%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP638+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 : n003.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 07:24:16 AM UTC 2026
% Result : Theorem 8.65s 2.73s
% Output : CNFRefutation 8.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 10
% Syntax : Number of formulae : 103 ( 34 unt; 0 def)
% Number of atoms : 341 ( 13 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 417 ( 179 ~; 166 |; 39 &)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 82 ( 4 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relset_1,axiom,
! [X0,X1,X2] :
( 'm1$usubset$u1'(X2,'k1$uzfmisc$u1'('k2$uzfmisc$u1'(X0,X1)))
=> 'v1$urelat$u1'(X2) ) ).
fof(d5_group_2,axiom,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( ( 'l1$ugroup$u1'(X1)
& 'v3$ugroup$u1'(X1)
& ~ 'v3$ustruct$u0'(X1) )
=> ( 'm1$ugroup$u2'(X1,X0)
<=> ( 'u1$ugroup$u1'(X1) = 'k1$urealset1'('u1$ugroup$u1'(X0),'u1$ustruct$u0'(X1))
& 'r1$utarski'('u1$ustruct$u0'(X1),'u1$ustruct$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(dt_m2_relset_1,axiom,
! [X0,X1,X2] :
( 'm2$urelset$u1'(X2,X0,X1)
=> 'm1$usubset$u1'(X2,'k1$uzfmisc$u1'('k2$uzfmisc$u1'(X0,X1))) ) ).
fof(redefinition_k3_funct_2,axiom,
! [X0,X1,X2,X3] :
( ( 'm1$urelset$u1'(X2,X0,X1)
& 'v1$ufunct$u1'(X2) )
=> 'k3$ufunct$u2'(X0,X1,X2,X3) = 'k10$urelat$u1'(X2,X3) ) ).
fof(redefinition_m1_group_6,axiom,
! [X0,X1] :
( ( 'm1$ugroup$u2'(X1,X0)
& 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X2] :
( 'm1$ugroup$u6'(X2,X0,X1)
<=> 'm1$ugroup$u2'(X2,X1) ) ) ).
fof(redefinition_m2_relset_1,axiom,
! [X0,X1,X2] :
( 'm2$urelset$u1'(X2,X0,X1)
<=> 'm1$urelset$u1'(X2,X0,X1) ) ).
fof(t178_relat_1,axiom,
! [X0,X1,X2] :
( 'v1$urelat$u1'(X2)
=> ( 'r1$utarski'(X0,X1)
=> 'r1$utarski'('k10$urelat$u1'(X2,X0),'k10$urelat$u1'(X2,X1)) ) ) ).
fof(t66_group_2,axiom,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( 'm1$ugroup$u2'(X1,X0)
=> ! [X2] :
( 'm1$ugroup$u2'(X2,X0)
=> ( 'r1$utarski'('u1$ustruct$u0'(X1),'u1$ustruct$u0'(X2))
=> 'm1$ugroup$u2'(X1,X2) ) ) ) ) ).
fof(t11_latsubgr,conjecture,
! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( ( 'l1$ugroup$u1'(X1)
& 'v4$ugroup$u1'(X1)
& 'v3$ugroup$u1'(X1)
& ~ 'v3$ustruct$u0'(X1) )
=> ! [X2] :
( ( 'm2$urelset$u1'(X2,'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1))
& 'v1$ugroup$u6'(X2,X0,X1)
& 'v1$ufunct$u2'(X2,'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1))
& 'v1$ufunct$u1'(X2) )
=> ! [X3] :
( 'm1$ugroup$u2'(X3,X1)
=> ! [X4] :
( 'm1$ugroup$u2'(X4,X1)
=> ! [X5] :
( 'm1$ugroup$u2'(X5,X0)
=> ! [X6] :
( 'm1$ugroup$u2'(X6,X0)
=> ( ( 'm1$ugroup$u6'(X3,X1,X4)
& 'u1$ustruct$u0'(X6) = 'k3$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1),X2,'u1$ustruct$u0'(X4))
& 'u1$ustruct$u0'(X5) = 'k3$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1),X2,'u1$ustruct$u0'(X3)) )
=> 'm1$ugroup$u6'(X5,X0,X6) ) ) ) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'l1$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v3$ugroup$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( ( 'l1$ugroup$u1'(X1)
& 'v4$ugroup$u1'(X1)
& 'v3$ugroup$u1'(X1)
& ~ 'v3$ustruct$u0'(X1) )
=> ! [X2] :
( ( 'm2$urelset$u1'(X2,'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1))
& 'v1$ugroup$u6'(X2,X0,X1)
& 'v1$ufunct$u2'(X2,'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1))
& 'v1$ufunct$u1'(X2) )
=> ! [X3] :
( 'm1$ugroup$u2'(X3,X1)
=> ! [X4] :
( 'm1$ugroup$u2'(X4,X1)
=> ! [X5] :
( 'm1$ugroup$u2'(X5,X0)
=> ! [X6] :
( 'm1$ugroup$u2'(X6,X0)
=> ( ( 'm1$ugroup$u6'(X3,X1,X4)
& 'u1$ustruct$u0'(X6) = 'k3$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1),X2,'u1$ustruct$u0'(X4))
& 'u1$ustruct$u0'(X5) = 'k3$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1),X2,'u1$ustruct$u0'(X3)) )
=> 'm1$ugroup$u6'(X5,X0,X6) ) ) ) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t11_latsubgr]) ).
cnf(c3,plain,
( 'v1$urelat$u1'(X0)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k2$uzfmisc$u1'(X1,X2))) ),
inference(clausification,[status(esa)],[cc1_relset_1]) ).
cnf(c11,plain,
( ~ 'v3$ugroup$u1'(X1)
| 'r1$utarski'('u1$ustruct$u0'(X1),'u1$ustruct$u0'(X0))
| 'v3$ustruct$u0'(X0)
| ~ 'v3$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X1)
| ~ 'l1$ugroup$u1'(X1)
| ~ 'm1$ugroup$u2'(X1,X0)
| ~ 'l1$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[d5_group_2]) ).
cnf(c16,plain,
( ~ 'v3$ugroup$u1'(X1)
| ~ 'm1$ugroup$u2'(X0,X1)
| ~ 'l1$ugroup$u1'(X1)
| 'v3$ustruct$u0'(X1)
| ~ 'v3$ustruct$u0'(X0) ),
inference(clausification,[status(esa)],[dt_m1_group_2]) ).
cnf(c17,plain,
( ~ 'v3$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| 'v3$ugroup$u1'(X1)
| ~ 'l1$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0) ),
inference(clausification,[status(esa)],[dt_m1_group_2]) ).
cnf(c18,plain,
( ~ 'v3$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X1,X0)
| ~ 'l1$ugroup$u1'(X0)
| 'l1$ugroup$u1'(X1)
| 'v3$ustruct$u0'(X0) ),
inference(clausification,[status(esa)],[dt_m1_group_2]) ).
cnf(c20,plain,
( 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k2$uzfmisc$u1'(X1,X2)))
| ~ 'm2$urelset$u1'(X0,X1,X2) ),
inference(clausification,[status(esa)],[dt_m2_relset_1]) ).
cnf(c52,plain,
( 'k3$ufunct$u2'(X1,X2,X0,X3) = 'k10$urelat$u1'(X0,X3)
| ~ 'm1$urelset$u1'(X0,X1,X2)
| ~ 'v1$ufunct$u1'(X0) ),
inference(clausification,[status(esa)],[redefinition_k3_funct_2]) ).
cnf(c53,plain,
( ~ 'v4$ugroup$u1'(X2)
| ~ 'l1$ugroup$u1'(X2)
| ~ 'v3$ugroup$u1'(X2)
| ~ 'm1$ugroup$u6'(X0,X2,X1)
| 'v3$ustruct$u0'(X2)
| ~ 'm1$ugroup$u2'(X1,X2)
| 'm1$ugroup$u2'(X0,X1) ),
inference(clausification,[status(esa)],[redefinition_m1_group_6]) ).
cnf(c54,plain,
( ~ 'v4$ugroup$u1'(X1)
| ~ 'l1$ugroup$u1'(X1)
| ~ 'v3$ugroup$u1'(X1)
| 'v3$ustruct$u0'(X1)
| ~ 'm1$ugroup$u2'(X0,X2)
| ~ 'm1$ugroup$u2'(X2,X1)
| 'm1$ugroup$u6'(X0,X1,X2) ),
inference(clausification,[status(esa)],[redefinition_m1_group_6]) ).
cnf(c55,plain,
( 'm1$urelset$u1'(X0,X1,X2)
| ~ 'm2$urelset$u1'(X0,X1,X2) ),
inference(clausification,[status(esa)],[redefinition_m2_relset_1]) ).
cnf(c58,plain,
( 'r1$utarski'('k10$urelat$u1'(X0,X1),'k10$urelat$u1'(X0,X2))
| ~ 'r1$utarski'(X1,X2)
| ~ 'v1$urelat$u1'(X0) ),
inference(clausification,[status(esa)],[t178_relat_1]) ).
cnf(c65,plain,
( ~ 'm1$ugroup$u2'(X1,X0)
| 'v3$ustruct$u0'(X0)
| ~ 'l1$ugroup$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'm1$ugroup$u2'(X2,X0)
| 'm1$ugroup$u2'(X1,X2)
| ~ 'r1$utarski'('u1$ustruct$u0'(X1),'u1$ustruct$u0'(X2))
| ~ 'v3$ugroup$u1'(X0) ),
inference(clausification,[status(esa)],[t66_group_2]) ).
cnf(c69,plain,
~ 'v3$ustruct$u0'(sK99),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c70,plain,
'v3$ugroup$u1'(sK99),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c71,plain,
'v4$ugroup$u1'(sK99),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c72,plain,
'l1$ugroup$u1'(sK99),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c73,plain,
~ 'v3$ustruct$u0'(sK100),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c74,plain,
'v3$ugroup$u1'(sK100),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c75,plain,
'v4$ugroup$u1'(sK100),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c76,plain,
'l1$ugroup$u1'(sK100),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c77,plain,
'v1$ufunct$u1'(sK101),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c80,plain,
'm2$urelset$u1'(sK101,'u1$ustruct$u0'(sK99),'u1$ustruct$u0'(sK100)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c81,plain,
'm1$ugroup$u2'(sK102,sK100),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c82,plain,
'm1$ugroup$u2'(sK103,sK100),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c83,plain,
'm1$ugroup$u2'(sK104,sK99),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c84,plain,
'm1$ugroup$u2'(sK105,sK99),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c85,plain,
'u1$ustruct$u0'(sK104) = 'k3$ufunct$u2'('u1$ustruct$u0'(sK99),'u1$ustruct$u0'(sK100),sK101,'u1$ustruct$u0'(sK102)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c86,plain,
'u1$ustruct$u0'(sK105) = 'k3$ufunct$u2'('u1$ustruct$u0'(sK99),'u1$ustruct$u0'(sK100),sK101,'u1$ustruct$u0'(sK103)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c87,plain,
'm1$ugroup$u6'(sK102,sK100,sK103),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c88,plain,
~ 'm1$ugroup$u6'(sK104,sK99,sK105),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'm1$urelset$u1'(sK101,'u1$ustruct$u0'(sK99),'u1$ustruct$u0'(sK100)),
inference(resolution,[status(thm)],[c55,c80]) ).
cnf(d1,plain,
( ~ 'v1$ufunct$u1'(sK101)
| 'k3$ufunct$u2'('u1$ustruct$u0'(sK99),'u1$ustruct$u0'(sK100),sK101,X0) = 'k10$urelat$u1'(sK101,X0) ),
inference(resolution,[status(thm)],[d0,c52]) ).
cnf(d2,plain,
'k3$ufunct$u2'('u1$ustruct$u0'(sK99),'u1$ustruct$u0'(sK100),sK101,X0) = 'k10$urelat$u1'(sK101,X0),
inference(resolution,[status(thm)],[c77,d1]) ).
cnf(d3,plain,
'u1$ustruct$u0'(sK105) = 'k10$urelat$u1'(sK101,'u1$ustruct$u0'(sK103)),
inference(demodulation,[status(thm)],[c86,d2]) ).
cnf(d4,plain,
( ~ 'r1$utarski'(X0,'u1$ustruct$u0'(sK103))
| ~ 'v1$urelat$u1'(sK101)
| 'r1$utarski'('k10$urelat$u1'(sK101,X0),'u1$ustruct$u0'(sK105)) ),
inference(superposition,[status(thm)],[d3,c58]) ).
cnf(d5,plain,
( 'v1$urelat$u1'(X0)
| ~ 'm2$urelset$u1'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c20,c3]) ).
cnf(d6,plain,
'v1$urelat$u1'(sK101),
inference(resolution,[status(thm)],[d5,c80]) ).
cnf(d7,plain,
( 'r1$utarski'('k10$urelat$u1'(sK101,X0),'u1$ustruct$u0'(sK105))
| ~ 'r1$utarski'(X0,'u1$ustruct$u0'(sK103)) ),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
'u1$ustruct$u0'(sK104) = 'k10$urelat$u1'(sK101,'u1$ustruct$u0'(sK102)),
inference(demodulation,[status(thm)],[c85,d2]) ).
cnf(d9,plain,
( ~ 'r1$utarski'('u1$ustruct$u0'(sK102),'u1$ustruct$u0'(sK103))
| 'r1$utarski'('u1$ustruct$u0'(sK104),'u1$ustruct$u0'(sK105)) ),
inference(superposition,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( 'v3$ustruct$u0'(sK103)
| 'v3$ustruct$u0'(sK102)
| ~ 'm1$ugroup$u2'(sK102,sK103)
| ~ 'v3$ugroup$u1'(sK103)
| ~ 'v3$ugroup$u1'(sK102)
| ~ 'l1$ugroup$u1'(sK103)
| ~ 'l1$ugroup$u1'(sK102)
| 'r1$utarski'('u1$ustruct$u0'(sK104),'u1$ustruct$u0'(sK105)) ),
inference(resolution,[status(thm)],[d9,c11]) ).
cnf(d11,plain,
( 'v3$ustruct$u0'(sK100)
| ~ 'v3$ustruct$u0'(sK103)
| ~ 'v3$ugroup$u1'(sK100)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c16,c82]) ).
cnf(d12,plain,
( ~ 'v3$ustruct$u0'(sK103)
| ~ 'v3$ugroup$u1'(sK100)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c73,d11]) ).
cnf(d13,plain,
( ~ 'v3$ustruct$u0'(sK103)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c74,d12]) ).
cnf(d14,plain,
~ 'v3$ustruct$u0'(sK103),
inference(resolution,[status(thm)],[c76,d13]) ).
cnf(d15,plain,
( 'v3$ustruct$u0'(sK102)
| 'r1$utarski'('u1$ustruct$u0'(sK104),'u1$ustruct$u0'(sK105))
| ~ 'm1$ugroup$u2'(sK102,sK103)
| ~ 'v3$ugroup$u1'(sK103)
| ~ 'v3$ugroup$u1'(sK102)
| ~ 'l1$ugroup$u1'(sK103)
| ~ 'l1$ugroup$u1'(sK102) ),
inference(resolution,[status(thm)],[d14,d10]) ).
cnf(d16,plain,
( 'v3$ustruct$u0'(sK100)
| ~ 'v3$ustruct$u0'(sK102)
| ~ 'v3$ugroup$u1'(sK100)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c16,c81]) ).
cnf(d17,plain,
( ~ 'v3$ustruct$u0'(sK102)
| ~ 'v3$ugroup$u1'(sK100)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c73,d16]) ).
cnf(d18,plain,
( ~ 'v3$ustruct$u0'(sK102)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c74,d17]) ).
cnf(d19,plain,
~ 'v3$ustruct$u0'(sK102),
inference(resolution,[status(thm)],[c76,d18]) ).
cnf(d20,plain,
( 'r1$utarski'('u1$ustruct$u0'(sK104),'u1$ustruct$u0'(sK105))
| ~ 'm1$ugroup$u2'(sK102,sK103)
| ~ 'v3$ugroup$u1'(sK103)
| ~ 'v3$ugroup$u1'(sK102)
| ~ 'l1$ugroup$u1'(sK103)
| ~ 'l1$ugroup$u1'(sK102) ),
inference(resolution,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
( 'v3$ustruct$u0'(sK100)
| ~ 'v3$ugroup$u1'(sK100)
| 'v3$ugroup$u1'(sK103)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c17,c82]) ).
cnf(d22,plain,
( 'v3$ugroup$u1'(sK103)
| ~ 'v3$ugroup$u1'(sK100)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c73,d21]) ).
cnf(d23,plain,
( 'v3$ugroup$u1'(sK103)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c74,d22]) ).
cnf(d24,plain,
'v3$ugroup$u1'(sK103),
inference(resolution,[status(thm)],[c76,d23]) ).
cnf(d25,plain,
( 'r1$utarski'('u1$ustruct$u0'(sK104),'u1$ustruct$u0'(sK105))
| ~ 'm1$ugroup$u2'(sK102,sK103)
| ~ 'v3$ugroup$u1'(sK102)
| ~ 'l1$ugroup$u1'(sK103)
| ~ 'l1$ugroup$u1'(sK102) ),
inference(resolution,[status(thm)],[d24,d20]) ).
cnf(d26,plain,
( 'v3$ustruct$u0'(sK100)
| ~ 'v3$ugroup$u1'(sK100)
| 'v3$ugroup$u1'(sK102)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c17,c81]) ).
cnf(d27,plain,
( 'v3$ugroup$u1'(sK102)
| ~ 'v3$ugroup$u1'(sK100)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c73,d26]) ).
cnf(d28,plain,
( 'v3$ugroup$u1'(sK102)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c74,d27]) ).
cnf(d29,plain,
'v3$ugroup$u1'(sK102),
inference(resolution,[status(thm)],[c76,d28]) ).
cnf(d30,plain,
( 'r1$utarski'('u1$ustruct$u0'(sK104),'u1$ustruct$u0'(sK105))
| ~ 'm1$ugroup$u2'(sK102,sK103)
| ~ 'l1$ugroup$u1'(sK103)
| ~ 'l1$ugroup$u1'(sK102) ),
inference(resolution,[status(thm)],[d29,d25]) ).
cnf(d31,plain,
( 'v3$ustruct$u0'(sK100)
| ~ 'v3$ugroup$u1'(sK100)
| ~ 'l1$ugroup$u1'(sK100)
| 'l1$ugroup$u1'(sK103) ),
inference(resolution,[status(thm)],[c18,c82]) ).
cnf(d32,plain,
( ~ 'v3$ugroup$u1'(sK100)
| 'l1$ugroup$u1'(sK103)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c73,d31]) ).
cnf(d33,plain,
( 'l1$ugroup$u1'(sK103)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c74,d32]) ).
cnf(d34,plain,
'l1$ugroup$u1'(sK103),
inference(resolution,[status(thm)],[c76,d33]) ).
cnf(d35,plain,
( 'r1$utarski'('u1$ustruct$u0'(sK104),'u1$ustruct$u0'(sK105))
| ~ 'm1$ugroup$u2'(sK102,sK103)
| ~ 'l1$ugroup$u1'(sK102) ),
inference(resolution,[status(thm)],[d34,d30]) ).
cnf(d36,plain,
( 'v3$ustruct$u0'(sK100)
| ~ 'v3$ugroup$u1'(sK100)
| ~ 'l1$ugroup$u1'(sK100)
| 'l1$ugroup$u1'(sK102) ),
inference(resolution,[status(thm)],[c18,c81]) ).
cnf(d37,plain,
( ~ 'v3$ugroup$u1'(sK100)
| 'l1$ugroup$u1'(sK102)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c73,d36]) ).
cnf(d38,plain,
( 'l1$ugroup$u1'(sK102)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c74,d37]) ).
cnf(d39,plain,
'l1$ugroup$u1'(sK102),
inference(resolution,[status(thm)],[c76,d38]) ).
cnf(d40,plain,
( 'r1$utarski'('u1$ustruct$u0'(sK104),'u1$ustruct$u0'(sK105))
| ~ 'm1$ugroup$u2'(sK102,sK103) ),
inference(resolution,[status(thm)],[d39,d35]) ).
cnf(d41,plain,
( ~ 'v4$ugroup$u1'(sK100)
| 'v3$ustruct$u0'(sK100)
| 'm1$ugroup$u2'(sK102,sK103)
| ~ 'm1$ugroup$u2'(sK103,sK100)
| ~ 'v3$ugroup$u1'(sK100)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c53,c87]) ).
cnf(d42,plain,
( ~ 'v4$ugroup$u1'(sK100)
| ~ 'm1$ugroup$u2'(sK103,sK100)
| 'm1$ugroup$u2'(sK102,sK103)
| ~ 'v3$ugroup$u1'(sK100)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c73,d41]) ).
cnf(d43,plain,
( ~ 'v4$ugroup$u1'(sK100)
| ~ 'm1$ugroup$u2'(sK103,sK100)
| 'm1$ugroup$u2'(sK102,sK103)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c74,d42]) ).
cnf(d44,plain,
( ~ 'm1$ugroup$u2'(sK103,sK100)
| 'm1$ugroup$u2'(sK102,sK103)
| ~ 'l1$ugroup$u1'(sK100) ),
inference(resolution,[status(thm)],[c75,d43]) ).
cnf(d45,plain,
( ~ 'm1$ugroup$u2'(sK103,sK100)
| 'm1$ugroup$u2'(sK102,sK103) ),
inference(resolution,[status(thm)],[c76,d44]) ).
cnf(d46,plain,
'm1$ugroup$u2'(sK102,sK103),
inference(resolution,[status(thm)],[c82,d45]) ).
cnf(d47,plain,
'r1$utarski'('u1$ustruct$u0'(sK104),'u1$ustruct$u0'(sK105)),
inference(resolution,[status(thm)],[d46,d40]) ).
cnf(d48,plain,
( ~ 'v4$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$ugroup$u2'(sK105,X0)
| ~ 'm1$ugroup$u2'(sK104,X0)
| 'm1$ugroup$u2'(sK104,sK105)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0) ),
inference(resolution,[status(thm)],[d47,c65]) ).
cnf(d49,plain,
( ~ 'v4$ugroup$u1'(sK99)
| 'v3$ustruct$u0'(sK99)
| ~ 'm1$ugroup$u2'(sK104,sK105)
| ~ 'm1$ugroup$u2'(sK105,sK99)
| ~ 'v3$ugroup$u1'(sK99)
| ~ 'l1$ugroup$u1'(sK99) ),
inference(resolution,[status(thm)],[c54,c88]) ).
cnf(d50,plain,
( ~ 'v4$ugroup$u1'(sK99)
| ~ 'm1$ugroup$u2'(sK105,sK99)
| ~ 'm1$ugroup$u2'(sK104,sK105)
| ~ 'v3$ugroup$u1'(sK99)
| ~ 'l1$ugroup$u1'(sK99) ),
inference(resolution,[status(thm)],[c69,d49]) ).
cnf(d51,plain,
( ~ 'v4$ugroup$u1'(sK99)
| ~ 'm1$ugroup$u2'(sK105,sK99)
| ~ 'm1$ugroup$u2'(sK104,sK105)
| ~ 'l1$ugroup$u1'(sK99) ),
inference(resolution,[status(thm)],[c70,d50]) ).
cnf(d52,plain,
( ~ 'm1$ugroup$u2'(sK105,sK99)
| ~ 'm1$ugroup$u2'(sK104,sK105)
| ~ 'l1$ugroup$u1'(sK99) ),
inference(resolution,[status(thm)],[c71,d51]) ).
cnf(d53,plain,
( ~ 'm1$ugroup$u2'(sK105,sK99)
| ~ 'm1$ugroup$u2'(sK104,sK105) ),
inference(resolution,[status(thm)],[c72,d52]) ).
cnf(d54,plain,
~ 'm1$ugroup$u2'(sK104,sK105),
inference(resolution,[status(thm)],[c84,d53]) ).
cnf(d55,plain,
( ~ 'v4$ugroup$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$ugroup$u2'(sK105,X0)
| ~ 'm1$ugroup$u2'(sK104,X0)
| ~ 'v3$ugroup$u1'(X0)
| ~ 'l1$ugroup$u1'(X0) ),
inference(resolution,[status(thm)],[d54,d48]) ).
cnf(d56,plain,
( ~ 'v4$ugroup$u1'(sK99)
| 'v3$ustruct$u0'(sK99)
| ~ 'm1$ugroup$u2'(sK104,sK99)
| ~ 'v3$ugroup$u1'(sK99)
| ~ 'l1$ugroup$u1'(sK99) ),
inference(resolution,[status(thm)],[d55,c84]) ).
cnf(d57,plain,
( ~ 'v4$ugroup$u1'(sK99)
| ~ 'm1$ugroup$u2'(sK104,sK99)
| ~ 'v3$ugroup$u1'(sK99)
| ~ 'l1$ugroup$u1'(sK99) ),
inference(resolution,[status(thm)],[c69,d56]) ).
cnf(d58,plain,
( ~ 'v4$ugroup$u1'(sK99)
| ~ 'm1$ugroup$u2'(sK104,sK99)
| ~ 'l1$ugroup$u1'(sK99) ),
inference(resolution,[status(thm)],[c70,d57]) ).
cnf(d59,plain,
( ~ 'm1$ugroup$u2'(sK104,sK99)
| ~ 'l1$ugroup$u1'(sK99) ),
inference(resolution,[status(thm)],[c71,d58]) ).
cnf(d60,plain,
~ 'm1$ugroup$u2'(sK104,sK99),
inference(resolution,[status(thm)],[c72,d59]) ).
cnf(d61,plain,
$false,
inference(resolution,[status(thm)],[c83,d60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP638+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n003.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Fri Sep 25 15:18:07 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.65/2.73 % SZS status Theorem for theBenchmark.p
% 8.65/2.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------