%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT002-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 06:55:31 AM UTC 2026
% Result : Unsatisfiable 15.24s 7.34s
% Output : CNFRefutation 15.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 46 ( 27 unt; 0 nHn; 37 RR)
% Number of literals : 69 ( 49 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cancellation_for_compose1,hypothesis,
( X0 = X2
| compose(a,X2) != X1
| compose(a,X0) != X1 ) ).
cnf(cancellation_for_compose2,hypothesis,
( X0 = X2
| compose(b,X2) != X1
| compose(b,X0) != X1 ) ).
cnf(assume_h_exists,hypothesis,
'there$uexists'(h) ).
cnf(ab_h_equals_ab_g,hypothesis,
compose(compose(a,b),h) = compose(compose(a,b),g) ).
cnf(prove_g_equals_h,negated_conjecture,
g != h ).
cnf(domain_has_elements,axiom,
( 'there$uexists'(X0)
| ~ 'there$uexists'(domain(X0)) ) ).
cnf(composition_implies_domain,axiom,
( 'there$uexists'(domain(X0))
| ~ 'there$uexists'(compose(X0,X1)) ) ).
cnf(domain_codomain_composition1,axiom,
( domain(X0) = codomain(X1)
| ~ 'there$uexists'(compose(X0,X1)) ) ).
cnf(associativity_of_compose,axiom,
compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2) ).
cnf(compose_domain,axiom,
compose(X0,domain(X0)) = X0 ).
cnf(compose_codomain,axiom,
compose(codomain(X0),X0) = X0 ).
cnf(c1,plain,
( X0 = X2
| compose(a,X2) != X1
| compose(a,X0) != X1 ),
inference(clausification,[status(esa)],[cancellation_for_compose1]) ).
cnf(c2,plain,
( X0 = X2
| compose(b,X2) != X1
| compose(b,X0) != X1 ),
inference(clausification,[status(esa)],[cancellation_for_compose2]) ).
cnf(c3,plain,
'there$uexists'(h),
inference(clausification,[status(esa)],[assume_h_exists]) ).
cnf(c4,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(clausification,[status(esa)],[ab_h_equals_ab_g]) ).
cnf(c5,plain,
g != h,
inference(clausification,[status(esa)],[prove_g_equals_h]) ).
cnf(c9,plain,
( 'there$uexists'(X0)
| ~ 'there$uexists'(domain(X0)) ),
inference(clausification,[status(esa)],[domain_has_elements]) ).
cnf(c11,plain,
( 'there$uexists'(domain(X0))
| ~ 'there$uexists'(compose(X0,X1)) ),
inference(clausification,[status(esa)],[composition_implies_domain]) ).
cnf(c12,plain,
( domain(X0) = codomain(X1)
| ~ 'there$uexists'(compose(X0,X1)) ),
inference(clausification,[status(esa)],[domain_codomain_composition1]) ).
cnf(c14,plain,
compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
inference(clausification,[status(esa)],[associativity_of_compose]) ).
cnf(c15,plain,
compose(X0,domain(X0)) = X0,
inference(clausification,[status(esa)],[compose_domain]) ).
cnf(c16,plain,
compose(codomain(X0),X0) = X0,
inference(clausification,[status(esa)],[compose_codomain]) ).
cnf(d0,plain,
( compose(b,X0) != compose(b,X1)
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(d1,plain,
( compose(a,X0) != compose(a,X1)
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(d2,plain,
compose(a,compose(b,h)) = compose(compose(a,b),g),
inference(demodulation,[status(thm)],[c4,c14]) ).
cnf(d3,plain,
compose(a,compose(b,h)) = compose(a,compose(b,g)),
inference(demodulation,[status(thm)],[d2,c14]) ).
cnf(d4,plain,
( compose(b,g) = X0
| compose(a,compose(b,h)) != compose(a,X0) ),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
compose(b,g) = compose(b,h),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( X0 = g
| compose(b,X0) != compose(b,h) ),
inference(superposition,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
h = g,
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
h != h,
inference(demodulation,[status(thm)],[c5,d7]) ).
cnf(d9,plain,
compose(codomain(X0),compose(X0,X1)) = compose(X0,X1),
inference(superposition,[status(thm)],[c16,c14]) ).
cnf(d10,plain,
compose(codomain(codomain(X0)),X0) = compose(codomain(X0),X0),
inference(superposition,[status(thm)],[c16,d9]) ).
cnf(d11,plain,
compose(codomain(codomain(X0)),X0) = X0,
inference(demodulation,[status(thm)],[d10,c16]) ).
cnf(d12,plain,
( domain(codomain(X0)) = codomain(X0)
| ~ 'there$uexists'(X0) ),
inference(superposition,[status(thm)],[c16,c12]) ).
cnf(d13,plain,
domain(codomain(h)) = codomain(h),
inference(resolution,[status(thm)],[d12,c3]) ).
cnf(d14,plain,
( 'there$uexists'(domain(codomain(X0)))
| ~ 'there$uexists'(X0) ),
inference(superposition,[status(thm)],[c16,c11]) ).
cnf(d15,plain,
( 'there$uexists'(codomain(X0))
| ~ 'there$uexists'(X0) ),
inference(resolution,[status(thm)],[d14,c9]) ).
cnf(d16,plain,
( domain(X0) = codomain(domain(X0))
| ~ 'there$uexists'(X0) ),
inference(superposition,[status(thm)],[c15,c12]) ).
cnf(d17,plain,
( ~ 'there$uexists'(X0)
| domain(codomain(X0)) = codomain(domain(codomain(X0))) ),
inference(resolution,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
domain(codomain(h)) = codomain(domain(codomain(h))),
inference(resolution,[status(thm)],[d17,c3]) ).
cnf(d19,plain,
codomain(h) = codomain(domain(codomain(h))),
inference(demodulation,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
codomain(h) = codomain(codomain(h)),
inference(demodulation,[status(thm)],[d19,d13]) ).
cnf(d21,plain,
compose(codomain(h),h) = h,
inference(superposition,[status(thm)],[d20,d11]) ).
cnf(d22,plain,
h = h,
inference(demodulation,[status(thm)],[d21,c16]) ).
cnf(d23,plain,
$false,
inference(resolution,[status(thm)],[d22,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n014.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sat Sep 26 22:47:52 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.24/7.34 % SZS status Unsatisfiable for theBenchmark.p
% 15.24/7.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------