%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU261+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:24:29 PM UTC 2026
% Result : Theorem 1.25s 0.65s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 24 unt; 0 def)
% Number of atoms : 380 ( 14 equ)
% Maximal formula atoms : 90 ( 5 avg)
% Number of connectives : 502 ( 190 ~; 193 |; 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] :
( ( function(X3)
& relation(X3) )
=> ( ( relation_isomorphism(X1,X2,X3)
& well_ordering(X1) )
=> well_ordering(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_wellord1) ).
fof(d7_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( relation_isomorphism(X1,X2,X3)
<=> ( ! [X4,X5] :
( in(ordered_pair(X4,X5),X1)
<=> ( in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
& in(X5,relation_field(X1))
& in(X4,relation_field(X1)) ) )
& one_to_one(X3)
& relation_rng(X3) = relation_field(X2)
& relation_dom(X3) = relation_field(X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_wellord1) ).
fof(t8_wellord1,lemma,
! [X1] :
( relation(X1)
=> ( well_orders(X1,relation_field(X1))
<=> well_ordering(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_wellord1) ).
fof(t53_wellord1,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( relation_isomorphism(X1,X2,X3)
=> ( ( well_founded_relation(X1)
=> well_founded_relation(X2) )
& ( antisymmetric(X1)
=> antisymmetric(X2) )
& ( connected(X1)
=> connected(X2) )
& ( transitive(X1)
=> transitive(X2) )
& ( reflexive(X1)
=> reflexive(X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_wellord1) ).
fof(d9_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_2) ).
fof(d5_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( well_orders(X1,X2)
<=> ( is_well_founded_in(X1,X2)
& is_connected_in(X1,X2)
& is_antisymmetric_in(X1,X2)
& is_transitive_in(X1,X2)
& is_reflexive_in(X1,X2) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',d16_relat_2) ).
fof(d4_wellord1,axiom,
! [X1] :
( relation(X1)
=> ( well_ordering(X1)
<=> ( well_founded_relation(X1)
& connected(X1)
& antisymmetric(X1)
& transitive(X1)
& reflexive(X1) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',d12_relat_2) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( ( relation_isomorphism(X1,X2,X3)
& well_ordering(X1) )
=> well_ordering(X2) ) ) ) ),
inference(assume_negation,[status(cth)],[t54_wellord1]) ).
fof(c_0_11,plain,
! [X16,X17,X18,X19,X20,X21,X22] :
( ( ~ relation(X16)
| ~ relation(X17)
| ~ function(X18)
| ~ relation(X18)
| relation_isomorphism(X16,X17,X18)
| ~ one_to_one(X18)
| relation_rng(X18) != relation_field(X17)
| relation_dom(X18) != relation_field(X16)
| in(ordered_pair(esk4_3(X16,X17,X18),esk5_3(X16,X17,X18)),X16)
| in(ordered_pair(apply(X18,esk4_3(X16,X17,X18)),apply(X18,esk5_3(X16,X17,X18))),X17) )
& ( ~ relation(X16)
| ~ relation(X17)
| ~ function(X18)
| ~ relation(X18)
| relation_isomorphism(X16,X17,X18)
| ~ one_to_one(X18)
| relation_rng(X18) != relation_field(X17)
| relation_dom(X18) != relation_field(X16)
| in(ordered_pair(esk4_3(X16,X17,X18),esk5_3(X16,X17,X18)),X16)
| in(esk5_3(X16,X17,X18),relation_field(X16)) )
& ( ~ relation(X16)
| ~ relation(X17)
| ~ function(X18)
| ~ relation(X18)
| relation_isomorphism(X16,X17,X18)
| ~ one_to_one(X18)
| relation_rng(X18) != relation_field(X17)
| relation_dom(X18) != relation_field(X16)
| in(ordered_pair(esk4_3(X16,X17,X18),esk5_3(X16,X17,X18)),X16)
| in(esk4_3(X16,X17,X18),relation_field(X16)) )
& ( ~ relation(X16)
| ~ relation(X17)
| ~ function(X18)
| ~ relation(X18)
| relation_isomorphism(X16,X17,X18)
| ~ one_to_one(X18)
| relation_rng(X18) != relation_field(X17)
| relation_dom(X18) != relation_field(X16)
| ~ in(ordered_pair(apply(X18,esk4_3(X16,X17,X18)),apply(X18,esk5_3(X16,X17,X18))),X17)
| ~ in(esk5_3(X16,X17,X18),relation_field(X16))
| ~ in(esk4_3(X16,X17,X18),relation_field(X16))
| ~ in(ordered_pair(esk4_3(X16,X17,X18),esk5_3(X16,X17,X18)),X16) )
& ( ~ relation(X16)
| ~ relation(X17)
| ~ function(X18)
| ~ relation(X18)
| ~ relation_isomorphism(X16,X17,X18)
| in(ordered_pair(X21,X22),X16)
| ~ in(ordered_pair(apply(X18,X21),apply(X18,X22)),X17)
| ~ in(X22,relation_field(X16))
| ~ in(X21,relation_field(X16)) )
& ( ~ relation(X16)
| ~ relation(X17)
| ~ function(X18)
| ~ relation(X18)
| ~ relation_isomorphism(X16,X17,X18)
| ~ in(ordered_pair(X19,X20),X16)
| in(ordered_pair(apply(X18,X19),apply(X18,X20)),X17) )
& ( ~ relation(X16)
| ~ relation(X17)
| ~ function(X18)
| ~ relation(X18)
| ~ relation_isomorphism(X16,X17,X18)
| ~ in(ordered_pair(X19,X20),X16)
| in(X20,relation_field(X16)) )
& ( ~ relation(X16)
| ~ relation(X17)
| ~ function(X18)
| ~ relation(X18)
| ~ relation_isomorphism(X16,X17,X18)
| ~ in(ordered_pair(X19,X20),X16)
| in(X19,relation_field(X16)) )
& ( ~ relation(X16)
| ~ relation(X17)
| ~ function(X18)
| ~ relation(X18)
| ~ relation_isomorphism(X16,X17,X18)
| one_to_one(X18) )
& ( ~ relation(X16)
| ~ relation(X17)
| ~ function(X18)
| ~ relation(X18)
| ~ relation_isomorphism(X16,X17,X18)
| relation_rng(X18) = relation_field(X17) )
& ( ~ relation(X16)
| ~ relation(X17)
| ~ function(X18)
| ~ relation(X18)
| ~ relation_isomorphism(X16,X17,X18)
| relation_dom(X18) = relation_field(X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_12,negated_conjecture,
( ~ well_ordering(esk2_0)
& relation_isomorphism(esk1_0,esk2_0,esk3_0)
& well_ordering(esk1_0)
& function(esk3_0)
& relation(esk3_0)
& relation(esk2_0)
& relation(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_13,plain,
! [X1,X2] :
( epred1_2(X2,X1)
<=> ( ( well_founded_relation(X1)
=> well_founded_relation(X2) )
& ( antisymmetric(X1)
=> antisymmetric(X2) )
& ( connected(X1)
=> connected(X2) )
& ( transitive(X1)
=> transitive(X2) )
& ( reflexive(X1)
=> reflexive(X2) ) ) ),
introduced(definition) ).
fof(c_0_14,lemma,
! [X15] :
( ( ~ relation(X15)
| well_orders(X15,relation_field(X15))
| ~ well_ordering(X15) )
& ( ~ relation(X15)
| well_ordering(X15)
| ~ well_orders(X15,relation_field(X15)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_wellord1])])])]) ).
cnf(c_0_15,plain,
( ~ relation(X2)
| ~ relation(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ relation_isomorphism(X2,X3,X1)
| relation_dom(X1) = relation_field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
relation_isomorphism(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
relation(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
relation(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
function(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_21,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( relation_isomorphism(X1,X2,X3)
=> epred1_2(X2,X1) ) ) ) ),
inference(apply_def,[status(thm)],[t53_wellord1,c_0_13]) ).
fof(c_0_22,plain,
! [X209] :
( ( ~ relation(X209)
| reflexive(X209)
| ~ is_reflexive_in(X209,relation_field(X209)) )
& ( ~ relation(X209)
| is_reflexive_in(X209,relation_field(X209))
| ~ reflexive(X209) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_relat_2])])])]) ).
fof(c_0_23,plain,
! [X316,X317] :
( ( ~ relation(X316)
| well_orders(X316,X317)
| ~ is_well_founded_in(X316,X317)
| ~ is_connected_in(X316,X317)
| ~ is_antisymmetric_in(X316,X317)
| ~ is_transitive_in(X316,X317)
| ~ is_reflexive_in(X316,X317) )
& ( ~ relation(X316)
| ~ well_orders(X316,X317)
| is_well_founded_in(X316,X317) )
& ( ~ relation(X316)
| ~ well_orders(X316,X317)
| is_connected_in(X316,X317) )
& ( ~ relation(X316)
| ~ well_orders(X316,X317)
| is_antisymmetric_in(X316,X317) )
& ( ~ relation(X316)
| ~ well_orders(X316,X317)
| is_transitive_in(X316,X317) )
& ( ~ relation(X316)
| ~ well_orders(X316,X317)
| is_reflexive_in(X316,X317) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_wellord1])])])])]) ).
cnf(c_0_24,lemma,
( ~ relation(X1)
| ~ well_ordering(X1)
| well_orders(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,negated_conjecture,
relation_field(esk1_0) = relation_dom(esk3_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_15,c_0_16]),c_0_17]),c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_26,negated_conjecture,
well_ordering(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_27,plain,
! [X1,X2] :
( epred1_2(X2,X1)
=> ( ( well_founded_relation(X1)
=> well_founded_relation(X2) )
& ( antisymmetric(X1)
=> antisymmetric(X2) )
& ( connected(X1)
=> connected(X2) )
& ( transitive(X1)
=> transitive(X2) )
& ( reflexive(X1)
=> reflexive(X2) ) ) ),
inference(split_equiv,[status(thm)],[c_0_13]) ).
fof(c_0_28,lemma,
! [X28,X29,X30] :
( epred1_2(X29,X28)
| ~ relation_isomorphism(X28,X29,X30)
| ~ function(X30)
| ~ relation(X30)
| ~ relation(X29)
| ~ relation(X28) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_29,plain,
( ~ relation(X1)
| ~ is_reflexive_in(X1,relation_field(X1))
| reflexive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_30,lemma,
! [X182] :
( ( ~ relation(X182)
| well_founded_relation(X182)
| ~ is_well_founded_in(X182,relation_field(X182)) )
& ( ~ relation(X182)
| is_well_founded_in(X182,relation_field(X182))
| ~ well_founded_relation(X182) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_wellord1])])])]) ).
cnf(c_0_31,plain,
( ~ relation(X1)
| ~ well_orders(X1,X2)
| is_well_founded_in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,lemma,
well_orders(esk1_0,relation_dom(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_18])]) ).
fof(c_0_33,plain,
! [X199] :
( ( ~ relation(X199)
| transitive(X199)
| ~ is_transitive_in(X199,relation_field(X199)) )
& ( ~ relation(X199)
| is_transitive_in(X199,relation_field(X199))
| ~ transitive(X199) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d16_relat_2])])])]) ).
cnf(c_0_34,plain,
( ~ relation(X1)
| ~ well_orders(X1,X2)
| is_transitive_in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_35,plain,
! [X10] :
( ( ~ relation(X10)
| well_ordering(X10)
| ~ well_founded_relation(X10)
| ~ connected(X10)
| ~ antisymmetric(X10)
| ~ transitive(X10)
| ~ reflexive(X10) )
& ( ~ relation(X10)
| ~ well_ordering(X10)
| well_founded_relation(X10) )
& ( ~ relation(X10)
| ~ well_ordering(X10)
| connected(X10) )
& ( ~ relation(X10)
| ~ well_ordering(X10)
| antisymmetric(X10) )
& ( ~ relation(X10)
| ~ well_ordering(X10)
| transitive(X10) )
& ( ~ relation(X10)
| ~ well_ordering(X10)
| reflexive(X10) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_wellord1])])])]) ).
fof(c_0_36,plain,
! [X191] :
( ( ~ relation(X191)
| antisymmetric(X191)
| ~ is_antisymmetric_in(X191,relation_field(X191)) )
& ( ~ relation(X191)
| is_antisymmetric_in(X191,relation_field(X191))
| ~ antisymmetric(X191) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d12_relat_2])])])]) ).
cnf(c_0_37,plain,
( ~ relation(X1)
| ~ well_orders(X1,X2)
| is_antisymmetric_in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_38,plain,
! [X844,X845] :
( ( ~ epred1_2(X845,X844)
| well_founded_relation(X845)
| ~ well_founded_relation(X844) )
& ( ~ epred1_2(X845,X844)
| antisymmetric(X845)
| ~ antisymmetric(X844) )
& ( ~ epred1_2(X845,X844)
| connected(X845)
| ~ connected(X844) )
& ( ~ epred1_2(X845,X844)
| transitive(X845)
| ~ transitive(X844) )
& ( ~ epred1_2(X845,X844)
| reflexive(X845)
| ~ reflexive(X844) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
cnf(c_0_39,lemma,
( ~ relation_isomorphism(X1,X2,X3)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_40,negated_conjecture,
( ~ is_reflexive_in(esk1_0,relation_dom(esk3_0))
| reflexive(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_18])]) ).
cnf(c_0_41,plain,
( ~ relation(X1)
| ~ well_orders(X1,X2)
| is_reflexive_in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_42,lemma,
( ~ relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1))
| well_founded_relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,lemma,
is_well_founded_in(esk1_0,relation_dom(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_18])]) ).
cnf(c_0_44,plain,
( ~ relation(X1)
| ~ is_transitive_in(X1,relation_field(X1))
| transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_45,lemma,
is_transitive_in(esk1_0,relation_dom(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_32]),c_0_18])]) ).
cnf(c_0_46,plain,
( ~ relation(X1)
| ~ well_ordering(X1)
| connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,plain,
( ~ relation(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1))
| antisymmetric(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,lemma,
is_antisymmetric_in(esk1_0,relation_dom(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_32]),c_0_18])]) ).
cnf(c_0_49,plain,
( ~ epred1_2(X2,X1)
| ~ reflexive(X1)
| reflexive(X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_50,negated_conjecture,
epred1_2(esk2_0,esk1_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_39,c_0_16]),c_0_19]),c_0_17]),c_0_18]),c_0_20])]) ).
cnf(c_0_51,negated_conjecture,
reflexive(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_32]),c_0_18])]) ).
cnf(c_0_52,plain,
( ~ epred1_2(X2,X1)
| ~ well_founded_relation(X1)
| well_founded_relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_53,lemma,
well_founded_relation(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_25]),c_0_18])]),c_0_43])]) ).
cnf(c_0_54,plain,
( ~ epred1_2(X2,X1)
| ~ transitive(X1)
| transitive(X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_55,negated_conjecture,
transitive(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_25]),c_0_18])]),c_0_45])]) ).
cnf(c_0_56,plain,
( ~ epred1_2(X2,X1)
| ~ connected(X1)
| connected(X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_57,negated_conjecture,
connected(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_26]),c_0_18])]) ).
cnf(c_0_58,plain,
( ~ epred1_2(X2,X1)
| ~ antisymmetric(X1)
| antisymmetric(X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_59,negated_conjecture,
antisymmetric(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_25]),c_0_18])]),c_0_48])]) ).
cnf(c_0_60,plain,
( ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(X1)
| well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_61,plain,
reflexive(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_62,plain,
well_founded_relation(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_50]),c_0_53])]) ).
cnf(c_0_63,plain,
transitive(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_50]),c_0_55])]) ).
cnf(c_0_64,plain,
connected(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_50]),c_0_57])]) ).
cnf(c_0_65,plain,
antisymmetric(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_50]),c_0_59])]) ).
cnf(c_0_66,negated_conjecture,
~ well_ordering(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_67,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_60,c_0_61]),c_0_62]),c_0_63]),c_0_64]),c_0_65]),c_0_17])]),c_0_66]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU261+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 05:59:57 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.25/0.65 % Version: 3.5.1
% 1.25/0.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.25/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.25/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.25/0.65 % Starting new_bool_3 with 300s (1) cores
% 1.25/0.65 % Starting new_bool_1 with 300s (1) cores
% 1.25/0.65 % Starting sh5l with 300s (1) cores
% 1.25/0.65 % sh5l with pid 1588185 completed with status 0
% 1.25/0.65 % Result found by sh5l
% 1.25/0.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.25/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.25/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.25/0.65 % Starting new_bool_3 with 300s (1) cores
% 1.25/0.65 % Starting new_bool_1 with 300s (1) cores
% 1.25/0.65 % Starting sh5l with 300s (1) cores
% 1.25/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 1.25/0.65 % SinE strategy is gf500_gu_R04_F100_L20000
% 1.25/0.65 % Search class: FGHSM-FSLM32-MFFFFFNN
% 1.25/0.65 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 1.25/0.65 % Starting SubtermCWHack with 28s (1) cores
% 1.25/0.65 % SubtermCWHack with pid 1588188 completed with status 0
% 1.25/0.65 % Result found by SubtermCWHack
% 1.25/0.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.25/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.25/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.25/0.65 % Starting new_bool_3 with 300s (1) cores
% 1.25/0.65 % Starting new_bool_1 with 300s (1) cores
% 1.25/0.65 % Starting sh5l with 300s (1) cores
% 1.25/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 1.25/0.65 % SinE strategy is gf500_gu_R04_F100_L20000
% 1.25/0.65 % Search class: FGHSM-FSLM32-MFFFFFNN
% 1.25/0.65 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 1.25/0.65 % Starting SubtermCWHack with 28s (1) cores
% 1.25/0.65 % Preprocessing time : 0.006 s
% 1.25/0.65
% 1.25/0.65 % Proof found!
% 1.25/0.65 % SZS status Theorem
% 1.25/0.65 % SZS output start CNFRefutation
% See solution above
% 1.25/0.66 % Parsed axioms : 321
% 1.25/0.66 % Removed by relevancy pruning/SinE : 29
% 1.25/0.66 % Initial clauses : 648
% 1.25/0.66 % Removed in clause preprocessing : 4
% 1.25/0.66 % Initial clauses in saturation : 644
% 1.25/0.66 % Processed clauses : 3207
% 1.25/0.66 % ...of these trivial : 40
% 1.25/0.66 % ...subsumed : 1826
% 1.25/0.66 % ...remaining for further processing : 1341
% 1.25/0.66 % Other redundant clauses eliminated : 92
% 1.25/0.66 % Clauses deleted for lack of memory : 0
% 1.25/0.66 % Backward-subsumed : 74
% 1.25/0.66 % Backward-rewritten : 65
% 1.25/0.66 % Generated clauses : 7876
% 1.25/0.66 % ...of the previous two non-redundant : 6696
% 1.25/0.66 % ...aggressively subsumed : 0
% 1.25/0.66 % Contextual simplify-reflections : 11
% 1.25/0.66 % Paramodulations : 7790
% 1.25/0.66 % Factorizations : 2
% 1.25/0.66 % NegExts : 0
% 1.25/0.66 % Equation resolutions : 95
% 1.25/0.66 % Disequality decompositions : 0
% 1.25/0.66 % Total rewrite steps : 2349
% 1.25/0.66 % ...of those cached : 2110
% 1.25/0.66 % Propositional unsat checks : 0
% 1.25/0.66 % Propositional check models : 0
% 1.25/0.66 % Propositional check unsatisfiable : 0
% 1.25/0.66 % Propositional clauses : 0
% 1.25/0.66 % Propositional clauses after purity: 0
% 1.25/0.66 % Propositional unsat core size : 0
% 1.25/0.66 % Propositional preprocessing time : 0.000
% 1.25/0.66 % Propositional encoding time : 0.000
% 1.25/0.66 % Propositional solver time : 0.000
% 1.25/0.66 % Success case prop preproc time : 0.000
% 1.25/0.66 % Success case prop encoding time : 0.000
% 1.25/0.66 % Success case prop solver time : 0.000
% 1.25/0.66 % Current number of processed clauses : 1145
% 1.25/0.66 % Positive orientable unit clauses : 175
% 1.25/0.66 % Positive unorientable unit clauses: 4
% 1.25/0.66 % Negative unit clauses : 325
% 1.25/0.66 % Non-unit-clauses : 641
% 1.25/0.66 % Current number of unprocessed clauses: 4095
% 1.25/0.66 % ...number of literals in the above : 12369
% 1.25/0.66 % Current number of archived formulas : 0
% 1.25/0.66 % Current number of archived clauses : 139
% 1.25/0.66 % Clause-clause subsumption calls (NU) : 136330
% 1.25/0.66 % Rec. Clause-clause subsumption calls : 90094
% 1.25/0.66 % Non-unit clause-clause subsumptions : 675
% 1.25/0.66 % Unit Clause-clause subsumption calls : 24837
% 1.25/0.66 % Rewrite failures with RHS unbound : 0
% 1.25/0.66 % BW rewrite match attempts : 99
% 1.25/0.66 % BW rewrite match successes : 45
% 1.25/0.66 % Condensation attempts : 0
% 1.25/0.66 % Condensation successes : 0
% 1.25/0.66 % Termbank termtop insertions : 117825
% 1.25/0.66 % Search garbage collected termcells : 11389
% 1.25/0.66
% 1.25/0.66 % -------------------------------------------------
% 1.25/0.66 % User time : 0.185 s
% 1.25/0.66 % System time : 0.012 s
% 1.25/0.66 % Total time : 0.197 s
% 1.25/0.66 % Maximum resident set size: 5780 pages
% 1.25/0.66
% 1.25/0.66 % -------------------------------------------------
% 1.25/0.66 % User time : 0.191 s
% 1.25/0.66 % System time : 0.013 s
% 1.25/0.66 % Total time : 0.204 s
% 1.25/0.66 % Maximum resident set size: 4864 pages
% 1.25/0.66 % E exiting
%------------------------------------------------------------------------------