%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP620+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 : n013.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 01:34:52 PM UTC 2026
% Result : Theorem 8.88s 12.13s
% Output : CNFRefutation 8.88s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f143ERROR: Could not build tree for root c_9483ERROR: 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))
=> m2_fraenkel(k2_funct_1(X1),u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_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))
=> m2_fraenkel(k2_funct_1(X1),u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f17,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(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(f39,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(f57,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(f60,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f61,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(f64,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(f66,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
=> ( m2_relset_1(k2_funct_1(X1),u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(k2_funct_1(X1),X0,X0)
& v1_funct_2(k2_funct_1(X1),u1_struct_0(X0),u1_struct_0(X0))
& v1_funct_1(k2_funct_1(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_autgroup) ).
fof(f68,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] :
( ( m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(X0))
& v1_group_6(X2,X1,X0)
& v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X0))
& v1_funct_1(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) )
=> ( ( X3 = k2_funct_1(X2)
& v4_group_6(X2,X1,X0) )
=> v4_group_6(X3,X0,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_group_6) ).
fof(f76,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))
& ~ m2_fraenkel(k2_funct_1(X1),u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f77,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))
& ~ m2_fraenkel(k2_funct_1(X1),u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
inference(flattening,[],[f76]) ).
fof(f102,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,[],[f17]) ).
fof(f103,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,[],[f102]) ).
fof(f106,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| ( v1_fraenkel(X2)
& ~ v1_xboole_0(X2) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f108,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(f109,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,[],[f108]) ).
fof(f116,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f117,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f116]) ).
fof(f124,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,[],[f57]) ).
fof(f125,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,[],[f124]) ).
fof(f126,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f60]) ).
fof(f127,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f128,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f127]) ).
fof(f132,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,[],[f64]) ).
fof(f133,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,[],[f132]) ).
fof(f135,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))
| ( m2_relset_1(k2_funct_1(X1),u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(k2_funct_1(X1),X0,X0)
& v1_funct_2(k2_funct_1(X1),u1_struct_0(X0),u1_struct_0(X0))
& v1_funct_1(k2_funct_1(X1)) ) ) ),
inference(ennf_transformation,[],[f66]) ).
fof(f136,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))
| ( m2_relset_1(k2_funct_1(X1),u1_struct_0(X0),u1_struct_0(X0))
& v1_group_6(k2_funct_1(X1),X0,X0)
& v1_funct_2(k2_funct_1(X1),u1_struct_0(X0),u1_struct_0(X0))
& v1_funct_1(k2_funct_1(X1)) ) ) ),
inference(flattening,[],[f135]) ).
fof(f138,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] :
( ~ m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(X0))
| ~ v1_group_6(X2,X1,X0)
| ~ v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X0))
| ~ v1_funct_1(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)
| k2_funct_1(X2) != X3
| ~ v4_group_6(X2,X1,X0)
| v4_group_6(X3,X0,X1) ) ) ) ),
inference(ennf_transformation,[],[f68]) ).
fof(f139,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] :
( ~ m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(X0))
| ~ v1_group_6(X2,X1,X0)
| ~ v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X0))
| ~ v1_funct_1(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)
| k2_funct_1(X2) != X3
| ~ v4_group_6(X2,X1,X0)
| v4_group_6(X3,X0,X1) ) ) ) ),
inference(flattening,[],[f138]) ).
fof(f144,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(k2_funct_1(sK2),u1_struct_0(sK1),u1_struct_0(sK1),k1_autgroup(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f77]) ).
fof(f152,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,[],[f143]) ).
fof(f153,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,[],[f152]) ).
fof(f154,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,[],[f153]) ).
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)
& ! [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(sK4(X0,X1),u1_struct_0(X0),u1_struct_0(X0),X1)
& ( ~ m2_relset_1(sK4(X0,X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(sK4(X0,X1),X0,X0)
| ~ v1_funct_2(sK4(X0,X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(sK4(X0,X1)) ) )
| X1 = k1_autgroup(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f154]) ).
fof(f178,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,[],[f125]) ).
fof(f180,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,[],[f133]) ).
fof(f181,plain,
l1_group_1(sK1),
inference(cnf_transformation,[],[f144]) ).
fof(f182,plain,
v4_group_1(sK1),
inference(cnf_transformation,[],[f144]) ).
fof(f183,plain,
v3_group_1(sK1),
inference(cnf_transformation,[],[f144]) ).
fof(f184,plain,
v1_group_1(sK1),
inference(cnf_transformation,[],[f144]) ).
fof(f185,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f144]) ).
fof(f186,plain,
m2_fraenkel(sK2,u1_struct_0(sK1),u1_struct_0(sK1),k1_autgroup(sK1)),
inference(cnf_transformation,[],[f144]) ).
fof(f187,plain,
~ m2_fraenkel(k2_funct_1(sK2),u1_struct_0(sK1),u1_struct_0(sK1),k1_autgroup(sK1)),
inference(cnf_transformation,[],[f144]) ).
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)
| m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f155]) ).
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_group_6(X3,X0,X0) ),
inference(cnf_transformation,[],[f155]) ).
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_2(X3,u1_struct_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f155]) ).
fof(f226,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,[],[f155]) ).
fof(f231,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,[],[f103]) ).
fof(f234,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f236,plain,
! [X2,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| ~ v1_xboole_0(X2) ),
inference(cnf_transformation,[],[f107]) ).
fof(f238,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,[],[f109]) ).
fof(f253,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f301,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,[],[f178]) ).
fof(f302,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,[],[f178]) ).
fof(f306,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f307,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f128]) ).
fof(f310,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,[],[f180]) ).
fof(f311,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,[],[f180]) ).
fof(f313,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| m2_relset_1(k2_funct_1(X1),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f314,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| v1_group_6(k2_funct_1(X1),X0,X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f315,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| v1_funct_2(k2_funct_1(X1),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f316,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| v1_funct_1(k2_funct_1(X1)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f318,plain,
! [X2,X3,X0,X1] :
( ~ 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)
| ~ m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(X0))
| ~ v1_group_6(X2,X1,X0)
| ~ v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X0))
| ~ v1_funct_1(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)
| k2_funct_1(X2) != X3
| ~ v4_group_6(X2,X1,X0)
| v4_group_6(X3,X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f321,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,[],[f226]) ).
fof(f322,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,[],[f225]) ).
fof(f323,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,[],[f224]) ).
fof(f324,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,[],[f223]) ).
fof(f326,plain,
! [X2,X0,X1] :
( ~ 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)
| ~ m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(X0))
| ~ v1_group_6(X2,X1,X0)
| ~ v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X0))
| ~ v1_funct_1(X2)
| ~ m2_relset_1(k2_funct_1(X2),u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(k2_funct_1(X2),X0,X1)
| ~ v1_funct_2(k2_funct_1(X2),u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(k2_funct_1(X2))
| ~ v4_group_6(X2,X1,X0)
| v4_group_6(k2_funct_1(X2),X0,X1) ),
inference(equality_resolution,[],[f318]) ).
tcf(c_49,negated_conjecture,
~ m2_fraenkel(k2_funct_1(sK2),u1_struct_0(sK1),u1_struct_0(sK1),k1_autgroup(sK1)),
inference(cnf_transformation,[],[f187]) ).
tcf(c_50,negated_conjecture,
m2_fraenkel(sK2,u1_struct_0(sK1),u1_struct_0(sK1),k1_autgroup(sK1)),
inference(cnf_transformation,[],[f186]) ).
tcf(c_51,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f185]) ).
tcf(c_52,negated_conjecture,
v1_group_1(sK1),
inference(cnf_transformation,[],[f184]) ).
tcf(c_53,negated_conjecture,
v3_group_1(sK1),
inference(cnf_transformation,[],[f183]) ).
tcf(c_54,negated_conjecture,
v4_group_1(sK1),
inference(cnf_transformation,[],[f182]) ).
tcf(c_55,negated_conjecture,
l1_group_1(sK1),
inference(cnf_transformation,[],[f181]) ).
tcf(c_84,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,[],[f321]) ).
tcf(c_85,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,[],[f322]) ).
tcf(c_86,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,[],[f323]) ).
tcf(c_87,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,[],[f324]) ).
tcf(c_91,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,[],[f231]) ).
tcf(c_94,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_98,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,[],[f238]) ).
tcf(c_113,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f253]) ).
tcf(c_161,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,[],[f302]) ).
tcf(c_162,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,[],[f301]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f306]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f307]) ).
tcf(c_170,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,[],[f311]) ).
tcf(c_171,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,[],[f310]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_funct_1(k2_funct_1(X0))
| ~ 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(cnf_transformation,[],[f316]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_funct_2(k2_funct_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(cnf_transformation,[],[f315]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_group_6(k2_funct_1(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(cnf_transformation,[],[f314]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m2_relset_1(k2_funct_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(cnf_transformation,[],[f313]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| v4_group_6(k2_funct_1(X0),X1,X2)
| ~ v1_funct_1(X0)
| ~ l1_group_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X2)
| ~ v4_group_1(X1)
| ~ v3_group_1(X2)
| ~ v3_group_1(X1)
| ~ v1_funct_1(k2_funct_1(X0))
| ~ v4_group_6(X0,X2,X1)
| ~ v1_group_6(X0,X2,X1)
| ~ v1_group_6(k2_funct_1(X0),X1,X2)
| ~ m2_relset_1(X0,u1_struct_0(X2),u1_struct_0(X1))
| ~ v1_funct_2(X0,u1_struct_0(X2),u1_struct_0(X1))
| ~ m2_relset_1(k2_funct_1(X0),u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_2(k2_funct_1(X0),u1_struct_0(X1),u1_struct_0(X2)) ),
inference(cnf_transformation,[],[f326]) ).
tcf(c_228,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_91]) ).
tcf(c_320,plain,
( v3_struct_0(sK1)
| v1_funct_1(k2_funct_1(sK2))
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_1(sK1) ),
inference(superposition,[status(thm)],[c_50,c_173]) ).
tcf(c_337,plain,
( v3_struct_0(sK1)
| v1_group_6(k2_funct_1(sK2),sK1,sK1)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_1(sK1) ),
inference(superposition,[status(thm)],[c_50,c_175]) ).
tcf(c_354,plain,
( v3_struct_0(sK1)
| m2_relset_1(k2_funct_1(sK2),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(superposition,[status(thm)],[c_50,c_176]) ).
tcf(c_371,plain,
( v3_struct_0(sK1)
| v1_funct_2(k2_funct_1(sK2),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(superposition,[status(thm)],[c_50,c_174]) ).
tcf(c_382,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(forward_subsumption_resolution,[status(thm)],[c_84,c_91]) ).
tcf(c_404,plain,
( v1_funct_1(sK2)
| v3_struct_0(sK1)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_1(sK1) ),
inference(superposition,[status(thm)],[c_50,c_382]) ).
tcf(c_415,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(forward_subsumption_resolution,[status(thm)],[c_86,c_91]) ).
tcf(c_437,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) ),
inference(superposition,[status(thm)],[c_50,c_415]) ).
tcf(c_448,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(forward_subsumption_resolution,[status(thm)],[c_87,c_91]) ).
tcf(c_470,plain,
( v3_struct_0(sK1)
| m2_relset_1(sK2,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(superposition,[status(thm)],[c_50,c_448]) ).
tcf(c_481,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(forward_subsumption_resolution,[status(thm)],[c_85,c_91]) ).
tcf(c_503,plain,
( v3_struct_0(sK1)
| v1_funct_2(sK2,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(superposition,[status(thm)],[c_50,c_481]) ).
tcf(c_854,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(superposition,[status(thm)],[c_91,c_95]) ).
tcf(c_855,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_854]) ).
tcf(c_2411,plain,
( l1_struct_0(sK1)
| ~ l1_group_1(sK1) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_2428,plain,
( v3_struct_0(sK1)
| ~ l1_struct_0(sK1)
| ~ v1_xboole_0(u1_struct_0(sK1)) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_2791,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_50,c_162]) ).
tcf(c_2802,plain,
( v1_xboole_0(u1_struct_0(sK1))
| ~ m1_subset_1(k2_funct_1(sK2),k1_autgroup(sK1))
| ~ m1_fraenkel(k1_autgroup(sK1),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_161,c_49]) ).
tcf(c_2826,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(superposition,[status(thm)],[c_50,c_98]) ).
tcf(c_3091,plain,
( v3_struct_0(sK1)
| v1_funct_2(k2_funct_1(sK2),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(superposition,[status(thm)],[c_50,c_174]) ).
tcf(c_4312,plain,
m1_subset_1(sK2,k1_autgroup(sK1)),
inference(global_subsumption_just,[status(thm)],[c_2791,c_55,c_54,c_53,c_52,c_51,c_228,c_2411,c_2428,c_2791]) ).
tcf(c_4316,plain,
( v1_xboole_0(k1_autgroup(sK1))
| r2_hidden(sK2,k1_autgroup(sK1)) ),
inference(superposition,[status(thm)],[c_4312,c_167]) ).
tcf(c_4355,plain,
~ m1_subset_1(k2_funct_1(sK2),k1_autgroup(sK1)),
inference(global_subsumption_just,[status(thm)],[c_2802,c_55,c_54,c_53,c_52,c_51,c_228,c_2411,c_2428,c_2802]) ).
tcf(c_4504,plain,
v1_funct_2(sK2,u1_struct_0(sK1),u1_struct_0(sK1)),
inference(global_subsumption_just,[status(thm)],[c_2826,c_55,c_54,c_53,c_52,c_51,c_503]) ).
tcf(c_4512,plain,
( v3_struct_0(sK1)
| v4_group_6(sK2,sK1,sK1)
| ~ v1_funct_1(sK2)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_1(sK1)
| ~ v1_group_6(sK2,sK1,sK1)
| ~ r2_hidden(sK2,k1_autgroup(sK1))
| ~ m2_relset_1(sK2,u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_4504,c_171]) ).
tcf(c_4995,plain,
v1_funct_2(k2_funct_1(sK2),u1_struct_0(sK1),u1_struct_0(sK1)),
inference(global_subsumption_just,[status(thm)],[c_3091,c_55,c_54,c_53,c_52,c_51,c_371]) ).
tcf(c_5002,plain,
( v3_struct_0(sK1)
| r2_hidden(k2_funct_1(sK2),k1_autgroup(sK1))
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_group_1(sK1)
| ~ v1_funct_1(k2_funct_1(sK2))
| ~ v4_group_6(k2_funct_1(sK2),sK1,sK1)
| ~ v1_group_6(k2_funct_1(sK2),sK1,sK1)
| ~ m2_relset_1(k2_funct_1(sK2),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_4995,c_170]) ).
tcf(c_5007,plain,
( v3_struct_0(sK1)
| v4_group_6(k2_funct_1(sK2),sK1,sK1)
| ~ v1_funct_1(sK2)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ v1_funct_1(k2_funct_1(sK2))
| ~ v4_group_6(sK2,sK1,sK1)
| ~ v1_group_6(sK2,sK1,sK1)
| ~ v1_group_6(k2_funct_1(sK2),sK1,sK1)
| ~ m2_relset_1(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ v1_funct_2(sK2,u1_struct_0(sK1),u1_struct_0(sK1))
| ~ m2_relset_1(k2_funct_1(sK2),u1_struct_0(sK1),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_4995,c_178]) ).
tcf(c_9476,plain,
r2_hidden(k2_funct_1(sK2),k1_autgroup(sK1)),
inference(global_subsumption_just,[status(thm)],[c_5002,c_55,c_54,c_53,c_52,c_51,c_320,c_337,c_354,c_404,c_437,c_470,c_503,c_855,c_4316,c_4512,c_5002,c_5007]) ).
tcf(c_9481,plain,
m1_subset_1(k2_funct_1(sK2),k1_autgroup(sK1)),
inference(superposition,[status(thm)],[c_9476,c_166]) ).
tcf(c_9483,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_4355,c_9481]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP620+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/10.62 % Computer : n013.cluster.edu
% 0.13/10.62 % Model : x86_64 x86_64
% 0.13/10.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.62 % Memory : 8046.5625MB
% 0.13/10.62 % OS : Linux 6.8.0-71-generic
% 0.13/10.62 % CPULimit : 300
% 0.13/10.62 % WCLimit : 300
% 0.13/10.62 % DateTime : Wed Sep 23 15:15:07 UTC 2026
% 0.13/10.63 % CPUTime :
% 0.13/10.63 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/10.69 Running first-order theorem proving
% 0.13/10.69 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
% 0.19/10.71
% 0.19/10.71 % ======== iProver multi-core TPTP/SMT =========
% 0.19/10.71
% 0.19/10.71 % Detected problem language: tptp
% 0.19/10.73 % Proving...
% 8.88/12.13 % SZS status Started for theBenchmark.p
% 8.88/12.13 % SZS status Theorem for theBenchmark.p
% 8.88/12.13
% 8.88/12.13 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.88/12.13
% 8.88/12.13 % ------ iProver source info
% 8.88/12.13
% 8.88/12.13 % git: date: 2026-07-19 20:42:38 +0200
% 8.88/12.13 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.88/12.13 % git: non_committed_changes: false
% 8.88/12.13
% 8.88/12.13 % ------ Parsing...
% 8.88/12.13 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 8.88/12.13 % ------ Proving...
% 8.88/12.13 % ------ Problem Properties
% 8.88/12.13
% 8.88/12.13 %
% 8.88/12.13 % clauses 132
% 8.88/12.13 % conjectures 7
% 8.88/12.13 % EPR 61
% 8.88/12.13 % Horn 87
% 8.88/12.13 % unary 50
% 8.88/12.13 % binary 20
% 8.88/12.13 % lits 502
% 8.88/12.13 % lits eq 9
% 8.88/12.13 % fd_pure 0
% 8.88/12.13 % fd_pseudo 0
% 8.88/12.13 % fd_cond 1
% 8.88/12.13 % fd_pseudo_cond 5
% 8.88/12.13 % AC symbols 0
% 8.88/12.13
% 8.88/12.13 % ------ Input Options Time Limit: Unbounded
% 8.88/12.13
% 8.88/12.13
% 8.88/12.13 % ------
% 8.88/12.13 % Current options:
% 8.88/12.13 % ------
% 8.88/12.13
% 8.88/12.13
% 8.88/12.13 %
% 8.88/12.13
% 8.88/12.13 % ------ Proving...
% 8.88/12.13 %
% 8.88/12.13
% 8.88/12.13 % ------ Proving...
% 8.88/12.13 %
% 8.88/12.13
% 8.88/12.13 % ------ Proving...
% 8.88/12.13 %
% 8.88/12.13
% 8.88/12.13 % ------ Proving...
% 8.88/12.13 %
% 8.88/12.13
% 8.88/12.13 % ------ Proving...
% 8.88/12.13 %
% 8.88/12.13
% 8.88/12.13 % SZS status Theorem for theBenchmark.p
% 8.88/12.13
% 8.88/12.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.88/12.13
% 8.88/12.13
%------------------------------------------------------------------------------