf(c_10258,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_368,c_241]) ).
tcf(c_10262,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_241]) ).
tcf(c_10263,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,h),X0)),compose(compose(codomain(X1),compose(a,h)),X0)),compose(compose(codomain(X1),compose(a,h)),X0)) = compose(compose(codomain(X1),compose(a,h)),X0),
inference(superposition,[status(thm)],[c_506,c_241]) ).
tcf(c_10320,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_10262,c_64]) ).
tcf(c_10321,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_10257,c_101]) ).
tcf(c_10326,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,h),X0)),compose(compose(codomain(X1),compose(a,h)),X0)),compose(compose(codomain(X1),compose(a,h)),X0)) = compose(compose(codomain(X1),compose(a,h)),X0),
inference(light_normalisation,[status(thm)],[c_10263,c_841]) ).
tcf(c_10327,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_10258,c_682]) ).
tcf(c_10399,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_368,c_288]) ).
tcf(c_10404,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),compose(a,h))),compose(compose(X1,domain(X0)),compose(a,h))),compose(compose(X1,domain(X0)),compose(a,h))) = compose(compose(X1,domain(X0)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_288]) ).
tcf(c_10408,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),X1)),compose(compose(compose(a,h),domain(X0)),X1)),compose(compose(compose(a,h),domain(X0)),X1)) = compose(compose(compose(a,h),domain(X0)),X1),
inference(superposition,[status(thm)],[c_841,c_288]) ).
tcf(c_10409,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_682,c_288]) ).
tcf(c_10518,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_368,c_289]) ).
tcf(c_10523,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),compose(a,h))),compose(compose(X1,codomain(X0)),compose(a,h))),compose(compose(X1,codomain(X0)),compose(a,h))) = compose(compose(X1,codomain(X0)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_289]) ).
tcf(c_10528,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),X1)),compose(compose(compose(a,h),codomain(X0)),X1)),compose(compose(compose(a,h),codomain(X0)),X1)) = compose(compose(compose(a,h),codomain(X0)),X1),
inference(superposition,[status(thm)],[c_841,c_289]) ).
tcf(c_10529,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_682,c_289]) ).
tcf(c_10590,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(X0,compose(a,b)),X1,X0,domain(a)),domain(a)),domain(a)) = domain(a),
inference(demodulation,[status(thm)],[c_395,c_63,c_64]) ).
tcf(c_10591,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(domain(X0),compose(a,b)),X1,domain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_64,c_10590]) ).
tcf(c_10592,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(codomain(X0),compose(a,b)),X1,codomain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_101,c_10590]) ).
tcf(c_10593,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(compose(a,b),X0,ifeq(compose(g,compose(a,b)),X0,g,domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_960,c_10590]) ).
tcf(c_10594,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(compose(a,b),X0,ifeq(compose(compose(a,h),compose(a,b)),X0,compose(a,h),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_841,c_10590]) ).
tcf(c_10595,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(compose(a,b),compose(a,b)),X0,compose(a,b),domain(a)),domain(a)),domain(a)) = domain(a),
inference(superposition,[status(thm)],[c_682,c_10590]) ).
tcf(c_10705,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(codomain(X0),compose(a,b)),compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_3947]) ).
tcf(c_10707,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(compose(a,h),compose(a,b)),compose(a,b),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_3947]) ).
tcf(c_10731,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),codomain(a),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),b)),compose(compose(domain(X1),codomain(X0)),b)),compose(compose(domain(X1),codomain(X0)),b)) = compose(compose(domain(X1),codomain(X0)),b),
inference(superposition,[status(thm)],[c_65,c_4547]) ).
tcf(c_10732,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),b)),compose(compose(domain(X0),compose(a,b)),b)),compose(compose(domain(X0),compose(a,b)),b)) = compose(compose(domain(X0),compose(a,b)),b),
inference(superposition,[status(thm)],[c_368,c_4547]) ).
tcf(c_10736,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(a),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),b)),compose(compose(domain(X1),domain(X0)),b)),compose(compose(domain(X1),domain(X0)),b)) = compose(compose(domain(X1),domain(X0)),b),
inference(superposition,[status(thm)],[c_100,c_4547]) ).
tcf(c_10737,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),b)),compose(compose(domain(X0),compose(a,h)),b)),compose(compose(domain(X0),compose(a,h)),b)) = compose(compose(domain(X0),compose(a,h)),b),
inference(superposition,[status(thm)],[c_506,c_4547]) ).
tcf(c_10738,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(domain(compose(X0,b)),domain(X0),compose(X0,b),compose(compose(domain(compose(X0,b)),X0),b)),compose(compose(domain(compose(X0,b)),X0),b)) = compose(compose(domain(compose(X0,b)),X0),b),
inference(superposition,[status(thm)],[c_66,c_4547]) ).
tcf(c_10782,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(a),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),b)),compose(compose(domain(X1),domain(X0)),b)),compose(compose(domain(X1),domain(X0)),b)) = compose(compose(domain(X1),domain(X0)),b),
inference(light_normalisation,[status(thm)],[c_10736,c_64]) ).
tcf(c_10783,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),b)),compose(compose(domain(X1),codomain(X0)),b)),compose(compose(domain(X1),codomain(X0)),b)) = compose(compose(domain(X1),codomain(X0)),b),
inference(light_normalisation,[status(thm)],[c_10731,c_101]) ).
tcf(c_10786,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),b)),compose(compose(domain(X0),compose(a,h)),b)),compose(compose(domain(X0),compose(a,h)),b)) = compose(compose(domain(X0),compose(a,h)),b),
inference(light_normalisation,[status(thm)],[c_10737,c_841]) ).
tcf(c_10787,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),b)),compose(compose(domain(X0),compose(a,b)),b)),compose(compose(domain(X0),compose(a,b)),b)) = compose(compose(domain(X0),compose(a,b)),b),
inference(light_normalisation,[status(thm)],[c_10732,c_682]) ).
tcf(c_10819,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(compose(a,h),compose(a,b)),compose(a,h),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_4079]) ).
tcf(c_10822,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(compose(a,h),compose(a,b)),compose(a,h),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_4079]) ).
tcf(c_10830,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(compose(a,b),compose(a,b)),compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_4080]) ).
tcf(c_10832,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(compose(a,b),compose(a,b)),compose(a,b),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_4080]) ).
tcf(c_10848,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),b)),compose(compose(codomain(X1),codomain(X0)),b)),compose(compose(codomain(X1),codomain(X0)),b)) = compose(compose(codomain(X1),codomain(X0)),b),
inference(superposition,[status(thm)],[c_101,c_4603]) ).
tcf(c_10849,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),b)),compose(compose(g,codomain(X0)),b)),compose(compose(g,codomain(X0)),b)) = compose(compose(g,codomain(X0)),b),
inference(superposition,[status(thm)],[c_960,c_4603]) ).
tcf(c_10850,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),b)),compose(compose(compose(a,h),codomain(X0)),b)),compose(compose(compose(a,h),codomain(X0)),b)) = compose(compose(compose(a,h),codomain(X0)),b),
inference(superposition,[status(thm)],[c_841,c_4603]) ).
tcf(c_10851,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),b)),compose(compose(compose(a,b),codomain(X0)),b)),compose(compose(compose(a,b),codomain(X0)),b)) = compose(compose(compose(a,b),codomain(X0)),b),
inference(superposition,[status(thm)],[c_682,c_4603]) ).
tcf(c_10929,plain,
ifeq(codomain(compose(a,b)),codomain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),b)),compose(compose(g,compose(a,b)),b)),compose(compose(g,compose(a,b)),b)) = compose(compose(g,compose(a,b)),b),
inference(superposition,[status(thm)],[c_368,c_4549]) ).
tcf(c_10933,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(a),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),b)),compose(compose(g,domain(X0)),b)),compose(compose(g,domain(X0)),b)) = compose(compose(g,domain(X0)),b),
inference(superposition,[status(thm)],[c_100,c_4549]) ).
tcf(c_10934,plain,
ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),b)),compose(compose(g,compose(a,h)),b)),compose(compose(g,compose(a,h)),b)) = compose(compose(g,compose(a,h)),b),
inference(superposition,[status(thm)],[c_506,c_4549]) ).
tcf(c_10946,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),b)),compose(compose(g,domain(X0)),b)),compose(compose(g,domain(X0)),b)) = compose(compose(g,domain(X0)),b),
inference(light_normalisation,[status(thm)],[c_10933,c_64]) ).
tcf(c_10950,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),b)),compose(compose(g,compose(a,h)),b)),compose(compose(g,compose(a,h)),b)) = compose(compose(g,compose(a,h)),b),
inference(light_normalisation,[status(thm)],[c_10934,c_841]) ).
tcf(c_10951,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),b)),compose(compose(g,compose(a,b)),b)),compose(compose(g,compose(a,b)),b)) = compose(compose(g,compose(a,b)),b),
inference(light_normalisation,[status(thm)],[c_10929,c_682]) ).
tcf(c_10984,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),codomain(a),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),h)),compose(compose(domain(X1),codomain(X0)),h)),compose(compose(domain(X1),codomain(X0)),h)) = compose(compose(domain(X1),codomain(X0)),h),
inference(superposition,[status(thm)],[c_65,c_4753]) ).
tcf(c_10985,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),h)),compose(compose(domain(X0),compose(a,b)),h)),compose(compose(domain(X0),compose(a,b)),h)) = compose(compose(domain(X0),compose(a,b)),h),
inference(superposition,[status(thm)],[c_368,c_4753]) ).
tcf(c_10989,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(a),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),h)),compose(compose(domain(X1),domain(X0)),h)),compose(compose(domain(X1),domain(X0)),h)) = compose(compose(domain(X1),domain(X0)),h),
inference(superposition,[status(thm)],[c_100,c_4753]) ).
tcf(c_10990,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),h)),compose(compose(domain(X0),compose(a,h)),h)),compose(compose(domain(X0),compose(a,h)),h)) = compose(compose(domain(X0),compose(a,h)),h),
inference(superposition,[status(thm)],[c_506,c_4753]) ).
tcf(c_10991,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(domain(compose(X0,h)),domain(X0),compose(X0,h),compose(compose(domain(compose(X0,h)),X0),h)),compose(compose(domain(compose(X0,h)),X0),h)) = compose(compose(domain(compose(X0,h)),X0),h),
inference(superposition,[status(thm)],[c_66,c_4753]) ).
tcf(c_11035,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(a),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),h)),compose(compose(domain(X1),domain(X0)),h)),compose(compose(domain(X1),domain(X0)),h)) = compose(compose(domain(X1),domain(X0)),h),
inference(light_normalisation,[status(thm)],[c_10989,c_64]) ).
tcf(c_11036,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),h)),compose(compose(domain(X1),codomain(X0)),h)),compose(compose(domain(X1),codomain(X0)),h)) = compose(compose(domain(X1),codomain(X0)),h),
inference(light_normalisation,[status(thm)],[c_10984,c_101]) ).
tcf(c_11039,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),h)),compose(compose(domain(X0),compose(a,h)),h)),compose(compose(domain(X0),compose(a,h)),h)) = compose(compose(domain(X0),compose(a,h)),h),
inference(light_normalisation,[status(thm)],[c_10990,c_841]) ).
tcf(c_11040,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),h)),compose(compose(domain(X0),compose(a,b)),h)),compose(compose(domain(X0),compose(a,b)),h)) = compose(compose(domain(X0),compose(a,b)),h),
inference(light_normalisation,[status(thm)],[c_10985,c_682]) ).
tcf(c_11075,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),codomain(a),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),h)),compose(compose(g,codomain(X0)),h)),compose(compose(g,codomain(X0)),h)) = compose(compose(g,codomain(X0)),h),
inference(superposition,[status(thm)],[c_65,c_4755]) ).
tcf(c_11076,plain,
ifeq(codomain(compose(a,b)),codomain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),h)),compose(compose(g,compose(a,b)),h)),compose(compose(g,compose(a,b)),h)) = compose(compose(g,compose(a,b)),h),
inference(superposition,[status(thm)],[c_368,c_4755]) ).
tcf(c_11080,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(a),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),h)),compose(compose(g,domain(X0)),h)),compose(compose(g,domain(X0)),h)) = compose(compose(g,domain(X0)),h),
inference(superposition,[status(thm)],[c_100,c_4755]) ).
tcf(c_11081,plain,
ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),h)),compose(compose(g,compose(a,h)),h)),compose(compose(g,compose(a,h)),h)) = compose(compose(g,compose(a,h)),h),
inference(superposition,[status(thm)],[c_506,c_4755]) ).
tcf(c_11093,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),h)),compose(compose(g,domain(X0)),h)),compose(compose(g,domain(X0)),h)) = compose(compose(g,domain(X0)),h),
inference(light_normalisation,[status(thm)],[c_11080,c_64]) ).
tcf(c_11094,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),h)),compose(compose(g,codomain(X0)),h)),compose(compose(g,codomain(X0)),h)) = compose(compose(g,codomain(X0)),h),
inference(light_normalisation,[status(thm)],[c_11075,c_101]) ).
tcf(c_11097,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),h)),compose(compose(g,compose(a,h)),h)),compose(compose(g,compose(a,h)),h)) = compose(compose(g,compose(a,h)),h),
inference(light_normalisation,[status(thm)],[c_11081,c_841]) ).
tcf(c_11098,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),h)),compose(compose(g,compose(a,b)),h)),compose(compose(g,compose(a,b)),h)) = compose(compose(g,compose(a,b)),h),
inference(light_normalisation,[status(thm)],[c_11076,c_682]) ).
tcf(c_11159,plain,
! [X0: $i] : ifeq(codomain(codomain(X0)),codomain(a),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),g)),compose(compose(g,codomain(X0)),g)),compose(compose(g,codomain(X0)),g)) = compose(compose(g,codomain(X0)),g),
inference(superposition,[status(thm)],[c_65,c_5005]) ).
tcf(c_11160,plain,
ifeq(codomain(compose(a,b)),codomain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),g)),compose(compose(g,compose(a,b)),g)),compose(compose(g,compose(a,b)),g)) = compose(compose(g,compose(a,b)),g),
inference(superposition,[status(thm)],[c_368,c_5005]) ).
tcf(c_11164,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(a),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),g)),compose(compose(g,domain(X0)),g)),compose(compose(g,domain(X0)),g)) = compose(compose(g,domain(X0)),g),
inference(superposition,[status(thm)],[c_100,c_5005]) ).
tcf(c_11165,plain,
ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),g)),compose(compose(g,compose(a,h)),g)),compose(compose(g,compose(a,h)),g)) = compose(compose(g,compose(a,h)),g),
inference(superposition,[status(thm)],[c_506,c_5005]) ).
tcf(c_11180,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),g)),compose(compose(g,domain(X0)),g)),compose(compose(g,domain(X0)),g)) = compose(compose(g,domain(X0)),g),
inference(light_normalisation,[status(thm)],[c_11164,c_64]) ).
tcf(c_11181,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),g)),compose(compose(g,codomain(X0)),g)),compose(compose(g,codomain(X0)),g)) = compose(compose(g,codomain(X0)),g),
inference(light_normalisation,[status(thm)],[c_11159,c_101]) ).
tcf(c_11184,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),g)),compose(compose(g,compose(a,h)),g)),compose(compose(g,compose(a,h)),g)) = compose(compose(g,compose(a,h)),g),
inference(light_normalisation,[status(thm)],[c_11165,c_841]) ).
tcf(c_11185,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),g)),compose(compose(g,compose(a,b)),g)),compose(compose(g,compose(a,b)),g)) = compose(compose(g,compose(a,b)),g),
inference(light_normalisation,[status(thm)],[c_11160,c_682]) ).
tcf(c_11198,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),h)),compose(compose(codomain(X1),codomain(X0)),h)),compose(compose(codomain(X1),codomain(X0)),h)) = compose(compose(codomain(X1),codomain(X0)),h),
inference(superposition,[status(thm)],[c_101,c_4809]) ).
tcf(c_11200,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),h)),compose(compose(compose(a,h),codomain(X0)),h)),compose(compose(compose(a,h),codomain(X0)),h)) = compose(compose(compose(a,h),codomain(X0)),h),
inference(superposition,[status(thm)],[c_841,c_4809]) ).
tcf(c_11201,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),h)),compose(compose(compose(a,b),codomain(X0)),h)),compose(compose(compose(a,b),codomain(X0)),h)) = compose(compose(compose(a,b),codomain(X0)),h),
inference(superposition,[status(thm)],[c_682,c_4809]) ).
tcf(c_11272,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(h),codomain(a),compose(g,compose(b,codomain(X0))),compose(compose(g,b),codomain(X0))),compose(compose(g,b),codomain(X0))) = compose(compose(g,b),codomain(X0)),
inference(superposition,[status(thm)],[c_65,c_5262]) ).
tcf(c_11273,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),codomain(a),compose(g,compose(b,compose(a,b))),compose(compose(g,b),compose(a,b))),compose(compose(g,b),compose(a,b))) = compose(compose(g,b),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_5262]) ).
tcf(c_11277,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),codomain(a),compose(g,compose(b,domain(X0))),compose(compose(g,b),domain(X0))),compose(compose(g,b),domain(X0))) = compose(compose(g,b),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_5262]) ).
tcf(c_11278,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),codomain(a),compose(g,compose(b,compose(a,h))),compose(compose(g,b),compose(a,h))),compose(compose(g,b),compose(a,h))) = compose(compose(g,b),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5262]) ).
tcf(c_11336,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),codomain(a),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_65,c_5346]) ).
tcf(c_11337,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),codomain(a),compose(g,compose(h,compose(a,b))),compose(compose(g,h),compose(a,b))),compose(compose(g,h),compose(a,b))) = compose(compose(g,h),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_5346]) ).
tcf(c_11341,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),codomain(a),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_5346]) ).
tcf(c_11342,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),codomain(a),compose(g,compose(h,compose(a,h))),compose(compose(g,h),compose(a,h))),compose(compose(g,h),compose(a,h))) = compose(compose(g,h),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5346]) ).
tcf(c_11411,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),codomain(a),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_65,c_5003]) ).
tcf(c_11412,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(a),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_368,c_5003]) ).
tcf(c_11416,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(a),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_5003]) ).
tcf(c_11417,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),g)),compose(compose(domain(X0),compose(a,h)),g)),compose(compose(domain(X0),compose(a,h)),g)) = compose(compose(domain(X0),compose(a,h)),g),
inference(superposition,[status(thm)],[c_506,c_5003]) ).
tcf(c_11418,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),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_66,c_5003]) ).
tcf(c_11464,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(a),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_11416,c_64]) ).
tcf(c_11465,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),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_11411,c_101]) ).
tcf(c_11468,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),g)),compose(compose(domain(X0),compose(a,h)),g)),compose(compose(domain(X0),compose(a,h)),g)) = compose(compose(domain(X0),compose(a,h)),g),
inference(light_normalisation,[status(thm)],[c_11417,c_841]) ).
tcf(c_11469,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),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_11412,c_682]) ).
tcf(c_11485,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(a),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_101,c_5060]) ).
tcf(c_11487,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),g)),compose(compose(compose(a,h),codomain(X0)),g)),compose(compose(compose(a,h),codomain(X0)),g)) = compose(compose(compose(a,h),codomain(X0)),g),
inference(superposition,[status(thm)],[c_841,c_5060]) ).
tcf(c_11488,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),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_682,c_5060]) ).
tcf(c_11557,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),codomain(X0),ifeq(domain(X1),codomain(a),compose(domain(X1),compose(b,codomain(X0))),compose(compose(domain(X1),b),codomain(X0))),compose(compose(domain(X1),b),codomain(X0))) = compose(compose(domain(X1),b),codomain(X0)),
inference(superposition,[status(thm)],[c_64,c_5252]) ).
tcf(c_11558,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(X1),codomain(a),compose(codomain(X1),compose(b,codomain(X0))),compose(compose(codomain(X1),b),codomain(X0))),compose(compose(codomain(X1),b),codomain(X0))) = compose(compose(codomain(X1),b),codomain(X0)),
inference(superposition,[status(thm)],[c_101,c_5252]) ).
tcf(c_11560,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(b,codomain(X0))),compose(compose(compose(a,h),b),codomain(X0))),compose(compose(compose(a,h),b),codomain(X0))) = compose(compose(compose(a,h),b),codomain(X0)),
inference(superposition,[status(thm)],[c_841,c_5252]) ).
tcf(c_11561,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(b,codomain(X0))),compose(compose(compose(a,b),b),codomain(X0))),compose(compose(compose(a,b),b),codomain(X0))) = compose(compose(compose(a,b),b),codomain(X0)),
inference(superposition,[status(thm)],[c_682,c_5252]) ).
tcf(c_11655,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),codomain(a),compose(domain(X0),compose(b,compose(a,b))),compose(compose(domain(X0),b),compose(a,b))),compose(compose(domain(X0),b),compose(a,b))) = compose(compose(domain(X0),b),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_5260]) ).
tcf(c_11659,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(X1),codomain(a),compose(domain(X1),compose(b,domain(X0))),compose(compose(domain(X1),b),domain(X0))),compose(compose(domain(X1),b),domain(X0))) = compose(compose(domain(X1),b),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_5260]) ).
tcf(c_11660,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),codomain(a),compose(domain(X0),compose(b,compose(a,h))),compose(compose(domain(X0),b),compose(a,h))),compose(compose(domain(X0),b),compose(a,h))) = compose(compose(domain(X0),b),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5260]) ).
tcf(c_11668,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(compose(b,X0)),codomain(a),compose(b,X0),compose(compose(domain(compose(b,X0)),b),X0)),compose(compose(domain(compose(b,X0)),b),X0)) = compose(compose(domain(compose(b,X0)),b),X0),
inference(superposition,[status(thm)],[c_66,c_5260]) ).
tcf(c_11738,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),codomain(X0),ifeq(domain(X1),codomain(a),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_64,c_5336]) ).
tcf(c_11739,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(X1),codomain(a),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_101,c_5336]) ).
tcf(c_11741,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(h,codomain(X0))),compose(compose(compose(a,h),h),codomain(X0))),compose(compose(compose(a,h),h),codomain(X0))) = compose(compose(compose(a,h),h),codomain(X0)),
inference(superposition,[status(thm)],[c_841,c_5336]) ).
tcf(c_11742,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(b),codomain(a),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_682,c_5336]) ).
tcf(c_11778,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(domain(X0),codomain(a),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),h),compose(a,b))),compose(compose(domain(X0),h),compose(a,b))) = compose(compose(domain(X0),h),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_5344]) ).
tcf(c_11782,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(domain(X1),codomain(a),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_5344]) ).
tcf(c_11783,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(domain(X0),codomain(a),compose(domain(X0),compose(h,compose(a,h))),compose(compose(domain(X0),h),compose(a,h))),compose(compose(domain(X0),h),compose(a,h))) = compose(compose(domain(X0),h),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5344]) ).
tcf(c_11791,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(domain(compose(h,X0)),codomain(a),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_66,c_5344]) ).
tcf(c_11873,plain,
! [X0: $i,X1: $i] : ifeq(codomain(codomain(X0)),codomain(X1),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),codomain(X1))),compose(compose(g,codomain(X0)),codomain(X1))),compose(compose(g,codomain(X0)),codomain(X1))) = compose(compose(g,codomain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_65,c_6002]) ).
tcf(c_11874,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),codomain(X0))),compose(compose(g,compose(a,b)),codomain(X0))),compose(compose(g,compose(a,b)),codomain(X0))) = compose(compose(g,compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_368,c_6002]) ).
tcf(c_11878,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),codomain(X1))),compose(compose(g,domain(X0)),codomain(X1))),compose(compose(g,domain(X0)),codomain(X1))) = compose(compose(g,domain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_100,c_6002]) ).
tcf(c_11879,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),codomain(X0))),compose(compose(g,compose(a,h)),codomain(X0))),compose(compose(g,compose(a,h)),codomain(X0))) = compose(compose(g,compose(a,h)),codomain(X0)),
inference(superposition,[status(thm)],[c_506,c_6002]) ).
tcf(c_11914,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),codomain(X1))),compose(compose(g,domain(X0)),codomain(X1))),compose(compose(g,domain(X0)),codomain(X1))) = compose(compose(g,domain(X0)),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_11878,c_64]) ).
tcf(c_11915,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),codomain(X1))),compose(compose(g,codomain(X0)),codomain(X1))),compose(compose(g,codomain(X0)),codomain(X1))) = compose(compose(g,codomain(X0)),codomain(X1)),
inference(light_normalisation,[status(thm)],[c_11873,c_101]) ).
tcf(c_11921,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),codomain(X0))),compose(compose(g,compose(a,h)),codomain(X0))),compose(compose(g,compose(a,h)),codomain(X0))) = compose(compose(g,compose(a,h)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_11879,c_841]) ).
tcf(c_11922,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),codomain(X0))),compose(compose(g,compose(a,b)),codomain(X0))),compose(compose(g,compose(a,b)),codomain(X0))) = compose(compose(g,compose(a,b)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_11874,c_682]) ).
tcf(c_11935,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),compose(a,b))),compose(compose(g,codomain(X0)),compose(a,b))),compose(compose(g,codomain(X0)),compose(a,b))) = compose(compose(g,codomain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_6050]) ).
tcf(c_11939,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),domain(X1))),compose(compose(g,codomain(X0)),domain(X1))),compose(compose(g,codomain(X0)),domain(X1))) = compose(compose(g,codomain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_6050]) ).
tcf(c_11940,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),compose(a,h))),compose(compose(g,codomain(X0)),compose(a,h))),compose(compose(g,codomain(X0)),compose(a,h))) = compose(compose(g,codomain(X0)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_6050]) ).
tcf(c_12001,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),codomain(X0),ifeq(domain(X1),codomain(a),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_64,c_6150]) ).
tcf(c_12002,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(X1),codomain(a),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_101,c_6150]) ).
tcf(c_12004,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(g,codomain(X0))),compose(compose(compose(a,h),g),codomain(X0))),compose(compose(compose(a,h),g),codomain(X0))) = compose(compose(compose(a,h),g),codomain(X0)),
inference(superposition,[status(thm)],[c_841,c_6150]) ).
tcf(c_12005,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(b),codomain(a),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_682,c_6150]) ).
tcf(c_12080,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(domain(X0),codomain(a),compose(domain(X0),compose(g,compose(a,b))),compose(compose(domain(X0),g),compose(a,b))),compose(compose(domain(X0),g),compose(a,b))) = compose(compose(domain(X0),g),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_6158]) ).
tcf(c_12084,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(domain(X1),codomain(a),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_6158]) ).
tcf(c_12085,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(domain(X0),codomain(a),compose(domain(X0),compose(g,compose(a,h))),compose(compose(domain(X0),g),compose(a,h))),compose(compose(domain(X0),g),compose(a,h))) = compose(compose(domain(X0),g),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_6158]) ).
tcf(c_12093,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(domain(compose(g,X0)),codomain(a),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_66,c_6158]) ).
tcf(c_12137,plain,
ifeq(codomain(b),codomain(a),ifeq(domain(compose(b,b)),codomain(a),compose(b,b),compose(compose(domain(compose(b,b)),b),b)),compose(compose(domain(compose(b,b)),b),b)) = compose(compose(domain(compose(b,b)),b),b),
inference(superposition,[status(thm)],[c_66,c_6269]) ).
tcf(c_12170,plain,
ifeq(codomain(h),codomain(a),ifeq(domain(compose(h,b)),codomain(a),compose(h,b),compose(compose(domain(compose(h,b)),h),b)),compose(compose(domain(compose(h,b)),h),b)) = compose(compose(domain(compose(h,b)),h),b),
inference(superposition,[status(thm)],[c_66,c_6406]) ).
tcf(c_12203,plain,
ifeq(codomain(h),codomain(a),ifeq(domain(compose(g,b)),codomain(a),compose(g,b),compose(compose(domain(compose(g,b)),g),b)),compose(compose(domain(compose(g,b)),g),b)) = compose(compose(domain(compose(g,b)),g),b),
inference(superposition,[status(thm)],[c_66,c_6501]) ).
tcf(c_12236,plain,
ifeq(codomain(b),codomain(a),ifeq(domain(compose(b,h)),codomain(a),compose(b,h),compose(compose(domain(compose(b,h)),b),h)),compose(compose(domain(compose(b,h)),b),h)) = compose(compose(domain(compose(b,h)),b),h),
inference(superposition,[status(thm)],[c_66,c_6529]) ).
tcf(c_12269,plain,
ifeq(codomain(h),codomain(a),ifeq(domain(compose(h,h)),codomain(a),compose(h,h),compose(compose(domain(compose(h,h)),h),h)),compose(compose(domain(compose(h,h)),h),h)) = compose(compose(domain(compose(h,h)),h),h),
inference(superposition,[status(thm)],[c_66,c_6567]) ).
tcf(c_12302,plain,
ifeq(codomain(h),codomain(a),ifeq(domain(compose(g,h)),codomain(a),compose(g,h),compose(compose(domain(compose(g,h)),g),h)),compose(compose(domain(compose(g,h)),g),h)) = compose(compose(domain(compose(g,h)),g),h),
inference(superposition,[status(thm)],[c_66,c_6581]) ).
tcf(c_12335,plain,
ifeq(codomain(b),codomain(a),ifeq(domain(compose(b,g)),codomain(a),compose(b,g),compose(compose(domain(compose(b,g)),b),g)),compose(compose(domain(compose(b,g)),b),g)) = compose(compose(domain(compose(b,g)),b),g),
inference(superposition,[status(thm)],[c_66,c_6598]) ).
tcf(c_12368,plain,
ifeq(codomain(h),codomain(a),ifeq(domain(compose(h,g)),codomain(a),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_66,c_6620]) ).
tcf(c_12403,plain,
ifeq(codomain(h),codomain(a),ifeq(domain(compose(g,g)),codomain(a),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_66,c_6658]) ).
tcf(c_12659,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(domain(X0),compose(a,b)),X2,ifeq(compose(codomain(X1),compose(a,b)),X2,codomain(X1),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_64,c_389]) ).
tcf(c_12660,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X2,ifeq(compose(codomain(X1),compose(a,b)),X2,codomain(X1),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_389]) ).
tcf(c_12662,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X1,ifeq(compose(codomain(X0),compose(a,b)),X1,codomain(X0),compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_389]) ).
tcf(c_12663,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X1,ifeq(compose(codomain(X0),compose(a,b)),X1,codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_389]) ).
tcf(c_12921,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_65,c_5528]) ).
tcf(c_12922,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_368,c_5528]) ).
tcf(c_12926,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_5528]) ).
tcf(c_12927,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(compose(domain(X0),compose(a,h))),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),codomain(compose(domain(X0),compose(a,h))))),compose(domain(X0),compose(a,h))),compose(domain(X0),compose(a,h))) = compose(domain(X0),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5528]) ).
tcf(c_12979,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_12926,c_64]) ).
tcf(c_12980,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_12921,c_101]) ).
tcf(c_12983,plain,
! [X0: $i] : ifeq(codomain(h),codomain(compose(domain(X0),compose(a,h))),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),codomain(compose(domain(X0),compose(a,h))))),compose(domain(X0),compose(a,h))),compose(domain(X0),compose(a,h))) = compose(domain(X0),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_12927,c_841]) ).
tcf(c_12984,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_12922,c_682]) ).
tcf(c_13009,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_101,c_5597]) ).
tcf(c_13011,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(compose(compose(a,h),codomain(X0))),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),codomain(compose(compose(a,h),codomain(X0))))),compose(compose(a,h),codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(a,h),codomain(X0)),
inference(superposition,[status(thm)],[c_841,c_5597]) ).
tcf(c_13012,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_682,c_5597]) ).
tcf(c_13464,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(domain(X0),compose(a,b)),X1,ifeq(compose(compose(a,h),compose(a,b)),X1,compose(a,h),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_841,c_386]) ).
tcf(c_13465,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(domain(X0),compose(a,b)),X1,ifeq(compose(compose(a,b),compose(a,b)),X1,compose(a,b),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c_682,c_386]) ).
tcf(c_13569,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X1,ifeq(compose(compose(a,b),compose(a,b)),X1,compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_711]) ).
tcf(c_13571,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X0,ifeq(compose(compose(a,b),compose(a,b)),X0,compose(a,b),compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_711]) ).
tcf(c_13572,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X0,ifeq(compose(compose(a,b),compose(a,b)),X0,compose(a,b),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_711]) ).
tcf(c_13583,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X1,ifeq(compose(compose(a,h),compose(a,b)),X1,compose(a,h),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_101,c_859]) ).
tcf(c_13585,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X0,ifeq(compose(compose(a,h),compose(a,b)),X0,compose(a,h),compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(superposition,[status(thm)],[c_841,c_859]) ).
tcf(c_13586,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X0,ifeq(compose(compose(a,h),compose(a,b)),X0,compose(a,h),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(superposition,[status(thm)],[c_682,c_859]) ).
tcf(c_13609,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),b)),compose(compose(codomain(X0),compose(a,b)),b)),compose(compose(codomain(X0),compose(a,b)),b)) = compose(compose(codomain(X0),compose(a,b)),b),
inference(superposition,[status(thm)],[c_368,c_4548]) ).
tcf(c_13613,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(a),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),b)),compose(compose(codomain(X1),domain(X0)),b)),compose(compose(codomain(X1),domain(X0)),b)) = compose(compose(codomain(X1),domain(X0)),b),
inference(superposition,[status(thm)],[c_100,c_4548]) ).
tcf(c_13614,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),b)),compose(compose(codomain(X0),compose(a,h)),b)),compose(compose(codomain(X0),compose(a,h)),b)) = compose(compose(codomain(X0),compose(a,h)),b),
inference(superposition,[status(thm)],[c_506,c_4548]) ).
tcf(c_13651,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(a),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),b)),compose(compose(codomain(X1),domain(X0)),b)),compose(compose(codomain(X1),domain(X0)),b)) = compose(compose(codomain(X1),domain(X0)),b),
inference(light_normalisation,[status(thm)],[c_13613,c_64]) ).
tcf(c_13655,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),b)),compose(compose(codomain(X0),compose(a,h)),b)),compose(compose(codomain(X0),compose(a,h)),b)) = compose(compose(codomain(X0),compose(a,h)),b),
inference(light_normalisation,[status(thm)],[c_13614,c_841]) ).
tcf(c_13656,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),b)),compose(compose(codomain(X0),compose(a,b)),b)),compose(compose(codomain(X0),compose(a,b)),b)) = compose(compose(codomain(X0),compose(a,b)),b),
inference(light_normalisation,[status(thm)],[c_13609,c_682]) ).
tcf(c_13672,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),b)),compose(compose(compose(a,h),domain(X0)),b)),compose(compose(compose(a,h),domain(X0)),b)) = compose(compose(compose(a,h),domain(X0)),b),
inference(superposition,[status(thm)],[c_841,c_4602]) ).
tcf(c_13673,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),b)),compose(compose(compose(a,b),domain(X0)),b)),compose(compose(compose(a,b),domain(X0)),b)) = compose(compose(compose(a,b),domain(X0)),b),
inference(superposition,[status(thm)],[c_682,c_4602]) ).
tcf(c_13728,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),h)),compose(compose(codomain(X0),compose(a,b)),h)),compose(compose(codomain(X0),compose(a,b)),h)) = compose(compose(codomain(X0),compose(a,b)),h),
inference(superposition,[status(thm)],[c_368,c_4754]) ).
tcf(c_13732,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(a),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),h)),compose(compose(codomain(X1),domain(X0)),h)),compose(compose(codomain(X1),domain(X0)),h)) = compose(compose(codomain(X1),domain(X0)),h),
inference(superposition,[status(thm)],[c_100,c_4754]) ).
tcf(c_13733,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),h)),compose(compose(codomain(X0),compose(a,h)),h)),compose(compose(codomain(X0),compose(a,h)),h)) = compose(compose(codomain(X0),compose(a,h)),h),
inference(superposition,[status(thm)],[c_506,c_4754]) ).
tcf(c_13770,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(a),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),h)),compose(compose(codomain(X1),domain(X0)),h)),compose(compose(codomain(X1),domain(X0)),h)) = compose(compose(codomain(X1),domain(X0)),h),
inference(light_normalisation,[status(thm)],[c_13732,c_64]) ).
tcf(c_13774,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),h)),compose(compose(codomain(X0),compose(a,h)),h)),compose(compose(codomain(X0),compose(a,h)),h)) = compose(compose(codomain(X0),compose(a,h)),h),
inference(light_normalisation,[status(thm)],[c_13733,c_841]) ).
tcf(c_13775,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),h)),compose(compose(codomain(X0),compose(a,b)),h)),compose(compose(codomain(X0),compose(a,b)),h)) = compose(compose(codomain(X0),compose(a,b)),h),
inference(light_normalisation,[status(thm)],[c_13728,c_682]) ).
tcf(c_13791,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),h)),compose(compose(compose(a,h),domain(X0)),h)),compose(compose(compose(a,h),domain(X0)),h)) = compose(compose(compose(a,h),domain(X0)),h),
inference(superposition,[status(thm)],[c_841,c_4808]) ).
tcf(c_13792,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),h)),compose(compose(compose(a,b),domain(X0)),h)),compose(compose(compose(a,b),domain(X0)),h)) = compose(compose(compose(a,b),domain(X0)),h),
inference(superposition,[status(thm)],[c_682,c_4808]) ).
tcf(c_13846,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(a),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_368,c_5004]) ).
tcf(c_13850,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),codomain(a),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_5004]) ).
tcf(c_13851,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),g)),compose(compose(codomain(X0),compose(a,h)),g)),compose(compose(codomain(X0),compose(a,h)),g)) = compose(compose(codomain(X0),compose(a,h)),g),
inference(superposition,[status(thm)],[c_506,c_5004]) ).
tcf(c_13891,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(a),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_13850,c_64]) ).
tcf(c_13895,plain,
! [X0: $i] : ifeq(codomain(h),codomain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),g)),compose(compose(codomain(X0),compose(a,h)),g)),compose(compose(codomain(X0),compose(a,h)),g)) = compose(compose(codomain(X0),compose(a,h)),g),
inference(light_normalisation,[status(thm)],[c_13851,c_841]) ).
tcf(c_13896,plain,
! [X0: $i] : ifeq(codomain(b),codomain(a),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_13846,c_682]) ).
tcf(c_13912,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),g)),compose(compose(compose(a,h),domain(X0)),g)),compose(compose(compose(a,h),domain(X0)),g)) = compose(compose(compose(a,h),domain(X0)),g),
inference(superposition,[status(thm)],[c_841,c_5059]) ).
tcf(c_13913,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),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_682,c_5059]) ).
tcf(c_13964,plain,
! [X0: $i,X1: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),codomain(a),compose(codomain(X1),compose(b,domain(X0))),compose(compose(codomain(X1),b),domain(X0))),compose(compose(codomain(X1),b),domain(X0))) = compose(compose(codomain(X1),b),domain(X0)),
inference(superposition,[status(thm)],[c_101,c_5257]) ).
tcf(c_13966,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(b,domain(X0))),compose(compose(compose(a,h),b),domain(X0))),compose(compose(compose(a,h),b),domain(X0))) = compose(compose(compose(a,h),b),domain(X0)),
inference(superposition,[status(thm)],[c_841,c_5257]) ).
tcf(c_13967,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(b,domain(X0))),compose(compose(compose(a,b),b),domain(X0))),compose(compose(compose(a,b),b),domain(X0))) = compose(compose(compose(a,b),b),domain(X0)),
inference(superposition,[status(thm)],[c_682,c_5257]) ).
tcf(c_14000,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(b,compose(a,b))),compose(compose(codomain(X0),b),compose(a,b))),compose(compose(codomain(X0),b),compose(a,b))) = compose(compose(codomain(X0),b),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_5261]) ).
tcf(c_14005,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(b,compose(a,h))),compose(compose(codomain(X0),b),compose(a,h))),compose(compose(codomain(X0),b),compose(a,h))) = compose(compose(codomain(X0),b),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5261]) ).
tcf(c_14047,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),codomain(a),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_101,c_5341]) ).
tcf(c_14049,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(h,domain(X0))),compose(compose(compose(a,h),h),domain(X0))),compose(compose(compose(a,h),h),domain(X0))) = compose(compose(compose(a,h),h),domain(X0)),
inference(superposition,[status(thm)],[c_841,c_5341]) ).
tcf(c_14050,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(b),codomain(a),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_682,c_5341]) ).
tcf(c_14090,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,compose(a,b))),compose(compose(compose(a,h),X0),compose(a,b))),compose(compose(compose(a,h),X0),compose(a,b))) = compose(compose(compose(a,h),X0),compose(a,b)),
inference(superposition,[status(thm)],[c_841,c_434]) ).
tcf(c_14091,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_682,c_434]) ).
tcf(c_14093,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_368,c_434]) ).
tcf(c_14098,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),compose(a,b))),compose(compose(X0,compose(a,h)),compose(a,b))),compose(compose(X0,compose(a,h)),compose(a,b))) = compose(compose(X0,compose(a,h)),compose(a,b)),
inference(superposition,[status(thm)],[c_506,c_434]) ).
tcf(c_14147,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),compose(a,b))),compose(compose(X0,compose(a,h)),compose(a,b))),compose(compose(X0,compose(a,h)),compose(a,b))) = compose(compose(X0,compose(a,h)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_14098,c_841]) ).
tcf(c_14148,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_14093,c_682]) ).
tcf(c_14169,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,compose(a,h))),compose(compose(compose(a,h),X0),compose(a,h))),compose(compose(compose(a,h),X0),compose(a,h))) = compose(compose(compose(a,h),X0),compose(a,h)),
inference(superposition,[status(thm)],[c_841,c_543]) ).
tcf(c_14170,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,compose(a,h))),compose(compose(compose(a,b),X0),compose(a,h))),compose(compose(compose(a,b),X0),compose(a,h))) = compose(compose(compose(a,b),X0),compose(a,h)),
inference(superposition,[status(thm)],[c_682,c_543]) ).
tcf(c_14172,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(a,h))),compose(compose(X0,compose(a,b)),compose(a,h))),compose(compose(X0,compose(a,b)),compose(a,h))) = compose(compose(X0,compose(a,b)),compose(a,h)),
inference(superposition,[status(thm)],[c_368,c_543]) ).
tcf(c_14177,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),compose(a,h))),compose(compose(X0,compose(a,h)),compose(a,h))),compose(compose(X0,compose(a,h)),compose(a,h))) = compose(compose(X0,compose(a,h)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_543]) ).
tcf(c_14226,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),compose(a,h))),compose(compose(X0,compose(a,h)),compose(a,h))),compose(compose(X0,compose(a,h)),compose(a,h))) = compose(compose(X0,compose(a,h)),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_14177,c_841]) ).
tcf(c_14227,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(a,h))),compose(compose(X0,compose(a,b)),compose(a,h))),compose(compose(X0,compose(a,b)),compose(a,h))) = compose(compose(X0,compose(a,b)),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_14172,c_682]) ).
tcf(c_14584,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_368,c_713]) ).
tcf(c_14589,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),X0)),compose(compose(compose(a,b),compose(a,h)),X0)),compose(compose(compose(a,b),compose(a,h)),X0)) = compose(compose(compose(a,b),compose(a,h)),X0),
inference(superposition,[status(thm)],[c_506,c_713]) ).
tcf(c_14627,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),X0)),compose(compose(compose(a,b),compose(a,h)),X0)),compose(compose(compose(a,b),compose(a,h)),X0)) = compose(compose(compose(a,b),compose(a,h)),X0),
inference(light_normalisation,[status(thm)],[c_14589,c_841]) ).
tcf(c_14628,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_14584,c_682]) ).
tcf(c_14803,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),h),compose(a,b))),compose(compose(codomain(X0),h),compose(a,b))) = compose(compose(codomain(X0),h),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_5345]) ).
tcf(c_14808,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(h,compose(a,h))),compose(compose(codomain(X0),h),compose(a,h))),compose(compose(codomain(X0),h),compose(a,h))) = compose(compose(codomain(X0),h),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5345]) ).
tcf(c_14887,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),domain(X0))),compose(compose(g,compose(a,b)),domain(X0))),compose(compose(g,compose(a,b)),domain(X0))) = compose(compose(g,compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_368,c_6007]) ).
tcf(c_14891,plain,
! [X0: $i,X1: $i] : ifeq(codomain(domain(X0)),domain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),domain(X1))),compose(compose(g,domain(X0)),domain(X1))),compose(compose(g,domain(X0)),domain(X1))) = compose(compose(g,domain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_100,c_6007]) ).
tcf(c_14892,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),domain(X0))),compose(compose(g,compose(a,h)),domain(X0))),compose(compose(g,compose(a,h)),domain(X0))) = compose(compose(g,compose(a,h)),domain(X0)),
inference(superposition,[status(thm)],[c_506,c_6007]) ).
tcf(c_14924,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),domain(X1))),compose(compose(g,domain(X0)),domain(X1))),compose(compose(g,domain(X0)),domain(X1))) = compose(compose(g,domain(X0)),domain(X1)),
inference(light_normalisation,[status(thm)],[c_14891,c_64]) ).
tcf(c_14929,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),domain(X0))),compose(compose(g,compose(a,h)),domain(X0))),compose(compose(g,compose(a,h)),domain(X0))) = compose(compose(g,compose(a,h)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_14892,c_841]) ).
tcf(c_14930,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),domain(X0))),compose(compose(g,compose(a,b)),domain(X0))),compose(compose(g,compose(a,b)),domain(X0))) = compose(compose(g,compose(a,b)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_14887,c_682]) ).
tcf(c_14946,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),X0)),compose(compose(compose(a,h),compose(a,b)),X0)),compose(compose(compose(a,h),compose(a,b)),X0)) = compose(compose(compose(a,h),compose(a,b)),X0),
inference(superposition,[status(thm)],[c_841,c_721]) ).
tcf(c_14972,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),compose(a,b))),compose(compose(g,domain(X0)),compose(a,b))),compose(compose(g,domain(X0)),compose(a,b))) = compose(compose(g,domain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_6049]) ).
tcf(c_14977,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),compose(a,h))),compose(compose(g,domain(X0)),compose(a,h))),compose(compose(g,domain(X0)),compose(a,h))) = compose(compose(g,domain(X0)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_6049]) ).
tcf(c_15031,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),codomain(a),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_101,c_6155]) ).
tcf(c_15033,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(g,domain(X0))),compose(compose(compose(a,h),g),domain(X0))),compose(compose(compose(a,h),g),domain(X0))) = compose(compose(compose(a,h),g),domain(X0)),
inference(superposition,[status(thm)],[c_841,c_6155]) ).
tcf(c_15034,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(b),codomain(a),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_682,c_6155]) ).
tcf(c_15137,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(g,compose(a,b))),compose(compose(codomain(X0),g),compose(a,b))),compose(compose(codomain(X0),g),compose(a,b))) = compose(compose(codomain(X0),g),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_6159]) ).
tcf(c_15142,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),codomain(a),compose(codomain(X0),compose(g,compose(a,h))),compose(compose(codomain(X0),g),compose(a,h))),compose(compose(codomain(X0),g),compose(a,h))) = compose(compose(codomain(X0),g),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_6159]) ).
tcf(c_15718,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),X0)),compose(compose(compose(a,h),compose(a,h)),X0)),compose(compose(compose(a,h),compose(a,h)),X0)) = compose(compose(compose(a,h),compose(a,h)),X0),
inference(superposition,[status(thm)],[c_506,c_861]) ).
tcf(c_15756,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),X0)),compose(compose(compose(a,h),compose(a,h)),X0)),compose(compose(compose(a,h),compose(a,h)),X0)) = compose(compose(compose(a,h),compose(a,h)),X0),
inference(light_normalisation,[status(thm)],[c_15718,c_841]) ).
tcf(c_16070,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_65,c_9364]) ).
tcf(c_16071,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_368,c_9364]) ).
tcf(c_16075,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_9364]) ).
tcf(c_16076,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,h)),codomain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,h),codomain(X0))),compose(compose(domain(X1),compose(a,h)),codomain(X0))),compose(compose(domain(X1),compose(a,h)),codomain(X0))) = compose(compose(domain(X1),compose(a,h)),codomain(X0)),
inference(superposition,[status(thm)],[c_506,c_9364]) ).
tcf(c_16077,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_66,c_9364]) ).
tcf(c_16142,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_16075,c_64]) ).
tcf(c_16143,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_16070,c_101]) ).
tcf(c_16149,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),codomain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,h),codomain(X0))),compose(compose(domain(X1),compose(a,h)),codomain(X0))),compose(compose(domain(X1),compose(a,h)),codomain(X0))) = compose(compose(domain(X1),compose(a,h)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_16076,c_841]) ).
tcf(c_16150,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_16071,c_682]) ).
tcf(c_16198,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_101,c_9445]) ).
tcf(c_16200,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),codomain(X1))),compose(compose(compose(a,h),codomain(X0)),codomain(X1))),compose(compose(compose(a,h),codomain(X0)),codomain(X1))) = compose(compose(compose(a,h),codomain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_841,c_9445]) ).
tcf(c_16201,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_682,c_9445]) ).
tcf(c_16322,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_65,c_9518]) ).
tcf(c_16323,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_368,c_9518]) ).
tcf(c_16327,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_9518]) ).
tcf(c_16328,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,h),domain(X0))),compose(compose(domain(X1),compose(a,h)),domain(X0))),compose(compose(domain(X1),compose(a,h)),domain(X0))) = compose(compose(domain(X1),compose(a,h)),domain(X0)),
inference(superposition,[status(thm)],[c_506,c_9518]) ).
tcf(c_16329,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_66,c_9518]) ).
tcf(c_16392,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_16327,c_64]) ).
tcf(c_16393,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_16322,c_101]) ).
tcf(c_16397,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,h),domain(X0))),compose(compose(domain(X1),compose(a,h)),domain(X0))),compose(compose(domain(X1),compose(a,h)),domain(X0))) = compose(compose(domain(X1),compose(a,h)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_16328,c_841]) ).
tcf(c_16398,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_16323,c_682]) ).
tcf(c_16511,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_101,c_9593]) ).
tcf(c_16513,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),domain(X1))),compose(compose(compose(a,h),codomain(X0)),domain(X1))),compose(compose(compose(a,h),codomain(X0)),domain(X1))) = compose(compose(compose(a,h),codomain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_841,c_9593]) ).
tcf(c_16514,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_682,c_9593]) ).
tcf(c_16616,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_368,c_10107]) ).
tcf(c_16621,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),compose(a,h))),compose(compose(domain(X1),codomain(X0)),compose(a,h))),compose(compose(domain(X1),codomain(X0)),compose(a,h))) = compose(compose(domain(X1),codomain(X0)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_10107]) ).
tcf(c_16634,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_66,c_10107]) ).
tcf(c_16740,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_368,c_10321]) ).
tcf(c_16745,plain,
! [X0: $i,X1: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),compose(a,h))),compose(compose(codomain(X1),codomain(X0)),compose(a,h))),compose(compose(codomain(X1),codomain(X0)),compose(a,h))) = compose(compose(codomain(X1),codomain(X0)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_10321]) ).
tcf(c_16864,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(domain(compose(codomain(X0),b)),codomain(X0),compose(codomain(X0),b),compose(compose(domain(compose(codomain(X0),b)),codomain(X0)),b)),compose(compose(domain(compose(codomain(X0),b)),codomain(X0)),b)) = compose(compose(domain(compose(codomain(X0),b)),codomain(X0)),b),
inference(superposition,[status(thm)],[c_66,c_10783]) ).
tcf(c_17006,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),ifeq(domain(compose(codomain(X0),h)),codomain(X0),compose(codomain(X0),h),compose(compose(domain(compose(codomain(X0),h)),codomain(X0)),h)),compose(compose(domain(compose(codomain(X0),h)),codomain(X0)),h)) = compose(compose(domain(compose(codomain(X0),h)),codomain(X0)),h),
inference(superposition,[status(thm)],[c_66,c_11036]) ).
tcf(c_17138,plain,
! [X0: $i] : ifeq(codomain(X0),codomain(a),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_66,c_11465]) ).
tcf(c_17227,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(domain(compose(b,codomain(X0))),codomain(a),compose(b,codomain(X0)),compose(compose(domain(compose(b,codomain(X0))),b),codomain(X0))),compose(compose(domain(compose(b,codomain(X0))),b),codomain(X0))) = compose(compose(domain(compose(b,codomain(X0))),b),codomain(X0)),
inference(superposition,[status(thm)],[c_66,c_11557]) ).
tcf(c_17289,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),ifeq(domain(compose(h,codomain(X0))),codomain(a),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_66,c_11738]) ).
tcf(c_17411,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),ifeq(domain(compose(g,codomain(X0))),codomain(a),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_66,c_12001]) ).
tcf(c_17549,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_368,c_5529]) ).
tcf(c_17553,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_5529]) ).
tcf(c_17554,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(compose(codomain(X0),compose(a,h))),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),codomain(compose(codomain(X0),compose(a,h))))),compose(codomain(X0),compose(a,h))),compose(codomain(X0),compose(a,h))) = compose(codomain(X0),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5529]) ).
tcf(c_17597,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_17553,c_64]) ).
tcf(c_17601,plain,
! [X0: $i] : ifeq(codomain(h),codomain(compose(codomain(X0),compose(a,h))),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),codomain(compose(codomain(X0),compose(a,h))))),compose(codomain(X0),compose(a,h))),compose(codomain(X0),compose(a,h))) = compose(codomain(X0),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_17554,c_841]) ).
tcf(c_17602,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_17549,c_682]) ).
tcf(c_17627,plain,
! [X0: $i] : ifeq(domain(X0),codomain(compose(compose(a,h),domain(X0))),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),codomain(compose(compose(a,h),domain(X0))))),compose(compose(a,h),domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(a,h),domain(X0)),
inference(superposition,[status(thm)],[c_841,c_5596]) ).
tcf(c_17628,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_682,c_5596]) ).
tcf(c_18169,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_368,c_10039]) ).
tcf(c_18174,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(compose(X0,compose(a,h))),domain(X0),compose(X0,compose(a,h)),compose(compose(domain(compose(X0,compose(a,h))),X0),compose(a,h))),compose(compose(domain(compose(X0,compose(a,h))),X0),compose(a,h))) = compose(compose(domain(compose(X0,compose(a,h))),X0),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_10039]) ).
tcf(c_18191,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_368,c_10039]) ).
tcf(c_18195,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_10039]) ).
tcf(c_18196,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(domain(compose(compose(a,h),X0)),domain(a),compose(compose(a,h),X0),compose(compose(domain(compose(compose(a,h),X0)),compose(a,h)),X0)),compose(compose(domain(compose(compose(a,h),X0)),compose(a,h)),X0)) = compose(compose(domain(compose(compose(a,h),X0)),compose(a,h)),X0),
inference(superposition,[status(thm)],[c_506,c_10039]) ).
tcf(c_18251,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_18195,c_64]) ).
tcf(c_18259,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(domain(compose(compose(a,h),X0)),domain(a),compose(compose(a,h),X0),compose(compose(domain(compose(compose(a,h),X0)),compose(a,h)),X0)),compose(compose(domain(compose(compose(a,h),X0)),compose(a,h)),X0)) = compose(compose(domain(compose(compose(a,h),X0)),compose(a,h)),X0),
inference(light_normalisation,[status(thm)],[c_18196,c_841]) ).
tcf(c_18260,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_18191,c_682]) ).
tcf(c_18279,plain,
ifeq(codomain(compose(a,b)),codomain(a),ifeq(domain(compose(compose(a,b),b)),domain(a),compose(compose(a,b),b),compose(compose(domain(compose(compose(a,b),b)),compose(a,b)),b)),compose(compose(domain(compose(compose(a,b),b)),compose(a,b)),b)) = compose(compose(domain(compose(compose(a,b),b)),compose(a,b)),b),
inference(superposition,[status(thm)],[c_368,c_10738]) ).
tcf(c_18283,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(a),ifeq(domain(compose(domain(X0),b)),domain(X0),compose(domain(X0),b),compose(compose(domain(compose(domain(X0),b)),domain(X0)),b)),compose(compose(domain(compose(domain(X0),b)),domain(X0)),b)) = compose(compose(domain(compose(domain(X0),b)),domain(X0)),b),
inference(superposition,[status(thm)],[c_100,c_10738]) ).
tcf(c_18284,plain,
ifeq(codomain(compose(a,h)),codomain(a),ifeq(domain(compose(compose(a,h),b)),domain(a),compose(compose(a,h),b),compose(compose(domain(compose(compose(a,h),b)),compose(a,h)),b)),compose(compose(domain(compose(compose(a,h),b)),compose(a,h)),b)) = compose(compose(domain(compose(compose(a,h),b)),compose(a,h)),b),
inference(superposition,[status(thm)],[c_506,c_10738]) ).
tcf(c_18298,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),ifeq(domain(compose(domain(X0),b)),domain(X0),compose(domain(X0),b),compose(compose(domain(compose(domain(X0),b)),domain(X0)),b)),compose(compose(domain(compose(domain(X0),b)),domain(X0)),b)) = compose(compose(domain(compose(domain(X0),b)),domain(X0)),b),
inference(light_normalisation,[status(thm)],[c_18283,c_64]) ).
tcf(c_18302,plain,
ifeq(codomain(h),codomain(a),ifeq(domain(compose(compose(a,h),b)),domain(a),compose(compose(a,h),b),compose(compose(domain(compose(compose(a,h),b)),compose(a,h)),b)),compose(compose(domain(compose(compose(a,h),b)),compose(a,h)),b)) = compose(compose(domain(compose(compose(a,h),b)),compose(a,h)),b),
inference(light_normalisation,[status(thm)],[c_18284,c_841]) ).
tcf(c_18303,plain,
ifeq(codomain(b),codomain(a),ifeq(domain(compose(compose(a,b),b)),domain(a),compose(compose(a,b),b),compose(compose(domain(compose(compose(a,b),b)),compose(a,b)),b)),compose(compose(domain(compose(compose(a,b),b)),compose(a,b)),b)) = compose(compose(domain(compose(compose(a,b),b)),compose(a,b)),b),
inference(light_normalisation,[status(thm)],[c_18279,c_682]) ).
tcf(c_18317,plain,
ifeq(codomain(compose(a,b)),codomain(a),ifeq(domain(compose(compose(a,b),h)),domain(a),compose(compose(a,b),h),compose(compose(domain(compose(compose(a,b),h)),compose(a,b)),h)),compose(compose(domain(compose(compose(a,b),h)),compose(a,b)),h)) = compose(compose(domain(compose(compose(a,b),h)),compose(a,b)),h),
inference(superposition,[status(thm)],[c_368,c_10991]) ).
tcf(c_18321,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(a),ifeq(domain(compose(domain(X0),h)),domain(X0),compose(domain(X0),h),compose(compose(domain(compose(domain(X0),h)),domain(X0)),h)),compose(compose(domain(compose(domain(X0),h)),domain(X0)),h)) = compose(compose(domain(compose(domain(X0),h)),domain(X0)),h),
inference(superposition,[status(thm)],[c_100,c_10991]) ).
tcf(c_18322,plain,
ifeq(codomain(compose(a,h)),codomain(a),ifeq(domain(compose(compose(a,h),h)),domain(a),compose(compose(a,h),h),compose(compose(domain(compose(compose(a,h),h)),compose(a,h)),h)),compose(compose(domain(compose(compose(a,h),h)),compose(a,h)),h)) = compose(compose(domain(compose(compose(a,h),h)),compose(a,h)),h),
inference(superposition,[status(thm)],[c_506,c_10991]) ).
tcf(c_18336,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),ifeq(domain(compose(domain(X0),h)),domain(X0),compose(domain(X0),h),compose(compose(domain(compose(domain(X0),h)),domain(X0)),h)),compose(compose(domain(compose(domain(X0),h)),domain(X0)),h)) = compose(compose(domain(compose(domain(X0),h)),domain(X0)),h),
inference(light_normalisation,[status(thm)],[c_18321,c_64]) ).
tcf(c_18340,plain,
ifeq(codomain(h),codomain(a),ifeq(domain(compose(compose(a,h),h)),domain(a),compose(compose(a,h),h),compose(compose(domain(compose(compose(a,h),h)),compose(a,h)),h)),compose(compose(domain(compose(compose(a,h),h)),compose(a,h)),h)) = compose(compose(domain(compose(compose(a,h),h)),compose(a,h)),h),
inference(light_normalisation,[status(thm)],[c_18322,c_841]) ).
tcf(c_18341,plain,
ifeq(codomain(b),codomain(a),ifeq(domain(compose(compose(a,b),h)),domain(a),compose(compose(a,b),h),compose(compose(domain(compose(compose(a,b),h)),compose(a,b)),h)),compose(compose(domain(compose(compose(a,b),h)),compose(a,b)),h)) = compose(compose(domain(compose(compose(a,b),h)),compose(a,b)),h),
inference(light_normalisation,[status(thm)],[c_18317,c_682]) ).
tcf(c_18364,plain,
ifeq(codomain(compose(a,b)),codomain(a),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_368,c_11418]) ).
tcf(c_18368,plain,
! [X0: $i] : ifeq(codomain(domain(X0)),codomain(a),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_11418]) ).
tcf(c_18369,plain,
ifeq(codomain(compose(a,h)),codomain(a),ifeq(domain(compose(compose(a,h),g)),domain(a),compose(compose(a,h),g),compose(compose(domain(compose(compose(a,h),g)),compose(a,h)),g)),compose(compose(domain(compose(compose(a,h),g)),compose(a,h)),g)) = compose(compose(domain(compose(compose(a,h),g)),compose(a,h)),g),
inference(superposition,[status(thm)],[c_506,c_11418]) ).
tcf(c_18386,plain,
! [X0: $i] : ifeq(domain(X0),codomain(a),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_18368,c_64]) ).
tcf(c_18390,plain,
ifeq(codomain(h),codomain(a),ifeq(domain(compose(compose(a,h),g)),domain(a),compose(compose(a,h),g),compose(compose(domain(compose(compose(a,h),g)),compose(a,h)),g)),compose(compose(domain(compose(compose(a,h),g)),compose(a,h)),g)) = compose(compose(domain(compose(compose(a,h),g)),compose(a,h)),g),
inference(light_normalisation,[status(thm)],[c_18369,c_841]) ).
tcf(c_18391,plain,
ifeq(codomain(b),codomain(a),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_18364,c_682]) ).
tcf(c_18405,plain,
ifeq(codomain(b),domain(a),ifeq(domain(compose(b,compose(a,b))),codomain(a),compose(b,compose(a,b)),compose(compose(domain(compose(b,compose(a,b))),b),compose(a,b))),compose(compose(domain(compose(b,compose(a,b))),b),compose(a,b))) = compose(compose(domain(compose(b,compose(a,b))),b),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_11668]) ).
tcf(c_18409,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(domain(compose(b,domain(X0))),codomain(a),compose(b,domain(X0)),compose(compose(domain(compose(b,domain(X0))),b),domain(X0))),compose(compose(domain(compose(b,domain(X0))),b),domain(X0))) = compose(compose(domain(compose(b,domain(X0))),b),domain(X0)),
inference(superposition,[status(thm)],[c_100,c_11668]) ).
tcf(c_18410,plain,
ifeq(codomain(b),domain(a),ifeq(domain(compose(b,compose(a,h))),codomain(a),compose(b,compose(a,h)),compose(compose(domain(compose(b,compose(a,h))),b),compose(a,h))),compose(compose(domain(compose(b,compose(a,h))),b),compose(a,h))) = compose(compose(domain(compose(b,compose(a,h))),b),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_11668]) ).
tcf(c_18418,plain,
ifeq(codomain(h),domain(a),ifeq(domain(compose(h,compose(a,b))),codomain(a),compose(h,compose(a,b)),compose(compose(domain(compose(h,compose(a,b))),h),compose(a,b))),compose(compose(domain(compose(h,compose(a,b))),h),compose(a,b))) = compose(compose(domain(compose(h,compose(a,b))),h),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_11791]) ).
tcf(c_18422,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(domain(compose(h,domain(X0))),codomain(a),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_11791]) ).
tcf(c_18423,plain,
ifeq(codomain(h),domain(a),ifeq(domain(compose(h,compose(a,h))),codomain(a),compose(h,compose(a,h)),compose(compose(domain(compose(h,compose(a,h))),h),compose(a,h))),compose(compose(domain(compose(h,compose(a,h))),h),compose(a,h))) = compose(compose(domain(compose(h,compose(a,h))),h),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_11791]) ).
tcf(c_18439,plain,
ifeq(codomain(h),domain(a),ifeq(domain(compose(g,compose(a,b))),codomain(a),compose(g,compose(a,b)),compose(compose(domain(compose(g,compose(a,b))),g),compose(a,b))),compose(compose(domain(compose(g,compose(a,b))),g),compose(a,b))) = compose(compose(domain(compose(g,compose(a,b))),g),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_12093]) ).
tcf(c_18443,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(domain(compose(g,domain(X0))),codomain(a),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_12093]) ).
tcf(c_18444,plain,
ifeq(codomain(h),domain(a),ifeq(domain(compose(g,compose(a,h))),codomain(a),compose(g,compose(a,h)),compose(compose(domain(compose(g,compose(a,h))),g),compose(a,h))),compose(compose(domain(compose(g,compose(a,h))),g),compose(a,h))) = compose(compose(domain(compose(g,compose(a,h))),g),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_12093]) ).
tcf(c_18605,plain,
ifeq(codomain(compose(a,b)),codomain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),b)),compose(compose(compose(a,h),compose(a,b)),b)),compose(compose(compose(a,h),compose(a,b)),b)) = compose(compose(compose(a,h),compose(a,b)),b),
inference(superposition,[status(thm)],[c_368,c_4550]) ).
tcf(c_18610,plain,
ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),b)),compose(compose(compose(a,h),compose(a,h)),b)),compose(compose(compose(a,h),compose(a,h)),b)) = compose(compose(compose(a,h),compose(a,h)),b),
inference(superposition,[status(thm)],[c_506,c_4550]) ).
tcf(c_18626,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),b)),compose(compose(compose(a,h),compose(a,h)),b)),compose(compose(compose(a,h),compose(a,h)),b)) = compose(compose(compose(a,h),compose(a,h)),b),
inference(light_normalisation,[status(thm)],[c_18610,c_841]) ).
tcf(c_18627,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),b)),compose(compose(compose(a,h),compose(a,b)),b)),compose(compose(compose(a,h),compose(a,b)),b)) = compose(compose(compose(a,h),compose(a,b)),b),
inference(light_normalisation,[status(thm)],[c_18605,c_682]) ).
tcf(c_18638,plain,
ifeq(codomain(compose(a,b)),codomain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),b)),compose(compose(compose(a,b),compose(a,b)),b)),compose(compose(compose(a,b),compose(a,b)),b)) = compose(compose(compose(a,b),compose(a,b)),b),
inference(superposition,[status(thm)],[c_368,c_4551]) ).
tcf(c_18643,plain,
ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),b)),compose(compose(compose(a,b),compose(a,h)),b)),compose(compose(compose(a,b),compose(a,h)),b)) = compose(compose(compose(a,b),compose(a,h)),b),
inference(superposition,[status(thm)],[c_506,c_4551]) ).
tcf(c_18659,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),b)),compose(compose(compose(a,b),compose(a,h)),b)),compose(compose(compose(a,b),compose(a,h)),b)) = compose(compose(compose(a,b),compose(a,h)),b),
inference(light_normalisation,[status(thm)],[c_18643,c_841]) ).
tcf(c_18660,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),b)),compose(compose(compose(a,b),compose(a,b)),b)),compose(compose(compose(a,b),compose(a,b)),b)) = compose(compose(compose(a,b),compose(a,b)),b),
inference(light_normalisation,[status(thm)],[c_18638,c_682]) ).
tcf(c_18693,plain,
ifeq(codomain(compose(a,b)),codomain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),h)),compose(compose(compose(a,h),compose(a,b)),h)),compose(compose(compose(a,h),compose(a,b)),h)) = compose(compose(compose(a,h),compose(a,b)),h),
inference(superposition,[status(thm)],[c_368,c_4756]) ).
tcf(c_18698,plain,
ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),h)),compose(compose(compose(a,h),compose(a,h)),h)),compose(compose(compose(a,h),compose(a,h)),h)) = compose(compose(compose(a,h),compose(a,h)),h),
inference(superposition,[status(thm)],[c_506,c_4756]) ).
tcf(c_18714,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),h)),compose(compose(compose(a,h),compose(a,h)),h)),compose(compose(compose(a,h),compose(a,h)),h)) = compose(compose(compose(a,h),compose(a,h)),h),
inference(light_normalisation,[status(thm)],[c_18698,c_841]) ).
tcf(c_18715,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),h)),compose(compose(compose(a,h),compose(a,b)),h)),compose(compose(compose(a,h),compose(a,b)),h)) = compose(compose(compose(a,h),compose(a,b)),h),
inference(light_normalisation,[status(thm)],[c_18693,c_682]) ).
tcf(c_18726,plain,
ifeq(codomain(compose(a,b)),codomain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),h)),compose(compose(compose(a,b),compose(a,b)),h)),compose(compose(compose(a,b),compose(a,b)),h)) = compose(compose(compose(a,b),compose(a,b)),h),
inference(superposition,[status(thm)],[c_368,c_4757]) ).
tcf(c_18731,plain,
ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),h)),compose(compose(compose(a,b),compose(a,h)),h)),compose(compose(compose(a,b),compose(a,h)),h)) = compose(compose(compose(a,b),compose(a,h)),h),
inference(superposition,[status(thm)],[c_506,c_4757]) ).
tcf(c_18747,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),h)),compose(compose(compose(a,b),compose(a,h)),h)),compose(compose(compose(a,b),compose(a,h)),h)) = compose(compose(compose(a,b),compose(a,h)),h),
inference(light_normalisation,[status(thm)],[c_18731,c_841]) ).
tcf(c_18748,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),h)),compose(compose(compose(a,b),compose(a,b)),h)),compose(compose(compose(a,b),compose(a,b)),h)) = compose(compose(compose(a,b),compose(a,b)),h),
inference(light_normalisation,[status(thm)],[c_18726,c_682]) ).
tcf(c_18780,plain,
ifeq(codomain(compose(a,b)),codomain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),g)),compose(compose(compose(a,h),compose(a,b)),g)),compose(compose(compose(a,h),compose(a,b)),g)) = compose(compose(compose(a,h),compose(a,b)),g),
inference(superposition,[status(thm)],[c_368,c_5006]) ).
tcf(c_18785,plain,
ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),g)),compose(compose(compose(a,h),compose(a,h)),g)),compose(compose(compose(a,h),compose(a,h)),g)) = compose(compose(compose(a,h),compose(a,h)),g),
inference(superposition,[status(thm)],[c_506,c_5006]) ).
tcf(c_18804,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),g)),compose(compose(compose(a,h),compose(a,h)),g)),compose(compose(compose(a,h),compose(a,h)),g)) = compose(compose(compose(a,h),compose(a,h)),g),
inference(light_normalisation,[status(thm)],[c_18785,c_841]) ).
tcf(c_18805,plain,
ifeq(codomain(b),codomain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),g)),compose(compose(compose(a,h),compose(a,b)),g)),compose(compose(compose(a,h),compose(a,b)),g)) = compose(compose(compose(a,h),compose(a,b)),g),
inference(light_normalisation,[status(thm)],[c_18780,c_682]) ).
tcf(c_18815,plain,
ifeq(codomain(compose(a,b)),codomain(a),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_368,c_5007]) ).
tcf(c_18820,plain,
ifeq(codomain(compose(a,h)),codomain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),g)),compose(compose(compose(a,b),compose(a,h)),g)),compose(compose(compose(a,b),compose(a,h)),g)) = compose(compose(compose(a,b),compose(a,h)),g),
inference(superposition,[status(thm)],[c_506,c_5007]) ).
tcf(c_18839,plain,
ifeq(codomain(h),codomain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),g)),compose(compose(compose(a,b),compose(a,h)),g)),compose(compose(compose(a,b),compose(a,h)),g)) = compose(compose(compose(a,b),compose(a,h)),g),
inference(light_normalisation,[status(thm)],[c_18820,c_841]) ).
tcf(c_18840,plain,
ifeq(codomain(b),codomain(a),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_18815,c_682]) ).
tcf(c_18869,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(b,compose(a,b))),compose(compose(compose(a,h),b),compose(a,b))),compose(compose(compose(a,h),b),compose(a,b))) = compose(compose(compose(a,h),b),compose(a,b)),
inference(superposition,[status(thm)],[c_841,c_5253]) ).
tcf(c_18870,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(b,compose(a,b))),compose(compose(compose(a,b),b),compose(a,b))),compose(compose(compose(a,b),b),compose(a,b))) = compose(compose(compose(a,b),b),compose(a,b)),
inference(superposition,[status(thm)],[c_682,c_5253]) ).
tcf(c_18881,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(b,compose(a,h))),compose(compose(compose(a,h),b),compose(a,h))),compose(compose(compose(a,h),b),compose(a,h))) = compose(compose(compose(a,h),b),compose(a,h)),
inference(superposition,[status(thm)],[c_841,c_5258]) ).
tcf(c_18882,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(b,compose(a,h))),compose(compose(compose(a,b),b),compose(a,h))),compose(compose(compose(a,b),b),compose(a,h))) = compose(compose(compose(a,b),b),compose(a,h)),
inference(superposition,[status(thm)],[c_682,c_5258]) ).
tcf(c_18915,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(h,compose(a,b))),compose(compose(compose(a,h),h),compose(a,b))),compose(compose(compose(a,h),h),compose(a,b))) = compose(compose(compose(a,h),h),compose(a,b)),
inference(superposition,[status(thm)],[c_841,c_5337]) ).
tcf(c_18916,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),h),compose(a,b))),compose(compose(compose(a,b),h),compose(a,b))) = compose(compose(compose(a,b),h),compose(a,b)),
inference(superposition,[status(thm)],[c_682,c_5337]) ).
tcf(c_18927,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(h,compose(a,h))),compose(compose(compose(a,h),h),compose(a,h))),compose(compose(compose(a,h),h),compose(a,h))) = compose(compose(compose(a,h),h),compose(a,h)),
inference(superposition,[status(thm)],[c_841,c_5342]) ).
tcf(c_18928,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(h,compose(a,h))),compose(compose(compose(a,b),h),compose(a,h))),compose(compose(compose(a,b),h),compose(a,h))) = compose(compose(compose(a,b),h),compose(a,h)),
inference(superposition,[status(thm)],[c_682,c_5342]) ).
tcf(c_18963,plain,
ifeq(codomain(compose(a,b)),domain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),compose(a,b))),compose(compose(g,compose(a,b)),compose(a,b))),compose(compose(g,compose(a,b)),compose(a,b))) = compose(compose(g,compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_6003]) ).
tcf(c_18968,plain,
ifeq(codomain(compose(a,h)),domain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),compose(a,b))),compose(compose(g,compose(a,h)),compose(a,b))),compose(compose(g,compose(a,h)),compose(a,b))) = compose(compose(g,compose(a,h)),compose(a,b)),
inference(superposition,[status(thm)],[c_506,c_6003]) ).
tcf(c_18982,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),compose(a,b))),compose(compose(g,compose(a,h)),compose(a,b))),compose(compose(g,compose(a,h)),compose(a,b))) = compose(compose(g,compose(a,h)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_18968,c_841]) ).
tcf(c_18983,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),compose(a,b))),compose(compose(g,compose(a,b)),compose(a,b))),compose(compose(g,compose(a,b)),compose(a,b))) = compose(compose(g,compose(a,b)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_18963,c_682]) ).
tcf(c_18993,plain,
ifeq(codomain(compose(a,b)),domain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),compose(a,h))),compose(compose(g,compose(a,b)),compose(a,h))),compose(compose(g,compose(a,b)),compose(a,h))) = compose(compose(g,compose(a,b)),compose(a,h)),
inference(superposition,[status(thm)],[c_368,c_6008]) ).
tcf(c_18998,plain,
ifeq(codomain(compose(a,h)),domain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),compose(a,h))),compose(compose(g,compose(a,h)),compose(a,h))),compose(compose(g,compose(a,h)),compose(a,h))) = compose(compose(g,compose(a,h)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_6008]) ).
tcf(c_19012,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),compose(a,h))),compose(compose(g,compose(a,h)),compose(a,h))),compose(compose(g,compose(a,h)),compose(a,h))) = compose(compose(g,compose(a,h)),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_18998,c_841]) ).
tcf(c_19013,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),compose(a,h))),compose(compose(g,compose(a,b)),compose(a,h))),compose(compose(g,compose(a,b)),compose(a,h))) = compose(compose(g,compose(a,b)),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_18993,c_682]) ).
tcf(c_19045,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(g,compose(a,b))),compose(compose(compose(a,h),g),compose(a,b))),compose(compose(compose(a,h),g),compose(a,b))) = compose(compose(compose(a,h),g),compose(a,b)),
inference(superposition,[status(thm)],[c_841,c_6151]) ).
tcf(c_19046,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(g,compose(a,b))),compose(compose(compose(a,b),g),compose(a,b))),compose(compose(compose(a,b),g),compose(a,b))) = compose(compose(compose(a,b),g),compose(a,b)),
inference(superposition,[status(thm)],[c_682,c_6151]) ).
tcf(c_19060,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),codomain(a),compose(compose(a,h),compose(g,compose(a,h))),compose(compose(compose(a,h),g),compose(a,h))),compose(compose(compose(a,h),g),compose(a,h))) = compose(compose(compose(a,h),g),compose(a,h)),
inference(superposition,[status(thm)],[c_841,c_6156]) ).
tcf(c_19061,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),codomain(a),compose(compose(a,b),compose(g,compose(a,h))),compose(compose(compose(a,b),g),compose(a,h))),compose(compose(compose(a,b),g),compose(a,h))) = compose(compose(compose(a,b),g),compose(a,h)),
inference(superposition,[status(thm)],[c_682,c_6156]) ).
tcf(c_19207,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_66,c_16143]) ).
tcf(c_19297,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_66,c_16393]) ).
tcf(c_19498,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_368,c_9365]) ).
tcf(c_19502,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_9365]) ).
tcf(c_19503,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,h)),codomain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,h),codomain(X0))),compose(compose(codomain(X1),compose(a,h)),codomain(X0))),compose(compose(codomain(X1),compose(a,h)),codomain(X0))) = compose(compose(codomain(X1),compose(a,h)),codomain(X0)),
inference(superposition,[status(thm)],[c_506,c_9365]) ).
tcf(c_19562,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_19502,c_64]) ).
tcf(c_19569,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,h),codomain(X0))),compose(compose(codomain(X1),compose(a,h)),codomain(X0))),compose(compose(codomain(X1),compose(a,h)),codomain(X0))) = compose(compose(codomain(X1),compose(a,h)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_19503,c_841]) ).
tcf(c_19570,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_19498,c_682]) ).
tcf(c_19592,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),codomain(X1),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),codomain(X1))),compose(compose(compose(a,h),domain(X0)),codomain(X1))),compose(compose(compose(a,h),domain(X0)),codomain(X1))) = compose(compose(compose(a,h),domain(X0)),codomain(X1)),
inference(superposition,[status(thm)],[c_841,c_9444]) ).
tcf(c_19593,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_682,c_9444]) ).
tcf(c_19671,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_368,c_9519]) ).
tcf(c_19675,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_9519]) ).
tcf(c_19676,plain,
! [X0: $i,X1: $i] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,h),domain(X0))),compose(compose(codomain(X1),compose(a,h)),domain(X0))),compose(compose(codomain(X1),compose(a,h)),domain(X0))) = compose(compose(codomain(X1),compose(a,h)),domain(X0)),
inference(superposition,[status(thm)],[c_506,c_9519]) ).
tcf(c_19733,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_19675,c_64]) ).
tcf(c_19738,plain,
! [X0: $i,X1: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,h),domain(X0))),compose(compose(codomain(X1),compose(a,h)),domain(X0))),compose(compose(codomain(X1),compose(a,h)),domain(X0))) = compose(compose(codomain(X1),compose(a,h)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_19676,c_841]) ).
tcf(c_19739,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_19671,c_682]) ).
tcf(c_19766,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),domain(X1))),compose(compose(compose(a,h),domain(X0)),domain(X1))),compose(compose(compose(a,h),domain(X0)),domain(X1))) = compose(compose(compose(a,h),domain(X0)),domain(X1)),
inference(superposition,[status(thm)],[c_841,c_9592]) ).
tcf(c_19767,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_682,c_9592]) ).
tcf(c_19841,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_368,c_10106]) ).
tcf(c_19846,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),compose(a,h))),compose(compose(domain(X1),domain(X0)),compose(a,h))),compose(compose(domain(X1),domain(X0)),compose(a,h))) = compose(compose(domain(X1),domain(X0)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_10106]) ).
tcf(c_19936,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_368,c_10320]) ).
tcf(c_19941,plain,
! [X0: $i,X1: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),compose(a,h))),compose(compose(codomain(X1),domain(X0)),compose(a,h))),compose(compose(codomain(X1),domain(X0)),compose(a,h))) = compose(compose(codomain(X1),domain(X0)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_10320]) ).
tcf(c_20291,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_368,c_16077]) ).
tcf(c_20295,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_16077]) ).
tcf(c_20296,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(X0),ifeq(domain(compose(compose(a,h),codomain(X0))),domain(a),compose(compose(a,h),codomain(X0)),compose(compose(domain(compose(compose(a,h),codomain(X0))),compose(a,h)),codomain(X0))),compose(compose(domain(compose(compose(a,h),codomain(X0))),compose(a,h)),codomain(X0))) = compose(compose(domain(compose(compose(a,h),codomain(X0))),compose(a,h)),codomain(X0)),
inference(superposition,[status(thm)],[c_506,c_16077]) ).
tcf(c_20350,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_20295,c_64]) ).
tcf(c_20354,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),ifeq(domain(compose(compose(a,h),codomain(X0))),domain(a),compose(compose(a,h),codomain(X0)),compose(compose(domain(compose(compose(a,h),codomain(X0))),compose(a,h)),codomain(X0))),compose(compose(domain(compose(compose(a,h),codomain(X0))),compose(a,h)),codomain(X0))) = compose(compose(domain(compose(compose(a,h),codomain(X0))),compose(a,h)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_20296,c_841]) ).
tcf(c_20355,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_20291,c_682]) ).
tcf(c_20383,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_368,c_16329]) ).
tcf(c_20387,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_16329]) ).
tcf(c_20388,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(domain(compose(compose(a,h),domain(X0))),domain(a),compose(compose(a,h),domain(X0)),compose(compose(domain(compose(compose(a,h),domain(X0))),compose(a,h)),domain(X0))),compose(compose(domain(compose(compose(a,h),domain(X0))),compose(a,h)),domain(X0))) = compose(compose(domain(compose(compose(a,h),domain(X0))),compose(a,h)),domain(X0)),
inference(superposition,[status(thm)],[c_506,c_16329]) ).
tcf(c_20434,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_20387,c_64]) ).
tcf(c_20438,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(domain(compose(compose(a,h),domain(X0))),domain(a),compose(compose(a,h),domain(X0)),compose(compose(domain(compose(compose(a,h),domain(X0))),compose(a,h)),domain(X0))),compose(compose(domain(compose(compose(a,h),domain(X0))),compose(a,h)),domain(X0))) = compose(compose(domain(compose(compose(a,h),domain(X0))),compose(a,h)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_20388,c_841]) ).
tcf(c_20439,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_20383,c_682]) ).
tcf(c_20451,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_368,c_16634]) ).
tcf(c_20456,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(domain(compose(codomain(X0),compose(a,h))),codomain(X0),compose(codomain(X0),compose(a,h)),compose(compose(domain(compose(codomain(X0),compose(a,h))),codomain(X0)),compose(a,h))),compose(compose(domain(compose(codomain(X0),compose(a,h))),codomain(X0)),compose(a,h))) = compose(compose(domain(compose(codomain(X0),compose(a,h))),codomain(X0)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_16634]) ).
tcf(c_22054,plain,
ifeq(codomain(compose(a,b)),codomain(compose(compose(a,h),compose(a,b))),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),codomain(compose(compose(a,h),compose(a,b))))),compose(compose(a,h),compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_5531]) ).
tcf(c_22059,plain,
ifeq(codomain(compose(a,h)),codomain(compose(compose(a,h),compose(a,h))),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),codomain(compose(compose(a,h),compose(a,h))))),compose(compose(a,h),compose(a,h))),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5531]) ).
tcf(c_22074,plain,
ifeq(codomain(h),codomain(compose(compose(a,h),compose(a,h))),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),codomain(compose(compose(a,h),compose(a,h))))),compose(compose(a,h),compose(a,h))),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_22059,c_841]) ).
tcf(c_22075,plain,
ifeq(codomain(b),codomain(compose(compose(a,h),compose(a,b))),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),codomain(compose(compose(a,h),compose(a,b))))),compose(compose(a,h),compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_22054,c_682]) ).
tcf(c_22086,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_368,c_5532]) ).
tcf(c_22091,plain,
ifeq(codomain(compose(a,h)),codomain(compose(compose(a,b),compose(a,h))),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),codomain(compose(compose(a,b),compose(a,h))))),compose(compose(a,b),compose(a,h))),compose(compose(a,b),compose(a,h))) = compose(compose(a,b),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_5532]) ).
tcf(c_22106,plain,
ifeq(codomain(h),codomain(compose(compose(a,b),compose(a,h))),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),codomain(compose(compose(a,b),compose(a,h))))),compose(compose(a,b),compose(a,h))),compose(compose(a,b),compose(a,h))) = compose(compose(a,b),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_22091,c_841]) ).
tcf(c_22107,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_22086,c_682]) ).
tcf(c_22610,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),codomain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),codomain(X0))),compose(compose(compose(a,h),compose(a,b)),codomain(X0))),compose(compose(compose(a,h),compose(a,b)),codomain(X0))) = compose(compose(compose(a,h),compose(a,b)),codomain(X0)),
inference(superposition,[status(thm)],[c_368,c_9367]) ).
tcf(c_22615,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),codomain(X0))),compose(compose(compose(a,h),compose(a,h)),codomain(X0))),compose(compose(compose(a,h),compose(a,h)),codomain(X0))) = compose(compose(compose(a,h),compose(a,h)),codomain(X0)),
inference(superposition,[status(thm)],[c_506,c_9367]) ).
tcf(c_22658,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),codomain(X0))),compose(compose(compose(a,h),compose(a,h)),codomain(X0))),compose(compose(compose(a,h),compose(a,h)),codomain(X0))) = compose(compose(compose(a,h),compose(a,h)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_22615,c_841]) ).
tcf(c_22659,plain,
! [X0: $i] : ifeq(codomain(b),codomain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),codomain(X0))),compose(compose(compose(a,h),compose(a,b)),codomain(X0))),compose(compose(compose(a,h),compose(a,b)),codomain(X0))) = compose(compose(compose(a,h),compose(a,b)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_22610,c_682]) ).
tcf(c_22676,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_368,c_9368]) ).
tcf(c_22681,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),codomain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),codomain(X0))),compose(compose(compose(a,b),compose(a,h)),codomain(X0))),compose(compose(compose(a,b),compose(a,h)),codomain(X0))) = compose(compose(compose(a,b),compose(a,h)),codomain(X0)),
inference(superposition,[status(thm)],[c_506,c_9368]) ).
tcf(c_22724,plain,
! [X0: $i] : ifeq(codomain(h),codomain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),codomain(X0))),compose(compose(compose(a,b),compose(a,h)),codomain(X0))),compose(compose(compose(a,b),compose(a,h)),codomain(X0))) = compose(compose(compose(a,b),compose(a,h)),codomain(X0)),
inference(light_normalisation,[status(thm)],[c_22681,c_841]) ).
tcf(c_22725,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_22676,c_682]) ).
tcf(c_22825,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),domain(X0))),compose(compose(compose(a,h),compose(a,b)),domain(X0))),compose(compose(compose(a,h),compose(a,b)),domain(X0))) = compose(compose(compose(a,h),compose(a,b)),domain(X0)),
inference(superposition,[status(thm)],[c_368,c_9521]) ).
tcf(c_22830,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),domain(X0))),compose(compose(compose(a,h),compose(a,h)),domain(X0))),compose(compose(compose(a,h),compose(a,h)),domain(X0))) = compose(compose(compose(a,h),compose(a,h)),domain(X0)),
inference(superposition,[status(thm)],[c_506,c_9521]) ).
tcf(c_22867,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),domain(X0))),compose(compose(compose(a,h),compose(a,h)),domain(X0))),compose(compose(compose(a,h),compose(a,h)),domain(X0))) = compose(compose(compose(a,h),compose(a,h)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_22830,c_841]) ).
tcf(c_22868,plain,
! [X0: $i] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),domain(X0))),compose(compose(compose(a,h),compose(a,b)),domain(X0))),compose(compose(compose(a,h),compose(a,b)),domain(X0))) = compose(compose(compose(a,h),compose(a,b)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_22825,c_682]) ).
tcf(c_22886,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_368,c_9522]) ).
tcf(c_22891,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),domain(X0))),compose(compose(compose(a,b),compose(a,h)),domain(X0))),compose(compose(compose(a,b),compose(a,h)),domain(X0))) = compose(compose(compose(a,b),compose(a,h)),domain(X0)),
inference(superposition,[status(thm)],[c_506,c_9522]) ).
tcf(c_22928,plain,
! [X0: $i] : ifeq(codomain(h),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),domain(X0))),compose(compose(compose(a,b),compose(a,h)),domain(X0))),compose(compose(compose(a,b),compose(a,h)),domain(X0))) = compose(compose(compose(a,b),compose(a,h)),domain(X0)),
inference(light_normalisation,[status(thm)],[c_22891,c_841]) ).
tcf(c_22929,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_22886,c_682]) ).
tcf(c_23032,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_368,c_10016]) ).
tcf(c_23037,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),compose(a,b))),compose(compose(domain(X0),compose(a,h)),compose(a,b))),compose(compose(domain(X0),compose(a,h)),compose(a,b))) = compose(compose(domain(X0),compose(a,h)),compose(a,b)),
inference(superposition,[status(thm)],[c_506,c_10016]) ).
tcf(c_23083,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),compose(a,b))),compose(compose(domain(X0),compose(a,h)),compose(a,b))),compose(compose(domain(X0),compose(a,h)),compose(a,b))) = compose(compose(domain(X0),compose(a,h)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_23037,c_841]) ).
tcf(c_23084,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_23032,c_682]) ).
tcf(c_23104,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),compose(a,h))),compose(compose(domain(X0),compose(a,b)),compose(a,h))),compose(compose(domain(X0),compose(a,b)),compose(a,h))) = compose(compose(domain(X0),compose(a,b)),compose(a,h)),
inference(superposition,[status(thm)],[c_368,c_10021]) ).
tcf(c_23109,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),compose(a,h))),compose(compose(domain(X0),compose(a,h)),compose(a,h))),compose(compose(domain(X0),compose(a,h)),compose(a,h))) = compose(compose(domain(X0),compose(a,h)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_10021]) ).
tcf(c_23155,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),compose(a,h))),compose(compose(domain(X0),compose(a,h)),compose(a,h))),compose(compose(domain(X0),compose(a,h)),compose(a,h))) = compose(compose(domain(X0),compose(a,h)),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_23109,c_841]) ).
tcf(c_23156,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),compose(a,h))),compose(compose(domain(X0),compose(a,b)),compose(a,h))),compose(compose(domain(X0),compose(a,b)),compose(a,h))) = compose(compose(domain(X0),compose(a,b)),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_23104,c_682]) ).
tcf(c_23273,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_368,c_10244]) ).
tcf(c_23278,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),compose(a,b))),compose(compose(codomain(X0),compose(a,h)),compose(a,b))),compose(compose(codomain(X0),compose(a,h)),compose(a,b))) = compose(compose(codomain(X0),compose(a,h)),compose(a,b)),
inference(superposition,[status(thm)],[c_506,c_10244]) ).
tcf(c_23317,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),compose(a,b))),compose(compose(codomain(X0),compose(a,h)),compose(a,b))),compose(compose(codomain(X0),compose(a,h)),compose(a,b))) = compose(compose(codomain(X0),compose(a,h)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_23278,c_841]) ).
tcf(c_23318,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_23273,c_682]) ).
tcf(c_23335,plain,
! [X0: $i] : ifeq(codomain(compose(a,b)),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),compose(a,h))),compose(compose(codomain(X0),compose(a,b)),compose(a,h))),compose(compose(codomain(X0),compose(a,b)),compose(a,h))) = compose(compose(codomain(X0),compose(a,b)),compose(a,h)),
inference(superposition,[status(thm)],[c_368,c_10249]) ).
tcf(c_23340,plain,
! [X0: $i] : ifeq(codomain(compose(a,h)),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),compose(a,h))),compose(compose(codomain(X0),compose(a,h)),compose(a,h))),compose(compose(codomain(X0),compose(a,h)),compose(a,h))) = compose(compose(codomain(X0),compose(a,h)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_10249]) ).
tcf(c_23379,plain,
! [X0: $i] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),compose(a,h))),compose(compose(codomain(X0),compose(a,h)),compose(a,h))),compose(compose(codomain(X0),compose(a,h)),compose(a,h))) = compose(compose(codomain(X0),compose(a,h)),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_23340,c_841]) ).
tcf(c_23380,plain,
! [X0: $i] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),compose(a,h))),compose(compose(codomain(X0),compose(a,b)),compose(a,h))),compose(compose(codomain(X0),compose(a,b)),compose(a,h))) = compose(compose(codomain(X0),compose(a,b)),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_23335,c_682]) ).
tcf(c_23465,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),compose(a,b))),compose(compose(compose(a,h),domain(X0)),compose(a,b))),compose(compose(compose(a,h),domain(X0)),compose(a,b))) = compose(compose(compose(a,h),domain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_841,c_10399]) ).
tcf(c_23466,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_682,c_10399]) ).
tcf(c_23474,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_66,c_10399]) ).
tcf(c_23522,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),compose(a,h))),compose(compose(compose(a,h),domain(X0)),compose(a,h))),compose(compose(compose(a,h),domain(X0)),compose(a,h))) = compose(compose(compose(a,h),domain(X0)),compose(a,h)),
inference(superposition,[status(thm)],[c_841,c_10404]) ).
tcf(c_23523,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),compose(a,h))),compose(compose(compose(a,b),domain(X0)),compose(a,h))),compose(compose(compose(a,b),domain(X0)),compose(a,h))) = compose(compose(compose(a,b),domain(X0)),compose(a,h)),
inference(superposition,[status(thm)],[c_682,c_10404]) ).
tcf(c_23531,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(codomain(domain(compose(domain(X0),compose(a,h)))),domain(X0),compose(domain(X0),compose(a,h)),compose(compose(domain(compose(domain(X0),compose(a,h))),domain(X0)),compose(a,h))),compose(compose(domain(compose(domain(X0),compose(a,h))),domain(X0)),compose(a,h))) = compose(compose(domain(compose(domain(X0),compose(a,h))),domain(X0)),compose(a,h)),
inference(superposition,[status(thm)],[c_66,c_10404]) ).
tcf(c_23693,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),compose(a,b))),compose(compose(compose(a,h),codomain(X0)),compose(a,b))),compose(compose(compose(a,h),codomain(X0)),compose(a,b))) = compose(compose(compose(a,h),codomain(X0)),compose(a,b)),
inference(superposition,[status(thm)],[c_841,c_10518]) ).
tcf(c_23694,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_682,c_10518]) ).
tcf(c_23746,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),compose(a,h))),compose(compose(compose(a,h),codomain(X0)),compose(a,h))),compose(compose(compose(a,h),codomain(X0)),compose(a,h))) = compose(compose(compose(a,h),codomain(X0)),compose(a,h)),
inference(superposition,[status(thm)],[c_841,c_10523]) ).
tcf(c_23747,plain,
! [X0: $i] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),compose(a,h))),compose(compose(compose(a,b),codomain(X0)),compose(a,h))),compose(compose(compose(a,b),codomain(X0)),compose(a,h))) = compose(compose(compose(a,b),codomain(X0)),compose(a,h)),
inference(superposition,[status(thm)],[c_682,c_10523]) ).
tcf(c_25086,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_23474,c_64]) ).
tcf(c_25260,plain,
! [X0: $i] : ifeq(domain(X0),domain(a),ifeq(domain(compose(domain(X0),compose(a,h))),domain(X0),compose(domain(X0),compose(a,h)),compose(compose(domain(compose(domain(X0),compose(a,h))),domain(X0)),compose(a,h))),compose(compose(domain(compose(domain(X0),compose(a,h))),domain(X0)),compose(a,h))) = compose(compose(domain(compose(domain(X0),compose(a,h))),domain(X0)),compose(a,h)),
inference(demodulation,[status(thm)],[c_23531,c_64]) ).
tcf(c_26392,plain,
ifeq(codomain(compose(a,b)),domain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),compose(a,b))),compose(compose(compose(a,h),compose(a,b)),compose(a,b))),compose(compose(compose(a,h),compose(a,b)),compose(a,b))) = compose(compose(compose(a,h),compose(a,b)),compose(a,b)),
inference(superposition,[status(thm)],[c_368,c_14090]) ).
tcf(c_26397,plain,
ifeq(codomain(compose(a,h)),domain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),compose(a,b))),compose(compose(compose(a,h),compose(a,h)),compose(a,b))),compose(compose(compose(a,h),compose(a,h)),compose(a,b))) = compose(compose(compose(a,h),compose(a,h)),compose(a,b)),
inference(superposition,[status(thm)],[c_506,c_14090]) ).
tcf(c_26411,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),compose(a,b))),compose(compose(compose(a,h),compose(a,h)),compose(a,b))),compose(compose(compose(a,h),compose(a,h)),compose(a,b))) = compose(compose(compose(a,h),compose(a,h)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_26397,c_841]) ).
tcf(c_26412,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),compose(a,b))),compose(compose(compose(a,h),compose(a,b)),compose(a,b))),compose(compose(compose(a,h),compose(a,b)),compose(a,b))) = compose(compose(compose(a,h),compose(a,b)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_26392,c_682]) ).
tcf(c_26422,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_368,c_14091]) ).
tcf(c_26427,plain,
ifeq(codomain(compose(a,h)),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),compose(a,b))),compose(compose(compose(a,b),compose(a,h)),compose(a,b))),compose(compose(compose(a,b),compose(a,h)),compose(a,b))) = compose(compose(compose(a,b),compose(a,h)),compose(a,b)),
inference(superposition,[status(thm)],[c_506,c_14091]) ).
tcf(c_26441,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),compose(a,b))),compose(compose(compose(a,b),compose(a,h)),compose(a,b))),compose(compose(compose(a,b),compose(a,h)),compose(a,b))) = compose(compose(compose(a,b),compose(a,h)),compose(a,b)),
inference(light_normalisation,[status(thm)],[c_26427,c_841]) ).
tcf(c_26442,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_26422,c_682]) ).
tcf(c_26451,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(domain(compose(compose(a,h),compose(a,b)))),domain(a),compose(compose(a,h),compose(a,b)),compose(compose(domain(compose(compose(a,h),compose(a,b))),compose(a,h)),compose(a,b))),compose(compose(domain(compose(compose(a,h),compose(a,b))),compose(a,h)),compose(a,b))) = compose(compose(domain(compose(compose(a,h),compose(a,b))),compose(a,h)),compose(a,b)),
inference(superposition,[status(thm)],[c_66,c_14147]) ).
tcf(c_26462,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_66,c_14148]) ).
tcf(c_26468,plain,
ifeq(codomain(h),domain(a),ifeq(domain(compose(compose(a,h),compose(a,b))),domain(a),compose(compose(a,h),compose(a,b)),compose(compose(domain(compose(compose(a,h),compose(a,b))),compose(a,h)),compose(a,b))),compose(compose(domain(compose(compose(a,h),compose(a,b))),compose(a,h)),compose(a,b))) = compose(compose(domain(compose(compose(a,h),compose(a,b))),compose(a,h)),compose(a,b)),
inference(demodulation,[status(thm)],[c_26451,c_64]) ).
tcf(c_26475,plain,
ifeq(codomain(compose(a,b)),domain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),compose(a,h))),compose(compose(compose(a,h),compose(a,b)),compose(a,h))),compose(compose(compose(a,h),compose(a,b)),compose(a,h))) = compose(compose(compose(a,h),compose(a,b)),compose(a,h)),
inference(superposition,[status(thm)],[c_368,c_14169]) ).
tcf(c_26480,plain,
ifeq(codomain(compose(a,h)),domain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),compose(a,h))),compose(compose(compose(a,h),compose(a,h)),compose(a,h))),compose(compose(compose(a,h),compose(a,h)),compose(a,h))) = compose(compose(compose(a,h),compose(a,h)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_14169]) ).
tcf(c_26494,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),compose(a,h))),compose(compose(compose(a,h),compose(a,h)),compose(a,h))),compose(compose(compose(a,h),compose(a,h)),compose(a,h))) = compose(compose(compose(a,h),compose(a,h)),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_26480,c_841]) ).
tcf(c_26495,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),compose(a,h))),compose(compose(compose(a,h),compose(a,b)),compose(a,h))),compose(compose(compose(a,h),compose(a,b)),compose(a,h))) = compose(compose(compose(a,h),compose(a,b)),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_26475,c_682]) ).
tcf(c_26505,plain,
ifeq(codomain(compose(a,b)),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),compose(a,h))),compose(compose(compose(a,b),compose(a,b)),compose(a,h))),compose(compose(compose(a,b),compose(a,b)),compose(a,h))) = compose(compose(compose(a,b),compose(a,b)),compose(a,h)),
inference(superposition,[status(thm)],[c_368,c_14170]) ).
tcf(c_26510,plain,
ifeq(codomain(compose(a,h)),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),compose(a,h))),compose(compose(compose(a,b),compose(a,h)),compose(a,h))),compose(compose(compose(a,b),compose(a,h)),compose(a,h))) = compose(compose(compose(a,b),compose(a,h)),compose(a,h)),
inference(superposition,[status(thm)],[c_506,c_14170]) ).
tcf(c_26524,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),compose(a,h))),compose(compose(compose(a,b),compose(a,h)),compose(a,h))),compose(compose(compose(a,b),compose(a,h)),compose(a,h))) = compose(compose(compose(a,b),compose(a,h)),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_26510,c_841]) ).
tcf(c_26525,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),compose(a,h))),compose(compose(compose(a,b),compose(a,b)),compose(a,h))),compose(compose(compose(a,b),compose(a,b)),compose(a,h))) = compose(compose(compose(a,b),compose(a,b)),compose(a,h)),
inference(light_normalisation,[status(thm)],[c_26505,c_682]) ).
tcf(c_26529,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_26462,c_64]) ).
tcf(c_26535,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(domain(compose(compose(a,h),compose(a,h)))),domain(a),compose(compose(a,h),compose(a,h)),compose(compose(domain(compose(compose(a,h),compose(a,h))),compose(a,h)),compose(a,h))),compose(compose(domain(compose(compose(a,h),compose(a,h))),compose(a,h)),compose(a,h))) = compose(compose(domain(compose(compose(a,h),compose(a,h))),compose(a,h)),compose(a,h)),
inference(superposition,[status(thm)],[c_66,c_14226]) ).
tcf(c_26546,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(domain(compose(compose(a,b),compose(a,h)))),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(domain(compose(compose(a,b),compose(a,h))),compose(a,b)),compose(a,h))),compose(compose(domain(compose(compose(a,b),compose(a,h))),compose(a,b)),compose(a,h))) = compose(compose(domain(compose(compose(a,b),compose(a,h))),compose(a,b)),compose(a,h)),
inference(superposition,[status(thm)],[c_66,c_14227]) ).
tcf(c_26552,plain,
ifeq(codomain(h),domain(a),ifeq(domain(compose(compose(a,h),compose(a,h))),domain(a),compose(compose(a,h),compose(a,h)),compose(compose(domain(compose(compose(a,h),compose(a,h))),compose(a,h)),compose(a,h))),compose(compose(domain(compose(compose(a,h),compose(a,h))),compose(a,h)),compose(a,h))) = compose(compose(domain(compose(compose(a,h),compose(a,h))),compose(a,h)),compose(a,h)),
inference(demodulation,[status(thm)],[c_26535,c_64]) ).
tcf(c_27329,plain,
ifeq(codomain(b),domain(a),ifeq(domain(compose(compose(a,b),compose(a,h))),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(domain(compose(compose(a,b),compose(a,h))),compose(a,b)),compose(a,h))),compose(compose(domain(compose(compose(a,b),compose(a,h))),compose(a,b)),compose(a,h))) = compose(compose(domain(compose(compose(a,b),compose(a,h))),compose(a,b)),compose(a,h)),
inference(demodulation,[status(thm)],[c_26546,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT001-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p SAT
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 06:51:55 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p SAT
% 0.10/0.42 Running model finding
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 10.29/2.21 % SZS status Started for theBenchmark.p
% 10.29/2.21 % SZS status Satisfiable for theBenchmark.p
% 10.29/2.21
% 10.29/2.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.29/2.21
% 10.29/2.21 ------ iProver source info
% 10.29/2.21
% 10.29/2.21 git: date: 2026-07-19 20:42:38 +0200
% 10.29/2.21 git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.29/2.21 git: non_committed_changes: false
% 10.29/2.21
% 10.29/2.21 ------ Parsing...successful
% 10.29/2.21
% 10.29/2.21
% 10.29/2.21 ------ Clausification by vclausify_rel & Parsing by iProver...------ preprocesses with Option_UEQ
% 10.29/2.21
% 10.29/2.21 ------ Proving...
% 10.29/2.21 ------ Problem Properties
% 10.29/2.21
% 10.29/2.21
% 10.29/2.21 clauses 14
% 10.29/2.21 conjectures 1
% 10.29/2.21 EPR 1
% 10.29/2.21 Horn 14
% 10.29/2.21 unary 14
% 10.29/2.21 binary 0
% 10.29/2.21 lits 14
% 10.29/2.21 lits eq 14
% 10.29/2.21 fd_pure 0
% 10.29/2.21 fd_pseudo 0
% 10.29/2.21 fd_cond 0
% 10.29/2.21 fd_pseudo_cond 0
% 10.29/2.21 AC symbols 0
% 10.29/2.21
% 10.29/2.21 ------ Schedule Sat is on
% 10.29/2.21
% 10.29/2.21 ------ Input Options sat_mode off Time Limit: 30.
% 10.29/2.21
% 10.29/2.21
% 10.29/2.21 ------
% 10.29/2.21 Current options:
% 10.29/2.21 ------
% 10.29/2.21
% 10.29/2.21 ------ Input Options
% 10.29/2.21
% 10.29/2.21 --out_options all
% 10.29/2.21 --tptp_safe_out true
% 10.29/2.21 --problem_path ""
% 10.29/2.21 --include_path ""
% 10.29/2.21 --clausifier res/vclausify_rel
% 10.29/2.21 --clausifier_options --mode clausify -t 101.66 -updr off
% 10.29/2.21 --stdin false
% 10.29/2.21 --proof_out true
% 10.29/2.21 --proof_dot_file ""
% 10.29/2.21 --proof_reduce_dot []
% 10.29/2.21 --suppress_sat_res false
% 10.29/2.21 --suppress_unsat_res true
% 10.29/2.21 --stats_out none
% 10.29/2.21 --stats_mem false
% 10.29/2.21 --theory_stats_out false
% 10.29/2.21
% 10.29/2.21 ------ General Options
% 10.29/2.21
% 10.29/2.21 --fof false
% 10.29/2.21 --time_out_real 304.99
% 10.29/2.21 --time_out_virtual -1.
% 10.29/2.21 --rnd_seed 13
% 10.29/2.21 --symbol_type_check false
% 10.29/2.21 --clausify_out false
% 10.29/2.21 --sig_cnt_out false
% 10.29/2.21 --trig_cnt_out false
% 10.29/2.21 --trig_cnt_out_tolerance 1.
% 10.29/2.21 --trig_cnt_out_sk_spl false
% 10.29/2.21 --abstr_cl_out false
% 10.29/2.21
% 10.29/2.21 ------ Interactive Mode
% 10.29/2.21
% 10.29/2.21 --interactive_mode false
% 10.29/2.21 --external_ip_address ""
% 10.29/2.21 --external_port 0
% 10.29/2.21
% 10.29/2.21 ------ Global Options
% 10.29/2.21
% 10.29/2.21 --schedule sat
% 10.29/2.21 --add_important_lit false
% 10.29/2.21 --prop_solver_per_cl 500
% 10.29/2.21 --subs_bck_mult 8
% 10.29/2.21 --min_unsat_core false
% 10.29/2.21 --soft_assumptions false
% 10.29/2.21 --soft_lemma_size 3
% 10.29/2.21 --prop_impl_unit_size 0
% 10.29/2.21 --prop_impl_unit []
% 10.29/2.21 --share_sel_clauses true
% 10.29/2.21 --reset_solvers false
% 10.29/2.21 --bc_imp_inh [conj_cone]
% 10.29/2.21 --conj_cone_tolerance 3.
% 10.29/2.21 --extra_neg_conj none
% 10.29/2.21 --large_theory_mode true
% 10.29/2.21 --prolific_symb_bound 200
% 10.29/2.21 --lt_threshold 2000
% 10.29/2.21 --clause_weak_htbl true
% 10.29/2.21 --gc_record_bc_elim false
% 10.29/2.21
% 10.29/2.21 ------ Preprocessing Options
% 10.29/2.21
% 10.29/2.21 --preprocessing_flag false
% 10.29/2.21 --time_out_prep_mult 0.1
% 10.29/2.21 --splitting_mode input
% 10.29/2.21 --splitting_grd true
% 10.29/2.21 --splitting_cvd false
% 10.29/2.21 --splitting_cvd_svl false
% 10.29/2.21 --splitting_nvd 32
% 10.29/2.21 --sub_typing false
% 10.29/2.21 --prep_eq_flat_conj false
% 10.29/2.21 --prep_ineq_split false
% 10.29/2.21 --prep_eq_flat_all_gr false
% 10.29/2.21 --prep_gs_sim true
% 10.29/2.21 --prep_unflatten true
% 10.29/2.21 --prep_res_sim true
% 10.29/2.21 --prep_sup_sim_all true
% 10.29/2.21 --prep_sup_sim_sup false
% 10.29/2.21 --prep_upred true
% 10.29/2.21 --prep_well_definedness true
% 10.29/2.21 --prep_sem_filter exhaustive
% 10.29/2.21 --prep_sem_filter_out false
% 10.29/2.21 --pred_elim true
% 10.29/2.21 --res_sim_input true
% 10.29/2.21 --eq_ax_congr_red true
% 10.29/2.21 --pure_diseq_elim true
% 10.29/2.21 --brand_transform false
% 10.29/2.21 --non_eq_to_eq false
% 10.29/2.21 --prep_eq_proxy false
% 10.29/2.21 --prep_def_merge true
% 10.29/2.21 --prep_def_merge_prop_impl false
% 10.29/2.21 --prep_def_merge_mbd true
% 10.29/2.21 --prep_def_merge_tr_red false
% 10.29/2.21 --prep_def_merge_tr_cl false
% 10.29/2.21 --smt_preprocessing false
% 10.29/2.21 --smt_ac_axioms fast
% 10.29/2.21 --preprocessed_out false
% 10.29/2.21 --preprocessed_stats false
% 10.29/2.21
% 10.29/2.21 ------ Abstraction refinement Options
% 10.29/2.21
% 10.29/2.21 --abstr_ref []
% 10.29/2.21 --abstr_ref_prep false
% 10.29/2.21 --abstr_ref_until_sat false
% 10.29/2.21 --abstr_ref_sig_restrict funpre
% 10.29/2.21 --abstr_ref_af_restrict_to_split_sk false
% 10.29/2.21 --abstr_ref_under []
% 10.29/2.21
% 10.29/2.21 ------ SAT Options
% 10.29/2.21
% 10.29/2.21 --sat_mode false
% 10.29/2.21 --sat_fm_restart_options ""
% 10.29/2.21 --sat_gr_def false
% 10.29/2.21 --sat_epr_types true
% 10.29/2.21 --sat_non_cyclic_types false
% 10.29/2.21 --sat_finite_models false
% 10.29/2.21 --sat_fm_lemmas false
% 10.29/2.21 --sat_fm_prep false
% 10.29/2.21 --sat_fm_uc_incr true
% 10.29/2.21 --sat_out_model small
% 10.29/2.21 --sat_out_clauses false
% 10.29/2.21
% 10.29/2.21 ------ QBF Options
% 10.29/2.21
% 10.29/2.21 --qbf_mode false
% 10.29/2.21 --qbf_elim_univ false
% 10.29/2.21 --qbf_dom_inst none
% 10.29/2.21 --qbf_dom_pre_inst false
% 10.29/2.21 --qbf_sk_in false
% 10.29/2.21 --qbf_pred_elim true
% 10.29/2.21 --qbf_split 512
% 10.29/2.21
% 10.29/2.21 ------ BMC1 Options
% 10.29/2.21
% 10.29/2.21 --bmc1_incremental false
% 10.29/2.21 --bmc1_axioms reachable_all
% 10.29/2.21 --bmc1_min_bound 0
% 10.29/2.21 --bmc1_max_bound -1
% 10.29/2.21 --bmc1_max_bound_default -1
% 10.29/2.21 --bmc1_symbol_reachability true
% 10.29/2.21 --bmc1_property_lemmas false
% 10.29/2.21 --bmc1_k_induction false
% 10.29/2.21 --bmc1_non_equiv_states false
% 10.29/2.21 --bmc1_deadlock false
% 10.29/2.21 --bmc1_ucm false
% 10.29/2.21 --bmc1_add_unsat_core none
% 10.29/2.21 --bmc1_unsat_core_children false
% 10.29/2.21 --bmc1_unsat_core_extrapolate_axioms false
% 10.29/2.21 --bmc1_out_stat full
% 10.29/2.21 --bmc1_ground_init false
% 10.29/2.21 --bmc1_pre_inst_next_state false
% 10.29/2.21 --bmc1_pre_inst_state false
% 10.29/2.21 --bmc1_pre_inst_reach_state false
% 10.29/2.21 --bmc1_out_unsat_core false
% 10.29/2.21 --bmc1_aig_witness_out false
% 10.29/2.21 --bmc1_verbose false
% 10.29/2.21 --bmc1_dump_clauses_tptp false
% 10.29/2.21 --bmc1_dump_unsat_core_tptp false
% 10.29/2.21 --bmc1_dump_file -
% 10.29/2.21 --bmc1_ucm_expand_uc_limit 128
% 10.29/2.21 --bmc1_ucm_n_expand_iterations 6
% 10.29/2.21 --bmc1_ucm_extend_mode 1
% 10.29/2.21 --bmc1_ucm_init_mode 2
% 10.29/2.21 --bmc1_ucm_cone_mode none
% 10.29/2.21 --bmc1_ucm_reduced_relation_type 0
% 10.29/2.21 --bmc1_ucm_relax_model 4
% 10.29/2.21 --bmc1_ucm_full_tr_after_sat true
% 10.29/2.21 --bmc1_ucm_expand_neg_assumptions false
% 10.29/2.21 --bmc1_ucm_layered_model none
% 10.29/2.21 --bmc1_ucm_max_lemma_size 10
% 10.29/2.21
% 10.29/2.21 ------ AIG Options
% 10.29/2.21
% 10.29/2.21 --aig_mode false
% 10.29/2.21
% 10.29/2.21 ------ Instantiation Options
% 10.29/2.21
% 10.29/2.21 --instantiation_flag true
% 10.29/2.21 --inst_sos_flag false
% 10.29/2.21 --inst_sos_phase true
% 10.29/2.21 --inst_sos_sth_lit_sel [+prop;+non_prol_conj_symb;-eq;+ground;-num_var;-num_symb]
% 10.29/2.21 --inst_lit_sel [-sign;+ground;-num_var;-num_symb]
% 10.29/2.21 --inst_lit_sel_side num_symb
% 10.29/2.21 --inst_solver_per_active 1400
% 10.29/2.21 --inst_solver_calls_frac 1.
% 10.29/2.21 --inst_to_smt_solver true
% 10.29/2.21 --inst_passive_queue_type priority_queues
% 10.29/2.21 --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 10.29/2.21 --inst_passive_queues_freq [25;2]
% 10.29/2.21 --inst_dismatching true
% 10.29/2.21 --inst_eager_unprocessed_to_passive true
% 10.29/2.21 --inst_unprocessed_bound 1000
% 10.29/2.21 --inst_prop_sim_given true
% 10.29/2.21 --inst_prop_sim_new false
% 10.29/2.21 --inst_subs_new false
% 10.29/2.21 --inst_eq_res_simp false
% 10.29/2.21 --inst_subs_given false
% 10.29/2.21 --inst_orphan_elimination true
% 10.29/2.21 --inst_learning_loop_flag true
% 10.29/2.21 --inst_learning_start 3000
% 10.29/2.21 --inst_learning_factor 2
% 10.29/2.21 --inst_start_prop_sim_after_learn 3
% 10.29/2.21 --inst_sel_renew solver
% 10.29/2.21 --inst_lit_activity_flag true
% 10.29/2.21 --inst_restr_to_given false
% 10.29/2.21 --inst_activity_threshold 500
% 10.29/2.21
% 10.29/2.21 ------ Resolution Options
% 10.29/2.21
% 10.29/2.21 --resolution_flag true
% 10.29/2.21 --res_lit_sel neg_min
% 10.29/2.21 --res_lit_sel_side none
% 10.29/2.21 --res_ordering kbo
% 10.29/2.21 --res_to_prop_solver active
% 10.29/2.21 --res_prop_simpl_new false
% 10.29/2.21 --res_prop_simpl_given true
% 10.29/2.21 --res_to_smt_solver true
% 10.29/2.21 --res_passive_queue_type priority_queues
% 10.29/2.21 --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 10.29/2.21 --res_passive_queues_freq [15;5]
% 10.29/2.21 --res_forward_subs full
% 10.29/2.21 --res_backward_subs full
% 10.29/2.21 --res_forward_subs_resolution true
% 10.29/2.21 --res_backward_subs_resolution true
% 10.29/2.21 --res_orphan_elimination true
% 10.29/2.21 --res_time_limit 300.
% 10.29/2.21
% 10.29/2.21 ------ Superposition Options
% 10.29/2.21
% 10.29/2.21 --superposition_flag true
% 10.29/2.21 --sup_passive_queue_type priority_queues
% 10.29/2.21 --sup_passive_queues [[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]
% 10.29/2.21 --sup_passive_queues_freq [1;1;1]
% 10.29/2.21 --twee_lhs_weight 4
% 10.29/2.21 --sup_set_join false
% 10.29/2.21 --sup_set_join_goals true
% 10.29/2.21 --sup_set_join_limit 1000
% 10.29/2.21 --demod_completeness_check fast
% 10.29/2.21 --demod_use_ground true
% 10.29/2.21 --sup_unprocessed_bound 0
% 10.29/2.21 --sup_to_prop_solver passive
% 10.29/2.21 --sup_prop_simpl_new true
% 10.29/2.21 --sup_prop_simpl_given true
% 10.29/2.21 --sup_fun_splitting false
% 10.29/2.21 --sup_iter_deepening 2
% 10.29/2.21 --sup_restarts_mult 12
% 10.29/2.21 --sup_score sim_d_gen
% 10.29/2.21 --sup_share_score_frac 0.2
% 10.29/2.21 --sup_share_max_num_cl 500
% 10.29/2.21 --sup_ordering lpo
% 10.29/2.21 --sup_symb_ordering invfreq
% 10.29/2.21 --sup_term_weight default
% 10.29/2.21
% 10.29/2.21 ------ Superposition Simplification Setup
% 10.29/2.21
% 10.29/2.21 --sup_indices_passive [LightNormIndex;FwDemodIndex]
% 10.29/2.21 --sup_full_triv [SMTSimplify;PropSubs]
% 10.29/2.21 --sup_full_fw [ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability]
% 10.29/2.21 --sup_full_bw [BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes]
% 10.29/2.21 --sup_immed_triv []
% 10.29/2.21 --sup_immed_fw_main [ACNormalisation;FwLightNorm;FwUnitSubsAndRes]
% 10.29/2.21 --sup_immed_fw_immed [ACNormalisation;FwUnitSubsAndRes]
% 10.29/2.21 --sup_immed_bw_main [BwUnitSubsAndRes;BwDemod]
% 10.29/2.21 --sup_immed_bw_immed [BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes]
% 10.29/2.21 --sup_input_triv [Unflattening;SMTSimplify]
% 10.29/2.21 --sup_input_fw [FwACDemod;ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability]
% 10.29/2.21 --sup_input_bw [BwACDemod;BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes]
% 10.29/2.21 --sup_full_fixpoint true
% 10.29/2.21 --sup_main_fixpoint true
% 10.29/2.21 --sup_immed_fixpoint false
% 10.29/2.21 --sup_input_fixpoint true
% 10.29/2.21 --sup_cache_sim none
% 10.29/2.21 --sup_smt_interval 500
% 10.29/2.21 --sup_bw_gjoin_interval 0
% 10.29/2.21
% 10.29/2.21 ------ Combination Options
% 10.29/2.21
% 10.29/2.21 --comb_mode clause_based
% 10.29/2.21 --comb_inst_mult 5
% 10.29/2.21 --comb_res_mult 1
% 10.29/2.21 --comb_sup_mult 8
% 10.29/2.21 --comb_sup_deep_mult 2
% 10.29/2.21
% 10.29/2.21 ------ Debug Options
% 10.29/2.21
% 10.29/2.21 --dbg_backtrace false
% 10.29/2.21 --dbg_dump_prop_clauses false
% 10.29/2.21 --dbg_dump_prop_clauses_file -
% 10.29/2.21 --dbg_out_stat false
% 10.29/2.21 --dbg_just_parse false
% 10.29/2.21
% 10.29/2.21
% 10.29/2.21
% 10.29/2.21
% 10.29/2.21 ------ Proving...
% 10.29/2.21
% 10.29/2.21
% 10.29/2.21 % SZS status Satisfiable for theBenchmark.p
% 10.29/2.21
% 10.29/2.21 % SZS output start Saturation for theBenchmark.p
% See solution above
% 12.32/2.24
% 12.32/2.24
%------------------------------------------------------------------------------