TSTP Solution File: KLE146+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE146+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 : n002.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 05:34:41 EDT 2023
% Result : Theorem 14.24s 2.63s
% Output : Proof 33.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE146+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 12:53:05 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.60 ________ _____
% 0.21/0.60 ___ __ \_________(_)________________________________
% 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60 (2023-06-19)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2023
% 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60 Amanda Stjerna.
% 0.21/0.60 Free software under BSD-3-Clause.
% 0.21/0.60
% 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60
% 0.21/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.61 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.28/1.01 Prover 4: Preprocessing ...
% 2.28/1.01 Prover 1: Preprocessing ...
% 2.77/1.05 Prover 2: Preprocessing ...
% 2.77/1.05 Prover 3: Preprocessing ...
% 2.77/1.05 Prover 0: Preprocessing ...
% 2.77/1.05 Prover 5: Preprocessing ...
% 2.77/1.06 Prover 6: Preprocessing ...
% 4.63/1.35 Prover 6: Constructing countermodel ...
% 4.63/1.36 Prover 1: Constructing countermodel ...
% 4.63/1.37 Prover 3: Constructing countermodel ...
% 5.27/1.40 Prover 5: Proving ...
% 5.53/1.43 Prover 4: Constructing countermodel ...
% 5.53/1.44 Prover 0: Proving ...
% 6.15/1.51 Prover 2: Proving ...
% 6.15/1.51 Prover 3: gave up
% 6.15/1.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.15/1.52 Prover 6: gave up
% 6.15/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.15/1.53 Prover 1: gave up
% 6.15/1.53 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 6.15/1.55 Prover 8: Preprocessing ...
% 6.15/1.57 Prover 9: Preprocessing ...
% 6.15/1.58 Prover 7: Preprocessing ...
% 7.38/1.67 Prover 8: Warning: ignoring some quantifiers
% 7.38/1.68 Prover 7: Constructing countermodel ...
% 7.49/1.69 Prover 8: Constructing countermodel ...
% 7.76/1.73 Prover 9: Constructing countermodel ...
% 7.76/1.78 Prover 8: gave up
% 7.76/1.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.41/1.83 Prover 10: Preprocessing ...
% 8.41/1.89 Prover 10: Constructing countermodel ...
% 8.41/1.91 Prover 10: gave up
% 8.41/1.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.12/1.96 Prover 11: Preprocessing ...
% 10.09/2.09 Prover 11: Constructing countermodel ...
% 14.24/2.62 Prover 9: proved (1090ms)
% 14.24/2.62
% 14.24/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.24/2.63
% 14.24/2.63 Prover 0: stopped
% 14.24/2.64 Prover 2: stopped
% 14.24/2.65 Prover 5: stopped
% 14.24/2.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.79/2.68 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 14.79/2.68 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 14.79/2.68 Prover 13: Preprocessing ...
% 14.79/2.68 Prover 19: Preprocessing ...
% 14.79/2.68 Prover 16: Preprocessing ...
% 15.15/2.71 Prover 13: Warning: ignoring some quantifiers
% 15.15/2.72 Prover 13: Constructing countermodel ...
% 15.15/2.74 Prover 13: gave up
% 15.15/2.74 Prover 16: Warning: ignoring some quantifiers
% 15.15/2.75 Prover 16: Constructing countermodel ...
% 15.45/2.75 Prover 19: Warning: ignoring some quantifiers
% 15.45/2.76 Prover 19: Constructing countermodel ...
% 15.45/2.80 Prover 19: gave up
% 32.79/5.31 Prover 11: Found proof (size 73)
% 32.79/5.31 Prover 11: proved (3379ms)
% 32.79/5.31 Prover 16: stopped
% 33.48/5.31 Prover 7: stopped
% 33.48/5.31 Prover 4: stopped
% 33.48/5.32
% 33.48/5.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.48/5.32
% 33.48/5.32 % SZS output start Proof for theBenchmark
% 33.48/5.33 Assumptions after simplification:
% 33.48/5.33 ---------------------------------
% 33.48/5.33
% 33.48/5.33 (additive_associativity)
% 33.48/5.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 33.48/5.35 (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 33.48/5.35 | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & addition(v1, v0) = v5 &
% 33.48/5.35 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 33.48/5.35 : ! [v4: $i] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~
% 33.48/5.35 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 &
% 33.48/5.35 addition(v2, v1) = v5 & $i(v5) & $i(v4)))
% 33.48/5.36
% 33.48/5.36 (additive_commutativity)
% 33.48/5.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~
% 33.48/5.36 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 33.48/5.36 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 33.48/5.36 (addition(v1, v0) = v2 & $i(v2)))
% 33.48/5.36
% 33.48/5.36 (distributivity1)
% 33.48/5.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 33.48/5.36 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) |
% 33.48/5.36 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 33.48/5.36 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5))) &
% 33.48/5.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 33.48/5.36 (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~ $i(v2) | ~
% 33.48/5.36 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v0, v2) =
% 33.48/5.36 v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5)
% 33.48/5.36 & $i(v4)))
% 33.48/5.36
% 33.48/5.36 (goals)
% 33.48/5.36 $i(one) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 33.48/5.36 strong_iteration(v0) = v1 & leq(one, v1) = v2 & $i(v1) & $i(v0))
% 33.48/5.36
% 33.48/5.36 (idempotence)
% 33.48/5.36 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~ $i(v0))
% 33.48/5.36
% 33.48/5.36 (infty_unfold1)
% 33.48/5.36 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~
% 33.48/5.36 $i(v0) | ? [v2: $i] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1
% 33.48/5.36 & $i(v2) & $i(v1)))
% 33.48/5.36
% 33.48/5.36 (isolation)
% 33.48/5.36 $i(zero) & ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~
% 33.48/5.36 $i(v0) | ? [v2: $i] : ? [v3: $i] : (star(v0) = v2 & multiplication(v1,
% 33.48/5.36 zero) = v3 & addition(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & !
% 33.48/5.36 [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 33.48/5.36 [v3: $i] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 &
% 33.48/5.36 addition(v1, v3) = v2 & $i(v3) & $i(v2)))
% 33.48/5.36
% 33.48/5.36 (order)
% 33.48/5.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (addition(v0, v1) =
% 33.48/5.37 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1) =
% 33.48/5.37 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0,
% 33.48/5.37 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 33.48/5.37 addition(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 33.48/5.37 (leq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | addition(v0, v1) = v1) & ! [v0:
% 33.48/5.37 $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) | ~ $i(v0) |
% 33.48/5.37 leq(v0, v1) = 0)
% 33.48/5.37
% 33.48/5.37 (star_unfold1)
% 33.48/5.37 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ?
% 33.48/5.37 [v2: $i] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1 & $i(v2) &
% 33.48/5.37 $i(v1)))
% 33.48/5.37
% 33.48/5.37 (star_unfold2)
% 33.48/5.37 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ?
% 33.48/5.37 [v2: $i] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1 & $i(v2) &
% 33.48/5.37 $i(v1)))
% 33.48/5.37
% 33.48/5.37 (function-axioms)
% 33.48/5.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 33.48/5.37 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 33.48/5.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.48/5.37 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 33.48/5.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 33.48/5.37 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 33.48/5.37 [v2: $i] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~
% 33.48/5.37 (strong_iteration(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 33.48/5.37 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0))
% 33.48/5.37
% 33.48/5.37 Further assumptions not needed in the proof:
% 33.48/5.37 --------------------------------------------
% 33.48/5.37 additive_identity, distributivity2, infty_coinduction, left_annihilation,
% 33.48/5.37 multiplicative_associativity, multiplicative_left_identity,
% 33.48/5.37 multiplicative_right_identity, star_induction1, star_induction2
% 33.48/5.37
% 33.48/5.37 Those formulas are unsatisfiable:
% 33.48/5.37 ---------------------------------
% 33.48/5.37
% 33.48/5.37 Begin of proof
% 33.48/5.37 |
% 33.48/5.37 | ALPHA: (additive_commutativity) implies:
% 33.48/5.37 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) |
% 33.48/5.37 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2)))
% 33.48/5.37 |
% 33.48/5.37 | ALPHA: (additive_associativity) implies:
% 33.48/5.37 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 33.48/5.37 | ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~ $i(v2) |
% 33.48/5.37 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 &
% 33.48/5.37 | addition(v2, v1) = v5 & $i(v5) & $i(v4)))
% 33.48/5.37 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 33.48/5.37 | ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) |
% 33.48/5.37 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 &
% 33.48/5.37 | addition(v1, v0) = v5 & $i(v5) & $i(v4)))
% 33.48/5.38 |
% 33.48/5.38 | ALPHA: (distributivity1) implies:
% 33.48/5.38 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 33.48/5.38 | ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~
% 33.48/5.38 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 33.48/5.38 | (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 &
% 33.48/5.38 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4)))
% 33.48/5.38 |
% 33.48/5.38 | ALPHA: (star_unfold1) implies:
% 33.48/5.38 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2:
% 33.48/5.38 | $i] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1 &
% 33.48/5.38 | $i(v2) & $i(v1)))
% 33.48/5.38 |
% 33.48/5.38 | ALPHA: (star_unfold2) implies:
% 33.48/5.38 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2:
% 33.48/5.38 | $i] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1 &
% 33.48/5.38 | $i(v2) & $i(v1)))
% 33.48/5.38 |
% 33.48/5.38 | ALPHA: (infty_unfold1) implies:
% 33.48/5.38 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~ $i(v0)
% 33.48/5.38 | | ? [v2: $i] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1
% 33.48/5.38 | & $i(v2) & $i(v1)))
% 33.48/5.38 |
% 33.48/5.38 | ALPHA: (isolation) implies:
% 33.48/5.38 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~ $i(v0)
% 33.48/5.38 | | ? [v2: $i] : ? [v3: $i] : (star(v0) = v2 & multiplication(v1,
% 33.48/5.38 | zero) = v3 & addition(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1)))
% 33.48/5.38 |
% 33.48/5.38 | ALPHA: (order) implies:
% 33.48/5.38 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) =
% 33.48/5.38 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 33.48/5.38 | addition(v0, v1) = v3 & $i(v3)))
% 33.48/5.38 |
% 33.48/5.38 | ALPHA: (goals) implies:
% 33.48/5.38 | (10) $i(one)
% 33.48/5.38 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 33.48/5.38 | strong_iteration(v0) = v1 & leq(one, v1) = v2 & $i(v1) & $i(v0))
% 33.48/5.38 |
% 33.48/5.38 | ALPHA: (function-axioms) implies:
% 33.48/5.38 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.48/5.38 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 33.48/5.38 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.48/5.38 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 33.48/5.38 |
% 33.48/5.38 | DELTA: instantiating (11) with fresh symbols all_22_0, all_22_1, all_22_2
% 33.48/5.38 | gives:
% 33.48/5.38 | (14) ~ (all_22_0 = 0) & strong_iteration(all_22_2) = all_22_1 & leq(one,
% 33.48/5.38 | all_22_1) = all_22_0 & $i(all_22_1) & $i(all_22_2)
% 33.48/5.38 |
% 33.48/5.38 | ALPHA: (14) implies:
% 33.48/5.38 | (15) ~ (all_22_0 = 0)
% 33.48/5.38 | (16) $i(all_22_2)
% 33.48/5.38 | (17) $i(all_22_1)
% 33.48/5.38 | (18) leq(one, all_22_1) = all_22_0
% 33.48/5.38 | (19) strong_iteration(all_22_2) = all_22_1
% 33.48/5.38 |
% 33.48/5.38 | GROUND_INST: instantiating (9) with one, all_22_1, all_22_0, simplifying with
% 33.48/5.38 | (10), (17), (18) gives:
% 33.48/5.38 | (20) all_22_0 = 0 | ? [v0: any] : ( ~ (v0 = all_22_1) & addition(one,
% 33.48/5.38 | all_22_1) = v0 & $i(v0))
% 33.48/5.38 |
% 33.48/5.38 | GROUND_INST: instantiating (8) with all_22_2, all_22_1, simplifying with (16),
% 33.48/5.38 | (19) gives:
% 33.48/5.39 | (21) ? [v0: $i] : ? [v1: $i] : (star(all_22_2) = v0 &
% 33.48/5.39 | multiplication(all_22_1, zero) = v1 & addition(v0, v1) = all_22_1 &
% 33.48/5.39 | $i(v1) & $i(v0) & $i(all_22_1))
% 33.48/5.39 |
% 33.48/5.39 | GROUND_INST: instantiating (7) with all_22_2, all_22_1, simplifying with (16),
% 33.48/5.39 | (19) gives:
% 33.48/5.39 | (22) ? [v0: $i] : (multiplication(all_22_2, all_22_1) = v0 & addition(v0,
% 33.48/5.39 | one) = all_22_1 & $i(v0) & $i(all_22_1))
% 33.48/5.39 |
% 33.48/5.39 | DELTA: instantiating (22) with fresh symbol all_29_0 gives:
% 33.48/5.39 | (23) multiplication(all_22_2, all_22_1) = all_29_0 & addition(all_29_0,
% 33.48/5.39 | one) = all_22_1 & $i(all_29_0) & $i(all_22_1)
% 33.48/5.39 |
% 33.48/5.39 | ALPHA: (23) implies:
% 33.48/5.39 | (24) $i(all_29_0)
% 33.48/5.39 | (25) addition(all_29_0, one) = all_22_1
% 33.48/5.39 | (26) multiplication(all_22_2, all_22_1) = all_29_0
% 33.48/5.39 |
% 33.48/5.39 | DELTA: instantiating (21) with fresh symbols all_31_0, all_31_1 gives:
% 33.48/5.39 | (27) star(all_22_2) = all_31_1 & multiplication(all_22_1, zero) = all_31_0
% 33.48/5.39 | & addition(all_31_1, all_31_0) = all_22_1 & $i(all_31_0) &
% 33.48/5.39 | $i(all_31_1) & $i(all_22_1)
% 33.48/5.39 |
% 33.48/5.39 | ALPHA: (27) implies:
% 33.48/5.39 | (28) $i(all_31_1)
% 33.48/5.39 | (29) $i(all_31_0)
% 33.48/5.39 | (30) addition(all_31_1, all_31_0) = all_22_1
% 33.48/5.39 | (31) star(all_22_2) = all_31_1
% 33.48/5.39 |
% 33.48/5.39 | BETA: splitting (20) gives:
% 33.48/5.39 |
% 33.48/5.39 | Case 1:
% 33.48/5.39 | |
% 33.48/5.39 | | (32) all_22_0 = 0
% 33.48/5.39 | |
% 33.48/5.39 | | REDUCE: (15), (32) imply:
% 33.48/5.39 | | (33) $false
% 33.48/5.39 | |
% 33.48/5.39 | | CLOSE: (33) is inconsistent.
% 33.48/5.39 | |
% 33.48/5.39 | Case 2:
% 33.48/5.39 | |
% 33.48/5.39 | | (34) ? [v0: any] : ( ~ (v0 = all_22_1) & addition(one, all_22_1) = v0 &
% 33.48/5.39 | | $i(v0))
% 33.48/5.39 | |
% 33.48/5.39 | | DELTA: instantiating (34) with fresh symbol all_37_0 gives:
% 33.48/5.39 | | (35) ~ (all_37_0 = all_22_1) & addition(one, all_22_1) = all_37_0 &
% 33.48/5.39 | | $i(all_37_0)
% 33.48/5.39 | |
% 33.48/5.39 | | ALPHA: (35) implies:
% 33.48/5.39 | | (36) ~ (all_37_0 = all_22_1)
% 33.48/5.39 | | (37) addition(one, all_22_1) = all_37_0
% 33.48/5.39 | |
% 33.48/5.39 | | GROUND_INST: instantiating (2) with one, all_29_0, one, all_22_1, all_37_0,
% 33.48/5.39 | | simplifying with (10), (24), (25), (37) gives:
% 33.48/5.39 | | (38) ? [v0: $i] : (addition(v0, one) = all_37_0 & addition(one,
% 33.48/5.39 | | all_29_0) = v0 & $i(v0) & $i(all_37_0))
% 33.48/5.39 | |
% 33.48/5.39 | | GROUND_INST: instantiating (1) with one, all_29_0, all_22_1, simplifying
% 33.48/5.39 | | with (10), (24), (25) gives:
% 33.48/5.39 | | (39) addition(one, all_29_0) = all_22_1 & $i(all_22_1)
% 33.48/5.39 | |
% 33.48/5.39 | | ALPHA: (39) implies:
% 33.88/5.39 | | (40) addition(one, all_29_0) = all_22_1
% 33.88/5.39 | |
% 33.88/5.39 | | GROUND_INST: instantiating (2) with all_31_0, all_31_1, one, all_22_1,
% 33.88/5.39 | | all_37_0, simplifying with (10), (28), (29), (30), (37) gives:
% 33.88/5.39 | | (41) ? [v0: $i] : (addition(v0, all_31_0) = all_37_0 & addition(one,
% 33.88/5.39 | | all_31_1) = v0 & $i(v0) & $i(all_37_0))
% 33.88/5.39 | |
% 33.88/5.39 | | GROUND_INST: instantiating (4) with all_22_2, all_31_1, all_31_0, all_22_1,
% 33.88/5.39 | | all_29_0, simplifying with (16), (26), (28), (29), (30) gives:
% 33.88/5.39 | | (42) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_2, all_31_0) = v1
% 33.88/5.39 | | & multiplication(all_22_2, all_31_1) = v0 & addition(v0, v1) =
% 33.88/5.39 | | all_29_0 & $i(v1) & $i(v0) & $i(all_29_0))
% 33.88/5.39 | |
% 33.88/5.39 | | GROUND_INST: instantiating (6) with all_22_2, all_31_1, simplifying with
% 33.88/5.39 | | (16), (31) gives:
% 33.88/5.40 | | (43) ? [v0: $i] : (multiplication(all_31_1, all_22_2) = v0 &
% 33.88/5.40 | | addition(one, v0) = all_31_1 & $i(v0) & $i(all_31_1))
% 33.88/5.40 | |
% 33.88/5.40 | | GROUND_INST: instantiating (5) with all_22_2, all_31_1, simplifying with
% 33.88/5.40 | | (16), (31) gives:
% 33.88/5.40 | | (44) ? [v0: $i] : (multiplication(all_22_2, all_31_1) = v0 &
% 33.88/5.40 | | addition(one, v0) = all_31_1 & $i(v0) & $i(all_31_1))
% 33.88/5.40 | |
% 33.88/5.40 | | DELTA: instantiating (44) with fresh symbol all_45_0 gives:
% 33.88/5.40 | | (45) multiplication(all_22_2, all_31_1) = all_45_0 & addition(one,
% 33.88/5.40 | | all_45_0) = all_31_1 & $i(all_45_0) & $i(all_31_1)
% 33.88/5.40 | |
% 33.88/5.40 | | ALPHA: (45) implies:
% 33.88/5.40 | | (46) addition(one, all_45_0) = all_31_1
% 33.88/5.40 | | (47) multiplication(all_22_2, all_31_1) = all_45_0
% 33.88/5.40 | |
% 33.88/5.40 | | DELTA: instantiating (41) with fresh symbol all_47_0 gives:
% 33.88/5.40 | | (48) addition(all_47_0, all_31_0) = all_37_0 & addition(one, all_31_1) =
% 33.88/5.40 | | all_47_0 & $i(all_47_0) & $i(all_37_0)
% 33.88/5.40 | |
% 33.88/5.40 | | ALPHA: (48) implies:
% 33.88/5.40 | | (49) addition(one, all_31_1) = all_47_0
% 33.88/5.40 | |
% 33.88/5.40 | | DELTA: instantiating (43) with fresh symbol all_49_0 gives:
% 33.88/5.40 | | (50) multiplication(all_31_1, all_22_2) = all_49_0 & addition(one,
% 33.88/5.40 | | all_49_0) = all_31_1 & $i(all_49_0) & $i(all_31_1)
% 33.88/5.40 | |
% 33.88/5.40 | | ALPHA: (50) implies:
% 33.88/5.40 | | (51) $i(all_49_0)
% 33.88/5.40 | | (52) addition(one, all_49_0) = all_31_1
% 33.88/5.40 | |
% 33.88/5.40 | | DELTA: instantiating (38) with fresh symbol all_51_0 gives:
% 33.88/5.40 | | (53) addition(all_51_0, one) = all_37_0 & addition(one, all_29_0) =
% 33.88/5.40 | | all_51_0 & $i(all_51_0) & $i(all_37_0)
% 33.88/5.40 | |
% 33.88/5.40 | | ALPHA: (53) implies:
% 33.88/5.40 | | (54) addition(one, all_29_0) = all_51_0
% 33.88/5.40 | | (55) addition(all_51_0, one) = all_37_0
% 33.88/5.40 | |
% 33.88/5.40 | | DELTA: instantiating (42) with fresh symbols all_59_0, all_59_1 gives:
% 33.88/5.40 | | (56) multiplication(all_22_2, all_31_0) = all_59_0 &
% 33.88/5.40 | | multiplication(all_22_2, all_31_1) = all_59_1 & addition(all_59_1,
% 33.88/5.40 | | all_59_0) = all_29_0 & $i(all_59_0) & $i(all_59_1) & $i(all_29_0)
% 33.88/5.40 | |
% 33.88/5.40 | | ALPHA: (56) implies:
% 33.88/5.40 | | (57) $i(all_59_1)
% 33.88/5.40 | | (58) multiplication(all_22_2, all_31_1) = all_59_1
% 33.88/5.40 | |
% 33.88/5.40 | | GROUND_INST: instantiating (12) with all_22_1, all_51_0, all_29_0, one,
% 33.88/5.40 | | simplifying with (40), (54) gives:
% 33.88/5.40 | | (59) all_51_0 = all_22_1
% 33.88/5.40 | |
% 33.88/5.40 | | GROUND_INST: instantiating (13) with all_45_0, all_59_1, all_31_1, all_22_2,
% 33.88/5.40 | | simplifying with (47), (58) gives:
% 33.88/5.40 | | (60) all_59_1 = all_45_0
% 33.88/5.40 | |
% 33.88/5.40 | | REDUCE: (55), (59) imply:
% 33.88/5.40 | | (61) addition(all_22_1, one) = all_37_0
% 33.88/5.40 | |
% 33.88/5.40 | | REDUCE: (57), (60) imply:
% 33.88/5.40 | | (62) $i(all_45_0)
% 33.88/5.40 | |
% 33.88/5.40 | | GROUND_INST: instantiating (2) with all_29_0, one, one, all_22_1, all_37_0,
% 33.88/5.40 | | simplifying with (10), (24), (37), (40) gives:
% 33.88/5.40 | | (63) ? [v0: $i] : (addition(v0, all_29_0) = all_37_0 & addition(one,
% 33.88/5.40 | | one) = v0 & $i(v0) & $i(all_37_0))
% 33.88/5.40 | |
% 33.88/5.40 | | GROUND_INST: instantiating (2) with all_45_0, one, one, all_31_1, all_47_0,
% 33.88/5.40 | | simplifying with (10), (46), (49), (62) gives:
% 33.88/5.40 | | (64) ? [v0: $i] : (addition(v0, all_45_0) = all_47_0 & addition(one,
% 33.88/5.40 | | one) = v0 & $i(v0) & $i(all_47_0))
% 33.88/5.40 | |
% 33.88/5.40 | | GROUND_INST: instantiating (2) with all_49_0, one, one, all_31_1, all_47_0,
% 33.88/5.40 | | simplifying with (10), (49), (51), (52) gives:
% 33.88/5.40 | | (65) ? [v0: $i] : (addition(v0, all_49_0) = all_47_0 & addition(one,
% 33.88/5.40 | | one) = v0 & $i(v0) & $i(all_47_0))
% 33.88/5.40 | |
% 33.88/5.40 | | GROUND_INST: instantiating (3) with one, one, all_29_0, all_22_1, all_37_0,
% 33.88/5.40 | | simplifying with (10), (24), (25), (61) gives:
% 33.88/5.40 | | (66) ? [v0: $i] : (addition(all_29_0, v0) = all_37_0 & addition(one,
% 33.88/5.40 | | one) = v0 & $i(v0) & $i(all_37_0))
% 33.88/5.40 | |
% 33.88/5.40 | | DELTA: instantiating (65) with fresh symbol all_100_0 gives:
% 33.88/5.40 | | (67) addition(all_100_0, all_49_0) = all_47_0 & addition(one, one) =
% 33.88/5.40 | | all_100_0 & $i(all_100_0) & $i(all_47_0)
% 33.88/5.40 | |
% 33.88/5.40 | | ALPHA: (67) implies:
% 33.88/5.40 | | (68) addition(one, one) = all_100_0
% 33.88/5.40 | |
% 33.88/5.40 | | DELTA: instantiating (63) with fresh symbol all_106_0 gives:
% 33.88/5.41 | | (69) addition(all_106_0, all_29_0) = all_37_0 & addition(one, one) =
% 33.88/5.41 | | all_106_0 & $i(all_106_0) & $i(all_37_0)
% 33.88/5.41 | |
% 33.88/5.41 | | ALPHA: (69) implies:
% 33.88/5.41 | | (70) addition(one, one) = all_106_0
% 33.88/5.41 | |
% 33.88/5.41 | | DELTA: instantiating (64) with fresh symbol all_108_0 gives:
% 33.88/5.41 | | (71) addition(all_108_0, all_45_0) = all_47_0 & addition(one, one) =
% 33.88/5.41 | | all_108_0 & $i(all_108_0) & $i(all_47_0)
% 33.88/5.41 | |
% 33.88/5.41 | | ALPHA: (71) implies:
% 33.88/5.41 | | (72) addition(one, one) = all_108_0
% 33.88/5.41 | |
% 33.88/5.41 | | DELTA: instantiating (66) with fresh symbol all_116_0 gives:
% 33.88/5.41 | | (73) addition(all_29_0, all_116_0) = all_37_0 & addition(one, one) =
% 33.88/5.41 | | all_116_0 & $i(all_116_0) & $i(all_37_0)
% 33.88/5.41 | |
% 33.88/5.41 | | ALPHA: (73) implies:
% 33.88/5.41 | | (74) addition(one, one) = all_116_0
% 33.88/5.41 | | (75) addition(all_29_0, all_116_0) = all_37_0
% 33.88/5.41 | |
% 33.88/5.41 | | GROUND_INST: instantiating (12) with all_108_0, all_116_0, one, one,
% 33.88/5.41 | | simplifying with (72), (74) gives:
% 33.88/5.41 | | (76) all_116_0 = all_108_0
% 33.88/5.41 | |
% 33.88/5.41 | | GROUND_INST: instantiating (12) with all_106_0, all_116_0, one, one,
% 33.88/5.41 | | simplifying with (70), (74) gives:
% 33.88/5.41 | | (77) all_116_0 = all_106_0
% 33.88/5.41 | |
% 33.88/5.41 | | GROUND_INST: instantiating (12) with all_100_0, all_116_0, one, one,
% 33.88/5.41 | | simplifying with (68), (74) gives:
% 33.88/5.41 | | (78) all_116_0 = all_100_0
% 33.88/5.41 | |
% 33.88/5.41 | | COMBINE_EQS: (76), (77) imply:
% 33.88/5.41 | | (79) all_108_0 = all_106_0
% 33.88/5.41 | |
% 33.88/5.41 | | COMBINE_EQS: (76), (78) imply:
% 33.88/5.41 | | (80) all_108_0 = all_100_0
% 33.88/5.41 | |
% 33.88/5.41 | | COMBINE_EQS: (79), (80) imply:
% 33.88/5.41 | | (81) all_106_0 = all_100_0
% 33.88/5.41 | |
% 33.88/5.41 | | SIMP: (81) implies:
% 33.88/5.41 | | (82) all_106_0 = all_100_0
% 33.88/5.41 | |
% 33.88/5.41 | | REDUCE: (75), (78) imply:
% 33.88/5.41 | | (83) addition(all_29_0, all_100_0) = all_37_0
% 33.88/5.41 | |
% 33.88/5.41 | | GROUND_INST: instantiating (idempotence) with one, all_100_0, simplifying
% 33.88/5.41 | | with (10), (68) gives:
% 33.88/5.41 | | (84) all_100_0 = one
% 33.88/5.41 | |
% 33.88/5.41 | | REDUCE: (83), (84) imply:
% 33.88/5.41 | | (85) addition(all_29_0, one) = all_37_0
% 33.88/5.41 | |
% 33.88/5.41 | | GROUND_INST: instantiating (12) with all_22_1, all_37_0, one, all_29_0,
% 33.88/5.41 | | simplifying with (25), (85) gives:
% 33.88/5.41 | | (86) all_37_0 = all_22_1
% 33.88/5.41 | |
% 33.88/5.41 | | REDUCE: (36), (86) imply:
% 33.88/5.41 | | (87) $false
% 33.88/5.41 | |
% 33.88/5.41 | | CLOSE: (87) is inconsistent.
% 33.88/5.41 | |
% 33.88/5.41 | End of split
% 33.88/5.41 |
% 33.88/5.41 End of proof
% 33.88/5.41 % SZS output end Proof for theBenchmark
% 33.88/5.41
% 33.88/5.41 4808ms
%------------------------------------------------------------------------------