TSTP Solution File: KLE022+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE022+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n020.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 05:34:16 EDT 2023
% Result : Theorem 106.17s 15.31s
% Output : Proof 107.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE022+4 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 11:58:13 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.53/0.66 ________ _____
% 0.53/0.66 ___ __ \_________(_)________________________________
% 0.53/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.53/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.53/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.53/0.66
% 0.53/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.53/0.66 (2023-06-19)
% 0.53/0.66
% 0.53/0.66 (c) Philipp Rümmer, 2009-2023
% 0.53/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.53/0.66 Amanda Stjerna.
% 0.53/0.66 Free software under BSD-3-Clause.
% 0.53/0.66
% 0.53/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.53/0.66
% 0.53/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.53/0.68 Running up to 7 provers in parallel.
% 0.53/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.53/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.53/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.53/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.53/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.53/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.53/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.69/1.16 Prover 1: Preprocessing ...
% 2.69/1.16 Prover 4: Preprocessing ...
% 2.89/1.22 Prover 6: Preprocessing ...
% 2.89/1.22 Prover 3: Preprocessing ...
% 2.89/1.22 Prover 0: Preprocessing ...
% 2.89/1.22 Prover 2: Preprocessing ...
% 2.89/1.24 Prover 5: Preprocessing ...
% 6.49/1.74 Prover 1: Constructing countermodel ...
% 6.49/1.75 Prover 3: Constructing countermodel ...
% 6.91/1.76 Prover 6: Proving ...
% 6.91/1.80 Prover 5: Proving ...
% 6.91/1.84 Prover 0: Proving ...
% 6.91/1.84 Prover 4: Constructing countermodel ...
% 7.56/1.86 Prover 2: Proving ...
% 9.30/2.16 Prover 3: gave up
% 9.30/2.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.87/2.22 Prover 7: Preprocessing ...
% 12.10/2.50 Prover 7: Constructing countermodel ...
% 65.17/9.81 Prover 2: stopped
% 65.17/9.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 66.06/9.87 Prover 8: Preprocessing ...
% 67.08/9.97 Prover 8: Warning: ignoring some quantifiers
% 67.16/9.97 Prover 8: Constructing countermodel ...
% 68.88/10.23 Prover 8: gave up
% 68.88/10.24 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 69.52/10.28 Prover 9: Preprocessing ...
% 70.54/10.51 Prover 9: Constructing countermodel ...
% 96.95/14.02 Prover 5: stopped
% 97.72/14.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 97.72/14.06 Prover 10: Preprocessing ...
% 98.75/14.17 Prover 10: Constructing countermodel ...
% 98.99/14.31 Prover 10: gave up
% 98.99/14.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 99.60/14.36 Prover 11: Preprocessing ...
% 99.60/14.43 Prover 11: Constructing countermodel ...
% 104.63/14.97 Prover 11: Found proof (size 112)
% 104.63/14.97 Prover 11: proved (656ms)
% 104.63/14.98 Prover 7: stopped
% 104.63/14.98 Prover 9: stopped
% 104.63/14.98 Prover 1: stopped
% 104.63/14.99 Prover 6: stopped
% 104.63/14.99 Prover 4: stopped
% 106.17/15.31 Prover 0: stopped
% 106.17/15.31
% 106.17/15.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.17/15.31
% 106.17/15.32 % SZS output start Proof for theBenchmark
% 106.17/15.33 Assumptions after simplification:
% 106.17/15.33 ---------------------------------
% 106.17/15.33
% 106.17/15.33 (additive_commutativity)
% 106.50/15.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~
% 106.50/15.37 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 106.50/15.37 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 106.50/15.37 (addition(v1, v0) = v2 & $i(v2)))
% 106.50/15.37
% 106.50/15.37 (additive_idempotence)
% 106.50/15.37 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~ $i(v0))
% 106.50/15.37
% 106.50/15.37 (goals)
% 106.55/15.38 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 106.55/15.38 $i] : ? [v6: int] : ? [v7: int] : (c(v1) = v3 & test(v1) = 0 &
% 106.55/15.38 multiplication(v0, v3) = v4 & multiplication(v0, v1) = v2 & addition(v2, v4)
% 106.55/15.38 = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (( ~ (v7 = 0) &
% 106.55/15.38 leq(v5, v0) = v7) | ( ~ (v6 = 0) & leq(v0, v5) = v6)))
% 106.55/15.38
% 106.55/15.38 (multiplicative_right_identity)
% 106.55/15.38 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 106.55/15.38 v1) | ~ $i(v0))
% 106.55/15.38
% 106.55/15.38 (order)
% 106.55/15.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (addition(v0, v1) =
% 106.55/15.39 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1) =
% 106.55/15.39 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0,
% 106.55/15.39 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 106.55/15.39 addition(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 106.55/15.39 (leq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | addition(v0, v1) = v1) & ! [v0:
% 106.55/15.39 $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) | ~ $i(v0) |
% 106.55/15.39 leq(v0, v1) = 0)
% 106.55/15.39
% 106.55/15.39 (right_distributivity)
% 106.55/15.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 106.55/15.39 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) |
% 106.55/15.39 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 106.55/15.39 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5))) &
% 106.55/15.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 106.55/15.39 (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~ $i(v2) | ~
% 106.55/15.39 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v0, v2) =
% 106.55/15.39 v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5)
% 106.55/15.39 & $i(v4)))
% 106.55/15.39
% 106.55/15.39 (test_1)
% 106.55/15.40 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (test(v0) = v1) | ~
% 106.55/15.40 (complement(v2, v0) = 0) | ~ $i(v2) | ~ $i(v0)) & ! [v0: $i] : ( ~
% 106.55/15.40 (test(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (complement(v1, v0) = 0 &
% 106.55/15.40 $i(v1)))
% 106.55/15.40
% 106.55/15.40 (test_2)
% 106.72/15.41 $i(one) & $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 106.72/15.41 (complement(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 106.72/15.41 $i] : ? [v5: $i] : (( ~ (v5 = one) & addition(v0, v1) = v5 & $i(v5)) | (
% 106.72/15.41 ~ (v4 = zero) & multiplication(v1, v0) = v4 & $i(v4)) | ( ~ (v3 = zero)
% 106.72/15.41 & multiplication(v0, v1) = v3 & $i(v3)))) & ! [v0: $i] : ! [v1: $i] :
% 106.72/15.41 ! [v2: $i] : ( ~ (multiplication(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 106.72/15.41 [v3: int] : ? [v4: $i] : ? [v5: $i] : ((v5 = one & v4 = zero & v2 = zero &
% 106.72/15.41 multiplication(v0, v1) = zero & addition(v0, v1) = one) | ( ~ (v3 = 0) &
% 106.72/15.41 complement(v1, v0) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 106.72/15.41 ~ (multiplication(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ?
% 106.72/15.41 [v4: $i] : ? [v5: $i] : ((v5 = one & v4 = zero & v2 = zero &
% 106.72/15.41 multiplication(v1, v0) = zero & addition(v0, v1) = one) | ( ~ (v3 = 0) &
% 106.72/15.41 complement(v1, v0) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 106.72/15.41 ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4:
% 106.72/15.41 $i] : ? [v5: $i] : ((v5 = zero & v4 = zero & v2 = one &
% 106.72/15.41 multiplication(v1, v0) = zero & multiplication(v0, v1) = zero) | ( ~ (v3
% 106.72/15.41 = 0) & complement(v1, v0) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 106.72/15.41 (complement(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | (multiplication(v1, v0) =
% 106.72/15.41 zero & multiplication(v0, v1) = zero & addition(v0, v1) = one)) & ! [v0:
% 106.72/15.41 $i] : ! [v1: $i] : ( ~ (multiplication(v1, v0) = zero) | ~ $i(v1) | ~
% 106.72/15.41 $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 &
% 106.72/15.41 complement(v1, v0) = 0) | ( ~ (v3 = one) & addition(v0, v1) = v3 &
% 106.72/15.41 $i(v3)) | ( ~ (v2 = zero) & multiplication(v0, v1) = v2 & $i(v2)))) & !
% 106.72/15.41 [v0: $i] : ! [v1: $i] : ( ~ (multiplication(v0, v1) = zero) | ~ $i(v1) | ~
% 106.72/15.41 $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 &
% 106.72/15.41 complement(v1, v0) = 0) | ( ~ (v3 = one) & addition(v0, v1) = v3 &
% 106.72/15.41 $i(v3)) | ( ~ (v2 = zero) & multiplication(v1, v0) = v2 & $i(v2)))) & !
% 106.72/15.41 [v0: $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = one) | ~ $i(v1) | ~ $i(v0)
% 106.72/15.41 | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 & complement(v1, v0) =
% 106.72/15.41 0) | ( ~ (v3 = zero) & multiplication(v1, v0) = v3 & $i(v3)) | ( ~ (v2 =
% 106.72/15.41 zero) & multiplication(v0, v1) = v2 & $i(v2))))
% 106.72/15.41
% 106.72/15.41 (test_3)
% 106.72/15.42 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (complement(v0, v1) = v2) | ~
% 106.72/15.42 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : (( ~ (v3 = 0) & test(v0) =
% 106.72/15.42 v3) | (( ~ (v2 = 0) | (v4 = v1 & c(v0) = v1)) & (v2 = 0 | ( ~ (v4 = v1)
% 106.72/15.42 & c(v0) = v4 & $i(v4))))))
% 106.72/15.42
% 106.72/15.42 (function-axioms)
% 106.72/15.42 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 106.72/15.42 [v3: $i] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3, v2) =
% 106.72/15.42 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 106.72/15.42 $i] : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) =
% 106.72/15.42 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 106.72/15.42 ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & !
% 106.72/15.42 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 106.72/15.42 (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : !
% 106.72/15.42 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) & !
% 106.72/15.42 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 106.72/15.42 | ~ (test(v2) = v1) | ~ (test(v2) = v0))
% 106.72/15.42
% 106.72/15.42 Further assumptions not needed in the proof:
% 106.72/15.42 --------------------------------------------
% 106.72/15.42 additive_associativity, additive_identity, left_annihilation,
% 106.72/15.42 left_distributivity, multiplicative_associativity, multiplicative_left_identity,
% 106.72/15.42 right_annihilation, test_4, test_deMorgan1, test_deMorgan2
% 106.72/15.42
% 106.72/15.42 Those formulas are unsatisfiable:
% 106.72/15.42 ---------------------------------
% 106.72/15.42
% 106.72/15.42 Begin of proof
% 106.72/15.42 |
% 106.72/15.42 | ALPHA: (additive_commutativity) implies:
% 106.72/15.43 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) |
% 106.72/15.43 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2)))
% 106.72/15.43 |
% 106.72/15.43 | ALPHA: (multiplicative_right_identity) implies:
% 106.72/15.43 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 106.72/15.43 | v1) | ~ $i(v0))
% 106.72/15.43 |
% 106.72/15.43 | ALPHA: (right_distributivity) implies:
% 106.83/15.43 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 106.83/15.43 | ! [v5: $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0,
% 106.83/15.43 | v1) = v3) | ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) |
% 106.83/15.43 | ~ $i(v0) | ? [v6: $i] : (multiplication(v0, v6) = v5 & addition(v1,
% 106.83/15.43 | v2) = v6 & $i(v6) & $i(v5)))
% 106.83/15.43 |
% 106.83/15.43 | ALPHA: (order) implies:
% 106.83/15.43 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) =
% 106.83/15.43 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 106.83/15.43 | addition(v0, v1) = v3 & $i(v3)))
% 106.83/15.43 |
% 106.83/15.43 | ALPHA: (test_1) implies:
% 106.83/15.43 | (5) ! [v0: $i] : ( ~ (test(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 106.83/15.43 | (complement(v1, v0) = 0 & $i(v1)))
% 106.83/15.43 |
% 106.83/15.43 | ALPHA: (test_2) implies:
% 106.83/15.44 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (multiplication(v1, v0) = zero) | ~
% 106.83/15.44 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ((v4
% 106.83/15.44 | = 0 & complement(v1, v0) = 0) | ( ~ (v3 = one) & addition(v0, v1)
% 106.83/15.44 | = v3 & $i(v3)) | ( ~ (v2 = zero) & multiplication(v0, v1) = v2 &
% 106.83/15.44 | $i(v2))))
% 106.83/15.44 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (complement(v1, v0) = 0) | ~ $i(v1) |
% 106.83/15.44 | ~ $i(v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) =
% 106.83/15.44 | zero & addition(v0, v1) = one))
% 106.83/15.44 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) |
% 106.83/15.44 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: $i] :
% 106.83/15.44 | ((v5 = zero & v4 = zero & v2 = one & multiplication(v1, v0) = zero &
% 106.83/15.44 | multiplication(v0, v1) = zero) | ( ~ (v3 = 0) & complement(v1,
% 106.83/15.44 | v0) = v3)))
% 106.83/15.44 |
% 106.83/15.44 | ALPHA: (function-axioms) implies:
% 106.83/15.44 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 106.83/15.44 | (v1 = v0 | ~ (test(v2) = v1) | ~ (test(v2) = v0))
% 106.83/15.44 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) |
% 106.83/15.44 | ~ (c(v2) = v0))
% 106.83/15.44 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 106.83/15.44 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 106.83/15.44 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 106.83/15.44 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 106.83/15.45 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 106.83/15.45 | : ! [v3: $i] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~
% 106.83/15.45 | (complement(v3, v2) = v0))
% 106.83/15.45 |
% 106.83/15.45 | DELTA: instantiating (goals) with fresh symbols all_22_0, all_22_1, all_22_2,
% 106.83/15.45 | all_22_3, all_22_4, all_22_5, all_22_6, all_22_7 gives:
% 106.83/15.45 | (14) c(all_22_6) = all_22_4 & test(all_22_6) = 0 & multiplication(all_22_7,
% 106.83/15.45 | all_22_4) = all_22_3 & multiplication(all_22_7, all_22_6) = all_22_5
% 106.83/15.45 | & addition(all_22_5, all_22_3) = all_22_2 & $i(all_22_2) &
% 106.83/15.45 | $i(all_22_3) & $i(all_22_4) & $i(all_22_5) & $i(all_22_6) &
% 106.83/15.45 | $i(all_22_7) & (( ~ (all_22_0 = 0) & leq(all_22_2, all_22_7) =
% 106.83/15.45 | all_22_0) | ( ~ (all_22_1 = 0) & leq(all_22_7, all_22_2) =
% 106.83/15.45 | all_22_1))
% 106.83/15.45 |
% 106.83/15.45 | ALPHA: (14) implies:
% 106.83/15.45 | (15) $i(all_22_7)
% 106.83/15.45 | (16) $i(all_22_6)
% 106.83/15.45 | (17) $i(all_22_5)
% 106.83/15.45 | (18) $i(all_22_4)
% 106.83/15.45 | (19) $i(all_22_3)
% 106.83/15.45 | (20) addition(all_22_5, all_22_3) = all_22_2
% 106.83/15.45 | (21) multiplication(all_22_7, all_22_6) = all_22_5
% 106.83/15.45 | (22) multiplication(all_22_7, all_22_4) = all_22_3
% 106.83/15.45 | (23) test(all_22_6) = 0
% 106.83/15.45 | (24) c(all_22_6) = all_22_4
% 106.83/15.45 | (25) ( ~ (all_22_0 = 0) & leq(all_22_2, all_22_7) = all_22_0) | ( ~
% 106.83/15.45 | (all_22_1 = 0) & leq(all_22_7, all_22_2) = all_22_1)
% 106.83/15.45 |
% 106.83/15.45 | GROUND_INST: instantiating (1) with all_22_3, all_22_5, all_22_2, simplifying
% 106.83/15.45 | with (17), (19), (20) gives:
% 106.83/15.46 | (26) addition(all_22_3, all_22_5) = all_22_2 & $i(all_22_2)
% 106.83/15.46 |
% 106.83/15.46 | ALPHA: (26) implies:
% 106.83/15.46 | (27) addition(all_22_3, all_22_5) = all_22_2
% 106.83/15.46 |
% 106.83/15.46 | GROUND_INST: instantiating (3) with all_22_7, all_22_6, all_22_4, all_22_5,
% 106.83/15.46 | all_22_3, all_22_2, simplifying with (15), (16), (18), (20),
% 106.83/15.46 | (21), (22) gives:
% 106.83/15.46 | (28) ? [v0: $i] : (multiplication(all_22_7, v0) = all_22_2 &
% 106.83/15.46 | addition(all_22_6, all_22_4) = v0 & $i(v0) & $i(all_22_2))
% 106.83/15.46 |
% 106.83/15.46 | GROUND_INST: instantiating (5) with all_22_6, simplifying with (16), (23)
% 106.83/15.46 | gives:
% 106.83/15.46 | (29) ? [v0: $i] : (complement(v0, all_22_6) = 0 & $i(v0))
% 106.83/15.46 |
% 106.83/15.46 | DELTA: instantiating (29) with fresh symbol all_30_0 gives:
% 106.83/15.46 | (30) complement(all_30_0, all_22_6) = 0 & $i(all_30_0)
% 106.83/15.46 |
% 106.83/15.46 | ALPHA: (30) implies:
% 106.83/15.46 | (31) $i(all_30_0)
% 106.83/15.46 | (32) complement(all_30_0, all_22_6) = 0
% 106.83/15.46 |
% 106.83/15.46 | DELTA: instantiating (28) with fresh symbol all_32_0 gives:
% 106.83/15.46 | (33) multiplication(all_22_7, all_32_0) = all_22_2 & addition(all_22_6,
% 106.83/15.46 | all_22_4) = all_32_0 & $i(all_32_0) & $i(all_22_2)
% 106.83/15.46 |
% 106.83/15.46 | ALPHA: (33) implies:
% 106.83/15.46 | (34) addition(all_22_6, all_22_4) = all_32_0
% 106.83/15.46 |
% 106.83/15.46 | GROUND_INST: instantiating (1) with all_22_4, all_22_6, all_32_0, simplifying
% 106.83/15.46 | with (16), (18), (34) gives:
% 106.83/15.46 | (35) addition(all_22_4, all_22_6) = all_32_0 & $i(all_32_0)
% 106.83/15.46 |
% 106.83/15.46 | ALPHA: (35) implies:
% 106.83/15.46 | (36) addition(all_22_4, all_22_6) = all_32_0
% 106.83/15.46 |
% 106.83/15.46 | GROUND_INST: instantiating (8) with all_22_6, all_22_4, all_32_0, simplifying
% 106.83/15.46 | with (16), (18), (34) gives:
% 106.83/15.47 | (37) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ((v2 = zero & v1 = zero &
% 106.83/15.47 | all_32_0 = one & multiplication(all_22_4, all_22_6) = zero &
% 106.83/15.47 | multiplication(all_22_6, all_22_4) = zero) | ( ~ (v0 = 0) &
% 106.83/15.47 | complement(all_22_4, all_22_6) = v0))
% 106.83/15.47 |
% 106.83/15.47 | GROUND_INST: instantiating (3) with all_22_7, all_22_4, all_22_6, all_22_3,
% 106.83/15.47 | all_22_5, all_22_2, simplifying with (15), (16), (18), (21),
% 106.83/15.47 | (22), (27) gives:
% 106.83/15.47 | (38) ? [v0: $i] : (multiplication(all_22_7, v0) = all_22_2 &
% 106.83/15.47 | addition(all_22_4, all_22_6) = v0 & $i(v0) & $i(all_22_2))
% 106.83/15.47 |
% 106.83/15.47 | GROUND_INST: instantiating (7) with all_22_6, all_30_0, simplifying with (16),
% 106.83/15.47 | (31), (32) gives:
% 106.83/15.47 | (39) multiplication(all_30_0, all_22_6) = zero & multiplication(all_22_6,
% 106.83/15.47 | all_30_0) = zero & addition(all_22_6, all_30_0) = one
% 106.83/15.47 |
% 106.83/15.47 | ALPHA: (39) implies:
% 106.83/15.47 | (40) addition(all_22_6, all_30_0) = one
% 106.83/15.47 | (41) multiplication(all_22_6, all_30_0) = zero
% 106.83/15.47 | (42) multiplication(all_30_0, all_22_6) = zero
% 106.83/15.47 |
% 106.83/15.47 | DELTA: instantiating (38) with fresh symbol all_48_0 gives:
% 106.83/15.47 | (43) multiplication(all_22_7, all_48_0) = all_22_2 & addition(all_22_4,
% 106.83/15.47 | all_22_6) = all_48_0 & $i(all_48_0) & $i(all_22_2)
% 106.83/15.47 |
% 106.83/15.47 | ALPHA: (43) implies:
% 106.83/15.47 | (44) $i(all_22_2)
% 106.83/15.47 | (45) addition(all_22_4, all_22_6) = all_48_0
% 106.83/15.47 | (46) multiplication(all_22_7, all_48_0) = all_22_2
% 106.83/15.47 |
% 106.83/15.47 | DELTA: instantiating (37) with fresh symbols all_52_0, all_52_1, all_52_2
% 106.83/15.47 | gives:
% 106.83/15.47 | (47) (all_52_0 = zero & all_52_1 = zero & all_32_0 = one &
% 106.83/15.47 | multiplication(all_22_4, all_22_6) = zero & multiplication(all_22_6,
% 106.83/15.47 | all_22_4) = zero) | ( ~ (all_52_2 = 0) & complement(all_22_4,
% 106.83/15.47 | all_22_6) = all_52_2)
% 106.83/15.47 |
% 106.83/15.47 | GROUND_INST: instantiating (11) with all_32_0, all_48_0, all_22_6, all_22_4,
% 106.83/15.47 | simplifying with (36), (45) gives:
% 106.83/15.47 | (48) all_48_0 = all_32_0
% 106.83/15.47 |
% 106.83/15.47 | REDUCE: (46), (48) imply:
% 106.83/15.48 | (49) multiplication(all_22_7, all_32_0) = all_22_2
% 106.83/15.48 |
% 106.83/15.48 | GROUND_INST: instantiating (1) with all_30_0, all_22_6, one, simplifying with
% 106.83/15.48 | (16), (31), (40) gives:
% 106.83/15.48 | (50) addition(all_30_0, all_22_6) = one & $i(one)
% 106.83/15.48 |
% 106.83/15.48 | ALPHA: (50) implies:
% 106.83/15.48 | (51) addition(all_30_0, all_22_6) = one
% 106.83/15.48 |
% 106.83/15.48 | GROUND_INST: instantiating (6) with all_30_0, all_22_6, simplifying with (16),
% 106.83/15.48 | (31), (41) gives:
% 106.83/15.48 | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ((v2 = 0 &
% 106.83/15.48 | complement(all_22_6, all_30_0) = 0) | ( ~ (v1 = one) &
% 106.83/15.48 | addition(all_30_0, all_22_6) = v1 & $i(v1)) | ( ~ (v0 = zero) &
% 106.83/15.48 | multiplication(all_30_0, all_22_6) = v0 & $i(v0)))
% 106.83/15.48 |
% 106.83/15.48 | DELTA: instantiating (52) with fresh symbols all_71_0, all_71_1, all_71_2
% 106.83/15.48 | gives:
% 106.83/15.48 | (53) (all_71_0 = 0 & complement(all_22_6, all_30_0) = 0) | ( ~ (all_71_1 =
% 106.83/15.48 | one) & addition(all_30_0, all_22_6) = all_71_1 & $i(all_71_1)) | (
% 106.83/15.48 | ~ (all_71_2 = zero) & multiplication(all_30_0, all_22_6) = all_71_2
% 106.83/15.48 | & $i(all_71_2))
% 106.83/15.48 |
% 106.83/15.48 | BETA: splitting (53) gives:
% 106.83/15.48 |
% 106.83/15.48 | Case 1:
% 106.83/15.48 | |
% 106.83/15.48 | | (54) all_71_0 = 0 & complement(all_22_6, all_30_0) = 0
% 106.83/15.48 | |
% 106.83/15.48 | | ALPHA: (54) implies:
% 106.83/15.48 | | (55) complement(all_22_6, all_30_0) = 0
% 106.83/15.48 | |
% 106.83/15.48 | | GROUND_INST: instantiating (test_3) with all_22_6, all_30_0, 0, simplifying
% 106.83/15.48 | | with (16), (31), (55) gives:
% 106.83/15.48 | | (56) ? [v0: int] : ? [v1: int] : ((v1 = all_30_0 & c(all_22_6) =
% 106.83/15.48 | | all_30_0) | ( ~ (v0 = 0) & test(all_22_6) = v0))
% 106.83/15.48 | |
% 106.83/15.48 | | DELTA: instantiating (56) with fresh symbols all_98_0, all_98_1 gives:
% 106.83/15.48 | | (57) (all_98_0 = all_30_0 & c(all_22_6) = all_30_0) | ( ~ (all_98_1 = 0)
% 106.83/15.48 | | & test(all_22_6) = all_98_1)
% 106.83/15.48 | |
% 106.83/15.49 | | BETA: splitting (25) gives:
% 106.83/15.49 | |
% 106.83/15.49 | | Case 1:
% 106.83/15.49 | | |
% 106.83/15.49 | | | (58) ~ (all_22_0 = 0) & leq(all_22_2, all_22_7) = all_22_0
% 106.83/15.49 | | |
% 106.83/15.49 | | | ALPHA: (58) implies:
% 106.83/15.49 | | | (59) ~ (all_22_0 = 0)
% 106.83/15.49 | | | (60) leq(all_22_2, all_22_7) = all_22_0
% 106.83/15.49 | | |
% 106.83/15.49 | | | BETA: splitting (57) gives:
% 106.83/15.49 | | |
% 106.83/15.49 | | | Case 1:
% 106.83/15.49 | | | |
% 106.83/15.49 | | | | (61) all_98_0 = all_30_0 & c(all_22_6) = all_30_0
% 106.83/15.49 | | | |
% 106.83/15.49 | | | | ALPHA: (61) implies:
% 106.83/15.49 | | | | (62) c(all_22_6) = all_30_0
% 106.83/15.49 | | | |
% 106.83/15.49 | | | | GROUND_INST: instantiating (10) with all_22_4, all_30_0, all_22_6,
% 106.83/15.49 | | | | simplifying with (24), (62) gives:
% 106.83/15.49 | | | | (63) all_30_0 = all_22_4
% 106.83/15.49 | | | |
% 106.83/15.49 | | | | REDUCE: (32), (63) imply:
% 106.83/15.49 | | | | (64) complement(all_22_4, all_22_6) = 0
% 106.83/15.49 | | | |
% 106.83/15.49 | | | | BETA: splitting (47) gives:
% 106.83/15.49 | | | |
% 106.83/15.49 | | | | Case 1:
% 106.83/15.49 | | | | |
% 106.83/15.49 | | | | | (65) all_52_0 = zero & all_52_1 = zero & all_32_0 = one &
% 106.83/15.49 | | | | | multiplication(all_22_4, all_22_6) = zero &
% 106.83/15.49 | | | | | multiplication(all_22_6, all_22_4) = zero
% 106.83/15.49 | | | | |
% 106.83/15.49 | | | | | ALPHA: (65) implies:
% 106.83/15.49 | | | | | (66) all_32_0 = one
% 106.83/15.49 | | | | |
% 106.83/15.49 | | | | | REDUCE: (49), (66) imply:
% 106.83/15.49 | | | | | (67) multiplication(all_22_7, one) = all_22_2
% 106.83/15.49 | | | | |
% 106.83/15.49 | | | | | GROUND_INST: instantiating (2) with all_22_7, all_22_2, simplifying
% 106.83/15.49 | | | | | with (15), (67) gives:
% 106.83/15.49 | | | | | (68) all_22_2 = all_22_7
% 106.83/15.49 | | | | |
% 106.83/15.49 | | | | | GROUND_INST: instantiating (4) with all_22_2, all_22_7, all_22_0,
% 106.83/15.49 | | | | | simplifying with (15), (44), (60) gives:
% 106.83/15.49 | | | | | (69) all_22_0 = 0 | ? [v0: any] : ( ~ (v0 = all_22_7) &
% 106.83/15.49 | | | | | addition(all_22_2, all_22_7) = v0 & $i(v0))
% 106.83/15.49 | | | | |
% 106.83/15.49 | | | | | BETA: splitting (69) gives:
% 106.83/15.49 | | | | |
% 106.83/15.49 | | | | | Case 1:
% 106.83/15.49 | | | | | |
% 106.83/15.49 | | | | | | (70) all_22_0 = 0
% 106.83/15.49 | | | | | |
% 106.83/15.49 | | | | | | REDUCE: (59), (70) imply:
% 106.83/15.49 | | | | | | (71) $false
% 106.83/15.49 | | | | | |
% 106.83/15.49 | | | | | | CLOSE: (71) is inconsistent.
% 106.83/15.49 | | | | | |
% 106.83/15.49 | | | | | Case 2:
% 106.83/15.49 | | | | | |
% 106.83/15.50 | | | | | | (72) ? [v0: any] : ( ~ (v0 = all_22_7) & addition(all_22_2,
% 106.83/15.50 | | | | | | all_22_7) = v0 & $i(v0))
% 106.83/15.50 | | | | | |
% 106.83/15.50 | | | | | | DELTA: instantiating (72) with fresh symbol all_128_0 gives:
% 106.83/15.50 | | | | | | (73) ~ (all_128_0 = all_22_7) & addition(all_22_2, all_22_7) =
% 106.83/15.50 | | | | | | all_128_0 & $i(all_128_0)
% 106.83/15.50 | | | | | |
% 106.83/15.50 | | | | | | ALPHA: (73) implies:
% 106.83/15.50 | | | | | | (74) ~ (all_128_0 = all_22_7)
% 106.83/15.50 | | | | | | (75) addition(all_22_2, all_22_7) = all_128_0
% 106.83/15.50 | | | | | |
% 106.83/15.50 | | | | | | REDUCE: (68), (75) imply:
% 106.83/15.50 | | | | | | (76) addition(all_22_7, all_22_7) = all_128_0
% 106.83/15.50 | | | | | |
% 106.83/15.50 | | | | | | GROUND_INST: instantiating (additive_idempotence) with all_22_7,
% 106.83/15.50 | | | | | | all_128_0, simplifying with (15), (76) gives:
% 106.83/15.50 | | | | | | (77) all_128_0 = all_22_7
% 106.83/15.50 | | | | | |
% 106.83/15.50 | | | | | | REDUCE: (74), (77) imply:
% 106.83/15.50 | | | | | | (78) $false
% 106.83/15.50 | | | | | |
% 106.83/15.50 | | | | | | CLOSE: (78) is inconsistent.
% 106.83/15.50 | | | | | |
% 106.83/15.50 | | | | | End of split
% 106.83/15.50 | | | | |
% 106.83/15.50 | | | | Case 2:
% 106.83/15.50 | | | | |
% 106.83/15.50 | | | | | (79) ~ (all_52_2 = 0) & complement(all_22_4, all_22_6) = all_52_2
% 106.83/15.50 | | | | |
% 106.83/15.50 | | | | | REF_CLOSE: (13), (64), (79) are inconsistent by sub-proof #1.
% 106.83/15.50 | | | | |
% 106.83/15.50 | | | | End of split
% 106.83/15.50 | | | |
% 106.83/15.50 | | | Case 2:
% 106.83/15.50 | | | |
% 106.83/15.50 | | | | (80) ~ (all_98_1 = 0) & test(all_22_6) = all_98_1
% 106.83/15.50 | | | |
% 106.83/15.50 | | | | ALPHA: (80) implies:
% 106.83/15.50 | | | | (81) ~ (all_98_1 = 0)
% 106.83/15.50 | | | | (82) test(all_22_6) = all_98_1
% 106.83/15.50 | | | |
% 106.83/15.50 | | | | GROUND_INST: instantiating (9) with 0, all_98_1, all_22_6, simplifying
% 106.83/15.50 | | | | with (23), (82) gives:
% 106.83/15.50 | | | | (83) all_98_1 = 0
% 106.83/15.50 | | | |
% 106.83/15.50 | | | | REDUCE: (81), (83) imply:
% 106.83/15.50 | | | | (84) $false
% 106.83/15.50 | | | |
% 106.83/15.50 | | | | CLOSE: (84) is inconsistent.
% 106.83/15.50 | | | |
% 106.83/15.50 | | | End of split
% 106.83/15.50 | | |
% 106.83/15.50 | | Case 2:
% 106.83/15.50 | | |
% 106.83/15.50 | | | (85) ~ (all_22_1 = 0) & leq(all_22_7, all_22_2) = all_22_1
% 106.83/15.50 | | |
% 106.83/15.50 | | | ALPHA: (85) implies:
% 106.83/15.50 | | | (86) ~ (all_22_1 = 0)
% 106.83/15.50 | | | (87) leq(all_22_7, all_22_2) = all_22_1
% 106.83/15.50 | | |
% 106.83/15.50 | | | BETA: splitting (57) gives:
% 106.83/15.50 | | |
% 106.83/15.50 | | | Case 1:
% 106.83/15.50 | | | |
% 106.83/15.50 | | | | (88) all_98_0 = all_30_0 & c(all_22_6) = all_30_0
% 106.83/15.50 | | | |
% 106.83/15.50 | | | | ALPHA: (88) implies:
% 106.83/15.50 | | | | (89) c(all_22_6) = all_30_0
% 106.83/15.50 | | | |
% 106.83/15.50 | | | | GROUND_INST: instantiating (10) with all_22_4, all_30_0, all_22_6,
% 106.83/15.50 | | | | simplifying with (24), (89) gives:
% 106.83/15.50 | | | | (90) all_30_0 = all_22_4
% 106.83/15.50 | | | |
% 106.83/15.50 | | | | REDUCE: (32), (90) imply:
% 106.83/15.51 | | | | (91) complement(all_22_4, all_22_6) = 0
% 106.83/15.51 | | | |
% 106.83/15.51 | | | | BETA: splitting (47) gives:
% 106.83/15.51 | | | |
% 106.83/15.51 | | | | Case 1:
% 106.83/15.51 | | | | |
% 106.83/15.51 | | | | | (92) all_52_0 = zero & all_52_1 = zero & all_32_0 = one &
% 106.83/15.51 | | | | | multiplication(all_22_4, all_22_6) = zero &
% 106.83/15.51 | | | | | multiplication(all_22_6, all_22_4) = zero
% 106.83/15.51 | | | | |
% 106.83/15.51 | | | | | ALPHA: (92) implies:
% 106.83/15.51 | | | | | (93) all_32_0 = one
% 106.83/15.51 | | | | |
% 106.83/15.51 | | | | | REDUCE: (49), (93) imply:
% 106.83/15.51 | | | | | (94) multiplication(all_22_7, one) = all_22_2
% 106.83/15.51 | | | | |
% 106.83/15.51 | | | | | GROUND_INST: instantiating (2) with all_22_7, all_22_2, simplifying
% 106.83/15.51 | | | | | with (15), (94) gives:
% 106.83/15.51 | | | | | (95) all_22_2 = all_22_7
% 106.83/15.51 | | | | |
% 106.83/15.51 | | | | | GROUND_INST: instantiating (4) with all_22_7, all_22_2, all_22_1,
% 106.83/15.51 | | | | | simplifying with (15), (44), (87) gives:
% 106.83/15.51 | | | | | (96) all_22_1 = 0 | ? [v0: any] : ( ~ (v0 = all_22_2) &
% 106.83/15.51 | | | | | addition(all_22_7, all_22_2) = v0 & $i(v0))
% 106.83/15.51 | | | | |
% 106.83/15.51 | | | | | BETA: splitting (96) gives:
% 106.83/15.51 | | | | |
% 106.83/15.51 | | | | | Case 1:
% 106.83/15.51 | | | | | |
% 106.83/15.51 | | | | | | (97) all_22_1 = 0
% 106.83/15.51 | | | | | |
% 106.83/15.51 | | | | | | REDUCE: (86), (97) imply:
% 106.83/15.51 | | | | | | (98) $false
% 106.83/15.51 | | | | | |
% 106.83/15.51 | | | | | | CLOSE: (98) is inconsistent.
% 106.83/15.51 | | | | | |
% 106.83/15.51 | | | | | Case 2:
% 106.83/15.51 | | | | | |
% 106.83/15.51 | | | | | | (99) ? [v0: any] : ( ~ (v0 = all_22_2) & addition(all_22_7,
% 106.83/15.51 | | | | | | all_22_2) = v0 & $i(v0))
% 106.83/15.51 | | | | | |
% 106.83/15.51 | | | | | | DELTA: instantiating (99) with fresh symbol all_128_0 gives:
% 106.83/15.51 | | | | | | (100) ~ (all_128_0 = all_22_2) & addition(all_22_7, all_22_2) =
% 106.83/15.51 | | | | | | all_128_0 & $i(all_128_0)
% 106.83/15.51 | | | | | |
% 106.83/15.51 | | | | | | ALPHA: (100) implies:
% 106.83/15.51 | | | | | | (101) ~ (all_128_0 = all_22_2)
% 106.83/15.51 | | | | | | (102) addition(all_22_7, all_22_2) = all_128_0
% 106.83/15.51 | | | | | |
% 106.83/15.51 | | | | | | REDUCE: (95), (101) imply:
% 106.83/15.51 | | | | | | (103) ~ (all_128_0 = all_22_7)
% 106.83/15.51 | | | | | |
% 106.83/15.51 | | | | | | REDUCE: (95), (102) imply:
% 106.83/15.51 | | | | | | (104) addition(all_22_7, all_22_7) = all_128_0
% 106.83/15.51 | | | | | |
% 106.83/15.51 | | | | | | GROUND_INST: instantiating (additive_idempotence) with all_22_7,
% 106.83/15.51 | | | | | | all_128_0, simplifying with (15), (104) gives:
% 106.83/15.51 | | | | | | (105) all_128_0 = all_22_7
% 106.83/15.51 | | | | | |
% 106.83/15.51 | | | | | | REDUCE: (103), (105) imply:
% 106.83/15.51 | | | | | | (106) $false
% 106.83/15.51 | | | | | |
% 106.83/15.51 | | | | | | CLOSE: (106) is inconsistent.
% 106.83/15.51 | | | | | |
% 106.83/15.51 | | | | | End of split
% 106.83/15.51 | | | | |
% 106.83/15.51 | | | | Case 2:
% 106.83/15.51 | | | | |
% 106.83/15.51 | | | | | (107) ~ (all_52_2 = 0) & complement(all_22_4, all_22_6) = all_52_2
% 106.83/15.51 | | | | |
% 106.83/15.51 | | | | | REF_CLOSE: (13), (91), (107) are inconsistent by sub-proof #1.
% 106.83/15.51 | | | | |
% 106.83/15.51 | | | | End of split
% 106.83/15.51 | | | |
% 106.83/15.51 | | | Case 2:
% 106.83/15.51 | | | |
% 106.83/15.51 | | | | (108) ~ (all_98_1 = 0) & test(all_22_6) = all_98_1
% 106.83/15.51 | | | |
% 106.83/15.52 | | | | ALPHA: (108) implies:
% 106.83/15.52 | | | | (109) ~ (all_98_1 = 0)
% 106.83/15.52 | | | | (110) test(all_22_6) = all_98_1
% 106.83/15.52 | | | |
% 106.83/15.52 | | | | GROUND_INST: instantiating (9) with 0, all_98_1, all_22_6, simplifying
% 106.83/15.52 | | | | with (23), (110) gives:
% 106.83/15.52 | | | | (111) all_98_1 = 0
% 106.83/15.52 | | | |
% 106.83/15.52 | | | | REDUCE: (109), (111) imply:
% 106.83/15.52 | | | | (112) $false
% 106.83/15.52 | | | |
% 106.83/15.52 | | | | CLOSE: (112) is inconsistent.
% 106.83/15.52 | | | |
% 106.83/15.52 | | | End of split
% 106.83/15.52 | | |
% 106.83/15.52 | | End of split
% 106.83/15.52 | |
% 106.83/15.52 | Case 2:
% 106.83/15.52 | |
% 106.83/15.52 | | (113) ( ~ (all_71_1 = one) & addition(all_30_0, all_22_6) = all_71_1 &
% 106.83/15.52 | | $i(all_71_1)) | ( ~ (all_71_2 = zero) & multiplication(all_30_0,
% 106.83/15.52 | | all_22_6) = all_71_2 & $i(all_71_2))
% 106.83/15.52 | |
% 106.83/15.52 | | BETA: splitting (113) gives:
% 106.83/15.52 | |
% 106.83/15.52 | | Case 1:
% 106.83/15.52 | | |
% 106.83/15.52 | | | (114) ~ (all_71_1 = one) & addition(all_30_0, all_22_6) = all_71_1 &
% 106.83/15.52 | | | $i(all_71_1)
% 106.83/15.52 | | |
% 106.83/15.52 | | | ALPHA: (114) implies:
% 106.83/15.52 | | | (115) ~ (all_71_1 = one)
% 106.83/15.52 | | | (116) addition(all_30_0, all_22_6) = all_71_1
% 106.83/15.52 | | |
% 106.83/15.52 | | | GROUND_INST: instantiating (11) with one, all_71_1, all_22_6, all_30_0,
% 106.83/15.52 | | | simplifying with (51), (116) gives:
% 106.83/15.52 | | | (117) all_71_1 = one
% 106.83/15.52 | | |
% 107.25/15.52 | | | REDUCE: (115), (117) imply:
% 107.25/15.52 | | | (118) $false
% 107.25/15.52 | | |
% 107.25/15.52 | | | CLOSE: (118) is inconsistent.
% 107.25/15.52 | | |
% 107.25/15.52 | | Case 2:
% 107.25/15.52 | | |
% 107.25/15.52 | | | (119) ~ (all_71_2 = zero) & multiplication(all_30_0, all_22_6) =
% 107.25/15.52 | | | all_71_2 & $i(all_71_2)
% 107.25/15.52 | | |
% 107.25/15.52 | | | ALPHA: (119) implies:
% 107.25/15.52 | | | (120) ~ (all_71_2 = zero)
% 107.25/15.52 | | | (121) multiplication(all_30_0, all_22_6) = all_71_2
% 107.25/15.52 | | |
% 107.25/15.52 | | | GROUND_INST: instantiating (12) with zero, all_71_2, all_22_6, all_30_0,
% 107.25/15.52 | | | simplifying with (42), (121) gives:
% 107.25/15.52 | | | (122) all_71_2 = zero
% 107.25/15.52 | | |
% 107.25/15.52 | | | REDUCE: (120), (122) imply:
% 107.25/15.52 | | | (123) $false
% 107.25/15.52 | | |
% 107.25/15.52 | | | CLOSE: (123) is inconsistent.
% 107.25/15.52 | | |
% 107.25/15.52 | | End of split
% 107.25/15.52 | |
% 107.25/15.52 | End of split
% 107.25/15.52 |
% 107.25/15.52 End of proof
% 107.25/15.52
% 107.25/15.52 Sub-proof #1 shows that the following formulas are inconsistent:
% 107.25/15.52 ----------------------------------------------------------------
% 107.25/15.52 (1) ~ (all_52_2 = 0) & complement(all_22_4, all_22_6) = all_52_2
% 107.25/15.52 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 107.25/15.52 ! [v3: $i] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3,
% 107.25/15.52 v2) = v0))
% 107.25/15.52 (3) complement(all_22_4, all_22_6) = 0
% 107.25/15.52
% 107.25/15.52 Begin of proof
% 107.25/15.52 |
% 107.25/15.52 | ALPHA: (1) implies:
% 107.25/15.52 | (4) ~ (all_52_2 = 0)
% 107.25/15.53 | (5) complement(all_22_4, all_22_6) = all_52_2
% 107.25/15.53 |
% 107.25/15.53 | GROUND_INST: instantiating (2) with 0, all_52_2, all_22_6, all_22_4,
% 107.25/15.53 | simplifying with (3), (5) gives:
% 107.25/15.53 | (6) all_52_2 = 0
% 107.25/15.53 |
% 107.25/15.53 | REDUCE: (4), (6) imply:
% 107.25/15.53 | (7) $false
% 107.25/15.53 |
% 107.25/15.53 | CLOSE: (7) is inconsistent.
% 107.25/15.53 |
% 107.25/15.53 End of proof
% 107.25/15.53 % SZS output end Proof for theBenchmark
% 107.25/15.53
% 107.25/15.53 14861ms
%------------------------------------------------------------------------------