%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP642+2 : 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 : n007.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 67.90s 10.22s
% Output : CNFRefutation 67.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 12 unt; 0 def)
% Number of atoms : 71 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 83 ( 36 ~; 28 |; 13 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 1 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(fc1_xboole_0,axiom,
'v1$uxboole$u0'('k1$uxboole$u0') ).
fof(t7_boole,axiom,
! [X0,X1] :
~ ( 'v1$uxboole$u0'(X1)
& 'r2$uhidden'(X0,X1) ) ).
fof(t20_latsubgr,conjecture,
! [X0] :
( ( 'l1$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$u0' ) ),
inference(negate_conjecture,[status(cth)],[t20_latsubgr]) ).
cnf(c34,plain,
( ~ 'v4$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| 'v3$ustruct$u0'(X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v1$ugroup$u1'(X1)
| 'r2$uhidden'('k2$ugroup$u1'(X0),'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1)) ),
inference(clausification,[status(esa)],[t19_latsubgr]) ).
cnf(c106,plain,
'v1$uxboole$u0'('k1$uxboole$u0'),
inference(clausification,[status(esa)],[fc1_xboole_0]) ).
cnf(c241,plain,
( ~ 'v1$uxboole$u0'(X1)
| ~ 'r2$uhidden'(X0,X1) ),
inference(clausification,[status(esa)],[t7_boole]) ).
cnf(c10996,plain,
~ 'v3$ustruct$u0'(sK14695),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c10997,plain,
'v3$ugroup$u1'(sK14695),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c10998,plain,
'v4$ugroup$u1'(sK14695),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c10999,plain,
'l1$ugroup$u1'(sK14695),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c11000,plain,
'v1$ugroup$u1'(sK14696),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c11001,plain,
'm1$ugroup$u2'(sK14696,sK14695),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c11002,plain,
'k1$ufunct$u1'('k1$ulatsubgr'(sK14695),sK14696) = 'k1$uxboole$u0',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'm1$ugroup$u2'(sK14696,sK14695)
| ~ 'v1$ugroup$u1'(sK14696)
| 'v3$ustruct$u0'(sK14695)
| ~ 'v4$ugroup$u1'(sK14695)
| ~ 'l1$ugroup$u1'(sK14695)
| ~ 'v3$ugroup$u1'(sK14695)
| 'r2$uhidden'('k2$ugroup$u1'(sK14695),'k1$uxboole$u0') ),
inference(superposition,[status(thm)],[c11002,c34]) ).
cnf(d1,plain,
( 'r2$uhidden'('k2$ugroup$u1'(sK14695),'k1$uxboole$u0')
| ~ 'm1$ugroup$u2'(sK14696,sK14695)
| ~ 'v1$ugroup$u1'(sK14696)
| ~ 'v4$ugroup$u1'(sK14695)
| ~ 'l1$ugroup$u1'(sK14695)
| ~ 'v3$ugroup$u1'(sK14695) ),
inference(resolution,[status(thm)],[c10996,d0]) ).
cnf(d2,plain,
( 'r2$uhidden'('k2$ugroup$u1'(sK14695),'k1$uxboole$u0')
| ~ 'm1$ugroup$u2'(sK14696,sK14695)
| ~ 'v1$ugroup$u1'(sK14696)
| ~ 'v4$ugroup$u1'(sK14695)
| ~ 'l1$ugroup$u1'(sK14695) ),
inference(resolution,[status(thm)],[c10997,d1]) ).
cnf(d3,plain,
( 'r2$uhidden'('k2$ugroup$u1'(sK14695),'k1$uxboole$u0')
| ~ 'm1$ugroup$u2'(sK14696,sK14695)
| ~ 'v1$ugroup$u1'(sK14696)
| ~ 'l1$ugroup$u1'(sK14695) ),
inference(resolution,[status(thm)],[c10998,d2]) ).
cnf(d4,plain,
( 'r2$uhidden'('k2$ugroup$u1'(sK14695),'k1$uxboole$u0')
| ~ 'm1$ugroup$u2'(sK14696,sK14695)
| ~ 'v1$ugroup$u1'(sK14696) ),
inference(resolution,[status(thm)],[c10999,d3]) ).
cnf(d5,plain,
( 'r2$uhidden'('k2$ugroup$u1'(sK14695),'k1$uxboole$u0')
| ~ 'm1$ugroup$u2'(sK14696,sK14695) ),
inference(resolution,[status(thm)],[c11000,d4]) ).
cnf(d6,plain,
'r2$uhidden'('k2$ugroup$u1'(sK14695),'k1$uxboole$u0'),
inference(resolution,[status(thm)],[c11001,d5]) ).
cnf(d7,plain,
~ 'v1$uxboole$u0'('k1$uxboole$u0'),
inference(resolution,[status(thm)],[c241,d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c106,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP642+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 15:17:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 67.90/10.22 % SZS status Theorem for theBenchmark.p
% 67.90/10.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------