%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO500_8 : TPTP v9.3.1. Released v8.0.0.
% 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 03:47:16 PM UTC 2026
% Result : Theorem 0.15s 0.63s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 5 unt; 0 def)
% Number of atoms : 455 ( 0 equ)
% Maximal formula atoms : 131 ( 12 avg)
% Number of connectives : 639 ( 220 ~; 331 |; 83 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 6 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-1 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
tff(decl_23,type,
f: $o > $o ).
tff(decl_24,type,
x: $o ).
tff(decl_25,type,
epred1_0: $o ).
tff(decl_26,type,
epred2_0: $o ).
fof(con,conjecture,
( f(f(f(x)))
<=> f(x) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(c_0_1,negated_conjecture,
~ ( f(f(f(x)))
<=> f(x) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_2,plain,
( epred1_0
<=> ( ( ~ f($false)
| ( ( f($false)
| x )
& ( f($true)
| ~ x ) ) )
& ( ~ f($true)
| ( ( ~ f($false)
| x )
& ( ~ f($true)
| ~ x ) ) ) ) ),
introduced(definition) ).
fof(c_0_3,plain,
( epred2_0
<=> ( ( f($false)
| ( ( f($false)
| x )
& ( f($true)
| ~ x ) ) )
& ( f($true)
| ( ( ~ f($false)
| x )
& ( ~ f($true)
| ~ x ) ) ) ) ),
introduced(definition) ).
fof(c_0_4,negated_conjecture,
~ ( ( ( f($false)
| epred2_0 )
& ( f($true)
| epred1_0 ) )
<=> ( ( f($false)
| x )
& ( f($true)
| ~ x ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[c_0_1]),c_0_2]),c_0_3]) ).
fof(c_0_5,plain,
( ( epred2_0
| ~ f($true)
| ~ f($false) )
& ( epred2_0
| ~ f($true)
| ~ f($true)
| ~ f($false) )
& ( epred2_0
| ~ f($true)
| ~ f($true)
| ~ x )
& ( epred2_0
| ~ f($true)
| x
| ~ f($false) )
& ( epred2_0
| ~ f($true)
| x
| ~ x )
& ( epred2_0
| f($true)
| f($false)
| ~ f($false) )
& ( epred2_0
| f($true)
| f($false)
| ~ f($true)
| ~ f($false) )
& ( epred2_0
| f($true)
| f($false)
| ~ f($true)
| ~ x )
& ( epred2_0
| f($true)
| f($false)
| x
| ~ f($false) )
& ( epred2_0
| f($true)
| f($false)
| x
| ~ x )
& ( epred2_0
| f($true)
| ~ x
| ~ f($false) )
& ( epred2_0
| f($true)
| ~ x
| ~ f($true)
| ~ f($false) )
& ( epred2_0
| f($true)
| ~ x
| ~ f($true)
| ~ x )
& ( epred2_0
| f($true)
| ~ x
| x
| ~ f($false) )
& ( epred2_0
| f($true)
| ~ x
| x
| ~ x )
& ( epred2_0
| x
| f($false)
| ~ f($false) )
& ( epred2_0
| x
| f($false)
| ~ f($true)
| ~ f($false) )
& ( epred2_0
| x
| f($false)
| ~ f($true)
| ~ x )
& ( epred2_0
| x
| f($false)
| x
| ~ f($false) )
& ( epred2_0
| x
| f($false)
| x
| ~ x )
& ( epred2_0
| x
| ~ x
| ~ f($false) )
& ( epred2_0
| x
| ~ x
| ~ f($true)
| ~ f($false) )
& ( epred2_0
| x
| ~ x
| ~ f($true)
| ~ x )
& ( epred2_0
| x
| ~ x
| x
| ~ f($false) )
& ( epred2_0
| x
| ~ x
| x
| ~ x )
& ( ~ epred2_0
| f($false)
| f($false)
| x )
& ( ~ epred2_0
| f($false)
| f($true)
| ~ x )
& ( ~ epred2_0
| f($true)
| ~ f($false)
| x )
& ( ~ epred2_0
| f($true)
| ~ f($true)
| ~ x ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_6,negated_conjecture,
( ( f($false)
| epred2_0
| f($false)
| x )
& ( f($false)
| epred2_0
| f($true)
| ~ x )
& ( f($true)
| epred1_0
| f($false)
| x )
& ( f($true)
| epred1_0
| f($true)
| ~ x )
& ( ~ f($true)
| ~ f($false)
| ~ f($true)
| ~ f($false) )
& ( ~ f($true)
| ~ f($false)
| ~ f($true)
| ~ x )
& ( ~ f($true)
| ~ f($false)
| x
| ~ f($false) )
& ( ~ f($true)
| ~ f($false)
| x
| ~ x )
& ( ~ f($true)
| ~ epred2_0
| ~ f($true)
| ~ f($false) )
& ( ~ f($true)
| ~ epred2_0
| ~ f($true)
| ~ x )
& ( ~ f($true)
| ~ epred2_0
| x
| ~ f($false) )
& ( ~ f($true)
| ~ epred2_0
| x
| ~ x )
& ( ~ epred1_0
| ~ f($false)
| ~ f($true)
| ~ f($false) )
& ( ~ epred1_0
| ~ f($false)
| ~ f($true)
| ~ x )
& ( ~ epred1_0
| ~ f($false)
| x
| ~ f($false) )
& ( ~ epred1_0
| ~ f($false)
| x
| ~ x )
& ( ~ epred1_0
| ~ epred2_0
| ~ f($true)
| ~ f($false) )
& ( ~ epred1_0
| ~ epred2_0
| ~ f($true)
| ~ x )
& ( ~ epred1_0
| ~ epred2_0
| x
| ~ f($false) )
& ( ~ epred1_0
| ~ epred2_0
| x
| ~ x ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_7,plain,
( ~ epred2_0
| f($false)
| f($false)
| x ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( f($false)
| epred2_0
| f($false)
| x ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( ~ f($true)
| ~ epred2_0
| ~ f($true)
| ~ x ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ f($true)
| ~ f($true)
| ~ x
| epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
( ~ f($true)
| ~ f($false)
| ~ f($true)
| ~ f($false) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( ~ epred2_0
| f($false)
| x ),
inference(cn,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
( f($false)
| epred2_0
| x ),
inference(cn,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( ~ f($true)
| ~ epred2_0
| ~ x ),
inference(cn,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ f($true)
| ~ x
| epred2_0 ),
inference(cn,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( ~ f($false)
| ~ f($true) ),
inference(cn,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( f($false)
| x ),
inference(csr,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( ~ f($true)
| ~ x ),
inference(csr,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( ~ x
| f($false)
| epred2_0
| f($true) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,plain,
~ f($true),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( ~ x
| f($true)
| epred1_0
| f($true) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
( ~ epred1_0
| ~ f($false)
| ~ f($false)
| x ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_23,plain,
( ( epred1_0
| f($true)
| f($false) )
& ( epred1_0
| f($true)
| ~ f($true)
| ~ f($false) )
& ( epred1_0
| f($true)
| ~ f($true)
| ~ x )
& ( epred1_0
| f($true)
| x
| ~ f($false) )
& ( epred1_0
| f($true)
| x
| ~ x )
& ( epred1_0
| f($true)
| f($false)
| f($false) )
& ( epred1_0
| f($true)
| f($false)
| ~ f($true)
| ~ f($false) )
& ( epred1_0
| f($true)
| f($false)
| ~ f($true)
| ~ x )
& ( epred1_0
| f($true)
| f($false)
| x
| ~ f($false) )
& ( epred1_0
| f($true)
| f($false)
| x
| ~ x )
& ( epred1_0
| f($true)
| ~ x
| f($false) )
& ( epred1_0
| f($true)
| ~ x
| ~ f($true)
| ~ f($false) )
& ( epred1_0
| f($true)
| ~ x
| ~ f($true)
| ~ x )
& ( epred1_0
| f($true)
| ~ x
| x
| ~ f($false) )
& ( epred1_0
| f($true)
| ~ x
| x
| ~ x )
& ( epred1_0
| x
| f($false)
| f($false) )
& ( epred1_0
| x
| f($false)
| ~ f($true)
| ~ f($false) )
& ( epred1_0
| x
| f($false)
| ~ f($true)
| ~ x )
& ( epred1_0
| x
| f($false)
| x
| ~ f($false) )
& ( epred1_0
| x
| f($false)
| x
| ~ x )
& ( epred1_0
| x
| ~ x
| f($false) )
& ( epred1_0
| x
| ~ x
| ~ f($true)
| ~ f($false) )
& ( epred1_0
| x
| ~ x
| ~ f($true)
| ~ x )
& ( epred1_0
| x
| ~ x
| x
| ~ f($false) )
& ( epred1_0
| x
| ~ x
| x
| ~ x )
& ( ~ epred1_0
| ~ f($false)
| f($false)
| x )
& ( ~ epred1_0
| ~ f($false)
| f($true)
| ~ x )
& ( ~ epred1_0
| ~ f($true)
| ~ f($false)
| x )
& ( ~ epred1_0
| ~ f($true)
| ~ f($true)
| ~ x ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).
cnf(c_0_24,plain,
( ~ epred2_0
| ~ x
| f($false)
| f($true) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_25,negated_conjecture,
( f($false)
| epred2_0 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_19,c_0_20]),c_0_17]) ).
cnf(c_0_26,negated_conjecture,
( ~ x
| f($true)
| epred1_0 ),
inference(cn,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( ~ f($false)
| ~ epred1_0
| x ),
inference(cn,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( ~ f($false)
| epred1_0
| f($true)
| x ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
f($false),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_24,c_0_20]),c_0_17]),c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( ~ x
| epred1_0 ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( ~ epred1_0
| x ),
inference(csr,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_32,plain,
epred1_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]),c_0_20]),c_0_30]) ).
cnf(c_0_33,plain,
( ~ epred1_0
| ~ f($false)
| ~ x
| f($true) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,negated_conjecture,
x,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_35,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_32]),c_0_29])]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO500_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.57 % Computer : n005.cluster.edu
% 0.12/0.57 % Model : x86_64 x86_64
% 0.12/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.57 % Memory : 8046.5625MB
% 0.12/0.57 % OS : Linux 6.8.0-71-generic
% 0.12/0.57 % CPULimit : 300
% 0.12/0.57 % WCLimit : 300
% 0.12/0.57 % DateTime : Mon Sep 21 11:53:35 UTC 2026
% 0.12/0.57 % CPUTime :
% 0.12/0.57 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.61 Running first-order theorem proving
% 0.15/0.61 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
% 0.15/0.63 % Version: 3.5.1
% 0.15/0.63 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.63 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.63 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.63 % Starting sh5l with 300s (1) cores
% 0.15/0.63 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3405147 completed with status 0
% 0.15/0.63 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.15/0.63 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.63 % No SInE strategy applied
% 0.15/0.63 % Search class: FGHNF-FFSS00-SFFFFFNN
% 0.15/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.63 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.15/0.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/0.63 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.63 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.63 % SubtermCWHack with pid 3405151 completed with status 0
% 0.15/0.63 % Result found by SubtermCWHack
% 0.15/0.63 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.63 % No SInE strategy applied
% 0.15/0.63 % Search class: FGHNF-FFSS00-SFFFFFNN
% 0.15/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.63 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.63 % Preprocessing time : 0.001 s
% 0.15/0.63
% 0.15/0.63 % Proof found!
% 0.15/0.63 % SZS status Theorem
% 0.15/0.63 % SZS output start CNFRefutation
% See solution above
% 0.15/0.64 % Parsed axioms : 3
% 0.15/0.64 % Removed by relevancy pruning/SinE : 0
% 0.15/0.64 % Initial clauses : 80
% 0.15/0.64 % Removed in clause preprocessing : 48
% 0.15/0.64 % Initial clauses in saturation : 32
% 0.15/0.64 % Processed clauses : 32
% 0.15/0.64 % ...of these trivial : 1
% 0.15/0.64 % ...subsumed : 11
% 0.15/0.64 % ...remaining for further processing : 19
% 0.15/0.64 % Other redundant clauses eliminated : 0
% 0.15/0.64 % Clauses deleted for lack of memory : 0
% 0.15/0.64 % Backward-subsumed : 12
% 0.15/0.64 % Backward-rewritten : 1
% 0.15/0.64 % Generated clauses : 7
% 0.15/0.64 % ...of the previous two non-redundant : 5
% 0.15/0.64 % ...aggressively subsumed : 0
% 0.15/0.64 % Contextual simplify-reflections : 9
% 0.15/0.64 % Paramodulations : 6
% 0.15/0.64 % Factorizations : 0
% 0.15/0.64 % NegExts : 0
% 0.15/0.64 % Equation resolutions : 0
% 0.15/0.64 % Disequality decompositions : 0
% 0.15/0.64 % Total rewrite steps : 9
% 0.15/0.64 % ...of those cached : 6
% 0.15/0.64 % Propositional unsat checks : 0
% 0.15/0.64 % Propositional check models : 0
% 0.15/0.64 % Propositional check unsatisfiable : 0
% 0.15/0.64 % Propositional clauses : 0
% 0.15/0.64 % Propositional clauses after purity: 0
% 0.15/0.64 % Propositional unsat core size : 0
% 0.15/0.64 % Propositional preprocessing time : 0.000
% 0.15/0.64 % Propositional encoding time : 0.000
% 0.15/0.64 % Propositional solver time : 0.000
% 0.15/0.64 % Success case prop preproc time : 0.000
% 0.15/0.64 % Success case prop encoding time : 0.000
% 0.15/0.64 % Success case prop solver time : 0.000
% 0.15/0.64 % Current number of processed clauses : 5
% 0.15/0.64 % Positive orientable unit clauses : 4
% 0.15/0.64 % Positive unorientable unit clauses: 0
% 0.15/0.64 % Negative unit clauses : 1
% 0.15/0.64 % Non-unit-clauses : 0
% 0.15/0.64 % Current number of unprocessed clauses: 5
% 0.15/0.64 % ...number of literals in the above : 20
% 0.15/0.64 % Current number of archived formulas : 0
% 0.15/0.64 % Current number of archived clauses : 14
% 0.15/0.64 % Clause-clause subsumption calls (NU) : 18
% 0.15/0.64 % Rec. Clause-clause subsumption calls : 18
% 0.15/0.64 % Non-unit clause-clause subsumptions : 18
% 0.15/0.64 % Unit Clause-clause subsumption calls : 7
% 0.15/0.64 % Rewrite failures with RHS unbound : 0
% 0.15/0.64 % BW rewrite match attempts : 2
% 0.15/0.64 % BW rewrite match successes : 2
% 0.15/0.64 % Condensation attempts : 0
% 0.15/0.64 % Condensation successes : 0
% 0.15/0.64 % Termbank termtop insertions : 2527
% 0.15/0.64 % Search garbage collected termcells : 474
% 0.15/0.64
% 0.15/0.64 % -------------------------------------------------
% 0.15/0.64 % User time : 0.002 s
% 0.15/0.64 % System time : 0.004 s
% 0.15/0.64 % Total time : 0.007 s
% 0.15/0.64 % Maximum resident set size: 3572 pages
% 0.15/0.64
% 0.15/0.64 % -------------------------------------------------
% 0.15/0.64 % User time : 0.010 s
% 0.15/0.64 % System time : 0.015 s
% 0.15/0.64 % Total time : 0.025 s
% 0.15/0.64 % Maximum resident set size: 4864 pages
% 0.15/0.64 % E exiting
%------------------------------------------------------------------------------