%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO219+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 : n001.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 11.79s 2.39s % Output : Proof 17.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : GEO219+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n001.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 23:04:08 EDT 2023 % 0.13/0.35 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.63 % 0.19/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.63 (2023-06-19) % 0.19/0.63 % 0.19/0.63 (c) Philipp Rümmer, 2009-2023 % 0.19/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.63 Amanda Stjerna. % 0.19/0.63 Free software under BSD-3-Clause. % 0.19/0.63 % 0.19/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.63 % 0.19/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.64 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.03/1.17 Prover 1: Preprocessing ... % 3.03/1.17 Prover 4: Preprocessing ... % 3.76/1.21 Prover 3: Preprocessing ... % 3.76/1.21 Prover 0: Preprocessing ... % 3.76/1.21 Prover 2: Preprocessing ... % 3.76/1.21 Prover 5: Preprocessing ... % 3.76/1.21 Prover 6: Preprocessing ... % 6.00/1.57 Prover 5: Proving ... % 6.00/1.57 Prover 2: Proving ... % 6.74/1.65 Prover 6: Constructing countermodel ... % 6.74/1.68 Prover 3: Constructing countermodel ... % 6.74/1.69 Prover 1: Constructing countermodel ... % 8.49/1.91 Prover 3: gave up % 8.49/1.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.49/1.92 Prover 4: Constructing countermodel ... % 8.49/1.96 Prover 7: Preprocessing ... % 8.49/1.97 Prover 0: Proving ... % 8.49/1.98 Prover 6: gave up % 8.49/1.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.57/2.01 Prover 7: Warning: ignoring some quantifiers % 9.57/2.04 Prover 8: Preprocessing ... % 9.57/2.05 Prover 7: Constructing countermodel ... % 10.25/2.13 Prover 1: gave up % 10.25/2.14 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 10.25/2.17 Prover 9: Preprocessing ... % 10.94/2.21 Prover 8: Warning: ignoring some quantifiers % 10.94/2.21 Prover 7: gave up % 10.94/2.22 Prover 8: Constructing countermodel ... % 10.94/2.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.94/2.26 Prover 10: Preprocessing ... % 11.79/2.31 Prover 10: Warning: ignoring some quantifiers % 11.79/2.33 Prover 10: Constructing countermodel ... % 11.79/2.39 Prover 0: proved (1748ms) % 11.79/2.39 % 11.79/2.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.79/2.39 % 11.79/2.40 Prover 2: stopped % 11.79/2.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.79/2.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.79/2.40 Prover 5: stopped % 11.79/2.40 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 12.55/2.42 Prover 13: Preprocessing ... % 12.55/2.43 Prover 11: Preprocessing ... % 12.55/2.44 Prover 16: Preprocessing ... % 12.55/2.44 Prover 10: gave up % 12.55/2.44 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 12.55/2.50 Prover 9: Constructing countermodel ... % 13.26/2.50 Prover 19: Preprocessing ... % 13.26/2.50 Prover 8: gave up % 13.26/2.50 Prover 16: Warning: ignoring some quantifiers % 13.26/2.50 Prover 9: stopped % 13.26/2.51 Prover 13: Warning: ignoring some quantifiers % 13.26/2.51 Prover 16: Constructing countermodel ... % 13.26/2.52 Prover 13: Constructing countermodel ... % 14.00/2.61 Prover 13: gave up % 14.00/2.62 Prover 19: Warning: ignoring some quantifiers % 14.00/2.63 Prover 19: Constructing countermodel ... % 14.00/2.66 Prover 11: Constructing countermodel ... % 15.02/2.80 Prover 16: gave up % 15.52/2.85 Prover 19: gave up % 16.51/3.03 Prover 11: Found proof (size 163) % 16.51/3.03 Prover 11: proved (629ms) % 16.51/3.03 Prover 4: stopped % 16.51/3.03 % 16.51/3.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.51/3.03 % 16.51/3.05 % SZS output start Proof for theBenchmark % 16.51/3.06 Assumptions after simplification: % 16.51/3.06 --------------------------------- % 16.51/3.06 % 16.51/3.06 (a3) % 17.03/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (parallel_lines(v0, % 17.03/3.10 v1) = v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v1) = 0) & ! % 17.03/3.10 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (convergent_lines(v0, v1) % 17.03/3.10 = v2) | ~ $i(v1) | ~ $i(v0) | parallel_lines(v0, v1) = 0) & ! [v0: $i] % 17.03/3.10 : ! [v1: $i] : ( ~ (parallel_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 17.03/3.10 [v2: int] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0: $i] : % 17.03/3.10 ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 17.03/3.10 [v2: int] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) % 17.03/3.10 % 17.03/3.10 (a5) % 17.03/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (orthogonal_lines(v0, % 17.03/3.10 v1) = v2) | ~ $i(v1) | ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) & ! % 17.03/3.10 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (unorthogonal_lines(v0, % 17.03/3.10 v1) = v2) | ~ $i(v1) | ~ $i(v0) | orthogonal_lines(v0, v1) = 0) & ! % 17.03/3.10 [v0: $i] : ! [v1: $i] : ( ~ (orthogonal_lines(v0, v1) = 0) | ~ $i(v1) | ~ % 17.03/3.10 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & % 17.03/3.10 ! [v0: $i] : ! [v1: $i] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v1) | % 17.03/3.10 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) % 17.03/3.10 % 17.03/3.10 (ax6) % 17.03/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 17.03/3.10 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 17.03/3.10 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 17.03/3.10 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 17.03/3.10 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ % 17.03/3.11 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 17.03/3.11 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.03/3.11 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 17.03/3.11 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 17.03/3.11 convergent_lines(v1, v2) = 0) % 17.03/3.11 % 17.03/3.11 (coipo1) % 17.03/3.11 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 17.03/3.11 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 17.03/3.11 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 17.03/3.11 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 17.03/3.11 unorthogonal_lines(v0, v1) = 0) % 17.12/3.11 % 17.12/3.11 (con) % 17.12/3.11 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 17.12/3.11 orthogonal_lines(v1, v2) = v3 & orthogonal_lines(v0, v1) = 0 & % 17.12/3.11 parallel_lines(v0, v2) = 0 & $i(v2) & $i(v1) & $i(v0)) % 17.12/3.11 % 17.12/3.11 (cotno1) % 17.16/3.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 17.16/3.13 (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | % 17.16/3.13 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 17.16/3.13 int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | % 17.16/3.13 (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 17.16/3.13 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, % 17.16/3.13 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 17.16/3.13 ! [v4: any] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 17.16/3.13 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.16/3.13 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 17.16/3.13 convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 17.16/3.13 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1, % 17.16/3.13 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: % 17.16/3.13 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 17.16/3.13 (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ~ % 17.16/3.13 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 17.16/3.13 : ? [v8: int] : ((v6 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = % 17.16/3.13 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 17.16/3.13 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, % 17.16/3.13 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 17.16/3.13 ! [v4: any] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, % 17.16/3.13 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 17.16/3.13 int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 17.16/3.13 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 17.16/3.13 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1, % 17.16/3.13 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: % 17.16/3.13 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, % 17.16/3.13 v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 17.16/3.13 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 17.16/3.13 ((v6 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 17.16/3.13 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 17.16/3.13 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : % 17.16/3.13 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 17.16/3.13 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.16/3.13 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 17.16/3.13 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 17.16/3.13 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 17.16/3.13 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.16/3.13 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 17.16/3.13 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.16/3.13 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 17.16/3.13 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 17.16/3.13 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 17.16/3.13 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : % 17.16/3.13 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 17.16/3.13 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.16/3.13 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 17.16/3.13 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 17.16/3.13 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 17.16/3.13 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.16/3.13 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 17.16/3.13 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 17.16/3.13 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 17.16/3.13 convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 17.16/3.13 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 17.16/3.13 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] % 17.16/3.13 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ % 17.16/3.13 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 17.16/3.13 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 17.16/3.13 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 17.16/3.13 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 17.16/3.13 unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.16/3.13 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 17.16/3.13 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.16/3.13 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 17.16/3.13 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 17.16/3.13 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 17.16/3.13 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] % 17.16/3.13 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 17.16/3.13 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.16/3.13 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 17.16/3.13 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 17.16/3.13 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 17.16/3.13 unorthogonal_lines(v1, v2) = v7))) % 17.16/3.13 % 17.16/3.13 (couo1) % 17.16/3.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 17.16/3.13 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 17.16/3.13 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.16/3.13 [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0: $i] : % 17.16/3.13 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, % 17.16/3.13 v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | % 17.16/3.13 ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! % 17.16/3.13 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ % 17.16/3.13 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 17.16/3.13 unorthogonal_lines(v0, v2) = 0) % 17.16/3.13 % 17.16/3.13 (oac1) % 17.16/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 17.16/3.14 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | % 17.16/3.14 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 17.16/3.14 int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | % 17.16/3.14 (v7 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 17.16/3.14 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, % 17.16/3.14 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 17.16/3.14 ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ % 17.16/3.14 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.16/3.14 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 17.16/3.14 convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 17.16/3.14 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0, % 17.16/3.14 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0: % 17.16/3.14 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 17.16/3.14 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~ % 17.16/3.14 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 17.16/3.14 : ? [v8: int] : ((v8 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v7 = % 17.16/3.14 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 17.16/3.14 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, % 17.16/3.14 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 17.16/3.14 ! [v4: any] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 17.16/3.14 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 17.16/3.14 int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 17.16/3.14 unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 17.16/3.14 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0, % 17.16/3.14 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0: % 17.16/3.14 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, % 17.16/3.14 v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) % 17.16/3.15 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 17.16/3.15 ((v7 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 17.16/3.15 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 17.16/3.15 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 17.16/3.15 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ % 17.16/3.15 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 17.16/3.15 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 17.16/3.15 convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 17.16/3.15 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 17.16/3.15 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 17.16/3.15 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 17.16/3.15 (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.16/3.15 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 17.16/3.15 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 17.16/3.15 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 17.16/3.15 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.16/3.15 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 17.16/3.15 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 17.16/3.15 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 17.16/3.15 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 17.16/3.15 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 17.16/3.15 unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.16/3.15 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 17.16/3.15 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.16/3.15 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 17.16/3.15 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 17.16/3.15 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 17.16/3.15 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 17.16/3.15 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 17.16/3.15 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.16/3.15 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 17.16/3.15 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 17.16/3.15 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 17.16/3.15 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.16/3.15 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~ % 17.16/3.15 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 17.16/3.15 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 17.16/3.15 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 17.16/3.15 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 17.16/3.15 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 17.16/3.15 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) | ~ % 17.16/3.15 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 17.16/3.15 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 17.16/3.15 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 17.16/3.15 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 17.16/3.15 unorthogonal_lines(v0, v1) = v4))) % 17.16/3.15 % 17.16/3.15 (occu1) % 17.16/3.15 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 17.16/3.15 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 17.16/3.15 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 17.16/3.15 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 17.16/3.15 unorthogonal_lines(v0, v1) = 0) % 17.16/3.15 % 17.16/3.15 (function-axioms) % 17.16/3.15 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 17.16/3.15 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 17.16/3.15 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.16/3.15 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.16/3.15 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 17.16/3.15 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 17.16/3.15 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 17.16/3.15 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.16/3.15 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.16/3.15 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 17.16/3.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.16/3.15 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 17.16/3.15 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.16/3.15 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 17.16/3.15 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 17.16/3.15 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 17.16/3.15 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.16/3.15 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 17.16/3.15 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.16/3.15 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 17.16/3.15 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 17.16/3.15 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 17.16/3.15 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.16/3.15 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.16/3.15 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 17.16/3.15 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 17.16/3.15 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 17.16/3.15 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.16/3.15 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.16/3.15 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 17.16/3.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.16/3.15 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 17.16/3.15 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 17.16/3.15 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 17.16/3.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 17.16/3.15 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 17.16/3.15 % 17.16/3.15 Further assumptions not needed in the proof: % 17.16/3.15 -------------------------------------------- % 17.16/3.15 a4, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ceq1, ceq2, ceq3, ci1, % 17.16/3.15 ci2, ci3, ci4, con1, cp1, cp2, cu1, cup1, int1, ooc1, ooc2, orth1, ouo1, p1, % 17.16/3.15 par1 % 17.16/3.15 % 17.16/3.15 Those formulas are unsatisfiable: % 17.16/3.15 --------------------------------- % 17.16/3.15 % 17.16/3.15 Begin of proof % 17.16/3.16 | % 17.16/3.16 | ALPHA: (ax6) implies: % 17.16/3.16 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 17.16/3.16 | (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 17.16/3.16 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 17.16/3.16 | % 17.16/3.16 | ALPHA: (oac1) implies: % 17.16/3.16 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 17.16/3.16 | ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) % 17.16/3.16 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 17.16/3.16 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 17.16/3.16 | convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 17.16/3.16 | convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 17.16/3.16 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 17.16/3.16 | convergent_lines(v0, v1) = v5))) % 17.16/3.16 | % 17.16/3.16 | ALPHA: (occu1) implies: % 17.16/3.16 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 17.16/3.16 | (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 17.16/3.16 | convergent_lines(v0, v1) = 0) % 17.16/3.16 | % 17.16/3.16 | ALPHA: (cotno1) implies: % 17.16/3.16 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 17.16/3.16 | (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) % 17.16/3.16 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : % 17.16/3.16 | ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 17.16/3.16 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 17.16/3.16 | unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | % 17.16/3.16 | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) % 17.16/3.16 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 17.16/3.16 | (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = % 17.16/3.16 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 17.16/3.16 | int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 17.16/3.16 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | % 17.16/3.16 | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 17.16/3.16 | convergent_lines(v1, v2) = v7))) % 17.16/3.17 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 17.16/3.17 | (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = % 17.16/3.17 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 17.16/3.17 | int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 17.16/3.17 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 17.16/3.17 | unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | % 17.16/3.17 | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) % 17.16/3.17 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 17.16/3.17 | ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = % 17.16/3.17 | v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 17.16/3.17 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 17.16/3.17 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 17.16/3.17 | convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 17.16/3.17 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 17.16/3.17 | convergent_lines(v1, v2) = v7))) % 17.16/3.17 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 17.16/3.17 | ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) % 17.16/3.17 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 17.16/3.17 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 17.16/3.17 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 17.16/3.17 | convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 17.16/3.17 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 17.16/3.17 | convergent_lines(v1, v2) = v7))) % 17.16/3.17 | % 17.16/3.17 | ALPHA: (couo1) implies: % 17.16/3.17 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 17.16/3.17 | (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 17.16/3.17 | (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 17.16/3.17 | | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) % 17.16/3.17 | % 17.16/3.17 | ALPHA: (a3) implies: % 17.16/3.17 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (parallel_lines(v0, v1) = 0) | ~ % 17.16/3.17 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 17.16/3.17 | convergent_lines(v0, v1) = v2)) % 17.16/3.17 | % 17.16/3.17 | ALPHA: (a5) implies: % 17.16/3.17 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (orthogonal_lines(v0, v1) = 0) | ~ % 17.16/3.17 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 17.16/3.17 | unorthogonal_lines(v0, v1) = v2)) % 17.16/3.17 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 17.16/3.17 | (orthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 17.16/3.17 | unorthogonal_lines(v0, v1) = 0) % 17.16/3.17 | % 17.16/3.17 | ALPHA: (function-axioms) implies: % 17.16/3.17 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.16/3.17 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 17.16/3.17 | (convergent_lines(v3, v2) = v0)) % 17.16/3.17 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.16/3.17 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 17.16/3.17 | (unorthogonal_lines(v3, v2) = v0)) % 17.16/3.17 | % 17.16/3.17 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 17.16/3.17 | all_38_3 gives: % 17.16/3.18 | (15) ~ (all_38_0 = 0) & orthogonal_lines(all_38_2, all_38_1) = all_38_0 & % 17.16/3.18 | orthogonal_lines(all_38_3, all_38_2) = 0 & parallel_lines(all_38_3, % 17.16/3.18 | all_38_1) = 0 & $i(all_38_1) & $i(all_38_2) & $i(all_38_3) % 17.16/3.18 | % 17.16/3.18 | ALPHA: (15) implies: % 17.16/3.18 | (16) ~ (all_38_0 = 0) % 17.16/3.18 | (17) $i(all_38_3) % 17.16/3.18 | (18) $i(all_38_2) % 17.16/3.18 | (19) $i(all_38_1) % 17.16/3.18 | (20) parallel_lines(all_38_3, all_38_1) = 0 % 17.16/3.18 | (21) orthogonal_lines(all_38_3, all_38_2) = 0 % 17.16/3.18 | (22) orthogonal_lines(all_38_2, all_38_1) = all_38_0 % 17.16/3.18 | % 17.16/3.18 | GROUND_INST: instantiating (10) with all_38_3, all_38_1, simplifying with % 17.16/3.18 | (17), (19), (20) gives: % 17.16/3.18 | (23) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_3, all_38_1) = % 17.16/3.18 | v0) % 17.16/3.18 | % 17.16/3.18 | GROUND_INST: instantiating (11) with all_38_3, all_38_2, simplifying with % 17.16/3.18 | (17), (18), (21) gives: % 17.16/3.18 | (24) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_38_3, all_38_2) = % 17.16/3.18 | v0) % 17.16/3.18 | % 17.16/3.18 | GROUND_INST: instantiating (12) with all_38_2, all_38_1, all_38_0, simplifying % 17.16/3.18 | with (18), (19), (22) gives: % 17.16/3.18 | (25) all_38_0 = 0 | unorthogonal_lines(all_38_2, all_38_1) = 0 % 17.16/3.18 | % 17.16/3.18 | DELTA: instantiating (24) with fresh symbol all_45_0 gives: % 17.16/3.18 | (26) ~ (all_45_0 = 0) & unorthogonal_lines(all_38_3, all_38_2) = all_45_0 % 17.16/3.18 | % 17.16/3.18 | ALPHA: (26) implies: % 17.16/3.18 | (27) ~ (all_45_0 = 0) % 17.16/3.18 | (28) unorthogonal_lines(all_38_3, all_38_2) = all_45_0 % 17.16/3.18 | % 17.16/3.18 | DELTA: instantiating (23) with fresh symbol all_47_0 gives: % 17.16/3.18 | (29) ~ (all_47_0 = 0) & convergent_lines(all_38_3, all_38_1) = all_47_0 % 17.16/3.18 | % 17.16/3.18 | ALPHA: (29) implies: % 17.16/3.18 | (30) ~ (all_47_0 = 0) % 17.16/3.18 | (31) convergent_lines(all_38_3, all_38_1) = all_47_0 % 17.16/3.18 | % 17.16/3.18 | BETA: splitting (25) gives: % 17.16/3.18 | % 17.16/3.18 | Case 1: % 17.16/3.18 | | % 17.16/3.18 | | (32) unorthogonal_lines(all_38_2, all_38_1) = 0 % 17.16/3.18 | | % 17.16/3.18 | | GROUND_INST: instantiating (9) with all_38_3, all_38_2, all_38_2, all_45_0, % 17.16/3.18 | | all_45_0, simplifying with (17), (18), (28) gives: % 17.16/3.18 | | (33) all_45_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 17.16/3.18 | | convergent_lines(all_38_2, all_38_2) = v0) % 17.16/3.18 | | % 17.16/3.18 | | GROUND_INST: instantiating (8) with all_38_3, all_38_2, all_38_2, all_45_0, % 17.16/3.18 | | all_45_0, simplifying with (17), (18), (28) gives: % 17.16/3.18 | | (34) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0 % 17.16/3.18 | | & all_45_0 = 0 & convergent_lines(all_38_3, all_38_2) = 0) | (v0 % 17.16/3.18 | | = 0 & all_45_0 = 0 & convergent_lines(all_38_3, all_38_2) = 0) | % 17.16/3.18 | | ( ~ (v3 = 0) & unorthogonal_lines(all_38_2, all_38_2) = v3) | ( ~ % 17.16/3.18 | | (v2 = 0) & convergent_lines(all_38_2, all_38_2) = v2)) % 17.16/3.18 | | % 17.16/3.18 | | GROUND_INST: instantiating (7) with all_38_3, all_38_2, all_38_1, all_45_0, % 17.16/3.18 | | all_47_0, simplifying with (17), (18), (19), (28), (31) gives: % 17.16/3.19 | | (35) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0 % 17.16/3.19 | | & all_47_0 = 0 & unorthogonal_lines(all_38_3, all_38_1) = 0) | % 17.16/3.19 | | (v0 = 0 & all_45_0 = 0 & convergent_lines(all_38_3, all_38_2) = 0) % 17.16/3.19 | | | ( ~ (v3 = 0) & unorthogonal_lines(all_38_2, all_38_1) = v3) | ( % 17.16/3.19 | | ~ (v2 = 0) & convergent_lines(all_38_2, all_38_1) = v2)) % 17.16/3.19 | | % 17.16/3.19 | | GROUND_INST: instantiating (3) with all_38_3, all_38_2, all_45_0, % 17.16/3.19 | | simplifying with (17), (18), (28) gives: % 17.16/3.19 | | (36) all_45_0 = 0 | convergent_lines(all_38_3, all_38_2) = 0 % 17.16/3.19 | | % 17.16/3.19 | | GROUND_INST: instantiating (6) with all_38_2, all_38_2, all_38_1, 0, % 17.16/3.19 | | simplifying with (18), (19), (32) gives: % 17.16/3.19 | | (37) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 % 17.16/3.19 | | & convergent_lines(all_38_2, all_38_1) = 0) | (v1 = 0 & v0 = 0 & % 17.16/3.19 | | unorthogonal_lines(all_38_2, all_38_2) = 0 & % 17.16/3.19 | | convergent_lines(all_38_2, all_38_2) = 0) | ( ~ (v3 = 0) & % 17.16/3.19 | | convergent_lines(all_38_2, all_38_1) = v3)) % 17.16/3.19 | | % 17.16/3.19 | | GROUND_INST: instantiating (2) with all_38_2, all_38_2, all_38_1, 0, 0, % 17.16/3.19 | | simplifying with (18), (19), (32) gives: % 17.16/3.19 | | (38) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 % 17.16/3.19 | | & convergent_lines(all_38_2, all_38_1) = 0) | (v2 = 0 & % 17.16/3.19 | | convergent_lines(all_38_2, all_38_1) = 0) | ( ~ (v1 = 0) & % 17.16/3.19 | | unorthogonal_lines(all_38_2, all_38_2) = v1) | ( ~ (v0 = 0) & % 17.16/3.19 | | convergent_lines(all_38_2, all_38_2) = v0)) % 17.16/3.19 | | % 17.16/3.19 | | GROUND_INST: instantiating (5) with all_38_3, all_38_2, all_38_1, all_45_0, % 17.16/3.19 | | simplifying with (17), (18), (19), (28), (32) gives: % 17.16/3.19 | | (39) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 % 17.16/3.19 | | & v1 = 0 & unorthogonal_lines(all_38_3, all_38_1) = 0 & % 17.16/3.19 | | convergent_lines(all_38_3, all_38_1) = 0) | (v0 = 0 & all_45_0 = % 17.16/3.19 | | 0 & convergent_lines(all_38_3, all_38_2) = 0) | ( ~ (v3 = 0) & % 17.16/3.19 | | convergent_lines(all_38_2, all_38_1) = v3)) % 17.16/3.19 | | % 17.16/3.19 | | GROUND_INST: instantiating (4) with all_38_3, all_38_2, all_38_1, all_47_0, % 17.16/3.19 | | simplifying with (17), (18), (19), (31), (32) gives: % 17.16/3.19 | | (40) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 % 17.16/3.19 | | & all_47_0 = 0 & unorthogonal_lines(all_38_3, all_38_1) = 0) | % 17.16/3.19 | | (v1 = 0 & v0 = 0 & unorthogonal_lines(all_38_3, all_38_2) = 0 & % 17.16/3.19 | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ (v3 = 0) & % 17.16/3.19 | | convergent_lines(all_38_2, all_38_1) = v3)) % 17.16/3.19 | | % 17.16/3.19 | | DELTA: instantiating (38) with fresh symbols all_58_0, all_58_1, all_58_2, % 17.16/3.19 | | all_58_3 gives: % 17.16/3.19 | | (41) (all_58_0 = 0 & convergent_lines(all_38_2, all_38_1) = 0) | % 17.16/3.19 | | (all_58_1 = 0 & convergent_lines(all_38_2, all_38_1) = 0) | ( ~ % 17.16/3.19 | | (all_58_2 = 0) & unorthogonal_lines(all_38_2, all_38_2) = % 17.16/3.19 | | all_58_2) | ( ~ (all_58_3 = 0) & convergent_lines(all_38_2, % 17.16/3.19 | | all_38_2) = all_58_3) % 17.16/3.19 | | % 17.16/3.19 | | DELTA: instantiating (37) with fresh symbols all_60_0, all_60_1, all_60_2, % 17.16/3.19 | | all_60_3 gives: % 17.16/3.19 | | (42) (all_60_1 = 0 & convergent_lines(all_38_2, all_38_1) = 0) | % 17.16/3.19 | | (all_60_2 = 0 & all_60_3 = 0 & unorthogonal_lines(all_38_2, % 17.16/3.19 | | all_38_2) = 0 & convergent_lines(all_38_2, all_38_2) = 0) | ( ~ % 17.16/3.19 | | (all_60_0 = 0) & convergent_lines(all_38_2, all_38_1) = all_60_0) % 17.16/3.19 | | % 17.16/3.19 | | DELTA: instantiating (40) with fresh symbols all_62_0, all_62_1, all_62_2, % 17.16/3.19 | | all_62_3 gives: % 17.16/3.19 | | (43) (all_62_1 = 0 & all_47_0 = 0 & unorthogonal_lines(all_38_3, % 17.16/3.19 | | all_38_1) = 0) | (all_62_2 = 0 & all_62_3 = 0 & % 17.16/3.19 | | unorthogonal_lines(all_38_3, all_38_2) = 0 & % 17.16/3.19 | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ (all_62_0 = 0) & % 17.16/3.19 | | convergent_lines(all_38_2, all_38_1) = all_62_0) % 17.16/3.19 | | % 17.16/3.19 | | DELTA: instantiating (39) with fresh symbols all_63_0, all_63_1, all_63_2, % 17.16/3.19 | | all_63_3 gives: % 17.16/3.19 | | (44) (all_63_1 = 0 & all_63_2 = 0 & unorthogonal_lines(all_38_3, % 17.16/3.19 | | all_38_1) = 0 & convergent_lines(all_38_3, all_38_1) = 0) | % 17.16/3.19 | | (all_63_3 = 0 & all_45_0 = 0 & convergent_lines(all_38_3, all_38_2) % 17.16/3.19 | | = 0) | ( ~ (all_63_0 = 0) & convergent_lines(all_38_2, all_38_1) = % 17.16/3.19 | | all_63_0) % 17.16/3.19 | | % 17.16/3.19 | | DELTA: instantiating (35) with fresh symbols all_67_0, all_67_1, all_67_2, % 17.16/3.19 | | all_67_3 gives: % 17.16/3.19 | | (45) (all_67_2 = 0 & all_47_0 = 0 & unorthogonal_lines(all_38_3, % 17.16/3.19 | | all_38_1) = 0) | (all_67_3 = 0 & all_45_0 = 0 & % 17.16/3.19 | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ (all_67_0 = 0) & % 17.16/3.19 | | unorthogonal_lines(all_38_2, all_38_1) = all_67_0) | ( ~ (all_67_1 % 17.16/3.19 | | = 0) & convergent_lines(all_38_2, all_38_1) = all_67_1) % 17.16/3.19 | | % 17.16/3.19 | | DELTA: instantiating (34) with fresh symbols all_68_0, all_68_1, all_68_2, % 17.16/3.19 | | all_68_3 gives: % 17.16/3.19 | | (46) (all_68_2 = 0 & all_45_0 = 0 & convergent_lines(all_38_3, all_38_2) % 17.16/3.19 | | = 0) | (all_68_3 = 0 & all_45_0 = 0 & convergent_lines(all_38_3, % 17.16/3.19 | | all_38_2) = 0) | ( ~ (all_68_0 = 0) & % 17.16/3.19 | | unorthogonal_lines(all_38_2, all_38_2) = all_68_0) | ( ~ (all_68_1 % 17.16/3.19 | | = 0) & convergent_lines(all_38_2, all_38_2) = all_68_1) % 17.16/3.20 | | % 17.16/3.20 | | BETA: splitting (36) gives: % 17.16/3.20 | | % 17.16/3.20 | | Case 1: % 17.16/3.20 | | | % 17.16/3.20 | | | (47) convergent_lines(all_38_3, all_38_2) = 0 % 17.16/3.20 | | | % 17.16/3.20 | | | BETA: splitting (44) gives: % 17.16/3.20 | | | % 17.16/3.20 | | | Case 1: % 17.16/3.20 | | | | % 17.16/3.20 | | | | (48) all_63_1 = 0 & all_63_2 = 0 & unorthogonal_lines(all_38_3, % 17.16/3.20 | | | | all_38_1) = 0 & convergent_lines(all_38_3, all_38_1) = 0 % 17.16/3.20 | | | | % 17.16/3.20 | | | | ALPHA: (48) implies: % 17.16/3.20 | | | | (49) convergent_lines(all_38_3, all_38_1) = 0 % 17.16/3.20 | | | | % 17.16/3.20 | | | | GROUND_INST: instantiating (13) with all_47_0, 0, all_38_1, all_38_3, % 17.16/3.20 | | | | simplifying with (31), (49) gives: % 17.16/3.20 | | | | (50) all_47_0 = 0 % 17.16/3.20 | | | | % 17.16/3.20 | | | | REDUCE: (30), (50) imply: % 17.16/3.20 | | | | (51) $false % 17.16/3.20 | | | | % 17.16/3.20 | | | | CLOSE: (51) is inconsistent. % 17.16/3.20 | | | | % 17.16/3.20 | | | Case 2: % 17.16/3.20 | | | | % 17.16/3.20 | | | | (52) (all_63_3 = 0 & all_45_0 = 0 & convergent_lines(all_38_3, % 17.16/3.20 | | | | all_38_2) = 0) | ( ~ (all_63_0 = 0) & % 17.16/3.20 | | | | convergent_lines(all_38_2, all_38_1) = all_63_0) % 17.16/3.20 | | | | % 17.16/3.20 | | | | BETA: splitting (52) gives: % 17.16/3.20 | | | | % 17.16/3.20 | | | | Case 1: % 17.16/3.20 | | | | | % 17.16/3.20 | | | | | (53) all_63_3 = 0 & all_45_0 = 0 & convergent_lines(all_38_3, % 17.16/3.20 | | | | | all_38_2) = 0 % 17.16/3.20 | | | | | % 17.16/3.20 | | | | | ALPHA: (53) implies: % 17.16/3.20 | | | | | (54) all_45_0 = 0 % 17.16/3.20 | | | | | % 17.16/3.20 | | | | | REDUCE: (27), (54) imply: % 17.16/3.20 | | | | | (55) $false % 17.16/3.20 | | | | | % 17.16/3.20 | | | | | CLOSE: (55) is inconsistent. % 17.16/3.20 | | | | | % 17.16/3.20 | | | | Case 2: % 17.16/3.20 | | | | | % 17.16/3.20 | | | | | (56) ~ (all_63_0 = 0) & convergent_lines(all_38_2, all_38_1) = % 17.16/3.20 | | | | | all_63_0 % 17.16/3.20 | | | | | % 17.16/3.20 | | | | | ALPHA: (56) implies: % 17.16/3.20 | | | | | (57) convergent_lines(all_38_2, all_38_1) = all_63_0 % 17.16/3.20 | | | | | % 17.16/3.20 | | | | | BETA: splitting (33) gives: % 17.16/3.20 | | | | | % 17.16/3.20 | | | | | Case 1: % 17.16/3.20 | | | | | | % 17.16/3.20 | | | | | | (58) all_45_0 = 0 % 17.16/3.20 | | | | | | % 17.16/3.20 | | | | | | REDUCE: (27), (58) imply: % 17.16/3.20 | | | | | | (59) $false % 17.16/3.20 | | | | | | % 17.16/3.20 | | | | | | CLOSE: (59) is inconsistent. % 17.16/3.20 | | | | | | % 17.16/3.20 | | | | | Case 2: % 17.16/3.20 | | | | | | % 17.16/3.20 | | | | | | (60) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_2, % 17.16/3.20 | | | | | | all_38_2) = v0) % 17.16/3.20 | | | | | | % 17.16/3.20 | | | | | | DELTA: instantiating (60) with fresh symbol all_85_0 gives: % 17.16/3.20 | | | | | | (61) ~ (all_85_0 = 0) & convergent_lines(all_38_2, all_38_2) = % 17.16/3.20 | | | | | | all_85_0 % 17.16/3.20 | | | | | | % 17.16/3.20 | | | | | | ALPHA: (61) implies: % 17.16/3.20 | | | | | | (62) convergent_lines(all_38_2, all_38_2) = all_85_0 % 17.16/3.20 | | | | | | % 17.16/3.20 | | | | | | BETA: splitting (43) gives: % 17.16/3.20 | | | | | | % 17.16/3.20 | | | | | | Case 1: % 17.16/3.20 | | | | | | | % 17.16/3.20 | | | | | | | (63) all_62_1 = 0 & all_47_0 = 0 & unorthogonal_lines(all_38_3, % 17.16/3.20 | | | | | | | all_38_1) = 0 % 17.16/3.20 | | | | | | | % 17.16/3.20 | | | | | | | ALPHA: (63) implies: % 17.16/3.20 | | | | | | | (64) all_47_0 = 0 % 17.16/3.20 | | | | | | | % 17.16/3.20 | | | | | | | REDUCE: (30), (64) imply: % 17.16/3.20 | | | | | | | (65) $false % 17.16/3.20 | | | | | | | % 17.16/3.20 | | | | | | | CLOSE: (65) is inconsistent. % 17.16/3.20 | | | | | | | % 17.16/3.20 | | | | | | Case 2: % 17.16/3.20 | | | | | | | % 17.16/3.20 | | | | | | | (66) (all_62_2 = 0 & all_62_3 = 0 & % 17.16/3.20 | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 & % 17.16/3.20 | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ % 17.16/3.20 | | | | | | | (all_62_0 = 0) & convergent_lines(all_38_2, all_38_1) = % 17.16/3.20 | | | | | | | all_62_0) % 17.16/3.20 | | | | | | | % 17.16/3.20 | | | | | | | BETA: splitting (66) gives: % 17.16/3.20 | | | | | | | % 17.16/3.20 | | | | | | | Case 1: % 17.16/3.20 | | | | | | | | % 17.16/3.20 | | | | | | | | (67) all_62_2 = 0 & all_62_3 = 0 & % 17.16/3.20 | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 & % 17.16/3.20 | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0 % 17.16/3.20 | | | | | | | | % 17.16/3.20 | | | | | | | | ALPHA: (67) implies: % 17.16/3.20 | | | | | | | | (68) unorthogonal_lines(all_38_3, all_38_2) = 0 % 17.16/3.20 | | | | | | | | % 17.16/3.20 | | | | | | | | GROUND_INST: instantiating (14) with all_45_0, 0, all_38_2, % 17.58/3.20 | | | | | | | | all_38_3, simplifying with (28), (68) gives: % 17.58/3.20 | | | | | | | | (69) all_45_0 = 0 % 17.58/3.20 | | | | | | | | % 17.58/3.20 | | | | | | | | REDUCE: (27), (69) imply: % 17.58/3.20 | | | | | | | | (70) $false % 17.58/3.20 | | | | | | | | % 17.58/3.20 | | | | | | | | CLOSE: (70) is inconsistent. % 17.58/3.20 | | | | | | | | % 17.58/3.20 | | | | | | | Case 2: % 17.58/3.20 | | | | | | | | % 17.58/3.20 | | | | | | | | (71) ~ (all_62_0 = 0) & convergent_lines(all_38_2, all_38_1) % 17.58/3.20 | | | | | | | | = all_62_0 % 17.58/3.20 | | | | | | | | % 17.58/3.20 | | | | | | | | ALPHA: (71) implies: % 17.58/3.20 | | | | | | | | (72) ~ (all_62_0 = 0) % 17.58/3.20 | | | | | | | | (73) convergent_lines(all_38_2, all_38_1) = all_62_0 % 17.58/3.20 | | | | | | | | % 17.58/3.20 | | | | | | | | BETA: splitting (42) gives: % 17.58/3.20 | | | | | | | | % 17.58/3.20 | | | | | | | | Case 1: % 17.58/3.20 | | | | | | | | | % 17.58/3.20 | | | | | | | | | (74) all_60_1 = 0 & convergent_lines(all_38_2, all_38_1) = % 17.58/3.20 | | | | | | | | | 0 % 17.58/3.20 | | | | | | | | | % 17.58/3.20 | | | | | | | | | ALPHA: (74) implies: % 17.58/3.20 | | | | | | | | | (75) convergent_lines(all_38_2, all_38_1) = 0 % 17.58/3.20 | | | | | | | | | % 17.58/3.21 | | | | | | | | | REF_CLOSE: (13), (57), (72), (73), (75) are inconsistent by % 17.58/3.21 | | | | | | | | | sub-proof #1. % 17.58/3.21 | | | | | | | | | % 17.58/3.21 | | | | | | | | Case 2: % 17.58/3.21 | | | | | | | | | % 17.58/3.21 | | | | | | | | | (76) (all_60_2 = 0 & all_60_3 = 0 & % 17.58/3.21 | | | | | | | | | unorthogonal_lines(all_38_2, all_38_2) = 0 & % 17.58/3.21 | | | | | | | | | convergent_lines(all_38_2, all_38_2) = 0) | ( ~ % 17.58/3.21 | | | | | | | | | (all_60_0 = 0) & convergent_lines(all_38_2, % 17.58/3.21 | | | | | | | | | all_38_1) = all_60_0) % 17.58/3.21 | | | | | | | | | % 17.58/3.21 | | | | | | | | | BETA: splitting (76) gives: % 17.58/3.21 | | | | | | | | | % 17.58/3.21 | | | | | | | | | Case 1: % 17.58/3.21 | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | (77) all_60_2 = 0 & all_60_3 = 0 & % 17.58/3.21 | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_2) = 0 & % 17.58/3.21 | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = 0 % 17.58/3.21 | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | ALPHA: (77) implies: % 17.58/3.21 | | | | | | | | | | (78) convergent_lines(all_38_2, all_38_2) = 0 % 17.58/3.21 | | | | | | | | | | (79) unorthogonal_lines(all_38_2, all_38_2) = 0 % 17.58/3.21 | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | BETA: splitting (46) gives: % 17.58/3.21 | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | Case 1: % 17.58/3.21 | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | (80) (all_68_2 = 0 & all_45_0 = 0 & % 17.58/3.21 | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | % 17.58/3.21 | | | | | | | | | | | (all_68_3 = 0 & all_45_0 = 0 & % 17.58/3.21 | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) % 17.58/3.21 | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | BETA: splitting (80) gives: % 17.58/3.21 | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | Case 1: % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | (81) all_68_2 = 0 & all_45_0 = 0 & % 17.58/3.21 | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0 % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | ALPHA: (81) implies: % 17.58/3.21 | | | | | | | | | | | | (82) all_45_0 = 0 % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | REDUCE: (27), (82) imply: % 17.58/3.21 | | | | | | | | | | | | (83) $false % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | CLOSE: (83) is inconsistent. % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | Case 2: % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | (84) all_68_3 = 0 & all_45_0 = 0 & % 17.58/3.21 | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0 % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | ALPHA: (84) implies: % 17.58/3.21 | | | | | | | | | | | | (85) all_45_0 = 0 % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | REDUCE: (27), (85) imply: % 17.58/3.21 | | | | | | | | | | | | (86) $false % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | CLOSE: (86) is inconsistent. % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | End of split % 17.58/3.21 | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | Case 2: % 17.58/3.21 | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | (87) ( ~ (all_68_0 = 0) & unorthogonal_lines(all_38_2, % 17.58/3.21 | | | | | | | | | | | all_38_2) = all_68_0) | ( ~ (all_68_1 = 0) & % 17.58/3.21 | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = all_68_1) % 17.58/3.21 | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | BETA: splitting (87) gives: % 17.58/3.21 | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | Case 1: % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | (88) ~ (all_68_0 = 0) & unorthogonal_lines(all_38_2, % 17.58/3.21 | | | | | | | | | | | | all_38_2) = all_68_0 % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | ALPHA: (88) implies: % 17.58/3.21 | | | | | | | | | | | | (89) ~ (all_68_0 = 0) % 17.58/3.21 | | | | | | | | | | | | (90) unorthogonal_lines(all_38_2, all_38_2) = all_68_0 % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_68_0, all_38_2, % 17.58/3.21 | | | | | | | | | | | | all_38_2, simplifying with (79), (90) gives: % 17.58/3.21 | | | | | | | | | | | | (91) all_68_0 = 0 % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | REDUCE: (89), (91) imply: % 17.58/3.21 | | | | | | | | | | | | (92) $false % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | CLOSE: (92) is inconsistent. % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | Case 2: % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | (93) ~ (all_68_1 = 0) & convergent_lines(all_38_2, % 17.58/3.21 | | | | | | | | | | | | all_38_2) = all_68_1 % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | ALPHA: (93) implies: % 17.58/3.21 | | | | | | | | | | | | (94) convergent_lines(all_38_2, all_38_2) = all_68_1 % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | BETA: splitting (41) gives: % 17.58/3.21 | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | Case 1: % 17.58/3.21 | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | (95) (all_58_0 = 0 & convergent_lines(all_38_2, % 17.58/3.21 | | | | | | | | | | | | | all_38_1) = 0) | (all_58_1 = 0 & % 17.58/3.21 | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0) % 17.58/3.21 | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | BETA: splitting (95) gives: % 17.58/3.21 | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | Case 1: % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | | (96) all_58_0 = 0 & convergent_lines(all_38_2, % 17.58/3.21 | | | | | | | | | | | | | | all_38_1) = 0 % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | | ALPHA: (96) implies: % 17.58/3.21 | | | | | | | | | | | | | | (97) convergent_lines(all_38_2, all_38_1) = 0 % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | | REF_CLOSE: (13), (57), (72), (73), (97) are inconsistent by % 17.58/3.21 | | | | | | | | | | | | | | sub-proof #1. % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | Case 2: % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | | (98) all_58_1 = 0 & convergent_lines(all_38_2, % 17.58/3.21 | | | | | | | | | | | | | | all_38_1) = 0 % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | | ALPHA: (98) implies: % 17.58/3.21 | | | | | | | | | | | | | | (99) convergent_lines(all_38_2, all_38_1) = 0 % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | | REF_CLOSE: (13), (57), (72), (73), (99) are inconsistent by % 17.58/3.21 | | | | | | | | | | | | | | sub-proof #1. % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | End of split % 17.58/3.21 | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | Case 2: % 17.58/3.21 | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | (100) ( ~ (all_58_2 = 0) & unorthogonal_lines(all_38_2, % 17.58/3.21 | | | | | | | | | | | | | all_38_2) = all_58_2) | ( ~ (all_58_3 = 0) & % 17.58/3.21 | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = all_58_3) % 17.58/3.21 | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | BETA: splitting (100) gives: % 17.58/3.21 | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | Case 1: % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | | (101) ~ (all_58_2 = 0) & unorthogonal_lines(all_38_2, % 17.58/3.21 | | | | | | | | | | | | | | all_38_2) = all_58_2 % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | | ALPHA: (101) implies: % 17.58/3.21 | | | | | | | | | | | | | | (102) ~ (all_58_2 = 0) % 17.58/3.21 | | | | | | | | | | | | | | (103) unorthogonal_lines(all_38_2, all_38_2) = all_58_2 % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_58_2, all_38_2, % 17.58/3.21 | | | | | | | | | | | | | | all_38_2, simplifying with (79), (103) gives: % 17.58/3.21 | | | | | | | | | | | | | | (104) all_58_2 = 0 % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | | REDUCE: (102), (104) imply: % 17.58/3.21 | | | | | | | | | | | | | | (105) $false % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | | CLOSE: (105) is inconsistent. % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | Case 2: % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | | (106) ~ (all_58_3 = 0) & convergent_lines(all_38_2, % 17.58/3.21 | | | | | | | | | | | | | | all_38_2) = all_58_3 % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | | ALPHA: (106) implies: % 17.58/3.21 | | | | | | | | | | | | | | (107) ~ (all_58_3 = 0) % 17.58/3.21 | | | | | | | | | | | | | | (108) convergent_lines(all_38_2, all_38_2) = all_58_3 % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.21 | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_58_3, all_68_1, % 17.58/3.21 | | | | | | | | | | | | | | all_38_2, all_38_2, simplifying with (94), (108) % 17.58/3.21 | | | | | | | | | | | | | | gives: % 17.58/3.21 | | | | | | | | | | | | | | (109) all_68_1 = all_58_3 % 17.58/3.21 | | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_68_1, all_85_0, % 17.58/3.22 | | | | | | | | | | | | | | all_38_2, all_38_2, simplifying with (62), (94) % 17.58/3.22 | | | | | | | | | | | | | | gives: % 17.58/3.22 | | | | | | | | | | | | | | (110) all_85_0 = all_68_1 % 17.58/3.22 | | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_85_0, all_38_2, % 17.58/3.22 | | | | | | | | | | | | | | all_38_2, simplifying with (62), (78) gives: % 17.58/3.22 | | | | | | | | | | | | | | (111) all_85_0 = 0 % 17.58/3.22 | | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | | COMBINE_EQS: (110), (111) imply: % 17.58/3.22 | | | | | | | | | | | | | | (112) all_68_1 = 0 % 17.58/3.22 | | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | | SIMP: (112) implies: % 17.58/3.22 | | | | | | | | | | | | | | (113) all_68_1 = 0 % 17.58/3.22 | | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | | COMBINE_EQS: (109), (113) imply: % 17.58/3.22 | | | | | | | | | | | | | | (114) all_58_3 = 0 % 17.58/3.22 | | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | | SIMP: (114) implies: % 17.58/3.22 | | | | | | | | | | | | | | (115) all_58_3 = 0 % 17.58/3.22 | | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | | REDUCE: (107), (115) imply: % 17.58/3.22 | | | | | | | | | | | | | | (116) $false % 17.58/3.22 | | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | | CLOSE: (116) is inconsistent. % 17.58/3.22 | | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | End of split % 17.58/3.22 | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | End of split % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | End of split % 17.58/3.22 | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | End of split % 17.58/3.22 | | | | | | | | | | % 17.58/3.22 | | | | | | | | | Case 2: % 17.58/3.22 | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | (117) ~ (all_60_0 = 0) & convergent_lines(all_38_2, % 17.58/3.22 | | | | | | | | | | all_38_1) = all_60_0 % 17.58/3.22 | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | ALPHA: (117) implies: % 17.58/3.22 | | | | | | | | | | (118) convergent_lines(all_38_2, all_38_1) = all_60_0 % 17.58/3.22 | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | BETA: splitting (45) gives: % 17.58/3.22 | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | Case 1: % 17.58/3.22 | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | (119) (all_67_2 = 0 & all_47_0 = 0 & % 17.58/3.22 | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0) | % 17.58/3.22 | | | | | | | | | | | (all_67_3 = 0 & all_45_0 = 0 & % 17.58/3.22 | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) % 17.58/3.22 | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | BETA: splitting (119) gives: % 17.58/3.22 | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | Case 1: % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | (120) all_67_2 = 0 & all_47_0 = 0 & % 17.58/3.22 | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | ALPHA: (120) implies: % 17.58/3.22 | | | | | | | | | | | | (121) all_47_0 = 0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | REDUCE: (30), (121) imply: % 17.58/3.22 | | | | | | | | | | | | (122) $false % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | CLOSE: (122) is inconsistent. % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | Case 2: % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | (123) all_67_3 = 0 & all_45_0 = 0 & % 17.58/3.22 | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | ALPHA: (123) implies: % 17.58/3.22 | | | | | | | | | | | | (124) all_45_0 = 0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | REDUCE: (27), (124) imply: % 17.58/3.22 | | | | | | | | | | | | (125) $false % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | CLOSE: (125) is inconsistent. % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | End of split % 17.58/3.22 | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | Case 2: % 17.58/3.22 | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | (126) ( ~ (all_67_0 = 0) & unorthogonal_lines(all_38_2, % 17.58/3.22 | | | | | | | | | | | all_38_1) = all_67_0) | ( ~ (all_67_1 = 0) & % 17.58/3.22 | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = all_67_1) % 17.58/3.22 | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | BETA: splitting (126) gives: % 17.58/3.22 | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | Case 1: % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | (127) ~ (all_67_0 = 0) & unorthogonal_lines(all_38_2, % 17.58/3.22 | | | | | | | | | | | | all_38_1) = all_67_0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | ALPHA: (127) implies: % 17.58/3.22 | | | | | | | | | | | | (128) ~ (all_67_0 = 0) % 17.58/3.22 | | | | | | | | | | | | (129) unorthogonal_lines(all_38_2, all_38_1) = all_67_0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_67_0, all_38_1, % 17.58/3.22 | | | | | | | | | | | | all_38_2, simplifying with (32), (129) gives: % 17.58/3.22 | | | | | | | | | | | | (130) all_67_0 = 0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | REDUCE: (128), (130) imply: % 17.58/3.22 | | | | | | | | | | | | (131) $false % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | CLOSE: (131) is inconsistent. % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | Case 2: % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | (132) ~ (all_67_1 = 0) & convergent_lines(all_38_2, % 17.58/3.22 | | | | | | | | | | | | all_38_1) = all_67_1 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | ALPHA: (132) implies: % 17.58/3.22 | | | | | | | | | | | | (133) convergent_lines(all_38_2, all_38_1) = all_67_1 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_62_0, all_63_0, % 17.58/3.22 | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (57), (73) % 17.58/3.22 | | | | | | | | | | | | gives: % 17.58/3.22 | | | | | | | | | | | | (134) all_63_0 = all_62_0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_63_0, all_67_1, % 17.58/3.22 | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (57), (133) % 17.58/3.22 | | | | | | | | | | | | gives: % 17.58/3.22 | | | | | | | | | | | | (135) all_67_1 = all_63_0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_60_0, all_67_1, % 17.58/3.22 | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (118), (133) % 17.58/3.22 | | | | | | | | | | | | gives: % 17.58/3.22 | | | | | | | | | | | | (136) all_67_1 = all_60_0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | COMBINE_EQS: (135), (136) imply: % 17.58/3.22 | | | | | | | | | | | | (137) all_63_0 = all_60_0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | SIMP: (137) implies: % 17.58/3.22 | | | | | | | | | | | | (138) all_63_0 = all_60_0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | COMBINE_EQS: (134), (138) imply: % 17.58/3.22 | | | | | | | | | | | | (139) all_62_0 = all_60_0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | SIMP: (139) implies: % 17.58/3.22 | | | | | | | | | | | | (140) all_62_0 = all_60_0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | REDUCE: (72), (140) imply: % 17.58/3.22 | | | | | | | | | | | | (141) ~ (all_60_0 = 0) % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_38_3, all_38_2, % 17.58/3.22 | | | | | | | | | | | | all_38_1, all_60_0, simplifying with (17), (18), % 17.58/3.22 | | | | | | | | | | | | (19), (47), (118) gives: % 17.58/3.22 | | | | | | | | | | | | (142) all_60_0 = 0 | convergent_lines(all_38_3, % 17.58/3.22 | | | | | | | | | | | | all_38_1) = 0 % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | BETA: splitting (142) gives: % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | Case 1: % 17.58/3.22 | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | (143) convergent_lines(all_38_3, all_38_1) = 0 % 17.58/3.22 | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_47_0, 0, all_38_1, % 17.58/3.22 | | | | | | | | | | | | | all_38_3, simplifying with (31), (143) gives: % 17.58/3.22 | | | | | | | | | | | | | (144) all_47_0 = 0 % 17.58/3.22 | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | REDUCE: (30), (144) imply: % 17.58/3.22 | | | | | | | | | | | | | (145) $false % 17.58/3.22 | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | CLOSE: (145) is inconsistent. % 17.58/3.22 | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | Case 2: % 17.58/3.22 | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | (146) all_60_0 = 0 % 17.58/3.22 | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | REDUCE: (141), (146) imply: % 17.58/3.22 | | | | | | | | | | | | | (147) $false % 17.58/3.22 | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | | CLOSE: (147) is inconsistent. % 17.58/3.22 | | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | | End of split % 17.58/3.22 | | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | | End of split % 17.58/3.22 | | | | | | | | | | | % 17.58/3.22 | | | | | | | | | | End of split % 17.58/3.22 | | | | | | | | | | % 17.58/3.22 | | | | | | | | | End of split % 17.58/3.22 | | | | | | | | | % 17.58/3.22 | | | | | | | | End of split % 17.58/3.22 | | | | | | | | % 17.58/3.22 | | | | | | | End of split % 17.58/3.22 | | | | | | | % 17.58/3.22 | | | | | | End of split % 17.58/3.22 | | | | | | % 17.58/3.22 | | | | | End of split % 17.58/3.22 | | | | | % 17.58/3.22 | | | | End of split % 17.58/3.22 | | | | % 17.58/3.22 | | | End of split % 17.58/3.22 | | | % 17.58/3.22 | | Case 2: % 17.58/3.22 | | | % 17.58/3.22 | | | (148) all_45_0 = 0 % 17.58/3.22 | | | % 17.58/3.22 | | | REDUCE: (27), (148) imply: % 17.58/3.22 | | | (149) $false % 17.58/3.22 | | | % 17.58/3.22 | | | CLOSE: (149) is inconsistent. % 17.58/3.22 | | | % 17.58/3.22 | | End of split % 17.58/3.22 | | % 17.58/3.22 | Case 2: % 17.58/3.22 | | % 17.58/3.22 | | (150) all_38_0 = 0 % 17.58/3.22 | | % 17.58/3.22 | | REDUCE: (16), (150) imply: % 17.58/3.22 | | (151) $false % 17.58/3.22 | | % 17.58/3.22 | | CLOSE: (151) is inconsistent. % 17.58/3.22 | | % 17.58/3.22 | End of split % 17.58/3.22 | % 17.58/3.22 End of proof % 17.58/3.22 % 17.58/3.22 Sub-proof #1 shows that the following formulas are inconsistent: % 17.58/3.22 ---------------------------------------------------------------- % 17.58/3.22 (1) ~ (all_62_0 = 0) % 17.58/3.22 (2) convergent_lines(all_38_2, all_38_1) = all_62_0 % 17.58/3.23 (3) convergent_lines(all_38_2, all_38_1) = all_63_0 % 17.58/3.23 (4) convergent_lines(all_38_2, all_38_1) = 0 % 17.58/3.23 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.58/3.23 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 17.58/3.23 (convergent_lines(v3, v2) = v0)) % 17.58/3.23 % 17.58/3.23 Begin of proof % 17.58/3.23 | % 17.58/3.23 | GROUND_INST: instantiating (5) with all_62_0, all_63_0, all_38_1, all_38_2, % 17.58/3.23 | simplifying with (2), (3) gives: % 17.58/3.23 | (6) all_63_0 = all_62_0 % 17.58/3.23 | % 17.58/3.23 | GROUND_INST: instantiating (5) with 0, all_63_0, all_38_1, all_38_2, % 17.58/3.23 | simplifying with (3), (4) gives: % 17.58/3.23 | (7) all_63_0 = 0 % 17.58/3.23 | % 17.58/3.23 | COMBINE_EQS: (6), (7) imply: % 17.58/3.23 | (8) all_62_0 = 0 % 17.58/3.23 | % 17.58/3.23 | SIMP: (8) implies: % 17.58/3.23 | (9) all_62_0 = 0 % 17.58/3.23 | % 17.58/3.23 | REDUCE: (1), (9) imply: % 17.58/3.23 | (10) $false % 17.58/3.23 | % 17.58/3.23 | CLOSE: (10) is inconsistent. % 17.58/3.23 | % 17.58/3.23 End of proof % 17.58/3.23 % SZS output end Proof for theBenchmark % 17.58/3.23 % 17.58/3.23 2600ms %------------------------------------------------------------------------------