%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP629+3 : 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 : n006.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 07:24:14 AM UTC 2026
% Result : Theorem 115.40s 33.22s
% Output : CNFRefutation 115.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 17 unt; 0 def)
% Number of atoms : 204 ( 49 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 247 ( 97 ~; 108 |; 27 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-5 aty)
% Number of variables : 51 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t23_autgroup,axiom,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& 'v1$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
=> ! [X2] :
( 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X0))
=> 'k6$uautgroup'(X0,'k1$ugroup$u1'(X0,X1,X2)) = 'k7$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X0),'k6$uautgroup'(X0,X1),'k6$uautgroup'(X0,X2)) ) ) ) ).
fof(t24_autgroup,axiom,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& 'v1$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> 'k6$uautgroup'(X0,'k2$ugroup$u1'(X0)) = 'k6$upartfun1'('u1$ustruct$u0'(X0)) ) ).
fof(d6_group_1,axiom,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
=> ! [X2] :
( 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X0))
=> ( X2 = 'k3$ugroup$u1'(X0,X1)
<=> ( 'k1$ugroup$u1'(X0,X2,X1) = 'k2$ugroup$u1'(X0)
& 'k1$ugroup$u1'(X0,X1,X2) = 'k2$ugroup$u1'(X0) ) ) ) ) ) ).
fof(t19_group_1,axiom,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
=> 'k3$ugroup$u1'(X0,'k3$ugroup$u1'(X0,X1)) = X1 ) ) ).
fof(dt_k3_group_1,axiom,
! [X0,X1] :
( ( 'm1$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$u0'(X0)) ) ).
fof(t26_autgroup,conjecture,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& 'v1$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
=> 'k7$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X0),'k6$uautgroup'(X0,'k3$ugroup$u1'(X0,X1)),'k6$uautgroup'(X0,X1)) = 'k6$uautgroup'(X0,'k2$ugroup$u1'(X0)) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& 'v1$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
=> 'k7$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X0),'k6$uautgroup'(X0,'k3$ugroup$u1'(X0,X1)),'k6$uautgroup'(X0,X1)) = 'k6$uautgroup'(X0,'k2$ugroup$u1'(X0)) ) ),
inference(negate_conjecture,[status(cth)],[t26_autgroup]) ).
cnf(c4,plain,
( ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X0))
| ~ 'v4$ugroup$u1'(X0)
| ~ 'v1$ugroup$u1'(X0)
| 'k7$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X0),'k6$uautgroup'(X0,X1),'k6$uautgroup'(X0,X2)) = 'k6$uautgroup'(X0,'k1$ugroup$u1'(X0,X1,X2))
| ~ 'v3$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[t23_autgroup]) ).
cnf(c5,plain,
( ~ 'v4$ugroup$u1'(X0)
| ~ 'v1$ugroup$u1'(X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| 'k6$upartfun1'('u1$ustruct$u0'(X0)) = 'k6$uautgroup'(X0,'k2$ugroup$u1'(X0)) ),
inference(clausification,[status(esa)],[t24_autgroup]) ).
cnf(c25,plain,
( ~ 'v4$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| 'k2$ugroup$u1'(X0) = 'k1$ugroup$u1'(X0,X2,X1)
| ~ 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X0))
| 'k3$ugroup$u1'(X0,X2) != X1
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
| ~ 'v3$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[d6_group_1]) ).
cnf(c34,plain,
( 'k3$ugroup$u1'(X0,'k3$ugroup$u1'(X0,X1)) = X1
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
| ~ 'v3$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[t19_group_1]) ).
cnf(c60,plain,
( ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
| ~ 'v3$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| 'm1$usubset$u1'('k3$ugroup$u1'(X0,X1),'u1$ustruct$u0'(X0)) ),
inference(clausification,[status(esa)],[dt_k3_group_1]) ).
cnf(c119,plain,
'v1$ugroup$u1'(sK177),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c120,plain,
'v4$ugroup$u1'(sK177),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c121,plain,
'l1$ugroup$u1'(sK177),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c122,plain,
'v3$ugroup$u1'(sK177),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c123,plain,
~ 'v3$ustruct$u0'(sK177),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c124,plain,
'm1$usubset$u1'(sK178,'u1$ustruct$u0'(sK177)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c125,plain,
'k6$uautgroup'(sK177,'k2$ugroup$u1'(sK177)) != 'k7$ufunct$u2'('u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'k6$uautgroup'(sK177,'k3$ugroup$u1'(sK177,sK178)),'k6$uautgroup'(sK177,sK178)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'v3$ugroup$u1'(sK177)
| ~ 'v1$ugroup$u1'(sK177)
| ~ 'v4$ugroup$u1'(sK177)
| 'k6$upartfun1'('u1$ustruct$u0'(sK177)) = 'k6$uautgroup'(sK177,'k2$ugroup$u1'(sK177)) ),
inference(resolution,[status(thm)],[c5,c121]) ).
cnf(d1,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'v3$ugroup$u1'(sK177)
| ~ 'v4$ugroup$u1'(sK177)
| 'k6$upartfun1'('u1$ustruct$u0'(sK177)) = 'k6$uautgroup'(sK177,'k2$ugroup$u1'(sK177)) ),
inference(resolution,[status(thm)],[c119,d0]) ).
cnf(d2,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'v3$ugroup$u1'(sK177)
| 'k6$upartfun1'('u1$ustruct$u0'(sK177)) = 'k6$uautgroup'(sK177,'k2$ugroup$u1'(sK177)) ),
inference(resolution,[status(thm)],[c120,d1]) ).
cnf(d3,plain,
( 'v3$ustruct$u0'(sK177)
| 'k6$upartfun1'('u1$ustruct$u0'(sK177)) = 'k6$uautgroup'(sK177,'k2$ugroup$u1'(sK177)) ),
inference(resolution,[status(thm)],[c122,d2]) ).
cnf(d4,plain,
'k6$upartfun1'('u1$ustruct$u0'(sK177)) = 'k6$uautgroup'(sK177,'k2$ugroup$u1'(sK177)),
inference(resolution,[status(thm)],[c123,d3]) ).
cnf(d5,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'v3$ugroup$u1'(sK177)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| ~ 'v4$ugroup$u1'(sK177)
| 'k3$ugroup$u1'(sK177,'k3$ugroup$u1'(sK177,X0)) = X0 ),
inference(resolution,[status(thm)],[c34,c121]) ).
cnf(d6,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'v3$ugroup$u1'(sK177)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| 'k3$ugroup$u1'(sK177,'k3$ugroup$u1'(sK177,X0)) = X0 ),
inference(resolution,[status(thm)],[c120,d5]) ).
cnf(d7,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| 'k3$ugroup$u1'(sK177,'k3$ugroup$u1'(sK177,X0)) = X0 ),
inference(resolution,[status(thm)],[c122,d6]) ).
cnf(d8,plain,
( ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| 'k3$ugroup$u1'(sK177,'k3$ugroup$u1'(sK177,X0)) = X0 ),
inference(resolution,[status(thm)],[c123,d7]) ).
cnf(d9,plain,
'k3$ugroup$u1'(sK177,'k3$ugroup$u1'(sK177,sK178)) = sK178,
inference(resolution,[status(thm)],[d8,c124]) ).
cnf(d10,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'v3$ugroup$u1'(sK177)
| ~ 'm1$usubset$u1'('k3$ugroup$u1'(sK177,sK178),'u1$ustruct$u0'(sK177))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| ~ 'v4$ugroup$u1'(sK177)
| ~ 'l1$ugroup$u1'(sK177)
| 'k2$ugroup$u1'(sK177) = 'k1$ugroup$u1'(sK177,'k3$ugroup$u1'(sK177,sK178),X0)
| sK178 != X0 ),
inference(superposition,[status(thm)],[d9,c25]) ).
cnf(d11,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'v3$ugroup$u1'(sK177)
| ~ 'm1$usubset$u1'('k3$ugroup$u1'(sK177,sK178),'u1$ustruct$u0'(sK177))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| ~ 'l1$ugroup$u1'(sK177)
| sK178 != X0
| 'k2$ugroup$u1'(sK177) = 'k1$ugroup$u1'(sK177,'k3$ugroup$u1'(sK177,sK178),X0) ),
inference(resolution,[status(thm)],[c120,d10]) ).
cnf(d12,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'v3$ugroup$u1'(sK177)
| ~ 'm1$usubset$u1'('k3$ugroup$u1'(sK177,sK178),'u1$ustruct$u0'(sK177))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| sK178 != X0
| 'k2$ugroup$u1'(sK177) = 'k1$ugroup$u1'(sK177,'k3$ugroup$u1'(sK177,sK178),X0) ),
inference(resolution,[status(thm)],[c121,d11]) ).
cnf(d13,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'm1$usubset$u1'('k3$ugroup$u1'(sK177,sK178),'u1$ustruct$u0'(sK177))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| sK178 != X0
| 'k2$ugroup$u1'(sK177) = 'k1$ugroup$u1'(sK177,'k3$ugroup$u1'(sK177,sK178),X0) ),
inference(resolution,[status(thm)],[c122,d12]) ).
cnf(d14,plain,
( ~ 'm1$usubset$u1'('k3$ugroup$u1'(sK177,sK178),'u1$ustruct$u0'(sK177))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| sK178 != X0
| 'k2$ugroup$u1'(sK177) = 'k1$ugroup$u1'(sK177,'k3$ugroup$u1'(sK177,sK178),X0) ),
inference(resolution,[status(thm)],[c123,d13]) ).
cnf(d15,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'v3$ugroup$u1'(sK177)
| 'm1$usubset$u1'('k3$ugroup$u1'(sK177,X0),'u1$ustruct$u0'(sK177))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| ~ 'v4$ugroup$u1'(sK177) ),
inference(resolution,[status(thm)],[c60,c121]) ).
cnf(d16,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'v3$ugroup$u1'(sK177)
| 'm1$usubset$u1'('k3$ugroup$u1'(sK177,X0),'u1$ustruct$u0'(sK177))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177)) ),
inference(resolution,[status(thm)],[c120,d15]) ).
cnf(d17,plain,
( 'v3$ustruct$u0'(sK177)
| 'm1$usubset$u1'('k3$ugroup$u1'(sK177,X0),'u1$ustruct$u0'(sK177))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177)) ),
inference(resolution,[status(thm)],[c122,d16]) ).
cnf(d18,plain,
( 'm1$usubset$u1'('k3$ugroup$u1'(sK177,X0),'u1$ustruct$u0'(sK177))
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177)) ),
inference(resolution,[status(thm)],[c123,d17]) ).
cnf(d19,plain,
'm1$usubset$u1'('k3$ugroup$u1'(sK177,sK178),'u1$ustruct$u0'(sK177)),
inference(resolution,[status(thm)],[d18,c124]) ).
cnf(d20,plain,
( ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| sK178 != X0
| 'k2$ugroup$u1'(sK177) = 'k1$ugroup$u1'(sK177,'k3$ugroup$u1'(sK177,sK178),X0) ),
inference(resolution,[status(thm)],[d19,d14]) ).
cnf(d21,plain,
( ~ 'm1$usubset$u1'(sK178,'u1$ustruct$u0'(sK177))
| 'k2$ugroup$u1'(sK177) = 'k1$ugroup$u1'(sK177,'k3$ugroup$u1'(sK177,sK178),sK178) ),
inference(equality_resolution,[status(thm)],[d20]) ).
cnf(d22,plain,
'k2$ugroup$u1'(sK177) = 'k1$ugroup$u1'(sK177,'k3$ugroup$u1'(sK177,sK178),sK178),
inference(resolution,[status(thm)],[c124,d21]) ).
cnf(d23,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'v3$ugroup$u1'(sK177)
| ~ 'v1$ugroup$u1'(sK177)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK177))
| ~ 'v4$ugroup$u1'(sK177)
| 'k7$ufunct$u2'('u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'k6$uautgroup'(sK177,X0),'k6$uautgroup'(sK177,X1)) = 'k6$uautgroup'(sK177,'k1$ugroup$u1'(sK177,X0,X1)) ),
inference(resolution,[status(thm)],[c4,c121]) ).
cnf(d24,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'v3$ugroup$u1'(sK177)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK177))
| ~ 'v4$ugroup$u1'(sK177)
| 'k7$ufunct$u2'('u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'k6$uautgroup'(sK177,X0),'k6$uautgroup'(sK177,X1)) = 'k6$uautgroup'(sK177,'k1$ugroup$u1'(sK177,X0,X1)) ),
inference(resolution,[status(thm)],[c119,d23]) ).
cnf(d25,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'v3$ugroup$u1'(sK177)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK177))
| 'k7$ufunct$u2'('u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'k6$uautgroup'(sK177,X0),'k6$uautgroup'(sK177,X1)) = 'k6$uautgroup'(sK177,'k1$ugroup$u1'(sK177,X0,X1)) ),
inference(resolution,[status(thm)],[c120,d24]) ).
cnf(d26,plain,
( 'v3$ustruct$u0'(sK177)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK177))
| 'k7$ufunct$u2'('u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'k6$uautgroup'(sK177,X0),'k6$uautgroup'(sK177,X1)) = 'k6$uautgroup'(sK177,'k1$ugroup$u1'(sK177,X0,X1)) ),
inference(resolution,[status(thm)],[c122,d25]) ).
cnf(d27,plain,
( ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(sK177))
| 'k7$ufunct$u2'('u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'k6$uautgroup'(sK177,X0),'k6$uautgroup'(sK177,X1)) = 'k6$uautgroup'(sK177,'k1$ugroup$u1'(sK177,X0,X1)) ),
inference(resolution,[status(thm)],[c123,d26]) ).
cnf(d28,plain,
( ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK177))
| 'k7$ufunct$u2'('u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'k6$uautgroup'(sK177,X0),'k6$uautgroup'(sK177,sK178)) = 'k6$uautgroup'(sK177,'k1$ugroup$u1'(sK177,X0,sK178)) ),
inference(resolution,[status(thm)],[d27,c124]) ).
cnf(d29,plain,
'k7$ufunct$u2'('u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'k6$uautgroup'(sK177,'k3$ugroup$u1'(sK177,sK178)),'k6$uautgroup'(sK177,sK178)) = 'k6$uautgroup'(sK177,'k1$ugroup$u1'(sK177,'k3$ugroup$u1'(sK177,sK178),sK178)),
inference(resolution,[status(thm)],[d28,d19]) ).
cnf(d30,plain,
'k7$ufunct$u2'('u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'k6$uautgroup'(sK177,'k3$ugroup$u1'(sK177,sK178)),'k6$uautgroup'(sK177,sK178)) = 'k6$uautgroup'(sK177,'k2$ugroup$u1'(sK177)),
inference(demodulation,[status(thm)],[d29,d22]) ).
cnf(d31,plain,
'k7$ufunct$u2'('u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'k6$uautgroup'(sK177,'k3$ugroup$u1'(sK177,sK178)),'k6$uautgroup'(sK177,sK178)) = 'k6$upartfun1'('u1$ustruct$u0'(sK177)),
inference(demodulation,[status(thm)],[d30,d4]) ).
cnf(d32,plain,
'k6$upartfun1'('u1$ustruct$u0'(sK177)) != 'k7$ufunct$u2'('u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'u1$ustruct$u0'(sK177),'k6$uautgroup'(sK177,'k3$ugroup$u1'(sK177,sK178)),'k6$uautgroup'(sK177,sK178)),
inference(demodulation,[status(thm)],[c125,d4]) ).
cnf(d33,plain,
'k6$upartfun1'('u1$ustruct$u0'(sK177)) != 'k6$upartfun1'('u1$ustruct$u0'(sK177)),
inference(demodulation,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
$false,
inference(equality_resolution,[status(thm)],[d33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP629+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.58 % Computer : n006.cluster.edu
% 0.10/10.58 % Model : x86_64 x86_64
% 0.10/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.58 % Memory : 8046.5625MB
% 0.10/10.58 % OS : Linux 6.8.0-71-generic
% 0.10/10.58 % CPULimit : 300
% 0.10/10.58 % WCLimit : 300
% 0.10/10.58 % DateTime : Fri Sep 25 15:08:33 UTC 2026
% 0.10/10.59 % CPUTime :
% 0.10/10.59 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 115.40/33.22 % SZS status Theorem for theBenchmark.p
% 115.40/33.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------