%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM488+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 : n015.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 01:49:16 PM UTC 2026
% Result : Theorem 51.25s 8.04s
% Output : CNFRefutation 51.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 16 unt; 0 def)
% Number of atoms : 144 ( 23 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 184 ( 80 ~; 76 |; 19 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 27 !; 1 ?)
% 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(mDivMin,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,sdtpldt0(X2,X3))
& doDivides0(X1,X2) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivMin) ).
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(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(m__,conjecture,
doDivides0(xp,sdtasdt0(xr,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(c_0_10,plain,
! [X63,X64,X66] :
( ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| doDivides0(X63,X64)
| X64 != sdtasdt0(X63,X66)
| ~ aNaturalNumber0(X66) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| X64 = sdtasdt0(X63,esk2_2(X63,X64)) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| aNaturalNumber0(esk2_2(X63,X64)) ) ),
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_11,plain,
! [X7,X8] :
( aNaturalNumber0(sdtasdt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_12,plain,
! [X76,X77,X78] :
( doDivides0(X76,X78)
| ~ doDivides0(X76,sdtpldt0(X77,X78))
| ~ doDivides0(X76,X77)
| ~ aNaturalNumber0(X78)
| ~ aNaturalNumber0(X77)
| ~ aNaturalNumber0(X76) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])])]) ).
cnf(c_0_13,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,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])])])])]) ).
cnf(c_0_16,plain,
( ~ doDivides0(X1,sdtpldt0(X2,X3))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_13]),c_0_14]) ).
fof(c_0_18,plain,
! [X22,X23,X24] :
( ( ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X22)
| sdtasdt0(sdtpldt0(X23,X24),X22) = sdtpldt0(sdtasdt0(X23,X22),sdtasdt0(X24,X22)) )
& ( ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X22)
| sdtasdt0(X22,sdtpldt0(X23,X24)) = sdtpldt0(sdtasdt0(X22,X23),sdtasdt0(X22,X24)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])])]) ).
cnf(c_0_19,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X3)
| X2 != sdtmndt0(X3,X1)
| sdtpldt0(X1,X2) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X3,X2)
| X1 != sdtmndt0(X2,X3)
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_22,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,sdtpldt0(sdtasdt0(X1,X3),X2))
| doDivides0(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14]) ).
cnf(c_0_23,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,sdtmndt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_25,hypothesis,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[m__1870]) ).
cnf(c_0_26,hypothesis,
xr = sdtmndt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_29,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| aNaturalNumber0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_20]) ).
fof(c_0_30,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,sdtasdt0(sdtpldt0(X1,X2),X3))
| doDivides0(X1,sdtasdt0(X2,X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14]) ).
cnf(c_0_32,hypothesis,
sdtpldt0(xp,xr) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_33,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_29,c_0_25]),c_0_26]),c_0_28]),c_0_27])]) ).
fof(c_0_34,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(fof_nnf,[status(thm)],[c_0_30]) ).
cnf(c_0_35,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(xp,sdtasdt0(xn,X1))
| doDivides0(xp,sdtasdt0(xr,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_28]),c_0_33])]) ).
cnf(c_0_36,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_37,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_38,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_39,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_35,c_0_36,c_0_37,c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM488+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.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 02:37:05 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 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
% 51.25/8.03 % Version: 3.5.1
% 51.25/8.03 % Preprocessing class: FSLSSMSSSSSNFFN.
% 51.25/8.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 51.25/8.03 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 51.25/8.03 % Starting new_bool_3 with 300s (1) cores
% 51.25/8.03 % Starting new_bool_1 with 300s (1) cores
% 51.25/8.03 % Starting sh5l with 300s (1) cores
% 51.25/8.03 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 371796 completed with status 0
% 51.25/8.03 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 51.25/8.03 % Preprocessing class: FSLSSMSSSSSNFFN.
% 51.25/8.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 51.25/8.03 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 51.25/8.03 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 51.25/8.03 % No SInE strategy applied
% 51.25/8.03 % Search class: FGHSF-FFMM21-SFFFFFNN
% 51.25/8.03 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 51.25/8.03 % Starting SubtermCWHack with 136s (1) cores
% 51.25/8.03 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 51.25/8.03 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 51.25/8.04 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 51.25/8.04 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 51.25/8.04 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with pid 371802 completed with status 0
% 51.25/8.04 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m
% 51.25/8.04 % Preprocessing class: FSLSSMSSSSSNFFN.
% 51.25/8.04 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 51.25/8.04 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 51.25/8.04 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 51.25/8.04 % No SInE strategy applied
% 51.25/8.04 % Search class: FGHSF-FFMM21-SFFFFFNN
% 51.25/8.04 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 51.25/8.04 % Starting SubtermCWHack with 136s (1) cores
% 51.25/8.04 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 51.25/8.04 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 51.25/8.04 % Preprocessing time : 0.003 s
% 51.25/8.04 % Presaturation interreduction done
% 51.25/8.04 % SatCheck found unsatisfiable ground set
% 51.25/8.04
% 51.25/8.04 % Proof found!
% 51.25/8.04 % SZS status Theorem
% 51.25/8.04 % SZS output start CNFRefutation
% See solution above
% 51.25/8.04 % Parsed axioms : 45
% 51.25/8.04 % Removed by relevancy pruning/SinE : 0
% 51.25/8.04 % Initial clauses : 81
% 51.25/8.04 % Removed in clause preprocessing : 3
% 51.25/8.04 % Initial clauses in saturation : 78
% 51.25/8.04 % Processed clauses : 16743
% 51.25/8.04 % ...of these trivial : 1511
% 51.25/8.04 % ...subsumed : 10232
% 51.25/8.04 % ...remaining for further processing : 5000
% 51.25/8.04 % Other redundant clauses eliminated : 298
% 51.25/8.04 % Clauses deleted for lack of memory : 0
% 51.25/8.04 % Backward-subsumed : 135
% 51.25/8.04 % Backward-rewritten : 890
% 51.25/8.04 % Generated clauses : 189298
% 51.25/8.04 % ...of the previous two non-redundant : 160016
% 51.25/8.04 % ...aggressively subsumed : 0
% 51.25/8.04 % Contextual simplify-reflections : 487
% 51.25/8.04 % Paramodulations : 188971
% 51.25/8.04 % Factorizations : 15
% 51.25/8.04 % NegExts : 0
% 51.25/8.04 % Equation resolutions : 312
% 51.25/8.04 % Disequality decompositions : 0
% 51.25/8.04 % Total rewrite steps : 265806
% 51.25/8.04 % ...of those cached : 264131
% 51.25/8.04 % Propositional unsat checks : 1
% 51.25/8.04 % Propositional check models : 0
% 51.25/8.04 % Propositional check unsatisfiable : 1
% 51.25/8.04 % Propositional clauses : 145189
% 51.25/8.04 % Propositional clauses after purity: 13609
% 51.25/8.04 % Propositional unsat core size : 4
% 51.25/8.04 % Propositional preprocessing time : 0.000
% 51.25/8.04 % Propositional encoding time : 0.483
% 51.25/8.04 % Propositional solver time : 0.075
% 51.25/8.04 % Success case prop preproc time : 0.000
% 51.25/8.04 % Success case prop encoding time : 0.483
% 51.25/8.04 % Success case prop solver time : 0.075
% 51.25/8.04 % Current number of processed clauses : 3891
% 51.25/8.04 % Positive orientable unit clauses : 1624
% 51.25/8.04 % Positive unorientable unit clauses: 0
% 51.25/8.04 % Negative unit clauses : 126
% 51.25/8.04 % Non-unit-clauses : 2141
% 51.25/8.04 % Current number of unprocessed clauses: 141298
% 51.25/8.04 % ...number of literals in the above : 580594
% 51.25/8.04 % Current number of archived formulas : 0
% 51.25/8.04 % Current number of archived clauses : 1098
% 51.25/8.04 % Clause-clause subsumption calls (NU) : 600827
% 51.25/8.04 % Rec. Clause-clause subsumption calls : 348757
% 51.25/8.04 % Non-unit clause-clause subsumptions : 7989
% 51.25/8.04 % Unit Clause-clause subsumption calls : 57462
% 51.25/8.04 % Rewrite failures with RHS unbound : 0
% 51.25/8.04 % BW rewrite match attempts : 13259
% 51.25/8.04 % BW rewrite match successes : 647
% 51.25/8.04 % Condensation attempts : 0
% 51.25/8.04 % Condensation successes : 0
% 51.25/8.04 % Termbank termtop insertions : 5531663
% 51.25/8.04 % Search garbage collected termcells : 1342
% 51.25/8.04
% 51.25/8.04 % -------------------------------------------------
% 51.25/8.04 % User time : 6.980 s
% 51.25/8.04 % System time : 0.311 s
% 51.25/8.04 % Total time : 7.291 s
% 51.25/8.04 % Maximum resident set size: 3428 pages
% 51.25/8.04
% 51.25/8.04 % -------------------------------------------------
% 51.25/8.04 % User time : 34.724 s
% 51.25/8.04 % System time : 1.401 s
% 51.25/8.04 % Total time : 36.125 s
% 51.25/8.04 % Maximum resident set size: 4864 pages
% 51.25/8.04 % E exiting
%------------------------------------------------------------------------------