%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM423+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 : n020.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 01:49:01 PM UTC 2026
% Result : Theorem 0.09s 0.46s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 13 unt; 0 def)
% Number of atoms : 129 ( 32 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 150 ( 58 ~; 53 |; 28 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 25 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( ? [X3] :
( sdtasdt0(X2,X3) = X1
& aInteger0(X3) )
& X2 != sz00
& aInteger0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(m__671,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__671) ).
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(m__,conjecture,
sdteqdtlpzmzozddtrp0(xa,xa,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtpldt0(smndt0(X1),X1)
& sdtpldt0(X1,smndt0(X1)) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(c_0_8,plain,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( ? [X3] :
( sdtasdt0(X2,X3) = X1
& aInteger0(X3) )
& X2 != sz00
& aInteger0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[mDivisor]) ).
fof(c_0_9,plain,
! [X30,X31,X33,X34] :
( ( ~ aInteger0(X30)
| aDivisorOf0(X33,X30)
| sdtasdt0(X33,X34) != X30
| ~ aInteger0(X34)
| X33 = sz00
| ~ aInteger0(X33) )
& ( ~ aInteger0(X30)
| ~ aDivisorOf0(X31,X30)
| sdtasdt0(X31,esk1_2(X30,X31)) = X30 )
& ( ~ aInteger0(X30)
| ~ aDivisorOf0(X31,X30)
| aInteger0(esk1_2(X30,X31)) )
& ( ~ aInteger0(X30)
| ~ aDivisorOf0(X31,X30)
| X31 != sz00 )
& ( ~ aInteger0(X30)
| ~ aDivisorOf0(X31,X30)
| aInteger0(X31) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])])])]) ).
fof(c_0_10,plain,
! [X8,X9] :
( aInteger0(sdtasdt0(X8,X9))
| ~ aInteger0(X9)
| ~ aInteger0(X8) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])])]) ).
cnf(c_0_11,plain,
( ~ aInteger0(X3)
| sdtasdt0(X1,X2) != X3
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| aDivisorOf0(X1,X3)
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
inference(fof_simplification,[status(thm)],[m__671]) ).
fof(c_0_14,plain,
! [X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
inference(fof_simplification,[status(thm)],[mEquMod]) ).
cnf(c_0_15,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| X1 = sz00 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_11]),c_0_12]) ).
cnf(c_0_16,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
fof(c_0_17,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
inference(fof_nnf,[status(thm)],[c_0_13]) ).
fof(c_0_18,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_19,plain,
! [X35,X36,X37] :
( ( X37 = sz00
| ~ aInteger0(X37)
| ~ aInteger0(X36)
| ~ aInteger0(X35)
| sdteqdtlpzmzozddtrp0(X35,X36,X37)
| ~ aDivisorOf0(X37,sdtpldt0(X35,smndt0(X36))) )
& ( X37 = sz00
| ~ aInteger0(X37)
| ~ aInteger0(X36)
| ~ aInteger0(X35)
| aDivisorOf0(X37,sdtpldt0(X35,smndt0(X36)))
| ~ sdteqdtlpzmzozddtrp0(X35,X36,X37) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
fof(c_0_20,plain,
! [X16] :
( ( ~ aInteger0(X16)
| sz00 = sdtpldt0(smndt0(X16),X16) )
& ( ~ aInteger0(X16)
| sdtpldt0(X16,smndt0(X16)) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])])]) ).
cnf(c_0_21,plain,
( ~ aInteger0(X1)
| aDivisorOf0(X1,sdtasdt0(X1,sz00))
| X1 = sz00 ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_24,plain,
! [X26] :
( ( ~ aInteger0(X26)
| sz00 = sdtasdt0(sz00,X26) )
& ( ~ aInteger0(X26)
| sdtasdt0(X26,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])])]) ).
fof(c_0_25,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X3)))
| X1 = sz00
| sdteqdtlpzmzozddtrp0(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,hypothesis,
aDivisorOf0(xq,sdtasdt0(xq,sz00)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_29,plain,
( ~ aInteger0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(fof_nnf,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aDivisorOf0(X1,sz00)
| sdteqdtlpzmzozddtrp0(X2,X2,X1)
| X1 = sz00 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,hypothesis,
aDivisorOf0(xq,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_22])]) ).
cnf(c_0_33,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,hypothesis,
( ~ aInteger0(X1)
| sdteqdtlpzmzozddtrp0(X1,X1,xq) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_22])]),c_0_23]) ).
cnf(c_0_35,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM423+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 02:29:02 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.43 Running first-order theorem proving
% 0.09/0.43 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
% 0.09/0.46 % Version: 3.5.1
% 0.09/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.46 % Starting sh5l with 300s (1) cores
% 0.09/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1796415 completed with status 0
% 0.09/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.09/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.46 % No SInE strategy applied
% 0.09/0.46 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.09/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.09/0.46 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.09/0.46 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.09/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.09/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1796420 completed with status 0
% 0.09/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.09/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.46 % No SInE strategy applied
% 0.09/0.46 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.09/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.09/0.46 % Preprocessing time : 0.002 s
% 0.09/0.46 % Presaturation interreduction done
% 0.09/0.46
% 0.09/0.46 % Proof found!
% 0.09/0.46 % SZS status Theorem
% 0.09/0.46 % SZS output start CNFRefutation
% See solution above
% 0.09/0.46 % Parsed axioms : 21
% 0.09/0.46 % Removed by relevancy pruning/SinE : 0
% 0.09/0.46 % Initial clauses : 34
% 0.09/0.46 % Removed in clause preprocessing : 1
% 0.09/0.46 % Initial clauses in saturation : 33
% 0.09/0.46 % Processed clauses : 155
% 0.09/0.46 % ...of these trivial : 7
% 0.09/0.46 % ...subsumed : 36
% 0.09/0.46 % ...remaining for further processing : 112
% 0.09/0.46 % Other redundant clauses eliminated : 4
% 0.09/0.46 % Clauses deleted for lack of memory : 0
% 0.09/0.46 % Backward-subsumed : 2
% 0.09/0.46 % Backward-rewritten : 3
% 0.09/0.46 % Generated clauses : 281
% 0.09/0.46 % ...of the previous two non-redundant : 226
% 0.09/0.46 % ...aggressively subsumed : 0
% 0.09/0.46 % Contextual simplify-reflections : 4
% 0.09/0.46 % Paramodulations : 277
% 0.09/0.46 % Factorizations : 0
% 0.09/0.46 % NegExts : 0
% 0.09/0.46 % Equation resolutions : 4
% 0.09/0.46 % Disequality decompositions : 0
% 0.09/0.46 % Total rewrite steps : 233
% 0.09/0.46 % ...of those cached : 219
% 0.09/0.46 % Propositional unsat checks : 0
% 0.09/0.46 % Propositional check models : 0
% 0.09/0.46 % Propositional check unsatisfiable : 0
% 0.09/0.46 % Propositional clauses : 0
% 0.09/0.46 % Propositional clauses after purity: 0
% 0.09/0.46 % Propositional unsat core size : 0
% 0.09/0.46 % Propositional preprocessing time : 0.000
% 0.09/0.46 % Propositional encoding time : 0.000
% 0.09/0.46 % Propositional solver time : 0.000
% 0.09/0.46 % Success case prop preproc time : 0.000
% 0.09/0.46 % Success case prop encoding time : 0.000
% 0.09/0.46 % Success case prop solver time : 0.000
% 0.09/0.46 % Current number of processed clauses : 72
% 0.09/0.46 % Positive orientable unit clauses : 16
% 0.09/0.46 % Positive unorientable unit clauses: 0
% 0.09/0.46 % Negative unit clauses : 2
% 0.09/0.46 % Non-unit-clauses : 54
% 0.09/0.46 % Current number of unprocessed clauses: 137
% 0.09/0.46 % ...number of literals in the above : 556
% 0.09/0.46 % Current number of archived formulas : 0
% 0.09/0.46 % Current number of archived clauses : 38
% 0.09/0.46 % Clause-clause subsumption calls (NU) : 425
% 0.09/0.46 % Rec. Clause-clause subsumption calls : 306
% 0.09/0.46 % Non-unit clause-clause subsumptions : 42
% 0.09/0.46 % Unit Clause-clause subsumption calls : 69
% 0.09/0.46 % Rewrite failures with RHS unbound : 0
% 0.09/0.46 % BW rewrite match attempts : 3
% 0.09/0.46 % BW rewrite match successes : 3
% 0.09/0.46 % Condensation attempts : 0
% 0.09/0.46 % Condensation successes : 0
% 0.09/0.46 % Termbank termtop insertions : 6360
% 0.09/0.46 % Search garbage collected termcells : 406
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.014 s
% 0.09/0.46 % System time : 0.004 s
% 0.09/0.46 % Total time : 0.018 s
% 0.09/0.46 % Maximum resident set size: 3652 pages
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.039 s
% 0.09/0.46 % System time : 0.012 s
% 0.09/0.46 % Total time : 0.051 s
% 0.09/0.46 % Maximum resident set size: 4864 pages
% 0.09/0.46 % E exiting
%------------------------------------------------------------------------------