TSTP Solution File: GEO232+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO232+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n021.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 23:22:37 EDT 2023
% Result : Theorem 11.06s 3.09s
% Output : Proof 13.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GEO232+3 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.37 % Computer : n021.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Tue Aug 29 20:18:44 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.44/0.67 ________ _____
% 0.44/0.67 ___ __ \_________(_)________________________________
% 0.44/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.44/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.44/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.44/0.67
% 0.44/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.44/0.67 (2023-06-19)
% 0.44/0.67
% 0.44/0.67 (c) Philipp Rümmer, 2009-2023
% 0.44/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.44/0.67 Amanda Stjerna.
% 0.44/0.67 Free software under BSD-3-Clause.
% 0.44/0.67
% 0.44/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.44/0.67
% 0.44/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.44/0.68 Running up to 7 provers in parallel.
% 0.72/0.72 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.72/0.72 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.72/0.72 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.72/0.72 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.72/0.72 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.72/0.72 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.72/0.72 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.49/1.32 Prover 1: Preprocessing ...
% 2.49/1.32 Prover 4: Preprocessing ...
% 2.49/1.35 Prover 5: Preprocessing ...
% 2.49/1.35 Prover 0: Preprocessing ...
% 2.49/1.35 Prover 3: Preprocessing ...
% 2.49/1.35 Prover 2: Preprocessing ...
% 2.49/1.35 Prover 6: Preprocessing ...
% 6.21/2.12 Prover 5: Proving ...
% 6.88/2.23 Prover 2: Proving ...
% 6.88/2.25 Prover 1: Constructing countermodel ...
% 6.88/2.25 Prover 6: Constructing countermodel ...
% 6.88/2.26 Prover 3: Constructing countermodel ...
% 7.27/2.37 Prover 6: gave up
% 7.27/2.37 Prover 3: gave up
% 7.27/2.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.27/2.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.27/2.38 Prover 1: gave up
% 7.65/2.42 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 8.16/2.50 Prover 7: Preprocessing ...
% 8.16/2.51 Prover 8: Preprocessing ...
% 8.16/2.51 Prover 9: Preprocessing ...
% 8.81/2.67 Prover 7: Warning: ignoring some quantifiers
% 9.32/2.73 Prover 7: Constructing countermodel ...
% 9.32/2.76 Prover 8: Warning: ignoring some quantifiers
% 9.85/2.81 Prover 8: Constructing countermodel ...
% 9.85/2.83 Prover 4: Constructing countermodel ...
% 9.85/2.85 Prover 0: Proving ...
% 10.55/2.94 Prover 7: gave up
% 10.55/2.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.06/3.02 Prover 10: Preprocessing ...
% 11.06/3.04 Prover 8: gave up
% 11.06/3.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.06/3.09 Prover 0: proved (2402ms)
% 11.06/3.09
% 11.06/3.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.06/3.09
% 11.51/3.14 Prover 5: stopped
% 11.51/3.15 Prover 2: stopped
% 11.51/3.15 Prover 11: Preprocessing ...
% 11.51/3.15 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.51/3.15 Prover 10: Warning: ignoring some quantifiers
% 11.51/3.15 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 11.51/3.15 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 11.96/3.19 Prover 10: Constructing countermodel ...
% 11.96/3.23 Prover 19: Preprocessing ...
% 11.96/3.24 Prover 13: Preprocessing ...
% 11.96/3.27 Prover 9: Constructing countermodel ...
% 11.96/3.27 Prover 16: Preprocessing ...
% 12.49/3.29 Prover 9: stopped
% 12.49/3.33 Prover 10: gave up
% 12.49/3.34 Prover 4: Found proof (size 56)
% 12.49/3.34 Prover 4: proved (2628ms)
% 12.49/3.34 Prover 16: stopped
% 12.49/3.36 Prover 11: stopped
% 12.98/3.40 Prover 19: Warning: ignoring some quantifiers
% 12.98/3.40 Prover 13: Warning: ignoring some quantifiers
% 12.98/3.42 Prover 19: Constructing countermodel ...
% 12.98/3.42 Prover 19: stopped
% 12.98/3.44 Prover 13: Constructing countermodel ...
% 12.98/3.45 Prover 13: stopped
% 12.98/3.45
% 12.98/3.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.98/3.45
% 12.98/3.46 % SZS output start Proof for theBenchmark
% 12.98/3.46 Assumptions after simplification:
% 12.98/3.46 ---------------------------------
% 12.98/3.47
% 12.98/3.47 (a1_defns)
% 13.42/3.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.42/3.50 (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ~
% 13.42/3.50 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) &
% 13.42/3.50 unequally_directed_opposite_lines(v0, v1) = v4)) & ! [v0: $i] : ! [v1:
% 13.42/3.50 $i] : ! [v2: int] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1)
% 13.42/3.50 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0)
% 13.42/3.50 & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4 & $i(v3)))
% 13.42/3.50 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) | ~
% 13.42/3.50 (unequally_directed_lines(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 13.42/3.50 unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] :
% 13.42/3.50 ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 13.42/3.50 ? [v2: $i] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0 &
% 13.42/3.50 $i(v2)))
% 13.42/3.50
% 13.42/3.50 (a5_defns)
% 13.45/3.50 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 13.45/3.50 (equally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 13.45/3.50 unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] :
% 13.45/3.50 ! [v2: int] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) |
% 13.45/3.50 ~ $i(v1) | ~ $i(v0) | equally_directed_opposite_lines(v0, v1) = 0) & !
% 13.45/3.50 [v0: $i] : ! [v1: $i] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) |
% 13.45/3.50 ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 13.45/3.50 unequally_directed_opposite_lines(v0, v1) = v2)) & ! [v0: $i] : ! [v1:
% 13.45/3.50 $i] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ~ $i(v1) | ~
% 13.45/3.50 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0,
% 13.45/3.50 v1) = v2))
% 13.45/3.50
% 13.45/3.50 (ax6_basics)
% 13.48/3.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 13.48/3.50 0 | v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v4) | ~
% 13.48/3.50 (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 13.48/3.50 | ? [v5: int] : ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)) & !
% 13.48/3.50 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.48/3.50 (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0,
% 13.48/3.50 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 13.48/3.51 unequally_directed_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 13.48/3.51 $i] : ! [v3: int] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) |
% 13.48/3.51 ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 13.48/3.51 | unequally_directed_lines(v1, v2) = 0)
% 13.48/3.51
% 13.48/3.51 (ax7_basics)
% 13.48/3.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.48/3.52 any] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~
% 13.48/3.52 (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0,
% 13.48/3.52 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 13.48/3.52 any] : ? [v8: any] : ? [v9: any] : (unequally_directed_lines(v1, v2) =
% 13.48/3.52 v9 & unequally_directed_lines(v0, v4) = v8 & unequally_directed_lines(v0,
% 13.48/3.52 v2) = v7 & unequally_directed_lines(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 =
% 13.48/3.52 0 & v5 = 0) | (v8 = 0 & v7 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 13.48/3.52 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (reverse_line(v2) =
% 13.48/3.52 v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v4) =
% 13.48/3.52 v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) |
% 13.48/3.52 ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: any] :
% 13.48/3.52 (unequally_directed_lines(v1, v4) = v9 & unequally_directed_lines(v1, v2) =
% 13.48/3.52 v8 & unequally_directed_lines(v0, v2) = v7 & unequally_directed_lines(v0,
% 13.48/3.52 v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 & v5 = 0)))) & !
% 13.48/3.52 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: $i] : ! [v5:
% 13.48/3.52 any] : ( ~ (reverse_line(v2) = v4) | ~ (unequally_directed_lines(v1, v4) =
% 13.48/3.52 v5) | ~ (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 13.48/3.52 ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ?
% 13.48/3.52 [v10: any] : (reverse_line(v1) = v7 & unequally_directed_lines(v1, v2) = v10
% 13.48/3.52 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v4)
% 13.48/3.52 = v9 & unequally_directed_lines(v0, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~
% 13.48/3.52 (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v3 = 0)))) & ! [v0: $i] : !
% 13.48/3.52 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ! [v5: any] : ( ~
% 13.48/3.52 (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v5) | ~
% 13.48/3.52 (unequally_directed_lines(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 13.48/3.52 | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ? [v10: any] :
% 13.48/3.52 (reverse_line(v1) = v7 & unequally_directed_lines(v1, v2) = v10 &
% 13.48/3.52 unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v2) =
% 13.48/3.52 v9 & unequally_directed_lines(v0, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~
% 13.48/3.53 (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v4 = 0)))) & ! [v0: $i] : !
% 13.48/3.53 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ! [v5: any] : ( ~
% 13.48/3.53 (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = v5) | ~
% 13.48/3.53 (unequally_directed_lines(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 13.48/3.53 | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ? [v10: any] :
% 13.48/3.53 (reverse_line(v1) = v7 & unequally_directed_lines(v1, v3) = v10 &
% 13.48/3.53 unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v2) =
% 13.48/3.53 v9 & unequally_directed_lines(v0, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~
% 13.48/3.53 (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v4 = 0)))) & ! [v0: $i] : !
% 13.48/3.53 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (reverse_line(v2) =
% 13.48/3.53 v3) | ~ (unequally_directed_lines(v1, v3) = v4) | ~
% 13.48/3.53 (unequally_directed_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 13.48/3.53 ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: any] :
% 13.48/3.53 (reverse_line(v1) = v5 & unequally_directed_lines(v1, v2) = v9 &
% 13.48/3.53 unequally_directed_lines(v0, v5) = v6 & unequally_directed_lines(v0, v3) =
% 13.48/3.53 v8 & unequally_directed_lines(v0, v2) = v7 & $i(v5) & ( ~ (v6 = 0) | (v9 =
% 13.48/3.53 0 & v4 = 0) | (v8 = 0 & v7 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 13.48/3.53 [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (reverse_line(v2) = v3) | ~
% 13.48/3.53 (unequally_directed_lines(v0, v3) = v4) | ~ (unequally_directed_lines(v0,
% 13.48/3.53 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6:
% 13.48/3.53 any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : (reverse_line(v1) = v5
% 13.48/3.53 & unequally_directed_lines(v1, v3) = v9 & unequally_directed_lines(v1, v2)
% 13.48/3.53 = v8 & unequally_directed_lines(v0, v5) = v6 &
% 13.48/3.53 unequally_directed_lines(v0, v2) = v7 & $i(v5) & ( ~ (v6 = 0) | (v9 = 0 &
% 13.48/3.53 v8 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 13.48/3.53 $i] : ! [v3: $i] : ! [v4: any] : ( ~ (reverse_line(v1) = v3) | ~
% 13.48/3.53 (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0,
% 13.48/3.53 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 13.48/3.53 any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : (reverse_line(v2) = v7
% 13.48/3.53 & unequally_directed_lines(v1, v7) = v9 & unequally_directed_lines(v0, v7)
% 13.48/3.53 = v8 & unequally_directed_lines(v0, v2) = v6 &
% 13.48/3.53 unequally_directed_lines(v0, v1) = v5 & $i(v7) & ( ~ (v5 = 0) | (v9 = 0 &
% 13.48/3.53 v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 13.48/3.53 $i] : ! [v3: $i] : ! [v4: any] : ( ~ (reverse_line(v1) = v3) | ~
% 13.48/3.53 (unequally_directed_lines(v0, v3) = 0) | ~ (unequally_directed_lines(v0,
% 13.48/3.53 v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 13.48/3.53 $i] : ? [v7: any] : ? [v8: any] : ? [v9: any] : (reverse_line(v2) = v6
% 13.48/3.53 & unequally_directed_lines(v1, v6) = v9 & unequally_directed_lines(v1, v2)
% 13.48/3.53 = v8 & unequally_directed_lines(v0, v6) = v7 &
% 13.48/3.53 unequally_directed_lines(v0, v1) = v5 & $i(v6) & ( ~ (v5 = 0) | (v9 = 0 &
% 13.48/3.53 v8 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 13.48/3.53 $i] : ! [v3: any] : ! [v4: any] : ( ~ (unequally_directed_lines(v1, v2) =
% 13.48/3.53 v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 13.48/3.53 ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ?
% 13.48/3.53 [v9: any] : ? [v10: any] : (reverse_line(v2) = v8 & reverse_line(v1) = v6 &
% 13.48/3.53 unequally_directed_lines(v1, v8) = v10 & unequally_directed_lines(v0, v8)
% 13.48/3.53 = v9 & unequally_directed_lines(v0, v6) = v7 &
% 13.48/3.53 unequally_directed_lines(v0, v1) = v5 & $i(v8) & $i(v6) & ( ~ (v7 = 0) |
% 13.48/3.53 ~ (v5 = 0) | (v10 = 0 & v4 = 0) | (v9 = 0 & v3 = 0)))) & ! [v0: $i] :
% 13.48/3.53 ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unequally_directed_lines(v1,
% 13.48/3.53 v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v2) | ~
% 13.48/3.53 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: $i]
% 13.48/3.53 : ? [v8: any] : ? [v9: any] : (reverse_line(v2) = v7 & reverse_line(v1) =
% 13.48/3.53 v4 & unequally_directed_lines(v1, v7) = v9 & unequally_directed_lines(v0,
% 13.48/3.53 v7) = v8 & unequally_directed_lines(v0, v4) = v5 &
% 13.48/3.53 unequally_directed_lines(v0, v2) = v6 & $i(v7) & $i(v4) & ( ~ (v5 = 0) |
% 13.48/3.53 (v9 = 0 & v3 = 0) | (v8 = 0 & v6 = 0)))) & ! [v0: $i] : ! [v1: $i] :
% 13.48/3.53 ! [v2: $i] : ! [v3: any] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~
% 13.48/3.53 (unequally_directed_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 13.48/3.53 ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : ?
% 13.48/3.53 [v9: any] : (reverse_line(v2) = v6 & reverse_line(v1) = v4 &
% 13.48/3.53 unequally_directed_lines(v1, v6) = v9 & unequally_directed_lines(v1, v2) =
% 13.48/3.53 v8 & unequally_directed_lines(v0, v6) = v7 & unequally_directed_lines(v0,
% 13.48/3.53 v4) = v5 & $i(v6) & $i(v4) & ( ~ (v5 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0
% 13.48/3.53 & v3 = 0))))
% 13.48/3.53
% 13.48/3.53 (ax8_basics)
% 13.48/3.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.48/3.53 (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ~
% 13.48/3.53 $i(v1) | ~ $i(v0) | unequally_directed_lines(v0, v1) = 0) & ! [v0: $i] :
% 13.48/3.53 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) =
% 13.48/3.53 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (reverse_line(v1) = v3 &
% 13.48/3.53 unequally_directed_lines(v0, v3) = 0 & $i(v3)))
% 13.48/3.53
% 13.48/3.53 (con)
% 13.48/3.53 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 13.48/3.53 unequally_directed_opposite_lines(v0, v0) = v1 & $i(v0))
% 13.48/3.53
% 13.48/3.53 (function-axioms)
% 13.48/3.54 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.48/3.54 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4,
% 13.48/3.54 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0:
% 13.48/3.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.48/3.54 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~
% 13.48/3.54 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.48/3.54 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 13.48/3.54 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) &
% 13.48/3.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.48/3.54 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) =
% 13.48/3.54 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 13.48/3.54 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 13.48/3.54 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.48/3.54 [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~
% 13.48/3.54 (distinct_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 13.48/3.54 ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 13.48/3.54 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.48/3.54 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.48/3.54 (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & !
% 13.48/3.54 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 13.48/3.54 $i] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~
% 13.48/3.54 (incident_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.48/3.54 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.48/3.54 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 13.48/3.54 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 13.48/3.54 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 13.48/3.54 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.48/3.54 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.48/3.54 (equally_directed_opposite_lines(v3, v2) = v1) | ~
% 13.48/3.54 (equally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 13.48/3.54 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.48/3.54 (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) =
% 13.48/3.54 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.48/3.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~
% 13.48/3.54 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.48/3.54 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.48/3.54 (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) =
% 13.48/3.54 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.48/3.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~
% 13.48/3.54 (left_apart_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.48/3.54 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.48/3.54 (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0)) & !
% 13.48/3.54 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 13.48/3.54 $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~
% 13.48/3.54 (unequally_directed_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.48/3.54 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.48/3.54 (unequally_directed_opposite_lines(v3, v2) = v1) | ~
% 13.48/3.54 (unequally_directed_opposite_lines(v3, v2) = v0)) & ! [v0:
% 13.48/3.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 13.48/3.54 ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.48/3.54 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~
% 13.48/3.54 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 13.48/3.54 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 13.48/3.54
% 13.48/3.54 Further assumptions not needed in the proof:
% 13.48/3.54 --------------------------------------------
% 13.48/3.54 a2_defns, a3_defns, a4_defns, a6_defns, a7_defns, a8_defns, a9_defns,
% 13.48/3.54 ax10_basics, ax10_cons_objs, ax11_basics, ax1_basics, ax1_cons_objs, ax1_subs,
% 13.48/3.54 ax1_uniq_cons, ax2_basics, ax2_cons_objs, ax2_subs, ax2_uniq_cons, ax3_basics,
% 13.48/3.54 ax3_cons_objs, ax3_subs, ax4_basics, ax4_cons_objs, ax4_defns, ax5_basics,
% 13.48/3.54 ax5_cons_objs, ax6_cons_objs, ax7_cons_objs, ax8_cons_objs, ax9_basics,
% 13.48/3.54 ax9_cons_objs
% 13.48/3.54
% 13.48/3.54 Those formulas are unsatisfiable:
% 13.48/3.54 ---------------------------------
% 13.48/3.54
% 13.48/3.54 Begin of proof
% 13.48/3.54 |
% 13.48/3.54 | ALPHA: (a1_defns) implies:
% 13.48/3.54 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 13.48/3.54 | (unequally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~
% 13.48/3.54 | $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & reverse_line(v1)
% 13.48/3.54 | = v3 & unequally_directed_lines(v0, v3) = v4 & $i(v3)))
% 13.48/3.54 |
% 13.48/3.54 | ALPHA: (a5_defns) implies:
% 13.48/3.54 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 13.48/3.54 | (unequally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~
% 13.48/3.54 | $i(v0) | equally_directed_opposite_lines(v0, v1) = 0)
% 13.48/3.54 |
% 13.48/3.54 | ALPHA: (ax6_basics) implies:
% 13.48/3.54 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] :
% 13.48/3.54 | (v4 = 0 | v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v4) | ~
% 13.48/3.54 | (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 13.48/3.54 | $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & unequally_directed_lines(v0,
% 13.48/3.54 | v1) = v5))
% 13.48/3.54 |
% 13.48/3.54 | ALPHA: (ax7_basics) implies:
% 13.48/3.55 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] :
% 13.48/3.55 | ( ~ (unequally_directed_lines(v1, v2) = v4) | ~
% 13.48/3.55 | (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 13.48/3.55 | $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ?
% 13.48/3.55 | [v9: any] : ? [v10: any] : (reverse_line(v2) = v8 & reverse_line(v1)
% 13.48/3.55 | = v6 & unequally_directed_lines(v1, v8) = v10 &
% 13.48/3.55 | unequally_directed_lines(v0, v8) = v9 &
% 13.48/3.55 | unequally_directed_lines(v0, v6) = v7 &
% 13.48/3.55 | unequally_directed_lines(v0, v1) = v5 & $i(v8) & $i(v6) & ( ~ (v7 =
% 13.48/3.55 | 0) | ~ (v5 = 0) | (v10 = 0 & v4 = 0) | (v9 = 0 & v3 = 0))))
% 13.48/3.55 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 13.48/3.55 | ! [v5: any] : ( ~ (reverse_line(v2) = v3) | ~
% 13.48/3.55 | (unequally_directed_lines(v1, v3) = v5) | ~
% 13.48/3.55 | (unequally_directed_lines(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 13.48/3.55 | $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] :
% 13.48/3.55 | ? [v10: any] : (reverse_line(v1) = v7 & unequally_directed_lines(v1,
% 13.48/3.55 | v2) = v10 & unequally_directed_lines(v0, v7) = v8 &
% 13.48/3.55 | unequally_directed_lines(v0, v2) = v9 &
% 13.48/3.55 | unequally_directed_lines(v0, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~
% 13.48/3.55 | (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v4 = 0))))
% 13.48/3.55 |
% 13.48/3.55 | ALPHA: (ax8_basics) implies:
% 13.48/3.55 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.48/3.55 | (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3)
% 13.48/3.55 | | ~ $i(v1) | ~ $i(v0) | unequally_directed_lines(v0, v1) = 0)
% 13.48/3.55 |
% 13.48/3.55 | ALPHA: (function-axioms) implies:
% 13.48/3.55 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.48/3.55 | ! [v3: $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) |
% 13.48/3.55 | ~ (unequally_directed_lines(v3, v2) = v0))
% 13.48/3.55 |
% 13.48/3.55 | DELTA: instantiating (con) with fresh symbols all_39_0, all_39_1 gives:
% 13.48/3.55 | (8) ~ (all_39_0 = 0) & unequally_directed_opposite_lines(all_39_1,
% 13.48/3.55 | all_39_1) = all_39_0 & $i(all_39_1)
% 13.48/3.55 |
% 13.48/3.55 | ALPHA: (8) implies:
% 13.48/3.55 | (9) ~ (all_39_0 = 0)
% 13.48/3.55 | (10) $i(all_39_1)
% 13.48/3.55 | (11) unequally_directed_opposite_lines(all_39_1, all_39_1) = all_39_0
% 13.48/3.55 |
% 13.48/3.55 | GROUND_INST: instantiating (2) with all_39_1, all_39_1, all_39_0, simplifying
% 13.48/3.55 | with (10), (11) gives:
% 13.48/3.55 | (12) all_39_0 = 0 | equally_directed_opposite_lines(all_39_1, all_39_1) = 0
% 13.48/3.55 |
% 13.48/3.55 | GROUND_INST: instantiating (1) with all_39_1, all_39_1, all_39_0, simplifying
% 13.48/3.55 | with (10), (11) gives:
% 13.48/3.56 | (13) all_39_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 13.48/3.56 | reverse_line(all_39_1) = v0 & unequally_directed_lines(all_39_1, v0)
% 13.48/3.56 | = v1 & $i(v0))
% 13.48/3.56 |
% 13.48/3.56 | BETA: splitting (13) gives:
% 13.48/3.56 |
% 13.48/3.56 | Case 1:
% 13.48/3.56 | |
% 13.48/3.56 | | (14) all_39_0 = 0
% 13.48/3.56 | |
% 13.48/3.56 | | REDUCE: (9), (14) imply:
% 13.48/3.56 | | (15) $false
% 13.48/3.56 | |
% 13.48/3.56 | | CLOSE: (15) is inconsistent.
% 13.48/3.56 | |
% 13.48/3.56 | Case 2:
% 13.48/3.56 | |
% 13.48/3.56 | | (16) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & reverse_line(all_39_1) =
% 13.48/3.56 | | v0 & unequally_directed_lines(all_39_1, v0) = v1 & $i(v0))
% 13.48/3.56 | |
% 13.48/3.56 | | DELTA: instantiating (16) with fresh symbols all_55_0, all_55_1 gives:
% 13.48/3.56 | | (17) ~ (all_55_0 = 0) & reverse_line(all_39_1) = all_55_1 &
% 13.48/3.56 | | unequally_directed_lines(all_39_1, all_55_1) = all_55_0 &
% 13.48/3.56 | | $i(all_55_1)
% 13.48/3.56 | |
% 13.48/3.56 | | ALPHA: (17) implies:
% 13.48/3.56 | | (18) ~ (all_55_0 = 0)
% 13.48/3.56 | | (19) $i(all_55_1)
% 13.48/3.56 | | (20) unequally_directed_lines(all_39_1, all_55_1) = all_55_0
% 13.48/3.56 | | (21) reverse_line(all_39_1) = all_55_1
% 13.48/3.56 | |
% 13.48/3.56 | | BETA: splitting (12) gives:
% 13.48/3.56 | |
% 13.48/3.56 | | Case 1:
% 13.48/3.56 | | |
% 13.48/3.56 | | |
% 13.48/3.56 | | | GROUND_INST: instantiating (3) with all_39_1, all_39_1, all_55_1,
% 13.48/3.56 | | | all_55_0, all_55_0, simplifying with (10), (19), (20) gives:
% 13.48/3.56 | | | (22) all_55_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 13.48/3.56 | | | unequally_directed_lines(all_39_1, all_39_1) = v0)
% 13.48/3.56 | | |
% 13.48/3.56 | | | GROUND_INST: instantiating (4) with all_39_1, all_39_1, all_55_1,
% 13.48/3.56 | | | all_55_0, all_55_0, simplifying with (10), (19), (20) gives:
% 13.48/3.56 | | | (23) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 13.48/3.56 | | | any] : ? [v5: any] : (reverse_line(all_55_1) = v3 &
% 13.48/3.56 | | | reverse_line(all_39_1) = v1 & unequally_directed_lines(all_39_1,
% 13.48/3.56 | | | v3) = v5 & unequally_directed_lines(all_39_1, v3) = v4 &
% 13.48/3.56 | | | unequally_directed_lines(all_39_1, v1) = v2 &
% 13.48/3.56 | | | unequally_directed_lines(all_39_1, all_39_1) = v0 & $i(v3) &
% 13.48/3.56 | | | $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | (v5 = 0 & all_55_0 = 0) |
% 13.48/3.56 | | | (v4 = 0 & all_55_0 = 0)))
% 13.48/3.56 | | |
% 13.48/3.56 | | | GROUND_INST: instantiating (5) with all_39_1, all_39_1, all_39_1,
% 13.48/3.56 | | | all_55_1, all_55_0, all_55_0, simplifying with (10), (20),
% 13.48/3.56 | | | (21) gives:
% 13.48/3.56 | | | (24) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : ? [v4:
% 13.48/3.57 | | | any] : (reverse_line(all_39_1) = v1 &
% 13.48/3.57 | | | unequally_directed_lines(all_39_1, v1) = v2 &
% 13.48/3.57 | | | unequally_directed_lines(all_39_1, all_39_1) = v4 &
% 13.48/3.57 | | | unequally_directed_lines(all_39_1, all_39_1) = v3 &
% 13.48/3.57 | | | unequally_directed_lines(all_39_1, all_39_1) = v0 & $i(v1) & ( ~
% 13.48/3.57 | | | (v2 = 0) | ~ (v0 = 0) | (v4 = 0 & all_55_0 = 0) | (v3 = 0 &
% 13.48/3.57 | | | all_55_0 = 0)))
% 13.48/3.57 | | |
% 13.48/3.57 | | | GROUND_INST: instantiating (6) with all_39_1, all_39_1, all_55_1,
% 13.48/3.57 | | | all_55_0, simplifying with (10), (20), (21) gives:
% 13.48/3.57 | | | (25) all_55_0 = 0 | unequally_directed_lines(all_39_1, all_39_1) = 0
% 13.48/3.57 | | |
% 13.48/3.57 | | | DELTA: instantiating (24) with fresh symbols all_72_0, all_72_1, all_72_2,
% 13.48/3.57 | | | all_72_3, all_72_4 gives:
% 13.48/3.57 | | | (26) reverse_line(all_39_1) = all_72_3 &
% 13.48/3.57 | | | unequally_directed_lines(all_39_1, all_72_3) = all_72_2 &
% 13.48/3.57 | | | unequally_directed_lines(all_39_1, all_39_1) = all_72_0 &
% 13.48/3.57 | | | unequally_directed_lines(all_39_1, all_39_1) = all_72_1 &
% 13.48/3.57 | | | unequally_directed_lines(all_39_1, all_39_1) = all_72_4 &
% 13.48/3.57 | | | $i(all_72_3) & ( ~ (all_72_2 = 0) | ~ (all_72_4 = 0) | (all_72_0
% 13.48/3.57 | | | = 0 & all_55_0 = 0) | (all_72_1 = 0 & all_55_0 = 0))
% 13.48/3.57 | | |
% 13.48/3.57 | | | ALPHA: (26) implies:
% 13.48/3.57 | | | (27) unequally_directed_lines(all_39_1, all_39_1) = all_72_4
% 13.48/3.57 | | | (28) unequally_directed_lines(all_39_1, all_39_1) = all_72_1
% 13.48/3.57 | | | (29) unequally_directed_lines(all_39_1, all_39_1) = all_72_0
% 13.48/3.57 | | |
% 13.48/3.57 | | | DELTA: instantiating (23) with fresh symbols all_74_0, all_74_1, all_74_2,
% 13.48/3.57 | | | all_74_3, all_74_4, all_74_5 gives:
% 13.48/3.57 | | | (30) reverse_line(all_55_1) = all_74_2 & reverse_line(all_39_1) =
% 13.48/3.57 | | | all_74_4 & unequally_directed_lines(all_39_1, all_74_2) = all_74_0
% 13.48/3.57 | | | & unequally_directed_lines(all_39_1, all_74_2) = all_74_1 &
% 13.48/3.57 | | | unequally_directed_lines(all_39_1, all_74_4) = all_74_3 &
% 13.48/3.57 | | | unequally_directed_lines(all_39_1, all_39_1) = all_74_5 &
% 13.48/3.57 | | | $i(all_74_2) & $i(all_74_4) & ( ~ (all_74_3 = 0) | ~ (all_74_5 =
% 13.48/3.57 | | | 0) | (all_74_0 = 0 & all_55_0 = 0) | (all_74_1 = 0 & all_55_0
% 13.48/3.57 | | | = 0))
% 13.48/3.57 | | |
% 13.48/3.57 | | | ALPHA: (30) implies:
% 13.48/3.57 | | | (31) unequally_directed_lines(all_39_1, all_39_1) = all_74_5
% 13.48/3.57 | | |
% 13.48/3.57 | | | BETA: splitting (25) gives:
% 13.48/3.57 | | |
% 13.48/3.57 | | | Case 1:
% 13.48/3.57 | | | |
% 13.48/3.57 | | | | (32) unequally_directed_lines(all_39_1, all_39_1) = 0
% 13.48/3.57 | | | |
% 13.48/3.57 | | | | BETA: splitting (22) gives:
% 13.48/3.57 | | | |
% 13.48/3.57 | | | | Case 1:
% 13.48/3.57 | | | | |
% 13.48/3.57 | | | | | (33) all_55_0 = 0
% 13.48/3.57 | | | | |
% 13.48/3.57 | | | | | REDUCE: (18), (33) imply:
% 13.48/3.57 | | | | | (34) $false
% 13.48/3.57 | | | | |
% 13.48/3.57 | | | | | CLOSE: (34) is inconsistent.
% 13.48/3.57 | | | | |
% 13.48/3.57 | | | | Case 2:
% 13.48/3.57 | | | | |
% 13.48/3.57 | | | | | (35) ? [v0: int] : ( ~ (v0 = 0) &
% 13.48/3.57 | | | | | unequally_directed_lines(all_39_1, all_39_1) = v0)
% 13.48/3.57 | | | | |
% 13.48/3.57 | | | | | DELTA: instantiating (35) with fresh symbol all_98_0 gives:
% 13.48/3.57 | | | | | (36) ~ (all_98_0 = 0) & unequally_directed_lines(all_39_1,
% 13.48/3.57 | | | | | all_39_1) = all_98_0
% 13.48/3.57 | | | | |
% 13.48/3.57 | | | | | ALPHA: (36) implies:
% 13.48/3.57 | | | | | (37) ~ (all_98_0 = 0)
% 13.48/3.57 | | | | | (38) unequally_directed_lines(all_39_1, all_39_1) = all_98_0
% 13.48/3.57 | | | | |
% 13.48/3.57 | | | | | GROUND_INST: instantiating (7) with all_72_4, all_74_5, all_39_1,
% 13.48/3.57 | | | | | all_39_1, simplifying with (27), (31) gives:
% 13.48/3.57 | | | | | (39) all_74_5 = all_72_4
% 13.48/3.57 | | | | |
% 13.48/3.57 | | | | | GROUND_INST: instantiating (7) with all_74_5, all_98_0, all_39_1,
% 13.48/3.57 | | | | | all_39_1, simplifying with (31), (38) gives:
% 13.48/3.57 | | | | | (40) all_98_0 = all_74_5
% 13.48/3.57 | | | | |
% 13.48/3.57 | | | | | GROUND_INST: instantiating (7) with all_72_0, all_98_0, all_39_1,
% 13.48/3.57 | | | | | all_39_1, simplifying with (29), (38) gives:
% 13.48/3.57 | | | | | (41) all_98_0 = all_72_0
% 13.48/3.57 | | | | |
% 13.48/3.57 | | | | | GROUND_INST: instantiating (7) with all_72_1, all_98_0, all_39_1,
% 13.48/3.57 | | | | | all_39_1, simplifying with (28), (38) gives:
% 13.48/3.57 | | | | | (42) all_98_0 = all_72_1
% 13.48/3.57 | | | | |
% 13.48/3.58 | | | | | GROUND_INST: instantiating (7) with 0, all_98_0, all_39_1, all_39_1,
% 13.48/3.58 | | | | | simplifying with (32), (38) gives:
% 13.48/3.58 | | | | | (43) all_98_0 = 0
% 13.48/3.58 | | | | |
% 13.48/3.58 | | | | | COMBINE_EQS: (40), (41) imply:
% 13.48/3.58 | | | | | (44) all_74_5 = all_72_0
% 13.48/3.58 | | | | |
% 13.48/3.58 | | | | | SIMP: (44) implies:
% 13.48/3.58 | | | | | (45) all_74_5 = all_72_0
% 13.48/3.58 | | | | |
% 13.48/3.58 | | | | | COMBINE_EQS: (41), (42) imply:
% 13.48/3.58 | | | | | (46) all_72_0 = all_72_1
% 13.48/3.58 | | | | |
% 13.48/3.58 | | | | | COMBINE_EQS: (41), (43) imply:
% 13.48/3.58 | | | | | (47) all_72_0 = 0
% 13.48/3.58 | | | | |
% 13.48/3.58 | | | | | COMBINE_EQS: (39), (45) imply:
% 13.48/3.58 | | | | | (48) all_72_0 = all_72_4
% 13.48/3.58 | | | | |
% 13.48/3.58 | | | | | SIMP: (48) implies:
% 13.48/3.58 | | | | | (49) all_72_0 = all_72_4
% 13.48/3.58 | | | | |
% 13.48/3.58 | | | | | COMBINE_EQS: (46), (47) imply:
% 13.48/3.58 | | | | | (50) all_72_1 = 0
% 13.48/3.58 | | | | |
% 13.48/3.58 | | | | | COMBINE_EQS: (46), (49) imply:
% 13.48/3.58 | | | | | (51) all_72_1 = all_72_4
% 13.48/3.58 | | | | |
% 13.48/3.58 | | | | | COMBINE_EQS: (50), (51) imply:
% 13.48/3.58 | | | | | (52) all_72_4 = 0
% 13.48/3.58 | | | | |
% 13.48/3.58 | | | | | REDUCE: (37), (43) imply:
% 13.48/3.58 | | | | | (53) $false
% 13.48/3.58 | | | | |
% 13.48/3.58 | | | | | CLOSE: (53) is inconsistent.
% 13.48/3.58 | | | | |
% 13.48/3.58 | | | | End of split
% 13.48/3.58 | | | |
% 13.48/3.58 | | | Case 2:
% 13.48/3.58 | | | |
% 13.48/3.58 | | | | (54) all_55_0 = 0
% 13.48/3.58 | | | |
% 13.48/3.58 | | | | REDUCE: (18), (54) imply:
% 13.48/3.58 | | | | (55) $false
% 13.48/3.58 | | | |
% 13.48/3.58 | | | | CLOSE: (55) is inconsistent.
% 13.48/3.58 | | | |
% 13.48/3.58 | | | End of split
% 13.48/3.58 | | |
% 13.48/3.58 | | Case 2:
% 13.48/3.58 | | |
% 13.48/3.58 | | | (56) all_39_0 = 0
% 13.48/3.58 | | |
% 13.48/3.58 | | | REDUCE: (9), (56) imply:
% 13.48/3.58 | | | (57) $false
% 13.48/3.58 | | |
% 13.48/3.58 | | | CLOSE: (57) is inconsistent.
% 13.48/3.58 | | |
% 13.48/3.58 | | End of split
% 13.48/3.58 | |
% 13.48/3.58 | End of split
% 13.48/3.58 |
% 13.48/3.58 End of proof
% 13.48/3.58 % SZS output end Proof for theBenchmark
% 13.48/3.58
% 13.48/3.58 2909ms
%------------------------------------------------------------------------------