%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM476+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 : n019.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 01:49:14 PM UTC 2026
% Result : Theorem 0.17s 0.67s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 139 ( 82 equ)
% Maximal formula atoms : 31 ( 4 avg)
% Number of connectives : 126 ( 18 ~; 27 |; 73 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 5 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( xl != sz00
=> ? [X1] :
( ? [X2] :
( ? [X3] :
( xn = sdtasdt0(xl,X3)
& sdtpldt0(sdtasdt0(xl,X1),sdtasdt0(xl,X3)) = sdtpldt0(sdtasdt0(xl,X1),xn)
& X3 = sdtmndt0(X2,X1)
& sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) )
& sdtlseqdt0(X1,X2)
& ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) )
& X2 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X2)
& aNaturalNumber0(X2) )
& X1 = sdtsldt0(xm,xl)
& 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(m__1324_04,hypothesis,
( doDivides0(xl,sdtpldt0(xm,xn))
& ? [X1] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) )
& doDivides0(xl,xm)
& ? [X1] :
( xm = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324_04) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(m__1324,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
fof(c_0_5,negated_conjecture,
~ ( ( xl != sz00
=> ? [X1] :
( ? [X2] :
( ? [X3] :
( xn = sdtasdt0(xl,X3)
& sdtpldt0(sdtasdt0(xl,X1),sdtasdt0(xl,X3)) = sdtpldt0(sdtasdt0(xl,X1),xn)
& X3 = sdtmndt0(X2,X1)
& sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) )
& sdtlseqdt0(X1,X2)
& ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) )
& X2 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X2)
& aNaturalNumber0(X2) )
& X1 = sdtsldt0(xm,xl)
& 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,negated_conjecture,
~ ( ( xl != sz00
=> ? [X1] :
( ? [X2] :
( ? [X3] :
( xn = sdtasdt0(xl,X3)
& sdtpldt0(sdtasdt0(xl,X1),sdtasdt0(xl,X3)) = sdtpldt0(sdtasdt0(xl,X1),xn)
& X3 = sdtmndt0(X2,X1)
& sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) )
& sdtlseqdt0(X1,X2)
& ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) )
& X2 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X2)
& aNaturalNumber0(X2) )
& X1 = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) ) )
=> ( doDivides0(xl,xn)
| ? [X1] :
( xn = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,negated_conjecture,
! [X10] :
( ~ doDivides0(xl,xn)
& ( xn != sdtasdt0(xl,X10)
| ~ aNaturalNumber0(X10) )
& ( xl = sz00
| xn = sdtasdt0(xl,esk6_0) )
& ( xl = sz00
| sdtpldt0(sdtasdt0(xl,esk3_0),sdtasdt0(xl,esk6_0)) = sdtpldt0(sdtasdt0(xl,esk3_0),xn) )
& ( xl = sz00
| esk6_0 = sdtmndt0(esk4_0,esk3_0) )
& ( xl = sz00
| sdtpldt0(esk3_0,esk6_0) = esk4_0 )
& ( xl = sz00
| aNaturalNumber0(esk6_0) )
& ( xl = sz00
| sdtlseqdt0(esk3_0,esk4_0) )
& ( xl = sz00
| sdtpldt0(esk3_0,esk5_0) = esk4_0 )
& ( xl = sz00
| aNaturalNumber0(esk5_0) )
& ( xl = sz00
| esk4_0 = sdtsldt0(sdtpldt0(xm,xn),xl) )
& ( xl = sz00
| sdtpldt0(xm,xn) = sdtasdt0(xl,esk4_0) )
& ( xl = sz00
| aNaturalNumber0(esk4_0) )
& ( xl = sz00
| esk3_0 = sdtsldt0(xm,xl) )
& ( xl = sz00
| xm = sdtasdt0(xl,esk3_0) )
& ( xl = sz00
| aNaturalNumber0(esk3_0) ) ),
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)],[c_0_6])])])])])]) ).
fof(c_0_8,hypothesis,
( doDivides0(xl,sdtpldt0(xm,xn))
& sdtpldt0(xm,xn) = sdtasdt0(xl,esk2_0)
& aNaturalNumber0(esk2_0)
& doDivides0(xl,xm)
& xm = sdtasdt0(xl,esk1_0)
& aNaturalNumber0(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1324_04])]) ).
cnf(c_0_9,negated_conjecture,
( xn != sdtasdt0(xl,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
( xl = sz00
| xn = sdtasdt0(xl,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( xl = sz00
| aNaturalNumber0(esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X52] :
( ( ~ aNaturalNumber0(X52)
| sz00 = sdtasdt0(sz00,X52) )
& ( ~ aNaturalNumber0(X52)
| sdtasdt0(X52,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
cnf(c_0_13,hypothesis,
xm = sdtasdt0(xl,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
xl = sz00,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_15,plain,
( ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,hypothesis,
sdtasdt0(sz00,esk1_0) = xm,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,hypothesis,
aNaturalNumber0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,hypothesis,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,hypothesis,
sdtpldt0(xm,xn) = sdtasdt0(xl,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_20,plain,
! [X29] :
( ( ~ aNaturalNumber0(X29)
| X29 = sdtpldt0(sz00,X29) )
& ( ~ aNaturalNumber0(X29)
| sdtpldt0(X29,sz00) = X29 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
cnf(c_0_21,hypothesis,
xm = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_22,hypothesis,
doDivides0(xl,sdtasdt0(xl,esk2_0)),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,hypothesis,
sdtpldt0(sz00,xn) = sdtasdt0(sz00,esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_14]),c_0_21]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_26,negated_conjecture,
~ doDivides0(xl,xn),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,hypothesis,
doDivides0(sz00,sdtasdt0(sz00,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_14]),c_0_14]) ).
cnf(c_0_28,hypothesis,
sdtasdt0(sz00,esk2_0) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_29,negated_conjecture,
~ doDivides0(sz00,xn),
inference(rw,[status(thm)],[c_0_26,c_0_14]) ).
cnf(c_0_30,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM476+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.60 % Computer : n019.cluster.edu
% 0.14/0.60 % Model : x86_64 x86_64
% 0.14/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.60 % Memory : 8046.5625MB
% 0.14/0.60 % OS : Linux 6.8.0-71-generic
% 0.14/0.60 % CPULimit : 300
% 0.14/0.60 % WCLimit : 300
% 0.14/0.60 % DateTime : Mon Sep 21 02:33:51 UTC 2026
% 0.14/0.60 % CPUTime :
% 0.14/0.60 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.64 Running first-order theorem proving
% 0.17/0.65 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
% 0.17/0.67 % Version: 3.5.1
% 0.17/0.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.67 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.67 % Starting sh5l with 300s (1) cores
% 0.17/0.67 % new_bool_3 with pid 1500845 completed with status 0
% 0.17/0.67 % Result found by new_bool_3
% 0.17/0.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.67 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.67 % Search class: FGHSF-FFMM22-SFFFFFNN
% 0.17/0.67 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.67 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.67 % SubtermCWHack with pid 1500849 completed with status 0
% 0.17/0.67 % Result found by SubtermCWHack
% 0.17/0.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.67 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.67 % Search class: FGHSF-FFMM22-SFFFFFNN
% 0.17/0.67 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.67 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.67 % Preprocessing time : 0.001 s
% 0.17/0.67
% 0.17/0.67 % Proof found!
% 0.17/0.67 % SZS status Theorem
% 0.17/0.67 % SZS output start CNFRefutation
% See solution above
% 0.17/0.67 % Parsed axioms : 36
% 0.17/0.67 % Removed by relevancy pruning/SinE : 5
% 0.17/0.67 % Initial clauses : 74
% 0.17/0.67 % Removed in clause preprocessing : 1
% 0.17/0.67 % Initial clauses in saturation : 73
% 0.17/0.67 % Processed clauses : 43
% 0.17/0.67 % ...of these trivial : 1
% 0.17/0.67 % ...subsumed : 4
% 0.17/0.67 % ...remaining for further processing : 38
% 0.17/0.67 % Other redundant clauses eliminated : 0
% 0.17/0.67 % Clauses deleted for lack of memory : 0
% 0.17/0.67 % Backward-subsumed : 0
% 0.17/0.67 % Backward-rewritten : 21
% 0.17/0.67 % Generated clauses : 12
% 0.17/0.67 % ...of the previous two non-redundant : 20
% 0.17/0.67 % ...aggressively subsumed : 0
% 0.17/0.67 % Contextual simplify-reflections : 1
% 0.17/0.67 % Paramodulations : 12
% 0.17/0.67 % Factorizations : 0
% 0.17/0.67 % NegExts : 0
% 0.17/0.67 % Equation resolutions : 0
% 0.17/0.67 % Disequality decompositions : 0
% 0.17/0.67 % Total rewrite steps : 38
% 0.17/0.67 % ...of those cached : 28
% 0.17/0.67 % Propositional unsat checks : 0
% 0.17/0.67 % Propositional check models : 0
% 0.17/0.67 % Propositional check unsatisfiable : 0
% 0.17/0.67 % Propositional clauses : 0
% 0.17/0.67 % Propositional clauses after purity: 0
% 0.17/0.67 % Propositional unsat core size : 0
% 0.17/0.67 % Propositional preprocessing time : 0.000
% 0.17/0.67 % Propositional encoding time : 0.000
% 0.17/0.67 % Propositional solver time : 0.000
% 0.17/0.67 % Success case prop preproc time : 0.000
% 0.17/0.67 % Success case prop encoding time : 0.000
% 0.17/0.67 % Success case prop solver time : 0.000
% 0.17/0.67 % Current number of processed clauses : 17
% 0.17/0.67 % Positive orientable unit clauses : 9
% 0.17/0.67 % Positive unorientable unit clauses: 0
% 0.17/0.67 % Negative unit clauses : 2
% 0.17/0.67 % Non-unit-clauses : 6
% 0.17/0.67 % Current number of unprocessed clauses: 49
% 0.17/0.67 % ...number of literals in the above : 226
% 0.17/0.67 % Current number of archived formulas : 0
% 0.17/0.67 % Current number of archived clauses : 21
% 0.17/0.67 % Clause-clause subsumption calls (NU) : 9
% 0.17/0.67 % Rec. Clause-clause subsumption calls : 9
% 0.17/0.67 % Non-unit clause-clause subsumptions : 1
% 0.17/0.67 % Unit Clause-clause subsumption calls : 17
% 0.17/0.67 % Rewrite failures with RHS unbound : 0
% 0.17/0.67 % BW rewrite match attempts : 4
% 0.17/0.67 % BW rewrite match successes : 4
% 0.17/0.67 % Condensation attempts : 0
% 0.17/0.67 % Condensation successes : 0
% 0.17/0.67 % Termbank termtop insertions : 5705
% 0.17/0.67 % Search garbage collected termcells : 1233
% 0.17/0.67
% 0.17/0.67 % -------------------------------------------------
% 0.17/0.67 % User time : 0.008 s
% 0.17/0.67 % System time : 0.002 s
% 0.17/0.67 % Total time : 0.010 s
% 0.17/0.67 % Maximum resident set size: 3676 pages
% 0.17/0.67
% 0.17/0.67 % -------------------------------------------------
% 0.17/0.67 % User time : 0.009 s
% 0.17/0.67 % System time : 0.007 s
% 0.17/0.67 % Total time : 0.017 s
% 0.17/0.67 % Maximum resident set size: 4608 pages
% 0.17/0.67 % E exiting
%------------------------------------------------------------------------------