%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT007-3 : 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 : n008.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 04:11:39 PM UTC 2026
% Result : Unsatisfiable 0.25s 1.62s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 12
% Syntax : Number of clauses : 25 ( 11 unt; 4 nHn; 19 RR)
% Number of literals : 47 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(indiscernibles3,axiom,
( equalish(X1,X2)
| ~ equalish(X1,f1(X1,X2))
| ~ equalish(X2,f1(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles3) ).
cnf(indiscernibles2,axiom,
( equalish(X1,f1(X1,X2))
| equalish(X2,f1(X1,X2))
| equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles2) ).
cnf(domain_codomain_composition2,axiom,
( there_exists(compose(X1,X2))
| ~ there_exists(domain(X1))
| ~ equalish(domain(X1),codomain(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition2) ).
cnf(transitivity,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
cnf(indiscernibles1,axiom,
( there_exists(f1(X1,X2))
| equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles1) ).
cnf(prove_c1_c2_is_defined,negated_conjecture,
~ there_exists(compose(c2,c1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c1_c2_is_defined) ).
cnf(symmetry,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
cnf(domain_has_elements,axiom,
( there_exists(X1)
| ~ there_exists(domain(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
cnf(domain_of_c2_equals_codomain_of_c1,hypothesis,
equalish(domain(c2),codomain(c1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_c2_equals_codomain_of_c1) ).
cnf(reflexivity,axiom,
equalish(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
cnf(domain_of_c1_exists,hypothesis,
there_exists(domain(c1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_c1_exists) ).
cnf(domain_of_c2_exists,hypothesis,
there_exists(domain(c2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_c2_exists) ).
cnf(i_0_12,axiom,
( equalish(X1,X2)
| ~ equalish(X1,f1(X1,X2))
| ~ equalish(X2,f1(X1,X2)) ),
indiscernibles3,
[final] ).
cnf(i_0_13,axiom,
( equalish(X1,f1(X1,X2))
| equalish(X2,f1(X1,X2))
| equalish(X1,X2) ),
indiscernibles2,
[final] ).
cnf(i_0_14,axiom,
( there_exists(compose(X1,X2))
| ~ there_exists(domain(X1))
| ~ equalish(domain(X1),codomain(X2)) ),
domain_codomain_composition2,
[final] ).
cnf(i_0_15,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
transitivity,
[final] ).
cnf(i_0_16,axiom,
( there_exists(f1(X1,X2))
| equalish(X1,X2) ),
indiscernibles1,
[final] ).
cnf(i_0_17,negated_conjecture,
~ there_exists(compose(c2,c1)),
prove_c1_c2_is_defined,
[final] ).
cnf(i_0_18,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
symmetry,
[final] ).
cnf(i_0_19,axiom,
( there_exists(X1)
| ~ there_exists(domain(X1)) ),
domain_has_elements,
[final] ).
cnf(i_0_20,hypothesis,
equalish(domain(c2),codomain(c1)),
domain_of_c2_equals_codomain_of_c1,
[final] ).
cnf(i_0_21,axiom,
equalish(X1,X1),
reflexivity,
[final] ).
cnf(i_0_22,hypothesis,
there_exists(domain(c1)),
domain_of_c1_exists,
[final] ).
cnf(i_0_23,hypothesis,
there_exists(domain(c2)),
domain_of_c2_exists,
[final] ).
cnf(i_0_24,plain,
$false,
inference(scs_inference,[],[i_0_17,i_0_23,i_0_20,i_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT007-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n008.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 10:46:43 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.25/1.62 % Version : CSE_E---1.7
% 0.25/1.62 % Problem : theBenchmark.p
% 0.25/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.25/1.62 % SZS output start CNFRefutation
% See solution above
% 0.25/1.64 % Total time : 1.271s
%------------------------------------------------------------------------------