%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET016+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 : Theorem 14.20s 7.41s
% Output : CNFRefutation 14.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 8 unt; 0 def)
% Number of atoms : 49 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 11 ~; 15 |; 1 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 3 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(equal_set,axiom,
! [X0,X1] :
( 'equal$uset'(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(singleton,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ) ).
fof(unordered_pair,axiom,
! [X0,X1,X2] :
( member(X0,'unordered$upair'(X1,X2))
<=> ( X0 = X2
| X0 = X1 ) ) ).
fof(thI50a,conjecture,
! [X0,X1,X2,X3] :
( 'equal$uset'('unordered$upair'(singleton(X0),'unordered$upair'(X0,X1)),'unordered$upair'(singleton(X2),'unordered$upair'(X2,X3)))
=> X0 = X2 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( 'equal$uset'('unordered$upair'(singleton(X0),'unordered$upair'(X0,X1)),'unordered$upair'(singleton(X2),'unordered$upair'(X2,X3)))
=> X0 = X2 ),
inference(negate_conjecture,[status(cth)],[thI50a]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c3,plain,
( subset(X0,X1)
| ~ 'equal$uset'(X0,X1) ),
inference(clausification,[status(esa)],[equal_set]) ).
cnf(c18,plain,
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(clausification,[status(esa)],[singleton]) ).
cnf(c19,plain,
( X0 != X1
| member(X0,singleton(X1)) ),
inference(clausification,[status(esa)],[singleton]) ).
cnf(c20,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair]) ).
cnf(c21,plain,
( X0 != X1
| member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair]) ).
cnf(c29,plain,
'equal$uset'('unordered$upair'(singleton(sK31),'unordered$upair'(sK31,sK32)),'unordered$upair'(singleton(sK33),'unordered$upair'(sK33,sK34))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c30,plain,
sK31 != sK33,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
member(X0,singleton(X0)),
inference(equality_resolution,[status(thm)],[c19]) ).
cnf(d1,plain,
member(X0,'unordered$upair'(X0,X1)),
inference(equality_resolution,[status(thm)],[c21]) ).
cnf(d2,plain,
subset('unordered$upair'(singleton(sK31),'unordered$upair'(sK31,sK32)),'unordered$upair'(singleton(sK33),'unordered$upair'(sK33,sK34))),
inference(resolution,[status(thm)],[c3,c29]) ).
cnf(d3,plain,
( member(X0,X2)
| ~ subset('unordered$upair'(X0,X1),X2) ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d4,plain,
member(singleton(sK31),'unordered$upair'(singleton(sK33),'unordered$upair'(sK33,sK34))),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( singleton(sK31) = singleton(sK33)
| singleton(sK31) = 'unordered$upair'(sK33,sK34) ),
inference(resolution,[status(thm)],[d4,c20]) ).
cnf(d6,plain,
( singleton(sK31) = singleton(sK33)
| member(sK33,singleton(sK31)) ),
inference(superposition,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( sK33 = sK31
| singleton(sK31) = singleton(sK33) ),
inference(resolution,[status(thm)],[d6,c18]) ).
cnf(d8,plain,
( sK33 = sK31
| member(sK33,singleton(sK31)) ),
inference(superposition,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
( sK33 = sK31
| sK33 = sK31 ),
inference(resolution,[status(thm)],[d8,c18]) ).
cnf(d10,plain,
sK31 != sK31,
inference(demodulation,[status(thm)],[c30,d9]) ).
cnf(d11,plain,
$false,
inference(equality_resolution,[status(thm)],[d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.59 % Computer : n026.cluster.edu
% 0.12/5.59 % Model : x86_64 x86_64
% 0.12/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.59 % Memory : 8046.5625MB
% 0.12/5.59 % OS : Linux 6.8.0-71-generic
% 0.12/5.59 % CPULimit : 300
% 0.12/5.59 % WCLimit : 300
% 0.12/5.59 % DateTime : Sat Sep 26 06:53:32 UTC 2026
% 0.12/5.59 % CPUTime :
% 0.12/5.59 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.20/7.41 % SZS status Theorem for theBenchmark.p
% 14.20/7.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------