%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU307+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 : 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 12.86s 3.84s
% Output : CNFRefutation 12.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 23 unt; 0 def)
% Number of atoms : 71 ( 33 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 18 ~; 14 |; 3 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 44 ( 2 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [X0,X1] : 'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0) ).
fof(idempotence_k3_xboole_0,axiom,
! [X0,X1] : 'set$uintersection2'(X0,X0) = X0 ).
fof(commutativity_k5_subset_1,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> 'subset$uintersection2'(X0,X1,X2) = 'subset$uintersection2'(X0,X2,X1) ) ).
fof(idempotence_k5_subset_1,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> 'subset$uintersection2'(X0,X1,X1) = X1 ) ).
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(dt_k2_pre_topc,axiom,
! [X0] :
( 'one$usorted$ustr'(X0)
=> element('cast$uas$ucarrier$usubset'(X0),powerset('the$ucarrier'(X0))) ) ).
fof(t3_subset,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ) ).
fof(d3_pre_topc,axiom,
! [X0] :
( 'one$usorted$ustr'(X0)
=> 'cast$uas$ucarrier$usubset'(X0) = 'the$ucarrier'(X0) ) ).
fof(t28_xboole_1,axiom,
! [X0,X1] :
( subset(X0,X1)
=> 'set$uintersection2'(X0,X1) = X0 ) ).
fof(t15_pre_topc,conjecture,
! [X0] :
( 'one$usorted$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> 'subset$uintersection2'('the$ucarrier'(X0),X1,'cast$uas$ucarrier$usubset'(X0)) = X1 ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'one$usorted$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> 'subset$uintersection2'('the$ucarrier'(X0),X1,'cast$uas$ucarrier$usubset'(X0)) = X1 ) ),
inference(negate_conjecture,[status(cth)],[t15_pre_topc]) ).
cnf(c99,plain,
'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k3_xboole_0]) ).
cnf(c100,plain,
'set$uintersection2'(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_k3_xboole_0]) ).
cnf(c101,plain,
( 'subset$uintersection2'(X1,X0,X2) = 'subset$uintersection2'(X1,X2,X0)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[commutativity_k5_subset_1]) ).
cnf(c102,plain,
( 'subset$uintersection2'(X1,X0,X0) = X0
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[idempotence_k5_subset_1]) ).
cnf(c106,plain,
( 'subset$uintersection2'(X1,X0,X2) = 'set$uintersection2'(X0,X2)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[redefinition_k5_subset_1]) ).
cnf(c107,plain,
( element('cast$uas$ucarrier$usubset'(X0),powerset('the$ucarrier'(X0)))
| ~ 'one$usorted$ustr'(X0) ),
inference(clausification,[status(esa)],[dt_k2_pre_topc]) ).
cnf(c110,plain,
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c112,plain,
( 'cast$uas$ucarrier$usubset'(X0) = 'the$ucarrier'(X0)
| ~ 'one$usorted$ustr'(X0) ),
inference(clausification,[status(esa)],[d3_pre_topc]) ).
cnf(c113,plain,
( 'set$uintersection2'(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t28_xboole_1]) ).
cnf(c114,plain,
'one$usorted$ustr'(sK101),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c115,plain,
element(sK102,powerset('the$ucarrier'(sK101))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c116,plain,
'subset$uintersection2'('the$ucarrier'(sK101),sK102,'cast$uas$ucarrier$usubset'(sK101)) != sK102,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
subset(sK102,'the$ucarrier'(sK101)),
inference(resolution,[status(thm)],[c110,c115]) ).
cnf(d1,plain,
'set$uintersection2'(sK102,'the$ucarrier'(sK101)) = sK102,
inference(resolution,[status(thm)],[c113,d0]) ).
cnf(d2,plain,
'cast$uas$ucarrier$usubset'(sK101) = 'the$ucarrier'(sK101),
inference(resolution,[status(thm)],[c112,c114]) ).
cnf(d3,plain,
( ~ 'one$usorted$ustr'(sK101)
| element('the$ucarrier'(sK101),powerset('the$ucarrier'(sK101))) ),
inference(superposition,[status(thm)],[d2,c107]) ).
cnf(d4,plain,
element('the$ucarrier'(sK101),powerset('the$ucarrier'(sK101))),
inference(resolution,[status(thm)],[c114,d3]) ).
cnf(d5,plain,
( ~ element(X0,powerset('the$ucarrier'(sK101)))
| 'subset$uintersection2'('the$ucarrier'(sK101),X0,sK102) = 'set$uintersection2'(X0,sK102) ),
inference(resolution,[status(thm)],[c106,c115]) ).
cnf(d6,plain,
'subset$uintersection2'('the$ucarrier'(sK101),'the$ucarrier'(sK101),sK102) = 'set$uintersection2'('the$ucarrier'(sK101),sK102),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
'subset$uintersection2'('the$ucarrier'(sK101),'the$ucarrier'(sK101),sK102) = 'set$uintersection2'(sK102,'the$ucarrier'(sK101)),
inference(demodulation,[status(thm)],[d6,c99]) ).
cnf(d8,plain,
'subset$uintersection2'('the$ucarrier'(sK101),'the$ucarrier'(sK101),sK102) = sK102,
inference(demodulation,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
( ~ element(X0,powerset('the$ucarrier'(sK101)))
| 'subset$uintersection2'('the$ucarrier'(sK101),X0,sK102) = 'subset$uintersection2'('the$ucarrier'(sK101),sK102,X0) ),
inference(resolution,[status(thm)],[c101,c115]) ).
cnf(d10,plain,
'subset$uintersection2'('the$ucarrier'(sK101),'the$ucarrier'(sK101),sK102) = 'subset$uintersection2'('the$ucarrier'(sK101),sK102,'the$ucarrier'(sK101)),
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
sK102 = 'subset$uintersection2'('the$ucarrier'(sK101),sK102,'the$ucarrier'(sK101)),
inference(demodulation,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
'subset$uintersection2'('the$ucarrier'(sK101),sK102,'the$ucarrier'(sK101)) != sK102,
inference(demodulation,[status(thm)],[c116,d2]) ).
cnf(d13,plain,
sK102 != sK102,
inference(demodulation,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
( ~ element(X0,powerset('the$ucarrier'(sK101)))
| 'subset$uintersection2'('the$ucarrier'(sK101),X0,X0) = X0 ),
inference(resolution,[status(thm)],[c102,c115]) ).
cnf(d15,plain,
'subset$uintersection2'('the$ucarrier'(sK101),sK102,sK102) = sK102,
inference(resolution,[status(thm)],[d14,c115]) ).
cnf(d16,plain,
'subset$uintersection2'('the$ucarrier'(sK101),sK102,sK102) = 'set$uintersection2'(sK102,sK102),
inference(resolution,[status(thm)],[d5,c115]) ).
cnf(d17,plain,
sK102 = 'set$uintersection2'(sK102,sK102),
inference(demodulation,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
sK102 = sK102,
inference(demodulation,[status(thm)],[d17,c100]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[d18,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU307+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.36 % Computer : n016.cluster.edu
% 0.06/0.36 % Model : x86_64 x86_64
% 0.06/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.36 % Memory : 8046.5625MB
% 0.06/0.36 % OS : Linux 6.8.0-71-generic
% 0.06/0.36 % CPULimit : 300
% 0.06/0.36 % WCLimit : 300
% 0.06/0.36 % DateTime : Sat Sep 26 09:14:14 UTC 2026
% 0.06/0.37 % CPUTime :
% 0.06/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.86/3.84 % SZS status Theorem for theBenchmark.p
% 12.86/3.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------