%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU268+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n029.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 03:45:02 PM UTC 2025
% Result : Theorem 43.15s 5.76s
% Output : CNFRefutation 43.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 25 unt; 0 def)
% Number of atoms : 81 ( 18 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 71 ( 30 ~; 30 |; 2 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 3 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t2_wellord2,plain,
! [A] : reflexive(inclusion_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_wellord2) ).
fof(t2_wellord2_negated,plain,
~ ! [A] : reflexive(inclusion_relation(A)),
inference(negate_conjecture,[status(cth)],[t2_wellord2]) ).
cnf(73,plain,
~ reflexive(inclusion_relation(sK14)),
inference(cnf,[status(esa)],[t2_wellord2_negated]) ).
cnf(l0,plain,
~ reflexive(inclusion_relation(sK14)),
inference(instantiation,[status(thm)],[73]) ).
fof(d9_relat_2,plain,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
cnf(26,plain,
( ~ relation(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0) ),
inference(cnf,[status(esa)],[d9_relat_2]) ).
cnf(l1,plain,
( ~ relation(inclusion_relation(sK14))
| ~ is_reflexive_in(inclusion_relation(sK14),relation_field(inclusion_relation(sK14)))
| reflexive(inclusion_relation(sK14)) ),
inference(instantiation,[status(thm)],[26]) ).
fof(d1_relat_2,plain,
! [A] :
( relation(A)
=> ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(C,B)
=> in(ordered_pair(C,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).
cnf(13,plain,
( ~ in(ordered_pair(sK1(X0,X1),sK1(X0,X1)),X0)
| ~ relation(X0)
| is_reflexive_in(X0,X1) ),
inference(cnf,[status(esa)],[d1_relat_2]) ).
cnf(l3,plain,
( ~ in(ordered_pair(sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14)))),inclusion_relation(sK14))
| ~ relation(inclusion_relation(sK14))
| is_reflexive_in(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))) ),
inference(instantiation,[status(thm)],[13]) ).
fof(dt_k1_wellord2,plain,
! [A] : relation(inclusion_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
cnf(27,plain,
relation(inclusion_relation(X0)),
inference(cnf,[status(esa)],[dt_k1_wellord2]) ).
cnf(l2,plain,
relation(inclusion_relation(sK14)),
inference(instantiation,[status(thm)],[27]) ).
fof(d1_wellord2,plain,
! [A,B] :
( relation(B)
=> ( B = inclusion_relation(A)
<=> ( relation_field(B) = A
& ! [C,D] :
( ( in(C,A)
& in(D,A) )
=> ( in(ordered_pair(C,D),B)
<=> subset(C,D) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord2) ).
cnf(16,plain,
( ~ in(X0,X1)
| ~ in(X2,X1)
| X3 != inclusion_relation(X1)
| ~ relation(X3)
| ~ subset(X0,X2)
| in(ordered_pair(X0,X2),X3) ),
inference(cnf,[status(esa)],[d1_wellord2]) ).
cnf(l6,plain,
( ~ in(sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),sK14)
| ~ in(sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),sK14)
| inclusion_relation(sK14) != inclusion_relation(sK14)
| ~ relation(inclusion_relation(sK14))
| ~ subset(sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))))
| in(ordered_pair(sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14)))),inclusion_relation(sK14)) ),
inference(instantiation,[status(thm)],[16]) ).
fof(t1_boole,plain,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
cnf(70,plain,
set_union2(X0,empty_set) = X0,
inference(cnf,[status(esa)],[t1_boole]) ).
cnf(l562,plain,
set_union2(sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),empty_set) = sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),
inference(instantiation,[status(thm)],[70]) ).
fof(idempotence_k2_xboole_0,plain,
! [A,B] : set_union2(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
cnf(41,plain,
set_union2(X0,X0) = X0,
inference(cnf,[status(esa)],[idempotence_k2_xboole_0]) ).
cnf(l23,plain,
set_union2(sK14,sK14) = sK14,
inference(instantiation,[status(thm)],[41]) ).
cnf(l557,plain,
relation(inclusion_relation(sK14)),
inference(instantiation,[status(thm)],[27]) ).
cnf(12,plain,
( ~ relation(X0)
| in(sK1(X0,X1),X1)
| is_reflexive_in(X0,X1) ),
inference(cnf,[status(esa)],[d1_relat_2]) ).
cnf(l332,plain,
( ~ relation(inclusion_relation(sK14))
| in(sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),relation_field(inclusion_relation(sK14)))
| is_reflexive_in(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l333,plain,
relation(inclusion_relation(sK14)),
inference(instantiation,[status(thm)],[27]) ).
fof(reflexivity_r1_tarski,plain,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
cnf(69,plain,
subset(X0,X0),
inference(cnf,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(l563,plain,
subset(set_union2(sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),empty_set),set_union2(sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),empty_set)),
inference(instantiation,[status(thm)],[69]) ).
cnf(14,plain,
( X0 != inclusion_relation(X1)
| ~ relation(X0)
| relation_field(X0) = X1 ),
inference(cnf,[status(esa)],[d1_wellord2]) ).
cnf(l251,plain,
( inclusion_relation(sK14) != inclusion_relation(sK14)
| ~ relation(inclusion_relation(sK14))
| relation_field(inclusion_relation(sK14)) = sK14 ),
inference(instantiation,[status(thm)],[14]) ).
cnf(l62,plain,
relation(inclusion_relation(set_union2(set_union2(sK14,sK14),set_union2(sK14,sK14)))),
inference(instantiation,[status(thm)],[27]) ).
cnf(l218,plain,
( ~ relation(inclusion_relation(sK14))
| in(sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),relation_field(inclusion_relation(sK14)))
| is_reflexive_in(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l252,plain,
relation(inclusion_relation(sK14)),
inference(instantiation,[status(thm)],[27]) ).
cnf(l572,plain,
set_union2(sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),empty_set) = sK1(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),
inference(instantiation,[status(thm)],[70]) ).
cnf(l353,plain,
relation(inclusion_relation(sK14)),
inference(instantiation,[status(thm)],[27]) ).
cnf(l63,plain,
set_union2(set_union2(sK14,sK14),set_union2(sK14,sK14)) = set_union2(sK14,sK14),
inference(instantiation,[status(thm)],[41]) ).
cnf(l75,plain,
( inclusion_relation(sK14) != inclusion_relation(sK14)
| ~ relation(inclusion_relation(sK14))
| relation_field(inclusion_relation(sK14)) = sK14 ),
inference(instantiation,[status(thm)],[14]) ).
cnf(l79,plain,
relation(inclusion_relation(sK14)),
inference(instantiation,[status(thm)],[27]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l2,l6,l562,l23,l557,l332,l333,l563,l251,l62,l218,l252,l572,l353,l63,l75,l79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU268+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Jul 22 00:24:04 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % launching worker at depth: 7
% 0.13/0.34 % launching worker at depth: 2
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 3
% 0.13/0.34 % launching worker at depth: 4
% 0.13/0.34 % launching worker at depth: 5
% 0.13/0.34 % launching worker at depth: 6
% 0.13/0.34 % launching worker at depth: 8
% 0.13/0.34 % launching worker at depth: 9
% 0.13/0.34 % launching worker at depth: 10
% 0.13/0.34 % launching worker at depth: 11
% 0.20/0.37 % launching worker at depth: 12
% 4.13/0.84 % launching worker at depth: 13
% 43.15/5.76 % SZS status Theorem for theBenchmark
% 43.15/5.76 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------