%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET072-7 : 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 : n011.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 08:31:53 AM UTC 2026
% Result : Unsatisfiable 36.65s 5.17s
% Output : CNFRefutation 36.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 26 ( 12 unt; 6 nHn; 24 RR)
% Number of literals : 44 ( 19 equ; 15 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(corollary_1_to_cartesian_product,axiom,
( member(X0,'universal$uclass')
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ) ).
cnf(corollary_2_to_cartesian_product,axiom,
( member(X1,'universal$uclass')
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ) ).
cnf(prove_right_cancellation_1,negated_conjecture,
'unordered$upair'(x,z) = 'unordered$upair'(y,z) ).
cnf(prove_right_cancellation_2,negated_conjecture,
member('ordered$upair'(x,y),'cross$uproduct'('universal$uclass','universal$uclass')) ).
cnf(prove_right_cancellation_3,negated_conjecture,
x != y ).
cnf(unordered_pair_member,axiom,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ) ).
cnf(unordered_pair2,axiom,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ) ).
cnf(c2,plain,
( member(X0,'universal$uclass')
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ),
inference(clausification,[status(esa)],[corollary_1_to_cartesian_product]) ).
cnf(c3,plain,
( member(X1,'universal$uclass')
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ),
inference(clausification,[status(esa)],[corollary_2_to_cartesian_product]) ).
cnf(c23,plain,
'unordered$upair'(x,z) = 'unordered$upair'(y,z),
inference(clausification,[status(esa)],[prove_right_cancellation_1]) ).
cnf(c24,plain,
member('ordered$upair'(x,y),'cross$uproduct'('universal$uclass','universal$uclass')),
inference(clausification,[status(esa)],[prove_right_cancellation_2]) ).
cnf(c25,plain,
x != y,
inference(clausification,[status(esa)],[prove_right_cancellation_3]) ).
cnf(c33,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c34,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair2]) ).
cnf(d0,plain,
( X0 = y
| X0 = z
| ~ member(X0,'unordered$upair'(x,z)) ),
inference(superposition,[status(thm)],[c23,c33]) ).
cnf(d1,plain,
( ~ member(x,'universal$uclass')
| x = y
| x = z ),
inference(resolution,[status(thm)],[d0,c34]) ).
cnf(d2,plain,
( ~ member(x,'universal$uclass')
| x = z ),
inference(resolution,[status(thm)],[c25,d1]) ).
cnf(d3,plain,
member(x,'universal$uclass'),
inference(resolution,[status(thm)],[c24,c2]) ).
cnf(d4,plain,
x = z,
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ member(y,'universal$uclass')
| member(y,'unordered$upair'(x,z)) ),
inference(superposition,[status(thm)],[c23,c34]) ).
cnf(d6,plain,
member(y,'universal$uclass'),
inference(resolution,[status(thm)],[c24,c3]) ).
cnf(d7,plain,
member(y,'unordered$upair'(x,z)),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( y = x
| y = z ),
inference(resolution,[status(thm)],[d7,c33]) ).
cnf(d9,plain,
( y = x
| y = x ),
inference(demodulation,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
x != x,
inference(demodulation,[status(thm)],[c25,d9]) ).
cnf(d11,plain,
$false,
inference(equality_resolution,[status(thm)],[d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET072-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n011.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 07:02:58 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.65/5.17 % SZS status Unsatisfiable for theBenchmark.p
% 36.65/5.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------