%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU309+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 16.65s 6.09s
% Output : CNFRefutation 16.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 23 unt; 0 def)
% Number of atoms : 87 ( 33 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 28 ~; 23 |; 3 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [X0,X1] : 'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0) ).
fof(d3_pre_topc,axiom,
! [X0] :
( 'one$usorted$ustr'(X0)
=> 'cast$uas$ucarrier$usubset'(X0) = 'the$ucarrier'(X0) ) ).
fof(dt_k2_pre_topc,axiom,
! [X0] :
( 'one$usorted$ustr'(X0)
=> element('cast$uas$ucarrier$usubset'(X0),powerset('the$ucarrier'(X0))) ) ).
fof(dt_k6_subset_1,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> element('subset$udifference'(X0,X1,X2),powerset(X0)) ) ).
fof(redefinition_k5_subset_1,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> 'subset$uintersection2'(X0,X1,X2) = 'set$uintersection2'(X1,X2) ) ).
fof(redefinition_k6_subset_1,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> 'subset$udifference'(X0,X1,X2) = 'set$udifference'(X1,X2) ) ).
fof(t15_pre_topc,axiom,
! [X0] :
( 'one$usorted$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> 'subset$uintersection2'('the$ucarrier'(X0),X1,'cast$uas$ucarrier$usubset'(X0)) = X1 ) ) ).
fof(t3_subset,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ) ).
fof(t48_xboole_1,axiom,
! [X0,X1] : 'set$udifference'(X0,'set$udifference'(X0,X1)) = 'set$uintersection2'(X0,X1) ).
fof(t22_pre_topc,conjecture,
! [X0] :
( 'one$usorted$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> 'subset$udifference'('the$ucarrier'(X0),'cast$uas$ucarrier$usubset'(X0),'subset$udifference'('the$ucarrier'(X0),'cast$uas$ucarrier$usubset'(X0),X1)) = X1 ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'one$usorted$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> 'subset$udifference'('the$ucarrier'(X0),'cast$uas$ucarrier$usubset'(X0),'subset$udifference'('the$ucarrier'(X0),'cast$uas$ucarrier$usubset'(X0),X1)) = X1 ) ),
inference(negate_conjecture,[status(cth)],[t22_pre_topc]) ).
cnf(c43,plain,
'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k3_xboole_0]) ).
cnf(c45,plain,
( 'cast$uas$ucarrier$usubset'(X0) = 'the$ucarrier'(X0)
| ~ 'one$usorted$ustr'(X0) ),
inference(clausification,[status(esa)],[d3_pre_topc]) ).
cnf(c46,plain,
( element('cast$uas$ucarrier$usubset'(X0),powerset('the$ucarrier'(X0)))
| ~ 'one$usorted$ustr'(X0) ),
inference(clausification,[status(esa)],[dt_k2_pre_topc]) ).
cnf(c48,plain,
( element('subset$udifference'(X1,X0,X2),powerset(X1))
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[dt_k6_subset_1]) ).
cnf(c118,plain,
( 'subset$uintersection2'(X1,X0,X2) = 'set$uintersection2'(X0,X2)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[redefinition_k5_subset_1]) ).
cnf(c119,plain,
( 'subset$udifference'(X1,X0,X2) = 'set$udifference'(X0,X2)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[redefinition_k6_subset_1]) ).
cnf(c121,plain,
( 'subset$uintersection2'('the$ucarrier'(X0),X1,'cast$uas$ucarrier$usubset'(X0)) = X1
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'one$usorted$ustr'(X0) ),
inference(clausification,[status(esa)],[t15_pre_topc]) ).
cnf(c126,plain,
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c127,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c128,plain,
'set$udifference'(X0,'set$udifference'(X0,X1)) = 'set$uintersection2'(X0,X1),
inference(clausification,[status(esa)],[t48_xboole_1]) ).
cnf(c135,plain,
'one$usorted$ustr'(sK122),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c136,plain,
element(sK123,powerset('the$ucarrier'(sK122))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c137,plain,
'subset$udifference'('the$ucarrier'(sK122),'cast$uas$ucarrier$usubset'(sK122),'subset$udifference'('the$ucarrier'(sK122),'cast$uas$ucarrier$usubset'(sK122),sK123)) != sK123,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'cast$uas$ucarrier$usubset'(sK122) = 'the$ucarrier'(sK122),
inference(resolution,[status(thm)],[c45,c135]) ).
cnf(d1,plain,
( ~ 'one$usorted$ustr'(sK122)
| 'subset$uintersection2'('the$ucarrier'(sK122),sK123,'cast$uas$ucarrier$usubset'(sK122)) = sK123 ),
inference(resolution,[status(thm)],[c121,c136]) ).
cnf(d2,plain,
( ~ 'one$usorted$ustr'(sK122)
| 'subset$uintersection2'('the$ucarrier'(sK122),sK123,'the$ucarrier'(sK122)) = sK123 ),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
'subset$uintersection2'('the$ucarrier'(sK122),sK123,'the$ucarrier'(sK122)) = sK123,
inference(resolution,[status(thm)],[c135,d2]) ).
cnf(d4,plain,
( ~ 'one$usorted$ustr'(sK122)
| element('the$ucarrier'(sK122),powerset('the$ucarrier'(sK122))) ),
inference(superposition,[status(thm)],[d0,c46]) ).
cnf(d5,plain,
element('the$ucarrier'(sK122),powerset('the$ucarrier'(sK122))),
inference(resolution,[status(thm)],[c135,d4]) ).
cnf(d6,plain,
( ~ element(X0,powerset('the$ucarrier'(sK122)))
| 'subset$uintersection2'('the$ucarrier'(sK122),sK123,X0) = 'set$uintersection2'(sK123,X0) ),
inference(resolution,[status(thm)],[c118,c136]) ).
cnf(d7,plain,
'subset$uintersection2'('the$ucarrier'(sK122),sK123,'the$ucarrier'(sK122)) = 'set$uintersection2'(sK123,'the$ucarrier'(sK122)),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
sK123 = 'set$uintersection2'(sK123,'the$ucarrier'(sK122)),
inference(demodulation,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( ~ element(X0,powerset('the$ucarrier'(sK122)))
| 'subset$udifference'('the$ucarrier'(sK122),X0,sK123) = 'set$udifference'(X0,sK123) ),
inference(resolution,[status(thm)],[c119,c136]) ).
cnf(d10,plain,
'subset$udifference'('the$ucarrier'(sK122),'the$ucarrier'(sK122),sK123) = 'set$udifference'('the$ucarrier'(sK122),sK123),
inference(resolution,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
( ~ element(sK123,powerset('the$ucarrier'(sK122)))
| ~ element('the$ucarrier'(sK122),powerset('the$ucarrier'(sK122)))
| element('set$udifference'('the$ucarrier'(sK122),sK123),powerset('the$ucarrier'(sK122))) ),
inference(superposition,[status(thm)],[d10,c48]) ).
cnf(d12,plain,
( element('set$udifference'('the$ucarrier'(sK122),sK123),powerset('the$ucarrier'(sK122)))
| ~ element('the$ucarrier'(sK122),powerset('the$ucarrier'(sK122))) ),
inference(resolution,[status(thm)],[c136,d11]) ).
cnf(d13,plain,
element('set$udifference'('the$ucarrier'(sK122),sK123),powerset('the$ucarrier'(sK122))),
inference(resolution,[status(thm)],[d5,d12]) ).
cnf(d14,plain,
subset('set$udifference'('the$ucarrier'(sK122),sK123),'the$ucarrier'(sK122)),
inference(resolution,[status(thm)],[d13,c126]) ).
cnf(d15,plain,
( ~ element(X2,powerset(X1))
| 'subset$udifference'(X1,X2,X0) = 'set$udifference'(X2,X0)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[c127,c119]) ).
cnf(d16,plain,
( ~ subset(X0,'the$ucarrier'(sK122))
| 'subset$udifference'('the$ucarrier'(sK122),'the$ucarrier'(sK122),X0) = 'set$udifference'('the$ucarrier'(sK122),X0) ),
inference(resolution,[status(thm)],[d15,d5]) ).
cnf(d17,plain,
'subset$udifference'('the$ucarrier'(sK122),'the$ucarrier'(sK122),'set$udifference'('the$ucarrier'(sK122),sK123)) = 'set$udifference'('the$ucarrier'(sK122),'set$udifference'('the$ucarrier'(sK122),sK123)),
inference(resolution,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
'subset$udifference'('the$ucarrier'(sK122),'the$ucarrier'(sK122),'set$udifference'('the$ucarrier'(sK122),sK123)) = 'set$uintersection2'('the$ucarrier'(sK122),sK123),
inference(demodulation,[status(thm)],[d17,c128]) ).
cnf(d19,plain,
'subset$udifference'('the$ucarrier'(sK122),'the$ucarrier'(sK122),'set$udifference'('the$ucarrier'(sK122),sK123)) = 'set$uintersection2'(sK123,'the$ucarrier'(sK122)),
inference(demodulation,[status(thm)],[d18,c43]) ).
cnf(d20,plain,
'subset$udifference'('the$ucarrier'(sK122),'the$ucarrier'(sK122),'set$udifference'('the$ucarrier'(sK122),sK123)) = sK123,
inference(demodulation,[status(thm)],[d19,d8]) ).
cnf(d21,plain,
'subset$udifference'('the$ucarrier'(sK122),'the$ucarrier'(sK122),'subset$udifference'('the$ucarrier'(sK122),'cast$uas$ucarrier$usubset'(sK122),sK123)) != sK123,
inference(demodulation,[status(thm)],[c137,d0]) ).
cnf(d22,plain,
'subset$udifference'('the$ucarrier'(sK122),'the$ucarrier'(sK122),'subset$udifference'('the$ucarrier'(sK122),'the$ucarrier'(sK122),sK123)) != sK123,
inference(demodulation,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
'subset$udifference'('the$ucarrier'(sK122),'the$ucarrier'(sK122),'set$udifference'('the$ucarrier'(sK122),sK123)) != sK123,
inference(demodulation,[status(thm)],[d22,d10]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[d23,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU309+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 09:14:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.65/6.09 % SZS status Theorem for theBenchmark.p
% 16.65/6.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------