TSTP Solution File: NUM924_4 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM924_4 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.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 11:33:39 EDT 2023
% Result : Theorem 50.61s 7.73s
% Output : CNFRefutation 50.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 61 ( 61 unt; 0 typ; 0 def)
% Number of atoms : 568 ( 46 equ)
% Maximal formula atoms : 1 ( 9 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 507 ( 507 fml; 0 var)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 35 ( 33 usr; 22 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 26 ( 1 sgn; 19 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
tff(f3,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
tff(f4,axiom,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
tff(f54,axiom,
! [X10: int] : ( hAPP_int_int(number_number_of_int,X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_number__of__is__id) ).
tff(f55,axiom,
! [X11: int,X9: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X11),X9) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X9),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_zmult__commute) ).
tff(f244,axiom,
one_one_int = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_one__is__num__one) ).
tff(f257,axiom,
zero_zero_int = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_Pls__def) ).
tff(f303,axiom,
! [X72: int] : ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X72),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X72),X72) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_power2__eq__square) ).
tff(f591,axiom,
! [X156: int] : ( zero_zero_int = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X156),zero_zero_int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
tff(f1837,axiom,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t) = hAPP_P1175774780nt_int(twoSqu2000912462sum2sq,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,s),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1836__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
tff(f3058,axiom,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3057_One__nat__def) ).
tff(f3196,axiom,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3195_numeral__2__eq__2) ).
tff(f3295,axiom,
! [X10: int] : ( hAPP_int_int(succ,X10) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X10),one_one_int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3294_succ__def) ).
tff(f5421,conjecture,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f5422,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)),zero_zero_int)),
inference(negated_conjecture,[],[f5421]) ).
tff(f5449,plain,
! [X0: int] : ( hAPP_int_int(number_number_of_int,X0) = X0 ),
inference(rectify,[],[f54]) ).
tff(f5450,plain,
! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) ),
inference(rectify,[],[f55]) ).
tff(f5685,plain,
! [X0: int] : ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X0),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X0) ),
inference(rectify,[],[f303]) ).
tff(f5928,plain,
! [X0: int] : ( zero_zero_int = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),zero_zero_int) ),
inference(rectify,[],[f591]) ).
tff(f8489,plain,
! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int) = hAPP_int_int(succ,X0) ),
inference(rectify,[],[f3295]) ).
tff(f10177,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)),zero_zero_int)),
inference(flattening,[],[f5422]) ).
tff(f16021,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))),
inference(cnf_transformation,[],[f3]) ).
tff(f16022,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int),
inference(cnf_transformation,[],[f4]) ).
tff(f16091,plain,
! [X0: int] : ( hAPP_int_int(number_number_of_int,X0) = X0 ),
inference(cnf_transformation,[],[f5449]) ).
tff(f16092,plain,
! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) ),
inference(cnf_transformation,[],[f5450]) ).
tff(f16376,plain,
one_one_int = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),
inference(cnf_transformation,[],[f244]) ).
tff(f16396,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f257]) ).
tff(f16446,plain,
! [X0: int] : ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X0),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X0) ),
inference(cnf_transformation,[],[f5685]) ).
tff(f16779,plain,
! [X0: int] : ( zero_zero_int = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),zero_zero_int) ),
inference(cnf_transformation,[],[f5928]) ).
tff(f18448,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t) = hAPP_P1175774780nt_int(twoSqu2000912462sum2sq,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,s),one_one_int)),
inference(cnf_transformation,[],[f1837]) ).
tff(f20087,plain,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
inference(cnf_transformation,[],[f3058]) ).
tff(f20278,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat)),
inference(cnf_transformation,[],[f3196]) ).
tff(f20442,plain,
! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int) = hAPP_int_int(succ,X0) ),
inference(cnf_transformation,[],[f8489]) ).
tff(f23447,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)),zero_zero_int)),
inference(cnf_transformation,[],[f10177]) ).
tff(f23458,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),pls))),
inference(definition_unfolding,[],[f16021,f16396]) ).
tff(f23551,plain,
! [X0: int] : ( pls = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),pls) ),
inference(definition_unfolding,[],[f16779,f16396,f16396]) ).
tff(f24805,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)),pls)),
inference(definition_unfolding,[],[f23447,f16396]) ).
cnf(c_51,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),pls))),
inference(cnf_transformation,[],[f23458]) ).
cnf(c_52,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int),
inference(cnf_transformation,[],[f16022]) ).
cnf(c_121,plain,
hAPP_int_int(number_number_of_int,X0_16) = X0_16,
inference(cnf_transformation,[],[f16091]) ).
cnf(c_122,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0_16),X1_16) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1_16),X0_16),
inference(cnf_transformation,[],[f16092]) ).
cnf(c_385,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) = one_one_int,
inference(cnf_transformation,[],[f16376]) ).
cnf(c_454,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X0_16),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0_16),X0_16),
inference(cnf_transformation,[],[f16446]) ).
cnf(c_787,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0_16),pls) = pls,
inference(cnf_transformation,[],[f23551]) ).
cnf(c_2398,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t) = hAPP_P1175774780nt_int(twoSqu2000912462sum2sq,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,s),one_one_int)),
inference(cnf_transformation,[],[f18448]) ).
cnf(c_3924,plain,
hAPP_nat_nat(suc,zero_zero_nat) = one_one_nat,
inference(cnf_transformation,[],[f20087]) ).
cnf(c_4113,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat)),
inference(cnf_transformation,[],[f20278]) ).
cnf(c_4273,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0_16),one_one_int) = hAPP_int_int(succ,X0_16),
inference(cnf_transformation,[],[f20442]) ).
cnf(c_7223,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)),pls)),
inference(cnf_transformation,[],[f24805]) ).
cnf(c_24958,plain,
hAPP_int_int(bit1,pls) = one_one_int,
inference(demodulation,[status(thm)],[c_385,c_121]) ).
cnf(c_26574,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)) = hAPP_nat_nat(suc,one_one_nat),
inference(light_normalisation,[status(thm)],[c_4113,c_3924,c_24958]) ).
cnf(c_30164,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X0_16),hAPP_nat_nat(suc,one_one_nat)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0_16),X0_16),
inference(light_normalisation,[status(thm)],[c_454,c_24958,c_26574]) ).
cnf(c_31445,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_nat_nat(suc,one_one_nat))),one_one_int)),pls)),
inference(light_normalisation,[status(thm)],[c_7223,c_24958,c_26574]) ).
cnf(c_31446,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(succ,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,s),s))),pls)),
inference(demodulation,[status(thm)],[c_31445,c_4273,c_30164]) ).
cnf(c_39293,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,one_one_int)))),m)),one_one_int)),t) = hAPP_P1175774780nt_int(twoSqu2000912462sum2sq,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,s),one_one_int)),
inference(light_normalisation,[status(thm)],[c_2398,c_24958]) ).
cnf(c_39294,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,t),hAPP_int_int(succ,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,m),hAPP_int_int(bit0,hAPP_int_int(bit0,one_one_int))))) = hAPP_P1175774780nt_int(twoSqu2000912462sum2sq,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,s),one_one_int)),
inference(demodulation,[status(thm)],[c_39293,c_121,c_122,c_4273]) ).
cnf(c_42589,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,one_one_int)))),m)),one_one_int)),t) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_nat_nat(suc,one_one_nat))),one_one_int),
inference(light_normalisation,[status(thm)],[c_52,c_24958,c_26574]) ).
cnf(c_42590,plain,
hAPP_int_int(succ,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,s),s)) = hAPP_P1175774780nt_int(twoSqu2000912462sum2sq,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,s),one_one_int)),
inference(demodulation,[status(thm)],[c_42589,c_121,c_122,c_4273,c_30164,c_39294]) ).
cnf(c_42591,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,t),hAPP_int_int(succ,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,m),hAPP_int_int(bit0,hAPP_int_int(bit0,one_one_int))))) = hAPP_int_int(succ,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,s),s)),
inference(demodulation,[status(thm)],[c_39294,c_42590]) ).
cnf(c_44619,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,one_one_int)))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,one_one_int)))),m)),one_one_int)),pls))),
inference(light_normalisation,[status(thm)],[c_51,c_24958]) ).
cnf(c_44620,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(succ,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,s),s))),pls)),
inference(demodulation,[status(thm)],[c_44619,c_121,c_122,c_787,c_4273,c_42591]) ).
cnf(c_44621,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_44620,c_31446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM924_4 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 17:21:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 50.61/7.73 % SZS status Started for theBenchmark.p
% 50.61/7.73 % SZS status Theorem for theBenchmark.p
% 50.61/7.73
% 50.61/7.73 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 50.61/7.73
% 50.61/7.73 ------ iProver source info
% 50.61/7.73
% 50.61/7.73 git: date: 2023-05-31 18:12:56 +0000
% 50.61/7.73 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 50.61/7.73 git: non_committed_changes: false
% 50.61/7.73 git: last_make_outside_of_git: false
% 50.61/7.73
% 50.61/7.73 ------ Parsing...
% 50.61/7.73 ------ Clausification by vclausify_rel & Parsing by iProver...
% 50.61/7.73
% 50.61/7.73 ------ Preprocessing...
% 50.61/7.73
% 50.61/7.73 % SZS status Theorem for theBenchmark.p
% 50.61/7.73
% 50.61/7.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 50.61/7.73
% 50.61/7.73
%------------------------------------------------------------------------------