TSTP Solution File: GEO206+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO206+3 : TPTP v8.1.2. Bugfixed v4.0.1.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.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 23:22:18 EDT 2023
% Result : Theorem 7.74s 1.67s
% Output : Proof 9.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : GEO206+3 : TPTP v8.1.2. Bugfixed v4.0.1.
% 0.06/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Aug 29 23:34:17 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.16/0.52 ________ _____
% 0.16/0.52 ___ __ \_________(_)________________________________
% 0.16/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.52
% 0.16/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.52 (2023-06-19)
% 0.16/0.52
% 0.16/0.52 (c) Philipp Rümmer, 2009-2023
% 0.16/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.52 Amanda Stjerna.
% 0.16/0.52 Free software under BSD-3-Clause.
% 0.16/0.52
% 0.16/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.52
% 0.16/0.52 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.53 Running up to 7 provers in parallel.
% 0.16/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.81/0.99 Prover 1: Preprocessing ...
% 2.81/0.99 Prover 4: Preprocessing ...
% 3.14/1.03 Prover 2: Preprocessing ...
% 3.14/1.03 Prover 3: Preprocessing ...
% 3.14/1.03 Prover 6: Preprocessing ...
% 3.14/1.03 Prover 0: Preprocessing ...
% 3.14/1.03 Prover 5: Preprocessing ...
% 6.24/1.45 Prover 5: Proving ...
% 6.25/1.45 Prover 2: Proving ...
% 6.25/1.50 Prover 6: Constructing countermodel ...
% 6.64/1.51 Prover 3: Constructing countermodel ...
% 6.64/1.52 Prover 1: Constructing countermodel ...
% 7.74/1.66 Prover 3: proved (1125ms)
% 7.74/1.66
% 7.74/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.74/1.67
% 7.74/1.67 Prover 6: stopped
% 7.74/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.74/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.74/1.67 Prover 2: stopped
% 7.74/1.67 Prover 5: stopped
% 7.74/1.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.74/1.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.16/1.74 Prover 1: Found proof (size 32)
% 8.16/1.74 Prover 1: proved (1204ms)
% 8.16/1.74 Prover 7: Preprocessing ...
% 8.16/1.75 Prover 8: Preprocessing ...
% 8.54/1.76 Prover 11: Preprocessing ...
% 8.54/1.78 Prover 10: Preprocessing ...
% 8.54/1.79 Prover 7: stopped
% 8.54/1.80 Prover 4: Constructing countermodel ...
% 8.54/1.81 Prover 10: stopped
% 8.54/1.82 Prover 4: stopped
% 8.54/1.83 Prover 0: Proving ...
% 8.54/1.83 Prover 0: stopped
% 8.54/1.84 Prover 11: stopped
% 9.20/1.87 Prover 8: Warning: ignoring some quantifiers
% 9.20/1.88 Prover 8: Constructing countermodel ...
% 9.20/1.89 Prover 8: stopped
% 9.20/1.89
% 9.20/1.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.20/1.89
% 9.20/1.90 % SZS output start Proof for theBenchmark
% 9.20/1.90 Assumptions after simplification:
% 9.20/1.90 ---------------------------------
% 9.20/1.90
% 9.20/1.90 (a3)
% 9.20/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (parallel_lines(v0,
% 9.20/1.93 v1) = v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v1) = 0) & !
% 9.20/1.93 [v0: $i] : ! [v1: $i] : ( ~ (parallel_lines(v0, v1) = 0) | ~ $i(v1) | ~
% 9.20/1.93 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 9.20/1.93
% 9.20/1.93 (a4)
% 9.20/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 9.20/1.93 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 9.20/1.93 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 9.20/1.93 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int]
% 9.20/1.93 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 9.20/1.93
% 9.20/1.93 (ax2)
% 9.20/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_lines(v0, v1) =
% 9.20/1.93 v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, v1) = 0) & ! [v0: $i] :
% 9.20/1.93 ! [v1: $i] : ( ~ (equal_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 9.20/1.93 int] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 9.20/1.93
% 9.20/1.93 (ax6)
% 9.20/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 9.20/1.93 (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ~
% 9.20/1.93 $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0)
% 9.20/1.93
% 9.20/1.93 (con)
% 9.20/1.94 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 9.20/1.94 = 0) & incident_point_and_line(v0, v1) = 0 & parallel_lines(v1, v2) = 0 &
% 9.20/1.94 equal_lines(v1, v3) = v4 & parallel_through_point(v2, v0) = v3 & $i(v3) &
% 9.20/1.94 $i(v2) & $i(v1) & $i(v0))
% 9.20/1.94
% 9.20/1.94 (cp1)
% 9.20/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (parallel_through_point(v1, v0)
% 9.20/1.94 = v2) | ~ (convergent_lines(v2, v1) = 0) | ~ $i(v1) | ~ $i(v0))
% 9.20/1.94
% 9.20/1.94 (cup1)
% 9.20/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 9.20/1.94 (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~
% 9.20/1.94 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 9.20/1.94 (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0
% 9.20/1.94 | v4 = 0)))
% 9.20/1.94
% 9.20/1.94 (p1)
% 9.20/1.94 ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_lines(v0, v1) = 0) | ~ $i(v1) | ~
% 9.20/1.94 $i(v0) | convergent_lines(v0, v1) = 0)
% 9.20/1.94
% 9.20/1.94 (function-axioms)
% 9.20/1.96 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 9.20/1.96 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~
% 9.20/1.96 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.20/1.96 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.20/1.96 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2)
% 9.20/1.96 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.20/1.96 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~
% 9.20/1.96 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.20/1.96 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.20/1.96 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0:
% 9.20/1.96 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.20/1.96 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 9.20/1.96 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.20/1.96 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 9.20/1.96 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 9.20/1.96 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 9.20/1.96 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 9.20/1.96 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 9.20/1.96 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 9.20/1.96 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 9.20/1.96 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 9.20/1.96 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 9.20/1.96 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.20/1.96 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.20/1.96 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 9.20/1.96 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.20/1.96 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 9.20/1.96 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.20/1.96 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.20/1.96 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 9.20/1.96 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.20/1.96 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 9.20/1.96 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.20/1.96 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 9.20/1.96 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.20/1.96 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 9.20/1.96
% 9.20/1.96 Further assumptions not needed in the proof:
% 9.20/1.96 --------------------------------------------
% 9.20/1.96 a5, apart1, apart2, apart3, apart4, apart5, ax1, ceq1, ceq2, ceq3, ci1, ci2,
% 9.20/1.96 ci3, ci4, coipo1, con1, cotno1, couo1, cp2, cu1, int1, oac1, occu1, ooc1, ooc2,
% 9.20/1.96 orth1, ouo1, par1
% 9.20/1.96
% 9.20/1.96 Those formulas are unsatisfiable:
% 9.20/1.96 ---------------------------------
% 9.20/1.96
% 9.20/1.96 Begin of proof
% 9.20/1.96 |
% 9.20/1.96 | ALPHA: (ax2) implies:
% 9.20/1.96 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 9.20/1.96 | (equal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 9.20/1.96 | distinct_lines(v0, v1) = 0)
% 9.20/1.96 |
% 9.20/1.96 | ALPHA: (a3) implies:
% 9.20/1.96 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (parallel_lines(v0, v1) = 0) | ~
% 9.20/1.96 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 9.20/1.96 | convergent_lines(v0, v1) = v2))
% 9.20/1.96 |
% 9.20/1.96 | ALPHA: (a4) implies:
% 9.20/1.96 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (incident_point_and_line(v0, v1) = 0) |
% 9.20/1.96 | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 9.20/1.96 | apart_point_and_line(v0, v1) = v2))
% 9.20/1.96 |
% 9.20/1.96 | ALPHA: (function-axioms) implies:
% 9.20/1.96 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.20/1.96 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 9.20/1.96 | (convergent_lines(v3, v2) = v0))
% 9.20/1.96 |
% 9.20/1.96 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2,
% 9.20/1.96 | all_38_3, all_38_4 gives:
% 9.20/1.96 | (5) ~ (all_38_0 = 0) & incident_point_and_line(all_38_4, all_38_3) = 0 &
% 9.20/1.96 | parallel_lines(all_38_3, all_38_2) = 0 & equal_lines(all_38_3,
% 9.20/1.96 | all_38_1) = all_38_0 & parallel_through_point(all_38_2, all_38_4) =
% 9.20/1.96 | all_38_1 & $i(all_38_1) & $i(all_38_2) & $i(all_38_3) & $i(all_38_4)
% 9.20/1.96 |
% 9.20/1.96 | ALPHA: (5) implies:
% 9.20/1.97 | (6) ~ (all_38_0 = 0)
% 9.20/1.97 | (7) $i(all_38_4)
% 9.20/1.97 | (8) $i(all_38_3)
% 9.20/1.97 | (9) $i(all_38_2)
% 9.20/1.97 | (10) $i(all_38_1)
% 9.20/1.97 | (11) parallel_through_point(all_38_2, all_38_4) = all_38_1
% 9.20/1.97 | (12) equal_lines(all_38_3, all_38_1) = all_38_0
% 9.20/1.97 | (13) parallel_lines(all_38_3, all_38_2) = 0
% 9.20/1.97 | (14) incident_point_and_line(all_38_4, all_38_3) = 0
% 9.20/1.97 |
% 9.20/1.97 | GROUND_INST: instantiating (1) with all_38_3, all_38_1, all_38_0, simplifying
% 9.20/1.97 | with (8), (10), (12) gives:
% 9.20/1.97 | (15) all_38_0 = 0 | distinct_lines(all_38_3, all_38_1) = 0
% 9.20/1.97 |
% 9.20/1.97 | GROUND_INST: instantiating (2) with all_38_3, all_38_2, simplifying with (8),
% 9.20/1.97 | (9), (13) gives:
% 9.20/1.97 | (16) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_3, all_38_2) =
% 9.20/1.97 | v0)
% 9.20/1.97 |
% 9.20/1.97 | GROUND_INST: instantiating (3) with all_38_4, all_38_3, simplifying with (7),
% 9.20/1.97 | (8), (14) gives:
% 9.20/1.97 | (17) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_4, all_38_3)
% 9.20/1.97 | = v0)
% 9.20/1.97 |
% 9.20/1.97 | DELTA: instantiating (17) with fresh symbol all_45_0 gives:
% 9.20/1.97 | (18) ~ (all_45_0 = 0) & apart_point_and_line(all_38_4, all_38_3) =
% 9.20/1.97 | all_45_0
% 9.20/1.97 |
% 9.20/1.97 | ALPHA: (18) implies:
% 9.20/1.97 | (19) ~ (all_45_0 = 0)
% 9.20/1.97 | (20) apart_point_and_line(all_38_4, all_38_3) = all_45_0
% 9.20/1.97 |
% 9.20/1.97 | DELTA: instantiating (16) with fresh symbol all_47_0 gives:
% 9.20/1.97 | (21) ~ (all_47_0 = 0) & convergent_lines(all_38_3, all_38_2) = all_47_0
% 9.20/1.97 |
% 9.20/1.97 | ALPHA: (21) implies:
% 9.20/1.97 | (22) ~ (all_47_0 = 0)
% 9.20/1.97 | (23) convergent_lines(all_38_3, all_38_2) = all_47_0
% 9.20/1.97 |
% 9.20/1.97 | BETA: splitting (15) gives:
% 9.20/1.97 |
% 9.20/1.97 | Case 1:
% 9.20/1.97 | |
% 9.20/1.97 | | (24) distinct_lines(all_38_3, all_38_1) = 0
% 9.20/1.97 | |
% 9.20/1.97 | | GROUND_INST: instantiating (p1) with all_38_3, all_38_1, simplifying with
% 9.20/1.97 | | (8), (10), (24) gives:
% 9.20/1.97 | | (25) convergent_lines(all_38_3, all_38_1) = 0
% 9.20/1.97 | |
% 9.52/1.97 | | GROUND_INST: instantiating (cup1) with all_38_4, all_38_3, all_38_1,
% 9.52/1.97 | | all_45_0, simplifying with (7), (8), (10), (20), (24) gives:
% 9.52/1.97 | | (26) all_45_0 = 0 | ? [v0: any] : ? [v1: any] :
% 9.52/1.97 | | (apart_point_and_line(all_38_4, all_38_1) = v0 &
% 9.52/1.97 | | convergent_lines(all_38_3, all_38_1) = v1 & (v1 = 0 | v0 = 0))
% 9.52/1.97 | |
% 9.52/1.97 | | BETA: splitting (26) gives:
% 9.52/1.97 | |
% 9.52/1.97 | | Case 1:
% 9.52/1.97 | | |
% 9.52/1.97 | | | (27) all_45_0 = 0
% 9.52/1.97 | | |
% 9.52/1.97 | | | REDUCE: (19), (27) imply:
% 9.52/1.97 | | | (28) $false
% 9.52/1.98 | | |
% 9.52/1.98 | | | CLOSE: (28) is inconsistent.
% 9.52/1.98 | | |
% 9.52/1.98 | | Case 2:
% 9.52/1.98 | | |
% 9.52/1.98 | | | (29) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_4,
% 9.52/1.98 | | | all_38_1) = v0 & convergent_lines(all_38_3, all_38_1) = v1 &
% 9.52/1.98 | | | (v1 = 0 | v0 = 0))
% 9.52/1.98 | | |
% 9.52/1.98 | | | DELTA: instantiating (29) with fresh symbols all_65_0, all_65_1 gives:
% 9.52/1.98 | | | (30) apart_point_and_line(all_38_4, all_38_1) = all_65_1 &
% 9.52/1.98 | | | convergent_lines(all_38_3, all_38_1) = all_65_0 & (all_65_0 = 0 |
% 9.52/1.98 | | | all_65_1 = 0)
% 9.52/1.98 | | |
% 9.52/1.98 | | | ALPHA: (30) implies:
% 9.52/1.98 | | | (31) convergent_lines(all_38_3, all_38_1) = all_65_0
% 9.52/1.98 | | |
% 9.52/1.98 | | | GROUND_INST: instantiating (4) with 0, all_65_0, all_38_1, all_38_3,
% 9.52/1.98 | | | simplifying with (25), (31) gives:
% 9.52/1.98 | | | (32) all_65_0 = 0
% 9.52/1.98 | | |
% 9.52/1.98 | | | GROUND_INST: instantiating (ax6) with all_38_3, all_38_1, all_38_2,
% 9.52/1.98 | | | all_47_0, simplifying with (8), (9), (10), (23), (25) gives:
% 9.52/1.98 | | | (33) all_47_0 = 0 | convergent_lines(all_38_1, all_38_2) = 0
% 9.52/1.98 | | |
% 9.52/1.98 | | | BETA: splitting (33) gives:
% 9.52/1.98 | | |
% 9.52/1.98 | | | Case 1:
% 9.52/1.98 | | | |
% 9.52/1.98 | | | | (34) convergent_lines(all_38_1, all_38_2) = 0
% 9.52/1.98 | | | |
% 9.52/1.98 | | | | GROUND_INST: instantiating (cp1) with all_38_4, all_38_2, all_38_1,
% 9.52/1.98 | | | | simplifying with (7), (9), (11), (34) gives:
% 9.52/1.98 | | | | (35) $false
% 9.52/1.98 | | | |
% 9.52/1.98 | | | | CLOSE: (35) is inconsistent.
% 9.52/1.98 | | | |
% 9.52/1.98 | | | Case 2:
% 9.52/1.98 | | | |
% 9.52/1.98 | | | | (36) all_47_0 = 0
% 9.52/1.98 | | | |
% 9.52/1.98 | | | | REDUCE: (22), (36) imply:
% 9.52/1.98 | | | | (37) $false
% 9.52/1.98 | | | |
% 9.52/1.98 | | | | CLOSE: (37) is inconsistent.
% 9.52/1.98 | | | |
% 9.52/1.98 | | | End of split
% 9.52/1.98 | | |
% 9.52/1.98 | | End of split
% 9.52/1.98 | |
% 9.52/1.98 | Case 2:
% 9.52/1.98 | |
% 9.52/1.98 | | (38) all_38_0 = 0
% 9.52/1.98 | |
% 9.52/1.98 | | REDUCE: (6), (38) imply:
% 9.52/1.98 | | (39) $false
% 9.52/1.98 | |
% 9.52/1.98 | | CLOSE: (39) is inconsistent.
% 9.52/1.98 | |
% 9.52/1.98 | End of split
% 9.52/1.98 |
% 9.52/1.98 End of proof
% 9.52/1.98 % SZS output end Proof for theBenchmark
% 9.52/1.98
% 9.52/1.98 1463ms
%------------------------------------------------------------------------------