%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM475+2 : 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 : n016.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 01:49:13 PM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 17 unt; 0 def)
% Number of atoms : 104 ( 31 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 118 ( 49 ~; 44 |; 18 &)
% ( 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 34 ( 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(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__,conjecture,
xn = sdtasdt0(xl,xr),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1459,hypothesis,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1459) ).
fof(m__1360,hypothesis,
( xp = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,xp)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).
fof(m__1379,hypothesis,
( xq = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& aNaturalNumber0(xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).
fof(m__1324,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
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__1422,hypothesis,
( xr = sdtmndt0(xq,xp)
& sdtpldt0(xp,xr) = xq
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1422) ).
fof(c_0_10,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_11,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_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_10]) ).
cnf(c_0_14,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(assume_negation,[status(cth)],[m__]) ).
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,
xn != sdtasdt0(xl,xr),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
cnf(c_0_19,hypothesis,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(split_conjunct,[status(thm)],[m__1459]) ).
cnf(c_0_20,hypothesis,
xm = sdtasdt0(xl,xp),
inference(split_conjunct,[status(thm)],[m__1360]) ).
cnf(c_0_21,hypothesis,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(split_conjunct,[status(thm)],[m__1379]) ).
cnf(c_0_22,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_23,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1324]) ).
fof(c_0_25,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
cnf(c_0_26,hypothesis,
sdtpldt0(xm,sdtasdt0(xl,xr)) = sdtasdt0(xl,xq),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20]),c_0_21]) ).
cnf(c_0_27,hypothesis,
sdtmndt0(sdtasdt0(xl,xq),xm) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_21]),c_0_23]),c_0_24])]) ).
cnf(c_0_28,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_29,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_30,hypothesis,
~ aNaturalNumber0(sdtasdt0(xl,xr)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_26]),c_0_23])]),c_0_27]),c_0_28]) ).
cnf(c_0_31,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__1422]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_34,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM475+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:38:07 UTC 2026
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.46 % Version: 3.5.1
% 0.15/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.46 % Starting sh5l with 300s (1) cores
% 0.15/0.46 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1373590 completed with status 0
% 0.15/0.46 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.15/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.46 % No SInE strategy applied
% 0.15/0.46 % Search class: FGUSF-FFMM22-SFFFFFNN
% 0.15/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.15/0.46 % Starting G-E--_107_B42_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.15/0.46 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.46 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1373598 completed with status 0
% 0.15/0.46 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.15/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.46 % No SInE strategy applied
% 0.15/0.46 % Search class: FGUSF-FFMM22-SFFFFFNN
% 0.15/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.15/0.46 % Preprocessing time : 0.002 s
% 0.15/0.46 % Presaturation interreduction done
% 0.15/0.46
% 0.15/0.46 % Proof found!
% 0.15/0.46 % SZS status Theorem
% 0.15/0.46 % SZS output start CNFRefutation
% See solution above
% 0.15/0.46 % Parsed axioms : 42
% 0.15/0.46 % Removed by relevancy pruning/SinE : 0
% 0.15/0.46 % Initial clauses : 81
% 0.15/0.46 % Removed in clause preprocessing : 3
% 0.15/0.46 % Initial clauses in saturation : 78
% 0.15/0.46 % Processed clauses : 268
% 0.15/0.46 % ...of these trivial : 0
% 0.15/0.46 % ...subsumed : 49
% 0.15/0.46 % ...remaining for further processing : 219
% 0.15/0.46 % Other redundant clauses eliminated : 37
% 0.15/0.46 % Clauses deleted for lack of memory : 0
% 0.15/0.46 % Backward-subsumed : 16
% 0.15/0.46 % Backward-rewritten : 9
% 0.15/0.46 % Generated clauses : 763
% 0.15/0.46 % ...of the previous two non-redundant : 658
% 0.15/0.46 % ...aggressively subsumed : 0
% 0.15/0.46 % Contextual simplify-reflections : 8
% 0.15/0.46 % Paramodulations : 722
% 0.15/0.46 % Factorizations : 0
% 0.15/0.46 % NegExts : 0
% 0.15/0.46 % Equation resolutions : 41
% 0.15/0.46 % Disequality decompositions : 0
% 0.15/0.46 % Total rewrite steps : 747
% 0.15/0.46 % ...of those cached : 721
% 0.15/0.46 % Propositional unsat checks : 0
% 0.15/0.46 % Propositional check models : 0
% 0.15/0.46 % Propositional check unsatisfiable : 0
% 0.15/0.46 % Propositional clauses : 0
% 0.15/0.46 % Propositional clauses after purity: 0
% 0.15/0.46 % Propositional unsat core size : 0
% 0.15/0.46 % Propositional preprocessing time : 0.000
% 0.15/0.46 % Propositional encoding time : 0.000
% 0.15/0.46 % Propositional solver time : 0.000
% 0.15/0.46 % Success case prop preproc time : 0.000
% 0.15/0.46 % Success case prop encoding time : 0.000
% 0.15/0.46 % Success case prop solver time : 0.000
% 0.15/0.46 % Current number of processed clauses : 112
% 0.15/0.46 % Positive orientable unit clauses : 25
% 0.15/0.46 % Positive unorientable unit clauses: 0
% 0.15/0.46 % Negative unit clauses : 6
% 0.15/0.46 % Non-unit-clauses : 81
% 0.15/0.46 % Current number of unprocessed clauses: 500
% 0.15/0.46 % ...number of literals in the above : 2462
% 0.15/0.46 % Current number of archived formulas : 0
% 0.15/0.46 % Current number of archived clauses : 98
% 0.15/0.46 % Clause-clause subsumption calls (NU) : 2126
% 0.15/0.46 % Rec. Clause-clause subsumption calls : 875
% 0.15/0.46 % Non-unit clause-clause subsumptions : 56
% 0.15/0.46 % Unit Clause-clause subsumption calls : 121
% 0.15/0.46 % Rewrite failures with RHS unbound : 0
% 0.15/0.46 % BW rewrite match attempts : 5
% 0.15/0.46 % BW rewrite match successes : 5
% 0.15/0.46 % Condensation attempts : 0
% 0.15/0.46 % Condensation successes : 0
% 0.15/0.46 % Termbank termtop insertions : 16897
% 0.15/0.46 % Search garbage collected termcells : 1055
% 0.15/0.46
% 0.15/0.46 % -------------------------------------------------
% 0.15/0.46 % User time : 0.031 s
% 0.15/0.46 % System time : 0.003 s
% 0.15/0.46 % Total time : 0.034 s
% 0.15/0.46 % Maximum resident set size: 3676 pages
% 0.15/0.46
% 0.15/0.46 % -------------------------------------------------
% 0.15/0.46 % User time : 0.108 s
% 0.15/0.46 % System time : 0.014 s
% 0.15/0.46 % Total time : 0.121 s
% 0.15/0.46 % Maximum resident set size: 4608 pages
% 0.15/0.46 % E exiting
%------------------------------------------------------------------------------