%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM523+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 : n017.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 01:49:25 PM UTC 2026
% Result : Theorem 0.26s 0.57s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 138 ( 37 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 172 ( 64 ~; 58 |; 43 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 21 !; 7 ?)
% 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)
| ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) )
& ( doDivides0(xp,sdtasdt0(xn,xn))
| ? [X1] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ) ),
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(m__3025,hypothesis,
( isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( xp = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xp
| X1 = sz10 ) )
& xp != sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
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(c_0_7,plain,
! [X65,X66,X68] :
( ( ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X65)
| doDivides0(X65,X66)
| X66 != sdtasdt0(X65,X68)
| ~ aNaturalNumber0(X68) )
& ( ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X65)
| ~ doDivides0(X65,X66)
| X66 = sdtasdt0(X65,esk2_2(X65,X66)) )
& ( ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X65)
| ~ doDivides0(X65,X66)
| aNaturalNumber0(esk2_2(X65,X66)) ) ),
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,
! [X9,X10] :
( aNaturalNumber0(sdtasdt0(X9,X10))
| ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X9) ),
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)
| ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) )
& ( doDivides0(xp,sdtasdt0(xn,xn))
| ? [X1] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ) ),
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,hypothesis,
( isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( xp = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xp
| X1 = sz10 ) )
& xp != sz10 ),
inference(fof_simplification,[status(thm)],[m__3025]) ).
fof(c_0_18,negated_conjecture,
! [X101,X102] :
( ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ doDivides0(xp,xn) )
& ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| xn != sdtasdt0(xp,X102)
| ~ aNaturalNumber0(X102) )
& ( sdtasdt0(xn,xn) != sdtasdt0(xp,X101)
| ~ aNaturalNumber0(X101)
| ~ doDivides0(xp,xn) )
& ( sdtasdt0(xn,xn) != sdtasdt0(xp,X101)
| ~ aNaturalNumber0(X101)
| xn != sdtasdt0(xp,X102)
| ~ aNaturalNumber0(X102) ) ),
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_13])])])])]) ).
cnf(c_0_19,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_20,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_21,plain,
! [X91,X92,X93] :
( doDivides0(X93,X92)
| doDivides0(X93,X91)
| ~ doDivides0(X93,sdtasdt0(X91,X92))
| ~ isPrime0(X93)
| ~ aNaturalNumber0(X93)
| ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X91) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPDP])])]) ).
fof(c_0_22,hypothesis,
! [X99,X100] :
( isPrime0(xp)
& ( X99 = xp
| X99 = sz10
| ~ aNaturalNumber0(X99)
| ~ doDivides0(X99,xp) )
& ( X99 = xp
| X99 = sz10
| ~ aNaturalNumber0(X99)
| xp != sdtasdt0(X99,X100)
| ~ aNaturalNumber0(X100) )
& xp != sz10 ),
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_17])])])])]) ).
cnf(c_0_23,negated_conjecture,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ doDivides0(xp,xn) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,hypothesis,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_11]),c_0_20])]) ).
cnf(c_0_25,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_21]) ).
cnf(c_0_26,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_28,negated_conjecture,
~ doDivides0(xp,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_29,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_25,c_0_24]),c_0_26]),c_0_16]),c_0_27])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM523+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.43 % Computer : n017.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 02:32:41 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 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
% 0.26/0.57 % Version: 3.5.1
% 0.26/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.57 % Starting sh5l with 300s (1) cores
% 0.26/0.57 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1234280 completed with status 0
% 0.26/0.57 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.26/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.57 % No SInE strategy applied
% 0.26/0.57 % Search class: FGHSF-FSMM32-SFFFFFNN
% 0.26/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.26/0.57 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 0.26/0.57 % Starting new_bool_3 with 136s (1) cores
% 0.26/0.57 % Starting new_bool_1 with 136s (1) cores
% 0.26/0.57 % new_bool_3 with pid 1234290 completed with status 0
% 0.26/0.57 % Result found by new_bool_3
% 0.26/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.57 % No SInE strategy applied
% 0.26/0.57 % Search class: FGHSF-FSMM32-SFFFFFNN
% 0.26/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.26/0.57 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 0.26/0.57 % Starting new_bool_3 with 136s (1) cores
% 0.26/0.57 % Preprocessing time : 0.002 s
% 0.26/0.57 % Presaturation interreduction done
% 0.26/0.57
% 0.26/0.57 % Proof found!
% 0.26/0.57 % SZS status Theorem
% 0.26/0.57 % SZS output start CNFRefutation
% See solution above
% 0.26/0.57 % Parsed axioms : 44
% 0.26/0.57 % Removed by relevancy pruning/SinE : 0
% 0.26/0.57 % Initial clauses : 93
% 0.26/0.57 % Removed in clause preprocessing : 3
% 0.26/0.57 % Initial clauses in saturation : 90
% 0.26/0.57 % Processed clauses : 358
% 0.26/0.57 % ...of these trivial : 4
% 0.26/0.57 % ...subsumed : 87
% 0.26/0.57 % ...remaining for further processing : 267
% 0.26/0.57 % Other redundant clauses eliminated : 19
% 0.26/0.57 % Clauses deleted for lack of memory : 0
% 0.26/0.57 % Backward-subsumed : 13
% 0.26/0.57 % Backward-rewritten : 14
% 0.26/0.57 % Generated clauses : 619
% 0.26/0.57 % ...of the previous two non-redundant : 497
% 0.26/0.57 % ...aggressively subsumed : 0
% 0.26/0.57 % Contextual simplify-reflections : 6
% 0.26/0.57 % Paramodulations : 593
% 0.26/0.57 % Factorizations : 3
% 0.26/0.57 % NegExts : 0
% 0.26/0.57 % Equation resolutions : 23
% 0.26/0.57 % Disequality decompositions : 0
% 0.26/0.57 % Total rewrite steps : 723
% 0.26/0.57 % ...of those cached : 690
% 0.26/0.57 % Propositional unsat checks : 0
% 0.26/0.57 % Propositional check models : 0
% 0.26/0.57 % Propositional check unsatisfiable : 0
% 0.26/0.57 % Propositional clauses : 0
% 0.26/0.57 % Propositional clauses after purity: 0
% 0.26/0.57 % Propositional unsat core size : 0
% 0.26/0.57 % Propositional preprocessing time : 0.000
% 0.26/0.57 % Propositional encoding time : 0.000
% 0.26/0.57 % Propositional solver time : 0.000
% 0.26/0.57 % Success case prop preproc time : 0.000
% 0.26/0.57 % Success case prop encoding time : 0.000
% 0.26/0.57 % Success case prop solver time : 0.000
% 0.26/0.57 % Current number of processed clauses : 144
% 0.26/0.57 % Positive orientable unit clauses : 49
% 0.26/0.57 % Positive unorientable unit clauses: 0
% 0.26/0.57 % Negative unit clauses : 11
% 0.26/0.57 % Non-unit-clauses : 84
% 0.26/0.57 % Current number of unprocessed clauses: 304
% 0.26/0.57 % ...number of literals in the above : 1247
% 0.26/0.57 % Current number of archived formulas : 0
% 0.26/0.57 % Current number of archived clauses : 112
% 0.26/0.57 % Clause-clause subsumption calls (NU) : 1684
% 0.26/0.57 % Rec. Clause-clause subsumption calls : 450
% 0.26/0.57 % Non-unit clause-clause subsumptions : 72
% 0.26/0.57 % Unit Clause-clause subsumption calls : 403
% 0.26/0.57 % Rewrite failures with RHS unbound : 0
% 0.26/0.57 % BW rewrite match attempts : 9
% 0.26/0.57 % BW rewrite match successes : 9
% 0.26/0.57 % Condensation attempts : 0
% 0.26/0.57 % Condensation successes : 0
% 0.26/0.57 % Termbank termtop insertions : 18331
% 0.26/0.57 % Search garbage collected termcells : 1680
% 0.26/0.57
% 0.26/0.57 % -------------------------------------------------
% 0.26/0.57 % User time : 0.030 s
% 0.26/0.57 % System time : 0.008 s
% 0.26/0.57 % Total time : 0.038 s
% 0.26/0.57 % Maximum resident set size: 3944 pages
% 0.26/0.57
% 0.26/0.57 % -------------------------------------------------
% 0.26/0.57 % User time : 0.124 s
% 0.26/0.57 % System time : 0.025 s
% 0.26/0.57 % Total time : 0.149 s
% 0.26/0.57 % Maximum resident set size: 4608 pages
% 0.26/0.57 % E exiting
%------------------------------------------------------------------------------