%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET018+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 08:31:37 AM UTC 2026
% Result : Theorem 23.14s 4.18s
% Output : CNFRefutation 23.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 18 unt; 0 def)
% Number of atoms : 90 ( 40 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 15 ~; 32 |; 1 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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 : 49 ( 6 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(thI50b,conjecture,
! [X0,X1,X2,X3] :
( 'equal$uset'('unordered$upair'(singleton(X0),'unordered$upair'(X0,X1)),'unordered$upair'(singleton(X2),'unordered$upair'(X2,X3)))
=> X1 = X3 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( 'equal$uset'('unordered$upair'(singleton(X0),'unordered$upair'(X0,X1)),'unordered$upair'(singleton(X2),'unordered$upair'(X2,X3)))
=> X1 = X3 ),
inference(negate_conjecture,[status(cth)],[thI50b]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c3,plain,
( subset(X0,X1)
| ~ 'equal$uset'(X0,X1) ),
inference(clausification,[status(esa)],[equal_set]) ).
cnf(c4,plain,
( subset(X1,X0)
| ~ 'equal$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(c22,plain,
( X0 != X2
| 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,
sK32 != sK34,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
member(X0,'unordered$upair'(X1,X0)),
inference(equality_resolution,[status(thm)],[c22]) ).
cnf(d1,plain,
member(X0,singleton(X0)),
inference(equality_resolution,[status(thm)],[c19]) ).
cnf(d2,plain,
member(X0,'unordered$upair'(X0,X1)),
inference(equality_resolution,[status(thm)],[c21]) ).
cnf(d3,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(d4,plain,
( member(X0,X2)
| ~ subset('unordered$upair'(X0,X1),X2) ),
inference(resolution,[status(thm)],[d2,c0]) ).
cnf(d5,plain,
member(singleton(sK31),'unordered$upair'(singleton(sK33),'unordered$upair'(sK33,sK34))),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( singleton(sK31) = singleton(sK33)
| singleton(sK31) = 'unordered$upair'(sK33,sK34) ),
inference(resolution,[status(thm)],[c20,d5]) ).
cnf(d7,plain,
( singleton(sK31) = singleton(sK33)
| member(sK33,singleton(sK31)) ),
inference(superposition,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( member(sK33,singleton(sK31))
| member(sK33,singleton(sK31)) ),
inference(superposition,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
sK33 = sK31,
inference(resolution,[status(thm)],[d8,c18]) ).
cnf(d10,plain,
subset('unordered$upair'(singleton(sK33),'unordered$upair'(sK33,sK34)),'unordered$upair'(singleton(sK31),'unordered$upair'(sK31,sK32))),
inference(resolution,[status(thm)],[c4,c29]) ).
cnf(d11,plain,
( member(X1,X2)
| ~ subset('unordered$upair'(X0,X1),X2) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d12,plain,
member('unordered$upair'(sK33,sK34),'unordered$upair'(singleton(sK31),'unordered$upair'(sK31,sK32))),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( 'unordered$upair'(sK33,sK34) = singleton(sK31)
| 'unordered$upair'(sK33,sK34) = 'unordered$upair'(sK31,sK32) ),
inference(resolution,[status(thm)],[c20,d12]) ).
cnf(d14,plain,
( 'unordered$upair'(sK33,sK34) = 'unordered$upair'(sK31,sK32)
| 'unordered$upair'(sK31,sK34) = singleton(sK31) ),
inference(demodulation,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
( 'unordered$upair'(sK31,sK34) = 'unordered$upair'(sK31,sK32)
| 'unordered$upair'(sK31,sK34) = singleton(sK31) ),
inference(demodulation,[status(thm)],[d14,d9]) ).
cnf(d16,plain,
( 'unordered$upair'(sK31,sK34) = singleton(sK31)
| member(sK34,'unordered$upair'(sK31,sK32)) ),
inference(superposition,[status(thm)],[d15,d0]) ).
cnf(d17,plain,
( member(sK34,'unordered$upair'(sK31,sK32))
| member(sK34,singleton(sK31)) ),
inference(superposition,[status(thm)],[d16,d0]) ).
cnf(d18,plain,
( sK34 = sK31
| sK34 = sK32
| member(sK34,singleton(sK31)) ),
inference(resolution,[status(thm)],[d17,c20]) ).
cnf(d19,plain,
( sK34 = sK31
| sK34 = sK32
| sK34 = sK31 ),
inference(resolution,[status(thm)],[d18,c18]) ).
cnf(d20,plain,
( sK34 = sK31
| sK32 != sK32 ),
inference(superposition,[status(thm)],[d19,c30]) ).
cnf(d21,plain,
sK34 = sK31,
inference(equality_resolution,[status(thm)],[d20]) ).
cnf(d22,plain,
member('unordered$upair'(sK31,sK32),'unordered$upair'(singleton(sK33),'unordered$upair'(sK33,sK34))),
inference(resolution,[status(thm)],[d11,d3]) ).
cnf(d23,plain,
member('unordered$upair'(sK31,sK32),'unordered$upair'(singleton(sK31),'unordered$upair'(sK33,sK34))),
inference(demodulation,[status(thm)],[d22,d9]) ).
cnf(d24,plain,
member('unordered$upair'(sK31,sK32),'unordered$upair'(singleton(sK31),'unordered$upair'(sK31,sK34))),
inference(demodulation,[status(thm)],[d23,d9]) ).
cnf(d25,plain,
( 'unordered$upair'(sK31,sK32) = singleton(sK31)
| 'unordered$upair'(sK31,sK32) = 'unordered$upair'(sK31,sK34) ),
inference(resolution,[status(thm)],[d24,c20]) ).
cnf(d26,plain,
( 'unordered$upair'(sK31,sK32) = 'unordered$upair'(sK31,sK31)
| 'unordered$upair'(sK31,sK32) = singleton(sK31) ),
inference(demodulation,[status(thm)],[d25,d21]) ).
cnf(d27,plain,
( 'unordered$upair'(sK31,sK32) = singleton(sK31)
| member(sK32,'unordered$upair'(sK31,sK31)) ),
inference(superposition,[status(thm)],[d26,d0]) ).
cnf(d28,plain,
( member(sK32,'unordered$upair'(sK31,sK31))
| member(sK32,singleton(sK31)) ),
inference(superposition,[status(thm)],[d27,d0]) ).
cnf(d29,plain,
( sK32 = sK31
| sK32 = sK31
| member(sK32,singleton(sK31)) ),
inference(resolution,[status(thm)],[d28,c20]) ).
cnf(d30,plain,
sK32 != sK31,
inference(demodulation,[status(thm)],[c30,d21]) ).
cnf(d31,plain,
member(sK32,singleton(sK31)),
inference(resolution,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
sK32 = sK31,
inference(resolution,[status(thm)],[d31,c18]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[d30,d32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET018+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 06:49:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.14/4.18 % SZS status Theorem for theBenchmark.p
% 23.14/4.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------