%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM457+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 : n015.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 01:49:09 PM UTC 2026
% Result : Theorem 0.05s 0.44s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 63 ( 36 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 67 ( 24 ~; 24 |; 8 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(m__,conjecture,
( sdtasdt0(xm,xn) = sz00
=> ( xn = sz00
| xm = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__624,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__624) ).
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(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_5,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[mMulCanc]) ).
fof(c_0_6,negated_conjecture,
~ ( sdtasdt0(xm,xn) = sz00
=> ( xn = sz00
| xm = sz00 ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_7,plain,
! [X7,X8,X9] :
( ( ~ aNaturalNumber0(X7)
| X7 = sz00
| ~ aNaturalNumber0(X9)
| ~ aNaturalNumber0(X8)
| X8 = X9
| sdtasdt0(X8,X7) != sdtasdt0(X9,X7) )
& ( ~ aNaturalNumber0(X7)
| X7 = sz00
| ~ aNaturalNumber0(X9)
| ~ aNaturalNumber0(X8)
| X8 = X9
| sdtasdt0(X7,X8) != sdtasdt0(X7,X9) ) ),
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,
( xn != sz00
& xm != sz00
& sdtasdt0(xm,xn) = sz00 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
cnf(c_0_9,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| X1 = sz00
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
sdtasdt0(xm,xn) = sz00,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__624]) ).
cnf(c_0_12,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__624]) ).
cnf(c_0_13,negated_conjecture,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,plain,
! [X6] :
( ( ~ aNaturalNumber0(X6)
| sz00 = sdtasdt0(sz00,X6) )
& ( ~ aNaturalNumber0(X6)
| sdtasdt0(X6,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_15,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xm,X1) != sz00
| X1 = xn ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12])]),c_0_13]) ).
cnf(c_0_16,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_18,negated_conjecture,
xn != sz00,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_12])]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM457+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n015.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 21 02:34:52 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.42 Running first-order theorem proving
% 0.05/0.42 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
% 0.05/0.44 % Version: 3.5.1
% 0.05/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.05/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.05/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.05/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.05/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.05/0.44 % Starting sh5l with 300s (1) cores
% 0.05/0.44 % new_bool_3 with pid 367741 completed with status 0
% 0.05/0.44 % Result found by new_bool_3
% 0.05/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.05/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.05/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.05/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.05/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.05/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.05/0.44 % Search class: FGUSF-FFMS22-SFFFFFNN
% 0.05/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.05/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.05/0.44 % SubtermCWHack with pid 367746 completed with status 0
% 0.05/0.44 % Result found by SubtermCWHack
% 0.05/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.05/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.05/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.05/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.05/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.05/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.05/0.44 % Search class: FGUSF-FFMS22-SFFFFFNN
% 0.05/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.05/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.05/0.44 % Preprocessing time : 0.001 s
% 0.05/0.44
% 0.05/0.44 % Proof found!
% 0.05/0.44 % SZS status Theorem
% 0.05/0.44 % SZS output start CNFRefutation
% See solution above
% 0.05/0.44 % Parsed axioms : 18
% 0.05/0.44 % Removed by relevancy pruning/SinE : 2
% 0.05/0.44 % Initial clauses : 25
% 0.05/0.44 % Removed in clause preprocessing : 1
% 0.05/0.44 % Initial clauses in saturation : 24
% 0.05/0.44 % Processed clauses : 45
% 0.05/0.44 % ...of these trivial : 0
% 0.05/0.44 % ...subsumed : 23
% 0.05/0.44 % ...remaining for further processing : 22
% 0.05/0.44 % Other redundant clauses eliminated : 4
% 0.05/0.44 % Clauses deleted for lack of memory : 0
% 0.05/0.44 % Backward-subsumed : 0
% 0.05/0.44 % Backward-rewritten : 0
% 0.05/0.44 % Generated clauses : 63
% 0.05/0.44 % ...of the previous two non-redundant : 44
% 0.05/0.44 % ...aggressively subsumed : 0
% 0.05/0.44 % Contextual simplify-reflections : 0
% 0.05/0.44 % Paramodulations : 56
% 0.05/0.44 % Factorizations : 0
% 0.05/0.44 % NegExts : 0
% 0.05/0.44 % Equation resolutions : 7
% 0.05/0.44 % Disequality decompositions : 0
% 0.05/0.44 % Total rewrite steps : 37
% 0.05/0.44 % ...of those cached : 34
% 0.05/0.44 % Propositional unsat checks : 0
% 0.05/0.44 % Propositional check models : 0
% 0.05/0.44 % Propositional check unsatisfiable : 0
% 0.05/0.44 % Propositional clauses : 0
% 0.05/0.44 % Propositional clauses after purity: 0
% 0.05/0.44 % Propositional unsat core size : 0
% 0.05/0.44 % Propositional preprocessing time : 0.000
% 0.05/0.44 % Propositional encoding time : 0.000
% 0.05/0.44 % Propositional solver time : 0.000
% 0.05/0.44 % Success case prop preproc time : 0.000
% 0.05/0.44 % Success case prop encoding time : 0.000
% 0.05/0.44 % Success case prop solver time : 0.000
% 0.05/0.44 % Current number of processed clauses : 22
% 0.05/0.44 % Positive orientable unit clauses : 4
% 0.05/0.44 % Positive unorientable unit clauses: 0
% 0.05/0.44 % Negative unit clauses : 2
% 0.05/0.44 % Non-unit-clauses : 16
% 0.05/0.44 % Current number of unprocessed clauses: 23
% 0.05/0.44 % ...number of literals in the above : 110
% 0.05/0.44 % Current number of archived formulas : 0
% 0.05/0.44 % Current number of archived clauses : 0
% 0.05/0.44 % Clause-clause subsumption calls (NU) : 58
% 0.05/0.44 % Rec. Clause-clause subsumption calls : 45
% 0.05/0.44 % Non-unit clause-clause subsumptions : 23
% 0.05/0.44 % Unit Clause-clause subsumption calls : 0
% 0.05/0.44 % Rewrite failures with RHS unbound : 0
% 0.05/0.44 % BW rewrite match attempts : 0
% 0.05/0.44 % BW rewrite match successes : 0
% 0.05/0.44 % Condensation attempts : 0
% 0.05/0.44 % Condensation successes : 0
% 0.05/0.44 % Termbank termtop insertions : 2525
% 0.05/0.44 % Search garbage collected termcells : 324
% 0.05/0.44
% 0.05/0.44 % -------------------------------------------------
% 0.05/0.44 % User time : 0.008 s
% 0.05/0.44 % System time : 0.001 s
% 0.05/0.44 % Total time : 0.009 s
% 0.05/0.44 % Maximum resident set size: 3648 pages
% 0.05/0.44
% 0.05/0.44 % -------------------------------------------------
% 0.05/0.44 % User time : 0.010 s
% 0.05/0.44 % System time : 0.003 s
% 0.05/0.44 % Total time : 0.012 s
% 0.05/0.44 % Maximum resident set size: 4608 pages
% 0.05/0.44 % E exiting
%------------------------------------------------------------------------------