%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP644+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 : n008.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 16.05s 2.60s
% Output : CNFRefutation 16.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 13 unt; 0 def)
% Number of atoms : 203 ( 0 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 296 ( 140 ~; 120 |; 19 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(c17,plain,
( ~ 'l1$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
| 'm1$usubset$u1'('k3$ugroup$u1'(X0,X1),'u1$ustruct$u0'(X0))
| ~ 'v3$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[dt_k3_group_1]) ).
cnf(c59,plain,
( ~ 'v4$ugroup$u1'(X2)
| ~ 'l1$ugroup$u1'(X2)
| ~ 'v3$ugroup$u1'(X2)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X2))
| ~ 'v1$ugroup$u1'(X0)
| ~ 'r2$uhidden'(X1,'k1$ufunct$u1'('k1$ulatsubgr'(X2),X0))
| 'v3$ustruct$u0'(X2)
| ~ 'm1$ugroup$u2'(X0,X2)
| 'r1$urlvect$u1'(X0,X1) ),
inference(clausification,[status(esa)],[t18_latsubgr]) ).
cnf(c60,plain,
( ~ 'v4$ugroup$u1'(X1)
| ~ 'l1$ugroup$u1'(X1)
| ~ 'v3$ugroup$u1'(X1)
| ~ 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X1))
| ~ 'v1$ugroup$u1'(X0)
| ~ 'r1$urlvect$u1'(X0,X2)
| 'v3$ustruct$u0'(X1)
| 'r2$uhidden'(X2,'k1$ufunct$u1'('k1$ulatsubgr'(X1),X0))
| ~ 'm1$ugroup$u2'(X0,X1) ),
inference(clausification,[status(esa)],[t18_latsubgr]) ).
cnf(c67,plain,
( ~ 'v3$ugroup$u1'(X1)
| 'r1$urlvect$u1'(X0,'k3$ugroup$u1'(X1,X2))
| ~ 'v4$ugroup$u1'(X1)
| ~ 'l1$ugroup$u1'(X1)
| 'v3$ustruct$u0'(X1)
| ~ 'r1$urlvect$u1'(X0,X2)
| ~ 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X1))
| ~ 'm1$ugroup$u2'(X0,X1) ),
inference(clausification,[status(esa)],[t60_group_2]) ).
cnf(c71,plain,
~ 'v3$ustruct$u0'(sK91),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c72,plain,
'v3$ugroup$u1'(sK91),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c73,plain,
'v4$ugroup$u1'(sK91),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c74,plain,
'l1$ugroup$u1'(sK91),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c75,plain,
'v1$ugroup$u1'(sK92),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c76,plain,
'm1$ugroup$u2'(sK92,sK91),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c77,plain,
'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c78,plain,
'r2$uhidden'(sK93,'k1$ufunct$u1'('k1$ulatsubgr'(sK91),sK92)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c79,plain,
~ 'r2$uhidden'('k3$ugroup$u1'(sK91,sK93),'k1$ufunct$u1'('k1$ulatsubgr'(sK91),sK92)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'r1$urlvect$u1'(sK92,'k3$ugroup$u1'(sK91,sK93))
| ~ 'm1$ugroup$u2'(sK92,sK91)
| 'v3$ustruct$u0'(sK91)
| ~ 'v4$ugroup$u1'(sK91)
| ~ 'v3$ugroup$u1'(sK91)
| ~ 'm1$usubset$u1'('k3$ugroup$u1'(sK91,sK93),'u1$ustruct$u0'(sK91))
| ~ 'v1$ugroup$u1'(sK92)
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c60,c79]) ).
cnf(d1,plain,
( ~ 'r1$urlvect$u1'(sK92,'k3$ugroup$u1'(sK91,sK93))
| ~ 'm1$ugroup$u2'(sK92,sK91)
| ~ 'v4$ugroup$u1'(sK91)
| ~ 'v3$ugroup$u1'(sK91)
| ~ 'm1$usubset$u1'('k3$ugroup$u1'(sK91,sK93),'u1$ustruct$u0'(sK91))
| ~ 'v1$ugroup$u1'(sK92)
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c71,d0]) ).
cnf(d2,plain,
( ~ 'r1$urlvect$u1'(sK92,'k3$ugroup$u1'(sK91,sK93))
| ~ 'm1$ugroup$u2'(sK92,sK91)
| ~ 'v4$ugroup$u1'(sK91)
| ~ 'm1$usubset$u1'('k3$ugroup$u1'(sK91,sK93),'u1$ustruct$u0'(sK91))
| ~ 'v1$ugroup$u1'(sK92)
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c72,d1]) ).
cnf(d3,plain,
( ~ 'r1$urlvect$u1'(sK92,'k3$ugroup$u1'(sK91,sK93))
| ~ 'm1$ugroup$u2'(sK92,sK91)
| ~ 'm1$usubset$u1'('k3$ugroup$u1'(sK91,sK93),'u1$ustruct$u0'(sK91))
| ~ 'v1$ugroup$u1'(sK92)
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c73,d2]) ).
cnf(d4,plain,
( ~ 'r1$urlvect$u1'(sK92,'k3$ugroup$u1'(sK91,sK93))
| ~ 'm1$ugroup$u2'(sK92,sK91)
| ~ 'm1$usubset$u1'('k3$ugroup$u1'(sK91,sK93),'u1$ustruct$u0'(sK91))
| ~ 'v1$ugroup$u1'(sK92) ),
inference(resolution,[status(thm)],[c74,d3]) ).
cnf(d5,plain,
( ~ 'r1$urlvect$u1'(sK92,'k3$ugroup$u1'(sK91,sK93))
| ~ 'm1$ugroup$u2'(sK92,sK91)
| ~ 'm1$usubset$u1'('k3$ugroup$u1'(sK91,sK93),'u1$ustruct$u0'(sK91)) ),
inference(resolution,[status(thm)],[c75,d4]) ).
cnf(d6,plain,
( ~ 'r1$urlvect$u1'(sK92,'k3$ugroup$u1'(sK91,sK93))
| ~ 'm1$usubset$u1'('k3$ugroup$u1'(sK91,sK93),'u1$ustruct$u0'(sK91)) ),
inference(resolution,[status(thm)],[c76,d5]) ).
cnf(d7,plain,
( 'v3$ustruct$u0'(sK91)
| ~ 'v4$ugroup$u1'(sK91)
| ~ 'v3$ugroup$u1'(sK91)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91))
| ~ 'l1$ugroup$u1'(sK91)
| ~ 'r1$urlvect$u1'(sK92,'k3$ugroup$u1'(sK91,sK93)) ),
inference(resolution,[status(thm)],[d6,c17]) ).
cnf(d8,plain,
( ~ 'r1$urlvect$u1'(sK92,'k3$ugroup$u1'(sK91,sK93))
| ~ 'v4$ugroup$u1'(sK91)
| ~ 'v3$ugroup$u1'(sK91)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91))
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c71,d7]) ).
cnf(d9,plain,
( ~ 'r1$urlvect$u1'(sK92,'k3$ugroup$u1'(sK91,sK93))
| ~ 'v4$ugroup$u1'(sK91)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91))
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c72,d8]) ).
cnf(d10,plain,
( ~ 'r1$urlvect$u1'(sK92,'k3$ugroup$u1'(sK91,sK93))
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91))
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c73,d9]) ).
cnf(d11,plain,
( ~ 'r1$urlvect$u1'(sK92,'k3$ugroup$u1'(sK91,sK93))
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91)) ),
inference(resolution,[status(thm)],[c74,d10]) ).
cnf(d12,plain,
~ 'r1$urlvect$u1'(sK92,'k3$ugroup$u1'(sK91,sK93)),
inference(resolution,[status(thm)],[c77,d11]) ).
cnf(d13,plain,
( ~ 'r1$urlvect$u1'(sK92,sK93)
| ~ 'm1$ugroup$u2'(sK92,sK91)
| 'v3$ustruct$u0'(sK91)
| ~ 'v4$ugroup$u1'(sK91)
| ~ 'v3$ugroup$u1'(sK91)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91))
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c67,d12]) ).
cnf(d14,plain,
( ~ 'r1$urlvect$u1'(sK92,sK93)
| ~ 'm1$ugroup$u2'(sK92,sK91)
| ~ 'v4$ugroup$u1'(sK91)
| ~ 'v3$ugroup$u1'(sK91)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91))
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c71,d13]) ).
cnf(d15,plain,
( ~ 'r1$urlvect$u1'(sK92,sK93)
| ~ 'm1$ugroup$u2'(sK92,sK91)
| ~ 'v4$ugroup$u1'(sK91)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91))
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c72,d14]) ).
cnf(d16,plain,
( ~ 'r1$urlvect$u1'(sK92,sK93)
| ~ 'm1$ugroup$u2'(sK92,sK91)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91))
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c73,d15]) ).
cnf(d17,plain,
( ~ 'r1$urlvect$u1'(sK92,sK93)
| ~ 'm1$ugroup$u2'(sK92,sK91)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91)) ),
inference(resolution,[status(thm)],[c74,d16]) ).
cnf(d18,plain,
( ~ 'r1$urlvect$u1'(sK92,sK93)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91)) ),
inference(resolution,[status(thm)],[c76,d17]) ).
cnf(d19,plain,
~ 'r1$urlvect$u1'(sK92,sK93),
inference(resolution,[status(thm)],[c77,d18]) ).
cnf(d20,plain,
( 'r1$urlvect$u1'(sK92,sK93)
| ~ 'm1$ugroup$u2'(sK92,sK91)
| 'v3$ustruct$u0'(sK91)
| ~ 'v4$ugroup$u1'(sK91)
| ~ 'v3$ugroup$u1'(sK91)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91))
| ~ 'v1$ugroup$u1'(sK92)
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c59,c78]) ).
cnf(d21,plain,
( 'r1$urlvect$u1'(sK92,sK93)
| ~ 'm1$ugroup$u2'(sK92,sK91)
| ~ 'v4$ugroup$u1'(sK91)
| ~ 'v3$ugroup$u1'(sK91)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91))
| ~ 'v1$ugroup$u1'(sK92)
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c71,d20]) ).
cnf(d22,plain,
( 'r1$urlvect$u1'(sK92,sK93)
| ~ 'm1$ugroup$u2'(sK92,sK91)
| ~ 'v4$ugroup$u1'(sK91)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91))
| ~ 'v1$ugroup$u1'(sK92)
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c72,d21]) ).
cnf(d23,plain,
( 'r1$urlvect$u1'(sK92,sK93)
| ~ 'm1$ugroup$u2'(sK92,sK91)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91))
| ~ 'v1$ugroup$u1'(sK92)
| ~ 'l1$ugroup$u1'(sK91) ),
inference(resolution,[status(thm)],[c73,d22]) ).
cnf(d24,plain,
( 'r1$urlvect$u1'(sK92,sK93)
| ~ 'm1$ugroup$u2'(sK92,sK91)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91))
| ~ 'v1$ugroup$u1'(sK92) ),
inference(resolution,[status(thm)],[c74,d23]) ).
cnf(d25,plain,
( 'r1$urlvect$u1'(sK92,sK93)
| ~ 'm1$ugroup$u2'(sK92,sK91)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91)) ),
inference(resolution,[status(thm)],[c75,d24]) ).
cnf(d26,plain,
( 'r1$urlvect$u1'(sK92,sK93)
| ~ 'm1$usubset$u1'(sK93,'u1$ustruct$u0'(sK91)) ),
inference(resolution,[status(thm)],[c76,d25]) ).
cnf(d27,plain,
'r1$urlvect$u1'(sK92,sK93),
inference(resolution,[status(thm)],[c77,d26]) ).
cnf(d28,plain,
$false,
inference(resolution,[status(thm)],[d27,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP644+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
% 0.09/0.37 % Computer : n008.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 15:21:39 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.05/2.60 % SZS status Theorem for theBenchmark.p
% 16.05/2.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------