%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM925+2 : 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 : n002.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 0.18s 0.55s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 34 unt; 0 def)
% Number of atoms : 60 ( 50 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 21 ~; 9 |; 2 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-2 aty)
% Number of variables : 45 ( 3 sgn 27 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_176_number__of__is__id,axiom,
! [X21] : number_number_of_int(X21) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_number__of__is__id) ).
fof(conj_0,conjecture,
hAPP_nat_int(power_power_int(hAPP_int_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) ).
fof(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) ).
fof(fact_98_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Pls__def) ).
fof(fact_128_Bit1__def,axiom,
! [X21] : bit1(X21) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X21)),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Bit1__def) ).
fof(fact_67_zadd__commute,axiom,
! [X17,X14] : hAPP_int_int(plus_plus_int(X17),X14) = hAPP_int_int(plus_plus_int(X14),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_zadd__commute) ).
fof(fact_231_field__power__not__zero,axiom,
! [X64,X65] :
( X65 != zero_zero_int
=> hAPP_nat_int(power_power_int(X65),X64) != zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
fof(fact_19_semiring__one__add__one__is__two,axiom,
hAPP_nat_nat(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) ).
fof(fact_529_zle__iff__zadd,axiom,
! [X25,X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X25),X30))
<=> ? [X90] : X30 = hAPP_int_int(plus_plus_int(X25),hAPP_nat_int(semiri1621563631at_int,X90)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_zle__iff__zadd) ).
fof(fact_351_add__0__iff,axiom,
! [X81,X5] :
( X81 = hAPP_int_int(plus_plus_int(X81),X5)
<=> X5 = zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_add__0__iff) ).
fof(fact_494_not__one__le__zero,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_not__one__le__zero) ).
fof(fact_104_zadd__0__right,axiom,
! [X17] : hAPP_int_int(plus_plus_int(X17),zero_zero_int) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_zadd__0__right) ).
fof(c_0_12,plain,
! [X1021] : number_number_of_int(X1021) = X1021,
inference(variable_rename,[status(thm)],[fact_176_number__of__is__id]) ).
fof(c_0_13,negated_conjecture,
~ ( hAPP_nat_int(power_power_int(hAPP_int_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]) ).
cnf(c_0_14,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(split_conjunct,[status(thm)],[fact_25_semiring__norm_I110_J]) ).
cnf(c_0_15,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_98_Pls__def]) ).
cnf(c_0_16,plain,
number_number_of_int(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X696] : bit1(X696) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X696)),X696),
inference(variable_rename,[status(thm)],[fact_128_Bit1__def]) ).
fof(c_0_18,plain,
! [X524,X525] : hAPP_int_int(plus_plus_int(X524),X525) = hAPP_int_int(plus_plus_int(X525),X524),
inference(variable_rename,[status(thm)],[fact_67_zadd__commute]) ).
fof(c_0_19,plain,
! [X64,X65] :
( X65 != zero_zero_int
=> hAPP_nat_int(power_power_int(X65),X64) != zero_zero_int ),
inference(fof_simplification,[status(thm)],[fact_231_field__power__not__zero]) ).
fof(c_0_20,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_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_13]) ).
cnf(c_0_21,plain,
hAPP_nat_nat(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]) ).
cnf(c_0_22,plain,
bit1(zero_zero_int) = one_one_int,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
fof(c_0_23,plain,
! [X672,X673,X675,X676,X677] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X675),X676))
| X676 != hAPP_int_int(plus_plus_int(X675),hAPP_nat_int(semiri1621563631at_int,X677)) )
& ( X673 = hAPP_int_int(plus_plus_int(X672),hAPP_nat_int(semiri1621563631at_int,esk6_2(X672,X673)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X672),X673)) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_529_zle__iff__zadd])])])])])]) ).
fof(c_0_24,plain,
! [X296,X297] :
( ( X296 = hAPP_int_int(plus_plus_int(X296),X297)
| X297 != zero_zero_int )
& ( X297 = zero_zero_int
| X296 != hAPP_int_int(plus_plus_int(X296),X297) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_351_add__0__iff])])]) ).
cnf(c_0_25,plain,
bit1(X1) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X2),X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_27,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
inference(fof_simplification,[status(thm)],[fact_494_not__one__le__zero]) ).
fof(c_0_28,plain,
! [X459,X460] :
( hAPP_nat_int(power_power_int(X460),X459) != zero_zero_int
| X460 = zero_zero_int ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_29,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_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_20]) ).
cnf(c_0_30,plain,
number_number_of_nat(bit0(one_one_int)) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_15]),c_0_22]) ).
cnf(c_0_31,plain,
( X1 != hAPP_int_int(plus_plus_int(X2),hAPP_nat_int(semiri1621563631at_int,X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( X1 != hAPP_int_int(plus_plus_int(X1),X2)
| X2 = zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(one_one_int),X1)) = bit1(X1),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_34,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
inference(fof_nnf,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
( hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int
| X1 = zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) = zero_zero_int,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_15]),c_0_22]),c_0_30]) ).
fof(c_0_37,plain,
! [X288] : hAPP_int_int(plus_plus_int(X288),zero_zero_int) = X288,
inference(variable_rename,[status(thm)],[fact_104_zadd__0__right]) ).
cnf(c_0_38,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(plus_plus_int(X1),hAPP_nat_int(semiri1621563631at_int,X2)))),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( bit1(X1) != X1
| hAPP_int_int(plus_plus_int(one_one_int),X1) = zero_zero_int ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,negated_conjecture,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
hAPP_int_int(plus_plus_int(X1),zero_zero_int) = X1,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
bit1(hAPP_nat_int(semiri1621563631at_int,X1)) != hAPP_nat_int(semiri1621563631at_int,X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_41]),c_0_42]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+2 : 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 : n002.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 03:20:17 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
% 0.18/0.55 % Version: 3.5.1
% 0.18/0.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.18/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.18/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.55 % Starting sh5l with 300s (1) cores
% 0.18/0.55 % new_bool_3 with pid 2314627 completed with status 0
% 0.18/0.55 % Result found by new_bool_3
% 0.18/0.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.18/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.18/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.18/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.18/0.55 % Search class: FGHSM-FSLM31-DFFFFFNN
% 0.18/0.55 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.55 % Starting SubtermCWHack with 28s (1) cores
% 0.18/0.55 % SubtermCWHack with pid 2314632 completed with status 0
% 0.18/0.55 % Result found by SubtermCWHack
% 0.18/0.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.18/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.18/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.18/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.18/0.55 % Search class: FGHSM-FSLM31-DFFFFFNN
% 0.18/0.55 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.55 % Starting SubtermCWHack with 28s (1) cores
% 0.18/0.55 % Preprocessing time : 0.010 s
% 0.18/0.55
% 0.18/0.55 % Proof found!
% 0.18/0.55 % SZS status Theorem
% 0.18/0.55 % SZS output start CNFRefutation
% See solution above
% 0.18/0.55 % Parsed axioms : 708
% 0.18/0.55 % Removed by relevancy pruning/SinE : 185
% 0.18/0.55 % Initial clauses : 757
% 0.18/0.55 % Removed in clause preprocessing : 69
% 0.18/0.55 % Initial clauses in saturation : 688
% 0.18/0.55 % Processed clauses : 1057
% 0.18/0.55 % ...of these trivial : 124
% 0.18/0.55 % ...subsumed : 525
% 0.18/0.55 % ...remaining for further processing : 408
% 0.18/0.55 % Other redundant clauses eliminated : 102
% 0.18/0.55 % Clauses deleted for lack of memory : 0
% 0.18/0.55 % Backward-subsumed : 13
% 0.18/0.55 % Backward-rewritten : 26
% 0.18/0.55 % Generated clauses : 2603
% 0.18/0.55 % ...of the previous two non-redundant : 1902
% 0.18/0.55 % ...aggressively subsumed : 0
% 0.18/0.55 % Contextual simplify-reflections : 0
% 0.18/0.55 % Paramodulations : 2483
% 0.18/0.55 % Factorizations : 8
% 0.18/0.55 % NegExts : 0
% 0.18/0.55 % Equation resolutions : 113
% 0.18/0.55 % Disequality decompositions : 0
% 0.18/0.55 % Total rewrite steps : 1653
% 0.18/0.55 % ...of those cached : 1405
% 0.18/0.55 % Propositional unsat checks : 0
% 0.18/0.55 % Propositional check models : 0
% 0.18/0.55 % Propositional check unsatisfiable : 0
% 0.18/0.55 % Propositional clauses : 0
% 0.18/0.55 % Propositional clauses after purity: 0
% 0.18/0.55 % Propositional unsat core size : 0
% 0.18/0.55 % Propositional preprocessing time : 0.000
% 0.18/0.55 % Propositional encoding time : 0.000
% 0.18/0.55 % Propositional solver time : 0.000
% 0.18/0.55 % Success case prop preproc time : 0.000
% 0.18/0.55 % Success case prop encoding time : 0.000
% 0.18/0.55 % Success case prop solver time : 0.000
% 0.18/0.55 % Current number of processed clauses : 324
% 0.18/0.55 % Positive orientable unit clauses : 149
% 0.18/0.55 % Positive unorientable unit clauses: 5
% 0.18/0.55 % Negative unit clauses : 45
% 0.18/0.55 % Non-unit-clauses : 125
% 0.18/0.55 % Current number of unprocessed clauses: 1478
% 0.18/0.55 % ...number of literals in the above : 3047
% 0.18/0.55 % Current number of archived formulas : 0
% 0.18/0.55 % Current number of archived clauses : 39
% 0.18/0.55 % Clause-clause subsumption calls (NU) : 2880
% 0.18/0.55 % Rec. Clause-clause subsumption calls : 2535
% 0.18/0.55 % Non-unit clause-clause subsumptions : 205
% 0.18/0.55 % Unit Clause-clause subsumption calls : 624
% 0.18/0.55 % Rewrite failures with RHS unbound : 0
% 0.18/0.55 % BW rewrite match attempts : 453
% 0.18/0.55 % BW rewrite match successes : 45
% 0.18/0.55 % Condensation attempts : 0
% 0.18/0.55 % Condensation successes : 0
% 0.18/0.55 % Termbank termtop insertions : 90404
% 0.18/0.55 % Search garbage collected termcells : 9111
% 0.18/0.55
% 0.18/0.55 % -------------------------------------------------
% 0.18/0.55 % User time : 0.080 s
% 0.18/0.55 % System time : 0.013 s
% 0.18/0.55 % Total time : 0.093 s
% 0.18/0.55 % Maximum resident set size: 6532 pages
% 0.18/0.55
% 0.18/0.55 % -------------------------------------------------
% 0.18/0.55 % User time : 0.103 s
% 0.18/0.55 % System time : 0.018 s
% 0.18/0.55 % Total time : 0.121 s
% 0.18/0.55 % Maximum resident set size: 5888 pages
% 0.18/0.55 % E exiting
%------------------------------------------------------------------------------