TSTP Solution File: NUM924+3 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM924+3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 09:37:42 EDT 2022
% Result : Theorem 0.34s 1.52s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 109 ( 103 unt; 0 def)
% Number of atoms : 115 ( 90 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 3 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 18 ( 3 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-2 aty)
% Number of variables : 79 ( 2 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_182_Bit0__def,axiom,
! [X13] : bit0(X13) = hAPP_int_int(plus_plus_int(X13),X13),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_182_Bit0__def) ).
fof(fact_236_Bit1__def,axiom,
! [X13] : bit1(X13) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X13)),X13),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_236_Bit1__def) ).
fof(fact_87_nat__1__add__1,axiom,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_87_nat__1__add__1) ).
fof(fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X140,X141,X142] : hAPP_int_int(plus_plus_int(X140),hAPP_int_int(plus_plus_int(X141),X142)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X140),X141)),X142),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_171_Bit0__Pls,axiom,
bit0(pls) = pls,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_171_Bit0__Pls) ).
fof(fact_3_t,axiom,
hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_3_t) ).
fof(fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X159] : hAPP_int_int(times_times_int(X159),zero_zero_int) = zero_zero_int,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_,axiom,
~ ! [X11] :
( is_int(X11)
=> hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) != hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),X11) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
fof(fact_26_add__special_I2_J,axiom,
! [X9] : hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X9)) = number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),X9)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_26_add__special_I2_J) ).
fof(fact_248_number__of__Bit1,axiom,
! [X89] : number_number_of_int(bit1(X89)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X89))),number_number_of_int(X89)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_248_number__of__Bit1) ).
fof(fact_134_zadd__commute,axiom,
! [X14,X12] : hAPP_int_int(plus_plus_int(X14),X12) = hAPP_int_int(plus_plus_int(X12),X14),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_134_zadd__commute) ).
fof(fact_133_zadd__left__commute,axiom,
! [X3,X4,X14] : hAPP_int_int(plus_plus_int(X3),hAPP_int_int(plus_plus_int(X4),X14)) = hAPP_int_int(plus_plus_int(X4),hAPP_int_int(plus_plus_int(X3),X14)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_133_zadd__left__commute) ).
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(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int))),
file('/export/starexec/sandbox/solver/bin/../tmp/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) ).
fof(fact_172_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_172_Pls__def) ).
fof(fact_224_number__of__add,axiom,
! [X83,X84] : number_number_of_int(hAPP_int_int(plus_plus_int(X83),X84)) = hAPP_int_int(plus_plus_int(number_number_of_int(X83)),number_number_of_int(X84)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_224_number__of__add) ).
fof(fact_28_add__special_I3_J,axiom,
! [X10] : hAPP_int_int(plus_plus_int(number_number_of_int(X10)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(X10),bit1(pls))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_28_add__special_I3_J) ).
fof(fact_184_zadd__0,axiom,
! [X14] :
( is_int(X14)
=> hAPP_int_int(plus_plus_int(zero_zero_int),X14) = X14 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_184_zadd__0) ).
fof(fact_160_one__is__num__one,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_160_one__is__num__one) ).
fof(fact_35_zmult__commute,axiom,
! [X14,X12] : hAPP_int_int(times_times_int(X14),X12) = hAPP_int_int(times_times_int(X12),X14),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_35_zmult__commute) ).
fof(fact_246_number__of__Bit0,axiom,
! [X88] : number_number_of_int(bit0(X88)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(X88))),number_number_of_int(X88)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_246_number__of__Bit0) ).
fof(gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint,hypothesis,
is_int(one_one_int),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
fof(fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X96] : hAPP_int_int(times_times_int(X96),X96) = hAPP_nat_int(power_power_int(X96),number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(conj_0,conjecture,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',conj_0) ).
fof(c_0_23,plain,
! [X14] : bit0(X14) = hAPP_int_int(plus_plus_int(X14),X14),
inference(variable_rename,[status(thm)],[fact_182_Bit0__def]) ).
fof(c_0_24,plain,
! [X14] : bit1(X14) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X14)),X14),
inference(variable_rename,[status(thm)],[fact_236_Bit1__def]) ).
cnf(c_0_25,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_87_nat__1__add__1]) ).
cnf(c_0_26,plain,
bit0(X1) = hAPP_int_int(plus_plus_int(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,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_24]) ).
fof(c_0_28,plain,
! [X143,X144,X145] : hAPP_int_int(plus_plus_int(X143),hAPP_int_int(plus_plus_int(X144),X145)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X143),X144)),X145),
inference(variable_rename,[status(thm)],[fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
cnf(c_0_29,plain,
bit0(pls) = pls,
inference(split_conjunct,[status(thm)],[fact_171_Bit0__Pls]) ).
cnf(c_0_30,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
inference(split_conjunct,[status(thm)],[fact_3_t]) ).
cnf(c_0_31,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_27]) ).
cnf(c_0_32,plain,
hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
hAPP_int_int(plus_plus_int(pls),pls) = pls,
inference(rw,[status(thm)],[c_0_29,c_0_26]) ).
fof(c_0_34,plain,
! [X160] : hAPP_int_int(times_times_int(X160),zero_zero_int) = zero_zero_int,
inference(variable_rename,[status(thm)],[fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
fof(c_0_35,plain,
( is_int(esk1_0)
& hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_])])]) ).
fof(c_0_36,plain,
! [X10] : hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X10)) = number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),X10)),
inference(variable_rename,[status(thm)],[fact_26_add__special_I2_J]) ).
fof(c_0_37,plain,
! [X90] : number_number_of_int(bit1(X90)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X90))),number_number_of_int(X90)),
inference(variable_rename,[status(thm)],[fact_248_number__of__Bit1]) ).
fof(c_0_38,plain,
! [X15,X16] : hAPP_int_int(plus_plus_int(X15),X16) = hAPP_int_int(plus_plus_int(X16),X15),
inference(variable_rename,[status(thm)],[fact_134_zadd__commute]) ).
fof(c_0_39,plain,
! [X15,X16,X17] : hAPP_int_int(plus_plus_int(X15),hAPP_int_int(plus_plus_int(X16),X17)) = hAPP_int_int(plus_plus_int(X16),hAPP_int_int(plus_plus_int(X15),X17)),
inference(variable_rename,[status(thm)],[fact_133_zadd__left__commute]) ).
cnf(c_0_40,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(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_41,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t),
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_30,c_0_26]),c_0_26]),c_0_26]),c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_27]) ).
cnf(c_0_42,plain,
number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),pls))))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]),c_0_33]),c_0_32]) ).
cnf(c_0_43,plain,
hAPP_int_int(times_times_int(X1),zero_zero_int) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_172_Pls__def]) ).
cnf(c_0_45,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_46,plain,
hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),X1)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_47,plain,
number_number_of_int(bit1(X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1))),number_number_of_int(X1)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_48,plain,
! [X85,X86] : number_number_of_int(hAPP_int_int(plus_plus_int(X85),X86)) = hAPP_int_int(plus_plus_int(number_number_of_int(X85)),number_number_of_int(X86)),
inference(variable_rename,[status(thm)],[fact_224_number__of__add]) ).
cnf(c_0_49,plain,
hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X2),X1),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_50,plain,
hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_51,plain,
! [X11] : hAPP_int_int(plus_plus_int(number_number_of_int(X11)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(X11),bit1(pls))),
inference(variable_rename,[status(thm)],[fact_28_add__special_I3_J]) ).
fof(c_0_52,plain,
! [X15] :
( ~ is_int(X15)
| hAPP_int_int(plus_plus_int(zero_zero_int),X15) = X15 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_184_zadd__0])]) ).
cnf(c_0_53,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(split_conjunct,[status(thm)],[fact_160_one__is__num__one]) ).
cnf(c_0_54,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),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)],[c_0_40,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_27]) ).
cnf(c_0_55,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),pls))))))))))),m)),one_one_int)),t) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),one_one_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)],[c_0_41,c_0_32]),c_0_32]),c_0_33]),c_0_32]),c_0_32]),c_0_32]),c_0_33]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_33]),c_0_32]),c_0_42]) ).
cnf(c_0_56,plain,
hAPP_int_int(times_times_int(X1),pls) = pls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_44]) ).
cnf(c_0_57,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),esk1_0),
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_45,c_0_26]),c_0_26]),c_0_26]),c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_27]) ).
cnf(c_0_58,plain,
hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),X1)),
inference(rw,[status(thm)],[c_0_46,c_0_27]) ).
cnf(c_0_59,plain,
number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1))),number_number_of_int(X1)),
inference(rw,[status(thm)],[c_0_47,c_0_27]) ).
cnf(c_0_60,plain,
number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_61,plain,
! [X15,X16] : hAPP_int_int(times_times_int(X15),X16) = hAPP_int_int(times_times_int(X16),X15),
inference(variable_rename,[status(thm)],[fact_35_zmult__commute]) ).
cnf(c_0_62,plain,
number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_49]),c_0_50]),c_0_50]),c_0_50]) ).
cnf(c_0_63,plain,
hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),X1)) = hAPP_int_int(plus_plus_int(pls),X1),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_64,plain,
! [X89] : number_number_of_int(bit0(X89)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(X89))),number_number_of_int(X89)),
inference(variable_rename,[status(thm)],[fact_246_number__of__Bit0]) ).
cnf(c_0_65,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(X1)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),bit1(pls))),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_66,plain,
( hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1
| ~ is_int(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_67,plain,
one_one_int = number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),
inference(rw,[status(thm)],[c_0_53,c_0_27]) ).
cnf(c_0_68,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),one_one_int)),pls)),
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)],[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_54,c_0_32]),c_0_32]),c_0_33]),c_0_32]),c_0_32]),c_0_32]),c_0_33]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_55]),c_0_32]),c_0_32]),c_0_33]),c_0_32]),c_0_32]),c_0_32]),c_0_33]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_44]),c_0_56]) ).
cnf(c_0_69,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),pls))))))))))),m)),one_one_int)),esk1_0) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),one_one_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)],[c_0_57,c_0_32]),c_0_32]),c_0_33]),c_0_32]),c_0_32]),c_0_32]),c_0_33]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_33]),c_0_32]),c_0_42]) ).
cnf(c_0_70,plain,
number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),X1))) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_32]),c_0_33]),c_0_49]),c_0_32]) ).
cnf(c_0_71,plain,
number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(X1),X1))) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_32]),c_0_60]),c_0_32]) ).
cnf(c_0_72,plain,
hAPP_int_int(times_times_int(X1),X2) = hAPP_int_int(times_times_int(X2),X1),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_73,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63]),c_0_63]) ).
cnf(c_0_74,plain,
number_number_of_int(bit0(X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(X1))),number_number_of_int(X1)),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_75,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(X1)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),
inference(rw,[status(thm)],[c_0_65,c_0_27]) ).
cnf(c_0_76,plain,
( hAPP_int_int(plus_plus_int(pls),X1) = X1
| ~ is_int(X1) ),
inference(rw,[status(thm)],[c_0_66,c_0_44]) ).
cnf(c_0_77,hypothesis,
is_int(one_one_int),
inference(split_conjunct,[status(thm)],[gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint]) ).
cnf(c_0_78,plain,
number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),pls)) = one_one_int,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_32]),c_0_33]) ).
fof(c_0_79,plain,
! [X97] : hAPP_int_int(times_times_int(X97),X97) = hAPP_nat_int(power_power_int(X97),number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
fof(c_0_80,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_81,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),pls)),
inference(rw,[status(thm)],[c_0_68,c_0_49]) ).
cnf(c_0_82,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))) = hAPP_int_int(times_times_int(esk1_0),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_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)],[c_0_69,c_0_49]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_50]),c_0_63]),c_0_63]),c_0_63]),c_0_50]),c_0_63]),c_0_63]),c_0_50]),c_0_70]),c_0_71]),c_0_72]),c_0_72]),c_0_73]) ).
cnf(c_0_83,plain,
number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(X1))),number_number_of_int(X1)),
inference(rw,[status(thm)],[c_0_74,c_0_26]) ).
cnf(c_0_84,plain,
number_number_of_int(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(pls),one_one_int))) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_32]),c_0_33]),c_0_49]),c_0_49]) ).
cnf(c_0_85,hypothesis,
hAPP_int_int(plus_plus_int(pls),one_one_int) = one_one_int,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_86,plain,
number_number_of_int(hAPP_int_int(plus_plus_int(pls),one_one_int)) = one_one_int,
inference(rw,[status(thm)],[c_0_78,c_0_49]) ).
cnf(c_0_87,plain,
hAPP_int_int(times_times_int(X1),X1) = hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
fof(c_0_88,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
cnf(c_0_89,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))),pls)),
inference(rw,[status(thm)],[c_0_81,c_0_73]) ).
cnf(c_0_90,plain,
hAPP_int_int(times_times_int(esk1_0),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))) = hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_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_55,c_0_49]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_50]),c_0_63]),c_0_63]),c_0_63]),c_0_50]),c_0_63]),c_0_63]),c_0_50]),c_0_70]),c_0_71]),c_0_72]),c_0_72]),c_0_73]),c_0_82]) ).
cnf(c_0_91,plain,
hAPP_int_int(plus_plus_int(pls),number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1))) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_44]),c_0_32]),c_0_60]) ).
cnf(c_0_92,plain,
number_number_of_int(hAPP_int_int(plus_plus_int(X1),one_one_int)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)),
inference(rw,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_93,plain,
number_number_of_int(one_one_int) = one_one_int,
inference(rw,[status(thm)],[c_0_86,c_0_85]) ).
cnf(c_0_94,plain,
hAPP_int_int(times_times_int(X1),X1) = hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_26]),c_0_27]),c_0_27]) ).
cnf(c_0_95,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_96,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(esk1_0),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))),pls)),
inference(rw,[status(thm)],[c_0_89,c_0_82]) ).
cnf(c_0_97,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))) = hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),
inference(rw,[status(thm)],[c_0_82,c_0_90]) ).
cnf(c_0_98,plain,
hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) = hAPP_int_int(plus_plus_int(one_one_int),one_one_int),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_93]) ).
cnf(c_0_99,plain,
hAPP_int_int(times_times_int(X1),X1) = hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_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)],[c_0_94,c_0_32]),c_0_49]),c_0_32]),c_0_33]),c_0_49]),c_0_32]),c_0_50]),c_0_50]) ).
cnf(c_0_100,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int)),zero_zero_int)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_26]),c_0_27]),c_0_27]) ).
cnf(c_0_101,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))),pls)),
inference(rw,[status(thm)],[c_0_96,c_0_90]) ).
cnf(c_0_102,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))) = hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_92]),c_0_93]),c_0_98]) ).
cnf(c_0_103,plain,
hAPP_int_int(times_times_int(X1),X1) = hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_62]),c_0_73]),c_0_98]) ).
cnf(c_0_104,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int)),pls)),
inference(rw,[status(thm)],[c_0_100,c_0_44]) ).
cnf(c_0_105,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))),pls)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_92]),c_0_93]) ).
cnf(c_0_106,plain,
hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)),
inference(rw,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_107,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s))),pls)),
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_104,c_0_32]),c_0_32]),c_0_33]),c_0_32]),c_0_49]),c_0_50]),c_0_50]),c_0_50]),c_0_99]),c_0_49]) ).
cnf(c_0_108,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106]),c_0_107]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM924+3 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 22:21:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.34/1.52 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.34/1.52 # Preprocessing time : 0.173 s
% 0.34/1.52
% 0.34/1.52 # Proof found!
% 0.34/1.52 # SZS status Theorem
% 0.34/1.52 # SZS output start CNFRefutation
% See solution above
% 0.34/1.52 # Proof object total steps : 109
% 0.34/1.52 # Proof object clause steps : 69
% 0.34/1.52 # Proof object formula steps : 40
% 0.34/1.52 # Proof object conjectures : 7
% 0.34/1.52 # Proof object clause conjectures : 4
% 0.34/1.52 # Proof object formula conjectures : 3
% 0.34/1.52 # Proof object initial clauses used : 23
% 0.34/1.52 # Proof object initial formulas used : 23
% 0.34/1.52 # Proof object generating inferences : 3
% 0.34/1.52 # Proof object simplifying inferences : 212
% 0.34/1.52 # Training examples: 0 positive, 0 negative
% 0.34/1.52 # Parsed axioms : 1230
% 0.34/1.52 # Removed by relevancy pruning/SinE : 0
% 0.34/1.52 # Initial clauses : 1824
% 0.34/1.52 # Removed in clause preprocessing : 95
% 0.34/1.52 # Initial clauses in saturation : 1729
% 0.34/1.52 # Processed clauses : 2143
% 0.34/1.52 # ...of these trivial : 136
% 0.34/1.52 # ...subsumed : 464
% 0.34/1.52 # ...remaining for further processing : 1543
% 0.34/1.52 # Other redundant clauses eliminated : 212
% 0.34/1.52 # Clauses deleted for lack of memory : 0
% 0.34/1.52 # Backward-subsumed : 13
% 0.34/1.52 # Backward-rewritten : 279
% 0.34/1.52 # Generated clauses : 45396
% 0.34/1.52 # ...of the previous two non-trivial : 40585
% 0.34/1.52 # Contextual simplify-reflections : 33
% 0.34/1.52 # Paramodulations : 45125
% 0.34/1.52 # Factorizations : 13
% 0.34/1.52 # Equation resolutions : 258
% 0.34/1.52 # Current number of processed clauses : 1222
% 0.34/1.52 # Positive orientable unit clauses : 215
% 0.34/1.52 # Positive unorientable unit clauses: 36
% 0.34/1.52 # Negative unit clauses : 48
% 0.34/1.52 # Non-unit-clauses : 923
% 0.34/1.52 # Current number of unprocessed clauses: 28640
% 0.34/1.52 # ...number of literals in the above : 91465
% 0.34/1.52 # Current number of archived formulas : 0
% 0.34/1.52 # Current number of archived clauses : 297
% 0.34/1.52 # Clause-clause subsumption calls (NU) : 150211
% 0.34/1.52 # Rec. Clause-clause subsumption calls : 67858
% 0.34/1.52 # Non-unit clause-clause subsumptions : 319
% 0.34/1.52 # Unit Clause-clause subsumption calls : 3413
% 0.34/1.52 # Rewrite failures with RHS unbound : 0
% 0.34/1.52 # BW rewrite match attempts : 3710
% 0.34/1.52 # BW rewrite match successes : 302
% 0.34/1.52 # Condensation attempts : 0
% 0.34/1.52 # Condensation successes : 0
% 0.34/1.52 # Termbank termtop insertions : 1444047
% 0.34/1.52
% 0.34/1.52 # -------------------------------------------------
% 0.34/1.52 # User time : 0.834 s
% 0.34/1.52 # System time : 0.032 s
% 0.34/1.52 # Total time : 0.866 s
% 0.34/1.52 # Maximum resident set size: 47868 pages
% 0.34/23.51 eprover: CPU time limit exceeded, terminating
% 0.34/23.52 eprover: CPU time limit exceeded, terminating
% 0.34/23.53 eprover: CPU time limit exceeded, terminating
% 0.34/23.53 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.53 eprover: No such file or directory
% 0.34/23.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.54 eprover: No such file or directory
% 0.34/23.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.34/23.54 eprover: No such file or directory
% 0.34/23.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.34/23.54 eprover: No such file or directory
% 0.34/23.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.54 eprover: No such file or directory
% 0.34/23.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.54 eprover: No such file or directory
% 0.34/23.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.55 eprover: No such file or directory
% 0.34/23.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.34/23.55 eprover: No such file or directory
% 0.34/23.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.55 eprover: No such file or directory
% 0.34/23.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.55 eprover: No such file or directory
% 0.34/23.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.34/23.55 eprover: No such file or directory
% 0.34/23.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.55 eprover: No such file or directory
% 0.34/23.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.56 eprover: No such file or directory
% 0.34/23.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.56 eprover: No such file or directory
% 0.34/23.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.34/23.56 eprover: No such file or directory
% 0.34/23.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.56 eprover: No such file or directory
% 0.34/23.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.56 eprover: No such file or directory
% 0.34/23.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.34/23.57 eprover: No such file or directory
% 0.34/23.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.57 eprover: No such file or directory
% 0.34/23.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.57 eprover: No such file or directory
% 0.34/23.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.57 eprover: No such file or directory
% 0.34/23.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.34/23.57 eprover: No such file or directory
% 0.34/23.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.57 eprover: No such file or directory
% 0.34/23.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.34/23.57 eprover: No such file or directory
% 0.34/23.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.58 eprover: No such file or directory
% 0.34/23.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.58 eprover: No such file or directory
% 0.34/23.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.34/23.58 eprover: No such file or directory
% 0.34/23.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.58 eprover: No such file or directory
% 0.34/23.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.34/23.58 eprover: No such file or directory
% 0.34/23.59 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.59 eprover: No such file or directory
% 0.34/23.59 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.34/23.59 eprover: No such file or directory
% 0.34/23.59 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.59 eprover: No such file or directory
% 0.34/23.60 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.60 eprover: No such file or directory
%------------------------------------------------------------------------------