%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM504+3 : 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 : n019.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 01:49:21 PM UTC 2026
% Result : ContradictoryAxioms 0.23s 0.63s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 16 unt; 0 def)
% Number of atoms : 128 ( 48 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 129 ( 35 ~; 27 |; 61 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 16 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2414,hypothesis,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& ? [X1] :
( sdtpldt0(sdtasdt0(xp,xm),X1) = sdtasdt0(xp,xk)
& aNaturalNumber0(X1) )
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& ? [X1] :
( sdtpldt0(sdtasdt0(xn,xm),X1) = sdtasdt0(xp,xm)
& aNaturalNumber0(X1) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2414) ).
fof(m__2362,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X1] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
& ? [X1] :
( sdtpldt0(xr,X1) = xk
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
fof(m__2342,hypothesis,
( isPrime0(xr)
& ! [X1] :
( ( ( doDivides0(X1,xr)
| ? [X2] :
( xr = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xr
| X1 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X1] :
( xk = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__2306,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(c_0_7,hypothesis,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& ? [X1] :
( sdtpldt0(sdtasdt0(xp,xm),X1) = sdtasdt0(xp,xk)
& aNaturalNumber0(X1) )
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& ? [X1] :
( sdtpldt0(sdtasdt0(xn,xm),X1) = sdtasdt0(xp,xm)
& aNaturalNumber0(X1) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
inference(fof_simplification,[status(thm)],[m__2414]) ).
fof(c_0_8,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0)
& aNaturalNumber0(esk14_0)
& sdtpldt0(xr,esk13_0) = xk
& aNaturalNumber0(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2362])]) ).
fof(c_0_9,hypothesis,
( isPrime0(xr)
& ! [X1] :
( ( ( doDivides0(X1,xr)
| ? [X2] :
( xr = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xr
| X1 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X1] :
( xk = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
& aNaturalNumber0(xr) ),
inference(fof_simplification,[status(thm)],[m__2342]) ).
fof(c_0_10,hypothesis,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& sdtpldt0(sdtasdt0(xp,xm),esk17_0) = sdtasdt0(xp,xk)
& aNaturalNumber0(esk17_0)
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtpldt0(sdtasdt0(xn,xm),esk16_0) = sdtasdt0(xp,xm)
& aNaturalNumber0(esk16_0)
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_7])])]) ).
fof(c_0_11,plain,
! [X9,X10] :
( aNaturalNumber0(sdtasdt0(X9,X10))
| ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_12,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
fof(c_0_14,hypothesis,
! [X107,X108] :
( isPrime0(xr)
& ( X107 = xr
| X107 = sz10
| ~ aNaturalNumber0(X107)
| ~ doDivides0(X107,xr) )
& ( X107 = xr
| X107 = sz10
| ~ aNaturalNumber0(X107)
| xr != sdtasdt0(X107,X108)
| ~ aNaturalNumber0(X108) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,esk12_0)
& aNaturalNumber0(esk12_0)
& aNaturalNumber0(xr) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])])]) ).
fof(c_0_15,plain,
! [X7,X8] :
( aNaturalNumber0(sdtpldt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
cnf(c_0_16,hypothesis,
sdtpldt0(sdtasdt0(xn,xm),esk16_0) = sdtasdt0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,hypothesis,
sdtasdt0(xr,esk14_0) = sdtasdt0(xp,xk),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,hypothesis,
aNaturalNumber0(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,plain,
! [X45,X46] :
( X45 = X46
| ~ sdtlseqdt0(X46,X45)
| ~ sdtlseqdt0(X45,X46)
| ~ aNaturalNumber0(X46)
| ~ aNaturalNumber0(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).
cnf(c_0_22,hypothesis,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,hypothesis,
sdtpldt0(sdtasdt0(xp,xk),esk16_0) = sdtasdt0(xp,xm),
inference(rw,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(sdtasdt0(xp,xk)),
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_27,hypothesis,
sdtasdt0(xn,xm) != sdtasdt0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,hypothesis,
sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)),
inference(rw,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_30,hypothesis,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_32,hypothesis,
sdtasdt0(xp,xk) != sdtasdt0(xp,xm),
inference(rw,[status(thm)],[c_0_27,c_0_13]) ).
cnf(c_0_33,hypothesis,
$false,
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_28,c_0_29]),c_0_30]),c_0_26]),c_0_31])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM504+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n019.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 02:36:05 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 0.23/0.63 % Version: 3.5.1
% 0.23/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/0.63 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.63 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.63 % Starting sh5l with 300s (1) cores
% 0.23/0.63 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1504444 completed with status 0
% 0.23/0.63 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.23/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.63 % No SInE strategy applied
% 0.23/0.63 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.23/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.63 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.23/0.63 % Starting G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.23/0.63 % Starting new_bool_3 with 136s (1) cores
% 0.23/0.63 % Starting U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1 with 136s (1) cores
% 0.23/0.63 % SubtermCWHack with pid 1504452 completed with status 0
% 0.23/0.63 % Result found by SubtermCWHack
% 0.23/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.63 % No SInE strategy applied
% 0.23/0.63 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.23/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.63 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.63 % Preprocessing time : 0.004 s
% 0.23/0.63
% 0.23/0.63 % Proof found!
% 0.23/0.63 % SZS status ContradictoryAxioms
% 0.23/0.63 % SZS output start CNFRefutation
% See solution above
% 0.23/0.63 % Parsed axioms : 52
% 0.23/0.63 % Removed by relevancy pruning/SinE : 0
% 0.23/0.63 % Initial clauses : 252
% 0.23/0.63 % Removed in clause preprocessing : 4
% 0.23/0.63 % Initial clauses in saturation : 248
% 0.23/0.63 % Processed clauses : 308
% 0.23/0.63 % ...of these trivial : 3
% 0.23/0.63 % ...subsumed : 76
% 0.23/0.63 % ...remaining for further processing : 229
% 0.23/0.63 % Other redundant clauses eliminated : 5
% 0.23/0.63 % Clauses deleted for lack of memory : 0
% 0.23/0.63 % Backward-subsumed : 0
% 0.23/0.63 % Backward-rewritten : 2
% 0.23/0.63 % Generated clauses : 604
% 0.23/0.63 % ...of the previous two non-redundant : 473
% 0.23/0.63 % ...aggressively subsumed : 0
% 0.23/0.63 % Contextual simplify-reflections : 0
% 0.23/0.63 % Paramodulations : 599
% 0.23/0.63 % Factorizations : 0
% 0.23/0.63 % NegExts : 0
% 0.23/0.63 % Equation resolutions : 5
% 0.23/0.63 % Disequality decompositions : 0
% 0.23/0.63 % Total rewrite steps : 605
% 0.23/0.63 % ...of those cached : 580
% 0.23/0.63 % Propositional unsat checks : 0
% 0.23/0.63 % Propositional check models : 0
% 0.23/0.63 % Propositional check unsatisfiable : 0
% 0.23/0.63 % Propositional clauses : 0
% 0.23/0.63 % Propositional clauses after purity: 0
% 0.23/0.63 % Propositional unsat core size : 0
% 0.23/0.63 % Propositional preprocessing time : 0.000
% 0.23/0.63 % Propositional encoding time : 0.000
% 0.23/0.63 % Propositional solver time : 0.000
% 0.23/0.63 % Success case prop preproc time : 0.000
% 0.23/0.63 % Success case prop encoding time : 0.000
% 0.23/0.63 % Success case prop solver time : 0.000
% 0.23/0.63 % Current number of processed clauses : 222
% 0.23/0.63 % Positive orientable unit clauses : 54
% 0.23/0.63 % Positive unorientable unit clauses: 0
% 0.23/0.63 % Negative unit clauses : 16
% 0.23/0.63 % Non-unit-clauses : 152
% 0.23/0.63 % Current number of unprocessed clauses: 409
% 0.23/0.63 % ...number of literals in the above : 2268
% 0.23/0.63 % Current number of archived formulas : 0
% 0.23/0.63 % Current number of archived clauses : 2
% 0.23/0.63 % Clause-clause subsumption calls (NU) : 6009
% 0.23/0.63 % Rec. Clause-clause subsumption calls : 5697
% 0.23/0.63 % Non-unit clause-clause subsumptions : 58
% 0.23/0.63 % Unit Clause-clause subsumption calls : 607
% 0.23/0.63 % Rewrite failures with RHS unbound : 0
% 0.23/0.63 % BW rewrite match attempts : 1
% 0.23/0.63 % BW rewrite match successes : 1
% 0.23/0.63 % Condensation attempts : 0
% 0.23/0.63 % Condensation successes : 0
% 0.23/0.63 % Termbank termtop insertions : 24389
% 0.23/0.63 % Search garbage collected termcells : 2436
% 0.23/0.63
% 0.23/0.63 % -------------------------------------------------
% 0.23/0.63 % User time : 0.033 s
% 0.23/0.63 % System time : 0.009 s
% 0.23/0.63 % Total time : 0.042 s
% 0.23/0.63 % Maximum resident set size: 3960 pages
% 0.23/0.63
% 0.23/0.63 % -------------------------------------------------
% 0.23/0.63 % User time : 0.127 s
% 0.23/0.63 % System time : 0.028 s
% 0.23/0.63 % Total time : 0.155 s
% 0.23/0.63 % Maximum resident set size: 4608 pages
% 0.23/0.63 % E exiting
%------------------------------------------------------------------------------