%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM468+2 : 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 : n014.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 1.35s 0.79s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% Number of atoms : 148 ( 56 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 176 ( 62 ~; 55 |; 40 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 24 !; 3 ?)
% 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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
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(m__,conjecture,
( xl != sz00
=> ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1240_04,hypothesis,
( doDivides0(xl,xn)
& ? [X1] :
( xn = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) )
& doDivides0(xl,xm)
& ? [X1] :
( xm = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240_04) ).
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__1240,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240) ).
fof(c_0_7,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_8,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_9,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_10,negated_conjecture,
~ ( xl != sz00
=> ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_11,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_7])])])])]) ).
cnf(c_0_12,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,negated_conjecture,
~ ( xl != sz00
=> ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| X3 = sz00
| X1 = sdtsldt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_12]),c_0_13]) ).
fof(c_0_17,hypothesis,
( doDivides0(xl,xn)
& xn = sdtasdt0(xl,esk4_0)
& aNaturalNumber0(esk4_0)
& doDivides0(xl,xm)
& xm = sdtasdt0(xl,esk3_0)
& aNaturalNumber0(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1240_04])]) ).
fof(c_0_18,negated_conjecture,
( sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl))
& xl != sz00 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).
fof(c_0_19,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_20,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtsldt0(sdtasdt0(X1,X2),X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_15]),c_0_13]),c_0_16]) ).
cnf(c_0_21,hypothesis,
xm = sdtasdt0(xl,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1240]) ).
cnf(c_0_23,hypothesis,
aNaturalNumber0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
xl != sz00,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,hypothesis,
xn = sdtasdt0(xl,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,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_19]) ).
cnf(c_0_28,negated_conjecture,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,hypothesis,
sdtsldt0(xm,xl) = esk3_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]),c_0_24]) ).
cnf(c_0_30,hypothesis,
sdtsldt0(xn,xl) = esk4_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_22]),c_0_26])]),c_0_24]) ).
cnf(c_0_31,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(sdtasdt0(xl,X1),xn) = sdtasdt0(xl,sdtpldt0(X1,esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_26]),c_0_22])]) ).
cnf(c_0_32,negated_conjecture,
sdtasdt0(xl,sdtpldt0(esk3_0,esk4_0)) != sdtpldt0(xm,xn),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_33,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_21]),c_0_23])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM468+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.40 % Computer : n014.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Mon Sep 21 02:32:50 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.49 Running first-order theorem proving
% 0.20/0.49 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
% 1.35/0.79 % Version: 3.5.1
% 1.35/0.79 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.35/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.35/0.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.35/0.79 % Starting new_bool_3 with 300s (1) cores
% 1.35/0.79 % Starting new_bool_1 with 300s (1) cores
% 1.35/0.79 % Starting sh5l with 300s (1) cores
% 1.35/0.79 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2952824 completed with status 0
% 1.35/0.79 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.35/0.79 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.35/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.35/0.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.35/0.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.35/0.79 % No SInE strategy applied
% 1.35/0.79 % Search class: FGUSF-FFMM22-MFFFFFNN
% 1.35/0.79 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.35/0.79 % Starting SubtermCWHack with 136s (1) cores
% 1.35/0.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.35/0.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 1.35/0.79 % Starting new_bool_3 with 136s (1) cores
% 1.35/0.79 % Starting new_bool_1 with 136s (1) cores
% 1.35/0.79 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2952830 completed with status 0
% 1.35/0.79 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.35/0.79 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.35/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.35/0.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.35/0.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.35/0.79 % No SInE strategy applied
% 1.35/0.79 % Search class: FGUSF-FFMM22-MFFFFFNN
% 1.35/0.79 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.35/0.79 % Starting SubtermCWHack with 136s (1) cores
% 1.35/0.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.35/0.79 % Preprocessing time : 0.003 s
% 1.35/0.79 % Presaturation interreduction done
% 1.35/0.79
% 1.35/0.79 % Proof found!
% 1.35/0.79 % SZS status Theorem
% 1.35/0.79 % SZS output start CNFRefutation
% See solution above
% 1.35/0.79 % Parsed axioms : 35
% 1.35/0.79 % Removed by relevancy pruning/SinE : 0
% 1.35/0.79 % Initial clauses : 71
% 1.35/0.79 % Removed in clause preprocessing : 3
% 1.35/0.79 % Initial clauses in saturation : 68
% 1.35/0.79 % Processed clauses : 1810
% 1.35/0.79 % ...of these trivial : 57
% 1.35/0.79 % ...subsumed : 969
% 1.35/0.79 % ...remaining for further processing : 784
% 1.35/0.79 % Other redundant clauses eliminated : 72
% 1.35/0.79 % Clauses deleted for lack of memory : 0
% 1.35/0.79 % Backward-subsumed : 21
% 1.35/0.79 % Backward-rewritten : 92
% 1.35/0.79 % Generated clauses : 12576
% 1.35/0.79 % ...of the previous two non-redundant : 9921
% 1.35/0.79 % ...aggressively subsumed : 0
% 1.35/0.79 % Contextual simplify-reflections : 166
% 1.35/0.79 % Paramodulations : 12496
% 1.35/0.79 % Factorizations : 2
% 1.35/0.79 % NegExts : 0
% 1.35/0.79 % Equation resolutions : 78
% 1.35/0.79 % Disequality decompositions : 0
% 1.35/0.79 % Total rewrite steps : 14560
% 1.35/0.79 % ...of those cached : 14417
% 1.35/0.79 % Propositional unsat checks : 0
% 1.35/0.79 % Propositional check models : 0
% 1.35/0.79 % Propositional check unsatisfiable : 0
% 1.35/0.79 % Propositional clauses : 0
% 1.35/0.79 % Propositional clauses after purity: 0
% 1.35/0.79 % Propositional unsat core size : 0
% 1.35/0.79 % Propositional preprocessing time : 0.000
% 1.35/0.79 % Propositional encoding time : 0.000
% 1.35/0.79 % Propositional solver time : 0.000
% 1.35/0.79 % Success case prop preproc time : 0.000
% 1.35/0.79 % Success case prop encoding time : 0.000
% 1.35/0.79 % Success case prop solver time : 0.000
% 1.35/0.79 % Current number of processed clauses : 599
% 1.35/0.79 % Positive orientable unit clauses : 126
% 1.35/0.79 % Positive unorientable unit clauses: 0
% 1.35/0.79 % Negative unit clauses : 10
% 1.35/0.79 % Non-unit-clauses : 463
% 1.35/0.79 % Current number of unprocessed clauses: 7997
% 1.35/0.79 % ...number of literals in the above : 37096
% 1.35/0.79 % Current number of archived formulas : 0
% 1.35/0.79 % Current number of archived clauses : 176
% 1.35/0.79 % Clause-clause subsumption calls (NU) : 27872
% 1.35/0.79 % Rec. Clause-clause subsumption calls : 16524
% 1.35/0.79 % Non-unit clause-clause subsumptions : 1115
% 1.35/0.79 % Unit Clause-clause subsumption calls : 1862
% 1.35/0.79 % Rewrite failures with RHS unbound : 0
% 1.35/0.79 % BW rewrite match attempts : 33
% 1.35/0.79 % BW rewrite match successes : 32
% 1.35/0.79 % Condensation attempts : 0
% 1.35/0.79 % Condensation successes : 0
% 1.35/0.79 % Termbank termtop insertions : 221980
% 1.35/0.79 % Search garbage collected termcells : 1054
% 1.35/0.79
% 1.35/0.79 % -------------------------------------------------
% 1.35/0.79 % User time : 0.218 s
% 1.35/0.79 % System time : 0.011 s
% 1.35/0.79 % Total time : 0.229 s
% 1.35/0.79 % Maximum resident set size: 3928 pages
% 1.35/0.79
% 1.35/0.79 % -------------------------------------------------
% 1.35/0.79 % User time : 0.948 s
% 1.35/0.79 % System time : 0.045 s
% 1.35/0.79 % Total time : 0.993 s
% 1.35/0.79 % Maximum resident set size: 4864 pages
% 1.35/0.79 % E exiting
%------------------------------------------------------------------------------