%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT004-1 : 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 : n005.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 06:55:32 AM UTC 2026
% Result : Unsatisfiable 36.47s 5.41s
% Output : CNFRefutation 36.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 39 ( 20 unt; 0 nHn; 39 RR)
% Number of literals : 70 ( 10 equ; 33 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 53 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cancellation_for_product1,hypothesis,
( X0 = X2
| ~ product(X2,a,X1)
| ~ product(X0,a,X1) ) ).
cnf(cancellation_for_product2,hypothesis,
( X0 = X2
| ~ product(X2,b,X1)
| ~ product(X0,b,X1) ) ).
cnf(ab_equals_c,hypothesis,
product(a,b,c) ).
cnf(hc_equals_d,hypothesis,
product(h,c,d) ).
cnf(gc_equals_d,hypothesis,
product(g,c,d) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g ).
cnf(closure_of_composition,axiom,
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ) ).
cnf(associative_property1,axiom,
( defined(X0,X1)
| ~ product(X0,X1,X2) ) ).
cnf(category_theory_axiom3,axiom,
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ) ).
cnf(category_theory_axiom5,axiom,
( product(X5,X1,X4)
| ~ product(X3,X0,X5)
| ~ product(X3,X2,X4)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
( X0 = X2
| ~ product(X2,a,X1)
| ~ product(X0,a,X1) ),
inference(clausification,[status(esa)],[cancellation_for_product1]) ).
cnf(c1,plain,
( X0 = X2
| ~ product(X2,b,X1)
| ~ product(X0,b,X1) ),
inference(clausification,[status(esa)],[cancellation_for_product2]) ).
cnf(c2,plain,
product(a,b,c),
inference(clausification,[status(esa)],[ab_equals_c]) ).
cnf(c3,plain,
product(h,c,d),
inference(clausification,[status(esa)],[hc_equals_d]) ).
cnf(c4,plain,
product(g,c,d),
inference(clausification,[status(esa)],[gc_equals_d]) ).
cnf(c5,plain,
g != h,
inference(clausification,[status(esa)],[prove_h_equals_g]) ).
cnf(c6,plain,
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[closure_of_composition]) ).
cnf(c7,plain,
( defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associative_property1]) ).
cnf(c11,plain,
( defined(X0,X2)
| ~ product(X2,X3,X1)
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[category_theory_axiom3]) ).
cnf(c13,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[category_theory_axiom5]) ).
cnf(d0,plain,
defined(h,c),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(d1,plain,
( defined(X0,a)
| ~ defined(X0,c) ),
inference(resolution,[status(thm)],[c11,c2]) ).
cnf(d2,plain,
defined(h,a),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
product(h,a,compose(h,a)),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
( ~ product(X0,a,compose(h,a))
| X0 = h ),
inference(resolution,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
( ~ product(X2,X1,c)
| ~ product(h,X2,X0)
| product(X0,X1,d) ),
inference(resolution,[status(thm)],[c13,c3]) ).
cnf(d6,plain,
( ~ product(h,a,X0)
| product(X0,b,d) ),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
product(compose(h,a),b,d),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
defined(g,c),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(d9,plain,
defined(g,a),
inference(resolution,[status(thm)],[d1,d8]) ).
cnf(d10,plain,
product(g,a,compose(g,a)),
inference(resolution,[status(thm)],[d9,c6]) ).
cnf(d11,plain,
( ~ product(X2,X1,c)
| ~ product(g,X2,X0)
| product(X0,X1,d) ),
inference(resolution,[status(thm)],[c13,c4]) ).
cnf(d12,plain,
( ~ product(g,a,X0)
| product(X0,b,d) ),
inference(resolution,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
product(compose(g,a),b,d),
inference(resolution,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
( ~ product(X0,b,d)
| compose(g,a) = X0 ),
inference(resolution,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
compose(g,a) = compose(h,a),
inference(resolution,[status(thm)],[d14,d7]) ).
cnf(d16,plain,
product(g,a,compose(h,a)),
inference(demodulation,[status(thm)],[d10,d15]) ).
cnf(d17,plain,
g = h,
inference(resolution,[status(thm)],[d16,d4]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[c5,d17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 22:48:31 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.47/5.41 % SZS status Unsatisfiable for theBenchmark.p
% 36.47/5.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------