TSTP Solution File: GEO179+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO179+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 : n012.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 23:21:54 EDT 2023
% Result : Theorem 6.39s 1.61s
% Output : Proof 8.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO179+2 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 20:41:08 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 2.21/1.06 Prover 1: Preprocessing ...
% 2.21/1.06 Prover 4: Preprocessing ...
% 2.90/1.10 Prover 2: Preprocessing ...
% 2.90/1.10 Prover 0: Preprocessing ...
% 2.90/1.10 Prover 6: Preprocessing ...
% 2.90/1.10 Prover 5: Preprocessing ...
% 2.90/1.10 Prover 3: Preprocessing ...
% 3.59/1.35 Prover 6: Constructing countermodel ...
% 3.59/1.35 Prover 1: Constructing countermodel ...
% 3.59/1.35 Prover 5: Proving ...
% 3.59/1.36 Prover 3: Constructing countermodel ...
% 3.59/1.36 Prover 2: Proving ...
% 4.44/1.43 Prover 4: Constructing countermodel ...
% 5.44/1.47 Prover 0: Proving ...
% 6.39/1.61 Prover 3: proved (980ms)
% 6.39/1.61
% 6.39/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.39/1.61
% 6.39/1.61 Prover 6: stopped
% 6.39/1.61 Prover 2: stopped
% 6.39/1.61 Prover 5: stopped
% 6.39/1.61 Prover 0: stopped
% 6.39/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.39/1.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.39/1.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.39/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.39/1.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.68/1.66 Prover 8: Preprocessing ...
% 6.68/1.67 Prover 13: Preprocessing ...
% 6.68/1.67 Prover 10: Preprocessing ...
% 6.68/1.67 Prover 11: Preprocessing ...
% 6.68/1.68 Prover 7: Preprocessing ...
% 7.13/1.70 Prover 10: Warning: ignoring some quantifiers
% 7.13/1.71 Prover 10: Constructing countermodel ...
% 7.13/1.72 Prover 13: Warning: ignoring some quantifiers
% 7.13/1.72 Prover 13: Constructing countermodel ...
% 7.13/1.73 Prover 7: Warning: ignoring some quantifiers
% 7.13/1.74 Prover 8: Warning: ignoring some quantifiers
% 7.13/1.74 Prover 8: Constructing countermodel ...
% 7.59/1.77 Prover 7: Constructing countermodel ...
% 7.59/1.78 Prover 10: gave up
% 7.59/1.78 Prover 1: Found proof (size 51)
% 7.59/1.78 Prover 1: proved (1165ms)
% 7.59/1.79 Prover 13: stopped
% 7.59/1.79 Prover 7: stopped
% 7.59/1.79 Prover 8: stopped
% 7.59/1.79 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.59/1.79 Prover 4: stopped
% 7.59/1.81 Prover 16: Preprocessing ...
% 7.59/1.82 Prover 16: stopped
% 7.59/1.82 Prover 11: Constructing countermodel ...
% 7.59/1.83 Prover 11: stopped
% 7.59/1.83
% 7.59/1.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.59/1.83
% 7.59/1.84 % SZS output start Proof for theBenchmark
% 7.59/1.84 Assumptions after simplification:
% 7.59/1.84 ---------------------------------
% 7.59/1.84
% 7.59/1.84 (apart1)
% 8.15/1.87 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0))
% 8.15/1.87
% 8.15/1.87 (ceq2)
% 8.15/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 8.15/1.87 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | ~
% 8.15/1.87 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v0, v2) = 0)
% 8.15/1.87
% 8.15/1.87 (con)
% 8.15/1.88 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 8.15/1.88 any] : ? [v6: $i] : ? [v7: any] : (line_connecting(v2, v1) = v6 &
% 8.15/1.88 line_connecting(v2, v0) = v4 & line_connecting(v0, v1) = v3 &
% 8.15/1.88 apart_point_and_line(v2, v3) = 0 & distinct_lines(v3, v6) = v7 &
% 8.15/1.88 distinct_lines(v3, v4) = v5 & distinct_points(v0, v1) = 0 & $i(v6) & $i(v4)
% 8.15/1.88 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v7 = 0) | ~ (v5 = 0)))
% 8.15/1.88
% 8.15/1.88 (con1)
% 8.15/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.15/1.88 (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ~
% 8.15/1.88 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any]
% 8.15/1.88 : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 &
% 8.15/1.88 distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 8.15/1.88
% 8.15/1.88 (function-axioms)
% 8.15/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.15/1.88 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) &
% 8.15/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.15/1.89 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 8.15/1.89 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 8.15/1.89 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 8.15/1.89 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.15/1.89 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.15/1.89 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 8.15/1.89 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 8.15/1.89 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3,
% 8.15/1.89 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 8.15/1.89 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 8.15/1.89 (distinct_points(v3, v2) = v0))
% 8.15/1.89
% 8.15/1.89 Further assumptions not needed in the proof:
% 8.15/1.89 --------------------------------------------
% 8.15/1.89 apart2, apart3, apart4, apart5, apart6, ceq1, ceq3, con2, cu1
% 8.15/1.89
% 8.15/1.89 Those formulas are unsatisfiable:
% 8.15/1.89 ---------------------------------
% 8.15/1.89
% 8.15/1.89 Begin of proof
% 8.15/1.89 |
% 8.15/1.89 | ALPHA: (function-axioms) implies:
% 8.15/1.89 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.15/1.89 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 8.15/1.89 | (distinct_points(v3, v2) = v0))
% 8.15/1.89 |
% 8.15/1.89 | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2,
% 8.15/1.89 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives:
% 8.15/1.89 | (2) line_connecting(all_15_5, all_15_6) = all_15_1 &
% 8.15/1.89 | line_connecting(all_15_5, all_15_7) = all_15_3 &
% 8.15/1.89 | line_connecting(all_15_7, all_15_6) = all_15_4 &
% 8.15/1.89 | apart_point_and_line(all_15_5, all_15_4) = 0 & distinct_lines(all_15_4,
% 8.15/1.89 | all_15_1) = all_15_0 & distinct_lines(all_15_4, all_15_3) = all_15_2
% 8.15/1.89 | & distinct_points(all_15_7, all_15_6) = 0 & $i(all_15_1) & $i(all_15_3)
% 8.15/1.89 | & $i(all_15_4) & $i(all_15_5) & $i(all_15_6) & $i(all_15_7) & ( ~
% 8.15/1.89 | (all_15_0 = 0) | ~ (all_15_2 = 0))
% 8.15/1.89 |
% 8.15/1.89 | ALPHA: (2) implies:
% 8.35/1.90 | (3) $i(all_15_7)
% 8.35/1.90 | (4) $i(all_15_6)
% 8.35/1.90 | (5) $i(all_15_5)
% 8.35/1.90 | (6) $i(all_15_4)
% 8.35/1.90 | (7) $i(all_15_3)
% 8.35/1.90 | (8) $i(all_15_1)
% 8.35/1.90 | (9) distinct_points(all_15_7, all_15_6) = 0
% 8.35/1.90 | (10) distinct_lines(all_15_4, all_15_3) = all_15_2
% 8.35/1.90 | (11) distinct_lines(all_15_4, all_15_1) = all_15_0
% 8.35/1.90 | (12) apart_point_and_line(all_15_5, all_15_4) = 0
% 8.35/1.90 | (13) line_connecting(all_15_7, all_15_6) = all_15_4
% 8.35/1.90 | (14) line_connecting(all_15_5, all_15_7) = all_15_3
% 8.35/1.90 | (15) line_connecting(all_15_5, all_15_6) = all_15_1
% 8.35/1.90 | (16) ~ (all_15_0 = 0) | ~ (all_15_2 = 0)
% 8.35/1.90 |
% 8.35/1.90 | GROUND_INST: instantiating (ceq2) with all_15_5, all_15_4, all_15_1, all_15_0,
% 8.35/1.90 | simplifying with (5), (6), (8), (11), (12) gives:
% 8.35/1.90 | (17) all_15_0 = 0 | apart_point_and_line(all_15_5, all_15_1) = 0
% 8.35/1.90 |
% 8.35/1.90 | GROUND_INST: instantiating (ceq2) with all_15_5, all_15_4, all_15_3, all_15_2,
% 8.35/1.90 | simplifying with (5), (6), (7), (10), (12) gives:
% 8.35/1.90 | (18) all_15_2 = 0 | apart_point_and_line(all_15_5, all_15_3) = 0
% 8.35/1.90 |
% 8.35/1.90 | GROUND_INST: instantiating (con1) with all_15_7, all_15_6, all_15_5, all_15_4,
% 8.35/1.90 | simplifying with (3), (4), (5), (12), (13) gives:
% 8.35/1.90 | (19) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 8.35/1.90 | (distinct_points(all_15_5, all_15_6) = v2 & distinct_points(all_15_5,
% 8.35/1.90 | all_15_7) = v1 & distinct_points(all_15_7, all_15_6) = v0 & ( ~
% 8.35/1.90 | (v0 = 0) | (v2 = 0 & v1 = 0)))
% 8.35/1.90 |
% 8.35/1.90 | DELTA: instantiating (19) with fresh symbols all_22_0, all_22_1, all_22_2
% 8.35/1.90 | gives:
% 8.35/1.91 | (20) distinct_points(all_15_5, all_15_6) = all_22_0 &
% 8.35/1.91 | distinct_points(all_15_5, all_15_7) = all_22_1 &
% 8.35/1.91 | distinct_points(all_15_7, all_15_6) = all_22_2 & ( ~ (all_22_2 = 0) |
% 8.35/1.91 | (all_22_0 = 0 & all_22_1 = 0))
% 8.35/1.91 |
% 8.35/1.91 | ALPHA: (20) implies:
% 8.35/1.91 | (21) distinct_points(all_15_7, all_15_6) = all_22_2
% 8.35/1.91 | (22) distinct_points(all_15_5, all_15_7) = all_22_1
% 8.35/1.91 | (23) distinct_points(all_15_5, all_15_6) = all_22_0
% 8.35/1.91 | (24) ~ (all_22_2 = 0) | (all_22_0 = 0 & all_22_1 = 0)
% 8.35/1.91 |
% 8.35/1.91 | GROUND_INST: instantiating (1) with 0, all_22_2, all_15_6, all_15_7,
% 8.35/1.91 | simplifying with (9), (21) gives:
% 8.35/1.91 | (25) all_22_2 = 0
% 8.35/1.91 |
% 8.35/1.91 | BETA: splitting (24) gives:
% 8.35/1.91 |
% 8.35/1.91 | Case 1:
% 8.35/1.91 | |
% 8.35/1.91 | | (26) ~ (all_22_2 = 0)
% 8.35/1.91 | |
% 8.35/1.91 | | REDUCE: (25), (26) imply:
% 8.35/1.91 | | (27) $false
% 8.35/1.91 | |
% 8.35/1.91 | | CLOSE: (27) is inconsistent.
% 8.35/1.91 | |
% 8.35/1.91 | Case 2:
% 8.35/1.91 | |
% 8.35/1.91 | | (28) all_22_0 = 0 & all_22_1 = 0
% 8.35/1.91 | |
% 8.35/1.91 | | ALPHA: (28) implies:
% 8.35/1.91 | | (29) all_22_1 = 0
% 8.35/1.91 | | (30) all_22_0 = 0
% 8.35/1.91 | |
% 8.35/1.91 | | REDUCE: (23), (30) imply:
% 8.35/1.91 | | (31) distinct_points(all_15_5, all_15_6) = 0
% 8.35/1.91 | |
% 8.35/1.91 | | REDUCE: (22), (29) imply:
% 8.35/1.91 | | (32) distinct_points(all_15_5, all_15_7) = 0
% 8.35/1.91 | |
% 8.35/1.91 | | BETA: splitting (16) gives:
% 8.35/1.91 | |
% 8.35/1.91 | | Case 1:
% 8.35/1.91 | | |
% 8.35/1.91 | | | (33) ~ (all_15_0 = 0)
% 8.35/1.91 | | |
% 8.35/1.91 | | | BETA: splitting (17) gives:
% 8.35/1.91 | | |
% 8.35/1.91 | | | Case 1:
% 8.35/1.91 | | | |
% 8.35/1.91 | | | | (34) apart_point_and_line(all_15_5, all_15_1) = 0
% 8.35/1.91 | | | |
% 8.35/1.91 | | | | GROUND_INST: instantiating (con1) with all_15_5, all_15_6, all_15_5,
% 8.35/1.91 | | | | all_15_1, simplifying with (4), (5), (15), (34) gives:
% 8.35/1.91 | | | | (35) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 8.35/1.91 | | | | (distinct_points(all_15_5, all_15_5) = v1 &
% 8.35/1.91 | | | | distinct_points(all_15_5, all_15_6) = v2 &
% 8.35/1.91 | | | | distinct_points(all_15_5, all_15_6) = v0 & ( ~ (v0 = 0) | (v2
% 8.35/1.91 | | | | = 0 & v1 = 0)))
% 8.35/1.91 | | | |
% 8.35/1.91 | | | | DELTA: instantiating (35) with fresh symbols all_48_0, all_48_1,
% 8.35/1.91 | | | | all_48_2 gives:
% 8.35/1.92 | | | | (36) distinct_points(all_15_5, all_15_5) = all_48_1 &
% 8.35/1.92 | | | | distinct_points(all_15_5, all_15_6) = all_48_0 &
% 8.35/1.92 | | | | distinct_points(all_15_5, all_15_6) = all_48_2 & ( ~ (all_48_2 =
% 8.35/1.92 | | | | 0) | (all_48_0 = 0 & all_48_1 = 0))
% 8.35/1.92 | | | |
% 8.35/1.92 | | | | ALPHA: (36) implies:
% 8.35/1.92 | | | | (37) distinct_points(all_15_5, all_15_6) = all_48_2
% 8.35/1.92 | | | | (38) distinct_points(all_15_5, all_15_6) = all_48_0
% 8.35/1.92 | | | | (39) distinct_points(all_15_5, all_15_5) = all_48_1
% 8.35/1.92 | | | | (40) ~ (all_48_2 = 0) | (all_48_0 = 0 & all_48_1 = 0)
% 8.35/1.92 | | | |
% 8.35/1.92 | | | | GROUND_INST: instantiating (1) with 0, all_48_0, all_15_6, all_15_5,
% 8.35/1.92 | | | | simplifying with (31), (38) gives:
% 8.35/1.92 | | | | (41) all_48_0 = 0
% 8.35/1.92 | | | |
% 8.35/1.92 | | | | GROUND_INST: instantiating (1) with all_48_2, all_48_0, all_15_6,
% 8.35/1.92 | | | | all_15_5, simplifying with (37), (38) gives:
% 8.35/1.92 | | | | (42) all_48_0 = all_48_2
% 8.35/1.92 | | | |
% 8.35/1.92 | | | | COMBINE_EQS: (41), (42) imply:
% 8.35/1.92 | | | | (43) all_48_2 = 0
% 8.35/1.92 | | | |
% 8.35/1.92 | | | | BETA: splitting (40) gives:
% 8.35/1.92 | | | |
% 8.35/1.92 | | | | Case 1:
% 8.35/1.92 | | | | |
% 8.35/1.92 | | | | | (44) ~ (all_48_2 = 0)
% 8.35/1.92 | | | | |
% 8.35/1.92 | | | | | REDUCE: (43), (44) imply:
% 8.35/1.92 | | | | | (45) $false
% 8.35/1.92 | | | | |
% 8.35/1.92 | | | | | CLOSE: (45) is inconsistent.
% 8.35/1.92 | | | | |
% 8.35/1.92 | | | | Case 2:
% 8.35/1.92 | | | | |
% 8.35/1.92 | | | | | (46) all_48_0 = 0 & all_48_1 = 0
% 8.35/1.92 | | | | |
% 8.35/1.92 | | | | | ALPHA: (46) implies:
% 8.35/1.92 | | | | | (47) all_48_1 = 0
% 8.35/1.92 | | | | |
% 8.35/1.92 | | | | | REDUCE: (39), (47) imply:
% 8.35/1.92 | | | | | (48) distinct_points(all_15_5, all_15_5) = 0
% 8.35/1.92 | | | | |
% 8.35/1.92 | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying with
% 8.35/1.92 | | | | | (5), (48) gives:
% 8.35/1.92 | | | | | (49) $false
% 8.35/1.92 | | | | |
% 8.35/1.92 | | | | | CLOSE: (49) is inconsistent.
% 8.35/1.92 | | | | |
% 8.35/1.92 | | | | End of split
% 8.35/1.92 | | | |
% 8.35/1.92 | | | Case 2:
% 8.35/1.92 | | | |
% 8.35/1.92 | | | | (50) all_15_0 = 0
% 8.35/1.92 | | | |
% 8.35/1.92 | | | | REDUCE: (33), (50) imply:
% 8.35/1.92 | | | | (51) $false
% 8.35/1.92 | | | |
% 8.35/1.92 | | | | CLOSE: (51) is inconsistent.
% 8.35/1.92 | | | |
% 8.35/1.92 | | | End of split
% 8.35/1.92 | | |
% 8.35/1.92 | | Case 2:
% 8.35/1.92 | | |
% 8.35/1.92 | | | (52) ~ (all_15_2 = 0)
% 8.35/1.92 | | |
% 8.35/1.92 | | | BETA: splitting (18) gives:
% 8.35/1.92 | | |
% 8.35/1.92 | | | Case 1:
% 8.35/1.92 | | | |
% 8.35/1.92 | | | | (53) apart_point_and_line(all_15_5, all_15_3) = 0
% 8.35/1.92 | | | |
% 8.35/1.92 | | | | GROUND_INST: instantiating (con1) with all_15_5, all_15_7, all_15_5,
% 8.35/1.92 | | | | all_15_3, simplifying with (3), (5), (14), (53) gives:
% 8.35/1.92 | | | | (54) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 8.35/1.92 | | | | (distinct_points(all_15_5, all_15_5) = v1 &
% 8.35/1.92 | | | | distinct_points(all_15_5, all_15_7) = v2 &
% 8.35/1.92 | | | | distinct_points(all_15_5, all_15_7) = v0 & ( ~ (v0 = 0) | (v2
% 8.35/1.92 | | | | = 0 & v1 = 0)))
% 8.35/1.92 | | | |
% 8.35/1.92 | | | | DELTA: instantiating (54) with fresh symbols all_48_0, all_48_1,
% 8.35/1.92 | | | | all_48_2 gives:
% 8.35/1.92 | | | | (55) distinct_points(all_15_5, all_15_5) = all_48_1 &
% 8.35/1.92 | | | | distinct_points(all_15_5, all_15_7) = all_48_0 &
% 8.35/1.92 | | | | distinct_points(all_15_5, all_15_7) = all_48_2 & ( ~ (all_48_2 =
% 8.35/1.92 | | | | 0) | (all_48_0 = 0 & all_48_1 = 0))
% 8.35/1.92 | | | |
% 8.35/1.92 | | | | ALPHA: (55) implies:
% 8.35/1.92 | | | | (56) distinct_points(all_15_5, all_15_7) = all_48_2
% 8.35/1.92 | | | | (57) distinct_points(all_15_5, all_15_7) = all_48_0
% 8.35/1.92 | | | | (58) distinct_points(all_15_5, all_15_5) = all_48_1
% 8.35/1.92 | | | | (59) ~ (all_48_2 = 0) | (all_48_0 = 0 & all_48_1 = 0)
% 8.35/1.92 | | | |
% 8.35/1.93 | | | | GROUND_INST: instantiating (1) with 0, all_48_0, all_15_7, all_15_5,
% 8.35/1.93 | | | | simplifying with (32), (57) gives:
% 8.35/1.93 | | | | (60) all_48_0 = 0
% 8.35/1.93 | | | |
% 8.35/1.93 | | | | GROUND_INST: instantiating (1) with all_48_2, all_48_0, all_15_7,
% 8.35/1.93 | | | | all_15_5, simplifying with (56), (57) gives:
% 8.35/1.93 | | | | (61) all_48_0 = all_48_2
% 8.35/1.93 | | | |
% 8.35/1.93 | | | | COMBINE_EQS: (60), (61) imply:
% 8.35/1.93 | | | | (62) all_48_2 = 0
% 8.35/1.93 | | | |
% 8.35/1.93 | | | | SIMP: (62) implies:
% 8.35/1.93 | | | | (63) all_48_2 = 0
% 8.35/1.93 | | | |
% 8.35/1.93 | | | | BETA: splitting (59) gives:
% 8.35/1.93 | | | |
% 8.35/1.93 | | | | Case 1:
% 8.35/1.93 | | | | |
% 8.35/1.93 | | | | | (64) ~ (all_48_2 = 0)
% 8.35/1.93 | | | | |
% 8.35/1.93 | | | | | REDUCE: (63), (64) imply:
% 8.35/1.93 | | | | | (65) $false
% 8.35/1.93 | | | | |
% 8.35/1.93 | | | | | CLOSE: (65) is inconsistent.
% 8.35/1.93 | | | | |
% 8.35/1.93 | | | | Case 2:
% 8.35/1.93 | | | | |
% 8.35/1.93 | | | | | (66) all_48_0 = 0 & all_48_1 = 0
% 8.35/1.93 | | | | |
% 8.35/1.93 | | | | | ALPHA: (66) implies:
% 8.35/1.93 | | | | | (67) all_48_1 = 0
% 8.35/1.93 | | | | |
% 8.35/1.93 | | | | | REDUCE: (58), (67) imply:
% 8.35/1.93 | | | | | (68) distinct_points(all_15_5, all_15_5) = 0
% 8.35/1.93 | | | | |
% 8.35/1.93 | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying with
% 8.35/1.93 | | | | | (5), (68) gives:
% 8.35/1.93 | | | | | (69) $false
% 8.35/1.93 | | | | |
% 8.35/1.93 | | | | | CLOSE: (69) is inconsistent.
% 8.35/1.93 | | | | |
% 8.35/1.93 | | | | End of split
% 8.35/1.93 | | | |
% 8.35/1.93 | | | Case 2:
% 8.35/1.93 | | | |
% 8.35/1.93 | | | | (70) all_15_2 = 0
% 8.35/1.93 | | | |
% 8.35/1.93 | | | | REDUCE: (52), (70) imply:
% 8.35/1.93 | | | | (71) $false
% 8.35/1.93 | | | |
% 8.35/1.93 | | | | CLOSE: (71) is inconsistent.
% 8.35/1.93 | | | |
% 8.35/1.93 | | | End of split
% 8.35/1.93 | | |
% 8.35/1.93 | | End of split
% 8.35/1.93 | |
% 8.35/1.93 | End of split
% 8.35/1.93 |
% 8.35/1.93 End of proof
% 8.35/1.93 % SZS output end Proof for theBenchmark
% 8.35/1.93
% 8.35/1.93 1333ms
%------------------------------------------------------------------------------