%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP630+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 : n001.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 10:15:07 AM UTC 2026
% Result : Theorem 9.43s 2.17s
% Output : Refutation 9.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 35
% Syntax : Number of formulae : 343 ( 60 unt; 15 def)
% Number of atoms : 1646 ( 177 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 2283 ( 980 ~;1069 |; 178 &)
% ( 24 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 10 prp; 0-4 aty)
% Number of functors : 24 ( 24 usr; 8 con; 0-6 aty)
% Number of variables : 364 ( 0 sgn 354 !; 10 ?)
% 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] :
( m1_subset_1(X1,u1_struct_0(X0))
=> k6_autgroup(X0,k3_group_1(X0,X1)) = k2_funct_1(k6_autgroup(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_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] :
( m1_subset_1(X1,u1_struct_0(X0))
=> k6_autgroup(X0,k3_group_1(X0,X1)) = k2_funct_1(k6_autgroup(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f17,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
=> ( X1 = k1_autgroup(X0)
<=> ( ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1)
=> ( v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X2,X0,X0)
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0)) ) )
& ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X2,X0,X0)
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0)) )
=> ( r2_hidden(X2,X1)
<=> ( v2_funct_1(X2)
& v3_group_6(X2,X0,X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_autgroup) ).
fof(f19,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_autgroup) ).
fof(f28,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0)
& m1_subset_1(X1,u1_struct_0(X0)) )
=> m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_group_1) ).
fof(f31,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(f35,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f37,axiom,
! [X0,X1,X2] :
( m1_fraenkel(X2,X0,X1)
=> ( ~ v1_xboole_0(X2)
& v1_fraenkel(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
fof(f53,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(f54,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f58,axiom,
! [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),k1_autgroup(X0))
=> ( k1_relat_1(X1) = k2_relat_1(X1)
& k1_relat_1(X1) = u1_struct_0(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l9_autgroup) ).
fof(f76,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( v1_funct_1(X4)
& m1_relset_1(X4,X0,X1)
& v1_funct_1(X5)
& m1_relset_1(X5,X2,X3) )
=> k1_partfun1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_partfun1) ).
fof(f77,axiom,
! [X0] : k6_partfun1(X0) = k6_relat_1(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
fof(f78,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(f79,axiom,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X1)
& m1_fraenkel(X2,X0,X1) )
=> ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
fof(f80,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(f82,axiom,
! [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))
=> m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_autgroup) ).
fof(f84,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,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,X1),k6_autgroup(X0,k3_group_1(X0,X1))) = k6_autgroup(X0,k2_group_1(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_autgroup) ).
fof(f86,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( v1_xboole_0(X1)
| r2_hidden(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f87,axiom,
! [X0,X1,X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,X0,X1)
& m2_relset_1(X2,X0,X1) )
=> ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,X1,X0)
& m2_relset_1(X3,X1,X0) )
=> ( ( k2_relat_1(X2) = X1
& k1_partfun1(X0,X1,X1,X0,X2,X3) = k6_partfun1(X0)
& v2_funct_1(X2) )
=> ( X0 = k1_xboole_0
| X1 = k1_xboole_0
| X3 = k2_funct_1(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_funct_2) ).
fof(f94,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
=> ( X1 = k1_autgroup(X0)
<=> ( ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1)
=> ( v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X2,X0,X0)
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0)) ) )
& ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X3,X0,X0)
& m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0)) )
=> ( r2_hidden(X3,X1)
<=> ( v2_funct_1(X3)
& v3_group_6(X3,X0,X0) ) ) ) ) ) ) ),
inference(rectify,[],[f17]) ).
fof(f101,plain,
? [X0] :
( ? [X1] :
( k6_autgroup(X0,k3_group_1(X0,X1)) != k2_funct_1(k6_autgroup(X0,X1))
& m1_subset_1(X1,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,[],[f2]) ).
fof(f102,plain,
? [X0] :
( ? [X1] :
( k6_autgroup(X0,k3_group_1(X0,X1)) != k2_funct_1(k6_autgroup(X0,X1))
& m1_subset_1(X1,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,[],[f101]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ( X1 = k1_autgroup(X0)
<=> ( ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X2,X0,X0)
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0)) )
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1) )
& ! [X3] :
( ( r2_hidden(X3,X1)
<=> ( v2_funct_1(X3)
& v3_group_6(X3,X0,X0) ) )
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X3,X0,X0)
| ~ m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0)) ) ) )
| ~ m1_fraenkel(X1,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,[],[f94]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ( X1 = k1_autgroup(X0)
<=> ( ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X2,X0,X0)
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0)) )
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1) )
& ! [X3] :
( ( r2_hidden(X3,X1)
<=> ( v2_funct_1(X3)
& v3_group_6(X3,X0,X0) ) )
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X3,X0,X0)
| ~ m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0)) ) ) )
| ~ m1_fraenkel(X1,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,[],[f127]) ).
fof(f131,plain,
! [X0] :
( m1_fraenkel(k1_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,[],[f19]) ).
fof(f132,plain,
! [X0] :
( m1_fraenkel(k1_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,[],[f131]) ).
fof(f139,plain,
! [X0,X1] :
( m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f140,plain,
! [X0,X1] :
( m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(flattening,[],[f139]) ).
fof(f145,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,[],[f31]) ).
fof(f146,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,[],[f145]) ).
fof(f149,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X2)
& v1_fraenkel(X2) )
| ~ m1_fraenkel(X2,X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f161,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f162,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(flattening,[],[f161]) ).
fof(f165,plain,
! [X0] :
( ! [X1] :
( ( k1_relat_1(X1) = k2_relat_1(X1)
& k1_relat_1(X1) = u1_struct_0(X0) )
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_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,[],[f58]) ).
fof(f166,plain,
! [X0] :
( ! [X1] :
( ( k1_relat_1(X1) = k2_relat_1(X1)
& k1_relat_1(X1) = u1_struct_0(X0) )
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f165]) ).
fof(f171,plain,
! [X0,X1,X2,X3,X4,X5] :
( k1_partfun1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5)
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X4,X0,X1)
| ~ v1_funct_1(X5)
| ~ m1_relset_1(X5,X2,X3) ),
inference(ennf_transformation,[],[f76]) ).
fof(f172,plain,
! [X0,X1,X2,X3,X4,X5] :
( k1_partfun1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5)
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X4,X0,X1)
| ~ v1_funct_1(X5)
| ~ m1_relset_1(X5,X2,X3) ),
inference(flattening,[],[f171]) ).
fof(f173,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,[],[f78]) ).
fof(f174,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,[],[f173]) ).
fof(f175,plain,
! [X0,X1,X2] :
( ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) )
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(ennf_transformation,[],[f79]) ).
fof(f176,plain,
! [X0,X1,X2] :
( ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) )
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(flattening,[],[f175]) ).
fof(f177,plain,
! [X0] :
( ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ 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,[],[f82]) ).
fof(f178,plain,
! [X0] :
( ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ 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,[],[f177]) ).
fof(f180,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,[],[f84]) ).
fof(f181,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,[],[f180]) ).
fof(f182,plain,
! [X0] :
( ! [X1] :
( k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,X1),k6_autgroup(X0,k3_group_1(X0,X1))) = k6_autgroup(X0,k2_group_1(X0))
| ~ m1_subset_1(X1,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,[],[f85]) ).
fof(f183,plain,
! [X0] :
( ! [X1] :
( k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,X1),k6_autgroup(X0,k3_group_1(X0,X1))) = k6_autgroup(X0,k2_group_1(X0))
| ~ m1_subset_1(X1,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,[],[f182]) ).
fof(f184,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f86]) ).
fof(f185,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f184]) ).
fof(f186,plain,
! [X0,X1,X2] :
( ! [X3] :
( X0 = k1_xboole_0
| X1 = k1_xboole_0
| X3 = k2_funct_1(X2)
| k2_relat_1(X2) != X1
| k6_partfun1(X0) != k1_partfun1(X0,X1,X1,X0,X2,X3)
| ~ v2_funct_1(X2)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,X1,X0)
| ~ m2_relset_1(X3,X1,X0) )
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f87]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ! [X3] :
( X0 = k1_xboole_0
| X1 = k1_xboole_0
| X3 = k2_funct_1(X2)
| k2_relat_1(X2) != X1
| k6_partfun1(X0) != k1_partfun1(X0,X1,X1,X0,X2,X3)
| ~ v2_funct_1(X2)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,X1,X0)
| ~ m2_relset_1(X3,X1,X0) )
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(flattening,[],[f186]) ).
fof(f195,definition,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X3] :
( ( r2_hidden(X3,X1)
<=> ( v2_funct_1(X3)
& v3_group_6(X3,X0,X0) ) )
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X3,X0,X0)
| ~ m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0)) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( ( X1 = k1_autgroup(X0)
<=> ( ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X2,X0,X0)
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0)) )
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1) )
& sP0(X0,X1) ) )
| ~ m1_fraenkel(X1,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(definition_folding,[],[f128,f195]) ).
fof(f197,plain,
( k6_autgroup(sK1,k3_group_1(sK1,sK2)) != k2_funct_1(k6_autgroup(sK1,sK2))
& m1_subset_1(sK2,u1_struct_0(sK1))
& ~ v3_struct_0(sK1)
& v1_group_1(sK1)
& v3_group_1(sK1)
& v4_group_1(sK1)
& l1_group_1(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f102]) ).
fof(f198,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X3] :
( ( ~ v2_funct_1(X3)
| ~ v3_group_6(X3,X0,X0)
| ~ r2_hidden(X3,X1) )
& ( ( v2_funct_1(X3)
& v3_group_6(X3,X0,X0) )
| r2_hidden(X3,X1) )
& v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X3,X0,X0)
& m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0)) ) )
& ( ! [X3] :
( ( ( r2_hidden(X3,X1)
| ~ v2_funct_1(X3)
| ~ v3_group_6(X3,X0,X0) )
& ( ( v2_funct_1(X3)
& v3_group_6(X3,X0,X0) )
| ~ r2_hidden(X3,X1) ) )
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X3,X0,X0)
| ~ m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0)) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f195]) ).
fof(f199,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X3] :
( ( ~ v2_funct_1(X3)
| ~ v3_group_6(X3,X0,X0)
| ~ r2_hidden(X3,X1) )
& ( ( v2_funct_1(X3)
& v3_group_6(X3,X0,X0) )
| r2_hidden(X3,X1) )
& v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X3,X0,X0)
& m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0)) ) )
& ( ! [X3] :
( ( ( r2_hidden(X3,X1)
| ~ v2_funct_1(X3)
| ~ v3_group_6(X3,X0,X0) )
& ( ( v2_funct_1(X3)
& v3_group_6(X3,X0,X0) )
| ~ r2_hidden(X3,X1) ) )
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X3,X0,X0)
| ~ m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0)) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f198]) ).
fof(f200,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ~ v2_funct_1(X2)
| ~ v3_group_6(X2,X0,X0)
| ~ r2_hidden(X2,X1) )
& ( ( v2_funct_1(X2)
& v3_group_6(X2,X0,X0) )
| r2_hidden(X2,X1) )
& v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X2,X0,X0)
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0)) ) )
& ( ! [X3] :
( ( ( r2_hidden(X3,X1)
| ~ v2_funct_1(X3)
| ~ v3_group_6(X3,X0,X0) )
& ( ( v2_funct_1(X3)
& v3_group_6(X3,X0,X0) )
| ~ r2_hidden(X3,X1) ) )
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X3,X0,X0)
| ~ m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0)) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f199]) ).
fof(f201,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ~ v2_funct_1(sK3(X0,X1))
| ~ v3_group_6(sK3(X0,X1),X0,X0)
| ~ r2_hidden(sK3(X0,X1),X1) )
& ( ( v2_funct_1(sK3(X0,X1))
& v3_group_6(sK3(X0,X1),X0,X0) )
| r2_hidden(sK3(X0,X1),X1) )
& v1_funct_1(sK3(X0,X1))
& v1_funct_2(sK3(X0,X1),u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(sK3(X0,X1),X0,X0)
& m2_relset_1(sK3(X0,X1),u1_struct_0(X0),u1_struct_0(X0)) ) )
& ( ! [X3] :
( ( ( r2_hidden(X3,X1)
| ~ v2_funct_1(X3)
| ~ v3_group_6(X3,X0,X0) )
& ( ( v2_funct_1(X3)
& v3_group_6(X3,X0,X0) )
| ~ r2_hidden(X3,X1) ) )
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X3,X0,X0)
| ~ m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0)) )
| ~ sP0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f200]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k1_autgroup(X0)
| ? [X2] :
( ( ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X2,X0,X0)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0)) )
& m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1) )
| ~ sP0(X0,X1) )
& ( ( ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X2,X0,X0)
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0)) )
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1) )
& sP0(X0,X1) )
| k1_autgroup(X0) != X1 ) )
| ~ m1_fraenkel(X1,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(nnf_transformation,[],[f196]) ).
fof(f203,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k1_autgroup(X0)
| ? [X2] :
( ( ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X2,X0,X0)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0)) )
& m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1) )
| ~ sP0(X0,X1) )
& ( ( ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X2,X0,X0)
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0)) )
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1) )
& sP0(X0,X1) )
| k1_autgroup(X0) != X1 ) )
| ~ m1_fraenkel(X1,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,[],[f202]) ).
fof(f204,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k1_autgroup(X0)
| ? [X2] :
( ( ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X2,X0,X0)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0)) )
& m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1) )
| ~ sP0(X0,X1) )
& ( ( ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X3,X0,X0)
& m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0)) )
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),X1) )
& sP0(X0,X1) )
| k1_autgroup(X0) != X1 ) )
| ~ m1_fraenkel(X1,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(rectify,[],[f203]) ).
fof(f205,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k1_autgroup(X0)
| ( ( ~ v1_funct_1(sK4(X0,X1))
| ~ v1_funct_2(sK4(X0,X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(sK4(X0,X1),X0,X0)
| ~ m2_relset_1(sK4(X0,X1),u1_struct_0(X0),u1_struct_0(X0)) )
& m2_fraenkel(sK4(X0,X1),u1_struct_0(X0),u1_struct_0(X0),X1) )
| ~ sP0(X0,X1) )
& ( ( ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X3,X0,X0)
& m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0)) )
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),X1) )
& sP0(X0,X1) )
| k1_autgroup(X0) != X1 ) )
| ~ m1_fraenkel(X1,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(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f204]) ).
fof(f230,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( m2_fraenkel(X3,X0,X1,X2)
| ~ m1_subset_1(X3,X2) )
& ( m1_subset_1(X3,X2)
| ~ m2_fraenkel(X3,X0,X1,X2) ) )
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(nnf_transformation,[],[f176]) ).
fof(f231,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,[],[f80]) ).
fof(f232,plain,
l1_group_1(sK1),
inference(cnf_transformation,[],[f197]) ).
fof(f233,plain,
v4_group_1(sK1),
inference(cnf_transformation,[],[f197]) ).
fof(f234,plain,
v3_group_1(sK1),
inference(cnf_transformation,[],[f197]) ).
fof(f235,plain,
v1_group_1(sK1),
inference(cnf_transformation,[],[f197]) ).
fof(f236,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f197]) ).
fof(f237,plain,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f197]) ).
fof(f238,plain,
k6_autgroup(sK1,k3_group_1(sK1,sK2)) != k2_funct_1(k6_autgroup(sK1,sK2)),
inference(cnf_transformation,[],[f197]) ).
fof(f273,plain,
! [X3,X0,X1] :
( ~ m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0))
| ~ r2_hidden(X3,X1)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X3,X0,X0)
| v2_funct_1(X3)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f282,plain,
! [X0,X1] :
( sP0(X0,X1)
| k1_autgroup(X0) != X1
| ~ m1_fraenkel(X1,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,[],[f205]) ).
fof(f283,plain,
! [X3,X0,X1] :
( m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0))
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),X1)
| k1_autgroup(X0) != X1
| ~ m1_fraenkel(X1,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,[],[f205]) ).
fof(f284,plain,
! [X3,X0,X1] :
( v1_group_6(X3,X0,X0)
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),X1)
| k1_autgroup(X0) != X1
| ~ m1_fraenkel(X1,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,[],[f205]) ).
fof(f285,plain,
! [X3,X0,X1] :
( v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),X1)
| k1_autgroup(X0) != X1
| ~ m1_fraenkel(X1,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,[],[f205]) ).
fof(f286,plain,
! [X3,X0,X1] :
( v1_funct_1(X3)
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),X1)
| k1_autgroup(X0) != X1
| ~ m1_fraenkel(X1,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,[],[f205]) ).
fof(f291,plain,
! [X0] :
( m1_fraenkel(k1_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,[],[f132]) ).
fof(f297,plain,
! [X0,X1] :
( m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f300,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,[],[f146]) ).
fof(f307,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f309,plain,
! [X2,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| ~ v1_xboole_0(X2) ),
inference(cnf_transformation,[],[f150]) ).
fof(f328,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f329,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f54]) ).
fof(f339,plain,
! [X0,X1] :
( ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| u1_struct_0(X0) = k1_relat_1(X1)
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f166]) ).
fof(f340,plain,
! [X0,X1] :
( ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| k1_relat_1(X1) = k2_relat_1(X1)
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f166]) ).
fof(f398,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ m1_relset_1(X5,X2,X3)
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X4,X0,X1)
| ~ v1_funct_1(X5)
| k1_partfun1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
inference(cnf_transformation,[],[f172]) ).
fof(f399,plain,
! [X0] : k6_partfun1(X0) = k6_relat_1(X0),
inference(cnf_transformation,[],[f77]) ).
fof(f400,plain,
! [X2,X3,X0,X1,X4] :
( ~ v1_funct_2(X4,X1,X2)
| v1_xboole_0(X1)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,X0,X1)
| ~ m1_relset_1(X3,X0,X1)
| ~ v1_funct_1(X4)
| k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4)
| ~ m1_relset_1(X4,X1,X2) ),
inference(cnf_transformation,[],[f174]) ).
fof(f401,plain,
! [X2,X3,X0,X1] :
( ~ m2_fraenkel(X3,X0,X1,X2)
| m1_subset_1(X3,X2)
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f230]) ).
fof(f403,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f406,plain,
! [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))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f408,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,[],[f181]) ).
fof(f409,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| k6_autgroup(X0,k2_group_1(X0)) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,X1),k6_autgroup(X0,k3_group_1(X0,X1)))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f410,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f185]) ).
fof(f411,plain,
! [X2,X3,X0,X1] :
( k1_xboole_0 = X0
| k1_xboole_0 = X1
| k2_funct_1(X2) = X3
| k2_relat_1(X2) != X1
| k6_partfun1(X0) != k1_partfun1(X0,X1,X1,X0,X2,X3)
| ~ v2_funct_1(X2)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,X1,X0)
| ~ m2_relset_1(X3,X1,X0)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f187]) ).
fof(f420,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,[],[f408,f399]) ).
fof(f421,plain,
! [X2,X3,X0,X1] :
( k1_xboole_0 = X0
| k1_xboole_0 = X1
| k2_funct_1(X2) = X3
| k2_relat_1(X2) != X1
| k6_relat_1(X0) != k1_partfun1(X0,X1,X1,X0,X2,X3)
| ~ v2_funct_1(X2)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,X1,X0)
| ~ m2_relset_1(X3,X1,X0)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(definition_unfolding,[],[f411,f399]) ).
fof(f422,plain,
! [X3,X0] :
( v1_funct_1(X3)
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m1_fraenkel(k1_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(equality_resolution,[],[f286]) ).
fof(f423,plain,
! [X3,X0] :
( v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m1_fraenkel(k1_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(equality_resolution,[],[f285]) ).
fof(f424,plain,
! [X3,X0] :
( v1_group_6(X3,X0,X0)
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m1_fraenkel(k1_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(equality_resolution,[],[f284]) ).
fof(f425,plain,
! [X3,X0] :
( m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0))
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m1_fraenkel(k1_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(equality_resolution,[],[f283]) ).
fof(f426,plain,
! [X0] :
( sP0(X0,k1_autgroup(X0))
| ~ m1_fraenkel(k1_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(equality_resolution,[],[f282]) ).
fof(f427,plain,
! [X2,X3,X0] :
( k6_relat_1(X0) != k1_partfun1(X0,k2_relat_1(X2),k2_relat_1(X2),X0,X2,X3)
| k1_xboole_0 = k2_relat_1(X2)
| k2_funct_1(X2) = X3
| k1_xboole_0 = X0
| ~ v2_funct_1(X2)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,k2_relat_1(X2),X0)
| ~ m2_relset_1(X3,k2_relat_1(X2),X0)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,k2_relat_1(X2))
| ~ m2_relset_1(X2,X0,k2_relat_1(X2)) ),
inference(equality_resolution,[],[f421]) ).
fof(f428,definition,
sF29 = k3_group_1(sK1,sK2),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f429,plain,
k3_group_1(sK1,sK2) = sF29,
inference(reorient_equations,[],[f428]) ).
fof(f430,definition,
sF30 = k6_autgroup(sK1,sF29),
introduced(definition,[new_symbols(definition,[sF30])],[function_definition]) ).
fof(f431,plain,
k6_autgroup(sK1,sF29) = sF30,
inference(reorient_equations,[],[f430]) ).
fof(f432,definition,
sF31 = k6_autgroup(sK1,sK2),
introduced(definition,[new_symbols(definition,[sF31])],[function_definition]) ).
fof(f433,plain,
k6_autgroup(sK1,sK2) = sF31,
inference(reorient_equations,[],[f432]) ).
fof(f434,definition,
sF32 = k2_funct_1(sF31),
introduced(definition,[new_symbols(definition,[sF32])],[function_definition]) ).
fof(f435,plain,
k2_funct_1(sF31) = sF32,
inference(reorient_equations,[],[f434]) ).
fof(f436,plain,
sF30 != sF32,
inference(definition_folding,[],[f238,f435,f433,f431,f429]) ).
fof(f437,definition,
sF33 = u1_struct_0(sK1),
introduced(definition,[new_symbols(definition,[sF33])],[function_definition]) ).
fof(f438,plain,
u1_struct_0(sK1) = sF33,
inference(reorient_equations,[],[f437]) ).
fof(f439,plain,
m1_subset_1(sK2,sF33),
inference(definition_folding,[],[f237,f438]) ).
fof(f440,plain,
! [X0] :
( sP0(X0,k1_autgroup(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f426,f291]) ).
fof(f441,plain,
! [X3,X0] :
( ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| m2_relset_1(X3,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(forward_subsumption_resolution,[],[f425,f291]) ).
fof(f442,plain,
! [X3,X0] :
( ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| v1_group_6(X3,X0,X0)
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f424,f291]) ).
fof(f443,plain,
! [X3,X0] :
( ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| v1_funct_2(X3,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(forward_subsumption_resolution,[],[f423,f291]) ).
fof(f444,plain,
! [X3,X0] :
( ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| v1_funct_1(X3)
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f422,f291]) ).
fof(f445,plain,
( m1_subset_1(sF29,u1_struct_0(sK1))
| v3_struct_0(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(sK2,u1_struct_0(sK1)) ),
inference(superposition,[],[f297,f429]) ).
fof(f448,plain,
( m1_subset_1(sF29,u1_struct_0(sK1))
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(sK2,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f445,f236]) ).
fof(f450,plain,
( m1_subset_1(sF29,u1_struct_0(sK1))
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(sK2,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f448,f234]) ).
fof(f452,plain,
( m1_subset_1(sF29,u1_struct_0(sK1))
| ~ l1_group_1(sK1)
| ~ m1_subset_1(sK2,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f450,f233]) ).
fof(f454,plain,
( m1_subset_1(sF29,u1_struct_0(sK1))
| ~ m1_subset_1(sK2,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f452,f232]) ).
fof(f455,plain,
( m1_subset_1(sF29,sF33)
| ~ m1_subset_1(sK2,u1_struct_0(sK1)) ),
inference(forward_demodulation,[],[f454,f438]) ).
fof(f456,plain,
( ~ m1_subset_1(sK2,sF33)
| m1_subset_1(sF29,sF33) ),
inference(forward_demodulation,[],[f455,f438]) ).
fof(f457,plain,
m1_subset_1(sF29,sF33),
inference(forward_subsumption_resolution,[],[f456,f439]) ).
fof(f458,plain,
( m2_fraenkel(sF30,u1_struct_0(sK1),u1_struct_0(sK1),k4_autgroup(sK1))
| v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(sF29,u1_struct_0(sK1)) ),
inference(superposition,[],[f300,f431]) ).
fof(f459,plain,
( m2_fraenkel(sF31,u1_struct_0(sK1),u1_struct_0(sK1),k4_autgroup(sK1))
| v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(sK2,u1_struct_0(sK1)) ),
inference(superposition,[],[f300,f433]) ).
fof(f460,plain,
! [X0] :
( m2_fraenkel(k6_autgroup(sK1,X0),sF33,sF33,k4_autgroup(sK1))
| v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(X0,sF33) ),
inference(superposition,[],[f300,f438]) ).
fof(f461,plain,
! [X0] :
( m2_fraenkel(k6_autgroup(sK1,X0),sF33,sF33,k4_autgroup(sK1))
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(X0,sF33) ),
inference(forward_subsumption_resolution,[],[f460,f236]) ).
fof(f462,plain,
( m2_fraenkel(sF31,u1_struct_0(sK1),u1_struct_0(sK1),k4_autgroup(sK1))
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(sK2,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f459,f236]) ).
fof(f463,plain,
( m2_fraenkel(sF30,u1_struct_0(sK1),u1_struct_0(sK1),k4_autgroup(sK1))
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(sF29,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f458,f236]) ).
fof(f464,plain,
! [X0] :
( m2_fraenkel(k6_autgroup(sK1,X0),sF33,sF33,k4_autgroup(sK1))
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(X0,sF33) ),
inference(forward_subsumption_resolution,[],[f461,f235]) ).
fof(f465,plain,
( m2_fraenkel(sF31,u1_struct_0(sK1),u1_struct_0(sK1),k4_autgroup(sK1))
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(sK2,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f462,f235]) ).
fof(f466,plain,
( m2_fraenkel(sF30,u1_struct_0(sK1),u1_struct_0(sK1),k4_autgroup(sK1))
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(sF29,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f463,f235]) ).
fof(f467,plain,
! [X0] :
( m2_fraenkel(k6_autgroup(sK1,X0),sF33,sF33,k4_autgroup(sK1))
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(X0,sF33) ),
inference(forward_subsumption_resolution,[],[f464,f234]) ).
fof(f468,plain,
( m2_fraenkel(sF31,u1_struct_0(sK1),u1_struct_0(sK1),k4_autgroup(sK1))
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(sK2,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f465,f234]) ).
fof(f469,plain,
( m2_fraenkel(sF30,u1_struct_0(sK1),u1_struct_0(sK1),k4_autgroup(sK1))
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_subset_1(sF29,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f466,f234]) ).
fof(f470,plain,
! [X0] :
( m2_fraenkel(k6_autgroup(sK1,X0),sF33,sF33,k4_autgroup(sK1))
| ~ l1_group_1(sK1)
| ~ m1_subset_1(X0,sF33) ),
inference(forward_subsumption_resolution,[],[f467,f233]) ).
fof(f471,plain,
( m2_fraenkel(sF31,u1_struct_0(sK1),u1_struct_0(sK1),k4_autgroup(sK1))
| ~ l1_group_1(sK1)
| ~ m1_subset_1(sK2,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f468,f233]) ).
fof(f472,plain,
( m2_fraenkel(sF30,u1_struct_0(sK1),u1_struct_0(sK1),k4_autgroup(sK1))
| ~ l1_group_1(sK1)
| ~ m1_subset_1(sF29,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f469,f233]) ).
fof(f473,plain,
! [X0] :
( m2_fraenkel(k6_autgroup(sK1,X0),sF33,sF33,k4_autgroup(sK1))
| ~ m1_subset_1(X0,sF33) ),
inference(forward_subsumption_resolution,[],[f470,f232]) ).
fof(f474,plain,
( m2_fraenkel(sF31,u1_struct_0(sK1),u1_struct_0(sK1),k4_autgroup(sK1))
| ~ m1_subset_1(sK2,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f471,f232]) ).
fof(f475,plain,
( m2_fraenkel(sF30,u1_struct_0(sK1),u1_struct_0(sK1),k4_autgroup(sK1))
| ~ m1_subset_1(sF29,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f472,f232]) ).
fof(f476,plain,
( m2_fraenkel(sF31,sF33,sF33,k4_autgroup(sK1))
| ~ m1_subset_1(sK2,u1_struct_0(sK1)) ),
inference(forward_demodulation,[],[f474,f438]) ).
fof(f477,plain,
( m2_fraenkel(sF30,sF33,sF33,k4_autgroup(sK1))
| ~ m1_subset_1(sF29,u1_struct_0(sK1)) ),
inference(forward_demodulation,[],[f475,f438]) ).
fof(f478,plain,
( ~ m1_subset_1(sK2,sF33)
| m2_fraenkel(sF31,sF33,sF33,k4_autgroup(sK1)) ),
inference(forward_demodulation,[],[f476,f438]) ).
fof(f479,plain,
( ~ m1_subset_1(sF29,sF33)
| m2_fraenkel(sF30,sF33,sF33,k4_autgroup(sK1)) ),
inference(forward_demodulation,[],[f477,f438]) ).
fof(f480,plain,
m2_fraenkel(sF31,sF33,sF33,k4_autgroup(sK1)),
inference(forward_subsumption_resolution,[],[f478,f439]) ).
fof(f481,plain,
m2_fraenkel(sF30,sF33,sF33,k4_autgroup(sK1)),
inference(forward_subsumption_resolution,[],[f479,f457]) ).
fof(f485,plain,
! [X0] :
( ~ m1_subset_1(X0,sF33)
| k6_autgroup(sK1,k2_group_1(sK1)) = k7_funct_2(sF33,sF33,sF33,k6_autgroup(sK1,X0),k6_autgroup(sK1,k3_group_1(sK1,X0)))
| v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(superposition,[],[f409,f438]) ).
fof(f487,plain,
! [X0] :
( ~ m1_subset_1(X0,sF33)
| k6_autgroup(sK1,k2_group_1(sK1)) = k7_funct_2(sF33,sF33,sF33,k6_autgroup(sK1,X0),k6_autgroup(sK1,k3_group_1(sK1,X0)))
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f485,f236]) ).
fof(f488,plain,
! [X0] :
( ~ m1_subset_1(X0,sF33)
| k6_autgroup(sK1,k2_group_1(sK1)) = k7_funct_2(sF33,sF33,sF33,k6_autgroup(sK1,X0),k6_autgroup(sK1,k3_group_1(sK1,X0)))
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f487,f235]) ).
fof(f489,plain,
! [X0] :
( ~ m1_subset_1(X0,sF33)
| k6_autgroup(sK1,k2_group_1(sK1)) = k7_funct_2(sF33,sF33,sF33,k6_autgroup(sK1,X0),k6_autgroup(sK1,k3_group_1(sK1,X0)))
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f488,f234]) ).
fof(f490,plain,
! [X0] :
( ~ m1_subset_1(X0,sF33)
| k6_autgroup(sK1,k2_group_1(sK1)) = k7_funct_2(sF33,sF33,sF33,k6_autgroup(sK1,X0),k6_autgroup(sK1,k3_group_1(sK1,X0)))
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f489,f233]) ).
fof(f491,plain,
! [X0] :
( ~ m1_subset_1(X0,sF33)
| k6_autgroup(sK1,k2_group_1(sK1)) = k7_funct_2(sF33,sF33,sF33,k6_autgroup(sK1,X0),k6_autgroup(sK1,k3_group_1(sK1,X0))) ),
inference(forward_subsumption_resolution,[],[f490,f232]) ).
fof(f492,plain,
( v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| k6_autgroup(sK1,k2_group_1(sK1)) = k6_relat_1(u1_struct_0(sK1)) ),
inference(resolution,[],[f420,f232]) ).
fof(f493,plain,
( ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| k6_autgroup(sK1,k2_group_1(sK1)) = k6_relat_1(u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f492,f236]) ).
fof(f494,plain,
( ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| k6_autgroup(sK1,k2_group_1(sK1)) = k6_relat_1(u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f493,f235]) ).
fof(f495,plain,
( ~ v4_group_1(sK1)
| k6_autgroup(sK1,k2_group_1(sK1)) = k6_relat_1(u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f494,f234]) ).
fof(f496,plain,
k6_autgroup(sK1,k2_group_1(sK1)) = k6_relat_1(u1_struct_0(sK1)),
inference(forward_subsumption_resolution,[],[f495,f233]) ).
fof(f497,plain,
k6_autgroup(sK1,k2_group_1(sK1)) = k6_relat_1(sF33),
inference(forward_demodulation,[],[f496,f438]) ).
fof(f518,plain,
k6_autgroup(sK1,k2_group_1(sK1)) = k7_funct_2(sF33,sF33,sF33,k6_autgroup(sK1,sK2),k6_autgroup(sK1,k3_group_1(sK1,sK2))),
inference(resolution,[],[f491,f439]) ).
fof(f523,plain,
k6_autgroup(sK1,k2_group_1(sK1)) = k7_funct_2(sF33,sF33,sF33,k6_autgroup(sK1,sK2),k6_autgroup(sK1,sF29)),
inference(forward_demodulation,[],[f518,f429]) ).
fof(f525,plain,
k6_autgroup(sK1,k2_group_1(sK1)) = k7_funct_2(sF33,sF33,sF33,k6_autgroup(sK1,sK2),sF30),
inference(forward_demodulation,[],[f523,f431]) ).
fof(f526,plain,
k6_autgroup(sK1,k2_group_1(sK1)) = k7_funct_2(sF33,sF33,sF33,sF31,sF30),
inference(forward_demodulation,[],[f525,f433]) ).
fof(f527,plain,
k6_relat_1(sF33) = k7_funct_2(sF33,sF33,sF33,sF31,sF30),
inference(forward_demodulation,[],[f526,f497]) ).
fof(f528,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| sF33 = k1_relat_1(X0)
| v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(superposition,[],[f339,f438]) ).
fof(f529,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| sF33 = k1_relat_1(X0)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f528,f236]) ).
fof(f530,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| sF33 = k1_relat_1(X0)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f529,f235]) ).
fof(f531,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| sF33 = k1_relat_1(X0)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f530,f234]) ).
fof(f532,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| sF33 = k1_relat_1(X0)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f531,f233]) ).
fof(f533,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| sF33 = k1_relat_1(X0) ),
inference(forward_subsumption_resolution,[],[f532,f232]) ).
fof(f535,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k4_autgroup(sK1))
| m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(superposition,[],[f406,f438]) ).
fof(f537,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k4_autgroup(sK1))
| m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f535,f236]) ).
fof(f538,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k4_autgroup(sK1))
| m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f537,f235]) ).
fof(f539,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k4_autgroup(sK1))
| m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f538,f234]) ).
fof(f540,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k4_autgroup(sK1))
| m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f539,f233]) ).
fof(f541,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k4_autgroup(sK1))
| m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1)) ),
inference(forward_subsumption_resolution,[],[f540,f232]) ).
fof(f542,plain,
! [X0] :
( m2_fraenkel(k6_autgroup(sK1,X0),sF33,sF33,k1_autgroup(sK1))
| ~ m1_subset_1(X0,sF33) ),
inference(resolution,[],[f541,f473]) ).
fof(f543,plain,
m2_fraenkel(sF30,sF33,sF33,k1_autgroup(sK1)),
inference(resolution,[],[f541,f481]) ).
fof(f544,plain,
m2_fraenkel(sF31,sF33,sF33,k1_autgroup(sK1)),
inference(resolution,[],[f541,f480]) ).
fof(f550,definition,
( spl34_3
<=> v1_xboole_0(sF33) ),
introduced(definition,[new_symbols(definition,[spl34_3])],[avatar_definition]) ).
fof(f551,plain,
( ~ v1_xboole_0(sF33)
| spl34_3 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f552,plain,
( v1_xboole_0(sF33)
| ~ spl34_3 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f574,plain,
( ~ v1_xboole_0(sF33)
| v3_struct_0(sK1)
| ~ l1_struct_0(sK1) ),
inference(superposition,[],[f328,f438]) ).
fof(f575,plain,
( v3_struct_0(sK1)
| ~ l1_struct_0(sK1)
| ~ spl34_3 ),
inference(forward_subsumption_resolution,[],[f574,f552]) ).
fof(f576,plain,
( ~ l1_struct_0(sK1)
| ~ spl34_3 ),
inference(forward_subsumption_resolution,[],[f575,f236]) ).
fof(f578,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_funct_2(X0,sF33,sF33)
| v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(superposition,[],[f443,f438]) ).
fof(f579,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_funct_2(X0,sF33,sF33)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f578,f236]) ).
fof(f581,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_funct_2(X0,sF33,sF33)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f579,f235]) ).
fof(f582,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_funct_2(X0,sF33,sF33)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f581,f234]) ).
fof(f583,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_funct_2(X0,sF33,sF33)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f582,f233]) ).
fof(f584,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_funct_2(X0,sF33,sF33) ),
inference(forward_subsumption_resolution,[],[f583,f232]) ).
fof(f585,plain,
v1_funct_2(sF30,sF33,sF33),
inference(resolution,[],[f584,f543]) ).
fof(f595,plain,
v1_funct_2(sF31,sF33,sF33),
inference(resolution,[],[f544,f584]) ).
fof(f596,plain,
sF33 = k1_relat_1(sF31),
inference(resolution,[],[f544,f533]) ).
fof(f599,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| m2_relset_1(X0,sF33,sF33)
| v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(superposition,[],[f441,f438]) ).
fof(f600,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| m2_relset_1(X0,sF33,sF33)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f599,f236]) ).
fof(f602,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| m2_relset_1(X0,sF33,sF33)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f600,f235]) ).
fof(f603,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| m2_relset_1(X0,sF33,sF33)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f602,f234]) ).
fof(f604,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| m2_relset_1(X0,sF33,sF33)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f603,f233]) ).
fof(f605,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| m2_relset_1(X0,sF33,sF33) ),
inference(forward_subsumption_resolution,[],[f604,f232]) ).
fof(f606,plain,
m2_relset_1(sF30,sF33,sF33),
inference(resolution,[],[f605,f543]) ).
fof(f607,plain,
m2_relset_1(sF31,sF33,sF33),
inference(resolution,[],[f605,f544]) ).
fof(f619,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_funct_1(X0)
| v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(superposition,[],[f444,f438]) ).
fof(f620,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_funct_1(X0)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f619,f236]) ).
fof(f621,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_funct_1(X0)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f620,f235]) ).
fof(f622,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_funct_1(X0)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f621,f234]) ).
fof(f623,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_funct_1(X0)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f622,f233]) ).
fof(f624,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_funct_1(X0) ),
inference(forward_subsumption_resolution,[],[f623,f232]) ).
fof(f625,plain,
v1_funct_1(sF30),
inference(resolution,[],[f624,f543]) ).
fof(f626,plain,
v1_funct_1(sF31),
inference(resolution,[],[f624,f544]) ).
fof(f648,plain,
l1_struct_0(sK1),
inference(resolution,[],[f307,f232]) ).
fof(f649,plain,
( $false
| ~ spl34_3 ),
inference(forward_subsumption_resolution,[],[f648,f576]) ).
fof(f650,plain,
~ spl34_3,
inference(avatar_contradiction_clause,[],[f649]) ).
fof(f665,definition,
( spl34_11
<=> m1_fraenkel(k1_autgroup(sK1),sF33,sF33) ),
introduced(definition,[new_symbols(definition,[spl34_11])],[avatar_definition]) ).
fof(f666,plain,
( m1_fraenkel(k1_autgroup(sK1),sF33,sF33)
| ~ spl34_11 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f667,plain,
( ~ m1_fraenkel(k1_autgroup(sK1),sF33,sF33)
| spl34_11 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f681,definition,
( spl34_15
<=> ! [X0] :
( m2_relset_1(k6_autgroup(sK1,X0),sF33,sF33)
| ~ m1_subset_1(X0,sF33) ) ),
introduced(definition,[new_symbols(definition,[spl34_15])],[avatar_definition]) ).
fof(f682,plain,
( ! [X0] :
( m2_relset_1(k6_autgroup(sK1,X0),sF33,sF33)
| ~ m1_subset_1(X0,sF33) )
| ~ spl34_15 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f685,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| k1_relat_1(X0) = k2_relat_1(X0)
| v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(superposition,[],[f340,f438]) ).
fof(f686,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| k1_relat_1(X0) = k2_relat_1(X0)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f685,f236]) ).
fof(f688,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| k1_relat_1(X0) = k2_relat_1(X0)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f686,f235]) ).
fof(f689,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| k1_relat_1(X0) = k2_relat_1(X0)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f688,f234]) ).
fof(f690,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| k1_relat_1(X0) = k2_relat_1(X0)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f689,f233]) ).
fof(f691,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| k1_relat_1(X0) = k2_relat_1(X0) ),
inference(forward_subsumption_resolution,[],[f690,f232]) ).
fof(f693,plain,
k1_relat_1(sF31) = k2_relat_1(sF31),
inference(resolution,[],[f691,f544]) ).
fof(f695,plain,
sF33 = k2_relat_1(sF31),
inference(forward_demodulation,[],[f693,f596]) ).
fof(f698,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_group_6(X0,sK1,sK1)
| v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(superposition,[],[f442,f438]) ).
fof(f699,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_group_6(X0,sK1,sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f698,f236]) ).
fof(f701,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_group_6(X0,sK1,sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f699,f235]) ).
fof(f702,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_group_6(X0,sK1,sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f701,f234]) ).
fof(f703,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_group_6(X0,sK1,sK1)
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f702,f233]) ).
fof(f704,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF33,sF33,k1_autgroup(sK1))
| v1_group_6(X0,sK1,sK1) ),
inference(forward_subsumption_resolution,[],[f703,f232]) ).
fof(f706,plain,
v1_group_6(sF31,sK1,sK1),
inference(resolution,[],[f704,f544]) ).
fof(f711,plain,
! [X0] :
( ~ m1_subset_1(X0,sF33)
| m2_relset_1(k6_autgroup(sK1,X0),sF33,sF33) ),
inference(resolution,[],[f542,f605]) ).
fof(f721,plain,
spl34_15,
inference(avatar_split_clause,[],[f711,f681]) ).
fof(f737,plain,
( ! [X0] :
( m1_relset_1(k6_autgroup(sK1,X0),sF33,sF33)
| ~ m1_subset_1(X0,sF33) )
| ~ spl34_15 ),
inference(resolution,[],[f682,f403]) ).
fof(f746,plain,
( m1_subset_1(sF31,k1_autgroup(sK1))
| v1_xboole_0(sF33)
| ~ m1_fraenkel(k1_autgroup(sK1),sF33,sF33) ),
inference(resolution,[],[f401,f544]) ).
fof(f835,plain,
! [X0,X1] :
( v1_xboole_0(sF33)
| ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,X1,sF33)
| ~ m1_relset_1(X0,X1,sF33)
| ~ v1_funct_1(sF30)
| k7_funct_2(X1,sF33,sF33,X0,sF30) = k5_relat_1(X0,sF30)
| ~ m1_relset_1(sF30,sF33,sF33) ),
inference(resolution,[],[f585,f400]) ).
fof(f837,plain,
( ! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,X1,sF33)
| ~ m1_relset_1(X0,X1,sF33)
| ~ v1_funct_1(sF30)
| k7_funct_2(X1,sF33,sF33,X0,sF30) = k5_relat_1(X0,sF30)
| ~ m1_relset_1(sF30,sF33,sF33) )
| spl34_3 ),
inference(forward_subsumption_resolution,[],[f835,f551]) ).
fof(f839,plain,
( ! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,X1,sF33)
| ~ m1_relset_1(X0,X1,sF33)
| k7_funct_2(X1,sF33,sF33,X0,sF30) = k5_relat_1(X0,sF30)
| ~ m1_relset_1(sF30,sF33,sF33) )
| spl34_3 ),
inference(forward_subsumption_resolution,[],[f837,f625]) ).
fof(f842,definition,
( spl34_16
<=> m1_relset_1(sF30,sF33,sF33) ),
introduced(definition,[new_symbols(definition,[spl34_16])],[avatar_definition]) ).
fof(f843,plain,
( m1_relset_1(sF30,sF33,sF33)
| ~ spl34_16 ),
inference(avatar_component_clause,[],[f842]) ).
fof(f844,plain,
( ~ m1_relset_1(sF30,sF33,sF33)
| spl34_16 ),
inference(avatar_component_clause,[],[f842]) ).
fof(f846,definition,
( spl34_17
<=> ! [X0,X1] :
( ~ v1_funct_1(X0)
| k7_funct_2(X1,sF33,sF33,X0,sF30) = k5_relat_1(X0,sF30)
| ~ m1_relset_1(X0,X1,sF33)
| ~ v1_funct_2(X0,X1,sF33) ) ),
introduced(definition,[new_symbols(definition,[spl34_17])],[avatar_definition]) ).
fof(f847,plain,
( ! [X0,X1] :
( ~ v1_funct_2(X0,X1,sF33)
| k7_funct_2(X1,sF33,sF33,X0,sF30) = k5_relat_1(X0,sF30)
| ~ m1_relset_1(X0,X1,sF33)
| ~ v1_funct_1(X0) )
| ~ spl34_17 ),
inference(avatar_component_clause,[],[f846]) ).
fof(f848,plain,
( ~ spl34_16
| spl34_17
| spl34_3 ),
inference(avatar_split_clause,[],[f839,f550,f846,f842]) ).
fof(f1133,plain,
( m1_relset_1(sF30,sF33,sF33)
| ~ m1_subset_1(sF29,sF33)
| ~ spl34_15 ),
inference(superposition,[],[f737,f431]) ).
fof(f1134,plain,
( m1_relset_1(sF31,sF33,sF33)
| ~ m1_subset_1(sK2,sF33)
| ~ spl34_15 ),
inference(superposition,[],[f737,f433]) ).
fof(f1137,plain,
( m1_relset_1(sF31,sF33,sF33)
| ~ spl34_15 ),
inference(forward_subsumption_resolution,[],[f1134,f439]) ).
fof(f1138,plain,
( ~ m1_subset_1(sF29,sF33)
| ~ spl34_15
| spl34_16 ),
inference(forward_subsumption_resolution,[],[f1133,f844]) ).
fof(f1142,plain,
( $false
| ~ spl34_15
| spl34_16 ),
inference(forward_subsumption_resolution,[],[f1138,f457]) ).
fof(f1143,plain,
( ~ spl34_15
| spl34_16 ),
inference(avatar_contradiction_clause,[],[f1142]) ).
fof(f1147,plain,
( ! [X2,X0,X1] :
( ~ v1_funct_1(X0)
| ~ m1_relset_1(X0,X1,X2)
| ~ v1_funct_1(sF30)
| k5_relat_1(X0,sF30) = k1_partfun1(X1,X2,sF33,sF33,X0,sF30) )
| ~ spl34_16 ),
inference(resolution,[],[f843,f398]) ).
fof(f1149,plain,
( ! [X2,X0,X1] :
( ~ m1_relset_1(X0,X1,X2)
| ~ v1_funct_1(X0)
| k5_relat_1(X0,sF30) = k1_partfun1(X1,X2,sF33,sF33,X0,sF30) )
| ~ spl34_16 ),
inference(forward_subsumption_resolution,[],[f1147,f625]) ).
fof(f1173,plain,
( ~ v1_funct_1(sF31)
| k5_relat_1(sF31,sF30) = k1_partfun1(sF33,sF33,sF33,sF33,sF31,sF30)
| ~ spl34_15
| ~ spl34_16 ),
inference(resolution,[],[f1149,f1137]) ).
fof(f1176,plain,
( k5_relat_1(sF31,sF30) = k1_partfun1(sF33,sF33,sF33,sF33,sF31,sF30)
| ~ spl34_15
| ~ spl34_16 ),
inference(forward_subsumption_resolution,[],[f1173,f626]) ).
fof(f1232,plain,
( k7_funct_2(sF33,sF33,sF33,sF31,sF30) = k5_relat_1(sF31,sF30)
| ~ m1_relset_1(sF31,sF33,sF33)
| ~ v1_funct_1(sF31)
| ~ spl34_17 ),
inference(resolution,[],[f595,f847]) ).
fof(f1238,plain,
( k7_funct_2(sF33,sF33,sF33,sF31,sF30) = k5_relat_1(sF31,sF30)
| ~ v1_funct_1(sF31)
| ~ spl34_15
| ~ spl34_17 ),
inference(forward_subsumption_resolution,[],[f1232,f1137]) ).
fof(f1240,plain,
( k7_funct_2(sF33,sF33,sF33,sF31,sF30) = k5_relat_1(sF31,sF30)
| ~ spl34_15
| ~ spl34_17 ),
inference(forward_subsumption_resolution,[],[f1238,f626]) ).
fof(f1242,plain,
( k6_relat_1(sF33) = k5_relat_1(sF31,sF30)
| ~ spl34_15
| ~ spl34_17 ),
inference(forward_demodulation,[],[f1240,f527]) ).
fof(f1275,plain,
( m1_fraenkel(k1_autgroup(sK1),sF33,sF33)
| v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1) ),
inference(superposition,[],[f291,f438]) ).
fof(f1276,plain,
( v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| spl34_11 ),
inference(forward_subsumption_resolution,[],[f1275,f667]) ).
fof(f1277,plain,
( ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| spl34_11 ),
inference(forward_subsumption_resolution,[],[f1276,f236]) ).
fof(f1278,plain,
( ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| spl34_11 ),
inference(forward_subsumption_resolution,[],[f1277,f235]) ).
fof(f1279,plain,
( ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| spl34_11 ),
inference(forward_subsumption_resolution,[],[f1278,f234]) ).
fof(f1280,plain,
( ~ l1_group_1(sK1)
| spl34_11 ),
inference(forward_subsumption_resolution,[],[f1279,f233]) ).
fof(f1281,plain,
( $false
| spl34_11 ),
inference(forward_subsumption_resolution,[],[f1280,f232]) ).
fof(f1282,plain,
spl34_11,
inference(avatar_contradiction_clause,[],[f1281]) ).
fof(f1286,plain,
( m1_subset_1(sF31,k1_autgroup(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),sF33,sF33)
| spl34_3 ),
inference(forward_subsumption_resolution,[],[f746,f551]) ).
fof(f1292,plain,
( m1_subset_1(sF31,k1_autgroup(sK1))
| spl34_3
| ~ spl34_11 ),
inference(forward_subsumption_resolution,[],[f1286,f666]) ).
fof(f1299,plain,
( ~ v1_xboole_0(k1_autgroup(sK1))
| ~ spl34_11 ),
inference(resolution,[],[f666,f309]) ).
fof(f1313,plain,
( r2_hidden(sF31,k1_autgroup(sK1))
| v1_xboole_0(k1_autgroup(sK1))
| spl34_3
| ~ spl34_11 ),
inference(resolution,[],[f1292,f410]) ).
fof(f1314,plain,
( r2_hidden(sF31,k1_autgroup(sK1))
| spl34_3
| ~ spl34_11 ),
inference(forward_subsumption_resolution,[],[f1313,f1299]) ).
fof(f1397,definition,
( spl34_36
<=> ! [X0] :
( ~ r2_hidden(sF31,X0)
| ~ sP0(sK1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl34_36])],[avatar_definition]) ).
fof(f1398,plain,
( ! [X0] :
( ~ sP0(sK1,X0)
| ~ r2_hidden(sF31,X0) )
| ~ spl34_36 ),
inference(avatar_component_clause,[],[f1397]) ).
fof(f1409,definition,
( spl34_38
<=> v2_funct_1(sF31) ),
introduced(definition,[new_symbols(definition,[spl34_38])],[avatar_definition]) ).
fof(f1410,plain,
( v2_funct_1(sF31)
| ~ spl34_38 ),
inference(avatar_component_clause,[],[f1409]) ).
fof(f1411,plain,
( ~ v2_funct_1(sF31)
| spl34_38 ),
inference(avatar_component_clause,[],[f1409]) ).
fof(f1476,plain,
! [X0,X1] :
( k6_relat_1(X0) != k1_partfun1(X0,sF33,sF33,X0,sF31,X1)
| k1_xboole_0 = sF33
| k2_funct_1(sF31) = X1
| k1_xboole_0 = X0
| ~ v2_funct_1(sF31)
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,sF33,X0)
| ~ m2_relset_1(X1,sF33,X0)
| ~ v1_funct_1(sF31)
| ~ v1_funct_2(sF31,X0,sF33)
| ~ m2_relset_1(sF31,X0,sF33) ),
inference(superposition,[],[f427,f695]) ).
fof(f1481,definition,
( spl34_42
<=> k1_xboole_0 = sF33 ),
introduced(definition,[new_symbols(definition,[spl34_42])],[avatar_definition]) ).
fof(f1482,plain,
( k1_xboole_0 != sF33
| spl34_42 ),
inference(avatar_component_clause,[],[f1481]) ).
fof(f1483,plain,
( k1_xboole_0 = sF33
| ~ spl34_42 ),
inference(avatar_component_clause,[],[f1481]) ).
fof(f1617,plain,
! [X0,X1] :
( ~ m2_relset_1(X0,sF33,sF33)
| ~ r2_hidden(X0,X1)
| ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,sF33,sF33)
| ~ v1_group_6(X0,sK1,sK1)
| v2_funct_1(X0)
| ~ sP0(sK1,X1) ),
inference(superposition,[],[f273,f438]) ).
fof(f2128,plain,
! [X0] :
( ~ r2_hidden(sF31,X0)
| ~ v1_funct_1(sF31)
| ~ v1_funct_2(sF31,sF33,sF33)
| ~ v1_group_6(sF31,sK1,sK1)
| v2_funct_1(sF31)
| ~ sP0(sK1,X0) ),
inference(resolution,[],[f1617,f607]) ).
fof(f2129,plain,
! [X0] :
( ~ r2_hidden(sF31,X0)
| ~ v1_funct_2(sF31,sF33,sF33)
| ~ v1_group_6(sF31,sK1,sK1)
| v2_funct_1(sF31)
| ~ sP0(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f2128,f626]) ).
fof(f2133,plain,
! [X0] :
( ~ r2_hidden(sF31,X0)
| ~ v1_group_6(sF31,sK1,sK1)
| v2_funct_1(sF31)
| ~ sP0(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f2129,f595]) ).
fof(f2137,plain,
! [X0] :
( ~ r2_hidden(sF31,X0)
| v2_funct_1(sF31)
| ~ sP0(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f2133,f706]) ).
fof(f2140,plain,
( ! [X0] :
( ~ r2_hidden(sF31,X0)
| ~ sP0(sK1,X0) )
| spl34_38 ),
inference(forward_subsumption_resolution,[],[f2137,f1411]) ).
fof(f2142,plain,
( spl34_36
| spl34_38 ),
inference(avatar_split_clause,[],[f2140,f1409,f1397]) ).
fof(f2144,plain,
( ~ r2_hidden(sF31,k1_autgroup(sK1))
| v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ spl34_36 ),
inference(resolution,[],[f1398,f440]) ).
fof(f2145,plain,
( v3_struct_0(sK1)
| ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| spl34_3
| ~ spl34_11
| ~ spl34_36 ),
inference(forward_subsumption_resolution,[],[f2144,f1314]) ).
fof(f2146,plain,
( ~ v1_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| spl34_3
| ~ spl34_11
| ~ spl34_36 ),
inference(forward_subsumption_resolution,[],[f2145,f236]) ).
fof(f2147,plain,
( ~ v3_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| spl34_3
| ~ spl34_11
| ~ spl34_36 ),
inference(forward_subsumption_resolution,[],[f2146,f235]) ).
fof(f2148,plain,
( ~ v4_group_1(sK1)
| ~ l1_group_1(sK1)
| spl34_3
| ~ spl34_11
| ~ spl34_36 ),
inference(forward_subsumption_resolution,[],[f2147,f234]) ).
fof(f2149,plain,
( ~ l1_group_1(sK1)
| spl34_3
| ~ spl34_11
| ~ spl34_36 ),
inference(forward_subsumption_resolution,[],[f2148,f233]) ).
fof(f2150,plain,
( $false
| spl34_3
| ~ spl34_11
| ~ spl34_36 ),
inference(forward_subsumption_resolution,[],[f2149,f232]) ).
fof(f2151,plain,
( spl34_3
| ~ spl34_11
| ~ spl34_36 ),
inference(avatar_contradiction_clause,[],[f2150]) ).
fof(f2152,plain,
( ! [X0,X1] :
( k6_relat_1(X0) != k1_partfun1(X0,sF33,sF33,X0,sF31,X1)
| k1_xboole_0 = sF33
| k2_funct_1(sF31) = X1
| k1_xboole_0 = X0
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,sF33,X0)
| ~ m2_relset_1(X1,sF33,X0)
| ~ v1_funct_1(sF31)
| ~ v1_funct_2(sF31,X0,sF33)
| ~ m2_relset_1(sF31,X0,sF33) )
| ~ spl34_38 ),
inference(forward_subsumption_resolution,[],[f1476,f1410]) ).
fof(f2153,plain,
( ! [X0,X1] :
( k6_relat_1(X0) != k1_partfun1(X0,sF33,sF33,X0,sF31,X1)
| k1_xboole_0 = sF33
| k2_funct_1(sF31) = X1
| k1_xboole_0 = X0
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,sF33,X0)
| ~ m2_relset_1(X1,sF33,X0)
| ~ v1_funct_2(sF31,X0,sF33)
| ~ m2_relset_1(sF31,X0,sF33) )
| ~ spl34_38 ),
inference(forward_subsumption_resolution,[],[f2152,f626]) ).
fof(f2154,plain,
( ! [X0,X1] :
( sF32 = X1
| k6_relat_1(X0) != k1_partfun1(X0,sF33,sF33,X0,sF31,X1)
| k1_xboole_0 = sF33
| k1_xboole_0 = X0
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,sF33,X0)
| ~ m2_relset_1(X1,sF33,X0)
| ~ v1_funct_2(sF31,X0,sF33)
| ~ m2_relset_1(sF31,X0,sF33) )
| ~ spl34_38 ),
inference(forward_demodulation,[],[f2153,f435]) ).
fof(f2156,definition,
( spl34_48
<=> ! [X0,X1] :
( sF32 = X1
| ~ m2_relset_1(sF31,X0,sF33)
| ~ v1_funct_2(sF31,X0,sF33)
| ~ m2_relset_1(X1,sF33,X0)
| ~ v1_funct_2(X1,sF33,X0)
| ~ v1_funct_1(X1)
| k1_xboole_0 = X0
| k6_relat_1(X0) != k1_partfun1(X0,sF33,sF33,X0,sF31,X1) ) ),
introduced(definition,[new_symbols(definition,[spl34_48])],[avatar_definition]) ).
fof(f2157,plain,
( ! [X0,X1] :
( k6_relat_1(X0) != k1_partfun1(X0,sF33,sF33,X0,sF31,X1)
| ~ m2_relset_1(sF31,X0,sF33)
| ~ v1_funct_2(sF31,X0,sF33)
| ~ m2_relset_1(X1,sF33,X0)
| ~ v1_funct_2(X1,sF33,X0)
| ~ v1_funct_1(X1)
| k1_xboole_0 = X0
| sF32 = X1 )
| ~ spl34_48 ),
inference(avatar_component_clause,[],[f2156]) ).
fof(f2158,plain,
( spl34_42
| spl34_48
| ~ spl34_38 ),
inference(avatar_split_clause,[],[f2154,f1409,f2156,f1481]) ).
fof(f2177,plain,
( ~ v1_xboole_0(k1_xboole_0)
| spl34_3
| ~ spl34_42 ),
inference(superposition,[],[f551,f1483]) ).
fof(f2247,plain,
( $false
| spl34_3
| ~ spl34_42 ),
inference(forward_subsumption_resolution,[],[f2177,f329]) ).
fof(f2248,plain,
( spl34_3
| ~ spl34_42 ),
inference(avatar_contradiction_clause,[],[f2247]) ).
fof(f2264,plain,
( k6_relat_1(sF33) != k5_relat_1(sF31,sF30)
| ~ m2_relset_1(sF31,sF33,sF33)
| ~ v1_funct_2(sF31,sF33,sF33)
| ~ m2_relset_1(sF30,sF33,sF33)
| ~ v1_funct_2(sF30,sF33,sF33)
| ~ v1_funct_1(sF30)
| k1_xboole_0 = sF33
| sF30 = sF32
| ~ spl34_15
| ~ spl34_16
| ~ spl34_48 ),
inference(superposition,[],[f2157,f1176]) ).
fof(f2270,plain,
( ~ m2_relset_1(sF31,sF33,sF33)
| ~ v1_funct_2(sF31,sF33,sF33)
| ~ m2_relset_1(sF30,sF33,sF33)
| ~ v1_funct_2(sF30,sF33,sF33)
| ~ v1_funct_1(sF30)
| k1_xboole_0 = sF33
| sF30 = sF32
| ~ spl34_15
| ~ spl34_16
| ~ spl34_17
| ~ spl34_48 ),
inference(forward_subsumption_resolution,[],[f2264,f1242]) ).
fof(f2273,plain,
( ~ v1_funct_2(sF31,sF33,sF33)
| ~ m2_relset_1(sF30,sF33,sF33)
| ~ v1_funct_2(sF30,sF33,sF33)
| ~ v1_funct_1(sF30)
| k1_xboole_0 = sF33
| sF30 = sF32
| ~ spl34_15
| ~ spl34_16
| ~ spl34_17
| ~ spl34_48 ),
inference(forward_subsumption_resolution,[],[f2270,f607]) ).
fof(f2276,plain,
( ~ m2_relset_1(sF30,sF33,sF33)
| ~ v1_funct_2(sF30,sF33,sF33)
| ~ v1_funct_1(sF30)
| k1_xboole_0 = sF33
| sF30 = sF32
| ~ spl34_15
| ~ spl34_16
| ~ spl34_17
| ~ spl34_48 ),
inference(forward_subsumption_resolution,[],[f2273,f595]) ).
fof(f2279,plain,
( ~ v1_funct_2(sF30,sF33,sF33)
| ~ v1_funct_1(sF30)
| k1_xboole_0 = sF33
| sF30 = sF32
| ~ spl34_15
| ~ spl34_16
| ~ spl34_17
| ~ spl34_48 ),
inference(forward_subsumption_resolution,[],[f2276,f606]) ).
fof(f2290,plain,
( ~ v1_funct_1(sF30)
| k1_xboole_0 = sF33
| sF30 = sF32
| ~ spl34_15
| ~ spl34_16
| ~ spl34_17
| ~ spl34_48 ),
inference(forward_subsumption_resolution,[],[f2279,f585]) ).
fof(f2292,plain,
( k1_xboole_0 = sF33
| sF30 = sF32
| ~ spl34_15
| ~ spl34_16
| ~ spl34_17
| ~ spl34_48 ),
inference(forward_subsumption_resolution,[],[f2290,f625]) ).
fof(f2302,plain,
( sF30 = sF32
| ~ spl34_15
| ~ spl34_16
| ~ spl34_17
| spl34_42
| ~ spl34_48 ),
inference(forward_subsumption_resolution,[],[f2292,f1482]) ).
fof(f2303,plain,
( $false
| ~ spl34_15
| ~ spl34_16
| ~ spl34_17
| spl34_42
| ~ spl34_48 ),
inference(forward_subsumption_resolution,[],[f2302,f436]) ).
fof(f2304,plain,
( ~ spl34_15
| ~ spl34_16
| ~ spl34_17
| spl34_42
| ~ spl34_48 ),
inference(avatar_contradiction_clause,[],[f2303]) ).
cnf(s7,plain,
~ spl34_3,
inference(sat_conversion,[],[f650]) ).
cnf(s14,plain,
spl34_15,
inference(sat_conversion,[],[f721]) ).
cnf(s17,plain,
( spl34_3
| ~ spl34_16
| spl34_17 ),
inference(sat_conversion,[],[f848]) ).
cnf(s27,plain,
( ~ spl34_15
| spl34_16 ),
inference(sat_conversion,[],[f1143]) ).
cnf(s28,plain,
spl34_11,
inference(sat_conversion,[],[f1282]) ).
cnf(s39,plain,
( spl34_36
| spl34_38 ),
inference(sat_conversion,[],[f2142]) ).
cnf(s41,plain,
( spl34_3
| ~ spl34_11
| ~ spl34_36 ),
inference(sat_conversion,[],[f2151]) ).
cnf(s42,plain,
( ~ spl34_38
| spl34_42
| spl34_48 ),
inference(sat_conversion,[],[f2158]) ).
cnf(s43,plain,
( spl34_3
| ~ spl34_42 ),
inference(sat_conversion,[],[f2248]) ).
cnf(s47,plain,
( ~ spl34_15
| ~ spl34_16
| ~ spl34_17
| spl34_42
| ~ spl34_48 ),
inference(sat_conversion,[],[f2304]) ).
cnf(s48,plain,
spl34_16,
inference(rat,[],[s27,s14]) ).
cnf(s53,plain,
~ spl34_42,
inference(rat,[],[s43,s7]) ).
cnf(s54,plain,
~ spl34_36,
inference(rat,[],[s41,s28,s7]) ).
cnf(s57,plain,
spl34_17,
inference(rat,[],[s17,s48,s7]) ).
cnf(s62,plain,
spl34_38,
inference(rat,[],[s39,s54]) ).
cnf(s64,plain,
~ spl34_48,
inference(rat,[],[s47,s53,s48,s14,s57]) ).
cnf(s67,plain,
$false,
inference(rat,[],[s42,s53,s64,s62]) ).
fof(f2305,plain,
$false,
inference(avatar_sat_refutation,[],[s67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP630+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:21:30 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 9.43/2.17 % (3348523)Detected formulas, will run a generic FOF schedule.
% 9.43/2.17 % (3348532)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2658895600:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.43/2.17 % (3348532)Refutation not found, incomplete strategy
% 9.43/2.17 % (3348532)------------------------------
% 9.43/2.17 % (3348532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.17 % (3348532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.17 % (3348532)CaDiCaL version: 2.1.3
% 9.43/2.17 % (3348532)Termination reason: Refutation not found, incomplete strategy
% 9.43/2.17 % (3348532)Time elapsed: 0.017 s
% 9.43/2.17 % (3348532)Peak memory usage: 88 MB
% 9.43/2.17 % (3348532)Instructions burned: 52 (million)
% 9.43/2.17 % (3348531)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2131575435:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.43/2.17 % (3348530)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=2076823918:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.43/2.17 % (3348533)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2882786836:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.43/2.17 % (3348534)dis-21_1_sil=8000:lcm=predicate:random_seed=2812044921: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)
% 9.43/2.17 % (3348529)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=3452497793:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.43/2.17 % (3348528)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=3464709610:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.43/2.17 % (3348531)Refutation not found, incomplete strategy
% 9.43/2.17 % (3348531)------------------------------
% 9.43/2.17 % (3348531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.17 % (3348531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.17 % (3348531)CaDiCaL version: 2.1.3
% 9.43/2.17 % (3348531)Termination reason: Refutation not found, incomplete strategy
% 9.43/2.17 % (3348531)Time elapsed: 0.002 s
% 9.43/2.17 % (3348531)Peak memory usage: 88 MB
% 9.43/2.17 % (3348531)Instructions burned: 1 (million)
% 9.43/2.17 % (3348534)Instruction limit reached!
% 9.43/2.17 % (3348534)------------------------------
% 9.43/2.17 % (3348534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.17 % (3348534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.17 % (3348534)CaDiCaL version: 2.1.3
% 9.43/2.17 % (3348534)Termination reason: Instruction limit
% 9.43/2.17 % (3348534)Termination phase: Saturation
% 9.43/2.17 % (3348534)Time elapsed: 0.068 s
% 9.43/2.17 % (3348534)Peak memory usage: 90 MB
% 9.43/2.17 % (3348534)Instructions burned: 131 (million)
% 9.43/2.17 % (3348533)Instruction limit reached!
% 9.43/2.17 % (3348533)------------------------------
% 9.43/2.17 % (3348533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.17 % (3348533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.17 % (3348533)CaDiCaL version: 2.1.3
% 9.43/2.17 % (3348533)Termination reason: Instruction limit
% 9.43/2.17 % (3348533)Termination phase: Saturation
% 9.43/2.17 % (3348533)Time elapsed: 0.106 s
% 9.43/2.17 % (3348533)Peak memory usage: 90 MB
% 9.43/2.17 % (3348533)Instructions burned: 141 (million)
% 9.43/2.17 % (3348532)------------------------------
% 9.43/2.17 % (3348532)------------------------------
% 9.43/2.17 % (3348542)lrs+10_1_sil=8000:sp=occurrence:random_seed=1110320319:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 9.43/2.17 % (3348531)------------------------------
% 9.43/2.17 % (3348531)------------------------------
% 9.43/2.17 % (3348543)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3294740298:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.43/2.17 % (3348544)lrs+1011_1_sil=32000:sp=occurrence:random_seed=147044557:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 9.43/2.17 % (3348543)Instruction limit reached!
% 9.43/2.17 % (3348543)------------------------------
% 9.43/2.17 % (3348543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.17 % (3348543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.17 % (3348543)CaDiCaL version: 2.1.3
% 9.43/2.17 % (3348543)Termination reason: Instruction limit
% 9.43/2.17 % (3348543)Termination phase: Saturation
% 9.43/2.17 % (3348543)Time elapsed: 0.074 s
% 9.43/2.17 % (3348543)Peak memory usage: 88 MB
% 9.43/2.17 % (3348543)Instructions burned: 158 (million)
% 9.43/2.17 % (3348544)Instruction limit reached!
% 9.43/2.17 % (3348544)------------------------------
% 9.43/2.17 % (3348544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.17 % (3348544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.17 % (3348544)CaDiCaL version: 2.1.3
% 9.43/2.17 % (3348544)Termination reason: Instruction limit
% 9.43/2.17 % (3348544)Termination phase: Saturation
% 9.43/2.17 % (3348544)Time elapsed: 0.120 s
% 9.43/2.17 % (3348544)Peak memory usage: 92 MB
% 9.43/2.17 % (3348544)Instructions burned: 325 (million)
% 9.43/2.17 % (3348542)Instruction limit reached!
% 9.43/2.17 % (3348542)------------------------------
% 9.43/2.17 % (3348542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.17 % (3348542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.17 % (3348542)CaDiCaL version: 2.1.3
% 9.43/2.17 % (3348542)Termination reason: Instruction limit
% 9.43/2.17 % (3348542)Termination phase: Saturation
% 9.43/2.17 % (3348542)Time elapsed: 0.183 s
% 9.43/2.17 % (3348542)Peak memory usage: 92 MB
% 9.43/2.17 % (3348542)Instructions burned: 285 (million)
% 9.43/2.17 % (3348547)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=2998662490:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 9.43/2.17 % (3348549)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3985356059:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 9.43/2.17 % (3348549)Refutation not found, incomplete strategy
% 9.43/2.17 % (3348549)------------------------------
% 9.43/2.17 % (3348549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.17 % (3348549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.17 % (3348549)CaDiCaL version: 2.1.3
% 9.43/2.17 % (3348549)Termination reason: Refutation not found, incomplete strategy
% 9.43/2.17 % (3348549)Time elapsed: 0.005 s
% 9.43/2.17 % (3348549)Peak memory usage: 88 MB
% 9.43/2.17 % (3348549)Instructions burned: 6 (million)
% 9.43/2.17 % (3348550)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=456394249:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 9.43/2.17 % (3348547)Instruction limit reached!
% 9.43/2.17 % (3348547)------------------------------
% 9.43/2.17 % (3348547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.17 % (3348547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.17 % (3348547)CaDiCaL version: 2.1.3
% 9.43/2.17 % (3348547)Termination reason: Instruction limit
% 9.43/2.17 % (3348547)Termination phase: Saturation
% 9.43/2.17 % (3348547)Time elapsed: 0.149 s
% 9.43/2.17 % (3348547)Peak memory usage: 92 MB
% 9.43/2.17 % (3348547)Instructions burned: 249 (million)
% 9.43/2.17 % (3348552)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1880913472:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 9.43/2.17 % (3348552)Instruction limit reached!
% 9.43/2.17 % (3348552)------------------------------
% 9.43/2.17 % (3348552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.17 % (3348552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.17 % (3348552)CaDiCaL version: 2.1.3
% 9.43/2.17 % (3348552)Termination reason: Instruction limit
% 9.43/2.17 % (3348552)Termination phase: Saturation
% 9.43/2.17 % (3348552)Time elapsed: 0.073 s
% 9.43/2.17 % (3348552)Peak memory usage: 91 MB
% 9.43/2.17 % (3348552)Instructions burned: 113 (million)
% 9.43/2.17 % (3348549)------------------------------
% 9.43/2.17 % (3348549)------------------------------
% 9.43/2.17 % (3348555)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=553100575:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 9.43/2.17 % (3348555)Instruction limit reached!
% 9.43/2.17 % (3348555)------------------------------
% 9.43/2.17 % (3348555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.17 % (3348555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.17 % (3348555)CaDiCaL version: 2.1.3
% 9.43/2.17 % (3348555)Termination reason: Instruction limit
% 9.43/2.17 % (3348555)Termination phase: Saturation
% 9.43/2.17 % (3348555)Time elapsed: 0.067 s
% 9.43/2.17 % (3348555)Peak memory usage: 89 MB
% 9.43/2.17 % (3348555)Instructions burned: 129 (million)
% 9.43/2.17 % (3348557)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3558461142:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 9.43/2.17 % (3348528)First to succeed.
% 9.43/2.17 % (3348528)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3348523"
% 9.43/2.17 % (3348557)Instruction limit reached!
% 9.43/2.17 % (3348557)------------------------------
% 9.43/2.17 % (3348557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.17 % (3348557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.17 % (3348557)CaDiCaL version: 2.1.3
% 9.43/2.17 % (3348557)Termination reason: Instruction limit
% 9.43/2.17 % (3348557)Termination phase: Saturation
% 9.43/2.17 % (3348557)Time elapsed: 0.066 s
% 9.43/2.17 % (3348557)Peak memory usage: 89 MB
% 9.43/2.17 % (3348557)Instructions burned: 115 (million)
% 9.43/2.17 % (3348559)lrs+10_1_sil=8000:sp=occurrence:random_seed=386141974:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 9.43/2.17 % (3348560)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1049825821:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 9.43/2.17 % (3348560)Refutation not found, incomplete strategy
% 9.43/2.17 % (3348560)------------------------------
% 9.43/2.17 % (3348560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.17 % (3348560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.17 % (3348560)CaDiCaL version: 2.1.3
% 9.43/2.17 % (3348560)Termination reason: Refutation not found, incomplete strategy
% 9.43/2.17 % (3348560)Time elapsed: 0.006 s
% 9.43/2.17 % (3348560)Peak memory usage: 88 MB
% 9.43/2.17 % (3348560)Instructions burned: 9 (million)
% 9.43/2.17 % (3348550)Also succeeded, but the first one will report.
% 9.43/2.17 % (3348562)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3579909136:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 9.43/2.17 % (3348528)Refutation found. Thanks to Tanya!
% 9.43/2.17 % SZS status Theorem for theBenchmark
% 9.43/2.17 % SZS output start Proof for theBenchmark
% See solution above
% 9.89/2.36 % (3348528)------------------------------
% 9.89/2.36 % (3348528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.89/2.36 % (3348528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.89/2.36 % (3348528)CaDiCaL version: 2.1.3
% 9.89/2.36 % (3348528)Termination reason: Refutation
% 9.89/2.36 % (3348528)Time elapsed: 0.874 s
% 9.89/2.36 % (3348528)Peak memory usage: 131 MB
% 9.89/2.36 % (3348528)Instructions burned: 1281 (million)
% 9.89/2.36 % (3348528)------------------------------
% 9.89/2.36 % (3348528)------------------------------
% 9.89/2.36 % (3348523)Success in time 1.318 s
% 9.89/2.36 % Vampire exiting
%------------------------------------------------------------------------------