%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM925+6 : 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 01:51:03 PM UTC 2026
% Result : Theorem 1.33s 0.70s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 24 unt; 0 def)
% Number of atoms : 57 ( 32 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 44 ( 22 ~; 11 |; 4 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-4 aty)
% Number of variables : 31 ( 1 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_37_one__is__num__one,axiom,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_one__is__num__one) ).
fof(fact_73_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Pls__def) ).
fof(fact_119_number__of__is__id,axiom,
! [X20] : number_number_of(int,X20) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_number__of__is__id) ).
fof(fact_164_field__power__not__zero,axiom,
! [X1] :
( ring_11004092258visors(X1)
=> ! [X15,X31] :
( ti(X1,X31) != zero_zero(X1)
=> hAPP(nat,X1,power_power(X1,X31),X15) != zero_zero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_field__power__not__zero) ).
fof(tsy_c_Int_Onumber__class_Onumber__of_res,axiom,
! [X2,X1] :
( number(X1)
=> ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).
fof(fact_254_zless__le,axiom,
! [X29,X24] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X29),X24))
<=> ( X29 != X24
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X29),X24)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_zless__le) ).
fof(arity_Int_Oint___Int_Onumber,axiom,
number(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
fof(arity_Int_Oint___Rings_Oring__1__no__zero__divisors,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
fof(fact_0_n1pos,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(c_0_10,negated_conjecture,
~ ( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_11,plain,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
inference(split_conjunct,[status(thm)],[fact_37_one__is__num__one]) ).
cnf(c_0_12,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_73_Pls__def]) ).
fof(c_0_13,plain,
! [X324] : number_number_of(int,X324) = X324,
inference(variable_rename,[status(thm)],[fact_119_number__of__is__id]) ).
fof(c_0_14,plain,
! [X1] :
( ring_11004092258visors(X1)
=> ! [X15,X31] :
( ti(X1,X31) != zero_zero(X1)
=> hAPP(nat,X1,power_power(X1,X31),X15) != zero_zero(X1) ) ),
inference(fof_simplification,[status(thm)],[fact_164_field__power__not__zero]) ).
fof(c_0_15,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
number_number_of(int,hAPP(int,int,bit1,zero_zero(int))) = one_one(int),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
number_number_of(int,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X87,X88] :
( ti(X88,number_number_of(X88,X87)) = number_number_of(X88,X87)
| ~ number(X88) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Int_Onumber__class_Onumber__of_res])])]) ).
fof(c_0_19,plain,
! [X29,X24] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X29),X24))
<=> ( X29 != X24
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X29),X24)) ) ),
inference(fof_simplification,[status(thm)],[fact_254_zless__le]) ).
fof(c_0_20,plain,
! [X420,X421,X422] :
( hAPP(nat,X420,power_power(X420,X422),X421) != zero_zero(X420)
| ti(X420,X422) = zero_zero(X420)
| ~ ring_11004092258visors(X420) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
cnf(c_0_21,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
hAPP(int,int,bit1,zero_zero(int)) = one_one(int),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( ~ number(X1)
| ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
number(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Int_Onumber]) ).
fof(c_0_25,plain,
! [X665,X666] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X665),X666))
| X665 = X666
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X665),X666)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X665),X666))
| X665 != X666 )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X665),X666))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X665),X666)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_26,plain,
( hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| ~ ring_11004092258visors(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = zero_zero(int),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_12]),c_0_22]) ).
cnf(c_0_28,plain,
ti(int,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17]),c_0_17]) ).
cnf(c_0_29,plain,
ring_11004092258visors(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Oring__1__no__zero__divisors]) ).
cnf(c_0_30,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
cnf(c_0_32,negated_conjecture,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)) = zero_zero(int),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_33,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X1)),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+6 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 03:18:55 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 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
% 1.33/0.70 % Version: 3.5.1
% 1.33/0.70 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.33/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.33/0.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.33/0.70 % Starting new_bool_3 with 300s (1) cores
% 1.33/0.70 % Starting new_bool_1 with 300s (1) cores
% 1.33/0.70 % Starting sh5l with 300s (1) cores
% 1.33/0.70 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 33402 completed with status 0
% 1.33/0.70 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.33/0.70 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.33/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.33/0.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.33/0.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.33/0.70 % No SInE strategy applied
% 1.33/0.70 % Search class: FGHSM-FSLM33-DFFFFFNN
% 1.33/0.70 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 1.33/0.70 % Starting SubtermCWHack with 136s (1) cores
% 1.33/0.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.33/0.70 % Starting U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.33/0.70 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 1.33/0.70 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 1.33/0.70 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 33414 completed with status 0
% 1.33/0.70 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.33/0.70 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.33/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.33/0.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.33/0.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.33/0.70 % No SInE strategy applied
% 1.33/0.70 % Search class: FGHSM-FSLM33-DFFFFFNN
% 1.33/0.70 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 1.33/0.70 % Starting SubtermCWHack with 136s (1) cores
% 1.33/0.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.33/0.70 % Preprocessing time : 0.014 s
% 1.33/0.70 % Presaturation interreduction done
% 1.33/0.70
% 1.33/0.70 % Proof found!
% 1.33/0.70 % SZS status Theorem
% 1.33/0.70 % SZS output start CNFRefutation
% See solution above
% 1.33/0.70 % Parsed axioms : 660
% 1.33/0.70 % Removed by relevancy pruning/SinE : 0
% 1.33/0.70 % Initial clauses : 904
% 1.33/0.70 % Removed in clause preprocessing : 51
% 1.33/0.70 % Initial clauses in saturation : 853
% 1.33/0.70 % Processed clauses : 1304
% 1.33/0.70 % ...of these trivial : 27
% 1.33/0.70 % ...subsumed : 207
% 1.33/0.70 % ...remaining for further processing : 1069
% 1.33/0.70 % Other redundant clauses eliminated : 69
% 1.33/0.70 % Clauses deleted for lack of memory : 0
% 1.33/0.70 % Backward-subsumed : 2
% 1.33/0.70 % Backward-rewritten : 20
% 1.33/0.70 % Generated clauses : 961
% 1.33/0.70 % ...of the previous two non-redundant : 667
% 1.33/0.70 % ...aggressively subsumed : 0
% 1.33/0.70 % Contextual simplify-reflections : 2
% 1.33/0.70 % Paramodulations : 887
% 1.33/0.70 % Factorizations : 2
% 1.33/0.70 % NegExts : 0
% 1.33/0.70 % Equation resolutions : 74
% 1.33/0.70 % Disequality decompositions : 0
% 1.33/0.70 % Total rewrite steps : 1157
% 1.33/0.70 % ...of those cached : 923
% 1.33/0.70 % Propositional unsat checks : 0
% 1.33/0.70 % Propositional check models : 0
% 1.33/0.70 % Propositional check unsatisfiable : 0
% 1.33/0.70 % Propositional clauses : 0
% 1.33/0.70 % Propositional clauses after purity: 0
% 1.33/0.70 % Propositional unsat core size : 0
% 1.33/0.70 % Propositional preprocessing time : 0.000
% 1.33/0.70 % Propositional encoding time : 0.000
% 1.33/0.70 % Propositional solver time : 0.000
% 1.33/0.70 % Success case prop preproc time : 0.000
% 1.33/0.70 % Success case prop encoding time : 0.000
% 1.33/0.70 % Success case prop solver time : 0.000
% 1.33/0.70 % Current number of processed clauses : 332
% 1.33/0.70 % Positive orientable unit clauses : 194
% 1.33/0.70 % Positive unorientable unit clauses: 3
% 1.33/0.70 % Negative unit clauses : 27
% 1.33/0.70 % Non-unit-clauses : 108
% 1.33/0.70 % Current number of unprocessed clauses: 898
% 1.33/0.70 % ...number of literals in the above : 2119
% 1.33/0.70 % Current number of archived formulas : 0
% 1.33/0.70 % Current number of archived clauses : 704
% 1.33/0.70 % Clause-clause subsumption calls (NU) : 47127
% 1.33/0.70 % Rec. Clause-clause subsumption calls : 24244
% 1.33/0.70 % Non-unit clause-clause subsumptions : 140
% 1.33/0.70 % Unit Clause-clause subsumption calls : 224
% 1.33/0.70 % Rewrite failures with RHS unbound : 0
% 1.33/0.70 % BW rewrite match attempts : 2456
% 1.33/0.70 % BW rewrite match successes : 103
% 1.33/0.70 % Condensation attempts : 0
% 1.33/0.70 % Condensation successes : 0
% 1.33/0.70 % Termbank termtop insertions : 151792
% 1.33/0.70 % Search garbage collected termcells : 11703
% 1.33/0.70
% 1.33/0.70 % -------------------------------------------------
% 1.33/0.70 % User time : 0.189 s
% 1.33/0.70 % System time : 0.025 s
% 1.33/0.70 % Total time : 0.214 s
% 1.33/0.70 % Maximum resident set size: 7524 pages
% 1.33/0.70
% 1.33/0.70 % -------------------------------------------------
% 1.33/0.70 % User time : 0.746 s
% 1.33/0.70 % System time : 0.082 s
% 1.33/0.70 % Total time : 0.828 s
% 1.33/0.70 % Maximum resident set size: 5632 pages
% 1.33/0.70 % E exiting
%------------------------------------------------------------------------------