%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP618+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 : n013.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 01:34:52 PM UTC 2026
% Result : Theorem 3.57s 1.28s
% Output : CNFRefutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 6
% Syntax : Number of formulae : 91 ( 29 unt; 3 def)
% Number of atoms : 494 ( 5 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 601 ( 243 ~; 255 |; 77 &)
% ( 2 <=>; 22 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 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 : 14 ( 12 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 109 ( 0 sgn 89 !; 20 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ( ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
=> ( m1_subset_1(X3,u1_struct_0(X1))
=> r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) ) )
<=> v1_group_3(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_autgroup) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ( ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
=> ( m1_subset_1(X3,u1_struct_0(X1))
=> r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) ) )
<=> v1_group_3(X1,X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f61,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ( ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
=> ( m1_subset_1(X3,u1_struct_0(X1))
=> r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) ) )
=> v1_group_3(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_autgroup) ).
fof(f62,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ( v1_group_3(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
=> ( m1_subset_1(X3,u1_struct_0(X1))
=> r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_autgroup) ).
fof(f72,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_group_2(X1,X0)
& ( ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) )
<~> v1_group_3(X1,X0) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f73,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_group_2(X1,X0)
& ( ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) )
<~> v1_group_3(X1,X0) ) ) ),
inference(flattening,[],[f72]) ).
fof(f124,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& m1_subset_1(X3,u1_struct_0(X1))
& ~ r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) )
| v1_group_3(X1,X0) ) ),
inference(ennf_transformation,[],[f61]) ).
fof(f125,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& m1_subset_1(X3,u1_struct_0(X1))
& ~ r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) )
| v1_group_3(X1,X0) ) ),
inference(flattening,[],[f124]) ).
fof(f126,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| ~ v1_group_3(X1,X0)
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) ) ) ),
inference(ennf_transformation,[],[f62]) ).
fof(f127,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| ~ v1_group_3(X1,X0)
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) ) ) ),
inference(flattening,[],[f126]) ).
fof(f128,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_group_2(X1,X0)
& ( ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) )
| v1_group_3(X1,X0) )
& ( ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& m1_subset_1(X3,u1_struct_0(X1))
& ~ r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) )
| ~ v1_group_3(X1,X0) ) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f129,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_group_2(X1,X0)
& ( ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) )
| v1_group_3(X1,X0) )
& ( ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& m1_subset_1(X3,u1_struct_0(X1))
& ~ r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) )
| ~ v1_group_3(X1,X0) ) ) ),
inference(flattening,[],[f128]) ).
fof(f130,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_group_2(X1,X0)
& ( ! [X4] :
( ~ m1_subset_1(X4,u1_struct_0(X0))
| ! [X5] :
( ~ m1_subset_1(X5,u1_struct_0(X0))
| ~ m1_subset_1(X5,u1_struct_0(X1))
| r1_rlvect_1(X1,k2_group_3(X0,X5,X4)) ) )
| v1_group_3(X1,X0) )
& ( ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& m1_subset_1(X3,u1_struct_0(X1))
& ~ r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ) )
| ~ v1_group_3(X1,X0) ) ) ),
inference(rectify,[],[f129]) ).
fof(f131,plain,
( l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& v1_group_1(sK0)
& ~ v3_struct_0(sK0)
& m1_group_2(sK1,sK0)
& ( ! [X4] :
( ~ m1_subset_1(X4,u1_struct_0(sK0))
| ! [X5] :
( ~ m1_subset_1(X5,u1_struct_0(sK0))
| ~ m1_subset_1(X5,u1_struct_0(sK1))
| r1_rlvect_1(sK1,k2_group_3(sK0,X5,X4)) ) )
| v1_group_3(sK1,sK0) )
& ( ( m1_subset_1(sK2,u1_struct_0(sK0))
& m1_subset_1(sK3,u1_struct_0(sK0))
& m1_subset_1(sK3,u1_struct_0(sK1))
& ~ r1_rlvect_1(sK1,k2_group_3(sK0,sK3,sK2)) )
| ~ v1_group_3(sK1,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f130]) ).
fof(f154,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_group_2(X1,X0)
| ( m1_subset_1(sK25(X0,X1),u1_struct_0(X0))
& m1_subset_1(sK26(X0,X1),u1_struct_0(X0))
& m1_subset_1(sK26(X0,X1),u1_struct_0(X1))
& ~ r1_rlvect_1(X1,k2_group_3(X0,sK26(X0,X1),sK25(X0,X1))) )
| v1_group_3(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26]),skolemize(X2,sK25(X0,X1)),skolemize(X3,sK26(X0,X1))],[f125]) ).
fof(f155,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f131]) ).
fof(f156,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f131]) ).
fof(f157,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f131]) ).
fof(f158,plain,
v1_group_1(sK0),
inference(cnf_transformation,[],[f131]) ).
fof(f159,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f131]) ).
fof(f160,plain,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f131]) ).
fof(f161,plain,
! [X4,X5] :
( ~ m1_subset_1(X4,u1_struct_0(sK0))
| ~ m1_subset_1(X5,u1_struct_0(sK0))
| ~ m1_subset_1(X5,u1_struct_0(sK1))
| r1_rlvect_1(sK1,k2_group_3(sK0,X5,X4))
| v1_group_3(sK1,sK0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f162,plain,
( m1_subset_1(sK2,u1_struct_0(sK0))
| ~ v1_group_3(sK1,sK0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f163,plain,
( m1_subset_1(sK3,u1_struct_0(sK0))
| ~ v1_group_3(sK1,sK0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f164,plain,
( m1_subset_1(sK3,u1_struct_0(sK1))
| ~ v1_group_3(sK1,sK0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f165,plain,
( ~ r1_rlvect_1(sK1,k2_group_3(sK0,sK3,sK2))
| ~ v1_group_3(sK1,sK0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f261,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| m1_subset_1(sK25(X0,X1),u1_struct_0(X0))
| v1_group_3(X1,X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f262,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| m1_subset_1(sK26(X0,X1),u1_struct_0(X0))
| v1_group_3(X1,X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f263,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| m1_subset_1(sK26(X0,X1),u1_struct_0(X1))
| v1_group_3(X1,X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f264,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| ~ r1_rlvect_1(X1,k2_group_3(X0,sK26(X0,X1),sK25(X0,X1)))
| v1_group_3(X1,X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f265,plain,
! [X2,X3,X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| ~ v1_group_3(X1,X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| r1_rlvect_1(X1,k2_group_3(X0,X3,X2)) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_49,negated_conjecture,
( ~ v1_group_3(sK1,sK0)
| ~ r1_rlvect_1(sK1,k2_group_3(sK0,sK3,sK2)) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_50,negated_conjecture,
( m1_subset_1(sK3,u1_struct_0(sK1))
| ~ v1_group_3(sK1,sK0) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_51,negated_conjecture,
( m1_subset_1(sK3,u1_struct_0(sK0))
| ~ v1_group_3(sK1,sK0) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_52,negated_conjecture,
( m1_subset_1(sK2,u1_struct_0(sK0))
| ~ v1_group_3(sK1,sK0) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i] :
( v1_group_3(sK1,sK0)
| r1_rlvect_1(sK1,k2_group_3(sK0,X0,X1))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_54,negated_conjecture,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f160]) ).
tcf(c_55,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f159]) ).
tcf(c_56,negated_conjecture,
v1_group_1(sK0),
inference(cnf_transformation,[],[f158]) ).
tcf(c_57,negated_conjecture,
v3_group_1(sK0),
inference(cnf_transformation,[],[f157]) ).
tcf(c_58,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f156]) ).
tcf(c_59,negated_conjecture,
l1_group_1(sK0),
inference(cnf_transformation,[],[f155]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_group_3(X0,X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_group_2(X0,X1)
| ~ r1_rlvect_1(X0,k2_group_3(X1,sK26(X1,X0),sK25(X1,X0))) ),
inference(cnf_transformation,[],[f264]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_group_3(X0,X1)
| m1_subset_1(sK26(X1,X0),u1_struct_0(X0))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_group_2(X0,X1) ),
inference(cnf_transformation,[],[f263]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_group_3(X0,X1)
| m1_subset_1(sK26(X1,X0),u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_group_2(X0,X1) ),
inference(cnf_transformation,[],[f262]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_group_3(X0,X1)
| m1_subset_1(sK25(X1,X0),u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_group_2(X0,X1) ),
inference(cnf_transformation,[],[f261]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| r1_rlvect_1(X3,k2_group_3(X1,X2,X0))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_group_2(X3,X1)
| ~ v1_group_3(X3,X1)
| ~ m1_subset_1(X2,u1_struct_0(X3))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f265]) ).
tcf(c_2724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| r1_rlvect_1(X0,k2_group_3(X1,X3,X2))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ v1_group_3(X0,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ( X1 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_151]) ).
tcf(c_2725,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| r1_rlvect_1(sK1,k2_group_3(sK0,X1,X0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| ~ v1_group_3(sK1,sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK1))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_2724]) ).
tcf(c_2726,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK1))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ v1_group_3(sK1,sK0)
| r1_rlvect_1(sK1,k2_group_3(sK0,X1,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_2725,c_59,c_58,c_57,c_56,c_55,c_2725]) ).
tcf(c_2727,plain,
! [X0: $i,X1: $i] :
( r1_rlvect_1(sK1,k2_group_3(sK0,X1,X0))
| ~ v1_group_3(sK1,sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK1))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_2726]) ).
tcf(c_2738,plain,
! [X0: $i,X1: $i] :
( r1_rlvect_1(sK1,k2_group_3(sK0,X1,X0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK1))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2727,c_53]) ).
tcf(c_8615,definition,
iPr_def_10 = u1_struct_0(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8616,definition,
iPr_def_11 = u1_struct_0(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8617,definition,
iPr_def_12 = k2_group_3(sK0,sK3,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8618,plain,
! [X0: $i,X1: $i] :
( r1_rlvect_1(sK1,k2_group_3(sK0,X1,X0))
| ~ m1_subset_1(X1,iPr_def_11)
| ~ m1_subset_1(X1,iPr_def_10)
| ~ m1_subset_1(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_2738,c_8616,c_8615]) ).
tcf(c_8619,negated_conjecture,
l1_group_1(sK0),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_8620,negated_conjecture,
v4_group_1(sK0),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_8621,negated_conjecture,
v3_group_1(sK0),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_8622,negated_conjecture,
v1_group_1(sK0),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_8623,negated_conjecture,
~ v3_struct_0(sK0),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_8624,negated_conjecture,
m1_group_2(sK1,sK0),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_8625,negated_conjecture,
( m1_subset_1(sK2,iPr_def_10)
| ~ v1_group_3(sK1,sK0) ),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_8626,negated_conjecture,
( m1_subset_1(sK3,iPr_def_10)
| ~ v1_group_3(sK1,sK0) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_8627,negated_conjecture,
( m1_subset_1(sK3,iPr_def_11)
| ~ v1_group_3(sK1,sK0) ),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_8628,negated_conjecture,
( ~ r1_rlvect_1(sK1,iPr_def_12)
| ~ v1_group_3(sK1,sK0) ),
inference(demodulation,[status(thm)],[c_49,c_8617]) ).
tcf(c_9920,plain,
( r1_rlvect_1(sK1,iPr_def_12)
| ~ m1_subset_1(sK2,iPr_def_10)
| ~ m1_subset_1(sK3,iPr_def_11)
| ~ m1_subset_1(sK3,iPr_def_10) ),
inference(superposition,[status(thm)],[c_8617,c_8618]) ).
tcf(c_10785,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v1_group_3(sK1,X0)
| m1_subset_1(sK26(X0,sK1),iPr_def_11)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ~ m1_group_2(sK1,X0) ),
inference(superposition,[status(thm)],[c_8616,c_148]) ).
tcf(c_10814,plain,
( v3_struct_0(sK0)
| v1_group_3(sK1,sK0)
| m1_subset_1(sK26(sK0,sK1),iPr_def_11)
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| ~ m1_group_2(sK1,sK0) ),
inference(instantiation,[status(thm)],[c_10785]) ).
tcf(c_10833,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| v1_group_3(X0,sK0)
| m1_subset_1(sK26(sK0,X0),iPr_def_10)
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| ~ m1_group_2(X0,sK0) ),
inference(superposition,[status(thm)],[c_8615,c_149]) ).
tcf(c_10835,plain,
! [X0: $i] :
( v1_group_3(X0,sK0)
| m1_subset_1(sK26(sK0,X0),iPr_def_10)
| ~ m1_group_2(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10833,c_8623,c_8619,c_8620,c_8621,c_8622]) ).
tcf(c_10881,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| v1_group_3(X0,sK0)
| m1_subset_1(sK25(sK0,X0),iPr_def_10)
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| ~ m1_group_2(X0,sK0) ),
inference(superposition,[status(thm)],[c_8615,c_150]) ).
tcf(c_10883,plain,
! [X0: $i] :
( v1_group_3(X0,sK0)
| m1_subset_1(sK25(sK0,X0),iPr_def_10)
| ~ m1_group_2(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10881,c_8623,c_8619,c_8620,c_8621,c_8622]) ).
tcf(c_11106,plain,
( v3_struct_0(sK0)
| v1_group_3(sK1,sK0)
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_subset_1(sK25(sK0,sK1),iPr_def_10)
| ~ m1_subset_1(sK26(sK0,sK1),iPr_def_11)
| ~ m1_subset_1(sK26(sK0,sK1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8618,c_147]) ).
tcf(c_11107,plain,
( v1_group_3(sK1,sK0)
| ~ m1_subset_1(sK25(sK0,sK1),iPr_def_10)
| ~ m1_subset_1(sK26(sK0,sK1),iPr_def_11)
| ~ m1_subset_1(sK26(sK0,sK1),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11106,c_8623,c_8619,c_8620,c_8621,c_8622,c_8624]) ).
tcf(c_11206,plain,
( v1_group_3(sK1,sK0)
| ~ m1_subset_1(sK25(sK0,sK1),iPr_def_10)
| ~ m1_subset_1(sK26(sK0,sK1),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_11107,c_59,c_58,c_57,c_56,c_55,c_54,c_8625,c_8626,c_8627,c_8628,c_9920,c_10814,c_11107]) ).
tcf(c_11208,plain,
( ~ m1_subset_1(sK26(sK0,sK1),iPr_def_10)
| ~ m1_subset_1(sK25(sK0,sK1),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_11206,c_8625,c_8626,c_8627,c_8628,c_9920,c_11206]) ).
tcf(c_11209,plain,
( ~ m1_subset_1(sK25(sK0,sK1),iPr_def_10)
| ~ m1_subset_1(sK26(sK0,sK1),iPr_def_10) ),
inference(renaming,[status(thm)],[c_11208]) ).
tcf(c_11214,plain,
( v1_group_3(sK1,sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_subset_1(sK26(sK0,sK1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_10883,c_11209]) ).
tcf(c_11215,plain,
( v1_group_3(sK1,sK0)
| ~ m1_subset_1(sK26(sK0,sK1),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11214,c_8624]) ).
tcf(c_11218,plain,
~ m1_subset_1(sK26(sK0,sK1),iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_11215,c_8625,c_8626,c_8627,c_8628,c_9920,c_11215]) ).
tcf(c_11220,plain,
( v1_group_3(sK1,sK0)
| ~ m1_group_2(sK1,sK0) ),
inference(superposition,[status(thm)],[c_10835,c_11218]) ).
tcf(c_11221,plain,
v1_group_3(sK1,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_11220,c_8624]) ).
tcf(c_11222,plain,
~ r1_rlvect_1(sK1,iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_8628,c_11221]) ).
tcf(c_11223,plain,
m1_subset_1(sK3,iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_8627,c_11221]) ).
tcf(c_11224,plain,
m1_subset_1(sK3,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_8626,c_11221]) ).
tcf(c_11225,plain,
m1_subset_1(sK2,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_8625,c_11221]) ).
tcf(c_11226,plain,
( ~ m1_subset_1(sK2,iPr_def_10)
| ~ m1_subset_1(sK3,iPr_def_11)
| ~ m1_subset_1(sK3,iPr_def_10) ),
inference(backward_subsumption_resolution,[status(thm)],[c_9920,c_11222]) ).
tcf(c_11230,plain,
( ~ m1_subset_1(sK2,iPr_def_10)
| ~ m1_subset_1(sK3,iPr_def_10) ),
inference(backward_subsumption_resolution,[status(thm)],[c_11226,c_11223]) ).
tcf(c_11233,plain,
~ m1_subset_1(sK2,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_11230,c_11224]) ).
tcf(c_11234,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11225,c_11233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP618+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 15:13:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 3.57/1.28 % SZS status Started for theBenchmark.p
% 3.57/1.28 % SZS status Theorem for theBenchmark.p
% 3.57/1.28
% 3.57/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.57/1.28
% 3.57/1.28 % ------ iProver source info
% 3.57/1.28
% 3.57/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.57/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.57/1.28 % git: non_committed_changes: false
% 3.57/1.28
% 3.57/1.28 % ------ Parsing...
% 3.57/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.57/1.28
% 3.57/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 9 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe_e %
% 3.57/1.28
% 3.57/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.57/1.28
% 3.57/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.57/1.28 % ------ Proving...
% 3.57/1.28 % ------ Problem Properties
% 3.57/1.28
% 3.57/1.28 %
% 3.57/1.28 % clauses 90
% 3.57/1.28 % conjectures 10
% 3.57/1.28 % EPR 37
% 3.57/1.28 % Horn 66
% 3.57/1.28 % unary 37
% 3.57/1.28 % binary 17
% 3.57/1.28 % lits 245
% 3.57/1.28 % lits eq 14
% 3.57/1.28 % fd_pure 0
% 3.57/1.28 % fd_pseudo 0
% 3.57/1.28 % fd_cond 1
% 3.57/1.28 % fd_pseudo_cond 5
% 3.57/1.28 % AC symbols 0
% 3.57/1.28
% 3.57/1.28 % ------ Schedule dynamic 5 is on
% 3.57/1.28
% 3.57/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.57/1.28
% 3.57/1.28
% 3.57/1.28 % ------
% 3.57/1.28 % Current options:
% 3.57/1.28 % ------
% 3.57/1.28
% 3.57/1.28
% 3.57/1.28 %
% 3.57/1.28
% 3.57/1.28 % ------ Proving...
% 3.57/1.28 %
% 3.57/1.28
% 3.57/1.28 % SZS status Theorem for theBenchmark.p
% 3.57/1.28
% 3.57/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.57/1.28
% 3.57/1.28
%------------------------------------------------------------------------------