%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP644+2 : 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 : n006.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 07:24:19 AM UTC 2026
% Result : Theorem 102.66s 15.01s
% Output : CNFRefutation 102.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 79 ( 20 unt; 0 def)
% Number of atoms : 337 ( 14 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 443 ( 185 ~; 206 |; 30 &)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k1_latsubgr,axiom,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ( 'm2$urelset$u1'('k1$ulatsubgr'(X0),'k1$ugroup$u3'(X0),'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
& 'v1$ufunct$u2'('k1$ulatsubgr'(X0),'k1$ugroup$u3'(X0),'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
& 'v1$ufunct$u1'('k1$ulatsubgr'(X0)) ) ) ).
fof(d1_latsubgr,axiom,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( ( 'm2$urelset$u1'(X1,'k1$ugroup$u3'(X0),'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
& 'v1$ufunct$u2'(X1,'k1$ugroup$u3'(X0),'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
& 'v1$ufunct$u1'(X1) )
=> ( X1 = 'k1$ulatsubgr'(X0)
<=> ! [X2] :
( ( 'm1$ugroup$u2'(X2,X0)
& 'v1$ugroup$u1'(X2) )
=> 'k1$ufunct$u1'(X1,X2) = 'u1$ustruct$u0'(X2) ) ) ) ) ).
fof(t18_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)
& 'v1$ugroup$u1'(X1) )
=> ! [X2] :
( 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X0))
=> ( 'r2$uhidden'(X2,'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1))
<=> 'r1$urlvect$u1'(X1,X2) ) ) ) ) ).
fof(dt_k3_group_1,axiom,
! [X0,X1] :
( ( 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
& 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> 'm1$usubset$u1'('k3$ugroup$u1'(X0,X1),'u1$ustruct$u0'(X0)) ) ).
fof(t60_group_2,axiom,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
=> ! [X2] :
( 'm1$ugroup$u2'(X2,X0)
=> ( 'r1$urlvect$u1'(X2,X1)
=> 'r1$urlvect$u1'(X2,'k3$ugroup$u1'(X0,X1)) ) ) ) ) ).
fof(t22_latsubgr,conjecture,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( ( 'm1$ugroup$u2'(X1,X0)
& 'v1$ugroup$u1'(X1) )
=> ! [X2] :
( 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X0))
=> ( 'r2$uhidden'(X2,'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1))
=> 'r2$uhidden'('k3$ugroup$u1'(X0,X2),'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1)) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( ( 'm1$ugroup$u2'(X1,X0)
& 'v1$ugroup$u1'(X1) )
=> ! [X2] :
( 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X0))
=> ( 'r2$uhidden'(X2,'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1))
=> 'r2$uhidden'('k3$ugroup$u1'(X0,X2),'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1)) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t22_latsubgr]) ).
cnf(c0,plain,
( ~ 'l1$ugroup$u1'(X0)
| ~ 'v3$ugroup$u1'(X0)
| 'v1$ufunct$u1'('k1$ulatsubgr'(X0))
| 'v3$ustruct$u0'(X0)
| ~ 'v4$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[dt_k1_latsubgr]) ).
cnf(c1,plain,
( ~ 'l1$ugroup$u1'(X0)
| ~ 'v3$ugroup$u1'(X0)
| 'm2$urelset$u1'('k1$ulatsubgr'(X0),'k1$ugroup$u3'(X0),'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
| 'v3$ustruct$u0'(X0)
| ~ 'v4$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[dt_k1_latsubgr]) ).
cnf(c2,plain,
( 'v1$ufunct$u2'('k1$ulatsubgr'(X0),'k1$ugroup$u3'(X0),'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
| ~ 'l1$ugroup$u1'(X0)
| ~ 'v3$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'v4$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[dt_k1_latsubgr]) ).
cnf(c3,plain,
( 'u1$ustruct$u0'(X2) = 'k1$ufunct$u1'(X0,X2)
| ~ 'l1$ugroup$u1'(X1)
| ~ 'v1$ufunct$u1'(X0)
| 'v3$ustruct$u0'(X1)
| ~ 'm2$urelset$u1'(X0,'k1$ugroup$u3'(X1),'k1$uzfmisc$u1'('u1$ustruct$u0'(X1)))
| ~ 'v1$ugroup$u1'(X2)
| ~ 'v3$ugroup$u1'(X1)
| 'k1$ulatsubgr'(X1) != X0
| ~ 'v4$ugroup$u1'(X1)
| ~ 'm1$ugroup$u2'(X2,X1)
| ~ 'v1$ufunct$u2'(X0,'k1$ugroup$u3'(X1),'k1$uzfmisc$u1'('u1$ustruct$u0'(X1))) ),
inference(clausification,[status(esa)],[d1_latsubgr]) ).
cnf(c7,plain,
( 'r1$urlvect$u1'(X2,X1)
| ~ 'v1$ugroup$u1'(X2)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'r2$uhidden'(X1,'k1$ufunct$u1'('k1$ulatsubgr'(X0),X2))
| ~ 'l1$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X2,X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
| ~ 'v3$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[t18_latsubgr]) ).
cnf(c8,plain,
( ~ 'l1$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| 'r2$uhidden'(X2,'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1))
| 'v3$ustruct$u0'(X0)
| ~ 'v1$ugroup$u1'(X1)
| ~ 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X0))
| ~ 'v3$ugroup$u1'(X0)
| ~ 'r1$urlvect$u1'(X1,X2)
| ~ 'v4$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[t18_latsubgr]) ).
cnf(c99,plain,
( ~ 'v4$ugroup$u1'(X1)
| ~ 'v3$ugroup$u1'(X1)
| 'm1$usubset$u1'('k3$ugroup$u1'(X1,X0),'u1$ustruct$u0'(X1))
| 'v3$ustruct$u0'(X1)
| ~ 'l1$ugroup$u1'(X1)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(X1)) ),
inference(clausification,[status(esa)],[dt_k3_group_1]) ).
cnf(c111,plain,
( ~ 'l1$ugroup$u1'(X0)
| ~ 'r1$urlvect$u1'(X1,X2)
| ~ 'v4$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| 'r1$urlvect$u1'(X1,'k3$ugroup$u1'(X0,X2))
| ~ 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X0))
| ~ 'm1$ugroup$u2'(X1,X0)
| ~ 'v3$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[t60_group_2]) ).
cnf(c150,plain,
'v3$ugroup$u1'(sK241),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c151,plain,
'l1$ugroup$u1'(sK241),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c152,plain,
'v4$ugroup$u1'(sK241),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c153,plain,
~ 'v3$ustruct$u0'(sK241),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c154,plain,
'm1$ugroup$u2'(sK242,sK241),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c155,plain,
'v1$ugroup$u1'(sK242),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c156,plain,
'm1$usubset$u1'(sK243,'u1$ustruct$u0'(sK241)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c157,plain,
~ 'r2$uhidden'('k3$ugroup$u1'(sK241,sK243),'k1$ufunct$u1'('k1$ulatsubgr'(sK241),sK242)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c158,plain,
'r2$uhidden'(sK243,'k1$ufunct$u1'('k1$ulatsubgr'(sK241),sK242)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'm1$usubset$u1'('k3$ugroup$u1'(sK241,X0),'u1$ustruct$u0'(sK241))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK241))
| 'v3$ustruct$u0'(sK241)
| ~ 'v4$ugroup$u1'(sK241)
| ~ 'l1$ugroup$u1'(sK241) ),
inference(resolution,[status(thm)],[c99,c150]) ).
cnf(d1,plain,
( 'm1$usubset$u1'('k3$ugroup$u1'(sK241,X0),'u1$ustruct$u0'(sK241))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK241))
| 'v3$ustruct$u0'(sK241)
| ~ 'v4$ugroup$u1'(sK241) ),
inference(resolution,[status(thm)],[c151,d0]) ).
cnf(d2,plain,
( 'm1$usubset$u1'('k3$ugroup$u1'(sK241,X0),'u1$ustruct$u0'(sK241))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK241))
| 'v3$ustruct$u0'(sK241) ),
inference(resolution,[status(thm)],[c152,d1]) ).
cnf(d3,plain,
( 'm1$usubset$u1'('k3$ugroup$u1'(sK241,X0),'u1$ustruct$u0'(sK241))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK241)) ),
inference(resolution,[status(thm)],[c153,d2]) ).
cnf(d4,plain,
'm1$usubset$u1'('k3$ugroup$u1'(sK241,sK243),'u1$ustruct$u0'(sK241)),
inference(resolution,[status(thm)],[d3,c156]) ).
cnf(d5,plain,
( ~ 'm1$ugroup$u2'(X0,X1)
| ~ 'v1$ugroup$u1'(X0)
| ~ 'v1$ufunct$u2'('k1$ulatsubgr'(X1),'k1$ugroup$u3'(X1),'k1$uzfmisc$u1'('u1$ustruct$u0'(X1)))
| ~ 'm2$urelset$u1'('k1$ulatsubgr'(X1),'k1$ugroup$u3'(X1),'k1$uzfmisc$u1'('u1$ustruct$u0'(X1)))
| 'v3$ustruct$u0'(X1)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(X1))
| ~ 'v4$ugroup$u1'(X1)
| ~ 'l1$ugroup$u1'(X1)
| ~ 'v3$ugroup$u1'(X1)
| 'u1$ustruct$u0'(X0) = 'k1$ufunct$u1'('k1$ulatsubgr'(X1),X0) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(d6,plain,
( ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0)
| ~ 'v1$ufunct$u2'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| ~ 'm2$urelset$u1'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| 'v3$ustruct$u0'(sK241)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK241))
| ~ 'v4$ugroup$u1'(sK241)
| ~ 'l1$ugroup$u1'(sK241)
| 'u1$ustruct$u0'(X0) = 'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0) ),
inference(resolution,[status(thm)],[d5,c150]) ).
cnf(d7,plain,
( ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0)
| ~ 'v1$ufunct$u2'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| ~ 'm2$urelset$u1'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| 'v3$ustruct$u0'(sK241)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK241))
| ~ 'v4$ugroup$u1'(sK241)
| 'u1$ustruct$u0'(X0) = 'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0) ),
inference(resolution,[status(thm)],[c151,d6]) ).
cnf(d8,plain,
( ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0)
| ~ 'v1$ufunct$u2'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| ~ 'm2$urelset$u1'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| 'v3$ustruct$u0'(sK241)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK241))
| 'u1$ustruct$u0'(X0) = 'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0) ),
inference(resolution,[status(thm)],[c152,d7]) ).
cnf(d9,plain,
( ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0)
| ~ 'v1$ufunct$u2'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| ~ 'm2$urelset$u1'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK241))
| 'u1$ustruct$u0'(X0) = 'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0) ),
inference(resolution,[status(thm)],[c153,d8]) ).
cnf(d10,plain,
( 'v3$ustruct$u0'(sK241)
| 'v1$ufunct$u1'('k1$ulatsubgr'(sK241))
| ~ 'v4$ugroup$u1'(sK241)
| ~ 'l1$ugroup$u1'(sK241) ),
inference(resolution,[status(thm)],[c0,c150]) ).
cnf(d11,plain,
( 'v3$ustruct$u0'(sK241)
| 'v1$ufunct$u1'('k1$ulatsubgr'(sK241))
| ~ 'v4$ugroup$u1'(sK241) ),
inference(resolution,[status(thm)],[c151,d10]) ).
cnf(d12,plain,
( 'v3$ustruct$u0'(sK241)
| 'v1$ufunct$u1'('k1$ulatsubgr'(sK241)) ),
inference(resolution,[status(thm)],[c152,d11]) ).
cnf(d13,plain,
'v1$ufunct$u1'('k1$ulatsubgr'(sK241)),
inference(resolution,[status(thm)],[c153,d12]) ).
cnf(d14,plain,
( ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0)
| ~ 'v1$ufunct$u2'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| ~ 'm2$urelset$u1'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| 'u1$ustruct$u0'(X0) = 'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0) ),
inference(resolution,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
( 'm2$urelset$u1'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| 'v3$ustruct$u0'(sK241)
| ~ 'v4$ugroup$u1'(sK241)
| ~ 'l1$ugroup$u1'(sK241) ),
inference(resolution,[status(thm)],[c1,c150]) ).
cnf(d16,plain,
( 'm2$urelset$u1'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| 'v3$ustruct$u0'(sK241)
| ~ 'v4$ugroup$u1'(sK241) ),
inference(resolution,[status(thm)],[c151,d15]) ).
cnf(d17,plain,
( 'm2$urelset$u1'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| 'v3$ustruct$u0'(sK241) ),
inference(resolution,[status(thm)],[c152,d16]) ).
cnf(d18,plain,
'm2$urelset$u1'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241))),
inference(resolution,[status(thm)],[c153,d17]) ).
cnf(d19,plain,
( ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0)
| ~ 'v1$ufunct$u2'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| 'u1$ustruct$u0'(X0) = 'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0) ),
inference(resolution,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
( 'v1$ufunct$u2'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| 'v3$ustruct$u0'(sK241)
| ~ 'v4$ugroup$u1'(sK241)
| ~ 'l1$ugroup$u1'(sK241) ),
inference(resolution,[status(thm)],[c2,c150]) ).
cnf(d21,plain,
( 'v1$ufunct$u2'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| 'v3$ustruct$u0'(sK241)
| ~ 'v4$ugroup$u1'(sK241) ),
inference(resolution,[status(thm)],[c151,d20]) ).
cnf(d22,plain,
( 'v1$ufunct$u2'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241)))
| 'v3$ustruct$u0'(sK241) ),
inference(resolution,[status(thm)],[c152,d21]) ).
cnf(d23,plain,
'v1$ufunct$u2'('k1$ulatsubgr'(sK241),'k1$ugroup$u3'(sK241),'k1$uzfmisc$u1'('u1$ustruct$u0'(sK241))),
inference(resolution,[status(thm)],[c153,d22]) ).
cnf(d24,plain,
( ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0)
| 'u1$ustruct$u0'(X0) = 'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0) ),
inference(resolution,[status(thm)],[d23,d19]) ).
cnf(d25,plain,
( ~ 'm1$ugroup$u2'(sK242,sK241)
| 'u1$ustruct$u0'(sK242) = 'k1$ufunct$u1'('k1$ulatsubgr'(sK241),sK242) ),
inference(resolution,[status(thm)],[d24,c155]) ).
cnf(d26,plain,
'u1$ustruct$u0'(sK242) = 'k1$ufunct$u1'('k1$ulatsubgr'(sK241),sK242),
inference(resolution,[status(thm)],[c154,d25]) ).
cnf(d27,plain,
( ~ 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK241))
| 'r2$uhidden'(X1,'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0))
| ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(sK241)
| ~ 'v4$ugroup$u1'(sK241)
| ~ 'l1$ugroup$u1'(sK241) ),
inference(resolution,[status(thm)],[c8,c150]) ).
cnf(d28,plain,
( ~ 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK241))
| 'r2$uhidden'(X1,'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0))
| ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(sK241)
| ~ 'v4$ugroup$u1'(sK241) ),
inference(resolution,[status(thm)],[c151,d27]) ).
cnf(d29,plain,
( ~ 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK241))
| 'r2$uhidden'(X1,'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0))
| ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(sK241) ),
inference(resolution,[status(thm)],[c152,d28]) ).
cnf(d30,plain,
( ~ 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK241))
| 'r2$uhidden'(X1,'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0))
| ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0) ),
inference(resolution,[status(thm)],[c153,d29]) ).
cnf(d31,plain,
( ~ 'r1$urlvect$u1'(sK242,X0)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK241))
| 'r2$uhidden'(X0,'k1$ufunct$u1'('k1$ulatsubgr'(sK241),sK242))
| ~ 'm1$ugroup$u2'(sK242,sK241) ),
inference(resolution,[status(thm)],[d30,c155]) ).
cnf(d32,plain,
( ~ 'r1$urlvect$u1'(sK242,X0)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK241))
| 'r2$uhidden'(X0,'u1$ustruct$u0'(sK242))
| ~ 'm1$ugroup$u2'(sK242,sK241) ),
inference(demodulation,[status(thm)],[d31,d26]) ).
cnf(d33,plain,
( ~ 'r1$urlvect$u1'(sK242,X0)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK241))
| 'r2$uhidden'(X0,'u1$ustruct$u0'(sK242)) ),
inference(resolution,[status(thm)],[c154,d32]) ).
cnf(d34,plain,
( ~ 'r1$urlvect$u1'(sK242,'k3$ugroup$u1'(sK241,sK243))
| 'r2$uhidden'('k3$ugroup$u1'(sK241,sK243),'u1$ustruct$u0'(sK242)) ),
inference(resolution,[status(thm)],[d33,d4]) ).
cnf(d35,plain,
~ 'r2$uhidden'('k3$ugroup$u1'(sK241,sK243),'u1$ustruct$u0'(sK242)),
inference(demodulation,[status(thm)],[c157,d26]) ).
cnf(d36,plain,
~ 'r1$urlvect$u1'(sK242,'k3$ugroup$u1'(sK241,sK243)),
inference(resolution,[status(thm)],[d35,d34]) ).
cnf(d37,plain,
( 'r1$urlvect$u1'(X0,'k3$ugroup$u1'(sK241,X1))
| ~ 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK241))
| ~ 'm1$ugroup$u2'(X0,sK241)
| 'v3$ustruct$u0'(sK241)
| ~ 'v4$ugroup$u1'(sK241)
| ~ 'l1$ugroup$u1'(sK241) ),
inference(resolution,[status(thm)],[c111,c150]) ).
cnf(d38,plain,
( 'r1$urlvect$u1'(X0,'k3$ugroup$u1'(sK241,X1))
| ~ 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK241))
| ~ 'm1$ugroup$u2'(X0,sK241)
| 'v3$ustruct$u0'(sK241)
| ~ 'v4$ugroup$u1'(sK241) ),
inference(resolution,[status(thm)],[c151,d37]) ).
cnf(d39,plain,
( 'r1$urlvect$u1'(X0,'k3$ugroup$u1'(sK241,X1))
| ~ 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK241))
| ~ 'm1$ugroup$u2'(X0,sK241)
| 'v3$ustruct$u0'(sK241) ),
inference(resolution,[status(thm)],[c152,d38]) ).
cnf(d40,plain,
( 'r1$urlvect$u1'(X0,'k3$ugroup$u1'(sK241,X1))
| ~ 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK241))
| ~ 'm1$ugroup$u2'(X0,sK241) ),
inference(resolution,[status(thm)],[c153,d39]) ).
cnf(d41,plain,
( 'r1$urlvect$u1'(sK242,'k3$ugroup$u1'(sK241,X0))
| ~ 'r1$urlvect$u1'(sK242,X0)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK241)) ),
inference(resolution,[status(thm)],[d40,c154]) ).
cnf(d42,plain,
( 'r1$urlvect$u1'(sK242,'k3$ugroup$u1'(sK241,sK243))
| ~ 'r1$urlvect$u1'(sK242,sK243) ),
inference(resolution,[status(thm)],[d41,c156]) ).
cnf(d43,plain,
( 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK241))
| ~ 'r2$uhidden'(X1,'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0))
| ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(sK241)
| ~ 'v4$ugroup$u1'(sK241)
| ~ 'l1$ugroup$u1'(sK241) ),
inference(resolution,[status(thm)],[c7,c150]) ).
cnf(d44,plain,
( 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK241))
| ~ 'r2$uhidden'(X1,'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0))
| ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(sK241)
| ~ 'v4$ugroup$u1'(sK241) ),
inference(resolution,[status(thm)],[c151,d43]) ).
cnf(d45,plain,
( 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK241))
| ~ 'r2$uhidden'(X1,'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0))
| ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(sK241) ),
inference(resolution,[status(thm)],[c152,d44]) ).
cnf(d46,plain,
( 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK241))
| ~ 'r2$uhidden'(X1,'k1$ufunct$u1'('k1$ulatsubgr'(sK241),X0))
| ~ 'm1$ugroup$u2'(X0,sK241)
| ~ 'v1$ugroup$u1'(X0) ),
inference(resolution,[status(thm)],[c153,d45]) ).
cnf(d47,plain,
( 'r1$urlvect$u1'(sK242,X0)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK241))
| ~ 'r2$uhidden'(X0,'k1$ufunct$u1'('k1$ulatsubgr'(sK241),sK242))
| ~ 'm1$ugroup$u2'(sK242,sK241) ),
inference(resolution,[status(thm)],[d46,c155]) ).
cnf(d48,plain,
( 'r1$urlvect$u1'(sK242,X0)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK241))
| ~ 'r2$uhidden'(X0,'u1$ustruct$u0'(sK242))
| ~ 'm1$ugroup$u2'(sK242,sK241) ),
inference(demodulation,[status(thm)],[d47,d26]) ).
cnf(d49,plain,
( 'r1$urlvect$u1'(sK242,X0)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK241))
| ~ 'r2$uhidden'(X0,'u1$ustruct$u0'(sK242)) ),
inference(resolution,[status(thm)],[c154,d48]) ).
cnf(d50,plain,
'r2$uhidden'(sK243,'u1$ustruct$u0'(sK242)),
inference(demodulation,[status(thm)],[c158,d26]) ).
cnf(d51,plain,
( 'r1$urlvect$u1'(sK242,sK243)
| ~ 'm1$usubset$u1'(sK243,'u1$ustruct$u0'(sK241)) ),
inference(resolution,[status(thm)],[d50,d49]) ).
cnf(d52,plain,
'r1$urlvect$u1'(sK242,sK243),
inference(resolution,[status(thm)],[c156,d51]) ).
cnf(d53,plain,
'r1$urlvect$u1'(sK242,'k3$ugroup$u1'(sK241,sK243)),
inference(resolution,[status(thm)],[d52,d42]) ).
cnf(d54,plain,
$false,
inference(resolution,[status(thm)],[d53,d36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP644+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n006.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % 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 15:20:41 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 102.66/15.01 % SZS status Theorem for theBenchmark.p
% 102.66/15.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------