TSTP Solution File: KLE065+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE065+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 : n029.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 28.13s 4.43s
% Output : Proof 90.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE065+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 11:18:11 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.59/0.60 ________ _____
% 0.59/0.60 ___ __ \_________(_)________________________________
% 0.59/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.59/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.59/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.59/0.60
% 0.59/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.59/0.60 (2023-06-19)
% 0.59/0.60
% 0.59/0.60 (c) Philipp Rümmer, 2009-2023
% 0.59/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.59/0.60 Amanda Stjerna.
% 0.59/0.60 Free software under BSD-3-Clause.
% 0.59/0.60
% 0.59/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.59/0.60
% 0.59/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.59/0.61 Running up to 7 provers in parallel.
% 0.59/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.59/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.59/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.59/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.59/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.59/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.59/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.16/0.99 Prover 1: Preprocessing ...
% 2.16/0.99 Prover 4: Preprocessing ...
% 2.64/1.03 Prover 6: Preprocessing ...
% 2.64/1.03 Prover 5: Preprocessing ...
% 2.64/1.03 Prover 2: Preprocessing ...
% 2.64/1.03 Prover 0: Preprocessing ...
% 2.64/1.04 Prover 3: Preprocessing ...
% 4.55/1.34 Prover 6: Constructing countermodel ...
% 4.55/1.35 Prover 3: Constructing countermodel ...
% 4.99/1.37 Prover 4: Constructing countermodel ...
% 4.99/1.38 Prover 1: Constructing countermodel ...
% 4.99/1.38 Prover 5: Proving ...
% 4.99/1.44 Prover 0: Proving ...
% 6.25/1.53 Prover 2: Proving ...
% 28.13/4.43 Prover 0: proved (3812ms)
% 28.13/4.43
% 28.13/4.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.13/4.43
% 28.13/4.43 Prover 3: stopped
% 28.13/4.44 Prover 5: stopped
% 28.13/4.44 Prover 6: stopped
% 28.13/4.44 Prover 2: stopped
% 28.13/4.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 28.13/4.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 28.13/4.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 28.13/4.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 28.13/4.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 28.74/4.47 Prover 10: Preprocessing ...
% 28.74/4.47 Prover 7: Preprocessing ...
% 28.74/4.48 Prover 11: Preprocessing ...
% 28.74/4.48 Prover 8: Preprocessing ...
% 28.74/4.48 Prover 13: Preprocessing ...
% 29.01/4.52 Prover 8: Warning: ignoring some quantifiers
% 29.01/4.52 Prover 8: Constructing countermodel ...
% 29.33/4.53 Prover 7: Constructing countermodel ...
% 29.33/4.54 Prover 10: Constructing countermodel ...
% 29.38/4.55 Prover 13: Warning: ignoring some quantifiers
% 29.38/4.55 Prover 13: Constructing countermodel ...
% 29.38/4.58 Prover 11: Constructing countermodel ...
% 70.23/9.74 Prover 13: stopped
% 70.23/9.74 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 70.23/9.77 Prover 16: Preprocessing ...
% 70.69/9.83 Prover 16: Warning: ignoring some quantifiers
% 70.69/9.83 Prover 16: Constructing countermodel ...
% 90.41/12.35 Prover 7: Found proof (size 150)
% 90.41/12.35 Prover 7: proved (7897ms)
% 90.41/12.35 Prover 16: stopped
% 90.41/12.36 Prover 11: stopped
% 90.41/12.36 Prover 10: stopped
% 90.41/12.36 Prover 8: stopped
% 90.41/12.36 Prover 4: stopped
% 90.41/12.36 Prover 1: stopped
% 90.41/12.36
% 90.41/12.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 90.41/12.36
% 90.41/12.37 % SZS output start Proof for theBenchmark
% 90.41/12.38 Assumptions after simplification:
% 90.41/12.38 ---------------------------------
% 90.41/12.38
% 90.41/12.38 (additive_identity)
% 90.41/12.40 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1)
% 90.41/12.40 | ~ $i(v0))
% 90.41/12.40
% 90.41/12.40 (domain1)
% 90.41/12.41 ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 90.41/12.41 (multiplication(v1, v0) = v2 & addition(v0, v2) = v2 & $i(v2)))
% 90.41/12.41
% 90.41/12.41 (domain2)
% 90.41/12.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (domain(v1) = v2)
% 90.41/12.41 | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 90.41/12.41 ? [v5: $i] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) =
% 90.41/12.41 v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 90.41/12.41 (multiplication(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 90.41/12.41 [v4: $i] : ? [v5: $i] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) =
% 90.41/12.41 v4 & multiplication(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3)))
% 90.41/12.41
% 90.41/12.41 (domain3)
% 90.41/12.41 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) |
% 90.41/12.41 addition(v1, one) = one)
% 90.41/12.41
% 90.41/12.41 (domain4)
% 90.41/12.41 domain(zero) = zero & $i(zero)
% 90.41/12.41
% 90.41/12.41 (domain5)
% 90.41/12.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 90.41/12.41 (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ~
% 90.41/12.41 $i(v1) | ~ $i(v0) | ? [v5: $i] : (domain(v5) = v4 & addition(v0, v1) = v5
% 90.41/12.41 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 90.41/12.41 (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i]
% 90.41/12.41 : ? [v5: $i] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 &
% 90.41/12.41 addition(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3)))
% 90.41/12.41
% 90.41/12.41 (goals)
% 90.41/12.41 $i(zero) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 90.41/12.41 zero) & domain(v1) = v2 & multiplication(v0, v2) = v3 & multiplication(v0,
% 90.41/12.41 v1) = zero & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 90.41/12.41
% 90.41/12.41 (left_annihilation)
% 90.41/12.42 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero,
% 90.41/12.42 v0) = v1) | ~ $i(v0))
% 90.41/12.42
% 90.41/12.42 (left_distributivity)
% 90.41/12.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 90.41/12.42 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) |
% 90.41/12.42 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 90.41/12.42 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5))) &
% 90.41/12.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 90.41/12.42 (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ $i(v2) | ~
% 90.41/12.42 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v1, v2) =
% 90.41/12.42 v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5)
% 90.41/12.42 & $i(v4)))
% 90.41/12.42
% 90.41/12.42 (right_annihilation)
% 90.41/12.42 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(v0,
% 90.41/12.42 zero) = v1) | ~ $i(v0))
% 90.41/12.42
% 90.41/12.42 (function-axioms)
% 90.41/12.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 90.41/12.42 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 90.41/12.42 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 90.41/12.42 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 90.41/12.42 [v2: $i] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0))
% 90.41/12.42
% 90.41/12.42 Further assumptions not needed in the proof:
% 90.41/12.42 --------------------------------------------
% 90.95/12.42 additive_associativity, additive_commutativity, additive_idempotence,
% 90.95/12.42 multiplicative_associativity, multiplicative_left_identity,
% 90.95/12.42 multiplicative_right_identity, order, right_distributivity
% 90.95/12.42
% 90.95/12.42 Those formulas are unsatisfiable:
% 90.95/12.42 ---------------------------------
% 90.95/12.42
% 90.95/12.42 Begin of proof
% 90.95/12.42 |
% 90.95/12.42 | ALPHA: (additive_identity) implies:
% 90.95/12.42 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) |
% 90.95/12.42 | ~ $i(v0))
% 90.95/12.42 |
% 90.95/12.42 | ALPHA: (left_distributivity) implies:
% 90.95/12.43 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 90.95/12.43 | ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~
% 90.95/12.43 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 90.95/12.43 | (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 &
% 90.95/12.43 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4)))
% 90.95/12.43 |
% 90.95/12.43 | ALPHA: (right_annihilation) implies:
% 90.95/12.43 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(v0, zero) =
% 90.95/12.43 | v1) | ~ $i(v0))
% 90.95/12.43 |
% 90.95/12.43 | ALPHA: (left_annihilation) implies:
% 90.95/12.43 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero, v0) =
% 90.95/12.43 | v1) | ~ $i(v0))
% 90.95/12.43 |
% 90.95/12.43 | ALPHA: (domain2) implies:
% 90.95/12.43 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (multiplication(v0, v1) =
% 90.95/12.43 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 90.95/12.43 | $i] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 &
% 90.95/12.43 | multiplication(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3)))
% 90.95/12.43 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (domain(v1)
% 90.95/12.43 | = v2) | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) |
% 90.95/12.43 | ? [v4: $i] : ? [v5: $i] : (domain(v4) = v5 & domain(v3) = v5 &
% 90.95/12.43 | multiplication(v0, v1) = v4 & $i(v5) & $i(v4)))
% 90.95/12.43 |
% 90.95/12.43 | ALPHA: (domain3) implies:
% 90.95/12.43 | (7) $i(one)
% 90.95/12.43 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) |
% 90.95/12.43 | addition(v1, one) = one)
% 90.95/12.43 |
% 90.95/12.43 | ALPHA: (domain4) implies:
% 90.95/12.43 | (9) domain(zero) = zero
% 90.95/12.43 |
% 90.95/12.43 | ALPHA: (domain5) implies:
% 90.95/12.43 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2)
% 90.95/12.43 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 90.95/12.43 | (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4,
% 90.95/12.43 | v5) = v3 & $i(v5) & $i(v4) & $i(v3)))
% 90.95/12.43 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 90.95/12.43 | ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) =
% 90.95/12.43 | v4) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (domain(v5) = v4 &
% 90.95/12.43 | addition(v0, v1) = v5 & $i(v5) & $i(v4)))
% 90.95/12.43 |
% 90.95/12.43 | ALPHA: (goals) implies:
% 90.95/12.43 | (12) $i(zero)
% 90.95/12.43 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 90.95/12.43 | zero) & domain(v1) = v2 & multiplication(v0, v2) = v3 &
% 90.95/12.43 | multiplication(v0, v1) = zero & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 90.95/12.43 |
% 90.95/12.43 | ALPHA: (function-axioms) implies:
% 90.95/12.43 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (domain(v2) =
% 90.95/12.43 | v1) | ~ (domain(v2) = v0))
% 90.95/12.43 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 90.95/12.43 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 90.95/12.44 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 90.95/12.44 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 90.95/12.44 |
% 90.95/12.44 | DELTA: instantiating (13) with fresh symbols all_20_0, all_20_1, all_20_2,
% 90.95/12.44 | all_20_3 gives:
% 90.95/12.44 | (17) ~ (all_20_0 = zero) & domain(all_20_2) = all_20_1 &
% 90.95/12.44 | multiplication(all_20_3, all_20_1) = all_20_0 &
% 90.95/12.44 | multiplication(all_20_3, all_20_2) = zero & $i(all_20_0) &
% 90.95/12.44 | $i(all_20_1) & $i(all_20_2) & $i(all_20_3)
% 90.95/12.44 |
% 90.95/12.44 | ALPHA: (17) implies:
% 90.95/12.44 | (18) ~ (all_20_0 = zero)
% 90.95/12.44 | (19) $i(all_20_3)
% 90.95/12.44 | (20) $i(all_20_2)
% 90.95/12.44 | (21) $i(all_20_1)
% 90.95/12.44 | (22) multiplication(all_20_3, all_20_2) = zero
% 90.95/12.44 | (23) multiplication(all_20_3, all_20_1) = all_20_0
% 90.95/12.44 | (24) domain(all_20_2) = all_20_1
% 90.95/12.44 |
% 90.95/12.44 | GROUND_INST: instantiating (16) with zero, all_20_0, all_20_2, all_20_3,
% 90.95/12.44 | simplifying with (22) gives:
% 90.95/12.44 | (25) all_20_0 = zero | ~ (multiplication(all_20_3, all_20_2) = all_20_0)
% 90.95/12.44 |
% 90.95/12.44 | GROUND_INST: instantiating (5) with all_20_3, all_20_2, zero, simplifying with
% 90.95/12.44 | (19), (20), (22) gives:
% 90.95/12.44 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(v2) = v0 &
% 90.95/12.44 | domain(all_20_2) = v1 & domain(zero) = v0 & multiplication(all_20_3,
% 90.95/12.44 | v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 90.95/12.44 |
% 90.95/12.44 | GROUND_INST: instantiating (4) with all_20_1, all_20_0, simplifying with (21)
% 90.95/12.44 | gives:
% 90.95/12.44 | (27) all_20_0 = zero | ~ (multiplication(zero, all_20_1) = all_20_0)
% 90.95/12.44 |
% 90.95/12.44 | GROUND_INST: instantiating (8) with zero, zero, simplifying with (9), (12)
% 90.95/12.44 | gives:
% 90.95/12.44 | (28) addition(zero, one) = one
% 90.95/12.44 |
% 90.95/12.44 | GROUND_INST: instantiating (domain1) with zero, zero, simplifying with (9),
% 90.95/12.44 | (12) gives:
% 90.95/12.44 | (29) ? [v0: $i] : (multiplication(zero, zero) = v0 & addition(zero, v0) =
% 90.95/12.44 | v0 & $i(v0))
% 90.95/12.44 |
% 90.95/12.44 | GROUND_INST: instantiating (6) with all_20_3, all_20_2, all_20_1, all_20_0,
% 90.95/12.44 | simplifying with (19), (20), (23), (24) gives:
% 90.95/12.44 | (30) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_20_0) = v1 &
% 90.95/12.44 | multiplication(all_20_3, all_20_2) = v0 & $i(v1) & $i(v0))
% 90.95/12.44 |
% 90.95/12.44 | DELTA: instantiating (29) with fresh symbol all_28_0 gives:
% 90.95/12.44 | (31) multiplication(zero, zero) = all_28_0 & addition(zero, all_28_0) =
% 90.95/12.44 | all_28_0 & $i(all_28_0)
% 90.95/12.44 |
% 90.95/12.44 | ALPHA: (31) implies:
% 90.95/12.44 | (32) $i(all_28_0)
% 90.95/12.44 | (33) addition(zero, all_28_0) = all_28_0
% 90.95/12.44 | (34) multiplication(zero, zero) = all_28_0
% 90.95/12.44 |
% 90.95/12.44 | DELTA: instantiating (30) with fresh symbols all_32_0, all_32_1 gives:
% 90.95/12.44 | (35) domain(all_32_1) = all_32_0 & domain(all_20_0) = all_32_0 &
% 90.95/12.44 | multiplication(all_20_3, all_20_2) = all_32_1 & $i(all_32_0) &
% 90.95/12.44 | $i(all_32_1)
% 90.95/12.44 |
% 90.95/12.44 | ALPHA: (35) implies:
% 90.95/12.44 | (36) $i(all_32_1)
% 90.95/12.44 | (37) multiplication(all_20_3, all_20_2) = all_32_1
% 90.95/12.44 |
% 90.95/12.44 | DELTA: instantiating (26) with fresh symbols all_34_0, all_34_1, all_34_2
% 90.95/12.44 | gives:
% 90.95/12.45 | (38) domain(all_34_0) = all_34_2 & domain(all_20_2) = all_34_1 &
% 90.95/12.45 | domain(zero) = all_34_2 & multiplication(all_20_3, all_34_1) =
% 90.95/12.45 | all_34_0 & $i(all_34_0) & $i(all_34_1) & $i(all_34_2)
% 90.95/12.45 |
% 90.95/12.45 | ALPHA: (38) implies:
% 90.95/12.45 | (39) $i(all_34_0)
% 90.95/12.45 | (40) multiplication(all_20_3, all_34_1) = all_34_0
% 90.95/12.45 | (41) domain(zero) = all_34_2
% 90.95/12.45 | (42) domain(all_20_2) = all_34_1
% 90.95/12.45 | (43) domain(all_34_0) = all_34_2
% 90.95/12.45 |
% 90.95/12.45 | BETA: splitting (25) gives:
% 90.95/12.45 |
% 90.95/12.45 | Case 1:
% 90.95/12.45 | |
% 90.95/12.45 | | (44) ~ (multiplication(all_20_3, all_20_2) = all_20_0)
% 90.95/12.45 | |
% 90.95/12.45 | | BETA: splitting (27) gives:
% 90.95/12.45 | |
% 90.95/12.45 | | Case 1:
% 90.95/12.45 | | |
% 90.95/12.45 | | |
% 90.95/12.45 | | | GROUND_INST: instantiating (16) with zero, all_32_1, all_20_2, all_20_3,
% 90.95/12.45 | | | simplifying with (22), (37) gives:
% 90.95/12.45 | | | (45) all_32_1 = zero
% 90.95/12.45 | | |
% 90.95/12.45 | | | GROUND_INST: instantiating (16) with all_20_0, all_34_0, all_20_1,
% 90.95/12.45 | | | all_20_3, simplifying with (23) gives:
% 90.95/12.45 | | | (46) all_34_0 = all_20_0 | ~ (multiplication(all_20_3, all_20_1) =
% 90.95/12.45 | | | all_34_0)
% 90.95/12.45 | | |
% 90.95/12.45 | | | GROUND_INST: instantiating (14) with zero, all_34_2, zero, simplifying
% 90.95/12.45 | | | with (9), (41) gives:
% 90.95/12.45 | | | (47) all_34_2 = zero
% 90.95/12.45 | | |
% 90.95/12.45 | | | GROUND_INST: instantiating (14) with all_20_1, all_34_1, all_20_2,
% 90.95/12.45 | | | simplifying with (24), (42) gives:
% 90.95/12.45 | | | (48) all_34_1 = all_20_1
% 90.95/12.45 | | |
% 90.95/12.45 | | | PRED_UNIFY: (37), (44) imply:
% 90.95/12.45 | | | (49) ~ (all_32_1 = all_20_0)
% 90.95/12.45 | | |
% 90.95/12.45 | | | REDUCE: (45), (49) imply:
% 90.95/12.45 | | | (50) ~ (all_20_0 = zero)
% 90.95/12.45 | | |
% 90.95/12.45 | | | REDUCE: (43), (47) imply:
% 90.95/12.45 | | | (51) domain(all_34_0) = zero
% 90.95/12.45 | | |
% 90.95/12.45 | | | REDUCE: (40), (48) imply:
% 90.95/12.45 | | | (52) multiplication(all_20_3, all_20_1) = all_34_0
% 90.95/12.45 | | |
% 90.95/12.45 | | | BETA: splitting (46) gives:
% 90.95/12.45 | | |
% 90.95/12.45 | | | Case 1:
% 90.95/12.45 | | | |
% 90.95/12.45 | | | | (53) ~ (multiplication(all_20_3, all_20_1) = all_34_0)
% 90.95/12.45 | | | |
% 90.95/12.45 | | | | PRED_UNIFY: (52), (53) imply:
% 90.95/12.45 | | | | (54) $false
% 90.95/12.45 | | | |
% 90.95/12.45 | | | | CLOSE: (54) is inconsistent.
% 90.95/12.45 | | | |
% 90.95/12.45 | | | Case 2:
% 90.95/12.45 | | | |
% 90.95/12.45 | | | | (55) all_34_0 = all_20_0
% 90.95/12.45 | | | |
% 90.95/12.45 | | | | REDUCE: (51), (55) imply:
% 90.95/12.45 | | | | (56) domain(all_20_0) = zero
% 90.95/12.45 | | | |
% 90.95/12.45 | | | | REDUCE: (39), (55) imply:
% 90.95/12.45 | | | | (57) $i(all_20_0)
% 90.95/12.45 | | | |
% 90.95/12.45 | | | | GROUND_INST: instantiating (10) with zero, one, one, simplifying with
% 90.95/12.45 | | | | (7), (12), (28) gives:
% 90.95/12.45 | | | | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(one) = v2 &
% 90.95/12.45 | | | | domain(one) = v0 & domain(zero) = v1 & addition(v1, v2) = v0 &
% 90.95/12.45 | | | | $i(v2) & $i(v1) & $i(v0))
% 90.95/12.45 | | | |
% 90.95/12.45 | | | | GROUND_INST: instantiating (10) with zero, all_28_0, all_28_0,
% 90.95/12.45 | | | | simplifying with (12), (32), (33) gives:
% 90.95/12.45 | | | | (59) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_28_0) = v2
% 90.95/12.45 | | | | & domain(all_28_0) = v0 & domain(zero) = v1 & addition(v1, v2)
% 90.95/12.45 | | | | = v0 & $i(v2) & $i(v1) & $i(v0))
% 90.95/12.45 | | | |
% 90.95/12.45 | | | | GROUND_INST: instantiating (2) with zero, zero, zero, zero, zero,
% 90.95/12.45 | | | | simplifying with (12) gives:
% 90.95/12.46 | | | | (60) ~ (multiplication(zero, zero) = zero) | ~ (addition(zero,
% 90.95/12.46 | | | | zero) = zero) | ? [v0: $i] : ? [v1: $i] :
% 90.95/12.46 | | | | (multiplication(zero, zero) = v1 & multiplication(zero, zero) =
% 90.95/12.46 | | | | v0 & addition(v0, v1) = zero & $i(v1) & $i(v0))
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | GROUND_INST: instantiating (2) with zero, zero, zero, zero, all_28_0,
% 90.95/12.46 | | | | simplifying with (12), (34) gives:
% 90.95/12.46 | | | | (61) ~ (addition(zero, zero) = zero) | ? [v0: $i] : ? [v1: $i] :
% 90.95/12.46 | | | | (multiplication(zero, zero) = v1 & multiplication(zero, zero) =
% 90.95/12.46 | | | | v0 & addition(v0, v1) = all_28_0 & $i(v1) & $i(v0) &
% 90.95/12.46 | | | | $i(all_28_0))
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | GROUND_INST: instantiating (6) with zero, zero, zero, all_28_0,
% 90.95/12.46 | | | | simplifying with (9), (12), (34) gives:
% 90.95/12.46 | | | | (62) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_28_0)
% 90.95/12.46 | | | | = v1 & multiplication(zero, zero) = v0 & $i(v1) & $i(v0))
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | GROUND_INST: instantiating (3) with zero, all_28_0, simplifying with
% 90.95/12.46 | | | | (12), (34) gives:
% 90.95/12.46 | | | | (63) all_28_0 = zero
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | GROUND_INST: instantiating (5) with zero, zero, all_28_0, simplifying
% 90.95/12.46 | | | | with (12), (34) gives:
% 90.95/12.46 | | | | (64) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(v2) = v0 &
% 90.95/12.46 | | | | domain(all_28_0) = v0 & domain(zero) = v1 &
% 90.95/12.46 | | | | multiplication(zero, v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | GROUND_INST: instantiating (11) with all_20_0, zero, zero, zero, zero,
% 90.95/12.46 | | | | simplifying with (9), (12), (56), (57) gives:
% 90.95/12.46 | | | | (65) ~ (addition(zero, zero) = zero) | ? [v0: $i] : (domain(v0) =
% 90.95/12.46 | | | | zero & addition(all_20_0, zero) = v0 & $i(v0))
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | GROUND_INST: instantiating (6) with zero, all_20_0, zero, all_28_0,
% 90.95/12.46 | | | | simplifying with (12), (34), (56), (57) gives:
% 90.95/12.46 | | | | (66) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_28_0)
% 90.95/12.46 | | | | = v1 & multiplication(zero, all_20_0) = v0 & $i(v1) & $i(v0))
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | GROUND_INST: instantiating (domain1) with all_20_0, zero, simplifying
% 90.95/12.46 | | | | with (56), (57) gives:
% 90.95/12.46 | | | | (67) ? [v0: $i] : (multiplication(zero, all_20_0) = v0 &
% 90.95/12.46 | | | | addition(all_20_0, v0) = v0 & $i(v0))
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | DELTA: instantiating (67) with fresh symbol all_100_0 gives:
% 90.95/12.46 | | | | (68) multiplication(zero, all_20_0) = all_100_0 & addition(all_20_0,
% 90.95/12.46 | | | | all_100_0) = all_100_0 & $i(all_100_0)
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | ALPHA: (68) implies:
% 90.95/12.46 | | | | (69) addition(all_20_0, all_100_0) = all_100_0
% 90.95/12.46 | | | | (70) multiplication(zero, all_20_0) = all_100_0
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | DELTA: instantiating (62) with fresh symbols all_112_0, all_112_1 gives:
% 90.95/12.46 | | | | (71) domain(all_112_1) = all_112_0 & domain(all_28_0) = all_112_0 &
% 90.95/12.46 | | | | multiplication(zero, zero) = all_112_1 & $i(all_112_0) &
% 90.95/12.46 | | | | $i(all_112_1)
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | ALPHA: (71) implies:
% 90.95/12.46 | | | | (72) multiplication(zero, zero) = all_112_1
% 90.95/12.46 | | | | (73) domain(all_28_0) = all_112_0
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | DELTA: instantiating (66) with fresh symbols all_114_0, all_114_1 gives:
% 90.95/12.46 | | | | (74) domain(all_114_1) = all_114_0 & domain(all_28_0) = all_114_0 &
% 90.95/12.46 | | | | multiplication(zero, all_20_0) = all_114_1 & $i(all_114_0) &
% 90.95/12.46 | | | | $i(all_114_1)
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | ALPHA: (74) implies:
% 90.95/12.46 | | | | (75) multiplication(zero, all_20_0) = all_114_1
% 90.95/12.46 | | | | (76) domain(all_28_0) = all_114_0
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | DELTA: instantiating (64) with fresh symbols all_116_0, all_116_1,
% 90.95/12.46 | | | | all_116_2 gives:
% 90.95/12.46 | | | | (77) domain(all_116_0) = all_116_2 & domain(all_28_0) = all_116_2 &
% 90.95/12.46 | | | | domain(zero) = all_116_1 & multiplication(zero, all_116_1) =
% 90.95/12.46 | | | | all_116_0 & $i(all_116_0) & $i(all_116_1) & $i(all_116_2)
% 90.95/12.46 | | | |
% 90.95/12.46 | | | | ALPHA: (77) implies:
% 90.95/12.46 | | | | (78) multiplication(zero, all_116_1) = all_116_0
% 90.95/12.47 | | | | (79) domain(zero) = all_116_1
% 90.95/12.47 | | | | (80) domain(all_28_0) = all_116_2
% 90.95/12.47 | | | |
% 90.95/12.47 | | | | DELTA: instantiating (58) with fresh symbols all_120_0, all_120_1,
% 90.95/12.47 | | | | all_120_2 gives:
% 90.95/12.47 | | | | (81) domain(one) = all_120_0 & domain(one) = all_120_2 & domain(zero)
% 90.95/12.47 | | | | = all_120_1 & addition(all_120_1, all_120_0) = all_120_2 &
% 90.95/12.47 | | | | $i(all_120_0) & $i(all_120_1) & $i(all_120_2)
% 90.95/12.47 | | | |
% 90.95/12.47 | | | | ALPHA: (81) implies:
% 90.95/12.47 | | | | (82) domain(zero) = all_120_1
% 90.95/12.47 | | | |
% 90.95/12.47 | | | | DELTA: instantiating (59) with fresh symbols all_122_0, all_122_1,
% 90.95/12.47 | | | | all_122_2 gives:
% 90.95/12.47 | | | | (83) domain(all_28_0) = all_122_0 & domain(all_28_0) = all_122_2 &
% 90.95/12.47 | | | | domain(zero) = all_122_1 & addition(all_122_1, all_122_0) =
% 90.95/12.47 | | | | all_122_2 & $i(all_122_0) & $i(all_122_1) & $i(all_122_2)
% 90.95/12.47 | | | |
% 90.95/12.47 | | | | ALPHA: (83) implies:
% 90.95/12.47 | | | | (84) domain(all_28_0) = all_122_0
% 90.95/12.47 | | | |
% 90.95/12.47 | | | | REDUCE: (63), (84) imply:
% 90.95/12.47 | | | | (85) domain(zero) = all_122_0
% 90.95/12.47 | | | |
% 90.95/12.47 | | | | REDUCE: (63), (80) imply:
% 90.95/12.47 | | | | (86) domain(zero) = all_116_2
% 90.95/12.47 | | | |
% 90.95/12.47 | | | | REDUCE: (63), (76) imply:
% 90.95/12.47 | | | | (87) domain(zero) = all_114_0
% 90.95/12.47 | | | |
% 90.95/12.47 | | | | REDUCE: (63), (73) imply:
% 90.95/12.47 | | | | (88) domain(zero) = all_112_0
% 90.95/12.47 | | | |
% 90.95/12.47 | | | | REDUCE: (34), (63) imply:
% 90.95/12.47 | | | | (89) multiplication(zero, zero) = zero
% 90.95/12.47 | | | |
% 90.95/12.47 | | | | REDUCE: (33), (63) imply:
% 90.95/12.47 | | | | (90) addition(zero, zero) = zero
% 90.95/12.47 | | | |
% 90.95/12.47 | | | | BETA: splitting (61) gives:
% 90.95/12.47 | | | |
% 90.95/12.47 | | | | Case 1:
% 90.95/12.47 | | | | |
% 90.95/12.47 | | | | | (91) ~ (addition(zero, zero) = zero)
% 90.95/12.47 | | | | |
% 90.95/12.47 | | | | | PRED_UNIFY: (90), (91) imply:
% 90.95/12.47 | | | | | (92) $false
% 90.95/12.47 | | | | |
% 90.95/12.47 | | | | | CLOSE: (92) is inconsistent.
% 90.95/12.47 | | | | |
% 90.95/12.47 | | | | Case 2:
% 90.95/12.47 | | | | |
% 90.95/12.47 | | | | | (93) ? [v0: $i] : ? [v1: $i] : (multiplication(zero, zero) = v1 &
% 90.95/12.47 | | | | | multiplication(zero, zero) = v0 & addition(v0, v1) =
% 90.95/12.47 | | | | | all_28_0 & $i(v1) & $i(v0) & $i(all_28_0))
% 90.95/12.47 | | | | |
% 90.95/12.47 | | | | | DELTA: instantiating (93) with fresh symbols all_215_0, all_215_1
% 90.95/12.47 | | | | | gives:
% 90.95/12.47 | | | | | (94) multiplication(zero, zero) = all_215_0 & multiplication(zero,
% 90.95/12.47 | | | | | zero) = all_215_1 & addition(all_215_1, all_215_0) =
% 90.95/12.47 | | | | | all_28_0 & $i(all_215_0) & $i(all_215_1) & $i(all_28_0)
% 90.95/12.47 | | | | |
% 90.95/12.47 | | | | | ALPHA: (94) implies:
% 90.95/12.47 | | | | | (95) multiplication(zero, zero) = all_215_1
% 90.95/12.47 | | | | | (96) multiplication(zero, zero) = all_215_0
% 90.95/12.47 | | | | |
% 90.95/12.47 | | | | | BETA: splitting (65) gives:
% 90.95/12.47 | | | | |
% 90.95/12.47 | | | | | Case 1:
% 90.95/12.47 | | | | | |
% 90.95/12.47 | | | | | | (97) ~ (addition(zero, zero) = zero)
% 90.95/12.47 | | | | | |
% 90.95/12.47 | | | | | | PRED_UNIFY: (90), (97) imply:
% 90.95/12.47 | | | | | | (98) $false
% 90.95/12.47 | | | | | |
% 90.95/12.47 | | | | | | CLOSE: (98) is inconsistent.
% 90.95/12.47 | | | | | |
% 90.95/12.47 | | | | | Case 2:
% 90.95/12.47 | | | | | |
% 90.95/12.47 | | | | | | (99) ? [v0: $i] : (domain(v0) = zero & addition(all_20_0, zero)
% 90.95/12.47 | | | | | | = v0 & $i(v0))
% 90.95/12.47 | | | | | |
% 90.95/12.47 | | | | | | DELTA: instantiating (99) with fresh symbol all_220_0 gives:
% 90.95/12.47 | | | | | | (100) domain(all_220_0) = zero & addition(all_20_0, zero) =
% 90.95/12.47 | | | | | | all_220_0 & $i(all_220_0)
% 90.95/12.47 | | | | | |
% 90.95/12.47 | | | | | | ALPHA: (100) implies:
% 90.95/12.47 | | | | | | (101) addition(all_20_0, zero) = all_220_0
% 90.95/12.47 | | | | | |
% 90.95/12.47 | | | | | | BETA: splitting (60) gives:
% 90.95/12.47 | | | | | |
% 90.95/12.47 | | | | | | Case 1:
% 90.95/12.47 | | | | | | |
% 90.95/12.47 | | | | | | | (102) ~ (multiplication(zero, zero) = zero)
% 90.95/12.47 | | | | | | |
% 90.95/12.47 | | | | | | | PRED_UNIFY: (89), (102) imply:
% 90.95/12.47 | | | | | | | (103) $false
% 90.95/12.47 | | | | | | |
% 90.95/12.47 | | | | | | | CLOSE: (103) is inconsistent.
% 90.95/12.47 | | | | | | |
% 90.95/12.47 | | | | | | Case 2:
% 90.95/12.47 | | | | | | |
% 90.95/12.47 | | | | | | | (104) ~ (addition(zero, zero) = zero) | ? [v0: $i] : ? [v1:
% 90.95/12.47 | | | | | | | $i] : (multiplication(zero, zero) = v1 &
% 90.95/12.47 | | | | | | | multiplication(zero, zero) = v0 & addition(v0, v1) =
% 90.95/12.47 | | | | | | | zero & $i(v1) & $i(v0))
% 90.95/12.47 | | | | | | |
% 90.95/12.47 | | | | | | | BETA: splitting (104) gives:
% 90.95/12.47 | | | | | | |
% 90.95/12.47 | | | | | | | Case 1:
% 90.95/12.47 | | | | | | | |
% 90.95/12.47 | | | | | | | | (105) ~ (addition(zero, zero) = zero)
% 90.95/12.47 | | | | | | | |
% 90.95/12.47 | | | | | | | | PRED_UNIFY: (90), (105) imply:
% 90.95/12.47 | | | | | | | | (106) $false
% 90.95/12.47 | | | | | | | |
% 90.95/12.47 | | | | | | | | CLOSE: (106) is inconsistent.
% 90.95/12.47 | | | | | | | |
% 90.95/12.47 | | | | | | | Case 2:
% 90.95/12.47 | | | | | | | |
% 90.95/12.47 | | | | | | | | (107) ? [v0: $i] : ? [v1: $i] : (multiplication(zero, zero)
% 90.95/12.47 | | | | | | | | = v1 & multiplication(zero, zero) = v0 & addition(v0,
% 90.95/12.48 | | | | | | | | v1) = zero & $i(v1) & $i(v0))
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | DELTA: instantiating (107) with fresh symbols all_230_0,
% 90.95/12.48 | | | | | | | | all_230_1 gives:
% 90.95/12.48 | | | | | | | | (108) multiplication(zero, zero) = all_230_0 &
% 90.95/12.48 | | | | | | | | multiplication(zero, zero) = all_230_1 &
% 90.95/12.48 | | | | | | | | addition(all_230_1, all_230_0) = zero & $i(all_230_0) &
% 90.95/12.48 | | | | | | | | $i(all_230_1)
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | ALPHA: (108) implies:
% 90.95/12.48 | | | | | | | | (109) multiplication(zero, zero) = all_230_1
% 90.95/12.48 | | | | | | | | (110) multiplication(zero, zero) = all_230_0
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | GROUND_INST: instantiating (15) with all_220_0, zero, zero,
% 90.95/12.48 | | | | | | | | all_20_0, simplifying with (101) gives:
% 90.95/12.48 | | | | | | | | (111) all_220_0 = zero | ~ (addition(all_20_0, zero) = zero)
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | GROUND_INST: instantiating (16) with all_112_1, all_215_1, zero,
% 90.95/12.48 | | | | | | | | zero, simplifying with (72), (95) gives:
% 90.95/12.48 | | | | | | | | (112) all_215_1 = all_112_1
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | GROUND_INST: instantiating (16) with all_215_0, all_230_1, zero,
% 90.95/12.48 | | | | | | | | zero, simplifying with (96), (109) gives:
% 90.95/12.48 | | | | | | | | (113) all_230_1 = all_215_0
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | GROUND_INST: instantiating (16) with all_215_1, all_230_1, zero,
% 90.95/12.48 | | | | | | | | zero, simplifying with (95), (109) gives:
% 90.95/12.48 | | | | | | | | (114) all_230_1 = all_215_1
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | GROUND_INST: instantiating (16) with all_230_1, all_230_0, zero,
% 90.95/12.48 | | | | | | | | zero, simplifying with (109), (110) gives:
% 90.95/12.48 | | | | | | | | (115) all_230_0 = all_230_1
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | GROUND_INST: instantiating (16) with zero, all_230_0, zero,
% 90.95/12.48 | | | | | | | | zero, simplifying with (89), (110) gives:
% 90.95/12.48 | | | | | | | | (116) all_230_0 = zero
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | GROUND_INST: instantiating (16) with all_100_0, all_114_1,
% 90.95/12.48 | | | | | | | | all_20_0, zero, simplifying with (70), (75) gives:
% 90.95/12.48 | | | | | | | | (117) all_114_1 = all_100_0
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | GROUND_INST: instantiating (16) with all_116_0, zero, all_116_1,
% 90.95/12.48 | | | | | | | | zero, simplifying with (78) gives:
% 90.95/12.48 | | | | | | | | (118) all_116_0 = zero | ~ (multiplication(zero, all_116_1)
% 90.95/12.48 | | | | | | | | = zero)
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | GROUND_INST: instantiating (14) with zero, all_116_2, zero,
% 90.95/12.48 | | | | | | | | simplifying with (9), (86) gives:
% 90.95/12.48 | | | | | | | | (119) all_116_2 = zero
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | GROUND_INST: instantiating (14) with all_112_0, all_116_2, zero,
% 90.95/12.48 | | | | | | | | simplifying with (86), (88) gives:
% 90.95/12.48 | | | | | | | | (120) all_116_2 = all_112_0
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | GROUND_INST: instantiating (14) with all_116_2, all_116_1, zero,
% 90.95/12.48 | | | | | | | | simplifying with (79), (86) gives:
% 90.95/12.48 | | | | | | | | (121) all_116_1 = all_116_2
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | GROUND_INST: instantiating (14) with all_116_1, all_120_1, zero,
% 90.95/12.48 | | | | | | | | simplifying with (79), (82) gives:
% 90.95/12.48 | | | | | | | | (122) all_120_1 = all_116_1
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | GROUND_INST: instantiating (14) with all_120_1, all_122_0, zero,
% 90.95/12.48 | | | | | | | | simplifying with (82), (85) gives:
% 90.95/12.48 | | | | | | | | (123) all_122_0 = all_120_1
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | GROUND_INST: instantiating (14) with all_114_0, all_122_0, zero,
% 90.95/12.48 | | | | | | | | simplifying with (85), (87) gives:
% 90.95/12.48 | | | | | | | | (124) all_122_0 = all_114_0
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | COMBINE_EQS: (115), (116) imply:
% 90.95/12.48 | | | | | | | | (125) all_230_1 = zero
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | SIMP: (125) implies:
% 90.95/12.48 | | | | | | | | (126) all_230_1 = zero
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | COMBINE_EQS: (113), (114) imply:
% 90.95/12.48 | | | | | | | | (127) all_215_0 = all_215_1
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | COMBINE_EQS: (113), (126) imply:
% 90.95/12.48 | | | | | | | | (128) all_215_0 = zero
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | COMBINE_EQS: (127), (128) imply:
% 90.95/12.48 | | | | | | | | (129) all_215_1 = zero
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | SIMP: (129) implies:
% 90.95/12.48 | | | | | | | | (130) all_215_1 = zero
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | COMBINE_EQS: (112), (130) imply:
% 90.95/12.48 | | | | | | | | (131) all_112_1 = zero
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | SIMP: (131) implies:
% 90.95/12.48 | | | | | | | | (132) all_112_1 = zero
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | COMBINE_EQS: (123), (124) imply:
% 90.95/12.48 | | | | | | | | (133) all_120_1 = all_114_0
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | SIMP: (133) implies:
% 90.95/12.48 | | | | | | | | (134) all_120_1 = all_114_0
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | COMBINE_EQS: (122), (134) imply:
% 90.95/12.48 | | | | | | | | (135) all_116_1 = all_114_0
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | SIMP: (135) implies:
% 90.95/12.48 | | | | | | | | (136) all_116_1 = all_114_0
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | COMBINE_EQS: (121), (136) imply:
% 90.95/12.48 | | | | | | | | (137) all_116_2 = all_114_0
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | SIMP: (137) implies:
% 90.95/12.48 | | | | | | | | (138) all_116_2 = all_114_0
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | COMBINE_EQS: (119), (138) imply:
% 90.95/12.48 | | | | | | | | (139) all_114_0 = zero
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | COMBINE_EQS: (120), (138) imply:
% 90.95/12.48 | | | | | | | | (140) all_114_0 = all_112_0
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | COMBINE_EQS: (139), (140) imply:
% 90.95/12.48 | | | | | | | | (141) all_112_0 = zero
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | COMBINE_EQS: (136), (139) imply:
% 90.95/12.48 | | | | | | | | (142) all_116_1 = zero
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | BETA: splitting (118) gives:
% 90.95/12.48 | | | | | | | |
% 90.95/12.48 | | | | | | | | Case 1:
% 90.95/12.48 | | | | | | | | |
% 90.95/12.48 | | | | | | | | | (143) ~ (multiplication(zero, all_116_1) = zero)
% 90.95/12.48 | | | | | | | | |
% 90.95/12.48 | | | | | | | | | REDUCE: (142), (143) imply:
% 90.95/12.48 | | | | | | | | | (144) ~ (multiplication(zero, zero) = zero)
% 90.95/12.48 | | | | | | | | |
% 90.95/12.48 | | | | | | | | | PRED_UNIFY: (89), (144) imply:
% 90.95/12.48 | | | | | | | | | (145) $false
% 90.95/12.49 | | | | | | | | |
% 90.95/12.49 | | | | | | | | | CLOSE: (145) is inconsistent.
% 90.95/12.49 | | | | | | | | |
% 90.95/12.49 | | | | | | | | Case 2:
% 90.95/12.49 | | | | | | | | |
% 90.95/12.49 | | | | | | | | |
% 90.95/12.49 | | | | | | | | | GROUND_INST: instantiating (1) with all_20_0, all_220_0,
% 90.95/12.49 | | | | | | | | | simplifying with (57), (101) gives:
% 90.95/12.49 | | | | | | | | | (146) all_220_0 = all_20_0
% 90.95/12.49 | | | | | | | | |
% 90.95/12.49 | | | | | | | | | GROUND_INST: instantiating (4) with all_20_0, all_100_0,
% 90.95/12.49 | | | | | | | | | simplifying with (57), (70) gives:
% 90.95/12.49 | | | | | | | | | (147) all_100_0 = zero
% 90.95/12.49 | | | | | | | | |
% 90.95/12.49 | | | | | | | | | REDUCE: (69), (147) imply:
% 90.95/12.49 | | | | | | | | | (148) addition(all_20_0, zero) = zero
% 90.95/12.49 | | | | | | | | |
% 90.95/12.49 | | | | | | | | | BETA: splitting (111) gives:
% 90.95/12.49 | | | | | | | | |
% 90.95/12.49 | | | | | | | | | Case 1:
% 90.95/12.49 | | | | | | | | | |
% 90.95/12.49 | | | | | | | | | | (149) ~ (addition(all_20_0, zero) = zero)
% 90.95/12.49 | | | | | | | | | |
% 90.95/12.49 | | | | | | | | | | PRED_UNIFY: (148), (149) imply:
% 90.95/12.49 | | | | | | | | | | (150) $false
% 90.95/12.49 | | | | | | | | | |
% 90.95/12.49 | | | | | | | | | | CLOSE: (150) is inconsistent.
% 90.95/12.49 | | | | | | | | | |
% 90.95/12.49 | | | | | | | | | Case 2:
% 90.95/12.49 | | | | | | | | | |
% 90.95/12.49 | | | | | | | | | | (151) all_220_0 = zero
% 90.95/12.49 | | | | | | | | | |
% 90.95/12.49 | | | | | | | | | | COMBINE_EQS: (146), (151) imply:
% 90.95/12.49 | | | | | | | | | | (152) all_20_0 = zero
% 90.95/12.49 | | | | | | | | | |
% 90.95/12.49 | | | | | | | | | | REDUCE: (18), (152) imply:
% 90.95/12.49 | | | | | | | | | | (153) $false
% 90.95/12.49 | | | | | | | | | |
% 90.95/12.49 | | | | | | | | | | CLOSE: (153) is inconsistent.
% 90.95/12.49 | | | | | | | | | |
% 90.95/12.49 | | | | | | | | | End of split
% 90.95/12.49 | | | | | | | | |
% 90.95/12.49 | | | | | | | | End of split
% 90.95/12.49 | | | | | | | |
% 90.95/12.49 | | | | | | | End of split
% 90.95/12.49 | | | | | | |
% 90.95/12.49 | | | | | | End of split
% 90.95/12.49 | | | | | |
% 90.95/12.49 | | | | | End of split
% 90.95/12.49 | | | | |
% 90.95/12.49 | | | | End of split
% 90.95/12.49 | | | |
% 90.95/12.49 | | | End of split
% 90.95/12.49 | | |
% 90.95/12.49 | | Case 2:
% 90.95/12.49 | | |
% 90.95/12.49 | | | (154) all_20_0 = zero
% 90.95/12.49 | | |
% 90.95/12.49 | | | REDUCE: (18), (154) imply:
% 90.95/12.49 | | | (155) $false
% 90.95/12.49 | | |
% 90.95/12.49 | | | CLOSE: (155) is inconsistent.
% 90.95/12.49 | | |
% 90.95/12.49 | | End of split
% 90.95/12.49 | |
% 90.95/12.49 | Case 2:
% 90.95/12.49 | |
% 90.95/12.49 | | (156) all_20_0 = zero
% 90.95/12.49 | |
% 90.95/12.49 | | REDUCE: (18), (156) imply:
% 90.95/12.49 | | (157) $false
% 90.95/12.49 | |
% 90.95/12.49 | | CLOSE: (157) is inconsistent.
% 90.95/12.49 | |
% 90.95/12.49 | End of split
% 90.95/12.49 |
% 90.95/12.49 End of proof
% 90.95/12.49 % SZS output end Proof for theBenchmark
% 90.95/12.49
% 90.95/12.49 11889ms
%------------------------------------------------------------------------------