%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU328+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 : n018.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 08:41:41 AM UTC 2026
% Result : Theorem 22.00s 4.18s
% Output : CNFRefutation 22.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 20 unt; 0 def)
% Number of atoms : 71 ( 38 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 21 ~; 16 |; 1 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 45 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_subset_1,axiom,
! [X0] : 'cast$uto$usubset'(X0) = X0 ).
fof(d5_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> 'subset$ucomplement'(X0,X1) = 'set$udifference'(X0,X1) ) ).
fof(dt_k2_subset_1,axiom,
! [X0] : element('cast$uto$usubset'(X0),powerset(X0)) ).
fof(dt_k6_setfam_1,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element('meet$uof$usubsets'(X0,X1),powerset(X0)) ) ).
fof(dt_k7_setfam_1,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element('complements$uof$usubsets'(X0,X1),powerset(powerset(X0))) ) ).
fof(redefinition_k5_setfam_1,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> 'union$uof$usubsets'(X0,X1) = union(X1) ) ).
fof(redefinition_k6_setfam_1,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> 'meet$uof$usubsets'(X0,X1) = 'set$umeet'(X1) ) ).
fof(redefinition_k6_subset_1,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> 'subset$udifference'(X0,X1,X2) = 'set$udifference'(X1,X2) ) ).
fof(t48_setfam_1,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != 'empty$uset'
=> 'union$uof$usubsets'(X0,'complements$uof$usubsets'(X0,X1)) = 'subset$udifference'(X0,'cast$uto$usubset'(X0),'meet$uof$usubsets'(X0,X1)) ) ) ).
fof(t12_tops_2,conjecture,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != 'empty$uset'
=> 'union$uof$usubsets'(X0,'complements$uof$usubsets'(X0,X1)) = 'subset$ucomplement'(X0,'meet$uof$usubsets'(X0,X1)) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != 'empty$uset'
=> 'union$uof$usubsets'(X0,'complements$uof$usubsets'(X0,X1)) = 'subset$ucomplement'(X0,'meet$uof$usubsets'(X0,X1)) ) ),
inference(negate_conjecture,[status(cth)],[t12_tops_2]) ).
cnf(c43,plain,
'cast$uto$usubset'(X0) = X0,
inference(clausification,[status(esa)],[d4_subset_1]) ).
cnf(c44,plain,
( 'subset$ucomplement'(X1,X0) = 'set$udifference'(X1,X0)
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[d5_subset_1]) ).
cnf(c45,plain,
element('cast$uto$usubset'(X0),powerset(X0)),
inference(clausification,[status(esa)],[dt_k2_subset_1]) ).
cnf(c48,plain,
( element('meet$uof$usubsets'(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(clausification,[status(esa)],[dt_k6_setfam_1]) ).
cnf(c50,plain,
( element('complements$uof$usubsets'(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(clausification,[status(esa)],[dt_k7_setfam_1]) ).
cnf(c87,plain,
( 'union$uof$usubsets'(X1,X0) = union(X0)
| ~ element(X0,powerset(powerset(X1))) ),
inference(clausification,[status(esa)],[redefinition_k5_setfam_1]) ).
cnf(c88,plain,
( 'meet$uof$usubsets'(X1,X0) = 'set$umeet'(X0)
| ~ element(X0,powerset(powerset(X1))) ),
inference(clausification,[status(esa)],[redefinition_k6_setfam_1]) ).
cnf(c89,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(c96,plain,
( 'union$uof$usubsets'(X1,'complements$uof$usubsets'(X1,X0)) = 'subset$udifference'(X1,'cast$uto$usubset'(X1),'meet$uof$usubsets'(X1,X0))
| X0 = 'empty$uset'
| ~ element(X0,powerset(powerset(X1))) ),
inference(clausification,[status(esa)],[t48_setfam_1]) ).
cnf(c103,plain,
element(sK99,powerset(powerset(sK98))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c104,plain,
sK99 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c105,plain,
'union$uof$usubsets'(sK98,'complements$uof$usubsets'(sK98,sK99)) != 'subset$ucomplement'(sK98,'meet$uof$usubsets'(sK98,sK99)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'meet$uof$usubsets'(sK98,sK99) = 'set$umeet'(sK99),
inference(resolution,[status(thm)],[c88,c103]) ).
cnf(d1,plain,
( ~ element(sK99,powerset(powerset(sK98)))
| element('set$umeet'(sK99),powerset(sK98)) ),
inference(superposition,[status(thm)],[d0,c48]) ).
cnf(d2,plain,
element('set$umeet'(sK99),powerset(sK98)),
inference(resolution,[status(thm)],[c103,d1]) ).
cnf(d3,plain,
element(X0,powerset(X0)),
inference(demodulation,[status(thm)],[c45,c43]) ).
cnf(d4,plain,
( ~ element(X1,powerset(X0))
| 'subset$udifference'(X0,X0,X1) = 'set$udifference'(X0,X1) ),
inference(resolution,[status(thm)],[c89,d3]) ).
cnf(d5,plain,
'subset$udifference'(sK98,sK98,'set$umeet'(sK99)) = 'set$udifference'(sK98,'set$umeet'(sK99)),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( ~ element(X1,powerset(powerset(X0)))
| 'union$uof$usubsets'(X0,'complements$uof$usubsets'(X0,X1)) = union('complements$uof$usubsets'(X0,X1)) ),
inference(resolution,[status(thm)],[c87,c50]) ).
cnf(d7,plain,
'union$uof$usubsets'(sK98,'complements$uof$usubsets'(sK98,sK99)) = union('complements$uof$usubsets'(sK98,sK99)),
inference(resolution,[status(thm)],[d6,c103]) ).
cnf(d8,plain,
( ~ element(X1,powerset(powerset(X0)))
| 'union$uof$usubsets'(X0,'complements$uof$usubsets'(X0,X1)) = 'subset$udifference'(X0,X0,'meet$uof$usubsets'(X0,X1))
| X1 = 'empty$uset' ),
inference(demodulation,[status(thm)],[c96,c43]) ).
cnf(d9,plain,
( 'union$uof$usubsets'(sK98,'complements$uof$usubsets'(sK98,sK99)) = 'subset$udifference'(sK98,sK98,'meet$uof$usubsets'(sK98,sK99))
| sK99 = 'empty$uset' ),
inference(resolution,[status(thm)],[d8,c103]) ).
cnf(d10,plain,
( sK99 = 'empty$uset'
| 'union$uof$usubsets'(sK98,'complements$uof$usubsets'(sK98,sK99)) = 'subset$udifference'(sK98,sK98,'set$umeet'(sK99)) ),
inference(demodulation,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
'union$uof$usubsets'(sK98,'complements$uof$usubsets'(sK98,sK99)) = 'subset$udifference'(sK98,sK98,'set$umeet'(sK99)),
inference(resolution,[status(thm)],[c104,d10]) ).
cnf(d12,plain,
union('complements$uof$usubsets'(sK98,sK99)) = 'subset$udifference'(sK98,sK98,'set$umeet'(sK99)),
inference(demodulation,[status(thm)],[d11,d7]) ).
cnf(d13,plain,
union('complements$uof$usubsets'(sK98,sK99)) = 'set$udifference'(sK98,'set$umeet'(sK99)),
inference(demodulation,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
'subset$ucomplement'(sK98,'set$umeet'(sK99)) = 'set$udifference'(sK98,'set$umeet'(sK99)),
inference(resolution,[status(thm)],[d2,c44]) ).
cnf(d15,plain,
'union$uof$usubsets'(sK98,'complements$uof$usubsets'(sK98,sK99)) != 'subset$ucomplement'(sK98,'set$umeet'(sK99)),
inference(demodulation,[status(thm)],[c105,d0]) ).
cnf(d16,plain,
'union$uof$usubsets'(sK98,'complements$uof$usubsets'(sK98,sK99)) != 'set$udifference'(sK98,'set$umeet'(sK99)),
inference(demodulation,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
union('complements$uof$usubsets'(sK98,sK99)) != 'set$udifference'(sK98,'set$umeet'(sK99)),
inference(demodulation,[status(thm)],[d16,d7]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d17,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU328+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
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 09:15:22 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.00/4.18 % SZS status Theorem for theBenchmark.p
% 22.00/4.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------