%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU145+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 08:41:00 AM UTC 2026
% Result : Theorem 20.86s 3.02s
% Output : CNFRefutation 20.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 6 unt; 0 def)
% Number of atoms : 55 ( 9 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 46 ( 15 ~; 22 |; 1 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ) ).
fof(d3_tarski,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ) ).
fof(d4_xboole_0,axiom,
! [X0,X1,X2] :
( X2 = 'set$udifference'(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ) ).
fof(l3_zfmisc_1,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,'set$udifference'(X1,singleton(X2)))
| in(X2,X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,'set$udifference'(X1,singleton(X2)))
| in(X2,X0) ) ),
inference(negate_conjecture,[status(cth)],[l3_zfmisc_1]) ).
cnf(c1,plain,
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c7,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c8,plain,
( in(sK9(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c9,plain,
( ~ in(sK9(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c12,plain,
( ~ in(X3,X0)
| in(X3,X1)
| in(X3,X2)
| 'set$udifference'(X0,X1) != X2 ),
inference(clausification,[status(esa)],[d4_xboole_0]) ).
cnf(c19,plain,
subset(sK18,sK19),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c20,plain,
~ subset(sK18,'set$udifference'(sK19,singleton(sK20))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c21,plain,
~ in(sK20,sK18),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ in(X1,singleton(X0))
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(d1,plain,
( ~ in(X0,sK18)
| in(X0,sK19) ),
inference(resolution,[status(thm)],[c7,c19]) ).
cnf(d2,plain,
( subset(sK18,X0)
| in(sK9(sK18,X0),sK19) ),
inference(resolution,[status(thm)],[d1,c8]) ).
cnf(d3,plain,
( ~ in(X0,X1)
| in(X0,X2)
| in(X0,'set$udifference'(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c12]) ).
cnf(d4,plain,
( subset(X0,'set$udifference'(X1,X2))
| ~ in(sK9(X0,'set$udifference'(X1,X2)),X1)
| in(sK9(X0,'set$udifference'(X1,X2)),X2) ),
inference(resolution,[status(thm)],[d3,c9]) ).
cnf(d5,plain,
( subset(sK18,'set$udifference'(sK19,X0))
| subset(sK18,'set$udifference'(sK19,X0))
| in(sK9(sK18,'set$udifference'(sK19,X0)),X0) ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( X0 = sK9(sK18,'set$udifference'(sK19,singleton(X0)))
| subset(sK18,'set$udifference'(sK19,singleton(X0))) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
sK20 = sK9(sK18,'set$udifference'(sK19,singleton(sK20))),
inference(resolution,[status(thm)],[d6,c20]) ).
cnf(d8,plain,
( subset(sK18,'set$udifference'(sK19,singleton(sK20)))
| in(sK20,sK18) ),
inference(superposition,[status(thm)],[d7,c8]) ).
cnf(d9,plain,
subset(sK18,'set$udifference'(sK19,singleton(sK20))),
inference(resolution,[status(thm)],[c21,d8]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c20,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU145+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:41:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.86/3.02 % SZS status Theorem for theBenchmark.p
% 20.86/3.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------