%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM521+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 : n012.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 01:49:24 PM UTC 2026
% Result : Theorem 0.07s 0.34s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 11 unt; 0 def)
% Number of atoms : 128 ( 47 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 151 ( 59 ~; 53 |; 36 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 14 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(m__,conjecture,
( doDivides0(xp,xm)
| ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
| doDivides0(xp,xn)
| ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__2287,hypothesis,
~ ( ( sdtlseqdt0(xm,xp)
| ? [X1] :
( sdtpldt0(xm,X1) = xp
& aNaturalNumber0(X1) ) )
& xm != xp
& ( sdtlseqdt0(xn,xp)
| ? [X1] :
( sdtpldt0(xn,X1) = xp
& aNaturalNumber0(X1) ) )
& xn != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(m__1870,hypothesis,
~ ( sdtlseqdt0(xp,xn)
| ? [X1] :
( sdtpldt0(xp,X1) = xn
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
fof(m__2075,hypothesis,
~ ( sdtlseqdt0(xp,xm)
| ? [X1] :
( sdtpldt0(xp,X1) = xm
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2075) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(c_0_8,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
fof(c_0_9,plain,
! [X97,X98] :
( ( ~ aNaturalNumber0(X98)
| ~ aNaturalNumber0(X97)
| sdtlseqdt0(X97,X98)
| sdtlseqdt0(X98,X97) )
& ( ~ aNaturalNumber0(X98)
| ~ aNaturalNumber0(X97)
| sdtlseqdt0(X97,X98)
| X98 != X97 ) ),
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_10,negated_conjecture,
~ ( doDivides0(xp,xm)
| ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
| doDivides0(xp,xn)
| ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_11,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_12,hypothesis,
~ ( ( sdtlseqdt0(xm,xp)
| ? [X1] :
( sdtpldt0(xm,X1) = xp
& aNaturalNumber0(X1) ) )
& xm != xp
& ( sdtlseqdt0(xn,xp)
| ? [X1] :
( sdtpldt0(xn,X1) = xp
& aNaturalNumber0(X1) ) )
& xn != xp ),
inference(fof_simplification,[status(thm)],[m__2287]) ).
cnf(c_0_13,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_15,hypothesis,
! [X17] :
( ~ sdtlseqdt0(xp,xn)
& ( sdtpldt0(xp,X17) != xn
| ~ aNaturalNumber0(X17) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1870])])])]) ).
fof(c_0_16,hypothesis,
! [X18] :
( ~ sdtlseqdt0(xp,xm)
& ( sdtpldt0(xp,X18) != xm
| ~ aNaturalNumber0(X18) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2075])])])]) ).
fof(c_0_17,negated_conjecture,
! [X21,X22] :
( ~ doDivides0(xp,xm)
& ( xm != sdtasdt0(xp,X22)
| ~ aNaturalNumber0(X22) )
& ~ doDivides0(xp,xn)
& ( xn != sdtasdt0(xp,X21)
| ~ aNaturalNumber0(X21) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_18,plain,
! [X89] :
( ( ~ aNaturalNumber0(X89)
| X89 = sdtasdt0(sz10,X89) )
& ( ~ aNaturalNumber0(X89)
| sdtasdt0(X89,sz10) = X89 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_19,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
fof(c_0_20,hypothesis,
! [X19,X20] :
( ( xm = xp
| xn = xp
| ~ sdtlseqdt0(xn,xp)
| ~ sdtlseqdt0(xm,xp) )
& ( xm = xp
| xn = xp
| ~ sdtlseqdt0(xn,xp)
| sdtpldt0(xm,X20) != xp
| ~ aNaturalNumber0(X20) )
& ( xm = xp
| xn = xp
| sdtpldt0(xn,X19) != xp
| ~ aNaturalNumber0(X19)
| ~ sdtlseqdt0(xm,xp) )
& ( xm = xp
| xn = xp
| sdtpldt0(xn,X19) != xp
| ~ aNaturalNumber0(X19)
| sdtpldt0(xm,X20) != xp
| ~ aNaturalNumber0(X20) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])]) ).
cnf(c_0_21,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,xp)
| sdtlseqdt0(xp,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_22,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_23,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_25,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( xn != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,negated_conjecture,
( xm != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,hypothesis,
( ~ sdtlseqdt0(xn,xp)
| ~ sdtlseqdt0(xm,xp)
| xm = xp
| xn = xp ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,hypothesis,
sdtlseqdt0(xn,xp),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_32,hypothesis,
sdtlseqdt0(xm,xp),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_24]),c_0_25]) ).
cnf(c_0_33,negated_conjecture,
xn != xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_14])]) ).
cnf(c_0_34,negated_conjecture,
xm != xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_28]),c_0_14])]) ).
cnf(c_0_35,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),c_0_33]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM521+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 02:37:06 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.32 Running first-order theorem proving
% 0.07/0.32 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
% 0.07/0.34 % Version: 3.5.1
% 0.07/0.34 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.07/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.34 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.07/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.34 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.34 % Starting sh5l with 300s (1) cores
% 0.07/0.34 % new_bool_3 with pid 1388465 completed with status 0
% 0.07/0.34 % Result found by new_bool_3
% 0.07/0.34 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.07/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.34 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.07/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.34 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.34 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.07/0.34 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.34 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.34 % SubtermCWHack with pid 1388468 completed with status 0
% 0.07/0.34 % Result found by SubtermCWHack
% 0.07/0.34 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.07/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.34 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.07/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.34 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.34 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.07/0.34 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.34 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.34 % Preprocessing time : 0.002 s
% 0.07/0.34
% 0.07/0.34 % Proof found!
% 0.07/0.34 % SZS status Theorem
% 0.07/0.34 % SZS output start CNFRefutation
% See solution above
% 0.07/0.34 % Parsed axioms : 45
% 0.07/0.34 % Removed by relevancy pruning/SinE : 3
% 0.07/0.34 % Initial clauses : 212
% 0.07/0.34 % Removed in clause preprocessing : 3
% 0.07/0.34 % Initial clauses in saturation : 209
% 0.07/0.34 % Processed clauses : 121
% 0.07/0.34 % ...of these trivial : 0
% 0.07/0.34 % ...subsumed : 32
% 0.07/0.34 % ...remaining for further processing : 88
% 0.07/0.34 % Other redundant clauses eliminated : 3
% 0.07/0.34 % Clauses deleted for lack of memory : 0
% 0.07/0.34 % Backward-subsumed : 0
% 0.07/0.34 % Backward-rewritten : 1
% 0.07/0.34 % Generated clauses : 129
% 0.07/0.34 % ...of the previous two non-redundant : 121
% 0.07/0.34 % ...aggressively subsumed : 0
% 0.07/0.34 % Contextual simplify-reflections : 0
% 0.07/0.34 % Paramodulations : 126
% 0.07/0.34 % Factorizations : 0
% 0.07/0.34 % NegExts : 0
% 0.07/0.34 % Equation resolutions : 3
% 0.07/0.34 % Disequality decompositions : 0
% 0.07/0.34 % Total rewrite steps : 66
% 0.07/0.34 % ...of those cached : 57
% 0.07/0.34 % Propositional unsat checks : 0
% 0.07/0.34 % Propositional check models : 0
% 0.07/0.34 % Propositional check unsatisfiable : 0
% 0.07/0.34 % Propositional clauses : 0
% 0.07/0.34 % Propositional clauses after purity: 0
% 0.07/0.34 % Propositional unsat core size : 0
% 0.07/0.34 % Propositional preprocessing time : 0.000
% 0.07/0.34 % Propositional encoding time : 0.000
% 0.07/0.34 % Propositional solver time : 0.000
% 0.07/0.34 % Success case prop preproc time : 0.000
% 0.07/0.34 % Success case prop encoding time : 0.000
% 0.07/0.34 % Success case prop solver time : 0.000
% 0.07/0.34 % Current number of processed clauses : 84
% 0.07/0.34 % Positive orientable unit clauses : 18
% 0.07/0.34 % Positive unorientable unit clauses: 0
% 0.07/0.34 % Negative unit clauses : 13
% 0.07/0.34 % Non-unit-clauses : 53
% 0.07/0.34 % Current number of unprocessed clauses: 209
% 0.07/0.34 % ...number of literals in the above : 1661
% 0.07/0.34 % Current number of archived formulas : 0
% 0.07/0.34 % Current number of archived clauses : 1
% 0.07/0.34 % Clause-clause subsumption calls (NU) : 274
% 0.07/0.34 % Rec. Clause-clause subsumption calls : 234
% 0.07/0.34 % Non-unit clause-clause subsumptions : 26
% 0.07/0.34 % Unit Clause-clause subsumption calls : 124
% 0.07/0.34 % Rewrite failures with RHS unbound : 0
% 0.07/0.34 % BW rewrite match attempts : 1
% 0.07/0.34 % BW rewrite match successes : 1
% 0.07/0.34 % Condensation attempts : 0
% 0.07/0.34 % Condensation successes : 0
% 0.07/0.34 % Termbank termtop insertions : 16619
% 0.07/0.34 % Search garbage collected termcells : 2227
% 0.07/0.34
% 0.07/0.34 % -------------------------------------------------
% 0.07/0.34 % User time : 0.010 s
% 0.07/0.34 % System time : 0.002 s
% 0.07/0.34 % Total time : 0.012 s
% 0.07/0.34 % Maximum resident set size: 4208 pages
% 0.07/0.34
% 0.07/0.34 % -------------------------------------------------
% 0.07/0.34 % User time : 0.012 s
% 0.07/0.34 % System time : 0.004 s
% 0.07/0.34 % Total time : 0.016 s
% 0.07/0.34 % Maximum resident set size: 4864 pages
% 0.07/0.34 % E exiting
%------------------------------------------------------------------------------