%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO219+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n026.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:22:28 EDT 2023 % Result : Theorem 9.33s 2.02s % Output : Proof 12.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : GEO219+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n026.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 21:38:35 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.51/1.09 Prover 1: Preprocessing ... % 2.51/1.10 Prover 4: Preprocessing ... % 3.01/1.13 Prover 0: Preprocessing ... % 3.01/1.13 Prover 3: Preprocessing ... % 3.01/1.13 Prover 2: Preprocessing ... % 3.01/1.13 Prover 5: Preprocessing ... % 3.01/1.13 Prover 6: Preprocessing ... % 4.62/1.35 Prover 5: Proving ... % 4.62/1.36 Prover 2: Proving ... % 4.62/1.42 Prover 1: Constructing countermodel ... % 4.62/1.42 Prover 6: Constructing countermodel ... % 4.62/1.43 Prover 3: Constructing countermodel ... % 5.67/1.64 Prover 4: Constructing countermodel ... % 5.67/1.64 Prover 0: Proving ... % 6.83/1.68 Prover 3: gave up % 6.83/1.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.98/1.69 Prover 6: gave up % 6.98/1.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.27/1.73 Prover 8: Preprocessing ... % 7.27/1.74 Prover 7: Preprocessing ... % 7.27/1.77 Prover 1: gave up % 7.27/1.78 Prover 7: Warning: ignoring some quantifiers % 7.27/1.78 Prover 7: Constructing countermodel ... % 7.27/1.79 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 7.87/1.82 Prover 8: Warning: ignoring some quantifiers % 7.87/1.83 Prover 7: gave up % 7.87/1.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.87/1.84 Prover 8: Constructing countermodel ... % 7.87/1.85 Prover 9: Preprocessing ... % 8.38/1.88 Prover 10: Preprocessing ... % 8.38/1.92 Prover 10: Warning: ignoring some quantifiers % 8.38/1.94 Prover 10: Constructing countermodel ... % 9.04/1.97 Prover 10: gave up % 9.14/1.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.14/2.01 Prover 11: Preprocessing ... % 9.14/2.01 Prover 8: gave up % 9.33/2.02 Prover 0: proved (1376ms) % 9.33/2.02 % 9.33/2.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.33/2.02 % 9.33/2.03 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 9.33/2.03 Prover 5: stopped % 9.41/2.03 Prover 2: stopped % 9.41/2.04 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.41/2.04 Prover 12: Preprocessing ... % 9.41/2.04 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 9.41/2.04 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.41/2.05 Prover 13: Preprocessing ... % 9.41/2.06 Prover 19: Preprocessing ... % 9.41/2.06 Prover 16: Preprocessing ... % 9.41/2.07 Prover 12: stopped % 9.41/2.09 Prover 16: Warning: ignoring some quantifiers % 9.41/2.09 Prover 13: Warning: ignoring some quantifiers % 9.41/2.09 Prover 16: Constructing countermodel ... % 9.41/2.09 Prover 13: Constructing countermodel ... % 9.41/2.12 Prover 9: Constructing countermodel ... % 9.41/2.12 Prover 16: gave up % 9.41/2.13 Prover 13: gave up % 9.41/2.13 Prover 9: stopped % 9.41/2.14 Prover 19: Warning: ignoring some quantifiers % 9.41/2.14 Prover 19: Constructing countermodel ... % 9.41/2.19 Prover 11: Constructing countermodel ... % 10.20/2.23 Prover 19: gave up % 11.95/2.41 Prover 11: Found proof (size 69) % 11.95/2.41 Prover 11: proved (424ms) % 11.95/2.41 Prover 4: stopped % 11.95/2.41 % 11.95/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.95/2.41 % 11.95/2.42 % SZS output start Proof for theBenchmark % 11.95/2.43 Assumptions after simplification: % 11.95/2.43 --------------------------------- % 11.95/2.43 % 11.95/2.43 (apart6) % 11.95/2.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 11.95/2.45 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 11.95/2.45 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 11.95/2.45 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 11.95/2.45 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ % 11.95/2.45 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 11.95/2.45 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 11.95/2.45 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 11.95/2.45 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 11.95/2.45 convergent_lines(v1, v2) = 0) % 11.95/2.45 % 11.95/2.45 (coipo1) % 11.95/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 11.95/2.46 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 11.95/2.46 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 11.95/2.46 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 11.95/2.46 unorthogonal_lines(v0, v1) = 0) % 11.95/2.46 % 11.95/2.46 (con) % 11.95/2.46 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( ~ % 11.95/2.46 (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v1, v2) = 0 & % 11.95/2.46 unorthogonal_lines(v0, v1) = v3 & convergent_lines(v0, v2) = v4 & $i(v2) & % 11.95/2.46 $i(v1) & $i(v0)) % 11.95/2.46 % 11.95/2.46 (cotno1) % 11.95/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 11.95/2.49 (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | % 11.95/2.49 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 11.95/2.49 int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | % 11.95/2.49 (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 11.95/2.49 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, % 11.95/2.49 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 11.95/2.49 ! [v4: any] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 11.95/2.49 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 11.95/2.49 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 11.95/2.49 convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 11.95/2.49 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1, % 11.95/2.49 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: % 11.95/2.49 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 11.95/2.49 (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ~ % 11.95/2.49 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 11.95/2.49 : ? [v8: int] : ((v6 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = % 11.95/2.49 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 11.95/2.49 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, % 11.95/2.49 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 11.95/2.49 ! [v4: any] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, % 11.95/2.49 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 11.95/2.49 int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 11.95/2.49 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 11.95/2.49 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1, % 11.95/2.49 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: % 11.95/2.49 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, % 11.95/2.49 v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 11.95/2.49 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 11.95/2.49 ((v6 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 11.95/2.49 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 11.95/2.49 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : % 11.95/2.49 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 11.95/2.49 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 11.95/2.49 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 11.95/2.49 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 11.95/2.49 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 11.95/2.49 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 11.95/2.49 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 11.95/2.49 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 11.95/2.49 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 11.95/2.49 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 11.95/2.49 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 11.95/2.49 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : % 11.95/2.49 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 11.95/2.49 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 11.95/2.49 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 11.95/2.49 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 11.95/2.49 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 11.95/2.49 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 11.95/2.49 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 11.95/2.49 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 11.95/2.49 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 11.95/2.49 convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 11.95/2.49 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 11.95/2.49 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] % 11.95/2.49 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ % 11.95/2.49 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 11.95/2.49 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 11.95/2.49 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 11.95/2.49 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 11.95/2.49 unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 11.95/2.49 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 11.95/2.49 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 11.95/2.49 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 11.95/2.49 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 11.95/2.49 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 11.95/2.49 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] % 11.95/2.49 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 11.95/2.49 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 11.95/2.49 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 11.95/2.49 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 11.95/2.49 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 11.95/2.49 unorthogonal_lines(v1, v2) = v7))) % 11.95/2.49 % 11.95/2.49 (function-axioms) % 11.95/2.50 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 11.95/2.50 [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 11.95/2.50 (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 11.95/2.50 : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 11.95/2.50 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 11.95/2.50 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 11.95/2.50 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.95/2.50 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.95/2.50 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 11.95/2.50 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.95/2.50 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 11.95/2.50 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.95/2.50 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.95/2.50 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 11.95/2.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.95/2.50 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 11.95/2.50 v0)) % 11.95/2.50 % 11.95/2.50 Further assumptions not needed in the proof: % 11.95/2.50 -------------------------------------------- % 11.95/2.50 apart1, apart2, apart3, apart4, apart5, ceq1, ceq2, ceq3, con1, con2, couo1, cu1 % 11.95/2.50 % 11.95/2.50 Those formulas are unsatisfiable: % 11.95/2.50 --------------------------------- % 11.95/2.50 % 11.95/2.50 Begin of proof % 11.95/2.50 | % 11.95/2.50 | ALPHA: (apart6) implies: % 11.95/2.50 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 11.95/2.50 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 11.95/2.50 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0) % 11.95/2.50 | % 11.95/2.50 | ALPHA: (coipo1) implies: % 11.95/2.50 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 11.95/2.50 | (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 11.95/2.50 | convergent_lines(v0, v1) = 0) % 11.95/2.50 | % 11.95/2.50 | ALPHA: (cotno1) implies: % 11.95/2.50 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 11.95/2.50 | (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) % 11.95/2.50 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : % 11.95/2.50 | ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 11.95/2.50 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 11.95/2.50 | unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | % 11.95/2.50 | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) % 12.42/2.51 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 12.42/2.51 | (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = % 12.42/2.51 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 12.42/2.51 | int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 12.42/2.51 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | % 12.42/2.51 | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 12.42/2.51 | convergent_lines(v1, v2) = v7))) % 12.42/2.51 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 12.42/2.51 | ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = % 12.42/2.51 | v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 12.42/2.51 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 12.42/2.51 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 12.42/2.51 | convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 12.42/2.51 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 12.42/2.51 | convergent_lines(v1, v2) = v7))) % 12.42/2.51 | % 12.42/2.51 | ALPHA: (function-axioms) implies: % 12.42/2.51 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.42/2.51 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 12.42/2.51 | (convergent_lines(v3, v2) = v0)) % 12.42/2.51 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.42/2.51 | ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 12.42/2.51 | (unorthogonal_lines(v3, v2) = v0)) % 12.42/2.51 | % 12.42/2.51 | DELTA: instantiating (con) with fresh symbols all_18_0, all_18_1, all_18_2, % 12.42/2.51 | all_18_3, all_18_4 gives: % 12.42/2.51 | (8) ~ (all_18_0 = 0) & ~ (all_18_1 = 0) & unorthogonal_lines(all_18_3, % 12.42/2.51 | all_18_2) = 0 & unorthogonal_lines(all_18_4, all_18_3) = all_18_1 & % 12.42/2.51 | convergent_lines(all_18_4, all_18_2) = all_18_0 & $i(all_18_2) & % 12.42/2.51 | $i(all_18_3) & $i(all_18_4) % 12.42/2.51 | % 12.42/2.51 | ALPHA: (8) implies: % 12.42/2.51 | (9) ~ (all_18_1 = 0) % 12.42/2.51 | (10) ~ (all_18_0 = 0) % 12.42/2.51 | (11) $i(all_18_4) % 12.42/2.51 | (12) $i(all_18_3) % 12.42/2.51 | (13) $i(all_18_2) % 12.42/2.51 | (14) convergent_lines(all_18_4, all_18_2) = all_18_0 % 12.42/2.51 | (15) unorthogonal_lines(all_18_4, all_18_3) = all_18_1 % 12.42/2.51 | (16) unorthogonal_lines(all_18_3, all_18_2) = 0 % 12.42/2.51 | % 12.42/2.51 | GROUND_INST: instantiating (5) with all_18_4, all_18_3, all_18_2, all_18_1, % 12.42/2.51 | all_18_0, simplifying with (11), (12), (13), (14), (15) gives: % 12.42/2.52 | (17) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0 & % 12.42/2.52 | all_18_0 = 0 & unorthogonal_lines(all_18_4, all_18_2) = 0) | (v0 = % 12.42/2.52 | 0 & all_18_1 = 0 & convergent_lines(all_18_4, all_18_3) = 0) | ( ~ % 12.42/2.52 | (v3 = 0) & unorthogonal_lines(all_18_3, all_18_2) = v3) | ( ~ (v2 % 12.42/2.52 | = 0) & convergent_lines(all_18_3, all_18_2) = v2)) % 12.42/2.52 | % 12.42/2.52 | GROUND_INST: instantiating (2) with all_18_4, all_18_3, all_18_1, simplifying % 12.42/2.52 | with (11), (12), (15) gives: % 12.42/2.52 | (18) all_18_1 = 0 | convergent_lines(all_18_4, all_18_3) = 0 % 12.42/2.52 | % 12.42/2.52 | GROUND_INST: instantiating (4) with all_18_4, all_18_3, all_18_2, all_18_1, % 12.42/2.52 | simplifying with (11), (12), (13), (15), (16) gives: % 12.42/2.52 | (19) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 & % 12.42/2.52 | v1 = 0 & unorthogonal_lines(all_18_4, all_18_2) = 0 & % 12.42/2.52 | convergent_lines(all_18_4, all_18_2) = 0) | (v0 = 0 & all_18_1 = 0 % 12.42/2.52 | & convergent_lines(all_18_4, all_18_3) = 0) | ( ~ (v3 = 0) & % 12.42/2.52 | convergent_lines(all_18_3, all_18_2) = v3)) % 12.42/2.52 | % 12.42/2.52 | GROUND_INST: instantiating (3) with all_18_4, all_18_3, all_18_2, all_18_0, % 12.42/2.52 | simplifying with (11), (12), (13), (14), (16) gives: % 12.42/2.52 | (20) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 & % 12.42/2.52 | all_18_0 = 0 & unorthogonal_lines(all_18_4, all_18_2) = 0) | (v1 = % 12.42/2.52 | 0 & v0 = 0 & unorthogonal_lines(all_18_4, all_18_3) = 0 & % 12.42/2.52 | convergent_lines(all_18_4, all_18_3) = 0) | ( ~ (v3 = 0) & % 12.42/2.52 | convergent_lines(all_18_3, all_18_2) = v3)) % 12.42/2.52 | % 12.42/2.52 | DELTA: instantiating (20) with fresh symbols all_27_0, all_27_1, all_27_2, % 12.42/2.52 | all_27_3 gives: % 12.42/2.52 | (21) (all_27_1 = 0 & all_18_0 = 0 & unorthogonal_lines(all_18_4, all_18_2) % 12.42/2.52 | = 0) | (all_27_2 = 0 & all_27_3 = 0 & unorthogonal_lines(all_18_4, % 12.42/2.52 | all_18_3) = 0 & convergent_lines(all_18_4, all_18_3) = 0) | ( ~ % 12.42/2.52 | (all_27_0 = 0) & convergent_lines(all_18_3, all_18_2) = all_27_0) % 12.42/2.52 | % 12.42/2.52 | DELTA: instantiating (19) with fresh symbols all_28_0, all_28_1, all_28_2, % 12.42/2.52 | all_28_3 gives: % 12.42/2.52 | (22) (all_28_1 = 0 & all_28_2 = 0 & unorthogonal_lines(all_18_4, all_18_2) % 12.42/2.52 | = 0 & convergent_lines(all_18_4, all_18_2) = 0) | (all_28_3 = 0 & % 12.42/2.52 | all_18_1 = 0 & convergent_lines(all_18_4, all_18_3) = 0) | ( ~ % 12.42/2.52 | (all_28_0 = 0) & convergent_lines(all_18_3, all_18_2) = all_28_0) % 12.42/2.52 | % 12.42/2.52 | DELTA: instantiating (17) with fresh symbols all_29_0, all_29_1, all_29_2, % 12.42/2.52 | all_29_3 gives: % 12.42/2.52 | (23) (all_29_2 = 0 & all_18_0 = 0 & unorthogonal_lines(all_18_4, all_18_2) % 12.42/2.52 | = 0) | (all_29_3 = 0 & all_18_1 = 0 & convergent_lines(all_18_4, % 12.42/2.52 | all_18_3) = 0) | ( ~ (all_29_0 = 0) & unorthogonal_lines(all_18_3, % 12.42/2.52 | all_18_2) = all_29_0) | ( ~ (all_29_1 = 0) & % 12.42/2.52 | convergent_lines(all_18_3, all_18_2) = all_29_1) % 12.42/2.52 | % 12.42/2.52 | BETA: splitting (18) gives: % 12.42/2.52 | % 12.42/2.52 | Case 1: % 12.42/2.52 | | % 12.42/2.52 | | (24) convergent_lines(all_18_4, all_18_3) = 0 % 12.42/2.52 | | % 12.42/2.52 | | BETA: splitting (21) gives: % 12.42/2.52 | | % 12.42/2.52 | | Case 1: % 12.42/2.52 | | | % 12.42/2.52 | | | (25) all_27_1 = 0 & all_18_0 = 0 & unorthogonal_lines(all_18_4, % 12.42/2.52 | | | all_18_2) = 0 % 12.42/2.52 | | | % 12.42/2.52 | | | ALPHA: (25) implies: % 12.42/2.52 | | | (26) all_18_0 = 0 % 12.42/2.52 | | | % 12.42/2.52 | | | REDUCE: (10), (26) imply: % 12.42/2.52 | | | (27) $false % 12.42/2.52 | | | % 12.42/2.52 | | | CLOSE: (27) is inconsistent. % 12.42/2.52 | | | % 12.42/2.52 | | Case 2: % 12.42/2.52 | | | % 12.42/2.53 | | | (28) (all_27_2 = 0 & all_27_3 = 0 & unorthogonal_lines(all_18_4, % 12.42/2.53 | | | all_18_3) = 0 & convergent_lines(all_18_4, all_18_3) = 0) | ( % 12.42/2.53 | | | ~ (all_27_0 = 0) & convergent_lines(all_18_3, all_18_2) = % 12.42/2.53 | | | all_27_0) % 12.42/2.53 | | | % 12.42/2.53 | | | BETA: splitting (28) gives: % 12.42/2.53 | | | % 12.42/2.53 | | | Case 1: % 12.42/2.53 | | | | % 12.42/2.53 | | | | (29) all_27_2 = 0 & all_27_3 = 0 & unorthogonal_lines(all_18_4, % 12.42/2.53 | | | | all_18_3) = 0 & convergent_lines(all_18_4, all_18_3) = 0 % 12.42/2.53 | | | | % 12.42/2.53 | | | | ALPHA: (29) implies: % 12.42/2.53 | | | | (30) unorthogonal_lines(all_18_4, all_18_3) = 0 % 12.42/2.53 | | | | % 12.42/2.53 | | | | GROUND_INST: instantiating (7) with all_18_1, 0, all_18_3, all_18_4, % 12.42/2.53 | | | | simplifying with (15), (30) gives: % 12.42/2.53 | | | | (31) all_18_1 = 0 % 12.42/2.53 | | | | % 12.42/2.53 | | | | REDUCE: (9), (31) imply: % 12.42/2.53 | | | | (32) $false % 12.42/2.53 | | | | % 12.42/2.53 | | | | CLOSE: (32) is inconsistent. % 12.42/2.53 | | | | % 12.42/2.53 | | | Case 2: % 12.42/2.53 | | | | % 12.42/2.53 | | | | (33) ~ (all_27_0 = 0) & convergent_lines(all_18_3, all_18_2) = % 12.42/2.53 | | | | all_27_0 % 12.42/2.53 | | | | % 12.42/2.53 | | | | ALPHA: (33) implies: % 12.42/2.53 | | | | (34) ~ (all_27_0 = 0) % 12.42/2.53 | | | | (35) convergent_lines(all_18_3, all_18_2) = all_27_0 % 12.42/2.53 | | | | % 12.42/2.53 | | | | BETA: splitting (23) gives: % 12.42/2.53 | | | | % 12.42/2.53 | | | | Case 1: % 12.42/2.53 | | | | | % 12.42/2.53 | | | | | (36) (all_29_2 = 0 & all_18_0 = 0 & unorthogonal_lines(all_18_4, % 12.42/2.53 | | | | | all_18_2) = 0) | (all_29_3 = 0 & all_18_1 = 0 & % 12.42/2.53 | | | | | convergent_lines(all_18_4, all_18_3) = 0) % 12.42/2.53 | | | | | % 12.42/2.53 | | | | | BETA: splitting (36) gives: % 12.42/2.53 | | | | | % 12.42/2.53 | | | | | Case 1: % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | (37) all_29_2 = 0 & all_18_0 = 0 & unorthogonal_lines(all_18_4, % 12.42/2.53 | | | | | | all_18_2) = 0 % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | ALPHA: (37) implies: % 12.42/2.53 | | | | | | (38) all_18_0 = 0 % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | REDUCE: (10), (38) imply: % 12.42/2.53 | | | | | | (39) $false % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | CLOSE: (39) is inconsistent. % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | Case 2: % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | (40) all_29_3 = 0 & all_18_1 = 0 & convergent_lines(all_18_4, % 12.42/2.53 | | | | | | all_18_3) = 0 % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | ALPHA: (40) implies: % 12.42/2.53 | | | | | | (41) all_18_1 = 0 % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | REDUCE: (9), (41) imply: % 12.42/2.53 | | | | | | (42) $false % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | CLOSE: (42) is inconsistent. % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | End of split % 12.42/2.53 | | | | | % 12.42/2.53 | | | | Case 2: % 12.42/2.53 | | | | | % 12.42/2.53 | | | | | (43) ( ~ (all_29_0 = 0) & unorthogonal_lines(all_18_3, all_18_2) = % 12.42/2.53 | | | | | all_29_0) | ( ~ (all_29_1 = 0) & convergent_lines(all_18_3, % 12.42/2.53 | | | | | all_18_2) = all_29_1) % 12.42/2.53 | | | | | % 12.42/2.53 | | | | | BETA: splitting (43) gives: % 12.42/2.53 | | | | | % 12.42/2.53 | | | | | Case 1: % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | (44) ~ (all_29_0 = 0) & unorthogonal_lines(all_18_3, all_18_2) = % 12.42/2.53 | | | | | | all_29_0 % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | ALPHA: (44) implies: % 12.42/2.53 | | | | | | (45) ~ (all_29_0 = 0) % 12.42/2.53 | | | | | | (46) unorthogonal_lines(all_18_3, all_18_2) = all_29_0 % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | GROUND_INST: instantiating (7) with 0, all_29_0, all_18_2, all_18_3, % 12.42/2.53 | | | | | | simplifying with (16), (46) gives: % 12.42/2.53 | | | | | | (47) all_29_0 = 0 % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | REDUCE: (45), (47) imply: % 12.42/2.53 | | | | | | (48) $false % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | CLOSE: (48) is inconsistent. % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | Case 2: % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | (49) ~ (all_29_1 = 0) & convergent_lines(all_18_3, all_18_2) = % 12.42/2.53 | | | | | | all_29_1 % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | ALPHA: (49) implies: % 12.42/2.53 | | | | | | (50) convergent_lines(all_18_3, all_18_2) = all_29_1 % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | BETA: splitting (22) gives: % 12.42/2.53 | | | | | | % 12.42/2.53 | | | | | | Case 1: % 12.42/2.53 | | | | | | | % 12.42/2.53 | | | | | | | (51) all_28_1 = 0 & all_28_2 = 0 & unorthogonal_lines(all_18_4, % 12.42/2.53 | | | | | | | all_18_2) = 0 & convergent_lines(all_18_4, all_18_2) = 0 % 12.42/2.53 | | | | | | | % 12.42/2.53 | | | | | | | ALPHA: (51) implies: % 12.42/2.53 | | | | | | | (52) convergent_lines(all_18_4, all_18_2) = 0 % 12.42/2.53 | | | | | | | % 12.42/2.53 | | | | | | | GROUND_INST: instantiating (6) with all_18_0, 0, all_18_2, % 12.42/2.53 | | | | | | | all_18_4, simplifying with (14), (52) gives: % 12.42/2.53 | | | | | | | (53) all_18_0 = 0 % 12.42/2.53 | | | | | | | % 12.42/2.53 | | | | | | | REDUCE: (10), (53) imply: % 12.42/2.54 | | | | | | | (54) $false % 12.42/2.54 | | | | | | | % 12.42/2.54 | | | | | | | CLOSE: (54) is inconsistent. % 12.42/2.54 | | | | | | | % 12.42/2.54 | | | | | | Case 2: % 12.42/2.54 | | | | | | | % 12.42/2.54 | | | | | | | (55) (all_28_3 = 0 & all_18_1 = 0 & convergent_lines(all_18_4, % 12.42/2.54 | | | | | | | all_18_3) = 0) | ( ~ (all_28_0 = 0) & % 12.42/2.54 | | | | | | | convergent_lines(all_18_3, all_18_2) = all_28_0) % 12.42/2.54 | | | | | | | % 12.42/2.54 | | | | | | | BETA: splitting (55) gives: % 12.42/2.54 | | | | | | | % 12.42/2.54 | | | | | | | Case 1: % 12.42/2.54 | | | | | | | | % 12.42/2.54 | | | | | | | | (56) all_28_3 = 0 & all_18_1 = 0 & convergent_lines(all_18_4, % 12.42/2.54 | | | | | | | | all_18_3) = 0 % 12.42/2.54 | | | | | | | | % 12.42/2.54 | | | | | | | | ALPHA: (56) implies: % 12.42/2.54 | | | | | | | | (57) all_18_1 = 0 % 12.42/2.54 | | | | | | | | % 12.42/2.54 | | | | | | | | REDUCE: (9), (57) imply: % 12.42/2.54 | | | | | | | | (58) $false % 12.42/2.54 | | | | | | | | % 12.42/2.54 | | | | | | | | CLOSE: (58) is inconsistent. % 12.42/2.54 | | | | | | | | % 12.42/2.54 | | | | | | | Case 2: % 12.42/2.54 | | | | | | | | % 12.42/2.54 | | | | | | | | (59) ~ (all_28_0 = 0) & convergent_lines(all_18_3, all_18_2) % 12.42/2.54 | | | | | | | | = all_28_0 % 12.42/2.54 | | | | | | | | % 12.42/2.54 | | | | | | | | ALPHA: (59) implies: % 12.42/2.54 | | | | | | | | (60) convergent_lines(all_18_3, all_18_2) = all_28_0 % 12.42/2.54 | | | | | | | | % 12.42/2.54 | | | | | | | | GROUND_INST: instantiating (1) with all_18_4, all_18_3, % 12.42/2.54 | | | | | | | | all_18_2, all_18_0, simplifying with (11), (12), % 12.42/2.54 | | | | | | | | (13), (14), (24) gives: % 12.42/2.54 | | | | | | | | (61) all_18_0 = 0 | convergent_lines(all_18_3, all_18_2) = 0 % 12.42/2.54 | | | | | | | | % 12.42/2.54 | | | | | | | | BETA: splitting (61) gives: % 12.42/2.54 | | | | | | | | % 12.42/2.54 | | | | | | | | Case 1: % 12.42/2.54 | | | | | | | | | % 12.42/2.54 | | | | | | | | | (62) convergent_lines(all_18_3, all_18_2) = 0 % 12.42/2.54 | | | | | | | | | % 12.42/2.54 | | | | | | | | | GROUND_INST: instantiating (6) with all_27_0, all_28_0, % 12.42/2.54 | | | | | | | | | all_18_2, all_18_3, simplifying with (35), (60) % 12.42/2.54 | | | | | | | | | gives: % 12.42/2.54 | | | | | | | | | (63) all_28_0 = all_27_0 % 12.42/2.54 | | | | | | | | | % 12.42/2.54 | | | | | | | | | GROUND_INST: instantiating (6) with all_28_0, all_29_1, % 12.42/2.54 | | | | | | | | | all_18_2, all_18_3, simplifying with (50), (60) % 12.42/2.54 | | | | | | | | | gives: % 12.42/2.54 | | | | | | | | | (64) all_29_1 = all_28_0 % 12.42/2.54 | | | | | | | | | % 12.42/2.54 | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_29_1, all_18_2, % 12.42/2.54 | | | | | | | | | all_18_3, simplifying with (50), (62) gives: % 12.42/2.54 | | | | | | | | | (65) all_29_1 = 0 % 12.42/2.54 | | | | | | | | | % 12.42/2.54 | | | | | | | | | COMBINE_EQS: (64), (65) imply: % 12.42/2.54 | | | | | | | | | (66) all_28_0 = 0 % 12.42/2.54 | | | | | | | | | % 12.42/2.54 | | | | | | | | | SIMP: (66) implies: % 12.42/2.54 | | | | | | | | | (67) all_28_0 = 0 % 12.42/2.54 | | | | | | | | | % 12.42/2.54 | | | | | | | | | COMBINE_EQS: (63), (67) imply: % 12.42/2.54 | | | | | | | | | (68) all_27_0 = 0 % 12.42/2.54 | | | | | | | | | % 12.42/2.54 | | | | | | | | | REDUCE: (34), (68) imply: % 12.42/2.54 | | | | | | | | | (69) $false % 12.42/2.54 | | | | | | | | | % 12.42/2.54 | | | | | | | | | CLOSE: (69) is inconsistent. % 12.42/2.54 | | | | | | | | | % 12.42/2.54 | | | | | | | | Case 2: % 12.42/2.54 | | | | | | | | | % 12.42/2.54 | | | | | | | | | (70) all_18_0 = 0 % 12.42/2.54 | | | | | | | | | % 12.42/2.54 | | | | | | | | | REDUCE: (10), (70) imply: % 12.42/2.54 | | | | | | | | | (71) $false % 12.42/2.54 | | | | | | | | | % 12.42/2.54 | | | | | | | | | CLOSE: (71) is inconsistent. % 12.42/2.54 | | | | | | | | | % 12.42/2.54 | | | | | | | | End of split % 12.42/2.54 | | | | | | | | % 12.42/2.54 | | | | | | | End of split % 12.42/2.54 | | | | | | | % 12.42/2.54 | | | | | | End of split % 12.42/2.54 | | | | | | % 12.42/2.54 | | | | | End of split % 12.42/2.54 | | | | | % 12.42/2.54 | | | | End of split % 12.42/2.54 | | | | % 12.42/2.54 | | | End of split % 12.42/2.54 | | | % 12.42/2.54 | | End of split % 12.42/2.54 | | % 12.42/2.54 | Case 2: % 12.42/2.54 | | % 12.42/2.54 | | (72) all_18_1 = 0 % 12.42/2.54 | | % 12.42/2.54 | | REDUCE: (9), (72) imply: % 12.42/2.54 | | (73) $false % 12.42/2.54 | | % 12.42/2.54 | | CLOSE: (73) is inconsistent. % 12.42/2.54 | | % 12.42/2.54 | End of split % 12.42/2.54 | % 12.42/2.54 End of proof % 12.42/2.54 % SZS output end Proof for theBenchmark % 12.42/2.54 % 12.42/2.54 1920ms %------------------------------------------------------------------------------