%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP628+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 : 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 07:30:33 AM UTC 2026
% Result : Theorem 2.89s 0.87s
% Output : CNFRefutation 2.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 91 ( 20 unt; 0 def)
% Number of atoms : 440 ( 60 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 587 ( 238 ~; 274 |; 51 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k3_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ( l1_group_1(k3_autgroup(A))
& v4_group_1(k3_autgroup(A))
& v3_group_1(k3_autgroup(A))
& v1_group_1(k3_autgroup(A))
& ~ v3_struct_0(k3_autgroup(A)) ) ),
file('theBenchmark.p',dt_k3_autgroup) ).
fof(dt_k5_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ( m1_group_2(k5_autgroup(A),k3_autgroup(A))
& v1_group_3(k5_autgroup(A),k3_autgroup(A))
& v1_group_1(k5_autgroup(A)) ) ),
file('theBenchmark.p',dt_k5_autgroup) ).
fof(t11_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),k1_autgroup(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_autgroup(A)))
=> ( B = C
=> k2_funct_1(B) = k3_group_1(k3_autgroup(A),C) ) ) ) ),
file('theBenchmark.p',t11_autgroup) ).
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(t51_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> m1_subset_1(C,u1_struct_0(A)) ) ) ),
file('theBenchmark.p',t51_group_2) ).
fof(t57_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_group_2(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ( D = B
=> k3_group_1(C,D) = k3_group_1(A,B) ) ) ) ) ),
file('theBenchmark.p',t57_group_2) ).
fof(t22_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] :
( m1_subset_1(C,u1_struct_0(k5_autgroup(A)))
=> ( B = C
=> k2_funct_1(B) = k3_group_1(k5_autgroup(A),C) ) ) ) ),
file('theBenchmark.p',t22_autgroup) ).
fof(t22_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] :
( m1_subset_1(C,u1_struct_0(k5_autgroup(A)))
=> ( B = C
=> k2_funct_1(B) = k3_group_1(k5_autgroup(A),C) ) ) ) ),
inference(assume_negation,[status(cth)],[t22_autgroup]) ).
cnf(c_85,plain,
( m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t51_group_2]) ).
cnf(c_86,plain,
( k3_group_1(C,D) = k3_group_1(A,B)
| D != B
| ~ m1_subset_1(D,u1_struct_0(C))
| ~ m1_group_2(C,A)
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t57_group_2]) ).
cnf(c_92,plain,
( m1_group_2(k5_autgroup(A),k3_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_k5_autgroup]) ).
cnf(c_156,plain,
( k3_group_1(k5_autgroup(A),C) = k3_group_1(k3_autgroup(A),B)
| C != B
| ~ m1_subset_1(C,u1_struct_0(k5_autgroup(A)))
| ~ m1_subset_1(B,u1_struct_0(k3_autgroup(A)))
| ~ l1_group_1(k3_autgroup(A))
| ~ v4_group_1(k3_autgroup(A))
| ~ v3_group_1(k3_autgroup(A))
| v3_struct_0(k3_autgroup(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(resolve,[status(thm)],[c_92,c_86]) ).
cnf(c_157,plain,
( k3_group_1(k3_autgroup(A),B) = k3_group_1(k5_autgroup(A),C)
| C != B
| ~ m1_subset_1(C,u1_struct_0(k5_autgroup(A)))
| ~ m1_subset_1(B,u1_struct_0(k3_autgroup(A)))
| ~ l1_group_1(k3_autgroup(A))
| ~ v4_group_1(k3_autgroup(A))
| ~ v3_group_1(k3_autgroup(A))
| v3_struct_0(k3_autgroup(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(copy,[status(thm)],[c_156]) ).
cnf(c_158,plain,
( m1_subset_1(B,u1_struct_0(k3_autgroup(A)))
| ~ m1_subset_1(B,u1_struct_0(k5_autgroup(A)))
| ~ l1_group_1(k3_autgroup(A))
| ~ v3_group_1(k3_autgroup(A))
| v3_struct_0(k3_autgroup(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(resolve,[status(thm)],[c_92,c_85]) ).
cnf(c_205,plain,
( ~ v3_struct_0(k3_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_k3_autgroup]) ).
cnf(c_207,plain,
( v3_group_1(k3_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_k3_autgroup]) ).
cnf(c_208,plain,
( v4_group_1(k3_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_k3_autgroup]) ).
cnf(c_209,plain,
( l1_group_1(k3_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_k3_autgroup]) ).
cnf(c_254,plain,
( k3_group_1(k3_autgroup(A),C) = k2_funct_1(B)
| C != B
| ~ m1_subset_1(C,u1_struct_0(k3_autgroup(A)))
| ~ m2_fraenkel(B,u1_struct_0(A),u1_struct_0(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)],[t11_autgroup]) ).
cnf(c_255,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_76,plain,
? [A] :
( ? [B] :
( ? [C] :
( k3_group_1(k5_autgroup(A),C) != k2_funct_1(B)
& C = B
& m1_subset_1(C,u1_struct_0(k5_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)],[t22_autgroup_neg]) ).
fof(sk_t22_autgroup_neg,plain,
( k3_group_1(k5_autgroup(sK0),sK2) != k2_funct_1(sK1)
& sK2 = sK1
& m1_subset_1(sK2,u1_struct_0(k5_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_76]) ).
cnf(c_263,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t22_autgroup_neg]) ).
cnf(c_264,negated_conjecture,
v1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t22_autgroup_neg]) ).
cnf(c_265,negated_conjecture,
v3_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t22_autgroup_neg]) ).
cnf(c_266,negated_conjecture,
v4_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t22_autgroup_neg]) ).
cnf(c_267,negated_conjecture,
l1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t22_autgroup_neg]) ).
cnf(c_268,negated_conjecture,
m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(split_conjunct,[status(thm)],[sk_t22_autgroup_neg]) ).
cnf(c_269,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0))),
inference(split_conjunct,[status(thm)],[sk_t22_autgroup_neg]) ).
cnf(c_270,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_t22_autgroup_neg]) ).
cnf(c_271,negated_conjecture,
k3_group_1(k5_autgroup(sK0),sK2) != k2_funct_1(sK1),
inference(split_conjunct,[status(thm)],[sk_t22_autgroup_neg]) ).
cnf(c_272,negated_conjecture,
k3_group_1(k5_autgroup(sK0),sK1) != k2_funct_1(sK1),
inference(paramod,[status(thm)],[c_270,c_271]) ).
cnf(c_302,negated_conjecture,
m1_subset_1(sK1,u1_struct_0(k5_autgroup(sK0))),
inference(paramod,[status(thm)],[c_270,c_269]) ).
cnf(c_2658,negated_conjecture,
( l1_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_264,c_209]) ).
cnf(c_2659,negated_conjecture,
( l1_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_263,c_2658]) ).
cnf(c_2660,negated_conjecture,
( l1_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_265,c_2659]) ).
cnf(c_2661,negated_conjecture,
( l1_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_266,c_2660]) ).
cnf(c_440,negated_conjecture,
l1_group_1(k3_autgroup(sK0)),
inference(resolve,[status(thm)],[c_267,c_2661]) ).
cnf(c_2662,negated_conjecture,
( v4_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_264,c_208]) ).
cnf(c_2663,negated_conjecture,
( v4_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_263,c_2662]) ).
cnf(c_2664,negated_conjecture,
( v4_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_265,c_2663]) ).
cnf(c_2665,negated_conjecture,
( v4_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_266,c_2664]) ).
cnf(c_441,negated_conjecture,
v4_group_1(k3_autgroup(sK0)),
inference(resolve,[status(thm)],[c_267,c_2665]) ).
cnf(c_2666,negated_conjecture,
( v3_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_264,c_207]) ).
cnf(c_2667,negated_conjecture,
( v3_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_263,c_2666]) ).
cnf(c_2668,negated_conjecture,
( v3_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_265,c_2667]) ).
cnf(c_2669,negated_conjecture,
( v3_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_266,c_2668]) ).
cnf(c_442,negated_conjecture,
v3_group_1(k3_autgroup(sK0)),
inference(resolve,[status(thm)],[c_267,c_2669]) ).
cnf(c_2670,negated_conjecture,
( ~ v3_struct_0(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_264,c_205]) ).
cnf(c_2671,negated_conjecture,
( ~ v3_struct_0(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_263,c_2670]) ).
cnf(c_2672,negated_conjecture,
( ~ v3_struct_0(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_265,c_2671]) ).
cnf(c_2673,negated_conjecture,
( ~ v3_struct_0(k3_autgroup(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_266,c_2672]) ).
cnf(c_444,negated_conjecture,
~ v3_struct_0(k3_autgroup(sK0)),
inference(resolve,[status(thm)],[c_267,c_2673]) ).
cnf(c_2674,negated_conjecture,
( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_268,c_255]) ).
cnf(c_2675,negated_conjecture,
( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_263,c_2674]) ).
cnf(c_2676,negated_conjecture,
( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_264,c_2675]) ).
cnf(c_2677,negated_conjecture,
( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_265,c_2676]) ).
cnf(c_2678,negated_conjecture,
( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_266,c_2677]) ).
cnf(c_481,negated_conjecture,
m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)),
inference(resolve,[status(thm)],[c_267,c_2678]) ).
cnf(c_2679,negated_conjecture,
( m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0))
| v3_struct_0(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_302,c_158]) ).
cnf(c_2680,negated_conjecture,
( m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0))
| v3_struct_0(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_263,c_2679]) ).
cnf(c_2681,negated_conjecture,
( m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0))
| v3_struct_0(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_264,c_2680]) ).
cnf(c_2682,negated_conjecture,
( m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0))
| v3_struct_0(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_265,c_2681]) ).
cnf(c_2683,negated_conjecture,
( m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0))
| v3_struct_0(k3_autgroup(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_266,c_2682]) ).
cnf(c_2684,negated_conjecture,
( m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0))
| v3_struct_0(k3_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_267,c_2683]) ).
cnf(c_2685,negated_conjecture,
( m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_444,c_2684]) ).
cnf(c_2686,negated_conjecture,
( m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_442,c_2685]) ).
cnf(c_526,negated_conjecture,
m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0))),
inference(resolve,[status(thm)],[c_440,c_2686]) ).
cnf(c_2687,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),B) = k2_funct_1(A)
| B != A
| ~ m1_subset_1(B,u1_struct_0(k3_autgroup(sK0)))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(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_254,c_264]) ).
cnf(c_2688,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),B) = k2_funct_1(A)
| B != A
| ~ m1_subset_1(B,u1_struct_0(k3_autgroup(sK0)))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_2687,c_265]) ).
cnf(c_2689,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),B) = k2_funct_1(A)
| B != A
| ~ m1_subset_1(B,u1_struct_0(k3_autgroup(sK0)))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_2688,c_266]) ).
cnf(c_2690,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),B) = k2_funct_1(A)
| B != A
| ~ m1_subset_1(B,u1_struct_0(k3_autgroup(sK0)))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_2689,c_267]) ).
cnf(c_2691,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),A) = k2_funct_1(sK1)
| A != sK1
| ~ m1_subset_1(A,u1_struct_0(k3_autgroup(sK0)))
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_2690,c_481]) ).
cnf(c_2692,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),sK1) = k2_funct_1(sK1)
| sK1 != sK1
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_2691,c_526]) ).
cnf(c_2693,plain,
( k3_group_1(k3_autgroup(sK0),sK1) = k2_funct_1(sK1)
| v3_struct_0(sK0) ),
inference(xxres,[status(thm)],[c_2692]) ).
cnf(c_2655,negated_conjecture,
k3_group_1(k3_autgroup(sK0),sK1) = k2_funct_1(sK1),
inference(resolve,[status(thm)],[c_263,c_2693]) ).
cnf(c_2694,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),A) = k3_group_1(k5_autgroup(sK0),B)
| B != A
| ~ m1_subset_1(B,u1_struct_0(k5_autgroup(sK0)))
| ~ m1_subset_1(A,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v4_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0))
| v3_struct_0(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_157,c_264]) ).
cnf(c_2695,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),A) = k3_group_1(k5_autgroup(sK0),B)
| B != A
| ~ m1_subset_1(B,u1_struct_0(k5_autgroup(sK0)))
| ~ m1_subset_1(A,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v4_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0))
| v3_struct_0(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_2694,c_265]) ).
cnf(c_2696,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),A) = k3_group_1(k5_autgroup(sK0),B)
| B != A
| ~ m1_subset_1(B,u1_struct_0(k5_autgroup(sK0)))
| ~ m1_subset_1(A,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v4_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0))
| v3_struct_0(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_2695,c_266]) ).
cnf(c_2697,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),A) = k3_group_1(k5_autgroup(sK0),B)
| B != A
| ~ m1_subset_1(B,u1_struct_0(k5_autgroup(sK0)))
| ~ m1_subset_1(A,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v4_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0))
| v3_struct_0(k3_autgroup(sK0))
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_2696,c_267]) ).
cnf(c_2698,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),A) = k3_group_1(k5_autgroup(sK0),B)
| B != A
| ~ m1_subset_1(B,u1_struct_0(k5_autgroup(sK0)))
| ~ m1_subset_1(A,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v4_group_1(k3_autgroup(sK0))
| v3_struct_0(k3_autgroup(sK0))
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_2697,c_442]) ).
cnf(c_2699,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),A) = k3_group_1(k5_autgroup(sK0),B)
| B != A
| ~ m1_subset_1(B,u1_struct_0(k5_autgroup(sK0)))
| ~ m1_subset_1(A,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| v3_struct_0(k3_autgroup(sK0))
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_2698,c_441]) ).
cnf(c_2700,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),A) = k3_group_1(k5_autgroup(sK0),B)
| B != A
| ~ m1_subset_1(B,u1_struct_0(k5_autgroup(sK0)))
| ~ m1_subset_1(A,u1_struct_0(k3_autgroup(sK0)))
| v3_struct_0(k3_autgroup(sK0))
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_2699,c_440]) ).
cnf(c_2701,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),sK1) = k3_group_1(k5_autgroup(sK0),A)
| A != sK1
| ~ m1_subset_1(A,u1_struct_0(k5_autgroup(sK0)))
| v3_struct_0(k3_autgroup(sK0))
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_2700,c_526]) ).
cnf(c_2702,negated_conjecture,
( k3_group_1(k3_autgroup(sK0),sK1) = k3_group_1(k5_autgroup(sK0),sK1)
| sK1 != sK1
| v3_struct_0(k3_autgroup(sK0))
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_2701,c_302]) ).
cnf(c_2703,plain,
( k3_group_1(k3_autgroup(sK0),sK1) = k3_group_1(k5_autgroup(sK0),sK1)
| v3_struct_0(k3_autgroup(sK0))
| v3_struct_0(sK0) ),
inference(xxres,[status(thm)],[c_2702]) ).
cnf(c_2704,plain,
( k2_funct_1(sK1) = k3_group_1(k5_autgroup(sK0),sK1)
| v3_struct_0(k3_autgroup(sK0))
| v3_struct_0(sK0) ),
inference(paramod,[status(thm)],[c_2655,c_2703]) ).
cnf(c_2705,plain,
( k3_group_1(k5_autgroup(sK0),sK1) = k2_funct_1(sK1)
| v3_struct_0(k3_autgroup(sK0))
| v3_struct_0(sK0) ),
inference(copy,[status(thm)],[c_2704]) ).
cnf(c_2706,negated_conjecture,
( k3_group_1(k5_autgroup(sK0),sK1) = k2_funct_1(sK1)
| v3_struct_0(k3_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_263,c_2705]) ).
cnf(c_2707,negated_conjecture,
k3_group_1(k5_autgroup(sK0),sK1) = k2_funct_1(sK1),
inference(resolve,[status(thm)],[c_444,c_2706]) ).
cnf(c_2657,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_272,c_2707]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP628+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 15:14:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2726046 was started by sandbox on n016,
% 0.10/0.37 % Fri Sep 25 15:14:45 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 2.89/0.87
% 2.89/0.87 % given #500 (F,wt=25): 1824 -v3_struct_0(f9(f8(f9(c12)))). [resolve(751,a,163,e),unit_del(a,748),unit_del(b,746),unit_del(c,744)].
% 2.89/0.87
% 2.89/0.87 % SZS status Theorem for theBenchmark
% 2.89/0.87
% 2.89/0.87 % Proof 1 at 0.35 (+ 0.11) seconds.
% 2.89/0.87 % Length of proof is 38.
% 2.89/0.87 % Level of proof is 5.
% 2.89/0.87 % Maximum clause weight is 59.000.
% 2.89/0.87 % Given clauses 623.
% 2.89/0.87
% 2.89/0.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------