%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT009-4 : 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 : n013.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 04:11:40 PM UTC 2026
% Result : Unsatisfiable 1.27s 1.73s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 15 unt; 0 nHn; 18 RR)
% Number of literals : 31 ( 14 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(compose_domain,axiom,
compose(X1,domain(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',compose_domain) ).
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_composition1,axiom,
( domain(X1) = codomain(X2)
| ~ there_exists(compose(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',domain_codomain_composition1) ).
cnf(ab_exists,hypothesis,
there_exists(compose(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_exists) ).
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(codomain_has_elements,axiom,
( there_exists(X1)
| ~ there_exists(codomain(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',codomain_has_elements) ).
cnf(prove_domain_of_ab_equals_domain_of_b,negated_conjecture,
domain(compose(a,b)) != domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_ab_equals_domain_of_b) ).
cnf(c_0_7,axiom,
compose(X1,domain(X1)) = X1,
compose_domain ).
cnf(c_0_8,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
associativity_of_compose ).
cnf(c_0_9,axiom,
( domain(X1) = codomain(X2)
| ~ there_exists(compose(X1,X2)) ),
domain_codomain_composition1 ).
cnf(c_0_10,plain,
compose(X1,compose(X2,domain(compose(X1,X2)))) = compose(X1,X2),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,hypothesis,
there_exists(compose(a,b)),
ab_exists ).
cnf(c_0_12,plain,
( codomain(compose(X1,domain(compose(X2,X1)))) = domain(X2)
| ~ there_exists(compose(X2,X1)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,hypothesis,
domain(a) = codomain(b),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_14,axiom,
( there_exists(domain(X1))
| ~ there_exists(compose(X1,X2)) ),
composition_implies_domain ).
cnf(c_0_15,axiom,
( there_exists(X1)
| ~ there_exists(codomain(X1)) ),
codomain_has_elements ).
cnf(c_0_16,hypothesis,
codomain(compose(b,domain(compose(a,b)))) = codomain(b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_11]),c_0_13]) ).
cnf(c_0_17,hypothesis,
there_exists(codomain(b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_11]),c_0_13]) ).
cnf(c_0_18,plain,
( codomain(domain(X1)) = domain(X1)
| ~ there_exists(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_7]) ).
cnf(c_0_19,hypothesis,
there_exists(compose(b,domain(compose(a,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_20,hypothesis,
codomain(domain(compose(a,b))) = domain(compose(a,b)),
inference(spm,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_21,negated_conjecture,
domain(compose(a,b)) != domain(b),
prove_domain_of_ab_equals_domain_of_b ).
cnf(c_0_22,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_19]),c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : CAT009-4 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n013.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 10:46:26 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.27/1.73 % Version : CSE_E---1.7
% 1.27/1.73 % Problem : theBenchmark.p
% 1.27/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/1.73 % SZS output start CNFRefutation
% See solution above
% 1.27/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------