%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET017-7 : 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 : n008.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 08:31:36 AM UTC 2026
% Result : Unsatisfiable 22.54s 13.34s
% Output : CNFRefutation 22.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 30 ( 16 unt; 6 nHn; 26 RR)
% Number of literals : 48 ( 23 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 : 31 ( 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(commutativity_of_unordered_pair,axiom,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0) ).
cnf(prove_left_cancellation_1,negated_conjecture,
'unordered$upair'(x,y) = 'unordered$upair'(x,z) ).
cnf(prove_left_cancellation_2,negated_conjecture,
member('ordered$upair'(y,z),'cross$uproduct'('universal$uclass','universal$uclass')) ).
cnf(prove_left_cancellation_3,negated_conjecture,
y != z ).
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$uproduct'(X2,X3)) ),
inference(clausification,[status(esa)],[corollary_2_to_cartesian_product]) ).
cnf(c16,plain,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_unordered_pair]) ).
cnf(c22,plain,
'unordered$upair'(x,y) = 'unordered$upair'(x,z),
inference(clausification,[status(esa)],[prove_left_cancellation_1]) ).
cnf(c23,plain,
member('ordered$upair'(y,z),'cross$uproduct'('universal$uclass','universal$uclass')),
inference(clausification,[status(esa)],[prove_left_cancellation_2]) ).
cnf(c24,plain,
y != z,
inference(clausification,[status(esa)],[prove_left_cancellation_3]) ).
cnf(c32,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c33,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair2]) ).
cnf(d0,plain,
'unordered$upair'(y,x) = 'unordered$upair'(x,z),
inference(demodulation,[status(thm)],[c22,c16]) ).
cnf(d1,plain,
'unordered$upair'(y,x) = 'unordered$upair'(z,x),
inference(demodulation,[status(thm)],[d0,c16]) ).
cnf(d2,plain,
( X0 = z
| X0 = x
| ~ member(X0,'unordered$upair'(y,x)) ),
inference(superposition,[status(thm)],[d1,c32]) ).
cnf(d3,plain,
( ~ member(y,'universal$uclass')
| y = z
| y = x ),
inference(resolution,[status(thm)],[d2,c33]) ).
cnf(d4,plain,
( ~ member(y,'universal$uclass')
| y = x ),
inference(resolution,[status(thm)],[c24,d3]) ).
cnf(d5,plain,
member(y,'universal$uclass'),
inference(resolution,[status(thm)],[c23,c2]) ).
cnf(d6,plain,
y = x,
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( ~ member(z,'universal$uclass')
| member(z,'unordered$upair'(y,x)) ),
inference(superposition,[status(thm)],[d1,c33]) ).
cnf(d8,plain,
member(z,'universal$uclass'),
inference(resolution,[status(thm)],[c23,c3]) ).
cnf(d9,plain,
member(z,'unordered$upair'(y,x)),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( z = y
| z = x ),
inference(resolution,[status(thm)],[d9,c32]) ).
cnf(d11,plain,
( z = y
| z = y ),
inference(demodulation,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
y != y,
inference(demodulation,[status(thm)],[c24,d11]) ).
cnf(d13,plain,
$false,
inference(equality_resolution,[status(thm)],[d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET017-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/10.37 % Computer : n008.cluster.edu
% 0.11/10.37 % Model : x86_64 x86_64
% 0.11/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.37 % Memory : 8046.5625MB
% 0.11/10.37 % OS : Linux 6.8.0-71-generic
% 0.11/10.37 % CPULimit : 300
% 0.11/10.37 % WCLimit : 300
% 0.11/10.37 % DateTime : Sat Sep 26 06:53:08 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.54/13.34 % SZS status Unsatisfiable for theBenchmark.p
% 22.54/13.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------