%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET800+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 : 7
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 96 ( 30 ~; 30 |; 24 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 62 ( 3 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV12,conjecture,
! [X6,X4] :
( order(X6,X4)
=> ! [X9,X10] :
( ( subset(X9,X10)
& subset(X10,X4)
& subset(X9,X4) )
=> ! [X11,X12] :
( ( greatest_lower_bound(X12,X10,X6,X4)
& greatest_lower_bound(X11,X9,X6,X4) )
=> apply(X6,X12,X11) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV12) ).
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/sandbox/benchmark/Axioms/SET006+3.ax',greatest_lower_bound) ).
fof(lower_bound,axiom,
! [X6,X4,X8] :
( lower_bound(X8,X6,X4)
<=> ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',lower_bound) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(c_0_4,negated_conjecture,
~ ! [X6,X4] :
( order(X6,X4)
=> ! [X9,X10] :
( ( subset(X9,X10)
& subset(X10,X4)
& subset(X9,X4) )
=> ! [X11,X12] :
( ( greatest_lower_bound(X12,X10,X6,X4)
& greatest_lower_bound(X11,X9,X6,X4) )
=> apply(X6,X12,X11) ) ) ),
inference(assume_negation,[status(cth)],[thIV12]) ).
fof(c_0_5,plain,
! [X19,X20,X21,X22,X23,X24,X25,X26,X27] :
( ( greatest_lower_bound(X24,X25,X26,X27)
| ~ lower_bound(X24,X26,X25)
| ~ member(X24,X25)
| ~ apply(X26,esk7_4(X24,X25,X26,X27),X24) )
& ( greatest_lower_bound(X24,X25,X26,X27)
| ~ lower_bound(X24,X26,X25)
| ~ member(X24,X25)
| lower_bound(esk7_4(X24,X25,X26,X27),X26,X25) )
& ( greatest_lower_bound(X24,X25,X26,X27)
| ~ lower_bound(X24,X26,X25)
| ~ member(X24,X25)
| member(esk7_4(X24,X25,X26,X27),X27) )
& ( ~ greatest_lower_bound(X19,X20,X21,X22)
| apply(X21,X23,X19)
| ~ lower_bound(X23,X21,X20)
| ~ member(X23,X22) )
& ( ~ greatest_lower_bound(X19,X20,X21,X22)
| lower_bound(X19,X21,X20) )
& ( ~ greatest_lower_bound(X19,X20,X21,X22)
| member(X19,X20) ) ),
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])])])])])])]) ).
fof(c_0_6,negated_conjecture,
( ~ apply(esk1_0,esk6_0,esk5_0)
& greatest_lower_bound(esk6_0,esk4_0,esk1_0,esk2_0)
& greatest_lower_bound(esk5_0,esk3_0,esk1_0,esk2_0)
& subset(esk3_0,esk4_0)
& subset(esk4_0,esk2_0)
& subset(esk3_0,esk2_0)
& order(esk1_0,esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_7,plain,
! [X37,X38,X39,X40,X41,X42,X43] :
( ( lower_bound(X43,X41,X42)
| ~ apply(X41,X43,esk9_3(X41,X42,X43)) )
& ( lower_bound(X43,X41,X42)
| member(esk9_3(X41,X42,X43),X42) )
& ( apply(X37,X39,X40)
| ~ member(X40,X38)
| ~ lower_bound(X39,X37,X38) ) ),
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_8,plain,
( ~ greatest_lower_bound(X1,X3,X2,X4)
| lower_bound(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
greatest_lower_bound(esk6_0,esk4_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ member(X4,X3)
| ~ lower_bound(X1,X2,X3)
| apply(X2,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
lower_bound(esk6_0,esk1_0,esk4_0),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
fof(c_0_12,plain,
! [X29,X30,X31,X32,X33] :
( ( subset(X32,X33)
| ~ member(esk8_2(X32,X33),X33) )
& ( subset(X32,X33)
| member(esk8_2(X32,X33),X32) )
& ( member(X31,X30)
| ~ member(X31,X29)
| ~ subset(X29,X30) ) ),
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)],[subset])])])])])])]) ).
cnf(c_0_13,negated_conjecture,
~ apply(esk1_0,esk6_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( ~ member(X1,esk4_0)
| apply(esk1_0,esk6_0,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,plain,
( ~ greatest_lower_bound(X1,X2,X3,X4)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
greatest_lower_bound(esk5_0,esk3_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
~ member(esk5_0,esk4_0),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( ~ member(X1,esk3_0)
| member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
member(esk5_0,esk3_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET800+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % 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 05:38:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.45 % 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 2665196 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: FGUSF-FFLM32-SFFFFFNN
% 0.11/0.45 % partial match(1): FGUSF-FFMM32-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 2665198 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: FGUSF-FFLM32-SFFFFFNN
% 0.11/0.45 % partial match(1): FGUSF-FFMM32-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 : 0.003 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 : 17
% 0.11/0.45 % Initial clauses : 84
% 0.11/0.45 % Removed in clause preprocessing : 0
% 0.11/0.45 % Initial clauses in saturation : 84
% 0.11/0.45 % Processed clauses : 38
% 0.11/0.45 % ...of these trivial : 0
% 0.11/0.45 % ...subsumed : 1
% 0.11/0.45 % ...remaining for further processing : 37
% 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 : 0
% 0.11/0.45 % Backward-rewritten : 0
% 0.11/0.45 % Generated clauses : 29
% 0.11/0.45 % ...of the previous two non-redundant : 23
% 0.11/0.45 % ...aggressively subsumed : 0
% 0.11/0.45 % Contextual simplify-reflections : 0
% 0.11/0.45 % Paramodulations : 29
% 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 : 4
% 0.11/0.45 % ...of those cached : 0
% 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 : 37
% 0.11/0.45 % Positive orientable unit clauses : 14
% 0.11/0.45 % Positive unorientable unit clauses: 0
% 0.11/0.45 % Negative unit clauses : 2
% 0.11/0.45 % Non-unit-clauses : 21
% 0.11/0.45 % Current number of unprocessed clauses: 69
% 0.11/0.45 % ...number of literals in the above : 277
% 0.11/0.45 % Current number of archived formulas : 0
% 0.11/0.45 % Current number of archived clauses : 0
% 0.11/0.45 % Clause-clause subsumption calls (NU) : 104
% 0.11/0.45 % Rec. Clause-clause subsumption calls : 57
% 0.11/0.45 % Non-unit clause-clause subsumptions : 1
% 0.11/0.45 % Unit Clause-clause subsumption calls : 24
% 0.11/0.45 % Rewrite failures with RHS unbound : 0
% 0.11/0.45 % BW rewrite match attempts : 4
% 0.11/0.45 % BW rewrite match successes : 0
% 0.11/0.45 % Condensation attempts : 0
% 0.11/0.45 % Condensation successes : 0
% 0.11/0.45 % Termbank termtop insertions : 4527
% 0.11/0.45 % Search garbage collected termcells : 1139
% 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 : 0.013 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 : 0.013 s
% 0.11/0.45 % System time : 0.010 s
% 0.11/0.45 % Total time : 0.023 s
% 0.11/0.45 % Maximum resident set size: 4864 pages
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------