%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM468+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 : n026.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 01:49:12 PM UTC 2026
% Result : Theorem 0.24s 15.89s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 99 ( 40 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 118 ( 48 ~; 44 |; 16 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(m__,conjecture,
( xl != sz00
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(m__1240_04,hypothesis,
( doDivides0(xl,xn)
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240_04) ).
fof(m__1240,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).
fof(c_0_5,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefQuot]) ).
fof(c_0_6,negated_conjecture,
~ ( xl != sz00
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_7,plain,
! [X67,X68,X69] :
( ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 = sdtsldt0(X68,X67)
| X68 != sdtasdt0(X67,X69)
| ~ aNaturalNumber0(X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| X68 = sdtasdt0(X67,X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| aNaturalNumber0(X69) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
fof(c_0_8,negated_conjecture,
~ ( xl != sz00
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2)
| X2 = sz00
| X1 = sdtasdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,negated_conjecture,
( sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
& xl != sz00 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
cnf(c_0_11,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,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_13,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| sdtasdt0(X1,sdtsldt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
doDivides0(xl,xn),
inference(split_conjunct,[status(thm)],[m__1240_04]) ).
cnf(c_0_15,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1240]) ).
cnf(c_0_16,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1240]) ).
cnf(c_0_17,negated_conjecture,
xl != sz00,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,hypothesis,
sdtasdt0(xl,sdtsldt0(xn,xl)) = xn,
inference(sr,[status(thm)],[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])]),c_0_17]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(sdtsldt0(xn,xl)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_14]),c_0_15]),c_0_16])]),c_0_17]) ).
cnf(c_0_22,hypothesis,
doDivides0(xl,xm),
inference(split_conjunct,[status(thm)],[m__1240_04]) ).
cnf(c_0_23,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1240]) ).
cnf(c_0_24,negated_conjecture,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xl,sdtpldt0(X1,sdtsldt0(xn,xl))) = sdtpldt0(sdtasdt0(xl,X1),xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_15])]) ).
cnf(c_0_26,hypothesis,
sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_22]),c_0_15]),c_0_23])]),c_0_17]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_22]),c_0_15]),c_0_23])]),c_0_17]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[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])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM468+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/15.51 % Computer : n026.cluster.edu
% 0.19/15.51 % Model : x86_64 x86_64
% 0.19/15.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/15.51 % Memory : 8046.5625MB
% 0.19/15.51 % OS : Linux 6.8.0-71-generic
% 0.19/15.51 % CPULimit : 300
% 0.19/15.51 % WCLimit : 300
% 0.19/15.51 % DateTime : Mon Sep 21 02:35:54 UTC 2026
% 0.19/15.52 % CPUTime :
% 0.19/15.52 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/15.56 Running first-order theorem proving
% 0.19/15.57 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
% 0.24/15.89 % Version: 3.5.1
% 0.24/15.89 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/15.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/15.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/15.89 % Starting new_bool_3 with 300s (1) cores
% 0.24/15.89 % Starting new_bool_1 with 300s (1) cores
% 0.24/15.89 % Starting sh5l with 300s (1) cores
% 0.24/15.89 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1178648 completed with status 0
% 0.24/15.89 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.24/15.89 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/15.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/15.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/15.89 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/15.89 % No SInE strategy applied
% 0.24/15.89 % Search class: FGUSF-FFMM22-MFFFFFNN
% 0.24/15.89 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/15.89 % Starting SubtermCWHack with 136s (1) cores
% 0.24/15.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.24/15.89 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.24/15.89 % Starting new_bool_3 with 136s (1) cores
% 0.24/15.89 % Starting new_bool_1 with 136s (1) cores
% 0.24/15.89 % new_bool_1 with pid 1178658 completed with status 0
% 0.24/15.89 % Result found by new_bool_1
% 0.24/15.89 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/15.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/15.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/15.89 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/15.89 % No SInE strategy applied
% 0.24/15.89 % Search class: FGUSF-FFMM22-MFFFFFNN
% 0.24/15.89 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/15.89 % Starting SubtermCWHack with 136s (1) cores
% 0.24/15.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.24/15.89 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.24/15.89 % Starting new_bool_3 with 136s (1) cores
% 0.24/15.89 % Starting new_bool_1 with 136s (1) cores
% 0.24/15.89 % Preprocessing time : 0.002 s
% 0.24/15.89 % Presaturation interreduction done
% 0.24/15.89
% 0.24/15.89 % Proof found!
% 0.24/15.89 % SZS status Theorem
% 0.24/15.89 % SZS output start CNFRefutation
% See solution above
% 0.24/15.89 % Parsed axioms : 35
% 0.24/15.89 % Removed by relevancy pruning/SinE : 0
% 0.24/15.89 % Initial clauses : 63
% 0.24/15.89 % Removed in clause preprocessing : 3
% 0.24/15.89 % Initial clauses in saturation : 60
% 0.24/15.89 % Processed clauses : 1986
% 0.24/15.89 % ...of these trivial : 46
% 0.24/15.89 % ...subsumed : 1036
% 0.24/15.89 % ...remaining for further processing : 904
% 0.24/15.89 % Other redundant clauses eliminated : 69
% 0.24/15.89 % Clauses deleted for lack of memory : 0
% 0.24/15.89 % Backward-subsumed : 38
% 0.24/15.89 % Backward-rewritten : 152
% 0.24/15.89 % Generated clauses : 12323
% 0.24/15.89 % ...of the previous two non-redundant : 10059
% 0.24/15.89 % ...aggressively subsumed : 0
% 0.24/15.89 % Contextual simplify-reflections : 98
% 0.24/15.89 % Paramodulations : 12240
% 0.24/15.89 % Factorizations : 6
% 0.24/15.89 % NegExts : 0
% 0.24/15.89 % Equation resolutions : 77
% 0.24/15.89 % Disequality decompositions : 0
% 0.24/15.89 % Total rewrite steps : 15305
% 0.24/15.89 % ...of those cached : 15145
% 0.24/15.89 % Propositional unsat checks : 0
% 0.24/15.89 % Propositional check models : 0
% 0.24/15.89 % Propositional check unsatisfiable : 0
% 0.24/15.89 % Propositional clauses : 0
% 0.24/15.89 % Propositional clauses after purity: 0
% 0.24/15.89 % Propositional unsat core size : 0
% 0.24/15.89 % Propositional preprocessing time : 0.000
% 0.24/15.89 % Propositional encoding time : 0.000
% 0.24/15.89 % Propositional solver time : 0.000
% 0.24/15.89 % Success case prop preproc time : 0.000
% 0.24/15.89 % Success case prop encoding time : 0.000
% 0.24/15.89 % Success case prop solver time : 0.000
% 0.24/15.89 % Current number of processed clauses : 650
% 0.24/15.89 % Positive orientable unit clauses : 139
% 0.24/15.89 % Positive unorientable unit clauses: 0
% 0.24/15.89 % Negative unit clauses : 3
% 0.24/15.89 % Non-unit-clauses : 508
% 0.24/15.89 % Current number of unprocessed clauses: 7984
% 0.24/15.89 % ...number of literals in the above : 35412
% 0.24/15.89 % Current number of archived formulas : 0
% 0.24/15.89 % Current number of archived clauses : 245
% 0.24/15.89 % Clause-clause subsumption calls (NU) : 34472
% 0.24/15.89 % Rec. Clause-clause subsumption calls : 20892
% 0.24/15.89 % Non-unit clause-clause subsumptions : 1161
% 0.24/15.89 % Unit Clause-clause subsumption calls : 5846
% 0.24/15.89 % Rewrite failures with RHS unbound : 0
% 0.24/15.89 % BW rewrite match attempts : 40
% 0.24/15.89 % BW rewrite match successes : 38
% 0.24/15.89 % Condensation attempts : 0
% 0.24/15.89 % Condensation successes : 0
% 0.24/15.89 % Termbank termtop insertions : 223651
% 0.24/15.89 % Search garbage collected termcells : 1006
% 0.24/15.89
% 0.24/15.89 % -------------------------------------------------
% 0.24/15.89 % User time : 0.221 s
% 0.24/15.89 % System time : 0.013 s
% 0.24/15.89 % Total time : 0.235 s
% 0.24/15.89 % Maximum resident set size: 3928 pages
% 0.24/15.89
% 0.24/15.89 % -------------------------------------------------
% 0.24/15.89 % User time : 1.159 s
% 0.24/15.89 % System time : 0.057 s
% 0.24/15.89 % Total time : 1.216 s
% 0.24/15.89 % Maximum resident set size: 4608 pages
% 0.24/15.89 % E exiting
%------------------------------------------------------------------------------