%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU255+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n015.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 17:43:41 EDT 2023 % Result : Theorem 9.03s 1.93s % Output : Proof 14.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU255+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n015.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 : Wed Aug 23 15:09:50 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 ... % 0.20/0.63 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 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 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 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 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 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.29/1.04 Prover 1: Preprocessing ... % 2.29/1.04 Prover 4: Preprocessing ... % 2.93/1.08 Prover 2: Preprocessing ... % 2.93/1.08 Prover 5: Preprocessing ... % 2.93/1.08 Prover 0: Preprocessing ... % 2.93/1.08 Prover 3: Preprocessing ... % 2.93/1.08 Prover 6: Preprocessing ... % 4.99/1.46 Prover 5: Proving ... % 4.99/1.48 Prover 6: Proving ... % 4.99/1.48 Prover 1: Warning: ignoring some quantifiers % 4.99/1.48 Prover 3: Warning: ignoring some quantifiers % 4.99/1.48 Prover 2: Proving ... % 4.99/1.49 Prover 1: Constructing countermodel ... % 5.82/1.51 Prover 3: Constructing countermodel ... % 5.82/1.53 Prover 4: Warning: ignoring some quantifiers % 6.21/1.55 Prover 4: Constructing countermodel ... % 6.36/1.58 Prover 0: Proving ... % 8.01/1.82 Prover 3: gave up % 8.01/1.82 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.59/1.86 Prover 7: Preprocessing ... % 9.03/1.92 Prover 1: gave up % 9.03/1.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.03/1.92 Prover 0: proved (1292ms) % 9.03/1.93 % 9.03/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.03/1.93 % 9.03/1.94 Prover 5: stopped % 9.03/1.94 Prover 6: stopped % 9.03/1.95 Prover 2: stopped % 9.34/1.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.34/1.97 Prover 8: Preprocessing ... % 9.34/1.97 Prover 7: Warning: ignoring some quantifiers % 9.34/1.97 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.34/1.97 Prover 7: Constructing countermodel ... % 9.34/1.97 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.34/1.97 Prover 10: Preprocessing ... % 9.34/1.99 Prover 11: Preprocessing ... % 9.34/2.01 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.34/2.01 Prover 13: Preprocessing ... % 9.34/2.03 Prover 10: Warning: ignoring some quantifiers % 9.34/2.03 Prover 10: Constructing countermodel ... % 9.34/2.04 Prover 16: Preprocessing ... % 9.34/2.04 Prover 8: Warning: ignoring some quantifiers % 9.34/2.05 Prover 8: Constructing countermodel ... % 9.34/2.10 Prover 13: Warning: ignoring some quantifiers % 9.34/2.10 Prover 13: Constructing countermodel ... % 9.34/2.11 Prover 16: Warning: ignoring some quantifiers % 9.34/2.11 Prover 16: Constructing countermodel ... % 9.34/2.14 Prover 11: Warning: ignoring some quantifiers % 9.34/2.15 Prover 10: gave up % 9.34/2.15 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 9.34/2.16 Prover 11: Constructing countermodel ... % 9.34/2.17 Prover 19: Preprocessing ... % 11.22/2.27 Prover 19: Warning: ignoring some quantifiers % 11.22/2.29 Prover 8: gave up % 11.22/2.29 Prover 19: Constructing countermodel ... % 13.39/2.56 Prover 4: Found proof (size 136) % 13.39/2.56 Prover 4: proved (1916ms) % 13.39/2.56 Prover 7: stopped % 13.39/2.56 Prover 13: stopped % 13.39/2.56 Prover 16: stopped % 13.39/2.56 Prover 19: stopped % 13.39/2.56 Prover 11: stopped % 13.39/2.56 % 13.39/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.39/2.56 % 13.39/2.58 % SZS output start Proof for theBenchmark % 13.39/2.58 Assumptions after simplification: % 13.39/2.58 --------------------------------- % 13.39/2.58 % 13.39/2.58 (cc2_funct_1) % 13.75/2.61 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2: % 13.75/2.61 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) = % 13.75/2.61 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) % 13.75/2.61 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 13.75/2.61 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0) % 13.75/2.61 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ % 13.75/2.61 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] % 13.75/2.61 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) | % 13.75/2.61 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) % 13.75/2.61 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & % 13.75/2.61 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = % 13.75/2.61 0))) % 13.75/2.61 % 13.75/2.61 (dt_k2_wellord1) % 13.75/2.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) = % 13.75/2.61 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (relation(v2) % 13.75/2.61 = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 13.75/2.61 % 13.75/2.61 (l3_wellord1) % 13.75/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 13.75/2.62 (antisymmetric(v0) = 0) | ~ (ordered_pair(v2, v1) = v3) | ~ $i(v2) | ~ % 13.75/2.62 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : (( ~ (v4 = % 13.75/2.62 0) & relation(v0) = v4) | (ordered_pair(v1, v2) = v4 & in(v4, v0) = v5 % 13.75/2.62 & in(v3, v0) = v6 & $i(v4) & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ! [v0: % 13.75/2.62 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 13.75/2.62 (antisymmetric(v0) = 0) | ~ (ordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ % 13.75/2.62 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: any] : (( ~ (v4 = % 13.75/2.62 0) & relation(v0) = v4) | (ordered_pair(v2, v1) = v5 & in(v5, v0) = v6 % 13.75/2.62 & in(v3, v0) = v4 & $i(v5) & ( ~ (v6 = 0) | ~ (v4 = 0))))) & ! [v0: % 13.75/2.62 $i] : ! [v1: int] : (v1 = 0 | ~ (antisymmetric(v0) = v1) | ~ $i(v0) | ? % 13.75/2.62 [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: % 13.75/2.62 $i] : ? [v8: int] : ($i(v4) & $i(v3) & ((v8 = 0 & v6 = 0 & ~ (v4 = v3) & % 13.75/2.62 ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = 0 % 13.75/2.62 & in(v5, v0) = 0 & $i(v7) & $i(v5)) | ( ~ (v2 = 0) & relation(v0) = % 13.75/2.62 v2)))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: % 13.75/2.62 any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ? [v6: % 13.75/2.62 $i] : ? [v7: int] : (antisymmetric(v0) = v1 & $i(v3) & $i(v2) & ( ~ (v1 = % 13.75/2.62 0) | ( ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : (v9 = v8 | ~ % 13.75/2.62 (ordered_pair(v9, v8) = v10) | ~ $i(v9) | ~ $i(v8) | ? [v11: $i] % 13.75/2.62 : ? [v12: any] : ? [v13: any] : (ordered_pair(v8, v9) = v11 & % 13.75/2.62 in(v11, v0) = v12 & in(v10, v0) = v13 & $i(v11) & ( ~ (v13 = 0) | % 13.75/2.62 ~ (v12 = 0)))) & ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : (v9 % 13.75/2.62 = v8 | ~ (ordered_pair(v8, v9) = v10) | ~ $i(v9) | ~ $i(v8) | ? % 13.75/2.62 [v11: any] : ? [v12: $i] : ? [v13: any] : (ordered_pair(v9, v8) = % 13.75/2.62 v12 & in(v12, v0) = v13 & in(v10, v0) = v11 & $i(v12) & ( ~ (v13 = % 13.75/2.62 0) | ~ (v11 = 0)))))) & (v1 = 0 | (v7 = 0 & v5 = 0 & ~ (v3 = % 13.75/2.62 v2) & ordered_pair(v3, v2) = v6 & ordered_pair(v2, v3) = v4 & in(v6, % 13.75/2.62 v0) = 0 & in(v4, v0) = 0 & $i(v6) & $i(v4))))) % 13.75/2.62 % 13.75/2.62 (t16_wellord1) % 13.75/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 13.75/2.62 (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~ $i(v2) | ~ % 13.75/2.62 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: % 13.75/2.62 any] : (cartesian_product2(v1, v1) = v7 & relation(v2) = v5 & in(v0, v7) = % 13.75/2.62 v8 & in(v0, v2) = v6 & $i(v7) & ( ~ (v5 = 0) | (( ~ (v8 = 0) | ~ (v6 = 0) % 13.75/2.62 | v4 = 0) & ( ~ (v4 = 0) | (v8 = 0 & v6 = 0)))))) % 13.75/2.62 % 13.75/2.62 (t25_wellord1) % 13.75/2.62 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 13.75/2.62 antisymmetric(v2) = v3 & antisymmetric(v1) = 0 & relation_restriction(v1, % 13.75/2.62 v0) = v2 & relation(v1) = 0 & $i(v2) & $i(v1) & $i(v0)) % 13.75/2.62 % 13.75/2.62 (function-axioms) % 13.75/2.63 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.75/2.63 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 13.75/2.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.75/2.63 (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = % 13.75/2.63 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 13.75/2.63 ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 13.75/2.63 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.75/2.63 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] % 13.75/2.63 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.75/2.63 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 13.75/2.63 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.75/2.63 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 13.75/2.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.75/2.63 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 13.75/2.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 13.75/2.63 ~ (antisymmetric(v2) = v1) | ~ (antisymmetric(v2) = v0)) & ! [v0: $i] : ! % 13.75/2.63 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 13.75/2.63 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.75/2.63 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ % 13.75/2.63 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.75/2.63 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 13.75/2.63 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.75/2.63 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 13.75/2.63 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.75/2.63 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 13.75/2.63 (empty(v2) = v0)) % 13.75/2.63 % 13.75/2.63 Further assumptions not needed in the proof: % 13.75/2.63 -------------------------------------------- % 13.75/2.63 antisymmetry_r2_hidden, cc1_funct_1, commutativity_k2_tarski, % 13.75/2.63 commutativity_k3_xboole_0, d5_tarski, d6_wellord1, dt_k1_tarski, dt_k1_xboole_0, % 13.75/2.63 dt_k2_tarski, dt_k2_zfmisc_1, dt_k3_xboole_0, dt_k4_tarski, dt_m1_subset_1, % 13.75/2.63 existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, idempotence_k3_xboole_0, % 13.75/2.63 rc1_funct_1, rc1_xboole_0, rc2_funct_1, rc2_xboole_0, rc3_funct_1, t1_subset, % 13.75/2.63 t2_boole, t2_subset, t6_boole, t7_boole, t8_boole % 13.75/2.63 % 13.75/2.63 Those formulas are unsatisfiable: % 13.75/2.63 --------------------------------- % 13.75/2.63 % 13.75/2.63 Begin of proof % 13.75/2.63 | % 13.75/2.63 | ALPHA: (cc2_funct_1) implies: % 13.75/2.63 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 13.75/2.63 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & % 13.75/2.63 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 13.75/2.63 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? % 13.75/2.63 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & % 13.75/2.63 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | % 13.75/2.63 | ~ (v2 = 0) | v1 = 0))) % 13.75/2.63 | % 13.75/2.63 | ALPHA: (l3_wellord1) implies: % 13.75/2.63 | (3) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 13.75/2.63 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ? [v6: $i] : % 13.75/2.63 | ? [v7: int] : (antisymmetric(v0) = v1 & $i(v3) & $i(v2) & ( ~ (v1 = % 13.75/2.63 | 0) | ( ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : (v9 = v8 | ~ % 13.75/2.63 | (ordered_pair(v9, v8) = v10) | ~ $i(v9) | ~ $i(v8) | ? % 13.75/2.63 | [v11: $i] : ? [v12: any] : ? [v13: any] : (ordered_pair(v8, % 13.75/2.63 | v9) = v11 & in(v11, v0) = v12 & in(v10, v0) = v13 & % 13.75/2.63 | $i(v11) & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v8: $i] : % 13.75/2.63 | ! [v9: $i] : ! [v10: $i] : (v9 = v8 | ~ (ordered_pair(v8, v9) % 13.75/2.63 | = v10) | ~ $i(v9) | ~ $i(v8) | ? [v11: any] : ? [v12: % 13.75/2.63 | $i] : ? [v13: any] : (ordered_pair(v9, v8) = v12 & in(v12, % 13.75/2.63 | v0) = v13 & in(v10, v0) = v11 & $i(v12) & ( ~ (v13 = 0) | % 13.75/2.63 | ~ (v11 = 0)))))) & (v1 = 0 | (v7 = 0 & v5 = 0 & ~ (v3 = % 13.75/2.63 | v2) & ordered_pair(v3, v2) = v6 & ordered_pair(v2, v3) = v4 & % 13.75/2.63 | in(v6, v0) = 0 & in(v4, v0) = 0 & $i(v6) & $i(v4))))) % 13.75/2.64 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (antisymmetric(v0) = v1) | ~ % 13.75/2.64 | $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 13.75/2.64 | [v6: int] : ? [v7: $i] : ? [v8: int] : ($i(v4) & $i(v3) & ((v8 = 0 % 13.75/2.64 | & v6 = 0 & ~ (v4 = v3) & ordered_pair(v4, v3) = v7 & % 13.75/2.64 | ordered_pair(v3, v4) = v5 & in(v7, v0) = 0 & in(v5, v0) = 0 & % 13.75/2.64 | $i(v7) & $i(v5)) | ( ~ (v2 = 0) & relation(v0) = v2)))) % 13.75/2.64 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 13.75/2.64 | (antisymmetric(v0) = 0) | ~ (ordered_pair(v2, v1) = v3) | ~ $i(v2) % 13.75/2.64 | | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] % 13.75/2.64 | : (( ~ (v4 = 0) & relation(v0) = v4) | (ordered_pair(v1, v2) = v4 & % 13.75/2.64 | in(v4, v0) = v5 & in(v3, v0) = v6 & $i(v4) & ( ~ (v6 = 0) | ~ % 13.75/2.64 | (v5 = 0))))) % 13.75/2.64 | % 13.75/2.64 | ALPHA: (function-axioms) implies: % 13.75/2.64 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.75/2.64 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 13.75/2.64 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.75/2.64 | (v1 = v0 | ~ (antisymmetric(v2) = v1) | ~ (antisymmetric(v2) = v0)) % 13.75/2.64 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.75/2.64 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 13.75/2.64 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.75/2.64 | (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 13.75/2.64 | % 13.75/2.64 | DELTA: instantiating (t25_wellord1) with fresh symbols all_33_0, all_33_1, % 13.75/2.64 | all_33_2, all_33_3 gives: % 13.75/2.64 | (10) ~ (all_33_0 = 0) & antisymmetric(all_33_1) = all_33_0 & % 13.75/2.64 | antisymmetric(all_33_2) = 0 & relation_restriction(all_33_2, all_33_3) % 13.75/2.64 | = all_33_1 & relation(all_33_2) = 0 & $i(all_33_1) & $i(all_33_2) & % 13.75/2.64 | $i(all_33_3) % 13.75/2.64 | % 13.75/2.64 | ALPHA: (10) implies: % 13.75/2.64 | (11) ~ (all_33_0 = 0) % 13.75/2.64 | (12) $i(all_33_3) % 13.75/2.64 | (13) $i(all_33_2) % 13.75/2.64 | (14) $i(all_33_1) % 13.75/2.64 | (15) relation(all_33_2) = 0 % 13.75/2.64 | (16) relation_restriction(all_33_2, all_33_3) = all_33_1 % 13.75/2.64 | (17) antisymmetric(all_33_2) = 0 % 13.75/2.64 | (18) antisymmetric(all_33_1) = all_33_0 % 13.75/2.64 | % 13.75/2.64 | GROUND_INST: instantiating (3) with all_33_2, simplifying with (13), (15) % 13.75/2.64 | gives: % 13.75/2.64 | (19) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] % 13.75/2.64 | : ? [v5: $i] : ? [v6: int] : (antisymmetric(all_33_2) = v0 & $i(v2) % 13.75/2.64 | & $i(v1) & ( ~ (v0 = 0) | ( ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 13.75/2.64 | (v8 = v7 | ~ (ordered_pair(v8, v7) = v9) | ~ $i(v8) | ~ % 13.75/2.64 | $i(v7) | ? [v10: $i] : ? [v11: any] : ? [v12: any] : % 13.75/2.64 | (ordered_pair(v7, v8) = v10 & in(v10, all_33_2) = v11 & in(v9, % 13.75/2.64 | all_33_2) = v12 & $i(v10) & ( ~ (v12 = 0) | ~ (v11 = % 13.75/2.64 | 0)))) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v8 = % 13.75/2.64 | v7 | ~ (ordered_pair(v7, v8) = v9) | ~ $i(v8) | ~ $i(v7) | % 13.75/2.64 | ? [v10: any] : ? [v11: $i] : ? [v12: any] : % 13.75/2.64 | (ordered_pair(v8, v7) = v11 & in(v11, all_33_2) = v12 & in(v9, % 13.75/2.64 | all_33_2) = v10 & $i(v11) & ( ~ (v12 = 0) | ~ (v10 = % 13.75/2.64 | 0)))))) & (v0 = 0 | (v6 = 0 & v4 = 0 & ~ (v2 = v1) & % 13.75/2.64 | ordered_pair(v2, v1) = v5 & ordered_pair(v1, v2) = v3 & in(v5, % 13.75/2.64 | all_33_2) = 0 & in(v3, all_33_2) = 0 & $i(v5) & $i(v3)))) % 13.75/2.64 | % 13.75/2.64 | GROUND_INST: instantiating (1) with all_33_2, simplifying with (13), (15) % 13.75/2.64 | gives: % 13.75/2.64 | (20) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_33_2) = % 13.75/2.64 | v2 & function(all_33_2) = v1 & empty(all_33_2) = v0 & ( ~ (v1 = 0) | % 13.75/2.64 | ~ (v0 = 0) | v2 = 0)) % 13.75/2.64 | % 13.75/2.65 | GROUND_INST: instantiating (dt_k2_wellord1) with all_33_2, all_33_3, all_33_1, % 13.75/2.65 | simplifying with (12), (13), (16) gives: % 13.75/2.65 | (21) ? [v0: any] : ? [v1: any] : (relation(all_33_1) = v1 & % 13.75/2.65 | relation(all_33_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 13.75/2.65 | % 13.75/2.65 | GROUND_INST: instantiating (4) with all_33_1, all_33_0, simplifying with (14), % 13.75/2.65 | (18) gives: % 13.75/2.65 | (22) all_33_0 = 0 | ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 13.75/2.65 | : ? [v4: int] : ? [v5: $i] : ? [v6: int] : ($i(v2) & $i(v1) & ((v6 % 13.75/2.65 | = 0 & v4 = 0 & ~ (v2 = v1) & ordered_pair(v2, v1) = v5 & % 13.75/2.65 | ordered_pair(v1, v2) = v3 & in(v5, all_33_1) = 0 & in(v3, % 13.75/2.65 | all_33_1) = 0 & $i(v5) & $i(v3)) | ( ~ (v0 = 0) & % 13.75/2.65 | relation(all_33_1) = v0))) % 13.75/2.65 | % 13.75/2.65 | DELTA: instantiating (21) with fresh symbols all_45_0, all_45_1 gives: % 13.75/2.65 | (23) relation(all_33_1) = all_45_0 & relation(all_33_2) = all_45_1 & ( ~ % 13.75/2.65 | (all_45_1 = 0) | all_45_0 = 0) % 13.75/2.65 | % 13.75/2.65 | ALPHA: (23) implies: % 13.75/2.65 | (24) relation(all_33_2) = all_45_1 % 13.75/2.65 | (25) relation(all_33_1) = all_45_0 % 13.75/2.65 | (26) ~ (all_45_1 = 0) | all_45_0 = 0 % 13.75/2.65 | % 13.75/2.65 | DELTA: instantiating (20) with fresh symbols all_61_0, all_61_1, all_61_2 % 13.75/2.65 | gives: % 13.75/2.65 | (27) one_to_one(all_33_2) = all_61_0 & function(all_33_2) = all_61_1 & % 13.75/2.65 | empty(all_33_2) = all_61_2 & ( ~ (all_61_1 = 0) | ~ (all_61_2 = 0) | % 13.75/2.65 | all_61_0 = 0) % 13.75/2.65 | % 13.75/2.65 | ALPHA: (27) implies: % 13.75/2.65 | (28) one_to_one(all_33_2) = all_61_0 % 13.75/2.65 | % 13.75/2.65 | DELTA: instantiating (19) with fresh symbols all_73_0, all_73_1, all_73_2, % 13.75/2.65 | all_73_3, all_73_4, all_73_5, all_73_6 gives: % 13.75/2.65 | (29) antisymmetric(all_33_2) = all_73_6 & $i(all_73_4) & $i(all_73_5) & ( ~ % 13.75/2.65 | (all_73_6 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 13.75/2.65 | | ~ (ordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 13.75/2.65 | [v3: $i] : ? [v4: any] : ? [v5: any] : (ordered_pair(v0, v1) = % 13.75/2.65 | v3 & in(v3, all_33_2) = v4 & in(v2, all_33_2) = v5 & $i(v3) & % 13.75/2.65 | ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 13.75/2.65 | [v2: $i] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | % 13.75/2.65 | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 13.75/2.65 | (ordered_pair(v1, v0) = v4 & in(v4, all_33_2) = v5 & in(v2, % 13.75/2.65 | all_33_2) = v3 & $i(v4) & ( ~ (v5 = 0) | ~ (v3 = 0)))))) & % 13.75/2.65 | (all_73_6 = 0 | (all_73_0 = 0 & all_73_2 = 0 & ~ (all_73_4 = % 13.75/2.65 | all_73_5) & ordered_pair(all_73_4, all_73_5) = all_73_1 & % 13.75/2.65 | ordered_pair(all_73_5, all_73_4) = all_73_3 & in(all_73_1, % 13.75/2.65 | all_33_2) = 0 & in(all_73_3, all_33_2) = 0 & $i(all_73_1) & % 13.75/2.65 | $i(all_73_3))) % 13.75/2.65 | % 13.75/2.65 | ALPHA: (29) implies: % 13.75/2.65 | (30) antisymmetric(all_33_2) = all_73_6 % 13.75/2.65 | (31) ~ (all_73_6 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 13.75/2.65 | v0 | ~ (ordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 13.75/2.65 | [v3: $i] : ? [v4: any] : ? [v5: any] : (ordered_pair(v0, v1) = % 13.75/2.65 | v3 & in(v3, all_33_2) = v4 & in(v2, all_33_2) = v5 & $i(v3) & ( % 13.75/2.65 | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 13.75/2.65 | [v2: $i] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | % 13.75/2.65 | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 13.75/2.65 | (ordered_pair(v1, v0) = v4 & in(v4, all_33_2) = v5 & in(v2, % 13.75/2.65 | all_33_2) = v3 & $i(v4) & ( ~ (v5 = 0) | ~ (v3 = 0))))) % 13.75/2.65 | % 13.75/2.65 | BETA: splitting (22) gives: % 13.75/2.65 | % 13.75/2.65 | Case 1: % 13.75/2.65 | | % 13.75/2.65 | | (32) all_33_0 = 0 % 13.75/2.65 | | % 13.75/2.65 | | REDUCE: (11), (32) imply: % 13.75/2.65 | | (33) $false % 14.08/2.65 | | % 14.08/2.65 | | CLOSE: (33) is inconsistent. % 14.08/2.65 | | % 14.08/2.65 | Case 2: % 14.08/2.65 | | % 14.08/2.66 | | (34) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 14.08/2.66 | | int] : ? [v5: $i] : ? [v6: int] : ($i(v2) & $i(v1) & ((v6 = 0 & % 14.08/2.66 | | v4 = 0 & ~ (v2 = v1) & ordered_pair(v2, v1) = v5 & % 14.08/2.66 | | ordered_pair(v1, v2) = v3 & in(v5, all_33_1) = 0 & in(v3, % 14.08/2.66 | | all_33_1) = 0 & $i(v5) & $i(v3)) | ( ~ (v0 = 0) & % 14.08/2.66 | | relation(all_33_1) = v0))) % 14.08/2.66 | | % 14.08/2.66 | | DELTA: instantiating (34) with fresh symbols all_79_0, all_79_1, all_79_2, % 14.08/2.66 | | all_79_3, all_79_4, all_79_5, all_79_6 gives: % 14.08/2.66 | | (35) $i(all_79_4) & $i(all_79_5) & ((all_79_0 = 0 & all_79_2 = 0 & ~ % 14.08/2.66 | | (all_79_4 = all_79_5) & ordered_pair(all_79_4, all_79_5) = % 14.08/2.66 | | all_79_1 & ordered_pair(all_79_5, all_79_4) = all_79_3 & % 14.08/2.66 | | in(all_79_1, all_33_1) = 0 & in(all_79_3, all_33_1) = 0 & % 14.08/2.66 | | $i(all_79_1) & $i(all_79_3)) | ( ~ (all_79_6 = 0) & % 14.08/2.66 | | relation(all_33_1) = all_79_6)) % 14.08/2.66 | | % 14.08/2.66 | | ALPHA: (35) implies: % 14.08/2.66 | | (36) $i(all_79_5) % 14.08/2.66 | | (37) $i(all_79_4) % 14.08/2.66 | | (38) (all_79_0 = 0 & all_79_2 = 0 & ~ (all_79_4 = all_79_5) & % 14.08/2.66 | | ordered_pair(all_79_4, all_79_5) = all_79_1 & % 14.08/2.66 | | ordered_pair(all_79_5, all_79_4) = all_79_3 & in(all_79_1, % 14.08/2.66 | | all_33_1) = 0 & in(all_79_3, all_33_1) = 0 & $i(all_79_1) & % 14.08/2.66 | | $i(all_79_3)) | ( ~ (all_79_6 = 0) & relation(all_33_1) = % 14.08/2.66 | | all_79_6) % 14.08/2.66 | | % 14.08/2.66 | | GROUND_INST: instantiating (6) with 0, all_45_1, all_33_2, simplifying with % 14.08/2.66 | | (15), (24) gives: % 14.08/2.66 | | (39) all_45_1 = 0 % 14.08/2.66 | | % 14.08/2.66 | | GROUND_INST: instantiating (7) with 0, all_73_6, all_33_2, simplifying with % 14.08/2.66 | | (17), (30) gives: % 14.08/2.66 | | (40) all_73_6 = 0 % 14.08/2.66 | | % 14.08/2.66 | | BETA: splitting (26) gives: % 14.08/2.66 | | % 14.08/2.66 | | Case 1: % 14.08/2.66 | | | % 14.08/2.66 | | | (41) ~ (all_45_1 = 0) % 14.08/2.66 | | | % 14.08/2.66 | | | REDUCE: (39), (41) imply: % 14.08/2.66 | | | (42) $false % 14.08/2.66 | | | % 14.08/2.66 | | | CLOSE: (42) is inconsistent. % 14.08/2.66 | | | % 14.08/2.66 | | Case 2: % 14.08/2.66 | | | % 14.08/2.66 | | | (43) all_45_0 = 0 % 14.08/2.66 | | | % 14.08/2.66 | | | REDUCE: (25), (43) imply: % 14.08/2.66 | | | (44) relation(all_33_1) = 0 % 14.08/2.66 | | | % 14.08/2.66 | | | BETA: splitting (38) gives: % 14.08/2.66 | | | % 14.08/2.66 | | | Case 1: % 14.08/2.66 | | | | % 14.08/2.66 | | | | (45) all_79_0 = 0 & all_79_2 = 0 & ~ (all_79_4 = all_79_5) & % 14.08/2.66 | | | | ordered_pair(all_79_4, all_79_5) = all_79_1 & % 14.08/2.66 | | | | ordered_pair(all_79_5, all_79_4) = all_79_3 & in(all_79_1, % 14.08/2.66 | | | | all_33_1) = 0 & in(all_79_3, all_33_1) = 0 & $i(all_79_1) & % 14.08/2.66 | | | | $i(all_79_3) % 14.08/2.66 | | | | % 14.08/2.66 | | | | ALPHA: (45) implies: % 14.08/2.66 | | | | (46) ~ (all_79_4 = all_79_5) % 14.08/2.66 | | | | (47) $i(all_79_3) % 14.08/2.66 | | | | (48) $i(all_79_1) % 14.08/2.66 | | | | (49) in(all_79_3, all_33_1) = 0 % 14.08/2.66 | | | | (50) in(all_79_1, all_33_1) = 0 % 14.08/2.66 | | | | (51) ordered_pair(all_79_5, all_79_4) = all_79_3 % 14.08/2.66 | | | | (52) ordered_pair(all_79_4, all_79_5) = all_79_1 % 14.08/2.66 | | | | % 14.08/2.66 | | | | BETA: splitting (31) gives: % 14.08/2.66 | | | | % 14.08/2.66 | | | | Case 1: % 14.08/2.66 | | | | | % 14.12/2.66 | | | | | (53) ~ (all_73_6 = 0) % 14.12/2.66 | | | | | % 14.12/2.66 | | | | | REDUCE: (40), (53) imply: % 14.12/2.66 | | | | | (54) $false % 14.12/2.66 | | | | | % 14.12/2.66 | | | | | CLOSE: (54) is inconsistent. % 14.12/2.66 | | | | | % 14.12/2.66 | | | | Case 2: % 14.12/2.66 | | | | | % 14.12/2.66 | | | | | (55) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.12/2.66 | | | | | (ordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 14.12/2.66 | | | | | [v3: $i] : ? [v4: any] : ? [v5: any] : (ordered_pair(v0, % 14.12/2.66 | | | | | v1) = v3 & in(v3, all_33_2) = v4 & in(v2, all_33_2) = v5 % 14.12/2.66 | | | | | & $i(v3) & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : % 14.12/2.66 | | | | | ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (ordered_pair(v0, v1) % 14.12/2.66 | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] % 14.12/2.66 | | | | | : ? [v5: any] : (ordered_pair(v1, v0) = v4 & in(v4, % 14.12/2.66 | | | | | all_33_2) = v5 & in(v2, all_33_2) = v3 & $i(v4) & ( ~ % 14.12/2.66 | | | | | (v5 = 0) | ~ (v3 = 0)))) % 14.12/2.66 | | | | | % 14.12/2.66 | | | | | ALPHA: (55) implies: % 14.12/2.67 | | | | | (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.12/2.67 | | | | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 14.12/2.67 | | | | | [v3: any] : ? [v4: $i] : ? [v5: any] : (ordered_pair(v1, % 14.12/2.67 | | | | | v0) = v4 & in(v4, all_33_2) = v5 & in(v2, all_33_2) = v3 % 14.12/2.67 | | | | | & $i(v4) & ( ~ (v5 = 0) | ~ (v3 = 0)))) % 14.12/2.67 | | | | | (57) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.12/2.67 | | | | | (ordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 14.12/2.67 | | | | | [v3: $i] : ? [v4: any] : ? [v5: any] : (ordered_pair(v0, % 14.12/2.67 | | | | | v1) = v3 & in(v3, all_33_2) = v4 & in(v2, all_33_2) = v5 % 14.12/2.67 | | | | | & $i(v3) & ( ~ (v5 = 0) | ~ (v4 = 0)))) % 14.12/2.67 | | | | | % 14.12/2.67 | | | | | GROUND_INST: instantiating (t16_wellord1) with all_79_3, all_33_3, % 14.12/2.67 | | | | | all_33_2, all_33_1, 0, simplifying with (12), (13), (16), % 14.12/2.67 | | | | | (47), (49) gives: % 14.12/2.67 | | | | | (58) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 14.12/2.67 | | | | | (cartesian_product2(all_33_3, all_33_3) = v2 & % 14.12/2.67 | | | | | relation(all_33_2) = v0 & in(all_79_3, v2) = v3 & % 14.12/2.67 | | | | | in(all_79_3, all_33_2) = v1 & $i(v2) & ( ~ (v0 = 0) | (v3 = % 14.12/2.67 | | | | | 0 & v1 = 0))) % 14.12/2.67 | | | | | % 14.12/2.67 | | | | | GROUND_INST: instantiating (t16_wellord1) with all_79_1, all_33_3, % 14.12/2.67 | | | | | all_33_2, all_33_1, 0, simplifying with (12), (13), (16), % 14.12/2.67 | | | | | (48), (50) gives: % 14.12/2.67 | | | | | (59) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 14.12/2.67 | | | | | (cartesian_product2(all_33_3, all_33_3) = v2 & % 14.12/2.67 | | | | | relation(all_33_2) = v0 & in(all_79_1, v2) = v3 & % 14.12/2.67 | | | | | in(all_79_1, all_33_2) = v1 & $i(v2) & ( ~ (v0 = 0) | (v3 = % 14.12/2.67 | | | | | 0 & v1 = 0))) % 14.12/2.67 | | | | | % 14.12/2.67 | | | | | GROUND_INST: instantiating (2) with all_33_2, all_61_0, simplifying % 14.12/2.67 | | | | | with (13), (28) gives: % 14.12/2.67 | | | | | (60) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 14.12/2.67 | | | | | (relation(all_33_2) = v0 & function(all_33_2) = v2 & % 14.12/2.67 | | | | | empty(all_33_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 14.12/2.67 | | | | | 0) | all_61_0 = 0)) % 14.12/2.67 | | | | | % 14.12/2.67 | | | | | GROUND_INST: instantiating (5) with all_33_2, all_79_4, all_79_5, % 14.12/2.67 | | | | | all_79_3, simplifying with (13), (17), (36), (37), (51) % 14.12/2.67 | | | | | gives: % 14.12/2.67 | | | | | (61) all_79_4 = all_79_5 | ? [v0: any] : ? [v1: any] : ? [v2: % 14.12/2.67 | | | | | any] : (( ~ (v0 = 0) & relation(all_33_2) = v0) | % 14.12/2.67 | | | | | (ordered_pair(all_79_4, all_79_5) = v0 & in(v0, all_33_2) = % 14.12/2.67 | | | | | v1 & in(all_79_3, all_33_2) = v2 & $i(v0) & ( ~ (v2 = 0) | % 14.12/2.67 | | | | | ~ (v1 = 0)))) % 14.12/2.67 | | | | | % 14.12/2.67 | | | | | GROUND_INST: instantiating (5) with all_33_2, all_79_5, all_79_4, % 14.12/2.67 | | | | | all_79_1, simplifying with (13), (17), (36), (37), (52) % 14.12/2.67 | | | | | gives: % 14.12/2.67 | | | | | (62) all_79_4 = all_79_5 | ? [v0: any] : ? [v1: any] : ? [v2: % 14.12/2.67 | | | | | any] : (( ~ (v0 = 0) & relation(all_33_2) = v0) | % 14.12/2.67 | | | | | (ordered_pair(all_79_5, all_79_4) = v0 & in(v0, all_33_2) = % 14.12/2.67 | | | | | v1 & in(all_79_1, all_33_2) = v2 & $i(v0) & ( ~ (v2 = 0) | % 14.12/2.67 | | | | | ~ (v1 = 0)))) % 14.12/2.67 | | | | | % 14.12/2.67 | | | | | GROUND_INST: instantiating (57) with all_79_5, all_79_4, all_79_1, % 14.12/2.67 | | | | | simplifying with (36), (37), (52) gives: % 14.12/2.67 | | | | | (63) all_79_4 = all_79_5 | ? [v0: $i] : ? [v1: any] : ? [v2: % 14.12/2.67 | | | | | any] : (ordered_pair(all_79_5, all_79_4) = v0 & in(v0, % 14.12/2.67 | | | | | all_33_2) = v1 & in(all_79_1, all_33_2) = v2 & $i(v0) & ( % 14.12/2.67 | | | | | ~ (v2 = 0) | ~ (v1 = 0))) % 14.12/2.67 | | | | | % 14.12/2.67 | | | | | GROUND_INST: instantiating (56) with all_79_4, all_79_5, all_79_1, % 14.12/2.67 | | | | | simplifying with (36), (37), (52) gives: % 14.12/2.67 | | | | | (64) all_79_4 = all_79_5 | ? [v0: any] : ? [v1: $i] : ? [v2: % 14.12/2.67 | | | | | any] : (ordered_pair(all_79_5, all_79_4) = v1 & in(v1, % 14.12/2.67 | | | | | all_33_2) = v2 & in(all_79_1, all_33_2) = v0 & $i(v1) & ( % 14.12/2.67 | | | | | ~ (v2 = 0) | ~ (v0 = 0))) % 14.12/2.67 | | | | | % 14.12/2.67 | | | | | DELTA: instantiating (60) with fresh symbols all_135_0, all_135_1, % 14.12/2.67 | | | | | all_135_2 gives: % 14.12/2.67 | | | | | (65) relation(all_33_2) = all_135_2 & function(all_33_2) = % 14.12/2.67 | | | | | all_135_0 & empty(all_33_2) = all_135_1 & ( ~ (all_135_0 = 0) % 14.12/2.67 | | | | | | ~ (all_135_1 = 0) | ~ (all_135_2 = 0) | all_61_0 = 0) % 14.12/2.67 | | | | | % 14.12/2.67 | | | | | ALPHA: (65) implies: % 14.12/2.67 | | | | | (66) relation(all_33_2) = all_135_2 % 14.12/2.67 | | | | | % 14.12/2.67 | | | | | DELTA: instantiating (59) with fresh symbols all_139_0, all_139_1, % 14.12/2.67 | | | | | all_139_2, all_139_3 gives: % 14.12/2.67 | | | | | (67) cartesian_product2(all_33_3, all_33_3) = all_139_1 & % 14.12/2.67 | | | | | relation(all_33_2) = all_139_3 & in(all_79_1, all_139_1) = % 14.12/2.67 | | | | | all_139_0 & in(all_79_1, all_33_2) = all_139_2 & $i(all_139_1) % 14.12/2.67 | | | | | & ( ~ (all_139_3 = 0) | (all_139_0 = 0 & all_139_2 = 0)) % 14.12/2.67 | | | | | % 14.12/2.67 | | | | | ALPHA: (67) implies: % 14.12/2.68 | | | | | (68) in(all_79_1, all_33_2) = all_139_2 % 14.12/2.68 | | | | | (69) relation(all_33_2) = all_139_3 % 14.12/2.68 | | | | | (70) ~ (all_139_3 = 0) | (all_139_0 = 0 & all_139_2 = 0) % 14.12/2.68 | | | | | % 14.12/2.68 | | | | | DELTA: instantiating (58) with fresh symbols all_141_0, all_141_1, % 14.12/2.68 | | | | | all_141_2, all_141_3 gives: % 14.12/2.68 | | | | | (71) cartesian_product2(all_33_3, all_33_3) = all_141_1 & % 14.12/2.68 | | | | | relation(all_33_2) = all_141_3 & in(all_79_3, all_141_1) = % 14.12/2.68 | | | | | all_141_0 & in(all_79_3, all_33_2) = all_141_2 & $i(all_141_1) % 14.12/2.68 | | | | | & ( ~ (all_141_3 = 0) | (all_141_0 = 0 & all_141_2 = 0)) % 14.12/2.68 | | | | | % 14.12/2.68 | | | | | ALPHA: (71) implies: % 14.12/2.68 | | | | | (72) in(all_79_3, all_33_2) = all_141_2 % 14.12/2.68 | | | | | (73) relation(all_33_2) = all_141_3 % 14.12/2.68 | | | | | (74) ~ (all_141_3 = 0) | (all_141_0 = 0 & all_141_2 = 0) % 14.12/2.68 | | | | | % 14.12/2.68 | | | | | BETA: splitting (62) gives: % 14.12/2.68 | | | | | % 14.12/2.68 | | | | | Case 1: % 14.12/2.68 | | | | | | % 14.12/2.68 | | | | | | (75) all_79_4 = all_79_5 % 14.12/2.68 | | | | | | % 14.12/2.68 | | | | | | REDUCE: (46), (75) imply: % 14.12/2.68 | | | | | | (76) $false % 14.12/2.68 | | | | | | % 14.12/2.68 | | | | | | CLOSE: (76) is inconsistent. % 14.12/2.68 | | | | | | % 14.12/2.68 | | | | | Case 2: % 14.12/2.68 | | | | | | % 14.12/2.68 | | | | | | (77) ? [v0: any] : ? [v1: any] : ? [v2: any] : (( ~ (v0 = 0) & % 14.12/2.68 | | | | | | relation(all_33_2) = v0) | (ordered_pair(all_79_5, % 14.12/2.68 | | | | | | all_79_4) = v0 & in(v0, all_33_2) = v1 & in(all_79_1, % 14.12/2.68 | | | | | | all_33_2) = v2 & $i(v0) & ( ~ (v2 = 0) | ~ (v1 = % 14.12/2.68 | | | | | | 0)))) % 14.12/2.68 | | | | | | % 14.12/2.68 | | | | | | DELTA: instantiating (77) with fresh symbols all_149_0, all_149_1, % 14.12/2.68 | | | | | | all_149_2 gives: % 14.12/2.68 | | | | | | (78) ( ~ (all_149_2 = 0) & relation(all_33_2) = all_149_2) | % 14.12/2.68 | | | | | | (ordered_pair(all_79_5, all_79_4) = all_149_2 & % 14.12/2.68 | | | | | | in(all_149_2, all_33_2) = all_149_1 & in(all_79_1, % 14.12/2.68 | | | | | | all_33_2) = all_149_0 & $i(all_149_2) & ( ~ (all_149_0 = % 14.12/2.68 | | | | | | 0) | ~ (all_149_1 = 0))) % 14.12/2.68 | | | | | | % 14.12/2.68 | | | | | | BETA: splitting (61) gives: % 14.12/2.68 | | | | | | % 14.12/2.68 | | | | | | Case 1: % 14.12/2.68 | | | | | | | % 14.12/2.68 | | | | | | | (79) all_79_4 = all_79_5 % 14.12/2.68 | | | | | | | % 14.12/2.68 | | | | | | | REDUCE: (46), (79) imply: % 14.12/2.68 | | | | | | | (80) $false % 14.12/2.68 | | | | | | | % 14.12/2.68 | | | | | | | CLOSE: (80) is inconsistent. % 14.12/2.68 | | | | | | | % 14.12/2.68 | | | | | | Case 2: % 14.12/2.68 | | | | | | | % 14.12/2.68 | | | | | | | (81) ? [v0: any] : ? [v1: any] : ? [v2: any] : (( ~ (v0 = 0) % 14.12/2.68 | | | | | | | & relation(all_33_2) = v0) | (ordered_pair(all_79_4, % 14.12/2.68 | | | | | | | all_79_5) = v0 & in(v0, all_33_2) = v1 & % 14.12/2.68 | | | | | | | in(all_79_3, all_33_2) = v2 & $i(v0) & ( ~ (v2 = 0) | % 14.12/2.68 | | | | | | | ~ (v1 = 0)))) % 14.12/2.68 | | | | | | | % 14.12/2.68 | | | | | | | DELTA: instantiating (81) with fresh symbols all_157_0, all_157_1, % 14.12/2.68 | | | | | | | all_157_2 gives: % 14.12/2.68 | | | | | | | (82) ( ~ (all_157_2 = 0) & relation(all_33_2) = all_157_2) | % 14.12/2.68 | | | | | | | (ordered_pair(all_79_4, all_79_5) = all_157_2 & % 14.12/2.68 | | | | | | | in(all_157_2, all_33_2) = all_157_1 & in(all_79_3, % 14.12/2.68 | | | | | | | all_33_2) = all_157_0 & $i(all_157_2) & ( ~ (all_157_0 % 14.12/2.68 | | | | | | | = 0) | ~ (all_157_1 = 0))) % 14.12/2.68 | | | | | | | % 14.12/2.68 | | | | | | | BETA: splitting (82) gives: % 14.12/2.68 | | | | | | | % 14.12/2.68 | | | | | | | Case 1: % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | (83) ~ (all_157_2 = 0) & relation(all_33_2) = all_157_2 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | ALPHA: (83) implies: % 14.12/2.68 | | | | | | | | (84) ~ (all_157_2 = 0) % 14.12/2.68 | | | | | | | | (85) relation(all_33_2) = all_157_2 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | GROUND_INST: instantiating (6) with 0, all_139_3, all_33_2, % 14.12/2.68 | | | | | | | | simplifying with (15), (69) gives: % 14.12/2.68 | | | | | | | | (86) all_139_3 = 0 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | GROUND_INST: instantiating (6) with all_139_3, all_141_3, % 14.12/2.68 | | | | | | | | all_33_2, simplifying with (69), (73) gives: % 14.12/2.68 | | | | | | | | (87) all_141_3 = all_139_3 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | GROUND_INST: instantiating (6) with all_141_3, all_157_2, % 14.12/2.68 | | | | | | | | all_33_2, simplifying with (73), (85) gives: % 14.12/2.68 | | | | | | | | (88) all_157_2 = all_141_3 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | GROUND_INST: instantiating (6) with all_135_2, all_157_2, % 14.12/2.68 | | | | | | | | all_33_2, simplifying with (66), (85) gives: % 14.12/2.68 | | | | | | | | (89) all_157_2 = all_135_2 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | COMBINE_EQS: (88), (89) imply: % 14.12/2.68 | | | | | | | | (90) all_141_3 = all_135_2 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | SIMP: (90) implies: % 14.12/2.68 | | | | | | | | (91) all_141_3 = all_135_2 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | COMBINE_EQS: (87), (91) imply: % 14.12/2.68 | | | | | | | | (92) all_139_3 = all_135_2 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | SIMP: (92) implies: % 14.12/2.68 | | | | | | | | (93) all_139_3 = all_135_2 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | COMBINE_EQS: (86), (93) imply: % 14.12/2.68 | | | | | | | | (94) all_135_2 = 0 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | COMBINE_EQS: (89), (94) imply: % 14.12/2.68 | | | | | | | | (95) all_157_2 = 0 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | REDUCE: (84), (95) imply: % 14.12/2.68 | | | | | | | | (96) $false % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | CLOSE: (96) is inconsistent. % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | Case 2: % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | (97) ordered_pair(all_79_4, all_79_5) = all_157_2 & % 14.12/2.68 | | | | | | | | in(all_157_2, all_33_2) = all_157_1 & in(all_79_3, % 14.12/2.68 | | | | | | | | all_33_2) = all_157_0 & $i(all_157_2) & ( ~ (all_157_0 % 14.12/2.68 | | | | | | | | = 0) | ~ (all_157_1 = 0)) % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | ALPHA: (97) implies: % 14.12/2.68 | | | | | | | | (98) in(all_79_3, all_33_2) = all_157_0 % 14.12/2.68 | | | | | | | | (99) in(all_157_2, all_33_2) = all_157_1 % 14.12/2.68 | | | | | | | | (100) ordered_pair(all_79_4, all_79_5) = all_157_2 % 14.12/2.68 | | | | | | | | (101) ~ (all_157_0 = 0) | ~ (all_157_1 = 0) % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | GROUND_INST: instantiating (8) with all_141_2, all_157_0, % 14.12/2.68 | | | | | | | | all_33_2, all_79_3, simplifying with (72), (98) % 14.12/2.68 | | | | | | | | gives: % 14.12/2.68 | | | | | | | | (102) all_157_0 = all_141_2 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | GROUND_INST: instantiating (6) with 0, all_139_3, all_33_2, % 14.12/2.68 | | | | | | | | simplifying with (15), (69) gives: % 14.12/2.68 | | | | | | | | (103) all_139_3 = 0 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | GROUND_INST: instantiating (6) with all_139_3, all_141_3, % 14.12/2.68 | | | | | | | | all_33_2, simplifying with (69), (73) gives: % 14.12/2.68 | | | | | | | | (104) all_141_3 = all_139_3 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | GROUND_INST: instantiating (6) with all_135_2, all_141_3, % 14.12/2.68 | | | | | | | | all_33_2, simplifying with (66), (73) gives: % 14.12/2.68 | | | | | | | | (105) all_141_3 = all_135_2 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | GROUND_INST: instantiating (9) with all_79_1, all_157_2, % 14.12/2.68 | | | | | | | | all_79_5, all_79_4, simplifying with (52), (100) % 14.12/2.68 | | | | | | | | gives: % 14.12/2.68 | | | | | | | | (106) all_157_2 = all_79_1 % 14.12/2.68 | | | | | | | | % 14.12/2.68 | | | | | | | | COMBINE_EQS: (104), (105) imply: % 14.12/2.68 | | | | | | | | (107) all_139_3 = all_135_2 % 14.12/2.68 | | | | | | | | % 14.12/2.69 | | | | | | | | SIMP: (107) implies: % 14.12/2.69 | | | | | | | | (108) all_139_3 = all_135_2 % 14.12/2.69 | | | | | | | | % 14.12/2.69 | | | | | | | | COMBINE_EQS: (103), (108) imply: % 14.12/2.69 | | | | | | | | (109) all_135_2 = 0 % 14.12/2.69 | | | | | | | | % 14.12/2.69 | | | | | | | | COMBINE_EQS: (105), (109) imply: % 14.12/2.69 | | | | | | | | (110) all_141_3 = 0 % 14.12/2.69 | | | | | | | | % 14.12/2.69 | | | | | | | | REDUCE: (99), (106) imply: % 14.12/2.69 | | | | | | | | (111) in(all_79_1, all_33_2) = all_157_1 % 14.12/2.69 | | | | | | | | % 14.12/2.69 | | | | | | | | BETA: splitting (70) gives: % 14.12/2.69 | | | | | | | | % 14.12/2.69 | | | | | | | | Case 1: % 14.12/2.69 | | | | | | | | | % 14.12/2.69 | | | | | | | | | (112) ~ (all_139_3 = 0) % 14.12/2.69 | | | | | | | | | % 14.12/2.69 | | | | | | | | | REDUCE: (103), (112) imply: % 14.12/2.69 | | | | | | | | | (113) $false % 14.12/2.69 | | | | | | | | | % 14.12/2.69 | | | | | | | | | CLOSE: (113) is inconsistent. % 14.12/2.69 | | | | | | | | | % 14.12/2.69 | | | | | | | | Case 2: % 14.12/2.69 | | | | | | | | | % 14.12/2.69 | | | | | | | | | (114) all_139_0 = 0 & all_139_2 = 0 % 14.12/2.69 | | | | | | | | | % 14.12/2.69 | | | | | | | | | ALPHA: (114) implies: % 14.12/2.69 | | | | | | | | | (115) all_139_2 = 0 % 14.12/2.69 | | | | | | | | | % 14.12/2.69 | | | | | | | | | REDUCE: (68), (115) imply: % 14.12/2.69 | | | | | | | | | (116) in(all_79_1, all_33_2) = 0 % 14.12/2.69 | | | | | | | | | % 14.12/2.69 | | | | | | | | | BETA: splitting (63) gives: % 14.12/2.69 | | | | | | | | | % 14.12/2.69 | | | | | | | | | Case 1: % 14.12/2.69 | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | (117) all_79_4 = all_79_5 % 14.12/2.69 | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | REDUCE: (46), (117) imply: % 14.12/2.69 | | | | | | | | | | (118) $false % 14.12/2.69 | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | CLOSE: (118) is inconsistent. % 14.12/2.69 | | | | | | | | | | % 14.12/2.69 | | | | | | | | | Case 2: % 14.12/2.69 | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | (119) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 14.12/2.69 | | | | | | | | | | (ordered_pair(all_79_5, all_79_4) = v0 & in(v0, % 14.12/2.69 | | | | | | | | | | all_33_2) = v1 & in(all_79_1, all_33_2) = v2 & % 14.12/2.69 | | | | | | | | | | $i(v0) & ( ~ (v2 = 0) | ~ (v1 = 0))) % 14.12/2.69 | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | DELTA: instantiating (119) with fresh symbols all_190_0, % 14.12/2.69 | | | | | | | | | | all_190_1, all_190_2 gives: % 14.12/2.69 | | | | | | | | | | (120) ordered_pair(all_79_5, all_79_4) = all_190_2 & % 14.12/2.69 | | | | | | | | | | in(all_190_2, all_33_2) = all_190_1 & in(all_79_1, % 14.12/2.69 | | | | | | | | | | all_33_2) = all_190_0 & $i(all_190_2) & ( ~ % 14.12/2.69 | | | | | | | | | | (all_190_0 = 0) | ~ (all_190_1 = 0)) % 14.12/2.69 | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | ALPHA: (120) implies: % 14.12/2.69 | | | | | | | | | | (121) in(all_79_1, all_33_2) = all_190_0 % 14.12/2.69 | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | BETA: splitting (78) gives: % 14.12/2.69 | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | Case 1: % 14.12/2.69 | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | (122) ~ (all_149_2 = 0) & relation(all_33_2) = % 14.12/2.69 | | | | | | | | | | | all_149_2 % 14.12/2.69 | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | ALPHA: (122) implies: % 14.12/2.69 | | | | | | | | | | | (123) ~ (all_149_2 = 0) % 14.12/2.69 | | | | | | | | | | | (124) relation(all_33_2) = all_149_2 % 14.12/2.69 | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_149_2, all_33_2, % 14.12/2.69 | | | | | | | | | | | simplifying with (15), (124) gives: % 14.12/2.69 | | | | | | | | | | | (125) all_149_2 = 0 % 14.12/2.69 | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | REDUCE: (123), (125) imply: % 14.12/2.69 | | | | | | | | | | | (126) $false % 14.12/2.69 | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | CLOSE: (126) is inconsistent. % 14.12/2.69 | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | Case 2: % 14.12/2.69 | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | (127) ordered_pair(all_79_5, all_79_4) = all_149_2 & % 14.12/2.69 | | | | | | | | | | | in(all_149_2, all_33_2) = all_149_1 & in(all_79_1, % 14.12/2.69 | | | | | | | | | | | all_33_2) = all_149_0 & $i(all_149_2) & ( ~ % 14.12/2.69 | | | | | | | | | | | (all_149_0 = 0) | ~ (all_149_1 = 0)) % 14.12/2.69 | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | ALPHA: (127) implies: % 14.12/2.69 | | | | | | | | | | | (128) in(all_79_1, all_33_2) = all_149_0 % 14.12/2.69 | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | BETA: splitting (74) gives: % 14.12/2.69 | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | Case 1: % 14.12/2.69 | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | (129) ~ (all_141_3 = 0) % 14.12/2.69 | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | REDUCE: (110), (129) imply: % 14.12/2.69 | | | | | | | | | | | | (130) $false % 14.12/2.69 | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | CLOSE: (130) is inconsistent. % 14.12/2.69 | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | Case 2: % 14.12/2.69 | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | (131) all_141_0 = 0 & all_141_2 = 0 % 14.12/2.69 | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | ALPHA: (131) implies: % 14.12/2.69 | | | | | | | | | | | | (132) all_141_2 = 0 % 14.12/2.69 | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | COMBINE_EQS: (102), (132) imply: % 14.12/2.69 | | | | | | | | | | | | (133) all_157_0 = 0 % 14.12/2.69 | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | BETA: splitting (101) gives: % 14.12/2.69 | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | Case 1: % 14.12/2.69 | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | (134) ~ (all_157_0 = 0) % 14.12/2.69 | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | REDUCE: (133), (134) imply: % 14.12/2.69 | | | | | | | | | | | | | (135) $false % 14.12/2.69 | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | CLOSE: (135) is inconsistent. % 14.12/2.69 | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | Case 2: % 14.12/2.69 | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | (136) ~ (all_157_1 = 0) % 14.12/2.69 | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | BETA: splitting (64) gives: % 14.12/2.69 | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | Case 1: % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | (137) all_79_4 = all_79_5 % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | REDUCE: (46), (137) imply: % 14.12/2.69 | | | | | | | | | | | | | | (138) $false % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | CLOSE: (138) is inconsistent. % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | Case 2: % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | (139) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 14.12/2.69 | | | | | | | | | | | | | | (ordered_pair(all_79_5, all_79_4) = v1 & in(v1, % 14.12/2.69 | | | | | | | | | | | | | | all_33_2) = v2 & in(all_79_1, all_33_2) = v0 & % 14.12/2.69 | | | | | | | | | | | | | | $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0))) % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | DELTA: instantiating (139) with fresh symbols all_220_0, % 14.12/2.69 | | | | | | | | | | | | | | all_220_1, all_220_2 gives: % 14.12/2.69 | | | | | | | | | | | | | | (140) ordered_pair(all_79_5, all_79_4) = all_220_1 & % 14.12/2.69 | | | | | | | | | | | | | | in(all_220_1, all_33_2) = all_220_0 & in(all_79_1, % 14.12/2.69 | | | | | | | | | | | | | | all_33_2) = all_220_2 & $i(all_220_1) & ( ~ % 14.12/2.69 | | | | | | | | | | | | | | (all_220_0 = 0) | ~ (all_220_2 = 0)) % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | ALPHA: (140) implies: % 14.12/2.69 | | | | | | | | | | | | | | (141) in(all_79_1, all_33_2) = all_220_2 % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_149_0, all_157_1, % 14.12/2.69 | | | | | | | | | | | | | | all_33_2, all_79_1, simplifying with (111), (128) % 14.12/2.69 | | | | | | | | | | | | | | gives: % 14.12/2.69 | | | | | | | | | | | | | | (142) all_157_1 = all_149_0 % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_157_1, all_190_0, % 14.12/2.69 | | | | | | | | | | | | | | all_33_2, all_79_1, simplifying with (111), (121) % 14.12/2.69 | | | | | | | | | | | | | | gives: % 14.12/2.69 | | | | | | | | | | | | | | (143) all_190_0 = all_157_1 % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_190_0, all_220_2, % 14.12/2.69 | | | | | | | | | | | | | | all_33_2, all_79_1, simplifying with (121), (141) % 14.12/2.69 | | | | | | | | | | | | | | gives: % 14.12/2.69 | | | | | | | | | | | | | | (144) all_220_2 = all_190_0 % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_220_2, all_33_2, % 14.12/2.69 | | | | | | | | | | | | | | all_79_1, simplifying with (116), (141) gives: % 14.12/2.69 | | | | | | | | | | | | | | (145) all_220_2 = 0 % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | COMBINE_EQS: (144), (145) imply: % 14.12/2.69 | | | | | | | | | | | | | | (146) all_190_0 = 0 % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | SIMP: (146) implies: % 14.12/2.69 | | | | | | | | | | | | | | (147) all_190_0 = 0 % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | COMBINE_EQS: (143), (147) imply: % 14.12/2.69 | | | | | | | | | | | | | | (148) all_157_1 = 0 % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | SIMP: (148) implies: % 14.12/2.69 | | | | | | | | | | | | | | (149) all_157_1 = 0 % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | COMBINE_EQS: (142), (149) imply: % 14.12/2.69 | | | | | | | | | | | | | | (150) all_149_0 = 0 % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | REDUCE: (136), (149) imply: % 14.12/2.69 | | | | | | | | | | | | | | (151) $false % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | | CLOSE: (151) is inconsistent. % 14.12/2.69 | | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | | End of split % 14.12/2.69 | | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | | End of split % 14.12/2.69 | | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | | End of split % 14.12/2.69 | | | | | | | | | | | % 14.12/2.69 | | | | | | | | | | End of split % 14.12/2.69 | | | | | | | | | | % 14.12/2.69 | | | | | | | | | End of split % 14.12/2.69 | | | | | | | | | % 14.12/2.69 | | | | | | | | End of split % 14.12/2.69 | | | | | | | | % 14.12/2.69 | | | | | | | End of split % 14.12/2.69 | | | | | | | % 14.12/2.69 | | | | | | End of split % 14.12/2.69 | | | | | | % 14.12/2.69 | | | | | End of split % 14.12/2.69 | | | | | % 14.12/2.69 | | | | End of split % 14.12/2.69 | | | | % 14.12/2.69 | | | Case 2: % 14.12/2.69 | | | | % 14.12/2.69 | | | | (152) ~ (all_79_6 = 0) & relation(all_33_1) = all_79_6 % 14.12/2.69 | | | | % 14.12/2.69 | | | | ALPHA: (152) implies: % 14.12/2.69 | | | | (153) ~ (all_79_6 = 0) % 14.12/2.69 | | | | (154) relation(all_33_1) = all_79_6 % 14.12/2.69 | | | | % 14.12/2.69 | | | | GROUND_INST: instantiating (6) with 0, all_79_6, all_33_1, simplifying % 14.12/2.69 | | | | with (44), (154) gives: % 14.12/2.69 | | | | (155) all_79_6 = 0 % 14.12/2.69 | | | | % 14.12/2.69 | | | | REDUCE: (153), (155) imply: % 14.12/2.69 | | | | (156) $false % 14.12/2.69 | | | | % 14.12/2.69 | | | | CLOSE: (156) is inconsistent. % 14.12/2.69 | | | | % 14.12/2.69 | | | End of split % 14.12/2.69 | | | % 14.12/2.69 | | End of split % 14.12/2.69 | | % 14.12/2.69 | End of split % 14.12/2.69 | % 14.12/2.69 End of proof % 14.12/2.69 % SZS output end Proof for theBenchmark % 14.12/2.69 % 14.12/2.69 2080ms %------------------------------------------------------------------------------