%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET075-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 08:31:54 AM UTC 2026
% Result : Unsatisfiable 15.11s 2.23s
% Output : CNFRefutation 15.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 11 RR)
% Number of literals : 13 ( 2 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(corollary_1_to_unordered_pair,axiom,
( member(X0,'unordered$upair'(X0,X1))
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ) ).
cnf(existence_of_null_class,axiom,
~ member(X0,'null$uclass') ).
cnf(prove_corollary_to_unordered_pair_axiom3_1,negated_conjecture,
member('ordered$upair'(x,y),'cross$uproduct'(u,v)) ).
cnf(prove_corollary_to_unordered_pair_axiom3_2,negated_conjecture,
'unordered$upair'(x,y) = 'null$uclass' ).
cnf(c0,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ),
inference(clausification,[status(esa)],[corollary_1_to_unordered_pair]) ).
cnf(c11,plain,
~ member(X0,'null$uclass'),
inference(clausification,[status(esa)],[existence_of_null_class]) ).
cnf(c24,plain,
member('ordered$upair'(x,y),'cross$uproduct'(u,v)),
inference(clausification,[status(esa)],[prove_corollary_to_unordered_pair_axiom3_1]) ).
cnf(c25,plain,
'unordered$upair'(x,y) = 'null$uclass',
inference(clausification,[status(esa)],[prove_corollary_to_unordered_pair_axiom3_2]) ).
cnf(d0,plain,
member(x,'unordered$upair'(x,y)),
inference(resolution,[status(thm)],[c24,c0]) ).
cnf(d1,plain,
member(x,'null$uclass'),
inference(demodulation,[status(thm)],[d0,c25]) ).
cnf(d2,plain,
$false,
inference(resolution,[status(thm)],[c11,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET075-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 07:04:18 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.11/2.23 % SZS status Unsatisfiable for theBenchmark.p
% 15.11/2.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------