TSTP Solution File: KLE066+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE066+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.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 05:34:26 EDT 2023
% Result : Theorem 34.83s 5.26s
% Output : Proof 141.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : KLE066+1 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.09 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.28 % CPULimit : 300
% 0.13/0.28 % WCLimit : 300
% 0.13/0.28 % DateTime : Tue Aug 29 12:27:01 EDT 2023
% 0.13/0.29 % CPUTime :
% 0.13/0.48 ________ _____
% 0.13/0.48 ___ __ \_________(_)________________________________
% 0.13/0.48 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.13/0.48 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.13/0.48 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.13/0.48
% 0.13/0.48 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.13/0.48 (2023-06-19)
% 0.13/0.48
% 0.13/0.48 (c) Philipp Rümmer, 2009-2023
% 0.13/0.48 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.13/0.48 Amanda Stjerna.
% 0.13/0.48 Free software under BSD-3-Clause.
% 0.13/0.48
% 0.13/0.48 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.13/0.48
% 0.13/0.48 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.13/0.49 Running up to 7 provers in parallel.
% 0.13/0.50 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.13/0.50 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.13/0.50 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.13/0.50 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.13/0.50 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.13/0.50 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.13/0.50 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.19/0.85 Prover 4: Preprocessing ...
% 2.19/0.85 Prover 1: Preprocessing ...
% 2.19/0.89 Prover 5: Preprocessing ...
% 2.19/0.89 Prover 3: Preprocessing ...
% 2.19/0.89 Prover 6: Preprocessing ...
% 2.19/0.89 Prover 2: Preprocessing ...
% 2.19/0.89 Prover 0: Preprocessing ...
% 4.42/1.19 Prover 6: Constructing countermodel ...
% 4.42/1.20 Prover 1: Constructing countermodel ...
% 4.42/1.21 Prover 3: Constructing countermodel ...
% 4.42/1.25 Prover 4: Constructing countermodel ...
% 4.42/1.27 Prover 5: Proving ...
% 4.42/1.32 Prover 0: Proving ...
% 6.68/1.48 Prover 2: Proving ...
% 34.83/5.25 Prover 0: proved (4736ms)
% 34.83/5.26
% 34.83/5.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.83/5.26
% 34.83/5.26 Prover 6: stopped
% 34.83/5.26 Prover 3: stopped
% 34.83/5.27 Prover 2: stopped
% 34.83/5.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 34.83/5.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 34.83/5.28 Prover 5: stopped
% 34.83/5.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 34.83/5.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 34.83/5.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 34.83/5.31 Prover 8: Preprocessing ...
% 35.37/5.32 Prover 13: Preprocessing ...
% 35.37/5.32 Prover 7: Preprocessing ...
% 35.37/5.33 Prover 10: Preprocessing ...
% 35.37/5.34 Prover 11: Preprocessing ...
% 35.78/5.39 Prover 10: Constructing countermodel ...
% 35.78/5.40 Prover 8: Warning: ignoring some quantifiers
% 35.78/5.40 Prover 8: Constructing countermodel ...
% 35.78/5.45 Prover 13: Warning: ignoring some quantifiers
% 36.41/5.46 Prover 13: Constructing countermodel ...
% 36.41/5.46 Prover 7: Constructing countermodel ...
% 36.41/5.47 Prover 11: Constructing countermodel ...
% 71.94/10.26 Prover 13: stopped
% 71.94/10.26 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 71.94/10.29 Prover 16: Preprocessing ...
% 73.05/10.38 Prover 16: Warning: ignoring some quantifiers
% 73.05/10.40 Prover 16: Constructing countermodel ...
% 114.54/15.78 Prover 16: stopped
% 114.54/15.79 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 114.81/15.83 Prover 19: Preprocessing ...
% 114.81/15.85 Prover 1: stopped
% 114.81/15.88 Prover 19: Warning: ignoring some quantifiers
% 114.81/15.88 Prover 19: Constructing countermodel ...
% 140.50/19.53 Prover 19: stopped
% 140.50/19.58 Prover 7: Found proof (size 146)
% 140.50/19.58 Prover 7: proved (14238ms)
% 140.50/19.59 Prover 4: stopped
% 140.50/19.59 Prover 10: stopped
% 140.50/19.59 Prover 8: stopped
% 140.50/19.59 Prover 11: stopped
% 140.50/19.60
% 140.50/19.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 140.50/19.60
% 140.90/19.62 % SZS output start Proof for theBenchmark
% 140.90/19.62 Assumptions after simplification:
% 140.90/19.62 ---------------------------------
% 140.90/19.62
% 140.90/19.62 (additive_identity)
% 140.90/19.66 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1)
% 140.90/19.66 | ~ $i(v0))
% 140.90/19.66
% 140.90/19.66 (domain1)
% 140.90/19.66 ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 140.90/19.67 (multiplication(v1, v0) = v2 & addition(v0, v2) = v2 & $i(v2)))
% 140.90/19.67
% 140.90/19.67 (domain2)
% 141.21/19.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (domain(v1) = v2)
% 141.21/19.67 | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 141.21/19.67 ? [v5: $i] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) =
% 141.21/19.67 v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 141.21/19.67 (multiplication(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 141.21/19.67 [v4: $i] : ? [v5: $i] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) =
% 141.21/19.67 v4 & multiplication(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3)))
% 141.21/19.67
% 141.21/19.67 (domain3)
% 141.21/19.67 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) |
% 141.21/19.67 addition(v1, one) = one)
% 141.21/19.67
% 141.21/19.67 (domain4)
% 141.21/19.67 domain(zero) = zero & $i(zero)
% 141.21/19.67
% 141.21/19.67 (domain5)
% 141.21/19.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 141.21/19.68 (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ~
% 141.21/19.68 $i(v1) | ~ $i(v0) | ? [v5: $i] : (domain(v5) = v4 & addition(v0, v1) = v5
% 141.21/19.68 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 141.21/19.68 (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i]
% 141.21/19.68 : ? [v5: $i] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 &
% 141.21/19.68 addition(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3)))
% 141.21/19.68
% 141.21/19.68 (goals)
% 141.21/19.68 $i(zero) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 141.21/19.68 zero) & domain(v1) = v2 & multiplication(v0, v2) = zero &
% 141.21/19.68 multiplication(v0, v1) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 141.21/19.68
% 141.21/19.68 (left_annihilation)
% 141.21/19.68 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero,
% 141.21/19.68 v0) = v1) | ~ $i(v0))
% 141.21/19.68
% 141.21/19.68 (left_distributivity)
% 141.21/19.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 141.21/19.69 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) |
% 141.21/19.69 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 141.21/19.69 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5))) &
% 141.21/19.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 141.21/19.69 (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ $i(v2) | ~
% 141.21/19.69 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v1, v2) =
% 141.21/19.69 v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5)
% 141.21/19.69 & $i(v4)))
% 141.21/19.69
% 141.21/19.69 (multiplicative_right_identity)
% 141.21/19.69 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 141.21/19.69 v1) | ~ $i(v0))
% 141.21/19.69
% 141.21/19.69 (right_annihilation)
% 141.21/19.69 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(v0,
% 141.21/19.69 zero) = v1) | ~ $i(v0))
% 141.21/19.69
% 141.21/19.69 (function-axioms)
% 141.21/19.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/19.70 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 141.21/19.70 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 141.21/19.70 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 141.21/19.70 [v2: $i] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0))
% 141.21/19.70
% 141.21/19.70 Further assumptions not needed in the proof:
% 141.21/19.70 --------------------------------------------
% 141.21/19.70 additive_associativity, additive_commutativity, additive_idempotence,
% 141.21/19.70 multiplicative_associativity, multiplicative_left_identity, order,
% 141.21/19.70 right_distributivity
% 141.21/19.70
% 141.21/19.70 Those formulas are unsatisfiable:
% 141.21/19.70 ---------------------------------
% 141.21/19.70
% 141.21/19.70 Begin of proof
% 141.21/19.70 |
% 141.21/19.70 | ALPHA: (additive_identity) implies:
% 141.21/19.70 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) |
% 141.21/19.70 | ~ $i(v0))
% 141.21/19.70 |
% 141.21/19.70 | ALPHA: (multiplicative_right_identity) implies:
% 141.21/19.70 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 141.21/19.70 | v1) | ~ $i(v0))
% 141.21/19.70 |
% 141.21/19.70 | ALPHA: (left_distributivity) implies:
% 141.21/19.70 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 141.21/19.70 | ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~
% 141.21/19.70 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 141.21/19.70 | (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 &
% 141.21/19.70 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4)))
% 141.21/19.70 |
% 141.21/19.70 | ALPHA: (right_annihilation) implies:
% 141.21/19.70 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(v0, zero) =
% 141.21/19.70 | v1) | ~ $i(v0))
% 141.21/19.70 |
% 141.21/19.70 | ALPHA: (left_annihilation) implies:
% 141.21/19.71 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero, v0) =
% 141.21/19.71 | v1) | ~ $i(v0))
% 141.21/19.71 |
% 141.21/19.71 | ALPHA: (domain2) implies:
% 141.21/19.71 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (multiplication(v0, v1) =
% 141.21/19.71 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 141.21/19.71 | $i] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 &
% 141.21/19.71 | multiplication(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3)))
% 141.21/19.71 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (domain(v1)
% 141.21/19.71 | = v2) | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) |
% 141.21/19.71 | ? [v4: $i] : ? [v5: $i] : (domain(v4) = v5 & domain(v3) = v5 &
% 141.21/19.71 | multiplication(v0, v1) = v4 & $i(v5) & $i(v4)))
% 141.21/19.71 |
% 141.21/19.71 | ALPHA: (domain3) implies:
% 141.21/19.71 | (8) $i(one)
% 141.21/19.71 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) |
% 141.21/19.71 | addition(v1, one) = one)
% 141.21/19.71 |
% 141.21/19.71 | ALPHA: (domain4) implies:
% 141.21/19.71 | (10) domain(zero) = zero
% 141.21/19.71 |
% 141.21/19.71 | ALPHA: (domain5) implies:
% 141.21/19.71 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2)
% 141.21/19.71 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 141.21/19.71 | (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4,
% 141.21/19.71 | v5) = v3 & $i(v5) & $i(v4) & $i(v3)))
% 141.21/19.72 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 141.21/19.72 | ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) =
% 141.21/19.72 | v4) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (domain(v5) = v4 &
% 141.21/19.72 | addition(v0, v1) = v5 & $i(v5) & $i(v4)))
% 141.21/19.72 |
% 141.21/19.72 | ALPHA: (goals) implies:
% 141.21/19.72 | (13) $i(zero)
% 141.21/19.72 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 141.21/19.72 | zero) & domain(v1) = v2 & multiplication(v0, v2) = zero &
% 141.21/19.72 | multiplication(v0, v1) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 141.21/19.72 |
% 141.21/19.72 | ALPHA: (function-axioms) implies:
% 141.21/19.72 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (domain(v2) =
% 141.21/19.72 | v1) | ~ (domain(v2) = v0))
% 141.21/19.72 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/19.72 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 141.21/19.72 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/19.72 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 141.21/19.72 |
% 141.21/19.72 | DELTA: instantiating (14) with fresh symbols all_20_0, all_20_1, all_20_2,
% 141.21/19.72 | all_20_3 gives:
% 141.21/19.72 | (18) ~ (all_20_0 = zero) & domain(all_20_2) = all_20_1 &
% 141.21/19.72 | multiplication(all_20_3, all_20_1) = zero & multiplication(all_20_3,
% 141.21/19.72 | all_20_2) = all_20_0 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) &
% 141.21/19.72 | $i(all_20_3)
% 141.21/19.72 |
% 141.21/19.72 | ALPHA: (18) implies:
% 141.21/19.72 | (19) ~ (all_20_0 = zero)
% 141.21/19.72 | (20) $i(all_20_3)
% 141.21/19.72 | (21) $i(all_20_2)
% 141.21/19.72 | (22) $i(all_20_1)
% 141.21/19.72 | (23) multiplication(all_20_3, all_20_2) = all_20_0
% 141.21/19.72 | (24) multiplication(all_20_3, all_20_1) = zero
% 141.21/19.73 | (25) domain(all_20_2) = all_20_1
% 141.21/19.73 |
% 141.21/19.73 | GROUND_INST: instantiating (5) with all_20_2, all_20_0, simplifying with (21)
% 141.21/19.73 | gives:
% 141.21/19.73 | (26) all_20_0 = zero | ~ (multiplication(zero, all_20_2) = all_20_0)
% 141.21/19.73 |
% 141.21/19.73 | GROUND_INST: instantiating (2) with all_20_3, zero, simplifying with (20)
% 141.21/19.73 | gives:
% 141.21/19.73 | (27) all_20_3 = zero | ~ (multiplication(all_20_3, one) = zero)
% 141.21/19.73 |
% 141.21/19.73 | GROUND_INST: instantiating (6) with all_20_3, all_20_1, zero, simplifying with
% 141.21/19.73 | (20), (22), (24) gives:
% 141.21/19.73 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(v2) = v0 &
% 141.21/19.73 | domain(all_20_1) = v1 & domain(zero) = v0 & multiplication(all_20_3,
% 141.21/19.73 | v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 141.21/19.73 |
% 141.21/19.73 | GROUND_INST: instantiating (9) with zero, zero, simplifying with (10), (13)
% 141.21/19.73 | gives:
% 141.21/19.73 | (29) addition(zero, one) = one
% 141.21/19.73 |
% 141.21/19.73 | GROUND_INST: instantiating (domain1) with zero, zero, simplifying with (10),
% 141.21/19.73 | (13) gives:
% 141.21/19.73 | (30) ? [v0: $i] : (multiplication(zero, zero) = v0 & addition(zero, v0) =
% 141.21/19.73 | v0 & $i(v0))
% 141.21/19.73 |
% 141.21/19.73 | GROUND_INST: instantiating (7) with all_20_3, all_20_2, all_20_1, zero,
% 141.21/19.73 | simplifying with (20), (21), (24), (25) gives:
% 141.21/19.73 | (31) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(zero) = v1 &
% 141.21/19.73 | multiplication(all_20_3, all_20_2) = v0 & $i(v1) & $i(v0))
% 141.21/19.73 |
% 141.21/19.73 | DELTA: instantiating (30) with fresh symbol all_30_0 gives:
% 141.21/19.73 | (32) multiplication(zero, zero) = all_30_0 & addition(zero, all_30_0) =
% 141.21/19.73 | all_30_0 & $i(all_30_0)
% 141.21/19.73 |
% 141.21/19.73 | ALPHA: (32) implies:
% 141.21/19.73 | (33) $i(all_30_0)
% 141.21/19.73 | (34) addition(zero, all_30_0) = all_30_0
% 141.21/19.74 | (35) multiplication(zero, zero) = all_30_0
% 141.21/19.74 |
% 141.21/19.74 | DELTA: instantiating (31) with fresh symbols all_32_0, all_32_1 gives:
% 141.21/19.74 | (36) domain(all_32_1) = all_32_0 & domain(zero) = all_32_0 &
% 141.21/19.74 | multiplication(all_20_3, all_20_2) = all_32_1 & $i(all_32_0) &
% 141.21/19.74 | $i(all_32_1)
% 141.21/19.74 |
% 141.21/19.74 | ALPHA: (36) implies:
% 141.21/19.74 | (37) $i(all_32_1)
% 141.21/19.74 | (38) $i(all_32_0)
% 141.21/19.74 | (39) multiplication(all_20_3, all_20_2) = all_32_1
% 141.21/19.74 | (40) domain(zero) = all_32_0
% 141.21/19.74 | (41) domain(all_32_1) = all_32_0
% 141.21/19.74 |
% 141.21/19.74 | DELTA: instantiating (28) with fresh symbols all_34_0, all_34_1, all_34_2
% 141.21/19.74 | gives:
% 141.21/19.74 | (42) domain(all_34_0) = all_34_2 & domain(all_20_1) = all_34_1 &
% 141.21/19.74 | domain(zero) = all_34_2 & multiplication(all_20_3, all_34_1) =
% 141.21/19.74 | all_34_0 & $i(all_34_0) & $i(all_34_1) & $i(all_34_2)
% 141.21/19.74 |
% 141.21/19.74 | ALPHA: (42) implies:
% 141.21/19.74 | (43) domain(zero) = all_34_2
% 141.21/19.74 |
% 141.21/19.74 | BETA: splitting (26) gives:
% 141.21/19.74 |
% 141.21/19.74 | Case 1:
% 141.21/19.74 | |
% 141.21/19.74 | | (44) ~ (multiplication(zero, all_20_2) = all_20_0)
% 141.21/19.74 | |
% 141.21/19.74 | | GROUND_INST: instantiating (17) with all_20_0, all_32_1, all_20_2, all_20_3,
% 141.21/19.74 | | simplifying with (23), (39) gives:
% 141.21/19.74 | | (45) all_32_1 = all_20_0
% 141.21/19.74 | |
% 141.21/19.74 | | GROUND_INST: instantiating (15) with zero, all_34_2, zero, simplifying with
% 141.21/19.74 | | (10), (43) gives:
% 141.21/19.74 | | (46) all_34_2 = zero
% 141.21/19.74 | |
% 141.21/19.74 | | GROUND_INST: instantiating (15) with all_32_0, all_34_2, zero, simplifying
% 141.21/19.74 | | with (40), (43) gives:
% 141.21/19.74 | | (47) all_34_2 = all_32_0
% 141.21/19.74 | |
% 141.21/19.74 | | PRED_UNIFY: (23), (44) imply:
% 141.21/19.74 | | (48) ~ (all_20_3 = zero)
% 141.21/19.74 | |
% 141.21/19.74 | | COMBINE_EQS: (46), (47) imply:
% 141.21/19.74 | | (49) all_32_0 = zero
% 141.21/19.74 | |
% 141.21/19.74 | | REDUCE: (41), (45), (49) imply:
% 141.21/19.74 | | (50) domain(all_20_0) = zero
% 141.21/19.74 | |
% 141.21/19.74 | | REDUCE: (37), (45) imply:
% 141.21/19.74 | | (51) $i(all_20_0)
% 141.21/19.74 | |
% 141.21/19.74 | | BETA: splitting (27) gives:
% 141.21/19.74 | |
% 141.21/19.74 | | Case 1:
% 141.21/19.74 | | |
% 141.21/19.75 | | |
% 141.21/19.75 | | | GROUND_INST: instantiating (11) with zero, one, one, simplifying with (8),
% 141.21/19.75 | | | (13), (29) gives:
% 141.21/19.75 | | | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(one) = v2 &
% 141.21/19.75 | | | domain(one) = v0 & domain(zero) = v1 & addition(v1, v2) = v0 &
% 141.21/19.75 | | | $i(v2) & $i(v1) & $i(v0))
% 141.21/19.75 | | |
% 141.21/19.75 | | | GROUND_INST: instantiating (11) with zero, all_30_0, all_30_0, simplifying
% 141.21/19.75 | | | with (13), (33), (34) gives:
% 141.21/19.75 | | | (53) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_30_0) = v2 &
% 141.21/19.75 | | | domain(all_30_0) = v0 & domain(zero) = v1 & addition(v1, v2) =
% 141.21/19.75 | | | v0 & $i(v2) & $i(v1) & $i(v0))
% 141.21/19.75 | | |
% 141.21/19.75 | | | GROUND_INST: instantiating (3) with zero, zero, zero, zero, zero,
% 141.21/19.75 | | | simplifying with (13) gives:
% 141.21/19.75 | | | (54) ~ (multiplication(zero, zero) = zero) | ~ (addition(zero, zero)
% 141.21/19.75 | | | = zero) | ? [v0: $i] : ? [v1: $i] : (multiplication(zero,
% 141.21/19.75 | | | zero) = v1 & multiplication(zero, zero) = v0 & addition(v0,
% 141.21/19.75 | | | v1) = zero & $i(v1) & $i(v0))
% 141.21/19.75 | | |
% 141.21/19.75 | | | GROUND_INST: instantiating (3) with zero, zero, zero, zero, all_30_0,
% 141.21/19.75 | | | simplifying with (13), (35) gives:
% 141.21/19.75 | | | (55) ~ (addition(zero, zero) = zero) | ? [v0: $i] : ? [v1: $i] :
% 141.21/19.75 | | | (multiplication(zero, zero) = v1 & multiplication(zero, zero) = v0
% 141.21/19.75 | | | & addition(v0, v1) = all_30_0 & $i(v1) & $i(v0) & $i(all_30_0))
% 141.21/19.75 | | |
% 141.21/19.75 | | | GROUND_INST: instantiating (7) with zero, zero, zero, all_30_0,
% 141.21/19.75 | | | simplifying with (10), (13), (35) gives:
% 141.21/19.76 | | | (56) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_30_0) =
% 141.21/19.76 | | | v1 & multiplication(zero, zero) = v0 & $i(v1) & $i(v0))
% 141.21/19.76 | | |
% 141.21/19.76 | | | GROUND_INST: instantiating (4) with zero, all_30_0, simplifying with (13),
% 141.21/19.76 | | | (35) gives:
% 141.21/19.76 | | | (57) all_30_0 = zero
% 141.21/19.76 | | |
% 141.21/19.76 | | | GROUND_INST: instantiating (6) with zero, zero, all_30_0, simplifying with
% 141.21/19.76 | | | (13), (35) gives:
% 141.21/19.76 | | | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(v2) = v0 &
% 141.21/19.76 | | | domain(all_30_0) = v0 & domain(zero) = v1 & multiplication(zero,
% 141.21/19.76 | | | v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 141.21/19.76 | | |
% 141.21/19.76 | | | GROUND_INST: instantiating (12) with all_20_0, zero, zero, zero, zero,
% 141.21/19.76 | | | simplifying with (10), (13), (50), (51) gives:
% 141.21/19.76 | | | (59) ~ (addition(zero, zero) = zero) | ? [v0: $i] : (domain(v0) =
% 141.21/19.76 | | | zero & addition(all_20_0, zero) = v0 & $i(v0))
% 141.21/19.76 | | |
% 141.21/19.76 | | | GROUND_INST: instantiating (7) with zero, all_20_0, zero, all_30_0,
% 141.21/19.76 | | | simplifying with (13), (35), (50), (51) gives:
% 141.21/19.76 | | | (60) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_30_0) =
% 141.21/19.76 | | | v1 & multiplication(zero, all_20_0) = v0 & $i(v1) & $i(v0))
% 141.21/19.76 | | |
% 141.21/19.76 | | | GROUND_INST: instantiating (domain1) with all_20_0, zero, simplifying with
% 141.21/19.76 | | | (50), (51) gives:
% 141.21/19.76 | | | (61) ? [v0: $i] : (multiplication(zero, all_20_0) = v0 &
% 141.21/19.76 | | | addition(all_20_0, v0) = v0 & $i(v0))
% 141.21/19.76 | | |
% 141.21/19.76 | | | DELTA: instantiating (61) with fresh symbol all_78_0 gives:
% 141.21/19.76 | | | (62) multiplication(zero, all_20_0) = all_78_0 & addition(all_20_0,
% 141.21/19.77 | | | all_78_0) = all_78_0 & $i(all_78_0)
% 141.21/19.77 | | |
% 141.21/19.77 | | | ALPHA: (62) implies:
% 141.21/19.77 | | | (63) addition(all_20_0, all_78_0) = all_78_0
% 141.71/19.77 | | | (64) multiplication(zero, all_20_0) = all_78_0
% 141.71/19.77 | | |
% 141.71/19.77 | | | DELTA: instantiating (56) with fresh symbols all_94_0, all_94_1 gives:
% 141.71/19.77 | | | (65) domain(all_94_1) = all_94_0 & domain(all_30_0) = all_94_0 &
% 141.71/19.77 | | | multiplication(zero, zero) = all_94_1 & $i(all_94_0) &
% 141.71/19.77 | | | $i(all_94_1)
% 141.71/19.77 | | |
% 141.71/19.77 | | | ALPHA: (65) implies:
% 141.71/19.77 | | | (66) multiplication(zero, zero) = all_94_1
% 141.71/19.77 | | |
% 141.71/19.77 | | | DELTA: instantiating (60) with fresh symbols all_98_0, all_98_1 gives:
% 141.71/19.77 | | | (67) domain(all_98_1) = all_98_0 & domain(all_30_0) = all_98_0 &
% 141.71/19.77 | | | multiplication(zero, all_20_0) = all_98_1 & $i(all_98_0) &
% 141.71/19.77 | | | $i(all_98_1)
% 141.71/19.77 | | |
% 141.71/19.77 | | | ALPHA: (67) implies:
% 141.71/19.77 | | | (68) multiplication(zero, all_20_0) = all_98_1
% 141.71/19.77 | | | (69) domain(all_30_0) = all_98_0
% 141.71/19.77 | | |
% 141.71/19.77 | | | DELTA: instantiating (58) with fresh symbols all_100_0, all_100_1,
% 141.71/19.77 | | | all_100_2 gives:
% 141.71/19.77 | | | (70) domain(all_100_0) = all_100_2 & domain(all_30_0) = all_100_2 &
% 141.71/19.77 | | | domain(zero) = all_100_1 & multiplication(zero, all_100_1) =
% 141.71/19.77 | | | all_100_0 & $i(all_100_0) & $i(all_100_1) & $i(all_100_2)
% 141.71/19.77 | | |
% 141.71/19.77 | | | ALPHA: (70) implies:
% 141.71/19.77 | | | (71) multiplication(zero, all_100_1) = all_100_0
% 141.71/19.77 | | | (72) domain(zero) = all_100_1
% 141.71/19.77 | | | (73) domain(all_30_0) = all_100_2
% 141.71/19.77 | | |
% 141.71/19.77 | | | DELTA: instantiating (53) with fresh symbols all_104_0, all_104_1,
% 141.71/19.77 | | | all_104_2 gives:
% 141.71/19.77 | | | (74) domain(all_30_0) = all_104_0 & domain(all_30_0) = all_104_2 &
% 141.71/19.77 | | | domain(zero) = all_104_1 & addition(all_104_1, all_104_0) =
% 141.71/19.77 | | | all_104_2 & $i(all_104_0) & $i(all_104_1) & $i(all_104_2)
% 141.71/19.77 | | |
% 141.71/19.77 | | | ALPHA: (74) implies:
% 141.71/19.77 | | | (75) domain(zero) = all_104_1
% 141.71/19.77 | | | (76) domain(all_30_0) = all_104_2
% 141.71/19.77 | | |
% 141.71/19.77 | | | DELTA: instantiating (52) with fresh symbols all_106_0, all_106_1,
% 141.71/19.77 | | | all_106_2 gives:
% 141.71/19.77 | | | (77) domain(one) = all_106_0 & domain(one) = all_106_2 & domain(zero) =
% 141.71/19.77 | | | all_106_1 & addition(all_106_1, all_106_0) = all_106_2 &
% 141.71/19.77 | | | $i(all_106_0) & $i(all_106_1) & $i(all_106_2)
% 141.71/19.78 | | |
% 141.71/19.78 | | | ALPHA: (77) implies:
% 141.71/19.78 | | | (78) domain(zero) = all_106_1
% 141.71/19.78 | | |
% 141.71/19.78 | | | REDUCE: (57), (76) imply:
% 141.71/19.78 | | | (79) domain(zero) = all_104_2
% 141.71/19.78 | | |
% 141.71/19.78 | | | REDUCE: (57), (73) imply:
% 141.71/19.78 | | | (80) domain(zero) = all_100_2
% 141.71/19.78 | | |
% 141.71/19.78 | | | REDUCE: (57), (69) imply:
% 141.71/19.78 | | | (81) domain(zero) = all_98_0
% 141.71/19.78 | | |
% 141.71/19.78 | | | REDUCE: (35), (57) imply:
% 141.71/19.78 | | | (82) multiplication(zero, zero) = zero
% 141.71/19.78 | | |
% 141.71/19.78 | | | REDUCE: (34), (57) imply:
% 141.71/19.78 | | | (83) addition(zero, zero) = zero
% 141.71/19.78 | | |
% 141.71/19.78 | | | BETA: splitting (59) gives:
% 141.71/19.78 | | |
% 141.71/19.78 | | | Case 1:
% 141.71/19.78 | | | |
% 141.71/19.78 | | | | (84) ~ (addition(zero, zero) = zero)
% 141.71/19.78 | | | |
% 141.71/19.78 | | | | PRED_UNIFY: (83), (84) imply:
% 141.71/19.78 | | | | (85) $false
% 141.71/19.78 | | | |
% 141.71/19.78 | | | | CLOSE: (85) is inconsistent.
% 141.71/19.78 | | | |
% 141.71/19.78 | | | Case 2:
% 141.71/19.78 | | | |
% 141.71/19.78 | | | | (86) ? [v0: $i] : (domain(v0) = zero & addition(all_20_0, zero) = v0
% 141.71/19.78 | | | | & $i(v0))
% 141.71/19.78 | | | |
% 141.71/19.78 | | | | DELTA: instantiating (86) with fresh symbol all_131_0 gives:
% 141.71/19.78 | | | | (87) domain(all_131_0) = zero & addition(all_20_0, zero) = all_131_0
% 141.71/19.78 | | | | & $i(all_131_0)
% 141.71/19.78 | | | |
% 141.71/19.78 | | | | ALPHA: (87) implies:
% 141.71/19.78 | | | | (88) addition(all_20_0, zero) = all_131_0
% 141.71/19.78 | | | |
% 141.71/19.78 | | | | BETA: splitting (55) gives:
% 141.71/19.78 | | | |
% 141.71/19.78 | | | | Case 1:
% 141.71/19.78 | | | | |
% 141.71/19.78 | | | | | (89) ~ (addition(zero, zero) = zero)
% 141.71/19.78 | | | | |
% 141.71/19.78 | | | | | PRED_UNIFY: (83), (89) imply:
% 141.71/19.78 | | | | | (90) $false
% 141.71/19.78 | | | | |
% 141.71/19.78 | | | | | CLOSE: (90) is inconsistent.
% 141.71/19.78 | | | | |
% 141.71/19.78 | | | | Case 2:
% 141.71/19.78 | | | | |
% 141.71/19.79 | | | | | (91) ? [v0: $i] : ? [v1: $i] : (multiplication(zero, zero) = v1 &
% 141.71/19.79 | | | | | multiplication(zero, zero) = v0 & addition(v0, v1) =
% 141.71/19.79 | | | | | all_30_0 & $i(v1) & $i(v0) & $i(all_30_0))
% 141.71/19.79 | | | | |
% 141.71/19.79 | | | | | DELTA: instantiating (91) with fresh symbols all_143_0, all_143_1
% 141.71/19.79 | | | | | gives:
% 141.71/19.79 | | | | | (92) multiplication(zero, zero) = all_143_0 & multiplication(zero,
% 141.71/19.79 | | | | | zero) = all_143_1 & addition(all_143_1, all_143_0) =
% 141.71/19.79 | | | | | all_30_0 & $i(all_143_0) & $i(all_143_1) & $i(all_30_0)
% 141.71/19.79 | | | | |
% 141.71/19.79 | | | | | ALPHA: (92) implies:
% 141.71/19.79 | | | | | (93) multiplication(zero, zero) = all_143_1
% 141.71/19.79 | | | | | (94) multiplication(zero, zero) = all_143_0
% 141.71/19.79 | | | | |
% 141.71/19.79 | | | | | BETA: splitting (54) gives:
% 141.71/19.79 | | | | |
% 141.71/19.79 | | | | | Case 1:
% 141.71/19.79 | | | | | |
% 141.71/19.79 | | | | | | (95) ~ (multiplication(zero, zero) = zero)
% 141.71/19.79 | | | | | |
% 141.71/19.79 | | | | | | PRED_UNIFY: (82), (95) imply:
% 141.71/19.79 | | | | | | (96) $false
% 141.71/19.79 | | | | | |
% 141.71/19.79 | | | | | | CLOSE: (96) is inconsistent.
% 141.71/19.79 | | | | | |
% 141.71/19.79 | | | | | Case 2:
% 141.71/19.79 | | | | | |
% 141.71/19.79 | | | | | | (97) ~ (addition(zero, zero) = zero) | ? [v0: $i] : ? [v1: $i]
% 141.71/19.79 | | | | | | : (multiplication(zero, zero) = v1 & multiplication(zero,
% 141.71/19.79 | | | | | | zero) = v0 & addition(v0, v1) = zero & $i(v1) & $i(v0))
% 141.71/19.79 | | | | | |
% 141.71/19.79 | | | | | | BETA: splitting (97) gives:
% 141.71/19.79 | | | | | |
% 141.71/19.79 | | | | | | Case 1:
% 141.71/19.79 | | | | | | |
% 141.71/19.79 | | | | | | | (98) ~ (addition(zero, zero) = zero)
% 141.71/19.79 | | | | | | |
% 141.71/19.79 | | | | | | | PRED_UNIFY: (83), (98) imply:
% 141.71/19.79 | | | | | | | (99) $false
% 141.71/19.79 | | | | | | |
% 141.71/19.79 | | | | | | | CLOSE: (99) is inconsistent.
% 141.71/19.79 | | | | | | |
% 141.71/19.79 | | | | | | Case 2:
% 141.71/19.79 | | | | | | |
% 141.71/19.79 | | | | | | | (100) ? [v0: $i] : ? [v1: $i] : (multiplication(zero, zero) =
% 141.71/19.79 | | | | | | | v1 & multiplication(zero, zero) = v0 & addition(v0, v1)
% 141.71/19.79 | | | | | | | = zero & $i(v1) & $i(v0))
% 141.71/19.79 | | | | | | |
% 141.71/19.79 | | | | | | | DELTA: instantiating (100) with fresh symbols all_188_0, all_188_1
% 141.71/19.79 | | | | | | | gives:
% 141.71/19.79 | | | | | | | (101) multiplication(zero, zero) = all_188_0 &
% 141.71/19.79 | | | | | | | multiplication(zero, zero) = all_188_1 &
% 141.71/19.79 | | | | | | | addition(all_188_1, all_188_0) = zero & $i(all_188_0) &
% 141.71/19.79 | | | | | | | $i(all_188_1)
% 141.71/19.79 | | | | | | |
% 141.71/19.79 | | | | | | | ALPHA: (101) implies:
% 141.71/19.79 | | | | | | | (102) multiplication(zero, zero) = all_188_1
% 141.71/19.79 | | | | | | | (103) multiplication(zero, zero) = all_188_0
% 141.71/19.79 | | | | | | |
% 141.71/19.79 | | | | | | | GROUND_INST: instantiating (16) with all_131_0, zero, zero,
% 141.71/19.79 | | | | | | | all_20_0, simplifying with (88) gives:
% 141.71/19.80 | | | | | | | (104) all_131_0 = zero | ~ (addition(all_20_0, zero) = zero)
% 141.71/19.80 | | | | | | |
% 141.71/19.80 | | | | | | | GROUND_INST: instantiating (17) with all_94_1, all_143_1, zero,
% 141.71/19.80 | | | | | | | zero, simplifying with (66), (93) gives:
% 141.71/19.80 | | | | | | | (105) all_143_1 = all_94_1
% 141.71/19.80 | | | | | | |
% 141.71/19.80 | | | | | | | GROUND_INST: instantiating (17) with all_143_1, all_143_0, zero,
% 141.71/19.80 | | | | | | | zero, simplifying with (93), (94) gives:
% 141.85/19.80 | | | | | | | (106) all_143_0 = all_143_1
% 141.85/19.80 | | | | | | |
% 141.85/19.80 | | | | | | | GROUND_INST: instantiating (17) with all_143_0, all_188_1, zero,
% 141.85/19.80 | | | | | | | zero, simplifying with (94), (102) gives:
% 141.85/19.80 | | | | | | | (107) all_188_1 = all_143_0
% 141.85/19.80 | | | | | | |
% 141.85/19.80 | | | | | | | GROUND_INST: instantiating (17) with all_188_1, all_188_0, zero,
% 141.85/19.80 | | | | | | | zero, simplifying with (102), (103) gives:
% 141.85/19.80 | | | | | | | (108) all_188_0 = all_188_1
% 141.85/19.80 | | | | | | |
% 141.85/19.80 | | | | | | | GROUND_INST: instantiating (17) with zero, all_188_0, zero, zero,
% 141.85/19.80 | | | | | | | simplifying with (82), (103) gives:
% 141.85/19.80 | | | | | | | (109) all_188_0 = zero
% 141.85/19.80 | | | | | | |
% 141.85/19.80 | | | | | | | GROUND_INST: instantiating (17) with all_78_0, all_98_1, all_20_0,
% 141.85/19.80 | | | | | | | zero, simplifying with (64), (68) gives:
% 141.85/19.80 | | | | | | | (110) all_98_1 = all_78_0
% 141.85/19.80 | | | | | | |
% 141.85/19.80 | | | | | | | GROUND_INST: instantiating (17) with all_100_0, zero, all_100_1,
% 141.85/19.80 | | | | | | | zero, simplifying with (71) gives:
% 141.85/19.80 | | | | | | | (111) all_100_0 = zero | ~ (multiplication(zero, all_100_1) =
% 141.85/19.80 | | | | | | | zero)
% 141.85/19.80 | | | | | | |
% 141.85/19.80 | | | | | | | GROUND_INST: instantiating (15) with zero, all_104_2, zero,
% 141.85/19.80 | | | | | | | simplifying with (10), (79) gives:
% 141.85/19.80 | | | | | | | (112) all_104_2 = zero
% 141.85/19.80 | | | | | | |
% 141.85/19.80 | | | | | | | GROUND_INST: instantiating (15) with all_100_2, all_104_1, zero,
% 141.85/19.80 | | | | | | | simplifying with (75), (80) gives:
% 141.85/19.80 | | | | | | | (113) all_104_1 = all_100_2
% 141.85/19.80 | | | | | | |
% 141.85/19.80 | | | | | | | GROUND_INST: instantiating (15) with all_104_1, all_106_1, zero,
% 141.85/19.80 | | | | | | | simplifying with (75), (78) gives:
% 141.85/19.80 | | | | | | | (114) all_106_1 = all_104_1
% 141.85/19.80 | | | | | | |
% 141.85/19.80 | | | | | | | GROUND_INST: instantiating (15) with all_104_2, all_106_1, zero,
% 141.85/19.80 | | | | | | | simplifying with (78), (79) gives:
% 141.85/19.80 | | | | | | | (115) all_106_1 = all_104_2
% 141.85/19.80 | | | | | | |
% 141.85/19.80 | | | | | | | GROUND_INST: instantiating (15) with all_100_1, all_106_1, zero,
% 141.85/19.80 | | | | | | | simplifying with (72), (78) gives:
% 141.85/19.80 | | | | | | | (116) all_106_1 = all_100_1
% 141.85/19.80 | | | | | | |
% 141.85/19.80 | | | | | | | GROUND_INST: instantiating (15) with all_98_0, all_106_1, zero,
% 141.85/19.80 | | | | | | | simplifying with (78), (81) gives:
% 141.85/19.80 | | | | | | | (117) all_106_1 = all_98_0
% 141.85/19.80 | | | | | | |
% 141.85/19.81 | | | | | | | COMBINE_EQS: (108), (109) imply:
% 141.85/19.81 | | | | | | | (118) all_188_1 = zero
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | SIMP: (118) implies:
% 141.85/19.81 | | | | | | | (119) all_188_1 = zero
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | COMBINE_EQS: (107), (119) imply:
% 141.85/19.81 | | | | | | | (120) all_143_0 = zero
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | SIMP: (120) implies:
% 141.85/19.81 | | | | | | | (121) all_143_0 = zero
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | COMBINE_EQS: (106), (121) imply:
% 141.85/19.81 | | | | | | | (122) all_143_1 = zero
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | SIMP: (122) implies:
% 141.85/19.81 | | | | | | | (123) all_143_1 = zero
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | COMBINE_EQS: (105), (123) imply:
% 141.85/19.81 | | | | | | | (124) all_94_1 = zero
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | SIMP: (124) implies:
% 141.85/19.81 | | | | | | | (125) all_94_1 = zero
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | COMBINE_EQS: (115), (116) imply:
% 141.85/19.81 | | | | | | | (126) all_104_2 = all_100_1
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | SIMP: (126) implies:
% 141.85/19.81 | | | | | | | (127) all_104_2 = all_100_1
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | COMBINE_EQS: (114), (116) imply:
% 141.85/19.81 | | | | | | | (128) all_104_1 = all_100_1
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | SIMP: (128) implies:
% 141.85/19.81 | | | | | | | (129) all_104_1 = all_100_1
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | COMBINE_EQS: (116), (117) imply:
% 141.85/19.81 | | | | | | | (130) all_100_1 = all_98_0
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | COMBINE_EQS: (113), (129) imply:
% 141.85/19.81 | | | | | | | (131) all_100_1 = all_100_2
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | SIMP: (131) implies:
% 141.85/19.81 | | | | | | | (132) all_100_1 = all_100_2
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | COMBINE_EQS: (112), (127) imply:
% 141.85/19.81 | | | | | | | (133) all_100_1 = zero
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | SIMP: (133) implies:
% 141.85/19.81 | | | | | | | (134) all_100_1 = zero
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | COMBINE_EQS: (132), (134) imply:
% 141.85/19.81 | | | | | | | (135) all_100_2 = zero
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | COMBINE_EQS: (130), (132) imply:
% 141.85/19.81 | | | | | | | (136) all_100_2 = all_98_0
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | COMBINE_EQS: (135), (136) imply:
% 141.85/19.81 | | | | | | | (137) all_98_0 = zero
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | BETA: splitting (111) gives:
% 141.85/19.81 | | | | | | |
% 141.85/19.81 | | | | | | | Case 1:
% 141.85/19.81 | | | | | | | |
% 141.85/19.81 | | | | | | | | (138) ~ (multiplication(zero, all_100_1) = zero)
% 141.85/19.81 | | | | | | | |
% 141.85/19.81 | | | | | | | | REDUCE: (134), (138) imply:
% 141.85/19.81 | | | | | | | | (139) ~ (multiplication(zero, zero) = zero)
% 141.85/19.81 | | | | | | | |
% 141.85/19.81 | | | | | | | | PRED_UNIFY: (82), (139) imply:
% 141.85/19.81 | | | | | | | | (140) $false
% 141.85/19.81 | | | | | | | |
% 141.85/19.81 | | | | | | | | CLOSE: (140) is inconsistent.
% 141.85/19.81 | | | | | | | |
% 141.85/19.81 | | | | | | | Case 2:
% 141.85/19.81 | | | | | | | |
% 141.85/19.81 | | | | | | | |
% 141.85/19.81 | | | | | | | | GROUND_INST: instantiating (1) with all_20_0, all_131_0,
% 141.85/19.81 | | | | | | | | simplifying with (51), (88) gives:
% 141.85/19.82 | | | | | | | | (141) all_131_0 = all_20_0
% 141.85/19.82 | | | | | | | |
% 141.85/19.82 | | | | | | | | GROUND_INST: instantiating (5) with all_20_0, all_78_0,
% 141.85/19.82 | | | | | | | | simplifying with (51), (64) gives:
% 141.85/19.82 | | | | | | | | (142) all_78_0 = zero
% 141.85/19.82 | | | | | | | |
% 141.85/19.82 | | | | | | | | REDUCE: (63), (142) imply:
% 141.85/19.82 | | | | | | | | (143) addition(all_20_0, zero) = zero
% 141.85/19.82 | | | | | | | |
% 141.85/19.82 | | | | | | | | BETA: splitting (104) gives:
% 141.85/19.82 | | | | | | | |
% 141.85/19.82 | | | | | | | | Case 1:
% 141.85/19.82 | | | | | | | | |
% 141.85/19.82 | | | | | | | | | (144) ~ (addition(all_20_0, zero) = zero)
% 141.85/19.82 | | | | | | | | |
% 141.85/19.82 | | | | | | | | | PRED_UNIFY: (143), (144) imply:
% 141.85/19.82 | | | | | | | | | (145) $false
% 141.85/19.82 | | | | | | | | |
% 141.85/19.82 | | | | | | | | | CLOSE: (145) is inconsistent.
% 141.85/19.82 | | | | | | | | |
% 141.85/19.82 | | | | | | | | Case 2:
% 141.85/19.82 | | | | | | | | |
% 141.85/19.82 | | | | | | | | | (146) all_131_0 = zero
% 141.85/19.82 | | | | | | | | |
% 141.85/19.82 | | | | | | | | | COMBINE_EQS: (141), (146) imply:
% 141.85/19.82 | | | | | | | | | (147) all_20_0 = zero
% 141.85/19.82 | | | | | | | | |
% 141.85/19.82 | | | | | | | | | SIMP: (147) implies:
% 141.85/19.82 | | | | | | | | | (148) all_20_0 = zero
% 141.85/19.82 | | | | | | | | |
% 141.85/19.82 | | | | | | | | | REDUCE: (19), (148) imply:
% 141.85/19.82 | | | | | | | | | (149) $false
% 141.85/19.82 | | | | | | | | |
% 141.85/19.82 | | | | | | | | | CLOSE: (149) is inconsistent.
% 141.85/19.82 | | | | | | | | |
% 141.85/19.82 | | | | | | | | End of split
% 141.85/19.82 | | | | | | | |
% 141.85/19.82 | | | | | | | End of split
% 141.85/19.82 | | | | | | |
% 141.85/19.82 | | | | | | End of split
% 141.85/19.82 | | | | | |
% 141.85/19.82 | | | | | End of split
% 141.85/19.82 | | | | |
% 141.85/19.82 | | | | End of split
% 141.85/19.82 | | | |
% 141.85/19.82 | | | End of split
% 141.85/19.82 | | |
% 141.85/19.82 | | Case 2:
% 141.85/19.82 | | |
% 141.85/19.82 | | | (150) all_20_3 = zero
% 141.85/19.82 | | |
% 141.85/19.82 | | | REDUCE: (48), (150) imply:
% 141.85/19.82 | | | (151) $false
% 141.85/19.82 | | |
% 141.85/19.82 | | | CLOSE: (151) is inconsistent.
% 141.85/19.82 | | |
% 141.85/19.82 | | End of split
% 141.85/19.82 | |
% 141.85/19.82 | Case 2:
% 141.85/19.82 | |
% 141.85/19.82 | | (152) all_20_0 = zero
% 141.85/19.82 | |
% 141.85/19.82 | | REDUCE: (19), (152) imply:
% 141.85/19.82 | | (153) $false
% 141.85/19.82 | |
% 141.85/19.82 | | CLOSE: (153) is inconsistent.
% 141.85/19.82 | |
% 141.85/19.82 | End of split
% 141.85/19.82 |
% 141.85/19.82 End of proof
% 141.85/19.82 % SZS output end Proof for theBenchmark
% 141.85/19.82
% 141.85/19.82 19340ms
%------------------------------------------------------------------------------