%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP637+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 07:30:35 AM UTC 2026
% Result : Theorem 0.86s 0.50s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 108 ( 38 unt; 0 def)
% Number of atoms : 381 ( 19 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 442 ( 169 ~; 162 |; 78 &)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 4 avg)
% Maximal term depth : 4 ( 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 : 121 ( 6 sgn 40 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relset_1,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(d5_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ( m1_group_2(B,A)
<=> ( u1_group_1(B) = k1_realset1(u1_group_1(A),u1_struct_0(B))
& r1_tarski(u1_struct_0(B),u1_struct_0(A)) ) ) ) ),
file('theBenchmark.p',d5_group_2) ).
fof(dt_m1_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) ) ) ),
file('theBenchmark.p',dt_m1_group_2) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(redefinition_k2_funct_2,axiom,
! [A,B,C,D] :
( ( m1_relset_1(C,A,B)
& v1_funct_2(C,A,B)
& v1_funct_1(C) )
=> k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ),
file('theBenchmark.p',redefinition_k2_funct_2) ).
fof(redefinition_m1_group_6,axiom,
! [A,B] :
( ( m1_group_2(B,A)
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [C] :
( m1_group_6(C,A,B)
<=> m1_group_2(C,B) ) ),
file('theBenchmark.p',redefinition_m1_group_6) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(t156_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) ) ),
file('theBenchmark.p',t156_relat_1) ).
fof(t66_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ! [C] :
( m1_group_2(C,A)
=> ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
=> m1_group_2(B,C) ) ) ) ),
file('theBenchmark.p',t66_group_2) ).
fof(t10_latsubgr,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ! [D] :
( m1_group_2(D,A)
=> ! [E] :
( m1_group_2(E,A)
=> ! [F] :
( m1_group_2(F,B)
=> ! [G] :
( m1_group_2(G,B)
=> ( ( m1_group_6(D,A,E)
& u1_struct_0(G) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(E))
& u1_struct_0(F) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D)) )
=> m1_group_6(F,B,G) ) ) ) ) ) ) ) ),
file('theBenchmark.p',t10_latsubgr) ).
fof(t10_latsubgr_neg,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ! [D] :
( m1_group_2(D,A)
=> ! [E] :
( m1_group_2(E,A)
=> ! [F] :
( m1_group_2(F,B)
=> ! [G] :
( m1_group_2(G,B)
=> ( ( m1_group_6(D,A,E)
& u1_struct_0(G) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(E))
& u1_struct_0(F) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D)) )
=> m1_group_6(F,B,G) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t10_latsubgr]) ).
fof(nnf_54,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ? [G] :
( ~ m1_group_6(F,B,G)
& m1_group_6(D,A,E)
& k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(E)) = u1_struct_0(G)
& k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D)) = u1_struct_0(F)
& m1_group_2(G,B) )
& m1_group_2(F,B) )
& m1_group_2(E,A) )
& m1_group_2(D,A) )
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
& l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t10_latsubgr_neg]) ).
fof(sk_t10_latsubgr_neg,plain,
( ~ m1_group_6(sK5,sK1,sK6)
& m1_group_6(sK3,sK0,sK4)
& k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(sK4)) = u1_struct_0(sK6)
& k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(sK3)) = u1_struct_0(sK5)
& m1_group_2(sK6,sK1)
& m1_group_2(sK5,sK1)
& m1_group_2(sK4,sK0)
& m1_group_2(sK3,sK0)
& m2_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
& v1_group_6(sK2,sK0,sK1)
& v1_funct_2(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
& v1_funct_1(sK2)
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1)
& l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3),skolemize(E,sK4),skolemize(F,sK5),skolemize(G,sK6)],[nnf_54]) ).
cnf(c_55,negated_conjecture,
v4_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_56,plain,
( m1_group_2(B,C)
| ~ r1_tarski(u1_struct_0(B),u1_struct_0(C))
| ~ m1_group_2(C,A)
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t66_group_2]) ).
cnf(c_57,plain,
( ~ m1_group_2(C,B)
| m1_group_6(C,A,B)
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[redefinition_m1_group_6]) ).
cnf(c_58,plain,
( m1_group_2(C,B)
| ~ m1_group_6(C,A,B)
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[redefinition_m1_group_6]) ).
cnf(c_61,negated_conjecture,
v4_group_1(sK1),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_62,plain,
( k9_relat_1(A,D) = k2_funct_2(B,C,A,D)
| ~ m1_relset_1(A,B,C)
| ~ v1_funct_2(A,B,C)
| ~ v1_funct_1(A) ),
inference(clausify,[status(thm)],[redefinition_k2_funct_2]) ).
cnf(c_63,negated_conjecture,
v1_funct_1(sK2),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_72,plain,
( m1_relset_1(A,B,C)
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_74,negated_conjecture,
m2_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_77,plain,
( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C)))
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[dt_m2_relset_1]) ).
cnf(c_78,plain,
( r1_tarski(k9_relat_1(A,B),k9_relat_1(A,C))
| ~ r1_tarski(B,C)
| ~ v1_relat_1(A) ),
inference(clausify,[status(thm)],[t156_relat_1]) ).
cnf(c_81,plain,
( v1_relat_1(A)
| ~ m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) ),
inference(clausify,[status(thm)],[cc1_relset_1]) ).
cnf(c_97,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK1)))),
inference(resolve,[status(thm)],[c_77,c_74]) ).
cnf(c_103,negated_conjecture,
m1_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(resolve,[status(thm)],[c_72,c_74]) ).
cnf(c_126,negated_conjecture,
( k9_relat_1(sK2,C) = k2_funct_2(A,B,sK2,C)
| ~ m1_relset_1(sK2,A,B)
| ~ v1_funct_2(sK2,A,B) ),
inference(resolve,[status(thm)],[c_62,c_63]) ).
cnf(c_127,negated_conjecture,
( k2_funct_2(A,B,sK2,C) = k9_relat_1(sK2,C)
| ~ m1_relset_1(sK2,A,B)
| ~ v1_funct_2(sK2,A,B) ),
inference(copy,[status(thm)],[c_126]) ).
cnf(c_129,plain,
( r1_tarski(u1_struct_0(B),u1_struct_0(A))
| ~ m1_group_2(B,A)
| ~ l1_group_1(B)
| ~ v3_group_1(B)
| v3_struct_0(B)
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[d5_group_2]) ).
cnf(c_132,plain,
( ~ v3_struct_0(B)
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_m1_group_2]) ).
cnf(c_133,plain,
( v3_group_1(B)
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_m1_group_2]) ).
cnf(c_134,plain,
( l1_group_1(B)
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_m1_group_2]) ).
cnf(c_163,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_164,negated_conjecture,
v3_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_165,negated_conjecture,
l1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_166,negated_conjecture,
~ v3_struct_0(sK1),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_167,negated_conjecture,
v3_group_1(sK1),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_168,negated_conjecture,
l1_group_1(sK1),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_169,negated_conjecture,
v1_funct_2(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_170,negated_conjecture,
m1_group_2(sK3,sK0),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_171,negated_conjecture,
m1_group_2(sK4,sK0),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_172,negated_conjecture,
m1_group_2(sK5,sK1),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_173,negated_conjecture,
m1_group_2(sK6,sK1),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_174,negated_conjecture,
k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(sK3)) = u1_struct_0(sK5),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_175,negated_conjecture,
k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(sK4)) = u1_struct_0(sK6),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_176,negated_conjecture,
m1_group_6(sK3,sK0,sK4),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_177,negated_conjecture,
~ m1_group_6(sK5,sK1,sK6),
inference(split_conjunct,[status(thm)],[sk_t10_latsubgr_neg]) ).
cnf(c_182,negated_conjecture,
( m1_group_2(B,A)
| ~ m1_group_6(B,sK0,A)
| ~ m1_group_2(A,sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_55,c_58]) ).
cnf(c_614,negated_conjecture,
( m1_group_2(B,A)
| ~ m1_group_6(B,sK0,A)
| ~ m1_group_2(A,sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_163,c_182]) ).
cnf(c_615,negated_conjecture,
( m1_group_2(B,A)
| ~ m1_group_6(B,sK0,A)
| ~ m1_group_2(A,sK0)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_164,c_614]) ).
cnf(c_183,negated_conjecture,
( m1_group_2(B,A)
| ~ m1_group_6(B,sK0,A)
| ~ m1_group_2(A,sK0) ),
inference(resolve,[status(thm)],[c_165,c_615]) ).
cnf(c_188,negated_conjecture,
( m1_group_2(A,B)
| ~ r1_tarski(u1_struct_0(A),u1_struct_0(B))
| ~ m1_group_2(B,sK1)
| ~ m1_group_2(A,sK1)
| ~ l1_group_1(sK1)
| ~ v3_group_1(sK1)
| v3_struct_0(sK1) ),
inference(resolve,[status(thm)],[c_61,c_56]) ).
cnf(c_616,negated_conjecture,
( m1_group_2(A,B)
| ~ r1_tarski(u1_struct_0(A),u1_struct_0(B))
| ~ m1_group_2(B,sK1)
| ~ m1_group_2(A,sK1)
| ~ l1_group_1(sK1)
| ~ v3_group_1(sK1) ),
inference(resolve,[status(thm)],[c_166,c_188]) ).
cnf(c_617,negated_conjecture,
( m1_group_2(A,B)
| ~ r1_tarski(u1_struct_0(A),u1_struct_0(B))
| ~ m1_group_2(B,sK1)
| ~ m1_group_2(A,sK1)
| ~ l1_group_1(sK1) ),
inference(resolve,[status(thm)],[c_167,c_616]) ).
cnf(c_189,negated_conjecture,
( m1_group_2(A,B)
| ~ r1_tarski(u1_struct_0(A),u1_struct_0(B))
| ~ m1_group_2(B,sK1)
| ~ m1_group_2(A,sK1) ),
inference(resolve,[status(thm)],[c_168,c_617]) ).
cnf(c_190,negated_conjecture,
( ~ m1_group_2(B,A)
| m1_group_6(B,sK1,A)
| ~ m1_group_2(A,sK1)
| ~ l1_group_1(sK1)
| ~ v3_group_1(sK1)
| v3_struct_0(sK1) ),
inference(resolve,[status(thm)],[c_61,c_57]) ).
cnf(c_618,negated_conjecture,
( ~ m1_group_2(B,A)
| m1_group_6(B,sK1,A)
| ~ m1_group_2(A,sK1)
| ~ l1_group_1(sK1)
| ~ v3_group_1(sK1) ),
inference(resolve,[status(thm)],[c_166,c_190]) ).
cnf(c_619,negated_conjecture,
( ~ m1_group_2(B,A)
| m1_group_6(B,sK1,A)
| ~ m1_group_2(A,sK1)
| ~ l1_group_1(sK1) ),
inference(resolve,[status(thm)],[c_167,c_618]) ).
cnf(c_191,negated_conjecture,
( ~ m1_group_2(B,A)
| m1_group_6(B,sK1,A)
| ~ m1_group_2(A,sK1) ),
inference(resolve,[status(thm)],[c_168,c_619]) ).
cnf(c_200,plain,
( ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(D,E)))
| r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B))
| ~ r1_tarski(A,B) ),
inference(resolve,[status(thm)],[c_78,c_81]) ).
cnf(c_620,negated_conjecture,
( k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,A) = k9_relat_1(sK2,A)
| ~ m1_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)) ),
inference(resolve,[status(thm)],[c_169,c_127]) ).
cnf(c_262,negated_conjecture,
k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,A) = k9_relat_1(sK2,A),
inference(resolve,[status(thm)],[c_103,c_620]) ).
cnf(c_266,negated_conjecture,
k9_relat_1(sK2,u1_struct_0(sK4)) = u1_struct_0(sK6),
inference(paramod,[status(thm)],[c_262,c_175]) ).
cnf(c_267,negated_conjecture,
k9_relat_1(sK2,u1_struct_0(sK3)) = u1_struct_0(sK5),
inference(paramod,[status(thm)],[c_262,c_174]) ).
cnf(c_621,negated_conjecture,
( l1_group_1(sK3)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_170,c_134]) ).
cnf(c_622,negated_conjecture,
( l1_group_1(sK3)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_163,c_621]) ).
cnf(c_623,negated_conjecture,
( l1_group_1(sK3)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_164,c_622]) ).
cnf(c_268,negated_conjecture,
l1_group_1(sK3),
inference(resolve,[status(thm)],[c_165,c_623]) ).
cnf(c_624,negated_conjecture,
( v3_group_1(sK3)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_170,c_133]) ).
cnf(c_625,negated_conjecture,
( v3_group_1(sK3)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_163,c_624]) ).
cnf(c_626,negated_conjecture,
( v3_group_1(sK3)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_164,c_625]) ).
cnf(c_269,negated_conjecture,
v3_group_1(sK3),
inference(resolve,[status(thm)],[c_165,c_626]) ).
cnf(c_627,negated_conjecture,
( ~ v3_struct_0(sK3)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_170,c_132]) ).
cnf(c_628,negated_conjecture,
( ~ v3_struct_0(sK3)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_163,c_627]) ).
cnf(c_629,negated_conjecture,
( ~ v3_struct_0(sK3)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_164,c_628]) ).
cnf(c_270,negated_conjecture,
~ v3_struct_0(sK3),
inference(resolve,[status(thm)],[c_165,c_629]) ).
cnf(c_630,negated_conjecture,
( l1_group_1(sK4)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_171,c_134]) ).
cnf(c_631,negated_conjecture,
( l1_group_1(sK4)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_163,c_630]) ).
cnf(c_632,negated_conjecture,
( l1_group_1(sK4)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_164,c_631]) ).
cnf(c_273,negated_conjecture,
l1_group_1(sK4),
inference(resolve,[status(thm)],[c_165,c_632]) ).
cnf(c_633,negated_conjecture,
( v3_group_1(sK4)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_171,c_133]) ).
cnf(c_634,negated_conjecture,
( v3_group_1(sK4)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_163,c_633]) ).
cnf(c_635,negated_conjecture,
( v3_group_1(sK4)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_164,c_634]) ).
cnf(c_274,negated_conjecture,
v3_group_1(sK4),
inference(resolve,[status(thm)],[c_165,c_635]) ).
cnf(c_636,negated_conjecture,
( ~ v3_struct_0(sK4)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_171,c_132]) ).
cnf(c_637,negated_conjecture,
( ~ v3_struct_0(sK4)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_163,c_636]) ).
cnf(c_638,negated_conjecture,
( ~ v3_struct_0(sK4)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_164,c_637]) ).
cnf(c_275,negated_conjecture,
~ v3_struct_0(sK4),
inference(resolve,[status(thm)],[c_165,c_638]) ).
cnf(c_639,negated_conjecture,
( m1_group_2(sK3,sK4)
| ~ m1_group_2(sK4,sK0) ),
inference(resolve,[status(thm)],[c_183,c_176]) ).
cnf(c_296,negated_conjecture,
m1_group_2(sK3,sK4),
inference(resolve,[status(thm)],[c_171,c_639]) ).
cnf(c_301,plain,
( ~ m1_group_2(A,sK6)
| m1_group_6(A,sK1,sK6) ),
inference(resolve,[status(thm)],[c_191,c_173]) ).
cnf(c_640,plain,
( r1_tarski(u1_struct_0(sK3),u1_struct_0(sK4))
| ~ l1_group_1(sK3)
| ~ v3_group_1(sK3)
| v3_struct_0(sK3)
| ~ l1_group_1(sK4)
| ~ v3_group_1(sK4)
| v3_struct_0(sK4) ),
inference(resolve,[status(thm)],[c_296,c_129]) ).
cnf(c_641,plain,
( r1_tarski(u1_struct_0(sK3),u1_struct_0(sK4))
| ~ l1_group_1(sK3)
| ~ v3_group_1(sK3)
| v3_struct_0(sK3)
| ~ l1_group_1(sK4)
| ~ v3_group_1(sK4) ),
inference(resolve,[status(thm)],[c_275,c_640]) ).
cnf(c_642,plain,
( r1_tarski(u1_struct_0(sK3),u1_struct_0(sK4))
| ~ l1_group_1(sK3)
| ~ v3_group_1(sK3)
| v3_struct_0(sK3)
| ~ l1_group_1(sK4) ),
inference(resolve,[status(thm)],[c_274,c_641]) ).
cnf(c_643,plain,
( r1_tarski(u1_struct_0(sK3),u1_struct_0(sK4))
| ~ l1_group_1(sK3)
| ~ v3_group_1(sK3)
| v3_struct_0(sK3) ),
inference(resolve,[status(thm)],[c_273,c_642]) ).
cnf(c_644,plain,
( r1_tarski(u1_struct_0(sK3),u1_struct_0(sK4))
| ~ l1_group_1(sK3)
| ~ v3_group_1(sK3) ),
inference(resolve,[status(thm)],[c_270,c_643]) ).
cnf(c_645,plain,
( r1_tarski(u1_struct_0(sK3),u1_struct_0(sK4))
| ~ l1_group_1(sK3) ),
inference(resolve,[status(thm)],[c_269,c_644]) ).
cnf(c_363,plain,
r1_tarski(u1_struct_0(sK3),u1_struct_0(sK4)),
inference(resolve,[status(thm)],[c_268,c_645]) ).
cnf(c_646,plain,
( ~ m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C)))
| r1_tarski(k9_relat_1(A,u1_struct_0(sK3)),k9_relat_1(A,u1_struct_0(sK4))) ),
inference(resolve,[status(thm)],[c_200,c_363]) ).
cnf(c_647,negated_conjecture,
r1_tarski(k9_relat_1(sK2,u1_struct_0(sK3)),k9_relat_1(sK2,u1_struct_0(sK4))),
inference(resolve,[status(thm)],[c_646,c_97]) ).
cnf(c_648,negated_conjecture,
r1_tarski(u1_struct_0(sK5),k9_relat_1(sK2,u1_struct_0(sK4))),
inference(paramod,[status(thm)],[c_267,c_647]) ).
cnf(c_558,negated_conjecture,
r1_tarski(u1_struct_0(sK5),u1_struct_0(sK6)),
inference(paramod,[status(thm)],[c_266,c_648]) ).
cnf(c_649,negated_conjecture,
( m1_group_2(sK5,sK6)
| ~ m1_group_2(sK6,sK1)
| ~ m1_group_2(sK5,sK1) ),
inference(resolve,[status(thm)],[c_558,c_189]) ).
cnf(c_650,negated_conjecture,
( m1_group_2(sK5,sK6)
| ~ m1_group_2(sK6,sK1) ),
inference(resolve,[status(thm)],[c_172,c_649]) ).
cnf(c_602,negated_conjecture,
m1_group_2(sK5,sK6),
inference(resolve,[status(thm)],[c_173,c_650]) ).
cnf(c_651,plain,
m1_group_6(sK5,sK1,sK6),
inference(resolve,[status(thm)],[c_602,c_301]) ).
cnf(c_613,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_177,c_651]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP637+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 15:20:13 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2731448 was started by sandbox2 on n016,
% 0.08/0.36 % Fri Sep 25 15:20:13 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.86/0.50
% 0.86/0.50 % SZS status Theorem for theBenchmark
% 0.86/0.50
% 0.86/0.50 % Proof 1 at 0.06 (+ 0.03) seconds.
% 0.86/0.50 % Length of proof is 67.
% 0.86/0.50 % Level of proof is 8.
% 0.86/0.50 % Maximum clause weight is 31.000.
% 0.86/0.50 % Given clauses 237.
% 0.86/0.50
% 0.86/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------