%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM500+1 : 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 : n013.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 0.26s 0.59s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 12 unt; 0 def)
% Number of atoms : 177 ( 68 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 212 ( 75 ~; 83 |; 39 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 23 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ! [X2] :
( ( doDivides0(X2,X1)
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(m__,conjecture,
? [X1] :
( isPrime0(X1)
& doDivides0(X1,xk)
& 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(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
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),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(c_0_9,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ! [X2] :
( ( doDivides0(X2,X1)
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) ) ),
inference(fof_simplification,[status(thm)],[mDefPrime]) ).
fof(c_0_10,negated_conjecture,
~ ? [X1] :
( isPrime0(X1)
& doDivides0(X1,xk)
& aNaturalNumber0(X1) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_11,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_12,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefQuot]) ).
fof(c_0_13,plain,
! [X84,X85] :
( ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| esk3_1(X84) != X84 )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| esk3_1(X84) != sz10 )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| doDivides0(esk3_1(X84),X84) )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| aNaturalNumber0(esk3_1(X84)) )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X85 = X84
| X85 = sz10
| ~ doDivides0(X85,X84)
| ~ aNaturalNumber0(X85) )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X84 != sz10 )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X84 != sz00 ) ),
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_9])])])])])]) ).
fof(c_0_14,negated_conjecture,
! [X92] :
( ~ isPrime0(X92)
| ~ doDivides0(X92,xk)
| ~ aNaturalNumber0(X92) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_15,plain,
! [X87] :
( ( X87 = sz10
| X87 = sz00
| ~ aNaturalNumber0(X87)
| isPrime0(esk4_1(X87)) )
& ( X87 = sz10
| X87 = sz00
| ~ aNaturalNumber0(X87)
| doDivides0(esk4_1(X87),X87) )
& ( X87 = sz10
| X87 = sz00
| ~ aNaturalNumber0(X87)
| aNaturalNumber0(esk4_1(X87)) ) ),
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_11])])])])]) ).
fof(c_0_16,plain,
! [X67,X68,X69] :
( ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 = sdtsldt0(X68,X67)
| X68 != sdtasdt0(X67,X69)
| ~ aNaturalNumber0(X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| X68 = sdtasdt0(X67,X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| aNaturalNumber0(X69) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])]) ).
cnf(c_0_17,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_19,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_20,negated_conjecture,
( ~ isPrime0(X1)
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz10
| X1 = sz00
| isPrime0(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_23,hypothesis,
( xk != sz10
& xk != sz00 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2315])]) ).
cnf(c_0_24,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_26,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_27,hypothesis,
xp != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
fof(c_0_28,plain,
! [X7,X8] :
( aNaturalNumber0(sdtasdt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_29,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(esk4_1(X1),xk)
| X1 = sz00
| X1 = sz10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_30,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz10
| X1 = sz00
| doDivides0(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_31,hypothesis,
xk != sz10,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| X1 != xk
| aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_19])]),c_0_27]) ).
cnf(c_0_34,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_36,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_37,negated_conjecture,
~ aNaturalNumber0(xk),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]) ).
cnf(c_0_38,hypothesis,
( X1 != xk
| aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36])]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_37,c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM500+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n013.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 02:34:51 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.52 Running first-order theorem proving
% 0.26/0.52 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
% 0.26/0.59 % Version: 3.5.1
% 0.26/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.59 % Starting sh5l with 300s (1) cores
% 0.26/0.59 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3959346 completed with status 0
% 0.26/0.59 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.26/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.59 % No SInE strategy applied
% 0.26/0.59 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.26/0.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.26/0.59 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.26/0.59 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.26/0.59 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.26/0.59 % G-E--_208_C18_F1_AE_CS_SP_PS_S3S with pid 3959356 completed with status 0
% 0.26/0.59 % Result found by G-E--_208_C18_F1_AE_CS_SP_PS_S3S
% 0.26/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.59 % No SInE strategy applied
% 0.26/0.59 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.26/0.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.26/0.59 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.26/0.59 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.26/0.59 % Preprocessing time : 0.004 s
% 0.26/0.59 % Presaturation interreduction done
% 0.26/0.59
% 0.26/0.59 % Proof found!
% 0.26/0.59 % SZS status Theorem
% 0.26/0.59 % SZS output start CNFRefutation
% See solution above
% 0.26/0.59 % Parsed axioms : 48
% 0.26/0.59 % Removed by relevancy pruning/SinE : 0
% 0.26/0.59 % Initial clauses : 88
% 0.26/0.59 % Removed in clause preprocessing : 3
% 0.26/0.59 % Initial clauses in saturation : 85
% 0.26/0.59 % Processed clauses : 185
% 0.26/0.59 % ...of these trivial : 0
% 0.26/0.59 % ...subsumed : 18
% 0.26/0.59 % ...remaining for further processing : 167
% 0.26/0.59 % Other redundant clauses eliminated : 9
% 0.26/0.59 % Clauses deleted for lack of memory : 0
% 0.26/0.59 % Backward-subsumed : 3
% 0.26/0.59 % Backward-rewritten : 0
% 0.26/0.59 % Generated clauses : 187
% 0.26/0.59 % ...of the previous two non-redundant : 150
% 0.26/0.59 % ...aggressively subsumed : 0
% 0.26/0.59 % Contextual simplify-reflections : 5
% 0.26/0.59 % Paramodulations : 168
% 0.26/0.59 % Factorizations : 2
% 0.26/0.59 % NegExts : 0
% 0.26/0.59 % Equation resolutions : 17
% 0.26/0.59 % Disequality decompositions : 0
% 0.26/0.59 % Total rewrite steps : 96
% 0.26/0.59 % ...of those cached : 90
% 0.26/0.59 % Propositional unsat checks : 0
% 0.26/0.59 % Propositional check models : 0
% 0.26/0.59 % Propositional check unsatisfiable : 0
% 0.26/0.59 % Propositional clauses : 0
% 0.26/0.59 % Propositional clauses after purity: 0
% 0.26/0.59 % Propositional unsat core size : 0
% 0.26/0.59 % Propositional preprocessing time : 0.000
% 0.26/0.59 % Propositional encoding time : 0.000
% 0.26/0.59 % Propositional solver time : 0.000
% 0.26/0.59 % Success case prop preproc time : 0.000
% 0.26/0.59 % Success case prop encoding time : 0.000
% 0.26/0.59 % Success case prop solver time : 0.000
% 0.26/0.59 % Current number of processed clauses : 85
% 0.26/0.59 % Positive orientable unit clauses : 12
% 0.26/0.59 % Positive unorientable unit clauses: 0
% 0.26/0.59 % Negative unit clauses : 11
% 0.26/0.59 % Non-unit-clauses : 62
% 0.26/0.59 % Current number of unprocessed clauses: 128
% 0.26/0.59 % ...number of literals in the above : 586
% 0.26/0.59 % Current number of archived formulas : 0
% 0.26/0.59 % Current number of archived clauses : 81
% 0.26/0.59 % Clause-clause subsumption calls (NU) : 1388
% 0.26/0.59 % Rec. Clause-clause subsumption calls : 153
% 0.26/0.59 % Non-unit clause-clause subsumptions : 22
% 0.26/0.59 % Unit Clause-clause subsumption calls : 77
% 0.26/0.59 % Rewrite failures with RHS unbound : 0
% 0.26/0.59 % BW rewrite match attempts : 0
% 0.26/0.59 % BW rewrite match successes : 0
% 0.26/0.59 % Condensation attempts : 0
% 0.26/0.59 % Condensation successes : 0
% 0.26/0.59 % Termbank termtop insertions : 10402
% 0.26/0.59 % Search garbage collected termcells : 1375
% 0.26/0.59
% 0.26/0.59 % -------------------------------------------------
% 0.26/0.59 % User time : 0.031 s
% 0.26/0.59 % System time : 0.007 s
% 0.26/0.59 % Total time : 0.038 s
% 0.26/0.59 % Maximum resident set size: 3940 pages
% 0.26/0.59
% 0.26/0.59 % -------------------------------------------------
% 0.26/0.59 % User time : 0.121 s
% 0.26/0.59 % System time : 0.029 s
% 0.26/0.59 % Total time : 0.150 s
% 0.26/0.59 % Maximum resident set size: 4864 pages
% 0.26/0.59 % E exiting
%------------------------------------------------------------------------------