%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT002-1 : 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 : n019.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 30.32s 5.88s
% Output : CNFRefutation 30.32s
% 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(a,X2,X1)
| ~ product(a,X0,X1) ) ).
cnf(cancellation_for_product2,hypothesis,
( X0 = X2
| ~ product(b,X2,X1)
| ~ product(b,X0,X1) ) ).
cnf(ab_equals_c,hypothesis,
product(a,b,c) ).
cnf(ch_equals_d,hypothesis,
product(c,h,d) ).
cnf(cg_equals_d,hypothesis,
product(c,g,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(associative_property2,axiom,
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ) ).
cnf(category_theory_axiom2,axiom,
( product(X0,X5,X4)
| ~ product(X1,X3,X5)
| ~ product(X2,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
( X0 = X2
| ~ product(a,X2,X1)
| ~ product(a,X0,X1) ),
inference(clausification,[status(esa)],[cancellation_for_product1]) ).
cnf(c1,plain,
( X0 = X2
| ~ product(b,X2,X1)
| ~ product(b,X0,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(c,h,d),
inference(clausification,[status(esa)],[ch_equals_d]) ).
cnf(c4,plain,
product(c,g,d),
inference(clausification,[status(esa)],[cg_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(c8,plain,
( defined(X3,X1)
| ~ product(X2,X3,X0)
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[associative_property2]) ).
cnf(c10,plain,
( product(X3,X2,X5)
| ~ product(X4,X1,X5)
| ~ product(X3,X0,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[category_theory_axiom2]) ).
cnf(d0,plain,
defined(c,h),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(d1,plain,
( defined(b,X0)
| ~ defined(c,X0) ),
inference(resolution,[status(thm)],[c8,c2]) ).
cnf(d2,plain,
defined(b,h),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
product(b,h,compose(b,h)),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
( ~ product(b,X0,compose(b,h))
| X0 = h ),
inference(resolution,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
( ~ product(X2,X0,c)
| product(X2,X1,d)
| ~ product(X0,h,X1) ),
inference(resolution,[status(thm)],[c10,c3]) ).
cnf(d6,plain,
( ~ product(b,h,X0)
| product(a,X0,d) ),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
product(a,compose(b,h),d),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
defined(c,g),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(d9,plain,
defined(b,g),
inference(resolution,[status(thm)],[d1,d8]) ).
cnf(d10,plain,
product(b,g,compose(b,g)),
inference(resolution,[status(thm)],[d9,c6]) ).
cnf(d11,plain,
( ~ product(X2,X0,c)
| product(X2,X1,d)
| ~ product(X0,g,X1) ),
inference(resolution,[status(thm)],[c10,c4]) ).
cnf(d12,plain,
( ~ product(b,g,X0)
| product(a,X0,d) ),
inference(resolution,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
product(a,compose(b,g),d),
inference(resolution,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
( ~ product(a,X0,d)
| X0 = compose(b,g) ),
inference(resolution,[status(thm)],[d13,c0]) ).
cnf(d15,plain,
compose(b,h) = compose(b,g),
inference(resolution,[status(thm)],[d14,d7]) ).
cnf(d16,plain,
product(b,g,compose(b,h)),
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 : CAT002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 22:48:03 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.32/5.88 % SZS status Unsatisfiable for theBenchmark.p
% 30.32/5.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------