%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU243+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 : n013.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 02:24:25 PM UTC 2026
% Result : Theorem 0.26s 0.57s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 4 unt; 0 def)
% Number of atoms : 137 ( 16 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 184 ( 76 ~; 74 |; 22 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 51 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_well_founded_in(X1,X2)
<=> ! [X3] :
~ ( ! [X4] :
~ ( disjoint(fiber(X1,X4),X3)
& in(X4,X3) )
& X3 != empty_set
& subset(X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_wellord1) ).
fof(d2_wellord1,axiom,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> ! [X2] :
~ ( ! [X3] :
~ ( disjoint(fiber(X1,X3),X2)
& in(X3,X2) )
& X2 != empty_set
& subset(X2,relation_field(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_wellord1) ).
fof(t5_wellord1,conjecture,
! [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(c_0_3,plain,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_well_founded_in(X1,X2)
<=> ! [X3] :
~ ( ! [X4] :
~ ( disjoint(fiber(X1,X4),X3)
& in(X4,X3) )
& X3 != empty_set
& subset(X3,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d3_wellord1]) ).
fof(c_0_4,plain,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> ! [X2] :
~ ( ! [X3] :
~ ( disjoint(fiber(X1,X3),X2)
& in(X3,X2) )
& X2 != empty_set
& subset(X2,relation_field(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[d2_wellord1]) ).
fof(c_0_5,plain,
! [X6,X7,X8,X10,X12] :
( ( ~ relation(X6)
| is_well_founded_in(X6,X10)
| ~ disjoint(fiber(X6,X12),esk3_2(X6,X10))
| ~ in(X12,esk3_2(X6,X10)) )
& ( ~ relation(X6)
| is_well_founded_in(X6,X10)
| esk3_2(X6,X10) != empty_set )
& ( ~ relation(X6)
| is_well_founded_in(X6,X10)
| subset(esk3_2(X6,X10),X10) )
& ( ~ relation(X6)
| ~ is_well_founded_in(X6,X7)
| X8 = empty_set
| ~ subset(X8,X7)
| disjoint(fiber(X6,esk2_3(X6,X7,X8)),X8) )
& ( ~ relation(X6)
| ~ is_well_founded_in(X6,X7)
| X8 = empty_set
| ~ subset(X8,X7)
| in(esk2_3(X6,X7,X8),X8) ) ),
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)],[c_0_3])])])])])])]) ).
fof(c_0_6,plain,
! [X13,X14,X17] :
( ( ~ relation(X13)
| well_founded_relation(X13)
| ~ disjoint(fiber(X13,X17),esk5_1(X13))
| ~ in(X17,esk5_1(X13)) )
& ( ~ relation(X13)
| well_founded_relation(X13)
| esk5_1(X13) != empty_set )
& ( ~ relation(X13)
| well_founded_relation(X13)
| subset(esk5_1(X13),relation_field(X13)) )
& ( ~ relation(X13)
| ~ well_founded_relation(X13)
| X14 = empty_set
| ~ subset(X14,relation_field(X13))
| disjoint(fiber(X13,esk4_2(X13,X14)),X14) )
& ( ~ relation(X13)
| ~ well_founded_relation(X13)
| X14 = empty_set
| ~ subset(X14,relation_field(X13))
| in(esk4_2(X13,X14),X14) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
inference(assume_negation,[status(cth)],[t5_wellord1]) ).
cnf(c_0_8,plain,
( ~ relation(X2)
| ~ disjoint(fiber(X2,X1),esk3_2(X2,X3))
| ~ in(X1,esk3_2(X2,X3))
| is_well_founded_in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1))
| X2 = empty_set
| disjoint(fiber(X1,esk4_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1))
| X2 = empty_set
| in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( ~ relation(X1)
| esk3_2(X1,X2) != empty_set
| is_well_founded_in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_12,negated_conjecture,
( ( is_well_founded_in(esk1_0,relation_field(esk1_0))
| well_founded_relation(esk1_0) )
& ( ~ is_well_founded_in(esk1_0,relation_field(esk1_0))
| ~ well_founded_relation(esk1_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_7])])])]) ).
cnf(c_0_13,plain,
( ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(esk3_2(X1,X2),relation_field(X1))
| is_well_founded_in(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]),c_0_11]) ).
cnf(c_0_14,plain,
( ~ relation(X1)
| is_well_founded_in(X1,X2)
| subset(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,plain,
( ~ relation(X2)
| ~ disjoint(fiber(X2,X1),esk5_1(X2))
| ~ in(X1,esk5_1(X2))
| well_founded_relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2)
| X3 = empty_set
| disjoint(fiber(X1,esk2_3(X1,X2,X3)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,plain,
( ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2)
| X3 = empty_set
| in(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,plain,
( ~ relation(X1)
| esk5_1(X1) != empty_set
| well_founded_relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( ~ is_well_founded_in(esk1_0,relation_field(esk1_0))
| ~ well_founded_relation(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( ~ relation(X1)
| ~ well_founded_relation(X1)
| is_well_founded_in(X1,relation_field(X1)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,negated_conjecture,
relation(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,plain,
( ~ relation(X1)
| ~ subset(esk5_1(X1),X2)
| ~ is_well_founded_in(X1,X2)
| well_founded_relation(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]) ).
cnf(c_0_23,plain,
( ~ relation(X1)
| well_founded_relation(X1)
| subset(esk5_1(X1),relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
( is_well_founded_in(esk1_0,relation_field(esk1_0))
| well_founded_relation(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,negated_conjecture,
~ well_founded_relation(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_26,plain,
( ~ relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1))
| well_founded_relation(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
is_well_founded_in(esk1_0,relation_field(esk1_0)),
inference(sr,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_21])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU243+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n013.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 06:02:21 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 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
% 0.26/0.57 % Version: 3.5.1
% 0.26/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.57 % Starting sh5l with 300s (1) cores
% 0.26/0.57 % new_bool_3 with pid 88617 completed with status 0
% 0.26/0.57 % Result found by new_bool_3
% 0.26/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.57 % Search class: FGHSM-FFMS31-SFFFFFNN
% 0.26/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.57 % SubtermCWHack with pid 88620 completed with status 0
% 0.26/0.57 % Result found by SubtermCWHack
% 0.26/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.57 % Search class: FGHSM-FFMS31-SFFFFFNN
% 0.26/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.57 % Preprocessing time : 0.001 s
% 0.26/0.57
% 0.26/0.57 % Proof found!
% 0.26/0.57 % SZS status Theorem
% 0.26/0.57 % SZS output start CNFRefutation
% See solution above
% 0.26/0.57 % Parsed axioms : 37
% 0.26/0.57 % Removed by relevancy pruning/SinE : 14
% 0.26/0.57 % Initial clauses : 34
% 0.26/0.57 % Removed in clause preprocessing : 0
% 0.26/0.57 % Initial clauses in saturation : 34
% 0.26/0.57 % Processed clauses : 465
% 0.26/0.57 % ...of these trivial : 1
% 0.26/0.57 % ...subsumed : 322
% 0.26/0.57 % ...remaining for further processing : 142
% 0.26/0.57 % Other redundant clauses eliminated : 0
% 0.26/0.57 % Clauses deleted for lack of memory : 0
% 0.26/0.57 % Backward-subsumed : 13
% 0.26/0.57 % Backward-rewritten : 3
% 0.26/0.57 % Generated clauses : 986
% 0.26/0.57 % ...of the previous two non-redundant : 758
% 0.26/0.57 % ...aggressively subsumed : 0
% 0.26/0.57 % Contextual simplify-reflections : 8
% 0.26/0.57 % Paramodulations : 985
% 0.26/0.57 % Factorizations : 0
% 0.26/0.57 % NegExts : 0
% 0.26/0.57 % Equation resolutions : 0
% 0.26/0.57 % Disequality decompositions : 0
% 0.26/0.57 % Total rewrite steps : 448
% 0.26/0.57 % ...of those cached : 436
% 0.26/0.57 % Propositional unsat checks : 0
% 0.26/0.57 % Propositional check models : 0
% 0.26/0.57 % Propositional check unsatisfiable : 0
% 0.26/0.57 % Propositional clauses : 0
% 0.26/0.57 % Propositional clauses after purity: 0
% 0.26/0.57 % Propositional unsat core size : 0
% 0.26/0.57 % Propositional preprocessing time : 0.000
% 0.26/0.57 % Propositional encoding time : 0.000
% 0.26/0.57 % Propositional solver time : 0.000
% 0.26/0.57 % Success case prop preproc time : 0.000
% 0.26/0.57 % Success case prop encoding time : 0.000
% 0.26/0.57 % Success case prop solver time : 0.000
% 0.26/0.57 % Current number of processed clauses : 125
% 0.26/0.57 % Positive orientable unit clauses : 12
% 0.26/0.57 % Positive unorientable unit clauses: 1
% 0.26/0.57 % Negative unit clauses : 3
% 0.26/0.57 % Non-unit-clauses : 109
% 0.26/0.57 % Current number of unprocessed clauses: 297
% 0.26/0.57 % ...number of literals in the above : 1327
% 0.26/0.57 % Current number of archived formulas : 0
% 0.26/0.57 % Current number of archived clauses : 17
% 0.26/0.57 % Clause-clause subsumption calls (NU) : 3389
% 0.26/0.57 % Rec. Clause-clause subsumption calls : 2404
% 0.26/0.57 % Non-unit clause-clause subsumptions : 289
% 0.26/0.57 % Unit Clause-clause subsumption calls : 54
% 0.26/0.57 % Rewrite failures with RHS unbound : 0
% 0.26/0.57 % BW rewrite match attempts : 14
% 0.26/0.57 % BW rewrite match successes : 11
% 0.26/0.57 % Condensation attempts : 0
% 0.26/0.57 % Condensation successes : 0
% 0.26/0.57 % Termbank termtop insertions : 15877
% 0.26/0.57 % Search garbage collected termcells : 533
% 0.26/0.57
% 0.26/0.57 % -------------------------------------------------
% 0.26/0.57 % User time : 0.026 s
% 0.26/0.57 % System time : 0.002 s
% 0.26/0.57 % Total time : 0.028 s
% 0.26/0.57 % Maximum resident set size: 3656 pages
% 0.26/0.57
% 0.26/0.57 % -------------------------------------------------
% 0.26/0.57 % User time : 0.028 s
% 0.26/0.57 % System time : 0.009 s
% 0.26/0.57 % Total time : 0.037 s
% 0.26/0.57 % Maximum resident set size: 4864 pages
% 0.26/0.57 % E exiting
%------------------------------------------------------------------------------