%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM505+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 01:49:21 PM UTC 2026
% Result : Theorem 0.37s 0.46s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 12 unt; 0 def)
% Number of atoms : 165 ( 54 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 200 ( 75 ~; 73 |; 33 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 27 !; 0 ?)
% 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/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(m__,conjecture,
( ~ sdtlseqdt0(xp,xk)
=> ( sdtlseqdt0(xk,xp)
& xk != xp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mLERefl,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
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,
~ ( ~ sdtlseqdt0(xp,xk)
=> ( sdtlseqdt0(xk,xp)
& xk != xp ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_11,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_12,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_13,negated_conjecture,
~ ( ~ sdtlseqdt0(xp,xk)
=> ( sdtlseqdt0(xk,xp)
& xk != xp ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
fof(c_0_15,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_11])])])])]) ).
cnf(c_0_16,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_18,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_19,negated_conjecture,
( ( ~ sdtlseqdt0(xk,xp)
| xk = xp )
& ~ sdtlseqdt0(xp,xk) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])]) ).
fof(c_0_20,plain,
! [X48,X49] :
( ( ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X48)
| sdtlseqdt0(X48,X49)
| sdtlseqdt0(X49,X48) )
& ( ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X48)
| sdtlseqdt0(X48,X49)
| X49 != X48 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
cnf(c_0_21,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_23,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_24,hypothesis,
xp != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
fof(c_0_25,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_26,negated_conjecture,
( ~ sdtlseqdt0(xk,xp)
| xk = xp ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
~ sdtlseqdt0(xp,xk),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,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_21,c_0_22]),c_0_23]),c_0_18])]),c_0_24]) ).
cnf(c_0_30,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_33,negated_conjecture,
( ~ aNaturalNumber0(xk)
| xk = xp ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_18])]),c_0_28]) ).
cnf(c_0_34,hypothesis,
( X1 != xk
| aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_35,negated_conjecture,
xk = xp,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_36,plain,
! [X42] :
( sdtlseqdt0(X42,X42)
| ~ aNaturalNumber0(X42) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERefl])])]) ).
cnf(c_0_37,negated_conjecture,
~ sdtlseqdt0(xp,xp),
inference(rw,[status(thm)],[c_0_28,c_0_35]) ).
cnf(c_0_38,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM505+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 02:37:43 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.37/0.46 % Version: 3.5.1
% 0.37/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.37/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.37/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.37/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.37/0.46 % Starting sh5l with 300s (1) cores
% 0.37/0.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 783936 completed with status 0
% 0.37/0.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.37/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.37/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.37/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.37/0.46 % No SInE strategy applied
% 0.37/0.46 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.37/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.37/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.37/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.37/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.37/0.46 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.37/0.46 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.37/0.46 % G-E--_208_C18_F1_AE_CS_SP_PS_S3S with pid 783944 completed with status 0
% 0.37/0.46 % Result found by G-E--_208_C18_F1_AE_CS_SP_PS_S3S
% 0.37/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.37/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.37/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.37/0.46 % No SInE strategy applied
% 0.37/0.46 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.37/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.37/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.37/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.37/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.37/0.46 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.37/0.46 % Preprocessing time : 0.003 s
% 0.37/0.46 % Presaturation interreduction done
% 0.37/0.46
% 0.37/0.46 % Proof found!
% 0.37/0.46 % SZS status Theorem
% 0.37/0.46 % SZS output start CNFRefutation
% See solution above
% 0.37/0.46 % Parsed axioms : 50
% 0.37/0.46 % Removed by relevancy pruning/SinE : 0
% 0.37/0.46 % Initial clauses : 94
% 0.37/0.46 % Removed in clause preprocessing : 3
% 0.37/0.46 % Initial clauses in saturation : 91
% 0.37/0.46 % Processed clauses : 211
% 0.37/0.46 % ...of these trivial : 0
% 0.37/0.46 % ...subsumed : 24
% 0.37/0.46 % ...remaining for further processing : 187
% 0.37/0.46 % Other redundant clauses eliminated : 9
% 0.37/0.46 % Clauses deleted for lack of memory : 0
% 0.37/0.46 % Backward-subsumed : 1
% 0.37/0.46 % Backward-rewritten : 12
% 0.37/0.46 % Generated clauses : 201
% 0.37/0.46 % ...of the previous two non-redundant : 170
% 0.37/0.46 % ...aggressively subsumed : 0
% 0.37/0.46 % Contextual simplify-reflections : 4
% 0.37/0.46 % Paramodulations : 183
% 0.37/0.46 % Factorizations : 2
% 0.37/0.46 % NegExts : 0
% 0.37/0.46 % Equation resolutions : 16
% 0.37/0.46 % Disequality decompositions : 0
% 0.37/0.46 % Total rewrite steps : 173
% 0.37/0.46 % ...of those cached : 160
% 0.37/0.46 % Propositional unsat checks : 0
% 0.37/0.46 % Propositional check models : 0
% 0.37/0.46 % Propositional check unsatisfiable : 0
% 0.37/0.46 % Propositional clauses : 0
% 0.37/0.46 % Propositional clauses after purity: 0
% 0.37/0.46 % Propositional unsat core size : 0
% 0.37/0.46 % Propositional preprocessing time : 0.000
% 0.37/0.46 % Propositional encoding time : 0.000
% 0.37/0.46 % Propositional solver time : 0.000
% 0.37/0.46 % Success case prop preproc time : 0.000
% 0.37/0.46 % Success case prop encoding time : 0.000
% 0.37/0.46 % Success case prop solver time : 0.000
% 0.37/0.46 % Current number of processed clauses : 89
% 0.37/0.46 % Positive orientable unit clauses : 17
% 0.37/0.46 % Positive unorientable unit clauses: 0
% 0.37/0.46 % Negative unit clauses : 11
% 0.37/0.46 % Non-unit-clauses : 61
% 0.37/0.46 % Current number of unprocessed clauses: 134
% 0.37/0.46 % ...number of literals in the above : 584
% 0.37/0.46 % Current number of archived formulas : 0
% 0.37/0.46 % Current number of archived clauses : 97
% 0.37/0.46 % Clause-clause subsumption calls (NU) : 1739
% 0.37/0.46 % Rec. Clause-clause subsumption calls : 316
% 0.37/0.46 % Non-unit clause-clause subsumptions : 23
% 0.37/0.46 % Unit Clause-clause subsumption calls : 198
% 0.37/0.46 % Rewrite failures with RHS unbound : 0
% 0.37/0.46 % BW rewrite match attempts : 1
% 0.37/0.46 % BW rewrite match successes : 1
% 0.37/0.46 % Condensation attempts : 0
% 0.37/0.46 % Condensation successes : 0
% 0.37/0.46 % Termbank termtop insertions : 10567
% 0.37/0.46 % Search garbage collected termcells : 1366
% 0.37/0.46
% 0.37/0.46 % -------------------------------------------------
% 0.37/0.46 % User time : 0.019 s
% 0.37/0.46 % System time : 0.007 s
% 0.37/0.46 % Total time : 0.025 s
% 0.37/0.46 % Maximum resident set size: 3944 pages
% 0.37/0.46
% 0.37/0.46 % -------------------------------------------------
% 0.37/0.46 % User time : 0.072 s
% 0.37/0.46 % System time : 0.022 s
% 0.37/0.46 % Total time : 0.093 s
% 0.37/0.46 % Maximum resident set size: 4608 pages
% 0.37/0.46 % E exiting
%------------------------------------------------------------------------------