%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET016-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 08:31:35 AM UTC 2026
% Result : Unsatisfiable 24.35s 17.30s
% Output : CNFRefutation 24.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of clauses : 36 ( 22 unt; 8 nHn; 24 RR)
% Number of literals : 57 ( 27 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(little_set_a,hypothesis,
'little$uset'(a) ).
cnf(little_set_b,hypothesis,
'little$uset'(b) ).
cnf(equal_ordered_pairs,hypothesis,
'ordered$upair'(a,c) = 'ordered$upair'(b,d) ).
cnf(prove_first_components_equal,negated_conjecture,
a != b ).
cnf(non_ordered_pair1,axiom,
( X0 = X2
| X0 = X1
| ~ member(X0,'non$uordered$upair'(X1,X2)) ) ).
cnf(non_ordered_pair2,axiom,
( X0 != X1
| ~ 'little$uset'(X0)
| member(X0,'non$uordered$upair'(X1,X2)) ) ).
cnf(non_ordered_pair4,axiom,
'little$uset'('non$uordered$upair'(X0,X1)) ).
cnf(singleton_set,axiom,
'singleton$uset'(X0) = 'non$uordered$upair'(X0,X0) ).
cnf(ordered_pair,axiom,
'ordered$upair'(X0,X1) = 'non$uordered$upair'('singleton$uset'(X0),'non$uordered$upair'(X0,X1)) ).
cnf(c0,plain,
'little$uset'(a),
inference(clausification,[status(esa)],[little_set_a]) ).
cnf(c1,plain,
'little$uset'(b),
inference(clausification,[status(esa)],[little_set_b]) ).
cnf(c2,plain,
'ordered$upair'(b,d) = 'ordered$upair'(a,c),
inference(clausification,[status(esa)],[equal_ordered_pairs]) ).
cnf(c3,plain,
b != a,
inference(clausification,[status(esa)],[prove_first_components_equal]) ).
cnf(c8,plain,
( X2 = X1
| ~ member(X1,'non$uordered$upair'(X0,X2))
| X0 = X1 ),
inference(clausification,[status(esa)],[non_ordered_pair1]) ).
cnf(c9,plain,
( X1 != X0
| member(X0,'non$uordered$upair'(X1,X2))
| ~ 'little$uset'(X0) ),
inference(clausification,[status(esa)],[non_ordered_pair2]) ).
cnf(c11,plain,
'little$uset'('non$uordered$upair'(X0,X1)),
inference(clausification,[status(esa)],[non_ordered_pair4]) ).
cnf(c12,plain,
'non$uordered$upair'(X0,X0) = 'singleton$uset'(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c13,plain,
'non$uordered$upair'('singleton$uset'(X0),'non$uordered$upair'(X0,X1)) = 'ordered$upair'(X0,X1),
inference(clausification,[status(esa)],[ordered_pair]) ).
cnf(d0,plain,
( X0 = X1
| X0 = X1
| ~ member(X1,'singleton$uset'(X0)) ),
inference(superposition,[status(thm)],[c12,c8]) ).
cnf(d1,plain,
( member(X0,'non$uordered$upair'(X0,X1))
| ~ 'little$uset'(X0) ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(d2,plain,
( ~ 'little$uset'(X0)
| member(X0,'singleton$uset'(X0)) ),
inference(superposition,[status(thm)],[c12,d1]) ).
cnf(d3,plain,
( 'singleton$uset'(X0) = X2
| 'non$uordered$upair'(X0,X1) = X2
| ~ member(X2,'ordered$upair'(X0,X1)) ),
inference(superposition,[status(thm)],[c13,c8]) ).
cnf(d4,plain,
( ~ 'little$uset'('singleton$uset'(X0))
| member('singleton$uset'(X0),'ordered$upair'(X0,X1)) ),
inference(superposition,[status(thm)],[c13,d1]) ).
cnf(d5,plain,
'little$uset'('singleton$uset'(X0)),
inference(superposition,[status(thm)],[c12,c11]) ).
cnf(d6,plain,
member('singleton$uset'(X0),'ordered$upair'(X0,X1)),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
member('singleton$uset'(b),'ordered$upair'(a,c)),
inference(superposition,[status(thm)],[c2,d6]) ).
cnf(d8,plain,
( 'singleton$uset'(a) = 'singleton$uset'(b)
| 'non$uordered$upair'(a,c) = 'singleton$uset'(b) ),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( 'singleton$uset'(a) = 'singleton$uset'(b)
| ~ 'little$uset'(a)
| member(a,'singleton$uset'(b)) ),
inference(superposition,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
( member(a,'singleton$uset'(b))
| 'singleton$uset'(a) = 'singleton$uset'(b) ),
inference(resolution,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
( b = a
| 'singleton$uset'(a) = 'singleton$uset'(b) ),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
'singleton$uset'(a) = 'singleton$uset'(b),
inference(resolution,[status(thm)],[c3,d11]) ).
cnf(d13,plain,
( ~ 'little$uset'(b)
| member(b,'singleton$uset'(a)) ),
inference(superposition,[status(thm)],[d12,d2]) ).
cnf(d14,plain,
member(b,'singleton$uset'(a)),
inference(resolution,[status(thm)],[c1,d13]) ).
cnf(d15,plain,
a = b,
inference(resolution,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
a != a,
inference(demodulation,[status(thm)],[c3,d15]) ).
cnf(d17,plain,
$false,
inference(equality_resolution,[status(thm)],[d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET016-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n018.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 06:52:52 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.35/17.30 % SZS status Unsatisfiable for theBenchmark.p
% 24.35/17.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------