%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET930+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 : 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 30.23s 4.25s
% Output : CNFRefutation 30.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 61 ( 26 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 69 ( 35 ~; 22 |; 9 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [X0,X1] : 'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0) ).
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(t72_zfmisc_1,axiom,
! [X0,X1,X2] :
( 'set$udifference'('unordered$upair'(X0,X1),X2) = 'unordered$upair'(X0,X1)
<=> ( ~ in(X1,X2)
& ~ in(X0,X2) ) ) ).
fof(t73_zfmisc_1,axiom,
! [X0,X1,X2] :
( 'set$udifference'('unordered$upair'(X0,X1),X2) = 'empty$uset'
<=> ( in(X1,X2)
& in(X0,X2) ) ) ).
fof(t74_zfmisc_1,conjecture,
! [X0,X1,X2] :
~ ( 'set$udifference'('unordered$upair'(X0,X1),X2) != 'unordered$upair'(X0,X1)
& 'set$udifference'('unordered$upair'(X0,X1),X2) != singleton(X1)
& 'set$udifference'('unordered$upair'(X0,X1),X2) != singleton(X0)
& 'set$udifference'('unordered$upair'(X0,X1),X2) != 'empty$uset' ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( 'set$udifference'('unordered$upair'(X0,X1),X2) != 'unordered$upair'(X0,X1)
& 'set$udifference'('unordered$upair'(X0,X1),X2) != singleton(X1)
& 'set$udifference'('unordered$upair'(X0,X1),X2) != singleton(X0)
& 'set$udifference'('unordered$upair'(X0,X1),X2) != 'empty$uset' ),
inference(negate_conjecture,[status(cth)],[t74_zfmisc_1]) ).
cnf(c1,plain,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_tarski]) ).
cnf(c5,plain,
( ~ in(X1,X2)
| in(X0,X2)
| 'set$udifference'('unordered$upair'(X0,X1),X2) = singleton(X0) ),
inference(clausification,[status(esa)],[l39_zfmisc_1]) ).
cnf(c11,plain,
( in(X1,X2)
| in(X0,X2)
| 'set$udifference'('unordered$upair'(X0,X1),X2) = 'unordered$upair'(X0,X1) ),
inference(clausification,[status(esa)],[t72_zfmisc_1]) ).
cnf(c14,plain,
( ~ in(X1,X2)
| ~ in(X0,X2)
| 'set$udifference'('unordered$upair'(X0,X1),X2) = 'empty$uset' ),
inference(clausification,[status(esa)],[t73_zfmisc_1]) ).
cnf(c15,plain,
'set$udifference'('unordered$upair'(sK15,sK16),sK17) != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
'set$udifference'('unordered$upair'(sK15,sK16),sK17) != singleton(sK15),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c17,plain,
'set$udifference'('unordered$upair'(sK15,sK16),sK17) != singleton(sK16),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c18,plain,
'set$udifference'('unordered$upair'(sK15,sK16),sK17) != 'unordered$upair'(sK15,sK16),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ in(X1,X2)
| in(X0,X2)
| 'set$udifference'('unordered$upair'(X1,X0),X2) = singleton(X0) ),
inference(superposition,[status(thm)],[c1,c5]) ).
cnf(d1,plain,
( in(sK16,sK17)
| ~ in(sK15,sK17)
| singleton(sK16) != singleton(sK16) ),
inference(superposition,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
( in(sK16,sK17)
| ~ in(sK15,sK17) ),
inference(equality_resolution,[status(thm)],[d1]) ).
cnf(d3,plain,
( ~ in(sK16,sK17)
| in(sK15,sK17)
| singleton(sK15) != singleton(sK15) ),
inference(superposition,[status(thm)],[c5,c16]) ).
cnf(d4,plain,
( ~ in(sK16,sK17)
| in(sK15,sK17) ),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
( in(sK15,sK17)
| in(sK16,sK17)
| 'unordered$upair'(sK15,sK16) != 'unordered$upair'(sK15,sK16) ),
inference(superposition,[status(thm)],[c11,c18]) ).
cnf(d6,plain,
( in(sK16,sK17)
| in(sK15,sK17) ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( in(sK15,sK17)
| in(sK15,sK17) ),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
in(sK16,sK17),
inference(resolution,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
( ~ in(sK16,sK17)
| ~ in(sK15,sK17)
| 'empty$uset' != 'empty$uset' ),
inference(superposition,[status(thm)],[c14,c15]) ).
cnf(d10,plain,
( ~ in(sK16,sK17)
| ~ in(sK15,sK17) ),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
~ in(sK16,sK17),
inference(resolution,[status(thm)],[d7,d10]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET930+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 08:28:08 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.23/4.25 % SZS status Theorem for theBenchmark.p
% 30.23/4.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------