TSTP Solution File: NUM924+5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM924+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 10:48:57 EDT 2023
% Result : Theorem 0.21s 0.75s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : NUM924+5 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.15 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 13:55:53 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.75 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.vhANNvhjJ0/cvc5---1.0.5_1817.p...
% 0.21/0.75 ------- get file name : TPTP file name is NUM924+5
% 0.21/0.75 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1817.smt2...
% 0.21/0.75 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.75 % SZS status Theorem for NUM924+5
% 0.21/0.75 % SZS output start Proof for NUM924+5
% 0.21/0.75 (
% 0.21/0.75 (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.one_one tptp.int))) (let ((_let_3 (tptp.bit1 tptp.pls))) (let ((_let_4 (tptp.bit0 _let_3))) (let ((_let_5 (tptp.number_number_of tptp.nat _let_4))) (let ((_let_6 (tptp.plus_plus tptp.int (tptp.power_power tptp.int tptp.s _let_5) _let_2))) (let ((_let_7 (tptp.ord_less tptp.int _let_6 _let_1))) (let ((_let_8 (not _let_7))) (let ((_let_9 (tptp.number_number_of tptp.int tptp.pls))) (let ((_let_10 (= _let_1 _let_9))) (let ((_let_11 (forall ((W_1 $$unsorted) (Z_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int W_1 (tptp.one_one tptp.int)) Z_1) (tptp.ord_less tptp.int W_1 Z_1))))) (let ((_let_12 (forall ((W $$unsorted) (Z $$unsorted)) (=> (tptp.ord_less tptp.int W Z) (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int W (tptp.one_one tptp.int)) Z))))) (let ((_let_13 (tptp.number_number_of tptp.nat _let_3))) (let ((_let_14 (tptp.one_one tptp.nat))) (let ((_let_15 (forall ((W $$unsorted)) (= (tptp.times_times tptp.int tptp.pls W) tptp.pls)))) (let ((_let_16 (tptp.number_number_of tptp.nat tptp.pls))) (let ((_let_17 (tptp.zero_zero tptp.nat))) (let ((_let_18 (forall ((Z $$unsorted) (W $$unsorted)) (= (tptp.times_times tptp.int Z W) (tptp.times_times tptp.int W Z))))) (let ((_let_19 (forall ((K_1 $$unsorted)) (= (tptp.number_number_of tptp.int K_1) K_1)))) (let ((_let_20 (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_4)) tptp.m) _let_2))) (let ((_let_21 (tptp.times_times tptp.int _let_20 tptp.t))) (let ((_let_22 (= _let_6 _let_21))) (let ((_let_23 (tptp.times_times tptp.int _let_20 _let_1))) (let ((_let_24 (tptp.ord_less tptp.int _let_21 _let_23))) (let ((_let_25 (= _let_21 _let_6))) (let ((_let_26 (= tptp.pls _let_9))) (let ((_let_27 (= _let_23 (tptp.times_times tptp.int _let_1 _let_20)))) (let ((_let_28 (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int _let_21 _let_2) _let_23))) (let ((_let_29 (tptp.plus_plus tptp.int _let_6 _let_2))) (let ((_let_30 (tptp.ord_less_eq tptp.int _let_29 _let_1))) (let ((_let_31 (= tptp.pls (tptp.times_times tptp.int tptp.pls _let_20)))) (let ((_let_32 (SYMM (ASSUME :args (_let_22))))) (let ((_let_33 (ASSUME :args (_let_10)))) (let ((_let_34 (forall ((K_1 $$unsorted)) (= K_1 (tptp.number_number_of tptp.int K_1))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (_let_18))) (let ((_let_37 (ASSUME :args _let_36))) (let ((_let_38 (not _let_24))) (let ((_let_39 (or _let_38 _let_28))) (let ((_let_40 (forall ((W $$unsorted) (Z $$unsorted)) (or (not (tptp.ord_less tptp.int W Z)) (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int W (tptp.one_one tptp.int)) Z))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (= _let_7 _let_30))) (let ((_let_43 (not _let_30))) (let ((_let_44 (_let_11))) (let ((_let_45 (ASSUME :args _let_44))) (let ((_let_46 (forall ((W $$unsorted)) (= tptp.pls (tptp.times_times tptp.int tptp.pls W))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (not _let_31))) (let ((_let_49 (not _let_28))) (let ((_let_50 (not _let_27))) (let ((_let_51 (not _let_26))) (let ((_let_52 (not _let_10))) (let ((_let_53 (not _let_25))) (let ((_let_54 (ASSUME :args (_let_28)))) (let ((_let_55 (APPLY_UF tptp.ord_less_eq))) (let ((_let_56 (ASSUME :args (_let_27)))) (let ((_let_57 (ASSUME :args (_let_26)))) (let ((_let_58 (TRANS (SYMM (SYMM _let_57)) (SYMM _let_33)))) (let ((_let_59 (REFL :args (tptp.int)))) (let ((_let_60 (ASSUME :args (_let_31)))) (let ((_let_61 (ASSUME :args (_let_43)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_54 _let_32 _let_56 _let_33 _let_57 _let_60 _let_61) :args (_let_10 _let_25 _let_26 _let_27 _let_28 _let_43 _let_31)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_61)) (CONG _let_59 (REFL :args (_let_29)) (SYMM _let_58) :args _let_55) (CONG _let_59 (CONG _let_59 (SYMM _let_32) (REFL :args (_let_2)) :args (APPLY_UF tptp.plus_plus)) (TRANS (SYMM (SYMM _let_60)) (CONG _let_59 _let_58 (REFL :args (_let_20)) :args (APPLY_UF tptp.times_times)) (SYMM _let_56)) :args _let_55) (TRUE_INTRO _let_54))) :args (_let_28 _let_25 _let_27 _let_10 _let_26 _let_31 _let_43)) :args ((not (and _let_10 _let_25 _let_26 _let_27 _let_28 _let_43 _let_31)) SB_LITERAL))) (CONG (REFL :args (_let_52)) (REFL :args (_let_53)) (REFL :args (_let_51)) (REFL :args (_let_50)) (REFL :args (_let_49)) (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_30))) (REFL :args (_let_48)) :args (or))) :args ((or _let_53 _let_52 _let_30 _let_51 _let_50 _let_49 _let_48))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (_let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.times_times tptp.int tptp.pls W) tptp.pls))))) :args (_let_46))) _let_47 :args (_let_31 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_42)) :args ((or _let_7 _let_43 (not _let_42)))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_45 :args (_let_6 _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ord_less tptp.int W_1 Z_1)))) :args _let_44))) _let_45 :args (_let_42 false _let_11)) :args (_let_43 true _let_7 false _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_38 _let_28 (not _let_39)))) (ASSUME :args (_let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_21 _let_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ord_less tptp.int W Z) false))))) :args (_let_40))) _let_41 :args (_let_39 false _let_40)) :args (_let_28 false _let_24 false _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (_let_20 _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.times_times tptp.int Z W)))) :args _let_36)) _let_37 :args (_let_27 false _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.pls QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.number_number_of tptp.int K_1)))) :args (_let_34))) _let_35 :args (_let_26 false _let_34)) _let_33 _let_32 :args (false false _let_31 true _let_30 false _let_28 false _let_27 false _let_26 false _let_10 false _let_25)) :args ((forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (= (tptp.plus_plus X_b (tptp.ti X_b B_1) B_2) (tptp.plus_plus X_b B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (= (tptp.plus_plus X_b B_1 (tptp.ti X_b B_2)) (tptp.plus_plus X_b B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.plus_plus X_b B_1 B_2))) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (= (tptp.ti X_b _let_1) _let_1)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (= (tptp.plus_plus X_a (tptp.ti X_a B_1) B_2) (tptp.plus_plus X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (= (tptp.plus_plus X_a B_1 (tptp.ti X_a B_2)) (tptp.plus_plus X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a B_1 B_2))) (=> (tptp.linordered_ring X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (= (tptp.times_times X_b (tptp.ti X_b B_1) B_2) (tptp.times_times X_b B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (= (tptp.times_times X_b B_1 (tptp.ti X_b B_2)) (tptp.times_times X_b B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.times_times X_b B_1 B_2))) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (= (tptp.ti X_b _let_1) _let_1)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (= (tptp.times_times X_a (tptp.ti X_a B_1) B_2) (tptp.times_times X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (= (tptp.times_times X_a B_1 (tptp.ti X_a B_2)) (tptp.times_times X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a B_1 B_2))) (=> (tptp.linordered_ring X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.linordered_ring X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.undefined X_a))) (= (tptp.ti X_a _let_1) _let_1))) (forall ((B_1 $$unsorted)) (= (tptp.zprime (tptp.ti tptp.int B_1)) (tptp.zprime B_1))) (forall ((B_1 $$unsorted)) (= (tptp.bit0 (tptp.ti tptp.int B_1)) (tptp.bit0 B_1))) (forall ((B_1 $$unsorted)) (let ((_let_1 (tptp.bit0 B_1))) (= (tptp.ti tptp.int _let_1) _let_1))) (forall ((B_1 $$unsorted)) (= (tptp.bit1 (tptp.ti tptp.int B_1)) (tptp.bit1 B_1))) (forall ((B_1 $$unsorted)) (let ((_let_1 (tptp.bit1 B_1))) (= (tptp.ti tptp.int _let_1) _let_1))) (= (tptp.ti tptp.int tptp.pls) tptp.pls) (forall ((B_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.number X_a) (= (tptp.number_number_of X_a (tptp.ti tptp.int B_1)) (tptp.number_number_of X_a B_1)))) (forall ((B_1 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a B_1))) (=> (tptp.number X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (and (tptp.number X_a) (tptp.linorder X_a)) (= (tptp.ord_less X_a (tptp.ti X_a B_1) B_2) (tptp.ord_less X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (and (tptp.number X_a) (tptp.linorder X_a)) (= (tptp.ord_less X_a B_1 (tptp.ti X_a B_2)) (tptp.ord_less X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (= (tptp.ord_less X_a (tptp.ti X_a B_1) B_2) (tptp.ord_less X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (= (tptp.ord_less X_a B_1 (tptp.ti X_a B_2)) (tptp.ord_less X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (and (tptp.number X_a) (tptp.linorder X_a)) (= (tptp.ord_less_eq X_a (tptp.ti X_a B_1) B_2) (tptp.ord_less_eq X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (and (tptp.number X_a) (tptp.linorder X_a)) (= (tptp.ord_less_eq X_a B_1 (tptp.ti X_a B_2)) (tptp.ord_less_eq X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (= (tptp.ord_less_eq X_a (tptp.ti X_a B_1) B_2) (tptp.ord_less_eq X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (= (tptp.ord_less_eq X_a B_1 (tptp.ti X_a B_2)) (tptp.ord_less_eq X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (= (tptp.power_power X_a (tptp.ti X_a B_1) B_2) (tptp.power_power X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (= (tptp.power_power X_a B_1 (tptp.ti tptp.nat B_2)) (tptp.power_power X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.power_power X_a B_1 B_2))) (=> (tptp.semiring_1 X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((B_1 $$unsorted)) (= (tptp.twoSqu33214720sum2sq (tptp.ti tptp.int B_1)) (tptp.twoSqu33214720sum2sq B_1))) (= (tptp.ti tptp.int tptp.m) tptp.m) (= (tptp.ti tptp.int tptp.s) tptp.s) (= (tptp.ti tptp.int tptp.t) tptp.t) (tptp.ord_less tptp.int tptp.t _let_1) (tptp.ord_less tptp.int tptp.t _let_2) _let_24 _let_22 (=> (= tptp.t _let_1) (= _let_6 _let_1)) (not (tptp.ord_less_eq tptp.int _let_2 tptp.t)) (tptp.ord_less tptp.int _let_1 _let_20) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (tptp.ord_less X_a (tptp.plus_plus X_a (tptp.power_power X_a X _let_1) (tptp.power_power X_a Y _let_1)) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.ord_less X_a _let_1 (tptp.plus_plus X_a (tptp.power_power X_a X_1 _let_2) (tptp.power_power X_a Y_1 _let_2))) (or (not (= (tptp.ti X_a X_1) _let_1)) (not (= (tptp.ti X_a Y_1) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.plus_plus X_a (tptp.power_power X_a X_1 _let_2) (tptp.power_power X_a Y_1 _let_2)) _let_1) (and (= (tptp.ti X_a X_1) _let_1) (= (tptp.ti X_a Y_1) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (not (tptp.ord_less X_a (tptp.power_power X_a A_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.ord_less X_a _let_1 (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (= (tptp.ti X_a A_2) _let_1))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.power_power X_a _let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.power_power X_a _let_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) _let_1) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (= (tptp.plus_plus X_a (tptp.one_one X_a) (tptp.number_number_of X_a W)) (tptp.number_number_of X_a (tptp.plus_plus tptp.int (tptp.bit1 tptp.pls) W)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a V) (tptp.one_one X_a)) (tptp.number_number_of X_a (tptp.plus_plus tptp.int V (tptp.bit1 tptp.pls))))))) (tptp.ord_less tptp.int tptp.t _let_20) (not (forall ((T_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (= (tptp.plus_plus tptp.int (tptp.power_power tptp.int tptp.s (tptp.number_number_of tptp.nat _let_2)) _let_1) (tptp.times_times tptp.int (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 _let_2)) tptp.m) _let_1) T_1))))))) (tptp.zprime _let_20) (tptp.twoSqu33214720sum2sq _let_21) (forall ((W $$unsorted)) (tptp.ord_less_eq tptp.int W W)) _let_19 _let_18 (forall ((Z $$unsorted) (W $$unsorted)) (or (tptp.ord_less_eq tptp.int Z W) (tptp.ord_less_eq tptp.int W Z))) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.times_times tptp.int (tptp.number_number_of tptp.int V) (tptp.number_number_of tptp.int W)) (tptp.number_number_of tptp.int (tptp.times_times tptp.int V W)))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.number_number_of tptp.int K) (tptp.number_number_of tptp.int L)) (tptp.ord_less_eq tptp.int K L))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.ord_less_eq X_a (tptp.number_number_of X_a X_1) (tptp.number_number_of X_a Y_1)) (tptp.ord_less_eq tptp.int X_1 Y_1))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (= (tptp.times_times tptp.int (tptp.times_times tptp.int Z1 Z2) Z3) (tptp.times_times tptp.int Z1 (tptp.times_times tptp.int Z2 Z3)))) (forall ((K_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (tptp.ord_less_eq tptp.int I J) (=> (tptp.ord_less_eq tptp.int J K_1) (tptp.ord_less_eq tptp.int I K_1)))) (forall ((Z $$unsorted) (W $$unsorted)) (=> (tptp.ord_less_eq tptp.int Z W) (=> (tptp.ord_less_eq tptp.int W Z) (= Z W)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.power_power tptp.int X (tptp.plus_plus tptp.nat Y Z)) (tptp.times_times tptp.int (tptp.power_power tptp.int X Y) (tptp.power_power tptp.int X Z)))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit1 K1) (tptp.bit1 K2)) (tptp.ord_less_eq tptp.int K1 K2))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit1 K) (tptp.bit1 L)) (tptp.ord_less_eq tptp.int K L))) (tptp.ord_less_eq tptp.int tptp.pls tptp.pls) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit0 K1) (tptp.bit0 K2)) (tptp.ord_less_eq tptp.int K1 K2))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit0 K) (tptp.bit0 L)) (tptp.ord_less_eq tptp.int K L))) (forall ((Z_1 $$unsorted) (W_1 $$unsorted)) (= (tptp.ord_less tptp.int Z_1 W_1) (and (tptp.ord_less_eq tptp.int Z_1 W_1) (not (= Z_1 W_1))))) (forall ((K_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (tptp.ord_less_eq tptp.int I J) (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int K_1 I) (tptp.plus_plus tptp.int K_1 J)))) (forall ((V_3 $$unsorted)) (= (= (tptp.number_number_of tptp.nat V_3) (tptp.zero_zero tptp.nat)) (tptp.ord_less_eq tptp.int V_3 tptp.pls))) (forall ((V_3 $$unsorted)) (= (= (tptp.zero_zero tptp.nat) (tptp.number_number_of tptp.nat V_3)) (tptp.ord_less_eq tptp.int V_3 tptp.pls))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((V_1 $$unsorted) (V $$unsorted)) (=> (tptp.ord_less_eq tptp.int tptp.pls V) (=> (tptp.ord_less_eq tptp.int tptp.pls V_1) (= (tptp.times_times X_a (tptp.number_number_of X_a V) (tptp.number_number_of X_a V_1)) (tptp.number_number_of X_a (tptp.times_times tptp.int V V_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted) (Z $$unsorted)) (= (tptp.times_times X_a (tptp.number_number_of X_a V) (tptp.times_times X_a (tptp.number_number_of X_a W) Z)) (tptp.times_times X_a (tptp.number_number_of X_a (tptp.times_times tptp.int V W)) Z))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.times_times X_a (tptp.number_number_of X_a V) (tptp.number_number_of X_a W)) (tptp.number_number_of X_a (tptp.times_times tptp.int V W)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.number_number_of X_a (tptp.times_times tptp.int V W)) (tptp.times_times X_a (tptp.number_number_of X_a V) (tptp.number_number_of X_a W)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.ord_less_eq X_a (tptp.plus_plus X_a (tptp.times_times X_a X_1 X_1) (tptp.times_times X_a Y_1 Y_1)) _let_1) (and (= (tptp.ti X_a X_1) _let_1) (= (tptp.ti X_a Y_1) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.ord_less_eq X_a (tptp.zero_zero X_a) (tptp.plus_plus X_a (tptp.times_times X_a X X) (tptp.times_times X_a Y Y)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_1 $$unsorted)) (= (tptp.ord_less_eq X_a (tptp.number_number_of X_a X_1) (tptp.zero_zero X_a)) (tptp.ord_less_eq tptp.int X_1 tptp.pls))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Y_1 $$unsorted)) (= (tptp.ord_less_eq X_a (tptp.zero_zero X_a) (tptp.number_number_of X_a Y_1)) (tptp.ord_less_eq tptp.int tptp.pls Y_1))))) (forall ((V_3 $$unsorted)) (= (tptp.ord_less tptp.nat (tptp.zero_zero tptp.nat) (tptp.number_number_of tptp.nat V_3)) (tptp.ord_less tptp.int tptp.pls V_3))) (forall ((X_a $$unsorted)) (=> (and (tptp.number X_a) (tptp.linorder X_a)) (forall ((V_3 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a V_3))) (let ((_let_2 (tptp.number_number_of X_a W_1))) (= (tptp.ord_less_eq X_a _let_1 _let_2) (not (tptp.ord_less X_a _let_2 _let_1)))))))) (forall ((K $$unsorted)) (= (tptp.ord_less_eq tptp.int tptp.pls (tptp.bit1 K)) (tptp.ord_less_eq tptp.int tptp.pls K))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit0 K1) (tptp.bit1 K2)) (tptp.ord_less_eq tptp.int K1 K2))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit0 K) (tptp.bit1 L)) (tptp.ord_less_eq tptp.int K L))) (forall ((K $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit0 K) tptp.pls) (tptp.ord_less_eq tptp.int K tptp.pls))) (forall ((K $$unsorted)) (= (tptp.ord_less_eq tptp.int tptp.pls (tptp.bit0 K)) (tptp.ord_less_eq tptp.int tptp.pls K))) (forall ((Z_2 $$unsorted) (Z $$unsorted) (W_2 $$unsorted) (W $$unsorted)) (=> (tptp.ord_less tptp.int W_2 W) (=> (tptp.ord_less_eq tptp.int Z_2 Z) (tptp.ord_less tptp.int (tptp.plus_plus tptp.int W_2 Z_2) (tptp.plus_plus tptp.int W Z))))) (= _let_16 _let_17) (= _let_17 _let_16) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_1 $$unsorted)) (= (tptp.ord_less_eq X_a (tptp.number_number_of X_a X_1) (tptp.one_one X_a)) (tptp.ord_less_eq tptp.int X_1 (tptp.bit1 tptp.pls)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Y_1 $$unsorted)) (= (tptp.ord_less_eq X_a (tptp.one_one X_a) (tptp.number_number_of X_a Y_1)) (tptp.ord_less_eq tptp.int (tptp.bit1 tptp.pls) Y_1))))) (= (tptp.plus_plus tptp.nat _let_14 _let_14) _let_5) _let_15 (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.times_times tptp.int (tptp.bit0 K_1) L_1) (tptp.bit0 (tptp.times_times tptp.int K_1 L_1)))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less tptp.int (tptp.number_number_of tptp.int K) (tptp.number_number_of tptp.int L)) (tptp.ord_less tptp.int K L))) (forall ((Z $$unsorted)) (= (tptp.times_times tptp.int Z (tptp.one_one tptp.int)) Z)) (forall ((Z $$unsorted)) (= (tptp.times_times tptp.int (tptp.one_one tptp.int) Z) Z)) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.number_number_of tptp.int V) (tptp.number_number_of tptp.int W)) (tptp.number_number_of tptp.int (tptp.plus_plus tptp.int V W)))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (tptp.times_times tptp.int (tptp.plus_plus tptp.int Z1 Z2) W) (tptp.plus_plus tptp.int (tptp.times_times tptp.int Z1 W) (tptp.times_times tptp.int Z2 W)))) (forall ((W $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (= (tptp.times_times tptp.int W (tptp.plus_plus tptp.int Z1 Z2)) (tptp.plus_plus tptp.int (tptp.times_times tptp.int W Z1) (tptp.times_times tptp.int W Z2)))) (forall ((K $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit1 K) tptp.pls) (tptp.ord_less tptp.int K tptp.pls))) (forall ((K $$unsorted)) (= (tptp.ord_less tptp.int tptp.pls (tptp.bit1 K)) (tptp.ord_less_eq tptp.int tptp.pls K))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit1 K1) (tptp.bit0 K2)) (tptp.ord_less tptp.int K1 K2))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.bit1 K) (tptp.bit0 L)) (tptp.ord_less tptp.int K L))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit0 K1) (tptp.bit1 K2)) (tptp.ord_less_eq tptp.int K1 K2))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit0 K) (tptp.bit1 L)) (tptp.ord_less_eq tptp.int K L))) (forall ((V_3 $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int V_3 V_2))) (= (tptp.ord_less tptp.nat (tptp.number_number_of tptp.nat V_3) (tptp.number_number_of tptp.nat V_2)) (and (=> _let_1 (tptp.ord_less tptp.int tptp.pls V_2)) _let_1)))) (forall ((Z_1 $$unsorted)) (= (tptp.ord_less_eq tptp.int (tptp.one_one tptp.int) Z_1) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) Z_1))) (= _let_13 _let_14) (= _let_14 _let_13) _let_12 _let_11 (forall ((W_1 $$unsorted) (Z_1 $$unsorted)) (= (tptp.ord_less tptp.int W_1 (tptp.plus_plus tptp.int Z_1 (tptp.one_one tptp.int))) (tptp.ord_less_eq tptp.int W_1 Z_1))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((V_1 $$unsorted) (V $$unsorted)) (=> (tptp.ord_less_eq tptp.int tptp.pls V) (=> (tptp.ord_less_eq tptp.int tptp.pls V_1) (= (tptp.plus_plus X_a (tptp.number_number_of X_a V) (tptp.number_number_of X_a V_1)) (tptp.number_number_of X_a (tptp.plus_plus tptp.int V V_1)))))))) (forall ((V_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat V_1))) (let ((_let_2 (tptp.number_number_of tptp.nat V))) (let ((_let_3 (tptp.plus_plus tptp.nat _let_2 _let_1))) (let ((_let_4 (tptp.ord_less tptp.int V_1 tptp.pls))) (let ((_let_5 (tptp.ord_less tptp.int V tptp.pls))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.number_number_of tptp.nat (tptp.plus_plus tptp.int V V_1))))))))))))) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.ord_less_eq tptp.int _let_1 Z) (tptp.ord_less tptp.int _let_1 (tptp.plus_plus tptp.int (tptp.one_one tptp.int) Z))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.ring_char_0 X_a)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (tptp.number_number_of X_a X_1) (tptp.number_number_of X_a Y_1)) (= X_1 Y_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number X_a) (forall ((W_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a W_1))) (let ((_let_2 (tptp.ti X_a X_1))) (= (= _let_1 _let_2) (= _let_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 ((X $$unsorted) (Y $$unsorted)) (or (tptp.ord_less tptp.int X Y) (= X Y) (tptp.ord_less tptp.int Y X))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.plus_plus X_a (tptp.times_times X_a X_1 X_1) (tptp.times_times X_a Y_1 Y_1)) _let_1) (and (= (tptp.ti X_a X_1) _let_1) (= (tptp.ti X_a Y_1) _let_1))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (forall ((A_1 $$unsorted) (B $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b V))) (= (tptp.times_times X_b (tptp.plus_plus X_b A_1 B) _let_1) (tptp.plus_plus X_b (tptp.times_times X_b A_1 _let_1) (tptp.times_times X_b B _let_1))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (forall ((V $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b V))) (= (tptp.times_times X_b _let_1 (tptp.plus_plus X_b B C)) (tptp.plus_plus X_b (tptp.times_times X_b _let_1 B) (tptp.times_times X_b _let_1 C))))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int Z1 Z2) Z3) (tptp.plus_plus tptp.int Z1 (tptp.plus_plus tptp.int Z2 Z3)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.plus_plus tptp.int X (tptp.plus_plus tptp.int Y Z)) (tptp.plus_plus tptp.int Y (tptp.plus_plus tptp.int X Z)))) (forall ((Z $$unsorted) (W $$unsorted)) (= (tptp.plus_plus tptp.int Z W) (tptp.plus_plus tptp.int W Z))) _let_10 (tptp.ring_11004092258visors tptp.int) (tptp.linord581940658strict tptp.int) (tptp.linordered_ring tptp.int) (tptp.linordered_idom tptp.int) (tptp.number_semiring tptp.int) (tptp.linorder tptp.int) (tptp.semiring_1 tptp.int) (tptp.ring_char_0 tptp.int) (tptp.number_ring tptp.int) (tptp.semiring tptp.int) (tptp.number tptp.int) (tptp.number_semiring tptp.nat) (tptp.linorder tptp.nat) (tptp.semiring_1 tptp.nat) (tptp.semiring tptp.nat) (tptp.number tptp.nat) (forall ((T $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.ti T A))) (= (tptp.ti T _let_1) _let_1))) _let_8 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.75 )
% 0.21/0.75 % SZS output end Proof for NUM924+5
% 0.21/0.75 % cvc5---1.0.5 exiting
% 0.21/0.76 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------