%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET873+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 08:33:28 AM UTC 2026
% Result : Theorem 11.09s 2.86s
% Output : CNFRefutation 11.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 30 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 9 ~; 6 |; 0 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 1 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0) ).
fof(d1_tarski,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ) ).
fof(l21_zfmisc_1,axiom,
! [X0,X1] :
( subset('set$uunion2'(singleton(X0),X1),X1)
=> in(X0,X1) ) ).
fof(reflexivity_r1_tarski,axiom,
! [X0,X1] : subset(X0,X0) ).
fof(t13_zfmisc_1,conjecture,
! [X0,X1] :
( 'set$uunion2'(singleton(X0),singleton(X1)) = singleton(X0)
=> X0 = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( 'set$uunion2'(singleton(X0),singleton(X1)) = singleton(X0)
=> X0 = X1 ),
inference(negate_conjecture,[status(cth)],[t13_zfmisc_1]) ).
cnf(c1,plain,
'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(c2,plain,
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c11,plain,
( in(X0,X1)
| ~ subset('set$uunion2'(singleton(X0),X1),X1) ),
inference(clausification,[status(esa)],[l21_zfmisc_1]) ).
cnf(c14,plain,
subset(X0,X0),
inference(clausification,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(c15,plain,
'set$uunion2'(singleton(sK20),singleton(sK21)) = singleton(sK20),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
sK20 != sK21,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(d1,plain,
( in(X0,X1)
| ~ subset('set$uunion2'(X1,singleton(X0)),X1) ),
inference(superposition,[status(thm)],[c1,c11]) ).
cnf(d2,plain,
( in(sK21,singleton(sK20))
| ~ subset(singleton(sK20),singleton(sK20)) ),
inference(superposition,[status(thm)],[c15,d1]) ).
cnf(d3,plain,
in(sK21,singleton(sK20)),
inference(resolution,[status(thm)],[c14,d2]) ).
cnf(d4,plain,
sK21 = sK20,
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
sK20 != sK20,
inference(demodulation,[status(thm)],[c16,d4]) ).
cnf(d6,plain,
$false,
inference(equality_resolution,[status(thm)],[d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET873+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:25:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.09/2.86 % SZS status Theorem for theBenchmark.p
% 11.09/2.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------