%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO218+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 : n016.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 23:22:28 EDT 2023 % Result : Theorem 19.97s 3.41s % Output : Proof 39.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : GEO218+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.30 % Computer : n016.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 300 % 0.10/0.30 % DateTime : Tue Aug 29 21:55:46 EDT 2023 % 0.10/0.30 % CPUTime : % 0.15/0.58 ________ _____ % 0.15/0.58 ___ __ \_________(_)________________________________ % 0.15/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.15/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.15/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.15/0.58 % 0.15/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.15/0.58 (2023-06-19) % 0.15/0.58 % 0.15/0.58 (c) Philipp Rümmer, 2009-2023 % 0.15/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.15/0.58 Amanda Stjerna. % 0.15/0.58 Free software under BSD-3-Clause. % 0.15/0.58 % 0.15/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.15/0.58 % 0.15/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.15/0.60 Running up to 7 provers in parallel. % 0.61/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.61/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.61/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.61/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.61/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.61/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.61/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.69/1.17 Prover 4: Preprocessing ... % 2.69/1.17 Prover 1: Preprocessing ... % 3.70/1.23 Prover 5: Preprocessing ... % 3.70/1.23 Prover 6: Preprocessing ... % 3.70/1.23 Prover 0: Preprocessing ... % 3.70/1.23 Prover 3: Preprocessing ... % 3.70/1.23 Prover 2: Preprocessing ... % 7.45/1.74 Prover 2: Proving ... % 7.45/1.74 Prover 5: Proving ... % 7.97/1.85 Prover 1: Constructing countermodel ... % 7.97/1.86 Prover 3: Constructing countermodel ... % 7.97/1.88 Prover 6: Constructing countermodel ... % 10.95/2.19 Prover 3: gave up % 10.95/2.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.60/2.28 Prover 7: Preprocessing ... % 11.96/2.38 Prover 4: Constructing countermodel ... % 11.96/2.40 Prover 7: Warning: ignoring some quantifiers % 12.64/2.43 Prover 6: gave up % 12.64/2.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.64/2.45 Prover 7: Constructing countermodel ... % 12.64/2.50 Prover 8: Preprocessing ... % 12.64/2.50 Prover 1: gave up % 13.35/2.51 Prover 0: Proving ... % 13.35/2.51 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 13.35/2.56 Prover 9: Preprocessing ... % 15.55/2.81 Prover 7: gave up % 15.55/2.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.55/2.83 Prover 8: Warning: ignoring some quantifiers % 15.55/2.87 Prover 8: Constructing countermodel ... % 16.47/2.93 Prover 10: Preprocessing ... % 17.18/3.06 Prover 10: Warning: ignoring some quantifiers % 17.18/3.09 Prover 10: Constructing countermodel ... % 18.07/3.15 Prover 9: Constructing countermodel ... % 18.78/3.29 Prover 8: gave up % 18.78/3.29 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 19.43/3.34 Prover 10: gave up % 19.43/3.36 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 19.43/3.36 Prover 11: Preprocessing ... % 19.97/3.40 Prover 0: proved (2795ms) % 19.97/3.41 % 19.97/3.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 19.97/3.41 % 19.97/3.41 Prover 9: stopped % 19.97/3.41 Prover 2: stopped % 19.97/3.41 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 19.97/3.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 19.97/3.41 Prover 5: stopped % 19.97/3.41 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 19.97/3.42 Prover 12: Preprocessing ... % 19.97/3.45 Prover 16: Preprocessing ... % 20.71/3.48 Prover 19: Preprocessing ... % 20.71/3.49 Prover 13: Preprocessing ... % 20.84/3.51 Prover 12: stopped % 21.06/3.55 Prover 13: Warning: ignoring some quantifiers % 21.06/3.55 Prover 16: Warning: ignoring some quantifiers % 21.06/3.57 Prover 16: Constructing countermodel ... % 21.06/3.57 Prover 13: Constructing countermodel ... % 21.70/3.62 Prover 19: Warning: ignoring some quantifiers % 21.70/3.63 Prover 19: Constructing countermodel ... % 22.32/3.73 Prover 13: gave up % 22.32/3.75 Prover 11: Constructing countermodel ... % 24.19/3.96 Prover 19: gave up % 24.63/3.99 Prover 16: gave up % 37.78/6.53 Prover 11: Found proof (size 176) % 37.78/6.53 Prover 11: proved (3242ms) % 37.78/6.53 Prover 4: stopped % 37.78/6.54 % 37.78/6.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 37.78/6.54 % 37.78/6.55 % SZS output start Proof for theBenchmark % 37.78/6.56 Assumptions after simplification: % 37.78/6.56 --------------------------------- % 37.78/6.56 % 37.78/6.56 (a3) % 38.25/6.60 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (parallel_lines(v0, % 38.25/6.60 v1) = v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v1) = 0) & ! % 38.25/6.60 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (convergent_lines(v0, v1) % 38.25/6.60 = v2) | ~ $i(v1) | ~ $i(v0) | parallel_lines(v0, v1) = 0) & ! [v0: $i] % 38.25/6.60 : ! [v1: $i] : ( ~ (parallel_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 38.25/6.60 [v2: int] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0: $i] : % 38.25/6.60 ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 38.25/6.60 [v2: int] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) % 38.25/6.60 % 38.25/6.60 (a5) % 38.25/6.61 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (orthogonal_lines(v0, % 38.25/6.61 v1) = v2) | ~ $i(v1) | ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) & ! % 38.25/6.61 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (unorthogonal_lines(v0, % 38.25/6.61 v1) = v2) | ~ $i(v1) | ~ $i(v0) | orthogonal_lines(v0, v1) = 0) & ! % 38.25/6.61 [v0: $i] : ! [v1: $i] : ( ~ (orthogonal_lines(v0, v1) = 0) | ~ $i(v1) | ~ % 38.25/6.61 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & % 38.25/6.61 ! [v0: $i] : ! [v1: $i] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v1) | % 38.25/6.61 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) % 38.25/6.61 % 38.25/6.61 (ax6) % 38.25/6.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 38.25/6.61 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 38.25/6.61 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 38.25/6.61 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 38.25/6.61 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ % 38.25/6.61 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 38.25/6.61 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 38.25/6.61 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 38.25/6.61 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 38.25/6.61 convergent_lines(v1, v2) = 0) % 38.25/6.61 % 38.25/6.61 (coipo1) % 38.37/6.62 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 38.37/6.62 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 38.37/6.62 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 38.37/6.62 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 38.37/6.62 unorthogonal_lines(v0, v1) = 0) % 38.37/6.62 % 38.37/6.62 (con) % 38.37/6.62 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 38.37/6.62 orthogonal_lines(v1, v2) = v3 & orthogonal_lines(v0, v2) = 0 & % 38.37/6.62 parallel_lines(v0, v1) = 0 & $i(v2) & $i(v1) & $i(v0)) % 38.37/6.62 % 38.37/6.62 (cotno1) % 38.40/6.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 38.40/6.65 (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | % 38.40/6.65 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 38.40/6.65 int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | % 38.40/6.65 (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 38.40/6.65 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, % 38.40/6.65 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 38.40/6.65 ! [v4: any] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 38.40/6.65 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 38.40/6.65 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 38.40/6.65 convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 38.40/6.65 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1, % 38.40/6.65 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: % 38.40/6.65 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 38.40/6.65 (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ~ % 38.40/6.65 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 38.40/6.65 : ? [v8: int] : ((v6 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = % 38.40/6.65 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 38.40/6.65 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, % 38.40/6.65 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 38.40/6.65 ! [v4: any] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, % 38.40/6.65 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 38.40/6.65 int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 38.40/6.65 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 38.40/6.65 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1, % 38.40/6.65 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: % 38.40/6.65 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, % 38.40/6.65 v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 38.40/6.65 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 38.40/6.65 ((v6 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 38.40/6.65 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 38.40/6.65 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : % 38.40/6.65 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 38.40/6.65 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 38.40/6.65 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 38.40/6.65 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 38.40/6.65 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 38.40/6.65 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 38.40/6.65 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 38.40/6.65 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 38.40/6.65 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 38.40/6.65 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 38.40/6.65 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 38.40/6.65 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : % 38.40/6.65 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 38.40/6.65 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 38.40/6.65 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 38.40/6.65 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 38.40/6.65 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 38.40/6.65 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 38.40/6.65 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 38.40/6.65 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 38.40/6.65 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 38.40/6.65 convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 38.40/6.65 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 38.40/6.65 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] % 38.40/6.65 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ % 38.40/6.65 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 38.40/6.65 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 38.40/6.65 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 38.40/6.65 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 38.40/6.65 unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 38.40/6.65 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 38.40/6.65 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 38.40/6.65 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 38.40/6.65 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 38.40/6.65 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 38.40/6.65 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] % 38.40/6.65 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 38.40/6.65 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 38.40/6.65 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 38.40/6.65 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 38.40/6.65 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 38.40/6.65 unorthogonal_lines(v1, v2) = v7))) % 38.40/6.65 % 38.40/6.65 (couo1) % 38.40/6.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 38.40/6.66 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 38.40/6.66 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 38.40/6.66 [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0: $i] : % 38.40/6.66 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, % 38.40/6.66 v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | % 38.40/6.66 ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! % 38.40/6.66 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ % 38.40/6.66 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 38.40/6.66 unorthogonal_lines(v0, v2) = 0) % 38.40/6.66 % 38.40/6.66 (oac1) % 38.40/6.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 38.40/6.67 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | % 38.40/6.67 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 38.40/6.67 int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | % 38.40/6.67 (v7 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 38.40/6.67 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, % 38.40/6.67 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 38.40/6.67 ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ % 38.40/6.67 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 38.40/6.67 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 38.40/6.67 convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 38.40/6.67 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0, % 38.40/6.67 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0: % 38.40/6.67 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 38.40/6.68 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~ % 38.40/6.68 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 38.40/6.68 : ? [v8: int] : ((v8 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v7 = % 38.40/6.68 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 38.40/6.68 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, % 38.40/6.68 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 38.40/6.68 ! [v4: any] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 38.40/6.68 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 38.40/6.68 int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 38.40/6.68 unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 38.40/6.68 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0, % 38.40/6.68 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0: % 38.40/6.68 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, % 38.40/6.68 v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) % 38.40/6.68 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 38.40/6.68 ((v7 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 38.40/6.68 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 38.40/6.68 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 38.40/6.68 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ % 38.40/6.68 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 38.40/6.68 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 38.40/6.68 convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 38.40/6.68 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 38.40/6.68 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 38.40/6.68 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 38.40/6.68 (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 38.40/6.68 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 38.40/6.68 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 38.40/6.68 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 38.40/6.68 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 38.40/6.68 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 38.40/6.68 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 38.40/6.68 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 38.40/6.68 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 38.40/6.68 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 38.40/6.68 unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 38.40/6.68 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 38.40/6.68 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 38.40/6.68 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 38.40/6.68 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 38.40/6.68 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 38.40/6.68 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 38.40/6.68 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 38.40/6.68 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 38.40/6.68 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 38.40/6.68 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 38.40/6.68 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 38.40/6.68 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 38.40/6.68 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~ % 38.40/6.68 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 38.40/6.68 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 38.40/6.68 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 38.40/6.68 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 38.40/6.68 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 38.40/6.68 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) | ~ % 38.40/6.68 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 38.40/6.68 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 38.40/6.68 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 38.40/6.68 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 38.40/6.68 unorthogonal_lines(v0, v1) = v4))) % 38.40/6.68 % 38.40/6.68 (occu1) % 38.40/6.68 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 38.40/6.68 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 38.40/6.68 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 38.40/6.68 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 38.40/6.68 unorthogonal_lines(v0, v1) = 0) % 38.40/6.68 % 38.40/6.68 (function-axioms) % 38.40/6.69 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 38.40/6.69 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 38.40/6.69 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.40/6.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.40/6.69 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 38.40/6.69 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 38.40/6.69 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 38.40/6.69 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.40/6.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.40/6.69 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 38.40/6.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 38.40/6.69 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 38.40/6.69 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.40/6.69 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 38.40/6.69 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 38.40/6.69 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 38.40/6.69 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 38.40/6.69 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 38.40/6.69 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 38.40/6.69 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 38.40/6.69 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 38.40/6.69 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 38.40/6.69 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.40/6.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.40/6.69 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 38.40/6.69 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 38.40/6.69 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 38.40/6.69 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.40/6.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.40/6.69 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 38.40/6.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 38.40/6.69 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 38.40/6.69 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 38.40/6.69 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 38.40/6.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 38.40/6.69 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 38.40/6.69 % 38.40/6.69 Further assumptions not needed in the proof: % 38.40/6.69 -------------------------------------------- % 38.40/6.69 a4, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ceq1, ceq2, ceq3, ci1, % 38.40/6.69 ci2, ci3, ci4, con1, cp1, cp2, cu1, cup1, int1, ooc1, ooc2, orth1, ouo1, p1, % 38.40/6.69 par1 % 38.40/6.69 % 38.40/6.69 Those formulas are unsatisfiable: % 38.40/6.69 --------------------------------- % 38.40/6.69 % 38.40/6.69 Begin of proof % 38.40/6.69 | % 38.40/6.69 | ALPHA: (ax6) implies: % 38.40/6.69 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 38.40/6.69 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 38.40/6.70 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0) % 38.40/6.70 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 38.40/6.70 | (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ % 38.40/6.70 | (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 38.40/6.70 | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) % 38.40/6.70 | % 38.40/6.70 | ALPHA: (oac1) implies: % 38.40/6.70 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 38.40/6.70 | (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = % 38.40/6.70 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 38.40/6.70 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 38.40/6.70 | unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | % 38.40/6.70 | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 38.40/6.70 | convergent_lines(v0, v1) = v4))) % 38.40/6.70 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 38.40/6.70 | ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) % 38.40/6.70 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 38.40/6.70 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 38.40/6.70 | convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 38.40/6.70 | convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 38.40/6.70 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 38.40/6.70 | convergent_lines(v0, v1) = v5))) % 38.40/6.70 | % 38.40/6.70 | ALPHA: (occu1) implies: % 38.40/6.70 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 38.40/6.70 | (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 38.40/6.70 | unorthogonal_lines(v0, v1) = 0) % 38.40/6.70 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 38.40/6.70 | (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 38.40/6.70 | convergent_lines(v0, v1) = 0) % 38.40/6.70 | % 38.40/6.70 | ALPHA: (cotno1) implies: % 38.40/6.71 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 38.40/6.71 | (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) % 38.40/6.71 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : % 38.40/6.71 | ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 38.40/6.71 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | % 38.40/6.71 | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 38.40/6.71 | convergent_lines(v1, v2) = v7))) % 38.40/6.71 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 38.40/6.71 | (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = % 38.40/6.71 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 38.40/6.71 | int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 38.40/6.71 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 38.40/6.71 | unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | % 38.40/6.71 | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) % 38.40/6.71 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 38.40/6.71 | ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = % 38.40/6.71 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 38.40/6.71 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 38.40/6.71 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 38.40/6.71 | unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 38.40/6.71 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 38.40/6.71 | convergent_lines(v1, v2) = v7))) % 38.40/6.71 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 38.40/6.71 | : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, % 38.40/6.71 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : % 38.40/6.71 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 38.40/6.71 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 38.40/6.71 | convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 38.40/6.71 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 38.40/6.71 | convergent_lines(v1, v2) = v7))) % 38.40/6.71 | % 38.40/6.71 | ALPHA: (couo1) implies: % 38.40/6.71 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] % 38.40/6.71 | : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 38.40/6.71 | (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 38.40/6.71 | $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = % 38.40/6.71 | v5)) % 38.40/6.71 | % 38.40/6.71 | ALPHA: (a3) implies: % 38.40/6.71 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (parallel_lines(v0, v1) = 0) | ~ % 38.40/6.71 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 38.40/6.71 | convergent_lines(v0, v1) = v2)) % 38.40/6.71 | % 38.40/6.71 | ALPHA: (a5) implies: % 38.40/6.72 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (orthogonal_lines(v0, v1) = 0) | ~ % 38.40/6.72 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 38.40/6.72 | unorthogonal_lines(v0, v1) = v2)) % 38.40/6.72 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 38.40/6.72 | (orthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 38.40/6.72 | unorthogonal_lines(v0, v1) = 0) % 38.40/6.72 | % 38.40/6.72 | ALPHA: (function-axioms) implies: % 38.88/6.72 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 38.88/6.72 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 38.88/6.72 | (convergent_lines(v3, v2) = v0)) % 38.88/6.72 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 38.88/6.72 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 38.88/6.72 | (unorthogonal_lines(v3, v2) = v0)) % 38.88/6.72 | % 38.88/6.72 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 38.88/6.72 | all_38_3 gives: % 38.88/6.72 | (17) ~ (all_38_0 = 0) & orthogonal_lines(all_38_2, all_38_1) = all_38_0 & % 38.88/6.72 | orthogonal_lines(all_38_3, all_38_1) = 0 & parallel_lines(all_38_3, % 38.88/6.72 | all_38_2) = 0 & $i(all_38_1) & $i(all_38_2) & $i(all_38_3) % 38.88/6.72 | % 38.88/6.72 | ALPHA: (17) implies: % 38.88/6.72 | (18) ~ (all_38_0 = 0) % 38.88/6.72 | (19) $i(all_38_3) % 38.88/6.72 | (20) $i(all_38_2) % 38.88/6.72 | (21) $i(all_38_1) % 38.88/6.72 | (22) parallel_lines(all_38_3, all_38_2) = 0 % 38.88/6.72 | (23) orthogonal_lines(all_38_3, all_38_1) = 0 % 38.88/6.72 | (24) orthogonal_lines(all_38_2, all_38_1) = all_38_0 % 38.88/6.72 | % 38.88/6.72 | GROUND_INST: instantiating (12) with all_38_3, all_38_2, simplifying with % 38.88/6.72 | (19), (20), (22) gives: % 38.88/6.72 | (25) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_3, all_38_2) = % 38.88/6.72 | v0) % 38.88/6.72 | % 38.88/6.72 | GROUND_INST: instantiating (13) with all_38_3, all_38_1, simplifying with % 38.88/6.72 | (19), (21), (23) gives: % 38.88/6.72 | (26) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_38_3, all_38_1) = % 38.88/6.72 | v0) % 38.88/6.72 | % 38.88/6.73 | GROUND_INST: instantiating (14) with all_38_2, all_38_1, all_38_0, simplifying % 38.88/6.73 | with (20), (21), (24) gives: % 38.88/6.73 | (27) all_38_0 = 0 | unorthogonal_lines(all_38_2, all_38_1) = 0 % 38.88/6.73 | % 38.88/6.73 | DELTA: instantiating (26) with fresh symbol all_45_0 gives: % 38.88/6.73 | (28) ~ (all_45_0 = 0) & unorthogonal_lines(all_38_3, all_38_1) = all_45_0 % 38.88/6.73 | % 38.88/6.73 | ALPHA: (28) implies: % 38.88/6.73 | (29) ~ (all_45_0 = 0) % 38.88/6.73 | (30) unorthogonal_lines(all_38_3, all_38_1) = all_45_0 % 38.88/6.73 | % 38.88/6.73 | DELTA: instantiating (25) with fresh symbol all_47_0 gives: % 38.88/6.73 | (31) ~ (all_47_0 = 0) & convergent_lines(all_38_3, all_38_2) = all_47_0 % 38.88/6.73 | % 38.88/6.73 | ALPHA: (31) implies: % 38.88/6.73 | (32) ~ (all_47_0 = 0) % 38.88/6.73 | (33) convergent_lines(all_38_3, all_38_2) = all_47_0 % 38.88/6.73 | % 38.88/6.73 | BETA: splitting (27) gives: % 38.88/6.73 | % 38.88/6.73 | Case 1: % 38.88/6.73 | | % 38.88/6.73 | | (34) unorthogonal_lines(all_38_2, all_38_1) = 0 % 38.88/6.73 | | % 38.88/6.73 | | GROUND_INST: instantiating (5) with all_38_3, all_38_2, all_47_0, % 38.88/6.73 | | simplifying with (19), (20), (33) gives: % 38.88/6.73 | | (35) all_47_0 = 0 | unorthogonal_lines(all_38_3, all_38_2) = 0 % 38.88/6.73 | | % 38.88/6.73 | | GROUND_INST: instantiating (11) with all_38_3, all_38_1, all_38_1, all_45_0, % 38.88/6.73 | | all_45_0, simplifying with (19), (21), (30) gives: % 38.88/6.73 | | (36) all_45_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 38.88/6.73 | | convergent_lines(all_38_1, all_38_1) = v0) % 38.88/6.73 | | % 38.88/6.73 | | GROUND_INST: instantiating (9) with all_38_3, all_38_2, all_38_1, all_47_0, % 38.88/6.73 | | all_45_0, simplifying with (19), (20), (21), (30), (33) gives: % 38.88/6.73 | | (37) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0 % 38.88/6.73 | | & all_45_0 = 0 & convergent_lines(all_38_3, all_38_1) = 0) | (v0 % 38.88/6.73 | | = 0 & all_47_0 = 0 & unorthogonal_lines(all_38_3, all_38_2) = 0) % 38.88/6.73 | | | ( ~ (v3 = 0) & unorthogonal_lines(all_38_2, all_38_1) = v3) | ( % 38.88/6.73 | | ~ (v2 = 0) & convergent_lines(all_38_2, all_38_1) = v2)) % 38.88/6.73 | | % 38.88/6.74 | | GROUND_INST: instantiating (6) with all_38_3, all_38_1, all_45_0, % 38.88/6.74 | | simplifying with (19), (21), (30) gives: % 38.88/6.74 | | (38) all_45_0 = 0 | convergent_lines(all_38_3, all_38_1) = 0 % 38.88/6.74 | | % 38.88/6.74 | | GROUND_INST: instantiating (3) with all_38_2, all_38_1, all_38_1, 0, % 38.88/6.74 | | simplifying with (20), (21), (34) gives: % 38.88/6.74 | | (39) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 % 38.88/6.74 | | & v2 = 0 & unorthogonal_lines(all_38_1, all_38_1) = 0 & % 38.88/6.74 | | convergent_lines(all_38_1, all_38_1) = 0) | (v1 = 0 & % 38.88/6.74 | | convergent_lines(all_38_2, all_38_1) = 0) | ( ~ (v0 = 0) & % 38.88/6.74 | | convergent_lines(all_38_2, all_38_1) = v0)) % 38.88/6.74 | | % 38.88/6.74 | | GROUND_INST: instantiating (10) with all_38_2, all_38_1, all_38_1, 0, 0, % 38.88/6.74 | | simplifying with (20), (21), (34) gives: % 38.88/6.74 | | (40) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0 % 38.88/6.74 | | & convergent_lines(all_38_2, all_38_1) = 0) | (v0 = 0 & % 38.88/6.74 | | convergent_lines(all_38_2, all_38_1) = 0) | ( ~ (v3 = 0) & % 38.88/6.74 | | unorthogonal_lines(all_38_1, all_38_1) = v3) | ( ~ (v2 = 0) & % 38.88/6.74 | | convergent_lines(all_38_1, all_38_1) = v2)) % 38.88/6.74 | | % 38.88/6.74 | | GROUND_INST: instantiating (4) with all_38_3, all_38_2, all_38_1, all_45_0, % 38.88/6.74 | | 0, simplifying with (19), (20), (21), (30), (34) gives: % 38.88/6.74 | | (41) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 % 38.88/6.74 | | & convergent_lines(all_38_2, all_38_1) = 0) | (v2 = 0 & all_45_0 % 38.88/6.74 | | = 0 & convergent_lines(all_38_3, all_38_1) = 0) | ( ~ (v1 = 0) & % 38.88/6.74 | | unorthogonal_lines(all_38_3, all_38_2) = v1) | ( ~ (v0 = 0) & % 38.88/6.74 | | convergent_lines(all_38_3, all_38_2) = v0)) % 38.88/6.74 | | % 38.88/6.74 | | GROUND_INST: instantiating (8) with all_38_3, all_38_2, all_38_1, all_45_0, % 38.88/6.74 | | simplifying with (19), (20), (21), (30), (34) gives: % 38.88/6.74 | | (42) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 % 38.88/6.74 | | & all_45_0 = 0 & convergent_lines(all_38_3, all_38_1) = 0) | (v1 % 38.88/6.74 | | = 0 & v0 = 0 & unorthogonal_lines(all_38_3, all_38_2) = 0 & % 38.88/6.74 | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ (v3 = 0) & % 38.88/6.74 | | convergent_lines(all_38_2, all_38_1) = v3)) % 38.88/6.74 | | % 38.88/6.74 | | GROUND_INST: instantiating (7) with all_38_3, all_38_2, all_38_1, all_47_0, % 38.88/6.74 | | simplifying with (19), (20), (21), (33), (34) gives: % 38.88/6.74 | | (43) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 % 38.88/6.74 | | & v1 = 0 & unorthogonal_lines(all_38_3, all_38_1) = 0 & % 38.88/6.74 | | convergent_lines(all_38_3, all_38_1) = 0) | (v0 = 0 & all_47_0 = % 38.88/6.74 | | 0 & unorthogonal_lines(all_38_3, all_38_2) = 0) | ( ~ (v3 = 0) & % 38.88/6.74 | | convergent_lines(all_38_2, all_38_1) = v3)) % 38.88/6.74 | | % 38.88/6.74 | | DELTA: instantiating (39) with fresh symbols all_59_0, all_59_1, all_59_2, % 38.88/6.74 | | all_59_3 gives: % 38.88/6.74 | | (44) (all_59_0 = 0 & all_59_1 = 0 & unorthogonal_lines(all_38_1, % 38.88/6.74 | | all_38_1) = 0 & convergent_lines(all_38_1, all_38_1) = 0) | % 38.88/6.74 | | (all_59_2 = 0 & convergent_lines(all_38_2, all_38_1) = 0) | ( ~ % 38.88/6.74 | | (all_59_3 = 0) & convergent_lines(all_38_2, all_38_1) = all_59_3) % 38.88/6.74 | | % 38.88/6.74 | | DELTA: instantiating (40) with fresh symbols all_61_0, all_61_1, all_61_2, % 38.88/6.74 | | all_61_3 gives: % 38.88/6.74 | | (45) (all_61_2 = 0 & convergent_lines(all_38_2, all_38_1) = 0) | % 38.88/6.74 | | (all_61_3 = 0 & convergent_lines(all_38_2, all_38_1) = 0) | ( ~ % 38.88/6.74 | | (all_61_0 = 0) & unorthogonal_lines(all_38_1, all_38_1) = % 38.88/6.74 | | all_61_0) | ( ~ (all_61_1 = 0) & convergent_lines(all_38_1, % 38.88/6.74 | | all_38_1) = all_61_1) % 38.88/6.74 | | % 38.88/6.74 | | DELTA: instantiating (43) with fresh symbols all_62_0, all_62_1, all_62_2, % 38.88/6.74 | | all_62_3 gives: % 38.88/6.74 | | (46) (all_62_1 = 0 & all_62_2 = 0 & unorthogonal_lines(all_38_3, % 38.88/6.74 | | all_38_1) = 0 & convergent_lines(all_38_3, all_38_1) = 0) | % 38.88/6.75 | | (all_62_3 = 0 & all_47_0 = 0 & unorthogonal_lines(all_38_3, % 38.88/6.75 | | all_38_2) = 0) | ( ~ (all_62_0 = 0) & convergent_lines(all_38_2, % 38.88/6.75 | | all_38_1) = all_62_0) % 38.88/6.75 | | % 38.88/6.75 | | DELTA: instantiating (42) with fresh symbols all_63_0, all_63_1, all_63_2, % 38.88/6.75 | | all_63_3 gives: % 38.88/6.75 | | (47) (all_63_1 = 0 & all_45_0 = 0 & convergent_lines(all_38_3, all_38_1) % 38.88/6.75 | | = 0) | (all_63_2 = 0 & all_63_3 = 0 & unorthogonal_lines(all_38_3, % 38.88/6.75 | | all_38_2) = 0 & convergent_lines(all_38_3, all_38_2) = 0) | ( ~ % 38.88/6.75 | | (all_63_0 = 0) & convergent_lines(all_38_2, all_38_1) = all_63_0) % 38.88/6.75 | | % 38.88/6.75 | | DELTA: instantiating (41) with fresh symbols all_65_0, all_65_1, all_65_2, % 38.88/6.75 | | all_65_3 gives: % 38.88/6.75 | | (48) (all_65_0 = 0 & convergent_lines(all_38_2, all_38_1) = 0) | % 38.88/6.75 | | (all_65_1 = 0 & all_45_0 = 0 & convergent_lines(all_38_3, all_38_1) % 38.88/6.75 | | = 0) | ( ~ (all_65_2 = 0) & unorthogonal_lines(all_38_3, all_38_2) % 38.88/6.75 | | = all_65_2) | ( ~ (all_65_3 = 0) & convergent_lines(all_38_3, % 38.88/6.75 | | all_38_2) = all_65_3) % 38.88/6.75 | | % 38.88/6.75 | | DELTA: instantiating (37) with fresh symbols all_70_0, all_70_1, all_70_2, % 38.88/6.75 | | all_70_3 gives: % 38.88/6.75 | | (49) (all_70_2 = 0 & all_45_0 = 0 & convergent_lines(all_38_3, all_38_1) % 38.88/6.75 | | = 0) | (all_70_3 = 0 & all_47_0 = 0 & unorthogonal_lines(all_38_3, % 38.88/6.75 | | all_38_2) = 0) | ( ~ (all_70_0 = 0) & % 38.88/6.75 | | unorthogonal_lines(all_38_2, all_38_1) = all_70_0) | ( ~ (all_70_1 % 38.88/6.75 | | = 0) & convergent_lines(all_38_2, all_38_1) = all_70_1) % 38.88/6.75 | | % 38.88/6.75 | | BETA: splitting (38) gives: % 38.88/6.75 | | % 38.88/6.75 | | Case 1: % 38.88/6.75 | | | % 38.88/6.75 | | | (50) convergent_lines(all_38_3, all_38_1) = 0 % 38.88/6.75 | | | % 38.88/6.75 | | | BETA: splitting (35) gives: % 38.88/6.75 | | | % 38.88/6.75 | | | Case 1: % 38.88/6.75 | | | | % 38.88/6.75 | | | | (51) unorthogonal_lines(all_38_3, all_38_2) = 0 % 38.88/6.75 | | | | % 38.88/6.75 | | | | BETA: splitting (47) gives: % 38.88/6.75 | | | | % 38.88/6.75 | | | | Case 1: % 38.88/6.75 | | | | | % 38.88/6.75 | | | | | (52) all_63_1 = 0 & all_45_0 = 0 & convergent_lines(all_38_3, % 38.88/6.75 | | | | | all_38_1) = 0 % 38.88/6.75 | | | | | % 38.88/6.75 | | | | | ALPHA: (52) implies: % 38.88/6.75 | | | | | (53) all_45_0 = 0 % 38.88/6.75 | | | | | % 38.88/6.75 | | | | | REDUCE: (29), (53) imply: % 38.88/6.75 | | | | | (54) $false % 38.88/6.75 | | | | | % 38.88/6.75 | | | | | CLOSE: (54) is inconsistent. % 38.88/6.75 | | | | | % 38.88/6.75 | | | | Case 2: % 38.88/6.75 | | | | | % 38.88/6.75 | | | | | (55) (all_63_2 = 0 & all_63_3 = 0 & unorthogonal_lines(all_38_3, % 38.88/6.75 | | | | | all_38_2) = 0 & convergent_lines(all_38_3, all_38_2) = 0) % 38.88/6.75 | | | | | | ( ~ (all_63_0 = 0) & convergent_lines(all_38_2, all_38_1) = % 38.88/6.75 | | | | | all_63_0) % 38.88/6.75 | | | | | % 38.88/6.75 | | | | | BETA: splitting (55) gives: % 38.88/6.75 | | | | | % 38.88/6.75 | | | | | Case 1: % 38.88/6.75 | | | | | | % 38.88/6.76 | | | | | | (56) all_63_2 = 0 & all_63_3 = 0 & unorthogonal_lines(all_38_3, % 38.88/6.76 | | | | | | all_38_2) = 0 & convergent_lines(all_38_3, all_38_2) = 0 % 38.88/6.76 | | | | | | % 38.88/6.76 | | | | | | ALPHA: (56) implies: % 38.88/6.76 | | | | | | (57) convergent_lines(all_38_3, all_38_2) = 0 % 38.88/6.76 | | | | | | % 38.88/6.76 | | | | | | GROUND_INST: instantiating (15) with all_47_0, 0, all_38_2, % 38.88/6.76 | | | | | | all_38_3, simplifying with (33), (57) gives: % 38.88/6.76 | | | | | | (58) all_47_0 = 0 % 38.88/6.76 | | | | | | % 38.88/6.76 | | | | | | REDUCE: (32), (58) imply: % 38.88/6.76 | | | | | | (59) $false % 38.88/6.76 | | | | | | % 38.88/6.76 | | | | | | CLOSE: (59) is inconsistent. % 38.88/6.76 | | | | | | % 38.88/6.76 | | | | | Case 2: % 38.88/6.76 | | | | | | % 38.88/6.76 | | | | | | (60) ~ (all_63_0 = 0) & convergent_lines(all_38_2, all_38_1) = % 38.88/6.76 | | | | | | all_63_0 % 38.88/6.76 | | | | | | % 38.88/6.76 | | | | | | ALPHA: (60) implies: % 38.88/6.76 | | | | | | (61) convergent_lines(all_38_2, all_38_1) = all_63_0 % 38.88/6.76 | | | | | | % 38.88/6.76 | | | | | | BETA: splitting (36) gives: % 38.88/6.76 | | | | | | % 38.88/6.76 | | | | | | Case 1: % 38.88/6.76 | | | | | | | % 38.88/6.76 | | | | | | | (62) all_45_0 = 0 % 38.88/6.76 | | | | | | | % 38.88/6.76 | | | | | | | REDUCE: (29), (62) imply: % 38.88/6.76 | | | | | | | (63) $false % 38.88/6.76 | | | | | | | % 38.88/6.76 | | | | | | | CLOSE: (63) is inconsistent. % 38.88/6.76 | | | | | | | % 38.88/6.76 | | | | | | Case 2: % 38.88/6.76 | | | | | | | % 38.88/6.76 | | | | | | | (64) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_1, % 38.88/6.76 | | | | | | | all_38_1) = v0) % 38.88/6.76 | | | | | | | % 38.88/6.76 | | | | | | | DELTA: instantiating (64) with fresh symbol all_85_0 gives: % 38.88/6.76 | | | | | | | (65) ~ (all_85_0 = 0) & convergent_lines(all_38_1, all_38_1) = % 38.88/6.76 | | | | | | | all_85_0 % 38.88/6.76 | | | | | | | % 38.88/6.76 | | | | | | | ALPHA: (65) implies: % 38.88/6.76 | | | | | | | (66) ~ (all_85_0 = 0) % 38.88/6.76 | | | | | | | (67) convergent_lines(all_38_1, all_38_1) = all_85_0 % 38.88/6.76 | | | | | | | % 38.88/6.76 | | | | | | | BETA: splitting (46) gives: % 38.88/6.76 | | | | | | | % 38.88/6.76 | | | | | | | Case 1: % 38.88/6.76 | | | | | | | | % 38.88/6.76 | | | | | | | | (68) all_62_1 = 0 & all_62_2 = 0 & % 38.88/6.76 | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0 & % 38.88/6.76 | | | | | | | | convergent_lines(all_38_3, all_38_1) = 0 % 38.88/6.76 | | | | | | | | % 38.88/6.76 | | | | | | | | ALPHA: (68) implies: % 38.88/6.76 | | | | | | | | (69) unorthogonal_lines(all_38_3, all_38_1) = 0 % 38.88/6.76 | | | | | | | | % 38.88/6.76 | | | | | | | | GROUND_INST: instantiating (16) with all_45_0, 0, all_38_1, % 38.88/6.76 | | | | | | | | all_38_3, simplifying with (30), (69) gives: % 38.88/6.76 | | | | | | | | (70) all_45_0 = 0 % 38.88/6.76 | | | | | | | | % 38.88/6.76 | | | | | | | | REDUCE: (29), (70) imply: % 38.88/6.76 | | | | | | | | (71) $false % 38.88/6.76 | | | | | | | | % 38.88/6.76 | | | | | | | | CLOSE: (71) is inconsistent. % 38.88/6.76 | | | | | | | | % 38.88/6.76 | | | | | | | Case 2: % 38.88/6.76 | | | | | | | | % 38.88/6.76 | | | | | | | | (72) (all_62_3 = 0 & all_47_0 = 0 & % 38.88/6.76 | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0) | ( ~ % 38.88/6.76 | | | | | | | | (all_62_0 = 0) & convergent_lines(all_38_2, all_38_1) % 38.88/6.76 | | | | | | | | = all_62_0) % 38.88/6.76 | | | | | | | | % 38.88/6.76 | | | | | | | | BETA: splitting (72) gives: % 38.88/6.76 | | | | | | | | % 38.88/6.76 | | | | | | | | Case 1: % 38.88/6.76 | | | | | | | | | % 38.88/6.77 | | | | | | | | | (73) all_62_3 = 0 & all_47_0 = 0 & % 38.88/6.77 | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 % 38.88/6.77 | | | | | | | | | % 38.88/6.77 | | | | | | | | | ALPHA: (73) implies: % 38.88/6.77 | | | | | | | | | (74) all_47_0 = 0 % 38.88/6.77 | | | | | | | | | % 38.88/6.77 | | | | | | | | | REDUCE: (32), (74) imply: % 38.88/6.77 | | | | | | | | | (75) $false % 38.88/6.77 | | | | | | | | | % 38.88/6.77 | | | | | | | | | CLOSE: (75) is inconsistent. % 38.88/6.77 | | | | | | | | | % 38.88/6.77 | | | | | | | | Case 2: % 38.88/6.77 | | | | | | | | | % 38.88/6.77 | | | | | | | | | (76) ~ (all_62_0 = 0) & convergent_lines(all_38_2, % 38.88/6.77 | | | | | | | | | all_38_1) = all_62_0 % 38.88/6.77 | | | | | | | | | % 38.88/6.77 | | | | | | | | | ALPHA: (76) implies: % 38.88/6.77 | | | | | | | | | (77) ~ (all_62_0 = 0) % 38.88/6.77 | | | | | | | | | (78) convergent_lines(all_38_2, all_38_1) = all_62_0 % 38.88/6.77 | | | | | | | | | % 38.88/6.77 | | | | | | | | | BETA: splitting (44) gives: % 38.88/6.77 | | | | | | | | | % 38.88/6.77 | | | | | | | | | Case 1: % 38.88/6.77 | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | (79) all_59_0 = 0 & all_59_1 = 0 & % 38.88/6.77 | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 & % 38.88/6.77 | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0 % 38.88/6.77 | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | ALPHA: (79) implies: % 38.88/6.77 | | | | | | | | | | (80) convergent_lines(all_38_1, all_38_1) = 0 % 38.88/6.77 | | | | | | | | | | (81) unorthogonal_lines(all_38_1, all_38_1) = 0 % 38.88/6.77 | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | BETA: splitting (45) gives: % 38.88/6.77 | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | Case 1: % 38.88/6.77 | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | (82) (all_61_2 = 0 & convergent_lines(all_38_2, % 38.88/6.77 | | | | | | | | | | | all_38_1) = 0) | (all_61_3 = 0 & % 38.88/6.77 | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0) % 38.88/6.77 | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | BETA: splitting (82) gives: % 38.88/6.77 | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | Case 1: % 38.88/6.77 | | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | | (83) all_61_2 = 0 & convergent_lines(all_38_2, % 38.88/6.77 | | | | | | | | | | | | all_38_1) = 0 % 38.88/6.77 | | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | | ALPHA: (83) implies: % 38.88/6.77 | | | | | | | | | | | | (84) convergent_lines(all_38_2, all_38_1) = 0 % 38.88/6.77 | | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | | REF_CLOSE: (15), (61), (77), (78), (84) are inconsistent by % 38.88/6.77 | | | | | | | | | | | | sub-proof #1. % 38.88/6.77 | | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | Case 2: % 38.88/6.77 | | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | | (85) all_61_3 = 0 & convergent_lines(all_38_2, % 38.88/6.77 | | | | | | | | | | | | all_38_1) = 0 % 38.88/6.77 | | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | | ALPHA: (85) implies: % 38.88/6.77 | | | | | | | | | | | | (86) convergent_lines(all_38_2, all_38_1) = 0 % 38.88/6.77 | | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | | REF_CLOSE: (15), (61), (77), (78), (86) are inconsistent by % 38.88/6.77 | | | | | | | | | | | | sub-proof #1. % 38.88/6.77 | | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | End of split % 38.88/6.77 | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | Case 2: % 38.88/6.77 | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | (87) ( ~ (all_61_0 = 0) & unorthogonal_lines(all_38_1, % 38.88/6.77 | | | | | | | | | | | all_38_1) = all_61_0) | ( ~ (all_61_1 = 0) & % 38.88/6.77 | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = all_61_1) % 38.88/6.77 | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | BETA: splitting (87) gives: % 38.88/6.77 | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | Case 1: % 38.88/6.77 | | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | | (88) ~ (all_61_0 = 0) & unorthogonal_lines(all_38_1, % 38.88/6.77 | | | | | | | | | | | | all_38_1) = all_61_0 % 38.88/6.77 | | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | | ALPHA: (88) implies: % 38.88/6.77 | | | | | | | | | | | | (89) ~ (all_61_0 = 0) % 38.88/6.77 | | | | | | | | | | | | (90) unorthogonal_lines(all_38_1, all_38_1) = all_61_0 % 38.88/6.77 | | | | | | | | | | | | % 38.88/6.77 | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_61_0, all_38_1, % 38.88/6.77 | | | | | | | | | | | | all_38_1, simplifying with (81), (90) gives: % 38.88/6.77 | | | | | | | | | | | | (91) all_61_0 = 0 % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | REDUCE: (89), (91) imply: % 38.88/6.78 | | | | | | | | | | | | (92) $false % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | CLOSE: (92) is inconsistent. % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | Case 2: % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | (93) ~ (all_61_1 = 0) & convergent_lines(all_38_1, % 38.88/6.78 | | | | | | | | | | | | all_38_1) = all_61_1 % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | ALPHA: (93) implies: % 38.88/6.78 | | | | | | | | | | | | (94) ~ (all_61_1 = 0) % 38.88/6.78 | | | | | | | | | | | | (95) convergent_lines(all_38_1, all_38_1) = all_61_1 % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_61_1, all_85_0, % 38.88/6.78 | | | | | | | | | | | | all_38_1, all_38_1, simplifying with (67), (95) % 38.88/6.78 | | | | | | | | | | | | gives: % 38.88/6.78 | | | | | | | | | | | | (96) all_85_0 = all_61_1 % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_85_0, all_38_1, % 38.88/6.78 | | | | | | | | | | | | all_38_1, simplifying with (67), (80) gives: % 38.88/6.78 | | | | | | | | | | | | (97) all_85_0 = 0 % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | COMBINE_EQS: (96), (97) imply: % 38.88/6.78 | | | | | | | | | | | | (98) all_61_1 = 0 % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | SIMP: (98) implies: % 38.88/6.78 | | | | | | | | | | | | (99) all_61_1 = 0 % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | REDUCE: (94), (99) imply: % 38.88/6.78 | | | | | | | | | | | | (100) $false % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | CLOSE: (100) is inconsistent. % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | End of split % 38.88/6.78 | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | End of split % 38.88/6.78 | | | | | | | | | | % 38.88/6.78 | | | | | | | | | Case 2: % 38.88/6.78 | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | (101) (all_59_2 = 0 & convergent_lines(all_38_2, % 38.88/6.78 | | | | | | | | | | all_38_1) = 0) | ( ~ (all_59_3 = 0) & % 38.88/6.78 | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = all_59_3) % 38.88/6.78 | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | BETA: splitting (101) gives: % 38.88/6.78 | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | Case 1: % 38.88/6.78 | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | (102) all_59_2 = 0 & convergent_lines(all_38_2, % 38.88/6.78 | | | | | | | | | | | all_38_1) = 0 % 38.88/6.78 | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | ALPHA: (102) implies: % 38.88/6.78 | | | | | | | | | | | (103) convergent_lines(all_38_2, all_38_1) = 0 % 38.88/6.78 | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | REF_CLOSE: (15), (61), (77), (78), (103) are inconsistent by % 38.88/6.78 | | | | | | | | | | | sub-proof #1. % 38.88/6.78 | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | Case 2: % 38.88/6.78 | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | (104) ~ (all_59_3 = 0) & convergent_lines(all_38_2, % 38.88/6.78 | | | | | | | | | | | all_38_1) = all_59_3 % 38.88/6.78 | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | ALPHA: (104) implies: % 38.88/6.78 | | | | | | | | | | | (105) convergent_lines(all_38_2, all_38_1) = all_59_3 % 38.88/6.78 | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | BETA: splitting (48) gives: % 38.88/6.78 | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | Case 1: % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | (106) (all_65_0 = 0 & convergent_lines(all_38_2, % 38.88/6.78 | | | | | | | | | | | | all_38_1) = 0) | (all_65_1 = 0 & all_45_0 = 0 % 38.88/6.78 | | | | | | | | | | | | & convergent_lines(all_38_3, all_38_1) = 0) % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | BETA: splitting (106) gives: % 38.88/6.78 | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | Case 1: % 38.88/6.78 | | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | | (107) all_65_0 = 0 & convergent_lines(all_38_2, % 38.88/6.78 | | | | | | | | | | | | | all_38_1) = 0 % 38.88/6.78 | | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | | ALPHA: (107) implies: % 38.88/6.78 | | | | | | | | | | | | | (108) convergent_lines(all_38_2, all_38_1) = 0 % 38.88/6.78 | | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | | REF_CLOSE: (15), (61), (77), (78), (108) are inconsistent by % 38.88/6.78 | | | | | | | | | | | | | sub-proof #1. % 38.88/6.78 | | | | | | | | | | | | | % 38.88/6.78 | | | | | | | | | | | | Case 2: % 38.88/6.78 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | (109) all_65_1 = 0 & all_45_0 = 0 & % 38.88/6.79 | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_1) = 0 % 38.88/6.79 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | ALPHA: (109) implies: % 38.88/6.79 | | | | | | | | | | | | | (110) all_45_0 = 0 % 38.88/6.79 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | REDUCE: (29), (110) imply: % 38.88/6.79 | | | | | | | | | | | | | (111) $false % 38.88/6.79 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | CLOSE: (111) is inconsistent. % 38.88/6.79 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | End of split % 38.88/6.79 | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | Case 2: % 38.88/6.79 | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | (112) ( ~ (all_65_2 = 0) & unorthogonal_lines(all_38_3, % 38.88/6.79 | | | | | | | | | | | | all_38_2) = all_65_2) | ( ~ (all_65_3 = 0) & % 38.88/6.79 | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = all_65_3) % 38.88/6.79 | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | BETA: splitting (112) gives: % 38.88/6.79 | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | Case 1: % 38.88/6.79 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | (113) ~ (all_65_2 = 0) & unorthogonal_lines(all_38_3, % 38.88/6.79 | | | | | | | | | | | | | all_38_2) = all_65_2 % 38.88/6.79 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | ALPHA: (113) implies: % 38.88/6.79 | | | | | | | | | | | | | (114) ~ (all_65_2 = 0) % 38.88/6.79 | | | | | | | | | | | | | (115) unorthogonal_lines(all_38_3, all_38_2) = all_65_2 % 38.88/6.79 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_65_2, all_38_2, % 38.88/6.79 | | | | | | | | | | | | | all_38_3, simplifying with (51), (115) gives: % 38.88/6.79 | | | | | | | | | | | | | (116) all_65_2 = 0 % 38.88/6.79 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | REDUCE: (114), (116) imply: % 38.88/6.79 | | | | | | | | | | | | | (117) $false % 38.88/6.79 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | CLOSE: (117) is inconsistent. % 38.88/6.79 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | Case 2: % 38.88/6.79 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | (118) ~ (all_65_3 = 0) & convergent_lines(all_38_3, % 38.88/6.79 | | | | | | | | | | | | | all_38_2) = all_65_3 % 38.88/6.79 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | ALPHA: (118) implies: % 38.88/6.79 | | | | | | | | | | | | | (119) ~ (all_65_3 = 0) % 38.88/6.79 | | | | | | | | | | | | | (120) convergent_lines(all_38_3, all_38_2) = all_65_3 % 38.88/6.79 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | BETA: splitting (49) gives: % 38.88/6.79 | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | Case 1: % 38.88/6.79 | | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | | (121) (all_70_2 = 0 & all_45_0 = 0 & % 38.88/6.79 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_1) = 0) | % 38.88/6.79 | | | | | | | | | | | | | | (all_70_3 = 0 & all_47_0 = 0 & % 38.88/6.79 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0) % 38.88/6.79 | | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | | BETA: splitting (121) gives: % 38.88/6.79 | | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | | Case 1: % 38.88/6.79 | | | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | | | (122) all_70_2 = 0 & all_45_0 = 0 & % 38.88/6.79 | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_1) = 0 % 38.88/6.79 | | | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | | | ALPHA: (122) implies: % 38.88/6.79 | | | | | | | | | | | | | | | (123) all_45_0 = 0 % 38.88/6.79 | | | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | | | REDUCE: (29), (123) imply: % 38.88/6.79 | | | | | | | | | | | | | | | (124) $false % 38.88/6.79 | | | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | | | CLOSE: (124) is inconsistent. % 38.88/6.79 | | | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | | Case 2: % 38.88/6.79 | | | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | | | (125) all_70_3 = 0 & all_47_0 = 0 & % 38.88/6.79 | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 % 38.88/6.79 | | | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | | | ALPHA: (125) implies: % 38.88/6.79 | | | | | | | | | | | | | | | (126) all_47_0 = 0 % 38.88/6.79 | | | | | | | | | | | | | | | % 38.88/6.79 | | | | | | | | | | | | | | | REDUCE: (32), (126) imply: % 38.88/6.79 | | | | | | | | | | | | | | | (127) $false % 38.88/6.79 | | | | | | | | | | | | | | | % 39.22/6.79 | | | | | | | | | | | | | | | CLOSE: (127) is inconsistent. % 39.22/6.79 | | | | | | | | | | | | | | | % 39.22/6.79 | | | | | | | | | | | | | | End of split % 39.22/6.79 | | | | | | | | | | | | | | % 39.22/6.79 | | | | | | | | | | | | | Case 2: % 39.22/6.79 | | | | | | | | | | | | | | % 39.22/6.79 | | | | | | | | | | | | | | (128) ( ~ (all_70_0 = 0) & unorthogonal_lines(all_38_2, % 39.22/6.79 | | | | | | | | | | | | | | all_38_1) = all_70_0) | ( ~ (all_70_1 = 0) & % 39.22/6.79 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = all_70_1) % 39.22/6.79 | | | | | | | | | | | | | | % 39.22/6.79 | | | | | | | | | | | | | | BETA: splitting (128) gives: % 39.22/6.79 | | | | | | | | | | | | | | % 39.22/6.79 | | | | | | | | | | | | | | Case 1: % 39.22/6.79 | | | | | | | | | | | | | | | % 39.22/6.79 | | | | | | | | | | | | | | | (129) ~ (all_70_0 = 0) & unorthogonal_lines(all_38_2, % 39.22/6.79 | | | | | | | | | | | | | | | all_38_1) = all_70_0 % 39.22/6.79 | | | | | | | | | | | | | | | % 39.22/6.79 | | | | | | | | | | | | | | | ALPHA: (129) implies: % 39.22/6.79 | | | | | | | | | | | | | | | (130) ~ (all_70_0 = 0) % 39.22/6.79 | | | | | | | | | | | | | | | (131) unorthogonal_lines(all_38_2, all_38_1) = all_70_0 % 39.22/6.79 | | | | | | | | | | | | | | | % 39.22/6.79 | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_70_0, all_38_1, % 39.22/6.79 | | | | | | | | | | | | | | | all_38_2, simplifying with (34), (131) gives: % 39.22/6.79 | | | | | | | | | | | | | | | (132) all_70_0 = 0 % 39.22/6.79 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | REDUCE: (130), (132) imply: % 39.22/6.80 | | | | | | | | | | | | | | | (133) $false % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | CLOSE: (133) is inconsistent. % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | Case 2: % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | (134) ~ (all_70_1 = 0) & convergent_lines(all_38_2, % 39.22/6.80 | | | | | | | | | | | | | | | all_38_1) = all_70_1 % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | ALPHA: (134) implies: % 39.22/6.80 | | | | | | | | | | | | | | | (135) convergent_lines(all_38_2, all_38_1) = all_70_1 % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_47_0, all_65_3, % 39.22/6.80 | | | | | | | | | | | | | | | all_38_2, all_38_3, simplifying with (33), (120) % 39.22/6.80 | | | | | | | | | | | | | | | gives: % 39.22/6.80 | | | | | | | | | | | | | | | (136) all_65_3 = all_47_0 % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_62_0, all_63_0, % 39.22/6.80 | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (61), (78) % 39.22/6.80 | | | | | | | | | | | | | | | gives: % 39.22/6.80 | | | | | | | | | | | | | | | (137) all_63_0 = all_62_0 % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_63_0, all_70_1, % 39.22/6.80 | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (61), (135) % 39.22/6.80 | | | | | | | | | | | | | | | gives: % 39.22/6.80 | | | | | | | | | | | | | | | (138) all_70_1 = all_63_0 % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_59_3, all_70_1, % 39.22/6.80 | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (105), (135) % 39.22/6.80 | | | | | | | | | | | | | | | gives: % 39.22/6.80 | | | | | | | | | | | | | | | (139) all_70_1 = all_59_3 % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | COMBINE_EQS: (138), (139) imply: % 39.22/6.80 | | | | | | | | | | | | | | | (140) all_63_0 = all_59_3 % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | SIMP: (140) implies: % 39.22/6.80 | | | | | | | | | | | | | | | (141) all_63_0 = all_59_3 % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | COMBINE_EQS: (137), (141) imply: % 39.22/6.80 | | | | | | | | | | | | | | | (142) all_62_0 = all_59_3 % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | REDUCE: (77), (142) imply: % 39.22/6.80 | | | | | | | | | | | | | | | (143) ~ (all_59_3 = 0) % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_38_3, all_38_1, % 39.22/6.80 | | | | | | | | | | | | | | | all_38_2, all_47_0, simplifying with (19), (20), % 39.22/6.80 | | | | | | | | | | | | | | | (21), (33), (50) gives: % 39.22/6.80 | | | | | | | | | | | | | | | (144) all_47_0 = 0 | convergent_lines(all_38_1, % 39.22/6.80 | | | | | | | | | | | | | | | all_38_2) = 0 % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_38_1, all_38_2, % 39.22/6.80 | | | | | | | | | | | | | | | all_38_1, all_85_0, all_59_3, simplifying with % 39.22/6.80 | | | | | | | | | | | | | | | (20), (21), (67), (105) gives: % 39.22/6.80 | | | | | | | | | | | | | | | (145) all_85_0 = 0 | all_59_3 = 0 | ? [v0: int] : ( ~ % 39.22/6.80 | | | | | | | | | | | | | | | (v0 = 0) & convergent_lines(all_38_1, all_38_2) % 39.22/6.80 | | | | | | | | | | | | | | | = v0) % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 39.22/6.80 | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | Case 1: % 39.22/6.80 | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | (146) all_85_0 = 0 % 39.22/6.80 | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | REDUCE: (66), (146) imply: % 39.22/6.80 | | | | | | | | | | | | | | | | (147) $false % 39.22/6.80 | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | CLOSE: (147) is inconsistent. % 39.22/6.80 | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | Case 2: % 39.22/6.80 | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | (148) all_59_3 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 39.22/6.80 | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = v0) % 39.22/6.80 | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | BETA: splitting (144) gives: % 39.22/6.80 | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | Case 1: % 39.22/6.80 | | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | | (149) convergent_lines(all_38_1, all_38_2) = 0 % 39.22/6.80 | | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 39.22/6.80 | | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | | Case 1: % 39.22/6.80 | | | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | | | (150) all_59_3 = 0 % 39.22/6.80 | | | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | | | REDUCE: (143), (150) imply: % 39.22/6.80 | | | | | | | | | | | | | | | | | | (151) $false % 39.22/6.80 | | | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | | | CLOSE: (151) is inconsistent. % 39.22/6.80 | | | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | | Case 2: % 39.22/6.80 | | | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | | | (152) ? [v0: int] : ( ~ (v0 = 0) & % 39.22/6.80 | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = v0) % 39.22/6.80 | | | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | | | DELTA: instantiating (152) with fresh symbol all_305_0 % 39.22/6.80 | | | | | | | | | | | | | | | | | | gives: % 39.22/6.80 | | | | | | | | | | | | | | | | | | (153) ~ (all_305_0 = 0) & convergent_lines(all_38_1, % 39.22/6.80 | | | | | | | | | | | | | | | | | | all_38_2) = all_305_0 % 39.22/6.80 | | | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | | | ALPHA: (153) implies: % 39.22/6.80 | | | | | | | | | | | | | | | | | | (154) ~ (all_305_0 = 0) % 39.22/6.80 | | | | | | | | | | | | | | | | | | (155) convergent_lines(all_38_1, all_38_2) = all_305_0 % 39.22/6.80 | | | | | | | | | | | | | | | | | | % 39.22/6.80 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_305_0, all_38_2, % 39.22/6.80 | | | | | | | | | | | | | | | | | | all_38_1, simplifying with (149), (155) gives: % 39.22/6.80 | | | | | | | | | | | | | | | | | | (156) all_305_0 = 0 % 39.22/6.80 | | | | | | | | | | | | | | | | | | % 39.22/6.81 | | | | | | | | | | | | | | | | | | REDUCE: (154), (156) imply: % 39.22/6.81 | | | | | | | | | | | | | | | | | | (157) $false % 39.22/6.81 | | | | | | | | | | | | | | | | | | % 39.22/6.81 | | | | | | | | | | | | | | | | | | CLOSE: (157) is inconsistent. % 39.22/6.81 | | | | | | | | | | | | | | | | | | % 39.22/6.81 | | | | | | | | | | | | | | | | | End of split % 39.22/6.81 | | | | | | | | | | | | | | | | | % 39.22/6.81 | | | | | | | | | | | | | | | | Case 2: % 39.22/6.81 | | | | | | | | | | | | | | | | | % 39.22/6.81 | | | | | | | | | | | | | | | | | (158) all_47_0 = 0 % 39.22/6.81 | | | | | | | | | | | | | | | | | % 39.22/6.81 | | | | | | | | | | | | | | | | | REDUCE: (32), (158) imply: % 39.22/6.81 | | | | | | | | | | | | | | | | | (159) $false % 39.22/6.81 | | | | | | | | | | | | | | | | | % 39.22/6.81 | | | | | | | | | | | | | | | | | CLOSE: (159) is inconsistent. % 39.22/6.81 | | | | | | | | | | | | | | | | | % 39.22/6.81 | | | | | | | | | | | | | | | | End of split % 39.22/6.81 | | | | | | | | | | | | | | | | % 39.22/6.81 | | | | | | | | | | | | | | | End of split % 39.22/6.81 | | | | | | | | | | | | | | | % 39.22/6.81 | | | | | | | | | | | | | | End of split % 39.22/6.81 | | | | | | | | | | | | | | % 39.22/6.81 | | | | | | | | | | | | | End of split % 39.22/6.81 | | | | | | | | | | | | | % 39.22/6.81 | | | | | | | | | | | | End of split % 39.22/6.81 | | | | | | | | | | | | % 39.22/6.81 | | | | | | | | | | | End of split % 39.22/6.81 | | | | | | | | | | | % 39.22/6.81 | | | | | | | | | | End of split % 39.22/6.81 | | | | | | | | | | % 39.22/6.81 | | | | | | | | | End of split % 39.22/6.81 | | | | | | | | | % 39.22/6.81 | | | | | | | | End of split % 39.22/6.81 | | | | | | | | % 39.22/6.81 | | | | | | | End of split % 39.22/6.81 | | | | | | | % 39.22/6.81 | | | | | | End of split % 39.22/6.81 | | | | | | % 39.22/6.81 | | | | | End of split % 39.22/6.81 | | | | | % 39.22/6.81 | | | | End of split % 39.22/6.81 | | | | % 39.22/6.81 | | | Case 2: % 39.22/6.81 | | | | % 39.22/6.81 | | | | (160) all_47_0 = 0 % 39.22/6.81 | | | | % 39.22/6.81 | | | | REDUCE: (32), (160) imply: % 39.22/6.81 | | | | (161) $false % 39.22/6.81 | | | | % 39.22/6.81 | | | | CLOSE: (161) is inconsistent. % 39.22/6.81 | | | | % 39.22/6.81 | | | End of split % 39.22/6.81 | | | % 39.22/6.81 | | Case 2: % 39.22/6.81 | | | % 39.22/6.81 | | | (162) all_45_0 = 0 % 39.22/6.81 | | | % 39.22/6.81 | | | REDUCE: (29), (162) imply: % 39.22/6.81 | | | (163) $false % 39.22/6.81 | | | % 39.22/6.81 | | | CLOSE: (163) is inconsistent. % 39.22/6.81 | | | % 39.22/6.81 | | End of split % 39.22/6.81 | | % 39.22/6.81 | Case 2: % 39.22/6.81 | | % 39.22/6.81 | | (164) all_38_0 = 0 % 39.22/6.81 | | % 39.22/6.81 | | REDUCE: (18), (164) imply: % 39.22/6.81 | | (165) $false % 39.22/6.81 | | % 39.22/6.81 | | CLOSE: (165) is inconsistent. % 39.22/6.81 | | % 39.22/6.81 | End of split % 39.22/6.81 | % 39.22/6.81 End of proof % 39.22/6.81 % 39.22/6.81 Sub-proof #1 shows that the following formulas are inconsistent: % 39.22/6.81 ---------------------------------------------------------------- % 39.22/6.81 (1) convergent_lines(all_38_2, all_38_1) = 0 % 39.22/6.81 (2) ~ (all_62_0 = 0) % 39.22/6.81 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 39.22/6.81 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 39.22/6.81 (convergent_lines(v3, v2) = v0)) % 39.22/6.81 (4) convergent_lines(all_38_2, all_38_1) = all_63_0 % 39.22/6.81 (5) convergent_lines(all_38_2, all_38_1) = all_62_0 % 39.22/6.81 % 39.22/6.81 Begin of proof % 39.22/6.81 | % 39.22/6.81 | GROUND_INST: instantiating (3) with all_62_0, all_63_0, all_38_1, all_38_2, % 39.22/6.81 | simplifying with (4), (5) gives: % 39.22/6.81 | (6) all_63_0 = all_62_0 % 39.22/6.81 | % 39.22/6.81 | GROUND_INST: instantiating (3) with 0, all_63_0, all_38_1, all_38_2, % 39.22/6.81 | simplifying with (1), (4) gives: % 39.22/6.81 | (7) all_63_0 = 0 % 39.22/6.81 | % 39.22/6.81 | COMBINE_EQS: (6), (7) imply: % 39.22/6.81 | (8) all_62_0 = 0 % 39.22/6.81 | % 39.22/6.81 | REDUCE: (2), (8) imply: % 39.22/6.81 | (9) $false % 39.22/6.81 | % 39.22/6.81 | CLOSE: (9) is inconsistent. % 39.22/6.81 | % 39.22/6.81 End of proof % 39.22/6.81 % SZS output end Proof for theBenchmark % 39.22/6.81 % 39.22/6.81 6229ms %------------------------------------------------------------------------------