%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET042-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 08:31:44 AM UTC 2026
% Result : Unsatisfiable 26.88s 4.80s
% Output : CNFRefutation 26.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 34 ( 15 unt; 0 nHn; 32 RR)
% Number of literals : 75 ( 10 equ; 51 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(property_of_first,axiom,
( first('ordered$upair'(X0,X1)) = X0
| ~ 'little$uset'(X1)
| ~ 'little$uset'(X0) ) ).
cnf(property_of_second,axiom,
( second('ordered$upair'(X0,X1)) = X1
| ~ 'little$uset'(X1)
| ~ 'little$uset'(X0) ) ).
cnf(ordered_pairs_are_small1,axiom,
'little$uset'('ordered$upair'(X0,X1)) ).
cnf(member_of_set_a,hypothesis,
member(a,'set$ua') ).
cnf(member_of_set_b,hypothesis,
member(b,'set$ub') ).
cnf(prove_ordered_pair_is_in_cross_product,negated_conjecture,
~ member('ordered$upair'(a,b),'cross$uproduct'('set$ua','set$ub')) ).
cnf(a2,axiom,
( 'little$uset'(X0)
| ~ member(X0,X1) ) ).
cnf(ordered_pair_predicate4,axiom,
( X0 != 'ordered$upair'(X1,X2)
| ~ 'little$uset'(X2)
| ~ 'little$uset'(X1)
| 'ordered$upair$upredicate'(X0) ) ).
cnf(cross_product4,axiom,
( ~ member(second(X0),X2)
| ~ member(first(X0),X1)
| ~ 'ordered$upair$upredicate'(X0)
| ~ 'little$uset'(X0)
| member(X0,'cross$uproduct'(X1,X2)) ) ).
cnf(c4,plain,
( first('ordered$upair'(X1,X0)) = X1
| ~ 'little$uset'(X1)
| ~ 'little$uset'(X0) ),
inference(clausification,[status(esa)],[property_of_first]) ).
cnf(c5,plain,
( second('ordered$upair'(X1,X0)) = X0
| ~ 'little$uset'(X1)
| ~ 'little$uset'(X0) ),
inference(clausification,[status(esa)],[property_of_second]) ).
cnf(c9,plain,
'little$uset'('ordered$upair'(X0,X1)),
inference(clausification,[status(esa)],[ordered_pairs_are_small1]) ).
cnf(c26,plain,
member(a,'set$ua'),
inference(clausification,[status(esa)],[member_of_set_a]) ).
cnf(c27,plain,
member(b,'set$ub'),
inference(clausification,[status(esa)],[member_of_set_b]) ).
cnf(c28,plain,
~ member('ordered$upair'(a,b),'cross$uproduct'('set$ua','set$ub')),
inference(clausification,[status(esa)],[prove_ordered_pair_is_in_cross_product]) ).
cnf(c29,plain,
( 'little$uset'(X0)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[a2]) ).
cnf(c42,plain,
( 'ordered$upair'(X2,X0) != X1
| ~ 'little$uset'(X2)
| 'ordered$upair$upredicate'(X1)
| ~ 'little$uset'(X0) ),
inference(clausification,[status(esa)],[ordered_pair_predicate4]) ).
cnf(c69,plain,
( ~ 'ordered$upair$upredicate'(X0)
| ~ member(first(X0),X2)
| member(X0,'cross$uproduct'(X2,X1))
| ~ member(second(X0),X1)
| ~ 'little$uset'(X0) ),
inference(clausification,[status(esa)],[cross_product4]) ).
cnf(d0,plain,
( 'ordered$upair$upredicate'('ordered$upair'(X1,X0))
| ~ 'little$uset'(X1)
| ~ 'little$uset'(X0) ),
inference(equality_resolution,[status(thm)],[c42]) ).
cnf(d1,plain,
'little$uset'(b),
inference(resolution,[status(thm)],[c29,c27]) ).
cnf(d2,plain,
'little$uset'(a),
inference(resolution,[status(thm)],[c29,c26]) ).
cnf(d3,plain,
( ~ 'little$uset'(X0)
| second('ordered$upair'(a,X0)) = X0 ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
second('ordered$upair'(a,b)) = b,
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( ~ 'little$uset'(X0)
| first('ordered$upair'(X0,b)) = X0 ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d6,plain,
first('ordered$upair'(a,b)) = a,
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( ~ member(second('ordered$upair'(a,b)),'set$ub')
| ~ member(first('ordered$upair'(a,b)),'set$ua')
| ~ 'ordered$upair$upredicate'('ordered$upair'(a,b))
| ~ 'little$uset'('ordered$upair'(a,b)) ),
inference(resolution,[status(thm)],[c69,c28]) ).
cnf(d8,plain,
( ~ member(second('ordered$upair'(a,b)),'set$ub')
| ~ member(a,'set$ua')
| ~ 'ordered$upair$upredicate'('ordered$upair'(a,b))
| ~ 'little$uset'('ordered$upair'(a,b)) ),
inference(demodulation,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( ~ member(b,'set$ub')
| ~ member(a,'set$ua')
| ~ 'ordered$upair$upredicate'('ordered$upair'(a,b))
| ~ 'little$uset'('ordered$upair'(a,b)) ),
inference(demodulation,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
( ~ member(b,'set$ub')
| ~ 'ordered$upair$upredicate'('ordered$upair'(a,b))
| ~ 'little$uset'('ordered$upair'(a,b)) ),
inference(resolution,[status(thm)],[c26,d9]) ).
cnf(d11,plain,
( ~ 'ordered$upair$upredicate'('ordered$upair'(a,b))
| ~ 'little$uset'('ordered$upair'(a,b)) ),
inference(resolution,[status(thm)],[c27,d10]) ).
cnf(d12,plain,
~ 'ordered$upair$upredicate'('ordered$upair'(a,b)),
inference(resolution,[status(thm)],[c9,d11]) ).
cnf(d13,plain,
( ~ 'little$uset'(b)
| ~ 'little$uset'(a) ),
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
~ 'little$uset'(b),
inference(resolution,[status(thm)],[d2,d13]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d1,d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET042-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.32 % Computer : n012.cluster.edu
% 0.07/0.32 % Model : x86_64 x86_64
% 0.07/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.32 % Memory : 8046.5625MB
% 0.07/0.32 % OS : Linux 6.8.0-71-generic
% 0.07/0.32 % CPULimit : 300
% 0.07/0.32 % WCLimit : 300
% 0.07/0.32 % DateTime : Sat Sep 26 06:58:50 UTC 2026
% 0.07/0.32 % CPUTime :
% 0.07/0.32 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.88/4.80 % SZS status Unsatisfiable for theBenchmark.p
% 26.88/4.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------