TSTP Solution File: KLE005+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE005+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 : n011.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 05:34:09 EDT 2023
% Result : Theorem 8.17s 1.90s
% Output : Proof 11.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE005+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 : n011.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 11:10:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.65 ________ _____
% 0.21/0.65 ___ __ \_________(_)________________________________
% 0.21/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.65
% 0.21/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.65 (2023-06-19)
% 0.21/0.65
% 0.21/0.65 (c) Philipp Rümmer, 2009-2023
% 0.21/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.65 Amanda Stjerna.
% 0.21/0.65 Free software under BSD-3-Clause.
% 0.21/0.65
% 0.21/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.65
% 0.21/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.67 Running up to 7 provers in parallel.
% 0.21/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.71/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.60/1.08 Prover 4: Preprocessing ...
% 2.60/1.08 Prover 1: Preprocessing ...
% 2.72/1.12 Prover 3: Preprocessing ...
% 2.72/1.12 Prover 2: Preprocessing ...
% 2.72/1.12 Prover 5: Preprocessing ...
% 2.72/1.12 Prover 0: Preprocessing ...
% 2.72/1.12 Prover 6: Preprocessing ...
% 4.78/1.42 Prover 1: Constructing countermodel ...
% 4.78/1.42 Prover 3: Constructing countermodel ...
% 4.78/1.45 Prover 6: Proving ...
% 4.78/1.46 Prover 4: Constructing countermodel ...
% 4.78/1.48 Prover 5: Proving ...
% 5.56/1.50 Prover 0: Proving ...
% 5.73/1.52 Prover 3: gave up
% 5.73/1.52 Prover 1: gave up
% 5.73/1.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.73/1.53 Prover 6: gave up
% 5.73/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.73/1.54 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.73/1.54 Prover 2: Proving ...
% 5.73/1.55 Prover 8: Preprocessing ...
% 5.73/1.56 Prover 7: Preprocessing ...
% 5.73/1.59 Prover 9: Preprocessing ...
% 6.36/1.67 Prover 8: Warning: ignoring some quantifiers
% 6.36/1.68 Prover 8: Constructing countermodel ...
% 7.00/1.72 Prover 7: Constructing countermodel ...
% 7.00/1.73 Prover 9: Constructing countermodel ...
% 7.00/1.76 Prover 8: gave up
% 7.00/1.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.80/1.80 Prover 10: Preprocessing ...
% 7.80/1.82 Prover 7: gave up
% 7.80/1.82 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.80/1.85 Prover 11: Preprocessing ...
% 7.80/1.89 Prover 10: Constructing countermodel ...
% 7.80/1.90 Prover 0: proved (1220ms)
% 8.17/1.90
% 8.17/1.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.17/1.90
% 8.17/1.90 Prover 2: stopped
% 8.17/1.90 Prover 5: stopped
% 8.53/1.92 Prover 9: stopped
% 8.53/1.95 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.53/1.95 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.53/1.95 Prover 13: Preprocessing ...
% 8.53/1.95 Prover 16: Preprocessing ...
% 8.53/1.95 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 8.53/1.95 Prover 19: Preprocessing ...
% 8.53/1.96 Prover 10: gave up
% 8.53/1.97 Prover 11: Constructing countermodel ...
% 9.20/2.01 Prover 16: Warning: ignoring some quantifiers
% 9.20/2.02 Prover 16: Constructing countermodel ...
% 9.20/2.02 Prover 19: Warning: ignoring some quantifiers
% 9.20/2.03 Prover 19: Constructing countermodel ...
% 9.20/2.03 Prover 13: Warning: ignoring some quantifiers
% 9.20/2.04 Prover 13: Constructing countermodel ...
% 9.20/2.06 Prover 19: gave up
% 9.86/2.13 Prover 13: gave up
% 11.35/2.33 Prover 4: Found proof (size 97)
% 11.35/2.33 Prover 4: proved (1648ms)
% 11.35/2.33 Prover 16: stopped
% 11.35/2.33 Prover 11: stopped
% 11.35/2.33
% 11.35/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.35/2.33
% 11.35/2.35 % SZS output start Proof for theBenchmark
% 11.35/2.35 Assumptions after simplification:
% 11.35/2.35 ---------------------------------
% 11.35/2.35
% 11.35/2.35 (additive_commutativity)
% 11.35/2.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~
% 11.35/2.37 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 11.35/2.37 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 11.35/2.37 (addition(v1, v0) = v2 & $i(v2)))
% 11.35/2.37
% 11.35/2.37 (goals)
% 11.35/2.37 $i(one) & $i(zero) & ? [v0: $i] : ( ~ (v0 = zero) & c(one) = v0 & $i(v0))
% 11.35/2.37
% 11.35/2.37 (multiplicative_right_identity)
% 11.35/2.38 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 11.35/2.38 v1) | ~ $i(v0))
% 11.35/2.38
% 11.35/2.38 (right_distributivity)
% 11.35/2.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 11.35/2.38 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) |
% 11.35/2.38 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 11.35/2.38 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5))) &
% 11.35/2.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 11.35/2.38 (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~ $i(v2) | ~
% 11.35/2.38 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v0, v2) =
% 11.35/2.38 v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5)
% 11.35/2.38 & $i(v4)))
% 11.35/2.38
% 11.35/2.38 (test_1)
% 11.35/2.38 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (test(v0) = v1) | ~
% 11.35/2.38 (complement(v2, v0) = 0) | ~ $i(v2) | ~ $i(v0)) & ! [v0: $i] : ( ~
% 11.35/2.38 (test(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (complement(v1, v0) = 0 &
% 11.35/2.38 $i(v1)))
% 11.35/2.38
% 11.35/2.38 (test_2)
% 11.84/2.40 $i(one) & $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 11.84/2.40 (complement(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 11.84/2.40 $i] : ? [v5: $i] : (multiplication(v1, v0) = v4 & multiplication(v0, v1)
% 11.84/2.40 = v3 & addition(v0, v1) = v5 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v5 = one) |
% 11.84/2.40 ~ (v4 = zero) | ~ (v3 = zero)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 11.84/2.40 $i] : ( ~ (multiplication(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 11.84/2.40 any] : ? [v4: $i] : ? [v5: $i] : (complement(v1, v0) = v3 &
% 11.84/2.40 multiplication(v0, v1) = v4 & addition(v0, v1) = v5 & $i(v5) & $i(v4) & (
% 11.84/2.40 ~ (v3 = 0) | (v5 = one & v4 = zero & v2 = zero)))) & ! [v0: $i] : !
% 11.84/2.40 [v1: $i] : ! [v2: $i] : ( ~ (multiplication(v0, v1) = v2) | ~ $i(v1) | ~
% 11.84/2.40 $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : (complement(v1, v0) = v3
% 11.84/2.40 & multiplication(v1, v0) = v4 & addition(v0, v1) = v5 & $i(v5) & $i(v4) &
% 11.84/2.40 ( ~ (v3 = 0) | (v5 = one & v4 = zero & v2 = zero)))) & ! [v0: $i] : !
% 11.84/2.40 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 11.84/2.40 ? [v3: any] : ? [v4: $i] : ? [v5: $i] : (complement(v1, v0) = v3 &
% 11.84/2.40 multiplication(v1, v0) = v5 & multiplication(v0, v1) = v4 & $i(v5) &
% 11.84/2.40 $i(v4) & ( ~ (v3 = 0) | (v5 = zero & v4 = zero & v2 = one)))) & ! [v0:
% 11.84/2.40 $i] : ! [v1: $i] : ( ~ (complement(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 11.84/2.40 (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero &
% 11.84/2.40 addition(v0, v1) = one)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 11.84/2.40 (multiplication(v1, v0) = zero) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 11.84/2.40 [v3: $i] : ? [v4: any] : (complement(v1, v0) = v4 & multiplication(v0, v1)
% 11.84/2.40 = v2 & addition(v0, v1) = v3 & $i(v3) & $i(v2) & ( ~ (v3 = one) | ~ (v2 =
% 11.84/2.40 zero) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 11.84/2.40 (multiplication(v0, v1) = zero) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 11.84/2.40 [v3: $i] : ? [v4: any] : (complement(v1, v0) = v4 & multiplication(v1, v0)
% 11.84/2.40 = v2 & addition(v0, v1) = v3 & $i(v3) & $i(v2) & ( ~ (v3 = one) | ~ (v2 =
% 11.84/2.40 zero) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (addition(v0, v1)
% 11.84/2.40 = one) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: any]
% 11.84/2.40 : (complement(v1, v0) = v4 & multiplication(v1, v0) = v3 &
% 11.84/2.40 multiplication(v0, v1) = v2 & $i(v3) & $i(v2) & ( ~ (v3 = zero) | ~ (v2 =
% 11.84/2.40 zero) | v4 = 0)))
% 11.84/2.40
% 11.84/2.40 (test_3)
% 11.84/2.40 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (complement(v0, v1) = v2) | ~
% 11.84/2.40 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : (c(v0) = v4 & test(v0) =
% 11.84/2.40 v3 & $i(v4) & ( ~ (v3 = 0) | (( ~ (v4 = v1) | v2 = 0) & ( ~ (v2 = 0) | v4
% 11.84/2.40 = v1)))))
% 11.84/2.40
% 11.84/2.40 (test_4)
% 11.84/2.40 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (c(v0) = v1) | ~
% 11.84/2.40 $i(v0) | test(v0) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (test(v0)
% 11.84/2.40 = v1) | ~ $i(v0) | c(v0) = zero)
% 11.84/2.40
% 11.84/2.40 (function-axioms)
% 11.84/2.40 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.84/2.40 [v3: $i] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3, v2) =
% 11.84/2.40 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.84/2.40 $i] : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) =
% 11.84/2.40 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 11.84/2.40 ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & !
% 11.84/2.40 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.84/2.40 (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : !
% 11.84/2.40 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) & !
% 11.84/2.40 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 11.84/2.40 | ~ (test(v2) = v1) | ~ (test(v2) = v0))
% 11.84/2.40
% 11.84/2.40 Further assumptions not needed in the proof:
% 11.84/2.40 --------------------------------------------
% 11.84/2.40 additive_associativity, additive_idempotence, additive_identity,
% 11.84/2.40 left_annihilation, left_distributivity, multiplicative_associativity,
% 11.84/2.40 multiplicative_left_identity, order, right_annihilation
% 11.84/2.40
% 11.84/2.40 Those formulas are unsatisfiable:
% 11.84/2.40 ---------------------------------
% 11.84/2.40
% 11.84/2.40 Begin of proof
% 11.84/2.40 |
% 11.84/2.40 | ALPHA: (additive_commutativity) implies:
% 11.84/2.41 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) |
% 11.84/2.41 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2)))
% 11.84/2.41 |
% 11.84/2.41 | ALPHA: (multiplicative_right_identity) implies:
% 11.84/2.41 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 11.84/2.41 | v1) | ~ $i(v0))
% 11.84/2.41 |
% 11.84/2.41 | ALPHA: (right_distributivity) implies:
% 11.84/2.41 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 11.84/2.41 | ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~
% 11.84/2.41 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 11.84/2.41 | (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 &
% 11.84/2.41 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4)))
% 11.84/2.41 |
% 11.84/2.41 | ALPHA: (test_1) implies:
% 11.84/2.41 | (4) ! [v0: $i] : ( ~ (test(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 11.84/2.41 | (complement(v1, v0) = 0 & $i(v1)))
% 11.84/2.41 |
% 11.84/2.41 | ALPHA: (test_2) implies:
% 11.84/2.41 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (multiplication(v0, v1) = zero) | ~
% 11.84/2.41 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: any] :
% 11.84/2.41 | (complement(v1, v0) = v4 & multiplication(v1, v0) = v2 & addition(v0,
% 11.84/2.41 | v1) = v3 & $i(v3) & $i(v2) & ( ~ (v3 = one) | ~ (v2 = zero) | v4
% 11.84/2.41 | = 0)))
% 11.84/2.41 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (multiplication(v1, v0) = zero) | ~
% 11.84/2.41 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: any] :
% 11.84/2.41 | (complement(v1, v0) = v4 & multiplication(v0, v1) = v2 & addition(v0,
% 11.84/2.41 | v1) = v3 & $i(v3) & $i(v2) & ( ~ (v3 = one) | ~ (v2 = zero) | v4
% 11.84/2.41 | = 0)))
% 11.84/2.41 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (complement(v1, v0) = 0) | ~ $i(v1) |
% 11.84/2.41 | ~ $i(v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) =
% 11.84/2.41 | zero & addition(v0, v1) = one))
% 11.84/2.41 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (multiplication(v0, v1) =
% 11.84/2.41 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5:
% 11.84/2.41 | $i] : (complement(v1, v0) = v3 & multiplication(v1, v0) = v4 &
% 11.84/2.41 | addition(v0, v1) = v5 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = one
% 11.84/2.41 | & v4 = zero & v2 = zero))))
% 11.84/2.41 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (multiplication(v1, v0) =
% 11.84/2.41 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5:
% 11.84/2.41 | $i] : (complement(v1, v0) = v3 & multiplication(v0, v1) = v4 &
% 11.84/2.41 | addition(v0, v1) = v5 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = one
% 11.84/2.41 | & v4 = zero & v2 = zero))))
% 11.84/2.41 |
% 11.84/2.41 | ALPHA: (test_4) implies:
% 11.84/2.41 | (10) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (c(v0) = v1) | ~ $i(v0) |
% 11.84/2.41 | test(v0) = 0)
% 11.84/2.41 |
% 11.84/2.41 | ALPHA: (goals) implies:
% 11.84/2.41 | (11) $i(one)
% 11.84/2.41 | (12) ? [v0: $i] : ( ~ (v0 = zero) & c(one) = v0 & $i(v0))
% 11.84/2.41 |
% 11.84/2.41 | ALPHA: (function-axioms) implies:
% 11.84/2.42 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 11.84/2.42 | : (v1 = v0 | ~ (test(v2) = v1) | ~ (test(v2) = v0))
% 11.84/2.42 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) |
% 11.84/2.42 | ~ (c(v2) = v0))
% 11.84/2.42 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.84/2.42 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 11.84/2.42 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.84/2.42 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 11.84/2.42 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 11.84/2.42 | : ! [v3: $i] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~
% 11.84/2.42 | (complement(v3, v2) = v0))
% 11.84/2.42 |
% 11.84/2.42 | DELTA: instantiating (12) with fresh symbol all_20_0 gives:
% 11.84/2.42 | (18) ~ (all_20_0 = zero) & c(one) = all_20_0 & $i(all_20_0)
% 11.84/2.42 |
% 11.84/2.42 | ALPHA: (18) implies:
% 11.84/2.42 | (19) ~ (all_20_0 = zero)
% 11.84/2.42 | (20) c(one) = all_20_0
% 11.84/2.42 |
% 11.84/2.42 | GROUND_INST: instantiating (10) with one, all_20_0, simplifying with (11),
% 11.84/2.42 | (20) gives:
% 11.84/2.42 | (21) all_20_0 = zero | test(one) = 0
% 11.84/2.42 |
% 11.84/2.42 | BETA: splitting (21) gives:
% 11.84/2.42 |
% 11.84/2.42 | Case 1:
% 11.84/2.42 | |
% 11.84/2.42 | | (22) test(one) = 0
% 11.84/2.42 | |
% 11.84/2.42 | | GROUND_INST: instantiating (4) with one, simplifying with (11), (22) gives:
% 11.84/2.42 | | (23) ? [v0: $i] : (complement(v0, one) = 0 & $i(v0))
% 11.84/2.42 | |
% 11.84/2.42 | | DELTA: instantiating (23) with fresh symbol all_34_0 gives:
% 11.84/2.42 | | (24) complement(all_34_0, one) = 0 & $i(all_34_0)
% 11.84/2.42 | |
% 11.84/2.42 | | ALPHA: (24) implies:
% 11.84/2.42 | | (25) $i(all_34_0)
% 11.84/2.42 | | (26) complement(all_34_0, one) = 0
% 11.84/2.42 | |
% 11.84/2.42 | | GROUND_INST: instantiating (7) with one, all_34_0, simplifying with (11),
% 11.84/2.42 | | (25), (26) gives:
% 11.84/2.42 | | (27) multiplication(all_34_0, one) = zero & multiplication(one, all_34_0)
% 11.84/2.42 | | = zero & addition(one, all_34_0) = one
% 11.84/2.42 | |
% 11.84/2.42 | | ALPHA: (27) implies:
% 11.84/2.42 | | (28) addition(one, all_34_0) = one
% 11.84/2.42 | | (29) multiplication(one, all_34_0) = zero
% 11.84/2.42 | | (30) multiplication(all_34_0, one) = zero
% 11.84/2.42 | |
% 11.84/2.42 | | GROUND_INST: instantiating (1) with all_34_0, one, one, simplifying with
% 11.84/2.42 | | (11), (25), (28) gives:
% 11.84/2.42 | | (31) addition(all_34_0, one) = one
% 11.84/2.42 | |
% 11.84/2.42 | | GROUND_INST: instantiating (6) with all_34_0, one, simplifying with (11),
% 11.84/2.42 | | (25), (29) gives:
% 11.84/2.42 | | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : (complement(one,
% 11.84/2.42 | | all_34_0) = v2 & multiplication(all_34_0, one) = v0 &
% 11.84/2.42 | | addition(all_34_0, one) = v1 & $i(v1) & $i(v0) & ( ~ (v1 = one) |
% 11.84/2.42 | | ~ (v0 = zero) | v2 = 0))
% 11.84/2.43 | |
% 11.84/2.43 | | GROUND_INST: instantiating (9) with all_34_0, one, zero, simplifying with
% 11.84/2.43 | | (11), (25), (29) gives:
% 11.84/2.43 | | (33) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (complement(one,
% 11.84/2.43 | | all_34_0) = v0 & multiplication(all_34_0, one) = v1 &
% 11.84/2.43 | | addition(all_34_0, one) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) |
% 11.84/2.43 | | (v2 = one & v1 = zero)))
% 11.84/2.43 | |
% 11.84/2.43 | | GROUND_INST: instantiating (3) with all_34_0, one, all_34_0, one, zero,
% 11.84/2.43 | | simplifying with (11), (25), (28), (30) gives:
% 11.84/2.43 | | (34) ? [v0: $i] : ? [v1: $i] : (multiplication(all_34_0, all_34_0) = v1
% 11.84/2.43 | | & multiplication(all_34_0, one) = v0 & addition(v0, v1) = zero &
% 11.84/2.43 | | $i(v1) & $i(v0) & $i(zero))
% 11.84/2.43 | |
% 11.84/2.43 | | GROUND_INST: instantiating (5) with all_34_0, one, simplifying with (11),
% 11.84/2.43 | | (25), (30) gives:
% 11.84/2.43 | | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : (complement(one,
% 11.84/2.43 | | all_34_0) = v2 & multiplication(one, all_34_0) = v0 &
% 11.84/2.43 | | addition(all_34_0, one) = v1 & $i(v1) & $i(v0) & ( ~ (v1 = one) |
% 11.84/2.43 | | ~ (v0 = zero) | v2 = 0))
% 11.84/2.43 | |
% 11.84/2.43 | | GROUND_INST: instantiating (2) with all_34_0, zero, simplifying with (25),
% 11.84/2.43 | | (30) gives:
% 11.84/2.43 | | (36) all_34_0 = zero
% 11.84/2.43 | |
% 11.84/2.43 | | GROUND_INST: instantiating (8) with all_34_0, one, zero, simplifying with
% 11.84/2.43 | | (11), (25), (30) gives:
% 11.84/2.43 | | (37) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (complement(one,
% 11.84/2.43 | | all_34_0) = v0 & multiplication(one, all_34_0) = v1 &
% 11.84/2.43 | | addition(all_34_0, one) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) |
% 11.84/2.43 | | (v2 = one & v1 = zero)))
% 11.84/2.43 | |
% 11.84/2.43 | | DELTA: instantiating (34) with fresh symbols all_52_0, all_52_1 gives:
% 11.84/2.43 | | (38) multiplication(all_34_0, all_34_0) = all_52_0 &
% 11.84/2.43 | | multiplication(all_34_0, one) = all_52_1 & addition(all_52_1,
% 11.84/2.43 | | all_52_0) = zero & $i(all_52_0) & $i(all_52_1) & $i(zero)
% 11.84/2.43 | |
% 11.84/2.43 | | ALPHA: (38) implies:
% 11.84/2.43 | | (39) $i(all_52_1)
% 11.84/2.43 | | (40) multiplication(all_34_0, one) = all_52_1
% 11.84/2.43 | |
% 11.84/2.43 | | DELTA: instantiating (37) with fresh symbols all_56_0, all_56_1, all_56_2
% 11.84/2.43 | | gives:
% 11.84/2.43 | | (41) complement(one, all_34_0) = all_56_2 & multiplication(one, all_34_0)
% 11.84/2.43 | | = all_56_1 & addition(all_34_0, one) = all_56_0 & $i(all_56_0) &
% 11.84/2.43 | | $i(all_56_1) & ( ~ (all_56_2 = 0) | (all_56_0 = one & all_56_1 =
% 11.84/2.43 | | zero))
% 11.84/2.43 | |
% 11.84/2.43 | | ALPHA: (41) implies:
% 11.84/2.43 | | (42) $i(all_56_0)
% 11.84/2.43 | | (43) addition(all_34_0, one) = all_56_0
% 11.84/2.43 | | (44) complement(one, all_34_0) = all_56_2
% 11.84/2.43 | |
% 11.84/2.43 | | DELTA: instantiating (32) with fresh symbols all_58_0, all_58_1, all_58_2
% 11.84/2.43 | | gives:
% 11.84/2.43 | | (45) complement(one, all_34_0) = all_58_0 & multiplication(all_34_0, one)
% 11.84/2.43 | | = all_58_2 & addition(all_34_0, one) = all_58_1 & $i(all_58_1) &
% 11.84/2.43 | | $i(all_58_2) & ( ~ (all_58_1 = one) | ~ (all_58_2 = zero) |
% 11.84/2.43 | | all_58_0 = 0)
% 11.84/2.43 | |
% 11.84/2.43 | | ALPHA: (45) implies:
% 11.84/2.43 | | (46) addition(all_34_0, one) = all_58_1
% 11.84/2.43 | | (47) multiplication(all_34_0, one) = all_58_2
% 11.84/2.43 | | (48) complement(one, all_34_0) = all_58_0
% 11.84/2.43 | | (49) ~ (all_58_1 = one) | ~ (all_58_2 = zero) | all_58_0 = 0
% 11.84/2.43 | |
% 11.84/2.43 | | DELTA: instantiating (33) with fresh symbols all_60_0, all_60_1, all_60_2
% 11.84/2.43 | | gives:
% 11.84/2.43 | | (50) complement(one, all_34_0) = all_60_2 & multiplication(all_34_0, one)
% 11.84/2.43 | | = all_60_1 & addition(all_34_0, one) = all_60_0 & $i(all_60_0) &
% 11.84/2.43 | | $i(all_60_1) & ( ~ (all_60_2 = 0) | (all_60_0 = one & all_60_1 =
% 11.84/2.43 | | zero))
% 11.84/2.43 | |
% 11.84/2.43 | | ALPHA: (50) implies:
% 11.84/2.43 | | (51) addition(all_34_0, one) = all_60_0
% 11.84/2.43 | | (52) multiplication(all_34_0, one) = all_60_1
% 11.84/2.43 | | (53) complement(one, all_34_0) = all_60_2
% 11.84/2.43 | |
% 11.84/2.43 | | DELTA: instantiating (35) with fresh symbols all_62_0, all_62_1, all_62_2
% 11.84/2.43 | | gives:
% 11.84/2.44 | | (54) complement(one, all_34_0) = all_62_0 & multiplication(one, all_34_0)
% 11.84/2.44 | | = all_62_2 & addition(all_34_0, one) = all_62_1 & $i(all_62_1) &
% 11.84/2.44 | | $i(all_62_2) & ( ~ (all_62_1 = one) | ~ (all_62_2 = zero) |
% 11.84/2.44 | | all_62_0 = 0)
% 11.84/2.44 | |
% 11.84/2.44 | | ALPHA: (54) implies:
% 11.84/2.44 | | (55) addition(all_34_0, one) = all_62_1
% 11.84/2.44 | | (56) complement(one, all_34_0) = all_62_0
% 11.84/2.44 | |
% 11.84/2.44 | | REDUCE: (36), (56) imply:
% 11.84/2.44 | | (57) complement(one, zero) = all_62_0
% 11.84/2.44 | |
% 11.84/2.44 | | REDUCE: (36), (53) imply:
% 11.84/2.44 | | (58) complement(one, zero) = all_60_2
% 11.84/2.44 | |
% 11.84/2.44 | | REDUCE: (36), (48) imply:
% 11.84/2.44 | | (59) complement(one, zero) = all_58_0
% 11.84/2.44 | |
% 11.84/2.44 | | REDUCE: (36), (44) imply:
% 11.84/2.44 | | (60) complement(one, zero) = all_56_2
% 11.84/2.44 | |
% 11.84/2.44 | | REDUCE: (36), (52) imply:
% 11.84/2.44 | | (61) multiplication(zero, one) = all_60_1
% 11.84/2.44 | |
% 11.84/2.44 | | REDUCE: (36), (47) imply:
% 11.84/2.44 | | (62) multiplication(zero, one) = all_58_2
% 11.84/2.44 | |
% 11.84/2.44 | | REDUCE: (36), (40) imply:
% 11.84/2.44 | | (63) multiplication(zero, one) = all_52_1
% 11.84/2.44 | |
% 11.84/2.44 | | REDUCE: (30), (36) imply:
% 11.84/2.44 | | (64) multiplication(zero, one) = zero
% 11.84/2.44 | |
% 11.84/2.44 | | REDUCE: (36), (55) imply:
% 11.84/2.44 | | (65) addition(zero, one) = all_62_1
% 11.84/2.44 | |
% 11.84/2.44 | | REDUCE: (36), (51) imply:
% 11.84/2.44 | | (66) addition(zero, one) = all_60_0
% 11.84/2.44 | |
% 11.84/2.44 | | REDUCE: (36), (46) imply:
% 11.84/2.44 | | (67) addition(zero, one) = all_58_1
% 11.84/2.44 | |
% 11.84/2.44 | | REDUCE: (36), (43) imply:
% 11.84/2.44 | | (68) addition(zero, one) = all_56_0
% 11.84/2.44 | |
% 11.84/2.44 | | REDUCE: (31), (36) imply:
% 11.84/2.44 | | (69) addition(zero, one) = one
% 11.84/2.44 | |
% 11.84/2.44 | | GROUND_INST: instantiating (15) with all_56_0, all_58_1, one, zero,
% 11.84/2.44 | | simplifying with (67), (68) gives:
% 11.84/2.44 | | (70) all_58_1 = all_56_0
% 11.84/2.44 | |
% 11.84/2.44 | | GROUND_INST: instantiating (15) with all_58_1, all_60_0, one, zero,
% 11.84/2.44 | | simplifying with (66), (67) gives:
% 11.84/2.44 | | (71) all_60_0 = all_58_1
% 11.84/2.44 | |
% 11.84/2.44 | | GROUND_INST: instantiating (15) with all_60_0, all_62_1, one, zero,
% 11.84/2.44 | | simplifying with (65), (66) gives:
% 11.84/2.44 | | (72) all_62_1 = all_60_0
% 11.84/2.44 | |
% 11.84/2.44 | | GROUND_INST: instantiating (15) with one, all_62_1, one, zero, simplifying
% 11.84/2.44 | | with (65), (69) gives:
% 11.84/2.44 | | (73) all_62_1 = one
% 11.84/2.44 | |
% 11.84/2.44 | | GROUND_INST: instantiating (16) with all_58_2, all_60_1, one, zero,
% 11.84/2.44 | | simplifying with (61), (62) gives:
% 11.84/2.44 | | (74) all_60_1 = all_58_2
% 11.84/2.44 | |
% 11.84/2.44 | | GROUND_INST: instantiating (16) with all_52_1, all_60_1, one, zero,
% 11.84/2.44 | | simplifying with (61), (63) gives:
% 11.84/2.44 | | (75) all_60_1 = all_52_1
% 11.84/2.44 | |
% 11.84/2.44 | | GROUND_INST: instantiating (16) with zero, all_60_1, one, zero, simplifying
% 11.84/2.44 | | with (61), (64) gives:
% 11.84/2.44 | | (76) all_60_1 = zero
% 11.84/2.44 | |
% 11.84/2.44 | | GROUND_INST: instantiating (17) with all_58_0, all_60_2, zero, one,
% 11.84/2.44 | | simplifying with (58), (59) gives:
% 11.84/2.44 | | (77) all_60_2 = all_58_0
% 11.84/2.44 | |
% 11.84/2.44 | | GROUND_INST: instantiating (17) with all_60_2, all_62_0, zero, one,
% 11.84/2.44 | | simplifying with (57), (58) gives:
% 11.84/2.44 | | (78) all_62_0 = all_60_2
% 11.84/2.44 | |
% 11.84/2.44 | | GROUND_INST: instantiating (17) with all_56_2, all_62_0, zero, one,
% 11.84/2.44 | | simplifying with (57), (60) gives:
% 11.84/2.44 | | (79) all_62_0 = all_56_2
% 11.84/2.44 | |
% 11.84/2.44 | | COMBINE_EQS: (78), (79) imply:
% 11.84/2.44 | | (80) all_60_2 = all_56_2
% 11.84/2.44 | |
% 11.84/2.44 | | SIMP: (80) implies:
% 11.84/2.44 | | (81) all_60_2 = all_56_2
% 11.84/2.44 | |
% 11.84/2.44 | | COMBINE_EQS: (72), (73) imply:
% 11.84/2.45 | | (82) all_60_0 = one
% 11.84/2.45 | |
% 11.84/2.45 | | SIMP: (82) implies:
% 11.84/2.45 | | (83) all_60_0 = one
% 11.84/2.45 | |
% 11.84/2.45 | | COMBINE_EQS: (71), (83) imply:
% 11.84/2.45 | | (84) all_58_1 = one
% 11.84/2.45 | |
% 11.84/2.45 | | SIMP: (84) implies:
% 11.84/2.45 | | (85) all_58_1 = one
% 11.84/2.45 | |
% 11.84/2.45 | | COMBINE_EQS: (74), (76) imply:
% 11.84/2.45 | | (86) all_58_2 = zero
% 11.84/2.45 | |
% 11.84/2.45 | | COMBINE_EQS: (74), (75) imply:
% 11.84/2.45 | | (87) all_58_2 = all_52_1
% 11.84/2.45 | |
% 11.84/2.45 | | COMBINE_EQS: (77), (81) imply:
% 11.84/2.45 | | (88) all_58_0 = all_56_2
% 11.84/2.45 | |
% 11.84/2.45 | | SIMP: (88) implies:
% 11.84/2.45 | | (89) all_58_0 = all_56_2
% 11.84/2.45 | |
% 11.84/2.45 | | COMBINE_EQS: (70), (85) imply:
% 11.84/2.45 | | (90) all_56_0 = one
% 11.84/2.45 | |
% 11.84/2.45 | | COMBINE_EQS: (86), (87) imply:
% 11.84/2.45 | | (91) all_52_1 = zero
% 11.84/2.45 | |
% 11.84/2.45 | | REDUCE: (39), (91) imply:
% 11.84/2.45 | | (92) $i(zero)
% 11.84/2.45 | |
% 11.84/2.45 | | BETA: splitting (49) gives:
% 11.84/2.45 | |
% 11.84/2.45 | | Case 1:
% 11.84/2.45 | | |
% 11.84/2.45 | | | (93) ~ (all_58_2 = zero)
% 11.84/2.45 | | |
% 11.84/2.45 | | | REDUCE: (86), (93) imply:
% 11.84/2.45 | | | (94) $false
% 11.84/2.45 | | |
% 11.84/2.45 | | | CLOSE: (94) is inconsistent.
% 11.84/2.45 | | |
% 11.84/2.45 | | Case 2:
% 11.84/2.45 | | |
% 11.84/2.45 | | | (95) ~ (all_58_1 = one) | all_58_0 = 0
% 11.84/2.45 | | |
% 11.84/2.45 | | | BETA: splitting (95) gives:
% 11.84/2.45 | | |
% 11.84/2.45 | | | Case 1:
% 11.84/2.45 | | | |
% 11.84/2.45 | | | | (96) ~ (all_58_1 = one)
% 11.84/2.45 | | | |
% 11.84/2.45 | | | | REDUCE: (85), (96) imply:
% 11.84/2.45 | | | | (97) $false
% 11.84/2.45 | | | |
% 11.84/2.45 | | | | CLOSE: (97) is inconsistent.
% 11.84/2.45 | | | |
% 11.84/2.45 | | | Case 2:
% 11.84/2.45 | | | |
% 11.84/2.45 | | | | (98) all_58_0 = 0
% 11.84/2.45 | | | |
% 11.84/2.45 | | | | COMBINE_EQS: (89), (98) imply:
% 11.84/2.45 | | | | (99) all_56_2 = 0
% 11.84/2.45 | | | |
% 11.84/2.45 | | | | SIMP: (99) implies:
% 11.84/2.45 | | | | (100) all_56_2 = 0
% 11.84/2.45 | | | |
% 11.84/2.45 | | | | REDUCE: (60), (100) imply:
% 11.84/2.45 | | | | (101) complement(one, zero) = 0
% 11.84/2.45 | | | |
% 11.84/2.45 | | | | GROUND_INST: instantiating (test_3) with one, zero, 0, simplifying with
% 11.84/2.45 | | | | (11), (92), (101) gives:
% 11.84/2.45 | | | | (102) ? [v0: any] : ? [v1: $i] : (c(one) = v1 & test(one) = v0 &
% 11.84/2.45 | | | | $i(v1) & ( ~ (v0 = 0) | v1 = zero))
% 11.84/2.45 | | | |
% 11.84/2.45 | | | | DELTA: instantiating (102) with fresh symbols all_128_0, all_128_1
% 11.84/2.45 | | | | gives:
% 11.84/2.45 | | | | (103) c(one) = all_128_0 & test(one) = all_128_1 & $i(all_128_0) & (
% 11.84/2.45 | | | | ~ (all_128_1 = 0) | all_128_0 = zero)
% 11.84/2.45 | | | |
% 11.84/2.45 | | | | ALPHA: (103) implies:
% 11.84/2.45 | | | | (104) test(one) = all_128_1
% 11.84/2.45 | | | | (105) c(one) = all_128_0
% 11.84/2.45 | | | | (106) ~ (all_128_1 = 0) | all_128_0 = zero
% 11.84/2.45 | | | |
% 11.84/2.45 | | | | GROUND_INST: instantiating (13) with 0, all_128_1, one, simplifying with
% 11.84/2.45 | | | | (22), (104) gives:
% 11.84/2.45 | | | | (107) all_128_1 = 0
% 11.84/2.45 | | | |
% 11.84/2.45 | | | | GROUND_INST: instantiating (14) with all_20_0, all_128_0, one,
% 11.84/2.45 | | | | simplifying with (20), (105) gives:
% 11.84/2.45 | | | | (108) all_128_0 = all_20_0
% 11.84/2.45 | | | |
% 11.84/2.45 | | | | BETA: splitting (106) gives:
% 11.84/2.45 | | | |
% 11.84/2.45 | | | | Case 1:
% 11.84/2.45 | | | | |
% 11.84/2.45 | | | | | (109) ~ (all_128_1 = 0)
% 11.84/2.45 | | | | |
% 11.84/2.45 | | | | | REDUCE: (107), (109) imply:
% 11.84/2.45 | | | | | (110) $false
% 11.84/2.45 | | | | |
% 11.84/2.45 | | | | | CLOSE: (110) is inconsistent.
% 11.84/2.45 | | | | |
% 11.84/2.46 | | | | Case 2:
% 11.84/2.46 | | | | |
% 11.84/2.46 | | | | | (111) all_128_0 = zero
% 11.84/2.46 | | | | |
% 11.84/2.46 | | | | | COMBINE_EQS: (108), (111) imply:
% 11.84/2.46 | | | | | (112) all_20_0 = zero
% 11.84/2.46 | | | | |
% 11.84/2.46 | | | | | REDUCE: (19), (112) imply:
% 11.84/2.46 | | | | | (113) $false
% 11.84/2.46 | | | | |
% 11.84/2.46 | | | | | CLOSE: (113) is inconsistent.
% 11.84/2.46 | | | | |
% 11.84/2.46 | | | | End of split
% 11.84/2.46 | | | |
% 11.84/2.46 | | | End of split
% 11.84/2.46 | | |
% 11.84/2.46 | | End of split
% 11.84/2.46 | |
% 11.84/2.46 | Case 2:
% 11.84/2.46 | |
% 11.84/2.46 | | (114) all_20_0 = zero
% 11.84/2.46 | |
% 11.84/2.46 | | REDUCE: (19), (114) imply:
% 11.84/2.46 | | (115) $false
% 11.84/2.46 | |
% 11.84/2.46 | | CLOSE: (115) is inconsistent.
% 11.84/2.46 | |
% 11.84/2.46 | End of split
% 11.84/2.46 |
% 11.84/2.46 End of proof
% 11.84/2.46 % SZS output end Proof for theBenchmark
% 11.84/2.46
% 11.84/2.46 1808ms
%------------------------------------------------------------------------------