%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO214+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n005.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 23:22:24 EDT 2023 % Result : Theorem 11.05s 2.32s % Output : Proof 13.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : GEO214+2 : TPTP v8.1.2. Released v3.3.0. % 0.08/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.36 % Computer : n005.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Tue Aug 29 19:25:37 EDT 2023 % 0.15/0.37 % CPUTime : % 0.22/0.67 ________ _____ % 0.22/0.67 ___ __ \_________(_)________________________________ % 0.22/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.67 % 0.22/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.67 (2023-06-19) % 0.22/0.67 % 0.22/0.67 (c) Philipp Rümmer, 2009-2023 % 0.22/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.67 Amanda Stjerna. % 0.22/0.67 Free software under BSD-3-Clause. % 0.22/0.67 % 0.22/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.67 % 0.22/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.68 Running up to 7 provers in parallel. % 0.22/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.75/1.12 Prover 4: Preprocessing ... % 2.75/1.13 Prover 1: Preprocessing ... % 2.98/1.17 Prover 6: Preprocessing ... % 2.98/1.17 Prover 3: Preprocessing ... % 2.98/1.17 Prover 5: Preprocessing ... % 2.98/1.17 Prover 2: Preprocessing ... % 2.98/1.17 Prover 0: Preprocessing ... % 5.41/1.48 Prover 5: Proving ... % 5.41/1.49 Prover 2: Proving ... % 5.81/1.53 Prover 6: Constructing countermodel ... % 5.81/1.53 Prover 3: Constructing countermodel ... % 5.81/1.55 Prover 1: Constructing countermodel ... % 5.81/1.62 Prover 3: gave up % 6.50/1.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.50/1.66 Prover 7: Preprocessing ... % 6.50/1.68 Prover 6: gave up % 6.50/1.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.03/1.70 Prover 1: gave up % 7.03/1.70 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 7.03/1.73 Prover 4: Constructing countermodel ... % 7.03/1.73 Prover 9: Preprocessing ... % 7.03/1.75 Prover 7: Warning: ignoring some quantifiers % 7.03/1.76 Prover 8: Preprocessing ... % 7.62/1.77 Prover 0: Proving ... % 7.62/1.79 Prover 7: Constructing countermodel ... % 8.04/1.84 Prover 7: gave up % 8.04/1.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.04/1.86 Prover 8: Warning: ignoring some quantifiers % 8.04/1.87 Prover 8: Constructing countermodel ... % 8.04/1.88 Prover 10: Preprocessing ... % 8.76/1.94 Prover 10: Warning: ignoring some quantifiers % 8.76/1.96 Prover 8: gave up % 8.76/1.96 Prover 10: Constructing countermodel ... % 8.76/1.97 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.76/1.99 Prover 10: gave up % 8.76/1.99 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 8.76/2.00 Prover 11: Preprocessing ... % 8.76/2.01 Prover 12: Preprocessing ... % 8.76/2.02 Prover 9: Constructing countermodel ... % 9.44/2.13 Prover 12: Proving ... % 11.05/2.25 Prover 11: Constructing countermodel ... % 11.05/2.32 Prover 0: proved (1634ms) % 11.05/2.32 % 11.05/2.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.05/2.32 % 11.05/2.32 Prover 5: stopped % 11.05/2.32 Prover 12: stopped % 11.79/2.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.79/2.34 Prover 2: stopped % 11.79/2.34 Prover 9: stopped % 11.79/2.34 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.79/2.34 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.79/2.34 Prover 13: Preprocessing ... % 11.79/2.37 Prover 16: Preprocessing ... % 11.79/2.37 Prover 19: Preprocessing ... % 11.79/2.38 Prover 13: Warning: ignoring some quantifiers % 11.79/2.39 Prover 13: Constructing countermodel ... % 12.27/2.44 Prover 13: gave up % 12.27/2.44 Prover 19: Warning: ignoring some quantifiers % 12.27/2.44 Prover 16: Warning: ignoring some quantifiers % 12.27/2.45 Prover 19: Constructing countermodel ... % 12.27/2.45 Prover 16: Constructing countermodel ... % 12.80/2.49 Prover 19: gave up % 13.10/2.50 Prover 16: gave up % 13.31/2.59 Prover 4: Found proof (size 108) % 13.31/2.59 Prover 4: proved (1894ms) % 13.31/2.59 Prover 11: stopped % 13.31/2.59 % 13.31/2.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.31/2.59 % 13.31/2.61 % SZS output start Proof for theBenchmark % 13.31/2.61 Assumptions after simplification: % 13.31/2.61 --------------------------------- % 13.31/2.61 % 13.31/2.61 (apart3) % 13.31/2.63 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 13.31/2.63 % 13.31/2.63 (apart6) % 13.31/2.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 13.31/2.64 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 13.31/2.64 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 13.31/2.64 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 13.31/2.64 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ % 13.31/2.64 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 13.31/2.64 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.31/2.64 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 13.31/2.64 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 13.31/2.64 convergent_lines(v1, v2) = 0) % 13.31/2.64 % 13.31/2.64 (con) % 13.31/2.64 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 13.31/2.64 unorthogonal_lines(v1, v0) = v2 & unorthogonal_lines(v0, v1) = 0 & $i(v1) & % 13.31/2.64 $i(v0)) % 13.31/2.64 % 13.31/2.64 (oac1) % 13.31/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 13.31/2.67 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | % 13.31/2.67 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: % 13.31/2.67 any] : ? [v8: any] : (unorthogonal_lines(v0, v1) = v6 & % 13.31/2.67 convergent_lines(v1, v2) = v8 & convergent_lines(v0, v2) = v7 & % 13.31/2.67 convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 % 13.31/2.67 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 13.31/2.67 : ! [v3: any] : ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ % 13.31/2.67 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 13.31/2.67 [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 13.31/2.67 (unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & % 13.31/2.67 convergent_lines(v1, v2) = v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = % 13.31/2.67 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0: % 13.31/2.67 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 13.31/2.67 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~ % 13.31/2.67 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] % 13.31/2.67 : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, % 13.31/2.67 v1) = v6 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 % 13.31/2.67 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & % 13.31/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 13.31/2.67 (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ~ % 13.31/2.67 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] % 13.31/2.67 : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, % 13.31/2.67 v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v1) = % 13.31/2.67 v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 13.31/2.67 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 13.31/2.67 (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 13.31/2.67 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] % 13.31/2.67 : ? [v7: any] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) % 13.31/2.67 = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ % 13.31/2.67 (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! % 13.31/2.67 [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) % 13.31/2.67 | ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 13.31/2.67 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 13.31/2.67 (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & % 13.31/2.67 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = % 13.31/2.67 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: % 13.31/2.67 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | % 13.31/2.67 ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 13.31/2.67 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 13.31/2.67 (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & % 13.31/2.67 convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = % 13.31/2.67 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: % 13.31/2.67 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | % 13.31/2.67 ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 13.31/2.67 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 13.31/2.67 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v4 & % 13.31/2.67 convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = % 13.31/2.67 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: % 13.31/2.67 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 13.31/2.67 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 13.31/2.67 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 13.31/2.67 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & % 13.31/2.67 convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = % 13.31/2.67 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: % 13.31/2.67 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 13.31/2.67 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 13.31/2.67 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 13.31/2.67 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & % 13.31/2.67 convergent_lines(v1, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = % 13.31/2.67 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: % 13.31/2.67 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~ % 13.31/2.67 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 13.31/2.67 any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 13.31/2.67 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & % 13.31/2.67 unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v4 % 13.31/2.67 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! % 13.31/2.67 [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) | % 13.31/2.67 ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 13.31/2.67 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 13.31/2.67 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & % 13.31/2.67 unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & ( ~ (v4 % 13.31/2.67 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) % 13.31/2.67 % 13.31/2.67 (occu1) % 13.31/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 13.31/2.67 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 13.31/2.67 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 13.31/2.67 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 13.31/2.67 unorthogonal_lines(v0, v1) = 0) % 13.31/2.67 % 13.31/2.67 (function-axioms) % 13.31/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.31/2.67 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 13.31/2.67 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 13.31/2.67 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 13.31/2.67 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 13.31/2.67 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 13.31/2.67 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 13.31/2.67 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 13.31/2.67 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 13.31/2.67 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 13.31/2.67 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.31/2.67 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.31/2.67 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 13.31/2.67 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.31/2.67 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 13.31/2.67 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.31/2.67 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.31/2.67 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 13.31/2.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.31/2.67 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 13.31/2.67 v0)) % 13.31/2.67 % 13.31/2.67 Further assumptions not needed in the proof: % 13.31/2.67 -------------------------------------------- % 13.31/2.68 apart1, apart2, apart4, apart5, ceq1, ceq2, ceq3, con1, con2, cp1, cp2, cu1, % 13.31/2.68 cup1, ooc1, ooc2, ouo1 % 13.31/2.68 % 13.31/2.68 Those formulas are unsatisfiable: % 13.31/2.68 --------------------------------- % 13.31/2.68 % 13.31/2.68 Begin of proof % 13.31/2.68 | % 13.31/2.68 | ALPHA: (apart6) implies: % 13.31/2.68 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.31/2.68 | (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 13.31/2.68 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 13.31/2.68 | % 13.31/2.68 | ALPHA: (occu1) implies: % 13.31/2.68 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 13.31/2.68 | (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 13.31/2.68 | convergent_lines(v0, v1) = 0) % 13.31/2.68 | % 13.31/2.68 | ALPHA: (oac1) implies: % 13.31/2.68 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 13.31/2.68 | (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) % 13.31/2.68 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 13.31/2.68 | ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) = v7 & % 13.31/2.68 | unorthogonal_lines(v0, v2) = v6 & convergent_lines(v0, v2) = v5 & % 13.31/2.68 | convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | % 13.31/2.68 | (v6 = 0 & v5 = 0)))) % 13.31/2.68 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 13.31/2.68 | (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = % 13.31/2.68 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 13.31/2.68 | any] : ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) = % 13.31/2.68 | v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 % 13.31/2.68 | & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) % 13.31/2.68 | | (v5 = 0 & v3 = 0)))) % 13.31/2.68 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 13.31/2.68 | (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = % 13.31/2.68 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 13.31/2.68 | any] : ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v0, v2) = % 13.31/2.68 | v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 % 13.31/2.68 | & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) % 13.31/2.68 | | (v6 = 0 & v5 = 0)))) % 13.31/2.69 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 13.31/2.69 | ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = % 13.31/2.69 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 13.31/2.69 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1, v2) = % 13.31/2.69 | v8 & unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = % 13.31/2.69 | v6 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | % 13.31/2.69 | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 13.31/2.69 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 13.31/2.69 | ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = % 13.31/2.69 | v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 13.31/2.69 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1, v2) = % 13.31/2.69 | v8 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v2) = % 13.31/2.69 | v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | % 13.31/2.69 | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 13.31/2.69 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 13.31/2.69 | ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = % 13.31/2.69 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 13.31/2.69 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v0, v2) = % 13.31/2.69 | v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = % 13.31/2.69 | v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | % 13.31/2.69 | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 13.31/2.69 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 13.31/2.69 | ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) % 13.31/2.69 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 13.31/2.69 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v0, v1) = % 13.31/2.69 | v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, v2) = v7 % 13.31/2.69 | & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 % 13.31/2.69 | = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 13.31/2.69 | % 13.31/2.69 | ALPHA: (function-axioms) implies: % 13.31/2.69 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 13.31/2.69 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 13.31/2.69 | (convergent_lines(v3, v2) = v0)) % 13.31/2.69 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 13.31/2.69 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 13.31/2.69 | (unorthogonal_lines(v3, v2) = v0)) % 13.31/2.69 | % 13.31/2.69 | DELTA: instantiating (con) with fresh symbols all_23_0, all_23_1, all_23_2 % 13.31/2.69 | gives: % 13.31/2.69 | (12) ~ (all_23_0 = 0) & unorthogonal_lines(all_23_1, all_23_2) = all_23_0 % 13.31/2.69 | & unorthogonal_lines(all_23_2, all_23_1) = 0 & $i(all_23_1) & % 13.31/2.69 | $i(all_23_2) % 13.31/2.69 | % 13.31/2.69 | ALPHA: (12) implies: % 13.31/2.69 | (13) ~ (all_23_0 = 0) % 13.31/2.69 | (14) $i(all_23_2) % 13.31/2.69 | (15) $i(all_23_1) % 13.31/2.69 | (16) unorthogonal_lines(all_23_2, all_23_1) = 0 % 13.31/2.69 | (17) unorthogonal_lines(all_23_1, all_23_2) = all_23_0 % 13.31/2.69 | % 13.31/2.69 | GROUND_INST: instantiating (9) with all_23_2, all_23_2, all_23_1, 0, 0, % 13.31/2.69 | simplifying with (14), (15), (16) gives: % 13.31/2.70 | (18) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 13.31/2.70 | (unorthogonal_lines(all_23_2, all_23_2) = v1 & % 13.31/2.70 | convergent_lines(all_23_2, all_23_1) = v3 & % 13.31/2.70 | convergent_lines(all_23_2, all_23_1) = v2 & % 13.31/2.70 | convergent_lines(all_23_2, all_23_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 13.31/2.70 | 0) | v3 = 0 | v2 = 0)) % 13.31/2.70 | % 13.31/2.70 | GROUND_INST: instantiating (4) with all_23_2, all_23_1, all_23_1, 0, % 13.31/2.70 | simplifying with (14), (15), (16) gives: % 13.31/2.70 | (19) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 13.31/2.70 | (unorthogonal_lines(all_23_1, all_23_1) = v3 & % 13.31/2.70 | convergent_lines(all_23_1, all_23_1) = v2 & % 13.31/2.70 | convergent_lines(all_23_2, all_23_1) = v1 & % 13.31/2.70 | convergent_lines(all_23_2, all_23_1) = v0 & ( ~ (v0 = 0) | v1 = 0 | % 13.31/2.70 | (v3 = 0 & v2 = 0))) % 13.31/2.70 | % 13.88/2.70 | GROUND_INST: instantiating (9) with all_23_1, all_23_1, all_23_2, all_23_0, % 13.88/2.70 | all_23_0, simplifying with (14), (15), (17) gives: % 13.88/2.70 | (20) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 13.88/2.70 | (unorthogonal_lines(all_23_1, all_23_1) = v1 & % 13.88/2.70 | convergent_lines(all_23_1, all_23_1) = v0 & % 13.88/2.70 | convergent_lines(all_23_1, all_23_2) = v3 & % 13.88/2.70 | convergent_lines(all_23_1, all_23_2) = v2 & ( ~ (v1 = 0) | ~ (v0 = % 13.88/2.70 | 0) | (v3 = 0 & all_23_0 = 0) | (v2 = 0 & all_23_0 = 0))) % 13.88/2.70 | % 13.88/2.70 | GROUND_INST: instantiating (5) with all_23_2, all_23_1, all_23_2, all_23_0, % 13.88/2.70 | simplifying with (14), (15), (16), (17) gives: % 13.88/2.70 | (21) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 13.88/2.70 | (unorthogonal_lines(all_23_2, all_23_2) = v2 & % 13.88/2.70 | convergent_lines(all_23_1, all_23_2) = v3 & % 13.88/2.70 | convergent_lines(all_23_2, all_23_1) = v0 & % 13.88/2.70 | convergent_lines(all_23_2, all_23_2) = v1 & ( ~ (v0 = 0) | (v3 = 0 & % 13.88/2.70 | all_23_0 = 0) | (v2 = 0 & v1 = 0))) % 13.88/2.70 | % 13.88/2.70 | GROUND_INST: instantiating (2) with all_23_1, all_23_2, all_23_0, simplifying % 13.88/2.70 | with (14), (15), (17) gives: % 13.88/2.70 | (22) all_23_0 = 0 | convergent_lines(all_23_1, all_23_2) = 0 % 13.88/2.70 | % 13.88/2.70 | DELTA: instantiating (19) with fresh symbols all_30_0, all_30_1, all_30_2, % 13.88/2.70 | all_30_3 gives: % 13.88/2.70 | (23) unorthogonal_lines(all_23_1, all_23_1) = all_30_0 & % 13.88/2.70 | convergent_lines(all_23_1, all_23_1) = all_30_1 & % 13.88/2.70 | convergent_lines(all_23_2, all_23_1) = all_30_2 & % 13.88/2.70 | convergent_lines(all_23_2, all_23_1) = all_30_3 & ( ~ (all_30_3 = 0) | % 13.88/2.70 | all_30_2 = 0 | (all_30_0 = 0 & all_30_1 = 0)) % 13.88/2.70 | % 13.88/2.70 | ALPHA: (23) implies: % 13.88/2.70 | (24) convergent_lines(all_23_2, all_23_1) = all_30_3 % 13.88/2.70 | (25) convergent_lines(all_23_2, all_23_1) = all_30_2 % 13.88/2.70 | % 13.88/2.70 | DELTA: instantiating (18) with fresh symbols all_32_0, all_32_1, all_32_2, % 13.88/2.70 | all_32_3 gives: % 13.88/2.70 | (26) unorthogonal_lines(all_23_2, all_23_2) = all_32_2 & % 13.88/2.70 | convergent_lines(all_23_2, all_23_1) = all_32_0 & % 13.88/2.70 | convergent_lines(all_23_2, all_23_1) = all_32_1 & % 13.88/2.70 | convergent_lines(all_23_2, all_23_2) = all_32_3 & ( ~ (all_32_2 = 0) | % 13.88/2.70 | ~ (all_32_3 = 0) | all_32_0 = 0 | all_32_1 = 0) % 13.88/2.70 | % 13.88/2.70 | ALPHA: (26) implies: % 13.88/2.70 | (27) convergent_lines(all_23_2, all_23_2) = all_32_3 % 13.88/2.70 | (28) convergent_lines(all_23_2, all_23_1) = all_32_1 % 13.88/2.70 | (29) convergent_lines(all_23_2, all_23_1) = all_32_0 % 13.88/2.70 | (30) unorthogonal_lines(all_23_2, all_23_2) = all_32_2 % 13.88/2.70 | % 13.88/2.70 | DELTA: instantiating (21) with fresh symbols all_34_0, all_34_1, all_34_2, % 13.88/2.70 | all_34_3 gives: % 13.88/2.71 | (31) unorthogonal_lines(all_23_2, all_23_2) = all_34_1 & % 13.88/2.71 | convergent_lines(all_23_1, all_23_2) = all_34_0 & % 13.88/2.71 | convergent_lines(all_23_2, all_23_1) = all_34_3 & % 13.88/2.71 | convergent_lines(all_23_2, all_23_2) = all_34_2 & ( ~ (all_34_3 = 0) | % 13.88/2.71 | (all_34_0 = 0 & all_23_0 = 0) | (all_34_1 = 0 & all_34_2 = 0)) % 13.88/2.71 | % 13.88/2.71 | ALPHA: (31) implies: % 13.88/2.71 | (32) convergent_lines(all_23_2, all_23_2) = all_34_2 % 13.88/2.71 | (33) convergent_lines(all_23_2, all_23_1) = all_34_3 % 13.88/2.71 | (34) convergent_lines(all_23_1, all_23_2) = all_34_0 % 13.88/2.71 | (35) unorthogonal_lines(all_23_2, all_23_2) = all_34_1 % 13.88/2.71 | (36) ~ (all_34_3 = 0) | (all_34_0 = 0 & all_23_0 = 0) | (all_34_1 = 0 & % 13.88/2.71 | all_34_2 = 0) % 13.88/2.71 | % 13.88/2.71 | DELTA: instantiating (20) with fresh symbols all_36_0, all_36_1, all_36_2, % 13.88/2.71 | all_36_3 gives: % 13.88/2.71 | (37) unorthogonal_lines(all_23_1, all_23_1) = all_36_2 & % 13.88/2.71 | convergent_lines(all_23_1, all_23_1) = all_36_3 & % 13.88/2.71 | convergent_lines(all_23_1, all_23_2) = all_36_0 & % 13.88/2.71 | convergent_lines(all_23_1, all_23_2) = all_36_1 & ( ~ (all_36_2 = 0) | % 13.88/2.71 | ~ (all_36_3 = 0) | (all_36_0 = 0 & all_23_0 = 0) | (all_36_1 = 0 & % 13.88/2.71 | all_23_0 = 0)) % 13.88/2.71 | % 13.88/2.71 | ALPHA: (37) implies: % 13.88/2.71 | (38) convergent_lines(all_23_1, all_23_2) = all_36_1 % 13.88/2.71 | (39) convergent_lines(all_23_1, all_23_2) = all_36_0 % 13.88/2.71 | % 13.88/2.71 | BETA: splitting (22) gives: % 13.88/2.71 | % 13.88/2.71 | Case 1: % 13.88/2.71 | | % 13.88/2.71 | | (40) convergent_lines(all_23_1, all_23_2) = 0 % 13.88/2.71 | | % 13.88/2.71 | | GROUND_INST: instantiating (10) with all_32_3, all_34_2, all_23_2, all_23_2, % 13.88/2.71 | | simplifying with (27), (32) gives: % 13.88/2.71 | | (41) all_34_2 = all_32_3 % 13.88/2.71 | | % 13.88/2.71 | | GROUND_INST: instantiating (10) with all_30_3, all_32_0, all_23_1, all_23_2, % 13.88/2.71 | | simplifying with (24), (29) gives: % 13.88/2.71 | | (42) all_32_0 = all_30_3 % 13.88/2.71 | | % 13.88/2.71 | | GROUND_INST: instantiating (10) with all_32_0, all_34_3, all_23_1, all_23_2, % 13.88/2.71 | | simplifying with (29), (33) gives: % 13.88/2.71 | | (43) all_34_3 = all_32_0 % 13.88/2.71 | | % 13.88/2.71 | | GROUND_INST: instantiating (10) with all_32_1, all_34_3, all_23_1, all_23_2, % 13.88/2.71 | | simplifying with (28), (33) gives: % 13.88/2.71 | | (44) all_34_3 = all_32_1 % 13.88/2.71 | | % 13.88/2.71 | | GROUND_INST: instantiating (10) with all_30_2, all_34_3, all_23_1, all_23_2, % 13.88/2.71 | | simplifying with (25), (33) gives: % 13.88/2.71 | | (45) all_34_3 = all_30_2 % 13.88/2.71 | | % 13.88/2.71 | | GROUND_INST: instantiating (10) with all_34_0, all_36_1, all_23_2, all_23_1, % 13.88/2.71 | | simplifying with (34), (38) gives: % 13.88/2.71 | | (46) all_36_1 = all_34_0 % 13.88/2.71 | | % 13.88/2.71 | | GROUND_INST: instantiating (10) with all_36_1, all_36_0, all_23_2, all_23_1, % 13.88/2.71 | | simplifying with (38), (39) gives: % 13.88/2.71 | | (47) all_36_0 = all_36_1 % 13.88/2.71 | | % 13.88/2.71 | | GROUND_INST: instantiating (10) with 0, all_36_0, all_23_2, all_23_1, % 13.88/2.71 | | simplifying with (39), (40) gives: % 13.88/2.71 | | (48) all_36_0 = 0 % 13.88/2.71 | | % 13.88/2.71 | | GROUND_INST: instantiating (11) with all_32_2, all_34_1, all_23_2, all_23_2, % 13.88/2.71 | | simplifying with (30), (35) gives: % 13.88/2.71 | | (49) all_34_1 = all_32_2 % 13.88/2.71 | | % 13.88/2.71 | | COMBINE_EQS: (47), (48) imply: % 13.88/2.71 | | (50) all_36_1 = 0 % 13.88/2.71 | | % 13.88/2.71 | | SIMP: (50) implies: % 13.88/2.71 | | (51) all_36_1 = 0 % 13.88/2.71 | | % 13.88/2.71 | | COMBINE_EQS: (46), (51) imply: % 13.88/2.71 | | (52) all_34_0 = 0 % 13.88/2.71 | | % 13.88/2.71 | | SIMP: (52) implies: % 13.88/2.71 | | (53) all_34_0 = 0 % 13.88/2.71 | | % 13.88/2.72 | | COMBINE_EQS: (44), (45) imply: % 13.88/2.72 | | (54) all_32_1 = all_30_2 % 13.88/2.72 | | % 13.88/2.72 | | COMBINE_EQS: (43), (44) imply: % 13.88/2.72 | | (55) all_32_0 = all_32_1 % 13.88/2.72 | | % 13.88/2.72 | | SIMP: (55) implies: % 13.88/2.72 | | (56) all_32_0 = all_32_1 % 13.88/2.72 | | % 13.88/2.72 | | COMBINE_EQS: (42), (56) imply: % 13.88/2.72 | | (57) all_32_1 = all_30_3 % 13.88/2.72 | | % 13.88/2.72 | | SIMP: (57) implies: % 13.88/2.72 | | (58) all_32_1 = all_30_3 % 13.88/2.72 | | % 13.88/2.72 | | COMBINE_EQS: (54), (58) imply: % 13.88/2.72 | | (59) all_30_2 = all_30_3 % 13.88/2.72 | | % 13.88/2.72 | | COMBINE_EQS: (44), (58) imply: % 13.88/2.72 | | (60) all_34_3 = all_30_3 % 13.88/2.72 | | % 13.88/2.72 | | GROUND_INST: instantiating (6) with all_23_2, all_23_2, all_23_1, all_30_3, % 13.88/2.72 | | all_30_3, simplifying with (14), (15), (24) gives: % 13.88/2.72 | | (61) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 13.88/2.72 | | (unorthogonal_lines(all_23_2, all_23_1) = v3 & % 13.88/2.72 | | unorthogonal_lines(all_23_2, all_23_1) = v2 & % 13.88/2.72 | | unorthogonal_lines(all_23_2, all_23_2) = v1 & % 13.88/2.72 | | convergent_lines(all_23_2, all_23_2) = v0 & ( ~ (v1 = 0) | ~ (v0 % 13.88/2.72 | | = 0) | (v3 = 0 & all_30_3 = 0) | (v2 = 0 & all_30_3 = 0))) % 13.88/2.72 | | % 13.88/2.72 | | GROUND_INST: instantiating (8) with all_23_2, all_23_2, all_23_1, all_30_3, % 13.88/2.72 | | 0, simplifying with (14), (15), (16), (24) gives: % 13.88/2.72 | | (62) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 13.88/2.72 | | (unorthogonal_lines(all_23_2, all_23_1) = v2 & % 13.88/2.72 | | unorthogonal_lines(all_23_2, all_23_2) = v1 & % 13.88/2.72 | | convergent_lines(all_23_2, all_23_1) = v3 & % 13.88/2.72 | | convergent_lines(all_23_2, all_23_2) = v0 & ( ~ (v1 = 0) | ~ (v0 % 13.88/2.72 | | = 0) | v3 = 0 | (v2 = 0 & all_30_3 = 0))) % 13.88/2.72 | | % 13.88/2.72 | | GROUND_INST: instantiating (7) with all_23_2, all_23_2, all_23_1, 0, % 13.88/2.72 | | all_30_3, simplifying with (14), (15), (16), (24) gives: % 13.88/2.72 | | (63) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 13.88/2.72 | | (unorthogonal_lines(all_23_2, all_23_1) = v3 & % 13.88/2.72 | | unorthogonal_lines(all_23_2, all_23_2) = v1 & % 13.88/2.72 | | convergent_lines(all_23_2, all_23_1) = v2 & % 13.88/2.72 | | convergent_lines(all_23_2, all_23_2) = v0 & ( ~ (v1 = 0) | ~ (v0 % 13.88/2.72 | | = 0) | v2 = 0 | (v3 = 0 & all_30_3 = 0))) % 13.88/2.72 | | % 13.88/2.72 | | GROUND_INST: instantiating (3) with all_23_2, all_23_1, all_23_2, 0, % 13.88/2.72 | | simplifying with (14), (15), (16), (40) gives: % 13.88/2.72 | | (64) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 13.88/2.72 | | (unorthogonal_lines(all_23_1, all_23_2) = v3 & % 13.88/2.72 | | unorthogonal_lines(all_23_2, all_23_2) = v2 & % 13.88/2.72 | | convergent_lines(all_23_2, all_23_1) = v0 & % 13.88/2.72 | | convergent_lines(all_23_2, all_23_2) = v1 & ( ~ (v0 = 0) | v3 = 0 % 13.88/2.72 | | | (v2 = 0 & v1 = 0))) % 13.88/2.72 | | % 13.88/2.72 | | GROUND_INST: instantiating (1) with all_23_1, all_23_2, all_23_1, all_30_3, % 13.88/2.72 | | simplifying with (14), (15), (24), (40) gives: % 13.88/2.72 | | (65) all_30_3 = 0 | convergent_lines(all_23_1, all_23_1) = 0 % 13.88/2.72 | | % 13.88/2.72 | | GROUND_INST: instantiating (9) with all_23_2, all_23_1, all_23_2, all_32_2, % 13.88/2.72 | | all_23_0, simplifying with (14), (15), (17), (30) gives: % 13.88/2.72 | | (66) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 13.88/2.72 | | (unorthogonal_lines(all_23_2, all_23_1) = v1 & % 13.88/2.72 | | convergent_lines(all_23_1, all_23_2) = v3 & % 13.88/2.72 | | convergent_lines(all_23_2, all_23_1) = v0 & % 13.88/2.72 | | convergent_lines(all_23_2, all_23_2) = v2 & ( ~ (v1 = 0) | ~ (v0 % 13.88/2.72 | | = 0) | (v3 = 0 & all_23_0 = 0) | (v2 = 0 & all_32_2 = 0))) % 13.88/2.72 | | % 13.88/2.73 | | GROUND_INST: instantiating (4) with all_23_2, all_23_1, all_23_2, all_32_2, % 13.88/2.73 | | simplifying with (14), (15), (16), (30) gives: % 13.88/2.73 | | (67) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 13.88/2.73 | | (unorthogonal_lines(all_23_1, all_23_2) = v3 & % 13.88/2.73 | | convergent_lines(all_23_1, all_23_2) = v2 & % 13.88/2.73 | | convergent_lines(all_23_2, all_23_1) = v0 & % 13.88/2.73 | | convergent_lines(all_23_2, all_23_2) = v1 & ( ~ (v0 = 0) | (v3 = 0 % 13.88/2.73 | | & v2 = 0) | (v1 = 0 & all_32_2 = 0))) % 13.88/2.73 | | % 13.88/2.73 | | GROUND_INST: instantiating (7) with all_23_2, all_23_1, all_23_2, all_32_2, % 13.88/2.73 | | 0, simplifying with (14), (15), (30), (40) gives: % 13.88/2.73 | | (68) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 13.88/2.73 | | (unorthogonal_lines(all_23_1, all_23_2) = v3 & % 13.88/2.73 | | unorthogonal_lines(all_23_2, all_23_1) = v1 & % 13.88/2.73 | | convergent_lines(all_23_2, all_23_1) = v0 & % 13.88/2.73 | | convergent_lines(all_23_2, all_23_2) = v2 & ( ~ (v1 = 0) | ~ (v0 % 13.88/2.73 | | = 0) | v3 = 0 | (v2 = 0 & all_32_2 = 0))) % 13.88/2.73 | | % 13.88/2.73 | | DELTA: instantiating (64) with fresh symbols all_52_0, all_52_1, all_52_2, % 13.88/2.73 | | all_52_3 gives: % 13.88/2.73 | | (69) unorthogonal_lines(all_23_1, all_23_2) = all_52_0 & % 13.88/2.73 | | unorthogonal_lines(all_23_2, all_23_2) = all_52_1 & % 13.88/2.73 | | convergent_lines(all_23_2, all_23_1) = all_52_3 & % 13.88/2.73 | | convergent_lines(all_23_2, all_23_2) = all_52_2 & ( ~ (all_52_3 = 0) % 13.88/2.73 | | | all_52_0 = 0 | (all_52_1 = 0 & all_52_2 = 0)) % 13.88/2.73 | | % 13.88/2.73 | | ALPHA: (69) implies: % 13.88/2.73 | | (70) convergent_lines(all_23_2, all_23_2) = all_52_2 % 13.88/2.73 | | % 13.88/2.73 | | DELTA: instantiating (68) with fresh symbols all_56_0, all_56_1, all_56_2, % 13.88/2.73 | | all_56_3 gives: % 13.88/2.73 | | (71) unorthogonal_lines(all_23_1, all_23_2) = all_56_0 & % 13.88/2.73 | | unorthogonal_lines(all_23_2, all_23_1) = all_56_2 & % 13.88/2.73 | | convergent_lines(all_23_2, all_23_1) = all_56_3 & % 13.88/2.73 | | convergent_lines(all_23_2, all_23_2) = all_56_1 & ( ~ (all_56_2 = 0) % 13.88/2.73 | | | ~ (all_56_3 = 0) | all_56_0 = 0 | (all_56_1 = 0 & all_32_2 = % 13.88/2.73 | | 0)) % 13.88/2.73 | | % 13.88/2.73 | | ALPHA: (71) implies: % 13.88/2.73 | | (72) convergent_lines(all_23_2, all_23_2) = all_56_1 % 13.88/2.73 | | % 13.88/2.73 | | DELTA: instantiating (67) with fresh symbols all_58_0, all_58_1, all_58_2, % 13.88/2.73 | | all_58_3 gives: % 13.88/2.73 | | (73) unorthogonal_lines(all_23_1, all_23_2) = all_58_0 & % 13.88/2.73 | | convergent_lines(all_23_1, all_23_2) = all_58_1 & % 13.88/2.73 | | convergent_lines(all_23_2, all_23_1) = all_58_3 & % 13.88/2.73 | | convergent_lines(all_23_2, all_23_2) = all_58_2 & ( ~ (all_58_3 = 0) % 13.88/2.73 | | | (all_58_0 = 0 & all_58_1 = 0) | (all_58_2 = 0 & all_32_2 = 0)) % 13.88/2.73 | | % 13.88/2.73 | | ALPHA: (73) implies: % 13.88/2.73 | | (74) convergent_lines(all_23_2, all_23_2) = all_58_2 % 13.88/2.73 | | % 13.88/2.73 | | DELTA: instantiating (62) with fresh symbols all_66_0, all_66_1, all_66_2, % 13.88/2.73 | | all_66_3 gives: % 13.88/2.73 | | (75) unorthogonal_lines(all_23_2, all_23_1) = all_66_1 & % 13.88/2.73 | | unorthogonal_lines(all_23_2, all_23_2) = all_66_2 & % 13.88/2.73 | | convergent_lines(all_23_2, all_23_1) = all_66_0 & % 13.88/2.73 | | convergent_lines(all_23_2, all_23_2) = all_66_3 & ( ~ (all_66_2 = 0) % 13.88/2.73 | | | ~ (all_66_3 = 0) | all_66_0 = 0 | (all_66_1 = 0 & all_30_3 = % 13.88/2.73 | | 0)) % 13.88/2.73 | | % 13.88/2.73 | | ALPHA: (75) implies: % 13.88/2.73 | | (76) convergent_lines(all_23_2, all_23_2) = all_66_3 % 13.88/2.73 | | % 13.88/2.73 | | DELTA: instantiating (63) with fresh symbols all_70_0, all_70_1, all_70_2, % 13.88/2.73 | | all_70_3 gives: % 13.88/2.73 | | (77) unorthogonal_lines(all_23_2, all_23_1) = all_70_0 & % 13.88/2.73 | | unorthogonal_lines(all_23_2, all_23_2) = all_70_2 & % 13.88/2.73 | | convergent_lines(all_23_2, all_23_1) = all_70_1 & % 13.88/2.73 | | convergent_lines(all_23_2, all_23_2) = all_70_3 & ( ~ (all_70_2 = 0) % 13.88/2.73 | | | ~ (all_70_3 = 0) | all_70_1 = 0 | (all_70_0 = 0 & all_30_3 = % 13.88/2.73 | | 0)) % 13.88/2.73 | | % 13.88/2.73 | | ALPHA: (77) implies: % 13.88/2.73 | | (78) convergent_lines(all_23_2, all_23_2) = all_70_3 % 13.88/2.73 | | % 13.88/2.73 | | DELTA: instantiating (66) with fresh symbols all_74_0, all_74_1, all_74_2, % 13.88/2.73 | | all_74_3 gives: % 13.88/2.74 | | (79) unorthogonal_lines(all_23_2, all_23_1) = all_74_2 & % 13.88/2.74 | | convergent_lines(all_23_1, all_23_2) = all_74_0 & % 13.88/2.74 | | convergent_lines(all_23_2, all_23_1) = all_74_3 & % 13.88/2.74 | | convergent_lines(all_23_2, all_23_2) = all_74_1 & ( ~ (all_74_2 = 0) % 13.88/2.74 | | | ~ (all_74_3 = 0) | (all_74_0 = 0 & all_23_0 = 0) | (all_74_1 = % 13.88/2.74 | | 0 & all_32_2 = 0)) % 13.88/2.74 | | % 13.88/2.74 | | ALPHA: (79) implies: % 13.88/2.74 | | (80) convergent_lines(all_23_2, all_23_2) = all_74_1 % 13.88/2.74 | | % 13.88/2.74 | | DELTA: instantiating (61) with fresh symbols all_76_0, all_76_1, all_76_2, % 13.88/2.74 | | all_76_3 gives: % 13.88/2.74 | | (81) unorthogonal_lines(all_23_2, all_23_1) = all_76_0 & % 13.88/2.74 | | unorthogonal_lines(all_23_2, all_23_1) = all_76_1 & % 13.88/2.74 | | unorthogonal_lines(all_23_2, all_23_2) = all_76_2 & % 13.88/2.74 | | convergent_lines(all_23_2, all_23_2) = all_76_3 & ( ~ (all_76_2 = 0) % 13.88/2.74 | | | ~ (all_76_3 = 0) | (all_76_0 = 0 & all_30_3 = 0) | (all_76_1 = % 13.88/2.74 | | 0 & all_30_3 = 0)) % 13.88/2.74 | | % 13.88/2.74 | | ALPHA: (81) implies: % 13.88/2.74 | | (82) convergent_lines(all_23_2, all_23_2) = all_76_3 % 13.88/2.74 | | % 13.88/2.74 | | GROUND_INST: instantiating (10) with all_56_1, all_58_2, all_23_2, all_23_2, % 13.88/2.74 | | simplifying with (72), (74) gives: % 13.88/2.74 | | (83) all_58_2 = all_56_1 % 13.88/2.74 | | % 13.88/2.74 | | GROUND_INST: instantiating (10) with all_58_2, all_66_3, all_23_2, all_23_2, % 13.88/2.74 | | simplifying with (74), (76) gives: % 13.88/2.74 | | (84) all_66_3 = all_58_2 % 13.88/2.74 | | % 13.88/2.74 | | GROUND_INST: instantiating (10) with all_56_1, all_70_3, all_23_2, all_23_2, % 13.88/2.74 | | simplifying with (72), (78) gives: % 13.88/2.74 | | (85) all_70_3 = all_56_1 % 13.88/2.74 | | % 13.88/2.74 | | GROUND_INST: instantiating (10) with all_32_3, all_74_1, all_23_2, all_23_2, % 13.88/2.74 | | simplifying with (27), (80) gives: % 13.88/2.74 | | (86) all_74_1 = all_32_3 % 13.88/2.74 | | % 13.88/2.74 | | GROUND_INST: instantiating (10) with all_66_3, all_74_1, all_23_2, all_23_2, % 13.88/2.74 | | simplifying with (76), (80) gives: % 13.88/2.74 | | (87) all_74_1 = all_66_3 % 13.88/2.74 | | % 13.88/2.74 | | GROUND_INST: instantiating (10) with all_70_3, all_76_3, all_23_2, all_23_2, % 13.88/2.74 | | simplifying with (78), (82) gives: % 13.88/2.74 | | (88) all_76_3 = all_70_3 % 13.88/2.74 | | % 13.88/2.74 | | GROUND_INST: instantiating (10) with all_52_2, all_76_3, all_23_2, all_23_2, % 13.88/2.74 | | simplifying with (70), (82) gives: % 13.88/2.74 | | (89) all_76_3 = all_52_2 % 13.88/2.74 | | % 13.88/2.74 | | COMBINE_EQS: (88), (89) imply: % 13.88/2.74 | | (90) all_70_3 = all_52_2 % 13.88/2.74 | | % 13.88/2.74 | | SIMP: (90) implies: % 13.88/2.74 | | (91) all_70_3 = all_52_2 % 13.88/2.74 | | % 13.88/2.74 | | COMBINE_EQS: (86), (87) imply: % 13.88/2.74 | | (92) all_66_3 = all_32_3 % 13.88/2.74 | | % 13.88/2.74 | | SIMP: (92) implies: % 13.88/2.74 | | (93) all_66_3 = all_32_3 % 13.88/2.74 | | % 13.88/2.74 | | COMBINE_EQS: (85), (91) imply: % 13.88/2.74 | | (94) all_56_1 = all_52_2 % 13.88/2.74 | | % 13.88/2.74 | | SIMP: (94) implies: % 13.88/2.74 | | (95) all_56_1 = all_52_2 % 13.88/2.74 | | % 13.88/2.74 | | COMBINE_EQS: (84), (93) imply: % 13.88/2.74 | | (96) all_58_2 = all_32_3 % 13.88/2.74 | | % 13.88/2.74 | | SIMP: (96) implies: % 13.88/2.74 | | (97) all_58_2 = all_32_3 % 13.88/2.74 | | % 13.88/2.74 | | COMBINE_EQS: (83), (97) imply: % 13.88/2.74 | | (98) all_56_1 = all_32_3 % 13.88/2.74 | | % 13.88/2.74 | | SIMP: (98) implies: % 13.88/2.74 | | (99) all_56_1 = all_32_3 % 13.88/2.74 | | % 13.88/2.74 | | COMBINE_EQS: (95), (99) imply: % 13.88/2.74 | | (100) all_52_2 = all_32_3 % 13.88/2.74 | | % 13.88/2.74 | | SIMP: (100) implies: % 13.88/2.74 | | (101) all_52_2 = all_32_3 % 13.88/2.74 | | % 13.88/2.74 | | BETA: splitting (36) gives: % 13.88/2.74 | | % 13.88/2.74 | | Case 1: % 13.88/2.74 | | | % 13.88/2.75 | | | (102) ~ (all_34_3 = 0) % 13.88/2.75 | | | % 13.88/2.75 | | | REDUCE: (60), (102) imply: % 13.88/2.75 | | | (103) ~ (all_30_3 = 0) % 13.88/2.75 | | | % 13.88/2.75 | | | BETA: splitting (65) gives: % 13.88/2.75 | | | % 13.88/2.75 | | | Case 1: % 13.88/2.75 | | | | % 13.88/2.75 | | | | (104) convergent_lines(all_23_1, all_23_1) = 0 % 13.88/2.75 | | | | % 13.88/2.75 | | | | GROUND_INST: instantiating (apart3) with all_23_1, simplifying with % 13.88/2.75 | | | | (15), (104) gives: % 13.88/2.75 | | | | (105) $false % 13.88/2.75 | | | | % 13.88/2.75 | | | | CLOSE: (105) is inconsistent. % 13.88/2.75 | | | | % 13.88/2.75 | | | Case 2: % 13.88/2.75 | | | | % 13.88/2.75 | | | | (106) all_30_3 = 0 % 13.88/2.75 | | | | % 13.88/2.75 | | | | REDUCE: (103), (106) imply: % 13.88/2.75 | | | | (107) $false % 13.88/2.75 | | | | % 13.88/2.75 | | | | CLOSE: (107) is inconsistent. % 13.88/2.75 | | | | % 13.88/2.75 | | | End of split % 13.88/2.75 | | | % 13.88/2.75 | | Case 2: % 13.88/2.75 | | | % 13.88/2.75 | | | (108) (all_34_0 = 0 & all_23_0 = 0) | (all_34_1 = 0 & all_34_2 = 0) % 13.88/2.75 | | | % 13.88/2.75 | | | BETA: splitting (108) gives: % 13.88/2.75 | | | % 13.88/2.75 | | | Case 1: % 13.88/2.75 | | | | % 13.88/2.75 | | | | (109) all_34_0 = 0 & all_23_0 = 0 % 13.88/2.75 | | | | % 13.88/2.75 | | | | ALPHA: (109) implies: % 13.88/2.75 | | | | (110) all_23_0 = 0 % 13.88/2.75 | | | | % 13.88/2.75 | | | | REDUCE: (13), (110) imply: % 13.88/2.75 | | | | (111) $false % 13.88/2.75 | | | | % 13.88/2.75 | | | | CLOSE: (111) is inconsistent. % 13.88/2.75 | | | | % 13.88/2.75 | | | Case 2: % 13.88/2.75 | | | | % 13.88/2.75 | | | | (112) all_34_1 = 0 & all_34_2 = 0 % 13.88/2.75 | | | | % 13.88/2.75 | | | | ALPHA: (112) implies: % 13.88/2.75 | | | | (113) all_34_2 = 0 % 13.88/2.75 | | | | % 13.88/2.75 | | | | COMBINE_EQS: (41), (113) imply: % 13.88/2.75 | | | | (114) all_32_3 = 0 % 13.88/2.75 | | | | % 13.88/2.75 | | | | SIMP: (114) implies: % 13.88/2.75 | | | | (115) all_32_3 = 0 % 13.88/2.75 | | | | % 13.88/2.75 | | | | REDUCE: (27), (115) imply: % 13.88/2.75 | | | | (116) convergent_lines(all_23_2, all_23_2) = 0 % 13.88/2.75 | | | | % 13.88/2.75 | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying with % 13.88/2.75 | | | | (14), (116) gives: % 13.88/2.75 | | | | (117) $false % 13.88/2.75 | | | | % 13.88/2.75 | | | | CLOSE: (117) is inconsistent. % 13.88/2.75 | | | | % 13.88/2.75 | | | End of split % 13.88/2.75 | | | % 13.88/2.75 | | End of split % 13.88/2.75 | | % 13.88/2.75 | Case 2: % 13.88/2.75 | | % 13.88/2.75 | | (118) all_23_0 = 0 % 13.88/2.75 | | % 13.88/2.75 | | REDUCE: (13), (118) imply: % 13.88/2.75 | | (119) $false % 13.88/2.75 | | % 13.88/2.75 | | CLOSE: (119) is inconsistent. % 13.88/2.75 | | % 13.88/2.75 | End of split % 13.88/2.75 | % 13.88/2.75 End of proof % 13.88/2.75 % SZS output end Proof for theBenchmark % 13.88/2.75 % 13.88/2.75 2084ms %------------------------------------------------------------------------------