%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET085-7 : 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 : n004.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 08:31:58 AM UTC 2026
% Result : Unsatisfiable 26.31s 6.05s
% Output : CNFRefutation 26.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 14 unt; 4 nHn; 22 RR)
% Number of literals : 40 ( 17 equ; 16 neg)
% Maximal clause size : 3 ( 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; 4 con; 0-2 aty)
% Number of variables : 31 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(corollary_1_to_unordered_pair,axiom,
( member(X0,'unordered$upair'(X0,X1))
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ) ).
cnf(prove_singleton_in_unordered_pair3_1,negated_conjecture,
'unordered$upair'(y,z) = singleton(x) ).
cnf(prove_singleton_in_unordered_pair3_2,negated_conjecture,
member(x,'universal$uclass') ).
cnf(prove_singleton_in_unordered_pair3_3,negated_conjecture,
x != y ).
cnf(prove_singleton_in_unordered_pair3_4,negated_conjecture,
x != z ).
cnf(unordered_pair_member,axiom,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ) ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(cartesian_product3,axiom,
( member('ordered$upair'(X0,X2),'cross$uproduct'(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ) ).
cnf(c0,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ),
inference(clausification,[status(esa)],[corollary_1_to_unordered_pair]) ).
cnf(c37,plain,
'unordered$upair'(y,z) = singleton(x),
inference(clausification,[status(esa)],[prove_singleton_in_unordered_pair3_1]) ).
cnf(c38,plain,
member(x,'universal$uclass'),
inference(clausification,[status(esa)],[prove_singleton_in_unordered_pair3_2]) ).
cnf(c39,plain,
x != y,
inference(clausification,[status(esa)],[prove_singleton_in_unordered_pair3_3]) ).
cnf(c40,plain,
x != z,
inference(clausification,[status(esa)],[prove_singleton_in_unordered_pair3_4]) ).
cnf(c48,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c52,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c56,plain,
( member('ordered$upair'(X0,X2),'cross$uproduct'(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[cartesian_product3]) ).
cnf(d0,plain,
( X0 = y
| X0 = z
| ~ member(X0,singleton(x)) ),
inference(superposition,[status(thm)],[c37,c48]) ).
cnf(d1,plain,
( member(X0,'unordered$upair'(X0,X2))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[c56,c0]) ).
cnf(d2,plain,
( member(x,'unordered$upair'(x,X0))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[d1,c38]) ).
cnf(d3,plain,
member(x,'unordered$upair'(x,x)),
inference(resolution,[status(thm)],[d2,c38]) ).
cnf(d4,plain,
member(x,singleton(x)),
inference(demodulation,[status(thm)],[d3,c52]) ).
cnf(d5,plain,
( x = z
| x = y ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
x = z,
inference(resolution,[status(thm)],[c39,d5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c40,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET085-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n004.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 07:04:21 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.31/6.05 % SZS status Unsatisfiable for theBenchmark.p
% 26.31/6.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------