%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU261+1 : 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 : n010.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 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 46 ( 11 unt; 0 def)
% Number of atoms : 201 ( 0 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 250 ( 95 ~; 83 |; 37 &)
% ( 2 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 42 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t53_wellord1,axiom,
! [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(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(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(c_0_3,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_4,axiom,
! [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_3]) ).
fof(c_0_5,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_6,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_3]) ).
fof(c_0_7,plain,
! [X14,X15,X16] :
( ~ relation(X14)
| ~ relation(X15)
| ~ relation(X16)
| ~ function(X16)
| ~ relation_isomorphism(X14,X15,X16)
| epred1_2(X15,X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,negated_conjecture,
( relation(esk2_0)
& relation(esk3_0)
& relation(esk4_0)
& function(esk4_0)
& well_ordering(esk2_0)
& relation_isomorphism(esk2_0,esk3_0,esk4_0)
& ~ well_ordering(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_9,plain,
! [X20,X21] :
( ( ~ reflexive(X20)
| reflexive(X21)
| ~ epred1_2(X21,X20) )
& ( ~ transitive(X20)
| transitive(X21)
| ~ epred1_2(X21,X20) )
& ( ~ connected(X20)
| connected(X21)
| ~ epred1_2(X21,X20) )
& ( ~ antisymmetric(X20)
| antisymmetric(X21)
| ~ epred1_2(X21,X20) )
& ( ~ well_founded_relation(X20)
| well_founded_relation(X21)
| ~ epred1_2(X21,X20) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_10,plain,
( epred1_2(X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
relation_isomorphism(esk2_0,esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
function(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
relation(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
relation(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_16,plain,
! [X12] :
( ( reflexive(X12)
| ~ well_ordering(X12)
| ~ relation(X12) )
& ( transitive(X12)
| ~ well_ordering(X12)
| ~ relation(X12) )
& ( antisymmetric(X12)
| ~ well_ordering(X12)
| ~ relation(X12) )
& ( connected(X12)
| ~ well_ordering(X12)
| ~ relation(X12) )
& ( well_founded_relation(X12)
| ~ well_ordering(X12)
| ~ relation(X12) )
& ( ~ reflexive(X12)
| ~ transitive(X12)
| ~ antisymmetric(X12)
| ~ connected(X12)
| ~ well_founded_relation(X12)
| well_ordering(X12)
| ~ relation(X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_wellord1])])]) ).
cnf(c_0_17,plain,
( well_founded_relation(X2)
| ~ well_founded_relation(X1)
| ~ epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
epred1_2(esk3_0,esk2_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_10,c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_19,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_16]) ).
cnf(c_0_20,plain,
( well_founded_relation(esk3_0)
| ~ well_founded_relation(esk2_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
~ well_ordering(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,plain,
( ~ well_founded_relation(esk2_0)
| ~ connected(esk3_0)
| ~ antisymmetric(esk3_0)
| ~ transitive(esk3_0)
| ~ reflexive(esk3_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_14])]),c_0_21]) ).
cnf(c_0_23,plain,
( well_founded_relation(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
well_ordering(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,plain,
( connected(X2)
| ~ connected(X1)
| ~ epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,plain,
( ~ connected(esk3_0)
| ~ antisymmetric(esk3_0)
| ~ transitive(esk3_0)
| ~ reflexive(esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_15])]) ).
cnf(c_0_27,plain,
( connected(esk3_0)
| ~ connected(esk2_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_28,plain,
( ~ connected(esk2_0)
| ~ antisymmetric(esk3_0)
| ~ transitive(esk3_0)
| ~ reflexive(esk3_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,plain,
( connected(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_30,plain,
( antisymmetric(X2)
| ~ antisymmetric(X1)
| ~ epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_31,plain,
( ~ antisymmetric(esk3_0)
| ~ transitive(esk3_0)
| ~ reflexive(esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_24]),c_0_15])]) ).
cnf(c_0_32,plain,
( antisymmetric(esk3_0)
| ~ antisymmetric(esk2_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_18]) ).
cnf(c_0_33,plain,
( ~ antisymmetric(esk2_0)
| ~ transitive(esk3_0)
| ~ reflexive(esk3_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,plain,
( antisymmetric(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_35,plain,
( transitive(X2)
| ~ transitive(X1)
| ~ epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_36,plain,
( ~ transitive(esk3_0)
| ~ reflexive(esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_24]),c_0_15])]) ).
cnf(c_0_37,plain,
( transitive(esk3_0)
| ~ transitive(esk2_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_18]) ).
cnf(c_0_38,plain,
( ~ transitive(esk2_0)
| ~ reflexive(esk3_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,plain,
( transitive(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_40,plain,
( reflexive(X2)
| ~ reflexive(X1)
| ~ epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_41,plain,
~ reflexive(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_24]),c_0_15])]) ).
cnf(c_0_42,plain,
( reflexive(esk3_0)
| ~ reflexive(esk2_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_18]) ).
cnf(c_0_43,plain,
~ reflexive(esk2_0),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_44,plain,
( reflexive(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_45,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_24]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU261+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n010.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:53:06 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Theorem for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.372s
%------------------------------------------------------------------------------