%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET927+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 08:33:35 AM UTC 2026
% Result : Theorem 10.91s 1.73s
% Output : CNFRefutation 10.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 30 ( 3 unt; 0 def)
% Number of atoms : 80 ( 47 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 77 ( 27 ~; 44 |; 3 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l39_zfmisc_1,axiom,
! [X0,X1,X2] :
( 'set$udifference'('unordered$upair'(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ) ).
fof(t70_zfmisc_1,conjecture,
! [X0,X1,X2] :
( 'set$udifference'('unordered$upair'(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( 'set$udifference'('unordered$upair'(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
inference(negate_conjecture,[status(cth)],[t70_zfmisc_1]) ).
cnf(c4,plain,
( ~ in(X0,X2)
| 'set$udifference'('unordered$upair'(X0,X1),X2) != singleton(X0) ),
inference(clausification,[status(esa)],[l39_zfmisc_1]) ).
cnf(c5,plain,
( X0 = X1
| in(X1,X2)
| 'set$udifference'('unordered$upair'(X0,X1),X2) != singleton(X0) ),
inference(clausification,[status(esa)],[l39_zfmisc_1]) ).
cnf(c6,plain,
( ~ in(X1,X2)
| in(X0,X2)
| 'set$udifference'('unordered$upair'(X0,X1),X2) = singleton(X0) ),
inference(clausification,[status(esa)],[l39_zfmisc_1]) ).
cnf(c7,plain,
( X0 != X1
| in(X0,X2)
| 'set$udifference'('unordered$upair'(X0,X1),X2) = singleton(X0) ),
inference(clausification,[status(esa)],[l39_zfmisc_1]) ).
cnf(c9,plain,
( ~ in(sK9,sK11)
| 'set$udifference'('unordered$upair'(sK9,sK10),sK11) = singleton(sK9) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c10,plain,
( sK9 = sK10
| in(sK10,sK11)
| 'set$udifference'('unordered$upair'(sK9,sK10),sK11) = singleton(sK9) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c11,plain,
( 'set$udifference'('unordered$upair'(sK9,sK10),sK11) != singleton(sK9)
| ~ in(sK10,sK11)
| in(sK9,sK11) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c14,plain,
( 'set$udifference'('unordered$upair'(sK9,sK10),sK11) != singleton(sK9)
| sK9 != sK10
| in(sK9,sK11) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( in(X0,X1)
| 'set$udifference'('unordered$upair'(X0,X0),X1) = singleton(X0) ),
inference(equality_resolution,[status(thm)],[c7]) ).
cnf(d1,plain,
( sK9 = sK10
| 'set$udifference'('unordered$upair'(sK9,sK10),sK11) = singleton(sK9)
| in(X0,sK11)
| 'set$udifference'('unordered$upair'(X0,sK10),sK11) = singleton(X0) ),
inference(resolution,[status(thm)],[c6,c10]) ).
cnf(d2,plain,
( 'set$udifference'('unordered$upair'(sK9,sK10),sK11) = singleton(sK9)
| sK9 = sK10
| 'set$udifference'('unordered$upair'(sK9,sK10),sK11) = singleton(sK9)
| 'set$udifference'('unordered$upair'(sK9,sK10),sK11) = singleton(sK9) ),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
( sK9 = sK10
| ~ in(sK9,sK11)
| singleton(sK9) != singleton(sK9) ),
inference(superposition,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
( ~ in(sK9,sK11)
| sK9 = sK10 ),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
( sK9 = sK10
| in(sK10,sK11)
| sK9 = sK10
| singleton(sK9) != singleton(sK9) ),
inference(superposition,[status(thm)],[d2,c5]) ).
cnf(d6,plain,
( in(sK10,sK11)
| sK9 = sK10 ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( sK9 = sK10
| ~ in(sK10,sK11)
| in(sK9,sK11)
| singleton(sK9) != singleton(sK9) ),
inference(superposition,[status(thm)],[d2,c11]) ).
cnf(d8,plain,
( ~ in(sK10,sK11)
| in(sK9,sK11)
| sK9 = sK10 ),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
( sK9 = sK10
| in(sK9,sK11)
| sK9 = sK10 ),
inference(resolution,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( sK9 = sK10
| sK9 = sK10 ),
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
( ~ in(sK9,sK11)
| 'set$udifference'('unordered$upair'(sK9,sK9),sK11) = singleton(sK9) ),
inference(demodulation,[status(thm)],[c9,d10]) ).
cnf(d12,plain,
( 'set$udifference'('unordered$upair'(sK9,sK9),sK11) = singleton(sK9)
| 'set$udifference'('unordered$upair'(sK9,sK9),sK11) = singleton(sK9) ),
inference(resolution,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
( ~ in(sK9,sK11)
| singleton(sK9) != singleton(sK9) ),
inference(superposition,[status(thm)],[d12,c4]) ).
cnf(d14,plain,
( in(sK9,sK11)
| 'set$udifference'('unordered$upair'(sK9,sK10),sK11) != singleton(sK9) ),
inference(resolution,[status(thm)],[d10,c14]) ).
cnf(d15,plain,
( in(sK9,sK11)
| 'set$udifference'('unordered$upair'(sK9,sK9),sK11) != singleton(sK9) ),
inference(demodulation,[status(thm)],[d14,d10]) ).
cnf(d16,plain,
in(sK9,sK11),
inference(resolution,[status(thm)],[d12,d15]) ).
cnf(d17,plain,
singleton(sK9) != singleton(sK9),
inference(resolution,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
$false,
inference(equality_resolution,[status(thm)],[d17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET927+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
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:27:39 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.91/1.73 % SZS status Theorem for theBenchmark.p
% 10.91/1.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------