%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM489+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 : n009.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 01:49:17 PM UTC 2026
% Result : Theorem 0.24s 0.57s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 12 unt; 0 def)
% Number of atoms : 46 ( 17 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 53 ( 24 ~; 20 |; 6 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
xn = sdtpldt0(xp,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__1870,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(c_0_5,negated_conjecture,
xn != sdtpldt0(xp,xr),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,plain,
! [X39,X40,X41] :
( ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 = sdtmndt0(X40,X39)
| sdtpldt0(X39,X41) != X40
| ~ aNaturalNumber0(X41) )
& ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 != sdtmndt0(X40,X39)
| sdtpldt0(X39,X41) = X40 )
& ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 != sdtmndt0(X40,X39)
| aNaturalNumber0(X41) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])])]) ).
fof(c_0_7,negated_conjecture,
xn != sdtpldt0(xp,xr),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X3)
| X2 != sdtmndt0(X3,X1)
| sdtpldt0(X1,X2) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,negated_conjecture,
xn != sdtpldt0(xp,xr),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,sdtmndt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_11,hypothesis,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[m__1870]) ).
cnf(c_0_12,hypothesis,
xr = sdtmndt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_13,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_15,negated_conjecture,
xn != sdtpldt0(xp,xr),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,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_10,c_0_11]),c_0_12]),c_0_13]),c_0_14])]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM489+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n009.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 02:34:42 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 0.24/0.57 % Version: 3.5.1
% 0.24/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.57 % Starting sh5l with 300s (1) cores
% 0.24/0.57 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 657444 completed with status 0
% 0.24/0.57 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.24/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.57 % No SInE strategy applied
% 0.24/0.57 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.24/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.24/0.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.24/0.57 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.24/0.57 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.24/0.57 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 657450 completed with status 0
% 0.24/0.57 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.24/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.57 % No SInE strategy applied
% 0.24/0.57 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.24/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.24/0.57 % Preprocessing time : 0.003 s
% 0.24/0.57 % Presaturation interreduction done
% 0.24/0.57
% 0.24/0.57 % Proof found!
% 0.24/0.57 % SZS status Theorem
% 0.24/0.57 % SZS output start CNFRefutation
% See solution above
% 0.24/0.57 % Parsed axioms : 45
% 0.24/0.57 % Removed by relevancy pruning/SinE : 0
% 0.24/0.57 % Initial clauses : 81
% 0.24/0.57 % Removed in clause preprocessing : 3
% 0.24/0.57 % Initial clauses in saturation : 78
% 0.24/0.57 % Processed clauses : 136
% 0.24/0.57 % ...of these trivial : 0
% 0.24/0.57 % ...subsumed : 5
% 0.24/0.57 % ...remaining for further processing : 131
% 0.24/0.57 % Other redundant clauses eliminated : 15
% 0.24/0.57 % Clauses deleted for lack of memory : 0
% 0.24/0.57 % Backward-subsumed : 0
% 0.24/0.57 % Backward-rewritten : 0
% 0.24/0.57 % Generated clauses : 109
% 0.24/0.57 % ...of the previous two non-redundant : 89
% 0.24/0.57 % ...aggressively subsumed : 0
% 0.24/0.57 % Contextual simplify-reflections : 6
% 0.24/0.57 % Paramodulations : 92
% 0.24/0.57 % Factorizations : 0
% 0.24/0.57 % NegExts : 0
% 0.24/0.57 % Equation resolutions : 17
% 0.24/0.57 % Disequality decompositions : 0
% 0.24/0.57 % Total rewrite steps : 65
% 0.24/0.57 % ...of those cached : 60
% 0.24/0.57 % Propositional unsat checks : 0
% 0.24/0.57 % Propositional check models : 0
% 0.24/0.57 % Propositional check unsatisfiable : 0
% 0.24/0.57 % Propositional clauses : 0
% 0.24/0.57 % Propositional clauses after purity: 0
% 0.24/0.57 % Propositional unsat core size : 0
% 0.24/0.57 % Propositional preprocessing time : 0.000
% 0.24/0.57 % Propositional encoding time : 0.000
% 0.24/0.57 % Propositional solver time : 0.000
% 0.24/0.57 % Success case prop preproc time : 0.000
% 0.24/0.57 % Success case prop encoding time : 0.000
% 0.24/0.57 % Success case prop solver time : 0.000
% 0.24/0.57 % Current number of processed clauses : 47
% 0.24/0.57 % Positive orientable unit clauses : 10
% 0.24/0.57 % Positive unorientable unit clauses: 0
% 0.24/0.57 % Negative unit clauses : 5
% 0.24/0.57 % Non-unit-clauses : 32
% 0.24/0.57 % Current number of unprocessed clauses: 103
% 0.24/0.57 % ...number of literals in the above : 379
% 0.24/0.57 % Current number of archived formulas : 0
% 0.24/0.57 % Current number of archived clauses : 73
% 0.24/0.57 % Clause-clause subsumption calls (NU) : 481
% 0.24/0.57 % Rec. Clause-clause subsumption calls : 126
% 0.24/0.57 % Non-unit clause-clause subsumptions : 11
% 0.24/0.57 % Unit Clause-clause subsumption calls : 106
% 0.24/0.57 % Rewrite failures with RHS unbound : 0
% 0.24/0.57 % BW rewrite match attempts : 0
% 0.24/0.57 % BW rewrite match successes : 0
% 0.24/0.57 % Condensation attempts : 0
% 0.24/0.57 % Condensation successes : 0
% 0.24/0.57 % Termbank termtop insertions : 8724
% 0.24/0.57 % Search garbage collected termcells : 1342
% 0.24/0.57
% 0.24/0.57 % -------------------------------------------------
% 0.24/0.57 % User time : 0.021 s
% 0.24/0.57 % System time : 0.010 s
% 0.24/0.57 % Total time : 0.031 s
% 0.24/0.57 % Maximum resident set size: 3940 pages
% 0.24/0.57
% 0.24/0.57 % -------------------------------------------------
% 0.24/0.57 % User time : 0.087 s
% 0.24/0.57 % System time : 0.026 s
% 0.24/0.57 % Total time : 0.113 s
% 0.24/0.57 % Maximum resident set size: 4608 pages
% 0.24/0.57 % E exiting
%------------------------------------------------------------------------------