TSTP Solution File: NUM924_2 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM924_2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.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 : 300s
% DateTime : Thu Aug 31 11:33:38 EDT 2023
% Result : Theorem 2.39s 1.20s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 23
% Syntax : Number of formulae : 132 ( 132 unt; 0 typ; 0 def)
% Number of atoms : 585 ( 104 equ)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 12 ( 12 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 453 ( 453 fml; 0 var)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 24 ( 22 usr; 11 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 150 ( 1 sgn; 110 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
tff(f3,axiom,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
tff(f4,axiom,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
tff(f35,axiom,
! [X10: int] : ( number_number_of_int(X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_number__of__is__id) ).
tff(f36,axiom,
! [X11: int,X9: int] : ( times_times_int(X11,X9) = times_times_int(X9,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zmult__commute) ).
tff(f42,axiom,
! [X15: int,X16: int,X17: int] : ( times_times_int(times_times_int(X15,X16),X17) = times_times_int(X15,times_times_int(X16,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_zmult__assoc) ).
tff(f88,axiom,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_nat__1__add__1) ).
tff(f131,axiom,
! [X15: int,X16: int,X17: int] : ( plus_plus_int(plus_plus_int(X15,X16),X17) = plus_plus_int(X15,plus_plus_int(X16,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_zadd__assoc) ).
tff(f133,axiom,
! [X11: int,X9: int] : ( plus_plus_int(X9,X11) = plus_plus_int(X11,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_zadd__commute) ).
tff(f171,axiom,
zero_zero_int = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_Pls__def) ).
tff(f179,axiom,
! [X10: int] : ( plus_plus_int(pls,X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_add__Pls) ).
tff(f181,axiom,
! [X10: int] : ( bit0(X10) = plus_plus_int(X10,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Bit0__def) ).
tff(f202,axiom,
! [X70: int] : ( power_power_int(X70,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(X70,X70) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_power2__eq__square) ).
tff(f235,axiom,
! [X10: int] : ( bit1(X10) = plus_plus_int(plus_plus_int(one_one_int,X10),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_Bit1__def) ).
tff(f315,axiom,
! [X118: real,X119: real,X120: real] : ( times_times_real(times_times_real(X118,X119),X120) = times_times_real(X118,times_times_real(X119,X120)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
tff(f316,axiom,
! [X118: nat,X119: nat,X120: nat] : ( times_times_nat(times_times_nat(X118,X119),X120) = times_times_nat(X118,times_times_nat(X119,X120)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
tff(f324,axiom,
! [X127: real,X128: real] : ( times_times_real(X127,X128) = times_times_real(X128,X127) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(f325,axiom,
! [X127: nat,X128: nat] : ( times_times_nat(X127,X128) = times_times_nat(X128,X127) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(f327,axiom,
! [X129: real,X130: real] : ( plus_plus_real(X129,X130) = plus_plus_real(X130,X129) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f328,axiom,
! [X129: nat,X130: nat] : ( plus_plus_nat(X129,X130) = plus_plus_nat(X130,X129) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f333,axiom,
! [X134: real,X135: real,X136: real] : ( plus_plus_real(X134,plus_plus_real(X135,X136)) = plus_plus_real(plus_plus_real(X134,X135),X136) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
tff(f334,axiom,
! [X134: nat,X135: nat,X136: nat] : ( plus_plus_nat(X134,plus_plus_nat(X135,X136)) = plus_plus_nat(plus_plus_nat(X134,X135),X136) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
tff(f363,axiom,
! [X153: int] : ( zero_zero_int = times_times_int(X153,zero_zero_int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
tff(f699,conjecture,
ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f700,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(negated_conjecture,[],[f699]) ).
tff(f717,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(rectify,[],[f35]) ).
tff(f718,plain,
! [X0: int,X1: int] : ( times_times_int(X0,X1) = times_times_int(X1,X0) ),
inference(rectify,[],[f36]) ).
tff(f724,plain,
! [X0: int,X1: int,X2: int] : ( times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X1,X2)) ),
inference(rectify,[],[f42]) ).
tff(f806,plain,
! [X0: int,X1: int,X2: int] : ( plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)) ),
inference(rectify,[],[f131]) ).
tff(f808,plain,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
inference(rectify,[],[f133]) ).
tff(f848,plain,
! [X0: int] : ( plus_plus_int(pls,X0) = X0 ),
inference(rectify,[],[f179]) ).
tff(f850,plain,
! [X0: int] : ( bit0(X0) = plus_plus_int(X0,X0) ),
inference(rectify,[],[f181]) ).
tff(f871,plain,
! [X0: int] : ( power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(X0,X0) ),
inference(rectify,[],[f202]) ).
tff(f895,plain,
! [X0: int] : ( bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0) ),
inference(rectify,[],[f235]) ).
tff(f955,plain,
! [X0: real,X1: real,X2: real] : ( times_times_real(times_times_real(X0,X1),X2) = times_times_real(X0,times_times_real(X1,X2)) ),
inference(rectify,[],[f315]) ).
tff(f956,plain,
! [X0: nat,X1: nat,X2: nat] : ( times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(X0,times_times_nat(X1,X2)) ),
inference(rectify,[],[f316]) ).
tff(f964,plain,
! [X0: real,X1: real] : ( times_times_real(X0,X1) = times_times_real(X1,X0) ),
inference(rectify,[],[f324]) ).
tff(f965,plain,
! [X0: nat,X1: nat] : ( times_times_nat(X0,X1) = times_times_nat(X1,X0) ),
inference(rectify,[],[f325]) ).
tff(f967,plain,
! [X0: real,X1: real] : ( plus_plus_real(X0,X1) = plus_plus_real(X1,X0) ),
inference(rectify,[],[f327]) ).
tff(f968,plain,
! [X0: nat,X1: nat] : ( plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0) ),
inference(rectify,[],[f328]) ).
tff(f973,plain,
! [X0: real,X1: real,X2: real] : ( plus_plus_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(plus_plus_real(X0,X1),X2) ),
inference(rectify,[],[f333]) ).
tff(f974,plain,
! [X0: nat,X1: nat,X2: nat] : ( plus_plus_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(plus_plus_nat(X0,X1),X2) ),
inference(rectify,[],[f334]) ).
tff(f1003,plain,
! [X0: int] : ( zero_zero_int = times_times_int(X0,zero_zero_int) ),
inference(rectify,[],[f363]) ).
tff(f1313,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(flattening,[],[f700]) ).
tff(f1850,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
inference(cnf_transformation,[],[f3]) ).
tff(f1851,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(cnf_transformation,[],[f4]) ).
tff(f1894,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(cnf_transformation,[],[f717]) ).
tff(f1895,plain,
! [X0: int,X1: int] : ( times_times_int(X0,X1) = times_times_int(X1,X0) ),
inference(cnf_transformation,[],[f718]) ).
tff(f1904,plain,
! [X2: int,X0: int,X1: int] : ( times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X1,X2)) ),
inference(cnf_transformation,[],[f724]) ).
tff(f1979,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnf_transformation,[],[f88]) ).
tff(f2048,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)) ),
inference(cnf_transformation,[],[f806]) ).
tff(f2050,plain,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
inference(cnf_transformation,[],[f808]) ).
tff(f2102,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f171]) ).
tff(f2114,plain,
! [X0: int] : ( plus_plus_int(pls,X0) = X0 ),
inference(cnf_transformation,[],[f848]) ).
tff(f2116,plain,
! [X0: int] : ( bit0(X0) = plus_plus_int(X0,X0) ),
inference(cnf_transformation,[],[f850]) ).
tff(f2137,plain,
! [X0: int] : ( power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(X0,X0) ),
inference(cnf_transformation,[],[f871]) ).
tff(f2181,plain,
! [X0: int] : ( bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0) ),
inference(cnf_transformation,[],[f895]) ).
tff(f2285,plain,
! [X2: real,X0: real,X1: real] : ( times_times_real(times_times_real(X0,X1),X2) = times_times_real(X0,times_times_real(X1,X2)) ),
inference(cnf_transformation,[],[f955]) ).
tff(f2286,plain,
! [X2: nat,X0: nat,X1: nat] : ( times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(X0,times_times_nat(X1,X2)) ),
inference(cnf_transformation,[],[f956]) ).
tff(f2294,plain,
! [X0: real,X1: real] : ( times_times_real(X0,X1) = times_times_real(X1,X0) ),
inference(cnf_transformation,[],[f964]) ).
tff(f2295,plain,
! [X0: nat,X1: nat] : ( times_times_nat(X0,X1) = times_times_nat(X1,X0) ),
inference(cnf_transformation,[],[f965]) ).
tff(f2297,plain,
! [X0: real,X1: real] : ( plus_plus_real(X0,X1) = plus_plus_real(X1,X0) ),
inference(cnf_transformation,[],[f967]) ).
tff(f2298,plain,
! [X0: nat,X1: nat] : ( plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0) ),
inference(cnf_transformation,[],[f968]) ).
tff(f2303,plain,
! [X2: real,X0: real,X1: real] : ( plus_plus_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(plus_plus_real(X0,X1),X2) ),
inference(cnf_transformation,[],[f973]) ).
tff(f2304,plain,
! [X2: nat,X0: nat,X1: nat] : ( plus_plus_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(plus_plus_nat(X0,X1),X2) ),
inference(cnf_transformation,[],[f974]) ).
tff(f2337,plain,
! [X0: int] : ( zero_zero_int = times_times_int(X0,zero_zero_int) ),
inference(cnf_transformation,[],[f1003]) ).
tff(f2778,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(cnf_transformation,[],[f1313]) ).
tff(f2780,plain,
ord_less_int(times_times_int(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),t),times_times_int(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),pls)),
inference(definition_unfolding,[],[f1850,f2116,f2116,f2181,f2116,f2116,f2181,f2102]) ).
tff(f2781,plain,
times_times_int(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),t) = plus_plus_int(power_power_int(s,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)))),one_one_int),
inference(definition_unfolding,[],[f1851,f2116,f2116,f2181,f2116,f2181]) ).
tff(f2856,plain,
plus_plus_nat(one_one_nat,one_one_nat) = 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))),
inference(definition_unfolding,[],[f1979,f2116,f2181]) ).
tff(f2956,plain,
! [X0: int] : ( times_times_int(X0,X0) = power_power_int(X0,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)))) ),
inference(definition_unfolding,[],[f2137,f2116,f2181]) ).
tff(f3054,plain,
! [X0: int] : ( pls = times_times_int(X0,pls) ),
inference(definition_unfolding,[],[f2337,f2102,f2102]) ).
tff(f3187,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,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)))),one_one_int),pls),
inference(definition_unfolding,[],[f2778,f2116,f2181,f2102]) ).
cnf(c_51,plain,
ord_less_int(times_times_int(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),t),times_times_int(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),pls)),
inference(cnf_transformation,[],[f2780]) ).
cnf(c_52,plain,
times_times_int(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),t) = plus_plus_int(power_power_int(s,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)))),one_one_int),
inference(cnf_transformation,[],[f2781]) ).
cnf(c_95,plain,
number_number_of_int(X0_13) = X0_13,
inference(cnf_transformation,[],[f1894]) ).
cnf(c_96,plain,
times_times_int(X0_13,X1_13) = times_times_int(X1_13,X0_13),
inference(cnf_transformation,[],[f1895]) ).
cnf(c_105,plain,
times_times_int(times_times_int(X0_13,X1_13),X2_13) = times_times_int(X0_13,times_times_int(X1_13,X2_13)),
inference(cnf_transformation,[],[f1904]) ).
cnf(c_180,plain,
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_nat(one_one_nat,one_one_nat),
inference(cnf_transformation,[],[f2856]) ).
cnf(c_238,plain,
plus_plus_int(plus_plus_int(X0_13,X1_13),X2_13) = plus_plus_int(X0_13,plus_plus_int(X1_13,X2_13)),
inference(cnf_transformation,[],[f2048]) ).
cnf(c_240,plain,
plus_plus_int(X0_13,X1_13) = plus_plus_int(X1_13,X0_13),
inference(cnf_transformation,[],[f2050]) ).
cnf(c_303,plain,
plus_plus_int(pls,X0_13) = X0_13,
inference(cnf_transformation,[],[f2114]) ).
cnf(c_325,plain,
power_power_int(X0_13,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)))) = times_times_int(X0_13,X0_13),
inference(cnf_transformation,[],[f2956]) ).
cnf(c_472,plain,
times_times_real(times_times_real(X0_15,X1_15),X2_15) = times_times_real(X0_15,times_times_real(X1_15,X2_15)),
inference(cnf_transformation,[],[f2285]) ).
cnf(c_473,plain,
times_times_nat(times_times_nat(X0_14,X1_14),X2_14) = times_times_nat(X0_14,times_times_nat(X1_14,X2_14)),
inference(cnf_transformation,[],[f2286]) ).
cnf(c_481,plain,
times_times_real(X0_15,X1_15) = times_times_real(X1_15,X0_15),
inference(cnf_transformation,[],[f2294]) ).
cnf(c_482,plain,
times_times_nat(X0_14,X1_14) = times_times_nat(X1_14,X0_14),
inference(cnf_transformation,[],[f2295]) ).
cnf(c_484,plain,
plus_plus_real(X0_15,X1_15) = plus_plus_real(X1_15,X0_15),
inference(cnf_transformation,[],[f2297]) ).
cnf(c_485,plain,
plus_plus_nat(X0_14,X1_14) = plus_plus_nat(X1_14,X0_14),
inference(cnf_transformation,[],[f2298]) ).
cnf(c_490,plain,
plus_plus_real(plus_plus_real(X0_15,X1_15),X2_15) = plus_plus_real(X0_15,plus_plus_real(X1_15,X2_15)),
inference(cnf_transformation,[],[f2303]) ).
cnf(c_491,plain,
plus_plus_nat(plus_plus_nat(X0_14,X1_14),X2_14) = plus_plus_nat(X0_14,plus_plus_nat(X1_14,X2_14)),
inference(cnf_transformation,[],[f2304]) ).
cnf(c_524,plain,
times_times_int(X0_13,pls) = pls,
inference(cnf_transformation,[],[f3054]) ).
cnf(c_954,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,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)))),one_one_int),pls),
inference(cnf_transformation,[],[f3187]) ).
cnf(c_1409,plain,
ord_less_int(times_times_int(t,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))))))))))))))),times_times_int(pls,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(theory_normalisation,[status(thm)],[c_51,c_472,c_481,c_473,c_482,c_105,c_96,c_490,c_484,c_491,c_485,c_238,c_240]) ).
cnf(c_1410,plain,
times_times_int(t,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))))))))))))))) = plus_plus_int(one_one_int,power_power_int(s,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)))))))),
inference(theory_normalisation,[status(thm)],[c_52,c_472,c_481,c_473,c_482,c_105,c_96,c_490,c_484,c_491,c_485,c_238,c_240]) ).
cnf(c_1463,plain,
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_nat(one_one_nat,one_one_nat),
inference(theory_normalisation,[status(thm)],[c_180,c_472,c_481,c_473,c_482,c_105,c_96,c_490,c_484,c_491,c_485,c_238,c_240]) ).
cnf(c_1514,plain,
power_power_int(X0_13,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))))))) = times_times_int(X0_13,X0_13),
inference(theory_normalisation,[status(thm)],[c_325,c_472,c_481,c_473,c_482,c_105,c_96,c_490,c_484,c_491,c_485,c_238,c_240]) ).
cnf(c_1619,negated_conjecture,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,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)))))))),pls),
inference(theory_normalisation,[status(thm)],[c_954,c_472,c_481,c_473,c_482,c_105,c_96,c_490,c_484,c_491,c_485,c_238,c_240]) ).
cnf(c_7322,plain,
number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(ac_demodulation,[status(thm)],[c_1463,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_7323,plain,
number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls)))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(ac_demodulation,[status(thm)],[c_7322,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_7324,plain,
number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(pls,one_one_int))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(ac_demodulation,[status(thm)],[c_7323,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_7325,plain,
number_number_of_nat(plus_plus_int(one_one_int,one_one_int)) = plus_plus_nat(one_one_nat,one_one_nat),
inference(ac_demodulation,[status(thm)],[c_7324,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_7511,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))))))),pls),
inference(ac_demodulation,[status(thm)],[c_1619,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_7512,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls)))))),pls),
inference(ac_demodulation,[status(thm)],[c_7511,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_7513,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(pls,one_one_int))))),pls),
inference(ac_demodulation,[status(thm)],[c_7512,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_7514,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,one_one_int)))),pls),
inference(ac_demodulation,[status(thm)],[c_7513,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_7515,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),pls),
inference(light_normalisation,[status(thm)],[c_7514,c_7325]) ).
cnf(c_7528,plain,
power_power_int(X0_13,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls)))))) = times_times_int(X0_13,X0_13),
inference(ac_demodulation,[status(thm)],[c_1514,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_7529,plain,
power_power_int(X0_13,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls))))) = times_times_int(X0_13,X0_13),
inference(ac_demodulation,[status(thm)],[c_7528,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_7530,plain,
power_power_int(X0_13,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(pls,one_one_int)))) = times_times_int(X0_13,X0_13),
inference(ac_demodulation,[status(thm)],[c_7529,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_7531,plain,
power_power_int(X0_13,number_number_of_nat(plus_plus_int(one_one_int,one_one_int))) = times_times_int(X0_13,X0_13),
inference(ac_demodulation,[status(thm)],[c_7530,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_7532,plain,
power_power_int(X0_13,plus_plus_nat(one_one_nat,one_one_nat)) = times_times_int(X0_13,X0_13),
inference(light_normalisation,[status(thm)],[c_7531,c_7325]) ).
cnf(c_7534,plain,
~ ord_less_int(plus_plus_int(one_one_int,times_times_int(s,s)),pls),
inference(demodulation,[status(thm)],[c_7515,c_7532]) ).
cnf(c_8423,plain,
times_times_int(t,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(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls)))))))))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))))))),
inference(ac_demodulation,[status(thm)],[c_1410,c_303,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8424,plain,
times_times_int(t,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(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls))))))))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls)))))),
inference(ac_demodulation,[status(thm)],[c_8423,c_303,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8425,plain,
times_times_int(t,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(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,pls)))))))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(pls,one_one_int))))),
inference(ac_demodulation,[status(thm)],[c_8424,c_303,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8426,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,pls))))))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,one_one_int)))),
inference(ac_demodulation,[status(thm)],[c_8425,c_303,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8427,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,one_one_int)))))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,one_one_int)))),
inference(ac_demodulation,[status(thm)],[c_8426,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8428,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int))))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,one_one_int)))),
inference(ac_demodulation,[status(thm)],[c_8427,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8429,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int)))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,one_one_int)))),
inference(ac_demodulation,[status(thm)],[c_8428,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8430,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,one_one_int)))),
inference(ac_demodulation,[status(thm)],[c_8429,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8431,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int))))))) = plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),
inference(light_normalisation,[status(thm)],[c_8430,c_7325]) ).
cnf(c_8432,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int)))))) = plus_plus_int(one_one_int,times_times_int(s,s)),
inference(demodulation,[status(thm)],[c_8431,c_95,c_7532]) ).
cnf(c_8455,plain,
ord_less_int(times_times_int(t,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(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls)))))))))))))),pls),
inference(ac_demodulation,[status(thm)],[c_1409,c_524,c_303,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8456,plain,
ord_less_int(times_times_int(t,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(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls))))))))))))),pls),
inference(ac_demodulation,[status(thm)],[c_8455,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8457,plain,
ord_less_int(times_times_int(t,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(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,pls)))))))))))),pls),
inference(ac_demodulation,[status(thm)],[c_8456,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8458,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,pls))))))))))),pls),
inference(ac_demodulation,[status(thm)],[c_8457,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8459,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,one_one_int)))))))))),pls),
inference(ac_demodulation,[status(thm)],[c_8458,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8460,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int))))))))),pls),
inference(ac_demodulation,[status(thm)],[c_8459,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8461,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int)))))))),pls),
inference(ac_demodulation,[status(thm)],[c_8460,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8462,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int))))))),pls),
inference(ac_demodulation,[status(thm)],[c_8461,c_303,c_238,c_240,c_491,c_485,c_490,c_484,c_105,c_96,c_473,c_482,c_472,c_481]) ).
cnf(c_8463,plain,
ord_less_int(plus_plus_int(one_one_int,times_times_int(s,s)),pls),
inference(demodulation,[status(thm)],[c_8462,c_95,c_8432]) ).
cnf(c_8464,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_8463,c_7534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM924_2 : TPTP v8.1.2. Released v5.3.0.
% 0.08/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 12:31:53 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.49 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.39/1.20 % SZS status Started for theBenchmark.p
% 2.39/1.20 % SZS status Theorem for theBenchmark.p
% 2.39/1.20
% 2.39/1.20 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.39/1.20
% 2.39/1.20 ------ iProver source info
% 2.39/1.20
% 2.39/1.20 git: date: 2023-05-31 18:12:56 +0000
% 2.39/1.20 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.39/1.20 git: non_committed_changes: false
% 2.39/1.20 git: last_make_outside_of_git: false
% 2.39/1.20
% 2.39/1.20 ------ Parsing...
% 2.39/1.20 ------ Clausification by vclausify_rel & Parsing by iProver...------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 2.39/1.20
% 2.39/1.20
% 2.39/1.20 ------ Preprocessing...
% 2.39/1.20
% 2.39/1.20 % SZS status Theorem for theBenchmark.p
% 2.39/1.20
% 2.39/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.39/1.21
% 2.39/1.21
%------------------------------------------------------------------------------