%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM924+4 : 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 01:51:00 PM UTC 2026
% Result : Theorem 9.26s 7.42s
% Output : CNFRefutation 9.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 59 ( 59 unt; 0 def)
% Number of atoms : 59 ( 48 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 18 con; 0-2 aty)
% Number of variables : 37 ( 1 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_399_semiring__one__add__one__is__two,axiom,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_semiring__one__add__one__is__two) ).
fof(fact_256_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_Pls__def) ).
fof(fact_266_Bit0__def,axiom,
! [X14] : hAPP_int_int(bit0,X14) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_Bit0__def) ).
fof(fact_2750_transfer__nat__int__numerals_I3_J,axiom,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2750_transfer__nat__int__numerals_I3_J) ).
fof(fact_691_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [X189] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X189),X189) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),X189),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(conj_0,conjecture,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X97] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X97),X97) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X97),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_3196_semiring__norm_I115_J,axiom,
hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat)) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3196_semiring__norm_I115_J) ).
fof(fact_3057_One__nat__def,axiom,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3057_One__nat__def) ).
fof(fact_270_double__number__of__Bit0,axiom,
! [X70] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,X70)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,X70)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_double__number__of__Bit0) ).
fof(fact_126_mult__Bit0,axiom,
! [X14,X42] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(bit0,X14)),X42) = hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X14),X42)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_mult__Bit0) ).
fof(fact_199_zadd__commute,axiom,
! [X15,X13] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X15),X13) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X13),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_zadd__commute) ).
fof(fact_243_one__is__num__one,axiom,
one_one_int = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_one__is__num__one) ).
fof(fact_54_zmult__commute,axiom,
! [X15,X13] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X15),X13) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X13),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_zmult__commute) ).
fof(fact_3_t,axiom,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
fof(fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X160] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X160),zero_zero_int) = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(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,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))),
file('/export/starexec/sandbox2/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) ).
cnf(c_0_17,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),
inference(split_conjunct,[status(thm)],[fact_399_semiring__one__add__one__is__two]) ).
cnf(c_0_18,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_256_Pls__def]) ).
fof(c_0_19,plain,
! [X1523] : hAPP_int_int(bit0,X1523) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1523),X1523),
inference(variable_rename,[status(thm)],[fact_266_Bit0__def]) ).
cnf(c_0_20,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
hAPP_int_int(bit0,X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(split_conjunct,[status(thm)],[fact_2750_transfer__nat__int__numerals_I3_J]) ).
cnf(c_0_23,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))) = hAPP_int_int(bit0,one_one_int),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_24,plain,
! [X1078] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1078),X1078) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),X1078),
inference(variable_rename,[status(thm)],[fact_691_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).
fof(c_0_25,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)),zero_zero_int)),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_26,plain,
! [X1289] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1289),X1289) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1289),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(variable_rename,[status(thm)],[fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
cnf(c_0_27,plain,
hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat)) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),
inference(split_conjunct,[status(thm)],[fact_3196_semiring__norm_I115_J]) ).
cnf(c_0_28,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))) = hAPP_int_nat(nat,hAPP_int_int(bit0,one_one_int)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_18]),c_0_23]),c_0_18]) ).
cnf(c_0_29,plain,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
inference(split_conjunct,[status(thm)],[fact_3057_One__nat__def]) ).
fof(c_0_30,plain,
! [X1065] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,X1065)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,X1065)),
inference(variable_rename,[status(thm)],[fact_270_double__number__of__Bit0]) ).
cnf(c_0_31,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X1) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_32,plain,
! [X1217,X1218] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(bit0,X1217)),X1218) = hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1217),X1218)),
inference(variable_rename,[status(thm)],[fact_126_mult__Bit0]) ).
fof(c_0_33,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)),zero_zero_int)),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X1) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
hAPP_int_nat(nat,hAPP_int_int(bit0,one_one_int)) = hAPP_nat_nat(suc,one_one_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_18]),c_0_28]),c_0_29]) ).
fof(c_0_36,plain,
! [X1515,X1516] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1515),X1516) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1516),X1515),
inference(variable_rename,[status(thm)],[fact_199_zadd__commute]) ).
cnf(c_0_37,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,X1)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(bit0,one_one_int)),X1) = hAPP_int_int(bit0,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_21]),c_0_21]) ).
cnf(c_0_39,plain,
one_one_int = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),
inference(split_conjunct,[status(thm)],[fact_243_one__is__num__one]) ).
cnf(c_0_40,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(bit0,X1)),X2) = hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_41,plain,
! [X1830,X1831] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1830),X1831) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1831),X1830),
inference(variable_rename,[status(thm)],[fact_54_zmult__commute]) ).
fof(c_0_42,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)),zero_zero_int)),
inference(fof_nnf,[status(thm)],[c_0_33]) ).
cnf(c_0_43,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t),
inference(split_conjunct,[status(thm)],[fact_3_t]) ).
cnf(c_0_44,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X1) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),hAPP_nat_nat(suc,one_one_nat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_18]),c_0_28]),c_0_35]) ).
cnf(c_0_45,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,X1)) = hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_21]),c_0_38]) ).
cnf(c_0_47,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,zero_zero_int)) = one_one_int,
inference(rw,[status(thm)],[c_0_39,c_0_18]) ).
cnf(c_0_48,plain,
hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X1)) = hAPP_int_int(bit0,X1),
inference(rw,[status(thm)],[c_0_38,c_0_40]) ).
cnf(c_0_49,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_50,plain,
! [X1106] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1106),zero_zero_int) = zero_zero_int,
inference(variable_rename,[status(thm)],[fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
cnf(c_0_51,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_52,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(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]) ).
cnf(c_0_53,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,t),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(bit0,hAPP_int_int(bit0,m)))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,s),s)),
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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_18]),c_0_28]),c_0_35]),c_0_44]),c_0_45]),c_0_18]),c_0_46]),c_0_46]),c_0_47]),c_0_40]),c_0_40]),c_0_48]),c_0_45]),c_0_49]) ).
cnf(c_0_54,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),zero_zero_int) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))),one_one_int)),zero_zero_int)),
inference(rw,[status(thm)],[c_0_51,c_0_18]) ).
cnf(c_0_56,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,s),s))),zero_zero_int)),
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)],[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_52,c_0_18]),c_0_46]),c_0_46]),c_0_47]),c_0_40]),c_0_40]),c_0_48]),c_0_45]),c_0_49]),c_0_53]),c_0_18]),c_0_46]),c_0_46]),c_0_47]),c_0_40]),c_0_40]),c_0_48]),c_0_45]),c_0_54]) ).
cnf(c_0_57,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,s),s))),zero_zero_int)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_45]),c_0_28]),c_0_35]),c_0_44]) ).
cnf(c_0_58,plain,
$false,
inference(sr,[status(thm)],[c_0_56,c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+4 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/5.39 % Computer : n008.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Mon Sep 21 03:18:00 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/5.44 Running first-order theorem proving
% 0.17/5.44 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
% 9.26/7.42 % Version: 3.5.1
% 9.26/7.42 % Preprocessing class: FMLLSMLLSSSNFFN.
% 9.26/7.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.26/7.42 % Starting new_bool_3 with 900s (3) cores
% 9.26/7.42 % Starting new_bool_1 with 900s (3) cores
% 9.26/7.42 % Starting sh5l with 300s (1) cores
% 9.26/7.42 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 9.26/7.42 % new_bool_1 with pid 30702 completed with status 0
% 9.26/7.42 % Result found by new_bool_1
% 9.26/7.42 % Preprocessing class: FMLLSMLLSSSNFFN.
% 9.26/7.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.26/7.42 % Starting new_bool_3 with 900s (3) cores
% 9.26/7.42 % Starting new_bool_1 with 900s (3) cores
% 9.26/7.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 9.26/7.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.26/7.42 % Search class: FGHSM-SMLM32-DFFFFFNN
% 9.26/7.42 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 9.26/7.42 % Starting SubtermCWHack with 82s (1) cores
% 9.26/7.42 % Starting new_bool_1 with 91s (1) cores
% 9.26/7.42 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 9.26/7.42 % new_bool_1 with pid 30707 completed with status 0
% 9.26/7.42 % Result found by new_bool_1
% 9.26/7.42 % Preprocessing class: FMLLSMLLSSSNFFN.
% 9.26/7.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.26/7.42 % Starting new_bool_3 with 900s (3) cores
% 9.26/7.42 % Starting new_bool_1 with 900s (3) cores
% 9.26/7.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 9.26/7.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.26/7.42 % Search class: FGHSM-SMLM32-DFFFFFNN
% 9.26/7.42 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 9.26/7.42 % Starting SubtermCWHack with 82s (1) cores
% 9.26/7.42 % Starting new_bool_1 with 91s (1) cores
% 9.26/7.42 % Preprocessing time : 0.095 s
% 9.26/7.42 % Presaturation interreduction done
% 9.26/7.42
% 9.26/7.42 % Proof found!
% 9.26/7.42 % SZS status Theorem
% 9.26/7.42 % SZS output start CNFRefutation
% See solution above
% 9.26/7.42 % Parsed axioms : 5480
% 9.26/7.42 % Removed by relevancy pruning/SinE : 3055
% 9.26/7.42 % Initial clauses : 3692
% 9.26/7.42 % Removed in clause preprocessing : 166
% 9.26/7.42 % Initial clauses in saturation : 3526
% 9.26/7.42 % Processed clauses : 3789
% 9.26/7.42 % ...of these trivial : 359
% 9.26/7.42 % ...subsumed : 659
% 9.26/7.42 % ...remaining for further processing : 2770
% 9.26/7.42 % Other redundant clauses eliminated : 304
% 9.26/7.42 % Clauses deleted for lack of memory : 0
% 9.26/7.42 % Backward-subsumed : 14
% 9.26/7.42 % Backward-rewritten : 46
% 9.26/7.42 % Generated clauses : 299
% 9.26/7.42 % ...of the previous two non-redundant : 176
% 9.26/7.42 % ...aggressively subsumed : 0
% 9.26/7.42 % Contextual simplify-reflections : 9
% 9.26/7.42 % Paramodulations : 31
% 9.26/7.42 % Factorizations : 0
% 9.26/7.42 % NegExts : 0
% 9.26/7.42 % Equation resolutions : 304
% 9.26/7.42 % Disequality decompositions : 0
% 9.26/7.42 % Total rewrite steps : 2968
% 9.26/7.42 % ...of those cached : 2361
% 9.26/7.42 % Propositional unsat checks : 0
% 9.26/7.42 % Propositional check models : 0
% 9.26/7.42 % Propositional check unsatisfiable : 0
% 9.26/7.42 % Propositional clauses : 0
% 9.26/7.42 % Propositional clauses after purity: 0
% 9.26/7.42 % Propositional unsat core size : 0
% 9.26/7.42 % Propositional preprocessing time : 0.000
% 9.26/7.42 % Propositional encoding time : 0.000
% 9.26/7.42 % Propositional solver time : 0.000
% 9.26/7.42 % Success case prop preproc time : 0.000
% 9.26/7.42 % Success case prop encoding time : 0.000
% 9.26/7.42 % Success case prop solver time : 0.000
% 9.26/7.42 % Current number of processed clauses : 98
% 9.26/7.42 % Positive orientable unit clauses : 61
% 9.26/7.42 % Positive unorientable unit clauses: 0
% 9.26/7.42 % Negative unit clauses : 29
% 9.26/7.42 % Non-unit-clauses : 8
% 9.26/7.42 % Current number of unprocessed clauses: 2257
% 9.26/7.42 % ...number of literals in the above : 5812
% 9.26/7.42 % Current number of archived formulas : 0
% 9.26/7.42 % Current number of archived clauses : 2404
% 9.26/7.42 % Clause-clause subsumption calls (NU) : 486897
% 9.26/7.42 % Rec. Clause-clause subsumption calls : 193436
% 9.26/7.42 % Non-unit clause-clause subsumptions : 566
% 9.26/7.42 % Unit Clause-clause subsumption calls : 2424
% 9.26/7.42 % Rewrite failures with RHS unbound : 0
% 9.26/7.42 % BW rewrite match attempts : 4464
% 9.26/7.42 % BW rewrite match successes : 312
% 9.26/7.42 % Condensation attempts : 0
% 9.26/7.42 % Condensation successes : 0
% 9.26/7.42 % Termbank termtop insertions : 499013
% 9.26/7.42 % Search garbage collected termcells : 67001
% 9.26/7.42
% 9.26/7.42 % -------------------------------------------------
% 9.26/7.42 % User time : 1.214 s
% 9.26/7.42 % System time : 0.065 s
% 9.26/7.42 % Total time : 1.279 s
% 9.26/7.42 % Maximum resident set size: 21700 pages
% 9.26/7.42
% 9.26/7.42 % -------------------------------------------------
% 9.26/7.42 % User time : 3.571 s
% 9.26/7.42 % System time : 0.203 s
% 9.26/7.42 % Total time : 3.774 s
% 9.26/7.42 % Maximum resident set size: 13312 pages
% 9.26/7.42 % E exiting
%------------------------------------------------------------------------------