TSTP Solution File: SYN352+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN352+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 : n023.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 03:27:19 EDT 2023
% Result : Theorem 4.79s 1.35s
% Output : Proof 6.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN352+1 : TPTP v8.1.2. Released v2.0.0.
% 0.03/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 18:21:56 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.51/0.60 ________ _____
% 0.51/0.60 ___ __ \_________(_)________________________________
% 0.51/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.51/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.51/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.51/0.60
% 0.51/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.51/0.60 (2023-06-19)
% 0.51/0.60
% 0.51/0.60 (c) Philipp Rümmer, 2009-2023
% 0.51/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.51/0.60 Amanda Stjerna.
% 0.51/0.60 Free software under BSD-3-Clause.
% 0.51/0.60
% 0.51/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.51/0.60
% 0.51/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.51/0.62 Running up to 7 provers in parallel.
% 0.74/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.74/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.74/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.74/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.74/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.74/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.74/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 1.96/0.96 Prover 4: Preprocessing ...
% 1.96/0.96 Prover 1: Preprocessing ...
% 2.25/1.00 Prover 2: Preprocessing ...
% 2.25/1.00 Prover 3: Preprocessing ...
% 2.25/1.00 Prover 6: Preprocessing ...
% 2.25/1.00 Prover 5: Preprocessing ...
% 2.25/1.00 Prover 0: Preprocessing ...
% 2.87/1.08 Prover 1: Constructing countermodel ...
% 2.87/1.08 Prover 3: Constructing countermodel ...
% 2.87/1.08 Prover 4: Constructing countermodel ...
% 2.87/1.08 Prover 2: Proving ...
% 2.87/1.08 Prover 5: Proving ...
% 2.87/1.09 Prover 6: Proving ...
% 2.87/1.11 Prover 0: Proving ...
% 4.79/1.35 Prover 3: proved (719ms)
% 4.79/1.35
% 4.79/1.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.79/1.35
% 4.79/1.35 Prover 6: stopped
% 4.79/1.35 Prover 0: stopped
% 4.79/1.35 Prover 5: stopped
% 4.79/1.35 Prover 2: stopped
% 4.79/1.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.79/1.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.79/1.36 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.79/1.36 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.79/1.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.03/1.38 Prover 8: Preprocessing ...
% 5.03/1.38 Prover 7: Preprocessing ...
% 5.03/1.38 Prover 10: Preprocessing ...
% 5.03/1.38 Prover 13: Preprocessing ...
% 5.03/1.39 Prover 10: Warning: ignoring some quantifiers
% 5.03/1.39 Prover 13: Warning: ignoring some quantifiers
% 5.03/1.40 Prover 10: Constructing countermodel ...
% 5.03/1.40 Prover 8: Warning: ignoring some quantifiers
% 5.03/1.40 Prover 8: Constructing countermodel ...
% 5.03/1.40 Prover 11: Preprocessing ...
% 5.03/1.40 Prover 7: Warning: ignoring some quantifiers
% 5.03/1.40 Prover 7: Constructing countermodel ...
% 5.03/1.41 Prover 10: gave up
% 5.03/1.41 Prover 13: Constructing countermodel ...
% 5.03/1.41 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 5.03/1.42 Prover 13: gave up
% 5.03/1.42 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 5.03/1.43 Prover 16: Preprocessing ...
% 5.03/1.43 Prover 7: gave up
% 5.53/1.43 Prover 11: Constructing countermodel ...
% 5.53/1.44 Prover 19: Preprocessing ...
% 5.53/1.44 Prover 16: Warning: ignoring some quantifiers
% 5.53/1.44 Prover 16: Constructing countermodel ...
% 5.79/1.47 Prover 16: gave up
% 5.79/1.48 Prover 19: Warning: ignoring some quantifiers
% 5.79/1.48 Prover 19: Constructing countermodel ...
% 5.79/1.51 Prover 4: Found proof (size 57)
% 5.79/1.51 Prover 4: proved (880ms)
% 5.79/1.51 Prover 11: stopped
% 5.79/1.51 Prover 8: stopped
% 5.79/1.51 Prover 19: stopped
% 5.79/1.51 Prover 1: stopped
% 5.79/1.51
% 5.79/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.79/1.51
% 5.79/1.52 % SZS output start Proof for theBenchmark
% 5.79/1.52 Assumptions after simplification:
% 5.79/1.52 ---------------------------------
% 5.79/1.52
% 5.79/1.52 (church_46_18_4)
% 6.22/1.56 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : (big_f(v0, v1) = v2 & $i(v1) &
% 6.22/1.56 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (big_f(v3, v4) = v5)
% 6.22/1.56 | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : ?
% 6.22/1.56 [v9: any] : ? [v10: any] : (v2 = 0 & big_f(v6, v6) = v10 & big_f(v4, v6)
% 6.22/1.56 = v8 & big_f(v3, v6) = v9 & big_f(v1, v6) = v7 & $i(v6) & ( ~ (v5 = 0) |
% 6.22/1.56 v8 = 0 | v7 = 0) & ( ~ (v5 = 0) | (( ~ (v9 = 0) | ~ (v8 = 0)) & (v9 =
% 6.22/1.56 0 | v8 = 0))) & (v10 = 0 | (v5 = 0 & ( ~ (v9 = 0) | ~ (v7 = 0)) &
% 6.22/1.56 (v9 = 0 | v7 = 0))))))
% 6.22/1.56
% 6.22/1.56 (function-axioms)
% 6.22/1.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.22/1.56 [v3: $i] : (v1 = v0 | ~ (big_f(v3, v2) = v1) | ~ (big_f(v3, v2) = v0))
% 6.22/1.56
% 6.22/1.56 Those formulas are unsatisfiable:
% 6.22/1.56 ---------------------------------
% 6.22/1.56
% 6.22/1.56 Begin of proof
% 6.22/1.56 |
% 6.22/1.56 | DELTA: instantiating (church_46_18_4) with fresh symbols all_3_0, all_3_1,
% 6.22/1.56 | all_3_2 gives:
% 6.37/1.57 | (1) big_f(all_3_2, all_3_1) = all_3_0 & $i(all_3_1) & $i(all_3_2) & ! [v0:
% 6.37/1.57 | $i] : ! [v1: $i] : ! [v2: any] : ( ~ (big_f(v0, v1) = v2) | ~
% 6.37/1.57 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ?
% 6.37/1.57 | [v6: any] : ? [v7: any] : (all_3_0 = 0 & big_f(v3, v3) = v7 &
% 6.37/1.57 | big_f(v1, v3) = v5 & big_f(v0, v3) = v6 & big_f(all_3_1, v3) = v4 &
% 6.37/1.57 | $i(v3) & ( ~ (v2 = 0) | v5 = 0 | v4 = 0) & ( ~ (v2 = 0) | (( ~ (v6
% 6.37/1.57 | = 0) | ~ (v5 = 0)) & (v6 = 0 | v5 = 0))) & (v7 = 0 | (v2 =
% 6.37/1.57 | 0 & ( ~ (v6 = 0) | ~ (v4 = 0)) & (v6 = 0 | v4 = 0)))))
% 6.37/1.57 |
% 6.37/1.57 | ALPHA: (1) implies:
% 6.37/1.57 | (2) $i(all_3_2)
% 6.37/1.57 | (3) $i(all_3_1)
% 6.37/1.57 | (4) big_f(all_3_2, all_3_1) = all_3_0
% 6.37/1.57 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (big_f(v0, v1) = v2) |
% 6.37/1.57 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ?
% 6.37/1.57 | [v6: any] : ? [v7: any] : (all_3_0 = 0 & big_f(v3, v3) = v7 &
% 6.37/1.57 | big_f(v1, v3) = v5 & big_f(v0, v3) = v6 & big_f(all_3_1, v3) = v4 &
% 6.37/1.57 | $i(v3) & ( ~ (v2 = 0) | v5 = 0 | v4 = 0) & ( ~ (v2 = 0) | (( ~ (v6
% 6.37/1.57 | = 0) | ~ (v5 = 0)) & (v6 = 0 | v5 = 0))) & (v7 = 0 | (v2 =
% 6.37/1.57 | 0 & ( ~ (v6 = 0) | ~ (v4 = 0)) & (v6 = 0 | v4 = 0)))))
% 6.37/1.57 |
% 6.37/1.58 | GROUND_INST: instantiating (5) with all_3_2, all_3_1, all_3_0, simplifying
% 6.37/1.58 | with (2), (3), (4) gives:
% 6.37/1.58 | (6) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: any]
% 6.37/1.58 | : (all_3_0 = 0 & big_f(v0, v0) = v4 & big_f(all_3_1, v0) = v2 &
% 6.37/1.58 | big_f(all_3_1, v0) = v1 & big_f(all_3_2, v0) = v3 & $i(v0) & ( ~ (v3
% 6.37/1.58 | = 0) | ~ (v2 = 0)) & (v4 = 0 | (( ~ (v3 = 0) | ~ (v1 = 0)) &
% 6.37/1.58 | (v3 = 0 | v1 = 0))) & (v3 = 0 | v2 = 0) & (v2 = 0 | v1 = 0))
% 6.37/1.58 |
% 6.37/1.58 | DELTA: instantiating (6) with fresh symbols all_11_0, all_11_1, all_11_2,
% 6.37/1.58 | all_11_3, all_11_4 gives:
% 6.37/1.58 | (7) all_3_0 = 0 & big_f(all_11_4, all_11_4) = all_11_0 & big_f(all_3_1,
% 6.37/1.58 | all_11_4) = all_11_2 & big_f(all_3_1, all_11_4) = all_11_3 &
% 6.37/1.58 | big_f(all_3_2, all_11_4) = all_11_1 & $i(all_11_4) & ( ~ (all_11_1 = 0)
% 6.37/1.58 | | ~ (all_11_2 = 0)) & (all_11_0 = 0 | (( ~ (all_11_1 = 0) | ~
% 6.37/1.58 | (all_11_3 = 0)) & (all_11_1 = 0 | all_11_3 = 0))) & (all_11_1 = 0
% 6.37/1.58 | | all_11_2 = 0) & (all_11_2 = 0 | all_11_3 = 0)
% 6.37/1.58 |
% 6.37/1.58 | ALPHA: (7) implies:
% 6.37/1.58 | (8) all_3_0 = 0
% 6.37/1.58 | (9) $i(all_11_4)
% 6.37/1.58 | (10) big_f(all_3_2, all_11_4) = all_11_1
% 6.37/1.58 | (11) big_f(all_3_1, all_11_4) = all_11_3
% 6.37/1.58 | (12) big_f(all_3_1, all_11_4) = all_11_2
% 6.37/1.58 | (13) all_11_2 = 0 | all_11_3 = 0
% 6.37/1.58 | (14) ~ (all_11_1 = 0) | ~ (all_11_2 = 0)
% 6.37/1.58 |
% 6.37/1.58 | REDUCE: (4), (8) imply:
% 6.37/1.58 | (15) big_f(all_3_2, all_3_1) = 0
% 6.37/1.58 |
% 6.37/1.59 | GROUND_INST: instantiating (function-axioms) with all_11_3, all_11_2,
% 6.37/1.59 | all_11_4, all_3_1, simplifying with (11), (12) gives:
% 6.37/1.59 | (16) all_11_2 = all_11_3
% 6.37/1.59 |
% 6.37/1.59 | BETA: splitting (13) gives:
% 6.37/1.59 |
% 6.37/1.59 | Case 1:
% 6.37/1.59 | |
% 6.37/1.59 | | (17) all_11_2 = 0
% 6.37/1.59 | |
% 6.37/1.59 | | COMBINE_EQS: (16), (17) imply:
% 6.37/1.59 | | (18) all_11_3 = 0
% 6.37/1.59 | |
% 6.37/1.59 | | BETA: splitting (14) gives:
% 6.37/1.59 | |
% 6.37/1.59 | | Case 1:
% 6.37/1.59 | | |
% 6.37/1.59 | | | (19) ~ (all_11_1 = 0)
% 6.37/1.59 | | |
% 6.37/1.59 | | | GROUND_INST: instantiating (5) with all_3_2, all_11_4, all_11_1,
% 6.37/1.59 | | | simplifying with (2), (9), (10) gives:
% 6.37/1.59 | | | (20) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 6.37/1.59 | | | any] : (all_3_0 = 0 & big_f(v0, v0) = v4 & big_f(all_11_4, v0) =
% 6.37/1.59 | | | v2 & big_f(all_3_1, v0) = v1 & big_f(all_3_2, v0) = v3 & $i(v0)
% 6.37/1.59 | | | & ( ~ (all_11_1 = 0) | v2 = 0 | v1 = 0) & ( ~ (all_11_1 = 0) |
% 6.37/1.59 | | | (( ~ (v3 = 0) | ~ (v2 = 0)) & (v3 = 0 | v2 = 0))) & (v4 = 0 |
% 6.37/1.59 | | | (all_11_1 = 0 & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 =
% 6.37/1.59 | | | 0))))
% 6.37/1.59 | | |
% 6.37/1.59 | | | DELTA: instantiating (6) with fresh symbols all_32_0, all_32_1, all_32_2,
% 6.37/1.59 | | | all_32_3, all_32_4 gives:
% 6.37/1.59 | | | (21) all_3_0 = 0 & big_f(all_32_4, all_32_4) = all_32_0 &
% 6.37/1.59 | | | big_f(all_3_1, all_32_4) = all_32_2 & big_f(all_3_1, all_32_4) =
% 6.37/1.59 | | | all_32_3 & big_f(all_3_2, all_32_4) = all_32_1 & $i(all_32_4) & (
% 6.37/1.59 | | | ~ (all_32_1 = 0) | ~ (all_32_2 = 0)) & (all_32_0 = 0 | (( ~
% 6.37/1.59 | | | (all_32_1 = 0) | ~ (all_32_3 = 0)) & (all_32_1 = 0 |
% 6.37/1.59 | | | all_32_3 = 0))) & (all_32_1 = 0 | all_32_2 = 0) & (all_32_2
% 6.37/1.59 | | | = 0 | all_32_3 = 0)
% 6.37/1.59 | | |
% 6.37/1.59 | | | ALPHA: (21) implies:
% 6.37/1.59 | | | (22) big_f(all_3_1, all_32_4) = all_32_3
% 6.37/1.59 | | | (23) big_f(all_3_1, all_32_4) = all_32_2
% 6.37/1.59 | | | (24) all_32_2 = 0 | all_32_3 = 0
% 6.37/1.59 | | | (25) ~ (all_32_1 = 0) | ~ (all_32_2 = 0)
% 6.37/1.59 | | |
% 6.37/1.59 | | | DELTA: instantiating (20) with fresh symbols all_34_0, all_34_1, all_34_2,
% 6.37/1.59 | | | all_34_3, all_34_4 gives:
% 6.37/1.59 | | | (26) all_3_0 = 0 & big_f(all_34_4, all_34_4) = all_34_0 &
% 6.37/1.59 | | | big_f(all_11_4, all_34_4) = all_34_2 & big_f(all_3_1, all_34_4) =
% 6.37/1.59 | | | all_34_3 & big_f(all_3_2, all_34_4) = all_34_1 & $i(all_34_4) & (
% 6.37/1.59 | | | ~ (all_11_1 = 0) | all_34_2 = 0 | all_34_3 = 0) & ( ~ (all_11_1
% 6.37/1.59 | | | = 0) | (( ~ (all_34_1 = 0) | ~ (all_34_2 = 0)) & (all_34_1 =
% 6.37/1.60 | | | 0 | all_34_2 = 0))) & (all_34_0 = 0 | (all_11_1 = 0 & ( ~
% 6.37/1.60 | | | (all_34_1 = 0) | ~ (all_34_3 = 0)) & (all_34_1 = 0 |
% 6.37/1.60 | | | all_34_3 = 0)))
% 6.37/1.60 | | |
% 6.37/1.60 | | | ALPHA: (26) implies:
% 6.37/1.60 | | | (27) $i(all_34_4)
% 6.37/1.60 | | | (28) big_f(all_34_4, all_34_4) = all_34_0
% 6.37/1.60 | | | (29) all_34_0 = 0 | (all_11_1 = 0 & ( ~ (all_34_1 = 0) | ~ (all_34_3 =
% 6.37/1.60 | | | 0)) & (all_34_1 = 0 | all_34_3 = 0))
% 6.37/1.60 | | |
% 6.37/1.60 | | | BETA: splitting (29) gives:
% 6.37/1.60 | | |
% 6.37/1.60 | | | Case 1:
% 6.37/1.60 | | | |
% 6.37/1.60 | | | | (30) all_34_0 = 0
% 6.37/1.60 | | | |
% 6.37/1.60 | | | | REDUCE: (28), (30) imply:
% 6.37/1.60 | | | | (31) big_f(all_34_4, all_34_4) = 0
% 6.37/1.60 | | | |
% 6.37/1.60 | | | | GROUND_INST: instantiating (function-axioms) with all_32_3, all_32_2,
% 6.37/1.60 | | | | all_32_4, all_3_1, simplifying with (22), (23) gives:
% 6.37/1.60 | | | | (32) all_32_2 = all_32_3
% 6.37/1.60 | | | |
% 6.37/1.60 | | | | BETA: splitting (24) gives:
% 6.37/1.60 | | | |
% 6.37/1.60 | | | | Case 1:
% 6.37/1.60 | | | | |
% 6.37/1.60 | | | | | (33) all_32_2 = 0
% 6.37/1.60 | | | | |
% 6.37/1.60 | | | | | BETA: splitting (25) gives:
% 6.37/1.60 | | | | |
% 6.37/1.60 | | | | | Case 1:
% 6.37/1.60 | | | | | |
% 6.37/1.60 | | | | | |
% 6.37/1.60 | | | | | | GROUND_INST: instantiating (5) with all_34_4, all_34_4, 0,
% 6.37/1.60 | | | | | | simplifying with (27), (31) gives:
% 6.37/1.60 | | | | | | (34) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 6.37/1.60 | | | | | | ? [v4: any] : (all_3_0 = 0 & big_f(v0, v0) = v4 &
% 6.37/1.60 | | | | | | big_f(all_34_4, v0) = v3 & big_f(all_34_4, v0) = v2 &
% 6.37/1.60 | | | | | | big_f(all_3_1, v0) = v1 & $i(v0) & ( ~ (v3 = 0) | ~ (v2 =
% 6.37/1.60 | | | | | | 0)) & (v4 = 0 | (( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0
% 6.37/1.60 | | | | | | | v1 = 0))) & (v3 = 0 | v2 = 0) & (v2 = 0 | v1 = 0))
% 6.37/1.60 | | | | | |
% 6.37/1.60 | | | | | | DELTA: instantiating (34) with fresh symbols all_61_0, all_61_1,
% 6.37/1.60 | | | | | | all_61_2, all_61_3, all_61_4 gives:
% 6.37/1.60 | | | | | | (35) all_3_0 = 0 & big_f(all_61_4, all_61_4) = all_61_0 &
% 6.37/1.60 | | | | | | big_f(all_34_4, all_61_4) = all_61_1 & big_f(all_34_4,
% 6.37/1.60 | | | | | | all_61_4) = all_61_2 & big_f(all_3_1, all_61_4) = all_61_3
% 6.37/1.60 | | | | | | & $i(all_61_4) & ( ~ (all_61_1 = 0) | ~ (all_61_2 = 0)) &
% 6.37/1.60 | | | | | | (all_61_0 = 0 | (( ~ (all_61_1 = 0) | ~ (all_61_3 = 0)) &
% 6.37/1.60 | | | | | | (all_61_1 = 0 | all_61_3 = 0))) & (all_61_1 = 0 |
% 6.37/1.60 | | | | | | all_61_2 = 0) & (all_61_2 = 0 | all_61_3 = 0)
% 6.37/1.60 | | | | | |
% 6.37/1.60 | | | | | | ALPHA: (35) implies:
% 6.37/1.60 | | | | | | (36) big_f(all_34_4, all_61_4) = all_61_2
% 6.37/1.60 | | | | | | (37) big_f(all_34_4, all_61_4) = all_61_1
% 6.37/1.60 | | | | | | (38) all_61_1 = 0 | all_61_2 = 0
% 6.37/1.60 | | | | | | (39) ~ (all_61_1 = 0) | ~ (all_61_2 = 0)
% 6.37/1.60 | | | | | |
% 6.37/1.60 | | | | | | GROUND_INST: instantiating (function-axioms) with all_61_2,
% 6.37/1.60 | | | | | | all_61_1, all_61_4, all_34_4, simplifying with (36),
% 6.37/1.60 | | | | | | (37) gives:
% 6.37/1.60 | | | | | | (40) all_61_1 = all_61_2
% 6.37/1.60 | | | | | |
% 6.37/1.60 | | | | | | BETA: splitting (38) gives:
% 6.37/1.60 | | | | | |
% 6.37/1.60 | | | | | | Case 1:
% 6.37/1.60 | | | | | | |
% 6.37/1.60 | | | | | | | (41) all_61_1 = 0
% 6.37/1.60 | | | | | | |
% 6.37/1.60 | | | | | | | COMBINE_EQS: (40), (41) imply:
% 6.37/1.60 | | | | | | | (42) all_61_2 = 0
% 6.37/1.61 | | | | | | |
% 6.37/1.61 | | | | | | | REF_CLOSE: (39), (41), (42) are inconsistent by sub-proof #1.
% 6.37/1.61 | | | | | | |
% 6.37/1.61 | | | | | | Case 2:
% 6.37/1.61 | | | | | | |
% 6.37/1.61 | | | | | | | (43) all_61_2 = 0
% 6.37/1.61 | | | | | | |
% 6.37/1.61 | | | | | | | COMBINE_EQS: (40), (43) imply:
% 6.37/1.61 | | | | | | | (44) all_61_1 = 0
% 6.37/1.61 | | | | | | |
% 6.37/1.61 | | | | | | | REF_CLOSE: (39), (43), (44) are inconsistent by sub-proof #1.
% 6.37/1.61 | | | | | | |
% 6.37/1.61 | | | | | | End of split
% 6.37/1.61 | | | | | |
% 6.37/1.61 | | | | | Case 2:
% 6.37/1.61 | | | | | |
% 6.37/1.61 | | | | | | (45) ~ (all_32_2 = 0)
% 6.37/1.61 | | | | | |
% 6.37/1.61 | | | | | | REDUCE: (33), (45) imply:
% 6.37/1.61 | | | | | | (46) $false
% 6.37/1.61 | | | | | |
% 6.37/1.61 | | | | | | CLOSE: (46) is inconsistent.
% 6.37/1.61 | | | | | |
% 6.37/1.61 | | | | | End of split
% 6.37/1.61 | | | | |
% 6.37/1.61 | | | | Case 2:
% 6.37/1.61 | | | | |
% 6.37/1.61 | | | | | (47) all_32_3 = 0
% 6.37/1.61 | | | | | (48) ~ (all_32_2 = 0)
% 6.37/1.61 | | | | |
% 6.37/1.61 | | | | | COMBINE_EQS: (32), (47) imply:
% 6.37/1.61 | | | | | (49) all_32_2 = 0
% 6.37/1.61 | | | | |
% 6.37/1.61 | | | | | REDUCE: (48), (49) imply:
% 6.37/1.61 | | | | | (50) $false
% 6.37/1.61 | | | | |
% 6.37/1.61 | | | | | CLOSE: (50) is inconsistent.
% 6.37/1.61 | | | | |
% 6.37/1.61 | | | | End of split
% 6.37/1.61 | | | |
% 6.37/1.61 | | | Case 2:
% 6.37/1.61 | | | |
% 6.37/1.61 | | | | (51) all_11_1 = 0 & ( ~ (all_34_1 = 0) | ~ (all_34_3 = 0)) &
% 6.37/1.61 | | | | (all_34_1 = 0 | all_34_3 = 0)
% 6.37/1.61 | | | |
% 6.37/1.61 | | | | ALPHA: (51) implies:
% 6.37/1.61 | | | | (52) all_11_1 = 0
% 6.37/1.61 | | | |
% 6.37/1.61 | | | | REDUCE: (19), (52) imply:
% 6.37/1.61 | | | | (53) $false
% 6.37/1.61 | | | |
% 6.37/1.61 | | | | CLOSE: (53) is inconsistent.
% 6.37/1.61 | | | |
% 6.37/1.61 | | | End of split
% 6.37/1.61 | | |
% 6.37/1.61 | | Case 2:
% 6.37/1.61 | | |
% 6.37/1.61 | | | (54) ~ (all_11_2 = 0)
% 6.37/1.61 | | |
% 6.37/1.61 | | | REDUCE: (17), (54) imply:
% 6.37/1.61 | | | (55) $false
% 6.37/1.61 | | |
% 6.37/1.61 | | | CLOSE: (55) is inconsistent.
% 6.37/1.61 | | |
% 6.37/1.61 | | End of split
% 6.37/1.61 | |
% 6.37/1.61 | Case 2:
% 6.37/1.61 | |
% 6.37/1.61 | | (56) all_11_3 = 0
% 6.37/1.61 | | (57) ~ (all_11_2 = 0)
% 6.37/1.61 | |
% 6.37/1.61 | | COMBINE_EQS: (16), (56) imply:
% 6.37/1.61 | | (58) all_11_2 = 0
% 6.37/1.61 | |
% 6.37/1.61 | | REDUCE: (57), (58) imply:
% 6.37/1.61 | | (59) $false
% 6.37/1.61 | |
% 6.37/1.61 | | CLOSE: (59) is inconsistent.
% 6.37/1.61 | |
% 6.37/1.61 | End of split
% 6.37/1.61 |
% 6.37/1.61 End of proof
% 6.37/1.61
% 6.37/1.61 Sub-proof #1 shows that the following formulas are inconsistent:
% 6.37/1.61 ----------------------------------------------------------------
% 6.37/1.61 (1) ~ (all_61_1 = 0) | ~ (all_61_2 = 0)
% 6.37/1.61 (2) all_61_1 = 0
% 6.37/1.61 (3) all_61_2 = 0
% 6.37/1.61
% 6.37/1.61 Begin of proof
% 6.37/1.61 |
% 6.37/1.61 | BETA: splitting (1) gives:
% 6.37/1.61 |
% 6.37/1.61 | Case 1:
% 6.37/1.61 | |
% 6.37/1.61 | | (4) ~ (all_61_1 = 0)
% 6.37/1.61 | |
% 6.37/1.61 | | REDUCE: (2), (4) imply:
% 6.37/1.61 | | (5) $false
% 6.37/1.61 | |
% 6.37/1.61 | | CLOSE: (5) is inconsistent.
% 6.37/1.61 | |
% 6.37/1.61 | Case 2:
% 6.37/1.61 | |
% 6.37/1.61 | | (6) ~ (all_61_2 = 0)
% 6.37/1.61 | |
% 6.37/1.61 | | REDUCE: (3), (6) imply:
% 6.37/1.61 | | (7) $false
% 6.37/1.61 | |
% 6.37/1.61 | | CLOSE: (7) is inconsistent.
% 6.37/1.61 | |
% 6.37/1.61 | End of split
% 6.37/1.61 |
% 6.37/1.61 End of proof
% 6.37/1.61 % SZS output end Proof for theBenchmark
% 6.37/1.61
% 6.37/1.61 1008ms
%------------------------------------------------------------------------------