%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM425+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 : n004.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 0.27s 0.54s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 10 unt; 0 def)
% Number of atoms : 114 ( 23 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 134 ( 53 ~; 42 |; 29 &)
% ( 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xb))
& aInteger0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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(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(m__724,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__724) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(c_0_7,negated_conjecture,
~ ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xb))
& aInteger0(X1) ),
inference(assume_negation,[status(cth)],[m__]) ).
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,
! [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_10,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(fof_simplification,[status(thm)],[m__704]) ).
fof(c_0_11,negated_conjecture,
! [X40] :
( sdtasdt0(xq,X40) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_12,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_13,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_9])])])]) ).
fof(c_0_14,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(fof_nnf,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( sdtasdt0(xq,X1) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ aInteger0(X2)
| ~ aDivisorOf0(X1,X2)
| sdtasdt0(X1,esk1_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( ~ aInteger0(X1)
| ~ aDivisorOf0(X2,X1)
| aInteger0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X3 = sz00
| aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
inference(split_conjunct,[status(thm)],[m__724]) ).
cnf(c_0_20,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,negated_conjecture,
( ~ aInteger0(X1)
| ~ aDivisorOf0(xq,X1)
| X1 != sdtpldt0(xa,smndt0(xb)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_25,hypothesis,
aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
fof(c_0_26,plain,
! [X6,X7] :
( aInteger0(sdtpldt0(X6,X7))
| ~ aInteger0(X7)
| ~ aInteger0(X6) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])])]) ).
cnf(c_0_27,negated_conjecture,
~ aInteger0(sdtpldt0(xa,smndt0(xb))),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
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,negated_conjecture,
~ aInteger0(smndt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_22])]) ).
cnf(c_0_31,plain,
( ~ aInteger0(X1)
| aInteger0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM425+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n004.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 02:28:19 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.50 Running first-order theorem proving
% 0.16/0.50 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
% 0.27/0.54 % Version: 3.5.1
% 0.27/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.54 % Starting sh5l with 300s (1) cores
% 0.27/0.54 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2054616 completed with status 0
% 0.27/0.54 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.27/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.54 % No SInE strategy applied
% 0.27/0.54 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.27/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.27/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.27/0.54 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.27/0.54 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.27/0.54 % G-E--_208_C18_F1_AE_CS_SP_PS_S3S with pid 2054625 completed with status 0
% 0.27/0.54 % Result found by G-E--_208_C18_F1_AE_CS_SP_PS_S3S
% 0.27/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.54 % No SInE strategy applied
% 0.27/0.54 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.27/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.27/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.27/0.54 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.27/0.54 % Preprocessing time : 0.001 s
% 0.27/0.54 % Presaturation interreduction done
% 0.27/0.54
% 0.27/0.54 % Proof found!
% 0.27/0.54 % SZS status Theorem
% 0.27/0.54 % SZS output start CNFRefutation
% See solution above
% 0.27/0.54 % Parsed axioms : 23
% 0.27/0.54 % Removed by relevancy pruning/SinE : 0
% 0.27/0.54 % Initial clauses : 37
% 0.27/0.54 % Removed in clause preprocessing : 1
% 0.27/0.54 % Initial clauses in saturation : 36
% 0.27/0.54 % Processed clauses : 119
% 0.27/0.54 % ...of these trivial : 0
% 0.27/0.54 % ...subsumed : 29
% 0.27/0.54 % ...remaining for further processing : 90
% 0.27/0.54 % Other redundant clauses eliminated : 3
% 0.27/0.54 % Clauses deleted for lack of memory : 0
% 0.27/0.54 % Backward-subsumed : 1
% 0.27/0.54 % Backward-rewritten : 1
% 0.27/0.54 % Generated clauses : 208
% 0.27/0.54 % ...of the previous two non-redundant : 182
% 0.27/0.54 % ...aggressively subsumed : 0
% 0.27/0.54 % Contextual simplify-reflections : 3
% 0.27/0.54 % Paramodulations : 204
% 0.27/0.54 % Factorizations : 0
% 0.27/0.54 % NegExts : 0
% 0.27/0.54 % Equation resolutions : 4
% 0.27/0.54 % Disequality decompositions : 0
% 0.27/0.54 % Total rewrite steps : 118
% 0.27/0.54 % ...of those cached : 110
% 0.27/0.54 % Propositional unsat checks : 0
% 0.27/0.54 % Propositional check models : 0
% 0.27/0.54 % Propositional check unsatisfiable : 0
% 0.27/0.54 % Propositional clauses : 0
% 0.27/0.54 % Propositional clauses after purity: 0
% 0.27/0.54 % Propositional unsat core size : 0
% 0.27/0.54 % Propositional preprocessing time : 0.000
% 0.27/0.54 % Propositional encoding time : 0.000
% 0.27/0.54 % Propositional solver time : 0.000
% 0.27/0.54 % Success case prop preproc time : 0.000
% 0.27/0.54 % Success case prop encoding time : 0.000
% 0.27/0.54 % Success case prop solver time : 0.000
% 0.27/0.54 % Current number of processed clauses : 52
% 0.27/0.54 % Positive orientable unit clauses : 9
% 0.27/0.54 % Positive unorientable unit clauses: 0
% 0.27/0.54 % Negative unit clauses : 3
% 0.27/0.54 % Non-unit-clauses : 40
% 0.27/0.54 % Current number of unprocessed clauses: 135
% 0.27/0.54 % ...number of literals in the above : 596
% 0.27/0.54 % Current number of archived formulas : 0
% 0.27/0.54 % Current number of archived clauses : 38
% 0.27/0.54 % Clause-clause subsumption calls (NU) : 467
% 0.27/0.54 % Rec. Clause-clause subsumption calls : 222
% 0.27/0.54 % Non-unit clause-clause subsumptions : 33
% 0.27/0.54 % Unit Clause-clause subsumption calls : 82
% 0.27/0.54 % Rewrite failures with RHS unbound : 0
% 0.27/0.54 % BW rewrite match attempts : 1
% 0.27/0.54 % BW rewrite match successes : 1
% 0.27/0.54 % Condensation attempts : 0
% 0.27/0.54 % Condensation successes : 0
% 0.27/0.54 % Termbank termtop insertions : 5847
% 0.27/0.54 % Search garbage collected termcells : 440
% 0.27/0.54
% 0.27/0.54 % -------------------------------------------------
% 0.27/0.54 % User time : 0.014 s
% 0.27/0.54 % System time : 0.004 s
% 0.27/0.54 % Total time : 0.018 s
% 0.27/0.54 % Maximum resident set size: 3652 pages
% 0.27/0.54
% 0.27/0.54 % -------------------------------------------------
% 0.27/0.54 % User time : 0.048 s
% 0.27/0.54 % System time : 0.021 s
% 0.27/0.54 % Total time : 0.069 s
% 0.27/0.54 % Maximum resident set size: 4608 pages
% 0.27/0.54 % E exiting
%------------------------------------------------------------------------------