%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM427+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 : n011.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 01:49:02 PM UTC 2026
% Result : Theorem 0.15s 0.52s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 14 unt; 0 def)
% Number of atoms : 117 ( 24 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 135 ( 52 ~; 45 |; 28 &)
% ( 4 <=>; 6 =>; 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 23 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(m__704,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__704) ).
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(m__,conjecture,
sdteqdtlpzmzozddtrp0(xb,xa,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(m__767,hypothesis,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__767) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(m__747,hypothesis,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__747) ).
fof(c_0_8,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]) ).
fof(c_0_9,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(fof_simplification,[status(thm)],[m__704]) ).
fof(c_0_10,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_11,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,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_8])])])]) ).
fof(c_0_13,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
fof(c_0_14,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_10])])])])])])]) ).
fof(c_0_15,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])])]) ).
fof(c_0_16,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
cnf(c_0_17,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_12]) ).
cnf(c_0_18,hypothesis,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(split_conjunct,[status(thm)],[m__767]) ).
cnf(c_0_19,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( ~ aInteger0(X3)
| sdtasdt0(X1,X2) != X3
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| aDivisorOf0(X1,X3)
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_23,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(fof_nnf,[status(thm)],[c_0_16]) ).
cnf(c_0_24,hypothesis,
( ~ aInteger0(X1)
| ~ aDivisorOf0(X1,sdtasdt0(xq,smndt0(xn)))
| sdteqdtlpzmzozddtrp0(xb,xa,X1)
| X1 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_25,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| X1 = sz00 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_21]),c_0_22]) ).
cnf(c_0_26,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_27,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_28,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_29,plain,
! [X5] :
( aInteger0(smndt0(X5))
| ~ aInteger0(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).
cnf(c_0_30,hypothesis,
~ aInteger0(smndt0(xn)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27]),c_0_28]) ).
cnf(c_0_31,plain,
( ~ aInteger0(X1)
| aInteger0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,hypothesis,
aInteger0(xn),
inference(split_conjunct,[status(thm)],[m__747]) ).
cnf(c_0_33,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM427+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:28:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 0.15/0.52 % Version: 3.5.1
% 0.15/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.52 % Starting sh5l with 300s (1) cores
% 0.15/0.52 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 770821 completed with status 0
% 0.15/0.52 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.52 % No SInE strategy applied
% 0.15/0.52 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.15/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.52 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.15/0.52 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.15/0.52 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.15/0.52 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with pid 770827 completed with status 0
% 0.15/0.52 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m
% 0.15/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.52 % No SInE strategy applied
% 0.15/0.52 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.15/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.52 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.15/0.52 % Preprocessing time : 0.002 s
% 0.15/0.52 % Presaturation interreduction done
% 0.15/0.52
% 0.15/0.52 % Proof found!
% 0.15/0.52 % SZS status Theorem
% 0.15/0.52 % SZS output start CNFRefutation
% See solution above
% 0.15/0.52 % Parsed axioms : 25
% 0.15/0.52 % Removed by relevancy pruning/SinE : 0
% 0.15/0.52 % Initial clauses : 40
% 0.15/0.52 % Removed in clause preprocessing : 1
% 0.15/0.52 % Initial clauses in saturation : 39
% 0.15/0.52 % Processed clauses : 228
% 0.15/0.52 % ...of these trivial : 9
% 0.15/0.52 % ...subsumed : 61
% 0.15/0.52 % ...remaining for further processing : 158
% 0.15/0.52 % Other redundant clauses eliminated : 2
% 0.15/0.52 % Clauses deleted for lack of memory : 0
% 0.15/0.52 % Backward-subsumed : 4
% 0.15/0.52 % Backward-rewritten : 12
% 0.15/0.52 % Generated clauses : 619
% 0.15/0.52 % ...of the previous two non-redundant : 432
% 0.15/0.52 % ...aggressively subsumed : 0
% 0.15/0.52 % Contextual simplify-reflections : 3
% 0.15/0.52 % Paramodulations : 617
% 0.15/0.52 % Factorizations : 0
% 0.15/0.52 % NegExts : 0
% 0.15/0.52 % Equation resolutions : 2
% 0.15/0.52 % Disequality decompositions : 0
% 0.15/0.52 % Total rewrite steps : 925
% 0.15/0.52 % ...of those cached : 891
% 0.15/0.52 % Propositional unsat checks : 0
% 0.15/0.52 % Propositional check models : 0
% 0.15/0.52 % Propositional check unsatisfiable : 0
% 0.15/0.52 % Propositional clauses : 0
% 0.15/0.52 % Propositional clauses after purity: 0
% 0.15/0.52 % Propositional unsat core size : 0
% 0.15/0.52 % Propositional preprocessing time : 0.000
% 0.15/0.52 % Propositional encoding time : 0.000
% 0.15/0.52 % Propositional solver time : 0.000
% 0.15/0.52 % Success case prop preproc time : 0.000
% 0.15/0.52 % Success case prop encoding time : 0.000
% 0.15/0.52 % Success case prop solver time : 0.000
% 0.15/0.52 % Current number of processed clauses : 101
% 0.15/0.52 % Positive orientable unit clauses : 36
% 0.15/0.52 % Positive unorientable unit clauses: 0
% 0.15/0.52 % Negative unit clauses : 3
% 0.15/0.52 % Non-unit-clauses : 62
% 0.15/0.52 % Current number of unprocessed clauses: 259
% 0.15/0.52 % ...number of literals in the above : 864
% 0.15/0.52 % Current number of archived formulas : 0
% 0.15/0.52 % Current number of archived clauses : 55
% 0.15/0.52 % Clause-clause subsumption calls (NU) : 555
% 0.15/0.52 % Rec. Clause-clause subsumption calls : 404
% 0.15/0.52 % Non-unit clause-clause subsumptions : 68
% 0.15/0.52 % Unit Clause-clause subsumption calls : 60
% 0.15/0.52 % Rewrite failures with RHS unbound : 0
% 0.15/0.52 % BW rewrite match attempts : 12
% 0.15/0.52 % BW rewrite match successes : 9
% 0.15/0.52 % Condensation attempts : 0
% 0.15/0.52 % Condensation successes : 0
% 0.15/0.52 % Termbank termtop insertions : 12442
% 0.15/0.52 % Search garbage collected termcells : 430
% 0.15/0.52
% 0.15/0.52 % -------------------------------------------------
% 0.15/0.52 % User time : 0.031 s
% 0.15/0.52 % System time : 0.008 s
% 0.15/0.52 % Total time : 0.040 s
% 0.15/0.52 % Maximum resident set size: 3656 pages
% 0.15/0.52
% 0.15/0.52 % -------------------------------------------------
% 0.15/0.52 % User time : 0.123 s
% 0.15/0.52 % System time : 0.023 s
% 0.15/0.52 % Total time : 0.146 s
% 0.15/0.52 % Maximum resident set size: 4608 pages
% 0.15/0.52 % E exiting
%------------------------------------------------------------------------------