%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP632+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 : Tue Sep 29 10:15:08 AM UTC 2026
% Result : Theorem 4.92s 1.62s
% Output : Refutation 6.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 25
% Syntax : Number of formulae : 186 ( 27 unt; 10 def)
% Number of atoms : 687 ( 72 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 868 ( 367 ~; 409 |; 66 &)
% ( 11 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 11 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-6 aty)
% Number of variables : 204 ( 0 sgn 200 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(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),k6_autgroup(X0,k2_group_1(X0)),X1) = X1
& k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X1,k6_autgroup(X0,k2_group_1(X0))) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_autgroup) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(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),k6_autgroup(X0,k2_group_1(X0)),X1) = X1
& k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X1,k6_autgroup(X0,k2_group_1(X0))) = X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f20,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_group_1(X0) )
=> m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_group_1) ).
fof(f22,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_autgroup) ).
fof(f24,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0)
& m1_subset_1(X1,u1_struct_0(X0)) )
=> m2_fraenkel(k6_autgroup(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_autgroup) ).
fof(f25,axiom,
! [X0] :
( v1_partfun1(k6_partfun1(X0),X0,X0)
& m2_relset_1(k6_partfun1(X0),X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_partfun1) ).
fof(f29,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X1)
& m1_fraenkel(X2,X0,X1) )
=> ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
=> ( v1_funct_1(X3)
& v1_funct_2(X3,X0,X1)
& m2_relset_1(X3,X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_fraenkel) ).
fof(f47,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f50,axiom,
! [X0] :
( v1_relat_1(k6_relat_1(X0))
& v1_funct_1(k6_relat_1(X0))
& v1_relat_2(k6_relat_1(X0))
& v3_relat_2(k6_relat_1(X0))
& v4_relat_2(k6_relat_1(X0))
& v8_relat_2(k6_relat_1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_partfun1) ).
fof(f68,axiom,
! [X0] : k6_partfun1(X0) = k6_relat_1(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
fof(f69,axiom,
! [X0,X1,X2,X3,X4] :
( ( ~ v1_xboole_0(X1)
& v1_funct_1(X3)
& v1_funct_2(X3,X0,X1)
& m1_relset_1(X3,X0,X1)
& v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m1_relset_1(X4,X1,X2) )
=> k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
fof(f70,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( m1_relset_1(X4,X0,X1)
& m1_relset_1(X5,X2,X3) )
=> k7_relset_1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f75,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> ( k7_relset_1(X0,X0,X0,X1,k6_partfun1(X0),X2) = X2
& k7_relset_1(X0,X1,X1,X1,X2,k6_partfun1(X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_2) ).
fof(f76,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> k6_autgroup(X0,k2_group_1(X0)) = k6_partfun1(u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_autgroup) ).
fof(f85,plain,
? [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
| k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X1,k6_autgroup(X0,k2_group_1(X0))) != X1 )
& m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) )
& ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f86,plain,
? [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
| k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X1,k6_autgroup(X0,k2_group_1(X0))) != X1 )
& m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) )
& ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(flattening,[],[f85]) ).
fof(f113,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f114,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
! [X0] :
( m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f116,plain,
! [X0] :
( m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f115]) ).
fof(f119,plain,
! [X0,X1] :
( m2_fraenkel(k6_autgroup(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f120,plain,
! [X0,X1] :
( m2_fraenkel(k6_autgroup(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(flattening,[],[f119]) ).
fof(f125,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,X0,X1)
& m2_relset_1(X3,X0,X1) )
| ~ m2_fraenkel(X3,X0,X1,X2) )
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f128,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,X0,X1)
& m2_relset_1(X3,X0,X1) )
| ~ m2_fraenkel(X3,X0,X1,X2) )
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(flattening,[],[f127]) ).
fof(f137,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f138,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(flattening,[],[f137]) ).
fof(f143,plain,
! [X0,X1,X2,X3,X4] :
( k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4)
| v1_xboole_0(X1)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,X0,X1)
| ~ m1_relset_1(X3,X0,X1)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,X1,X2)
| ~ m1_relset_1(X4,X1,X2) ),
inference(ennf_transformation,[],[f69]) ).
fof(f144,plain,
! [X0,X1,X2,X3,X4] :
( k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4)
| v1_xboole_0(X1)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,X0,X1)
| ~ m1_relset_1(X3,X0,X1)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,X1,X2)
| ~ m1_relset_1(X4,X1,X2) ),
inference(flattening,[],[f143]) ).
fof(f145,plain,
! [X0,X1,X2,X3,X4,X5] :
( k7_relset_1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5)
| ~ m1_relset_1(X4,X0,X1)
| ~ m1_relset_1(X5,X2,X3) ),
inference(ennf_transformation,[],[f70]) ).
fof(f146,plain,
! [X0,X1,X2,X3,X4,X5] :
( k7_relset_1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5)
| ~ m1_relset_1(X4,X0,X1)
| ~ m1_relset_1(X5,X2,X3) ),
inference(flattening,[],[f145]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ( k7_relset_1(X0,X0,X0,X1,k6_partfun1(X0),X2) = X2
& k7_relset_1(X0,X1,X1,X1,X2,k6_partfun1(X1)) = X2 )
| ~ m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f75]) ).
fof(f151,plain,
! [X0] :
( k6_autgroup(X0,k2_group_1(X0)) = k6_partfun1(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f152,plain,
! [X0] :
( k6_autgroup(X0,k2_group_1(X0)) = k6_partfun1(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f151]) ).
fof(f161,plain,
( ( 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 != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_autgroup(sK0,k2_group_1(sK0))) )
& m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
& ~ v3_struct_0(sK0)
& v1_group_1(sK0)
& v3_group_1(sK0)
& v4_group_1(sK0)
& l1_group_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f86]) ).
fof(f186,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(f188,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f161]) ).
fof(f189,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f161]) ).
fof(f190,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f161]) ).
fof(f191,plain,
v1_group_1(sK0),
inference(cnf_transformation,[],[f161]) ).
fof(f192,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f161]) ).
fof(f193,plain,
m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(cnf_transformation,[],[f161]) ).
fof(f194,plain,
( 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 != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_autgroup(sK0,k2_group_1(sK0))) ),
inference(cnf_transformation,[],[f161]) ).
fof(f231,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f232,plain,
! [X0] :
( m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f234,plain,
! [X0,X1] :
( m2_fraenkel(k6_autgroup(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f235,plain,
! [X0] : m2_relset_1(k6_partfun1(X0),X0,X0),
inference(cnf_transformation,[],[f25]) ).
fof(f242,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f245,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| v1_xboole_0(X1)
| m2_relset_1(X3,X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
fof(f246,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| v1_xboole_0(X1)
| v1_funct_2(X3,X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
fof(f247,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| v1_xboole_0(X1)
| v1_funct_1(X3) ),
inference(cnf_transformation,[],[f128]) ).
fof(f263,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f271,plain,
! [X0] : v1_funct_1(k6_relat_1(X0)),
inference(cnf_transformation,[],[f50]) ).
fof(f327,plain,
! [X0] : k6_partfun1(X0) = k6_relat_1(X0),
inference(cnf_transformation,[],[f68]) ).
fof(f328,plain,
! [X2,X3,X0,X1,X4] :
( ~ v1_funct_1(X4)
| v1_xboole_0(X1)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,X0,X1)
| ~ m1_relset_1(X3,X0,X1)
| k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4)
| ~ v1_funct_2(X4,X1,X2)
| ~ m1_relset_1(X4,X1,X2) ),
inference(cnf_transformation,[],[f144]) ).
fof(f329,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,[],[f146]) ).
fof(f332,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
fof(f336,plain,
! [X2,X0,X1] :
( k7_relset_1(X0,X1,X1,X1,X2,k6_partfun1(X1)) = X2
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f337,plain,
! [X2,X0,X1] :
( k7_relset_1(X0,X0,X0,X1,k6_partfun1(X0),X2) = X2
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f338,plain,
! [X0] :
( k6_autgroup(X0,k2_group_1(X0)) = k6_partfun1(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f348,plain,
! [X0] : m2_relset_1(k6_relat_1(X0),X0,X0),
inference(definition_unfolding,[],[f235,f327]) ).
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,[],[f337,f327]) ).
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,[],[f336,f327]) ).
fof(f351,plain,
! [X0] :
( ~ l1_group_1(X0)
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| k6_autgroup(X0,k2_group_1(X0)) = k6_relat_1(u1_struct_0(X0)) ),
inference(definition_unfolding,[],[f338,f327]) ).
fof(f353,definition,
( spl25_1
<=> sK1 = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_autgroup(sK0,k2_group_1(sK0))) ),
introduced(definition,[new_symbols(definition,[spl25_1])],[avatar_definition]) ).
fof(f354,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)))
| spl25_1 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f356,definition,
( spl25_2
<=> sK1 = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_autgroup(sK0,k2_group_1(sK0)),sK1) ),
introduced(definition,[new_symbols(definition,[spl25_2])],[avatar_definition]) ).
fof(f357,plain,
( sK1 != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_autgroup(sK0,k2_group_1(sK0)),sK1)
| spl25_2 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f358,plain,
( ~ spl25_1
| ~ spl25_2 ),
inference(avatar_split_clause,[],[f194,f356,f353]) ).
fof(f359,plain,
( v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| k6_autgroup(sK0,k2_group_1(sK0)) = k6_relat_1(u1_struct_0(sK0)) ),
inference(resolution,[],[f351,f188]) ).
fof(f360,plain,
( ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| k6_autgroup(sK0,k2_group_1(sK0)) = k6_relat_1(u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f359,f192]) ).
fof(f361,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| k6_autgroup(sK0,k2_group_1(sK0)) = k6_relat_1(u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f360,f191]) ).
fof(f362,plain,
( ~ v4_group_1(sK0)
| k6_autgroup(sK0,k2_group_1(sK0)) = k6_relat_1(u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f361,f190]) ).
fof(f363,plain,
k6_autgroup(sK0,k2_group_1(sK0)) = k6_relat_1(u1_struct_0(sK0)),
inference(forward_subsumption_resolution,[],[f362,f189]) ).
fof(f364,plain,
( sK1 != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_relat_1(u1_struct_0(sK0)))
| spl25_1 ),
inference(superposition,[],[f354,f363]) ).
fof(f367,plain,
! [X0,X1] :
( ~ l1_group_1(X1)
| v1_xboole_0(u1_struct_0(X1))
| m2_relset_1(X0,u1_struct_0(X1),u1_struct_0(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
inference(resolution,[],[f245,f232]) ).
fof(f368,plain,
! [X0,X1] :
( ~ l1_group_1(X1)
| v1_xboole_0(u1_struct_0(X1))
| v1_funct_2(X0,u1_struct_0(X1),u1_struct_0(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
inference(resolution,[],[f246,f232]) ).
fof(f369,plain,
! [X0,X1] :
( ~ l1_group_1(X1)
| v1_xboole_0(u1_struct_0(X1))
| v1_funct_1(X0)
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
inference(resolution,[],[f247,f232]) ).
fof(f371,plain,
( m2_fraenkel(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(k2_group_1(sK0),u1_struct_0(sK0)) ),
inference(superposition,[],[f234,f363]) ).
fof(f372,plain,
( m2_fraenkel(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(k2_group_1(sK0),u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f371,f192]) ).
fof(f373,plain,
( m2_fraenkel(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(k2_group_1(sK0),u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f372,f191]) ).
fof(f374,plain,
( m2_fraenkel(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(k2_group_1(sK0),u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f373,f190]) ).
fof(f375,plain,
( m2_fraenkel(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ m1_subset_1(k2_group_1(sK0),u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f374,f189]) ).
fof(f376,plain,
( m2_fraenkel(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ m1_subset_1(k2_group_1(sK0),u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f375,f188]) ).
fof(f378,definition,
( spl25_3
<=> m1_subset_1(k2_group_1(sK0),u1_struct_0(sK0)) ),
introduced(definition,[new_symbols(definition,[spl25_3])],[avatar_definition]) ).
fof(f379,plain,
( ~ m1_subset_1(k2_group_1(sK0),u1_struct_0(sK0))
| spl25_3 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f381,definition,
( spl25_4
<=> m2_fraenkel(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl25_4])],[avatar_definition]) ).
fof(f382,plain,
( m2_fraenkel(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ spl25_4 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f383,plain,
( ~ spl25_3
| spl25_4 ),
inference(avatar_split_clause,[],[f376,f381,f378]) ).
fof(f385,plain,
( v3_struct_0(sK0)
| ~ l1_group_1(sK0)
| spl25_3 ),
inference(resolution,[],[f379,f231]) ).
fof(f387,plain,
( ~ l1_group_1(sK0)
| spl25_3 ),
inference(forward_subsumption_resolution,[],[f385,f192]) ).
fof(f388,plain,
( $false
| spl25_3 ),
inference(forward_subsumption_resolution,[],[f387,f188]) ).
fof(f389,plain,
spl25_3,
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f393,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK0))
| m2_relset_1(X0,u1_struct_0(sK0),u1_struct_0(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(resolution,[],[f367,f188]) ).
fof(f394,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK0))
| m2_relset_1(X0,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[],[f393,f192]) ).
fof(f395,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK0))
| m2_relset_1(X0,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[],[f394,f191]) ).
fof(f396,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK0))
| m2_relset_1(X0,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ v4_group_1(sK0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[],[f395,f190]) ).
fof(f397,plain,
! [X0] :
( 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(forward_subsumption_resolution,[],[f396,f189]) ).
fof(f399,definition,
( spl25_5
<=> ! [X0] :
( 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)) ) ),
introduced(definition,[new_symbols(definition,[spl25_5])],[avatar_definition]) ).
fof(f400,plain,
( ! [X0] :
( ~ 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)) )
| ~ spl25_5 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f402,definition,
( spl25_6
<=> v1_xboole_0(u1_struct_0(sK0)) ),
introduced(definition,[new_symbols(definition,[spl25_6])],[avatar_definition]) ).
fof(f403,plain,
( v1_xboole_0(u1_struct_0(sK0))
| ~ spl25_6 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f404,plain,
( spl25_5
| spl25_6 ),
inference(avatar_split_clause,[],[f397,f402,f399]) ).
fof(f405,plain,
( m2_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ spl25_5 ),
inference(resolution,[],[f400,f193]) ).
fof(f413,plain,
( sK1 = 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)))
| ~ spl25_5 ),
inference(resolution,[],[f405,f350]) ).
fof(f414,plain,
( sK1 = 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)
| ~ spl25_5 ),
inference(resolution,[],[f405,f349]) ).
fof(f419,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK0))
| v1_funct_2(X0,u1_struct_0(sK0),u1_struct_0(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(resolution,[],[f368,f188]) ).
fof(f420,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK0))
| v1_funct_2(X0,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[],[f419,f192]) ).
fof(f421,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK0))
| v1_funct_2(X0,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[],[f420,f191]) ).
fof(f422,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK0))
| v1_funct_2(X0,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ v4_group_1(sK0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[],[f421,f190]) ).
fof(f423,plain,
! [X0] :
( 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(forward_subsumption_resolution,[],[f422,f189]) ).
fof(f425,definition,
( spl25_7
<=> ! [X0] :
( 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)) ) ),
introduced(definition,[new_symbols(definition,[spl25_7])],[avatar_definition]) ).
fof(f426,plain,
( ! [X0] :
( ~ 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)) )
| ~ spl25_7 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f427,plain,
( spl25_7
| spl25_6 ),
inference(avatar_split_clause,[],[f423,f402,f425]) ).
fof(f428,plain,
( v3_struct_0(sK0)
| ~ l1_struct_0(sK0)
| ~ spl25_6 ),
inference(resolution,[],[f403,f263]) ).
fof(f430,plain,
( ~ l1_struct_0(sK0)
| ~ spl25_6 ),
inference(forward_subsumption_resolution,[],[f428,f192]) ).
fof(f432,plain,
( ~ l1_group_1(sK0)
| ~ spl25_6 ),
inference(resolution,[],[f430,f242]) ).
fof(f434,plain,
( $false
| ~ spl25_6 ),
inference(forward_subsumption_resolution,[],[f432,f188]) ).
fof(f435,plain,
~ spl25_6,
inference(avatar_contradiction_clause,[],[f434]) ).
fof(f436,plain,
( v1_funct_2(sK1,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ spl25_7 ),
inference(resolution,[],[f426,f193]) ).
fof(f438,plain,
( v1_funct_2(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ spl25_4
| ~ spl25_7 ),
inference(resolution,[],[f426,f382]) ).
fof(f446,plain,
( m1_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ spl25_5 ),
inference(resolution,[],[f332,f405]) ).
fof(f447,plain,
( ! [X2,X0,X1] :
( ~ m1_relset_1(X0,X1,X2)
| k5_relat_1(X0,sK1) = k7_relset_1(X1,X2,u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) )
| ~ spl25_5 ),
inference(resolution,[],[f446,f329]) ).
fof(f451,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK0))
| v1_funct_1(X0)
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(resolution,[],[f369,f188]) ).
fof(f452,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK0))
| v1_funct_1(X0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[],[f451,f192]) ).
fof(f453,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK0))
| v1_funct_1(X0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[],[f452,f191]) ).
fof(f454,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK0))
| v1_funct_1(X0)
| ~ v4_group_1(sK0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[],[f453,f190]) ).
fof(f455,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK0))
| v1_funct_1(X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[],[f454,f189]) ).
fof(f457,definition,
( spl25_8
<=> ! [X0] :
( v1_funct_1(X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl25_8])],[avatar_definition]) ).
fof(f458,plain,
( ! [X0] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| v1_funct_1(X0) )
| ~ spl25_8 ),
inference(avatar_component_clause,[],[f457]) ).
fof(f459,plain,
( spl25_8
| spl25_6 ),
inference(avatar_split_clause,[],[f455,f402,f457]) ).
fof(f460,plain,
( v1_funct_1(sK1)
| ~ spl25_8 ),
inference(resolution,[],[f458,f193]) ).
fof(f469,plain,
( ! [X2,X3,X0,X1] :
( ~ v1_funct_2(sK1,X0,X3)
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,X2,X0)
| ~ m1_relset_1(X1,X2,X0)
| k7_funct_2(X2,X0,X3,X1,sK1) = k5_relat_1(X1,sK1)
| v1_xboole_0(X0)
| ~ m1_relset_1(sK1,X0,X3) )
| ~ spl25_8 ),
inference(resolution,[],[f460,f328]) ).
fof(f484,plain,
! [X2,X3,X0,X1,X4] :
( ~ v1_funct_2(k6_relat_1(X4),X0,X3)
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,X2,X0)
| ~ m1_relset_1(X1,X2,X0)
| k7_funct_2(X2,X0,X3,X1,k6_relat_1(X4)) = k5_relat_1(X1,k6_relat_1(X4))
| v1_xboole_0(X0)
| ~ m1_relset_1(k6_relat_1(X4),X0,X3) ),
inference(resolution,[],[f271,f328]) ).
fof(f614,plain,
( ! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,X1,u1_struct_0(sK0))
| ~ m1_relset_1(X0,X1,u1_struct_0(sK0))
| k7_funct_2(X1,u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k5_relat_1(X0,sK1)
| v1_xboole_0(u1_struct_0(sK0))
| ~ m1_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK0)) )
| ~ spl25_7
| ~ spl25_8 ),
inference(resolution,[],[f469,f436]) ).
fof(f615,plain,
( ! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,X1,u1_struct_0(sK0))
| ~ m1_relset_1(X0,X1,u1_struct_0(sK0))
| k7_funct_2(X1,u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k5_relat_1(X0,sK1)
| v1_xboole_0(u1_struct_0(sK0)) )
| ~ spl25_5
| ~ spl25_7
| ~ spl25_8 ),
inference(forward_subsumption_resolution,[],[f614,f446]) ).
fof(f617,definition,
( spl25_22
<=> ! [X0,X1] :
( ~ v1_funct_1(X0)
| k7_funct_2(X1,u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k5_relat_1(X0,sK1)
| ~ m1_relset_1(X0,X1,u1_struct_0(sK0))
| ~ v1_funct_2(X0,X1,u1_struct_0(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl25_22])],[avatar_definition]) ).
fof(f618,plain,
( ! [X0,X1] :
( ~ v1_funct_1(X0)
| k7_funct_2(X1,u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k5_relat_1(X0,sK1)
| ~ m1_relset_1(X0,X1,u1_struct_0(sK0))
| ~ v1_funct_2(X0,X1,u1_struct_0(sK0)) )
| ~ spl25_22 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f619,plain,
( spl25_6
| spl25_22
| ~ spl25_5
| ~ spl25_7
| ~ spl25_8 ),
inference(avatar_split_clause,[],[f615,f457,f425,f399,f617,f402]) ).
fof(f621,plain,
( ! [X0,X1] :
( ~ v1_funct_2(k6_relat_1(X1),X0,u1_struct_0(sK0))
| ~ m1_relset_1(k6_relat_1(X1),X0,u1_struct_0(sK0))
| k7_funct_2(X0,u1_struct_0(sK0),u1_struct_0(sK0),k6_relat_1(X1),sK1) = k5_relat_1(k6_relat_1(X1),sK1) )
| ~ spl25_22 ),
inference(resolution,[],[f618,f271]) ).
fof(f731,plain,
! [X0] : m1_relset_1(k6_relat_1(X0),X0,X0),
inference(resolution,[],[f348,f332]) ).
fof(f736,plain,
! [X2,X3,X0,X1] :
( ~ m1_relset_1(X0,X1,X2)
| k7_relset_1(X1,X2,X3,X3,X0,k6_relat_1(X3)) = k5_relat_1(X0,k6_relat_1(X3)) ),
inference(resolution,[],[f731,f329]) ).
fof(f738,plain,
( ! [X0] : k5_relat_1(k6_relat_1(X0),sK1) = k7_relset_1(X0,X0,u1_struct_0(sK0),u1_struct_0(sK0),k6_relat_1(X0),sK1)
| ~ spl25_5 ),
inference(resolution,[],[f731,f447]) ).
fof(f780,plain,
( ! [X0] : 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))
| ~ spl25_5 ),
inference(resolution,[],[f736,f446]) ).
fof(f785,plain,
( sK1 = k5_relat_1(sK1,k6_relat_1(u1_struct_0(sK0)))
| ~ spl25_5 ),
inference(superposition,[],[f413,f780]) ).
fof(f797,plain,
( sK1 = k5_relat_1(k6_relat_1(u1_struct_0(sK0)),sK1)
| ~ spl25_5 ),
inference(superposition,[],[f414,f738]) ).
fof(f962,plain,
( ! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,X1,u1_struct_0(sK0))
| ~ m1_relset_1(X0,X1,u1_struct_0(sK0))
| k7_funct_2(X1,u1_struct_0(sK0),u1_struct_0(sK0),X0,k6_relat_1(u1_struct_0(sK0))) = k5_relat_1(X0,k6_relat_1(u1_struct_0(sK0)))
| v1_xboole_0(u1_struct_0(sK0))
| ~ m1_relset_1(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0)) )
| ~ spl25_4
| ~ spl25_7 ),
inference(resolution,[],[f484,f438]) ).
fof(f963,plain,
( ! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,X1,u1_struct_0(sK0))
| ~ m1_relset_1(X0,X1,u1_struct_0(sK0))
| k7_funct_2(X1,u1_struct_0(sK0),u1_struct_0(sK0),X0,k6_relat_1(u1_struct_0(sK0))) = k5_relat_1(X0,k6_relat_1(u1_struct_0(sK0)))
| v1_xboole_0(u1_struct_0(sK0)) )
| ~ spl25_4
| ~ spl25_7 ),
inference(forward_subsumption_resolution,[],[f962,f731]) ).
fof(f965,definition,
( spl25_44
<=> ! [X0,X1] :
( ~ v1_funct_1(X0)
| k7_funct_2(X1,u1_struct_0(sK0),u1_struct_0(sK0),X0,k6_relat_1(u1_struct_0(sK0))) = k5_relat_1(X0,k6_relat_1(u1_struct_0(sK0)))
| ~ m1_relset_1(X0,X1,u1_struct_0(sK0))
| ~ v1_funct_2(X0,X1,u1_struct_0(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl25_44])],[avatar_definition]) ).
fof(f966,plain,
( ! [X0,X1] :
( ~ v1_funct_1(X0)
| k7_funct_2(X1,u1_struct_0(sK0),u1_struct_0(sK0),X0,k6_relat_1(u1_struct_0(sK0))) = k5_relat_1(X0,k6_relat_1(u1_struct_0(sK0)))
| ~ m1_relset_1(X0,X1,u1_struct_0(sK0))
| ~ v1_funct_2(X0,X1,u1_struct_0(sK0)) )
| ~ spl25_44 ),
inference(avatar_component_clause,[],[f965]) ).
fof(f967,plain,
( spl25_6
| spl25_44
| ~ spl25_4
| ~ spl25_7 ),
inference(avatar_split_clause,[],[f963,f425,f381,f965,f402]) ).
fof(f968,plain,
( ! [X0] :
( k5_relat_1(sK1,k6_relat_1(u1_struct_0(sK0))) = k7_funct_2(X0,u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_relat_1(u1_struct_0(sK0)))
| ~ m1_relset_1(sK1,X0,u1_struct_0(sK0))
| ~ v1_funct_2(sK1,X0,u1_struct_0(sK0)) )
| ~ spl25_8
| ~ spl25_44 ),
inference(resolution,[],[f966,f460]) ).
fof(f971,plain,
( ! [X0] :
( ~ v1_funct_2(sK1,X0,u1_struct_0(sK0))
| ~ m1_relset_1(sK1,X0,u1_struct_0(sK0))
| sK1 = k7_funct_2(X0,u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_relat_1(u1_struct_0(sK0))) )
| ~ spl25_5
| ~ spl25_8
| ~ spl25_44 ),
inference(forward_demodulation,[],[f968,f785]) ).
fof(f973,plain,
( ~ m1_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK0))
| sK1 = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_relat_1(u1_struct_0(sK0)))
| ~ spl25_5
| ~ spl25_7
| ~ spl25_8
| ~ spl25_44 ),
inference(resolution,[],[f971,f436]) ).
fof(f975,plain,
( sK1 = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_relat_1(u1_struct_0(sK0)))
| ~ spl25_5
| ~ spl25_7
| ~ spl25_8
| ~ spl25_44 ),
inference(forward_subsumption_resolution,[],[f973,f446]) ).
fof(f976,plain,
( $false
| spl25_1
| ~ spl25_5
| ~ spl25_7
| ~ spl25_8
| ~ spl25_44 ),
inference(forward_subsumption_resolution,[],[f975,f364]) ).
fof(f977,plain,
( spl25_1
| ~ spl25_5
| ~ spl25_7
| ~ spl25_8
| ~ spl25_44 ),
inference(avatar_contradiction_clause,[],[f976]) ).
fof(f978,plain,
( sK1 != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_relat_1(u1_struct_0(sK0)),sK1)
| spl25_2 ),
inference(forward_demodulation,[],[f357,f363]) ).
fof(f1496,plain,
( ~ m1_relset_1(k6_relat_1(u1_struct_0(sK0)),u1_struct_0(sK0),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)
| ~ spl25_4
| ~ spl25_7
| ~ spl25_22 ),
inference(resolution,[],[f621,f438]) ).
fof(f1497,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)
| ~ spl25_4
| ~ spl25_7
| ~ spl25_22 ),
inference(forward_subsumption_resolution,[],[f1496,f731]) ).
fof(f1498,plain,
( sK1 = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_relat_1(u1_struct_0(sK0)),sK1)
| ~ spl25_4
| ~ spl25_5
| ~ spl25_7
| ~ spl25_22 ),
inference(forward_demodulation,[],[f1497,f797]) ).
fof(f1499,plain,
( $false
| spl25_2
| ~ spl25_4
| ~ spl25_5
| ~ spl25_7
| ~ spl25_22 ),
inference(forward_subsumption_resolution,[],[f1498,f978]) ).
fof(f1500,plain,
( spl25_2
| ~ spl25_4
| ~ spl25_5
| ~ spl25_7
| ~ spl25_22 ),
inference(avatar_contradiction_clause,[],[f1499]) ).
cnf(s1,plain,
( ~ spl25_1
| ~ spl25_2 ),
inference(sat_conversion,[],[f358]) ).
cnf(s2,plain,
( ~ spl25_3
| spl25_4 ),
inference(sat_conversion,[],[f383]) ).
cnf(s4,plain,
spl25_3,
inference(sat_conversion,[],[f389]) ).
cnf(s5,plain,
( spl25_5
| spl25_6 ),
inference(sat_conversion,[],[f404]) ).
cnf(s6,plain,
( spl25_6
| spl25_7 ),
inference(sat_conversion,[],[f427]) ).
cnf(s8,plain,
~ spl25_6,
inference(sat_conversion,[],[f435]) ).
cnf(s9,plain,
( spl25_6
| spl25_8 ),
inference(sat_conversion,[],[f459]) ).
cnf(s23,plain,
( ~ spl25_5
| spl25_6
| ~ spl25_7
| ~ spl25_8
| spl25_22 ),
inference(sat_conversion,[],[f619]) ).
cnf(s37,plain,
( ~ spl25_4
| spl25_6
| ~ spl25_7
| spl25_44 ),
inference(sat_conversion,[],[f967]) ).
cnf(s39,plain,
( spl25_1
| ~ spl25_5
| ~ spl25_7
| ~ spl25_8
| ~ spl25_44 ),
inference(sat_conversion,[],[f977]) ).
cnf(s54,plain,
( spl25_2
| ~ spl25_4
| ~ spl25_5
| ~ spl25_7
| ~ spl25_22 ),
inference(sat_conversion,[],[f1500]) ).
cnf(s58,plain,
spl25_8,
inference(rat,[],[s9,s8]) ).
cnf(s60,plain,
spl25_7,
inference(rat,[],[s6,s8]) ).
cnf(s61,plain,
spl25_5,
inference(rat,[],[s5,s8]) ).
cnf(s62,plain,
spl25_22,
inference(rat,[],[s23,s60,s58,s8,s61]) ).
cnf(s68,plain,
spl25_4,
inference(rat,[],[s2,s4]) ).
cnf(s69,plain,
spl25_2,
inference(rat,[],[s54,s62,s60,s61,s68]) ).
cnf(s70,plain,
spl25_44,
inference(rat,[],[s37,s60,s8,s68]) ).
cnf(s73,plain,
spl25_1,
inference(rat,[],[s39,s61,s58,s60,s70]) ).
cnf(s74,plain,
$false,
inference(rat,[],[s1,s69,s73]) ).
fof(f1501,plain,
$false,
inference(avatar_sat_refutation,[],[s74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP632+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n020.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 : Sun Sep 27 10:17:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.92/1.62 % (3171412)Detected formulas, will run a generic FOF schedule.
% 4.92/1.62 % (3171418)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1976606245:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.92/1.62 % (3171422)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3706569211:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.92/1.62 % (3171419)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1701733142:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.92/1.62 % (3171423)dis-21_1_sil=8000:lcm=predicate:random_seed=2754519997:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.92/1.62 % (3171420)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3934495566:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.92/1.62 % (3171421)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=617729961:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.92/1.62 % (3171417)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2578998165:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.92/1.62 % (3171420)Refutation not found, incomplete strategy
% 4.92/1.62 % (3171420)------------------------------
% 4.92/1.62 % (3171420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.62 % (3171420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.62 % (3171420)CaDiCaL version: 2.1.3
% 4.92/1.62 % (3171420)Termination reason: Refutation not found, incomplete strategy
% 4.92/1.62 % (3171420)Time elapsed: 0.003 s
% 4.92/1.62 % (3171420)Peak memory usage: 88 MB
% 4.92/1.62 % (3171420)Instructions burned: 2 (million)
% 4.92/1.62 % (3171421)Refutation not found, incomplete strategy
% 4.92/1.62 % (3171421)------------------------------
% 4.92/1.62 % (3171421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.62 % (3171421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.62 % (3171421)CaDiCaL version: 2.1.3
% 4.92/1.62 % (3171421)Termination reason: Refutation not found, incomplete strategy
% 4.92/1.62 % (3171421)Time elapsed: 0.047 s
% 4.92/1.62 % (3171421)Peak memory usage: 89 MB
% 4.92/1.62 % (3171421)Instructions burned: 77 (million)
% 4.92/1.62 % (3171423)Instruction limit reached!
% 4.92/1.62 % (3171423)------------------------------
% 4.92/1.62 % (3171423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.62 % (3171423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.62 % (3171423)CaDiCaL version: 2.1.3
% 4.92/1.62 % (3171423)Termination reason: Instruction limit
% 4.92/1.62 % (3171423)Termination phase: Saturation
% 4.92/1.62 % (3171423)Time elapsed: 0.067 s
% 4.92/1.62 % (3171423)Peak memory usage: 90 MB
% 4.92/1.62 % (3171423)Instructions burned: 131 (million)
% 4.92/1.62 % (3171422)Instruction limit reached!
% 4.92/1.62 % (3171422)------------------------------
% 4.92/1.62 % (3171422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.62 % (3171422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.62 % (3171422)CaDiCaL version: 2.1.3
% 4.92/1.62 % (3171422)Termination reason: Instruction limit
% 4.92/1.62 % (3171422)Termination phase: Saturation
% 4.92/1.62 % (3171422)Time elapsed: 0.102 s
% 4.92/1.62 % (3171422)Peak memory usage: 90 MB
% 4.92/1.62 % (3171422)Instructions burned: 139 (million)
% 4.92/1.62 % (3171431)lrs+10_1_sil=8000:sp=occurrence:random_seed=3599081777:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.92/1.62 % (3171420)------------------------------
% 4.92/1.62 % (3171420)------------------------------
% 4.92/1.62 % (3171432)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1332930602:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.92/1.62 % (3171432)Refutation not found, incomplete strategy
% 4.92/1.62 % (3171432)------------------------------
% 4.92/1.62 % (3171432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.62 % (3171432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.62 % (3171432)CaDiCaL version: 2.1.3
% 4.92/1.62 % (3171432)Termination reason: Refutation not found, incomplete strategy
% 4.92/1.62 % (3171432)Time elapsed: 0.004 s
% 4.92/1.62 % (3171432)Peak memory usage: 89 MB
% 4.92/1.62 % (3171432)Instructions burned: 3 (million)
% 4.92/1.62 % (3171421)------------------------------
% 4.92/1.62 % (3171421)------------------------------
% 4.92/1.62 % (3171431)Instruction limit reached!
% 4.92/1.62 % (3171431)------------------------------
% 4.92/1.62 % (3171431)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.62 % (3171431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.62 % (3171431)CaDiCaL version: 2.1.3
% 4.92/1.62 % (3171431)Termination reason: Instruction limit
% 4.92/1.62 % (3171431)Termination phase: Saturation
% 4.92/1.62 % (3171431)Time elapsed: 0.162 s
% 4.92/1.62 % (3171431)Peak memory usage: 92 MB
% 4.92/1.62 % (3171431)Instructions burned: 286 (million)
% 4.92/1.62 % (3171434)lrs+1011_1_sil=32000:sp=occurrence:random_seed=711888374:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 4.92/1.62 % (3171434)Refutation not found, incomplete strategy
% 4.92/1.62 % (3171434)------------------------------
% 4.92/1.62 % (3171434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.62 % (3171434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.62 % (3171434)CaDiCaL version: 2.1.3
% 4.92/1.62 % (3171434)Termination reason: Refutation not found, incomplete strategy
% 4.92/1.62 % (3171434)Time elapsed: 0.005 s
% 4.92/1.62 % (3171434)Peak memory usage: 89 MB
% 4.92/1.62 % (3171434)Instructions burned: 5 (million)
% 4.92/1.62 % (3171418)First to succeed.
% 4.92/1.62 % (3171418)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3171412"
% 4.92/1.62 % (3171436)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=341161066:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.92/1.62 % (3171432)------------------------------
% 4.92/1.62 % (3171432)------------------------------
% 4.92/1.62 % (3171438)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3898630463:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 4.92/1.62 % (3171418)Refutation found. Thanks to Tanya!
% 4.92/1.62 % SZS status Theorem for theBenchmark
% 4.92/1.62 % SZS output start Proof for theBenchmark
% See solution above
% 6.05/1.82 % (3171418)------------------------------
% 6.05/1.82 % (3171418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.05/1.82 % (3171418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.82 % (3171418)CaDiCaL version: 2.1.3
% 6.05/1.82 % (3171418)Termination reason: Refutation
% 6.05/1.82 % (3171418)Time elapsed: 0.474 s
% 6.05/1.82 % (3171418)Peak memory usage: 133 MB
% 6.05/1.82 % (3171418)Instructions burned: 1242 (million)
% 6.05/1.82 % (3171418)------------------------------
% 6.05/1.82 % (3171418)------------------------------
% 6.05/1.82 % (3171412)Success in time 0.765 s
% 6.05/1.82 % Vampire exiting
%------------------------------------------------------------------------------