%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU308+1 : 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 : n008.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 08:41:37 AM UTC 2026
% Result : Theorem 13.60s 2.21s
% Output : CNFRefutation 13.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 39 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 12 ~; 7 |; 1 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 19 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_k6_subset_1,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> 'subset$udifference'(X0,X1,X2) = 'set$udifference'(X1,X2) ) ).
fof(dt_k2_pre_topc,axiom,
! [X0] :
( 'one$usorted$ustr'(X0)
=> element('cast$uas$ucarrier$usubset'(X0),powerset('the$ucarrier'(X0))) ) ).
fof(d3_pre_topc,axiom,
! [X0] :
( 'one$usorted$ustr'(X0)
=> 'cast$uas$ucarrier$usubset'(X0) = 'the$ucarrier'(X0) ) ).
fof(d5_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> 'subset$ucomplement'(X0,X1) = 'set$udifference'(X0,X1) ) ).
fof(t17_pre_topc,conjecture,
! [X0] :
( 'one$usorted$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> 'subset$ucomplement'('the$ucarrier'(X0),X1) = 'subset$udifference'('the$ucarrier'(X0),'cast$uas$ucarrier$usubset'(X0),X1) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'one$usorted$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> 'subset$ucomplement'('the$ucarrier'(X0),X1) = 'subset$udifference'('the$ucarrier'(X0),'cast$uas$ucarrier$usubset'(X0),X1) ) ),
inference(negate_conjecture,[status(cth)],[t17_pre_topc]) ).
cnf(c88,plain,
( 'subset$udifference'(X1,X0,X2) = 'set$udifference'(X0,X2)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[redefinition_k6_subset_1]) ).
cnf(c89,plain,
( element('cast$uas$ucarrier$usubset'(X0),powerset('the$ucarrier'(X0)))
| ~ 'one$usorted$ustr'(X0) ),
inference(clausification,[status(esa)],[dt_k2_pre_topc]) ).
cnf(c95,plain,
( 'cast$uas$ucarrier$usubset'(X0) = 'the$ucarrier'(X0)
| ~ 'one$usorted$ustr'(X0) ),
inference(clausification,[status(esa)],[d3_pre_topc]) ).
cnf(c96,plain,
( 'subset$ucomplement'(X1,X0) = 'set$udifference'(X1,X0)
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[d5_subset_1]) ).
cnf(c97,plain,
'one$usorted$ustr'(sK85),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c98,plain,
element(sK86,powerset('the$ucarrier'(sK85))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c99,plain,
'subset$ucomplement'('the$ucarrier'(sK85),sK86) != 'subset$udifference'('the$ucarrier'(sK85),'cast$uas$ucarrier$usubset'(sK85),sK86),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'cast$uas$ucarrier$usubset'(sK85) = 'the$ucarrier'(sK85),
inference(resolution,[status(thm)],[c95,c97]) ).
cnf(d1,plain,
( ~ 'one$usorted$ustr'(sK85)
| element('the$ucarrier'(sK85),powerset('the$ucarrier'(sK85))) ),
inference(superposition,[status(thm)],[d0,c89]) ).
cnf(d2,plain,
element('the$ucarrier'(sK85),powerset('the$ucarrier'(sK85))),
inference(resolution,[status(thm)],[c97,d1]) ).
cnf(d3,plain,
( ~ element(X0,powerset('the$ucarrier'(sK85)))
| 'subset$udifference'('the$ucarrier'(sK85),X0,sK86) = 'set$udifference'(X0,sK86) ),
inference(resolution,[status(thm)],[c88,c98]) ).
cnf(d4,plain,
'subset$udifference'('the$ucarrier'(sK85),'the$ucarrier'(sK85),sK86) = 'set$udifference'('the$ucarrier'(sK85),sK86),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
'subset$ucomplement'('the$ucarrier'(sK85),sK86) = 'set$udifference'('the$ucarrier'(sK85),sK86),
inference(resolution,[status(thm)],[c96,c98]) ).
cnf(d6,plain,
'subset$ucomplement'('the$ucarrier'(sK85),sK86) != 'subset$udifference'('the$ucarrier'(sK85),'the$ucarrier'(sK85),sK86),
inference(demodulation,[status(thm)],[c99,d0]) ).
cnf(d7,plain,
'set$udifference'('the$ucarrier'(sK85),sK86) != 'subset$udifference'('the$ucarrier'(sK85),'the$ucarrier'(sK85),sK86),
inference(demodulation,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
'set$udifference'('the$ucarrier'(sK85),sK86) != 'set$udifference'('the$ucarrier'(sK85),sK86),
inference(demodulation,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
$false,
inference(equality_resolution,[status(thm)],[d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU308+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 09:10:09 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.60/2.21 % SZS status Theorem for theBenchmark.p
% 13.60/2.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------