%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP624+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 07:30:32 AM UTC 2026
% Result : Theorem 38.32s 6.05s
% Output : CNFRefutation 38.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 95 ( 19 unt; 0 def)
% Number of atoms : 389 ( 39 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 502 ( 208 ~; 221 |; 51 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-6 aty)
% Number of variables : 112 ( 2 sgn 32 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m2_relset_1(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& v1_funct_2(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& v1_funct_1(B) )
=> ( B = k2_autgroup(A)
<=> ! [C] :
( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
=> ! [D] :
( m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
=> k2_binop_1(k1_autgroup(A),k1_autgroup(A),k1_autgroup(A),B,C,D) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D,C) ) ) ) ) ),
file('theBenchmark.p',d2_autgroup) ).
fof(dt_k1_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_fraenkel(k1_autgroup(A),u1_struct_0(A),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k1_autgroup) ).
fof(dt_k2_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ( m2_relset_1(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& v1_funct_2(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& v1_funct_1(k2_autgroup(A)) ) ),
file('theBenchmark.p',dt_k2_autgroup) ).
fof(dt_l1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_group_1) ).
fof(dt_m1_fraenkel,axiom,
! [A,B,C] :
( m1_fraenkel(C,A,B)
=> ( v1_fraenkel(C)
& ~ v1_xboole_0(C) ) ),
file('theBenchmark.p',dt_m1_fraenkel) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(redefinition_k2_binop_1,axiom,
! [A,B,C,D,E,F] :
( ( m1_subset_1(F,B)
& m1_subset_1(E,A)
& m1_relset_1(D,k2_zfmisc_1(A,B),C)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& v1_funct_1(D)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(A) )
=> k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ),
file('theBenchmark.p',redefinition_k2_binop_1) ).
fof(redefinition_m2_fraenkel,axiom,
! [A,B,C] :
( ( m1_fraenkel(C,A,B)
& ~ v1_xboole_0(B) )
=> ! [D] :
( m2_fraenkel(D,A,B,C)
<=> m1_subset_1(D,C) ) ),
file('theBenchmark.p',redefinition_m2_fraenkel) ).
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(t13_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
=> m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) ) ),
file('theBenchmark.p',t13_autgroup) ).
fof(t15_autgroup,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
=> ! [C] :
( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
=> k1_binop_1(k2_autgroup(A),B,C) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B) ) ) ),
file('theBenchmark.p',t15_autgroup) ).
fof(t15_autgroup_neg,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
=> ! [C] :
( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
=> k1_binop_1(k2_autgroup(A),B,C) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B) ) ) ),
inference(assume_negation,[status(cth)],[t15_autgroup]) ).
cnf(c_83,plain,
( k2_binop_1(k1_autgroup(A),k1_autgroup(A),k1_autgroup(A),B,C,D) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D,C)
| ~ m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
| ~ m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
| k2_autgroup(A) != B
| ~ m2_relset_1(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
| ~ v1_funct_2(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
| ~ v1_funct_1(B)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[d2_autgroup]) ).
cnf(c_85,plain,
( m1_fraenkel(k1_autgroup(A),u1_struct_0(A),u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k1_autgroup]) ).
cnf(c_86,plain,
( v1_funct_1(k2_autgroup(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k2_autgroup]) ).
cnf(c_87,plain,
( v1_funct_2(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k2_autgroup]) ).
cnf(c_88,plain,
( m2_relset_1(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k2_autgroup]) ).
cnf(c_94,plain,
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
| ~ m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t13_autgroup]) ).
fof(nnf_78,plain,
? [A] :
( ? [B] :
( ? [C] :
( k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B) != k1_binop_1(k2_autgroup(A),B,C)
& m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) )
& m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) )
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t15_autgroup_neg]) ).
fof(sk_t15_autgroup_neg,plain,
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1) != k1_binop_1(k2_autgroup(sK0),sK1,sK2)
& m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
& m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
& l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& v1_group_1(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_78]) ).
cnf(c_95,negated_conjecture,
v1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t15_autgroup_neg]) ).
cnf(c_113,negated_conjecture,
( m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_95,c_85]) ).
cnf(c_114,plain,
( m1_subset_1(D,B)
| ~ m2_fraenkel(D,C,A,B)
| ~ m1_fraenkel(B,C,A)
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[redefinition_m2_fraenkel]) ).
cnf(c_120,plain,
( ~ v1_xboole_0(A)
| ~ m1_fraenkel(A,B,C) ),
inference(clausify,[status(thm)],[dt_m1_fraenkel]) ).
cnf(c_123,plain,
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[fc1_struct_0]) ).
cnf(c_125,plain,
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(clausify,[status(thm)],[dt_l1_group_1]) ).
cnf(c_155,negated_conjecture,
( ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0)
| ~ v1_xboole_0(k1_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_120,c_113]) ).
cnf(c_212,negated_conjecture,
( ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0)
| m1_subset_1(A,k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_114,c_113]) ).
cnf(c_289,plain,
( k2_binop_1(A,B,D,C,E,F) = k1_binop_1(C,E,F)
| ~ m1_subset_1(F,B)
| ~ m1_subset_1(E,A)
| ~ m1_relset_1(C,k2_zfmisc_1(A,B),D)
| ~ v1_funct_2(C,k2_zfmisc_1(A,B),D)
| ~ v1_funct_1(C)
| v1_xboole_0(B)
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[redefinition_k2_binop_1]) ).
cnf(c_292,plain,
( m1_relset_1(A,B,C)
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_301,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t15_autgroup_neg]) ).
cnf(c_302,negated_conjecture,
v3_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t15_autgroup_neg]) ).
cnf(c_303,negated_conjecture,
v4_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t15_autgroup_neg]) ).
cnf(c_304,negated_conjecture,
l1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t15_autgroup_neg]) ).
cnf(c_305,negated_conjecture,
m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(split_conjunct,[status(thm)],[sk_t15_autgroup_neg]) ).
cnf(c_306,negated_conjecture,
m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(split_conjunct,[status(thm)],[sk_t15_autgroup_neg]) ).
cnf(c_307,negated_conjecture,
k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1) != k1_binop_1(k2_autgroup(sK0),sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t15_autgroup_neg]) ).
cnf(c_372,negated_conjecture,
( m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_95,c_94]) ).
cnf(c_18319,negated_conjecture,
( m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_301,c_372]) ).
cnf(c_18320,negated_conjecture,
( m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_302,c_18319]) ).
cnf(c_18321,negated_conjecture,
( m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_303,c_18320]) ).
cnf(c_373,negated_conjecture,
( m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_304,c_18321]) ).
cnf(c_374,negated_conjecture,
( m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_95,c_88]) ).
cnf(c_18322,negated_conjecture,
( m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_301,c_374]) ).
cnf(c_18323,negated_conjecture,
( m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_302,c_18322]) ).
cnf(c_18324,negated_conjecture,
( m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_303,c_18323]) ).
cnf(c_375,negated_conjecture,
m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)),
inference(resolve,[status(thm)],[c_304,c_18324]) ).
cnf(c_376,negated_conjecture,
( v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_95,c_87]) ).
cnf(c_18325,negated_conjecture,
( v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_301,c_376]) ).
cnf(c_18326,negated_conjecture,
( v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_302,c_18325]) ).
cnf(c_18327,negated_conjecture,
( v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_303,c_18326]) ).
cnf(c_377,negated_conjecture,
v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)),
inference(resolve,[status(thm)],[c_304,c_18327]) ).
cnf(c_378,negated_conjecture,
( v1_funct_1(k2_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_95,c_86]) ).
cnf(c_18328,negated_conjecture,
( v1_funct_1(k2_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_301,c_378]) ).
cnf(c_18329,negated_conjecture,
( v1_funct_1(k2_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_302,c_18328]) ).
cnf(c_18330,negated_conjecture,
( v1_funct_1(k2_autgroup(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_303,c_18329]) ).
cnf(c_379,negated_conjecture,
v1_funct_1(k2_autgroup(sK0)),
inference(resolve,[status(thm)],[c_304,c_18330]) ).
cnf(c_386,negated_conjecture,
( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),A,B,C) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),C,B)
| ~ m2_fraenkel(C,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(B,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| k2_autgroup(sK0) != A
| ~ m2_relset_1(A,k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v1_funct_2(A,k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v1_funct_1(A)
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_95,c_83]) ).
cnf(c_18331,negated_conjecture,
( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),A,B,C) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),C,B)
| ~ m2_fraenkel(C,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(B,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| k2_autgroup(sK0) != A
| ~ m2_relset_1(A,k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v1_funct_2(A,k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v1_funct_1(A)
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_301,c_386]) ).
cnf(c_18332,negated_conjecture,
( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),A,B,C) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),C,B)
| ~ m2_fraenkel(C,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(B,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| k2_autgroup(sK0) != A
| ~ m2_relset_1(A,k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v1_funct_2(A,k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v1_funct_1(A)
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_302,c_18331]) ).
cnf(c_18333,negated_conjecture,
( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),A,B,C) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),C,B)
| ~ m2_fraenkel(C,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(B,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| k2_autgroup(sK0) != A
| ~ m2_relset_1(A,k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v1_funct_2(A,k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v1_funct_1(A)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_303,c_18332]) ).
cnf(c_387,negated_conjecture,
( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),A,B,C) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),C,B)
| ~ m2_fraenkel(C,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(B,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| k2_autgroup(sK0) != A
| ~ m2_relset_1(A,k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v1_funct_2(A,k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v1_funct_1(A) ),
inference(resolve,[status(thm)],[c_304,c_18333]) ).
cnf(c_391,plain,
( ~ l1_group_1(A)
| ~ v1_xboole_0(u1_struct_0(A))
| v3_struct_0(A) ),
inference(resolve,[status(thm)],[c_123,c_125]) ).
cnf(c_469,plain,
( k2_binop_1(A,A,C,B,D,E) = k1_binop_1(B,D,E)
| ~ m1_subset_1(E,A)
| ~ m1_subset_1(D,A)
| ~ m1_relset_1(B,k2_zfmisc_1(A,A),C)
| ~ v1_funct_2(B,k2_zfmisc_1(A,A),C)
| ~ v1_funct_1(B)
| v1_xboole_0(A) ),
inference(factor,[status(thm)],[c_289]) ).
cnf(c_18334,negated_conjecture,
( ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| m1_subset_1(A,k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_301,c_212]) ).
cnf(c_18335,negated_conjecture,
( ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| m1_subset_1(A,k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_302,c_18334]) ).
cnf(c_18336,negated_conjecture,
( ~ l1_group_1(sK0)
| m1_subset_1(A,k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_303,c_18335]) ).
cnf(c_476,negated_conjecture,
( m1_subset_1(A,k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_304,c_18336]) ).
cnf(c_18337,negated_conjecture,
( ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_xboole_0(k1_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_301,c_155]) ).
cnf(c_18338,negated_conjecture,
( ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v1_xboole_0(k1_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_302,c_18337]) ).
cnf(c_18339,negated_conjecture,
( ~ l1_group_1(sK0)
| ~ v1_xboole_0(k1_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_303,c_18338]) ).
cnf(c_486,negated_conjecture,
~ v1_xboole_0(k1_autgroup(sK0)),
inference(resolve,[status(thm)],[c_304,c_18339]) ).
cnf(c_790,plain,
m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)),
inference(resolve,[status(thm)],[c_373,c_306]) ).
cnf(c_791,plain,
m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)),
inference(resolve,[status(thm)],[c_373,c_305]) ).
cnf(c_792,plain,
m1_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)),
inference(resolve,[status(thm)],[c_375,c_292]) ).
cnf(c_3618,plain,
( m1_subset_1(sK2,k1_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_790,c_476]) ).
cnf(c_3671,plain,
( m1_subset_1(sK1,k1_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_791,c_476]) ).
cnf(c_18340,negated_conjecture,
( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),A,B) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),B,A)
| ~ m2_fraenkel(B,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| k2_autgroup(sK0) != k2_autgroup(sK0)
| ~ m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_387,c_379]) ).
cnf(c_18341,negated_conjecture,
( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),A,B) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),B,A)
| ~ m2_fraenkel(B,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| k2_autgroup(sK0) != k2_autgroup(sK0)
| ~ m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_18340,c_377]) ).
cnf(c_18342,negated_conjecture,
( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),A,B) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),B,A)
| ~ m2_fraenkel(B,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| k2_autgroup(sK0) != k2_autgroup(sK0) ),
inference(resolve,[status(thm)],[c_18341,c_375]) ).
cnf(c_18343,plain,
( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),A,B) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),B,A)
| ~ m2_fraenkel(B,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
inference(xxres,[status(thm)],[c_18342]) ).
cnf(c_18344,plain,
( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,A) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),A,sK1)
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_18343,c_791]) ).
cnf(c_3677,plain,
k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,sK2) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1),
inference(resolve,[status(thm)],[c_18344,c_790]) ).
cnf(c_18345,negated_conjecture,
( k2_binop_1(A,A,B,k2_autgroup(sK0),C,D) = k1_binop_1(k2_autgroup(sK0),C,D)
| ~ m1_subset_1(D,A)
| ~ m1_subset_1(C,A)
| ~ m1_relset_1(k2_autgroup(sK0),k2_zfmisc_1(A,A),B)
| ~ v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(A,A),B)
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_469,c_379]) ).
cnf(c_18346,negated_conjecture,
( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),A,B) = k1_binop_1(k2_autgroup(sK0),A,B)
| ~ m1_subset_1(B,k1_autgroup(sK0))
| ~ m1_subset_1(A,k1_autgroup(sK0))
| ~ m1_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| v1_xboole_0(k1_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_18345,c_377]) ).
cnf(c_18347,negated_conjecture,
( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),A,B) = k1_binop_1(k2_autgroup(sK0),A,B)
| ~ m1_subset_1(B,k1_autgroup(sK0))
| ~ m1_subset_1(A,k1_autgroup(sK0))
| v1_xboole_0(k1_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_18346,c_792]) ).
cnf(c_18348,negated_conjecture,
( v1_xboole_0(u1_struct_0(sK0))
| k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,A) = k1_binop_1(k2_autgroup(sK0),sK1,A)
| ~ m1_subset_1(A,k1_autgroup(sK0))
| v1_xboole_0(k1_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_18347,c_3671]) ).
cnf(c_18349,negated_conjecture,
( v1_xboole_0(u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,sK2) = k1_binop_1(k2_autgroup(sK0),sK1,sK2)
| v1_xboole_0(k1_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_18348,c_3618]) ).
cnf(c_18350,negated_conjecture,
( v1_xboole_0(u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1) = k1_binop_1(k2_autgroup(sK0),sK1,sK2)
| v1_xboole_0(k1_autgroup(sK0)) ),
inference(paramod,[status(thm)],[c_3677,c_18349]) ).
cnf(c_18351,negated_conjecture,
( v1_xboole_0(u1_struct_0(sK0))
| k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1) = k1_binop_1(k2_autgroup(sK0),sK1,sK2)
| v1_xboole_0(k1_autgroup(sK0)) ),
inference(copy,[status(thm)],[c_18350]) ).
cnf(c_18352,negated_conjecture,
( v1_xboole_0(u1_struct_0(sK0))
| k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1) = k1_binop_1(k2_autgroup(sK0),sK1,sK2) ),
inference(resolve,[status(thm)],[c_486,c_18351]) ).
cnf(c_18314,negated_conjecture,
v1_xboole_0(u1_struct_0(sK0)),
inference(resolve,[status(thm)],[c_307,c_18352]) ).
cnf(c_18353,plain,
( ~ l1_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_18314,c_391]) ).
cnf(c_18354,negated_conjecture,
~ l1_group_1(sK0),
inference(resolve,[status(thm)],[c_301,c_18353]) ).
cnf(c_18318,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_304,c_18354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP624+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n019.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Fri Sep 25 15:06:34 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.47 % Process 3067083 was started by sandbox on n019,
% 0.20/0.47 % Fri Sep 25 15:06:34 2026
% 0.20/0.47 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.49
% 0.20/0.49 % From the command line: assign(max_seconds, 300).
% 38.32/6.05
% 38.32/6.05 % given #500 (A,wt=23): 542 m1_subset_1(f7(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))). [resolve(255,a,248,a)].
% 38.32/6.05
% 38.32/6.05 % SZS status Theorem for theBenchmark
% 38.32/6.05
% 38.32/6.05 % Proof 1 at 4.40 (+ 1.09) seconds.
% 38.32/6.05 % Length of proof is 56.
% 38.32/6.05 % Level of proof is 7.
% 38.32/6.05 % Maximum clause weight is 75.000.
% 38.32/6.05 % Given clauses 709.
% 38.32/6.05
% 38.32/6.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------