%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP642+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 07:24:18 AM UTC 2026
% Result : Theorem 106.45s 15.92s
% Output : CNFRefutation 106.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 10 unt; 0 def)
% Number of atoms : 69 ( 5 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 83 ( 36 ~; 28 |; 12 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t19_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) )
=> 'r2$uhidden'('k2$ugroup$u1'(X0),'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1)) ) ) ).
fof(d1_xboole_0,axiom,
! [X0] :
( X0 = 'k1$uxboole$u0'
<=> ! [X1] : ~ 'r2$uhidden'(X1,X0) ) ).
fof(t20_latsubgr,conjecture,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( ( 'm1$ugroup$u2'(X1,X0)
& 'v1$ugroup$u1'(X1) )
=> 'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1) != 'k1$uxboole$u0' ) ) ).
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) )
=> 'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1) != 'k1$uxboole$u0' ) ),
inference(negate_conjecture,[status(cth)],[t20_latsubgr]) ).
cnf(c13,plain,
( ~ 'v4$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| 'r2$uhidden'('k2$ugroup$u1'(X0),'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1))
| ~ 'l1$ugroup$u1'(X0)
| ~ 'v1$ugroup$u1'(X1)
| ~ 'm1$ugroup$u2'(X1,X0)
| ~ 'v3$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[t19_latsubgr]) ).
cnf(c28,plain,
( ~ 'r2$uhidden'(X1,X0)
| X0 != 'k1$uxboole$u0' ),
inference(clausification,[status(esa)],[d1_xboole_0]) ).
cnf(c391,plain,
~ 'v3$ustruct$u0'(sK563),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c392,plain,
'v3$ugroup$u1'(sK563),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c393,plain,
'v4$ugroup$u1'(sK563),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c394,plain,
'l1$ugroup$u1'(sK563),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c395,plain,
'v1$ugroup$u1'(sK564),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c396,plain,
'm1$ugroup$u2'(sK564,sK563),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c397,plain,
'k1$ufunct$u1'('k1$ulatsubgr'(sK563),sK564) = 'k1$uxboole$u0',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'm1$ugroup$u2'(sK564,sK563)
| ~ 'v1$ugroup$u1'(sK564)
| 'v3$ustruct$u0'(sK563)
| ~ 'v4$ugroup$u1'(sK563)
| ~ 'l1$ugroup$u1'(sK563)
| ~ 'v3$ugroup$u1'(sK563)
| 'r2$uhidden'('k2$ugroup$u1'(sK563),'k1$uxboole$u0') ),
inference(superposition,[status(thm)],[c397,c13]) ).
cnf(d1,plain,
( ~ 'm1$ugroup$u2'(sK564,sK563)
| ~ 'v1$ugroup$u1'(sK564)
| 'r2$uhidden'('k2$ugroup$u1'(sK563),'k1$uxboole$u0')
| ~ 'v4$ugroup$u1'(sK563)
| ~ 'l1$ugroup$u1'(sK563)
| ~ 'v3$ugroup$u1'(sK563) ),
inference(resolution,[status(thm)],[c391,d0]) ).
cnf(d2,plain,
( ~ 'm1$ugroup$u2'(sK564,sK563)
| ~ 'v1$ugroup$u1'(sK564)
| 'r2$uhidden'('k2$ugroup$u1'(sK563),'k1$uxboole$u0')
| ~ 'v4$ugroup$u1'(sK563)
| ~ 'l1$ugroup$u1'(sK563) ),
inference(resolution,[status(thm)],[c392,d1]) ).
cnf(d3,plain,
( ~ 'm1$ugroup$u2'(sK564,sK563)
| ~ 'v1$ugroup$u1'(sK564)
| 'r2$uhidden'('k2$ugroup$u1'(sK563),'k1$uxboole$u0')
| ~ 'l1$ugroup$u1'(sK563) ),
inference(resolution,[status(thm)],[c393,d2]) ).
cnf(d4,plain,
( ~ 'm1$ugroup$u2'(sK564,sK563)
| ~ 'v1$ugroup$u1'(sK564)
| 'r2$uhidden'('k2$ugroup$u1'(sK563),'k1$uxboole$u0') ),
inference(resolution,[status(thm)],[c394,d3]) ).
cnf(d5,plain,
( ~ 'm1$ugroup$u2'(sK564,sK563)
| 'r2$uhidden'('k2$ugroup$u1'(sK563),'k1$uxboole$u0') ),
inference(resolution,[status(thm)],[c395,d4]) ).
cnf(d6,plain,
'r2$uhidden'('k2$ugroup$u1'(sK563),'k1$uxboole$u0'),
inference(resolution,[status(thm)],[c396,d5]) ).
cnf(d7,plain,
~ 'r2$uhidden'(X0,'k1$uxboole$u0'),
inference(equality_resolution,[status(thm)],[c28]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP642+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n005.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Fri Sep 25 15:19:19 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.45/15.92 % SZS status Theorem for theBenchmark.p
% 106.45/15.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------