%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT011-4 : 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 : n025.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 1.19s 1.66s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 12 unt; 0 nHn; 14 RR)
% Number of literals : 24 ( 12 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(domain_codomain_composition1,axiom,
( domain(X1) = codomain(X2)
| ~ there_exists(compose(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',domain_codomain_composition1) ).
cnf(compose_codomain,axiom,
compose(codomain(X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',compose_codomain) ).
cnf(compose_domain,axiom,
compose(X1,domain(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',compose_domain) ).
cnf(domain_has_elements,axiom,
( there_exists(X1)
| ~ there_exists(domain(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',domain_has_elements) ).
cnf(assume_domain_exists,hypothesis,
there_exists(domain(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_domain_exists) ).
cnf(prove_domain_is_idempotent,negated_conjecture,
domain(domain(a)) != domain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_is_idempotent) ).
cnf(c_0_6,axiom,
( domain(X1) = codomain(X2)
| ~ there_exists(compose(X1,X2)) ),
domain_codomain_composition1 ).
cnf(c_0_7,axiom,
compose(codomain(X1),X1) = X1,
compose_codomain ).
cnf(c_0_8,axiom,
compose(X1,domain(X1)) = X1,
compose_domain ).
cnf(c_0_9,axiom,
( there_exists(X1)
| ~ there_exists(domain(X1)) ),
domain_has_elements ).
cnf(c_0_10,hypothesis,
there_exists(domain(a)),
assume_domain_exists ).
cnf(c_0_11,plain,
( domain(codomain(X1)) = codomain(X1)
| ~ there_exists(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_12,plain,
( codomain(domain(X1)) = domain(X1)
| ~ there_exists(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_13,hypothesis,
there_exists(a),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,hypothesis,
domain(codomain(domain(a))) = codomain(domain(a)),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_15,hypothesis,
codomain(domain(a)) = domain(a),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
domain(domain(a)) != domain(a),
prove_domain_is_idempotent ).
cnf(c_0_17,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : CAT011-4 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.09 % 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
% 0.11/0.28 % Computer : n025.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8042.1875MB
% 0.11/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Tue May 5 10:49:58 EDT 2026
% 0.11/0.28 % CPUTime :
% 0.11/0.29 % start to proof: theBenchmark
% 1.19/1.66 % Version : CSE_E---1.7
% 1.19/1.66 % Problem : theBenchmark.p
% 1.19/1.66 % SZS status Unsatisfiable for theBenchmark.p
% 1.19/1.66 % SZS output start CNFRefutation
% See solution above
% 1.19/1.66 % Total time : 1.367s
%------------------------------------------------------------------------------