TSTP Solution File: GEO170+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO170+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 : n015.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 23:21:48 EDT 2023
% Result : Theorem 8.20s 1.92s
% Output : Proof 10.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO170+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34 % Computer : n015.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Aug 29 23:51:11 EDT 2023
% 0.16/0.34 % 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/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.99/1.16 Prover 1: Preprocessing ...
% 2.99/1.16 Prover 4: Preprocessing ...
% 3.58/1.21 Prover 6: Preprocessing ...
% 3.58/1.21 Prover 3: Preprocessing ...
% 3.58/1.21 Prover 2: Preprocessing ...
% 3.58/1.21 Prover 0: Preprocessing ...
% 3.58/1.21 Prover 5: Preprocessing ...
% 5.53/1.59 Prover 2: Proving ...
% 5.53/1.59 Prover 5: Proving ...
% 6.56/1.67 Prover 3: Constructing countermodel ...
% 6.56/1.68 Prover 6: Constructing countermodel ...
% 7.29/1.74 Prover 1: Constructing countermodel ...
% 8.20/1.92 Prover 3: proved (1277ms)
% 8.20/1.92
% 8.20/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.20/1.92
% 8.20/1.93 Prover 5: stopped
% 8.20/1.93 Prover 2: stopped
% 8.20/1.94 Prover 6: stopped
% 8.20/1.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.20/1.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.20/1.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.20/1.96 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.20/2.01 Prover 11: Preprocessing ...
% 9.20/2.03 Prover 7: Preprocessing ...
% 9.20/2.03 Prover 8: Preprocessing ...
% 9.48/2.04 Prover 10: Preprocessing ...
% 9.48/2.06 Prover 4: Constructing countermodel ...
% 9.48/2.07 Prover 0: Proving ...
% 9.48/2.10 Prover 0: stopped
% 9.48/2.12 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.48/2.12 Prover 10: Warning: ignoring some quantifiers
% 9.48/2.13 Prover 7: Warning: ignoring some quantifiers
% 10.20/2.14 Prover 1: Found proof (size 50)
% 10.20/2.15 Prover 1: proved (1496ms)
% 10.20/2.15 Prover 4: stopped
% 10.20/2.15 Prover 11: stopped
% 10.20/2.15 Prover 7: Constructing countermodel ...
% 10.20/2.16 Prover 10: Constructing countermodel ...
% 10.20/2.16 Prover 13: Preprocessing ...
% 10.20/2.16 Prover 7: stopped
% 10.20/2.16 Prover 10: stopped
% 10.20/2.18 Prover 13: stopped
% 10.57/2.22 Prover 8: Warning: ignoring some quantifiers
% 10.57/2.22 Prover 8: Constructing countermodel ...
% 10.57/2.23 Prover 8: stopped
% 10.57/2.23
% 10.57/2.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.57/2.23
% 10.57/2.24 % SZS output start Proof for theBenchmark
% 10.57/2.25 Assumptions after simplification:
% 10.57/2.25 ---------------------------------
% 10.57/2.25
% 10.57/2.25 (a4)
% 10.87/2.27 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 10.87/2.27 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 10.87/2.27 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 10.87/2.27 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int]
% 10.87/2.27 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 10.87/2.27
% 10.87/2.27 (ax2)
% 10.87/2.28 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_lines(v0, v1) =
% 10.87/2.28 v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, v1) = 0) & ! [v0: $i] :
% 10.87/2.28 ! [v1: $i] : ( ~ (equal_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 10.87/2.28 int] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 10.87/2.28
% 10.87/2.28 (ci1)
% 10.87/2.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 10.87/2.28 ~ (apart_point_and_line(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 10.87/2.28 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 10.87/2.28
% 10.87/2.28 (ci2)
% 10.87/2.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 10.87/2.28 ~ (apart_point_and_line(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 10.87/2.28 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 10.87/2.28
% 10.87/2.28 (con)
% 10.87/2.28 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 10.87/2.28 = 0) & incident_point_and_line(v1, v2) = 0 & incident_point_and_line(v0,
% 10.87/2.28 v2) = 0 & equal_lines(v2, v3) = v4 & line_connecting(v0, v1) = v3 &
% 10.87/2.28 distinct_points(v0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.87/2.28
% 10.87/2.28 (con1)
% 10.87/2.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 10.87/2.28 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6:
% 10.87/2.28 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 &
% 10.87/2.28 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) |
% 10.87/2.28 v6 = 0)))
% 10.87/2.28
% 10.87/2.28 (cu1)
% 10.87/2.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.87/2.29 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 10.87/2.29 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 10.87/2.29 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 10.87/2.29 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 10.87/2.29 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 10.87/2.29
% 10.87/2.29 (function-axioms)
% 10.87/2.30 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.87/2.30 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~
% 10.87/2.30 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.87/2.30 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.87/2.30 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2)
% 10.87/2.30 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.87/2.30 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~
% 10.87/2.30 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.87/2.30 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.87/2.30 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0:
% 10.87/2.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.87/2.30 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 10.87/2.30 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.87/2.30 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 10.87/2.30 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 10.87/2.30 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 10.87/2.30 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 10.87/2.30 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 10.87/2.30 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 10.87/2.30 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 10.87/2.30 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 10.87/2.30 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 10.87/2.30 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.87/2.30 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.87/2.30 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 10.87/2.30 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.87/2.30 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 10.87/2.30 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.87/2.30 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.87/2.30 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 10.87/2.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.87/2.30 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 10.87/2.30 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.87/2.30 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 10.87/2.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.87/2.30 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 10.87/2.30
% 10.87/2.30 Further assumptions not needed in the proof:
% 10.87/2.30 --------------------------------------------
% 10.87/2.30 a3, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax6, ceq1, ceq2, ceq3, ci3,
% 10.87/2.30 ci4, coipo1, cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1, ooc2,
% 10.87/2.30 orth1, ouo1, p1, par1
% 10.87/2.30
% 10.87/2.30 Those formulas are unsatisfiable:
% 10.87/2.30 ---------------------------------
% 10.87/2.30
% 10.87/2.30 Begin of proof
% 10.87/2.30 |
% 10.87/2.30 | ALPHA: (ax2) implies:
% 10.87/2.30 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 10.87/2.30 | (equal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 10.87/2.30 | distinct_lines(v0, v1) = 0)
% 10.87/2.30 |
% 10.87/2.30 | ALPHA: (a4) implies:
% 10.87/2.30 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (incident_point_and_line(v0, v1) = 0) |
% 10.87/2.30 | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 10.87/2.30 | apart_point_and_line(v0, v1) = v2))
% 10.87/2.30 |
% 10.87/2.30 | ALPHA: (function-axioms) implies:
% 10.87/2.30 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.87/2.30 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 10.87/2.30 | (distinct_points(v3, v2) = v0))
% 10.87/2.30 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.87/2.30 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 10.87/2.30 | (apart_point_and_line(v3, v2) = v0))
% 10.87/2.30 |
% 10.87/2.30 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2,
% 10.87/2.30 | all_38_3, all_38_4 gives:
% 10.87/2.31 | (5) ~ (all_38_0 = 0) & incident_point_and_line(all_38_3, all_38_2) = 0 &
% 10.87/2.31 | incident_point_and_line(all_38_4, all_38_2) = 0 & equal_lines(all_38_2,
% 10.87/2.31 | all_38_1) = all_38_0 & line_connecting(all_38_4, all_38_3) = all_38_1
% 10.87/2.31 | & distinct_points(all_38_4, all_38_3) = 0 & $i(all_38_1) & $i(all_38_2)
% 10.87/2.31 | & $i(all_38_3) & $i(all_38_4)
% 10.87/2.31 |
% 10.87/2.31 | ALPHA: (5) implies:
% 10.87/2.31 | (6) ~ (all_38_0 = 0)
% 10.87/2.31 | (7) $i(all_38_4)
% 10.87/2.31 | (8) $i(all_38_3)
% 10.87/2.31 | (9) $i(all_38_2)
% 10.87/2.31 | (10) $i(all_38_1)
% 10.87/2.31 | (11) distinct_points(all_38_4, all_38_3) = 0
% 10.87/2.31 | (12) line_connecting(all_38_4, all_38_3) = all_38_1
% 10.87/2.31 | (13) equal_lines(all_38_2, all_38_1) = all_38_0
% 10.87/2.31 | (14) incident_point_and_line(all_38_4, all_38_2) = 0
% 10.87/2.31 | (15) incident_point_and_line(all_38_3, all_38_2) = 0
% 10.87/2.31 |
% 10.87/2.31 | GROUND_INST: instantiating (con1) with all_38_4, all_38_3, all_38_1,
% 10.87/2.31 | simplifying with (7), (8), (12) gives:
% 10.87/2.31 | (16) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 10.87/2.31 | (point(all_38_3) = v1 & point(all_38_4) = v0 & line(all_38_1) = v3 &
% 10.87/2.31 | distinct_points(all_38_4, all_38_3) = v2 & ( ~ (v2 = 0) | ~ (v1 =
% 10.87/2.31 | 0) | ~ (v0 = 0) | v3 = 0))
% 10.87/2.31 |
% 10.87/2.31 | GROUND_INST: instantiating (1) with all_38_2, all_38_1, all_38_0, simplifying
% 10.87/2.31 | with (9), (10), (13) gives:
% 10.87/2.31 | (17) all_38_0 = 0 | distinct_lines(all_38_2, all_38_1) = 0
% 10.87/2.31 |
% 10.87/2.31 | GROUND_INST: instantiating (2) with all_38_4, all_38_2, simplifying with (7),
% 10.87/2.31 | (9), (14) gives:
% 10.87/2.31 | (18) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_4, all_38_2)
% 10.87/2.31 | = v0)
% 10.87/2.31 |
% 10.87/2.31 | GROUND_INST: instantiating (2) with all_38_3, all_38_2, simplifying with (8),
% 10.87/2.31 | (9), (15) gives:
% 10.87/2.31 | (19) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_3, all_38_2)
% 10.87/2.31 | = v0)
% 10.87/2.31 |
% 10.87/2.31 | DELTA: instantiating (19) with fresh symbol all_45_0 gives:
% 10.87/2.31 | (20) ~ (all_45_0 = 0) & apart_point_and_line(all_38_3, all_38_2) =
% 10.87/2.31 | all_45_0
% 10.87/2.31 |
% 10.87/2.31 | ALPHA: (20) implies:
% 10.87/2.31 | (21) ~ (all_45_0 = 0)
% 10.87/2.31 | (22) apart_point_and_line(all_38_3, all_38_2) = all_45_0
% 10.87/2.31 |
% 10.87/2.31 | DELTA: instantiating (18) with fresh symbol all_47_0 gives:
% 10.87/2.31 | (23) ~ (all_47_0 = 0) & apart_point_and_line(all_38_4, all_38_2) =
% 10.87/2.31 | all_47_0
% 10.87/2.31 |
% 10.87/2.31 | ALPHA: (23) implies:
% 10.87/2.31 | (24) ~ (all_47_0 = 0)
% 10.87/2.31 | (25) apart_point_and_line(all_38_4, all_38_2) = all_47_0
% 10.87/2.31 |
% 10.87/2.31 | DELTA: instantiating (16) with fresh symbols all_49_0, all_49_1, all_49_2,
% 10.87/2.31 | all_49_3 gives:
% 10.87/2.31 | (26) point(all_38_3) = all_49_2 & point(all_38_4) = all_49_3 &
% 10.87/2.31 | line(all_38_1) = all_49_0 & distinct_points(all_38_4, all_38_3) =
% 10.87/2.31 | all_49_1 & ( ~ (all_49_1 = 0) | ~ (all_49_2 = 0) | ~ (all_49_3 = 0)
% 10.87/2.31 | | all_49_0 = 0)
% 10.87/2.31 |
% 10.87/2.31 | ALPHA: (26) implies:
% 10.87/2.31 | (27) distinct_points(all_38_4, all_38_3) = all_49_1
% 10.87/2.31 |
% 10.87/2.31 | BETA: splitting (17) gives:
% 10.87/2.31 |
% 10.87/2.31 | Case 1:
% 10.87/2.31 | |
% 10.87/2.31 | | (28) distinct_lines(all_38_2, all_38_1) = 0
% 10.87/2.31 | |
% 10.87/2.32 | | GROUND_INST: instantiating (3) with 0, all_49_1, all_38_3, all_38_4,
% 10.87/2.32 | | simplifying with (11), (27) gives:
% 10.87/2.32 | | (29) all_49_1 = 0
% 10.87/2.32 | |
% 10.87/2.32 | | GROUND_INST: instantiating (cu1) with all_38_4, all_38_3, all_38_2,
% 10.87/2.32 | | all_38_1, simplifying with (7), (8), (9), (10), (11), (28)
% 10.87/2.32 | | gives:
% 10.87/2.32 | | (30) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 10.87/2.32 | | (apart_point_and_line(all_38_3, all_38_1) = v3 &
% 10.87/2.32 | | apart_point_and_line(all_38_3, all_38_2) = v2 &
% 10.87/2.32 | | apart_point_and_line(all_38_4, all_38_1) = v1 &
% 10.87/2.32 | | apart_point_and_line(all_38_4, all_38_2) = v0 & (v3 = 0 | v2 = 0 |
% 10.87/2.32 | | v1 = 0 | v0 = 0))
% 10.87/2.32 | |
% 10.87/2.32 | | DELTA: instantiating (30) with fresh symbols all_65_0, all_65_1, all_65_2,
% 10.87/2.32 | | all_65_3 gives:
% 10.87/2.32 | | (31) apart_point_and_line(all_38_3, all_38_1) = all_65_0 &
% 10.87/2.32 | | apart_point_and_line(all_38_3, all_38_2) = all_65_1 &
% 10.87/2.32 | | apart_point_and_line(all_38_4, all_38_1) = all_65_2 &
% 10.87/2.32 | | apart_point_and_line(all_38_4, all_38_2) = all_65_3 & (all_65_0 = 0
% 10.87/2.32 | | | all_65_1 = 0 | all_65_2 = 0 | all_65_3 = 0)
% 10.87/2.32 | |
% 10.87/2.32 | | ALPHA: (31) implies:
% 10.87/2.32 | | (32) apart_point_and_line(all_38_4, all_38_2) = all_65_3
% 10.87/2.32 | | (33) apart_point_and_line(all_38_4, all_38_1) = all_65_2
% 10.87/2.32 | | (34) apart_point_and_line(all_38_3, all_38_2) = all_65_1
% 10.87/2.32 | | (35) apart_point_and_line(all_38_3, all_38_1) = all_65_0
% 10.87/2.32 | | (36) all_65_0 = 0 | all_65_1 = 0 | all_65_2 = 0 | all_65_3 = 0
% 10.87/2.32 | |
% 10.87/2.32 | | GROUND_INST: instantiating (4) with all_47_0, all_65_3, all_38_2, all_38_4,
% 10.87/2.32 | | simplifying with (25), (32) gives:
% 10.87/2.32 | | (37) all_65_3 = all_47_0
% 10.87/2.32 | |
% 10.87/2.32 | | GROUND_INST: instantiating (4) with all_45_0, all_65_1, all_38_2, all_38_3,
% 10.87/2.32 | | simplifying with (22), (34) gives:
% 10.87/2.32 | | (38) all_65_1 = all_45_0
% 10.87/2.32 | |
% 10.87/2.32 | | BETA: splitting (36) gives:
% 10.87/2.32 | |
% 10.87/2.32 | | Case 1:
% 10.87/2.32 | | |
% 10.87/2.32 | | | (39) all_65_0 = 0
% 10.87/2.32 | | |
% 10.87/2.32 | | | REDUCE: (35), (39) imply:
% 10.87/2.32 | | | (40) apart_point_and_line(all_38_3, all_38_1) = 0
% 10.87/2.32 | | |
% 10.87/2.32 | | | GROUND_INST: instantiating (ci2) with all_38_4, all_38_3, all_38_1,
% 10.87/2.32 | | | simplifying with (7), (8), (12), (40) gives:
% 10.87/2.32 | | | (41) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_4, all_38_3)
% 10.87/2.32 | | | = v0)
% 10.87/2.32 | | |
% 10.87/2.32 | | | DELTA: instantiating (41) with fresh symbol all_90_0 gives:
% 10.87/2.32 | | | (42) ~ (all_90_0 = 0) & distinct_points(all_38_4, all_38_3) = all_90_0
% 10.87/2.32 | | |
% 10.87/2.32 | | | ALPHA: (42) implies:
% 10.87/2.32 | | | (43) ~ (all_90_0 = 0)
% 10.87/2.32 | | | (44) distinct_points(all_38_4, all_38_3) = all_90_0
% 10.87/2.32 | | |
% 10.87/2.32 | | | GROUND_INST: instantiating (3) with 0, all_90_0, all_38_3, all_38_4,
% 10.87/2.32 | | | simplifying with (11), (44) gives:
% 10.87/2.32 | | | (45) all_90_0 = 0
% 10.87/2.32 | | |
% 10.87/2.32 | | | REDUCE: (43), (45) imply:
% 10.87/2.32 | | | (46) $false
% 10.87/2.32 | | |
% 10.87/2.32 | | | CLOSE: (46) is inconsistent.
% 10.87/2.32 | | |
% 10.87/2.32 | | Case 2:
% 10.87/2.32 | | |
% 10.87/2.32 | | | (47) all_65_1 = 0 | all_65_2 = 0 | all_65_3 = 0
% 10.87/2.32 | | |
% 10.87/2.32 | | | BETA: splitting (47) gives:
% 10.87/2.32 | | |
% 10.87/2.32 | | | Case 1:
% 10.87/2.32 | | | |
% 10.87/2.33 | | | | (48) all_65_1 = 0
% 10.87/2.33 | | | |
% 10.87/2.33 | | | | COMBINE_EQS: (38), (48) imply:
% 10.87/2.33 | | | | (49) all_45_0 = 0
% 10.87/2.33 | | | |
% 10.87/2.33 | | | | REDUCE: (21), (49) imply:
% 10.87/2.33 | | | | (50) $false
% 10.87/2.33 | | | |
% 10.87/2.33 | | | | CLOSE: (50) is inconsistent.
% 10.87/2.33 | | | |
% 10.87/2.33 | | | Case 2:
% 10.87/2.33 | | | |
% 10.87/2.33 | | | | (51) all_65_2 = 0 | all_65_3 = 0
% 10.87/2.33 | | | |
% 10.87/2.33 | | | | BETA: splitting (51) gives:
% 10.87/2.33 | | | |
% 10.87/2.33 | | | | Case 1:
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | | (52) all_65_2 = 0
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | | REDUCE: (33), (52) imply:
% 10.87/2.33 | | | | | (53) apart_point_and_line(all_38_4, all_38_1) = 0
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | | GROUND_INST: instantiating (ci1) with all_38_4, all_38_3, all_38_1,
% 10.87/2.33 | | | | | simplifying with (7), (8), (12), (53) gives:
% 10.87/2.33 | | | | | (54) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_4,
% 10.87/2.33 | | | | | all_38_3) = v0)
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | | DELTA: instantiating (54) with fresh symbol all_98_0 gives:
% 10.87/2.33 | | | | | (55) ~ (all_98_0 = 0) & distinct_points(all_38_4, all_38_3) =
% 10.87/2.33 | | | | | all_98_0
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | | ALPHA: (55) implies:
% 10.87/2.33 | | | | | (56) ~ (all_98_0 = 0)
% 10.87/2.33 | | | | | (57) distinct_points(all_38_4, all_38_3) = all_98_0
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | | GROUND_INST: instantiating (3) with 0, all_98_0, all_38_3, all_38_4,
% 10.87/2.33 | | | | | simplifying with (11), (57) gives:
% 10.87/2.33 | | | | | (58) all_98_0 = 0
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | | REDUCE: (56), (58) imply:
% 10.87/2.33 | | | | | (59) $false
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | | CLOSE: (59) is inconsistent.
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | Case 2:
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | | (60) all_65_3 = 0
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | | COMBINE_EQS: (37), (60) imply:
% 10.87/2.33 | | | | | (61) all_47_0 = 0
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | | SIMP: (61) implies:
% 10.87/2.33 | | | | | (62) all_47_0 = 0
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | | REDUCE: (24), (62) imply:
% 10.87/2.33 | | | | | (63) $false
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | | CLOSE: (63) is inconsistent.
% 10.87/2.33 | | | | |
% 10.87/2.33 | | | | End of split
% 10.87/2.33 | | | |
% 10.87/2.33 | | | End of split
% 10.87/2.33 | | |
% 10.87/2.33 | | End of split
% 10.87/2.33 | |
% 10.87/2.33 | Case 2:
% 10.87/2.33 | |
% 10.87/2.33 | | (64) all_38_0 = 0
% 10.87/2.33 | |
% 10.87/2.33 | | REDUCE: (6), (64) imply:
% 10.87/2.33 | | (65) $false
% 10.87/2.33 | |
% 10.87/2.33 | | CLOSE: (65) is inconsistent.
% 10.87/2.33 | |
% 10.87/2.33 | End of split
% 10.87/2.33 |
% 10.87/2.33 End of proof
% 10.87/2.33 % SZS output end Proof for theBenchmark
% 10.87/2.33
% 10.87/2.33 1709ms
%------------------------------------------------------------------------------