%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT014-1 : 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 : n018.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 04:11:42 PM UTC 2026
% Result : Unsatisfiable 0.31s 1.63s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 39
% Syntax : Number of clauses : 68 ( 24 unt; 0 nHn; 50 RR)
% Number of literals : 158 ( 35 equ; 95 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 172 ( 11 sgn)
% 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_is_idempotent,negated_conjecture,
codomain(codomain(a)) != codomain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_is_idempotent) ).
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(codomain(a)) != codomain(a),
prove_codomain_is_idempotent,
[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
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_43,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_44,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_45,axiom,
( X1 != X2
| ~ defined(X1,X3)
| defined(X2,X3) ) ).
cnf(i_0_46,axiom,
( X1 != X2
| ~ defined(X3,X1)
| defined(X3,X2) ) ).
cnf(i_0_47,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
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_43_006,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_44_007,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_45_008,axiom,
( X1 != X2
| ~ defined(X1,X3)
| defined(X2,X3) ) ).
cnf(i_0_46_009,axiom,
( X1 != X2
| ~ defined(X3,X1)
| defined(X3,X2) ) ).
cnf(i_0_47_010,axiom,
( X1 != X2
| ~ identity_map(X1)
| identity_map(X2) ) ).
cnf(i_0_48,plain,
codomain(a) != a,
inference(scs_inference,[],[i_0_35,i_0_41]) ).
cnf(i_0_49,plain,
~ product(codomain(codomain(a)),codomain(a),codomain(codomain(a))),
inference(scs_inference,[],[i_0_35,i_0_31,i_0_41,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,
codomain(a) != codomain(codomain(a)),
inference(scs_inference,[],[i_0_35,i_0_31,i_0_50,i_0_41,i_0_23,i_0_44]) ).
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_41,i_0_23,i_0_44,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,
$false,
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_41,i_0_23,i_0_44,i_0_25,i_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : CAT014-1 : TPTP v9.2.1. Released v1.0.0.
% 0.11/0.13 % 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
% 0.16/0.34 % Computer : n018.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 10:49:47 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.36 % start to proof: theBenchmark
% 0.31/1.63 % Version : CSE_E---1.7
% 0.31/1.63 % Problem : theBenchmark.p
% 0.31/1.63 % SZS status Unsatisfiable for theBenchmark.p
% 0.31/1.63 % SZS output start CNFRefutation
% See solution above
% 0.31/1.66 % Total time : 1.272s
%------------------------------------------------------------------------------