TSTP Solution File: NUM925_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM925_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.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 11:50:50 EDT 2023
% Result : Theorem 12.81s 2.54s
% Output : Proof 22.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM925_1 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n001.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 09:41:58 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.85/1.32 Prover 1: Preprocessing ...
% 3.85/1.32 Prover 4: Preprocessing ...
% 3.85/1.36 Prover 6: Preprocessing ...
% 3.85/1.36 Prover 3: Preprocessing ...
% 4.37/1.36 Prover 0: Preprocessing ...
% 4.37/1.36 Prover 2: Preprocessing ...
% 4.37/1.36 Prover 5: Preprocessing ...
% 10.63/2.23 Prover 6: Constructing countermodel ...
% 10.63/2.26 Prover 3: Constructing countermodel ...
% 11.08/2.32 Prover 1: Constructing countermodel ...
% 11.84/2.39 Prover 5: Proving ...
% 11.84/2.41 Prover 0: Proving ...
% 12.26/2.45 Prover 4: Constructing countermodel ...
% 12.26/2.45 Prover 2: Proving ...
% 12.81/2.54 Prover 3: proved (1911ms)
% 12.81/2.54
% 12.81/2.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.81/2.54
% 12.81/2.54 Prover 6: stopped
% 12.81/2.54 Prover 2: stopped
% 12.81/2.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.81/2.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.81/2.55 Prover 0: stopped
% 12.81/2.57 Prover 5: stopped
% 12.81/2.57 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.81/2.57 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.81/2.57 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.01/2.72 Prover 10: Preprocessing ...
% 14.01/2.73 Prover 13: Preprocessing ...
% 14.01/2.75 Prover 7: Preprocessing ...
% 14.01/2.77 Prover 8: Preprocessing ...
% 14.01/2.77 Prover 11: Preprocessing ...
% 17.30/3.15 Prover 10: Warning: ignoring some quantifiers
% 17.30/3.16 Prover 8: Warning: ignoring some quantifiers
% 17.30/3.17 Prover 8: Constructing countermodel ...
% 17.30/3.19 Prover 10: Constructing countermodel ...
% 18.03/3.24 Prover 7: Warning: ignoring some quantifiers
% 18.03/3.26 Prover 7: Constructing countermodel ...
% 18.03/3.28 Prover 13: Warning: ignoring some quantifiers
% 18.59/3.31 Prover 13: Constructing countermodel ...
% 18.59/3.32 Prover 11: Constructing countermodel ...
% 20.77/3.64 Prover 1: Found proof (size 313)
% 20.77/3.64 Prover 1: proved (3023ms)
% 20.77/3.64 Prover 10: stopped
% 20.77/3.64 Prover 7: stopped
% 20.77/3.64 Prover 4: stopped
% 20.77/3.64 Prover 11: stopped
% 20.77/3.64 Prover 13: stopped
% 20.77/3.66 Prover 8: stopped
% 20.77/3.66
% 20.77/3.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.77/3.66
% 21.53/3.79 % SZS output start Proof for theBenchmark
% 21.53/3.80 Assumptions after simplification:
% 21.53/3.80 ---------------------------------
% 21.53/3.80
% 21.53/3.80 (conj_0)
% 21.89/3.82 nat(n) & int(pls) & int(zero_zero_int) & int(one_one_int) & ? [v0: int] : ?
% 21.89/3.82 [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: nat] : (bit1(pls) = v2 &
% 21.89/3.82 bit0(v2) = v3 & number_number_of_nat(v3) = v4 & power_power_int(v1, v4) =
% 21.89/3.82 zero_zero_int & semiri1621563631at_int(n) = v0 & plus_plus_int(one_one_int,
% 21.89/3.82 v0) = v1 & nat(v4) & int(v3) & int(v2) & int(v1) & int(v0))
% 21.89/3.82
% 21.89/3.82 (fact_0_n1pos)
% 21.89/3.82 nat(n) & int(zero_zero_int) & int(one_one_int) & ? [v0: int] : ? [v1: int] :
% 21.89/3.82 (semiri1621563631at_int(n) = v0 & plus_plus_int(one_one_int, v0) = v1 &
% 21.89/3.82 ord_less_int(zero_zero_int, v1) = 0 & int(v1) & int(v0))
% 21.89/3.82
% 21.89/3.82 (fact_103_zero__less__power2)
% 21.89/3.82 int(pls) & int(zero_zero_int) & ? [v0: int] : ? [v1: int] : ? [v2: nat] :
% 21.89/3.82 (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & nat(v2) &
% 21.89/3.82 int(v1) & int(v0) & ! [v3: int] : ! [v4: int] : (v3 = zero_zero_int | ~
% 21.89/3.82 (power_power_int(v3, v2) = v4) | ~ int(v3) | ord_less_int(zero_zero_int,
% 21.89/3.82 v4) = 0) & ! [v3: int] : ( ~ (power_power_int(zero_zero_int, v2) = v3)
% 21.89/3.82 | ? [v4: int] : ( ~ (v4 = 0) & ord_less_int(zero_zero_int, v3) = v4)))
% 21.89/3.82
% 21.89/3.82 (fact_104_power2__less__0)
% 21.89/3.82 int(pls) & int(zero_zero_int) & ? [v0: int] : ? [v1: int] : ? [v2: nat] :
% 21.89/3.82 (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & nat(v2) &
% 21.89/3.82 int(v1) & int(v0) & ! [v3: int] : ! [v4: int] : ( ~ (power_power_int(v3,
% 21.89/3.82 v2) = v4) | ~ int(v3) | ? [v5: int] : ( ~ (v5 = 0) &
% 21.89/3.82 ord_less_int(v4, zero_zero_int) = v5)))
% 21.89/3.82
% 21.89/3.82 (fact_105_sum__power2__gt__zero__iff)
% 21.89/3.83 int(pls) & int(zero_zero_int) & ? [v0: int] : ? [v1: int] : ? [v2: nat] :
% 21.89/3.83 (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & nat(v2) &
% 21.89/3.83 int(v1) & int(v0) & ! [v3: int] : ! [v4: int] : ! [v5: int] : ! [v6:
% 21.89/3.83 int] : ! [v7: int] : ( ~ (power_power_int(v4, v2) = v6) | ~
% 21.89/3.83 (power_power_int(v3, v2) = v5) | ~ (plus_plus_int(v5, v6) = v7) | ~
% 21.89/3.83 int(v4) | ~ int(v3) | ord_less_int(zero_zero_int, v7) = 0 | (v4 =
% 21.89/3.83 zero_zero_int & v3 = zero_zero_int)) & ! [v3: int] : ! [v4: int] : ( ~
% 21.89/3.83 (power_power_int(zero_zero_int, v2) = v3) | ~ (plus_plus_int(v3, v3) =
% 21.89/3.83 v4) | ? [v5: int] : ( ~ (v5 = 0) & ord_less_int(zero_zero_int, v4) =
% 21.89/3.83 v5)))
% 21.89/3.83
% 21.89/3.83 (fact_10_one__add__one__is__two)
% 21.89/3.83 int(pls) & int(one_one_int) & ? [v0: int] : ? [v1: int] : ? [v2: int] :
% 21.89/3.83 (number_number_of_int(v2) = v0 & bit1(pls) = v1 & bit0(v1) = v2 &
% 21.89/3.83 plus_plus_int(one_one_int, one_one_int) = v0 & int(v2) & int(v1) & int(v0))
% 21.89/3.83
% 21.89/3.83 (fact_11_semiring__one__add__one__is__two)
% 21.89/3.83 int(pls) & int(one_one_int) & ? [v0: int] : ? [v1: int] : ? [v2: int] :
% 21.89/3.83 (number_number_of_int(v2) = v0 & bit1(pls) = v1 & bit0(v1) = v2 &
% 21.89/3.83 plus_plus_int(one_one_int, one_one_int) = v0 & int(v2) & int(v1) & int(v0))
% 21.89/3.83
% 21.89/3.83 (fact_12_semiring__one__add__one__is__two)
% 21.89/3.83 nat(one_one_nat) & int(pls) & ? [v0: nat] : ? [v1: int] : ? [v2: int] :
% 21.89/3.83 (plus_plus_nat(one_one_nat, one_one_nat) = v0 & bit1(pls) = v1 & bit0(v1) = v2
% 21.89/3.83 & number_number_of_nat(v2) = v0 & nat(v0) & int(v2) & int(v1))
% 21.89/3.83
% 21.89/3.83 (fact_13_quartic__square__square)
% 21.89/3.83 int(pls) & ? [v0: int] : ? [v1: int] : ? [v2: nat] : ? [v3: int] : ? [v4:
% 21.89/3.83 nat] : (bit1(pls) = v0 & bit0(v1) = v3 & bit0(v0) = v1 &
% 21.89/3.83 number_number_of_nat(v3) = v4 & number_number_of_nat(v1) = v2 & nat(v4) &
% 21.89/3.83 nat(v2) & int(v3) & int(v1) & int(v0) & ! [v5: int] : ! [v6: int] : ( ~
% 21.89/3.83 (power_power_int(v5, v4) = v6) | ~ int(v5) | ? [v7: int] :
% 21.89/3.83 (power_power_int(v7, v2) = v6 & power_power_int(v5, v2) = v7 & int(v7) &
% 21.89/3.83 int(v6))))
% 21.89/3.83
% 21.89/3.83 (fact_16_semiring__norm_I110_J)
% 21.89/3.83 int(pls) & int(one_one_int) & ? [v0: int] : (number_number_of_int(v0) =
% 21.89/3.83 one_one_int & bit1(pls) = v0 & int(v0))
% 21.89/3.83
% 21.89/3.83 (fact_17_numeral__1__eq__1)
% 21.89/3.83 int(pls) & int(one_one_int) & ? [v0: int] : (number_number_of_int(v0) =
% 21.89/3.83 one_one_int & bit1(pls) = v0 & int(v0))
% 21.89/3.83
% 21.89/3.83 (fact_2_sum__power2__eq__zero__iff)
% 21.89/3.83 int(pls) & int(zero_zero_int) & ? [v0: int] : ? [v1: int] : ? [v2: nat] :
% 21.89/3.83 (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & nat(v2) &
% 21.89/3.83 int(v1) & int(v0) & ! [v3: int] : ! [v4: int] : ! [v5: int] : ! [v6:
% 21.89/3.83 int] : ( ~ (power_power_int(v4, v2) = v6) | ~ (power_power_int(v3, v2) =
% 21.89/3.83 v5) | ~ (plus_plus_int(v5, v6) = zero_zero_int) | ~ int(v4) | ~
% 21.89/3.83 int(v3) | (v4 = zero_zero_int & v3 = zero_zero_int)) & ! [v3: int] : !
% 21.89/3.83 [v4: int] : (v4 = zero_zero_int | ~ (power_power_int(zero_zero_int, v2) =
% 21.89/3.83 v3) | ~ (plus_plus_int(v3, v3) = v4)))
% 21.89/3.83
% 21.89/3.83 (fact_33_nat__1__add__1)
% 21.89/3.83 nat(one_one_nat) & int(pls) & ? [v0: nat] : ? [v1: int] : ? [v2: int] :
% 21.89/3.83 (plus_plus_nat(one_one_nat, one_one_nat) = v0 & bit1(pls) = v1 & bit0(v1) = v2
% 21.89/3.83 & number_number_of_nat(v2) = v0 & nat(v0) & int(v2) & int(v1))
% 21.89/3.83
% 21.89/3.83 (fact_36_rel__simps_I2_J)
% 21.89/3.83 int(pls) & ? [v0: int] : ( ~ (v0 = 0) & ord_less_int(pls, pls) = v0)
% 21.89/3.83
% 21.89/3.83 (fact_3_one__power2)
% 21.89/3.84 int(pls) & int(one_one_int) & ? [v0: int] : ? [v1: int] : ? [v2: nat] :
% 21.89/3.84 (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 &
% 21.89/3.84 power_power_int(one_one_int, v2) = one_one_int & nat(v2) & int(v1) &
% 21.89/3.84 int(v0))
% 21.89/3.84
% 21.89/3.84 (fact_41_one__is__num__one)
% 21.89/3.84 int(pls) & int(one_one_int) & ? [v0: int] : (number_number_of_int(v0) =
% 21.89/3.84 one_one_int & bit1(pls) = v0 & int(v0))
% 21.89/3.84
% 21.89/3.84 (fact_42_nat__numeral__1__eq__1)
% 21.89/3.84 nat(one_one_nat) & int(pls) & ? [v0: int] : (bit1(pls) = v0 &
% 21.89/3.84 number_number_of_nat(v0) = one_one_nat & int(v0))
% 21.89/3.84
% 21.89/3.84 (fact_43_Numeral1__eq1__nat)
% 21.89/3.84 nat(one_one_nat) & int(pls) & ? [v0: int] : (bit1(pls) = v0 &
% 21.89/3.84 number_number_of_nat(v0) = one_one_nat & int(v0))
% 21.89/3.84
% 21.89/3.84 (fact_4_one__power2)
% 21.89/3.84 nat(one_one_nat) & int(pls) & ? [v0: int] : ? [v1: int] : ? [v2: nat] :
% 21.89/3.84 (power_power_nat(one_one_nat, v2) = one_one_nat & bit1(pls) = v0 & bit0(v0) =
% 21.89/3.84 v1 & number_number_of_nat(v1) = v2 & nat(v2) & int(v1) & int(v0))
% 21.89/3.84
% 21.89/3.84 (fact_52_zadd__commute)
% 21.89/3.84 ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ (plus_plus_int(v0, v1) = v2)
% 21.89/3.84 | ~ int(v1) | ~ int(v0) | (plus_plus_int(v1, v0) = v2 & int(v2)))
% 21.89/3.84
% 21.89/3.84 (fact_5_zero__power2)
% 21.89/3.84 int(pls) & int(zero_zero_int) & ? [v0: int] : ? [v1: int] : ? [v2: nat] :
% 21.89/3.84 (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 &
% 21.89/3.84 power_power_int(zero_zero_int, v2) = zero_zero_int & nat(v2) & int(v1) &
% 21.89/3.84 int(v0))
% 21.89/3.84
% 21.89/3.84 (fact_62_bin__less__0__simps_I1_J)
% 21.89/3.84 int(pls) & int(zero_zero_int) & ? [v0: int] : ( ~ (v0 = 0) &
% 21.89/3.84 ord_less_int(pls, zero_zero_int) = v0)
% 21.89/3.84
% 21.89/3.84 (fact_67_less__special_I4_J)
% 21.89/3.84 int(pls) & int(one_one_int) & ? [v0: int] : (bit1(pls) = v0 & int(v0) & !
% 21.89/3.84 [v1: int] : ! [v2: int] : (v2 = 0 | ~ (ord_less_int(v1, v0) = v2) | ~
% 21.89/3.84 int(v1) | ? [v3: int] : ? [v4: int] : ( ~ (v4 = 0) &
% 21.89/3.84 number_number_of_int(v1) = v3 & ord_less_int(v3, one_one_int) = v4 &
% 21.89/3.84 int(v3))) & ! [v1: int] : ( ~ (ord_less_int(v1, v0) = 0) | ~ int(v1) |
% 21.89/3.84 ? [v2: int] : (number_number_of_int(v1) = v2 & ord_less_int(v2,
% 21.89/3.84 one_one_int) = 0 & int(v2))))
% 21.89/3.84
% 21.89/3.84 (fact_68_less__special_I2_J)
% 21.89/3.84 int(pls) & int(one_one_int) & ? [v0: int] : (bit1(pls) = v0 & int(v0) & !
% 21.89/3.84 [v1: int] : ! [v2: int] : (v2 = 0 | ~ (ord_less_int(v0, v1) = v2) | ~
% 21.89/3.84 int(v1) | ? [v3: int] : ? [v4: int] : ( ~ (v4 = 0) &
% 21.89/3.84 number_number_of_int(v1) = v3 & ord_less_int(one_one_int, v3) = v4 &
% 21.89/3.84 int(v3))) & ! [v1: int] : ( ~ (ord_less_int(v0, v1) = 0) | ~ int(v1) |
% 21.89/3.84 ? [v2: int] : (number_number_of_int(v1) = v2 & ord_less_int(one_one_int,
% 21.89/3.84 v2) = 0 & int(v2))))
% 21.89/3.84
% 21.89/3.84 (fact_6_zero__power2)
% 21.89/3.84 nat(zero_zero_nat) & int(pls) & ? [v0: int] : ? [v1: int] : ? [v2: nat] :
% 21.89/3.84 (power_power_nat(zero_zero_nat, v2) = zero_zero_nat & bit1(pls) = v0 &
% 21.89/3.84 bit0(v0) = v1 & number_number_of_nat(v1) = v2 & nat(v2) & int(v1) & int(v0))
% 21.89/3.84
% 21.89/3.84 (fact_78_Pls__def)
% 21.89/3.84 pls = zero_zero_int & int(zero_zero_int)
% 21.89/3.84
% 21.89/3.84 (fact_7_zero__eq__power2)
% 21.89/3.84 int(pls) & int(zero_zero_int) & ? [v0: int] : ? [v1: int] : ? [v2: nat] :
% 21.89/3.84 (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & nat(v2) &
% 21.89/3.84 int(v1) & int(v0) & ! [v3: int] : (v3 = zero_zero_int | ~
% 21.89/3.84 (power_power_int(v3, v2) = zero_zero_int) | ~ int(v3)) & ! [v3: int] :
% 21.89/3.84 (v3 = zero_zero_int | ~ (power_power_int(zero_zero_int, v2) = v3)))
% 21.89/3.84
% 21.89/3.84 (fact_8_add__special_I2_J)
% 21.89/3.84 int(pls) & int(one_one_int) & ? [v0: int] : (bit1(pls) = v0 & int(v0) & !
% 21.89/3.84 [v1: int] : ! [v2: int] : ( ~ (plus_plus_int(v0, v1) = v2) | ~ int(v1) |
% 21.89/3.84 ? [v3: int] : ? [v4: int] : (number_number_of_int(v2) = v4 &
% 21.89/3.84 number_number_of_int(v1) = v3 & plus_plus_int(one_one_int, v3) = v4 &
% 21.89/3.84 int(v4) & int(v3))))
% 21.89/3.84
% 21.89/3.84 (fact_92_power__eq__0__iff__number__of)
% 21.89/3.85 nat(zero_zero_nat) & int(zero_zero_int) & ! [v0: int] : ! [v1: nat] : !
% 21.89/3.85 [v2: int] : (v2 = zero_zero_int | v1 = zero_zero_nat | ~
% 21.89/3.85 (number_number_of_nat(v0) = v1) | ~ (power_power_int(zero_zero_int, v1) =
% 21.89/3.85 v2) | ~ int(v0)) & ! [v0: int] : ! [v1: int] : ! [v2: nat] : ( ~
% 21.89/3.85 (number_number_of_nat(v1) = v2) | ~ (power_power_int(v0, v2) =
% 21.89/3.85 zero_zero_int) | ~ int(v1) | ~ int(v0) | (v0 = zero_zero_int & ~ (v2 =
% 21.89/3.85 zero_zero_nat)))
% 21.89/3.85
% 21.89/3.85 (fact_9_add__special_I3_J)
% 21.89/3.85 int(pls) & int(one_one_int) & ? [v0: int] : (bit1(pls) = v0 & int(v0) & !
% 21.89/3.85 [v1: int] : ! [v2: int] : ( ~ (plus_plus_int(v1, v0) = v2) | ~ int(v1) |
% 21.89/3.85 ? [v3: int] : ? [v4: int] : (number_number_of_int(v2) = v4 &
% 21.89/3.85 number_number_of_int(v1) = v3 & plus_plus_int(v3, one_one_int) = v4 &
% 21.89/3.85 int(v4) & int(v3))))
% 21.89/3.85
% 21.89/3.85 (function-axioms)
% 21.89/3.85 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: nat] : !
% 21.89/3.85 [v3: nat] : (v1 = v0 | ~ (ord_less_nat(v3, v2) = v1) | ~ (ord_less_nat(v3,
% 21.89/3.85 v2) = v0)) & ! [v0: nat] : ! [v1: nat] : ! [v2: nat] : ! [v3: nat] :
% 21.89/3.85 (v1 = v0 | ~ (plus_plus_nat(v3, v2) = v1) | ~ (plus_plus_nat(v3, v2) = v0))
% 21.89/3.85 & ! [v0: nat] : ! [v1: nat] : ! [v2: nat] : ! [v3: nat] : (v1 = v0 | ~
% 21.89/3.85 (power_power_nat(v3, v2) = v1) | ~ (power_power_nat(v3, v2) = v0)) & !
% 21.89/3.85 [v0: int] : ! [v1: int] : ! [v2: nat] : ! [v3: int] : (v1 = v0 | ~
% 21.89/3.85 (power_power_int(v3, v2) = v1) | ~ (power_power_int(v3, v2) = v0)) & !
% 21.89/3.85 [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~
% 21.89/3.85 (plus_plus_int(v3, v2) = v1) | ~ (plus_plus_int(v3, v2) = v0)) & ! [v0:
% 21.89/3.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3:
% 21.89/3.85 int] : (v1 = v0 | ~ (ord_less_int(v3, v2) = v1) | ~ (ord_less_int(v3, v2)
% 21.89/3.85 = v0)) & ! [v0: nat] : ! [v1: nat] : ! [v2: nat] : (v1 = v0 | ~
% 21.89/3.85 (semiri984289939at_nat(v2) = v1) | ~ (semiri984289939at_nat(v2) = v0)) & !
% 21.89/3.85 [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~
% 21.89/3.85 (number_number_of_int(v2) = v1) | ~ (number_number_of_int(v2) = v0)) & !
% 21.89/3.85 [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (bit1(v2) = v1) | ~
% 21.89/3.85 (bit1(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 |
% 21.89/3.85 ~ (bit0(v2) = v1) | ~ (bit0(v2) = v0)) & ! [v0: nat] : ! [v1: nat] : !
% 21.89/3.85 [v2: int] : (v1 = v0 | ~ (number_number_of_nat(v2) = v1) | ~
% 21.89/3.85 (number_number_of_nat(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 21.89/3.85 nat] : (v1 = v0 | ~ (semiri1621563631at_int(v2) = v1) | ~
% 21.89/3.85 (semiri1621563631at_int(v2) = v0))
% 21.89/3.85
% 21.89/3.85 Further assumptions not needed in the proof:
% 21.89/3.85 --------------------------------------------
% 21.89/3.85 fact_100_odd__nonzero, fact_101_number__of__int, fact_102_number__of__int,
% 21.89/3.85 fact_14_power__0__left__number__of, fact_15_power__0__left__number__of,
% 21.89/3.85 fact_18_n0, fact_19_zless__linear, fact_1_t1,
% 21.89/3.85 fact_20_less__number__of__int__code, fact_21_plus__numeral__code_I9_J,
% 21.89/3.85 fact_22_less__number__of, fact_23_zero__is__num__zero, fact_24_zpower__int,
% 21.89/3.85 fact_25_int__power, fact_26_zadd__int__left, fact_27_zadd__int, fact_28_int__1,
% 21.89/3.85 fact_29_nat__number__of__Pls, fact_30_semiring__norm_I113_J,
% 21.89/3.85 fact_31_int__eq__0__conv, fact_32_int__0, fact_34_less__int__code_I16_J,
% 21.89/3.85 fact_35_rel__simps_I17_J, fact_37_less__int__code_I13_J,
% 21.89/3.85 fact_38_rel__simps_I14_J, fact_39_zadd__strict__right__mono,
% 21.89/3.85 fact_40_add__nat__number__of, fact_44_eq__number__of,
% 21.89/3.85 fact_45_number__of__reorient, fact_46_number__of__reorient,
% 21.89/3.85 fact_47_rel__simps_I51_J, fact_48_rel__simps_I48_J, fact_49_even__less__0__iff,
% 21.89/3.85 fact_50_zadd__assoc, fact_51_zadd__left__commute, fact_53_int__int__eq,
% 21.89/3.85 fact_54_less__special_I3_J, fact_55_less__special_I1_J,
% 21.89/3.85 fact_56_rel__simps_I12_J, fact_57_less__int__code_I15_J,
% 21.89/3.85 fact_58_rel__simps_I16_J, fact_59_rel__simps_I10_J, fact_60_rel__simps_I4_J,
% 21.89/3.85 fact_61_bin__less__0__simps_I4_J, fact_63_bin__less__0__simps_I3_J,
% 21.89/3.85 fact_64_int__0__less__1, fact_65_zless__add1__eq, fact_66_int__less__0__conv,
% 21.89/3.85 fact_69_odd__less__0, fact_70_double__eq__0__iff, fact_71_rel__simps_I46_J,
% 21.89/3.85 fact_72_rel__simps_I39_J, fact_73_rel__simps_I50_J, fact_74_rel__simps_I49_J,
% 21.89/3.85 fact_75_rel__simps_I44_J, fact_76_rel__simps_I38_J, fact_77_Bit0__Pls,
% 21.89/3.85 fact_79_int__0__neq__1, fact_80_add__Pls__right, fact_81_add__Pls,
% 21.89/3.85 fact_82_add__Bit0__Bit0, fact_83_Bit0__def, fact_84_zadd__0__right,
% 21.89/3.85 fact_85_zadd__0, fact_86_semiring__numeral__0__eq__0,
% 21.89/3.85 fact_87_semiring__numeral__0__eq__0, fact_88_number__of__Pls,
% 21.89/3.85 fact_89_semiring__norm_I112_J, fact_90_add__numeral__0,
% 21.89/3.85 fact_91_add__numeral__0__right, fact_93_power__eq__0__iff__number__of,
% 21.89/3.85 fact_94_add__number__of__left, fact_95_add__number__of__eq,
% 21.89/3.85 fact_96_number__of__add, fact_97_add__Bit1__Bit0, fact_98_add__Bit0__Bit1,
% 21.89/3.85 fact_99_Bit1__def
% 21.89/3.85
% 21.89/3.85 Those formulas are unsatisfiable:
% 21.89/3.85 ---------------------------------
% 21.89/3.85
% 21.89/3.85 Begin of proof
% 21.89/3.85 |
% 21.89/3.85 | ALPHA: (fact_0_n1pos) implies:
% 21.89/3.85 | (1) ? [v0: int] : ? [v1: int] : (semiri1621563631at_int(n) = v0 &
% 21.89/3.85 | plus_plus_int(one_one_int, v0) = v1 & ord_less_int(zero_zero_int, v1)
% 21.89/3.85 | = 0 & int(v1) & int(v0))
% 21.89/3.85 |
% 21.89/3.85 | ALPHA: (fact_2_sum__power2__eq__zero__iff) implies:
% 21.89/3.86 | (2) ? [v0: int] : ? [v1: int] : ? [v2: nat] : (bit1(pls) = v0 & bit0(v0)
% 21.89/3.86 | = v1 & number_number_of_nat(v1) = v2 & nat(v2) & int(v1) & int(v0) &
% 21.89/3.86 | ! [v3: int] : ! [v4: int] : ! [v5: int] : ! [v6: int] : ( ~
% 21.89/3.86 | (power_power_int(v4, v2) = v6) | ~ (power_power_int(v3, v2) = v5)
% 21.89/3.86 | | ~ (plus_plus_int(v5, v6) = zero_zero_int) | ~ int(v4) | ~
% 21.89/3.86 | int(v3) | (v4 = zero_zero_int & v3 = zero_zero_int)) & ! [v3: int]
% 21.89/3.86 | : ! [v4: int] : (v4 = zero_zero_int | ~
% 21.89/3.86 | (power_power_int(zero_zero_int, v2) = v3) | ~ (plus_plus_int(v3,
% 21.89/3.86 | v3) = v4)))
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_3_one__power2) implies:
% 21.89/3.86 | (3) ? [v0: int] : ? [v1: int] : ? [v2: nat] : (bit1(pls) = v0 & bit0(v0)
% 21.89/3.86 | = v1 & number_number_of_nat(v1) = v2 & power_power_int(one_one_int,
% 21.89/3.86 | v2) = one_one_int & nat(v2) & int(v1) & int(v0))
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_4_one__power2) implies:
% 21.89/3.86 | (4) ? [v0: int] : ? [v1: int] : ? [v2: nat] :
% 21.89/3.86 | (power_power_nat(one_one_nat, v2) = one_one_nat & bit1(pls) = v0 &
% 21.89/3.86 | bit0(v0) = v1 & number_number_of_nat(v1) = v2 & nat(v2) & int(v1) &
% 21.89/3.86 | int(v0))
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_5_zero__power2) implies:
% 21.89/3.86 | (5) ? [v0: int] : ? [v1: int] : ? [v2: nat] : (bit1(pls) = v0 & bit0(v0)
% 21.89/3.86 | = v1 & number_number_of_nat(v1) = v2 & power_power_int(zero_zero_int,
% 21.89/3.86 | v2) = zero_zero_int & nat(v2) & int(v1) & int(v0))
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_6_zero__power2) implies:
% 21.89/3.86 | (6) ? [v0: int] : ? [v1: int] : ? [v2: nat] :
% 21.89/3.86 | (power_power_nat(zero_zero_nat, v2) = zero_zero_nat & bit1(pls) = v0 &
% 21.89/3.86 | bit0(v0) = v1 & number_number_of_nat(v1) = v2 & nat(v2) & int(v1) &
% 21.89/3.86 | int(v0))
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_7_zero__eq__power2) implies:
% 21.89/3.86 | (7) ? [v0: int] : ? [v1: int] : ? [v2: nat] : (bit1(pls) = v0 & bit0(v0)
% 21.89/3.86 | = v1 & number_number_of_nat(v1) = v2 & nat(v2) & int(v1) & int(v0) &
% 21.89/3.86 | ! [v3: int] : (v3 = zero_zero_int | ~ (power_power_int(v3, v2) =
% 21.89/3.86 | zero_zero_int) | ~ int(v3)) & ! [v3: int] : (v3 = zero_zero_int
% 21.89/3.86 | | ~ (power_power_int(zero_zero_int, v2) = v3)))
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_8_add__special_I2_J) implies:
% 21.89/3.86 | (8) ? [v0: int] : (bit1(pls) = v0 & int(v0) & ! [v1: int] : ! [v2: int]
% 21.89/3.86 | : ( ~ (plus_plus_int(v0, v1) = v2) | ~ int(v1) | ? [v3: int] : ?
% 21.89/3.86 | [v4: int] : (number_number_of_int(v2) = v4 &
% 21.89/3.86 | number_number_of_int(v1) = v3 & plus_plus_int(one_one_int, v3) =
% 21.89/3.86 | v4 & int(v4) & int(v3))))
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_9_add__special_I3_J) implies:
% 21.89/3.86 | (9) ? [v0: int] : (bit1(pls) = v0 & int(v0) & ! [v1: int] : ! [v2: int]
% 21.89/3.86 | : ( ~ (plus_plus_int(v1, v0) = v2) | ~ int(v1) | ? [v3: int] : ?
% 21.89/3.86 | [v4: int] : (number_number_of_int(v2) = v4 &
% 21.89/3.86 | number_number_of_int(v1) = v3 & plus_plus_int(v3, one_one_int) =
% 21.89/3.86 | v4 & int(v4) & int(v3))))
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_11_semiring__one__add__one__is__two) implies:
% 21.89/3.86 | (10) ? [v0: int] : ? [v1: int] : ? [v2: int] : (number_number_of_int(v2)
% 21.89/3.86 | = v0 & bit1(pls) = v1 & bit0(v1) = v2 & plus_plus_int(one_one_int,
% 21.89/3.86 | one_one_int) = v0 & int(v2) & int(v1) & int(v0))
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_13_quartic__square__square) implies:
% 21.89/3.86 | (11) ? [v0: int] : ? [v1: int] : ? [v2: nat] : ? [v3: int] : ? [v4:
% 21.89/3.86 | nat] : (bit1(pls) = v0 & bit0(v1) = v3 & bit0(v0) = v1 &
% 21.89/3.86 | number_number_of_nat(v3) = v4 & number_number_of_nat(v1) = v2 &
% 21.89/3.86 | nat(v4) & nat(v2) & int(v3) & int(v1) & int(v0) & ! [v5: int] : !
% 21.89/3.86 | [v6: int] : ( ~ (power_power_int(v5, v4) = v6) | ~ int(v5) | ?
% 21.89/3.86 | [v7: int] : (power_power_int(v7, v2) = v6 & power_power_int(v5,
% 21.89/3.86 | v2) = v7 & int(v7) & int(v6))))
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_33_nat__1__add__1) implies:
% 21.89/3.86 | (12) ? [v0: nat] : ? [v1: int] : ? [v2: int] :
% 21.89/3.86 | (plus_plus_nat(one_one_nat, one_one_nat) = v0 & bit1(pls) = v1 &
% 21.89/3.86 | bit0(v1) = v2 & number_number_of_nat(v2) = v0 & nat(v0) & int(v2) &
% 21.89/3.86 | int(v1))
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_36_rel__simps_I2_J) implies:
% 21.89/3.86 | (13) ? [v0: int] : ( ~ (v0 = 0) & ord_less_int(pls, pls) = v0)
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_41_one__is__num__one) implies:
% 21.89/3.86 | (14) ? [v0: int] : (number_number_of_int(v0) = one_one_int & bit1(pls) =
% 21.89/3.86 | v0 & int(v0))
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_43_Numeral1__eq1__nat) implies:
% 21.89/3.86 | (15) ? [v0: int] : (bit1(pls) = v0 & number_number_of_nat(v0) =
% 21.89/3.86 | one_one_nat & int(v0))
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_62_bin__less__0__simps_I1_J) implies:
% 21.89/3.86 | (16) ? [v0: int] : ( ~ (v0 = 0) & ord_less_int(pls, zero_zero_int) = v0)
% 21.89/3.86 |
% 21.89/3.86 | ALPHA: (fact_67_less__special_I4_J) implies:
% 21.89/3.87 | (17) ? [v0: int] : (bit1(pls) = v0 & int(v0) & ! [v1: int] : ! [v2: int]
% 21.89/3.87 | : (v2 = 0 | ~ (ord_less_int(v1, v0) = v2) | ~ int(v1) | ? [v3:
% 21.89/3.87 | int] : ? [v4: int] : ( ~ (v4 = 0) & number_number_of_int(v1) =
% 21.89/3.87 | v3 & ord_less_int(v3, one_one_int) = v4 & int(v3))) & ! [v1:
% 21.89/3.87 | int] : ( ~ (ord_less_int(v1, v0) = 0) | ~ int(v1) | ? [v2: int]
% 21.89/3.87 | : (number_number_of_int(v1) = v2 & ord_less_int(v2, one_one_int) =
% 21.89/3.87 | 0 & int(v2))))
% 21.89/3.87 |
% 21.89/3.87 | ALPHA: (fact_68_less__special_I2_J) implies:
% 21.89/3.87 | (18) ? [v0: int] : (bit1(pls) = v0 & int(v0) & ! [v1: int] : ! [v2: int]
% 21.89/3.87 | : (v2 = 0 | ~ (ord_less_int(v0, v1) = v2) | ~ int(v1) | ? [v3:
% 21.89/3.87 | int] : ? [v4: int] : ( ~ (v4 = 0) & number_number_of_int(v1) =
% 21.89/3.87 | v3 & ord_less_int(one_one_int, v3) = v4 & int(v3))) & ! [v1:
% 21.89/3.87 | int] : ( ~ (ord_less_int(v0, v1) = 0) | ~ int(v1) | ? [v2: int]
% 21.89/3.87 | : (number_number_of_int(v1) = v2 & ord_less_int(one_one_int, v2) =
% 21.89/3.87 | 0 & int(v2))))
% 21.89/3.87 |
% 21.89/3.87 | ALPHA: (fact_78_Pls__def) implies:
% 21.89/3.87 | (19) pls = zero_zero_int
% 21.89/3.87 |
% 21.89/3.87 | ALPHA: (fact_92_power__eq__0__iff__number__of) implies:
% 21.89/3.87 | (20) ! [v0: int] : ! [v1: int] : ! [v2: nat] : ( ~
% 21.89/3.87 | (number_number_of_nat(v1) = v2) | ~ (power_power_int(v0, v2) =
% 21.89/3.87 | zero_zero_int) | ~ int(v1) | ~ int(v0) | (v0 = zero_zero_int &
% 21.89/3.87 | ~ (v2 = zero_zero_nat)))
% 21.89/3.87 |
% 21.89/3.87 | ALPHA: (fact_103_zero__less__power2) implies:
% 21.89/3.87 | (21) ? [v0: int] : ? [v1: int] : ? [v2: nat] : (bit1(pls) = v0 &
% 21.89/3.87 | bit0(v0) = v1 & number_number_of_nat(v1) = v2 & nat(v2) & int(v1) &
% 21.89/3.87 | int(v0) & ! [v3: int] : ! [v4: int] : (v3 = zero_zero_int | ~
% 21.89/3.87 | (power_power_int(v3, v2) = v4) | ~ int(v3) |
% 21.89/3.87 | ord_less_int(zero_zero_int, v4) = 0) & ! [v3: int] : ( ~
% 21.89/3.87 | (power_power_int(zero_zero_int, v2) = v3) | ? [v4: int] : ( ~ (v4
% 21.89/3.87 | = 0) & ord_less_int(zero_zero_int, v3) = v4)))
% 21.89/3.87 |
% 21.89/3.87 | ALPHA: (fact_104_power2__less__0) implies:
% 21.89/3.87 | (22) ? [v0: int] : ? [v1: int] : ? [v2: nat] : (bit1(pls) = v0 &
% 21.89/3.87 | bit0(v0) = v1 & number_number_of_nat(v1) = v2 & nat(v2) & int(v1) &
% 21.89/3.87 | int(v0) & ! [v3: int] : ! [v4: int] : ( ~ (power_power_int(v3, v2)
% 21.89/3.87 | = v4) | ~ int(v3) | ? [v5: int] : ( ~ (v5 = 0) &
% 21.89/3.87 | ord_less_int(v4, zero_zero_int) = v5)))
% 21.89/3.87 |
% 21.89/3.87 | ALPHA: (fact_105_sum__power2__gt__zero__iff) implies:
% 21.89/3.87 | (23) ? [v0: int] : ? [v1: int] : ? [v2: nat] : (bit1(pls) = v0 &
% 21.89/3.87 | bit0(v0) = v1 & number_number_of_nat(v1) = v2 & nat(v2) & int(v1) &
% 21.89/3.87 | int(v0) & ! [v3: int] : ! [v4: int] : ! [v5: int] : ! [v6: int]
% 21.89/3.87 | : ! [v7: int] : ( ~ (power_power_int(v4, v2) = v6) | ~
% 21.89/3.87 | (power_power_int(v3, v2) = v5) | ~ (plus_plus_int(v5, v6) = v7) |
% 21.89/3.87 | ~ int(v4) | ~ int(v3) | ord_less_int(zero_zero_int, v7) = 0 |
% 21.89/3.87 | (v4 = zero_zero_int & v3 = zero_zero_int)) & ! [v3: int] : !
% 21.89/3.87 | [v4: int] : ( ~ (power_power_int(zero_zero_int, v2) = v3) | ~
% 21.89/3.87 | (plus_plus_int(v3, v3) = v4) | ? [v5: int] : ( ~ (v5 = 0) &
% 21.89/3.87 | ord_less_int(zero_zero_int, v4) = v5)))
% 21.89/3.87 |
% 21.89/3.87 | ALPHA: (conj_0) implies:
% 21.89/3.87 | (24) int(one_one_int)
% 21.89/3.87 | (25) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4:
% 21.89/3.87 | nat] : (bit1(pls) = v2 & bit0(v2) = v3 & number_number_of_nat(v3) =
% 21.89/3.87 | v4 & power_power_int(v1, v4) = zero_zero_int &
% 21.89/3.87 | semiri1621563631at_int(n) = v0 & plus_plus_int(one_one_int, v0) = v1
% 21.89/3.87 | & nat(v4) & int(v3) & int(v2) & int(v1) & int(v0))
% 21.89/3.87 |
% 21.89/3.87 | ALPHA: (function-axioms) implies:
% 21.89/3.87 | (26) ! [v0: int] : ! [v1: int] : ! [v2: nat] : (v1 = v0 | ~
% 21.89/3.87 | (semiri1621563631at_int(v2) = v1) | ~ (semiri1621563631at_int(v2) =
% 21.89/3.87 | v0))
% 21.89/3.87 | (27) ! [v0: nat] : ! [v1: nat] : ! [v2: int] : (v1 = v0 | ~
% 21.89/3.87 | (number_number_of_nat(v2) = v1) | ~ (number_number_of_nat(v2) =
% 21.89/3.87 | v0))
% 21.89/3.87 | (28) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (bit0(v2) =
% 21.89/3.87 | v1) | ~ (bit0(v2) = v0))
% 21.89/3.88 | (29) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (bit1(v2) =
% 21.89/3.88 | v1) | ~ (bit1(v2) = v0))
% 21.89/3.88 | (30) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int]
% 21.89/3.88 | : ! [v3: int] : (v1 = v0 | ~ (ord_less_int(v3, v2) = v1) | ~
% 21.89/3.88 | (ord_less_int(v3, v2) = v0))
% 21.89/3.88 | (31) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 |
% 21.89/3.88 | ~ (plus_plus_int(v3, v2) = v1) | ~ (plus_plus_int(v3, v2) = v0))
% 21.89/3.88 |
% 21.89/3.88 | DELTA: instantiating (13) with fresh symbol all_69_0 gives:
% 21.89/3.88 | (32) ~ (all_69_0 = 0) & ord_less_int(pls, pls) = all_69_0
% 21.89/3.88 |
% 21.89/3.88 | ALPHA: (32) implies:
% 21.89/3.88 | (33) ord_less_int(pls, pls) = all_69_0
% 21.89/3.88 |
% 21.89/3.88 | DELTA: instantiating (16) with fresh symbol all_71_0 gives:
% 21.89/3.88 | (34) ~ (all_71_0 = 0) & ord_less_int(pls, zero_zero_int) = all_71_0
% 21.89/3.88 |
% 21.89/3.88 | ALPHA: (34) implies:
% 21.89/3.88 | (35) ~ (all_71_0 = 0)
% 21.89/3.88 | (36) ord_less_int(pls, zero_zero_int) = all_71_0
% 21.89/3.88 |
% 21.89/3.88 | DELTA: instantiating (14) with fresh symbol all_73_0 gives:
% 21.89/3.88 | (37) number_number_of_int(all_73_0) = one_one_int & bit1(pls) = all_73_0 &
% 21.89/3.88 | int(all_73_0)
% 21.89/3.88 |
% 21.89/3.88 | ALPHA: (37) implies:
% 21.89/3.88 | (38) bit1(pls) = all_73_0
% 21.89/3.88 |
% 21.89/3.88 | DELTA: instantiating (14) with fresh symbol all_79_0 gives:
% 21.89/3.88 | (39) number_number_of_int(all_79_0) = one_one_int & bit1(pls) = all_79_0 &
% 21.89/3.88 | int(all_79_0)
% 21.89/3.88 |
% 21.89/3.88 | ALPHA: (39) implies:
% 21.89/3.88 | (40) bit1(pls) = all_79_0
% 21.89/3.88 |
% 21.89/3.88 | DELTA: instantiating (15) with fresh symbol all_81_0 gives:
% 21.89/3.88 | (41) bit1(pls) = all_81_0 & number_number_of_nat(all_81_0) = one_one_nat &
% 21.89/3.88 | int(all_81_0)
% 21.89/3.88 |
% 21.89/3.88 | ALPHA: (41) implies:
% 21.89/3.88 | (42) bit1(pls) = all_81_0
% 21.89/3.88 |
% 21.89/3.88 | DELTA: instantiating (1) with fresh symbols all_86_0, all_86_1 gives:
% 21.89/3.88 | (43) semiri1621563631at_int(n) = all_86_1 & plus_plus_int(one_one_int,
% 21.89/3.88 | all_86_1) = all_86_0 & ord_less_int(zero_zero_int, all_86_0) = 0 &
% 21.89/3.88 | int(all_86_0) & int(all_86_1)
% 21.89/3.88 |
% 21.89/3.88 | ALPHA: (43) implies:
% 21.89/3.88 | (44) ord_less_int(zero_zero_int, all_86_0) = 0
% 21.89/3.88 | (45) plus_plus_int(one_one_int, all_86_1) = all_86_0
% 21.89/3.88 | (46) semiri1621563631at_int(n) = all_86_1
% 21.89/3.88 |
% 21.89/3.88 | DELTA: instantiating (10) with fresh symbols all_91_0, all_91_1, all_91_2
% 21.89/3.88 | gives:
% 21.89/3.88 | (47) number_number_of_int(all_91_0) = all_91_2 & bit1(pls) = all_91_1 &
% 21.89/3.88 | bit0(all_91_1) = all_91_0 & plus_plus_int(one_one_int, one_one_int) =
% 21.89/3.88 | all_91_2 & int(all_91_0) & int(all_91_1) & int(all_91_2)
% 21.89/3.88 |
% 21.89/3.88 | ALPHA: (47) implies:
% 21.89/3.88 | (48) bit0(all_91_1) = all_91_0
% 21.89/3.88 | (49) bit1(pls) = all_91_1
% 21.89/3.88 |
% 21.89/3.88 | DELTA: instantiating (12) with fresh symbols all_93_0, all_93_1, all_93_2
% 21.89/3.88 | gives:
% 21.89/3.88 | (50) plus_plus_nat(one_one_nat, one_one_nat) = all_93_2 & bit1(pls) =
% 21.89/3.88 | all_93_1 & bit0(all_93_1) = all_93_0 & number_number_of_nat(all_93_0)
% 21.89/3.88 | = all_93_2 & nat(all_93_2) & int(all_93_0) & int(all_93_1)
% 21.89/3.88 |
% 21.89/3.88 | ALPHA: (50) implies:
% 22.27/3.88 | (51) int(all_93_0)
% 22.27/3.88 | (52) number_number_of_nat(all_93_0) = all_93_2
% 22.27/3.88 | (53) bit0(all_93_1) = all_93_0
% 22.27/3.88 | (54) bit1(pls) = all_93_1
% 22.27/3.88 |
% 22.27/3.88 | DELTA: instantiating (10) with fresh symbols all_95_0, all_95_1, all_95_2
% 22.27/3.88 | gives:
% 22.27/3.88 | (55) number_number_of_int(all_95_0) = all_95_2 & bit1(pls) = all_95_1 &
% 22.27/3.88 | bit0(all_95_1) = all_95_0 & plus_plus_int(one_one_int, one_one_int) =
% 22.27/3.88 | all_95_2 & int(all_95_0) & int(all_95_1) & int(all_95_2)
% 22.27/3.88 |
% 22.27/3.88 | ALPHA: (55) implies:
% 22.27/3.88 | (56) bit0(all_95_1) = all_95_0
% 22.27/3.88 | (57) bit1(pls) = all_95_1
% 22.27/3.88 |
% 22.27/3.88 | DELTA: instantiating (12) with fresh symbols all_97_0, all_97_1, all_97_2
% 22.27/3.88 | gives:
% 22.27/3.88 | (58) plus_plus_nat(one_one_nat, one_one_nat) = all_97_2 & bit1(pls) =
% 22.27/3.88 | all_97_1 & bit0(all_97_1) = all_97_0 & number_number_of_nat(all_97_0)
% 22.27/3.88 | = all_97_2 & nat(all_97_2) & int(all_97_0) & int(all_97_1)
% 22.27/3.88 |
% 22.27/3.88 | ALPHA: (58) implies:
% 22.27/3.88 | (59) bit0(all_97_1) = all_97_0
% 22.27/3.88 | (60) bit1(pls) = all_97_1
% 22.27/3.88 |
% 22.27/3.88 | DELTA: instantiating (6) with fresh symbols all_99_0, all_99_1, all_99_2
% 22.27/3.88 | gives:
% 22.27/3.88 | (61) power_power_nat(zero_zero_nat, all_99_0) = zero_zero_nat & bit1(pls) =
% 22.27/3.88 | all_99_2 & bit0(all_99_2) = all_99_1 & number_number_of_nat(all_99_1)
% 22.27/3.88 | = all_99_0 & nat(all_99_0) & int(all_99_1) & int(all_99_2)
% 22.27/3.88 |
% 22.27/3.88 | ALPHA: (61) implies:
% 22.27/3.89 | (62) number_number_of_nat(all_99_1) = all_99_0
% 22.27/3.89 | (63) bit0(all_99_2) = all_99_1
% 22.27/3.89 | (64) bit1(pls) = all_99_2
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (4) with fresh symbols all_101_0, all_101_1, all_101_2
% 22.27/3.89 | gives:
% 22.27/3.89 | (65) power_power_nat(one_one_nat, all_101_0) = one_one_nat & bit1(pls) =
% 22.27/3.89 | all_101_2 & bit0(all_101_2) = all_101_1 &
% 22.27/3.89 | number_number_of_nat(all_101_1) = all_101_0 & nat(all_101_0) &
% 22.27/3.89 | int(all_101_1) & int(all_101_2)
% 22.27/3.89 |
% 22.27/3.89 | ALPHA: (65) implies:
% 22.27/3.89 | (66) number_number_of_nat(all_101_1) = all_101_0
% 22.27/3.89 | (67) bit0(all_101_2) = all_101_1
% 22.27/3.89 | (68) bit1(pls) = all_101_2
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (3) with fresh symbols all_103_0, all_103_1, all_103_2
% 22.27/3.89 | gives:
% 22.27/3.89 | (69) bit1(pls) = all_103_2 & bit0(all_103_2) = all_103_1 &
% 22.27/3.89 | number_number_of_nat(all_103_1) = all_103_0 &
% 22.27/3.89 | power_power_int(one_one_int, all_103_0) = one_one_int & nat(all_103_0)
% 22.27/3.89 | & int(all_103_1) & int(all_103_2)
% 22.27/3.89 |
% 22.27/3.89 | ALPHA: (69) implies:
% 22.27/3.89 | (70) number_number_of_nat(all_103_1) = all_103_0
% 22.27/3.89 | (71) bit0(all_103_2) = all_103_1
% 22.27/3.89 | (72) bit1(pls) = all_103_2
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (5) with fresh symbols all_105_0, all_105_1, all_105_2
% 22.27/3.89 | gives:
% 22.27/3.89 | (73) bit1(pls) = all_105_2 & bit0(all_105_2) = all_105_1 &
% 22.27/3.89 | number_number_of_nat(all_105_1) = all_105_0 &
% 22.27/3.89 | power_power_int(zero_zero_int, all_105_0) = zero_zero_int &
% 22.27/3.89 | nat(all_105_0) & int(all_105_1) & int(all_105_2)
% 22.27/3.89 |
% 22.27/3.89 | ALPHA: (73) implies:
% 22.27/3.89 | (74) number_number_of_nat(all_105_1) = all_105_0
% 22.27/3.89 | (75) bit0(all_105_2) = all_105_1
% 22.27/3.89 | (76) bit1(pls) = all_105_2
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (8) with fresh symbol all_107_0 gives:
% 22.27/3.89 | (77) bit1(pls) = all_107_0 & int(all_107_0) & ! [v0: int] : ! [v1: int] :
% 22.27/3.89 | ( ~ (plus_plus_int(all_107_0, v0) = v1) | ~ int(v0) | ? [v2: int] :
% 22.27/3.89 | ? [v3: int] : (number_number_of_int(v1) = v3 &
% 22.27/3.89 | number_number_of_int(v0) = v2 & plus_plus_int(one_one_int, v2) =
% 22.27/3.89 | v3 & int(v3) & int(v2)))
% 22.27/3.89 |
% 22.27/3.89 | ALPHA: (77) implies:
% 22.27/3.89 | (78) bit1(pls) = all_107_0
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (9) with fresh symbol all_110_0 gives:
% 22.27/3.89 | (79) bit1(pls) = all_110_0 & int(all_110_0) & ! [v0: int] : ! [v1: int] :
% 22.27/3.89 | ( ~ (plus_plus_int(v0, all_110_0) = v1) | ~ int(v0) | ? [v2: int] :
% 22.27/3.89 | ? [v3: int] : (number_number_of_int(v1) = v3 &
% 22.27/3.89 | number_number_of_int(v0) = v2 & plus_plus_int(v2, one_one_int) =
% 22.27/3.89 | v3 & int(v3) & int(v2)))
% 22.27/3.89 |
% 22.27/3.89 | ALPHA: (79) implies:
% 22.27/3.89 | (80) bit1(pls) = all_110_0
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (22) with fresh symbols all_113_0, all_113_1, all_113_2
% 22.27/3.89 | gives:
% 22.27/3.89 | (81) bit1(pls) = all_113_2 & bit0(all_113_2) = all_113_1 &
% 22.27/3.89 | number_number_of_nat(all_113_1) = all_113_0 & nat(all_113_0) &
% 22.27/3.89 | int(all_113_1) & int(all_113_2) & ! [v0: int] : ! [v1: int] : ( ~
% 22.27/3.89 | (power_power_int(v0, all_113_0) = v1) | ~ int(v0) | ? [v2: int] :
% 22.27/3.89 | ( ~ (v2 = 0) & ord_less_int(v1, zero_zero_int) = v2))
% 22.27/3.89 |
% 22.27/3.89 | ALPHA: (81) implies:
% 22.27/3.89 | (82) number_number_of_nat(all_113_1) = all_113_0
% 22.27/3.89 | (83) bit0(all_113_2) = all_113_1
% 22.27/3.89 | (84) bit1(pls) = all_113_2
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (25) with fresh symbols all_116_0, all_116_1, all_116_2,
% 22.27/3.89 | all_116_3, all_116_4 gives:
% 22.27/3.89 | (85) bit1(pls) = all_116_2 & bit0(all_116_2) = all_116_1 &
% 22.27/3.89 | number_number_of_nat(all_116_1) = all_116_0 &
% 22.27/3.89 | power_power_int(all_116_3, all_116_0) = zero_zero_int &
% 22.27/3.89 | semiri1621563631at_int(n) = all_116_4 & plus_plus_int(one_one_int,
% 22.27/3.89 | all_116_4) = all_116_3 & nat(all_116_0) & int(all_116_1) &
% 22.27/3.89 | int(all_116_2) & int(all_116_3) & int(all_116_4)
% 22.27/3.89 |
% 22.27/3.89 | ALPHA: (85) implies:
% 22.27/3.89 | (86) int(all_116_4)
% 22.27/3.89 | (87) plus_plus_int(one_one_int, all_116_4) = all_116_3
% 22.27/3.89 | (88) semiri1621563631at_int(n) = all_116_4
% 22.27/3.89 | (89) power_power_int(all_116_3, all_116_0) = zero_zero_int
% 22.27/3.89 | (90) number_number_of_nat(all_116_1) = all_116_0
% 22.27/3.89 | (91) bit0(all_116_2) = all_116_1
% 22.27/3.89 | (92) bit1(pls) = all_116_2
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (7) with fresh symbols all_118_0, all_118_1, all_118_2
% 22.27/3.89 | gives:
% 22.27/3.89 | (93) bit1(pls) = all_118_2 & bit0(all_118_2) = all_118_1 &
% 22.27/3.89 | number_number_of_nat(all_118_1) = all_118_0 & nat(all_118_0) &
% 22.27/3.89 | int(all_118_1) & int(all_118_2) & ! [v0: int] : (v0 = zero_zero_int |
% 22.27/3.89 | ~ (power_power_int(v0, all_118_0) = zero_zero_int) | ~ int(v0)) &
% 22.27/3.89 | ! [v0: int] : (v0 = zero_zero_int | ~ (power_power_int(zero_zero_int,
% 22.27/3.89 | all_118_0) = v0))
% 22.27/3.89 |
% 22.27/3.89 | ALPHA: (93) implies:
% 22.27/3.89 | (94) number_number_of_nat(all_118_1) = all_118_0
% 22.27/3.89 | (95) bit0(all_118_2) = all_118_1
% 22.27/3.89 | (96) bit1(pls) = all_118_2
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (21) with fresh symbols all_121_0, all_121_1, all_121_2
% 22.27/3.89 | gives:
% 22.27/3.89 | (97) bit1(pls) = all_121_2 & bit0(all_121_2) = all_121_1 &
% 22.27/3.89 | number_number_of_nat(all_121_1) = all_121_0 & nat(all_121_0) &
% 22.27/3.89 | int(all_121_1) & int(all_121_2) & ! [v0: int] : ! [v1: int] : (v0 =
% 22.27/3.89 | zero_zero_int | ~ (power_power_int(v0, all_121_0) = v1) | ~
% 22.27/3.89 | int(v0) | ord_less_int(zero_zero_int, v1) = 0) & ! [v0: int] : ( ~
% 22.27/3.89 | (power_power_int(zero_zero_int, all_121_0) = v0) | ? [v1: int] : (
% 22.27/3.89 | ~ (v1 = 0) & ord_less_int(zero_zero_int, v0) = v1))
% 22.27/3.89 |
% 22.27/3.89 | ALPHA: (97) implies:
% 22.27/3.89 | (98) number_number_of_nat(all_121_1) = all_121_0
% 22.27/3.89 | (99) bit0(all_121_2) = all_121_1
% 22.27/3.89 | (100) bit1(pls) = all_121_2
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (17) with fresh symbol all_124_0 gives:
% 22.27/3.90 | (101) bit1(pls) = all_124_0 & int(all_124_0) & ! [v0: int] : ! [v1: int]
% 22.27/3.90 | : (v1 = 0 | ~ (ord_less_int(v0, all_124_0) = v1) | ~ int(v0) | ?
% 22.27/3.90 | [v2: int] : ? [v3: int] : ( ~ (v3 = 0) & number_number_of_int(v0)
% 22.27/3.90 | = v2 & ord_less_int(v2, one_one_int) = v3 & int(v2))) & ! [v0:
% 22.27/3.90 | int] : ( ~ (ord_less_int(v0, all_124_0) = 0) | ~ int(v0) | ? [v1:
% 22.27/3.90 | int] : (number_number_of_int(v0) = v1 & ord_less_int(v1,
% 22.27/3.90 | one_one_int) = 0 & int(v1)))
% 22.27/3.90 |
% 22.27/3.90 | ALPHA: (101) implies:
% 22.27/3.90 | (102) bit1(pls) = all_124_0
% 22.27/3.90 |
% 22.27/3.90 | DELTA: instantiating (18) with fresh symbol all_127_0 gives:
% 22.27/3.90 | (103) bit1(pls) = all_127_0 & int(all_127_0) & ! [v0: int] : ! [v1: int]
% 22.27/3.90 | : (v1 = 0 | ~ (ord_less_int(all_127_0, v0) = v1) | ~ int(v0) | ?
% 22.27/3.90 | [v2: int] : ? [v3: int] : ( ~ (v3 = 0) & number_number_of_int(v0)
% 22.27/3.90 | = v2 & ord_less_int(one_one_int, v2) = v3 & int(v2))) & ! [v0:
% 22.27/3.90 | int] : ( ~ (ord_less_int(all_127_0, v0) = 0) | ~ int(v0) | ? [v1:
% 22.27/3.90 | int] : (number_number_of_int(v0) = v1 & ord_less_int(one_one_int,
% 22.27/3.90 | v1) = 0 & int(v1)))
% 22.27/3.90 |
% 22.27/3.90 | ALPHA: (103) implies:
% 22.27/3.90 | (104) bit1(pls) = all_127_0
% 22.27/3.90 |
% 22.27/3.90 | DELTA: instantiating (2) with fresh symbols all_130_0, all_130_1, all_130_2
% 22.27/3.90 | gives:
% 22.27/3.90 | (105) bit1(pls) = all_130_2 & bit0(all_130_2) = all_130_1 &
% 22.27/3.90 | number_number_of_nat(all_130_1) = all_130_0 & nat(all_130_0) &
% 22.27/3.90 | int(all_130_1) & int(all_130_2) & ! [v0: int] : ! [v1: int] : !
% 22.27/3.90 | [v2: int] : ! [v3: int] : ( ~ (power_power_int(v1, all_130_0) = v3)
% 22.27/3.90 | | ~ (power_power_int(v0, all_130_0) = v2) | ~ (plus_plus_int(v2,
% 22.27/3.90 | v3) = zero_zero_int) | ~ int(v1) | ~ int(v0) | (v1 =
% 22.27/3.90 | zero_zero_int & v0 = zero_zero_int)) & ! [v0: int] : ! [v1:
% 22.27/3.90 | int] : (v1 = zero_zero_int | ~ (power_power_int(zero_zero_int,
% 22.27/3.90 | all_130_0) = v0) | ~ (plus_plus_int(v0, v0) = v1))
% 22.27/3.90 |
% 22.27/3.90 | ALPHA: (105) implies:
% 22.27/3.90 | (106) number_number_of_nat(all_130_1) = all_130_0
% 22.27/3.90 | (107) bit0(all_130_2) = all_130_1
% 22.27/3.90 | (108) bit1(pls) = all_130_2
% 22.27/3.90 |
% 22.27/3.90 | DELTA: instantiating (11) with fresh symbols all_133_0, all_133_1, all_133_2,
% 22.27/3.90 | all_133_3, all_133_4 gives:
% 22.27/3.90 | (109) bit1(pls) = all_133_4 & bit0(all_133_3) = all_133_1 & bit0(all_133_4)
% 22.27/3.90 | = all_133_3 & number_number_of_nat(all_133_1) = all_133_0 &
% 22.27/3.90 | number_number_of_nat(all_133_3) = all_133_2 & nat(all_133_0) &
% 22.27/3.90 | nat(all_133_2) & int(all_133_1) & int(all_133_3) & int(all_133_4) &
% 22.27/3.90 | ! [v0: int] : ! [v1: int] : ( ~ (power_power_int(v0, all_133_0) =
% 22.27/3.90 | v1) | ~ int(v0) | ? [v2: int] : (power_power_int(v2, all_133_2)
% 22.27/3.90 | = v1 & power_power_int(v0, all_133_2) = v2 & int(v2) & int(v1)))
% 22.27/3.90 |
% 22.27/3.90 | ALPHA: (109) implies:
% 22.27/3.90 | (110) number_number_of_nat(all_133_3) = all_133_2
% 22.27/3.90 | (111) bit0(all_133_4) = all_133_3
% 22.27/3.90 | (112) bit1(pls) = all_133_4
% 22.27/3.90 |
% 22.27/3.90 | DELTA: instantiating (23) with fresh symbols all_136_0, all_136_1, all_136_2
% 22.27/3.90 | gives:
% 22.27/3.90 | (113) bit1(pls) = all_136_2 & bit0(all_136_2) = all_136_1 &
% 22.27/3.90 | number_number_of_nat(all_136_1) = all_136_0 & nat(all_136_0) &
% 22.27/3.90 | int(all_136_1) & int(all_136_2) & ! [v0: int] : ! [v1: int] : !
% 22.27/3.90 | [v2: int] : ! [v3: int] : ! [v4: int] : ( ~ (power_power_int(v1,
% 22.27/3.90 | all_136_0) = v3) | ~ (power_power_int(v0, all_136_0) = v2) |
% 22.27/3.90 | ~ (plus_plus_int(v2, v3) = v4) | ~ int(v1) | ~ int(v0) |
% 22.27/3.90 | ord_less_int(zero_zero_int, v4) = 0 | (v1 = zero_zero_int & v0 =
% 22.27/3.90 | zero_zero_int)) & ! [v0: int] : ! [v1: int] : ( ~
% 22.27/3.90 | (power_power_int(zero_zero_int, all_136_0) = v0) | ~
% 22.27/3.90 | (plus_plus_int(v0, v0) = v1) | ? [v2: int] : ( ~ (v2 = 0) &
% 22.27/3.90 | ord_less_int(zero_zero_int, v1) = v2))
% 22.27/3.90 |
% 22.27/3.90 | ALPHA: (113) implies:
% 22.27/3.90 | (114) number_number_of_nat(all_136_1) = all_136_0
% 22.27/3.90 | (115) bit0(all_136_2) = all_136_1
% 22.27/3.90 | (116) bit1(pls) = all_136_2
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (116) imply:
% 22.27/3.90 | (117) bit1(zero_zero_int) = all_136_2
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (112) imply:
% 22.27/3.90 | (118) bit1(zero_zero_int) = all_133_4
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (108) imply:
% 22.27/3.90 | (119) bit1(zero_zero_int) = all_130_2
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (104) imply:
% 22.27/3.90 | (120) bit1(zero_zero_int) = all_127_0
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (102) imply:
% 22.27/3.90 | (121) bit1(zero_zero_int) = all_124_0
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (100) imply:
% 22.27/3.90 | (122) bit1(zero_zero_int) = all_121_2
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (96) imply:
% 22.27/3.90 | (123) bit1(zero_zero_int) = all_118_2
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (92) imply:
% 22.27/3.90 | (124) bit1(zero_zero_int) = all_116_2
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (84) imply:
% 22.27/3.90 | (125) bit1(zero_zero_int) = all_113_2
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (80) imply:
% 22.27/3.90 | (126) bit1(zero_zero_int) = all_110_0
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (78) imply:
% 22.27/3.90 | (127) bit1(zero_zero_int) = all_107_0
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (76) imply:
% 22.27/3.90 | (128) bit1(zero_zero_int) = all_105_2
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (72) imply:
% 22.27/3.90 | (129) bit1(zero_zero_int) = all_103_2
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (68) imply:
% 22.27/3.90 | (130) bit1(zero_zero_int) = all_101_2
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (64) imply:
% 22.27/3.90 | (131) bit1(zero_zero_int) = all_99_2
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (60) imply:
% 22.27/3.90 | (132) bit1(zero_zero_int) = all_97_1
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (57) imply:
% 22.27/3.90 | (133) bit1(zero_zero_int) = all_95_1
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (54) imply:
% 22.27/3.90 | (134) bit1(zero_zero_int) = all_93_1
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (49) imply:
% 22.27/3.90 | (135) bit1(zero_zero_int) = all_91_1
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (42) imply:
% 22.27/3.90 | (136) bit1(zero_zero_int) = all_81_0
% 22.27/3.90 |
% 22.27/3.90 | REDUCE: (19), (40) imply:
% 22.27/3.91 | (137) bit1(zero_zero_int) = all_79_0
% 22.27/3.91 |
% 22.27/3.91 | REDUCE: (19), (38) imply:
% 22.27/3.91 | (138) bit1(zero_zero_int) = all_73_0
% 22.27/3.91 |
% 22.27/3.91 | REDUCE: (19), (33) imply:
% 22.27/3.91 | (139) ord_less_int(zero_zero_int, zero_zero_int) = all_69_0
% 22.27/3.91 |
% 22.27/3.91 | REDUCE: (19), (36) imply:
% 22.27/3.91 | (140) ord_less_int(zero_zero_int, zero_zero_int) = all_71_0
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (30) with all_69_0, all_71_0, zero_zero_int,
% 22.27/3.91 | zero_zero_int, simplifying with (139), (140) gives:
% 22.27/3.91 | (141) all_71_0 = all_69_0
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (26) with all_86_1, all_116_4, n, simplifying with
% 22.27/3.91 | (46), (88) gives:
% 22.27/3.91 | (142) all_116_4 = all_86_1
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_81_0, all_91_1, zero_zero_int,
% 22.27/3.91 | simplifying with (135), (136) gives:
% 22.27/3.91 | (143) all_91_1 = all_81_0
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_99_2, all_103_2, zero_zero_int,
% 22.27/3.91 | simplifying with (129), (131) gives:
% 22.27/3.91 | (144) all_103_2 = all_99_2
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_99_2, all_105_2, zero_zero_int,
% 22.27/3.91 | simplifying with (128), (131) gives:
% 22.27/3.91 | (145) all_105_2 = all_99_2
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_105_2, all_110_0, zero_zero_int,
% 22.27/3.91 | simplifying with (126), (128) gives:
% 22.27/3.91 | (146) all_110_0 = all_105_2
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_97_1, all_110_0, zero_zero_int,
% 22.27/3.91 | simplifying with (126), (132) gives:
% 22.27/3.91 | (147) all_110_0 = all_97_1
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_113_2, all_118_2, zero_zero_int,
% 22.27/3.91 | simplifying with (123), (125) gives:
% 22.27/3.91 | (148) all_118_2 = all_113_2
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_105_2, all_121_2, zero_zero_int,
% 22.27/3.91 | simplifying with (122), (128) gives:
% 22.27/3.91 | (149) all_121_2 = all_105_2
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_95_1, all_121_2, zero_zero_int,
% 22.27/3.91 | simplifying with (122), (133) gives:
% 22.27/3.91 | (150) all_121_2 = all_95_1
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_113_2, all_124_0, zero_zero_int,
% 22.27/3.91 | simplifying with (121), (125) gives:
% 22.27/3.91 | (151) all_124_0 = all_113_2
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_103_2, all_124_0, zero_zero_int,
% 22.27/3.91 | simplifying with (121), (129) gives:
% 22.27/3.91 | (152) all_124_0 = all_103_2
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_121_2, all_127_0, zero_zero_int,
% 22.27/3.91 | simplifying with (120), (122) gives:
% 22.27/3.91 | (153) all_127_0 = all_121_2
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_116_2, all_127_0, zero_zero_int,
% 22.27/3.91 | simplifying with (120), (124) gives:
% 22.27/3.91 | (154) all_127_0 = all_116_2
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_101_2, all_127_0, zero_zero_int,
% 22.27/3.91 | simplifying with (120), (130) gives:
% 22.27/3.91 | (155) all_127_0 = all_101_2
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_93_1, all_127_0, zero_zero_int,
% 22.27/3.91 | simplifying with (120), (134) gives:
% 22.27/3.91 | (156) all_127_0 = all_93_1
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_91_1, all_127_0, zero_zero_int,
% 22.27/3.91 | simplifying with (120), (135) gives:
% 22.27/3.91 | (157) all_127_0 = all_91_1
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_124_0, all_130_2, zero_zero_int,
% 22.27/3.91 | simplifying with (119), (121) gives:
% 22.27/3.91 | (158) all_130_2 = all_124_0
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_107_0, all_130_2, zero_zero_int,
% 22.27/3.91 | simplifying with (119), (127) gives:
% 22.27/3.91 | (159) all_130_2 = all_107_0
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_118_2, all_133_4, zero_zero_int,
% 22.27/3.91 | simplifying with (118), (123) gives:
% 22.27/3.91 | (160) all_133_4 = all_118_2
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_79_0, all_133_4, zero_zero_int,
% 22.27/3.91 | simplifying with (118), (137) gives:
% 22.27/3.91 | (161) all_133_4 = all_79_0
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_81_0, all_136_2, zero_zero_int,
% 22.27/3.91 | simplifying with (117), (136) gives:
% 22.27/3.91 | (162) all_136_2 = all_81_0
% 22.27/3.91 |
% 22.27/3.91 | GROUND_INST: instantiating (29) with all_73_0, all_136_2, zero_zero_int,
% 22.27/3.91 | simplifying with (117), (138) gives:
% 22.27/3.91 | (163) all_136_2 = all_73_0
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (162), (163) imply:
% 22.27/3.91 | (164) all_81_0 = all_73_0
% 22.27/3.91 |
% 22.27/3.91 | SIMP: (164) implies:
% 22.27/3.91 | (165) all_81_0 = all_73_0
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (160), (161) imply:
% 22.27/3.91 | (166) all_118_2 = all_79_0
% 22.27/3.91 |
% 22.27/3.91 | SIMP: (166) implies:
% 22.27/3.91 | (167) all_118_2 = all_79_0
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (158), (159) imply:
% 22.27/3.91 | (168) all_124_0 = all_107_0
% 22.27/3.91 |
% 22.27/3.91 | SIMP: (168) implies:
% 22.27/3.91 | (169) all_124_0 = all_107_0
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (154), (157) imply:
% 22.27/3.91 | (170) all_116_2 = all_91_1
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (154), (156) imply:
% 22.27/3.91 | (171) all_116_2 = all_93_1
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (153), (154) imply:
% 22.27/3.91 | (172) all_121_2 = all_116_2
% 22.27/3.91 |
% 22.27/3.91 | SIMP: (172) implies:
% 22.27/3.91 | (173) all_121_2 = all_116_2
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (154), (155) imply:
% 22.27/3.91 | (174) all_116_2 = all_101_2
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (151), (169) imply:
% 22.27/3.91 | (175) all_113_2 = all_107_0
% 22.27/3.91 |
% 22.27/3.91 | SIMP: (175) implies:
% 22.27/3.91 | (176) all_113_2 = all_107_0
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (152), (169) imply:
% 22.27/3.91 | (177) all_107_0 = all_103_2
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (149), (150) imply:
% 22.27/3.91 | (178) all_105_2 = all_95_1
% 22.27/3.91 |
% 22.27/3.91 | SIMP: (178) implies:
% 22.27/3.91 | (179) all_105_2 = all_95_1
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (150), (173) imply:
% 22.27/3.91 | (180) all_116_2 = all_95_1
% 22.27/3.91 |
% 22.27/3.91 | SIMP: (180) implies:
% 22.27/3.91 | (181) all_116_2 = all_95_1
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (148), (167) imply:
% 22.27/3.91 | (182) all_113_2 = all_79_0
% 22.27/3.91 |
% 22.27/3.91 | SIMP: (182) implies:
% 22.27/3.91 | (183) all_113_2 = all_79_0
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (174), (181) imply:
% 22.27/3.91 | (184) all_101_2 = all_95_1
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (171), (174) imply:
% 22.27/3.91 | (185) all_101_2 = all_93_1
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (170), (174) imply:
% 22.27/3.91 | (186) all_101_2 = all_91_1
% 22.27/3.91 |
% 22.27/3.91 | COMBINE_EQS: (176), (183) imply:
% 22.27/3.91 | (187) all_107_0 = all_79_0
% 22.27/3.91 |
% 22.27/3.91 | SIMP: (187) implies:
% 22.27/3.92 | (188) all_107_0 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (146), (147) imply:
% 22.27/3.92 | (189) all_105_2 = all_97_1
% 22.27/3.92 |
% 22.27/3.92 | SIMP: (189) implies:
% 22.27/3.92 | (190) all_105_2 = all_97_1
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (177), (188) imply:
% 22.27/3.92 | (191) all_103_2 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | SIMP: (191) implies:
% 22.27/3.92 | (192) all_103_2 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (145), (190) imply:
% 22.27/3.92 | (193) all_99_2 = all_97_1
% 22.27/3.92 |
% 22.27/3.92 | SIMP: (193) implies:
% 22.27/3.92 | (194) all_99_2 = all_97_1
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (179), (190) imply:
% 22.27/3.92 | (195) all_97_1 = all_95_1
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (144), (192) imply:
% 22.27/3.92 | (196) all_99_2 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | SIMP: (196) implies:
% 22.27/3.92 | (197) all_99_2 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (185), (186) imply:
% 22.27/3.92 | (198) all_93_1 = all_91_1
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (184), (185) imply:
% 22.27/3.92 | (199) all_95_1 = all_93_1
% 22.27/3.92 |
% 22.27/3.92 | SIMP: (199) implies:
% 22.27/3.92 | (200) all_95_1 = all_93_1
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (194), (197) imply:
% 22.27/3.92 | (201) all_97_1 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | SIMP: (201) implies:
% 22.27/3.92 | (202) all_97_1 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (195), (202) imply:
% 22.27/3.92 | (203) all_95_1 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | SIMP: (203) implies:
% 22.27/3.92 | (204) all_95_1 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (200), (204) imply:
% 22.27/3.92 | (205) all_93_1 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | SIMP: (205) implies:
% 22.27/3.92 | (206) all_93_1 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (198), (206) imply:
% 22.27/3.92 | (207) all_91_1 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | SIMP: (207) implies:
% 22.27/3.92 | (208) all_91_1 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (143), (208) imply:
% 22.27/3.92 | (209) all_81_0 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | SIMP: (209) implies:
% 22.27/3.92 | (210) all_81_0 = all_79_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (165), (210) imply:
% 22.27/3.92 | (211) all_79_0 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (208), (211) imply:
% 22.27/3.92 | (212) all_91_1 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (206), (211) imply:
% 22.27/3.92 | (213) all_93_1 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (204), (211) imply:
% 22.27/3.92 | (214) all_95_1 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (202), (211) imply:
% 22.27/3.92 | (215) all_97_1 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (197), (211) imply:
% 22.27/3.92 | (216) all_99_2 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (185), (213) imply:
% 22.27/3.92 | (217) all_101_2 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (192), (211) imply:
% 22.27/3.92 | (218) all_103_2 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (190), (215) imply:
% 22.27/3.92 | (219) all_105_2 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (188), (211) imply:
% 22.27/3.92 | (220) all_107_0 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (183), (211) imply:
% 22.27/3.92 | (221) all_113_2 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (174), (217) imply:
% 22.27/3.92 | (222) all_116_2 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (167), (211) imply:
% 22.27/3.92 | (223) all_118_2 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (150), (214) imply:
% 22.27/3.92 | (224) all_121_2 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (159), (220) imply:
% 22.27/3.92 | (225) all_130_2 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (161), (211) imply:
% 22.27/3.92 | (226) all_133_4 = all_73_0
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (35), (141) imply:
% 22.27/3.92 | (227) ~ (all_69_0 = 0)
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (115), (163) imply:
% 22.27/3.92 | (228) bit0(all_73_0) = all_136_1
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (111), (226) imply:
% 22.27/3.92 | (229) bit0(all_73_0) = all_133_3
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (107), (225) imply:
% 22.27/3.92 | (230) bit0(all_73_0) = all_130_1
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (99), (224) imply:
% 22.27/3.92 | (231) bit0(all_73_0) = all_121_1
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (95), (223) imply:
% 22.27/3.92 | (232) bit0(all_73_0) = all_118_1
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (91), (222) imply:
% 22.27/3.92 | (233) bit0(all_73_0) = all_116_1
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (83), (221) imply:
% 22.27/3.92 | (234) bit0(all_73_0) = all_113_1
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (75), (219) imply:
% 22.27/3.92 | (235) bit0(all_73_0) = all_105_1
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (71), (218) imply:
% 22.27/3.92 | (236) bit0(all_73_0) = all_103_1
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (67), (217) imply:
% 22.27/3.92 | (237) bit0(all_73_0) = all_101_1
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (63), (216) imply:
% 22.27/3.92 | (238) bit0(all_73_0) = all_99_1
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (59), (215) imply:
% 22.27/3.92 | (239) bit0(all_73_0) = all_97_0
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (56), (214) imply:
% 22.27/3.92 | (240) bit0(all_73_0) = all_95_0
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (53), (213) imply:
% 22.27/3.92 | (241) bit0(all_73_0) = all_93_0
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (48), (212) imply:
% 22.27/3.92 | (242) bit0(all_73_0) = all_91_0
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (87), (142) imply:
% 22.27/3.92 | (243) plus_plus_int(one_one_int, all_86_1) = all_116_3
% 22.27/3.92 |
% 22.27/3.92 | REDUCE: (86), (142) imply:
% 22.27/3.92 | (244) int(all_86_1)
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (31) with all_86_0, all_116_3, all_86_1,
% 22.27/3.92 | one_one_int, simplifying with (45), (243) gives:
% 22.27/3.92 | (245) all_116_3 = all_86_0
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (28) with all_95_0, all_101_1, all_73_0,
% 22.27/3.92 | simplifying with (237), (240) gives:
% 22.27/3.92 | (246) all_101_1 = all_95_0
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (28) with all_105_1, all_113_1, all_73_0,
% 22.27/3.92 | simplifying with (234), (235) gives:
% 22.27/3.92 | (247) all_113_1 = all_105_1
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (28) with all_103_1, all_113_1, all_73_0,
% 22.27/3.92 | simplifying with (234), (236) gives:
% 22.27/3.92 | (248) all_113_1 = all_103_1
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (28) with all_99_1, all_113_1, all_73_0,
% 22.27/3.92 | simplifying with (234), (238) gives:
% 22.27/3.92 | (249) all_113_1 = all_99_1
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (28) with all_97_0, all_113_1, all_73_0,
% 22.27/3.92 | simplifying with (234), (239) gives:
% 22.27/3.92 | (250) all_113_1 = all_97_0
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (28) with all_95_0, all_113_1, all_73_0,
% 22.27/3.92 | simplifying with (234), (240) gives:
% 22.27/3.92 | (251) all_113_1 = all_95_0
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (28) with all_105_1, all_116_1, all_73_0,
% 22.27/3.92 | simplifying with (233), (235) gives:
% 22.27/3.92 | (252) all_116_1 = all_105_1
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (28) with all_101_1, all_118_1, all_73_0,
% 22.27/3.92 | simplifying with (232), (237) gives:
% 22.27/3.92 | (253) all_118_1 = all_101_1
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (28) with all_116_1, all_121_1, all_73_0,
% 22.27/3.92 | simplifying with (231), (233) gives:
% 22.27/3.92 | (254) all_121_1 = all_116_1
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (28) with all_121_1, all_130_1, all_73_0,
% 22.27/3.92 | simplifying with (230), (231) gives:
% 22.27/3.92 | (255) all_130_1 = all_121_1
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (28) with all_118_1, all_133_3, all_73_0,
% 22.27/3.92 | simplifying with (229), (232) gives:
% 22.27/3.92 | (256) all_133_3 = all_118_1
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (28) with all_93_0, all_133_3, all_73_0,
% 22.27/3.92 | simplifying with (229), (241) gives:
% 22.27/3.92 | (257) all_133_3 = all_93_0
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (28) with all_130_1, all_136_1, all_73_0,
% 22.27/3.92 | simplifying with (228), (230) gives:
% 22.27/3.92 | (258) all_136_1 = all_130_1
% 22.27/3.92 |
% 22.27/3.92 | GROUND_INST: instantiating (28) with all_91_0, all_136_1, all_73_0,
% 22.27/3.92 | simplifying with (228), (242) gives:
% 22.27/3.92 | (259) all_136_1 = all_91_0
% 22.27/3.92 |
% 22.27/3.92 | COMBINE_EQS: (258), (259) imply:
% 22.27/3.93 | (260) all_130_1 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (260) implies:
% 22.27/3.93 | (261) all_130_1 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (256), (257) imply:
% 22.27/3.93 | (262) all_118_1 = all_93_0
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (262) implies:
% 22.27/3.93 | (263) all_118_1 = all_93_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (255), (261) imply:
% 22.27/3.93 | (264) all_121_1 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (264) implies:
% 22.27/3.93 | (265) all_121_1 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (254), (265) imply:
% 22.27/3.93 | (266) all_116_1 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (266) implies:
% 22.27/3.93 | (267) all_116_1 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (253), (263) imply:
% 22.27/3.93 | (268) all_101_1 = all_93_0
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (268) implies:
% 22.27/3.93 | (269) all_101_1 = all_93_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (252), (267) imply:
% 22.27/3.93 | (270) all_105_1 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (270) implies:
% 22.27/3.93 | (271) all_105_1 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (247), (248) imply:
% 22.27/3.93 | (272) all_105_1 = all_103_1
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (272) implies:
% 22.27/3.93 | (273) all_105_1 = all_103_1
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (248), (249) imply:
% 22.27/3.93 | (274) all_103_1 = all_99_1
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (248), (250) imply:
% 22.27/3.93 | (275) all_103_1 = all_97_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (248), (251) imply:
% 22.27/3.93 | (276) all_103_1 = all_95_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (271), (273) imply:
% 22.27/3.93 | (277) all_103_1 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (277) implies:
% 22.27/3.93 | (278) all_103_1 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (274), (275) imply:
% 22.27/3.93 | (279) all_99_1 = all_97_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (274), (276) imply:
% 22.27/3.93 | (280) all_99_1 = all_95_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (274), (278) imply:
% 22.27/3.93 | (281) all_99_1 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (246), (269) imply:
% 22.27/3.93 | (282) all_95_0 = all_93_0
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (282) implies:
% 22.27/3.93 | (283) all_95_0 = all_93_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (279), (280) imply:
% 22.27/3.93 | (284) all_97_0 = all_95_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (279), (281) imply:
% 22.27/3.93 | (285) all_97_0 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (284), (285) imply:
% 22.27/3.93 | (286) all_95_0 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (286) implies:
% 22.27/3.93 | (287) all_95_0 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (283), (287) imply:
% 22.27/3.93 | (288) all_93_0 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (288) implies:
% 22.27/3.93 | (289) all_93_0 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (269), (289) imply:
% 22.27/3.93 | (290) all_101_1 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (248), (278) imply:
% 22.27/3.93 | (291) all_113_1 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (263), (289) imply:
% 22.27/3.93 | (292) all_118_1 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (257), (289) imply:
% 22.27/3.93 | (293) all_133_3 = all_91_0
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (114), (259) imply:
% 22.27/3.93 | (294) number_number_of_nat(all_91_0) = all_136_0
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (110), (293) imply:
% 22.27/3.93 | (295) number_number_of_nat(all_91_0) = all_133_2
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (106), (261) imply:
% 22.27/3.93 | (296) number_number_of_nat(all_91_0) = all_130_0
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (98), (265) imply:
% 22.27/3.93 | (297) number_number_of_nat(all_91_0) = all_121_0
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (94), (292) imply:
% 22.27/3.93 | (298) number_number_of_nat(all_91_0) = all_118_0
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (90), (267) imply:
% 22.27/3.93 | (299) number_number_of_nat(all_91_0) = all_116_0
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (82), (291) imply:
% 22.27/3.93 | (300) number_number_of_nat(all_91_0) = all_113_0
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (74), (271) imply:
% 22.27/3.93 | (301) number_number_of_nat(all_91_0) = all_105_0
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (70), (278) imply:
% 22.27/3.93 | (302) number_number_of_nat(all_91_0) = all_103_0
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (66), (290) imply:
% 22.27/3.93 | (303) number_number_of_nat(all_91_0) = all_101_0
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (62), (281) imply:
% 22.27/3.93 | (304) number_number_of_nat(all_91_0) = all_99_0
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (52), (289) imply:
% 22.27/3.93 | (305) number_number_of_nat(all_91_0) = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (89), (245) imply:
% 22.27/3.93 | (306) power_power_int(all_86_0, all_116_0) = zero_zero_int
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (51), (289) imply:
% 22.27/3.93 | (307) int(all_91_0)
% 22.27/3.93 |
% 22.27/3.93 | GROUND_INST: instantiating (27) with all_99_0, all_101_0, all_91_0,
% 22.27/3.93 | simplifying with (303), (304) gives:
% 22.27/3.93 | (308) all_101_0 = all_99_0
% 22.27/3.93 |
% 22.27/3.93 | GROUND_INST: instantiating (27) with all_101_0, all_103_0, all_91_0,
% 22.27/3.93 | simplifying with (302), (303) gives:
% 22.27/3.93 | (309) all_103_0 = all_101_0
% 22.27/3.93 |
% 22.27/3.93 | GROUND_INST: instantiating (27) with all_103_0, all_105_0, all_91_0,
% 22.27/3.93 | simplifying with (301), (302) gives:
% 22.27/3.93 | (310) all_105_0 = all_103_0
% 22.27/3.93 |
% 22.27/3.93 | GROUND_INST: instantiating (27) with all_105_0, all_113_0, all_91_0,
% 22.27/3.93 | simplifying with (300), (301) gives:
% 22.27/3.93 | (311) all_113_0 = all_105_0
% 22.27/3.93 |
% 22.27/3.93 | GROUND_INST: instantiating (27) with all_113_0, all_116_0, all_91_0,
% 22.27/3.93 | simplifying with (299), (300) gives:
% 22.27/3.93 | (312) all_116_0 = all_113_0
% 22.27/3.93 |
% 22.27/3.93 | GROUND_INST: instantiating (27) with all_121_0, all_130_0, all_91_0,
% 22.27/3.93 | simplifying with (296), (297) gives:
% 22.27/3.93 | (313) all_130_0 = all_121_0
% 22.27/3.93 |
% 22.27/3.93 | GROUND_INST: instantiating (27) with all_121_0, all_133_2, all_91_0,
% 22.27/3.93 | simplifying with (295), (297) gives:
% 22.27/3.93 | (314) all_133_2 = all_121_0
% 22.27/3.93 |
% 22.27/3.93 | GROUND_INST: instantiating (27) with all_118_0, all_133_2, all_91_0,
% 22.27/3.93 | simplifying with (295), (298) gives:
% 22.27/3.93 | (315) all_133_2 = all_118_0
% 22.27/3.93 |
% 22.27/3.93 | GROUND_INST: instantiating (27) with all_116_0, all_133_2, all_91_0,
% 22.27/3.93 | simplifying with (295), (299) gives:
% 22.27/3.93 | (316) all_133_2 = all_116_0
% 22.27/3.93 |
% 22.27/3.93 | GROUND_INST: instantiating (27) with all_130_0, all_136_0, all_91_0,
% 22.27/3.93 | simplifying with (294), (296) gives:
% 22.27/3.93 | (317) all_136_0 = all_130_0
% 22.27/3.93 |
% 22.27/3.93 | GROUND_INST: instantiating (27) with all_93_2, all_136_0, all_91_0,
% 22.27/3.93 | simplifying with (294), (305) gives:
% 22.27/3.93 | (318) all_136_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (317), (318) imply:
% 22.27/3.93 | (319) all_130_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (319) implies:
% 22.27/3.93 | (320) all_130_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (314), (315) imply:
% 22.27/3.93 | (321) all_121_0 = all_118_0
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (321) implies:
% 22.27/3.93 | (322) all_121_0 = all_118_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (315), (316) imply:
% 22.27/3.93 | (323) all_118_0 = all_116_0
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (313), (320) imply:
% 22.27/3.93 | (324) all_121_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (324) implies:
% 22.27/3.93 | (325) all_121_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (322), (325) imply:
% 22.27/3.93 | (326) all_118_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (326) implies:
% 22.27/3.93 | (327) all_118_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (323), (327) imply:
% 22.27/3.93 | (328) all_116_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (328) implies:
% 22.27/3.93 | (329) all_116_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (312), (329) imply:
% 22.27/3.93 | (330) all_113_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (330) implies:
% 22.27/3.93 | (331) all_113_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (311), (331) imply:
% 22.27/3.93 | (332) all_105_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (332) implies:
% 22.27/3.93 | (333) all_105_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (310), (333) imply:
% 22.27/3.93 | (334) all_103_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (334) implies:
% 22.27/3.93 | (335) all_103_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (309), (335) imply:
% 22.27/3.93 | (336) all_101_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (336) implies:
% 22.27/3.93 | (337) all_101_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | COMBINE_EQS: (308), (337) imply:
% 22.27/3.93 | (338) all_99_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | SIMP: (338) implies:
% 22.27/3.93 | (339) all_99_0 = all_93_2
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (306), (329) imply:
% 22.27/3.93 | (340) power_power_int(all_86_0, all_93_2) = zero_zero_int
% 22.27/3.93 |
% 22.27/3.93 | GROUND_INST: instantiating (fact_52_zadd__commute) with one_one_int, all_86_1,
% 22.27/3.93 | all_86_0, simplifying with (24), (45), (244) gives:
% 22.27/3.93 | (341) plus_plus_int(all_86_1, one_one_int) = all_86_0 & int(all_86_0)
% 22.27/3.93 |
% 22.27/3.93 | ALPHA: (341) implies:
% 22.27/3.93 | (342) int(all_86_0)
% 22.27/3.93 |
% 22.27/3.93 | GROUND_INST: instantiating (20) with all_86_0, all_91_0, all_93_2, simplifying
% 22.27/3.93 | with (305), (307), (340), (342) gives:
% 22.27/3.93 | (343) all_86_0 = zero_zero_int & ~ (all_93_2 = zero_zero_nat)
% 22.27/3.93 |
% 22.27/3.93 | ALPHA: (343) implies:
% 22.27/3.93 | (344) all_86_0 = zero_zero_int
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (44), (344) imply:
% 22.27/3.93 | (345) ord_less_int(zero_zero_int, zero_zero_int) = 0
% 22.27/3.93 |
% 22.27/3.93 | GROUND_INST: instantiating (30) with all_69_0, 0, zero_zero_int,
% 22.27/3.93 | zero_zero_int, simplifying with (139), (345) gives:
% 22.27/3.93 | (346) all_69_0 = 0
% 22.27/3.93 |
% 22.27/3.93 | REDUCE: (227), (346) imply:
% 22.27/3.93 | (347) $false
% 22.27/3.94 |
% 22.27/3.94 | CLOSE: (347) is inconsistent.
% 22.27/3.94 |
% 22.27/3.94 End of proof
% 22.27/3.94 % SZS output end Proof for theBenchmark
% 22.27/3.94
% 22.27/3.94 3334ms
%------------------------------------------------------------------------------