%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP641+4 : 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 : n012.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 37.94s 35.68s
% Output : CNFRefutation 37.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 134 ( 53 ~; 54 |; 16 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_k2_group_1,axiom,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> 'm1$usubset$u1'('k2$ugroup$u1'(X0),'u1$ustruct$u0'(X0)) ) ).
fof(t55_group_2,axiom,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( 'm1$ugroup$u2'(X1,X0)
=> 'r1$urlvect$u1'(X1,'k2$ugroup$u1'(X0)) ) ) ).
fof(t19_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) )
=> 'r2$uhidden'('k2$ugroup$u1'(X0),'k1$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) )
=> 'r2$uhidden'('k2$ugroup$u1'(X0),'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1)) ) ),
inference(negate_conjecture,[status(cth)],[t19_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(c112,plain,
( 'm1$usubset$u1'('k2$ugroup$u1'(X0),'u1$ustruct$u0'(X0))
| 'v3$ustruct$u0'(X0)
| ~ 'l1$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[dt_k2_group_1]) ).
cnf(c139,plain,
( ~ 'v3$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| 'r1$urlvect$u1'(X1,'k2$ugroup$u1'(X0))
| ~ 'l1$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[t55_group_2]) ).
cnf(c155,plain,
'v3$ugroup$u1'(sK183),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c156,plain,
'l1$ugroup$u1'(sK183),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c157,plain,
'v4$ugroup$u1'(sK183),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c158,plain,
~ 'v3$ustruct$u0'(sK183),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c159,plain,
'm1$ugroup$u2'(sK184,sK183),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c160,plain,
'v1$ugroup$u1'(sK184),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c161,plain,
~ 'r2$uhidden'('k2$ugroup$u1'(sK183),'k1$ufunct$u1'('k1$ulatsubgr'(sK183),sK184)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'r1$urlvect$u1'(X0,'k2$ugroup$u1'(sK183))
| ~ 'm1$ugroup$u2'(X0,sK183)
| 'v3$ustruct$u0'(sK183)
| ~ 'v4$ugroup$u1'(sK183)
| ~ 'l1$ugroup$u1'(sK183) ),
inference(resolution,[status(thm)],[c139,c155]) ).
cnf(d1,plain,
( 'r1$urlvect$u1'(X0,'k2$ugroup$u1'(sK183))
| ~ 'm1$ugroup$u2'(X0,sK183)
| 'v3$ustruct$u0'(sK183)
| ~ 'v4$ugroup$u1'(sK183) ),
inference(resolution,[status(thm)],[c156,d0]) ).
cnf(d2,plain,
( 'r1$urlvect$u1'(X0,'k2$ugroup$u1'(sK183))
| ~ 'm1$ugroup$u2'(X0,sK183)
| 'v3$ustruct$u0'(sK183) ),
inference(resolution,[status(thm)],[c157,d1]) ).
cnf(d3,plain,
( 'r1$urlvect$u1'(X0,'k2$ugroup$u1'(sK183))
| ~ 'm1$ugroup$u2'(X0,sK183) ),
inference(resolution,[status(thm)],[c158,d2]) ).
cnf(d4,plain,
'r1$urlvect$u1'(sK184,'k2$ugroup$u1'(sK183)),
inference(resolution,[status(thm)],[d3,c159]) ).
cnf(d5,plain,
( ~ 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK183))
| 'r2$uhidden'(X1,'k1$ufunct$u1'('k1$ulatsubgr'(sK183),X0))
| ~ 'm1$ugroup$u2'(X0,sK183)
| ~ 'v1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(sK183)
| ~ 'v4$ugroup$u1'(sK183)
| ~ 'l1$ugroup$u1'(sK183) ),
inference(resolution,[status(thm)],[c8,c155]) ).
cnf(d6,plain,
( ~ 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK183))
| 'r2$uhidden'(X1,'k1$ufunct$u1'('k1$ulatsubgr'(sK183),X0))
| ~ 'm1$ugroup$u2'(X0,sK183)
| ~ 'v1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(sK183)
| ~ 'v4$ugroup$u1'(sK183) ),
inference(resolution,[status(thm)],[c156,d5]) ).
cnf(d7,plain,
( ~ 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK183))
| 'r2$uhidden'(X1,'k1$ufunct$u1'('k1$ulatsubgr'(sK183),X0))
| ~ 'm1$ugroup$u2'(X0,sK183)
| ~ 'v1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(sK183) ),
inference(resolution,[status(thm)],[c157,d6]) ).
cnf(d8,plain,
( ~ 'r1$urlvect$u1'(X0,X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK183))
| 'r2$uhidden'(X1,'k1$ufunct$u1'('k1$ulatsubgr'(sK183),X0))
| ~ 'm1$ugroup$u2'(X0,sK183)
| ~ 'v1$ugroup$u1'(X0) ),
inference(resolution,[status(thm)],[c158,d7]) ).
cnf(d9,plain,
( ~ 'r1$urlvect$u1'(sK184,X0)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK183))
| 'r2$uhidden'(X0,'k1$ufunct$u1'('k1$ulatsubgr'(sK183),sK184))
| ~ 'm1$ugroup$u2'(sK184,sK183) ),
inference(resolution,[status(thm)],[d8,c160]) ).
cnf(d10,plain,
( ~ 'r1$urlvect$u1'(sK184,X0)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK183))
| 'r2$uhidden'(X0,'k1$ufunct$u1'('k1$ulatsubgr'(sK183),sK184)) ),
inference(resolution,[status(thm)],[c159,d9]) ).
cnf(d11,plain,
( 'm1$usubset$u1'('k2$ugroup$u1'(sK183),'u1$ustruct$u0'(sK183))
| 'v3$ustruct$u0'(sK183) ),
inference(resolution,[status(thm)],[c112,c156]) ).
cnf(d12,plain,
'm1$usubset$u1'('k2$ugroup$u1'(sK183),'u1$ustruct$u0'(sK183)),
inference(resolution,[status(thm)],[c158,d11]) ).
cnf(d13,plain,
( ~ 'r1$urlvect$u1'(sK184,'k2$ugroup$u1'(sK183))
| 'r2$uhidden'('k2$ugroup$u1'(sK183),'k1$ufunct$u1'('k1$ulatsubgr'(sK183),sK184)) ),
inference(resolution,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
~ 'r1$urlvect$u1'(sK184,'k2$ugroup$u1'(sK183)),
inference(resolution,[status(thm)],[c161,d13]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d14,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP641+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.78 % Computer : n012.cluster.edu
% 0.09/10.78 % Model : x86_64 x86_64
% 0.09/10.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.78 % Memory : 8046.5625MB
% 0.09/10.78 % OS : Linux 6.8.0-71-generic
% 0.09/10.78 % CPULimit : 300
% 0.09/10.78 % WCLimit : 300
% 0.09/10.78 % DateTime : Fri Sep 25 15:19:21 UTC 2026
% 0.09/10.79 % CPUTime :
% 0.09/10.79 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.94/35.68 % SZS status Theorem for theBenchmark.p
% 37.94/35.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------