TSTP Solution File: GEO209+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO209+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 : n027.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 23:22:20 EDT 2023
% Result : Theorem 5.30s 1.43s
% Output : Proof 7.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO209+2 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n027.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 19:43:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.64/0.63 Running up to 7 provers in parallel.
% 0.64/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.64/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.64/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.64/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.64/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.64/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.64/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.52/1.05 Prover 4: Preprocessing ...
% 2.52/1.05 Prover 1: Preprocessing ...
% 2.96/1.09 Prover 5: Preprocessing ...
% 2.96/1.09 Prover 2: Preprocessing ...
% 2.96/1.09 Prover 3: Preprocessing ...
% 2.96/1.09 Prover 0: Preprocessing ...
% 2.96/1.09 Prover 6: Preprocessing ...
% 4.45/1.30 Prover 5: Proving ...
% 4.66/1.32 Prover 2: Proving ...
% 4.66/1.34 Prover 3: Constructing countermodel ...
% 4.66/1.35 Prover 6: Constructing countermodel ...
% 4.66/1.36 Prover 1: Constructing countermodel ...
% 5.30/1.43 Prover 3: proved (793ms)
% 5.30/1.43
% 5.30/1.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.30/1.43
% 5.30/1.44 Prover 2: stopped
% 5.30/1.44 Prover 6: stopped
% 5.30/1.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.30/1.44 Prover 5: stopped
% 5.30/1.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.30/1.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.30/1.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.30/1.47 Prover 7: Preprocessing ...
% 5.30/1.48 Prover 8: Preprocessing ...
% 5.30/1.48 Prover 11: Preprocessing ...
% 5.91/1.49 Prover 10: Preprocessing ...
% 5.91/1.51 Prover 7: Warning: ignoring some quantifiers
% 5.91/1.52 Prover 7: Constructing countermodel ...
% 5.91/1.52 Prover 10: Warning: ignoring some quantifiers
% 5.91/1.53 Prover 0: Proving ...
% 5.91/1.54 Prover 4: Constructing countermodel ...
% 5.91/1.54 Prover 0: stopped
% 5.91/1.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.91/1.55 Prover 10: Constructing countermodel ...
% 5.91/1.56 Prover 1: Found proof (size 22)
% 5.91/1.56 Prover 1: proved (921ms)
% 5.91/1.56 Prover 7: stopped
% 5.91/1.57 Prover 10: stopped
% 5.91/1.57 Prover 4: stopped
% 5.91/1.57 Prover 13: Preprocessing ...
% 5.91/1.57 Prover 8: Warning: ignoring some quantifiers
% 6.63/1.58 Prover 8: Constructing countermodel ...
% 6.63/1.59 Prover 13: stopped
% 6.63/1.59 Prover 8: stopped
% 6.86/1.65 Prover 11: Constructing countermodel ...
% 6.86/1.66 Prover 11: stopped
% 6.86/1.66
% 6.86/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.86/1.66
% 6.86/1.67 % SZS output start Proof for theBenchmark
% 6.86/1.67 Assumptions after simplification:
% 6.86/1.67 ---------------------------------
% 6.86/1.67
% 6.86/1.67 (apart6)
% 6.86/1.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 6.86/1.70 (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ~
% 6.86/1.70 $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0)
% 6.86/1.70
% 6.86/1.70 (con)
% 7.27/1.70 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5:
% 7.27/1.70 int] : ? [v6: int] : ? [v7: int] : ( ~ (v7 = 0) & ~ (v6 = 0) & ~ (v5 =
% 7.27/1.70 0) & ~ (v4 = 0) & apart_point_and_line(v0, v3) = v5 &
% 7.27/1.70 apart_point_and_line(v0, v2) = v4 & apart_point_and_line(v0, v1) = 0 &
% 7.27/1.70 convergent_lines(v3, v1) = v7 & convergent_lines(v2, v1) = v6 &
% 7.27/1.70 distinct_lines(v2, v3) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.27/1.70
% 7.27/1.70 (cup1)
% 7.27/1.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 7.27/1.70 (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~
% 7.27/1.70 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 7.27/1.70 (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0
% 7.27/1.70 | v4 = 0)))
% 7.27/1.70
% 7.27/1.70 (function-axioms)
% 7.27/1.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.27/1.71 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) =
% 7.27/1.71 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 7.27/1.71 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 7.27/1.71 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.27/1.71 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 7.27/1.71 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.27/1.71 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 7.27/1.71 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.27/1.71 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.27/1.71 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 7.27/1.71 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.27/1.71 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3,
% 7.27/1.71 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 7.27/1.71 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 7.27/1.71 (distinct_points(v3, v2) = v0))
% 7.27/1.71
% 7.27/1.71 Further assumptions not needed in the proof:
% 7.27/1.71 --------------------------------------------
% 7.27/1.71 apart1, apart2, apart3, apart4, apart5, ceq1, ceq2, ceq3, con1, con2, cp1, cp2,
% 7.27/1.71 cu1
% 7.27/1.71
% 7.27/1.71 Those formulas are unsatisfiable:
% 7.27/1.71 ---------------------------------
% 7.27/1.71
% 7.27/1.71 Begin of proof
% 7.27/1.71 |
% 7.27/1.71 | ALPHA: (function-axioms) implies:
% 7.27/1.71 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.27/1.71 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 7.27/1.71 | (convergent_lines(v3, v2) = v0))
% 7.27/1.72 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.27/1.72 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 7.27/1.72 | (apart_point_and_line(v3, v2) = v0))
% 7.27/1.72 |
% 7.27/1.72 | DELTA: instantiating (con) with fresh symbols all_18_0, all_18_1, all_18_2,
% 7.27/1.72 | all_18_3, all_18_4, all_18_5, all_18_6, all_18_7 gives:
% 7.27/1.72 | (3) ~ (all_18_0 = 0) & ~ (all_18_1 = 0) & ~ (all_18_2 = 0) & ~
% 7.27/1.72 | (all_18_3 = 0) & apart_point_and_line(all_18_7, all_18_4) = all_18_2 &
% 7.27/1.72 | apart_point_and_line(all_18_7, all_18_5) = all_18_3 &
% 7.27/1.72 | apart_point_and_line(all_18_7, all_18_6) = 0 &
% 7.27/1.72 | convergent_lines(all_18_4, all_18_6) = all_18_0 &
% 7.27/1.72 | convergent_lines(all_18_5, all_18_6) = all_18_1 &
% 7.27/1.72 | distinct_lines(all_18_5, all_18_4) = 0 & $i(all_18_4) & $i(all_18_5) &
% 7.27/1.72 | $i(all_18_6) & $i(all_18_7)
% 7.27/1.72 |
% 7.27/1.72 | ALPHA: (3) implies:
% 7.27/1.72 | (4) ~ (all_18_3 = 0)
% 7.27/1.72 | (5) ~ (all_18_2 = 0)
% 7.27/1.72 | (6) ~ (all_18_1 = 0)
% 7.27/1.72 | (7) ~ (all_18_0 = 0)
% 7.27/1.72 | (8) $i(all_18_7)
% 7.27/1.72 | (9) $i(all_18_6)
% 7.27/1.72 | (10) $i(all_18_5)
% 7.27/1.72 | (11) $i(all_18_4)
% 7.27/1.72 | (12) distinct_lines(all_18_5, all_18_4) = 0
% 7.27/1.72 | (13) convergent_lines(all_18_5, all_18_6) = all_18_1
% 7.27/1.72 | (14) convergent_lines(all_18_4, all_18_6) = all_18_0
% 7.27/1.72 | (15) apart_point_and_line(all_18_7, all_18_5) = all_18_3
% 7.27/1.72 | (16) apart_point_and_line(all_18_7, all_18_4) = all_18_2
% 7.27/1.72 |
% 7.27/1.72 | GROUND_INST: instantiating (cup1) with all_18_7, all_18_5, all_18_4, all_18_3,
% 7.27/1.72 | simplifying with (8), (10), (11), (12), (15) gives:
% 7.27/1.72 | (17) all_18_3 = 0 | ? [v0: any] : ? [v1: any] :
% 7.27/1.72 | (apart_point_and_line(all_18_7, all_18_4) = v0 &
% 7.27/1.72 | convergent_lines(all_18_5, all_18_4) = v1 & (v1 = 0 | v0 = 0))
% 7.27/1.72 |
% 7.27/1.72 | BETA: splitting (17) gives:
% 7.27/1.72 |
% 7.27/1.72 | Case 1:
% 7.27/1.72 | |
% 7.27/1.73 | | (18) all_18_3 = 0
% 7.27/1.73 | |
% 7.27/1.73 | | REDUCE: (4), (18) imply:
% 7.27/1.73 | | (19) $false
% 7.27/1.73 | |
% 7.27/1.73 | | CLOSE: (19) is inconsistent.
% 7.27/1.73 | |
% 7.27/1.73 | Case 2:
% 7.27/1.73 | |
% 7.27/1.73 | | (20) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_18_7,
% 7.27/1.73 | | all_18_4) = v0 & convergent_lines(all_18_5, all_18_4) = v1 & (v1
% 7.27/1.73 | | = 0 | v0 = 0))
% 7.27/1.73 | |
% 7.27/1.73 | | DELTA: instantiating (20) with fresh symbols all_27_0, all_27_1 gives:
% 7.27/1.73 | | (21) apart_point_and_line(all_18_7, all_18_4) = all_27_1 &
% 7.27/1.73 | | convergent_lines(all_18_5, all_18_4) = all_27_0 & (all_27_0 = 0 |
% 7.27/1.73 | | all_27_1 = 0)
% 7.27/1.73 | |
% 7.27/1.73 | | ALPHA: (21) implies:
% 7.27/1.73 | | (22) convergent_lines(all_18_5, all_18_4) = all_27_0
% 7.27/1.73 | | (23) apart_point_and_line(all_18_7, all_18_4) = all_27_1
% 7.27/1.73 | | (24) all_27_0 = 0 | all_27_1 = 0
% 7.27/1.73 | |
% 7.27/1.73 | | GROUND_INST: instantiating (2) with all_18_2, all_27_1, all_18_4, all_18_7,
% 7.27/1.73 | | simplifying with (16), (23) gives:
% 7.27/1.73 | | (25) all_27_1 = all_18_2
% 7.27/1.73 | |
% 7.27/1.73 | | BETA: splitting (24) gives:
% 7.27/1.73 | |
% 7.27/1.73 | | Case 1:
% 7.27/1.73 | | |
% 7.27/1.73 | | | (26) all_27_0 = 0
% 7.27/1.73 | | |
% 7.27/1.73 | | | REDUCE: (22), (26) imply:
% 7.27/1.73 | | | (27) convergent_lines(all_18_5, all_18_4) = 0
% 7.27/1.73 | | |
% 7.27/1.73 | | | GROUND_INST: instantiating (apart6) with all_18_5, all_18_4, all_18_6,
% 7.27/1.73 | | | all_18_1, simplifying with (9), (10), (11), (13), (27) gives:
% 7.27/1.73 | | | (28) all_18_1 = 0 | convergent_lines(all_18_4, all_18_6) = 0
% 7.27/1.73 | | |
% 7.27/1.73 | | | BETA: splitting (28) gives:
% 7.27/1.73 | | |
% 7.27/1.73 | | | Case 1:
% 7.27/1.73 | | | |
% 7.27/1.73 | | | | (29) convergent_lines(all_18_4, all_18_6) = 0
% 7.27/1.73 | | | |
% 7.27/1.73 | | | | GROUND_INST: instantiating (1) with all_18_0, 0, all_18_6, all_18_4,
% 7.27/1.73 | | | | simplifying with (14), (29) gives:
% 7.27/1.73 | | | | (30) all_18_0 = 0
% 7.27/1.73 | | | |
% 7.27/1.73 | | | | REDUCE: (7), (30) imply:
% 7.27/1.73 | | | | (31) $false
% 7.27/1.73 | | | |
% 7.27/1.73 | | | | CLOSE: (31) is inconsistent.
% 7.27/1.73 | | | |
% 7.27/1.73 | | | Case 2:
% 7.27/1.73 | | | |
% 7.27/1.73 | | | | (32) all_18_1 = 0
% 7.27/1.73 | | | |
% 7.27/1.73 | | | | REDUCE: (6), (32) imply:
% 7.27/1.73 | | | | (33) $false
% 7.27/1.73 | | | |
% 7.27/1.73 | | | | CLOSE: (33) is inconsistent.
% 7.27/1.73 | | | |
% 7.27/1.73 | | | End of split
% 7.27/1.73 | | |
% 7.27/1.73 | | Case 2:
% 7.27/1.73 | | |
% 7.27/1.73 | | | (34) all_27_1 = 0
% 7.27/1.73 | | |
% 7.27/1.73 | | | COMBINE_EQS: (25), (34) imply:
% 7.27/1.73 | | | (35) all_18_2 = 0
% 7.27/1.73 | | |
% 7.27/1.73 | | | REDUCE: (5), (35) imply:
% 7.27/1.73 | | | (36) $false
% 7.27/1.73 | | |
% 7.27/1.73 | | | CLOSE: (36) is inconsistent.
% 7.27/1.73 | | |
% 7.27/1.73 | | End of split
% 7.27/1.73 | |
% 7.27/1.73 | End of split
% 7.27/1.73 |
% 7.27/1.73 End of proof
% 7.27/1.74 % SZS output end Proof for theBenchmark
% 7.27/1.74
% 7.27/1.74 1118ms
%------------------------------------------------------------------------------