%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP644+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 01:27:48 PM UTC 2026
% Result : Theorem 9.02s 6.69s
% Output : Proof 9.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 55 ( 11 unt; 0 def)
% Number of atoms : 273 ( 0 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 354 ( 136 ~; 164 |; 37 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f45,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))
<=> r1_rlvect_1(B,C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_latsubgr) ).
fof(f45_nnf,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ~ r1_rlvect_1(B,C)
| r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) )
& ( r1_rlvect_1(B,C)
| ~ r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) ) )
| ~ m1_subset_1(C,u1_struct_0(A)) )
| ~ m1_group_2(B,A)
| ~ v1_group_1(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [A,B,C] :
( ( ( ~ r1_rlvect_1(B,C)
| r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) )
& ( r1_rlvect_1(B,C)
| ~ r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) ) )
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_group_2(B,A)
| ~ v1_group_1(B)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c78,plain,
( ~ r1_rlvect_1(X1,X2)
| r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
fof(f0,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))
=> r2_hidden(k3_group_1(A,C),k1_funct_1(k1_latsubgr(A),B)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_latsubgr) ).
fof(f0_neg,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))
=> r2_hidden(k3_group_1(A,C),k1_funct_1(k1_latsubgr(A),B)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ r2_hidden(k3_group_1(A,C),k1_funct_1(k1_latsubgr(A),B))
& r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))
& m1_subset_1(C,u1_struct_0(A)) )
& m1_group_2(B,A)
& v1_group_1(B) )
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
( ~ r2_hidden(k3_group_1(sk0,sk2),k1_funct_1(k1_latsubgr(sk0),sk1))
& r2_hidden(sk2,k1_funct_1(k1_latsubgr(sk0),sk1))
& m1_subset_1(sk2,u1_struct_0(sk0))
& m1_group_2(sk1,sk0)
& v1_group_1(sk1)
& l1_group_1(sk0)
& v4_group_1(sk0)
& v3_group_1(sk0)
& ~ v3_struct_0(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f0_nnf]) ).
cnf(c1,plain,
v3_group_1(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p276,plain,
( ~ r1_rlvect_1(X0,X1)
| r2_hidden(X1,k1_funct_1(k1_latsubgr(sk0),X0))
| ~ m1_subset_1(X1,u1_struct_0(sk0))
| ~ m1_group_2(X0,sk0)
| ~ v1_group_1(X0)
| ~ l1_group_1(sk0)
| ~ v4_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c78,c1]) ).
cnf(c2,plain,
v4_group_1(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p745,plain,
( ~ r1_rlvect_1(X0,X1)
| r2_hidden(X1,k1_funct_1(k1_latsubgr(sk0),X0))
| ~ m1_subset_1(X1,u1_struct_0(sk0))
| ~ m1_group_2(X0,sk0)
| ~ v1_group_1(X0)
| ~ l1_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p276,c2]) ).
cnf(c3,plain,
l1_group_1(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p960,plain,
( ~ r1_rlvect_1(X0,X1)
| r2_hidden(X1,k1_funct_1(k1_latsubgr(sk0),X0))
| ~ m1_subset_1(X1,u1_struct_0(sk0))
| ~ m1_group_2(X0,sk0)
| ~ v1_group_1(X0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p745,c3]) ).
cnf(c4,plain,
v1_group_1(sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p961,plain,
( ~ r1_rlvect_1(sk1,X0)
| r2_hidden(X0,k1_funct_1(k1_latsubgr(sk0),sk1))
| ~ m1_subset_1(X0,u1_struct_0(sk0))
| ~ m1_group_2(sk1,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p960,c4]) ).
cnf(c5,plain,
m1_group_2(sk1,sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p965,plain,
( ~ r1_rlvect_1(sk1,X0)
| r2_hidden(X0,k1_funct_1(k1_latsubgr(sk0),sk1))
| ~ m1_subset_1(X0,u1_struct_0(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p961,c5]) ).
fof(f14,axiom,
! [A,B] :
( ( m1_subset_1(B,u1_struct_0(A))
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k3_group_1(A,B),u1_struct_0(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_group_1) ).
fof(f14_nnf,plain,
! [A,B] :
( m1_subset_1(k3_group_1(A,B),u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B] :
( m1_subset_1(k3_group_1(A,B),u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c31,plain,
( m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p137,plain,
( m1_subset_1(k3_group_1(sk0,X0),u1_struct_0(sk0))
| ~ m1_subset_1(X0,u1_struct_0(sk0))
| ~ l1_group_1(sk0)
| ~ v4_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c31,c1]) ).
cnf(p138,plain,
( m1_subset_1(k3_group_1(sk0,X0),u1_struct_0(sk0))
| ~ m1_subset_1(X0,u1_struct_0(sk0))
| ~ l1_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p137,c2]) ).
cnf(p139,plain,
( m1_subset_1(k3_group_1(sk0,X0),u1_struct_0(sk0))
| ~ m1_subset_1(X0,u1_struct_0(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p138,c3]) ).
cnf(c6,plain,
m1_subset_1(sk2,u1_struct_0(sk0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p140,plain,
( m1_subset_1(k3_group_1(sk0,sk2),u1_struct_0(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p139,c6]) ).
cnf(p967,plain,
( v3_struct_0(sk0)
| ~ r1_rlvect_1(sk1,k3_group_1(sk0,sk2))
| r2_hidden(k3_group_1(sk0,sk2),k1_funct_1(k1_latsubgr(sk0),sk1))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p965,p140]) ).
cnf(p982,plain,
( ~ r1_rlvect_1(sk1,k3_group_1(sk0,sk2))
| r2_hidden(k3_group_1(sk0,sk2),k1_funct_1(k1_latsubgr(sk0),sk1))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p967]) ).
cnf(c77,plain,
( r1_rlvect_1(X1,X2)
| ~ r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p269,plain,
( r1_rlvect_1(X0,X1)
| ~ r2_hidden(X1,k1_funct_1(k1_latsubgr(sk0),X0))
| ~ m1_subset_1(X1,u1_struct_0(sk0))
| ~ m1_group_2(X0,sk0)
| ~ v1_group_1(X0)
| ~ l1_group_1(sk0)
| ~ v4_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c77,c1]) ).
cnf(p728,plain,
( r1_rlvect_1(X0,X1)
| ~ r2_hidden(X1,k1_funct_1(k1_latsubgr(sk0),X0))
| ~ m1_subset_1(X1,u1_struct_0(sk0))
| ~ m1_group_2(X0,sk0)
| ~ v1_group_1(X0)
| ~ l1_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p269,c2]) ).
cnf(p929,plain,
( r1_rlvect_1(X0,X1)
| ~ r2_hidden(X1,k1_funct_1(k1_latsubgr(sk0),X0))
| ~ m1_subset_1(X1,u1_struct_0(sk0))
| ~ m1_group_2(X0,sk0)
| ~ v1_group_1(X0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p728,c3]) ).
cnf(p930,plain,
( r1_rlvect_1(sk1,X0)
| ~ r2_hidden(X0,k1_funct_1(k1_latsubgr(sk0),sk1))
| ~ m1_subset_1(X0,u1_struct_0(sk0))
| ~ m1_group_2(sk1,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p929,c4]) ).
cnf(p934,plain,
( r1_rlvect_1(sk1,X0)
| ~ r2_hidden(X0,k1_funct_1(k1_latsubgr(sk0),sk1))
| ~ m1_subset_1(X0,u1_struct_0(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p930,c5]) ).
cnf(p935,plain,
( r1_rlvect_1(sk1,sk2)
| ~ r2_hidden(sk2,k1_funct_1(k1_latsubgr(sk0),sk1))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p934,c6]) ).
cnf(c7,plain,
r2_hidden(sk2,k1_funct_1(k1_latsubgr(sk0),sk1)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p951,plain,
( r1_rlvect_1(sk1,sk2)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p935,c7]) ).
fof(f51,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_group_2(C,A)
=> ( r1_rlvect_1(C,B)
=> r1_rlvect_1(C,k3_group_1(A,B)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_group_2) ).
fof(f51_nnf,plain,
! [A] :
( ! [B] :
( ! [C] :
( r1_rlvect_1(C,k3_group_1(A,B))
| ~ r1_rlvect_1(C,B)
| ~ m1_group_2(C,A) )
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
! [A,B,C] :
( r1_rlvect_1(C,k3_group_1(A,B))
| ~ r1_rlvect_1(C,B)
| ~ m1_group_2(C,A)
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c85,plain,
( r1_rlvect_1(X2,k3_group_1(X0,X1))
| ~ r1_rlvect_1(X2,X1)
| ~ m1_group_2(X2,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(p324,plain,
( r1_rlvect_1(X1,k3_group_1(sk0,X0))
| ~ r1_rlvect_1(X1,X0)
| ~ m1_group_2(X1,sk0)
| ~ m1_subset_1(X0,u1_struct_0(sk0))
| ~ l1_group_1(sk0)
| ~ v4_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c85,c1]) ).
cnf(p813,plain,
( r1_rlvect_1(X1,k3_group_1(sk0,X0))
| ~ r1_rlvect_1(X1,X0)
| ~ m1_group_2(X1,sk0)
| ~ m1_subset_1(X0,u1_struct_0(sk0))
| ~ l1_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p324,c2]) ).
cnf(p814,plain,
( r1_rlvect_1(X1,k3_group_1(sk0,X0))
| ~ r1_rlvect_1(X1,X0)
| ~ m1_group_2(X1,sk0)
| ~ m1_subset_1(X0,u1_struct_0(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p813,c3]) ).
cnf(p815,plain,
( r1_rlvect_1(X0,k3_group_1(sk0,sk2))
| ~ r1_rlvect_1(X0,sk2)
| ~ m1_group_2(X0,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p814,c6]) ).
cnf(p832,plain,
( r1_rlvect_1(sk1,k3_group_1(sk0,sk2))
| ~ r1_rlvect_1(sk1,sk2)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p815,c5]) ).
cnf(p952,plain,
( r1_rlvect_1(sk1,k3_group_1(sk0,sk2))
| v3_struct_0(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p951,p832]) ).
cnf(p953,plain,
( r1_rlvect_1(sk1,k3_group_1(sk0,sk2))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p952]) ).
cnf(p983,plain,
( v3_struct_0(sk0)
| r2_hidden(k3_group_1(sk0,sk2),k1_funct_1(k1_latsubgr(sk0),sk1))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p982,p953]) ).
cnf(p984,plain,
( r2_hidden(k3_group_1(sk0,sk2),k1_funct_1(k1_latsubgr(sk0),sk1))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p983]) ).
cnf(c8,plain,
~ r2_hidden(k3_group_1(sk0,sk2),k1_funct_1(k1_latsubgr(sk0),sk1)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p985,plain,
v3_struct_0(sk0),
inference(resolution,[status(thm)],[p984,c8]) ).
cnf(c0,plain,
~ v3_struct_0(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p986,plain,
$false,
inference(resolution,[status(thm)],[p985,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP644+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/5.43 % Computer : n015.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Wed Sep 23 15:29:15 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.02/6.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.02/6.69 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------