%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP642+1 : 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 : n016.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 14.91s 17.35s
% Output : CNFRefutation 14.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 15 unt; 0 def)
% Number of atoms : 206 ( 22 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 273 ( 119 ~; 117 |; 24 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 12 !; 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_l1_group_1,axiom,
! [X0] :
( 'l1$ugroup$u1'(X0)
=> 'l1$ustruct$u0'(X0) ) ).
fof(dt_m1_group_2,axiom,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( 'm1$ugroup$u2'(X1,X0)
=> ( 'l1$ugroup$u1'(X1)
& 'v3$ugroup$u1'(X1)
& ~ 'v3$ustruct$u0'(X1) ) ) ) ).
fof(fc1_struct_0,axiom,
! [X0] :
( ( 'l1$ustruct$u0'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ~ 'v1$uxboole$u0'('u1$ustruct$u0'(X0)) ) ).
fof(fc1_xboole_0,axiom,
'v1$uxboole$u0'('k1$uxboole$u0') ).
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(c12,plain,
( 'v3$ustruct$u0'(X1)
| ~ 'v1$ugroup$u1'(X2)
| ~ 'm2$urelset$u1'(X0,'k1$ugroup$u3'(X1),'k1$uzfmisc$u1'('u1$ustruct$u0'(X1)))
| ~ 'v3$ugroup$u1'(X1)
| ~ 'm1$ugroup$u2'(X2,X1)
| ~ 'v1$ufunct$u2'(X0,'k1$ugroup$u3'(X1),'k1$uzfmisc$u1'('u1$ustruct$u0'(X1)))
| ~ 'l1$ugroup$u1'(X1)
| ~ 'v1$ufunct$u1'(X0)
| 'k1$ufunct$u1'(X0,X2) = 'u1$ustruct$u0'(X2)
| ~ 'v4$ugroup$u1'(X1)
| X0 != 'k1$ulatsubgr'(X1) ),
inference(clausification,[status(esa)],[d1_latsubgr]) ).
cnf(c18,plain,
( ~ 'l1$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'v3$ugroup$u1'(X0)
| 'v1$ufunct$u1'('k1$ulatsubgr'(X0)) ),
inference(clausification,[status(esa)],[dt_k1_latsubgr]) ).
cnf(c19,plain,
( ~ 'l1$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| 'v1$ufunct$u2'('k1$ulatsubgr'(X0),'k1$ugroup$u3'(X0),'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
| 'v3$ustruct$u0'(X0)
| ~ 'v3$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[dt_k1_latsubgr]) ).
cnf(c20,plain,
( ~ 'l1$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| 'm2$urelset$u1'('k1$ulatsubgr'(X0),'k1$ugroup$u3'(X0),'k1$uzfmisc$u1'('u1$ustruct$u0'(X0)))
| ~ 'v3$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[dt_k1_latsubgr]) ).
cnf(c21,plain,
( 'l1$ustruct$u0'(X0)
| ~ 'l1$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[dt_l1_group_1]) ).
cnf(c22,plain,
( ~ 'v3$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| ~ 'v3$ustruct$u0'(X1)
| 'v3$ustruct$u0'(X0) ),
inference(clausification,[status(esa)],[dt_m1_group_2]) ).
cnf(c24,plain,
( ~ 'l1$ugroup$u1'(X0)
| 'l1$ugroup$u1'(X1)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| 'v3$ustruct$u0'(X0) ),
inference(clausification,[status(esa)],[dt_m1_group_2]) ).
cnf(c36,plain,
( ~ 'v1$uxboole$u0'('u1$ustruct$u0'(X0))
| ~ 'l1$ustruct$u0'(X0)
| 'v3$ustruct$u0'(X0) ),
inference(clausification,[status(esa)],[fc1_struct_0]) ).
cnf(c38,plain,
'v1$uxboole$u0'('k1$uxboole$u0'),
inference(clausification,[status(esa)],[fc1_xboole_0]) ).
cnf(c71,plain,
~ 'v3$ustruct$u0'(sK87),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c72,plain,
'v3$ugroup$u1'(sK87),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c73,plain,
'v4$ugroup$u1'(sK87),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c74,plain,
'l1$ugroup$u1'(sK87),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c75,plain,
'v1$ugroup$u1'(sK88),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c76,plain,
'm1$ugroup$u2'(sK88,sK87),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c77,plain,
'k1$ufunct$u1'('k1$ulatsubgr'(sK87),sK88) = 'k1$uxboole$u0',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'v3$ustruct$u0'(X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| ~ 'm2$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))
| ~ 'v1$ugroup$u1'(X1)
| ~ 'l1$ugroup$u1'(X0)
| 'k1$ufunct$u1'('k1$ulatsubgr'(X0),X1) = 'u1$ustruct$u0'(X1) ),
inference(equality_resolution,[status(thm)],[c12]) ).
cnf(d1,plain,
( 'v3$ustruct$u0'(X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| ~ 'v1$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)],[d0,c20]) ).
cnf(d2,plain,
( 'v3$ustruct$u0'(X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X1,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)],[d1,c19]) ).
cnf(d3,plain,
( 'v3$ustruct$u0'(sK87)
| ~ 'v3$ugroup$u1'(sK87)
| ~ 'v4$ugroup$u1'(sK87)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK87))
| ~ 'v1$ugroup$u1'(sK88)
| ~ 'l1$ugroup$u1'(sK87)
| 'k1$ufunct$u1'('k1$ulatsubgr'(sK87),sK88) = 'u1$ustruct$u0'(sK88) ),
inference(resolution,[status(thm)],[d2,c76]) ).
cnf(d4,plain,
( 'v3$ustruct$u0'(sK87)
| ~ 'v3$ugroup$u1'(sK87)
| ~ 'v4$ugroup$u1'(sK87)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK87))
| ~ 'v1$ugroup$u1'(sK88)
| ~ 'l1$ugroup$u1'(sK87)
| 'k1$uxboole$u0' = 'u1$ustruct$u0'(sK88) ),
inference(demodulation,[status(thm)],[d3,c77]) ).
cnf(d5,plain,
( ~ 'v3$ugroup$u1'(sK87)
| ~ 'v4$ugroup$u1'(sK87)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK87))
| ~ 'v1$ugroup$u1'(sK88)
| ~ 'l1$ugroup$u1'(sK87)
| 'k1$uxboole$u0' = 'u1$ustruct$u0'(sK88) ),
inference(resolution,[status(thm)],[c71,d4]) ).
cnf(d6,plain,
( ~ 'v4$ugroup$u1'(sK87)
| ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK87))
| ~ 'v1$ugroup$u1'(sK88)
| ~ 'l1$ugroup$u1'(sK87)
| 'k1$uxboole$u0' = 'u1$ustruct$u0'(sK88) ),
inference(resolution,[status(thm)],[c72,d5]) ).
cnf(d7,plain,
( ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK87))
| ~ 'v1$ugroup$u1'(sK88)
| ~ 'l1$ugroup$u1'(sK87)
| 'k1$uxboole$u0' = 'u1$ustruct$u0'(sK88) ),
inference(resolution,[status(thm)],[c73,d6]) ).
cnf(d8,plain,
( ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK87))
| ~ 'v1$ugroup$u1'(sK88)
| 'k1$uxboole$u0' = 'u1$ustruct$u0'(sK88) ),
inference(resolution,[status(thm)],[c74,d7]) ).
cnf(d9,plain,
( ~ 'v1$ufunct$u1'('k1$ulatsubgr'(sK87))
| 'k1$uxboole$u0' = 'u1$ustruct$u0'(sK88) ),
inference(resolution,[status(thm)],[c75,d8]) ).
cnf(d10,plain,
( 'v3$ustruct$u0'(sK87)
| ~ 'v3$ugroup$u1'(sK87)
| ~ 'v4$ugroup$u1'(sK87)
| ~ 'l1$ugroup$u1'(sK87)
| 'k1$uxboole$u0' = 'u1$ustruct$u0'(sK88) ),
inference(resolution,[status(thm)],[d9,c18]) ).
cnf(d11,plain,
( ~ 'v3$ugroup$u1'(sK87)
| ~ 'v4$ugroup$u1'(sK87)
| ~ 'l1$ugroup$u1'(sK87)
| 'k1$uxboole$u0' = 'u1$ustruct$u0'(sK88) ),
inference(resolution,[status(thm)],[c71,d10]) ).
cnf(d12,plain,
( ~ 'v4$ugroup$u1'(sK87)
| ~ 'l1$ugroup$u1'(sK87)
| 'k1$uxboole$u0' = 'u1$ustruct$u0'(sK88) ),
inference(resolution,[status(thm)],[c72,d11]) ).
cnf(d13,plain,
( ~ 'l1$ugroup$u1'(sK87)
| 'k1$uxboole$u0' = 'u1$ustruct$u0'(sK88) ),
inference(resolution,[status(thm)],[c73,d12]) ).
cnf(d14,plain,
'k1$uxboole$u0' = 'u1$ustruct$u0'(sK88),
inference(resolution,[status(thm)],[c74,d13]) ).
cnf(d15,plain,
( ~ 'l1$ustruct$u0'(sK88)
| 'v3$ustruct$u0'(sK88)
| ~ 'v1$uxboole$u0'('k1$uxboole$u0') ),
inference(superposition,[status(thm)],[d14,c36]) ).
cnf(d16,plain,
( ~ 'l1$ustruct$u0'(sK88)
| 'v3$ustruct$u0'(sK88) ),
inference(resolution,[status(thm)],[c38,d15]) ).
cnf(d17,plain,
( 'v3$ustruct$u0'(sK87)
| ~ 'v3$ustruct$u0'(sK88)
| ~ 'v3$ugroup$u1'(sK87)
| ~ 'l1$ugroup$u1'(sK87) ),
inference(resolution,[status(thm)],[c22,c76]) ).
cnf(d18,plain,
( ~ 'v3$ustruct$u0'(sK88)
| ~ 'v3$ugroup$u1'(sK87)
| ~ 'l1$ugroup$u1'(sK87) ),
inference(resolution,[status(thm)],[c71,d17]) ).
cnf(d19,plain,
( ~ 'v3$ustruct$u0'(sK88)
| ~ 'l1$ugroup$u1'(sK87) ),
inference(resolution,[status(thm)],[c72,d18]) ).
cnf(d20,plain,
~ 'v3$ustruct$u0'(sK88),
inference(resolution,[status(thm)],[c74,d19]) ).
cnf(d21,plain,
~ 'l1$ustruct$u0'(sK88),
inference(resolution,[status(thm)],[d20,d16]) ).
cnf(d22,plain,
( 'v3$ustruct$u0'(sK87)
| ~ 'v3$ugroup$u1'(sK87)
| ~ 'l1$ugroup$u1'(sK87)
| 'l1$ugroup$u1'(sK88) ),
inference(resolution,[status(thm)],[c24,c76]) ).
cnf(d23,plain,
( ~ 'v3$ugroup$u1'(sK87)
| 'l1$ugroup$u1'(sK88)
| ~ 'l1$ugroup$u1'(sK87) ),
inference(resolution,[status(thm)],[c71,d22]) ).
cnf(d24,plain,
( 'l1$ugroup$u1'(sK88)
| ~ 'l1$ugroup$u1'(sK87) ),
inference(resolution,[status(thm)],[c72,d23]) ).
cnf(d25,plain,
'l1$ugroup$u1'(sK88),
inference(resolution,[status(thm)],[c74,d24]) ).
cnf(d26,plain,
'l1$ustruct$u0'(sK88),
inference(resolution,[status(thm)],[d25,c21]) ).
cnf(d27,plain,
$false,
inference(resolution,[status(thm)],[d26,d21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP642+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/15.40 % Computer : n016.cluster.edu
% 0.02/15.40 % Model : x86_64 x86_64
% 0.02/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/15.40 % Memory : 8046.5625MB
% 0.02/15.40 % OS : Linux 6.8.0-71-generic
% 0.02/15.40 % CPULimit : 300
% 0.02/15.40 % WCLimit : 300
% 0.02/15.40 % DateTime : Fri Sep 25 15:24:45 UTC 2026
% 0.02/15.40 % CPUTime :
% 0.02/15.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.91/17.35 % SZS status Theorem for theBenchmark.p
% 14.91/17.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------