%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU183+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 : n007.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 17:43:06 EDT 2023 % Result : Theorem 14.57s 2.80s % Output : Proof 18.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU183+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n007.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 22:43:10 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.64 ________ _____ % 0.20/0.64 ___ __ \_________(_)________________________________ % 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.64 % 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.64 (2023-06-19) % 0.20/0.64 % 0.20/0.64 (c) Philipp Rümmer, 2009-2023 % 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.64 Amanda Stjerna. % 0.20/0.64 Free software under BSD-3-Clause. % 0.20/0.64 % 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.64 % 0.20/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.55/0.66 Running up to 7 provers in parallel. % 0.55/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.55/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.55/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.55/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.55/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.55/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.55/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.80/1.18 Prover 4: Preprocessing ... % 2.80/1.18 Prover 1: Preprocessing ... % 3.32/1.25 Prover 0: Preprocessing ... % 3.32/1.25 Prover 3: Preprocessing ... % 3.32/1.25 Prover 6: Preprocessing ... % 3.32/1.25 Prover 5: Preprocessing ... % 3.32/1.25 Prover 2: Preprocessing ... % 7.76/1.92 Prover 1: Warning: ignoring some quantifiers % 7.76/1.98 Prover 6: Proving ... % 7.76/1.98 Prover 1: Constructing countermodel ... % 7.76/1.98 Prover 5: Proving ... % 7.76/2.00 Prover 3: Warning: ignoring some quantifiers % 7.76/2.04 Prover 4: Warning: ignoring some quantifiers % 7.76/2.04 Prover 3: Constructing countermodel ... % 8.65/2.10 Prover 4: Constructing countermodel ... % 9.82/2.23 Prover 2: Proving ... % 10.49/2.24 Prover 0: Proving ... % 14.19/2.79 Prover 3: proved (2109ms) % 14.19/2.80 % 14.57/2.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.57/2.80 % 14.57/2.80 Prover 0: stopped % 14.57/2.81 Prover 6: stopped % 14.57/2.82 Prover 2: stopped % 14.57/2.83 Prover 5: stopped % 14.57/2.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.57/2.83 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.57/2.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.57/2.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.57/2.83 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.91/2.86 Prover 7: Preprocessing ... % 14.91/2.89 Prover 13: Preprocessing ... % 14.91/2.89 Prover 11: Preprocessing ... % 14.91/2.91 Prover 8: Preprocessing ... % 14.91/2.92 Prover 10: Preprocessing ... % 16.01/3.03 Prover 10: Warning: ignoring some quantifiers % 16.41/3.04 Prover 7: Warning: ignoring some quantifiers % 16.43/3.05 Prover 10: Constructing countermodel ... % 16.43/3.06 Prover 8: Warning: ignoring some quantifiers % 16.43/3.08 Prover 7: Constructing countermodel ... % 16.43/3.09 Prover 8: Constructing countermodel ... % 16.85/3.10 Prover 1: Found proof (size 74) % 16.85/3.10 Prover 1: proved (2428ms) % 16.85/3.10 Prover 7: stopped % 16.85/3.10 Prover 10: stopped % 16.85/3.11 Prover 8: stopped % 16.85/3.11 Prover 4: stopped % 16.85/3.13 Prover 13: Warning: ignoring some quantifiers % 17.14/3.16 Prover 13: Constructing countermodel ... % 17.14/3.17 Prover 13: stopped % 17.14/3.20 Prover 11: Warning: ignoring some quantifiers % 17.14/3.21 Prover 11: Constructing countermodel ... % 17.14/3.22 Prover 11: stopped % 17.14/3.22 % 17.14/3.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.14/3.22 % 17.14/3.23 % SZS output start Proof for theBenchmark % 17.14/3.24 Assumptions after simplification: % 17.14/3.24 --------------------------------- % 17.14/3.24 % 17.14/3.24 (d3_tarski) % 17.65/3.28 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 17.65/3.28 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 17.65/3.28 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 17.65/3.28 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 17.65/3.28 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 17.65/3.28 % 17.65/3.28 (d5_relat_1) % 17.65/3.29 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 17.65/3.29 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~ % 17.65/3.29 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~ % 17.65/3.29 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) = % 17.65/3.29 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i] % 17.65/3.29 : ? [v6: $i] : (ordered_pair(v5, v3) = v6 & in(v6, v0) = 0 & $i(v6) % 17.65/3.29 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 % 17.65/3.29 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 17.65/3.29 (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) & % 17.65/3.29 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: % 17.65/3.29 $i] : (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0 & $i(v4) & % 17.65/3.29 $i(v3))))))) % 17.65/3.29 % 17.65/3.29 (d8_relat_1) % 17.65/3.31 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : % 17.65/3.31 ( ~ (relation_composition(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 % 17.65/3.31 = 0) & relation(v1) = v3) | ! [v3: $i] : ( ~ (relation(v3) = 0) | ~ % 17.65/3.31 $i(v3) | (( ~ (v3 = v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 17.65/3.31 [v7: int] : (v7 = 0 | ~ (ordered_pair(v4, v5) = v6) | ~ (in(v6, % 17.65/3.31 v2) = v7) | ~ $i(v5) | ~ $i(v4) | ! [v8: $i] : ! [v9: % 17.65/3.31 $i] : ( ~ (ordered_pair(v4, v8) = v9) | ~ (in(v9, v0) = 0) | % 17.65/3.31 ~ $i(v8) | ? [v10: $i] : ? [v11: int] : ( ~ (v11 = 0) & % 17.65/3.31 ordered_pair(v8, v5) = v10 & in(v10, v1) = v11 & $i(v10)))) % 17.65/3.31 & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v4, % 17.65/3.31 v5) = v6) | ~ (in(v6, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ? % 17.65/3.31 [v7: $i] : ? [v8: $i] : ? [v9: $i] : (ordered_pair(v7, v5) = % 17.65/3.31 v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) = 0 & in(v8, v0) = % 17.65/3.31 0 & $i(v9) & $i(v8) & $i(v7))))) & (v3 = v2 | ? [v4: $i] : ? % 17.65/3.31 [v5: $i] : ? [v6: $i] : ? [v7: any] : (ordered_pair(v4, v5) = v6 & % 17.65/3.31 in(v6, v3) = v7 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v7 = 0) | ! % 17.65/3.31 [v8: $i] : ! [v9: $i] : ( ~ (ordered_pair(v4, v8) = v9) | ~ % 17.65/3.31 (in(v9, v0) = 0) | ~ $i(v8) | ? [v10: $i] : ? [v11: int] : % 17.65/3.31 ( ~ (v11 = 0) & ordered_pair(v8, v5) = v10 & in(v10, v1) = v11 % 17.65/3.31 & $i(v10)))) & (v7 = 0 | ? [v8: $i] : ? [v9: $i] : ? % 17.65/3.31 [v10: $i] : (ordered_pair(v8, v5) = v10 & ordered_pair(v4, v8) = % 17.65/3.31 v9 & in(v10, v1) = 0 & in(v9, v0) = 0 & $i(v10) & $i(v9) & % 17.65/3.31 $i(v8))))))))) % 17.65/3.31 % 17.65/3.31 (dt_k5_relat_1) % 17.65/3.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) = % 17.65/3.32 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 17.65/3.32 (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | % 17.65/3.32 ~ (v3 = 0) | v5 = 0))) % 17.65/3.32 % 17.65/3.32 (t45_relat_1) % 17.65/3.32 ? [v0: $i] : (relation(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ? [v3: % 17.65/3.32 $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & relation_composition(v0, % 17.65/3.32 v1) = v2 & relation_rng(v2) = v3 & relation_rng(v1) = v4 & relation(v1) % 17.65/3.32 = 0 & subset(v3, v4) = v5 & $i(v4) & $i(v3) & $i(v2) & $i(v1))) % 17.65/3.32 % 17.65/3.32 (function-axioms) % 17.65/3.32 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 17.65/3.32 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 17.65/3.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.65/3.32 (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = % 17.65/3.32 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 17.65/3.33 ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: % 17.65/3.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.65/3.33 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 17.65/3.33 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.65/3.33 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 17.65/3.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.65/3.33 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 17.65/3.33 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) % 17.65/3.33 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 17.65/3.33 $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : % 17.65/3.33 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 17.65/3.33 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 17.65/3.33 ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: % 17.65/3.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 17.65/3.33 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 17.65/3.33 % 17.65/3.33 Further assumptions not needed in the proof: % 17.65/3.33 -------------------------------------------- % 17.65/3.33 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, dt_k1_tarski, % 17.65/3.33 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_tarski, dt_k4_tarski, % 17.65/3.33 dt_m1_subset_1, existence_m1_subset_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, % 17.65/3.33 fc2_subset_1, fc3_subset_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, % 17.65/3.33 rc2_subset_1, rc2_xboole_0, reflexivity_r1_tarski, t1_subset, t2_subset, % 17.65/3.33 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 17.65/3.33 % 17.65/3.33 Those formulas are unsatisfiable: % 17.65/3.33 --------------------------------- % 17.65/3.33 % 17.65/3.33 Begin of proof % 17.65/3.33 | % 17.65/3.33 | ALPHA: (d3_tarski) implies: % 17.65/3.33 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 17.65/3.33 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 17.65/3.33 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 17.65/3.33 | % 17.65/3.33 | ALPHA: (function-axioms) implies: % 17.65/3.33 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.65/3.33 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 17.65/3.33 | % 17.65/3.33 | DELTA: instantiating (t45_relat_1) with fresh symbol all_34_0 gives: % 17.65/3.34 | (3) relation(all_34_0) = 0 & $i(all_34_0) & ? [v0: $i] : ? [v1: $i] : ? % 17.65/3.34 | [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 17.65/3.34 | relation_composition(all_34_0, v0) = v1 & relation_rng(v1) = v2 & % 17.65/3.34 | relation_rng(v0) = v3 & relation(v0) = 0 & subset(v2, v3) = v4 & % 17.65/3.34 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.65/3.34 | % 17.65/3.34 | ALPHA: (3) implies: % 17.65/3.34 | (4) $i(all_34_0) % 17.65/3.34 | (5) relation(all_34_0) = 0 % 17.65/3.34 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : % 17.65/3.34 | ( ~ (v4 = 0) & relation_composition(all_34_0, v0) = v1 & % 17.65/3.34 | relation_rng(v1) = v2 & relation_rng(v0) = v3 & relation(v0) = 0 & % 17.65/3.34 | subset(v2, v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.65/3.34 | % 17.65/3.34 | DELTA: instantiating (6) with fresh symbols all_36_0, all_36_1, all_36_2, % 17.65/3.34 | all_36_3, all_36_4 gives: % 17.65/3.34 | (7) ~ (all_36_0 = 0) & relation_composition(all_34_0, all_36_4) = all_36_3 % 17.65/3.34 | & relation_rng(all_36_3) = all_36_2 & relation_rng(all_36_4) = all_36_1 % 17.65/3.34 | & relation(all_36_4) = 0 & subset(all_36_2, all_36_1) = all_36_0 & % 17.65/3.34 | $i(all_36_1) & $i(all_36_2) & $i(all_36_3) & $i(all_36_4) % 17.65/3.34 | % 17.65/3.34 | ALPHA: (7) implies: % 17.65/3.34 | (8) ~ (all_36_0 = 0) % 17.65/3.34 | (9) $i(all_36_4) % 17.65/3.34 | (10) $i(all_36_3) % 17.65/3.34 | (11) $i(all_36_2) % 17.65/3.34 | (12) $i(all_36_1) % 17.65/3.34 | (13) subset(all_36_2, all_36_1) = all_36_0 % 17.65/3.34 | (14) relation(all_36_4) = 0 % 17.65/3.34 | (15) relation_rng(all_36_4) = all_36_1 % 17.65/3.34 | (16) relation_rng(all_36_3) = all_36_2 % 17.65/3.34 | (17) relation_composition(all_34_0, all_36_4) = all_36_3 % 17.65/3.34 | % 17.65/3.34 | GROUND_INST: instantiating (1) with all_36_2, all_36_1, all_36_0, simplifying % 17.65/3.34 | with (11), (12), (13) gives: % 17.65/3.35 | (18) all_36_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 17.65/3.35 | all_36_1) = v1 & in(v0, all_36_2) = 0 & $i(v0)) % 17.65/3.35 | % 17.65/3.35 | GROUND_INST: instantiating (d8_relat_1) with all_34_0, simplifying with (4), % 17.65/3.35 | (5) gives: % 17.65/3.35 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_composition(all_34_0, v0) = % 17.65/3.35 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & relation(v0) = v2) % 17.65/3.35 | | ! [v2: $i] : ( ~ (relation(v2) = 0) | ~ $i(v2) | (( ~ (v2 = v1) % 17.65/3.35 | | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] : % 17.65/3.35 | (v6 = 0 | ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v1) = % 17.65/3.35 | v6) | ~ $i(v4) | ~ $i(v3) | ! [v7: $i] : ! [v8: $i] % 17.65/3.35 | : ( ~ (ordered_pair(v3, v7) = v8) | ~ (in(v8, all_34_0) = % 17.65/3.35 | 0) | ~ $i(v7) | ? [v9: $i] : ? [v10: int] : ( ~ % 17.65/3.35 | (v10 = 0) & ordered_pair(v7, v4) = v9 & in(v9, v0) = % 17.65/3.35 | v10 & $i(v9)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.65/3.35 | $i] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v1) = % 17.65/3.35 | 0) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: $i] : % 17.65/3.35 | ? [v8: $i] : (ordered_pair(v6, v4) = v8 & % 17.65/3.35 | ordered_pair(v3, v6) = v7 & in(v8, v0) = 0 & in(v7, % 17.65/3.35 | all_34_0) = 0 & $i(v8) & $i(v7) & $i(v6))))) & (v2 = % 17.65/3.35 | v1 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] : % 17.65/3.35 | (ordered_pair(v3, v4) = v5 & in(v5, v2) = v6 & $i(v5) & $i(v4) % 17.65/3.35 | & $i(v3) & ( ~ (v6 = 0) | ! [v7: $i] : ! [v8: $i] : ( ~ % 17.65/3.35 | (ordered_pair(v3, v7) = v8) | ~ (in(v8, all_34_0) = 0) % 17.65/3.35 | | ~ $i(v7) | ? [v9: $i] : ? [v10: int] : ( ~ (v10 = % 17.65/3.35 | 0) & ordered_pair(v7, v4) = v9 & in(v9, v0) = v10 & % 17.65/3.35 | $i(v9)))) & (v6 = 0 | ? [v7: $i] : ? [v8: $i] : ? % 17.65/3.35 | [v9: $i] : (ordered_pair(v7, v4) = v9 & ordered_pair(v3, % 17.65/3.35 | v7) = v8 & in(v9, v0) = 0 & in(v8, all_34_0) = 0 & % 17.65/3.35 | $i(v9) & $i(v8) & $i(v7)))))))) % 17.65/3.35 | % 17.65/3.35 | GROUND_INST: instantiating (d5_relat_1) with all_36_4, all_36_1, simplifying % 17.65/3.35 | with (9), (15) gives: % 17.65/3.36 | (20) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_4) = v0) | ( ? [v0: any] % 17.65/3.36 | : (v0 = all_36_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1, % 17.65/3.36 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] : % 17.65/3.36 | ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4, all_36_4) = 0) | % 17.65/3.36 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] : % 17.65/3.36 | (ordered_pair(v3, v1) = v4 & in(v4, all_36_4) = 0 & $i(v4) & % 17.65/3.36 | $i(v3))))) & ( ~ $i(all_36_1) | ( ! [v0: $i] : ! [v1: int] % 17.65/3.36 | : (v1 = 0 | ~ (in(v0, all_36_1) = v1) | ~ $i(v0) | ! [v2: $i] % 17.65/3.36 | : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, % 17.65/3.36 | all_36_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, % 17.65/3.36 | all_36_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 17.65/3.36 | (ordered_pair(v1, v0) = v2 & in(v2, all_36_4) = 0 & $i(v2) & % 17.65/3.36 | $i(v1)))))) % 17.65/3.36 | % 17.65/3.36 | GROUND_INST: instantiating (d5_relat_1) with all_36_3, all_36_2, simplifying % 17.65/3.36 | with (10), (16) gives: % 17.65/3.36 | (21) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_3) = v0) | ( ? [v0: any] % 17.65/3.36 | : (v0 = all_36_2 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1, % 17.65/3.36 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] : % 17.65/3.36 | ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4, all_36_3) = 0) | % 17.65/3.36 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] : % 17.65/3.36 | (ordered_pair(v3, v1) = v4 & in(v4, all_36_3) = 0 & $i(v4) & % 17.65/3.36 | $i(v3))))) & ( ~ $i(all_36_2) | ( ! [v0: $i] : ! [v1: int] % 17.65/3.36 | : (v1 = 0 | ~ (in(v0, all_36_2) = v1) | ~ $i(v0) | ! [v2: $i] % 17.65/3.36 | : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, % 17.65/3.36 | all_36_3) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, % 17.65/3.36 | all_36_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 17.65/3.36 | (ordered_pair(v1, v0) = v2 & in(v2, all_36_3) = 0 & $i(v2) & % 17.65/3.36 | $i(v1)))))) % 17.65/3.36 | % 17.65/3.37 | GROUND_INST: instantiating (dt_k5_relat_1) with all_34_0, all_36_4, all_36_3, % 17.65/3.37 | simplifying with (4), (9), (17) gives: % 17.65/3.37 | (22) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_36_3) = v2 % 17.65/3.37 | & relation(all_36_4) = v1 & relation(all_34_0) = v0 & ( ~ (v1 = 0) | % 17.65/3.37 | ~ (v0 = 0) | v2 = 0)) % 17.65/3.37 | % 17.65/3.37 | GROUND_INST: instantiating (19) with all_36_4, all_36_3, simplifying with (9), % 17.65/3.37 | (17) gives: % 17.65/3.37 | (23) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_4) = v0) | ! [v0: $i] : % 17.65/3.37 | ( ~ (relation(v0) = 0) | ~ $i(v0) | (( ~ (v0 = all_36_3) | ( ! [v1: % 17.65/3.37 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | % 17.65/3.37 | ~ (ordered_pair(v1, v2) = v3) | ~ (in(v3, all_36_3) = v4) | % 17.65/3.37 | ~ $i(v2) | ~ $i(v1) | ! [v5: $i] : ! [v6: $i] : ( ~ % 17.65/3.37 | (ordered_pair(v1, v5) = v6) | ~ (in(v6, all_34_0) = 0) | % 17.65/3.37 | ~ $i(v5) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 17.65/3.37 | ordered_pair(v5, v2) = v7 & in(v7, all_36_4) = v8 & % 17.65/3.37 | $i(v7)))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 17.65/3.37 | ~ (ordered_pair(v1, v2) = v3) | ~ (in(v3, all_36_3) = 0) | % 17.65/3.37 | ~ $i(v2) | ~ $i(v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: % 17.65/3.37 | $i] : (ordered_pair(v4, v2) = v6 & ordered_pair(v1, v4) = % 17.65/3.37 | v5 & in(v6, all_36_4) = 0 & in(v5, all_34_0) = 0 & $i(v6) % 17.65/3.37 | & $i(v5) & $i(v4))))) & (v0 = all_36_3 | ? [v1: $i] : ? % 17.65/3.37 | [v2: $i] : ? [v3: $i] : ? [v4: any] : (ordered_pair(v1, v2) = % 17.65/3.37 | v3 & in(v3, v0) = v4 & $i(v3) & $i(v2) & $i(v1) & ( ~ (v4 = 0) % 17.65/3.37 | | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v1, v5) = % 17.65/3.37 | v6) | ~ (in(v6, all_34_0) = 0) | ~ $i(v5) | ? [v7: % 17.65/3.37 | $i] : ? [v8: int] : ( ~ (v8 = 0) & ordered_pair(v5, v2) % 17.65/3.37 | = v7 & in(v7, all_36_4) = v8 & $i(v7)))) & (v4 = 0 | ? % 17.65/3.37 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (ordered_pair(v5, v2) % 17.65/3.37 | = v7 & ordered_pair(v1, v5) = v6 & in(v7, all_36_4) = 0 & % 17.65/3.37 | in(v6, all_34_0) = 0 & $i(v7) & $i(v6) & $i(v5))))))) % 17.65/3.37 | % 17.65/3.37 | DELTA: instantiating (22) with fresh symbols all_47_0, all_47_1, all_47_2 % 17.65/3.38 | gives: % 17.65/3.38 | (24) relation(all_36_3) = all_47_0 & relation(all_36_4) = all_47_1 & % 17.65/3.38 | relation(all_34_0) = all_47_2 & ( ~ (all_47_1 = 0) | ~ (all_47_2 = 0) % 17.65/3.38 | | all_47_0 = 0) % 17.65/3.38 | % 17.65/3.38 | ALPHA: (24) implies: % 17.65/3.38 | (25) relation(all_34_0) = all_47_2 % 17.65/3.38 | (26) relation(all_36_4) = all_47_1 % 17.65/3.38 | (27) relation(all_36_3) = all_47_0 % 17.65/3.38 | (28) ~ (all_47_1 = 0) | ~ (all_47_2 = 0) | all_47_0 = 0 % 17.65/3.38 | % 17.65/3.38 | BETA: splitting (18) gives: % 17.65/3.38 | % 17.65/3.38 | Case 1: % 17.65/3.38 | | % 17.65/3.38 | | (29) all_36_0 = 0 % 17.65/3.38 | | % 17.65/3.38 | | REDUCE: (8), (29) imply: % 17.65/3.38 | | (30) $false % 17.65/3.38 | | % 17.65/3.38 | | CLOSE: (30) is inconsistent. % 17.65/3.38 | | % 17.65/3.38 | Case 2: % 17.65/3.38 | | % 17.65/3.38 | | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_36_1) = v1 & % 17.65/3.38 | | in(v0, all_36_2) = 0 & $i(v0)) % 17.65/3.38 | | % 17.65/3.38 | | DELTA: instantiating (31) with fresh symbols all_53_0, all_53_1 gives: % 17.65/3.38 | | (32) ~ (all_53_0 = 0) & in(all_53_1, all_36_1) = all_53_0 & in(all_53_1, % 17.65/3.38 | | all_36_2) = 0 & $i(all_53_1) % 17.65/3.38 | | % 17.65/3.38 | | ALPHA: (32) implies: % 17.65/3.38 | | (33) ~ (all_53_0 = 0) % 17.65/3.38 | | (34) $i(all_53_1) % 17.65/3.38 | | (35) in(all_53_1, all_36_2) = 0 % 17.65/3.38 | | (36) in(all_53_1, all_36_1) = all_53_0 % 17.65/3.38 | | % 17.65/3.38 | | GROUND_INST: instantiating (2) with 0, all_47_2, all_34_0, simplifying with % 17.65/3.38 | | (5), (25) gives: % 17.65/3.38 | | (37) all_47_2 = 0 % 17.65/3.38 | | % 17.65/3.38 | | GROUND_INST: instantiating (2) with 0, all_47_1, all_36_4, simplifying with % 17.65/3.38 | | (14), (26) gives: % 17.65/3.39 | | (38) all_47_1 = 0 % 17.65/3.39 | | % 17.65/3.39 | | BETA: splitting (28) gives: % 17.65/3.39 | | % 17.65/3.39 | | Case 1: % 17.65/3.39 | | | % 17.65/3.39 | | | (39) ~ (all_47_1 = 0) % 17.65/3.39 | | | % 17.65/3.39 | | | REDUCE: (38), (39) imply: % 17.65/3.39 | | | (40) $false % 17.65/3.39 | | | % 17.65/3.39 | | | CLOSE: (40) is inconsistent. % 17.65/3.39 | | | % 17.65/3.39 | | Case 2: % 17.65/3.39 | | | % 17.65/3.39 | | | (41) ~ (all_47_2 = 0) | all_47_0 = 0 % 17.65/3.39 | | | % 17.65/3.39 | | | BETA: splitting (20) gives: % 17.65/3.39 | | | % 17.65/3.39 | | | Case 1: % 17.65/3.39 | | | | % 17.65/3.39 | | | | (42) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_4) = v0) % 17.65/3.39 | | | | % 17.65/3.39 | | | | DELTA: instantiating (42) with fresh symbol all_67_0 gives: % 17.65/3.39 | | | | (43) ~ (all_67_0 = 0) & relation(all_36_4) = all_67_0 % 17.65/3.39 | | | | % 17.65/3.39 | | | | ALPHA: (43) implies: % 17.65/3.39 | | | | (44) ~ (all_67_0 = 0) % 17.65/3.39 | | | | (45) relation(all_36_4) = all_67_0 % 17.65/3.39 | | | | % 17.65/3.39 | | | | GROUND_INST: instantiating (2) with 0, all_67_0, all_36_4, simplifying % 17.65/3.39 | | | | with (14), (45) gives: % 17.65/3.39 | | | | (46) all_67_0 = 0 % 17.65/3.39 | | | | % 18.03/3.39 | | | | REDUCE: (44), (46) imply: % 18.03/3.39 | | | | (47) $false % 18.03/3.39 | | | | % 18.03/3.39 | | | | CLOSE: (47) is inconsistent. % 18.03/3.39 | | | | % 18.03/3.39 | | | Case 2: % 18.03/3.39 | | | | % 18.03/3.39 | | | | (48) ? [v0: any] : (v0 = all_36_1 | ~ $i(v0) | ? [v1: $i] : ? % 18.03/3.39 | | | | [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: % 18.03/3.39 | | | | $i] : ! [v4: $i] : ( ~ (ordered_pair(v3, v1) = v4) | ~ % 18.03/3.39 | | | | (in(v4, all_36_4) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: % 18.03/3.39 | | | | $i] : ? [v4: $i] : (ordered_pair(v3, v1) = v4 & in(v4, % 18.03/3.39 | | | | all_36_4) = 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_36_1) % 18.03/3.39 | | | | | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_36_1) % 18.03/3.39 | | | | = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ % 18.03/3.39 | | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_36_4) = 0) % 18.03/3.39 | | | | | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_36_1) = 0) % 18.03/3.39 | | | | | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 18.03/3.39 | | | | (ordered_pair(v1, v0) = v2 & in(v2, all_36_4) = 0 & $i(v2) % 18.03/3.39 | | | | & $i(v1))))) % 18.03/3.39 | | | | % 18.03/3.39 | | | | ALPHA: (48) implies: % 18.03/3.40 | | | | (49) ~ $i(all_36_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 18.03/3.40 | | | | (in(v0, all_36_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: % 18.03/3.40 | | | | $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, % 18.03/3.40 | | | | all_36_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ % 18.03/3.40 | | | | (in(v0, all_36_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 18.03/3.40 | | | | $i] : (ordered_pair(v1, v0) = v2 & in(v2, all_36_4) = 0 & % 18.03/3.40 | | | | $i(v2) & $i(v1)))) % 18.03/3.40 | | | | % 18.03/3.40 | | | | BETA: splitting (23) gives: % 18.03/3.40 | | | | % 18.03/3.40 | | | | Case 1: % 18.03/3.40 | | | | | % 18.03/3.40 | | | | | (50) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_4) = v0) % 18.03/3.40 | | | | | % 18.03/3.40 | | | | | DELTA: instantiating (50) with fresh symbol all_66_0 gives: % 18.03/3.40 | | | | | (51) ~ (all_66_0 = 0) & relation(all_36_4) = all_66_0 % 18.03/3.40 | | | | | % 18.03/3.40 | | | | | ALPHA: (51) implies: % 18.03/3.40 | | | | | (52) ~ (all_66_0 = 0) % 18.03/3.40 | | | | | (53) relation(all_36_4) = all_66_0 % 18.03/3.40 | | | | | % 18.03/3.40 | | | | | GROUND_INST: instantiating (2) with 0, all_66_0, all_36_4, simplifying % 18.03/3.40 | | | | | with (14), (53) gives: % 18.03/3.40 | | | | | (54) all_66_0 = 0 % 18.03/3.40 | | | | | % 18.03/3.40 | | | | | REDUCE: (52), (54) imply: % 18.03/3.40 | | | | | (55) $false % 18.03/3.40 | | | | | % 18.03/3.40 | | | | | CLOSE: (55) is inconsistent. % 18.03/3.40 | | | | | % 18.03/3.40 | | | | Case 2: % 18.03/3.40 | | | | | % 18.03/3.41 | | | | | (56) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | (( ~ (v0 = % 18.03/3.41 | | | | | all_36_3) | ( ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 18.03/3.41 | | | | | ! [v4: int] : (v4 = 0 | ~ (ordered_pair(v1, v2) = % 18.03/3.41 | | | | | v3) | ~ (in(v3, all_36_3) = v4) | ~ $i(v2) | ~ % 18.03/3.41 | | | | | $i(v1) | ! [v5: $i] : ! [v6: $i] : ( ~ % 18.03/3.41 | | | | | (ordered_pair(v1, v5) = v6) | ~ (in(v6, all_34_0) % 18.03/3.41 | | | | | = 0) | ~ $i(v5) | ? [v7: $i] : ? [v8: int] : % 18.03/3.41 | | | | | ( ~ (v8 = 0) & ordered_pair(v5, v2) = v7 & in(v7, % 18.03/3.41 | | | | | all_36_4) = v8 & $i(v7)))) & ! [v1: $i] : ! % 18.03/3.41 | | | | | [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v1, v2) = % 18.03/3.41 | | | | | v3) | ~ (in(v3, all_36_3) = 0) | ~ $i(v2) | ~ % 18.03/3.41 | | | | | $i(v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 18.03/3.41 | | | | | (ordered_pair(v4, v2) = v6 & ordered_pair(v1, v4) = % 18.03/3.41 | | | | | v5 & in(v6, all_36_4) = 0 & in(v5, all_34_0) = 0 & % 18.03/3.41 | | | | | $i(v6) & $i(v5) & $i(v4))))) & (v0 = all_36_3 | ? % 18.03/3.41 | | | | | [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : % 18.03/3.41 | | | | | (ordered_pair(v1, v2) = v3 & in(v3, v0) = v4 & $i(v3) & % 18.03/3.41 | | | | | $i(v2) & $i(v1) & ( ~ (v4 = 0) | ! [v5: $i] : ! [v6: % 18.03/3.41 | | | | | $i] : ( ~ (ordered_pair(v1, v5) = v6) | ~ (in(v6, % 18.03/3.41 | | | | | all_34_0) = 0) | ~ $i(v5) | ? [v7: $i] : ? % 18.03/3.41 | | | | | [v8: int] : ( ~ (v8 = 0) & ordered_pair(v5, v2) = % 18.03/3.41 | | | | | v7 & in(v7, all_36_4) = v8 & $i(v7)))) & (v4 = 0 % 18.03/3.41 | | | | | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 18.03/3.41 | | | | | (ordered_pair(v5, v2) = v7 & ordered_pair(v1, v5) = % 18.03/3.41 | | | | | v6 & in(v7, all_36_4) = 0 & in(v6, all_34_0) = 0 & % 18.03/3.41 | | | | | $i(v7) & $i(v6) & $i(v5))))))) % 18.03/3.41 | | | | | % 18.03/3.41 | | | | | BETA: splitting (41) gives: % 18.03/3.41 | | | | | % 18.03/3.41 | | | | | Case 1: % 18.03/3.41 | | | | | | % 18.03/3.41 | | | | | | (57) ~ (all_47_2 = 0) % 18.03/3.41 | | | | | | % 18.03/3.41 | | | | | | REDUCE: (37), (57) imply: % 18.03/3.41 | | | | | | (58) $false % 18.03/3.41 | | | | | | % 18.03/3.41 | | | | | | CLOSE: (58) is inconsistent. % 18.03/3.41 | | | | | | % 18.03/3.41 | | | | | Case 2: % 18.03/3.41 | | | | | | % 18.03/3.41 | | | | | | (59) all_47_0 = 0 % 18.03/3.41 | | | | | | % 18.03/3.41 | | | | | | REDUCE: (27), (59) imply: % 18.03/3.41 | | | | | | (60) relation(all_36_3) = 0 % 18.03/3.41 | | | | | | % 18.03/3.41 | | | | | | BETA: splitting (21) gives: % 18.03/3.41 | | | | | | % 18.03/3.41 | | | | | | Case 1: % 18.03/3.41 | | | | | | | % 18.03/3.41 | | | | | | | (61) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_3) = v0) % 18.03/3.41 | | | | | | | % 18.03/3.41 | | | | | | | DELTA: instantiating (61) with fresh symbol all_77_0 gives: % 18.03/3.41 | | | | | | | (62) ~ (all_77_0 = 0) & relation(all_36_3) = all_77_0 % 18.03/3.41 | | | | | | | % 18.03/3.41 | | | | | | | ALPHA: (62) implies: % 18.03/3.41 | | | | | | | (63) ~ (all_77_0 = 0) % 18.03/3.41 | | | | | | | (64) relation(all_36_3) = all_77_0 % 18.03/3.41 | | | | | | | % 18.03/3.41 | | | | | | | GROUND_INST: instantiating (2) with 0, all_77_0, all_36_3, % 18.03/3.41 | | | | | | | simplifying with (60), (64) gives: % 18.03/3.41 | | | | | | | (65) all_77_0 = 0 % 18.03/3.41 | | | | | | | % 18.03/3.41 | | | | | | | REDUCE: (63), (65) imply: % 18.03/3.41 | | | | | | | (66) $false % 18.03/3.41 | | | | | | | % 18.03/3.41 | | | | | | | CLOSE: (66) is inconsistent. % 18.03/3.41 | | | | | | | % 18.03/3.41 | | | | | | Case 2: % 18.03/3.41 | | | | | | | % 18.03/3.42 | | | | | | | (67) ? [v0: any] : (v0 = all_36_2 | ~ $i(v0) | ? [v1: $i] : % 18.03/3.42 | | | | | | | ? [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | % 18.03/3.42 | | | | | | | ! [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v3, % 18.03/3.42 | | | | | | | v1) = v4) | ~ (in(v4, all_36_3) = 0) | ~ % 18.03/3.42 | | | | | | | $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] : % 18.03/3.42 | | | | | | | (ordered_pair(v3, v1) = v4 & in(v4, all_36_3) = 0 & % 18.03/3.42 | | | | | | | $i(v4) & $i(v3))))) & ( ~ $i(all_36_2) | ( ! [v0: % 18.03/3.42 | | | | | | | $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_36_2) % 18.03/3.42 | | | | | | | = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( % 18.03/3.42 | | | | | | | ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, % 18.03/3.42 | | | | | | | all_36_3) = 0) | ~ $i(v2))) & ! [v0: $i] : ( % 18.03/3.42 | | | | | | | ~ (in(v0, all_36_2) = 0) | ~ $i(v0) | ? [v1: $i] : % 18.03/3.42 | | | | | | | ? [v2: $i] : (ordered_pair(v1, v0) = v2 & in(v2, % 18.03/3.42 | | | | | | | all_36_3) = 0 & $i(v2) & $i(v1))))) % 18.03/3.42 | | | | | | | % 18.03/3.42 | | | | | | | ALPHA: (67) implies: % 18.03/3.42 | | | | | | | (68) ~ $i(all_36_2) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 18.03/3.42 | | | | | | | ~ (in(v0, all_36_2) = v1) | ~ $i(v0) | ! [v2: $i] : % 18.03/3.42 | | | | | | | ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ % 18.03/3.42 | | | | | | | (in(v3, all_36_3) = 0) | ~ $i(v2))) & ! [v0: $i] : % 18.03/3.42 | | | | | | | ( ~ (in(v0, all_36_2) = 0) | ~ $i(v0) | ? [v1: $i] : % 18.03/3.42 | | | | | | | ? [v2: $i] : (ordered_pair(v1, v0) = v2 & in(v2, % 18.03/3.42 | | | | | | | all_36_3) = 0 & $i(v2) & $i(v1)))) % 18.03/3.42 | | | | | | | % 18.03/3.42 | | | | | | | BETA: splitting (49) gives: % 18.03/3.42 | | | | | | | % 18.03/3.42 | | | | | | | Case 1: % 18.03/3.42 | | | | | | | | % 18.03/3.42 | | | | | | | | (69) ~ $i(all_36_1) % 18.03/3.42 | | | | | | | | % 18.03/3.42 | | | | | | | | PRED_UNIFY: (12), (69) imply: % 18.03/3.42 | | | | | | | | (70) $false % 18.03/3.42 | | | | | | | | % 18.03/3.42 | | | | | | | | CLOSE: (70) is inconsistent. % 18.03/3.42 | | | | | | | | % 18.03/3.42 | | | | | | | Case 2: % 18.03/3.42 | | | | | | | | % 18.03/3.42 | | | | | | | | (71) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 18.03/3.42 | | | | | | | | all_36_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! % 18.03/3.42 | | | | | | | | [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ % 18.03/3.42 | | | | | | | | (in(v3, all_36_4) = 0) | ~ $i(v2))) & ! [v0: $i] : % 18.03/3.42 | | | | | | | | ( ~ (in(v0, all_36_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 18.03/3.42 | | | | | | | | ? [v2: $i] : (ordered_pair(v1, v0) = v2 & in(v2, % 18.03/3.42 | | | | | | | | all_36_4) = 0 & $i(v2) & $i(v1))) % 18.03/3.42 | | | | | | | | % 18.03/3.42 | | | | | | | | ALPHA: (71) implies: % 18.03/3.42 | | | | | | | | (72) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 18.03/3.42 | | | | | | | | all_36_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! % 18.03/3.42 | | | | | | | | [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ % 18.03/3.42 | | | | | | | | (in(v3, all_36_4) = 0) | ~ $i(v2))) % 18.03/3.42 | | | | | | | | % 18.03/3.42 | | | | | | | | BETA: splitting (68) gives: % 18.03/3.42 | | | | | | | | % 18.03/3.42 | | | | | | | | Case 1: % 18.03/3.42 | | | | | | | | | % 18.03/3.42 | | | | | | | | | (73) ~ $i(all_36_2) % 18.03/3.42 | | | | | | | | | % 18.03/3.42 | | | | | | | | | PRED_UNIFY: (11), (73) imply: % 18.03/3.42 | | | | | | | | | (74) $false % 18.03/3.42 | | | | | | | | | % 18.03/3.42 | | | | | | | | | CLOSE: (74) is inconsistent. % 18.03/3.42 | | | | | | | | | % 18.03/3.42 | | | | | | | | Case 2: % 18.03/3.42 | | | | | | | | | % 18.03/3.42 | | | | | | | | | (75) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 18.03/3.42 | | | | | | | | | all_36_2) = v1) | ~ $i(v0) | ! [v2: $i] : ! % 18.03/3.42 | | | | | | | | | [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ % 18.03/3.42 | | | | | | | | | (in(v3, all_36_3) = 0) | ~ $i(v2))) & ! [v0: $i] % 18.03/3.42 | | | | | | | | | : ( ~ (in(v0, all_36_2) = 0) | ~ $i(v0) | ? [v1: $i] % 18.03/3.42 | | | | | | | | | : ? [v2: $i] : (ordered_pair(v1, v0) = v2 & in(v2, % 18.03/3.42 | | | | | | | | | all_36_3) = 0 & $i(v2) & $i(v1))) % 18.03/3.43 | | | | | | | | | % 18.03/3.43 | | | | | | | | | ALPHA: (75) implies: % 18.03/3.43 | | | | | | | | | (76) ! [v0: $i] : ( ~ (in(v0, all_36_2) = 0) | ~ $i(v0) | % 18.03/3.43 | | | | | | | | | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) = % 18.03/3.43 | | | | | | | | | v2 & in(v2, all_36_3) = 0 & $i(v2) & $i(v1))) % 18.03/3.43 | | | | | | | | | % 18.03/3.43 | | | | | | | | | GROUND_INST: instantiating (76) with all_53_1, simplifying with % 18.03/3.43 | | | | | | | | | (34), (35) gives: % 18.03/3.43 | | | | | | | | | (77) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, % 18.03/3.43 | | | | | | | | | all_53_1) = v1 & in(v1, all_36_3) = 0 & $i(v1) & % 18.03/3.43 | | | | | | | | | $i(v0)) % 18.03/3.43 | | | | | | | | | % 18.03/3.43 | | | | | | | | | GROUND_INST: instantiating (72) with all_53_1, all_53_0, % 18.03/3.43 | | | | | | | | | simplifying with (34), (36) gives: % 18.03/3.43 | | | | | | | | | (78) all_53_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ % 18.03/3.43 | | | | | | | | | (ordered_pair(v0, all_53_1) = v1) | ~ (in(v1, % 18.03/3.43 | | | | | | | | | all_36_4) = 0) | ~ $i(v0)) % 18.03/3.43 | | | | | | | | | % 18.03/3.43 | | | | | | | | | GROUND_INST: instantiating (56) with all_36_3, simplifying with % 18.03/3.43 | | | | | | | | | (10), (60) gives: % 18.03/3.43 | | | | | | | | | (79) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] % 18.03/3.43 | | | | | | | | | : (v3 = 0 | ~ (ordered_pair(v0, v1) = v2) | ~ % 18.03/3.43 | | | | | | | | | (in(v2, all_36_3) = v3) | ~ $i(v1) | ~ $i(v0) | ! % 18.03/3.43 | | | | | | | | | [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v0, v4) = % 18.03/3.43 | | | | | | | | | v5) | ~ (in(v5, all_34_0) = 0) | ~ $i(v4) | ? % 18.03/3.43 | | | | | | | | | [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & % 18.03/3.43 | | | | | | | | | ordered_pair(v4, v1) = v6 & in(v6, all_36_4) = % 18.03/3.43 | | | | | | | | | v7 & $i(v6)))) & ! [v0: $i] : ! [v1: $i] : ! % 18.03/3.43 | | | | | | | | | [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 18.03/3.43 | | | | | | | | | (in(v2, all_36_3) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 18.03/3.43 | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 18.03/3.43 | | | | | | | | | (ordered_pair(v3, v1) = v5 & ordered_pair(v0, v3) = % 18.03/3.43 | | | | | | | | | v4 & in(v5, all_36_4) = 0 & in(v4, all_34_0) = 0 & % 18.03/3.43 | | | | | | | | | $i(v5) & $i(v4) & $i(v3))) % 18.03/3.43 | | | | | | | | | % 18.03/3.43 | | | | | | | | | ALPHA: (79) implies: % 18.03/3.43 | | | | | | | | | (80) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 18.03/3.43 | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_36_3) = % 18.03/3.43 | | | | | | | | | 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 18.03/3.43 | | | | | | | | | $i] : ? [v5: $i] : (ordered_pair(v3, v1) = v5 & % 18.03/3.43 | | | | | | | | | ordered_pair(v0, v3) = v4 & in(v5, all_36_4) = 0 & % 18.03/3.43 | | | | | | | | | in(v4, all_34_0) = 0 & $i(v5) & $i(v4) & $i(v3))) % 18.03/3.43 | | | | | | | | | % 18.03/3.43 | | | | | | | | | DELTA: instantiating (77) with fresh symbols all_94_0, % 18.03/3.43 | | | | | | | | | all_94_1 gives: % 18.03/3.43 | | | | | | | | | (81) ordered_pair(all_94_1, all_53_1) = all_94_0 & % 18.03/3.43 | | | | | | | | | in(all_94_0, all_36_3) = 0 & $i(all_94_0) & % 18.03/3.43 | | | | | | | | | $i(all_94_1) % 18.03/3.43 | | | | | | | | | % 18.03/3.43 | | | | | | | | | ALPHA: (81) implies: % 18.03/3.43 | | | | | | | | | (82) $i(all_94_1) % 18.03/3.43 | | | | | | | | | (83) in(all_94_0, all_36_3) = 0 % 18.03/3.43 | | | | | | | | | (84) ordered_pair(all_94_1, all_53_1) = all_94_0 % 18.03/3.43 | | | | | | | | | % 18.03/3.43 | | | | | | | | | BETA: splitting (78) gives: % 18.03/3.43 | | | | | | | | | % 18.03/3.43 | | | | | | | | | Case 1: % 18.03/3.43 | | | | | | | | | | % 18.03/3.43 | | | | | | | | | | (85) all_53_0 = 0 % 18.03/3.43 | | | | | | | | | | % 18.03/3.43 | | | | | | | | | | REDUCE: (33), (85) imply: % 18.03/3.43 | | | | | | | | | | (86) $false % 18.03/3.43 | | | | | | | | | | % 18.03/3.43 | | | | | | | | | | CLOSE: (86) is inconsistent. % 18.03/3.43 | | | | | | | | | | % 18.03/3.43 | | | | | | | | | Case 2: % 18.03/3.43 | | | | | | | | | | % 18.03/3.44 | | | | | | | | | | (87) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, % 18.03/3.44 | | | | | | | | | | all_53_1) = v1) | ~ (in(v1, all_36_4) = 0) | % 18.03/3.44 | | | | | | | | | | ~ $i(v0)) % 18.03/3.44 | | | | | | | | | | % 18.03/3.44 | | | | | | | | | | GROUND_INST: instantiating (80) with all_94_1, all_53_1, % 18.03/3.44 | | | | | | | | | | all_94_0, simplifying with (34), (82), (83), (84) % 18.03/3.44 | | | | | | | | | | gives: % 18.03/3.44 | | | | | | | | | | (88) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 18.03/3.44 | | | | | | | | | | (ordered_pair(v0, all_53_1) = v2 & % 18.03/3.44 | | | | | | | | | | ordered_pair(all_94_1, v0) = v1 & in(v2, all_36_4) % 18.03/3.44 | | | | | | | | | | = 0 & in(v1, all_34_0) = 0 & $i(v2) & $i(v1) & % 18.03/3.44 | | | | | | | | | | $i(v0)) % 18.03/3.44 | | | | | | | | | | % 18.03/3.44 | | | | | | | | | | DELTA: instantiating (88) with fresh symbols all_112_0, % 18.03/3.44 | | | | | | | | | | all_112_1, all_112_2 gives: % 18.03/3.44 | | | | | | | | | | (89) ordered_pair(all_112_2, all_53_1) = all_112_0 & % 18.03/3.44 | | | | | | | | | | ordered_pair(all_94_1, all_112_2) = all_112_1 & % 18.03/3.44 | | | | | | | | | | in(all_112_0, all_36_4) = 0 & in(all_112_1, % 18.03/3.44 | | | | | | | | | | all_34_0) = 0 & $i(all_112_0) & $i(all_112_1) & % 18.03/3.44 | | | | | | | | | | $i(all_112_2) % 18.03/3.44 | | | | | | | | | | % 18.03/3.44 | | | | | | | | | | ALPHA: (89) implies: % 18.03/3.44 | | | | | | | | | | (90) $i(all_112_2) % 18.03/3.44 | | | | | | | | | | (91) in(all_112_0, all_36_4) = 0 % 18.03/3.44 | | | | | | | | | | (92) ordered_pair(all_112_2, all_53_1) = all_112_0 % 18.03/3.44 | | | | | | | | | | % 18.03/3.44 | | | | | | | | | | GROUND_INST: instantiating (87) with all_112_2, all_112_0, % 18.59/3.44 | | | | | | | | | | simplifying with (90), (91), (92) gives: % 18.59/3.44 | | | | | | | | | | (93) $false % 18.59/3.44 | | | | | | | | | | % 18.59/3.44 | | | | | | | | | | CLOSE: (93) is inconsistent. % 18.59/3.44 | | | | | | | | | | % 18.59/3.44 | | | | | | | | | End of split % 18.59/3.44 | | | | | | | | | % 18.59/3.44 | | | | | | | | End of split % 18.59/3.44 | | | | | | | | % 18.59/3.44 | | | | | | | End of split % 18.59/3.44 | | | | | | | % 18.59/3.44 | | | | | | End of split % 18.59/3.44 | | | | | | % 18.59/3.44 | | | | | End of split % 18.59/3.44 | | | | | % 18.59/3.44 | | | | End of split % 18.59/3.44 | | | | % 18.59/3.44 | | | End of split % 18.59/3.44 | | | % 18.59/3.44 | | End of split % 18.59/3.44 | | % 18.59/3.44 | End of split % 18.59/3.44 | % 18.59/3.44 End of proof % 18.59/3.44 % SZS output end Proof for theBenchmark % 18.59/3.44 % 18.59/3.44 2796ms %------------------------------------------------------------------------------