%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU257+1 : 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 : n007.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 02:24:28 PM UTC 2026
% Result : Theorem 0.23s 0.56s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 5 unt; 0 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 224 ( 102 ~; 94 |; 11 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 7 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t31_wellord1,axiom,
! [X1,X2] :
( relation(X2)
=> ( well_founded_relation(X2)
=> well_founded_relation(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_wellord1) ).
fof(dt_k2_wellord1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(t23_wellord1,axiom,
! [X1,X2] :
( relation(X2)
=> ( connected(X2)
=> connected(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_wellord1) ).
fof(t25_wellord1,axiom,
! [X1,X2] :
( relation(X2)
=> ( antisymmetric(X2)
=> antisymmetric(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_wellord1) ).
fof(t24_wellord1,axiom,
! [X1,X2] :
( relation(X2)
=> ( transitive(X2)
=> transitive(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_wellord1) ).
fof(t32_wellord1,conjecture,
! [X1,X2] :
( relation(X2)
=> ( well_ordering(X2)
=> well_ordering(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_wellord1) ).
fof(t22_wellord1,axiom,
! [X1,X2] :
( relation(X2)
=> ( reflexive(X2)
=> reflexive(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_wellord1) ).
fof(c_0_8,plain,
! [X5] :
( ( ~ relation(X5)
| well_ordering(X5)
| ~ well_founded_relation(X5)
| ~ connected(X5)
| ~ antisymmetric(X5)
| ~ transitive(X5)
| ~ reflexive(X5) )
& ( ~ relation(X5)
| ~ well_ordering(X5)
| well_founded_relation(X5) )
& ( ~ relation(X5)
| ~ well_ordering(X5)
| connected(X5) )
& ( ~ relation(X5)
| ~ well_ordering(X5)
| antisymmetric(X5) )
& ( ~ relation(X5)
| ~ well_ordering(X5)
| transitive(X5) )
& ( ~ relation(X5)
| ~ well_ordering(X5)
| reflexive(X5) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_wellord1])])])]) ).
fof(c_0_9,plain,
! [X8,X9] :
( well_founded_relation(relation_restriction(X9,X8))
| ~ well_founded_relation(X9)
| ~ relation(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t31_wellord1])])]) ).
fof(c_0_10,plain,
! [X6,X7] :
( relation(relation_restriction(X6,X7))
| ~ relation(X6) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_wellord1])])]) ).
cnf(c_0_11,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_8]) ).
cnf(c_0_12,plain,
( ~ well_founded_relation(X1)
| ~ relation(X1)
| well_founded_relation(relation_restriction(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( ~ relation(X1)
| relation(relation_restriction(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X10,X11] :
( connected(relation_restriction(X11,X10))
| ~ connected(X11)
| ~ relation(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_wellord1])])]) ).
cnf(c_0_15,plain,
( ~ relation(X1)
| ~ reflexive(relation_restriction(X1,X2))
| ~ transitive(relation_restriction(X1,X2))
| ~ antisymmetric(relation_restriction(X1,X2))
| ~ connected(relation_restriction(X1,X2))
| ~ well_founded_relation(X1)
| well_ordering(relation_restriction(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_16,plain,
( ~ connected(X1)
| ~ relation(X1)
| connected(relation_restriction(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_17,plain,
! [X12,X13] :
( antisymmetric(relation_restriction(X13,X12))
| ~ antisymmetric(X13)
| ~ relation(X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t25_wellord1])])]) ).
cnf(c_0_18,plain,
( ~ relation(X1)
| ~ reflexive(relation_restriction(X1,X2))
| ~ transitive(relation_restriction(X1,X2))
| ~ antisymmetric(relation_restriction(X1,X2))
| ~ connected(X1)
| ~ well_founded_relation(X1)
| well_ordering(relation_restriction(X1,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( ~ antisymmetric(X1)
| ~ relation(X1)
| antisymmetric(relation_restriction(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X14,X15] :
( transitive(relation_restriction(X15,X14))
| ~ transitive(X15)
| ~ relation(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t24_wellord1])])]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> ( well_ordering(X2)
=> well_ordering(relation_restriction(X2,X1)) ) ),
inference(assume_negation,[status(cth)],[t32_wellord1]) ).
cnf(c_0_22,plain,
( ~ relation(X1)
| ~ reflexive(relation_restriction(X1,X2))
| ~ transitive(relation_restriction(X1,X2))
| ~ antisymmetric(X1)
| ~ connected(X1)
| ~ well_founded_relation(X1)
| well_ordering(relation_restriction(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ transitive(X1)
| ~ relation(X1)
| transitive(relation_restriction(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_24,plain,
! [X16,X17] :
( reflexive(relation_restriction(X17,X16))
| ~ reflexive(X17)
| ~ relation(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_wellord1])])]) ).
fof(c_0_25,negated_conjecture,
( ~ well_ordering(relation_restriction(esk2_0,esk1_0))
& well_ordering(esk2_0)
& relation(esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_26,plain,
( ~ relation(X1)
| ~ reflexive(relation_restriction(X1,X2))
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ connected(X1)
| ~ well_founded_relation(X1)
| well_ordering(relation_restriction(X1,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( ~ reflexive(X1)
| ~ relation(X1)
| reflexive(relation_restriction(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
~ well_ordering(relation_restriction(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,plain,
( ~ relation(X1)
| ~ reflexive(X1)
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ connected(X1)
| ~ well_founded_relation(X1)
| well_ordering(relation_restriction(X1,X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
relation(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( ~ reflexive(esk2_0)
| ~ transitive(esk2_0)
| ~ antisymmetric(esk2_0)
| ~ connected(esk2_0)
| ~ well_founded_relation(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_32,plain,
( ~ relation(X1)
| ~ well_ordering(X1)
| well_founded_relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_33,negated_conjecture,
well_ordering(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,negated_conjecture,
( ~ reflexive(esk2_0)
| ~ transitive(esk2_0)
| ~ antisymmetric(esk2_0)
| ~ connected(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_30])]) ).
cnf(c_0_35,plain,
( ~ relation(X1)
| ~ well_ordering(X1)
| connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_36,negated_conjecture,
( ~ reflexive(esk2_0)
| ~ transitive(esk2_0)
| ~ antisymmetric(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_33]),c_0_30])]) ).
cnf(c_0_37,plain,
( ~ relation(X1)
| ~ well_ordering(X1)
| antisymmetric(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_38,negated_conjecture,
( ~ reflexive(esk2_0)
| ~ transitive(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_33]),c_0_30])]) ).
cnf(c_0_39,plain,
( ~ relation(X1)
| ~ well_ordering(X1)
| transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_40,negated_conjecture,
~ reflexive(esk2_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_33]),c_0_30])]) ).
cnf(c_0_41,plain,
( ~ relation(X1)
| ~ well_ordering(X1)
| reflexive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_33]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU257+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.46 % Computer : n007.cluster.edu
% 0.17/0.46 % Model : x86_64 x86_64
% 0.17/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.46 % Memory : 8046.5625MB
% 0.17/0.46 % OS : Linux 6.8.0-71-generic
% 0.17/0.46 % CPULimit : 300
% 0.17/0.46 % WCLimit : 300
% 0.17/0.46 % DateTime : Mon Sep 21 06:02:21 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.53 Running first-order theorem proving
% 0.23/0.53 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
% 0.23/0.56 % Version: 3.5.1
% 0.23/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.56 % Starting sh5l with 300s (1) cores
% 0.23/0.56 % new_bool_3 with pid 338150 completed with status 0
% 0.23/0.56 % Result found by new_bool_3
% 0.23/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.56 % Search class: FHUNF-FFSF22-SFFFFFNN
% 0.23/0.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.56 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.56 % SubtermCWHack with pid 338155 completed with status 0
% 0.23/0.56 % Result found by SubtermCWHack
% 0.23/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.56 % Search class: FHUNF-FFSF22-SFFFFFNN
% 0.23/0.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.56 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.56 % Preprocessing time : 0.002 s
% 0.23/0.56
% 0.23/0.56 % Proof found!
% 0.23/0.56 % SZS status Theorem
% 0.23/0.56 % SZS output start CNFRefutation
% See solution above
% 0.23/0.56 % Parsed axioms : 13
% 0.23/0.56 % Removed by relevancy pruning/SinE : 5
% 0.23/0.56 % Initial clauses : 15
% 0.23/0.56 % Removed in clause preprocessing : 0
% 0.23/0.56 % Initial clauses in saturation : 15
% 0.23/0.56 % Processed clauses : 25
% 0.23/0.56 % ...of these trivial : 0
% 0.23/0.56 % ...subsumed : 0
% 0.23/0.56 % ...remaining for further processing : 25
% 0.23/0.56 % Other redundant clauses eliminated : 0
% 0.23/0.56 % Clauses deleted for lack of memory : 0
% 0.23/0.56 % Backward-subsumed : 4
% 0.23/0.56 % Backward-rewritten : 0
% 0.23/0.56 % Generated clauses : 16
% 0.23/0.56 % ...of the previous two non-redundant : 10
% 0.23/0.57 % ...aggressively subsumed : 0
% 0.23/0.57 % Contextual simplify-reflections : 1
% 0.23/0.57 % Paramodulations : 16
% 0.23/0.57 % Factorizations : 0
% 0.23/0.57 % NegExts : 0
% 0.23/0.57 % Equation resolutions : 0
% 0.23/0.57 % Disequality decompositions : 0
% 0.23/0.57 % Total rewrite steps : 11
% 0.23/0.57 % ...of those cached : 9
% 0.23/0.57 % Propositional unsat checks : 0
% 0.23/0.57 % Propositional check models : 0
% 0.23/0.57 % Propositional check unsatisfiable : 0
% 0.23/0.57 % Propositional clauses : 0
% 0.23/0.57 % Propositional clauses after purity: 0
% 0.23/0.57 % Propositional unsat core size : 0
% 0.23/0.57 % Propositional preprocessing time : 0.000
% 0.23/0.57 % Propositional encoding time : 0.000
% 0.23/0.57 % Propositional solver time : 0.000
% 0.23/0.57 % Success case prop preproc time : 0.000
% 0.23/0.57 % Success case prop encoding time : 0.000
% 0.23/0.57 % Success case prop solver time : 0.000
% 0.23/0.57 % Current number of processed clauses : 21
% 0.23/0.57 % Positive orientable unit clauses : 2
% 0.23/0.57 % Positive unorientable unit clauses: 0
% 0.23/0.57 % Negative unit clauses : 2
% 0.23/0.57 % Non-unit-clauses : 17
% 0.23/0.57 % Current number of unprocessed clauses: 0
% 0.23/0.57 % ...number of literals in the above : 0
% 0.23/0.57 % Current number of archived formulas : 0
% 0.23/0.57 % Current number of archived clauses : 4
% 0.23/0.57 % Clause-clause subsumption calls (NU) : 70
% 0.23/0.57 % Rec. Clause-clause subsumption calls : 20
% 0.23/0.57 % Non-unit clause-clause subsumptions : 4
% 0.23/0.57 % Unit Clause-clause subsumption calls : 8
% 0.23/0.57 % Rewrite failures with RHS unbound : 0
% 0.23/0.57 % BW rewrite match attempts : 0
% 0.23/0.57 % BW rewrite match successes : 0
% 0.23/0.57 % Condensation attempts : 0
% 0.23/0.57 % Condensation successes : 0
% 0.23/0.57 % Termbank termtop insertions : 1490
% 0.23/0.57 % Search garbage collected termcells : 232
% 0.23/0.57
% 0.23/0.57 % -------------------------------------------------
% 0.23/0.57 % User time : 0.006 s
% 0.23/0.57 % System time : 0.005 s
% 0.23/0.57 % Total time : 0.011 s
% 0.23/0.57 % Maximum resident set size: 3640 pages
% 0.23/0.57
% 0.23/0.57 % -------------------------------------------------
% 0.23/0.57 % User time : 0.008 s
% 0.23/0.57 % System time : 0.011 s
% 0.23/0.57 % Total time : 0.020 s
% 0.23/0.57 % Maximum resident set size: 4864 pages
% 0.23/0.57 % E exiting
%------------------------------------------------------------------------------