%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM926+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 : n020.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 01:51:04 PM UTC 2026
% Result : Theorem 1.98s 0.79s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 29
% Syntax : Number of formulae : 117 ( 90 unt; 0 def)
% Number of atoms : 184 ( 111 equ)
% Maximal formula atoms : 13 ( 1 avg)
% Number of connectives : 115 ( 48 ~; 36 |; 18 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-2 aty)
% Number of variables : 126 ( 9 sgn 66 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_251_Bit1__def,axiom,
! [X23] : bit1(X23) = plus_plus_int(plus_plus_int(one_one_int,X23),X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_Bit1__def) ).
fof(fact_50_le__number__of__eq__not__less,axiom,
! [X30,X20] :
( ord_less_eq_int(number_number_of_int(X30),number_number_of_int(X20))
<=> ~ ord_less_int(number_number_of_int(X20),number_number_of_int(X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_le__number__of__eq__not__less) ).
fof(fact_264_semiring__norm_I110_J,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_semiring__norm_I110_J) ).
fof(fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X84,X85] : plus_plus_int(X84,X85) = plus_plus_int(X85,X84),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X105] : times_times_nat(one_one_nat,X105) = X105,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_79_Numeral1__eq1__nat,axiom,
one_one_nat = number_number_of_nat(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Numeral1__eq1__nat) ).
fof(fact_201_add__Pls__right,axiom,
! [X23] :
( is_int(X23)
=> plus_plus_int(X23,pls) = X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_add__Pls__right) ).
fof(conj_0,conjecture,
? [X3,X4] : plus_plus_int(power_power_int(X3,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X4,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_31_add__special_I3_J,axiom,
! [X15] : plus_plus_int(number_number_of_int(X15),one_one_int) = number_number_of_int(plus_plus_int(X15,bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add__special_I3_J) ).
fof(gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint,hypothesis,
is_int(one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
fof(fact_562_mult__nat__number__of,axiom,
! [X40,X41] :
( ( ~ ord_less_int(X41,pls)
=> times_times_nat(number_number_of_nat(X41),number_number_of_nat(X40)) = number_number_of_nat(times_times_int(X41,X40)) )
& ( ord_less_int(X41,pls)
=> times_times_nat(number_number_of_nat(X41),number_number_of_nat(X40)) = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_mult__nat__number__of) ).
fof(fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [X122,X123] : plus_plus_int(X122,times_times_int(X123,X122)) = times_times_int(plus_plus_int(X123,one_one_int),X122),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_199_mult__Pls,axiom,
! [X17] : times_times_int(pls,X17) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_mult__Pls) ).
fof(fact_390_semiring__norm_I112_J,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_semiring__norm_I112_J) ).
fof(fact_356_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_Pls__def) ).
fof(fact_692_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
ord_less_eq_int(zero_zero_int,one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_204_Bit0__def,axiom,
! [X23] : bit0(X23) = plus_plus_int(X23,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_Bit0__def) ).
fof(fact_280_semiring__mult__2__right,axiom,
! [X148] : times_times_int(X148,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(X148,X148),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_semiring__mult__2__right) ).
fof(fact_29_add__special_I2_J,axiom,
! [X14] : plus_plus_int(one_one_int,number_number_of_int(X14)) = number_number_of_int(plus_plus_int(bit1(pls),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_add__special_I2_J) ).
fof(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( t = one_one_int
=> ? [X3,X4] :
( plus_plus_int(power_power_int(X3,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X4,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
& is_int(X4)
& is_int(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [X124] : plus_plus_int(X124,X124) = times_times_int(plus_plus_int(one_one_int,one_one_int),X124),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X66,X67] : times_times_int(X66,X67) = times_times_int(X67,X66),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X78,X79,X80] : plus_plus_int(X78,plus_plus_int(X79,X80)) = plus_plus_int(plus_plus_int(X78,X79),X80),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_248_number__of__add,axiom,
! [X139,X140] : number_number_of_int(plus_plus_int(X139,X140)) = plus_plus_int(number_number_of_int(X139),number_number_of_int(X140)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_number__of__add) ).
fof(fact_37_zless__le,axiom,
! [X19,X20] :
( ( is_int(X20)
& is_int(X19) )
=> ( ord_less_int(X19,X20)
<=> ( X19 != X20
& ord_less_eq_int(X19,X20) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zless__le) ).
fof(fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X81,X82,X83] : plus_plus_int(X81,plus_plus_int(X82,X83)) = plus_plus_int(X82,plus_plus_int(X81,X83)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( ord_less_int(one_one_int,t)
=> ? [X3,X4] :
( plus_plus_int(power_power_int(X3,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X4,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
& is_int(X4)
& is_int(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(fact_0_tpos,axiom,
ord_less_eq_int(one_one_int,t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).
fof(gsy_v_t____,axiom,
is_int(t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_t____) ).
fof(c_0_29,plain,
! [X804] : bit1(X804) = plus_plus_int(plus_plus_int(one_one_int,X804),X804),
inference(variable_rename,[status(thm)],[fact_251_Bit1__def]) ).
fof(c_0_30,plain,
! [X30,X20] :
( ord_less_eq_int(number_number_of_int(X30),number_number_of_int(X20))
<=> ~ ord_less_int(number_number_of_int(X20),number_number_of_int(X30)) ),
inference(fof_simplification,[status(thm)],[fact_50_le__number__of__eq__not__less]) ).
cnf(c_0_31,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(split_conjunct,[status(thm)],[fact_264_semiring__norm_I110_J]) ).
cnf(c_0_32,plain,
bit1(X1) = plus_plus_int(plus_plus_int(one_one_int,X1),X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_33,plain,
! [X568,X569] : plus_plus_int(X568,X569) = plus_plus_int(X569,X568),
inference(variable_rename,[status(thm)],[fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(c_0_34,plain,
! [X683] : times_times_nat(one_one_nat,X683) = X683,
inference(variable_rename,[status(thm)],[fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J]) ).
cnf(c_0_35,plain,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(split_conjunct,[status(thm)],[fact_79_Numeral1__eq1__nat]) ).
fof(c_0_36,plain,
! [X705] :
( plus_plus_int(X705,pls) = X705
| ~ is_int(X705) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_201_add__Pls__right])])]) ).
fof(c_0_37,plain,
! [X364,X365] :
( ( ord_less_eq_int(number_number_of_int(X364),number_number_of_int(X365))
| ord_less_int(number_number_of_int(X365),number_number_of_int(X364)) )
& ( ~ ord_less_int(number_number_of_int(X365),number_number_of_int(X364))
| ~ ord_less_eq_int(number_number_of_int(X364),number_number_of_int(X365)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
cnf(c_0_38,plain,
one_one_int = number_number_of_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls)),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
plus_plus_int(X1,X2) = plus_plus_int(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_40,negated_conjecture,
~ ? [X3,X4] : plus_plus_int(power_power_int(X3,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X4,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_41,plain,
! [X331] : plus_plus_int(number_number_of_int(X331),one_one_int) = number_number_of_int(plus_plus_int(X331,bit1(pls))),
inference(variable_rename,[status(thm)],[fact_31_add__special_I3_J]) ).
cnf(c_0_42,plain,
times_times_nat(one_one_nat,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,plain,
one_one_nat = number_number_of_nat(plus_plus_int(plus_plus_int(one_one_int,pls),pls)),
inference(rw,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_44,plain,
( ~ is_int(X1)
| plus_plus_int(X1,pls) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,hypothesis,
is_int(one_one_int),
inference(split_conjunct,[status(thm)],[gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint]) ).
fof(c_0_46,plain,
! [X40,X41] :
( ( ~ ord_less_int(X41,pls)
=> times_times_nat(number_number_of_nat(X41),number_number_of_nat(X40)) = number_number_of_nat(times_times_int(X41,X40)) )
& ( ord_less_int(X41,pls)
=> times_times_nat(number_number_of_nat(X41),number_number_of_nat(X40)) = zero_zero_nat ) ),
inference(fof_simplification,[status(thm)],[fact_562_mult__nat__number__of]) ).
fof(c_0_47,plain,
! [X763,X764] : plus_plus_int(X763,times_times_int(X764,X763)) = times_times_int(plus_plus_int(X764,one_one_int),X763),
inference(variable_rename,[status(thm)],[fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).
fof(c_0_48,plain,
! [X702] : times_times_int(pls,X702) = pls,
inference(variable_rename,[status(thm)],[fact_199_mult__Pls]) ).
cnf(c_0_49,plain,
( ~ ord_less_int(number_number_of_int(X2),number_number_of_int(X1))
| ~ ord_less_eq_int(number_number_of_int(X1),number_number_of_int(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_50,plain,
number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,one_one_int))) = one_one_int,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_39]) ).
cnf(c_0_51,plain,
zero_zero_int = number_number_of_int(pls),
inference(split_conjunct,[status(thm)],[fact_390_semiring__norm_I112_J]) ).
cnf(c_0_52,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_356_Pls__def]) ).
cnf(c_0_53,plain,
ord_less_eq_int(zero_zero_int,one_one_int),
inference(split_conjunct,[status(thm)],[fact_692_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]) ).
fof(c_0_54,negated_conjecture,
! [X1659,X1660] : plus_plus_int(power_power_int(X1659,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1660,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])]) ).
fof(c_0_55,plain,
! [X709] : bit0(X709) = plus_plus_int(X709,X709),
inference(variable_rename,[status(thm)],[fact_204_Bit0__def]) ).
fof(c_0_56,plain,
! [X826] : times_times_int(X826,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(X826,X826),
inference(variable_rename,[status(thm)],[fact_280_semiring__mult__2__right]) ).
fof(c_0_57,plain,
! [X329] : plus_plus_int(one_one_int,number_number_of_int(X329)) = number_number_of_int(plus_plus_int(bit1(pls),X329)),
inference(variable_rename,[status(thm)],[fact_29_add__special_I2_J]) ).
cnf(c_0_58,plain,
plus_plus_int(number_number_of_int(X1),one_one_int) = number_number_of_int(plus_plus_int(X1,bit1(pls))),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_59,plain,
( ( t != one_one_int
| plus_plus_int(power_power_int(esk1_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk2_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) )
& ( t != one_one_int
| is_int(esk2_0) )
& ( t != one_one_int
| is_int(esk1_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])])])]) ).
cnf(c_0_60,plain,
times_times_nat(number_number_of_nat(plus_plus_int(plus_plus_int(one_one_int,pls),pls)),X1) = X1,
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_61,hypothesis,
plus_plus_int(pls,one_one_int) = one_one_int,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_39]) ).
fof(c_0_62,plain,
! [X1325,X1326] :
( ( times_times_nat(number_number_of_nat(X1326),number_number_of_nat(X1325)) = number_number_of_nat(times_times_int(X1326,X1325))
| ord_less_int(X1326,pls) )
& ( times_times_nat(number_number_of_nat(X1326),number_number_of_nat(X1325)) = zero_zero_nat
| ~ ord_less_int(X1326,pls) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])]) ).
cnf(c_0_63,plain,
plus_plus_int(X1,times_times_int(X2,X1)) = times_times_int(plus_plus_int(X2,one_one_int),X1),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_64,plain,
times_times_int(pls,X1) = pls,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_65,plain,
( ~ ord_less_eq_int(number_number_of_int(X1),one_one_int)
| ~ ord_less_int(one_one_int,number_number_of_int(X1)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_66,plain,
number_number_of_int(pls) = pls,
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_67,plain,
ord_less_eq_int(pls,one_one_int),
inference(rw,[status(thm)],[c_0_53,c_0_52]) ).
cnf(c_0_68,negated_conjecture,
plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_69,plain,
bit0(X1) = plus_plus_int(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_70,plain,
! [X767] : plus_plus_int(X767,X767) = times_times_int(plus_plus_int(one_one_int,one_one_int),X767),
inference(variable_rename,[status(thm)],[fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).
fof(c_0_71,plain,
! [X514,X515] : times_times_int(X514,X515) = times_times_int(X515,X514),
inference(variable_rename,[status(thm)],[fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
fof(c_0_72,plain,
! [X552,X553,X554] : plus_plus_int(X552,plus_plus_int(X553,X554)) = plus_plus_int(plus_plus_int(X552,X553),X554),
inference(variable_rename,[status(thm)],[fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
cnf(c_0_73,plain,
times_times_int(X1,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_74,plain,
plus_plus_int(one_one_int,number_number_of_int(X1)) = number_number_of_int(plus_plus_int(bit1(pls),X1)),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
fof(c_0_75,plain,
! [X798,X799] : number_number_of_int(plus_plus_int(X798,X799)) = plus_plus_int(number_number_of_int(X798),number_number_of_int(X799)),
inference(variable_rename,[status(thm)],[fact_248_number__of__add]) ).
cnf(c_0_76,plain,
plus_plus_int(number_number_of_int(X1),one_one_int) = number_number_of_int(plus_plus_int(X1,plus_plus_int(plus_plus_int(one_one_int,pls),pls))),
inference(rw,[status(thm)],[c_0_58,c_0_32]) ).
fof(c_0_77,plain,
! [X19,X20] :
( ( is_int(X20)
& is_int(X19) )
=> ( ord_less_int(X19,X20)
<=> ( X19 != X20
& ord_less_eq_int(X19,X20) ) ) ),
inference(fof_simplification,[status(thm)],[fact_37_zless__le]) ).
cnf(c_0_78,plain,
( t != one_one_int
| plus_plus_int(power_power_int(esk1_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk2_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_79,plain,
! [X561,X562,X563] : plus_plus_int(X561,plus_plus_int(X562,X563)) = plus_plus_int(X562,plus_plus_int(X561,X563)),
inference(variable_rename,[status(thm)],[fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
cnf(c_0_80,plain,
times_times_nat(number_number_of_nat(one_one_int),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_39]),c_0_39]),c_0_61]),c_0_61]) ).
cnf(c_0_81,plain,
( times_times_nat(number_number_of_nat(X1),number_number_of_nat(X2)) = number_number_of_nat(times_times_int(X1,X2))
| ord_less_int(X1,pls) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_82,hypothesis,
times_times_int(one_one_int,X1) = plus_plus_int(X1,pls),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_61]),c_0_64]) ).
cnf(c_0_83,plain,
~ ord_less_int(one_one_int,pls),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67])]) ).
cnf(c_0_84,negated_conjecture,
plus_plus_int(power_power_int(X1,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),power_power_int(X2,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))))) != plus_plus_int(times_times_int(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)),plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),m),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)],[c_0_68,c_0_69]),c_0_69]),c_0_69]),c_0_69]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_85,plain,
plus_plus_int(X1,X1) = times_times_int(plus_plus_int(one_one_int,one_one_int),X1),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_86,plain,
times_times_int(X1,X2) = times_times_int(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_87,plain,
plus_plus_int(X1,plus_plus_int(X2,X3)) = plus_plus_int(plus_plus_int(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_88,plain,
times_times_int(X1,number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))) = plus_plus_int(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_69]),c_0_32]),c_0_32]) ).
cnf(c_0_89,plain,
plus_plus_int(one_one_int,number_number_of_int(X1)) = number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),X1)),
inference(rw,[status(thm)],[c_0_74,c_0_32]) ).
cnf(c_0_90,plain,
number_number_of_int(plus_plus_int(X1,X2)) = plus_plus_int(number_number_of_int(X1),number_number_of_int(X2)),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_91,hypothesis,
number_number_of_int(one_one_int) = one_one_int,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_61]),c_0_61]) ).
cnf(c_0_92,plain,
number_number_of_int(plus_plus_int(X1,plus_plus_int(pls,plus_plus_int(pls,one_one_int)))) = plus_plus_int(one_one_int,number_number_of_int(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_39]),c_0_39]),c_0_39]) ).
fof(c_0_93,plain,
( ( ~ ord_less_int(one_one_int,t)
| plus_plus_int(power_power_int(esk3_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk4_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) )
& ( ~ ord_less_int(one_one_int,t)
| is_int(esk4_0) )
& ( ~ ord_less_int(one_one_int,t)
| is_int(esk3_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])])])]) ).
fof(c_0_94,plain,
! [X336,X337] :
( ( ~ is_int(X337)
| ~ is_int(X336)
| ord_less_int(X336,X337)
| X336 = X337
| ~ ord_less_eq_int(X336,X337) )
& ( ~ is_int(X337)
| ~ is_int(X336)
| ~ ord_less_int(X336,X337)
| X336 != X337 )
& ( ~ is_int(X337)
| ~ is_int(X336)
| ~ ord_less_int(X336,X337)
| ord_less_eq_int(X336,X337) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])])]) ).
cnf(c_0_95,plain,
( t != one_one_int
| plus_plus_int(power_power_int(esk1_0,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),power_power_int(esk2_0,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))))) = plus_plus_int(times_times_int(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)),plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),m),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)],[c_0_78,c_0_69]),c_0_69]),c_0_69]),c_0_69]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_96,plain,
plus_plus_int(X1,plus_plus_int(X2,X3)) = plus_plus_int(X2,plus_plus_int(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_97,plain,
number_number_of_nat(plus_plus_int(X1,pls)) = number_number_of_nat(X1),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_83]) ).
cnf(c_0_98,negated_conjecture,
plus_plus_int(power_power_int(X1,number_number_of_nat(plus_plus_int(plus_plus_int(pls,plus_plus_int(pls,one_one_int)),plus_plus_int(pls,plus_plus_int(pls,one_one_int))))),power_power_int(X2,number_number_of_nat(plus_plus_int(plus_plus_int(pls,plus_plus_int(pls,one_one_int)),plus_plus_int(pls,plus_plus_int(pls,one_one_int)))))) != plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(plus_plus_int(pls,plus_plus_int(pls,one_one_int)),plus_plus_int(pls,plus_plus_int(pls,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_84,c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_85]),c_0_86]),c_0_39]) ).
cnf(c_0_99,hypothesis,
plus_plus_int(pls,plus_plus_int(one_one_int,X1)) = plus_plus_int(one_one_int,X1),
inference(spm,[status(thm)],[c_0_87,c_0_61]) ).
cnf(c_0_100,plain,
times_times_int(X1,plus_plus_int(one_one_int,one_one_int)) = plus_plus_int(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89]),c_0_39]),c_0_39]),c_0_50]) ).
cnf(c_0_101,hypothesis,
number_number_of_int(plus_plus_int(one_one_int,X1)) = plus_plus_int(one_one_int,number_number_of_int(X1)),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_102,plain,
number_number_of_int(plus_plus_int(X1,one_one_int)) = plus_plus_int(one_one_int,number_number_of_int(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_61]),c_0_61]) ).
cnf(c_0_103,plain,
( ~ ord_less_int(one_one_int,t)
| plus_plus_int(power_power_int(esk3_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk4_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_104,plain,
( ~ is_int(X2)
| ~ is_int(X1)
| ~ ord_less_eq_int(X1,X2)
| ord_less_int(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_105,plain,
ord_less_eq_int(one_one_int,t),
inference(split_conjunct,[status(thm)],[fact_0_tpos]) ).
cnf(c_0_106,plain,
is_int(t),
inference(split_conjunct,[status(thm)],[gsy_v_t____]) ).
cnf(c_0_107,plain,
( t != one_one_int
| plus_plus_int(power_power_int(esk1_0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int))))))),power_power_int(esk2_0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int)))))))) = plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_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)],[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)],[inference(rw,[status(thm)],[c_0_95,c_0_87]),c_0_39]),c_0_39]),c_0_39]),c_0_87]),c_0_96]),c_0_96]),c_0_96]),c_0_87]),c_0_39]),c_0_39]),c_0_39]),c_0_87]),c_0_96]),c_0_96]),c_0_96]),c_0_87]),c_0_39]),c_0_39]),c_0_39]),c_0_87]),c_0_96]),c_0_96]),c_0_96]),c_0_87]),c_0_39]),c_0_39]),c_0_39]),c_0_87]),c_0_96]),c_0_96]),c_0_96]),c_0_87]),c_0_87]),c_0_87]),c_0_87]),c_0_87]),c_0_96]),c_0_96]),c_0_96]),c_0_96]),c_0_96]),c_0_96]),c_0_96]),c_0_96]),c_0_86]),c_0_39]) ).
cnf(c_0_108,plain,
number_number_of_nat(plus_plus_int(pls,X1)) = number_number_of_nat(X1),
inference(spm,[status(thm)],[c_0_97,c_0_39]) ).
cnf(c_0_109,plain,
number_number_of_int(plus_plus_int(pls,X1)) = plus_plus_int(pls,number_number_of_int(X1)),
inference(spm,[status(thm)],[c_0_90,c_0_66]) ).
cnf(c_0_110,negated_conjecture,
plus_plus_int(power_power_int(X1,number_number_of_nat(plus_plus_int(one_one_int,one_one_int))),power_power_int(X2,number_number_of_nat(plus_plus_int(one_one_int,one_one_int)))) != plus_plus_int(one_one_int,times_times_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int))),m)),
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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_87]),c_0_87]),c_0_96]),c_0_96]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_87]),c_0_87]),c_0_96]),c_0_96]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_87]),c_0_87]),c_0_96]),c_0_96]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_100]),c_0_87]),c_0_101]),c_0_101]),c_0_102]),c_0_91]),c_0_86]) ).
cnf(c_0_111,plain,
( ~ ord_less_int(one_one_int,t)
| plus_plus_int(power_power_int(esk3_0,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),power_power_int(esk4_0,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))))) = plus_plus_int(times_times_int(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)),plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),m),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)],[c_0_103,c_0_69]),c_0_69]),c_0_69]),c_0_69]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_112,plain,
( ord_less_int(one_one_int,t)
| t = one_one_int ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]),c_0_45])]) ).
cnf(c_0_113,plain,
t != one_one_int,
inference(sr,[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108]),c_0_99]),c_0_99]),c_0_99]),c_0_108]),c_0_99]),c_0_99]),c_0_99]),c_0_109]),c_0_109]),c_0_109]),c_0_109]),c_0_109]),c_0_109]),c_0_109]),c_0_109]),c_0_101]),c_0_101]),c_0_102]),c_0_91]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_86]),c_0_110]) ).
cnf(c_0_114,plain,
( ~ ord_less_int(one_one_int,t)
| plus_plus_int(power_power_int(esk3_0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int))))))),power_power_int(esk4_0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int)))))))) = plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_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)],[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)],[inference(rw,[status(thm)],[c_0_111,c_0_87]),c_0_39]),c_0_39]),c_0_39]),c_0_87]),c_0_96]),c_0_96]),c_0_96]),c_0_87]),c_0_39]),c_0_39]),c_0_39]),c_0_87]),c_0_96]),c_0_96]),c_0_96]),c_0_87]),c_0_39]),c_0_39]),c_0_39]),c_0_87]),c_0_96]),c_0_96]),c_0_96]),c_0_87]),c_0_39]),c_0_39]),c_0_39]),c_0_87]),c_0_96]),c_0_96]),c_0_96]),c_0_87]),c_0_87]),c_0_87]),c_0_87]),c_0_87]),c_0_96]),c_0_96]),c_0_96]),c_0_96]),c_0_96]),c_0_96]),c_0_96]),c_0_96]),c_0_86]),c_0_39]) ).
cnf(c_0_115,plain,
ord_less_int(one_one_int,t),
inference(sr,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_116,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_108]),c_0_99]),c_0_99]),c_0_99]),c_0_108]),c_0_99]),c_0_99]),c_0_99]),c_0_109]),c_0_109]),c_0_109]),c_0_109]),c_0_109]),c_0_109]),c_0_109]),c_0_109]),c_0_101]),c_0_101]),c_0_102]),c_0_91]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_86]),c_0_115])]),c_0_110]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM926+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 03:18:47 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.02/0.41 Running first-order theorem proving
% 0.02/0.41 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
% 1.98/0.79 % Version: 3.5.1
% 1.98/0.79 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.98/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.98/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.98/0.79 % Starting new_bool_3 with 300s (1) cores
% 1.98/0.79 % Starting new_bool_1 with 300s (1) cores
% 1.98/0.79 % Starting sh5l with 300s (1) cores
% 1.98/0.79 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1889258 completed with status 0
% 1.98/0.79 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.98/0.79 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.98/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.98/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.98/0.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.98/0.79 % No SInE strategy applied
% 1.98/0.79 % Search class: FGHSM-FSLM31-DFFFFFNN
% 1.98/0.79 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.98/0.79 % Starting SubtermCWHack with 136s (1) cores
% 1.98/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.98/0.79 % Starting C07_19_nc_SAT001_MinMin_p005000_rr with 354s (1) cores
% 1.98/0.79 % Starting U----_206c_10_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.98/0.79 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 1.98/0.79 % C07_19_nc_SAT001_MinMin_p005000_rr with pid 1889267 completed with status 0
% 1.98/0.79 % Result found by C07_19_nc_SAT001_MinMin_p005000_rr
% 1.98/0.79 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.98/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.98/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.98/0.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.98/0.79 % No SInE strategy applied
% 1.98/0.79 % Search class: FGHSM-FSLM31-DFFFFFNN
% 1.98/0.79 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.98/0.79 % Starting SubtermCWHack with 136s (1) cores
% 1.98/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.98/0.79 % Starting C07_19_nc_SAT001_MinMin_p005000_rr with 354s (1) cores
% 1.98/0.79 % Preprocessing time : 0.009 s
% 1.98/0.79 % Presaturation interreduction done
% 1.98/0.79
% 1.98/0.79 % Proof found!
% 1.98/0.79 % SZS status Theorem
% 1.98/0.79 % SZS output start CNFRefutation
% See solution above
% 1.98/0.79 % Parsed axioms : 717
% 1.98/0.79 % Removed by relevancy pruning/SinE : 0
% 1.98/0.79 % Initial clauses : 964
% 1.98/0.79 % Removed in clause preprocessing : 24
% 1.98/0.79 % Initial clauses in saturation : 940
% 1.98/0.79 % Processed clauses : 5825
% 1.98/0.79 % ...of these trivial : 175
% 1.98/0.79 % ...subsumed : 3575
% 1.98/0.79 % ...remaining for further processing : 2074
% 1.98/0.79 % Other redundant clauses eliminated : 104
% 1.98/0.79 % Clauses deleted for lack of memory : 0
% 1.98/0.79 % Backward-subsumed : 95
% 1.98/0.79 % Backward-rewritten : 170
% 1.98/0.79 % Generated clauses : 20771
% 1.98/0.79 % ...of the previous two non-redundant : 18197
% 1.98/0.79 % ...aggressively subsumed : 0
% 1.98/0.79 % Contextual simplify-reflections : 1
% 1.98/0.79 % Paramodulations : 20670
% 1.98/0.79 % Factorizations : 5
% 1.98/0.79 % NegExts : 0
% 1.98/0.79 % Equation resolutions : 109
% 1.98/0.79 % Disequality decompositions : 0
% 1.98/0.79 % Total rewrite steps : 20388
% 1.98/0.79 % ...of those cached : 18200
% 1.98/0.79 % Propositional unsat checks : 0
% 1.98/0.79 % Propositional check models : 0
% 1.98/0.79 % Propositional check unsatisfiable : 0
% 1.98/0.79 % Propositional clauses : 0
% 1.98/0.79 % Propositional clauses after purity: 0
% 1.98/0.79 % Propositional unsat core size : 0
% 1.98/0.79 % Propositional preprocessing time : 0.000
% 1.98/0.79 % Propositional encoding time : 0.000
% 1.98/0.79 % Propositional solver time : 0.000
% 1.98/0.79 % Success case prop preproc time : 0.000
% 1.98/0.79 % Success case prop encoding time : 0.000
% 1.98/0.79 % Success case prop solver time : 0.000
% 1.98/0.79 % Current number of processed clauses : 1080
% 1.98/0.79 % Positive orientable unit clauses : 313
% 1.98/0.79 % Positive unorientable unit clauses: 46
% 1.98/0.79 % Negative unit clauses : 303
% 1.98/0.79 % Non-unit-clauses : 418
% 1.98/0.79 % Current number of unprocessed clauses: 13838
% 1.98/0.79 % ...number of literals in the above : 25316
% 1.98/0.79 % Current number of archived formulas : 0
% 1.98/0.79 % Current number of archived clauses : 920
% 1.98/0.79 % Clause-clause subsumption calls (NU) : 51593
% 1.98/0.79 % Rec. Clause-clause subsumption calls : 26273
% 1.98/0.79 % Non-unit clause-clause subsumptions : 475
% 1.98/0.79 % Unit Clause-clause subsumption calls : 10447
% 1.98/0.79 % Rewrite failures with RHS unbound : 6
% 1.98/0.79 % BW rewrite match attempts : 2189
% 1.98/0.79 % BW rewrite match successes : 666
% 1.98/0.79 % Condensation attempts : 0
% 1.98/0.79 % Condensation successes : 0
% 1.98/0.79 % Termbank termtop insertions : 347234
% 1.98/0.79 % Search garbage collected termcells : 9050
% 1.98/0.79
% 1.98/0.79 % -------------------------------------------------
% 1.98/0.79 % User time : 0.308 s
% 1.98/0.79 % System time : 0.024 s
% 1.98/0.79 % Total time : 0.332 s
% 1.98/0.79 % Maximum resident set size: 7160 pages
% 1.98/0.79
% 1.98/0.79 % -------------------------------------------------
% 1.98/0.79 % User time : 1.345 s
% 1.98/0.79 % System time : 0.102 s
% 1.98/0.79 % Total time : 1.447 s
% 1.98/0.79 % Maximum resident set size: 5888 pages
% 1.98/0.79 % E exiting
%------------------------------------------------------------------------------