%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM482+3 : 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 : n016.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 01:49:15 PM UTC 2026
% Result : Theorem 0.15s 10.67s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 5 unt; 0 def)
% Number of atoms : 167 ( 78 equ)
% Maximal formula atoms : 83 ( 10 avg)
% Number of connectives : 215 ( 64 ~; 87 |; 54 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 12 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( isPrime0(xk)
& ! [X1] :
( ( ( doDivides0(X1,xk)
| ? [X2] :
( xk = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xk
| X1 = sz10 ) ) )
=> ? [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/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(m__1716,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1716) ).
fof(c_0_4,negated_conjecture,
~ ( ( isPrime0(xk)
& ! [X1] :
( ( ( doDivides0(X1,xk)
| ? [X2] :
( xk = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xk
| X1 = sz10 ) ) )
=> ? [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,
~ ( ( isPrime0(xk)
& ! [X1] :
( ( ( doDivides0(X1,xk)
| ? [X2] :
( xk = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xk
| X1 = sz10 ) ) )
=> ? [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,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_7,negated_conjecture,
! [X10,X11,X12,X13] :
( ( ~ aNaturalNumber0(X12)
| ~ doDivides0(X12,xk)
| ~ isPrime0(X12) )
& ( ~ aNaturalNumber0(X12)
| ~ doDivides0(X12,xk)
| X12 = sz10
| X12 = sz00
| esk3_1(X12) != X12 )
& ( ~ aNaturalNumber0(X12)
| ~ doDivides0(X12,xk)
| X12 = sz10
| X12 = sz00
| esk3_1(X12) != sz10 )
& ( ~ aNaturalNumber0(X12)
| ~ doDivides0(X12,xk)
| X12 = sz10
| X12 = sz00
| doDivides0(esk3_1(X12),X12) )
& ( ~ aNaturalNumber0(X12)
| ~ doDivides0(X12,xk)
| X12 = sz10
| X12 = sz00
| X12 = sdtasdt0(esk3_1(X12),esk4_1(X12)) )
& ( ~ aNaturalNumber0(X12)
| ~ doDivides0(X12,xk)
| X12 = sz10
| X12 = sz00
| aNaturalNumber0(esk4_1(X12)) )
& ( ~ aNaturalNumber0(X12)
| ~ doDivides0(X12,xk)
| X12 = sz10
| X12 = sz00
| aNaturalNumber0(esk3_1(X12)) )
& ( ~ aNaturalNumber0(X12)
| xk != sdtasdt0(X12,X13)
| ~ aNaturalNumber0(X13)
| ~ isPrime0(X12) )
& ( ~ aNaturalNumber0(X12)
| xk != sdtasdt0(X12,X13)
| ~ aNaturalNumber0(X13)
| X12 = sz10
| X12 = sz00
| esk3_1(X12) != X12 )
& ( ~ aNaturalNumber0(X12)
| xk != sdtasdt0(X12,X13)
| ~ aNaturalNumber0(X13)
| X12 = sz10
| X12 = sz00
| esk3_1(X12) != sz10 )
& ( ~ aNaturalNumber0(X12)
| xk != sdtasdt0(X12,X13)
| ~ aNaturalNumber0(X13)
| X12 = sz10
| X12 = sz00
| doDivides0(esk3_1(X12),X12) )
& ( ~ aNaturalNumber0(X12)
| xk != sdtasdt0(X12,X13)
| ~ aNaturalNumber0(X13)
| X12 = sz10
| X12 = sz00
| X12 = sdtasdt0(esk3_1(X12),esk4_1(X12)) )
& ( ~ aNaturalNumber0(X12)
| xk != sdtasdt0(X12,X13)
| ~ aNaturalNumber0(X13)
| X12 = sz10
| X12 = sz00
| aNaturalNumber0(esk4_1(X12)) )
& ( ~ aNaturalNumber0(X12)
| xk != sdtasdt0(X12,X13)
| ~ aNaturalNumber0(X13)
| X12 = sz10
| X12 = sz00
| aNaturalNumber0(esk3_1(X12)) )
& isPrime0(xk)
& ( X10 = xk
| X10 = sz10
| ~ aNaturalNumber0(X10)
| ~ doDivides0(X10,xk) )
& ( X10 = xk
| X10 = sz10
| ~ aNaturalNumber0(X10)
| xk != sdtasdt0(X10,X11)
| ~ aNaturalNumber0(X11) ) ),
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,
! [X20] :
( ( ~ aNaturalNumber0(X20)
| X20 = sdtasdt0(sz10,X20) )
& ( ~ aNaturalNumber0(X20)
| sdtasdt0(X20,sz10) = X20 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_9,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( ~ aNaturalNumber0(X1)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ isPrime0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
isPrime0(xk),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__1716]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[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])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM482+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/10.59 % Computer : n016.cluster.edu
% 0.10/10.59 % Model : x86_64 x86_64
% 0.10/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.59 % Memory : 8046.5625MB
% 0.10/10.59 % OS : Linux 6.8.0-71-generic
% 0.10/10.59 % CPULimit : 300
% 0.10/10.59 % WCLimit : 300
% 0.10/10.59 % DateTime : Mon Sep 21 02:38:33 UTC 2026
% 0.10/10.59 % CPUTime :
% 0.10/10.59 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/10.64 Running first-order theorem proving
% 0.15/10.64 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
% 0.15/10.67 % Version: 3.5.1
% 0.15/10.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/10.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/10.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/10.67 % Starting new_bool_3 with 300s (1) cores
% 0.15/10.67 % Starting new_bool_1 with 300s (1) cores
% 0.15/10.67 % Starting sh5l with 300s (1) cores
% 0.15/10.67 % new_bool_1 with pid 1374384 completed with status 0
% 0.15/10.67 % Result found by new_bool_1
% 0.15/10.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/10.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/10.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/10.67 % Starting new_bool_3 with 300s (1) cores
% 0.15/10.67 % Starting new_bool_1 with 300s (1) cores
% 0.15/10.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/10.67 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/10.67 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.15/10.67 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/10.67 % Starting SubtermCWHack with 31s (1) cores
% 0.15/10.67 % SubtermCWHack with pid 1374390 completed with status 0
% 0.15/10.67 % Result found by SubtermCWHack
% 0.15/10.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/10.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/10.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/10.67 % Starting new_bool_3 with 300s (1) cores
% 0.15/10.67 % Starting new_bool_1 with 300s (1) cores
% 0.15/10.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/10.67 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/10.67 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.15/10.67 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/10.67 % Starting SubtermCWHack with 31s (1) cores
% 0.15/10.67 % Preprocessing time : 0.001 s
% 0.15/10.67
% 0.15/10.67 % Proof found!
% 0.15/10.67 % SZS status Theorem
% 0.15/10.67 % SZS output start CNFRefutation
% See solution above
% 0.15/10.67 % Parsed axioms : 41
% 0.15/10.67 % Removed by relevancy pruning/SinE : 3
% 0.15/10.67 % Initial clauses : 89
% 0.15/10.67 % Removed in clause preprocessing : 3
% 0.15/10.67 % Initial clauses in saturation : 86
% 0.15/10.67 % Processed clauses : 61
% 0.15/10.67 % ...of these trivial : 0
% 0.15/10.67 % ...subsumed : 20
% 0.15/10.67 % ...remaining for further processing : 41
% 0.15/10.67 % Other redundant clauses eliminated : 5
% 0.15/10.67 % Clauses deleted for lack of memory : 0
% 0.15/10.67 % Backward-subsumed : 0
% 0.15/10.67 % Backward-rewritten : 0
% 0.15/10.67 % Generated clauses : 58
% 0.15/10.67 % ...of the previous two non-redundant : 49
% 0.15/10.67 % ...aggressively subsumed : 0
% 0.15/10.67 % Contextual simplify-reflections : 0
% 0.15/10.67 % Paramodulations : 53
% 0.15/10.67 % Factorizations : 0
% 0.15/10.67 % NegExts : 0
% 0.15/10.67 % Equation resolutions : 5
% 0.15/10.67 % Disequality decompositions : 0
% 0.15/10.67 % Total rewrite steps : 30
% 0.15/10.67 % ...of those cached : 26
% 0.15/10.67 % Propositional unsat checks : 0
% 0.15/10.67 % Propositional check models : 0
% 0.15/10.67 % Propositional check unsatisfiable : 0
% 0.15/10.67 % Propositional clauses : 0
% 0.15/10.67 % Propositional clauses after purity: 0
% 0.15/10.67 % Propositional unsat core size : 0
% 0.15/10.67 % Propositional preprocessing time : 0.000
% 0.15/10.67 % Propositional encoding time : 0.000
% 0.15/10.67 % Propositional solver time : 0.000
% 0.15/10.67 % Success case prop preproc time : 0.000
% 0.15/10.67 % Success case prop encoding time : 0.000
% 0.15/10.67 % Success case prop solver time : 0.000
% 0.15/10.67 % Current number of processed clauses : 38
% 0.15/10.67 % Positive orientable unit clauses : 7
% 0.15/10.67 % Positive unorientable unit clauses: 0
% 0.15/10.67 % Negative unit clauses : 6
% 0.15/10.67 % Non-unit-clauses : 25
% 0.15/10.67 % Current number of unprocessed clauses: 69
% 0.15/10.67 % ...number of literals in the above : 365
% 0.15/10.67 % Current number of archived formulas : 0
% 0.15/10.67 % Current number of archived clauses : 0
% 0.15/10.67 % Clause-clause subsumption calls (NU) : 70
% 0.15/10.67 % Rec. Clause-clause subsumption calls : 56
% 0.15/10.67 % Non-unit clause-clause subsumptions : 20
% 0.15/10.67 % Unit Clause-clause subsumption calls : 12
% 0.15/10.67 % Rewrite failures with RHS unbound : 0
% 0.15/10.67 % BW rewrite match attempts : 0
% 0.15/10.67 % BW rewrite match successes : 0
% 0.15/10.67 % Condensation attempts : 0
% 0.15/10.67 % Condensation successes : 0
% 0.15/10.67 % Termbank termtop insertions : 7692
% 0.15/10.67 % Search garbage collected termcells : 1564
% 0.15/10.67
% 0.15/10.67 % -------------------------------------------------
% 0.15/10.67 % User time : 0.005 s
% 0.15/10.67 % System time : 0.003 s
% 0.15/10.67 % Total time : 0.008 s
% 0.15/10.67 % Maximum resident set size: 3936 pages
% 0.15/10.67
% 0.15/10.67 % -------------------------------------------------
% 0.15/10.67 % User time : 0.008 s
% 0.15/10.67 % System time : 0.008 s
% 0.15/10.67 % Total time : 0.015 s
% 0.15/10.67 % Maximum resident set size: 4608 pages
% 0.15/10.67 % E exiting
%------------------------------------------------------------------------------