%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP640+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 : n009.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 01:34:59 PM UTC 2026
% Result : Theorem 2.73s 1.27s
% Output : CNFRefutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of formulae : 139 ( 55 unt; 11 def)
% Number of atoms : 653 ( 76 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 742 ( 307 ~; 318 |; 90 &)
% ( 4 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 26 ( 24 usr; 13 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 208 ( 0 sgn 196 !; 12 ?; 100 :)
% 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] :
( m1_group_2(X2,X0)
=> ! [X3] :
( m1_group_2(X3,X0)
=> ! [X4] :
( ( m2_relset_1(X4,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_2(X4,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X4) )
=> ! [X5] :
( m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X0)))
=> ( X5 = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
=> k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k8_group_4(X0,X2,X3))) = k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k5_group_4(X0,X5))) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_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] :
( m1_group_2(X2,X0)
=> ! [X3] :
( m1_group_2(X3,X0)
=> ! [X4] :
( ( m2_relset_1(X4,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_2(X4,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X4) )
=> ! [X5] :
( m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X0)))
=> ( X5 = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
=> k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k8_group_4(X0,X2,X3))) = k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k5_group_4(X0,X5))) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f49,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(f50,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(f51,axiom,
! [X0,X1,X2] :
( ( m1_group_2(X2,X0)
& v1_group_1(X2)
& m1_group_2(X1,X0)
& v1_group_1(X1)
& l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ( r1_group_2(X0,X1,X2)
<=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_group_2) ).
fof(f55,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(f56,axiom,
! [X0,X1,X2] :
( ( m1_group_2(X2,X0)
& m1_group_2(X1,X0)
& l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ( m1_group_2(k8_group_4(X0,X1,X2),X0)
& v1_group_1(k8_group_4(X0,X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_group_4) ).
fof(f64,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ! [X2] :
( m1_group_2(X2,X0)
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
=> ( X3 = k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2))
=> r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_latsubgr) ).
fof(f71,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] :
( m1_group_2(X2,X0)
& ? [X3] :
( m1_group_2(X3,X0)
& ? [X4] :
( m2_relset_1(X4,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_2(X4,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X4)
& ? [X5] :
( m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X0)))
& X5 = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
& k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k8_group_4(X0,X2,X3))) != k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k5_group_4(X0,X5))) ) ) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f72,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] :
( m1_group_2(X2,X0)
& ? [X3] :
( m1_group_2(X3,X0)
& ? [X4] :
( m2_relset_1(X4,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_2(X4,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X4)
& ? [X5] :
( m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X0)))
& X5 = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
& k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k8_group_4(X0,X2,X3))) != k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k5_group_4(X0,X5))) ) ) ) ) ) ),
inference(flattening,[],[f71]) ).
fof(f111,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,[],[f49]) ).
fof(f112,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,[],[f111]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ( r1_group_2(X0,X1,X2)
<=> X1 = X2 ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ( r1_group_2(X0,X1,X2)
<=> X1 = X2 ) ),
inference(flattening,[],[f113]) ).
fof(f117,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,[],[f55]) ).
fof(f118,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,[],[f117]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ( m1_group_2(k8_group_4(X0,X1,X2),X0)
& v1_group_1(k8_group_4(X0,X1,X2)) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ( m1_group_2(k8_group_4(X0,X1,X2),X0)
& v1_group_1(k8_group_4(X0,X1,X2)) ) ),
inference(flattening,[],[f119]) ).
fof(f126,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| ! [X2] :
( ~ m1_group_2(X2,X0)
| ! [X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
| k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)) != X3
| r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,X3)) ) ) ) ),
inference(ennf_transformation,[],[f64]) ).
fof(f127,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| ! [X2] :
( ~ m1_group_2(X2,X0)
| ! [X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
| k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)) != X3
| r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,X3)) ) ) ) ),
inference(flattening,[],[f126]) ).
fof(f128,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)
& m1_group_2(sK2,sK0)
& m1_group_2(sK3,sK0)
& m2_relset_1(sK4,u1_struct_0(sK0),u1_struct_0(sK1))
& v1_funct_2(sK4,u1_struct_0(sK0),u1_struct_0(sK1))
& v1_funct_1(sK4)
& m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(sK0)))
& sK5 = k2_xboole_0(u1_struct_0(sK2),u1_struct_0(sK3))
& k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK4,u1_struct_0(k8_group_4(sK0,sK2,sK3))) != k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK4,u1_struct_0(k5_group_4(sK0,sK5))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f72]) ).
fof(f143,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,[],[f50]) ).
fof(f144,plain,
! [X0,X1,X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ( ( ~ r1_group_2(X0,X1,X2)
| X1 = X2 )
& ( X1 != X2
| r1_group_2(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f114]) ).
fof(f145,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f128]) ).
fof(f146,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f128]) ).
fof(f147,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f128]) ).
fof(f148,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f128]) ).
fof(f153,plain,
m1_group_2(sK2,sK0),
inference(cnf_transformation,[],[f128]) ).
fof(f154,plain,
m1_group_2(sK3,sK0),
inference(cnf_transformation,[],[f128]) ).
fof(f155,plain,
m2_relset_1(sK4,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f128]) ).
fof(f156,plain,
v1_funct_2(sK4,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f128]) ).
fof(f157,plain,
v1_funct_1(sK4),
inference(cnf_transformation,[],[f128]) ).
fof(f158,plain,
m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f128]) ).
fof(f159,plain,
sK5 = k2_xboole_0(u1_struct_0(sK2),u1_struct_0(sK3)),
inference(cnf_transformation,[],[f128]) ).
fof(f160,plain,
k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK4,u1_struct_0(k8_group_4(sK0,sK2,sK3))) != k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK4,u1_struct_0(k5_group_4(sK0,sK5))),
inference(cnf_transformation,[],[f128]) ).
fof(f218,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,[],[f112]) ).
fof(f219,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ r1_group_2(X0,X1,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f144]) ).
fof(f224,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,[],[f118]) ).
fof(f225,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,[],[f118]) ).
fof(f226,plain,
! [X2,X0,X1] :
( ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| m1_group_2(k8_group_4(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f227,plain,
! [X2,X0,X1] :
( ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| v1_group_1(k8_group_4(X0,X1,X2)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f235,plain,
! [X2,X3,X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
| k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)) != X3
| r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,X3)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f237,plain,
! [X2,X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0)
| ~ m1_subset_1(k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X0)))
| r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)))) ),
inference(equality_resolution,[],[f235]) ).
tcf(c_49,negated_conjecture,
k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK4,u1_struct_0(k8_group_4(sK0,sK2,sK3))) != k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK4,u1_struct_0(k5_group_4(sK0,sK5))),
inference(cnf_transformation,[],[f160]) ).
tcf(c_50,negated_conjecture,
k2_xboole_0(u1_struct_0(sK2),u1_struct_0(sK3)) = sK5,
inference(cnf_transformation,[],[f159]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f158]) ).
tcf(c_52,negated_conjecture,
v1_funct_1(sK4),
inference(cnf_transformation,[],[f157]) ).
tcf(c_53,negated_conjecture,
v1_funct_2(sK4,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f156]) ).
tcf(c_54,negated_conjecture,
m2_relset_1(sK4,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f155]) ).
tcf(c_55,negated_conjecture,
m1_group_2(sK3,sK0),
inference(cnf_transformation,[],[f154]) ).
tcf(c_56,negated_conjecture,
m1_group_2(sK2,sK0),
inference(cnf_transformation,[],[f153]) ).
tcf(c_61,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f148]) ).
tcf(c_62,negated_conjecture,
v3_group_1(sK0),
inference(cnf_transformation,[],[f147]) ).
tcf(c_63,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f146]) ).
tcf(c_64,negated_conjecture,
l1_group_1(sK0),
inference(cnf_transformation,[],[f145]) ).
tcf(c_117,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,[],[f218]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ( X1 = X2 )
| ~ v1_group_1(X2)
| ~ v1_group_1(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| ~ r1_group_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_123,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,[],[f225]) ).
tcf(c_124,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,[],[f224]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v1_group_1(k8_group_4(X1,X2,X0))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_group_2(X2,X1)
| ~ m1_group_2(X0,X1) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| m1_group_2(k8_group_4(X1,X2,X0),X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_group_2(X2,X1)
| ~ m1_group_2(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| r1_group_2(X2,k8_group_4(X2,X0,X1),k5_group_4(X2,k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))))
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ m1_group_2(X1,X2)
| ~ m1_group_2(X0,X2)
| ~ m1_subset_1(k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X2))) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_189,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_119]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_189]) ).
tcf(c_1207,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X2,X0,X1)
| ( X2 != sK4 )
| ( u1_struct_0(sK1) != X1 )
| ( u1_struct_0(sK0) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_190]) ).
tcf(c_1208,plain,
m1_relset_1(sK4,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(unflattening,[status(thm)],[c_1207]) ).
tcf(c_1403,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 != sK4 )
| ( u1_struct_0(sK1) != X1 )
| ( u1_struct_0(sK0) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_117]) ).
tcf(c_1404,plain,
! [X0: $i] :
( ( k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK4,X0) = k9_relat_1(sK4,X0) )
| ~ v1_funct_1(sK4)
| ~ m1_relset_1(sK4,u1_struct_0(sK0),u1_struct_0(sK1)) ),
inference(unflattening,[status(thm)],[c_1403]) ).
tcf(c_1406,plain,
! [X0: $i] : k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK4,X0) = k9_relat_1(sK4,X0),
inference(global_subsumption_just,[status(thm)],[c_1404,c_52,c_1208,c_1404]) ).
tcf(c_2300,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ( X1 = X2 )
| ~ v1_group_1(X2)
| ~ v1_group_1(X1)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| ~ r1_group_2(X0,X1,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_121]) ).
tcf(c_2301,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| ( X0 = X1 )
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(X1)
| ~ v1_group_1(X0)
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0)
| ~ r1_group_2(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_2300]) ).
tcf(c_2303,plain,
! [X0: $i,X1: $i] :
( ~ r1_group_2(sK0,X0,X1)
| ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| ~ v1_group_1(X0)
| ~ v1_group_1(X1)
| ( X0 = X1 ) ),
inference(global_subsumption_just,[status(thm)],[c_2301,c_64,c_62,c_61,c_2301]) ).
tcf(c_2304,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ v1_group_1(X1)
| ~ v1_group_1(X0)
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0)
| ~ r1_group_2(sK0,X0,X1) ),
inference(renaming,[status(thm)],[c_2303]) ).
tcf(c_2346,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| m1_group_2(k8_group_4(X0,X2,X1),X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_126]) ).
tcf(c_2347,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| m1_group_2(k8_group_4(sK0,X1,X0),sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0) ),
inference(unflattening,[status(thm)],[c_2346]) ).
tcf(c_2349,plain,
! [X0: $i,X1: $i] :
( ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| m1_group_2(k8_group_4(sK0,X1,X0),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_2347,c_64,c_62,c_61,c_2347]) ).
tcf(c_2350,plain,
! [X0: $i,X1: $i] :
( m1_group_2(k8_group_4(sK0,X1,X0),sK0)
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0) ),
inference(renaming,[status(thm)],[c_2349]) ).
tcf(c_2361,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| v1_group_1(k8_group_4(X0,X2,X1))
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_125]) ).
tcf(c_2362,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v1_group_1(k8_group_4(sK0,X1,X0))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0) ),
inference(unflattening,[status(thm)],[c_2361]) ).
tcf(c_2364,plain,
! [X0: $i,X1: $i] :
( ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| v1_group_1(k8_group_4(sK0,X1,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_2362,c_64,c_62,c_61,c_2362]) ).
tcf(c_2365,plain,
! [X0: $i,X1: $i] :
( v1_group_1(k8_group_4(sK0,X1,X0))
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0) ),
inference(renaming,[status(thm)],[c_2364]) ).
tcf(c_2376,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| m1_group_2(k5_group_4(X0,X1),X0)
| ~ 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_63,c_124]) ).
tcf(c_2377,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| m1_group_2(k5_group_4(sK0,X0),sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(unflattening,[status(thm)],[c_2376]) ).
tcf(c_2379,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| m1_group_2(k5_group_4(sK0,X0),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_2377,c_64,c_62,c_61,c_2377]) ).
tcf(c_2380,plain,
! [X0: $i] :
( m1_group_2(k5_group_4(sK0,X0),sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(renaming,[status(thm)],[c_2379]) ).
tcf(c_2388,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| v1_group_1(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_63,c_123]) ).
tcf(c_2389,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| v1_group_1(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_2388]) ).
tcf(c_2391,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_group_1(k5_group_4(sK0,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_2389,c_64,c_62,c_61,c_2389]) ).
tcf(c_2392,plain,
! [X0: $i] :
( v1_group_1(k5_group_4(sK0,X0))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(renaming,[status(thm)],[c_2391]) ).
tcf(c_2415,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2))))
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| ~ m1_subset_1(k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_134]) ).
tcf(c_2416,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| r1_group_2(sK0,k8_group_4(sK0,X0,X1),k5_group_4(sK0,k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0)
| ~ m1_subset_1(k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(unflattening,[status(thm)],[c_2415]) ).
tcf(c_2418,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| r1_group_2(sK0,k8_group_4(sK0,X0,X1),k5_group_4(sK0,k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)))) ),
inference(global_subsumption_just,[status(thm)],[c_2416,c_64,c_62,c_61,c_2416]) ).
tcf(c_2419,plain,
! [X0: $i,X1: $i] :
( r1_group_2(sK0,k8_group_4(sK0,X0,X1),k5_group_4(sK0,k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))))
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0)
| ~ m1_subset_1(k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(renaming,[status(thm)],[c_2418]) ).
tcf(c_2495,definition,
iPr_def_12 = u1_struct_0(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2496,definition,
iPr_def_13 = k1_zfmisc_1(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2501,definition,
iPr_def_18 = u1_struct_0(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_2502,definition,
iPr_def_19 = u1_struct_0(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_2503,definition,
iPr_def_20 = k2_xboole_0(iPr_def_18,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_2504,definition,
iPr_def_21 = k8_group_4(sK0,sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_2505,definition,
iPr_def_22 = u1_struct_0(iPr_def_21),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_2506,definition,
iPr_def_23 = k2_funct_2(iPr_def_12,iPr_def_14,sK4,iPr_def_22),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_2507,definition,
iPr_def_24 = k5_group_4(sK0,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_2508,definition,
iPr_def_25 = u1_struct_0(iPr_def_24),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_2509,definition,
iPr_def_26 = k2_funct_2(iPr_def_12,iPr_def_14,sK4,iPr_def_25),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_2510,plain,
! [X0: $i,X1: $i] :
( r1_group_2(sK0,k8_group_4(sK0,X0,X1),k5_group_4(sK0,k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))))
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0)
| ~ m1_subset_1(k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),iPr_def_13) ),
inference(demodulation,[status(thm)],[c_2419,c_2495,c_2496]) ).
tcf(c_2512,plain,
! [X0: $i] :
( v1_group_1(k5_group_4(sK0,X0))
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_2392]) ).
tcf(c_2513,plain,
! [X0: $i] :
( m1_group_2(k5_group_4(sK0,X0),sK0)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_2380]) ).
tcf(c_2514,plain,
! [X0: $i,X1: $i] :
( v1_group_1(k8_group_4(sK0,X1,X0))
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0) ),
inference(demodulation,[status(thm)],[c_2365]) ).
tcf(c_2515,plain,
! [X0: $i,X1: $i] :
( m1_group_2(k8_group_4(sK0,X1,X0),sK0)
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0) ),
inference(demodulation,[status(thm)],[c_2350]) ).
tcf(c_2517,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ v1_group_1(X1)
| ~ v1_group_1(X0)
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0)
| ~ r1_group_2(sK0,X0,X1) ),
inference(demodulation,[status(thm)],[c_2304]) ).
tcf(c_2527,plain,
! [X0: $i] : k2_funct_2(iPr_def_12,iPr_def_14,sK4,X0) = k9_relat_1(sK4,X0),
inference(demodulation,[status(thm)],[c_1406]) ).
tcf(c_2542,negated_conjecture,
m1_group_2(sK2,sK0),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_2543,negated_conjecture,
m1_group_2(sK3,sK0),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_2544,negated_conjecture,
m1_subset_1(sK5,iPr_def_13),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_2545,negated_conjecture,
iPr_def_20 = sK5,
inference(demodulation,[status(thm)],[c_50,c_2502,c_2501,c_2503]) ).
tcf(c_2546,negated_conjecture,
iPr_def_23 != iPr_def_26,
inference(demodulation,[status(thm)],[c_49,c_2507,c_2508,c_2509,c_2504,c_2505,c_2506]) ).
tcf(c_3794,plain,
m1_subset_1(iPr_def_20,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_2544,c_2545]) ).
tcf(c_3961,plain,
! [X0: $i] :
( r1_group_2(sK0,k8_group_4(sK0,sK2,X0),k5_group_4(sK0,k2_xboole_0(iPr_def_18,u1_struct_0(X0))))
| ~ m1_group_2(sK2,sK0)
| ~ m1_group_2(X0,sK0)
| ~ m1_subset_1(k2_xboole_0(u1_struct_0(sK2),u1_struct_0(X0)),iPr_def_13) ),
inference(superposition,[status(thm)],[c_2501,c_2510]) ).
tcf(c_4021,plain,
! [X0: $i] :
( r1_group_2(sK0,k8_group_4(sK0,sK2,X0),k5_group_4(sK0,k2_xboole_0(iPr_def_18,u1_struct_0(X0))))
| ~ m1_group_2(sK2,sK0)
| ~ m1_group_2(X0,sK0)
| ~ m1_subset_1(k2_xboole_0(iPr_def_18,u1_struct_0(X0)),iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_3961,c_2501]) ).
tcf(c_4022,plain,
! [X0: $i] :
( r1_group_2(sK0,k8_group_4(sK0,sK2,X0),k5_group_4(sK0,k2_xboole_0(iPr_def_18,u1_struct_0(X0))))
| ~ m1_group_2(X0,sK0)
| ~ m1_subset_1(k2_xboole_0(iPr_def_18,u1_struct_0(X0)),iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4021,c_2542]) ).
tcf(c_4228,plain,
k5_group_4(sK0,iPr_def_20) = iPr_def_24,
inference(light_normalisation,[status(thm)],[c_2507,c_2545]) ).
tcf(c_4347,plain,
! [X0: $i] :
( ( k5_group_4(sK0,k2_xboole_0(iPr_def_18,u1_struct_0(X0))) = k8_group_4(sK0,sK2,X0) )
| ~ m1_group_2(X0,sK0)
| ~ v1_group_1(k8_group_4(sK0,sK2,X0))
| ~ m1_group_2(k8_group_4(sK0,sK2,X0),sK0)
| ~ m1_subset_1(k2_xboole_0(iPr_def_18,u1_struct_0(X0)),iPr_def_13)
| ~ v1_group_1(k5_group_4(sK0,k2_xboole_0(iPr_def_18,u1_struct_0(X0))))
| ~ m1_group_2(k5_group_4(sK0,k2_xboole_0(iPr_def_18,u1_struct_0(X0))),sK0) ),
inference(superposition,[status(thm)],[c_4022,c_2517]) ).
tcf(c_4525,plain,
( m1_group_2(iPr_def_21,sK0)
| ~ m1_group_2(sK3,sK0)
| ~ m1_group_2(sK2,sK0) ),
inference(superposition,[status(thm)],[c_2504,c_2515]) ).
tcf(c_4526,plain,
( v1_group_1(iPr_def_21)
| ~ m1_group_2(sK3,sK0)
| ~ m1_group_2(sK2,sK0) ),
inference(superposition,[status(thm)],[c_2504,c_2514]) ).
tcf(c_4530,plain,
v1_group_1(iPr_def_21),
inference(forward_subsumption_resolution,[status(thm)],[c_4526,c_2543,c_2542]) ).
tcf(c_4531,plain,
m1_group_2(iPr_def_21,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_4525,c_2543,c_2542]) ).
tcf(c_4715,plain,
k9_relat_1(sK4,iPr_def_22) = iPr_def_23,
inference(demodulation,[status(thm)],[c_2506,c_2527]) ).
tcf(c_4742,plain,
k9_relat_1(sK4,iPr_def_25) = iPr_def_26,
inference(demodulation,[status(thm)],[c_2509,c_2527]) ).
tcf(c_4881,plain,
! [X0: $i] :
( ( k5_group_4(sK0,k2_xboole_0(iPr_def_18,u1_struct_0(X0))) = k8_group_4(sK0,sK2,X0) )
| ~ m1_group_2(X0,sK0)
| ~ v1_group_1(k8_group_4(sK0,sK2,X0))
| ~ m1_group_2(k8_group_4(sK0,sK2,X0),sK0)
| ~ m1_subset_1(k2_xboole_0(iPr_def_18,u1_struct_0(X0)),iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4347,c_2512,c_2513]) ).
tcf(c_4900,plain,
( ( k5_group_4(sK0,k2_xboole_0(iPr_def_18,u1_struct_0(sK3))) = k8_group_4(sK0,sK2,sK3) )
| ~ m1_group_2(sK3,sK0)
| ~ v1_group_1(k8_group_4(sK0,sK2,sK3))
| ~ m1_subset_1(k2_xboole_0(iPr_def_18,iPr_def_19),iPr_def_13)
| ~ m1_group_2(k8_group_4(sK0,sK2,sK3),sK0) ),
inference(superposition,[status(thm)],[c_2502,c_4881]) ).
tcf(c_4915,plain,
( ( iPr_def_21 = iPr_def_24 )
| ~ v1_group_1(iPr_def_21)
| ~ m1_group_2(iPr_def_21,sK0)
| ~ m1_group_2(sK3,sK0)
| ~ m1_subset_1(iPr_def_20,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_4900,c_2502,c_2503,c_2504,c_4228]) ).
tcf(c_4916,plain,
iPr_def_21 = iPr_def_24,
inference(forward_subsumption_resolution,[status(thm)],[c_4915,c_4530,c_4531,c_2543,c_3794]) ).
tcf(c_4940,plain,
u1_struct_0(iPr_def_21) = iPr_def_25,
inference(demodulation,[status(thm)],[c_2508,c_4916]) ).
tcf(c_4941,plain,
iPr_def_22 = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_4940,c_2505]) ).
tcf(c_4942,plain,
k9_relat_1(sK4,iPr_def_22) = iPr_def_26,
inference(demodulation,[status(thm)],[c_4742,c_4941]) ).
tcf(c_4943,plain,
iPr_def_23 = iPr_def_26,
inference(light_normalisation,[status(thm)],[c_4942,c_4715]) ).
tcf(c_4944,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4943,c_2546]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP640+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 15:23:30 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.42 % Proving...
% 2.73/1.27 % SZS status Started for theBenchmark.p
% 2.73/1.27 % SZS status Theorem for theBenchmark.p
% 2.73/1.27
% 2.73/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.73/1.27
% 2.73/1.27 % ------ iProver source info
% 2.73/1.27
% 2.73/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.73/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.73/1.27 % git: non_committed_changes: false
% 2.73/1.27
% 2.73/1.27 % ------ Parsing...
% 2.73/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.73/1.27
% 2.73/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 2.73/1.27
% 2.73/1.27 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.73/1.27
% 2.73/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.73/1.27 % ------ Proving...
% 2.73/1.27 % ------ Problem Properties
% 2.73/1.27
% 2.73/1.27 %
% 2.73/1.27 % clauses 112
% 2.73/1.27 % conjectures 11
% 2.73/1.27 % EPR 37
% 2.73/1.27 % Horn 102
% 2.73/1.27 % unary 53
% 2.73/1.27 % binary 22
% 2.73/1.27 % lits 232
% 2.73/1.27 % lits eq 48
% 2.73/1.27 % fd_pure 0
% 2.73/1.27 % fd_pseudo 0
% 2.73/1.27 % fd_cond 3
% 2.73/1.27 % fd_pseudo_cond 7
% 2.73/1.27 % AC symbols 0
% 2.73/1.27
% 2.73/1.27 % ------ Schedule dynamic 5 is on
% 2.73/1.27
% 2.73/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.73/1.27
% 2.73/1.27
% 2.73/1.27 % ------
% 2.73/1.27 % Current options:
% 2.73/1.27 % ------
% 2.73/1.27
% 2.73/1.27
% 2.73/1.27 %
% 2.73/1.27
% 2.73/1.27 % ------ Proving...
% 2.73/1.27 %
% 2.73/1.27
% 2.73/1.27 % SZS status Theorem for theBenchmark.p
% 2.73/1.27
% 2.73/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.73/1.27
% 2.73/1.27
%------------------------------------------------------------------------------