%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU244+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 05:11:14 PM UTC 2026
% Result : Theorem 13.83s 8.78s
% Output : CNFRefutation 13.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 7 unt; 0 def)
% Number of atoms : 247 ( 0 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 321 ( 139 ~; 139 |; 25 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 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 : 48 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t8_wellord1,conjecture,
! [X1] :
( relation(X1)
=> ( well_orders(X1,relation_field(X1))
<=> well_ordering(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_wellord1) ).
fof(d5_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( well_orders(X1,X2)
<=> ( is_reflexive_in(X1,X2)
& is_transitive_in(X1,X2)
& is_antisymmetric_in(X1,X2)
& is_connected_in(X1,X2)
& is_well_founded_in(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_wellord1) ).
fof(d9_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
fof(t5_wellord1,lemma,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
fof(d14_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( connected(X1)
<=> is_connected_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
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/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
fof(d12_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> is_antisymmetric_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
fof(d16_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( transitive(X1)
<=> is_transitive_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( well_orders(X1,relation_field(X1))
<=> well_ordering(X1) ) ),
inference(assume_negation,[status(cth)],[t8_wellord1]) ).
fof(c_0_9,plain,
! [X943,X944] :
( ( is_reflexive_in(X943,X944)
| ~ well_orders(X943,X944)
| ~ relation(X943) )
& ( is_transitive_in(X943,X944)
| ~ well_orders(X943,X944)
| ~ relation(X943) )
& ( is_antisymmetric_in(X943,X944)
| ~ well_orders(X943,X944)
| ~ relation(X943) )
& ( is_connected_in(X943,X944)
| ~ well_orders(X943,X944)
| ~ relation(X943) )
& ( is_well_founded_in(X943,X944)
| ~ well_orders(X943,X944)
| ~ relation(X943) )
& ( ~ is_reflexive_in(X943,X944)
| ~ is_transitive_in(X943,X944)
| ~ is_antisymmetric_in(X943,X944)
| ~ is_connected_in(X943,X944)
| ~ is_well_founded_in(X943,X944)
| well_orders(X943,X944)
| ~ relation(X943) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_wellord1])])])]) ).
fof(c_0_10,negated_conjecture,
( relation(esk120_0)
& ( ~ well_orders(esk120_0,relation_field(esk120_0))
| ~ well_ordering(esk120_0) )
& ( well_orders(esk120_0,relation_field(esk120_0))
| well_ordering(esk120_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_11,plain,
! [X999] :
( ( ~ reflexive(X999)
| is_reflexive_in(X999,relation_field(X999))
| ~ relation(X999) )
& ( ~ is_reflexive_in(X999,relation_field(X999))
| reflexive(X999)
| ~ relation(X999) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_relat_2])])]) ).
fof(c_0_12,lemma,
! [X1379] :
( ( ~ well_founded_relation(X1379)
| is_well_founded_in(X1379,relation_field(X1379))
| ~ relation(X1379) )
& ( ~ is_well_founded_in(X1379,relation_field(X1379))
| well_founded_relation(X1379)
| ~ relation(X1379) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_wellord1])])]) ).
cnf(c_0_13,plain,
( is_well_founded_in(X1,X2)
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( well_orders(esk120_0,relation_field(esk120_0))
| well_ordering(esk120_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
relation(esk120_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X730] :
( ( ~ connected(X730)
| is_connected_in(X730,relation_field(X730))
| ~ relation(X730) )
& ( ~ is_connected_in(X730,relation_field(X730))
| connected(X730)
| ~ relation(X730) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d14_relat_2])])]) ).
cnf(c_0_17,plain,
( is_connected_in(X1,X2)
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,plain,
( reflexive(X1)
| ~ is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( is_reflexive_in(X1,X2)
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_20,plain,
! [X909] :
( ( reflexive(X909)
| ~ well_ordering(X909)
| ~ relation(X909) )
& ( transitive(X909)
| ~ well_ordering(X909)
| ~ relation(X909) )
& ( antisymmetric(X909)
| ~ well_ordering(X909)
| ~ relation(X909) )
& ( connected(X909)
| ~ well_ordering(X909)
| ~ relation(X909) )
& ( well_founded_relation(X909)
| ~ well_ordering(X909)
| ~ relation(X909) )
& ( ~ reflexive(X909)
| ~ transitive(X909)
| ~ antisymmetric(X909)
| ~ connected(X909)
| ~ well_founded_relation(X909)
| well_ordering(X909)
| ~ relation(X909) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_wellord1])])]) ).
cnf(c_0_21,lemma,
( well_founded_relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
( well_ordering(esk120_0)
| is_well_founded_in(esk120_0,relation_field(esk120_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_23,plain,
( connected(X1)
| ~ is_connected_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( well_ordering(esk120_0)
| is_connected_in(esk120_0,relation_field(esk120_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15])]) ).
fof(c_0_25,plain,
! [X697] :
( ( ~ antisymmetric(X697)
| is_antisymmetric_in(X697,relation_field(X697))
| ~ relation(X697) )
& ( ~ is_antisymmetric_in(X697,relation_field(X697))
| antisymmetric(X697)
| ~ relation(X697) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d12_relat_2])])]) ).
cnf(c_0_26,plain,
( is_antisymmetric_in(X1,X2)
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_27,plain,
! [X731] :
( ( ~ transitive(X731)
| is_transitive_in(X731,relation_field(X731))
| ~ relation(X731) )
& ( ~ is_transitive_in(X731,relation_field(X731))
| transitive(X731)
| ~ relation(X731) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d16_relat_2])])]) ).
cnf(c_0_28,plain,
( is_transitive_in(X1,X2)
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_29,plain,
( reflexive(X1)
| ~ well_orders(X1,relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_30,plain,
( well_founded_relation(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,lemma,
( well_ordering(esk120_0)
| well_founded_relation(esk120_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_15])]) ).
cnf(c_0_32,plain,
( connected(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,negated_conjecture,
( well_ordering(esk120_0)
| connected(esk120_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_15])]) ).
cnf(c_0_34,plain,
( antisymmetric(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,negated_conjecture,
( well_ordering(esk120_0)
| is_antisymmetric_in(esk120_0,relation_field(esk120_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_14]),c_0_15])]) ).
cnf(c_0_36,plain,
( transitive(X1)
| ~ is_transitive_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,negated_conjecture,
( well_ordering(esk120_0)
| is_transitive_in(esk120_0,relation_field(esk120_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_14]),c_0_15])]) ).
cnf(c_0_38,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_20]) ).
cnf(c_0_39,negated_conjecture,
( reflexive(esk120_0)
| well_ordering(esk120_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_14]),c_0_15])]) ).
cnf(c_0_40,lemma,
well_founded_relation(esk120_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_15])]) ).
cnf(c_0_41,negated_conjecture,
connected(esk120_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_15])]) ).
cnf(c_0_42,negated_conjecture,
( well_ordering(esk120_0)
| antisymmetric(esk120_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_15])]) ).
cnf(c_0_43,negated_conjecture,
( well_ordering(esk120_0)
| transitive(esk120_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_15])]) ).
cnf(c_0_44,negated_conjecture,
( ~ well_orders(esk120_0,relation_field(esk120_0))
| ~ well_ordering(esk120_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_45,negated_conjecture,
well_ordering(esk120_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41]),c_0_15])]),c_0_42]),c_0_43]) ).
cnf(c_0_46,plain,
( well_orders(X1,X2)
| ~ is_reflexive_in(X1,X2)
| ~ is_transitive_in(X1,X2)
| ~ is_antisymmetric_in(X1,X2)
| ~ is_connected_in(X1,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_47,plain,
( is_reflexive_in(X1,relation_field(X1))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_48,negated_conjecture,
~ well_orders(esk120_0,relation_field(esk120_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
cnf(c_0_49,plain,
( well_orders(X1,relation_field(X1))
| ~ reflexive(X1)
| ~ is_well_founded_in(X1,relation_field(X1))
| ~ is_transitive_in(X1,relation_field(X1))
| ~ is_connected_in(X1,relation_field(X1))
| ~ is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( ~ reflexive(esk120_0)
| ~ is_well_founded_in(esk120_0,relation_field(esk120_0))
| ~ is_transitive_in(esk120_0,relation_field(esk120_0))
| ~ is_connected_in(esk120_0,relation_field(esk120_0))
| ~ is_antisymmetric_in(esk120_0,relation_field(esk120_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_15])]) ).
cnf(c_0_51,lemma,
( is_well_founded_in(X1,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_52,lemma,
( ~ reflexive(esk120_0)
| ~ is_transitive_in(esk120_0,relation_field(esk120_0))
| ~ is_connected_in(esk120_0,relation_field(esk120_0))
| ~ is_antisymmetric_in(esk120_0,relation_field(esk120_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_40]),c_0_15])]) ).
cnf(c_0_53,plain,
( is_connected_in(X1,relation_field(X1))
| ~ connected(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_54,lemma,
( ~ reflexive(esk120_0)
| ~ is_transitive_in(esk120_0,relation_field(esk120_0))
| ~ is_antisymmetric_in(esk120_0,relation_field(esk120_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_41]),c_0_15])]) ).
cnf(c_0_55,plain,
( is_antisymmetric_in(X1,relation_field(X1))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_56,lemma,
( ~ reflexive(esk120_0)
| ~ is_transitive_in(esk120_0,relation_field(esk120_0))
| ~ antisymmetric(esk120_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_15])]) ).
cnf(c_0_57,plain,
( is_transitive_in(X1,relation_field(X1))
| ~ transitive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_58,lemma,
( ~ reflexive(esk120_0)
| ~ transitive(esk120_0)
| ~ antisymmetric(esk120_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_15])]) ).
cnf(c_0_59,plain,
( reflexive(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_60,lemma,
( ~ transitive(esk120_0)
| ~ antisymmetric(esk120_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_45]),c_0_15])]) ).
cnf(c_0_61,plain,
( transitive(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_62,lemma,
~ antisymmetric(esk120_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_45]),c_0_15])]) ).
cnf(c_0_63,plain,
( antisymmetric(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_64,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_45]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU244+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n018.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:52:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 13.83/8.78 % Version : CSE_E---1.7
% 13.83/8.78 % Problem : theBenchmark.p
% 13.83/8.78 % SZS status Theorem for theBenchmark.p
% 13.83/8.78 % SZS output start CNFRefutation
% See solution above
% 13.92/8.83 % Total time : 6.446s
%------------------------------------------------------------------------------