TSTP Solution File: SYN551+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN551+3 : TPTP v8.1.2. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.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 3.69s 1.28s
% Output : Proof 5.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN551+3 : TPTP v8.1.2. Bugfixed v3.1.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 21:28:08 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.79/0.96 Prover 4: Preprocessing ...
% 1.79/0.96 Prover 1: Preprocessing ...
% 1.79/1.01 Prover 2: Preprocessing ...
% 1.79/1.01 Prover 3: Preprocessing ...
% 1.79/1.01 Prover 0: Preprocessing ...
% 1.79/1.01 Prover 5: Preprocessing ...
% 1.79/1.01 Prover 6: Preprocessing ...
% 2.73/1.12 Prover 1: Constructing countermodel ...
% 2.73/1.12 Prover 3: Constructing countermodel ...
% 2.73/1.12 Prover 6: Proving ...
% 2.73/1.12 Prover 4: Constructing countermodel ...
% 2.73/1.13 Prover 5: Constructing countermodel ...
% 2.73/1.15 Prover 0: Proving ...
% 3.34/1.18 Prover 2: Proving ...
% 3.69/1.27 Prover 5: proved (618ms)
% 3.69/1.28
% 3.69/1.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.69/1.28
% 3.69/1.28 Prover 3: stopped
% 3.69/1.28 Prover 6: stopped
% 3.69/1.29 Prover 2: stopped
% 3.69/1.29 Prover 0: stopped
% 3.69/1.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.69/1.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.69/1.29 Prover 7: Preprocessing ...
% 3.69/1.29 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.69/1.29 Prover 8: Preprocessing ...
% 3.69/1.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.69/1.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.69/1.31 Prover 13: Preprocessing ...
% 4.26/1.32 Prover 10: Preprocessing ...
% 4.26/1.32 Prover 11: Preprocessing ...
% 4.26/1.35 Prover 7: Constructing countermodel ...
% 4.26/1.35 Prover 8: Warning: ignoring some quantifiers
% 4.26/1.36 Prover 8: Constructing countermodel ...
% 4.26/1.36 Prover 13: Constructing countermodel ...
% 4.26/1.36 Prover 10: Constructing countermodel ...
% 4.26/1.39 Prover 11: Constructing countermodel ...
% 4.96/1.41 Prover 1: Found proof (size 51)
% 4.96/1.41 Prover 1: proved (759ms)
% 4.96/1.41 Prover 11: stopped
% 4.96/1.41 Prover 8: stopped
% 4.96/1.41 Prover 10: stopped
% 4.96/1.41 Prover 4: stopped
% 4.96/1.41 Prover 7: stopped
% 4.96/1.41 Prover 13: stopped
% 4.96/1.41
% 4.96/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.96/1.41
% 4.96/1.42 % SZS output start Proof for theBenchmark
% 4.96/1.42 Assumptions after simplification:
% 4.96/1.42 ---------------------------------
% 4.96/1.42
% 4.96/1.42 (prove_this_cute_thing)
% 4.96/1.46 ( ! [v0: $i] : ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 4.96/1.46 [v3: $i] : ( ~ (v2 = v0) & g(v2) = v3 & f(v3) = v2 & $i(v3) & $i(v2)) | ?
% 4.96/1.46 [v2: $i] : ( ~ (v2 = v0) & f(v1) = v2 & $i(v2))) & ? [v0: $i] : ? [v1:
% 4.96/1.46 $i] : (g(v1) = v0 & f(v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3:
% 4.96/1.46 $i] : (v2 = v0 | ~ (f(v2) = v3) | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 =
% 4.96/1.46 v2) & g(v3) = v4 & $i(v4))))) | ( ! [v0: $i] : ! [v1: $i] : ( ~
% 4.96/1.46 (f(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v2 = v0) &
% 4.96/1.46 g(v3) = v2 & f(v2) = v3 & $i(v3) & $i(v2)) | ? [v2: $i] : ( ~ (v2 = v0)
% 4.96/1.46 & g(v1) = v2 & $i(v2))) & ? [v0: $i] : ? [v1: $i] : (g(v0) = v1 &
% 4.96/1.46 f(v1) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~
% 4.96/1.46 (g(v2) = v3) | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 = v2) & f(v3) = v4 &
% 4.96/1.46 $i(v4)))))
% 4.96/1.46
% 4.96/1.46 (function-axioms)
% 4.96/1.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (g(v2) = v1) | ~
% 4.96/1.46 (g(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 4.96/1.46 (f(v2) = v1) | ~ (f(v2) = v0))
% 4.96/1.46
% 4.96/1.46 Those formulas are unsatisfiable:
% 4.96/1.46 ---------------------------------
% 4.96/1.46
% 4.96/1.46 Begin of proof
% 4.96/1.46 |
% 4.96/1.46 | ALPHA: (function-axioms) implies:
% 4.96/1.46 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (f(v2) = v1) |
% 4.96/1.46 | ~ (f(v2) = v0))
% 4.96/1.46 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (g(v2) = v1) |
% 4.96/1.46 | ~ (g(v2) = v0))
% 4.96/1.46 |
% 4.96/1.46 | BETA: splitting (prove_this_cute_thing) gives:
% 4.96/1.46 |
% 5.34/1.46 | Case 1:
% 5.34/1.46 | |
% 5.34/1.47 | | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) | ? [v2:
% 5.34/1.47 | | $i] : ? [v3: $i] : ( ~ (v2 = v0) & g(v2) = v3 & f(v3) = v2 &
% 5.34/1.47 | | $i(v3) & $i(v2)) | ? [v2: $i] : ( ~ (v2 = v0) & f(v1) = v2 &
% 5.34/1.47 | | $i(v2))) & ? [v0: $i] : ? [v1: $i] : (g(v1) = v0 & f(v0) = v1 &
% 5.34/1.47 | | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ (f(v2)
% 5.34/1.47 | | = v3) | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 = v2) & g(v3) = v4 &
% 5.34/1.47 | | $i(v4))))
% 5.34/1.47 | |
% 5.34/1.47 | | ALPHA: (3) implies:
% 5.34/1.47 | | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (g(v0) = v1) | ~ $i(v0) | ? [v2:
% 5.34/1.47 | | $i] : ? [v3: $i] : ( ~ (v2 = v0) & g(v2) = v3 & f(v3) = v2 &
% 5.34/1.47 | | $i(v3) & $i(v2)) | ? [v2: $i] : ( ~ (v2 = v0) & f(v1) = v2 &
% 5.34/1.47 | | $i(v2)))
% 5.34/1.47 | | (5) ? [v0: $i] : ? [v1: $i] : (g(v1) = v0 & f(v0) = v1 & $i(v1) &
% 5.34/1.47 | | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ (f(v2) = v3) |
% 5.34/1.47 | | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 = v2) & g(v3) = v4 & $i(v4))))
% 5.34/1.47 | |
% 5.34/1.47 | | DELTA: instantiating (5) with fresh symbols all_10_0, all_10_1 gives:
% 5.34/1.48 | | (6) g(all_10_0) = all_10_1 & f(all_10_1) = all_10_0 & $i(all_10_0) &
% 5.34/1.48 | | $i(all_10_1) & ! [v0: any] : ! [v1: $i] : (v0 = all_10_1 | ~
% 5.34/1.48 | | (f(v0) = v1) | ~ $i(v0) | ? [v2: any] : ( ~ (v2 = v0) & g(v1) =
% 5.34/1.48 | | v2 & $i(v2)))
% 5.34/1.48 | |
% 5.34/1.48 | | ALPHA: (6) implies:
% 5.34/1.48 | | (7) $i(all_10_0)
% 5.34/1.48 | | (8) f(all_10_1) = all_10_0
% 5.34/1.48 | | (9) g(all_10_0) = all_10_1
% 5.34/1.48 | | (10) ! [v0: any] : ! [v1: $i] : (v0 = all_10_1 | ~ (f(v0) = v1) | ~
% 5.34/1.48 | | $i(v0) | ? [v2: any] : ( ~ (v2 = v0) & g(v1) = v2 & $i(v2)))
% 5.34/1.48 | |
% 5.34/1.48 | | GROUND_INST: instantiating (4) with all_10_0, all_10_1, simplifying with
% 5.34/1.48 | | (7), (9) gives:
% 5.34/1.48 | | (11) ? [v0: any] : ? [v1: $i] : ( ~ (v0 = all_10_0) & g(v0) = v1 &
% 5.34/1.48 | | f(v1) = v0 & $i(v1) & $i(v0)) | ? [v0: any] : ( ~ (v0 = all_10_0)
% 5.34/1.48 | | & f(all_10_1) = v0 & $i(v0))
% 5.34/1.48 | |
% 5.34/1.48 | | BETA: splitting (11) gives:
% 5.34/1.48 | |
% 5.34/1.48 | | Case 1:
% 5.34/1.48 | | |
% 5.34/1.48 | | | (12) ? [v0: any] : ? [v1: $i] : ( ~ (v0 = all_10_0) & g(v0) = v1 &
% 5.34/1.48 | | | f(v1) = v0 & $i(v1) & $i(v0))
% 5.34/1.48 | | |
% 5.34/1.48 | | | DELTA: instantiating (12) with fresh symbols all_19_0, all_19_1 gives:
% 5.34/1.48 | | | (13) ~ (all_19_1 = all_10_0) & g(all_19_1) = all_19_0 & f(all_19_0) =
% 5.34/1.48 | | | all_19_1 & $i(all_19_0) & $i(all_19_1)
% 5.34/1.48 | | |
% 5.34/1.48 | | | ALPHA: (13) implies:
% 5.34/1.48 | | | (14) ~ (all_19_1 = all_10_0)
% 5.34/1.48 | | | (15) $i(all_19_0)
% 5.34/1.48 | | | (16) f(all_19_0) = all_19_1
% 5.34/1.48 | | | (17) g(all_19_1) = all_19_0
% 5.34/1.48 | | |
% 5.34/1.48 | | | GROUND_INST: instantiating (10) with all_19_0, all_19_1, simplifying with
% 5.34/1.48 | | | (15), (16) gives:
% 5.34/1.48 | | | (18) all_19_0 = all_10_1 | ? [v0: any] : ( ~ (v0 = all_19_0) &
% 5.34/1.48 | | | g(all_19_1) = v0 & $i(v0))
% 5.34/1.48 | | |
% 5.34/1.48 | | | BETA: splitting (18) gives:
% 5.34/1.48 | | |
% 5.34/1.48 | | | Case 1:
% 5.34/1.48 | | | |
% 5.34/1.48 | | | | (19) all_19_0 = all_10_1
% 5.34/1.48 | | | |
% 5.34/1.48 | | | | REDUCE: (16), (19) imply:
% 5.34/1.48 | | | | (20) f(all_10_1) = all_19_1
% 5.34/1.48 | | | |
% 5.34/1.48 | | | | GROUND_INST: instantiating (1) with all_10_0, all_19_1, all_10_1,
% 5.34/1.48 | | | | simplifying with (8), (20) gives:
% 5.34/1.49 | | | | (21) all_19_1 = all_10_0
% 5.34/1.49 | | | |
% 5.34/1.49 | | | | REDUCE: (14), (21) imply:
% 5.34/1.49 | | | | (22) $false
% 5.34/1.49 | | | |
% 5.34/1.49 | | | | CLOSE: (22) is inconsistent.
% 5.34/1.49 | | | |
% 5.34/1.49 | | | Case 2:
% 5.34/1.49 | | | |
% 5.34/1.49 | | | | (23) ? [v0: any] : ( ~ (v0 = all_19_0) & g(all_19_1) = v0 & $i(v0))
% 5.34/1.49 | | | |
% 5.34/1.49 | | | | DELTA: instantiating (23) with fresh symbol all_33_0 gives:
% 5.34/1.49 | | | | (24) ~ (all_33_0 = all_19_0) & g(all_19_1) = all_33_0 & $i(all_33_0)
% 5.34/1.49 | | | |
% 5.34/1.49 | | | | ALPHA: (24) implies:
% 5.34/1.49 | | | | (25) ~ (all_33_0 = all_19_0)
% 5.34/1.49 | | | | (26) g(all_19_1) = all_33_0
% 5.34/1.49 | | | |
% 5.34/1.49 | | | | GROUND_INST: instantiating (2) with all_19_0, all_33_0, all_19_1,
% 5.34/1.49 | | | | simplifying with (17), (26) gives:
% 5.34/1.49 | | | | (27) all_33_0 = all_19_0
% 5.34/1.49 | | | |
% 5.34/1.49 | | | | REDUCE: (25), (27) imply:
% 5.34/1.49 | | | | (28) $false
% 5.34/1.49 | | | |
% 5.34/1.49 | | | | CLOSE: (28) is inconsistent.
% 5.34/1.49 | | | |
% 5.34/1.49 | | | End of split
% 5.34/1.49 | | |
% 5.34/1.49 | | Case 2:
% 5.34/1.49 | | |
% 5.34/1.49 | | | (29) ? [v0: any] : ( ~ (v0 = all_10_0) & f(all_10_1) = v0 & $i(v0))
% 5.34/1.49 | | |
% 5.34/1.49 | | | DELTA: instantiating (29) with fresh symbol all_19_0 gives:
% 5.34/1.49 | | | (30) ~ (all_19_0 = all_10_0) & f(all_10_1) = all_19_0 & $i(all_19_0)
% 5.34/1.49 | | |
% 5.34/1.49 | | | ALPHA: (30) implies:
% 5.34/1.49 | | | (31) ~ (all_19_0 = all_10_0)
% 5.34/1.49 | | | (32) f(all_10_1) = all_19_0
% 5.34/1.49 | | |
% 5.34/1.49 | | | GROUND_INST: instantiating (1) with all_10_0, all_19_0, all_10_1,
% 5.34/1.49 | | | simplifying with (8), (32) gives:
% 5.34/1.49 | | | (33) all_19_0 = all_10_0
% 5.34/1.49 | | |
% 5.34/1.49 | | | REDUCE: (31), (33) imply:
% 5.34/1.49 | | | (34) $false
% 5.34/1.49 | | |
% 5.34/1.49 | | | CLOSE: (34) is inconsistent.
% 5.34/1.49 | | |
% 5.34/1.49 | | End of split
% 5.34/1.49 | |
% 5.34/1.49 | Case 2:
% 5.34/1.49 | |
% 5.34/1.49 | | (35) ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ? [v2:
% 5.34/1.49 | | $i] : ? [v3: $i] : ( ~ (v2 = v0) & g(v3) = v2 & f(v2) = v3 &
% 5.34/1.49 | | $i(v3) & $i(v2)) | ? [v2: $i] : ( ~ (v2 = v0) & g(v1) = v2 &
% 5.34/1.49 | | $i(v2))) & ? [v0: $i] : ? [v1: $i] : (g(v0) = v1 & f(v1) = v0
% 5.34/1.49 | | & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~
% 5.34/1.49 | | (g(v2) = v3) | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 = v2) & f(v3) =
% 5.34/1.49 | | v4 & $i(v4))))
% 5.34/1.49 | |
% 5.34/1.49 | | ALPHA: (35) implies:
% 5.34/1.49 | | (36) ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ? [v2:
% 5.34/1.49 | | $i] : ? [v3: $i] : ( ~ (v2 = v0) & g(v3) = v2 & f(v2) = v3 &
% 5.34/1.49 | | $i(v3) & $i(v2)) | ? [v2: $i] : ( ~ (v2 = v0) & g(v1) = v2 &
% 5.34/1.50 | | $i(v2)))
% 5.34/1.50 | | (37) ? [v0: $i] : ? [v1: $i] : (g(v0) = v1 & f(v1) = v0 & $i(v1) &
% 5.34/1.50 | | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ (g(v2) = v3) |
% 5.34/1.50 | | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 = v2) & f(v3) = v4 & $i(v4))))
% 5.49/1.50 | |
% 5.49/1.50 | | DELTA: instantiating (37) with fresh symbols all_10_0, all_10_1 gives:
% 5.49/1.50 | | (38) g(all_10_1) = all_10_0 & f(all_10_0) = all_10_1 & $i(all_10_0) &
% 5.49/1.50 | | $i(all_10_1) & ! [v0: any] : ! [v1: $i] : (v0 = all_10_1 | ~
% 5.49/1.50 | | (g(v0) = v1) | ~ $i(v0) | ? [v2: any] : ( ~ (v2 = v0) & f(v1) =
% 5.49/1.50 | | v2 & $i(v2)))
% 5.49/1.50 | |
% 5.49/1.50 | | ALPHA: (38) implies:
% 5.49/1.50 | | (39) $i(all_10_0)
% 5.49/1.50 | | (40) f(all_10_0) = all_10_1
% 5.49/1.50 | | (41) g(all_10_1) = all_10_0
% 5.49/1.50 | | (42) ! [v0: any] : ! [v1: $i] : (v0 = all_10_1 | ~ (g(v0) = v1) | ~
% 5.49/1.50 | | $i(v0) | ? [v2: any] : ( ~ (v2 = v0) & f(v1) = v2 & $i(v2)))
% 5.49/1.50 | |
% 5.49/1.50 | | GROUND_INST: instantiating (36) with all_10_0, all_10_1, simplifying with
% 5.49/1.50 | | (39), (40) gives:
% 5.49/1.50 | | (43) ? [v0: any] : ? [v1: $i] : ( ~ (v0 = all_10_0) & g(v1) = v0 &
% 5.49/1.50 | | f(v0) = v1 & $i(v1) & $i(v0)) | ? [v0: any] : ( ~ (v0 = all_10_0)
% 5.49/1.50 | | & g(all_10_1) = v0 & $i(v0))
% 5.49/1.50 | |
% 5.49/1.50 | | BETA: splitting (43) gives:
% 5.49/1.50 | |
% 5.49/1.50 | | Case 1:
% 5.49/1.50 | | |
% 5.49/1.50 | | | (44) ? [v0: any] : ? [v1: $i] : ( ~ (v0 = all_10_0) & g(v1) = v0 &
% 5.49/1.50 | | | f(v0) = v1 & $i(v1) & $i(v0))
% 5.49/1.50 | | |
% 5.49/1.50 | | | DELTA: instantiating (44) with fresh symbols all_19_0, all_19_1 gives:
% 5.49/1.50 | | | (45) ~ (all_19_1 = all_10_0) & g(all_19_0) = all_19_1 & f(all_19_1) =
% 5.49/1.50 | | | all_19_0 & $i(all_19_0) & $i(all_19_1)
% 5.49/1.50 | | |
% 5.49/1.50 | | | ALPHA: (45) implies:
% 5.49/1.50 | | | (46) ~ (all_19_1 = all_10_0)
% 5.49/1.50 | | | (47) $i(all_19_0)
% 5.49/1.50 | | | (48) f(all_19_1) = all_19_0
% 5.49/1.51 | | | (49) g(all_19_0) = all_19_1
% 5.49/1.51 | | |
% 5.49/1.51 | | | GROUND_INST: instantiating (42) with all_19_0, all_19_1, simplifying with
% 5.49/1.51 | | | (47), (49) gives:
% 5.49/1.51 | | | (50) all_19_0 = all_10_1 | ? [v0: any] : ( ~ (v0 = all_19_0) &
% 5.49/1.51 | | | f(all_19_1) = v0 & $i(v0))
% 5.49/1.51 | | |
% 5.49/1.51 | | | BETA: splitting (50) gives:
% 5.49/1.51 | | |
% 5.49/1.51 | | | Case 1:
% 5.49/1.51 | | | |
% 5.49/1.51 | | | | (51) all_19_0 = all_10_1
% 5.49/1.51 | | | |
% 5.49/1.51 | | | | REDUCE: (49), (51) imply:
% 5.49/1.51 | | | | (52) g(all_10_1) = all_19_1
% 5.49/1.51 | | | |
% 5.49/1.51 | | | | GROUND_INST: instantiating (2) with all_10_0, all_19_1, all_10_1,
% 5.49/1.51 | | | | simplifying with (41), (52) gives:
% 5.49/1.51 | | | | (53) all_19_1 = all_10_0
% 5.49/1.51 | | | |
% 5.49/1.51 | | | | REDUCE: (46), (53) imply:
% 5.49/1.51 | | | | (54) $false
% 5.49/1.51 | | | |
% 5.49/1.51 | | | | CLOSE: (54) is inconsistent.
% 5.49/1.51 | | | |
% 5.49/1.51 | | | Case 2:
% 5.49/1.51 | | | |
% 5.49/1.51 | | | | (55) ? [v0: any] : ( ~ (v0 = all_19_0) & f(all_19_1) = v0 & $i(v0))
% 5.49/1.51 | | | |
% 5.49/1.51 | | | | DELTA: instantiating (55) with fresh symbol all_28_0 gives:
% 5.49/1.51 | | | | (56) ~ (all_28_0 = all_19_0) & f(all_19_1) = all_28_0 & $i(all_28_0)
% 5.49/1.51 | | | |
% 5.49/1.51 | | | | ALPHA: (56) implies:
% 5.49/1.51 | | | | (57) ~ (all_28_0 = all_19_0)
% 5.49/1.51 | | | | (58) f(all_19_1) = all_28_0
% 5.49/1.51 | | | |
% 5.49/1.51 | | | | GROUND_INST: instantiating (1) with all_19_0, all_28_0, all_19_1,
% 5.49/1.51 | | | | simplifying with (48), (58) gives:
% 5.49/1.51 | | | | (59) all_28_0 = all_19_0
% 5.49/1.51 | | | |
% 5.49/1.51 | | | | REDUCE: (57), (59) imply:
% 5.49/1.51 | | | | (60) $false
% 5.49/1.51 | | | |
% 5.49/1.51 | | | | CLOSE: (60) is inconsistent.
% 5.49/1.51 | | | |
% 5.49/1.51 | | | End of split
% 5.49/1.51 | | |
% 5.49/1.51 | | Case 2:
% 5.49/1.51 | | |
% 5.49/1.51 | | | (61) ? [v0: any] : ( ~ (v0 = all_10_0) & g(all_10_1) = v0 & $i(v0))
% 5.49/1.51 | | |
% 5.49/1.51 | | | DELTA: instantiating (61) with fresh symbol all_19_0 gives:
% 5.49/1.51 | | | (62) ~ (all_19_0 = all_10_0) & g(all_10_1) = all_19_0 & $i(all_19_0)
% 5.49/1.51 | | |
% 5.49/1.51 | | | ALPHA: (62) implies:
% 5.49/1.51 | | | (63) ~ (all_19_0 = all_10_0)
% 5.49/1.51 | | | (64) g(all_10_1) = all_19_0
% 5.49/1.51 | | |
% 5.49/1.51 | | | GROUND_INST: instantiating (2) with all_10_0, all_19_0, all_10_1,
% 5.49/1.51 | | | simplifying with (41), (64) gives:
% 5.49/1.51 | | | (65) all_19_0 = all_10_0
% 5.49/1.51 | | |
% 5.49/1.51 | | | REDUCE: (63), (65) imply:
% 5.49/1.51 | | | (66) $false
% 5.49/1.51 | | |
% 5.49/1.51 | | | CLOSE: (66) is inconsistent.
% 5.49/1.51 | | |
% 5.49/1.51 | | End of split
% 5.49/1.51 | |
% 5.49/1.51 | End of split
% 5.49/1.51 |
% 5.49/1.51 End of proof
% 5.49/1.51 % SZS output end Proof for theBenchmark
% 5.49/1.51
% 5.49/1.51 881ms
%------------------------------------------------------------------------------