%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP640+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:24:17 AM UTC 2026
% Result : Theorem 13.44s 2.49s
% Output : CNFRefutation 13.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 66 ( 21 unt; 0 def)
% Number of atoms : 308 ( 37 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 418 ( 176 ~; 178 |; 39 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 63 ( 0 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_k2_funct_2,axiom,
! [X0,X1,X2,X3] :
( ( 'm1$urelset$u1'(X2,X0,X1)
& 'v1$ufunct$u2'(X2,X0,X1)
& 'v1$ufunct$u1'(X2) )
=> 'k2$ufunct$u2'(X0,X1,X2,X3) = 'k9$urelat$u1'(X2,X3) ) ).
fof(redefinition_m2_relset_1,axiom,
! [X0,X1,X2] :
( 'm2$urelset$u1'(X2,X0,X1)
<=> 'm1$urelset$u1'(X2,X0,X1) ) ).
fof(redefinition_r1_group_2,axiom,
! [X0,X1,X2] :
( ( 'm1$ugroup$u2'(X2,X0)
& 'v1$ugroup$u1'(X2)
& 'm1$ugroup$u2'(X1,X0)
& 'v1$ugroup$u1'(X1)
& 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ( 'r1$ugroup$u2'(X0,X1,X2)
<=> X1 = X2 ) ) ).
fof(dt_k5_group_4,axiom,
! [X0,X1] :
( ( 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
& 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ( 'm1$ugroup$u2'('k5$ugroup$u4'(X0,X1),X0)
& 'v1$ugroup$u1'('k5$ugroup$u4'(X0,X1)) ) ) ).
fof(dt_k8_group_4,axiom,
! [X0,X1,X2] :
( ( 'm1$ugroup$u2'(X2,X0)
& 'm1$ugroup$u2'(X1,X0)
& 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ( 'm1$ugroup$u2'('k8$ugroup$u4'(X0,X1,X2),X0)
& 'v1$ugroup$u1'('k8$ugroup$u4'(X0,X1,X2)) ) ) ).
fof(t4_latsubgr,axiom,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( 'm1$ugroup$u2'(X1,X0)
=> ! [X2] :
( 'm1$ugroup$u2'(X2,X0)
=> ! [X3] :
( 'm1$usubset$u1'(X3,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
=> ( X3 = 'k2$uxboole$u0'('u1$ustruct$u0'(X1),'u1$ustruct$u0'(X2))
=> 'r1$ugroup$u2'(X0,'k8$ugroup$u4'(X0,X1,X2),'k5$ugroup$u4'(X0,X3)) ) ) ) ) ) ).
fof(t13_latsubgr,conjecture,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( ( 'l1$ugroup$u1'(X1)
& 'v4$ugroup$u1'(X1)
& 'v3$ugroup$u1'(X1)
& ~ 'v3$ustruct$u0'(X1) )
=> ! [X2] :
( 'm1$ugroup$u2'(X2,X0)
=> ! [X3] :
( 'm1$ugroup$u2'(X3,X0)
=> ! [X4] :
( ( 'm2$urelset$u1'(X4,'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1))
& 'v1$ufunct$u2'(X4,'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1))
& 'v1$ufunct$u1'(X4) )
=> ! [X5] :
( 'm1$usubset$u1'(X5,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
=> ( X5 = 'k2$uxboole$u0'('u1$ustruct$u0'(X2),'u1$ustruct$u0'(X3))
=> 'k2$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1),X4,'u1$ustruct$u0'('k8$ugroup$u4'(X0,X2,X3))) = 'k2$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1),X4,'u1$ustruct$u0'('k5$ugroup$u4'(X0,X5))) ) ) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( ( 'l1$ugroup$u1'(X1)
& 'v4$ugroup$u1'(X1)
& 'v3$ugroup$u1'(X1)
& ~ 'v3$ustruct$u0'(X1) )
=> ! [X2] :
( 'm1$ugroup$u2'(X2,X0)
=> ! [X3] :
( 'm1$ugroup$u2'(X3,X0)
=> ! [X4] :
( ( 'm2$urelset$u1'(X4,'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1))
& 'v1$ufunct$u2'(X4,'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1))
& 'v1$ufunct$u1'(X4) )
=> ! [X5] :
( 'm1$usubset$u1'(X5,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
=> ( X5 = 'k2$uxboole$u0'('u1$ustruct$u0'(X2),'u1$ustruct$u0'(X3))
=> 'k2$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1),X4,'u1$ustruct$u0'('k8$ugroup$u4'(X0,X2,X3))) = 'k2$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1),X4,'u1$ustruct$u0'('k5$ugroup$u4'(X0,X5))) ) ) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t13_latsubgr]) ).
cnf(c60,plain,
( 'k2$ufunct$u2'(X1,X2,X0,X3) = 'k9$urelat$u1'(X0,X3)
| ~ 'm1$urelset$u1'(X0,X1,X2)
| ~ 'v1$ufunct$u2'(X0,X1,X2)
| ~ 'v1$ufunct$u1'(X0) ),
inference(clausification,[status(esa)],[redefinition_k2_funct_2]) ).
cnf(c61,plain,
( 'm1$urelset$u1'(X0,X1,X2)
| ~ 'm2$urelset$u1'(X0,X1,X2) ),
inference(clausification,[status(esa)],[redefinition_m2_relset_1]) ).
cnf(c63,plain,
( ~ 'm1$ugroup$u2'(X1,X0)
| 'v3$ustruct$u0'(X0)
| ~ 'l1$ugroup$u1'(X0)
| ~ 'v3$ugroup$u1'(X0)
| X1 = X2
| ~ 'v4$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X2,X0)
| ~ 'v1$ugroup$u1'(X2)
| ~ 'v1$ugroup$u1'(X1)
| ~ 'r1$ugroup$u2'(X0,X1,X2) ),
inference(clausification,[status(esa)],[redefinition_r1_group_2]) ).
cnf(c66,plain,
( 'v1$ugroup$u1'('k5$ugroup$u4'(X0,X1))
| ~ 'v3$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'l1$ugroup$u1'(X0)
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
| ~ 'v4$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[dt_k5_group_4]) ).
cnf(c67,plain,
( ~ 'v3$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'l1$ugroup$u1'(X0)
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
| 'm1$ugroup$u2'('k5$ugroup$u4'(X0,X1),X0)
| ~ 'v4$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[dt_k5_group_4]) ).
cnf(c68,plain,
( 'v3$ustruct$u0'(X1)
| ~ 'm1$ugroup$u2'(X2,X1)
| ~ 'v3$ugroup$u1'(X1)
| 'v1$ugroup$u1'('k8$ugroup$u4'(X1,X0,X2))
| ~ 'l1$ugroup$u1'(X1)
| ~ 'v4$ugroup$u1'(X1)
| ~ 'm1$ugroup$u2'(X0,X1) ),
inference(clausification,[status(esa)],[dt_k8_group_4]) ).
cnf(c69,plain,
( 'm1$ugroup$u2'('k8$ugroup$u4'(X0,X2,X1),X0)
| ~ 'm1$ugroup$u2'(X2,X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[dt_k8_group_4]) ).
cnf(c78,plain,
( ~ 'l1$ugroup$u1'(X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'm1$usubset$u1'(X3,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
| X3 != 'k2$uxboole$u0'('u1$ustruct$u0'(X1),'u1$ustruct$u0'(X2))
| 'v3$ustruct$u0'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| ~ 'm1$ugroup$u2'(X2,X0)
| 'r1$ugroup$u2'(X0,'k8$ugroup$u4'(X0,X1,X2),'k5$ugroup$u4'(X0,X3)) ),
inference(clausification,[status(esa)],[t4_latsubgr]) ).
cnf(c79,plain,
~ 'v3$ustruct$u0'(sK116),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c80,plain,
'v3$ugroup$u1'(sK116),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c81,plain,
'v4$ugroup$u1'(sK116),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c82,plain,
'l1$ugroup$u1'(sK116),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c87,plain,
'm1$ugroup$u2'(sK118,sK116),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c88,plain,
'm1$ugroup$u2'(sK119,sK116),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c89,plain,
'v1$ufunct$u1'(sK120),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c90,plain,
'v1$ufunct$u2'(sK120,'u1$ustruct$u0'(sK116),'u1$ustruct$u0'(sK117)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c91,plain,
'm2$urelset$u1'(sK120,'u1$ustruct$u0'(sK116),'u1$ustruct$u0'(sK117)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c92,plain,
'm1$usubset$u1'(sK121,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK116))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c93,plain,
sK121 = 'k2$uxboole$u0'('u1$ustruct$u0'(sK118),'u1$ustruct$u0'(sK119)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c94,plain,
'k2$ufunct$u2'('u1$ustruct$u0'(sK116),'u1$ustruct$u0'(sK117),sK120,'u1$ustruct$u0'('k8$ugroup$u4'(sK116,sK118,sK119))) != 'k2$ufunct$u2'('u1$ustruct$u0'(sK116),'u1$ustruct$u0'(sK117),sK120,'u1$ustruct$u0'('k5$ugroup$u4'(sK116,sK121))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'v3$ugroup$u1'(sK116)
| 'm1$ugroup$u2'('k5$ugroup$u4'(sK116,sK121),sK116)
| ~ 'v4$ugroup$u1'(sK116)
| 'v3$ustruct$u0'(sK116)
| ~ 'l1$ugroup$u1'(sK116) ),
inference(resolution,[status(thm)],[c67,c92]) ).
cnf(d1,plain,
( ~ 'v3$ugroup$u1'(sK116)
| 'm1$ugroup$u2'('k5$ugroup$u4'(sK116,sK121),sK116)
| ~ 'v4$ugroup$u1'(sK116)
| ~ 'l1$ugroup$u1'(sK116) ),
inference(resolution,[status(thm)],[c79,d0]) ).
cnf(d2,plain,
( 'm1$ugroup$u2'('k5$ugroup$u4'(sK116,sK121),sK116)
| ~ 'v4$ugroup$u1'(sK116)
| ~ 'l1$ugroup$u1'(sK116) ),
inference(resolution,[status(thm)],[c80,d1]) ).
cnf(d3,plain,
( 'm1$ugroup$u2'('k5$ugroup$u4'(sK116,sK121),sK116)
| ~ 'l1$ugroup$u1'(sK116) ),
inference(resolution,[status(thm)],[c81,d2]) ).
cnf(d4,plain,
'm1$ugroup$u2'('k5$ugroup$u4'(sK116,sK121),sK116),
inference(resolution,[status(thm)],[c82,d3]) ).
cnf(d5,plain,
( ~ 'v3$ugroup$u1'(X1)
| ~ 'm1$ugroup$u2'(sK119,X1)
| ~ 'm1$ugroup$u2'(sK118,X1)
| 'r1$ugroup$u2'(X1,'k8$ugroup$u4'(X1,sK118,sK119),'k5$ugroup$u4'(X1,X0))
| ~ 'v4$ugroup$u1'(X1)
| 'v3$ustruct$u0'(X1)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('u1$ustruct$u0'(X1)))
| ~ 'l1$ugroup$u1'(X1)
| X0 != sK121 ),
inference(superposition,[status(thm)],[c93,c78]) ).
cnf(d6,plain,
( ~ 'v3$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(sK119,X0)
| ~ 'm1$ugroup$u2'(sK118,X0)
| 'r1$ugroup$u2'(X0,'k8$ugroup$u4'(X0,sK118,sK119),'k5$ugroup$u4'(X0,sK121))
| ~ 'v4$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'(sK121,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
| ~ 'l1$ugroup$u1'(X0) ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( ~ 'v3$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'('k5$ugroup$u4'(X0,sK121),X0)
| ~ 'm1$ugroup$u2'('k8$ugroup$u4'(X0,sK118,sK119),X0)
| ~ 'v4$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'l1$ugroup$u1'(X0)
| ~ 'v1$ugroup$u1'('k5$ugroup$u4'(X0,sK121))
| ~ 'v1$ugroup$u1'('k8$ugroup$u4'(X0,sK118,sK119))
| 'k8$ugroup$u4'(X0,sK118,sK119) = 'k5$ugroup$u4'(X0,sK121)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(sK119,X0)
| ~ 'm1$ugroup$u2'(sK118,X0)
| ~ 'v4$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'(sK121,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
| ~ 'l1$ugroup$u1'(X0) ),
inference(resolution,[status(thm)],[d6,c63]) ).
cnf(d8,plain,
( ~ 'v3$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(sK118,X0)
| ~ 'm1$ugroup$u2'(sK119,X0)
| ~ 'v4$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'l1$ugroup$u1'(X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(sK119,X0)
| ~ 'm1$ugroup$u2'(sK118,X0)
| ~ 'm1$ugroup$u2'('k5$ugroup$u4'(X0,sK121),X0)
| ~ 'v4$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'(sK121,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
| ~ 'l1$ugroup$u1'(X0)
| ~ 'v1$ugroup$u1'('k8$ugroup$u4'(X0,sK118,sK119))
| ~ 'v1$ugroup$u1'('k5$ugroup$u4'(X0,sK121))
| 'k8$ugroup$u4'(X0,sK118,sK119) = 'k5$ugroup$u4'(X0,sK121) ),
inference(resolution,[status(thm)],[d7,c69]) ).
cnf(d9,plain,
( ~ 'v3$ugroup$u1'(sK116)
| ~ 'm1$ugroup$u2'(sK119,sK116)
| ~ 'm1$ugroup$u2'(sK118,sK116)
| ~ 'v4$ugroup$u1'(sK116)
| 'v3$ustruct$u0'(sK116)
| ~ 'm1$usubset$u1'(sK121,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK116)))
| ~ 'l1$ugroup$u1'(sK116)
| ~ 'v1$ugroup$u1'('k8$ugroup$u4'(sK116,sK118,sK119))
| ~ 'v1$ugroup$u1'('k5$ugroup$u4'(sK116,sK121))
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
( ~ 'v3$ugroup$u1'(sK116)
| ~ 'm1$ugroup$u2'(sK119,sK116)
| ~ 'm1$ugroup$u2'(sK118,sK116)
| ~ 'v4$ugroup$u1'(sK116)
| ~ 'm1$usubset$u1'(sK121,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK116)))
| ~ 'l1$ugroup$u1'(sK116)
| ~ 'v1$ugroup$u1'('k8$ugroup$u4'(sK116,sK118,sK119))
| ~ 'v1$ugroup$u1'('k5$ugroup$u4'(sK116,sK121))
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[c79,d9]) ).
cnf(d11,plain,
( ~ 'm1$ugroup$u2'(sK119,sK116)
| ~ 'm1$ugroup$u2'(sK118,sK116)
| ~ 'v4$ugroup$u1'(sK116)
| ~ 'm1$usubset$u1'(sK121,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK116)))
| ~ 'l1$ugroup$u1'(sK116)
| ~ 'v1$ugroup$u1'('k8$ugroup$u4'(sK116,sK118,sK119))
| ~ 'v1$ugroup$u1'('k5$ugroup$u4'(sK116,sK121))
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[c80,d10]) ).
cnf(d12,plain,
( ~ 'm1$ugroup$u2'(sK119,sK116)
| ~ 'm1$ugroup$u2'(sK118,sK116)
| ~ 'm1$usubset$u1'(sK121,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK116)))
| ~ 'l1$ugroup$u1'(sK116)
| ~ 'v1$ugroup$u1'('k8$ugroup$u4'(sK116,sK118,sK119))
| ~ 'v1$ugroup$u1'('k5$ugroup$u4'(sK116,sK121))
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[c81,d11]) ).
cnf(d13,plain,
( ~ 'm1$ugroup$u2'(sK119,sK116)
| ~ 'm1$ugroup$u2'(sK118,sK116)
| ~ 'm1$usubset$u1'(sK121,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK116)))
| ~ 'v1$ugroup$u1'('k8$ugroup$u4'(sK116,sK118,sK119))
| ~ 'v1$ugroup$u1'('k5$ugroup$u4'(sK116,sK121))
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[c82,d12]) ).
cnf(d14,plain,
( ~ 'm1$ugroup$u2'(sK119,sK116)
| ~ 'm1$usubset$u1'(sK121,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK116)))
| ~ 'v1$ugroup$u1'('k8$ugroup$u4'(sK116,sK118,sK119))
| ~ 'v1$ugroup$u1'('k5$ugroup$u4'(sK116,sK121))
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[c87,d13]) ).
cnf(d15,plain,
( ~ 'm1$usubset$u1'(sK121,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK116)))
| ~ 'v1$ugroup$u1'('k8$ugroup$u4'(sK116,sK118,sK119))
| ~ 'v1$ugroup$u1'('k5$ugroup$u4'(sK116,sK121))
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[c88,d14]) ).
cnf(d16,plain,
( ~ 'v1$ugroup$u1'('k8$ugroup$u4'(sK116,sK118,sK119))
| ~ 'v1$ugroup$u1'('k5$ugroup$u4'(sK116,sK121))
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[c92,d15]) ).
cnf(d17,plain,
( ~ 'v3$ugroup$u1'(sK116)
| ~ 'v4$ugroup$u1'(sK116)
| 'v3$ustruct$u0'(sK116)
| ~ 'l1$ugroup$u1'(sK116)
| 'v1$ugroup$u1'('k5$ugroup$u4'(sK116,sK121)) ),
inference(resolution,[status(thm)],[c66,c92]) ).
cnf(d18,plain,
( ~ 'v3$ugroup$u1'(sK116)
| ~ 'v4$ugroup$u1'(sK116)
| ~ 'l1$ugroup$u1'(sK116)
| 'v1$ugroup$u1'('k5$ugroup$u4'(sK116,sK121)) ),
inference(resolution,[status(thm)],[c79,d17]) ).
cnf(d19,plain,
( ~ 'v4$ugroup$u1'(sK116)
| ~ 'l1$ugroup$u1'(sK116)
| 'v1$ugroup$u1'('k5$ugroup$u4'(sK116,sK121)) ),
inference(resolution,[status(thm)],[c80,d18]) ).
cnf(d20,plain,
( ~ 'l1$ugroup$u1'(sK116)
| 'v1$ugroup$u1'('k5$ugroup$u4'(sK116,sK121)) ),
inference(resolution,[status(thm)],[c81,d19]) ).
cnf(d21,plain,
'v1$ugroup$u1'('k5$ugroup$u4'(sK116,sK121)),
inference(resolution,[status(thm)],[c82,d20]) ).
cnf(d22,plain,
( ~ 'v1$ugroup$u1'('k8$ugroup$u4'(sK116,sK118,sK119))
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[d21,d16]) ).
cnf(d23,plain,
( ~ 'v3$ugroup$u1'(sK116)
| ~ 'm1$ugroup$u2'(sK118,sK116)
| ~ 'm1$ugroup$u2'(sK119,sK116)
| ~ 'v4$ugroup$u1'(sK116)
| 'v3$ustruct$u0'(sK116)
| ~ 'l1$ugroup$u1'(sK116)
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[d22,c68]) ).
cnf(d24,plain,
( ~ 'v3$ugroup$u1'(sK116)
| ~ 'm1$ugroup$u2'(sK119,sK116)
| ~ 'm1$ugroup$u2'(sK118,sK116)
| ~ 'v4$ugroup$u1'(sK116)
| ~ 'l1$ugroup$u1'(sK116)
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[c79,d23]) ).
cnf(d25,plain,
( ~ 'm1$ugroup$u2'(sK119,sK116)
| ~ 'm1$ugroup$u2'(sK118,sK116)
| ~ 'v4$ugroup$u1'(sK116)
| ~ 'l1$ugroup$u1'(sK116)
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[c80,d24]) ).
cnf(d26,plain,
( ~ 'm1$ugroup$u2'(sK119,sK116)
| ~ 'm1$ugroup$u2'(sK118,sK116)
| ~ 'l1$ugroup$u1'(sK116)
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[c81,d25]) ).
cnf(d27,plain,
( ~ 'm1$ugroup$u2'(sK119,sK116)
| ~ 'm1$ugroup$u2'(sK118,sK116)
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[c82,d26]) ).
cnf(d28,plain,
( ~ 'm1$ugroup$u2'(sK119,sK116)
| 'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121) ),
inference(resolution,[status(thm)],[c87,d27]) ).
cnf(d29,plain,
'k8$ugroup$u4'(sK116,sK118,sK119) = 'k5$ugroup$u4'(sK116,sK121),
inference(resolution,[status(thm)],[c88,d28]) ).
cnf(d30,plain,
'm1$urelset$u1'(sK120,'u1$ustruct$u0'(sK116),'u1$ustruct$u0'(sK117)),
inference(resolution,[status(thm)],[c61,c91]) ).
cnf(d31,plain,
( ~ 'v1$ufunct$u2'(sK120,'u1$ustruct$u0'(sK116),'u1$ustruct$u0'(sK117))
| ~ 'v1$ufunct$u1'(sK120)
| 'k2$ufunct$u2'('u1$ustruct$u0'(sK116),'u1$ustruct$u0'(sK117),sK120,X0) = 'k9$urelat$u1'(sK120,X0) ),
inference(resolution,[status(thm)],[d30,c60]) ).
cnf(d32,plain,
( ~ 'v1$ufunct$u2'(sK120,'u1$ustruct$u0'(sK116),'u1$ustruct$u0'(sK117))
| 'k2$ufunct$u2'('u1$ustruct$u0'(sK116),'u1$ustruct$u0'(sK117),sK120,X0) = 'k9$urelat$u1'(sK120,X0) ),
inference(resolution,[status(thm)],[c89,d31]) ).
cnf(d33,plain,
'k2$ufunct$u2'('u1$ustruct$u0'(sK116),'u1$ustruct$u0'(sK117),sK120,X0) = 'k9$urelat$u1'(sK120,X0),
inference(resolution,[status(thm)],[c90,d32]) ).
cnf(d34,plain,
'k9$urelat$u1'(sK120,'u1$ustruct$u0'('k8$ugroup$u4'(sK116,sK118,sK119))) != 'k2$ufunct$u2'('u1$ustruct$u0'(sK116),'u1$ustruct$u0'(sK117),sK120,'u1$ustruct$u0'('k5$ugroup$u4'(sK116,sK121))),
inference(demodulation,[status(thm)],[c94,d33]) ).
cnf(d35,plain,
'k9$urelat$u1'(sK120,'u1$ustruct$u0'('k8$ugroup$u4'(sK116,sK118,sK119))) != 'k9$urelat$u1'(sK120,'u1$ustruct$u0'('k5$ugroup$u4'(sK116,sK121))),
inference(demodulation,[status(thm)],[d34,d33]) ).
cnf(d36,plain,
'k9$urelat$u1'(sK120,'u1$ustruct$u0'('k5$ugroup$u4'(sK116,sK121))) != 'k9$urelat$u1'(sK120,'u1$ustruct$u0'('k5$ugroup$u4'(sK116,sK121))),
inference(demodulation,[status(thm)],[d35,d29]) ).
cnf(d37,plain,
$false,
inference(equality_resolution,[status(thm)],[d36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP640+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 15:21:13 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.44/2.49 % SZS status Theorem for theBenchmark.p
% 13.44/2.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------