%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GRP645+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Jul 24 06:27:45 PM UTC 2025
% Result : Theorem 17.40s 2.57s
% Output : CNFRefutation 17.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 75 ( 51 unt; 0 def)
% Number of atoms : 230 ( 17 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 252 ( 97 ~; 102 |; 37 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 37 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t24_latsubgr,plain,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& m1_group_2(B,A) )
=> ! [C] :
( ( v1_group_1(C)
& m1_group_2(C,A) )
=> k1_funct_1(k1_latsubgr(A),k9_group_2(A,B,C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A),B),k1_funct_1(k1_latsubgr(A),C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_latsubgr) ).
fof(t24_latsubgr_negated,plain,
~ ! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& m1_group_2(B,A) )
=> ! [C] :
( ( v1_group_1(C)
& m1_group_2(C,A) )
=> k1_funct_1(k1_latsubgr(A),k9_group_2(A,B,C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A),B),k1_funct_1(k1_latsubgr(A),C)) ) ) ),
inference(negate_conjecture,[status(cth)],[t24_latsubgr]) ).
cnf(0,plain,
~ v3_struct_0(sK1),
inference(cnf,[status(esa)],[t24_latsubgr_negated]) ).
cnf(l0,plain,
~ v3_struct_0(sK1),
inference(instantiation,[status(thm)],[0]) ).
fof(dt_k1_latsubgr,plain,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_funct_1(k1_latsubgr(A))
& v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_latsubgr) ).
cnf(25,plain,
( ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0)
| v3_struct_0(X0)
| v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf,[status(esa)],[dt_k1_latsubgr]) ).
cnf(l1,plain,
( ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ l1_group_1(sK1)
| v3_struct_0(sK1)
| v1_funct_2(k1_latsubgr(sK1),k1_group_3(sK1),k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(instantiation,[status(thm)],[25]) ).
cnf(3,plain,
l1_group_1(sK1),
inference(cnf,[status(esa)],[t24_latsubgr_negated]) ).
cnf(l6,plain,
l1_group_1(sK1),
inference(instantiation,[status(thm)],[3]) ).
cnf(2,plain,
v4_group_1(sK1),
inference(cnf,[status(esa)],[t24_latsubgr_negated]) ).
cnf(l3,plain,
v4_group_1(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(1,plain,
v3_group_1(sK1),
inference(cnf,[status(esa)],[t24_latsubgr_negated]) ).
cnf(l2,plain,
v3_group_1(sK1),
inference(instantiation,[status(thm)],[1]) ).
fof(d1_latsubgr,plain,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) )
=> ( B = k1_latsubgr(A)
<=> ! [C] :
( ( v1_group_1(C)
& m1_group_2(C,A) )
=> k1_funct_1(B,C) = u1_struct_0(C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_latsubgr) ).
cnf(18,plain,
( X0 != k1_latsubgr(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X1)
| ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ~ m2_relset_1(X0,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| k1_funct_1(X0,X2) = u1_struct_0(X2)
| v3_struct_0(X1) ),
inference(cnf,[status(esa)],[d1_latsubgr]) ).
cnf(l39,plain,
( k1_latsubgr(sK1) != k1_latsubgr(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ v1_group_1(k9_group_2(sK1,sK2,sK3))
| ~ m1_group_2(k9_group_2(sK1,sK2,sK3),sK1)
| ~ v1_funct_1(k1_latsubgr(sK1))
| ~ v1_funct_2(k1_latsubgr(sK1),k1_group_3(sK1),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m2_relset_1(k1_latsubgr(sK1),k1_group_3(sK1),k1_zfmisc_1(u1_struct_0(sK1)))
| k1_funct_1(k1_latsubgr(sK1),k9_group_2(sK1,sK2,sK3)) = u1_struct_0(k9_group_2(sK1,sK2,sK3))
| v3_struct_0(sK1) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(l75,plain,
v4_group_1(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(l57,plain,
l1_group_1(sK1),
inference(instantiation,[status(thm)],[3]) ).
cnf(24,plain,
( ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0)
| v3_struct_0(X0)
| v1_funct_1(k1_latsubgr(X0)) ),
inference(cnf,[status(esa)],[dt_k1_latsubgr]) ).
cnf(l104,plain,
( ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ l1_group_1(sK1)
| v3_struct_0(sK1)
| v1_funct_1(k1_latsubgr(sK1)) ),
inference(instantiation,[status(thm)],[24]) ).
cnf(l80,plain,
v3_group_1(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(26,plain,
( ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0)
| v3_struct_0(X0)
| m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf,[status(esa)],[dt_k1_latsubgr]) ).
cnf(l105,plain,
( ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ l1_group_1(sK1)
| v3_struct_0(sK1)
| m2_relset_1(k1_latsubgr(sK1),k1_group_3(sK1),k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(l430,plain,
v3_group_1(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(l429,plain,
l1_group_1(sK1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l107,plain,
v4_group_1(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(l285,plain,
l1_group_1(sK1),
inference(instantiation,[status(thm)],[3]) ).
fof(dt_k9_group_2,plain,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_group_2(B,A)
& m1_group_2(C,A) )
=> ( v1_group_1(k9_group_2(A,B,C))
& m1_group_2(k9_group_2(A,B,C),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_group_2) ).
cnf(29,plain,
( ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0)
| v3_struct_0(X0)
| v1_group_1(k9_group_2(X0,X1,X2)) ),
inference(cnf,[status(esa)],[dt_k9_group_2]) ).
cnf(l99,plain,
( ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_group_2(sK3,sK1)
| ~ m1_group_2(sK2,sK1)
| v3_struct_0(sK1)
| v1_group_1(k9_group_2(sK1,sK3,sK2)) ),
inference(instantiation,[status(thm)],[29]) ).
cnf(8,plain,
k1_funct_1(k1_latsubgr(sK1),k9_group_2(sK1,sK2,sK3)) != k3_xboole_0(k1_funct_1(k1_latsubgr(sK1),sK2),k1_funct_1(k1_latsubgr(sK1),sK3)),
inference(cnf,[status(esa)],[t24_latsubgr_negated]) ).
cnf(l92,plain,
k1_funct_1(k1_latsubgr(sK1),k9_group_2(sK1,sK2,sK3)) != k3_xboole_0(k1_funct_1(k1_latsubgr(sK1),sK2),k1_funct_1(k1_latsubgr(sK1),sK3)),
inference(instantiation,[status(thm)],[8]) ).
cnf(l278,plain,
v4_group_1(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(l204,plain,
l1_group_1(sK1),
inference(instantiation,[status(thm)],[3]) ).
fof(t23_latsubgr,plain,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& m1_group_2(B,A) )
=> ! [C] :
( ( v1_group_1(C)
& m1_group_2(C,A) )
=> u1_struct_0(k9_group_2(A,B,C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A),B),k1_funct_1(k1_latsubgr(A),C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_latsubgr) ).
cnf(75,plain,
( ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_group_1(X1)
| ~ v1_group_1(X2)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0)
| u1_struct_0(k9_group_2(X0,X1,X2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),X2))
| v3_struct_0(X0) ),
inference(cnf,[status(esa)],[t23_latsubgr]) ).
cnf(l93,plain,
( ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ v1_group_1(sK2)
| ~ v1_group_1(sK3)
| ~ m1_group_2(sK2,sK1)
| ~ m1_group_2(sK3,sK1)
| u1_struct_0(k9_group_2(sK1,sK2,sK3)) = k3_xboole_0(k1_funct_1(k1_latsubgr(sK1),sK2),k1_funct_1(k1_latsubgr(sK1),sK3))
| v3_struct_0(sK1) ),
inference(instantiation,[status(thm)],[75]) ).
cnf(l201,plain,
v3_group_1(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(l989,plain,
l1_group_1(sK1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l96,plain,
v4_group_1(sK1),
inference(instantiation,[status(thm)],[2]) ).
fof(commutativity_k9_group_2,plain,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_group_2(B,A)
& m1_group_2(C,A) )
=> k9_group_2(A,B,C) = k9_group_2(A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k9_group_2) ).
cnf(17,plain,
( ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0)
| k9_group_2(X0,X1,X2) = k9_group_2(X0,X2,X1)
| v3_struct_0(X0) ),
inference(cnf,[status(esa)],[commutativity_k9_group_2]) ).
cnf(l62,plain,
( ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_group_2(sK3,sK1)
| ~ m1_group_2(sK2,sK1)
| k9_group_2(sK1,sK3,sK2) = k9_group_2(sK1,sK2,sK3)
| v3_struct_0(sK1) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(l286,plain,
v3_group_1(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(l242,plain,
v4_group_1(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(4,plain,
v1_group_1(sK2),
inference(cnf,[status(esa)],[t24_latsubgr_negated]) ).
cnf(l1246,plain,
v1_group_1(sK2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l98,plain,
v3_group_1(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(l261,plain,
v3_group_1(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(7,plain,
m1_group_2(sK3,sK1),
inference(cnf,[status(esa)],[t24_latsubgr_negated]) ).
cnf(l209,plain,
m1_group_2(sK3,sK1),
inference(instantiation,[status(thm)],[7]) ).
cnf(l1256,plain,
m1_group_2(sK3,sK1),
inference(instantiation,[status(thm)],[7]) ).
cnf(l205,plain,
v4_group_1(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(5,plain,
m1_group_2(sK2,sK1),
inference(cnf,[status(esa)],[t24_latsubgr_negated]) ).
cnf(l449,plain,
m1_group_2(sK2,sK1),
inference(instantiation,[status(thm)],[5]) ).
cnf(l1252,plain,
m1_group_2(sK2,sK1),
inference(instantiation,[status(thm)],[5]) ).
cnf(6,plain,
v1_group_1(sK3),
inference(cnf,[status(esa)],[t24_latsubgr_negated]) ).
cnf(l995,plain,
v1_group_1(sK3),
inference(instantiation,[status(thm)],[6]) ).
cnf(l100,plain,
m1_group_2(sK2,sK1),
inference(instantiation,[status(thm)],[5]) ).
cnf(l112,plain,
( ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_group_2(sK3,sK1)
| ~ m1_group_2(sK2,sK1)
| k9_group_2(sK1,sK3,sK2) = k9_group_2(sK1,sK2,sK3)
| v3_struct_0(sK1) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(30,plain,
( ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0)
| v3_struct_0(X0)
| m1_group_2(k9_group_2(X0,X1,X2),X0) ),
inference(cnf,[status(esa)],[dt_k9_group_2]) ).
cnf(l293,plain,
( ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| ~ l1_group_1(sK1)
| ~ m1_group_2(sK3,sK1)
| ~ m1_group_2(sK2,sK1)
| v3_struct_0(sK1)
| m1_group_2(k9_group_2(sK1,sK3,sK2),sK1) ),
inference(instantiation,[status(thm)],[30]) ).
cnf(l340,plain,
l1_group_1(sK1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l472,plain,
l1_group_1(sK1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l471,plain,
m1_group_2(sK3,sK1),
inference(instantiation,[status(thm)],[7]) ).
cnf(l299,plain,
v3_group_1(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(l1250,plain,
m1_group_2(sK2,sK1),
inference(instantiation,[status(thm)],[5]) ).
cnf(l1234,plain,
m1_group_2(sK3,sK1),
inference(instantiation,[status(thm)],[7]) ).
cnf(l1235,plain,
l1_group_1(sK1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l367,plain,
m1_group_2(sK3,sK1),
inference(instantiation,[status(thm)],[7]) ).
cnf(l114,plain,
v4_group_1(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(l475,plain,
v4_group_1(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(l474,plain,
v3_group_1(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(l344,plain,
m1_group_2(sK2,sK1),
inference(instantiation,[status(thm)],[5]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l6,l3,l2,l39,l75,l57,l104,l80,l105,l430,l429,l107,l285,l99,l92,l278,l204,l93,l201,l989,l96,l62,l286,l242,l1246,l98,l261,l209,l1256,l205,l449,l1252,l995,l100,l112,l293,l340,l472,l471,l299,l1250,l1234,l1235,l367,l114,l475,l474,l344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP645+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Jul 20 16:23:04 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 8
% 0.18/0.35 % launching worker at depth: 9
% 0.18/0.36 % launching worker at depth: 10
% 1.92/0.62 % launching worker at depth: 11
% 17.40/2.57 % SZS status Theorem for theBenchmark
% 17.40/2.57 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------