%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO269+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 : n009.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 23:22:53 EDT 2023 % Result : Theorem 46.56s 6.68s % Output : Proof 47.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO269+3 : TPTP v8.1.2. Released v4.0.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n009.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 19:47:50 EDT 2023 % 0.12/0.34 % CPUTime : % 0.56/0.60 ________ _____ % 0.56/0.60 ___ __ \_________(_)________________________________ % 0.56/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.56/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.56/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.56/0.60 % 0.56/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.56/0.60 (2023-06-19) % 0.56/0.60 % 0.56/0.60 (c) Philipp Rümmer, 2009-2023 % 0.56/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.56/0.60 Amanda Stjerna. % 0.56/0.60 Free software under BSD-3-Clause. % 0.56/0.60 % 0.56/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.56/0.60 % 0.56/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.56/0.61 Running up to 7 provers in parallel. % 0.56/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.56/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.56/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.56/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.56/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.56/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.56/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.60/1.16 Prover 1: Preprocessing ... % 3.60/1.16 Prover 4: Preprocessing ... % 3.60/1.18 Prover 5: Preprocessing ... % 3.60/1.18 Prover 2: Preprocessing ... % 3.60/1.18 Prover 6: Preprocessing ... % 3.60/1.18 Prover 3: Preprocessing ... % 3.60/1.18 Prover 0: Preprocessing ... % 7.43/1.71 Prover 5: Proving ... % 7.43/1.73 Prover 6: Constructing countermodel ... % 7.43/1.74 Prover 2: Proving ... % 8.13/1.77 Prover 1: Constructing countermodel ... % 8.13/1.77 Prover 3: Constructing countermodel ... % 8.76/1.88 Prover 6: gave up % 8.76/1.88 Prover 3: gave up % 8.76/1.89 Prover 1: gave up % 8.76/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.76/1.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.22/1.91 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 9.67/2.00 Prover 7: Preprocessing ... % 9.67/2.01 Prover 9: Preprocessing ... % 9.67/2.01 Prover 8: Preprocessing ... % 10.38/2.08 Prover 7: Warning: ignoring some quantifiers % 10.64/2.11 Prover 7: Constructing countermodel ... % 10.64/2.13 Prover 4: Constructing countermodel ... % 11.12/2.17 Prover 0: Proving ... % 11.12/2.20 Prover 8: Warning: ignoring some quantifiers % 11.66/2.22 Prover 8: Constructing countermodel ... % 11.66/2.26 Prover 7: gave up % 11.66/2.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.12/2.32 Prover 10: Preprocessing ... % 12.12/2.35 Prover 8: gave up % 12.12/2.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.90/2.39 Prover 10: Warning: ignoring some quantifiers % 12.90/2.40 Prover 11: Preprocessing ... % 12.90/2.40 Prover 10: Constructing countermodel ... % 13.39/2.51 Prover 10: gave up % 13.39/2.52 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 13.99/2.54 Prover 9: Constructing countermodel ... % 13.99/2.55 Prover 12: Preprocessing ... % 15.82/2.81 Prover 12: Proving ... % 16.46/2.83 Prover 11: Constructing countermodel ... % 37.05/5.45 Prover 12: stopped % 37.05/5.47 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 37.05/5.52 Prover 13: Preprocessing ... % 38.06/5.62 Prover 13: Warning: ignoring some quantifiers % 38.06/5.63 Prover 13: Constructing countermodel ... % 39.33/5.76 Prover 13: gave up % 39.33/5.76 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379 % 39.33/5.78 Prover 14: Preprocessing ... % 41.75/6.10 Prover 14: Proving ... % 46.56/6.68 Prover 11: Found proof (size 88) % 46.56/6.68 Prover 11: proved (4331ms) % 46.56/6.68 Prover 2: stopped % 46.56/6.68 Prover 9: stopped % 46.56/6.68 Prover 5: stopped % 46.56/6.68 Prover 0: stopped % 46.56/6.68 Prover 14: stopped % 46.56/6.68 Prover 4: stopped % 46.56/6.68 % 46.56/6.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 46.56/6.68 % 46.56/6.69 % SZS output start Proof for theBenchmark % 46.56/6.69 Assumptions after simplification: % 46.56/6.69 --------------------------------- % 46.56/6.69 % 46.56/6.69 (a1_defns) % 46.56/6.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 46.56/6.72 (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ~ % 46.56/6.72 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & % 46.56/6.72 unequally_directed_opposite_lines(v0, v1) = v4)) & ! [v0: $i] : ! [v1: % 46.56/6.72 $i] : ! [v2: int] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) % 46.56/6.72 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) % 46.56/6.72 & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4 & $i(v3))) % 46.56/6.72 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) | ~ % 46.56/6.72 (unequally_directed_lines(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | % 46.56/6.72 unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : % 46.56/6.72 ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 46.56/6.72 ? [v2: $i] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0 & % 46.56/6.72 $i(v2))) % 46.56/6.72 % 46.56/6.72 (a5_defns) % 46.56/6.72 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 46.56/6.72 (equally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 46.56/6.72 unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : % 46.56/6.72 ! [v2: int] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | % 46.56/6.72 ~ $i(v1) | ~ $i(v0) | equally_directed_opposite_lines(v0, v1) = 0) & ! % 46.56/6.73 [v0: $i] : ! [v1: $i] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) | % 46.56/6.73 ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 46.56/6.73 unequally_directed_opposite_lines(v0, v1) = v2)) & ! [v0: $i] : ! [v1: % 46.56/6.73 $i] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ~ $i(v1) | ~ % 46.56/6.73 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0, % 46.56/6.73 v1) = v2)) % 46.56/6.73 % 46.56/6.73 (a7_defns) % 46.96/6.73 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (convergent_lines(v0, % 46.96/6.73 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ % 46.96/6.73 (v4 = 0) & unequally_directed_opposite_lines(v0, v1) = v4) | ( ~ (v3 = % 46.96/6.73 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: % 46.96/6.73 $i] : ! [v2: any] : ( ~ (unequally_directed_lines(v0, v1) = v2) | ~ $i(v1) % 46.96/6.73 | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & v2 = 0 & % 46.96/6.73 unequally_directed_opposite_lines(v0, v1) = 0) | ( ~ (v3 = 0) & % 46.96/6.73 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 46.96/6.73 any] : ( ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~ % 46.96/6.73 $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & v2 = 0 & % 46.96/6.73 unequally_directed_lines(v0, v1) = 0) | ( ~ (v3 = 0) & % 46.96/6.73 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 46.96/6.73 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 46.96/6.73 (unequally_directed_lines(v0, v1) = 0 & % 46.96/6.73 unequally_directed_opposite_lines(v0, v1) = 0)) & ! [v0: $i] : ! [v1: % 46.96/6.73 $i] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 46.96/6.73 ? [v2: int] : ? [v3: int] : ((v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ % 46.96/6.73 (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))) & ! [v0: % 46.96/6.73 $i] : ! [v1: $i] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ~ % 46.96/6.73 $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 46.96/6.73 convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & % 46.96/6.73 unequally_directed_lines(v0, v1) = v2))) % 46.96/6.73 % 46.96/6.73 (ax11_basics) % 46.96/6.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (left_convergent_lines(v0, v2) = % 46.96/6.73 0) | ~ (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : % 46.96/6.73 ! [v1: $i] : ( ~ (left_convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)) % 46.96/6.73 % 46.96/6.73 (ax4_basics) % 46.96/6.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 46.96/6.74 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = % 46.96/6.74 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 46.96/6.74 distinct_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 46.96/6.74 ! [v3: int] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ % 46.96/6.74 (distinct_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 46.96/6.74 distinct_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 46.96/6.74 [v3: int] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ % 46.96/6.74 (distinct_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 46.96/6.74 distinct_lines(v1, v2) = 0) % 46.96/6.74 % 46.96/6.74 (ax6_basics) % 46.96/6.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 46.96/6.74 0 | v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v4) | ~ % 46.96/6.74 (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 46.96/6.74 | ? [v5: int] : ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)) & ! % 46.96/6.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 46.96/6.74 (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, % 46.96/6.74 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 46.96/6.74 unequally_directed_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 46.96/6.74 $i] : ! [v3: int] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | % 46.96/6.74 ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 46.96/6.74 | unequally_directed_lines(v1, v2) = 0) % 46.96/6.74 % 46.96/6.74 (ax8_basics) % 46.96/6.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 46.96/6.74 (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ~ % 46.96/6.74 $i(v1) | ~ $i(v0) | unequally_directed_lines(v0, v1) = 0) & ! [v0: $i] : % 46.96/6.74 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = % 46.96/6.74 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (reverse_line(v1) = v3 & % 46.96/6.74 unequally_directed_lines(v0, v3) = 0 & $i(v3))) % 46.96/6.74 % 46.96/6.74 (ax8_cons_objs) % 46.96/6.74 ! [v0: $i] : ! [v1: $i] : ( ~ (reverse_line(v0) = v1) | ~ $i(v0) | ? [v2: % 46.96/6.74 int] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 46.96/6.74 % 46.96/6.74 (ax9_basics) % 46.96/6.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 46.96/6.74 (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ~ % 46.96/6.74 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ((v6 = 0 & % 46.96/6.74 left_convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & % 46.96/6.74 unequally_directed_lines(v0, v2) = v5) | ( ~ (v4 = 0) & % 46.96/6.74 unequally_directed_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 46.96/6.74 ! [v2: int] : (v2 = 0 | ~ (left_convergent_lines(v0, v1) = v2) | ~ $i(v1) | % 46.96/6.74 ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : ((v6 = % 46.96/6.74 0 & left_convergent_lines(v0, v4) = 0 & reverse_line(v1) = v4 & $i(v4)) % 46.96/6.74 | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) % 46.96/6.74 = v5 & $i(v4)) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) % 46.96/6.74 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) | ~ % 46.96/6.74 (unequally_directed_lines(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 46.96/6.74 int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & left_convergent_lines(v0, % 46.96/6.74 v2) = 0) | (v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) % 46.96/6.74 & unequally_directed_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : % 46.96/6.74 ( ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 46.96/6.74 $i] : ? [v3: int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & % 46.96/6.74 left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2 & $i(v2)) | % 46.96/6.74 (v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & % 46.96/6.74 reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3 & % 46.96/6.74 $i(v2)))) % 46.96/6.74 % 46.96/6.74 (con) % 46.96/6.74 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 46.96/6.74 equally_directed_opposite_lines(v0, v1) = v2 & reverse_line(v0) = v1 & % 46.96/6.74 $i(v1) & $i(v0)) % 46.96/6.74 % 46.96/6.75 (function-axioms) % 46.96/6.75 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 46.96/6.75 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4, % 46.96/6.75 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0: % 46.96/6.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 46.96/6.75 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ % 46.96/6.75 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 46.96/6.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 46.96/6.75 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) & % 46.96/6.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 46.96/6.75 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = % 46.96/6.75 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 46.96/6.75 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 46.96/6.75 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 46.96/6.75 [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 46.96/6.75 (distinct_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 46.96/6.75 ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 46.96/6.75 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 46.96/6.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 46.96/6.75 (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! % 46.96/6.75 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 46.96/6.75 $i] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ % 46.96/6.75 (incident_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 46.96/6.75 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 46.96/6.75 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 46.96/6.75 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 46.96/6.75 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 46.96/6.75 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 46.96/6.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 46.96/6.75 (equally_directed_opposite_lines(v3, v2) = v1) | ~ % 46.96/6.75 (equally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 46.96/6.75 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 46.96/6.75 (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = % 46.96/6.75 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 46.96/6.75 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ % 46.96/6.75 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 46.96/6.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 46.96/6.75 (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = % 46.96/6.75 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 46.96/6.75 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ % 46.96/6.75 (left_apart_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 46.96/6.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 46.96/6.75 (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0)) & ! % 46.96/6.75 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 46.96/6.75 $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ % 46.96/6.75 (unequally_directed_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 46.96/6.75 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 46.96/6.75 (unequally_directed_opposite_lines(v3, v2) = v1) | ~ % 46.96/6.75 (unequally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: % 46.96/6.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 46.96/6.75 ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 46.96/6.75 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~ % 46.96/6.75 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 46.96/6.75 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 46.96/6.75 % 46.96/6.75 Further assumptions not needed in the proof: % 46.96/6.75 -------------------------------------------- % 46.96/6.75 a2_defns, a3_defns, a4_defns, a6_defns, a8_defns, a9_defns, ax10_basics, % 46.96/6.75 ax10_cons_objs, ax1_basics, ax1_cons_objs, ax1_subs, ax1_uniq_cons, ax2_basics, % 46.96/6.75 ax2_cons_objs, ax2_subs, ax2_uniq_cons, ax3_basics, ax3_cons_objs, ax3_subs, % 46.96/6.75 ax4_cons_objs, ax4_defns, ax5_basics, ax5_cons_objs, ax6_cons_objs, ax7_basics, % 46.96/6.75 ax7_cons_objs, ax9_cons_objs % 46.96/6.75 % 46.96/6.75 Those formulas are unsatisfiable: % 46.96/6.75 --------------------------------- % 46.96/6.75 % 46.96/6.75 Begin of proof % 46.96/6.75 | % 46.96/6.75 | ALPHA: (a1_defns) implies: % 46.96/6.76 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (unequally_directed_opposite_lines(v0, % 46.96/6.76 | v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : % 46.96/6.76 | (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0 & % 46.96/6.76 | $i(v2))) % 46.96/6.76 | % 46.96/6.76 | ALPHA: (a5_defns) implies: % 46.96/6.76 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 46.96/6.76 | (equally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~ % 46.96/6.76 | $i(v0) | unequally_directed_opposite_lines(v0, v1) = 0) % 46.96/6.76 | % 46.96/6.76 | ALPHA: (a7_defns) implies: % 46.96/6.76 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (unequally_directed_opposite_lines(v0, % 46.96/6.76 | v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : % 46.96/6.76 | ((v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & % 46.96/6.76 | unequally_directed_lines(v0, v1) = v2))) % 46.96/6.76 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 46.96/6.76 | (unequally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~ % 46.96/6.76 | $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & v2 = 0 & % 46.96/6.76 | unequally_directed_lines(v0, v1) = 0) | ( ~ (v3 = 0) & % 46.96/6.76 | convergent_lines(v0, v1) = v3))) % 46.96/6.76 | % 46.96/6.76 | ALPHA: (ax4_basics) implies: % 46.96/6.76 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 46.96/6.76 | (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ % 46.96/6.76 | (distinct_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 46.96/6.76 | ? [v5: int] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) % 46.96/6.76 | % 46.96/6.76 | ALPHA: (ax6_basics) implies: % 46.96/6.76 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 46.96/6.76 | (v4 = 0 | v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v4) | ~ % 46.96/6.76 | (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 46.96/6.76 | $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & unequally_directed_lines(v0, % 46.96/6.76 | v1) = v5)) % 46.96/6.76 | % 46.96/6.76 | ALPHA: (ax8_basics) implies: % 46.96/6.76 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 46.96/6.76 | (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) % 46.96/6.76 | | ~ $i(v1) | ~ $i(v0) | unequally_directed_lines(v0, v1) = 0) % 46.96/6.76 | % 46.96/6.76 | ALPHA: (ax9_basics) implies: % 46.96/6.76 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) | % 46.96/6.76 | ~ (unequally_directed_lines(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | % 46.96/6.76 | ? [v3: int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & % 46.96/6.76 | left_convergent_lines(v0, v2) = 0) | (v4 = 0 & % 46.96/6.76 | left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & % 46.96/6.76 | unequally_directed_lines(v0, v1) = v3))) % 46.96/6.76 | % 46.96/6.76 | ALPHA: (ax11_basics) implies: % 46.96/6.76 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (left_convergent_lines(v0, v1) = 0) | % 46.96/6.76 | ~ $i(v1) | ~ $i(v0)) % 46.96/6.76 | % 46.96/6.76 | ALPHA: (function-axioms) implies: % 46.96/6.76 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 46.96/6.76 | : ! [v3: $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) % 46.96/6.76 | | ~ (unequally_directed_lines(v3, v2) = v0)) % 46.96/6.77 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 46.96/6.77 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 46.96/6.77 | (convergent_lines(v3, v2) = v0)) % 46.96/6.77 | % 46.96/6.77 | DELTA: instantiating (con) with fresh symbols all_39_0, all_39_1, all_39_2 % 46.96/6.77 | gives: % 47.14/6.77 | (12) ~ (all_39_0 = 0) & equally_directed_opposite_lines(all_39_2, % 47.14/6.77 | all_39_1) = all_39_0 & reverse_line(all_39_2) = all_39_1 & % 47.14/6.77 | $i(all_39_1) & $i(all_39_2) % 47.14/6.77 | % 47.14/6.77 | ALPHA: (12) implies: % 47.14/6.77 | (13) ~ (all_39_0 = 0) % 47.14/6.77 | (14) $i(all_39_2) % 47.14/6.77 | (15) $i(all_39_1) % 47.14/6.77 | (16) reverse_line(all_39_2) = all_39_1 % 47.14/6.77 | (17) equally_directed_opposite_lines(all_39_2, all_39_1) = all_39_0 % 47.14/6.77 | % 47.14/6.77 | GROUND_INST: instantiating (ax8_cons_objs) with all_39_2, all_39_1, % 47.14/6.77 | simplifying with (14), (16) gives: % 47.14/6.77 | (18) ? [v0: int] : ( ~ (v0 = 0) & distinct_lines(all_39_2, all_39_1) = v0) % 47.14/6.77 | % 47.14/6.77 | GROUND_INST: instantiating (2) with all_39_2, all_39_1, all_39_0, simplifying % 47.14/6.77 | with (14), (15), (17) gives: % 47.14/6.77 | (19) all_39_0 = 0 | unequally_directed_opposite_lines(all_39_2, all_39_1) = % 47.14/6.77 | 0 % 47.14/6.77 | % 47.14/6.77 | DELTA: instantiating (18) with fresh symbol all_46_0 gives: % 47.14/6.77 | (20) ~ (all_46_0 = 0) & distinct_lines(all_39_2, all_39_1) = all_46_0 % 47.14/6.77 | % 47.14/6.77 | ALPHA: (20) implies: % 47.14/6.77 | (21) ~ (all_46_0 = 0) % 47.14/6.77 | (22) distinct_lines(all_39_2, all_39_1) = all_46_0 % 47.14/6.77 | % 47.14/6.77 | BETA: splitting (19) gives: % 47.14/6.77 | % 47.14/6.77 | Case 1: % 47.14/6.77 | | % 47.14/6.77 | | (23) unequally_directed_opposite_lines(all_39_2, all_39_1) = 0 % 47.14/6.77 | | % 47.14/6.77 | | GROUND_INST: instantiating (3) with all_39_2, all_39_1, simplifying with % 47.14/6.77 | | (14), (15), (23) gives: % 47.14/6.77 | | (24) ? [v0: int] : ? [v1: int] : ((v1 = 0 & convergent_lines(all_39_2, % 47.14/6.77 | | all_39_1) = 0) | ( ~ (v0 = 0) & % 47.14/6.77 | | unequally_directed_lines(all_39_2, all_39_1) = v0)) % 47.14/6.77 | | % 47.14/6.77 | | GROUND_INST: instantiating (1) with all_39_2, all_39_1, simplifying with % 47.14/6.77 | | (14), (15), (23) gives: % 47.14/6.77 | | (25) ? [v0: $i] : (reverse_line(all_39_1) = v0 & % 47.14/6.77 | | unequally_directed_lines(all_39_2, v0) = 0 & $i(v0)) % 47.14/6.77 | | % 47.14/6.77 | | GROUND_INST: instantiating (4) with all_39_2, all_39_1, 0, simplifying with % 47.14/6.77 | | (14), (15), (23) gives: % 47.14/6.77 | | (26) ? [v0: int] : ? [v1: int] : ((v1 = 0 & % 47.14/6.77 | | unequally_directed_lines(all_39_2, all_39_1) = 0) | ( ~ (v0 = 0) % 47.14/6.77 | | & convergent_lines(all_39_2, all_39_1) = v0)) % 47.14/6.77 | | % 47.14/6.77 | | GROUND_INST: instantiating (5) with all_39_2, all_39_2, all_39_1, all_46_0, % 47.14/6.77 | | all_46_0, simplifying with (14), (15), (22) gives: % 47.14/6.77 | | (27) all_46_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 47.14/6.77 | | distinct_lines(all_39_2, all_39_2) = v0) % 47.14/6.77 | | % 47.14/6.77 | | DELTA: instantiating (25) with fresh symbol all_58_0 gives: % 47.14/6.78 | | (28) reverse_line(all_39_1) = all_58_0 & % 47.14/6.78 | | unequally_directed_lines(all_39_2, all_58_0) = 0 & $i(all_58_0) % 47.14/6.78 | | % 47.14/6.78 | | ALPHA: (28) implies: % 47.14/6.78 | | (29) $i(all_58_0) % 47.14/6.78 | | (30) unequally_directed_lines(all_39_2, all_58_0) = 0 % 47.14/6.78 | | (31) reverse_line(all_39_1) = all_58_0 % 47.14/6.78 | | % 47.14/6.78 | | DELTA: instantiating (26) with fresh symbols all_60_0, all_60_1 gives: % 47.14/6.78 | | (32) (all_60_0 = 0 & unequally_directed_lines(all_39_2, all_39_1) = 0) | % 47.14/6.78 | | ( ~ (all_60_1 = 0) & convergent_lines(all_39_2, all_39_1) = % 47.14/6.78 | | all_60_1) % 47.14/6.78 | | % 47.14/6.78 | | DELTA: instantiating (24) with fresh symbols all_61_0, all_61_1 gives: % 47.14/6.78 | | (33) (all_61_0 = 0 & convergent_lines(all_39_2, all_39_1) = 0) | ( ~ % 47.14/6.78 | | (all_61_1 = 0) & unequally_directed_lines(all_39_2, all_39_1) = % 47.14/6.78 | | all_61_1) % 47.14/6.78 | | % 47.14/6.78 | | BETA: splitting (27) gives: % 47.14/6.78 | | % 47.14/6.78 | | Case 1: % 47.14/6.78 | | | % 47.14/6.78 | | | (34) all_46_0 = 0 % 47.14/6.78 | | | % 47.14/6.78 | | | REDUCE: (21), (34) imply: % 47.14/6.78 | | | (35) $false % 47.14/6.78 | | | % 47.14/6.78 | | | CLOSE: (35) is inconsistent. % 47.14/6.78 | | | % 47.14/6.78 | | Case 2: % 47.14/6.78 | | | % 47.14/6.78 | | | % 47.14/6.78 | | | GROUND_INST: instantiating (8) with all_39_2, all_39_1, all_58_0, % 47.14/6.78 | | | simplifying with (14), (15), (30), (31) gives: % 47.14/6.78 | | | (36) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & % 47.14/6.78 | | | left_convergent_lines(all_39_2, all_58_0) = 0) | (v1 = 0 & % 47.14/6.78 | | | left_convergent_lines(all_39_2, all_39_1) = 0) | ( ~ (v0 = 0) % 47.14/6.78 | | | & unequally_directed_lines(all_39_2, all_39_1) = v0)) % 47.14/6.78 | | | % 47.14/6.78 | | | GROUND_INST: instantiating (ax8_cons_objs) with all_39_1, all_58_0, % 47.14/6.78 | | | simplifying with (15), (31) gives: % 47.14/6.78 | | | (37) ? [v0: int] : ( ~ (v0 = 0) & distinct_lines(all_39_1, all_58_0) = % 47.14/6.78 | | | v0) % 47.14/6.78 | | | % 47.14/6.78 | | | DELTA: instantiating (37) with fresh symbol all_73_0 gives: % 47.14/6.78 | | | (38) ~ (all_73_0 = 0) & distinct_lines(all_39_1, all_58_0) = all_73_0 % 47.14/6.78 | | | % 47.14/6.78 | | | ALPHA: (38) implies: % 47.14/6.78 | | | (39) ~ (all_73_0 = 0) % 47.14/6.78 | | | (40) distinct_lines(all_39_1, all_58_0) = all_73_0 % 47.14/6.78 | | | % 47.14/6.78 | | | DELTA: instantiating (36) with fresh symbols all_80_0, all_80_1, all_80_2 % 47.14/6.78 | | | gives: % 47.14/6.78 | | | (41) (all_80_0 = 0 & left_convergent_lines(all_39_2, all_58_0) = 0) | % 47.14/6.78 | | | (all_80_1 = 0 & left_convergent_lines(all_39_2, all_39_1) = 0) | ( % 47.14/6.78 | | | ~ (all_80_2 = 0) & unequally_directed_lines(all_39_2, all_39_1) % 47.14/6.78 | | | = all_80_2) % 47.14/6.78 | | | % 47.14/6.78 | | | GROUND_INST: instantiating (5) with all_39_1, all_39_1, all_58_0, % 47.14/6.78 | | | all_73_0, all_73_0, simplifying with (15), (29), (40) gives: % 47.14/6.78 | | | (42) all_73_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 47.14/6.78 | | | distinct_lines(all_39_1, all_39_1) = v0) % 47.14/6.78 | | | % 47.14/6.78 | | | BETA: splitting (42) gives: % 47.14/6.78 | | | % 47.14/6.78 | | | Case 1: % 47.14/6.78 | | | | % 47.14/6.78 | | | | (43) all_73_0 = 0 % 47.14/6.78 | | | | % 47.14/6.78 | | | | REDUCE: (39), (43) imply: % 47.14/6.78 | | | | (44) $false % 47.14/6.78 | | | | % 47.14/6.78 | | | | CLOSE: (44) is inconsistent. % 47.14/6.78 | | | | % 47.14/6.78 | | | Case 2: % 47.14/6.78 | | | | % 47.14/6.78 | | | | (45) ? [v0: int] : ( ~ (v0 = 0) & distinct_lines(all_39_1, all_39_1) % 47.14/6.78 | | | | = v0) % 47.14/6.78 | | | | % 47.14/6.78 | | | | DELTA: instantiating (45) with fresh symbol all_103_0 gives: % 47.14/6.78 | | | | (46) ~ (all_103_0 = 0) & distinct_lines(all_39_1, all_39_1) = % 47.14/6.78 | | | | all_103_0 % 47.14/6.78 | | | | % 47.14/6.78 | | | | ALPHA: (46) implies: % 47.14/6.78 | | | | (47) ~ (all_103_0 = 0) % 47.14/6.78 | | | | (48) distinct_lines(all_39_1, all_39_1) = all_103_0 % 47.14/6.78 | | | | % 47.14/6.78 | | | | GROUND_INST: instantiating (5) with all_39_1, all_39_2, all_39_1, % 47.14/6.78 | | | | all_103_0, all_46_0, simplifying with (14), (15), (22), % 47.14/6.78 | | | | (48) gives: % 47.14/6.78 | | | | (49) all_103_0 = 0 | all_46_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 47.14/6.78 | | | | distinct_lines(all_39_1, all_39_2) = v0) % 47.14/6.78 | | | | % 47.14/6.78 | | | | BETA: splitting (32) gives: % 47.14/6.78 | | | | % 47.14/6.78 | | | | Case 1: % 47.14/6.78 | | | | | % 47.14/6.78 | | | | | (50) all_60_0 = 0 & unequally_directed_lines(all_39_2, all_39_1) = % 47.14/6.78 | | | | | 0 % 47.14/6.79 | | | | | % 47.14/6.79 | | | | | ALPHA: (50) implies: % 47.14/6.79 | | | | | (51) unequally_directed_lines(all_39_2, all_39_1) = 0 % 47.14/6.79 | | | | | % 47.14/6.79 | | | | | BETA: splitting (41) gives: % 47.14/6.79 | | | | | % 47.14/6.79 | | | | | Case 1: % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | (52) all_80_0 = 0 & left_convergent_lines(all_39_2, all_58_0) = 0 % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | ALPHA: (52) implies: % 47.14/6.79 | | | | | | (53) left_convergent_lines(all_39_2, all_58_0) = 0 % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | GROUND_INST: instantiating (9) with all_39_2, all_58_0, simplifying % 47.14/6.79 | | | | | | with (14), (29), (53) gives: % 47.14/6.79 | | | | | | (54) $false % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | CLOSE: (54) is inconsistent. % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | Case 2: % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | (55) (all_80_1 = 0 & left_convergent_lines(all_39_2, all_39_1) = % 47.14/6.79 | | | | | | 0) | ( ~ (all_80_2 = 0) & % 47.14/6.79 | | | | | | unequally_directed_lines(all_39_2, all_39_1) = all_80_2) % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | BETA: splitting (55) gives: % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | Case 1: % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | (56) all_80_1 = 0 & left_convergent_lines(all_39_2, all_39_1) = % 47.14/6.79 | | | | | | | 0 % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | ALPHA: (56) implies: % 47.14/6.79 | | | | | | | (57) left_convergent_lines(all_39_2, all_39_1) = 0 % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | GROUND_INST: instantiating (9) with all_39_2, all_39_1, % 47.14/6.79 | | | | | | | simplifying with (14), (15), (57) gives: % 47.14/6.79 | | | | | | | (58) $false % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | CLOSE: (58) is inconsistent. % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | Case 2: % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | (59) ~ (all_80_2 = 0) & unequally_directed_lines(all_39_2, % 47.14/6.79 | | | | | | | all_39_1) = all_80_2 % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | ALPHA: (59) implies: % 47.14/6.79 | | | | | | | (60) ~ (all_80_2 = 0) % 47.14/6.79 | | | | | | | (61) unequally_directed_lines(all_39_2, all_39_1) = all_80_2 % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | GROUND_INST: instantiating (10) with 0, all_80_2, all_39_1, % 47.14/6.79 | | | | | | | all_39_2, simplifying with (51), (61) gives: % 47.14/6.79 | | | | | | | (62) all_80_2 = 0 % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | REDUCE: (60), (62) imply: % 47.14/6.79 | | | | | | | (63) $false % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | CLOSE: (63) is inconsistent. % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | End of split % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | End of split % 47.14/6.79 | | | | | % 47.14/6.79 | | | | Case 2: % 47.14/6.79 | | | | | % 47.14/6.79 | | | | | (64) ~ (all_60_1 = 0) & convergent_lines(all_39_2, all_39_1) = % 47.14/6.79 | | | | | all_60_1 % 47.14/6.79 | | | | | % 47.14/6.79 | | | | | ALPHA: (64) implies: % 47.14/6.79 | | | | | (65) ~ (all_60_1 = 0) % 47.14/6.79 | | | | | (66) convergent_lines(all_39_2, all_39_1) = all_60_1 % 47.14/6.79 | | | | | % 47.14/6.79 | | | | | BETA: splitting (33) gives: % 47.14/6.79 | | | | | % 47.14/6.79 | | | | | Case 1: % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | (67) all_61_0 = 0 & convergent_lines(all_39_2, all_39_1) = 0 % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | ALPHA: (67) implies: % 47.14/6.79 | | | | | | (68) convergent_lines(all_39_2, all_39_1) = 0 % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | GROUND_INST: instantiating (11) with 0, all_60_1, all_39_1, % 47.14/6.79 | | | | | | all_39_2, simplifying with (66), (68) gives: % 47.14/6.79 | | | | | | (69) all_60_1 = 0 % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | REDUCE: (65), (69) imply: % 47.14/6.79 | | | | | | (70) $false % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | CLOSE: (70) is inconsistent. % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | Case 2: % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | (71) ~ (all_61_1 = 0) & unequally_directed_lines(all_39_2, % 47.14/6.79 | | | | | | all_39_1) = all_61_1 % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | ALPHA: (71) implies: % 47.14/6.79 | | | | | | (72) ~ (all_61_1 = 0) % 47.14/6.79 | | | | | | (73) unequally_directed_lines(all_39_2, all_39_1) = all_61_1 % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | BETA: splitting (49) gives: % 47.14/6.79 | | | | | | % 47.14/6.79 | | | | | | Case 1: % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | (74) all_103_0 = 0 % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | REDUCE: (47), (74) imply: % 47.14/6.79 | | | | | | | (75) $false % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | CLOSE: (75) is inconsistent. % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | Case 2: % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | (76) all_46_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 47.14/6.79 | | | | | | | distinct_lines(all_39_1, all_39_2) = v0) % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | BETA: splitting (76) gives: % 47.14/6.79 | | | | | | | % 47.14/6.79 | | | | | | | Case 1: % 47.14/6.79 | | | | | | | | % 47.14/6.79 | | | | | | | | (77) all_46_0 = 0 % 47.14/6.79 | | | | | | | | % 47.14/6.79 | | | | | | | | REDUCE: (21), (77) imply: % 47.14/6.79 | | | | | | | | (78) $false % 47.14/6.79 | | | | | | | | % 47.14/6.79 | | | | | | | | CLOSE: (78) is inconsistent. % 47.14/6.79 | | | | | | | | % 47.14/6.79 | | | | | | | Case 2: % 47.14/6.79 | | | | | | | | % 47.14/6.79 | | | | | | | | % 47.14/6.79 | | | | | | | | GROUND_INST: instantiating (7) with all_39_2, all_39_2, % 47.14/6.79 | | | | | | | | all_39_1, all_61_1, simplifying with (14), (16), % 47.14/6.79 | | | | | | | | (73) gives: % 47.14/6.79 | | | | | | | | (79) all_61_1 = 0 | unequally_directed_lines(all_39_2, % 47.14/6.79 | | | | | | | | all_39_2) = 0 % 47.14/6.79 | | | | | | | | % 47.14/6.79 | | | | | | | | GROUND_INST: instantiating (6) with all_39_2, all_39_2, % 47.14/6.79 | | | | | | | | all_39_1, all_61_1, all_61_1, simplifying with % 47.14/6.79 | | | | | | | | (14), (15), (73) gives: % 47.14/6.79 | | | | | | | | (80) all_61_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 47.14/6.79 | | | | | | | | unequally_directed_lines(all_39_2, all_39_2) = v0) % 47.14/6.79 | | | | | | | | % 47.14/6.79 | | | | | | | | BETA: splitting (79) gives: % 47.14/6.79 | | | | | | | | % 47.14/6.79 | | | | | | | | Case 1: % 47.14/6.79 | | | | | | | | | % 47.14/6.79 | | | | | | | | | (81) unequally_directed_lines(all_39_2, all_39_2) = 0 % 47.14/6.79 | | | | | | | | | % 47.14/6.79 | | | | | | | | | BETA: splitting (80) gives: % 47.14/6.79 | | | | | | | | | % 47.14/6.79 | | | | | | | | | Case 1: % 47.14/6.79 | | | | | | | | | | % 47.14/6.79 | | | | | | | | | | (82) all_61_1 = 0 % 47.14/6.79 | | | | | | | | | | % 47.14/6.79 | | | | | | | | | | REDUCE: (72), (82) imply: % 47.14/6.79 | | | | | | | | | | (83) $false % 47.14/6.79 | | | | | | | | | | % 47.14/6.79 | | | | | | | | | | CLOSE: (83) is inconsistent. % 47.14/6.79 | | | | | | | | | | % 47.14/6.79 | | | | | | | | | Case 2: % 47.14/6.79 | | | | | | | | | | % 47.14/6.79 | | | | | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & % 47.14/6.79 | | | | | | | | | | unequally_directed_lines(all_39_2, all_39_2) = v0) % 47.14/6.79 | | | | | | | | | | % 47.14/6.79 | | | | | | | | | | DELTA: instantiating (84) with fresh symbol all_149_0 gives: % 47.14/6.79 | | | | | | | | | | (85) ~ (all_149_0 = 0) & % 47.14/6.79 | | | | | | | | | | unequally_directed_lines(all_39_2, all_39_2) = % 47.14/6.79 | | | | | | | | | | all_149_0 % 47.14/6.79 | | | | | | | | | | % 47.14/6.79 | | | | | | | | | | ALPHA: (85) implies: % 47.14/6.80 | | | | | | | | | | (86) ~ (all_149_0 = 0) % 47.14/6.80 | | | | | | | | | | (87) unequally_directed_lines(all_39_2, all_39_2) = % 47.14/6.80 | | | | | | | | | | all_149_0 % 47.14/6.80 | | | | | | | | | | % 47.14/6.80 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_149_0, all_39_2, % 47.14/6.80 | | | | | | | | | | all_39_2, simplifying with (81), (87) gives: % 47.14/6.80 | | | | | | | | | | (88) all_149_0 = 0 % 47.14/6.80 | | | | | | | | | | % 47.14/6.80 | | | | | | | | | | REDUCE: (86), (88) imply: % 47.14/6.80 | | | | | | | | | | (89) $false % 47.14/6.80 | | | | | | | | | | % 47.14/6.80 | | | | | | | | | | CLOSE: (89) is inconsistent. % 47.14/6.80 | | | | | | | | | | % 47.14/6.80 | | | | | | | | | End of split % 47.14/6.80 | | | | | | | | | % 47.14/6.80 | | | | | | | | Case 2: % 47.14/6.80 | | | | | | | | | % 47.14/6.80 | | | | | | | | | (90) all_61_1 = 0 % 47.14/6.80 | | | | | | | | | % 47.14/6.80 | | | | | | | | | REDUCE: (72), (90) imply: % 47.14/6.80 | | | | | | | | | (91) $false % 47.14/6.80 | | | | | | | | | % 47.14/6.80 | | | | | | | | | CLOSE: (91) is inconsistent. % 47.14/6.80 | | | | | | | | | % 47.14/6.80 | | | | | | | | End of split % 47.14/6.80 | | | | | | | | % 47.14/6.80 | | | | | | | End of split % 47.14/6.80 | | | | | | | % 47.14/6.80 | | | | | | End of split % 47.14/6.80 | | | | | | % 47.14/6.80 | | | | | End of split % 47.14/6.80 | | | | | % 47.14/6.80 | | | | End of split % 47.14/6.80 | | | | % 47.14/6.80 | | | End of split % 47.14/6.80 | | | % 47.14/6.80 | | End of split % 47.14/6.80 | | % 47.14/6.80 | Case 2: % 47.14/6.80 | | % 47.14/6.80 | | (92) all_39_0 = 0 % 47.14/6.80 | | % 47.14/6.80 | | REDUCE: (13), (92) imply: % 47.14/6.80 | | (93) $false % 47.14/6.80 | | % 47.14/6.80 | | CLOSE: (93) is inconsistent. % 47.14/6.80 | | % 47.14/6.80 | End of split % 47.14/6.80 | % 47.14/6.80 End of proof % 47.14/6.80 % SZS output end Proof for theBenchmark % 47.14/6.80 % 47.14/6.80 6199ms %------------------------------------------------------------------------------