%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT013-3 : 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 : n027.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 0.28s 1.61s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 28)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_compose,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',associativity_of_compose) ).
cnf(domain_codomain_composition2,axiom,
( there_exists(compose(X1,X2))
| ~ there_exists(domain(X1))
| domain(X1) != codomain(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',domain_codomain_composition2) ).
cnf(composition_implies_codomain,axiom,
( there_exists(codomain(X1))
| ~ there_exists(compose(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',composition_implies_codomain) ).
cnf(composition_implies_domain,axiom,
( there_exists(domain(X1))
| ~ there_exists(compose(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',composition_implies_domain) ).
cnf(domain_codomain_composition1,axiom,
( domain(X1) = codomain(X2)
| ~ there_exists(compose(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',domain_codomain_composition1) ).
cnf(indiscernibles2,axiom,
( X1 = f1(X1,X2)
| X2 = f1(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',indiscernibles2) ).
cnf(indiscernibles1,axiom,
( there_exists(f1(X1,X2))
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',indiscernibles1) ).
cnf(existence_and_equality_implies_equivalence2,axiom,
( equivalent(X1,X2)
| ~ there_exists(X1)
| ~ there_exists(X2)
| X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',existence_and_equality_implies_equivalence2) ).
cnf(equivalence_implies_existence1,axiom,
( there_exists(X1)
| ~ equivalent(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',equivalence_implies_existence1) ).
cnf(equivalence_implies_existence3,axiom,
( there_exists(X2)
| ~ equivalent(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',equivalence_implies_existence3) ).
cnf(existence_and_equality_implies_equivalence1,axiom,
( equivalent(X1,X2)
| ~ there_exists(X1)
| X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',existence_and_equality_implies_equivalence1) ).
cnf(equivalence_implies_existence2,axiom,
( X1 = X2
| ~ equivalent(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',equivalence_implies_existence2) ).
cnf(codomain_has_elements,axiom,
( there_exists(X1)
| ~ there_exists(codomain(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',codomain_has_elements) ).
cnf(domain_has_elements,axiom,
( there_exists(X1)
| ~ there_exists(domain(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',domain_has_elements) ).
cnf(compose_codomain,axiom,
compose(codomain(X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',compose_codomain) ).
cnf(compose_domain,axiom,
compose(X1,domain(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',compose_domain) ).
cnf(prove_domain_of_codomain_is_codomain,negated_conjecture,
domain(codomain(a)) != codomain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_codomain_is_codomain) ).
cnf(assume_codomain_exists,hypothesis,
there_exists(codomain(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_codomain_exists) ).
cnf(i_0_18,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
associativity_of_compose,
[final] ).
cnf(i_0_19,axiom,
( there_exists(compose(X1,X2))
| ~ there_exists(domain(X1))
| domain(X1) != codomain(X2) ),
domain_codomain_composition2,
[final] ).
cnf(i_0_20,axiom,
( there_exists(codomain(X1))
| ~ there_exists(compose(X1,X2)) ),
composition_implies_codomain,
[final] ).
cnf(i_0_21,axiom,
( there_exists(domain(X1))
| ~ there_exists(compose(X1,X2)) ),
composition_implies_domain,
[final] ).
cnf(i_0_22,axiom,
( domain(X1) = codomain(X2)
| ~ there_exists(compose(X1,X2)) ),
domain_codomain_composition1,
[final] ).
cnf(i_0_23,axiom,
( X1 = f1(X1,X2)
| X2 = f1(X1,X2)
| X1 = X2 ),
indiscernibles2,
[final] ).
cnf(i_0_24,axiom,
( there_exists(f1(X1,X2))
| X1 = X2 ),
indiscernibles1,
[final] ).
cnf(i_0_25,axiom,
( equivalent(X1,X2)
| ~ there_exists(X1)
| ~ there_exists(X2)
| X1 != X2 ),
existence_and_equality_implies_equivalence2,
[final] ).
cnf(i_0_26,axiom,
( there_exists(X1)
| ~ equivalent(X1,X2) ),
equivalence_implies_existence1,
[final] ).
cnf(i_0_27,axiom,
( there_exists(X2)
| ~ equivalent(X1,X2) ),
equivalence_implies_existence3,
[final] ).
cnf(i_0_28,axiom,
( equivalent(X1,X2)
| ~ there_exists(X1)
| X1 != X2 ),
existence_and_equality_implies_equivalence1,
[final] ).
cnf(i_0_29,axiom,
( X1 = X2
| ~ equivalent(X1,X2) ),
equivalence_implies_existence2,
[final] ).
cnf(i_0_30,axiom,
( there_exists(X1)
| ~ there_exists(codomain(X1)) ),
codomain_has_elements,
[final] ).
cnf(i_0_31,axiom,
( there_exists(X1)
| ~ there_exists(domain(X1)) ),
domain_has_elements,
[final] ).
cnf(i_0_32,axiom,
compose(codomain(X1),X1) = X1,
compose_codomain,
[final] ).
cnf(i_0_33,axiom,
compose(X1,domain(X1)) = X1,
compose_domain,
[final] ).
cnf(i_0_34,negated_conjecture,
domain(codomain(a)) != codomain(a),
prove_domain_of_codomain_is_codomain,
[final] ).
cnf(i_0_35,hypothesis,
there_exists(codomain(a)),
assume_codomain_exists,
[final] ).
cnf(i_0_36,axiom,
X1 = X1 ).
cnf(i_0_37,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_38,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_39,axiom,
( X1 != X2
| compose(X1,X3) = compose(X2,X3) ) ).
cnf(i_0_40,axiom,
( X1 != X2
| compose(X3,X1) = compose(X3,X2) ) ).
cnf(i_0_41,axiom,
( X1 != X2
| domain(X1) = domain(X2) ) ).
cnf(i_0_42,axiom,
( X1 != X2
| codomain(X1) = codomain(X2) ) ).
cnf(i_0_43,axiom,
( X1 != X2
| f1(X1,X3) = f1(X2,X3) ) ).
cnf(i_0_44,axiom,
( X1 != X2
| f1(X3,X1) = f1(X3,X2) ) ).
cnf(i_0_45,axiom,
( X1 != X2
| ~ there_exists(X1)
| there_exists(X2) ) ).
cnf(i_0_46,axiom,
( X1 != X2
| ~ equivalent(X1,X3)
| equivalent(X2,X3) ) ).
cnf(i_0_47,axiom,
( X1 != X2
| ~ equivalent(X3,X1)
| equivalent(X3,X2) ) ).
cnf(i_0_36_001,axiom,
X1 = X1 ).
cnf(i_0_37_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_38_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_39_004,axiom,
( X1 != X2
| compose(X1,X3) = compose(X2,X3) ) ).
cnf(i_0_40_005,axiom,
( X1 != X2
| compose(X3,X1) = compose(X3,X2) ) ).
cnf(i_0_41_006,axiom,
( X1 != X2
| domain(X1) = domain(X2) ) ).
cnf(i_0_42_007,axiom,
( X1 != X2
| codomain(X1) = codomain(X2) ) ).
cnf(i_0_43_008,axiom,
( X1 != X2
| f1(X1,X3) = f1(X2,X3) ) ).
cnf(i_0_44_009,axiom,
( X1 != X2
| f1(X3,X1) = f1(X3,X2) ) ).
cnf(i_0_45_010,axiom,
( X1 != X2
| ~ there_exists(X1)
| there_exists(X2) ) ).
cnf(i_0_46_011,axiom,
( X1 != X2
| ~ equivalent(X1,X3)
| equivalent(X2,X3) ) ).
cnf(i_0_47_012,axiom,
( X1 != X2
| ~ equivalent(X3,X1)
| equivalent(X3,X2) ) ).
cnf(i_0_48,plain,
( ~ there_exists(X1)
| equivalent(X1,X1) ),
inference(equality_inference,[],[28]) ).
cnf(i_0_49,plain,
X1 = compose(codomain(X1),X1),
inference(scs_inference,[],[i_0_32,i_0_37]) ).
cnf(i_0_50,plain,
there_exists(a),
inference(scs_inference,[],[i_0_32,i_0_35,i_0_37,i_0_30]) ).
cnf(i_0_51,plain,
( ~ there_exists(codomain(X1))
| there_exists(X1) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_52,plain,
domain(codomain(a)) != compose(codomain(codomain(a)),codomain(a)),
inference(scs_inference,[],[i_0_34,i_0_32,i_0_35,i_0_37,i_0_30,i_0_38]) ).
cnf(i_0_53,plain,
compose(codomain(X1),X1) = X1,
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_54,plain,
equivalent(codomain(a),compose(codomain(codomain(a)),codomain(a))),
inference(scs_inference,[],[i_0_34,i_0_32,i_0_35,i_0_37,i_0_30,i_0_38,i_0_28]) ).
cnf(i_0_55,plain,
( ~ there_exists(X1)
| X1 != X2
| equivalent(X1,X2) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_56,plain,
there_exists(compose(codomain(codomain(a)),codomain(a))),
inference(scs_inference,[],[i_0_34,i_0_32,i_0_35,i_0_37,i_0_30,i_0_38,i_0_28,i_0_45]) ).
cnf(i_0_57,plain,
X1 = compose(X1,domain(X1)),
inference(scs_inference,[],[i_0_33,i_0_37]) ).
cnf(i_0_58,plain,
equivalent(a,compose(codomain(a),a)),
inference(scs_inference,[],[i_0_49,i_0_50,i_0_33,i_0_37,i_0_28]) ).
cnf(i_0_59,plain,
X1 = compose(codomain(X1),X1),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_60,plain,
( ~ there_exists(X1)
| X1 != X2
| equivalent(X1,X2) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_61,plain,
there_exists(compose(codomain(a),a)),
inference(scs_inference,[],[i_0_49,i_0_59,i_0_50,i_0_33,i_0_37,i_0_28,i_0_45]) ).
cnf(i_0_62,plain,
X1 = compose(codomain(X1),X1),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_63,plain,
$false,
inference(scs_inference,[],[i_0_34,i_0_49,i_0_59,i_0_50,i_0_33,i_0_37,i_0_28,i_0_45,i_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT013-3 : 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
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 10:50:05 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.28/1.61 % Version : CSE_E---1.7
% 0.28/1.61 % Problem : theBenchmark.p
% 0.28/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.28/1.61 % SZS output start CNFRefutation
% See solution above
% 0.28/1.66 % Total time : 1.271s
%------------------------------------------------------------------------------