TSTP Solution File: SYN551+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN551+1 : TPTP v8.1.2. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n009.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 03:28:15 EDT 2023
% Result : Theorem 4.28s 1.30s
% Output : Proof 6.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN551+1 : TPTP v8.1.2. Bugfixed v3.1.0.
% 0.03/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n009.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 19:27:50 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.54/0.60 ________ _____
% 0.54/0.60 ___ __ \_________(_)________________________________
% 0.54/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.54/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.54/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.54/0.60
% 0.54/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.54/0.60 (2023-06-19)
% 0.54/0.60
% 0.54/0.60 (c) Philipp Rümmer, 2009-2023
% 0.54/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.54/0.60 Amanda Stjerna.
% 0.54/0.60 Free software under BSD-3-Clause.
% 0.54/0.60
% 0.54/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.54/0.60
% 0.54/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.54/0.62 Running up to 7 provers in parallel.
% 0.54/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.54/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.54/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.54/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.54/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.54/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.54/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.03/0.94 Prover 1: Preprocessing ...
% 2.03/0.94 Prover 4: Preprocessing ...
% 2.21/0.99 Prover 2: Preprocessing ...
% 2.21/0.99 Prover 0: Preprocessing ...
% 2.21/0.99 Prover 5: Preprocessing ...
% 2.21/0.99 Prover 6: Preprocessing ...
% 2.21/0.99 Prover 3: Preprocessing ...
% 2.96/1.12 Prover 3: Constructing countermodel ...
% 2.96/1.12 Prover 5: Constructing countermodel ...
% 2.96/1.12 Prover 1: Constructing countermodel ...
% 2.96/1.12 Prover 6: Proving ...
% 2.96/1.13 Prover 4: Constructing countermodel ...
% 2.96/1.13 Prover 0: Proving ...
% 3.49/1.15 Prover 2: Proving ...
% 4.28/1.30 Prover 3: proved (675ms)
% 4.28/1.30 Prover 5: proved (674ms)
% 4.28/1.30
% 4.28/1.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.28/1.30
% 4.28/1.30
% 4.28/1.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.28/1.30
% 4.28/1.30 Prover 6: stopped
% 4.28/1.30 Prover 2: stopped
% 4.73/1.32 Prover 0: stopped
% 4.73/1.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.73/1.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.73/1.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.73/1.32 Prover 7: Preprocessing ...
% 4.73/1.32 Prover 8: Preprocessing ...
% 4.73/1.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.73/1.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.73/1.33 Prover 11: Preprocessing ...
% 4.73/1.33 Prover 13: Preprocessing ...
% 4.73/1.34 Prover 10: Preprocessing ...
% 5.05/1.37 Prover 8: Warning: ignoring some quantifiers
% 5.05/1.38 Prover 8: Constructing countermodel ...
% 5.05/1.38 Prover 7: Constructing countermodel ...
% 5.05/1.39 Prover 13: Constructing countermodel ...
% 5.05/1.41 Prover 11: Constructing countermodel ...
% 5.05/1.42 Prover 10: Constructing countermodel ...
% 5.05/1.44 Prover 4: Found proof (size 44)
% 5.05/1.44 Prover 4: proved (815ms)
% 5.05/1.44 Prover 13: stopped
% 5.05/1.44 Prover 8: stopped
% 5.05/1.44 Prover 1: stopped
% 5.05/1.44 Prover 11: stopped
% 5.05/1.44 Prover 7: stopped
% 5.66/1.44 Prover 10: stopped
% 5.66/1.44
% 5.66/1.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.66/1.44
% 5.66/1.45 % SZS output start Proof for theBenchmark
% 5.66/1.46 Assumptions after simplification:
% 5.66/1.46 ---------------------------------
% 5.66/1.46
% 5.66/1.46 (prove_this_cute_thing)
% 5.83/1.50 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 5.83/1.50 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 5.83/1.50 ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ?
% 5.83/1.50 [v16: $i] : ? [v17: $i] : ($i(v15) & $i(v10) & $i(v9) & $i(v6) & $i(v1) &
% 5.83/1.50 $i(v0) & ((v17 = v15 & g(v15) = v16 & f(v16) = v15 & $i(v16) & ! [v18: $i]
% 5.83/1.50 : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : (v19 = v18 | ~ (g(v19) =
% 5.83/1.50 v21) | ~ (g(v18) = v20) | ~ (f(v21) = v19) | ~ (f(v20) = v18) |
% 5.83/1.50 ~ $i(v19) | ~ $i(v18)) & ( ! [v18: $i] : ! [v19: $i] : ( ~ (f(v18) =
% 5.83/1.50 v19) | ~ $i(v18) | ? [v20: $i] : ( ~ (v20 = v18) & g(v19) = v20
% 5.83/1.50 & $i(v20))) | (v14 = v10 & v12 = v9 & ~ (v10 = v9) & g(v13) = v10
% 5.83/1.50 & g(v11) = v9 & f(v10) = v13 & f(v9) = v11 & $i(v13) & $i(v11)))) |
% 5.83/1.50 (v8 = v6 & g(v7) = v6 & f(v6) = v7 & $i(v7) & ! [v18: $i] : ! [v19: $i]
% 5.83/1.50 : ! [v20: $i] : ! [v21: $i] : (v19 = v18 | ~ (g(v21) = v19) | ~
% 5.83/1.50 (g(v20) = v18) | ~ (f(v19) = v21) | ~ (f(v18) = v20) | ~ $i(v19) |
% 5.83/1.50 ~ $i(v18)) & ( ! [v18: $i] : ! [v19: $i] : ( ~ (g(v18) = v19) | ~
% 5.83/1.50 $i(v18) | ? [v20: $i] : ( ~ (v20 = v18) & f(v19) = v20 & $i(v20)))
% 5.83/1.50 | (v5 = v1 & v3 = v0 & ~ (v1 = v0) & g(v1) = v4 & g(v0) = v2 & f(v4)
% 5.83/1.50 = v1 & f(v2) = v0 & $i(v4) & $i(v2))))))
% 5.83/1.50
% 5.83/1.50 (function-axioms)
% 5.83/1.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (g(v2) = v1) | ~
% 5.83/1.50 (g(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 5.83/1.50 (f(v2) = v1) | ~ (f(v2) = v0))
% 5.83/1.50
% 5.83/1.50 Those formulas are unsatisfiable:
% 5.83/1.50 ---------------------------------
% 5.83/1.50
% 5.83/1.50 Begin of proof
% 5.83/1.50 |
% 5.83/1.50 | ALPHA: (function-axioms) implies:
% 5.83/1.50 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (f(v2) = v1) |
% 5.83/1.50 | ~ (f(v2) = v0))
% 5.83/1.50 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (g(v2) = v1) |
% 5.83/1.50 | ~ (g(v2) = v0))
% 5.83/1.50 |
% 5.83/1.51 | DELTA: instantiating (prove_this_cute_thing) with fresh symbols all_3_0,
% 5.83/1.51 | all_3_1, all_3_2, all_3_3, all_3_4, all_3_5, all_3_6, all_3_7, all_3_8,
% 5.83/1.51 | all_3_9, all_3_10, all_3_11, all_3_12, all_3_13, all_3_14, all_3_15,
% 5.83/1.51 | all_3_16, all_3_17 gives:
% 5.83/1.51 | (3) $i(all_3_2) & $i(all_3_7) & $i(all_3_8) & $i(all_3_11) & $i(all_3_16) &
% 5.83/1.51 | $i(all_3_17) & ((all_3_0 = all_3_2 & g(all_3_2) = all_3_1 & f(all_3_1)
% 5.83/1.51 | = all_3_2 & $i(all_3_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 5.83/1.51 | ! [v3: $i] : (v1 = v0 | ~ (g(v1) = v3) | ~ (g(v0) = v2) | ~
% 5.83/1.51 | (f(v3) = v1) | ~ (f(v2) = v0) | ~ $i(v1) | ~ $i(v0)) & ( !
% 5.83/1.51 | [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ? [v2:
% 5.83/1.51 | $i] : ( ~ (v2 = v0) & g(v1) = v2 & $i(v2))) | (all_3_3 =
% 5.83/1.51 | all_3_7 & all_3_5 = all_3_8 & ~ (all_3_7 = all_3_8) &
% 5.83/1.52 | g(all_3_4) = all_3_7 & g(all_3_6) = all_3_8 & f(all_3_7) =
% 5.83/1.52 | all_3_4 & f(all_3_8) = all_3_6 & $i(all_3_4) & $i(all_3_6)))) |
% 5.83/1.52 | (all_3_9 = all_3_11 & g(all_3_10) = all_3_11 & f(all_3_11) = all_3_10
% 5.83/1.52 | & $i(all_3_10) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 5.83/1.52 | $i] : (v1 = v0 | ~ (g(v3) = v1) | ~ (g(v2) = v0) | ~ (f(v1) =
% 5.83/1.52 | v3) | ~ (f(v0) = v2) | ~ $i(v1) | ~ $i(v0)) & ( ! [v0: $i] :
% 5.83/1.52 | ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ( ~
% 5.83/1.52 | (v2 = v0) & f(v1) = v2 & $i(v2))) | (all_3_12 = all_3_16 &
% 5.83/1.52 | all_3_14 = all_3_17 & ~ (all_3_16 = all_3_17) & g(all_3_16) =
% 5.83/1.52 | all_3_13 & g(all_3_17) = all_3_15 & f(all_3_13) = all_3_16 &
% 5.83/1.52 | f(all_3_15) = all_3_17 & $i(all_3_13) & $i(all_3_15)))))
% 5.83/1.52 |
% 5.83/1.52 | ALPHA: (3) implies:
% 5.83/1.52 | (4) $i(all_3_11)
% 5.83/1.52 | (5) $i(all_3_2)
% 5.83/1.52 | (6) (all_3_0 = all_3_2 & g(all_3_2) = all_3_1 & f(all_3_1) = all_3_2 &
% 5.83/1.52 | $i(all_3_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 5.83/1.52 | (v1 = v0 | ~ (g(v1) = v3) | ~ (g(v0) = v2) | ~ (f(v3) = v1) | ~
% 5.83/1.52 | (f(v2) = v0) | ~ $i(v1) | ~ $i(v0)) & ( ! [v0: $i] : ! [v1: $i]
% 5.83/1.52 | : ( ~ (f(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ( ~ (v2 = v0) &
% 5.83/1.52 | g(v1) = v2 & $i(v2))) | (all_3_3 = all_3_7 & all_3_5 = all_3_8
% 5.83/1.52 | & ~ (all_3_7 = all_3_8) & g(all_3_4) = all_3_7 & g(all_3_6) =
% 5.83/1.52 | all_3_8 & f(all_3_7) = all_3_4 & f(all_3_8) = all_3_6 &
% 5.83/1.52 | $i(all_3_4) & $i(all_3_6)))) | (all_3_9 = all_3_11 & g(all_3_10)
% 5.83/1.52 | = all_3_11 & f(all_3_11) = all_3_10 & $i(all_3_10) & ! [v0: $i] : !
% 5.83/1.52 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (g(v3) = v1) |
% 5.83/1.52 | ~ (g(v2) = v0) | ~ (f(v1) = v3) | ~ (f(v0) = v2) | ~ $i(v1) | ~
% 5.83/1.52 | $i(v0)) & ( ! [v0: $i] : ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0)
% 5.83/1.52 | | ? [v2: $i] : ( ~ (v2 = v0) & f(v1) = v2 & $i(v2))) | (all_3_12
% 5.83/1.52 | = all_3_16 & all_3_14 = all_3_17 & ~ (all_3_16 = all_3_17) &
% 5.83/1.52 | g(all_3_16) = all_3_13 & g(all_3_17) = all_3_15 & f(all_3_13) =
% 5.83/1.52 | all_3_16 & f(all_3_15) = all_3_17 & $i(all_3_13) &
% 5.83/1.52 | $i(all_3_15))))
% 5.83/1.52 |
% 5.83/1.52 | BETA: splitting (6) gives:
% 5.83/1.52 |
% 5.83/1.52 | Case 1:
% 5.83/1.52 | |
% 5.83/1.53 | | (7) all_3_0 = all_3_2 & g(all_3_2) = all_3_1 & f(all_3_1) = all_3_2 &
% 5.83/1.53 | | $i(all_3_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 5.83/1.53 | | (v1 = v0 | ~ (g(v1) = v3) | ~ (g(v0) = v2) | ~ (f(v3) = v1) | ~
% 5.83/1.53 | | (f(v2) = v0) | ~ $i(v1) | ~ $i(v0)) & ( ! [v0: $i] : ! [v1: $i]
% 5.83/1.53 | | : ( ~ (f(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ( ~ (v2 = v0) &
% 5.83/1.53 | | g(v1) = v2 & $i(v2))) | (all_3_3 = all_3_7 & all_3_5 = all_3_8
% 5.83/1.53 | | & ~ (all_3_7 = all_3_8) & g(all_3_4) = all_3_7 & g(all_3_6) =
% 5.83/1.53 | | all_3_8 & f(all_3_7) = all_3_4 & f(all_3_8) = all_3_6 &
% 5.83/1.53 | | $i(all_3_4) & $i(all_3_6)))
% 5.83/1.53 | |
% 5.83/1.53 | | ALPHA: (7) implies:
% 5.83/1.53 | | (8) $i(all_3_1)
% 5.83/1.53 | | (9) f(all_3_1) = all_3_2
% 5.83/1.53 | | (10) g(all_3_2) = all_3_1
% 5.83/1.53 | | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ? [v2:
% 5.83/1.53 | | $i] : ( ~ (v2 = v0) & g(v1) = v2 & $i(v2))) | (all_3_3 = all_3_7
% 5.83/1.53 | | & all_3_5 = all_3_8 & ~ (all_3_7 = all_3_8) & g(all_3_4) =
% 5.83/1.53 | | all_3_7 & g(all_3_6) = all_3_8 & f(all_3_7) = all_3_4 & f(all_3_8)
% 5.83/1.53 | | = all_3_6 & $i(all_3_4) & $i(all_3_6))
% 6.10/1.53 | | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 6.10/1.53 | | ~ (g(v1) = v3) | ~ (g(v0) = v2) | ~ (f(v3) = v1) | ~ (f(v2) =
% 6.10/1.53 | | v0) | ~ $i(v1) | ~ $i(v0))
% 6.10/1.53 | |
% 6.10/1.53 | | BETA: splitting (11) gives:
% 6.10/1.53 | |
% 6.10/1.53 | | Case 1:
% 6.10/1.53 | | |
% 6.10/1.53 | | | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ? [v2:
% 6.10/1.53 | | | $i] : ( ~ (v2 = v0) & g(v1) = v2 & $i(v2)))
% 6.10/1.53 | | |
% 6.10/1.53 | | | GROUND_INST: instantiating (13) with all_3_1, all_3_2, simplifying with
% 6.10/1.53 | | | (8), (9) gives:
% 6.10/1.53 | | | (14) ? [v0: any] : ( ~ (v0 = all_3_1) & g(all_3_2) = v0 & $i(v0))
% 6.10/1.53 | | |
% 6.10/1.53 | | | DELTA: instantiating (14) with fresh symbol all_20_0 gives:
% 6.10/1.53 | | | (15) ~ (all_20_0 = all_3_1) & g(all_3_2) = all_20_0 & $i(all_20_0)
% 6.10/1.53 | | |
% 6.10/1.53 | | | ALPHA: (15) implies:
% 6.10/1.54 | | | (16) ~ (all_20_0 = all_3_1)
% 6.10/1.54 | | | (17) g(all_3_2) = all_20_0
% 6.10/1.54 | | |
% 6.10/1.54 | | | GROUND_INST: instantiating (2) with all_3_1, all_20_0, all_3_2,
% 6.10/1.54 | | | simplifying with (10), (17) gives:
% 6.10/1.54 | | | (18) all_20_0 = all_3_1
% 6.10/1.54 | | |
% 6.10/1.54 | | | REDUCE: (16), (18) imply:
% 6.10/1.54 | | | (19) $false
% 6.10/1.54 | | |
% 6.10/1.54 | | | CLOSE: (19) is inconsistent.
% 6.10/1.54 | | |
% 6.10/1.54 | | Case 2:
% 6.10/1.54 | | |
% 6.10/1.54 | | | (20) all_3_3 = all_3_7 & all_3_5 = all_3_8 & ~ (all_3_7 = all_3_8) &
% 6.10/1.54 | | | g(all_3_4) = all_3_7 & g(all_3_6) = all_3_8 & f(all_3_7) = all_3_4
% 6.10/1.54 | | | & f(all_3_8) = all_3_6 & $i(all_3_4) & $i(all_3_6)
% 6.10/1.54 | | |
% 6.10/1.54 | | | ALPHA: (20) implies:
% 6.10/1.54 | | | (21) ~ (all_3_7 = all_3_8)
% 6.10/1.54 | | | (22) $i(all_3_6)
% 6.10/1.54 | | | (23) $i(all_3_4)
% 6.10/1.54 | | | (24) f(all_3_8) = all_3_6
% 6.10/1.54 | | | (25) f(all_3_7) = all_3_4
% 6.10/1.54 | | | (26) g(all_3_6) = all_3_8
% 6.10/1.54 | | | (27) g(all_3_4) = all_3_7
% 6.10/1.54 | | |
% 6.10/1.54 | | | GROUND_INST: instantiating (12) with all_3_6, all_3_2, all_3_8, all_3_1,
% 6.10/1.54 | | | simplifying with (5), (9), (10), (22), (24), (26) gives:
% 6.10/1.54 | | | (28) all_3_2 = all_3_6
% 6.10/1.54 | | |
% 6.10/1.54 | | | GROUND_INST: instantiating (12) with all_3_4, all_3_2, all_3_7, all_3_1,
% 6.10/1.54 | | | simplifying with (5), (9), (10), (23), (25), (27) gives:
% 6.10/1.54 | | | (29) all_3_2 = all_3_4
% 6.10/1.54 | | |
% 6.10/1.54 | | | COMBINE_EQS: (28), (29) imply:
% 6.10/1.54 | | | (30) all_3_4 = all_3_6
% 6.10/1.54 | | |
% 6.10/1.54 | | | REDUCE: (10), (28) imply:
% 6.10/1.54 | | | (31) g(all_3_6) = all_3_1
% 6.10/1.54 | | |
% 6.10/1.54 | | | REDUCE: (27), (30) imply:
% 6.10/1.54 | | | (32) g(all_3_6) = all_3_7
% 6.10/1.54 | | |
% 6.10/1.54 | | | GROUND_INST: instantiating (2) with all_3_8, all_3_1, all_3_6, simplifying
% 6.10/1.54 | | | with (26), (31) gives:
% 6.10/1.54 | | | (33) all_3_1 = all_3_8
% 6.10/1.54 | | |
% 6.10/1.54 | | | GROUND_INST: instantiating (2) with all_3_7, all_3_1, all_3_6, simplifying
% 6.10/1.54 | | | with (31), (32) gives:
% 6.10/1.54 | | | (34) all_3_1 = all_3_7
% 6.10/1.54 | | |
% 6.10/1.54 | | | COMBINE_EQS: (33), (34) imply:
% 6.10/1.54 | | | (35) all_3_7 = all_3_8
% 6.10/1.54 | | |
% 6.10/1.55 | | | REDUCE: (21), (35) imply:
% 6.10/1.55 | | | (36) $false
% 6.10/1.55 | | |
% 6.10/1.55 | | | CLOSE: (36) is inconsistent.
% 6.10/1.55 | | |
% 6.10/1.55 | | End of split
% 6.10/1.55 | |
% 6.10/1.55 | Case 2:
% 6.10/1.55 | |
% 6.10/1.55 | | (37) all_3_9 = all_3_11 & g(all_3_10) = all_3_11 & f(all_3_11) = all_3_10
% 6.10/1.55 | | & $i(all_3_10) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 6.10/1.55 | | $i] : (v1 = v0 | ~ (g(v3) = v1) | ~ (g(v2) = v0) | ~ (f(v1) =
% 6.10/1.55 | | v3) | ~ (f(v0) = v2) | ~ $i(v1) | ~ $i(v0)) & ( ! [v0: $i] :
% 6.10/1.55 | | ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ( ~ (v2
% 6.10/1.55 | | = v0) & f(v1) = v2 & $i(v2))) | (all_3_12 = all_3_16 &
% 6.10/1.55 | | all_3_14 = all_3_17 & ~ (all_3_16 = all_3_17) & g(all_3_16) =
% 6.10/1.55 | | all_3_13 & g(all_3_17) = all_3_15 & f(all_3_13) = all_3_16 &
% 6.10/1.55 | | f(all_3_15) = all_3_17 & $i(all_3_13) & $i(all_3_15)))
% 6.10/1.55 | |
% 6.10/1.55 | | ALPHA: (37) implies:
% 6.10/1.55 | | (38) $i(all_3_10)
% 6.10/1.55 | | (39) f(all_3_11) = all_3_10
% 6.10/1.55 | | (40) g(all_3_10) = all_3_11
% 6.18/1.55 | | (41) ! [v0: $i] : ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) | ? [v2:
% 6.18/1.55 | | $i] : ( ~ (v2 = v0) & f(v1) = v2 & $i(v2))) | (all_3_12 =
% 6.18/1.55 | | all_3_16 & all_3_14 = all_3_17 & ~ (all_3_16 = all_3_17) &
% 6.18/1.55 | | g(all_3_16) = all_3_13 & g(all_3_17) = all_3_15 & f(all_3_13) =
% 6.18/1.55 | | all_3_16 & f(all_3_15) = all_3_17 & $i(all_3_13) & $i(all_3_15))
% 6.18/1.55 | | (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 6.18/1.55 | | ~ (g(v3) = v1) | ~ (g(v2) = v0) | ~ (f(v1) = v3) | ~ (f(v0) =
% 6.18/1.55 | | v2) | ~ $i(v1) | ~ $i(v0))
% 6.18/1.55 | |
% 6.18/1.55 | | BETA: splitting (41) gives:
% 6.18/1.55 | |
% 6.18/1.55 | | Case 1:
% 6.18/1.55 | | |
% 6.18/1.55 | | | (43) ! [v0: $i] : ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) | ? [v2:
% 6.18/1.55 | | | $i] : ( ~ (v2 = v0) & f(v1) = v2 & $i(v2)))
% 6.18/1.55 | | |
% 6.18/1.55 | | | GROUND_INST: instantiating (43) with all_3_10, all_3_11, simplifying with
% 6.18/1.55 | | | (38), (40) gives:
% 6.18/1.55 | | | (44) ? [v0: any] : ( ~ (v0 = all_3_10) & f(all_3_11) = v0 & $i(v0))
% 6.18/1.55 | | |
% 6.18/1.55 | | | DELTA: instantiating (44) with fresh symbol all_20_0 gives:
% 6.18/1.55 | | | (45) ~ (all_20_0 = all_3_10) & f(all_3_11) = all_20_0 & $i(all_20_0)
% 6.18/1.55 | | |
% 6.18/1.55 | | | ALPHA: (45) implies:
% 6.18/1.55 | | | (46) ~ (all_20_0 = all_3_10)
% 6.18/1.55 | | | (47) f(all_3_11) = all_20_0
% 6.18/1.55 | | |
% 6.18/1.55 | | | GROUND_INST: instantiating (1) with all_3_10, all_20_0, all_3_11,
% 6.18/1.55 | | | simplifying with (39), (47) gives:
% 6.18/1.55 | | | (48) all_20_0 = all_3_10
% 6.18/1.55 | | |
% 6.18/1.55 | | | REDUCE: (46), (48) imply:
% 6.18/1.55 | | | (49) $false
% 6.18/1.55 | | |
% 6.18/1.55 | | | CLOSE: (49) is inconsistent.
% 6.18/1.55 | | |
% 6.18/1.55 | | Case 2:
% 6.18/1.55 | | |
% 6.18/1.56 | | | (50) all_3_12 = all_3_16 & all_3_14 = all_3_17 & ~ (all_3_16 =
% 6.18/1.56 | | | all_3_17) & g(all_3_16) = all_3_13 & g(all_3_17) = all_3_15 &
% 6.18/1.56 | | | f(all_3_13) = all_3_16 & f(all_3_15) = all_3_17 & $i(all_3_13) &
% 6.18/1.56 | | | $i(all_3_15)
% 6.18/1.56 | | |
% 6.18/1.56 | | | ALPHA: (50) implies:
% 6.18/1.56 | | | (51) ~ (all_3_16 = all_3_17)
% 6.18/1.56 | | | (52) $i(all_3_15)
% 6.18/1.56 | | | (53) $i(all_3_13)
% 6.18/1.56 | | | (54) f(all_3_15) = all_3_17
% 6.18/1.56 | | | (55) f(all_3_13) = all_3_16
% 6.18/1.56 | | | (56) g(all_3_17) = all_3_15
% 6.18/1.56 | | | (57) g(all_3_16) = all_3_13
% 6.18/1.56 | | |
% 6.18/1.56 | | | GROUND_INST: instantiating (42) with all_3_15, all_3_11, all_3_17,
% 6.18/1.56 | | | all_3_10, simplifying with (4), (39), (40), (52), (54), (56)
% 6.18/1.56 | | | gives:
% 6.18/1.56 | | | (58) all_3_11 = all_3_15
% 6.18/1.56 | | |
% 6.18/1.56 | | | GROUND_INST: instantiating (42) with all_3_13, all_3_11, all_3_16,
% 6.18/1.56 | | | all_3_10, simplifying with (4), (39), (40), (53), (55), (57)
% 6.18/1.56 | | | gives:
% 6.18/1.56 | | | (59) all_3_11 = all_3_13
% 6.18/1.56 | | |
% 6.18/1.56 | | | COMBINE_EQS: (58), (59) imply:
% 6.18/1.56 | | | (60) all_3_13 = all_3_15
% 6.18/1.56 | | |
% 6.18/1.56 | | | REDUCE: (39), (58) imply:
% 6.18/1.56 | | | (61) f(all_3_15) = all_3_10
% 6.18/1.56 | | |
% 6.18/1.56 | | | REDUCE: (55), (60) imply:
% 6.18/1.56 | | | (62) f(all_3_15) = all_3_16
% 6.18/1.56 | | |
% 6.18/1.56 | | | GROUND_INST: instantiating (1) with all_3_17, all_3_10, all_3_15,
% 6.18/1.56 | | | simplifying with (54), (61) gives:
% 6.18/1.56 | | | (63) all_3_10 = all_3_17
% 6.18/1.56 | | |
% 6.18/1.56 | | | GROUND_INST: instantiating (1) with all_3_16, all_3_10, all_3_15,
% 6.18/1.56 | | | simplifying with (61), (62) gives:
% 6.18/1.56 | | | (64) all_3_10 = all_3_16
% 6.18/1.56 | | |
% 6.18/1.56 | | | COMBINE_EQS: (63), (64) imply:
% 6.18/1.56 | | | (65) all_3_16 = all_3_17
% 6.18/1.56 | | |
% 6.18/1.56 | | | REDUCE: (51), (65) imply:
% 6.18/1.56 | | | (66) $false
% 6.18/1.56 | | |
% 6.18/1.56 | | | CLOSE: (66) is inconsistent.
% 6.18/1.56 | | |
% 6.18/1.56 | | End of split
% 6.18/1.56 | |
% 6.18/1.56 | End of split
% 6.18/1.56 |
% 6.18/1.56 End of proof
% 6.18/1.56 % SZS output end Proof for theBenchmark
% 6.18/1.56
% 6.18/1.56 958ms
%------------------------------------------------------------------------------