%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET094-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 08:32:00 AM UTC 2026
% Result : Unsatisfiable 24.10s 13.52s
% Output : CNFRefutation 24.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 11 unt; 3 nHn; 13 RR)
% Number of literals : 22 ( 15 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_property_of_singletons1_1,negated_conjecture,
singleton('member$uof'(x)) = x ).
cnf(prove_property_of_singletons1_2,negated_conjecture,
member(y,x) ).
cnf(prove_property_of_singletons1_3,negated_conjecture,
'member$uof'(x) != y ).
cnf(unordered_pair_member,axiom,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ) ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(c0,plain,
singleton('member$uof'(x)) = x,
inference(clausification,[status(esa)],[prove_property_of_singletons1_1]) ).
cnf(c1,plain,
member(y,x),
inference(clausification,[status(esa)],[prove_property_of_singletons1_2]) ).
cnf(c2,plain,
'member$uof'(x) != y,
inference(clausification,[status(esa)],[prove_property_of_singletons1_3]) ).
cnf(c10,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c14,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(d0,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c14,c10]) ).
cnf(d1,plain,
( X0 = 'member$uof'(x)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
y = 'member$uof'(x),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
y != y,
inference(demodulation,[status(thm)],[c2,d2]) ).
cnf(d4,plain,
$false,
inference(equality_resolution,[status(thm)],[d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET094-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/10.44 % Computer : n017.cluster.edu
% 0.15/10.44 % Model : x86_64 x86_64
% 0.15/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.44 % Memory : 8046.5625MB
% 0.15/10.44 % OS : Linux 6.8.0-71-generic
% 0.15/10.44 % CPULimit : 300
% 0.15/10.44 % WCLimit : 300
% 0.15/10.44 % DateTime : Sat Sep 26 07:01:58 UTC 2026
% 0.15/10.44 % CPUTime :
% 0.15/10.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.10/13.52 % SZS status Unsatisfiable for theBenchmark.p
% 24.10/13.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------