TSTP Solution File: GEO220+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO220+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 : 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 23:22:29 EDT 2023
% Result : Theorem 5.66s 1.57s
% Output : Proof 8.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO220+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % 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 22:37:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.58/1.08 Prover 1: Preprocessing ...
% 2.64/1.09 Prover 4: Preprocessing ...
% 2.89/1.12 Prover 2: Preprocessing ...
% 2.89/1.12 Prover 5: Preprocessing ...
% 2.89/1.12 Prover 3: Preprocessing ...
% 2.89/1.12 Prover 6: Preprocessing ...
% 2.89/1.12 Prover 0: Preprocessing ...
% 3.97/1.39 Prover 2: Proving ...
% 3.97/1.40 Prover 5: Proving ...
% 3.97/1.43 Prover 3: Constructing countermodel ...
% 3.97/1.43 Prover 6: Constructing countermodel ...
% 3.97/1.44 Prover 1: Constructing countermodel ...
% 5.66/1.57 Prover 6: proved (941ms)
% 5.66/1.57
% 5.66/1.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.66/1.57
% 5.66/1.57 Prover 3: proved (947ms)
% 5.66/1.57
% 5.66/1.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.66/1.57
% 5.66/1.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.66/1.58 Prover 5: stopped
% 5.66/1.58 Prover 2: stopped
% 5.66/1.60 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.66/1.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.66/1.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.21/1.63 Prover 10: Preprocessing ...
% 6.21/1.63 Prover 7: Preprocessing ...
% 6.21/1.65 Prover 11: Preprocessing ...
% 6.21/1.65 Prover 8: Preprocessing ...
% 6.21/1.67 Prover 7: Warning: ignoring some quantifiers
% 6.21/1.67 Prover 4: Constructing countermodel ...
% 6.71/1.69 Prover 7: Constructing countermodel ...
% 6.71/1.69 Prover 10: Warning: ignoring some quantifiers
% 6.71/1.71 Prover 10: Constructing countermodel ...
% 6.71/1.71 Prover 0: Proving ...
% 6.71/1.73 Prover 0: stopped
% 6.71/1.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.71/1.75 Prover 8: Warning: ignoring some quantifiers
% 6.71/1.75 Prover 8: Constructing countermodel ...
% 6.71/1.76 Prover 13: Preprocessing ...
% 7.59/1.79 Prover 10: gave up
% 7.59/1.82 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.84/1.82 Prover 13: Warning: ignoring some quantifiers
% 7.92/1.83 Prover 13: Constructing countermodel ...
% 7.92/1.84 Prover 16: Preprocessing ...
% 7.92/1.84 Prover 1: Found proof (size 24)
% 7.92/1.84 Prover 1: proved (1218ms)
% 7.92/1.84 Prover 8: stopped
% 7.92/1.84 Prover 7: stopped
% 7.92/1.84 Prover 4: stopped
% 7.92/1.85 Prover 13: stopped
% 7.92/1.85 Prover 16: stopped
% 7.92/1.91 Prover 11: Constructing countermodel ...
% 7.92/1.92 Prover 11: stopped
% 7.92/1.92
% 7.92/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.92/1.92
% 7.92/1.93 % SZS output start Proof for theBenchmark
% 7.92/1.93 Assumptions after simplification:
% 7.92/1.93 ---------------------------------
% 7.92/1.93
% 7.92/1.93 (con)
% 7.92/1.96 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( ~
% 7.92/1.96 (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v0, v2) = v4 &
% 7.92/1.96 unorthogonal_lines(v0, v1) = v3 & convergent_lines(v1, v2) = 0 & $i(v2) &
% 7.92/1.96 $i(v1) & $i(v0))
% 7.92/1.96
% 7.92/1.96 (cotno1)
% 7.92/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 7.92/1.96 (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) |
% 7.92/1.96 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7:
% 7.92/1.96 any] : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 &
% 7.92/1.97 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 &
% 7.92/1.97 convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4
% 7.92/1.97 = 0) | (v5 = 0 & v3 = 0))))
% 7.92/1.97
% 7.92/1.97 (couo1)
% 7.92/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 7.92/1.97 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~
% 7.92/1.97 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 7.92/1.97 [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))
% 7.92/1.97
% 7.92/1.97 (function-axioms)
% 8.66/1.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.66/1.97 [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 8.66/1.97 (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 8.66/1.97 : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 8.66/1.97 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 8.66/1.97 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 8.66/1.97 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.66/1.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.66/1.97 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 8.66/1.97 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.66/1.97 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 8.66/1.97 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.66/1.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.66/1.97 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 8.66/1.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.66/1.97 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 8.66/1.97 v0))
% 8.66/1.97
% 8.66/1.97 Further assumptions not needed in the proof:
% 8.66/1.97 --------------------------------------------
% 8.66/1.98 apart1, apart2, apart3, apart4, apart5, apart6, ceq1, ceq2, ceq3, coipo1, con1,
% 8.66/1.98 con2, cu1
% 8.66/1.98
% 8.66/1.98 Those formulas are unsatisfiable:
% 8.66/1.98 ---------------------------------
% 8.66/1.98
% 8.66/1.98 Begin of proof
% 8.66/1.98 |
% 8.66/1.98 | ALPHA: (function-axioms) implies:
% 8.66/1.98 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.66/1.98 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 8.66/1.98 | (convergent_lines(v3, v2) = v0))
% 8.66/1.98 |
% 8.66/1.98 | DELTA: instantiating (con) with fresh symbols all_18_0, all_18_1, all_18_2,
% 8.66/1.98 | all_18_3, all_18_4 gives:
% 8.66/1.98 | (2) ~ (all_18_0 = 0) & ~ (all_18_1 = 0) & unorthogonal_lines(all_18_4,
% 8.66/1.98 | all_18_2) = all_18_0 & unorthogonal_lines(all_18_4, all_18_3) =
% 8.66/1.98 | all_18_1 & convergent_lines(all_18_3, all_18_2) = 0 & $i(all_18_2) &
% 8.66/1.98 | $i(all_18_3) & $i(all_18_4)
% 8.66/1.98 |
% 8.66/1.98 | ALPHA: (2) implies:
% 8.66/1.98 | (3) ~ (all_18_1 = 0)
% 8.66/1.98 | (4) ~ (all_18_0 = 0)
% 8.66/1.98 | (5) $i(all_18_4)
% 8.66/1.98 | (6) $i(all_18_3)
% 8.66/1.98 | (7) $i(all_18_2)
% 8.66/1.98 | (8) convergent_lines(all_18_3, all_18_2) = 0
% 8.66/1.98 | (9) unorthogonal_lines(all_18_4, all_18_3) = all_18_1
% 8.66/1.98 | (10) unorthogonal_lines(all_18_4, all_18_2) = all_18_0
% 8.66/1.98 |
% 8.66/1.98 | GROUND_INST: instantiating (couo1) with all_18_4, all_18_3, all_18_2,
% 8.66/1.98 | all_18_1, all_18_0, simplifying with (5), (6), (7), (9), (10)
% 8.66/1.98 | gives:
% 8.66/1.99 | (11) all_18_0 = 0 | all_18_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 8.66/1.99 | convergent_lines(all_18_3, all_18_2) = v0)
% 8.66/1.99 |
% 8.66/1.99 | GROUND_INST: instantiating (cotno1) with all_18_4, all_18_3, all_18_2,
% 8.66/1.99 | all_18_1, all_18_0, simplifying with (5), (6), (7), (9), (10)
% 8.66/1.99 | gives:
% 8.66/1.99 | (12) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 8.66/1.99 | (unorthogonal_lines(all_18_3, all_18_2) = v3 &
% 8.66/1.99 | convergent_lines(all_18_3, all_18_2) = v2 &
% 8.66/1.99 | convergent_lines(all_18_4, all_18_2) = v1 &
% 8.66/1.99 | convergent_lines(all_18_4, all_18_3) = v0 & ( ~ (v3 = 0) | ~ (v2 =
% 8.66/1.99 | 0) | (v1 = 0 & all_18_0 = 0) | (v0 = 0 & all_18_1 = 0)))
% 8.66/1.99 |
% 8.66/1.99 | DELTA: instantiating (12) with fresh symbols all_27_0, all_27_1, all_27_2,
% 8.66/1.99 | all_27_3 gives:
% 8.66/1.99 | (13) unorthogonal_lines(all_18_3, all_18_2) = all_27_0 &
% 8.66/1.99 | convergent_lines(all_18_3, all_18_2) = all_27_1 &
% 8.66/1.99 | convergent_lines(all_18_4, all_18_2) = all_27_2 &
% 8.66/1.99 | convergent_lines(all_18_4, all_18_3) = all_27_3 & ( ~ (all_27_0 = 0) |
% 8.66/1.99 | ~ (all_27_1 = 0) | (all_27_2 = 0 & all_18_0 = 0) | (all_27_3 = 0 &
% 8.66/1.99 | all_18_1 = 0))
% 8.66/1.99 |
% 8.66/1.99 | ALPHA: (13) implies:
% 8.66/1.99 | (14) convergent_lines(all_18_3, all_18_2) = all_27_1
% 8.66/1.99 |
% 8.66/1.99 | BETA: splitting (11) gives:
% 8.66/1.99 |
% 8.66/1.99 | Case 1:
% 8.66/1.99 | |
% 8.66/1.99 | | (15) all_18_0 = 0
% 8.66/1.99 | |
% 8.66/1.99 | | REDUCE: (4), (15) imply:
% 8.66/1.99 | | (16) $false
% 8.66/1.99 | |
% 8.66/1.99 | | CLOSE: (16) is inconsistent.
% 8.66/1.99 | |
% 8.66/1.99 | Case 2:
% 8.66/1.99 | |
% 8.66/1.99 | | (17) all_18_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 8.66/1.99 | | convergent_lines(all_18_3, all_18_2) = v0)
% 8.66/1.99 | |
% 8.66/1.99 | | BETA: splitting (17) gives:
% 8.66/1.99 | |
% 8.66/1.99 | | Case 1:
% 8.66/1.99 | | |
% 8.66/1.99 | | | (18) all_18_1 = 0
% 8.66/1.99 | | |
% 8.66/1.99 | | | REDUCE: (3), (18) imply:
% 8.66/1.99 | | | (19) $false
% 8.66/1.99 | | |
% 8.66/1.99 | | | CLOSE: (19) is inconsistent.
% 8.66/1.99 | | |
% 8.66/1.99 | | Case 2:
% 8.66/1.99 | | |
% 8.66/1.99 | | | (20) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_18_3, all_18_2)
% 8.66/1.99 | | | = v0)
% 8.66/1.99 | | |
% 8.66/1.99 | | | DELTA: instantiating (20) with fresh symbol all_65_0 gives:
% 8.66/1.99 | | | (21) ~ (all_65_0 = 0) & convergent_lines(all_18_3, all_18_2) =
% 8.66/1.99 | | | all_65_0
% 8.66/1.99 | | |
% 8.66/1.99 | | | ALPHA: (21) implies:
% 8.66/1.99 | | | (22) ~ (all_65_0 = 0)
% 8.66/1.99 | | | (23) convergent_lines(all_18_3, all_18_2) = all_65_0
% 8.66/1.99 | | |
% 8.66/1.99 | | | GROUND_INST: instantiating (1) with 0, all_65_0, all_18_2, all_18_3,
% 8.66/1.99 | | | simplifying with (8), (23) gives:
% 8.66/1.99 | | | (24) all_65_0 = 0
% 8.66/1.99 | | |
% 8.66/1.99 | | | GROUND_INST: instantiating (1) with all_27_1, all_65_0, all_18_2,
% 8.66/1.99 | | | all_18_3, simplifying with (14), (23) gives:
% 8.66/1.99 | | | (25) all_65_0 = all_27_1
% 8.66/1.99 | | |
% 8.66/1.99 | | | COMBINE_EQS: (24), (25) imply:
% 8.66/1.99 | | | (26) all_27_1 = 0
% 8.66/1.99 | | |
% 8.66/1.99 | | | REDUCE: (22), (24) imply:
% 8.66/1.99 | | | (27) $false
% 8.66/1.99 | | |
% 8.66/1.99 | | | CLOSE: (27) is inconsistent.
% 8.66/1.99 | | |
% 8.66/1.99 | | End of split
% 8.66/1.99 | |
% 8.66/1.99 | End of split
% 8.66/1.99 |
% 8.66/1.99 End of proof
% 8.66/2.00 % SZS output end Proof for theBenchmark
% 8.66/2.00
% 8.66/2.00 1391ms
%------------------------------------------------------------------------------