%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT004-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 06:55:33 AM UTC 2026
% Result : Unsatisfiable 2.44s 9.13s
% Output : CNFRefutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 46 ( 25 unt; 0 nHn; 37 RR)
% Number of literals : 71 ( 51 equ; 28 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 : 52 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cancellation_for_product1,hypothesis,
( X0 = X2
| compose(X2,a) != X1
| compose(X0,a) != X1 ) ).
cnf(cancellation_for_product2,hypothesis,
( X0 = X2
| compose(X2,b) != X1
| compose(X0,b) != X1 ) ).
cnf(assume_h_exists,hypothesis,
'there$uexists'(h) ).
cnf(h_ab_equals_g_ab,hypothesis,
compose(h,compose(a,b)) = compose(g,compose(a,b)) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g ).
cnf(domain_has_elements,axiom,
( 'there$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(X2,a) != X1
| compose(X0,a) != X1 ),
inference(clausification,[status(esa)],[cancellation_for_product1]) ).
cnf(c2,plain,
( X0 = X2
| compose(X2,b) != X1
| compose(X0,b) != X1 ),
inference(clausification,[status(esa)],[cancellation_for_product2]) ).
cnf(c3,plain,
'there$uexists'(h),
inference(clausification,[status(esa)],[assume_h_exists]) ).
cnf(c4,plain,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
inference(clausification,[status(esa)],[h_ab_equals_g_ab]) ).
cnf(c5,plain,
h != g,
inference(clausification,[status(esa)],[prove_h_equals_g]) ).
cnf(c9,plain,
( 'there$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(X0,a) != compose(X1,a)
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(d1,plain,
( compose(X0,b) != compose(X1,b)
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(d2,plain,
( compose(X0,X1) = X2
| compose(X0,compose(X1,b)) != compose(X2,b) ),
inference(superposition,[status(thm)],[c14,d1]) ).
cnf(d3,plain,
( compose(g,a) = X0
| compose(h,compose(a,b)) != compose(X0,b) ),
inference(superposition,[status(thm)],[c4,d2]) ).
cnf(d4,plain,
( compose(g,a) = compose(X0,X1)
| compose(h,compose(a,b)) != compose(X0,compose(X1,b)) ),
inference(superposition,[status(thm)],[c14,d3]) ).
cnf(d5,plain,
compose(g,a) = compose(h,a),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( g = X0
| compose(h,a) != compose(X0,a) ),
inference(superposition,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
g = h,
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
% 0.00/0.03 % Problem : CAT004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 22:53:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.44/9.13 % SZS status Unsatisfiable for theBenchmark.p
% 2.44/9.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------