%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM924_1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 01:50:59 PM UTC 2026
% Result : Theorem 0.24s 0.57s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
int: $tType ).
tff(decl_sort2,type,
nat: $tType ).
tff(decl_23,type,
one_one_int: int ).
tff(decl_25,type,
plus_plus_int: ( int * int ) > int ).
tff(decl_27,type,
times_times_int: ( int * int ) > int ).
tff(decl_29,type,
zero_zero_int: int ).
tff(decl_32,type,
bit0: int > int ).
tff(decl_33,type,
bit1: int > int ).
tff(decl_34,type,
pls: int ).
tff(decl_35,type,
number_number_of_int: int > int ).
tff(decl_36,type,
number_number_of_nat: int > nat ).
tff(decl_37,type,
ord_less_int: ( int * int ) > $o ).
tff(decl_41,type,
power_power_int: ( nat * int ) > int ).
tff(decl_44,type,
m: int ).
tff(decl_45,type,
s: int ).
tff(decl_46,type,
t: int ).
tff(conj_0,conjecture,
ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(fact_24_number__of__is__id,axiom,
! [X11: int] : ( number_number_of_int(X11) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_number__of__is__id) ).
tff(fact_105_zero__is__num__zero,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_zero__is__num__zero) ).
tff(fact_18_add__special_I3_J,axiom,
! [X8: int] : ( plus_plus_int(number_number_of_int(X8),one_one_int) = number_number_of_int(plus_plus_int(X8,bit1(pls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_add__special_I3_J) ).
tff(fact_3_t,axiom,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
tff(fact_25_zmult__commute,axiom,
! [X12: int,X10: int] : ( times_times_int(X12,X10) = times_times_int(X10,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zmult__commute) ).
tff(fact_104_zadd__commute,axiom,
! [X12: int,X10: int] : ( plus_plus_int(X12,X10) = plus_plus_int(X10,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_zadd__commute) ).
tff(fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096,axiom,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
tff(fact_66_mult__Pls,axiom,
! [X10: int] : ( times_times_int(pls,X10) = pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_mult__Pls) ).
tff(c_0_9,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(assume_negation,[status(cth)],[conj_0]) ).
tff(c_0_10,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
tff(c_0_11,plain,
! [X70: int] : ( number_number_of_int(X70) = X70 ),
inference(variable_rename,[status(thm)],[fact_24_number__of__is__id]) ).
tff(c_0_12,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(fof_nnf,[status(thm)],[c_0_10]) ).
tcf(c_0_13,plain,
zero_zero_int = number_number_of_int(pls),
inference(split_conjunct,[status(thm)],[fact_105_zero__is__num__zero]) ).
tcf(c_0_14,plain,
! [X1: int] : number_number_of_int(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tff(c_0_15,plain,
! [X67: int] : ( plus_plus_int(number_number_of_int(X67),one_one_int) = number_number_of_int(plus_plus_int(X67,bit1(pls))) ),
inference(variable_rename,[status(thm)],[fact_18_add__special_I3_J]) ).
tcf(c_0_16,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_17,plain,
pls = zero_zero_int,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
tcf(c_0_18,plain,
! [X1: int] : plus_plus_int(number_number_of_int(X1),one_one_int) = number_number_of_int(plus_plus_int(X1,bit1(pls))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
tcf(c_0_19,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),
inference(split_conjunct,[status(thm)],[fact_3_t]) ).
tff(c_0_20,plain,
! [X71: int,X72: int] : ( times_times_int(X71,X72) = times_times_int(X72,X71) ),
inference(variable_rename,[status(thm)],[fact_25_zmult__commute]) ).
tff(c_0_21,plain,
! [X215: int,X216: int] : ( plus_plus_int(X215,X216) = plus_plus_int(X216,X215) ),
inference(variable_rename,[status(thm)],[fact_104_zadd__commute]) ).
tcf(c_0_22,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),pls),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
tcf(c_0_23,plain,
! [X1: int] : plus_plus_int(X1,one_one_int) = plus_plus_int(X1,bit1(pls)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_14]),c_0_14]) ).
tcf(c_0_24,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
inference(split_conjunct,[status(thm)],[fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096]) ).
tcf(c_0_25,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),t),
inference(rw,[status(thm)],[c_0_19,c_0_14]) ).
tcf(c_0_26,plain,
! [X2: int,X1: int] : times_times_int(X1,X2) = times_times_int(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
tcf(c_0_27,plain,
! [X2: int,X1: int] : plus_plus_int(X1,X2) = plus_plus_int(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
tff(c_0_28,plain,
! [X142: int] : ( times_times_int(pls,X142) = pls ),
inference(variable_rename,[status(thm)],[fact_66_mult__Pls]) ).
tcf(c_0_29,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),bit1(pls)),pls),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
tcf(c_0_30,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),zero_zero_int)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_14]),c_0_14]) ).
tcf(c_0_31,plain,
times_times_int(t,plus_plus_int(bit1(pls),times_times_int(m,bit0(bit0(bit1(pls)))))) = plus_plus_int(bit1(pls),power_power_int(s,number_number_of_nat(bit0(bit1(pls))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_23]),c_0_27]),c_0_26]),c_0_23]),c_0_27]) ).
tcf(c_0_32,plain,
! [X1: int] : times_times_int(pls,X1) = pls,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
tcf(c_0_33,negated_conjecture,
~ ord_less_int(plus_plus_int(bit1(pls),power_power_int(s,number_number_of_nat(bit0(bit1(pls))))),pls),
inference(rw,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_34,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_26]),c_0_23]),c_0_27]),c_0_26]),c_0_31]),c_0_26]),c_0_23]),c_0_27]),c_0_17]),c_0_26]),c_0_32]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM924_1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n009.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 03:16:42 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.51 Running first-order theorem proving
% 0.24/0.51 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
% 0.24/0.57 % Version: 3.5.1
% 0.24/0.57 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.24/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.57 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr 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 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 720097 completed with status 0
% 0.24/0.57 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.24/0.57 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.24/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.57 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr 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: FGHSM-FFMM21-DFFFFFNN
% 0.24/0.57 % partial match(1): FGHSM-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 C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.24/0.57 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.24/0.57 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.24/0.57 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 136s (1) cores
% 0.24/0.57 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 720105 completed with status 0
% 0.24/0.57 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.24/0.57 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.24/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.57 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr 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: FGHSM-FFMM21-DFFFFFNN
% 0.24/0.57 % partial match(1): FGHSM-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 C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.24/0.57 % Preprocessing time : 0.004 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 : 133
% 0.24/0.57 % Removed by relevancy pruning/SinE : 0
% 0.24/0.57 % Initial clauses : 185
% 0.24/0.57 % Removed in clause preprocessing : 48
% 0.24/0.57 % Initial clauses in saturation : 137
% 0.24/0.57 % Processed clauses : 145
% 0.24/0.57 % ...of these trivial : 9
% 0.24/0.57 % ...subsumed : 15
% 0.24/0.57 % ...remaining for further processing : 120
% 0.24/0.57 % Other redundant clauses eliminated : 11
% 0.24/0.57 % Clauses deleted for lack of memory : 0
% 0.24/0.57 % Backward-subsumed : 1
% 0.24/0.57 % Backward-rewritten : 6
% 0.24/0.57 % Generated clauses : 7
% 0.24/0.57 % ...of the previous two non-redundant : 9
% 0.24/0.57 % ...aggressively subsumed : 0
% 0.24/0.57 % Contextual simplify-reflections : 1
% 0.24/0.57 % Paramodulations : 0
% 0.24/0.57 % Factorizations : 0
% 0.24/0.57 % NegExts : 0
% 0.24/0.57 % Equation resolutions : 11
% 0.24/0.57 % Disequality decompositions : 0
% 0.24/0.57 % Total rewrite steps : 133
% 0.24/0.57 % ...of those cached : 109
% 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 : 106
% 0.24/0.57 % Positive orientable unit clauses : 31
% 0.24/0.57 % Positive unorientable unit clauses: 3
% 0.24/0.57 % Negative unit clauses : 5
% 0.24/0.57 % Non-unit-clauses : 67
% 0.24/0.57 % Current number of unprocessed clauses: 1
% 0.24/0.57 % ...number of literals in the above : 1
% 0.24/0.57 % Current number of archived formulas : 0
% 0.24/0.57 % Current number of archived clauses : 8
% 0.24/0.57 % Clause-clause subsumption calls (NU) : 877
% 0.24/0.57 % Rec. Clause-clause subsumption calls : 821
% 0.24/0.57 % Non-unit clause-clause subsumptions : 15
% 0.24/0.57 % Unit Clause-clause subsumption calls : 12
% 0.24/0.57 % Rewrite failures with RHS unbound : 0
% 0.24/0.57 % BW rewrite match attempts : 30
% 0.24/0.57 % BW rewrite match successes : 23
% 0.24/0.57 % Condensation attempts : 0
% 0.24/0.57 % Condensation successes : 0
% 0.24/0.57 % Termbank termtop insertions : 9768
% 0.24/0.57 % Search garbage collected termcells : 1150
% 0.24/0.57
% 0.24/0.57 % -------------------------------------------------
% 0.24/0.57 % User time : 0.024 s
% 0.24/0.57 % System time : 0.007 s
% 0.24/0.57 % Total time : 0.032 s
% 0.24/0.57 % Maximum resident set size: 3772 pages
% 0.24/0.57
% 0.24/0.57 % -------------------------------------------------
% 0.24/0.57 % User time : 0.077 s
% 0.24/0.57 % System time : 0.035 s
% 0.24/0.57 % Total time : 0.112 s
% 0.24/0.57 % Maximum resident set size: 4608 pages
% 0.24/0.57 % E exiting
%------------------------------------------------------------------------------