%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM423+3 : 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 : n007.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 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 5 unt; 0 def)
% Number of atoms : 48 ( 18 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 47 ( 18 ~; 13 |; 14 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 5 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( sdteqdtlpzmzozddtrp0(xa,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xa))
& aInteger0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__671,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__671) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtpldt0(smndt0(X1),X1)
& sdtpldt0(X1,smndt0(X1)) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(c_0_5,negated_conjecture,
~ ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xa))
& aInteger0(X1) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
inference(fof_simplification,[status(thm)],[m__671]) ).
fof(c_0_7,negated_conjecture,
! [X4] :
( ~ sdteqdtlpzmzozddtrp0(xa,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
& ( sdtasdt0(xq,X4) != sdtpldt0(xa,smndt0(xa))
| ~ aInteger0(X4) ) ),
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,plain,
! [X29] :
( ( ~ aInteger0(X29)
| sz00 = sdtpldt0(smndt0(X29),X29) )
& ( ~ aInteger0(X29)
| sdtpldt0(X29,smndt0(X29)) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])])]) ).
fof(c_0_9,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( sdtasdt0(xq,X1) != sdtpldt0(xa,smndt0(xa))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X6] :
( ( ~ aInteger0(X6)
| sz00 = sdtasdt0(sz00,X6) )
& ( ~ aInteger0(X6)
| sdtasdt0(X6,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])])]) ).
cnf(c_0_14,negated_conjecture,
( ~ aInteger0(X1)
| sdtasdt0(xq,X1) != sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_15,plain,
( ~ aInteger0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_17,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM423+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 02:26:05 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 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
% 0.16/0.44 % Version: 3.5.1
% 0.16/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.44 % Starting sh5l with 300s (1) cores
% 0.16/0.44 % new_bool_3 with pid 4166292 completed with status 0
% 0.16/0.44 % Result found by new_bool_3
% 0.16/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.44 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.16/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.44 % SubtermCWHack with pid 4166300 completed with status 0
% 0.16/0.44 % Result found by SubtermCWHack
% 0.16/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.44 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.16/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.44 % Preprocessing time : 0.001 s
% 0.16/0.44
% 0.16/0.44 % Proof found!
% 0.16/0.44 % SZS status Theorem
% 0.16/0.44 % SZS output start CNFRefutation
% See solution above
% 0.16/0.44 % Parsed axioms : 21
% 0.16/0.44 % Removed by relevancy pruning/SinE : 3
% 0.16/0.44 % Initial clauses : 31
% 0.16/0.44 % Removed in clause preprocessing : 1
% 0.16/0.44 % Initial clauses in saturation : 30
% 0.16/0.44 % Processed clauses : 26
% 0.16/0.44 % ...of these trivial : 0
% 0.16/0.44 % ...subsumed : 0
% 0.16/0.44 % ...remaining for further processing : 26
% 0.16/0.44 % Other redundant clauses eliminated : 1
% 0.16/0.44 % Clauses deleted for lack of memory : 0
% 0.16/0.44 % Backward-subsumed : 0
% 0.16/0.44 % Backward-rewritten : 1
% 0.16/0.44 % Generated clauses : 17
% 0.16/0.44 % ...of the previous two non-redundant : 6
% 0.16/0.44 % ...aggressively subsumed : 0
% 0.16/0.44 % Contextual simplify-reflections : 0
% 0.16/0.44 % Paramodulations : 16
% 0.16/0.44 % Factorizations : 0
% 0.16/0.44 % NegExts : 0
% 0.16/0.44 % Equation resolutions : 1
% 0.16/0.44 % Disequality decompositions : 0
% 0.16/0.44 % Total rewrite steps : 28
% 0.16/0.44 % ...of those cached : 23
% 0.16/0.44 % Propositional unsat checks : 0
% 0.16/0.44 % Propositional check models : 0
% 0.16/0.44 % Propositional check unsatisfiable : 0
% 0.16/0.44 % Propositional clauses : 0
% 0.16/0.44 % Propositional clauses after purity: 0
% 0.16/0.44 % Propositional unsat core size : 0
% 0.16/0.44 % Propositional preprocessing time : 0.000
% 0.16/0.44 % Propositional encoding time : 0.000
% 0.16/0.44 % Propositional solver time : 0.000
% 0.16/0.44 % Success case prop preproc time : 0.000
% 0.16/0.44 % Success case prop encoding time : 0.000
% 0.16/0.44 % Success case prop solver time : 0.000
% 0.16/0.44 % Current number of processed clauses : 24
% 0.16/0.44 % Positive orientable unit clauses : 5
% 0.16/0.44 % Positive unorientable unit clauses: 0
% 0.16/0.44 % Negative unit clauses : 4
% 0.16/0.44 % Non-unit-clauses : 15
% 0.16/0.44 % Current number of unprocessed clauses: 10
% 0.16/0.44 % ...number of literals in the above : 43
% 0.16/0.44 % Current number of archived formulas : 0
% 0.16/0.44 % Current number of archived clauses : 1
% 0.16/0.44 % Clause-clause subsumption calls (NU) : 14
% 0.16/0.44 % Rec. Clause-clause subsumption calls : 11
% 0.16/0.44 % Non-unit clause-clause subsumptions : 0
% 0.16/0.44 % Unit Clause-clause subsumption calls : 0
% 0.16/0.44 % Rewrite failures with RHS unbound : 0
% 0.16/0.44 % BW rewrite match attempts : 1
% 0.16/0.44 % BW rewrite match successes : 1
% 0.16/0.44 % Condensation attempts : 0
% 0.16/0.44 % Condensation successes : 0
% 0.16/0.44 % Termbank termtop insertions : 2425
% 0.16/0.44 % Search garbage collected termcells : 419
% 0.16/0.44
% 0.16/0.44 % -------------------------------------------------
% 0.16/0.44 % User time : 0.006 s
% 0.16/0.44 % System time : 0.002 s
% 0.16/0.44 % Total time : 0.008 s
% 0.16/0.44 % Maximum resident set size: 3652 pages
% 0.16/0.44
% 0.16/0.44 % -------------------------------------------------
% 0.16/0.44 % User time : 0.008 s
% 0.16/0.44 % System time : 0.006 s
% 0.16/0.44 % Total time : 0.015 s
% 0.16/0.44 % Maximum resident set size: 4608 pages
% 0.16/0.44 % E exiting
%------------------------------------------------------------------------------