TSTP Solution File: GEO218+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO218+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n029.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 : Wed Aug 30 23:22:27 EDT 2023
% Result : Theorem 8.92s 1.97s
% Output : Proof 18.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO218+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 30 00:02:12 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.60/0.62 ________ _____
% 0.60/0.62 ___ __ \_________(_)________________________________
% 0.60/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.60/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.60/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.60/0.62
% 0.60/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.60/0.62 (2023-06-19)
% 0.60/0.62
% 0.60/0.62 (c) Philipp Rümmer, 2009-2023
% 0.60/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.60/0.62 Amanda Stjerna.
% 0.60/0.62 Free software under BSD-3-Clause.
% 0.60/0.62
% 0.60/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.60/0.62
% 0.60/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.60/0.63 Running up to 7 provers in parallel.
% 0.71/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.71/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.71/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.71/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.71/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.71/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.71/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.60/1.11 Prover 1: Preprocessing ...
% 2.60/1.11 Prover 4: Preprocessing ...
% 2.60/1.16 Prover 6: Preprocessing ...
% 2.60/1.16 Prover 0: Preprocessing ...
% 2.60/1.16 Prover 5: Preprocessing ...
% 2.60/1.16 Prover 3: Preprocessing ...
% 2.60/1.16 Prover 2: Preprocessing ...
% 4.45/1.39 Prover 5: Proving ...
% 4.94/1.41 Prover 2: Proving ...
% 4.94/1.42 Prover 3: Constructing countermodel ...
% 4.94/1.43 Prover 6: Constructing countermodel ...
% 4.94/1.43 Prover 1: Constructing countermodel ...
% 6.04/1.60 Prover 3: gave up
% 6.04/1.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.04/1.62 Prover 6: gave up
% 6.74/1.63 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.74/1.65 Prover 7: Preprocessing ...
% 6.74/1.66 Prover 8: Preprocessing ...
% 6.74/1.66 Prover 4: Constructing countermodel ...
% 6.74/1.68 Prover 7: Warning: ignoring some quantifiers
% 6.74/1.69 Prover 0: Proving ...
% 6.74/1.70 Prover 7: Constructing countermodel ...
% 7.30/1.71 Prover 1: gave up
% 7.30/1.73 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 7.30/1.73 Prover 7: gave up
% 7.30/1.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.30/1.75 Prover 9: Preprocessing ...
% 7.81/1.77 Prover 10: Preprocessing ...
% 7.81/1.77 Prover 8: Warning: ignoring some quantifiers
% 7.85/1.80 Prover 10: Warning: ignoring some quantifiers
% 7.85/1.80 Prover 8: Constructing countermodel ...
% 8.05/1.80 Prover 10: Constructing countermodel ...
% 8.21/1.86 Prover 10: gave up
% 8.21/1.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.21/1.88 Prover 11: Preprocessing ...
% 8.92/1.93 Prover 8: gave up
% 8.92/1.95 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 8.92/1.95 Prover 9: Constructing countermodel ...
% 8.92/1.97 Prover 12: Preprocessing ...
% 8.92/1.97 Prover 0: proved (1337ms)
% 8.92/1.97
% 8.92/1.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.92/1.97
% 8.92/1.97 Prover 9: stopped
% 8.92/1.98 Prover 2: stopped
% 8.92/1.98 Prover 5: stopped
% 8.92/1.98 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.92/1.98 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 8.92/1.98 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.48/1.99 Prover 13: Preprocessing ...
% 9.48/2.00 Prover 16: Preprocessing ...
% 9.48/2.01 Prover 19: Preprocessing ...
% 9.48/2.02 Prover 13: Warning: ignoring some quantifiers
% 9.48/2.03 Prover 13: Constructing countermodel ...
% 9.48/2.04 Prover 16: Warning: ignoring some quantifiers
% 9.48/2.04 Prover 12: stopped
% 9.48/2.04 Prover 16: Constructing countermodel ...
% 9.48/2.06 Prover 16: gave up
% 10.09/2.07 Prover 13: gave up
% 10.12/2.08 Prover 11: Constructing countermodel ...
% 10.12/2.10 Prover 19: Warning: ignoring some quantifiers
% 10.30/2.10 Prover 19: Constructing countermodel ...
% 10.45/2.18 Prover 19: gave up
% 17.76/3.44 Prover 11: Found proof (size 86)
% 17.76/3.44 Prover 11: proved (1575ms)
% 17.76/3.44 Prover 4: stopped
% 17.76/3.44
% 17.76/3.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.76/3.44
% 17.76/3.45 % SZS output start Proof for theBenchmark
% 17.88/3.46 Assumptions after simplification:
% 17.88/3.46 ---------------------------------
% 17.88/3.46
% 17.88/3.46 (apart6)
% 17.88/3.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 17.88/3.51 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0,
% 17.88/3.51 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 =
% 17.88/3.51 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : !
% 17.88/3.51 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~
% 17.88/3.51 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.88/3.51 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.88/3.51 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~
% 17.88/3.51 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.88/3.51 convergent_lines(v1, v2) = 0)
% 17.88/3.51
% 17.88/3.51 (coipo1)
% 17.88/3.52 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 17.88/3.52 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 17.88/3.52 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 17.88/3.52 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 17.88/3.52 unorthogonal_lines(v0, v1) = 0)
% 17.88/3.52
% 17.88/3.52 (con)
% 17.88/3.52 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( ~
% 17.88/3.52 (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v1, v2) = 0 &
% 18.20/3.52 unorthogonal_lines(v0, v2) = v4 & convergent_lines(v0, v1) = v3 & $i(v2) &
% 18.20/3.52 $i(v1) & $i(v0))
% 18.20/3.52
% 18.20/3.52 (cotno1)
% 18.20/3.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 18.20/3.55 (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) |
% 18.20/3.55 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7:
% 18.20/3.55 int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) |
% 18.20/3.55 (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) &
% 18.20/3.55 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1,
% 18.20/3.55 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] :
% 18.20/3.55 ! [v4: any] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~
% 18.20/3.55 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 18.20/3.55 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 &
% 18.20/3.55 convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 &
% 18.20/3.55 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1,
% 18.20/3.55 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0:
% 18.20/3.55 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 18.20/3.55 (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ~
% 18.20/3.55 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int]
% 18.20/3.55 : ? [v8: int] : ((v6 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 =
% 18.20/3.55 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) &
% 18.20/3.55 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1,
% 18.20/3.55 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] :
% 18.20/3.55 ! [v4: any] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0,
% 18.20/3.55 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 18.20/3.55 int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 &
% 18.20/3.56 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 &
% 18.20/3.56 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1,
% 18.20/3.56 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0:
% 18.20/3.56 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1,
% 18.20/3.56 v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 18.20/3.56 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] :
% 18.20/3.56 ((v6 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 &
% 18.20/3.56 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7
% 18.20/3.56 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] :
% 18.20/3.56 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~
% 18.20/3.56 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 18.20/3.56 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 &
% 18.20/3.56 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0
% 18.20/3.56 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) &
% 18.20/3.56 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 18.20/3.56 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~
% 18.20/3.56 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 18.20/3.56 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 &
% 18.20/3.56 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 &
% 18.20/3.56 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7
% 18.20/3.56 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] :
% 18.20/3.56 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~
% 18.20/3.56 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 18.20/3.56 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 &
% 18.20/3.56 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0
% 18.20/3.56 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) &
% 18.20/3.56 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 18.20/3.56 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~
% 18.20/3.56 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 18.20/3.56 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 &
% 18.20/3.56 convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 &
% 18.20/3.56 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7
% 18.20/3.56 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i]
% 18.20/3.56 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~
% 18.20/3.56 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 18.20/3.56 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 &
% 18.20/3.56 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0
% 18.20/3.56 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) &
% 18.20/3.56 unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 18.20/3.56 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~
% 18.20/3.56 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 18.20/3.56 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 &
% 18.20/3.56 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 &
% 18.20/3.56 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7
% 18.20/3.56 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i]
% 18.20/3.56 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~
% 18.20/3.56 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 18.20/3.56 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 &
% 18.20/3.56 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0
% 18.20/3.56 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) &
% 18.20/3.56 unorthogonal_lines(v1, v2) = v7)))
% 18.20/3.56
% 18.20/3.56 (couo1)
% 18.20/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 18.20/3.56 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~
% 18.20/3.56 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 18.20/3.56 [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0: $i] :
% 18.20/3.56 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0,
% 18.20/3.56 v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) |
% 18.20/3.56 ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : !
% 18.20/3.56 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~
% 18.20/3.56 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 18.20/3.56 unorthogonal_lines(v0, v2) = 0)
% 18.20/3.56
% 18.20/3.56 (function-axioms)
% 18.41/3.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 18.41/3.56 [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 18.41/3.56 (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 18.41/3.56 : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 18.41/3.56 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 18.41/3.56 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 18.41/3.56 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.41/3.56 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.41/3.56 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 18.41/3.56 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 18.41/3.56 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 18.41/3.56 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.41/3.56 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.41/3.57 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 18.41/3.57 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.41/3.57 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 18.41/3.57 v0))
% 18.41/3.57
% 18.41/3.57 Further assumptions not needed in the proof:
% 18.41/3.57 --------------------------------------------
% 18.41/3.57 apart1, apart2, apart3, apart4, apart5, ceq1, ceq2, ceq3, con1, con2, cu1
% 18.41/3.57
% 18.41/3.57 Those formulas are unsatisfiable:
% 18.41/3.57 ---------------------------------
% 18.41/3.57
% 18.41/3.57 Begin of proof
% 18.41/3.57 |
% 18.41/3.57 | ALPHA: (apart6) implies:
% 18.41/3.57 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 18.41/3.57 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) |
% 18.41/3.57 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0)
% 18.41/3.57 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] :
% 18.41/3.57 | (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~
% 18.41/3.57 | (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 18.41/3.57 | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 18.41/3.57 |
% 18.41/3.57 | ALPHA: (coipo1) implies:
% 18.41/3.57 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 18.41/3.57 | (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 18.41/3.57 | convergent_lines(v0, v1) = 0)
% 18.41/3.57 |
% 18.41/3.57 | ALPHA: (cotno1) implies:
% 18.41/3.57 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 18.41/3.57 | (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3)
% 18.41/3.57 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] :
% 18.41/3.57 | ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 &
% 18.41/3.57 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) |
% 18.41/3.57 | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) &
% 18.41/3.57 | convergent_lines(v1, v2) = v7)))
% 18.41/3.58 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 18.41/3.58 | (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) =
% 18.41/3.58 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5:
% 18.41/3.58 | int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 &
% 18.41/3.58 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 &
% 18.41/3.58 | unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) |
% 18.41/3.58 | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7)))
% 18.41/3.58 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] :
% 18.41/3.58 | ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) =
% 18.41/3.58 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 18.41/3.58 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 &
% 18.41/3.58 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 &
% 18.41/3.58 | unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) &
% 18.41/3.58 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) &
% 18.41/3.58 | convergent_lines(v1, v2) = v7)))
% 18.41/3.58 |
% 18.41/3.58 | ALPHA: (couo1) implies:
% 18.41/3.58 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] :
% 18.41/3.58 | (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~
% 18.41/3.58 | (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 18.41/3.58 | | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))
% 18.41/3.58 |
% 18.41/3.58 | ALPHA: (function-axioms) implies:
% 18.41/3.58 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 18.41/3.58 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 18.41/3.58 | (convergent_lines(v3, v2) = v0))
% 18.41/3.58 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 18.41/3.58 | ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 18.41/3.58 | (unorthogonal_lines(v3, v2) = v0))
% 18.41/3.58 |
% 18.41/3.58 | DELTA: instantiating (con) with fresh symbols all_18_0, all_18_1, all_18_2,
% 18.41/3.58 | all_18_3, all_18_4 gives:
% 18.41/3.58 | (10) ~ (all_18_0 = 0) & ~ (all_18_1 = 0) & unorthogonal_lines(all_18_3,
% 18.41/3.58 | all_18_2) = 0 & unorthogonal_lines(all_18_4, all_18_2) = all_18_0 &
% 18.41/3.58 | convergent_lines(all_18_4, all_18_3) = all_18_1 & $i(all_18_2) &
% 18.41/3.58 | $i(all_18_3) & $i(all_18_4)
% 18.41/3.58 |
% 18.41/3.58 | ALPHA: (10) implies:
% 18.41/3.58 | (11) ~ (all_18_1 = 0)
% 18.41/3.58 | (12) ~ (all_18_0 = 0)
% 18.41/3.58 | (13) $i(all_18_4)
% 18.41/3.58 | (14) $i(all_18_3)
% 18.41/3.58 | (15) $i(all_18_2)
% 18.41/3.58 | (16) convergent_lines(all_18_4, all_18_3) = all_18_1
% 18.41/3.58 | (17) unorthogonal_lines(all_18_4, all_18_2) = all_18_0
% 18.41/3.58 | (18) unorthogonal_lines(all_18_3, all_18_2) = 0
% 18.41/3.58 |
% 18.41/3.58 | GROUND_INST: instantiating (7) with all_18_4, all_18_2, all_18_2, all_18_0,
% 18.41/3.58 | all_18_0, simplifying with (13), (15), (17) gives:
% 18.41/3.59 | (19) all_18_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 18.41/3.59 | convergent_lines(all_18_2, all_18_2) = v0)
% 18.41/3.59 |
% 18.41/3.59 | GROUND_INST: instantiating (6) with all_18_4, all_18_3, all_18_2, all_18_1,
% 18.41/3.59 | all_18_0, simplifying with (13), (14), (15), (16), (17) gives:
% 18.41/3.59 | (20) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0 &
% 18.41/3.59 | all_18_0 = 0 & convergent_lines(all_18_4, all_18_2) = 0) | (v0 = 0
% 18.41/3.59 | & all_18_1 = 0 & unorthogonal_lines(all_18_4, all_18_3) = 0) | ( ~
% 18.41/3.59 | (v3 = 0) & unorthogonal_lines(all_18_3, all_18_2) = v3) | ( ~ (v2
% 18.41/3.59 | = 0) & convergent_lines(all_18_3, all_18_2) = v2))
% 18.41/3.59 |
% 18.41/3.59 | GROUND_INST: instantiating (3) with all_18_4, all_18_2, all_18_0, simplifying
% 18.41/3.59 | with (13), (15), (17) gives:
% 18.41/3.59 | (21) all_18_0 = 0 | convergent_lines(all_18_4, all_18_2) = 0
% 18.41/3.59 |
% 18.41/3.59 | GROUND_INST: instantiating (5) with all_18_4, all_18_3, all_18_2, all_18_0,
% 18.41/3.59 | simplifying with (13), (14), (15), (17), (18) gives:
% 18.41/3.59 | (22) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 &
% 18.41/3.59 | all_18_0 = 0 & convergent_lines(all_18_4, all_18_2) = 0) | (v1 = 0
% 18.41/3.59 | & v0 = 0 & unorthogonal_lines(all_18_4, all_18_3) = 0 &
% 18.41/3.59 | convergent_lines(all_18_4, all_18_3) = 0) | ( ~ (v3 = 0) &
% 18.41/3.59 | convergent_lines(all_18_3, all_18_2) = v3))
% 18.41/3.59 |
% 18.41/3.59 | GROUND_INST: instantiating (4) with all_18_4, all_18_3, all_18_2, all_18_1,
% 18.41/3.59 | simplifying with (13), (14), (15), (16), (18) gives:
% 18.41/3.59 | (23) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 &
% 18.41/3.59 | v1 = 0 & unorthogonal_lines(all_18_4, all_18_2) = 0 &
% 18.41/3.59 | convergent_lines(all_18_4, all_18_2) = 0) | (v0 = 0 & all_18_1 = 0
% 18.41/3.59 | & unorthogonal_lines(all_18_4, all_18_3) = 0) | ( ~ (v3 = 0) &
% 18.41/3.59 | convergent_lines(all_18_3, all_18_2) = v3))
% 18.41/3.59 |
% 18.41/3.59 | DELTA: instantiating (23) with fresh symbols all_27_0, all_27_1, all_27_2,
% 18.41/3.59 | all_27_3 gives:
% 18.41/3.59 | (24) (all_27_1 = 0 & all_27_2 = 0 & unorthogonal_lines(all_18_4, all_18_2)
% 18.41/3.59 | = 0 & convergent_lines(all_18_4, all_18_2) = 0) | (all_27_3 = 0 &
% 18.41/3.59 | all_18_1 = 0 & unorthogonal_lines(all_18_4, all_18_3) = 0) | ( ~
% 18.41/3.59 | (all_27_0 = 0) & convergent_lines(all_18_3, all_18_2) = all_27_0)
% 18.41/3.59 |
% 18.41/3.59 | DELTA: instantiating (22) with fresh symbols all_28_0, all_28_1, all_28_2,
% 18.41/3.59 | all_28_3 gives:
% 18.41/3.59 | (25) (all_28_1 = 0 & all_18_0 = 0 & convergent_lines(all_18_4, all_18_2) =
% 18.41/3.59 | 0) | (all_28_2 = 0 & all_28_3 = 0 & unorthogonal_lines(all_18_4,
% 18.41/3.59 | all_18_3) = 0 & convergent_lines(all_18_4, all_18_3) = 0) | ( ~
% 18.41/3.59 | (all_28_0 = 0) & convergent_lines(all_18_3, all_18_2) = all_28_0)
% 18.41/3.59 |
% 18.41/3.59 | DELTA: instantiating (20) with fresh symbols all_31_0, all_31_1, all_31_2,
% 18.41/3.59 | all_31_3 gives:
% 18.41/3.59 | (26) (all_31_2 = 0 & all_18_0 = 0 & convergent_lines(all_18_4, all_18_2) =
% 18.41/3.59 | 0) | (all_31_3 = 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4,
% 18.41/3.59 | all_18_3) = 0) | ( ~ (all_31_0 = 0) & unorthogonal_lines(all_18_3,
% 18.41/3.59 | all_18_2) = all_31_0) | ( ~ (all_31_1 = 0) &
% 18.41/3.59 | convergent_lines(all_18_3, all_18_2) = all_31_1)
% 18.41/3.59 |
% 18.41/3.59 | BETA: splitting (21) gives:
% 18.41/3.59 |
% 18.41/3.59 | Case 1:
% 18.41/3.59 | |
% 18.41/3.59 | | (27) convergent_lines(all_18_4, all_18_2) = 0
% 18.41/3.59 | |
% 18.41/3.59 | | BETA: splitting (24) gives:
% 18.41/3.59 | |
% 18.41/3.59 | | Case 1:
% 18.41/3.59 | | |
% 18.41/3.59 | | | (28) all_27_1 = 0 & all_27_2 = 0 & unorthogonal_lines(all_18_4,
% 18.41/3.59 | | | all_18_2) = 0 & convergent_lines(all_18_4, all_18_2) = 0
% 18.41/3.59 | | |
% 18.41/3.59 | | | ALPHA: (28) implies:
% 18.41/3.59 | | | (29) unorthogonal_lines(all_18_4, all_18_2) = 0
% 18.41/3.59 | | |
% 18.41/3.60 | | | GROUND_INST: instantiating (9) with all_18_0, 0, all_18_2, all_18_4,
% 18.41/3.60 | | | simplifying with (17), (29) gives:
% 18.41/3.60 | | | (30) all_18_0 = 0
% 18.41/3.60 | | |
% 18.41/3.60 | | | REDUCE: (12), (30) imply:
% 18.41/3.60 | | | (31) $false
% 18.41/3.60 | | |
% 18.41/3.60 | | | CLOSE: (31) is inconsistent.
% 18.41/3.60 | | |
% 18.41/3.60 | | Case 2:
% 18.41/3.60 | | |
% 18.41/3.60 | | | (32) (all_27_3 = 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4,
% 18.41/3.60 | | | all_18_3) = 0) | ( ~ (all_27_0 = 0) &
% 18.41/3.60 | | | convergent_lines(all_18_3, all_18_2) = all_27_0)
% 18.41/3.60 | | |
% 18.41/3.60 | | | BETA: splitting (32) gives:
% 18.41/3.60 | | |
% 18.41/3.60 | | | Case 1:
% 18.41/3.60 | | | |
% 18.41/3.60 | | | | (33) all_27_3 = 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4,
% 18.41/3.60 | | | | all_18_3) = 0
% 18.41/3.60 | | | |
% 18.41/3.60 | | | | ALPHA: (33) implies:
% 18.41/3.60 | | | | (34) all_18_1 = 0
% 18.41/3.60 | | | |
% 18.41/3.60 | | | | REDUCE: (11), (34) imply:
% 18.41/3.60 | | | | (35) $false
% 18.41/3.60 | | | |
% 18.41/3.60 | | | | CLOSE: (35) is inconsistent.
% 18.41/3.60 | | | |
% 18.41/3.60 | | | Case 2:
% 18.41/3.60 | | | |
% 18.41/3.60 | | | | (36) ~ (all_27_0 = 0) & convergent_lines(all_18_3, all_18_2) =
% 18.41/3.60 | | | | all_27_0
% 18.41/3.60 | | | |
% 18.41/3.60 | | | | ALPHA: (36) implies:
% 18.41/3.60 | | | | (37) convergent_lines(all_18_3, all_18_2) = all_27_0
% 18.41/3.60 | | | |
% 18.41/3.60 | | | | BETA: splitting (25) gives:
% 18.41/3.60 | | | |
% 18.41/3.60 | | | | Case 1:
% 18.41/3.60 | | | | |
% 18.41/3.60 | | | | | (38) all_28_1 = 0 & all_18_0 = 0 & convergent_lines(all_18_4,
% 18.41/3.60 | | | | | all_18_2) = 0
% 18.41/3.60 | | | | |
% 18.41/3.60 | | | | | ALPHA: (38) implies:
% 18.41/3.60 | | | | | (39) all_18_0 = 0
% 18.41/3.60 | | | | |
% 18.41/3.60 | | | | | REDUCE: (12), (39) imply:
% 18.41/3.60 | | | | | (40) $false
% 18.41/3.60 | | | | |
% 18.41/3.60 | | | | | CLOSE: (40) is inconsistent.
% 18.41/3.60 | | | | |
% 18.41/3.60 | | | | Case 2:
% 18.41/3.60 | | | | |
% 18.41/3.60 | | | | | (41) (all_28_2 = 0 & all_28_3 = 0 & unorthogonal_lines(all_18_4,
% 18.41/3.60 | | | | | all_18_3) = 0 & convergent_lines(all_18_4, all_18_3) = 0)
% 18.41/3.60 | | | | | | ( ~ (all_28_0 = 0) & convergent_lines(all_18_3, all_18_2) =
% 18.41/3.60 | | | | | all_28_0)
% 18.41/3.60 | | | | |
% 18.41/3.60 | | | | | BETA: splitting (41) gives:
% 18.41/3.60 | | | | |
% 18.41/3.60 | | | | | Case 1:
% 18.41/3.60 | | | | | |
% 18.41/3.60 | | | | | | (42) all_28_2 = 0 & all_28_3 = 0 & unorthogonal_lines(all_18_4,
% 18.41/3.60 | | | | | | all_18_3) = 0 & convergent_lines(all_18_4, all_18_3) = 0
% 18.41/3.60 | | | | | |
% 18.41/3.60 | | | | | | ALPHA: (42) implies:
% 18.41/3.60 | | | | | | (43) convergent_lines(all_18_4, all_18_3) = 0
% 18.41/3.60 | | | | | |
% 18.41/3.60 | | | | | | GROUND_INST: instantiating (8) with all_18_1, 0, all_18_3, all_18_4,
% 18.41/3.60 | | | | | | simplifying with (16), (43) gives:
% 18.41/3.60 | | | | | | (44) all_18_1 = 0
% 18.41/3.60 | | | | | |
% 18.41/3.60 | | | | | | REDUCE: (11), (44) imply:
% 18.41/3.60 | | | | | | (45) $false
% 18.41/3.60 | | | | | |
% 18.41/3.60 | | | | | | CLOSE: (45) is inconsistent.
% 18.41/3.60 | | | | | |
% 18.41/3.60 | | | | | Case 2:
% 18.41/3.60 | | | | | |
% 18.41/3.60 | | | | | | (46) ~ (all_28_0 = 0) & convergent_lines(all_18_3, all_18_2) =
% 18.41/3.60 | | | | | | all_28_0
% 18.41/3.60 | | | | | |
% 18.41/3.60 | | | | | | ALPHA: (46) implies:
% 18.41/3.60 | | | | | | (47) ~ (all_28_0 = 0)
% 18.41/3.60 | | | | | | (48) convergent_lines(all_18_3, all_18_2) = all_28_0
% 18.41/3.60 | | | | | |
% 18.41/3.60 | | | | | | BETA: splitting (19) gives:
% 18.41/3.60 | | | | | |
% 18.41/3.60 | | | | | | Case 1:
% 18.41/3.60 | | | | | | |
% 18.41/3.60 | | | | | | | (49) all_18_0 = 0
% 18.41/3.60 | | | | | | |
% 18.41/3.60 | | | | | | | REDUCE: (12), (49) imply:
% 18.41/3.60 | | | | | | | (50) $false
% 18.41/3.60 | | | | | | |
% 18.41/3.60 | | | | | | | CLOSE: (50) is inconsistent.
% 18.41/3.60 | | | | | | |
% 18.41/3.60 | | | | | | Case 2:
% 18.41/3.60 | | | | | | |
% 18.41/3.60 | | | | | | | (51) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_18_2,
% 18.41/3.60 | | | | | | | all_18_2) = v0)
% 18.41/3.60 | | | | | | |
% 18.41/3.60 | | | | | | | DELTA: instantiating (51) with fresh symbol all_50_0 gives:
% 18.41/3.60 | | | | | | | (52) ~ (all_50_0 = 0) & convergent_lines(all_18_2, all_18_2) =
% 18.41/3.60 | | | | | | | all_50_0
% 18.41/3.60 | | | | | | |
% 18.41/3.60 | | | | | | | ALPHA: (52) implies:
% 18.41/3.60 | | | | | | | (53) ~ (all_50_0 = 0)
% 18.41/3.60 | | | | | | | (54) convergent_lines(all_18_2, all_18_2) = all_50_0
% 18.41/3.60 | | | | | | |
% 18.41/3.60 | | | | | | | BETA: splitting (26) gives:
% 18.41/3.60 | | | | | | |
% 18.41/3.60 | | | | | | | Case 1:
% 18.41/3.60 | | | | | | | |
% 18.41/3.60 | | | | | | | | (55) (all_31_2 = 0 & all_18_0 = 0 &
% 18.41/3.60 | | | | | | | | convergent_lines(all_18_4, all_18_2) = 0) | (all_31_3
% 18.41/3.60 | | | | | | | | = 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4,
% 18.41/3.60 | | | | | | | | all_18_3) = 0)
% 18.41/3.60 | | | | | | | |
% 18.41/3.60 | | | | | | | | BETA: splitting (55) gives:
% 18.41/3.60 | | | | | | | |
% 18.41/3.60 | | | | | | | | Case 1:
% 18.41/3.60 | | | | | | | | |
% 18.41/3.60 | | | | | | | | | (56) all_31_2 = 0 & all_18_0 = 0 &
% 18.41/3.60 | | | | | | | | | convergent_lines(all_18_4, all_18_2) = 0
% 18.41/3.60 | | | | | | | | |
% 18.41/3.60 | | | | | | | | | ALPHA: (56) implies:
% 18.41/3.60 | | | | | | | | | (57) all_18_0 = 0
% 18.41/3.60 | | | | | | | | |
% 18.41/3.60 | | | | | | | | | REDUCE: (12), (57) imply:
% 18.41/3.60 | | | | | | | | | (58) $false
% 18.41/3.60 | | | | | | | | |
% 18.41/3.60 | | | | | | | | | CLOSE: (58) is inconsistent.
% 18.41/3.60 | | | | | | | | |
% 18.41/3.60 | | | | | | | | Case 2:
% 18.41/3.60 | | | | | | | | |
% 18.41/3.60 | | | | | | | | | (59) all_31_3 = 0 & all_18_1 = 0 &
% 18.41/3.60 | | | | | | | | | unorthogonal_lines(all_18_4, all_18_3) = 0
% 18.41/3.60 | | | | | | | | |
% 18.41/3.60 | | | | | | | | | ALPHA: (59) implies:
% 18.41/3.60 | | | | | | | | | (60) all_18_1 = 0
% 18.41/3.60 | | | | | | | | |
% 18.41/3.60 | | | | | | | | | REDUCE: (11), (60) imply:
% 18.41/3.61 | | | | | | | | | (61) $false
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | CLOSE: (61) is inconsistent.
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | End of split
% 18.41/3.61 | | | | | | | |
% 18.41/3.61 | | | | | | | Case 2:
% 18.41/3.61 | | | | | | | |
% 18.41/3.61 | | | | | | | | (62) ( ~ (all_31_0 = 0) & unorthogonal_lines(all_18_3,
% 18.41/3.61 | | | | | | | | all_18_2) = all_31_0) | ( ~ (all_31_1 = 0) &
% 18.41/3.61 | | | | | | | | convergent_lines(all_18_3, all_18_2) = all_31_1)
% 18.41/3.61 | | | | | | | |
% 18.41/3.61 | | | | | | | | BETA: splitting (62) gives:
% 18.41/3.61 | | | | | | | |
% 18.41/3.61 | | | | | | | | Case 1:
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | (63) ~ (all_31_0 = 0) & unorthogonal_lines(all_18_3,
% 18.41/3.61 | | | | | | | | | all_18_2) = all_31_0
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | ALPHA: (63) implies:
% 18.41/3.61 | | | | | | | | | (64) ~ (all_31_0 = 0)
% 18.41/3.61 | | | | | | | | | (65) unorthogonal_lines(all_18_3, all_18_2) = all_31_0
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_31_0, all_18_2,
% 18.41/3.61 | | | | | | | | | all_18_3, simplifying with (18), (65) gives:
% 18.41/3.61 | | | | | | | | | (66) all_31_0 = 0
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | REDUCE: (64), (66) imply:
% 18.41/3.61 | | | | | | | | | (67) $false
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | CLOSE: (67) is inconsistent.
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | Case 2:
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | (68) ~ (all_31_1 = 0) & convergent_lines(all_18_3,
% 18.41/3.61 | | | | | | | | | all_18_2) = all_31_1
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | ALPHA: (68) implies:
% 18.41/3.61 | | | | | | | | | (69) convergent_lines(all_18_3, all_18_2) = all_31_1
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | GROUND_INST: instantiating (8) with all_28_0, all_31_1,
% 18.41/3.61 | | | | | | | | | all_18_2, all_18_3, simplifying with (48), (69)
% 18.41/3.61 | | | | | | | | | gives:
% 18.41/3.61 | | | | | | | | | (70) all_31_1 = all_28_0
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | GROUND_INST: instantiating (8) with all_27_0, all_31_1,
% 18.41/3.61 | | | | | | | | | all_18_2, all_18_3, simplifying with (37), (69)
% 18.41/3.61 | | | | | | | | | gives:
% 18.41/3.61 | | | | | | | | | (71) all_31_1 = all_27_0
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | COMBINE_EQS: (70), (71) imply:
% 18.41/3.61 | | | | | | | | | (72) all_28_0 = all_27_0
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | SIMP: (72) implies:
% 18.41/3.61 | | | | | | | | | (73) all_28_0 = all_27_0
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | REDUCE: (47), (73) imply:
% 18.41/3.61 | | | | | | | | | (74) ~ (all_27_0 = 0)
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | GROUND_INST: instantiating (1) with all_18_4, all_18_2,
% 18.41/3.61 | | | | | | | | | all_18_3, all_18_1, simplifying with (13), (14),
% 18.41/3.61 | | | | | | | | | (15), (16), (27) gives:
% 18.41/3.61 | | | | | | | | | (75) all_18_1 = 0 | convergent_lines(all_18_2, all_18_3) =
% 18.41/3.61 | | | | | | | | | 0
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | GROUND_INST: instantiating (2) with all_18_2, all_18_3,
% 18.41/3.61 | | | | | | | | | all_18_2, all_50_0, all_27_0, simplifying with
% 18.41/3.61 | | | | | | | | | (14), (15), (37), (54) gives:
% 18.41/3.61 | | | | | | | | | (76) all_50_0 = 0 | all_27_0 = 0 | ? [v0: int] : ( ~ (v0 =
% 18.41/3.61 | | | | | | | | | 0) & convergent_lines(all_18_2, all_18_3) = v0)
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | BETA: splitting (75) gives:
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | | Case 1:
% 18.41/3.61 | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | (77) convergent_lines(all_18_2, all_18_3) = 0
% 18.41/3.61 | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | BETA: splitting (76) gives:
% 18.41/3.61 | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | Case 1:
% 18.41/3.61 | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | (78) all_50_0 = 0
% 18.41/3.61 | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | REDUCE: (53), (78) imply:
% 18.41/3.61 | | | | | | | | | | | (79) $false
% 18.41/3.61 | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | CLOSE: (79) is inconsistent.
% 18.41/3.61 | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | Case 2:
% 18.41/3.61 | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | (80) all_27_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 18.41/3.61 | | | | | | | | | | | convergent_lines(all_18_2, all_18_3) = v0)
% 18.41/3.61 | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | BETA: splitting (80) gives:
% 18.41/3.61 | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | Case 1:
% 18.41/3.61 | | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | | (81) all_27_0 = 0
% 18.41/3.61 | | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | | REDUCE: (74), (81) imply:
% 18.41/3.61 | | | | | | | | | | | | (82) $false
% 18.41/3.61 | | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | | CLOSE: (82) is inconsistent.
% 18.41/3.61 | | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | Case 2:
% 18.41/3.61 | | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | | (83) ? [v0: int] : ( ~ (v0 = 0) &
% 18.41/3.61 | | | | | | | | | | | | convergent_lines(all_18_2, all_18_3) = v0)
% 18.41/3.61 | | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | | DELTA: instantiating (83) with fresh symbol all_191_0
% 18.41/3.61 | | | | | | | | | | | | gives:
% 18.41/3.61 | | | | | | | | | | | | (84) ~ (all_191_0 = 0) & convergent_lines(all_18_2,
% 18.41/3.61 | | | | | | | | | | | | all_18_3) = all_191_0
% 18.41/3.61 | | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | | ALPHA: (84) implies:
% 18.41/3.61 | | | | | | | | | | | | (85) ~ (all_191_0 = 0)
% 18.41/3.61 | | | | | | | | | | | | (86) convergent_lines(all_18_2, all_18_3) = all_191_0
% 18.41/3.61 | | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_191_0, all_18_3,
% 18.41/3.61 | | | | | | | | | | | | all_18_2, simplifying with (77), (86) gives:
% 18.41/3.61 | | | | | | | | | | | | (87) all_191_0 = 0
% 18.41/3.61 | | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | | REDUCE: (85), (87) imply:
% 18.41/3.61 | | | | | | | | | | | | (88) $false
% 18.41/3.61 | | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | | CLOSE: (88) is inconsistent.
% 18.41/3.61 | | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | | End of split
% 18.41/3.61 | | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | End of split
% 18.41/3.61 | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | Case 2:
% 18.41/3.61 | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | (89) all_18_1 = 0
% 18.41/3.61 | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | REDUCE: (11), (89) imply:
% 18.41/3.61 | | | | | | | | | | (90) $false
% 18.41/3.61 | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | | CLOSE: (90) is inconsistent.
% 18.41/3.61 | | | | | | | | | |
% 18.41/3.61 | | | | | | | | | End of split
% 18.41/3.61 | | | | | | | | |
% 18.41/3.61 | | | | | | | | End of split
% 18.41/3.61 | | | | | | | |
% 18.41/3.61 | | | | | | | End of split
% 18.41/3.61 | | | | | | |
% 18.41/3.61 | | | | | | End of split
% 18.41/3.61 | | | | | |
% 18.41/3.61 | | | | | End of split
% 18.41/3.61 | | | | |
% 18.41/3.61 | | | | End of split
% 18.41/3.61 | | | |
% 18.41/3.61 | | | End of split
% 18.41/3.61 | | |
% 18.41/3.61 | | End of split
% 18.41/3.61 | |
% 18.41/3.61 | Case 2:
% 18.41/3.61 | |
% 18.41/3.61 | | (91) all_18_0 = 0
% 18.41/3.61 | |
% 18.41/3.61 | | REDUCE: (12), (91) imply:
% 18.41/3.61 | | (92) $false
% 18.41/3.61 | |
% 18.41/3.61 | | CLOSE: (92) is inconsistent.
% 18.41/3.61 | |
% 18.41/3.61 | End of split
% 18.41/3.61 |
% 18.41/3.61 End of proof
% 18.41/3.61 % SZS output end Proof for theBenchmark
% 18.41/3.61
% 18.41/3.61 2997ms
%------------------------------------------------------------------------------