%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET146+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 : n001.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 08:32:10 AM UTC 2026
% Result : Theorem 10.59s 2.93s
% Output : CNFRefutation 10.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 14 unt; 0 def)
% Number of atoms : 44 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 15 ~; 10 |; 2 &)
% ( 4 <=>; 1 =>; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 8 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ) ).
fof(empty_set_defn,axiom,
! [X0] : ~ member(X0,'empty$uset') ).
fof(equal_defn,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(commutativity_of_intersection,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0) ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(empty_defn,axiom,
! [X0] :
( empty(X0)
<=> ! [X1] : ~ member(X1,X0) ) ).
fof(prove_th61,conjecture,
! [X0] : intersection(X0,'empty$uset') = 'empty$uset' ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : intersection(X0,'empty$uset') = 'empty$uset',
inference(negate_conjecture,[status(cth)],[prove_th61]) ).
cnf(c1,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c3,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set_defn]) ).
cnf(c6,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_defn]) ).
cnf(c7,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_intersection]) ).
cnf(c9,plain,
( member(sK11(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c12,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c13,plain,
( member(sK15(X0),X0)
| empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c20,plain,
intersection(sK20,'empty$uset') != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ empty(X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c9,c12]) ).
cnf(d1,plain,
subset('empty$uset',X0),
inference(resolution,[status(thm)],[c9,c3]) ).
cnf(d2,plain,
( ~ subset(X0,'empty$uset')
| 'empty$uset' = X0 ),
inference(resolution,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
( ~ empty(X0)
| 'empty$uset' = X0 ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( member(sK15(intersection(X0,X1)),X1)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[c13,c1]) ).
cnf(d5,plain,
empty(intersection(X0,'empty$uset')),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
empty(intersection('empty$uset',X0)),
inference(superposition,[status(thm)],[c7,d5]) ).
cnf(d7,plain,
'empty$uset' = intersection('empty$uset',X0),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
intersection('empty$uset',sK20) != 'empty$uset',
inference(demodulation,[status(thm)],[c20,c7]) ).
cnf(d9,plain,
'empty$uset' != 'empty$uset',
inference(demodulation,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
$false,
inference(equality_resolution,[status(thm)],[d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET146+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.37 % Computer : n001.cluster.edu
% 0.06/0.37 % Model : x86_64 x86_64
% 0.06/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.37 % Memory : 8046.5625MB
% 0.06/0.37 % OS : Linux 6.8.0-71-generic
% 0.06/0.37 % CPULimit : 300
% 0.06/0.37 % WCLimit : 300
% 0.06/0.37 % DateTime : Sat Sep 26 07:18:56 UTC 2026
% 0.06/0.38 % CPUTime :
% 0.06/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.59/2.93 % SZS status Theorem for theBenchmark.p
% 10.59/2.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------