%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM388+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 12:28:03 PM UTC 2025
% Result : Theorem 3.53s 0.82s
% Output : CNFRefutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 13 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 67 ( 25 ~; 22 |; 6 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 35 ( 2 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t19_ordinal1,plain,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( epsilon_transitive(C)
=> ( ( in(C,A)
& in(A,B) )
=> in(C,B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_ordinal1) ).
fof(t19_ordinal1_negated,plain,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( epsilon_transitive(C)
=> ( ( in(C,A)
& in(A,B) )
=> in(C,B) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t19_ordinal1]) ).
cnf(46,plain,
in(sK16,sK14),
inference(cnf,[status(esa)],[t19_ordinal1_negated]) ).
cnf(l0,plain,
in(sK16,sK14),
inference(instantiation,[status(thm)],[46]) ).
fof(t4_subset,plain,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
cnf(53,plain,
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| element(X0,X2) ),
inference(cnf,[status(esa)],[t4_subset]) ).
cnf(l1,plain,
( ~ in(sK16,sK14)
| ~ element(sK14,powerset(sK15))
| element(sK16,sK15) ),
inference(instantiation,[status(thm)],[53]) ).
fof(t3_subset,plain,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
cnf(52,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf,[status(esa)],[t3_subset]) ).
cnf(l2,plain,
( ~ subset(sK14,sK15)
| element(sK14,powerset(sK15)) ),
inference(instantiation,[status(thm)],[52]) ).
fof(d2_ordinal1,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
cnf(7,plain,
( ~ in(X0,X1)
| ~ epsilon_transitive(X1)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[d2_ordinal1]) ).
cnf(l3,plain,
( ~ in(sK14,sK15)
| ~ epsilon_transitive(sK15)
| subset(sK14,sK15) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(47,plain,
in(sK14,sK15),
inference(cnf,[status(esa)],[t19_ordinal1_negated]) ).
cnf(l5,plain,
in(sK14,sK15),
inference(instantiation,[status(thm)],[47]) ).
fof(cc1_ordinal1,plain,
! [A] :
( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
cnf(2,plain,
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf,[status(esa)],[cc1_ordinal1]) ).
cnf(l17,plain,
( ~ ordinal(sK15)
| epsilon_transitive(sK15) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(44,plain,
ordinal(sK15),
inference(cnf,[status(esa)],[t19_ordinal1_negated]) ).
cnf(l18,plain,
ordinal(sK15),
inference(instantiation,[status(thm)],[44]) ).
fof(t2_subset,plain,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
cnf(50,plain,
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf,[status(esa)],[t2_subset]) ).
cnf(l30,plain,
( ~ element(sK16,sK15)
| empty(sK15)
| in(sK16,sK15) ),
inference(instantiation,[status(thm)],[50]) ).
cnf(48,plain,
~ in(sK16,sK15),
inference(cnf,[status(esa)],[t19_ordinal1_negated]) ).
cnf(l31,plain,
~ in(sK16,sK15),
inference(instantiation,[status(thm)],[48]) ).
fof(t5_subset,plain,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
cnf(54,plain,
( ~ empty(X0)
| ~ in(X1,X2)
| ~ element(X2,powerset(X0)) ),
inference(cnf,[status(esa)],[t5_subset]) ).
cnf(l58,plain,
( ~ empty(sK15)
| ~ in(sK14,sK15)
| ~ element(sK15,powerset(sK15)) ),
inference(instantiation,[status(thm)],[54]) ).
cnf(l102,plain,
in(sK14,sK15),
inference(instantiation,[status(thm)],[47]) ).
cnf(l59,plain,
( ~ subset(sK15,sK15)
| element(sK15,powerset(sK15)) ),
inference(instantiation,[status(thm)],[52]) ).
fof(reflexivity_r1_tarski,plain,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
cnf(42,plain,
subset(X0,X0),
inference(cnf,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(l61,plain,
subset(sK15,sK15),
inference(instantiation,[status(thm)],[42]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l5,l17,l18,l30,l31,l58,l102,l59,l61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM388+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 21 11:54:34 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % launching worker at depth: 3
% 0.13/0.35 % launching worker at depth: 5
% 0.13/0.35 % launching worker at depth: 2
% 0.13/0.35 % launching worker at depth: 1
% 0.13/0.35 % launching worker at depth: 4
% 0.13/0.35 % launching worker at depth: 6
% 0.13/0.35 % launching worker at depth: 7
% 0.13/0.35 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.35 % launching worker at depth: 10
% 0.13/0.37 % launching worker at depth: 11
% 0.20/0.45 % launching worker at depth: 12
% 3.53/0.82 % SZS status Theorem for theBenchmark
% 3.53/0.82 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------