%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM466+2 : 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 : n004.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 01:55:07 PM UTC 2026
% Result : Theorem 0.24s 0.61s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 8 unt; 0 def)
% Number of atoms : 90 ( 19 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 101 ( 35 ~; 32 |; 28 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 16 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( doDivides0(xm,xn)
& ? [X1] :
( xn = sdtasdt0(xm,X1)
& aNaturalNumber0(X1) )
& doDivides0(xl,xm)
& ? [X1] :
( xm = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) ) )
=> ( doDivides0(xl,xn)
| ? [X1] :
( xn = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(m__1218,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1218) ).
fof(c_0_5,negated_conjecture,
~ ( ( doDivides0(xm,xn)
& ? [X1] :
( xn = sdtasdt0(xm,X1)
& aNaturalNumber0(X1) )
& doDivides0(xl,xm)
& ? [X1] :
( xm = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) ) )
=> ( doDivides0(xl,xn)
| ? [X1] :
( xn = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,plain,
! [X8,X9,X11] :
( ( ~ aNaturalNumber0(X9)
| ~ aNaturalNumber0(X8)
| doDivides0(X8,X9)
| X9 != sdtasdt0(X8,X11)
| ~ aNaturalNumber0(X11) )
& ( ~ aNaturalNumber0(X9)
| ~ aNaturalNumber0(X8)
| ~ doDivides0(X8,X9)
| X9 = sdtasdt0(X8,esk3_2(X8,X9)) )
& ( ~ aNaturalNumber0(X9)
| ~ aNaturalNumber0(X8)
| ~ doDivides0(X8,X9)
| aNaturalNumber0(esk3_2(X8,X9)) ) ),
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_7,plain,
! [X12,X13] :
( aNaturalNumber0(sdtasdt0(X12,X13))
| ~ aNaturalNumber0(X13)
| ~ aNaturalNumber0(X12) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_8,plain,
! [X16,X17,X18] :
( sdtasdt0(sdtasdt0(X16,X17),X18) = sdtasdt0(X16,sdtasdt0(X17,X18))
| ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17)
| ~ aNaturalNumber0(X16) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
fof(c_0_9,negated_conjecture,
! [X6] :
( ~ doDivides0(xl,xn)
& ( xn != sdtasdt0(xl,X6)
| ~ aNaturalNumber0(X6) )
& doDivides0(xm,xn)
& xn = sdtasdt0(xm,esk2_0)
& aNaturalNumber0(esk2_0)
& doDivides0(xl,xm)
& xm = sdtasdt0(xl,esk1_0)
& aNaturalNumber0(esk1_0) ),
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_5])])])])]) ).
cnf(c_0_10,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
xm = sdtasdt0(xl,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
aNaturalNumber0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1218]) ).
cnf(c_0_16,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_10]),c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xl,sdtasdt0(esk1_0,X1)) = sdtasdt0(xm,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_18,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(esk1_0,X1))
| doDivides0(xl,sdtasdt0(xm,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_15])]) ).
cnf(c_0_19,negated_conjecture,
xn = sdtasdt0(xm,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,negated_conjecture,
aNaturalNumber0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,negated_conjecture,
~ doDivides0(xl,xn),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,negated_conjecture,
~ aNaturalNumber0(sdtasdt0(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),c_0_21]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_11]),c_0_20]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM466+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.46 % Computer : n004.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Mon Sep 21 02:32:22 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 0.24/0.61 % Version: 3.5.1
% 0.24/0.61 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.61 % Starting sh5l with 300s (1) cores
% 0.24/0.61 % new_bool_1 with pid 2059896 completed with status 0
% 0.24/0.61 % Result found by new_bool_1
% 0.24/0.61 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.61 % Search class: FGHSF-FFMM22-SFFFFFNN
% 0.24/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.61 % SubtermCWHack with pid 2059904 completed with status 0
% 0.24/0.61 % Result found by SubtermCWHack
% 0.24/0.61 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.61 % Search class: FGHSF-FFMM22-SFFFFFNN
% 0.24/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.61 % Preprocessing time : 0.002 s
% 0.24/0.61
% 0.24/0.61 % Proof found!
% 0.24/0.61 % SZS status Theorem
% 0.24/0.61 % SZS output start CNFRefutation
% See solution above
% 0.24/0.61 % Parsed axioms : 33
% 0.24/0.61 % Removed by relevancy pruning/SinE : 7
% 0.24/0.61 % Initial clauses : 52
% 0.24/0.61 % Removed in clause preprocessing : 1
% 0.24/0.61 % Initial clauses in saturation : 51
% 0.24/0.61 % Processed clauses : 915
% 0.24/0.61 % ...of these trivial : 6
% 0.24/0.61 % ...subsumed : 561
% 0.24/0.61 % ...remaining for further processing : 348
% 0.24/0.61 % Other redundant clauses eliminated : 24
% 0.24/0.61 % Clauses deleted for lack of memory : 0
% 0.24/0.61 % Backward-subsumed : 30
% 0.24/0.61 % Backward-rewritten : 10
% 0.24/0.61 % Generated clauses : 2892
% 0.24/0.61 % ...of the previous two non-redundant : 2494
% 0.24/0.61 % ...aggressively subsumed : 0
% 0.24/0.61 % Contextual simplify-reflections : 5
% 0.24/0.61 % Paramodulations : 2862
% 0.24/0.61 % Factorizations : 0
% 0.24/0.61 % NegExts : 0
% 0.24/0.61 % Equation resolutions : 30
% 0.24/0.61 % Disequality decompositions : 0
% 0.24/0.61 % Total rewrite steps : 3267
% 0.24/0.61 % ...of those cached : 3234
% 0.24/0.61 % Propositional unsat checks : 0
% 0.24/0.61 % Propositional check models : 0
% 0.24/0.61 % Propositional check unsatisfiable : 0
% 0.24/0.61 % Propositional clauses : 0
% 0.24/0.61 % Propositional clauses after purity: 0
% 0.24/0.61 % Propositional unsat core size : 0
% 0.24/0.61 % Propositional preprocessing time : 0.000
% 0.24/0.61 % Propositional encoding time : 0.000
% 0.24/0.61 % Propositional solver time : 0.000
% 0.24/0.61 % Success case prop preproc time : 0.000
% 0.24/0.61 % Success case prop encoding time : 0.000
% 0.24/0.61 % Success case prop solver time : 0.000
% 0.24/0.61 % Current number of processed clauses : 305
% 0.24/0.61 % Positive orientable unit clauses : 39
% 0.24/0.61 % Positive unorientable unit clauses: 0
% 0.24/0.61 % Negative unit clauses : 5
% 0.24/0.61 % Non-unit-clauses : 261
% 0.24/0.61 % Current number of unprocessed clauses: 1586
% 0.24/0.61 % ...number of literals in the above : 7585
% 0.24/0.61 % Current number of archived formulas : 0
% 0.24/0.61 % Current number of archived clauses : 40
% 0.24/0.61 % Clause-clause subsumption calls (NU) : 10636
% 0.24/0.61 % Rec. Clause-clause subsumption calls : 4466
% 0.24/0.61 % Non-unit clause-clause subsumptions : 576
% 0.24/0.61 % Unit Clause-clause subsumption calls : 122
% 0.24/0.61 % Rewrite failures with RHS unbound : 0
% 0.24/0.61 % BW rewrite match attempts : 8
% 0.24/0.61 % BW rewrite match successes : 8
% 0.24/0.61 % Condensation attempts : 0
% 0.24/0.61 % Condensation successes : 0
% 0.24/0.61 % Termbank termtop insertions : 48650
% 0.24/0.61 % Search garbage collected termcells : 885
% 0.24/0.61
% 0.24/0.61 % -------------------------------------------------
% 0.24/0.61 % User time : 0.055 s
% 0.24/0.61 % System time : 0.008 s
% 0.24/0.61 % Total time : 0.063 s
% 0.24/0.61 % Maximum resident set size: 3664 pages
% 0.24/0.61
% 0.24/0.61 % -------------------------------------------------
% 0.24/0.61 % User time : 0.057 s
% 0.24/0.61 % System time : 0.013 s
% 0.24/0.61 % Total time : 0.070 s
% 0.24/0.61 % Maximum resident set size: 4608 pages
% 0.24/0.61 % E exiting
%------------------------------------------------------------------------------