%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP639+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 : n015.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 01:34:58 PM UTC 2026
% Result : Theorem 3.06s 1.18s
% Output : CNFRefutation 3.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 85 ( 24 unt; 0 def)
% Number of atoms : 393 ( 29 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 506 ( 198 ~; 195 |; 90 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 176 ( 0 sgn 165 !; 11 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [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(X0),u1_struct_0(X1))
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X2) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
=> r1_tarski(k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(X0,X3)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_latsubgr) ).
fof(f2,negated_conjecture,
~ ! [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(X0),u1_struct_0(X1))
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X2) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
=> r1_tarski(k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(X0,X3)))) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> v1_relat_1(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f9,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> ! [X2] :
( ( m1_group_2(X2,X0)
& v1_group_1(X2) )
=> ( X2 = k5_group_4(X0,X1)
<=> ( ! [X3] :
( ( m1_group_2(X3,X0)
& v1_group_1(X3) )
=> ( r1_tarski(X1,u1_struct_0(X3))
=> m1_group_2(X2,X3) ) )
& r1_tarski(X1,u1_struct_0(X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_group_4) ).
fof(f15,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ( m1_group_2(k5_group_4(X0,X1),X0)
& v1_group_1(k5_group_4(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_group_4) ).
fof(f22,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f44,axiom,
! [X0,X1,X2,X3] :
( ( m1_relset_1(X2,X0,X1)
& v1_funct_2(X2,X0,X1)
& v1_funct_1(X2) )
=> k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
fof(f45,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(f47,axiom,
! [X0,X1,X2] :
( v1_relat_1(X2)
=> ( r1_tarski(X0,X1)
=> r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_relat_1) ).
fof(f57,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(X0),u1_struct_0(X1))
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X2)
& ? [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
& ~ r1_tarski(k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(X0,X3)))) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f58,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(X0),u1_struct_0(X1))
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X2)
& ? [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
& ~ r1_tarski(k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(X0,X3)))) ) ) ) ),
inference(flattening,[],[f57]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( ~ m1_relset_1(X2,X0,X1)
| ~ v1_funct_2(X2,X0,X1)
| ~ v1_funct_1(X2)
| k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
inference(ennf_transformation,[],[f44]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( ~ m1_relset_1(X2,X0,X1)
| ~ v1_funct_2(X2,X0,X1)
| ~ v1_funct_1(X2)
| k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
inference(flattening,[],[f68]) ).
fof(f72,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ( m1_group_2(k5_group_4(X0,X1),X0)
& v1_group_1(k5_group_4(X0,X1)) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f73,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ( m1_group_2(k5_group_4(X0,X1),X0)
& v1_group_1(k5_group_4(X0,X1)) ) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ! [X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| ( X2 = k5_group_4(X0,X1)
<=> ( ! [X3] :
( ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3)
| ~ r1_tarski(X1,u1_struct_0(X3))
| m1_group_2(X2,X3) )
& r1_tarski(X1,u1_struct_0(X2)) ) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f75,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ! [X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| ( X2 = k5_group_4(X0,X1)
<=> ( ! [X3] :
( ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3)
| ~ r1_tarski(X1,u1_struct_0(X3))
| m1_group_2(X2,X3) )
& r1_tarski(X1,u1_struct_0(X2)) ) ) ) ) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ m2_relset_1(X2,X0,X1)
| m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f22]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ v1_relat_1(X2)
| ~ r1_tarski(X0,X1)
| r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ v1_relat_1(X2)
| ~ r1_tarski(X0,X1)
| r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1)) ),
inference(flattening,[],[f79]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f91,plain,
( l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& ~ v3_struct_0(sK0)
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1)
& m2_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
& v1_funct_2(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
& v1_funct_1(sK2)
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0)))
& ~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,sK3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(k5_group_4(sK0,sK3)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f58]) ).
fof(f96,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ! [X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| ( ( k5_group_4(X0,X1) != X2
| ( ! [X3] :
( ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3)
| ~ r1_tarski(X1,u1_struct_0(X3))
| m1_group_2(X2,X3) )
& r1_tarski(X1,u1_struct_0(X2)) ) )
& ( ? [X3] :
( m1_group_2(X3,X0)
& v1_group_1(X3)
& r1_tarski(X1,u1_struct_0(X3))
& ~ m1_group_2(X2,X3) )
| ~ r1_tarski(X1,u1_struct_0(X2))
| X2 = k5_group_4(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f97,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ! [X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| ( ( k5_group_4(X0,X1) != X2
| ( ! [X3] :
( ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3)
| ~ r1_tarski(X1,u1_struct_0(X3))
| m1_group_2(X2,X3) )
& r1_tarski(X1,u1_struct_0(X2)) ) )
& ( ? [X3] :
( m1_group_2(X3,X0)
& v1_group_1(X3)
& r1_tarski(X1,u1_struct_0(X3))
& ~ m1_group_2(X2,X3) )
| ~ r1_tarski(X1,u1_struct_0(X2))
| X2 = k5_group_4(X0,X1) ) ) ) ) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ! [X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| ( ( k5_group_4(X0,X1) != X2
| ( ! [X4] :
( ~ m1_group_2(X4,X0)
| ~ v1_group_1(X4)
| ~ r1_tarski(X1,u1_struct_0(X4))
| m1_group_2(X2,X4) )
& r1_tarski(X1,u1_struct_0(X2)) ) )
& ( ? [X3] :
( m1_group_2(X3,X0)
& v1_group_1(X3)
& r1_tarski(X1,u1_struct_0(X3))
& ~ m1_group_2(X2,X3) )
| ~ r1_tarski(X1,u1_struct_0(X2))
| X2 = k5_group_4(X0,X1) ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ! [X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| ( ( k5_group_4(X0,X1) != X2
| ( ! [X4] :
( ~ m1_group_2(X4,X0)
| ~ v1_group_1(X4)
| ~ r1_tarski(X1,u1_struct_0(X4))
| m1_group_2(X2,X4) )
& r1_tarski(X1,u1_struct_0(X2)) ) )
& ( ( m1_group_2(sK8(X0,X1,X2),X0)
& v1_group_1(sK8(X0,X1,X2))
& r1_tarski(X1,u1_struct_0(sK8(X0,X1,X2)))
& ~ m1_group_2(X2,sK8(X0,X1,X2)) )
| ~ r1_tarski(X1,u1_struct_0(X2))
| X2 = k5_group_4(X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1,X2))],[f98]) ).
fof(f101,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,[],[f45]) ).
fof(f112,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f113,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f114,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f115,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f120,plain,
m2_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f91]) ).
fof(f121,plain,
v1_funct_2(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f91]) ).
fof(f122,plain,
v1_funct_1(sK2),
inference(cnf_transformation,[],[f91]) ).
fof(f123,plain,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f91]) ).
fof(f124,plain,
~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,sK3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(k5_group_4(sK0,sK3)))),
inference(cnf_transformation,[],[f91]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( ~ m1_relset_1(X2,X0,X1)
| ~ v1_funct_2(X2,X0,X1)
| ~ v1_funct_1(X2)
| k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
inference(cnf_transformation,[],[f69]) ).
fof(f139,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| m1_group_2(k5_group_4(X0,X1),X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f140,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| v1_group_1(k5_group_4(X0,X1)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f142,plain,
! [X2,X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| k5_group_4(X0,X1) != X2
| r1_tarski(X1,u1_struct_0(X2)) ),
inference(cnf_transformation,[],[f99]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ m1_relset_1(X2,X0,X1)
| m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f163,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| ~ r1_tarski(X0,X1)
| r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f182,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(k5_group_4(X0,X1),X0)
| ~ v1_group_1(k5_group_4(X0,X1))
| r1_tarski(X1,u1_struct_0(k5_group_4(X0,X1))) ),
inference(equality_resolution,[],[f142]) ).
tcf(c_49,negated_conjecture,
~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,sK3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(k5_group_4(sK0,sK3)))),
inference(cnf_transformation,[],[f124]) ).
tcf(c_50,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f123]) ).
tcf(c_51,negated_conjecture,
v1_funct_1(sK2),
inference(cnf_transformation,[],[f122]) ).
tcf(c_52,negated_conjecture,
v1_funct_2(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f121]) ).
tcf(c_53,negated_conjecture,
m2_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f120]) ).
tcf(c_58,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f115]) ).
tcf(c_59,negated_conjecture,
v3_group_1(sK0),
inference(cnf_transformation,[],[f114]) ).
tcf(c_60,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f113]) ).
tcf(c_61,negated_conjecture,
l1_group_1(sK0),
inference(cnf_transformation,[],[f112]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( k2_funct_2(X1,X2,X0,X3) = k9_relat_1(X0,X3) )
| ~ v1_funct_1(X0)
| ~ m1_relset_1(X0,X1,X2)
| ~ v1_funct_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_group_1(k5_group_4(X1,X0))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_group_2(k5_group_4(X1,X0),X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| r1_tarski(X1,u1_struct_0(k5_group_4(X0,X1)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(k5_group_4(X0,X1))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(k5_group_4(X0,X1),X0) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( m2_relset_1(X0,X1,X2)
| ~ m1_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1))
| ~ v1_relat_1(X2)
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_relat_1(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m2_relset_1(X0,X1,X2)
| m1_relset_1(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_86]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_164]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ m1_relset_1(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_85,c_88]) ).
tcf(c_578,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| r1_tarski(X1,u1_struct_0(k5_group_4(X0,X1)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(k5_group_4(X0,X1),X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_82,c_76]) ).
tcf(c_594,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| r1_tarski(X0,u1_struct_0(k5_group_4(X1,X0)))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_578,c_77]) ).
tcf(c_1046,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X2,X0,X1)
| ( X2 != sK2 )
| ( u1_struct_0(sK1) != X1 )
| ( u1_struct_0(sK0) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_165]) ).
tcf(c_1047,plain,
m1_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(unflattening,[status(thm)],[c_1046]) ).
tcf(c_1215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3) )
| ~ v1_funct_1(X2)
| ~ m1_relset_1(X2,X0,X1)
| ( X2 != sK2 )
| ( u1_struct_0(sK1) != X1 )
| ( u1_struct_0(sK0) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_74]) ).
tcf(c_1216,plain,
! [X0: $i] :
( ( k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,X0) = k9_relat_1(sK2,X0) )
| ~ v1_funct_1(sK2)
| ~ m1_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)) ),
inference(unflattening,[status(thm)],[c_1215]) ).
tcf(c_1218,plain,
! [X0: $i] : k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,X0) = k9_relat_1(sK2,X0),
inference(global_subsumption_just,[status(thm)],[c_1216,c_51,c_1047,c_1216]) ).
tcf(c_2142,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| r1_tarski(X1,u1_struct_0(k5_group_4(X0,X1)))
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_594]) ).
tcf(c_2143,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| r1_tarski(X0,u1_struct_0(k5_group_4(sK0,X0)))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(unflattening,[status(thm)],[c_2142]) ).
tcf(c_2145,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| r1_tarski(X0,u1_struct_0(k5_group_4(sK0,X0))) ),
inference(global_subsumption_just,[status(thm)],[c_2143,c_61,c_59,c_58,c_2143]) ).
tcf(c_2146,plain,
! [X0: $i] :
( r1_tarski(X0,u1_struct_0(k5_group_4(sK0,X0)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(renaming,[status(thm)],[c_2145]) ).
tcf(c_2628,plain,
! [X0: $i] :
( r1_tarski(X0,u1_struct_0(k5_group_4(sK0,X0)))
| ( X0 != sK3 )
| ( k1_zfmisc_1(u1_struct_0(sK0)) != k1_zfmisc_1(u1_struct_0(sK0)) ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_2146]) ).
tcf(c_2629,plain,
r1_tarski(sK3,u1_struct_0(k5_group_4(sK0,sK3))),
inference(unflattening,[status(thm)],[c_2628]) ).
tcf(c_8542,plain,
~ r1_tarski(k9_relat_1(sK2,sK3),k9_relat_1(sK2,u1_struct_0(k5_group_4(sK0,sK3)))),
inference(demodulation,[status(thm)],[c_49,c_1218]) ).
tcf(c_8962,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_relat_1(X0)
| ~ m1_relset_1(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_184,c_105]) ).
tcf(c_9145,plain,
( ~ v1_relat_1(sK2)
| ~ r1_tarski(sK3,u1_struct_0(k5_group_4(sK0,sK3))) ),
inference(superposition,[status(thm)],[c_100,c_8542]) ).
tcf(c_9787,plain,
v1_relat_1(sK2),
inference(superposition,[status(thm)],[c_1047,c_8962]) ).
tcf(c_9789,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9787,c_9145,c_2629]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP639+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 15:26:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.06/1.18 % SZS status Started for theBenchmark.p
% 3.06/1.18 % SZS status Theorem for theBenchmark.p
% 3.06/1.18
% 3.06/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.06/1.18
% 3.06/1.18 % ------ iProver source info
% 3.06/1.18
% 3.06/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.06/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.06/1.18 % git: non_committed_changes: false
% 3.06/1.18
% 3.06/1.18 % ------ Parsing...
% 3.06/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.06/1.18
% 3.06/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 3.06/1.18
% 3.06/1.18 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.06/1.18
% 3.06/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.06/1.18 % ------ Proving...
% 3.06/1.18 % ------ Problem Properties
% 3.06/1.18
% 3.06/1.18 %
% 3.06/1.18 % clauses 84
% 3.06/1.18 % conjectures 8
% 3.06/1.18 % EPR 15
% 3.06/1.18 % Horn 71
% 3.06/1.18 % unary 33
% 3.06/1.18 % binary 20
% 3.06/1.18 % lits 203
% 3.06/1.18 % lits eq 33
% 3.06/1.18 % fd_pure 0
% 3.06/1.18 % fd_pseudo 0
% 3.06/1.18 % fd_cond 2
% 3.06/1.18 % fd_pseudo_cond 13
% 3.06/1.18 % AC symbols 0
% 3.06/1.18
% 3.06/1.18 % ------ Schedule dynamic 5 is on
% 3.06/1.18
% 3.06/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.06/1.18
% 3.06/1.18
% 3.06/1.18 % ------
% 3.06/1.18 % Current options:
% 3.06/1.18 % ------
% 3.06/1.18
% 3.06/1.18
% 3.06/1.18 %
% 3.06/1.18
% 3.06/1.18 % ------ Proving...
% 3.06/1.18 %
% 3.06/1.18
% 3.06/1.18 % SZS status Theorem for theBenchmark.p
% 3.06/1.18
% 3.06/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.06/1.19
%------------------------------------------------------------------------------