%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:55:34 AM UTC 2026
% Result : Unsatisfiable 21.61s 13.66s
% Output : CNFRefutation 21.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 23 RR)
% Number of literals : 45 ( 44 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 42 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom_001,axiom,
ifeq2(X0,X0,X1,X2) = X1 ).
cnf(ifeq_axiom_002,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(equivalence_implies_existence2,axiom,
ifeq2(equivalent(X0,X1),true,X0,X1) = X1 ).
cnf(existence_and_equality_implies_equivalence1,axiom,
ifeq('there$uexists'(X0),true,equivalent(X0,X0),true) = true ).
cnf(domain_has_elements,axiom,
ifeq('there$uexists'(domain(X0)),true,'there$uexists'(X0),true) = true ).
cnf(composition_implies_domain,axiom,
ifeq('there$uexists'(compose(X0,X1)),true,'there$uexists'(domain(X0)),true) = true ).
cnf(domain_codomain_composition1,axiom,
ifeq2('there$uexists'(compose(X0,X1)),true,domain(X0),codomain(X1)) = codomain(X1) ).
cnf(associativity_of_compose,axiom,
compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2) ).
cnf(compose_codomain,axiom,
compose(codomain(X0),X0) = X0 ).
cnf(ab_exists,hypothesis,
'there$uexists'(compose(a,b)) = true ).
cnf(prove_codomain_of_ab_equals_codomain_of_a,negated_conjecture,
codomain(compose(a,b)) != codomain(a) ).
cnf(c1,plain,
ifeq2(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom_001]) ).
cnf(c2,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom_002]) ).
cnf(c4,plain,
ifeq2(equivalent(X0,X1),true,X0,X1) = X1,
inference(clausification,[status(esa)],[equivalence_implies_existence2]) ).
cnf(c5,plain,
ifeq('there$uexists'(X0),true,equivalent(X0,X0),true) = true,
inference(clausification,[status(esa)],[existence_and_equality_implies_equivalence1]) ).
cnf(c6,plain,
ifeq('there$uexists'(domain(X0)),true,'there$uexists'(X0),true) = true,
inference(clausification,[status(esa)],[domain_has_elements]) ).
cnf(c8,plain,
ifeq('there$uexists'(compose(X0,X1)),true,'there$uexists'(domain(X0)),true) = true,
inference(clausification,[status(esa)],[composition_implies_domain]) ).
cnf(c9,plain,
ifeq2('there$uexists'(compose(X0,X1)),true,domain(X0),codomain(X1)) = codomain(X1),
inference(clausification,[status(esa)],[domain_codomain_composition1]) ).
cnf(c11,plain,
compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
inference(clausification,[status(esa)],[associativity_of_compose]) ).
cnf(c13,plain,
compose(codomain(X0),X0) = X0,
inference(clausification,[status(esa)],[compose_codomain]) ).
cnf(c14,plain,
'there$uexists'(compose(a,b)) = true,
inference(clausification,[status(esa)],[ab_exists]) ).
cnf(c15,plain,
codomain(compose(a,b)) != codomain(a),
inference(clausification,[status(esa)],[prove_codomain_of_ab_equals_codomain_of_a]) ).
cnf(d0,plain,
ifeq2('there$uexists'(X0),true,domain(codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c13,c9]) ).
cnf(d1,plain,
ifeq(true,true,'there$uexists'(domain(a)),true) = true,
inference(superposition,[status(thm)],[c14,c8]) ).
cnf(d2,plain,
'there$uexists'(domain(a)) = true,
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
ifeq(true,true,'there$uexists'(a),true) = true,
inference(superposition,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
'there$uexists'(a) = true,
inference(demodulation,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
ifeq2(true,true,domain(codomain(a)),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
domain(codomain(a)) = codomain(a),
inference(demodulation,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
compose(codomain(X0),compose(X0,X1)) = compose(X0,X1),
inference(superposition,[status(thm)],[c13,c11]) ).
cnf(d8,plain,
ifeq2('there$uexists'(compose(X0,X1)),true,domain(codomain(X0)),codomain(compose(X0,X1))) = codomain(compose(X0,X1)),
inference(superposition,[status(thm)],[d7,c9]) ).
cnf(d9,plain,
ifeq2(true,true,domain(codomain(a)),codomain(compose(a,b))) = codomain(compose(a,b)),
inference(superposition,[status(thm)],[c14,d8]) ).
cnf(d10,plain,
domain(codomain(a)) = codomain(compose(a,b)),
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
codomain(a) = codomain(compose(a,b)),
inference(demodulation,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
codomain(a) != codomain(a),
inference(demodulation,[status(thm)],[c15,d11]) ).
cnf(d13,plain,
ifeq('there$uexists'(X0),true,'there$uexists'(domain(codomain(X0))),true) = true,
inference(superposition,[status(thm)],[c13,c8]) ).
cnf(d14,plain,
ifeq(true,true,'there$uexists'(domain(codomain(a))),true) = true,
inference(superposition,[status(thm)],[d4,d13]) ).
cnf(d15,plain,
'there$uexists'(domain(codomain(a))) = true,
inference(demodulation,[status(thm)],[d14,c2]) ).
cnf(d16,plain,
ifeq(true,true,'there$uexists'(codomain(a)),true) = true,
inference(superposition,[status(thm)],[d15,c6]) ).
cnf(d17,plain,
'there$uexists'(codomain(a)) = true,
inference(demodulation,[status(thm)],[d16,c2]) ).
cnf(d18,plain,
ifeq(true,true,equivalent(codomain(a),codomain(a)),true) = true,
inference(superposition,[status(thm)],[d17,c5]) ).
cnf(d19,plain,
equivalent(codomain(a),codomain(a)) = true,
inference(demodulation,[status(thm)],[d18,c2]) ).
cnf(d20,plain,
ifeq2(true,true,codomain(a),codomain(a)) = codomain(a),
inference(superposition,[status(thm)],[d19,c4]) ).
cnf(d21,plain,
codomain(a) = codomain(a),
inference(demodulation,[status(thm)],[d20,c1]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[d21,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/10.51 % Computer : n012.cluster.edu
% 0.06/10.51 % Model : x86_64 x86_64
% 0.06/10.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/10.51 % Memory : 8046.5625MB
% 0.06/10.51 % OS : Linux 6.8.0-71-generic
% 0.06/10.51 % CPULimit : 300
% 0.06/10.51 % WCLimit : 300
% 0.06/10.51 % DateTime : Sat Sep 26 22:49:14 UTC 2026
% 0.06/10.51 % CPUTime :
% 0.06/10.51 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.61/13.66 % SZS status Unsatisfiable for theBenchmark.p
% 21.61/13.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------