%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP645+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 : n018.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 31.79s 4.87s
% Output : CNFRefutation 31.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 5
% Syntax : Number of formulae : 59 ( 13 unt; 0 def)
% Number of atoms : 298 ( 26 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 456 ( 217 ~; 192 |; 32 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 37 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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$u0'(X2) ) ) ) ) ).
fof(dt_k1_latsubgr,axiom,
! [X0] :
( ( 'l1$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(dt_k9_group_2,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'('k9$ugroup$u2'(X0,X1,X2),X0)
& 'v1$ugroup$u1'('k9$ugroup$u2'(X0,X1,X2)) ) ) ).
fof(t23_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$ugroup$u2'(X2,X0)
& 'v1$ugroup$u1'(X2) )
=> 'u1$ustruct$u0'('k9$ugroup$u2'(X0,X1,X2)) = 'k3$uxboole$u0'('k1$ufunct$u1'('k1$ulatsubgr'(X0),X1),'k1$ufunct$u1'('k1$ulatsubgr'(X0),X2)) ) ) ) ).
fof(t24_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$ugroup$u2'(X2,X0)
& 'v1$ugroup$u1'(X2) )
=> 'k1$ufunct$u1'('k1$ulatsubgr'(X0),'k9$ugroup$u2'(X0,X1,X2)) = 'k3$uxboole$u0'('k1$ufunct$u1'('k1$ulatsubgr'(X0),X1),'k1$ufunct$u1'('k1$ulatsubgr'(X0),X2)) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( ( 'm1$ugroup$u2'(X1,X0)
& 'v1$ugroup$u1'(X1) )
=> ! [X2] :
( ( 'm1$ugroup$u2'(X2,X0)
& 'v1$ugroup$u1'(X2) )
=> 'k1$ufunct$u1'('k1$ulatsubgr'(X0),'k9$ugroup$u2'(X0,X1,X2)) = 'k3$uxboole$u0'('k1$ufunct$u1'('k1$ulatsubgr'(X0),X1),'k1$ufunct$u1'('k1$ulatsubgr'(X0),X2)) ) ) ),
inference(negate_conjecture,[status(cth)],[t24_latsubgr]) ).
cnf(c14,plain,
( ~ 'm2$urelset$u1'(X2,'k1$ugroup$u3'(X1),'k1$uzfmisc$u1'('u1$ustruct$u0'(X1)))
| X2 != 'k1$ulatsubgr'(X1)
| 'k1$ufunct$u1'(X2,X0) = 'u1$ustruct$u0'(X0)
| ~ 'v4$ugroup$u1'(X1)
| ~ 'v1$ufunct$u2'(X2,'k1$ugroup$u3'(X1),'k1$uzfmisc$u1'('u1$ustruct$u0'(X1)))
| 'v3$ustruct$u0'(X1)
| ~ 'v1$ufunct$u1'(X2)
| ~ 'v3$ugroup$u1'(X1)
| ~ 'l1$ugroup$u1'(X1)
| ~ 'v1$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X0,X1) ),
inference(clausification,[status(esa)],[d1_latsubgr]) ).
cnf(c20,plain,
( 'v1$ufunct$u1'('k1$ulatsubgr'(X0))
| ~ 'v4$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'v3$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[dt_k1_latsubgr]) ).
cnf(c21,plain,
( ~ 'l1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| 'v1$ufunct$u2'('k1$ulatsubgr'(X0),'k1$ugroup$u3'(X0),'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[dt_k1_latsubgr]) ).
cnf(c22,plain,
( ~ 'l1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| 'm2$urelset$u1'('k1$ulatsubgr'(X0),'k1$ugroup$u3'(X0),'k1$uzfmisc$u1'('u1$ustruct$u0'(X0))) ),
inference(clausification,[status(esa)],[dt_k1_latsubgr]) ).
cnf(c25,plain,
( ~ 'v3$ugroup$u1'(X1)
| ~ 'l1$ugroup$u1'(X1)
| 'v1$ugroup$u1'('k9$ugroup$u2'(X1,X2,X0))
| ~ 'v4$ugroup$u1'(X1)
| ~ 'm1$ugroup$u2'(X2,X1)
| 'v3$ustruct$u0'(X1)
| ~ 'm1$ugroup$u2'(X0,X1) ),
inference(clausification,[status(esa)],[dt_k9_group_2]) ).
cnf(c26,plain,
( ~ 'v3$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$ugroup$u2'(X2,X0)
| 'm1$ugroup$u2'('k9$ugroup$u2'(X0,X1,X2),X0) ),
inference(clausification,[status(esa)],[dt_k9_group_2]) ).
cnf(c71,plain,
( 'u1$ustruct$u0'('k9$ugroup$u2'(X1,X0,X2)) = 'k3$uxboole$u0'('k1$ufunct$u1'('k1$ulatsubgr'(X1),X0),'k1$ufunct$u1'('k1$ulatsubgr'(X1),X2))
| ~ 'v1$ugroup$u1'(X2)
| ~ 'l1$ugroup$u1'(X1)
| ~ 'm1$ugroup$u2'(X2,X1)
| 'v3$ustruct$u0'(X1)
| ~ 'v3$ugroup$u1'(X1)
| ~ 'v4$ugroup$u1'(X1)
| ~ 'v1$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X0,X1) ),
inference(clausification,[status(esa)],[t23_latsubgr]) ).
cnf(c81,plain,
~ 'v3$ustruct$u0'(sK107),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c82,plain,
'v3$ugroup$u1'(sK107),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c83,plain,
'v4$ugroup$u1'(sK107),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c84,plain,
'l1$ugroup$u1'(sK107),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c85,plain,
'v1$ugroup$u1'(sK108),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c86,plain,
'm1$ugroup$u2'(sK108,sK107),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c87,plain,
'v1$ugroup$u1'(sK109),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c88,plain,
'm1$ugroup$u2'(sK109,sK107),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c89,plain,
'k1$ufunct$u1'('k1$ulatsubgr'(sK107),'k9$ugroup$u2'(sK107,sK108,sK109)) != 'k3$uxboole$u0'('k1$ufunct$u1'('k1$ulatsubgr'(sK107),sK108),'k1$ufunct$u1'('k1$ulatsubgr'(sK107),sK109)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'v3$ustruct$u0'(sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'v3$ugroup$u1'(sK107)
| ~ 'v4$ugroup$u1'(sK107)
| ~ 'v1$ugroup$u1'(sK108)
| ~ 'v1$ugroup$u1'(sK109)
| ~ 'l1$ugroup$u1'(sK107)
| 'k1$ufunct$u1'('k1$ulatsubgr'(sK107),'k9$ugroup$u2'(sK107,sK108,sK109)) != 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(superposition,[status(thm)],[c71,c89]) ).
cnf(d1,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v3$ugroup$u1'(sK107)
| ~ 'v4$ugroup$u1'(sK107)
| ~ 'v1$ugroup$u1'(sK109)
| ~ 'v1$ugroup$u1'(sK108)
| ~ 'l1$ugroup$u1'(sK107)
| 'k1$ufunct$u1'('k1$ulatsubgr'(sK107),'k9$ugroup$u2'(sK107,sK108,sK109)) != 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[c81,d0]) ).
cnf(d2,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v4$ugroup$u1'(sK107)
| ~ 'v1$ugroup$u1'(sK109)
| ~ 'v1$ugroup$u1'(sK108)
| ~ 'l1$ugroup$u1'(sK107)
| 'k1$ufunct$u1'('k1$ulatsubgr'(sK107),'k9$ugroup$u2'(sK107,sK108,sK109)) != 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[c82,d1]) ).
cnf(d3,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v1$ugroup$u1'(sK109)
| ~ 'v1$ugroup$u1'(sK108)
| ~ 'l1$ugroup$u1'(sK107)
| 'k1$ufunct$u1'('k1$ulatsubgr'(sK107),'k9$ugroup$u2'(sK107,sK108,sK109)) != 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[c83,d2]) ).
cnf(d4,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v1$ugroup$u1'(sK109)
| ~ 'v1$ugroup$u1'(sK108)
| 'k1$ufunct$u1'('k1$ulatsubgr'(sK107),'k9$ugroup$u2'(sK107,sK108,sK109)) != 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[c84,d3]) ).
cnf(d5,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v1$ugroup$u1'(sK109)
| 'k1$ufunct$u1'('k1$ulatsubgr'(sK107),'k9$ugroup$u2'(sK107,sK108,sK109)) != 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[c85,d4]) ).
cnf(d6,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| 'k1$ufunct$u1'('k1$ulatsubgr'(sK107),'k9$ugroup$u2'(sK107,sK108,sK109)) != 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[c87,d5]) ).
cnf(d7,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| 'k1$ufunct$u1'('k1$ulatsubgr'(sK107),'k9$ugroup$u2'(sK107,sK108,sK109)) != 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[c86,d6]) ).
cnf(d8,plain,
'k1$ufunct$u1'('k1$ulatsubgr'(sK107),'k9$ugroup$u2'(sK107,sK108,sK109)) != 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)),
inference(resolution,[status(thm)],[c88,d7]) ).
cnf(d9,plain,
( ~ 'm2$urelset$u1'('k1$ulatsubgr'(X0),'k1$ugroup$u3'(X0),'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
| 'v3$ustruct$u0'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'v1$ufunct$u2'('k1$ulatsubgr'(X0),'k1$ugroup$u3'(X0),'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(X0))
| ~ 'v1$ugroup$u1'(X1)
| ~ 'l1$ugroup$u1'(X0)
| 'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1) = 'u1$ustruct$u0'(X1) ),
inference(equality_resolution,[status(thm)],[c14]) ).
cnf(d10,plain,
( 'v3$ustruct$u0'(X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'v1$ufunct$u2'('k1$ulatsubgr'(X0),'k1$ugroup$u3'(X0),'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(X0))
| ~ 'v1$ugroup$u1'(X1)
| ~ 'l1$ugroup$u1'(X0)
| 'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1) = 'u1$ustruct$u0'(X1) ),
inference(resolution,[status(thm)],[d9,c22]) ).
cnf(d11,plain,
( 'v3$ustruct$u0'(X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(X0))
| ~ 'v1$ugroup$u1'(X1)
| ~ 'l1$ugroup$u1'(X0)
| 'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1) = 'u1$ustruct$u0'(X1) ),
inference(resolution,[status(thm)],[d10,c21]) ).
cnf(d12,plain,
( 'v3$ustruct$u0'(sK107)
| ~ 'm1$ugroup$u2'('k9$ugroup$u2'(sK107,sK108,sK109),sK107)
| ~ 'v3$ugroup$u1'(sK107)
| ~ 'v4$ugroup$u1'(sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'v1$ugroup$u1'('k9$ugroup$u2'(sK107,sK108,sK109))
| ~ 'l1$ugroup$u1'(sK107)
| 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) != 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(superposition,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
( ~ 'm1$ugroup$u2'('k9$ugroup$u2'(sK107,sK108,sK109),sK107)
| ~ 'v3$ugroup$u1'(sK107)
| ~ 'v4$ugroup$u1'(sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'v1$ugroup$u1'('k9$ugroup$u2'(sK107,sK108,sK109))
| ~ 'l1$ugroup$u1'(sK107)
| 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) != 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[c81,d12]) ).
cnf(d14,plain,
( ~ 'm1$ugroup$u2'('k9$ugroup$u2'(sK107,sK108,sK109),sK107)
| ~ 'v4$ugroup$u1'(sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'v1$ugroup$u1'('k9$ugroup$u2'(sK107,sK108,sK109))
| ~ 'l1$ugroup$u1'(sK107)
| 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) != 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[c82,d13]) ).
cnf(d15,plain,
( ~ 'm1$ugroup$u2'('k9$ugroup$u2'(sK107,sK108,sK109),sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'v1$ugroup$u1'('k9$ugroup$u2'(sK107,sK108,sK109))
| ~ 'l1$ugroup$u1'(sK107)
| 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) != 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[c83,d14]) ).
cnf(d16,plain,
( ~ 'm1$ugroup$u2'('k9$ugroup$u2'(sK107,sK108,sK109),sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'v1$ugroup$u1'('k9$ugroup$u2'(sK107,sK108,sK109))
| 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) != 'u1$ustruct$u0'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[c84,d15]) ).
cnf(d17,plain,
( ~ 'm1$ugroup$u2'('k9$ugroup$u2'(sK107,sK108,sK109),sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'v1$ugroup$u1'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
( 'v3$ustruct$u0'(sK107)
| ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v3$ugroup$u1'(sK107)
| ~ 'v4$ugroup$u1'(sK107)
| ~ 'l1$ugroup$u1'(sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'v1$ugroup$u1'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[d17,c26]) ).
cnf(d19,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v3$ugroup$u1'(sK107)
| ~ 'v4$ugroup$u1'(sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'v1$ugroup$u1'('k9$ugroup$u2'(sK107,sK108,sK109))
| ~ 'l1$ugroup$u1'(sK107) ),
inference(resolution,[status(thm)],[c81,d18]) ).
cnf(d20,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v4$ugroup$u1'(sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'v1$ugroup$u1'('k9$ugroup$u2'(sK107,sK108,sK109))
| ~ 'l1$ugroup$u1'(sK107) ),
inference(resolution,[status(thm)],[c82,d19]) ).
cnf(d21,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'v1$ugroup$u1'('k9$ugroup$u2'(sK107,sK108,sK109))
| ~ 'l1$ugroup$u1'(sK107) ),
inference(resolution,[status(thm)],[c83,d20]) ).
cnf(d22,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'v1$ugroup$u1'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[c84,d21]) ).
cnf(d23,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'v1$ugroup$u1'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[c86,d22]) ).
cnf(d24,plain,
( ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'v1$ugroup$u1'('k9$ugroup$u2'(sK107,sK108,sK109)) ),
inference(resolution,[status(thm)],[c88,d23]) ).
cnf(d25,plain,
( 'v3$ustruct$u0'(sK107)
| ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v3$ugroup$u1'(sK107)
| ~ 'v4$ugroup$u1'(sK107)
| ~ 'l1$ugroup$u1'(sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107)) ),
inference(resolution,[status(thm)],[d24,c25]) ).
cnf(d26,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v3$ugroup$u1'(sK107)
| ~ 'v4$ugroup$u1'(sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'l1$ugroup$u1'(sK107) ),
inference(resolution,[status(thm)],[c81,d25]) ).
cnf(d27,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v4$ugroup$u1'(sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'l1$ugroup$u1'(sK107) ),
inference(resolution,[status(thm)],[c82,d26]) ).
cnf(d28,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107))
| ~ 'l1$ugroup$u1'(sK107) ),
inference(resolution,[status(thm)],[c83,d27]) ).
cnf(d29,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'm1$ugroup$u2'(sK108,sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107)) ),
inference(resolution,[status(thm)],[c84,d28]) ).
cnf(d30,plain,
( ~ 'm1$ugroup$u2'(sK109,sK107)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107)) ),
inference(resolution,[status(thm)],[c86,d29]) ).
cnf(d31,plain,
~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK107)),
inference(resolution,[status(thm)],[c88,d30]) ).
cnf(d32,plain,
( 'v3$ustruct$u0'(sK107)
| ~ 'v3$ugroup$u1'(sK107)
| ~ 'v4$ugroup$u1'(sK107)
| ~ 'l1$ugroup$u1'(sK107) ),
inference(resolution,[status(thm)],[d31,c20]) ).
cnf(d33,plain,
( ~ 'v3$ugroup$u1'(sK107)
| ~ 'v4$ugroup$u1'(sK107)
| ~ 'l1$ugroup$u1'(sK107) ),
inference(resolution,[status(thm)],[c81,d32]) ).
cnf(d34,plain,
( ~ 'v4$ugroup$u1'(sK107)
| ~ 'l1$ugroup$u1'(sK107) ),
inference(resolution,[status(thm)],[c82,d33]) ).
cnf(d35,plain,
~ 'l1$ugroup$u1'(sK107),
inference(resolution,[status(thm)],[c83,d34]) ).
cnf(d36,plain,
$false,
inference(resolution,[status(thm)],[c84,d35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP645+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 15:23:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.79/4.87 % SZS status Theorem for theBenchmark.p
% 31.79/4.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------