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CSE_E---1.7.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : CAT012-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n028.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 04:11:41 PM UTC 2026

% Result   : Unsatisfiable 0.32s 1.61s
% Output   : CNFRefutation 0.44s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named 71)

% 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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).

cnf(associative_property1,axiom,
    ( defined(X1,X2)
    | ~ product(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',associative_property1) ).

cnf(identity2,axiom,
    ( product(X1,X2,X1)
    | ~ defined(X1,X2)
    | ~ identity_map(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',identity2) ).

cnf(identity1,axiom,
    ( product(X1,X2,X2)
    | ~ defined(X1,X2)
    | ~ identity_map(X1) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom6) ).

cnf(product_on_codomain,axiom,
    product(codomain(X1),X1,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',product_on_codomain) ).

cnf(product_on_domain,axiom,
    product(X1,domain(X1),X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).

cnf(mapping_from_codomain_of_x_to_x,axiom,
    defined(codomain(X1),X1),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/CAT001-0.ax',mapping_from_x_to_its_domain) ).

cnf(prove_codomain_of_domain_is_domain,negated_conjecture,
    codomain(domain(a)) != domain(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_domain_is_domain) ).

cnf(codomain_is_an_identity_map,axiom,
    identity_map(codomain(X1)),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',codomain_is_an_identity_map) ).

cnf(domain_is_an_identity_map,axiom,
    identity_map(domain(X1)),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).

cnf(i_0_19,axiom,
    ( product(X1,X6,X5)
    | ~ product(X1,X2,X3)
    | ~ product(X3,X4,X5)
    | ~ product(X2,X4,X6) ),
    category_theory_axiom2,
    [final] ).

cnf(i_0_20,axiom,
    ( product(X6,X2,X5)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X3,X5)
    | ~ product(X4,X1,X6) ),
    category_theory_axiom5,
    [final] ).

cnf(i_0_21,axiom,
    ( defined(X1,X5)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ defined(X3,X4) ),
    category_theory_axiom1,
    [final] ).

cnf(i_0_22,axiom,
    ( defined(X5,X2)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X1,X5)
    | ~ defined(X4,X3) ),
    category_theory_axiom4,
    [final] ).

cnf(i_0_23,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    composition_is_well_defined,
    [final] ).

cnf(i_0_24,axiom,
    ( defined(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ defined(X3,X4) ),
    associative_property2,
    [final] ).

cnf(i_0_25,axiom,
    ( defined(X4,X1)
    | ~ product(X1,X2,X3)
    | ~ defined(X4,X3) ),
    category_theory_axiom3,
    [final] ).

cnf(i_0_26,axiom,
    ( product(X1,X2,compose(X1,X2))
    | ~ defined(X1,X2) ),
    closure_of_composition,
    [final] ).

cnf(i_0_27,axiom,
    ( defined(X1,X2)
    | ~ product(X1,X2,X3) ),
    associative_property1,
    [final] ).

cnf(i_0_28,axiom,
    ( product(X1,X2,X1)
    | ~ defined(X1,X2)
    | ~ identity_map(X2) ),
    identity2,
    [final] ).

cnf(i_0_29,axiom,
    ( product(X1,X2,X2)
    | ~ defined(X1,X2)
    | ~ identity_map(X1) ),
    identity1,
    [final] ).

cnf(i_0_30,axiom,
    ( defined(X1,X3)
    | ~ defined(X1,X2)
    | ~ defined(X2,X3)
    | ~ identity_map(X2) ),
    category_theory_axiom6,
    [final] ).

cnf(i_0_31,axiom,
    product(codomain(X1),X1,X1),
    product_on_codomain,
    [final] ).

cnf(i_0_32,axiom,
    product(X1,domain(X1),X1),
    product_on_domain,
    [final] ).

cnf(i_0_33,axiom,
    defined(codomain(X1),X1),
    mapping_from_codomain_of_x_to_x,
    [final] ).

cnf(i_0_34,axiom,
    defined(X1,domain(X1)),
    mapping_from_x_to_its_domain,
    [final] ).

cnf(i_0_35,negated_conjecture,
    codomain(domain(a)) != domain(a),
    prove_codomain_of_domain_is_domain,
    [final] ).

cnf(i_0_36,axiom,
    identity_map(codomain(X1)),
    codomain_is_an_identity_map,
    [final] ).

cnf(i_0_37,axiom,
    identity_map(domain(X1)),
    domain_is_an_identity_map,
    [final] ).

cnf(i_0_38,axiom,
    X1 = X1 ).

cnf(i_0_39,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_40,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_41,axiom,
    ( X1 != X2
    | codomain(X1) = codomain(X2) ) ).

cnf(i_0_42,axiom,
    ( X1 != X2
    | domain(X1) = domain(X2) ) ).

cnf(i_0_43,axiom,
    ( X1 != X2
    | ~ product(X1,X3,X4)
    | product(X2,X3,X4) ) ).

cnf(i_0_44,axiom,
    ( X1 != X2
    | ~ product(X3,X1,X4)
    | product(X3,X2,X4) ) ).

cnf(i_0_45,axiom,
    ( X1 != X2
    | ~ product(X3,X4,X1)
    | product(X3,X4,X2) ) ).

cnf(i_0_46,axiom,
    ( X1 != X2
    | ~ defined(X1,X3)
    | defined(X2,X3) ) ).

cnf(i_0_47,axiom,
    ( X1 != X2
    | ~ defined(X3,X1)
    | defined(X3,X2) ) ).

cnf(i_0_48,axiom,
    ( X1 != X2
    | ~ identity_map(X1)
    | identity_map(X2) ) ).

cnf(i_0_38_001,axiom,
    X1 = X1 ).

cnf(i_0_39_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_40_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_41_004,axiom,
    ( X1 != X2
    | codomain(X1) = codomain(X2) ) ).

cnf(i_0_42_005,axiom,
    ( X1 != X2
    | domain(X1) = domain(X2) ) ).

cnf(i_0_43_006,axiom,
    ( X1 != X2
    | ~ product(X1,X3,X4)
    | product(X2,X3,X4) ) ).

cnf(i_0_44_007,axiom,
    ( X1 != X2
    | ~ product(X3,X1,X4)
    | product(X3,X2,X4) ) ).

cnf(i_0_45_008,axiom,
    ( X1 != X2
    | ~ product(X3,X4,X1)
    | product(X3,X4,X2) ) ).

cnf(i_0_46_009,axiom,
    ( X1 != X2
    | ~ defined(X1,X3)
    | defined(X2,X3) ) ).

cnf(i_0_47_010,axiom,
    ( X1 != X2
    | ~ defined(X3,X1)
    | defined(X3,X2) ) ).

cnf(i_0_48_011,axiom,
    ( X1 != X2
    | ~ identity_map(X1)
    | identity_map(X2) ) ).

cnf(i_0_49,plain,
    ~ product(codomain(domain(a)),domain(a),codomain(domain(a))),
    inference(scs_inference,[],[i_0_35,i_0_31,i_0_23]) ).

cnf(i_0_50,plain,
    product(codomain(X1),X1,X1),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_51,plain,
    ( ~ product(X1,X2,X3)
    | X4 = X3
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_23]) ).

cnf(i_0_52,plain,
    domain(a) != codomain(domain(a)),
    inference(scs_inference,[],[i_0_35,i_0_31,i_0_50,i_0_23,i_0_45]) ).

cnf(i_0_53,plain,
    product(codomain(X1),X1,X1),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_54,plain,
    defined(codomain(X1),codomain(X1)),
    inference(scs_inference,[],[i_0_35,i_0_31,i_0_50,i_0_53,i_0_33,i_0_23,i_0_45,i_0_25]) ).

cnf(i_0_55,plain,
    defined(codomain(X1),X1),
    inference(rename_variables,[],[i_0_33]) ).

cnf(i_0_56,plain,
    ( ~ defined(X1,X2)
    | defined(X1,X3)
    | ~ product(X3,X4,X2) ),
    inference(rename_variables,[],[i_0_25]) ).

cnf(i_0_57,plain,
    product(codomain(codomain(X1)),codomain(X1),codomain(codomain(X1))),
    inference(scs_inference,[],[i_0_35,i_0_31,i_0_50,i_0_53,i_0_33,i_0_55,i_0_36,i_0_23,i_0_45,i_0_25,i_0_28]) ).

cnf(i_0_58,plain,
    defined(codomain(X1),X1),
    inference(rename_variables,[],[i_0_33]) ).

cnf(i_0_59,plain,
    ( ~ defined(X1,X2)
    | ~ identity_map(X2)
    | product(X1,X2,X1) ),
    inference(rename_variables,[],[i_0_28]) ).

cnf(i_0_60,plain,
    product(codomain(X1),domain(codomain(X1)),domain(codomain(X1))),
    inference(scs_inference,[],[i_0_35,i_0_31,i_0_50,i_0_53,i_0_33,i_0_55,i_0_34,i_0_36,i_0_23,i_0_45,i_0_25,i_0_28,i_0_29]) ).

cnf(i_0_61,plain,
    defined(X1,domain(X1)),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_62,plain,
    ( ~ defined(X1,X2)
    | ~ identity_map(X1)
    | product(X1,X2,X2) ),
    inference(rename_variables,[],[i_0_29]) ).

cnf(i_0_63,plain,
    ~ product(domain(a),domain(domain(a)),codomain(domain(a))),
    inference(scs_inference,[],[i_0_35,i_0_31,i_0_50,i_0_53,i_0_32,i_0_33,i_0_55,i_0_34,i_0_36,i_0_23,i_0_45,i_0_25,i_0_28,i_0_29,i_0_19]) ).

cnf(i_0_64,plain,
    product(X1,domain(X1),X1),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_65,plain,
    product(codomain(X1),X1,X1),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_66,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X3,X5)
    | ~ product(X4,X1,X6)
    | ~ product(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_19]) ).

cnf(i_0_67,plain,
    defined(codomain(codomain(X1)),domain(codomain(X1))),
    inference(scs_inference,[],[i_0_35,i_0_31,i_0_50,i_0_53,i_0_32,i_0_33,i_0_55,i_0_58,i_0_34,i_0_61,i_0_36,i_0_23,i_0_45,i_0_25,i_0_28,i_0_29,i_0_19,i_0_30]) ).

cnf(i_0_68,plain,
    defined(X1,domain(X1)),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_69,plain,
    defined(codomain(X1),X1),
    inference(rename_variables,[],[i_0_33]) ).

cnf(i_0_70,plain,
    ( ~ defined(X1,X2)
    | ~ identity_map(X1)
    | defined(X3,X2)
    | ~ defined(X3,X1) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_71,plain,
    ( X1 != codomain(domain(a))
    | ~ product(X1,domain(a),codomain(domain(a))) ),
    inference(scs_inference,[],[i_0_35,i_0_31,i_0_50,i_0_53,i_0_32,i_0_33,i_0_55,i_0_58,i_0_34,i_0_61,i_0_36,i_0_23,i_0_45,i_0_25,i_0_28,i_0_29,i_0_19,i_0_30,i_0_43]) ).

cnf(i_0_72,plain,
    ( X1 != domain(a)
    | ~ product(codomain(X1),domain(a),codomain(domain(a))) ),
    inference(scs_inference,[],[i_0_35,i_0_31,i_0_50,i_0_53,i_0_32,i_0_33,i_0_55,i_0_58,i_0_34,i_0_61,i_0_36,i_0_23,i_0_45,i_0_25,i_0_28,i_0_29,i_0_19,i_0_30,i_0_43,i_0_41]) ).

cnf(i_0_73,plain,
    ( X1 != a
    | ~ product(codomain(domain(X1)),domain(a),codomain(domain(a))) ),
    inference(scs_inference,[],[i_0_35,i_0_31,i_0_50,i_0_53,i_0_32,i_0_33,i_0_55,i_0_58,i_0_34,i_0_61,i_0_36,i_0_23,i_0_45,i_0_25,i_0_28,i_0_29,i_0_19,i_0_30,i_0_43,i_0_41,i_0_42]) ).

cnf(i_0_74,plain,
    ( ~ product(X1,X2,X3)
    | product(X3,X4,X5)
    | ~ product(X2,X4,X6)
    | ~ product(X1,X6,X5) ),
    inference(rename_variables,[],[i_0_20]) ).

cnf(i_0_75,plain,
    product(codomain(X1),X1,X1),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_76,plain,
    defined(codomain(X1),X1),
    inference(rename_variables,[],[i_0_33]) ).

cnf(i_0_77,plain,
    ( defined(X1,X2)
    | ~ product(codomain(domain(X3)),domain(a),codomain(domain(a)))
    | ~ product(codomain(X2),codomain(X2),X1)
    | ~ product(codomain(codomain(codomain(X2))),codomain(X2),X4) ),
    inference(scs_inference,[],[i_0_35,i_0_31,i_0_50,i_0_53,i_0_65,i_0_75,i_0_32,i_0_33,i_0_55,i_0_58,i_0_69,i_0_34,i_0_61,i_0_36,i_0_23,i_0_45,i_0_25,i_0_28,i_0_29,i_0_19,i_0_30,i_0_43,i_0_41,i_0_42,i_0_20,i_0_22]) ).

cnf(i_0_78,plain,
    ~ product(codomain(domain(a)),domain(a),codomain(domain(a))),
    inference(equality_inference,[],[71]) ).

cnf(i_0_79,plain,
    ~ product(codomain(domain(a)),domain(a),codomain(domain(a))),
    inference(equality_inference,[],[72]) ).

cnf(i_0_80,plain,
    ~ product(codomain(domain(a)),domain(a),codomain(domain(a))),
    inference(equality_inference,[],[73]) ).

cnf(i_0_81,plain,
    defined(codomain(X1),codomain(codomain(X1))),
    inference(scs_inference,[],[i_0_54,i_0_57,i_0_24]) ).

cnf(i_0_82,plain,
    defined(codomain(X1),codomain(X1)),
    inference(rename_variables,[],[i_0_54]) ).

cnf(i_0_83,plain,
    ( ~ defined(X1,X2)
    | defined(X3,X2)
    | ~ product(X4,X3,X1) ),
    inference(rename_variables,[],[i_0_24]) ).

cnf(i_0_84,plain,
    product(codomain(X1),codomain(X1),codomain(X1)),
    inference(scs_inference,[],[i_0_54,i_0_82,i_0_57,i_0_36,i_0_24,i_0_28]) ).

cnf(i_0_85,plain,
    defined(codomain(X1),codomain(X1)),
    inference(rename_variables,[],[i_0_54]) ).

cnf(i_0_86,plain,
    ( ~ defined(X1,X2)
    | ~ identity_map(X2)
    | product(X1,X2,X1) ),
    inference(rename_variables,[],[i_0_28]) ).

cnf(i_0_87,plain,
    product(domain(X1),domain(domain(X1)),domain(domain(X1))),
    inference(scs_inference,[],[i_0_54,i_0_82,i_0_57,i_0_37,i_0_34,i_0_36,i_0_24,i_0_28,i_0_29]) ).

cnf(i_0_88,plain,
    defined(X1,domain(X1)),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_89,plain,
    ( ~ defined(X1,X2)
    | ~ identity_map(X1)
    | product(X1,X2,X2) ),
    inference(rename_variables,[],[i_0_29]) ).

cnf(i_0_90,plain,
    ~ product(codomain(domain(a)),codomain(domain(a)),domain(a)),
    inference(scs_inference,[],[i_0_52,i_0_54,i_0_82,i_0_57,i_0_37,i_0_34,i_0_36,i_0_24,i_0_28,i_0_29,i_0_23]) ).

cnf(i_0_91,plain,
    ( ~ product(X1,X2,X3)
    | X4 = X3
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_23]) ).

cnf(i_0_92,plain,
    ( X1 != domain(a)
    | ~ product(X1,domain(domain(a)),codomain(domain(a))) ),
    inference(scs_inference,[],[i_0_52,i_0_54,i_0_82,i_0_57,i_0_63,i_0_37,i_0_34,i_0_36,i_0_24,i_0_28,i_0_29,i_0_23,i_0_43]) ).

cnf(i_0_93,plain,
    ( X1 != a
    | ~ product(domain(X1),domain(domain(a)),codomain(domain(a))) ),
    inference(scs_inference,[],[i_0_52,i_0_54,i_0_82,i_0_57,i_0_63,i_0_37,i_0_34,i_0_36,i_0_24,i_0_28,i_0_29,i_0_23,i_0_43,i_0_42]) ).

cnf(i_0_94,plain,
    product(X1,domain(X1),X1),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_95,plain,
    product(codomain(X1),domain(codomain(X1)),domain(codomain(X1))),
    inference(rename_variables,[],[i_0_60]) ).

cnf(i_0_96,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X3,X5)
    | ~ product(X4,X1,X6)
    | ~ product(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_19]) ).

cnf(i_0_97,plain,
    defined(codomain(X1),codomain(X1)),
    inference(rename_variables,[],[i_0_54]) ).

cnf(i_0_98,plain,
    product(codomain(codomain(X1)),codomain(X1),codomain(codomain(X1))),
    inference(rename_variables,[],[i_0_57]) ).

cnf(i_0_99,plain,
    defined(codomain(X1),codomain(X1)),
    inference(rename_variables,[],[i_0_54]) ).

cnf(i_0_100,plain,
    ( defined(codomain(codomain(X1)),X2)
    | ~ product(domain(X3),domain(domain(a)),codomain(domain(a)))
    | ~ product(codomain(X1),codomain(codomain(X1)),X2)
    | ~ product(codomain(codomain(X4)),domain(codomain(X4)),X5) ),
    inference(scs_inference,[],[i_0_52,i_0_54,i_0_82,i_0_85,i_0_97,i_0_57,i_0_98,i_0_60,i_0_95,i_0_63,i_0_37,i_0_32,i_0_34,i_0_36,i_0_24,i_0_28,i_0_29,i_0_23,i_0_43,i_0_42,i_0_44,i_0_45,i_0_19,i_0_20,i_0_21]) ).

cnf(i_0_101,plain,
    ~ product(domain(a),domain(domain(a)),codomain(domain(a))),
    inference(equality_inference,[],[92]) ).

cnf(i_0_102,plain,
    ~ product(domain(a),domain(domain(a)),codomain(domain(a))),
    inference(equality_inference,[],[93]) ).

cnf(i_0_103,plain,
    defined(X1,codomain(domain(X1))),
    inference(scs_inference,[],[i_0_31,i_0_34,i_0_25]) ).

cnf(i_0_104,plain,
    product(codomain(X1),X1,X1),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_105,plain,
    ( ~ defined(X1,X2)
    | defined(X1,X3)
    | ~ product(X3,X4,X2) ),
    inference(rename_variables,[],[i_0_25]) ).

cnf(i_0_106,plain,
    $false,
    inference(scs_inference,[],[i_0_49,i_0_31,i_0_33,i_0_34,i_0_37,i_0_25,i_0_28]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : CAT012-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33  % Computer : n028.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit   : 300
% 0.15/0.33  % WCLimit    : 300
% 0.15/0.33  % DateTime   : Tue May  5 10:50:01 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 0.32/1.61  % Version  : CSE_E---1.7
% 0.32/1.61  % Problem  : theBenchmark.p
% 0.32/1.61  % SZS status Unsatisfiable for theBenchmark.p
% 0.32/1.61  % SZS output start CNFRefutation
% See solution above
% 0.44/1.73  % Total time : 1.271s
%------------------------------------------------------------------------------