%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET587+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 08:32:49 AM UTC 2026
% Result : Theorem 12.96s 2.04s
% Output : CNFRefutation 12.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 6 unt; 0 def)
% Number of atoms : 76 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 66 ( 24 ~; 33 |; 1 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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; 3 con; 0-2 aty)
% Number of variables : 53 ( 4 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(member_equal,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
<=> member(X2,X1) )
=> X0 = X1 ) ).
fof(difference_defn,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ) ).
fof(empty_set_defn,axiom,
! [X0] : ~ member(X0,'empty$uset') ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(empty_defn,axiom,
! [X0] :
( empty(X0)
<=> ! [X1] : ~ member(X1,X0) ) ).
fof(prove_difference_empty_set,conjecture,
! [X0,X1] :
( difference(X0,X1) = 'empty$uset'
<=> subset(X0,X1) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( difference(X0,X1) = 'empty$uset'
<=> subset(X0,X1) ),
inference(negate_conjecture,[status(cth)],[prove_difference_empty_set]) ).
cnf(c1,plain,
( X0 = X1
| member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0) ),
inference(clausification,[status(esa)],[member_equal]) ).
cnf(c4,plain,
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c5,plain,
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c6,plain,
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c7,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set_defn]) ).
cnf(c8,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c9,plain,
( member(sK10(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c10,plain,
( ~ member(sK10(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c21,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c22,plain,
( member(sK20(X0),X0)
| empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c24,plain,
( subset(sK21,sK22)
| difference(sK21,sK22) = 'empty$uset' ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c25,plain,
( difference(sK21,sK22) != 'empty$uset'
| ~ subset(sK21,sK22) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ empty(difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(resolution,[status(thm)],[c6,c21]) ).
cnf(d1,plain,
( member(sK2(X0,'empty$uset'),X0)
| X0 = 'empty$uset' ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d2,plain,
( ~ member(sK2(difference(X0,X1),'empty$uset'),X1)
| difference(X0,X1) = 'empty$uset' ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
( difference(sK21,sK22) = 'empty$uset'
| ~ member(X0,sK21)
| member(X0,sK22) ),
inference(resolution,[status(thm)],[c8,c24]) ).
cnf(d4,plain,
( member(sK2(difference(X0,X1),X2),X2)
| difference(X0,X1) = X2
| member(sK2(difference(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(d5,plain,
( member(sK2(difference(sK21,X0),X1),sK22)
| difference(sK21,sK22) = 'empty$uset'
| member(sK2(difference(sK21,X0),X1),X1)
| difference(sK21,X0) = X1 ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( difference(sK21,sK22) = 'empty$uset'
| member(sK2(difference(sK21,sK22),'empty$uset'),'empty$uset')
| difference(sK21,sK22) = 'empty$uset'
| difference(sK21,sK22) = 'empty$uset' ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
difference(sK21,sK22) = 'empty$uset',
inference(resolution,[status(thm)],[c7,d6]) ).
cnf(d8,plain,
( member(X0,sK22)
| ~ member(X0,sK21)
| ~ empty('empty$uset') ),
inference(superposition,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
empty('empty$uset'),
inference(resolution,[status(thm)],[c22,c7]) ).
cnf(d10,plain,
( member(X0,sK22)
| ~ member(X0,sK21) ),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( subset(sK21,X0)
| member(sK10(sK21,X0),sK22) ),
inference(resolution,[status(thm)],[d10,c9]) ).
cnf(d12,plain,
( subset(sK21,sK22)
| subset(sK21,sK22) ),
inference(resolution,[status(thm)],[d11,c10]) ).
cnf(d13,plain,
~ subset(sK21,sK22),
inference(resolution,[status(thm)],[d7,c25]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET587+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:00:37 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.96/2.04 % SZS status Theorem for theBenchmark.p
% 12.96/2.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------