%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU422+1 : TPTP v9.3.1. Released v3.4.0.
% 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 08:41:58 AM UTC 2026
% Result : Theorem 12.68s 4.44s
% Output : CNFRefutation 12.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 90 ( 2 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 92 ( 37 ~; 41 |; 3 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 58 ( 1 sgn 17 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [X0,X1] :
( 'r1$utarski'(X0,X1)
<=> ! [X2] :
( 'r2$uhidden'(X2,X0)
=> 'r2$uhidden'(X2,X1) ) ) ).
fof(fc1_subset_1,axiom,
! [X0] : ~ 'v1$uxboole$u0'('k1$uzfmisc$u1'(X0)) ).
fof(fraenkel_a_2_0_relset_2,axiom,
! [X0,X1,X2] :
( ( 'm1$usubset$u1'(X2,'k1$uzfmisc$u1'(X1))
& ~ 'v1$uxboole$u0'(X1) )
=> ( 'r2$uhidden'(X0,'a$u2$u0$urelset$u2'(X1,X2))
<=> ? [X3] :
( 'r2$uhidden'(X3,X2)
& X0 = 'k1$utarski'(X3)
& 'm1$usubset$u1'(X3,X1) ) ) ) ).
fof(t2_subset,axiom,
! [X0,X1] :
( 'm1$usubset$u1'(X0,X1)
=> ( 'r2$uhidden'(X0,X1)
| 'v1$uxboole$u0'(X1) ) ) ).
fof(t37_zfmisc_1,axiom,
! [X0,X1] :
( 'r1$utarski'('k1$utarski'(X0),X1)
<=> 'r2$uhidden'(X0,X1) ) ).
fof(t3_subset,axiom,
! [X0,X1] :
( 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'(X1))
<=> 'r1$utarski'(X0,X1) ) ).
fof(t16_relset_2,conjecture,
! [X0] :
( ~ 'v1$uxboole$u0'(X0)
=> ! [X1] :
( 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'(X0))
=> 'm1$usubset$u1'('a$u2$u0$urelset$u2'(X0,X1),'k1$uzfmisc$u1'('k1$uzfmisc$u1'(X0))) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ~ 'v1$uxboole$u0'(X0)
=> ! [X1] :
( 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'(X0))
=> 'm1$usubset$u1'('a$u2$u0$urelset$u2'(X0,X1),'k1$uzfmisc$u1'('k1$uzfmisc$u1'(X0))) ) ),
inference(negate_conjecture,[status(cth)],[t16_relset_2]) ).
cnf(c2,plain,
( 'r2$uhidden'(X2,X1)
| ~ 'r2$uhidden'(X2,X0)
| ~ 'r1$utarski'(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c3,plain,
( 'r2$uhidden'(sK6(X0,X1),X0)
| 'r1$utarski'(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c4,plain,
( ~ 'r2$uhidden'(sK6(X0,X1),X1)
| 'r1$utarski'(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c9,plain,
~ 'v1$uxboole$u0'('k1$uzfmisc$u1'(X0)),
inference(clausification,[status(esa)],[fc1_subset_1]) ).
cnf(c14,plain,
( X2 = 'k1$utarski'(sK14(X2,X0,X1))
| ~ 'r2$uhidden'(X2,'a$u2$u0$urelset$u2'(X0,X1))
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'(X0))
| 'v1$uxboole$u0'(X0) ),
inference(clausification,[status(esa)],[fraenkel_a_2_0_relset_2]) ).
cnf(c15,plain,
( 'r2$uhidden'(sK14(X2,X0,X1),X1)
| ~ 'r2$uhidden'(X2,'a$u2$u0$urelset$u2'(X0,X1))
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'(X0))
| 'v1$uxboole$u0'(X0) ),
inference(clausification,[status(esa)],[fraenkel_a_2_0_relset_2]) ).
cnf(c29,plain,
( 'r2$uhidden'(X0,X1)
| 'v1$uxboole$u0'(X1)
| ~ 'm1$usubset$u1'(X0,X1) ),
inference(clausification,[status(esa)],[t2_subset]) ).
cnf(c35,plain,
( ~ 'r2$uhidden'(X0,X1)
| 'r1$utarski'('k1$utarski'(X0),X1) ),
inference(clausification,[status(esa)],[t37_zfmisc_1]) ).
cnf(c36,plain,
( 'r1$utarski'(X0,X1)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c37,plain,
( ~ 'r1$utarski'(X0,X1)
| 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c43,plain,
~ 'v1$uxboole$u0'(sK47),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c44,plain,
'm1$usubset$u1'(sK48,'k1$uzfmisc$u1'(sK47)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c45,plain,
~ 'm1$usubset$u1'('a$u2$u0$urelset$u2'(sK47,sK48),'k1$uzfmisc$u1'('k1$uzfmisc$u1'(sK47))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'r1$utarski'('a$u2$u0$urelset$u2'(sK47,sK48),'k1$uzfmisc$u1'(sK47)),
inference(resolution,[status(thm)],[c37,c45]) ).
cnf(d1,plain,
'r1$utarski'(sK48,sK47),
inference(resolution,[status(thm)],[c36,c44]) ).
cnf(d2,plain,
( ~ 'r2$uhidden'(X0,sK48)
| 'r2$uhidden'(X0,sK47) ),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
( 'r2$uhidden'(sK14(X0,X1,sK48),sK47)
| ~ 'm1$usubset$u1'(sK48,'k1$uzfmisc$u1'(X1))
| 'v1$uxboole$u0'(X1)
| ~ 'r2$uhidden'(X0,'a$u2$u0$urelset$u2'(X1,sK48)) ),
inference(resolution,[status(thm)],[c15,d2]) ).
cnf(d4,plain,
( ~ 'm1$usubset$u1'(X2,'k1$uzfmisc$u1'(X1))
| 'v1$uxboole$u0'(X1)
| ~ 'r2$uhidden'(X0,'a$u2$u0$urelset$u2'(X1,X2))
| ~ 'r2$uhidden'(sK14(X0,X1,X2),X3)
| 'r1$utarski'(X0,X3) ),
inference(superposition,[status(thm)],[c14,c35]) ).
cnf(d5,plain,
( ~ 'm1$usubset$u1'(sK48,'k1$uzfmisc$u1'(X1))
| 'v1$uxboole$u0'(X1)
| ~ 'r2$uhidden'(X0,'a$u2$u0$urelset$u2'(X1,sK48))
| ~ 'm1$usubset$u1'(sK48,'k1$uzfmisc$u1'(X1))
| 'r1$utarski'(X0,sK47)
| 'v1$uxboole$u0'(X1)
| ~ 'r2$uhidden'(X0,'a$u2$u0$urelset$u2'(X1,sK48)) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( 'r1$utarski'('a$u2$u0$urelset$u2'(X0,sK48),X1)
| ~ 'm1$usubset$u1'(sK48,'k1$uzfmisc$u1'(X0))
| 'r1$utarski'(sK6('a$u2$u0$urelset$u2'(X0,sK48),X1),sK47)
| 'v1$uxboole$u0'(X0) ),
inference(resolution,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
( ~ 'r1$utarski'(X0,X1)
| 'v1$uxboole$u0'('k1$uzfmisc$u1'(X1))
| 'r2$uhidden'(X0,'k1$uzfmisc$u1'(X1)) ),
inference(resolution,[status(thm)],[c29,c37]) ).
cnf(d8,plain,
( ~ 'r1$utarski'(X0,X1)
| 'r2$uhidden'(X0,'k1$uzfmisc$u1'(X1)) ),
inference(resolution,[status(thm)],[c9,d7]) ).
cnf(d9,plain,
( 'r1$utarski'(X0,'k1$uzfmisc$u1'(X1))
| ~ 'r1$utarski'(sK6(X0,'k1$uzfmisc$u1'(X1)),X1) ),
inference(resolution,[status(thm)],[d8,c4]) ).
cnf(d10,plain,
( ~ 'm1$usubset$u1'(sK48,'k1$uzfmisc$u1'(X0))
| 'r1$utarski'('a$u2$u0$urelset$u2'(X0,sK48),'k1$uzfmisc$u1'(sK47))
| 'v1$uxboole$u0'(X0)
| 'r1$utarski'('a$u2$u0$urelset$u2'(X0,sK48),'k1$uzfmisc$u1'(sK47)) ),
inference(resolution,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
( ~ 'm1$usubset$u1'(sK48,'k1$uzfmisc$u1'(sK47))
| 'v1$uxboole$u0'(sK47) ),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
~ 'm1$usubset$u1'(sK48,'k1$uzfmisc$u1'(sK47)),
inference(resolution,[status(thm)],[c43,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c44,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU422+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 09:45:12 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.68/4.44 % SZS status Theorem for theBenchmark.p
% 12.68/4.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------