TSTP Solution File: NUM924+2 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM924+2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n019.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 : Fri May 3 02:51:08 EDT 2024
% Result : Theorem 7.41s 1.67s
% Output : CNFRefutation 7.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 23
% Syntax : Number of formulae : 137 ( 129 unt; 0 def)
% Number of atoms : 153 ( 117 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 10 |; 1 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-2 aty)
% Number of variables : 148 ( 1 sgn 110 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,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/sandbox/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) ).
fof(f21,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/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
fof(f53,axiom,
! [X13,X11] : times_times_int(X13,X11) = times_times_int(X11,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zmult__commute) ).
fof(f59,axiom,
! [X17,X18,X19] : times_times_int(times_times_int(X17,X18),X19) = times_times_int(X17,times_times_int(X18,X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_zmult__assoc) ).
fof(f105,axiom,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_nat__1__add__1) ).
fof(f148,axiom,
! [X17,X18,X19] : plus_plus_int(plus_plus_int(X17,X18),X19) = plus_plus_int(X17,plus_plus_int(X18,X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_zadd__assoc) ).
fof(f150,axiom,
! [X13,X11] : plus_plus_int(X11,X13) = plus_plus_int(X13,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_zadd__commute) ).
fof(f180,axiom,
! [X7] :
( is_int(X7)
=> ( zero_zero_int = plus_plus_int(X7,X7)
<=> zero_zero_int = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_double__eq__0__iff) ).
fof(f187,axiom,
pls = bit0(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_Bit0__Pls) ).
fof(f188,axiom,
zero_zero_int = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Pls__def) ).
fof(f198,axiom,
! [X12] : bit0(X12) = plus_plus_int(X12,X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Bit0__def) ).
fof(f219,axiom,
! [X72] : power_power_int(X72,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(X72,X72),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_power2__eq__square) ).
fof(f252,axiom,
! [X12] : bit1(X12) = plus_plus_int(plus_plus_int(one_one_int,X12),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_Bit1__def) ).
fof(f332,axiom,
! [X120,X121,X122] : times_times_real(times_times_real(X120,X121),X122) = times_times_real(X120,times_times_real(X121,X122)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(f333,axiom,
! [X120,X121,X122] : times_times_nat(times_times_nat(X120,X121),X122) = times_times_nat(X120,times_times_nat(X121,X122)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(f341,axiom,
! [X129,X130] : times_times_real(X129,X130) = times_times_real(X130,X129),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f342,axiom,
! [X129,X130] : times_times_nat(X129,X130) = times_times_nat(X130,X129),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f344,axiom,
! [X131,X132] : plus_plus_real(X131,X132) = plus_plus_real(X132,X131),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f345,axiom,
! [X131,X132] : plus_plus_nat(X131,X132) = plus_plus_nat(X132,X131),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f350,axiom,
! [X136,X137,X138] : plus_plus_real(X136,plus_plus_real(X137,X138)) = plus_plus_real(plus_plus_real(X136,X137),X138),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(f351,axiom,
! [X136,X137,X138] : plus_plus_nat(X136,plus_plus_nat(X137,X138)) = plus_plus_nat(plus_plus_nat(X136,X137),X138),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(f380,axiom,
! [X155] : zero_zero_int = times_times_int(X155,zero_zero_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f716,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/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f717,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,[],[f716]) ).
fof(f737,plain,
! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0),
inference(rectify,[],[f53]) ).
fof(f743,plain,
! [X0,X1,X2] : times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X1,X2)),
inference(rectify,[],[f59]) ).
fof(f826,plain,
! [X0,X1,X2] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)),
inference(rectify,[],[f148]) ).
fof(f828,plain,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(rectify,[],[f150]) ).
fof(f856,plain,
! [X0] :
( is_int(X0)
=> ( zero_zero_int = plus_plus_int(X0,X0)
<=> zero_zero_int = X0 ) ),
inference(rectify,[],[f180]) ).
fof(f870,plain,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
inference(rectify,[],[f198]) ).
fof(f891,plain,
! [X0] : power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(X0,X0),
inference(rectify,[],[f219]) ).
fof(f915,plain,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
inference(rectify,[],[f252]) ).
fof(f977,plain,
! [X0,X1,X2] : times_times_real(times_times_real(X0,X1),X2) = times_times_real(X0,times_times_real(X1,X2)),
inference(rectify,[],[f332]) ).
fof(f978,plain,
! [X0,X1,X2] : times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(X0,times_times_nat(X1,X2)),
inference(rectify,[],[f333]) ).
fof(f986,plain,
! [X0,X1] : times_times_real(X0,X1) = times_times_real(X1,X0),
inference(rectify,[],[f341]) ).
fof(f987,plain,
! [X0,X1] : times_times_nat(X0,X1) = times_times_nat(X1,X0),
inference(rectify,[],[f342]) ).
fof(f989,plain,
! [X0,X1] : plus_plus_real(X0,X1) = plus_plus_real(X1,X0),
inference(rectify,[],[f344]) ).
fof(f990,plain,
! [X0,X1] : plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0),
inference(rectify,[],[f345]) ).
fof(f995,plain,
! [X0,X1,X2] : plus_plus_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(plus_plus_real(X0,X1),X2),
inference(rectify,[],[f350]) ).
fof(f996,plain,
! [X0,X1,X2] : plus_plus_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(plus_plus_nat(X0,X1),X2),
inference(rectify,[],[f351]) ).
fof(f1025,plain,
! [X0] : zero_zero_int = times_times_int(X0,zero_zero_int),
inference(rectify,[],[f380]) ).
fof(f1339,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,[],[f717]) ).
fof(f1431,plain,
! [X0] :
( ( zero_zero_int = plus_plus_int(X0,X0)
<=> zero_zero_int = X0 )
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f856]) ).
fof(f1818,plain,
! [X0] :
( ( ( zero_zero_int = plus_plus_int(X0,X0)
| zero_zero_int != X0 )
& ( zero_zero_int = X0
| zero_zero_int != plus_plus_int(X0,X0) ) )
| ~ is_int(X0) ),
inference(nnf_transformation,[],[f1431]) ).
fof(f1975,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,[],[f20]) ).
fof(f1976,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,[],[f21]) ).
fof(f2021,plain,
! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0),
inference(cnf_transformation,[],[f737]) ).
fof(f2030,plain,
! [X2,X0,X1] : times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X1,X2)),
inference(cnf_transformation,[],[f743]) ).
fof(f2105,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnf_transformation,[],[f105]) ).
fof(f2174,plain,
! [X2,X0,X1] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)),
inference(cnf_transformation,[],[f826]) ).
fof(f2176,plain,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[],[f828]) ).
fof(f2218,plain,
! [X0] :
( zero_zero_int = plus_plus_int(X0,X0)
| zero_zero_int != X0
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f1818]) ).
fof(f2227,plain,
pls = bit0(pls),
inference(cnf_transformation,[],[f187]) ).
fof(f2228,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f188]) ).
fof(f2242,plain,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
inference(cnf_transformation,[],[f870]) ).
fof(f2263,plain,
! [X0] : power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(X0,X0),
inference(cnf_transformation,[],[f891]) ).
fof(f2307,plain,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
inference(cnf_transformation,[],[f915]) ).
fof(f2413,plain,
! [X2,X0,X1] : times_times_real(times_times_real(X0,X1),X2) = times_times_real(X0,times_times_real(X1,X2)),
inference(cnf_transformation,[],[f977]) ).
fof(f2414,plain,
! [X2,X0,X1] : times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(X0,times_times_nat(X1,X2)),
inference(cnf_transformation,[],[f978]) ).
fof(f2422,plain,
! [X0,X1] : times_times_real(X0,X1) = times_times_real(X1,X0),
inference(cnf_transformation,[],[f986]) ).
fof(f2423,plain,
! [X0,X1] : times_times_nat(X0,X1) = times_times_nat(X1,X0),
inference(cnf_transformation,[],[f987]) ).
fof(f2425,plain,
! [X0,X1] : plus_plus_real(X0,X1) = plus_plus_real(X1,X0),
inference(cnf_transformation,[],[f989]) ).
fof(f2426,plain,
! [X0,X1] : plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0),
inference(cnf_transformation,[],[f990]) ).
fof(f2431,plain,
! [X2,X0,X1] : plus_plus_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(plus_plus_real(X0,X1),X2),
inference(cnf_transformation,[],[f995]) ).
fof(f2432,plain,
! [X2,X0,X1] : plus_plus_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(plus_plus_nat(X0,X1),X2),
inference(cnf_transformation,[],[f996]) ).
fof(f2465,plain,
! [X0] : zero_zero_int = times_times_int(X0,zero_zero_int),
inference(cnf_transformation,[],[f1025]) ).
fof(f2910,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,[],[f1339]) ).
fof(f2915,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,[],[f1975,f2242,f2242,f2307,f2242,f2242,f2307,f2228]) ).
fof(f2916,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,[],[f1976,f2242,f2242,f2307,f2242,f2307]) ).
fof(f2991,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,[],[f2105,f2242,f2307]) ).
fof(f3051,plain,
! [X0] :
( pls = plus_plus_int(X0,X0)
| pls != X0
| ~ is_int(X0) ),
inference(definition_unfolding,[],[f2218,f2228,f2228]) ).
fof(f3061,plain,
pls = plus_plus_int(pls,pls),
inference(definition_unfolding,[],[f2227,f2242]) ).
fof(f3091,plain,
! [X0] : 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,[],[f2263,f2242,f2307]) ).
fof(f3189,plain,
! [X0] : pls = times_times_int(X0,pls),
inference(definition_unfolding,[],[f2465,f2228,f2228]) ).
fof(f3322,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,[],[f2910,f2242,f2307,f2228]) ).
fof(f3365,plain,
( pls = plus_plus_int(pls,pls)
| ~ is_int(pls) ),
inference(equality_resolution,[],[f3051]) ).
cnf(c_68,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,[],[f2915]) ).
cnf(c_69,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,[],[f2916]) ).
cnf(c_114,plain,
times_times_int(X0,X1) = times_times_int(X1,X0),
inference(cnf_transformation,[],[f2021]) ).
cnf(c_123,plain,
times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X1,X2)),
inference(cnf_transformation,[],[f2030]) ).
cnf(c_198,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,[],[f2991]) ).
cnf(c_260,plain,
plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)),
inference(cnf_transformation,[],[f2174]) ).
cnf(c_262,plain,
plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[],[f2176]) ).
cnf(c_303,plain,
( ~ is_int(pls)
| plus_plus_int(pls,pls) = pls ),
inference(cnf_transformation,[],[f3365]) ).
cnf(c_313,plain,
plus_plus_int(pls,pls) = pls,
inference(cnf_transformation,[],[f3061]) ).
cnf(c_347,plain,
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)))) = times_times_int(X0,X0),
inference(cnf_transformation,[],[f3091]) ).
cnf(c_496,plain,
times_times_real(times_times_real(X0,X1),X2) = times_times_real(X0,times_times_real(X1,X2)),
inference(cnf_transformation,[],[f2413]) ).
cnf(c_497,plain,
times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(X0,times_times_nat(X1,X2)),
inference(cnf_transformation,[],[f2414]) ).
cnf(c_505,plain,
times_times_real(X0,X1) = times_times_real(X1,X0),
inference(cnf_transformation,[],[f2422]) ).
cnf(c_506,plain,
times_times_nat(X0,X1) = times_times_nat(X1,X0),
inference(cnf_transformation,[],[f2423]) ).
cnf(c_508,plain,
plus_plus_real(X0,X1) = plus_plus_real(X1,X0),
inference(cnf_transformation,[],[f2425]) ).
cnf(c_509,plain,
plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0),
inference(cnf_transformation,[],[f2426]) ).
cnf(c_514,plain,
plus_plus_real(plus_plus_real(X0,X1),X2) = plus_plus_real(X0,plus_plus_real(X1,X2)),
inference(cnf_transformation,[],[f2431]) ).
cnf(c_515,plain,
plus_plus_nat(plus_plus_nat(X0,X1),X2) = plus_plus_nat(X0,plus_plus_nat(X1,X2)),
inference(cnf_transformation,[],[f2432]) ).
cnf(c_548,plain,
times_times_int(X0,pls) = pls,
inference(cnf_transformation,[],[f3189]) ).
cnf(c_984,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,[],[f3322]) ).
cnf(c_1467,plain,
plus_plus_int(pls,pls) = pls,
inference(global_subsumption_just,[status(thm)],[c_303,c_313]) ).
cnf(c_1515,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_68,c_497,c_506,c_496,c_505,c_515,c_509,c_514,c_508,c_123,c_114,c_260,c_262]) ).
cnf(c_1516,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_69,c_497,c_506,c_496,c_505,c_515,c_509,c_514,c_508,c_123,c_114,c_260,c_262]) ).
cnf(c_1566,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_198,c_497,c_506,c_496,c_505,c_515,c_509,c_514,c_508,c_123,c_114,c_260,c_262]) ).
cnf(c_1616,plain,
power_power_int(X0,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,X0),
inference(theory_normalisation,[status(thm)],[c_347,c_497,c_506,c_496,c_505,c_515,c_509,c_514,c_508,c_123,c_114,c_260,c_262]) ).
cnf(c_1721,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_984,c_497,c_506,c_496,c_505,c_515,c_509,c_514,c_508,c_123,c_114,c_260,c_262]) ).
cnf(c_7792,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_1566,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_7793,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_7792,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_7794,plain,
number_number_of_nat(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_7793,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_7795,plain,
number_number_of_nat(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_7794,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_8026,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_1721,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_8027,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_8026,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_8028,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,pls))))),pls),
inference(ac_demodulation,[status(thm)],[c_8027,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_8029,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(one_one_int,one_one_int))))),pls),
inference(theory_normalisation,[status(thm)],[c_8028,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_8030,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_8029,c_7795]) ).
cnf(c_8043,plain,
power_power_int(X0,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,X0),
inference(ac_demodulation,[status(thm)],[c_1616,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_8044,plain,
power_power_int(X0,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,X0),
inference(ac_demodulation,[status(thm)],[c_8043,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_8045,plain,
power_power_int(X0,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls)))) = times_times_int(X0,X0),
inference(ac_demodulation,[status(thm)],[c_8044,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_8046,plain,
power_power_int(X0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int)))) = times_times_int(X0,X0),
inference(theory_normalisation,[status(thm)],[c_8045,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_8047,plain,
power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)) = times_times_int(X0,X0),
inference(light_normalisation,[status(thm)],[c_8046,c_7795]) ).
cnf(c_8049,plain,
~ ord_less_int(plus_plus_int(one_one_int,times_times_int(s,s)),pls),
inference(demodulation,[status(thm)],[c_8030,c_8047]) ).
cnf(c_9131,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_1516,c_1467,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9132,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_9131,c_1467,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9133,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(one_one_int,pls))))),
inference(ac_demodulation,[status(thm)],[c_9132,c_1467,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9134,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,plus_plus_int(one_one_int,pls))))),
inference(ac_demodulation,[status(thm)],[c_9133,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9135,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,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,pls))))),
inference(ac_demodulation,[status(thm)],[c_9134,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9136,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,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,pls))))),
inference(ac_demodulation,[status(thm)],[c_9135,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9137,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,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,pls))))),
inference(ac_demodulation,[status(thm)],[c_9136,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9138,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(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(one_one_int,one_one_int))))),
inference(theory_normalisation,[status(thm)],[c_9137,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9139,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(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_9138,c_7795]) ).
cnf(c_9140,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(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_9139,c_8047]) ).
cnf(c_9180,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_1515,c_548,c_1467,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9181,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_9180,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9182,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_9181,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9183,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_9182,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9184,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,pls)))))))))),pls),
inference(ac_demodulation,[status(thm)],[c_9183,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9185,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,pls))))))))),pls),
inference(ac_demodulation,[status(thm)],[c_9184,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9186,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,pls)))))))),pls),
inference(ac_demodulation,[status(thm)],[c_9185,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9187,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(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int)))))))),pls),
inference(theory_normalisation,[status(thm)],[c_9186,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
cnf(c_9188,plain,
ord_less_int(plus_plus_int(one_one_int,times_times_int(s,s)),pls),
inference(light_normalisation,[status(thm)],[c_9187,c_9140]) ).
cnf(c_9189,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9188,c_8049]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM924+2 : TPTP v8.1.2. Released v5.3.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 19:47:14 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.41/1.67 % SZS status Started for theBenchmark.p
% 7.41/1.67 % SZS status Theorem for theBenchmark.p
% 7.41/1.67
% 7.41/1.67 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.41/1.67
% 7.41/1.67 ------ iProver source info
% 7.41/1.67
% 7.41/1.67 git: date: 2024-05-02 19:28:25 +0000
% 7.41/1.67 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.41/1.67 git: non_committed_changes: false
% 7.41/1.67
% 7.41/1.67 ------ Parsing...
% 7.41/1.67 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.41/1.67
% 7.41/1.67 ------ Preprocessing...
% 7.41/1.67
% 7.41/1.67 % SZS status Theorem for theBenchmark.p
% 7.41/1.67
% 7.41/1.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.41/1.67
% 7.41/1.68
%------------------------------------------------------------------------------