%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP641+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 01:27:46 PM UTC 2026
% Result : Theorem 4.68s 1.13s
% Output : Proof 4.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 92 ( 9 unt; 0 def)
% Number of atoms : 394 ( 35 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 476 ( 174 ~; 231 |; 54 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 43 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f50,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> k2_group_1(B) = k2_group_1(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_group_2) ).
fof(f50_nnf,plain,
! [A] :
( ! [B] :
( k2_group_1(B) = k2_group_1(A)
| ~ m1_group_2(B,A) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f50]) ).
fof(f50_sk,plain,
! [A,B] :
( k2_group_1(B) = k2_group_1(A)
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f50_nnf]) ).
cnf(c84,plain,
( k2_group_1(X1) = k2_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f50_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) )
=> r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_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) )
=> r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B)) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [A] :
( ? [B] :
( ~ r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B))
& 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(k2_group_1(sk0),k1_funct_1(k1_latsubgr(sk0),sk1))
& 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])],[f0_nnf]) ).
cnf(c1,plain,
v3_group_1(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p333,plain,
( k2_group_1(X0) = k2_group_1(sk0)
| ~ m1_group_2(X0,sk0)
| ~ l1_group_1(sk0)
| ~ v4_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c84,c1]) ).
cnf(c2,plain,
v4_group_1(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p427,plain,
( k2_group_1(X0) = k2_group_1(sk0)
| ~ m1_group_2(X0,sk0)
| ~ l1_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p333,c2]) ).
cnf(c3,plain,
l1_group_1(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p428,plain,
( k2_group_1(X0) = k2_group_1(sk0)
| ~ m1_group_2(X0,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p427,c3]) ).
cnf(c5,plain,
m1_group_2(sk1,sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p429,plain,
( k2_group_1(sk1) = k2_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p428,c5]) ).
fof(f18,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_group_2) ).
fof(f18_nnf,plain,
! [A] :
( ! [B] :
( ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
| ~ m1_group_2(B,A) )
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B] :
( ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c38,plain,
( l1_group_1(X1)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p186,plain,
( l1_group_1(X0)
| ~ m1_group_2(X0,sk0)
| ~ l1_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c38,c1]) ).
cnf(p188,plain,
( l1_group_1(X0)
| ~ m1_group_2(X0,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p186,c3]) ).
cnf(p189,plain,
( l1_group_1(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p188,c5]) ).
fof(f14,axiom,
! [A] :
( ( l1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k2_group_1(A),u1_struct_0(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_group_1) ).
fof(f14_nnf,plain,
! [A] :
( m1_subset_1(k2_group_1(A),u1_struct_0(A))
| ~ l1_group_1(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A] :
( m1_subset_1(k2_group_1(A),u1_struct_0(A))
| ~ l1_group_1(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c32,plain,
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p193,plain,
( m1_subset_1(k2_group_1(sk1),u1_struct_0(sk1))
| v3_struct_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p189,c32]) ).
cnf(p431,plain,
( m1_subset_1(k2_group_1(sk0),u1_struct_0(sk1))
| v3_struct_0(sk1)
| v3_struct_0(sk0)
| v3_struct_0(sk0) ),
inference(superposition,[status(thm)],[p429,p193]) ).
cnf(p436,plain,
( m1_subset_1(k2_group_1(sk0),u1_struct_0(sk1))
| v3_struct_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p431]) ).
fof(f47,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f47_nnf,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(nnf_transformation,[status(thm)],[f47]) ).
fof(f47_sk,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(skolemisation,[status(esa)],[f47_nnf]) ).
cnf(c80,plain,
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(p437,plain,
( r2_hidden(k2_group_1(sk0),u1_struct_0(sk1))
| v1_xboole_0(u1_struct_0(sk1))
| v3_struct_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p436,c80]) ).
fof(f11,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(k1_latsubgr(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_latsubgr) ).
fof(f11_nnf,plain,
! [A] :
( ( m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(k1_latsubgr(A)) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] :
( ( m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(k1_latsubgr(A)) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c27,plain,
( v1_funct_1(k1_latsubgr(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p151,plain,
( v1_funct_1(k1_latsubgr(sk0))
| ~ l1_group_1(sk0)
| ~ v4_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c27,c1]) ).
cnf(p152,plain,
( v1_funct_1(k1_latsubgr(sk0))
| ~ l1_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p151,c2]) ).
cnf(p153,plain,
( v1_funct_1(k1_latsubgr(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p152,c3]) ).
fof(f7,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(B) )
=> ( B = k1_latsubgr(A)
<=> ! [C] :
( ( m1_group_2(C,A)
& v1_group_1(C) )
=> k1_funct_1(B,C) = u1_struct_0(C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_latsubgr) ).
fof(f7_nnf,plain,
! [A] :
( ! [B] :
( ( ( ? [C] :
( k1_funct_1(B,C) != u1_struct_0(C)
& m1_group_2(C,A)
& v1_group_1(C) )
| B = k1_latsubgr(A) )
& ( ! [C] :
( k1_funct_1(B,C) = u1_struct_0(C)
| ~ m1_group_2(C,A)
| ~ v1_group_1(C) )
| B != k1_latsubgr(A) ) )
| ~ m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_funct_1(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] :
( ( ( ( k1_funct_1(B,sk2(A,B)) != u1_struct_0(sk2(A,B))
& m1_group_2(sk2(A,B),A)
& v1_group_1(sk2(A,B)) )
| B = k1_latsubgr(A) )
& ( k1_funct_1(B,C) = u1_struct_0(C)
| ~ m1_group_2(C,A)
| ~ v1_group_1(C)
| B != k1_latsubgr(A) ) )
| ~ m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_funct_1(B)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f7_nnf]) ).
cnf(c19,plain,
( k1_funct_1(X1,X2) = u1_struct_0(X2)
| ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| X1 != k1_latsubgr(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)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p116,plain,
( k1_funct_1(X0,X1) = u1_struct_0(X1)
| ~ m1_group_2(X1,sk0)
| ~ v1_group_1(X1)
| X0 != k1_latsubgr(sk0)
| ~ m2_relset_1(X0,k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| ~ v1_funct_2(X0,k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| ~ v1_funct_1(X0)
| ~ l1_group_1(sk0)
| ~ v4_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c19,c1]) ).
cnf(p118,plain,
( k1_funct_1(X0,X1) = u1_struct_0(X1)
| ~ m1_group_2(X1,sk0)
| ~ v1_group_1(X1)
| X0 != k1_latsubgr(sk0)
| ~ m2_relset_1(X0,k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| ~ v1_funct_2(X0,k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| ~ v1_funct_1(X0)
| ~ l1_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p116,c2]) ).
cnf(p120,plain,
( k1_funct_1(X0,X1) = u1_struct_0(X1)
| ~ m1_group_2(X1,sk0)
| ~ v1_group_1(X1)
| X0 != k1_latsubgr(sk0)
| ~ m2_relset_1(X0,k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| ~ v1_funct_2(X0,k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| ~ v1_funct_1(X0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p118,c3]) ).
cnf(p121,plain,
( k1_funct_1(k1_latsubgr(sk0),X0) = u1_struct_0(X0)
| ~ m1_group_2(X0,sk0)
| ~ v1_group_1(X0)
| ~ m2_relset_1(k1_latsubgr(sk0),k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| ~ v1_funct_2(k1_latsubgr(sk0),k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| ~ v1_funct_1(k1_latsubgr(sk0))
| v3_struct_0(sk0) ),
inference(equality_resolution,[status(thm)],[p120]) ).
cnf(p155,plain,
( k1_funct_1(k1_latsubgr(sk0),X0) = u1_struct_0(X0)
| ~ m1_group_2(X0,sk0)
| ~ v1_group_1(X0)
| ~ m2_relset_1(k1_latsubgr(sk0),k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| ~ v1_funct_2(k1_latsubgr(sk0),k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| v3_struct_0(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p153,p121]) ).
cnf(p164,plain,
( k1_funct_1(k1_latsubgr(sk0),X0) = u1_struct_0(X0)
| ~ m1_group_2(X0,sk0)
| ~ v1_group_1(X0)
| ~ m2_relset_1(k1_latsubgr(sk0),k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| ~ v1_funct_2(k1_latsubgr(sk0),k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p155]) ).
cnf(c28,plain,
( 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)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p158,plain,
( v1_funct_2(k1_latsubgr(sk0),k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| ~ l1_group_1(sk0)
| ~ v4_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c28,c1]) ).
cnf(p159,plain,
( v1_funct_2(k1_latsubgr(sk0),k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| ~ l1_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p158,c2]) ).
cnf(p160,plain,
( v1_funct_2(k1_latsubgr(sk0),k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p159,c3]) ).
cnf(p167,plain,
( v3_struct_0(sk0)
| k1_funct_1(k1_latsubgr(sk0),X0) = u1_struct_0(X0)
| ~ m1_group_2(X0,sk0)
| ~ v1_group_1(X0)
| ~ m2_relset_1(k1_latsubgr(sk0),k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p164,p160]) ).
cnf(p168,plain,
( k1_funct_1(k1_latsubgr(sk0),X0) = u1_struct_0(X0)
| ~ m1_group_2(X0,sk0)
| ~ v1_group_1(X0)
| ~ m2_relset_1(k1_latsubgr(sk0),k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p167]) ).
cnf(c29,plain,
( 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)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p161,plain,
( m2_relset_1(k1_latsubgr(sk0),k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| ~ l1_group_1(sk0)
| ~ v4_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c29,c1]) ).
cnf(p162,plain,
( m2_relset_1(k1_latsubgr(sk0),k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| ~ l1_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p161,c2]) ).
cnf(p163,plain,
( m2_relset_1(k1_latsubgr(sk0),k1_group_3(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p162,c3]) ).
cnf(p169,plain,
( v3_struct_0(sk0)
| k1_funct_1(k1_latsubgr(sk0),X0) = u1_struct_0(X0)
| ~ m1_group_2(X0,sk0)
| ~ v1_group_1(X0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p168,p163]) ).
cnf(p173,plain,
( k1_funct_1(k1_latsubgr(sk0),X0) = u1_struct_0(X0)
| ~ m1_group_2(X0,sk0)
| ~ v1_group_1(X0)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p169]) ).
cnf(c4,plain,
v1_group_1(sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p378,plain,
( k1_funct_1(k1_latsubgr(sk0),sk1) = u1_struct_0(sk1)
| ~ m1_group_2(sk1,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p173,c4]) ).
cnf(p379,plain,
( k1_funct_1(k1_latsubgr(sk0),sk1) = u1_struct_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p378,c5]) ).
cnf(c6,plain,
~ r2_hidden(k2_group_1(sk0),k1_funct_1(k1_latsubgr(sk0),sk1)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p380,plain,
( ~ r2_hidden(k2_group_1(sk0),u1_struct_0(sk1))
| v3_struct_0(sk0) ),
inference(superposition,[status(thm)],[p379,c6]) ).
cnf(p440,plain,
( v3_struct_0(sk0)
| v1_xboole_0(u1_struct_0(sk1))
| v3_struct_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p437,p380]) ).
cnf(p441,plain,
( v1_xboole_0(u1_struct_0(sk1))
| v3_struct_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p440]) ).
fof(f31,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f31_nnf,plain,
! [A] :
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [A] :
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c53,plain,
( ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
fof(f16,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f16_nnf,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c34,plain,
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p191,plain,
( l1_struct_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p189,c34]) ).
cnf(p248,plain,
( v3_struct_0(sk0)
| ~ v1_xboole_0(u1_struct_0(sk1))
| v3_struct_0(sk1) ),
inference(resolution,[status(thm)],[c53,p191]) ).
cnf(p443,plain,
( v3_struct_0(sk0)
| v3_struct_0(sk1)
| v3_struct_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p441,p248]) ).
cnf(p463,plain,
( v3_struct_0(sk1)
| v3_struct_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p443]) ).
cnf(p465,plain,
( v3_struct_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p463]) ).
cnf(c36,plain,
( ~ v3_struct_0(X1)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p170,plain,
( ~ v3_struct_0(X0)
| ~ m1_group_2(X0,sk0)
| ~ l1_group_1(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c36,c1]) ).
cnf(p171,plain,
( ~ v3_struct_0(X0)
| ~ m1_group_2(X0,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p170,c3]) ).
cnf(p172,plain,
( ~ v3_struct_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p171,c5]) ).
cnf(p466,plain,
( v3_struct_0(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p465,p172]) ).
cnf(p467,plain,
v3_struct_0(sk0),
inference(factoring,[status(thm)],[p466]) ).
cnf(c0,plain,
~ v3_struct_0(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p468,plain,
$false,
inference(resolution,[status(thm)],[p467,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP641+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 15:22:22 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.68/1.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.68/1.13 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------