%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM498+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 : n014.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 01:49:19 PM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 20 unt; 0 def)
% Number of atoms : 165 ( 92 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 170 ( 53 ~; 48 |; 61 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 14 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( xk = sz10
| xk = sz00 )
=> ( doDivides0(xp,xm)
| ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
| doDivides0(xp,xn)
| ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
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/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(m__2287,hypothesis,
( sdtlseqdt0(xm,xp)
& ? [X1] :
( sdtpldt0(xm,X1) = xp
& aNaturalNumber0(X1) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X1] :
( sdtpldt0(xn,X1) = xp
& aNaturalNumber0(X1) )
& xn != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(m__2306,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
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(c_0_9,negated_conjecture,
~ ( ( xk = sz10
| xk = sz00 )
=> ( doDivides0(xp,xm)
| ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
| doDivides0(xp,xn)
| ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_10,negated_conjecture,
! [X21,X22] :
( ~ doDivides0(xp,xm)
& ( xm != sdtasdt0(xp,X22)
| ~ aNaturalNumber0(X22) )
& ~ doDivides0(xp,xn)
& ( xn != sdtasdt0(xp,X21)
| ~ aNaturalNumber0(X21) )
& ( xk = sz10
| xk = sz00 ) ),
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,
! [X46] :
( ( ~ aNaturalNumber0(X46)
| sz00 = sdtasdt0(sz00,X46) )
& ( ~ aNaturalNumber0(X46)
| sdtasdt0(X46,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
fof(c_0_12,plain,
! [X53,X54] :
( X54 = sz00
| X53 = sz00
| sdtasdt0(X53,X54) != sz00
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X53) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])])]) ).
cnf(c_0_13,negated_conjecture,
( xn != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_16,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_17,negated_conjecture,
( xm != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_18,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]) ).
fof(c_0_19,hypothesis,
( sdtlseqdt0(xm,xp)
& ? [X1] :
( sdtpldt0(xm,X1) = xp
& aNaturalNumber0(X1) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X1] :
( sdtpldt0(xn,X1) = xp
& aNaturalNumber0(X1) )
& xn != xp ),
inference(fof_simplification,[status(thm)],[m__2287]) ).
cnf(c_0_20,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_22,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_23,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_24,negated_conjecture,
xn != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_25,negated_conjecture,
xm != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15]),c_0_16])]) ).
fof(c_0_26,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_18])])])])])]) ).
fof(c_0_27,hypothesis,
( sdtlseqdt0(xm,xp)
& sdtpldt0(xm,esk7_0) = xp
& aNaturalNumber0(esk7_0)
& xm != xp
& sdtlseqdt0(xn,xp)
& sdtpldt0(xn,esk6_0) = xp
& aNaturalNumber0(esk6_0)
& xn != xp ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_19])])]) ).
cnf(c_0_28,hypothesis,
sdtasdt0(xp,xk) != sz00,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]),c_0_24]),c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( xk = sz10
| xk = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_30,hypothesis,
( ~ aNaturalNumber0(X2)
| xp != sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| X2 = xp
| X2 = sz10 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( sdtasdt0(xp,sz00) != sz00
| xk = sz10 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,hypothesis,
( sdtasdt0(xp,xk) != xp
| xn = sz10 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_21]),c_0_23]),c_0_22])]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
xk = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_14]),c_0_16])]) ).
fof(c_0_35,plain,
! [X89] :
( ( ~ aNaturalNumber0(X89)
| X89 = sdtasdt0(sz10,X89) )
& ( ~ aNaturalNumber0(X89)
| sdtasdt0(X89,sz10) = X89 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
cnf(c_0_36,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,hypothesis,
( sdtasdt0(xp,sz10) != xp
| xn = sz10 ),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,hypothesis,
sdtasdt0(xp,esk5_0) = sdtasdt0(xp,xk),
inference(rw,[status(thm)],[c_0_36,c_0_21]) ).
cnf(c_0_40,hypothesis,
aNaturalNumber0(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_41,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,sz10),
inference(rw,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_42,hypothesis,
xn = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_16])]) ).
cnf(c_0_43,hypothesis,
sdtasdt0(xp,xk) != xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_39]),c_0_40])]) ).
cnf(c_0_44,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,hypothesis,
sdtasdt0(sz10,xm) = sdtasdt0(xp,sz10),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,hypothesis,
sdtasdt0(xp,sz10) != xm,
inference(rw,[status(thm)],[c_0_43,c_0_34]) ).
cnf(c_0_47,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_22])]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM498+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:34:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.46 % Version: 3.5.1
% 0.11/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % Starting sh5l with 300s (1) cores
% 0.11/0.46 % new_bool_1 with pid 2958061 completed with status 0
% 0.11/0.46 % Result found by new_bool_1
% 0.11/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.46 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.11/0.46 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.46 % SubtermCWHack with pid 2958063 completed with status 0
% 0.11/0.46 % Result found by SubtermCWHack
% 0.11/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.46 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.11/0.46 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.46 % Preprocessing time : 0.004 s
% 0.11/0.46
% 0.11/0.46 % Proof found!
% 0.11/0.46 % SZS status Theorem
% 0.11/0.46 % SZS output start CNFRefutation
% See solution above
% 0.11/0.46 % Parsed axioms : 46
% 0.11/0.46 % Removed by relevancy pruning/SinE : 1
% 0.11/0.46 % Initial clauses : 224
% 0.11/0.46 % Removed in clause preprocessing : 3
% 0.11/0.46 % Initial clauses in saturation : 221
% 0.11/0.46 % Processed clauses : 306
% 0.11/0.46 % ...of these trivial : 2
% 0.11/0.46 % ...subsumed : 118
% 0.11/0.46 % ...remaining for further processing : 186
% 0.11/0.46 % Other redundant clauses eliminated : 6
% 0.11/0.46 % Clauses deleted for lack of memory : 0
% 0.11/0.46 % Backward-subsumed : 2
% 0.11/0.46 % Backward-rewritten : 54
% 0.11/0.46 % Generated clauses : 399
% 0.11/0.46 % ...of the previous two non-redundant : 383
% 0.11/0.46 % ...aggressively subsumed : 0
% 0.11/0.46 % Contextual simplify-reflections : 0
% 0.11/0.46 % Paramodulations : 391
% 0.11/0.46 % Factorizations : 1
% 0.11/0.46 % NegExts : 0
% 0.11/0.46 % Equation resolutions : 6
% 0.11/0.46 % Disequality decompositions : 0
% 0.11/0.46 % Total rewrite steps : 401
% 0.11/0.46 % ...of those cached : 378
% 0.11/0.46 % Propositional unsat checks : 0
% 0.11/0.46 % Propositional check models : 0
% 0.11/0.46 % Propositional check unsatisfiable : 0
% 0.11/0.46 % Propositional clauses : 0
% 0.11/0.46 % Propositional clauses after purity: 0
% 0.11/0.46 % Propositional unsat core size : 0
% 0.11/0.46 % Propositional preprocessing time : 0.000
% 0.11/0.46 % Propositional encoding time : 0.000
% 0.11/0.46 % Propositional solver time : 0.000
% 0.11/0.46 % Success case prop preproc time : 0.000
% 0.11/0.46 % Success case prop encoding time : 0.000
% 0.11/0.46 % Success case prop solver time : 0.000
% 0.11/0.46 % Current number of processed clauses : 123
% 0.11/0.46 % Positive orientable unit clauses : 34
% 0.11/0.46 % Positive unorientable unit clauses: 0
% 0.11/0.46 % Negative unit clauses : 14
% 0.11/0.46 % Non-unit-clauses : 75
% 0.11/0.46 % Current number of unprocessed clauses: 297
% 0.11/0.46 % ...number of literals in the above : 1967
% 0.11/0.46 % Current number of archived formulas : 0
% 0.11/0.46 % Current number of archived clauses : 57
% 0.11/0.46 % Clause-clause subsumption calls (NU) : 767
% 0.11/0.46 % Rec. Clause-clause subsumption calls : 626
% 0.11/0.46 % Non-unit clause-clause subsumptions : 83
% 0.11/0.46 % Unit Clause-clause subsumption calls : 417
% 0.11/0.46 % Rewrite failures with RHS unbound : 0
% 0.11/0.46 % BW rewrite match attempts : 5
% 0.11/0.46 % BW rewrite match successes : 5
% 0.11/0.46 % Condensation attempts : 0
% 0.11/0.46 % Condensation successes : 0
% 0.11/0.46 % Termbank termtop insertions : 20586
% 0.11/0.46 % Search garbage collected termcells : 2299
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.021 s
% 0.11/0.46 % System time : 0.003 s
% 0.11/0.46 % Total time : 0.023 s
% 0.11/0.46 % Maximum resident set size: 4208 pages
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.023 s
% 0.11/0.46 % System time : 0.007 s
% 0.11/0.46 % Total time : 0.031 s
% 0.11/0.46 % Maximum resident set size: 4608 pages
% 0.11/0.46 % E exiting
%------------------------------------------------------------------------------