%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET776+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 02:15:21 PM UTC 2026
% Result : Theorem 0.21s 0.59s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 151 ( 0 equ)
% Maximal formula atoms : 46 ( 6 avg)
% Number of connectives : 182 ( 56 ~; 68 |; 44 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIII12,conjecture,
! [X4,X8,X7] :
( ( ! [X1,X2] :
( ( member(X2,X4)
& member(X1,X4) )
=> ( apply(X7,X1,X2)
<=> ( apply(X8,X2,X1)
& apply(X8,X1,X2) ) ) )
& pre_order(X8,X4) )
=> ! [X9,X10,X11,X12] :
( ( member(X12,X4)
& member(X11,X4)
& member(X10,X4)
& member(X9,X4) )
=> ( ( apply(X8,X9,X10)
& apply(X7,X10,X12)
& apply(X7,X9,X11) )
=> apply(X8,X11,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII12) ).
fof(pre_order,axiom,
! [X7,X4] :
( pre_order(X7,X4)
<=> ( ! [X3,X5,X6] :
( ( member(X6,X4)
& member(X5,X4)
& member(X3,X4) )
=> ( ( apply(X7,X5,X6)
& apply(X7,X3,X5) )
=> apply(X7,X3,X6) ) )
& ! [X3] :
( member(X3,X4)
=> apply(X7,X3,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',pre_order) ).
fof(c_0_2,negated_conjecture,
~ ! [X4,X8,X7] :
( ( ! [X1,X2] :
( ( member(X2,X4)
& member(X1,X4) )
=> ( apply(X7,X1,X2)
<=> ( apply(X8,X2,X1)
& apply(X8,X1,X2) ) ) )
& pre_order(X8,X4) )
=> ! [X9,X10,X11,X12] :
( ( member(X12,X4)
& member(X11,X4)
& member(X10,X4)
& member(X9,X4) )
=> ( ( apply(X8,X9,X10)
& apply(X7,X10,X12)
& apply(X7,X9,X11) )
=> apply(X8,X11,X12) ) ) ),
inference(assume_negation,[status(cth)],[thIII12]) ).
fof(c_0_3,negated_conjecture,
! [X16,X17] :
( ~ apply(esk2_0,esk6_0,esk7_0)
& apply(esk2_0,esk4_0,esk5_0)
& apply(esk3_0,esk5_0,esk7_0)
& apply(esk3_0,esk4_0,esk6_0)
& member(esk7_0,esk1_0)
& member(esk6_0,esk1_0)
& member(esk5_0,esk1_0)
& member(esk4_0,esk1_0)
& ( ~ member(X17,esk1_0)
| ~ member(X16,esk1_0)
| apply(esk3_0,X16,X17)
| ~ apply(esk2_0,X17,X16)
| ~ apply(esk2_0,X16,X17) )
& ( ~ member(X17,esk1_0)
| ~ member(X16,esk1_0)
| ~ apply(esk3_0,X16,X17)
| apply(esk2_0,X17,X16) )
& ( ~ member(X17,esk1_0)
| ~ member(X16,esk1_0)
| ~ apply(esk3_0,X16,X17)
| apply(esk2_0,X16,X17) )
& pre_order(esk2_0,esk1_0) ),
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_2])])])])])]) ).
fof(c_0_4,plain,
! [X22,X23,X24,X25,X26,X27,X28,X29] :
( ( pre_order(X28,X29)
| ~ apply(X28,esk8_2(X28,X29),esk8_2(X28,X29))
| ~ apply(X28,esk9_2(X28,X29),esk11_2(X28,X29)) )
& ( pre_order(X28,X29)
| ~ apply(X28,esk8_2(X28,X29),esk8_2(X28,X29))
| apply(X28,esk10_2(X28,X29),esk11_2(X28,X29)) )
& ( pre_order(X28,X29)
| ~ apply(X28,esk8_2(X28,X29),esk8_2(X28,X29))
| apply(X28,esk9_2(X28,X29),esk10_2(X28,X29)) )
& ( pre_order(X28,X29)
| ~ apply(X28,esk8_2(X28,X29),esk8_2(X28,X29))
| member(esk11_2(X28,X29),X29) )
& ( pre_order(X28,X29)
| ~ apply(X28,esk8_2(X28,X29),esk8_2(X28,X29))
| member(esk10_2(X28,X29),X29) )
& ( pre_order(X28,X29)
| ~ apply(X28,esk8_2(X28,X29),esk8_2(X28,X29))
| member(esk9_2(X28,X29),X29) )
& ( pre_order(X28,X29)
| member(esk8_2(X28,X29),X29)
| ~ apply(X28,esk9_2(X28,X29),esk11_2(X28,X29)) )
& ( pre_order(X28,X29)
| member(esk8_2(X28,X29),X29)
| apply(X28,esk10_2(X28,X29),esk11_2(X28,X29)) )
& ( pre_order(X28,X29)
| member(esk8_2(X28,X29),X29)
| apply(X28,esk9_2(X28,X29),esk10_2(X28,X29)) )
& ( pre_order(X28,X29)
| member(esk8_2(X28,X29),X29)
| member(esk11_2(X28,X29),X29) )
& ( pre_order(X28,X29)
| member(esk8_2(X28,X29),X29)
| member(esk10_2(X28,X29),X29) )
& ( pre_order(X28,X29)
| member(esk8_2(X28,X29),X29)
| member(esk9_2(X28,X29),X29) )
& ( ~ pre_order(X22,X23)
| apply(X22,X25,X27)
| ~ apply(X22,X26,X27)
| ~ apply(X22,X25,X26)
| ~ member(X27,X23)
| ~ member(X26,X23)
| ~ member(X25,X23) )
& ( ~ pre_order(X22,X23)
| apply(X22,X24,X24)
| ~ member(X24,X23) ) ),
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)],[pre_order])])])])])])]) ).
cnf(c_0_5,negated_conjecture,
( ~ member(X2,esk1_0)
| ~ member(X1,esk1_0)
| ~ apply(esk3_0,X1,X2)
| apply(esk2_0,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
apply(esk3_0,esk5_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,negated_conjecture,
member(esk7_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_8,negated_conjecture,
member(esk5_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_9,plain,
( ~ pre_order(X5,X2)
| ~ apply(X5,X3,X4)
| ~ apply(X5,X1,X3)
| ~ member(X4,X2)
| ~ member(X3,X2)
| ~ member(X1,X2)
| apply(X5,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
apply(esk2_0,esk5_0,esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]),c_0_8])]) ).
cnf(c_0_11,negated_conjecture,
apply(esk2_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_12,negated_conjecture,
( ~ member(X1,X2)
| ~ member(esk5_0,X2)
| ~ member(esk7_0,X2)
| ~ apply(esk2_0,X1,esk5_0)
| ~ pre_order(esk2_0,X2)
| apply(esk2_0,X1,esk7_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
pre_order(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_14,negated_conjecture,
( ~ member(X1,X2)
| ~ member(esk4_0,X2)
| ~ member(esk5_0,X2)
| ~ apply(esk2_0,X1,esk4_0)
| ~ pre_order(esk2_0,X2)
| apply(esk2_0,X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
member(esk4_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_16,negated_conjecture,
( ~ member(X1,esk1_0)
| ~ member(X2,esk1_0)
| ~ apply(esk3_0,X2,X1)
| apply(esk2_0,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_17,negated_conjecture,
apply(esk3_0,esk4_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_18,negated_conjecture,
member(esk6_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_19,negated_conjecture,
( ~ member(X1,esk1_0)
| ~ apply(esk2_0,X1,esk5_0)
| apply(esk2_0,X1,esk7_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_7]),c_0_8])]) ).
cnf(c_0_20,negated_conjecture,
~ apply(esk2_0,esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_21,negated_conjecture,
( ~ member(X1,esk1_0)
| ~ apply(esk2_0,X1,esk4_0)
| apply(esk2_0,X1,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_8]),c_0_15])]) ).
cnf(c_0_22,negated_conjecture,
apply(esk2_0,esk6_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_15]),c_0_18])]) ).
cnf(c_0_23,negated_conjecture,
~ apply(esk2_0,esk6_0,esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_20]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_22])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET776+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.45 % Computer : n010.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 05:37:25 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.55 Running first-order theorem proving
% 0.21/0.55 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
% 0.21/0.59 % Version: 3.5.1
% 0.21/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.59 % Starting sh5l with 300s (1) cores
% 0.21/0.59 % new_bool_1 with pid 126290 completed with status 0
% 0.21/0.59 % Result found by new_bool_1
% 0.21/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.59 % Search class: FGUNF-FFMM22-SFFFFFNN
% 0.21/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.59 % SubtermCWHack with pid 126293 completed with status 0
% 0.21/0.59 % Result found by SubtermCWHack
% 0.21/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.59 % Search class: FGUNF-FFMM22-SFFFFFNN
% 0.21/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.59 % Preprocessing time : 0.002 s
% 0.21/0.59
% 0.21/0.59 % Proof found!
% 0.21/0.59 % SZS status Theorem
% 0.21/0.59 % SZS output start CNFRefutation
% See solution above
% 0.21/0.59 % Parsed axioms : 17
% 0.21/0.59 % Removed by relevancy pruning/SinE : 15
% 0.21/0.59 % Initial clauses : 26
% 0.21/0.59 % Removed in clause preprocessing : 0
% 0.21/0.59 % Initial clauses in saturation : 26
% 0.21/0.59 % Processed clauses : 76
% 0.21/0.59 % ...of these trivial : 0
% 0.21/0.59 % ...subsumed : 3
% 0.21/0.59 % ...remaining for further processing : 73
% 0.21/0.59 % Other redundant clauses eliminated : 0
% 0.21/0.59 % Clauses deleted for lack of memory : 0
% 0.21/0.59 % Backward-subsumed : 2
% 0.21/0.59 % Backward-rewritten : 2
% 0.21/0.59 % Generated clauses : 151
% 0.21/0.59 % ...of the previous two non-redundant : 101
% 0.21/0.59 % ...aggressively subsumed : 0
% 0.21/0.59 % Contextual simplify-reflections : 0
% 0.21/0.59 % Paramodulations : 151
% 0.21/0.59 % Factorizations : 0
% 0.21/0.59 % NegExts : 0
% 0.21/0.59 % Equation resolutions : 0
% 0.21/0.59 % Disequality decompositions : 0
% 0.21/0.59 % Total rewrite steps : 114
% 0.21/0.59 % ...of those cached : 98
% 0.21/0.59 % Propositional unsat checks : 0
% 0.21/0.59 % Propositional check models : 0
% 0.21/0.59 % Propositional check unsatisfiable : 0
% 0.21/0.59 % Propositional clauses : 0
% 0.21/0.59 % Propositional clauses after purity: 0
% 0.21/0.59 % Propositional unsat core size : 0
% 0.21/0.59 % Propositional preprocessing time : 0.000
% 0.21/0.59 % Propositional encoding time : 0.000
% 0.21/0.59 % Propositional solver time : 0.000
% 0.21/0.59 % Success case prop preproc time : 0.000
% 0.21/0.59 % Success case prop encoding time : 0.000
% 0.21/0.59 % Success case prop solver time : 0.000
% 0.21/0.59 % Current number of processed clauses : 69
% 0.21/0.60 % Positive orientable unit clauses : 23
% 0.21/0.60 % Positive unorientable unit clauses: 0
% 0.21/0.60 % Negative unit clauses : 2
% 0.21/0.60 % Non-unit-clauses : 44
% 0.21/0.60 % Current number of unprocessed clauses: 48
% 0.21/0.60 % ...number of literals in the above : 277
% 0.21/0.60 % Current number of archived formulas : 0
% 0.21/0.60 % Current number of archived clauses : 4
% 0.21/0.60 % Clause-clause subsumption calls (NU) : 382
% 0.21/0.60 % Rec. Clause-clause subsumption calls : 121
% 0.21/0.60 % Non-unit clause-clause subsumptions : 0
% 0.21/0.60 % Unit Clause-clause subsumption calls : 85
% 0.21/0.60 % Rewrite failures with RHS unbound : 0
% 0.21/0.60 % BW rewrite match attempts : 21
% 0.21/0.60 % BW rewrite match successes : 1
% 0.21/0.60 % Condensation attempts : 0
% 0.21/0.60 % Condensation successes : 0
% 0.21/0.60 % Termbank termtop insertions : 5145
% 0.21/0.60 % Search garbage collected termcells : 656
% 0.21/0.60
% 0.21/0.60 % -------------------------------------------------
% 0.21/0.60 % User time : 0.015 s
% 0.21/0.60 % System time : 0.003 s
% 0.21/0.60 % Total time : 0.018 s
% 0.21/0.60 % Maximum resident set size: 3668 pages
% 0.21/0.60
% 0.21/0.60 % -------------------------------------------------
% 0.21/0.60 % User time : 0.018 s
% 0.21/0.60 % System time : 0.009 s
% 0.21/0.60 % Total time : 0.027 s
% 0.21/0.60 % Maximum resident set size: 4608 pages
% 0.21/0.60 % E exiting
%------------------------------------------------------------------------------