TSTP Solution File: GEO184+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO184+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 : n007.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 23:21:59 EDT 2023
% Result : Theorem 8.64s 1.85s
% Output : Proof 10.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO184+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n007.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 23:19:29 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.62 Running up to 7 provers in parallel.
% 0.72/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.72/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.72/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.72/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.72/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.72/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.72/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.87/1.12 Prover 4: Preprocessing ...
% 2.87/1.12 Prover 1: Preprocessing ...
% 2.87/1.16 Prover 6: Preprocessing ...
% 2.87/1.16 Prover 0: Preprocessing ...
% 2.87/1.16 Prover 2: Preprocessing ...
% 2.87/1.16 Prover 3: Preprocessing ...
% 2.87/1.16 Prover 5: Preprocessing ...
% 6.39/1.57 Prover 5: Proving ...
% 6.39/1.57 Prover 2: Proving ...
% 6.39/1.63 Prover 6: Constructing countermodel ...
% 7.07/1.64 Prover 1: Constructing countermodel ...
% 7.07/1.66 Prover 3: Constructing countermodel ...
% 8.44/1.84 Prover 3: proved (1208ms)
% 8.64/1.85
% 8.64/1.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.64/1.85
% 8.64/1.85 Prover 6: stopped
% 8.64/1.87 Prover 2: stopped
% 8.64/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.64/1.88 Prover 5: stopped
% 8.64/1.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.64/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.64/1.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.64/1.91 Prover 7: Preprocessing ...
% 8.64/1.91 Prover 4: Constructing countermodel ...
% 9.19/1.93 Prover 8: Preprocessing ...
% 9.19/1.93 Prover 11: Preprocessing ...
% 9.19/1.94 Prover 10: Preprocessing ...
% 9.19/1.96 Prover 0: Proving ...
% 9.19/1.97 Prover 1: Found proof (size 50)
% 9.19/1.97 Prover 1: proved (1327ms)
% 9.19/1.97 Prover 4: stopped
% 9.19/1.97 Prover 0: stopped
% 9.19/1.97 Prover 7: Warning: ignoring some quantifiers
% 9.59/1.98 Prover 10: stopped
% 9.59/1.99 Prover 7: Constructing countermodel ...
% 9.59/2.00 Prover 7: stopped
% 9.59/2.02 Prover 11: stopped
% 10.01/2.06 Prover 8: Warning: ignoring some quantifiers
% 10.11/2.07 Prover 8: Constructing countermodel ...
% 10.11/2.08 Prover 8: stopped
% 10.11/2.08
% 10.11/2.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.11/2.08
% 10.11/2.09 % SZS output start Proof for theBenchmark
% 10.11/2.10 Assumptions after simplification:
% 10.11/2.10 ---------------------------------
% 10.11/2.10
% 10.11/2.10 (a4)
% 10.34/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 10.34/2.13 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 10.34/2.13 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 10.34/2.13 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int]
% 10.34/2.13 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 10.34/2.13
% 10.34/2.13 (ax2)
% 10.34/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_lines(v0, v1) =
% 10.34/2.14 v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, v1) = 0) & ! [v0: $i] :
% 10.34/2.14 ! [v1: $i] : ( ~ (equal_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 10.34/2.14 int] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 10.34/2.14
% 10.34/2.14 (ci1)
% 10.34/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 10.34/2.14 ~ (apart_point_and_line(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 10.34/2.14 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 10.34/2.14
% 10.34/2.14 (ci2)
% 10.34/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 10.34/2.14 ~ (apart_point_and_line(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 10.34/2.14 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 10.34/2.14
% 10.34/2.14 (con)
% 10.48/2.15 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 10.48/2.15 int] : ( ~ (v5 = 0) & incident_point_and_line(v1, v2) = 0 &
% 10.48/2.15 incident_point_and_line(v0, v2) = 0 & equal_lines(v2, v4) = v5 &
% 10.48/2.15 line_connecting(v0, v1) = v4 & convergent_lines(v2, v3) = 0 &
% 10.48/2.15 distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.48/2.15
% 10.48/2.15 (con1)
% 10.48/2.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 10.48/2.15 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6:
% 10.48/2.15 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 &
% 10.48/2.15 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) |
% 10.48/2.15 v6 = 0)))
% 10.48/2.15
% 10.48/2.15 (cu1)
% 10.48/2.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.48/2.15 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 10.48/2.15 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 10.48/2.15 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 10.48/2.15 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 10.48/2.15 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 10.48/2.15
% 10.48/2.15 (function-axioms)
% 10.48/2.17 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.48/2.17 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~
% 10.48/2.17 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.48/2.17 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.48/2.17 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2)
% 10.48/2.17 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.48/2.17 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~
% 10.48/2.17 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.48/2.17 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.48/2.17 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0:
% 10.48/2.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.48/2.17 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 10.48/2.17 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.48/2.17 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 10.48/2.17 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 10.48/2.17 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 10.48/2.17 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 10.48/2.17 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 10.48/2.17 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 10.48/2.17 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 10.48/2.17 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 10.48/2.17 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 10.48/2.17 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.48/2.17 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.48/2.17 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 10.48/2.17 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.48/2.17 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 10.48/2.17 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.48/2.17 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.48/2.17 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 10.48/2.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.48/2.17 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 10.48/2.17 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.48/2.17 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 10.48/2.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.48/2.17 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 10.48/2.17
% 10.48/2.17 Further assumptions not needed in the proof:
% 10.48/2.17 --------------------------------------------
% 10.48/2.17 a3, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax6, ceq1, ceq2, ceq3, ci3,
% 10.48/2.17 ci4, coipo1, cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1, ooc2,
% 10.48/2.17 orth1, ouo1, p1, par1
% 10.48/2.17
% 10.48/2.17 Those formulas are unsatisfiable:
% 10.48/2.17 ---------------------------------
% 10.48/2.17
% 10.48/2.17 Begin of proof
% 10.48/2.17 |
% 10.48/2.17 | ALPHA: (ax2) implies:
% 10.48/2.17 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 10.48/2.17 | (equal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 10.48/2.17 | distinct_lines(v0, v1) = 0)
% 10.48/2.17 |
% 10.48/2.17 | ALPHA: (a4) implies:
% 10.48/2.17 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (incident_point_and_line(v0, v1) = 0) |
% 10.48/2.17 | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 10.48/2.17 | apart_point_and_line(v0, v1) = v2))
% 10.48/2.17 |
% 10.48/2.17 | ALPHA: (function-axioms) implies:
% 10.48/2.17 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.48/2.17 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 10.48/2.17 | (distinct_points(v3, v2) = v0))
% 10.48/2.17 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.48/2.17 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 10.48/2.17 | (apart_point_and_line(v3, v2) = v0))
% 10.48/2.17 |
% 10.48/2.18 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2,
% 10.48/2.18 | all_38_3, all_38_4, all_38_5 gives:
% 10.48/2.18 | (5) ~ (all_38_0 = 0) & incident_point_and_line(all_38_4, all_38_3) = 0 &
% 10.48/2.18 | incident_point_and_line(all_38_5, all_38_3) = 0 & equal_lines(all_38_3,
% 10.48/2.18 | all_38_1) = all_38_0 & line_connecting(all_38_5, all_38_4) = all_38_1
% 10.48/2.18 | & convergent_lines(all_38_3, all_38_2) = 0 & distinct_points(all_38_5,
% 10.48/2.18 | all_38_4) = 0 & $i(all_38_1) & $i(all_38_2) & $i(all_38_3) &
% 10.48/2.18 | $i(all_38_4) & $i(all_38_5)
% 10.48/2.18 |
% 10.48/2.18 | ALPHA: (5) implies:
% 10.48/2.18 | (6) ~ (all_38_0 = 0)
% 10.48/2.18 | (7) $i(all_38_5)
% 10.48/2.18 | (8) $i(all_38_4)
% 10.48/2.18 | (9) $i(all_38_3)
% 10.48/2.18 | (10) $i(all_38_1)
% 10.48/2.18 | (11) distinct_points(all_38_5, all_38_4) = 0
% 10.48/2.18 | (12) line_connecting(all_38_5, all_38_4) = all_38_1
% 10.48/2.18 | (13) equal_lines(all_38_3, all_38_1) = all_38_0
% 10.48/2.18 | (14) incident_point_and_line(all_38_5, all_38_3) = 0
% 10.48/2.18 | (15) incident_point_and_line(all_38_4, all_38_3) = 0
% 10.48/2.18 |
% 10.48/2.18 | GROUND_INST: instantiating (con1) with all_38_5, all_38_4, all_38_1,
% 10.48/2.18 | simplifying with (7), (8), (12) gives:
% 10.48/2.18 | (16) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 10.48/2.18 | (point(all_38_4) = v1 & point(all_38_5) = v0 & line(all_38_1) = v3 &
% 10.48/2.18 | distinct_points(all_38_5, all_38_4) = v2 & ( ~ (v2 = 0) | ~ (v1 =
% 10.48/2.18 | 0) | ~ (v0 = 0) | v3 = 0))
% 10.48/2.18 |
% 10.48/2.18 | GROUND_INST: instantiating (1) with all_38_3, all_38_1, all_38_0, simplifying
% 10.48/2.18 | with (9), (10), (13) gives:
% 10.48/2.18 | (17) all_38_0 = 0 | distinct_lines(all_38_3, all_38_1) = 0
% 10.48/2.18 |
% 10.48/2.18 | GROUND_INST: instantiating (2) with all_38_5, all_38_3, simplifying with (7),
% 10.48/2.18 | (9), (14) gives:
% 10.48/2.18 | (18) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_5, all_38_3)
% 10.48/2.18 | = v0)
% 10.48/2.18 |
% 10.48/2.18 | GROUND_INST: instantiating (2) with all_38_4, all_38_3, simplifying with (8),
% 10.48/2.18 | (9), (15) gives:
% 10.48/2.18 | (19) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_4, all_38_3)
% 10.48/2.18 | = v0)
% 10.48/2.18 |
% 10.48/2.18 | DELTA: instantiating (19) with fresh symbol all_45_0 gives:
% 10.48/2.18 | (20) ~ (all_45_0 = 0) & apart_point_and_line(all_38_4, all_38_3) =
% 10.48/2.18 | all_45_0
% 10.48/2.18 |
% 10.48/2.18 | ALPHA: (20) implies:
% 10.48/2.18 | (21) ~ (all_45_0 = 0)
% 10.48/2.18 | (22) apart_point_and_line(all_38_4, all_38_3) = all_45_0
% 10.48/2.18 |
% 10.48/2.18 | DELTA: instantiating (18) with fresh symbol all_47_0 gives:
% 10.48/2.18 | (23) ~ (all_47_0 = 0) & apart_point_and_line(all_38_5, all_38_3) =
% 10.48/2.18 | all_47_0
% 10.48/2.18 |
% 10.48/2.18 | ALPHA: (23) implies:
% 10.48/2.19 | (24) ~ (all_47_0 = 0)
% 10.48/2.19 | (25) apart_point_and_line(all_38_5, all_38_3) = all_47_0
% 10.48/2.19 |
% 10.48/2.19 | DELTA: instantiating (16) with fresh symbols all_49_0, all_49_1, all_49_2,
% 10.48/2.19 | all_49_3 gives:
% 10.48/2.19 | (26) point(all_38_4) = all_49_2 & point(all_38_5) = all_49_3 &
% 10.48/2.19 | line(all_38_1) = all_49_0 & distinct_points(all_38_5, all_38_4) =
% 10.48/2.19 | all_49_1 & ( ~ (all_49_1 = 0) | ~ (all_49_2 = 0) | ~ (all_49_3 = 0)
% 10.48/2.19 | | all_49_0 = 0)
% 10.48/2.19 |
% 10.48/2.19 | ALPHA: (26) implies:
% 10.48/2.19 | (27) distinct_points(all_38_5, all_38_4) = all_49_1
% 10.48/2.19 |
% 10.48/2.19 | BETA: splitting (17) gives:
% 10.48/2.19 |
% 10.48/2.19 | Case 1:
% 10.48/2.19 | |
% 10.48/2.19 | | (28) distinct_lines(all_38_3, all_38_1) = 0
% 10.48/2.19 | |
% 10.48/2.19 | | GROUND_INST: instantiating (3) with 0, all_49_1, all_38_4, all_38_5,
% 10.48/2.19 | | simplifying with (11), (27) gives:
% 10.48/2.19 | | (29) all_49_1 = 0
% 10.48/2.19 | |
% 10.48/2.19 | | GROUND_INST: instantiating (cu1) with all_38_5, all_38_4, all_38_3,
% 10.48/2.19 | | all_38_1, simplifying with (7), (8), (9), (10), (11), (28)
% 10.48/2.19 | | gives:
% 10.48/2.19 | | (30) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 10.48/2.19 | | (apart_point_and_line(all_38_4, all_38_1) = v3 &
% 10.48/2.19 | | apart_point_and_line(all_38_4, all_38_3) = v2 &
% 10.48/2.19 | | apart_point_and_line(all_38_5, all_38_1) = v1 &
% 10.48/2.19 | | apart_point_and_line(all_38_5, all_38_3) = v0 & (v3 = 0 | v2 = 0 |
% 10.48/2.19 | | v1 = 0 | v0 = 0))
% 10.48/2.19 | |
% 10.48/2.19 | | DELTA: instantiating (30) with fresh symbols all_65_0, all_65_1, all_65_2,
% 10.48/2.19 | | all_65_3 gives:
% 10.48/2.19 | | (31) apart_point_and_line(all_38_4, all_38_1) = all_65_0 &
% 10.48/2.19 | | apart_point_and_line(all_38_4, all_38_3) = all_65_1 &
% 10.48/2.19 | | apart_point_and_line(all_38_5, all_38_1) = all_65_2 &
% 10.48/2.19 | | apart_point_and_line(all_38_5, all_38_3) = all_65_3 & (all_65_0 = 0
% 10.48/2.19 | | | all_65_1 = 0 | all_65_2 = 0 | all_65_3 = 0)
% 10.48/2.19 | |
% 10.48/2.19 | | ALPHA: (31) implies:
% 10.48/2.19 | | (32) apart_point_and_line(all_38_5, all_38_3) = all_65_3
% 10.48/2.19 | | (33) apart_point_and_line(all_38_5, all_38_1) = all_65_2
% 10.48/2.19 | | (34) apart_point_and_line(all_38_4, all_38_3) = all_65_1
% 10.48/2.19 | | (35) apart_point_and_line(all_38_4, all_38_1) = all_65_0
% 10.48/2.19 | | (36) all_65_0 = 0 | all_65_1 = 0 | all_65_2 = 0 | all_65_3 = 0
% 10.48/2.19 | |
% 10.48/2.19 | | GROUND_INST: instantiating (4) with all_47_0, all_65_3, all_38_3, all_38_5,
% 10.48/2.19 | | simplifying with (25), (32) gives:
% 10.48/2.19 | | (37) all_65_3 = all_47_0
% 10.48/2.19 | |
% 10.48/2.19 | | GROUND_INST: instantiating (4) with all_45_0, all_65_1, all_38_3, all_38_4,
% 10.48/2.19 | | simplifying with (22), (34) gives:
% 10.48/2.19 | | (38) all_65_1 = all_45_0
% 10.48/2.19 | |
% 10.48/2.19 | | BETA: splitting (36) gives:
% 10.48/2.19 | |
% 10.48/2.19 | | Case 1:
% 10.48/2.19 | | |
% 10.48/2.19 | | | (39) all_65_0 = 0
% 10.48/2.19 | | |
% 10.48/2.19 | | | REDUCE: (35), (39) imply:
% 10.48/2.19 | | | (40) apart_point_and_line(all_38_4, all_38_1) = 0
% 10.48/2.19 | | |
% 10.48/2.19 | | | GROUND_INST: instantiating (ci2) with all_38_5, all_38_4, all_38_1,
% 10.48/2.19 | | | simplifying with (7), (8), (12), (40) gives:
% 10.48/2.19 | | | (41) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_5, all_38_4)
% 10.48/2.19 | | | = v0)
% 10.48/2.19 | | |
% 10.48/2.19 | | | DELTA: instantiating (41) with fresh symbol all_90_0 gives:
% 10.48/2.19 | | | (42) ~ (all_90_0 = 0) & distinct_points(all_38_5, all_38_4) = all_90_0
% 10.48/2.19 | | |
% 10.48/2.19 | | | ALPHA: (42) implies:
% 10.48/2.20 | | | (43) ~ (all_90_0 = 0)
% 10.48/2.20 | | | (44) distinct_points(all_38_5, all_38_4) = all_90_0
% 10.48/2.20 | | |
% 10.48/2.20 | | | GROUND_INST: instantiating (3) with 0, all_90_0, all_38_4, all_38_5,
% 10.48/2.20 | | | simplifying with (11), (44) gives:
% 10.48/2.20 | | | (45) all_90_0 = 0
% 10.48/2.20 | | |
% 10.48/2.20 | | | REDUCE: (43), (45) imply:
% 10.48/2.20 | | | (46) $false
% 10.48/2.20 | | |
% 10.48/2.20 | | | CLOSE: (46) is inconsistent.
% 10.48/2.20 | | |
% 10.48/2.20 | | Case 2:
% 10.48/2.20 | | |
% 10.48/2.20 | | | (47) all_65_1 = 0 | all_65_2 = 0 | all_65_3 = 0
% 10.48/2.20 | | |
% 10.48/2.20 | | | BETA: splitting (47) gives:
% 10.48/2.20 | | |
% 10.48/2.20 | | | Case 1:
% 10.48/2.20 | | | |
% 10.48/2.20 | | | | (48) all_65_1 = 0
% 10.48/2.20 | | | |
% 10.48/2.20 | | | | COMBINE_EQS: (38), (48) imply:
% 10.48/2.20 | | | | (49) all_45_0 = 0
% 10.48/2.20 | | | |
% 10.48/2.20 | | | | REDUCE: (21), (49) imply:
% 10.48/2.20 | | | | (50) $false
% 10.48/2.20 | | | |
% 10.48/2.20 | | | | CLOSE: (50) is inconsistent.
% 10.48/2.20 | | | |
% 10.48/2.20 | | | Case 2:
% 10.48/2.20 | | | |
% 10.48/2.20 | | | | (51) all_65_2 = 0 | all_65_3 = 0
% 10.48/2.20 | | | |
% 10.48/2.20 | | | | BETA: splitting (51) gives:
% 10.48/2.20 | | | |
% 10.48/2.20 | | | | Case 1:
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | | (52) all_65_2 = 0
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | | REDUCE: (33), (52) imply:
% 10.48/2.20 | | | | | (53) apart_point_and_line(all_38_5, all_38_1) = 0
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | | GROUND_INST: instantiating (ci1) with all_38_5, all_38_4, all_38_1,
% 10.48/2.20 | | | | | simplifying with (7), (8), (12), (53) gives:
% 10.48/2.20 | | | | | (54) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_5,
% 10.48/2.20 | | | | | all_38_4) = v0)
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | | DELTA: instantiating (54) with fresh symbol all_98_0 gives:
% 10.48/2.20 | | | | | (55) ~ (all_98_0 = 0) & distinct_points(all_38_5, all_38_4) =
% 10.48/2.20 | | | | | all_98_0
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | | ALPHA: (55) implies:
% 10.48/2.20 | | | | | (56) ~ (all_98_0 = 0)
% 10.48/2.20 | | | | | (57) distinct_points(all_38_5, all_38_4) = all_98_0
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | | GROUND_INST: instantiating (3) with 0, all_98_0, all_38_4, all_38_5,
% 10.48/2.20 | | | | | simplifying with (11), (57) gives:
% 10.48/2.20 | | | | | (58) all_98_0 = 0
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | | REDUCE: (56), (58) imply:
% 10.48/2.20 | | | | | (59) $false
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | | CLOSE: (59) is inconsistent.
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | Case 2:
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | | (60) all_65_3 = 0
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | | COMBINE_EQS: (37), (60) imply:
% 10.48/2.20 | | | | | (61) all_47_0 = 0
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | | SIMP: (61) implies:
% 10.48/2.20 | | | | | (62) all_47_0 = 0
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | | REDUCE: (24), (62) imply:
% 10.48/2.20 | | | | | (63) $false
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | | CLOSE: (63) is inconsistent.
% 10.48/2.20 | | | | |
% 10.48/2.20 | | | | End of split
% 10.48/2.20 | | | |
% 10.48/2.20 | | | End of split
% 10.48/2.20 | | |
% 10.48/2.20 | | End of split
% 10.48/2.20 | |
% 10.48/2.20 | Case 2:
% 10.48/2.20 | |
% 10.48/2.20 | | (64) all_38_0 = 0
% 10.48/2.20 | |
% 10.48/2.20 | | REDUCE: (6), (64) imply:
% 10.48/2.20 | | (65) $false
% 10.48/2.20 | |
% 10.48/2.20 | | CLOSE: (65) is inconsistent.
% 10.48/2.20 | |
% 10.48/2.20 | End of split
% 10.48/2.20 |
% 10.48/2.20 End of proof
% 10.48/2.20 % SZS output end Proof for theBenchmark
% 10.48/2.20
% 10.48/2.20 1591ms
%------------------------------------------------------------------------------