%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT004-4 : 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 : n006.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 43.43s 11.10s
% Output : CNFRefutation 43.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of clauses : 19 ( 9 unt; 0 nHn; 17 RR)
% Number of literals : 33 ( 32 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 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(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(associativity_of_compose,axiom,
compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2) ).
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(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(c14,plain,
compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
inference(clausification,[status(esa)],[associativity_of_compose]) ).
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,
( X0 = g
| compose(X0,a) != compose(h,a) ),
inference(superposition,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
h = g,
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c5,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT004-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.52 % Computer : n006.cluster.edu
% 0.09/5.52 % Model : x86_64 x86_64
% 0.09/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.52 % Memory : 8046.5625MB
% 0.09/5.52 % OS : Linux 6.8.0-71-generic
% 0.09/5.52 % CPULimit : 300
% 0.09/5.52 % WCLimit : 300
% 0.09/5.52 % DateTime : Sat Sep 26 22:48:18 UTC 2026
% 0.09/5.52 % CPUTime :
% 0.09/5.52 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.43/11.10 % SZS status Unsatisfiable for theBenchmark.p
% 43.43/11.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------