%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM490+1 : 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 : 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 01:49:17 PM UTC 2026
% Result : Theorem 0.26s 0.56s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 17 unt; 0 def)
% Number of atoms : 106 ( 24 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 129 ( 58 ~; 52 |; 12 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 19 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(m__,conjecture,
sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__1951,hypothesis,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1951) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
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),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
fof(c_0_9,plain,
! [X35,X36,X38] :
( ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| sdtlseqdt0(X35,X36)
| sdtpldt0(X35,X38) != X36
| ~ aNaturalNumber0(X38) )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| sdtpldt0(X35,esk1_2(X35,X36)) = X36 )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| aNaturalNumber0(esk1_2(X35,X36)) ) ),
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)],[mDefLE])])])])])]) ).
fof(c_0_10,plain,
! [X5,X6] :
( aNaturalNumber0(sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
fof(c_0_11,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,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])])])])]) ).
cnf(c_0_13,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X3)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| X1 = sdtmndt0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_13]),c_0_14]) ).
fof(c_0_18,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(fof_nnf,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtmndt0(sdtpldt0(X1,X2),X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_14]),c_0_17]) ).
cnf(c_0_20,hypothesis,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(split_conjunct,[status(thm)],[m__1951]) ).
cnf(c_0_21,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X7,X8] :
( aNaturalNumber0(sdtasdt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_23,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X3,X2)
| X1 != sdtmndt0(X2,X3)
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_25,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_28,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| aNaturalNumber0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_29,hypothesis,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[m__1870]) ).
cnf(c_0_30,hypothesis,
xr = sdtmndt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_32,hypothesis,
~ aNaturalNumber0(sdtasdt0(xr,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27])]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(xr),
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_27]),c_0_31])]) ).
cnf(c_0_34,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_26]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM490+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 % Computer : n011.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 02:34:26 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 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
% 0.26/0.56 % Version: 3.5.1
% 0.26/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.56 % Starting sh5l with 300s (1) cores
% 0.26/0.56 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 780942 completed with status 0
% 0.26/0.56 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.26/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.56 % No SInE strategy applied
% 0.26/0.56 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.26/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.26/0.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.26/0.56 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.26/0.56 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.26/0.56 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 780947 completed with status 0
% 0.26/0.56 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.26/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.56 % No SInE strategy applied
% 0.26/0.56 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.26/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.26/0.56 % Preprocessing time : 0.003 s
% 0.26/0.56 % Presaturation interreduction done
% 0.26/0.56
% 0.26/0.56 % Proof found!
% 0.26/0.56 % SZS status Theorem
% 0.26/0.56 % SZS output start CNFRefutation
% See solution above
% 0.26/0.56 % Parsed axioms : 47
% 0.26/0.56 % Removed by relevancy pruning/SinE : 0
% 0.26/0.56 % Initial clauses : 83
% 0.26/0.56 % Removed in clause preprocessing : 3
% 0.26/0.56 % Initial clauses in saturation : 80
% 0.26/0.56 % Processed clauses : 176
% 0.26/0.56 % ...of these trivial : 0
% 0.26/0.56 % ...subsumed : 6
% 0.26/0.56 % ...remaining for further processing : 170
% 0.26/0.56 % Other redundant clauses eliminated : 19
% 0.26/0.56 % Clauses deleted for lack of memory : 0
% 0.26/0.56 % Backward-subsumed : 1
% 0.26/0.56 % Backward-rewritten : 0
% 0.26/0.56 % Generated clauses : 380
% 0.26/0.56 % ...of the previous two non-redundant : 343
% 0.26/0.56 % ...aggressively subsumed : 0
% 0.26/0.56 % Contextual simplify-reflections : 6
% 0.26/0.56 % Paramodulations : 355
% 0.26/0.56 % Factorizations : 2
% 0.26/0.56 % NegExts : 0
% 0.26/0.56 % Equation resolutions : 23
% 0.26/0.56 % Disequality decompositions : 0
% 0.26/0.56 % Total rewrite steps : 193
% 0.26/0.56 % ...of those cached : 183
% 0.26/0.56 % Propositional unsat checks : 0
% 0.26/0.56 % Propositional check models : 0
% 0.26/0.56 % Propositional check unsatisfiable : 0
% 0.26/0.56 % Propositional clauses : 0
% 0.26/0.56 % Propositional clauses after purity: 0
% 0.26/0.56 % Propositional unsat core size : 0
% 0.26/0.56 % Propositional preprocessing time : 0.000
% 0.26/0.56 % Propositional encoding time : 0.000
% 0.26/0.56 % Propositional solver time : 0.000
% 0.26/0.56 % Success case prop preproc time : 0.000
% 0.26/0.56 % Success case prop encoding time : 0.000
% 0.26/0.56 % Success case prop solver time : 0.000
% 0.26/0.56 % Current number of processed clauses : 83
% 0.26/0.56 % Positive orientable unit clauses : 14
% 0.26/0.56 % Positive unorientable unit clauses: 0
% 0.26/0.56 % Negative unit clauses : 8
% 0.26/0.56 % Non-unit-clauses : 61
% 0.26/0.56 % Current number of unprocessed clauses: 320
% 0.26/0.56 % ...number of literals in the above : 1488
% 0.26/0.56 % Current number of archived formulas : 0
% 0.26/0.56 % Current number of archived clauses : 76
% 0.26/0.56 % Clause-clause subsumption calls (NU) : 895
% 0.26/0.56 % Rec. Clause-clause subsumption calls : 196
% 0.26/0.56 % Non-unit clause-clause subsumptions : 11
% 0.26/0.56 % Unit Clause-clause subsumption calls : 165
% 0.26/0.56 % Rewrite failures with RHS unbound : 0
% 0.26/0.56 % BW rewrite match attempts : 0
% 0.26/0.56 % BW rewrite match successes : 0
% 0.26/0.56 % Condensation attempts : 0
% 0.26/0.56 % Condensation successes : 0
% 0.26/0.56 % Termbank termtop insertions : 13381
% 0.26/0.56 % Search garbage collected termcells : 1342
% 0.26/0.56
% 0.26/0.56 % -------------------------------------------------
% 0.26/0.56 % User time : 0.038 s
% 0.26/0.56 % System time : 0.004 s
% 0.26/0.56 % Total time : 0.042 s
% 0.26/0.56 % Maximum resident set size: 3940 pages
% 0.26/0.56
% 0.26/0.56 % -------------------------------------------------
% 0.26/0.56 % User time : 0.151 s
% 0.26/0.56 % System time : 0.022 s
% 0.26/0.56 % Total time : 0.173 s
% 0.26/0.56 % Maximum resident set size: 4608 pages
% 0.26/0.56 % E exiting
%------------------------------------------------------------------------------