%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM523+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 : n020.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 01:55:21 PM UTC 2026
% Result : Theorem 0.25s 0.56s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 94 ( 15 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 112 ( 46 ~; 36 |; 25 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 15 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__2987,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(m__,conjecture,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(mPDP,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X3,sdtasdt0(X1,X2))
& isPrime0(X3) )
=> ( doDivides0(X3,X2)
| doDivides0(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPDP) ).
fof(m__3025,hypothesis,
isPrime0(xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
fof(c_0_7,plain,
! [X63,X64,X66] :
( ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| doDivides0(X63,X64)
| X64 != sdtasdt0(X63,X66)
| ~ aNaturalNumber0(X66) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| X64 = sdtasdt0(X63,esk2_2(X63,X64)) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| aNaturalNumber0(esk2_2(X63,X64)) ) ),
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)],[mDefDiv])])])])])]) ).
fof(c_0_8,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])])]) ).
fof(c_0_9,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_simplification,[status(thm)],[m__2987]) ).
cnf(c_0_10,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
fof(c_0_13,negated_conjecture,
~ ( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_14,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_10]),c_0_11]) ).
cnf(c_0_15,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_16,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,negated_conjecture,
( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])]) ).
cnf(c_0_18,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_19,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X89,X90,X91] :
( doDivides0(X91,X90)
| doDivides0(X91,X89)
| ~ doDivides0(X91,sdtasdt0(X89,X90))
| ~ isPrime0(X91)
| ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X90)
| ~ aNaturalNumber0(X89) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPDP])])]) ).
cnf(c_0_21,negated_conjecture,
( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,hypothesis,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_11]),c_0_19])]) ).
cnf(c_0_23,plain,
( ~ doDivides0(X3,sdtasdt0(X1,X2))
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2)
| doDivides0(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__3025]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_26,negated_conjecture,
~ doDivides0(xp,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
cnf(c_0_27,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_24]),c_0_16]),c_0_25])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM523+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 02:38:17 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.51 Running first-order theorem proving
% 0.25/0.51 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
% 0.25/0.56 % Version: 3.5.1
% 0.25/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.56 % Starting sh5l with 300s (1) cores
% 0.25/0.56 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1812181 completed with status 0
% 0.25/0.56 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.25/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.56 % No SInE strategy applied
% 0.25/0.56 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.25/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.25/0.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.25/0.56 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.25/0.56 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.25/0.56 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1812189 completed with status 0
% 0.25/0.56 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.25/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.56 % No SInE strategy applied
% 0.25/0.56 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.25/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.25/0.56 % Preprocessing time : 0.002 s
% 0.25/0.56 % Presaturation interreduction done
% 0.25/0.56
% 0.25/0.56 % Proof found!
% 0.25/0.56 % SZS status Theorem
% 0.25/0.56 % SZS output start CNFRefutation
% See solution above
% 0.25/0.56 % Parsed axioms : 44
% 0.25/0.56 % Removed by relevancy pruning/SinE : 0
% 0.25/0.56 % Initial clauses : 81
% 0.25/0.56 % Removed in clause preprocessing : 3
% 0.25/0.56 % Initial clauses in saturation : 78
% 0.25/0.56 % Processed clauses : 170
% 0.25/0.56 % ...of these trivial : 0
% 0.25/0.56 % ...subsumed : 7
% 0.25/0.56 % ...remaining for further processing : 162
% 0.25/0.56 % Other redundant clauses eliminated : 19
% 0.25/0.56 % Clauses deleted for lack of memory : 0
% 0.25/0.56 % Backward-subsumed : 0
% 0.25/0.56 % Backward-rewritten : 2
% 0.25/0.56 % Generated clauses : 348
% 0.25/0.56 % ...of the previous two non-redundant : 314
% 0.25/0.56 % ...aggressively subsumed : 0
% 0.25/0.56 % Contextual simplify-reflections : 6
% 0.25/0.56 % Paramodulations : 323
% 0.25/0.56 % Factorizations : 2
% 0.25/0.56 % NegExts : 0
% 0.25/0.56 % Equation resolutions : 23
% 0.25/0.56 % Disequality decompositions : 0
% 0.25/0.56 % Total rewrite steps : 145
% 0.25/0.56 % ...of those cached : 137
% 0.25/0.56 % Propositional unsat checks : 0
% 0.25/0.56 % Propositional check models : 0
% 0.25/0.56 % Propositional check unsatisfiable : 0
% 0.25/0.56 % Propositional clauses : 0
% 0.25/0.56 % Propositional clauses after purity: 0
% 0.25/0.56 % Propositional unsat core size : 0
% 0.25/0.56 % Propositional preprocessing time : 0.000
% 0.25/0.56 % Propositional encoding time : 0.000
% 0.25/0.56 % Propositional solver time : 0.000
% 0.25/0.56 % Success case prop preproc time : 0.000
% 0.25/0.56 % Success case prop encoding time : 0.000
% 0.25/0.56 % Success case prop solver time : 0.000
% 0.25/0.56 % Current number of processed clauses : 76
% 0.25/0.56 % Positive orientable unit clauses : 8
% 0.25/0.56 % Positive unorientable unit clauses: 0
% 0.25/0.56 % Negative unit clauses : 7
% 0.25/0.56 % Non-unit-clauses : 61
% 0.25/0.56 % Current number of unprocessed clauses: 295
% 0.25/0.56 % ...number of literals in the above : 1402
% 0.25/0.56 % Current number of archived formulas : 0
% 0.25/0.56 % Current number of archived clauses : 75
% 0.25/0.56 % Clause-clause subsumption calls (NU) : 907
% 0.25/0.56 % Rec. Clause-clause subsumption calls : 198
% 0.25/0.56 % Non-unit clause-clause subsumptions : 13
% 0.25/0.56 % Unit Clause-clause subsumption calls : 123
% 0.25/0.56 % Rewrite failures with RHS unbound : 0
% 0.25/0.56 % BW rewrite match attempts : 1
% 0.25/0.56 % BW rewrite match successes : 1
% 0.25/0.56 % Condensation attempts : 0
% 0.25/0.56 % Condensation successes : 0
% 0.25/0.56 % Termbank termtop insertions : 13045
% 0.25/0.56 % Search garbage collected termcells : 1404
% 0.25/0.56
% 0.25/0.56 % -------------------------------------------------
% 0.25/0.56 % User time : 0.025 s
% 0.25/0.56 % System time : 0.006 s
% 0.25/0.56 % Total time : 0.031 s
% 0.25/0.56 % Maximum resident set size: 3940 pages
% 0.25/0.56
% 0.25/0.56 % -------------------------------------------------
% 0.25/0.56 % User time : 0.084 s
% 0.25/0.56 % System time : 0.020 s
% 0.25/0.56 % Total time : 0.104 s
% 0.25/0.56 % Maximum resident set size: 4864 pages
% 0.25/0.56 % E exiting
%------------------------------------------------------------------------------