TSTP Solution File: SYN070+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN070+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 03:26:28 EDT 2023
% Result : Theorem 3.88s 1.32s
% Output : Proof 6.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN070+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 19:15:03 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.64 ________ _____
% 0.21/0.64 ___ __ \_________(_)________________________________
% 0.21/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.64
% 0.21/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.64 (2023-06-19)
% 0.21/0.64
% 0.21/0.64 (c) Philipp Rümmer, 2009-2023
% 0.21/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.64 Amanda Stjerna.
% 0.21/0.64 Free software under BSD-3-Clause.
% 0.21/0.64
% 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.64
% 0.21/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.13/1.00 Prover 1: Preprocessing ...
% 2.13/1.00 Prover 4: Preprocessing ...
% 2.46/1.05 Prover 3: Preprocessing ...
% 2.46/1.05 Prover 0: Preprocessing ...
% 2.46/1.05 Prover 6: Preprocessing ...
% 2.46/1.05 Prover 2: Preprocessing ...
% 2.46/1.05 Prover 5: Preprocessing ...
% 2.88/1.14 Prover 5: Proving ...
% 2.88/1.15 Prover 2: Proving ...
% 2.88/1.16 Prover 6: Constructing countermodel ...
% 2.88/1.16 Prover 3: Constructing countermodel ...
% 3.29/1.17 Prover 1: Constructing countermodel ...
% 3.29/1.18 Prover 4: Constructing countermodel ...
% 3.29/1.22 Prover 0: Proving ...
% 3.88/1.26 Prover 3: gave up
% 3.88/1.26 Prover 6: gave up
% 3.88/1.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.88/1.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.88/1.28 Prover 7: Preprocessing ...
% 3.88/1.28 Prover 8: Preprocessing ...
% 3.88/1.30 Prover 1: gave up
% 3.88/1.31 Prover 7: Warning: ignoring some quantifiers
% 3.88/1.32 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 3.88/1.32 Prover 0: proved (658ms)
% 3.88/1.32
% 3.88/1.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.88/1.32
% 3.88/1.33 Prover 5: stopped
% 3.88/1.33 Prover 2: stopped
% 3.88/1.33 Prover 7: Constructing countermodel ...
% 3.88/1.33 Prover 9: Preprocessing ...
% 3.88/1.33 Prover 8: Warning: ignoring some quantifiers
% 3.88/1.34 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.88/1.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.88/1.34 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.88/1.35 Prover 8: Constructing countermodel ...
% 3.88/1.35 Prover 11: Preprocessing ...
% 3.88/1.36 Prover 13: Preprocessing ...
% 3.88/1.36 Prover 10: Preprocessing ...
% 4.28/1.37 Prover 13: Warning: ignoring some quantifiers
% 4.28/1.38 Prover 13: Constructing countermodel ...
% 4.28/1.38 Prover 10: Warning: ignoring some quantifiers
% 4.28/1.38 Prover 8: gave up
% 4.28/1.39 Prover 10: Constructing countermodel ...
% 4.28/1.40 Prover 7: gave up
% 4.28/1.41 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.28/1.41 Prover 16: Preprocessing ...
% 4.28/1.41 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 5.01/1.42 Prover 19: Preprocessing ...
% 5.09/1.43 Prover 11: Constructing countermodel ...
% 5.09/1.43 Prover 9: Constructing countermodel ...
% 5.09/1.43 Prover 10: gave up
% 5.09/1.43 Prover 9: stopped
% 5.09/1.43 Prover 13: gave up
% 5.09/1.44 Prover 16: Warning: ignoring some quantifiers
% 5.09/1.44 Prover 16: Constructing countermodel ...
% 5.09/1.46 Prover 19: Warning: ignoring some quantifiers
% 5.09/1.47 Prover 19: Constructing countermodel ...
% 5.09/1.48 Prover 16: gave up
% 5.09/1.50 Prover 4: Found proof (size 89)
% 5.09/1.50 Prover 4: proved (833ms)
% 5.09/1.50 Prover 11: stopped
% 5.09/1.50 Prover 19: stopped
% 5.09/1.50
% 5.09/1.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.09/1.50
% 5.69/1.51 % SZS output start Proof for theBenchmark
% 5.69/1.51 Assumptions after simplification:
% 5.69/1.51 ---------------------------------
% 5.69/1.51
% 5.69/1.51 (pel46)
% 5.69/1.54 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_f(v0) = 0 & big_g(v0) = v1 &
% 5.69/1.54 $i(v0))
% 5.69/1.54
% 5.69/1.54 (pel46_1)
% 5.69/1.54 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (big_h(v1, v0) = v2) | ~
% 5.69/1.54 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6:
% 5.69/1.54 any] : (big_f(v1) = v4 & big_f(v0) = v3 & big_g(v1) = v5 & big_g(v0) = v6
% 5.69/1.54 & ( ~ (v3 = 0) | v6 = 0 | (v4 = 0 & v2 = 0 & ~ (v5 = 0)))))
% 5.69/1.54
% 5.69/1.54 (pel46_2)
% 5.69/1.55 ? [v0: $i] : ? [v1: int] : ? [v2: int] : ($i(v0) & ((v1 = 0 & ~ (v2 = 0) &
% 5.69/1.55 big_f(v0) = 0 & big_g(v0) = v2 & ! [v3: $i] : ! [v4: int] : (v4 = 0 |
% 5.69/1.55 ~ (big_j(v0, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] :
% 5.69/1.55 (big_f(v3) = v5 & big_g(v3) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v3:
% 5.69/1.55 $i] : ! [v4: int] : (v4 = 0 | ~ (big_g(v3) = v4) | ~ $i(v3) | ?
% 5.69/1.55 [v5: any] : ? [v6: any] : (big_j(v0, v3) = v6 & big_f(v3) = v5 & ( ~
% 5.69/1.55 (v5 = 0) | v6 = 0))) & ! [v3: $i] : ( ~ (big_f(v3) = 0) | ~
% 5.69/1.55 $i(v3) | ? [v4: any] : ? [v5: any] : (big_j(v0, v3) = v5 & big_g(v3)
% 5.69/1.55 = v4 & (v5 = 0 | v4 = 0)))) | ( ! [v3: $i] : ! [v4: int] : (v4 = 0
% 5.69/1.55 | ~ (big_g(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) &
% 5.69/1.55 big_f(v3) = v5)) & ! [v3: $i] : ( ~ (big_f(v3) = 0) | ~ $i(v3) |
% 5.69/1.55 big_g(v3) = 0))))
% 5.69/1.55
% 5.69/1.55 (pel46_3)
% 5.69/1.55 ! [v0: $i] : ! [v1: $i] : ( ~ (big_j(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 5.69/1.55 ? [v2: any] : ? [v3: any] : ? [v4: any] : (big_h(v0, v1) = v4 & big_f(v1)
% 5.69/1.55 = v3 & big_f(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0)))) & !
% 5.69/1.55 [v0: $i] : ! [v1: $i] : ( ~ (big_h(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 5.69/1.55 [v2: any] : ? [v3: any] : ? [v4: any] : (big_j(v1, v0) = v4 & big_f(v1) =
% 5.69/1.55 v3 & big_f(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0))))
% 5.69/1.55
% 5.69/1.55 (function-axioms)
% 5.69/1.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 5.69/1.56 [v3: $i] : (v1 = v0 | ~ (big_j(v3, v2) = v1) | ~ (big_j(v3, v2) = v0)) & !
% 5.69/1.56 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 5.69/1.56 $i] : (v1 = v0 | ~ (big_h(v3, v2) = v1) | ~ (big_h(v3, v2) = v0)) & !
% 5.69/1.56 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 5.69/1.56 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0)) & ! [v0: MultipleValueBool] :
% 5.69/1.56 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (big_g(v2) = v1) | ~
% 5.69/1.56 (big_g(v2) = v0))
% 5.69/1.56
% 5.69/1.56 Those formulas are unsatisfiable:
% 5.69/1.56 ---------------------------------
% 5.69/1.56
% 5.69/1.56 Begin of proof
% 5.69/1.56 |
% 5.69/1.56 | ALPHA: (pel46_3) implies:
% 5.69/1.56 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (big_j(v1, v0) = 0) | ~ $i(v1) | ~
% 5.69/1.56 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (big_h(v0, v1)
% 5.69/1.56 | = v4 & big_f(v1) = v3 & big_f(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0)
% 5.69/1.56 | | ~ (v2 = 0))))
% 5.69/1.56 |
% 5.69/1.56 | ALPHA: (function-axioms) implies:
% 5.69/1.56 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.69/1.56 | (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0))
% 5.69/1.56 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.69/1.56 | (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0))
% 5.69/1.56 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.69/1.56 | ! [v3: $i] : (v1 = v0 | ~ (big_j(v3, v2) = v1) | ~ (big_j(v3, v2) =
% 5.69/1.56 | v0))
% 5.69/1.56 |
% 5.69/1.56 | DELTA: instantiating (pel46) with fresh symbols all_5_0, all_5_1 gives:
% 5.69/1.56 | (5) ~ (all_5_0 = 0) & big_f(all_5_1) = 0 & big_g(all_5_1) = all_5_0 &
% 5.69/1.56 | $i(all_5_1)
% 5.69/1.56 |
% 5.69/1.56 | ALPHA: (5) implies:
% 5.69/1.56 | (6) ~ (all_5_0 = 0)
% 5.69/1.57 | (7) $i(all_5_1)
% 5.69/1.57 | (8) big_g(all_5_1) = all_5_0
% 5.69/1.57 | (9) big_f(all_5_1) = 0
% 5.69/1.57 |
% 5.69/1.57 | DELTA: instantiating (pel46_2) with fresh symbols all_7_0, all_7_1, all_7_2
% 5.69/1.57 | gives:
% 5.69/1.57 | (10) $i(all_7_2) & ((all_7_1 = 0 & ~ (all_7_0 = 0) & big_f(all_7_2) = 0 &
% 5.69/1.57 | big_g(all_7_2) = all_7_0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 |
% 5.69/1.57 | ~ (big_j(all_7_2, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 5.69/1.57 | any] : (big_f(v0) = v2 & big_g(v0) = v3 & ( ~ (v2 = 0) | v3 =
% 5.69/1.57 | 0))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_g(v0)
% 5.69/1.57 | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 5.69/1.57 | (big_j(all_7_2, v0) = v3 & big_f(v0) = v2 & ( ~ (v2 = 0) | v3 =
% 5.69/1.57 | 0))) & ! [v0: $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | ?
% 5.69/1.57 | [v1: any] : ? [v2: any] : (big_j(all_7_2, v0) = v2 & big_g(v0)
% 5.69/1.57 | = v1 & (v2 = 0 | v1 = 0)))) | ( ! [v0: $i] : ! [v1: int] :
% 5.69/1.57 | (v1 = 0 | ~ (big_g(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2
% 5.69/1.57 | = 0) & big_f(v0) = v2)) & ! [v0: $i] : ( ~ (big_f(v0) = 0)
% 5.69/1.57 | | ~ $i(v0) | big_g(v0) = 0)))
% 5.69/1.57 |
% 5.69/1.57 | ALPHA: (10) implies:
% 5.69/1.57 | (11) $i(all_7_2)
% 5.69/1.57 | (12) (all_7_1 = 0 & ~ (all_7_0 = 0) & big_f(all_7_2) = 0 & big_g(all_7_2)
% 5.69/1.57 | = all_7_0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 5.69/1.57 | (big_j(all_7_2, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 5.69/1.57 | any] : (big_f(v0) = v2 & big_g(v0) = v3 & ( ~ (v2 = 0) | v3 =
% 5.69/1.57 | 0))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_g(v0) =
% 5.69/1.57 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (big_j(all_7_2,
% 5.69/1.57 | v0) = v3 & big_f(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0:
% 5.69/1.57 | $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 5.69/1.57 | any] : (big_j(all_7_2, v0) = v2 & big_g(v0) = v1 & (v2 = 0 | v1
% 5.69/1.57 | = 0)))) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 5.69/1.57 | (big_g(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 5.69/1.57 | big_f(v0) = v2)) & ! [v0: $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0)
% 5.69/1.57 | | big_g(v0) = 0))
% 5.69/1.57 |
% 5.69/1.57 | BETA: splitting (12) gives:
% 5.69/1.57 |
% 5.69/1.57 | Case 1:
% 5.69/1.57 | |
% 5.69/1.58 | | (13) all_7_1 = 0 & ~ (all_7_0 = 0) & big_f(all_7_2) = 0 & big_g(all_7_2)
% 5.69/1.58 | | = all_7_0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 5.69/1.58 | | (big_j(all_7_2, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 5.69/1.58 | | any] : (big_f(v0) = v2 & big_g(v0) = v3 & ( ~ (v2 = 0) | v3 =
% 5.69/1.58 | | 0))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_g(v0) =
% 5.69/1.58 | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (big_j(all_7_2,
% 5.69/1.58 | | v0) = v3 & big_f(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0:
% 5.69/1.58 | | $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 5.69/1.58 | | any] : (big_j(all_7_2, v0) = v2 & big_g(v0) = v1 & (v2 = 0 | v1
% 5.69/1.58 | | = 0)))
% 5.69/1.58 | |
% 5.69/1.58 | | ALPHA: (13) implies:
% 5.69/1.58 | | (14) ~ (all_7_0 = 0)
% 5.69/1.58 | | (15) big_g(all_7_2) = all_7_0
% 5.69/1.58 | | (16) big_f(all_7_2) = 0
% 5.69/1.58 | | (17) ! [v0: $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 5.69/1.58 | | [v2: any] : (big_j(all_7_2, v0) = v2 & big_g(v0) = v1 & (v2 = 0 |
% 5.69/1.58 | | v1 = 0)))
% 5.69/1.58 | | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_g(v0) = v1) | ~
% 5.69/1.58 | | $i(v0) | ? [v2: any] : ? [v3: any] : (big_j(all_7_2, v0) = v3 &
% 5.69/1.58 | | big_f(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 5.69/1.58 | |
% 5.69/1.58 | | GROUND_INST: instantiating (18) with all_5_1, all_5_0, simplifying with (7),
% 5.69/1.58 | | (8) gives:
% 6.03/1.58 | | (19) all_5_0 = 0 | ? [v0: any] : ? [v1: any] : (big_j(all_7_2, all_5_1)
% 6.03/1.58 | | = v1 & big_f(all_5_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 6.03/1.58 | |
% 6.03/1.58 | | GROUND_INST: instantiating (17) with all_5_1, simplifying with (7), (9)
% 6.03/1.58 | | gives:
% 6.03/1.58 | | (20) ? [v0: any] : ? [v1: any] : (big_j(all_7_2, all_5_1) = v1 &
% 6.03/1.58 | | big_g(all_5_1) = v0 & (v1 = 0 | v0 = 0))
% 6.03/1.58 | |
% 6.03/1.58 | | DELTA: instantiating (20) with fresh symbols all_17_0, all_17_1 gives:
% 6.03/1.58 | | (21) big_j(all_7_2, all_5_1) = all_17_0 & big_g(all_5_1) = all_17_1 &
% 6.03/1.58 | | (all_17_0 = 0 | all_17_1 = 0)
% 6.03/1.58 | |
% 6.03/1.58 | | ALPHA: (21) implies:
% 6.03/1.58 | | (22) big_j(all_7_2, all_5_1) = all_17_0
% 6.03/1.58 | |
% 6.03/1.58 | | BETA: splitting (19) gives:
% 6.03/1.58 | |
% 6.03/1.58 | | Case 1:
% 6.03/1.58 | | |
% 6.03/1.58 | | | (23) all_5_0 = 0
% 6.03/1.58 | | |
% 6.03/1.58 | | | REDUCE: (6), (23) imply:
% 6.03/1.58 | | | (24) $false
% 6.03/1.58 | | |
% 6.03/1.58 | | | CLOSE: (24) is inconsistent.
% 6.03/1.58 | | |
% 6.03/1.58 | | Case 2:
% 6.03/1.58 | | |
% 6.03/1.58 | | | (25) ? [v0: any] : ? [v1: any] : (big_j(all_7_2, all_5_1) = v1 &
% 6.03/1.58 | | | big_f(all_5_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 6.03/1.59 | | |
% 6.03/1.59 | | | DELTA: instantiating (25) with fresh symbols all_23_0, all_23_1 gives:
% 6.03/1.59 | | | (26) big_j(all_7_2, all_5_1) = all_23_0 & big_f(all_5_1) = all_23_1 & (
% 6.03/1.59 | | | ~ (all_23_1 = 0) | all_23_0 = 0)
% 6.03/1.59 | | |
% 6.03/1.59 | | | ALPHA: (26) implies:
% 6.03/1.59 | | | (27) big_f(all_5_1) = all_23_1
% 6.03/1.59 | | | (28) big_j(all_7_2, all_5_1) = all_23_0
% 6.03/1.59 | | | (29) ~ (all_23_1 = 0) | all_23_0 = 0
% 6.03/1.59 | | |
% 6.03/1.59 | | | GROUND_INST: instantiating (3) with 0, all_23_1, all_5_1, simplifying with
% 6.03/1.59 | | | (9), (27) gives:
% 6.03/1.59 | | | (30) all_23_1 = 0
% 6.03/1.59 | | |
% 6.03/1.59 | | | GROUND_INST: instantiating (4) with all_17_0, all_23_0, all_5_1, all_7_2,
% 6.03/1.59 | | | simplifying with (22), (28) gives:
% 6.03/1.59 | | | (31) all_23_0 = all_17_0
% 6.03/1.59 | | |
% 6.03/1.59 | | | BETA: splitting (29) gives:
% 6.03/1.59 | | |
% 6.03/1.59 | | | Case 1:
% 6.03/1.59 | | | |
% 6.03/1.59 | | | | (32) ~ (all_23_1 = 0)
% 6.03/1.59 | | | |
% 6.03/1.59 | | | | REDUCE: (30), (32) imply:
% 6.03/1.59 | | | | (33) $false
% 6.03/1.59 | | | |
% 6.03/1.59 | | | | CLOSE: (33) is inconsistent.
% 6.03/1.59 | | | |
% 6.03/1.59 | | | Case 2:
% 6.03/1.59 | | | |
% 6.03/1.59 | | | | (34) all_23_0 = 0
% 6.03/1.59 | | | |
% 6.03/1.59 | | | | COMBINE_EQS: (31), (34) imply:
% 6.03/1.59 | | | | (35) all_17_0 = 0
% 6.03/1.59 | | | |
% 6.03/1.59 | | | | REDUCE: (22), (35) imply:
% 6.03/1.59 | | | | (36) big_j(all_7_2, all_5_1) = 0
% 6.03/1.59 | | | |
% 6.03/1.59 | | | | GROUND_INST: instantiating (18) with all_7_2, all_7_0, simplifying with
% 6.03/1.59 | | | | (11), (15) gives:
% 6.03/1.59 | | | | (37) all_7_0 = 0 | ? [v0: any] : ? [v1: any] : (big_j(all_7_2,
% 6.03/1.59 | | | | all_7_2) = v1 & big_f(all_7_2) = v0 & ( ~ (v0 = 0) | v1 =
% 6.03/1.59 | | | | 0))
% 6.03/1.59 | | | |
% 6.03/1.59 | | | | GROUND_INST: instantiating (17) with all_7_2, simplifying with (11),
% 6.03/1.59 | | | | (16) gives:
% 6.03/1.59 | | | | (38) ? [v0: any] : ? [v1: any] : (big_j(all_7_2, all_7_2) = v1 &
% 6.03/1.59 | | | | big_g(all_7_2) = v0 & (v1 = 0 | v0 = 0))
% 6.03/1.59 | | | |
% 6.03/1.59 | | | | GROUND_INST: instantiating (1) with all_5_1, all_7_2, simplifying with
% 6.03/1.59 | | | | (7), (11), (36) gives:
% 6.03/1.59 | | | | (39) ? [v0: any] : ? [v1: any] : ? [v2: any] : (big_h(all_5_1,
% 6.03/1.59 | | | | all_7_2) = v2 & big_f(all_7_2) = v1 & big_f(all_5_1) = v0 &
% 6.03/1.59 | | | | ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 6.03/1.59 | | | |
% 6.03/1.59 | | | | DELTA: instantiating (38) with fresh symbols all_38_0, all_38_1 gives:
% 6.03/1.59 | | | | (40) big_j(all_7_2, all_7_2) = all_38_0 & big_g(all_7_2) = all_38_1 &
% 6.03/1.59 | | | | (all_38_0 = 0 | all_38_1 = 0)
% 6.03/1.59 | | | |
% 6.03/1.59 | | | | ALPHA: (40) implies:
% 6.03/1.59 | | | | (41) big_g(all_7_2) = all_38_1
% 6.03/1.59 | | | | (42) big_j(all_7_2, all_7_2) = all_38_0
% 6.03/1.59 | | | | (43) all_38_0 = 0 | all_38_1 = 0
% 6.03/1.59 | | | |
% 6.03/1.59 | | | | DELTA: instantiating (39) with fresh symbols all_40_0, all_40_1,
% 6.03/1.59 | | | | all_40_2 gives:
% 6.03/1.59 | | | | (44) big_h(all_5_1, all_7_2) = all_40_0 & big_f(all_7_2) = all_40_1 &
% 6.03/1.59 | | | | big_f(all_5_1) = all_40_2 & ( ~ (all_40_0 = 0) | ~ (all_40_1 =
% 6.03/1.59 | | | | 0) | ~ (all_40_2 = 0))
% 6.03/1.59 | | | |
% 6.03/1.59 | | | | ALPHA: (44) implies:
% 6.03/1.59 | | | | (45) big_f(all_5_1) = all_40_2
% 6.03/1.59 | | | | (46) big_f(all_7_2) = all_40_1
% 6.03/1.59 | | | | (47) big_h(all_5_1, all_7_2) = all_40_0
% 6.03/1.60 | | | | (48) ~ (all_40_0 = 0) | ~ (all_40_1 = 0) | ~ (all_40_2 = 0)
% 6.03/1.60 | | | |
% 6.03/1.60 | | | | GROUND_INST: instantiating (2) with all_7_0, all_38_1, all_7_2,
% 6.03/1.60 | | | | simplifying with (15), (41) gives:
% 6.03/1.60 | | | | (49) all_38_1 = all_7_0
% 6.03/1.60 | | | |
% 6.03/1.60 | | | | GROUND_INST: instantiating (3) with 0, all_40_2, all_5_1, simplifying
% 6.03/1.60 | | | | with (9), (45) gives:
% 6.03/1.60 | | | | (50) all_40_2 = 0
% 6.03/1.60 | | | |
% 6.03/1.60 | | | | GROUND_INST: instantiating (3) with 0, all_40_1, all_7_2, simplifying
% 6.03/1.60 | | | | with (16), (46) gives:
% 6.03/1.60 | | | | (51) all_40_1 = 0
% 6.03/1.60 | | | |
% 6.03/1.60 | | | | BETA: splitting (37) gives:
% 6.03/1.60 | | | |
% 6.03/1.60 | | | | Case 1:
% 6.03/1.60 | | | | |
% 6.03/1.60 | | | | | (52) all_7_0 = 0
% 6.03/1.60 | | | | |
% 6.03/1.60 | | | | | REDUCE: (14), (52) imply:
% 6.03/1.60 | | | | | (53) $false
% 6.03/1.60 | | | | |
% 6.03/1.60 | | | | | CLOSE: (53) is inconsistent.
% 6.03/1.60 | | | | |
% 6.03/1.60 | | | | Case 2:
% 6.03/1.60 | | | | |
% 6.03/1.60 | | | | | (54) ? [v0: any] : ? [v1: any] : (big_j(all_7_2, all_7_2) = v1 &
% 6.03/1.60 | | | | | big_f(all_7_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 6.03/1.60 | | | | |
% 6.03/1.60 | | | | | DELTA: instantiating (54) with fresh symbols all_50_0, all_50_1 gives:
% 6.03/1.60 | | | | | (55) big_j(all_7_2, all_7_2) = all_50_0 & big_f(all_7_2) = all_50_1
% 6.03/1.60 | | | | | & ( ~ (all_50_1 = 0) | all_50_0 = 0)
% 6.03/1.60 | | | | |
% 6.03/1.60 | | | | | ALPHA: (55) implies:
% 6.03/1.60 | | | | | (56) big_f(all_7_2) = all_50_1
% 6.03/1.60 | | | | | (57) big_j(all_7_2, all_7_2) = all_50_0
% 6.03/1.60 | | | | |
% 6.03/1.60 | | | | | BETA: splitting (48) gives:
% 6.03/1.60 | | | | |
% 6.03/1.60 | | | | | Case 1:
% 6.03/1.60 | | | | | |
% 6.03/1.60 | | | | | | (58) ~ (all_40_0 = 0)
% 6.03/1.60 | | | | | |
% 6.03/1.60 | | | | | | BETA: splitting (43) gives:
% 6.03/1.60 | | | | | |
% 6.03/1.60 | | | | | | Case 1:
% 6.03/1.60 | | | | | | |
% 6.03/1.60 | | | | | | | (59) all_38_0 = 0
% 6.03/1.60 | | | | | | |
% 6.03/1.60 | | | | | | | REDUCE: (42), (59) imply:
% 6.03/1.60 | | | | | | | (60) big_j(all_7_2, all_7_2) = 0
% 6.03/1.60 | | | | | | |
% 6.03/1.60 | | | | | | | GROUND_INST: instantiating (3) with 0, all_50_1, all_7_2,
% 6.03/1.60 | | | | | | | simplifying with (16), (56) gives:
% 6.03/1.60 | | | | | | | (61) all_50_1 = 0
% 6.03/1.60 | | | | | | |
% 6.03/1.60 | | | | | | | GROUND_INST: instantiating (4) with 0, all_50_0, all_7_2, all_7_2,
% 6.03/1.60 | | | | | | | simplifying with (57), (60) gives:
% 6.03/1.60 | | | | | | | (62) all_50_0 = 0
% 6.03/1.60 | | | | | | |
% 6.03/1.60 | | | | | | | GROUND_INST: instantiating (pel46_1) with all_7_2, all_5_1,
% 6.03/1.60 | | | | | | | all_40_0, simplifying with (7), (11), (47) gives:
% 6.03/1.60 | | | | | | | (63) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any]
% 6.03/1.60 | | | | | | | : (big_f(all_7_2) = v0 & big_f(all_5_1) = v1 &
% 6.03/1.60 | | | | | | | big_g(all_7_2) = v3 & big_g(all_5_1) = v2 & ( ~ (v0 = 0)
% 6.03/1.60 | | | | | | | | v3 = 0 | (v1 = 0 & all_40_0 = 0 & ~ (v2 = 0))))
% 6.03/1.60 | | | | | | |
% 6.03/1.60 | | | | | | | GROUND_INST: instantiating (1) with all_7_2, all_7_2, simplifying
% 6.03/1.60 | | | | | | | with (11), (60) gives:
% 6.03/1.60 | | | | | | | (64) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 6.03/1.60 | | | | | | | (big_h(all_7_2, all_7_2) = v2 & big_f(all_7_2) = v1 &
% 6.03/1.60 | | | | | | | big_f(all_7_2) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 6.03/1.60 | | | | | | | (v0 = 0)))
% 6.03/1.60 | | | | | | |
% 6.03/1.60 | | | | | | | DELTA: instantiating (64) with fresh symbols all_69_0, all_69_1,
% 6.03/1.60 | | | | | | | all_69_2 gives:
% 6.03/1.60 | | | | | | | (65) big_h(all_7_2, all_7_2) = all_69_0 & big_f(all_7_2) =
% 6.03/1.60 | | | | | | | all_69_1 & big_f(all_7_2) = all_69_2 & ( ~ (all_69_0 = 0)
% 6.03/1.60 | | | | | | | | ~ (all_69_1 = 0) | ~ (all_69_2 = 0))
% 6.03/1.60 | | | | | | |
% 6.03/1.60 | | | | | | | ALPHA: (65) implies:
% 6.03/1.60 | | | | | | | (66) big_f(all_7_2) = all_69_2
% 6.03/1.60 | | | | | | | (67) big_f(all_7_2) = all_69_1
% 6.03/1.60 | | | | | | |
% 6.03/1.60 | | | | | | | DELTA: instantiating (63) with fresh symbols all_71_0, all_71_1,
% 6.03/1.60 | | | | | | | all_71_2, all_71_3 gives:
% 6.03/1.60 | | | | | | | (68) big_f(all_7_2) = all_71_3 & big_f(all_5_1) = all_71_2 &
% 6.03/1.61 | | | | | | | big_g(all_7_2) = all_71_0 & big_g(all_5_1) = all_71_1 & (
% 6.03/1.61 | | | | | | | ~ (all_71_3 = 0) | all_71_0 = 0 | (all_71_2 = 0 &
% 6.03/1.61 | | | | | | | all_40_0 = 0 & ~ (all_71_1 = 0)))
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | ALPHA: (68) implies:
% 6.03/1.61 | | | | | | | (69) big_g(all_7_2) = all_71_0
% 6.03/1.61 | | | | | | | (70) big_f(all_7_2) = all_71_3
% 6.03/1.61 | | | | | | | (71) ~ (all_71_3 = 0) | all_71_0 = 0 | (all_71_2 = 0 &
% 6.03/1.61 | | | | | | | all_40_0 = 0 & ~ (all_71_1 = 0))
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | GROUND_INST: instantiating (2) with all_7_0, all_71_0, all_7_2,
% 6.03/1.61 | | | | | | | simplifying with (15), (69) gives:
% 6.03/1.61 | | | | | | | (72) all_71_0 = all_7_0
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | GROUND_INST: instantiating (3) with 0, all_71_3, all_7_2,
% 6.03/1.61 | | | | | | | simplifying with (16), (70) gives:
% 6.03/1.61 | | | | | | | (73) all_71_3 = 0
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | GROUND_INST: instantiating (3) with all_69_1, all_71_3, all_7_2,
% 6.03/1.61 | | | | | | | simplifying with (67), (70) gives:
% 6.03/1.61 | | | | | | | (74) all_71_3 = all_69_1
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | GROUND_INST: instantiating (3) with all_69_2, all_71_3, all_7_2,
% 6.03/1.61 | | | | | | | simplifying with (66), (70) gives:
% 6.03/1.61 | | | | | | | (75) all_71_3 = all_69_2
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | COMBINE_EQS: (73), (74) imply:
% 6.03/1.61 | | | | | | | (76) all_69_1 = 0
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | COMBINE_EQS: (74), (75) imply:
% 6.03/1.61 | | | | | | | (77) all_69_1 = all_69_2
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | COMBINE_EQS: (76), (77) imply:
% 6.03/1.61 | | | | | | | (78) all_69_2 = 0
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | BETA: splitting (71) gives:
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | Case 1:
% 6.03/1.61 | | | | | | | |
% 6.03/1.61 | | | | | | | | (79) ~ (all_71_3 = 0)
% 6.03/1.61 | | | | | | | |
% 6.03/1.61 | | | | | | | | REDUCE: (73), (79) imply:
% 6.03/1.61 | | | | | | | | (80) $false
% 6.03/1.61 | | | | | | | |
% 6.03/1.61 | | | | | | | | CLOSE: (80) is inconsistent.
% 6.03/1.61 | | | | | | | |
% 6.03/1.61 | | | | | | | Case 2:
% 6.03/1.61 | | | | | | | |
% 6.03/1.61 | | | | | | | | (81) all_71_0 = 0 | (all_71_2 = 0 & all_40_0 = 0 & ~
% 6.03/1.61 | | | | | | | | (all_71_1 = 0))
% 6.03/1.61 | | | | | | | |
% 6.03/1.61 | | | | | | | | BETA: splitting (81) gives:
% 6.03/1.61 | | | | | | | |
% 6.03/1.61 | | | | | | | | Case 1:
% 6.03/1.61 | | | | | | | | |
% 6.03/1.61 | | | | | | | | | (82) all_71_0 = 0
% 6.03/1.61 | | | | | | | | |
% 6.03/1.61 | | | | | | | | | COMBINE_EQS: (72), (82) imply:
% 6.03/1.61 | | | | | | | | | (83) all_7_0 = 0
% 6.03/1.61 | | | | | | | | |
% 6.03/1.61 | | | | | | | | | REDUCE: (14), (83) imply:
% 6.03/1.61 | | | | | | | | | (84) $false
% 6.03/1.61 | | | | | | | | |
% 6.03/1.61 | | | | | | | | | CLOSE: (84) is inconsistent.
% 6.03/1.61 | | | | | | | | |
% 6.03/1.61 | | | | | | | | Case 2:
% 6.03/1.61 | | | | | | | | |
% 6.03/1.61 | | | | | | | | | (85) all_71_2 = 0 & all_40_0 = 0 & ~ (all_71_1 = 0)
% 6.03/1.61 | | | | | | | | |
% 6.03/1.61 | | | | | | | | | ALPHA: (85) implies:
% 6.03/1.61 | | | | | | | | | (86) all_40_0 = 0
% 6.03/1.61 | | | | | | | | |
% 6.03/1.61 | | | | | | | | | REDUCE: (58), (86) imply:
% 6.03/1.61 | | | | | | | | | (87) $false
% 6.03/1.61 | | | | | | | | |
% 6.03/1.61 | | | | | | | | | CLOSE: (87) is inconsistent.
% 6.03/1.61 | | | | | | | | |
% 6.03/1.61 | | | | | | | | End of split
% 6.03/1.61 | | | | | | | |
% 6.03/1.61 | | | | | | | End of split
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | Case 2:
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | (88) all_38_1 = 0
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | COMBINE_EQS: (49), (88) imply:
% 6.03/1.61 | | | | | | | (89) all_7_0 = 0
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | REDUCE: (14), (89) imply:
% 6.03/1.61 | | | | | | | (90) $false
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | CLOSE: (90) is inconsistent.
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | End of split
% 6.03/1.61 | | | | | |
% 6.03/1.61 | | | | | Case 2:
% 6.03/1.61 | | | | | |
% 6.03/1.61 | | | | | | (91) ~ (all_40_1 = 0) | ~ (all_40_2 = 0)
% 6.03/1.61 | | | | | |
% 6.03/1.61 | | | | | | BETA: splitting (91) gives:
% 6.03/1.61 | | | | | |
% 6.03/1.61 | | | | | | Case 1:
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | (92) ~ (all_40_1 = 0)
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | REDUCE: (51), (92) imply:
% 6.03/1.61 | | | | | | | (93) $false
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | CLOSE: (93) is inconsistent.
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | Case 2:
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | (94) ~ (all_40_2 = 0)
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | REDUCE: (50), (94) imply:
% 6.03/1.61 | | | | | | | (95) $false
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | | CLOSE: (95) is inconsistent.
% 6.03/1.61 | | | | | | |
% 6.03/1.61 | | | | | | End of split
% 6.03/1.61 | | | | | |
% 6.03/1.61 | | | | | End of split
% 6.03/1.61 | | | | |
% 6.03/1.61 | | | | End of split
% 6.03/1.61 | | | |
% 6.03/1.61 | | | End of split
% 6.03/1.61 | | |
% 6.03/1.61 | | End of split
% 6.03/1.61 | |
% 6.03/1.61 | Case 2:
% 6.03/1.61 | |
% 6.03/1.62 | | (96) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_g(v0) = v1) | ~
% 6.03/1.62 | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & big_f(v0) = v2)) & ! [v0:
% 6.03/1.62 | | $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | big_g(v0) = 0)
% 6.03/1.62 | |
% 6.03/1.62 | | ALPHA: (96) implies:
% 6.03/1.62 | | (97) ! [v0: $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | big_g(v0) = 0)
% 6.03/1.62 | |
% 6.03/1.62 | | GROUND_INST: instantiating (97) with all_5_1, simplifying with (7), (9)
% 6.03/1.62 | | gives:
% 6.03/1.62 | | (98) big_g(all_5_1) = 0
% 6.03/1.62 | |
% 6.03/1.62 | | GROUND_INST: instantiating (2) with all_5_0, 0, all_5_1, simplifying with
% 6.03/1.62 | | (8), (98) gives:
% 6.03/1.62 | | (99) all_5_0 = 0
% 6.03/1.62 | |
% 6.03/1.62 | | REDUCE: (6), (99) imply:
% 6.03/1.62 | | (100) $false
% 6.03/1.62 | |
% 6.03/1.62 | | CLOSE: (100) is inconsistent.
% 6.03/1.62 | |
% 6.03/1.62 | End of split
% 6.03/1.62 |
% 6.03/1.62 End of proof
% 6.03/1.62 % SZS output end Proof for theBenchmark
% 6.03/1.62
% 6.03/1.62 979ms
%------------------------------------------------------------------------------