%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP632+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 01:34:56 PM UTC 2026
% Result : Theorem 42.13s 6.79s
% Output : CNFRefutation 42.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 176 ( 45 unt; 0 def)
% Number of atoms : 600 ( 106 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 729 ( 305 ~; 332 |; 74 &)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-6 aty)
% Number of variables : 284 ( 0 sgn 280 !; 4 ?; 131 :)
% 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))
=> ( k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X1,k6_autgroup(X0,k2_group_1(X0))) = X1
& k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,k2_group_1(X0)),X1) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_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))
=> ( k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X1,k6_autgroup(X0,k2_group_1(X0))) = X1
& k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,k2_group_1(X0)),X1) = X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( m1_relset_1(X2,X0,X1)
=> ( ( v1_partfun1(X2,X0,X1)
& v1_funct_1(X2) )
=> ( v1_funct_2(X2,X0,X1)
& v1_funct_1(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
fof(f20,axiom,
! [X0] :
( ( l1_group_1(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_group_1) ).
fof(f22,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_autgroup) ).
fof(f24,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,u1_struct_0(X0))
& l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> m2_fraenkel(k6_autgroup(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_autgroup) ).
fof(f25,axiom,
! [X0] :
( m2_relset_1(k6_partfun1(X0),X0,X0)
& v1_partfun1(k6_partfun1(X0),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
fof(f29,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( m1_fraenkel(X2,X0,X1)
& ~ v1_xboole_0(X1) )
=> ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
=> ( m2_relset_1(X3,X0,X1)
& v1_funct_2(X3,X0,X1)
& v1_funct_1(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_fraenkel) ).
fof(f47,axiom,
! [X0] :
( ( l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f50,axiom,
! [X0] :
( v8_relat_2(k6_relat_1(X0))
& v4_relat_2(k6_relat_1(X0))
& v3_relat_2(k6_relat_1(X0))
& v1_relat_2(k6_relat_1(X0))
& v1_funct_1(k6_relat_1(X0))
& v1_relat_1(k6_relat_1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_partfun1) ).
fof(f68,axiom,
! [X0] : k6_partfun1(X0) = k6_relat_1(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
fof(f69,axiom,
! [X0,X1,X2,X3,X4] :
( ( m1_relset_1(X4,X1,X2)
& v1_funct_2(X4,X1,X2)
& v1_funct_1(X4)
& m1_relset_1(X3,X0,X1)
& v1_funct_2(X3,X0,X1)
& v1_funct_1(X3)
& ~ v1_xboole_0(X1) )
=> k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
fof(f70,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( m1_relset_1(X5,X2,X3)
& m1_relset_1(X4,X0,X1) )
=> k7_relset_1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).
fof(f72,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f75,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> ( k7_relset_1(X0,X1,X1,X1,X2,k6_partfun1(X1)) = X2
& k7_relset_1(X0,X0,X0,X1,k6_partfun1(X0),X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_2) ).
fof(f76,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> k6_autgroup(X0,k2_group_1(X0)) = k6_partfun1(u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_autgroup) ).
fof(f87,plain,
! [X0] :
( v8_relat_2(k6_relat_1(X0))
& v3_relat_2(k6_relat_1(X0))
& v1_relat_2(k6_relat_1(X0))
& v1_funct_1(k6_relat_1(X0))
& v1_relat_1(k6_relat_1(X0)) ),
inference(pure_predicate_removal,[],[f50]) ).
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))
& ( k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X1,k6_autgroup(X0,k2_group_1(X0))) != X1
| k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,k2_group_1(X0)),X1) != X1 ) ) ),
inference(ennf_transformation,[],[f2]) ).
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))
& ( k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X1,k6_autgroup(X0,k2_group_1(X0))) != X1
| k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,k2_group_1(X0)),X1) != X1 ) ) ),
inference(flattening,[],[f90]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ~ m1_relset_1(X2,X0,X1)
| ~ v1_partfun1(X2,X0,X1)
| ~ v1_funct_1(X2)
| ( v1_funct_2(X2,X0,X1)
& v1_funct_1(X2) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ m1_relset_1(X2,X0,X1)
| ~ v1_partfun1(X2,X0,X1)
| ~ v1_funct_1(X2)
| ( v1_funct_2(X2,X0,X1)
& v1_funct_1(X2) ) ),
inference(flattening,[],[f97]) ).
fof(f118,plain,
! [X0] :
( ~ l1_group_1(X0)
| v3_struct_0(X0)
| m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f119,plain,
! [X0] :
( ~ l1_group_1(X0)
| v3_struct_0(X0)
| m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
inference(flattening,[],[f118]) ).
fof(f120,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f121,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(flattening,[],[f120]) ).
fof(f124,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m2_fraenkel(k6_autgroup(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f125,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m2_fraenkel(k6_autgroup(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) ),
inference(flattening,[],[f124]) ).
fof(f130,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( ~ m2_fraenkel(X3,X0,X1,X2)
| ( m2_relset_1(X3,X0,X1)
& v1_funct_2(X3,X0,X1)
& v1_funct_1(X3) ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( ~ m2_fraenkel(X3,X0,X1,X2)
| ( m2_relset_1(X3,X0,X1)
& v1_funct_2(X3,X0,X1)
& v1_funct_1(X3) ) ) ),
inference(flattening,[],[f132]) ).
fof(f142,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f143,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f142]) ).
fof(f148,plain,
! [X0,X1,X2,X3,X4] :
( ~ m1_relset_1(X4,X1,X2)
| ~ v1_funct_2(X4,X1,X2)
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,X0,X1)
| ~ v1_funct_2(X3,X0,X1)
| ~ v1_funct_1(X3)
| v1_xboole_0(X1)
| k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
inference(ennf_transformation,[],[f69]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4] :
( ~ m1_relset_1(X4,X1,X2)
| ~ v1_funct_2(X4,X1,X2)
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,X0,X1)
| ~ v1_funct_2(X3,X0,X1)
| ~ v1_funct_1(X3)
| v1_xboole_0(X1)
| k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
inference(flattening,[],[f148]) ).
fof(f150,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ m1_relset_1(X5,X2,X3)
| ~ m1_relset_1(X4,X0,X1)
| k7_relset_1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
inference(ennf_transformation,[],[f70]) ).
fof(f151,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ m1_relset_1(X5,X2,X3)
| ~ m1_relset_1(X4,X0,X1)
| k7_relset_1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
inference(flattening,[],[f150]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ~ m2_relset_1(X2,X0,X1)
| ( k7_relset_1(X0,X1,X1,X1,X2,k6_partfun1(X1)) = X2
& k7_relset_1(X0,X0,X0,X1,k6_partfun1(X0),X2) = X2 ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f156,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| k6_autgroup(X0,k2_group_1(X0)) = k6_partfun1(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f76]) ).
fof(f157,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| k6_autgroup(X0,k2_group_1(X0)) = k6_partfun1(u1_struct_0(X0)) ),
inference(flattening,[],[f156]) ).
fof(f167,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))
& ( sK1 != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_autgroup(sK0,k2_group_1(sK0)))
| sK1 != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_autgroup(sK0,k2_group_1(sK0)),sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f91]) ).
fof(f192,plain,
! [X0,X1,X2] :
( ( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) )
& ( ~ m1_relset_1(X2,X0,X1)
| m2_relset_1(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f193,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f167]) ).
fof(f194,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f167]) ).
fof(f195,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f167]) ).
fof(f196,plain,
v1_group_1(sK0),
inference(cnf_transformation,[],[f167]) ).
fof(f197,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f167]) ).
fof(f198,plain,
m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(cnf_transformation,[],[f167]) ).
fof(f199,plain,
( sK1 != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_autgroup(sK0,k2_group_1(sK0)))
| sK1 != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_autgroup(sK0,k2_group_1(sK0)),sK1) ),
inference(cnf_transformation,[],[f167]) ).
fof(f205,plain,
! [X2,X0,X1] :
( ~ m1_relset_1(X2,X0,X1)
| ~ v1_partfun1(X2,X0,X1)
| ~ v1_funct_1(X2)
| v1_funct_2(X2,X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f235,plain,
! [X0] :
( ~ l1_group_1(X0)
| v3_struct_0(X0)
| m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f236,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f121]) ).
fof(f238,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m2_fraenkel(k6_autgroup(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f239,plain,
! [X0] : m2_relset_1(k6_partfun1(X0),X0,X0),
inference(cnf_transformation,[],[f25]) ).
fof(f240,plain,
! [X0] : v1_partfun1(k6_partfun1(X0),X0,X0),
inference(cnf_transformation,[],[f25]) ).
fof(f246,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f249,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| m2_relset_1(X3,X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f250,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| v1_funct_2(X3,X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f251,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| v1_funct_1(X3) ),
inference(cnf_transformation,[],[f133]) ).
fof(f267,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f143]) ).
fof(f274,plain,
! [X0] : v1_funct_1(k6_relat_1(X0)),
inference(cnf_transformation,[],[f87]) ).
fof(f328,plain,
! [X0] : k6_partfun1(X0) = k6_relat_1(X0),
inference(cnf_transformation,[],[f68]) ).
fof(f329,plain,
! [X2,X3,X0,X1,X4] :
( ~ m1_relset_1(X4,X1,X2)
| ~ v1_funct_2(X4,X1,X2)
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,X0,X1)
| ~ v1_funct_2(X3,X0,X1)
| ~ v1_funct_1(X3)
| v1_xboole_0(X1)
| k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
inference(cnf_transformation,[],[f149]) ).
fof(f330,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ m1_relset_1(X5,X2,X3)
| ~ m1_relset_1(X4,X0,X1)
| k7_relset_1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
inference(cnf_transformation,[],[f151]) ).
fof(f333,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
fof(f337,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| k7_relset_1(X0,X1,X1,X1,X2,k6_partfun1(X1)) = X2 ),
inference(cnf_transformation,[],[f155]) ).
fof(f338,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| k7_relset_1(X0,X0,X0,X1,k6_partfun1(X0),X2) = X2 ),
inference(cnf_transformation,[],[f155]) ).
fof(f339,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| k6_autgroup(X0,k2_group_1(X0)) = k6_partfun1(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f157]) ).
fof(f347,plain,
! [X0] : v1_partfun1(k6_relat_1(X0),X0,X0),
inference(definition_unfolding,[],[f240,f328]) ).
fof(f348,plain,
! [X0] : m2_relset_1(k6_relat_1(X0),X0,X0),
inference(definition_unfolding,[],[f239,f328]) ).
fof(f349,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| k7_relset_1(X0,X0,X0,X1,k6_relat_1(X0),X2) = X2 ),
inference(definition_unfolding,[],[f338,f328]) ).
fof(f350,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| k7_relset_1(X0,X1,X1,X1,X2,k6_relat_1(X1)) = X2 ),
inference(definition_unfolding,[],[f337,f328]) ).
fof(f351,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| k6_autgroup(X0,k2_group_1(X0)) = k6_relat_1(u1_struct_0(X0)) ),
inference(definition_unfolding,[],[f339,f328]) ).
tcf(c_49,negated_conjecture,
( ( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_autgroup(sK0,k2_group_1(sK0))) != sK1 )
| ( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_autgroup(sK0,k2_group_1(sK0)),sK1) != sK1 ) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_50,negated_conjecture,
m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(cnf_transformation,[],[f198]) ).
tcf(c_51,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f197]) ).
tcf(c_52,negated_conjecture,
v1_group_1(sK0),
inference(cnf_transformation,[],[f196]) ).
tcf(c_53,negated_conjecture,
v3_group_1(sK0),
inference(cnf_transformation,[],[f195]) ).
tcf(c_54,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f194]) ).
tcf(c_55,negated_conjecture,
l1_group_1(sK0),
inference(cnf_transformation,[],[f193]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_funct_2(X0,X1,X2)
| ~ v1_funct_1(X0)
| ~ m1_relset_1(X0,X1,X2)
| ~ v1_partfun1(X0,X1,X2) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_76,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_77,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m2_fraenkel(k6_autgroup(X1,X0),u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f238]) ).
tcf(c_80,plain,
! [X0: $i] : v1_partfun1(k6_relat_1(X0),X0,X0),
inference(cnf_transformation,[],[f347]) ).
tcf(c_81,plain,
! [X0: $i] : m2_relset_1(k6_relat_1(X0),X0,X0),
inference(cnf_transformation,[],[f348]) ).
tcf(c_87,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| v1_funct_1(X0)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m2_fraenkel(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| v1_funct_2(X0,X1,X2)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m2_fraenkel(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f250]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| m2_relset_1(X0,X1,X2)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m2_fraenkel(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f249]) ).
tcf(c_108,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f267]) ).
tcf(c_113,plain,
! [X0: $i] : v1_funct_1(k6_relat_1(X0)),
inference(cnf_transformation,[],[f274]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v1_xboole_0(X2)
| ( k7_funct_2(X1,X2,X4,X0,X3) = k5_relat_1(X0,X3) )
| ~ v1_funct_1(X3)
| ~ v1_funct_1(X0)
| ~ m1_relset_1(X3,X2,X4)
| ~ m1_relset_1(X0,X1,X2)
| ~ v1_funct_2(X3,X2,X4)
| ~ v1_funct_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f329]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( k7_relset_1(X1,X2,X4,X5,X0,X3) = k5_relat_1(X0,X3) )
| ~ m1_relset_1(X3,X4,X5)
| ~ m1_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f330]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f333]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( k7_relset_1(X1,X1,X1,X2,k6_relat_1(X1),X0) = X0 )
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f349]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( k7_relset_1(X1,X2,X2,X2,X0,k6_relat_1(X2)) = X0 )
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f350]) ).
tcf(c_179,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ( k6_autgroup(X0,k2_group_1(X0)) = k6_relat_1(u1_struct_0(X0)) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0) ),
inference(cnf_transformation,[],[f351]) ).
tcf(c_211,plain,
( l1_struct_0(sK0)
| ~ l1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_233,plain,
( v3_struct_0(sK0)
| ~ l1_struct_0(sK0)
| ~ v1_xboole_0(u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_239,plain,
( v3_struct_0(sK0)
| m1_subset_1(k2_group_1(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_260,plain,
( v3_struct_0(sK0)
| m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_265,plain,
( v3_struct_0(sK0)
| ( k6_autgroup(sK0,k2_group_1(sK0)) = k6_relat_1(u1_struct_0(sK0)) )
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_179]) ).
tcf(c_279,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_174]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_funct_2(X0,X1,X2)
| ~ v1_funct_1(X0)
| ~ m2_relset_1(X0,X1,X2)
| ~ v1_partfun1(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_61,c_279]) ).
tcf(c_537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v1_xboole_0(X2)
| ( k7_funct_2(X1,X2,X4,X0,X3) = k5_relat_1(X0,X3) )
| ~ v1_funct_1(X3)
| ~ v1_funct_1(X0)
| ~ m2_relset_1(X0,X1,X2)
| ~ m1_relset_1(X3,X2,X4)
| ~ v1_funct_2(X3,X2,X4)
| ~ v1_funct_2(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_169,c_279]) ).
tcf(c_538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( k7_relset_1(X4,X5,X1,X2,X3,X0) = k5_relat_1(X3,X0) )
| ~ m2_relset_1(X3,X4,X5)
| ~ m1_relset_1(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_170,c_279]) ).
tcf(c_644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_funct_2(X1,X2,X3)
| ~ v1_funct_1(X1)
| ~ m2_relset_1(X1,X2,X3)
| ( X0 != X3 )
| ( X0 != X2 )
| ( k6_relat_1(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_526,c_80]) ).
tcf(c_645,plain,
! [X0: $i] :
( v1_funct_2(k6_relat_1(X0),X0,X0)
| ~ v1_funct_1(k6_relat_1(X0))
| ~ m2_relset_1(k6_relat_1(X0),X0,X0) ),
inference(unflattening,[status(thm)],[c_644]) ).
tcf(c_647,plain,
! [X0: $i] : v1_funct_2(k6_relat_1(X0),X0,X0),
inference(global_subsumption_just,[status(thm)],[c_645,c_113,c_81,c_645]) ).
tcf(c_768,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ( k6_autgroup(X0,k2_group_1(X0)) = k6_relat_1(u1_struct_0(X0)) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v1_group_1(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_179]) ).
tcf(c_769,plain,
( v3_struct_0(sK0)
| ( k6_autgroup(sK0,k2_group_1(sK0)) = k6_relat_1(u1_struct_0(sK0)) )
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(unflattening,[status(thm)],[c_768]) ).
tcf(c_770,plain,
k6_autgroup(sK0,k2_group_1(sK0)) = k6_relat_1(u1_struct_0(sK0)),
inference(global_subsumption_just,[status(thm)],[c_769,c_55,c_54,c_53,c_52,c_51,c_265]) ).
tcf(c_775,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v1_group_1(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_77]) ).
tcf(c_776,plain,
( v3_struct_0(sK0)
| m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(unflattening,[status(thm)],[c_775]) ).
tcf(c_777,plain,
m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)),
inference(global_subsumption_just,[status(thm)],[c_776,c_55,c_54,c_53,c_52,c_51,c_260]) ).
tcf(c_782,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| m2_fraenkel(k6_autgroup(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_79]) ).
tcf(c_783,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| m2_fraenkel(k6_autgroup(sK0,X0),u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v1_group_1(sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_782]) ).
tcf(c_785,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| m2_fraenkel(k6_autgroup(sK0,X0),u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_783,c_55,c_54,c_52,c_51,c_783]) ).
tcf(c_786,plain,
! [X0: $i] :
( m2_fraenkel(k6_autgroup(sK0,X0),u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_785]) ).
tcf(c_1034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| m2_relset_1(X3,X0,X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| ( k4_autgroup(sK0) != X2 )
| ( u1_struct_0(sK0) != X1 )
| ( u1_struct_0(sK0) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_92,c_777]) ).
tcf(c_1035,plain,
! [X0: $i] :
( v1_xboole_0(u1_struct_0(sK0))
| m2_relset_1(X0,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(unflattening,[status(thm)],[c_1034]) ).
tcf(c_1037,plain,
! [X0: $i] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| m2_relset_1(X0,u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_1035,c_55,c_51,c_211,c_233,c_1035]) ).
tcf(c_1038,plain,
! [X0: $i] :
( m2_relset_1(X0,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(renaming,[status(thm)],[c_1037]) ).
tcf(c_1046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| v1_funct_2(X3,X0,X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| ( k4_autgroup(sK0) != X2 )
| ( u1_struct_0(sK0) != X1 )
| ( u1_struct_0(sK0) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_91,c_777]) ).
tcf(c_1047,plain,
! [X0: $i] :
( v1_xboole_0(u1_struct_0(sK0))
| v1_funct_2(X0,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(unflattening,[status(thm)],[c_1046]) ).
tcf(c_1049,plain,
! [X0: $i] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| v1_funct_2(X0,u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_1047,c_55,c_51,c_211,c_233,c_1047]) ).
tcf(c_1050,plain,
! [X0: $i] :
( v1_funct_2(X0,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(renaming,[status(thm)],[c_1049]) ).
tcf(c_1058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| v1_funct_1(X3)
| ~ m2_fraenkel(X3,X0,X1,X2)
| ( k4_autgroup(sK0) != X2 )
| ( u1_struct_0(sK0) != X1 )
| ( u1_struct_0(sK0) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_777]) ).
tcf(c_1059,plain,
! [X0: $i] :
( v1_funct_1(X0)
| v1_xboole_0(u1_struct_0(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(unflattening,[status(thm)],[c_1058]) ).
tcf(c_1061,plain,
! [X0: $i] :
( v1_funct_1(X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_1059,c_55,c_51,c_211,c_233,c_1059]) ).
tcf(c_2278,plain,
! [X0: $i] :
( v1_funct_1(X0)
| ( X0 != sK1 )
| ( k4_autgroup(sK0) != k4_autgroup(sK0) )
| ( u1_struct_0(sK0) != u1_struct_0(sK0) ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_1061]) ).
tcf(c_2279,plain,
v1_funct_1(sK1),
inference(unflattening,[status(thm)],[c_2278]) ).
tcf(c_2283,plain,
! [X0: $i] :
( v1_funct_2(X0,u1_struct_0(sK0),u1_struct_0(sK0))
| ( X0 != sK1 )
| ( k4_autgroup(sK0) != k4_autgroup(sK0) )
| ( u1_struct_0(sK0) != u1_struct_0(sK0) ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_1050]) ).
tcf(c_2284,plain,
v1_funct_2(sK1,u1_struct_0(sK0),u1_struct_0(sK0)),
inference(unflattening,[status(thm)],[c_2283]) ).
tcf(c_2288,plain,
! [X0: $i] :
( m2_relset_1(X0,u1_struct_0(sK0),u1_struct_0(sK0))
| ( X0 != sK1 )
| ( k4_autgroup(sK0) != k4_autgroup(sK0) )
| ( u1_struct_0(sK0) != u1_struct_0(sK0) ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_1038]) ).
tcf(c_2289,plain,
m2_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK0)),
inference(unflattening,[status(thm)],[c_2288]) ).
tcf(c_2393,plain,
! [X0: $i,X1: $i] :
( v1_funct_1(X1)
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ( k4_autgroup(sK0) != k4_autgroup(sK0) )
| ( u1_struct_0(sK0) != u1_struct_0(sK0) )
| ( k6_autgroup(sK0,X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_786,c_1061]) ).
tcf(c_2394,plain,
! [X0: $i] :
( v1_funct_1(k6_autgroup(sK0,X0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_2393]) ).
tcf(c_2402,plain,
! [X0: $i,X1: $i] :
( v1_funct_2(X1,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ( k4_autgroup(sK0) != k4_autgroup(sK0) )
| ( u1_struct_0(sK0) != u1_struct_0(sK0) )
| ( k6_autgroup(sK0,X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_786,c_1050]) ).
tcf(c_2403,plain,
! [X0: $i] :
( v1_funct_2(k6_autgroup(sK0,X0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_2402]) ).
tcf(c_2411,plain,
! [X0: $i,X1: $i] :
( m2_relset_1(X1,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ( k4_autgroup(sK0) != k4_autgroup(sK0) )
| ( u1_struct_0(sK0) != u1_struct_0(sK0) )
| ( k6_autgroup(sK0,X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_786,c_1038]) ).
tcf(c_2412,plain,
! [X0: $i] :
( m2_relset_1(k6_autgroup(sK0,X0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_2411]) ).
tcf(c_6288,plain,
! [X0: $i] : m1_relset_1(k6_relat_1(X0),X0,X0),
inference(superposition,[status(thm)],[c_81,c_174]) ).
tcf(c_6290,plain,
m1_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK0)),
inference(superposition,[status(thm)],[c_2289,c_174]) ).
tcf(c_6485,plain,
( v3_struct_0(sK0)
| v1_funct_1(k6_autgroup(sK0,k2_group_1(sK0)))
| ~ l1_group_1(sK0) ),
inference(superposition,[status(thm)],[c_76,c_2394]) ).
tcf(c_6490,plain,
v1_funct_1(k6_autgroup(sK0,k2_group_1(sK0))),
inference(global_subsumption_just,[status(thm)],[c_6485,c_55,c_51,c_6485]) ).
tcf(c_6492,plain,
v1_funct_1(k6_relat_1(u1_struct_0(sK0))),
inference(light_normalisation,[status(thm)],[c_6490,c_770]) ).
tcf(c_7175,plain,
( m2_relset_1(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ m1_subset_1(k2_group_1(sK0),u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_770,c_2412]) ).
tcf(c_7178,plain,
m2_relset_1(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0)),
inference(global_subsumption_just,[status(thm)],[c_7175,c_55,c_51,c_239,c_7175]) ).
tcf(c_7190,plain,
( v1_funct_2(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ m1_subset_1(k2_group_1(sK0),u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_770,c_2403]) ).
tcf(c_7191,plain,
v1_funct_2(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0)),
inference(global_subsumption_just,[status(thm)],[c_7190,c_55,c_51,c_239,c_7190]) ).
tcf(c_7359,plain,
k7_relset_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_relat_1(u1_struct_0(sK0))) = sK1,
inference(superposition,[status(thm)],[c_2289,c_178]) ).
tcf(c_7504,plain,
k7_relset_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_relat_1(u1_struct_0(sK0)),sK1) = sK1,
inference(superposition,[status(thm)],[c_2289,c_177]) ).
tcf(c_8220,plain,
( ( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_relat_1(u1_struct_0(sK0)),sK1) != sK1 )
| ( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_autgroup(sK0,k2_group_1(sK0))) != sK1 ) ),
inference(superposition,[status(thm)],[c_770,c_49]) ).
tcf(c_8221,plain,
( ( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_relat_1(u1_struct_0(sK0))) != sK1 )
| ( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_relat_1(u1_struct_0(sK0)),sK1) != sK1 ) ),
inference(light_normalisation,[status(thm)],[c_8220,c_770]) ).
tcf(c_8461,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X0)
| ( k7_funct_2(X0,X0,X2,k6_relat_1(X0),X1) = k5_relat_1(k6_relat_1(X0),X1) )
| ~ v1_funct_1(X1)
| ~ v1_funct_1(k6_relat_1(X0))
| ~ m1_relset_1(X1,X0,X2)
| ~ v1_funct_2(X1,X0,X2)
| ~ m2_relset_1(k6_relat_1(X0),X0,X0) ),
inference(superposition,[status(thm)],[c_647,c_537]) ).
tcf(c_8467,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(u1_struct_0(sK0))
| ( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),X1,sK1,X0) = k5_relat_1(sK1,X0) )
| ~ v1_funct_1(sK1)
| ~ v1_funct_1(X0)
| ~ m1_relset_1(X0,u1_struct_0(sK0),X1)
| ~ v1_funct_2(X0,u1_struct_0(sK0),X1)
| ~ m2_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_2284,c_537]) ).
tcf(c_8480,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X0)
| ( k7_funct_2(X0,X0,X2,k6_relat_1(X0),X1) = k5_relat_1(k6_relat_1(X0),X1) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,X0,X2)
| ~ m1_relset_1(X1,X0,X2) ),
inference(global_subsumption_just,[status(thm)],[c_8461,c_113,c_81,c_8461]) ).
tcf(c_8481,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X1)
| ( k7_funct_2(X1,X1,X2,k6_relat_1(X1),X0) = k5_relat_1(k6_relat_1(X1),X0) )
| ~ v1_funct_1(X0)
| ~ m1_relset_1(X0,X1,X2)
| ~ v1_funct_2(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_8480]) ).
tcf(c_8488,plain,
! [X0: $i,X1: $i] :
( ~ v1_funct_1(X0)
| ~ m1_relset_1(X0,u1_struct_0(sK0),X1)
| ~ v1_funct_2(X0,u1_struct_0(sK0),X1)
| ( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),X1,sK1,X0) = k5_relat_1(sK1,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_8467,c_55,c_51,c_211,c_233,c_2279,c_2289,c_8467]) ).
tcf(c_8489,plain,
! [X0: $i,X1: $i] :
( ( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),X1,sK1,X0) = k5_relat_1(sK1,X0) )
| ~ v1_funct_1(X0)
| ~ m1_relset_1(X0,u1_struct_0(sK0),X1)
| ~ v1_funct_2(X0,u1_struct_0(sK0),X1) ),
inference(renaming,[status(thm)],[c_8488]) ).
tcf(c_8997,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( k7_relset_1(X1,X2,X3,X3,X0,k6_relat_1(X3)) = k5_relat_1(X0,k6_relat_1(X3)) )
| ~ m2_relset_1(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_6288,c_538]) ).
tcf(c_9005,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( k7_relset_1(X1,X2,u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k5_relat_1(X0,sK1) )
| ~ m2_relset_1(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_6290,c_538]) ).
tcf(c_10565,plain,
m1_relset_1(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0)),
inference(superposition,[status(thm)],[c_7178,c_174]) ).
tcf(c_15784,plain,
( ( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_relat_1(u1_struct_0(sK0))) = k5_relat_1(sK1,k6_relat_1(u1_struct_0(sK0))) )
| ~ v1_funct_1(k6_relat_1(u1_struct_0(sK0)))
| ~ m1_relset_1(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_7191,c_8489]) ).
tcf(c_15796,plain,
k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_relat_1(u1_struct_0(sK0))) = k5_relat_1(sK1,k6_relat_1(u1_struct_0(sK0))),
inference(global_subsumption_just,[status(thm)],[c_15784,c_6492,c_10565,c_15784]) ).
tcf(c_15849,plain,
( ( k5_relat_1(sK1,k6_relat_1(u1_struct_0(sK0))) != sK1 )
| ( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_relat_1(u1_struct_0(sK0)),sK1) != sK1 ) ),
inference(demodulation,[status(thm)],[c_8221,c_15796]) ).
tcf(c_16240,plain,
( v1_xboole_0(u1_struct_0(sK0))
| ( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_relat_1(u1_struct_0(sK0)),sK1) = k5_relat_1(k6_relat_1(u1_struct_0(sK0)),sK1) )
| ~ v1_funct_1(sK1)
| ~ m1_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_2284,c_8481]) ).
tcf(c_16267,plain,
k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_relat_1(u1_struct_0(sK0)),sK1) = k5_relat_1(k6_relat_1(u1_struct_0(sK0)),sK1),
inference(global_subsumption_just,[status(thm)],[c_16240,c_55,c_51,c_211,c_233,c_2279,c_6290,c_16240]) ).
tcf(c_20162,plain,
! [X0: $i] : k7_relset_1(u1_struct_0(sK0),u1_struct_0(sK0),X0,X0,sK1,k6_relat_1(X0)) = k5_relat_1(sK1,k6_relat_1(X0)),
inference(superposition,[status(thm)],[c_2289,c_8997]) ).
tcf(c_20273,plain,
k5_relat_1(sK1,k6_relat_1(u1_struct_0(sK0))) = sK1,
inference(demodulation,[status(thm)],[c_7359,c_20162]) ).
tcf(c_20538,plain,
k7_relset_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_relat_1(u1_struct_0(sK0)),sK1) = k5_relat_1(k6_relat_1(u1_struct_0(sK0)),sK1),
inference(superposition,[status(thm)],[c_7178,c_9005]) ).
tcf(c_20548,plain,
k5_relat_1(k6_relat_1(u1_struct_0(sK0)),sK1) = sK1,
inference(light_normalisation,[status(thm)],[c_20538,c_7504]) ).
tcf(c_20605,plain,
k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_relat_1(u1_struct_0(sK0)),sK1) = sK1,
inference(demodulation,[status(thm)],[c_16267,c_20548]) ).
tcf(c_20606,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_20605,c_20273,c_15849]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP632+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n010.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Wed Sep 23 15:20:42 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.39 % Detected problem language: tptp
% 0.13/0.40 % Proving...
% 42.13/6.79 % SZS status Started for theBenchmark.p
% 42.13/6.79 % SZS status Theorem for theBenchmark.p
% 42.13/6.79
% 42.13/6.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 42.13/6.79
% 42.13/6.79 % ------ iProver source info
% 42.13/6.79
% 42.13/6.79 % git: date: 2026-07-19 20:42:38 +0200
% 42.13/6.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 42.13/6.79 % git: non_committed_changes: false
% 42.13/6.79
% 42.13/6.79 % ------ Parsing...
% 42.13/6.79 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 42.13/6.79
% 42.13/6.79 % ------ Preprocessing... sf_s rm: 26 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 42.13/6.79
% 42.13/6.79 % ------ Preprocessing... gs_s sp: 12 0s gs_e scvd_s sp: 1 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 42.13/6.79
% 42.13/6.79 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 42.13/6.79 % ------ Proving...
% 42.13/6.79 % ------ Problem Properties
% 42.13/6.79
% 42.13/6.79 %
% 42.13/6.79 % clauses 193
% 42.13/6.79 % conjectures 4
% 42.13/6.79 % EPR 42
% 42.13/6.79 % Horn 178
% 42.13/6.79 % unary 72
% 42.13/6.79 % binary 50
% 42.13/6.79 % lits 420
% 42.13/6.79 % lits eq 78
% 42.13/6.79 % fd_pure 0
% 42.13/6.79 % fd_pseudo 0
% 42.13/6.79 % fd_cond 1
% 42.13/6.79 % fd_pseudo_cond 3
% 42.13/6.79 % AC symbols 0
% 42.13/6.79
% 42.13/6.79 % ------ Input Options Time Limit: Unbounded
% 42.13/6.79
% 42.13/6.79
% 42.13/6.79 % ------
% 42.13/6.79 % Current options:
% 42.13/6.79 % ------
% 42.13/6.79
% 42.13/6.79
% 42.13/6.79 %
% 42.13/6.79
% 42.13/6.79 % ------ Proving...
% 42.13/6.79 %
% 42.13/6.79
% 42.13/6.79 % SZS status Theorem for theBenchmark.p
% 42.13/6.79
% 42.13/6.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 42.13/6.79
% 42.13/6.79
%------------------------------------------------------------------------------