%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM500+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 01:49:19 PM UTC 2026
% Result : Theorem 0.27s 0.64s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 165 ( 79 equ)
% Maximal formula atoms : 73 ( 8 avg)
% Number of connectives : 215 ( 70 ~; 90 |; 50 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 8 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( ( isPrime0(X1)
| ( ! [X2] :
( ( doDivides0(X2,X1)
& ? [X3] :
( X1 = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) )
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) )
& ( doDivides0(X1,xk)
| ? [X2] :
( xk = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mPrimDiv,axiom,
! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ? [X2] :
( isPrime0(X2)
& doDivides0(X2,X1)
& aNaturalNumber0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).
fof(m__2315,hypothesis,
~ ( xk = sz10
| xk = sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
fof(m__2306,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(c_0_4,negated_conjecture,
~ ? [X1] :
( ( isPrime0(X1)
| ( ! [X2] :
( ( doDivides0(X2,X1)
& ? [X3] :
( X1 = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) )
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) )
& ( doDivides0(X1,xk)
| ? [X2] :
( xk = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_5,negated_conjecture,
~ ? [X1] :
( ( isPrime0(X1)
| ( ! [X2] :
( ( doDivides0(X2,X1)
& ? [X3] :
( X1 = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) )
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) )
& ( doDivides0(X1,xk)
| ? [X2] :
( xk = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_6,plain,
! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ? [X2] :
( isPrime0(X2)
& doDivides0(X2,X1)
& aNaturalNumber0(X2) ) ),
inference(fof_simplification,[status(thm)],[mPrimDiv]) ).
fof(c_0_7,negated_conjecture,
! [X106,X107] :
( ( ~ aNaturalNumber0(X106)
| ~ doDivides0(X106,xk)
| ~ isPrime0(X106) )
& ( ~ aNaturalNumber0(X106)
| ~ doDivides0(X106,xk)
| X106 = sz10
| X106 = sz00
| esk12_1(X106) != X106 )
& ( ~ aNaturalNumber0(X106)
| ~ doDivides0(X106,xk)
| X106 = sz10
| X106 = sz00
| esk12_1(X106) != sz10 )
& ( ~ aNaturalNumber0(X106)
| ~ doDivides0(X106,xk)
| X106 = sz10
| X106 = sz00
| doDivides0(esk12_1(X106),X106) )
& ( ~ aNaturalNumber0(X106)
| ~ doDivides0(X106,xk)
| X106 = sz10
| X106 = sz00
| X106 = sdtasdt0(esk12_1(X106),esk13_1(X106)) )
& ( ~ aNaturalNumber0(X106)
| ~ doDivides0(X106,xk)
| X106 = sz10
| X106 = sz00
| aNaturalNumber0(esk13_1(X106)) )
& ( ~ aNaturalNumber0(X106)
| ~ doDivides0(X106,xk)
| X106 = sz10
| X106 = sz00
| aNaturalNumber0(esk12_1(X106)) )
& ( ~ aNaturalNumber0(X106)
| xk != sdtasdt0(X106,X107)
| ~ aNaturalNumber0(X107)
| ~ isPrime0(X106) )
& ( ~ aNaturalNumber0(X106)
| xk != sdtasdt0(X106,X107)
| ~ aNaturalNumber0(X107)
| X106 = sz10
| X106 = sz00
| esk12_1(X106) != X106 )
& ( ~ aNaturalNumber0(X106)
| xk != sdtasdt0(X106,X107)
| ~ aNaturalNumber0(X107)
| X106 = sz10
| X106 = sz00
| esk12_1(X106) != sz10 )
& ( ~ aNaturalNumber0(X106)
| xk != sdtasdt0(X106,X107)
| ~ aNaturalNumber0(X107)
| X106 = sz10
| X106 = sz00
| doDivides0(esk12_1(X106),X106) )
& ( ~ aNaturalNumber0(X106)
| xk != sdtasdt0(X106,X107)
| ~ aNaturalNumber0(X107)
| X106 = sz10
| X106 = sz00
| X106 = sdtasdt0(esk12_1(X106),esk13_1(X106)) )
& ( ~ aNaturalNumber0(X106)
| xk != sdtasdt0(X106,X107)
| ~ aNaturalNumber0(X107)
| X106 = sz10
| X106 = sz00
| aNaturalNumber0(esk13_1(X106)) )
& ( ~ aNaturalNumber0(X106)
| xk != sdtasdt0(X106,X107)
| ~ aNaturalNumber0(X107)
| X106 = sz10
| X106 = sz00
| aNaturalNumber0(esk12_1(X106)) ) ),
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_5])])])])])]) ).
fof(c_0_8,plain,
! [X89] :
( ( X89 = sz10
| X89 = sz00
| ~ aNaturalNumber0(X89)
| isPrime0(esk4_1(X89)) )
& ( X89 = sz10
| X89 = sz00
| ~ aNaturalNumber0(X89)
| doDivides0(esk4_1(X89),X89) )
& ( X89 = sz10
| X89 = sz00
| ~ aNaturalNumber0(X89)
| aNaturalNumber0(esk4_1(X89)) ) ),
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_6])])])])]) ).
fof(c_0_9,hypothesis,
( xk != sz10
& xk != sz00 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2315])]) ).
cnf(c_0_10,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xk)
| ~ isPrime0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz10
| X1 = sz00
| doDivides0(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_13,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
xk != sz10,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( ~ aNaturalNumber0(esk4_1(xk))
| ~ isPrime0(esk4_1(xk)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),c_0_13]),c_0_14]) ).
cnf(c_0_16,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz10
| X1 = sz00
| isPrime0(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
~ aNaturalNumber0(esk4_1(xk)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_12])]),c_0_13]),c_0_14]) ).
cnf(c_0_18,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_12])]),c_0_13]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM500+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n002.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 02:38:02 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.50 Running first-order theorem proving
% 0.16/0.50 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
% 0.27/0.64 % Version: 3.5.1
% 0.27/0.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.64 % Starting sh5l with 300s (1) cores
% 0.27/0.64 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2245203 completed with status 0
% 0.27/0.64 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.27/0.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.64 % No SInE strategy applied
% 0.27/0.64 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.27/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.27/0.64 % Starting G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.27/0.64 % Starting new_bool_3 with 136s (1) cores
% 0.27/0.64 % Starting U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1 with 136s (1) cores
% 0.27/0.64 % new_bool_3 with pid 2245210 completed with status 0
% 0.27/0.64 % Result found by new_bool_3
% 0.27/0.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.64 % No SInE strategy applied
% 0.27/0.64 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.27/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.27/0.64 % Starting G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.27/0.64 % Starting new_bool_3 with 136s (1) cores
% 0.27/0.64 % Preprocessing time : 0.009 s
% 0.27/0.64 % Presaturation interreduction done
% 0.27/0.64
% 0.27/0.64 % Proof found!
% 0.27/0.64 % SZS status Theorem
% 0.27/0.64 % SZS output start CNFRefutation
% See solution above
% 0.27/0.64 % Parsed axioms : 48
% 0.27/0.64 % Removed by relevancy pruning/SinE : 0
% 0.27/0.64 % Initial clauses : 240
% 0.27/0.64 % Removed in clause preprocessing : 3
% 0.27/0.64 % Initial clauses in saturation : 237
% 0.27/0.64 % Processed clauses : 344
% 0.27/0.64 % ...of these trivial : 1
% 0.27/0.64 % ...subsumed : 18
% 0.27/0.64 % ...remaining for further processing : 325
% 0.27/0.64 % Other redundant clauses eliminated : 17
% 0.27/0.64 % Clauses deleted for lack of memory : 0
% 0.27/0.64 % Backward-subsumed : 2
% 0.27/0.64 % Backward-rewritten : 0
% 0.27/0.64 % Generated clauses : 103
% 0.27/0.64 % ...of the previous two non-redundant : 78
% 0.27/0.64 % ...aggressively subsumed : 0
% 0.27/0.64 % Contextual simplify-reflections : 6
% 0.27/0.64 % Paramodulations : 82
% 0.27/0.64 % Factorizations : 2
% 0.27/0.64 % NegExts : 0
% 0.27/0.64 % Equation resolutions : 19
% 0.27/0.64 % Disequality decompositions : 0
% 0.27/0.64 % Total rewrite steps : 116
% 0.27/0.64 % ...of those cached : 104
% 0.27/0.64 % Propositional unsat checks : 0
% 0.27/0.64 % Propositional check models : 0
% 0.27/0.64 % Propositional check unsatisfiable : 0
% 0.27/0.64 % Propositional clauses : 0
% 0.27/0.64 % Propositional clauses after purity: 0
% 0.27/0.64 % Propositional unsat core size : 0
% 0.27/0.64 % Propositional preprocessing time : 0.000
% 0.27/0.64 % Propositional encoding time : 0.000
% 0.27/0.64 % Propositional solver time : 0.000
% 0.27/0.64 % Success case prop preproc time : 0.000
% 0.27/0.64 % Success case prop encoding time : 0.000
% 0.27/0.64 % Success case prop solver time : 0.000
% 0.27/0.64 % Current number of processed clauses : 82
% 0.27/0.64 % Positive orientable unit clauses : 26
% 0.27/0.64 % Positive unorientable unit clauses: 0
% 0.27/0.64 % Negative unit clauses : 14
% 0.27/0.64 % Non-unit-clauses : 42
% 0.27/0.64 % Current number of unprocessed clauses: 201
% 0.27/0.64 % ...number of literals in the above : 1611
% 0.27/0.64 % Current number of archived formulas : 0
% 0.27/0.64 % Current number of archived clauses : 232
% 0.27/0.64 % Clause-clause subsumption calls (NU) : 33244
% 0.27/0.64 % Rec. Clause-clause subsumption calls : 175
% 0.27/0.64 % Non-unit clause-clause subsumptions : 11
% 0.27/0.64 % Unit Clause-clause subsumption calls : 122
% 0.27/0.64 % Rewrite failures with RHS unbound : 0
% 0.27/0.64 % BW rewrite match attempts : 0
% 0.27/0.64 % BW rewrite match successes : 0
% 0.27/0.64 % Condensation attempts : 0
% 0.27/0.64 % Condensation successes : 0
% 0.27/0.64 % Termbank termtop insertions : 23867
% 0.27/0.64 % Search garbage collected termcells : 2481
% 0.27/0.64
% 0.27/0.64 % -------------------------------------------------
% 0.27/0.64 % User time : 0.107 s
% 0.27/0.64 % System time : 0.008 s
% 0.27/0.64 % Total time : 0.115 s
% 0.27/0.64 % Maximum resident set size: 3956 pages
% 0.27/0.64
% 0.27/0.64 % -------------------------------------------------
% 0.27/0.64 % User time : 0.471 s
% 0.27/0.64 % System time : 0.035 s
% 0.27/0.64 % Total time : 0.506 s
% 0.27/0.64 % Maximum resident set size: 4864 pages
% 0.27/0.64 % E exiting
%------------------------------------------------------------------------------