%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET725+4 : TPTP v8.1.2. Bugfixed v2.2.1. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n011.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 : Thu Aug 31 15:26:10 EDT 2023 % Result : Theorem 30.04s 4.76s % Output : Proof 103.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET725+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n011.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 : Sat Aug 26 12:13:24 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.52/1.18 Prover 4: Preprocessing ... % 3.52/1.18 Prover 1: Preprocessing ... % 3.52/1.24 Prover 2: Preprocessing ... % 3.52/1.24 Prover 5: Preprocessing ... % 3.52/1.24 Prover 6: Preprocessing ... % 3.52/1.24 Prover 3: Preprocessing ... % 3.52/1.24 Prover 0: Preprocessing ... % 8.94/1.98 Prover 5: Proving ... % 8.94/1.98 Prover 2: Proving ... % 9.71/2.02 Prover 6: Proving ... % 9.71/2.04 Prover 3: Constructing countermodel ... % 9.71/2.04 Prover 1: Constructing countermodel ... % 11.14/2.20 Prover 3: gave up % 11.14/2.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.14/2.21 Prover 1: gave up % 11.14/2.24 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.51/2.28 Prover 7: Preprocessing ... % 11.51/2.28 Prover 8: Preprocessing ... % 12.31/2.39 Prover 7: Warning: ignoring some quantifiers % 13.06/2.46 Prover 7: Constructing countermodel ... % 13.40/2.57 Prover 4: Constructing countermodel ... % 13.40/2.61 Prover 8: Warning: ignoring some quantifiers % 14.28/2.63 Prover 8: Constructing countermodel ... % 14.66/2.72 Prover 0: Proving ... % 15.41/2.78 Prover 8: gave up % 15.41/2.78 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 15.41/2.81 Prover 9: Preprocessing ... % 19.97/3.38 Prover 9: Constructing countermodel ... % 30.04/4.76 Prover 9: proved (1980ms) % 30.04/4.76 % 30.04/4.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 30.04/4.76 % 30.04/4.76 Prover 6: stopped % 30.04/4.76 Prover 0: stopped % 30.04/4.76 Prover 5: stopped % 30.78/4.77 Prover 2: stopped % 30.78/4.79 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 30.78/4.79 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 30.78/4.79 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 30.78/4.79 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 30.78/4.79 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 31.14/4.86 Prover 10: Preprocessing ... % 31.14/4.86 Prover 13: Preprocessing ... % 31.14/4.86 Prover 16: Preprocessing ... % 31.14/4.87 Prover 11: Preprocessing ... % 31.14/4.88 Prover 19: Preprocessing ... % 31.56/4.99 Prover 10: Warning: ignoring some quantifiers % 32.57/5.01 Prover 10: Constructing countermodel ... % 32.57/5.02 Prover 16: Warning: ignoring some quantifiers % 32.57/5.03 Prover 13: Warning: ignoring some quantifiers % 32.57/5.03 Prover 16: Constructing countermodel ... % 32.57/5.05 Prover 13: Constructing countermodel ... % 33.14/5.14 Prover 10: gave up % 34.01/5.20 Prover 19: Warning: ignoring some quantifiers % 34.13/5.22 Prover 19: Constructing countermodel ... % 36.40/5.51 Prover 11: Constructing countermodel ... % 36.40/5.57 Prover 19: gave up % 73.88/10.44 Prover 13: stopped % 82.59/11.65 Prover 16: stopped % 102.34/15.50 Prover 11: Found proof (size 166) % 102.34/15.50 Prover 11: proved (10734ms) % 102.55/15.50 Prover 7: stopped % 102.55/15.50 Prover 4: stopped % 102.55/15.50 % 102.55/15.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 102.55/15.50 % 102.55/15.51 % SZS output start Proof for theBenchmark % 102.55/15.51 Assumptions after simplification: % 102.55/15.51 --------------------------------- % 102.55/15.51 % 102.55/15.51 (compose_function) % 102.76/15.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 102.76/15.55 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 102.76/15.55 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 102.76/15.55 ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 102.76/15.55 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: int] : ? [v11: int] % 102.76/15.55 : (( ~ (v11 = 0) & apply(v0, v9, v6) = v11) | ( ~ (v11 = 0) & member(v6, v4) % 102.76/15.55 = v11) | ( ~ (v10 = 0) & member(v9, v3) = v10) | ( ~ (v10 = 0) & % 102.76/15.55 member(v5, v2) = v10))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 102.76/15.55 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 102.76/15.55 int] : ! [v9: $i] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = % 102.76/15.55 v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) % 102.76/15.55 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 102.76/15.55 $i(v0) | ? [v10: int] : ? [v11: int] : (( ~ (v11 = 0) & apply(v1, v5, v9) % 102.76/15.55 = v11) | ( ~ (v11 = 0) & member(v6, v4) = v11) | ( ~ (v10 = 0) & % 102.76/15.55 member(v9, v3) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10))) & ! % 102.76/15.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 102.76/15.55 : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 102.76/15.56 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 102.76/15.56 ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ % 102.76/15.56 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: int] : ? [v11: int] : % 102.76/15.56 (( ~ (v11 = 0) & apply(v0, v9, v6) = v11) | ( ~ (v11 = 0) & member(v6, v4) = % 102.76/15.56 v11) | ( ~ (v10 = 0) & apply(v1, v5, v9) = v10) | ( ~ (v10 = 0) & % 102.76/15.56 member(v5, v2) = v10))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 102.76/15.56 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 102.76/15.56 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | % 102.76/15.56 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 102.76/15.56 $i(v0) | ? [v8: int] : ? [v9: int] : ? [v10: $i] : ? [v11: int] : ? % 102.76/15.56 [v12: int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 & % 102.76/15.56 apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, v3) = 0) % 102.76/15.56 | ( ~ (v9 = 0) & member(v6, v4) = v9) | ( ~ (v8 = 0) & member(v5, v2) = % 102.76/15.56 v8)))) % 102.76/15.56 % 102.76/15.56 (identity) % 102.76/15.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 102.76/15.56 (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 102.76/15.56 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0: % 102.76/15.56 $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ~ % 102.76/15.56 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v0, % 102.76/15.56 v3, v3) = v4 & member(v3, v1) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] % 102.76/15.56 : ! [v2: $i] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ~ % 102.76/15.56 $i(v2) | ~ $i(v1) | ~ $i(v0) | apply(v0, v2, v2) = 0) % 102.76/15.56 % 102.76/15.56 (injective) % 102.76/15.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 102.76/15.57 $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) % 102.76/15.57 | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 102.76/15.57 | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : (( ~ % 102.76/15.57 (v8 = 0) & member(v5, v2) = v8) | ( ~ (v7 = 0) & member(v4, v1) = v7) | % 102.76/15.57 ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! % 102.76/15.57 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ % 102.76/15.57 (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3, % 102.76/15.57 v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 102.76/15.57 ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : (( ~ (v8 = 0) & % 102.76/15.57 apply(v0, v3, v5) = v8) | ( ~ (v7 = 0) & member(v5, v2) = v7) | ( ~ (v6 % 102.76/15.57 = 0) & member(v4, v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 102.76/15.57 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (injective(v0, % 102.76/15.57 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ~ % 102.76/15.57 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 102.76/15.57 int] : ? [v7: int] : ? [v8: int] : (( ~ (v8 = 0) & apply(v0, v4, v5) = % 102.76/15.57 v8) | ( ~ (v7 = 0) & member(v5, v2) = v7) | ( ~ (v6 = 0) & member(v3, % 102.76/15.57 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 102.76/15.57 ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ % 102.76/15.57 (member(v5, v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | % 102.76/15.57 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 102.76/15.57 [v6: int] : ? [v7: int] : (( ~ (v7 = 0) & apply(v0, v4, v5) = v7) | ( ~ (v6 % 102.76/15.57 = 0) & apply(v0, v3, v5) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 102.76/15.57 $i] : ! [v3: int] : (v3 = 0 | ~ (injective(v0, v1, v2) = v3) | ~ $i(v2) | % 102.76/15.57 ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = % 102.76/15.57 v4) & apply(v0, v5, v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 % 102.76/15.57 & member(v5, v1) = 0 & member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4))) % 102.76/15.57 % 102.76/15.57 (maps) % 102.76/15.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 102.76/15.58 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ % 102.76/15.58 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 102.76/15.58 $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : (( ~ (v8 = % 102.76/15.58 0) & member(v5, v2) = v8) | ( ~ (v7 = 0) & member(v4, v2) = v7) | ( ~ % 102.76/15.58 (v6 = 0) & member(v3, v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 102.76/15.58 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, % 102.76/15.58 v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~ % 102.76/15.58 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 102.76/15.58 int] : ? [v7: int] : ? [v8: int] : (( ~ (v8 = 0) & apply(v0, v3, v4) = % 102.76/15.58 v8) | ( ~ (v7 = 0) & member(v5, v2) = v7) | ( ~ (v6 = 0) & member(v3, % 102.76/15.58 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 102.76/15.58 ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ % 102.76/15.58 (apply(v0, v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | % 102.76/15.58 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 102.76/15.58 ? [v8: int] : (( ~ (v8 = 0) & apply(v0, v3, v5) = v8) | ( ~ (v7 = 0) & % 102.76/15.58 member(v4, v2) = v7) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0: % 102.76/15.58 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 102.76/15.58 (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ % 102.76/15.58 (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 102.76/15.58 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 102.76/15.58 (( ~ (v7 = 0) & apply(v0, v3, v5) = v7) | ( ~ (v6 = 0) & apply(v0, v3, v4) = % 102.76/15.58 v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 % 102.76/15.58 | ~ (maps(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 102.76/15.58 $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: int] : ? [v9: % 102.76/15.58 int] : ? [v10: int] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : % 102.76/15.58 ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13 = 0 & member(v12, v1) = 0 & ! % 102.76/15.58 [v14: $i] : ( ~ (apply(v0, v12, v14) = 0) | ~ $i(v14) | ? [v15: int] % 102.76/15.58 : ( ~ (v15 = 0) & member(v14, v2) = v15)) & ! [v14: $i] : ( ~ % 102.76/15.58 (member(v14, v2) = 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & % 102.76/15.58 apply(v0, v12, v14) = v15))) | (v11 = 0 & v10 = 0 & v9 = 0 & v8 = % 102.76/15.58 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, v4, v5) % 102.76/15.58 = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = 0)))) % 102.76/15.58 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, % 102.76/15.58 v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 102.76/15.58 ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0 & % 102.76/15.58 $i(v4))) % 102.76/15.58 % 102.76/15.58 (one_to_one) % 102.76/15.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 102.76/15.58 (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 102.76/15.58 int] : ? [v5: int] : (( ~ (v5 = 0) & surjective(v0, v1, v2) = v5) | ( ~ % 102.76/15.58 (v4 = 0) & injective(v0, v1, v2) = v4))) & ! [v0: $i] : ! [v1: $i] : % 102.76/15.58 ! [v2: $i] : ! [v3: any] : ( ~ (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ % 102.76/15.58 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ((v5 = 0 & v3 = 0 & % 102.76/15.58 injective(v0, v1, v2) = 0) | ( ~ (v4 = 0) & one_to_one(v0, v1, v2) = % 102.76/15.58 v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 102.76/15.58 (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 102.76/15.58 int] : ? [v5: int] : ((v5 = 0 & v3 = 0 & surjective(v0, v1, v2) = 0) | ( % 102.76/15.58 ~ (v4 = 0) & one_to_one(v0, v1, v2) = v4))) & ! [v0: $i] : ! [v1: $i] % 102.76/15.58 : ! [v2: $i] : ( ~ (one_to_one(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 102.76/15.58 $i(v0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0: % 102.76/15.58 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ % 102.76/15.58 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & % 102.76/15.58 one_to_one(v0, v1, v2) = 0) | ( ~ (v3 = 0) & injective(v0, v1, v2) = % 102.76/15.58 v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, % 102.76/15.58 v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 102.76/15.58 int] : ((v4 = 0 & one_to_one(v0, v1, v2) = 0) | ( ~ (v3 = 0) & % 102.76/15.58 surjective(v0, v1, v2) = v3))) % 102.76/15.58 % 102.76/15.58 (surjective) % 102.76/15.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 102.76/15.59 (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 102.76/15.59 $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ (apply(v0, v5, v4) % 102.76/15.59 = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6)) % 102.76/15.59 & ! [v5: $i] : ( ~ (member(v5, v1) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ % 102.76/15.59 (v6 = 0) & apply(v0, v5, v4) = v6)))) & ! [v0: $i] : ! [v1: $i] : ! % 102.76/15.59 [v2: $i] : ! [v3: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) % 102.76/15.59 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 102.76/15.59 (apply(v0, v4, v3) = 0 & member(v4, v1) = 0 & $i(v4))) % 102.76/15.59 % 102.76/15.59 (thII16) % 102.76/15.59 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 102.76/15.59 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & one_to_one(v0, v3, v4) = % 102.76/15.59 v7 & identity(v6, v4) = 0 & identity(v5, v3) = 0 & compose_function(v1, v0, % 102.76/15.59 v3, v4, v3) = v5 & compose_function(v0, v2, v4, v3, v4) = v6 & maps(v2, % 102.76/15.59 v4, v3) = 0 & maps(v1, v4, v3) = 0 & maps(v0, v3, v4) = 0 & $i(v6) & % 102.76/15.59 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 102.76/15.59 % 102.76/15.59 (function-axioms) % 102.76/15.60 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 102.76/15.60 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 102.76/15.60 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 102.76/15.60 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 102.76/15.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 102.76/15.60 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 102.76/15.60 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 102.76/15.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 102.76/15.60 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 102.76/15.60 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 102.76/15.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 102.76/15.60 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 102.76/15.60 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 102.76/15.60 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 102.76/15.60 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 102.76/15.60 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 102.76/15.60 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 102.76/15.60 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 102.76/15.60 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 102.76/15.60 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 102.76/15.60 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 102.76/15.60 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 102.76/15.60 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 102.76/15.60 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 102.76/15.60 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 102.76/15.60 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 102.76/15.60 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 102.76/15.60 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 102.76/15.60 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 102.76/15.60 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 102.76/15.60 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 102.76/15.60 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 102.76/15.60 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 102.76/15.60 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 102.76/15.60 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 102.76/15.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 102.76/15.60 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 102.76/15.60 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 102.76/15.60 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 102.76/15.60 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 102.76/15.60 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 102.76/15.60 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 102.76/15.60 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 102.76/15.60 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 102.76/15.60 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 102.76/15.60 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 102.76/15.60 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 102.76/15.60 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 102.76/15.60 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 102.76/15.60 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 102.76/15.60 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 102.76/15.60 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 102.76/15.60 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 102.76/15.60 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 102.76/15.60 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 102.76/15.60 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 102.76/15.60 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 102.76/15.60 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 102.76/15.60 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 102.76/15.60 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 102.76/15.60 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 102.76/15.60 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 102.76/15.60 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 102.76/15.60 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 102.76/15.60 (power_set(v2) = v0)) % 102.76/15.60 % 102.76/15.60 Further assumptions not needed in the proof: % 102.76/15.60 -------------------------------------------- % 102.76/15.60 compose_predicate, decreasing_function, difference, empty_set, equal_maps, % 102.76/15.60 equal_set, image2, image3, increasing_function, intersection, inverse_function, % 102.76/15.60 inverse_image2, inverse_image3, inverse_predicate, isomorphism, power_set, % 102.76/15.60 product, singleton, subset, sum, union, unordered_pair % 102.76/15.60 % 102.76/15.60 Those formulas are unsatisfiable: % 102.76/15.60 --------------------------------- % 102.76/15.60 % 102.76/15.60 Begin of proof % 102.76/15.60 | % 102.76/15.60 | ALPHA: (maps) implies: % 102.76/15.60 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, % 102.76/15.60 | v1, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) | % 102.76/15.60 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 102.76/15.60 | member(v4, v2) = 0 & $i(v4))) % 102.76/15.60 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 102.76/15.60 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) % 102.76/15.60 | = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~ % 102.76/15.60 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 102.76/15.60 | ? [v6: int] : ? [v7: int] : (( ~ (v7 = 0) & apply(v0, v3, v5) = v7) % 102.76/15.60 | | ( ~ (v6 = 0) & apply(v0, v3, v4) = v6))) % 102.76/15.61 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 102.76/15.61 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, % 102.76/15.61 | v5) = 0) | ~ (member(v4, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 102.76/15.61 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: % 102.76/15.61 | int] : ? [v8: int] : (( ~ (v8 = 0) & apply(v0, v3, v4) = v8) | ( ~ % 102.76/15.61 | (v7 = 0) & member(v5, v2) = v7) | ( ~ (v6 = 0) & member(v3, v1) = % 102.76/15.61 | v6))) % 102.76/15.61 | % 102.76/15.61 | ALPHA: (compose_function) implies: % 102.76/15.61 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 102.76/15.61 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (compose_function(v0, v1, % 102.76/15.61 | v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | ~ $i(v6) | ~ % 102.76/15.61 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 102.76/15.61 | ? [v8: int] : ? [v9: int] : ? [v10: $i] : ? [v11: int] : ? [v12: % 102.76/15.61 | int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 & % 102.76/15.61 | apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, % 102.76/15.61 | v3) = 0) | ( ~ (v9 = 0) & member(v6, v4) = v9) | ( ~ (v8 = 0) % 102.76/15.61 | & member(v5, v2) = v8)))) % 102.76/15.61 | % 102.76/15.61 | ALPHA: (identity) implies: % 102.76/15.61 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (identity(v0, v1) = 0) | % 102.76/15.61 | ~ (member(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 102.76/15.61 | apply(v0, v2, v2) = 0) % 102.76/15.61 | % 102.76/15.61 | ALPHA: (injective) implies: % 102.76/15.61 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 102.76/15.61 | (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 102.76/15.61 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, % 102.76/15.61 | v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, % 102.76/15.61 | v1) = 0 & member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4))) % 102.76/15.61 | % 102.76/15.61 | ALPHA: (surjective) implies: % 102.76/15.61 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 102.76/15.61 | (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 102.76/15.61 | ? [v4: $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ % 102.76/15.61 | (apply(v0, v5, v4) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) % 102.76/15.61 | & member(v5, v1) = v6)) & ! [v5: $i] : ( ~ (member(v5, v1) = % 102.76/15.61 | 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & apply(v0, v5, % 102.76/15.61 | v4) = v6)))) % 102.76/15.61 | % 102.76/15.61 | ALPHA: (one_to_one) implies: % 102.76/15.61 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 102.76/15.61 | (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 102.76/15.61 | ? [v4: int] : ? [v5: int] : (( ~ (v5 = 0) & surjective(v0, v1, v2) = % 102.76/15.61 | v5) | ( ~ (v4 = 0) & injective(v0, v1, v2) = v4))) % 102.76/15.61 | % 102.76/15.61 | ALPHA: (function-axioms) implies: % 102.76/15.61 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 102.76/15.61 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 102.76/15.61 | = v0)) % 102.76/15.62 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 102.76/15.62 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 102.76/15.62 | ~ (apply(v4, v3, v2) = v0)) % 102.76/15.62 | % 102.76/15.62 | DELTA: instantiating (thII16) with fresh symbols all_32_0, all_32_1, all_32_2, % 102.76/15.62 | all_32_3, all_32_4, all_32_5, all_32_6, all_32_7 gives: % 102.76/15.62 | (11) ~ (all_32_0 = 0) & one_to_one(all_32_7, all_32_4, all_32_3) = % 102.76/15.62 | all_32_0 & identity(all_32_1, all_32_3) = 0 & identity(all_32_2, % 102.76/15.62 | all_32_4) = 0 & compose_function(all_32_6, all_32_7, all_32_4, % 102.76/15.62 | all_32_3, all_32_4) = all_32_2 & compose_function(all_32_7, % 102.76/15.62 | all_32_5, all_32_3, all_32_4, all_32_3) = all_32_1 & maps(all_32_5, % 102.76/15.62 | all_32_3, all_32_4) = 0 & maps(all_32_6, all_32_3, all_32_4) = 0 & % 102.76/15.62 | maps(all_32_7, all_32_4, all_32_3) = 0 & $i(all_32_1) & $i(all_32_2) & % 102.76/15.62 | $i(all_32_3) & $i(all_32_4) & $i(all_32_5) & $i(all_32_6) & % 102.76/15.62 | $i(all_32_7) % 102.76/15.62 | % 102.76/15.62 | ALPHA: (11) implies: % 102.76/15.62 | (12) ~ (all_32_0 = 0) % 102.76/15.62 | (13) $i(all_32_7) % 102.76/15.62 | (14) $i(all_32_6) % 102.76/15.62 | (15) $i(all_32_5) % 102.76/15.62 | (16) $i(all_32_4) % 102.76/15.62 | (17) $i(all_32_3) % 102.76/15.62 | (18) $i(all_32_2) % 102.76/15.62 | (19) $i(all_32_1) % 102.76/15.62 | (20) maps(all_32_7, all_32_4, all_32_3) = 0 % 102.76/15.62 | (21) maps(all_32_6, all_32_3, all_32_4) = 0 % 102.76/15.62 | (22) maps(all_32_5, all_32_3, all_32_4) = 0 % 102.76/15.62 | (23) compose_function(all_32_7, all_32_5, all_32_3, all_32_4, all_32_3) = % 102.76/15.62 | all_32_1 % 102.76/15.62 | (24) compose_function(all_32_6, all_32_7, all_32_4, all_32_3, all_32_4) = % 102.76/15.62 | all_32_2 % 102.76/15.62 | (25) identity(all_32_2, all_32_4) = 0 % 102.76/15.62 | (26) identity(all_32_1, all_32_3) = 0 % 102.76/15.62 | (27) one_to_one(all_32_7, all_32_4, all_32_3) = all_32_0 % 102.76/15.62 | % 102.76/15.62 | GROUND_INST: instantiating (8) with all_32_7, all_32_4, all_32_3, all_32_0, % 102.76/15.62 | simplifying with (13), (16), (17), (27) gives: % 102.76/15.62 | (28) all_32_0 = 0 | ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 102.76/15.62 | surjective(all_32_7, all_32_4, all_32_3) = v1) | ( ~ (v0 = 0) & % 102.76/15.62 | injective(all_32_7, all_32_4, all_32_3) = v0)) % 102.76/15.62 | % 102.76/15.62 | BETA: splitting (28) gives: % 102.76/15.62 | % 102.76/15.62 | Case 1: % 102.76/15.62 | | % 102.76/15.62 | | (29) all_32_0 = 0 % 102.76/15.62 | | % 102.76/15.62 | | REDUCE: (12), (29) imply: % 102.76/15.62 | | (30) $false % 102.76/15.62 | | % 102.76/15.62 | | CLOSE: (30) is inconsistent. % 102.76/15.62 | | % 102.76/15.62 | Case 2: % 102.76/15.62 | | % 102.76/15.62 | | (31) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & surjective(all_32_7, % 102.76/15.62 | | all_32_4, all_32_3) = v1) | ( ~ (v0 = 0) & injective(all_32_7, % 102.76/15.62 | | all_32_4, all_32_3) = v0)) % 102.76/15.62 | | % 102.76/15.62 | | DELTA: instantiating (31) with fresh symbols all_41_0, all_41_1 gives: % 102.76/15.62 | | (32) ( ~ (all_41_0 = 0) & surjective(all_32_7, all_32_4, all_32_3) = % 102.76/15.62 | | all_41_0) | ( ~ (all_41_1 = 0) & injective(all_32_7, all_32_4, % 102.76/15.62 | | all_32_3) = all_41_1) % 102.76/15.62 | | % 102.76/15.62 | | BETA: splitting (32) gives: % 102.76/15.62 | | % 102.76/15.62 | | Case 1: % 102.76/15.63 | | | % 102.76/15.63 | | | (33) ~ (all_41_0 = 0) & surjective(all_32_7, all_32_4, all_32_3) = % 102.76/15.63 | | | all_41_0 % 102.76/15.63 | | | % 102.76/15.63 | | | ALPHA: (33) implies: % 102.76/15.63 | | | (34) ~ (all_41_0 = 0) % 102.76/15.63 | | | (35) surjective(all_32_7, all_32_4, all_32_3) = all_41_0 % 102.76/15.63 | | | % 102.76/15.63 | | | GROUND_INST: instantiating (7) with all_32_7, all_32_4, all_32_3, % 102.76/15.63 | | | all_41_0, simplifying with (13), (16), (17), (35) gives: % 102.76/15.63 | | | (36) all_41_0 = 0 | ? [v0: $i] : (member(v0, all_32_3) = 0 & $i(v0) & % 102.76/15.63 | | | ! [v1: $i] : ( ~ (apply(all_32_7, v1, v0) = 0) | ~ $i(v1) | ? % 102.76/15.63 | | | [v2: int] : ( ~ (v2 = 0) & member(v1, all_32_4) = v2)) & ! % 102.76/15.63 | | | [v1: $i] : ( ~ (member(v1, all_32_4) = 0) | ~ $i(v1) | ? [v2: % 102.76/15.63 | | | int] : ( ~ (v2 = 0) & apply(all_32_7, v1, v0) = v2))) % 102.76/15.63 | | | % 102.76/15.63 | | | BETA: splitting (36) gives: % 102.76/15.63 | | | % 102.76/15.63 | | | Case 1: % 102.76/15.63 | | | | % 102.76/15.63 | | | | (37) all_41_0 = 0 % 102.76/15.63 | | | | % 102.76/15.63 | | | | REDUCE: (34), (37) imply: % 102.76/15.63 | | | | (38) $false % 102.76/15.63 | | | | % 102.76/15.63 | | | | CLOSE: (38) is inconsistent. % 102.76/15.63 | | | | % 102.76/15.63 | | | Case 2: % 102.76/15.63 | | | | % 102.76/15.63 | | | | (39) ? [v0: $i] : (member(v0, all_32_3) = 0 & $i(v0) & ! [v1: $i] : % 102.76/15.63 | | | | ( ~ (apply(all_32_7, v1, v0) = 0) | ~ $i(v1) | ? [v2: int] : % 102.76/15.63 | | | | ( ~ (v2 = 0) & member(v1, all_32_4) = v2)) & ! [v1: $i] : ( % 102.76/15.63 | | | | ~ (member(v1, all_32_4) = 0) | ~ $i(v1) | ? [v2: int] : ( % 102.76/15.63 | | | | ~ (v2 = 0) & apply(all_32_7, v1, v0) = v2))) % 102.76/15.63 | | | | % 102.76/15.63 | | | | DELTA: instantiating (39) with fresh symbol all_56_0 gives: % 102.76/15.63 | | | | (40) member(all_56_0, all_32_3) = 0 & $i(all_56_0) & ! [v0: $i] : ( % 102.76/15.63 | | | | ~ (apply(all_32_7, v0, all_56_0) = 0) | ~ $i(v0) | ? [v1: % 102.76/15.63 | | | | int] : ( ~ (v1 = 0) & member(v0, all_32_4) = v1)) & ! [v0: % 102.76/15.63 | | | | $i] : ( ~ (member(v0, all_32_4) = 0) | ~ $i(v0) | ? [v1: % 102.76/15.63 | | | | int] : ( ~ (v1 = 0) & apply(all_32_7, v0, all_56_0) = v1)) % 102.76/15.63 | | | | % 102.76/15.63 | | | | ALPHA: (40) implies: % 102.76/15.63 | | | | (41) $i(all_56_0) % 102.76/15.63 | | | | (42) member(all_56_0, all_32_3) = 0 % 102.76/15.63 | | | | (43) ! [v0: $i] : ( ~ (apply(all_32_7, v0, all_56_0) = 0) | ~ % 102.76/15.63 | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_4) = % 102.76/15.63 | | | | v1)) % 102.76/15.63 | | | | % 102.76/15.63 | | | | GROUND_INST: instantiating (5) with all_32_1, all_32_3, all_56_0, % 102.76/15.63 | | | | simplifying with (17), (19), (26), (41), (42) gives: % 102.76/15.63 | | | | (44) apply(all_32_1, all_56_0, all_56_0) = 0 % 102.76/15.63 | | | | % 102.76/15.63 | | | | GROUND_INST: instantiating (4) with all_32_7, all_32_5, all_32_3, % 102.76/15.63 | | | | all_32_4, all_32_3, all_56_0, all_56_0, all_32_1, % 102.76/15.63 | | | | simplifying with (13), (15), (16), (17), (23), (41), (44) % 102.76/15.63 | | | | gives: % 102.76/15.63 | | | | (45) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? [v3: int] : ? % 102.76/15.63 | | | | [v4: int] : ? [v5: int] : ($i(v2) & ((v5 = 0 & v4 = 0 & v3 = 0 % 102.76/15.63 | | | | & apply(all_32_5, all_56_0, v2) = 0 & apply(all_32_7, v2, % 102.76/15.63 | | | | all_56_0) = 0 & member(v2, all_32_4) = 0) | ( ~ (v1 = 0) % 102.76/15.63 | | | | & member(all_56_0, all_32_3) = v1) | ( ~ (v0 = 0) & % 102.76/15.63 | | | | member(all_56_0, all_32_3) = v0))) % 102.76/15.63 | | | | % 102.76/15.63 | | | | DELTA: instantiating (45) with fresh symbols all_83_0, all_83_1, % 102.76/15.63 | | | | all_83_2, all_83_3, all_83_4, all_83_5 gives: % 102.76/15.64 | | | | (46) $i(all_83_3) & ((all_83_0 = 0 & all_83_1 = 0 & all_83_2 = 0 & % 102.76/15.64 | | | | apply(all_32_5, all_56_0, all_83_3) = 0 & apply(all_32_7, % 102.76/15.64 | | | | all_83_3, all_56_0) = 0 & member(all_83_3, all_32_4) = 0) % 102.76/15.64 | | | | | ( ~ (all_83_4 = 0) & member(all_56_0, all_32_3) = all_83_4) % 102.76/15.64 | | | | | ( ~ (all_83_5 = 0) & member(all_56_0, all_32_3) = all_83_5)) % 102.76/15.64 | | | | % 102.76/15.64 | | | | ALPHA: (46) implies: % 102.76/15.64 | | | | (47) $i(all_83_3) % 102.76/15.64 | | | | (48) (all_83_0 = 0 & all_83_1 = 0 & all_83_2 = 0 & apply(all_32_5, % 102.76/15.64 | | | | all_56_0, all_83_3) = 0 & apply(all_32_7, all_83_3, % 102.76/15.64 | | | | all_56_0) = 0 & member(all_83_3, all_32_4) = 0) | ( ~ % 102.76/15.64 | | | | (all_83_4 = 0) & member(all_56_0, all_32_3) = all_83_4) | ( ~ % 102.76/15.64 | | | | (all_83_5 = 0) & member(all_56_0, all_32_3) = all_83_5) % 102.76/15.64 | | | | % 102.76/15.64 | | | | BETA: splitting (48) gives: % 102.76/15.64 | | | | % 102.76/15.64 | | | | Case 1: % 102.76/15.64 | | | | | % 102.76/15.64 | | | | | (49) all_83_0 = 0 & all_83_1 = 0 & all_83_2 = 0 & apply(all_32_5, % 102.76/15.64 | | | | | all_56_0, all_83_3) = 0 & apply(all_32_7, all_83_3, % 102.76/15.64 | | | | | all_56_0) = 0 & member(all_83_3, all_32_4) = 0 % 102.76/15.64 | | | | | % 102.76/15.64 | | | | | ALPHA: (49) implies: % 102.76/15.64 | | | | | (50) member(all_83_3, all_32_4) = 0 % 102.76/15.64 | | | | | (51) apply(all_32_7, all_83_3, all_56_0) = 0 % 102.76/15.64 | | | | | % 102.76/15.64 | | | | | GROUND_INST: instantiating (43) with all_83_3, simplifying with (47), % 102.76/15.64 | | | | | (51) gives: % 102.76/15.64 | | | | | (52) ? [v0: int] : ( ~ (v0 = 0) & member(all_83_3, all_32_4) = v0) % 102.76/15.64 | | | | | % 102.76/15.64 | | | | | DELTA: instantiating (52) with fresh symbol all_95_0 gives: % 102.76/15.64 | | | | | (53) ~ (all_95_0 = 0) & member(all_83_3, all_32_4) = all_95_0 % 102.76/15.64 | | | | | % 102.76/15.64 | | | | | ALPHA: (53) implies: % 102.76/15.64 | | | | | (54) ~ (all_95_0 = 0) % 102.76/15.64 | | | | | (55) member(all_83_3, all_32_4) = all_95_0 % 102.76/15.64 | | | | | % 102.76/15.64 | | | | | GROUND_INST: instantiating (9) with 0, all_95_0, all_32_4, all_83_3, % 102.76/15.64 | | | | | simplifying with (50), (55) gives: % 102.76/15.64 | | | | | (56) all_95_0 = 0 % 102.76/15.64 | | | | | % 102.76/15.64 | | | | | REDUCE: (54), (56) imply: % 102.76/15.64 | | | | | (57) $false % 103.23/15.64 | | | | | % 103.23/15.64 | | | | | CLOSE: (57) is inconsistent. % 103.23/15.64 | | | | | % 103.23/15.64 | | | | Case 2: % 103.23/15.64 | | | | | % 103.23/15.64 | | | | | (58) ( ~ (all_83_4 = 0) & member(all_56_0, all_32_3) = all_83_4) | % 103.23/15.64 | | | | | ( ~ (all_83_5 = 0) & member(all_56_0, all_32_3) = all_83_5) % 103.23/15.64 | | | | | % 103.23/15.64 | | | | | BETA: splitting (58) gives: % 103.23/15.64 | | | | | % 103.23/15.64 | | | | | Case 1: % 103.23/15.64 | | | | | | % 103.23/15.64 | | | | | | (59) ~ (all_83_4 = 0) & member(all_56_0, all_32_3) = all_83_4 % 103.23/15.64 | | | | | | % 103.23/15.64 | | | | | | ALPHA: (59) implies: % 103.23/15.64 | | | | | | (60) ~ (all_83_4 = 0) % 103.23/15.64 | | | | | | (61) member(all_56_0, all_32_3) = all_83_4 % 103.23/15.64 | | | | | | % 103.23/15.64 | | | | | | GROUND_INST: instantiating (9) with 0, all_83_4, all_32_3, all_56_0, % 103.23/15.64 | | | | | | simplifying with (42), (61) gives: % 103.23/15.64 | | | | | | (62) all_83_4 = 0 % 103.23/15.64 | | | | | | % 103.23/15.64 | | | | | | REDUCE: (60), (62) imply: % 103.23/15.64 | | | | | | (63) $false % 103.23/15.64 | | | | | | % 103.23/15.64 | | | | | | CLOSE: (63) is inconsistent. % 103.23/15.64 | | | | | | % 103.23/15.64 | | | | | Case 2: % 103.23/15.64 | | | | | | % 103.23/15.64 | | | | | | (64) ~ (all_83_5 = 0) & member(all_56_0, all_32_3) = all_83_5 % 103.23/15.64 | | | | | | % 103.23/15.64 | | | | | | ALPHA: (64) implies: % 103.23/15.64 | | | | | | (65) ~ (all_83_5 = 0) % 103.23/15.64 | | | | | | (66) member(all_56_0, all_32_3) = all_83_5 % 103.23/15.64 | | | | | | % 103.23/15.64 | | | | | | GROUND_INST: instantiating (9) with 0, all_83_5, all_32_3, all_56_0, % 103.23/15.64 | | | | | | simplifying with (42), (66) gives: % 103.23/15.64 | | | | | | (67) all_83_5 = 0 % 103.23/15.64 | | | | | | % 103.23/15.64 | | | | | | REDUCE: (65), (67) imply: % 103.23/15.64 | | | | | | (68) $false % 103.23/15.64 | | | | | | % 103.23/15.64 | | | | | | CLOSE: (68) is inconsistent. % 103.23/15.64 | | | | | | % 103.23/15.64 | | | | | End of split % 103.23/15.64 | | | | | % 103.23/15.64 | | | | End of split % 103.23/15.64 | | | | % 103.23/15.64 | | | End of split % 103.23/15.64 | | | % 103.23/15.64 | | Case 2: % 103.23/15.64 | | | % 103.23/15.64 | | | (69) ~ (all_41_1 = 0) & injective(all_32_7, all_32_4, all_32_3) = % 103.23/15.64 | | | all_41_1 % 103.23/15.64 | | | % 103.23/15.64 | | | ALPHA: (69) implies: % 103.23/15.64 | | | (70) ~ (all_41_1 = 0) % 103.23/15.64 | | | (71) injective(all_32_7, all_32_4, all_32_3) = all_41_1 % 103.23/15.64 | | | % 103.23/15.65 | | | GROUND_INST: instantiating (6) with all_32_7, all_32_4, all_32_3, % 103.23/15.65 | | | all_41_1, simplifying with (13), (16), (17), (71) gives: % 103.23/15.65 | | | (72) all_41_1 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = % 103.23/15.65 | | | v0) & apply(all_32_7, v1, v2) = 0 & apply(all_32_7, v0, v2) = % 103.23/15.65 | | | 0 & member(v2, all_32_3) = 0 & member(v1, all_32_4) = 0 & % 103.23/15.65 | | | member(v0, all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0)) % 103.23/15.65 | | | % 103.23/15.65 | | | BETA: splitting (72) gives: % 103.23/15.65 | | | % 103.23/15.65 | | | Case 1: % 103.23/15.65 | | | | % 103.23/15.65 | | | | (73) all_41_1 = 0 % 103.23/15.65 | | | | % 103.23/15.65 | | | | REDUCE: (70), (73) imply: % 103.23/15.65 | | | | (74) $false % 103.23/15.65 | | | | % 103.23/15.65 | | | | CLOSE: (74) is inconsistent. % 103.23/15.65 | | | | % 103.23/15.65 | | | Case 2: % 103.23/15.65 | | | | % 103.23/15.65 | | | | (75) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) & % 103.23/15.65 | | | | apply(all_32_7, v1, v2) = 0 & apply(all_32_7, v0, v2) = 0 & % 103.23/15.65 | | | | member(v2, all_32_3) = 0 & member(v1, all_32_4) = 0 & % 103.23/15.65 | | | | member(v0, all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0)) % 103.23/15.65 | | | | % 103.23/15.65 | | | | DELTA: instantiating (75) with fresh symbols all_56_0, all_56_1, % 103.23/15.65 | | | | all_56_2 gives: % 103.23/15.65 | | | | (76) ~ (all_56_1 = all_56_2) & apply(all_32_7, all_56_1, all_56_0) = % 103.23/15.65 | | | | 0 & apply(all_32_7, all_56_2, all_56_0) = 0 & member(all_56_0, % 103.23/15.65 | | | | all_32_3) = 0 & member(all_56_1, all_32_4) = 0 & % 103.23/15.65 | | | | member(all_56_2, all_32_4) = 0 & $i(all_56_0) & $i(all_56_1) & % 103.23/15.65 | | | | $i(all_56_2) % 103.23/15.65 | | | | % 103.23/15.65 | | | | ALPHA: (76) implies: % 103.23/15.65 | | | | (77) ~ (all_56_1 = all_56_2) % 103.23/15.65 | | | | (78) $i(all_56_2) % 103.23/15.65 | | | | (79) $i(all_56_1) % 103.23/15.65 | | | | (80) $i(all_56_0) % 103.23/15.65 | | | | (81) member(all_56_2, all_32_4) = 0 % 103.23/15.65 | | | | (82) member(all_56_1, all_32_4) = 0 % 103.23/15.65 | | | | (83) member(all_56_0, all_32_3) = 0 % 103.23/15.65 | | | | (84) apply(all_32_7, all_56_2, all_56_0) = 0 % 103.23/15.65 | | | | (85) apply(all_32_7, all_56_1, all_56_0) = 0 % 103.23/15.65 | | | | % 103.23/15.65 | | | | GROUND_INST: instantiating (5) with all_32_2, all_32_4, all_56_2, % 103.23/15.65 | | | | simplifying with (16), (18), (25), (78), (81) gives: % 103.23/15.65 | | | | (86) apply(all_32_2, all_56_2, all_56_2) = 0 % 103.23/15.65 | | | | % 103.23/15.65 | | | | GROUND_INST: instantiating (1) with all_32_7, all_32_4, all_32_3, % 103.23/15.65 | | | | all_56_1, simplifying with (13), (16), (17), (20), (79), % 103.23/15.65 | | | | (82) gives: % 103.23/15.65 | | | | (87) ? [v0: $i] : (apply(all_32_7, all_56_1, v0) = 0 & member(v0, % 103.23/15.65 | | | | all_32_3) = 0 & $i(v0)) % 103.23/15.65 | | | | % 103.23/15.65 | | | | GROUND_INST: instantiating (5) with all_32_2, all_32_4, all_56_1, % 103.23/15.65 | | | | simplifying with (16), (18), (25), (79), (82) gives: % 103.23/15.65 | | | | (88) apply(all_32_2, all_56_1, all_56_1) = 0 % 103.23/15.65 | | | | % 103.23/15.65 | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_3, all_32_4, % 103.23/15.65 | | | | all_56_0, all_56_2, all_56_1, simplifying with (14), (16), % 103.23/15.65 | | | | (17), (21), (78), (79), (80), (81), (82), (83) gives: % 103.23/15.65 | | | | (89) all_56_1 = all_56_2 | ? [v0: int] : ? [v1: int] : (( ~ (v1 = % 103.23/15.65 | | | | 0) & apply(all_32_6, all_56_0, all_56_1) = v1) | ( ~ (v0 = % 103.23/15.65 | | | | 0) & apply(all_32_6, all_56_0, all_56_2) = v0)) % 103.23/15.65 | | | | % 103.23/15.65 | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_3, all_32_4, % 103.23/15.65 | | | | all_56_0, all_56_1, all_56_2, simplifying with (14), (16), % 103.23/15.65 | | | | (17), (21), (78), (79), (80), (81), (82), (83) gives: % 103.23/15.65 | | | | (90) all_56_1 = all_56_2 | ? [v0: int] : ? [v1: int] : (( ~ (v1 = % 103.23/15.65 | | | | 0) & apply(all_32_6, all_56_0, all_56_2) = v1) | ( ~ (v0 = % 103.23/15.65 | | | | 0) & apply(all_32_6, all_56_0, all_56_1) = v0)) % 103.23/15.65 | | | | % 103.23/15.65 | | | | DELTA: instantiating (87) with fresh symbol all_70_0 gives: % 103.23/15.65 | | | | (91) apply(all_32_7, all_56_1, all_70_0) = 0 & member(all_70_0, % 103.23/15.65 | | | | all_32_3) = 0 & $i(all_70_0) % 103.23/15.65 | | | | % 103.23/15.65 | | | | ALPHA: (91) implies: % 103.23/15.65 | | | | (92) $i(all_70_0) % 103.23/15.65 | | | | (93) member(all_70_0, all_32_3) = 0 % 103.23/15.65 | | | | % 103.23/15.66 | | | | BETA: splitting (89) gives: % 103.23/15.66 | | | | % 103.23/15.66 | | | | Case 1: % 103.23/15.66 | | | | | % 103.23/15.66 | | | | | (94) all_56_1 = all_56_2 % 103.23/15.66 | | | | | % 103.23/15.66 | | | | | REDUCE: (77), (94) imply: % 103.23/15.66 | | | | | (95) $false % 103.23/15.66 | | | | | % 103.23/15.66 | | | | | CLOSE: (95) is inconsistent. % 103.23/15.66 | | | | | % 103.23/15.66 | | | | Case 2: % 103.23/15.66 | | | | | % 103.23/15.66 | | | | | (96) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & apply(all_32_6, % 103.23/15.66 | | | | | all_56_0, all_56_1) = v1) | ( ~ (v0 = 0) & % 103.23/15.66 | | | | | apply(all_32_6, all_56_0, all_56_2) = v0)) % 103.23/15.66 | | | | | % 103.23/15.66 | | | | | DELTA: instantiating (96) with fresh symbols all_76_0, all_76_1 gives: % 103.23/15.66 | | | | | (97) ( ~ (all_76_0 = 0) & apply(all_32_6, all_56_0, all_56_1) = % 103.23/15.66 | | | | | all_76_0) | ( ~ (all_76_1 = 0) & apply(all_32_6, all_56_0, % 103.23/15.66 | | | | | all_56_2) = all_76_1) % 103.23/15.66 | | | | | % 103.23/15.66 | | | | | BETA: splitting (90) gives: % 103.23/15.66 | | | | | % 103.23/15.66 | | | | | Case 1: % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | | (98) all_56_1 = all_56_2 % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | | REDUCE: (77), (98) imply: % 103.23/15.66 | | | | | | (99) $false % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | | CLOSE: (99) is inconsistent. % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | Case 2: % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | | (100) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 103.23/15.66 | | | | | | apply(all_32_6, all_56_0, all_56_2) = v1) | ( ~ (v0 = % 103.23/15.66 | | | | | | 0) & apply(all_32_6, all_56_0, all_56_1) = v0)) % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | | DELTA: instantiating (100) with fresh symbols all_80_0, all_80_1 % 103.23/15.66 | | | | | | gives: % 103.23/15.66 | | | | | | (101) ( ~ (all_80_0 = 0) & apply(all_32_6, all_56_0, all_56_2) = % 103.23/15.66 | | | | | | all_80_0) | ( ~ (all_80_1 = 0) & apply(all_32_6, % 103.23/15.66 | | | | | | all_56_0, all_56_1) = all_80_1) % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | | GROUND_INST: instantiating (2) with all_32_5, all_32_3, all_32_4, % 103.23/15.66 | | | | | | all_70_0, all_56_2, all_56_1, simplifying with (15), % 103.23/15.66 | | | | | | (16), (17), (22), (78), (79), (81), (82), (92), (93) % 103.23/15.66 | | | | | | gives: % 103.23/15.66 | | | | | | (102) all_56_1 = all_56_2 | ? [v0: int] : ? [v1: int] : (( ~ % 103.23/15.66 | | | | | | (v1 = 0) & apply(all_32_5, all_70_0, all_56_1) = v1) | % 103.23/15.66 | | | | | | ( ~ (v0 = 0) & apply(all_32_5, all_70_0, all_56_2) = v0)) % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | | GROUND_INST: instantiating (4) with all_32_6, all_32_7, all_32_4, % 103.23/15.66 | | | | | | all_32_3, all_32_4, all_56_2, all_56_2, all_32_2, % 103.23/15.66 | | | | | | simplifying with (13), (14), (16), (17), (24), (78), % 103.23/15.66 | | | | | | (86) gives: % 103.23/15.66 | | | | | | (103) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? [v3: int] : % 103.23/15.66 | | | | | | ? [v4: int] : ? [v5: int] : ($i(v2) & ((v5 = 0 & v4 = 0 & % 103.23/15.66 | | | | | | v3 = 0 & apply(all_32_6, v2, all_56_2) = 0 & % 103.23/15.66 | | | | | | apply(all_32_7, all_56_2, v2) = 0 & member(v2, % 103.23/15.66 | | | | | | all_32_3) = 0) | ( ~ (v1 = 0) & member(all_56_2, % 103.23/15.66 | | | | | | all_32_4) = v1) | ( ~ (v0 = 0) & member(all_56_2, % 103.23/15.66 | | | | | | all_32_4) = v0))) % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | | GROUND_INST: instantiating (4) with all_32_6, all_32_7, all_32_4, % 103.23/15.66 | | | | | | all_32_3, all_32_4, all_56_1, all_56_1, all_32_2, % 103.23/15.66 | | | | | | simplifying with (13), (14), (16), (17), (24), (79), % 103.23/15.66 | | | | | | (88) gives: % 103.23/15.66 | | | | | | (104) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? [v3: int] : % 103.23/15.66 | | | | | | ? [v4: int] : ? [v5: int] : ($i(v2) & ((v5 = 0 & v4 = 0 & % 103.23/15.66 | | | | | | v3 = 0 & apply(all_32_6, v2, all_56_1) = 0 & % 103.23/15.66 | | | | | | apply(all_32_7, all_56_1, v2) = 0 & member(v2, % 103.23/15.66 | | | | | | all_32_3) = 0) | ( ~ (v1 = 0) & member(all_56_1, % 103.23/15.66 | | | | | | all_32_4) = v1) | ( ~ (v0 = 0) & member(all_56_1, % 103.23/15.66 | | | | | | all_32_4) = v0))) % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | | DELTA: instantiating (104) with fresh symbols all_109_0, all_109_1, % 103.23/15.66 | | | | | | all_109_2, all_109_3, all_109_4, all_109_5 gives: % 103.23/15.66 | | | | | | (105) $i(all_109_3) & ((all_109_0 = 0 & all_109_1 = 0 & all_109_2 % 103.23/15.66 | | | | | | = 0 & apply(all_32_6, all_109_3, all_56_1) = 0 & % 103.23/15.66 | | | | | | apply(all_32_7, all_56_1, all_109_3) = 0 & % 103.23/15.66 | | | | | | member(all_109_3, all_32_3) = 0) | ( ~ (all_109_4 = 0) % 103.23/15.66 | | | | | | & member(all_56_1, all_32_4) = all_109_4) | ( ~ % 103.23/15.66 | | | | | | (all_109_5 = 0) & member(all_56_1, all_32_4) = % 103.23/15.66 | | | | | | all_109_5)) % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | | ALPHA: (105) implies: % 103.23/15.66 | | | | | | (106) $i(all_109_3) % 103.23/15.66 | | | | | | (107) (all_109_0 = 0 & all_109_1 = 0 & all_109_2 = 0 & % 103.23/15.66 | | | | | | apply(all_32_6, all_109_3, all_56_1) = 0 & % 103.23/15.66 | | | | | | apply(all_32_7, all_56_1, all_109_3) = 0 & % 103.23/15.66 | | | | | | member(all_109_3, all_32_3) = 0) | ( ~ (all_109_4 = 0) & % 103.23/15.66 | | | | | | member(all_56_1, all_32_4) = all_109_4) | ( ~ (all_109_5 % 103.23/15.66 | | | | | | = 0) & member(all_56_1, all_32_4) = all_109_5) % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | | DELTA: instantiating (103) with fresh symbols all_111_0, all_111_1, % 103.23/15.66 | | | | | | all_111_2, all_111_3, all_111_4, all_111_5 gives: % 103.23/15.66 | | | | | | (108) $i(all_111_3) & ((all_111_0 = 0 & all_111_1 = 0 & all_111_2 % 103.23/15.66 | | | | | | = 0 & apply(all_32_6, all_111_3, all_56_2) = 0 & % 103.23/15.66 | | | | | | apply(all_32_7, all_56_2, all_111_3) = 0 & % 103.23/15.66 | | | | | | member(all_111_3, all_32_3) = 0) | ( ~ (all_111_4 = 0) % 103.23/15.66 | | | | | | & member(all_56_2, all_32_4) = all_111_4) | ( ~ % 103.23/15.66 | | | | | | (all_111_5 = 0) & member(all_56_2, all_32_4) = % 103.23/15.66 | | | | | | all_111_5)) % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | | ALPHA: (108) implies: % 103.23/15.66 | | | | | | (109) $i(all_111_3) % 103.23/15.66 | | | | | | (110) (all_111_0 = 0 & all_111_1 = 0 & all_111_2 = 0 & % 103.23/15.66 | | | | | | apply(all_32_6, all_111_3, all_56_2) = 0 & % 103.23/15.66 | | | | | | apply(all_32_7, all_56_2, all_111_3) = 0 & % 103.23/15.66 | | | | | | member(all_111_3, all_32_3) = 0) | ( ~ (all_111_4 = 0) & % 103.23/15.66 | | | | | | member(all_56_2, all_32_4) = all_111_4) | ( ~ (all_111_5 % 103.23/15.66 | | | | | | = 0) & member(all_56_2, all_32_4) = all_111_5) % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | | BETA: splitting (110) gives: % 103.23/15.66 | | | | | | % 103.23/15.66 | | | | | | Case 1: % 103.23/15.66 | | | | | | | % 103.23/15.67 | | | | | | | (111) all_111_0 = 0 & all_111_1 = 0 & all_111_2 = 0 & % 103.23/15.67 | | | | | | | apply(all_32_6, all_111_3, all_56_2) = 0 & % 103.23/15.67 | | | | | | | apply(all_32_7, all_56_2, all_111_3) = 0 & % 103.23/15.67 | | | | | | | member(all_111_3, all_32_3) = 0 % 103.23/15.67 | | | | | | | % 103.23/15.67 | | | | | | | ALPHA: (111) implies: % 103.23/15.67 | | | | | | | (112) member(all_111_3, all_32_3) = 0 % 103.23/15.67 | | | | | | | (113) apply(all_32_7, all_56_2, all_111_3) = 0 % 103.23/15.67 | | | | | | | (114) apply(all_32_6, all_111_3, all_56_2) = 0 % 103.23/15.67 | | | | | | | % 103.23/15.67 | | | | | | | BETA: splitting (107) gives: % 103.23/15.67 | | | | | | | % 103.23/15.67 | | | | | | | Case 1: % 103.23/15.67 | | | | | | | | % 103.23/15.67 | | | | | | | | (115) all_109_0 = 0 & all_109_1 = 0 & all_109_2 = 0 & % 103.23/15.67 | | | | | | | | apply(all_32_6, all_109_3, all_56_1) = 0 & % 103.23/15.67 | | | | | | | | apply(all_32_7, all_56_1, all_109_3) = 0 & % 103.23/15.67 | | | | | | | | member(all_109_3, all_32_3) = 0 % 103.23/15.67 | | | | | | | | % 103.23/15.67 | | | | | | | | ALPHA: (115) implies: % 103.23/15.67 | | | | | | | | (116) member(all_109_3, all_32_3) = 0 % 103.23/15.67 | | | | | | | | (117) apply(all_32_7, all_56_1, all_109_3) = 0 % 103.23/15.67 | | | | | | | | (118) apply(all_32_6, all_109_3, all_56_1) = 0 % 103.23/15.67 | | | | | | | | % 103.23/15.67 | | | | | | | | BETA: splitting (102) gives: % 103.23/15.67 | | | | | | | | % 103.23/15.67 | | | | | | | | Case 1: % 103.23/15.67 | | | | | | | | | % 103.23/15.67 | | | | | | | | | (119) all_56_1 = all_56_2 % 103.23/15.67 | | | | | | | | | % 103.23/15.67 | | | | | | | | | REDUCE: (77), (119) imply: % 103.23/15.67 | | | | | | | | | (120) $false % 103.23/15.67 | | | | | | | | | % 103.23/15.67 | | | | | | | | | CLOSE: (120) is inconsistent. % 103.23/15.67 | | | | | | | | | % 103.23/15.67 | | | | | | | | Case 2: % 103.23/15.67 | | | | | | | | | % 103.23/15.67 | | | | | | | | | % 103.23/15.67 | | | | | | | | | GROUND_INST: instantiating (2) with all_32_7, all_32_4, % 103.23/15.67 | | | | | | | | | all_32_3, all_56_2, all_56_0, all_111_3, % 103.23/15.67 | | | | | | | | | simplifying with (13), (16), (17), (20), (78), % 103.23/15.67 | | | | | | | | | (80), (81), (83), (109), (112) gives: % 103.23/15.67 | | | | | | | | | (121) all_111_3 = all_56_0 | ? [v0: int] : ? [v1: int] : % 103.23/15.67 | | | | | | | | | (( ~ (v1 = 0) & apply(all_32_7, all_56_2, all_111_3) % 103.23/15.67 | | | | | | | | | = v1) | ( ~ (v0 = 0) & apply(all_32_7, all_56_2, % 103.23/15.67 | | | | | | | | | all_56_0) = v0)) % 103.23/15.67 | | | | | | | | | % 103.23/15.67 | | | | | | | | | GROUND_INST: instantiating (3) with all_32_7, all_32_4, % 103.23/15.67 | | | | | | | | | all_32_3, all_56_1, all_56_0, all_109_3, % 103.23/15.67 | | | | | | | | | simplifying with (13), (16), (17), (20), (79), % 103.23/15.67 | | | | | | | | | (80), (83), (106), (117) gives: % 103.23/15.67 | | | | | | | | | (122) all_109_3 = all_56_0 | ? [v0: int] : ? [v1: int] : % 103.23/15.67 | | | | | | | | | ? [v2: int] : (( ~ (v2 = 0) & apply(all_32_7, % 103.23/15.67 | | | | | | | | | all_56_1, all_56_0) = v2) | ( ~ (v1 = 0) & % 103.23/15.67 | | | | | | | | | member(all_109_3, all_32_3) = v1) | ( ~ (v0 = 0) % 103.23/15.67 | | | | | | | | | & member(all_56_1, all_32_4) = v0)) % 103.23/15.67 | | | | | | | | | % 103.23/15.67 | | | | | | | | | BETA: splitting (122) gives: % 103.23/15.67 | | | | | | | | | % 103.23/15.67 | | | | | | | | | Case 1: % 103.23/15.67 | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | (123) all_109_3 = all_56_0 % 103.23/15.67 | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | REDUCE: (118), (123) imply: % 103.23/15.67 | | | | | | | | | | (124) apply(all_32_6, all_56_0, all_56_1) = 0 % 103.23/15.67 | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | BETA: splitting (97) gives: % 103.23/15.67 | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | Case 1: % 103.23/15.67 | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | (125) ~ (all_76_0 = 0) & apply(all_32_6, all_56_0, % 103.23/15.67 | | | | | | | | | | | all_56_1) = all_76_0 % 103.23/15.67 | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | ALPHA: (125) implies: % 103.23/15.67 | | | | | | | | | | | (126) ~ (all_76_0 = 0) % 103.23/15.67 | | | | | | | | | | | (127) apply(all_32_6, all_56_0, all_56_1) = all_76_0 % 103.23/15.67 | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_76_0, all_56_1, % 103.23/15.67 | | | | | | | | | | | all_56_0, all_32_6, simplifying with (124), (127) % 103.23/15.67 | | | | | | | | | | | gives: % 103.23/15.67 | | | | | | | | | | | (128) all_76_0 = 0 % 103.23/15.67 | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | REDUCE: (126), (128) imply: % 103.23/15.67 | | | | | | | | | | | (129) $false % 103.23/15.67 | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | CLOSE: (129) is inconsistent. % 103.23/15.67 | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | Case 2: % 103.23/15.67 | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | (130) ~ (all_76_1 = 0) & apply(all_32_6, all_56_0, % 103.23/15.67 | | | | | | | | | | | all_56_2) = all_76_1 % 103.23/15.67 | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | ALPHA: (130) implies: % 103.23/15.67 | | | | | | | | | | | (131) ~ (all_76_1 = 0) % 103.23/15.67 | | | | | | | | | | | (132) apply(all_32_6, all_56_0, all_56_2) = all_76_1 % 103.23/15.67 | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | BETA: splitting (101) gives: % 103.23/15.67 | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | Case 1: % 103.23/15.67 | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | (133) ~ (all_80_0 = 0) & apply(all_32_6, all_56_0, % 103.23/15.67 | | | | | | | | | | | | all_56_2) = all_80_0 % 103.23/15.67 | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | ALPHA: (133) implies: % 103.23/15.67 | | | | | | | | | | | | (134) apply(all_32_6, all_56_0, all_56_2) = all_80_0 % 103.23/15.67 | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | BETA: splitting (121) gives: % 103.23/15.67 | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | Case 1: % 103.23/15.67 | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | | (135) all_111_3 = all_56_0 % 103.23/15.67 | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | | REDUCE: (114), (135) imply: % 103.23/15.67 | | | | | | | | | | | | | (136) apply(all_32_6, all_56_0, all_56_2) = 0 % 103.23/15.67 | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_76_1, all_80_0, % 103.23/15.67 | | | | | | | | | | | | | all_56_2, all_56_0, all_32_6, simplifying with % 103.23/15.67 | | | | | | | | | | | | | (132), (134) gives: % 103.23/15.67 | | | | | | | | | | | | | (137) all_80_0 = all_76_1 % 103.23/15.67 | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_80_0, all_56_2, % 103.23/15.67 | | | | | | | | | | | | | all_56_0, all_32_6, simplifying with (134), (136) % 103.23/15.67 | | | | | | | | | | | | | gives: % 103.23/15.67 | | | | | | | | | | | | | (138) all_80_0 = 0 % 103.23/15.67 | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | | COMBINE_EQS: (137), (138) imply: % 103.23/15.67 | | | | | | | | | | | | | (139) all_76_1 = 0 % 103.23/15.67 | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | | SIMP: (139) implies: % 103.23/15.67 | | | | | | | | | | | | | (140) all_76_1 = 0 % 103.23/15.67 | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | | REDUCE: (131), (140) imply: % 103.23/15.67 | | | | | | | | | | | | | (141) $false % 103.23/15.67 | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | | CLOSE: (141) is inconsistent. % 103.23/15.67 | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | Case 2: % 103.23/15.67 | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | | (142) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 103.23/15.67 | | | | | | | | | | | | | apply(all_32_7, all_56_2, all_111_3) = v1) | ( % 103.23/15.67 | | | | | | | | | | | | | ~ (v0 = 0) & apply(all_32_7, all_56_2, % 103.23/15.67 | | | | | | | | | | | | | all_56_0) = v0)) % 103.23/15.67 | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | | DELTA: instantiating (142) with fresh symbols all_254_0, % 103.23/15.67 | | | | | | | | | | | | | all_254_1 gives: % 103.23/15.67 | | | | | | | | | | | | | (143) ( ~ (all_254_0 = 0) & apply(all_32_7, all_56_2, % 103.23/15.67 | | | | | | | | | | | | | all_111_3) = all_254_0) | ( ~ (all_254_1 = 0) % 103.23/15.67 | | | | | | | | | | | | | & apply(all_32_7, all_56_2, all_56_0) = % 103.23/15.67 | | | | | | | | | | | | | all_254_1) % 103.23/15.67 | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | | BETA: splitting (143) gives: % 103.23/15.67 | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | | Case 1: % 103.23/15.67 | | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | | | (144) ~ (all_254_0 = 0) & apply(all_32_7, all_56_2, % 103.23/15.67 | | | | | | | | | | | | | | all_111_3) = all_254_0 % 103.23/15.67 | | | | | | | | | | | | | | % 103.23/15.67 | | | | | | | | | | | | | | ALPHA: (144) implies: % 103.23/15.67 | | | | | | | | | | | | | | (145) ~ (all_254_0 = 0) % 103.23/15.67 | | | | | | | | | | | | | | (146) apply(all_32_7, all_56_2, all_111_3) = all_254_0 % 103.23/15.67 | | | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_254_0, all_111_3, % 103.23/15.68 | | | | | | | | | | | | | | all_56_2, all_32_7, simplifying with (113), (146) % 103.23/15.68 | | | | | | | | | | | | | | gives: % 103.23/15.68 | | | | | | | | | | | | | | (147) all_254_0 = 0 % 103.23/15.68 | | | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | | | REDUCE: (145), (147) imply: % 103.23/15.68 | | | | | | | | | | | | | | (148) $false % 103.23/15.68 | | | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | | | CLOSE: (148) is inconsistent. % 103.23/15.68 | | | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | | Case 2: % 103.23/15.68 | | | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | | | (149) ~ (all_254_1 = 0) & apply(all_32_7, all_56_2, % 103.23/15.68 | | | | | | | | | | | | | | all_56_0) = all_254_1 % 103.23/15.68 | | | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | | | ALPHA: (149) implies: % 103.23/15.68 | | | | | | | | | | | | | | (150) ~ (all_254_1 = 0) % 103.23/15.68 | | | | | | | | | | | | | | (151) apply(all_32_7, all_56_2, all_56_0) = all_254_1 % 103.23/15.68 | | | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_254_1, all_56_0, % 103.23/15.68 | | | | | | | | | | | | | | all_56_2, all_32_7, simplifying with (84), (151) % 103.23/15.68 | | | | | | | | | | | | | | gives: % 103.23/15.68 | | | | | | | | | | | | | | (152) all_254_1 = 0 % 103.23/15.68 | | | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | | | REDUCE: (150), (152) imply: % 103.23/15.68 | | | | | | | | | | | | | | (153) $false % 103.23/15.68 | | | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | | | CLOSE: (153) is inconsistent. % 103.23/15.68 | | | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | | End of split % 103.23/15.68 | | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | End of split % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | Case 2: % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | (154) ~ (all_80_1 = 0) & apply(all_32_6, all_56_0, % 103.23/15.68 | | | | | | | | | | | | all_56_1) = all_80_1 % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | ALPHA: (154) implies: % 103.23/15.68 | | | | | | | | | | | | (155) ~ (all_80_1 = 0) % 103.23/15.68 | | | | | | | | | | | | (156) apply(all_32_6, all_56_0, all_56_1) = all_80_1 % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_80_1, all_56_1, % 103.23/15.68 | | | | | | | | | | | | all_56_0, all_32_6, simplifying with (124), (156) % 103.23/15.68 | | | | | | | | | | | | gives: % 103.23/15.68 | | | | | | | | | | | | (157) all_80_1 = 0 % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | REDUCE: (155), (157) imply: % 103.23/15.68 | | | | | | | | | | | | (158) $false % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | CLOSE: (158) is inconsistent. % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | End of split % 103.23/15.68 | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | End of split % 103.23/15.68 | | | | | | | | | | % 103.23/15.68 | | | | | | | | | Case 2: % 103.23/15.68 | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | (159) ? [v0: int] : ? [v1: int] : ? [v2: int] : (( ~ % 103.23/15.68 | | | | | | | | | | (v2 = 0) & apply(all_32_7, all_56_1, all_56_0) % 103.23/15.68 | | | | | | | | | | = v2) | ( ~ (v1 = 0) & member(all_109_3, % 103.23/15.68 | | | | | | | | | | all_32_3) = v1) | ( ~ (v0 = 0) & % 103.23/15.68 | | | | | | | | | | member(all_56_1, all_32_4) = v0)) % 103.23/15.68 | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | DELTA: instantiating (159) with fresh symbols all_238_0, % 103.23/15.68 | | | | | | | | | | all_238_1, all_238_2 gives: % 103.23/15.68 | | | | | | | | | | (160) ( ~ (all_238_0 = 0) & apply(all_32_7, all_56_1, % 103.23/15.68 | | | | | | | | | | all_56_0) = all_238_0) | ( ~ (all_238_1 = 0) & % 103.23/15.68 | | | | | | | | | | member(all_109_3, all_32_3) = all_238_1) | ( ~ % 103.23/15.68 | | | | | | | | | | (all_238_2 = 0) & member(all_56_1, all_32_4) = % 103.23/15.68 | | | | | | | | | | all_238_2) % 103.23/15.68 | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | BETA: splitting (160) gives: % 103.23/15.68 | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | Case 1: % 103.23/15.68 | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | (161) ~ (all_238_0 = 0) & apply(all_32_7, all_56_1, % 103.23/15.68 | | | | | | | | | | | all_56_0) = all_238_0 % 103.23/15.68 | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | ALPHA: (161) implies: % 103.23/15.68 | | | | | | | | | | | (162) ~ (all_238_0 = 0) % 103.23/15.68 | | | | | | | | | | | (163) apply(all_32_7, all_56_1, all_56_0) = all_238_0 % 103.23/15.68 | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_238_0, all_56_0, % 103.23/15.68 | | | | | | | | | | | all_56_1, all_32_7, simplifying with (85), (163) % 103.23/15.68 | | | | | | | | | | | gives: % 103.23/15.68 | | | | | | | | | | | (164) all_238_0 = 0 % 103.23/15.68 | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | REDUCE: (162), (164) imply: % 103.23/15.68 | | | | | | | | | | | (165) $false % 103.23/15.68 | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | CLOSE: (165) is inconsistent. % 103.23/15.68 | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | Case 2: % 103.23/15.68 | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | (166) ( ~ (all_238_1 = 0) & member(all_109_3, all_32_3) % 103.23/15.68 | | | | | | | | | | | = all_238_1) | ( ~ (all_238_2 = 0) & % 103.23/15.68 | | | | | | | | | | | member(all_56_1, all_32_4) = all_238_2) % 103.23/15.68 | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | BETA: splitting (166) gives: % 103.23/15.68 | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | Case 1: % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | (167) ~ (all_238_1 = 0) & member(all_109_3, all_32_3) = % 103.23/15.68 | | | | | | | | | | | | all_238_1 % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | ALPHA: (167) implies: % 103.23/15.68 | | | | | | | | | | | | (168) ~ (all_238_1 = 0) % 103.23/15.68 | | | | | | | | | | | | (169) member(all_109_3, all_32_3) = all_238_1 % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_238_1, all_32_3, % 103.23/15.68 | | | | | | | | | | | | all_109_3, simplifying with (116), (169) gives: % 103.23/15.68 | | | | | | | | | | | | (170) all_238_1 = 0 % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | REDUCE: (168), (170) imply: % 103.23/15.68 | | | | | | | | | | | | (171) $false % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | CLOSE: (171) is inconsistent. % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | Case 2: % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | (172) ~ (all_238_2 = 0) & member(all_56_1, all_32_4) = % 103.23/15.68 | | | | | | | | | | | | all_238_2 % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | ALPHA: (172) implies: % 103.23/15.68 | | | | | | | | | | | | (173) ~ (all_238_2 = 0) % 103.23/15.68 | | | | | | | | | | | | (174) member(all_56_1, all_32_4) = all_238_2 % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_238_2, all_32_4, % 103.23/15.68 | | | | | | | | | | | | all_56_1, simplifying with (82), (174) gives: % 103.23/15.68 | | | | | | | | | | | | (175) all_238_2 = 0 % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | REDUCE: (173), (175) imply: % 103.23/15.68 | | | | | | | | | | | | (176) $false % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | | CLOSE: (176) is inconsistent. % 103.23/15.68 | | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | | End of split % 103.23/15.68 | | | | | | | | | | | % 103.23/15.68 | | | | | | | | | | End of split % 103.23/15.68 | | | | | | | | | | % 103.23/15.68 | | | | | | | | | End of split % 103.23/15.68 | | | | | | | | | % 103.23/15.68 | | | | | | | | End of split % 103.23/15.68 | | | | | | | | % 103.23/15.68 | | | | | | | Case 2: % 103.23/15.68 | | | | | | | | % 103.23/15.68 | | | | | | | | (177) ( ~ (all_109_4 = 0) & member(all_56_1, all_32_4) = % 103.23/15.68 | | | | | | | | all_109_4) | ( ~ (all_109_5 = 0) & member(all_56_1, % 103.23/15.68 | | | | | | | | all_32_4) = all_109_5) % 103.23/15.68 | | | | | | | | % 103.23/15.68 | | | | | | | | BETA: splitting (177) gives: % 103.23/15.68 | | | | | | | | % 103.23/15.68 | | | | | | | | Case 1: % 103.23/15.68 | | | | | | | | | % 103.23/15.68 | | | | | | | | | (178) ~ (all_109_4 = 0) & member(all_56_1, all_32_4) = % 103.23/15.68 | | | | | | | | | all_109_4 % 103.23/15.68 | | | | | | | | | % 103.23/15.68 | | | | | | | | | ALPHA: (178) implies: % 103.23/15.68 | | | | | | | | | (179) ~ (all_109_4 = 0) % 103.23/15.68 | | | | | | | | | (180) member(all_56_1, all_32_4) = all_109_4 % 103.23/15.68 | | | | | | | | | % 103.23/15.68 | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_109_4, all_32_4, % 103.23/15.68 | | | | | | | | | all_56_1, simplifying with (82), (180) gives: % 103.23/15.68 | | | | | | | | | (181) all_109_4 = 0 % 103.23/15.68 | | | | | | | | | % 103.23/15.68 | | | | | | | | | REDUCE: (179), (181) imply: % 103.23/15.68 | | | | | | | | | (182) $false % 103.23/15.68 | | | | | | | | | % 103.23/15.68 | | | | | | | | | CLOSE: (182) is inconsistent. % 103.23/15.68 | | | | | | | | | % 103.23/15.68 | | | | | | | | Case 2: % 103.23/15.68 | | | | | | | | | % 103.23/15.68 | | | | | | | | | (183) ~ (all_109_5 = 0) & member(all_56_1, all_32_4) = % 103.23/15.68 | | | | | | | | | all_109_5 % 103.23/15.68 | | | | | | | | | % 103.23/15.68 | | | | | | | | | ALPHA: (183) implies: % 103.23/15.68 | | | | | | | | | (184) ~ (all_109_5 = 0) % 103.23/15.68 | | | | | | | | | (185) member(all_56_1, all_32_4) = all_109_5 % 103.23/15.68 | | | | | | | | | % 103.23/15.68 | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_109_5, all_32_4, % 103.23/15.68 | | | | | | | | | all_56_1, simplifying with (82), (185) gives: % 103.23/15.68 | | | | | | | | | (186) all_109_5 = 0 % 103.23/15.68 | | | | | | | | | % 103.23/15.68 | | | | | | | | | REDUCE: (184), (186) imply: % 103.23/15.68 | | | | | | | | | (187) $false % 103.23/15.68 | | | | | | | | | % 103.23/15.68 | | | | | | | | | CLOSE: (187) is inconsistent. % 103.23/15.68 | | | | | | | | | % 103.23/15.68 | | | | | | | | End of split % 103.23/15.68 | | | | | | | | % 103.23/15.68 | | | | | | | End of split % 103.23/15.68 | | | | | | | % 103.23/15.68 | | | | | | Case 2: % 103.23/15.68 | | | | | | | % 103.23/15.68 | | | | | | | (188) ( ~ (all_111_4 = 0) & member(all_56_2, all_32_4) = % 103.23/15.68 | | | | | | | all_111_4) | ( ~ (all_111_5 = 0) & member(all_56_2, % 103.23/15.68 | | | | | | | all_32_4) = all_111_5) % 103.23/15.68 | | | | | | | % 103.23/15.68 | | | | | | | BETA: splitting (188) gives: % 103.23/15.68 | | | | | | | % 103.23/15.68 | | | | | | | Case 1: % 103.23/15.68 | | | | | | | | % 103.23/15.68 | | | | | | | | (189) ~ (all_111_4 = 0) & member(all_56_2, all_32_4) = % 103.23/15.68 | | | | | | | | all_111_4 % 103.23/15.69 | | | | | | | | % 103.23/15.69 | | | | | | | | ALPHA: (189) implies: % 103.23/15.69 | | | | | | | | (190) ~ (all_111_4 = 0) % 103.23/15.69 | | | | | | | | (191) member(all_56_2, all_32_4) = all_111_4 % 103.23/15.69 | | | | | | | | % 103.23/15.69 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_111_4, all_32_4, % 103.23/15.69 | | | | | | | | all_56_2, simplifying with (81), (191) gives: % 103.23/15.69 | | | | | | | | (192) all_111_4 = 0 % 103.23/15.69 | | | | | | | | % 103.23/15.69 | | | | | | | | REDUCE: (190), (192) imply: % 103.23/15.69 | | | | | | | | (193) $false % 103.23/15.69 | | | | | | | | % 103.23/15.69 | | | | | | | | CLOSE: (193) is inconsistent. % 103.23/15.69 | | | | | | | | % 103.23/15.69 | | | | | | | Case 2: % 103.23/15.69 | | | | | | | | % 103.23/15.69 | | | | | | | | (194) ~ (all_111_5 = 0) & member(all_56_2, all_32_4) = % 103.23/15.69 | | | | | | | | all_111_5 % 103.23/15.69 | | | | | | | | % 103.23/15.69 | | | | | | | | ALPHA: (194) implies: % 103.23/15.69 | | | | | | | | (195) ~ (all_111_5 = 0) % 103.23/15.69 | | | | | | | | (196) member(all_56_2, all_32_4) = all_111_5 % 103.23/15.69 | | | | | | | | % 103.23/15.69 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_111_5, all_32_4, % 103.23/15.69 | | | | | | | | all_56_2, simplifying with (81), (196) gives: % 103.23/15.69 | | | | | | | | (197) all_111_5 = 0 % 103.23/15.69 | | | | | | | | % 103.23/15.69 | | | | | | | | REDUCE: (195), (197) imply: % 103.23/15.69 | | | | | | | | (198) $false % 103.23/15.69 | | | | | | | | % 103.23/15.69 | | | | | | | | CLOSE: (198) is inconsistent. % 103.23/15.69 | | | | | | | | % 103.23/15.69 | | | | | | | End of split % 103.23/15.69 | | | | | | | % 103.23/15.69 | | | | | | End of split % 103.23/15.69 | | | | | | % 103.23/15.69 | | | | | End of split % 103.23/15.69 | | | | | % 103.23/15.69 | | | | End of split % 103.23/15.69 | | | | % 103.23/15.69 | | | End of split % 103.23/15.69 | | | % 103.23/15.69 | | End of split % 103.23/15.69 | | % 103.23/15.69 | End of split % 103.23/15.69 | % 103.23/15.69 End of proof % 103.23/15.69 % SZS output end Proof for theBenchmark % 103.23/15.69 % 103.23/15.69 15073ms %------------------------------------------------------------------------------