%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET027+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 : n017.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 08:31:40 AM UTC 2026
% Result : Theorem 9.70s 6.63s
% Output : CNFRefutation 9.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 5 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 29 ( 10 ~; 13 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(prove_transitivity_of_subset,conjecture,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
inference(negate_conjecture,[status(cth)],[prove_transitivity_of_subset]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c2,plain,
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c4,plain,
subset(sK5,sK6),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c5,plain,
subset(sK6,sK7),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c6,plain,
~ subset(sK5,sK7),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( member(sK3(X0,X1),X2)
| ~ subset(X0,X2)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
( member(sK3(X0,X2),X3)
| ~ subset(X1,X3)
| subset(X0,X2)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( member(sK3(sK5,X1),X0)
| subset(sK5,X1)
| ~ subset(sK6,X0) ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( subset(sK5,X0)
| ~ subset(sK6,X0)
| subset(sK5,X0) ),
inference(resolution,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
subset(sK5,sK7),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c6,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET027+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
% 0.08/5.35 % Computer : n017.cluster.edu
% 0.08/5.35 % Model : x86_64 x86_64
% 0.08/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.35 % Memory : 8046.5625MB
% 0.08/5.35 % OS : Linux 6.8.0-71-generic
% 0.08/5.35 % CPULimit : 300
% 0.08/5.35 % WCLimit : 300
% 0.08/5.35 % DateTime : Sat Sep 26 06:50:08 UTC 2026
% 0.08/5.35 % CPUTime :
% 0.08/5.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.70/6.63 % SZS status Theorem for theBenchmark.p
% 9.70/6.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------