%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM925_1 : 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 : n008.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 01:51:01 PM UTC 2026
% Result : Theorem 0.14s 0.62s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 44 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 6 |; 4 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 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 : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?; 31 :)
% 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,
zero_zero_int: int ).
tff(decl_28,type,
zero_zero_nat: nat ).
tff(decl_29,type,
bit0: int > int ).
tff(decl_30,type,
bit1: int > int ).
tff(decl_31,type,
pls: int ).
tff(decl_33,type,
number_number_of_nat: int > nat ).
tff(decl_34,type,
semiri1621563631at_int: nat > int ).
tff(decl_36,type,
ord_less_int: ( int * int ) > $o ).
tff(decl_38,type,
power_power_int: ( nat * int ) > int ).
tff(decl_40,type,
n: nat ).
tff(fact_85_zadd__0,axiom,
! [X15: int] : ( plus_plus_int(zero_zero_int,X15) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_zadd__0) ).
tff(fact_99_Bit1__def,axiom,
! [X19: int] : ( bit1(X19) = plus_plus_int(plus_plus_int(one_one_int,X19),X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Bit1__def) ).
tff(fact_52_zadd__commute,axiom,
! [X15: int,X12: int] : ( plus_plus_int(X15,X12) = plus_plus_int(X12,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_zadd__commute) ).
tff(fact_84_zadd__0__right,axiom,
! [X15: int] : ( plus_plus_int(X15,zero_zero_int) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_zadd__0__right) ).
tff(fact_92_power__eq__0__iff__number__of,axiom,
! [X3: int,X23: int] :
( ( power_power_int(X3,number_number_of_nat(X23)) = zero_zero_int )
<=> ( ( number_number_of_nat(X23) != zero_zero_nat )
& ( X3 = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_power__eq__0__iff__number__of) ).
tff(conj_0,conjecture,
power_power_int(plus_plus_int(one_one_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_78_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Pls__def) ).
tff(fact_83_Bit0__def,axiom,
! [X19: int] : ( bit0(X19) = plus_plus_int(X19,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Bit0__def) ).
tff(fact_62_bin__less__0__simps_I1_J,axiom,
~ ord_less_int(pls,zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_bin__less__0__simps_I1_J) ).
tff(fact_0_n1pos,axiom,
ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(c_0_10,plain,
! [X52: int] : ( plus_plus_int(zero_zero_int,X52) = X52 ),
inference(variable_rename,[status(thm)],[fact_85_zadd__0]) ).
tff(c_0_11,plain,
! [X136: int] : ( bit1(X136) = plus_plus_int(plus_plus_int(one_one_int,X136),X136) ),
inference(variable_rename,[status(thm)],[fact_99_Bit1__def]) ).
tff(c_0_12,plain,
! [X114: int,X115: int] : ( plus_plus_int(X114,X115) = plus_plus_int(X115,X114) ),
inference(variable_rename,[status(thm)],[fact_52_zadd__commute]) ).
tff(c_0_13,plain,
! [X51: int] : ( plus_plus_int(X51,zero_zero_int) = X51 ),
inference(variable_rename,[status(thm)],[fact_84_zadd__0__right]) ).
tff(c_0_14,plain,
! [X3: int,X23: int] :
( ( power_power_int(X3,number_number_of_nat(X23)) = zero_zero_int )
<=> ( ( number_number_of_nat(X23) != zero_zero_nat )
& ( X3 = zero_zero_int ) ) ),
inference(fof_simplification,[status(thm)],[fact_92_power__eq__0__iff__number__of]) ).
tff(c_0_15,negated_conjecture,
~ ( ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
tcf(c_0_16,plain,
! [X1: int] : plus_plus_int(zero_zero_int,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_17,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_78_Pls__def]) ).
tcf(c_0_18,plain,
! [X1: int] : bit1(X1) = plus_plus_int(plus_plus_int(one_one_int,X1),X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_19,plain,
! [X2: int,X1: int] : plus_plus_int(X1,X2) = plus_plus_int(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_20,plain,
! [X1: int] : plus_plus_int(X1,zero_zero_int) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tff(c_0_21,plain,
! [X59: int,X60: int] :
( ( ( power_power_int(X59,number_number_of_nat(X60)) = zero_zero_int )
| ( number_number_of_nat(X60) = zero_zero_nat )
| ( X59 != zero_zero_int ) )
& ( ( power_power_int(X59,number_number_of_nat(X60)) != zero_zero_int )
| ( number_number_of_nat(X60) != zero_zero_nat ) )
& ( ( power_power_int(X59,number_number_of_nat(X60)) != zero_zero_int )
| ( X59 = zero_zero_int ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
tff(c_0_22,negated_conjecture,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(fof_simplification,[status(thm)],[c_0_15]) ).
tcf(c_0_23,plain,
! [X1: int] : plus_plus_int(pls,X1) = X1,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
tcf(c_0_24,plain,
! [X1: int] : plus_plus_int(X1,plus_plus_int(one_one_int,X1)) = bit1(X1),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
tcf(c_0_25,plain,
! [X1: int] : plus_plus_int(X1,pls) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_17]) ).
tff(c_0_26,plain,
! [X87: int] : ( bit0(X87) = plus_plus_int(X87,X87) ),
inference(variable_rename,[status(thm)],[fact_83_Bit0__def]) ).
tff(c_0_27,plain,
~ ord_less_int(pls,zero_zero_int),
inference(fof_simplification,[status(thm)],[fact_62_bin__less__0__simps_I1_J]) ).
tcf(c_0_28,plain,
! [X1: int,X2: int] :
( ( power_power_int(X1,number_number_of_nat(X2)) != zero_zero_int )
| ( X1 = zero_zero_int ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
tcf(c_0_29,negated_conjecture,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
tcf(c_0_30,plain,
bit1(pls) = one_one_int,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
tcf(c_0_31,plain,
! [X1: int] : bit0(X1) = plus_plus_int(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
tff(c_0_32,plain,
~ ord_less_int(pls,zero_zero_int),
inference(fof_nnf,[status(thm)],[c_0_27]) ).
tcf(c_0_33,plain,
ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
tcf(c_0_34,plain,
! [X1: int,X2: int] :
( ( power_power_int(X1,number_number_of_nat(X2)) != pls )
| ( X1 = pls ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_17]),c_0_17]) ).
tcf(c_0_35,negated_conjecture,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(plus_plus_int(one_one_int,one_one_int))) = pls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_17]) ).
tcf(c_0_36,plain,
~ ord_less_int(pls,zero_zero_int),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
tcf(c_0_37,plain,
ord_less_int(pls,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
inference(rw,[status(thm)],[c_0_33,c_0_17]) ).
tcf(c_0_38,negated_conjecture,
plus_plus_int(one_one_int,semiri1621563631at_int(n)) = pls,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
tcf(c_0_39,plain,
~ ord_less_int(pls,pls),
inference(rw,[status(thm)],[c_0_36,c_0_17]) ).
cnf(c_0_40,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM925_1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.53 % Computer : n008.cluster.edu
% 0.08/0.53 % Model : x86_64 x86_64
% 0.08/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.53 % Memory : 8046.5625MB
% 0.08/0.53 % OS : Linux 6.8.0-71-generic
% 0.08/0.53 % CPULimit : 300
% 0.08/0.53 % WCLimit : 300
% 0.08/0.53 % DateTime : Mon Sep 21 03:18:25 UTC 2026
% 0.08/0.53 % CPUTime :
% 0.08/0.54 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.58 Running first-order theorem proving
% 0.14/0.58 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
% 0.14/0.62 % Version: 3.5.1
% 0.14/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.62 % Starting sh5l with 300s (1) cores
% 0.14/0.62 % new_bool_3 with pid 32022 completed with status 0
% 0.14/0.62 % Result found by new_bool_3
% 0.14/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.62 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.62 % Search class: FGHSM-FFMM21-MFFFFFNN
% 0.14/0.62 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.62 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.62 % SubtermCWHack with pid 32025 completed with status 0
% 0.14/0.62 % Result found by SubtermCWHack
% 0.14/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.62 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.62 % Search class: FGHSM-FFMM21-MFFFFFNN
% 0.14/0.62 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.62 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.62 % Preprocessing time : 0.002 s
% 0.14/0.62
% 0.14/0.62 % Proof found!
% 0.14/0.62 % SZS status Theorem
% 0.14/0.62 % SZS output start CNFRefutation
% See solution above
% 0.14/0.62 % Parsed axioms : 128
% 0.14/0.62 % Removed by relevancy pruning/SinE : 38
% 0.14/0.62 % Initial clauses : 130
% 0.14/0.62 % Removed in clause preprocessing : 8
% 0.14/0.62 % Initial clauses in saturation : 122
% 0.14/0.62 % Processed clauses : 266
% 0.14/0.62 % ...of these trivial : 18
% 0.14/0.62 % ...subsumed : 123
% 0.14/0.62 % ...remaining for further processing : 125
% 0.14/0.62 % Other redundant clauses eliminated : 7
% 0.14/0.62 % Clauses deleted for lack of memory : 0
% 0.14/0.62 % Backward-subsumed : 1
% 0.14/0.62 % Backward-rewritten : 10
% 0.14/0.62 % Generated clauses : 474
% 0.14/0.62 % ...of the previous two non-redundant : 329
% 0.14/0.62 % ...aggressively subsumed : 0
% 0.14/0.62 % Contextual simplify-reflections : 0
% 0.14/0.62 % Paramodulations : 461
% 0.14/0.62 % Factorizations : 2
% 0.14/0.62 % NegExts : 0
% 0.14/0.62 % Equation resolutions : 11
% 0.14/0.62 % Disequality decompositions : 0
% 0.14/0.62 % Total rewrite steps : 263
% 0.14/0.62 % ...of those cached : 214
% 0.14/0.62 % Propositional unsat checks : 0
% 0.14/0.62 % Propositional check models : 0
% 0.14/0.62 % Propositional check unsatisfiable : 0
% 0.14/0.62 % Propositional clauses : 0
% 0.14/0.62 % Propositional clauses after purity: 0
% 0.14/0.62 % Propositional unsat core size : 0
% 0.14/0.62 % Propositional preprocessing time : 0.000
% 0.14/0.62 % Propositional encoding time : 0.000
% 0.14/0.62 % Propositional solver time : 0.000
% 0.14/0.62 % Success case prop preproc time : 0.000
% 0.14/0.62 % Success case prop encoding time : 0.000
% 0.14/0.62 % Success case prop solver time : 0.000
% 0.14/0.62 % Current number of processed clauses : 107
% 0.14/0.62 % Positive orientable unit clauses : 29
% 0.14/0.62 % Positive unorientable unit clauses: 2
% 0.14/0.62 % Negative unit clauses : 19
% 0.14/0.62 % Non-unit-clauses : 57
% 0.14/0.62 % Current number of unprocessed clauses: 183
% 0.14/0.62 % ...number of literals in the above : 343
% 0.14/0.62 % Current number of archived formulas : 0
% 0.14/0.62 % Current number of archived clauses : 11
% 0.14/0.62 % Clause-clause subsumption calls (NU) : 764
% 0.14/0.62 % Rec. Clause-clause subsumption calls : 699
% 0.14/0.62 % Non-unit clause-clause subsumptions : 47
% 0.14/0.62 % Unit Clause-clause subsumption calls : 386
% 0.14/0.62 % Rewrite failures with RHS unbound : 0
% 0.14/0.62 % BW rewrite match attempts : 21
% 0.14/0.62 % BW rewrite match successes : 18
% 0.14/0.62 % Condensation attempts : 0
% 0.14/0.62 % Condensation successes : 0
% 0.14/0.62 % Termbank termtop insertions : 10104
% 0.14/0.62 % Search garbage collected termcells : 901
% 0.14/0.62
% 0.14/0.62 % -------------------------------------------------
% 0.14/0.62 % User time : 0.016 s
% 0.14/0.62 % System time : 0.004 s
% 0.14/0.62 % Total time : 0.020 s
% 0.14/0.62 % Maximum resident set size: 3952 pages
% 0.14/0.62
% 0.14/0.62 % -------------------------------------------------
% 0.14/0.62 % User time : 0.022 s
% 0.14/0.62 % System time : 0.007 s
% 0.14/0.62 % Total time : 0.028 s
% 0.14/0.62 % Maximum resident set size: 4608 pages
% 0.14/0.62 % E exiting
%------------------------------------------------------------------------------