%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT008-1 : 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 : n001.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 04:11:40 PM UTC 2026
% Result : Unsatisfiable 0.35s 1.61s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 65)
% 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(ab_defined,hypothesis,
defined(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_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(prove_domain_of_a_equals_codomain_of_b,negated_conjecture,
domain(a) != codomain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_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,hypothesis,
defined(a,b),
ab_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,negated_conjecture,
domain(a) != codomain(b),
prove_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(codomain(codomain(b)),codomain(b),domain(a)),
inference(scs_inference,[],[i_0_39,i_0_32,i_0_24]) ).
cnf(i_0_52,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_53,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_54,plain,
codomain(b) != domain(a),
inference(scs_inference,[],[i_0_39,i_0_32,i_0_52,i_0_24,i_0_47]) ).
cnf(i_0_55,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_56,plain,
defined(codomain(X1),codomain(X1)),
inference(scs_inference,[],[i_0_39,i_0_32,i_0_52,i_0_55,i_0_34,i_0_24,i_0_47,i_0_26]) ).
cnf(i_0_57,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_58,plain,
( ~ defined(X1,X2)
| defined(X1,X3)
| ~ product(X3,X4,X2) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_59,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(scs_inference,[],[i_0_39,i_0_32,i_0_52,i_0_55,i_0_34,i_0_37,i_0_24,i_0_47,i_0_26,i_0_29]) ).
cnf(i_0_60,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_61,plain,
~ product(codomain(b),domain(codomain(b)),domain(a)),
inference(scs_inference,[],[i_0_39,i_0_32,i_0_52,i_0_55,i_0_33,i_0_34,i_0_37,i_0_24,i_0_47,i_0_26,i_0_29,i_0_20]) ).
cnf(i_0_62,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_63,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_64,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_65,plain,
( X1 != codomain(codomain(b))
| ~ product(X1,codomain(b),domain(a)) ),
inference(scs_inference,[],[i_0_39,i_0_32,i_0_52,i_0_55,i_0_33,i_0_34,i_0_37,i_0_24,i_0_47,i_0_26,i_0_29,i_0_20,i_0_45]) ).
cnf(i_0_66,plain,
( X1 != codomain(b)
| ~ product(codomain(codomain(b)),X1,domain(a)) ),
inference(scs_inference,[],[i_0_39,i_0_32,i_0_52,i_0_55,i_0_33,i_0_34,i_0_37,i_0_24,i_0_47,i_0_26,i_0_29,i_0_20,i_0_45,i_0_46]) ).
cnf(i_0_67,plain,
( identity_map(X1)
| codomain(codomain(b)) != X1 ),
inference(scs_inference,[],[i_0_39,i_0_32,i_0_52,i_0_55,i_0_33,i_0_34,i_0_37,i_0_24,i_0_47,i_0_26,i_0_29,i_0_20,i_0_45,i_0_46,i_0_50]) ).
cnf(i_0_68,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_69,plain,
( product(a,b,b)
| codomain(codomain(b)) != a ),
inference(scs_inference,[],[i_0_39,i_0_32,i_0_52,i_0_55,i_0_33,i_0_34,i_0_36,i_0_37,i_0_24,i_0_47,i_0_26,i_0_29,i_0_20,i_0_45,i_0_46,i_0_50,i_0_30]) ).
cnf(i_0_70,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_71,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_72,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_73,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_74,plain,
( defined(X1,domain(X2))
| codomain(codomain(b)) != a
| ~ product(X2,codomain(domain(X2)),X1) ),
inference(scs_inference,[],[i_0_39,i_0_32,i_0_52,i_0_55,i_0_63,i_0_71,i_0_72,i_0_33,i_0_34,i_0_57,i_0_35,i_0_36,i_0_37,i_0_24,i_0_47,i_0_26,i_0_29,i_0_20,i_0_50,i_0_30,i_0_23]) ).
cnf(i_0_75,plain,
~ product(codomain(codomain(b)),codomain(b),domain(a)),
inference(equality_inference,[],[65]) ).
cnf(i_0_76,plain,
~ product(codomain(codomain(b)),codomain(b),domain(a)),
inference(equality_inference,[],[66]) ).
cnf(i_0_77,plain,
identity_map(codomain(codomain(b))),
inference(equality_inference,[],[67]) ).
cnf(i_0_78,plain,
~ product(codomain(b),codomain(b),domain(a)),
inference(scs_inference,[],[i_0_39,i_0_59,i_0_24]) ).
cnf(i_0_79,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_80,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_81,plain,
defined(X1,codomain(domain(X1))),
inference(scs_inference,[],[i_0_39,i_0_35,i_0_59,i_0_32,i_0_24,i_0_26]) ).
cnf(i_0_82,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_83,plain,
( ~ defined(X1,X2)
| defined(X1,X3)
| ~ product(X3,X4,X2) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_84,plain,
product(X1,codomain(domain(X1)),X1),
inference(scs_inference,[],[i_0_39,i_0_35,i_0_59,i_0_32,i_0_37,i_0_24,i_0_26,i_0_29]) ).
cnf(i_0_85,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_86,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_87,plain,
( ~ identity_map(a)
| product(a,b,b) ),
inference(scs_inference,[],[i_0_39,i_0_35,i_0_36,i_0_59,i_0_32,i_0_37,i_0_24,i_0_26,i_0_29,i_0_30]) ).
cnf(i_0_88,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_89,plain,
( product(a,b,b)
| domain(X1) != a ),
inference(scs_inference,[],[i_0_39,i_0_35,i_0_36,i_0_59,i_0_38,i_0_32,i_0_37,i_0_24,i_0_26,i_0_29,i_0_30,i_0_50]) ).
cnf(i_0_90,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_91,plain,
defined(X1,domain(X1)),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_92,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_93,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| defined(X3,X2)
| ~ defined(X3,X1) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_94,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_95,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_96,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_97,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_98,plain,
defined(X1,domain(X1)),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_99,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_100,plain,
defined(X1,domain(X1)),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_101,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_103,plain,
defined(domain(X1),domain(X1)),
inference(scs_inference,[],[i_0_35,i_0_33,i_0_25]) ).
cnf(i_0_104,plain,
defined(X1,domain(X1)),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_105,plain,
( ~ defined(X1,X2)
| defined(X3,X2)
| ~ product(X4,X3,X1) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_106,plain,
product(domain(X1),domain(X1),domain(X1)),
inference(scs_inference,[],[i_0_35,i_0_33,i_0_38,i_0_25,i_0_29]) ).
cnf(i_0_107,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_108,plain,
~ product(domain(a),domain(a),codomain(b)),
inference(scs_inference,[],[i_0_54,i_0_35,i_0_33,i_0_38,i_0_25,i_0_29,i_0_24]) ).
cnf(i_0_109,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_110,plain,
( X1 != codomain(b)
| ~ product(X1,codomain(b),domain(a)) ),
inference(scs_inference,[],[i_0_78,i_0_54,i_0_35,i_0_33,i_0_38,i_0_25,i_0_29,i_0_24,i_0_45]) ).
cnf(i_0_111,plain,
( X1 != b
| ~ product(codomain(X1),codomain(b),domain(a)) ),
inference(scs_inference,[],[i_0_78,i_0_54,i_0_35,i_0_33,i_0_38,i_0_25,i_0_29,i_0_24,i_0_45,i_0_43]) ).
cnf(i_0_112,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_113,plain,
identity_map(domain(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_114,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_115,plain,
defined(X1,domain(X1)),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_116,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_117,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_118,plain,
product(X1,codomain(domain(X1)),X1),
inference(rename_variables,[],[i_0_84]) ).
cnf(i_0_119,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_120,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_121,plain,
defined(X1,domain(X1)),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_122,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_123,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_124,plain,
( product(a,b,b)
| defined(X1,domain(domain(X2)))
| ~ product(codomain(X3),codomain(b),domain(a))
| ~ product(X2,domain(X2),X1) ),
inference(scs_inference,[],[i_0_51,i_0_78,i_0_54,i_0_35,i_0_104,i_0_115,i_0_121,i_0_34,i_0_36,i_0_33,i_0_117,i_0_119,i_0_122,i_0_84,i_0_32,i_0_114,i_0_38,i_0_113,i_0_25,i_0_29,i_0_24,i_0_45,i_0_43,i_0_30,i_0_50,i_0_47,i_0_31,i_0_21,i_0_20,i_0_22,i_0_23]) ).
cnf(i_0_125,plain,
~ product(codomain(b),codomain(b),domain(a)),
inference(equality_inference,[],[110]) ).
cnf(i_0_126,plain,
~ product(codomain(b),codomain(b),domain(a)),
inference(equality_inference,[],[111]) ).
cnf(i_0_127,plain,
defined(domain(a),b),
inference(scs_inference,[],[i_0_36,i_0_33,i_0_25]) ).
cnf(i_0_128,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_129,plain,
( ~ defined(X1,X2)
| defined(X3,X2)
| ~ product(X4,X3,X1) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_130,plain,
product(domain(a),b,b),
inference(scs_inference,[],[i_0_36,i_0_33,i_0_38,i_0_25,i_0_30]) ).
cnf(i_0_131,plain,
identity_map(domain(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_132,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_133,plain,
defined(codomain(domain(a)),b),
inference(scs_inference,[],[i_0_34,i_0_36,i_0_33,i_0_38,i_0_131,i_0_25,i_0_30,i_0_31]) ).
cnf(i_0_134,plain,
identity_map(domain(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_135,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_136,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| defined(X3,X2)
| ~ defined(X3,X1) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_137,plain,
( ~ identity_map(b)
| product(a,b,a) ),
inference(scs_inference,[],[i_0_34,i_0_36,i_0_33,i_0_38,i_0_131,i_0_25,i_0_30,i_0_31,i_0_29]) ).
cnf(i_0_138,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_139,plain,
( product(a,b,a)
| codomain(X1) != b ),
inference(scs_inference,[],[i_0_34,i_0_36,i_0_33,i_0_37,i_0_38,i_0_131,i_0_25,i_0_30,i_0_31,i_0_29,i_0_50]) ).
cnf(i_0_140,plain,
( product(a,b,a)
| ~ product(domain(a),b,codomain(X1)) ),
inference(scs_inference,[],[i_0_34,i_0_36,i_0_33,i_0_37,i_0_38,i_0_131,i_0_25,i_0_30,i_0_31,i_0_29,i_0_50,i_0_24]) ).
cnf(i_0_141,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_142,plain,
( product(a,b,a)
| b != codomain(X1) ),
inference(scs_inference,[],[i_0_51,i_0_34,i_0_36,i_0_33,i_0_37,i_0_38,i_0_131,i_0_25,i_0_30,i_0_31,i_0_29,i_0_50,i_0_24,i_0_45,i_0_46,i_0_47]) ).
cnf(i_0_143,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_144,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_145,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_146,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_147,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_148,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_149,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_150,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_152,plain,
defined(a,codomain(b)),
inference(scs_inference,[],[i_0_36,i_0_32,i_0_26]) ).
cnf(i_0_153,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_154,plain,
( ~ defined(X1,X2)
| defined(X1,X3)
| ~ product(X3,X4,X2) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_155,plain,
product(codomain(domain(a)),b,b),
inference(scs_inference,[],[i_0_36,i_0_32,i_0_133,i_0_37,i_0_26,i_0_30]) ).
cnf(i_0_156,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_157,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_158,plain,
product(a,codomain(b),a),
inference(scs_inference,[],[i_0_36,i_0_32,i_0_133,i_0_37,i_0_156,i_0_26,i_0_30,i_0_29]) ).
cnf(i_0_159,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_160,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_161,plain,
( X1 != domain(a)
| ~ product(X1,domain(a),codomain(b)) ),
inference(scs_inference,[],[i_0_108,i_0_36,i_0_32,i_0_133,i_0_37,i_0_156,i_0_26,i_0_30,i_0_29,i_0_45]) ).
cnf(i_0_162,plain,
( X1 != a
| ~ product(domain(X1),domain(a),codomain(b)) ),
inference(scs_inference,[],[i_0_108,i_0_36,i_0_32,i_0_133,i_0_37,i_0_156,i_0_26,i_0_30,i_0_29,i_0_45,i_0_44]) ).
cnf(i_0_163,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_164,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_165,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_166,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_167,plain,
defined(codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_168,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_169,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_170,plain,
defined(codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_172,plain,
~ product(domain(a),domain(a),codomain(b)),
inference(equality_inference,[],[161]) ).
cnf(i_0_173,plain,
~ product(domain(a),domain(a),codomain(b)),
inference(equality_inference,[],[162]) ).
cnf(i_0_174,plain,
defined(domain(a),codomain(b)),
inference(scs_inference,[],[i_0_33,i_0_152,i_0_25]) ).
cnf(i_0_175,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_176,plain,
( ~ defined(X1,X2)
| defined(X3,X2)
| ~ product(X4,X3,X1) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_177,plain,
product(domain(a),codomain(b),codomain(b)),
inference(scs_inference,[],[i_0_33,i_0_152,i_0_38,i_0_25,i_0_30]) ).
cnf(i_0_178,plain,
identity_map(domain(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_179,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_180,plain,
product(domain(a),codomain(b),domain(a)),
inference(scs_inference,[],[i_0_33,i_0_152,i_0_37,i_0_38,i_0_25,i_0_30,i_0_29]) ).
cnf(i_0_181,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_182,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_183,plain,
$false,
inference(scs_inference,[],[i_0_39,i_0_33,i_0_152,i_0_37,i_0_38,i_0_25,i_0_30,i_0_29,i_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT008-1 : 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
% 0.16/0.32 % Computer : n001.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 10:47:18 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.35/1.61 % Version : CSE_E---1.7
% 0.35/1.61 % Problem : theBenchmark.p
% 0.35/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.35/1.61 % SZS output start CNFRefutation
% See solution above
% 0.56/1.82 % Total time : 1.271s
%------------------------------------------------------------------------------