%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT007-1 : 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 : n021.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 04:11:39 PM UTC 2026
% Result : Unsatisfiable 0.25s 1.61s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 85)
% Comments :
%------------------------------------------------------------------------------
cnf(category_theory_axiom2,axiom,
( product(X1,X6,X5)
| ~ product(X1,X2,X3)
| ~ product(X3,X4,X5)
| ~ product(X2,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom2) ).
cnf(category_theory_axiom5,axiom,
( product(X6,X2,X5)
| ~ product(X1,X2,X3)
| ~ product(X4,X3,X5)
| ~ product(X4,X1,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom5) ).
cnf(category_theory_axiom1,axiom,
( defined(X1,X5)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ defined(X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom1) ).
cnf(category_theory_axiom4,axiom,
( defined(X5,X2)
| ~ product(X1,X2,X3)
| ~ product(X4,X1,X5)
| ~ defined(X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom4) ).
cnf(composition_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',composition_is_well_defined) ).
cnf(associative_property2,axiom,
( defined(X2,X4)
| ~ product(X1,X2,X3)
| ~ defined(X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property2) ).
cnf(category_theory_axiom3,axiom,
( defined(X4,X1)
| ~ product(X1,X2,X3)
| ~ defined(X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom3) ).
cnf(closure_of_composition,axiom,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).
cnf(associative_property1,axiom,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property1) ).
cnf(identity2,axiom,
( product(X1,X2,X1)
| ~ defined(X1,X2)
| ~ identity_map(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity2) ).
cnf(identity1,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity1) ).
cnf(category_theory_axiom6,axiom,
( defined(X1,X3)
| ~ defined(X1,X2)
| ~ defined(X2,X3)
| ~ identity_map(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom6) ).
cnf(product_on_codomain,axiom,
product(codomain(X1),X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_codomain) ).
cnf(product_on_domain,axiom,
product(X1,domain(X1),X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).
cnf(mapping_from_codomain_of_x_to_x,axiom,
defined(codomain(X1),X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',mapping_from_codomain_of_x_to_x) ).
cnf(mapping_from_x_to_its_domain,axiom,
defined(X1,domain(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',mapping_from_x_to_its_domain) ).
cnf(prove_ab_is_defined,negated_conjecture,
~ defined(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ab_is_defined) ).
cnf(codomain_is_an_identity_map,axiom,
identity_map(codomain(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',codomain_is_an_identity_map) ).
cnf(domain_is_an_identity_map,axiom,
identity_map(domain(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).
cnf(domain_of_a_equals_codomain_of_b,hypothesis,
domain(a) = codomain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_a_equals_codomain_of_b) ).
cnf(i_0_20,axiom,
( product(X1,X6,X5)
| ~ product(X1,X2,X3)
| ~ product(X3,X4,X5)
| ~ product(X2,X4,X6) ),
category_theory_axiom2,
[final] ).
cnf(i_0_21,axiom,
( product(X6,X2,X5)
| ~ product(X1,X2,X3)
| ~ product(X4,X3,X5)
| ~ product(X4,X1,X6) ),
category_theory_axiom5,
[final] ).
cnf(i_0_22,axiom,
( defined(X1,X5)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ defined(X3,X4) ),
category_theory_axiom1,
[final] ).
cnf(i_0_23,axiom,
( defined(X5,X2)
| ~ product(X1,X2,X3)
| ~ product(X4,X1,X5)
| ~ defined(X4,X3) ),
category_theory_axiom4,
[final] ).
cnf(i_0_24,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
composition_is_well_defined,
[final] ).
cnf(i_0_25,axiom,
( defined(X2,X4)
| ~ product(X1,X2,X3)
| ~ defined(X3,X4) ),
associative_property2,
[final] ).
cnf(i_0_26,axiom,
( defined(X4,X1)
| ~ product(X1,X2,X3)
| ~ defined(X4,X3) ),
category_theory_axiom3,
[final] ).
cnf(i_0_27,axiom,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
closure_of_composition,
[final] ).
cnf(i_0_28,axiom,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
associative_property1,
[final] ).
cnf(i_0_29,axiom,
( product(X1,X2,X1)
| ~ defined(X1,X2)
| ~ identity_map(X2) ),
identity2,
[final] ).
cnf(i_0_30,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
identity1,
[final] ).
cnf(i_0_31,axiom,
( defined(X1,X3)
| ~ defined(X1,X2)
| ~ defined(X2,X3)
| ~ identity_map(X2) ),
category_theory_axiom6,
[final] ).
cnf(i_0_32,axiom,
product(codomain(X1),X1,X1),
product_on_codomain,
[final] ).
cnf(i_0_33,axiom,
product(X1,domain(X1),X1),
product_on_domain,
[final] ).
cnf(i_0_34,axiom,
defined(codomain(X1),X1),
mapping_from_codomain_of_x_to_x,
[final] ).
cnf(i_0_35,axiom,
defined(X1,domain(X1)),
mapping_from_x_to_its_domain,
[final] ).
cnf(i_0_36,negated_conjecture,
~ defined(a,b),
prove_ab_is_defined,
[final] ).
cnf(i_0_37,axiom,
identity_map(codomain(X1)),
codomain_is_an_identity_map,
[final] ).
cnf(i_0_38,axiom,
identity_map(domain(X1)),
domain_is_an_identity_map,
[final] ).
cnf(i_0_39,hypothesis,
domain(a) = codomain(b),
domain_of_a_equals_codomain_of_b,
[final] ).
cnf(i_0_40,axiom,
X1 = X1 ).
cnf(i_0_41,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_42,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_43,axiom,
( X1 != X2
| codomain(X1) = codomain(X2) ) ).
cnf(i_0_44,axiom,
( X1 != X2
| domain(X1) = domain(X2) ) ).
cnf(i_0_45,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_46,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_47,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_48,axiom,
( X1 != X2
| ~ defined(X1,X3)
| defined(X2,X3) ) ).
cnf(i_0_49,axiom,
( X1 != X2
| ~ defined(X3,X1)
| defined(X3,X2) ) ).
cnf(i_0_50,axiom,
( X1 != X2
| ~ identity_map(X1)
| identity_map(X2) ) ).
cnf(i_0_40_001,axiom,
X1 = X1 ).
cnf(i_0_41_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_42_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_43_004,axiom,
( X1 != X2
| codomain(X1) = codomain(X2) ) ).
cnf(i_0_44_005,axiom,
( X1 != X2
| domain(X1) = domain(X2) ) ).
cnf(i_0_45_006,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_46_007,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_47_008,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_48_009,axiom,
( X1 != X2
| ~ defined(X1,X3)
| defined(X2,X3) ) ).
cnf(i_0_49_010,axiom,
( X1 != X2
| ~ defined(X3,X1)
| defined(X3,X2) ) ).
cnf(i_0_50_011,axiom,
( X1 != X2
| ~ identity_map(X1)
| identity_map(X2) ) ).
cnf(i_0_51,plain,
~ product(a,b,X1),
inference(scs_inference,[],[i_0_36,i_0_28]) ).
cnf(i_0_52,plain,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_53,plain,
codomain(b) = domain(a),
inference(scs_inference,[],[i_0_36,i_0_39,i_0_28,i_0_41]) ).
cnf(i_0_54,plain,
~ product(X1,a,codomain(b)),
inference(scs_inference,[],[i_0_36,i_0_34,i_0_39,i_0_28,i_0_41,i_0_25]) ).
cnf(i_0_55,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_56,plain,
( ~ defined(X1,X2)
| defined(X3,X2)
| ~ product(X4,X3,X1) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_57,plain,
defined(codomain(X1),codomain(X1)),
inference(scs_inference,[],[i_0_36,i_0_32,i_0_34,i_0_55,i_0_39,i_0_28,i_0_41,i_0_25,i_0_26]) ).
cnf(i_0_58,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_59,plain,
( ~ defined(X1,X2)
| defined(X1,X3)
| ~ product(X3,X4,X2) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_60,plain,
codomain(b) != a,
inference(scs_inference,[],[i_0_36,i_0_32,i_0_34,i_0_55,i_0_58,i_0_39,i_0_28,i_0_41,i_0_25,i_0_26,i_0_48]) ).
cnf(i_0_61,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_62,plain,
~ product(a,domain(a),codomain(b)),
inference(scs_inference,[],[i_0_36,i_0_32,i_0_33,i_0_34,i_0_55,i_0_58,i_0_39,i_0_28,i_0_41,i_0_25,i_0_26,i_0_48,i_0_24]) ).
cnf(i_0_63,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_64,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_65,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(scs_inference,[],[i_0_36,i_0_32,i_0_33,i_0_34,i_0_55,i_0_58,i_0_37,i_0_39,i_0_28,i_0_41,i_0_25,i_0_26,i_0_48,i_0_24,i_0_29]) ).
cnf(i_0_66,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_67,plain,
domain(a) != b,
inference(scs_inference,[],[i_0_36,i_0_32,i_0_33,i_0_63,i_0_34,i_0_55,i_0_58,i_0_37,i_0_39,i_0_28,i_0_41,i_0_25,i_0_26,i_0_48,i_0_24,i_0_29,i_0_46]) ).
cnf(i_0_68,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_69,plain,
~ product(X1,a,domain(a)),
inference(scs_inference,[],[i_0_36,i_0_32,i_0_33,i_0_63,i_0_34,i_0_55,i_0_58,i_0_37,i_0_39,i_0_28,i_0_41,i_0_25,i_0_26,i_0_48,i_0_24,i_0_29,i_0_46,i_0_47]) ).
cnf(i_0_70,plain,
~ product(a,codomain(b),codomain(b)),
inference(scs_inference,[],[i_0_36,i_0_32,i_0_33,i_0_63,i_0_34,i_0_55,i_0_58,i_0_61,i_0_37,i_0_39,i_0_28,i_0_41,i_0_25,i_0_26,i_0_48,i_0_24,i_0_29,i_0_46,i_0_47,i_0_22]) ).
cnf(i_0_71,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_72,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_73,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X5,X2,X4) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_74,plain,
~ product(codomain(b),codomain(b),a),
inference(scs_inference,[],[i_0_36,i_0_32,i_0_72,i_0_33,i_0_63,i_0_34,i_0_55,i_0_58,i_0_61,i_0_71,i_0_37,i_0_39,i_0_28,i_0_41,i_0_25,i_0_26,i_0_48,i_0_24,i_0_29,i_0_46,i_0_47,i_0_22,i_0_23]) ).
cnf(i_0_75,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_76,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_77,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_78,plain,
~ defined(a,codomain(b)),
inference(scs_inference,[],[i_0_36,i_0_32,i_0_72,i_0_33,i_0_63,i_0_34,i_0_55,i_0_58,i_0_61,i_0_71,i_0_75,i_0_37,i_0_39,i_0_28,i_0_41,i_0_25,i_0_26,i_0_48,i_0_24,i_0_29,i_0_46,i_0_47,i_0_22,i_0_23,i_0_31]) ).
cnf(i_0_79,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_80,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_81,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| defined(X3,X2)
| ~ defined(X3,X1) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_82,plain,
~ product(domain(a),b,domain(a)),
inference(scs_inference,[],[i_0_36,i_0_32,i_0_72,i_0_33,i_0_63,i_0_68,i_0_34,i_0_55,i_0_58,i_0_61,i_0_71,i_0_75,i_0_37,i_0_39,i_0_28,i_0_41,i_0_25,i_0_26,i_0_48,i_0_24,i_0_29,i_0_46,i_0_47,i_0_22,i_0_23,i_0_31,i_0_21]) ).
cnf(i_0_83,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_84,plain,
( ~ product(X1,X2,X3)
| product(X3,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X1,X6,X5) ),
inference(rename_variables,[],[i_0_21]) ).
cnf(i_0_85,plain,
( X1 != a
| ~ product(X1,b,a) ),
inference(scs_inference,[],[i_0_36,i_0_32,i_0_72,i_0_33,i_0_63,i_0_68,i_0_34,i_0_55,i_0_58,i_0_61,i_0_71,i_0_75,i_0_37,i_0_39,i_0_28,i_0_41,i_0_25,i_0_26,i_0_48,i_0_24,i_0_29,i_0_46,i_0_47,i_0_22,i_0_23,i_0_31,i_0_21,i_0_45]) ).
cnf(i_0_86,plain,
defined(X1,domain(X1)),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_87,plain,
( ~ product(a,codomain(b),X1)
| ~ product(X1,b,a) ),
inference(scs_inference,[],[i_0_36,i_0_32,i_0_72,i_0_76,i_0_33,i_0_63,i_0_68,i_0_34,i_0_55,i_0_58,i_0_61,i_0_71,i_0_75,i_0_35,i_0_37,i_0_39,i_0_28,i_0_41,i_0_25,i_0_26,i_0_48,i_0_24,i_0_29,i_0_46,i_0_47,i_0_22,i_0_23,i_0_31,i_0_21,i_0_45,i_0_49,i_0_20]) ).
cnf(i_0_88,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_89,plain,
( ~ product(X1,X2,X3)
| product(X4,X3,X5)
| ~ product(X4,X1,X6)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_90,plain,
~ product(a,b,a),
inference(equality_inference,[],[85]) ).
cnf(i_0_91,plain,
~ product(a,codomain(b),X1),
inference(scs_inference,[],[i_0_78,i_0_28]) ).
cnf(i_0_92,plain,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_93,plain,
~ product(b,X1,domain(a)),
inference(scs_inference,[],[i_0_36,i_0_78,i_0_35,i_0_28,i_0_26]) ).
cnf(i_0_94,plain,
defined(X1,domain(X1)),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_95,plain,
( ~ defined(X1,X2)
| defined(X1,X3)
| ~ product(X3,X4,X2) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_96,plain,
~ product(codomain(b),domain(a),a),
inference(scs_inference,[],[i_0_36,i_0_74,i_0_78,i_0_35,i_0_39,i_0_28,i_0_26,i_0_46]) ).
cnf(i_0_97,plain,
~ product(a,domain(a),domain(a)),
inference(scs_inference,[],[i_0_36,i_0_74,i_0_78,i_0_62,i_0_35,i_0_39,i_0_28,i_0_26,i_0_46,i_0_47]) ).
cnf(i_0_98,plain,
$false,
inference(scs_inference,[],[i_0_36,i_0_74,i_0_78,i_0_62,i_0_35,i_0_94,i_0_39,i_0_28,i_0_26,i_0_46,i_0_47,i_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : CAT007-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % 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 : n021.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 10:47:25 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 0.25/1.61 % Version : CSE_E---1.7
% 0.25/1.61 % Problem : theBenchmark.p
% 0.25/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.25/1.61 % SZS output start CNFRefutation
% See solution above
% 0.35/1.77 % Total time : 1.270s
%------------------------------------------------------------------------------