%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET802+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 02:15:25 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 5 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 152 ( 55 ~; 65 |; 20 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 93 ( 3 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV14,conjecture,
! [X6,X4] :
( order(X6,X4)
=> ! [X3] :
( subset(X3,X4)
=> ! [X8] :
( least(X8,X6,X3)
<=> ( greatest_lower_bound(X8,X3,X6,X4)
& member(X8,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV14) ).
fof(least,axiom,
! [X6,X4,X8] :
( least(X8,X6,X4)
<=> ( ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) )
& member(X8,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',least) ).
fof(lower_bound,axiom,
! [X6,X4,X8] :
( lower_bound(X8,X6,X4)
<=> ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',lower_bound) ).
fof(greatest_lower_bound,axiom,
! [X1,X3,X6,X4] :
( greatest_lower_bound(X1,X3,X6,X4)
<=> ( ! [X8] :
( ( lower_bound(X8,X6,X3)
& member(X8,X4) )
=> apply(X6,X8,X1) )
& lower_bound(X1,X6,X3)
& member(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',greatest_lower_bound) ).
fof(c_0_4,negated_conjecture,
~ ! [X6,X4] :
( order(X6,X4)
=> ! [X3] :
( subset(X3,X4)
=> ! [X8] :
( least(X8,X6,X3)
<=> ( greatest_lower_bound(X8,X3,X6,X4)
& member(X8,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[thIV14]) ).
fof(c_0_5,plain,
! [X23,X24,X25,X26,X27,X28,X29] :
( ( least(X29,X27,X28)
| ~ member(X29,X28)
| ~ apply(X27,X29,esk6_3(X27,X28,X29)) )
& ( least(X29,X27,X28)
| ~ member(X29,X28)
| member(esk6_3(X27,X28,X29),X28) )
& ( ~ least(X25,X23,X24)
| apply(X23,X25,X26)
| ~ member(X26,X24) )
& ( ~ least(X25,X23,X24)
| member(X25,X24) ) ),
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)],[least])])])])])])]) ).
fof(c_0_6,negated_conjecture,
( ( least(esk4_0,esk1_0,esk3_0)
| greatest_lower_bound(esk4_0,esk3_0,esk1_0,esk2_0) )
& ( least(esk4_0,esk1_0,esk3_0)
| member(esk4_0,esk3_0) )
& ( ~ greatest_lower_bound(esk4_0,esk3_0,esk1_0,esk2_0)
| ~ member(esk4_0,esk3_0)
| ~ least(esk4_0,esk1_0,esk3_0) )
& subset(esk3_0,esk2_0)
& order(esk1_0,esk2_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
cnf(c_0_7,plain,
( ~ least(X4,X3,X2)
| ~ member(X1,X2)
| apply(X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( least(esk4_0,esk1_0,esk3_0)
| greatest_lower_bound(esk4_0,esk3_0,esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X39,X40,X41,X42,X43,X44,X45] :
( ( lower_bound(X45,X43,X44)
| ~ apply(X43,X45,esk8_3(X43,X44,X45)) )
& ( lower_bound(X45,X43,X44)
| member(esk8_3(X43,X44,X45),X44) )
& ( apply(X39,X41,X42)
| ~ member(X42,X40)
| ~ lower_bound(X41,X39,X40) ) ),
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)],[lower_bound])])])])])])]) ).
cnf(c_0_10,negated_conjecture,
( ~ member(X1,esk3_0)
| apply(esk1_0,esk4_0,X1)
| greatest_lower_bound(esk4_0,esk3_0,esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( lower_bound(X3,X1,X2)
| member(esk8_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20,X21] :
( ( greatest_lower_bound(X18,X19,X20,X21)
| ~ lower_bound(X18,X20,X19)
| ~ member(X18,X19)
| ~ apply(X20,esk5_4(X18,X19,X20,X21),X18) )
& ( greatest_lower_bound(X18,X19,X20,X21)
| ~ lower_bound(X18,X20,X19)
| ~ member(X18,X19)
| lower_bound(esk5_4(X18,X19,X20,X21),X20,X19) )
& ( greatest_lower_bound(X18,X19,X20,X21)
| ~ lower_bound(X18,X20,X19)
| ~ member(X18,X19)
| member(esk5_4(X18,X19,X20,X21),X21) )
& ( ~ greatest_lower_bound(X13,X14,X15,X16)
| apply(X15,X17,X13)
| ~ lower_bound(X17,X15,X14)
| ~ member(X17,X16) )
& ( ~ greatest_lower_bound(X13,X14,X15,X16)
| lower_bound(X13,X15,X14) )
& ( ~ greatest_lower_bound(X13,X14,X15,X16)
| member(X13,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(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[greatest_lower_bound])])])])])])]) ).
cnf(c_0_13,plain,
( ~ apply(X1,X2,esk8_3(X1,X3,X2))
| lower_bound(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( apply(esk1_0,esk4_0,esk8_3(X2,esk3_0,X1))
| lower_bound(X1,X2,esk3_0)
| greatest_lower_bound(esk4_0,esk3_0,esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( ~ greatest_lower_bound(X1,X3,X2,X4)
| lower_bound(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( ~ member(X4,X3)
| ~ lower_bound(X1,X2,X3)
| apply(X2,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
lower_bound(esk4_0,esk1_0,esk3_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
( ~ least(X1,X3,X2)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_19,negated_conjecture,
( least(esk4_0,esk1_0,esk3_0)
| member(esk4_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,plain,
( ~ member(X2,X3)
| ~ apply(X1,X2,esk6_3(X1,X3,X2))
| least(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,negated_conjecture,
( ~ member(X1,esk3_0)
| apply(esk1_0,esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( ~ greatest_lower_bound(esk4_0,esk3_0,esk1_0,esk2_0)
| ~ member(esk4_0,esk3_0)
| ~ least(esk4_0,esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,negated_conjecture,
member(esk4_0,esk3_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( ~ member(esk4_0,X1)
| ~ member(esk6_3(esk1_0,X1,esk4_0),esk3_0)
| least(esk4_0,esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( ~ member(X3,X2)
| least(X3,X1,X2)
| member(esk6_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_26,plain,
( ~ lower_bound(X1,X3,X2)
| ~ member(X1,X2)
| greatest_lower_bound(X1,X2,X3,X4)
| lower_bound(esk5_4(X1,X2,X3,X4),X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,negated_conjecture,
( ~ least(esk4_0,esk1_0,esk3_0)
| ~ greatest_lower_bound(esk4_0,esk3_0,esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_28,negated_conjecture,
least(esk4_0,esk1_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_23])]) ).
cnf(c_0_29,plain,
( ~ lower_bound(X2,X1,X3)
| ~ member(X2,X3)
| ~ apply(X1,esk5_4(X2,X3,X1,X4),X2)
| greatest_lower_bound(X2,X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,plain,
( ~ member(X1,X2)
| ~ member(X5,X2)
| ~ lower_bound(X1,X3,X2)
| apply(X3,esk5_4(X1,X2,X3,X4),X5)
| greatest_lower_bound(X1,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
~ greatest_lower_bound(esk4_0,esk3_0,esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_32,plain,
( ~ member(X1,X2)
| ~ lower_bound(X1,X3,X2)
| greatest_lower_bound(X1,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_17]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET802+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:34:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.11/0.45 % Version: 3.5.1
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % Starting sh5l with 300s (1) cores
% 0.11/0.45 % new_bool_1 with pid 1537708 completed with status 0
% 0.11/0.45 % Result found by new_bool_1
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.45 % Search class: FGHSF-FFLS32-SFFFFFNN
% 0.11/0.45 % partial match(1): FGHSF-FFMS32-SFFFFFNN
% 0.11/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.45 % SubtermCWHack with pid 1537710 completed with status 0
% 0.11/0.45 % Result found by SubtermCWHack
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.45 % Search class: FGHSF-FFLS32-SFFFFFNN
% 0.11/0.45 % partial match(1): FGHSF-FFMS32-SFFFFFNN
% 0.11/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.45 % Preprocessing time : 0.002 s
% 0.11/0.45
% 0.11/0.45 % Proof found!
% 0.11/0.45 % SZS status Theorem
% 0.11/0.45 % SZS output start CNFRefutation
% See solution above
% 0.11/0.45 % Parsed axioms : 22
% 0.11/0.45 % Removed by relevancy pruning/SinE : 16
% 0.11/0.45 % Initial clauses : 86
% 0.11/0.45 % Removed in clause preprocessing : 0
% 0.11/0.45 % Initial clauses in saturation : 86
% 0.11/0.45 % Processed clauses : 92
% 0.11/0.45 % ...of these trivial : 0
% 0.11/0.45 % ...subsumed : 1
% 0.11/0.45 % ...remaining for further processing : 91
% 0.11/0.45 % Other redundant clauses eliminated : 0
% 0.11/0.45 % Clauses deleted for lack of memory : 0
% 0.11/0.45 % Backward-subsumed : 6
% 0.11/0.45 % Backward-rewritten : 5
% 0.11/0.45 % Generated clauses : 70
% 0.11/0.45 % ...of the previous two non-redundant : 58
% 0.11/0.45 % ...aggressively subsumed : 0
% 0.11/0.45 % Contextual simplify-reflections : 1
% 0.11/0.45 % Paramodulations : 68
% 0.11/0.45 % Factorizations : 0
% 0.11/0.45 % NegExts : 0
% 0.11/0.45 % Equation resolutions : 0
% 0.11/0.45 % Disequality decompositions : 0
% 0.11/0.45 % Total rewrite steps : 15
% 0.11/0.45 % ...of those cached : 10
% 0.11/0.45 % Propositional unsat checks : 0
% 0.11/0.45 % Propositional check models : 0
% 0.11/0.45 % Propositional check unsatisfiable : 0
% 0.11/0.45 % Propositional clauses : 0
% 0.11/0.45 % Propositional clauses after purity: 0
% 0.11/0.45 % Propositional unsat core size : 0
% 0.11/0.45 % Propositional preprocessing time : 0.000
% 0.11/0.45 % Propositional encoding time : 0.000
% 0.11/0.45 % Propositional solver time : 0.000
% 0.11/0.45 % Success case prop preproc time : 0.000
% 0.11/0.45 % Success case prop encoding time : 0.000
% 0.11/0.45 % Success case prop solver time : 0.000
% 0.11/0.45 % Current number of processed clauses : 78
% 0.11/0.45 % Positive orientable unit clauses : 8
% 0.11/0.45 % Positive unorientable unit clauses: 0
% 0.11/0.45 % Negative unit clauses : 1
% 0.11/0.45 % Non-unit-clauses : 69
% 0.11/0.45 % Current number of unprocessed clauses: 48
% 0.11/0.45 % ...number of literals in the above : 262
% 0.11/0.45 % Current number of archived formulas : 0
% 0.11/0.45 % Current number of archived clauses : 13
% 0.11/0.45 % Clause-clause subsumption calls (NU) : 1354
% 0.11/0.45 % Rec. Clause-clause subsumption calls : 505
% 0.11/0.45 % Non-unit clause-clause subsumptions : 7
% 0.11/0.45 % Unit Clause-clause subsumption calls : 11
% 0.11/0.45 % Rewrite failures with RHS unbound : 0
% 0.11/0.45 % BW rewrite match attempts : 8
% 0.11/0.45 % BW rewrite match successes : 3
% 0.11/0.45 % Condensation attempts : 0
% 0.11/0.45 % Condensation successes : 0
% 0.11/0.45 % Termbank termtop insertions : 6621
% 0.11/0.45 % Search garbage collected termcells : 1228
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.011 s
% 0.11/0.45 % System time : 0.002 s
% 0.11/0.45 % Total time : 0.014 s
% 0.11/0.45 % Maximum resident set size: 3928 pages
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.012 s
% 0.11/0.45 % System time : 0.008 s
% 0.11/0.45 % Total time : 0.020 s
% 0.11/0.45 % Maximum resident set size: 4864 pages
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------