%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO504+1 : TPTP v8.1.2. Released v7.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n006.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 23:23:31 EDT 2023 % Result : Theorem 49.10s 7.13s % Output : Proof 93.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO504+1 : TPTP v8.1.2. Released v7.0.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n006.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Tue Aug 29 22:04:21 EDT 2023 % 0.13/0.33 % CPUTime : % 0.18/0.60 ________ _____ % 0.18/0.60 ___ __ \_________(_)________________________________ % 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.60 % 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.60 (2023-06-19) % 0.18/0.60 % 0.18/0.60 (c) Philipp Rümmer, 2009-2023 % 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.60 Amanda Stjerna. % 0.18/0.60 Free software under BSD-3-Clause. % 0.18/0.60 % 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.60 % 0.18/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.61 Running up to 7 provers in parallel. % 0.18/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 7.26/1.66 Prover 1: Preprocessing ... % 7.26/1.66 Prover 4: Preprocessing ... % 7.26/1.69 Prover 3: Preprocessing ... % 7.26/1.69 Prover 2: Preprocessing ... % 7.26/1.69 Prover 5: Preprocessing ... % 7.26/1.69 Prover 0: Preprocessing ... % 7.26/1.69 Prover 6: Preprocessing ... % 15.45/2.76 Prover 5: Proving ... % 15.45/2.81 Prover 2: Proving ... % 16.11/2.86 Prover 1: Warning: ignoring some quantifiers % 16.11/2.88 Prover 3: Warning: ignoring some quantifiers % 16.52/2.93 Prover 1: Constructing countermodel ... % 16.52/2.93 Prover 3: Constructing countermodel ... % 17.15/2.99 Prover 6: Proving ... % 17.68/3.08 Prover 3: gave up % 17.68/3.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.68/3.09 Prover 6: gave up % 17.68/3.09 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 18.78/3.21 Prover 4: Constructing countermodel ... % 18.78/3.23 Prover 1: gave up % 18.78/3.23 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 20.14/3.37 Prover 0: Proving ... % 20.14/3.42 Prover 7: Preprocessing ... % 21.05/3.52 Prover 8: Preprocessing ... % 21.05/3.53 Prover 9: Preprocessing ... % 22.45/3.68 Prover 7: Warning: ignoring some quantifiers % 22.45/3.74 Prover 7: Constructing countermodel ... % 23.67/3.88 Prover 8: Warning: ignoring some quantifiers % 24.28/3.93 Prover 8: Constructing countermodel ... % 26.60/4.26 Prover 8: gave up % 26.60/4.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 27.34/4.41 Prover 10: Preprocessing ... % 27.34/4.43 Prover 9: Warning: ignoring some quantifiers % 28.47/4.47 Prover 9: Constructing countermodel ... % 29.16/4.58 Prover 10: Warning: ignoring some quantifiers % 29.53/4.60 Prover 10: Constructing countermodel ... % 31.90/4.92 Prover 10: gave up % 31.90/4.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 32.25/5.08 Prover 11: Preprocessing ... % 35.43/5.37 Prover 7: gave up % 35.43/5.38 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 36.52/5.54 Prover 12: Preprocessing ... % 37.37/5.70 Prover 11: Constructing countermodel ... % 40.28/5.98 Prover 12: Proving ... % 49.10/7.13 Prover 0: proved (6475ms) % 49.10/7.13 % 49.10/7.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 49.10/7.13 % 49.10/7.13 Prover 9: stopped % 49.10/7.13 Prover 12: stopped % 49.10/7.13 Prover 2: stopped % 49.10/7.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 49.10/7.13 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 49.10/7.13 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 49.10/7.14 Prover 5: stopped % 49.72/7.25 Prover 16: Preprocessing ... % 49.72/7.25 Prover 13: Preprocessing ... % 49.72/7.25 Prover 19: Preprocessing ... % 50.72/7.39 Prover 16: Warning: ignoring some quantifiers % 50.72/7.39 Prover 13: Warning: ignoring some quantifiers % 51.41/7.41 Prover 16: Constructing countermodel ... % 51.41/7.41 Prover 13: Constructing countermodel ... % 52.04/7.49 Prover 19: Warning: ignoring some quantifiers % 52.04/7.51 Prover 19: Constructing countermodel ... % 55.17/7.93 Prover 19: gave up % 83.30/11.99 Prover 13: stopped % 89.19/13.17 Prover 16: stopped % 91.86/14.14 Prover 11: Found proof (size 100) % 91.86/14.14 Prover 11: proved (9212ms) % 91.86/14.15 Prover 4: stopped % 91.86/14.15 % 91.86/14.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 91.86/14.15 % 91.86/14.16 % SZS output start Proof for theBenchmark % 91.86/14.18 Assumptions after simplification: % 91.86/14.18 --------------------------------- % 91.86/14.18 % 91.86/14.18 (aA8) % 92.23/14.23 $i(gamma) & $i(beta) & $i(alpha) & ? [v0: int] : ? [v1: int] : ? [v2: int] % 92.23/14.23 : ( ~ (v2 = 0) & ~ (v1 = 0) & ~ (v0 = 0) & s_t(gamma, alpha, beta) = v2 & % 92.23/14.23 s_t(beta, gamma, alpha) = v1 & s_t(alpha, beta, gamma) = v0) % 92.23/14.23 % 92.23/14.23 (aSatz2_3) % 92.23/14.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 92.23/14.24 $i] : ! [v6: int] : (v6 = 0 | ~ (s_e(v2, v3, v4, v5) = 0) | ~ (s_e(v0, % 92.23/14.24 v1, v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 92.23/14.24 $i(v1) | ~ $i(v0) | ? [v7: int] : ( ~ (v7 = 0) & s_e(v0, v1, v2, v3) = % 92.23/14.24 v7)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 92.23/14.24 : ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (s_e(v0, v1, v4, v5) = v6) | ~ % 92.23/14.24 (s_e(v0, v1, v2, v3) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 92.23/14.24 ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ( ~ (v7 = 0) & s_e(v2, v3, v4, v5) = % 92.23/14.24 v7)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 92.23/14.24 : ! [v5: $i] : ( ~ (s_e(v2, v3, v4, v5) = 0) | ~ (s_e(v0, v1, v2, v3) = 0) | % 92.23/14.24 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 92.23/14.24 s_e(v0, v1, v4, v5) = 0) % 92.23/14.24 % 92.23/14.24 (aSatz2_4) % 92.23/14.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 92.23/14.25 | ~ (s_e(v1, v0, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 92.23/14.25 $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & s_e(v0, v1, v2, v3) = v5)) & ! [v0: % 92.23/14.25 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s_e(v0, v1, v2, v3) = % 92.23/14.25 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | s_e(v1, v0, v2, v3) = % 92.23/14.25 0) % 92.23/14.25 % 92.23/14.25 (aSatz2_5) % 92.23/14.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 92.23/14.25 | ~ (s_e(v0, v1, v3, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 92.23/14.25 $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & s_e(v0, v1, v2, v3) = v5)) & ! [v0: % 92.23/14.25 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s_e(v0, v1, v2, v3) = % 92.23/14.25 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | s_e(v0, v1, v3, v2) = % 92.23/14.25 0) % 92.23/14.25 % 92.23/14.25 (aSatz3_13b) % 92.23/14.25 ~ (gamma = beta) & $i(gamma) & $i(beta) % 92.23/14.25 % 92.23/14.25 (aSatz3_2) % 92.23/14.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (s_t(v2, % 92.23/14.26 v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ % 92.23/14.26 (v4 = 0) & s_t(v0, v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 92.23/14.26 $i] : ( ~ (s_t(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 92.23/14.26 s_t(v2, v1, v0) = 0) % 92.23/14.26 % 92.23/14.26 (aSatz6_4b) % 92.23/14.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 92.23/14.26 (sameside(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 92.23/14.26 int] : ? [v5: int] : ((v5 = 0 & s_t(v0, v1, v2) = 0) | ( ~ (v4 = 0) & % 92.23/14.26 s_col(v0, v1, v2) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 92.23/14.26 [v3: int] : (v3 = 0 | ~ (s_t(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 92.23/14.27 $i(v0) | ? [v4: int] : ? [v5: int] : ((v4 = 0 & sameside(v0, v1, v2) = 0) % 92.23/14.27 | ( ~ (v5 = 0) & s_col(v0, v1, v2) = v5))) & ! [v0: $i] : ! [v1: $i] : % 92.23/14.27 ! [v2: $i] : ( ~ (s_col(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 92.23/14.27 ? [v3: int] : ? [v4: int] : ((v4 = 0 & s_t(v0, v1, v2) = 0) | (v3 = 0 & % 92.23/14.27 sameside(v0, v1, v2) = 0))) % 92.23/14.27 % 92.23/14.27 (aSatz7_13) % 92.23/14.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 92.23/14.27 int] : (v5 = 0 | ~ (s(v2, v1) = v4) | ~ (s(v2, v0) = v3) | ~ (s_e(v0, v1, % 92.23/14.27 v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 92.23/14.27 % 92.23/14.27 (aSatz7_17) % 92.23/14.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (s_m(v0, % 92.23/14.27 v3, v2) = 0) | ~ (s_m(v0, v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 92.23/14.27 $i(v1) | ~ $i(v0)) % 92.23/14.27 % 92.23/14.27 (aSatz7_20) % 92.68/14.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 = v0 | % 92.68/14.27 ~ (s_m(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] % 92.68/14.27 : ? [v5: int] : (( ~ (v5 = 0) & s_e(v1, v0, v1, v2) = v5) | ( ~ (v4 = 0) & % 92.68/14.27 s_col(v0, v1, v2) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 92.68/14.27 (v2 = v0 | ~ (s_col(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 92.68/14.27 [v3: int] : ? [v4: int] : ((v4 = 0 & s_m(v0, v1, v2) = 0) | ( ~ (v3 = 0) & % 92.68/14.28 s_e(v1, v0, v1, v2) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 92.68/14.28 (v2 = v0 | ~ (s_e(v1, v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 92.68/14.28 ? [v3: int] : ? [v4: int] : ((v4 = 0 & s_m(v0, v1, v2) = 0) | ( ~ (v3 = 0) % 92.68/14.28 & s_col(v0, v1, v2) = v3))) % 92.68/14.28 % 92.68/14.28 (aSatz7_25) % 92.68/14.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (isomidpoint(v1, % 92.68/14.28 v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? % 92.68/14.28 [v5: int] : ((v5 = 0 & s_m(v1, v3, v2) = 0) | ( ~ (v4 = 0) & s_e(v0, v1, v0, % 92.68/14.28 v2) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (s_e(v0, % 92.68/14.28 v1, v0, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 92.68/14.28 (isomidpoint(v1, v2, v0) = v3 & s_m(v1, v3, v2) = 0 & $i(v3))) % 92.68/14.28 % 92.68/14.28 (aSatz7_4a) % 92.68/14.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (s(v1, v0) = v2) | ~ $i(v1) | % 92.68/14.28 ~ $i(v0) | s_m(v0, v1, v2) = 0) % 92.68/14.28 % 92.68/14.28 (aSatz7_7) % 92.68/14.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (s(v0, v1) = v2) | ~ $i(v1) | % 92.68/14.28 ~ $i(v0) | s(v0, v2) = v1) % 92.68/14.28 % 92.68/14.28 (aSatz8_2) % 92.68/14.28 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 92.68/14.28 s_r(v2, v1, v0) = v3 & s_r(v0, v1, v2) = 0 & $i(v2) & $i(v1) & $i(v0)) % 92.68/14.28 % 92.68/14.28 (d_Defn6_1) % 92.68/14.29 $i(xb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 % 92.68/14.29 = v1 | v1 = v0 | ~ (sameside(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 92.68/14.29 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & s_t(v1, v2, v0) = v4)) & ! [v0: $i] % 92.68/14.29 : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v1 = v0 | v1 = xb | ~ % 92.68/14.29 (sameside(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 92.68/14.29 int] : ( ~ (v4 = 0) & s_t(v1, v0, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : % 92.68/14.29 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (s_t(v1, v2, v0) = v3) | ~ $i(v2) | % 92.68/14.29 ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ((v5 = 0 & s_t(v1, v0, % 92.68/14.29 v2) = 0) | ( ~ (v4 = 0) & sameside(v0, v1, v2) = v4))) & ! [v0: $i] : % 92.68/14.29 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (s_t(v1, v0, v2) = v3) % 92.68/14.29 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ((v5 = 0 % 92.68/14.29 & s_t(v1, v2, v0) = 0) | ( ~ (v4 = 0) & sameside(v0, v1, v2) = v4))) & % 92.68/14.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | v1 = v0 | ~ (s_t(v1, v2, % 92.68/14.29 v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | sameside(v0, v1, v2) = 0) % 92.68/14.29 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | v1 = xb | ~ (s_t(v1, % 92.68/14.29 v0, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | sameside(v0, v1, v2) % 92.68/14.29 = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sameside(v0, v1, v2) = % 92.68/14.29 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 92.68/14.29 ((v4 = 0 & s_t(v1, v2, v0) = 0) | (v3 = 0 & s_t(v1, v0, v2) = 0))) & ! [v0: % 92.68/14.29 $i] : ! [v1: $i] : ( ~ (sameside(v0, v1, v1) = 0) | ~ $i(v1) | ~ $i(v0)) % 92.68/14.29 & ! [v0: $i] : ! [v1: $i] : ( ~ (sameside(v0, v0, v1) = 0) | ~ $i(v1) | ~ % 92.68/14.29 $i(v0)) % 92.68/14.29 % 92.68/14.29 (d_Defn7_1) % 92.68/14.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (s_m(v0, % 92.68/14.29 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? % 92.68/14.29 [v5: int] : (( ~ (v5 = 0) & s_e(v1, v0, v1, v2) = v5) | ( ~ (v4 = 0) & % 92.68/14.29 s_t(v0, v1, v2) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 92.68/14.29 [v3: int] : (v3 = 0 | ~ (s_t(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 92.68/14.29 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & s_m(v0, v1, v2) = v4)) & ! [v0: $i] % 92.68/14.29 : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (s_e(v1, v0, v1, v2) % 92.68/14.29 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & % 92.68/14.29 s_m(v0, v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 92.68/14.29 (s_m(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | s_t(v0, v1, v2) % 92.68/14.29 = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (s_m(v0, v1, v2) = 0) | % 92.68/14.29 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | s_e(v1, v0, v1, v2) = 0) & ! [v0: $i] : % 92.68/14.29 ! [v1: $i] : ! [v2: $i] : ( ~ (s_t(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) % 92.68/14.29 | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & s_m(v0, v1, v2) = 0) % 92.68/14.29 | ( ~ (v3 = 0) & s_e(v1, v0, v1, v2) = v3))) & ! [v0: $i] : ! [v1: $i] : % 92.68/14.29 ! [v2: $i] : ( ~ (s_e(v1, v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 92.68/14.29 $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & s_m(v0, v1, v2) = 0) | ( ~ % 92.68/14.29 (v3 = 0) & s_t(v0, v1, v2) = v3))) % 92.68/14.29 % 92.68/14.29 (d_Defn8_1) % 92.68/14.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 92.68/14.30 | ~ (s(v1, v2) = v3) | ~ (s_e(v0, v2, v0, v3) = v4) | ~ $i(v2) | ~ % 92.68/14.30 $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & s_r(v0, v1, v2) = v5)) & % 92.68/14.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (s_r(v0, % 92.68/14.30 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? % 92.68/14.30 [v5: int] : ( ~ (v5 = 0) & s(v1, v2) = v4 & s_e(v0, v2, v0, v4) = v5 & % 92.68/14.30 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 92.68/14.30 (s(v1, v2) = v3) | ~ (s_e(v0, v2, v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 92.68/14.30 $i(v0) | s_r(v0, v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( % 92.68/14.30 ~ (s_r(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 92.68/14.30 (s(v1, v2) = v3 & s_e(v0, v2, v0, v3) = 0 & $i(v3))) % 92.68/14.30 % 92.68/14.30 (d_insert) % 92.68/14.30 $i(gamma) & $i(alpha) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 92.68/14.30 : ! [v4: $i] : ! [v5: $i] : ( ~ (ext(v4, v2, v0, v1) = v5) | ~ (ext(v3, v2, % 92.68/14.30 alpha, gamma) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 92.68/14.30 (insert(v0, v1, v2, v3) = v5 & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! % 92.68/14.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (insert(v0, v1, v2, v3) = v4) | ~ % 92.68/14.30 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (ext(v5, v2, v0, % 92.68/14.30 v1) = v4 & ext(v3, v2, alpha, gamma) = v5 & $i(v5) & $i(v4))) % 92.68/14.30 % 92.68/14.30 (function-axioms) % 92.68/14.31 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 92.68/14.31 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] % 92.68/14.31 : ! [v9: $i] : (v1 = v0 | ~ (s_afs(v9, v8, v7, v6, v5, v4, v3, v2) = v1) | % 92.68/14.31 ~ (s_afs(v9, v8, v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] % 92.68/14.31 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 92.68/14.31 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v1 = v0 | % 92.68/14.31 ~ (s_fs(v9, v8, v7, v6, v5, v4, v3, v2) = v1) | ~ (s_fs(v9, v8, v7, v6, v5, % 92.68/14.31 v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 92.68/14.31 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 92.68/14.31 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v1 = v0 | ~ % 92.68/14.31 (s_ifs(v9, v8, v7, v6, v5, v4, v3, v2) = v1) | ~ (s_ifs(v9, v8, v7, v6, v5, % 92.68/14.31 v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 92.68/14.31 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 92.68/14.31 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v1 = v0 | ~ (s_kf(v8, v7, v6, v5, % 92.68/14.31 v4, v3, v2) = v1) | ~ (s_kf(v8, v7, v6, v5, v4, v3, v2) = v0)) & ! % 92.68/14.31 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 92.68/14.31 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ % 92.68/14.31 (s_e3(v7, v6, v5, v4, v3, v2) = v1) | ~ (s_e3(v7, v6, v5, v4, v3, v2) = % 92.68/14.31 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 92.68/14.31 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (crossbar(v7, v6, % 92.68/14.31 v5, v4, v3, v2) = v1) | ~ (crossbar(v7, v6, v5, v4, v3, v2) = v0)) & ! % 92.68/14.31 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 92.68/14.31 : ! [v6: $i] : (v1 = v0 | ~ (g811(v6, v5, v4, v3, v2) = v1) | ~ (g811(v6, % 92.68/14.31 v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 92.68/14.31 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (f811(v6, % 92.68/14.31 v5, v4, v3, v2) = v1) | ~ (f811(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 92.68/14.31 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 92.68/14.31 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (perpAt(v6, v5, v4, % 92.68/14.31 v3, v2) = v1) | ~ (perpAt(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! % 92.68/14.31 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 92.68/14.31 : (v1 = v0 | ~ (insert5(v6, v5, v4, v3, v2) = v1) | ~ (insert5(v6, v5, v4, % 92.68/14.31 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 92.68/14.31 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (ip(v6, v5, v4, v3, % 92.68/14.31 v2) = v1) | ~ (ip(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 92.68/14.31 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 92.68/14.31 (il(v5, v4, v3, v2) = v1) | ~ (il(v5, v4, v3, v2) = v0)) & ! [v0: % 92.68/14.31 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 92.68/14.31 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (perp(v5, v4, v3, v2) = v1) | ~ % 92.68/14.31 (perp(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 92.68/14.31 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (ins(v5, v4, v3, v2) = % 92.68/14.31 v1) | ~ (ins(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 92.68/14.31 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 92.68/14.31 $i] : (v1 = v0 | ~ (le(v5, v4, v3, v2) = v1) | ~ (le(v5, v4, v3, v2) = % 92.68/14.31 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 92.68/14.31 : ! [v5: $i] : (v1 = v0 | ~ (insert(v5, v4, v3, v2) = v1) | ~ (insert(v5, % 92.68/14.31 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 92.68/14.31 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (ext(v5, v4, v3, v2) = v1) | % 92.68/14.31 ~ (ext(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 92.68/14.31 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 92.68/14.31 (v1 = v0 | ~ (s_e(v5, v4, v3, v2) = v1) | ~ (s_e(v5, v4, v3, v2) = v0)) & ! % 92.68/14.31 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 92.68/14.31 $i] : ! [v4: $i] : (v1 = v0 | ~ (s_r(v4, v3, v2) = v1) | ~ (s_r(v4, v3, % 92.68/14.31 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 92.68/14.31 [v4: $i] : (v1 = v0 | ~ (isomidpoint(v4, v3, v2) = v1) | ~ (isomidpoint(v4, % 92.68/14.31 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 92.68/14.31 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (s_m(v4, v3, v2) = % 92.68/14.31 v1) | ~ (s_m(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 92.68/14.31 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c63(v4, v3, v2) = v1) | ~ % 92.68/14.31 (c63(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 92.68/14.31 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 92.68/14.31 (sameside(v4, v3, v2) = v1) | ~ (sameside(v4, v3, v2) = v0)) & ! [v0: % 92.68/14.31 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 92.68/14.31 : ! [v4: $i] : (v1 = v0 | ~ (s_col(v4, v3, v2) = v1) | ~ (s_col(v4, v3, v2) % 92.68/14.31 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 92.68/14.31 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (s_t(v4, v3, v2) = v1) | ~ % 92.68/14.31 (s_t(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 92.68/14.31 $i] : (v1 = v0 | ~ (s(v3, v2) = v1) | ~ (s(v3, v2) = v0)) & ! [v0: $i] : % 92.68/14.31 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (pointOffLine(v3, v2) = % 92.68/14.31 v1) | ~ (pointOffLine(v3, v2) = v0)) % 92.68/14.31 % 92.68/14.31 Further assumptions not needed in the proof: % 92.68/14.31 -------------------------------------------- % 92.68/14.31 aA1, aA2, aA3, aA4, aA5, aA6, aA7, aNarbouxLemma1, aSatz2_1, aSatz2_11, % 92.68/14.31 aSatz2_12, aSatz2_13, aSatz2_14, aSatz2_15, aSatz2_2, aSatz2_8, aSatz3_1, % 92.68/14.31 aSatz3_13a, aSatz3_13c, aSatz3_14a, aSatz3_14b, aSatz3_17, aSatz3_3, aSatz3_4, % 92.68/14.31 aSatz3_5a, aSatz3_5b, aSatz3_6a, aSatz3_6b, aSatz3_7a, aSatz3_7b, aSatz4_11a, % 92.68/14.31 aSatz4_11b, aSatz4_11c, aSatz4_11d, aSatz4_11e, aSatz4_12, aSatz4_12b, % 92.68/14.31 aSatz4_13, aSatz4_14, aSatz4_16, aSatz4_17, aSatz4_18, aSatz4_19, aSatz4_2, % 92.68/14.31 aSatz4_3, aSatz4_5, aSatz4_6, aSatz5_1, aSatz5_10, aSatz5_11, aSatz5_12a1, % 92.68/14.31 aSatz5_12a2, aSatz5_12b, aSatz5_2, aSatz5_3, aSatz5_5a, aSatz5_5b, aSatz5_6, % 92.68/14.31 aSatz5_7, aSatz5_8, aSatz5_9, aSatz6_11a, aSatz6_11b, aSatz6_13a, aSatz6_13b, % 92.68/14.31 aSatz6_15a, aSatz6_15b, aSatz6_15c, aSatz6_15d, aSatz6_16a, aSatz6_16b, % 92.68/14.31 aSatz6_17a, aSatz6_17b, aSatz6_18, aSatz6_21, aSatz6_25, aSatz6_28, aSatz6_2a, % 92.68/14.31 aSatz6_2b, aSatz6_3a, aSatz6_3b, aSatz6_4a, aSatz6_5, aSatz6_6, aSatz6_7, % 92.68/14.31 aSatz7_10a, aSatz7_10b, aSatz7_15a, aSatz7_15b, aSatz7_16a, aSatz7_16b, % 92.68/14.31 aSatz7_18, aSatz7_19, aSatz7_2, aSatz7_21, aSatz7_22, aSatz7_22a, aSatz7_22b, % 92.68/14.31 aSatz7_3a, aSatz7_3b, aSatz7_4b, aSatz7_6, aSatz7_8, aSatz7_9, d_Defn2_10, % 92.68/14.31 d_Defn4_1, d_Defn4_10, d_Defn4_15, d_Defn4_4, d_Defn5_4, d_Defn7_23, % 92.68/14.31 d_Defn8_11a, d_Defn8_11b % 92.68/14.31 % 92.68/14.31 Those formulas are unsatisfiable: % 92.68/14.31 --------------------------------- % 92.68/14.31 % 92.68/14.31 Begin of proof % 92.68/14.31 | % 92.68/14.32 | ALPHA: (aA8) implies: % 92.68/14.32 | (1) ? [v0: int] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = 0) & ~ (v1 = 0) % 92.68/14.32 | & ~ (v0 = 0) & s_t(gamma, alpha, beta) = v2 & s_t(beta, gamma, % 92.68/14.32 | alpha) = v1 & s_t(alpha, beta, gamma) = v0) % 92.68/14.32 | % 92.68/14.32 | ALPHA: (aSatz2_3) implies: % 92.68/14.32 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 92.68/14.32 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (s_e(v0, v1, v4, v5) = v6) | % 92.68/14.32 | ~ (s_e(v0, v1, v2, v3) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 92.68/14.32 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ( ~ (v7 = 0) & % 92.68/14.32 | s_e(v2, v3, v4, v5) = v7)) % 92.68/14.32 | % 92.68/14.32 | ALPHA: (aSatz2_4) implies: % 92.68/14.32 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 92.68/14.32 | (v4 = 0 | ~ (s_e(v1, v0, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 92.68/14.32 | $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & s_e(v0, v1, v2, % 92.68/14.32 | v3) = v5)) % 92.68/14.32 | % 92.68/14.32 | ALPHA: (aSatz2_5) implies: % 92.68/14.32 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s_e(v0, % 92.68/14.32 | v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 92.68/14.32 | | s_e(v0, v1, v3, v2) = 0) % 92.68/14.32 | % 92.68/14.32 | ALPHA: (aSatz3_2) implies: % 92.68/14.32 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 92.68/14.32 | (s_t(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 92.68/14.32 | int] : ( ~ (v4 = 0) & s_t(v0, v1, v2) = v4)) % 92.68/14.32 | % 92.68/14.32 | ALPHA: (aSatz3_13b) implies: % 92.68/14.32 | (6) ~ (gamma = beta) % 92.68/14.32 | (7) $i(beta) % 92.68/14.32 | % 92.68/14.32 | ALPHA: (aSatz6_4b) implies: % 92.68/14.32 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 92.68/14.32 | (s_t(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 92.68/14.32 | int] : ? [v5: int] : ((v4 = 0 & sameside(v0, v1, v2) = 0) | ( ~ % 92.68/14.32 | (v5 = 0) & s_col(v0, v1, v2) = v5))) % 92.68/14.32 | % 92.68/14.32 | ALPHA: (aSatz7_20) implies: % 92.68/14.32 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 = % 92.68/14.32 | v0 | ~ (s_m(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 92.68/14.32 | ? [v4: int] : ? [v5: int] : (( ~ (v5 = 0) & s_e(v1, v0, v1, v2) = % 92.68/14.32 | v5) | ( ~ (v4 = 0) & s_col(v0, v1, v2) = v4))) % 92.68/14.32 | % 92.68/14.32 | ALPHA: (aSatz7_25) implies: % 92.68/14.33 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (s_e(v0, v1, v0, v2) = % 92.68/14.33 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 92.68/14.33 | (isomidpoint(v1, v2, v0) = v3 & s_m(v1, v3, v2) = 0 & $i(v3))) % 92.68/14.33 | % 92.68/14.33 | ALPHA: (d_insert) implies: % 92.68/14.33 | (11) $i(alpha) % 92.68/14.33 | (12) $i(gamma) % 92.68/14.33 | % 92.68/14.33 | ALPHA: (d_Defn6_1) implies: % 92.68/14.33 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 92.68/14.33 | (s_t(v1, v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 92.68/14.33 | int] : ? [v5: int] : ((v5 = 0 & s_t(v1, v0, v2) = 0) | ( ~ (v4 = % 92.68/14.33 | 0) & sameside(v0, v1, v2) = v4))) % 92.68/14.33 | % 92.68/14.33 | ALPHA: (d_Defn7_1) implies: % 92.68/14.33 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 92.68/14.33 | (s_t(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 92.68/14.33 | int] : ( ~ (v4 = 0) & s_m(v0, v1, v2) = v4)) % 92.68/14.33 | % 92.68/14.33 | ALPHA: (d_Defn8_1) implies: % 92.68/14.33 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (s_r(v0, v1, v2) = 0) | % 92.68/14.33 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (s(v1, v2) = v3 & % 92.68/14.33 | s_e(v0, v2, v0, v3) = 0 & $i(v3))) % 92.68/14.33 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 92.68/14.33 | (s_r(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 92.68/14.33 | $i] : ? [v5: int] : ( ~ (v5 = 0) & s(v1, v2) = v4 & s_e(v0, v2, % 92.68/14.33 | v0, v4) = v5 & $i(v4))) % 92.68/14.33 | % 92.68/14.33 | ALPHA: (function-axioms) implies: % 92.68/14.33 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 92.68/14.33 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (s_t(v4, v3, v2) = v1) | % 92.68/14.33 | ~ (s_t(v4, v3, v2) = v0)) % 92.68/14.33 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 92.68/14.33 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sameside(v4, v3, v2) = % 92.68/14.33 | v1) | ~ (sameside(v4, v3, v2) = v0)) % 92.68/14.33 | % 92.68/14.33 | DELTA: instantiating (1) with fresh symbols all_130_0, all_130_1, all_130_2 % 92.68/14.33 | gives: % 92.68/14.33 | (19) ~ (all_130_0 = 0) & ~ (all_130_1 = 0) & ~ (all_130_2 = 0) & % 92.68/14.33 | s_t(gamma, alpha, beta) = all_130_0 & s_t(beta, gamma, alpha) = % 92.68/14.33 | all_130_1 & s_t(alpha, beta, gamma) = all_130_2 % 92.68/14.33 | % 92.68/14.33 | ALPHA: (19) implies: % 92.68/14.33 | (20) ~ (all_130_2 = 0) % 92.68/14.33 | (21) ~ (all_130_1 = 0) % 92.68/14.33 | (22) ~ (all_130_0 = 0) % 92.68/14.33 | (23) s_t(alpha, beta, gamma) = all_130_2 % 92.68/14.33 | (24) s_t(beta, gamma, alpha) = all_130_1 % 92.68/14.33 | (25) s_t(gamma, alpha, beta) = all_130_0 % 92.68/14.33 | % 92.68/14.33 | DELTA: instantiating (aSatz8_2) with fresh symbols all_132_0, all_132_1, % 92.68/14.33 | all_132_2, all_132_3 gives: % 92.68/14.33 | (26) ~ (all_132_0 = 0) & s_r(all_132_1, all_132_2, all_132_3) = all_132_0 % 92.68/14.33 | & s_r(all_132_3, all_132_2, all_132_1) = 0 & $i(all_132_1) & % 92.68/14.33 | $i(all_132_2) & $i(all_132_3) % 92.68/14.33 | % 92.68/14.33 | ALPHA: (26) implies: % 92.68/14.33 | (27) ~ (all_132_0 = 0) % 92.68/14.33 | (28) $i(all_132_3) % 92.68/14.33 | (29) $i(all_132_2) % 92.68/14.34 | (30) $i(all_132_1) % 92.68/14.34 | (31) s_r(all_132_3, all_132_2, all_132_1) = 0 % 92.68/14.34 | (32) s_r(all_132_1, all_132_2, all_132_3) = all_132_0 % 92.68/14.34 | % 92.68/14.34 | GROUND_INST: instantiating (13) with gamma, alpha, beta, all_130_2, % 92.68/14.34 | simplifying with (7), (11), (12), (23) gives: % 92.68/14.34 | (33) all_130_2 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 & s_t(alpha, % 92.68/14.34 | gamma, beta) = 0) | ( ~ (v0 = 0) & sameside(gamma, alpha, beta) % 92.68/14.34 | = v0)) % 92.68/14.34 | % 92.68/14.34 | GROUND_INST: instantiating (5) with alpha, gamma, beta, all_130_1, simplifying % 92.68/14.34 | with (7), (11), (12), (24) gives: % 92.68/14.34 | (34) all_130_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & s_t(alpha, gamma, beta) % 92.68/14.34 | = v0) % 92.68/14.34 | % 92.68/14.34 | GROUND_INST: instantiating (8) with gamma, alpha, beta, all_130_0, simplifying % 92.68/14.34 | with (7), (11), (12), (25) gives: % 92.68/14.34 | (35) all_130_0 = 0 | ? [v0: int] : ? [v1: int] : ((v0 = 0 & % 92.68/14.34 | sameside(gamma, alpha, beta) = 0) | ( ~ (v1 = 0) & s_col(gamma, % 92.68/14.34 | alpha, beta) = v1)) % 92.68/14.34 | % 92.68/14.34 | GROUND_INST: instantiating (14) with gamma, alpha, beta, all_130_0, % 92.68/14.34 | simplifying with (7), (11), (12), (25) gives: % 92.68/14.34 | (36) all_130_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & s_m(gamma, alpha, beta) % 92.68/14.34 | = v0) % 92.68/14.34 | % 92.68/14.34 | GROUND_INST: instantiating (15) with all_132_3, all_132_2, all_132_1, % 92.68/14.34 | simplifying with (28), (29), (30), (31) gives: % 92.68/14.34 | (37) ? [v0: $i] : (s(all_132_2, all_132_1) = v0 & s_e(all_132_3, % 92.68/14.34 | all_132_1, all_132_3, v0) = 0 & $i(v0)) % 92.68/14.34 | % 92.68/14.34 | GROUND_INST: instantiating (16) with all_132_1, all_132_2, all_132_3, % 92.68/14.34 | all_132_0, simplifying with (28), (29), (30), (32) gives: % 92.68/14.34 | (38) all_132_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 92.68/14.34 | s(all_132_2, all_132_3) = v0 & s_e(all_132_1, all_132_3, all_132_1, % 92.68/14.34 | v0) = v1 & $i(v0)) % 92.68/14.34 | % 92.68/14.34 | DELTA: instantiating (37) with fresh symbol all_139_0 gives: % 92.68/14.34 | (39) s(all_132_2, all_132_1) = all_139_0 & s_e(all_132_3, all_132_1, % 92.68/14.34 | all_132_3, all_139_0) = 0 & $i(all_139_0) % 92.68/14.34 | % 92.68/14.34 | ALPHA: (39) implies: % 92.68/14.34 | (40) $i(all_139_0) % 92.68/14.34 | (41) s_e(all_132_3, all_132_1, all_132_3, all_139_0) = 0 % 92.68/14.34 | (42) s(all_132_2, all_132_1) = all_139_0 % 92.68/14.34 | % 92.68/14.34 | BETA: splitting (36) gives: % 92.68/14.34 | % 92.68/14.34 | Case 1: % 92.68/14.34 | | % 92.68/14.34 | | (43) all_130_0 = 0 % 92.68/14.34 | | % 92.68/14.34 | | REDUCE: (22), (43) imply: % 92.68/14.34 | | (44) $false % 92.68/14.35 | | % 92.68/14.35 | | CLOSE: (44) is inconsistent. % 92.68/14.35 | | % 92.68/14.35 | Case 2: % 92.68/14.35 | | % 92.68/14.35 | | (45) ? [v0: int] : ( ~ (v0 = 0) & s_m(gamma, alpha, beta) = v0) % 92.68/14.35 | | % 92.68/14.35 | | DELTA: instantiating (45) with fresh symbol all_179_0 gives: % 93.00/14.35 | | (46) ~ (all_179_0 = 0) & s_m(gamma, alpha, beta) = all_179_0 % 93.00/14.35 | | % 93.00/14.35 | | ALPHA: (46) implies: % 93.00/14.35 | | (47) ~ (all_179_0 = 0) % 93.00/14.35 | | (48) s_m(gamma, alpha, beta) = all_179_0 % 93.00/14.35 | | % 93.00/14.35 | | BETA: splitting (34) gives: % 93.00/14.35 | | % 93.00/14.35 | | Case 1: % 93.00/14.35 | | | % 93.00/14.35 | | | (49) all_130_1 = 0 % 93.00/14.35 | | | % 93.00/14.35 | | | REDUCE: (21), (49) imply: % 93.00/14.35 | | | (50) $false % 93.00/14.35 | | | % 93.00/14.35 | | | CLOSE: (50) is inconsistent. % 93.00/14.35 | | | % 93.00/14.35 | | Case 2: % 93.00/14.35 | | | % 93.00/14.35 | | | (51) ? [v0: int] : ( ~ (v0 = 0) & s_t(alpha, gamma, beta) = v0) % 93.00/14.35 | | | % 93.00/14.35 | | | DELTA: instantiating (51) with fresh symbol all_184_0 gives: % 93.00/14.35 | | | (52) ~ (all_184_0 = 0) & s_t(alpha, gamma, beta) = all_184_0 % 93.00/14.35 | | | % 93.00/14.35 | | | ALPHA: (52) implies: % 93.00/14.35 | | | (53) ~ (all_184_0 = 0) % 93.00/14.35 | | | (54) s_t(alpha, gamma, beta) = all_184_0 % 93.00/14.35 | | | % 93.00/14.35 | | | BETA: splitting (33) gives: % 93.00/14.35 | | | % 93.00/14.35 | | | Case 1: % 93.00/14.35 | | | | % 93.00/14.35 | | | | (55) all_130_2 = 0 % 93.00/14.35 | | | | % 93.00/14.35 | | | | REDUCE: (20), (55) imply: % 93.00/14.35 | | | | (56) $false % 93.00/14.35 | | | | % 93.00/14.35 | | | | CLOSE: (56) is inconsistent. % 93.00/14.35 | | | | % 93.00/14.35 | | | Case 2: % 93.00/14.35 | | | | % 93.00/14.35 | | | | (57) ? [v0: int] : ? [v1: int] : ((v1 = 0 & s_t(alpha, gamma, beta) % 93.00/14.35 | | | | = 0) | ( ~ (v0 = 0) & sameside(gamma, alpha, beta) = v0)) % 93.00/14.35 | | | | % 93.00/14.35 | | | | DELTA: instantiating (57) with fresh symbols all_235_0, all_235_1 gives: % 93.00/14.35 | | | | (58) (all_235_0 = 0 & s_t(alpha, gamma, beta) = 0) | ( ~ (all_235_1 = % 93.00/14.35 | | | | 0) & sameside(gamma, alpha, beta) = all_235_1) % 93.00/14.35 | | | | % 93.00/14.35 | | | | BETA: splitting (35) gives: % 93.00/14.35 | | | | % 93.00/14.35 | | | | Case 1: % 93.00/14.35 | | | | | % 93.00/14.35 | | | | | (59) all_130_0 = 0 % 93.00/14.35 | | | | | % 93.00/14.35 | | | | | REDUCE: (22), (59) imply: % 93.00/14.35 | | | | | (60) $false % 93.00/14.35 | | | | | % 93.00/14.35 | | | | | CLOSE: (60) is inconsistent. % 93.00/14.35 | | | | | % 93.00/14.35 | | | | Case 2: % 93.00/14.35 | | | | | % 93.00/14.35 | | | | | (61) ? [v0: int] : ? [v1: int] : ((v0 = 0 & sameside(gamma, % 93.00/14.35 | | | | | alpha, beta) = 0) | ( ~ (v1 = 0) & s_col(gamma, alpha, % 93.00/14.35 | | | | | beta) = v1)) % 93.00/14.35 | | | | | % 93.00/14.35 | | | | | DELTA: instantiating (61) with fresh symbols all_251_0, all_251_1 % 93.00/14.35 | | | | | gives: % 93.00/14.35 | | | | | (62) (all_251_1 = 0 & sameside(gamma, alpha, beta) = 0) | ( ~ % 93.00/14.35 | | | | | (all_251_0 = 0) & s_col(gamma, alpha, beta) = all_251_0) % 93.00/14.35 | | | | | % 93.00/14.35 | | | | | BETA: splitting (38) gives: % 93.00/14.35 | | | | | % 93.00/14.35 | | | | | Case 1: % 93.00/14.35 | | | | | | % 93.00/14.35 | | | | | | (63) all_132_0 = 0 % 93.00/14.35 | | | | | | % 93.00/14.35 | | | | | | REDUCE: (27), (63) imply: % 93.00/14.35 | | | | | | (64) $false % 93.00/14.35 | | | | | | % 93.00/14.35 | | | | | | CLOSE: (64) is inconsistent. % 93.00/14.35 | | | | | | % 93.00/14.35 | | | | | Case 2: % 93.00/14.35 | | | | | | % 93.00/14.36 | | | | | | (65) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & s(all_132_2, % 93.00/14.36 | | | | | | all_132_3) = v0 & s_e(all_132_1, all_132_3, all_132_1, % 93.00/14.36 | | | | | | v0) = v1 & $i(v0)) % 93.00/14.36 | | | | | | % 93.00/14.36 | | | | | | DELTA: instantiating (65) with fresh symbols all_255_0, all_255_1 % 93.00/14.36 | | | | | | gives: % 93.00/14.36 | | | | | | (66) ~ (all_255_0 = 0) & s(all_132_2, all_132_3) = all_255_1 & % 93.00/14.36 | | | | | | s_e(all_132_1, all_132_3, all_132_1, all_255_1) = all_255_0 % 93.00/14.36 | | | | | | & $i(all_255_1) % 93.00/14.36 | | | | | | % 93.00/14.36 | | | | | | ALPHA: (66) implies: % 93.00/14.36 | | | | | | (67) ~ (all_255_0 = 0) % 93.00/14.36 | | | | | | (68) $i(all_255_1) % 93.00/14.36 | | | | | | (69) s_e(all_132_1, all_132_3, all_132_1, all_255_1) = all_255_0 % 93.00/14.36 | | | | | | (70) s(all_132_2, all_132_3) = all_255_1 % 93.00/14.36 | | | | | | % 93.00/14.36 | | | | | | BETA: splitting (58) gives: % 93.00/14.36 | | | | | | % 93.00/14.36 | | | | | | Case 1: % 93.00/14.36 | | | | | | | % 93.00/14.36 | | | | | | | (71) all_235_0 = 0 & s_t(alpha, gamma, beta) = 0 % 93.00/14.36 | | | | | | | % 93.00/14.36 | | | | | | | ALPHA: (71) implies: % 93.00/14.36 | | | | | | | (72) s_t(alpha, gamma, beta) = 0 % 93.00/14.36 | | | | | | | % 93.00/14.36 | | | | | | | GROUND_INST: instantiating (17) with 0, all_184_0, beta, gamma, % 93.00/14.36 | | | | | | | alpha, simplifying with (54), (72) gives: % 93.00/14.36 | | | | | | | (73) all_184_0 = 0 % 93.00/14.36 | | | | | | | % 93.00/14.36 | | | | | | | REDUCE: (53), (73) imply: % 93.00/14.36 | | | | | | | (74) $false % 93.00/14.36 | | | | | | | % 93.00/14.36 | | | | | | | CLOSE: (74) is inconsistent. % 93.00/14.36 | | | | | | | % 93.00/14.36 | | | | | | Case 2: % 93.00/14.36 | | | | | | | % 93.00/14.36 | | | | | | | (75) ~ (all_235_1 = 0) & sameside(gamma, alpha, beta) = % 93.00/14.36 | | | | | | | all_235_1 % 93.00/14.36 | | | | | | | % 93.00/14.36 | | | | | | | ALPHA: (75) implies: % 93.00/14.36 | | | | | | | (76) ~ (all_235_1 = 0) % 93.00/14.36 | | | | | | | (77) sameside(gamma, alpha, beta) = all_235_1 % 93.00/14.36 | | | | | | | % 93.00/14.36 | | | | | | | BETA: splitting (62) gives: % 93.00/14.36 | | | | | | | % 93.00/14.36 | | | | | | | Case 1: % 93.00/14.36 | | | | | | | | % 93.00/14.36 | | | | | | | | (78) all_251_1 = 0 & sameside(gamma, alpha, beta) = 0 % 93.00/14.36 | | | | | | | | % 93.00/14.36 | | | | | | | | ALPHA: (78) implies: % 93.00/14.36 | | | | | | | | (79) sameside(gamma, alpha, beta) = 0 % 93.00/14.36 | | | | | | | | % 93.00/14.36 | | | | | | | | GROUND_INST: instantiating (18) with 0, all_235_1, beta, alpha, % 93.00/14.36 | | | | | | | | gamma, simplifying with (77), (79) gives: % 93.00/14.36 | | | | | | | | (80) all_235_1 = 0 % 93.00/14.36 | | | | | | | | % 93.00/14.36 | | | | | | | | REDUCE: (76), (80) imply: % 93.00/14.36 | | | | | | | | (81) $false % 93.00/14.36 | | | | | | | | % 93.00/14.36 | | | | | | | | CLOSE: (81) is inconsistent. % 93.00/14.36 | | | | | | | | % 93.00/14.36 | | | | | | | Case 2: % 93.00/14.36 | | | | | | | | % 93.00/14.36 | | | | | | | | % 93.00/14.36 | | | | | | | | GROUND_INST: instantiating (10) with all_132_3, all_132_1, % 93.00/14.36 | | | | | | | | all_139_0, simplifying with (28), (30), (40), (41) % 93.00/14.36 | | | | | | | | gives: % 93.00/14.36 | | | | | | | | (82) ? [v0: $i] : (isomidpoint(all_132_1, all_139_0, % 93.00/14.36 | | | | | | | | all_132_3) = v0 & s_m(all_132_1, v0, all_139_0) = 0 % 93.00/14.36 | | | | | | | | & $i(v0)) % 93.00/14.36 | | | | | | | | % 93.00/14.36 | | | | | | | | GROUND_INST: instantiating (4) with all_132_3, all_132_1, % 93.00/14.36 | | | | | | | | all_132_3, all_139_0, simplifying with (28), (30), % 93.00/14.36 | | | | | | | | (40), (41) gives: % 93.00/14.36 | | | | | | | | (83) s_e(all_132_3, all_132_1, all_139_0, all_132_3) = 0 % 93.00/14.36 | | | | | | | | % 93.00/14.36 | | | | | | | | GROUND_INST: instantiating (3) with all_132_3, all_132_1, % 93.00/14.36 | | | | | | | | all_132_1, all_255_1, all_255_0, simplifying with % 93.00/14.36 | | | | | | | | (28), (30), (68), (69) gives: % 93.00/14.36 | | | | | | | | (84) all_255_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 93.00/14.36 | | | | | | | | s_e(all_132_3, all_132_1, all_132_1, all_255_1) = v0) % 93.00/14.36 | | | | | | | | % 93.00/14.36 | | | | | | | | GROUND_INST: instantiating (9) with gamma, alpha, beta, % 93.00/14.36 | | | | | | | | all_179_0, simplifying with (7), (11), (12), (48) % 93.00/14.36 | | | | | | | | gives: % 93.00/14.36 | | | | | | | | (85) all_179_0 = 0 | gamma = beta | ? [v0: int] : ? [v1: % 93.00/14.36 | | | | | | | | int] : (( ~ (v1 = 0) & s_e(alpha, gamma, alpha, beta) % 93.00/14.36 | | | | | | | | = v1) | ( ~ (v0 = 0) & s_col(gamma, alpha, beta) = % 93.00/14.36 | | | | | | | | v0)) % 93.00/14.36 | | | | | | | | % 93.00/14.36 | | | | | | | | GROUND_INST: instantiating (aSatz7_4a) with all_132_1, % 93.00/14.36 | | | | | | | | all_132_2, all_139_0, simplifying with (29), (30), % 93.00/14.36 | | | | | | | | (42) gives: % 93.00/14.36 | | | | | | | | (86) s_m(all_132_1, all_132_2, all_139_0) = 0 % 93.00/14.37 | | | | | | | | % 93.00/14.37 | | | | | | | | GROUND_INST: instantiating (aSatz7_7) with all_132_2, all_132_1, % 93.00/14.37 | | | | | | | | all_139_0, simplifying with (29), (30), (42) gives: % 93.00/14.37 | | | | | | | | (87) s(all_132_2, all_139_0) = all_132_1 % 93.00/14.37 | | | | | | | | % 93.00/14.37 | | | | | | | | DELTA: instantiating (82) with fresh symbol all_355_0 gives: % 93.00/14.37 | | | | | | | | (88) isomidpoint(all_132_1, all_139_0, all_132_3) = all_355_0 % 93.00/14.37 | | | | | | | | & s_m(all_132_1, all_355_0, all_139_0) = 0 & % 93.00/14.37 | | | | | | | | $i(all_355_0) % 93.00/14.37 | | | | | | | | % 93.00/14.37 | | | | | | | | ALPHA: (88) implies: % 93.00/14.37 | | | | | | | | (89) $i(all_355_0) % 93.00/14.37 | | | | | | | | (90) s_m(all_132_1, all_355_0, all_139_0) = 0 % 93.00/14.37 | | | | | | | | % 93.00/14.37 | | | | | | | | BETA: splitting (84) gives: % 93.00/14.37 | | | | | | | | % 93.00/14.37 | | | | | | | | Case 1: % 93.00/14.37 | | | | | | | | | % 93.00/14.37 | | | | | | | | | (91) all_255_0 = 0 % 93.00/14.37 | | | | | | | | | % 93.00/14.37 | | | | | | | | | REDUCE: (67), (91) imply: % 93.00/14.37 | | | | | | | | | (92) $false % 93.00/14.37 | | | | | | | | | % 93.00/14.37 | | | | | | | | | CLOSE: (92) is inconsistent. % 93.00/14.37 | | | | | | | | | % 93.00/14.37 | | | | | | | | Case 2: % 93.00/14.37 | | | | | | | | | % 93.00/14.37 | | | | | | | | | (93) ? [v0: int] : ( ~ (v0 = 0) & s_e(all_132_3, % 93.00/14.37 | | | | | | | | | all_132_1, all_132_1, all_255_1) = v0) % 93.00/14.37 | | | | | | | | | % 93.00/14.37 | | | | | | | | | DELTA: instantiating (93) with fresh symbol all_551_0 gives: % 93.00/14.37 | | | | | | | | | (94) ~ (all_551_0 = 0) & s_e(all_132_3, all_132_1, % 93.00/14.37 | | | | | | | | | all_132_1, all_255_1) = all_551_0 % 93.00/14.37 | | | | | | | | | % 93.00/14.37 | | | | | | | | | ALPHA: (94) implies: % 93.00/14.37 | | | | | | | | | (95) ~ (all_551_0 = 0) % 93.00/14.37 | | | | | | | | | (96) s_e(all_132_3, all_132_1, all_132_1, all_255_1) = % 93.00/14.37 | | | | | | | | | all_551_0 % 93.00/14.37 | | | | | | | | | % 93.00/14.37 | | | | | | | | | BETA: splitting (85) gives: % 93.00/14.37 | | | | | | | | | % 93.00/14.37 | | | | | | | | | Case 1: % 93.00/14.37 | | | | | | | | | | % 93.00/14.37 | | | | | | | | | | (97) gamma = beta % 93.00/14.37 | | | | | | | | | | % 93.00/14.37 | | | | | | | | | | REDUCE: (6), (97) imply: % 93.00/14.37 | | | | | | | | | | (98) $false % 93.00/14.37 | | | | | | | | | | % 93.00/14.37 | | | | | | | | | | CLOSE: (98) is inconsistent. % 93.00/14.37 | | | | | | | | | | % 93.00/14.37 | | | | | | | | | Case 2: % 93.00/14.37 | | | | | | | | | | % 93.00/14.37 | | | | | | | | | | (99) all_179_0 = 0 | ? [v0: int] : ? [v1: int] : (( ~ % 93.00/14.37 | | | | | | | | | | (v1 = 0) & s_e(alpha, gamma, alpha, beta) = v1) % 93.00/14.37 | | | | | | | | | | | ( ~ (v0 = 0) & s_col(gamma, alpha, beta) = v0)) % 93.00/14.37 | | | | | | | | | | % 93.00/14.37 | | | | | | | | | | BETA: splitting (99) gives: % 93.00/14.37 | | | | | | | | | | % 93.00/14.37 | | | | | | | | | | Case 1: % 93.00/14.37 | | | | | | | | | | | % 93.00/14.37 | | | | | | | | | | | (100) all_179_0 = 0 % 93.00/14.37 | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | REDUCE: (47), (100) imply: % 93.13/14.37 | | | | | | | | | | | (101) $false % 93.13/14.37 | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | CLOSE: (101) is inconsistent. % 93.13/14.37 | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | Case 2: % 93.13/14.37 | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | GROUND_INST: instantiating (2) with all_132_3, all_132_1, % 93.13/14.37 | | | | | | | | | | | all_139_0, all_132_3, all_132_1, all_255_1, % 93.13/14.37 | | | | | | | | | | | all_551_0, simplifying with (28), (30), (40), % 93.13/14.37 | | | | | | | | | | | (68), (83), (96) gives: % 93.13/14.37 | | | | | | | | | | | (102) all_551_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 93.13/14.37 | | | | | | | | | | | s_e(all_139_0, all_132_3, all_132_1, all_255_1) % 93.13/14.37 | | | | | | | | | | | = v0) % 93.13/14.37 | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | GROUND_INST: instantiating (aSatz7_17) with all_132_1, % 93.13/14.37 | | | | | | | | | | | all_132_2, all_139_0, all_355_0, simplifying with % 93.13/14.37 | | | | | | | | | | | (29), (30), (40), (86), (89), (90) gives: % 93.13/14.37 | | | | | | | | | | | (103) all_355_0 = all_132_2 % 93.13/14.37 | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | BETA: splitting (102) gives: % 93.13/14.37 | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | Case 1: % 93.13/14.37 | | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | | (104) all_551_0 = 0 % 93.13/14.37 | | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | | REDUCE: (95), (104) imply: % 93.13/14.37 | | | | | | | | | | | | (105) $false % 93.13/14.37 | | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | | CLOSE: (105) is inconsistent. % 93.13/14.37 | | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | Case 2: % 93.13/14.37 | | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | | (106) ? [v0: int] : ( ~ (v0 = 0) & s_e(all_139_0, % 93.13/14.37 | | | | | | | | | | | | all_132_3, all_132_1, all_255_1) = v0) % 93.13/14.37 | | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | | DELTA: instantiating (106) with fresh symbol all_845_0 % 93.13/14.37 | | | | | | | | | | | | gives: % 93.13/14.37 | | | | | | | | | | | | (107) ~ (all_845_0 = 0) & s_e(all_139_0, all_132_3, % 93.13/14.37 | | | | | | | | | | | | all_132_1, all_255_1) = all_845_0 % 93.13/14.37 | | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | | ALPHA: (107) implies: % 93.13/14.37 | | | | | | | | | | | | (108) ~ (all_845_0 = 0) % 93.13/14.37 | | | | | | | | | | | | (109) s_e(all_139_0, all_132_3, all_132_1, all_255_1) = % 93.13/14.37 | | | | | | | | | | | | all_845_0 % 93.13/14.37 | | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | | GROUND_INST: instantiating (aSatz7_13) with all_139_0, % 93.13/14.37 | | | | | | | | | | | | all_132_3, all_132_2, all_132_1, all_255_1, % 93.13/14.37 | | | | | | | | | | | | all_845_0, simplifying with (28), (29), (40), % 93.13/14.37 | | | | | | | | | | | | (70), (87), (109) gives: % 93.13/14.37 | | | | | | | | | | | | (110) all_845_0 = 0 % 93.13/14.37 | | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | | REDUCE: (108), (110) imply: % 93.13/14.37 | | | | | | | | | | | | (111) $false % 93.13/14.37 | | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | | CLOSE: (111) is inconsistent. % 93.13/14.37 | | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | | End of split % 93.13/14.37 | | | | | | | | | | | % 93.13/14.37 | | | | | | | | | | End of split % 93.13/14.37 | | | | | | | | | | % 93.13/14.37 | | | | | | | | | End of split % 93.13/14.37 | | | | | | | | | % 93.13/14.37 | | | | | | | | End of split % 93.13/14.37 | | | | | | | | % 93.13/14.37 | | | | | | | End of split % 93.13/14.37 | | | | | | | % 93.13/14.37 | | | | | | End of split % 93.13/14.37 | | | | | | % 93.13/14.37 | | | | | End of split % 93.13/14.37 | | | | | % 93.13/14.37 | | | | End of split % 93.13/14.37 | | | | % 93.13/14.37 | | | End of split % 93.13/14.37 | | | % 93.13/14.37 | | End of split % 93.13/14.37 | | % 93.13/14.37 | End of split % 93.13/14.37 | % 93.13/14.37 End of proof % 93.13/14.37 % SZS output end Proof for theBenchmark % 93.13/14.38 % 93.13/14.38 13776ms %------------------------------------------------------------------------------