%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU179+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 : n021.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 17:43:05 EDT 2023 % Result : Theorem 9.51s 2.19s % Output : Proof 13.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU179+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.18/0.34 % Computer : n021.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.35 % DateTime : Wed Aug 23 14:11:39 EDT 2023 % 0.18/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.54/1.08 Prover 1: Preprocessing ... % 2.54/1.08 Prover 4: Preprocessing ... % 2.97/1.12 Prover 2: Preprocessing ... % 2.97/1.12 Prover 5: Preprocessing ... % 2.97/1.12 Prover 0: Preprocessing ... % 2.97/1.13 Prover 6: Preprocessing ... % 2.97/1.13 Prover 3: Preprocessing ... % 6.00/1.57 Prover 1: Warning: ignoring some quantifiers % 6.00/1.60 Prover 3: Warning: ignoring some quantifiers % 6.44/1.62 Prover 5: Proving ... % 6.44/1.63 Prover 2: Proving ... % 6.44/1.63 Prover 6: Proving ... % 6.44/1.64 Prover 1: Constructing countermodel ... % 6.44/1.64 Prover 3: Constructing countermodel ... % 6.66/1.66 Prover 4: Warning: ignoring some quantifiers % 6.66/1.70 Prover 4: Constructing countermodel ... % 7.54/1.78 Prover 0: Proving ... % 9.51/2.19 Prover 3: proved (1549ms) % 9.51/2.19 % 9.51/2.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.51/2.19 % 9.51/2.19 Prover 2: stopped % 9.51/2.19 Prover 0: stopped % 9.51/2.19 Prover 6: stopped % 9.51/2.19 Prover 5: stopped % 9.51/2.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.51/2.20 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.51/2.20 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.51/2.20 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.51/2.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.82/2.24 Prover 10: Preprocessing ... % 10.82/2.25 Prover 7: Preprocessing ... % 10.82/2.26 Prover 13: Preprocessing ... % 10.82/2.26 Prover 11: Preprocessing ... % 10.82/2.26 Prover 8: Preprocessing ... % 11.62/2.35 Prover 10: Warning: ignoring some quantifiers % 11.62/2.36 Prover 7: Warning: ignoring some quantifiers % 11.62/2.37 Prover 7: Constructing countermodel ... % 11.62/2.37 Prover 10: Constructing countermodel ... % 11.62/2.39 Prover 1: Found proof (size 94) % 11.62/2.39 Prover 1: proved (1752ms) % 11.62/2.39 Prover 10: stopped % 11.62/2.39 Prover 7: stopped % 11.62/2.39 Prover 4: stopped % 11.62/2.40 Prover 8: Warning: ignoring some quantifiers % 11.62/2.41 Prover 13: Warning: ignoring some quantifiers % 11.62/2.42 Prover 8: Constructing countermodel ... % 12.34/2.42 Prover 13: Constructing countermodel ... % 12.34/2.43 Prover 8: stopped % 12.34/2.43 Prover 13: stopped % 12.34/2.44 Prover 11: Warning: ignoring some quantifiers % 12.34/2.45 Prover 11: Constructing countermodel ... % 12.34/2.46 Prover 11: stopped % 12.34/2.46 % 12.34/2.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.34/2.46 % 12.34/2.47 % SZS output start Proof for theBenchmark % 12.34/2.47 Assumptions after simplification: % 12.34/2.47 --------------------------------- % 12.34/2.47 % 12.34/2.47 (d3_tarski) % 12.68/2.50 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 12.68/2.50 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 12.68/2.50 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 12.68/2.50 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 12.68/2.50 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 12.68/2.50 % 12.68/2.50 (d4_relat_1) % 12.68/2.51 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 12.68/2.51 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~ % 12.68/2.51 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~ % 12.68/2.51 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) = % 12.68/2.51 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i] % 12.68/2.51 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6) % 12.68/2.51 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 % 12.68/2.51 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 12.68/2.51 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) & % 12.68/2.51 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: % 12.68/2.51 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) & % 12.68/2.51 $i(v3))))))) % 12.68/2.51 % 12.68/2.51 (d5_relat_1) % 12.68/2.51 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 12.68/2.51 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~ % 12.68/2.51 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~ % 12.68/2.51 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) = % 12.68/2.51 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i] % 12.68/2.51 : ? [v6: $i] : (ordered_pair(v5, v3) = v6 & in(v6, v0) = 0 & $i(v6) % 12.68/2.51 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 % 12.68/2.51 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 12.68/2.51 (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) & % 12.68/2.51 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: % 12.68/2.51 $i] : (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0 & $i(v4) & % 12.68/2.51 $i(v3))))))) % 12.68/2.51 % 12.68/2.51 (t25_relat_1) % 12.68/2.51 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_rng(v0) = v2 & % 12.68/2.51 relation_dom(v0) = v1 & relation(v0) = 0 & $i(v2) & $i(v1) & $i(v0) & ? % 12.68/2.51 [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : % 12.68/2.51 (relation_rng(v3) = v6 & relation_dom(v3) = v4 & relation(v3) = 0 & % 12.68/2.51 subset(v2, v6) = v7 & subset(v1, v4) = v5 & subset(v0, v3) = 0 & $i(v6) & % 12.68/2.51 $i(v4) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0)))) % 12.68/2.51 % 12.68/2.51 (function-axioms) % 12.68/2.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.68/2.52 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 12.68/2.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.68/2.52 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: % 12.68/2.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.68/2.52 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 12.68/2.52 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.68/2.52 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 12.68/2.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.68/2.52 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 12.68/2.52 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) % 12.68/2.52 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.68/2.52 $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : % 12.68/2.52 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 12.68/2.52 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 12.68/2.52 ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! % 12.68/2.52 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 12.68/2.52 (relation_dom(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.68/2.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 12.68/2.52 (relation(v2) = v0)) % 12.68/2.52 % 12.68/2.52 Further assumptions not needed in the proof: % 12.68/2.52 -------------------------------------------- % 12.68/2.52 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, dt_k1_relat_1, % 12.68/2.52 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_tarski, % 12.68/2.52 dt_k4_tarski, dt_m1_subset_1, existence_m1_subset_1, fc1_subset_1, fc1_xboole_0, % 12.68/2.52 fc1_zfmisc_1, fc2_subset_1, fc3_subset_1, rc1_relat_1, rc1_subset_1, % 12.68/2.52 rc1_xboole_0, rc2_subset_1, rc2_xboole_0, reflexivity_r1_tarski, t1_subset, % 12.68/2.52 t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 12.68/2.52 % 12.68/2.52 Those formulas are unsatisfiable: % 12.68/2.52 --------------------------------- % 12.68/2.52 % 12.68/2.52 Begin of proof % 12.68/2.52 | % 12.68/2.52 | ALPHA: (d3_tarski) implies: % 12.68/2.52 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 12.68/2.52 | $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | in(v2, v1) % 12.68/2.52 | = 0)) % 12.68/2.52 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 12.68/2.52 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 12.68/2.52 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 12.68/2.52 | % 12.68/2.52 | ALPHA: (function-axioms) implies: % 12.68/2.52 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.68/2.52 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 12.68/2.52 | % 12.68/2.52 | DELTA: instantiating (t25_relat_1) with fresh symbols all_33_0, all_33_1, % 12.68/2.52 | all_33_2 gives: % 12.68/2.53 | (4) relation_rng(all_33_2) = all_33_0 & relation_dom(all_33_2) = all_33_1 & % 12.68/2.53 | relation(all_33_2) = 0 & $i(all_33_0) & $i(all_33_1) & $i(all_33_2) & % 12.68/2.53 | ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 12.68/2.53 | (relation_rng(v0) = v3 & relation_dom(v0) = v1 & relation(v0) = 0 & % 12.68/2.53 | subset(all_33_0, v3) = v4 & subset(all_33_1, v1) = v2 & % 12.68/2.53 | subset(all_33_2, v0) = 0 & $i(v3) & $i(v1) & $i(v0) & ( ~ (v4 = 0) | % 12.68/2.53 | ~ (v2 = 0))) % 12.68/2.53 | % 12.68/2.53 | ALPHA: (4) implies: % 12.68/2.53 | (5) $i(all_33_2) % 12.68/2.53 | (6) $i(all_33_1) % 12.68/2.53 | (7) $i(all_33_0) % 12.68/2.53 | (8) relation(all_33_2) = 0 % 12.68/2.53 | (9) relation_dom(all_33_2) = all_33_1 % 12.68/2.53 | (10) relation_rng(all_33_2) = all_33_0 % 12.68/2.53 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] % 12.68/2.53 | : (relation_rng(v0) = v3 & relation_dom(v0) = v1 & relation(v0) = 0 & % 12.68/2.53 | subset(all_33_0, v3) = v4 & subset(all_33_1, v1) = v2 & % 12.68/2.53 | subset(all_33_2, v0) = 0 & $i(v3) & $i(v1) & $i(v0) & ( ~ (v4 = 0) | % 12.68/2.53 | ~ (v2 = 0))) % 12.68/2.53 | % 12.68/2.53 | DELTA: instantiating (11) with fresh symbols all_35_0, all_35_1, all_35_2, % 12.68/2.53 | all_35_3, all_35_4 gives: % 12.68/2.53 | (12) relation_rng(all_35_4) = all_35_1 & relation_dom(all_35_4) = all_35_3 % 12.68/2.53 | & relation(all_35_4) = 0 & subset(all_33_0, all_35_1) = all_35_0 & % 12.68/2.53 | subset(all_33_1, all_35_3) = all_35_2 & subset(all_33_2, all_35_4) = 0 % 12.68/2.53 | & $i(all_35_1) & $i(all_35_3) & $i(all_35_4) & ( ~ (all_35_0 = 0) | ~ % 12.68/2.53 | (all_35_2 = 0)) % 12.68/2.53 | % 12.68/2.53 | ALPHA: (12) implies: % 12.68/2.53 | (13) $i(all_35_4) % 12.68/2.53 | (14) $i(all_35_3) % 12.68/2.53 | (15) $i(all_35_1) % 12.68/2.53 | (16) subset(all_33_2, all_35_4) = 0 % 12.68/2.53 | (17) subset(all_33_1, all_35_3) = all_35_2 % 12.68/2.53 | (18) subset(all_33_0, all_35_1) = all_35_0 % 12.68/2.53 | (19) relation(all_35_4) = 0 % 12.68/2.53 | (20) relation_dom(all_35_4) = all_35_3 % 12.68/2.53 | (21) relation_rng(all_35_4) = all_35_1 % 12.68/2.53 | (22) ~ (all_35_0 = 0) | ~ (all_35_2 = 0) % 12.68/2.53 | % 12.68/2.53 | GROUND_INST: instantiating (1) with all_33_2, all_35_4, simplifying with (5), % 12.68/2.53 | (13), (16) gives: % 12.68/2.53 | (23) ! [v0: $i] : ( ~ (in(v0, all_33_2) = 0) | ~ $i(v0) | in(v0, % 12.68/2.53 | all_35_4) = 0) % 12.68/2.53 | % 12.68/2.53 | GROUND_INST: instantiating (2) with all_33_1, all_35_3, all_35_2, simplifying % 12.68/2.53 | with (6), (14), (17) gives: % 12.68/2.53 | (24) all_35_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 12.68/2.53 | all_35_3) = v1 & in(v0, all_33_1) = 0 & $i(v0)) % 12.68/2.53 | % 12.68/2.53 | GROUND_INST: instantiating (2) with all_33_0, all_35_1, all_35_0, simplifying % 12.68/2.53 | with (7), (15), (18) gives: % 12.68/2.53 | (25) all_35_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 12.68/2.53 | all_35_1) = v1 & in(v0, all_33_0) = 0 & $i(v0)) % 12.68/2.53 | % 12.68/2.54 | GROUND_INST: instantiating (d4_relat_1) with all_33_2, all_33_1, simplifying % 12.68/2.54 | with (5), (9) gives: % 12.68/2.54 | (26) ? [v0: int] : ( ~ (v0 = 0) & relation(all_33_2) = v0) | ( ? [v0: any] % 12.68/2.54 | : (v0 = all_33_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1, % 12.68/2.54 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] : % 12.68/2.54 | ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, all_33_2) = 0) | % 12.68/2.54 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] : % 12.68/2.54 | (ordered_pair(v1, v3) = v4 & in(v4, all_33_2) = 0 & $i(v4) & % 12.68/2.54 | $i(v3))))) & ( ~ $i(all_33_1) | ( ! [v0: $i] : ! [v1: int] % 12.68/2.54 | : (v1 = 0 | ~ (in(v0, all_33_1) = v1) | ~ $i(v0) | ! [v2: $i] % 12.68/2.54 | : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, % 12.68/2.54 | all_33_2) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, % 12.68/2.54 | all_33_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 12.68/2.54 | (ordered_pair(v0, v1) = v2 & in(v2, all_33_2) = 0 & $i(v2) & % 12.68/2.54 | $i(v1)))))) % 12.68/2.54 | % 12.68/2.54 | GROUND_INST: instantiating (d4_relat_1) with all_35_4, all_35_3, simplifying % 12.68/2.54 | with (13), (20) gives: % 12.68/2.54 | (27) ? [v0: int] : ( ~ (v0 = 0) & relation(all_35_4) = v0) | ( ? [v0: any] % 12.68/2.54 | : (v0 = all_35_3 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1, % 12.68/2.54 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] : % 12.68/2.54 | ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, all_35_4) = 0) | % 12.68/2.54 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] : % 12.68/2.54 | (ordered_pair(v1, v3) = v4 & in(v4, all_35_4) = 0 & $i(v4) & % 12.68/2.54 | $i(v3))))) & ( ~ $i(all_35_3) | ( ! [v0: $i] : ! [v1: int] % 12.68/2.54 | : (v1 = 0 | ~ (in(v0, all_35_3) = v1) | ~ $i(v0) | ! [v2: $i] % 12.68/2.54 | : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, % 12.68/2.54 | all_35_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, % 12.68/2.54 | all_35_3) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 12.68/2.54 | (ordered_pair(v0, v1) = v2 & in(v2, all_35_4) = 0 & $i(v2) & % 12.68/2.54 | $i(v1)))))) % 12.68/2.54 | % 12.68/2.54 | GROUND_INST: instantiating (d5_relat_1) with all_33_2, all_33_0, simplifying % 12.68/2.54 | with (5), (10) gives: % 12.68/2.54 | (28) ? [v0: int] : ( ~ (v0 = 0) & relation(all_33_2) = v0) | ( ? [v0: any] % 12.68/2.54 | : (v0 = all_33_0 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1, % 12.68/2.54 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] : % 12.68/2.54 | ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4, all_33_2) = 0) | % 12.68/2.54 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] : % 12.68/2.54 | (ordered_pair(v3, v1) = v4 & in(v4, all_33_2) = 0 & $i(v4) & % 12.68/2.54 | $i(v3))))) & ( ~ $i(all_33_0) | ( ! [v0: $i] : ! [v1: int] % 12.68/2.54 | : (v1 = 0 | ~ (in(v0, all_33_0) = v1) | ~ $i(v0) | ! [v2: $i] % 12.68/2.54 | : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, % 12.68/2.54 | all_33_2) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, % 12.68/2.54 | all_33_0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 12.68/2.54 | (ordered_pair(v1, v0) = v2 & in(v2, all_33_2) = 0 & $i(v2) & % 12.68/2.54 | $i(v1)))))) % 12.68/2.55 | % 12.68/2.55 | GROUND_INST: instantiating (d5_relat_1) with all_35_4, all_35_1, simplifying % 12.68/2.55 | with (13), (21) gives: % 12.68/2.55 | (29) ? [v0: int] : ( ~ (v0 = 0) & relation(all_35_4) = v0) | ( ? [v0: any] % 12.68/2.55 | : (v0 = all_35_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1, % 12.68/2.55 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] : % 12.68/2.55 | ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4, all_35_4) = 0) | % 12.68/2.55 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] : % 12.68/2.55 | (ordered_pair(v3, v1) = v4 & in(v4, all_35_4) = 0 & $i(v4) & % 12.68/2.55 | $i(v3))))) & ( ~ $i(all_35_1) | ( ! [v0: $i] : ! [v1: int] % 12.68/2.55 | : (v1 = 0 | ~ (in(v0, all_35_1) = v1) | ~ $i(v0) | ! [v2: $i] % 12.68/2.55 | : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, % 12.68/2.55 | all_35_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, % 12.68/2.55 | all_35_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 12.68/2.55 | (ordered_pair(v1, v0) = v2 & in(v2, all_35_4) = 0 & $i(v2) & % 12.68/2.55 | $i(v1)))))) % 12.68/2.55 | % 12.68/2.55 | BETA: splitting (29) gives: % 12.68/2.55 | % 12.68/2.55 | Case 1: % 12.68/2.55 | | % 12.68/2.55 | | (30) ? [v0: int] : ( ~ (v0 = 0) & relation(all_35_4) = v0) % 12.68/2.55 | | % 12.68/2.55 | | DELTA: instantiating (30) with fresh symbol all_50_0 gives: % 12.68/2.55 | | (31) ~ (all_50_0 = 0) & relation(all_35_4) = all_50_0 % 12.68/2.55 | | % 12.68/2.55 | | ALPHA: (31) implies: % 12.68/2.55 | | (32) ~ (all_50_0 = 0) % 12.68/2.55 | | (33) relation(all_35_4) = all_50_0 % 12.68/2.55 | | % 12.68/2.55 | | GROUND_INST: instantiating (3) with 0, all_50_0, all_35_4, simplifying with % 12.68/2.55 | | (19), (33) gives: % 12.68/2.55 | | (34) all_50_0 = 0 % 12.68/2.55 | | % 12.68/2.55 | | REDUCE: (32), (34) imply: % 12.68/2.55 | | (35) $false % 12.68/2.55 | | % 12.68/2.55 | | CLOSE: (35) is inconsistent. % 12.68/2.55 | | % 12.68/2.55 | Case 2: % 12.68/2.55 | | % 12.68/2.55 | | (36) ? [v0: any] : (v0 = all_35_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 12.68/2.55 | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : % 12.68/2.55 | | ! [v4: $i] : ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4, % 12.68/2.55 | | all_35_4) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : % 12.68/2.55 | | ? [v4: $i] : (ordered_pair(v3, v1) = v4 & in(v4, all_35_4) = 0 % 12.68/2.55 | | & $i(v4) & $i(v3))))) & ( ~ $i(all_35_1) | ( ! [v0: $i] : ! % 12.68/2.55 | | [v1: int] : (v1 = 0 | ~ (in(v0, all_35_1) = v1) | ~ $i(v0) | % 12.68/2.55 | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | % 12.68/2.55 | | ~ (in(v3, all_35_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ % 12.68/2.55 | | (in(v0, all_35_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] % 12.68/2.55 | | : (ordered_pair(v1, v0) = v2 & in(v2, all_35_4) = 0 & $i(v2) & % 12.68/2.55 | | $i(v1))))) % 12.68/2.56 | | % 12.68/2.56 | | ALPHA: (36) implies: % 12.68/2.56 | | (37) ~ $i(all_35_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 12.68/2.56 | | all_35_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( % 12.68/2.56 | | ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_35_4) = 0) | ~ % 12.68/2.56 | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_35_1) = 0) | ~ % 12.68/2.56 | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) = v2 % 12.68/2.56 | | & in(v2, all_35_4) = 0 & $i(v2) & $i(v1)))) % 12.68/2.56 | | % 12.68/2.56 | | BETA: splitting (28) gives: % 12.68/2.56 | | % 12.68/2.56 | | Case 1: % 12.68/2.56 | | | % 12.68/2.56 | | | (38) ? [v0: int] : ( ~ (v0 = 0) & relation(all_33_2) = v0) % 12.68/2.56 | | | % 12.68/2.56 | | | DELTA: instantiating (38) with fresh symbol all_50_0 gives: % 12.68/2.56 | | | (39) ~ (all_50_0 = 0) & relation(all_33_2) = all_50_0 % 12.68/2.56 | | | % 12.68/2.56 | | | ALPHA: (39) implies: % 12.68/2.56 | | | (40) ~ (all_50_0 = 0) % 12.68/2.56 | | | (41) relation(all_33_2) = all_50_0 % 12.68/2.56 | | | % 12.68/2.56 | | | GROUND_INST: instantiating (3) with 0, all_50_0, all_33_2, simplifying % 12.68/2.56 | | | with (8), (41) gives: % 12.68/2.56 | | | (42) all_50_0 = 0 % 12.68/2.56 | | | % 12.68/2.56 | | | REDUCE: (40), (42) imply: % 12.68/2.56 | | | (43) $false % 12.68/2.56 | | | % 12.68/2.56 | | | CLOSE: (43) is inconsistent. % 12.68/2.56 | | | % 12.68/2.56 | | Case 2: % 12.68/2.56 | | | % 12.68/2.56 | | | (44) ? [v0: any] : (v0 = all_33_0 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 12.68/2.56 | | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] % 12.68/2.56 | | | : ! [v4: $i] : ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4, % 12.68/2.56 | | | all_33_2) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : % 12.68/2.56 | | | ? [v4: $i] : (ordered_pair(v3, v1) = v4 & in(v4, all_33_2) % 12.68/2.56 | | | = 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_33_0) | ( ! [v0: % 12.68/2.56 | | | $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_33_0) = v1) | % 12.68/2.56 | | | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, % 12.68/2.56 | | | v0) = v3) | ~ (in(v3, all_33_2) = 0) | ~ $i(v2))) & % 12.68/2.56 | | | ! [v0: $i] : ( ~ (in(v0, all_33_0) = 0) | ~ $i(v0) | ? [v1: % 12.68/2.56 | | | $i] : ? [v2: $i] : (ordered_pair(v1, v0) = v2 & in(v2, % 12.68/2.56 | | | all_33_2) = 0 & $i(v2) & $i(v1))))) % 12.68/2.56 | | | % 12.68/2.56 | | | ALPHA: (44) implies: % 12.68/2.56 | | | (45) ~ $i(all_33_0) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 12.68/2.56 | | | (in(v0, all_33_0) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: % 12.68/2.56 | | | $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_33_2) % 12.68/2.56 | | | = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_33_0) = % 12.68/2.56 | | | 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 12.68/2.56 | | | (ordered_pair(v1, v0) = v2 & in(v2, all_33_2) = 0 & $i(v2) & % 12.68/2.56 | | | $i(v1)))) % 12.68/2.56 | | | % 12.68/2.56 | | | BETA: splitting (27) gives: % 12.68/2.56 | | | % 12.68/2.56 | | | Case 1: % 12.68/2.56 | | | | % 12.68/2.56 | | | | (46) ? [v0: int] : ( ~ (v0 = 0) & relation(all_35_4) = v0) % 12.68/2.56 | | | | % 12.68/2.56 | | | | DELTA: instantiating (46) with fresh symbol all_50_0 gives: % 12.68/2.56 | | | | (47) ~ (all_50_0 = 0) & relation(all_35_4) = all_50_0 % 12.68/2.56 | | | | % 12.68/2.56 | | | | ALPHA: (47) implies: % 12.68/2.56 | | | | (48) ~ (all_50_0 = 0) % 13.04/2.56 | | | | (49) relation(all_35_4) = all_50_0 % 13.04/2.56 | | | | % 13.04/2.56 | | | | GROUND_INST: instantiating (3) with 0, all_50_0, all_35_4, simplifying % 13.04/2.56 | | | | with (19), (49) gives: % 13.04/2.56 | | | | (50) all_50_0 = 0 % 13.04/2.56 | | | | % 13.04/2.57 | | | | REDUCE: (48), (50) imply: % 13.04/2.57 | | | | (51) $false % 13.04/2.57 | | | | % 13.04/2.57 | | | | CLOSE: (51) is inconsistent. % 13.04/2.57 | | | | % 13.04/2.57 | | | Case 2: % 13.04/2.57 | | | | % 13.04/2.57 | | | | (52) ? [v0: any] : (v0 = all_35_3 | ~ $i(v0) | ? [v1: $i] : ? % 13.04/2.57 | | | | [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: % 13.04/2.57 | | | | $i] : ! [v4: $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ % 13.04/2.57 | | | | (in(v4, all_35_4) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: % 13.04/2.57 | | | | $i] : ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4, % 13.04/2.57 | | | | all_35_4) = 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_35_3) % 13.04/2.57 | | | | | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_35_3) % 13.04/2.57 | | | | = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ % 13.04/2.57 | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_35_4) = 0) % 13.04/2.57 | | | | | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_35_3) = 0) % 13.04/2.57 | | | | | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 13.04/2.57 | | | | (ordered_pair(v0, v1) = v2 & in(v2, all_35_4) = 0 & $i(v2) % 13.04/2.57 | | | | & $i(v1))))) % 13.04/2.57 | | | | % 13.04/2.57 | | | | ALPHA: (52) implies: % 13.06/2.57 | | | | (53) ~ $i(all_35_3) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 13.06/2.57 | | | | (in(v0, all_35_3) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: % 13.06/2.57 | | | | $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, % 13.06/2.57 | | | | all_35_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ % 13.06/2.57 | | | | (in(v0, all_35_3) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 13.06/2.57 | | | | $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_35_4) = 0 & % 13.06/2.57 | | | | $i(v2) & $i(v1)))) % 13.06/2.57 | | | | % 13.06/2.57 | | | | BETA: splitting (26) gives: % 13.06/2.57 | | | | % 13.06/2.57 | | | | Case 1: % 13.06/2.57 | | | | | % 13.06/2.57 | | | | | (54) ? [v0: int] : ( ~ (v0 = 0) & relation(all_33_2) = v0) % 13.06/2.57 | | | | | % 13.06/2.57 | | | | | DELTA: instantiating (54) with fresh symbol all_50_0 gives: % 13.06/2.57 | | | | | (55) ~ (all_50_0 = 0) & relation(all_33_2) = all_50_0 % 13.06/2.57 | | | | | % 13.06/2.57 | | | | | ALPHA: (55) implies: % 13.06/2.57 | | | | | (56) ~ (all_50_0 = 0) % 13.06/2.57 | | | | | (57) relation(all_33_2) = all_50_0 % 13.06/2.57 | | | | | % 13.06/2.57 | | | | | GROUND_INST: instantiating (3) with 0, all_50_0, all_33_2, simplifying % 13.06/2.57 | | | | | with (8), (57) gives: % 13.06/2.57 | | | | | (58) all_50_0 = 0 % 13.06/2.57 | | | | | % 13.06/2.57 | | | | | REDUCE: (56), (58) imply: % 13.06/2.57 | | | | | (59) $false % 13.06/2.57 | | | | | % 13.06/2.57 | | | | | CLOSE: (59) is inconsistent. % 13.06/2.57 | | | | | % 13.06/2.57 | | | | Case 2: % 13.06/2.57 | | | | | % 13.06/2.57 | | | | | (60) ? [v0: any] : (v0 = all_33_1 | ~ $i(v0) | ? [v1: $i] : ? % 13.06/2.57 | | | | | [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! % 13.06/2.57 | | | | | [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v1, v3) = v4) % 13.06/2.57 | | | | | | ~ (in(v4, all_33_2) = 0) | ~ $i(v3))) & (v2 = 0 | % 13.06/2.57 | | | | | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v1, v3) = v4 & % 13.06/2.57 | | | | | in(v4, all_33_2) = 0 & $i(v4) & $i(v3))))) & ( ~ % 13.06/2.57 | | | | | $i(all_33_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 13.06/2.57 | | | | | (in(v0, all_33_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! % 13.06/2.57 | | | | | [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, % 13.06/2.57 | | | | | all_33_2) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ % 13.06/2.57 | | | | | (in(v0, all_33_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 13.06/2.57 | | | | | [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_33_2) % 13.06/2.57 | | | | | = 0 & $i(v2) & $i(v1))))) % 13.06/2.57 | | | | | % 13.06/2.57 | | | | | ALPHA: (60) implies: % 13.06/2.57 | | | | | (61) ~ $i(all_33_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 13.06/2.57 | | | | | (in(v0, all_33_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! % 13.06/2.57 | | | | | [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, % 13.06/2.58 | | | | | all_33_2) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ % 13.06/2.58 | | | | | (in(v0, all_33_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 13.06/2.58 | | | | | $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_33_2) = 0 % 13.06/2.58 | | | | | & $i(v2) & $i(v1)))) % 13.06/2.58 | | | | | % 13.06/2.58 | | | | | BETA: splitting (37) gives: % 13.06/2.58 | | | | | % 13.06/2.58 | | | | | Case 1: % 13.06/2.58 | | | | | | % 13.06/2.58 | | | | | | (62) ~ $i(all_35_1) % 13.06/2.58 | | | | | | % 13.06/2.58 | | | | | | PRED_UNIFY: (15), (62) imply: % 13.06/2.58 | | | | | | (63) $false % 13.06/2.58 | | | | | | % 13.06/2.58 | | | | | | CLOSE: (63) is inconsistent. % 13.06/2.58 | | | | | | % 13.06/2.58 | | | | | Case 2: % 13.06/2.58 | | | | | | % 13.06/2.58 | | | | | | (64) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_35_1) % 13.06/2.58 | | | | | | = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ % 13.06/2.58 | | | | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_35_4) = 0) % 13.06/2.58 | | | | | | | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_35_1) = 0) % 13.06/2.58 | | | | | | | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 13.06/2.58 | | | | | | (ordered_pair(v1, v0) = v2 & in(v2, all_35_4) = 0 & $i(v2) % 13.06/2.58 | | | | | | & $i(v1))) % 13.06/2.58 | | | | | | % 13.06/2.58 | | | | | | ALPHA: (64) implies: % 13.06/2.58 | | | | | | (65) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_35_1) % 13.06/2.58 | | | | | | = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ % 13.06/2.58 | | | | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_35_4) = 0) % 13.06/2.58 | | | | | | | ~ $i(v2))) % 13.06/2.58 | | | | | | % 13.06/2.58 | | | | | | BETA: splitting (53) gives: % 13.06/2.58 | | | | | | % 13.06/2.58 | | | | | | Case 1: % 13.06/2.58 | | | | | | | % 13.06/2.58 | | | | | | | (66) ~ $i(all_35_3) % 13.06/2.58 | | | | | | | % 13.06/2.58 | | | | | | | PRED_UNIFY: (14), (66) imply: % 13.06/2.58 | | | | | | | (67) $false % 13.06/2.58 | | | | | | | % 13.06/2.58 | | | | | | | CLOSE: (67) is inconsistent. % 13.06/2.58 | | | | | | | % 13.06/2.58 | | | | | | Case 2: % 13.06/2.58 | | | | | | | % 13.06/2.58 | | | | | | | (68) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 13.06/2.58 | | | | | | | all_35_3) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: % 13.06/2.58 | | | | | | | $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, % 13.06/2.58 | | | | | | | all_35_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ % 13.06/2.58 | | | | | | | (in(v0, all_35_3) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 13.06/2.58 | | | | | | | [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_35_4) % 13.06/2.58 | | | | | | | = 0 & $i(v2) & $i(v1))) % 13.06/2.58 | | | | | | | % 13.06/2.58 | | | | | | | ALPHA: (68) implies: % 13.06/2.58 | | | | | | | (69) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 13.06/2.58 | | | | | | | all_35_3) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: % 13.06/2.58 | | | | | | | $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, % 13.06/2.58 | | | | | | | all_35_4) = 0) | ~ $i(v2))) % 13.06/2.58 | | | | | | | % 13.06/2.58 | | | | | | | BETA: splitting (45) gives: % 13.06/2.58 | | | | | | | % 13.06/2.58 | | | | | | | Case 1: % 13.06/2.58 | | | | | | | | % 13.06/2.58 | | | | | | | | (70) ~ $i(all_33_0) % 13.06/2.58 | | | | | | | | % 13.06/2.58 | | | | | | | | PRED_UNIFY: (7), (70) imply: % 13.06/2.58 | | | | | | | | (71) $false % 13.06/2.58 | | | | | | | | % 13.06/2.58 | | | | | | | | CLOSE: (71) is inconsistent. % 13.06/2.58 | | | | | | | | % 13.06/2.58 | | | | | | | Case 2: % 13.06/2.58 | | | | | | | | % 13.06/2.58 | | | | | | | | (72) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 13.06/2.58 | | | | | | | | all_33_0) = v1) | ~ $i(v0) | ! [v2: $i] : ! % 13.06/2.58 | | | | | | | | [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ % 13.06/2.58 | | | | | | | | (in(v3, all_33_2) = 0) | ~ $i(v2))) & ! [v0: $i] : % 13.06/2.58 | | | | | | | | ( ~ (in(v0, all_33_0) = 0) | ~ $i(v0) | ? [v1: $i] : % 13.06/2.58 | | | | | | | | ? [v2: $i] : (ordered_pair(v1, v0) = v2 & in(v2, % 13.06/2.58 | | | | | | | | all_33_2) = 0 & $i(v2) & $i(v1))) % 13.06/2.58 | | | | | | | | % 13.06/2.58 | | | | | | | | ALPHA: (72) implies: % 13.06/2.58 | | | | | | | | (73) ! [v0: $i] : ( ~ (in(v0, all_33_0) = 0) | ~ $i(v0) | % 13.06/2.58 | | | | | | | | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) = v2 % 13.06/2.58 | | | | | | | | & in(v2, all_33_2) = 0 & $i(v2) & $i(v1))) % 13.06/2.58 | | | | | | | | % 13.06/2.58 | | | | | | | | BETA: splitting (61) gives: % 13.06/2.58 | | | | | | | | % 13.06/2.58 | | | | | | | | Case 1: % 13.06/2.58 | | | | | | | | | % 13.06/2.58 | | | | | | | | | (74) ~ $i(all_33_1) % 13.06/2.58 | | | | | | | | | % 13.06/2.58 | | | | | | | | | PRED_UNIFY: (6), (74) imply: % 13.06/2.58 | | | | | | | | | (75) $false % 13.06/2.58 | | | | | | | | | % 13.06/2.58 | | | | | | | | | CLOSE: (75) is inconsistent. % 13.06/2.58 | | | | | | | | | % 13.06/2.58 | | | | | | | | Case 2: % 13.06/2.58 | | | | | | | | | % 13.06/2.58 | | | | | | | | | (76) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 13.06/2.58 | | | | | | | | | all_33_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! % 13.06/2.58 | | | | | | | | | [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ % 13.06/2.58 | | | | | | | | | (in(v3, all_33_2) = 0) | ~ $i(v2))) & ! [v0: $i] % 13.06/2.58 | | | | | | | | | : ( ~ (in(v0, all_33_1) = 0) | ~ $i(v0) | ? [v1: $i] % 13.06/2.58 | | | | | | | | | : ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2, % 13.06/2.58 | | | | | | | | | all_33_2) = 0 & $i(v2) & $i(v1))) % 13.06/2.58 | | | | | | | | | % 13.06/2.58 | | | | | | | | | ALPHA: (76) implies: % 13.06/2.58 | | | | | | | | | (77) ! [v0: $i] : ( ~ (in(v0, all_33_1) = 0) | ~ $i(v0) | % 13.06/2.58 | | | | | | | | | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = % 13.06/2.58 | | | | | | | | | v2 & in(v2, all_33_2) = 0 & $i(v2) & $i(v1))) % 13.06/2.58 | | | | | | | | | % 13.06/2.58 | | | | | | | | | BETA: splitting (22) gives: % 13.06/2.58 | | | | | | | | | % 13.06/2.58 | | | | | | | | | Case 1: % 13.06/2.58 | | | | | | | | | | % 13.06/2.58 | | | | | | | | | | (78) ~ (all_35_0 = 0) % 13.06/2.58 | | | | | | | | | | % 13.06/2.58 | | | | | | | | | | BETA: splitting (25) gives: % 13.06/2.58 | | | | | | | | | | % 13.06/2.58 | | | | | | | | | | Case 1: % 13.06/2.58 | | | | | | | | | | | % 13.06/2.58 | | | | | | | | | | | (79) all_35_0 = 0 % 13.06/2.58 | | | | | | | | | | | % 13.06/2.58 | | | | | | | | | | | REDUCE: (78), (79) imply: % 13.06/2.58 | | | | | | | | | | | (80) $false % 13.06/2.58 | | | | | | | | | | | % 13.06/2.58 | | | | | | | | | | | CLOSE: (80) is inconsistent. % 13.06/2.58 | | | | | | | | | | | % 13.06/2.58 | | | | | | | | | | Case 2: % 13.06/2.58 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | (81) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 13.06/2.59 | | | | | | | | | | | all_35_1) = v1 & in(v0, all_33_0) = 0 & % 13.06/2.59 | | | | | | | | | | | $i(v0)) % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | DELTA: instantiating (81) with fresh symbols all_97_0, % 13.06/2.59 | | | | | | | | | | | all_97_1 gives: % 13.06/2.59 | | | | | | | | | | | (82) ~ (all_97_0 = 0) & in(all_97_1, all_35_1) = % 13.06/2.59 | | | | | | | | | | | all_97_0 & in(all_97_1, all_33_0) = 0 & % 13.06/2.59 | | | | | | | | | | | $i(all_97_1) % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | ALPHA: (82) implies: % 13.06/2.59 | | | | | | | | | | | (83) ~ (all_97_0 = 0) % 13.06/2.59 | | | | | | | | | | | (84) $i(all_97_1) % 13.06/2.59 | | | | | | | | | | | (85) in(all_97_1, all_33_0) = 0 % 13.06/2.59 | | | | | | | | | | | (86) in(all_97_1, all_35_1) = all_97_0 % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | GROUND_INST: instantiating (73) with all_97_1, simplifying with % 13.06/2.59 | | | | | | | | | | | (84), (85) gives: % 13.06/2.59 | | | | | | | | | | | (87) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, % 13.06/2.59 | | | | | | | | | | | all_97_1) = v1 & in(v1, all_33_2) = 0 & $i(v1) % 13.06/2.59 | | | | | | | | | | | & $i(v0)) % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | GROUND_INST: instantiating (65) with all_97_1, all_97_0, % 13.06/2.59 | | | | | | | | | | | simplifying with (84), (86) gives: % 13.06/2.59 | | | | | | | | | | | (88) all_97_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ % 13.06/2.59 | | | | | | | | | | | (ordered_pair(v0, all_97_1) = v1) | ~ (in(v1, % 13.06/2.59 | | | | | | | | | | | all_35_4) = 0) | ~ $i(v0)) % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | DELTA: instantiating (87) with fresh symbols all_108_0, % 13.06/2.59 | | | | | | | | | | | all_108_1 gives: % 13.06/2.59 | | | | | | | | | | | (89) ordered_pair(all_108_1, all_97_1) = all_108_0 & % 13.06/2.59 | | | | | | | | | | | in(all_108_0, all_33_2) = 0 & $i(all_108_0) & % 13.06/2.59 | | | | | | | | | | | $i(all_108_1) % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | ALPHA: (89) implies: % 13.06/2.59 | | | | | | | | | | | (90) $i(all_108_1) % 13.06/2.59 | | | | | | | | | | | (91) $i(all_108_0) % 13.06/2.59 | | | | | | | | | | | (92) in(all_108_0, all_33_2) = 0 % 13.06/2.59 | | | | | | | | | | | (93) ordered_pair(all_108_1, all_97_1) = all_108_0 % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | BETA: splitting (88) gives: % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | Case 1: % 13.06/2.59 | | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | | (94) all_97_0 = 0 % 13.06/2.59 | | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | | REDUCE: (83), (94) imply: % 13.06/2.59 | | | | | | | | | | | | (95) $false % 13.06/2.59 | | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | | CLOSE: (95) is inconsistent. % 13.06/2.59 | | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | Case 2: % 13.06/2.59 | | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | | (96) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, % 13.06/2.59 | | | | | | | | | | | | all_97_1) = v1) | ~ (in(v1, all_35_4) = 0) % 13.06/2.59 | | | | | | | | | | | | | ~ $i(v0)) % 13.06/2.59 | | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | | GROUND_INST: instantiating (23) with all_108_0, simplifying % 13.06/2.59 | | | | | | | | | | | | with (91), (92) gives: % 13.06/2.59 | | | | | | | | | | | | (97) in(all_108_0, all_35_4) = 0 % 13.06/2.59 | | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | | GROUND_INST: instantiating (96) with all_108_1, all_108_0, % 13.06/2.59 | | | | | | | | | | | | simplifying with (90), (93), (97) gives: % 13.06/2.59 | | | | | | | | | | | | (98) $false % 13.06/2.59 | | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | | CLOSE: (98) is inconsistent. % 13.06/2.59 | | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | End of split % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | End of split % 13.06/2.59 | | | | | | | | | | % 13.06/2.59 | | | | | | | | | Case 2: % 13.06/2.59 | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | (99) ~ (all_35_2 = 0) % 13.06/2.59 | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | BETA: splitting (24) gives: % 13.06/2.59 | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | Case 1: % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | (100) all_35_2 = 0 % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | REDUCE: (99), (100) imply: % 13.06/2.59 | | | | | | | | | | | (101) $false % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | CLOSE: (101) is inconsistent. % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | Case 2: % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | (102) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 13.06/2.59 | | | | | | | | | | | all_35_3) = v1 & in(v0, all_33_1) = 0 & % 13.06/2.59 | | | | | | | | | | | $i(v0)) % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | DELTA: instantiating (102) with fresh symbols all_97_0, % 13.06/2.59 | | | | | | | | | | | all_97_1 gives: % 13.06/2.59 | | | | | | | | | | | (103) ~ (all_97_0 = 0) & in(all_97_1, all_35_3) = % 13.06/2.59 | | | | | | | | | | | all_97_0 & in(all_97_1, all_33_1) = 0 & % 13.06/2.59 | | | | | | | | | | | $i(all_97_1) % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | ALPHA: (103) implies: % 13.06/2.59 | | | | | | | | | | | (104) ~ (all_97_0 = 0) % 13.06/2.59 | | | | | | | | | | | (105) $i(all_97_1) % 13.06/2.59 | | | | | | | | | | | (106) in(all_97_1, all_33_1) = 0 % 13.06/2.59 | | | | | | | | | | | (107) in(all_97_1, all_35_3) = all_97_0 % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | GROUND_INST: instantiating (77) with all_97_1, simplifying with % 13.06/2.59 | | | | | | | | | | | (105), (106) gives: % 13.06/2.59 | | | | | | | | | | | (108) ? [v0: $i] : ? [v1: $i] : % 13.06/2.59 | | | | | | | | | | | (ordered_pair(all_97_1, v0) = v1 & in(v1, % 13.06/2.59 | | | | | | | | | | | all_33_2) = 0 & $i(v1) & $i(v0)) % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | GROUND_INST: instantiating (69) with all_97_1, all_97_0, % 13.06/2.59 | | | | | | | | | | | simplifying with (105), (107) gives: % 13.06/2.59 | | | | | | | | | | | (109) all_97_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ % 13.06/2.59 | | | | | | | | | | | (ordered_pair(all_97_1, v0) = v1) | ~ (in(v1, % 13.06/2.59 | | | | | | | | | | | all_35_4) = 0) | ~ $i(v0)) % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | DELTA: instantiating (108) with fresh symbols all_109_0, % 13.06/2.59 | | | | | | | | | | | all_109_1 gives: % 13.06/2.59 | | | | | | | | | | | (110) ordered_pair(all_97_1, all_109_1) = all_109_0 & % 13.06/2.59 | | | | | | | | | | | in(all_109_0, all_33_2) = 0 & $i(all_109_0) & % 13.06/2.59 | | | | | | | | | | | $i(all_109_1) % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | ALPHA: (110) implies: % 13.06/2.59 | | | | | | | | | | | (111) $i(all_109_1) % 13.06/2.59 | | | | | | | | | | | (112) $i(all_109_0) % 13.06/2.59 | | | | | | | | | | | (113) in(all_109_0, all_33_2) = 0 % 13.06/2.59 | | | | | | | | | | | (114) ordered_pair(all_97_1, all_109_1) = all_109_0 % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | BETA: splitting (109) gives: % 13.06/2.59 | | | | | | | | | | | % 13.06/2.59 | | | | | | | | | | | Case 1: % 13.06/2.59 | | | | | | | | | | | | % 13.06/2.60 | | | | | | | | | | | | (115) all_97_0 = 0 % 13.06/2.60 | | | | | | | | | | | | % 13.06/2.60 | | | | | | | | | | | | REDUCE: (104), (115) imply: % 13.06/2.60 | | | | | | | | | | | | (116) $false % 13.06/2.60 | | | | | | | | | | | | % 13.06/2.60 | | | | | | | | | | | | CLOSE: (116) is inconsistent. % 13.06/2.60 | | | | | | | | | | | | % 13.06/2.60 | | | | | | | | | | | Case 2: % 13.06/2.60 | | | | | | | | | | | | % 13.06/2.60 | | | | | | | | | | | | (117) ! [v0: $i] : ! [v1: $i] : ( ~ % 13.06/2.60 | | | | | | | | | | | | (ordered_pair(all_97_1, v0) = v1) | ~ (in(v1, % 13.06/2.60 | | | | | | | | | | | | all_35_4) = 0) | ~ $i(v0)) % 13.06/2.60 | | | | | | | | | | | | % 13.06/2.60 | | | | | | | | | | | | GROUND_INST: instantiating (23) with all_109_0, simplifying % 13.06/2.60 | | | | | | | | | | | | with (112), (113) gives: % 13.06/2.60 | | | | | | | | | | | | (118) in(all_109_0, all_35_4) = 0 % 13.06/2.60 | | | | | | | | | | | | % 13.06/2.60 | | | | | | | | | | | | GROUND_INST: instantiating (117) with all_109_1, all_109_0, % 13.06/2.60 | | | | | | | | | | | | simplifying with (111), (114), (118) gives: % 13.06/2.60 | | | | | | | | | | | | (119) $false % 13.06/2.60 | | | | | | | | | | | | % 13.06/2.60 | | | | | | | | | | | | CLOSE: (119) is inconsistent. % 13.06/2.60 | | | | | | | | | | | | % 13.06/2.60 | | | | | | | | | | | End of split % 13.06/2.60 | | | | | | | | | | | % 13.06/2.60 | | | | | | | | | | End of split % 13.06/2.60 | | | | | | | | | | % 13.06/2.60 | | | | | | | | | End of split % 13.06/2.60 | | | | | | | | | % 13.06/2.60 | | | | | | | | End of split % 13.06/2.60 | | | | | | | | % 13.06/2.60 | | | | | | | End of split % 13.06/2.60 | | | | | | | % 13.06/2.60 | | | | | | End of split % 13.06/2.60 | | | | | | % 13.06/2.60 | | | | | End of split % 13.06/2.60 | | | | | % 13.06/2.60 | | | | End of split % 13.06/2.60 | | | | % 13.06/2.60 | | | End of split % 13.06/2.60 | | | % 13.06/2.60 | | End of split % 13.06/2.60 | | % 13.06/2.60 | End of split % 13.06/2.60 | % 13.06/2.60 End of proof % 13.06/2.60 % SZS output end Proof for theBenchmark % 13.06/2.60 % 13.06/2.60 1980ms %------------------------------------------------------------------------------