%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP641+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 3.96s 1.43s
% Output : CNFRefutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 108 ( 27 unt; 0 def)
% Number of atoms : 447 ( 51 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 577 ( 238 ~; 255 |; 65 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 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 : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn 115 !; 7 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( m1_group_2(X1,X0)
& v1_group_1(X1) )
=> r2_hidden(k2_group_1(X0),k1_funct_1(k1_latsubgr(X0),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_latsubgr) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( m1_group_2(X1,X0)
& v1_group_1(X1) )
=> r2_hidden(k2_group_1(X0),k1_funct_1(k1_latsubgr(X0),X1)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f9,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_1(X1) )
=> ( X1 = k1_latsubgr(X0)
<=> ! [X2] :
( ( m1_group_2(X2,X0)
& v1_group_1(X2) )
=> k1_funct_1(X1,X2) = u1_struct_0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_latsubgr) ).
fof(f13,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ( m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_1(k1_latsubgr(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsubgr) ).
fof(f16,axiom,
! [X0] :
( ( l1_group_1(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_group_1) ).
fof(f18,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f20,axiom,
! [X0] :
( ( l1_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ( l1_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_group_2) ).
fof(f33,axiom,
! [X0] :
( ( l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f40,axiom,
? [X0] : v1_xboole_0(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f49,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( r2_hidden(X0,X1)
| v1_xboole_0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f52,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> k2_group_1(X1) = k2_group_1(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_group_2) ).
fof(f56,axiom,
! [X0,X1] :
~ ( v1_xboole_0(X1)
& X0 != X1
& v1_xboole_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f57,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_group_2(X1,X0)
& v1_group_1(X1)
& ~ r2_hidden(k2_group_1(X0),k1_funct_1(k1_latsubgr(X0),X1)) ) ),
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] :
( m1_group_2(X1,X0)
& v1_group_1(X1)
& ~ r2_hidden(k2_group_1(X0),k1_funct_1(k1_latsubgr(X0),X1)) ) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| k2_group_1(X1) = k2_group_1(X0) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f60,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| k2_group_1(X1) = k2_group_1(X0) ) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0] :
( ~ l1_group_1(X0)
| v3_struct_0(X0)
| m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f62,plain,
! [X0] :
( ~ l1_group_1(X0)
| v3_struct_0(X0)
| m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ( m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_1(k1_latsubgr(X0)) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f64,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ( m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& v1_funct_1(k1_latsubgr(X0)) ) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(X1)
| ( X1 = k1_latsubgr(X0)
<=> ! [X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| k1_funct_1(X1,X2) = u1_struct_0(X2) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f66,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(X1)
| ( X1 = k1_latsubgr(X0)
<=> ! [X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| k1_funct_1(X1,X2) = u1_struct_0(X2) ) ) ) ),
inference(flattening,[],[f65]) ).
fof(f69,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| ( l1_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) ) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f70,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| ( l1_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) ) ) ),
inference(flattening,[],[f69]) ).
fof(f77,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f78,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f77]) ).
fof(f81,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f84,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f85,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f84]) ).
fof(f96,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f98,plain,
( l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& ~ v3_struct_0(sK0)
& m1_group_2(sK1,sK0)
& v1_group_1(sK1)
& ~ r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f58]) ).
fof(f99,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(X1)
| ( ( k1_latsubgr(X0) != X1
| ! [X2] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| k1_funct_1(X1,X2) = u1_struct_0(X2) ) )
& ( ? [X2] :
( m1_group_2(X2,X0)
& v1_group_1(X2)
& k1_funct_1(X1,X2) != u1_struct_0(X2) )
| X1 = k1_latsubgr(X0) ) ) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f100,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(X1)
| ( ( k1_latsubgr(X0) != X1
| ! [X3] :
( ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3)
| k1_funct_1(X1,X3) = u1_struct_0(X3) ) )
& ( ? [X2] :
( m1_group_2(X2,X0)
& v1_group_1(X2)
& k1_funct_1(X1,X2) != u1_struct_0(X2) )
| X1 = k1_latsubgr(X0) ) ) ) ),
inference(rectify,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(X1)
| ( ( k1_latsubgr(X0) != X1
| ! [X3] :
( ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3)
| k1_funct_1(X1,X3) = u1_struct_0(X3) ) )
& ( ( m1_group_2(sK2(X0,X1),X0)
& v1_group_1(sK2(X0,X1))
& k1_funct_1(X1,sK2(X0,X1)) != u1_struct_0(sK2(X0,X1)) )
| X1 = k1_latsubgr(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f100]) ).
fof(f112,plain,
v1_xboole_0(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f40]) ).
fof(f115,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f98]) ).
fof(f116,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f98]) ).
fof(f117,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f98]) ).
fof(f118,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f98]) ).
fof(f119,plain,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f98]) ).
fof(f120,plain,
v1_group_1(sK1),
inference(cnf_transformation,[],[f98]) ).
fof(f121,plain,
~ r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f98]) ).
fof(f122,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| k2_group_1(X0) = k2_group_1(X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f123,plain,
! [X0] :
( ~ l1_group_1(X0)
| v3_struct_0(X0)
| m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f124,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f64]) ).
fof(f125,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f64]) ).
fof(f126,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| v1_funct_1(k1_latsubgr(X0)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f127,plain,
! [X3,X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(X1)
| k1_latsubgr(X0) != X1
| ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3)
| k1_funct_1(X1,X3) = u1_struct_0(X3) ),
inference(cnf_transformation,[],[f101]) ).
fof(f132,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| l1_group_1(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f134,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| ~ v3_struct_0(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f141,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f144,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f147,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f165,plain,
v1_xboole_0(sK12),
inference(cnf_transformation,[],[f112]) ).
fof(f169,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f173,plain,
! [X3,X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(k1_latsubgr(X0))
| ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3)
| u1_struct_0(X3) = k1_funct_1(k1_latsubgr(X0),X3) ),
inference(equality_resolution,[],[f127]) ).
tcf(c_49,negated_conjecture,
~ r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f121]) ).
tcf(c_50,negated_conjecture,
v1_group_1(sK1),
inference(cnf_transformation,[],[f120]) ).
tcf(c_51,negated_conjecture,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f119]) ).
tcf(c_52,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f118]) ).
tcf(c_53,negated_conjecture,
v3_group_1(sK0),
inference(cnf_transformation,[],[f117]) ).
tcf(c_54,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f116]) ).
tcf(c_55,negated_conjecture,
l1_group_1(sK0),
inference(cnf_transformation,[],[f115]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k2_group_1(X0) = k2_group_1(X1) )
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_group_2(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_57,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_58,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v1_funct_1(k1_latsubgr(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_59,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_60,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ( k1_funct_1(k1_latsubgr(X0),X1) = u1_struct_0(X1) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X1)
| ~ v1_funct_1(k1_latsubgr(X0))
| ~ m1_group_2(X1,X0)
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v3_struct_0(X0)
| ~ m1_group_2(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( l1_group_1(X0)
| v3_struct_0(X1)
| ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_group_2(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ v1_xboole_0(X1)
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_81,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_99,plain,
v1_xboole_0(sK12),
inference(cnf_transformation,[],[f165]) ).
tcf(c_103,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ( k1_funct_1(k1_latsubgr(X0),X1) = u1_struct_0(X1) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_64,c_58,c_60,c_59,c_64]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k1_funct_1(k1_latsubgr(X1),X0) = u1_struct_0(X0) )
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,X1) ),
inference(renaming,[status(thm)],[c_146]) ).
tcf(c_153,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_103]) ).
tcf(c_947,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v1_xboole_0(u1_struct_0(X1))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_153,c_81]) ).
tcf(c_948,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_947]) ).
tcf(c_1437,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ( k1_funct_1(k1_latsubgr(X0),X1) = u1_struct_0(X1) )
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_147]) ).
tcf(c_1438,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| ( k1_funct_1(k1_latsubgr(sK0),X0) = u1_struct_0(X0) )
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0) ),
inference(unflattening,[status(thm)],[c_1437]) ).
tcf(c_1440,plain,
! [X0: $i] :
( ~ m1_group_2(X0,sK0)
| ~ v1_group_1(X0)
| ( k1_funct_1(k1_latsubgr(sK0),X0) = u1_struct_0(X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_1438,c_55,c_53,c_52,c_1438]) ).
tcf(c_1441,plain,
! [X0: $i] :
( ( k1_funct_1(k1_latsubgr(sK0),X0) = u1_struct_0(X0) )
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0) ),
inference(renaming,[status(thm)],[c_1440]) ).
tcf(c_1515,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ( k2_group_1(X0) = k2_group_1(X1) )
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ m1_group_2(X1,X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_56]) ).
tcf(c_1516,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| ( k2_group_1(sK0) = k2_group_1(X0) )
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ m1_group_2(X0,sK0) ),
inference(unflattening,[status(thm)],[c_1515]) ).
tcf(c_1518,plain,
! [X0: $i] :
( ~ m1_group_2(X0,sK0)
| ( k2_group_1(sK0) = k2_group_1(X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_1516,c_55,c_53,c_52,c_1516]) ).
tcf(c_1519,plain,
! [X0: $i] :
( ( k2_group_1(sK0) = k2_group_1(X0) )
| ~ m1_group_2(X0,sK0) ),
inference(renaming,[status(thm)],[c_1518]) ).
tcf(c_2405,plain,
! [X0: $i,X1: $i] :
( l1_group_1(X1)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_68]) ).
tcf(c_2406,plain,
( l1_group_1(sK1)
| v3_struct_0(sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(unflattening,[status(thm)],[c_2405]) ).
tcf(c_3940,plain,
k2_group_1(sK0) = k2_group_1(sK1),
inference(superposition,[status(thm)],[c_51,c_1519]) ).
tcf(c_3947,plain,
( ( k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1) )
| ~ v1_group_1(sK1) ),
inference(superposition,[status(thm)],[c_51,c_1441]) ).
tcf(c_3948,plain,
k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_3947,c_50]) ).
tcf(c_3949,plain,
~ r2_hidden(k2_group_1(sK0),u1_struct_0(sK1)),
inference(demodulation,[status(thm)],[c_49,c_3948]) ).
tcf(c_4045,plain,
( v3_struct_0(sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v3_struct_0(sK1) ),
inference(superposition,[status(thm)],[c_51,c_66]) ).
tcf(c_4046,plain,
~ v3_struct_0(sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_4045,c_52,c_55,c_53]) ).
tcf(c_4142,plain,
( v3_struct_0(sK1)
| m1_subset_1(k2_group_1(sK0),u1_struct_0(sK1))
| ~ l1_group_1(sK1) ),
inference(superposition,[status(thm)],[c_3940,c_57]) ).
tcf(c_4144,plain,
( m1_subset_1(k2_group_1(sK0),u1_struct_0(sK1))
| ~ l1_group_1(sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4142,c_4046]) ).
tcf(c_4159,plain,
! [X0: $i] :
( ( X0 = sK12 )
| ~ v1_xboole_0(X0) ),
inference(superposition,[status(thm)],[c_99,c_78]) ).
tcf(c_4229,plain,
m1_subset_1(k2_group_1(sK0),u1_struct_0(sK1)),
inference(global_subsumption_just,[status(thm)],[c_4144,c_55,c_53,c_52,c_2406,c_4144]) ).
tcf(c_4231,plain,
( v1_xboole_0(u1_struct_0(sK1))
| r2_hidden(k2_group_1(sK0),u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_4229,c_75]) ).
tcf(c_4232,plain,
v1_xboole_0(u1_struct_0(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_4231,c_3949]) ).
tcf(c_4234,plain,
u1_struct_0(sK1) = sK12,
inference(superposition,[status(thm)],[c_4232,c_4159]) ).
tcf(c_4369,plain,
( l1_group_1(sK1)
| v3_struct_0(sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(superposition,[status(thm)],[c_51,c_68]) ).
tcf(c_4371,plain,
l1_group_1(sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_4369,c_52,c_55,c_53]) ).
tcf(c_4428,plain,
( v3_struct_0(sK1)
| ~ v1_xboole_0(sK12)
| ~ l1_group_1(sK1) ),
inference(superposition,[status(thm)],[c_4234,c_948]) ).
tcf(c_4429,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4428,c_4046,c_99,c_4371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP641+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.44 % Computer : n017.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Wed Sep 23 15:19:31 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.50 Running first-order theorem proving
% 0.18/0.50 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.25/0.52
% 0.25/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.52
% 0.25/0.52 % Detected problem language: tptp
% 0.25/0.54 % Proving...
% 3.96/1.43 % SZS status Started for theBenchmark.p
% 3.96/1.43 % SZS status Theorem for theBenchmark.p
% 3.96/1.43
% 3.96/1.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.96/1.43
% 3.96/1.43 % ------ iProver source info
% 3.96/1.43
% 3.96/1.43 % git: date: 2026-07-19 20:42:38 +0200
% 3.96/1.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.96/1.43 % git: non_committed_changes: false
% 3.96/1.43
% 3.96/1.43 % ------ Parsing...
% 3.96/1.43 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.96/1.43
% 3.96/1.43 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 3.96/1.43
% 3.96/1.43 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.96/1.43
% 3.96/1.43 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.96/1.43 % ------ Proving...
% 3.96/1.43 % ------ Problem Properties
% 3.96/1.43
% 3.96/1.43 %
% 3.96/1.43 % clauses 60
% 3.96/1.43 % conjectures 6
% 3.96/1.43 % EPR 19
% 3.96/1.43 % Horn 49
% 3.96/1.43 % unary 23
% 3.96/1.43 % binary 15
% 3.96/1.43 % lits 138
% 3.96/1.43 % lits eq 12
% 3.96/1.43 % fd_pure 0
% 3.96/1.43 % fd_pseudo 0
% 3.96/1.43 % fd_cond 3
% 3.96/1.43 % fd_pseudo_cond 3
% 3.96/1.43 % AC symbols 0
% 3.96/1.43
% 3.96/1.43 % ------ Schedule dynamic 5 is on
% 3.96/1.43
% 3.96/1.43 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.96/1.43
% 3.96/1.43
% 3.96/1.43 % ------
% 3.96/1.43 % Current options:
% 3.96/1.43 % ------
% 3.96/1.43
% 3.96/1.43
% 3.96/1.43 %
% 3.96/1.43
% 3.96/1.43 % ------ Proving...
% 3.96/1.43 %
% 3.96/1.43
% 3.96/1.43 % SZS status Theorem for theBenchmark.p
% 3.96/1.43
% 3.96/1.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.96/1.43
% 3.96/1.43
%------------------------------------------------------------------------------