TSTP Solution File: GEO203+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO203+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 : n028.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 23:22:16 EDT 2023
% Result : Theorem 9.19s 2.03s
% Output : Proof 11.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO203+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n028.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 : Tue Aug 29 19:47:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.55/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.55/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.55/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.55/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.55/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.55/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.55/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.22/1.18 Prover 1: Preprocessing ...
% 3.22/1.18 Prover 4: Preprocessing ...
% 3.22/1.22 Prover 2: Preprocessing ...
% 3.22/1.22 Prover 0: Preprocessing ...
% 3.22/1.22 Prover 6: Preprocessing ...
% 3.22/1.22 Prover 5: Preprocessing ...
% 3.22/1.23 Prover 3: Preprocessing ...
% 6.31/1.66 Prover 5: Proving ...
% 6.31/1.66 Prover 2: Proving ...
% 6.95/1.72 Prover 6: Constructing countermodel ...
% 6.95/1.74 Prover 1: Constructing countermodel ...
% 6.95/1.76 Prover 3: Constructing countermodel ...
% 8.28/1.97 Prover 4: Constructing countermodel ...
% 9.19/2.02 Prover 3: proved (1381ms)
% 9.19/2.03
% 9.19/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.19/2.03
% 9.19/2.04 Prover 5: stopped
% 9.19/2.04 Prover 2: stopped
% 9.19/2.05 Prover 6: stopped
% 9.19/2.05 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.19/2.05 Prover 0: Proving ...
% 9.19/2.05 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.19/2.05 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.19/2.05 Prover 0: stopped
% 9.19/2.06 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.19/2.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.19/2.09 Prover 7: Preprocessing ...
% 9.19/2.10 Prover 8: Preprocessing ...
% 9.84/2.10 Prover 10: Preprocessing ...
% 9.84/2.12 Prover 11: Preprocessing ...
% 9.84/2.12 Prover 13: Preprocessing ...
% 9.84/2.16 Prover 7: Warning: ignoring some quantifiers
% 9.84/2.17 Prover 7: Constructing countermodel ...
% 9.84/2.17 Prover 10: Warning: ignoring some quantifiers
% 9.84/2.17 Prover 1: Found proof (size 60)
% 9.84/2.18 Prover 1: proved (1537ms)
% 9.84/2.18 Prover 4: stopped
% 9.84/2.18 Prover 7: stopped
% 10.50/2.19 Prover 13: stopped
% 10.50/2.19 Prover 10: Constructing countermodel ...
% 10.50/2.20 Prover 10: stopped
% 10.50/2.23 Prover 11: stopped
% 10.50/2.24 Prover 8: Warning: ignoring some quantifiers
% 10.50/2.25 Prover 8: Constructing countermodel ...
% 10.50/2.26 Prover 8: stopped
% 10.50/2.26
% 10.50/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.50/2.26
% 10.50/2.26 % SZS output start Proof for theBenchmark
% 10.50/2.27 Assumptions after simplification:
% 10.50/2.27 ---------------------------------
% 10.50/2.27
% 10.50/2.27 (ax2)
% 11.03/2.29 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_lines(v0, v1) =
% 11.03/2.29 v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, v1) = 0) & ! [v0: $i] :
% 11.03/2.29 ! [v1: $i] : ( ~ (equal_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 11.03/2.29 int] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 11.03/2.29
% 11.03/2.29 (ci1)
% 11.08/2.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 11.08/2.29 ~ (apart_point_and_line(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 11.08/2.29 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 11.08/2.29
% 11.08/2.29 (ci2)
% 11.08/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 11.08/2.30 ~ (apart_point_and_line(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 11.08/2.30 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 11.08/2.30
% 11.08/2.30 (ci3)
% 11.08/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 11.08/2.30 v2) | ~ (apart_point_and_line(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 11.08/2.30 [v3: int] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 11.08/2.30
% 11.08/2.30 (con)
% 11.08/2.30 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 11.08/2.30 $i] : ? [v6: int] : ( ~ (v6 = 0) & equal_lines(v5, v0) = v6 &
% 11.08/2.30 intersection_point(v0, v2) = v4 & intersection_point(v0, v1) = v3 &
% 11.08/2.30 line_connecting(v3, v4) = v5 & convergent_lines(v0, v2) = 0 &
% 11.08/2.30 convergent_lines(v0, v1) = 0 & distinct_points(v3, v4) = 0 & $i(v5) & $i(v4)
% 11.08/2.30 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.08/2.30
% 11.08/2.30 (con1)
% 11.08/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 11.08/2.30 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6:
% 11.08/2.30 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 &
% 11.08/2.30 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) |
% 11.08/2.30 v6 = 0)))
% 11.08/2.30
% 11.08/2.30 (cu1)
% 11.14/2.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 11.14/2.31 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 11.14/2.31 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 11.14/2.31 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 11.14/2.31 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 11.14/2.31 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 11.14/2.31
% 11.14/2.31 (int1)
% 11.14/2.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 11.14/2.31 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 11.14/2.31 ? [v6: any] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 &
% 11.14/2.31 convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) |
% 11.14/2.31 v6 = 0)))
% 11.14/2.31
% 11.14/2.31 (function-axioms)
% 11.14/2.32 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.14/2.32 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~
% 11.14/2.32 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.14/2.32 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.14/2.32 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2)
% 11.14/2.32 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.14/2.32 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~
% 11.14/2.32 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.14/2.32 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.14/2.32 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0:
% 11.14/2.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.14/2.32 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 11.14/2.32 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.14/2.32 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 11.14/2.32 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 11.14/2.32 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 11.14/2.32 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 11.14/2.32 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 11.14/2.32 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 11.14/2.32 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 11.14/2.32 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 11.14/2.32 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 11.14/2.32 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.14/2.32 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.14/2.32 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 11.14/2.32 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.14/2.32 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 11.14/2.32 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.14/2.32 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.14/2.32 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 11.14/2.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.14/2.32 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 11.14/2.32 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.14/2.32 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 11.14/2.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 11.14/2.32 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 11.14/2.32
% 11.14/2.32 Further assumptions not needed in the proof:
% 11.14/2.32 --------------------------------------------
% 11.14/2.32 a3, a4, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax6, ceq1, ceq2, ceq3,
% 11.14/2.32 ci4, coipo1, cotno1, couo1, cp1, cp2, cup1, oac1, occu1, ooc1, ooc2, orth1,
% 11.14/2.32 ouo1, p1, par1
% 11.14/2.32
% 11.14/2.32 Those formulas are unsatisfiable:
% 11.14/2.32 ---------------------------------
% 11.14/2.32
% 11.14/2.32 Begin of proof
% 11.14/2.32 |
% 11.14/2.32 | ALPHA: (ax2) implies:
% 11.14/2.32 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 11.14/2.32 | (equal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 11.14/2.32 | distinct_lines(v0, v1) = 0)
% 11.14/2.32 |
% 11.14/2.32 | ALPHA: (function-axioms) implies:
% 11.14/2.32 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.14/2.32 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 11.14/2.32 | (distinct_points(v3, v2) = v0))
% 11.14/2.32 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.14/2.32 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 11.14/2.32 | (convergent_lines(v3, v2) = v0))
% 11.14/2.32 |
% 11.14/2.33 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2,
% 11.14/2.33 | all_38_3, all_38_4, all_38_5, all_38_6 gives:
% 11.14/2.33 | (4) ~ (all_38_0 = 0) & equal_lines(all_38_1, all_38_6) = all_38_0 &
% 11.14/2.33 | intersection_point(all_38_6, all_38_4) = all_38_2 &
% 11.14/2.33 | intersection_point(all_38_6, all_38_5) = all_38_3 &
% 11.14/2.33 | line_connecting(all_38_3, all_38_2) = all_38_1 &
% 11.14/2.33 | convergent_lines(all_38_6, all_38_4) = 0 & convergent_lines(all_38_6,
% 11.14/2.33 | all_38_5) = 0 & distinct_points(all_38_3, all_38_2) = 0 &
% 11.14/2.33 | $i(all_38_1) & $i(all_38_2) & $i(all_38_3) & $i(all_38_4) &
% 11.14/2.33 | $i(all_38_5) & $i(all_38_6)
% 11.14/2.33 |
% 11.14/2.33 | ALPHA: (4) implies:
% 11.14/2.33 | (5) ~ (all_38_0 = 0)
% 11.14/2.33 | (6) $i(all_38_6)
% 11.14/2.33 | (7) $i(all_38_5)
% 11.14/2.33 | (8) $i(all_38_4)
% 11.14/2.33 | (9) $i(all_38_3)
% 11.14/2.33 | (10) $i(all_38_2)
% 11.14/2.33 | (11) $i(all_38_1)
% 11.14/2.33 | (12) distinct_points(all_38_3, all_38_2) = 0
% 11.14/2.33 | (13) convergent_lines(all_38_6, all_38_5) = 0
% 11.14/2.33 | (14) convergent_lines(all_38_6, all_38_4) = 0
% 11.14/2.33 | (15) line_connecting(all_38_3, all_38_2) = all_38_1
% 11.14/2.33 | (16) intersection_point(all_38_6, all_38_5) = all_38_3
% 11.14/2.33 | (17) intersection_point(all_38_6, all_38_4) = all_38_2
% 11.14/2.33 | (18) equal_lines(all_38_1, all_38_6) = all_38_0
% 11.14/2.33 |
% 11.14/2.33 | GROUND_INST: instantiating (con1) with all_38_3, all_38_2, all_38_1,
% 11.14/2.33 | simplifying with (9), (10), (15) gives:
% 11.14/2.33 | (19) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 11.14/2.33 | (point(all_38_2) = v1 & point(all_38_3) = v0 & line(all_38_1) = v3 &
% 11.14/2.33 | distinct_points(all_38_3, all_38_2) = v2 & ( ~ (v2 = 0) | ~ (v1 =
% 11.14/2.33 | 0) | ~ (v0 = 0) | v3 = 0))
% 11.14/2.33 |
% 11.14/2.33 | GROUND_INST: instantiating (int1) with all_38_6, all_38_5, all_38_3,
% 11.14/2.33 | simplifying with (6), (7), (16) gives:
% 11.14/2.33 | (20) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 11.14/2.33 | (point(all_38_3) = v3 & line(all_38_5) = v1 & line(all_38_6) = v0 &
% 11.14/2.33 | convergent_lines(all_38_6, all_38_5) = v2 & ( ~ (v2 = 0) | ~ (v1 =
% 11.14/2.33 | 0) | ~ (v0 = 0) | v3 = 0))
% 11.14/2.33 |
% 11.14/2.33 | GROUND_INST: instantiating (int1) with all_38_6, all_38_4, all_38_2,
% 11.14/2.33 | simplifying with (6), (8), (17) gives:
% 11.14/2.33 | (21) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 11.14/2.33 | (point(all_38_2) = v3 & line(all_38_4) = v1 & line(all_38_6) = v0 &
% 11.14/2.33 | convergent_lines(all_38_6, all_38_4) = v2 & ( ~ (v2 = 0) | ~ (v1 =
% 11.14/2.33 | 0) | ~ (v0 = 0) | v3 = 0))
% 11.14/2.33 |
% 11.14/2.34 | GROUND_INST: instantiating (1) with all_38_1, all_38_6, all_38_0, simplifying
% 11.14/2.34 | with (6), (11), (18) gives:
% 11.14/2.34 | (22) all_38_0 = 0 | distinct_lines(all_38_1, all_38_6) = 0
% 11.14/2.34 |
% 11.14/2.34 | DELTA: instantiating (21) with fresh symbols all_45_0, all_45_1, all_45_2,
% 11.14/2.34 | all_45_3 gives:
% 11.14/2.34 | (23) point(all_38_2) = all_45_0 & line(all_38_4) = all_45_2 &
% 11.14/2.34 | line(all_38_6) = all_45_3 & convergent_lines(all_38_6, all_38_4) =
% 11.14/2.34 | all_45_1 & ( ~ (all_45_1 = 0) | ~ (all_45_2 = 0) | ~ (all_45_3 = 0)
% 11.14/2.34 | | all_45_0 = 0)
% 11.14/2.34 |
% 11.14/2.34 | ALPHA: (23) implies:
% 11.14/2.34 | (24) convergent_lines(all_38_6, all_38_4) = all_45_1
% 11.14/2.34 |
% 11.14/2.34 | DELTA: instantiating (20) with fresh symbols all_47_0, all_47_1, all_47_2,
% 11.14/2.34 | all_47_3 gives:
% 11.14/2.34 | (25) point(all_38_3) = all_47_0 & line(all_38_5) = all_47_2 &
% 11.14/2.34 | line(all_38_6) = all_47_3 & convergent_lines(all_38_6, all_38_5) =
% 11.14/2.34 | all_47_1 & ( ~ (all_47_1 = 0) | ~ (all_47_2 = 0) | ~ (all_47_3 = 0)
% 11.14/2.34 | | all_47_0 = 0)
% 11.14/2.34 |
% 11.14/2.34 | ALPHA: (25) implies:
% 11.14/2.34 | (26) convergent_lines(all_38_6, all_38_5) = all_47_1
% 11.14/2.34 |
% 11.14/2.34 | DELTA: instantiating (19) with fresh symbols all_49_0, all_49_1, all_49_2,
% 11.14/2.34 | all_49_3 gives:
% 11.14/2.34 | (27) point(all_38_2) = all_49_2 & point(all_38_3) = all_49_3 &
% 11.14/2.34 | line(all_38_1) = all_49_0 & distinct_points(all_38_3, all_38_2) =
% 11.14/2.34 | all_49_1 & ( ~ (all_49_1 = 0) | ~ (all_49_2 = 0) | ~ (all_49_3 = 0)
% 11.14/2.34 | | all_49_0 = 0)
% 11.14/2.34 |
% 11.14/2.34 | ALPHA: (27) implies:
% 11.14/2.34 | (28) distinct_points(all_38_3, all_38_2) = all_49_1
% 11.14/2.34 |
% 11.14/2.34 | BETA: splitting (22) gives:
% 11.14/2.34 |
% 11.14/2.34 | Case 1:
% 11.14/2.34 | |
% 11.14/2.34 | | (29) distinct_lines(all_38_1, all_38_6) = 0
% 11.14/2.34 | |
% 11.14/2.34 | | GROUND_INST: instantiating (2) with 0, all_49_1, all_38_2, all_38_3,
% 11.14/2.34 | | simplifying with (12), (28) gives:
% 11.14/2.34 | | (30) all_49_1 = 0
% 11.14/2.34 | |
% 11.14/2.34 | | GROUND_INST: instantiating (3) with 0, all_47_1, all_38_5, all_38_6,
% 11.14/2.34 | | simplifying with (13), (26) gives:
% 11.14/2.34 | | (31) all_47_1 = 0
% 11.14/2.34 | |
% 11.14/2.34 | | GROUND_INST: instantiating (3) with 0, all_45_1, all_38_4, all_38_6,
% 11.14/2.34 | | simplifying with (14), (24) gives:
% 11.14/2.34 | | (32) all_45_1 = 0
% 11.14/2.34 | |
% 11.14/2.34 | | GROUND_INST: instantiating (cu1) with all_38_3, all_38_2, all_38_1,
% 11.14/2.34 | | all_38_6, simplifying with (6), (9), (10), (11), (12), (29)
% 11.14/2.34 | | gives:
% 11.14/2.34 | | (33) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 11.14/2.34 | | (apart_point_and_line(all_38_2, all_38_1) = v2 &
% 11.14/2.34 | | apart_point_and_line(all_38_2, all_38_6) = v3 &
% 11.14/2.34 | | apart_point_and_line(all_38_3, all_38_1) = v0 &
% 11.14/2.34 | | apart_point_and_line(all_38_3, all_38_6) = v1 & (v3 = 0 | v2 = 0 |
% 11.14/2.34 | | v1 = 0 | v0 = 0))
% 11.14/2.34 | |
% 11.14/2.34 | | DELTA: instantiating (33) with fresh symbols all_65_0, all_65_1, all_65_2,
% 11.14/2.34 | | all_65_3 gives:
% 11.14/2.34 | | (34) apart_point_and_line(all_38_2, all_38_1) = all_65_1 &
% 11.14/2.34 | | apart_point_and_line(all_38_2, all_38_6) = all_65_0 &
% 11.14/2.34 | | apart_point_and_line(all_38_3, all_38_1) = all_65_3 &
% 11.14/2.34 | | apart_point_and_line(all_38_3, all_38_6) = all_65_2 & (all_65_0 = 0
% 11.14/2.34 | | | all_65_1 = 0 | all_65_2 = 0 | all_65_3 = 0)
% 11.14/2.34 | |
% 11.14/2.34 | | ALPHA: (34) implies:
% 11.14/2.34 | | (35) apart_point_and_line(all_38_3, all_38_6) = all_65_2
% 11.14/2.34 | | (36) apart_point_and_line(all_38_3, all_38_1) = all_65_3
% 11.14/2.35 | | (37) apart_point_and_line(all_38_2, all_38_6) = all_65_0
% 11.14/2.35 | | (38) apart_point_and_line(all_38_2, all_38_1) = all_65_1
% 11.14/2.35 | | (39) all_65_0 = 0 | all_65_1 = 0 | all_65_2 = 0 | all_65_3 = 0
% 11.14/2.35 | |
% 11.14/2.35 | | BETA: splitting (39) gives:
% 11.14/2.35 | |
% 11.14/2.35 | | Case 1:
% 11.14/2.35 | | |
% 11.14/2.35 | | | (40) all_65_0 = 0
% 11.14/2.35 | | |
% 11.14/2.35 | | | REDUCE: (37), (40) imply:
% 11.14/2.35 | | | (41) apart_point_and_line(all_38_2, all_38_6) = 0
% 11.14/2.35 | | |
% 11.14/2.35 | | | GROUND_INST: instantiating (ci3) with all_38_6, all_38_4, all_38_2,
% 11.14/2.35 | | | simplifying with (6), (8), (17), (41) gives:
% 11.14/2.35 | | | (42) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_6, all_38_4)
% 11.14/2.35 | | | = v0)
% 11.14/2.35 | | |
% 11.14/2.35 | | | DELTA: instantiating (42) with fresh symbol all_100_0 gives:
% 11.14/2.35 | | | (43) ~ (all_100_0 = 0) & convergent_lines(all_38_6, all_38_4) =
% 11.14/2.35 | | | all_100_0
% 11.14/2.35 | | |
% 11.14/2.35 | | | ALPHA: (43) implies:
% 11.14/2.35 | | | (44) ~ (all_100_0 = 0)
% 11.14/2.35 | | | (45) convergent_lines(all_38_6, all_38_4) = all_100_0
% 11.14/2.35 | | |
% 11.14/2.35 | | | GROUND_INST: instantiating (3) with 0, all_100_0, all_38_4, all_38_6,
% 11.14/2.35 | | | simplifying with (14), (45) gives:
% 11.14/2.35 | | | (46) all_100_0 = 0
% 11.14/2.35 | | |
% 11.14/2.35 | | | REDUCE: (44), (46) imply:
% 11.14/2.35 | | | (47) $false
% 11.14/2.35 | | |
% 11.14/2.35 | | | CLOSE: (47) is inconsistent.
% 11.14/2.35 | | |
% 11.14/2.35 | | Case 2:
% 11.14/2.35 | | |
% 11.14/2.35 | | | (48) all_65_1 = 0 | all_65_2 = 0 | all_65_3 = 0
% 11.14/2.35 | | |
% 11.14/2.35 | | | BETA: splitting (48) gives:
% 11.14/2.35 | | |
% 11.14/2.35 | | | Case 1:
% 11.14/2.35 | | | |
% 11.14/2.35 | | | | (49) all_65_1 = 0
% 11.14/2.35 | | | |
% 11.14/2.35 | | | | REDUCE: (38), (49) imply:
% 11.14/2.35 | | | | (50) apart_point_and_line(all_38_2, all_38_1) = 0
% 11.14/2.35 | | | |
% 11.14/2.35 | | | | GROUND_INST: instantiating (ci2) with all_38_3, all_38_2, all_38_1,
% 11.14/2.35 | | | | simplifying with (9), (10), (15), (50) gives:
% 11.14/2.35 | | | | (51) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_3,
% 11.14/2.35 | | | | all_38_2) = v0)
% 11.14/2.35 | | | |
% 11.14/2.35 | | | | DELTA: instantiating (51) with fresh symbol all_128_0 gives:
% 11.14/2.35 | | | | (52) ~ (all_128_0 = 0) & distinct_points(all_38_3, all_38_2) =
% 11.14/2.35 | | | | all_128_0
% 11.14/2.35 | | | |
% 11.14/2.35 | | | | ALPHA: (52) implies:
% 11.14/2.35 | | | | (53) ~ (all_128_0 = 0)
% 11.14/2.35 | | | | (54) distinct_points(all_38_3, all_38_2) = all_128_0
% 11.14/2.35 | | | |
% 11.14/2.35 | | | | GROUND_INST: instantiating (2) with 0, all_128_0, all_38_2, all_38_3,
% 11.14/2.35 | | | | simplifying with (12), (54) gives:
% 11.14/2.35 | | | | (55) all_128_0 = 0
% 11.14/2.35 | | | |
% 11.14/2.35 | | | | REDUCE: (53), (55) imply:
% 11.14/2.35 | | | | (56) $false
% 11.14/2.35 | | | |
% 11.14/2.35 | | | | CLOSE: (56) is inconsistent.
% 11.14/2.35 | | | |
% 11.14/2.35 | | | Case 2:
% 11.14/2.35 | | | |
% 11.14/2.35 | | | | (57) all_65_2 = 0 | all_65_3 = 0
% 11.14/2.35 | | | |
% 11.14/2.35 | | | | BETA: splitting (57) gives:
% 11.14/2.35 | | | |
% 11.14/2.35 | | | | Case 1:
% 11.14/2.35 | | | | |
% 11.14/2.35 | | | | | (58) all_65_2 = 0
% 11.14/2.35 | | | | |
% 11.14/2.35 | | | | | REDUCE: (35), (58) imply:
% 11.14/2.35 | | | | | (59) apart_point_and_line(all_38_3, all_38_6) = 0
% 11.14/2.35 | | | | |
% 11.14/2.36 | | | | | GROUND_INST: instantiating (ci3) with all_38_6, all_38_5, all_38_3,
% 11.14/2.36 | | | | | simplifying with (6), (7), (16), (59) gives:
% 11.14/2.36 | | | | | (60) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_6,
% 11.14/2.36 | | | | | all_38_5) = v0)
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | | DELTA: instantiating (60) with fresh symbol all_142_0 gives:
% 11.14/2.36 | | | | | (61) ~ (all_142_0 = 0) & convergent_lines(all_38_6, all_38_5) =
% 11.14/2.36 | | | | | all_142_0
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | | ALPHA: (61) implies:
% 11.14/2.36 | | | | | (62) ~ (all_142_0 = 0)
% 11.14/2.36 | | | | | (63) convergent_lines(all_38_6, all_38_5) = all_142_0
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | | GROUND_INST: instantiating (3) with 0, all_142_0, all_38_5, all_38_6,
% 11.14/2.36 | | | | | simplifying with (13), (63) gives:
% 11.14/2.36 | | | | | (64) all_142_0 = 0
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | | REDUCE: (62), (64) imply:
% 11.14/2.36 | | | | | (65) $false
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | | CLOSE: (65) is inconsistent.
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | Case 2:
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | | (66) all_65_3 = 0
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | | REDUCE: (36), (66) imply:
% 11.14/2.36 | | | | | (67) apart_point_and_line(all_38_3, all_38_1) = 0
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | | GROUND_INST: instantiating (ci1) with all_38_3, all_38_2, all_38_1,
% 11.14/2.36 | | | | | simplifying with (9), (10), (15), (67) gives:
% 11.14/2.36 | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_3,
% 11.14/2.36 | | | | | all_38_2) = v0)
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | | DELTA: instantiating (68) with fresh symbol all_142_0 gives:
% 11.14/2.36 | | | | | (69) ~ (all_142_0 = 0) & distinct_points(all_38_3, all_38_2) =
% 11.14/2.36 | | | | | all_142_0
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | | ALPHA: (69) implies:
% 11.14/2.36 | | | | | (70) ~ (all_142_0 = 0)
% 11.14/2.36 | | | | | (71) distinct_points(all_38_3, all_38_2) = all_142_0
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | | GROUND_INST: instantiating (2) with 0, all_142_0, all_38_2, all_38_3,
% 11.14/2.36 | | | | | simplifying with (12), (71) gives:
% 11.14/2.36 | | | | | (72) all_142_0 = 0
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | | REDUCE: (70), (72) imply:
% 11.14/2.36 | | | | | (73) $false
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | | CLOSE: (73) is inconsistent.
% 11.14/2.36 | | | | |
% 11.14/2.36 | | | | End of split
% 11.14/2.36 | | | |
% 11.14/2.36 | | | End of split
% 11.14/2.36 | | |
% 11.14/2.36 | | End of split
% 11.14/2.36 | |
% 11.14/2.36 | Case 2:
% 11.14/2.36 | |
% 11.14/2.36 | | (74) all_38_0 = 0
% 11.14/2.36 | |
% 11.14/2.36 | | REDUCE: (5), (74) imply:
% 11.14/2.36 | | (75) $false
% 11.14/2.36 | |
% 11.14/2.36 | | CLOSE: (75) is inconsistent.
% 11.14/2.36 | |
% 11.14/2.36 | End of split
% 11.14/2.36 |
% 11.14/2.36 End of proof
% 11.22/2.36 % SZS output end Proof for theBenchmark
% 11.22/2.36
% 11.22/2.36 1743ms
%------------------------------------------------------------------------------