TSTP Solution File: GEO228+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO228+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n025.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 23:22:35 EDT 2023
% Result : Theorem 8.22s 1.87s
% Output : Proof 10.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO228+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 22:25:10 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.24/1.15 Prover 1: Preprocessing ...
% 3.24/1.15 Prover 4: Preprocessing ...
% 3.24/1.18 Prover 0: Preprocessing ...
% 3.24/1.18 Prover 6: Preprocessing ...
% 3.24/1.18 Prover 2: Preprocessing ...
% 3.24/1.18 Prover 5: Preprocessing ...
% 3.24/1.18 Prover 3: Preprocessing ...
% 7.07/1.69 Prover 5: Proving ...
% 7.07/1.72 Prover 2: Proving ...
% 7.07/1.73 Prover 3: Constructing countermodel ...
% 7.07/1.74 Prover 6: Constructing countermodel ...
% 7.07/1.74 Prover 1: Constructing countermodel ...
% 8.22/1.86 Prover 3: proved (1229ms)
% 8.22/1.86
% 8.22/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.22/1.87
% 8.22/1.87 Prover 6: stopped
% 8.22/1.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.22/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.22/1.88 Prover 5: stopped
% 8.22/1.88 Prover 2: stopped
% 8.22/1.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.22/1.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.76/1.96 Prover 8: Preprocessing ...
% 8.76/1.97 Prover 10: Preprocessing ...
% 9.23/1.99 Prover 11: Preprocessing ...
% 9.23/1.99 Prover 7: Preprocessing ...
% 9.23/2.01 Prover 1: Found proof (size 53)
% 9.23/2.02 Prover 1: proved (1393ms)
% 9.23/2.02 Prover 10: stopped
% 9.23/2.03 Prover 7: stopped
% 9.23/2.05 Prover 4: Constructing countermodel ...
% 9.23/2.07 Prover 4: stopped
% 9.23/2.09 Prover 11: stopped
% 9.23/2.11 Prover 8: Warning: ignoring some quantifiers
% 9.23/2.12 Prover 8: Constructing countermodel ...
% 9.23/2.12 Prover 0: Proving ...
% 9.23/2.13 Prover 8: stopped
% 9.23/2.13 Prover 0: stopped
% 9.23/2.13
% 9.23/2.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.23/2.13
% 9.23/2.14 % SZS output start Proof for theBenchmark
% 9.23/2.15 Assumptions after simplification:
% 9.23/2.15 ---------------------------------
% 9.23/2.15
% 9.23/2.15 (con)
% 10.30/2.17 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : ? [v4: $i] : ?
% 10.30/2.17 [v5: any] : (convergent_lines(v0, v1) = v2 & unequally_directed_lines(v0, v4)
% 10.30/2.17 = v5 & unequally_directed_lines(v0, v1) = v3 & reverse_line(v1) = v4 &
% 10.30/2.17 $i(v4) & $i(v1) & $i(v0) & ((v5 = 0 & v3 = 0 & ~ (v2 = 0)) | (v2 = 0 & ( ~
% 10.30/2.17 (v5 = 0) | ~ (v3 = 0)))))
% 10.30/2.17
% 10.30/2.17 (con_def)
% 10.30/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 10.30/2.18 (unequally_directed_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ~
% 10.30/2.18 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (convergent_lines(v0, v1)
% 10.30/2.18 = v4 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3
% 10.30/2.18 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 10.30/2.18 (unequally_directed_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | ~
% 10.30/2.18 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (convergent_lines(v0, v1)
% 10.30/2.18 = v4 & unequally_directed_lines(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 10.30/2.18
% 10.30/2.18 (oag7)
% 10.59/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 10.59/2.18 any] : ( ~ (unequally_directed_lines(v0, v4) = v5) | ~
% 10.59/2.18 (unequally_directed_lines(v0, v3) = 0) | ~ (reverse_line(v2) = v4) | ~
% 10.59/2.18 (reverse_line(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] :
% 10.59/2.18 ? [v7: any] : ? [v8: any] : ? [v9: any] : (unequally_directed_lines(v1,
% 10.59/2.18 v4) = v9 & unequally_directed_lines(v1, v2) = v8 &
% 10.59/2.18 unequally_directed_lines(v0, v2) = v7 & unequally_directed_lines(v0, v1) =
% 10.59/2.18 v6 & ( ~ (v6 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 & v5 = 0))))
% 10.59/2.18
% 10.59/2.18 (oagco2)
% 10.59/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unequally_directed_lines(v0,
% 10.59/2.18 v2) = 0) | ~ (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 10.59/2.18 any] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] :
% 10.59/2.18 (intersection_point(v0, v1) = v6 & point(v6) = v7 & line(v1) = v4 & line(v0)
% 10.59/2.18 = v3 & unequally_directed_lines(v0, v1) = v5 & $i(v6) & ( ~ (v5 = 0) | ~
% 10.59/2.18 (v4 = 0) | ~ (v3 = 0) | v7 = 0)))
% 10.59/2.18
% 10.59/2.18 (function-axioms)
% 10.59/2.19 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.59/2.19 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4,
% 10.59/2.19 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0:
% 10.59/2.19 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.59/2.19 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~
% 10.59/2.19 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.59/2.19 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 10.59/2.19 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) &
% 10.59/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.59/2.19 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) =
% 10.59/2.19 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 10.59/2.19 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 10.59/2.19 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.59/2.19 [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~
% 10.59/2.19 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.59/2.19 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.59/2.19 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 10.59/2.19 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.59/2.19 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 10.59/2.19 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 10.59/2.19 $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3,
% 10.59/2.19 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 10.59/2.19 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 10.59/2.19 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.59/2.19 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.59/2.19 (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3,
% 10.59/2.19 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 10.59/2.19 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) |
% 10.59/2.19 ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.59/2.20 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.59/2.20 (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0)) & !
% 10.59/2.20 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 10.59/2.20 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] :
% 10.59/2.20 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~
% 10.59/2.20 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 10.59/2.20 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 10.59/2.20
% 10.59/2.20 Further assumptions not needed in the proof:
% 10.59/2.20 --------------------------------------------
% 10.59/2.20 apt_def, bet_def, bf_def, div_def, oag1, oag10, oag11, oag2, oag3, oag4, oag5,
% 10.59/2.20 oag6, oag8, oag9, oagco1, oagco10, oagco3, oagco4, oagco5, oagco6, oagco7,
% 10.59/2.20 oagco8, oagco9, oagsub1, oagsub2, oagsub3, oaguc1, oaguc2
% 10.59/2.20
% 10.59/2.20 Those formulas are unsatisfiable:
% 10.59/2.20 ---------------------------------
% 10.59/2.20
% 10.59/2.20 Begin of proof
% 10.59/2.20 |
% 10.59/2.20 | ALPHA: (con_def) implies:
% 10.59/2.20 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 10.59/2.20 | (unequally_directed_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) |
% 10.59/2.20 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 10.59/2.20 | (convergent_lines(v0, v1) = v4 & unequally_directed_lines(v0, v1) =
% 10.59/2.20 | v3 & ( ~ (v3 = 0) | v4 = 0)))
% 10.59/2.20 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 10.59/2.20 | (unequally_directed_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2)
% 10.59/2.20 | | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 10.59/2.20 | (convergent_lines(v0, v1) = v4 & unequally_directed_lines(v0, v1) =
% 10.59/2.20 | v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0))))
% 10.59/2.20 |
% 10.59/2.20 | ALPHA: (function-axioms) implies:
% 10.59/2.20 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.59/2.20 | ! [v3: $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) |
% 10.59/2.20 | ~ (unequally_directed_lines(v3, v2) = v0))
% 10.59/2.20 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.59/2.20 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 10.59/2.20 | (convergent_lines(v3, v2) = v0))
% 10.59/2.20 |
% 10.59/2.20 | DELTA: instantiating (con) with fresh symbols all_34_0, all_34_1, all_34_2,
% 10.59/2.20 | all_34_3, all_34_4, all_34_5 gives:
% 10.59/2.20 | (5) convergent_lines(all_34_5, all_34_4) = all_34_3 &
% 10.59/2.20 | unequally_directed_lines(all_34_5, all_34_1) = all_34_0 &
% 10.59/2.20 | unequally_directed_lines(all_34_5, all_34_4) = all_34_2 &
% 10.59/2.20 | reverse_line(all_34_4) = all_34_1 & $i(all_34_1) & $i(all_34_4) &
% 10.59/2.20 | $i(all_34_5) & ((all_34_0 = 0 & all_34_2 = 0 & ~ (all_34_3 = 0)) |
% 10.59/2.20 | (all_34_3 = 0 & ( ~ (all_34_0 = 0) | ~ (all_34_2 = 0))))
% 10.59/2.20 |
% 10.59/2.20 | ALPHA: (5) implies:
% 10.59/2.20 | (6) $i(all_34_5)
% 10.59/2.21 | (7) $i(all_34_4)
% 10.59/2.21 | (8) reverse_line(all_34_4) = all_34_1
% 10.59/2.21 | (9) unequally_directed_lines(all_34_5, all_34_4) = all_34_2
% 10.59/2.21 | (10) unequally_directed_lines(all_34_5, all_34_1) = all_34_0
% 10.59/2.21 | (11) convergent_lines(all_34_5, all_34_4) = all_34_3
% 10.59/2.21 | (12) (all_34_0 = 0 & all_34_2 = 0 & ~ (all_34_3 = 0)) | (all_34_3 = 0 & (
% 10.59/2.21 | ~ (all_34_0 = 0) | ~ (all_34_2 = 0)))
% 10.59/2.21 |
% 10.59/2.21 | GROUND_INST: instantiating (2) with all_34_5, all_34_4, all_34_1, all_34_0,
% 10.59/2.21 | simplifying with (6), (7), (8), (10) gives:
% 10.59/2.21 | (13) ? [v0: any] : ? [v1: any] : (convergent_lines(all_34_5, all_34_4) =
% 10.59/2.21 | v0 & unequally_directed_lines(all_34_5, all_34_4) = v1 & ( ~ (v0 =
% 10.59/2.21 | 0) | (v1 = 0 & all_34_0 = 0)))
% 10.59/2.21 |
% 10.59/2.21 | DELTA: instantiating (13) with fresh symbols all_41_0, all_41_1 gives:
% 10.59/2.21 | (14) convergent_lines(all_34_5, all_34_4) = all_41_1 &
% 10.59/2.21 | unequally_directed_lines(all_34_5, all_34_4) = all_41_0 & ( ~
% 10.59/2.21 | (all_41_1 = 0) | (all_41_0 = 0 & all_34_0 = 0))
% 10.59/2.21 |
% 10.59/2.21 | ALPHA: (14) implies:
% 10.59/2.21 | (15) unequally_directed_lines(all_34_5, all_34_4) = all_41_0
% 10.59/2.21 | (16) convergent_lines(all_34_5, all_34_4) = all_41_1
% 10.59/2.21 | (17) ~ (all_41_1 = 0) | (all_41_0 = 0 & all_34_0 = 0)
% 10.59/2.21 |
% 10.59/2.21 | GROUND_INST: instantiating (3) with all_34_2, all_41_0, all_34_4, all_34_5,
% 10.59/2.21 | simplifying with (9), (15) gives:
% 10.59/2.21 | (18) all_41_0 = all_34_2
% 10.59/2.21 |
% 10.59/2.21 | GROUND_INST: instantiating (4) with all_34_3, all_41_1, all_34_4, all_34_5,
% 10.59/2.21 | simplifying with (11), (16) gives:
% 10.59/2.21 | (19) all_41_1 = all_34_3
% 10.59/2.21 |
% 10.59/2.21 | BETA: splitting (12) gives:
% 10.59/2.21 |
% 10.59/2.21 | Case 1:
% 10.59/2.21 | |
% 10.59/2.21 | | (20) all_34_0 = 0 & all_34_2 = 0 & ~ (all_34_3 = 0)
% 10.59/2.21 | |
% 10.59/2.21 | | ALPHA: (20) implies:
% 10.59/2.21 | | (21) all_34_2 = 0
% 10.59/2.21 | | (22) all_34_0 = 0
% 10.59/2.21 | | (23) ~ (all_34_3 = 0)
% 10.59/2.21 | |
% 10.59/2.21 | | REDUCE: (10), (22) imply:
% 10.59/2.21 | | (24) unequally_directed_lines(all_34_5, all_34_1) = 0
% 10.59/2.21 | |
% 10.59/2.21 | | REDUCE: (9), (21) imply:
% 10.59/2.21 | | (25) unequally_directed_lines(all_34_5, all_34_4) = 0
% 10.59/2.21 | |
% 10.59/2.21 | | GROUND_INST: instantiating (oag7) with all_34_5, all_34_4, all_34_4,
% 10.59/2.21 | | all_34_1, all_34_1, 0, simplifying with (6), (7), (8), (24)
% 10.59/2.21 | | gives:
% 10.59/2.21 | | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 10.59/2.21 | | (unequally_directed_lines(all_34_4, all_34_1) = v3 &
% 10.59/2.21 | | unequally_directed_lines(all_34_4, all_34_4) = v2 &
% 10.59/2.21 | | unequally_directed_lines(all_34_5, all_34_4) = v1 &
% 10.59/2.21 | | unequally_directed_lines(all_34_5, all_34_4) = v0 & ( ~ (v0 = 0) |
% 10.59/2.21 | | v1 = 0 | (v3 = 0 & v2 = 0)))
% 10.59/2.21 | |
% 10.59/2.22 | | GROUND_INST: instantiating (oagco2) with all_34_5, all_34_4, all_34_1,
% 10.59/2.22 | | simplifying with (6), (7), (8), (24) gives:
% 10.59/2.22 | | (27) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 10.59/2.22 | | any] : (intersection_point(all_34_5, all_34_4) = v3 & point(v3) =
% 10.59/2.22 | | v4 & line(all_34_4) = v1 & line(all_34_5) = v0 &
% 10.59/2.22 | | unequally_directed_lines(all_34_5, all_34_4) = v2 & $i(v3) & ( ~
% 10.59/2.22 | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 10.59/2.22 | |
% 10.59/2.22 | | GROUND_INST: instantiating (1) with all_34_5, all_34_4, all_34_1,
% 10.59/2.22 | | simplifying with (6), (7), (8), (24) gives:
% 10.59/2.22 | | (28) ? [v0: any] : ? [v1: any] : (convergent_lines(all_34_5, all_34_4)
% 10.59/2.22 | | = v1 & unequally_directed_lines(all_34_5, all_34_4) = v0 & ( ~ (v0
% 10.59/2.22 | | = 0) | v1 = 0))
% 10.59/2.22 | |
% 10.59/2.22 | | DELTA: instantiating (28) with fresh symbols all_59_0, all_59_1 gives:
% 10.59/2.22 | | (29) convergent_lines(all_34_5, all_34_4) = all_59_0 &
% 10.59/2.22 | | unequally_directed_lines(all_34_5, all_34_4) = all_59_1 & ( ~
% 10.59/2.22 | | (all_59_1 = 0) | all_59_0 = 0)
% 10.59/2.22 | |
% 10.59/2.22 | | ALPHA: (29) implies:
% 10.59/2.22 | | (30) unequally_directed_lines(all_34_5, all_34_4) = all_59_1
% 10.59/2.22 | | (31) convergent_lines(all_34_5, all_34_4) = all_59_0
% 10.59/2.22 | | (32) ~ (all_59_1 = 0) | all_59_0 = 0
% 10.59/2.22 | |
% 10.59/2.22 | | DELTA: instantiating (26) with fresh symbols all_61_0, all_61_1, all_61_2,
% 10.59/2.22 | | all_61_3 gives:
% 10.59/2.22 | | (33) unequally_directed_lines(all_34_4, all_34_1) = all_61_0 &
% 10.59/2.22 | | unequally_directed_lines(all_34_4, all_34_4) = all_61_1 &
% 10.59/2.22 | | unequally_directed_lines(all_34_5, all_34_4) = all_61_2 &
% 10.59/2.22 | | unequally_directed_lines(all_34_5, all_34_4) = all_61_3 & ( ~
% 10.59/2.22 | | (all_61_3 = 0) | all_61_2 = 0 | (all_61_0 = 0 & all_61_1 = 0))
% 10.59/2.22 | |
% 10.59/2.22 | | ALPHA: (33) implies:
% 10.59/2.22 | | (34) unequally_directed_lines(all_34_5, all_34_4) = all_61_3
% 10.59/2.22 | | (35) unequally_directed_lines(all_34_5, all_34_4) = all_61_2
% 10.59/2.22 | |
% 10.59/2.22 | | DELTA: instantiating (27) with fresh symbols all_63_0, all_63_1, all_63_2,
% 10.59/2.22 | | all_63_3, all_63_4 gives:
% 10.79/2.22 | | (36) intersection_point(all_34_5, all_34_4) = all_63_1 & point(all_63_1)
% 10.79/2.22 | | = all_63_0 & line(all_34_4) = all_63_3 & line(all_34_5) = all_63_4 &
% 10.79/2.22 | | unequally_directed_lines(all_34_5, all_34_4) = all_63_2 &
% 10.79/2.22 | | $i(all_63_1) & ( ~ (all_63_2 = 0) | ~ (all_63_3 = 0) | ~ (all_63_4
% 10.79/2.22 | | = 0) | all_63_0 = 0)
% 10.79/2.22 | |
% 10.79/2.22 | | ALPHA: (36) implies:
% 10.79/2.22 | | (37) unequally_directed_lines(all_34_5, all_34_4) = all_63_2
% 10.79/2.22 | |
% 10.79/2.22 | | GROUND_INST: instantiating (3) with 0, all_61_3, all_34_4, all_34_5,
% 10.79/2.22 | | simplifying with (25), (34) gives:
% 10.79/2.22 | | (38) all_61_3 = 0
% 10.79/2.22 | |
% 10.79/2.22 | | GROUND_INST: instantiating (3) with all_61_3, all_61_2, all_34_4, all_34_5,
% 10.79/2.22 | | simplifying with (34), (35) gives:
% 10.79/2.22 | | (39) all_61_2 = all_61_3
% 10.79/2.22 | |
% 10.79/2.22 | | GROUND_INST: instantiating (3) with all_61_2, all_63_2, all_34_4, all_34_5,
% 10.79/2.22 | | simplifying with (35), (37) gives:
% 10.79/2.22 | | (40) all_63_2 = all_61_2
% 10.79/2.22 | |
% 10.79/2.22 | | GROUND_INST: instantiating (3) with all_59_1, all_63_2, all_34_4, all_34_5,
% 10.79/2.22 | | simplifying with (30), (37) gives:
% 10.79/2.22 | | (41) all_63_2 = all_59_1
% 10.79/2.22 | |
% 10.79/2.22 | | GROUND_INST: instantiating (4) with all_34_3, all_59_0, all_34_4, all_34_5,
% 10.79/2.22 | | simplifying with (11), (31) gives:
% 10.79/2.22 | | (42) all_59_0 = all_34_3
% 10.79/2.22 | |
% 10.79/2.22 | | COMBINE_EQS: (40), (41) imply:
% 10.79/2.23 | | (43) all_61_2 = all_59_1
% 10.79/2.23 | |
% 10.79/2.23 | | SIMP: (43) implies:
% 10.79/2.23 | | (44) all_61_2 = all_59_1
% 10.79/2.23 | |
% 10.79/2.23 | | COMBINE_EQS: (39), (44) imply:
% 10.79/2.23 | | (45) all_61_3 = all_59_1
% 10.79/2.23 | |
% 10.79/2.23 | | SIMP: (45) implies:
% 10.79/2.23 | | (46) all_61_3 = all_59_1
% 10.79/2.23 | |
% 10.79/2.23 | | COMBINE_EQS: (38), (46) imply:
% 10.79/2.23 | | (47) all_59_1 = 0
% 10.79/2.23 | |
% 10.79/2.23 | | BETA: splitting (32) gives:
% 10.79/2.23 | |
% 10.79/2.23 | | Case 1:
% 10.79/2.23 | | |
% 10.79/2.23 | | | (48) ~ (all_59_1 = 0)
% 10.79/2.23 | | |
% 10.79/2.23 | | | REDUCE: (47), (48) imply:
% 10.79/2.23 | | | (49) $false
% 10.79/2.23 | | |
% 10.79/2.23 | | | CLOSE: (49) is inconsistent.
% 10.79/2.23 | | |
% 10.79/2.23 | | Case 2:
% 10.79/2.23 | | |
% 10.79/2.23 | | | (50) all_59_0 = 0
% 10.79/2.23 | | |
% 10.79/2.23 | | | COMBINE_EQS: (42), (50) imply:
% 10.79/2.23 | | | (51) all_34_3 = 0
% 10.79/2.23 | | |
% 10.79/2.23 | | | SIMP: (51) implies:
% 10.79/2.23 | | | (52) all_34_3 = 0
% 10.79/2.23 | | |
% 10.79/2.23 | | | REDUCE: (23), (52) imply:
% 10.79/2.23 | | | (53) $false
% 10.79/2.23 | | |
% 10.79/2.23 | | | CLOSE: (53) is inconsistent.
% 10.79/2.23 | | |
% 10.79/2.23 | | End of split
% 10.79/2.23 | |
% 10.79/2.23 | Case 2:
% 10.79/2.23 | |
% 10.79/2.23 | | (54) all_34_3 = 0 & ( ~ (all_34_0 = 0) | ~ (all_34_2 = 0))
% 10.79/2.23 | |
% 10.79/2.23 | | ALPHA: (54) implies:
% 10.79/2.23 | | (55) all_34_3 = 0
% 10.79/2.23 | | (56) ~ (all_34_0 = 0) | ~ (all_34_2 = 0)
% 10.79/2.23 | |
% 10.79/2.23 | | COMBINE_EQS: (19), (55) imply:
% 10.79/2.23 | | (57) all_41_1 = 0
% 10.79/2.23 | |
% 10.79/2.23 | | BETA: splitting (17) gives:
% 10.79/2.23 | |
% 10.79/2.23 | | Case 1:
% 10.79/2.23 | | |
% 10.79/2.23 | | | (58) ~ (all_41_1 = 0)
% 10.79/2.23 | | |
% 10.79/2.23 | | | REDUCE: (57), (58) imply:
% 10.79/2.23 | | | (59) $false
% 10.79/2.23 | | |
% 10.79/2.23 | | | CLOSE: (59) is inconsistent.
% 10.79/2.23 | | |
% 10.79/2.23 | | Case 2:
% 10.79/2.23 | | |
% 10.79/2.23 | | | (60) all_41_0 = 0 & all_34_0 = 0
% 10.79/2.23 | | |
% 10.79/2.23 | | | ALPHA: (60) implies:
% 10.79/2.23 | | | (61) all_34_0 = 0
% 10.79/2.23 | | | (62) all_41_0 = 0
% 10.79/2.23 | | |
% 10.79/2.23 | | | COMBINE_EQS: (18), (62) imply:
% 10.79/2.23 | | | (63) all_34_2 = 0
% 10.79/2.23 | | |
% 10.79/2.23 | | | BETA: splitting (56) gives:
% 10.79/2.23 | | |
% 10.79/2.23 | | | Case 1:
% 10.79/2.23 | | | |
% 10.79/2.23 | | | | (64) ~ (all_34_0 = 0)
% 10.79/2.23 | | | |
% 10.79/2.23 | | | | REDUCE: (61), (64) imply:
% 10.79/2.23 | | | | (65) $false
% 10.79/2.23 | | | |
% 10.79/2.23 | | | | CLOSE: (65) is inconsistent.
% 10.79/2.23 | | | |
% 10.79/2.23 | | | Case 2:
% 10.79/2.23 | | | |
% 10.79/2.23 | | | | (66) ~ (all_34_2 = 0)
% 10.79/2.23 | | | |
% 10.79/2.23 | | | | REDUCE: (63), (66) imply:
% 10.79/2.23 | | | | (67) $false
% 10.79/2.23 | | | |
% 10.79/2.23 | | | | CLOSE: (67) is inconsistent.
% 10.79/2.23 | | | |
% 10.79/2.23 | | | End of split
% 10.79/2.23 | | |
% 10.79/2.23 | | End of split
% 10.79/2.23 | |
% 10.79/2.23 | End of split
% 10.79/2.23 |
% 10.79/2.23 End of proof
% 10.79/2.23 % SZS output end Proof for theBenchmark
% 10.79/2.23
% 10.79/2.23 1628ms
%------------------------------------------------------------------------------