%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET929+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 : n013.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 10.37s 2.74s
% Output : CNFRefutation 10.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 5 unt; 0 def)
% Number of atoms : 47 ( 15 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 42 ( 17 ~; 18 |; 3 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 2 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t37_xboole_1,axiom,
! [X0,X1] :
( 'set$udifference'(X0,X1) = 'empty$uset'
<=> subset(X0,X1) ) ).
fof(t38_zfmisc_1,axiom,
! [X0,X1,X2] :
( subset('unordered$upair'(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ) ).
fof(t73_zfmisc_1,conjecture,
! [X0,X1,X2] :
( 'set$udifference'('unordered$upair'(X0,X1),X2) = 'empty$uset'
<=> ( in(X1,X2)
& in(X0,X2) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( 'set$udifference'('unordered$upair'(X0,X1),X2) = 'empty$uset'
<=> ( in(X1,X2)
& in(X0,X2) ) ),
inference(negate_conjecture,[status(cth)],[t73_zfmisc_1]) ).
cnf(c6,plain,
( subset(X0,X1)
| 'set$udifference'(X0,X1) != 'empty$uset' ),
inference(clausification,[status(esa)],[t37_xboole_1]) ).
cnf(c7,plain,
( ~ subset(X0,X1)
| 'set$udifference'(X0,X1) = 'empty$uset' ),
inference(clausification,[status(esa)],[t37_xboole_1]) ).
cnf(c8,plain,
( in(X0,X2)
| ~ subset('unordered$upair'(X0,X1),X2) ),
inference(clausification,[status(esa)],[t38_zfmisc_1]) ).
cnf(c9,plain,
( in(X1,X2)
| ~ subset('unordered$upair'(X0,X1),X2) ),
inference(clausification,[status(esa)],[t38_zfmisc_1]) ).
cnf(c10,plain,
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset('unordered$upair'(X0,X1),X2) ),
inference(clausification,[status(esa)],[t38_zfmisc_1]) ).
cnf(c12,plain,
( in(sK13,sK15)
| 'set$udifference'('unordered$upair'(sK13,sK14),sK15) = 'empty$uset' ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c13,plain,
( in(sK14,sK15)
| 'set$udifference'('unordered$upair'(sK13,sK14),sK15) = 'empty$uset' ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c14,plain,
( 'set$udifference'('unordered$upair'(sK13,sK14),sK15) != 'empty$uset'
| ~ in(sK14,sK15)
| ~ in(sK13,sK15) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'set$udifference'('unordered$upair'(X0,X2),X1) = 'empty$uset'
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[c10,c7]) ).
cnf(d1,plain,
( 'set$udifference'('unordered$upair'(sK13,sK14),sK15) = 'empty$uset'
| ~ in(X0,sK15)
| 'set$udifference'('unordered$upair'(sK13,X0),sK15) = 'empty$uset' ),
inference(resolution,[status(thm)],[d0,c12]) ).
cnf(d2,plain,
( 'set$udifference'('unordered$upair'(sK13,sK14),sK15) = 'empty$uset'
| 'set$udifference'('unordered$upair'(sK13,sK14),sK15) = 'empty$uset'
| 'set$udifference'('unordered$upair'(sK13,sK14),sK15) = 'empty$uset' ),
inference(resolution,[status(thm)],[d1,c13]) ).
cnf(d3,plain,
( ~ in(sK14,sK15)
| ~ in(sK13,sK15) ),
inference(resolution,[status(thm)],[d2,c14]) ).
cnf(d4,plain,
( subset('unordered$upair'(sK13,sK14),sK15)
| 'empty$uset' != 'empty$uset' ),
inference(superposition,[status(thm)],[d2,c6]) ).
cnf(d5,plain,
subset('unordered$upair'(sK13,sK14),sK15),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
in(sK14,sK15),
inference(resolution,[status(thm)],[d5,c9]) ).
cnf(d7,plain,
~ in(sK13,sK15),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
in(sK13,sK15),
inference(resolution,[status(thm)],[d5,c8]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET929+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n013.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 08:25:51 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.37/2.74 % SZS status Theorem for theBenchmark.p
% 10.37/2.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------