%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT010-4 : 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 : n001.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 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 29 ( 19 unt; 0 nHn; 20 RR)
% Number of literals : 39 ( 20 equ; 12 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 2 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(ab_exists,hypothesis,
there_exists(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_exists) ).
cnf(composition_implies_domain,axiom,
( there_exists(domain(X1))
| ~ there_exists(compose(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',composition_implies_domain) ).
cnf(compose_codomain,axiom,
compose(codomain(X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',compose_codomain) ).
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(associativity_of_compose,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',associativity_of_compose) ).
cnf(compose_domain,axiom,
compose(X1,domain(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',compose_domain) ).
cnf(prove_codomain_of_ab_equals_codomain_of_a,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
cnf(c_0_8,axiom,
( domain(X1) = codomain(X2)
| ~ there_exists(compose(X1,X2)) ),
domain_codomain_composition1 ).
cnf(c_0_9,hypothesis,
there_exists(compose(a,b)),
ab_exists ).
cnf(c_0_10,axiom,
( there_exists(domain(X1))
| ~ there_exists(compose(X1,X2)) ),
composition_implies_domain ).
cnf(c_0_11,hypothesis,
domain(a) = codomain(b),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,axiom,
compose(codomain(X1),X1) = X1,
compose_codomain ).
cnf(c_0_13,axiom,
( there_exists(X1)
| ~ there_exists(domain(X1)) ),
domain_has_elements ).
cnf(c_0_14,hypothesis,
there_exists(codomain(b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_9]),c_0_11]) ).
cnf(c_0_15,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
associativity_of_compose ).
cnf(c_0_16,axiom,
compose(X1,domain(X1)) = X1,
compose_domain ).
cnf(c_0_17,plain,
( domain(codomain(X1)) = codomain(X1)
| ~ there_exists(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_18,hypothesis,
there_exists(a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_14])]) ).
cnf(c_0_19,plain,
compose(X1,compose(domain(X1),X2)) = compose(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,hypothesis,
domain(codomain(a)) = codomain(a),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( codomain(X1) = domain(compose(X2,X3))
| ~ there_exists(compose(X2,compose(X3,X1))) ),
inference(spm,[status(thm)],[c_0_8,c_0_15]) ).
cnf(c_0_22,hypothesis,
compose(codomain(a),compose(codomain(a),X1)) = compose(codomain(a),X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,hypothesis,
compose(codomain(a),codomain(a)) = codomain(a),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_24,hypothesis,
( codomain(X1) = codomain(a)
| ~ there_exists(compose(codomain(a),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_20]) ).
cnf(c_0_25,plain,
compose(codomain(X1),compose(X1,X2)) = compose(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_26,hypothesis,
( codomain(compose(a,X1)) = codomain(a)
| ~ there_exists(compose(a,X1)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
prove_codomain_of_ab_equals_codomain_of_a ).
cnf(c_0_28,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_9]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT010-4 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.17/0.34 % Computer : n001.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 10:50:33 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.369s
%------------------------------------------------------------------------------