%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET095-7 : 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 : n012.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 08:32:01 AM UTC 2026
% Result : Unsatisfiable 14.63s 2.61s
% Output : CNFRefutation 14.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 11 unt; 0 nHn; 9 RR)
% Number of literals : 20 ( 5 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_unordered_pair,axiom,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0) ).
cnf(unordered_pair_is_subset,axiom,
( subclass('unordered$upair'(X0,X2),X1)
| ~ member(X2,X1)
| ~ member(X0,X1) ) ).
cnf(prove_property_of_singletons2_1,negated_conjecture,
member(x,y) ).
cnf(prove_property_of_singletons2_2,negated_conjecture,
~ subclass(singleton(x),y) ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(c16,plain,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_unordered_pair]) ).
cnf(c27,plain,
( subclass('unordered$upair'(X0,X2),X1)
| ~ member(X2,X1)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[unordered_pair_is_subset]) ).
cnf(c47,plain,
member(x,y),
inference(clausification,[status(esa)],[prove_property_of_singletons2_1]) ).
cnf(c48,plain,
~ subclass(singleton(x),y),
inference(clausification,[status(esa)],[prove_property_of_singletons2_2]) ).
cnf(c60,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(d0,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(superposition,[status(thm)],[c60,c16]) ).
cnf(d1,plain,
( ~ member(X0,X1)
| ~ member(X0,X1)
| subclass(singleton(X0),X1) ),
inference(superposition,[status(thm)],[d0,c27]) ).
cnf(d2,plain,
~ member(x,y),
inference(resolution,[status(thm)],[d1,c48]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c47,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET095-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.49 % Computer : n012.cluster.edu
% 0.04/0.49 % Model : x86_64 x86_64
% 0.04/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.49 % Memory : 8046.5625MB
% 0.04/0.49 % OS : Linux 6.8.0-71-generic
% 0.04/0.49 % CPULimit : 300
% 0.04/0.49 % WCLimit : 300
% 0.04/0.49 % DateTime : Sat Sep 26 07:06:09 UTC 2026
% 0.04/0.49 % CPUTime :
% 0.04/0.49 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.63/2.61 % SZS status Unsatisfiable for theBenchmark.p
% 14.63/2.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------