%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM496+1 : 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 : n006.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 0.08s 0.46s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 14 unt; 0 def)
% Number of atoms : 140 ( 26 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 167 ( 71 ~; 67 |; 20 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 23 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( doDivides0(xp,xm)
| doDivides0(xp,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mDivSum,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X3)
& doDivides0(X1,X2) )
=> doDivides0(X1,sdtpldt0(X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
fof(m__2027,hypothesis,
( doDivides0(xp,xm)
| doDivides0(xp,xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2027) ).
fof(m__1870,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
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_11,negated_conjecture,
~ ( doDivides0(xp,xm)
| doDivides0(xp,xn) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,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_13,negated_conjecture,
( ~ doDivides0(xp,xm)
& ~ doDivides0(xp,xn) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
cnf(c_0_14,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X3,X2)
| X1 != sdtmndt0(X2,X3)
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,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_16,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_17,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_18,plain,
! [X73,X74,X75] :
( doDivides0(X73,sdtpldt0(X74,X75))
| ~ doDivides0(X73,X75)
| ~ doDivides0(X73,X74)
| ~ aNaturalNumber0(X75)
| ~ aNaturalNumber0(X74)
| ~ aNaturalNumber0(X73) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])])]) ).
cnf(c_0_19,hypothesis,
( doDivides0(xp,xm)
| doDivides0(xp,xr) ),
inference(split_conjunct,[status(thm)],[m__2027]) ).
cnf(c_0_20,negated_conjecture,
~ doDivides0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| aNaturalNumber0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_22,hypothesis,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[m__1870]) ).
cnf(c_0_23,hypothesis,
xr = sdtmndt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_26,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_28,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_29,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_17]) ).
cnf(c_0_30,plain,
( ~ doDivides0(X1,X3)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,hypothesis,
doDivides0(xp,xr),
inference(sr,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_32,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_21,c_0_22]),c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_33,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_26]),c_0_27]) ).
cnf(c_0_34,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X3)
| X2 != sdtmndt0(X3,X1)
| sdtpldt0(X1,X2) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_37,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(xp,X1)
| doDivides0(xp,sdtpldt0(X1,xr)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_24])]) ).
cnf(c_0_38,plain,
( ~ aNaturalNumber0(X1)
| doDivides0(X1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_39,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,sdtmndt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_40,hypothesis,
doDivides0(xp,sdtpldt0(xp,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_24])]) ).
cnf(c_0_41,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_39,c_0_22]),c_0_23]),c_0_25]),c_0_24])]) ).
cnf(c_0_42,negated_conjecture,
~ doDivides0(xp,xn),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_43,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM496+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 02:34:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.46 % Version: 3.5.1
% 0.08/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.46 % Starting sh5l with 300s (1) cores
% 0.08/0.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1817518 completed with status 0
% 0.08/0.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.08/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.46 % No SInE strategy applied
% 0.08/0.46 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.08/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.08/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.08/0.46 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.08/0.46 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.08/0.46 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with pid 1817526 completed with status 0
% 0.08/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m
% 0.08/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.46 % No SInE strategy applied
% 0.08/0.46 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.08/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.08/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.08/0.46 % Preprocessing time : 0.002 s
% 0.08/0.46 % Presaturation interreduction done
% 0.08/0.46
% 0.08/0.46 % Proof found!
% 0.08/0.46 % SZS status Theorem
% 0.08/0.46 % SZS output start CNFRefutation
% See solution above
% 0.08/0.46 % Parsed axioms : 47
% 0.08/0.46 % Removed by relevancy pruning/SinE : 0
% 0.08/0.46 % Initial clauses : 84
% 0.08/0.46 % Removed in clause preprocessing : 3
% 0.08/0.46 % Initial clauses in saturation : 81
% 0.08/0.46 % Processed clauses : 315
% 0.08/0.46 % ...of these trivial : 6
% 0.08/0.46 % ...subsumed : 42
% 0.08/0.46 % ...remaining for further processing : 267
% 0.08/0.46 % Other redundant clauses eliminated : 19
% 0.08/0.46 % Clauses deleted for lack of memory : 0
% 0.08/0.46 % Backward-subsumed : 4
% 0.08/0.46 % Backward-rewritten : 9
% 0.08/0.46 % Generated clauses : 724
% 0.08/0.46 % ...of the previous two non-redundant : 604
% 0.08/0.46 % ...aggressively subsumed : 0
% 0.08/0.46 % Contextual simplify-reflections : 8
% 0.08/0.46 % Paramodulations : 699
% 0.08/0.46 % Factorizations : 2
% 0.08/0.46 % NegExts : 0
% 0.08/0.46 % Equation resolutions : 23
% 0.08/0.46 % Disequality decompositions : 0
% 0.08/0.46 % Total rewrite steps : 773
% 0.08/0.46 % ...of those cached : 741
% 0.08/0.46 % Propositional unsat checks : 0
% 0.08/0.46 % Propositional check models : 0
% 0.08/0.46 % Propositional check unsatisfiable : 0
% 0.08/0.46 % Propositional clauses : 0
% 0.08/0.46 % Propositional clauses after purity: 0
% 0.08/0.46 % Propositional unsat core size : 0
% 0.08/0.46 % Propositional preprocessing time : 0.000
% 0.08/0.46 % Propositional encoding time : 0.000
% 0.08/0.46 % Propositional solver time : 0.000
% 0.08/0.46 % Success case prop preproc time : 0.000
% 0.08/0.46 % Success case prop encoding time : 0.000
% 0.08/0.46 % Success case prop solver time : 0.000
% 0.08/0.46 % Current number of processed clauses : 167
% 0.08/0.46 % Positive orientable unit clauses : 47
% 0.08/0.46 % Positive unorientable unit clauses: 0
% 0.08/0.46 % Negative unit clauses : 7
% 0.08/0.46 % Non-unit-clauses : 113
% 0.08/0.46 % Current number of unprocessed clauses: 446
% 0.08/0.46 % ...number of literals in the above : 1613
% 0.08/0.46 % Current number of archived formulas : 0
% 0.08/0.46 % Current number of archived clauses : 89
% 0.08/0.46 % Clause-clause subsumption calls (NU) : 1355
% 0.08/0.46 % Rec. Clause-clause subsumption calls : 606
% 0.08/0.46 % Non-unit clause-clause subsumptions : 51
% 0.08/0.46 % Unit Clause-clause subsumption calls : 103
% 0.08/0.46 % Rewrite failures with RHS unbound : 0
% 0.08/0.46 % BW rewrite match attempts : 6
% 0.08/0.46 % BW rewrite match successes : 6
% 0.08/0.46 % Condensation attempts : 0
% 0.08/0.46 % Condensation successes : 0
% 0.08/0.46 % Termbank termtop insertions : 18680
% 0.08/0.46 % Search garbage collected termcells : 1342
% 0.08/0.46
% 0.08/0.46 % -------------------------------------------------
% 0.08/0.46 % User time : 0.026 s
% 0.08/0.46 % System time : 0.010 s
% 0.08/0.46 % Total time : 0.035 s
% 0.08/0.46 % Maximum resident set size: 3940 pages
% 0.08/0.46
% 0.08/0.46 % -------------------------------------------------
% 0.08/0.46 % User time : 0.127 s
% 0.08/0.46 % System time : 0.028 s
% 0.08/0.46 % Total time : 0.155 s
% 0.08/0.46 % Maximum resident set size: 4608 pages
% 0.08/0.46 % E exiting
%------------------------------------------------------------------------------