%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP644+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 : n012.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 0.19s 0.96s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 86 ( 25 unt; 2 def)
% Number of atoms : 410 ( 14 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 533 ( 232 ~; 238 |; 44 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn 112 !; 6 ?; 68 :)
% 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))
=> ( r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
=> r2_hidden(k3_group_1(X0,X2),k1_funct_1(k1_latsubgr(X0),X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_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))
=> ( r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
=> r2_hidden(k3_group_1(X0,X2),k1_funct_1(k1_latsubgr(X0),X1)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f16,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,u1_struct_0(X0))
& l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_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(f53,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_group_2(X2,X0)
=> ( r1_rlvect_1(X2,X1)
=> r1_rlvect_1(X2,k3_group_1(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_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))
& r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
& ~ r2_hidden(k3_group_1(X0,X2),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))
& r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
& ~ r2_hidden(k3_group_1(X0,X2),k1_funct_1(k1_latsubgr(X0),X1)) ) ) ),
inference(flattening,[],[f62]) ).
fof(f77,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f78,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0)) ),
inference(flattening,[],[f77]) ).
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(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_group_2(X2,X0)
| ~ r1_rlvect_1(X2,X1)
| r1_rlvect_1(X2,k3_group_1(X0,X1)) ) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f107,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_group_2(X2,X0)
| ~ r1_rlvect_1(X2,X1)
| r1_rlvect_1(X2,k3_group_1(X0,X1)) ) ) ),
inference(flattening,[],[f106]) ).
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))
& r2_hidden(sK2,k1_funct_1(k1_latsubgr(sK0),sK1))
& ~ r2_hidden(k3_group_1(sK0,sK2),k1_funct_1(k1_latsubgr(sK0),sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[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,
r2_hidden(sK2,k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f111]) ).
fof(f136,plain,
~ r2_hidden(k3_group_1(sK0,sK2),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f111]) ).
fof(f153,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f193,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(f194,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(f200,plain,
! [X2,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_group_2(X2,X0)
| ~ r1_rlvect_1(X2,X1)
| r1_rlvect_1(X2,k3_group_1(X0,X1)) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_49,negated_conjecture,
~ r2_hidden(k3_group_1(sK0,sK2),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f136]) ).
tcf(c_50,negated_conjecture,
r2_hidden(sK2,k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f135]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f134]) ).
tcf(c_52,negated_conjecture,
v1_group_1(sK1),
inference(cnf_transformation,[],[f133]) ).
tcf(c_53,negated_conjecture,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f132]) ).
tcf(c_54,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f131]) ).
tcf(c_55,negated_conjecture,
v3_group_1(sK0),
inference(cnf_transformation,[],[f130]) ).
tcf(c_56,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f129]) ).
tcf(c_57,negated_conjecture,
l1_group_1(sK0),
inference(cnf_transformation,[],[f128]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_subset_1(k3_group_1(X1,X0),u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_109,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,[],[f194]) ).
tcf(c_110,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,[],[f193]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r1_rlvect_1(X2,k3_group_1(X1,X0))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ r1_rlvect_1(X2,X0)
| ~ m1_group_2(X2,X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_1183,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r1_rlvect_1(X2,k3_group_1(X0,X1))
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ 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_56,c_116]) ).
tcf(c_1184,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| r1_rlvect_1(X1,k3_group_1(sK0,X0))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ m1_group_2(X1,sK0)
| ~ r1_rlvect_1(X1,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_1183]) ).
tcf(c_1186,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r1_rlvect_1(X1,X0)
| ~ m1_group_2(X1,sK0)
| r1_rlvect_1(X1,k3_group_1(sK0,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_1184,c_57,c_55,c_54,c_1184]) ).
tcf(c_1187,plain,
! [X0: $i,X1: $i] :
( r1_rlvect_1(X1,k3_group_1(sK0,X0))
| ~ m1_group_2(X1,sK0)
| ~ r1_rlvect_1(X1,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_1186]) ).
tcf(c_1201,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_56,c_110]) ).
tcf(c_1202,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_1201]) ).
tcf(c_1204,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_1202,c_57,c_55,c_54,c_1202]) ).
tcf(c_1205,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_1204]) ).
tcf(c_1222,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_56,c_109]) ).
tcf(c_1223,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_1222]) ).
tcf(c_1225,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_1223,c_57,c_55,c_54,c_1223]) ).
tcf(c_1226,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_1225]) ).
tcf(c_1243,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_69]) ).
tcf(c_1244,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| m1_subset_1(k3_group_1(sK0,X0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_1243]) ).
tcf(c_1246,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| m1_subset_1(k3_group_1(sK0,X0),u1_struct_0(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_1244,c_57,c_55,c_54,c_1244]) ).
tcf(c_1247,plain,
! [X0: $i] :
( m1_subset_1(k3_group_1(sK0,X0),u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_1246]) ).
tcf(c_1283,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_52,c_1226]) ).
tcf(c_1284,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_1283]) ).
tcf(c_1298,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_52,c_1205]) ).
tcf(c_1299,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_1298]) ).
tcf(c_2151,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_53,c_1226]) ).
tcf(c_2152,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_2151]) ).
tcf(c_2153,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_2152,c_53,c_1284]) ).
tcf(c_2154,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_2153]) ).
tcf(c_2164,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_53,c_1205]) ).
tcf(c_2165,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_2164]) ).
tcf(c_2166,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_2165,c_53,c_1299]) ).
tcf(c_2167,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_2166]) ).
tcf(c_2177,plain,
! [X0: $i,X1: $i] :
( r1_rlvect_1(X0,k3_group_1(sK0,X1))
| ~ r1_rlvect_1(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ( sK0 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_1187]) ).
tcf(c_2178,plain,
! [X0: $i] :
( r1_rlvect_1(sK1,k3_group_1(sK0,X0))
| ~ r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_2177]) ).
tcf(c_3038,definition,
iPr_def_23 = k1_funct_1(iPr_def_14,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_3039,definition,
iPr_def_24 = k3_group_1(sK0,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_3043,plain,
! [X0: $i] :
( r1_rlvect_1(sK1,k3_group_1(sK0,X0))
| ~ r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_2178]) ).
tcf(c_3057,plain,
! [X0: $i] :
( r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X0,iPr_def_12)
| ~ r2_hidden(X0,iPr_def_23) ),
inference(demodulation,[status(thm)],[c_2167,c_3038]) ).
tcf(c_3058,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_23)
| ~ r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_2154]) ).
tcf(c_3059,plain,
! [X0: $i] :
( m1_subset_1(k3_group_1(sK0,X0),iPr_def_12)
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_1247]) ).
tcf(c_3065,negated_conjecture,
m1_subset_1(sK2,iPr_def_12),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_3066,negated_conjecture,
r2_hidden(sK2,iPr_def_23),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_3067,negated_conjecture,
~ r2_hidden(iPr_def_24,iPr_def_23),
inference(demodulation,[status(thm)],[c_49,c_3039]) ).
tcf(c_4084,plain,
( r1_rlvect_1(sK1,sK2)
| ~ r2_hidden(sK2,iPr_def_23) ),
inference(superposition,[status(thm)],[c_3065,c_3057]) ).
tcf(c_4085,plain,
r1_rlvect_1(sK1,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_4084,c_3066]) ).
tcf(c_4103,plain,
! [X0: $i] :
( r2_hidden(k3_group_1(sK0,X0),iPr_def_23)
| ~ r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X0,iPr_def_12)
| ~ m1_subset_1(k3_group_1(sK0,X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_3043,c_3058]) ).
tcf(c_4248,plain,
! [X0: $i] :
( r2_hidden(k3_group_1(sK0,X0),iPr_def_23)
| ~ r1_rlvect_1(sK1,X0)
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_4103,c_3059,c_4103]) ).
tcf(c_4309,plain,
( r2_hidden(iPr_def_24,iPr_def_23)
| ~ r1_rlvect_1(sK1,sK2)
| ~ m1_subset_1(sK2,iPr_def_12) ),
inference(superposition,[status(thm)],[c_3039,c_4248]) ).
tcf(c_4321,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4309,c_3067,c_4085,c_3065]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP644+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Wed Sep 23 15:25:22 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 0.19/0.96 % SZS status Started for theBenchmark.p
% 0.19/0.96 % SZS status Theorem for theBenchmark.p
% 0.19/0.96
% 0.19/0.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.19/0.96
% 0.19/0.96 % ------ iProver source info
% 0.19/0.96
% 0.19/0.96 % git: date: 2026-07-19 20:42:38 +0200
% 0.19/0.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.19/0.96 % git: non_committed_changes: false
% 0.19/0.96
% 0.19/0.96 % ------ Parsing...
% 0.19/0.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.19/0.96
% 0.19/0.96 % ------ 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 %
% 0.19/0.96
% 0.19/0.96 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.19/0.96
% 0.19/0.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.19/0.96 % ------ Proving...
% 0.19/0.96 % ------ Problem Properties
% 0.19/0.96
% 0.19/0.96 %
% 0.19/0.96 % clauses 93
% 0.19/0.96 % conjectures 7
% 0.19/0.96 % EPR 34
% 0.19/0.96 % Horn 84
% 0.19/0.96 % unary 47
% 0.19/0.96 % binary 16
% 0.19/0.96 % lits 177
% 0.19/0.96 % lits eq 37
% 0.19/0.96 % fd_pure 0
% 0.19/0.96 % fd_pseudo 0
% 0.19/0.96 % fd_cond 3
% 0.19/0.96 % fd_pseudo_cond 5
% 0.19/0.96 % AC symbols 0
% 0.19/0.96
% 0.19/0.96 % ------ Schedule dynamic 5 is on
% 0.19/0.96
% 0.19/0.96 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.19/0.96
% 0.19/0.96
% 0.19/0.96 % ------
% 0.19/0.96 % Current options:
% 0.19/0.96 % ------
% 0.19/0.96
% 0.19/0.96
% 0.19/0.96 %
% 0.19/0.96
% 0.19/0.96 % ------ Proving...
% 0.19/0.96 %
% 0.19/0.96
% 0.19/0.96 % SZS status Theorem for theBenchmark.p
% 0.19/0.96
% 0.19/0.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.19/0.96
% 0.19/0.96
%------------------------------------------------------------------------------