%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM926+1 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n014.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 10:49:08 EDT 2023

% Result   : Theorem 0.22s 0.59s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM926+1 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n014.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri Aug 25 09:25:48 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.59  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.mCuiR2GXyn/cvc5---1.0.5_23431.p...
% 0.22/0.59  ------- get file name : TPTP file name is NUM926+1
% 0.22/0.59  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_23431.smt2...
% 0.22/0.59  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.59  % SZS status Theorem for NUM926+1
% 0.22/0.59  % SZS output start Proof for NUM926+1
% 0.22/0.59  (
% 0.22/0.59  (let ((_let_1 (not (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2)) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int)))))))) (let ((_let_2 (tptp.bit1 tptp.pls))) (let ((_let_3 (tptp.bit0 _let_2))) (let ((_let_4 (tptp.number_number_of_int _let_3))) (let ((_let_5 (tptp.number_number_of_nat _let_2))) (let ((_let_6 (tptp.number_number_of_nat _let_3))) (let ((_let_7 (forall ((Z_1 $$unsorted) (W_1 $$unsorted)) (= (tptp.ord_less_int Z_1 W_1) (and (tptp.ord_less_eq_int Z_1 W_1) (not (= Z_1 W_1))))))) (let ((_let_8 (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_3)) tptp.m) tptp.one_one_int))) (let ((_let_9 (tptp.times_times_int _let_8 tptp.t))) (let ((_let_10 (tptp.ord_less_int tptp.one_one_int tptp.t))) (let ((_let_11 (=> _let_10 (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2)) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int)))))))) (let ((_let_12 (=> (= tptp.t tptp.one_one_int) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2)) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int)))))))) (let ((_let_13 (tptp.ord_less_eq_int tptp.one_one_int tptp.t))) (let ((_let_14 (= tptp.one_one_int tptp.t))) (let ((_let_15 (not _let_14))) (let ((_let_16 (and _let_13 _let_15))) (let ((_let_17 (= _let_10 _let_16))) (let ((_let_18 (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int) (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2))))))))) (let ((_let_19 (not _let_10))) (let ((_let_20 (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2)) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int)))))))) (let ((_let_21 (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int) (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2))))))))) (let ((_let_22 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (TRANS (ALPHA_EQUIV :args (_let_20 (= X X) (= Y Y))) (MACRO_SR_PRED_INTRO :args ((= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2)) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int)))))) _let_21) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (_let_20 false _let_21)))) (let ((_let_23 (not _let_13))) (let ((_let_24 (_let_16))) (let ((_let_25 (_let_7))) (let ((_let_26 (ASSUME :args _let_25))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_17)) :args ((or _let_10 (not _let_16) (not _let_17)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (tptp.one_one_int tptp.t QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ord_less_int Z_1 W_1)))) :args _let_25)) _let_26 :args (_let_17 false _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_24) (CONG (REFL :args _let_24) (REFL :args (_let_23)) (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args (or))) :args ((or _let_14 _let_23 _let_16))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)))) :args ((or (not _let_20) _let_15))) _let_22 :args (_let_15 false _let_20)) (ASSUME :args (_let_13)) :args (_let_16 true _let_14 false _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT)))) :args ((or (not _let_18) _let_19))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_20 (= X X) (= Y Y))) (MACRO_SR_PRED_INTRO :args ((= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (not (= (tptp.plus_plus_int (tptp.power_power_int X _let_2) (tptp.power_power_int Y _let_2)) (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int)))))) _let_18) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) _let_22 :args (_let_18 false _let_20)) :args (_let_19 false _let_18)) :args (false false _let_17 false _let_16 true _let_10)) :args (_let_13 _let_12 _let_11 (tptp.ord_less_int tptp.t _let_8) (tptp.zprime _let_8) (= (tptp.plus_plus_int (tptp.power_power_int tptp.s _let_6) tptp.one_one_int) _let_9) (tptp.twoSqu526106917sum2sq _let_9) (forall ((A_8 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.power_power_int (tptp.plus_plus_int A_8 B_4) _let_2) (tptp.plus_plus_int (tptp.plus_plus_int (tptp.power_power_int A_8 _let_2) (tptp.times_times_int (tptp.times_times_int (tptp.number_number_of_int _let_1) A_8) B_4)) (tptp.power_power_int B_4 _let_2)))))) (forall ((A_8 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of_nat _let_2))) (let ((_let_4 (tptp.number_number_of_nat (tptp.bit0 _let_1)))) (let ((_let_5 (tptp.number_number_of_int _let_2))) (= (tptp.power_power_int (tptp.plus_plus_int A_8 B_4) _let_3) (tptp.plus_plus_int (tptp.plus_plus_int (tptp.plus_plus_int (tptp.power_power_int A_8 _let_3) (tptp.times_times_int (tptp.times_times_int _let_5 (tptp.power_power_int A_8 _let_4)) B_4)) (tptp.times_times_int (tptp.times_times_int _let_5 A_8) (tptp.power_power_int B_4 _let_4))) (tptp.power_power_int B_4 _let_3))))))))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.power_power_nat (tptp.plus_plus_nat X_2 Y_2) _let_1) (tptp.plus_plus_nat (tptp.plus_plus_nat (tptp.power_power_nat X_2 _let_1) (tptp.power_power_nat Y_2 _let_1)) (tptp.times_times_nat (tptp.times_times_nat _let_1 X_2) Y_2))))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of_nat _let_1))) (= (tptp.power_power_int (tptp.plus_plus_int X_2 Y_2) _let_2) (tptp.plus_plus_int (tptp.plus_plus_int (tptp.power_power_int X_2 _let_2) (tptp.power_power_int Y_2 _let_2)) (tptp.times_times_int (tptp.times_times_int (tptp.number_number_of_int _let_1) X_2) Y_2)))))) (forall ((W_4 $$unsorted)) (let ((_let_1 (tptp.number_number_of_int W_4))) (= (tptp.power_power_int _let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.times_times_int _let_1 _let_1)))) (forall ((W_4 $$unsorted)) (let ((_let_1 (tptp.number_number_of_nat W_4))) (= (tptp.power_power_nat _let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.times_times_nat _let_1 _let_1)))) (forall ((A_8 $$unsorted)) (let ((_let_1 (tptp.bit1 tptp.pls))) (= (tptp.times_times_int A_8 (tptp.power_power_int A_8 (tptp.number_number_of_nat (tptp.bit0 _let_1)))) (tptp.power_power_int A_8 (tptp.number_number_of_nat (tptp.bit1 _let_1)))))) (= (tptp.power_power_nat tptp.one_one_nat _let_6) tptp.one_one_nat) (= (tptp.power_power_int tptp.one_one_int _let_6) tptp.one_one_int) (forall ((X_7 $$unsorted)) (= (tptp.times_times_int X_7 X_7) (tptp.power_power_int X_7 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (forall ((X_7 $$unsorted)) (= (tptp.times_times_nat X_7 X_7) (tptp.power_power_nat X_7 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (forall ((A_7 $$unsorted)) (= (tptp.power_power_int A_7 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.times_times_int A_7 A_7))) (forall ((A_7 $$unsorted)) (= (tptp.power_power_nat A_7 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.times_times_nat A_7 A_7))) (forall ((X_6 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power_int X_6 N))) (= (tptp.power_power_int X_6 (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) N)) (tptp.times_times_int _let_1 _let_1)))) (forall ((X_6 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power_nat X_6 N))) (= (tptp.power_power_nat X_6 (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) N)) (tptp.times_times_nat _let_1 _let_1)))) (forall ((W_3 $$unsorted)) (= (tptp.plus_plus_int tptp.one_one_int (tptp.number_number_of_int W_3)) (tptp.number_number_of_int (tptp.plus_plus_int (tptp.bit1 tptp.pls) W_3)))) (forall ((V_3 $$unsorted)) (= (tptp.plus_plus_int (tptp.number_number_of_int V_3) tptp.one_one_int) (tptp.number_number_of_int (tptp.plus_plus_int V_3 (tptp.bit1 tptp.pls))))) (= (tptp.plus_plus_int tptp.one_one_int tptp.one_one_int) _let_4) (not (forall ((T $$unsorted)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (= (tptp.plus_plus_int (tptp.power_power_int tptp.s (tptp.number_number_of_nat _let_1)) tptp.one_one_int) (tptp.times_times_int (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int) T)))))) (forall ((W $$unsorted)) (tptp.ord_less_eq_int W W)) (forall ((Z $$unsorted) (W $$unsorted)) (or (tptp.ord_less_eq_int Z W) (tptp.ord_less_eq_int W Z))) _let_7 (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (tptp.ord_less_int X_1 Y_1) (= X_1 Y_1) (tptp.ord_less_int Y_1 X_1))) (forall ((K_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (tptp.ord_less_eq_int I J) (=> (tptp.ord_less_eq_int J K_1) (tptp.ord_less_eq_int I K_1)))) (forall ((Z $$unsorted) (W $$unsorted)) (=> (tptp.ord_less_eq_int Z W) (=> (tptp.ord_less_eq_int W Z) (= Z W)))) (forall ((X_5 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.power_power_int (tptp.power_power_int X_5 P_1) Q_1) (tptp.power_power_int X_5 (tptp.times_times_nat P_1 Q_1)))) (forall ((X_5 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.power_power_nat (tptp.power_power_nat X_5 P_1) Q_1) (tptp.power_power_nat X_5 (tptp.times_times_nat P_1 Q_1)))) (forall ((X_4 $$unsorted)) (= (tptp.power_power_int X_4 tptp.one_one_nat) X_4)) (forall ((X_4 $$unsorted)) (= (tptp.power_power_nat X_4 tptp.one_one_nat) X_4)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (= (tptp.power_power_int (tptp.power_power_int X_1 Y_1) Z) (tptp.power_power_int X_1 (tptp.times_times_nat Y_1 Z)))) (forall ((V_2 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of_nat V_2))) (let ((_let_2 (tptp.number_number_of_nat W_1))) (= (tptp.ord_less_eq_nat _let_1 _let_2) (not (tptp.ord_less_nat _let_2 _let_1)))))) (forall ((V_2 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of_int V_2))) (let ((_let_2 (tptp.number_number_of_int W_1))) (= (tptp.ord_less_eq_int _let_1 _let_2) (not (tptp.ord_less_int _let_2 _let_1)))))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (tptp.ord_less_int (tptp.number_number_of_int X_2) (tptp.number_number_of_int Y_2)) (tptp.ord_less_int X_2 Y_2))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (tptp.ord_less_eq_int (tptp.number_number_of_int X_2) (tptp.number_number_of_int Y_2)) (tptp.ord_less_eq_int X_2 Y_2))) (forall ((Z_2 $$unsorted) (Z $$unsorted) (W_2 $$unsorted) (W $$unsorted)) (=> (tptp.ord_less_int W_2 W) (=> (tptp.ord_less_eq_int Z_2 Z) (tptp.ord_less_int (tptp.plus_plus_int W_2 Z_2) (tptp.plus_plus_int W Z))))) (forall ((X_3 $$unsorted) (P $$unsorted) (Q $$unsorted)) (= (tptp.times_times_int (tptp.power_power_int X_3 P) (tptp.power_power_int X_3 Q)) (tptp.power_power_int X_3 (tptp.plus_plus_nat P Q)))) (forall ((X_3 $$unsorted) (P $$unsorted) (Q $$unsorted)) (= (tptp.times_times_nat (tptp.power_power_nat X_3 P) (tptp.power_power_nat X_3 Q)) (tptp.power_power_nat X_3 (tptp.plus_plus_nat P Q)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (= (tptp.power_power_int X_1 (tptp.plus_plus_nat Y_1 Z)) (tptp.times_times_int (tptp.power_power_int X_1 Y_1) (tptp.power_power_int X_1 Z)))) (forall ((Z $$unsorted)) (= (tptp.times_times_nat (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))) Z) (tptp.plus_plus_nat Z Z))) (forall ((Z $$unsorted)) (= (tptp.times_times_nat Z (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.plus_plus_nat Z Z))) (= (tptp.plus_plus_nat tptp.one_one_nat tptp.one_one_nat) _let_6) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_int (tptp.bit1 K1) (tptp.bit1 K2)) (tptp.ord_less_int K1 K2))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_int (tptp.bit1 K) (tptp.bit1 L)) (tptp.ord_less_int K L))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_eq_int (tptp.bit1 K1) (tptp.bit1 K2)) (tptp.ord_less_eq_int K1 K2))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_eq_int (tptp.bit1 K) (tptp.bit1 L)) (tptp.ord_less_eq_int K L))) (not (tptp.ord_less_int tptp.pls tptp.pls)) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_int (tptp.bit0 K1) (tptp.bit0 K2)) (tptp.ord_less_int K1 K2))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_int (tptp.bit0 K) (tptp.bit0 L)) (tptp.ord_less_int K L))) (tptp.ord_less_eq_int tptp.pls tptp.pls) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_eq_int (tptp.bit0 K1) (tptp.bit0 K2)) (tptp.ord_less_eq_int K1 K2))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_eq_int (tptp.bit0 K) (tptp.bit0 L)) (tptp.ord_less_eq_int K L))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_int (tptp.number_number_of_int K) (tptp.number_number_of_int L)) (tptp.ord_less_int K L))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_eq_int (tptp.number_number_of_int K) (tptp.number_number_of_int L)) (tptp.ord_less_eq_int K L))) (forall ((K_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (tptp.ord_less_int I J) (tptp.ord_less_int (tptp.plus_plus_int I K_1) (tptp.plus_plus_int J K_1)))) (forall ((K_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (tptp.ord_less_eq_int I J) (tptp.ord_less_eq_int (tptp.plus_plus_int K_1 I) (tptp.plus_plus_int K_1 J)))) (forall ((V_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of_nat V_1))) (let ((_let_2 (tptp.number_number_of_nat V))) (let ((_let_3 (tptp.plus_plus_nat _let_2 _let_1))) (let ((_let_4 (tptp.ord_less_int V_1 tptp.pls))) (let ((_let_5 (tptp.ord_less_int V tptp.pls))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.number_number_of_nat (tptp.plus_plus_int V V_1))))))))))))) (= _let_5 tptp.one_one_nat) (= tptp.one_one_nat _let_5) (forall ((K $$unsorted)) (= (tptp.ord_less_eq_int (tptp.bit1 K) tptp.pls) (tptp.ord_less_int K tptp.pls))) (forall ((K $$unsorted)) (= (tptp.ord_less_int tptp.pls (tptp.bit1 K)) (tptp.ord_less_eq_int tptp.pls K))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_eq_int (tptp.bit1 K1) (tptp.bit0 K2)) (tptp.ord_less_int K1 K2))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_eq_int (tptp.bit1 K) (tptp.bit0 L)) (tptp.ord_less_int K L))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_int (tptp.bit0 K1) (tptp.bit1 K2)) (tptp.ord_less_eq_int K1 K2))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_int (tptp.bit0 K) (tptp.bit1 L)) (tptp.ord_less_eq_int K L))) (forall ((W $$unsorted) (Z $$unsorted)) (=> (tptp.ord_less_int W Z) (tptp.ord_less_eq_int (tptp.plus_plus_int W tptp.one_one_int) Z))) (forall ((W_1 $$unsorted) (Z_1 $$unsorted)) (= (tptp.ord_less_eq_int (tptp.plus_plus_int W_1 tptp.one_one_int) Z_1) (tptp.ord_less_int W_1 Z_1))) (forall ((W_1 $$unsorted) (Z_1 $$unsorted)) (= (tptp.ord_less_int W_1 (tptp.plus_plus_int Z_1 tptp.one_one_int)) (tptp.ord_less_eq_int W_1 Z_1))) (tptp.zprime _let_4) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.twoSqu526106917sum2sq X_1) (=> (tptp.twoSqu526106917sum2sq Y_1) (tptp.twoSqu526106917sum2sq (tptp.times_times_int X_1 Y_1))))) (forall ((Lx_6 $$unsorted) (Ly_4 $$unsorted) (Rx_6 $$unsorted) (Ry_4 $$unsorted)) (= (tptp.times_times_int (tptp.times_times_int Lx_6 Ly_4) (tptp.times_times_int Rx_6 Ry_4)) (tptp.times_times_int (tptp.times_times_int Lx_6 Rx_6) (tptp.times_times_int Ly_4 Ry_4)))) (forall ((Lx_6 $$unsorted) (Ly_4 $$unsorted) (Rx_6 $$unsorted) (Ry_4 $$unsorted)) (= (tptp.times_times_nat (tptp.times_times_nat Lx_6 Ly_4) (tptp.times_times_nat Rx_6 Ry_4)) (tptp.times_times_nat (tptp.times_times_nat Lx_6 Rx_6) (tptp.times_times_nat Ly_4 Ry_4)))) (forall ((Lx_5 $$unsorted) (Ly_3 $$unsorted) (Rx_5 $$unsorted) (Ry_3 $$unsorted)) (let ((_let_1 (tptp.times_times_int Lx_5 Ly_3))) (= (tptp.times_times_int _let_1 (tptp.times_times_int Rx_5 Ry_3)) (tptp.times_times_int Rx_5 (tptp.times_times_int _let_1 Ry_3))))) (forall ((Lx_5 $$unsorted) (Ly_3 $$unsorted) (Rx_5 $$unsorted) (Ry_3 $$unsorted)) (let ((_let_1 (tptp.times_times_nat Lx_5 Ly_3))) (= (tptp.times_times_nat _let_1 (tptp.times_times_nat Rx_5 Ry_3)) (tptp.times_times_nat Rx_5 (tptp.times_times_nat _let_1 Ry_3))))) (forall ((Lx_4 $$unsorted) (Ly_2 $$unsorted) (Rx_4 $$unsorted) (Ry_2 $$unsorted)) (let ((_let_1 (tptp.times_times_int Rx_4 Ry_2))) (= (tptp.times_times_int (tptp.times_times_int Lx_4 Ly_2) _let_1) (tptp.times_times_int Lx_4 (tptp.times_times_int Ly_2 _let_1))))) (forall ((Lx_4 $$unsorted) (Ly_2 $$unsorted) (Rx_4 $$unsorted) (Ry_2 $$unsorted)) (let ((_let_1 (tptp.times_times_nat Rx_4 Ry_2))) (= (tptp.times_times_nat (tptp.times_times_nat Lx_4 Ly_2) _let_1) (tptp.times_times_nat Lx_4 (tptp.times_times_nat Ly_2 _let_1))))) (forall ((Lx_3 $$unsorted) (Ly_1 $$unsorted) (Rx_3 $$unsorted)) (= (tptp.times_times_int (tptp.times_times_int Lx_3 Ly_1) Rx_3) (tptp.times_times_int (tptp.times_times_int Lx_3 Rx_3) Ly_1))) (forall ((Lx_3 $$unsorted) (Ly_1 $$unsorted) (Rx_3 $$unsorted)) (= (tptp.times_times_nat (tptp.times_times_nat Lx_3 Ly_1) Rx_3) (tptp.times_times_nat (tptp.times_times_nat Lx_3 Rx_3) Ly_1))) (forall ((Lx_2 $$unsorted) (Ly $$unsorted) (Rx_2 $$unsorted)) (= (tptp.times_times_int (tptp.times_times_int Lx_2 Ly) Rx_2) (tptp.times_times_int Lx_2 (tptp.times_times_int Ly Rx_2)))) (forall ((Lx_2 $$unsorted) (Ly $$unsorted) (Rx_2 $$unsorted)) (= (tptp.times_times_nat (tptp.times_times_nat Lx_2 Ly) Rx_2) (tptp.times_times_nat Lx_2 (tptp.times_times_nat Ly Rx_2)))) (forall ((Lx_1 $$unsorted) (Rx_1 $$unsorted) (Ry_1 $$unsorted)) (= (tptp.times_times_int Lx_1 (tptp.times_times_int Rx_1 Ry_1)) (tptp.times_times_int (tptp.times_times_int Lx_1 Rx_1) Ry_1))) (forall ((Lx_1 $$unsorted) (Rx_1 $$unsorted) (Ry_1 $$unsorted)) (= (tptp.times_times_nat Lx_1 (tptp.times_times_nat Rx_1 Ry_1)) (tptp.times_times_nat (tptp.times_times_nat Lx_1 Rx_1) Ry_1))) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (= (tptp.times_times_int Lx (tptp.times_times_int Rx Ry)) (tptp.times_times_int Rx (tptp.times_times_int Lx Ry)))) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (= (tptp.times_times_nat Lx (tptp.times_times_nat Rx Ry)) (tptp.times_times_nat Rx (tptp.times_times_nat Lx Ry)))) (forall ((A_6 $$unsorted) (B_3 $$unsorted)) (= (tptp.times_times_int A_6 B_3) (tptp.times_times_int B_3 A_6))) (forall ((A_6 $$unsorted) (B_3 $$unsorted)) (= (tptp.times_times_nat A_6 B_3) (tptp.times_times_nat B_3 A_6))) (forall ((A_5 $$unsorted) (B_2 $$unsorted) (C_5 $$unsorted) (D_2 $$unsorted)) (= (tptp.plus_plus_int (tptp.plus_plus_int A_5 B_2) (tptp.plus_plus_int C_5 D_2)) (tptp.plus_plus_int (tptp.plus_plus_int A_5 C_5) (tptp.plus_plus_int B_2 D_2)))) (forall ((A_5 $$unsorted) (B_2 $$unsorted) (C_5 $$unsorted) (D_2 $$unsorted)) (= (tptp.plus_plus_nat (tptp.plus_plus_nat A_5 B_2) (tptp.plus_plus_nat C_5 D_2)) (tptp.plus_plus_nat (tptp.plus_plus_nat A_5 C_5) (tptp.plus_plus_nat B_2 D_2)))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (C_4 $$unsorted)) (= (tptp.plus_plus_int (tptp.plus_plus_int A_4 B_1) C_4) (tptp.plus_plus_int (tptp.plus_plus_int A_4 C_4) B_1))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (C_4 $$unsorted)) (= (tptp.plus_plus_nat (tptp.plus_plus_nat A_4 B_1) C_4) (tptp.plus_plus_nat (tptp.plus_plus_nat A_4 C_4) B_1))) (forall ((A_3 $$unsorted) (B $$unsorted) (C_3 $$unsorted)) (= (tptp.plus_plus_int (tptp.plus_plus_int A_3 B) C_3) (tptp.plus_plus_int A_3 (tptp.plus_plus_int B C_3)))) (forall ((A_3 $$unsorted) (B $$unsorted) (C_3 $$unsorted)) (= (tptp.plus_plus_nat (tptp.plus_plus_nat A_3 B) C_3) (tptp.plus_plus_nat A_3 (tptp.plus_plus_nat B C_3)))) (forall ((A_2 $$unsorted) (C_2 $$unsorted) (D_1 $$unsorted)) (= (tptp.plus_plus_int A_2 (tptp.plus_plus_int C_2 D_1)) (tptp.plus_plus_int (tptp.plus_plus_int A_2 C_2) D_1))) (forall ((A_2 $$unsorted) (C_2 $$unsorted) (D_1 $$unsorted)) (= (tptp.plus_plus_nat A_2 (tptp.plus_plus_nat C_2 D_1)) (tptp.plus_plus_nat (tptp.plus_plus_nat A_2 C_2) D_1))) (forall ((A_1 $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (= (tptp.plus_plus_int A_1 (tptp.plus_plus_int C_1 D)) (tptp.plus_plus_int C_1 (tptp.plus_plus_int A_1 D)))) (forall ((A_1 $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (= (tptp.plus_plus_nat A_1 (tptp.plus_plus_nat C_1 D)) (tptp.plus_plus_nat C_1 (tptp.plus_plus_nat A_1 D)))) (forall ((A $$unsorted) (C $$unsorted)) (= (tptp.plus_plus_int A C) (tptp.plus_plus_int C A))) (forall ((A $$unsorted) (C $$unsorted)) (= (tptp.plus_plus_nat A C) (tptp.plus_plus_nat C A))) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (= (tptp.number_number_of_int X_2) (tptp.number_number_of_int Y_2)) (= X_2 Y_2))) (forall ((W_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (= _let_1 X_2) (= X_2 _let_1)))) (forall ((W_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.number_number_of_int W_1))) (= (= _let_1 X_2) (= X_2 _let_1)))) (forall ((K $$unsorted) (L $$unsorted)) (= (= (tptp.bit1 K) (tptp.bit1 L)) (= K L))) (forall ((K $$unsorted) (L $$unsorted)) (= (= (tptp.bit0 K) (tptp.bit0 L)) (= K L))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (= (tptp.times_times_int (tptp.times_times_int Z1 Z2) Z3) (tptp.times_times_int Z1 (tptp.times_times_int Z2 Z3)))) (forall ((Z $$unsorted) (W $$unsorted)) (= (tptp.times_times_int Z W) (tptp.times_times_int W Z))) (forall ((K_1 $$unsorted)) (= (tptp.number_number_of_int K_1) K_1)) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (= (tptp.plus_plus_int (tptp.plus_plus_int Z1 Z2) Z3) (tptp.plus_plus_int Z1 (tptp.plus_plus_int Z2 Z3)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (= (tptp.plus_plus_int X_1 (tptp.plus_plus_int Y_1 Z)) (tptp.plus_plus_int Y_1 (tptp.plus_plus_int X_1 Z)))) (forall ((Z $$unsorted) (W $$unsorted)) (= (tptp.plus_plus_int Z W) (tptp.plus_plus_int W Z))) (forall ((K $$unsorted)) (= (tptp.ord_less_int (tptp.bit1 K) tptp.pls) (tptp.ord_less_int K tptp.pls))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_int (tptp.bit1 K1) (tptp.bit0 K2)) (tptp.ord_less_int K1 K2))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_int (tptp.bit1 K) (tptp.bit0 L)) (tptp.ord_less_int K L))) (forall ((K $$unsorted)) (= (tptp.ord_less_int (tptp.bit0 K) tptp.pls) (tptp.ord_less_int K tptp.pls))) (forall ((K $$unsorted)) (= (tptp.ord_less_int tptp.pls (tptp.bit0 K)) (tptp.ord_less_int tptp.pls K))) (forall ((K $$unsorted)) (= (tptp.ord_less_eq_int tptp.pls (tptp.bit1 K)) (tptp.ord_less_eq_int tptp.pls K))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_eq_int (tptp.bit0 K1) (tptp.bit1 K2)) (tptp.ord_less_eq_int K1 K2))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_eq_int (tptp.bit0 K) (tptp.bit1 L)) (tptp.ord_less_eq_int K L))) _let_1 true)))))))))))))))))))))))))))))
% 0.22/0.59  )
% 0.22/0.59  % SZS output end Proof for NUM926+1
% 0.22/0.59  % cvc5---1.0.5 exiting
% 0.22/0.59  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------