%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : LAT327+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n024.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 10:34:29 PM UTC 2025
% Result : Theorem 6.93s 1.23s
% Output : CNFRefutation 6.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 73 ( 51 unt; 0 def)
% Number of atoms : 189 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 198 ( 82 ~; 77 |; 22 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 27 ( 1 sgn 15 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t64_filter_2,plain,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_lattices(A,B,C)
=> ( r2_hidden(B,k22_filter_2(A,B,C))
& r2_hidden(C,k22_filter_2(A,B,C)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_filter_2) ).
fof(t64_filter_2_negated,plain,
~ ! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_lattices(A,B,C)
=> ( r2_hidden(B,k22_filter_2(A,B,C))
& r2_hidden(C,k22_filter_2(A,B,C)) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t64_filter_2]) ).
cnf(6,plain,
( ~ r2_hidden(sK2,k22_filter_2(sK1,sK2,sK3))
| ~ r2_hidden(sK3,k22_filter_2(sK1,sK2,sK3)) ),
inference(cnf,[status(esa)],[t64_filter_2_negated]) ).
cnf(l0,plain,
( ~ r2_hidden(sK2,k22_filter_2(sK1,sK2,sK3))
| ~ r2_hidden(sK3,k22_filter_2(sK1,sK2,sK3)) ),
inference(instantiation,[status(thm)],[6]) ).
fof(t63_filter_2,plain,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_lattices(A,B,C)
=> ( r2_hidden(D,k22_filter_2(A,B,C))
<=> ( r3_lattices(A,B,D)
& r3_lattices(A,D,C) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_filter_2) ).
cnf(59,plain,
( ~ l3_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ v10_lattices(X0)
| ~ r3_lattices(X0,X1,X2)
| ~ r3_lattices(X0,X1,X3)
| ~ r3_lattices(X0,X3,X2)
| v3_struct_0(X0)
| r2_hidden(X3,k22_filter_2(X0,X1,X2)) ),
inference(cnf,[status(esa)],[t63_filter_2]) ).
cnf(l1,plain,
( ~ l3_lattices(sK1)
| ~ m1_subset_1(sK2,u1_struct_0(sK1))
| ~ m1_subset_1(sK3,u1_struct_0(sK1))
| ~ m1_subset_1(sK2,u1_struct_0(sK1))
| ~ v10_lattices(sK1)
| ~ r3_lattices(sK1,sK2,sK3)
| ~ r3_lattices(sK1,sK2,sK2)
| ~ r3_lattices(sK1,sK2,sK3)
| v3_struct_0(sK1)
| r2_hidden(sK2,k22_filter_2(sK1,sK2,sK3)) ),
inference(instantiation,[status(thm)],[59]) ).
cnf(l614,plain,
( ~ l3_lattices(sK1)
| ~ m1_subset_1(sK2,u1_struct_0(sK1))
| ~ m1_subset_1(sK3,u1_struct_0(sK1))
| ~ m1_subset_1(sK3,u1_struct_0(sK1))
| ~ v10_lattices(sK1)
| ~ r3_lattices(sK1,sK2,sK3)
| ~ r3_lattices(sK1,sK2,sK3)
| ~ r3_lattices(sK1,sK3,sK3)
| v3_struct_0(sK1)
| r2_hidden(sK3,k22_filter_2(sK1,sK2,sK3)) ),
inference(instantiation,[status(thm)],[59]) ).
cnf(3,plain,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(cnf,[status(esa)],[t64_filter_2_negated]) ).
cnf(l663,plain,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(instantiation,[status(thm)],[3]) ).
cnf(0,plain,
~ v3_struct_0(sK1),
inference(cnf,[status(esa)],[t64_filter_2_negated]) ).
cnf(l617,plain,
~ v3_struct_0(sK1),
inference(instantiation,[status(thm)],[0]) ).
fof(reflexivity_r3_lattices,plain,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> r3_lattices(A,B,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
cnf(40,plain,
( ~ l3_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ v6_lattices(X0)
| ~ v8_lattices(X0)
| ~ v9_lattices(X0)
| v3_struct_0(X0)
| r3_lattices(X0,X1,X1) ),
inference(cnf,[status(esa)],[reflexivity_r3_lattices]) ).
cnf(l79,plain,
( ~ l3_lattices(sK1)
| ~ m1_subset_1(sK2,u1_struct_0(sK1))
| ~ m1_subset_1(sK2,u1_struct_0(sK1))
| ~ v6_lattices(sK1)
| ~ v8_lattices(sK1)
| ~ v9_lattices(sK1)
| v3_struct_0(sK1)
| r3_lattices(sK1,sK2,sK2) ),
inference(instantiation,[status(thm)],[40]) ).
fof(cc1_lattices,plain,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A) )
=> ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
cnf(54,plain,
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v9_lattices(X0) ),
inference(cnf,[status(esa)],[cc1_lattices]) ).
cnf(l268,plain,
( ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| v3_struct_0(sK1)
| v9_lattices(sK1) ),
inference(instantiation,[status(thm)],[54]) ).
cnf(l3,plain,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(instantiation,[status(thm)],[3]) ).
cnf(53,plain,
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v8_lattices(X0) ),
inference(cnf,[status(esa)],[cc1_lattices]) ).
cnf(l272,plain,
( ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| v3_struct_0(sK1)
| v8_lattices(sK1) ),
inference(instantiation,[status(thm)],[53]) ).
cnf(1,plain,
v10_lattices(sK1),
inference(cnf,[status(esa)],[t64_filter_2_negated]) ).
cnf(l618,plain,
v10_lattices(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(51,plain,
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v6_lattices(X0) ),
inference(cnf,[status(esa)],[cc1_lattices]) ).
cnf(l270,plain,
( ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| v3_struct_0(sK1)
| v6_lattices(sK1) ),
inference(instantiation,[status(thm)],[51]) ).
cnf(2,plain,
l3_lattices(sK1),
inference(cnf,[status(esa)],[t64_filter_2_negated]) ).
cnf(l2,plain,
l3_lattices(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(l294,plain,
~ v3_struct_0(sK1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l105,plain,
l3_lattices(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(4,plain,
m1_subset_1(sK3,u1_struct_0(sK1)),
inference(cnf,[status(esa)],[t64_filter_2_negated]) ).
cnf(l80,plain,
m1_subset_1(sK3,u1_struct_0(sK1)),
inference(instantiation,[status(thm)],[4]) ).
cnf(l269,plain,
~ v3_struct_0(sK1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l10,plain,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(instantiation,[status(thm)],[3]) ).
cnf(l655,plain,
m1_subset_1(sK3,u1_struct_0(sK1)),
inference(instantiation,[status(thm)],[4]) ).
cnf(l286,plain,
l3_lattices(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(5,plain,
r3_lattices(sK1,sK2,sK3),
inference(cnf,[status(esa)],[t64_filter_2_negated]) ).
cnf(l616,plain,
r3_lattices(sK1,sK2,sK3),
inference(instantiation,[status(thm)],[5]) ).
cnf(l275,plain,
l3_lattices(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(l296,plain,
v10_lattices(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(l81,plain,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(instantiation,[status(thm)],[3]) ).
cnf(l84,plain,
r3_lattices(sK1,sK2,sK3),
inference(instantiation,[status(thm)],[5]) ).
cnf(l271,plain,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(instantiation,[status(thm)],[3]) ).
cnf(l369,plain,
r3_lattices(sK1,sK2,sK3),
inference(instantiation,[status(thm)],[5]) ).
cnf(l283,plain,
~ v3_struct_0(sK1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l91,plain,
~ v3_struct_0(sK1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l299,plain,
l3_lattices(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(l273,plain,
v10_lattices(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(l628,plain,
l3_lattices(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(l307,plain,
~ v3_struct_0(sK1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l92,plain,
v10_lattices(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(l656,plain,
r3_lattices(sK1,sK2,sK3),
inference(instantiation,[status(thm)],[5]) ).
cnf(l642,plain,
m1_subset_1(sK3,u1_struct_0(sK1)),
inference(instantiation,[status(thm)],[4]) ).
cnf(l284,plain,
v10_lattices(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(l625,plain,
( ~ l3_lattices(sK1)
| ~ m1_subset_1(sK3,u1_struct_0(sK1))
| ~ m1_subset_1(sK16(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v6_lattices(sK1)
| ~ v8_lattices(sK1)
| ~ v9_lattices(sK1)
| v3_struct_0(sK1)
| r3_lattices(sK1,sK3,sK3) ),
inference(instantiation,[status(thm)],[40]) ).
fof(existence_m1_subset_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
cnf(42,plain,
m1_subset_1(sK16(X0),X0),
inference(cnf,[status(esa)],[existence_m1_subset_1]) ).
cnf(l724,plain,
m1_subset_1(sK16(u1_struct_0(sK1)),u1_struct_0(sK1)),
inference(instantiation,[status(thm)],[42]) ).
cnf(l710,plain,
( ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| v3_struct_0(sK1)
| v8_lattices(sK1) ),
inference(instantiation,[status(thm)],[53]) ).
cnf(l723,plain,
l3_lattices(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(l627,plain,
( ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| v3_struct_0(sK1)
| v9_lattices(sK1) ),
inference(instantiation,[status(thm)],[54]) ).
cnf(l732,plain,
( ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| v3_struct_0(sK1)
| v6_lattices(sK1) ),
inference(instantiation,[status(thm)],[51]) ).
cnf(l748,plain,
l3_lattices(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(l786,plain,
l3_lattices(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(l741,plain,
~ v3_struct_0(sK1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l752,plain,
~ v3_struct_0(sK1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l725,plain,
l3_lattices(sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(l745,plain,
~ v3_struct_0(sK1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l728,plain,
m1_subset_1(sK3,u1_struct_0(sK1)),
inference(instantiation,[status(thm)],[4]) ).
cnf(l722,plain,
v10_lattices(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(l727,plain,
~ v3_struct_0(sK1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l746,plain,
v10_lattices(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(l751,plain,
v10_lattices(sK1),
inference(instantiation,[status(thm)],[1]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l614,l663,l617,l79,l268,l3,l272,l618,l270,l2,l294,l105,l80,l269,l10,l655,l286,l616,l275,l296,l81,l84,l271,l369,l283,l91,l299,l273,l628,l307,l92,l656,l642,l284,l625,l724,l710,l723,l627,l732,l748,l786,l741,l752,l725,l745,l728,l722,l727,l746,l751]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT327+1 : TPTP v9.0.0. Released v3.4.0.
% 0.06/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 21 00:43:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 3
% 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: 8
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.35 % launching worker at depth: 10
% 0.18/0.45 % launching worker at depth: 11
% 6.93/1.23 % SZS status Theorem for theBenchmark
% 6.93/1.23 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------