%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM487+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 : n026.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 01:55:13 PM UTC 2026
% Result : Theorem 0.27s 0.65s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 120 ( 58 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 134 ( 45 ~; 43 |; 40 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 17 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( sdtlseqdt0(xr,xn)
| ? [X1] :
( sdtpldt0(xr,X1) = xn
& aNaturalNumber0(X1) ) )
& xr != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(m__1883,hypothesis,
( xr = sdtmndt0(xn,xp)
& sdtpldt0(xp,xr) = xn
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtpldt0(X2,X1) = sdtpldt0(X3,X1)
| sdtpldt0(X1,X2) = sdtpldt0(X1,X3) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X1] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
& isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( xp = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xp
| X1 = sz10 ) )
& xp != sz10
& xp != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_8,negated_conjecture,
~ ( ( sdtlseqdt0(xr,xn)
| ? [X1] :
( sdtpldt0(xr,X1) = xn
& aNaturalNumber0(X1) ) )
& xr != xn ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_9,negated_conjecture,
~ ( ( sdtlseqdt0(xr,xn)
| ? [X1] :
( sdtpldt0(xr,X1) = xn
& aNaturalNumber0(X1) ) )
& xr != xn ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_10,negated_conjecture,
! [X18] :
( ( xr = xn
| ~ sdtlseqdt0(xr,xn) )
& ( xr = xn
| sdtpldt0(xr,X18) != xn
| ~ aNaturalNumber0(X18) ) ),
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_9])])])])]) ).
fof(c_0_11,plain,
! [X62,X63] :
( sdtpldt0(X62,X63) = sdtpldt0(X63,X62)
| ~ aNaturalNumber0(X63)
| ~ aNaturalNumber0(X62) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_12,negated_conjecture,
( sdtpldt0(xr,X1) != xn
| ~ aNaturalNumber0(X1)
| xr = xn ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_15,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,xr) != xn
| xr = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_16,hypothesis,
sdtpldt0(xp,xr) = xn,
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_17,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_18,plain,
! [X68,X69,X70] :
( ( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69)
| ~ aNaturalNumber0(X68)
| X69 = X70
| sdtpldt0(X69,X68) != sdtpldt0(X70,X68) )
& ( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69)
| ~ aNaturalNumber0(X68)
| X69 = X70
| sdtpldt0(X68,X69) != sdtpldt0(X68,X70) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])])]) ).
cnf(c_0_19,hypothesis,
xr = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
fof(c_0_20,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X1] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
& isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( xp = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xp
| X1 = sz10 ) )
& xp != sz10
& xp != sz00 ),
inference(fof_simplification,[status(thm)],[m__1860]) ).
cnf(c_0_21,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,hypothesis,
sdtpldt0(xp,xn) = xn,
inference(rw,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_23,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_24,plain,
! [X67] :
( ( ~ aNaturalNumber0(X67)
| X67 = sdtpldt0(sz00,X67) )
& ( ~ aNaturalNumber0(X67)
| sdtpldt0(X67,sz00) = X67 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
fof(c_0_25,hypothesis,
! [X14,X15] :
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,esk5_0)
& aNaturalNumber0(esk5_0)
& isPrime0(xp)
& ( X14 = xp
| X14 = sz10
| ~ aNaturalNumber0(X14)
| ~ doDivides0(X14,xp) )
& ( X14 = xp
| X14 = sz10
| ~ aNaturalNumber0(X14)
| xp != sdtasdt0(X14,X15)
| ~ aNaturalNumber0(X15) )
& xp != sz10
& xp != 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_20])])])])])]) ).
cnf(c_0_26,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,xn) != xn
| X1 = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_17]),c_0_23])]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_29,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_23])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM487+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n026.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 02:36:51 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.56 Running first-order theorem proving
% 0.27/0.56 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
% 0.27/0.65 % Version: 3.5.1
% 0.27/0.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.65 % Starting sh5l with 300s (1) cores
% 0.27/0.65 % new_bool_3 with pid 1181478 completed with status 0
% 0.27/0.65 % Result found by new_bool_3
% 0.27/0.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.27/0.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.27/0.65 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.27/0.65 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.65 % Starting SubtermCWHack with 31s (1) cores
% 0.27/0.65 % SubtermCWHack with pid 1181483 completed with status 0
% 0.27/0.65 % Result found by SubtermCWHack
% 0.27/0.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.27/0.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.27/0.65 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.27/0.65 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.65 % Starting SubtermCWHack with 31s (1) cores
% 0.27/0.65 % Preprocessing time : 0.004 s
% 0.27/0.65
% 0.27/0.65 % Proof found!
% 0.27/0.65 % SZS status Theorem
% 0.27/0.65 % SZS output start CNFRefutation
% See solution above
% 0.27/0.65 % Parsed axioms : 44
% 0.27/0.65 % Removed by relevancy pruning/SinE : 2
% 0.27/0.65 % Initial clauses : 211
% 0.27/0.65 % Removed in clause preprocessing : 3
% 0.27/0.65 % Initial clauses in saturation : 208
% 0.27/0.65 % Processed clauses : 351
% 0.27/0.65 % ...of these trivial : 0
% 0.27/0.65 % ...subsumed : 113
% 0.27/0.65 % ...remaining for further processing : 238
% 0.27/0.65 % Other redundant clauses eliminated : 24
% 0.27/0.65 % Clauses deleted for lack of memory : 0
% 0.27/0.65 % Backward-subsumed : 7
% 0.27/0.65 % Backward-rewritten : 53
% 0.27/0.65 % Generated clauses : 582
% 0.27/0.65 % ...of the previous two non-redundant : 514
% 0.27/0.65 % ...aggressively subsumed : 0
% 0.27/0.65 % Contextual simplify-reflections : 0
% 0.27/0.65 % Paramodulations : 552
% 0.27/0.65 % Factorizations : 1
% 0.27/0.65 % NegExts : 0
% 0.27/0.65 % Equation resolutions : 28
% 0.27/0.65 % Disequality decompositions : 0
% 0.27/0.65 % Total rewrite steps : 670
% 0.27/0.65 % ...of those cached : 651
% 0.27/0.65 % Propositional unsat checks : 0
% 0.27/0.65 % Propositional check models : 0
% 0.27/0.65 % Propositional check unsatisfiable : 0
% 0.27/0.65 % Propositional clauses : 0
% 0.27/0.65 % Propositional clauses after purity: 0
% 0.27/0.65 % Propositional unsat core size : 0
% 0.27/0.65 % Propositional preprocessing time : 0.000
% 0.27/0.65 % Propositional encoding time : 0.000
% 0.27/0.65 % Propositional solver time : 0.000
% 0.27/0.65 % Success case prop preproc time : 0.000
% 0.27/0.65 % Success case prop encoding time : 0.000
% 0.27/0.65 % Success case prop solver time : 0.000
% 0.27/0.65 % Current number of processed clauses : 170
% 0.27/0.65 % Positive orientable unit clauses : 25
% 0.27/0.65 % Positive unorientable unit clauses: 0
% 0.27/0.65 % Negative unit clauses : 7
% 0.27/0.65 % Non-unit-clauses : 138
% 0.27/0.65 % Current number of unprocessed clauses: 349
% 0.27/0.65 % ...number of literals in the above : 2332
% 0.27/0.65 % Current number of archived formulas : 0
% 0.27/0.65 % Current number of archived clauses : 61
% 0.27/0.65 % Clause-clause subsumption calls (NU) : 2715
% 0.27/0.65 % Rec. Clause-clause subsumption calls : 1694
% 0.27/0.65 % Non-unit clause-clause subsumptions : 111
% 0.27/0.65 % Unit Clause-clause subsumption calls : 482
% 0.27/0.65 % Rewrite failures with RHS unbound : 0
% 0.27/0.65 % BW rewrite match attempts : 5
% 0.27/0.65 % BW rewrite match successes : 5
% 0.27/0.65 % Condensation attempts : 0
% 0.27/0.65 % Condensation successes : 0
% 0.27/0.65 % Termbank termtop insertions : 22757
% 0.27/0.65 % Search garbage collected termcells : 2161
% 0.27/0.65
% 0.27/0.65 % -------------------------------------------------
% 0.27/0.65 % User time : 0.036 s
% 0.27/0.65 % System time : 0.005 s
% 0.27/0.65 % Total time : 0.041 s
% 0.27/0.65 % Maximum resident set size: 3896 pages
% 0.27/0.65
% 0.27/0.65 % -------------------------------------------------
% 0.27/0.65 % User time : 0.041 s
% 0.27/0.65 % System time : 0.011 s
% 0.27/0.65 % Total time : 0.052 s
% 0.27/0.65 % Maximum resident set size: 4864 pages
% 0.27/0.65 % E exiting
%------------------------------------------------------------------------------