%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWW624_2 : TPTP v8.1.2. Released v6.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n018.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 : Fri Sep 1 00:50:56 EDT 2023 % Result : Theorem 26.00s 4.37s % Output : Proof 66.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWW624_2 : TPTP v8.1.2. Released v6.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n018.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 : Sun Aug 27 20:14:31 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.65 ________ _____ % 0.20/0.65 ___ __ \_________(_)________________________________ % 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.65 % 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.65 (2023-06-19) % 0.20/0.65 % 0.20/0.65 (c) Philipp Rümmer, 2009-2023 % 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.65 Amanda Stjerna. % 0.20/0.65 Free software under BSD-3-Clause. % 0.20/0.65 % 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.65 % 0.20/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.67 Running up to 7 provers in parallel. % 0.20/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 5.17/1.49 Prover 4: Preprocessing ... % 5.17/1.49 Prover 3: Preprocessing ... % 5.17/1.49 Prover 0: Preprocessing ... % 5.17/1.49 Prover 6: Preprocessing ... % 5.17/1.49 Prover 2: Preprocessing ... % 5.17/1.49 Prover 5: Preprocessing ... % 5.17/1.50 Prover 1: Preprocessing ... % 12.06/2.46 Prover 1: Warning: ignoring some quantifiers % 13.01/2.56 Prover 1: Constructing countermodel ... % 13.01/2.57 Prover 6: Proving ... % 13.01/2.63 Prover 3: Warning: ignoring some quantifiers % 13.01/2.64 Prover 5: Proving ... % 13.01/2.65 Prover 3: Constructing countermodel ... % 13.01/2.67 Prover 4: Warning: ignoring some quantifiers % 13.84/2.72 Prover 2: Proving ... % 13.84/2.73 Prover 4: Constructing countermodel ... % 13.84/2.74 Prover 0: Proving ... % 26.00/4.37 Prover 0: proved (3693ms) % 26.00/4.37 % 26.00/4.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 26.00/4.37 % 26.00/4.37 Prover 3: stopped % 26.00/4.37 Prover 2: stopped % 26.46/4.37 Prover 5: stopped % 26.46/4.38 Prover 6: stopped % 26.46/4.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 26.46/4.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 26.46/4.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 26.46/4.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 26.46/4.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 27.56/4.61 Prover 13: Preprocessing ... % 27.56/4.62 Prover 11: Preprocessing ... % 27.56/4.65 Prover 8: Preprocessing ... % 27.56/4.72 Prover 10: Preprocessing ... % 28.73/4.73 Prover 7: Preprocessing ... % 30.16/4.96 Prover 10: Warning: ignoring some quantifiers % 30.88/4.97 Prover 8: Warning: ignoring some quantifiers % 30.88/4.98 Prover 10: Constructing countermodel ... % 31.10/5.00 Prover 8: Constructing countermodel ... % 31.10/5.02 Prover 13: Warning: ignoring some quantifiers % 31.37/5.04 Prover 13: Constructing countermodel ... % 31.37/5.06 Prover 11: Warning: ignoring some quantifiers % 31.37/5.07 Prover 7: Warning: ignoring some quantifiers % 31.37/5.08 Prover 11: Constructing countermodel ... % 31.95/5.11 Prover 7: Constructing countermodel ... % 33.41/5.40 Prover 10: gave up % 33.41/5.40 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 35.15/5.53 Prover 16: Preprocessing ... % 36.24/5.72 Prover 16: Warning: ignoring some quantifiers % 36.69/5.73 Prover 16: Constructing countermodel ... % 57.18/8.53 Prover 13: gave up % 57.18/8.54 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 57.18/8.62 Prover 19: Preprocessing ... % 59.13/8.82 Prover 19: Warning: ignoring some quantifiers % 59.13/8.84 Prover 19: Constructing countermodel ... % 65.53/9.71 Prover 7: Found proof (size 168) % 65.53/9.71 Prover 7: proved (5336ms) % 65.53/9.71 Prover 8: stopped % 65.53/9.72 Prover 1: stopped % 65.53/9.72 Prover 11: stopped % 65.53/9.72 Prover 4: stopped % 65.53/9.72 Prover 19: stopped % 65.53/9.72 Prover 16: stopped % 65.53/9.72 % 65.53/9.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 65.53/9.72 % 66.34/9.73 % SZS output start Proof for theBenchmark % 66.34/9.74 Assumptions after simplification: % 66.34/9.74 --------------------------------- % 66.34/9.74 % 66.34/9.74 (infix_plpl_def) % 66.34/9.75 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : ! % 66.34/9.75 [v5: uni] : ( ~ (infix_plpl(v0, v4, v1) = v5) | ~ (cons(v0, v2, v3) = v4) | % 66.34/9.75 ~ ty(v0) | ~ uni(v3) | ~ uni(v2) | ~ uni(v1) | ? [v6: uni] : % 66.34/9.75 (infix_plpl(v0, v3, v1) = v6 & cons(v0, v2, v6) = v5 & uni(v6) & uni(v5))) & % 66.34/9.75 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : ! % 66.34/9.75 [v5: uni] : ( ~ (infix_plpl(v0, v3, v1) = v4) | ~ (cons(v0, v2, v4) = v5) | % 66.34/9.76 ~ ty(v0) | ~ uni(v3) | ~ uni(v2) | ~ uni(v1) | ? [v6: uni] : % 66.34/9.76 (infix_plpl(v0, v6, v1) = v5 & cons(v0, v2, v3) = v6 & uni(v6) & uni(v5))) & % 66.34/9.76 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : (v3 = v1 | ~ % 66.34/9.76 (infix_plpl(v0, v2, v1) = v3) | ~ (nil(v0) = v2) | ~ ty(v0) | ~ uni(v1)) % 66.34/9.76 % 66.34/9.76 (length_def) % 66.34/9.76 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ( ~ (cons(v0, v1, % 66.34/9.76 v2) = v3) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v4: int] : % 66.34/9.76 (length(v0, v3) = v4 & length(v0, v2) = $sum(v4, -1))) & ! [v0: ty] : ! % 66.34/9.76 [v1: uni] : ( ~ (nil(v0) = v1) | ~ ty(v0) | length(v0, v1) = 0) % 66.34/9.76 % 66.34/9.76 (length_nonnegative) % 66.34/9.76 ! [v0: ty] : ! [v1: uni] : ! [v2: int] : ( ~ ($lesseq(v2, -1)) | ~ % 66.34/9.76 (length(v0, v1) = v2) | ~ ty(v0) | ~ uni(v1)) % 66.34/9.76 % 66.34/9.76 (nil_sort) % 66.34/9.76 ! [v0: ty] : ! [v1: ty] : ( ~ (list(v0) = v1) | ~ ty(v0) | ? [v2: uni] : % 66.34/9.76 (nil(v0) = v2 & uni(v2) & sort(v1, v2))) & ! [v0: ty] : ! [v1: uni] : ( ~ % 66.34/9.76 (nil(v0) = v1) | ~ ty(v0) | ? [v2: ty] : (list(v0) = v2 & ty(v2) & % 66.34/9.76 sort(v2, v1))) % 66.34/9.76 % 66.34/9.76 (permut_append_swap) % 66.34/9.76 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ( ~ (infix_plpl(v0, % 66.34/9.76 v2, v1) = v3) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v4: uni] : % 66.34/9.76 (infix_plpl(v0, v1, v2) = v4 & uni(v4) & permut(v0, v4, v3))) & ! [v0: ty] % 66.34/9.76 : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ( ~ (infix_plpl(v0, v1, v2) = % 66.34/9.76 v3) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v4: uni] : (infix_plpl(v0, % 66.34/9.76 v2, v1) = v4 & uni(v4) & permut(v0, v3, v4))) % 66.34/9.76 % 66.34/9.76 (permut_assoc) % 66.34/9.77 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : ! % 66.34/9.77 [v5: uni] : ( ~ (infix_plpl(v0, v4, v3) = v5) | ~ (infix_plpl(v0, v1, v2) = % 66.34/9.77 v4) | ~ ty(v0) | ~ uni(v3) | ~ uni(v2) | ~ uni(v1) | ? [v6: uni] : ? % 66.34/9.77 [v7: uni] : (infix_plpl(v0, v2, v3) = v6 & infix_plpl(v0, v1, v6) = v7 & % 66.34/9.77 uni(v7) & uni(v6) & permut(v0, v5, v7))) & ! [v0: ty] : ! [v1: uni] : ! % 66.34/9.77 [v2: uni] : ! [v3: uni] : ! [v4: uni] : ! [v5: uni] : ( ~ (infix_plpl(v0, % 66.34/9.77 v2, v3) = v4) | ~ (infix_plpl(v0, v1, v4) = v5) | ~ ty(v0) | ~ % 66.34/9.77 uni(v3) | ~ uni(v2) | ~ uni(v1) | ? [v6: uni] : ? [v7: uni] : % 66.34/9.77 (infix_plpl(v0, v6, v3) = v7 & infix_plpl(v0, v1, v2) = v6 & uni(v7) & % 66.34/9.77 uni(v6) & permut(v0, v7, v5))) % 66.34/9.77 % 66.34/9.77 (permut_cons) % 66.34/9.77 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : ! % 66.34/9.77 [v5: uni] : ( ~ (cons(v0, v1, v3) = v5) | ~ (cons(v0, v1, v2) = v4) | ~ % 66.34/9.77 ty(v0) | ~ uni(v3) | ~ uni(v2) | ~ uni(v1) | ~ permut(v0, v2, v3) | % 66.34/9.77 permut(v0, v4, v5)) % 66.34/9.77 % 66.34/9.77 (permut_prefix) % 66.34/9.77 ty(elt1) & ? [v0: uni] : ? [v1: int] : ? [v2: uni] : ? [v3: elt] : ? [v4: % 66.34/9.77 list_elt] : ? [v5: uni] : ? [v6: int] : ? [v7: uni] : ? [v8: uni] : ? % 66.34/9.77 [v9: uni] : ? [v10: int] : ? [v11: uni] : (list_elt(v4) & elt(v3) & % 66.34/9.77 ((prefix(elt1, v10, v9) = v11 & prefix(elt1, v6, v5) = v7 & t2tb1(v3) = v8 & % 66.34/9.77 t2tb(v4) = v5 & length(elt1, v9) = v10 & length(elt1, v5) = v6 & % 66.34/9.77 cons(elt1, v8, v5) = v9 & uni(v11) & uni(v9) & uni(v8) & uni(v7) & % 66.34/9.77 uni(v5) & permut(elt1, v7, v5) & ~ permut(elt1, v11, v9)) | % 66.34/9.77 (prefix(elt1, v1, v0) = v2 & length(elt1, v0) = v1 & nil(elt1) = v0 & % 66.34/9.77 uni(v2) & uni(v0) & ~ permut(elt1, v2, v0)))) % 66.34/9.77 % 66.34/9.77 (prefix_append) % 66.34/9.77 ! [v0: ty] : ! [v1: int] : ! [v2: uni] : ! [v3: uni] : ! [v4: int] : ! % 66.34/9.77 [v5: uni] : ( ~ ($lesseq(v4, v1)) | ~ (prefix(v0, $difference(v1, v4), v3) = % 66.34/9.77 v5) | ~ (length(v0, v2) = v4) | ~ ty(v0) | ~ uni(v3) | ~ uni(v2) | ? % 66.34/9.77 [v6: int] : ? [v7: uni] : ? [v8: uni] : ? [v9: uni] : ? [v10: uni] : % 66.34/9.77 ((v10 = v8 & prefix(v0, v4, v2) = v9 & prefix(v0, v1, v7) = v8 & % 66.34/9.77 infix_plpl(v0, v9, v5) = v8 & infix_plpl(v0, v2, v3) = v7 & uni(v9) & % 66.34/9.77 uni(v8) & uni(v7)) | ($lesseq(1, $sum($difference($product(-1, v6), v4), % 66.34/9.77 v1)) & length(v0, v3) = v6))) & ! [v0: ty] : ! [v1: int] : ! [v2: % 66.34/9.77 uni] : ! [v3: uni] : ! [v4: uni] : ! [v5: uni] : ( ~ (prefix(v0, v1, v4) % 66.34/9.77 = v5) | ~ (infix_plpl(v0, v2, v3) = v4) | ~ ty(v0) | ~ uni(v3) | ~ % 66.34/9.77 uni(v2) | ? [v6: int] : ? [v7: int] : ? [v8: uni] : ? [v9: uni] : ? % 66.34/9.77 [v10: uni] : (length(v0, v2) = v6 & ( ~ ($lesseq(v6, v1)) | (v10 = v5 & % 66.34/9.77 prefix(v0, $difference(v1, v6), v3) = v9 & prefix(v0, v6, v2) = v8 & % 66.34/9.77 infix_plpl(v0, v8, v9) = v5 & uni(v9) & uni(v8) & uni(v5)) | % 66.34/9.77 ($lesseq(1, $sum($difference($product(-1, v7), v6), v1)) & length(v0, % 66.34/9.77 v3) = v7)))) % 66.34/9.77 % 66.34/9.77 (prefix_def1) % 66.34/9.77 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ( ~ (prefix(v0, 0, v1) = v2) | ~ % 66.34/9.77 ty(v0) | ~ uni(v1) | (nil(v0) = v2 & uni(v2))) % 66.34/9.77 % 66.34/9.77 (prefix_def2) % 66.34/9.78 ! [v0: ty] : ! [v1: int] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : ! % 66.34/9.78 [v5: uni] : ( ~ ($lesseq(1, v1)) | ~ (prefix(v0, $sum(v1, -1), v3) = v4) | ~ % 66.34/9.78 (cons(v0, v2, v4) = v5) | ~ ty(v0) | ~ uni(v3) | ~ uni(v2) | ? [v6: uni] % 66.34/9.78 : (prefix(v0, v1, v6) = v5 & cons(v0, v2, v3) = v6 & uni(v6) & uni(v5))) & % 66.34/9.78 ! [v0: ty] : ! [v1: int] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : ! % 66.34/9.78 [v5: uni] : ( ~ ($lesseq(1, v1)) | ~ (prefix(v0, v1, v4) = v5) | ~ (cons(v0, % 66.34/9.78 v2, v3) = v4) | ~ ty(v0) | ~ uni(v3) | ~ uni(v2) | ? [v6: uni] : % 66.34/9.78 (prefix(v0, $sum(v1, -1), v3) = v6 & cons(v0, v2, v6) = v5 & uni(v6) & % 66.34/9.78 uni(v5))) % 66.34/9.78 % 66.34/9.78 (sorted_Nil) % 66.34/9.78 ty(elt1) & ? [v0: uni] : ? [v1: list_elt] : (tb2t(v0) = v1 & nil(elt1) = v0 % 66.34/9.78 & list_elt(v1) & uni(v0) & sorted(v1)) % 66.34/9.78 % 66.34/9.78 (sorted_One) % 66.34/9.78 ty(elt1) & ? [v0: uni] : (nil(elt1) = v0 & uni(v0) & ! [v1: elt] : ! [v2: % 66.34/9.78 uni] : ( ~ (t2tb1(v1) = v2) | ~ elt(v1) | ? [v3: uni] : ? [v4: % 66.34/9.78 list_elt] : (tb2t(v3) = v4 & cons(elt1, v2, v0) = v3 & list_elt(v4) & % 66.34/9.78 uni(v3) & sorted(v4)))) % 66.34/9.78 % 66.34/9.78 (sorted_inversion) % 66.34/9.78 ty(elt1) & ? [v0: uni] : ? [v1: list_elt] : (tb2t(v0) = v1 & nil(elt1) = v0 % 66.34/9.78 & list_elt(v1) & uni(v0) & ! [v2: list_elt] : (v2 = v1 | ~ list_elt(v2) | % 66.34/9.78 ~ sorted(v2) | ? [v3: elt] : ? [v4: elt] : ? [v5: list_elt] : ? [v6: % 66.34/9.78 uni] : ? [v7: uni] : ? [v8: uni] : ? [v9: list_elt] : ? [v10: uni] : % 66.34/9.78 ? [v11: uni] : ? [v12: list_elt] : ? [v13: elt] : ? [v14: uni] : ? % 66.34/9.78 [v15: uni] : ? [v16: list_elt] : (list_elt(v5) & elt(v13) & elt(v4) & % 66.34/9.78 elt(v3) & ((v16 = v2 & t2tb1(v13) = v14 & tb2t(v15) = v2 & cons(elt1, % 66.34/9.78 v14, v0) = v15 & uni(v15) & uni(v14)) | (v12 = v2 & t2tb1(v4) = v6 % 66.34/9.78 & t2tb1(v3) = v10 & tb2t(v11) = v2 & tb2t(v8) = v9 & t2tb(v5) = v7 & % 66.34/9.78 cons(elt1, v10, v8) = v11 & cons(elt1, v6, v7) = v8 & list_elt(v9) & % 66.34/9.78 uni(v11) & uni(v10) & uni(v8) & uni(v7) & uni(v6) & sorted(v9) & % 66.34/9.78 le(v3, v4)))))) % 66.34/9.78 % 66.34/9.78 (t2tb_sort) % 66.34/9.78 ty(elt1) & ? [v0: ty] : (list(elt1) = v0 & ty(v0) & ! [v1: list_elt] : ! % 66.34/9.78 [v2: uni] : ( ~ (t2tb(v1) = v2) | ~ list_elt(v1) | sort(v0, v2))) % 66.34/9.78 % 66.34/9.78 (function-axioms) % 66.34/9.79 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : ! % 66.34/9.79 [v5: ty] : ! [v6: ty] : (v1 = v0 | ~ (match_list(v6, v5, v4, v3, v2) = v1) | % 66.34/9.79 ~ (match_list(v6, v5, v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! % 66.34/9.79 [v2: uni] : ! [v3: uni] : ! [v4: bool] : ! [v5: ty] : (v1 = v0 | ~ % 66.34/9.79 (match_bool(v5, v4, v3, v2) = v1) | ~ (match_bool(v5, v4, v3, v2) = v0)) & % 66.34/9.79 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: ty] : (v1 = % 66.34/9.79 v0 | ~ (prefix(v4, v3, v2) = v1) | ~ (prefix(v4, v3, v2) = v0)) & ! [v0: % 66.34/9.79 uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : (v1 = v0 | % 66.34/9.79 ~ (rev_append(v4, v3, v2) = v1) | ~ (rev_append(v4, v3, v2) = v0)) & ! % 66.34/9.79 [v0: int] : ! [v1: int] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : (v1 = % 66.34/9.79 v0 | ~ (num_occ(v4, v3, v2) = v1) | ~ (num_occ(v4, v3, v2) = v0)) & ! % 66.34/9.79 [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : (v1 = % 66.34/9.79 v0 | ~ (infix_plpl(v4, v3, v2) = v1) | ~ (infix_plpl(v4, v3, v2) = v0)) & % 66.34/9.79 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : (v1 = % 66.34/9.79 v0 | ~ (cons(v4, v3, v2) = v1) | ~ (cons(v4, v3, v2) = v0)) & ! [v0: int] % 66.34/9.79 : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~ (div(v3, v2) = % 66.34/9.79 v1) | ~ (div(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] % 66.34/9.79 : ! [v3: int] : (v1 = v0 | ~ (mod(v3, v2) = v1) | ~ (mod(v3, v2) = v0)) & % 66.34/9.79 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ % 66.34/9.79 (reverse(v3, v2) = v1) | ~ (reverse(v3, v2) = v0)) & ! [v0: int] : ! [v1: % 66.34/9.79 int] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (length(v3, v2) = v1) | ~ % 66.34/9.79 (length(v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! % 66.34/9.79 [v3: ty] : (v1 = v0 | ~ (cons_proj_2(v3, v2) = v1) | ~ (cons_proj_2(v3, v2) % 66.34/9.79 = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = % 66.34/9.79 v0 | ~ (cons_proj_1(v3, v2) = v1) | ~ (cons_proj_1(v3, v2) = v0)) & ! % 66.34/9.79 [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (abs(v2) = v1) | ~ % 66.34/9.79 (abs(v2) = v0)) & ! [v0: elt] : ! [v1: elt] : ! [v2: uni] : (v1 = v0 | ~ % 66.34/9.79 (tb2t1(v2) = v1) | ~ (tb2t1(v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! % 66.34/9.79 [v2: elt] : (v1 = v0 | ~ (t2tb1(v2) = v1) | ~ (t2tb1(v2) = v0)) & ! [v0: % 66.34/9.79 list_elt] : ! [v1: list_elt] : ! [v2: uni] : (v1 = v0 | ~ (tb2t(v2) = v1) % 66.34/9.79 | ~ (tb2t(v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: list_elt] : % 66.34/9.79 (v1 = v0 | ~ (t2tb(v2) = v1) | ~ (t2tb(v2) = v0)) & ! [v0: ty] : ! [v1: % 66.34/9.79 ty] : ! [v2: ty] : (v1 = v0 | ~ (list(v2) = v1) | ~ (list(v2) = v0)) & ! % 66.34/9.79 [v0: uni] : ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~ (nil(v2) = v1) | ~ % 66.34/9.79 (nil(v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~ % 66.34/9.79 (witness(v2) = v1) | ~ (witness(v2) = v0)) % 66.34/9.79 % 66.34/9.79 Further assumptions not needed in the proof: % 66.34/9.79 -------------------------------------------- % 66.34/9.79 abs_def, abs_le, abs_pos, append_Num_Occ, append_assoc, append_l_nil, % 66.34/9.79 append_length, bool_inversion, bridgeL, bridgeL1, bridgeR, bridgeR1, % 66.34/9.79 compatOrderMult, cons_proj_1_def, cons_proj_1_sort, cons_proj_2_def, % 66.34/9.79 cons_proj_2_sort, cons_sort, div_1, div_bound, div_inf, div_mod, div_mult, % 66.34/9.79 div_sign_neg, div_sign_pos, infix_plpl_sort, length_nil, list_inversion, % 66.34/9.79 match_bool_False, match_bool_True, match_bool_sort, match_list_Cons, % 66.34/9.79 match_list_Nil, match_list_sort, mem_Num_Occ, mem_append, mem_decomp, mem_def, % 66.34/9.79 mod_1, mod_bound, mod_inf, mod_mult, mod_sign_neg, mod_sign_pos, nil_Cons, % 66.34/9.79 num_occ_def, permut_append, permut_cons_append, permut_def, permut_length, % 66.34/9.79 permut_mem, permut_refl, permut_swap, permut_sym, permut_trans, prefix_length, % 66.34/9.79 prefix_sort, refl, rev_append_append_l, rev_append_append_r, rev_append_def, % 66.34/9.79 rev_append_def1, rev_append_length, rev_append_sort, reverse_append, % 66.34/9.79 reverse_cons, reverse_def, reverse_length, reverse_mem, reverse_num_occ, % 66.34/9.79 reverse_reverse, reverse_sort, rounds_toward_zero, sorted_Two, sorted_append, % 66.34/9.79 sorted_mem, sorted_rev_append, sorted_reverse_cons, sorted_reverse_cons2, % 66.34/9.79 sorted_reverse_mem, t2tb_sort1, total, trans, true_False, tuple0_inversion, % 66.34/9.79 witness_sort % 66.34/9.79 % 66.34/9.79 Those formulas are unsatisfiable: % 66.34/9.79 --------------------------------- % 66.34/9.79 % 66.34/9.79 Begin of proof % 66.34/9.79 | % 66.34/9.79 | ALPHA: (nil_sort) implies: % 66.34/9.79 | (1) ! [v0: ty] : ! [v1: ty] : ( ~ (list(v0) = v1) | ~ ty(v0) | ? [v2: % 66.34/9.79 | uni] : (nil(v0) = v2 & uni(v2) & sort(v1, v2))) % 66.34/9.79 | % 66.34/9.79 | ALPHA: (length_def) implies: % 66.34/9.79 | (2) ! [v0: ty] : ! [v1: uni] : ( ~ (nil(v0) = v1) | ~ ty(v0) | % 66.34/9.79 | length(v0, v1) = 0) % 66.34/9.79 | (3) ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ( ~ % 66.34/9.79 | (cons(v0, v1, v2) = v3) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? % 66.34/9.79 | [v4: int] : (length(v0, v3) = v4 & length(v0, v2) = $sum(v4, -1))) % 66.34/9.79 | % 66.34/9.79 | ALPHA: (infix_plpl_def) implies: % 66.34/9.80 | (4) ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : (v3 = v1 | % 66.34/9.80 | ~ (infix_plpl(v0, v2, v1) = v3) | ~ (nil(v0) = v2) | ~ ty(v0) | ~ % 66.34/9.80 | uni(v1)) % 66.34/9.80 | % 66.34/9.80 | ALPHA: (permut_assoc) implies: % 66.34/9.80 | (5) ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] % 66.34/9.80 | : ! [v5: uni] : ( ~ (infix_plpl(v0, v2, v3) = v4) | ~ (infix_plpl(v0, % 66.34/9.80 | v1, v4) = v5) | ~ ty(v0) | ~ uni(v3) | ~ uni(v2) | ~ uni(v1) % 66.34/9.80 | | ? [v6: uni] : ? [v7: uni] : (infix_plpl(v0, v6, v3) = v7 & % 66.34/9.80 | infix_plpl(v0, v1, v2) = v6 & uni(v7) & uni(v6) & permut(v0, v7, % 66.34/9.80 | v5))) % 66.34/9.80 | (6) ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] % 66.34/9.80 | : ! [v5: uni] : ( ~ (infix_plpl(v0, v4, v3) = v5) | ~ (infix_plpl(v0, % 66.34/9.80 | v1, v2) = v4) | ~ ty(v0) | ~ uni(v3) | ~ uni(v2) | ~ uni(v1) % 66.34/9.80 | | ? [v6: uni] : ? [v7: uni] : (infix_plpl(v0, v2, v3) = v6 & % 66.34/9.80 | infix_plpl(v0, v1, v6) = v7 & uni(v7) & uni(v6) & permut(v0, v5, % 66.34/9.80 | v7))) % 66.34/9.80 | % 66.34/9.80 | ALPHA: (permut_append_swap) implies: % 66.34/9.80 | (7) ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ( ~ % 66.34/9.80 | (infix_plpl(v0, v1, v2) = v3) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | % 66.34/9.80 | ? [v4: uni] : (infix_plpl(v0, v2, v1) = v4 & uni(v4) & permut(v0, % 66.34/9.80 | v3, v4))) % 66.34/9.80 | (8) ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ( ~ % 66.34/9.80 | (infix_plpl(v0, v2, v1) = v3) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | % 66.34/9.80 | ? [v4: uni] : (infix_plpl(v0, v1, v2) = v4 & uni(v4) & permut(v0, % 66.34/9.80 | v4, v3))) % 66.34/9.80 | % 66.34/9.80 | ALPHA: (t2tb_sort) implies: % 66.34/9.80 | (9) ? [v0: ty] : (list(elt1) = v0 & ty(v0) & ! [v1: list_elt] : ! [v2: % 66.34/9.80 | uni] : ( ~ (t2tb(v1) = v2) | ~ list_elt(v1) | sort(v0, v2))) % 66.34/9.80 | % 66.34/9.80 | ALPHA: (sorted_Nil) implies: % 66.34/9.80 | (10) ? [v0: uni] : ? [v1: list_elt] : (tb2t(v0) = v1 & nil(elt1) = v0 & % 66.34/9.80 | list_elt(v1) & uni(v0) & sorted(v1)) % 66.34/9.80 | % 66.34/9.80 | ALPHA: (sorted_One) implies: % 66.34/9.80 | (11) ? [v0: uni] : (nil(elt1) = v0 & uni(v0) & ! [v1: elt] : ! [v2: uni] % 66.34/9.80 | : ( ~ (t2tb1(v1) = v2) | ~ elt(v1) | ? [v3: uni] : ? [v4: % 66.34/9.80 | list_elt] : (tb2t(v3) = v4 & cons(elt1, v2, v0) = v3 & % 66.34/9.80 | list_elt(v4) & uni(v3) & sorted(v4)))) % 66.34/9.80 | % 66.34/9.80 | ALPHA: (sorted_inversion) implies: % 66.34/9.80 | (12) ? [v0: uni] : ? [v1: list_elt] : (tb2t(v0) = v1 & nil(elt1) = v0 & % 66.34/9.80 | list_elt(v1) & uni(v0) & ! [v2: list_elt] : (v2 = v1 | ~ % 66.34/9.81 | list_elt(v2) | ~ sorted(v2) | ? [v3: elt] : ? [v4: elt] : ? % 66.34/9.81 | [v5: list_elt] : ? [v6: uni] : ? [v7: uni] : ? [v8: uni] : ? % 66.34/9.81 | [v9: list_elt] : ? [v10: uni] : ? [v11: uni] : ? [v12: % 66.34/9.81 | list_elt] : ? [v13: elt] : ? [v14: uni] : ? [v15: uni] : ? % 66.34/9.81 | [v16: list_elt] : (list_elt(v5) & elt(v13) & elt(v4) & elt(v3) & % 66.34/9.81 | ((v16 = v2 & t2tb1(v13) = v14 & tb2t(v15) = v2 & cons(elt1, v14, % 66.34/9.81 | v0) = v15 & uni(v15) & uni(v14)) | (v12 = v2 & t2tb1(v4) = % 66.34/9.81 | v6 & t2tb1(v3) = v10 & tb2t(v11) = v2 & tb2t(v8) = v9 & % 66.34/9.81 | t2tb(v5) = v7 & cons(elt1, v10, v8) = v11 & cons(elt1, v6, % 66.34/9.81 | v7) = v8 & list_elt(v9) & uni(v11) & uni(v10) & uni(v8) & % 66.34/9.81 | uni(v7) & uni(v6) & sorted(v9) & le(v3, v4)))))) % 66.34/9.81 | % 66.34/9.81 | ALPHA: (prefix_def2) implies: % 66.34/9.81 | (13) ! [v0: ty] : ! [v1: int] : ! [v2: uni] : ! [v3: uni] : ! [v4: % 66.34/9.81 | uni] : ! [v5: uni] : ( ~ ($lesseq(1, v1)) | ~ (prefix(v0, v1, v4) % 66.34/9.81 | = v5) | ~ (cons(v0, v2, v3) = v4) | ~ ty(v0) | ~ uni(v3) | ~ % 66.34/9.81 | uni(v2) | ? [v6: uni] : (prefix(v0, $sum(v1, -1), v3) = v6 & % 66.34/9.81 | cons(v0, v2, v6) = v5 & uni(v6) & uni(v5))) % 66.34/9.81 | % 66.34/9.81 | ALPHA: (prefix_append) implies: % 66.34/9.81 | (14) ! [v0: ty] : ! [v1: int] : ! [v2: uni] : ! [v3: uni] : ! [v4: % 66.34/9.81 | int] : ! [v5: uni] : ( ~ ($lesseq(v4, v1)) | ~ (prefix(v0, % 66.34/9.81 | $difference(v1, v4), v3) = v5) | ~ (length(v0, v2) = v4) | ~ % 66.34/9.81 | ty(v0) | ~ uni(v3) | ~ uni(v2) | ? [v6: int] : ? [v7: uni] : ? % 66.34/9.81 | [v8: uni] : ? [v9: uni] : ? [v10: uni] : ((v10 = v8 & prefix(v0, % 66.34/9.81 | v4, v2) = v9 & prefix(v0, v1, v7) = v8 & infix_plpl(v0, v9, % 66.34/9.81 | v5) = v8 & infix_plpl(v0, v2, v3) = v7 & uni(v9) & uni(v8) & % 66.34/9.81 | uni(v7)) | ($lesseq(1, $sum($difference($product(-1, v6), v4), % 66.34/9.81 | v1)) & length(v0, v3) = v6))) % 66.34/9.81 | % 66.34/9.81 | ALPHA: (permut_prefix) implies: % 66.34/9.81 | (15) ty(elt1) % 66.34/9.81 | (16) ? [v0: uni] : ? [v1: int] : ? [v2: uni] : ? [v3: elt] : ? [v4: % 66.34/9.81 | list_elt] : ? [v5: uni] : ? [v6: int] : ? [v7: uni] : ? [v8: % 66.34/9.81 | uni] : ? [v9: uni] : ? [v10: int] : ? [v11: uni] : (list_elt(v4) % 66.34/9.81 | & elt(v3) & ((prefix(elt1, v10, v9) = v11 & prefix(elt1, v6, v5) = % 66.74/9.81 | v7 & t2tb1(v3) = v8 & t2tb(v4) = v5 & length(elt1, v9) = v10 & % 66.74/9.81 | length(elt1, v5) = v6 & cons(elt1, v8, v5) = v9 & uni(v11) & % 66.74/9.81 | uni(v9) & uni(v8) & uni(v7) & uni(v5) & permut(elt1, v7, v5) & % 66.74/9.81 | ~ permut(elt1, v11, v9)) | (prefix(elt1, v1, v0) = v2 & % 66.74/9.81 | length(elt1, v0) = v1 & nil(elt1) = v0 & uni(v2) & uni(v0) & ~ % 66.74/9.81 | permut(elt1, v2, v0)))) % 66.74/9.81 | % 66.74/9.81 | ALPHA: (function-axioms) implies: % 66.74/9.81 | (17) ! [v0: uni] : ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~ (nil(v2) = % 66.74/9.81 | v1) | ~ (nil(v2) = v0)) % 66.74/9.81 | (18) ! [v0: list_elt] : ! [v1: list_elt] : ! [v2: uni] : (v1 = v0 | ~ % 66.74/9.81 | (tb2t(v2) = v1) | ~ (tb2t(v2) = v0)) % 66.74/9.81 | (19) ! [v0: int] : ! [v1: int] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | % 66.74/9.81 | ~ (length(v3, v2) = v1) | ~ (length(v3, v2) = v0)) % 66.74/9.81 | (20) ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: % 66.74/9.81 | ty] : (v1 = v0 | ~ (infix_plpl(v4, v3, v2) = v1) | ~ % 66.74/9.81 | (infix_plpl(v4, v3, v2) = v0)) % 66.74/9.81 | (21) ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: % 66.74/9.81 | ty] : (v1 = v0 | ~ (prefix(v4, v3, v2) = v1) | ~ (prefix(v4, v3, % 66.74/9.81 | v2) = v0)) % 66.74/9.81 | % 66.74/9.81 | DELTA: instantiating (9) with fresh symbol all_108_0 gives: % 66.74/9.82 | (22) list(elt1) = all_108_0 & ty(all_108_0) & ! [v0: list_elt] : ! [v1: % 66.74/9.82 | uni] : ( ~ (t2tb(v0) = v1) | ~ list_elt(v0) | sort(all_108_0, v1)) % 66.74/9.82 | % 66.74/9.82 | ALPHA: (22) implies: % 66.74/9.82 | (23) list(elt1) = all_108_0 % 66.74/9.82 | % 66.74/9.82 | DELTA: instantiating (10) with fresh symbols all_111_0, all_111_1 gives: % 66.74/9.82 | (24) tb2t(all_111_1) = all_111_0 & nil(elt1) = all_111_1 & % 66.74/9.82 | list_elt(all_111_0) & uni(all_111_1) & sorted(all_111_0) % 66.74/9.82 | % 66.74/9.82 | ALPHA: (24) implies: % 66.74/9.82 | (25) nil(elt1) = all_111_1 % 66.74/9.82 | (26) tb2t(all_111_1) = all_111_0 % 66.74/9.82 | % 66.74/9.82 | DELTA: instantiating (11) with fresh symbol all_118_0 gives: % 66.74/9.82 | (27) nil(elt1) = all_118_0 & uni(all_118_0) & ! [v0: elt] : ! [v1: uni] : % 66.74/9.82 | ( ~ (t2tb1(v0) = v1) | ~ elt(v0) | ? [v2: uni] : ? [v3: list_elt] : % 66.74/9.82 | (tb2t(v2) = v3 & cons(elt1, v1, all_118_0) = v2 & list_elt(v3) & % 66.74/9.82 | uni(v2) & sorted(v3))) % 66.74/9.82 | % 66.74/9.82 | ALPHA: (27) implies: % 66.74/9.82 | (28) nil(elt1) = all_118_0 % 66.74/9.82 | % 66.74/9.82 | DELTA: instantiating (16) with fresh symbols all_122_0, all_122_1, all_122_2, % 66.74/9.82 | all_122_3, all_122_4, all_122_5, all_122_6, all_122_7, all_122_8, % 66.74/9.82 | all_122_9, all_122_10, all_122_11 gives: % 66.74/9.82 | (29) list_elt(all_122_7) & elt(all_122_8) & ((prefix(elt1, all_122_1, % 66.74/9.82 | all_122_2) = all_122_0 & prefix(elt1, all_122_5, all_122_6) = % 66.74/9.82 | all_122_4 & t2tb1(all_122_8) = all_122_3 & t2tb(all_122_7) = % 66.74/9.82 | all_122_6 & length(elt1, all_122_2) = all_122_1 & length(elt1, % 66.74/9.82 | all_122_6) = all_122_5 & cons(elt1, all_122_3, all_122_6) = % 66.74/9.82 | all_122_2 & uni(all_122_0) & uni(all_122_2) & uni(all_122_3) & % 66.74/9.82 | uni(all_122_4) & uni(all_122_6) & permut(elt1, all_122_4, % 66.74/9.82 | all_122_6) & ~ permut(elt1, all_122_0, all_122_2)) | % 66.74/9.82 | (prefix(elt1, all_122_10, all_122_11) = all_122_9 & length(elt1, % 66.74/9.82 | all_122_11) = all_122_10 & nil(elt1) = all_122_11 & % 66.74/9.82 | uni(all_122_9) & uni(all_122_11) & ~ permut(elt1, all_122_9, % 66.74/9.82 | all_122_11))) % 66.74/9.82 | % 66.74/9.82 | ALPHA: (29) implies: % 66.74/9.82 | (30) (prefix(elt1, all_122_1, all_122_2) = all_122_0 & prefix(elt1, % 66.74/9.82 | all_122_5, all_122_6) = all_122_4 & t2tb1(all_122_8) = all_122_3 & % 66.74/9.82 | t2tb(all_122_7) = all_122_6 & length(elt1, all_122_2) = all_122_1 & % 66.74/9.82 | length(elt1, all_122_6) = all_122_5 & cons(elt1, all_122_3, % 66.74/9.82 | all_122_6) = all_122_2 & uni(all_122_0) & uni(all_122_2) & % 66.74/9.82 | uni(all_122_3) & uni(all_122_4) & uni(all_122_6) & permut(elt1, % 66.74/9.82 | all_122_4, all_122_6) & ~ permut(elt1, all_122_0, all_122_2)) | % 66.74/9.82 | (prefix(elt1, all_122_10, all_122_11) = all_122_9 & length(elt1, % 66.74/9.82 | all_122_11) = all_122_10 & nil(elt1) = all_122_11 & uni(all_122_9) % 66.74/9.82 | & uni(all_122_11) & ~ permut(elt1, all_122_9, all_122_11)) % 66.74/9.82 | % 66.74/9.82 | DELTA: instantiating (12) with fresh symbols all_124_0, all_124_1 gives: % 66.74/9.82 | (31) tb2t(all_124_1) = all_124_0 & nil(elt1) = all_124_1 & % 66.74/9.82 | list_elt(all_124_0) & uni(all_124_1) & ! [v0: any] : (v0 = all_124_0 % 66.74/9.82 | | ~ list_elt(v0) | ~ sorted(v0) | ? [v1: elt] : ? [v2: elt] : ? % 66.74/9.82 | [v3: list_elt] : ? [v4: uni] : ? [v5: uni] : ? [v6: uni] : ? % 66.74/9.82 | [v7: list_elt] : ? [v8: uni] : ? [v9: uni] : ? [v10: any] : ? % 66.74/9.82 | [v11: elt] : ? [v12: uni] : ? [v13: uni] : ? [v14: any] : % 66.74/9.82 | (list_elt(v3) & elt(v11) & elt(v2) & elt(v1) & ((v14 = v0 & % 66.74/9.82 | t2tb1(v11) = v12 & tb2t(v13) = v0 & cons(elt1, v12, all_124_1) % 66.74/9.82 | = v13 & uni(v13) & uni(v12)) | (v10 = v0 & t2tb1(v2) = v4 & % 66.74/9.82 | t2tb1(v1) = v8 & tb2t(v9) = v0 & tb2t(v6) = v7 & t2tb(v3) = v5 % 66.74/9.82 | & cons(elt1, v8, v6) = v9 & cons(elt1, v4, v5) = v6 & % 66.74/9.82 | list_elt(v7) & uni(v9) & uni(v8) & uni(v6) & uni(v5) & uni(v4) % 66.74/9.82 | & sorted(v7) & le(v1, v2))))) % 66.74/9.82 | % 66.74/9.82 | ALPHA: (31) implies: % 66.74/9.82 | (32) nil(elt1) = all_124_1 % 66.74/9.82 | (33) tb2t(all_124_1) = all_124_0 % 66.74/9.82 | % 66.74/9.82 | GROUND_INST: instantiating (17) with all_118_0, all_124_1, elt1, simplifying % 66.74/9.82 | with (28), (32) gives: % 66.74/9.82 | (34) all_124_1 = all_118_0 % 66.74/9.82 | % 66.74/9.82 | GROUND_INST: instantiating (17) with all_111_1, all_124_1, elt1, simplifying % 66.74/9.82 | with (25), (32) gives: % 66.74/9.82 | (35) all_124_1 = all_111_1 % 66.74/9.82 | % 66.74/9.82 | GROUND_INST: instantiating (18) with all_111_0, all_124_0, all_111_1, % 66.74/9.82 | simplifying with (26) gives: % 66.74/9.82 | (36) all_124_0 = all_111_0 | ~ (tb2t(all_111_1) = all_124_0) % 66.74/9.82 | % 66.74/9.82 | COMBINE_EQS: (34), (35) imply: % 66.74/9.82 | (37) all_118_0 = all_111_1 % 66.74/9.82 | % 66.74/9.82 | SIMP: (37) implies: % 66.74/9.82 | (38) all_118_0 = all_111_1 % 66.74/9.82 | % 66.74/9.82 | REDUCE: (33), (35) imply: % 66.74/9.83 | (39) tb2t(all_111_1) = all_124_0 % 66.74/9.83 | % 66.74/9.83 | BETA: splitting (36) gives: % 66.74/9.83 | % 66.74/9.83 | Case 1: % 66.74/9.83 | | % 66.74/9.83 | | (40) ~ (tb2t(all_111_1) = all_124_0) % 66.74/9.83 | | % 66.74/9.83 | | PRED_UNIFY: (39), (40) imply: % 66.74/9.83 | | (41) $false % 66.74/9.83 | | % 66.74/9.83 | | CLOSE: (41) is inconsistent. % 66.74/9.83 | | % 66.74/9.83 | Case 2: % 66.74/9.83 | | % 66.74/9.83 | | % 66.74/9.83 | | GROUND_INST: instantiating (2) with elt1, all_111_1, simplifying with (15), % 66.74/9.83 | | (25) gives: % 66.74/9.83 | | (42) length(elt1, all_111_1) = 0 % 66.74/9.83 | | % 66.74/9.83 | | GROUND_INST: instantiating (1) with elt1, all_108_0, simplifying with (15), % 66.74/9.83 | | (23) gives: % 66.74/9.83 | | (43) ? [v0: uni] : (nil(elt1) = v0 & uni(v0) & sort(all_108_0, v0)) % 66.74/9.83 | | % 66.74/9.83 | | DELTA: instantiating (43) with fresh symbol all_145_0 gives: % 66.74/9.83 | | (44) nil(elt1) = all_145_0 & uni(all_145_0) & sort(all_108_0, all_145_0) % 66.74/9.83 | | % 66.74/9.83 | | ALPHA: (44) implies: % 66.74/9.83 | | (45) nil(elt1) = all_145_0 % 66.74/9.83 | | % 66.74/9.83 | | GROUND_INST: instantiating (17) with all_111_1, all_145_0, elt1, simplifying % 66.74/9.83 | | with (25), (45) gives: % 66.74/9.83 | | (46) all_145_0 = all_111_1 % 66.74/9.83 | | % 66.74/9.83 | | BETA: splitting (30) gives: % 66.74/9.83 | | % 66.74/9.83 | | Case 1: % 66.74/9.83 | | | % 66.74/9.83 | | | (47) prefix(elt1, all_122_1, all_122_2) = all_122_0 & prefix(elt1, % 66.74/9.83 | | | all_122_5, all_122_6) = all_122_4 & t2tb1(all_122_8) = all_122_3 % 66.74/9.83 | | | & t2tb(all_122_7) = all_122_6 & length(elt1, all_122_2) = % 66.74/9.83 | | | all_122_1 & length(elt1, all_122_6) = all_122_5 & cons(elt1, % 66.74/9.83 | | | all_122_3, all_122_6) = all_122_2 & uni(all_122_0) & % 66.74/9.83 | | | uni(all_122_2) & uni(all_122_3) & uni(all_122_4) & uni(all_122_6) % 66.74/9.83 | | | & permut(elt1, all_122_4, all_122_6) & ~ permut(elt1, all_122_0, % 66.74/9.83 | | | all_122_2) % 66.74/9.83 | | | % 66.74/9.83 | | | ALPHA: (47) implies: % 66.74/9.83 | | | (48) ~ permut(elt1, all_122_0, all_122_2) % 66.74/9.83 | | | (49) permut(elt1, all_122_4, all_122_6) % 66.74/9.83 | | | (50) uni(all_122_6) % 66.74/9.83 | | | (51) uni(all_122_3) % 66.74/9.83 | | | (52) uni(all_122_2) % 66.74/9.83 | | | (53) cons(elt1, all_122_3, all_122_6) = all_122_2 % 66.74/9.83 | | | (54) length(elt1, all_122_6) = all_122_5 % 66.74/9.83 | | | (55) length(elt1, all_122_2) = all_122_1 % 66.74/9.83 | | | (56) prefix(elt1, all_122_5, all_122_6) = all_122_4 % 66.74/9.83 | | | (57) prefix(elt1, all_122_1, all_122_2) = all_122_0 % 66.74/9.83 | | | % 66.74/9.83 | | | GROUND_INST: instantiating (3) with elt1, all_122_3, all_122_6, all_122_2, % 66.74/9.83 | | | simplifying with (15), (50), (51), (53) gives: % 66.74/9.83 | | | (58) ? [v0: int] : (length(elt1, all_122_2) = v0 & length(elt1, % 66.74/9.83 | | | all_122_6) = $sum(v0, -1)) % 66.74/9.83 | | | % 66.74/9.83 | | | GROUND_INST: instantiating (length_nonnegative) with elt1, all_122_6, % 66.74/9.83 | | | all_122_5, simplifying with (15), (50), (54) gives: % 66.74/9.83 | | | (59) $lesseq(0, all_122_5) % 66.74/9.83 | | | % 66.74/9.83 | | | GROUND_INST: instantiating (length_nonnegative) with elt1, all_122_2, % 66.74/9.83 | | | all_122_1, simplifying with (15), (52), (55) gives: % 66.74/9.83 | | | (60) $lesseq(0, all_122_1) % 66.74/9.83 | | | % 66.74/9.83 | | | GROUND_INST: instantiating (14) with elt1, $product(2, all_122_5), % 66.74/9.83 | | | all_122_6, all_122_6, all_122_5, all_122_4, simplifying with % 66.74/9.83 | | | (15), (50), (54), (56) gives: % 66.74/9.83 | | | (61) ~ ($lesseq(0, all_122_5)) | ? [v0: int] : ? [v1: uni] : ? [v2: % 66.74/9.83 | | | uni] : ? [v3: uni] : ? [v4: uni] : ((v4 = v2 & prefix(elt1, % 66.74/9.83 | | | $product(2, all_122_5), v1) = v2 & prefix(elt1, all_122_5, % 66.74/9.83 | | | all_122_6) = v3 & infix_plpl(elt1, v3, all_122_4) = v2 & % 66.74/9.83 | | | infix_plpl(elt1, all_122_6, all_122_6) = v1 & uni(v3) & % 66.74/9.83 | | | uni(v2) & uni(v1)) | ($lesseq(1, $difference(all_122_5, v0)) & % 66.74/9.83 | | | length(elt1, all_122_6) = v0)) % 66.74/9.83 | | | % 66.74/9.83 | | | GROUND_INST: instantiating (14) with elt1, $sum(all_122_1, all_122_5), % 66.74/9.83 | | | all_122_6, all_122_2, all_122_5, all_122_0, simplifying with % 66.74/9.83 | | | (15), (50), (52), (54), (57) gives: % 66.74/9.84 | | | (62) ~ ($lesseq(0, all_122_1)) | ? [v0: int] : ? [v1: uni] : ? [v2: % 66.74/9.84 | | | uni] : ? [v3: uni] : ? [v4: uni] : ((v4 = v2 & prefix(elt1, % 66.74/9.84 | | | $sum(all_122_1, all_122_5), v1) = v2 & prefix(elt1, % 66.74/9.84 | | | all_122_5, all_122_6) = v3 & infix_plpl(elt1, v3, all_122_0) % 66.74/9.84 | | | = v2 & infix_plpl(elt1, all_122_6, all_122_2) = v1 & uni(v3) & % 66.74/9.84 | | | uni(v2) & uni(v1)) | ($lesseq(1, $difference(all_122_1, v0)) & % 66.74/9.84 | | | length(elt1, all_122_2) = v0)) % 66.74/9.84 | | | % 66.74/9.84 | | | GROUND_INST: instantiating (13) with elt1, all_122_1, all_122_3, % 66.74/9.84 | | | all_122_6, all_122_2, all_122_0, simplifying with (15), (50), % 66.74/9.84 | | | (51), (53), (57) gives: % 66.74/9.84 | | | (63) ~ ($lesseq(1, all_122_1)) | ? [v0: uni] : (prefix(elt1, % 66.74/9.84 | | | $sum(all_122_1, -1), all_122_6) = v0 & cons(elt1, all_122_3, % 66.74/9.84 | | | v0) = all_122_0 & uni(v0) & uni(all_122_0)) % 66.74/9.84 | | | % 66.74/9.84 | | | DELTA: instantiating (58) with fresh symbol all_249_0 gives: % 66.74/9.84 | | | (64) length(elt1, all_122_2) = all_249_0 & length(elt1, all_122_6) = % 66.74/9.84 | | | $sum(all_249_0, -1) % 66.74/9.84 | | | % 66.74/9.84 | | | ALPHA: (64) implies: % 66.74/9.84 | | | (65) length(elt1, all_122_6) = $sum(all_249_0, -1) % 66.74/9.84 | | | (66) length(elt1, all_122_2) = all_249_0 % 66.74/9.84 | | | % 66.74/9.84 | | | BETA: splitting (61) gives: % 66.74/9.84 | | | % 66.74/9.84 | | | Case 1: % 66.74/9.84 | | | | % 66.74/9.84 | | | | (67) $lesseq(all_122_5, -1) % 66.74/9.84 | | | | % 66.74/9.84 | | | | COMBINE_INEQS: (59), (67) imply: % 66.74/9.84 | | | | (68) $false % 66.74/9.84 | | | | % 66.74/9.84 | | | | CLOSE: (68) is inconsistent. % 66.74/9.84 | | | | % 66.74/9.84 | | | Case 2: % 66.74/9.84 | | | | % 66.74/9.84 | | | | (69) ? [v0: int] : ? [v1: uni] : ? [v2: uni] : ? [v3: uni] : ? % 66.74/9.84 | | | | [v4: uni] : ((v4 = v2 & prefix(elt1, $product(2, all_122_5), v1) % 66.74/9.84 | | | | = v2 & prefix(elt1, all_122_5, all_122_6) = v3 & % 66.74/9.84 | | | | infix_plpl(elt1, v3, all_122_4) = v2 & infix_plpl(elt1, % 66.74/9.84 | | | | all_122_6, all_122_6) = v1 & uni(v3) & uni(v2) & uni(v1)) % 66.74/9.84 | | | | | ($lesseq(1, $difference(all_122_5, v0)) & length(elt1, % 66.74/9.84 | | | | all_122_6) = v0)) % 66.74/9.84 | | | | % 66.74/9.84 | | | | DELTA: instantiating (69) with fresh symbols all_294_0, all_294_1, % 66.74/9.84 | | | | all_294_2, all_294_3, all_294_4 gives: % 66.74/9.84 | | | | (70) (all_294_0 = all_294_2 & prefix(elt1, $product(2, all_122_5), % 66.74/9.84 | | | | all_294_3) = all_294_2 & prefix(elt1, all_122_5, all_122_6) % 66.74/9.84 | | | | = all_294_1 & infix_plpl(elt1, all_294_1, all_122_4) = % 66.74/9.84 | | | | all_294_2 & infix_plpl(elt1, all_122_6, all_122_6) = all_294_3 % 66.74/9.84 | | | | & uni(all_294_1) & uni(all_294_2) & uni(all_294_3)) | % 66.74/9.84 | | | | ($lesseq(1, $difference(all_122_5, all_294_4)) & length(elt1, % 66.74/9.84 | | | | all_122_6) = all_294_4) % 66.74/9.84 | | | | % 66.74/9.84 | | | | BETA: splitting (62) gives: % 66.74/9.84 | | | | % 66.74/9.84 | | | | Case 1: % 66.74/9.84 | | | | | % 66.74/9.84 | | | | | (71) $lesseq(all_122_1, -1) % 66.74/9.84 | | | | | % 66.74/9.84 | | | | | COMBINE_INEQS: (60), (71) imply: % 66.74/9.84 | | | | | (72) $false % 66.74/9.84 | | | | | % 66.74/9.84 | | | | | CLOSE: (72) is inconsistent. % 66.74/9.84 | | | | | % 66.74/9.84 | | | | Case 2: % 66.74/9.84 | | | | | % 66.74/9.84 | | | | | (73) ? [v0: int] : ? [v1: uni] : ? [v2: uni] : ? [v3: uni] : ? % 66.74/9.84 | | | | | [v4: uni] : ((v4 = v2 & prefix(elt1, $sum(all_122_1, % 66.74/9.84 | | | | | all_122_5), v1) = v2 & prefix(elt1, all_122_5, % 66.74/9.84 | | | | | all_122_6) = v3 & infix_plpl(elt1, v3, all_122_0) = v2 & % 66.74/9.84 | | | | | infix_plpl(elt1, all_122_6, all_122_2) = v1 & uni(v3) & % 66.74/9.84 | | | | | uni(v2) & uni(v1)) | ($lesseq(1, $difference(all_122_1, % 66.74/9.84 | | | | | v0)) & length(elt1, all_122_2) = v0)) % 66.74/9.84 | | | | | % 66.74/9.84 | | | | | DELTA: instantiating (73) with fresh symbols all_309_0, all_309_1, % 66.74/9.84 | | | | | all_309_2, all_309_3, all_309_4 gives: % 66.74/9.84 | | | | | (74) (all_309_0 = all_309_2 & prefix(elt1, $sum(all_122_1, % 66.74/9.84 | | | | | all_122_5), all_309_3) = all_309_2 & prefix(elt1, % 66.74/9.84 | | | | | all_122_5, all_122_6) = all_309_1 & infix_plpl(elt1, % 66.74/9.84 | | | | | all_309_1, all_122_0) = all_309_2 & infix_plpl(elt1, % 66.74/9.84 | | | | | all_122_6, all_122_2) = all_309_3 & uni(all_309_1) & % 66.74/9.84 | | | | | uni(all_309_2) & uni(all_309_3)) | ($lesseq(1, % 66.74/9.84 | | | | | $difference(all_122_1, all_309_4)) & length(elt1, % 66.74/9.84 | | | | | all_122_2) = all_309_4) % 66.74/9.84 | | | | | % 66.74/9.84 | | | | | GROUND_INST: instantiating (19) with all_122_5, $sum(all_249_0, -1), % 66.74/9.84 | | | | | all_122_6, elt1, simplifying with (54), (65) gives: % 66.74/9.84 | | | | | (75) $difference(all_249_0, all_122_5) = 1 % 66.74/9.84 | | | | | % 66.74/9.84 | | | | | GROUND_INST: instantiating (19) with all_122_1, all_249_0, all_122_2, % 66.74/9.84 | | | | | elt1, simplifying with (55), (66) gives: % 66.74/9.84 | | | | | (76) all_249_0 = all_122_1 % 66.74/9.84 | | | | | % 66.74/9.84 | | | | | COMBINE_EQS: (75), (76) imply: % 66.74/9.84 | | | | | (77) $difference(all_122_1, all_122_5) = 1 % 66.74/9.84 | | | | | % 66.74/9.84 | | | | | SIMP: (77) implies: % 66.74/9.84 | | | | | (78) $difference(all_122_1, all_122_5) = 1 % 66.74/9.84 | | | | | % 66.74/9.84 | | | | | REDUCE: (55), (78) imply: % 66.74/9.84 | | | | | (79) length(elt1, all_122_2) = $sum(all_122_5, 1) % 66.74/9.84 | | | | | % 66.74/9.84 | | | | | BETA: splitting (63) gives: % 66.74/9.84 | | | | | % 66.74/9.84 | | | | | Case 1: % 66.74/9.84 | | | | | | % 66.74/9.84 | | | | | | (80) $lesseq(all_122_1, 0) % 66.74/9.84 | | | | | | % 66.74/9.84 | | | | | | REDUCE: (78), (80) imply: % 66.74/9.84 | | | | | | (81) $lesseq(all_122_5, -1) % 66.74/9.84 | | | | | | % 66.74/9.84 | | | | | | COMBINE_INEQS: (59), (81) imply: % 66.74/9.84 | | | | | | (82) $false % 66.74/9.84 | | | | | | % 66.74/9.84 | | | | | | CLOSE: (82) is inconsistent. % 66.74/9.84 | | | | | | % 66.74/9.84 | | | | | Case 2: % 66.74/9.84 | | | | | | % 66.74/9.84 | | | | | | (83) ? [v0: uni] : (prefix(elt1, $sum(all_122_1, -1), all_122_6) % 66.74/9.84 | | | | | | = v0 & cons(elt1, all_122_3, v0) = all_122_0 & uni(v0) & % 66.74/9.84 | | | | | | uni(all_122_0)) % 66.74/9.84 | | | | | | % 66.74/9.84 | | | | | | DELTA: instantiating (83) with fresh symbol all_339_0 gives: % 66.74/9.84 | | | | | | (84) prefix(elt1, $sum(all_122_1, -1), all_122_6) = all_339_0 & % 66.74/9.84 | | | | | | cons(elt1, all_122_3, all_339_0) = all_122_0 & % 66.74/9.84 | | | | | | uni(all_339_0) & uni(all_122_0) % 66.74/9.84 | | | | | | % 66.74/9.84 | | | | | | ALPHA: (84) implies: % 66.74/9.84 | | | | | | (85) cons(elt1, all_122_3, all_339_0) = all_122_0 % 66.74/9.84 | | | | | | (86) prefix(elt1, $sum(all_122_1, -1), all_122_6) = all_339_0 % 66.74/9.84 | | | | | | % 66.74/9.84 | | | | | | REDUCE: (78), (86) imply: % 66.74/9.84 | | | | | | (87) prefix(elt1, all_122_5, all_122_6) = all_339_0 % 66.74/9.84 | | | | | | % 66.74/9.84 | | | | | | BETA: splitting (74) gives: % 66.74/9.84 | | | | | | % 66.74/9.84 | | | | | | Case 1: % 66.74/9.84 | | | | | | | % 66.74/9.84 | | | | | | | (88) all_309_0 = all_309_2 & prefix(elt1, $sum(all_122_1, % 66.74/9.84 | | | | | | | all_122_5), all_309_3) = all_309_2 & prefix(elt1, % 66.74/9.84 | | | | | | | all_122_5, all_122_6) = all_309_1 & infix_plpl(elt1, % 66.74/9.84 | | | | | | | all_309_1, all_122_0) = all_309_2 & infix_plpl(elt1, % 66.74/9.84 | | | | | | | all_122_6, all_122_2) = all_309_3 & uni(all_309_1) & % 66.74/9.84 | | | | | | | uni(all_309_2) & uni(all_309_3) % 66.74/9.84 | | | | | | | % 66.74/9.84 | | | | | | | ALPHA: (88) implies: % 66.74/9.84 | | | | | | | (89) prefix(elt1, all_122_5, all_122_6) = all_309_1 % 66.74/9.84 | | | | | | | % 66.74/9.84 | | | | | | | BETA: splitting (70) gives: % 66.74/9.84 | | | | | | | % 66.74/9.84 | | | | | | | Case 1: % 66.74/9.84 | | | | | | | | % 66.74/9.85 | | | | | | | | (90) all_294_0 = all_294_2 & prefix(elt1, $product(2, % 66.74/9.85 | | | | | | | | all_122_5), all_294_3) = all_294_2 & prefix(elt1, % 66.74/9.85 | | | | | | | | all_122_5, all_122_6) = all_294_1 & infix_plpl(elt1, % 66.74/9.85 | | | | | | | | all_294_1, all_122_4) = all_294_2 & infix_plpl(elt1, % 66.74/9.85 | | | | | | | | all_122_6, all_122_6) = all_294_3 & uni(all_294_1) & % 66.74/9.85 | | | | | | | | uni(all_294_2) & uni(all_294_3) % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | ALPHA: (90) implies: % 66.74/9.85 | | | | | | | | (91) uni(all_294_1) % 66.74/9.85 | | | | | | | | (92) prefix(elt1, all_122_5, all_122_6) = all_294_1 % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | GROUND_INST: instantiating (21) with all_122_4, all_309_1, % 66.74/9.85 | | | | | | | | all_122_6, all_122_5, elt1, simplifying with (56), % 66.74/9.85 | | | | | | | | (89) gives: % 66.74/9.85 | | | | | | | | (93) all_309_1 = all_122_4 % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | GROUND_INST: instantiating (21) with all_309_1, all_339_0, % 66.74/9.85 | | | | | | | | all_122_6, all_122_5, elt1, simplifying with (87), % 66.74/9.85 | | | | | | | | (89) gives: % 66.74/9.85 | | | | | | | | (94) all_339_0 = all_309_1 % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | GROUND_INST: instantiating (21) with all_294_1, all_339_0, % 66.74/9.85 | | | | | | | | all_122_6, all_122_5, elt1, simplifying with (87), % 66.74/9.85 | | | | | | | | (92) gives: % 66.74/9.85 | | | | | | | | (95) all_339_0 = all_294_1 % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | COMBINE_EQS: (94), (95) imply: % 66.74/9.85 | | | | | | | | (96) all_309_1 = all_294_1 % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | SIMP: (96) implies: % 66.74/9.85 | | | | | | | | (97) all_309_1 = all_294_1 % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | COMBINE_EQS: (93), (97) imply: % 66.74/9.85 | | | | | | | | (98) all_294_1 = all_122_4 % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | COMBINE_EQS: (95), (98) imply: % 66.74/9.85 | | | | | | | | (99) all_339_0 = all_122_4 % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | REDUCE: (85), (99) imply: % 66.74/9.85 | | | | | | | | (100) cons(elt1, all_122_3, all_122_4) = all_122_0 % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | REDUCE: (91), (98) imply: % 66.74/9.85 | | | | | | | | (101) uni(all_122_4) % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | GROUND_INST: instantiating (permut_cons) with elt1, all_122_3, % 66.74/9.85 | | | | | | | | all_122_4, all_122_6, all_122_0, all_122_2, % 66.74/9.85 | | | | | | | | simplifying with (15), (48), (49), (50), (51), % 66.74/9.85 | | | | | | | | (53), (100), (101) gives: % 66.74/9.85 | | | | | | | | (102) $false % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | CLOSE: (102) is inconsistent. % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | Case 2: % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | (103) $lesseq(1, $difference(all_122_5, all_294_4)) & % 66.74/9.85 | | | | | | | | length(elt1, all_122_6) = all_294_4 % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | ALPHA: (103) implies: % 66.74/9.85 | | | | | | | | (104) $lesseq(1, $difference(all_122_5, all_294_4)) % 66.74/9.85 | | | | | | | | (105) length(elt1, all_122_6) = all_294_4 % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | GROUND_INST: instantiating (19) with all_122_5, all_294_4, % 66.74/9.85 | | | | | | | | all_122_6, elt1, simplifying with (54), (105) % 66.74/9.85 | | | | | | | | gives: % 66.74/9.85 | | | | | | | | (106) all_294_4 = all_122_5 % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | REDUCE: (104), (106) imply: % 66.74/9.85 | | | | | | | | (107) $false % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | | CLOSE: (107) is inconsistent. % 66.74/9.85 | | | | | | | | % 66.74/9.85 | | | | | | | End of split % 66.74/9.85 | | | | | | | % 66.74/9.85 | | | | | | Case 2: % 66.74/9.85 | | | | | | | % 66.74/9.85 | | | | | | | (108) $lesseq(1, $difference(all_122_1, all_309_4)) & % 66.74/9.85 | | | | | | | length(elt1, all_122_2) = all_309_4 % 66.74/9.85 | | | | | | | % 66.74/9.85 | | | | | | | ALPHA: (108) implies: % 66.74/9.85 | | | | | | | (109) $lesseq(1, $difference(all_122_1, all_309_4)) % 66.74/9.85 | | | | | | | (110) length(elt1, all_122_2) = all_309_4 % 66.74/9.85 | | | | | | | % 66.74/9.85 | | | | | | | REDUCE: (78), (109) imply: % 66.74/9.85 | | | | | | | (111) $lesseq(all_309_4, all_122_5) % 66.74/9.85 | | | | | | | % 66.74/9.85 | | | | | | | GROUND_INST: instantiating (19) with $sum(all_122_5, 1), % 66.74/9.85 | | | | | | | all_309_4, all_122_2, elt1, simplifying with (79), % 66.74/9.85 | | | | | | | (110) gives: % 66.74/9.85 | | | | | | | (112) $difference(all_309_4, all_122_5) = 1 % 66.74/9.85 | | | | | | | % 66.74/9.85 | | | | | | | REDUCE: (111), (112) imply: % 66.74/9.85 | | | | | | | (113) $false % 66.74/9.85 | | | | | | | % 66.74/9.85 | | | | | | | CLOSE: (113) is inconsistent. % 66.74/9.85 | | | | | | | % 66.74/9.85 | | | | | | End of split % 66.74/9.85 | | | | | | % 66.74/9.85 | | | | | End of split % 66.74/9.85 | | | | | % 66.74/9.85 | | | | End of split % 66.74/9.85 | | | | % 66.74/9.85 | | | End of split % 66.74/9.85 | | | % 66.74/9.85 | | Case 2: % 66.74/9.85 | | | % 66.74/9.85 | | | (114) prefix(elt1, all_122_10, all_122_11) = all_122_9 & length(elt1, % 66.74/9.85 | | | all_122_11) = all_122_10 & nil(elt1) = all_122_11 & % 66.74/9.85 | | | uni(all_122_9) & uni(all_122_11) & ~ permut(elt1, all_122_9, % 66.74/9.85 | | | all_122_11) % 66.74/9.85 | | | % 66.74/9.85 | | | ALPHA: (114) implies: % 66.74/9.85 | | | (115) ~ permut(elt1, all_122_9, all_122_11) % 66.74/9.85 | | | (116) uni(all_122_11) % 66.74/9.85 | | | (117) nil(elt1) = all_122_11 % 66.74/9.85 | | | (118) length(elt1, all_122_11) = all_122_10 % 66.74/9.85 | | | (119) prefix(elt1, all_122_10, all_122_11) = all_122_9 % 66.74/9.85 | | | % 66.74/9.85 | | | GROUND_INST: instantiating (17) with all_111_1, all_122_11, elt1, % 66.74/9.85 | | | simplifying with (25), (117) gives: % 66.74/9.85 | | | (120) all_122_11 = all_111_1 % 66.74/9.85 | | | % 66.74/9.85 | | | GROUND_INST: instantiating (19) with 0, all_122_10, all_111_1, elt1, % 66.74/9.85 | | | simplifying with (42) gives: % 66.74/9.85 | | | (121) all_122_10 = 0 | ~ (length(elt1, all_111_1) = all_122_10) % 66.74/9.85 | | | % 66.74/9.85 | | | REDUCE: (119), (120) imply: % 66.74/9.85 | | | (122) prefix(elt1, all_122_10, all_111_1) = all_122_9 % 66.74/9.85 | | | % 66.74/9.85 | | | REDUCE: (118), (120) imply: % 66.74/9.85 | | | (123) length(elt1, all_111_1) = all_122_10 % 66.74/9.85 | | | % 66.74/9.85 | | | REDUCE: (116), (120) imply: % 66.74/9.85 | | | (124) uni(all_111_1) % 66.74/9.85 | | | % 66.74/9.85 | | | REDUCE: (115), (120) imply: % 66.74/9.85 | | | (125) ~ permut(elt1, all_122_9, all_111_1) % 66.74/9.85 | | | % 66.74/9.85 | | | BETA: splitting (121) gives: % 66.74/9.85 | | | % 66.74/9.85 | | | Case 1: % 66.74/9.85 | | | | % 66.74/9.85 | | | | (126) ~ (length(elt1, all_111_1) = all_122_10) % 66.74/9.85 | | | | % 66.74/9.85 | | | | PRED_UNIFY: (123), (126) imply: % 66.74/9.85 | | | | (127) $false % 66.74/9.85 | | | | % 66.74/9.85 | | | | CLOSE: (127) is inconsistent. % 66.74/9.85 | | | | % 66.74/9.85 | | | Case 2: % 66.74/9.85 | | | | % 66.74/9.85 | | | | (128) all_122_10 = 0 % 66.74/9.85 | | | | % 66.74/9.85 | | | | REDUCE: (122), (128) imply: % 66.74/9.85 | | | | (129) prefix(elt1, 0, all_111_1) = all_122_9 % 66.74/9.85 | | | | % 66.74/9.85 | | | | GROUND_INST: instantiating (14) with elt1, 0, all_111_1, all_111_1, 0, % 66.74/9.85 | | | | all_122_9, simplifying with (15), (42), (124), (129) gives: % 66.74/9.85 | | | | (130) ? [v0: int] : ? [v1: uni] : ? [v2: uni] : ? [v3: uni] : ? % 66.74/9.85 | | | | [v4: uni] : ((v4 = v2 & prefix(elt1, 0, v1) = v2 & prefix(elt1, % 66.74/9.85 | | | | 0, all_111_1) = v3 & infix_plpl(elt1, v3, all_122_9) = v2 % 66.74/9.85 | | | | & infix_plpl(elt1, all_111_1, all_111_1) = v1 & uni(v3) & % 66.74/9.85 | | | | uni(v2) & uni(v1)) | ($lesseq(v0, -1) & length(elt1, % 66.74/9.85 | | | | all_111_1) = v0)) % 66.74/9.85 | | | | % 66.74/9.86 | | | | GROUND_INST: instantiating (prefix_def1) with elt1, all_111_1, % 66.74/9.86 | | | | all_122_9, simplifying with (15), (124), (129) gives: % 66.74/9.86 | | | | (131) nil(elt1) = all_122_9 & uni(all_122_9) % 66.74/9.86 | | | | % 66.74/9.86 | | | | ALPHA: (131) implies: % 66.74/9.86 | | | | (132) uni(all_122_9) % 66.74/9.86 | | | | (133) nil(elt1) = all_122_9 % 66.74/9.86 | | | | % 66.74/9.86 | | | | DELTA: instantiating (130) with fresh symbols all_256_0, all_256_1, % 66.74/9.86 | | | | all_256_2, all_256_3, all_256_4 gives: % 66.74/9.86 | | | | (134) (all_256_0 = all_256_2 & prefix(elt1, 0, all_256_3) = all_256_2 % 66.74/9.86 | | | | & prefix(elt1, 0, all_111_1) = all_256_1 & infix_plpl(elt1, % 66.74/9.86 | | | | all_256_1, all_122_9) = all_256_2 & infix_plpl(elt1, % 66.74/9.86 | | | | all_111_1, all_111_1) = all_256_3 & uni(all_256_1) & % 66.74/9.86 | | | | uni(all_256_2) & uni(all_256_3)) | ($lesseq(all_256_4, -1) & % 66.74/9.86 | | | | length(elt1, all_111_1) = all_256_4) % 66.74/9.86 | | | | % 66.74/9.86 | | | | BETA: splitting (134) gives: % 66.74/9.86 | | | | % 66.74/9.86 | | | | Case 1: % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | (135) all_256_0 = all_256_2 & prefix(elt1, 0, all_256_3) = % 66.74/9.86 | | | | | all_256_2 & prefix(elt1, 0, all_111_1) = all_256_1 & % 66.74/9.86 | | | | | infix_plpl(elt1, all_256_1, all_122_9) = all_256_2 & % 66.74/9.86 | | | | | infix_plpl(elt1, all_111_1, all_111_1) = all_256_3 & % 66.74/9.86 | | | | | uni(all_256_1) & uni(all_256_2) & uni(all_256_3) % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | ALPHA: (135) implies: % 66.74/9.86 | | | | | (136) infix_plpl(elt1, all_111_1, all_111_1) = all_256_3 % 66.74/9.86 | | | | | (137) infix_plpl(elt1, all_256_1, all_122_9) = all_256_2 % 66.74/9.86 | | | | | (138) prefix(elt1, 0, all_111_1) = all_256_1 % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | GROUND_INST: instantiating (17) with all_111_1, all_122_9, elt1, % 66.74/9.86 | | | | | simplifying with (25), (133) gives: % 66.74/9.86 | | | | | (139) all_122_9 = all_111_1 % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | GROUND_INST: instantiating (21) with all_122_9, all_256_1, all_111_1, % 66.74/9.86 | | | | | 0, elt1, simplifying with (129), (138) gives: % 66.74/9.86 | | | | | (140) all_256_1 = all_122_9 % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | COMBINE_EQS: (139), (140) imply: % 66.74/9.86 | | | | | (141) all_256_1 = all_111_1 % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | REDUCE: (137), (139), (141) imply: % 66.74/9.86 | | | | | (142) infix_plpl(elt1, all_111_1, all_111_1) = all_256_2 % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | REDUCE: (125), (139) imply: % 66.74/9.86 | | | | | (143) ~ permut(elt1, all_111_1, all_111_1) % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | GROUND_INST: instantiating (20) with all_256_3, all_256_2, all_111_1, % 66.74/9.86 | | | | | all_111_1, elt1, simplifying with (136), (142) gives: % 66.74/9.86 | | | | | (144) all_256_2 = all_256_3 % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | GROUND_INST: instantiating (6) with elt1, all_111_1, all_111_1, % 66.74/9.86 | | | | | all_111_1, all_111_1, all_111_1, simplifying with (15), % 66.74/9.86 | | | | | (124) gives: % 66.74/9.86 | | | | | (145) ~ (infix_plpl(elt1, all_111_1, all_111_1) = all_111_1) | ? % 66.74/9.86 | | | | | [v0: uni] : ? [v1: uni] : (infix_plpl(elt1, all_111_1, v0) = % 66.74/9.86 | | | | | v1 & infix_plpl(elt1, all_111_1, all_111_1) = v0 & uni(v1) % 66.74/9.86 | | | | | & uni(v0) & permut(elt1, all_111_1, v1)) % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | GROUND_INST: instantiating (5) with elt1, all_111_1, all_111_1, % 66.74/9.86 | | | | | all_111_1, all_111_1, all_111_1, simplifying with (15), % 66.74/9.86 | | | | | (124) gives: % 66.74/9.86 | | | | | (146) ~ (infix_plpl(elt1, all_111_1, all_111_1) = all_111_1) | ? % 66.74/9.86 | | | | | [v0: uni] : ? [v1: uni] : (infix_plpl(elt1, v0, all_111_1) = % 66.74/9.86 | | | | | v1 & infix_plpl(elt1, all_111_1, all_111_1) = v0 & uni(v1) % 66.74/9.86 | | | | | & uni(v0) & permut(elt1, v1, all_111_1)) % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | GROUND_INST: instantiating (4) with elt1, all_111_1, all_111_1, % 66.74/9.86 | | | | | all_256_3, simplifying with (15), (25), (124), (136) % 66.74/9.86 | | | | | gives: % 66.74/9.86 | | | | | (147) all_256_3 = all_111_1 % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | GROUND_INST: instantiating (8) with elt1, all_111_1, all_111_1, % 66.74/9.86 | | | | | all_256_3, simplifying with (15), (124), (136) gives: % 66.74/9.86 | | | | | (148) ? [v0: uni] : (infix_plpl(elt1, all_111_1, all_111_1) = v0 & % 66.74/9.86 | | | | | uni(v0) & permut(elt1, v0, all_256_3)) % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | GROUND_INST: instantiating (7) with elt1, all_111_1, all_111_1, % 66.74/9.86 | | | | | all_256_3, simplifying with (15), (124), (136) gives: % 66.74/9.86 | | | | | (149) ? [v0: uni] : (infix_plpl(elt1, all_111_1, all_111_1) = v0 & % 66.74/9.86 | | | | | uni(v0) & permut(elt1, all_256_3, v0)) % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | DELTA: instantiating (149) with fresh symbol all_285_0 gives: % 66.74/9.86 | | | | | (150) infix_plpl(elt1, all_111_1, all_111_1) = all_285_0 & % 66.74/9.86 | | | | | uni(all_285_0) & permut(elt1, all_256_3, all_285_0) % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | ALPHA: (150) implies: % 66.74/9.86 | | | | | (151) permut(elt1, all_256_3, all_285_0) % 66.74/9.86 | | | | | (152) infix_plpl(elt1, all_111_1, all_111_1) = all_285_0 % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | DELTA: instantiating (148) with fresh symbol all_289_0 gives: % 66.74/9.86 | | | | | (153) infix_plpl(elt1, all_111_1, all_111_1) = all_289_0 & % 66.74/9.86 | | | | | uni(all_289_0) & permut(elt1, all_289_0, all_256_3) % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | ALPHA: (153) implies: % 66.74/9.86 | | | | | (154) infix_plpl(elt1, all_111_1, all_111_1) = all_289_0 % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | REDUCE: (136), (147) imply: % 66.74/9.86 | | | | | (155) infix_plpl(elt1, all_111_1, all_111_1) = all_111_1 % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | REDUCE: (147), (151) imply: % 66.74/9.86 | | | | | (156) permut(elt1, all_111_1, all_285_0) % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | BETA: splitting (146) gives: % 66.74/9.86 | | | | | % 66.74/9.86 | | | | | Case 1: % 66.74/9.86 | | | | | | % 66.74/9.86 | | | | | | (157) ~ (infix_plpl(elt1, all_111_1, all_111_1) = all_111_1) % 66.74/9.86 | | | | | | % 66.74/9.86 | | | | | | PRED_UNIFY: (155), (157) imply: % 66.74/9.86 | | | | | | (158) $false % 66.74/9.86 | | | | | | % 66.74/9.86 | | | | | | CLOSE: (158) is inconsistent. % 66.74/9.86 | | | | | | % 66.74/9.86 | | | | | Case 2: % 66.74/9.86 | | | | | | % 66.74/9.86 | | | | | | (159) ? [v0: uni] : ? [v1: uni] : (infix_plpl(elt1, v0, % 66.74/9.86 | | | | | | all_111_1) = v1 & infix_plpl(elt1, all_111_1, % 66.74/9.86 | | | | | | all_111_1) = v0 & uni(v1) & uni(v0) & permut(elt1, v1, % 66.74/9.86 | | | | | | all_111_1)) % 66.74/9.86 | | | | | | % 66.74/9.86 | | | | | | DELTA: instantiating (159) with fresh symbols all_302_0, all_302_1 % 66.74/9.86 | | | | | | gives: % 66.74/9.86 | | | | | | (160) infix_plpl(elt1, all_302_1, all_111_1) = all_302_0 & % 66.74/9.86 | | | | | | infix_plpl(elt1, all_111_1, all_111_1) = all_302_1 & % 66.74/9.86 | | | | | | uni(all_302_0) & uni(all_302_1) & permut(elt1, all_302_0, % 66.74/9.86 | | | | | | all_111_1) % 66.74/9.86 | | | | | | % 66.74/9.86 | | | | | | ALPHA: (160) implies: % 66.74/9.86 | | | | | | (161) infix_plpl(elt1, all_111_1, all_111_1) = all_302_1 % 66.74/9.86 | | | | | | % 66.74/9.86 | | | | | | BETA: splitting (145) gives: % 66.74/9.86 | | | | | | % 66.74/9.86 | | | | | | Case 1: % 66.74/9.86 | | | | | | | % 66.74/9.86 | | | | | | | (162) ~ (infix_plpl(elt1, all_111_1, all_111_1) = all_111_1) % 66.74/9.86 | | | | | | | % 66.74/9.86 | | | | | | | PRED_UNIFY: (155), (162) imply: % 66.74/9.86 | | | | | | | (163) $false % 66.74/9.86 | | | | | | | % 66.74/9.86 | | | | | | | CLOSE: (163) is inconsistent. % 66.74/9.86 | | | | | | | % 66.74/9.86 | | | | | | Case 2: % 66.74/9.86 | | | | | | | % 66.74/9.86 | | | | | | | (164) ? [v0: uni] : ? [v1: uni] : (infix_plpl(elt1, % 66.74/9.86 | | | | | | | all_111_1, v0) = v1 & infix_plpl(elt1, all_111_1, % 66.74/9.86 | | | | | | | all_111_1) = v0 & uni(v1) & uni(v0) & permut(elt1, % 66.74/9.86 | | | | | | | all_111_1, v1)) % 66.74/9.86 | | | | | | | % 66.74/9.86 | | | | | | | DELTA: instantiating (164) with fresh symbols all_307_0, all_307_1 % 66.74/9.86 | | | | | | | gives: % 66.74/9.87 | | | | | | | (165) infix_plpl(elt1, all_111_1, all_307_1) = all_307_0 & % 66.74/9.87 | | | | | | | infix_plpl(elt1, all_111_1, all_111_1) = all_307_1 & % 66.74/9.87 | | | | | | | uni(all_307_0) & uni(all_307_1) & permut(elt1, all_111_1, % 66.74/9.87 | | | | | | | all_307_0) % 66.74/9.87 | | | | | | | % 66.74/9.87 | | | | | | | ALPHA: (165) implies: % 66.74/9.87 | | | | | | | (166) infix_plpl(elt1, all_111_1, all_111_1) = all_307_1 % 66.74/9.87 | | | | | | | % 66.74/9.87 | | | | | | | PRED_UNIFY: (143), (156) imply: % 66.74/9.87 | | | | | | | (167) ~ (all_285_0 = all_111_1) % 66.74/9.87 | | | | | | | % 66.74/9.87 | | | | | | | GROUND_INST: instantiating (20) with all_289_0, all_302_1, % 66.74/9.87 | | | | | | | all_111_1, all_111_1, elt1, simplifying with (154), % 66.74/9.87 | | | | | | | (161) gives: % 66.74/9.87 | | | | | | | (168) all_302_1 = all_289_0 % 66.74/9.87 | | | | | | | % 66.74/9.87 | | | | | | | GROUND_INST: instantiating (20) with all_285_0, all_302_1, % 66.74/9.87 | | | | | | | all_111_1, all_111_1, elt1, simplifying with (152), % 66.74/9.87 | | | | | | | (161) gives: % 66.74/9.87 | | | | | | | (169) all_302_1 = all_285_0 % 66.74/9.87 | | | | | | | % 66.74/9.87 | | | | | | | GROUND_INST: instantiating (20) with all_289_0, all_307_1, % 66.74/9.87 | | | | | | | all_111_1, all_111_1, elt1, simplifying with (154), % 66.74/9.87 | | | | | | | (166) gives: % 66.74/9.87 | | | | | | | (170) all_307_1 = all_289_0 % 66.74/9.87 | | | | | | | % 66.74/9.87 | | | | | | | GROUND_INST: instantiating (20) with all_111_1, all_307_1, % 66.74/9.87 | | | | | | | all_111_1, all_111_1, elt1, simplifying with (155), % 66.74/9.87 | | | | | | | (166) gives: % 66.74/9.87 | | | | | | | (171) all_307_1 = all_111_1 % 66.74/9.87 | | | | | | | % 66.74/9.87 | | | | | | | COMBINE_EQS: (170), (171) imply: % 66.74/9.87 | | | | | | | (172) all_289_0 = all_111_1 % 66.74/9.87 | | | | | | | % 66.74/9.87 | | | | | | | SIMP: (172) implies: % 66.74/9.87 | | | | | | | (173) all_289_0 = all_111_1 % 66.74/9.87 | | | | | | | % 66.74/9.87 | | | | | | | COMBINE_EQS: (168), (169) imply: % 66.74/9.87 | | | | | | | (174) all_289_0 = all_285_0 % 66.74/9.87 | | | | | | | % 66.74/9.87 | | | | | | | SIMP: (174) implies: % 66.74/9.87 | | | | | | | (175) all_289_0 = all_285_0 % 66.74/9.87 | | | | | | | % 66.74/9.87 | | | | | | | COMBINE_EQS: (173), (175) imply: % 66.74/9.87 | | | | | | | (176) all_285_0 = all_111_1 % 66.74/9.87 | | | | | | | % 66.74/9.87 | | | | | | | REDUCE: (167), (176) imply: % 66.74/9.87 | | | | | | | (177) $false % 66.74/9.87 | | | | | | | % 66.74/9.87 | | | | | | | CLOSE: (177) is inconsistent. % 66.74/9.87 | | | | | | | % 66.74/9.87 | | | | | | End of split % 66.74/9.87 | | | | | | % 66.74/9.87 | | | | | End of split % 66.74/9.87 | | | | | % 66.74/9.87 | | | | Case 2: % 66.74/9.87 | | | | | % 66.74/9.87 | | | | | (178) $lesseq(all_256_4, -1) & length(elt1, all_111_1) = all_256_4 % 66.74/9.87 | | | | | % 66.74/9.87 | | | | | ALPHA: (178) implies: % 66.74/9.87 | | | | | (179) $lesseq(all_256_4, -1) % 66.74/9.87 | | | | | (180) length(elt1, all_111_1) = all_256_4 % 66.74/9.87 | | | | | % 66.74/9.87 | | | | | GROUND_INST: instantiating (19) with 0, all_256_4, all_111_1, elt1, % 66.74/9.87 | | | | | simplifying with (42), (180) gives: % 66.74/9.87 | | | | | (181) all_256_4 = 0 % 66.74/9.87 | | | | | % 66.74/9.87 | | | | | REDUCE: (179), (181) imply: % 66.74/9.87 | | | | | (182) $false % 66.74/9.87 | | | | | % 66.74/9.87 | | | | | CLOSE: (182) is inconsistent. % 66.74/9.87 | | | | | % 66.74/9.87 | | | | End of split % 66.74/9.87 | | | | % 66.74/9.87 | | | End of split % 66.74/9.87 | | | % 66.74/9.87 | | End of split % 66.74/9.87 | | % 66.74/9.87 | End of split % 66.74/9.87 | % 66.74/9.87 End of proof % 66.74/9.87 % SZS output end Proof for theBenchmark % 66.74/9.87 % 66.74/9.87 9214ms %------------------------------------------------------------------------------