%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM468+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 : n016.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 01:55:08 PM UTC 2026
% Result : Theorem 0.21s 15.81s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 102 ( 40 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 129 ( 54 ~; 49 |; 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 : 31 ( 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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(m__,conjecture,
( xl != sz00
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(m__1240_04,hypothesis,
( doDivides0(xl,xn)
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240_04) ).
fof(m__1240,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/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]) ).
fof(c_0_9,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_10,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]) ).
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,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_13,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_9]) ).
cnf(c_0_14,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| sdtasdt0(X1,sdtsldt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X3)
| X1 = sz00
| sdtasdt0(X1,sdtpldt0(X2,sdtsldt0(X3,X1))) = sdtpldt0(sdtasdt0(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,hypothesis,
doDivides0(xl,xn),
inference(split_conjunct,[status(thm)],[m__1240_04]) ).
cnf(c_0_19,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1240]) ).
cnf(c_0_20,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1240]) ).
cnf(c_0_21,negated_conjecture,
xl != sz00,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),xn) != sdtpldt0(xm,xn) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]),c_0_20])]),c_0_21]) ).
cnf(c_0_23,hypothesis,
doDivides0(xl,xm),
inference(split_conjunct,[status(thm)],[m__1240_04]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1240]) ).
cnf(c_0_25,negated_conjecture,
~ aNaturalNumber0(sdtsldt0(xm,xl)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_14]),c_0_23]),c_0_19]),c_0_24])]),c_0_21]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_15]),c_0_23]),c_0_19]),c_0_24])]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM468+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/15.43 % Computer : n016.cluster.edu
% 0.15/15.43 % Model : x86_64 x86_64
% 0.15/15.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/15.43 % Memory : 8046.5625MB
% 0.15/15.43 % OS : Linux 6.8.0-71-generic
% 0.15/15.43 % CPULimit : 300
% 0.15/15.43 % WCLimit : 300
% 0.15/15.43 % DateTime : Mon Sep 21 02:37:53 UTC 2026
% 0.15/15.44 % CPUTime :
% 0.15/15.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/15.48 Running first-order theorem proving
% 0.15/15.48 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
% 0.21/15.81 % Version: 3.5.1
% 0.21/15.81 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/15.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/15.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/15.81 % Starting new_bool_3 with 300s (1) cores
% 0.21/15.81 % Starting new_bool_1 with 300s (1) cores
% 0.21/15.81 % Starting sh5l with 300s (1) cores
% 0.21/15.81 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1372782 completed with status 0
% 0.21/15.81 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.21/15.81 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/15.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/15.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/15.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/15.81 % No SInE strategy applied
% 0.21/15.81 % Search class: FGUSF-FFMM22-MFFFFFNN
% 0.21/15.81 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/15.81 % Starting SubtermCWHack with 136s (1) cores
% 0.21/15.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.21/15.81 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.21/15.81 % Starting new_bool_3 with 136s (1) cores
% 0.21/15.81 % Starting new_bool_1 with 136s (1) cores
% 0.21/15.81 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 1372791 completed with status 0
% 0.21/15.81 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.21/15.81 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/15.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/15.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/15.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/15.81 % No SInE strategy applied
% 0.21/15.81 % Search class: FGUSF-FFMM22-MFFFFFNN
% 0.21/15.81 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/15.81 % Starting SubtermCWHack with 136s (1) cores
% 0.21/15.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.21/15.81 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.21/15.81 % Preprocessing time : 0.002 s
% 0.21/15.81 % Presaturation interreduction done
% 0.21/15.81
% 0.21/15.81 % Proof found!
% 0.21/15.81 % SZS status Theorem
% 0.21/15.81 % SZS output start CNFRefutation
% See solution above
% 0.21/15.81 % Parsed axioms : 35
% 0.21/15.81 % Removed by relevancy pruning/SinE : 0
% 0.21/15.81 % Initial clauses : 63
% 0.21/15.81 % Removed in clause preprocessing : 3
% 0.21/15.81 % Initial clauses in saturation : 60
% 0.21/15.81 % Processed clauses : 2071
% 0.21/15.81 % ...of these trivial : 14
% 0.21/15.81 % ...subsumed : 1448
% 0.21/15.81 % ...remaining for further processing : 609
% 0.21/15.81 % Other redundant clauses eliminated : 189
% 0.21/15.81 % Clauses deleted for lack of memory : 0
% 0.21/15.81 % Backward-subsumed : 18
% 0.21/15.81 % Backward-rewritten : 23
% 0.21/15.81 % Generated clauses : 14376
% 0.21/15.81 % ...of the previous two non-redundant : 12900
% 0.21/15.81 % ...aggressively subsumed : 0
% 0.21/15.81 % Contextual simplify-reflections : 104
% 0.21/15.81 % Paramodulations : 14170
% 0.21/15.81 % Factorizations : 0
% 0.21/15.81 % NegExts : 0
% 0.21/15.81 % Equation resolutions : 206
% 0.21/15.81 % Disequality decompositions : 0
% 0.21/15.81 % Total rewrite steps : 10816
% 0.21/15.81 % ...of those cached : 10788
% 0.21/15.81 % Propositional unsat checks : 0
% 0.21/15.81 % Propositional check models : 0
% 0.21/15.81 % Propositional check unsatisfiable : 0
% 0.21/15.81 % Propositional clauses : 0
% 0.21/15.81 % Propositional clauses after purity: 0
% 0.21/15.81 % Propositional unsat core size : 0
% 0.21/15.81 % Propositional preprocessing time : 0.000
% 0.21/15.81 % Propositional encoding time : 0.000
% 0.21/15.81 % Propositional solver time : 0.000
% 0.21/15.81 % Success case prop preproc time : 0.000
% 0.21/15.81 % Success case prop encoding time : 0.000
% 0.21/15.81 % Success case prop solver time : 0.000
% 0.21/15.81 % Current number of processed clauses : 504
% 0.21/15.81 % Positive orientable unit clauses : 29
% 0.21/15.81 % Positive unorientable unit clauses: 0
% 0.21/15.81 % Negative unit clauses : 6
% 0.21/15.81 % Non-unit-clauses : 469
% 0.21/15.81 % Current number of unprocessed clauses: 10877
% 0.21/15.81 % ...number of literals in the above : 64014
% 0.21/15.81 % Current number of archived formulas : 0
% 0.21/15.81 % Current number of archived clauses : 96
% 0.21/15.81 % Clause-clause subsumption calls (NU) : 31336
% 0.21/15.81 % Rec. Clause-clause subsumption calls : 14073
% 0.21/15.81 % Non-unit clause-clause subsumptions : 1491
% 0.21/15.81 % Unit Clause-clause subsumption calls : 222
% 0.21/15.81 % Rewrite failures with RHS unbound : 0
% 0.21/15.81 % BW rewrite match attempts : 10
% 0.21/15.81 % BW rewrite match successes : 10
% 0.21/15.81 % Condensation attempts : 0
% 0.21/15.81 % Condensation successes : 0
% 0.21/15.81 % Termbank termtop insertions : 274788
% 0.21/15.81 % Search garbage collected termcells : 1006
% 0.21/15.81
% 0.21/15.81 % -------------------------------------------------
% 0.21/15.81 % User time : 0.278 s
% 0.21/15.81 % System time : 0.014 s
% 0.21/15.81 % Total time : 0.292 s
% 0.21/15.81 % Maximum resident set size: 3928 pages
% 0.21/15.81
% 0.21/15.81 % -------------------------------------------------
% 0.21/15.81 % User time : 1.129 s
% 0.21/15.81 % System time : 0.045 s
% 0.21/15.81 % Total time : 1.174 s
% 0.21/15.81 % Maximum resident set size: 4608 pages
% 0.21/15.81 % E exiting
%------------------------------------------------------------------------------