%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LAT359+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 : n026.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 07:48:28 AM UTC 2026
% Result : Theorem 45.29s 7.11s
% Output : CNFRefutation 45.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 59 ( 8 unt; 0 def)
% Number of atoms : 199 ( 22 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 253 ( 113 ~; 96 |; 22 &)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 86 ( 9 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_binop_1,axiom,
! [X0] :
( ( 'v1$ufunct$u1'(X0)
& 'v1$urelat$u1'(X0) )
=> ! [X1,X2] : 'k1$ubinop$u1'(X0,X1,X2) = 'k1$ufunct$u1'(X0,'k4$utarski'(X1,X2)) ) ).
fof(d2_altcat_1,axiom,
! [X0] :
( 'l1$ualtcat$u1'(X0)
=> ! [X1] :
( 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
=> ! [X2] :
( 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X0))
=> 'k1$ualtcat$u1'(X0,X1,X2) = 'k1$ubinop$u1'('u1$ualtcat$u1'(X0),X1,X2) ) ) ) ).
fof(d3_pboole,axiom,
! [X0,X1] :
( ( 'v1$ufunct$u1'(X1)
& 'v1$urelat$u1'(X1) )
=> ( 'm1$upboole'(X1,X0)
<=> 'k1$urelat$u1'(X1) = X0 ) ) ).
fof(d4_funct_1,axiom,
! [X0] :
( ( 'v1$ufunct$u1'(X0)
& 'v1$urelat$u1'(X0) )
=> ! [X1,X2] :
( ( ~ 'r2$uhidden'(X1,'k1$urelat$u1'(X0))
=> ( X2 = 'k1$ufunct$u1'(X0,X1)
<=> X2 = 'k1$uxboole$u0' ) )
& ( 'r2$uhidden'(X1,'k1$urelat$u1'(X0))
=> ( X2 = 'k1$ufunct$u1'(X0,X1)
<=> 'r2$uhidden'('k4$utarski'(X1,X2),X0) ) ) ) ) ).
fof(dt_l2_altcat_1,axiom,
! [X0] :
( 'l2$ualtcat$u1'(X0)
=> 'l1$ualtcat$u1'(X0) ) ).
fof(dt_m1_pboole,axiom,
! [X0,X1] :
( 'm1$upboole'(X1,X0)
=> ( 'v1$ufunct$u1'(X1)
& 'v1$urelat$u1'(X1) ) ) ).
fof(dt_u1_altcat_1,axiom,
! [X0] :
( 'l1$ualtcat$u1'(X0)
=> 'm1$upboole'('u1$ualtcat$u1'(X0),'k2$uzfmisc$u1'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X0))) ) ).
fof(fc6_membered,axiom,
( 'v5$umembered'('k1$uxboole$u0')
& 'v4$umembered'('k1$uxboole$u0')
& 'v3$umembered'('k1$uxboole$u0')
& 'v2$umembered'('k1$uxboole$u0')
& 'v1$umembered'('k1$uxboole$u0')
& 'v1$uxboole$u0'('k1$uxboole$u0') ) ).
fof(t106_zfmisc_1,axiom,
! [X0,X1,X2,X3] :
( 'r2$uhidden'('k4$utarski'(X0,X1),'k2$uzfmisc$u1'(X2,X3))
<=> ( 'r2$uhidden'(X1,X3)
& 'r2$uhidden'(X0,X2) ) ) ).
fof(t1_subset,axiom,
! [X0,X1] :
( 'r2$uhidden'(X0,X1)
=> 'm1$usubset$u1'(X0,X1) ) ).
fof(t7_boole,axiom,
! [X0,X1] :
~ ( 'v1$uxboole$u0'(X1)
& 'r2$uhidden'(X0,X1) ) ).
fof(t12_waybel34,conjecture,
! [X0] :
( ( 'l2$ualtcat$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1,X2,X3] :
~ ( ! [X4] :
( 'm1$usubset$u1'(X4,'u1$ustruct$u0'(X0))
=> ! [X5] :
( 'm1$usubset$u1'(X5,'u1$ustruct$u0'(X0))
=> ~ ( 'm1$usubset$u1'(X3,'k1$ualtcat$u1'(X0,X4,X5))
& 'r2$uhidden'(X3,'k1$ualtcat$u1'(X0,X4,X5))
& X5 = X2
& X4 = X1 ) ) )
& 'r2$uhidden'(X3,'k1$ubinop$u1'('u1$ualtcat$u1'(X0),X1,X2)) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'l2$ualtcat$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1,X2,X3] :
~ ( ! [X4] :
( 'm1$usubset$u1'(X4,'u1$ustruct$u0'(X0))
=> ! [X5] :
( 'm1$usubset$u1'(X5,'u1$ustruct$u0'(X0))
=> ~ ( 'm1$usubset$u1'(X3,'k1$ualtcat$u1'(X0,X4,X5))
& 'r2$uhidden'(X3,'k1$ualtcat$u1'(X0,X4,X5))
& X5 = X2
& X4 = X1 ) ) )
& 'r2$uhidden'(X3,'k1$ubinop$u1'('u1$ualtcat$u1'(X0),X1,X2)) ) ),
inference(negate_conjecture,[status(cth)],[t12_waybel34]) ).
cnf(c34,plain,
( 'k1$ubinop$u1'(X0,X1,X2) = 'k1$ufunct$u1'(X0,'k4$utarski'(X1,X2))
| ~ 'v1$ufunct$u1'(X0)
| ~ 'v1$urelat$u1'(X0) ),
inference(clausification,[status(esa)],[d1_binop_1]) ).
cnf(c35,plain,
( 'k1$ualtcat$u1'(X0,X1,X2) = 'k1$ubinop$u1'('u1$ualtcat$u1'(X0),X1,X2)
| ~ 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X0))
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
| ~ 'l1$ualtcat$u1'(X0) ),
inference(clausification,[status(esa)],[d2_altcat_1]) ).
cnf(c36,plain,
( 'k1$urelat$u1'(X0) = X1
| ~ 'm1$upboole'(X0,X1)
| ~ 'v1$ufunct$u1'(X0)
| ~ 'v1$urelat$u1'(X0) ),
inference(clausification,[status(esa)],[d3_pboole]) ).
cnf(c40,plain,
( X0 = 'k1$uxboole$u0'
| ~ 'v1$urelat$u1'(X1)
| 'r2$uhidden'(X2,'k1$urelat$u1'(X1))
| ~ 'v1$ufunct$u1'(X1)
| X0 != 'k1$ufunct$u1'(X1,X2) ),
inference(clausification,[status(esa)],[d4_funct_1]) ).
cnf(c44,plain,
( 'l1$ualtcat$u1'(X0)
| ~ 'l2$ualtcat$u1'(X0) ),
inference(clausification,[status(esa)],[dt_l2_altcat_1]) ).
cnf(c45,plain,
( 'v1$urelat$u1'(X0)
| ~ 'm1$upboole'(X0,X1) ),
inference(clausification,[status(esa)],[dt_m1_pboole]) ).
cnf(c46,plain,
( 'v1$ufunct$u1'(X0)
| ~ 'm1$upboole'(X0,X1) ),
inference(clausification,[status(esa)],[dt_m1_pboole]) ).
cnf(c47,plain,
( 'm1$upboole'('u1$ualtcat$u1'(X0),'k2$uzfmisc$u1'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X0)))
| ~ 'l1$ualtcat$u1'(X0) ),
inference(clausification,[status(esa)],[dt_u1_altcat_1]) ).
cnf(c89,plain,
'v1$uxboole$u0'('k1$uxboole$u0'),
inference(clausification,[status(esa)],[fc6_membered]) ).
cnf(c121,plain,
( 'r2$uhidden'(X0,X2)
| ~ 'r2$uhidden'('k4$utarski'(X0,X1),'k2$uzfmisc$u1'(X2,X3)) ),
inference(clausification,[status(esa)],[t106_zfmisc_1]) ).
cnf(c122,plain,
( 'r2$uhidden'(X1,X3)
| ~ 'r2$uhidden'('k4$utarski'(X0,X1),'k2$uzfmisc$u1'(X2,X3)) ),
inference(clausification,[status(esa)],[t106_zfmisc_1]) ).
cnf(c124,plain,
( 'm1$usubset$u1'(X0,X1)
| ~ 'r2$uhidden'(X0,X1) ),
inference(clausification,[status(esa)],[t1_subset]) ).
cnf(c127,plain,
( ~ 'v1$uxboole$u0'(X1)
| ~ 'r2$uhidden'(X0,X1) ),
inference(clausification,[status(esa)],[t7_boole]) ).
cnf(c130,plain,
'l2$ualtcat$u1'(sK97),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c131,plain,
'r2$uhidden'(sK100,'k1$ubinop$u1'('u1$ualtcat$u1'(sK97),sK98,sK99)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c132,plain,
( ~ 'm1$usubset$u1'(sK100,'k1$ualtcat$u1'(sK97,X0,X1))
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK97))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK97))
| ~ 'r2$uhidden'(sK100,'k1$ualtcat$u1'(sK97,X0,X1))
| X1 != sK99
| X0 != sK98 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'v1$ufunct$u1'('u1$ualtcat$u1'(X0))
| ~ 'l1$ualtcat$u1'(X0) ),
inference(resolution,[status(thm)],[c47,c46]) ).
cnf(d1,plain,
( 'v1$urelat$u1'('u1$ualtcat$u1'(X0))
| ~ 'l1$ualtcat$u1'(X0) ),
inference(resolution,[status(thm)],[c47,c45]) ).
cnf(d2,plain,
( ~ 'l1$ualtcat$u1'(sK97)
| ~ 'm1$usubset$u1'(sK99,'u1$ustruct$u0'(sK97))
| ~ 'm1$usubset$u1'(sK98,'u1$ustruct$u0'(sK97))
| 'r2$uhidden'(sK100,'k1$ualtcat$u1'(sK97,sK98,sK99)) ),
inference(superposition,[status(thm)],[c35,c131]) ).
cnf(d3,plain,
'l1$ualtcat$u1'(sK97),
inference(resolution,[status(thm)],[c44,c130]) ).
cnf(d4,plain,
( ~ 'm1$usubset$u1'(sK99,'u1$ustruct$u0'(sK97))
| ~ 'm1$usubset$u1'(sK98,'u1$ustruct$u0'(sK97))
| 'r2$uhidden'(sK100,'k1$ualtcat$u1'(sK97,sK98,sK99)) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ 'm1$usubset$u1'(sK100,'k1$ualtcat$u1'(sK97,X0,sK99))
| ~ 'm1$usubset$u1'(sK99,'u1$ustruct$u0'(sK97))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK97))
| ~ 'r2$uhidden'(sK100,'k1$ualtcat$u1'(sK97,X0,sK99))
| X0 != sK98 ),
inference(equality_resolution,[status(thm)],[c132]) ).
cnf(d6,plain,
( ~ 'm1$usubset$u1'(sK99,'u1$ustruct$u0'(sK97))
| ~ 'm1$usubset$u1'(sK100,'k1$ualtcat$u1'(sK97,sK98,sK99))
| ~ 'm1$usubset$u1'(sK98,'u1$ustruct$u0'(sK97))
| ~ 'r2$uhidden'(sK100,'k1$ualtcat$u1'(sK97,sK98,sK99)) ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( 'm1$usubset$u1'(sK100,'k1$ualtcat$u1'(sK97,sK98,sK99))
| ~ 'm1$usubset$u1'(sK99,'u1$ustruct$u0'(sK97))
| ~ 'm1$usubset$u1'(sK98,'u1$ustruct$u0'(sK97)) ),
inference(resolution,[status(thm)],[d4,c124]) ).
cnf(d8,plain,
( ~ 'm1$usubset$u1'(sK99,'u1$ustruct$u0'(sK97))
| ~ 'm1$usubset$u1'(sK98,'u1$ustruct$u0'(sK97))
| ~ 'r2$uhidden'(sK100,'k1$ualtcat$u1'(sK97,sK98,sK99))
| ~ 'm1$usubset$u1'(sK99,'u1$ustruct$u0'(sK97))
| ~ 'm1$usubset$u1'(sK98,'u1$ustruct$u0'(sK97)) ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( ~ 'm1$usubset$u1'(sK99,'u1$ustruct$u0'(sK97))
| ~ 'm1$usubset$u1'(sK98,'u1$ustruct$u0'(sK97))
| ~ 'm1$usubset$u1'(sK99,'u1$ustruct$u0'(sK97))
| ~ 'm1$usubset$u1'(sK98,'u1$ustruct$u0'(sK97)) ),
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
~ 'v1$uxboole$u0'('k1$ubinop$u1'('u1$ualtcat$u1'(sK97),sK98,sK99)),
inference(resolution,[status(thm)],[c127,c131]) ).
cnf(d11,plain,
( ~ 'v1$urelat$u1'(X0)
| ~ 'v1$ufunct$u1'(X0)
| ~ 'v1$urelat$u1'(X0)
| ~ 'v1$ufunct$u1'(X0)
| 'r2$uhidden'('k4$utarski'(X1,X2),'k1$urelat$u1'(X0))
| X3 = 'k1$uxboole$u0'
| X3 != 'k1$ubinop$u1'(X0,X1,X2) ),
inference(superposition,[status(thm)],[c34,c40]) ).
cnf(d12,plain,
( ~ 'v1$urelat$u1'(X0)
| ~ 'v1$ufunct$u1'(X0)
| 'r2$uhidden'('k4$utarski'(X1,X2),'k1$urelat$u1'(X0))
| 'k1$ubinop$u1'(X0,X1,X2) = 'k1$uxboole$u0' ),
inference(equality_resolution,[status(thm)],[d11]) ).
cnf(d13,plain,
( ~ 'm1$upboole'(X0,X1)
| ~ 'v1$urelat$u1'(X0)
| ~ 'v1$ufunct$u1'(X0)
| ~ 'v1$urelat$u1'(X0)
| ~ 'v1$ufunct$u1'(X0)
| 'k1$ubinop$u1'(X0,X2,X3) = 'k1$uxboole$u0'
| 'r2$uhidden'('k4$utarski'(X2,X3),X1) ),
inference(superposition,[status(thm)],[c36,d12]) ).
cnf(d14,plain,
( ~ 'm1$upboole'('u1$ualtcat$u1'(sK97),X0)
| ~ 'v1$urelat$u1'('u1$ualtcat$u1'(sK97))
| ~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97))
| 'r2$uhidden'('k4$utarski'(sK98,sK99),X0)
| ~ 'v1$uxboole$u0'('k1$uxboole$u0') ),
inference(superposition,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
( ~ 'm1$upboole'('u1$ualtcat$u1'(sK97),X0)
| ~ 'v1$urelat$u1'('u1$ualtcat$u1'(sK97))
| ~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97))
| 'r2$uhidden'('k4$utarski'(sK98,sK99),X0) ),
inference(resolution,[status(thm)],[c89,d14]) ).
cnf(d16,plain,
( 'r2$uhidden'(sK99,X1)
| ~ 'm1$upboole'('u1$ualtcat$u1'(sK97),'k2$uzfmisc$u1'(X0,X1))
| ~ 'v1$urelat$u1'('u1$ualtcat$u1'(sK97))
| ~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97)) ),
inference(resolution,[status(thm)],[d15,c122]) ).
cnf(d17,plain,
( ~ 'l1$ualtcat$u1'(sK97)
| ~ 'v1$urelat$u1'('u1$ualtcat$u1'(sK97))
| ~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97))
| 'r2$uhidden'(sK99,'u1$ustruct$u0'(sK97)) ),
inference(resolution,[status(thm)],[d16,c47]) ).
cnf(d18,plain,
( ~ 'v1$urelat$u1'('u1$ualtcat$u1'(sK97))
| ~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97))
| 'r2$uhidden'(sK99,'u1$ustruct$u0'(sK97)) ),
inference(resolution,[status(thm)],[d3,d17]) ).
cnf(d19,plain,
( 'm1$usubset$u1'(sK99,'u1$ustruct$u0'(sK97))
| ~ 'v1$urelat$u1'('u1$ualtcat$u1'(sK97))
| ~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97)) ),
inference(resolution,[status(thm)],[d18,c124]) ).
cnf(d20,plain,
( ~ 'm1$usubset$u1'(sK98,'u1$ustruct$u0'(sK97))
| ~ 'v1$urelat$u1'('u1$ualtcat$u1'(sK97))
| ~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97)) ),
inference(resolution,[status(thm)],[d19,d9]) ).
cnf(d21,plain,
( 'r2$uhidden'(sK98,X0)
| ~ 'm1$upboole'('u1$ualtcat$u1'(sK97),'k2$uzfmisc$u1'(X0,X1))
| ~ 'v1$urelat$u1'('u1$ualtcat$u1'(sK97))
| ~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97)) ),
inference(resolution,[status(thm)],[d15,c121]) ).
cnf(d22,plain,
( ~ 'l1$ualtcat$u1'(sK97)
| ~ 'v1$urelat$u1'('u1$ualtcat$u1'(sK97))
| ~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97))
| 'r2$uhidden'(sK98,'u1$ustruct$u0'(sK97)) ),
inference(resolution,[status(thm)],[d21,c47]) ).
cnf(d23,plain,
( ~ 'v1$urelat$u1'('u1$ualtcat$u1'(sK97))
| ~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97))
| 'r2$uhidden'(sK98,'u1$ustruct$u0'(sK97)) ),
inference(resolution,[status(thm)],[d3,d22]) ).
cnf(d24,plain,
( 'm1$usubset$u1'(sK98,'u1$ustruct$u0'(sK97))
| ~ 'v1$urelat$u1'('u1$ualtcat$u1'(sK97))
| ~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97)) ),
inference(resolution,[status(thm)],[d23,c124]) ).
cnf(d25,plain,
( ~ 'v1$urelat$u1'('u1$ualtcat$u1'(sK97))
| ~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97))
| ~ 'v1$urelat$u1'('u1$ualtcat$u1'(sK97))
| ~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97)) ),
inference(resolution,[status(thm)],[d24,d20]) ).
cnf(d26,plain,
( ~ 'l1$ualtcat$u1'(sK97)
| ~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97)) ),
inference(resolution,[status(thm)],[d25,d1]) ).
cnf(d27,plain,
~ 'v1$ufunct$u1'('u1$ualtcat$u1'(sK97)),
inference(resolution,[status(thm)],[d3,d26]) ).
cnf(d28,plain,
~ 'l1$ualtcat$u1'(sK97),
inference(resolution,[status(thm)],[d27,d0]) ).
cnf(d29,plain,
$false,
inference(resolution,[status(thm)],[d3,d28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT359+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n026.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 21:21:25 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.29/7.11 % SZS status Theorem for theBenchmark.p
% 45.29/7.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------