%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM390+1 : TPTP v9.0.0. Released v3.2.0.
% 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 : Fri Jul 25 12:28:04 PM UTC 2025
% Result : Theorem 17.86s 2.59s
% Output : CNFRefutation 17.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 13 unt; 0 def)
% Number of atoms : 77 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 27 ~; 22 |; 6 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 30 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t22_ordinal1,plain,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ordinal(C)
=> ( ( subset(A,B)
& in(B,C) )
=> in(A,C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_ordinal1) ).
fof(t22_ordinal1_negated,plain,
~ ! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ordinal(C)
=> ( ( subset(A,B)
& in(B,C) )
=> in(A,C) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t22_ordinal1]) ).
cnf(53,plain,
ordinal(sK16),
inference(cnf,[status(esa)],[t22_ordinal1_negated]) ).
cnf(l0,plain,
ordinal(sK16),
inference(instantiation,[status(thm)],[53]) ).
fof(t21_ordinal1,plain,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_ordinal1) ).
cnf(50,plain,
( ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0)
| in(X0,X1) ),
inference(cnf,[status(esa)],[t21_ordinal1]) ).
cnf(l1,plain,
( ~ proper_subset(sK14,sK16)
| ~ ordinal(sK16)
| ~ epsilon_transitive(sK14)
| in(sK14,sK16) ),
inference(instantiation,[status(thm)],[50]) ).
fof(d8_xboole_0,plain,
! [A,B] :
( proper_subset(A,B)
<=> ( subset(A,B)
& A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
cnf(13,plain,
( ~ subset(X0,X1)
| proper_subset(X0,X1)
| X0 = X1 ),
inference(cnf,[status(esa)],[d8_xboole_0]) ).
cnf(l2,plain,
( ~ subset(sK14,sK16)
| proper_subset(sK14,sK16)
| sK14 = sK16 ),
inference(instantiation,[status(thm)],[13]) ).
fof(t1_xboole_1,plain,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
cnf(49,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| subset(X0,X2) ),
inference(cnf,[status(esa)],[t1_xboole_1]) ).
cnf(l7,plain,
( ~ subset(sK14,sK15)
| ~ subset(sK15,sK16)
| subset(sK14,sK16) ),
inference(instantiation,[status(thm)],[49]) ).
cnf(54,plain,
subset(sK14,sK15),
inference(cnf,[status(esa)],[t22_ordinal1_negated]) ).
cnf(l19,plain,
subset(sK14,sK15),
inference(instantiation,[status(thm)],[54]) ).
cnf(51,plain,
epsilon_transitive(sK14),
inference(cnf,[status(esa)],[t22_ordinal1_negated]) ).
cnf(l3,plain,
epsilon_transitive(sK14),
inference(instantiation,[status(thm)],[51]) ).
fof(d2_ordinal1,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
cnf(8,plain,
( ~ in(X0,X1)
| ~ epsilon_transitive(X1)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[d2_ordinal1]) ).
cnf(l9,plain,
( ~ in(sK15,sK16)
| ~ epsilon_transitive(sK16)
| subset(sK15,sK16) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(56,plain,
~ in(sK14,sK16),
inference(cnf,[status(esa)],[t22_ordinal1_negated]) ).
cnf(l140,plain,
~ in(sK14,sK16),
inference(instantiation,[status(thm)],[56]) ).
fof(cc1_ordinal1,plain,
! [A] :
( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
cnf(3,plain,
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf,[status(esa)],[cc1_ordinal1]) ).
cnf(l14,plain,
( ~ ordinal(sK16)
| epsilon_transitive(sK16) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(55,plain,
in(sK15,sK16),
inference(cnf,[status(esa)],[t22_ordinal1_negated]) ).
cnf(l17,plain,
in(sK15,sK16),
inference(instantiation,[status(thm)],[55]) ).
cnf(l113,plain,
subset(sK14,sK15),
inference(instantiation,[status(thm)],[54]) ).
fof(t7_ordinal1,plain,
! [A,B] :
~ ( in(A,B)
& subset(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
cnf(64,plain,
( ~ in(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf,[status(esa)],[t7_ordinal1]) ).
cnf(l161,plain,
( ~ in(sK15,sK16)
| ~ subset(sK16,sK15) ),
inference(instantiation,[status(thm)],[64]) ).
cnf(l166,plain,
in(sK15,sK16),
inference(instantiation,[status(thm)],[55]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l7,l19,l3,l9,l140,l14,l17,l113,l161,l166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : NUM390+1 : TPTP v9.0.0. Released v3.2.0.
% 0.05/0.09 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.29 % Computer : n021.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Jul 21 11:54:34 EDT 2025
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % launching worker at depth: 2
% 0.09/0.30 % launching worker at depth: 4
% 0.09/0.30 % launching worker at depth: 3
% 0.09/0.30 % launching worker at depth: 1
% 0.09/0.30 % launching worker at depth: 7
% 0.09/0.30 % launching worker at depth: 5
% 0.09/0.30 % launching worker at depth: 8
% 0.09/0.30 % launching worker at depth: 6
% 0.09/0.30 % launching worker at depth: 9
% 0.09/0.30 % launching worker at depth: 10
% 0.14/0.33 % launching worker at depth: 11
% 2.21/0.58 % launching worker at depth: 12
% 17.86/2.59 % SZS status Theorem for theBenchmark
% 17.86/2.59 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------