%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET047-5 : 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 : n002.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 08:31:46 AM UTC 2026
% Result : Unsatisfiable 10.33s 11.72s
% Output : CNFRefutation 10.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of clauses : 29 ( 5 unt; 13 nHn; 25 RR)
% Number of literals : 69 ( 0 equ; 24 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(element_substitution1,axiom,
( element(X2,X1)
| ~ element(X2,X0)
| ~ 'set$uequal'(X0,X1) ) ).
cnf(element_substitution2,axiom,
( element(X2,X0)
| ~ element(X2,X1)
| ~ 'set$uequal'(X0,X1) ) ).
cnf(clause_3,axiom,
( 'set$uequal'(X0,X1)
| element(f(X0,X1),X1)
| element(f(X0,X1),X0) ) ).
cnf(clause_4,axiom,
( 'set$uequal'(X0,X1)
| ~ element(f(X0,X1),X0)
| ~ element(f(X0,X1),X1) ) ).
cnf(prove_symmetry1,negated_conjecture,
( 'set$uequal'(b,a)
| 'set$uequal'(a,b) ) ).
cnf(prove_symmetry2,negated_conjecture,
( ~ 'set$uequal'(a,b)
| ~ 'set$uequal'(b,a) ) ).
cnf(c0,plain,
( element(X2,X1)
| ~ element(X2,X0)
| ~ 'set$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[element_substitution1]) ).
cnf(c1,plain,
( element(X2,X0)
| ~ element(X2,X1)
| ~ 'set$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[element_substitution2]) ).
cnf(c2,plain,
( 'set$uequal'(X0,X1)
| element(f(X0,X1),X1)
| element(f(X0,X1),X0) ),
inference(clausification,[status(esa)],[clause_3]) ).
cnf(c3,plain,
( 'set$uequal'(X0,X1)
| ~ element(f(X0,X1),X0)
| ~ element(f(X0,X1),X1) ),
inference(clausification,[status(esa)],[clause_4]) ).
cnf(c4,plain,
( 'set$uequal'(b,a)
| 'set$uequal'(a,b) ),
inference(clausification,[status(esa)],[prove_symmetry1]) ).
cnf(c5,plain,
( ~ 'set$uequal'(a,b)
| ~ 'set$uequal'(b,a) ),
inference(clausification,[status(esa)],[prove_symmetry2]) ).
cnf(d0,plain,
( 'set$uequal'(b,a)
| ~ element(X0,a)
| element(X0,b) ),
inference(resolution,[status(thm)],[c0,c4]) ).
cnf(d1,plain,
( 'set$uequal'(b,a)
| element(f(X0,a),b)
| 'set$uequal'(X0,a)
| element(f(X0,a),X0) ),
inference(resolution,[status(thm)],[c2,d0]) ).
cnf(d2,plain,
( 'set$uequal'(b,a)
| 'set$uequal'(b,a)
| element(f(b,a),b) ),
inference(factoring,[status(thm)],[d1]) ).
cnf(d3,plain,
( 'set$uequal'(b,a)
| ~ element(f(b,a),a)
| 'set$uequal'(b,a) ),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
( 'set$uequal'(b,a)
| ~ element(X0,b)
| element(X0,a) ),
inference(resolution,[status(thm)],[c1,c4]) ).
cnf(d5,plain,
( 'set$uequal'(b,a)
| element(f(b,a),a)
| 'set$uequal'(b,a) ),
inference(resolution,[status(thm)],[d2,d4]) ).
cnf(d6,plain,
( 'set$uequal'(b,a)
| 'set$uequal'(b,a) ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( ~ element(X0,b)
| element(X0,a) ),
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
( ~ element(X0,a)
| element(X0,b) ),
inference(resolution,[status(thm)],[d6,c1]) ).
cnf(d9,plain,
( 'set$uequal'(a,X0)
| element(f(a,X0),X0)
| element(f(a,X0),b) ),
inference(resolution,[status(thm)],[d8,c2]) ).
cnf(d10,plain,
( 'set$uequal'(a,b)
| element(f(a,b),b) ),
inference(factoring,[status(thm)],[d9]) ).
cnf(d11,plain,
~ 'set$uequal'(a,b),
inference(resolution,[status(thm)],[d6,c5]) ).
cnf(d12,plain,
element(f(a,b),b),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
element(f(a,b),a),
inference(resolution,[status(thm)],[d12,d7]) ).
cnf(d14,plain,
( 'set$uequal'(a,b)
| ~ element(f(a,b),b) ),
inference(resolution,[status(thm)],[d13,c3]) ).
cnf(d15,plain,
~ element(f(a,b),b),
inference(resolution,[status(thm)],[d11,d14]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[d12,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET047-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/10.44 % Computer : n002.cluster.edu
% 0.18/10.44 % Model : x86_64 x86_64
% 0.18/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/10.44 % Memory : 8046.5625MB
% 0.18/10.44 % OS : Linux 6.8.0-71-generic
% 0.18/10.44 % CPULimit : 300
% 0.18/10.44 % WCLimit : 300
% 0.18/10.44 % DateTime : Sat Sep 26 07:02:48 UTC 2026
% 0.18/10.44 % CPUTime :
% 0.18/10.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.33/11.72 % SZS status Unsatisfiable for theBenchmark.p
% 10.33/11.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------