%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET611+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 : n008.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 08:32:53 AM UTC 2026
% Result : Theorem 5.57s 9.37s
% Output : CNFRefutation 5.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 8 unt; 0 def)
% Number of atoms : 111 ( 30 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 99 ( 36 ~; 50 |; 3 &)
% ( 8 <=>; 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 6 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(member_equal,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
<=> member(X2,X1) )
=> X0 = X1 ) ).
fof(intersection_defn,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ) ).
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$uset') ).
fof(equal_defn,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(commutativity_of_intersection,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0) ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(empty_defn,axiom,
! [X0] :
( empty(X0)
<=> ! [X1] : ~ member(X1,X0) ) ).
fof(prove_th84,conjecture,
! [X0,X1] :
( intersection(X0,X1) = 'empty$uset'
<=> difference(X0,X1) = X0 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( intersection(X0,X1) = 'empty$uset'
<=> difference(X0,X1) = X0 ),
inference(negate_conjecture,[status(cth)],[prove_th84]) ).
cnf(c1,plain,
( X0 = X1
| member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0) ),
inference(clausification,[status(esa)],[member_equal]) ).
cnf(c4,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c5,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c6,plain,
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c7,plain,
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c8,plain,
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c9,plain,
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c10,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set_defn]) ).
cnf(c13,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_defn]) ).
cnf(c14,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_intersection]) ).
cnf(c22,plain,
( member(sK21(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c23,plain,
( ~ member(sK21(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c25,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c26,plain,
( member(sK25(X0),X0)
| empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c28,plain,
( difference(sK26,sK27) = sK26
| intersection(sK26,sK27) = 'empty$uset' ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c29,plain,
( intersection(sK26,sK27) != 'empty$uset'
| difference(sK26,sK27) != sK26 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ empty(intersection(X2,X1))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[c6,c25]) ).
cnf(d1,plain,
( member(sK2(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(sK2(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(d2,plain,
( intersection(sK26,sK27) = 'empty$uset'
| ~ member(X0,sK27)
| ~ member(X0,sK26) ),
inference(superposition,[status(thm)],[c28,c8]) ).
cnf(d3,plain,
( member(sK2(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(sK2(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(d4,plain,
( ~ member(sK2(intersection(sK27,X0),X1),sK26)
| intersection(sK26,sK27) = 'empty$uset'
| member(sK2(intersection(sK27,X0),X1),X1)
| intersection(sK27,X0) = X1 ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( member(sK2(intersection(sK27,sK26),X0),X0)
| intersection(sK27,sK26) = X0
| member(sK2(intersection(sK27,sK26),X0),X0)
| intersection(sK27,sK26) = X0
| intersection(sK26,sK27) = 'empty$uset' ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( member(sK2(intersection(sK27,sK26),X0),X0)
| intersection(sK26,sK27) = X0
| intersection(sK26,sK27) = 'empty$uset' ),
inference(demodulation,[status(thm)],[d5,c14]) ).
cnf(d7,plain,
( member(sK2(intersection(sK26,sK27),X0),X0)
| intersection(sK26,sK27) = X0
| intersection(sK26,sK27) = 'empty$uset' ),
inference(demodulation,[status(thm)],[d6,c14]) ).
cnf(d8,plain,
( intersection(sK26,sK27) = 'empty$uset'
| intersection(sK26,sK27) = 'empty$uset' ),
inference(resolution,[status(thm)],[d7,c10]) ).
cnf(d9,plain,
( ~ member(X0,sK27)
| ~ member(X0,sK26)
| ~ empty('empty$uset') ),
inference(superposition,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
empty('empty$uset'),
inference(resolution,[status(thm)],[c26,c10]) ).
cnf(d11,plain,
( ~ member(X0,sK27)
| ~ member(X0,sK26) ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( ~ member(sK21(X0,difference(X1,X2)),X1)
| member(sK21(X0,difference(X1,X2)),X2)
| subset(X0,difference(X1,X2)) ),
inference(resolution,[status(thm)],[c23,c9]) ).
cnf(d13,plain,
( subset(X0,difference(X0,X1))
| subset(X0,difference(X0,X1))
| member(sK21(X0,difference(X0,X1)),X1) ),
inference(resolution,[status(thm)],[d12,c22]) ).
cnf(d14,plain,
( ~ member(sK21(X0,difference(X0,sK27)),sK26)
| subset(X0,difference(X0,sK27)) ),
inference(resolution,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
( subset(sK26,difference(sK26,sK27))
| subset(sK26,difference(sK26,sK27)) ),
inference(resolution,[status(thm)],[d14,c22]) ).
cnf(d16,plain,
( ~ subset(difference(sK26,sK27),sK26)
| difference(sK26,sK27) = sK26 ),
inference(resolution,[status(thm)],[d15,c13]) ).
cnf(d17,plain,
difference(sK26,sK27) != sK26,
inference(resolution,[status(thm)],[d8,c29]) ).
cnf(d18,plain,
~ subset(difference(sK26,sK27),sK26),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
( member(sK21(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c22,c7]) ).
cnf(d20,plain,
( subset(difference(X0,X1),X0)
| subset(difference(X0,X1),X0) ),
inference(resolution,[status(thm)],[d19,c23]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[d20,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET611+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
% 0.09/0.35 % Computer : n008.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
% 0.09/0.36 % DateTime : Sat Sep 26 08:00:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.57/9.37 % SZS status Theorem for theBenchmark.p
% 5.57/9.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------