%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT001-2 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:11:36 PM UTC 2026
% Result : Satisfiable 1.44s 1.77s
% Output : Saturation 1.44s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(codomain_of_a_equals_domain_of_b,hypothesis,
codomain(a) = domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
cnf(codomain_of_a_equals_domain_of_h,hypothesis,
codomain(a) = domain(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_h) ).
cnf(codomain_of_a_equals_domain_of_g,hypothesis,
codomain(a) = domain(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_g) ).
cnf(codomain_domain2,axiom,
( codomain(compose(X1,X2)) = codomain(X2)
| codomain(X1) != domain(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_domain2) ).
cnf(ah_equals_ag,hypothesis,
compose(a,h) = compose(a,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ah_equals_ag) ).
cnf(domain_of_codomain_is_codomain,axiom,
domain(codomain(X1)) = codomain(X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',domain_of_codomain_is_codomain) ).
cnf(codomain_of_domain_is_domain,axiom,
codomain(domain(X1)) = domain(X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_of_domain_is_domain) ).
cnf(star_property,axiom,
( compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3)
| codomain(X1) != domain(X2)
| codomain(X2) != domain(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',star_property) ).
cnf(codomain_domain1,axiom,
( domain(compose(X1,X2)) = domain(X1)
| codomain(X1) != domain(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_domain1) ).
cnf(c1,hypothesis,
( X1 = X3
| codomain(X1) != domain(compose(a,b))
| compose(X1,compose(a,b)) != X2
| codomain(X3) != domain(compose(a,b))
| compose(X3,compose(a,b)) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c1) ).
cnf(codomain_composition,axiom,
compose(X1,codomain(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_composition) ).
cnf(domain_composition,axiom,
compose(domain(X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',domain_composition) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
cnf(c_0_13,hypothesis,
codomain(a) = domain(b),
codomain_of_a_equals_domain_of_b ).
cnf(c_0_14,hypothesis,
codomain(a) = domain(h),
codomain_of_a_equals_domain_of_h ).
cnf(c_0_15,hypothesis,
domain(h) = domain(b),
inference(rw,[status(thm)],[c_0_13,c_0_14]),
[final] ).
cnf(c_0_16,hypothesis,
codomain(a) = domain(g),
codomain_of_a_equals_domain_of_g ).
cnf(c_0_17,axiom,
( codomain(compose(X1,X2)) = codomain(X2)
| codomain(X1) != domain(X2) ),
codomain_domain2,
[final] ).
cnf(c_0_18,hypothesis,
codomain(a) = domain(b),
inference(rw,[status(thm)],[c_0_14,c_0_15]),
[final] ).
cnf(c_0_19,hypothesis,
domain(g) = domain(h),
inference(rw,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_20,hypothesis,
( codomain(compose(a,X1)) = codomain(X1)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]),
[final] ).
cnf(c_0_21,hypothesis,
domain(g) = domain(b),
inference(rw,[status(thm)],[c_0_19,c_0_15]),
[final] ).
cnf(c_0_22,hypothesis,
compose(a,h) = compose(a,g),
ah_equals_ag,
[final] ).
cnf(c_0_23,axiom,
domain(codomain(X1)) = codomain(X1),
domain_of_codomain_is_codomain,
[final] ).
cnf(c_0_24,axiom,
codomain(domain(X1)) = domain(X1),
codomain_of_domain_is_domain,
[final] ).
cnf(c_0_25,axiom,
( compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3)
| codomain(X1) != domain(X2)
| codomain(X2) != domain(X3) ),
star_property,
[final] ).
cnf(c_0_26,hypothesis,
codomain(compose(a,h)) = codomain(g),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_27,axiom,
( domain(compose(X1,X2)) = domain(X1)
| codomain(X1) != domain(X2) ),
codomain_domain1,
[final] ).
cnf(c_0_28,plain,
domain(domain(X1)) = domain(X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]),
[final] ).
cnf(c_0_29,plain,
( compose(compose(X1,X2),codomain(X3)) = compose(X1,compose(X2,codomain(X3)))
| codomain(X2) != codomain(X3)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_23]),
[final] ).
cnf(c_0_30,hypothesis,
codomain(g) = codomain(h),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_15]),c_0_26]),
[final] ).
cnf(c_0_31,hypothesis,
( domain(compose(a,X1)) = domain(a)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_18]),
[final] ).
cnf(c_0_32,plain,
( compose(compose(X1,domain(X2)),X3) = compose(X1,compose(domain(X2),X3))
| domain(X2) != domain(X3)
| codomain(X1) != domain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_28]),
[final] ).
cnf(c_0_33,hypothesis,
( X1 = X3
| codomain(X1) != domain(compose(a,b))
| compose(X1,compose(a,b)) != X2
| codomain(X3) != domain(compose(a,b))
| compose(X3,compose(a,b)) != X2 ),
c1 ).
cnf(c_0_34,plain,
( compose(compose(X1,domain(X2)),codomain(X3)) = compose(X1,compose(domain(X2),codomain(X3)))
| domain(X2) != codomain(X3)
| codomain(X1) != domain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_24]),c_0_28]),
[final] ).
cnf(c_0_35,hypothesis,
codomain(compose(a,b)) = codomain(b),
inference(er,[status(thm)],[c_0_20]),
[final] ).
cnf(c_0_36,hypothesis,
codomain(compose(a,h)) = codomain(h),
inference(rw,[status(thm)],[c_0_26,c_0_30]),
[final] ).
cnf(c_0_37,hypothesis,
domain(compose(a,b)) = domain(a),
inference(er,[status(thm)],[c_0_31]),
[final] ).
cnf(c_0_38,plain,
codomain(codomain(X1)) = codomain(X1),
inference(spm,[status(thm)],[c_0_24,c_0_23]),
[final] ).
cnf(c_0_39,hypothesis,
( compose(compose(g,domain(X1)),X2) = compose(g,compose(domain(X1),X2))
| codomain(h) != domain(X1)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_30]),
[final] ).
cnf(c_0_40,hypothesis,
( compose(compose(a,domain(X1)),X2) = compose(a,compose(domain(X1),X2))
| domain(b) != domain(X1)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_18]),
[final] ).
cnf(c_0_41,hypothesis,
domain(compose(a,h)) = domain(a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_21]),c_0_22]),
[final] ).
cnf(c_0_42,hypothesis,
( X1 = X2
| compose(X1,compose(a,b)) != compose(X2,compose(a,b))
| codomain(X2) != domain(compose(a,b))
| codomain(X1) != domain(compose(a,b)) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_43,axiom,
compose(X1,codomain(X1)) = X1,
codomain_composition,
[final] ).
cnf(c_0_44,plain,
( compose(compose(X1,X2),domain(X3)) = compose(X1,compose(X2,domain(X3)))
| codomain(X2) != domain(X3)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_28]),
[final] ).
cnf(c_0_45,hypothesis,
( compose(compose(compose(a,b),domain(X1)),codomain(X2)) = compose(compose(a,b),compose(domain(X1),codomain(X2)))
| codomain(b) != domain(X1)
| domain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]),
[final] ).
cnf(c_0_46,hypothesis,
( compose(compose(compose(a,h),domain(X1)),codomain(X2)) = compose(compose(a,h),compose(domain(X1),codomain(X2)))
| codomain(h) != domain(X1)
| domain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_36]),
[final] ).
cnf(c_0_47,plain,
( compose(compose(domain(X1),domain(X2)),X3) = compose(domain(X1),compose(domain(X2),X3))
| domain(X2) != domain(X3)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_24]),
[final] ).
cnf(c_0_48,hypothesis,
( compose(compose(compose(a,b),domain(X1)),X2) = compose(compose(a,b),compose(domain(X1),X2))
| codomain(b) != domain(X1)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_35]),
[final] ).
cnf(c_0_49,hypothesis,
( compose(compose(compose(a,h),domain(X1)),X2) = compose(compose(a,h),compose(domain(X1),X2))
| codomain(h) != domain(X1)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_36]),
[final] ).
cnf(c_0_50,hypothesis,
( compose(compose(X1,X2),compose(a,b)) = compose(X1,compose(X2,compose(a,b)))
| codomain(X2) != domain(a)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_37]),
[final] ).
cnf(c_0_51,axiom,
compose(domain(X1),X1) = X1,
domain_composition,
[final] ).
cnf(c_0_52,plain,
( compose(compose(X1,codomain(X2)),X3) = compose(X1,compose(codomain(X2),X3))
| codomain(X2) != domain(X3)
| codomain(X1) != codomain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_38]),c_0_23]),
[final] ).
cnf(c_0_53,hypothesis,
( compose(compose(g,codomain(X1)),X2) = compose(g,compose(codomain(X1),X2))
| codomain(h) != codomain(X1)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_23]),
[final] ).
cnf(c_0_54,hypothesis,
( compose(compose(a,codomain(X1)),X2) = compose(a,compose(codomain(X1),X2))
| codomain(X1) != domain(b)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_23]),
[final] ).
cnf(c_0_55,hypothesis,
( compose(compose(X1,X2),compose(a,h)) = compose(X1,compose(X2,compose(a,h)))
| codomain(X2) != domain(a)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_41]),
[final] ).
cnf(c_0_56,hypothesis,
( compose(compose(X1,a),X2) = compose(X1,compose(a,X2))
| domain(b) != domain(X2)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_25,c_0_18]),
[final] ).
cnf(c_0_57,hypothesis,
( X1 = X2
| compose(X1,compose(a,b)) != compose(X2,compose(a,b))
| codomain(X2) != domain(a)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_37]),c_0_37]),
[final] ).
cnf(c_0_58,plain,
( compose(compose(X1,X2),codomain(X2)) = compose(X1,X2)
| codomain(X1) != domain(X2) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_29]),c_0_43]),
[final] ).
cnf(c_0_59,plain,
( compose(compose(X1,domain(X2)),domain(X3)) = compose(X1,compose(domain(X2),domain(X3)))
| domain(X2) != domain(X3)
| codomain(X1) != domain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_24]),c_0_28]),
[final] ).
cnf(c_0_60,hypothesis,
( compose(compose(compose(a,b),codomain(X1)),codomain(X2)) = compose(compose(a,b),compose(codomain(X1),codomain(X2)))
| codomain(b) != codomain(X1)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_23]),
[final] ).
cnf(c_0_61,hypothesis,
( compose(compose(compose(a,h),codomain(X1)),codomain(X2)) = compose(compose(a,h),compose(codomain(X1),codomain(X2)))
| codomain(h) != codomain(X1)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_23]),
[final] ).
cnf(c_0_62,hypothesis,
( compose(compose(domain(X1),domain(X2)),compose(a,b)) = compose(domain(X1),compose(domain(X2),compose(a,b)))
| domain(X2) != domain(a)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_37]),
[final] ).
cnf(c_0_63,hypothesis,
( compose(compose(domain(X1),domain(X2)),compose(a,h)) = compose(domain(X1),compose(domain(X2),compose(a,h)))
| domain(X2) != domain(a)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_41]),
[final] ).
cnf(c_0_64,hypothesis,
( compose(compose(compose(a,b),codomain(X1)),X2) = compose(compose(a,b),compose(codomain(X1),X2))
| codomain(b) != codomain(X1)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_23]),
[final] ).
cnf(c_0_65,hypothesis,
compose(compose(a,b),codomain(b)) = compose(a,b),
inference(spm,[status(thm)],[c_0_43,c_0_35]),
[final] ).
cnf(c_0_66,hypothesis,
( compose(compose(compose(a,h),codomain(X1)),X2) = compose(compose(a,h),compose(codomain(X1),X2))
| codomain(h) != codomain(X1)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_23]),
[final] ).
cnf(c_0_67,hypothesis,
compose(compose(a,h),codomain(h)) = compose(a,h),
inference(spm,[status(thm)],[c_0_43,c_0_36]),
[final] ).
cnf(c_0_68,plain,
( compose(compose(codomain(X1),domain(X2)),X3) = compose(codomain(X1),compose(domain(X2),X3))
| domain(X2) != domain(X3)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_38]),
[final] ).
cnf(c_0_69,hypothesis,
( compose(compose(domain(X1),domain(X2)),h) = compose(domain(X1),compose(domain(X2),h))
| domain(X2) != domain(b)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_15]),
[final] ).
cnf(c_0_70,hypothesis,
( compose(compose(domain(X1),domain(X2)),g) = compose(domain(X1),compose(domain(X2),g))
| domain(X2) != domain(b)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_21]),
[final] ).
cnf(c_0_71,hypothesis,
( compose(compose(X1,domain(X2)),compose(a,b)) = compose(X1,compose(domain(X2),compose(a,b)))
| domain(X2) != domain(a)
| codomain(X1) != domain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_28]),c_0_24]),
[final] ).
cnf(c_0_72,hypothesis,
compose(domain(a),compose(a,b)) = compose(a,b),
inference(spm,[status(thm)],[c_0_51,c_0_37]),
[final] ).
cnf(c_0_73,hypothesis,
( compose(compose(X1,codomain(X2)),compose(a,b)) = compose(X1,compose(codomain(X2),compose(a,b)))
| codomain(X2) != domain(a)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_37]),
[final] ).
cnf(c_0_74,plain,
compose(domain(X1),domain(X1)) = domain(X1),
inference(spm,[status(thm)],[c_0_43,c_0_24]),
[final] ).
cnf(c_0_75,hypothesis,
( compose(compose(g,codomain(X1)),codomain(X2)) = compose(g,compose(codomain(X1),codomain(X2)))
| codomain(h) != codomain(X1)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_23]),
[final] ).
cnf(c_0_76,hypothesis,
( compose(compose(a,codomain(X1)),codomain(X2)) = compose(a,compose(codomain(X1),codomain(X2)))
| codomain(X1) != domain(b)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_23]),
[final] ).
cnf(c_0_77,hypothesis,
( compose(compose(X1,domain(X2)),compose(a,h)) = compose(X1,compose(domain(X2),compose(a,h)))
| domain(X2) != domain(a)
| codomain(X1) != domain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_28]),c_0_24]),
[final] ).
cnf(c_0_78,hypothesis,
compose(domain(a),compose(a,h)) = compose(a,h),
inference(spm,[status(thm)],[c_0_51,c_0_41]),
[final] ).
cnf(c_0_79,hypothesis,
( compose(compose(X1,codomain(X2)),compose(a,h)) = compose(X1,compose(codomain(X2),compose(a,h)))
| codomain(X2) != domain(a)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_41]),
[final] ).
cnf(c_0_80,plain,
( compose(compose(domain(X1),domain(X2)),X2) = compose(domain(X1),X2)
| domain(X1) != domain(X2) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_47]),c_0_51]),
[final] ).
cnf(c_0_81,hypothesis,
compose(a,domain(b)) = a,
inference(spm,[status(thm)],[c_0_43,c_0_18]),
[final] ).
cnf(c_0_82,hypothesis,
( compose(compose(domain(X1),a),X2) = compose(domain(X1),compose(a,X2))
| domain(b) != domain(X2)
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_56,c_0_24]),
[final] ).
cnf(c_0_83,hypothesis,
compose(g,codomain(h)) = g,
inference(spm,[status(thm)],[c_0_43,c_0_30]),
[final] ).
cnf(c_0_84,hypothesis,
( compose(compose(X1,a),codomain(X2)) = compose(X1,compose(a,codomain(X2)))
| codomain(X2) != domain(b)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_29,c_0_18]),
[final] ).
cnf(c_0_85,hypothesis,
( compose(compose(X1,g),codomain(X2)) = compose(X1,compose(g,codomain(X2)))
| codomain(h) != codomain(X2)
| codomain(X1) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_21]),
[final] ).
cnf(c_0_86,hypothesis,
( X1 = a
| compose(X1,compose(a,b)) != compose(a,compose(a,b))
| domain(b) != domain(a)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_57,c_0_18]),
[final] ).
cnf(c_0_87,plain,
( compose(compose(domain(X1),X2),codomain(X2)) = compose(domain(X1),X2)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_24]),
[final] ).
cnf(c_0_88,plain,
( domain(compose(domain(X1),X2)) = domain(X1)
| domain(X1) != domain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_24]),c_0_28]),
[final] ).
cnf(c_0_89,plain,
( codomain(compose(domain(X1),X2)) = codomain(X2)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_24]),
[final] ).
cnf(c_0_90,hypothesis,
( compose(compose(domain(X1),X2),compose(a,b)) = compose(domain(X1),compose(X2,compose(a,b)))
| codomain(X2) != domain(a)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_24]),
[final] ).
cnf(c_0_91,hypothesis,
( compose(compose(codomain(X1),X2),compose(a,b)) = compose(codomain(X1),compose(X2,compose(a,b)))
| codomain(X2) != domain(a)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_38]),
[final] ).
cnf(c_0_92,hypothesis,
( compose(compose(compose(a,b),X1),compose(a,b)) = compose(compose(a,b),compose(X1,compose(a,b)))
| codomain(X1) != domain(a)
| codomain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_35]),
[final] ).
cnf(c_0_93,hypothesis,
( compose(compose(compose(a,b),domain(X1)),domain(X2)) = compose(compose(a,b),compose(domain(X1),domain(X2)))
| codomain(b) != domain(X1)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_35]),
[final] ).
cnf(c_0_94,hypothesis,
( compose(compose(compose(a,b),codomain(X1)),codomain(b)) = compose(compose(a,b),compose(codomain(X1),codomain(b)))
| codomain(b) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_35]),
[final] ).
cnf(c_0_95,hypothesis,
( compose(compose(compose(a,h),X1),compose(a,b)) = compose(compose(a,h),compose(X1,compose(a,b)))
| codomain(X1) != domain(a)
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_36]),
[final] ).
cnf(c_0_96,hypothesis,
( compose(compose(a,X1),compose(a,b)) = compose(a,compose(X1,compose(a,b)))
| codomain(X1) != domain(a)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_18]),
[final] ).
cnf(c_0_97,hypothesis,
( compose(compose(domain(X1),X2),compose(a,h)) = compose(domain(X1),compose(X2,compose(a,h)))
| codomain(X2) != domain(a)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_24]),
[final] ).
cnf(c_0_98,hypothesis,
( compose(compose(compose(a,h),domain(X1)),domain(X2)) = compose(compose(a,h),compose(domain(X1),domain(X2)))
| codomain(h) != domain(X1)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_36]),
[final] ).
cnf(c_0_99,hypothesis,
( compose(compose(codomain(X1),X2),compose(a,h)) = compose(codomain(X1),compose(X2,compose(a,h)))
| codomain(X2) != domain(a)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_38]),
[final] ).
cnf(c_0_100,hypothesis,
( compose(compose(compose(a,h),codomain(X1)),codomain(h)) = compose(compose(a,h),compose(codomain(X1),codomain(h)))
| codomain(h) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_30]),
[final] ).
cnf(c_0_101,hypothesis,
( compose(compose(compose(a,b),X1),compose(a,h)) = compose(compose(a,b),compose(X1,compose(a,h)))
| codomain(X1) != domain(a)
| codomain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_35]),
[final] ).
cnf(c_0_102,hypothesis,
( compose(compose(compose(a,h),X1),compose(a,h)) = compose(compose(a,h),compose(X1,compose(a,h)))
| codomain(X1) != domain(a)
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_36]),
[final] ).
cnf(c_0_103,hypothesis,
( compose(compose(a,X1),compose(a,h)) = compose(a,compose(X1,compose(a,h)))
| codomain(X1) != domain(a)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_18]),
[final] ).
cnf(c_0_104,hypothesis,
( compose(compose(domain(a),domain(X1)),compose(a,b)) = compose(domain(a),compose(domain(X1),compose(a,b)))
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_62,c_0_41]),
[final] ).
cnf(c_0_105,hypothesis,
( compose(compose(domain(a),domain(X1)),compose(a,h)) = compose(domain(a),compose(domain(X1),compose(a,h)))
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_63,c_0_41]),
[final] ).
cnf(c_0_106,hypothesis,
( compose(compose(a,b),compose(codomain(b),X1)) = compose(compose(a,b),X1)
| codomain(b) != domain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_35]),c_0_65]),
[final] ).
cnf(c_0_107,hypothesis,
( compose(compose(g,X1),compose(a,b)) = compose(g,compose(X1,compose(a,b)))
| codomain(X1) != domain(a)
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_30]),
[final] ).
cnf(c_0_108,hypothesis,
( compose(compose(a,h),compose(codomain(h),X1)) = compose(compose(a,h),X1)
| codomain(h) != domain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_30]),c_0_67]),
[final] ).
cnf(c_0_109,plain,
( compose(compose(domain(X1),codomain(X2)),X3) = compose(domain(X1),compose(codomain(X2),X3))
| codomain(X2) != domain(X3)
| domain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_23]),
[final] ).
cnf(c_0_110,plain,
( compose(compose(codomain(X1),codomain(X2)),X3) = compose(codomain(X1),compose(codomain(X2),X3))
| codomain(X2) != domain(X3)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_23]),
[final] ).
cnf(c_0_111,hypothesis,
( compose(compose(g,X1),compose(a,h)) = compose(g,compose(X1,compose(a,h)))
| codomain(X1) != domain(a)
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_30]),
[final] ).
cnf(c_0_112,hypothesis,
( compose(compose(codomain(X1),domain(X2)),h) = compose(codomain(X1),compose(domain(X2),h))
| domain(X2) != domain(b)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_23]),
[final] ).
cnf(c_0_113,hypothesis,
( compose(compose(codomain(X1),domain(X2)),g) = compose(codomain(X1),compose(domain(X2),g))
| domain(X2) != domain(b)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_23]),
[final] ).
cnf(c_0_114,hypothesis,
( compose(compose(X1,a),domain(X2)) = compose(X1,compose(a,domain(X2)))
| domain(b) != domain(X2)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_44,c_0_18]),
[final] ).
cnf(c_0_115,hypothesis,
( compose(compose(X1,domain(a)),compose(a,b)) = compose(X1,compose(a,b))
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_41]),c_0_72]),
[final] ).
cnf(c_0_116,hypothesis,
( compose(X1,compose(codomain(X1),compose(a,b))) = compose(X1,compose(a,b))
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_73]),c_0_43]),
[final] ).
cnf(c_0_117,hypothesis,
( compose(compose(domain(b),domain(X1)),h) = compose(domain(b),compose(domain(X1),h))
| domain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_69,c_0_21]),
[final] ).
cnf(c_0_118,hypothesis,
( compose(domain(X1),compose(domain(X1),h)) = compose(domain(X1),h)
| domain(X1) != domain(b) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_69]),c_0_74]),
[final] ).
cnf(c_0_119,hypothesis,
( compose(compose(X1,compose(a,b)),codomain(b)) = compose(X1,compose(a,b))
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_120,hypothesis,
( compose(compose(domain(b),domain(X1)),g) = compose(domain(b),compose(domain(X1),g))
| domain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_70,c_0_21]),
[final] ).
cnf(c_0_121,hypothesis,
( compose(domain(X1),compose(domain(X1),g)) = compose(domain(X1),g)
| domain(X1) != domain(b) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_70]),c_0_74]),
[final] ).
cnf(c_0_122,hypothesis,
( compose(compose(g,codomain(X1)),codomain(h)) = compose(g,compose(codomain(X1),codomain(h)))
| codomain(h) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_75,c_0_30]),
[final] ).
cnf(c_0_123,hypothesis,
( compose(compose(a,codomain(X1)),domain(b)) = compose(a,compose(codomain(X1),domain(b)))
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_76,c_0_18]),
[final] ).
cnf(c_0_124,plain,
( compose(compose(X1,domain(X2)),domain(X2)) = compose(X1,domain(X2))
| codomain(X1) != domain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_28]),c_0_24]),
[final] ).
cnf(c_0_125,plain,
( compose(compose(X1,codomain(X2)),codomain(X2)) = compose(X1,codomain(X2))
| codomain(X1) != codomain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_23]),c_0_38]),
[final] ).
cnf(c_0_126,hypothesis,
( compose(compose(X1,domain(a)),compose(a,h)) = compose(X1,compose(a,h))
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_41]),c_0_78]),
[final] ).
cnf(c_0_127,hypothesis,
( compose(X1,compose(codomain(X1),compose(a,h))) = compose(X1,compose(a,h))
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_79]),c_0_43]),
[final] ).
cnf(c_0_128,hypothesis,
( compose(compose(compose(a,h),X1),codomain(X1)) = compose(compose(a,h),X1)
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_36]),
[final] ).
cnf(c_0_129,hypothesis,
( compose(compose(X1,compose(a,h)),codomain(h)) = compose(X1,compose(a,h))
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_41]),c_0_26]),c_0_30]),
[final] ).
cnf(c_0_130,plain,
( compose(compose(codomain(X1),domain(X2)),X2) = compose(codomain(X1),X2)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_23]),
[final] ).
cnf(c_0_131,plain,
( compose(compose(codomain(X1),X2),codomain(X2)) = compose(codomain(X1),X2)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_38]),
[final] ).
cnf(c_0_132,hypothesis,
( compose(compose(X1,g),X2) = compose(X1,compose(g,X2))
| codomain(h) != domain(X2)
| codomain(X1) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_30]),c_0_21]),
[final] ).
cnf(c_0_133,hypothesis,
( compose(compose(a,domain(X1)),X1) = compose(a,X1)
| domain(b) != domain(X1) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_40]),c_0_51]),
[final] ).
cnf(c_0_134,hypothesis,
( compose(compose(domain(X1),domain(b)),h) = compose(domain(X1),h)
| domain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_80,c_0_15]),
[final] ).
cnf(c_0_135,hypothesis,
( compose(compose(domain(X1),domain(b)),g) = compose(domain(X1),g)
| domain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_80,c_0_21]),
[final] ).
cnf(c_0_136,hypothesis,
( compose(a,compose(domain(b),X1)) = compose(a,X1)
| domain(b) != domain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_21]),c_0_81]),
[final] ).
cnf(c_0_137,hypothesis,
( compose(compose(a,domain(X1)),h) = compose(a,compose(domain(X1),h))
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_15]),
[final] ).
cnf(c_0_138,hypothesis,
( compose(compose(a,domain(X1)),g) = compose(a,compose(domain(X1),g))
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_21]),
[final] ).
cnf(c_0_139,hypothesis,
( X1 = domain(X2)
| compose(X1,compose(a,b)) != compose(domain(X2),compose(a,b))
| domain(X2) != domain(a)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_57,c_0_24]),
[final] ).
cnf(c_0_140,hypothesis,
( compose(compose(domain(X1),a),h) = compose(domain(X1),compose(a,h))
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_82,c_0_15]),
[final] ).
cnf(c_0_141,hypothesis,
( compose(compose(domain(X1),a),b) = compose(domain(X1),compose(a,b))
| domain(X1) != domain(a) ),
inference(er,[status(thm)],[c_0_82]),
[final] ).
cnf(c_0_142,hypothesis,
( compose(compose(domain(X1),a),g) = compose(domain(X1),compose(a,h))
| domain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_21]),c_0_22]),
[final] ).
cnf(c_0_143,hypothesis,
( compose(g,compose(codomain(h),X1)) = compose(g,X1)
| codomain(h) != domain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_30]),c_0_83]),
[final] ).
cnf(c_0_144,hypothesis,
( compose(compose(X1,a),domain(b)) = compose(X1,a)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_18]),c_0_81]),
[final] ).
cnf(c_0_145,hypothesis,
( compose(compose(a,X1),codomain(X1)) = compose(a,X1)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_18]),
[final] ).
cnf(c_0_146,hypothesis,
( compose(compose(X1,g),codomain(h)) = compose(X1,g)
| codomain(X1) != domain(b) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_85]),c_0_83]),
[final] ).
cnf(c_0_147,hypothesis,
( compose(compose(g,X1),codomain(X1)) = compose(g,X1)
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_30]),
[final] ).
cnf(c_0_148,hypothesis,
( codomain(compose(X1,compose(a,b))) = codomain(b)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_149,hypothesis,
( domain(compose(X1,compose(a,b))) = domain(X1)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_27,c_0_37]),
[final] ).
cnf(c_0_150,hypothesis,
( domain(compose(X1,compose(a,h))) = domain(X1)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_27,c_0_41]),
[final] ).
cnf(c_0_151,hypothesis,
( codomain(X1) = a
| compose(codomain(X1),compose(a,b)) != compose(a,compose(a,b))
| domain(b) != domain(a)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_86,c_0_38]),
[final] ).
cnf(c_0_152,hypothesis,
( compose(compose(domain(X1),h),codomain(h)) = compose(domain(X1),h)
| domain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_87,c_0_15]),
[final] ).
cnf(c_0_153,hypothesis,
( compose(compose(domain(X1),g),codomain(h)) = compose(domain(X1),g)
| domain(X1) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_21]),c_0_30]),
[final] ).
cnf(c_0_154,plain,
( codomain(compose(X1,domain(X2))) = domain(X2)
| codomain(X1) != domain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_28]),c_0_24]),
[final] ).
cnf(c_0_155,plain,
( codomain(compose(X1,codomain(X2))) = codomain(X2)
| codomain(X1) != codomain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_23]),c_0_38]),
[final] ).
cnf(c_0_156,plain,
( domain(compose(X1,domain(X2))) = domain(X1)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]),
[final] ).
cnf(c_0_157,plain,
( domain(compose(X1,codomain(X2))) = domain(X1)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_23]),
[final] ).
cnf(c_0_158,plain,
( codomain(compose(codomain(X1),X2)) = codomain(X2)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_38]),
[final] ).
cnf(c_0_159,plain,
( domain(compose(codomain(X1),X2)) = codomain(X1)
| codomain(X1) != domain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_38]),c_0_23]),
[final] ).
cnf(c_0_160,hypothesis,
( codomain(compose(X1,compose(a,h))) = codomain(h)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_41]),c_0_26]),c_0_30]),
[final] ).
cnf(c_0_161,hypothesis,
( codomain(compose(compose(a,h),X1)) = codomain(X1)
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_36]),
[final] ).
cnf(c_0_162,hypothesis,
( domain(compose(compose(a,h),X1)) = domain(a)
| codomain(h) != domain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_36]),c_0_41]),
[final] ).
cnf(c_0_163,hypothesis,
( domain(compose(domain(X1),h)) = domain(X1)
| domain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_88,c_0_15]),
[final] ).
cnf(c_0_164,hypothesis,
( domain(compose(domain(X1),g)) = domain(X1)
| domain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_88,c_0_21]),
[final] ).
cnf(c_0_165,hypothesis,
( codomain(compose(domain(X1),h)) = codomain(h)
| domain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_89,c_0_15]),
[final] ).
cnf(c_0_166,hypothesis,
( codomain(compose(domain(X1),g)) = codomain(h)
| domain(X1) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_21]),c_0_30]),
[final] ).
cnf(c_0_167,hypothesis,
( codomain(compose(g,X1)) = codomain(X1)
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_30]),
[final] ).
cnf(c_0_168,hypothesis,
( domain(compose(g,X1)) = domain(b)
| codomain(h) != domain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_30]),c_0_21]),
[final] ).
cnf(c_0_169,hypothesis,
( compose(compose(domain(X1),compose(a,b)),compose(a,b)) = compose(domain(X1),compose(compose(a,b),compose(a,b)))
| codomain(b) != domain(a)
| domain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_170,hypothesis,
( compose(compose(codomain(X1),compose(a,b)),compose(a,b)) = compose(codomain(X1),compose(compose(a,b),compose(a,b)))
| codomain(b) != domain(a)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_171,hypothesis,
( compose(compose(domain(X1),compose(a,h)),compose(a,b)) = compose(domain(X1),compose(compose(a,h),compose(a,b)))
| codomain(h) != domain(a)
| domain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_36]),c_0_41]),
[final] ).
cnf(c_0_172,hypothesis,
( compose(compose(compose(a,b),compose(a,h)),compose(a,b)) = compose(compose(a,b),compose(compose(a,h),compose(a,b)))
| codomain(h) != domain(a)
| codomain(b) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_36]),c_0_41]),
[final] ).
cnf(c_0_173,hypothesis,
( compose(compose(compose(a,b),codomain(X1)),domain(X2)) = compose(compose(a,b),compose(codomain(X1),domain(X2)))
| codomain(b) != codomain(X1)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_23]),
[final] ).
cnf(c_0_174,hypothesis,
( compose(compose(compose(a,b),domain(X1)),codomain(b)) = compose(compose(a,b),compose(domain(X1),codomain(b)))
| codomain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_24]),
[final] ).
cnf(c_0_175,hypothesis,
( compose(compose(compose(a,h),compose(a,b)),compose(a,b)) = compose(compose(a,h),compose(compose(a,b),compose(a,b)))
| codomain(b) != domain(a)
| codomain(h) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_176,hypothesis,
( compose(compose(codomain(X1),compose(a,h)),compose(a,b)) = compose(codomain(X1),compose(compose(a,h),compose(a,b)))
| codomain(h) != domain(a)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_41]),c_0_26]),c_0_30]),
[final] ).
cnf(c_0_177,hypothesis,
( compose(compose(compose(a,b),compose(a,b)),compose(a,b)) = compose(compose(a,b),compose(compose(a,b),compose(a,b)))
| codomain(b) != domain(a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_35]),c_0_37])]),
[final] ).
cnf(c_0_178,hypothesis,
( compose(compose(codomain(X1),domain(X2)),compose(a,b)) = compose(codomain(X1),compose(domain(X2),compose(a,b)))
| domain(X2) != domain(a)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_38]),
[final] ).
cnf(c_0_179,hypothesis,
( compose(compose(compose(a,b),domain(X1)),compose(a,b)) = compose(compose(a,b),compose(domain(X1),compose(a,b)))
| domain(X1) != domain(a)
| codomain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_35]),
[final] ).
cnf(c_0_180,hypothesis,
( compose(compose(compose(a,b),a),compose(a,b)) = compose(compose(a,b),compose(a,compose(a,b)))
| domain(b) != domain(a)
| codomain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_92,c_0_18]),
[final] ).
cnf(c_0_181,hypothesis,
( compose(compose(compose(a,h),domain(X1)),compose(a,b)) = compose(compose(a,h),compose(domain(X1),compose(a,b)))
| domain(X1) != domain(a)
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_36]),
[final] ).
cnf(c_0_182,hypothesis,
( compose(compose(a,compose(a,b)),compose(a,b)) = compose(a,compose(compose(a,b),compose(a,b)))
| codomain(b) != domain(a)
| domain(b) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_183,hypothesis,
( compose(compose(domain(X1),compose(a,b)),compose(a,h)) = compose(domain(X1),compose(compose(a,b),compose(a,h)))
| codomain(b) != domain(a)
| domain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_184,hypothesis,
( compose(compose(compose(a,h),codomain(X1)),domain(X2)) = compose(compose(a,h),compose(codomain(X1),domain(X2)))
| codomain(h) != codomain(X1)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_98,c_0_23]),
[final] ).
cnf(c_0_185,hypothesis,
( compose(compose(codomain(X1),compose(a,b)),compose(a,h)) = compose(codomain(X1),compose(compose(a,b),compose(a,h)))
| codomain(b) != domain(a)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_186,hypothesis,
( compose(compose(compose(a,h),domain(X1)),codomain(h)) = compose(compose(a,h),compose(domain(X1),codomain(h)))
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_24]),
[final] ).
cnf(c_0_187,hypothesis,
( compose(compose(compose(a,b),compose(a,h)),compose(a,h)) = compose(compose(a,b),compose(compose(a,h),compose(a,h)))
| codomain(h) != domain(a)
| codomain(b) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_36]),c_0_41]),
[final] ).
cnf(c_0_188,hypothesis,
( compose(compose(compose(a,b),compose(a,b)),compose(a,h)) = compose(compose(a,b),compose(compose(a,b),compose(a,h)))
| codomain(b) != domain(a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_35]),c_0_37])]),
[final] ).
cnf(c_0_189,hypothesis,
( compose(compose(compose(a,h),compose(a,b)),compose(a,h)) = compose(compose(a,h),compose(compose(a,b),compose(a,h)))
| codomain(b) != domain(a)
| codomain(h) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_190,hypothesis,
( compose(compose(compose(a,b),a),compose(a,h)) = compose(compose(a,b),compose(a,compose(a,h)))
| domain(b) != domain(a)
| codomain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_101,c_0_18]),
[final] ).
cnf(c_0_191,hypothesis,
( compose(compose(a,compose(a,b)),compose(a,h)) = compose(a,compose(compose(a,b),compose(a,h)))
| codomain(b) != domain(a)
| domain(b) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_192,hypothesis,
( compose(compose(codomain(X1),domain(X2)),compose(a,h)) = compose(codomain(X1),compose(domain(X2),compose(a,h)))
| domain(X2) != domain(a)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_38]),
[final] ).
cnf(c_0_193,hypothesis,
( compose(compose(compose(a,b),domain(X1)),compose(a,h)) = compose(compose(a,b),compose(domain(X1),compose(a,h)))
| domain(X1) != domain(a)
| codomain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_35]),
[final] ).
cnf(c_0_194,hypothesis,
( compose(compose(domain(a),codomain(X1)),compose(a,b)) = compose(domain(a),compose(codomain(X1),compose(a,b)))
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_104,c_0_23]),
[final] ).
cnf(c_0_195,hypothesis,
( compose(compose(compose(a,h),domain(X1)),compose(a,h)) = compose(compose(a,h),compose(domain(X1),compose(a,h)))
| domain(X1) != domain(a)
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_36]),
[final] ).
cnf(c_0_196,hypothesis,
( compose(compose(domain(a),codomain(X1)),compose(a,h)) = compose(domain(a),compose(codomain(X1),compose(a,h)))
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_105,c_0_23]),
[final] ).
cnf(c_0_197,hypothesis,
( compose(compose(a,b),compose(codomain(b),domain(X1))) = compose(compose(a,b),domain(X1))
| codomain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_28]),
[final] ).
cnf(c_0_198,hypothesis,
( compose(compose(a,domain(X1)),compose(a,b)) = compose(a,compose(domain(X1),compose(a,b)))
| domain(b) != domain(X1)
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_40,c_0_37]),
[final] ).
cnf(c_0_199,hypothesis,
( compose(compose(a,b),compose(codomain(b),codomain(X1))) = compose(compose(a,b),codomain(X1))
| codomain(b) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_23]),
[final] ).
cnf(c_0_200,hypothesis,
( compose(compose(domain(X1),codomain(X2)),compose(a,b)) = compose(domain(X1),compose(codomain(X2),compose(a,b)))
| codomain(X2) != domain(a)
| domain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_24]),
[final] ).
cnf(c_0_201,hypothesis,
( compose(compose(domain(X1),compose(a,h)),compose(a,h)) = compose(domain(X1),compose(compose(a,h),compose(a,h)))
| codomain(h) != domain(a)
| domain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_36]),c_0_41]),
[final] ).
cnf(c_0_202,hypothesis,
( compose(compose(codomain(X1),codomain(X2)),compose(a,b)) = compose(codomain(X1),compose(codomain(X2),compose(a,b)))
| codomain(X2) != domain(a)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_38]),
[final] ).
cnf(c_0_203,hypothesis,
( compose(compose(compose(a,b),codomain(X1)),compose(a,b)) = compose(compose(a,b),compose(codomain(X1),compose(a,b)))
| codomain(X1) != domain(a)
| codomain(b) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_35]),
[final] ).
cnf(c_0_204,hypothesis,
( compose(compose(compose(a,h),codomain(X1)),compose(a,b)) = compose(compose(a,h),compose(codomain(X1),compose(a,b)))
| codomain(X1) != domain(a)
| codomain(h) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_36]),
[final] ).
cnf(c_0_205,hypothesis,
( compose(compose(a,domain(X1)),compose(a,h)) = compose(a,compose(domain(X1),compose(a,h)))
| domain(b) != domain(X1)
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]),
[final] ).
cnf(c_0_206,hypothesis,
( compose(compose(g,compose(a,b)),compose(a,b)) = compose(g,compose(compose(a,b),compose(a,b)))
| codomain(b) != domain(a)
| codomain(h) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_207,hypothesis,
( compose(compose(codomain(X1),compose(a,h)),compose(a,h)) = compose(codomain(X1),compose(compose(a,h),compose(a,h)))
| codomain(h) != domain(a)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_41]),c_0_26]),c_0_30]),
[final] ).
cnf(c_0_208,hypothesis,
( compose(compose(compose(a,b),g),compose(a,b)) = compose(compose(a,b),compose(g,compose(a,b)))
| codomain(h) != domain(a)
| codomain(b) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_30]),c_0_21]),
[final] ).
cnf(c_0_209,hypothesis,
( compose(compose(compose(a,h),a),compose(a,b)) = compose(compose(a,h),compose(a,compose(a,b)))
| domain(b) != domain(a)
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_95,c_0_18]),
[final] ).
cnf(c_0_210,hypothesis,
( compose(compose(a,compose(a,h)),compose(a,b)) = compose(a,compose(compose(a,h),compose(a,b)))
| codomain(h) != domain(a)
| domain(b) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_36]),c_0_41]),
[final] ).
cnf(c_0_211,hypothesis,
( compose(compose(a,codomain(X1)),compose(a,b)) = compose(a,compose(codomain(X1),compose(a,b)))
| codomain(X1) != domain(a)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_73,c_0_18]),
[final] ).
cnf(c_0_212,hypothesis,
( compose(compose(domain(X1),codomain(X2)),compose(a,h)) = compose(domain(X1),compose(codomain(X2),compose(a,h)))
| codomain(X2) != domain(a)
| domain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_79,c_0_24]),
[final] ).
cnf(c_0_213,hypothesis,
( compose(compose(codomain(X1),codomain(X2)),compose(a,h)) = compose(codomain(X1),compose(codomain(X2),compose(a,h)))
| codomain(X2) != domain(a)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_79,c_0_38]),
[final] ).
cnf(c_0_214,hypothesis,
( compose(compose(compose(a,b),codomain(X1)),compose(a,h)) = compose(compose(a,b),compose(codomain(X1),compose(a,h)))
| codomain(X1) != domain(a)
| codomain(b) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_35]),
[final] ).
cnf(c_0_215,hypothesis,
( compose(compose(a,h),compose(codomain(h),domain(X1))) = compose(compose(a,h),domain(X1))
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_28]),
[final] ).
cnf(c_0_216,hypothesis,
( compose(compose(a,h),compose(codomain(h),codomain(X1))) = compose(compose(a,h),codomain(X1))
| codomain(h) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_23]),
[final] ).
cnf(c_0_217,hypothesis,
( compose(compose(compose(a,h),codomain(X1)),compose(a,h)) = compose(compose(a,h),compose(codomain(X1),compose(a,h)))
| codomain(X1) != domain(a)
| codomain(h) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_36]),
[final] ).
cnf(c_0_218,plain,
( compose(compose(domain(X1),codomain(X2)),domain(X3)) = compose(domain(X1),compose(codomain(X2),domain(X3)))
| codomain(X2) != domain(X3)
| domain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_109,c_0_28]),
[final] ).
cnf(c_0_219,plain,
( compose(compose(domain(X1),codomain(X2)),codomain(X3)) = compose(domain(X1),compose(codomain(X2),codomain(X3)))
| codomain(X2) != codomain(X3)
| domain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_109,c_0_23]),
[final] ).
cnf(c_0_220,plain,
( compose(compose(codomain(X1),codomain(X2)),domain(X3)) = compose(codomain(X1),compose(codomain(X2),domain(X3)))
| codomain(X2) != domain(X3)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_110,c_0_28]),
[final] ).
cnf(c_0_221,hypothesis,
( compose(compose(domain(X1),a),compose(a,b)) = compose(domain(X1),compose(a,compose(a,b)))
| domain(b) != domain(a)
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_82,c_0_37]),
[final] ).
cnf(c_0_222,plain,
( compose(compose(codomain(X1),codomain(X2)),codomain(X3)) = compose(codomain(X1),compose(codomain(X2),codomain(X3)))
| codomain(X2) != codomain(X3)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_110,c_0_23]),
[final] ).
cnf(c_0_223,hypothesis,
( compose(compose(domain(X1),a),compose(a,h)) = compose(domain(X1),compose(a,compose(a,h)))
| domain(b) != domain(a)
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_82,c_0_41]),
[final] ).
cnf(c_0_224,hypothesis,
( compose(compose(g,domain(X1)),compose(a,b)) = compose(g,compose(domain(X1),compose(a,b)))
| domain(X1) != domain(a)
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_30]),
[final] ).
cnf(c_0_225,hypothesis,
( compose(compose(compose(a,h),compose(a,h)),compose(a,b)) = compose(compose(a,h),compose(compose(a,h),compose(a,b)))
| codomain(h) != domain(a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_36]),c_0_41])]),
[final] ).
cnf(c_0_226,plain,
( compose(compose(domain(X1),domain(X2)),domain(X3)) = compose(domain(X1),compose(domain(X2),domain(X3)))
| domain(X2) != domain(X3)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_24]),
[final] ).
cnf(c_0_227,plain,
( compose(compose(codomain(X1),domain(X2)),domain(X3)) = compose(codomain(X1),compose(domain(X2),domain(X3)))
| domain(X2) != domain(X3)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_38]),
[final] ).
cnf(c_0_228,hypothesis,
( compose(compose(a,codomain(X1)),compose(a,h)) = compose(a,compose(codomain(X1),compose(a,h)))
| codomain(X1) != domain(a)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_79,c_0_18]),
[final] ).
cnf(c_0_229,hypothesis,
( compose(compose(g,codomain(X1)),compose(a,b)) = compose(g,compose(codomain(X1),compose(a,b)))
| codomain(h) != codomain(X1)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_53,c_0_37]),
[final] ).
cnf(c_0_230,hypothesis,
( compose(compose(domain(X1),g),compose(a,b)) = compose(domain(X1),compose(g,compose(a,b)))
| codomain(h) != domain(a)
| domain(X1) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_30]),c_0_21]),
[final] ).
cnf(c_0_231,hypothesis,
( compose(compose(g,compose(a,b)),compose(a,h)) = compose(g,compose(compose(a,b),compose(a,h)))
| codomain(b) != domain(a)
| codomain(h) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_232,hypothesis,
( compose(compose(codomain(X1),codomain(X2)),h) = compose(codomain(X1),compose(codomain(X2),h))
| codomain(X2) != domain(b)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_112,c_0_23]),
[final] ).
cnf(c_0_233,hypothesis,
( compose(compose(codomain(X1),codomain(X2)),g) = compose(codomain(X1),compose(codomain(X2),g))
| codomain(X2) != domain(b)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_113,c_0_23]),
[final] ).
cnf(c_0_234,hypothesis,
( compose(compose(domain(X1),a),domain(X2)) = compose(domain(X1),compose(a,domain(X2)))
| domain(b) != domain(X2)
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_114,c_0_24]),
[final] ).
cnf(c_0_235,hypothesis,
( compose(compose(compose(a,b),g),compose(a,h)) = compose(compose(a,b),compose(g,compose(a,h)))
| codomain(h) != domain(a)
| codomain(b) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_30]),c_0_21]),
[final] ).
cnf(c_0_236,hypothesis,
( compose(compose(compose(a,h),a),compose(a,h)) = compose(compose(a,h),compose(a,compose(a,h)))
| domain(b) != domain(a)
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_102,c_0_18]),
[final] ).
cnf(c_0_237,hypothesis,
( compose(compose(a,compose(a,h)),compose(a,h)) = compose(a,compose(compose(a,h),compose(a,h)))
| codomain(h) != domain(a)
| domain(b) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_36]),c_0_41]),
[final] ).
cnf(c_0_238,hypothesis,
( compose(compose(compose(a,b),a),domain(X1)) = compose(compose(a,b),compose(a,domain(X1)))
| codomain(b) != domain(a)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_35]),
[final] ).
cnf(c_0_239,hypothesis,
( compose(compose(compose(a,h),compose(a,h)),compose(a,h)) = compose(compose(a,h),compose(compose(a,h),compose(a,h)))
| codomain(h) != domain(a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_36]),c_0_41])]),
[final] ).
cnf(c_0_240,hypothesis,
( compose(compose(compose(a,b),domain(a)),compose(a,b)) = compose(compose(a,b),compose(a,b))
| codomain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_115,c_0_35]),
[final] ).
cnf(c_0_241,hypothesis,
( compose(compose(a,b),compose(codomain(b),compose(a,b))) = compose(compose(a,b),compose(a,b))
| codomain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_116,c_0_35]),
[final] ).
cnf(c_0_242,hypothesis,
( compose(compose(compose(a,h),a),domain(X1)) = compose(compose(a,h),compose(a,domain(X1)))
| codomain(h) != domain(a)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_36]),
[final] ).
cnf(c_0_243,hypothesis,
( compose(compose(domain(X1),codomain(X2)),h) = compose(domain(X1),compose(codomain(X2),h))
| codomain(X2) != domain(b)
| domain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_23]),
[final] ).
cnf(c_0_244,plain,
( compose(compose(domain(X1),domain(X2)),codomain(X3)) = compose(domain(X1),compose(domain(X2),codomain(X3)))
| domain(X2) != codomain(X3)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_24]),
[final] ).
cnf(c_0_245,plain,
( compose(compose(codomain(X1),domain(X2)),codomain(X3)) = compose(codomain(X1),compose(domain(X2),codomain(X3)))
| domain(X2) != codomain(X3)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_38]),
[final] ).
cnf(c_0_246,hypothesis,
( compose(compose(domain(b),codomain(X1)),h) = compose(domain(b),compose(codomain(X1),h))
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_117,c_0_23]),
[final] ).
cnf(c_0_247,hypothesis,
( compose(codomain(X1),compose(codomain(X1),h)) = compose(codomain(X1),h)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_118,c_0_23]),
[final] ).
cnf(c_0_248,hypothesis,
( compose(compose(domain(X1),codomain(X2)),g) = compose(domain(X1),compose(codomain(X2),g))
| codomain(X2) != domain(b)
| domain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_23]),
[final] ).
cnf(c_0_249,hypothesis,
( compose(compose(compose(a,b),compose(a,b)),codomain(b)) = compose(compose(a,b),compose(a,b))
| codomain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_119,c_0_35]),
[final] ).
cnf(c_0_250,hypothesis,
( compose(compose(domain(b),codomain(X1)),g) = compose(domain(b),compose(codomain(X1),g))
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_120,c_0_23]),
[final] ).
cnf(c_0_251,hypothesis,
( compose(codomain(X1),compose(codomain(X1),g)) = compose(codomain(X1),g)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_121,c_0_23]),
[final] ).
cnf(c_0_252,hypothesis,
( compose(compose(a,domain(X1)),domain(X2)) = compose(a,compose(domain(X1),domain(X2)))
| domain(b) != domain(X1)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_18]),
[final] ).
cnf(c_0_253,hypothesis,
( compose(compose(a,domain(X1)),codomain(X2)) = compose(a,compose(domain(X1),codomain(X2)))
| domain(b) != domain(X1)
| domain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_18]),
[final] ).
cnf(c_0_254,hypothesis,
( compose(compose(g,codomain(X1)),domain(X2)) = compose(g,compose(codomain(X1),domain(X2)))
| codomain(h) != codomain(X1)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_28]),
[final] ).
cnf(c_0_255,hypothesis,
( compose(compose(domain(X1),domain(a)),compose(a,b)) = compose(domain(X1),compose(a,b))
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_80,c_0_37]),
[final] ).
cnf(c_0_256,hypothesis,
( compose(domain(X1),compose(domain(X1),compose(a,b))) = compose(domain(X1),compose(a,b))
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_116,c_0_24]),
[final] ).
cnf(c_0_257,hypothesis,
( compose(compose(g,domain(X1)),codomain(h)) = compose(g,compose(domain(X1),codomain(h)))
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_24]),
[final] ).
cnf(c_0_258,hypothesis,
( compose(compose(g,domain(X1)),compose(a,h)) = compose(g,compose(domain(X1),compose(a,h)))
| domain(X1) != domain(a)
| codomain(h) != domain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_24]),c_0_28]),
[final] ).
cnf(c_0_259,hypothesis,
( compose(compose(compose(a,h),g),compose(a,b)) = compose(compose(a,h),compose(g,compose(a,b)))
| codomain(h) != domain(a)
| codomain(h) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_30]),c_0_21]),
[final] ).
cnf(c_0_260,hypothesis,
( compose(compose(domain(X1),compose(a,b)),codomain(b)) = compose(domain(X1),compose(a,b))
| domain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_261,hypothesis,
( compose(compose(a,codomain(X1)),domain(X2)) = compose(a,compose(codomain(X1),domain(X2)))
| codomain(X1) != domain(b)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_28]),
[final] ).
cnf(c_0_262,hypothesis,
( compose(compose(a,domain(X1)),domain(b)) = compose(a,compose(domain(X1),domain(b)))
| domain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_123,c_0_24]),
[final] ).
cnf(c_0_263,hypothesis,
( compose(compose(compose(a,b),domain(X1)),domain(X1)) = compose(compose(a,b),domain(X1))
| codomain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_35]),
[final] ).
cnf(c_0_264,hypothesis,
( compose(compose(compose(a,b),codomain(X1)),codomain(X1)) = compose(compose(a,b),codomain(X1))
| codomain(b) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_125,c_0_35]),
[final] ).
cnf(c_0_265,hypothesis,
( compose(compose(domain(X1),a),codomain(X2)) = compose(domain(X1),compose(a,codomain(X2)))
| codomain(X2) != domain(b)
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_82,c_0_23]),
[final] ).
cnf(c_0_266,hypothesis,
( compose(compose(compose(a,b),domain(a)),compose(a,h)) = compose(compose(a,b),compose(a,h))
| codomain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_126,c_0_35]),
[final] ).
cnf(c_0_267,hypothesis,
( compose(compose(g,domain(X1)),domain(X2)) = compose(g,compose(domain(X1),domain(X2)))
| codomain(h) != domain(X1)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_30]),
[final] ).
cnf(c_0_268,hypothesis,
( compose(compose(a,b),compose(codomain(b),compose(a,h))) = compose(compose(a,b),compose(a,h))
| codomain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_127,c_0_35]),
[final] ).
cnf(c_0_269,hypothesis,
( compose(compose(codomain(X1),a),domain(X2)) = compose(codomain(X1),compose(a,domain(X2)))
| domain(b) != domain(X2)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_114,c_0_38]),
[final] ).
cnf(c_0_270,hypothesis,
( compose(compose(g,domain(X1)),codomain(X2)) = compose(g,compose(domain(X1),codomain(X2)))
| codomain(h) != domain(X1)
| domain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_30]),
[final] ).
cnf(c_0_271,hypothesis,
( compose(compose(g,codomain(X1)),compose(a,h)) = compose(g,compose(codomain(X1),compose(a,h)))
| codomain(h) != codomain(X1)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_53,c_0_41]),
[final] ).
cnf(c_0_272,hypothesis,
( compose(compose(compose(a,h),domain(a)),compose(a,b)) = compose(compose(a,h),compose(a,b))
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_115,c_0_36]),
[final] ).
cnf(c_0_273,hypothesis,
( compose(compose(a,a),compose(a,b)) = compose(a,compose(a,compose(a,b)))
| domain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_96,c_0_18]),
[final] ).
cnf(c_0_274,hypothesis,
( compose(compose(a,h),compose(a,b)) = compose(a,compose(g,compose(a,b)))
| codomain(h) != domain(a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_30]),c_0_22]),c_0_21])]),
[final] ).
cnf(c_0_275,hypothesis,
( compose(compose(compose(a,h),compose(a,b)),codomain(b)) = compose(compose(a,h),compose(a,b))
| codomain(h) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_276,hypothesis,
( compose(compose(compose(a,b),compose(a,h)),codomain(h)) = compose(compose(a,b),compose(a,h))
| codomain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_129,c_0_35]),
[final] ).
cnf(c_0_277,hypothesis,
( compose(compose(g,a),compose(a,b)) = compose(g,compose(a,compose(a,b)))
| domain(b) != domain(a)
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_107,c_0_18]),
[final] ).
cnf(c_0_278,hypothesis,
( compose(compose(g,compose(a,h)),compose(a,b)) = compose(g,compose(compose(a,h),compose(a,b)))
| codomain(h) != domain(a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_36]),c_0_41])]),
[final] ).
cnf(c_0_279,hypothesis,
( compose(compose(g,g),compose(a,b)) = compose(g,compose(g,compose(a,b)))
| codomain(h) != domain(a)
| codomain(h) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_30]),c_0_21]),
[final] ).
cnf(c_0_280,hypothesis,
( compose(compose(g,domain(a)),compose(a,b)) = compose(g,compose(a,b))
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_115,c_0_30]),
[final] ).
cnf(c_0_281,hypothesis,
( compose(compose(domain(X1),domain(a)),compose(a,h)) = compose(domain(X1),compose(a,h))
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_80,c_0_41]),
[final] ).
cnf(c_0_282,hypothesis,
( compose(domain(X1),compose(domain(X1),compose(a,h))) = compose(domain(X1),compose(a,h))
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_127,c_0_24]),
[final] ).
cnf(c_0_283,hypothesis,
( compose(compose(codomain(X1),domain(a)),compose(a,b)) = compose(codomain(X1),compose(a,b))
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_130,c_0_37]),
[final] ).
cnf(c_0_284,hypothesis,
( compose(compose(X1,compose(a,b)),compose(a,b)) = compose(X1,compose(compose(a,b),compose(a,b)))
| codomain(b) != domain(a)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_285,hypothesis,
( compose(compose(domain(X1),g),compose(a,h)) = compose(domain(X1),compose(g,compose(a,h)))
| codomain(h) != domain(a)
| domain(X1) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_30]),c_0_21]),
[final] ).
cnf(c_0_286,hypothesis,
( compose(codomain(X1),compose(codomain(X1),compose(a,b))) = compose(codomain(X1),compose(a,b))
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_116,c_0_38]),
[final] ).
cnf(c_0_287,hypothesis,
( compose(compose(X1,compose(a,h)),compose(a,b)) = compose(X1,compose(compose(a,h),compose(a,b)))
| codomain(h) != domain(a)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_41]),c_0_26]),c_0_30]),
[final] ).
cnf(c_0_288,hypothesis,
( compose(compose(codomain(X1),compose(a,b)),codomain(b)) = compose(codomain(X1),compose(a,b))
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_289,hypothesis,
( compose(compose(a,a),domain(X1)) = compose(a,compose(a,domain(X1)))
| domain(b) != domain(a)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_18]),
[final] ).
cnf(c_0_290,hypothesis,
( compose(compose(codomain(X1),domain(a)),compose(a,h)) = compose(codomain(X1),compose(a,h))
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_130,c_0_41]),
[final] ).
cnf(c_0_291,hypothesis,
( compose(compose(X1,g),compose(a,b)) = compose(X1,compose(g,compose(a,b)))
| codomain(h) != domain(a)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_132,c_0_37]),
[final] ).
cnf(c_0_292,hypothesis,
( compose(compose(a,h),compose(codomain(h),compose(a,b))) = compose(compose(a,h),compose(a,b))
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_116,c_0_36]),
[final] ).
cnf(c_0_293,hypothesis,
( compose(compose(compose(a,h),g),compose(a,h)) = compose(compose(a,h),compose(g,compose(a,h)))
| codomain(h) != domain(a)
| codomain(h) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_30]),c_0_21]),
[final] ).
cnf(c_0_294,hypothesis,
( compose(a,b) = a
| compose(compose(a,b),compose(a,b)) != compose(a,compose(a,b))
| domain(b) != domain(a)
| codomain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_86,c_0_35]),
[final] ).
cnf(c_0_295,hypothesis,
( compose(compose(compose(a,h),domain(a)),compose(a,h)) = compose(compose(a,h),compose(a,h))
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_126,c_0_36]),
[final] ).
cnf(c_0_296,hypothesis,
( compose(compose(a,a),compose(a,h)) = compose(a,compose(a,compose(a,h)))
| domain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_103,c_0_18]),
[final] ).
cnf(c_0_297,hypothesis,
( compose(compose(a,h),compose(a,h)) = compose(a,compose(g,compose(a,h)))
| codomain(h) != domain(a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_30]),c_0_22]),c_0_21])]),
[final] ).
cnf(c_0_298,hypothesis,
( compose(compose(g,domain(a)),compose(a,h)) = compose(g,compose(a,h))
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_126,c_0_30]),
[final] ).
cnf(c_0_299,hypothesis,
( compose(compose(a,domain(a)),compose(a,b)) = compose(a,compose(a,b))
| domain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_133,c_0_37]),
[final] ).
cnf(c_0_300,hypothesis,
( compose(compose(codomain(X1),domain(b)),h) = compose(codomain(X1),h)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_134,c_0_23]),
[final] ).
cnf(c_0_301,hypothesis,
( compose(compose(X1,compose(a,b)),compose(a,h)) = compose(X1,compose(compose(a,b),compose(a,h)))
| codomain(b) != domain(a)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_302,hypothesis,
( compose(compose(codomain(X1),domain(b)),g) = compose(codomain(X1),g)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_135,c_0_23]),
[final] ).
cnf(c_0_303,hypothesis,
( compose(compose(X1,compose(a,h)),compose(a,h)) = compose(X1,compose(compose(a,h),compose(a,h)))
| codomain(h) != domain(a)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_41]),c_0_26]),c_0_30]),
[final] ).
cnf(c_0_304,hypothesis,
( compose(compose(a,domain(a)),compose(a,h)) = compose(a,compose(a,h))
| domain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_133,c_0_41]),
[final] ).
cnf(c_0_305,hypothesis,
( compose(a,compose(domain(b),domain(X1))) = compose(a,domain(X1))
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_136,c_0_28]),
[final] ).
cnf(c_0_306,hypothesis,
( compose(compose(a,codomain(X1)),h) = compose(a,compose(codomain(X1),h))
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_137,c_0_23]),
[final] ).
cnf(c_0_307,hypothesis,
( compose(compose(a,codomain(X1)),g) = compose(a,compose(codomain(X1),g))
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_138,c_0_23]),
[final] ).
cnf(c_0_308,hypothesis,
( compose(a,compose(domain(b),codomain(X1))) = compose(a,codomain(X1))
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_136,c_0_23]),
[final] ).
cnf(c_0_309,hypothesis,
( compose(compose(domain(X1),compose(a,h)),codomain(h)) = compose(domain(X1),compose(a,h))
| domain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_41]),c_0_26]),c_0_30]),
[final] ).
cnf(c_0_310,hypothesis,
( compose(codomain(X1),compose(codomain(X1),compose(a,h))) = compose(codomain(X1),compose(a,h))
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_127,c_0_38]),
[final] ).
cnf(c_0_311,hypothesis,
( domain(X1) = compose(a,b)
| compose(domain(X1),compose(a,b)) != compose(compose(a,b),compose(a,b))
| codomain(b) != domain(a)
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_139,c_0_35]),
[final] ).
cnf(c_0_312,hypothesis,
( domain(X1) = compose(a,h)
| compose(domain(X1),compose(a,b)) != compose(compose(a,h),compose(a,b))
| codomain(h) != domain(a)
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_139,c_0_36]),
[final] ).
cnf(c_0_313,hypothesis,
( compose(a,compose(domain(b),compose(a,b))) = compose(a,compose(a,b))
| domain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_116,c_0_18]),
[final] ).
cnf(c_0_314,hypothesis,
( compose(compose(compose(a,h),domain(X1)),domain(X1)) = compose(compose(a,h),domain(X1))
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_36]),
[final] ).
cnf(c_0_315,hypothesis,
( compose(compose(compose(a,h),codomain(X1)),codomain(X1)) = compose(compose(a,h),codomain(X1))
| codomain(h) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_125,c_0_36]),
[final] ).
cnf(c_0_316,hypothesis,
( compose(compose(a,h),compose(codomain(h),compose(a,h))) = compose(compose(a,h),compose(a,h))
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_127,c_0_36]),
[final] ).
cnf(c_0_317,hypothesis,
( compose(a,compose(domain(b),compose(a,h))) = compose(a,compose(a,h))
| domain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_127,c_0_18]),
[final] ).
cnf(c_0_318,hypothesis,
( compose(compose(codomain(X1),a),h) = compose(codomain(X1),compose(a,h))
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_140,c_0_23]),
[final] ).
cnf(c_0_319,hypothesis,
( compose(compose(codomain(X1),a),b) = compose(codomain(X1),compose(a,b))
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_141,c_0_23]),
[final] ).
cnf(c_0_320,hypothesis,
( compose(compose(codomain(X1),a),g) = compose(codomain(X1),compose(a,h))
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_142,c_0_23]),
[final] ).
cnf(c_0_321,hypothesis,
( compose(compose(codomain(X1),a),X2) = compose(codomain(X1),compose(a,X2))
| domain(b) != domain(X2)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_56,c_0_38]),
[final] ).
cnf(c_0_322,hypothesis,
( compose(g,compose(codomain(h),compose(a,b))) = compose(g,compose(a,b))
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_143,c_0_37]),
[final] ).
cnf(c_0_323,hypothesis,
( compose(compose(compose(a,b),a),X1) = compose(compose(a,b),compose(a,X1))
| codomain(b) != domain(a)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_35]),
[final] ).
cnf(c_0_324,hypothesis,
( compose(g,compose(codomain(h),domain(X1))) = compose(g,domain(X1))
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_143,c_0_28]),
[final] ).
cnf(c_0_325,hypothesis,
( compose(g,compose(codomain(h),codomain(X1))) = compose(g,codomain(X1))
| codomain(h) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_143,c_0_23]),
[final] ).
cnf(c_0_326,hypothesis,
( compose(g,compose(codomain(h),compose(a,h))) = compose(g,compose(a,h))
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_143,c_0_41]),
[final] ).
cnf(c_0_327,hypothesis,
( compose(compose(compose(a,h),a),X1) = compose(compose(a,h),compose(a,X1))
| codomain(h) != domain(a)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_36]),
[final] ).
cnf(c_0_328,hypothesis,
( compose(compose(g,a),compose(a,h)) = compose(g,compose(a,compose(a,h)))
| domain(b) != domain(a)
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_111,c_0_18]),
[final] ).
cnf(c_0_329,hypothesis,
( compose(compose(compose(a,b),X1),codomain(X1)) = compose(compose(a,b),X1)
| codomain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_35]),
[final] ).
cnf(c_0_330,hypothesis,
( compose(compose(g,compose(a,h)),compose(a,h)) = compose(g,compose(compose(a,h),compose(a,h)))
| codomain(h) != domain(a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_36]),c_0_41])]),
[final] ).
cnf(c_0_331,plain,
( compose(compose(X1,codomain(X2)),domain(X3)) = compose(X1,compose(codomain(X2),domain(X3)))
| codomain(X2) != domain(X3)
| codomain(X1) != codomain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_38]),c_0_23]),
[final] ).
cnf(c_0_332,hypothesis,
( compose(compose(g,g),compose(a,h)) = compose(g,compose(g,compose(a,h)))
| codomain(h) != domain(a)
| codomain(h) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_30]),c_0_21]),
[final] ).
cnf(c_0_333,hypothesis,
( compose(compose(X1,compose(a,b)),domain(X2)) = compose(X1,compose(compose(a,b),domain(X2)))
| codomain(b) != domain(X2)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_334,hypothesis,
( compose(compose(codomain(X1),compose(a,h)),codomain(h)) = compose(codomain(X1),compose(a,h))
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_41]),c_0_26]),c_0_30]),
[final] ).
cnf(c_0_335,hypothesis,
( compose(compose(X1,compose(a,h)),domain(X2)) = compose(X1,compose(compose(a,h),domain(X2)))
| codomain(h) != domain(X2)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_36]),c_0_41]),
[final] ).
cnf(c_0_336,hypothesis,
( compose(compose(g,a),domain(X1)) = compose(g,compose(a,domain(X1)))
| codomain(h) != domain(a)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_30]),
[final] ).
cnf(c_0_337,hypothesis,
( compose(compose(compose(a,b),a),domain(b)) = compose(compose(a,b),a)
| codomain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_144,c_0_35]),
[final] ).
cnf(c_0_338,hypothesis,
( compose(compose(X1,g),domain(X2)) = compose(X1,compose(g,domain(X2)))
| codomain(h) != domain(X2)
| codomain(X1) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_30]),c_0_21]),
[final] ).
cnf(c_0_339,hypothesis,
( compose(a,h) = a
| compose(compose(a,h),compose(a,b)) != compose(a,compose(a,b))
| domain(b) != domain(a)
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_86,c_0_36]),
[final] ).
cnf(c_0_340,plain,
( compose(compose(domain(X1),domain(X2)),domain(X2)) = compose(domain(X1),domain(X2))
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_24]),
[final] ).
cnf(c_0_341,plain,
( compose(compose(codomain(X1),domain(X2)),domain(X2)) = compose(codomain(X1),domain(X2))
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_38]),
[final] ).
cnf(c_0_342,plain,
( compose(compose(domain(X1),codomain(X2)),codomain(X2)) = compose(domain(X1),codomain(X2))
| domain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_125,c_0_24]),
[final] ).
cnf(c_0_343,plain,
( compose(compose(codomain(X1),codomain(X2)),codomain(X2)) = compose(codomain(X1),codomain(X2))
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_125,c_0_38]),
[final] ).
cnf(c_0_344,hypothesis,
( compose(compose(a,compose(a,b)),codomain(b)) = compose(a,compose(a,b))
| domain(b) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_345,hypothesis,
( compose(compose(a,a),X1) = compose(a,compose(a,X1))
| domain(b) != domain(a)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_18]),
[final] ).
cnf(c_0_346,hypothesis,
( compose(compose(domain(X1),a),domain(b)) = compose(domain(X1),a)
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_144,c_0_24]),
[final] ).
cnf(c_0_347,hypothesis,
( compose(compose(X1,g),compose(a,h)) = compose(X1,compose(g,compose(a,h)))
| codomain(h) != domain(a)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_132,c_0_41]),
[final] ).
cnf(c_0_348,hypothesis,
( compose(compose(compose(a,h),compose(a,h)),codomain(h)) = compose(compose(a,h),compose(a,h))
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_129,c_0_36]),
[final] ).
cnf(c_0_349,plain,
( compose(compose(X1,codomain(X2)),codomain(X3)) = compose(X1,compose(codomain(X2),codomain(X3)))
| codomain(X2) != codomain(X3)
| codomain(X1) != codomain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_38]),c_0_23]),
[final] ).
cnf(c_0_350,hypothesis,
( compose(compose(a,domain(X1)),domain(X1)) = compose(a,domain(X1))
| domain(b) != domain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_28]),c_0_24]),
[final] ).
cnf(c_0_351,hypothesis,
( compose(compose(X1,compose(a,b)),codomain(X2)) = compose(X1,compose(compose(a,b),codomain(X2)))
| codomain(b) != codomain(X2)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_352,hypothesis,
( domain(X1) = a
| compose(domain(X1),compose(a,b)) != compose(a,compose(a,b))
| domain(b) != domain(a)
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_86,c_0_24]),
[final] ).
cnf(c_0_353,hypothesis,
( compose(compose(codomain(X1),a),domain(b)) = compose(codomain(X1),a)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_144,c_0_38]),
[final] ).
cnf(c_0_354,hypothesis,
( compose(compose(X1,compose(a,h)),codomain(X2)) = compose(X1,compose(compose(a,h),codomain(X2)))
| codomain(h) != codomain(X2)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_36]),c_0_41]),
[final] ).
cnf(c_0_355,hypothesis,
( domain(X1) = g
| compose(domain(X1),compose(a,b)) != compose(g,compose(a,b))
| codomain(h) != domain(a)
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_139,c_0_30]),
[final] ).
cnf(c_0_356,hypothesis,
( compose(compose(compose(a,h),a),domain(b)) = compose(compose(a,h),a)
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_144,c_0_36]),
[final] ).
cnf(c_0_357,hypothesis,
( compose(compose(a,a),domain(b)) = compose(a,a)
| domain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_144,c_0_18]),
[final] ).
cnf(c_0_358,hypothesis,
( compose(compose(g,a),domain(b)) = compose(g,a)
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_144,c_0_30]),
[final] ).
cnf(c_0_359,hypothesis,
( compose(compose(compose(a,b),g),codomain(h)) = compose(compose(a,b),g)
| codomain(b) != domain(b) ),
inference(spm,[status(thm)],[c_0_146,c_0_35]),
[final] ).
cnf(c_0_360,hypothesis,
( compose(compose(compose(a,h),g),codomain(h)) = compose(compose(a,h),g)
| codomain(h) != domain(b) ),
inference(spm,[status(thm)],[c_0_146,c_0_36]),
[final] ).
cnf(c_0_361,hypothesis,
( compose(compose(g,g),codomain(h)) = compose(g,g)
| codomain(h) != domain(b) ),
inference(spm,[status(thm)],[c_0_146,c_0_30]),
[final] ).
cnf(c_0_362,hypothesis,
( compose(compose(a,compose(a,h)),codomain(h)) = compose(a,compose(a,h))
| domain(b) != domain(a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_41]),c_0_26]),c_0_30]),
[final] ).
cnf(c_0_363,hypothesis,
( compose(compose(g,compose(a,b)),codomain(b)) = compose(g,compose(a,b))
| codomain(h) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_364,hypothesis,
( compose(compose(g,a),X1) = compose(g,compose(a,X1))
| codomain(h) != domain(a)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_30]),
[final] ).
cnf(c_0_365,hypothesis,
( codomain(compose(compose(a,b),compose(a,b))) = codomain(b)
| codomain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_148,c_0_35]),
[final] ).
cnf(c_0_366,hypothesis,
( domain(compose(compose(a,b),compose(a,b))) = domain(a)
| codomain(b) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_367,hypothesis,
( domain(compose(compose(a,b),compose(a,h))) = domain(a)
| codomain(b) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_368,hypothesis,
( domain(b) = a
| compose(domain(b),compose(a,b)) != compose(a,compose(a,b))
| domain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_151,c_0_18]),
[final] ).
cnf(c_0_369,hypothesis,
( compose(compose(codomain(X1),h),codomain(h)) = compose(codomain(X1),h)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_152,c_0_23]),
[final] ).
cnf(c_0_370,hypothesis,
( compose(compose(codomain(X1),g),codomain(h)) = compose(codomain(X1),g)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_153,c_0_23]),
[final] ).
cnf(c_0_371,hypothesis,
( codomain(compose(domain(X1),compose(a,b))) = codomain(b)
| domain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_372,hypothesis,
( compose(compose(a,codomain(X1)),codomain(X1)) = compose(a,codomain(X1))
| codomain(X1) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_23]),c_0_38]),
[final] ).
cnf(c_0_373,hypothesis,
( codomain(compose(compose(a,b),domain(X1))) = domain(X1)
| codomain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_154,c_0_35]),
[final] ).
cnf(c_0_374,hypothesis,
( codomain(compose(compose(a,b),codomain(X1))) = codomain(X1)
| codomain(b) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_155,c_0_35]),
[final] ).
cnf(c_0_375,hypothesis,
( domain(compose(domain(X1),compose(a,b))) = domain(X1)
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_88,c_0_37]),
[final] ).
cnf(c_0_376,hypothesis,
( domain(compose(domain(X1),compose(a,h))) = domain(X1)
| domain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_88,c_0_41]),
[final] ).
cnf(c_0_377,hypothesis,
( domain(compose(compose(a,b),domain(X1))) = domain(a)
| codomain(b) != domain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_378,hypothesis,
( domain(compose(compose(a,b),codomain(X1))) = domain(a)
| codomain(b) != codomain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_379,hypothesis,
( compose(compose(g,domain(X1)),domain(X1)) = compose(g,domain(X1))
| codomain(h) != domain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_28]),c_0_24]),
[final] ).
cnf(c_0_380,hypothesis,
( codomain(compose(codomain(X1),compose(a,b))) = codomain(b)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_381,hypothesis,
( X1 = codomain(X2)
| compose(X1,compose(a,b)) != compose(codomain(X2),compose(a,b))
| codomain(X2) != domain(a)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_57,c_0_38]),
[final] ).
cnf(c_0_382,hypothesis,
( compose(compose(g,codomain(X1)),codomain(X1)) = compose(g,codomain(X1))
| codomain(h) != codomain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_23]),c_0_38]),
[final] ).
cnf(c_0_383,hypothesis,
( domain(compose(codomain(X1),compose(a,b))) = codomain(X1)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_159,c_0_37]),
[final] ).
cnf(c_0_384,hypothesis,
( X1 = compose(a,b)
| compose(X1,compose(a,b)) != compose(compose(a,b),compose(a,b))
| codomain(b) != domain(a)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_57,c_0_35]),
[final] ).
cnf(c_0_385,hypothesis,
( codomain(compose(compose(a,b),compose(a,h))) = codomain(h)
| codomain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_160,c_0_35]),
[final] ).
cnf(c_0_386,hypothesis,
( codomain(compose(compose(a,h),compose(a,b))) = codomain(b)
| codomain(h) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_387,hypothesis,
( domain(compose(compose(a,h),compose(a,b))) = domain(a)
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_162,c_0_37]),
[final] ).
cnf(c_0_388,hypothesis,
( X1 = compose(a,h)
| compose(X1,compose(a,b)) != compose(compose(a,h),compose(a,b))
| codomain(h) != domain(a)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_57,c_0_36]),
[final] ).
cnf(c_0_389,hypothesis,
( g = a
| compose(g,compose(a,b)) != compose(a,compose(a,b))
| domain(b) != domain(a)
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_86,c_0_30]),
[final] ).
cnf(c_0_390,hypothesis,
( codomain(compose(domain(X1),compose(a,h))) = codomain(h)
| domain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_41]),c_0_26]),c_0_30]),
[final] ).
cnf(c_0_391,hypothesis,
( X1 = g
| compose(X1,compose(a,b)) != compose(g,compose(a,b))
| codomain(h) != domain(a)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_57,c_0_30]),
[final] ).
cnf(c_0_392,hypothesis,
( domain(compose(codomain(X1),compose(a,h))) = codomain(X1)
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_159,c_0_41]),
[final] ).
cnf(c_0_393,hypothesis,
( compose(compose(X1,compose(a,h)),X2) = compose(X1,compose(compose(a,h),X2))
| codomain(h) != domain(X2)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_36]),c_0_41]),
[final] ).
cnf(c_0_394,hypothesis,
( compose(compose(g,compose(a,h)),codomain(h)) = compose(g,compose(a,h))
| codomain(h) != domain(a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_41]),c_0_26]),c_0_30]),
[final] ).
cnf(c_0_395,hypothesis,
( compose(compose(X1,compose(a,b)),X2) = compose(X1,compose(compose(a,b),X2))
| codomain(b) != domain(X2)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_396,plain,
( codomain(compose(domain(X1),domain(X2))) = domain(X2)
| domain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_154,c_0_24]),
[final] ).
cnf(c_0_397,plain,
( codomain(compose(codomain(X1),domain(X2))) = domain(X2)
| codomain(X1) != domain(X2) ),
inference(spm,[status(thm)],[c_0_154,c_0_38]),
[final] ).
cnf(c_0_398,hypothesis,
( codomain(compose(compose(a,b),X1)) = codomain(X1)
| codomain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_35]),
[final] ).
cnf(c_0_399,hypothesis,
( codomain(compose(compose(a,h),domain(X1))) = domain(X1)
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_154,c_0_36]),
[final] ).
cnf(c_0_400,hypothesis,
( codomain(compose(compose(a,h),codomain(X1))) = codomain(X1)
| codomain(h) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_155,c_0_36]),
[final] ).
cnf(c_0_401,plain,
( codomain(compose(domain(X1),codomain(X2))) = codomain(X2)
| domain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_155,c_0_24]),
[final] ).
cnf(c_0_402,hypothesis,
( domain(compose(compose(a,b),X1)) = domain(a)
| codomain(b) != domain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_35]),c_0_37]),
[final] ).
cnf(c_0_403,plain,
( codomain(compose(codomain(X1),codomain(X2))) = codomain(X2)
| codomain(X1) != codomain(X2) ),
inference(spm,[status(thm)],[c_0_155,c_0_38]),
[final] ).
cnf(c_0_404,hypothesis,
( domain(compose(compose(a,h),domain(X1))) = domain(a)
| codomain(h) != domain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_36]),c_0_41]),
[final] ).
cnf(c_0_405,hypothesis,
( domain(compose(compose(a,h),codomain(X1))) = domain(a)
| codomain(h) != codomain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_36]),c_0_41]),
[final] ).
cnf(c_0_406,plain,
( domain(compose(domain(X1),domain(X2))) = domain(X1)
| domain(X1) != domain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_24]),c_0_28]),
[final] ).
cnf(c_0_407,hypothesis,
( codomain(compose(a,compose(a,b))) = codomain(b)
| domain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_148,c_0_18]),
[final] ).
cnf(c_0_408,plain,
( domain(compose(codomain(X1),domain(X2))) = codomain(X1)
| codomain(X1) != domain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_38]),c_0_23]),
[final] ).
cnf(c_0_409,plain,
( domain(compose(domain(X1),codomain(X2))) = domain(X1)
| domain(X1) != codomain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_24]),c_0_28]),
[final] ).
cnf(c_0_410,plain,
( domain(compose(codomain(X1),codomain(X2))) = codomain(X1)
| codomain(X1) != codomain(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_38]),c_0_23]),
[final] ).
cnf(c_0_411,hypothesis,
( codomain(compose(codomain(X1),compose(a,h))) = codomain(h)
| codomain(X1) != domain(a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_41]),c_0_26]),c_0_30]),
[final] ).
cnf(c_0_412,hypothesis,
( domain(compose(a,compose(a,b))) = domain(a)
| domain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_31,c_0_37]),
[final] ).
cnf(c_0_413,hypothesis,
( domain(compose(compose(a,h),compose(a,h))) = domain(a)
| codomain(h) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_36]),c_0_41]),
[final] ).
cnf(c_0_414,hypothesis,
( codomain(compose(compose(a,h),compose(a,h))) = codomain(h)
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_160,c_0_36]),
[final] ).
cnf(c_0_415,hypothesis,
( codomain(compose(a,compose(a,h))) = codomain(h)
| domain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_160,c_0_18]),
[final] ).
cnf(c_0_416,hypothesis,
( domain(compose(codomain(X1),h)) = codomain(X1)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_163,c_0_23]),
[final] ).
cnf(c_0_417,hypothesis,
( domain(compose(codomain(X1),g)) = codomain(X1)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_164,c_0_23]),
[final] ).
cnf(c_0_418,hypothesis,
( domain(compose(a,compose(a,h))) = domain(a)
| domain(b) != domain(a) ),
inference(spm,[status(thm)],[c_0_31,c_0_41]),
[final] ).
cnf(c_0_419,hypothesis,
( codomain(compose(a,domain(X1))) = domain(X1)
| domain(b) != domain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_28]),c_0_24]),
[final] ).
cnf(c_0_420,hypothesis,
( codomain(compose(codomain(X1),h)) = codomain(h)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_165,c_0_23]),
[final] ).
cnf(c_0_421,hypothesis,
( domain(compose(a,domain(X1))) = domain(a)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_28]),
[final] ).
cnf(c_0_422,hypothesis,
( codomain(compose(codomain(X1),g)) = codomain(h)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_166,c_0_23]),
[final] ).
cnf(c_0_423,hypothesis,
( codomain(compose(g,compose(a,b))) = codomain(b)
| codomain(h) != domain(a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_37]),c_0_35]),
[final] ).
cnf(c_0_424,hypothesis,
( domain(compose(g,compose(a,b))) = domain(b)
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_168,c_0_37]),
[final] ).
cnf(c_0_425,hypothesis,
( codomain(compose(g,domain(X1))) = domain(X1)
| codomain(h) != domain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_28]),c_0_24]),
[final] ).
cnf(c_0_426,hypothesis,
( domain(compose(a,codomain(X1))) = domain(a)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_31,c_0_23]),
[final] ).
cnf(c_0_427,hypothesis,
( codomain(compose(g,codomain(X1))) = codomain(X1)
| codomain(h) != codomain(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_23]),c_0_38]),
[final] ).
cnf(c_0_428,hypothesis,
( domain(compose(g,domain(X1))) = domain(b)
| codomain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_168,c_0_28]),
[final] ).
cnf(c_0_429,hypothesis,
( domain(compose(g,codomain(X1))) = domain(b)
| codomain(h) != codomain(X1) ),
inference(spm,[status(thm)],[c_0_168,c_0_23]),
[final] ).
cnf(c_0_430,hypothesis,
( domain(compose(g,compose(a,h))) = domain(b)
| codomain(h) != domain(a) ),
inference(spm,[status(thm)],[c_0_168,c_0_41]),
[final] ).
cnf(c_0_431,hypothesis,
( codomain(compose(a,codomain(X1))) = codomain(X1)
| codomain(X1) != domain(b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_23]),c_0_38]),
[final] ).
cnf(c_0_432,hypothesis,
( codomain(compose(g,compose(a,h))) = codomain(h)
| codomain(h) != domain(a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_41]),c_0_26]),c_0_30]),
[final] ).
cnf(c_0_433,negated_conjecture,
h != g,
prove_h_equals_g,
[final] ).
cnf(c_0_434,plain,
compose(codomain(X1),codomain(X1)) = codomain(X1),
inference(spm,[status(thm)],[c_0_43,c_0_38]),
[final] ).
cnf(c_0_435,hypothesis,
compose(domain(b),h) = h,
inference(spm,[status(thm)],[c_0_51,c_0_15]),
[final] ).
cnf(c_0_436,hypothesis,
compose(domain(b),g) = g,
inference(spm,[status(thm)],[c_0_51,c_0_21]),
[final] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT001-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n004.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 10:47:17 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.44/1.77 % Version : CSE_E---1.7
% 1.44/1.77 % Problem : theBenchmark.p
% 1.44/1.77 % SZS status Satisfiable for theBenchmark.p
% 1.44/1.77 % SZS output start Saturation
% See solution above
% 1.44/1.77 % Total time : 1.371s
%------------------------------------------------------------------------------