%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU326+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 : 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 08:41:41 AM UTC 2026
% Result : Theorem 11.97s 2.81s
% Output : CNFRefutation 11.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 16 unt; 0 def)
% Number of atoms : 82 ( 39 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 80 ( 39 ~; 25 |; 8 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 4 sgn 17 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k7_setfam_1,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element('complements$uof$usubsets'(X0,X1),powerset(powerset(X0))) ) ).
fof(fc1_subset_1,axiom,
! [X0] : ~ empty(powerset(X0)) ).
fof(involutiveness_k7_setfam_1,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> 'complements$uof$usubsets'(X0,'complements$uof$usubsets'(X0,X1)) = X1 ) ).
fof(rc2_subset_1,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ) ).
fof(t1_subset,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ) ).
fof(t2_subset,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ) ).
fof(t46_setfam_1,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( 'complements$uof$usubsets'(X0,X1) = 'empty$uset'
& X1 != 'empty$uset' ) ) ).
fof(t6_boole,axiom,
! [X0] :
( empty(X0)
=> X0 = 'empty$uset' ) ).
fof(t10_tops_2,conjecture,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( ~ ( X1 = 'empty$uset'
& 'complements$uof$usubsets'(X0,X1) != 'empty$uset' )
& ~ ( 'complements$uof$usubsets'(X0,X1) = 'empty$uset'
& X1 != 'empty$uset' ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( ~ ( X1 = 'empty$uset'
& 'complements$uof$usubsets'(X0,X1) != 'empty$uset' )
& ~ ( 'complements$uof$usubsets'(X0,X1) = 'empty$uset'
& X1 != 'empty$uset' ) ) ),
inference(negate_conjecture,[status(cth)],[t10_tops_2]) ).
cnf(c43,plain,
( element('complements$uof$usubsets'(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(clausification,[status(esa)],[dt_k7_setfam_1]) ).
cnf(c45,plain,
~ empty(powerset(X0)),
inference(clausification,[status(esa)],[fc1_subset_1]) ).
cnf(c52,plain,
( 'complements$uof$usubsets'(X1,'complements$uof$usubsets'(X1,X0)) = X0
| ~ element(X0,powerset(powerset(X1))) ),
inference(clausification,[status(esa)],[involutiveness_k7_setfam_1]) ).
cnf(c61,plain,
element(sK41(X0),powerset(X0)),
inference(clausification,[status(esa)],[rc2_subset_1]) ).
cnf(c62,plain,
empty(sK41(X0)),
inference(clausification,[status(esa)],[rc2_subset_1]) ).
cnf(c64,plain,
( element(X0,X1)
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t1_subset]) ).
cnf(c65,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[t2_subset]) ).
cnf(c68,plain,
( 'complements$uof$usubsets'(X1,X0) != 'empty$uset'
| X0 = 'empty$uset'
| ~ element(X0,powerset(powerset(X1))) ),
inference(clausification,[status(esa)],[t46_setfam_1]) ).
cnf(c71,plain,
( X0 = 'empty$uset'
| ~ empty(X0) ),
inference(clausification,[status(esa)],[t6_boole]) ).
cnf(c74,plain,
element(sK64,powerset(powerset(sK63))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c75,plain,
( 'complements$uof$usubsets'(sK63,sK64) != 'empty$uset'
| sK64 != 'empty$uset' ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c78,plain,
( sK64 = 'empty$uset'
| 'complements$uof$usubsets'(sK63,sK64) = 'empty$uset' ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( sK64 = 'empty$uset'
| ~ element(sK64,powerset(powerset(sK63)))
| sK64 = 'empty$uset'
| 'empty$uset' != 'empty$uset' ),
inference(superposition,[status(thm)],[c78,c68]) ).
cnf(d1,plain,
( sK64 = 'empty$uset'
| 'empty$uset' != 'empty$uset' ),
inference(resolution,[status(thm)],[c74,d0]) ).
cnf(d2,plain,
sK64 = 'empty$uset',
inference(equality_resolution,[status(thm)],[d1]) ).
cnf(d3,plain,
'complements$uof$usubsets'(sK63,'complements$uof$usubsets'(sK63,sK64)) = sK64,
inference(resolution,[status(thm)],[c52,c74]) ).
cnf(d4,plain,
( ~ element('complements$uof$usubsets'(sK63,sK64),powerset(powerset(sK63)))
| 'complements$uof$usubsets'(sK63,sK64) = 'empty$uset'
| sK64 != 'empty$uset' ),
inference(superposition,[status(thm)],[d3,c68]) ).
cnf(d5,plain,
( ~ element('complements$uof$usubsets'(sK63,sK64),powerset(powerset(sK63)))
| sK64 != 'empty$uset'
| 'complements$uof$usubsets'(sK63,'empty$uset') = 'empty$uset' ),
inference(demodulation,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( ~ element('complements$uof$usubsets'(sK63,sK64),powerset(powerset(sK63)))
| 'empty$uset' != 'empty$uset'
| 'complements$uof$usubsets'(sK63,'empty$uset') = 'empty$uset' ),
inference(demodulation,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( ~ element('complements$uof$usubsets'(sK63,'empty$uset'),powerset(powerset(sK63)))
| 'empty$uset' != 'empty$uset'
| 'complements$uof$usubsets'(sK63,'empty$uset') = 'empty$uset' ),
inference(demodulation,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
'complements$uof$usubsets'(sK63,sK64) != 'empty$uset',
inference(resolution,[status(thm)],[d2,c75]) ).
cnf(d9,plain,
'complements$uof$usubsets'(sK63,'empty$uset') != 'empty$uset',
inference(demodulation,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
( ~ element('complements$uof$usubsets'(sK63,'empty$uset'),powerset(powerset(sK63)))
| 'empty$uset' != 'empty$uset' ),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
~ element('complements$uof$usubsets'(sK63,'empty$uset'),powerset(powerset(sK63))),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
~ element('empty$uset',powerset(powerset(sK63))),
inference(resolution,[status(thm)],[d11,c43]) ).
cnf(d13,plain,
sK41(X0) = 'empty$uset',
inference(resolution,[status(thm)],[c71,c62]) ).
cnf(d14,plain,
( empty(powerset(X0))
| in(sK41(X0),powerset(X0)) ),
inference(resolution,[status(thm)],[c65,c61]) ).
cnf(d15,plain,
in(sK41(X0),powerset(X0)),
inference(resolution,[status(thm)],[c45,d14]) ).
cnf(d16,plain,
element(sK41(X0),powerset(X0)),
inference(resolution,[status(thm)],[d15,c64]) ).
cnf(d17,plain,
element('empty$uset',powerset(X0)),
inference(demodulation,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d17,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU326+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
% 0.12/0.39 % Computer : n019.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 09:12:49 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.97/2.81 % SZS status Theorem for theBenchmark.p
% 11.97/2.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------