%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU261+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 : 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 05:11:17 PM UTC 2026
% Result : Theorem 2.40s 2.05s
% Output : CNFRefutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 72 ( 24 unt; 0 def)
% Number of atoms : 388 ( 14 equ)
% Maximal formula atoms : 90 ( 5 avg)
% Number of connectives : 510 ( 194 ~; 197 |; 67 &)
% ( 10 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 80 ( 0 sgn 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t54_wellord1,conjecture,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( well_ordering(X1)
& relation_isomorphism(X1,X2,X3) )
=> well_ordering(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_wellord1) ).
fof(d7_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( relation_isomorphism(X1,X2,X3)
<=> ( relation_dom(X3) = relation_field(X1)
& relation_rng(X3) = relation_field(X2)
& one_to_one(X3)
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X1)
<=> ( in(X4,relation_field(X1))
& in(X5,relation_field(X1))
& in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_wellord1) ).
fof(t53_wellord1,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( relation_isomorphism(X1,X2,X3)
=> ( ( reflexive(X1)
=> reflexive(X2) )
& ( transitive(X1)
=> transitive(X2) )
& ( connected(X1)
=> connected(X2) )
& ( antisymmetric(X1)
=> antisymmetric(X2) )
& ( well_founded_relation(X1)
=> well_founded_relation(X2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_wellord1) ).
fof(t8_wellord1,lemma,
! [X1] :
( relation(X1)
=> ( well_orders(X1,relation_field(X1))
<=> well_ordering(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_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(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(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(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(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(c_0_10,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( well_ordering(X1)
& relation_isomorphism(X1,X2,X3) )
=> well_ordering(X2) ) ) ) ),
inference(assume_negation,[status(cth)],[t54_wellord1]) ).
fof(c_0_11,plain,
! [X1,X2] :
( epred1_2(X2,X1)
<=> ( ( reflexive(X1)
=> reflexive(X2) )
& ( transitive(X1)
=> transitive(X2) )
& ( connected(X1)
=> connected(X2) )
& ( antisymmetric(X1)
=> antisymmetric(X2) )
& ( well_founded_relation(X1)
=> well_founded_relation(X2) ) ) ),
introduced(definition) ).
fof(c_0_12,plain,
! [X1027,X1028,X1029,X1030,X1031,X1032,X1033] :
( ( relation_dom(X1029) = relation_field(X1027)
| ~ relation_isomorphism(X1027,X1028,X1029)
| ~ relation(X1029)
| ~ function(X1029)
| ~ relation(X1028)
| ~ relation(X1027) )
& ( relation_rng(X1029) = relation_field(X1028)
| ~ relation_isomorphism(X1027,X1028,X1029)
| ~ relation(X1029)
| ~ function(X1029)
| ~ relation(X1028)
| ~ relation(X1027) )
& ( one_to_one(X1029)
| ~ relation_isomorphism(X1027,X1028,X1029)
| ~ relation(X1029)
| ~ function(X1029)
| ~ relation(X1028)
| ~ relation(X1027) )
& ( in(X1030,relation_field(X1027))
| ~ in(ordered_pair(X1030,X1031),X1027)
| ~ relation_isomorphism(X1027,X1028,X1029)
| ~ relation(X1029)
| ~ function(X1029)
| ~ relation(X1028)
| ~ relation(X1027) )
& ( in(X1031,relation_field(X1027))
| ~ in(ordered_pair(X1030,X1031),X1027)
| ~ relation_isomorphism(X1027,X1028,X1029)
| ~ relation(X1029)
| ~ function(X1029)
| ~ relation(X1028)
| ~ relation(X1027) )
& ( in(ordered_pair(apply(X1029,X1030),apply(X1029,X1031)),X1028)
| ~ in(ordered_pair(X1030,X1031),X1027)
| ~ relation_isomorphism(X1027,X1028,X1029)
| ~ relation(X1029)
| ~ function(X1029)
| ~ relation(X1028)
| ~ relation(X1027) )
& ( ~ in(X1032,relation_field(X1027))
| ~ in(X1033,relation_field(X1027))
| ~ in(ordered_pair(apply(X1029,X1032),apply(X1029,X1033)),X1028)
| in(ordered_pair(X1032,X1033),X1027)
| ~ relation_isomorphism(X1027,X1028,X1029)
| ~ relation(X1029)
| ~ function(X1029)
| ~ relation(X1028)
| ~ relation(X1027) )
& ( ~ in(ordered_pair(esk68_3(X1027,X1028,X1029),esk69_3(X1027,X1028,X1029)),X1027)
| ~ in(esk68_3(X1027,X1028,X1029),relation_field(X1027))
| ~ in(esk69_3(X1027,X1028,X1029),relation_field(X1027))
| ~ in(ordered_pair(apply(X1029,esk68_3(X1027,X1028,X1029)),apply(X1029,esk69_3(X1027,X1028,X1029))),X1028)
| relation_dom(X1029) != relation_field(X1027)
| relation_rng(X1029) != relation_field(X1028)
| ~ one_to_one(X1029)
| relation_isomorphism(X1027,X1028,X1029)
| ~ relation(X1029)
| ~ function(X1029)
| ~ relation(X1028)
| ~ relation(X1027) )
& ( in(esk68_3(X1027,X1028,X1029),relation_field(X1027))
| in(ordered_pair(esk68_3(X1027,X1028,X1029),esk69_3(X1027,X1028,X1029)),X1027)
| relation_dom(X1029) != relation_field(X1027)
| relation_rng(X1029) != relation_field(X1028)
| ~ one_to_one(X1029)
| relation_isomorphism(X1027,X1028,X1029)
| ~ relation(X1029)
| ~ function(X1029)
| ~ relation(X1028)
| ~ relation(X1027) )
& ( in(esk69_3(X1027,X1028,X1029),relation_field(X1027))
| in(ordered_pair(esk68_3(X1027,X1028,X1029),esk69_3(X1027,X1028,X1029)),X1027)
| relation_dom(X1029) != relation_field(X1027)
| relation_rng(X1029) != relation_field(X1028)
| ~ one_to_one(X1029)
| relation_isomorphism(X1027,X1028,X1029)
| ~ relation(X1029)
| ~ function(X1029)
| ~ relation(X1028)
| ~ relation(X1027) )
& ( in(ordered_pair(apply(X1029,esk68_3(X1027,X1028,X1029)),apply(X1029,esk69_3(X1027,X1028,X1029))),X1028)
| in(ordered_pair(esk68_3(X1027,X1028,X1029),esk69_3(X1027,X1028,X1029)),X1027)
| relation_dom(X1029) != relation_field(X1027)
| relation_rng(X1029) != relation_field(X1028)
| ~ one_to_one(X1029)
| relation_isomorphism(X1027,X1028,X1029)
| ~ relation(X1029)
| ~ function(X1029)
| ~ relation(X1028)
| ~ relation(X1027) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_wellord1])])])])])]) ).
fof(c_0_13,negated_conjecture,
( relation(esk119_0)
& relation(esk120_0)
& relation(esk121_0)
& function(esk121_0)
& well_ordering(esk119_0)
& relation_isomorphism(esk119_0,esk120_0,esk121_0)
& ~ well_ordering(esk120_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_14,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( relation_isomorphism(X1,X2,X3)
=> epred1_2(X2,X1) ) ) ) ),
inference(apply_def,[status(thm)],[t53_wellord1,c_0_11]) ).
fof(c_0_15,lemma,
! [X1548] :
( ( ~ well_orders(X1548,relation_field(X1548))
| well_ordering(X1548)
| ~ relation(X1548) )
& ( ~ well_ordering(X1548)
| well_orders(X1548,relation_field(X1548))
| ~ relation(X1548) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_wellord1])])]) ).
cnf(c_0_16,plain,
( relation_dom(X1) = relation_field(X2)
| ~ relation_isomorphism(X2,X3,X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
relation_isomorphism(esk119_0,esk120_0,esk121_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
relation(esk120_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
relation(esk119_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
relation(esk121_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
function(esk121_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_22,plain,
! [X1,X2] :
( epred1_2(X2,X1)
=> ( ( reflexive(X1)
=> reflexive(X2) )
& ( transitive(X1)
=> transitive(X2) )
& ( connected(X1)
=> connected(X2) )
& ( antisymmetric(X1)
=> antisymmetric(X2) )
& ( well_founded_relation(X1)
=> well_founded_relation(X2) ) ) ),
inference(split_equiv,[status(thm)],[c_0_11]) ).
fof(c_0_23,lemma,
! [X1469,X1470,X1471] :
( ~ relation(X1469)
| ~ relation(X1470)
| ~ relation(X1471)
| ~ function(X1471)
| ~ relation_isomorphism(X1469,X1470,X1471)
| epred1_2(X1470,X1469) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_24,plain,
! [X1073] :
( ( ~ reflexive(X1073)
| is_reflexive_in(X1073,relation_field(X1073))
| ~ relation(X1073) )
& ( ~ is_reflexive_in(X1073,relation_field(X1073))
| reflexive(X1073)
| ~ relation(X1073) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_relat_2])])]) ).
fof(c_0_25,plain,
! [X1006,X1007] :
( ( is_reflexive_in(X1006,X1007)
| ~ well_orders(X1006,X1007)
| ~ relation(X1006) )
& ( is_transitive_in(X1006,X1007)
| ~ well_orders(X1006,X1007)
| ~ relation(X1006) )
& ( is_antisymmetric_in(X1006,X1007)
| ~ well_orders(X1006,X1007)
| ~ relation(X1006) )
& ( is_connected_in(X1006,X1007)
| ~ well_orders(X1006,X1007)
| ~ relation(X1006) )
& ( is_well_founded_in(X1006,X1007)
| ~ well_orders(X1006,X1007)
| ~ relation(X1006) )
& ( ~ is_reflexive_in(X1006,X1007)
| ~ is_transitive_in(X1006,X1007)
| ~ is_antisymmetric_in(X1006,X1007)
| ~ is_connected_in(X1006,X1007)
| ~ is_well_founded_in(X1006,X1007)
| well_orders(X1006,X1007)
| ~ relation(X1006) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_wellord1])])])]) ).
cnf(c_0_26,lemma,
( well_orders(X1,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,negated_conjecture,
relation_field(esk119_0) = relation_dom(esk121_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_28,negated_conjecture,
well_ordering(esk119_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_29,plain,
! [X1575,X1576] :
( ( ~ reflexive(X1575)
| reflexive(X1576)
| ~ epred1_2(X1576,X1575) )
& ( ~ transitive(X1575)
| transitive(X1576)
| ~ epred1_2(X1576,X1575) )
& ( ~ connected(X1575)
| connected(X1576)
| ~ epred1_2(X1576,X1575) )
& ( ~ antisymmetric(X1575)
| antisymmetric(X1576)
| ~ epred1_2(X1576,X1575) )
& ( ~ well_founded_relation(X1575)
| well_founded_relation(X1576)
| ~ epred1_2(X1576,X1575) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
cnf(c_0_30,lemma,
( epred1_2(X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
( reflexive(X1)
| ~ is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_32,lemma,
! [X1497] :
( ( ~ well_founded_relation(X1497)
| is_well_founded_in(X1497,relation_field(X1497))
| ~ relation(X1497) )
& ( ~ is_well_founded_in(X1497,relation_field(X1497))
| well_founded_relation(X1497)
| ~ relation(X1497) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_wellord1])])]) ).
cnf(c_0_33,plain,
( is_well_founded_in(X1,X2)
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,lemma,
well_orders(esk119_0,relation_dom(esk121_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_19])]) ).
fof(c_0_35,plain,
! [X786] :
( ( ~ transitive(X786)
| is_transitive_in(X786,relation_field(X786))
| ~ relation(X786) )
& ( ~ is_transitive_in(X786,relation_field(X786))
| transitive(X786)
| ~ relation(X786) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d16_relat_2])])]) ).
cnf(c_0_36,plain,
( is_transitive_in(X1,X2)
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_37,plain,
! [X972] :
( ( reflexive(X972)
| ~ well_ordering(X972)
| ~ relation(X972) )
& ( transitive(X972)
| ~ well_ordering(X972)
| ~ relation(X972) )
& ( antisymmetric(X972)
| ~ well_ordering(X972)
| ~ relation(X972) )
& ( connected(X972)
| ~ well_ordering(X972)
| ~ relation(X972) )
& ( well_founded_relation(X972)
| ~ well_ordering(X972)
| ~ relation(X972) )
& ( ~ reflexive(X972)
| ~ transitive(X972)
| ~ antisymmetric(X972)
| ~ connected(X972)
| ~ well_founded_relation(X972)
| well_ordering(X972)
| ~ relation(X972) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_wellord1])])]) ).
fof(c_0_38,plain,
! [X752] :
( ( ~ antisymmetric(X752)
| is_antisymmetric_in(X752,relation_field(X752))
| ~ relation(X752) )
& ( ~ is_antisymmetric_in(X752,relation_field(X752))
| antisymmetric(X752)
| ~ relation(X752) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d12_relat_2])])]) ).
cnf(c_0_39,plain,
( is_antisymmetric_in(X1,X2)
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_40,plain,
( reflexive(X2)
| ~ reflexive(X1)
| ~ epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_41,negated_conjecture,
epred1_2(esk120_0,esk119_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_17]),c_0_20]),c_0_18]),c_0_19]),c_0_21])]) ).
cnf(c_0_42,negated_conjecture,
( reflexive(esk119_0)
| ~ is_reflexive_in(esk119_0,relation_dom(esk121_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_27]),c_0_19])]) ).
cnf(c_0_43,plain,
( is_reflexive_in(X1,X2)
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_44,plain,
( well_founded_relation(X2)
| ~ well_founded_relation(X1)
| ~ epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_45,lemma,
( well_founded_relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_46,lemma,
is_well_founded_in(esk119_0,relation_dom(esk121_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_19])]) ).
cnf(c_0_47,plain,
( transitive(X2)
| ~ transitive(X1)
| ~ epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_48,plain,
( transitive(X1)
| ~ is_transitive_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_49,lemma,
is_transitive_in(esk119_0,relation_dom(esk121_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_34]),c_0_19])]) ).
cnf(c_0_50,plain,
( connected(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_51,plain,
( antisymmetric(X2)
| ~ antisymmetric(X1)
| ~ epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_52,plain,
( antisymmetric(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_53,lemma,
is_antisymmetric_in(esk119_0,relation_dom(esk121_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_34]),c_0_19])]) ).
cnf(c_0_54,plain,
( reflexive(esk120_0)
| ~ reflexive(esk119_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_55,negated_conjecture,
reflexive(esk119_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_34]),c_0_19])]) ).
cnf(c_0_56,plain,
( well_founded_relation(esk120_0)
| ~ well_founded_relation(esk119_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_57,lemma,
well_founded_relation(esk119_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_27]),c_0_19])]),c_0_46])]) ).
cnf(c_0_58,plain,
( transitive(esk120_0)
| ~ transitive(esk119_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_41]) ).
cnf(c_0_59,negated_conjecture,
transitive(esk119_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_27]),c_0_19])]),c_0_49])]) ).
cnf(c_0_60,plain,
( connected(X2)
| ~ connected(X1)
| ~ epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_61,negated_conjecture,
connected(esk119_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_28]),c_0_19])]) ).
cnf(c_0_62,plain,
( antisymmetric(esk120_0)
| ~ antisymmetric(esk119_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_41]) ).
cnf(c_0_63,negated_conjecture,
antisymmetric(esk119_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_27]),c_0_19])]),c_0_53])]) ).
cnf(c_0_64,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_37]) ).
cnf(c_0_65,plain,
reflexive(esk120_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_66,plain,
well_founded_relation(esk120_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
cnf(c_0_67,plain,
transitive(esk120_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).
cnf(c_0_68,plain,
connected(esk120_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_41]),c_0_61])]) ).
cnf(c_0_69,plain,
antisymmetric(esk120_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
cnf(c_0_70,negated_conjecture,
~ well_ordering(esk120_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_71,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]),c_0_67]),c_0_68]),c_0_69]),c_0_18])]),c_0_70]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU261+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 : n013.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 02:53:11 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.40/2.05 % Version : CSE_E---1.7
% 2.40/2.05 % Problem : theBenchmark.p
% 2.40/2.05 % SZS status Theorem for theBenchmark.p
% 2.40/2.05 % SZS output start CNFRefutation
% See solution above
% 2.40/2.05 % Total time : 1.427s
%------------------------------------------------------------------------------