%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP643+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 : n010.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 01:35:00 PM UTC 2026
% Result : Theorem 4.14s 1.51s
% Output : CNFRefutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 95 ( 36 unt; 3 def)
% Number of atoms : 470 ( 14 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 592 ( 257 ~; 261 |; 52 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 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; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 133 ( 0 sgn 125 !; 8 ?; 71 :)
% 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) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
=> ( ( r2_hidden(X3,k1_funct_1(k1_latsubgr(X0),X1))
& r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1)) )
=> r2_hidden(k1_group_1(X0,X2,X3),k1_funct_1(k1_latsubgr(X0),X1)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_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) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
=> ( ( r2_hidden(X3,k1_funct_1(k1_latsubgr(X0),X1))
& r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1)) )
=> r2_hidden(k1_group_1(X0,X2,X3),k1_funct_1(k1_latsubgr(X0),X1)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f11,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X0))
& m1_subset_1(X1,u1_struct_0(X0))
& l1_group_1(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k1_group_1(X0,X1,X2),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_group_1) ).
fof(f47,axiom,
! [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) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
<=> r1_rlvect_1(X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_latsubgr) ).
fof(f52,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_group_2(X3,X0)
=> ( ( r1_rlvect_1(X3,X2)
& r1_rlvect_1(X3,X1) )
=> r1_rlvect_1(X3,k1_group_1(X0,X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_group_2) ).
fof(f62,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)
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& r2_hidden(X3,k1_funct_1(k1_latsubgr(X0),X1))
& r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
& ~ r2_hidden(k1_group_1(X0,X2,X3),k1_funct_1(k1_latsubgr(X0),X1)) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f63,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)
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& r2_hidden(X3,k1_funct_1(k1_latsubgr(X0),X1))
& r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
& ~ r2_hidden(k1_group_1(X0,X2,X3),k1_funct_1(k1_latsubgr(X0),X1)) ) ) ) ),
inference(flattening,[],[f62]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_group_1(X0)
| v3_struct_0(X0)
| m1_subset_1(k1_group_1(X0,X1,X2),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_group_1(X0)
| v3_struct_0(X0)
| m1_subset_1(k1_group_1(X0,X1,X2),u1_struct_0(X0)) ),
inference(flattening,[],[f75]) ).
fof(f97,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)
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ( r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
<=> r1_rlvect_1(X1,X2) ) ) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f98,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)
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ( r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
<=> r1_rlvect_1(X1,X2) ) ) ) ),
inference(flattening,[],[f97]) ).
fof(f105,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_group_2(X3,X0)
| ~ r1_rlvect_1(X3,X2)
| ~ r1_rlvect_1(X3,X1)
| r1_rlvect_1(X3,k1_group_1(X0,X1,X2)) ) ) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f106,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_group_2(X3,X0)
| ~ r1_rlvect_1(X3,X2)
| ~ r1_rlvect_1(X3,X1)
| r1_rlvect_1(X3,k1_group_1(X0,X1,X2)) ) ) ) ),
inference(flattening,[],[f105]) ).
fof(f111,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)
& m1_subset_1(sK2,u1_struct_0(sK0))
& m1_subset_1(sK3,u1_struct_0(sK0))
& r2_hidden(sK3,k1_funct_1(k1_latsubgr(sK0),sK1))
& r2_hidden(sK2,k1_funct_1(k1_latsubgr(sK0),sK1))
& ~ r2_hidden(k1_group_1(sK0,sK2,sK3),k1_funct_1(k1_latsubgr(sK0),sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f63]) ).
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)
| ~ v1_group_1(X1)
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ( ( ~ r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
| r1_rlvect_1(X1,X2) )
& ( ~ r1_rlvect_1(X1,X2)
| r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1)) ) ) ) ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f128,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f111]) ).
fof(f129,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f111]) ).
fof(f130,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f111]) ).
fof(f131,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f111]) ).
fof(f132,plain,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f111]) ).
fof(f133,plain,
v1_group_1(sK1),
inference(cnf_transformation,[],[f111]) ).
fof(f134,plain,
m1_subset_1(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f111]) ).
fof(f135,plain,
m1_subset_1(sK3,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f111]) ).
fof(f136,plain,
r2_hidden(sK3,k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f111]) ).
fof(f137,plain,
r2_hidden(sK2,k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f111]) ).
fof(f138,plain,
~ r2_hidden(k1_group_1(sK0,sK2,sK3),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f111]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_group_1(X0)
| v3_struct_0(X0)
| m1_subset_1(k1_group_1(X0,X1,X2),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f195,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)
| ~ v1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
| r1_rlvect_1(X1,X2) ),
inference(cnf_transformation,[],[f127]) ).
fof(f196,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)
| ~ v1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r1_rlvect_1(X1,X2)
| r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f201,plain,
! [X2,X3,X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_group_2(X3,X0)
| ~ r1_rlvect_1(X3,X2)
| ~ r1_rlvect_1(X3,X1)
| r1_rlvect_1(X3,k1_group_1(X0,X1,X2)) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_49,negated_conjecture,
~ r2_hidden(k1_group_1(sK0,sK2,sK3),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f138]) ).
tcf(c_50,negated_conjecture,
r2_hidden(sK2,k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f137]) ).
tcf(c_51,negated_conjecture,
r2_hidden(sK3,k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f136]) ).
tcf(c_52,negated_conjecture,
m1_subset_1(sK3,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f135]) ).
tcf(c_53,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f134]) ).
tcf(c_54,negated_conjecture,
v1_group_1(sK1),
inference(cnf_transformation,[],[f133]) ).
tcf(c_55,negated_conjecture,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f132]) ).
tcf(c_56,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f131]) ).
tcf(c_57,negated_conjecture,
v3_group_1(sK0),
inference(cnf_transformation,[],[f130]) ).
tcf(c_58,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f129]) ).
tcf(c_59,negated_conjecture,
l1_group_1(sK0),
inference(cnf_transformation,[],[f128]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| m1_subset_1(k1_group_1(X1,X0,X2),u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r2_hidden(X0,k1_funct_1(k1_latsubgr(X1),X2))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X2)
| ~ r1_rlvect_1(X2,X0)
| ~ m1_group_2(X2,X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r1_rlvect_1(X2,X0)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X1)
| ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ r2_hidden(X0,k1_funct_1(k1_latsubgr(X1),X2)) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| r1_rlvect_1(X3,k1_group_1(X1,X0,X2))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ r1_rlvect_1(X3,X2)
| ~ r1_rlvect_1(X3,X0)
| ~ m1_group_2(X3,X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_1199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X0)
| r1_rlvect_1(X3,k1_group_1(X0,X1,X2))
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ r1_rlvect_1(X3,X2)
| ~ r1_rlvect_1(X3,X1)
| ~ m1_group_2(X3,X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_117]) ).
tcf(c_1200,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(sK0)
| r1_rlvect_1(X2,k1_group_1(sK0,X0,X1))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ m1_group_2(X2,sK0)
| ~ r1_rlvect_1(X2,X1)
| ~ r1_rlvect_1(X2,X0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_1199]) ).
tcf(c_1202,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r1_rlvect_1(X2,X0)
| ~ r1_rlvect_1(X2,X1)
| ~ m1_group_2(X2,sK0)
| r1_rlvect_1(X2,k1_group_1(sK0,X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_1200,c_59,c_57,c_56,c_1200]) ).
tcf(c_1203,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1_rlvect_1(X2,k1_group_1(sK0,X0,X1))
| ~ m1_group_2(X2,sK0)
| ~ r1_rlvect_1(X2,X1)
| ~ r1_rlvect_1(X2,X0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_1202]) ).
tcf(c_1223,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r1_rlvect_1(X2,X1)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r2_hidden(X1,k1_funct_1(k1_latsubgr(X0),X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_112]) ).
tcf(c_1224,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| r1_rlvect_1(X1,X0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r2_hidden(X0,k1_funct_1(k1_latsubgr(sK0),X1)) ),
inference(unflattening,[status(thm)],[c_1223]) ).
tcf(c_1226,plain,
! [X0: $i,X1: $i] :
( ~ r2_hidden(X0,k1_funct_1(k1_latsubgr(sK0),X1))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ m1_group_2(X1,sK0)
| ~ v1_group_1(X1)
| r1_rlvect_1(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_1224,c_59,c_57,c_56,c_1224]) ).
tcf(c_1227,plain,
! [X0: $i,X1: $i] :
( r1_rlvect_1(X1,X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r2_hidden(X0,k1_funct_1(k1_latsubgr(sK0),X1)) ),
inference(renaming,[status(thm)],[c_1226]) ).
tcf(c_1244,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r2_hidden(X1,k1_funct_1(k1_latsubgr(X0),X2))
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X2)
| ~ r1_rlvect_1(X2,X1)
| ~ m1_group_2(X2,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_111]) ).
tcf(c_1245,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| r2_hidden(X0,k1_funct_1(k1_latsubgr(sK0),X1))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,sK0)
| ~ r1_rlvect_1(X1,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_1244]) ).
tcf(c_1247,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r1_rlvect_1(X1,X0)
| ~ m1_group_2(X1,sK0)
| ~ v1_group_1(X1)
| r2_hidden(X0,k1_funct_1(k1_latsubgr(sK0),X1)) ),
inference(global_subsumption_just,[status(thm)],[c_1245,c_59,c_57,c_56,c_1245]) ).
tcf(c_1248,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,k1_funct_1(k1_latsubgr(sK0),X1))
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,sK0)
| ~ r1_rlvect_1(X1,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_1247]) ).
tcf(c_1293,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X1,k1_funct_1(k1_latsubgr(sK0),X0))
| ~ m1_group_2(X0,sK0)
| ~ r1_rlvect_1(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_1248]) ).
tcf(c_1294,plain,
! [X0: $i] :
( r2_hidden(X0,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_group_2(sK1,sK0)
| ~ r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_1293]) ).
tcf(c_1308,plain,
! [X0: $i,X1: $i] :
( r1_rlvect_1(X0,X1)
| ~ m1_group_2(X0,sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X1,k1_funct_1(k1_latsubgr(sK0),X0))
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_1227]) ).
tcf(c_1309,plain,
! [X0: $i] :
( r1_rlvect_1(sK1,X0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r2_hidden(X0,k1_funct_1(k1_latsubgr(sK0),sK1)) ),
inference(unflattening,[status(thm)],[c_1308]) ).
tcf(c_2161,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1_rlvect_1(X0,k1_group_1(sK0,X1,X2))
| ~ r1_rlvect_1(X0,X2)
| ~ r1_rlvect_1(X0,X1)
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ( sK0 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_1203]) ).
tcf(c_2162,plain,
! [X0: $i,X1: $i] :
( r1_rlvect_1(sK1,k1_group_1(sK0,X0,X1))
| ~ r1_rlvect_1(sK1,X1)
| ~ r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_2161]) ).
tcf(c_2179,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X1,k1_funct_1(k1_latsubgr(sK0),X0))
| ~ v1_group_1(X0)
| ~ r1_rlvect_1(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ( sK0 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_1248]) ).
tcf(c_2180,plain,
! [X0: $i] :
( r2_hidden(X0,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ v1_group_1(sK1)
| ~ r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_2179]) ).
tcf(c_2181,plain,
! [X0: $i] :
( r2_hidden(X0,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r1_rlvect_1(sK1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_2180,c_55,c_1294]) ).
tcf(c_2182,plain,
! [X0: $i] :
( r2_hidden(X0,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_2181]) ).
tcf(c_2192,plain,
! [X0: $i,X1: $i] :
( r1_rlvect_1(X0,X1)
| ~ v1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X1,k1_funct_1(k1_latsubgr(sK0),X0))
| ( sK0 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_1227]) ).
tcf(c_2193,plain,
! [X0: $i] :
( r1_rlvect_1(sK1,X0)
| ~ v1_group_1(sK1)
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r2_hidden(X0,k1_funct_1(k1_latsubgr(sK0),sK1)) ),
inference(unflattening,[status(thm)],[c_2192]) ).
tcf(c_2194,plain,
! [X0: $i] :
( r1_rlvect_1(sK1,X0)
| ~ r2_hidden(X0,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_2193,c_55,c_1309]) ).
tcf(c_2195,plain,
! [X0: $i] :
( r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r2_hidden(X0,k1_funct_1(k1_latsubgr(sK0),sK1)) ),
inference(renaming,[status(thm)],[c_2194]) ).
tcf(c_3056,definition,
iPr_def_15 = u1_struct_0(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_3064,definition,
iPr_def_23 = k1_funct_1(iPr_def_12,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_3065,definition,
iPr_def_24 = k1_group_1(sK0,sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_3069,plain,
! [X0: $i,X1: $i] :
( r1_rlvect_1(sK1,k1_group_1(sK0,X0,X1))
| ~ r1_rlvect_1(sK1,X1)
| ~ r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X1,iPr_def_15)
| ~ m1_subset_1(X0,iPr_def_15) ),
inference(demodulation,[status(thm)],[c_2162]) ).
tcf(c_3083,plain,
! [X0: $i] :
( r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X0,iPr_def_15)
| ~ r2_hidden(X0,iPr_def_23) ),
inference(demodulation,[status(thm)],[c_2195,c_3064]) ).
tcf(c_3084,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_23)
| ~ r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X0,iPr_def_15) ),
inference(demodulation,[status(thm)],[c_2182]) ).
tcf(c_3086,negated_conjecture,
l1_group_1(sK0),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_3088,negated_conjecture,
~ v3_struct_0(sK0),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_3090,negated_conjecture,
m1_subset_1(sK2,iPr_def_15),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_3091,negated_conjecture,
m1_subset_1(sK3,iPr_def_15),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_3092,negated_conjecture,
r2_hidden(sK3,iPr_def_23),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_3093,negated_conjecture,
r2_hidden(sK2,iPr_def_23),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_3094,negated_conjecture,
~ r2_hidden(iPr_def_24,iPr_def_23),
inference(demodulation,[status(thm)],[c_49,c_3065]) ).
tcf(c_4144,plain,
( r1_rlvect_1(sK1,sK2)
| ~ r2_hidden(sK2,iPr_def_23) ),
inference(superposition,[status(thm)],[c_3090,c_3083]) ).
tcf(c_4145,plain,
( r1_rlvect_1(sK1,sK3)
| ~ r2_hidden(sK3,iPr_def_23) ),
inference(superposition,[status(thm)],[c_3091,c_3083]) ).
tcf(c_4146,plain,
r1_rlvect_1(sK1,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_4145,c_3092]) ).
tcf(c_4147,plain,
r1_rlvect_1(sK1,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_4144,c_3093]) ).
tcf(c_4166,plain,
! [X0: $i,X1: $i] :
( r2_hidden(k1_group_1(sK0,X0,X1),iPr_def_23)
| ~ r1_rlvect_1(sK1,X1)
| ~ r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X1,iPr_def_15)
| ~ m1_subset_1(X0,iPr_def_15)
| ~ m1_subset_1(k1_group_1(sK0,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_3069,c_3084]) ).
tcf(c_4364,plain,
( r2_hidden(k1_group_1(sK0,sK2,sK3),iPr_def_23)
| ~ r1_rlvect_1(sK1,sK3)
| ~ r1_rlvect_1(sK1,sK2)
| ~ m1_subset_1(iPr_def_24,iPr_def_15)
| ~ m1_subset_1(sK3,iPr_def_15)
| ~ m1_subset_1(sK2,iPr_def_15) ),
inference(superposition,[status(thm)],[c_3065,c_4166]) ).
tcf(c_4372,plain,
( r2_hidden(iPr_def_24,iPr_def_23)
| ~ r1_rlvect_1(sK1,sK3)
| ~ r1_rlvect_1(sK1,sK2)
| ~ m1_subset_1(iPr_def_24,iPr_def_15)
| ~ m1_subset_1(sK3,iPr_def_15)
| ~ m1_subset_1(sK2,iPr_def_15) ),
inference(light_normalisation,[status(thm)],[c_4364,c_3065]) ).
tcf(c_4373,plain,
~ m1_subset_1(iPr_def_24,iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_4372,c_3094,c_4146,c_4147,c_3091,c_3090]) ).
tcf(c_4636,plain,
( v3_struct_0(sK0)
| m1_subset_1(iPr_def_24,u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sK3,u1_struct_0(sK0))
| ~ m1_subset_1(sK2,u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_3065,c_68]) ).
tcf(c_4639,plain,
( v3_struct_0(sK0)
| m1_subset_1(iPr_def_24,iPr_def_15)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sK3,iPr_def_15)
| ~ m1_subset_1(sK2,iPr_def_15) ),
inference(light_normalisation,[status(thm)],[c_4636,c_3056]) ).
tcf(c_4640,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4639,c_3088,c_4373,c_3086,c_3091,c_3090]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP643+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.42 % Computer : n010.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Wed Sep 23 15:24:58 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.49 Running first-order theorem proving
% 0.16/0.49 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
% 0.25/0.51
% 0.25/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.51
% 0.25/0.51 % Detected problem language: tptp
% 0.25/0.53 % Proving...
% 4.14/1.51 % SZS status Started for theBenchmark.p
% 4.14/1.51 % SZS status Theorem for theBenchmark.p
% 4.14/1.51
% 4.14/1.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.14/1.51
% 4.14/1.51 % ------ iProver source info
% 4.14/1.51
% 4.14/1.51 % git: date: 2026-07-19 20:42:38 +0200
% 4.14/1.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.14/1.51 % git: non_committed_changes: false
% 4.14/1.51
% 4.14/1.51 % ------ Parsing...
% 4.14/1.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.14/1.51
% 4.14/1.51 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e %
% 4.14/1.51
% 4.14/1.51 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.14/1.51
% 4.14/1.51 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.14/1.51 % ------ Proving...
% 4.14/1.51 % ------ Problem Properties
% 4.14/1.51
% 4.14/1.51 %
% 4.14/1.51 % clauses 95
% 4.14/1.51 % conjectures 9
% 4.14/1.51 % EPR 36
% 4.14/1.51 % Horn 85
% 4.14/1.51 % unary 49
% 4.14/1.51 % binary 15
% 4.14/1.51 % lits 186
% 4.14/1.51 % lits eq 37
% 4.14/1.51 % fd_pure 0
% 4.14/1.51 % fd_pseudo 0
% 4.14/1.51 % fd_cond 3
% 4.14/1.51 % fd_pseudo_cond 5
% 4.14/1.51 % AC symbols 0
% 4.14/1.51
% 4.14/1.51 % ------ Schedule dynamic 5 is on
% 4.14/1.51
% 4.14/1.51 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.14/1.51
% 4.14/1.51
% 4.14/1.51 % ------
% 4.14/1.51 % Current options:
% 4.14/1.51 % ------
% 4.14/1.51
% 4.14/1.51
% 4.14/1.51 %
% 4.14/1.51
% 4.14/1.51 % ------ Proving...
% 4.14/1.51 %
% 4.14/1.51
% 4.14/1.51 % SZS status Theorem for theBenchmark.p
% 4.14/1.51
% 4.14/1.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.14/1.52
% 4.14/1.52
%------------------------------------------------------------------------------