%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP628+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 01:34:55 PM UTC 2026
% Result : Theorem 4.79s 1.41s
% Output : CNFRefutation 4.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 81 ( 24 unt; 0 def)
% Number of atoms : 440 ( 41 equ)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 600 ( 241 ~; 260 |; 74 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 97 ( 0 sgn 91 !; 6 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k5_autgroup(X0)))
=> ( X1 = X2
=> k2_funct_1(X1) = k3_group_1(k5_autgroup(X0),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_autgroup) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k5_autgroup(X0)))
=> ( X1 = X2
=> k2_funct_1(X1) = k3_group_1(k5_autgroup(X0),X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f22,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ( l1_group_1(k3_autgroup(X0))
& v4_group_1(k3_autgroup(X0))
& v3_group_1(k3_autgroup(X0))
& v1_group_1(k3_autgroup(X0))
& ~ v3_struct_0(k3_autgroup(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_autgroup) ).
fof(f25,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ( m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
& v1_group_3(k5_autgroup(X0),k3_autgroup(X0))
& v1_group_1(k5_autgroup(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_autgroup) ).
fof(f67,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k3_autgroup(X0)))
=> ( X1 = X2
=> k2_funct_1(X1) = k3_group_1(k3_autgroup(X0),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_autgroup) ).
fof(f68,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_autgroup) ).
fof(f73,axiom,
! [X0] :
( ( l1_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> m1_subset_1(X2,u1_struct_0(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_group_2) ).
fof(f74,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_group_2(X2,X0)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X2))
=> ( X3 = X1
=> k3_group_1(X2,X3) = k3_group_1(X0,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_group_2) ).
fof(f80,plain,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ( m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
& v1_group_1(k5_autgroup(X0)) ) ),
inference(pure_predicate_removal,[],[f25]) ).
fof(f85,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(k5_autgroup(X0)))
& X1 = X2
& k2_funct_1(X1) != k3_group_1(k5_autgroup(X0),X2) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f86,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(k5_autgroup(X0)))
& X1 = X2
& k2_funct_1(X1) != k3_group_1(k5_autgroup(X0),X2) ) ) ),
inference(flattening,[],[f85]) ).
fof(f88,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| m1_subset_1(X2,u1_struct_0(X0)) ) ) ),
inference(ennf_transformation,[],[f73]) ).
fof(f89,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| m1_subset_1(X2,u1_struct_0(X0)) ) ) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
inference(ennf_transformation,[],[f68]) ).
fof(f91,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
inference(flattening,[],[f90]) ).
fof(f94,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ( m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
& v1_group_1(k5_autgroup(X0)) ) ),
inference(ennf_transformation,[],[f80]) ).
fof(f95,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ( m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
& v1_group_1(k5_autgroup(X0)) ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X0)))
| X1 != X2
| k2_funct_1(X1) = k3_group_1(k3_autgroup(X0),X2) ) ) ),
inference(ennf_transformation,[],[f67]) ).
fof(f97,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X0)))
| X1 != X2
| k2_funct_1(X1) = k3_group_1(k3_autgroup(X0),X2) ) ) ),
inference(flattening,[],[f96]) ).
fof(f100,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_group_2(X2,X0)
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X2))
| X1 != X3
| k3_group_1(X2,X3) = k3_group_1(X0,X1) ) ) ) ),
inference(ennf_transformation,[],[f74]) ).
fof(f101,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_group_2(X2,X0)
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X2))
| X1 != X3
| k3_group_1(X2,X3) = k3_group_1(X0,X1) ) ) ) ),
inference(flattening,[],[f100]) ).
fof(f119,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ( l1_group_1(k3_autgroup(X0))
& v4_group_1(k3_autgroup(X0))
& v3_group_1(k3_autgroup(X0))
& v1_group_1(k3_autgroup(X0))
& ~ v3_struct_0(k3_autgroup(X0)) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f120,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ( l1_group_1(k3_autgroup(X0))
& v4_group_1(k3_autgroup(X0))
& v3_group_1(k3_autgroup(X0))
& v1_group_1(k3_autgroup(X0))
& ~ v3_struct_0(k3_autgroup(X0)) ) ),
inference(flattening,[],[f119]) ).
fof(f148,plain,
( l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& v1_group_1(sK0)
& ~ v3_struct_0(sK0)
& m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
& m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0)))
& sK1 = sK2
& k2_funct_1(sK1) != k3_group_1(k5_autgroup(sK0),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f86]) ).
fof(f172,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f173,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f174,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f175,plain,
v1_group_1(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f176,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f177,plain,
m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(cnf_transformation,[],[f148]) ).
fof(f178,plain,
m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0))),
inference(cnf_transformation,[],[f148]) ).
fof(f179,plain,
sK1 = sK2,
inference(cnf_transformation,[],[f148]) ).
fof(f180,plain,
k2_funct_1(sK1) != k3_group_1(k5_autgroup(sK0),sK2),
inference(cnf_transformation,[],[f148]) ).
fof(f182,plain,
! [X2,X0,X1] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| m1_subset_1(X2,u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f186,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f190,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_group_2(k5_autgroup(X0),k3_autgroup(X0)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X0)))
| X1 != X2
| k2_funct_1(X1) = k3_group_1(k3_autgroup(X0),X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f195,plain,
! [X2,X3,X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_group_2(X2,X0)
| ~ m1_subset_1(X3,u1_struct_0(X2))
| X1 != X3
| k3_group_1(X0,X1) = k3_group_1(X2,X3) ),
inference(cnf_transformation,[],[f101]) ).
fof(f215,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| l1_group_1(k3_autgroup(X0)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f216,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| v4_group_1(k3_autgroup(X0)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f217,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| v3_group_1(k3_autgroup(X0)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f219,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ v3_struct_0(k3_autgroup(X0)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f273,plain,
k3_group_1(k5_autgroup(sK0),sK2) != k2_funct_1(sK2),
inference(definition_unfolding,[],[f180,f179]) ).
fof(f274,plain,
m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(definition_unfolding,[],[f177,f179]) ).
fof(f275,plain,
! [X2,X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X0)))
| k3_group_1(k3_autgroup(X0),X2) = k2_funct_1(X2) ),
inference(equality_resolution,[],[f192]) ).
fof(f276,plain,
! [X2,X3,X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_group_2(X2,X0)
| ~ m1_subset_1(X3,u1_struct_0(X2))
| k3_group_1(X2,X3) = k3_group_1(X0,X3) ),
inference(equality_resolution,[],[f195]) ).
tcf(c_49,negated_conjecture,
k3_group_1(k5_autgroup(sK0),sK2) != k2_funct_1(sK2),
inference(cnf_transformation,[],[f273]) ).
tcf(c_50,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0))),
inference(cnf_transformation,[],[f178]) ).
tcf(c_51,negated_conjecture,
m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(cnf_transformation,[],[f274]) ).
tcf(c_52,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f176]) ).
tcf(c_53,negated_conjecture,
v1_group_1(sK0),
inference(cnf_transformation,[],[f175]) ).
tcf(c_54,negated_conjecture,
v3_group_1(sK0),
inference(cnf_transformation,[],[f174]) ).
tcf(c_55,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f173]) ).
tcf(c_56,negated_conjecture,
l1_group_1(sK0),
inference(cnf_transformation,[],[f172]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| m1_subset_1(X0,u1_struct_0(X2))
| ~ l1_group_1(X2)
| ~ v3_group_1(X2)
| ~ m1_group_2(X1,X2)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_67,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k3_group_1(k3_autgroup(X1),X0) = k2_funct_1(X0) )
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_subset_1(X0,u1_struct_0(k3_autgroup(X1)))
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| ( k3_group_1(X1,X0) = k3_group_1(X2,X0) )
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_group_2(X2,X1)
| ~ m1_subset_1(X0,u1_struct_0(X2))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_91,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ~ v3_struct_0(k3_autgroup(X0)) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_93,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v3_group_1(k3_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_94,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v4_group_1(k3_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_95,plain,
! [X0: $i] :
( v3_struct_0(X0)
| l1_group_1(k3_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_190,plain,
( v3_struct_0(sK0)
| l1_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_191,plain,
( v3_struct_0(sK0)
| v4_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_192,plain,
( v3_struct_0(sK0)
| v3_group_1(k3_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_197,plain,
( v3_struct_0(sK0)
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| ~ v3_struct_0(k3_autgroup(sK0)) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_894,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| ( k3_group_1(X2,X0) = k3_group_1(X1,X0) )
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ m1_group_2(X1,X2)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_71,c_58]) ).
tcf(c_4900,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_subset_1(sK2,u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ m1_group_2(k5_autgroup(sK0),X0) ),
inference(superposition,[status(thm)],[c_50,c_58]) ).
tcf(c_6306,plain,
( v3_struct_0(sK0)
| v3_struct_0(k3_autgroup(sK0))
| m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0)) ),
inference(superposition,[status(thm)],[c_67,c_4900]) ).
tcf(c_6334,plain,
( v3_struct_0(k3_autgroup(sK0))
| m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6306,c_52,c_56,c_55,c_54,c_53]) ).
tcf(c_6504,plain,
m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0))),
inference(global_subsumption_just,[status(thm)],[c_6334,c_56,c_55,c_54,c_53,c_52,c_190,c_192,c_197,c_6334]) ).
tcf(c_6736,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ( k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(X0,sK2) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ m1_group_2(k5_autgroup(sK0),X0) ),
inference(superposition,[status(thm)],[c_50,c_894]) ).
tcf(c_6883,plain,
( v3_struct_0(sK0)
| v3_struct_0(k3_autgroup(sK0))
| ( k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2) )
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v4_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0)) ),
inference(superposition,[status(thm)],[c_67,c_6736]) ).
tcf(c_6884,plain,
( v3_struct_0(k3_autgroup(sK0))
| ( k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2) )
| ~ l1_group_1(k3_autgroup(sK0))
| ~ v4_group_1(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6883,c_52,c_56,c_55,c_54,c_53]) ).
tcf(c_6890,plain,
k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2),
inference(global_subsumption_just,[status(thm)],[c_6884,c_56,c_55,c_54,c_53,c_52,c_190,c_191,c_192,c_197,c_6884]) ).
tcf(c_6893,plain,
k3_group_1(k3_autgroup(sK0),sK2) != k2_funct_1(sK2),
inference(demodulation,[status(thm)],[c_49,c_6890]) ).
tcf(c_7078,plain,
( v3_struct_0(sK0)
| m2_fraenkel(sK2,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(superposition,[status(thm)],[c_51,c_62]) ).
tcf(c_7081,plain,
m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_7078,c_52,c_56,c_55,c_54,c_53]) ).
tcf(c_7146,plain,
( v3_struct_0(sK0)
| ( k3_group_1(k3_autgroup(sK0),sK2) = k2_funct_1(sK2) )
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| ~ m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0))) ),
inference(superposition,[status(thm)],[c_7081,c_68]) ).
tcf(c_7153,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7146,c_52,c_6893,c_56,c_55,c_54,c_53,c_6504]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP628+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.42 % Computer : n016.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Wed Sep 23 15:23:42 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.48 Running first-order theorem proving
% 0.15/0.48 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.50
% 0.15/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.50
% 0.15/0.51 % Detected problem language: tptp
% 0.22/0.52 % Proving...
% 4.79/1.41 % SZS status Started for theBenchmark.p
% 4.79/1.41 % SZS status Theorem for theBenchmark.p
% 4.79/1.41
% 4.79/1.41 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.79/1.41
% 4.79/1.41 % ------ iProver source info
% 4.79/1.41
% 4.79/1.41 % git: date: 2026-07-19 20:42:38 +0200
% 4.79/1.41 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.79/1.41 % git: non_committed_changes: false
% 4.79/1.41
% 4.79/1.41 % ------ Parsing...
% 4.79/1.41 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.79/1.41
% 4.79/1.41 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 4.79/1.41
% 4.79/1.41 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.79/1.41
% 4.79/1.41 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.79/1.41 % ------ Proving...
% 4.79/1.41 % ------ Problem Properties
% 4.79/1.41
% 4.79/1.41 %
% 4.79/1.41 % clauses 99
% 4.79/1.41 % conjectures 8
% 4.79/1.41 % EPR 39
% 4.79/1.41 % Horn 65
% 4.79/1.41 % unary 41
% 4.79/1.41 % binary 9
% 4.79/1.41 % lits 295
% 4.79/1.41 % lits eq 8
% 4.79/1.41 % fd_pure 0
% 4.79/1.41 % fd_pseudo 0
% 4.79/1.41 % fd_cond 0
% 4.79/1.41 % fd_pseudo_cond 3
% 4.79/1.41 % AC symbols 0
% 4.79/1.41
% 4.79/1.41 % ------ Schedule dynamic 5 is on
% 4.79/1.41
% 4.79/1.41 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.79/1.41
% 4.79/1.41
% 4.79/1.41 % ------
% 4.79/1.41 % Current options:
% 4.79/1.41 % ------
% 4.79/1.41
% 4.79/1.41
% 4.79/1.41 %
% 4.79/1.41
% 4.79/1.41 % ------ Proving...
% 4.79/1.41 %
% 4.79/1.41
% 4.79/1.41 % SZS status Theorem for theBenchmark.p
% 4.79/1.41
% 4.79/1.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.79/1.41
% 4.79/1.41
%------------------------------------------------------------------------------