%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT018-1 : 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 : 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 04:11:43 PM UTC 2026
% Result : Unsatisfiable 1.29s 1.74s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 15 unt; 0 nHn; 22 RR)
% Number of literals : 45 ( 0 equ; 21 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
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(assume_bc_exists,hypothesis,
defined(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_bc_exists) ).
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(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(identity1,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity1) ).
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(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(assume_ab_exists,hypothesis,
defined(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_ab_exists) ).
cnf(prove_a_bc_exists,negated_conjecture,
~ defined(a,compose(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_bc_exists) ).
cnf(c_0_9,axiom,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
closure_of_composition ).
cnf(c_0_10,hypothesis,
defined(b,c),
assume_bc_exists ).
cnf(c_0_11,axiom,
( defined(X4,X1)
| ~ product(X1,X2,X3)
| ~ defined(X4,X3) ),
category_theory_axiom3 ).
cnf(c_0_12,hypothesis,
product(b,c,compose(b,c)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,hypothesis,
( defined(X1,b)
| ~ defined(X1,compose(b,c)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
defined(codomain(X1),X1),
mapping_from_codomain_of_x_to_x ).
cnf(c_0_15,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
identity1 ).
cnf(c_0_16,hypothesis,
defined(codomain(compose(b,c)),b),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
identity_map(codomain(X1)),
codomain_is_an_identity_map ).
cnf(c_0_18,hypothesis,
product(codomain(compose(b,c)),b,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_19,axiom,
( defined(X1,X3)
| ~ defined(X1,X2)
| ~ defined(X2,X3)
| ~ identity_map(X2) ),
category_theory_axiom6 ).
cnf(c_0_20,hypothesis,
( defined(X1,codomain(compose(b,c)))
| ~ defined(X1,b) ),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_21,hypothesis,
defined(a,b),
assume_ab_exists ).
cnf(c_0_22,plain,
( defined(X1,X2)
| ~ defined(X1,codomain(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_14]),c_0_17])]) ).
cnf(c_0_23,hypothesis,
defined(a,codomain(compose(b,c))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
~ defined(a,compose(b,c)),
prove_a_bc_exists ).
cnf(c_0_25,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT018-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.13 % 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
% 0.17/0.34 % Computer : n027.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 10:49:35 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.29/1.74 % Version : CSE_E---1.7
% 1.29/1.74 % Problem : theBenchmark.p
% 1.29/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.29/1.74 % SZS output start CNFRefutation
% See solution above
% 1.29/1.74 % Total time : 1.376s
%------------------------------------------------------------------------------