%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET902+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 08:33:31 AM UTC 2026
% Result : Theorem 14.97s 2.36s
% Output : CNFRefutation 14.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 18 unt; 0 def)
% Number of atoms : 79 ( 71 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 74 ( 32 ~; 29 |; 12 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 4 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0) ).
fof(idempotence_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X0) = X0 ).
fof(l1_zfmisc_1,axiom,
! [X0] : singleton(X0) != 'empty$uset' ).
fof(l4_zfmisc_1,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = 'empty$uset' ) ) ).
fof(t7_xboole_1,axiom,
! [X0,X1] : subset(X0,'set$uunion2'(X0,X1)) ).
fof(t43_zfmisc_1,conjecture,
! [X0,X1,X2] :
~ ( ~ ( X2 = 'empty$uset'
& X1 = singleton(X0) )
& ~ ( X2 = singleton(X0)
& X1 = 'empty$uset' )
& ~ ( X2 = singleton(X0)
& X1 = singleton(X0) )
& singleton(X0) = 'set$uunion2'(X1,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( ~ ( X2 = 'empty$uset'
& X1 = singleton(X0) )
& ~ ( X2 = singleton(X0)
& X1 = 'empty$uset' )
& ~ ( X2 = singleton(X0)
& X1 = singleton(X0) )
& singleton(X0) = 'set$uunion2'(X1,X2) ),
inference(negate_conjecture,[status(cth)],[t43_zfmisc_1]) ).
cnf(c0,plain,
'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(c4,plain,
'set$uunion2'(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_k2_xboole_0]) ).
cnf(c5,plain,
singleton(X0) != 'empty$uset',
inference(clausification,[status(esa)],[l1_zfmisc_1]) ).
cnf(c6,plain,
( X0 = singleton(X1)
| X0 = 'empty$uset'
| ~ subset(X0,singleton(X1)) ),
inference(clausification,[status(esa)],[l4_zfmisc_1]) ).
cnf(c12,plain,
subset(X0,'set$uunion2'(X0,X1)),
inference(clausification,[status(esa)],[t7_xboole_1]) ).
cnf(c13,plain,
singleton(sK17) = 'set$uunion2'(sK18,sK19),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c14,plain,
( sK19 != singleton(sK17)
| sK18 != singleton(sK17) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c15,plain,
( sK19 != singleton(sK17)
| sK18 != 'empty$uset' ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
( sK19 != 'empty$uset'
| sK18 != singleton(sK17) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
subset(X0,'set$uunion2'(X1,X0)),
inference(superposition,[status(thm)],[c0,c12]) ).
cnf(d1,plain,
subset(sK19,singleton(sK17)),
inference(superposition,[status(thm)],[c13,d0]) ).
cnf(d2,plain,
( sK19 = singleton(sK17)
| sK19 = 'empty$uset' ),
inference(resolution,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
( sK19 = 'empty$uset'
| sK18 != 'empty$uset'
| sK19 != sK19 ),
inference(superposition,[status(thm)],[d2,c15]) ).
cnf(d4,plain,
( sK19 = 'empty$uset'
| sK18 != 'empty$uset' ),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
subset(sK18,singleton(sK17)),
inference(superposition,[status(thm)],[c13,c12]) ).
cnf(d6,plain,
( sK18 = singleton(sK17)
| sK18 = 'empty$uset' ),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
( sK18 = 'empty$uset'
| sK19 != 'empty$uset'
| sK18 != sK18 ),
inference(superposition,[status(thm)],[d6,c16]) ).
cnf(d8,plain,
( sK18 = 'empty$uset'
| sK18 != singleton(sK17)
| sK19 != sK18 ),
inference(superposition,[status(thm)],[d6,c14]) ).
cnf(d9,plain,
( sK18 = 'empty$uset'
| sK19 != sK18
| sK18 = 'empty$uset'
| sK18 != sK18 ),
inference(superposition,[status(thm)],[d6,d8]) ).
cnf(d10,plain,
( sK19 = 'empty$uset'
| sK18 = 'empty$uset'
| sK18 = sK19 ),
inference(superposition,[status(thm)],[d2,d6]) ).
cnf(d11,plain,
( sK19 = 'empty$uset'
| sK18 = 'empty$uset'
| sK18 != sK18
| sK18 = 'empty$uset'
| sK18 != sK18 ),
inference(superposition,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( sK19 = 'empty$uset'
| sK18 = 'empty$uset' ),
inference(equality_resolution,[status(thm)],[d11]) ).
cnf(d13,plain,
( sK18 = 'empty$uset'
| sK18 != sK18
| sK18 = 'empty$uset'
| 'empty$uset' != 'empty$uset' ),
inference(superposition,[status(thm)],[d12,d7]) ).
cnf(d14,plain,
( sK18 = 'empty$uset'
| 'empty$uset' != 'empty$uset' ),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
sK18 = 'empty$uset',
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
sK19 = 'empty$uset',
inference(resolution,[status(thm)],[d15,d4]) ).
cnf(d17,plain,
singleton(sK17) = 'set$uunion2'('empty$uset',sK19),
inference(demodulation,[status(thm)],[c13,d15]) ).
cnf(d18,plain,
singleton(sK17) = 'set$uunion2'('empty$uset','empty$uset'),
inference(demodulation,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
singleton(sK17) = 'empty$uset',
inference(demodulation,[status(thm)],[d18,c4]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[c5,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET902+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n019.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 08:25:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.97/2.36 % SZS status Theorem for theBenchmark.p
% 14.97/2.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------