%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU321+2 : TPTP v9.3.1. Released v3.3.0.
% 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 08:41:39 AM UTC 2026
% Result : Theorem 125.21s 18.76s
% Output : CNFRefutation 125.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 19 unt; 0 def)
% Number of atoms : 114 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 105 ( 46 ~; 33 |; 6 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 3 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0) ).
fof(d2_subset_1,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ) ).
fof(d4_xboole_0,axiom,
! [X0,X1,X2] :
( X2 = 'set$udifference'(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ) ).
fof(d5_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> 'subset$ucomplement'(X0,X1) = 'set$udifference'(X0,X1) ) ).
fof(dt_k3_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element('subset$ucomplement'(X0,X1),powerset(X0)) ) ).
fof(fc1_finset_1,axiom,
! [X0] :
( finite(singleton(X0))
& ~ empty(singleton(X0)) ) ).
fof(fc1_struct_0,axiom,
! [X0] :
( ( 'one$usorted$ustr'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ~ empty('the$ucarrier'(X0)) ) ).
fof(fc3_xboole_0,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty('set$uunion2'(X1,X0)) ) ).
fof(involutiveness_k3_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> 'subset$ucomplement'(X0,'subset$ucomplement'(X0,X1)) = X1 ) ).
fof(l23_zfmisc_1,lemma,
! [X0,X1] :
( in(X0,X1)
=> 'set$uunion2'(singleton(X0),X1) = X1 ) ).
fof(l40_tops_1,conjecture,
! [X0] :
( ( 'one$usorted$ustr'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ! [X2] :
( element(X2,'the$ucarrier'(X0))
=> ( in(X2,'subset$ucomplement'('the$ucarrier'(X0),X1))
<=> ~ in(X2,X1) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'one$usorted$ustr'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ! [X2] :
( element(X2,'the$ucarrier'(X0))
=> ( in(X2,'subset$ucomplement'('the$ucarrier'(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
inference(negate_conjecture,[status(cth)],[l40_tops_1]) ).
cnf(c73,plain,
'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(c277,plain,
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(clausification,[status(esa)],[d2_subset_1]) ).
cnf(c388,plain,
( ~ in(X3,X1)
| ~ in(X3,X2)
| 'set$udifference'(X0,X1) != X2 ),
inference(clausification,[status(esa)],[d4_xboole_0]) ).
cnf(c389,plain,
( ~ in(X3,X0)
| in(X3,X1)
| in(X3,X2)
| 'set$udifference'(X0,X1) != X2 ),
inference(clausification,[status(esa)],[d4_xboole_0]) ).
cnf(c421,plain,
( 'set$udifference'(X1,X0) = 'subset$ucomplement'(X1,X0)
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[d5_subset_1]) ).
cnf(c518,plain,
( element('subset$ucomplement'(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[dt_k3_subset_1]) ).
cnf(c567,plain,
~ empty(singleton(X0)),
inference(clausification,[status(esa)],[fc1_finset_1]) ).
cnf(c588,plain,
( ~ empty('the$ucarrier'(X0))
| 'empty$ucarrier'(X0)
| ~ 'one$usorted$ustr'(X0) ),
inference(clausification,[status(esa)],[fc1_struct_0]) ).
cnf(c657,plain,
( ~ empty('set$uunion2'(X1,X0))
| empty(X0) ),
inference(clausification,[status(esa)],[fc3_xboole_0]) ).
cnf(c697,plain,
( 'subset$ucomplement'(X1,'subset$ucomplement'(X1,X0)) = X0
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[involutiveness_k3_subset_1]) ).
cnf(c705,plain,
( 'set$uunion2'(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[l23_zfmisc_1]) ).
cnf(c1497,plain,
'one$usorted$ustr'(sK1636),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c1498,plain,
~ 'empty$ucarrier'(sK1636),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c1499,plain,
element(sK1637,powerset('the$ucarrier'(sK1636))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c1500,plain,
element(sK1638,'the$ucarrier'(sK1636)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c1502,plain,
( ~ in(sK1638,sK1637)
| in(sK1638,'subset$ucomplement'('the$ucarrier'(sK1636),sK1637)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c1503,plain,
( ~ in(sK1638,'subset$ucomplement'('the$ucarrier'(sK1636),sK1637))
| in(sK1638,sK1637) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'set$udifference'('the$ucarrier'(sK1636),sK1637) = 'subset$ucomplement'('the$ucarrier'(sK1636),sK1637),
inference(resolution,[status(thm)],[c421,c1499]) ).
cnf(d1,plain,
( in(sK1638,sK1637)
| ~ in(sK1638,'set$udifference'('the$ucarrier'(sK1636),sK1637)) ),
inference(demodulation,[status(thm)],[c1503,d0]) ).
cnf(d2,plain,
( ~ in(sK1638,sK1637)
| in(sK1638,'set$udifference'('the$ucarrier'(sK1636),sK1637)) ),
inference(demodulation,[status(thm)],[c1502,d0]) ).
cnf(d3,plain,
'subset$ucomplement'('the$ucarrier'(sK1636),'subset$ucomplement'('the$ucarrier'(sK1636),sK1637)) = sK1637,
inference(resolution,[status(thm)],[c697,c1499]) ).
cnf(d4,plain,
'subset$ucomplement'('the$ucarrier'(sK1636),'set$udifference'('the$ucarrier'(sK1636),sK1637)) = sK1637,
inference(demodulation,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( ~ element(sK1637,powerset('the$ucarrier'(sK1636)))
| element('set$udifference'('the$ucarrier'(sK1636),sK1637),powerset('the$ucarrier'(sK1636))) ),
inference(superposition,[status(thm)],[d0,c518]) ).
cnf(d6,plain,
element('set$udifference'('the$ucarrier'(sK1636),sK1637),powerset('the$ucarrier'(sK1636))),
inference(resolution,[status(thm)],[c1499,d5]) ).
cnf(d7,plain,
'set$udifference'('the$ucarrier'(sK1636),'set$udifference'('the$ucarrier'(sK1636),sK1637)) = 'subset$ucomplement'('the$ucarrier'(sK1636),'set$udifference'('the$ucarrier'(sK1636),sK1637)),
inference(resolution,[status(thm)],[d6,c421]) ).
cnf(d8,plain,
'set$udifference'('the$ucarrier'(sK1636),'set$udifference'('the$ucarrier'(sK1636),sK1637)) = sK1637,
inference(demodulation,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
( ~ in(X1,'set$udifference'('the$ucarrier'(sK1636),sK1637))
| ~ in(X1,X0)
| sK1637 != X0 ),
inference(superposition,[status(thm)],[d8,c388]) ).
cnf(d10,plain,
( ~ in(X0,'set$udifference'('the$ucarrier'(sK1636),sK1637))
| ~ in(X0,sK1637) ),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
( ~ in(sK1638,sK1637)
| ~ in(sK1638,sK1637) ),
inference(resolution,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
~ in(sK1638,'set$udifference'('the$ucarrier'(sK1636),sK1637)),
inference(resolution,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
( ~ in(X0,X1)
| in(X0,X2)
| in(X0,'set$udifference'(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c389]) ).
cnf(d14,plain,
( ~ in(sK1638,'the$ucarrier'(sK1636))
| in(sK1638,sK1637) ),
inference(resolution,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
~ in(sK1638,'the$ucarrier'(sK1636)),
inference(resolution,[status(thm)],[d11,d14]) ).
cnf(d16,plain,
( empty('the$ucarrier'(sK1636))
| in(sK1638,'the$ucarrier'(sK1636)) ),
inference(resolution,[status(thm)],[c277,c1500]) ).
cnf(d17,plain,
( empty('the$ucarrier'(sK1636))
| 'set$uunion2'(singleton(sK1638),'the$ucarrier'(sK1636)) = 'the$ucarrier'(sK1636) ),
inference(resolution,[status(thm)],[c705,d16]) ).
cnf(d18,plain,
( empty('the$ucarrier'(sK1636))
| 'set$uunion2'('the$ucarrier'(sK1636),singleton(sK1638)) = 'the$ucarrier'(sK1636) ),
inference(demodulation,[status(thm)],[d17,c73]) ).
cnf(d19,plain,
( ~ 'one$usorted$ustr'(sK1636)
| 'empty$ucarrier'(sK1636)
| 'set$uunion2'('the$ucarrier'(sK1636),singleton(sK1638)) = 'the$ucarrier'(sK1636) ),
inference(resolution,[status(thm)],[d18,c588]) ).
cnf(d20,plain,
( 'empty$ucarrier'(sK1636)
| 'set$uunion2'('the$ucarrier'(sK1636),singleton(sK1638)) = 'the$ucarrier'(sK1636) ),
inference(resolution,[status(thm)],[c1497,d19]) ).
cnf(d21,plain,
'set$uunion2'('the$ucarrier'(sK1636),singleton(sK1638)) = 'the$ucarrier'(sK1636),
inference(resolution,[status(thm)],[c1498,d20]) ).
cnf(d22,plain,
( empty(singleton(sK1638))
| ~ empty('the$ucarrier'(sK1636)) ),
inference(superposition,[status(thm)],[d21,c657]) ).
cnf(d23,plain,
~ empty('the$ucarrier'(sK1636)),
inference(resolution,[status(thm)],[c567,d22]) ).
cnf(d24,plain,
in(sK1638,'the$ucarrier'(sK1636)),
inference(resolution,[status(thm)],[d23,d16]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[d24,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU321+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 09:12:18 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 125.21/18.76 % SZS status Theorem for theBenchmark.p
% 125.21/18.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------