TSTP Solution File: GEO178+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO178+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 23:21:54 EDT 2023
% Result : Theorem 5.09s 1.48s
% Output : Proof 6.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO178+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.35 % Computer : n026.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Aug 29 22:51:35 EDT 2023
% 0.16/0.35 % 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 ...
% 0.20/0.63 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 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 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 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 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
% 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
% 2.30/1.05 Prover 1: Preprocessing ...
% 2.30/1.06 Prover 4: Preprocessing ...
% 2.30/1.10 Prover 5: Preprocessing ...
% 2.30/1.10 Prover 0: Preprocessing ...
% 2.30/1.10 Prover 2: Preprocessing ...
% 2.30/1.10 Prover 6: Preprocessing ...
% 2.30/1.10 Prover 3: Preprocessing ...
% 4.47/1.33 Prover 5: Proving ...
% 4.47/1.34 Prover 2: Proving ...
% 4.47/1.35 Prover 6: Constructing countermodel ...
% 4.47/1.35 Prover 3: Constructing countermodel ...
% 4.47/1.36 Prover 1: Constructing countermodel ...
% 5.09/1.46 Prover 4: Constructing countermodel ...
% 5.09/1.48 Prover 3: proved (837ms)
% 5.09/1.48
% 5.09/1.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.09/1.48
% 5.09/1.48 Prover 6: proved (835ms)
% 5.09/1.48
% 5.09/1.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.09/1.48
% 5.73/1.49 Prover 2: stopped
% 5.73/1.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.73/1.50 Prover 5: proved (844ms)
% 5.73/1.50
% 5.73/1.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.73/1.50
% 5.73/1.50 Prover 0: Proving ...
% 5.73/1.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.73/1.50 Prover 0: stopped
% 5.73/1.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.73/1.51 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.73/1.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.73/1.54 Prover 7: Preprocessing ...
% 5.73/1.55 Prover 8: Preprocessing ...
% 5.73/1.55 Prover 11: Preprocessing ...
% 5.73/1.56 Prover 10: Preprocessing ...
% 5.73/1.56 Prover 13: Preprocessing ...
% 5.73/1.56 Prover 1: Found proof (size 20)
% 5.73/1.56 Prover 1: proved (922ms)
% 5.73/1.56 Prover 4: stopped
% 5.73/1.57 Prover 10: stopped
% 5.73/1.57 Prover 13: stopped
% 5.73/1.57 Prover 7: Warning: ignoring some quantifiers
% 5.73/1.58 Prover 7: Constructing countermodel ...
% 6.40/1.59 Prover 7: stopped
% 6.40/1.59 Prover 11: stopped
% 6.40/1.61 Prover 8: Warning: ignoring some quantifiers
% 6.40/1.62 Prover 8: Constructing countermodel ...
% 6.40/1.62 Prover 8: stopped
% 6.40/1.62
% 6.40/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.40/1.62
% 6.40/1.63 % SZS output start Proof for theBenchmark
% 6.40/1.63 Assumptions after simplification:
% 6.40/1.63 ---------------------------------
% 6.40/1.63
% 6.40/1.63 (con)
% 6.40/1.67 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5:
% 6.40/1.67 any] : (line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = 0 &
% 6.40/1.67 distinct_points(v2, v1) = v5 & distinct_points(v2, v0) = v4 &
% 6.40/1.67 distinct_points(v0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v5 =
% 6.40/1.67 0) | ~ (v4 = 0)))
% 6.40/1.67
% 6.40/1.67 (con1)
% 6.40/1.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 6.40/1.67 (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ~
% 6.40/1.67 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any]
% 6.40/1.67 : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 &
% 6.40/1.67 distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 6.40/1.67
% 6.40/1.67 (function-axioms)
% 6.40/1.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.40/1.68 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) &
% 6.40/1.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.40/1.68 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 6.40/1.68 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 6.40/1.68 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 6.40/1.68 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.40/1.68 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.40/1.68 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 6.40/1.68 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 6.40/1.68 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3,
% 6.40/1.68 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 6.40/1.68 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 6.40/1.68 (distinct_points(v3, v2) = v0))
% 6.40/1.68
% 6.40/1.68 Further assumptions not needed in the proof:
% 6.40/1.68 --------------------------------------------
% 6.40/1.68 apart1, apart2, apart3, apart4, apart5, apart6, ceq1, ceq2, ceq3, con2, cu1
% 6.40/1.68
% 6.40/1.68 Those formulas are unsatisfiable:
% 6.40/1.68 ---------------------------------
% 6.40/1.68
% 6.40/1.68 Begin of proof
% 6.40/1.68 |
% 6.40/1.68 | ALPHA: (function-axioms) implies:
% 6.40/1.68 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.40/1.68 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 6.40/1.68 | (distinct_points(v3, v2) = v0))
% 6.40/1.68 |
% 6.40/1.68 | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2,
% 6.40/1.68 | all_15_3, all_15_4, all_15_5 gives:
% 6.40/1.69 | (2) line_connecting(all_15_5, all_15_4) = all_15_2 &
% 6.40/1.69 | apart_point_and_line(all_15_3, all_15_2) = 0 &
% 6.40/1.69 | distinct_points(all_15_3, all_15_4) = all_15_0 &
% 6.40/1.69 | distinct_points(all_15_3, all_15_5) = all_15_1 &
% 6.40/1.69 | distinct_points(all_15_5, all_15_4) = 0 & $i(all_15_2) & $i(all_15_3) &
% 6.40/1.69 | $i(all_15_4) & $i(all_15_5) & ( ~ (all_15_0 = 0) | ~ (all_15_1 = 0))
% 6.40/1.69 |
% 6.40/1.69 | ALPHA: (2) implies:
% 6.40/1.69 | (3) $i(all_15_5)
% 6.40/1.69 | (4) $i(all_15_4)
% 6.40/1.69 | (5) $i(all_15_3)
% 6.40/1.69 | (6) distinct_points(all_15_5, all_15_4) = 0
% 6.40/1.69 | (7) distinct_points(all_15_3, all_15_5) = all_15_1
% 6.40/1.69 | (8) distinct_points(all_15_3, all_15_4) = all_15_0
% 6.40/1.69 | (9) apart_point_and_line(all_15_3, all_15_2) = 0
% 6.40/1.69 | (10) line_connecting(all_15_5, all_15_4) = all_15_2
% 6.40/1.69 | (11) ~ (all_15_0 = 0) | ~ (all_15_1 = 0)
% 6.40/1.69 |
% 6.40/1.69 | GROUND_INST: instantiating (con1) with all_15_5, all_15_4, all_15_3, all_15_2,
% 6.40/1.69 | simplifying with (3), (4), (5), (9), (10) gives:
% 6.40/1.69 | (12) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 6.40/1.69 | (distinct_points(all_15_3, all_15_4) = v2 & distinct_points(all_15_3,
% 6.40/1.69 | all_15_5) = v1 & distinct_points(all_15_5, all_15_4) = v0 & ( ~
% 6.40/1.69 | (v0 = 0) | (v2 = 0 & v1 = 0)))
% 6.40/1.69 |
% 6.40/1.69 | DELTA: instantiating (12) with fresh symbols all_22_0, all_22_1, all_22_2
% 6.40/1.69 | gives:
% 6.40/1.69 | (13) distinct_points(all_15_3, all_15_4) = all_22_0 &
% 6.40/1.69 | distinct_points(all_15_3, all_15_5) = all_22_1 &
% 6.40/1.69 | distinct_points(all_15_5, all_15_4) = all_22_2 & ( ~ (all_22_2 = 0) |
% 6.40/1.69 | (all_22_0 = 0 & all_22_1 = 0))
% 6.40/1.69 |
% 6.40/1.69 | ALPHA: (13) implies:
% 6.40/1.70 | (14) distinct_points(all_15_5, all_15_4) = all_22_2
% 6.40/1.70 | (15) distinct_points(all_15_3, all_15_5) = all_22_1
% 6.40/1.70 | (16) distinct_points(all_15_3, all_15_4) = all_22_0
% 6.40/1.70 | (17) ~ (all_22_2 = 0) | (all_22_0 = 0 & all_22_1 = 0)
% 6.40/1.70 |
% 6.40/1.70 | GROUND_INST: instantiating (1) with 0, all_22_2, all_15_4, all_15_5,
% 6.40/1.70 | simplifying with (6), (14) gives:
% 6.40/1.70 | (18) all_22_2 = 0
% 6.40/1.70 |
% 6.40/1.70 | GROUND_INST: instantiating (1) with all_15_1, all_22_1, all_15_5, all_15_3,
% 6.40/1.70 | simplifying with (7), (15) gives:
% 6.40/1.70 | (19) all_22_1 = all_15_1
% 6.40/1.70 |
% 6.40/1.70 | GROUND_INST: instantiating (1) with all_15_0, all_22_0, all_15_4, all_15_3,
% 6.40/1.70 | simplifying with (8), (16) gives:
% 6.40/1.70 | (20) all_22_0 = all_15_0
% 6.40/1.70 |
% 6.40/1.70 | BETA: splitting (17) gives:
% 6.40/1.70 |
% 6.40/1.70 | Case 1:
% 6.40/1.70 | |
% 6.40/1.70 | | (21) ~ (all_22_2 = 0)
% 6.40/1.70 | |
% 6.40/1.70 | | REDUCE: (18), (21) imply:
% 6.40/1.70 | | (22) $false
% 6.40/1.70 | |
% 6.40/1.70 | | CLOSE: (22) is inconsistent.
% 6.40/1.70 | |
% 6.40/1.70 | Case 2:
% 6.40/1.70 | |
% 6.40/1.70 | | (23) all_22_0 = 0 & all_22_1 = 0
% 6.40/1.70 | |
% 6.40/1.70 | | ALPHA: (23) implies:
% 6.40/1.70 | | (24) all_22_1 = 0
% 6.40/1.70 | | (25) all_22_0 = 0
% 6.40/1.70 | |
% 6.40/1.70 | | COMBINE_EQS: (20), (25) imply:
% 6.40/1.70 | | (26) all_15_0 = 0
% 6.40/1.70 | |
% 6.40/1.70 | | COMBINE_EQS: (19), (24) imply:
% 6.40/1.70 | | (27) all_15_1 = 0
% 6.40/1.70 | |
% 6.40/1.70 | | BETA: splitting (11) gives:
% 6.40/1.70 | |
% 6.40/1.70 | | Case 1:
% 6.40/1.70 | | |
% 6.40/1.70 | | | (28) ~ (all_15_0 = 0)
% 6.40/1.70 | | |
% 6.40/1.70 | | | REDUCE: (26), (28) imply:
% 6.40/1.70 | | | (29) $false
% 6.40/1.70 | | |
% 6.40/1.71 | | | CLOSE: (29) is inconsistent.
% 6.40/1.71 | | |
% 6.40/1.71 | | Case 2:
% 6.40/1.71 | | |
% 6.40/1.71 | | | (30) ~ (all_15_1 = 0)
% 6.40/1.71 | | |
% 6.40/1.71 | | | REDUCE: (27), (30) imply:
% 6.40/1.71 | | | (31) $false
% 6.40/1.71 | | |
% 6.40/1.71 | | | CLOSE: (31) is inconsistent.
% 6.40/1.71 | | |
% 6.40/1.71 | | End of split
% 6.40/1.71 | |
% 6.40/1.71 | End of split
% 6.40/1.71 |
% 6.40/1.71 End of proof
% 6.40/1.71 % SZS output end Proof for theBenchmark
% 6.40/1.71
% 6.40/1.71 1087ms
%------------------------------------------------------------------------------