%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM495+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 : n001.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 01:49:18 PM UTC 2026
% Result : Theorem 0.37s 0.56s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 19 unt; 0 def)
% Number of atoms : 124 ( 18 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 141 ( 60 ~; 51 |; 19 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__,conjecture,
( doDivides0(xp,xm)
| doDivides0(xp,xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(m__2062,hypothesis,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2062) ).
fof(m__1799,hypothesis,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X3,sdtasdt0(X1,X2))
& isPrime0(X3) )
=> ( iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(X3,X2)
| doDivides0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1799) ).
fof(m__1870,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp),
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(m__1913,hypothesis,
doDivides0(xp,sdtasdt0(xr,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1913) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(c_0_11,plain,
! [X39,X40,X41] :
( ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 = sdtmndt0(X40,X39)
| sdtpldt0(X39,X41) != X40
| ~ aNaturalNumber0(X41) )
& ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 != sdtmndt0(X40,X39)
| sdtpldt0(X39,X41) = X40 )
& ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 != sdtmndt0(X40,X39)
| aNaturalNumber0(X41) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])])]) ).
fof(c_0_12,negated_conjecture,
~ ( doDivides0(xp,xm)
| doDivides0(xp,xr) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_13,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X3,X2)
| X1 != sdtmndt0(X2,X3)
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> iLess0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mIH_03]) ).
fof(c_0_15,hypothesis,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(fof_simplification,[status(thm)],[m__2062]) ).
fof(c_0_16,hypothesis,
! [X89,X90,X91] :
( doDivides0(X91,X90)
| doDivides0(X91,X89)
| ~ iLess0(sdtpldt0(sdtpldt0(X89,X90),X91),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ 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)],[m__1799])])]) ).
fof(c_0_17,negated_conjecture,
( ~ doDivides0(xp,xm)
& ~ doDivides0(xp,xr) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
cnf(c_0_18,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| aNaturalNumber0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_19,hypothesis,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[m__1870]) ).
cnf(c_0_20,hypothesis,
xr = sdtmndt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_22,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_23,plain,
! [X61,X62] :
( iLess0(X61,X62)
| ~ sdtlseqdt0(X61,X62)
| X61 = X62
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X61) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_24,hypothesis,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(fof_nnf,[status(thm)],[c_0_15]) ).
cnf(c_0_25,hypothesis,
( ~ iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ 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_16]) ).
cnf(c_0_26,hypothesis,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(split_conjunct,[status(thm)],[m__1913]) ).
cnf(c_0_27,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_29,negated_conjecture,
~ doDivides0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,negated_conjecture,
~ doDivides0(xp,xr),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_32,plain,
( ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| iLess0(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,hypothesis,
sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,hypothesis,
sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,hypothesis,
~ iLess0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[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_26]),c_0_27]),c_0_21]),c_0_28])]),c_0_29]),c_0_30]),c_0_31])]) ).
fof(c_0_36,plain,
! [X5,X6] :
( aNaturalNumber0(sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
cnf(c_0_37,hypothesis,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]) ).
cnf(c_0_38,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_39,hypothesis,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_21])]) ).
cnf(c_0_40,hypothesis,
~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_38]),c_0_28]),c_0_22])]) ).
cnf(c_0_41,hypothesis,
~ aNaturalNumber0(sdtpldt0(xr,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_38]),c_0_21])]) ).
cnf(c_0_42,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_38]),c_0_28]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM495+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:40:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 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
% 0.37/0.56 % Version: 3.5.1
% 0.37/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.37/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.37/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.37/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.37/0.56 % Starting sh5l with 300s (1) cores
% 0.37/0.56 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2009968 completed with status 0
% 0.37/0.56 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.37/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.37/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.37/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.37/0.56 % No SInE strategy applied
% 0.37/0.56 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.37/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.37/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.37/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.37/0.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.37/0.56 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.37/0.56 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.37/0.56 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2009975 completed with status 0
% 0.37/0.56 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.37/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.37/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.37/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.37/0.56 % No SInE strategy applied
% 0.37/0.56 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.37/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.37/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.37/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.37/0.56 % Preprocessing time : 0.004 s
% 0.37/0.56 % Presaturation interreduction done
% 0.37/0.56
% 0.37/0.56 % Proof found!
% 0.37/0.56 % SZS status Theorem
% 0.37/0.56 % SZS output start CNFRefutation
% See solution above
% 0.37/0.56 % Parsed axioms : 47
% 0.37/0.56 % Removed by relevancy pruning/SinE : 0
% 0.37/0.56 % Initial clauses : 85
% 0.37/0.56 % Removed in clause preprocessing : 3
% 0.37/0.56 % Initial clauses in saturation : 82
% 0.37/0.56 % Processed clauses : 527
% 0.37/0.56 % ...of these trivial : 11
% 0.37/0.56 % ...subsumed : 154
% 0.37/0.56 % ...remaining for further processing : 362
% 0.37/0.56 % Other redundant clauses eliminated : 25
% 0.37/0.56 % Clauses deleted for lack of memory : 0
% 0.37/0.56 % Backward-subsumed : 14
% 0.37/0.56 % Backward-rewritten : 37
% 0.37/0.56 % Generated clauses : 1194
% 0.37/0.56 % ...of the previous two non-redundant : 1038
% 0.37/0.56 % ...aggressively subsumed : 0
% 0.37/0.56 % Contextual simplify-reflections : 15
% 0.37/0.56 % Paramodulations : 1163
% 0.37/0.56 % Factorizations : 2
% 0.37/0.56 % NegExts : 0
% 0.37/0.56 % Equation resolutions : 29
% 0.37/0.56 % Disequality decompositions : 0
% 0.37/0.56 % Total rewrite steps : 1536
% 0.37/0.56 % ...of those cached : 1484
% 0.37/0.56 % Propositional unsat checks : 0
% 0.37/0.56 % Propositional check models : 0
% 0.37/0.56 % Propositional check unsatisfiable : 0
% 0.37/0.56 % Propositional clauses : 0
% 0.37/0.56 % Propositional clauses after purity: 0
% 0.37/0.56 % Propositional unsat core size : 0
% 0.37/0.56 % Propositional preprocessing time : 0.000
% 0.37/0.56 % Propositional encoding time : 0.000
% 0.37/0.56 % Propositional solver time : 0.000
% 0.37/0.56 % Success case prop preproc time : 0.000
% 0.37/0.56 % Success case prop encoding time : 0.000
% 0.37/0.56 % Success case prop solver time : 0.000
% 0.37/0.56 % Current number of processed clauses : 223
% 0.37/0.56 % Positive orientable unit clauses : 45
% 0.37/0.56 % Positive unorientable unit clauses: 0
% 0.37/0.56 % Negative unit clauses : 45
% 0.37/0.56 % Non-unit-clauses : 133
% 0.37/0.56 % Current number of unprocessed clauses: 624
% 0.37/0.56 % ...number of literals in the above : 2579
% 0.37/0.56 % Current number of archived formulas : 0
% 0.37/0.56 % Current number of archived clauses : 128
% 0.37/0.56 % Clause-clause subsumption calls (NU) : 2663
% 0.37/0.56 % Rec. Clause-clause subsumption calls : 1343
% 0.37/0.56 % Non-unit clause-clause subsumptions : 127
% 0.37/0.56 % Unit Clause-clause subsumption calls : 823
% 0.37/0.56 % Rewrite failures with RHS unbound : 0
% 0.37/0.56 % BW rewrite match attempts : 22
% 0.37/0.56 % BW rewrite match successes : 19
% 0.37/0.56 % Condensation attempts : 0
% 0.37/0.56 % Condensation successes : 0
% 0.37/0.56 % Termbank termtop insertions : 26640
% 0.37/0.56 % Search garbage collected termcells : 1348
% 0.37/0.56
% 0.37/0.56 % -------------------------------------------------
% 0.37/0.56 % User time : 0.075 s
% 0.37/0.56 % System time : 0.006 s
% 0.37/0.56 % Total time : 0.082 s
% 0.37/0.56 % Maximum resident set size: 3684 pages
% 0.37/0.56
% 0.37/0.56 % -------------------------------------------------
% 0.37/0.56 % User time : 0.295 s
% 0.37/0.56 % System time : 0.038 s
% 0.37/0.56 % Total time : 0.332 s
% 0.37/0.56 % Maximum resident set size: 4608 pages
% 0.37/0.56 % E exiting
%------------------------------------------------------------------------------