%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU275+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n013.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 : Tue May 5 05:11:19 PM UTC 2026
% Result : Theorem 3.90s 3.22s
% Output : CNFRefutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 16 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 79 ( 34 ~; 29 |; 10 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 24 ( 4 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t7_wellord2,conjecture,
! [X1] :
( ordinal(X1)
=> well_ordering(inclusion_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_wellord2) ).
fof(d4_wellord1,axiom,
! [X1] :
( relation(X1)
=> ( well_ordering(X1)
<=> ( reflexive(X1)
& transitive(X1)
& antisymmetric(X1)
& connected(X1)
& well_founded_relation(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
fof(t2_wellord2,lemma,
! [X1] : reflexive(inclusion_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_wellord2) ).
fof(t3_wellord2,lemma,
! [X1] : transitive(inclusion_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_wellord2) ).
fof(t5_wellord2,lemma,
! [X1] : antisymmetric(inclusion_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord2) ).
fof(dt_k1_wellord2,axiom,
! [X1] : relation(inclusion_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(t6_wellord2,lemma,
! [X1] :
( ordinal(X1)
=> well_founded_relation(inclusion_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_wellord2) ).
fof(t4_wellord2,lemma,
! [X1] :
( ordinal(X1)
=> connected(inclusion_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_wellord2) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> well_ordering(inclusion_relation(X1)) ),
inference(assume_negation,[status(cth)],[t7_wellord2]) ).
fof(c_0_9,plain,
! [X1100] :
( ( reflexive(X1100)
| ~ well_ordering(X1100)
| ~ relation(X1100) )
& ( transitive(X1100)
| ~ well_ordering(X1100)
| ~ relation(X1100) )
& ( antisymmetric(X1100)
| ~ well_ordering(X1100)
| ~ relation(X1100) )
& ( connected(X1100)
| ~ well_ordering(X1100)
| ~ relation(X1100) )
& ( well_founded_relation(X1100)
| ~ well_ordering(X1100)
| ~ relation(X1100) )
& ( ~ reflexive(X1100)
| ~ transitive(X1100)
| ~ antisymmetric(X1100)
| ~ connected(X1100)
| ~ well_founded_relation(X1100)
| well_ordering(X1100)
| ~ relation(X1100) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_wellord1])])]) ).
fof(c_0_10,lemma,
! [X1567] : reflexive(inclusion_relation(X1567)),
inference(variable_rename,[status(thm)],[t2_wellord2]) ).
fof(c_0_11,lemma,
! [X1619] : transitive(inclusion_relation(X1619)),
inference(variable_rename,[status(thm)],[t3_wellord2]) ).
fof(c_0_12,lemma,
! [X1704] : antisymmetric(inclusion_relation(X1704)),
inference(variable_rename,[status(thm)],[t5_wellord2]) ).
fof(c_0_13,plain,
! [X1202] : relation(inclusion_relation(X1202)),
inference(variable_rename,[status(thm)],[dt_k1_wellord2]) ).
fof(c_0_14,negated_conjecture,
( ordinal(esk146_0)
& ~ well_ordering(inclusion_relation(esk146_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_15,plain,
( well_ordering(X1)
| ~ reflexive(X1)
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ connected(X1)
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,lemma,
reflexive(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,lemma,
transitive(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,lemma,
antisymmetric(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
relation(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
~ well_ordering(inclusion_relation(esk146_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,lemma,
( well_ordering(inclusion_relation(X1))
| ~ well_founded_relation(inclusion_relation(X1))
| ~ connected(inclusion_relation(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]),c_0_19])]) ).
fof(c_0_22,lemma,
! [X1722] :
( ~ ordinal(X1722)
| well_founded_relation(inclusion_relation(X1722)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_wellord2])]) ).
cnf(c_0_23,negated_conjecture,
( ~ well_founded_relation(inclusion_relation(esk146_0))
| ~ connected(inclusion_relation(esk146_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,lemma,
( well_founded_relation(inclusion_relation(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
ordinal(esk146_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_26,lemma,
! [X1665] :
( ~ ordinal(X1665)
| connected(inclusion_relation(X1665)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_wellord2])]) ).
cnf(c_0_27,lemma,
~ connected(inclusion_relation(esk146_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_28,lemma,
( connected(inclusion_relation(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU275+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.31 % Computer : n013.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Tue May 5 02:54:11 EDT 2026
% 0.14/0.31 % CPUTime :
% 0.14/0.32 % start to proof: theBenchmark
% 3.90/3.22 % Version : CSE_E---1.7
% 3.90/3.22 % Problem : theBenchmark.p
% 3.90/3.22 % SZS status Theorem for theBenchmark.p
% 3.90/3.22 % SZS output start CNFRefutation
% See solution above
% 3.90/3.23 % Total time : 2.476s
%------------------------------------------------------------------------------