TSTP Solution File: NUM925+5 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM925+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n031.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 11:50:54 EDT 2023
% Result : Theorem 20.12s 3.38s
% Output : Proof 35.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM925+5 : TPTP v8.1.2. Released v5.3.0.
% 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n031.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 13:39:07 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.68/1.37 Prover 1: Preprocessing ...
% 4.68/1.37 Prover 4: Preprocessing ...
% 4.68/1.40 Prover 2: Preprocessing ...
% 4.68/1.40 Prover 3: Preprocessing ...
% 4.68/1.40 Prover 0: Preprocessing ...
% 4.68/1.40 Prover 5: Preprocessing ...
% 4.68/1.40 Prover 6: Preprocessing ...
% 14.31/2.64 Prover 6: Proving ...
% 14.31/2.68 Prover 3: Constructing countermodel ...
% 15.08/2.74 Prover 1: Constructing countermodel ...
% 17.28/3.01 Prover 2: Proving ...
% 17.28/3.01 Prover 5: Proving ...
% 18.02/3.16 Prover 0: Proving ...
% 18.84/3.22 Prover 4: Constructing countermodel ...
% 19.45/3.37 Prover 3: proved (2762ms)
% 19.45/3.37
% 20.12/3.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.12/3.38
% 20.12/3.38 Prover 6: stopped
% 20.12/3.38 Prover 5: stopped
% 20.12/3.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 20.12/3.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 20.12/3.38 Prover 0: stopped
% 20.12/3.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 20.12/3.39 Prover 2: stopped
% 20.20/3.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 20.20/3.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 21.71/3.59 Prover 11: Preprocessing ...
% 21.71/3.59 Prover 10: Preprocessing ...
% 21.71/3.61 Prover 13: Preprocessing ...
% 21.71/3.63 Prover 7: Preprocessing ...
% 21.71/3.67 Prover 8: Preprocessing ...
% 24.67/4.00 Prover 10: Warning: ignoring some quantifiers
% 24.67/4.01 Prover 7: Warning: ignoring some quantifiers
% 24.96/4.02 Prover 10: Constructing countermodel ...
% 25.11/4.05 Prover 7: Constructing countermodel ...
% 25.74/4.16 Prover 8: Warning: ignoring some quantifiers
% 26.21/4.18 Prover 13: Warning: ignoring some quantifiers
% 26.21/4.19 Prover 8: Constructing countermodel ...
% 26.21/4.22 Prover 13: Constructing countermodel ...
% 28.91/4.55 Prover 11: Constructing countermodel ...
% 32.94/5.10 Prover 10: Found proof (size 439)
% 32.94/5.10 Prover 10: proved (1713ms)
% 32.94/5.10 Prover 11: stopped
% 32.94/5.10 Prover 13: stopped
% 32.94/5.10 Prover 1: stopped
% 32.94/5.10 Prover 8: stopped
% 32.94/5.10 Prover 4: stopped
% 32.94/5.12 Prover 7: stopped
% 32.94/5.12
% 32.94/5.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.94/5.12
% 34.09/5.39 % SZS output start Proof for theBenchmark
% 34.46/5.40 Assumptions after simplification:
% 34.46/5.40 ---------------------------------
% 34.46/5.40
% 34.46/5.40 (arity_Int_Oint___Groups_Olinordered__ab__group__add)
% 34.46/5.40 $i(int) & linord219039673up_add(int)
% 34.46/5.40
% 34.46/5.40 (arity_Int_Oint___Power_Opower)
% 34.46/5.40 $i(int) & power(int)
% 34.46/5.40
% 34.46/5.40 (arity_Int_Oint___Rings_Olinordered__idom)
% 34.46/5.40 $i(int) & linordered_idom(int)
% 34.46/5.40
% 34.46/5.40 (arity_Int_Oint___Rings_Omult__zero)
% 34.46/5.40 $i(int) & mult_zero(int)
% 34.46/5.40
% 34.46/5.40 (arity_Int_Oint___Rings_Ono__zero__divisors)
% 34.46/5.40 $i(int) & no_zero_divisors(int)
% 34.46/5.40
% 34.46/5.40 (arity_Int_Oint___Rings_Osemiring__0)
% 34.46/5.40 $i(int) & semiring_0(int)
% 34.46/5.40
% 34.46/5.40 (arity_Int_Oint___Rings_Ozero__neq__one)
% 34.46/5.40 $i(int) & zero_neq_one(int)
% 34.46/5.40
% 34.46/5.40 (conj_0)
% 34.46/5.43 $i(n) & $i(nat) & $i(pls) & $i(int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 34.46/5.43 : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (power_power(int,
% 34.46/5.43 v2, v5) = v6 & semiring_1_of_nat(int, n) = v1 & number_number_of(nat, v4)
% 34.46/5.43 = v5 & bit1(pls) = v3 & bit0(v3) = v4 & zero_zero(int) = v6 & plus_plus(int,
% 34.46/5.43 v0, v1) = v2 & one_one(int) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 34.46/5.43 $i(v2) & $i(v1) & $i(v0))
% 34.46/5.43
% 34.46/5.43 (fact_0_n1pos)
% 34.46/5.44 $i(n) & $i(int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 34.46/5.44 (semiring_1_of_nat(int, n) = v2 & zero_zero(int) = v0 & plus_plus(int, v1, v2)
% 34.46/5.44 = v3 & one_one(int) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ord_less(int,
% 34.46/5.44 v0, v3))
% 34.46/5.44
% 34.46/5.44 (fact_10_quartic__square__square)
% 34.46/5.44 $i(nat) & $i(pls) & $i(int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 34.46/5.44 [v3: $i] : ? [v4: $i] : (number_number_of(nat, v3) = v4 &
% 34.46/5.44 number_number_of(nat, v1) = v2 & bit1(pls) = v0 & bit0(v1) = v3 & bit0(v0) =
% 34.46/5.44 v1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i]
% 34.46/5.44 : ( ~ (power_power(int, v5, v4) = v6) | ~ $i(v5) | ? [v7: $i] :
% 34.46/5.44 (power_power(int, v7, v2) = v6 & power_power(int, v5, v2) = v7 & $i(v7) &
% 34.46/5.44 $i(v6))))
% 34.46/5.44
% 34.46/5.44 (fact_11_power__0__left__number__of)
% 34.46/5.45 $i(nat) & ? [v0: $i] : (zero_zero(nat) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.46/5.45 $i] : ( ~ (one_one(v1) = v2) | ~ $i(v1) | ~ semiring_0(v1) | ~
% 34.46/5.45 power(v1) | ? [v3: $i] : (zero_zero(v1) = v3 & $i(v3) & ! [v4: $i] : !
% 34.46/5.45 [v5: $i] : ! [v6: $i] : (v6 = v3 | v5 = v0 | ~ (power_power(v1, v3,
% 34.46/5.45 v5) = v6) | ~ (number_number_of(nat, v4) = v5) | ~ $i(v4)) & !
% 34.46/5.45 [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ (power_power(v1, v3, v0) = v5) |
% 34.46/5.45 ~ (number_number_of(nat, v4) = v0) | ~ $i(v4)))))
% 34.46/5.45
% 34.46/5.45 (fact_12_semiring__norm_I110_J)
% 34.46/5.45 $i(pls) & ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 34.46/5.45 ( ~ (number_number_of(v1, v0) = v2) | ~ $i(v1) | ~ number_ring(v1) |
% 34.46/5.45 (one_one(v1) = v2 & $i(v2))))
% 34.46/5.45
% 34.46/5.45 (fact_13_numeral__1__eq__1)
% 34.46/5.45 $i(pls) & ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 34.46/5.45 ( ~ (number_number_of(v1, v0) = v2) | ~ $i(v1) | ~ number_ring(v1) |
% 34.46/5.45 (one_one(v1) = v2 & $i(v2))))
% 34.46/5.45
% 34.46/5.45 (fact_19_zero__is__num__zero)
% 34.46/5.45 $i(pls) & $i(int) & ? [v0: $i] : (number_number_of(int, pls) = v0 &
% 34.46/5.45 zero_zero(int) = v0 & $i(v0))
% 34.46/5.45
% 34.46/5.45 (fact_1_t1)
% 34.46/5.45 $i(t) & $i(int) & ? [v0: $i] : (one_one(int) = v0 & $i(v0) & ord_less(int,
% 34.46/5.45 v0, t))
% 34.46/5.45
% 34.46/5.45 (fact_23_zadd__int)
% 34.46/5.46 $i(nat) & $i(int) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 34.46/5.46 [v4: $i] : ( ~ (semiring_1_of_nat(int, v1) = v3) | ~ (semiring_1_of_nat(int,
% 34.46/5.46 v0) = v2) | ~ (plus_plus(int, v2, v3) = v4) | ~ $i(v1) | ~ $i(v0) |
% 34.46/5.46 ? [v5: $i] : (semiring_1_of_nat(int, v5) = v4 & plus_plus(nat, v0, v1) = v5
% 34.46/5.46 & $i(v5) & $i(v4)))
% 34.46/5.46
% 34.46/5.46 (fact_24_int__1)
% 34.46/5.46 $i(nat) & $i(int) & ? [v0: $i] : ? [v1: $i] : (semiring_1_of_nat(int, v0) =
% 34.46/5.46 v1 & one_one(nat) = v0 & one_one(int) = v1 & $i(v1) & $i(v0))
% 34.46/5.46
% 34.46/5.46 (fact_27_int__eq__0__conv)
% 34.46/5.46 $i(nat) & $i(int) & ? [v0: $i] : ? [v1: $i] : (zero_zero(nat) = v1 &
% 34.46/5.46 zero_zero(int) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : (v2 = v1 | ~
% 34.46/5.46 (semiring_1_of_nat(int, v2) = v0) | ~ $i(v2)) & ! [v2: $i] : (v2 = v0 |
% 34.46/5.46 ~ (semiring_1_of_nat(int, v1) = v2)))
% 34.46/5.46
% 34.46/5.46 (fact_28_int__0)
% 34.46/5.46 $i(nat) & $i(int) & ? [v0: $i] : ? [v1: $i] : (semiring_1_of_nat(int, v0) =
% 34.46/5.46 v1 & zero_zero(nat) = v0 & zero_zero(int) = v1 & $i(v1) & $i(v0))
% 34.46/5.46
% 34.46/5.46 (fact_29_nat__1__add__1)
% 34.46/5.47 $i(nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 34.46/5.47 (number_number_of(nat, v3) = v1 & bit1(pls) = v2 & bit0(v2) = v3 &
% 34.46/5.47 plus_plus(nat, v0, v0) = v1 & one_one(nat) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 34.46/5.47 $i(v0))
% 34.46/5.47
% 34.46/5.47 (fact_2_sum__power2__eq__zero__iff)
% 34.46/5.47 $i(nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 34.46/5.47 (number_number_of(nat, v1) = v2 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v2) &
% 34.46/5.47 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 34.46/5.47 [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v9 = v4 | ~ (power_power(v3, v6,
% 34.46/5.47 v2) = v8) | ~ (power_power(v3, v5, v2) = v7) | ~ (zero_zero(v3) =
% 34.46/5.47 v4) | ~ (plus_plus(v3, v7, v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~
% 34.46/5.47 $i(v3) | ~ linordered_idom(v3) | ? [v10: $i] : ? [v11: $i] : (( ~ (v11
% 34.46/5.47 = v4) & ti(v3, v6) = v11 & $i(v11)) | ( ~ (v10 = v4) & ti(v3, v5) =
% 34.46/5.47 v10 & $i(v10)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 34.46/5.47 $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (power_power(v3, v6, v2) = v8) | ~
% 34.46/5.47 (power_power(v3, v5, v2) = v7) | ~ (zero_zero(v3) = v4) | ~
% 34.46/5.47 (plus_plus(v3, v7, v8) = v4) | ~ $i(v6) | ~ $i(v5) | ~ $i(v3) | ~
% 34.46/5.47 linordered_idom(v3) | (ti(v3, v6) = v4 & ti(v3, v5) = v4 & $i(v4))))
% 34.46/5.47
% 34.46/5.47 (fact_37_one__is__num__one)
% 34.46/5.47 $i(pls) & $i(int) & ? [v0: $i] : ? [v1: $i] : (number_number_of(int, v1) =
% 34.46/5.47 v0 & bit1(pls) = v1 & one_one(int) = v0 & $i(v1) & $i(v0))
% 34.46/5.47
% 34.46/5.47 (fact_38_nat__numeral__1__eq__1)
% 34.46/5.47 $i(nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : (number_number_of(nat, v0) =
% 34.46/5.47 v1 & bit1(pls) = v0 & one_one(nat) = v1 & $i(v1) & $i(v0))
% 34.46/5.47
% 34.46/5.47 (fact_39_Numeral1__eq1__nat)
% 34.46/5.48 $i(nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : (number_number_of(nat, v1) =
% 34.46/5.48 v0 & bit1(pls) = v1 & one_one(nat) = v0 & $i(v1) & $i(v0))
% 34.46/5.48
% 34.46/5.48 (fact_3_one__power2)
% 34.46/5.48 $i(nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 34.46/5.48 (number_number_of(nat, v1) = v2 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v2) &
% 34.46/5.48 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 34.46/5.48 (power_power(v3, v4, v2) = v5) | ~ (one_one(v3) = v4) | ~ $i(v3) | ~
% 34.46/5.48 semiring_1(v3)))
% 34.46/5.48
% 34.46/5.48 (fact_47_zadd__commute)
% 34.46/5.48 $i(int) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (plus_plus(int, v0,
% 34.46/5.48 v1) = v2) | ~ $i(v1) | ~ $i(v0) | (plus_plus(int, v1, v0) = v2 &
% 34.46/5.48 $i(v2)))
% 34.46/5.48
% 34.46/5.48 (fact_4_zero__power2)
% 34.46/5.48 $i(nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 34.46/5.48 (number_number_of(nat, v1) = v2 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v2) &
% 34.46/5.48 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 34.46/5.48 (power_power(v3, v4, v2) = v5) | ~ (zero_zero(v3) = v4) | ~ $i(v3) | ~
% 34.46/5.48 semiring_1(v3)))
% 34.46/5.48
% 34.46/5.48 (fact_56_bin__less__0__simps_I4_J)
% 34.46/5.48 $i(int) & ? [v0: $i] : (zero_zero(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.46/5.48 $i] : ( ~ (bit1(v1) = v2) | ~ $i(v1) | ~ ord_less(int, v2, v0) |
% 34.46/5.48 ord_less(int, v1, v0)) & ! [v1: $i] : ! [v2: $i] : ( ~ (bit1(v1) = v2) |
% 34.46/5.48 ~ $i(v1) | ~ ord_less(int, v1, v0) | ord_less(int, v2, v0)))
% 34.46/5.48
% 34.46/5.48 (fact_57_bin__less__0__simps_I1_J)
% 34.46/5.48 $i(pls) & $i(int) & ? [v0: $i] : (zero_zero(int) = v0 & $i(v0) & ~
% 34.46/5.48 ord_less(int, pls, v0))
% 34.46/5.48
% 34.46/5.48 (fact_58_bin__less__0__simps_I3_J)
% 34.46/5.48 $i(int) & ? [v0: $i] : (zero_zero(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.46/5.48 $i] : ( ~ (bit0(v1) = v2) | ~ $i(v1) | ~ ord_less(int, v2, v0) |
% 34.46/5.48 ord_less(int, v1, v0)) & ! [v1: $i] : ! [v2: $i] : ( ~ (bit0(v1) = v2) |
% 34.46/5.48 ~ $i(v1) | ~ ord_less(int, v1, v0) | ord_less(int, v2, v0)))
% 34.46/5.48
% 34.46/5.48 (fact_59_int__0__less__1)
% 34.46/5.49 $i(int) & ? [v0: $i] : ? [v1: $i] : (zero_zero(int) = v0 & one_one(int) = v1
% 34.46/5.49 & $i(v1) & $i(v0) & ord_less(int, v0, v1))
% 34.46/5.49
% 34.46/5.49 (fact_5_zero__eq__power2)
% 34.90/5.49 $i(nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 34.90/5.49 (number_number_of(nat, v1) = v2 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v2) &
% 34.90/5.49 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 34.90/5.49 (v6 = v4 | ~ (power_power(v3, v5, v2) = v6) | ~ (zero_zero(v3) = v4) | ~
% 34.90/5.49 $i(v5) | ~ $i(v3) | ~ ring_11004092258visors(v3) | ? [v7: $i] : ( ~ (v7
% 34.90/5.49 = v4) & ti(v3, v5) = v7 & $i(v7))) & ! [v3: $i] : ! [v4: $i] : !
% 34.90/5.49 [v5: $i] : ( ~ (power_power(v3, v5, v2) = v4) | ~ (zero_zero(v3) = v4) | ~
% 34.90/5.49 $i(v5) | ~ $i(v3) | ~ ring_11004092258visors(v3) | (ti(v3, v5) = v4 &
% 34.90/5.49 $i(v4))))
% 34.90/5.49
% 34.90/5.49 (fact_60_zless__add1__eq)
% 34.90/5.49 $i(int) & ? [v0: $i] : (one_one(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.90/5.49 $i] : ! [v3: $i] : (v2 = v1 | ~ (plus_plus(int, v2, v0) = v3) | ~
% 34.90/5.49 $i(v2) | ~ $i(v1) | ~ ord_less(int, v1, v3) | ord_less(int, v1, v2)) &
% 34.90/5.49 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (plus_plus(int, v2, v0) = v3) |
% 34.90/5.49 ~ $i(v2) | ~ $i(v1) | ~ ord_less(int, v1, v2) | ord_less(int, v1, v3))
% 34.90/5.49 & ! [v1: $i] : ! [v2: $i] : ( ~ (plus_plus(int, v1, v0) = v2) | ~ $i(v1)
% 34.90/5.49 | ord_less(int, v1, v2)))
% 34.90/5.49
% 34.90/5.49 (fact_61_int__less__0__conv)
% 34.90/5.49 $i(int) & ? [v0: $i] : (zero_zero(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.90/5.49 $i] : ( ~ (semiring_1_of_nat(int, v1) = v2) | ~ $i(v1) | ~ ord_less(int,
% 34.90/5.49 v2, v0)))
% 34.90/5.49
% 34.90/5.49 (fact_62_less__special_I4_J)
% 34.90/5.49 $i(pls) & $i(int) & ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : !
% 34.90/5.49 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (number_number_of(v1, v3) = v4) |
% 34.90/5.49 ~ (one_one(v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ number_ring(v1) | ~
% 34.90/5.49 ord_less(v1, v4, v2) | ~ linordered_idom(v1) | ord_less(int, v3, v0)) &
% 34.90/5.49 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 34.90/5.49 (number_number_of(v1, v3) = v4) | ~ (one_one(v1) = v2) | ~ $i(v3) | ~
% 34.90/5.49 $i(v1) | ~ number_ring(v1) | ~ ord_less(int, v3, v0) | ~
% 34.90/5.49 linordered_idom(v1) | ord_less(v1, v4, v2)))
% 34.90/5.49
% 34.90/5.49 (fact_63_less__special_I2_J)
% 34.90/5.50 $i(pls) & $i(int) & ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : !
% 34.90/5.50 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (number_number_of(v1, v3) = v4) |
% 34.90/5.50 ~ (one_one(v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ number_ring(v1) | ~
% 34.90/5.50 ord_less(v1, v2, v4) | ~ linordered_idom(v1) | ord_less(int, v0, v3)) &
% 34.90/5.50 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 34.90/5.50 (number_number_of(v1, v3) = v4) | ~ (one_one(v1) = v2) | ~ $i(v3) | ~
% 34.90/5.50 $i(v1) | ~ number_ring(v1) | ~ ord_less(int, v0, v3) | ~
% 34.90/5.50 linordered_idom(v1) | ord_less(v1, v2, v4)))
% 34.90/5.50
% 34.90/5.50 (fact_64_odd__less__0)
% 34.94/5.50 $i(int) & ? [v0: $i] : ? [v1: $i] : (zero_zero(int) = v1 & one_one(int) = v0
% 34.94/5.50 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 34.94/5.50 (plus_plus(int, v3, v2) = v4) | ~ (plus_plus(int, v0, v2) = v3) | ~
% 34.94/5.50 $i(v2) | ~ ord_less(int, v4, v1) | ord_less(int, v2, v1)) & ! [v2: $i] :
% 34.94/5.50 ! [v3: $i] : ! [v4: $i] : ( ~ (plus_plus(int, v3, v2) = v4) | ~
% 34.94/5.50 (plus_plus(int, v0, v2) = v3) | ~ $i(v2) | ~ ord_less(int, v2, v1) |
% 34.94/5.50 ord_less(int, v4, v1)))
% 34.94/5.50
% 34.94/5.50 (fact_65_double__eq__0__iff)
% 34.94/5.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 34.94/5.50 (zero_zero(v0) = v1) | ~ (ti(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~
% 34.94/5.50 linord219039673up_add(v0) | ? [v4: $i] : ( ~ (v4 = v1) & plus_plus(v0, v2,
% 34.94/5.50 v2) = v4 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 34.94/5.50 (zero_zero(v0) = v1) | ~ (ti(v0, v2) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 34.94/5.50 linord219039673up_add(v0) | (plus_plus(v0, v2, v2) = v1 & $i(v1)))
% 34.94/5.50
% 34.94/5.50 (fact_6_add__special_I2_J)
% 34.94/5.50 $i(pls) & $i(int) & ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : !
% 34.94/5.50 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 34.94/5.50 (number_number_of(v1, v4) = v5) | ~ (plus_plus(int, v0, v3) = v4) | ~
% 34.94/5.50 (one_one(v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ number_ring(v1) | ? [v6:
% 34.94/5.50 $i] : (number_number_of(v1, v3) = v6 & plus_plus(v1, v2, v6) = v5 &
% 34.94/5.50 $i(v6) & $i(v5))))
% 34.94/5.50
% 34.94/5.50 (fact_73_Pls__def)
% 34.94/5.50 zero_zero(int) = pls & $i(pls) & $i(int)
% 34.94/5.50
% 34.94/5.50 (fact_74_int__0__neq__1)
% 34.94/5.50 $i(int) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & zero_zero(int) = v0 &
% 34.94/5.50 one_one(int) = v1 & $i(v1) & $i(v0))
% 34.94/5.50
% 34.94/5.50 (fact_79_zadd__0__right)
% 34.94/5.50 $i(int) & ? [v0: $i] : (zero_zero(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.94/5.50 $i] : (v2 = v1 | ~ (plus_plus(int, v1, v0) = v2) | ~ $i(v1)))
% 34.94/5.50
% 34.94/5.50 (fact_7_add__special_I3_J)
% 34.97/5.51 $i(pls) & $i(int) & ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : !
% 34.97/5.51 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 34.97/5.51 (number_number_of(v1, v4) = v5) | ~ (plus_plus(int, v3, v0) = v4) | ~
% 34.97/5.51 (one_one(v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ number_ring(v1) | ? [v6:
% 34.97/5.51 $i] : (number_number_of(v1, v3) = v6 & plus_plus(v1, v6, v2) = v5 &
% 34.97/5.51 $i(v6) & $i(v5))))
% 34.97/5.51
% 34.97/5.51 (fact_80_zadd__0)
% 34.97/5.51 $i(int) & ? [v0: $i] : (zero_zero(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.97/5.51 $i] : (v2 = v1 | ~ (plus_plus(int, v0, v1) = v2) | ~ $i(v1)))
% 34.97/5.51
% 34.97/5.51 (fact_86_power__eq__0__iff__number__of)
% 34.97/5.51 $i(nat) & ? [v0: $i] : (zero_zero(nat) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.97/5.51 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 |
% 34.97/5.51 v5 = v0 | ~ (power_power(v1, v3, v5) = v6) | ~ (number_number_of(nat,
% 34.97/5.51 v4) = v5) | ~ (zero_zero(v1) = v2) | ~ $i(v4) | ~ $i(v3) | ~
% 34.97/5.51 $i(v1) | ~ zero_neq_one(v1) | ~ no_zero_divisors(v1) | ~ mult_zero(v1)
% 34.97/5.51 | ~ power(v1) | ? [v7: $i] : ( ~ (v7 = v2) & ti(v1, v3) = v7 & $i(v7)))
% 34.97/5.51 & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 34.97/5.51 (power_power(v1, v3, v5) = v2) | ~ (number_number_of(nat, v4) = v5) | ~
% 34.97/5.51 (zero_zero(v1) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~
% 34.97/5.51 zero_neq_one(v1) | ~ no_zero_divisors(v1) | ~ mult_zero(v1) | ~
% 34.97/5.51 power(v1) | (ti(v1, v3) = v2 & $i(v2))) & ! [v1: $i] : ! [v2: $i] : !
% 34.97/5.51 [v3: $i] : ! [v4: $i] : ( ~ (power_power(v1, v3, v0) = v2) | ~
% 34.97/5.51 (number_number_of(nat, v4) = v0) | ~ (zero_zero(v1) = v2) | ~ $i(v4) |
% 34.97/5.51 ~ $i(v3) | ~ $i(v1) | ~ zero_neq_one(v1) | ~ no_zero_divisors(v1) | ~
% 34.97/5.51 mult_zero(v1) | ~ power(v1)))
% 34.97/5.51
% 34.97/5.51 (fact_8_one__add__one__is__two)
% 34.97/5.51 $i(pls) & ? [v0: $i] : ? [v1: $i] : (bit1(pls) = v0 & bit0(v0) = v1 & $i(v1)
% 34.97/5.51 & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (number_number_of(v2, v1) = v3) |
% 34.97/5.51 ~ $i(v2) | ~ number_ring(v2) | ? [v4: $i] : (plus_plus(v2, v4, v4) = v3
% 34.97/5.51 & one_one(v2) = v4 & $i(v4) & $i(v3))))
% 34.97/5.51
% 34.97/5.51 (fact_92_Bit1__def)
% 34.97/5.51 $i(int) & ? [v0: $i] : (one_one(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.97/5.51 $i] : ! [v3: $i] : ( ~ (plus_plus(int, v2, v1) = v3) | ~ (plus_plus(int,
% 34.97/5.51 v0, v1) = v2) | ~ $i(v1) | (bit1(v1) = v3 & $i(v3))))
% 34.97/5.51
% 34.97/5.51 (fact_93_odd__nonzero)
% 34.97/5.51 $i(int) & ? [v0: $i] : ? [v1: $i] : (zero_zero(int) = v1 & one_one(int) = v0
% 34.97/5.51 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (plus_plus(int, v3, v2)
% 34.97/5.51 = v1) | ~ (plus_plus(int, v0, v2) = v3) | ~ $i(v2)))
% 34.97/5.51
% 34.97/5.51 (fact_95_zero__less__power2)
% 34.97/5.52 $i(nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 34.97/5.52 (number_number_of(nat, v1) = v2 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v2) &
% 34.97/5.52 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 34.97/5.52 ~ (power_power(v3, v5, v2) = v6) | ~ (zero_zero(v3) = v4) | ~ $i(v5) |
% 34.97/5.52 ~ $i(v3) | ~ ord_less(v3, v4, v6) | ~ linordered_idom(v3) | ? [v7: $i]
% 34.97/5.52 : ( ~ (v7 = v4) & ti(v3, v5) = v7 & $i(v7))) & ! [v3: $i] : ! [v4: $i] :
% 34.97/5.52 ! [v5: $i] : ! [v6: $i] : ( ~ (power_power(v3, v5, v2) = v6) | ~
% 34.97/5.52 (zero_zero(v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ linordered_idom(v3) |
% 34.97/5.52 ord_less(v3, v4, v6) | (ti(v3, v5) = v4 & $i(v4))))
% 34.97/5.52
% 34.97/5.52 (fact_96_power2__less__0)
% 34.97/5.52 $i(nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 34.97/5.52 (number_number_of(nat, v1) = v2 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v2) &
% 34.97/5.52 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 34.97/5.52 ~ (power_power(v3, v5, v2) = v6) | ~ (zero_zero(v3) = v4) | ~ $i(v5) |
% 34.97/5.52 ~ $i(v3) | ~ ord_less(v3, v6, v4) | ~ linordered_idom(v3)))
% 34.97/5.52
% 34.97/5.52 (fact_97_sum__power2__gt__zero__iff)
% 34.97/5.52 $i(nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 34.97/5.52 (number_number_of(nat, v1) = v2 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v2) &
% 34.97/5.52 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 34.97/5.52 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (power_power(v3, v6, v2) = v8) |
% 34.97/5.52 ~ (power_power(v3, v5, v2) = v7) | ~ (zero_zero(v3) = v4) | ~
% 34.97/5.52 (plus_plus(v3, v7, v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v3) | ~
% 34.97/5.52 ord_less(v3, v4, v9) | ~ linordered_idom(v3) | ? [v10: $i] : ? [v11:
% 34.97/5.52 $i] : (( ~ (v11 = v4) & ti(v3, v6) = v11 & $i(v11)) | ( ~ (v10 = v4) &
% 34.97/5.52 ti(v3, v5) = v10 & $i(v10)))) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 34.97/5.52 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 34.97/5.52 (power_power(v3, v6, v2) = v8) | ~ (power_power(v3, v5, v2) = v7) | ~
% 34.97/5.52 (zero_zero(v3) = v4) | ~ (plus_plus(v3, v7, v8) = v9) | ~ $i(v6) | ~
% 34.97/5.52 $i(v5) | ~ $i(v3) | ~ linordered_idom(v3) | ord_less(v3, v4, v9) |
% 34.97/5.52 (ti(v3, v6) = v4 & ti(v3, v5) = v4 & $i(v4))))
% 34.97/5.52
% 34.97/5.52 (fact_9_semiring__one__add__one__is__two)
% 34.97/5.52 $i(pls) & ? [v0: $i] : ? [v1: $i] : (bit1(pls) = v0 & bit0(v0) = v1 & $i(v1)
% 34.97/5.52 & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (number_number_of(v2, v1) = v3) |
% 34.97/5.52 ~ $i(v2) | ~ number_semiring(v2) | ? [v4: $i] : (plus_plus(v2, v4, v4)
% 34.97/5.52 = v3 & one_one(v2) = v4 & $i(v4) & $i(v3))))
% 34.97/5.52
% 34.97/5.52 (tsy_c_Int_OBit0_res)
% 34.97/5.53 $i(int) & ! [v0: $i] : ! [v1: $i] : ( ~ (bit0(v0) = v1) | ~ $i(v0) |
% 34.97/5.53 (ti(int, v1) = v1 & $i(v1)))
% 34.97/5.53
% 34.97/5.53 (tsy_c_Orderings_Oord__class_Oless_0_arg2)
% 34.97/5.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (ti(v2, v1) = v3)
% 34.97/5.53 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ord_less(v2, v0, v3) | ~
% 34.97/5.53 linordered_idom(v2) | ord_less(v2, v0, v1)) & ! [v0: $i] : ! [v1: $i] : !
% 34.97/5.53 [v2: $i] : ! [v3: $i] : ( ~ (ti(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 34.97/5.53 $i(v0) | ~ ord_less(v2, v0, v1) | ~ linordered_idom(v2) | ord_less(v2, v0,
% 34.97/5.53 v3))
% 34.97/5.53
% 34.97/5.53 (function-axioms)
% 34.97/5.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 34.97/5.53 | ~ (power_power(v4, v3, v2) = v1) | ~ (power_power(v4, v3, v2) = v0)) &
% 34.97/5.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 34.97/5.53 | ~ (plus_plus(v4, v3, v2) = v1) | ~ (plus_plus(v4, v3, v2) = v0)) & !
% 34.97/5.53 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 34.97/5.53 (semiring_1_of_nat(v3, v2) = v1) | ~ (semiring_1_of_nat(v3, v2) = v0)) & !
% 34.97/5.53 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 34.97/5.53 (number_number_of(v3, v2) = v1) | ~ (number_number_of(v3, v2) = v0)) & !
% 34.97/5.53 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ti(v3, v2)
% 34.97/5.53 = v1) | ~ (ti(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 34.97/5.53 (v1 = v0 | ~ (bit1(v2) = v1) | ~ (bit1(v2) = v0)) & ! [v0: $i] : ! [v1:
% 34.97/5.53 $i] : ! [v2: $i] : (v1 = v0 | ~ (bit0(v2) = v1) | ~ (bit0(v2) = v0)) & !
% 34.97/5.53 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (undefined(v2) = v1) | ~
% 34.97/5.53 (undefined(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 34.97/5.53 ~ (zero_zero(v2) = v1) | ~ (zero_zero(v2) = v0)) & ! [v0: $i] : ! [v1:
% 34.97/5.53 $i] : ! [v2: $i] : (v1 = v0 | ~ (one_one(v2) = v1) | ~ (one_one(v2) =
% 34.97/5.53 v0))
% 34.97/5.53
% 34.97/5.53 Further assumptions not needed in the proof:
% 34.97/5.53 --------------------------------------------
% 34.97/5.53 arity_Int_Oint___Int_Onumber, arity_Int_Oint___Int_Onumber__ring,
% 34.97/5.53 arity_Int_Oint___Int_Onumber__semiring, arity_Int_Oint___Int_Oring__char__0,
% 34.97/5.53 arity_Int_Oint___Rings_Oring__1__no__zero__divisors,
% 34.97/5.53 arity_Int_Oint___Rings_Osemiring__1, arity_Nat_Onat___Int_Onumber,
% 34.97/5.53 arity_Nat_Onat___Int_Onumber__semiring, arity_Nat_Onat___Power_Opower,
% 34.97/5.53 arity_Nat_Onat___Rings_Omult__zero, arity_Nat_Onat___Rings_Ono__zero__divisors,
% 34.97/5.53 arity_Nat_Onat___Rings_Osemiring__0, arity_Nat_Onat___Rings_Osemiring__1,
% 34.97/5.53 arity_Nat_Onat___Rings_Ozero__neq__one, fact_14_n0, fact_15_zless__linear,
% 34.97/5.53 fact_16_less__number__of__int__code, fact_17_plus__numeral__code_I9_J,
% 34.97/5.53 fact_18_less__number__of, fact_20_zpower__int, fact_21_int__power,
% 34.97/5.53 fact_22_zadd__int__left, fact_25_nat__number__of__Pls,
% 34.97/5.53 fact_26_semiring__norm_I113_J, fact_30_less__int__code_I16_J,
% 34.97/5.53 fact_31_rel__simps_I17_J, fact_32_rel__simps_I2_J,
% 34.97/5.53 fact_33_less__int__code_I13_J, fact_34_rel__simps_I14_J,
% 34.97/5.53 fact_35_zadd__strict__right__mono, fact_36_add__nat__number__of,
% 34.97/5.53 fact_40_eq__number__of, fact_41_number__of__reorient, fact_42_rel__simps_I51_J,
% 34.97/5.53 fact_43_rel__simps_I48_J, fact_44_even__less__0__iff, fact_45_zadd__assoc,
% 34.97/5.53 fact_46_zadd__left__commute, fact_48_int__int__eq, fact_49_less__special_I3_J,
% 34.97/5.53 fact_50_less__special_I1_J, fact_51_rel__simps_I12_J,
% 34.97/5.53 fact_52_less__int__code_I15_J, fact_53_rel__simps_I16_J,
% 34.97/5.53 fact_54_rel__simps_I10_J, fact_55_rel__simps_I4_J, fact_66_rel__simps_I46_J,
% 34.97/5.53 fact_67_rel__simps_I39_J, fact_68_rel__simps_I50_J, fact_69_rel__simps_I49_J,
% 34.97/5.53 fact_70_rel__simps_I44_J, fact_71_rel__simps_I38_J, fact_72_Bit0__Pls,
% 34.97/5.53 fact_75_add__Pls__right, fact_76_add__Pls, fact_77_add__Bit0__Bit0,
% 34.97/5.53 fact_78_Bit0__def, fact_81_semiring__numeral__0__eq__0, fact_82_number__of__Pls,
% 34.97/5.53 fact_83_semiring__norm_I112_J, fact_84_add__numeral__0,
% 34.97/5.53 fact_85_add__numeral__0__right, fact_87_add__number__of__left,
% 34.97/5.53 fact_88_add__number__of__eq, fact_89_number__of__add, fact_90_add__Bit1__Bit0,
% 34.97/5.53 fact_91_add__Bit0__Bit1, fact_94_number__of__int, help_ti_idem,
% 34.97/5.53 tsy_c_Groups_Oone__class_Oone_res, tsy_c_Groups_Oplus__class_Oplus_0_arg1,
% 34.97/5.53 tsy_c_Groups_Oplus__class_Oplus_0_arg2, tsy_c_Groups_Oplus__class_Oplus_0_res,
% 34.97/5.53 tsy_c_Groups_Oplus__class_Oplus_1_arg1, tsy_c_Groups_Oplus__class_Oplus_1_arg2,
% 34.97/5.53 tsy_c_Groups_Oplus__class_Oplus_1_res, tsy_c_Groups_Ozero__class_Ozero_0_res,
% 34.97/5.53 tsy_c_Groups_Ozero__class_Ozero_1_res, tsy_c_Groups_Ozero__class_Ozero_2_res,
% 34.97/5.53 tsy_c_HOL_Oundefined_res, tsy_c_Int_OBit0_arg1, tsy_c_Int_OBit1_arg1,
% 34.97/5.53 tsy_c_Int_OBit1_res, tsy_c_Int_OPls_res,
% 34.97/5.53 tsy_c_Int_Onumber__class_Onumber__of_arg1,
% 34.97/5.53 tsy_c_Int_Onumber__class_Onumber__of_res,
% 34.97/5.53 tsy_c_Nat_Osemiring__1__class_Oof__nat_arg1,
% 34.97/5.53 tsy_c_Nat_Osemiring__1__class_Oof__nat_res,
% 34.97/5.53 tsy_c_Orderings_Oord__class_Oless_0_arg1,
% 34.97/5.53 tsy_c_Orderings_Oord__class_Oless_1_arg1,
% 34.97/5.53 tsy_c_Orderings_Oord__class_Oless_1_arg2,
% 34.97/5.53 tsy_c_Power_Opower__class_Opower_0_arg1,
% 34.97/5.53 tsy_c_Power_Opower__class_Opower_0_arg2, tsy_c_Power_Opower__class_Opower_0_res,
% 34.97/5.53 tsy_c_Power_Opower__class_Opower_1_arg1,
% 34.97/5.53 tsy_c_Power_Opower__class_Opower_1_arg2, tsy_c_Power_Opower__class_Opower_1_res,
% 34.97/5.53 tsy_v_n_____res, tsy_v_t_____res
% 34.97/5.53
% 34.97/5.53 Those formulas are unsatisfiable:
% 34.97/5.53 ---------------------------------
% 34.97/5.53
% 34.97/5.53 Begin of proof
% 34.97/5.54 |
% 34.97/5.54 | ALPHA: (tsy_c_Int_OBit0_res) implies:
% 34.97/5.54 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (bit0(v0) = v1) | ~ $i(v0) | (ti(int,
% 34.97/5.54 | v1) = v1 & $i(v1)))
% 34.97/5.54 |
% 34.97/5.54 | ALPHA: (tsy_c_Orderings_Oord__class_Oless_0_arg2) implies:
% 34.97/5.54 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (ti(v2, v1)
% 34.97/5.54 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ord_less(v2, v0, v1)
% 34.97/5.54 | | ~ linordered_idom(v2) | ord_less(v2, v0, v3))
% 34.97/5.54 |
% 34.97/5.54 | ALPHA: (fact_0_n1pos) implies:
% 34.97/5.54 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 34.97/5.54 | (semiring_1_of_nat(int, n) = v2 & zero_zero(int) = v0 & plus_plus(int,
% 34.97/5.54 | v1, v2) = v3 & one_one(int) = v1 & $i(v3) & $i(v2) & $i(v1) &
% 34.97/5.54 | $i(v0) & ord_less(int, v0, v3))
% 34.97/5.54 |
% 34.97/5.54 | ALPHA: (fact_1_t1) implies:
% 34.97/5.54 | (4) ? [v0: $i] : (one_one(int) = v0 & $i(v0) & ord_less(int, v0, t))
% 34.97/5.54 |
% 34.97/5.54 | ALPHA: (fact_2_sum__power2__eq__zero__iff) implies:
% 34.97/5.55 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (number_number_of(nat, v1) =
% 34.97/5.55 | v2 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & !
% 34.97/5.55 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 34.97/5.55 | [v8: $i] : ! [v9: $i] : (v9 = v4 | ~ (power_power(v3, v6, v2) = v8)
% 34.97/5.55 | | ~ (power_power(v3, v5, v2) = v7) | ~ (zero_zero(v3) = v4) | ~
% 34.97/5.55 | (plus_plus(v3, v7, v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v3) |
% 34.97/5.55 | ~ linordered_idom(v3) | ? [v10: $i] : ? [v11: $i] : (( ~ (v11 =
% 34.97/5.55 | v4) & ti(v3, v6) = v11 & $i(v11)) | ( ~ (v10 = v4) & ti(v3,
% 34.97/5.55 | v5) = v10 & $i(v10)))) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 34.97/5.55 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 34.97/5.55 | (power_power(v3, v6, v2) = v8) | ~ (power_power(v3, v5, v2) = v7)
% 34.97/5.55 | | ~ (zero_zero(v3) = v4) | ~ (plus_plus(v3, v7, v8) = v4) | ~
% 34.97/5.55 | $i(v6) | ~ $i(v5) | ~ $i(v3) | ~ linordered_idom(v3) | (ti(v3,
% 34.97/5.55 | v6) = v4 & ti(v3, v5) = v4 & $i(v4))))
% 34.97/5.55 |
% 34.97/5.55 | ALPHA: (fact_3_one__power2) implies:
% 34.97/5.55 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (number_number_of(nat, v1) =
% 34.97/5.55 | v2 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & !
% 34.97/5.55 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (power_power(v3,
% 34.97/5.55 | v4, v2) = v5) | ~ (one_one(v3) = v4) | ~ $i(v3) | ~
% 34.97/5.55 | semiring_1(v3)))
% 34.97/5.55 |
% 34.97/5.55 | ALPHA: (fact_4_zero__power2) implies:
% 34.97/5.55 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (number_number_of(nat, v1) =
% 34.97/5.55 | v2 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & !
% 34.97/5.55 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (power_power(v3,
% 34.97/5.55 | v4, v2) = v5) | ~ (zero_zero(v3) = v4) | ~ $i(v3) | ~
% 34.97/5.55 | semiring_1(v3)))
% 34.97/5.55 |
% 34.97/5.55 | ALPHA: (fact_5_zero__eq__power2) implies:
% 34.97/5.55 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (number_number_of(nat, v1) =
% 34.97/5.55 | v2 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & !
% 34.97/5.55 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v4 | ~
% 34.97/5.55 | (power_power(v3, v5, v2) = v6) | ~ (zero_zero(v3) = v4) | ~
% 34.97/5.55 | $i(v5) | ~ $i(v3) | ~ ring_11004092258visors(v3) | ? [v7: $i] :
% 34.97/5.55 | ( ~ (v7 = v4) & ti(v3, v5) = v7 & $i(v7))) & ! [v3: $i] : ! [v4:
% 34.97/5.55 | $i] : ! [v5: $i] : ( ~ (power_power(v3, v5, v2) = v4) | ~
% 34.97/5.55 | (zero_zero(v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~
% 34.97/5.55 | ring_11004092258visors(v3) | (ti(v3, v5) = v4 & $i(v4))))
% 34.97/5.55 |
% 34.97/5.55 | ALPHA: (fact_6_add__special_I2_J) implies:
% 34.97/5.55 | (9) ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : !
% 34.97/5.55 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (number_number_of(v1, v4)
% 34.97/5.55 | = v5) | ~ (plus_plus(int, v0, v3) = v4) | ~ (one_one(v1) = v2)
% 34.97/5.55 | | ~ $i(v3) | ~ $i(v1) | ~ number_ring(v1) | ? [v6: $i] :
% 34.97/5.55 | (number_number_of(v1, v3) = v6 & plus_plus(v1, v2, v6) = v5 &
% 34.97/5.55 | $i(v6) & $i(v5))))
% 34.97/5.55 |
% 34.97/5.55 | ALPHA: (fact_7_add__special_I3_J) implies:
% 34.97/5.55 | (10) ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 34.97/5.55 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (number_number_of(v1,
% 34.97/5.55 | v4) = v5) | ~ (plus_plus(int, v3, v0) = v4) | ~ (one_one(v1)
% 34.97/5.55 | = v2) | ~ $i(v3) | ~ $i(v1) | ~ number_ring(v1) | ? [v6: $i]
% 34.97/5.55 | : (number_number_of(v1, v3) = v6 & plus_plus(v1, v6, v2) = v5 &
% 34.97/5.55 | $i(v6) & $i(v5))))
% 34.97/5.55 |
% 34.97/5.55 | ALPHA: (fact_8_one__add__one__is__two) implies:
% 34.97/5.56 | (11) ? [v0: $i] : ? [v1: $i] : (bit1(pls) = v0 & bit0(v0) = v1 & $i(v1) &
% 34.97/5.56 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (number_number_of(v2, v1) =
% 34.97/5.56 | v3) | ~ $i(v2) | ~ number_ring(v2) | ? [v4: $i] :
% 34.97/5.56 | (plus_plus(v2, v4, v4) = v3 & one_one(v2) = v4 & $i(v4) &
% 34.97/5.56 | $i(v3))))
% 34.97/5.56 |
% 34.97/5.56 | ALPHA: (fact_9_semiring__one__add__one__is__two) implies:
% 34.97/5.56 | (12) ? [v0: $i] : ? [v1: $i] : (bit1(pls) = v0 & bit0(v0) = v1 & $i(v1) &
% 34.97/5.56 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (number_number_of(v2, v1) =
% 34.97/5.56 | v3) | ~ $i(v2) | ~ number_semiring(v2) | ? [v4: $i] :
% 34.97/5.56 | (plus_plus(v2, v4, v4) = v3 & one_one(v2) = v4 & $i(v4) &
% 34.97/5.56 | $i(v3))))
% 34.97/5.56 |
% 34.97/5.56 | ALPHA: (fact_10_quartic__square__square) implies:
% 34.97/5.56 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 34.97/5.56 | (number_number_of(nat, v3) = v4 & number_number_of(nat, v1) = v2 &
% 34.97/5.56 | bit1(pls) = v0 & bit0(v1) = v3 & bit0(v0) = v1 & $i(v4) & $i(v3) &
% 34.97/5.56 | $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ( ~
% 34.97/5.56 | (power_power(int, v5, v4) = v6) | ~ $i(v5) | ? [v7: $i] :
% 34.97/5.56 | (power_power(int, v7, v2) = v6 & power_power(int, v5, v2) = v7 &
% 34.97/5.56 | $i(v7) & $i(v6))))
% 34.97/5.56 |
% 34.97/5.56 | ALPHA: (fact_11_power__0__left__number__of) implies:
% 34.97/5.56 | (14) ? [v0: $i] : (zero_zero(nat) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.97/5.56 | $i] : ( ~ (one_one(v1) = v2) | ~ $i(v1) | ~ semiring_0(v1) | ~
% 34.97/5.56 | power(v1) | ? [v3: $i] : (zero_zero(v1) = v3 & $i(v3) & ! [v4:
% 34.97/5.56 | $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v3 | v5 = v0 | ~
% 34.97/5.56 | (power_power(v1, v3, v5) = v6) | ~ (number_number_of(nat, v4)
% 34.97/5.56 | = v5) | ~ $i(v4)) & ! [v4: $i] : ! [v5: $i] : (v5 = v2 |
% 34.97/5.56 | ~ (power_power(v1, v3, v0) = v5) | ~ (number_number_of(nat,
% 34.97/5.56 | v4) = v0) | ~ $i(v4)))))
% 34.97/5.56 |
% 34.97/5.56 | ALPHA: (fact_13_numeral__1__eq__1) implies:
% 34.97/5.56 | (15) ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (
% 34.97/5.56 | ~ (number_number_of(v1, v0) = v2) | ~ $i(v1) | ~ number_ring(v1)
% 34.97/5.56 | | (one_one(v1) = v2 & $i(v2))))
% 34.97/5.56 |
% 34.97/5.56 | ALPHA: (fact_19_zero__is__num__zero) implies:
% 34.97/5.56 | (16) ? [v0: $i] : (number_number_of(int, pls) = v0 & zero_zero(int) = v0 &
% 34.97/5.56 | $i(v0))
% 34.97/5.56 |
% 34.97/5.56 | ALPHA: (fact_23_zadd__int) implies:
% 34.97/5.56 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 34.97/5.56 | ( ~ (semiring_1_of_nat(int, v1) = v3) | ~ (semiring_1_of_nat(int, v0)
% 34.97/5.56 | = v2) | ~ (plus_plus(int, v2, v3) = v4) | ~ $i(v1) | ~ $i(v0) |
% 34.97/5.56 | ? [v5: $i] : (semiring_1_of_nat(int, v5) = v4 & plus_plus(nat, v0,
% 34.97/5.56 | v1) = v5 & $i(v5) & $i(v4)))
% 34.97/5.56 |
% 34.97/5.56 | ALPHA: (fact_24_int__1) implies:
% 34.97/5.56 | (18) ? [v0: $i] : ? [v1: $i] : (semiring_1_of_nat(int, v0) = v1 &
% 34.97/5.56 | one_one(nat) = v0 & one_one(int) = v1 & $i(v1) & $i(v0))
% 34.97/5.56 |
% 34.97/5.56 | ALPHA: (fact_27_int__eq__0__conv) implies:
% 34.97/5.57 | (19) ? [v0: $i] : ? [v1: $i] : (zero_zero(nat) = v1 & zero_zero(int) = v0
% 34.97/5.57 | & $i(v1) & $i(v0) & ! [v2: $i] : (v2 = v1 | ~
% 34.97/5.57 | (semiring_1_of_nat(int, v2) = v0) | ~ $i(v2)) & ! [v2: $i] : (v2
% 34.97/5.57 | = v0 | ~ (semiring_1_of_nat(int, v1) = v2)))
% 34.97/5.57 |
% 34.97/5.57 | ALPHA: (fact_28_int__0) implies:
% 34.97/5.57 | (20) ? [v0: $i] : ? [v1: $i] : (semiring_1_of_nat(int, v0) = v1 &
% 34.97/5.57 | zero_zero(nat) = v0 & zero_zero(int) = v1 & $i(v1) & $i(v0))
% 34.97/5.57 |
% 34.97/5.57 | ALPHA: (fact_29_nat__1__add__1) implies:
% 34.97/5.57 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 34.97/5.57 | (number_number_of(nat, v3) = v1 & bit1(pls) = v2 & bit0(v2) = v3 &
% 34.97/5.57 | plus_plus(nat, v0, v0) = v1 & one_one(nat) = v0 & $i(v3) & $i(v2) &
% 34.97/5.57 | $i(v1) & $i(v0))
% 34.97/5.57 |
% 34.97/5.57 | ALPHA: (fact_37_one__is__num__one) implies:
% 34.97/5.57 | (22) ? [v0: $i] : ? [v1: $i] : (number_number_of(int, v1) = v0 &
% 34.97/5.57 | bit1(pls) = v1 & one_one(int) = v0 & $i(v1) & $i(v0))
% 34.97/5.57 |
% 34.97/5.57 | ALPHA: (fact_38_nat__numeral__1__eq__1) implies:
% 34.97/5.57 | (23) ? [v0: $i] : ? [v1: $i] : (number_number_of(nat, v0) = v1 &
% 34.97/5.57 | bit1(pls) = v0 & one_one(nat) = v1 & $i(v1) & $i(v0))
% 34.97/5.57 |
% 34.97/5.57 | ALPHA: (fact_39_Numeral1__eq1__nat) implies:
% 34.97/5.57 | (24) ? [v0: $i] : ? [v1: $i] : (number_number_of(nat, v1) = v0 &
% 34.97/5.57 | bit1(pls) = v1 & one_one(nat) = v0 & $i(v1) & $i(v0))
% 34.97/5.57 |
% 34.97/5.57 | ALPHA: (fact_47_zadd__commute) implies:
% 34.97/5.57 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (plus_plus(int, v0, v1)
% 34.97/5.57 | = v2) | ~ $i(v1) | ~ $i(v0) | (plus_plus(int, v1, v0) = v2 &
% 34.97/5.57 | $i(v2)))
% 34.97/5.57 |
% 34.97/5.57 | ALPHA: (fact_56_bin__less__0__simps_I4_J) implies:
% 34.97/5.57 | (26) ? [v0: $i] : (zero_zero(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.97/5.57 | $i] : ( ~ (bit1(v1) = v2) | ~ $i(v1) | ~ ord_less(int, v2, v0) |
% 34.97/5.57 | ord_less(int, v1, v0)) & ! [v1: $i] : ! [v2: $i] : ( ~ (bit1(v1)
% 34.97/5.57 | = v2) | ~ $i(v1) | ~ ord_less(int, v1, v0) | ord_less(int, v2,
% 34.97/5.57 | v0)))
% 34.97/5.57 |
% 34.97/5.57 | ALPHA: (fact_57_bin__less__0__simps_I1_J) implies:
% 34.97/5.57 | (27) ? [v0: $i] : (zero_zero(int) = v0 & $i(v0) & ~ ord_less(int, pls,
% 34.97/5.57 | v0))
% 34.97/5.57 |
% 34.97/5.57 | ALPHA: (fact_58_bin__less__0__simps_I3_J) implies:
% 34.97/5.57 | (28) ? [v0: $i] : (zero_zero(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.97/5.57 | $i] : ( ~ (bit0(v1) = v2) | ~ $i(v1) | ~ ord_less(int, v2, v0) |
% 34.97/5.57 | ord_less(int, v1, v0)) & ! [v1: $i] : ! [v2: $i] : ( ~ (bit0(v1)
% 34.97/5.57 | = v2) | ~ $i(v1) | ~ ord_less(int, v1, v0) | ord_less(int, v2,
% 34.97/5.57 | v0)))
% 34.97/5.57 |
% 34.97/5.57 | ALPHA: (fact_59_int__0__less__1) implies:
% 34.97/5.57 | (29) ? [v0: $i] : ? [v1: $i] : (zero_zero(int) = v0 & one_one(int) = v1 &
% 34.97/5.57 | $i(v1) & $i(v0) & ord_less(int, v0, v1))
% 34.97/5.57 |
% 34.97/5.57 | ALPHA: (fact_60_zless__add1__eq) implies:
% 34.97/5.57 | (30) ? [v0: $i] : (one_one(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i]
% 34.97/5.57 | : ! [v3: $i] : (v2 = v1 | ~ (plus_plus(int, v2, v0) = v3) | ~
% 34.97/5.57 | $i(v2) | ~ $i(v1) | ~ ord_less(int, v1, v3) | ord_less(int, v1,
% 34.97/5.57 | v2)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 34.97/5.57 | (plus_plus(int, v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 34.97/5.57 | ord_less(int, v1, v2) | ord_less(int, v1, v3)) & ! [v1: $i] : !
% 34.97/5.57 | [v2: $i] : ( ~ (plus_plus(int, v1, v0) = v2) | ~ $i(v1) |
% 34.97/5.57 | ord_less(int, v1, v2)))
% 34.97/5.57 |
% 34.97/5.57 | ALPHA: (fact_61_int__less__0__conv) implies:
% 34.97/5.58 | (31) ? [v0: $i] : (zero_zero(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.97/5.58 | $i] : ( ~ (semiring_1_of_nat(int, v1) = v2) | ~ $i(v1) | ~
% 34.97/5.58 | ord_less(int, v2, v0)))
% 34.97/5.58 |
% 34.97/5.58 | ALPHA: (fact_62_less__special_I4_J) implies:
% 34.97/5.58 | (32) ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 34.97/5.58 | ! [v3: $i] : ! [v4: $i] : ( ~ (number_number_of(v1, v3) = v4) | ~
% 34.97/5.58 | (one_one(v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ number_ring(v1) |
% 34.97/5.58 | ~ ord_less(v1, v4, v2) | ~ linordered_idom(v1) | ord_less(int,
% 34.97/5.58 | v3, v0)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 34.97/5.58 | : ( ~ (number_number_of(v1, v3) = v4) | ~ (one_one(v1) = v2) | ~
% 34.97/5.58 | $i(v3) | ~ $i(v1) | ~ number_ring(v1) | ~ ord_less(int, v3, v0)
% 34.97/5.58 | | ~ linordered_idom(v1) | ord_less(v1, v4, v2)))
% 34.97/5.58 |
% 34.97/5.58 | ALPHA: (fact_63_less__special_I2_J) implies:
% 34.97/5.58 | (33) ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 34.97/5.58 | ! [v3: $i] : ! [v4: $i] : ( ~ (number_number_of(v1, v3) = v4) | ~
% 34.97/5.58 | (one_one(v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ number_ring(v1) |
% 34.97/5.58 | ~ ord_less(v1, v2, v4) | ~ linordered_idom(v1) | ord_less(int,
% 34.97/5.58 | v0, v3)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 34.97/5.58 | : ( ~ (number_number_of(v1, v3) = v4) | ~ (one_one(v1) = v2) | ~
% 34.97/5.58 | $i(v3) | ~ $i(v1) | ~ number_ring(v1) | ~ ord_less(int, v0, v3)
% 34.97/5.58 | | ~ linordered_idom(v1) | ord_less(v1, v2, v4)))
% 34.97/5.58 |
% 34.97/5.58 | ALPHA: (fact_64_odd__less__0) implies:
% 34.97/5.58 | (34) ? [v0: $i] : ? [v1: $i] : (zero_zero(int) = v1 & one_one(int) = v0 &
% 34.97/5.58 | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 34.97/5.58 | (plus_plus(int, v3, v2) = v4) | ~ (plus_plus(int, v0, v2) = v3) |
% 34.97/5.58 | ~ $i(v2) | ~ ord_less(int, v4, v1) | ord_less(int, v2, v1)) & !
% 34.97/5.58 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (plus_plus(int, v3, v2) =
% 34.97/5.58 | v4) | ~ (plus_plus(int, v0, v2) = v3) | ~ $i(v2) | ~
% 34.97/5.58 | ord_less(int, v2, v1) | ord_less(int, v4, v1)))
% 34.97/5.58 |
% 34.97/5.58 | ALPHA: (fact_65_double__eq__0__iff) implies:
% 34.97/5.58 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (zero_zero(v0) = v1) |
% 34.97/5.58 | ~ (ti(v0, v2) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 34.97/5.58 | linord219039673up_add(v0) | (plus_plus(v0, v2, v2) = v1 & $i(v1)))
% 34.97/5.58 |
% 34.97/5.58 | ALPHA: (fact_73_Pls__def) implies:
% 34.97/5.58 | (36) zero_zero(int) = pls
% 34.97/5.58 |
% 34.97/5.58 | ALPHA: (fact_74_int__0__neq__1) implies:
% 34.97/5.58 | (37) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & zero_zero(int) = v0 &
% 34.97/5.58 | one_one(int) = v1 & $i(v1) & $i(v0))
% 34.97/5.58 |
% 34.97/5.58 | ALPHA: (fact_79_zadd__0__right) implies:
% 34.97/5.58 | (38) ? [v0: $i] : (zero_zero(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.97/5.58 | $i] : (v2 = v1 | ~ (plus_plus(int, v1, v0) = v2) | ~ $i(v1)))
% 34.97/5.58 |
% 34.97/5.58 | ALPHA: (fact_80_zadd__0) implies:
% 34.97/5.58 | (39) ? [v0: $i] : (zero_zero(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.97/5.58 | $i] : (v2 = v1 | ~ (plus_plus(int, v0, v1) = v2) | ~ $i(v1)))
% 34.97/5.58 |
% 34.97/5.58 | ALPHA: (fact_86_power__eq__0__iff__number__of) implies:
% 34.97/5.59 | (40) ? [v0: $i] : (zero_zero(nat) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 34.97/5.59 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6
% 34.97/5.59 | = v2 | v5 = v0 | ~ (power_power(v1, v3, v5) = v6) | ~
% 34.97/5.59 | (number_number_of(nat, v4) = v5) | ~ (zero_zero(v1) = v2) | ~
% 34.97/5.59 | $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ zero_neq_one(v1) | ~
% 34.97/5.59 | no_zero_divisors(v1) | ~ mult_zero(v1) | ~ power(v1) | ? [v7:
% 34.97/5.59 | $i] : ( ~ (v7 = v2) & ti(v1, v3) = v7 & $i(v7))) & ! [v1: $i] :
% 34.97/5.59 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 34.97/5.59 | (power_power(v1, v3, v5) = v2) | ~ (number_number_of(nat, v4) =
% 34.97/5.59 | v5) | ~ (zero_zero(v1) = v2) | ~ $i(v4) | ~ $i(v3) | ~
% 34.97/5.59 | $i(v1) | ~ zero_neq_one(v1) | ~ no_zero_divisors(v1) | ~
% 34.97/5.59 | mult_zero(v1) | ~ power(v1) | (ti(v1, v3) = v2 & $i(v2))) & !
% 34.97/5.59 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 34.97/5.59 | (power_power(v1, v3, v0) = v2) | ~ (number_number_of(nat, v4) =
% 34.97/5.59 | v0) | ~ (zero_zero(v1) = v2) | ~ $i(v4) | ~ $i(v3) | ~
% 34.97/5.59 | $i(v1) | ~ zero_neq_one(v1) | ~ no_zero_divisors(v1) | ~
% 34.97/5.59 | mult_zero(v1) | ~ power(v1)))
% 34.97/5.59 |
% 34.97/5.59 | ALPHA: (fact_92_Bit1__def) implies:
% 34.97/5.59 | (41) ? [v0: $i] : (one_one(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i]
% 34.97/5.59 | : ! [v3: $i] : ( ~ (plus_plus(int, v2, v1) = v3) | ~
% 34.97/5.59 | (plus_plus(int, v0, v1) = v2) | ~ $i(v1) | (bit1(v1) = v3 &
% 34.97/5.59 | $i(v3))))
% 34.97/5.59 |
% 34.97/5.59 | ALPHA: (fact_93_odd__nonzero) implies:
% 34.97/5.59 | (42) ? [v0: $i] : ? [v1: $i] : (zero_zero(int) = v1 & one_one(int) = v0 &
% 34.97/5.59 | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (plus_plus(int,
% 34.97/5.59 | v3, v2) = v1) | ~ (plus_plus(int, v0, v2) = v3) | ~ $i(v2)))
% 34.97/5.59 |
% 34.97/5.59 | ALPHA: (fact_95_zero__less__power2) implies:
% 34.97/5.59 | (43) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (number_number_of(nat, v1) =
% 34.97/5.59 | v2 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & !
% 34.97/5.59 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 34.97/5.59 | (power_power(v3, v5, v2) = v6) | ~ (zero_zero(v3) = v4) | ~
% 34.97/5.59 | $i(v5) | ~ $i(v3) | ~ ord_less(v3, v4, v6) | ~
% 34.97/5.59 | linordered_idom(v3) | ? [v7: $i] : ( ~ (v7 = v4) & ti(v3, v5) =
% 34.97/5.59 | v7 & $i(v7))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 34.97/5.59 | [v6: $i] : ( ~ (power_power(v3, v5, v2) = v6) | ~ (zero_zero(v3) =
% 34.97/5.59 | v4) | ~ $i(v5) | ~ $i(v3) | ~ linordered_idom(v3) |
% 34.97/5.59 | ord_less(v3, v4, v6) | (ti(v3, v5) = v4 & $i(v4))))
% 34.97/5.59 |
% 34.97/5.59 | ALPHA: (fact_96_power2__less__0) implies:
% 34.97/5.59 | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (number_number_of(nat, v1) =
% 34.97/5.59 | v2 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & !
% 34.97/5.59 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 34.97/5.59 | (power_power(v3, v5, v2) = v6) | ~ (zero_zero(v3) = v4) | ~
% 34.97/5.59 | $i(v5) | ~ $i(v3) | ~ ord_less(v3, v6, v4) | ~
% 34.97/5.59 | linordered_idom(v3)))
% 34.97/5.59 |
% 34.97/5.59 | ALPHA: (fact_97_sum__power2__gt__zero__iff) implies:
% 34.97/5.59 | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (number_number_of(nat, v1) =
% 34.97/5.59 | v2 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & !
% 34.97/5.59 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 34.97/5.59 | ! [v8: $i] : ! [v9: $i] : ( ~ (power_power(v3, v6, v2) = v8) | ~
% 34.97/5.59 | (power_power(v3, v5, v2) = v7) | ~ (zero_zero(v3) = v4) | ~
% 34.97/5.59 | (plus_plus(v3, v7, v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v3) |
% 34.97/5.59 | ~ ord_less(v3, v4, v9) | ~ linordered_idom(v3) | ? [v10: $i] :
% 34.97/5.59 | ? [v11: $i] : (( ~ (v11 = v4) & ti(v3, v6) = v11 & $i(v11)) | ( ~
% 34.97/5.59 | (v10 = v4) & ti(v3, v5) = v10 & $i(v10)))) & ! [v3: $i] : !
% 34.97/5.59 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] :
% 34.97/5.59 | ! [v9: $i] : ( ~ (power_power(v3, v6, v2) = v8) | ~
% 34.97/5.59 | (power_power(v3, v5, v2) = v7) | ~ (zero_zero(v3) = v4) | ~
% 34.97/5.59 | (plus_plus(v3, v7, v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v3) |
% 34.97/5.59 | ~ linordered_idom(v3) | ord_less(v3, v4, v9) | (ti(v3, v6) = v4 &
% 34.97/5.59 | ti(v3, v5) = v4 & $i(v4))))
% 34.97/5.59 |
% 34.97/5.59 | ALPHA: (arity_Int_Oint___Groups_Olinordered__ab__group__add) implies:
% 34.97/5.59 | (46) linord219039673up_add(int)
% 34.97/5.59 |
% 34.97/5.59 | ALPHA: (arity_Int_Oint___Rings_Ono__zero__divisors) implies:
% 34.97/5.59 | (47) no_zero_divisors(int)
% 34.97/5.59 |
% 34.97/5.59 | ALPHA: (arity_Int_Oint___Rings_Olinordered__idom) implies:
% 34.97/5.59 | (48) linordered_idom(int)
% 34.97/5.59 |
% 34.97/5.59 | ALPHA: (arity_Int_Oint___Rings_Ozero__neq__one) implies:
% 34.97/5.59 | (49) zero_neq_one(int)
% 34.97/5.59 |
% 34.97/5.59 | ALPHA: (arity_Int_Oint___Rings_Osemiring__0) implies:
% 34.97/5.59 | (50) semiring_0(int)
% 34.97/5.59 |
% 34.97/5.59 | ALPHA: (arity_Int_Oint___Rings_Omult__zero) implies:
% 34.97/5.59 | (51) mult_zero(int)
% 34.97/5.59 |
% 34.97/5.59 | ALPHA: (arity_Int_Oint___Power_Opower) implies:
% 34.97/5.59 | (52) power(int)
% 34.97/5.59 |
% 34.97/5.59 | ALPHA: (conj_0) implies:
% 34.97/5.60 | (53) $i(int)
% 34.97/5.60 | (54) $i(n)
% 34.97/5.60 | (55) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 34.97/5.60 | ? [v5: $i] : ? [v6: $i] : (power_power(int, v2, v5) = v6 &
% 34.97/5.60 | semiring_1_of_nat(int, n) = v1 & number_number_of(nat, v4) = v5 &
% 34.97/5.60 | bit1(pls) = v3 & bit0(v3) = v4 & zero_zero(int) = v6 &
% 34.97/5.60 | plus_plus(int, v0, v1) = v2 & one_one(int) = v0 & $i(v6) & $i(v5) &
% 34.97/5.60 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 34.97/5.60 |
% 34.97/5.60 | ALPHA: (function-axioms) implies:
% 34.97/5.60 | (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (one_one(v2) =
% 34.97/5.60 | v1) | ~ (one_one(v2) = v0))
% 34.97/5.60 | (57) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (zero_zero(v2)
% 34.97/5.60 | = v1) | ~ (zero_zero(v2) = v0))
% 34.97/5.60 | (58) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (bit0(v2) =
% 34.97/5.60 | v1) | ~ (bit0(v2) = v0))
% 34.97/5.60 | (59) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (bit1(v2) =
% 34.97/5.60 | v1) | ~ (bit1(v2) = v0))
% 34.97/5.60 | (60) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 34.97/5.60 | (number_number_of(v3, v2) = v1) | ~ (number_number_of(v3, v2) =
% 34.97/5.60 | v0))
% 34.97/5.60 | (61) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 34.97/5.60 | (semiring_1_of_nat(v3, v2) = v1) | ~ (semiring_1_of_nat(v3, v2) =
% 34.97/5.60 | v0))
% 34.97/5.60 | (62) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 34.97/5.60 | (v1 = v0 | ~ (plus_plus(v4, v3, v2) = v1) | ~ (plus_plus(v4, v3, v2)
% 34.97/5.60 | = v0))
% 34.97/5.60 |
% 34.97/5.60 | DELTA: instantiating (4) with fresh symbol all_86_0 gives:
% 34.97/5.60 | (63) one_one(int) = all_86_0 & $i(all_86_0) & ord_less(int, all_86_0, t)
% 34.97/5.60 |
% 34.97/5.60 | ALPHA: (63) implies:
% 34.97/5.60 | (64) one_one(int) = all_86_0
% 34.97/5.60 |
% 34.97/5.60 | DELTA: instantiating (16) with fresh symbol all_88_0 gives:
% 34.97/5.60 | (65) number_number_of(int, pls) = all_88_0 & zero_zero(int) = all_88_0 &
% 34.97/5.60 | $i(all_88_0)
% 34.97/5.60 |
% 34.97/5.60 | ALPHA: (65) implies:
% 34.97/5.60 | (66) zero_zero(int) = all_88_0
% 34.97/5.60 |
% 34.97/5.60 | DELTA: instantiating (27) with fresh symbol all_94_0 gives:
% 34.97/5.60 | (67) zero_zero(int) = all_94_0 & $i(all_94_0) & ~ ord_less(int, pls,
% 34.97/5.60 | all_94_0)
% 34.97/5.60 |
% 34.97/5.60 | ALPHA: (67) implies:
% 34.97/5.60 | (68) ~ ord_less(int, pls, all_94_0)
% 34.97/5.60 | (69) zero_zero(int) = all_94_0
% 34.97/5.60 |
% 34.97/5.60 | DELTA: instantiating (39) with fresh symbol all_96_0 gives:
% 34.97/5.60 | (70) zero_zero(int) = all_96_0 & $i(all_96_0) & ! [v0: $i] : ! [v1: $i] :
% 34.97/5.60 | (v1 = v0 | ~ (plus_plus(int, all_96_0, v0) = v1) | ~ $i(v0))
% 34.97/5.60 |
% 34.97/5.60 | ALPHA: (70) implies:
% 34.97/5.60 | (71) zero_zero(int) = all_96_0
% 34.97/5.60 |
% 34.97/5.60 | DELTA: instantiating (23) with fresh symbols all_99_0, all_99_1 gives:
% 34.97/5.60 | (72) number_number_of(nat, all_99_1) = all_99_0 & bit1(pls) = all_99_1 &
% 34.97/5.60 | one_one(nat) = all_99_0 & $i(all_99_0) & $i(all_99_1)
% 34.97/5.60 |
% 34.97/5.60 | ALPHA: (72) implies:
% 34.97/5.60 | (73) one_one(nat) = all_99_0
% 34.97/5.60 | (74) bit1(pls) = all_99_1
% 34.97/5.60 |
% 34.97/5.60 | DELTA: instantiating (18) with fresh symbols all_101_0, all_101_1 gives:
% 34.97/5.60 | (75) semiring_1_of_nat(int, all_101_1) = all_101_0 & one_one(nat) =
% 34.97/5.60 | all_101_1 & one_one(int) = all_101_0 & $i(all_101_0) & $i(all_101_1)
% 34.97/5.60 |
% 34.97/5.60 | ALPHA: (75) implies:
% 34.97/5.60 | (76) $i(all_101_1)
% 34.97/5.60 | (77) $i(all_101_0)
% 34.97/5.60 | (78) one_one(int) = all_101_0
% 34.97/5.60 | (79) one_one(nat) = all_101_1
% 34.97/5.60 | (80) semiring_1_of_nat(int, all_101_1) = all_101_0
% 34.97/5.60 |
% 34.97/5.60 | DELTA: instantiating (29) with fresh symbols all_103_0, all_103_1 gives:
% 35.46/5.60 | (81) zero_zero(int) = all_103_1 & one_one(int) = all_103_0 & $i(all_103_0)
% 35.46/5.60 | & $i(all_103_1) & ord_less(int, all_103_1, all_103_0)
% 35.46/5.60 |
% 35.46/5.60 | ALPHA: (81) implies:
% 35.46/5.60 | (82) one_one(int) = all_103_0
% 35.46/5.60 | (83) zero_zero(int) = all_103_1
% 35.46/5.60 |
% 35.46/5.60 | DELTA: instantiating (37) with fresh symbols all_105_0, all_105_1 gives:
% 35.46/5.61 | (84) ~ (all_105_0 = all_105_1) & zero_zero(int) = all_105_1 & one_one(int)
% 35.46/5.61 | = all_105_0 & $i(all_105_0) & $i(all_105_1)
% 35.46/5.61 |
% 35.46/5.61 | ALPHA: (84) implies:
% 35.46/5.61 | (85) one_one(int) = all_105_0
% 35.46/5.61 | (86) zero_zero(int) = all_105_1
% 35.46/5.61 |
% 35.46/5.61 | DELTA: instantiating (22) with fresh symbols all_107_0, all_107_1 gives:
% 35.46/5.61 | (87) number_number_of(int, all_107_0) = all_107_1 & bit1(pls) = all_107_0 &
% 35.46/5.61 | one_one(int) = all_107_1 & $i(all_107_0) & $i(all_107_1)
% 35.46/5.61 |
% 35.46/5.61 | ALPHA: (87) implies:
% 35.46/5.61 | (88) $i(all_107_0)
% 35.46/5.61 | (89) one_one(int) = all_107_1
% 35.46/5.61 | (90) bit1(pls) = all_107_0
% 35.46/5.61 |
% 35.46/5.61 | DELTA: instantiating (24) with fresh symbols all_109_0, all_109_1 gives:
% 35.46/5.61 | (91) number_number_of(nat, all_109_0) = all_109_1 & bit1(pls) = all_109_0 &
% 35.46/5.61 | one_one(nat) = all_109_1 & $i(all_109_0) & $i(all_109_1)
% 35.46/5.61 |
% 35.46/5.61 | ALPHA: (91) implies:
% 35.46/5.61 | (92) one_one(nat) = all_109_1
% 35.46/5.61 | (93) bit1(pls) = all_109_0
% 35.46/5.61 |
% 35.46/5.61 | DELTA: instantiating (20) with fresh symbols all_111_0, all_111_1 gives:
% 35.46/5.61 | (94) semiring_1_of_nat(int, all_111_1) = all_111_0 & zero_zero(nat) =
% 35.46/5.61 | all_111_1 & zero_zero(int) = all_111_0 & $i(all_111_0) & $i(all_111_1)
% 35.46/5.61 |
% 35.46/5.61 | ALPHA: (94) implies:
% 35.46/5.61 | (95) zero_zero(int) = all_111_0
% 35.46/5.61 |
% 35.46/5.61 | DELTA: instantiating (31) with fresh symbol all_113_0 gives:
% 35.46/5.61 | (96) zero_zero(int) = all_113_0 & $i(all_113_0) & ! [v0: $i] : ! [v1: $i]
% 35.46/5.61 | : ( ~ (semiring_1_of_nat(int, v0) = v1) | ~ $i(v0) | ~ ord_less(int,
% 35.46/5.61 | v1, all_113_0))
% 35.46/5.61 |
% 35.46/5.61 | ALPHA: (96) implies:
% 35.46/5.61 | (97) zero_zero(int) = all_113_0
% 35.46/5.61 |
% 35.46/5.61 | DELTA: instantiating (38) with fresh symbol all_116_0 gives:
% 35.46/5.61 | (98) zero_zero(int) = all_116_0 & $i(all_116_0) & ! [v0: $i] : ! [v1: $i]
% 35.46/5.61 | : (v1 = v0 | ~ (plus_plus(int, v0, all_116_0) = v1) | ~ $i(v0))
% 35.46/5.61 |
% 35.46/5.61 | ALPHA: (98) implies:
% 35.46/5.61 | (99) zero_zero(int) = all_116_0
% 35.46/5.61 |
% 35.46/5.61 | DELTA: instantiating (42) with fresh symbols all_120_0, all_120_1 gives:
% 35.46/5.61 | (100) zero_zero(int) = all_120_0 & one_one(int) = all_120_1 & $i(all_120_0)
% 35.46/5.61 | & $i(all_120_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (plus_plus(int, v1,
% 35.46/5.61 | v0) = all_120_0) | ~ (plus_plus(int, all_120_1, v0) = v1) | ~
% 35.46/5.61 | $i(v0))
% 35.46/5.61 |
% 35.46/5.61 | ALPHA: (100) implies:
% 35.46/5.61 | (101) one_one(int) = all_120_1
% 35.46/5.61 | (102) zero_zero(int) = all_120_0
% 35.46/5.61 |
% 35.46/5.61 | DELTA: instantiating (41) with fresh symbol all_123_0 gives:
% 35.46/5.61 | (103) one_one(int) = all_123_0 & $i(all_123_0) & ! [v0: $i] : ! [v1: $i]
% 35.46/5.61 | : ! [v2: $i] : ( ~ (plus_plus(int, v1, v0) = v2) | ~
% 35.46/5.61 | (plus_plus(int, all_123_0, v0) = v1) | ~ $i(v0) | (bit1(v0) = v2 &
% 35.46/5.61 | $i(v2)))
% 35.46/5.61 |
% 35.46/5.61 | ALPHA: (103) implies:
% 35.46/5.61 | (104) one_one(int) = all_123_0
% 35.46/5.61 |
% 35.46/5.61 | DELTA: instantiating (15) with fresh symbol all_126_0 gives:
% 35.46/5.61 | (105) bit1(pls) = all_126_0 & $i(all_126_0) & ! [v0: $i] : ! [v1: $i] : (
% 35.46/5.61 | ~ (number_number_of(v0, all_126_0) = v1) | ~ $i(v0) | ~
% 35.46/5.61 | number_ring(v0) | (one_one(v0) = v1 & $i(v1)))
% 35.46/5.61 |
% 35.46/5.61 | ALPHA: (105) implies:
% 35.46/5.61 | (106) bit1(pls) = all_126_0
% 35.46/5.61 |
% 35.46/5.61 | DELTA: instantiating (15) with fresh symbol all_129_0 gives:
% 35.46/5.61 | (107) bit1(pls) = all_129_0 & $i(all_129_0) & ! [v0: $i] : ! [v1: $i] : (
% 35.46/5.61 | ~ (number_number_of(v0, all_129_0) = v1) | ~ $i(v0) | ~
% 35.46/5.61 | number_ring(v0) | (one_one(v0) = v1 & $i(v1)))
% 35.46/5.61 |
% 35.46/5.61 | ALPHA: (107) implies:
% 35.46/5.61 | (108) bit1(pls) = all_129_0
% 35.46/5.61 |
% 35.46/5.61 | DELTA: instantiating (3) with fresh symbols all_132_0, all_132_1, all_132_2,
% 35.46/5.61 | all_132_3 gives:
% 35.46/5.61 | (109) semiring_1_of_nat(int, n) = all_132_1 & zero_zero(int) = all_132_3 &
% 35.46/5.61 | plus_plus(int, all_132_2, all_132_1) = all_132_0 & one_one(int) =
% 35.46/5.61 | all_132_2 & $i(all_132_0) & $i(all_132_1) & $i(all_132_2) &
% 35.46/5.61 | $i(all_132_3) & ord_less(int, all_132_3, all_132_0)
% 35.46/5.61 |
% 35.46/5.61 | ALPHA: (109) implies:
% 35.46/5.61 | (110) ord_less(int, all_132_3, all_132_0)
% 35.46/5.61 | (111) one_one(int) = all_132_2
% 35.46/5.61 | (112) plus_plus(int, all_132_2, all_132_1) = all_132_0
% 35.46/5.61 | (113) zero_zero(int) = all_132_3
% 35.46/5.61 | (114) semiring_1_of_nat(int, n) = all_132_1
% 35.46/5.61 |
% 35.46/5.61 | DELTA: instantiating (19) with fresh symbols all_134_0, all_134_1 gives:
% 35.46/5.62 | (115) zero_zero(nat) = all_134_0 & zero_zero(int) = all_134_1 &
% 35.46/5.62 | $i(all_134_0) & $i(all_134_1) & ! [v0: any] : (v0 = all_134_0 | ~
% 35.46/5.62 | (semiring_1_of_nat(int, v0) = all_134_1) | ~ $i(v0)) & ! [v0:
% 35.46/5.62 | int] : (v0 = all_134_1 | ~ (semiring_1_of_nat(int, all_134_0) =
% 35.46/5.62 | v0))
% 35.46/5.62 |
% 35.46/5.62 | ALPHA: (115) implies:
% 35.46/5.62 | (116) zero_zero(int) = all_134_1
% 35.46/5.62 |
% 35.46/5.62 | DELTA: instantiating (21) with fresh symbols all_137_0, all_137_1, all_137_2,
% 35.46/5.62 | all_137_3 gives:
% 35.46/5.62 | (117) number_number_of(nat, all_137_0) = all_137_2 & bit1(pls) = all_137_1
% 35.46/5.62 | & bit0(all_137_1) = all_137_0 & plus_plus(nat, all_137_3, all_137_3)
% 35.46/5.62 | = all_137_2 & one_one(nat) = all_137_3 & $i(all_137_0) &
% 35.46/5.62 | $i(all_137_1) & $i(all_137_2) & $i(all_137_3)
% 35.46/5.62 |
% 35.46/5.62 | ALPHA: (117) implies:
% 35.46/5.62 | (118) one_one(nat) = all_137_3
% 35.46/5.62 | (119) bit0(all_137_1) = all_137_0
% 35.46/5.62 | (120) bit1(pls) = all_137_1
% 35.46/5.62 | (121) number_number_of(nat, all_137_0) = all_137_2
% 35.46/5.62 |
% 35.46/5.62 | DELTA: instantiating (26) with fresh symbol all_139_0 gives:
% 35.46/5.62 | (122) zero_zero(int) = all_139_0 & $i(all_139_0) & ! [v0: $i] : ! [v1:
% 35.46/5.62 | $i] : ( ~ (bit1(v0) = v1) | ~ $i(v0) | ~ ord_less(int, v1,
% 35.46/5.62 | all_139_0) | ord_less(int, v0, all_139_0)) & ! [v0: $i] : !
% 35.46/5.62 | [v1: $i] : ( ~ (bit1(v0) = v1) | ~ $i(v0) | ~ ord_less(int, v0,
% 35.46/5.62 | all_139_0) | ord_less(int, v1, all_139_0))
% 35.46/5.62 |
% 35.46/5.62 | ALPHA: (122) implies:
% 35.46/5.62 | (123) zero_zero(int) = all_139_0
% 35.46/5.62 |
% 35.46/5.62 | DELTA: instantiating (28) with fresh symbol all_142_0 gives:
% 35.46/5.62 | (124) zero_zero(int) = all_142_0 & $i(all_142_0) & ! [v0: $i] : ! [v1:
% 35.46/5.62 | $i] : ( ~ (bit0(v0) = v1) | ~ $i(v0) | ~ ord_less(int, v1,
% 35.46/5.62 | all_142_0) | ord_less(int, v0, all_142_0)) & ! [v0: $i] : !
% 35.46/5.62 | [v1: $i] : ( ~ (bit0(v0) = v1) | ~ $i(v0) | ~ ord_less(int, v0,
% 35.46/5.62 | all_142_0) | ord_less(int, v1, all_142_0))
% 35.46/5.62 |
% 35.46/5.62 | ALPHA: (124) implies:
% 35.46/5.62 | (125) zero_zero(int) = all_142_0
% 35.46/5.62 |
% 35.46/5.62 | DELTA: instantiating (11) with fresh symbols all_145_0, all_145_1 gives:
% 35.46/5.62 | (126) bit1(pls) = all_145_1 & bit0(all_145_1) = all_145_0 & $i(all_145_0) &
% 35.46/5.62 | $i(all_145_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (number_number_of(v0,
% 35.46/5.62 | all_145_0) = v1) | ~ $i(v0) | ~ number_ring(v0) | ? [v2: $i]
% 35.46/5.62 | : (plus_plus(v0, v2, v2) = v1 & one_one(v0) = v2 & $i(v2) &
% 35.46/5.62 | $i(v1)))
% 35.46/5.62 |
% 35.46/5.62 | ALPHA: (126) implies:
% 35.46/5.62 | (127) bit0(all_145_1) = all_145_0
% 35.46/5.62 | (128) bit1(pls) = all_145_1
% 35.46/5.62 |
% 35.46/5.62 | DELTA: instantiating (7) with fresh symbols all_148_0, all_148_1, all_148_2
% 35.46/5.62 | gives:
% 35.46/5.62 | (129) number_number_of(nat, all_148_1) = all_148_0 & bit1(pls) = all_148_2
% 35.46/5.62 | & bit0(all_148_2) = all_148_1 & $i(all_148_0) & $i(all_148_1) &
% 35.46/5.62 | $i(all_148_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 |
% 35.46/5.62 | ~ (power_power(v0, v1, all_148_0) = v2) | ~ (zero_zero(v0) = v1) |
% 35.46/5.62 | ~ $i(v0) | ~ semiring_1(v0))
% 35.46/5.62 |
% 35.46/5.62 | ALPHA: (129) implies:
% 35.46/5.62 | (130) bit0(all_148_2) = all_148_1
% 35.46/5.62 | (131) bit1(pls) = all_148_2
% 35.46/5.62 | (132) number_number_of(nat, all_148_1) = all_148_0
% 35.46/5.62 |
% 35.46/5.62 | DELTA: instantiating (12) with fresh symbols all_151_0, all_151_1 gives:
% 35.46/5.62 | (133) bit1(pls) = all_151_1 & bit0(all_151_1) = all_151_0 & $i(all_151_0) &
% 35.46/5.62 | $i(all_151_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (number_number_of(v0,
% 35.46/5.62 | all_151_0) = v1) | ~ $i(v0) | ~ number_semiring(v0) | ? [v2:
% 35.46/5.62 | $i] : (plus_plus(v0, v2, v2) = v1 & one_one(v0) = v2 & $i(v2) &
% 35.46/5.62 | $i(v1)))
% 35.46/5.62 |
% 35.46/5.62 | ALPHA: (133) implies:
% 35.46/5.62 | (134) bit0(all_151_1) = all_151_0
% 35.46/5.62 | (135) bit1(pls) = all_151_1
% 35.46/5.62 |
% 35.46/5.62 | DELTA: instantiating (6) with fresh symbols all_154_0, all_154_1, all_154_2
% 35.46/5.62 | gives:
% 35.46/5.62 | (136) number_number_of(nat, all_154_1) = all_154_0 & bit1(pls) = all_154_2
% 35.46/5.62 | & bit0(all_154_2) = all_154_1 & $i(all_154_0) & $i(all_154_1) &
% 35.46/5.62 | $i(all_154_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 |
% 35.46/5.62 | ~ (power_power(v0, v1, all_154_0) = v2) | ~ (one_one(v0) = v1) |
% 35.46/5.62 | ~ $i(v0) | ~ semiring_1(v0))
% 35.46/5.62 |
% 35.46/5.62 | ALPHA: (136) implies:
% 35.46/5.62 | (137) bit0(all_154_2) = all_154_1
% 35.46/5.62 | (138) bit1(pls) = all_154_2
% 35.46/5.62 | (139) number_number_of(nat, all_154_1) = all_154_0
% 35.46/5.62 |
% 35.46/5.62 | DELTA: instantiating (10) with fresh symbol all_157_0 gives:
% 35.46/5.62 | (140) bit1(pls) = all_157_0 & $i(all_157_0) & ! [v0: $i] : ! [v1: $i] :
% 35.46/5.62 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (number_number_of(v0,
% 35.46/5.62 | v3) = v4) | ~ (plus_plus(int, v2, all_157_0) = v3) | ~
% 35.46/5.62 | (one_one(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ number_ring(v0) |
% 35.46/5.62 | ? [v5: $i] : (number_number_of(v0, v2) = v5 & plus_plus(v0, v5, v1)
% 35.46/5.62 | = v4 & $i(v5) & $i(v4)))
% 35.46/5.62 |
% 35.46/5.62 | ALPHA: (140) implies:
% 35.46/5.62 | (141) bit1(pls) = all_157_0
% 35.46/5.62 |
% 35.46/5.62 | DELTA: instantiating (9) with fresh symbol all_160_0 gives:
% 35.46/5.63 | (142) bit1(pls) = all_160_0 & $i(all_160_0) & ! [v0: $i] : ! [v1: $i] :
% 35.46/5.63 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (number_number_of(v0,
% 35.46/5.63 | v3) = v4) | ~ (plus_plus(int, all_160_0, v2) = v3) | ~
% 35.46/5.63 | (one_one(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ number_ring(v0) |
% 35.46/5.63 | ? [v5: $i] : (number_number_of(v0, v2) = v5 & plus_plus(v0, v1, v5)
% 35.46/5.63 | = v4 & $i(v5) & $i(v4)))
% 35.46/5.63 |
% 35.46/5.63 | ALPHA: (142) implies:
% 35.46/5.63 | (143) bit1(pls) = all_160_0
% 35.46/5.63 |
% 35.46/5.63 | DELTA: instantiating (44) with fresh symbols all_163_0, all_163_1, all_163_2
% 35.46/5.63 | gives:
% 35.46/5.63 | (144) number_number_of(nat, all_163_1) = all_163_0 & bit1(pls) = all_163_2
% 35.46/5.63 | & bit0(all_163_2) = all_163_1 & $i(all_163_0) & $i(all_163_1) &
% 35.46/5.63 | $i(all_163_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 35.46/5.63 | : ( ~ (power_power(v0, v2, all_163_0) = v3) | ~ (zero_zero(v0) = v1)
% 35.46/5.63 | | ~ $i(v2) | ~ $i(v0) | ~ ord_less(v0, v3, v1) | ~
% 35.46/5.63 | linordered_idom(v0))
% 35.46/5.63 |
% 35.46/5.63 | ALPHA: (144) implies:
% 35.46/5.63 | (145) bit0(all_163_2) = all_163_1
% 35.46/5.63 | (146) bit1(pls) = all_163_2
% 35.46/5.63 | (147) number_number_of(nat, all_163_1) = all_163_0
% 35.46/5.63 |
% 35.46/5.63 | DELTA: instantiating (34) with fresh symbols all_166_0, all_166_1 gives:
% 35.46/5.63 | (148) zero_zero(int) = all_166_0 & one_one(int) = all_166_1 & $i(all_166_0)
% 35.46/5.63 | & $i(all_166_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 35.46/5.63 | (plus_plus(int, v1, v0) = v2) | ~ (plus_plus(int, all_166_1, v0) =
% 35.46/5.63 | v1) | ~ $i(v0) | ~ ord_less(int, v2, all_166_0) | ord_less(int,
% 35.46/5.63 | v0, all_166_0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 35.46/5.63 | (plus_plus(int, v1, v0) = v2) | ~ (plus_plus(int, all_166_1, v0) =
% 35.46/5.63 | v1) | ~ $i(v0) | ~ ord_less(int, v0, all_166_0) | ord_less(int,
% 35.46/5.63 | v2, all_166_0))
% 35.46/5.63 |
% 35.46/5.63 | ALPHA: (148) implies:
% 35.46/5.63 | (149) one_one(int) = all_166_1
% 35.46/5.63 | (150) zero_zero(int) = all_166_0
% 35.46/5.63 |
% 35.46/5.63 | DELTA: instantiating (55) with fresh symbols all_169_0, all_169_1, all_169_2,
% 35.46/5.63 | all_169_3, all_169_4, all_169_5, all_169_6 gives:
% 35.46/5.63 | (151) power_power(int, all_169_4, all_169_1) = all_169_0 &
% 35.46/5.63 | semiring_1_of_nat(int, n) = all_169_5 & number_number_of(nat,
% 35.46/5.63 | all_169_2) = all_169_1 & bit1(pls) = all_169_3 & bit0(all_169_3) =
% 35.46/5.63 | all_169_2 & zero_zero(int) = all_169_0 & plus_plus(int, all_169_6,
% 35.46/5.63 | all_169_5) = all_169_4 & one_one(int) = all_169_6 & $i(all_169_0) &
% 35.46/5.63 | $i(all_169_1) & $i(all_169_2) & $i(all_169_3) & $i(all_169_4) &
% 35.46/5.63 | $i(all_169_5) & $i(all_169_6)
% 35.46/5.63 |
% 35.46/5.63 | ALPHA: (151) implies:
% 35.46/5.63 | (152) $i(all_169_5)
% 35.46/5.63 | (153) one_one(int) = all_169_6
% 35.46/5.63 | (154) plus_plus(int, all_169_6, all_169_5) = all_169_4
% 35.46/5.63 | (155) zero_zero(int) = all_169_0
% 35.46/5.63 | (156) bit0(all_169_3) = all_169_2
% 35.46/5.63 | (157) bit1(pls) = all_169_3
% 35.46/5.63 | (158) number_number_of(nat, all_169_2) = all_169_1
% 35.46/5.63 | (159) semiring_1_of_nat(int, n) = all_169_5
% 35.46/5.63 | (160) power_power(int, all_169_4, all_169_1) = all_169_0
% 35.46/5.63 |
% 35.46/5.63 | DELTA: instantiating (30) with fresh symbol all_171_0 gives:
% 35.46/5.63 | (161) one_one(int) = all_171_0 & $i(all_171_0) & ! [v0: $i] : ! [v1: $i]
% 35.46/5.63 | : ! [v2: $i] : (v1 = v0 | ~ (plus_plus(int, v1, all_171_0) = v2) |
% 35.46/5.63 | ~ $i(v1) | ~ $i(v0) | ~ ord_less(int, v0, v2) | ord_less(int, v0,
% 35.46/5.63 | v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 35.46/5.63 | (plus_plus(int, v1, all_171_0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 35.46/5.63 | ord_less(int, v0, v1) | ord_less(int, v0, v2)) & ! [v0: $i] : !
% 35.46/5.63 | [v1: $i] : ( ~ (plus_plus(int, v0, all_171_0) = v1) | ~ $i(v0) |
% 35.46/5.63 | ord_less(int, v0, v1))
% 35.46/5.63 |
% 35.46/5.63 | ALPHA: (161) implies:
% 35.46/5.63 | (162) one_one(int) = all_171_0
% 35.46/5.63 |
% 35.46/5.63 | DELTA: instantiating (13) with fresh symbols all_174_0, all_174_1, all_174_2,
% 35.46/5.63 | all_174_3, all_174_4 gives:
% 35.46/5.63 | (163) number_number_of(nat, all_174_1) = all_174_0 & number_number_of(nat,
% 35.46/5.63 | all_174_3) = all_174_2 & bit1(pls) = all_174_4 & bit0(all_174_3) =
% 35.46/5.63 | all_174_1 & bit0(all_174_4) = all_174_3 & $i(all_174_0) &
% 35.46/5.63 | $i(all_174_1) & $i(all_174_2) & $i(all_174_3) & $i(all_174_4) & !
% 35.46/5.63 | [v0: $i] : ! [v1: $i] : ( ~ (power_power(int, v0, all_174_0) = v1) |
% 35.46/5.63 | ~ $i(v0) | ? [v2: $i] : (power_power(int, v2, all_174_2) = v1 &
% 35.46/5.63 | power_power(int, v0, all_174_2) = v2 & $i(v2) & $i(v1)))
% 35.46/5.63 |
% 35.46/5.63 | ALPHA: (163) implies:
% 35.46/5.63 | (164) bit0(all_174_4) = all_174_3
% 35.46/5.63 | (165) bit1(pls) = all_174_4
% 35.46/5.63 | (166) number_number_of(nat, all_174_3) = all_174_2
% 35.46/5.63 |
% 35.46/5.63 | DELTA: instantiating (14) with fresh symbol all_177_0 gives:
% 35.46/5.64 | (167) zero_zero(nat) = all_177_0 & $i(all_177_0) & ! [v0: $i] : ! [v1:
% 35.46/5.64 | $i] : ( ~ (one_one(v0) = v1) | ~ $i(v0) | ~ semiring_0(v0) | ~
% 35.46/5.64 | power(v0) | ? [v2: $i] : (zero_zero(v0) = v2 & $i(v2) & ! [v3:
% 35.46/5.64 | $i] : ! [v4: any] : ! [v5: $i] : (v5 = v2 | v4 = all_177_0 |
% 35.46/5.64 | ~ (power_power(v0, v2, v4) = v5) | ~ (number_number_of(nat,
% 35.46/5.64 | v3) = v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: $i] : (v4 =
% 35.46/5.64 | v1 | ~ (power_power(v0, v2, all_177_0) = v4) | ~
% 35.46/5.64 | (number_number_of(nat, v3) = all_177_0) | ~ $i(v3))))
% 35.46/5.64 |
% 35.46/5.64 | ALPHA: (167) implies:
% 35.46/5.64 | (168) ! [v0: $i] : ! [v1: $i] : ( ~ (one_one(v0) = v1) | ~ $i(v0) | ~
% 35.46/5.64 | semiring_0(v0) | ~ power(v0) | ? [v2: $i] : (zero_zero(v0) = v2 &
% 35.46/5.64 | $i(v2) & ! [v3: $i] : ! [v4: any] : ! [v5: $i] : (v5 = v2 | v4
% 35.46/5.64 | = all_177_0 | ~ (power_power(v0, v2, v4) = v5) | ~
% 35.46/5.64 | (number_number_of(nat, v3) = v4) | ~ $i(v3)) & ! [v3: $i] :
% 35.46/5.64 | ! [v4: $i] : (v4 = v1 | ~ (power_power(v0, v2, all_177_0) = v4)
% 35.46/5.64 | | ~ (number_number_of(nat, v3) = all_177_0) | ~ $i(v3))))
% 35.46/5.64 |
% 35.46/5.64 | DELTA: instantiating (32) with fresh symbol all_180_0 gives:
% 35.46/5.64 | (169) bit1(pls) = all_180_0 & $i(all_180_0) & ! [v0: $i] : ! [v1: $i] :
% 35.46/5.64 | ! [v2: $i] : ! [v3: $i] : ( ~ (number_number_of(v0, v2) = v3) | ~
% 35.46/5.64 | (one_one(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ number_ring(v0) |
% 35.46/5.64 | ~ ord_less(v0, v3, v1) | ~ linordered_idom(v0) | ord_less(int, v2,
% 35.46/5.64 | all_180_0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 35.46/5.64 | $i] : ( ~ (number_number_of(v0, v2) = v3) | ~ (one_one(v0) = v1) |
% 35.46/5.64 | ~ $i(v2) | ~ $i(v0) | ~ number_ring(v0) | ~ ord_less(int, v2,
% 35.46/5.64 | all_180_0) | ~ linordered_idom(v0) | ord_less(v0, v3, v1))
% 35.46/5.64 |
% 35.46/5.64 | ALPHA: (169) implies:
% 35.46/5.64 | (170) bit1(pls) = all_180_0
% 35.46/5.64 |
% 35.46/5.64 | DELTA: instantiating (33) with fresh symbol all_183_0 gives:
% 35.46/5.64 | (171) bit1(pls) = all_183_0 & $i(all_183_0) & ! [v0: $i] : ! [v1: $i] :
% 35.46/5.64 | ! [v2: $i] : ! [v3: $i] : ( ~ (number_number_of(v0, v2) = v3) | ~
% 35.46/5.64 | (one_one(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ number_ring(v0) |
% 35.46/5.64 | ~ ord_less(v0, v1, v3) | ~ linordered_idom(v0) | ord_less(int,
% 35.46/5.64 | all_183_0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 35.46/5.64 | [v3: $i] : ( ~ (number_number_of(v0, v2) = v3) | ~ (one_one(v0) =
% 35.46/5.64 | v1) | ~ $i(v2) | ~ $i(v0) | ~ number_ring(v0) | ~
% 35.46/5.64 | ord_less(int, all_183_0, v2) | ~ linordered_idom(v0) |
% 35.46/5.64 | ord_less(v0, v1, v3))
% 35.46/5.64 |
% 35.46/5.64 | ALPHA: (171) implies:
% 35.46/5.64 | (172) bit1(pls) = all_183_0
% 35.46/5.64 |
% 35.46/5.64 | DELTA: instantiating (8) with fresh symbols all_186_0, all_186_1, all_186_2
% 35.46/5.64 | gives:
% 35.46/5.64 | (173) number_number_of(nat, all_186_1) = all_186_0 & bit1(pls) = all_186_2
% 35.46/5.64 | & bit0(all_186_2) = all_186_1 & $i(all_186_0) & $i(all_186_1) &
% 35.46/5.64 | $i(all_186_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 35.46/5.64 | : (v3 = v1 | ~ (power_power(v0, v2, all_186_0) = v3) | ~
% 35.46/5.64 | (zero_zero(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 35.46/5.64 | ring_11004092258visors(v0) | ? [v4: $i] : ( ~ (v4 = v1) & ti(v0,
% 35.46/5.64 | v2) = v4 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 35.46/5.64 | ( ~ (power_power(v0, v2, all_186_0) = v1) | ~ (zero_zero(v0) = v1) |
% 35.46/5.64 | ~ $i(v2) | ~ $i(v0) | ~ ring_11004092258visors(v0) | (ti(v0, v2)
% 35.46/5.64 | = v1 & $i(v1)))
% 35.46/5.64 |
% 35.46/5.64 | ALPHA: (173) implies:
% 35.46/5.64 | (174) bit0(all_186_2) = all_186_1
% 35.46/5.64 | (175) bit1(pls) = all_186_2
% 35.46/5.64 | (176) number_number_of(nat, all_186_1) = all_186_0
% 35.46/5.64 |
% 35.46/5.64 | DELTA: instantiating (43) with fresh symbols all_189_0, all_189_1, all_189_2
% 35.46/5.64 | gives:
% 35.46/5.64 | (177) number_number_of(nat, all_189_1) = all_189_0 & bit1(pls) = all_189_2
% 35.46/5.64 | & bit0(all_189_2) = all_189_1 & $i(all_189_0) & $i(all_189_1) &
% 35.46/5.64 | $i(all_189_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 35.46/5.64 | : ( ~ (power_power(v0, v2, all_189_0) = v3) | ~ (zero_zero(v0) = v1)
% 35.46/5.64 | | ~ $i(v2) | ~ $i(v0) | ~ ord_less(v0, v1, v3) | ~
% 35.46/5.64 | linordered_idom(v0) | ? [v4: $i] : ( ~ (v4 = v1) & ti(v0, v2) = v4
% 35.46/5.64 | & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 35.46/5.64 | $i] : ( ~ (power_power(v0, v2, all_189_0) = v3) | ~ (zero_zero(v0)
% 35.46/5.64 | = v1) | ~ $i(v2) | ~ $i(v0) | ~ linordered_idom(v0) |
% 35.46/5.64 | ord_less(v0, v1, v3) | (ti(v0, v2) = v1 & $i(v1)))
% 35.46/5.64 |
% 35.46/5.64 | ALPHA: (177) implies:
% 35.46/5.64 | (178) bit0(all_189_2) = all_189_1
% 35.46/5.64 | (179) bit1(pls) = all_189_2
% 35.46/5.64 | (180) number_number_of(nat, all_189_1) = all_189_0
% 35.46/5.64 |
% 35.46/5.64 | DELTA: instantiating (5) with fresh symbols all_192_0, all_192_1, all_192_2
% 35.46/5.64 | gives:
% 35.46/5.65 | (181) number_number_of(nat, all_192_1) = all_192_0 & bit1(pls) = all_192_2
% 35.46/5.65 | & bit0(all_192_2) = all_192_1 & $i(all_192_0) & $i(all_192_1) &
% 35.46/5.65 | $i(all_192_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 35.46/5.65 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v1 | ~
% 35.46/5.65 | (power_power(v0, v3, all_192_0) = v5) | ~ (power_power(v0, v2,
% 35.46/5.65 | all_192_0) = v4) | ~ (zero_zero(v0) = v1) | ~ (plus_plus(v0,
% 35.46/5.65 | v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 35.46/5.65 | linordered_idom(v0) | ? [v7: $i] : ? [v8: $i] : (( ~ (v8 = v1) &
% 35.46/5.65 | ti(v0, v3) = v8 & $i(v8)) | ( ~ (v7 = v1) & ti(v0, v2) = v7 &
% 35.46/5.65 | $i(v7)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 35.46/5.65 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (power_power(v0, v3,
% 35.46/5.65 | all_192_0) = v5) | ~ (power_power(v0, v2, all_192_0) = v4) |
% 35.46/5.65 | ~ (zero_zero(v0) = v1) | ~ (plus_plus(v0, v4, v5) = v1) | ~
% 35.46/5.65 | $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ linordered_idom(v0) | (ti(v0,
% 35.46/5.65 | v3) = v1 & ti(v0, v2) = v1 & $i(v1)))
% 35.46/5.65 |
% 35.46/5.65 | ALPHA: (181) implies:
% 35.46/5.65 | (182) bit0(all_192_2) = all_192_1
% 35.46/5.65 | (183) bit1(pls) = all_192_2
% 35.46/5.65 | (184) number_number_of(nat, all_192_1) = all_192_0
% 35.46/5.65 |
% 35.46/5.65 | DELTA: instantiating (45) with fresh symbols all_195_0, all_195_1, all_195_2
% 35.46/5.65 | gives:
% 35.46/5.65 | (185) number_number_of(nat, all_195_1) = all_195_0 & bit1(pls) = all_195_2
% 35.46/5.65 | & bit0(all_195_2) = all_195_1 & $i(all_195_0) & $i(all_195_1) &
% 35.46/5.65 | $i(all_195_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 35.46/5.65 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (power_power(v0, v3,
% 35.46/5.65 | all_195_0) = v5) | ~ (power_power(v0, v2, all_195_0) = v4) |
% 35.46/5.65 | ~ (zero_zero(v0) = v1) | ~ (plus_plus(v0, v4, v5) = v6) | ~
% 35.46/5.65 | $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ ord_less(v0, v1, v6) | ~
% 35.46/5.65 | linordered_idom(v0) | ? [v7: $i] : ? [v8: $i] : (( ~ (v8 = v1) &
% 35.46/5.65 | ti(v0, v3) = v8 & $i(v8)) | ( ~ (v7 = v1) & ti(v0, v2) = v7 &
% 35.46/5.65 | $i(v7)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 35.46/5.65 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 35.46/5.65 | (power_power(v0, v3, all_195_0) = v5) | ~ (power_power(v0, v2,
% 35.46/5.65 | all_195_0) = v4) | ~ (zero_zero(v0) = v1) | ~ (plus_plus(v0,
% 35.46/5.65 | v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 35.46/5.65 | linordered_idom(v0) | ord_less(v0, v1, v6) | (ti(v0, v3) = v1 &
% 35.46/5.65 | ti(v0, v2) = v1 & $i(v1)))
% 35.46/5.65 |
% 35.46/5.65 | ALPHA: (185) implies:
% 35.46/5.65 | (186) bit0(all_195_2) = all_195_1
% 35.46/5.65 | (187) bit1(pls) = all_195_2
% 35.46/5.65 | (188) number_number_of(nat, all_195_1) = all_195_0
% 35.46/5.65 |
% 35.46/5.65 | DELTA: instantiating (40) with fresh symbol all_198_0 gives:
% 35.46/5.65 | (189) zero_zero(nat) = all_198_0 & $i(all_198_0) & ! [v0: $i] : ! [v1:
% 35.46/5.65 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ! [v5: $i] : (v5
% 35.46/5.65 | = v1 | v4 = all_198_0 | ~ (power_power(v0, v2, v4) = v5) | ~
% 35.46/5.65 | (number_number_of(nat, v3) = v4) | ~ (zero_zero(v0) = v1) | ~
% 35.46/5.65 | $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ zero_neq_one(v0) | ~
% 35.46/5.65 | no_zero_divisors(v0) | ~ mult_zero(v0) | ~ power(v0) | ? [v6:
% 35.46/5.65 | $i] : ( ~ (v6 = v1) & ti(v0, v2) = v6 & $i(v6))) & ! [v0: $i] :
% 35.46/5.65 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 35.46/5.65 | (power_power(v0, v2, v4) = v1) | ~ (number_number_of(nat, v3) =
% 35.46/5.65 | v4) | ~ (zero_zero(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0)
% 35.46/5.65 | | ~ zero_neq_one(v0) | ~ no_zero_divisors(v0) | ~ mult_zero(v0)
% 35.46/5.65 | | ~ power(v0) | (ti(v0, v2) = v1 & $i(v1))) & ! [v0: $i] : !
% 35.46/5.65 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (power_power(v0, v2,
% 35.46/5.65 | all_198_0) = v1) | ~ (number_number_of(nat, v3) = all_198_0) |
% 35.46/5.65 | ~ (zero_zero(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 35.46/5.65 | zero_neq_one(v0) | ~ no_zero_divisors(v0) | ~ mult_zero(v0) | ~
% 35.46/5.65 | power(v0))
% 35.46/5.65 |
% 35.46/5.65 | ALPHA: (189) implies:
% 35.46/5.65 | (190) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 35.46/5.65 | ( ~ (power_power(v0, v2, v4) = v1) | ~ (number_number_of(nat, v3) =
% 35.46/5.65 | v4) | ~ (zero_zero(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0)
% 35.46/5.65 | | ~ zero_neq_one(v0) | ~ no_zero_divisors(v0) | ~ mult_zero(v0)
% 35.46/5.65 | | ~ power(v0) | (ti(v0, v2) = v1 & $i(v1)))
% 35.46/5.65 |
% 35.46/5.65 | GROUND_INST: instantiating (56) with all_86_0, all_103_0, int, simplifying
% 35.46/5.65 | with (64), (82) gives:
% 35.46/5.65 | (191) all_103_0 = all_86_0
% 35.46/5.65 |
% 35.46/5.65 | GROUND_INST: instantiating (56) with all_103_0, all_105_0, int, simplifying
% 35.46/5.65 | with (82), (85) gives:
% 35.46/5.65 | (192) all_105_0 = all_103_0
% 35.46/5.65 |
% 35.46/5.65 | GROUND_INST: instantiating (56) with all_105_0, all_107_1, int, simplifying
% 35.46/5.65 | with (85), (89) gives:
% 35.46/5.65 | (193) all_107_1 = all_105_0
% 35.46/5.65 |
% 35.46/5.65 | GROUND_INST: instantiating (56) with all_107_1, all_120_1, int, simplifying
% 35.46/5.65 | with (89), (101) gives:
% 35.46/5.65 | (194) all_120_1 = all_107_1
% 35.46/5.65 |
% 35.46/5.65 | GROUND_INST: instantiating (56) with all_120_1, all_123_0, int, simplifying
% 35.46/5.65 | with (101), (104) gives:
% 35.46/5.65 | (195) all_123_0 = all_120_1
% 35.46/5.65 |
% 35.46/5.65 | GROUND_INST: instantiating (56) with all_123_0, all_132_2, int, simplifying
% 35.46/5.65 | with (104), (111) gives:
% 35.46/5.65 | (196) all_132_2 = all_123_0
% 35.46/5.65 |
% 35.46/5.65 | GROUND_INST: instantiating (56) with all_132_2, all_166_1, int, simplifying
% 35.46/5.65 | with (111), (149) gives:
% 35.46/5.65 | (197) all_166_1 = all_132_2
% 35.46/5.65 |
% 35.46/5.66 | GROUND_INST: instantiating (56) with all_166_1, all_169_6, int, simplifying
% 35.46/5.66 | with (149), (153) gives:
% 35.46/5.66 | (198) all_169_6 = all_166_1
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (56) with all_169_6, all_171_0, int, simplifying
% 35.46/5.66 | with (153), (162) gives:
% 35.46/5.66 | (199) all_171_0 = all_169_6
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (56) with all_101_0, all_171_0, int, simplifying
% 35.46/5.66 | with (78), (162) gives:
% 35.46/5.66 | (200) all_171_0 = all_101_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (56) with all_99_0, all_109_1, nat, simplifying
% 35.46/5.66 | with (73), (92) gives:
% 35.46/5.66 | (201) all_109_1 = all_99_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (56) with all_109_1, all_137_3, nat, simplifying
% 35.46/5.66 | with (92), (118) gives:
% 35.46/5.66 | (202) all_137_3 = all_109_1
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (56) with all_101_1, all_137_3, nat, simplifying
% 35.46/5.66 | with (79), (118) gives:
% 35.46/5.66 | (203) all_137_3 = all_101_1
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with all_96_0, all_103_1, int, simplifying
% 35.46/5.66 | with (71), (83) gives:
% 35.46/5.66 | (204) all_103_1 = all_96_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with all_88_0, all_103_1, int, simplifying
% 35.46/5.66 | with (66), (83) gives:
% 35.46/5.66 | (205) all_103_1 = all_88_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with all_96_0, all_105_1, int, simplifying
% 35.46/5.66 | with (71), (86) gives:
% 35.46/5.66 | (206) all_105_1 = all_96_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with all_105_1, all_111_0, int, simplifying
% 35.46/5.66 | with (86), (95) gives:
% 35.46/5.66 | (207) all_111_0 = all_105_1
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with all_113_0, all_116_0, int, simplifying
% 35.46/5.66 | with (97), (99) gives:
% 35.46/5.66 | (208) all_116_0 = all_113_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with all_111_0, all_116_0, int, simplifying
% 35.46/5.66 | with (95), (99) gives:
% 35.46/5.66 | (209) all_116_0 = all_111_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with all_120_0, all_132_3, int, simplifying
% 35.46/5.66 | with (102), (113) gives:
% 35.46/5.66 | (210) all_132_3 = all_120_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with all_116_0, all_132_3, int, simplifying
% 35.46/5.66 | with (99), (113) gives:
% 35.46/5.66 | (211) all_132_3 = all_116_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with all_132_3, all_134_1, int, simplifying
% 35.46/5.66 | with (113), (116) gives:
% 35.46/5.66 | (212) all_134_1 = all_132_3
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with all_134_1, all_139_0, int, simplifying
% 35.46/5.66 | with (116), (123) gives:
% 35.46/5.66 | (213) all_139_0 = all_134_1
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with all_139_0, all_142_0, int, simplifying
% 35.46/5.66 | with (123), (125) gives:
% 35.46/5.66 | (214) all_142_0 = all_139_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with all_94_0, all_142_0, int, simplifying
% 35.46/5.66 | with (69), (125) gives:
% 35.46/5.66 | (215) all_142_0 = all_94_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with all_96_0, all_166_0, int, simplifying
% 35.46/5.66 | with (71), (150) gives:
% 35.46/5.66 | (216) all_166_0 = all_96_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with all_166_0, all_169_0, int, simplifying
% 35.46/5.66 | with (150), (155) gives:
% 35.46/5.66 | (217) all_169_0 = all_166_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (57) with pls, all_169_0, int, simplifying with
% 35.46/5.66 | (36), (155) gives:
% 35.46/5.66 | (218) all_169_0 = pls
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_99_1, all_145_1, pls, simplifying
% 35.46/5.66 | with (74), (128) gives:
% 35.46/5.66 | (219) all_145_1 = all_99_1
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_151_1, all_163_2, pls, simplifying
% 35.46/5.66 | with (135), (146) gives:
% 35.46/5.66 | (220) all_163_2 = all_151_1
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_145_1, all_163_2, pls, simplifying
% 35.46/5.66 | with (128), (146) gives:
% 35.46/5.66 | (221) all_163_2 = all_145_1
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_126_0, all_163_2, pls, simplifying
% 35.46/5.66 | with (106), (146) gives:
% 35.46/5.66 | (222) all_163_2 = all_126_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_154_2, all_169_3, pls, simplifying
% 35.46/5.66 | with (138), (157) gives:
% 35.46/5.66 | (223) all_169_3 = all_154_2
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_109_0, all_169_3, pls, simplifying
% 35.46/5.66 | with (93), (157) gives:
% 35.46/5.66 | (224) all_169_3 = all_109_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_160_0, all_180_0, pls, simplifying
% 35.46/5.66 | with (143), (170) gives:
% 35.46/5.66 | (225) all_180_0 = all_160_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_180_0, all_183_0, pls, simplifying
% 35.46/5.66 | with (170), (172) gives:
% 35.46/5.66 | (226) all_183_0 = all_180_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_129_0, all_183_0, pls, simplifying
% 35.46/5.66 | with (108), (172) gives:
% 35.46/5.66 | (227) all_183_0 = all_129_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_154_2, all_186_2, pls, simplifying
% 35.46/5.66 | with (138), (175) gives:
% 35.46/5.66 | (228) all_186_2 = all_154_2
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_137_1, all_186_2, pls, simplifying
% 35.46/5.66 | with (120), (175) gives:
% 35.46/5.66 | (229) all_186_2 = all_137_1
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_148_2, all_189_2, pls, simplifying
% 35.46/5.66 | with (131), (179) gives:
% 35.46/5.66 | (230) all_189_2 = all_148_2
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_186_2, all_192_2, pls, simplifying
% 35.46/5.66 | with (175), (183) gives:
% 35.46/5.66 | (231) all_192_2 = all_186_2
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_180_0, all_192_2, pls, simplifying
% 35.46/5.66 | with (170), (183) gives:
% 35.46/5.66 | (232) all_192_2 = all_180_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_163_2, all_192_2, pls, simplifying
% 35.46/5.66 | with (146), (183) gives:
% 35.46/5.66 | (233) all_192_2 = all_163_2
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_157_0, all_192_2, pls, simplifying
% 35.46/5.66 | with (141), (183) gives:
% 35.46/5.66 | (234) all_192_2 = all_157_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_107_0, all_192_2, pls, simplifying
% 35.46/5.66 | with (90), (183) gives:
% 35.46/5.66 | (235) all_192_2 = all_107_0
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_192_2, all_195_2, pls, simplifying
% 35.46/5.66 | with (183), (187) gives:
% 35.46/5.66 | (236) all_195_2 = all_192_2
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_189_2, all_195_2, pls, simplifying
% 35.46/5.66 | with (179), (187) gives:
% 35.46/5.66 | (237) all_195_2 = all_189_2
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (59) with all_174_4, all_195_2, pls, simplifying
% 35.46/5.66 | with (165), (187) gives:
% 35.46/5.66 | (238) all_195_2 = all_174_4
% 35.46/5.66 |
% 35.46/5.66 | GROUND_INST: instantiating (61) with all_132_1, all_169_5, n, int, simplifying
% 35.46/5.66 | with (114), (159) gives:
% 35.46/5.66 | (239) all_169_5 = all_132_1
% 35.46/5.66 |
% 35.46/5.66 | COMBINE_EQS: (236), (238) imply:
% 35.46/5.66 | (240) all_192_2 = all_174_4
% 35.46/5.66 |
% 35.46/5.66 | SIMP: (240) implies:
% 35.46/5.66 | (241) all_192_2 = all_174_4
% 35.46/5.66 |
% 35.46/5.66 | COMBINE_EQS: (237), (238) imply:
% 35.46/5.67 | (242) all_189_2 = all_174_4
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (242) implies:
% 35.46/5.67 | (243) all_189_2 = all_174_4
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (233), (234) imply:
% 35.46/5.67 | (244) all_163_2 = all_157_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (244) implies:
% 35.46/5.67 | (245) all_163_2 = all_157_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (232), (234) imply:
% 35.46/5.67 | (246) all_180_0 = all_157_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (246) implies:
% 35.46/5.67 | (247) all_180_0 = all_157_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (234), (235) imply:
% 35.46/5.67 | (248) all_157_0 = all_107_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (234), (241) imply:
% 35.46/5.67 | (249) all_174_4 = all_157_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (249) implies:
% 35.46/5.67 | (250) all_174_4 = all_157_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (231), (234) imply:
% 35.46/5.67 | (251) all_186_2 = all_157_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (251) implies:
% 35.46/5.67 | (252) all_186_2 = all_157_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (230), (243) imply:
% 35.46/5.67 | (253) all_174_4 = all_148_2
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (253) implies:
% 35.46/5.67 | (254) all_174_4 = all_148_2
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (228), (229) imply:
% 35.46/5.67 | (255) all_154_2 = all_137_1
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (255) implies:
% 35.46/5.67 | (256) all_154_2 = all_137_1
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (229), (252) imply:
% 35.46/5.67 | (257) all_157_0 = all_137_1
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (257) implies:
% 35.46/5.67 | (258) all_157_0 = all_137_1
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (226), (227) imply:
% 35.46/5.67 | (259) all_180_0 = all_129_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (259) implies:
% 35.46/5.67 | (260) all_180_0 = all_129_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (225), (260) imply:
% 35.46/5.67 | (261) all_160_0 = all_129_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (225), (247) imply:
% 35.46/5.67 | (262) all_160_0 = all_157_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (250), (254) imply:
% 35.46/5.67 | (263) all_157_0 = all_148_2
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (263) implies:
% 35.46/5.67 | (264) all_157_0 = all_148_2
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (199), (200) imply:
% 35.46/5.67 | (265) all_169_6 = all_101_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (265) implies:
% 35.46/5.67 | (266) all_169_6 = all_101_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (217), (218) imply:
% 35.46/5.67 | (267) all_166_0 = pls
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (267) implies:
% 35.46/5.67 | (268) all_166_0 = pls
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (223), (224) imply:
% 35.46/5.67 | (269) all_154_2 = all_109_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (269) implies:
% 35.46/5.67 | (270) all_154_2 = all_109_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (198), (266) imply:
% 35.46/5.67 | (271) all_166_1 = all_101_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (271) implies:
% 35.46/5.67 | (272) all_166_1 = all_101_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (216), (268) imply:
% 35.46/5.67 | (273) all_96_0 = pls
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (273) implies:
% 35.46/5.67 | (274) all_96_0 = pls
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (197), (272) imply:
% 35.46/5.67 | (275) all_132_2 = all_101_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (275) implies:
% 35.46/5.67 | (276) all_132_2 = all_101_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (220), (221) imply:
% 35.46/5.67 | (277) all_151_1 = all_145_1
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (220), (222) imply:
% 35.46/5.67 | (278) all_151_1 = all_126_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (220), (245) imply:
% 35.46/5.67 | (279) all_157_0 = all_151_1
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (279) implies:
% 35.46/5.67 | (280) all_157_0 = all_151_1
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (261), (262) imply:
% 35.46/5.67 | (281) all_157_0 = all_129_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (281) implies:
% 35.46/5.67 | (282) all_157_0 = all_129_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (248), (264) imply:
% 35.46/5.67 | (283) all_148_2 = all_107_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (258), (264) imply:
% 35.46/5.67 | (284) all_148_2 = all_137_1
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (264), (282) imply:
% 35.46/5.67 | (285) all_148_2 = all_129_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (264), (280) imply:
% 35.46/5.67 | (286) all_151_1 = all_148_2
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (286) implies:
% 35.46/5.67 | (287) all_151_1 = all_148_2
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (256), (270) imply:
% 35.46/5.67 | (288) all_137_1 = all_109_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (288) implies:
% 35.46/5.67 | (289) all_137_1 = all_109_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (277), (278) imply:
% 35.46/5.67 | (290) all_145_1 = all_126_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (290) implies:
% 35.46/5.67 | (291) all_145_1 = all_126_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (278), (287) imply:
% 35.46/5.67 | (292) all_148_2 = all_126_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (292) implies:
% 35.46/5.67 | (293) all_148_2 = all_126_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (283), (285) imply:
% 35.46/5.67 | (294) all_129_0 = all_107_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (284), (285) imply:
% 35.46/5.67 | (295) all_137_1 = all_129_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (295) implies:
% 35.46/5.67 | (296) all_137_1 = all_129_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (285), (293) imply:
% 35.46/5.67 | (297) all_129_0 = all_126_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (219), (291) imply:
% 35.46/5.67 | (298) all_126_0 = all_99_1
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (298) implies:
% 35.46/5.67 | (299) all_126_0 = all_99_1
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (214), (215) imply:
% 35.46/5.67 | (300) all_139_0 = all_94_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (300) implies:
% 35.46/5.67 | (301) all_139_0 = all_94_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (213), (301) imply:
% 35.46/5.67 | (302) all_134_1 = all_94_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (302) implies:
% 35.46/5.67 | (303) all_134_1 = all_94_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (289), (296) imply:
% 35.46/5.67 | (304) all_129_0 = all_109_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (304) implies:
% 35.46/5.67 | (305) all_129_0 = all_109_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (202), (203) imply:
% 35.46/5.67 | (306) all_109_1 = all_101_1
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (306) implies:
% 35.46/5.67 | (307) all_109_1 = all_101_1
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (212), (303) imply:
% 35.46/5.67 | (308) all_132_3 = all_94_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (308) implies:
% 35.46/5.67 | (309) all_132_3 = all_94_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (196), (276) imply:
% 35.46/5.67 | (310) all_123_0 = all_101_0
% 35.46/5.67 |
% 35.46/5.67 | SIMP: (310) implies:
% 35.46/5.67 | (311) all_123_0 = all_101_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (210), (309) imply:
% 35.46/5.67 | (312) all_120_0 = all_94_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (210), (211) imply:
% 35.46/5.67 | (313) all_120_0 = all_116_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (294), (305) imply:
% 35.46/5.67 | (314) all_109_0 = all_107_0
% 35.46/5.67 |
% 35.46/5.67 | COMBINE_EQS: (297), (305) imply:
% 35.46/5.67 | (315) all_126_0 = all_109_0
% 35.46/5.67 |
% 35.46/5.68 | SIMP: (315) implies:
% 35.46/5.68 | (316) all_126_0 = all_109_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (299), (316) imply:
% 35.46/5.68 | (317) all_109_0 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | SIMP: (317) implies:
% 35.46/5.68 | (318) all_109_0 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (195), (311) imply:
% 35.46/5.68 | (319) all_120_1 = all_101_0
% 35.46/5.68 |
% 35.46/5.68 | SIMP: (319) implies:
% 35.46/5.68 | (320) all_120_1 = all_101_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (312), (313) imply:
% 35.46/5.68 | (321) all_116_0 = all_94_0
% 35.46/5.68 |
% 35.46/5.68 | SIMP: (321) implies:
% 35.46/5.68 | (322) all_116_0 = all_94_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (194), (320) imply:
% 35.46/5.68 | (323) all_107_1 = all_101_0
% 35.46/5.68 |
% 35.46/5.68 | SIMP: (323) implies:
% 35.46/5.68 | (324) all_107_1 = all_101_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (208), (209) imply:
% 35.46/5.68 | (325) all_113_0 = all_111_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (208), (322) imply:
% 35.46/5.68 | (326) all_113_0 = all_94_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (325), (326) imply:
% 35.46/5.68 | (327) all_111_0 = all_94_0
% 35.46/5.68 |
% 35.46/5.68 | SIMP: (327) implies:
% 35.46/5.68 | (328) all_111_0 = all_94_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (207), (328) imply:
% 35.46/5.68 | (329) all_105_1 = all_94_0
% 35.46/5.68 |
% 35.46/5.68 | SIMP: (329) implies:
% 35.46/5.68 | (330) all_105_1 = all_94_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (314), (318) imply:
% 35.46/5.68 | (331) all_107_0 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | SIMP: (331) implies:
% 35.46/5.68 | (332) all_107_0 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (201), (307) imply:
% 35.46/5.68 | (333) all_101_1 = all_99_0
% 35.46/5.68 |
% 35.46/5.68 | SIMP: (333) implies:
% 35.46/5.68 | (334) all_101_1 = all_99_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (193), (324) imply:
% 35.46/5.68 | (335) all_105_0 = all_101_0
% 35.46/5.68 |
% 35.46/5.68 | SIMP: (335) implies:
% 35.46/5.68 | (336) all_105_0 = all_101_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (192), (336) imply:
% 35.46/5.68 | (337) all_103_0 = all_101_0
% 35.46/5.68 |
% 35.46/5.68 | SIMP: (337) implies:
% 35.46/5.68 | (338) all_103_0 = all_101_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (206), (330) imply:
% 35.46/5.68 | (339) all_96_0 = all_94_0
% 35.46/5.68 |
% 35.46/5.68 | SIMP: (339) implies:
% 35.46/5.68 | (340) all_96_0 = all_94_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (191), (338) imply:
% 35.46/5.68 | (341) all_101_0 = all_86_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (204), (205) imply:
% 35.46/5.68 | (342) all_96_0 = all_88_0
% 35.46/5.68 |
% 35.46/5.68 | SIMP: (342) implies:
% 35.46/5.68 | (343) all_96_0 = all_88_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (340), (343) imply:
% 35.46/5.68 | (344) all_94_0 = all_88_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (274), (340) imply:
% 35.46/5.68 | (345) all_94_0 = pls
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (344), (345) imply:
% 35.46/5.68 | (346) all_88_0 = pls
% 35.46/5.68 |
% 35.46/5.68 | SIMP: (346) implies:
% 35.46/5.68 | (347) all_88_0 = pls
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (312), (345) imply:
% 35.46/5.68 | (348) all_120_0 = pls
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (305), (318) imply:
% 35.46/5.68 | (349) all_129_0 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (210), (348) imply:
% 35.46/5.68 | (350) all_132_3 = pls
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (276), (341) imply:
% 35.46/5.68 | (351) all_132_2 = all_86_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (289), (318) imply:
% 35.46/5.68 | (352) all_137_1 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (285), (349) imply:
% 35.46/5.68 | (353) all_148_2 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (278), (299) imply:
% 35.46/5.68 | (354) all_151_1 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (270), (318) imply:
% 35.46/5.68 | (355) all_154_2 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (264), (353) imply:
% 35.46/5.68 | (356) all_157_0 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (220), (354) imply:
% 35.46/5.68 | (357) all_163_2 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (266), (341) imply:
% 35.46/5.68 | (358) all_169_6 = all_86_0
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (224), (318) imply:
% 35.46/5.68 | (359) all_169_3 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (254), (353) imply:
% 35.46/5.68 | (360) all_174_4 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (229), (352) imply:
% 35.46/5.68 | (361) all_186_2 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (230), (353) imply:
% 35.46/5.68 | (362) all_189_2 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (234), (356) imply:
% 35.46/5.68 | (363) all_192_2 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | COMBINE_EQS: (238), (360) imply:
% 35.46/5.68 | (364) all_195_2 = all_99_1
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (160), (218) imply:
% 35.46/5.68 | (365) power_power(int, all_169_4, all_169_1) = pls
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (80), (334), (341) imply:
% 35.46/5.68 | (366) semiring_1_of_nat(int, all_99_0) = all_86_0
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (186), (364) imply:
% 35.46/5.68 | (367) bit0(all_99_1) = all_195_1
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (182), (363) imply:
% 35.46/5.68 | (368) bit0(all_99_1) = all_192_1
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (178), (362) imply:
% 35.46/5.68 | (369) bit0(all_99_1) = all_189_1
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (174), (361) imply:
% 35.46/5.68 | (370) bit0(all_99_1) = all_186_1
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (164), (360) imply:
% 35.46/5.68 | (371) bit0(all_99_1) = all_174_3
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (156), (359) imply:
% 35.46/5.68 | (372) bit0(all_99_1) = all_169_2
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (145), (357) imply:
% 35.46/5.68 | (373) bit0(all_99_1) = all_163_1
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (137), (355) imply:
% 35.46/5.68 | (374) bit0(all_99_1) = all_154_1
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (134), (354) imply:
% 35.46/5.68 | (375) bit0(all_99_1) = all_151_0
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (130), (353) imply:
% 35.46/5.68 | (376) bit0(all_99_1) = all_148_1
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (127), (219) imply:
% 35.46/5.68 | (377) bit0(all_99_1) = all_145_0
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (119), (352) imply:
% 35.46/5.68 | (378) bit0(all_99_1) = all_137_0
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (154), (239), (358) imply:
% 35.46/5.68 | (379) plus_plus(int, all_86_0, all_132_1) = all_169_4
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (112), (351) imply:
% 35.46/5.68 | (380) plus_plus(int, all_86_0, all_132_1) = all_132_0
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (152), (239) imply:
% 35.46/5.68 | (381) $i(all_132_1)
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (88), (332) imply:
% 35.46/5.68 | (382) $i(all_99_1)
% 35.46/5.68 |
% 35.46/5.68 | REDUCE: (77), (341) imply:
% 35.46/5.69 | (383) $i(all_86_0)
% 35.46/5.69 |
% 35.46/5.69 | REDUCE: (76), (334) imply:
% 35.46/5.69 | (384) $i(all_99_0)
% 35.46/5.69 |
% 35.46/5.69 | REDUCE: (110), (350) imply:
% 35.46/5.69 | (385) ord_less(int, pls, all_132_0)
% 35.46/5.69 |
% 35.46/5.69 | REDUCE: (68), (345) imply:
% 35.46/5.69 | (386) ~ ord_less(int, pls, pls)
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (62) with all_132_0, all_169_4, all_132_1,
% 35.46/5.69 | all_86_0, int, simplifying with (379), (380) gives:
% 35.46/5.69 | (387) all_169_4 = all_132_0
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (58) with all_163_1, all_169_2, all_99_1,
% 35.46/5.69 | simplifying with (372), (373) gives:
% 35.46/5.69 | (388) all_169_2 = all_163_1
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (58) with all_154_1, all_169_2, all_99_1,
% 35.46/5.69 | simplifying with (372), (374) gives:
% 35.46/5.69 | (389) all_169_2 = all_154_1
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (58) with all_169_2, all_174_3, all_99_1,
% 35.46/5.69 | simplifying with (371), (372) gives:
% 35.46/5.69 | (390) all_174_3 = all_169_2
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (58) with all_137_0, all_174_3, all_99_1,
% 35.46/5.69 | simplifying with (371), (378) gives:
% 35.46/5.69 | (391) all_174_3 = all_137_0
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (58) with all_163_1, all_186_1, all_99_1,
% 35.46/5.69 | simplifying with (370), (373) gives:
% 35.46/5.69 | (392) all_186_1 = all_163_1
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (58) with all_148_1, all_186_1, all_99_1,
% 35.46/5.69 | simplifying with (370), (376) gives:
% 35.46/5.69 | (393) all_186_1 = all_148_1
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (58) with all_174_3, all_189_1, all_99_1,
% 35.46/5.69 | simplifying with (369), (371) gives:
% 35.46/5.69 | (394) all_189_1 = all_174_3
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (58) with all_174_3, all_192_1, all_99_1,
% 35.46/5.69 | simplifying with (368), (371) gives:
% 35.46/5.69 | (395) all_192_1 = all_174_3
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (58) with all_151_0, all_192_1, all_99_1,
% 35.46/5.69 | simplifying with (368), (375) gives:
% 35.46/5.69 | (396) all_192_1 = all_151_0
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (58) with all_189_1, all_195_1, all_99_1,
% 35.46/5.69 | simplifying with (367), (369) gives:
% 35.46/5.69 | (397) all_195_1 = all_189_1
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (58) with all_145_0, all_195_1, all_99_1,
% 35.46/5.69 | simplifying with (367), (377) gives:
% 35.46/5.69 | (398) all_195_1 = all_145_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (397), (398) imply:
% 35.46/5.69 | (399) all_189_1 = all_145_0
% 35.46/5.69 |
% 35.46/5.69 | SIMP: (399) implies:
% 35.46/5.69 | (400) all_189_1 = all_145_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (395), (396) imply:
% 35.46/5.69 | (401) all_174_3 = all_151_0
% 35.46/5.69 |
% 35.46/5.69 | SIMP: (401) implies:
% 35.46/5.69 | (402) all_174_3 = all_151_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (394), (400) imply:
% 35.46/5.69 | (403) all_174_3 = all_145_0
% 35.46/5.69 |
% 35.46/5.69 | SIMP: (403) implies:
% 35.46/5.69 | (404) all_174_3 = all_145_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (392), (393) imply:
% 35.46/5.69 | (405) all_163_1 = all_148_1
% 35.46/5.69 |
% 35.46/5.69 | SIMP: (405) implies:
% 35.46/5.69 | (406) all_163_1 = all_148_1
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (390), (402) imply:
% 35.46/5.69 | (407) all_169_2 = all_151_0
% 35.46/5.69 |
% 35.46/5.69 | SIMP: (407) implies:
% 35.46/5.69 | (408) all_169_2 = all_151_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (391), (402) imply:
% 35.46/5.69 | (409) all_151_0 = all_137_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (402), (404) imply:
% 35.46/5.69 | (410) all_151_0 = all_145_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (389), (408) imply:
% 35.46/5.69 | (411) all_154_1 = all_151_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (388), (389) imply:
% 35.46/5.69 | (412) all_163_1 = all_154_1
% 35.46/5.69 |
% 35.46/5.69 | SIMP: (412) implies:
% 35.46/5.69 | (413) all_163_1 = all_154_1
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (406), (413) imply:
% 35.46/5.69 | (414) all_154_1 = all_148_1
% 35.46/5.69 |
% 35.46/5.69 | SIMP: (414) implies:
% 35.46/5.69 | (415) all_154_1 = all_148_1
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (411), (415) imply:
% 35.46/5.69 | (416) all_151_0 = all_148_1
% 35.46/5.69 |
% 35.46/5.69 | SIMP: (416) implies:
% 35.46/5.69 | (417) all_151_0 = all_148_1
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (410), (417) imply:
% 35.46/5.69 | (418) all_148_1 = all_145_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (409), (417) imply:
% 35.46/5.69 | (419) all_148_1 = all_137_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (418), (419) imply:
% 35.46/5.69 | (420) all_145_0 = all_137_0
% 35.46/5.69 |
% 35.46/5.69 | SIMP: (420) implies:
% 35.46/5.69 | (421) all_145_0 = all_137_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (415), (419) imply:
% 35.46/5.69 | (422) all_154_1 = all_137_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (406), (419) imply:
% 35.46/5.69 | (423) all_163_1 = all_137_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (389), (422) imply:
% 35.46/5.69 | (424) all_169_2 = all_137_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (393), (419) imply:
% 35.46/5.69 | (425) all_186_1 = all_137_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (400), (421) imply:
% 35.46/5.69 | (426) all_189_1 = all_137_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (396), (409) imply:
% 35.46/5.69 | (427) all_192_1 = all_137_0
% 35.46/5.69 |
% 35.46/5.69 | COMBINE_EQS: (398), (421) imply:
% 35.46/5.69 | (428) all_195_1 = all_137_0
% 35.46/5.69 |
% 35.46/5.69 | REDUCE: (365), (387) imply:
% 35.46/5.69 | (429) power_power(int, all_132_0, all_169_1) = pls
% 35.46/5.69 |
% 35.46/5.69 | REDUCE: (188), (428) imply:
% 35.46/5.69 | (430) number_number_of(nat, all_137_0) = all_195_0
% 35.46/5.69 |
% 35.46/5.69 | REDUCE: (184), (427) imply:
% 35.46/5.69 | (431) number_number_of(nat, all_137_0) = all_192_0
% 35.46/5.69 |
% 35.46/5.69 | REDUCE: (180), (426) imply:
% 35.46/5.69 | (432) number_number_of(nat, all_137_0) = all_189_0
% 35.46/5.69 |
% 35.46/5.69 | REDUCE: (176), (425) imply:
% 35.46/5.69 | (433) number_number_of(nat, all_137_0) = all_186_0
% 35.46/5.69 |
% 35.46/5.69 | REDUCE: (166), (391) imply:
% 35.46/5.69 | (434) number_number_of(nat, all_137_0) = all_174_2
% 35.46/5.69 |
% 35.46/5.69 | REDUCE: (158), (424) imply:
% 35.46/5.69 | (435) number_number_of(nat, all_137_0) = all_169_1
% 35.46/5.69 |
% 35.46/5.69 | REDUCE: (147), (423) imply:
% 35.46/5.69 | (436) number_number_of(nat, all_137_0) = all_163_0
% 35.46/5.69 |
% 35.46/5.69 | REDUCE: (139), (422) imply:
% 35.46/5.69 | (437) number_number_of(nat, all_137_0) = all_154_0
% 35.46/5.69 |
% 35.46/5.69 | REDUCE: (132), (419) imply:
% 35.46/5.69 | (438) number_number_of(nat, all_137_0) = all_148_0
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (60) with all_137_2, all_169_1, all_137_0, nat,
% 35.46/5.69 | simplifying with (121), (435) gives:
% 35.46/5.69 | (439) all_169_1 = all_137_2
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (60) with all_154_0, all_174_2, all_137_0, nat,
% 35.46/5.69 | simplifying with (434), (437) gives:
% 35.46/5.69 | (440) all_174_2 = all_154_0
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (60) with all_174_2, all_186_0, all_137_0, nat,
% 35.46/5.69 | simplifying with (433), (434) gives:
% 35.46/5.69 | (441) all_186_0 = all_174_2
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (60) with all_174_2, all_189_0, all_137_0, nat,
% 35.46/5.69 | simplifying with (432), (434) gives:
% 35.46/5.69 | (442) all_189_0 = all_174_2
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (60) with all_169_1, all_189_0, all_137_0, nat,
% 35.46/5.69 | simplifying with (432), (435) gives:
% 35.46/5.69 | (443) all_189_0 = all_169_1
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (60) with all_163_0, all_189_0, all_137_0, nat,
% 35.46/5.69 | simplifying with (432), (436) gives:
% 35.46/5.69 | (444) all_189_0 = all_163_0
% 35.46/5.69 |
% 35.46/5.69 | GROUND_INST: instantiating (60) with all_186_0, all_192_0, all_137_0, nat,
% 35.46/5.69 | simplifying with (431), (433) gives:
% 35.46/5.69 | (445) all_192_0 = all_186_0
% 35.46/5.69 |
% 35.46/5.70 | GROUND_INST: instantiating (60) with all_192_0, all_195_0, all_137_0, nat,
% 35.46/5.70 | simplifying with (430), (431) gives:
% 35.46/5.70 | (446) all_195_0 = all_192_0
% 35.46/5.70 |
% 35.46/5.70 | GROUND_INST: instantiating (60) with all_148_0, all_195_0, all_137_0, nat,
% 35.46/5.70 | simplifying with (430), (438) gives:
% 35.46/5.70 | (447) all_195_0 = all_148_0
% 35.46/5.70 |
% 35.46/5.70 | COMBINE_EQS: (446), (447) imply:
% 35.46/5.70 | (448) all_192_0 = all_148_0
% 35.46/5.70 |
% 35.46/5.70 | SIMP: (448) implies:
% 35.46/5.70 | (449) all_192_0 = all_148_0
% 35.46/5.70 |
% 35.46/5.70 | COMBINE_EQS: (445), (449) imply:
% 35.46/5.70 | (450) all_186_0 = all_148_0
% 35.46/5.70 |
% 35.46/5.70 | SIMP: (450) implies:
% 35.46/5.70 | (451) all_186_0 = all_148_0
% 35.46/5.70 |
% 35.46/5.70 | COMBINE_EQS: (442), (444) imply:
% 35.46/5.70 | (452) all_174_2 = all_163_0
% 35.46/5.70 |
% 35.46/5.70 | SIMP: (452) implies:
% 35.46/5.70 | (453) all_174_2 = all_163_0
% 35.46/5.70 |
% 35.87/5.70 | COMBINE_EQS: (443), (444) imply:
% 35.87/5.70 | (454) all_169_1 = all_163_0
% 35.87/5.70 |
% 35.87/5.70 | SIMP: (454) implies:
% 35.87/5.70 | (455) all_169_1 = all_163_0
% 35.87/5.70 |
% 35.87/5.70 | COMBINE_EQS: (441), (451) imply:
% 35.87/5.70 | (456) all_174_2 = all_148_0
% 35.87/5.70 |
% 35.87/5.70 | SIMP: (456) implies:
% 35.87/5.70 | (457) all_174_2 = all_148_0
% 35.87/5.70 |
% 35.87/5.70 | COMBINE_EQS: (440), (453) imply:
% 35.87/5.70 | (458) all_163_0 = all_154_0
% 35.87/5.70 |
% 35.87/5.70 | SIMP: (458) implies:
% 35.87/5.70 | (459) all_163_0 = all_154_0
% 35.87/5.70 |
% 35.87/5.70 | COMBINE_EQS: (440), (457) imply:
% 35.87/5.70 | (460) all_154_0 = all_148_0
% 35.87/5.70 |
% 35.87/5.70 | COMBINE_EQS: (439), (455) imply:
% 35.87/5.70 | (461) all_163_0 = all_137_2
% 35.87/5.70 |
% 35.87/5.70 | SIMP: (461) implies:
% 35.87/5.70 | (462) all_163_0 = all_137_2
% 35.87/5.70 |
% 35.87/5.70 | COMBINE_EQS: (459), (462) imply:
% 35.87/5.70 | (463) all_154_0 = all_137_2
% 35.87/5.70 |
% 35.87/5.70 | SIMP: (463) implies:
% 35.87/5.70 | (464) all_154_0 = all_137_2
% 35.87/5.70 |
% 35.87/5.70 | COMBINE_EQS: (460), (464) imply:
% 35.87/5.70 | (465) all_148_0 = all_137_2
% 35.87/5.70 |
% 35.87/5.70 | SIMP: (465) implies:
% 35.87/5.70 | (466) all_148_0 = all_137_2
% 35.87/5.70 |
% 35.87/5.70 | REDUCE: (429), (439) imply:
% 35.87/5.70 | (467) power_power(int, all_132_0, all_137_2) = pls
% 35.87/5.70 |
% 35.87/5.70 | GROUND_INST: instantiating (168) with int, all_86_0, simplifying with (50),
% 35.87/5.70 | (52), (53), (64) gives:
% 35.87/5.70 | (468) ? [v0: $i] : (zero_zero(int) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 35.87/5.70 | any] : ! [v3: $i] : (v3 = v0 | v2 = all_177_0 | ~
% 35.87/5.70 | (power_power(int, v0, v2) = v3) | ~ (number_number_of(nat, v1) =
% 35.87/5.70 | v2) | ~ $i(v1)) & ! [v1: $i] : ! [v2: int] : (v2 = all_86_0
% 35.87/5.70 | | ~ (power_power(int, v0, all_177_0) = v2) | ~
% 35.87/5.70 | (number_number_of(nat, v1) = all_177_0) | ~ $i(v1)))
% 35.87/5.70 |
% 35.87/5.70 | GROUND_INST: instantiating (25) with all_86_0, all_132_1, all_132_0,
% 35.87/5.70 | simplifying with (380), (381), (383) gives:
% 35.87/5.70 | (469) plus_plus(int, all_132_1, all_86_0) = all_132_0 & $i(all_132_0)
% 35.87/5.70 |
% 35.87/5.70 | ALPHA: (469) implies:
% 35.87/5.70 | (470) $i(all_132_0)
% 35.87/5.70 |
% 35.87/5.70 | GROUND_INST: instantiating (1) with all_99_1, all_137_0, simplifying with
% 35.87/5.70 | (378), (382) gives:
% 35.87/5.70 | (471) ti(int, all_137_0) = all_137_0 & $i(all_137_0)
% 35.87/5.70 |
% 35.87/5.70 | ALPHA: (471) implies:
% 35.87/5.70 | (472) $i(all_137_0)
% 35.87/5.70 |
% 35.87/5.70 | GROUND_INST: instantiating (17) with all_99_0, n, all_86_0, all_132_1,
% 35.87/5.70 | all_132_0, simplifying with (54), (114), (366), (380), (384)
% 35.87/5.70 | gives:
% 35.87/5.70 | (473) ? [v0: $i] : (semiring_1_of_nat(int, v0) = all_132_0 &
% 35.87/5.70 | plus_plus(nat, all_99_0, n) = v0 & $i(v0) & $i(all_132_0))
% 35.87/5.70 |
% 35.87/5.70 | GROUND_INST: instantiating (190) with int, pls, all_132_0, all_137_0,
% 35.87/5.70 | all_137_2, simplifying with (36), (47), (49), (51), (52), (53),
% 35.87/5.70 | (121), (467), (470), (472) gives:
% 35.87/5.70 | (474) ti(int, all_132_0) = pls & $i(pls)
% 35.87/5.70 |
% 35.87/5.70 | ALPHA: (474) implies:
% 35.87/5.70 | (475) ti(int, all_132_0) = pls
% 35.87/5.70 |
% 35.87/5.70 | DELTA: instantiating (473) with fresh symbol all_223_0 gives:
% 35.87/5.70 | (476) semiring_1_of_nat(int, all_223_0) = all_132_0 & plus_plus(nat,
% 35.87/5.70 | all_99_0, n) = all_223_0 & $i(all_223_0) & $i(all_132_0)
% 35.87/5.70 |
% 35.87/5.70 | DELTA: instantiating (468) with fresh symbol all_225_0 gives:
% 35.87/5.70 | (477) zero_zero(int) = all_225_0 & $i(all_225_0) & ! [v0: $i] : ! [v1:
% 35.87/5.70 | any] : ! [v2: int] : (v2 = all_225_0 | v1 = all_177_0 | ~
% 35.87/5.70 | (power_power(int, all_225_0, v1) = v2) | ~ (number_number_of(nat,
% 35.87/5.70 | v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: int] : (v1 =
% 35.87/5.70 | all_86_0 | ~ (power_power(int, all_225_0, all_177_0) = v1) | ~
% 35.87/5.70 | (number_number_of(nat, v0) = all_177_0) | ~ $i(v0))
% 35.87/5.70 |
% 35.87/5.70 | ALPHA: (477) implies:
% 35.87/5.70 | (478) zero_zero(int) = all_225_0
% 35.87/5.70 |
% 35.87/5.70 | GROUND_INST: instantiating (57) with pls, all_225_0, int, simplifying with
% 35.87/5.70 | (36), (478) gives:
% 35.87/5.70 | (479) all_225_0 = pls
% 35.87/5.70 |
% 35.87/5.70 | GROUND_INST: instantiating (35) with int, pls, all_132_0, simplifying with
% 35.87/5.70 | (36), (46), (53), (470), (475) gives:
% 35.87/5.70 | (480) plus_plus(int, all_132_0, all_132_0) = pls & $i(pls)
% 35.87/5.70 |
% 35.87/5.70 | ALPHA: (480) implies:
% 35.87/5.70 | (481) $i(pls)
% 35.87/5.70 |
% 35.87/5.70 | GROUND_INST: instantiating (2) with pls, all_132_0, int, pls, simplifying with
% 35.87/5.70 | (48), (53), (385), (386), (470), (475), (481) gives:
% 35.87/5.70 | (482) $false
% 35.87/5.70 |
% 35.87/5.70 | CLOSE: (482) is inconsistent.
% 35.87/5.70 |
% 35.87/5.70 End of proof
% 35.87/5.70 % SZS output end Proof for theBenchmark
% 35.87/5.70
% 35.87/5.71 5117ms
%------------------------------------------------------------------------------