%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU244+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 : 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 : Fri Jul 25 03:44:58 PM UTC 2025
% Result : Theorem 1.80s 0.57s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 90 ( 24 unt; 0 def)
% Number of atoms : 233 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 252 ( 109 ~; 117 |; 8 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 38 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t8_wellord1,plain,
! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_wellord1) ).
fof(t8_wellord1_negated,plain,
~ ! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
inference(negate_conjecture,[status(cth)],[t8_wellord1]) ).
cnf(27,plain,
( ~ well_ordering(sK1)
| ~ well_orders(sK1,relation_field(sK1)) ),
inference(cnf,[status(esa)],[t8_wellord1_negated]) ).
cnf(l0,plain,
( ~ well_ordering(sK1)
| ~ well_orders(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[27]) ).
fof(d5_wellord1,plain,
! [A] :
( relation(A)
=> ! [B] :
( well_orders(A,B)
<=> ( is_reflexive_in(A,B)
& is_transitive_in(A,B)
& is_antisymmetric_in(A,B)
& is_connected_in(A,B)
& is_well_founded_in(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_wellord1) ).
cnf(18,plain,
( ~ relation(X0)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_reflexive_in(X0,X1)
| ~ is_well_founded_in(X0,X1)
| well_orders(X0,X1) ),
inference(cnf,[status(esa)],[d5_wellord1]) ).
cnf(l173,plain,
( ~ relation(sK1)
| ~ is_antisymmetric_in(sK1,relation_field(sK1))
| ~ is_transitive_in(sK1,relation_field(sK1))
| ~ is_connected_in(sK1,relation_field(sK1))
| ~ is_reflexive_in(sK1,relation_field(sK1))
| ~ is_well_founded_in(sK1,relation_field(sK1))
| well_orders(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(25,plain,
relation(sK1),
inference(cnf,[status(esa)],[t8_wellord1_negated]) ).
cnf(l174,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
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(20,plain,
( ~ relation(X0)
| ~ reflexive(X0)
| is_reflexive_in(X0,relation_field(X0)) ),
inference(cnf,[status(esa)],[d9_relat_2]) ).
cnf(l213,plain,
( ~ relation(sK1)
| ~ reflexive(sK1)
| is_reflexive_in(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[20]) ).
fof(d4_wellord1,plain,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( reflexive(A)
& transitive(A)
& antisymmetric(A)
& connected(A)
& well_founded_relation(A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
cnf(12,plain,
( ~ relation(X0)
| ~ reflexive(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| well_ordering(X0) ),
inference(cnf,[status(esa)],[d4_wellord1]) ).
cnf(l1,plain,
( ~ relation(sK1)
| ~ reflexive(sK1)
| ~ antisymmetric(sK1)
| ~ transitive(sK1)
| ~ well_founded_relation(sK1)
| ~ connected(sK1)
| well_ordering(sK1) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(21,plain,
( ~ relation(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0) ),
inference(cnf,[status(esa)],[d9_relat_2]) ).
cnf(l2,plain,
( ~ relation(sK1)
| ~ is_reflexive_in(sK1,relation_field(sK1))
| reflexive(sK1) ),
inference(instantiation,[status(thm)],[21]) ).
cnf(l230,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(7,plain,
( ~ relation(X0)
| ~ well_ordering(X0)
| reflexive(X0) ),
inference(cnf,[status(esa)],[d4_wellord1]) ).
cnf(l219,plain,
( ~ relation(sK1)
| ~ well_ordering(sK1)
| reflexive(sK1) ),
inference(instantiation,[status(thm)],[7]) ).
fof(d14_relat_2,plain,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
cnf(3,plain,
( ~ relation(X0)
| ~ connected(X0)
| is_connected_in(X0,relation_field(X0)) ),
inference(cnf,[status(esa)],[d14_relat_2]) ).
cnf(l177,plain,
( ~ relation(sK1)
| ~ connected(sK1)
| is_connected_in(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l240,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
fof(d16_relat_2,plain,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
cnf(5,plain,
( ~ relation(X0)
| ~ transitive(X0)
| is_transitive_in(X0,relation_field(X0)) ),
inference(cnf,[status(esa)],[d16_relat_2]) ).
cnf(l204,plain,
( ~ relation(sK1)
| ~ transitive(sK1)
| is_transitive_in(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[5]) ).
fof(t5_wellord1,plain,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
cnf(24,plain,
( ~ relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0))
| well_founded_relation(X0) ),
inference(cnf,[status(esa)],[t5_wellord1]) ).
cnf(l80,plain,
( ~ relation(sK1)
| ~ is_well_founded_in(sK1,relation_field(sK1))
| well_founded_relation(sK1) ),
inference(instantiation,[status(thm)],[24]) ).
cnf(l111,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(l11,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(4,plain,
( ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0))
| connected(X0) ),
inference(cnf,[status(esa)],[d14_relat_2]) ).
cnf(l82,plain,
( ~ relation(sK1)
| ~ is_connected_in(sK1,relation_field(sK1))
| connected(sK1) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(8,plain,
( ~ relation(X0)
| ~ well_ordering(X0)
| transitive(X0) ),
inference(cnf,[status(esa)],[d4_wellord1]) ).
cnf(l214,plain,
( ~ relation(sK1)
| ~ well_ordering(sK1)
| transitive(sK1) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l211,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(13,plain,
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_reflexive_in(X0,X1) ),
inference(cnf,[status(esa)],[d5_wellord1]) ).
cnf(l6,plain,
( ~ relation(sK1)
| ~ well_orders(sK1,relation_field(sK1))
| is_reflexive_in(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(17,plain,
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_well_founded_in(X0,X1) ),
inference(cnf,[status(esa)],[d5_wellord1]) ).
cnf(l86,plain,
( ~ relation(sK1)
| ~ well_orders(sK1,relation_field(sK1))
| is_well_founded_in(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(l183,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(16,plain,
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_connected_in(X0,X1) ),
inference(cnf,[status(esa)],[d5_wellord1]) ).
cnf(l93,plain,
( ~ relation(sK1)
| ~ well_orders(sK1,relation_field(sK1))
| is_connected_in(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(26,plain,
( well_ordering(sK1)
| well_orders(sK1,relation_field(sK1)) ),
inference(cnf,[status(esa)],[t8_wellord1_negated]) ).
cnf(l215,plain,
( well_ordering(sK1)
| well_orders(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(6,plain,
( ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0) ),
inference(cnf,[status(esa)],[d16_relat_2]) ).
cnf(l79,plain,
( ~ relation(sK1)
| ~ is_transitive_in(sK1,relation_field(sK1))
| transitive(sK1) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l232,plain,
( well_ordering(sK1)
| well_orders(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[26]) ).
fof(d12_relat_2,plain,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
cnf(2,plain,
( ~ relation(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0) ),
inference(cnf,[status(esa)],[d12_relat_2]) ).
cnf(l3,plain,
( ~ relation(sK1)
| ~ is_antisymmetric_in(sK1,relation_field(sK1))
| antisymmetric(sK1) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l106,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(l102,plain,
( well_ordering(sK1)
| well_orders(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(l64,plain,
( well_ordering(sK1)
| well_orders(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(l129,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(l95,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(l101,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(l97,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(15,plain,
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf,[status(esa)],[d5_wellord1]) ).
cnf(l23,plain,
( ~ relation(sK1)
| ~ well_orders(sK1,relation_field(sK1))
| is_antisymmetric_in(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(l43,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(l90,plain,
( well_ordering(sK1)
| well_orders(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(l26,plain,
( well_ordering(sK1)
| well_orders(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(l25,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(l233,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(10,plain,
( ~ relation(X0)
| ~ well_ordering(X0)
| connected(X0) ),
inference(cnf,[status(esa)],[d4_wellord1]) ).
cnf(l196,plain,
( ~ relation(sK1)
| ~ well_ordering(sK1)
| connected(sK1) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(14,plain,
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_transitive_in(X0,X1) ),
inference(cnf,[status(esa)],[d5_wellord1]) ).
cnf(l91,plain,
( ~ relation(sK1)
| ~ well_orders(sK1,relation_field(sK1))
| is_transitive_in(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(23,plain,
( ~ relation(X0)
| ~ well_founded_relation(X0)
| is_well_founded_in(X0,relation_field(X0)) ),
inference(cnf,[status(esa)],[t5_wellord1]) ).
cnf(l203,plain,
( ~ relation(sK1)
| ~ well_founded_relation(sK1)
| is_well_founded_in(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[23]) ).
cnf(l96,plain,
( well_ordering(sK1)
| well_orders(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(l227,plain,
( well_ordering(sK1)
| well_orders(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(11,plain,
( ~ relation(X0)
| ~ well_ordering(X0)
| well_founded_relation(X0) ),
inference(cnf,[status(esa)],[d4_wellord1]) ).
cnf(l208,plain,
( ~ relation(sK1)
| ~ well_ordering(sK1)
| well_founded_relation(sK1) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l228,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(l9,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(l225,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(1,plain,
( ~ relation(X0)
| ~ antisymmetric(X0)
| is_antisymmetric_in(X0,relation_field(X0)) ),
inference(cnf,[status(esa)],[d12_relat_2]) ).
cnf(l182,plain,
( ~ relation(sK1)
| ~ antisymmetric(sK1)
| is_antisymmetric_in(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l109,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(l238,plain,
( well_ordering(sK1)
| well_orders(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(l206,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(l186,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(9,plain,
( ~ relation(X0)
| ~ well_ordering(X0)
| antisymmetric(X0) ),
inference(cnf,[status(esa)],[d4_wellord1]) ).
cnf(l210,plain,
( ~ relation(sK1)
| ~ well_ordering(sK1)
| antisymmetric(sK1) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l234,plain,
( well_ordering(sK1)
| well_orders(sK1,relation_field(sK1)) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(l224,plain,
relation(sK1),
inference(instantiation,[status(thm)],[25]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l173,l174,l213,l1,l2,l230,l219,l177,l240,l204,l80,l111,l11,l82,l214,l211,l6,l86,l183,l93,l215,l79,l232,l3,l106,l102,l64,l129,l95,l101,l97,l23,l43,l90,l26,l25,l233,l196,l91,l203,l96,l227,l208,l228,l9,l225,l182,l109,l238,l206,l186,l210,l234,l224]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU244+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
% 0.12/0.33 % 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 : Tue Jul 22 00:15:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.19/0.40 % launching worker at depth: 11
% 1.80/0.57 % SZS status Theorem for theBenchmark
% 1.80/0.57 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------