TSTP Solution File: GEO216+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO216+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n006.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 23:22:26 EDT 2023
% Result : Theorem 7.43s 1.68s
% Output : Proof 9.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GEO216+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Aug 29 19:54:06 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.59 ________ _____
% 0.18/0.59 ___ __ \_________(_)________________________________
% 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59 (2023-06-19)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2023
% 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59 Amanda Stjerna.
% 0.18/0.59 Free software under BSD-3-Clause.
% 0.18/0.59
% 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.60 Running up to 7 provers in parallel.
% 0.61/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.61/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.61/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.61/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.61/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.61/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.61/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.32/1.11 Prover 4: Preprocessing ...
% 3.32/1.11 Prover 1: Preprocessing ...
% 3.32/1.16 Prover 5: Preprocessing ...
% 3.32/1.16 Prover 3: Preprocessing ...
% 3.32/1.16 Prover 2: Preprocessing ...
% 3.32/1.16 Prover 6: Preprocessing ...
% 3.32/1.17 Prover 0: Preprocessing ...
% 5.80/1.51 Prover 2: Proving ...
% 5.80/1.52 Prover 5: Proving ...
% 6.36/1.56 Prover 6: Constructing countermodel ...
% 6.72/1.58 Prover 1: Constructing countermodel ...
% 6.72/1.58 Prover 3: Constructing countermodel ...
% 7.43/1.67 Prover 3: proved (1062ms)
% 7.43/1.68
% 7.43/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.43/1.68
% 7.43/1.68 Prover 6: proved (1061ms)
% 7.43/1.68
% 7.43/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.43/1.68
% 7.43/1.68 Prover 2: stopped
% 7.43/1.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.43/1.69 Prover 5: stopped
% 7.43/1.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.43/1.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.43/1.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.84/1.76 Prover 8: Preprocessing ...
% 7.84/1.77 Prover 7: Preprocessing ...
% 7.84/1.77 Prover 11: Preprocessing ...
% 7.84/1.77 Prover 10: Preprocessing ...
% 8.30/1.83 Prover 1: Found proof (size 20)
% 8.30/1.83 Prover 1: proved (1221ms)
% 8.30/1.85 Prover 10: Warning: ignoring some quantifiers
% 8.30/1.87 Prover 7: Warning: ignoring some quantifiers
% 8.30/1.87 Prover 11: stopped
% 8.99/1.89 Prover 10: Constructing countermodel ...
% 8.99/1.90 Prover 10: stopped
% 8.99/1.90 Prover 7: Constructing countermodel ...
% 8.99/1.91 Prover 7: stopped
% 9.31/1.94 Prover 8: Warning: ignoring some quantifiers
% 9.40/1.94 Prover 4: Constructing countermodel ...
% 9.40/1.95 Prover 8: Constructing countermodel ...
% 9.40/1.96 Prover 8: stopped
% 9.40/1.96 Prover 0: Proving ...
% 9.40/1.97 Prover 4: stopped
% 9.40/1.97 Prover 0: stopped
% 9.40/1.97
% 9.40/1.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.40/1.97
% 9.40/1.98 % SZS output start Proof for theBenchmark
% 9.40/1.98 Assumptions after simplification:
% 9.40/1.98 ---------------------------------
% 9.40/1.98
% 9.40/1.98 (a5)
% 9.79/2.01 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (orthogonal_lines(v0,
% 9.79/2.01 v1) = v2) | ~ $i(v1) | ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) & !
% 9.79/2.01 [v0: $i] : ! [v1: $i] : ( ~ (orthogonal_lines(v0, v1) = 0) | ~ $i(v1) | ~
% 9.79/2.01 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 9.79/2.01
% 9.79/2.01 (coipo1)
% 9.79/2.01 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 9.79/2.01 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 9.79/2.01 convergent_lines(v0, v1) = 0)
% 9.79/2.01
% 9.79/2.01 (con)
% 9.79/2.01 ? [v0: $i] : (orthogonal_lines(v0, v0) = 0 & $i(v0))
% 9.79/2.01
% 9.79/2.01 (couo1)
% 9.79/2.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 9.79/2.01 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~
% 9.79/2.01 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 9.79/2.01 [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))
% 9.79/2.01
% 9.79/2.01 (occu1)
% 9.79/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 9.79/2.02 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 9.79/2.02 convergent_lines(v0, v1) = 0)
% 9.79/2.02
% 9.79/2.02 (function-axioms)
% 9.79/2.03 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 9.79/2.03 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~
% 9.79/2.03 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.79/2.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.79/2.03 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2)
% 9.79/2.03 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.79/2.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~
% 9.79/2.03 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.79/2.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.79/2.03 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0:
% 9.79/2.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.79/2.03 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 9.79/2.03 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.79/2.03 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 9.79/2.03 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 9.79/2.03 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 9.79/2.03 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 9.79/2.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 9.79/2.03 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 9.79/2.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 9.79/2.03 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 9.79/2.03 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 9.79/2.03 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.79/2.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.79/2.03 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 9.79/2.03 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.79/2.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 9.79/2.03 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.79/2.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.79/2.03 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 9.79/2.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.79/2.03 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 9.79/2.03 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.79/2.03 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 9.79/2.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.79/2.03 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 9.79/2.03
% 9.79/2.03 Further assumptions not needed in the proof:
% 9.79/2.03 --------------------------------------------
% 9.79/2.03 a3, a4, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq1, ceq2, ceq3,
% 9.79/2.03 ci1, ci2, ci3, ci4, con1, cotno1, cp1, cp2, cu1, cup1, int1, oac1, ooc1, ooc2,
% 9.79/2.03 orth1, ouo1, p1, par1
% 9.79/2.03
% 9.79/2.03 Those formulas are unsatisfiable:
% 9.79/2.03 ---------------------------------
% 9.79/2.03
% 9.79/2.03 Begin of proof
% 9.79/2.03 |
% 9.79/2.03 | ALPHA: (a5) implies:
% 9.79/2.03 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (orthogonal_lines(v0, v1) = 0) | ~
% 9.79/2.03 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 9.79/2.03 | unorthogonal_lines(v0, v1) = v2))
% 9.79/2.03 |
% 9.79/2.03 | ALPHA: (function-axioms) implies:
% 9.79/2.03 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.79/2.03 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 9.79/2.03 | (convergent_lines(v3, v2) = v0))
% 9.79/2.03 |
% 9.79/2.03 | DELTA: instantiating (con) with fresh symbol all_38_0 gives:
% 9.79/2.03 | (3) orthogonal_lines(all_38_0, all_38_0) = 0 & $i(all_38_0)
% 9.79/2.03 |
% 9.79/2.03 | ALPHA: (3) implies:
% 9.79/2.03 | (4) $i(all_38_0)
% 9.79/2.03 | (5) orthogonal_lines(all_38_0, all_38_0) = 0
% 9.79/2.03 |
% 9.79/2.04 | GROUND_INST: instantiating (1) with all_38_0, all_38_0, simplifying with (4),
% 9.79/2.04 | (5) gives:
% 9.79/2.04 | (6) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_38_0, all_38_0) =
% 9.79/2.04 | v0)
% 9.79/2.04 |
% 9.79/2.04 | DELTA: instantiating (6) with fresh symbol all_45_0 gives:
% 9.79/2.04 | (7) ~ (all_45_0 = 0) & unorthogonal_lines(all_38_0, all_38_0) = all_45_0
% 9.79/2.04 |
% 9.79/2.04 | ALPHA: (7) implies:
% 9.79/2.04 | (8) ~ (all_45_0 = 0)
% 9.79/2.04 | (9) unorthogonal_lines(all_38_0, all_38_0) = all_45_0
% 9.79/2.04 |
% 9.79/2.04 | GROUND_INST: instantiating (couo1) with all_38_0, all_38_0, all_38_0,
% 9.79/2.04 | all_45_0, all_45_0, simplifying with (4), (9) gives:
% 9.79/2.04 | (10) all_45_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 9.79/2.04 | convergent_lines(all_38_0, all_38_0) = v0)
% 9.79/2.04 |
% 9.79/2.04 | GROUND_INST: instantiating (occu1) with all_38_0, all_38_0, all_45_0,
% 9.79/2.04 | simplifying with (4), (9) gives:
% 9.79/2.04 | (11) all_45_0 = 0 | convergent_lines(all_38_0, all_38_0) = 0
% 9.79/2.04 |
% 9.79/2.04 | BETA: splitting (11) gives:
% 9.79/2.04 |
% 9.79/2.04 | Case 1:
% 9.79/2.04 | |
% 9.79/2.04 | | (12) convergent_lines(all_38_0, all_38_0) = 0
% 9.79/2.04 | |
% 9.79/2.04 | | BETA: splitting (10) gives:
% 9.79/2.04 | |
% 9.79/2.04 | | Case 1:
% 9.79/2.04 | | |
% 9.79/2.04 | | | (13) all_45_0 = 0
% 9.79/2.04 | | |
% 9.79/2.04 | | | REDUCE: (8), (13) imply:
% 9.79/2.04 | | | (14) $false
% 9.79/2.04 | | |
% 9.79/2.04 | | | CLOSE: (14) is inconsistent.
% 9.79/2.04 | | |
% 9.79/2.04 | | Case 2:
% 9.79/2.04 | | |
% 9.79/2.04 | | | (15) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_0, all_38_0)
% 9.79/2.04 | | | = v0)
% 9.79/2.04 | | |
% 9.79/2.04 | | | DELTA: instantiating (15) with fresh symbol all_62_0 gives:
% 9.79/2.04 | | | (16) ~ (all_62_0 = 0) & convergent_lines(all_38_0, all_38_0) =
% 9.79/2.04 | | | all_62_0
% 9.79/2.04 | | |
% 9.79/2.04 | | | ALPHA: (16) implies:
% 9.79/2.04 | | | (17) ~ (all_62_0 = 0)
% 9.79/2.04 | | | (18) convergent_lines(all_38_0, all_38_0) = all_62_0
% 9.79/2.04 | | |
% 9.79/2.04 | | | GROUND_INST: instantiating (2) with 0, all_62_0, all_38_0, all_38_0,
% 9.79/2.04 | | | simplifying with (12), (18) gives:
% 9.79/2.04 | | | (19) all_62_0 = 0
% 9.79/2.04 | | |
% 9.79/2.04 | | | REDUCE: (17), (19) imply:
% 9.79/2.04 | | | (20) $false
% 9.79/2.04 | | |
% 9.79/2.04 | | | CLOSE: (20) is inconsistent.
% 9.79/2.04 | | |
% 9.79/2.04 | | End of split
% 9.79/2.04 | |
% 9.79/2.04 | Case 2:
% 9.79/2.04 | |
% 9.79/2.04 | | (21) all_45_0 = 0
% 9.79/2.04 | |
% 9.79/2.04 | | REDUCE: (8), (21) imply:
% 9.79/2.04 | | (22) $false
% 9.79/2.04 | |
% 9.79/2.04 | | CLOSE: (22) is inconsistent.
% 9.79/2.04 | |
% 9.79/2.04 | End of split
% 9.79/2.04 |
% 9.79/2.04 End of proof
% 9.79/2.04 % SZS output end Proof for theBenchmark
% 9.79/2.04
% 9.79/2.04 1453ms
%------------------------------------------------------------------------------