TSTP Solution File: GEO203+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO203+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 23:22:15 EDT 2023
% Result : Theorem 5.54s 1.44s
% Output : Proof 7.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO203+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n011.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 21:47:11 EDT 2023
% 0.13/0.35 % 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/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.39/1.03 Prover 1: Preprocessing ...
% 2.39/1.03 Prover 4: Preprocessing ...
% 2.39/1.07 Prover 2: Preprocessing ...
% 2.39/1.07 Prover 6: Preprocessing ...
% 2.39/1.07 Prover 0: Preprocessing ...
% 2.39/1.07 Prover 5: Preprocessing ...
% 2.39/1.07 Prover 3: Preprocessing ...
% 4.31/1.28 Prover 5: Proving ...
% 4.31/1.29 Prover 2: Proving ...
% 4.31/1.34 Prover 3: Constructing countermodel ...
% 4.93/1.35 Prover 1: Constructing countermodel ...
% 4.93/1.36 Prover 6: Constructing countermodel ...
% 5.54/1.43 Prover 2: proved (798ms)
% 5.54/1.44
% 5.54/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.54/1.44
% 5.54/1.44 Prover 6: stopped
% 5.66/1.45 Prover 3: stopped
% 5.66/1.45 Prover 5: stopped
% 5.66/1.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.66/1.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.66/1.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.66/1.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.66/1.49 Prover 0: Proving ...
% 5.66/1.49 Prover 8: Preprocessing ...
% 5.66/1.49 Prover 10: Preprocessing ...
% 5.66/1.49 Prover 4: Constructing countermodel ...
% 5.66/1.50 Prover 11: Preprocessing ...
% 5.66/1.50 Prover 7: Preprocessing ...
% 5.66/1.51 Prover 0: stopped
% 5.66/1.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.16/1.54 Prover 13: Preprocessing ...
% 6.16/1.55 Prover 7: Warning: ignoring some quantifiers
% 6.16/1.56 Prover 7: Constructing countermodel ...
% 6.16/1.56 Prover 10: Warning: ignoring some quantifiers
% 6.50/1.57 Prover 10: Constructing countermodel ...
% 6.50/1.60 Prover 13: Warning: ignoring some quantifiers
% 6.50/1.61 Prover 8: Warning: ignoring some quantifiers
% 6.50/1.62 Prover 13: Constructing countermodel ...
% 6.50/1.62 Prover 8: Constructing countermodel ...
% 6.50/1.64 Prover 1: Found proof (size 37)
% 6.50/1.64 Prover 1: proved (1008ms)
% 6.50/1.64 Prover 8: stopped
% 6.50/1.64 Prover 7: stopped
% 6.50/1.64 Prover 13: stopped
% 6.50/1.64 Prover 10: stopped
% 6.50/1.64 Prover 4: stopped
% 7.32/1.69 Prover 11: Constructing countermodel ...
% 7.32/1.70 Prover 11: stopped
% 7.32/1.70
% 7.32/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.32/1.70
% 7.32/1.70 % SZS output start Proof for theBenchmark
% 7.32/1.71 Assumptions after simplification:
% 7.32/1.71 ---------------------------------
% 7.32/1.71
% 7.32/1.71 (ci1)
% 7.55/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 7.55/1.73 ~ (apart_point_and_line(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 7.55/1.73 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 7.55/1.73
% 7.55/1.73 (ci2)
% 7.55/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 7.55/1.74 ~ (apart_point_and_line(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 7.55/1.74 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 7.55/1.74
% 7.55/1.74 (ci3)
% 7.55/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 7.55/1.74 v2) | ~ (apart_point_and_line(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 7.55/1.74 [v3: int] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 7.55/1.74
% 7.55/1.74 (con)
% 7.55/1.74 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.55/1.74 $i] : (intersection_point(v0, v2) = v4 & intersection_point(v0, v1) = v3 &
% 7.55/1.74 line_connecting(v3, v4) = v5 & convergent_lines(v0, v2) = 0 &
% 7.55/1.74 convergent_lines(v0, v1) = 0 & distinct_lines(v5, v0) = 0 &
% 7.55/1.74 distinct_points(v3, v4) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 7.55/1.74 $i(v0))
% 7.55/1.74
% 7.55/1.74 (cu1)
% 7.55/1.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 7.55/1.75 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 7.55/1.75 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 7.55/1.75 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 7.55/1.75 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 7.55/1.75 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 7.55/1.75
% 7.55/1.75 (function-axioms)
% 7.55/1.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.55/1.75 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) &
% 7.55/1.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.55/1.75 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 7.55/1.75 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.55/1.75 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 7.55/1.75 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.55/1.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.55/1.75 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 7.55/1.75 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.55/1.75 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3,
% 7.55/1.75 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 7.55/1.75 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 7.55/1.75 (distinct_points(v3, v2) = v0))
% 7.55/1.75
% 7.55/1.75 Further assumptions not needed in the proof:
% 7.55/1.75 --------------------------------------------
% 7.55/1.75 apart1, apart2, apart3, apart4, apart5, ax6, ceq1, ceq2, ceq3, ci4
% 7.55/1.75
% 7.55/1.75 Those formulas are unsatisfiable:
% 7.55/1.75 ---------------------------------
% 7.55/1.75
% 7.55/1.75 Begin of proof
% 7.55/1.76 |
% 7.55/1.76 | ALPHA: (function-axioms) implies:
% 7.55/1.76 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.55/1.76 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 7.55/1.76 | (distinct_points(v3, v2) = v0))
% 7.55/1.76 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.55/1.76 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 7.55/1.76 | (convergent_lines(v3, v2) = v0))
% 7.55/1.76 |
% 7.55/1.76 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2,
% 7.55/1.76 | all_17_3, all_17_4, all_17_5 gives:
% 7.55/1.76 | (3) intersection_point(all_17_5, all_17_3) = all_17_1 &
% 7.55/1.76 | intersection_point(all_17_5, all_17_4) = all_17_2 &
% 7.55/1.76 | line_connecting(all_17_2, all_17_1) = all_17_0 &
% 7.55/1.76 | convergent_lines(all_17_5, all_17_3) = 0 & convergent_lines(all_17_5,
% 7.55/1.76 | all_17_4) = 0 & distinct_lines(all_17_0, all_17_5) = 0 &
% 7.55/1.76 | distinct_points(all_17_2, all_17_1) = 0 & $i(all_17_0) & $i(all_17_1) &
% 7.55/1.76 | $i(all_17_2) & $i(all_17_3) & $i(all_17_4) & $i(all_17_5)
% 7.55/1.76 |
% 7.55/1.76 | ALPHA: (3) implies:
% 7.55/1.77 | (4) $i(all_17_5)
% 7.55/1.77 | (5) $i(all_17_4)
% 7.55/1.77 | (6) $i(all_17_3)
% 7.55/1.77 | (7) $i(all_17_2)
% 7.55/1.77 | (8) $i(all_17_1)
% 7.55/1.77 | (9) $i(all_17_0)
% 7.55/1.77 | (10) distinct_points(all_17_2, all_17_1) = 0
% 7.55/1.77 | (11) distinct_lines(all_17_0, all_17_5) = 0
% 7.55/1.77 | (12) convergent_lines(all_17_5, all_17_4) = 0
% 7.55/1.77 | (13) convergent_lines(all_17_5, all_17_3) = 0
% 7.55/1.77 | (14) line_connecting(all_17_2, all_17_1) = all_17_0
% 7.55/1.77 | (15) intersection_point(all_17_5, all_17_4) = all_17_2
% 7.55/1.77 | (16) intersection_point(all_17_5, all_17_3) = all_17_1
% 7.55/1.77 |
% 7.55/1.77 | GROUND_INST: instantiating (cu1) with all_17_2, all_17_1, all_17_0, all_17_5,
% 7.55/1.77 | simplifying with (4), (7), (8), (9), (10), (11) gives:
% 7.55/1.77 | (17) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 7.55/1.77 | (apart_point_and_line(all_17_1, all_17_0) = v2 &
% 7.55/1.77 | apart_point_and_line(all_17_1, all_17_5) = v3 &
% 7.55/1.77 | apart_point_and_line(all_17_2, all_17_0) = v0 &
% 7.55/1.77 | apart_point_and_line(all_17_2, all_17_5) = v1 & (v3 = 0 | v2 = 0 |
% 7.55/1.77 | v1 = 0 | v0 = 0))
% 7.55/1.77 |
% 7.55/1.77 | DELTA: instantiating (17) with fresh symbols all_24_0, all_24_1, all_24_2,
% 7.55/1.77 | all_24_3 gives:
% 7.55/1.77 | (18) apart_point_and_line(all_17_1, all_17_0) = all_24_1 &
% 7.55/1.77 | apart_point_and_line(all_17_1, all_17_5) = all_24_0 &
% 7.55/1.77 | apart_point_and_line(all_17_2, all_17_0) = all_24_3 &
% 7.55/1.77 | apart_point_and_line(all_17_2, all_17_5) = all_24_2 & (all_24_0 = 0 |
% 7.55/1.77 | all_24_1 = 0 | all_24_2 = 0 | all_24_3 = 0)
% 7.55/1.77 |
% 7.55/1.77 | ALPHA: (18) implies:
% 7.55/1.77 | (19) apart_point_and_line(all_17_2, all_17_5) = all_24_2
% 7.55/1.77 | (20) apart_point_and_line(all_17_2, all_17_0) = all_24_3
% 7.55/1.77 | (21) apart_point_and_line(all_17_1, all_17_5) = all_24_0
% 7.55/1.77 | (22) apart_point_and_line(all_17_1, all_17_0) = all_24_1
% 7.55/1.77 | (23) all_24_0 = 0 | all_24_1 = 0 | all_24_2 = 0 | all_24_3 = 0
% 7.55/1.77 |
% 7.55/1.77 | BETA: splitting (23) gives:
% 7.55/1.77 |
% 7.55/1.78 | Case 1:
% 7.55/1.78 | |
% 7.55/1.78 | | (24) all_24_0 = 0
% 7.55/1.78 | |
% 7.55/1.78 | | REDUCE: (21), (24) imply:
% 7.55/1.78 | | (25) apart_point_and_line(all_17_1, all_17_5) = 0
% 7.55/1.78 | |
% 7.55/1.78 | | GROUND_INST: instantiating (ci3) with all_17_5, all_17_3, all_17_1,
% 7.55/1.78 | | simplifying with (4), (6), (16), (25) gives:
% 7.55/1.78 | | (26) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_17_5, all_17_3) =
% 7.55/1.78 | | v0)
% 7.55/1.78 | |
% 7.55/1.78 | | DELTA: instantiating (26) with fresh symbol all_38_0 gives:
% 7.55/1.78 | | (27) ~ (all_38_0 = 0) & convergent_lines(all_17_5, all_17_3) = all_38_0
% 7.55/1.78 | |
% 7.55/1.78 | | ALPHA: (27) implies:
% 7.55/1.78 | | (28) ~ (all_38_0 = 0)
% 7.55/1.78 | | (29) convergent_lines(all_17_5, all_17_3) = all_38_0
% 7.55/1.78 | |
% 7.55/1.78 | | GROUND_INST: instantiating (2) with 0, all_38_0, all_17_3, all_17_5,
% 7.55/1.78 | | simplifying with (13), (29) gives:
% 7.55/1.78 | | (30) all_38_0 = 0
% 7.55/1.78 | |
% 7.55/1.78 | | REDUCE: (28), (30) imply:
% 7.55/1.78 | | (31) $false
% 7.55/1.78 | |
% 7.55/1.78 | | CLOSE: (31) is inconsistent.
% 7.55/1.78 | |
% 7.55/1.78 | Case 2:
% 7.55/1.78 | |
% 7.55/1.78 | | (32) all_24_1 = 0 | all_24_2 = 0 | all_24_3 = 0
% 7.55/1.78 | |
% 7.55/1.78 | | BETA: splitting (32) gives:
% 7.55/1.78 | |
% 7.55/1.78 | | Case 1:
% 7.55/1.78 | | |
% 7.55/1.78 | | | (33) all_24_1 = 0
% 7.55/1.78 | | |
% 7.55/1.78 | | | REDUCE: (22), (33) imply:
% 7.55/1.78 | | | (34) apart_point_and_line(all_17_1, all_17_0) = 0
% 7.55/1.78 | | |
% 7.55/1.78 | | | GROUND_INST: instantiating (ci2) with all_17_2, all_17_1, all_17_0,
% 7.55/1.78 | | | simplifying with (7), (8), (14), (34) gives:
% 7.55/1.78 | | | (35) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_2, all_17_1)
% 7.55/1.78 | | | = v0)
% 7.55/1.78 | | |
% 7.55/1.78 | | | DELTA: instantiating (35) with fresh symbol all_45_0 gives:
% 7.55/1.78 | | | (36) ~ (all_45_0 = 0) & distinct_points(all_17_2, all_17_1) = all_45_0
% 7.55/1.78 | | |
% 7.55/1.78 | | | ALPHA: (36) implies:
% 7.55/1.78 | | | (37) ~ (all_45_0 = 0)
% 7.55/1.78 | | | (38) distinct_points(all_17_2, all_17_1) = all_45_0
% 7.55/1.78 | | |
% 7.55/1.78 | | | GROUND_INST: instantiating (1) with 0, all_45_0, all_17_1, all_17_2,
% 7.55/1.78 | | | simplifying with (10), (38) gives:
% 7.55/1.78 | | | (39) all_45_0 = 0
% 7.55/1.78 | | |
% 7.55/1.78 | | | REDUCE: (37), (39) imply:
% 7.55/1.79 | | | (40) $false
% 7.55/1.79 | | |
% 7.55/1.79 | | | CLOSE: (40) is inconsistent.
% 7.55/1.79 | | |
% 7.55/1.79 | | Case 2:
% 7.55/1.79 | | |
% 7.55/1.79 | | | (41) all_24_2 = 0 | all_24_3 = 0
% 7.55/1.79 | | |
% 7.55/1.79 | | | BETA: splitting (41) gives:
% 7.55/1.79 | | |
% 7.55/1.79 | | | Case 1:
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | (42) all_24_2 = 0
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | REDUCE: (19), (42) imply:
% 7.55/1.79 | | | | (43) apart_point_and_line(all_17_2, all_17_5) = 0
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | GROUND_INST: instantiating (ci3) with all_17_5, all_17_4, all_17_2,
% 7.55/1.79 | | | | simplifying with (4), (5), (15), (43) gives:
% 7.55/1.79 | | | | (44) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_17_5,
% 7.55/1.79 | | | | all_17_4) = v0)
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | DELTA: instantiating (44) with fresh symbol all_52_0 gives:
% 7.55/1.79 | | | | (45) ~ (all_52_0 = 0) & convergent_lines(all_17_5, all_17_4) =
% 7.55/1.79 | | | | all_52_0
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | ALPHA: (45) implies:
% 7.55/1.79 | | | | (46) ~ (all_52_0 = 0)
% 7.55/1.79 | | | | (47) convergent_lines(all_17_5, all_17_4) = all_52_0
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | GROUND_INST: instantiating (2) with 0, all_52_0, all_17_4, all_17_5,
% 7.55/1.79 | | | | simplifying with (12), (47) gives:
% 7.55/1.79 | | | | (48) all_52_0 = 0
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | REDUCE: (46), (48) imply:
% 7.55/1.79 | | | | (49) $false
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | CLOSE: (49) is inconsistent.
% 7.55/1.79 | | | |
% 7.55/1.79 | | | Case 2:
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | (50) all_24_3 = 0
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | REDUCE: (20), (50) imply:
% 7.55/1.79 | | | | (51) apart_point_and_line(all_17_2, all_17_0) = 0
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | GROUND_INST: instantiating (ci1) with all_17_2, all_17_1, all_17_0,
% 7.55/1.79 | | | | simplifying with (7), (8), (14), (51) gives:
% 7.55/1.79 | | | | (52) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_2,
% 7.55/1.79 | | | | all_17_1) = v0)
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | DELTA: instantiating (52) with fresh symbol all_52_0 gives:
% 7.55/1.79 | | | | (53) ~ (all_52_0 = 0) & distinct_points(all_17_2, all_17_1) =
% 7.55/1.79 | | | | all_52_0
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | ALPHA: (53) implies:
% 7.55/1.79 | | | | (54) ~ (all_52_0 = 0)
% 7.55/1.79 | | | | (55) distinct_points(all_17_2, all_17_1) = all_52_0
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | GROUND_INST: instantiating (1) with 0, all_52_0, all_17_1, all_17_2,
% 7.55/1.79 | | | | simplifying with (10), (55) gives:
% 7.55/1.79 | | | | (56) all_52_0 = 0
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | REDUCE: (54), (56) imply:
% 7.55/1.79 | | | | (57) $false
% 7.55/1.79 | | | |
% 7.55/1.79 | | | | CLOSE: (57) is inconsistent.
% 7.55/1.79 | | | |
% 7.55/1.79 | | | End of split
% 7.55/1.79 | | |
% 7.55/1.79 | | End of split
% 7.55/1.79 | |
% 7.55/1.79 | End of split
% 7.55/1.79 |
% 7.55/1.79 End of proof
% 7.55/1.79 % SZS output end Proof for theBenchmark
% 7.55/1.79
% 7.55/1.79 1185ms
%------------------------------------------------------------------------------