TSTP Solution File: GEO208+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO208+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 : n023.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 23:22:20 EDT 2023
% Result : Theorem 7.85s 1.81s
% Output : Proof 10.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO208+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 20:33:10 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.65/0.66 ________ _____
% 0.65/0.66 ___ __ \_________(_)________________________________
% 0.65/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.65/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.65/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.65/0.66
% 0.65/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.65/0.66 (2023-06-19)
% 0.65/0.66
% 0.65/0.66 (c) Philipp Rümmer, 2009-2023
% 0.65/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.65/0.66 Amanda Stjerna.
% 0.65/0.66 Free software under BSD-3-Clause.
% 0.65/0.66
% 0.65/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.65/0.67
% 0.65/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.65/0.69 Running up to 7 provers in parallel.
% 0.80/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.80/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.80/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.80/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.80/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.80/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.80/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.51/1.24 Prover 4: Preprocessing ...
% 3.51/1.24 Prover 1: Preprocessing ...
% 3.51/1.28 Prover 2: Preprocessing ...
% 3.51/1.28 Prover 5: Preprocessing ...
% 3.51/1.28 Prover 3: Preprocessing ...
% 3.51/1.28 Prover 0: Preprocessing ...
% 3.51/1.28 Prover 6: Preprocessing ...
% 5.74/1.60 Prover 5: Proving ...
% 5.74/1.60 Prover 2: Proving ...
% 6.43/1.66 Prover 1: Constructing countermodel ...
% 6.43/1.68 Prover 6: Constructing countermodel ...
% 7.03/1.71 Prover 3: Constructing countermodel ...
% 7.85/1.81 Prover 6: proved (1111ms)
% 7.85/1.81
% 7.85/1.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.85/1.81
% 7.85/1.82 Prover 5: stopped
% 7.92/1.82 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.92/1.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.92/1.82 Prover 2: stopped
% 7.92/1.82 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.92/1.82 Prover 3: stopped
% 7.92/1.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.92/1.87 Prover 8: Preprocessing ...
% 7.92/1.87 Prover 10: Preprocessing ...
% 7.92/1.89 Prover 7: Preprocessing ...
% 7.92/1.90 Prover 11: Preprocessing ...
% 8.60/1.97 Prover 1: Found proof (size 28)
% 8.60/1.97 Prover 1: proved (1271ms)
% 8.60/1.97 Prover 10: Warning: ignoring some quantifiers
% 8.60/1.98 Prover 7: Warning: ignoring some quantifiers
% 9.23/2.01 Prover 10: Constructing countermodel ...
% 9.23/2.01 Prover 7: Constructing countermodel ...
% 9.23/2.02 Prover 10: stopped
% 9.23/2.02 Prover 7: stopped
% 9.23/2.03 Prover 11: stopped
% 9.23/2.03 Prover 4: Constructing countermodel ...
% 9.23/2.04 Prover 8: Warning: ignoring some quantifiers
% 9.23/2.04 Prover 0: Proving ...
% 9.23/2.05 Prover 8: Constructing countermodel ...
% 9.23/2.05 Prover 0: stopped
% 9.23/2.06 Prover 8: stopped
% 9.23/2.06 Prover 4: stopped
% 9.23/2.06
% 9.23/2.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.23/2.06
% 9.23/2.07 % SZS output start Proof for theBenchmark
% 9.23/2.07 Assumptions after simplification:
% 9.23/2.07 ---------------------------------
% 9.23/2.07
% 9.23/2.07 (a3)
% 9.89/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (parallel_lines(v0,
% 9.89/2.10 v1) = v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v1) = 0) & !
% 9.89/2.10 [v0: $i] : ! [v1: $i] : ( ~ (parallel_lines(v0, v1) = 0) | ~ $i(v1) | ~
% 9.89/2.10 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 9.89/2.10
% 9.89/2.10 (a4)
% 9.89/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 9.89/2.10 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 9.89/2.10 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 9.89/2.10 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int]
% 9.89/2.10 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 9.89/2.10
% 9.89/2.10 (ax2)
% 9.89/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_lines(v0, v1) =
% 9.89/2.10 v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, v1) = 0) & ! [v0: $i] :
% 9.89/2.10 ! [v1: $i] : ( ~ (equal_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 9.89/2.10 int] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 9.89/2.10
% 9.89/2.10 (con)
% 9.89/2.10 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 9.89/2.10 incident_point_and_line(v0, v2) = 0 & incident_point_and_line(v0, v1) = 0 &
% 9.89/2.10 parallel_lines(v1, v2) = 0 & equal_lines(v1, v2) = v3 & $i(v2) & $i(v1) &
% 9.89/2.10 $i(v0))
% 9.89/2.10
% 9.89/2.10 (cup1)
% 9.89/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 9.89/2.10 (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~
% 9.89/2.10 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 9.89/2.10 (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0
% 9.89/2.10 | v4 = 0)))
% 9.89/2.10
% 9.89/2.10 (p1)
% 9.99/2.11 ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_lines(v0, v1) = 0) | ~ $i(v1) | ~
% 9.99/2.11 $i(v0) | convergent_lines(v0, v1) = 0)
% 9.99/2.11
% 9.99/2.11 (function-axioms)
% 9.99/2.11 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 9.99/2.11 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~
% 9.99/2.11 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.99/2.11 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.99/2.11 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2)
% 9.99/2.11 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.99/2.11 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~
% 9.99/2.11 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.99/2.11 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.99/2.11 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0:
% 9.99/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.99/2.11 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 9.99/2.11 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.99/2.11 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 9.99/2.11 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 9.99/2.11 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 9.99/2.11 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 9.99/2.11 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 9.99/2.11 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 9.99/2.11 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 9.99/2.11 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 9.99/2.11 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 9.99/2.11 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.99/2.11 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.99/2.11 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 9.99/2.11 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.99/2.11 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 9.99/2.11 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.99/2.11 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.99/2.11 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 9.99/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.99/2.11 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 9.99/2.11 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.99/2.11 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 9.99/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.99/2.11 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 9.99/2.11
% 9.99/2.11 Further assumptions not needed in the proof:
% 9.99/2.11 --------------------------------------------
% 9.99/2.11 a5, apart1, apart2, apart3, apart4, apart5, ax1, ax6, ceq1, ceq2, ceq3, ci1,
% 9.99/2.11 ci2, ci3, ci4, coipo1, con1, cotno1, couo1, cp1, cp2, cu1, int1, oac1, occu1,
% 9.99/2.11 ooc1, ooc2, orth1, ouo1, par1
% 9.99/2.11
% 9.99/2.11 Those formulas are unsatisfiable:
% 9.99/2.11 ---------------------------------
% 9.99/2.11
% 9.99/2.11 Begin of proof
% 10.04/2.12 |
% 10.04/2.12 | ALPHA: (ax2) implies:
% 10.04/2.12 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 10.04/2.12 | (equal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 10.04/2.12 | distinct_lines(v0, v1) = 0)
% 10.04/2.12 |
% 10.04/2.12 | ALPHA: (a3) implies:
% 10.04/2.12 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (parallel_lines(v0, v1) = 0) | ~
% 10.04/2.12 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 10.04/2.12 | convergent_lines(v0, v1) = v2))
% 10.04/2.12 |
% 10.04/2.12 | ALPHA: (a4) implies:
% 10.04/2.12 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (incident_point_and_line(v0, v1) = 0) |
% 10.04/2.12 | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 10.04/2.12 | apart_point_and_line(v0, v1) = v2))
% 10.04/2.12 |
% 10.04/2.12 | ALPHA: (function-axioms) implies:
% 10.04/2.12 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.04/2.12 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 10.04/2.12 | (convergent_lines(v3, v2) = v0))
% 10.04/2.12 |
% 10.04/2.12 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2,
% 10.04/2.12 | all_38_3 gives:
% 10.04/2.12 | (5) ~ (all_38_0 = 0) & incident_point_and_line(all_38_3, all_38_1) = 0 &
% 10.04/2.12 | incident_point_and_line(all_38_3, all_38_2) = 0 &
% 10.04/2.12 | parallel_lines(all_38_2, all_38_1) = 0 & equal_lines(all_38_2,
% 10.04/2.12 | all_38_1) = all_38_0 & $i(all_38_1) & $i(all_38_2) & $i(all_38_3)
% 10.04/2.12 |
% 10.04/2.12 | ALPHA: (5) implies:
% 10.04/2.12 | (6) ~ (all_38_0 = 0)
% 10.04/2.12 | (7) $i(all_38_3)
% 10.04/2.12 | (8) $i(all_38_2)
% 10.04/2.12 | (9) $i(all_38_1)
% 10.04/2.12 | (10) equal_lines(all_38_2, all_38_1) = all_38_0
% 10.04/2.12 | (11) parallel_lines(all_38_2, all_38_1) = 0
% 10.04/2.12 | (12) incident_point_and_line(all_38_3, all_38_2) = 0
% 10.04/2.12 |
% 10.04/2.12 | GROUND_INST: instantiating (1) with all_38_2, all_38_1, all_38_0, simplifying
% 10.04/2.12 | with (8), (9), (10) gives:
% 10.04/2.13 | (13) all_38_0 = 0 | distinct_lines(all_38_2, all_38_1) = 0
% 10.04/2.13 |
% 10.04/2.13 | GROUND_INST: instantiating (2) with all_38_2, all_38_1, simplifying with (8),
% 10.04/2.13 | (9), (11) gives:
% 10.04/2.13 | (14) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_2, all_38_1) =
% 10.04/2.13 | v0)
% 10.04/2.13 |
% 10.04/2.13 | GROUND_INST: instantiating (3) with all_38_3, all_38_2, simplifying with (7),
% 10.04/2.13 | (8), (12) gives:
% 10.04/2.13 | (15) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_3, all_38_2)
% 10.04/2.13 | = v0)
% 10.04/2.13 |
% 10.04/2.13 | DELTA: instantiating (14) with fresh symbol all_47_0 gives:
% 10.04/2.13 | (16) ~ (all_47_0 = 0) & convergent_lines(all_38_2, all_38_1) = all_47_0
% 10.04/2.13 |
% 10.04/2.13 | ALPHA: (16) implies:
% 10.04/2.13 | (17) ~ (all_47_0 = 0)
% 10.04/2.13 | (18) convergent_lines(all_38_2, all_38_1) = all_47_0
% 10.04/2.13 |
% 10.04/2.13 | DELTA: instantiating (15) with fresh symbol all_49_0 gives:
% 10.04/2.13 | (19) ~ (all_49_0 = 0) & apart_point_and_line(all_38_3, all_38_2) =
% 10.04/2.13 | all_49_0
% 10.04/2.13 |
% 10.04/2.13 | ALPHA: (19) implies:
% 10.04/2.13 | (20) ~ (all_49_0 = 0)
% 10.04/2.13 | (21) apart_point_and_line(all_38_3, all_38_2) = all_49_0
% 10.04/2.13 |
% 10.04/2.13 | BETA: splitting (13) gives:
% 10.04/2.13 |
% 10.04/2.13 | Case 1:
% 10.04/2.13 | |
% 10.04/2.13 | | (22) distinct_lines(all_38_2, all_38_1) = 0
% 10.04/2.13 | |
% 10.04/2.13 | | GROUND_INST: instantiating (p1) with all_38_2, all_38_1, simplifying with
% 10.04/2.13 | | (8), (9), (22) gives:
% 10.04/2.13 | | (23) convergent_lines(all_38_2, all_38_1) = 0
% 10.04/2.13 | |
% 10.04/2.13 | | GROUND_INST: instantiating (cup1) with all_38_3, all_38_2, all_38_1,
% 10.04/2.13 | | all_49_0, simplifying with (7), (8), (9), (21), (22) gives:
% 10.04/2.13 | | (24) all_49_0 = 0 | ? [v0: any] : ? [v1: any] :
% 10.04/2.13 | | (apart_point_and_line(all_38_3, all_38_1) = v0 &
% 10.04/2.13 | | convergent_lines(all_38_2, all_38_1) = v1 & (v1 = 0 | v0 = 0))
% 10.04/2.13 | |
% 10.04/2.13 | | BETA: splitting (24) gives:
% 10.04/2.13 | |
% 10.04/2.13 | | Case 1:
% 10.04/2.13 | | |
% 10.04/2.13 | | | (25) all_49_0 = 0
% 10.04/2.13 | | |
% 10.04/2.13 | | | REDUCE: (20), (25) imply:
% 10.04/2.13 | | | (26) $false
% 10.04/2.13 | | |
% 10.04/2.13 | | | CLOSE: (26) is inconsistent.
% 10.04/2.13 | | |
% 10.04/2.13 | | Case 2:
% 10.04/2.13 | | |
% 10.04/2.13 | | | (27) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_3,
% 10.04/2.13 | | | all_38_1) = v0 & convergent_lines(all_38_2, all_38_1) = v1 &
% 10.04/2.13 | | | (v1 = 0 | v0 = 0))
% 10.04/2.13 | | |
% 10.04/2.13 | | | DELTA: instantiating (27) with fresh symbols all_65_0, all_65_1 gives:
% 10.04/2.13 | | | (28) apart_point_and_line(all_38_3, all_38_1) = all_65_1 &
% 10.04/2.13 | | | convergent_lines(all_38_2, all_38_1) = all_65_0 & (all_65_0 = 0 |
% 10.04/2.13 | | | all_65_1 = 0)
% 10.04/2.13 | | |
% 10.04/2.13 | | | ALPHA: (28) implies:
% 10.04/2.13 | | | (29) convergent_lines(all_38_2, all_38_1) = all_65_0
% 10.04/2.13 | | |
% 10.04/2.13 | | | GROUND_INST: instantiating (4) with all_47_0, all_65_0, all_38_1,
% 10.04/2.13 | | | all_38_2, simplifying with (18), (29) gives:
% 10.04/2.13 | | | (30) all_65_0 = all_47_0
% 10.04/2.13 | | |
% 10.04/2.13 | | | GROUND_INST: instantiating (4) with 0, all_65_0, all_38_1, all_38_2,
% 10.04/2.14 | | | simplifying with (23), (29) gives:
% 10.04/2.14 | | | (31) all_65_0 = 0
% 10.04/2.14 | | |
% 10.04/2.14 | | | COMBINE_EQS: (30), (31) imply:
% 10.04/2.14 | | | (32) all_47_0 = 0
% 10.04/2.14 | | |
% 10.04/2.14 | | | REDUCE: (17), (32) imply:
% 10.04/2.14 | | | (33) $false
% 10.04/2.14 | | |
% 10.04/2.14 | | | CLOSE: (33) is inconsistent.
% 10.04/2.14 | | |
% 10.04/2.14 | | End of split
% 10.04/2.14 | |
% 10.04/2.14 | Case 2:
% 10.04/2.14 | |
% 10.04/2.14 | | (34) all_38_0 = 0
% 10.04/2.14 | |
% 10.04/2.14 | | REDUCE: (6), (34) imply:
% 10.04/2.14 | | (35) $false
% 10.04/2.14 | |
% 10.04/2.14 | | CLOSE: (35) is inconsistent.
% 10.04/2.14 | |
% 10.04/2.14 | End of split
% 10.04/2.14 |
% 10.04/2.14 End of proof
% 10.04/2.14 % SZS output end Proof for theBenchmark
% 10.04/2.14
% 10.04/2.14 1470ms
%------------------------------------------------------------------------------