%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET024-4 : 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 : n008.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 08:31:39 AM UTC 2026
% Result : Unsatisfiable 21.10s 13.42s
% Output : CNFRefutation 21.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 12 ( 8 unt; 0 nHn; 7 RR)
% Number of literals : 18 ( 4 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 11 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_little_set,hypothesis,
'little$uset'(a) ).
cnf(prove_membership_of_singleton_set,negated_conjecture,
~ member(a,'singleton$uset'(a)) ).
cnf(non_ordered_pair2,axiom,
( X0 != X1
| ~ 'little$uset'(X0)
| member(X0,'non$uordered$upair'(X1,X2)) ) ).
cnf(singleton_set,axiom,
'singleton$uset'(X0) = 'non$uordered$upair'(X0,X0) ).
cnf(c0,plain,
'little$uset'(a),
inference(clausification,[status(esa)],[a_little_set]) ).
cnf(c1,plain,
~ member(a,'singleton$uset'(a)),
inference(clausification,[status(esa)],[prove_membership_of_singleton_set]) ).
cnf(c7,plain,
( X0 != X1
| ~ 'little$uset'(X0)
| member(X0,'non$uordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[non_ordered_pair2]) ).
cnf(c10,plain,
'singleton$uset'(X0) = 'non$uordered$upair'(X0,X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(d0,plain,
( member(X0,'non$uordered$upair'(X0,X1))
| ~ 'little$uset'(X0) ),
inference(equality_resolution,[status(thm)],[c7]) ).
cnf(d1,plain,
( ~ 'little$uset'(X0)
| member(X0,'singleton$uset'(X0)) ),
inference(superposition,[status(thm)],[c10,d0]) ).
cnf(d2,plain,
~ 'little$uset'(a),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c0,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET024-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n008.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Sat Sep 26 06:55:05 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.10/13.42 % SZS status Unsatisfiable for theBenchmark.p
% 21.10/13.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------