%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM925_3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 01:56:57 PM UTC 2026
% Result : Theorem 0.77s 0.64s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 31 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 13 ~; 2 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
fun_int_bool: $tType ).
tff(decl_sort2,type,
int: $tType ).
tff(decl_sort3,type,
nat: $tType ).
tff(decl_sort4,type,
bool: $tType ).
tff(decl_sort5,type,
fun_nat_int: $tType ).
tff(decl_sort6,type,
fun_int_fun_int_bool: $tType ).
tff(decl_28,type,
one_one_int: int ).
tff(decl_29,type,
one_one_nat: nat ).
tff(decl_31,type,
plus_plus_int: ( int * int ) > int ).
tff(decl_32,type,
plus_plus_nat: ( nat * nat ) > nat ).
tff(decl_37,type,
zero_zero_int: int ).
tff(decl_44,type,
bit0: int > int ).
tff(decl_45,type,
bit1: int > int ).
tff(decl_47,type,
pls: int ).
tff(decl_49,type,
number_number_of_int: int > int ).
tff(decl_50,type,
number_number_of_nat: int > nat ).
tff(decl_53,type,
semiri1621563631at_int: fun_nat_int ).
tff(decl_56,type,
ord_less_int: fun_int_fun_int_bool ).
tff(decl_62,type,
power_power_int: int > fun_nat_int ).
tff(decl_72,type,
hAPP_int_bool: ( int * fun_int_bool ) > bool ).
tff(decl_73,type,
hAPP_i1948725293t_bool: ( int * fun_int_fun_int_bool ) > fun_int_bool ).
tff(decl_75,type,
hAPP_nat_int: ( nat * fun_nat_int ) > int ).
tff(decl_81,type,
hBOOL: bool > $o ).
tff(decl_84,type,
n: nat ).
tff(fact_177_number__of__is__id,axiom,
! [X22: int] : ( number_number_of_int(X22) = X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_number__of__is__id) ).
tff(conj_0,conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(fact_25_semiring__norm_I110_J,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_semiring__norm_I110_J) ).
tff(fact_98_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Pls__def) ).
tff(fact_103_Bit0__def,axiom,
! [X22: int] : ( bit0(X22) = plus_plus_int(X22,X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
tff(fact_231_field__power__not__zero,axiom,
! [X132: nat,X133: int] :
( ( X133 != zero_zero_int )
=> ( hAPP_nat_int(power_power_int(X133),X132) != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
tff(fact_19_semiring__one__add__one__is__two,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_semiring__one__add__one__is__two) ).
tff(fact_269_less__add__one,axiom,
! [X160: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X160),plus_plus_int(X160,one_one_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_less__add__one) ).
tff(fact_67_zadd__commute,axiom,
! [X18: int,X15: int] : ( plus_plus_int(X18,X15) = plus_plus_int(X15,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_zadd__commute) ).
tff(fact_83_int__less__0__conv,axiom,
! [X35: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X35)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_int__less__0__conv) ).
tff(c_0_10,plain,
! [X2584: int] : ( number_number_of_int(X2584) = X2584 ),
inference(variable_rename,[status(thm)],[fact_177_number__of__is__id]) ).
tff(c_0_11,negated_conjecture,
~ ( ( hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
tcf(c_0_12,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(split_conjunct,[status(thm)],[fact_25_semiring__norm_I110_J]) ).
tcf(c_0_13,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_98_Pls__def]) ).
tcf(c_0_14,plain,
! [X1: int] : number_number_of_int(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tff(c_0_15,plain,
! [X1772: int] : ( bit0(X1772) = plus_plus_int(X1772,X1772) ),
inference(variable_rename,[status(thm)],[fact_103_Bit0__def]) ).
tff(c_0_16,plain,
! [X132: nat,X133: int] :
( ( X133 != zero_zero_int )
=> ( hAPP_nat_int(power_power_int(X133),X132) != zero_zero_int ) ),
inference(fof_simplification,[status(thm)],[fact_231_field__power__not__zero]) ).
tff(c_0_17,negated_conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(fof_simplification,[status(thm)],[c_0_11]) ).
tcf(c_0_18,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_19_semiring__one__add__one__is__two]) ).
tcf(c_0_19,plain,
bit1(zero_zero_int) = one_one_int,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
tcf(c_0_20,plain,
! [X1: int] : bit0(X1) = plus_plus_int(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
tff(c_0_21,plain,
! [X1901: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1901),plus_plus_int(X1901,one_one_int))),
inference(variable_rename,[status(thm)],[fact_269_less__add__one]) ).
tff(c_0_22,plain,
! [X1891: int,X1892: int] : ( plus_plus_int(X1891,X1892) = plus_plus_int(X1892,X1891) ),
inference(variable_rename,[status(thm)],[fact_67_zadd__commute]) ).
tff(c_0_23,plain,
! [X1830: nat,X1831: int] :
( ( hAPP_nat_int(power_power_int(X1831),X1830) != zero_zero_int )
| ( X1831 = zero_zero_int ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
tcf(c_0_24,negated_conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
tcf(c_0_25,plain,
number_number_of_nat(plus_plus_int(one_one_int,one_one_int)) = plus_plus_nat(one_one_nat,one_one_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_13]),c_0_19]),c_0_20]) ).
tff(c_0_26,plain,
! [X35: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X35)),zero_zero_int)),
inference(fof_simplification,[status(thm)],[fact_83_int__less__0__conv]) ).
tcf(c_0_27,plain,
! [X1: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),plus_plus_int(X1,one_one_int))),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
tcf(c_0_28,plain,
! [X2: int,X1: int] : plus_plus_int(X1,X2) = plus_plus_int(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
tcf(c_0_29,plain,
! [X1: int,X16: nat] :
( ( hAPP_nat_int(power_power_int(X1),X16) != zero_zero_int )
| ( X1 = zero_zero_int ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
tcf(c_0_30,negated_conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(one_one_nat,one_one_nat)) = zero_zero_int,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_13]),c_0_19]),c_0_20]),c_0_25]) ).
tff(c_0_31,plain,
! [X2052: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X2052)),zero_zero_int)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_26])]) ).
tcf(c_0_32,plain,
! [X1: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),plus_plus_int(one_one_int,X1))),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
tcf(c_0_33,negated_conjecture,
plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
tcf(c_0_34,plain,
! [X16: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X16)),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925_3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n001.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 03:23:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.77/0.64 % Version: 3.5.1
% 0.77/0.64 % Preprocessing class: FMLSSMSMSSSNFFN.
% 0.77/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 0.77/0.64 % Starting new_bool_3 with 600s (2) cores
% 0.77/0.64 % Starting new_bool_1 with 600s (2) cores
% 0.77/0.64 % Starting sh5l with 300s (1) cores
% 0.77/0.64 % new_bool_3 with pid 2077453 completed with status 0
% 0.77/0.64 % Result found by new_bool_3
% 0.77/0.64 % Preprocessing class: FMLSSMSMSSSNFFN.
% 0.77/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 0.77/0.64 % Starting new_bool_3 with 600s (2) cores
% 0.77/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.77/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.77/0.64 % Search class: FGHSM-SSLM31-DFFFFFNN
% 0.77/0.64 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.77/0.64 % Starting SubtermCWHack with 55s (1) cores
% 0.77/0.64 % Starting new_bool_3 with 61s (1) cores
% 0.77/0.64 % SubtermCWHack with pid 2077456 completed with status 0
% 0.77/0.64 % Result found by SubtermCWHack
% 0.77/0.64 % Preprocessing class: FMLSSMSMSSSNFFN.
% 0.77/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 0.77/0.64 % Starting new_bool_3 with 600s (2) cores
% 0.77/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.77/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.77/0.64 % Search class: FGHSM-SSLM31-DFFFFFNN
% 0.77/0.64 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.77/0.64 % Starting SubtermCWHack with 55s (1) cores
% 0.77/0.64 % Preprocessing time : 0.011 s
% 0.77/0.64
% 0.77/0.64 % Proof found!
% 0.77/0.64 % SZS status Theorem
% 0.77/0.64 % SZS output start CNFRefutation
% See solution above
% 0.77/0.64 % Parsed axioms : 1286
% 0.77/0.64 % Removed by relevancy pruning/SinE : 428
% 0.77/0.64 % Initial clauses : 1265
% 0.77/0.64 % Removed in clause preprocessing : 98
% 0.77/0.64 % Initial clauses in saturation : 1167
% 0.77/0.64 % Processed clauses : 3015
% 0.77/0.64 % ...of these trivial : 235
% 0.77/0.64 % ...subsumed : 2139
% 0.77/0.64 % ...remaining for further processing : 641
% 0.77/0.64 % Other redundant clauses eliminated : 230
% 0.77/0.64 % Clauses deleted for lack of memory : 0
% 0.77/0.64 % Backward-subsumed : 16
% 0.77/0.64 % Backward-rewritten : 52
% 0.77/0.64 % Generated clauses : 7585
% 0.77/0.64 % ...of the previous two non-redundant : 6317
% 0.77/0.64 % ...aggressively subsumed : 0
% 0.77/0.64 % Contextual simplify-reflections : 0
% 0.77/0.64 % Paramodulations : 7344
% 0.77/0.64 % Factorizations : 9
% 0.77/0.64 % NegExts : 0
% 0.77/0.64 % Equation resolutions : 241
% 0.77/0.64 % Disequality decompositions : 0
% 0.77/0.64 % Total rewrite steps : 5148
% 0.77/0.64 % ...of those cached : 4097
% 0.77/0.64 % Propositional unsat checks : 0
% 0.77/0.64 % Propositional check models : 0
% 0.77/0.64 % Propositional check unsatisfiable : 0
% 0.77/0.64 % Propositional clauses : 0
% 0.77/0.64 % Propositional clauses after purity: 0
% 0.77/0.64 % Propositional unsat core size : 0
% 0.77/0.64 % Propositional preprocessing time : 0.000
% 0.77/0.64 % Propositional encoding time : 0.000
% 0.77/0.64 % Propositional solver time : 0.000
% 0.77/0.64 % Success case prop preproc time : 0.000
% 0.77/0.64 % Success case prop encoding time : 0.000
% 0.77/0.64 % Success case prop solver time : 0.000
% 0.77/0.64 % Current number of processed clauses : 479
% 0.77/0.64 % Positive orientable unit clauses : 190
% 0.77/0.64 % Positive unorientable unit clauses: 13
% 0.77/0.64 % Negative unit clauses : 169
% 0.77/0.64 % Non-unit-clauses : 107
% 0.77/0.64 % Current number of unprocessed clauses: 4370
% 0.77/0.64 % ...number of literals in the above : 7124
% 0.77/0.64 % Current number of archived formulas : 0
% 0.77/0.64 % Current number of archived clauses : 68
% 0.77/0.64 % Clause-clause subsumption calls (NU) : 11217
% 0.77/0.64 % Rec. Clause-clause subsumption calls : 10338
% 0.77/0.64 % Non-unit clause-clause subsumptions : 129
% 0.77/0.64 % Unit Clause-clause subsumption calls : 25776
% 0.77/0.64 % Rewrite failures with RHS unbound : 0
% 0.77/0.64 % BW rewrite match attempts : 286
% 0.77/0.64 % BW rewrite match successes : 98
% 0.77/0.64 % Condensation attempts : 0
% 0.77/0.64 % Condensation successes : 0
% 0.77/0.64 % Termbank termtop insertions : 162274
% 0.77/0.64 % Search garbage collected termcells : 16912
% 0.77/0.64
% 0.77/0.64 % -------------------------------------------------
% 0.77/0.64 % User time : 0.131 s
% 0.77/0.64 % System time : 0.023 s
% 0.77/0.64 % Total time : 0.155 s
% 0.77/0.64 % Maximum resident set size: 9324 pages
% 0.77/0.64
% 0.77/0.64 % -------------------------------------------------
% 0.77/0.64 % User time : 0.244 s
% 0.77/0.64 % System time : 0.043 s
% 0.77/0.64 % Total time : 0.287 s
% 0.77/0.64 % Maximum resident set size: 6912 pages
% 0.77/0.64 % E exiting
%------------------------------------------------------------------------------