%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP621+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:34:53 PM UTC 2026
% Result : Theorem 57.71s 19.59s
% Output : CNFRefutation 139.62s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f149ERROR: Could not build tree for root c_27757ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
=> m2_fraenkel(k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1),u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_autgroup) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
=> m2_fraenkel(k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1),u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f15,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_autgroup) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4] :
( ( m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X4,X1,X2)
& v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_funct_1(X4)
& m1_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
& v1_group_6(X3,X0,X1)
& v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X3)
& l1_group_1(X2)
& v4_group_1(X2)
& v3_group_1(X2)
& ~ v3_struct_0(X2)
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1)
& l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ( m2_relset_1(k8_group_6(X0,X1,X2,X3,X4),u1_struct_0(X0),u1_struct_0(X2))
& v1_group_6(k8_group_6(X0,X1,X2,X3,X4),X0,X2)
& v1_funct_2(k8_group_6(X0,X1,X2,X3,X4),u1_struct_0(X0),u1_struct_0(X2))
& v1_funct_1(k8_group_6(X0,X1,X2,X3,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_group_6) ).
fof(f22,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f24,axiom,
! [X0,X1,X2] :
( m1_fraenkel(X2,X0,X1)
=> ( v1_fraenkel(X2)
& ~ v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
fof(f27,axiom,
! [X0,X1,X2] :
( ( m1_fraenkel(X2,X0,X1)
& ~ v1_xboole_0(X1) )
=> ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
=> ( m2_relset_1(X3,X0,X1)
& v1_funct_2(X3,X0,X1)
& v1_funct_1(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_fraenkel) ).
fof(f40,axiom,
! [X0] :
( ( l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f58,axiom,
! [X0,X1,X2,X3,X4] :
( ( m1_relset_1(X4,X1,X2)
& v1_funct_2(X4,X1,X2)
& v1_funct_1(X4)
& m1_relset_1(X3,X0,X1)
& v1_funct_2(X3,X0,X1)
& v1_funct_1(X3)
& ~ v1_xboole_0(X1) )
=> k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
fof(f59,axiom,
! [X0,X1,X2,X3,X4] :
( ( m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X4,X1,X2)
& v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_funct_1(X4)
& m1_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
& v1_group_6(X3,X0,X1)
& v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X3)
& l1_group_1(X2)
& v4_group_1(X2)
& v3_group_1(X2)
& ~ v3_struct_0(X2)
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1)
& l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> k8_group_6(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_group_6) ).
fof(f60,axiom,
! [X0,X1,X2] :
( ( m1_fraenkel(X2,X0,X1)
& ~ v1_xboole_0(X1) )
=> ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
fof(f61,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f63,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f64,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( r2_hidden(X0,X1)
| v1_xboole_0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f67,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( m2_relset_1(X1,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X1,X0,X0)
& v1_funct_2(X1,u1_struct_0(X0),u1_struct_0(X0))
& v1_funct_1(X1) )
=> ( r2_hidden(X1,k1_autgroup(X0))
<=> v4_group_6(X1,X0,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_autgroup) ).
fof(f70,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_group_1(X2)
& v4_group_1(X2)
& v3_group_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( ( m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
& v1_group_6(X3,X0,X1)
& v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X3) )
=> ! [X4] :
( ( m2_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X4,X1,X2)
& v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_funct_1(X4) )
=> ( ( v4_group_6(X4,X1,X2)
& v4_group_6(X3,X0,X1) )
=> v4_group_6(k8_group_6(X0,X1,X2,X3,X4),X0,X2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_group_6) ).
fof(f78,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
& ? [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
& ~ m2_fraenkel(k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1),u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f79,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
& ? [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
& ~ m2_fraenkel(k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1),u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ) ),
inference(flattening,[],[f78]) ).
fof(f100,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f101,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(flattening,[],[f100]) ).
fof(f106,plain,
! [X0,X1,X2,X3,X4] :
( ~ m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X3,X0,X1)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| v3_struct_0(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ( m2_relset_1(k8_group_6(X0,X1,X2,X3,X4),u1_struct_0(X0),u1_struct_0(X2))
& v1_group_6(k8_group_6(X0,X1,X2,X3,X4),X0,X2)
& v1_funct_2(k8_group_6(X0,X1,X2,X3,X4),u1_struct_0(X0),u1_struct_0(X2))
& v1_funct_1(k8_group_6(X0,X1,X2,X3,X4)) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f107,plain,
! [X0,X1,X2,X3,X4] :
( ~ m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X3,X0,X1)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| v3_struct_0(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ( m2_relset_1(k8_group_6(X0,X1,X2,X3,X4),u1_struct_0(X0),u1_struct_0(X2))
& v1_group_6(k8_group_6(X0,X1,X2,X3,X4),X0,X2)
& v1_funct_2(k8_group_6(X0,X1,X2,X3,X4),u1_struct_0(X0),u1_struct_0(X2))
& v1_funct_1(k8_group_6(X0,X1,X2,X3,X4)) ) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| ( v1_fraenkel(X2)
& ~ v1_xboole_0(X2) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( ~ m2_fraenkel(X3,X0,X1,X2)
| ( m2_relset_1(X3,X0,X1)
& v1_funct_2(X3,X0,X1)
& v1_funct_1(X3) ) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( ~ m2_fraenkel(X3,X0,X1,X2)
| ( m2_relset_1(X3,X0,X1)
& v1_funct_2(X3,X0,X1)
& v1_funct_1(X3) ) ) ),
inference(flattening,[],[f110]) ).
fof(f120,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f121,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f120]) ).
fof(f128,plain,
! [X0,X1,X2,X3,X4] :
( ~ m1_relset_1(X4,X1,X2)
| ~ v1_funct_2(X4,X1,X2)
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,X0,X1)
| ~ v1_funct_2(X3,X0,X1)
| ~ v1_funct_1(X3)
| v1_xboole_0(X1)
| k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
inference(ennf_transformation,[],[f58]) ).
fof(f129,plain,
! [X0,X1,X2,X3,X4] :
( ~ m1_relset_1(X4,X1,X2)
| ~ v1_funct_2(X4,X1,X2)
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,X0,X1)
| ~ v1_funct_2(X3,X0,X1)
| ~ v1_funct_1(X3)
| v1_xboole_0(X1)
| k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
inference(flattening,[],[f128]) ).
fof(f130,plain,
! [X0,X1,X2,X3,X4] :
( ~ m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X3,X0,X1)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| v3_struct_0(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| k8_group_6(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
inference(ennf_transformation,[],[f59]) ).
fof(f131,plain,
! [X0,X1,X2,X3,X4] :
( ~ m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X3,X0,X1)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| v3_struct_0(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| k8_group_6(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
inference(flattening,[],[f130]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
inference(ennf_transformation,[],[f60]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
inference(flattening,[],[f132]) ).
fof(f134,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f63]) ).
fof(f135,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f64]) ).
fof(f136,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f135]) ).
fof(f140,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X1,X0,X0)
| ~ v1_funct_2(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X1)
| ( r2_hidden(X1,k1_autgroup(X0))
<=> v4_group_6(X1,X0,X0) ) ) ),
inference(ennf_transformation,[],[f67]) ).
fof(f141,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X1,X0,X0)
| ~ v1_funct_2(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X1)
| ( r2_hidden(X1,k1_autgroup(X0))
<=> v4_group_6(X1,X0,X0) ) ) ),
inference(flattening,[],[f140]) ).
fof(f144,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ! [X2] :
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| v3_struct_0(X2)
| ! [X3] :
( ~ m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X3,X0,X1)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ! [X4] :
( ~ m2_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X4)
| ~ v4_group_6(X4,X1,X2)
| ~ v4_group_6(X3,X0,X1)
| v4_group_6(k8_group_6(X0,X1,X2,X3,X4),X0,X2) ) ) ) ) ),
inference(ennf_transformation,[],[f70]) ).
fof(f145,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ! [X2] :
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| v3_struct_0(X2)
| ! [X3] :
( ~ m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X3,X0,X1)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ! [X4] :
( ~ m2_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X4)
| ~ v4_group_6(X4,X1,X2)
| ~ v4_group_6(X3,X0,X1)
| v4_group_6(k8_group_6(X0,X1,X2,X3,X4),X0,X2) ) ) ) ) ),
inference(flattening,[],[f144]) ).
fof(f150,plain,
( l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& v1_group_1(sK1)
& ~ v3_struct_0(sK1)
& m2_fraenkel(sK2,u1_struct_0(sK1),u1_struct_0(sK1),k1_autgroup(sK1))
& m2_fraenkel(sK3,u1_struct_0(sK1),u1_struct_0(sK1),k1_autgroup(sK1))
& ~ m2_fraenkel(k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2),u1_struct_0(sK1),u1_struct_0(sK1),k1_autgroup(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f79]) ).
fof(f155,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
| ( ( k1_autgroup(X0) != X1
| ( sP0(X0,X1)
& ! [X2] :
( ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1)
| ( m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X2,X0,X0)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
& v1_funct_1(X2) ) ) ) )
& ( ~ sP0(X0,X1)
| ? [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1)
& ( ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X2,X0,X0)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X2) ) )
| X1 = k1_autgroup(X0) ) ) ) ),
inference(nnf_transformation,[],[f149]) ).
fof(f156,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
| ( ( k1_autgroup(X0) != X1
| ( sP0(X0,X1)
& ! [X2] :
( ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1)
| ( m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X2,X0,X0)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
& v1_funct_1(X2) ) ) ) )
& ( ~ sP0(X0,X1)
| ? [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1)
& ( ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X2,X0,X0)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X2) ) )
| X1 = k1_autgroup(X0) ) ) ) ),
inference(flattening,[],[f155]) ).
fof(f157,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
| ( ( k1_autgroup(X0) != X1
| ( sP0(X0,X1)
& ! [X3] :
( ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),X1)
| ( m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X3,X0,X0)
& v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
& v1_funct_1(X3) ) ) ) )
& ( ~ sP0(X0,X1)
| ? [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),X1)
& ( ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X2,X0,X0)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X2) ) )
| X1 = k1_autgroup(X0) ) ) ) ),
inference(rectify,[],[f156]) ).
fof(f158,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
| ( ( k1_autgroup(X0) != X1
| ( sP0(X0,X1)
& ! [X3] :
( ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),X1)
| ( m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(X3,X0,X0)
& v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0))
& v1_funct_1(X3) ) ) ) )
& ( ~ sP0(X0,X1)
| ( m2_fraenkel(sK5(X0,X1),u1_struct_0(X0),u1_struct_0(X0),X1)
& ( ~ m2_relset_1(sK5(X0,X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(sK5(X0,X1),X0,X0)
| ~ v1_funct_2(sK5(X0,X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(sK5(X0,X1)) ) )
| X1 = k1_autgroup(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f157]) ).
fof(f181,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( ( ~ m2_fraenkel(X3,X0,X1,X2)
| m1_subset_1(X3,X2) )
& ( ~ m1_subset_1(X3,X2)
| m2_fraenkel(X3,X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f133]) ).
fof(f182,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,[],[f61]) ).
fof(f183,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X1,X0,X0)
| ~ v1_funct_2(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X1)
| ( ( ~ r2_hidden(X1,k1_autgroup(X0))
| v4_group_6(X1,X0,X0) )
& ( ~ v4_group_6(X1,X0,X0)
| r2_hidden(X1,k1_autgroup(X0)) ) ) ) ),
inference(nnf_transformation,[],[f141]) ).
fof(f184,plain,
l1_group_1(sK1),
inference(cnf_transformation,[],[f150]) ).
fof(f185,plain,
v4_group_1(sK1),
inference(cnf_transformation,[],[f150]) ).
fof(f186,plain,
v3_group_1(sK1),
inference(cnf_transformation,[],[f150]) ).
fof(f187,plain,
v1_group_1(sK1),
inference(cnf_transformation,[],[f150]) ).
fof(f188,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f150]) ).
fof(f189,plain,
m2_fraenkel(sK2,u1_struct_0(sK1),u1_struct_0(sK1),k1_autgroup(sK1)),
inference(cnf_transformation,[],[f150]) ).
fof(f190,plain,
m2_fraenkel(sK3,u1_struct_0(sK1),u1_struct_0(sK1),k1_autgroup(sK1)),
inference(cnf_transformation,[],[f150]) ).
fof(f191,plain,
~ m2_fraenkel(k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2),u1_struct_0(sK1),u1_struct_0(sK1),k1_autgroup(sK1)),
inference(cnf_transformation,[],[f150]) ).
fof(f222,plain,
! [X3,X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
| k1_autgroup(X0) != X1
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),X1)
| m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f158]) ).
fof(f223,plain,
! [X3,X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
| k1_autgroup(X0) != X1
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),X1)
| v1_group_6(X3,X0,X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f224,plain,
! [X3,X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
| k1_autgroup(X0) != X1
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),X1)
| v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f158]) ).
fof(f225,plain,
! [X3,X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
| k1_autgroup(X0) != X1
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),X1)
| v1_funct_1(X3) ),
inference(cnf_transformation,[],[f158]) ).
fof(f230,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f235,plain,
! [X2,X3,X0,X1,X4] :
( ~ m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X3,X0,X1)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| v3_struct_0(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| m2_relset_1(k8_group_6(X0,X1,X2,X3,X4),u1_struct_0(X0),u1_struct_0(X2)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f236,plain,
! [X2,X3,X0,X1,X4] :
( ~ m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X3,X0,X1)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| v3_struct_0(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| v1_group_6(k8_group_6(X0,X1,X2,X3,X4),X0,X2) ),
inference(cnf_transformation,[],[f107]) ).
fof(f237,plain,
! [X2,X3,X0,X1,X4] :
( ~ m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X3,X0,X1)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| v3_struct_0(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| v1_funct_2(k8_group_6(X0,X1,X2,X3,X4),u1_struct_0(X0),u1_struct_0(X2)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f238,plain,
! [X2,X3,X0,X1,X4] :
( ~ m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X3,X0,X1)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| v3_struct_0(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| v1_funct_1(k8_group_6(X0,X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f239,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f241,plain,
! [X2,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| ~ v1_xboole_0(X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f242,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| m2_relset_1(X3,X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f243,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| v1_funct_2(X3,X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f244,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| v1_funct_1(X3) ),
inference(cnf_transformation,[],[f111]) ).
fof(f260,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f121]) ).
fof(f308,plain,
! [X2,X3,X0,X1,X4] :
( ~ m1_relset_1(X4,X1,X2)
| ~ v1_funct_2(X4,X1,X2)
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,X0,X1)
| ~ v1_funct_2(X3,X0,X1)
| ~ v1_funct_1(X3)
| v1_xboole_0(X1)
| k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
inference(cnf_transformation,[],[f129]) ).
fof(f309,plain,
! [X2,X3,X0,X1,X4] :
( ~ m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X3,X0,X1)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| v3_struct_0(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| k8_group_6(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
inference(cnf_transformation,[],[f131]) ).
fof(f310,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| m1_subset_1(X3,X2) ),
inference(cnf_transformation,[],[f181]) ).
fof(f311,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X3,X2)
| m2_fraenkel(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f181]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f182]) ).
fof(f315,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f316,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f319,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m2_relset_1(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X1,X0,X0)
| ~ v1_funct_2(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X1)
| ~ r2_hidden(X1,k1_autgroup(X0))
| v4_group_6(X1,X0,X0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f320,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m2_relset_1(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X1,X0,X0)
| ~ v1_funct_2(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X1)
| ~ v4_group_6(X1,X0,X0)
| r2_hidden(X1,k1_autgroup(X0)) ),
inference(cnf_transformation,[],[f183]) ).
fof(f323,plain,
! [X2,X3,X0,X1,X4] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| v3_struct_0(X2)
| ~ m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X3,X0,X1)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ~ m2_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X4)
| ~ v4_group_6(X4,X1,X2)
| ~ v4_group_6(X3,X0,X1)
| v4_group_6(k8_group_6(X0,X1,X2,X3,X4),X0,X2) ),
inference(cnf_transformation,[],[f145]) ).
fof(f326,plain,
! [X3,X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| v1_funct_1(X3) ),
inference(equality_resolution,[],[f225]) ).
fof(f327,plain,
! [X3,X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(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)) ),
inference(equality_resolution,[],[f224]) ).
fof(f328,plain,
! [X3,X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| v1_group_6(X3,X0,X0) ),
inference(equality_resolution,[],[f223]) ).
fof(f329,plain,
! [X3,X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(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)) ),
inference(equality_resolution,[],[f222]) ).
tcf(c_49,negated_conjecture,
~ m2_fraenkel(k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2),u1_struct_0(sK1),u1_struct_0(sK1),k1_autgroup(sK1)),
inference(cnf_transformation,[],[f191]) ).
tcf(c_50,negated_conjecture,
m2_fraenkel(sK3,u1_struct_0(sK1),u1_struct_0(sK1),k1_autgroup(sK1)),
inference(cnf_transformation,[],[f190]) ).
tcf(c_51,negated_conjecture,
m2_fraenkel(sK2,u1_struct_0(sK1),u1_struct_0(sK1),k1_autgroup(sK1)),
inference(cnf_transformation,[],[f189]) ).
tcf(c_52,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f188]) ).
tcf(c_53,negated_conjecture,
v1_group_1(sK1),
inference(cnf_transformation,[],[f187]) ).
tcf(c_54,negated_conjecture,
v3_group_1(sK1),
inference(cnf_transformation,[],[f186]) ).
tcf(c_55,negated_conjecture,
v4_group_1(sK1),
inference(cnf_transformation,[],[f185]) ).
tcf(c_56,negated_conjecture,
l1_group_1(sK1),
inference(cnf_transformation,[],[f184]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( v1_funct_1(X0)
| v3_struct_0(X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ),
inference(cnf_transformation,[],[f326]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_funct_2(X0,u1_struct_0(X1),u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ),
inference(cnf_transformation,[],[f327]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_group_6(X0,X1,X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ),
inference(cnf_transformation,[],[f328]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m2_relset_1(X0,u1_struct_0(X1),u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ),
inference(cnf_transformation,[],[f329]) ).
tcf(c_87,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v3_struct_0(X4)
| v3_struct_0(X2)
| v3_struct_0(X1)
| v1_funct_1(k8_group_6(X1,X2,X4,X0,X3))
| ~ v1_funct_1(X3)
| ~ v1_funct_1(X0)
| ~ l1_group_1(X4)
| ~ l1_group_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X4)
| ~ v4_group_1(X2)
| ~ v4_group_1(X1)
| ~ v3_group_1(X4)
| ~ v3_group_1(X2)
| ~ v3_group_1(X1)
| ~ v1_group_6(X3,X2,X4)
| ~ v1_group_6(X0,X1,X2)
| ~ m1_relset_1(X3,u1_struct_0(X2),u1_struct_0(X4))
| ~ m1_relset_1(X0,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X4))
| ~ v1_funct_2(X0,u1_struct_0(X1),u1_struct_0(X2)) ),
inference(cnf_transformation,[],[f238]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v3_struct_0(X4)
| v3_struct_0(X2)
| v3_struct_0(X1)
| v1_funct_2(k8_group_6(X1,X2,X4,X0,X3),u1_struct_0(X1),u1_struct_0(X4))
| ~ v1_funct_1(X3)
| ~ v1_funct_1(X0)
| ~ l1_group_1(X4)
| ~ l1_group_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X4)
| ~ v4_group_1(X2)
| ~ v4_group_1(X1)
| ~ v3_group_1(X4)
| ~ v3_group_1(X2)
| ~ v3_group_1(X1)
| ~ v1_group_6(X3,X2,X4)
| ~ v1_group_6(X0,X1,X2)
| ~ m1_relset_1(X3,u1_struct_0(X2),u1_struct_0(X4))
| ~ m1_relset_1(X0,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X4))
| ~ v1_funct_2(X0,u1_struct_0(X1),u1_struct_0(X2)) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v3_struct_0(X4)
| v3_struct_0(X2)
| v3_struct_0(X1)
| v1_group_6(k8_group_6(X1,X2,X4,X0,X3),X1,X4)
| ~ v1_funct_1(X3)
| ~ v1_funct_1(X0)
| ~ l1_group_1(X4)
| ~ l1_group_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X4)
| ~ v4_group_1(X2)
| ~ v4_group_1(X1)
| ~ v3_group_1(X4)
| ~ v3_group_1(X2)
| ~ v3_group_1(X1)
| ~ v1_group_6(X3,X2,X4)
| ~ v1_group_6(X0,X1,X2)
| ~ m1_relset_1(X3,u1_struct_0(X2),u1_struct_0(X4))
| ~ m1_relset_1(X0,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X4))
| ~ v1_funct_2(X0,u1_struct_0(X1),u1_struct_0(X2)) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v3_struct_0(X4)
| v3_struct_0(X2)
| v3_struct_0(X1)
| m2_relset_1(k8_group_6(X1,X2,X4,X0,X3),u1_struct_0(X1),u1_struct_0(X4))
| ~ v1_funct_1(X3)
| ~ v1_funct_1(X0)
| ~ l1_group_1(X4)
| ~ l1_group_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X4)
| ~ v4_group_1(X2)
| ~ v4_group_1(X1)
| ~ v3_group_1(X4)
| ~ v3_group_1(X2)
| ~ v3_group_1(X1)
| ~ v1_group_6(X3,X2,X4)
| ~ v1_group_6(X0,X1,X2)
| ~ m1_relset_1(X3,u1_struct_0(X2),u1_struct_0(X4))
| ~ m1_relset_1(X0,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X4))
| ~ v1_funct_2(X0,u1_struct_0(X1),u1_struct_0(X2)) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_96,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f239]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| v1_funct_1(X0)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m2_fraenkel(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f244]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| v1_funct_2(X0,X1,X2)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m2_fraenkel(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| m2_relset_1(X0,X1,X2)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m2_fraenkel(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_117,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f260]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v1_xboole_0(X2)
| ( k7_funct_2(X1,X2,X4,X0,X3) = k5_relat_1(X0,X3) )
| ~ v1_funct_1(X3)
| ~ v1_funct_1(X0)
| ~ m1_relset_1(X3,X2,X4)
| ~ m1_relset_1(X0,X1,X2)
| ~ v1_funct_2(X3,X2,X4)
| ~ v1_funct_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f308]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v3_struct_0(X4)
| v3_struct_0(X2)
| v3_struct_0(X1)
| ( k8_group_6(X1,X2,X4,X0,X3) = k5_relat_1(X0,X3) )
| ~ v1_funct_1(X3)
| ~ v1_funct_1(X0)
| ~ l1_group_1(X4)
| ~ l1_group_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X4)
| ~ v4_group_1(X2)
| ~ v4_group_1(X1)
| ~ v3_group_1(X4)
| ~ v3_group_1(X2)
| ~ v3_group_1(X1)
| ~ v1_group_6(X3,X2,X4)
| ~ v1_group_6(X0,X1,X2)
| ~ m1_relset_1(X3,u1_struct_0(X2),u1_struct_0(X4))
| ~ m1_relset_1(X0,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X4))
| ~ v1_funct_2(X0,u1_struct_0(X1),u1_struct_0(X2)) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| m2_fraenkel(X3,X1,X2,X0)
| ~ m1_subset_1(X3,X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(cnf_transformation,[],[f311]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| m1_subset_1(X0,X3)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m2_fraenkel(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f312]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f315]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f316]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| r2_hidden(X0,k1_autgroup(X1))
| ~ v1_funct_1(X0)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ v4_group_6(X0,X1,X1)
| ~ v1_group_6(X0,X1,X1)
| ~ m2_relset_1(X0,u1_struct_0(X1),u1_struct_0(X1))
| ~ v1_funct_2(X0,u1_struct_0(X1),u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f320]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v4_group_6(X0,X1,X1)
| ~ v1_funct_1(X0)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ r2_hidden(X0,k1_autgroup(X1))
| ~ v1_group_6(X0,X1,X1)
| ~ m2_relset_1(X0,u1_struct_0(X1),u1_struct_0(X1))
| ~ v1_funct_2(X0,u1_struct_0(X1),u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f319]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v3_struct_0(X4)
| v3_struct_0(X2)
| v3_struct_0(X1)
| v4_group_6(k8_group_6(X1,X2,X4,X0,X3),X1,X4)
| ~ v1_funct_1(X3)
| ~ v1_funct_1(X0)
| ~ l1_group_1(X4)
| ~ l1_group_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X4)
| ~ v4_group_1(X2)
| ~ v4_group_1(X1)
| ~ v3_group_1(X4)
| ~ v3_group_1(X2)
| ~ v3_group_1(X1)
| ~ v4_group_6(X3,X2,X4)
| ~ v4_group_6(X0,X1,X2)
| ~ v1_group_6(X3,X2,X4)
| ~ v1_group_6(X0,X1,X2)
| ~ m2_relset_1(X3,u1_struct_0(X2),u1_struct_0(X4))
| ~ m2_relset_1(X0,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X4))
| ~ v1_funct_2(X0,u1_struct_0(X1),u1_struct_0(X2)) ),
inference(cnf_transformation,[],[f323]) ).
tcf(c_189,plain,
( l1_struct_0(sK1)
| ~ l1_group_1(sK1) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_210,plain,
( v3_struct_0(sK1)
| ~ l1_struct_0(sK1)
| ~ v1_xboole_0(u1_struct_0(sK1)) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_236,plain,
( v3_struct_0(sK1)
| m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1))
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_1(sK1) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_285,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_170]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m1_fraenkel(X0,X1,X2)
| ~ v1_xboole_0(X0) ),
inference(prop_impl_just,[status(thm)],[c_97]) ).
tcf(c_310,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_309]) ).
tcf(c_570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v1_xboole_0(X2)
| ( k7_funct_2(X1,X2,X4,X0,X3) = k5_relat_1(X0,X3) )
| ~ v1_funct_1(X3)
| ~ v1_funct_1(X0)
| ~ m2_relset_1(X0,X1,X2)
| ~ m1_relset_1(X3,X2,X4)
| ~ v1_funct_2(X3,X2,X4)
| ~ v1_funct_2(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_165,c_285]) ).
tcf(c_1005,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_funct_2(X0,u1_struct_0(X1),u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_81,c_87]) ).
tcf(c_1006,plain,
! [X0: $i,X1: $i] :
( v1_funct_1(X0)
| v3_struct_0(X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_80,c_87]) ).
tcf(c_1007,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_group_6(X0,X1,X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_82,c_87]) ).
tcf(c_1008,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m2_relset_1(X0,u1_struct_0(X1),u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_83,c_87]) ).
tcf(c_2473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X0)
| ~ v1_xboole_0(X3)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ( k1_autgroup(X0) != X3 )
| ( u1_struct_0(X0) != X2 )
| ( u1_struct_0(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_87,c_310]) ).
tcf(c_2474,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ~ v1_xboole_0(k1_autgroup(X0)) ),
inference(unflattening,[status(thm)],[c_2473]) ).
tcf(c_2475,plain,
( v3_struct_0(sK1)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_1(sK1)
| ~ v1_xboole_0(k1_autgroup(sK1)) ),
inference(instantiation,[status(thm)],[c_2474]) ).
tcf(c_2737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| ~ m1_subset_1(X0,X3)
| ~ m1_fraenkel(X3,X1,X2)
| ( k1_autgroup(sK1) != X3 )
| ( u1_struct_0(sK1) != X2 )
| ( u1_struct_0(sK1) != X1 )
| ( k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_167]) ).
tcf(c_2738,plain,
( v1_xboole_0(u1_struct_0(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2),k1_autgroup(sK1)) ),
inference(unflattening,[status(thm)],[c_2737]) ).
tcf(c_2771,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| v1_group_6(X1,X0,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ( X1 != sK3 )
| ( k1_autgroup(X0) != k1_autgroup(sK1) )
| ( u1_struct_0(X0) != u1_struct_0(sK1) ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_1007]) ).
tcf(c_2772,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v1_group_6(sK3,X0,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ( k1_autgroup(X0) != k1_autgroup(sK1) )
| ( u1_struct_0(X0) != u1_struct_0(sK1) ) ),
inference(unflattening,[status(thm)],[c_2771]) ).
tcf(c_2773,plain,
( v3_struct_0(sK1)
| v1_group_6(sK3,sK1,sK1)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_1(sK1)
| ( k1_autgroup(sK1) != k1_autgroup(sK1) )
| ( u1_struct_0(sK1) != u1_struct_0(sK1) ) ),
inference(instantiation,[status(thm)],[c_2772]) ).
tcf(c_2852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| m1_subset_1(X3,X2)
| ~ m1_fraenkel(X2,X0,X1)
| ( X3 != sK3 )
| ( k1_autgroup(sK1) != X2 )
| ( u1_struct_0(sK1) != X1 )
| ( u1_struct_0(sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_168]) ).
tcf(c_2853,plain,
( v1_xboole_0(u1_struct_0(sK1))
| m1_subset_1(sK3,k1_autgroup(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(unflattening,[status(thm)],[c_2852]) ).
tcf(c_2859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| m2_relset_1(X3,X0,X1)
| ~ m1_fraenkel(X2,X0,X1)
| ( X3 != sK3 )
| ( k1_autgroup(sK1) != X2 )
| ( u1_struct_0(sK1) != X1 )
| ( u1_struct_0(sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_101]) ).
tcf(c_2860,plain,
( v1_xboole_0(u1_struct_0(sK1))
| m2_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(unflattening,[status(thm)],[c_2859]) ).
tcf(c_2866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| v1_funct_2(X3,X0,X1)
| ~ m1_fraenkel(X2,X0,X1)
| ( X3 != sK3 )
| ( k1_autgroup(sK1) != X2 )
| ( u1_struct_0(sK1) != X1 )
| ( u1_struct_0(sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_100]) ).
tcf(c_2867,plain,
( v1_xboole_0(u1_struct_0(sK1))
| v1_funct_2(sK3,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(unflattening,[status(thm)],[c_2866]) ).
tcf(c_2873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| v1_funct_1(X3)
| ~ m1_fraenkel(X2,X0,X1)
| ( X3 != sK3 )
| ( k1_autgroup(sK1) != X2 )
| ( u1_struct_0(sK1) != X1 )
| ( u1_struct_0(sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_99]) ).
tcf(c_2874,plain,
( v1_funct_1(sK3)
| v1_xboole_0(u1_struct_0(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(unflattening,[status(thm)],[c_2873]) ).
tcf(c_2907,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| v1_group_6(X1,X0,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ( X1 != sK2 )
| ( k1_autgroup(X0) != k1_autgroup(sK1) )
| ( u1_struct_0(X0) != u1_struct_0(sK1) ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_1007]) ).
tcf(c_2908,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v1_group_6(sK2,X0,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ( k1_autgroup(X0) != k1_autgroup(sK1) )
| ( u1_struct_0(X0) != u1_struct_0(sK1) ) ),
inference(unflattening,[status(thm)],[c_2907]) ).
tcf(c_2909,plain,
( v3_struct_0(sK1)
| v1_group_6(sK2,sK1,sK1)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_1(sK1)
| ( k1_autgroup(sK1) != k1_autgroup(sK1) )
| ( u1_struct_0(sK1) != u1_struct_0(sK1) ) ),
inference(instantiation,[status(thm)],[c_2908]) ).
tcf(c_2988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| m1_subset_1(X3,X2)
| ~ m1_fraenkel(X2,X0,X1)
| ( X3 != sK2 )
| ( k1_autgroup(sK1) != X2 )
| ( u1_struct_0(sK1) != X1 )
| ( u1_struct_0(sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_168]) ).
tcf(c_2989,plain,
( v1_xboole_0(u1_struct_0(sK1))
| m1_subset_1(sK2,k1_autgroup(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(unflattening,[status(thm)],[c_2988]) ).
tcf(c_2995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| m2_relset_1(X3,X0,X1)
| ~ m1_fraenkel(X2,X0,X1)
| ( X3 != sK2 )
| ( k1_autgroup(sK1) != X2 )
| ( u1_struct_0(sK1) != X1 )
| ( u1_struct_0(sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_101]) ).
tcf(c_2996,plain,
( v1_xboole_0(u1_struct_0(sK1))
| m2_relset_1(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(unflattening,[status(thm)],[c_2995]) ).
tcf(c_3002,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| v1_funct_2(X3,X0,X1)
| ~ m1_fraenkel(X2,X0,X1)
| ( X3 != sK2 )
| ( k1_autgroup(sK1) != X2 )
| ( u1_struct_0(sK1) != X1 )
| ( u1_struct_0(sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_100]) ).
tcf(c_3003,plain,
( v1_xboole_0(u1_struct_0(sK1))
| v1_funct_2(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(unflattening,[status(thm)],[c_3002]) ).
tcf(c_3009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| v1_funct_1(X3)
| ~ m1_fraenkel(X2,X0,X1)
| ( X3 != sK2 )
| ( k1_autgroup(sK1) != X2 )
| ( u1_struct_0(sK1) != X1 )
| ( u1_struct_0(sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_99]) ).
tcf(c_3010,plain,
( v1_funct_1(sK2)
| v1_xboole_0(u1_struct_0(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(unflattening,[status(thm)],[c_3009]) ).
tcf(c_3440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( v1_xboole_0(X2)
| v3_struct_0(X0)
| m2_relset_1(X4,u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ~ m1_subset_1(X5,X3)
| ~ m1_fraenkel(X3,X1,X2)
| ( X4 != X5 )
| ( k1_autgroup(X0) != X3 )
| ( u1_struct_0(X0) != X2 )
| ( u1_struct_0(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1008,c_167]) ).
tcf(c_3441,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| v1_xboole_0(u1_struct_0(X0))
| m2_relset_1(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ~ m1_subset_1(X1,k1_autgroup(X0))
| ~ m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_3440]) ).
tcf(c_3443,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_autgroup(X0))
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| m2_relset_1(X1,u1_struct_0(X0),u1_struct_0(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_3441,c_96,c_117,c_87,c_3441]) ).
tcf(c_3444,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m2_relset_1(X0,u1_struct_0(X1),u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_subset_1(X0,k1_autgroup(X1)) ),
inference(renaming,[status(thm)],[c_3443]) ).
tcf(c_3467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( v1_xboole_0(X2)
| v3_struct_0(X0)
| v1_group_6(X4,X0,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ~ m1_subset_1(X5,X3)
| ~ m1_fraenkel(X3,X1,X2)
| ( X4 != X5 )
| ( k1_autgroup(X0) != X3 )
| ( u1_struct_0(X0) != X2 )
| ( u1_struct_0(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1007,c_167]) ).
tcf(c_3468,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| v1_xboole_0(u1_struct_0(X0))
| v1_group_6(X1,X0,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ~ m1_subset_1(X1,k1_autgroup(X0))
| ~ m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_3467]) ).
tcf(c_3470,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_autgroup(X0))
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| v1_group_6(X1,X0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_3468,c_96,c_117,c_87,c_3468]) ).
tcf(c_3471,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_group_6(X0,X1,X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_subset_1(X0,k1_autgroup(X1)) ),
inference(renaming,[status(thm)],[c_3470]) ).
tcf(c_3494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( v1_xboole_0(X2)
| v1_funct_1(X4)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ~ m1_subset_1(X5,X3)
| ~ m1_fraenkel(X3,X1,X2)
| ( X4 != X5 )
| ( k1_autgroup(X0) != X3 )
| ( u1_struct_0(X0) != X2 )
| ( u1_struct_0(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1006,c_167]) ).
tcf(c_3495,plain,
! [X0: $i,X1: $i] :
( v1_funct_1(X1)
| v3_struct_0(X0)
| v1_xboole_0(u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ~ m1_subset_1(X1,k1_autgroup(X0))
| ~ m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_3494]) ).
tcf(c_3497,plain,
! [X0: $i,X1: $i] :
( v1_funct_1(X1)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_autgroup(X0))
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3495,c_96,c_117,c_87,c_3495]) ).
tcf(c_3498,plain,
! [X0: $i,X1: $i] :
( v1_funct_1(X0)
| v3_struct_0(X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_subset_1(X0,k1_autgroup(X1)) ),
inference(renaming,[status(thm)],[c_3497]) ).
tcf(c_3521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( v1_xboole_0(X2)
| v3_struct_0(X0)
| v1_funct_2(X4,u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ~ m1_subset_1(X5,X3)
| ~ m1_fraenkel(X3,X1,X2)
| ( X4 != X5 )
| ( k1_autgroup(X0) != X3 )
| ( u1_struct_0(X0) != X2 )
| ( u1_struct_0(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1005,c_167]) ).
tcf(c_3522,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| v1_xboole_0(u1_struct_0(X0))
| v1_funct_2(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ~ m1_subset_1(X1,k1_autgroup(X0))
| ~ m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_3521]) ).
tcf(c_3524,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_autgroup(X0))
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| v1_funct_2(X1,u1_struct_0(X0),u1_struct_0(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_3522,c_96,c_117,c_87,c_3522]) ).
tcf(c_3525,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_funct_2(X0,u1_struct_0(X1),u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_subset_1(X0,k1_autgroup(X1)) ),
inference(renaming,[status(thm)],[c_3524]) ).
tcf(c_12551,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_12554,plain,
! [X0: $i,X1: $i] :
( ( u1_struct_0(X0) = u1_struct_0(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_12556,plain,
! [X0: $i,X1: $i] :
( ( k1_autgroup(X0) = k1_autgroup(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_12564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2_hidden(X0,X2)
| ~ r2_hidden(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_12582,plain,
( ( u1_struct_0(sK1) = u1_struct_0(sK1) )
| ( sK1 != sK1 ) ),
inference(instantiation,[status(thm)],[c_12554]) ).
tcf(c_12584,plain,
( ( k1_autgroup(sK1) = k1_autgroup(sK1) )
| ( sK1 != sK1 ) ),
inference(instantiation,[status(thm)],[c_12556]) ).
tcf(c_12589,plain,
sK1 = sK1,
inference(instantiation,[status(thm)],[c_12551]) ).
tcf(c_15746,plain,
( m1_subset_1(k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2),k1_autgroup(sK1))
| ~ r2_hidden(k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2),k1_autgroup(sK1)) ),
inference(instantiation,[status(thm)],[c_172]) ).
tcf(c_15800,plain,
! [X0: $i,X1: $i] :
( r2_hidden(k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2),k1_autgroup(sK1))
| ~ r2_hidden(X0,X1)
| ( k1_autgroup(sK1) != X1 )
| ( k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2) != X0 ) ),
inference(instantiation,[status(thm)],[c_12564]) ).
tcf(c_16173,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| r2_hidden(X0,k1_autgroup(sK1))
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_1(sK1)
| ~ v1_funct_1(X0)
| ~ v4_group_6(X0,sK1,sK1)
| ~ v1_group_6(X0,sK1,sK1)
| ~ m2_relset_1(X0,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(X0,u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(instantiation,[status(thm)],[c_176]) ).
tcf(c_16330,plain,
! [X0: $i,X1: $i] :
( r2_hidden(k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2),k1_autgroup(sK1))
| ~ r2_hidden(X0,k1_autgroup(X1))
| ( k1_autgroup(sK1) != k1_autgroup(X1) )
| ( k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2) != X0 ) ),
inference(instantiation,[status(thm)],[c_15800]) ).
tcf(c_16386,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,k1_autgroup(X1))
| ~ r2_hidden(X0,k1_autgroup(X1)) ),
inference(instantiation,[status(thm)],[c_172]) ).
tcf(c_16797,plain,
( m1_relset_1(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m2_relset_1(sK2,u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(instantiation,[status(thm)],[c_170]) ).
tcf(c_17453,plain,
! [X0: $i] :
( r2_hidden(k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2),k1_autgroup(sK1))
| ~ r2_hidden(k5_relat_1(sK3,sK2),k1_autgroup(X0))
| ( k1_autgroup(sK1) != k1_autgroup(X0) )
| ( k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2) != k5_relat_1(sK3,sK2) ) ),
inference(instantiation,[status(thm)],[c_16330]) ).
tcf(c_17454,plain,
( r2_hidden(k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2),k1_autgroup(sK1))
| ~ r2_hidden(k5_relat_1(sK3,sK2),k1_autgroup(sK1))
| ( k1_autgroup(sK1) != k1_autgroup(sK1) )
| ( k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2) != k5_relat_1(sK3,sK2) ) ),
inference(instantiation,[status(thm)],[c_17453]) ).
tcf(c_19247,plain,
( v1_xboole_0(u1_struct_0(sK1))
| m1_subset_1(sK3,k1_autgroup(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_50,c_168]) ).
tcf(c_19248,plain,
( v1_xboole_0(u1_struct_0(sK1))
| m1_subset_1(sK2,k1_autgroup(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_51,c_168]) ).
tcf(c_19375,plain,
m1_subset_1(sK3,k1_autgroup(sK1)),
inference(global_subsumption_just,[status(thm)],[c_19247,c_56,c_55,c_54,c_53,c_52,c_189,c_210,c_236,c_2853]) ).
tcf(c_19377,plain,
( v1_xboole_0(k1_autgroup(sK1))
| r2_hidden(sK3,k1_autgroup(sK1)) ),
inference(superposition,[status(thm)],[c_19375,c_173]) ).
tcf(c_19413,plain,
m1_subset_1(sK2,k1_autgroup(sK1)),
inference(global_subsumption_just,[status(thm)],[c_19248,c_56,c_55,c_54,c_53,c_52,c_189,c_210,c_236,c_2989]) ).
tcf(c_19415,plain,
( v1_xboole_0(k1_autgroup(sK1))
| r2_hidden(sK2,k1_autgroup(sK1)) ),
inference(superposition,[status(thm)],[c_19413,c_173]) ).
tcf(c_19461,plain,
r2_hidden(sK3,k1_autgroup(sK1)),
inference(global_subsumption_just,[status(thm)],[c_19377,c_56,c_55,c_54,c_53,c_52,c_2475,c_19377]) ).
tcf(c_19485,plain,
( v1_xboole_0(u1_struct_0(sK1))
| m2_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_50,c_101]) ).
tcf(c_19668,plain,
m2_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK1)),
inference(global_subsumption_just,[status(thm)],[c_19485,c_56,c_55,c_54,c_53,c_52,c_189,c_210,c_236,c_2860]) ).
tcf(c_19671,plain,
m1_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK1)),
inference(superposition,[status(thm)],[c_19668,c_170]) ).
tcf(c_19745,plain,
r2_hidden(sK2,k1_autgroup(sK1)),
inference(global_subsumption_just,[status(thm)],[c_19415,c_56,c_55,c_54,c_53,c_52,c_2475,c_19415]) ).
tcf(c_23752,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v4_group_6(X0,X1,X1)
| ~ r2_hidden(X0,k1_autgroup(X1))
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(global_subsumption_just,[status(thm)],[c_177,c_177,c_3444,c_3471,c_3498,c_3525,c_16386]) ).
tcf(c_23753,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v4_group_6(X0,X1,X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ r2_hidden(X0,k1_autgroup(X1)) ),
inference(renaming,[status(thm)],[c_23752]) ).
tcf(c_23758,plain,
( v3_struct_0(sK1)
| v4_group_6(sK3,sK1,sK1)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_1(sK1) ),
inference(superposition,[status(thm)],[c_19461,c_23753]) ).
tcf(c_23759,plain,
( v3_struct_0(sK1)
| v4_group_6(sK2,sK1,sK1)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_1(sK1) ),
inference(superposition,[status(thm)],[c_19745,c_23753]) ).
tcf(c_24519,plain,
( v1_xboole_0(u1_struct_0(sK1))
| m2_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_50,c_101]) ).
tcf(c_24520,plain,
( v1_xboole_0(u1_struct_0(sK1))
| m2_relset_1(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_51,c_101]) ).
tcf(c_24526,plain,
m2_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK1)),
inference(global_subsumption_just,[status(thm)],[c_24519,c_56,c_55,c_54,c_53,c_52,c_189,c_210,c_236,c_2860]) ).
tcf(c_24529,plain,
m1_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK1)),
inference(superposition,[status(thm)],[c_24526,c_170]) ).
tcf(c_24530,plain,
m2_relset_1(sK2,u1_struct_0(sK1),u1_struct_0(sK1)),
inference(global_subsumption_just,[status(thm)],[c_24520,c_56,c_55,c_54,c_53,c_52,c_189,c_210,c_236,c_2996]) ).
tcf(c_24533,plain,
m1_relset_1(sK2,u1_struct_0(sK1),u1_struct_0(sK1)),
inference(superposition,[status(thm)],[c_24530,c_170]) ).
tcf(c_24880,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK1)
| v3_struct_0(X1)
| ( k8_group_6(sK1,sK1,X1,sK3,X0) = k5_relat_1(sK3,X0) )
| ~ v1_funct_1(sK3)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_funct_1(X0)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_6(sK3,sK1,sK1)
| ~ v1_group_6(X0,sK1,X1)
| ~ v1_funct_2(sK3,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m1_relset_1(X0,u1_struct_0(sK1),u1_struct_0(X1))
| ~ v1_funct_2(X0,u1_struct_0(sK1),u1_struct_0(X1)) ),
inference(superposition,[status(thm)],[c_24529,c_166]) ).
tcf(c_24931,plain,
! [X0: $i,X1: $i] :
( ~ v1_group_6(X0,sK1,X1)
| ~ v1_funct_2(X0,u1_struct_0(sK1),u1_struct_0(X1))
| ~ m1_relset_1(X0,u1_struct_0(sK1),u1_struct_0(X1))
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ v1_funct_1(X0)
| ( k8_group_6(sK1,sK1,X1,sK3,X0) = k5_relat_1(sK3,X0) )
| v3_struct_0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_24880,c_56,c_55,c_54,c_53,c_52,c_189,c_210,c_236,c_2773,c_2867,c_2874,c_12582,c_12584,c_12589,c_24880]) ).
tcf(c_24932,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k8_group_6(sK1,sK1,X1,sK3,X0) = k5_relat_1(sK3,X0) )
| ~ v1_funct_1(X0)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_6(X0,sK1,X1)
| ~ m1_relset_1(X0,u1_struct_0(sK1),u1_struct_0(X1))
| ~ v1_funct_2(X0,u1_struct_0(sK1),u1_struct_0(X1)) ),
inference(renaming,[status(thm)],[c_24931]) ).
tcf(c_24938,plain,
( v3_struct_0(sK1)
| ( k8_group_6(sK1,sK1,sK1,sK3,sK2) = k5_relat_1(sK3,sK2) )
| ~ v1_funct_1(sK2)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_6(sK2,sK1,sK1)
| ~ v1_funct_2(sK2,u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_24533,c_24932]) ).
tcf(c_24946,plain,
k8_group_6(sK1,sK1,sK1,sK3,sK2) = k5_relat_1(sK3,sK2),
inference(global_subsumption_just,[status(thm)],[c_24938,c_56,c_55,c_54,c_53,c_52,c_189,c_210,c_236,c_2909,c_3003,c_3010,c_12582,c_12584,c_12589,c_24938]) ).
tcf(c_24948,plain,
( v3_struct_0(sK1)
| v4_group_6(k5_relat_1(sK3,sK2),sK1,sK1)
| ~ v1_funct_1(sK2)
| ~ v1_funct_1(sK3)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v4_group_6(sK2,sK1,sK1)
| ~ v4_group_6(sK3,sK1,sK1)
| ~ v1_group_6(sK2,sK1,sK1)
| ~ v1_group_6(sK3,sK1,sK1)
| ~ m2_relset_1(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m2_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(sK3,u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_24946,c_180]) ).
tcf(c_24949,plain,
( v3_struct_0(sK1)
| m2_relset_1(k5_relat_1(sK3,sK2),u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_1(sK2)
| ~ v1_funct_1(sK3)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_6(sK2,sK1,sK1)
| ~ v1_group_6(sK3,sK1,sK1)
| ~ m1_relset_1(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m1_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(sK3,u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_24946,c_95]) ).
tcf(c_24950,plain,
( v3_struct_0(sK1)
| v1_funct_2(k5_relat_1(sK3,sK2),u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_1(sK2)
| ~ v1_funct_1(sK3)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_6(sK2,sK1,sK1)
| ~ v1_group_6(sK3,sK1,sK1)
| ~ m1_relset_1(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m1_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(sK3,u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_24946,c_93]) ).
tcf(c_24951,plain,
( v3_struct_0(sK1)
| v1_group_6(k5_relat_1(sK3,sK2),sK1,sK1)
| ~ v1_funct_1(sK2)
| ~ v1_funct_1(sK3)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_6(sK2,sK1,sK1)
| ~ v1_group_6(sK3,sK1,sK1)
| ~ m1_relset_1(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m1_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(sK3,u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_24946,c_94]) ).
tcf(c_24952,plain,
( v3_struct_0(sK1)
| v1_funct_1(k5_relat_1(sK3,sK2))
| ~ v1_funct_1(sK2)
| ~ v1_funct_1(sK3)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_6(sK2,sK1,sK1)
| ~ v1_group_6(sK3,sK1,sK1)
| ~ m1_relset_1(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m1_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(sK3,u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_24946,c_92]) ).
tcf(c_27420,plain,
( v3_struct_0(sK1)
| r2_hidden(k5_relat_1(sK3,sK2),k1_autgroup(sK1))
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_1(sK1)
| ~ v1_funct_1(k5_relat_1(sK3,sK2))
| ~ v4_group_6(k5_relat_1(sK3,sK2),sK1,sK1)
| ~ v1_group_6(k5_relat_1(sK3,sK2),sK1,sK1)
| ~ m2_relset_1(k5_relat_1(sK3,sK2),u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(k5_relat_1(sK3,sK2),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(instantiation,[status(thm)],[c_16173]) ).
tcf(c_27756,plain,
( v1_xboole_0(u1_struct_0(sK1))
| ( k7_funct_2(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),sK3,sK2) = k5_relat_1(sK3,sK2) )
| ~ v1_funct_1(sK2)
| ~ v1_funct_1(sK3)
| ~ m2_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m1_relset_1(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(sK3,u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(instantiation,[status(thm)],[c_570]) ).
tcf(c_27757,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_27756,c_27420,c_24948,c_24949,c_24950,c_24951,c_24952,c_23758,c_23759,c_19671,c_17454,c_16797,c_15746,c_12589,c_12584,c_12582,c_3010,c_3003,c_2996,c_2909,c_2874,c_2867,c_2860,c_2773,c_2738,c_236,c_210,c_189,c_52,c_53,c_54,c_55,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP621+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 15:16:39 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 57.71/19.59 % SZS status Started for theBenchmark.p
% 57.71/19.59 % SZS status Theorem for theBenchmark.p
% 57.71/19.59
% 57.71/19.59 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 57.71/19.59
% 57.71/19.59 % ------ iProver source info
% 57.71/19.59
% 57.71/19.59 % git: date: 2026-07-19 20:42:38 +0200
% 57.71/19.59 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 57.71/19.59 % git: non_committed_changes: false
% 57.71/19.59
% 57.71/19.59 % ------ Parsing...
% 57.71/19.59 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 57.71/19.59
% 57.71/19.59 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 57.71/19.59
% 57.71/19.59 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 57.71/19.59
% 57.71/19.59 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 57.71/19.59 % ------ Proving...
% 57.71/19.59 % ------ Problem Properties
% 57.71/19.59
% 57.71/19.59 %
% 57.71/19.59 % clauses 130
% 57.71/19.59 % conjectures 8
% 57.71/19.59 % EPR 54
% 57.71/19.59 % Horn 88
% 57.71/19.59 % unary 52
% 57.71/19.59 % binary 21
% 57.71/19.59 % lits 515
% 57.71/19.59 % lits eq 11
% 57.71/19.59 % fd_pure 0
% 57.71/19.59 % fd_pseudo 0
% 57.71/19.59 % fd_cond 1
% 57.71/19.59 % fd_pseudo_cond 5
% 57.71/19.59 % AC symbols 0
% 57.71/19.59
% 57.71/19.59 % ------ Input Options Time Limit: Unbounded
% 57.71/19.59
% 57.71/19.59
% 57.71/19.59 % ------
% 57.71/19.59 % Current options:
% 57.71/19.59 % ------
% 57.71/19.59
% 57.71/19.59
% 57.71/19.59 %
% 57.71/19.59
% 57.71/19.59 % ------ Proving...
% 57.71/19.59 %
% 57.71/19.59
% 57.71/19.59 % SZS status Theorem for theBenchmark.p
% 57.71/19.59
% 57.71/19.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 139.62/19.60
% 139.62/19.60
%------------------------------------------------------------------------------