TSTP Solution File: GEO183+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO183+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n026.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 23:21:58 EDT 2023
% Result : Theorem 6.99s 1.75s
% Output : Proof 9.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO183+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n026.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 22:32:05 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 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 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 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 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
% 2.29/1.10 Prover 1: Preprocessing ...
% 2.29/1.10 Prover 4: Preprocessing ...
% 2.88/1.14 Prover 2: Preprocessing ...
% 2.88/1.14 Prover 6: Preprocessing ...
% 2.88/1.14 Prover 0: Preprocessing ...
% 2.88/1.14 Prover 3: Preprocessing ...
% 2.88/1.14 Prover 5: Preprocessing ...
% 4.48/1.44 Prover 5: Proving ...
% 4.79/1.47 Prover 2: Proving ...
% 4.79/1.47 Prover 3: Constructing countermodel ...
% 4.79/1.48 Prover 1: Constructing countermodel ...
% 4.79/1.48 Prover 6: Constructing countermodel ...
% 5.76/1.60 Prover 4: Constructing countermodel ...
% 5.76/1.63 Prover 0: Proving ...
% 6.99/1.75 Prover 3: proved (1101ms)
% 6.99/1.75
% 6.99/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.99/1.75
% 6.99/1.75 Prover 0: stopped
% 6.99/1.75 Prover 2: stopped
% 6.99/1.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.99/1.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.99/1.76 Prover 6: stopped
% 6.99/1.76 Prover 5: stopped
% 6.99/1.76 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.99/1.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.99/1.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.99/1.81 Prover 13: Preprocessing ...
% 6.99/1.81 Prover 11: Preprocessing ...
% 6.99/1.82 Prover 7: Preprocessing ...
% 6.99/1.82 Prover 10: Preprocessing ...
% 6.99/1.82 Prover 8: Preprocessing ...
% 7.99/1.88 Prover 7: Warning: ignoring some quantifiers
% 7.99/1.89 Prover 13: Warning: ignoring some quantifiers
% 7.99/1.89 Prover 10: Warning: ignoring some quantifiers
% 7.99/1.89 Prover 7: Constructing countermodel ...
% 7.99/1.90 Prover 13: Constructing countermodel ...
% 7.99/1.90 Prover 10: Constructing countermodel ...
% 7.99/1.93 Prover 8: Warning: ignoring some quantifiers
% 7.99/1.94 Prover 8: Constructing countermodel ...
% 8.47/1.97 Prover 1: Found proof (size 61)
% 8.47/1.98 Prover 1: proved (1343ms)
% 8.47/1.98 Prover 10: stopped
% 8.47/1.98 Prover 4: stopped
% 8.47/1.98 Prover 8: stopped
% 8.47/1.98 Prover 7: stopped
% 8.47/1.99 Prover 13: stopped
% 8.47/2.03 Prover 11: Constructing countermodel ...
% 8.47/2.04 Prover 11: stopped
% 8.47/2.04
% 8.47/2.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.47/2.04
% 8.47/2.05 % SZS output start Proof for theBenchmark
% 8.47/2.05 Assumptions after simplification:
% 8.47/2.05 ---------------------------------
% 8.47/2.05
% 8.47/2.05 (apart1)
% 8.47/2.08 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0))
% 8.47/2.08
% 8.47/2.08 (apart5)
% 8.47/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 8.47/2.09 (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | ~ $i(v2)
% 8.47/2.09 | ~ $i(v1) | ~ $i(v0) | distinct_lines(v1, v2) = 0)
% 8.47/2.09
% 8.47/2.09 (ceq2)
% 8.47/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 8.47/2.09 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | ~
% 8.47/2.09 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v0, v2) = 0)
% 8.47/2.09
% 8.47/2.09 (ceq3)
% 8.47/2.09 ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ $i(v1) |
% 8.47/2.09 ~ $i(v0) | distinct_lines(v0, v1) = 0)
% 8.47/2.09
% 8.47/2.09 (con)
% 8.47/2.09 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 8.47/2.09 int] : ? [v6: any] : ? [v7: any] : ( ~ (v5 = 0) & line_connecting(v0, v1)
% 8.47/2.09 = v4 & apart_point_and_line(v1, v2) = v7 & apart_point_and_line(v0, v2) = v6
% 8.47/2.09 & convergent_lines(v2, v3) = 0 & distinct_lines(v2, v4) = v5 &
% 8.47/2.09 distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 8.47/2.09 (v7 = 0 | v6 = 0))
% 8.47/2.09
% 8.47/2.09 (con1)
% 8.47/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.47/2.10 (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ~
% 8.47/2.10 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any]
% 8.47/2.10 : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 &
% 8.47/2.10 distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 8.47/2.10
% 8.47/2.10 (cu1)
% 8.47/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.47/2.10 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 8.47/2.10 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 8.47/2.10 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 8.47/2.10 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 8.47/2.10 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 8.47/2.10
% 8.47/2.10 (function-axioms)
% 8.47/2.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.47/2.11 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) &
% 8.47/2.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.47/2.11 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 8.47/2.11 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 8.47/2.11 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 8.47/2.11 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.47/2.11 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.47/2.11 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 8.47/2.11 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 8.47/2.11 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3,
% 8.47/2.11 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 8.47/2.11 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 8.47/2.11 (distinct_points(v3, v2) = v0))
% 8.47/2.11
% 8.47/2.11 Further assumptions not needed in the proof:
% 8.47/2.11 --------------------------------------------
% 8.47/2.11 apart2, apart3, apart4, apart6, ceq1, con2
% 8.47/2.11
% 8.47/2.11 Those formulas are unsatisfiable:
% 8.47/2.11 ---------------------------------
% 8.47/2.11
% 8.47/2.11 Begin of proof
% 8.47/2.11 |
% 8.47/2.11 | ALPHA: (function-axioms) implies:
% 8.47/2.11 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.47/2.11 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 8.47/2.11 | (distinct_points(v3, v2) = v0))
% 8.47/2.11 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.47/2.11 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 8.47/2.11 | (apart_point_and_line(v3, v2) = v0))
% 8.47/2.11 |
% 9.13/2.11 | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2,
% 9.13/2.11 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives:
% 9.13/2.11 | (3) ~ (all_15_2 = 0) & line_connecting(all_15_7, all_15_6) = all_15_3 &
% 9.13/2.11 | apart_point_and_line(all_15_6, all_15_5) = all_15_0 &
% 9.13/2.11 | apart_point_and_line(all_15_7, all_15_5) = all_15_1 &
% 9.13/2.11 | convergent_lines(all_15_5, all_15_4) = 0 & distinct_lines(all_15_5,
% 9.13/2.11 | all_15_3) = all_15_2 & distinct_points(all_15_7, all_15_6) = 0 &
% 9.13/2.11 | $i(all_15_3) & $i(all_15_4) & $i(all_15_5) & $i(all_15_6) &
% 9.13/2.11 | $i(all_15_7) & (all_15_0 = 0 | all_15_1 = 0)
% 9.13/2.11 |
% 9.13/2.11 | ALPHA: (3) implies:
% 9.13/2.11 | (4) ~ (all_15_2 = 0)
% 9.13/2.11 | (5) $i(all_15_7)
% 9.13/2.11 | (6) $i(all_15_6)
% 9.13/2.12 | (7) $i(all_15_5)
% 9.13/2.12 | (8) $i(all_15_4)
% 9.13/2.12 | (9) $i(all_15_3)
% 9.13/2.12 | (10) distinct_points(all_15_7, all_15_6) = 0
% 9.13/2.12 | (11) distinct_lines(all_15_5, all_15_3) = all_15_2
% 9.13/2.12 | (12) convergent_lines(all_15_5, all_15_4) = 0
% 9.13/2.12 | (13) apart_point_and_line(all_15_7, all_15_5) = all_15_1
% 9.13/2.12 | (14) apart_point_and_line(all_15_6, all_15_5) = all_15_0
% 9.13/2.12 | (15) line_connecting(all_15_7, all_15_6) = all_15_3
% 9.13/2.12 | (16) all_15_0 = 0 | all_15_1 = 0
% 9.13/2.12 |
% 9.13/2.12 | GROUND_INST: instantiating (ceq3) with all_15_5, all_15_4, simplifying with
% 9.13/2.12 | (7), (8), (12) gives:
% 9.13/2.12 | (17) distinct_lines(all_15_5, all_15_4) = 0
% 9.13/2.12 |
% 9.13/2.12 | GROUND_INST: instantiating (apart5) with all_15_5, all_15_4, all_15_3,
% 9.13/2.12 | all_15_2, simplifying with (7), (8), (9), (11), (17) gives:
% 9.13/2.12 | (18) all_15_2 = 0 | distinct_lines(all_15_4, all_15_3) = 0
% 9.13/2.12 |
% 9.13/2.12 | GROUND_INST: instantiating (cu1) with all_15_7, all_15_6, all_15_5, all_15_4,
% 9.13/2.12 | simplifying with (5), (6), (7), (8), (10), (17) gives:
% 9.13/2.12 | (19) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 9.13/2.12 | (apart_point_and_line(all_15_6, all_15_4) = v3 &
% 9.13/2.12 | apart_point_and_line(all_15_6, all_15_5) = v2 &
% 9.13/2.12 | apart_point_and_line(all_15_7, all_15_4) = v1 &
% 9.13/2.12 | apart_point_and_line(all_15_7, all_15_5) = v0 & (v3 = 0 | v2 = 0 |
% 9.13/2.12 | v1 = 0 | v0 = 0))
% 9.13/2.12 |
% 9.13/2.12 | DELTA: instantiating (19) with fresh symbols all_28_0, all_28_1, all_28_2,
% 9.13/2.12 | all_28_3 gives:
% 9.13/2.12 | (20) apart_point_and_line(all_15_6, all_15_4) = all_28_0 &
% 9.13/2.12 | apart_point_and_line(all_15_6, all_15_5) = all_28_1 &
% 9.13/2.12 | apart_point_and_line(all_15_7, all_15_4) = all_28_2 &
% 9.13/2.12 | apart_point_and_line(all_15_7, all_15_5) = all_28_3 & (all_28_0 = 0 |
% 9.13/2.12 | all_28_1 = 0 | all_28_2 = 0 | all_28_3 = 0)
% 9.13/2.12 |
% 9.13/2.12 | ALPHA: (20) implies:
% 9.13/2.12 | (21) apart_point_and_line(all_15_7, all_15_5) = all_28_3
% 9.13/2.12 | (22) apart_point_and_line(all_15_6, all_15_5) = all_28_1
% 9.13/2.12 |
% 9.13/2.12 | BETA: splitting (18) gives:
% 9.13/2.12 |
% 9.13/2.12 | Case 1:
% 9.13/2.12 | |
% 9.13/2.12 | | (23) distinct_lines(all_15_4, all_15_3) = 0
% 9.13/2.12 | |
% 9.13/2.13 | | GROUND_INST: instantiating (2) with all_15_1, all_28_3, all_15_5, all_15_7,
% 9.13/2.13 | | simplifying with (13), (21) gives:
% 9.13/2.13 | | (24) all_28_3 = all_15_1
% 9.13/2.13 | |
% 9.13/2.13 | | GROUND_INST: instantiating (2) with all_15_0, all_28_1, all_15_5, all_15_6,
% 9.13/2.13 | | simplifying with (14), (22) gives:
% 9.13/2.13 | | (25) all_28_1 = all_15_0
% 9.13/2.13 | |
% 9.13/2.13 | | GROUND_INST: instantiating (cu1) with all_15_7, all_15_6, all_15_4,
% 9.13/2.13 | | all_15_3, simplifying with (5), (6), (8), (9), (10), (23)
% 9.13/2.13 | | gives:
% 9.13/2.13 | | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 9.13/2.13 | | (apart_point_and_line(all_15_6, all_15_3) = v3 &
% 9.13/2.13 | | apart_point_and_line(all_15_6, all_15_4) = v2 &
% 9.13/2.13 | | apart_point_and_line(all_15_7, all_15_3) = v1 &
% 9.13/2.13 | | apart_point_and_line(all_15_7, all_15_4) = v0 & (v3 = 0 | v2 = 0 |
% 9.13/2.13 | | v1 = 0 | v0 = 0))
% 9.13/2.13 | |
% 9.13/2.13 | | DELTA: instantiating (26) with fresh symbols all_43_0, all_43_1, all_43_2,
% 9.13/2.13 | | all_43_3 gives:
% 9.13/2.13 | | (27) apart_point_and_line(all_15_6, all_15_3) = all_43_0 &
% 9.13/2.13 | | apart_point_and_line(all_15_6, all_15_4) = all_43_1 &
% 9.13/2.13 | | apart_point_and_line(all_15_7, all_15_3) = all_43_2 &
% 9.13/2.13 | | apart_point_and_line(all_15_7, all_15_4) = all_43_3 & (all_43_0 = 0
% 9.13/2.13 | | | all_43_1 = 0 | all_43_2 = 0 | all_43_3 = 0)
% 9.13/2.13 | |
% 9.13/2.13 | | ALPHA: (27) implies:
% 9.13/2.13 | | (28) apart_point_and_line(all_15_7, all_15_3) = all_43_2
% 9.13/2.13 | | (29) apart_point_and_line(all_15_6, all_15_3) = all_43_0
% 9.13/2.13 | | (30) all_43_0 = 0 | all_43_1 = 0 | all_43_2 = 0 | all_43_3 = 0
% 9.13/2.13 | |
% 9.13/2.13 | | BETA: splitting (16) gives:
% 9.13/2.13 | |
% 9.13/2.13 | | Case 1:
% 9.13/2.13 | | |
% 9.13/2.13 | | | (31) all_15_0 = 0
% 9.13/2.13 | | |
% 9.13/2.13 | | | REDUCE: (14), (31) imply:
% 9.13/2.13 | | | (32) apart_point_and_line(all_15_6, all_15_5) = 0
% 9.13/2.13 | | |
% 9.13/2.13 | | | GROUND_INST: instantiating (ceq2) with all_15_6, all_15_5, all_15_3,
% 9.13/2.13 | | | all_15_2, simplifying with (6), (7), (9), (11), (32) gives:
% 9.13/2.13 | | | (33) all_15_2 = 0 | apart_point_and_line(all_15_6, all_15_3) = 0
% 9.13/2.13 | | |
% 9.13/2.13 | | | BETA: splitting (30) gives:
% 9.13/2.13 | | |
% 9.13/2.13 | | | Case 1:
% 9.13/2.13 | | | |
% 9.13/2.13 | | | | (34) all_43_0 = 0
% 9.13/2.13 | | | |
% 9.13/2.13 | | | | REDUCE: (29), (34) imply:
% 9.13/2.13 | | | | (35) apart_point_and_line(all_15_6, all_15_3) = 0
% 9.13/2.13 | | | |
% 9.13/2.13 | | | | GROUND_INST: instantiating (con1) with all_15_7, all_15_6, all_15_6,
% 9.13/2.13 | | | | all_15_3, simplifying with (5), (6), (15), (35) gives:
% 9.13/2.13 | | | | (36) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 9.13/2.13 | | | | (distinct_points(all_15_6, all_15_6) = v2 &
% 9.13/2.13 | | | | distinct_points(all_15_6, all_15_7) = v1 &
% 9.13/2.13 | | | | distinct_points(all_15_7, all_15_6) = v0 & ( ~ (v0 = 0) | (v2
% 9.13/2.13 | | | | = 0 & v1 = 0)))
% 9.13/2.13 | | | |
% 9.13/2.13 | | | | DELTA: instantiating (36) with fresh symbols all_68_0, all_68_1,
% 9.13/2.13 | | | | all_68_2 gives:
% 9.13/2.13 | | | | (37) distinct_points(all_15_6, all_15_6) = all_68_0 &
% 9.13/2.13 | | | | distinct_points(all_15_6, all_15_7) = all_68_1 &
% 9.13/2.13 | | | | distinct_points(all_15_7, all_15_6) = all_68_2 & ( ~ (all_68_2 =
% 9.13/2.13 | | | | 0) | (all_68_0 = 0 & all_68_1 = 0))
% 9.13/2.13 | | | |
% 9.13/2.13 | | | | ALPHA: (37) implies:
% 9.13/2.13 | | | | (38) distinct_points(all_15_7, all_15_6) = all_68_2
% 9.13/2.13 | | | | (39) distinct_points(all_15_6, all_15_6) = all_68_0
% 9.13/2.13 | | | | (40) ~ (all_68_2 = 0) | (all_68_0 = 0 & all_68_1 = 0)
% 9.13/2.13 | | | |
% 9.13/2.14 | | | | GROUND_INST: instantiating (1) with 0, all_68_2, all_15_6, all_15_7,
% 9.13/2.14 | | | | simplifying with (10), (38) gives:
% 9.13/2.14 | | | | (41) all_68_2 = 0
% 9.13/2.14 | | | |
% 9.13/2.14 | | | | BETA: splitting (40) gives:
% 9.13/2.14 | | | |
% 9.13/2.14 | | | | Case 1:
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | (42) ~ (all_68_2 = 0)
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | REDUCE: (41), (42) imply:
% 9.13/2.14 | | | | | (43) $false
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | CLOSE: (43) is inconsistent.
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | Case 2:
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | (44) all_68_0 = 0 & all_68_1 = 0
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | ALPHA: (44) implies:
% 9.13/2.14 | | | | | (45) all_68_0 = 0
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | REDUCE: (39), (45) imply:
% 9.13/2.14 | | | | | (46) distinct_points(all_15_6, all_15_6) = 0
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | GROUND_INST: instantiating (apart1) with all_15_6, simplifying with
% 9.13/2.14 | | | | | (6), (46) gives:
% 9.13/2.14 | | | | | (47) $false
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | CLOSE: (47) is inconsistent.
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | End of split
% 9.13/2.14 | | | |
% 9.13/2.14 | | | Case 2:
% 9.13/2.14 | | | |
% 9.13/2.14 | | | | (48) ~ (all_43_0 = 0)
% 9.13/2.14 | | | |
% 9.13/2.14 | | | | BETA: splitting (33) gives:
% 9.13/2.14 | | | |
% 9.13/2.14 | | | | Case 1:
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | (49) apart_point_and_line(all_15_6, all_15_3) = 0
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | GROUND_INST: instantiating (2) with all_43_0, 0, all_15_3, all_15_6,
% 9.13/2.14 | | | | | simplifying with (29), (49) gives:
% 9.13/2.14 | | | | | (50) all_43_0 = 0
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | REDUCE: (48), (50) imply:
% 9.13/2.14 | | | | | (51) $false
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | CLOSE: (51) is inconsistent.
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | Case 2:
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | (52) all_15_2 = 0
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | REDUCE: (4), (52) imply:
% 9.13/2.14 | | | | | (53) $false
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | | CLOSE: (53) is inconsistent.
% 9.13/2.14 | | | | |
% 9.13/2.14 | | | | End of split
% 9.13/2.14 | | | |
% 9.13/2.14 | | | End of split
% 9.13/2.14 | | |
% 9.13/2.14 | | Case 2:
% 9.13/2.14 | | |
% 9.13/2.14 | | | (54) all_15_1 = 0
% 9.13/2.14 | | |
% 9.13/2.14 | | | REDUCE: (13), (54) imply:
% 9.13/2.14 | | | (55) apart_point_and_line(all_15_7, all_15_5) = 0
% 9.13/2.14 | | |
% 9.13/2.14 | | | GROUND_INST: instantiating (ceq2) with all_15_7, all_15_5, all_15_3,
% 9.13/2.14 | | | all_15_2, simplifying with (5), (7), (9), (11), (55) gives:
% 9.13/2.14 | | | (56) all_15_2 = 0 | apart_point_and_line(all_15_7, all_15_3) = 0
% 9.13/2.14 | | |
% 9.13/2.14 | | | BETA: splitting (56) gives:
% 9.13/2.14 | | |
% 9.13/2.14 | | | Case 1:
% 9.13/2.14 | | | |
% 9.13/2.14 | | | | (57) apart_point_and_line(all_15_7, all_15_3) = 0
% 9.13/2.14 | | | |
% 9.13/2.14 | | | | GROUND_INST: instantiating (2) with all_43_2, 0, all_15_3, all_15_7,
% 9.13/2.14 | | | | simplifying with (28), (57) gives:
% 9.13/2.14 | | | | (58) all_43_2 = 0
% 9.13/2.14 | | | |
% 9.13/2.14 | | | | GROUND_INST: instantiating (con1) with all_15_7, all_15_6, all_15_7,
% 9.13/2.14 | | | | all_15_3, simplifying with (5), (6), (15), (57) gives:
% 9.13/2.14 | | | | (59) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 9.13/2.14 | | | | (distinct_points(all_15_7, all_15_6) = v2 &
% 9.13/2.14 | | | | distinct_points(all_15_7, all_15_6) = v0 &
% 9.13/2.14 | | | | distinct_points(all_15_7, all_15_7) = v1 & ( ~ (v0 = 0) | (v2
% 9.13/2.14 | | | | = 0 & v1 = 0)))
% 9.13/2.14 | | | |
% 9.13/2.14 | | | | DELTA: instantiating (59) with fresh symbols all_76_0, all_76_1,
% 9.13/2.14 | | | | all_76_2 gives:
% 9.13/2.14 | | | | (60) distinct_points(all_15_7, all_15_6) = all_76_0 &
% 9.13/2.14 | | | | distinct_points(all_15_7, all_15_6) = all_76_2 &
% 9.13/2.14 | | | | distinct_points(all_15_7, all_15_7) = all_76_1 & ( ~ (all_76_2 =
% 9.13/2.14 | | | | 0) | (all_76_0 = 0 & all_76_1 = 0))
% 9.13/2.14 | | | |
% 9.13/2.14 | | | | ALPHA: (60) implies:
% 9.13/2.15 | | | | (61) distinct_points(all_15_7, all_15_7) = all_76_1
% 9.13/2.15 | | | | (62) distinct_points(all_15_7, all_15_6) = all_76_2
% 9.13/2.15 | | | | (63) distinct_points(all_15_7, all_15_6) = all_76_0
% 9.13/2.15 | | | | (64) ~ (all_76_2 = 0) | (all_76_0 = 0 & all_76_1 = 0)
% 9.13/2.15 | | | |
% 9.13/2.15 | | | | GROUND_INST: instantiating (1) with 0, all_76_0, all_15_6, all_15_7,
% 9.13/2.15 | | | | simplifying with (10), (63) gives:
% 9.13/2.15 | | | | (65) all_76_0 = 0
% 9.13/2.15 | | | |
% 9.13/2.15 | | | | GROUND_INST: instantiating (1) with all_76_2, all_76_0, all_15_6,
% 9.13/2.15 | | | | all_15_7, simplifying with (62), (63) gives:
% 9.13/2.15 | | | | (66) all_76_0 = all_76_2
% 9.13/2.15 | | | |
% 9.13/2.15 | | | | COMBINE_EQS: (65), (66) imply:
% 9.13/2.15 | | | | (67) all_76_2 = 0
% 9.13/2.15 | | | |
% 9.13/2.15 | | | | BETA: splitting (64) gives:
% 9.13/2.15 | | | |
% 9.13/2.15 | | | | Case 1:
% 9.13/2.15 | | | | |
% 9.13/2.15 | | | | | (68) ~ (all_76_2 = 0)
% 9.13/2.15 | | | | |
% 9.13/2.15 | | | | | REDUCE: (67), (68) imply:
% 9.13/2.15 | | | | | (69) $false
% 9.13/2.15 | | | | |
% 9.13/2.15 | | | | | CLOSE: (69) is inconsistent.
% 9.13/2.15 | | | | |
% 9.13/2.15 | | | | Case 2:
% 9.13/2.15 | | | | |
% 9.13/2.15 | | | | | (70) all_76_0 = 0 & all_76_1 = 0
% 9.13/2.15 | | | | |
% 9.13/2.15 | | | | | ALPHA: (70) implies:
% 9.13/2.15 | | | | | (71) all_76_1 = 0
% 9.13/2.15 | | | | |
% 9.13/2.15 | | | | | REDUCE: (61), (71) imply:
% 9.13/2.15 | | | | | (72) distinct_points(all_15_7, all_15_7) = 0
% 9.13/2.15 | | | | |
% 9.13/2.15 | | | | | GROUND_INST: instantiating (apart1) with all_15_7, simplifying with
% 9.13/2.15 | | | | | (5), (72) gives:
% 9.13/2.15 | | | | | (73) $false
% 9.13/2.15 | | | | |
% 9.13/2.15 | | | | | CLOSE: (73) is inconsistent.
% 9.13/2.15 | | | | |
% 9.13/2.15 | | | | End of split
% 9.13/2.15 | | | |
% 9.13/2.15 | | | Case 2:
% 9.13/2.15 | | | |
% 9.13/2.15 | | | | (74) all_15_2 = 0
% 9.13/2.15 | | | |
% 9.13/2.15 | | | | REDUCE: (4), (74) imply:
% 9.13/2.15 | | | | (75) $false
% 9.13/2.15 | | | |
% 9.13/2.15 | | | | CLOSE: (75) is inconsistent.
% 9.13/2.15 | | | |
% 9.13/2.15 | | | End of split
% 9.13/2.15 | | |
% 9.13/2.15 | | End of split
% 9.13/2.15 | |
% 9.13/2.15 | Case 2:
% 9.13/2.15 | |
% 9.13/2.15 | | (76) all_15_2 = 0
% 9.13/2.15 | |
% 9.13/2.15 | | REDUCE: (4), (76) imply:
% 9.13/2.15 | | (77) $false
% 9.13/2.15 | |
% 9.13/2.15 | | CLOSE: (77) is inconsistent.
% 9.13/2.15 | |
% 9.13/2.15 | End of split
% 9.13/2.15 |
% 9.13/2.15 End of proof
% 9.13/2.15 % SZS output end Proof for theBenchmark
% 9.13/2.15
% 9.13/2.15 1537ms
%------------------------------------------------------------------------------