TSTP Solution File: LCL897+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL897+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:13:16 EDT 2023
% Result : Theorem 7.34s 1.72s
% Output : Proof 10.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL897+1 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu Aug 24 18:38:57 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.52 ________ _____
% 0.16/0.52 ___ __ \_________(_)________________________________
% 0.16/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.52
% 0.16/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.52 (2023-06-19)
% 0.16/0.52
% 0.16/0.52 (c) Philipp Rümmer, 2009-2023
% 0.16/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.52 Amanda Stjerna.
% 0.16/0.52 Free software under BSD-3-Clause.
% 0.16/0.52
% 0.16/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.52
% 0.16/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.54 Running up to 7 provers in parallel.
% 0.16/0.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.55 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.55 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.55 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.55 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.55 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.72/0.88 Prover 1: Preprocessing ...
% 1.72/0.88 Prover 4: Preprocessing ...
% 1.72/0.93 Prover 2: Preprocessing ...
% 1.72/0.93 Prover 0: Preprocessing ...
% 1.72/0.93 Prover 6: Preprocessing ...
% 1.72/0.93 Prover 3: Preprocessing ...
% 1.72/0.93 Prover 5: Preprocessing ...
% 3.38/1.13 Prover 3: Constructing countermodel ...
% 3.38/1.13 Prover 1: Constructing countermodel ...
% 3.38/1.13 Prover 6: Constructing countermodel ...
% 3.38/1.13 Prover 4: Constructing countermodel ...
% 3.38/1.13 Prover 0: Proving ...
% 3.38/1.13 Prover 5: Proving ...
% 3.59/1.20 Prover 2: Proving ...
% 6.38/1.57 Prover 3: gave up
% 6.38/1.57 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.38/1.61 Prover 7: Preprocessing ...
% 7.15/1.67 Prover 1: gave up
% 7.15/1.69 Prover 7: Constructing countermodel ...
% 7.15/1.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.34/1.72 Prover 8: Preprocessing ...
% 7.34/1.72 Prover 0: proved (1172ms)
% 7.34/1.72
% 7.34/1.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.34/1.72
% 7.34/1.72 Prover 6: stopped
% 7.57/1.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.57/1.73 Prover 5: stopped
% 7.57/1.74 Prover 2: stopped
% 7.57/1.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.57/1.75 Prover 10: Preprocessing ...
% 7.57/1.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.57/1.75 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.57/1.75 Prover 13: Preprocessing ...
% 7.57/1.75 Prover 8: Warning: ignoring some quantifiers
% 7.57/1.76 Prover 11: Preprocessing ...
% 7.57/1.77 Prover 16: Preprocessing ...
% 7.57/1.78 Prover 8: Constructing countermodel ...
% 7.57/1.78 Prover 10: Constructing countermodel ...
% 7.57/1.81 Prover 13: Warning: ignoring some quantifiers
% 7.57/1.81 Prover 16: Warning: ignoring some quantifiers
% 7.57/1.82 Prover 13: Constructing countermodel ...
% 7.57/1.82 Prover 16: Constructing countermodel ...
% 8.33/1.84 Prover 11: Constructing countermodel ...
% 9.44/1.99 Prover 8: gave up
% 9.44/2.01 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.44/2.01 Prover 10: gave up
% 9.44/2.01 Prover 13: gave up
% 9.44/2.02 Prover 19: Preprocessing ...
% 10.18/2.09 Prover 19: Warning: ignoring some quantifiers
% 10.29/2.10 Prover 4: Found proof (size 132)
% 10.29/2.10 Prover 4: proved (1556ms)
% 10.29/2.10 Prover 11: stopped
% 10.29/2.10 Prover 7: stopped
% 10.29/2.10 Prover 16: stopped
% 10.29/2.10 Prover 19: Constructing countermodel ...
% 10.29/2.11 Prover 19: stopped
% 10.29/2.11
% 10.29/2.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.29/2.11
% 10.29/2.14 % SZS output start Proof for theBenchmark
% 10.29/2.15 Assumptions after simplification:
% 10.29/2.15 ---------------------------------
% 10.29/2.15
% 10.29/2.15 (goals_09)
% 10.29/2.18 $i(c) & $i(b) & $i(a) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 10.29/2.18 : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v3) &
% 10.29/2.18 ==>(v1, c) = v2 & ==>(b, c) = v4 & ==>(a, v5) = v6 & ==>(a, b) = v0 & +(v1,
% 10.29/2.18 v2) = v3 & +(b, v4) = v5 & +(a, v6) = v7 & +(a, v0) = v1 & $i(v7) & $i(v6)
% 10.29/2.18 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.29/2.18
% 10.29/2.18 (sos_01)
% 10.29/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 10.29/2.18 (+(v3, v2) = v4) | ~ (+(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 10.29/2.18 ? [v5: $i] : (+(v1, v2) = v5 & +(v0, v5) = v4 & $i(v5) & $i(v4))) & ! [v0:
% 10.29/2.18 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (+(v1, v2)
% 10.29/2.18 = v3) | ~ (+(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 10.29/2.18 $i] : (+(v5, v2) = v4 & +(v0, v1) = v5 & $i(v5) & $i(v4)))
% 10.29/2.18
% 10.29/2.18 (sos_02)
% 10.29/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (+(v1, v0) = v2) | ~ $i(v1) |
% 10.29/2.18 ~ $i(v0) | (+(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 10.29/2.18 $i] : ( ~ (+(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (+(v1, v0) = v2 &
% 10.29/2.18 $i(v2)))
% 10.29/2.18
% 10.29/2.18 (sos_07)
% 10.29/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 10.29/2.19 (==>(v3, v2) = v4) | ~ (+(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 10.29/2.19 | ? [v5: $i] : (==>(v1, v2) = v5 & ==>(v0, v5) = v4 & $i(v5) & $i(v4))) &
% 10.29/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 10.29/2.19 (==>(v1, v2) = v3) | ~ (==>(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 10.29/2.19 $i(v0) | ? [v5: $i] : (==>(v5, v2) = v4 & +(v0, v1) = v5 & $i(v5) &
% 10.29/2.19 $i(v4)))
% 10.29/2.19
% 10.29/2.19 (sos_08)
% 10.29/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (==>(v1, v0) = v2) | ~ $i(v1) |
% 10.29/2.19 ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (==>(v0, v1) = v3 & +(v1, v2) = v4 &
% 10.29/2.19 +(v0, v3) = v4 & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 10.29/2.19 $i] : ( ~ (==>(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 10.29/2.19 $i] : (==>(v1, v0) = v4 & +(v1, v4) = v3 & +(v0, v2) = v3 & $i(v4) &
% 10.29/2.19 $i(v3)))
% 10.29/2.19
% 10.29/2.19 (function-axioms)
% 10.29/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (==>(v3,
% 10.29/2.19 v2) = v1) | ~ (==>(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 10.29/2.19 $i] : ! [v3: $i] : (v1 = v0 | ~ (+(v3, v2) = v1) | ~ (+(v3, v2) = v0))
% 10.29/2.19
% 10.29/2.19 Further assumptions not needed in the proof:
% 10.29/2.19 --------------------------------------------
% 10.29/2.19 sos_03, sos_04, sos_05, sos_06
% 10.29/2.19
% 10.29/2.19 Those formulas are unsatisfiable:
% 10.29/2.19 ---------------------------------
% 10.29/2.19
% 10.29/2.19 Begin of proof
% 10.29/2.19 |
% 10.29/2.19 | ALPHA: (sos_01) implies:
% 10.29/2.20 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 10.29/2.20 | ~ (+(v1, v2) = v3) | ~ (+(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 10.29/2.20 | $i(v0) | ? [v5: $i] : (+(v5, v2) = v4 & +(v0, v1) = v5 & $i(v5) &
% 10.29/2.20 | $i(v4)))
% 10.29/2.20 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 10.29/2.20 | ~ (+(v3, v2) = v4) | ~ (+(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 10.29/2.20 | $i(v0) | ? [v5: $i] : (+(v1, v2) = v5 & +(v0, v5) = v4 & $i(v5) &
% 10.29/2.20 | $i(v4)))
% 10.29/2.20 |
% 10.29/2.20 | ALPHA: (sos_02) implies:
% 10.29/2.20 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (+(v1, v0) = v2) | ~
% 10.29/2.20 | $i(v1) | ~ $i(v0) | (+(v0, v1) = v2 & $i(v2)))
% 10.29/2.20 |
% 10.29/2.20 | ALPHA: (sos_07) implies:
% 10.29/2.20 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 10.29/2.20 | ~ (==>(v3, v2) = v4) | ~ (+(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 10.29/2.20 | ~ $i(v0) | ? [v5: $i] : (==>(v1, v2) = v5 & ==>(v0, v5) = v4 &
% 10.29/2.20 | $i(v5) & $i(v4)))
% 10.29/2.20 |
% 10.29/2.20 | ALPHA: (sos_08) implies:
% 10.29/2.20 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (==>(v0, v1) = v2) | ~
% 10.29/2.20 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (==>(v1, v0) = v4 &
% 10.29/2.20 | +(v1, v4) = v3 & +(v0, v2) = v3 & $i(v4) & $i(v3)))
% 10.29/2.20 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (==>(v1, v0) = v2) | ~
% 10.29/2.20 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (==>(v0, v1) = v3 &
% 10.29/2.20 | +(v1, v2) = v4 & +(v0, v3) = v4 & $i(v4) & $i(v3)))
% 10.29/2.20 |
% 10.29/2.20 | ALPHA: (goals_09) implies:
% 10.29/2.20 | (7) $i(a)
% 10.29/2.20 | (8) $i(b)
% 10.29/2.20 | (9) $i(c)
% 10.29/2.21 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 10.29/2.21 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v3) & ==>(v1, c) =
% 10.29/2.21 | v2 & ==>(b, c) = v4 & ==>(a, v5) = v6 & ==>(a, b) = v0 & +(v1, v2) =
% 10.29/2.21 | v3 & +(b, v4) = v5 & +(a, v6) = v7 & +(a, v0) = v1 & $i(v7) & $i(v6)
% 10.29/2.21 | & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.29/2.21 |
% 10.29/2.21 | ALPHA: (function-axioms) implies:
% 10.29/2.21 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.29/2.21 | (+(v3, v2) = v1) | ~ (+(v3, v2) = v0))
% 10.29/2.21 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.29/2.21 | (==>(v3, v2) = v1) | ~ (==>(v3, v2) = v0))
% 10.29/2.21 |
% 10.29/2.21 | DELTA: instantiating (10) with fresh symbols all_12_0, all_12_1, all_12_2,
% 10.29/2.21 | all_12_3, all_12_4, all_12_5, all_12_6, all_12_7 gives:
% 10.29/2.21 | (13) ~ (all_12_0 = all_12_4) & ==>(all_12_6, c) = all_12_5 & ==>(b, c) =
% 10.29/2.21 | all_12_3 & ==>(a, all_12_2) = all_12_1 & ==>(a, b) = all_12_7 &
% 10.29/2.21 | +(all_12_6, all_12_5) = all_12_4 & +(b, all_12_3) = all_12_2 & +(a,
% 10.29/2.21 | all_12_1) = all_12_0 & +(a, all_12_7) = all_12_6 & $i(all_12_0) &
% 10.29/2.21 | $i(all_12_1) & $i(all_12_2) & $i(all_12_3) & $i(all_12_4) &
% 10.29/2.21 | $i(all_12_5) & $i(all_12_6) & $i(all_12_7)
% 10.29/2.21 |
% 10.29/2.21 | ALPHA: (13) implies:
% 10.29/2.21 | (14) ~ (all_12_0 = all_12_4)
% 10.29/2.21 | (15) $i(all_12_7)
% 10.29/2.21 | (16) $i(all_12_5)
% 10.29/2.21 | (17) $i(all_12_3)
% 10.29/2.21 | (18) +(a, all_12_7) = all_12_6
% 10.29/2.21 | (19) +(a, all_12_1) = all_12_0
% 10.29/2.21 | (20) +(b, all_12_3) = all_12_2
% 10.29/2.21 | (21) +(all_12_6, all_12_5) = all_12_4
% 10.29/2.21 | (22) ==>(a, b) = all_12_7
% 10.29/2.21 | (23) ==>(a, all_12_2) = all_12_1
% 10.29/2.21 | (24) ==>(b, c) = all_12_3
% 10.29/2.21 | (25) ==>(all_12_6, c) = all_12_5
% 10.29/2.21 |
% 10.29/2.21 | GROUND_INST: instantiating (3) with all_12_7, a, all_12_6, simplifying with
% 10.29/2.21 | (7), (15), (18) gives:
% 10.29/2.21 | (26) +(all_12_7, a) = all_12_6 & $i(all_12_6)
% 10.29/2.21 |
% 10.29/2.21 | ALPHA: (26) implies:
% 10.29/2.21 | (27) $i(all_12_6)
% 10.29/2.21 |
% 10.29/2.21 | GROUND_INST: instantiating (3) with all_12_3, b, all_12_2, simplifying with
% 10.29/2.21 | (8), (17), (20) gives:
% 10.29/2.21 | (28) +(all_12_3, b) = all_12_2 & $i(all_12_2)
% 10.29/2.21 |
% 10.29/2.21 | ALPHA: (28) implies:
% 10.29/2.21 | (29) $i(all_12_2)
% 10.29/2.21 | (30) +(all_12_3, b) = all_12_2
% 10.29/2.21 |
% 10.29/2.21 | GROUND_INST: instantiating (3) with all_12_5, all_12_6, all_12_4, simplifying
% 10.29/2.21 | with (16), (21), (27) gives:
% 10.29/2.21 | (31) +(all_12_5, all_12_6) = all_12_4 & $i(all_12_4)
% 10.29/2.21 |
% 10.29/2.22 | ALPHA: (31) implies:
% 10.29/2.22 | (32) +(all_12_5, all_12_6) = all_12_4
% 10.29/2.22 |
% 10.29/2.22 | GROUND_INST: instantiating (6) with b, a, all_12_7, simplifying with (7), (8),
% 10.29/2.22 | (22) gives:
% 10.29/2.22 | (33) ? [v0: $i] : ? [v1: $i] : (==>(b, a) = v0 & +(b, v0) = v1 & +(a,
% 10.29/2.22 | all_12_7) = v1 & $i(v1) & $i(v0))
% 10.29/2.22 |
% 10.29/2.22 | GROUND_INST: instantiating (5) with a, b, all_12_7, simplifying with (7), (8),
% 10.29/2.22 | (22) gives:
% 10.29/2.22 | (34) ? [v0: $i] : ? [v1: $i] : (==>(b, a) = v1 & +(b, v1) = v0 & +(a,
% 10.29/2.22 | all_12_7) = v0 & $i(v1) & $i(v0))
% 10.29/2.22 |
% 10.29/2.22 | GROUND_INST: instantiating (6) with all_12_2, a, all_12_1, simplifying with
% 10.29/2.22 | (7), (23), (29) gives:
% 10.29/2.22 | (35) ? [v0: $i] : ? [v1: $i] : (==>(all_12_2, a) = v0 & +(all_12_2, v0) =
% 10.29/2.22 | v1 & +(a, all_12_1) = v1 & $i(v1) & $i(v0))
% 10.29/2.22 |
% 10.29/2.22 | GROUND_INST: instantiating (5) with a, all_12_2, all_12_1, simplifying with
% 10.29/2.22 | (7), (23), (29) gives:
% 10.29/2.22 | (36) ? [v0: $i] : ? [v1: $i] : (==>(all_12_2, a) = v1 & +(all_12_2, v1) =
% 10.29/2.22 | v0 & +(a, all_12_1) = v0 & $i(v1) & $i(v0))
% 10.29/2.22 |
% 10.29/2.22 | GROUND_INST: instantiating (6) with c, b, all_12_3, simplifying with (8), (9),
% 10.29/2.22 | (24) gives:
% 10.29/2.22 | (37) ? [v0: $i] : ? [v1: $i] : (==>(c, b) = v0 & +(c, v0) = v1 & +(b,
% 10.29/2.22 | all_12_3) = v1 & $i(v1) & $i(v0))
% 10.29/2.22 |
% 10.29/2.22 | GROUND_INST: instantiating (5) with b, c, all_12_3, simplifying with (8), (9),
% 10.29/2.22 | (24) gives:
% 10.29/2.22 | (38) ? [v0: $i] : ? [v1: $i] : (==>(c, b) = v1 & +(c, v1) = v0 & +(b,
% 10.29/2.22 | all_12_3) = v0 & $i(v1) & $i(v0))
% 10.29/2.22 |
% 10.29/2.22 | GROUND_INST: instantiating (4) with a, all_12_7, c, all_12_6, all_12_5,
% 10.29/2.22 | simplifying with (7), (9), (15), (18), (25) gives:
% 10.29/2.22 | (39) ? [v0: $i] : (==>(all_12_7, c) = v0 & ==>(a, v0) = all_12_5 & $i(v0)
% 10.29/2.22 | & $i(all_12_5))
% 10.29/2.22 |
% 10.29/2.22 | GROUND_INST: instantiating (6) with c, all_12_6, all_12_5, simplifying with
% 10.29/2.22 | (9), (25), (27) gives:
% 10.29/2.22 | (40) ? [v0: $i] : ? [v1: $i] : (==>(c, all_12_6) = v0 & +(all_12_6,
% 10.29/2.22 | all_12_5) = v1 & +(c, v0) = v1 & $i(v1) & $i(v0))
% 10.29/2.22 |
% 10.29/2.22 | GROUND_INST: instantiating (5) with all_12_6, c, all_12_5, simplifying with
% 10.29/2.22 | (9), (25), (27) gives:
% 10.29/2.22 | (41) ? [v0: $i] : ? [v1: $i] : (==>(c, all_12_6) = v1 & +(all_12_6,
% 10.29/2.22 | all_12_5) = v0 & +(c, v1) = v0 & $i(v1) & $i(v0))
% 10.29/2.22 |
% 10.29/2.22 | DELTA: instantiating (39) with fresh symbol all_20_0 gives:
% 10.29/2.22 | (42) ==>(all_12_7, c) = all_20_0 & ==>(a, all_20_0) = all_12_5 &
% 10.29/2.22 | $i(all_20_0) & $i(all_12_5)
% 10.29/2.22 |
% 10.29/2.22 | DELTA: instantiating (37) with fresh symbols all_24_0, all_24_1 gives:
% 10.29/2.22 | (43) ==>(c, b) = all_24_1 & +(c, all_24_1) = all_24_0 & +(b, all_12_3) =
% 10.29/2.22 | all_24_0 & $i(all_24_0) & $i(all_24_1)
% 10.29/2.22 |
% 10.29/2.22 | ALPHA: (43) implies:
% 10.29/2.22 | (44) +(b, all_12_3) = all_24_0
% 10.29/2.23 | (45) +(c, all_24_1) = all_24_0
% 10.29/2.23 | (46) ==>(c, b) = all_24_1
% 10.29/2.23 |
% 10.29/2.23 | DELTA: instantiating (36) with fresh symbols all_26_0, all_26_1 gives:
% 10.29/2.23 | (47) ==>(all_12_2, a) = all_26_0 & +(all_12_2, all_26_0) = all_26_1 & +(a,
% 10.29/2.23 | all_12_1) = all_26_1 & $i(all_26_0) & $i(all_26_1)
% 10.29/2.23 |
% 10.29/2.23 | ALPHA: (47) implies:
% 10.29/2.23 | (48) +(a, all_12_1) = all_26_1
% 10.29/2.23 | (49) +(all_12_2, all_26_0) = all_26_1
% 10.29/2.23 | (50) ==>(all_12_2, a) = all_26_0
% 10.29/2.23 |
% 10.29/2.23 | DELTA: instantiating (35) with fresh symbols all_28_0, all_28_1 gives:
% 10.29/2.23 | (51) ==>(all_12_2, a) = all_28_1 & +(all_12_2, all_28_1) = all_28_0 & +(a,
% 10.29/2.23 | all_12_1) = all_28_0 & $i(all_28_0) & $i(all_28_1)
% 10.29/2.23 |
% 10.29/2.23 | ALPHA: (51) implies:
% 10.29/2.23 | (52) $i(all_28_1)
% 10.29/2.23 | (53) +(a, all_12_1) = all_28_0
% 10.29/2.23 | (54) ==>(all_12_2, a) = all_28_1
% 10.29/2.23 |
% 10.29/2.23 | DELTA: instantiating (33) with fresh symbols all_30_0, all_30_1 gives:
% 10.29/2.23 | (55) ==>(b, a) = all_30_1 & +(b, all_30_1) = all_30_0 & +(a, all_12_7) =
% 10.29/2.23 | all_30_0 & $i(all_30_0) & $i(all_30_1)
% 10.29/2.23 |
% 10.29/2.23 | ALPHA: (55) implies:
% 10.29/2.23 | (56) +(a, all_12_7) = all_30_0
% 10.29/2.23 | (57) +(b, all_30_1) = all_30_0
% 10.29/2.23 | (58) ==>(b, a) = all_30_1
% 10.29/2.23 |
% 10.29/2.23 | DELTA: instantiating (41) with fresh symbols all_32_0, all_32_1 gives:
% 10.29/2.23 | (59) ==>(c, all_12_6) = all_32_0 & +(all_12_6, all_12_5) = all_32_1 & +(c,
% 10.29/2.23 | all_32_0) = all_32_1 & $i(all_32_0) & $i(all_32_1)
% 10.29/2.23 |
% 10.29/2.23 | ALPHA: (59) implies:
% 10.29/2.23 | (60) +(all_12_6, all_12_5) = all_32_1
% 10.29/2.23 |
% 10.29/2.23 | DELTA: instantiating (40) with fresh symbols all_34_0, all_34_1 gives:
% 10.29/2.23 | (61) ==>(c, all_12_6) = all_34_1 & +(all_12_6, all_12_5) = all_34_0 & +(c,
% 10.29/2.23 | all_34_1) = all_34_0 & $i(all_34_0) & $i(all_34_1)
% 10.29/2.23 |
% 10.29/2.23 | ALPHA: (61) implies:
% 10.29/2.23 | (62) +(all_12_6, all_12_5) = all_34_0
% 10.29/2.23 |
% 10.29/2.23 | DELTA: instantiating (38) with fresh symbols all_36_0, all_36_1 gives:
% 10.29/2.23 | (63) ==>(c, b) = all_36_0 & +(c, all_36_0) = all_36_1 & +(b, all_12_3) =
% 10.29/2.23 | all_36_1 & $i(all_36_0) & $i(all_36_1)
% 10.29/2.23 |
% 10.29/2.23 | ALPHA: (63) implies:
% 10.29/2.23 | (64) $i(all_36_0)
% 10.29/2.23 | (65) +(b, all_12_3) = all_36_1
% 10.29/2.23 | (66) ==>(c, b) = all_36_0
% 10.29/2.23 |
% 10.29/2.23 | DELTA: instantiating (34) with fresh symbols all_38_0, all_38_1 gives:
% 10.29/2.23 | (67) ==>(b, a) = all_38_0 & +(b, all_38_0) = all_38_1 & +(a, all_12_7) =
% 10.29/2.23 | all_38_1 & $i(all_38_0) & $i(all_38_1)
% 10.29/2.23 |
% 10.29/2.23 | ALPHA: (67) implies:
% 10.29/2.23 | (68) $i(all_38_0)
% 10.29/2.23 | (69) +(a, all_12_7) = all_38_1
% 10.29/2.23 | (70) ==>(b, a) = all_38_0
% 10.29/2.23 |
% 10.29/2.23 | GROUND_INST: instantiating (11) with all_12_6, all_38_1, all_12_7, a,
% 10.29/2.23 | simplifying with (18), (69) gives:
% 10.29/2.23 | (71) all_38_1 = all_12_6
% 10.29/2.23 |
% 10.29/2.23 | GROUND_INST: instantiating (11) with all_30_0, all_38_1, all_12_7, a,
% 10.29/2.23 | simplifying with (56), (69) gives:
% 10.29/2.23 | (72) all_38_1 = all_30_0
% 10.29/2.23 |
% 10.29/2.23 | GROUND_INST: instantiating (11) with all_12_0, all_28_0, all_12_1, a,
% 10.29/2.23 | simplifying with (19), (53) gives:
% 10.29/2.23 | (73) all_28_0 = all_12_0
% 10.29/2.23 |
% 10.29/2.23 | GROUND_INST: instantiating (11) with all_26_1, all_28_0, all_12_1, a,
% 10.29/2.23 | simplifying with (48), (53) gives:
% 10.29/2.23 | (74) all_28_0 = all_26_1
% 10.29/2.23 |
% 10.29/2.23 | GROUND_INST: instantiating (11) with all_12_2, all_36_1, all_12_3, b,
% 10.29/2.23 | simplifying with (20), (65) gives:
% 10.29/2.23 | (75) all_36_1 = all_12_2
% 10.29/2.23 |
% 10.29/2.23 | GROUND_INST: instantiating (11) with all_24_0, all_36_1, all_12_3, b,
% 10.29/2.23 | simplifying with (44), (65) gives:
% 10.29/2.23 | (76) all_36_1 = all_24_0
% 10.29/2.23 |
% 10.29/2.23 | GROUND_INST: instantiating (11) with all_12_4, all_34_0, all_12_5, all_12_6,
% 10.29/2.23 | simplifying with (21), (62) gives:
% 10.51/2.23 | (77) all_34_0 = all_12_4
% 10.51/2.23 |
% 10.51/2.24 | GROUND_INST: instantiating (11) with all_32_1, all_34_0, all_12_5, all_12_6,
% 10.51/2.24 | simplifying with (60), (62) gives:
% 10.51/2.24 | (78) all_34_0 = all_32_1
% 10.51/2.24 |
% 10.51/2.24 | GROUND_INST: instantiating (12) with all_30_1, all_38_0, a, b, simplifying
% 10.51/2.24 | with (58), (70) gives:
% 10.51/2.24 | (79) all_38_0 = all_30_1
% 10.51/2.24 |
% 10.51/2.24 | GROUND_INST: instantiating (12) with all_24_1, all_36_0, b, c, simplifying
% 10.51/2.24 | with (46), (66) gives:
% 10.51/2.24 | (80) all_36_0 = all_24_1
% 10.51/2.24 |
% 10.51/2.24 | GROUND_INST: instantiating (12) with all_26_0, all_28_1, a, all_12_2,
% 10.97/2.24 | simplifying with (50), (54) gives:
% 10.97/2.24 | (81) all_28_1 = all_26_0
% 10.97/2.24 |
% 10.97/2.24 | COMBINE_EQS: (71), (72) imply:
% 10.97/2.24 | (82) all_30_0 = all_12_6
% 10.97/2.24 |
% 10.97/2.24 | COMBINE_EQS: (75), (76) imply:
% 10.97/2.24 | (83) all_24_0 = all_12_2
% 10.97/2.24 |
% 10.97/2.24 | SIMP: (83) implies:
% 10.97/2.24 | (84) all_24_0 = all_12_2
% 10.97/2.24 |
% 10.97/2.24 | COMBINE_EQS: (77), (78) imply:
% 10.97/2.24 | (85) all_32_1 = all_12_4
% 10.97/2.24 |
% 10.97/2.24 | SIMP: (85) implies:
% 10.97/2.24 | (86) all_32_1 = all_12_4
% 10.97/2.24 |
% 10.97/2.24 | COMBINE_EQS: (73), (74) imply:
% 10.97/2.24 | (87) all_26_1 = all_12_0
% 10.97/2.24 |
% 10.97/2.24 | SIMP: (87) implies:
% 10.97/2.24 | (88) all_26_1 = all_12_0
% 10.97/2.24 |
% 10.97/2.24 | REDUCE: (49), (88) imply:
% 10.97/2.24 | (89) +(all_12_2, all_26_0) = all_12_0
% 10.97/2.24 |
% 10.97/2.24 | REDUCE: (45), (84) imply:
% 10.97/2.24 | (90) +(c, all_24_1) = all_12_2
% 10.97/2.24 |
% 10.97/2.24 | REDUCE: (57), (82) imply:
% 10.97/2.24 | (91) +(b, all_30_1) = all_12_6
% 10.97/2.24 |
% 10.97/2.24 | REDUCE: (68), (79) imply:
% 10.97/2.24 | (92) $i(all_30_1)
% 10.97/2.24 |
% 10.97/2.24 | REDUCE: (64), (80) imply:
% 10.97/2.24 | (93) $i(all_24_1)
% 10.97/2.24 |
% 10.97/2.24 | REDUCE: (52), (81) imply:
% 10.97/2.24 | (94) $i(all_26_0)
% 10.97/2.24 |
% 10.97/2.24 | GROUND_INST: instantiating (4) with b, all_30_1, c, all_12_6, all_12_5,
% 10.97/2.24 | simplifying with (8), (9), (25), (91), (92) gives:
% 10.97/2.24 | (95) ? [v0: $i] : (==>(all_30_1, c) = v0 & ==>(b, v0) = all_12_5 & $i(v0)
% 10.97/2.24 | & $i(all_12_5))
% 10.97/2.24 |
% 10.97/2.24 | GROUND_INST: instantiating (2) with b, all_30_1, all_12_5, all_12_6, all_12_4,
% 10.97/2.24 | simplifying with (8), (16), (21), (91), (92) gives:
% 10.97/2.24 | (96) ? [v0: $i] : (+(all_30_1, all_12_5) = v0 & +(b, v0) = all_12_4 &
% 10.97/2.24 | $i(v0) & $i(all_12_4))
% 10.97/2.24 |
% 10.97/2.24 | GROUND_INST: instantiating (3) with all_30_1, b, all_12_6, simplifying with
% 10.97/2.24 | (8), (91), (92) gives:
% 10.97/2.24 | (97) +(all_30_1, b) = all_12_6 & $i(all_12_6)
% 10.97/2.24 |
% 10.97/2.24 | ALPHA: (97) implies:
% 10.97/2.24 | (98) +(all_30_1, b) = all_12_6
% 10.97/2.24 |
% 10.97/2.24 | GROUND_INST: instantiating (3) with all_24_1, c, all_12_2, simplifying with
% 10.97/2.24 | (9), (90), (93) gives:
% 10.97/2.24 | (99) +(all_24_1, c) = all_12_2 & $i(all_12_2)
% 10.97/2.24 |
% 10.97/2.24 | GROUND_INST: instantiating (2) with b, all_12_3, all_26_0, all_12_2, all_12_0,
% 10.97/2.24 | simplifying with (8), (17), (20), (89), (94) gives:
% 10.97/2.24 | (100) ? [v0: $i] : (+(all_12_3, all_26_0) = v0 & +(b, v0) = all_12_0 &
% 10.97/2.24 | $i(v0) & $i(all_12_0))
% 10.97/2.24 |
% 10.97/2.24 | GROUND_INST: instantiating (3) with all_26_0, all_12_2, all_12_0, simplifying
% 10.97/2.24 | with (29), (89), (94) gives:
% 10.97/2.25 | (101) +(all_26_0, all_12_2) = all_12_0 & $i(all_12_0)
% 10.97/2.25 |
% 10.97/2.25 | ALPHA: (101) implies:
% 10.97/2.25 | (102) +(all_26_0, all_12_2) = all_12_0
% 10.97/2.25 |
% 10.97/2.25 | GROUND_INST: instantiating (4) with b, all_12_3, a, all_12_2, all_26_0,
% 10.97/2.25 | simplifying with (7), (8), (17), (20), (50) gives:
% 10.97/2.25 | (103) ? [v0: $i] : (==>(all_12_3, a) = v0 & ==>(b, v0) = all_26_0 & $i(v0)
% 10.97/2.25 | & $i(all_26_0))
% 10.97/2.25 |
% 10.97/2.25 | GROUND_INST: instantiating (4) with all_12_3, b, a, all_12_2, all_26_0,
% 10.97/2.25 | simplifying with (7), (8), (17), (30), (50) gives:
% 10.97/2.25 | (104) ? [v0: $i] : (==>(all_12_3, v0) = all_26_0 & ==>(b, a) = v0 & $i(v0)
% 10.97/2.25 | & $i(all_26_0))
% 10.97/2.25 |
% 10.97/2.25 | DELTA: instantiating (100) with fresh symbol all_52_0 gives:
% 10.97/2.25 | (105) +(all_12_3, all_26_0) = all_52_0 & +(b, all_52_0) = all_12_0 &
% 10.97/2.25 | $i(all_52_0) & $i(all_12_0)
% 10.97/2.25 |
% 10.97/2.25 | ALPHA: (105) implies:
% 10.97/2.25 | (106) +(all_12_3, all_26_0) = all_52_0
% 10.97/2.25 |
% 10.97/2.25 | DELTA: instantiating (96) with fresh symbol all_56_0 gives:
% 10.97/2.25 | (107) +(all_30_1, all_12_5) = all_56_0 & +(b, all_56_0) = all_12_4 &
% 10.97/2.25 | $i(all_56_0) & $i(all_12_4)
% 10.97/2.25 |
% 10.97/2.25 | ALPHA: (107) implies:
% 10.97/2.25 | (108) +(all_30_1, all_12_5) = all_56_0
% 10.97/2.25 |
% 10.97/2.25 | DELTA: instantiating (95) with fresh symbol all_62_0 gives:
% 10.97/2.25 | (109) ==>(all_30_1, c) = all_62_0 & ==>(b, all_62_0) = all_12_5 &
% 10.97/2.25 | $i(all_62_0) & $i(all_12_5)
% 10.97/2.25 |
% 10.97/2.25 | DELTA: instantiating (104) with fresh symbol all_66_0 gives:
% 10.97/2.25 | (110) ==>(all_12_3, all_66_0) = all_26_0 & ==>(b, a) = all_66_0 &
% 10.97/2.25 | $i(all_66_0) & $i(all_26_0)
% 10.97/2.25 |
% 10.97/2.25 | ALPHA: (110) implies:
% 10.97/2.25 | (111) $i(all_66_0)
% 10.97/2.25 | (112) ==>(b, a) = all_66_0
% 10.97/2.25 | (113) ==>(all_12_3, all_66_0) = all_26_0
% 10.97/2.25 |
% 10.97/2.25 | DELTA: instantiating (103) with fresh symbol all_68_0 gives:
% 10.97/2.25 | (114) ==>(all_12_3, a) = all_68_0 & ==>(b, all_68_0) = all_26_0 &
% 10.97/2.25 | $i(all_68_0) & $i(all_26_0)
% 10.97/2.25 |
% 10.97/2.25 | GROUND_INST: instantiating (12) with all_30_1, all_66_0, a, b, simplifying
% 10.97/2.25 | with (58), (112) gives:
% 10.97/2.25 | (115) all_66_0 = all_30_1
% 10.97/2.25 |
% 10.97/2.25 | REDUCE: (113), (115) imply:
% 10.97/2.25 | (116) ==>(all_12_3, all_30_1) = all_26_0
% 10.97/2.25 |
% 10.97/2.25 | GROUND_INST: instantiating (3) with all_26_0, all_12_3, all_52_0, simplifying
% 10.97/2.25 | with (17), (94), (106) gives:
% 10.97/2.25 | (117) +(all_26_0, all_12_3) = all_52_0 & $i(all_52_0)
% 10.97/2.25 |
% 10.97/2.25 | ALPHA: (117) implies:
% 10.97/2.25 | (118) +(all_26_0, all_12_3) = all_52_0
% 10.97/2.25 |
% 10.97/2.25 | GROUND_INST: instantiating (1) with all_26_0, all_12_3, b, all_12_2, all_12_0,
% 10.97/2.25 | simplifying with (8), (17), (30), (94), (102) gives:
% 10.97/2.25 | (119) ? [v0: $i] : (+(v0, b) = all_12_0 & +(all_26_0, all_12_3) = v0 &
% 10.97/2.25 | $i(v0) & $i(all_12_0))
% 10.97/2.25 |
% 10.97/2.25 | GROUND_INST: instantiating (4) with all_30_1, b, c, all_12_6, all_12_5,
% 10.97/2.25 | simplifying with (8), (9), (25), (92), (98) gives:
% 10.97/2.25 | (120) ? [v0: $i] : (==>(all_30_1, v0) = all_12_5 & ==>(b, c) = v0 & $i(v0)
% 10.97/2.25 | & $i(all_12_5))
% 10.97/2.25 |
% 10.97/2.25 | GROUND_INST: instantiating (1) with all_12_5, all_30_1, b, all_12_6, all_12_4,
% 10.97/2.25 | simplifying with (8), (16), (32), (92), (98) gives:
% 10.97/2.25 | (121) ? [v0: $i] : (+(v0, b) = all_12_4 & +(all_12_5, all_30_1) = v0 &
% 10.97/2.25 | $i(v0) & $i(all_12_4))
% 10.97/2.25 |
% 10.97/2.25 | GROUND_INST: instantiating (3) with all_12_5, all_30_1, all_56_0, simplifying
% 10.97/2.25 | with (16), (92), (108) gives:
% 10.97/2.25 | (122) +(all_12_5, all_30_1) = all_56_0 & $i(all_56_0)
% 10.97/2.25 |
% 10.97/2.25 | ALPHA: (122) implies:
% 10.97/2.26 | (123) +(all_12_5, all_30_1) = all_56_0
% 10.97/2.26 |
% 10.97/2.26 | GROUND_INST: instantiating (6) with all_30_1, all_12_3, all_26_0, simplifying
% 10.97/2.26 | with (17), (92), (116) gives:
% 10.97/2.26 | (124) ? [v0: $i] : ? [v1: $i] : (==>(all_30_1, all_12_3) = v0 &
% 10.97/2.26 | +(all_30_1, v0) = v1 & +(all_12_3, all_26_0) = v1 & $i(v1) &
% 10.97/2.26 | $i(v0))
% 10.97/2.26 |
% 10.97/2.26 | GROUND_INST: instantiating (5) with all_12_3, all_30_1, all_26_0, simplifying
% 10.97/2.26 | with (17), (92), (116) gives:
% 10.97/2.26 | (125) ? [v0: $i] : ? [v1: $i] : (==>(all_30_1, all_12_3) = v1 &
% 10.97/2.26 | +(all_30_1, v1) = v0 & +(all_12_3, all_26_0) = v0 & $i(v1) &
% 10.97/2.26 | $i(v0))
% 10.97/2.26 |
% 10.97/2.26 | DELTA: instantiating (120) with fresh symbol all_100_0 gives:
% 10.97/2.26 | (126) ==>(all_30_1, all_100_0) = all_12_5 & ==>(b, c) = all_100_0 &
% 10.97/2.26 | $i(all_100_0) & $i(all_12_5)
% 10.97/2.26 |
% 10.97/2.26 | ALPHA: (126) implies:
% 10.97/2.26 | (127) ==>(b, c) = all_100_0
% 10.97/2.26 | (128) ==>(all_30_1, all_100_0) = all_12_5
% 10.97/2.26 |
% 10.97/2.26 | DELTA: instantiating (121) with fresh symbol all_108_0 gives:
% 10.97/2.26 | (129) +(all_108_0, b) = all_12_4 & +(all_12_5, all_30_1) = all_108_0 &
% 10.97/2.26 | $i(all_108_0) & $i(all_12_4)
% 10.97/2.26 |
% 10.97/2.26 | ALPHA: (129) implies:
% 10.97/2.26 | (130) +(all_12_5, all_30_1) = all_108_0
% 10.97/2.26 | (131) +(all_108_0, b) = all_12_4
% 10.97/2.26 |
% 10.97/2.26 | DELTA: instantiating (119) with fresh symbol all_110_0 gives:
% 10.97/2.26 | (132) +(all_110_0, b) = all_12_0 & +(all_26_0, all_12_3) = all_110_0 &
% 10.97/2.26 | $i(all_110_0) & $i(all_12_0)
% 10.97/2.26 |
% 10.97/2.26 | ALPHA: (132) implies:
% 10.97/2.26 | (133) +(all_26_0, all_12_3) = all_110_0
% 10.97/2.26 | (134) +(all_110_0, b) = all_12_0
% 10.97/2.26 |
% 10.97/2.26 | DELTA: instantiating (125) with fresh symbols all_124_0, all_124_1 gives:
% 10.97/2.26 | (135) ==>(all_30_1, all_12_3) = all_124_0 & +(all_30_1, all_124_0) =
% 10.97/2.26 | all_124_1 & +(all_12_3, all_26_0) = all_124_1 & $i(all_124_0) &
% 10.97/2.26 | $i(all_124_1)
% 10.97/2.26 |
% 10.97/2.26 | ALPHA: (135) implies:
% 10.97/2.26 | (136) +(all_12_3, all_26_0) = all_124_1
% 10.97/2.26 | (137) +(all_30_1, all_124_0) = all_124_1
% 10.97/2.26 | (138) ==>(all_30_1, all_12_3) = all_124_0
% 10.97/2.26 |
% 10.97/2.26 | DELTA: instantiating (124) with fresh symbols all_146_0, all_146_1 gives:
% 10.97/2.26 | (139) ==>(all_30_1, all_12_3) = all_146_1 & +(all_30_1, all_146_1) =
% 10.97/2.26 | all_146_0 & +(all_12_3, all_26_0) = all_146_0 & $i(all_146_0) &
% 10.97/2.26 | $i(all_146_1)
% 10.97/2.26 |
% 10.97/2.26 | ALPHA: (139) implies:
% 10.97/2.26 | (140) +(all_12_3, all_26_0) = all_146_0
% 10.97/2.26 | (141) ==>(all_30_1, all_12_3) = all_146_1
% 10.97/2.26 |
% 10.97/2.26 | GROUND_INST: instantiating (11) with all_56_0, all_108_0, all_30_1, all_12_5,
% 10.97/2.26 | simplifying with (123), (130) gives:
% 10.97/2.26 | (142) all_108_0 = all_56_0
% 10.97/2.26 |
% 10.97/2.26 | GROUND_INST: instantiating (11) with all_52_0, all_146_0, all_26_0, all_12_3,
% 10.97/2.26 | simplifying with (106), (140) gives:
% 10.97/2.26 | (143) all_146_0 = all_52_0
% 10.97/2.26 |
% 10.97/2.26 | GROUND_INST: instantiating (11) with all_124_1, all_146_0, all_26_0, all_12_3,
% 10.97/2.26 | simplifying with (136), (140) gives:
% 10.97/2.26 | (144) all_146_0 = all_124_1
% 10.97/2.26 |
% 10.97/2.26 | GROUND_INST: instantiating (11) with all_52_0, all_110_0, all_12_3, all_26_0,
% 10.97/2.26 | simplifying with (118), (133) gives:
% 10.97/2.26 | (145) all_110_0 = all_52_0
% 10.97/2.26 |
% 10.97/2.26 | GROUND_INST: instantiating (12) with all_12_3, all_100_0, c, b, simplifying
% 10.97/2.26 | with (24), (127) gives:
% 10.97/2.26 | (146) all_100_0 = all_12_3
% 10.97/2.26 |
% 10.97/2.26 | GROUND_INST: instantiating (12) with all_124_0, all_146_1, all_12_3, all_30_1,
% 10.97/2.26 | simplifying with (138), (141) gives:
% 10.97/2.26 | (147) all_146_1 = all_124_0
% 10.97/2.26 |
% 10.97/2.26 | COMBINE_EQS: (143), (144) imply:
% 10.97/2.26 | (148) all_124_1 = all_52_0
% 10.97/2.26 |
% 10.97/2.26 | SIMP: (148) implies:
% 10.97/2.26 | (149) all_124_1 = all_52_0
% 10.97/2.26 |
% 10.97/2.26 | REDUCE: (128), (146) imply:
% 10.97/2.26 | (150) ==>(all_30_1, all_12_3) = all_12_5
% 10.97/2.26 |
% 10.97/2.26 | REDUCE: (134), (145) imply:
% 10.97/2.26 | (151) +(all_52_0, b) = all_12_0
% 10.97/2.26 |
% 10.97/2.26 | REDUCE: (131), (142) imply:
% 10.97/2.27 | (152) +(all_56_0, b) = all_12_4
% 10.97/2.27 |
% 10.97/2.27 | REDUCE: (137), (149) imply:
% 10.97/2.27 | (153) +(all_30_1, all_124_0) = all_52_0
% 10.97/2.27 |
% 10.97/2.27 | GROUND_INST: instantiating (12) with all_124_0, all_12_5, all_12_3, all_30_1,
% 10.97/2.27 | simplifying with (138), (150) gives:
% 10.97/2.27 | (154) all_124_0 = all_12_5
% 10.97/2.27 |
% 10.97/2.27 | REDUCE: (153), (154) imply:
% 10.97/2.27 | (155) +(all_30_1, all_12_5) = all_52_0
% 10.97/2.27 |
% 10.97/2.27 | GROUND_INST: instantiating (11) with all_56_0, all_52_0, all_12_5, all_30_1,
% 10.97/2.27 | simplifying with (108), (155) gives:
% 10.97/2.27 | (156) all_56_0 = all_52_0
% 10.97/2.27 |
% 10.97/2.27 | REDUCE: (152), (156) imply:
% 10.97/2.27 | (157) +(all_52_0, b) = all_12_4
% 10.97/2.27 |
% 10.97/2.27 | GROUND_INST: instantiating (11) with all_12_0, all_12_4, b, all_52_0,
% 10.97/2.27 | simplifying with (151), (157) gives:
% 10.97/2.27 | (158) all_12_0 = all_12_4
% 10.97/2.27 |
% 10.97/2.27 | REDUCE: (14), (158) imply:
% 10.97/2.27 | (159) $false
% 10.97/2.27 |
% 10.97/2.27 | CLOSE: (159) is inconsistent.
% 10.97/2.27 |
% 10.97/2.27 End of proof
% 10.97/2.27 % SZS output end Proof for theBenchmark
% 10.97/2.27
% 10.97/2.27 1743ms
%------------------------------------------------------------------------------