%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT012-4 : 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 : n016.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 1.01s 1.75s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 18)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_compose,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.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/sandbox/benchmark/Axioms/CAT004-0.ax',domain_codomain_composition2) ).
cnf(composition_implies_domain,axiom,
( there_exists(domain(X1))
| ~ there_exists(compose(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',composition_implies_domain) ).
cnf(domain_codomain_composition1,axiom,
( domain(X1) = codomain(X2)
| ~ there_exists(compose(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',domain_codomain_composition1) ).
cnf(equivalence_implies_existence1,axiom,
( there_exists(X1)
| ~ equivalent(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',equivalence_implies_existence1) ).
cnf(existence_and_equality_implies_equivalence1,axiom,
( equivalent(X1,X2)
| ~ there_exists(X1)
| X1 != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',existence_and_equality_implies_equivalence1) ).
cnf(equivalence_implies_existence2,axiom,
( X1 = X2
| ~ equivalent(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',equivalence_implies_existence2) ).
cnf(codomain_has_elements,axiom,
( there_exists(X1)
| ~ there_exists(codomain(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',codomain_has_elements) ).
cnf(domain_has_elements,axiom,
( there_exists(X1)
| ~ there_exists(domain(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',domain_has_elements) ).
cnf(compose_codomain,axiom,
compose(codomain(X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',compose_codomain) ).
cnf(compose_domain,axiom,
compose(X1,domain(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',compose_domain) ).
cnf(prove_codomain_of_domain_is_domain,negated_conjecture,
codomain(domain(a)) != domain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_domain_is_domain) ).
cnf(assume_domain_exists,hypothesis,
there_exists(domain(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_domain_exists) ).
cnf(i_0_13,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
associativity_of_compose,
[final] ).
cnf(i_0_14,axiom,
( there_exists(compose(X1,X2))
| ~ there_exists(domain(X1))
| domain(X1) != codomain(X2) ),
domain_codomain_composition2,
[final] ).
cnf(i_0_15,axiom,
( there_exists(domain(X1))
| ~ there_exists(compose(X1,X2)) ),
composition_implies_domain,
[final] ).
cnf(i_0_16,axiom,
( domain(X1) = codomain(X2)
| ~ there_exists(compose(X1,X2)) ),
domain_codomain_composition1,
[final] ).
cnf(i_0_17,axiom,
( there_exists(X1)
| ~ equivalent(X1,X2) ),
equivalence_implies_existence1,
[final] ).
cnf(i_0_18,axiom,
( equivalent(X1,X2)
| ~ there_exists(X1)
| X1 != X2 ),
existence_and_equality_implies_equivalence1,
[final] ).
cnf(i_0_19,axiom,
( X1 = X2
| ~ equivalent(X1,X2) ),
equivalence_implies_existence2,
[final] ).
cnf(i_0_20,axiom,
( there_exists(X1)
| ~ there_exists(codomain(X1)) ),
codomain_has_elements,
[final] ).
cnf(i_0_21,axiom,
( there_exists(X1)
| ~ there_exists(domain(X1)) ),
domain_has_elements,
[final] ).
cnf(i_0_22,axiom,
compose(codomain(X1),X1) = X1,
compose_codomain,
[final] ).
cnf(i_0_23,axiom,
compose(X1,domain(X1)) = X1,
compose_domain,
[final] ).
cnf(i_0_24,negated_conjecture,
codomain(domain(a)) != domain(a),
prove_codomain_of_domain_is_domain,
[final] ).
cnf(i_0_25,hypothesis,
there_exists(domain(a)),
assume_domain_exists,
[final] ).
cnf(i_0_26,axiom,
X1 = X1 ).
cnf(i_0_27,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_28,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_29,axiom,
( X1 != X2
| compose(X1,X3) = compose(X2,X3) ) ).
cnf(i_0_30,axiom,
( X1 != X2
| compose(X3,X1) = compose(X3,X2) ) ).
cnf(i_0_31,axiom,
( X1 != X2
| domain(X1) = domain(X2) ) ).
cnf(i_0_32,axiom,
( X1 != X2
| codomain(X1) = codomain(X2) ) ).
cnf(i_0_33,axiom,
( X1 != X2
| ~ there_exists(X1)
| there_exists(X2) ) ).
cnf(i_0_34,axiom,
( X1 != X2
| ~ equivalent(X1,X3)
| equivalent(X2,X3) ) ).
cnf(i_0_35,axiom,
( X1 != X2
| ~ equivalent(X3,X1)
| equivalent(X3,X2) ) ).
cnf(i_0_26_001,axiom,
X1 = X1 ).
cnf(i_0_27_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_28_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_29_004,axiom,
( X1 != X2
| compose(X1,X3) = compose(X2,X3) ) ).
cnf(i_0_30_005,axiom,
( X1 != X2
| compose(X3,X1) = compose(X3,X2) ) ).
cnf(i_0_31_006,axiom,
( X1 != X2
| domain(X1) = domain(X2) ) ).
cnf(i_0_32_007,axiom,
( X1 != X2
| codomain(X1) = codomain(X2) ) ).
cnf(i_0_33_008,axiom,
( X1 != X2
| ~ there_exists(X1)
| there_exists(X2) ) ).
cnf(i_0_34_009,axiom,
( X1 != X2
| ~ equivalent(X1,X3)
| equivalent(X2,X3) ) ).
cnf(i_0_35_010,axiom,
( X1 != X2
| ~ equivalent(X3,X1)
| equivalent(X3,X2) ) ).
cnf(i_0_36,plain,
( ~ there_exists(X1)
| equivalent(X1,X1) ),
inference(equality_inference,[],[18]) ).
cnf(i_0_37,plain,
X1 = compose(codomain(X1),X1),
inference(scs_inference,[],[i_0_22,i_0_27]) ).
cnf(i_0_38,plain,
there_exists(a),
inference(scs_inference,[],[i_0_22,i_0_25,i_0_27,i_0_21]) ).
cnf(i_0_39,plain,
( ~ there_exists(domain(X1))
| there_exists(X1) ),
inference(rename_variables,[],[i_0_21]) ).
cnf(i_0_40,plain,
codomain(domain(a)) != compose(codomain(domain(a)),domain(a)),
inference(scs_inference,[],[i_0_24,i_0_22,i_0_25,i_0_27,i_0_21,i_0_28]) ).
cnf(i_0_41,plain,
compose(codomain(X1),X1) = X1,
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_42,plain,
equivalent(domain(a),compose(codomain(domain(a)),domain(a))),
inference(scs_inference,[],[i_0_24,i_0_22,i_0_25,i_0_27,i_0_21,i_0_28,i_0_18]) ).
cnf(i_0_43,plain,
( ~ there_exists(X1)
| X1 != X2
| equivalent(X1,X2) ),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_44,plain,
there_exists(compose(codomain(domain(a)),domain(a))),
inference(scs_inference,[],[i_0_24,i_0_22,i_0_25,i_0_27,i_0_21,i_0_28,i_0_18,i_0_33]) ).
cnf(i_0_45,plain,
( domain(a) != codomain(X1)
| there_exists(compose(a,X1)) ),
inference(scs_inference,[],[i_0_24,i_0_22,i_0_25,i_0_27,i_0_21,i_0_28,i_0_18,i_0_33,i_0_14]) ).
cnf(i_0_46,plain,
( ~ there_exists(domain(X1))
| there_exists(compose(X1,X2))
| domain(X1) != codomain(X2) ),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_47,plain,
( domain(a) != codomain(X1)
| domain(a) = codomain(X1) ),
inference(scs_inference,[],[i_0_24,i_0_22,i_0_25,i_0_27,i_0_21,i_0_28,i_0_18,i_0_33,i_0_14,i_0_16]) ).
cnf(i_0_48,plain,
( ~ there_exists(compose(X1,X2))
| domain(X1) = codomain(X2) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_49,plain,
X1 = compose(X1,domain(X1)),
inference(scs_inference,[],[i_0_23,i_0_27]) ).
cnf(i_0_50,plain,
equivalent(a,compose(codomain(a),a)),
inference(scs_inference,[],[i_0_37,i_0_38,i_0_23,i_0_27,i_0_18]) ).
cnf(i_0_51,plain,
X1 = compose(codomain(X1),X1),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_52,plain,
( ~ there_exists(X1)
| X1 != X2
| equivalent(X1,X2) ),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_53,plain,
there_exists(compose(codomain(a),a)),
inference(scs_inference,[],[i_0_37,i_0_51,i_0_38,i_0_23,i_0_27,i_0_18,i_0_33]) ).
cnf(i_0_54,plain,
X1 = compose(codomain(X1),X1),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_55,plain,
domain(codomain(a)) = codomain(a),
inference(scs_inference,[],[i_0_37,i_0_51,i_0_38,i_0_23,i_0_27,i_0_18,i_0_33,i_0_16]) ).
cnf(i_0_56,plain,
( ~ there_exists(compose(X1,X2))
| domain(X1) = codomain(X2) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_57,plain,
codomain(a) = domain(codomain(a)),
inference(scs_inference,[],[i_0_55,i_0_27]) ).
cnf(i_0_58,plain,
equivalent(domain(a),compose(domain(a),domain(domain(a)))),
inference(scs_inference,[],[i_0_49,i_0_25,i_0_55,i_0_27,i_0_18]) ).
cnf(i_0_59,plain,
X1 = compose(X1,domain(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_18]) ).
cnf(i_0_61,plain,
there_exists(compose(domain(a),domain(domain(a)))),
inference(scs_inference,[],[i_0_49,i_0_59,i_0_25,i_0_55,i_0_27,i_0_18,i_0_33]) ).
cnf(i_0_62,plain,
X1 = compose(X1,domain(X1)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_63,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(scs_inference,[],[i_0_13,i_0_27]) ).
cnf(i_0_64,plain,
equivalent(compose(codomain(domain(a)),domain(a)),domain(a)),
inference(scs_inference,[],[i_0_22,i_0_44,i_0_18]) ).
cnf(i_0_65,plain,
compose(codomain(X1),X1) = X1,
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_66,plain,
( ~ there_exists(X1)
| X1 != X2
| equivalent(X1,X2) ),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_67,plain,
compose(codomain(codomain(a)),codomain(a)) = domain(codomain(a)),
inference(scs_inference,[],[i_0_22,i_0_65,i_0_57,i_0_44,i_0_18,i_0_28]) ).
cnf(i_0_68,plain,
compose(codomain(X1),X1) = X1,
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_69,plain,
domain(codomain(a)) = compose(codomain(codomain(a)),codomain(a)),
inference(scs_inference,[],[i_0_22,i_0_65,i_0_57,i_0_44,i_0_18,i_0_28,i_0_27]) ).
cnf(i_0_70,plain,
equivalent(compose(codomain(a),a),a),
inference(scs_inference,[],[i_0_22,i_0_53,i_0_18]) ).
cnf(i_0_71,plain,
compose(codomain(X1),X1) = X1,
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_72,plain,
( ~ there_exists(X1)
| X1 != X2
| equivalent(X1,X2) ),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_73,plain,
compose(codomain(X1),X1) = compose(X1,domain(X1)),
inference(scs_inference,[],[i_0_22,i_0_71,i_0_49,i_0_53,i_0_18,i_0_28]) ).
cnf(i_0_74,plain,
X1 = compose(X1,domain(X1)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_75,plain,
compose(X1,domain(X1)) = compose(codomain(X1),X1),
inference(scs_inference,[],[i_0_22,i_0_71,i_0_49,i_0_53,i_0_18,i_0_28,i_0_27]) ).
cnf(i_0_76,plain,
equivalent(compose(domain(a),domain(domain(a))),domain(a)),
inference(scs_inference,[],[i_0_23,i_0_61,i_0_18]) ).
cnf(i_0_77,plain,
compose(X1,domain(X1)) = X1,
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_78,plain,
( ~ there_exists(X1)
| X1 != X2
| equivalent(X1,X2) ),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_79,plain,
there_exists(compose(a,domain(a))),
inference(scs_inference,[],[i_0_23,i_0_73,i_0_61,i_0_53,i_0_18,i_0_33]) ).
cnf(i_0_80,plain,
compose(codomain(X1),X1) = compose(X1,domain(X1)),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_81,plain,
domain(a) = codomain(domain(a)),
inference(scs_inference,[],[i_0_23,i_0_73,i_0_61,i_0_53,i_0_18,i_0_33,i_0_16]) ).
cnf(i_0_82,plain,
( ~ there_exists(compose(X1,X2))
| domain(X1) = codomain(X2) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_83,plain,
$false,
inference(scs_inference,[],[i_0_23,i_0_24,i_0_73,i_0_61,i_0_53,i_0_18,i_0_33,i_0_16,i_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.20 % Problem : CAT012-4 : TPTP v9.2.1. Released v1.0.0.
% 0.03/0.20 % 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
% 0.11/0.43 % Computer : n016.cluster.edu
% 0.11/0.43 % Model : x86_64 x86_64
% 0.11/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.43 % Memory : 8042.1875MB
% 0.11/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.43 % CPULimit : 300
% 0.11/0.43 % WCLimit : 300
% 0.11/0.43 % DateTime : Tue May 5 10:50:21 EDT 2026
% 0.11/0.44 % CPUTime :
% 0.14/0.47 % start to proof: theBenchmark
% 1.01/1.75 % Version : CSE_E---1.7
% 1.01/1.75 % Problem : theBenchmark.p
% 1.01/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 1.01/1.75 % SZS output start CNFRefutation
% See solution above
% 1.07/1.84 % Total time : 1.280s
%------------------------------------------------------------------------------