%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU305+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 : n026.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 17:43:58 EDT 2023 % Result : Theorem 10.34s 2.21s % Output : Proof 16.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU305+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n026.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 12:32:01 EDT 2023 % 0.13/0.35 % 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. % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.05/1.18 Prover 1: Preprocessing ... % 3.05/1.18 Prover 4: Preprocessing ... % 3.40/1.21 Prover 3: Preprocessing ... % 3.40/1.21 Prover 0: Preprocessing ... % 3.40/1.21 Prover 5: Preprocessing ... % 3.40/1.22 Prover 6: Preprocessing ... % 3.40/1.22 Prover 2: Preprocessing ... % 7.41/1.86 Prover 1: Warning: ignoring some quantifiers % 7.82/1.87 Prover 5: Proving ... % 7.82/1.87 Prover 3: Warning: ignoring some quantifiers % 7.82/1.88 Prover 6: Proving ... % 7.82/1.90 Prover 2: Proving ... % 7.82/1.91 Prover 1: Constructing countermodel ... % 7.82/1.91 Prover 3: Constructing countermodel ... % 9.13/2.06 Prover 4: Warning: ignoring some quantifiers % 9.13/2.12 Prover 4: Constructing countermodel ... % 10.34/2.21 Prover 3: proved (1560ms) % 10.34/2.21 % 10.34/2.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.34/2.21 % 10.34/2.21 Prover 6: stopped % 10.34/2.21 Prover 5: stopped % 10.34/2.21 Prover 2: stopped % 10.34/2.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.34/2.23 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.34/2.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.34/2.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.34/2.25 Prover 0: Proving ... % 10.34/2.25 Prover 0: stopped % 10.34/2.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.34/2.31 Prover 7: Preprocessing ... % 10.34/2.32 Prover 8: Preprocessing ... % 10.34/2.33 Prover 11: Preprocessing ... % 10.34/2.34 Prover 10: Preprocessing ... % 10.34/2.36 Prover 13: Preprocessing ... % 10.34/2.41 Prover 7: Warning: ignoring some quantifiers % 11.24/2.43 Prover 7: Constructing countermodel ... % 11.24/2.48 Prover 10: Warning: ignoring some quantifiers % 11.24/2.51 Prover 10: Constructing countermodel ... % 11.24/2.51 Prover 13: Warning: ignoring some quantifiers % 11.24/2.52 Prover 8: Warning: ignoring some quantifiers % 12.56/2.53 Prover 8: Constructing countermodel ... % 12.56/2.54 Prover 13: Constructing countermodel ... % 13.40/2.65 Prover 11: Warning: ignoring some quantifiers % 13.70/2.68 Prover 11: Constructing countermodel ... % 13.70/2.71 Prover 10: gave up % 13.70/2.72 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 14.35/2.77 Prover 16: Preprocessing ... % 15.56/2.94 Prover 1: Found proof (size 206) % 15.56/2.94 Prover 1: proved (2302ms) % 15.56/2.94 Prover 7: stopped % 15.56/2.94 Prover 13: stopped % 15.56/2.94 Prover 11: stopped % 15.56/2.94 Prover 4: stopped % 15.56/2.94 Prover 16: Warning: ignoring some quantifiers % 15.56/2.95 Prover 8: stopped % 15.56/2.95 Prover 16: Constructing countermodel ... % 15.56/2.96 Prover 16: stopped % 15.56/2.96 % 15.56/2.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.56/2.96 % 15.77/3.00 % SZS output start Proof for theBenchmark % 15.77/3.01 Assumptions after simplification: % 15.77/3.01 --------------------------------- % 15.77/3.01 % 15.77/3.01 (commutativity_k3_lattices) % 15.77/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (the_carrier(v0) = % 15.77/3.04 v3) | ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ~ $i(v2) | ~ % 15.77/3.04 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: % 15.77/3.04 $i] : ? [v8: $i] : (empty_carrier(v0) = v4 & join_commutative(v0) = v5 & % 15.77/3.04 join_semilatt_str(v0) = v6 & join_commut(v0, v2, v1) = v8 & % 15.77/3.04 join_commut(v0, v1, v2) = v7 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = % 15.77/3.04 0) | v8 = v7 | v4 = 0))) % 15.77/3.04 % 15.77/3.04 (d3_lattices) % 15.77/3.04 ! [v0: $i] : ( ~ (join_semilatt_str(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 15.77/3.04 [v2: $i] : (the_carrier(v0) = v2 & empty_carrier(v0) = v1 & $i(v2) & (v1 = 0 % 15.77/3.04 | ! [v3: $i] : ( ~ (element(v3, v2) = 0) | ~ $i(v3) | ! [v4: $i] : ( % 15.77/3.04 ~ (element(v4, v2) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i] : % 15.77/3.04 (below(v0, v3, v4) = v5 & join(v0, v3, v4) = v6 & $i(v6) & ( ~ (v6 = % 15.77/3.04 v4) | v5 = 0) & ( ~ (v5 = 0) | v6 = v4))))))) % 15.77/3.04 % 15.77/3.04 (redefinition_k3_lattices) % 15.77/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (the_carrier(v0) = % 15.77/3.04 v3) | ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ~ $i(v2) | ~ % 15.77/3.05 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: % 15.77/3.05 $i] : ? [v8: $i] : (join(v0, v1, v2) = v8 & empty_carrier(v0) = v4 & % 15.77/3.05 join_commutative(v0) = v5 & join_semilatt_str(v0) = v6 & join_commut(v0, % 15.77/3.05 v1, v2) = v7 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v7 | % 15.77/3.05 v4 = 0))) % 15.77/3.05 % 15.77/3.05 (t26_lattices) % 15.77/3.05 ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ( ~ (v1 = 0) & the_carrier(v0) = v2 % 15.77/3.05 & empty_carrier(v0) = v1 & join_commutative(v0) = 0 & join_semilatt_str(v0) % 15.77/3.05 = 0 & $i(v2) & $i(v0) & ? [v3: $i] : (element(v3, v2) = 0 & $i(v3) & ? % 15.77/3.05 [v4: $i] : ( ~ (v4 = v3) & below(v0, v4, v3) = 0 & below(v0, v3, v4) = 0 & % 15.77/3.05 element(v4, v2) = 0 & $i(v4)))) % 15.77/3.05 % 15.77/3.05 (function-axioms) % 15.77/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.77/3.06 $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (apply_binary_as_element(v7, % 15.77/3.06 v6, v5, v4, v3, v2) = v1) | ~ (apply_binary_as_element(v7, v6, v5, v4, % 15.77/3.06 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 15.77/3.06 ! [v4: $i] : (v1 = v0 | ~ (apply_binary(v4, v3, v2) = v1) | ~ % 15.77/3.06 (apply_binary(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.77/3.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 15.77/3.06 (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, % 15.77/3.06 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 15.77/3.06 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (quasi_total(v4, v3, % 15.77/3.06 v2) = v1) | ~ (quasi_total(v4, v3, v2) = v0)) & ! [v0: % 15.77/3.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.77/3.06 : ! [v4: $i] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ % 15.77/3.06 (relation_of2(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.77/3.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 15.77/3.06 (below(v4, v3, v2) = v1) | ~ (below(v4, v3, v2) = v0)) & ! [v0: $i] : ! % 15.77/3.06 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (join(v4, % 15.77/3.06 v3, v2) = v1) | ~ (join(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 15.77/3.06 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (join_commut(v4, v3, % 15.77/3.06 v2) = v1) | ~ (join_commut(v4, v3, v2) = v0)) & ! [v0: % 15.77/3.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.77/3.06 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 15.77/3.06 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.77/3.06 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 15.77/3.06 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.77/3.06 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! % 15.77/3.06 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.77/3.06 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] % 15.77/3.06 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 15.77/3.06 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.77/3.06 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | % 15.77/3.06 ~ (one_sorted_str(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.77/3.06 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 15.77/3.06 (empty(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 15.77/3.06 : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & % 15.77/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_L_join(v2) = v1) | % 15.77/3.06 ~ (the_L_join(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 15.77/3.06 v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0: % 15.77/3.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 15.77/3.06 ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) = v0)) & ! [v0: % 15.77/3.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 15.77/3.06 ~ (join_commutative(v2) = v1) | ~ (join_commutative(v2) = v0)) & ! [v0: % 15.77/3.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 15.77/3.06 ~ (join_semilatt_str(v2) = v1) | ~ (join_semilatt_str(v2) = v0)) & ! [v0: % 15.77/3.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 15.77/3.06 ~ (preboolean(v2) = v1) | ~ (preboolean(v2) = v0)) & ! [v0: % 15.77/3.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 15.77/3.06 ~ (cup_closed(v2) = v1) | ~ (cup_closed(v2) = v0)) & ! [v0: % 15.77/3.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 15.77/3.06 ~ (diff_closed(v2) = v1) | ~ (diff_closed(v2) = v0)) % 15.77/3.06 % 15.77/3.06 Further assumptions not needed in the proof: % 15.77/3.06 -------------------------------------------- % 15.77/3.06 antisymmetry_r2_hidden, cc1_finsub_1, cc2_finsub_1, d1_lattices, dt_k1_binop_1, % 15.77/3.06 dt_k1_lattices, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_binop_1, dt_k2_zfmisc_1, % 15.77/3.06 dt_k3_lattices, dt_l1_struct_0, dt_l2_lattices, dt_m1_relset_1, dt_m1_subset_1, % 15.77/3.06 dt_m2_relset_1, dt_u1_struct_0, dt_u2_lattices, existence_l1_struct_0, % 15.77/3.06 existence_l2_lattices, existence_m1_relset_1, existence_m1_subset_1, % 15.77/3.06 existence_m2_relset_1, fc1_finsub_1, fc1_struct_0, rc3_struct_0, rc5_struct_0, % 15.77/3.06 redefinition_k2_binop_1, redefinition_m2_relset_1, reflexivity_r1_tarski, % 15.77/3.06 t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, % 15.77/3.06 t8_boole % 15.77/3.06 % 15.77/3.06 Those formulas are unsatisfiable: % 15.77/3.06 --------------------------------- % 15.77/3.06 % 15.77/3.06 Begin of proof % 15.77/3.06 | % 15.77/3.06 | ALPHA: (function-axioms) implies: % 15.77/3.07 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.77/3.07 | (v1 = v0 | ~ (join_semilatt_str(v2) = v1) | ~ (join_semilatt_str(v2) % 15.77/3.07 | = v0)) % 15.77/3.07 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.77/3.07 | (v1 = v0 | ~ (join_commutative(v2) = v1) | ~ (join_commutative(v2) = % 15.77/3.07 | v0)) % 15.77/3.07 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.77/3.07 | (v1 = v0 | ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) = v0)) % 15.77/3.07 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.77/3.07 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 15.77/3.07 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.77/3.07 | (v1 = v0 | ~ (join_commut(v4, v3, v2) = v1) | ~ (join_commut(v4, v3, % 15.77/3.07 | v2) = v0)) % 15.77/3.07 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.77/3.07 | (v1 = v0 | ~ (join(v4, v3, v2) = v1) | ~ (join(v4, v3, v2) = v0)) % 15.77/3.07 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.77/3.07 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (below(v4, v3, v2) = v1) | ~ % 15.77/3.07 | (below(v4, v3, v2) = v0)) % 15.77/3.07 | % 15.77/3.07 | DELTA: instantiating (t26_lattices) with fresh symbols all_41_0, all_41_1, % 15.77/3.07 | all_41_2 gives: % 15.77/3.07 | (8) ~ (all_41_1 = 0) & the_carrier(all_41_2) = all_41_0 & % 15.77/3.07 | empty_carrier(all_41_2) = all_41_1 & join_commutative(all_41_2) = 0 & % 15.77/3.07 | join_semilatt_str(all_41_2) = 0 & $i(all_41_0) & $i(all_41_2) & ? [v0: % 15.77/3.07 | $i] : (element(v0, all_41_0) = 0 & $i(v0) & ? [v1: $i] : ( ~ (v1 = % 15.77/3.07 | v0) & below(all_41_2, v1, v0) = 0 & below(all_41_2, v0, v1) = 0 & % 15.77/3.07 | element(v1, all_41_0) = 0 & $i(v1))) % 15.77/3.07 | % 15.77/3.07 | ALPHA: (8) implies: % 15.77/3.07 | (9) ~ (all_41_1 = 0) % 15.77/3.07 | (10) $i(all_41_2) % 15.77/3.07 | (11) join_semilatt_str(all_41_2) = 0 % 15.77/3.07 | (12) join_commutative(all_41_2) = 0 % 15.77/3.07 | (13) empty_carrier(all_41_2) = all_41_1 % 15.77/3.07 | (14) the_carrier(all_41_2) = all_41_0 % 15.77/3.08 | (15) ? [v0: $i] : (element(v0, all_41_0) = 0 & $i(v0) & ? [v1: $i] : ( ~ % 15.77/3.08 | (v1 = v0) & below(all_41_2, v1, v0) = 0 & below(all_41_2, v0, v1) % 15.77/3.08 | = 0 & element(v1, all_41_0) = 0 & $i(v1))) % 15.77/3.08 | % 15.77/3.08 | DELTA: instantiating (15) with fresh symbol all_43_0 gives: % 15.77/3.08 | (16) element(all_43_0, all_41_0) = 0 & $i(all_43_0) & ? [v0: any] : ( ~ % 15.77/3.08 | (v0 = all_43_0) & below(all_41_2, v0, all_43_0) = 0 & % 15.77/3.08 | below(all_41_2, all_43_0, v0) = 0 & element(v0, all_41_0) = 0 & % 15.77/3.08 | $i(v0)) % 15.77/3.08 | % 15.77/3.08 | ALPHA: (16) implies: % 15.77/3.08 | (17) $i(all_43_0) % 15.77/3.08 | (18) element(all_43_0, all_41_0) = 0 % 15.77/3.08 | (19) ? [v0: any] : ( ~ (v0 = all_43_0) & below(all_41_2, v0, all_43_0) = 0 % 15.77/3.08 | & below(all_41_2, all_43_0, v0) = 0 & element(v0, all_41_0) = 0 & % 15.77/3.08 | $i(v0)) % 15.77/3.08 | % 15.77/3.08 | DELTA: instantiating (19) with fresh symbol all_45_0 gives: % 15.77/3.08 | (20) ~ (all_45_0 = all_43_0) & below(all_41_2, all_45_0, all_43_0) = 0 & % 15.77/3.08 | below(all_41_2, all_43_0, all_45_0) = 0 & element(all_45_0, all_41_0) % 15.77/3.08 | = 0 & $i(all_45_0) % 15.77/3.08 | % 15.77/3.08 | ALPHA: (20) implies: % 15.77/3.08 | (21) ~ (all_45_0 = all_43_0) % 15.77/3.08 | (22) $i(all_45_0) % 15.77/3.08 | (23) element(all_45_0, all_41_0) = 0 % 15.77/3.08 | (24) below(all_41_2, all_43_0, all_45_0) = 0 % 15.77/3.08 | (25) below(all_41_2, all_45_0, all_43_0) = 0 % 15.77/3.08 | % 15.77/3.08 | GROUND_INST: instantiating (d3_lattices) with all_41_2, simplifying with (10), % 15.77/3.08 | (11) gives: % 15.77/3.08 | (26) ? [v0: any] : ? [v1: $i] : (the_carrier(all_41_2) = v1 & % 15.77/3.08 | empty_carrier(all_41_2) = v0 & $i(v1) & (v0 = 0 | ! [v2: $i] : ( ~ % 15.77/3.08 | (element(v2, v1) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ % 15.77/3.08 | (element(v3, v1) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: $i] % 15.77/3.08 | : (below(all_41_2, v2, v3) = v4 & join(all_41_2, v2, v3) = v5 % 15.77/3.08 | & $i(v5) & ( ~ (v5 = v3) | v4 = 0) & ( ~ (v4 = 0) | v5 = % 15.77/3.08 | v3)))))) % 15.77/3.08 | % 15.77/3.08 | GROUND_INST: instantiating (redefinition_k3_lattices) with all_41_2, all_45_0, % 15.77/3.08 | all_45_0, all_41_0, simplifying with (10), (14), (22), (23) % 15.77/3.08 | gives: % 15.77/3.08 | (27) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 15.77/3.08 | : (join(all_41_2, all_45_0, all_45_0) = v4 & empty_carrier(all_41_2) = % 15.77/3.08 | v0 & join_commutative(all_41_2) = v1 & join_semilatt_str(all_41_2) = % 15.77/3.08 | v2 & join_commut(all_41_2, all_45_0, all_45_0) = v3 & $i(v4) & % 15.77/3.08 | $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0)) % 15.77/3.09 | % 15.77/3.09 | GROUND_INST: instantiating (commutativity_k3_lattices) with all_41_2, % 15.77/3.09 | all_45_0, all_45_0, all_41_0, simplifying with (10), (14), (22), % 15.77/3.09 | (23) gives: % 15.77/3.09 | (28) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 15.77/3.09 | : (empty_carrier(all_41_2) = v0 & join_commutative(all_41_2) = v1 & % 15.77/3.09 | join_semilatt_str(all_41_2) = v2 & join_commut(all_41_2, all_45_0, % 15.77/3.09 | all_45_0) = v4 & join_commut(all_41_2, all_45_0, all_45_0) = v3 & % 15.77/3.09 | $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0)) % 15.77/3.09 | % 15.77/3.09 | GROUND_INST: instantiating (redefinition_k3_lattices) with all_41_2, all_43_0, % 15.77/3.09 | all_45_0, all_41_0, simplifying with (10), (14), (17), (18), % 15.77/3.09 | (22), (23) gives: % 15.77/3.09 | (29) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 15.77/3.09 | : (join(all_41_2, all_43_0, all_45_0) = v4 & empty_carrier(all_41_2) = % 15.77/3.09 | v0 & join_commutative(all_41_2) = v1 & join_semilatt_str(all_41_2) = % 15.77/3.09 | v2 & join_commut(all_41_2, all_43_0, all_45_0) = v3 & $i(v4) & % 15.77/3.09 | $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0)) % 15.77/3.09 | % 15.77/3.09 | GROUND_INST: instantiating (commutativity_k3_lattices) with all_41_2, % 15.77/3.09 | all_43_0, all_45_0, all_41_0, simplifying with (10), (14), (17), % 15.77/3.09 | (18), (22), (23) gives: % 15.77/3.09 | (30) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 15.77/3.09 | : (empty_carrier(all_41_2) = v0 & join_commutative(all_41_2) = v1 & % 15.77/3.09 | join_semilatt_str(all_41_2) = v2 & join_commut(all_41_2, all_45_0, % 15.77/3.09 | all_43_0) = v4 & join_commut(all_41_2, all_43_0, all_45_0) = v3 & % 15.77/3.09 | $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0)) % 15.77/3.09 | % 15.77/3.09 | GROUND_INST: instantiating (redefinition_k3_lattices) with all_41_2, all_45_0, % 15.77/3.09 | all_43_0, all_41_0, simplifying with (10), (14), (17), (18), % 15.77/3.09 | (22), (23) gives: % 15.77/3.09 | (31) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 15.77/3.09 | : (join(all_41_2, all_45_0, all_43_0) = v4 & empty_carrier(all_41_2) = % 15.77/3.09 | v0 & join_commutative(all_41_2) = v1 & join_semilatt_str(all_41_2) = % 15.77/3.09 | v2 & join_commut(all_41_2, all_45_0, all_43_0) = v3 & $i(v4) & % 15.77/3.09 | $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0)) % 15.77/3.09 | % 15.77/3.10 | GROUND_INST: instantiating (commutativity_k3_lattices) with all_41_2, % 15.77/3.10 | all_45_0, all_43_0, all_41_0, simplifying with (10), (14), (17), % 15.77/3.10 | (18), (22), (23) gives: % 15.77/3.10 | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 15.77/3.10 | : (empty_carrier(all_41_2) = v0 & join_commutative(all_41_2) = v1 & % 15.77/3.10 | join_semilatt_str(all_41_2) = v2 & join_commut(all_41_2, all_45_0, % 15.77/3.10 | all_43_0) = v3 & join_commut(all_41_2, all_43_0, all_45_0) = v4 & % 15.77/3.10 | $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0)) % 15.77/3.10 | % 15.77/3.10 | GROUND_INST: instantiating (redefinition_k3_lattices) with all_41_2, all_43_0, % 15.77/3.10 | all_43_0, all_41_0, simplifying with (10), (14), (17), (18) % 15.77/3.10 | gives: % 15.77/3.10 | (33) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 15.77/3.10 | : (join(all_41_2, all_43_0, all_43_0) = v4 & empty_carrier(all_41_2) = % 15.77/3.10 | v0 & join_commutative(all_41_2) = v1 & join_semilatt_str(all_41_2) = % 15.77/3.10 | v2 & join_commut(all_41_2, all_43_0, all_43_0) = v3 & $i(v4) & % 15.77/3.10 | $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0)) % 15.77/3.10 | % 15.77/3.10 | GROUND_INST: instantiating (commutativity_k3_lattices) with all_41_2, % 15.77/3.10 | all_43_0, all_43_0, all_41_0, simplifying with (10), (14), (17), % 15.77/3.10 | (18) gives: % 15.77/3.10 | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 15.77/3.10 | : (empty_carrier(all_41_2) = v0 & join_commutative(all_41_2) = v1 & % 15.77/3.10 | join_semilatt_str(all_41_2) = v2 & join_commut(all_41_2, all_43_0, % 15.77/3.10 | all_43_0) = v4 & join_commut(all_41_2, all_43_0, all_43_0) = v3 & % 15.77/3.10 | $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0)) % 15.77/3.10 | % 15.77/3.10 | DELTA: instantiating (34) with fresh symbols all_60_0, all_60_1, all_60_2, % 15.77/3.10 | all_60_3, all_60_4 gives: % 15.77/3.10 | (35) empty_carrier(all_41_2) = all_60_4 & join_commutative(all_41_2) = % 15.77/3.10 | all_60_3 & join_semilatt_str(all_41_2) = all_60_2 & % 15.77/3.10 | join_commut(all_41_2, all_43_0, all_43_0) = all_60_0 & % 15.77/3.10 | join_commut(all_41_2, all_43_0, all_43_0) = all_60_1 & $i(all_60_0) & % 15.77/3.10 | $i(all_60_1) & ( ~ (all_60_2 = 0) | ~ (all_60_3 = 0) | all_60_0 = % 15.77/3.10 | all_60_1 | all_60_4 = 0) % 15.77/3.10 | % 15.77/3.10 | ALPHA: (35) implies: % 15.77/3.10 | (36) join_semilatt_str(all_41_2) = all_60_2 % 15.77/3.10 | (37) empty_carrier(all_41_2) = all_60_4 % 15.77/3.10 | % 15.77/3.10 | DELTA: instantiating (33) with fresh symbols all_62_0, all_62_1, all_62_2, % 15.77/3.10 | all_62_3, all_62_4 gives: % 15.77/3.10 | (38) join(all_41_2, all_43_0, all_43_0) = all_62_0 & % 15.77/3.10 | empty_carrier(all_41_2) = all_62_4 & join_commutative(all_41_2) = % 15.77/3.10 | all_62_3 & join_semilatt_str(all_41_2) = all_62_2 & % 15.77/3.10 | join_commut(all_41_2, all_43_0, all_43_0) = all_62_1 & $i(all_62_0) & % 15.77/3.10 | $i(all_62_1) & ( ~ (all_62_2 = 0) | ~ (all_62_3 = 0) | all_62_0 = % 15.77/3.10 | all_62_1 | all_62_4 = 0) % 15.77/3.10 | % 15.77/3.10 | ALPHA: (38) implies: % 15.77/3.10 | (39) join_semilatt_str(all_41_2) = all_62_2 % 15.77/3.10 | (40) empty_carrier(all_41_2) = all_62_4 % 15.77/3.10 | % 15.77/3.10 | DELTA: instantiating (28) with fresh symbols all_64_0, all_64_1, all_64_2, % 15.77/3.10 | all_64_3, all_64_4 gives: % 15.77/3.11 | (41) empty_carrier(all_41_2) = all_64_4 & join_commutative(all_41_2) = % 15.77/3.11 | all_64_3 & join_semilatt_str(all_41_2) = all_64_2 & % 15.77/3.11 | join_commut(all_41_2, all_45_0, all_45_0) = all_64_0 & % 15.77/3.11 | join_commut(all_41_2, all_45_0, all_45_0) = all_64_1 & $i(all_64_0) & % 15.77/3.11 | $i(all_64_1) & ( ~ (all_64_2 = 0) | ~ (all_64_3 = 0) | all_64_0 = % 15.77/3.11 | all_64_1 | all_64_4 = 0) % 15.77/3.11 | % 15.77/3.11 | ALPHA: (41) implies: % 15.77/3.11 | (42) join_semilatt_str(all_41_2) = all_64_2 % 15.77/3.11 | (43) join_commutative(all_41_2) = all_64_3 % 15.77/3.11 | (44) empty_carrier(all_41_2) = all_64_4 % 15.77/3.11 | % 15.77/3.11 | DELTA: instantiating (32) with fresh symbols all_66_0, all_66_1, all_66_2, % 15.77/3.11 | all_66_3, all_66_4 gives: % 15.77/3.11 | (45) empty_carrier(all_41_2) = all_66_4 & join_commutative(all_41_2) = % 15.77/3.11 | all_66_3 & join_semilatt_str(all_41_2) = all_66_2 & % 15.77/3.11 | join_commut(all_41_2, all_45_0, all_43_0) = all_66_1 & % 15.77/3.11 | join_commut(all_41_2, all_43_0, all_45_0) = all_66_0 & $i(all_66_0) & % 15.77/3.11 | $i(all_66_1) & ( ~ (all_66_2 = 0) | ~ (all_66_3 = 0) | all_66_0 = % 15.77/3.11 | all_66_1 | all_66_4 = 0) % 15.77/3.11 | % 15.77/3.11 | ALPHA: (45) implies: % 15.77/3.11 | (46) join_commut(all_41_2, all_43_0, all_45_0) = all_66_0 % 15.77/3.11 | (47) join_commut(all_41_2, all_45_0, all_43_0) = all_66_1 % 15.77/3.11 | (48) join_semilatt_str(all_41_2) = all_66_2 % 15.77/3.11 | (49) join_commutative(all_41_2) = all_66_3 % 15.77/3.11 | (50) empty_carrier(all_41_2) = all_66_4 % 15.77/3.11 | (51) ~ (all_66_2 = 0) | ~ (all_66_3 = 0) | all_66_0 = all_66_1 | all_66_4 % 15.77/3.11 | = 0 % 15.77/3.11 | % 15.77/3.11 | DELTA: instantiating (31) with fresh symbols all_68_0, all_68_1, all_68_2, % 15.77/3.11 | all_68_3, all_68_4 gives: % 15.77/3.11 | (52) join(all_41_2, all_45_0, all_43_0) = all_68_0 & % 15.77/3.11 | empty_carrier(all_41_2) = all_68_4 & join_commutative(all_41_2) = % 15.77/3.11 | all_68_3 & join_semilatt_str(all_41_2) = all_68_2 & % 15.77/3.11 | join_commut(all_41_2, all_45_0, all_43_0) = all_68_1 & $i(all_68_0) & % 15.77/3.11 | $i(all_68_1) & ( ~ (all_68_2 = 0) | ~ (all_68_3 = 0) | all_68_0 = % 15.77/3.11 | all_68_1 | all_68_4 = 0) % 15.77/3.11 | % 15.77/3.11 | ALPHA: (52) implies: % 15.77/3.11 | (53) join_commut(all_41_2, all_45_0, all_43_0) = all_68_1 % 15.77/3.11 | (54) join_semilatt_str(all_41_2) = all_68_2 % 15.77/3.11 | (55) join_commutative(all_41_2) = all_68_3 % 15.77/3.11 | (56) empty_carrier(all_41_2) = all_68_4 % 15.77/3.11 | (57) join(all_41_2, all_45_0, all_43_0) = all_68_0 % 15.77/3.11 | (58) ~ (all_68_2 = 0) | ~ (all_68_3 = 0) | all_68_0 = all_68_1 | all_68_4 % 15.77/3.11 | = 0 % 15.77/3.11 | % 15.77/3.11 | DELTA: instantiating (30) with fresh symbols all_70_0, all_70_1, all_70_2, % 15.77/3.11 | all_70_3, all_70_4 gives: % 15.77/3.11 | (59) empty_carrier(all_41_2) = all_70_4 & join_commutative(all_41_2) = % 15.77/3.11 | all_70_3 & join_semilatt_str(all_41_2) = all_70_2 & % 15.77/3.11 | join_commut(all_41_2, all_45_0, all_43_0) = all_70_0 & % 15.77/3.11 | join_commut(all_41_2, all_43_0, all_45_0) = all_70_1 & $i(all_70_0) & % 15.77/3.11 | $i(all_70_1) & ( ~ (all_70_2 = 0) | ~ (all_70_3 = 0) | all_70_0 = % 15.77/3.11 | all_70_1 | all_70_4 = 0) % 15.77/3.11 | % 15.77/3.11 | ALPHA: (59) implies: % 15.77/3.11 | (60) join_commut(all_41_2, all_45_0, all_43_0) = all_70_0 % 15.77/3.11 | (61) join_semilatt_str(all_41_2) = all_70_2 % 15.77/3.11 | (62) join_commutative(all_41_2) = all_70_3 % 15.77/3.11 | (63) empty_carrier(all_41_2) = all_70_4 % 15.77/3.11 | % 15.77/3.11 | DELTA: instantiating (29) with fresh symbols all_72_0, all_72_1, all_72_2, % 15.77/3.11 | all_72_3, all_72_4 gives: % 15.77/3.12 | (64) join(all_41_2, all_43_0, all_45_0) = all_72_0 & % 15.77/3.12 | empty_carrier(all_41_2) = all_72_4 & join_commutative(all_41_2) = % 15.77/3.12 | all_72_3 & join_semilatt_str(all_41_2) = all_72_2 & % 15.77/3.12 | join_commut(all_41_2, all_43_0, all_45_0) = all_72_1 & $i(all_72_0) & % 15.77/3.12 | $i(all_72_1) & ( ~ (all_72_2 = 0) | ~ (all_72_3 = 0) | all_72_0 = % 15.77/3.12 | all_72_1 | all_72_4 = 0) % 15.77/3.12 | % 15.77/3.12 | ALPHA: (64) implies: % 15.77/3.12 | (65) join_commut(all_41_2, all_43_0, all_45_0) = all_72_1 % 15.77/3.12 | (66) join_semilatt_str(all_41_2) = all_72_2 % 15.77/3.12 | (67) join_commutative(all_41_2) = all_72_3 % 15.77/3.12 | (68) empty_carrier(all_41_2) = all_72_4 % 15.77/3.12 | (69) join(all_41_2, all_43_0, all_45_0) = all_72_0 % 15.77/3.12 | (70) ~ (all_72_2 = 0) | ~ (all_72_3 = 0) | all_72_0 = all_72_1 | all_72_4 % 15.77/3.12 | = 0 % 15.77/3.12 | % 15.77/3.12 | DELTA: instantiating (27) with fresh symbols all_74_0, all_74_1, all_74_2, % 15.77/3.12 | all_74_3, all_74_4 gives: % 15.77/3.12 | (71) join(all_41_2, all_45_0, all_45_0) = all_74_0 & % 15.77/3.12 | empty_carrier(all_41_2) = all_74_4 & join_commutative(all_41_2) = % 15.77/3.12 | all_74_3 & join_semilatt_str(all_41_2) = all_74_2 & % 15.77/3.12 | join_commut(all_41_2, all_45_0, all_45_0) = all_74_1 & $i(all_74_0) & % 15.77/3.12 | $i(all_74_1) & ( ~ (all_74_2 = 0) | ~ (all_74_3 = 0) | all_74_0 = % 15.77/3.12 | all_74_1 | all_74_4 = 0) % 15.77/3.12 | % 15.77/3.12 | ALPHA: (71) implies: % 15.77/3.12 | (72) join_semilatt_str(all_41_2) = all_74_2 % 15.77/3.12 | (73) join_commutative(all_41_2) = all_74_3 % 15.77/3.12 | (74) empty_carrier(all_41_2) = all_74_4 % 15.77/3.12 | % 15.77/3.12 | DELTA: instantiating (26) with fresh symbols all_76_0, all_76_1 gives: % 15.77/3.12 | (75) the_carrier(all_41_2) = all_76_0 & empty_carrier(all_41_2) = all_76_1 % 15.77/3.12 | & $i(all_76_0) & (all_76_1 = 0 | ! [v0: $i] : ( ~ (element(v0, % 15.77/3.12 | all_76_0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (element(v1, % 15.77/3.12 | all_76_0) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : % 15.77/3.12 | (below(all_41_2, v0, v1) = v2 & join(all_41_2, v0, v1) = v3 & % 15.77/3.12 | $i(v3) & ( ~ (v3 = v1) | v2 = 0) & ( ~ (v2 = 0) | v3 = v1))))) % 15.77/3.12 | % 15.77/3.12 | ALPHA: (75) implies: % 15.77/3.12 | (76) empty_carrier(all_41_2) = all_76_1 % 15.77/3.12 | (77) the_carrier(all_41_2) = all_76_0 % 15.77/3.12 | (78) all_76_1 = 0 | ! [v0: $i] : ( ~ (element(v0, all_76_0) = 0) | ~ % 15.77/3.12 | $i(v0) | ! [v1: $i] : ( ~ (element(v1, all_76_0) = 0) | ~ $i(v1) | % 15.77/3.12 | ? [v2: any] : ? [v3: $i] : (below(all_41_2, v0, v1) = v2 & % 15.77/3.12 | join(all_41_2, v0, v1) = v3 & $i(v3) & ( ~ (v3 = v1) | v2 = 0) & % 15.77/3.12 | ( ~ (v2 = 0) | v3 = v1)))) % 15.77/3.12 | % 15.77/3.12 | GROUND_INST: instantiating (5) with all_66_0, all_72_1, all_45_0, all_43_0, % 15.77/3.12 | all_41_2, simplifying with (46), (65) gives: % 15.77/3.12 | (79) all_72_1 = all_66_0 % 15.77/3.12 | % 15.77/3.12 | GROUND_INST: instantiating (5) with all_68_1, all_70_0, all_43_0, all_45_0, % 15.77/3.12 | all_41_2, simplifying with (53), (60) gives: % 15.77/3.12 | (80) all_70_0 = all_68_1 % 15.77/3.12 | % 15.77/3.12 | GROUND_INST: instantiating (5) with all_66_1, all_70_0, all_43_0, all_45_0, % 15.77/3.12 | all_41_2, simplifying with (47), (60) gives: % 15.77/3.12 | (81) all_70_0 = all_66_1 % 15.77/3.12 | % 15.77/3.12 | GROUND_INST: instantiating (1) with all_64_2, all_68_2, all_41_2, simplifying % 15.77/3.12 | with (42), (54) gives: % 15.77/3.12 | (82) all_68_2 = all_64_2 % 15.77/3.12 | % 15.77/3.12 | GROUND_INST: instantiating (1) with all_62_2, all_68_2, all_41_2, simplifying % 15.77/3.12 | with (39), (54) gives: % 15.77/3.12 | (83) all_68_2 = all_62_2 % 15.77/3.12 | % 15.77/3.12 | GROUND_INST: instantiating (1) with all_64_2, all_70_2, all_41_2, simplifying % 15.77/3.12 | with (42), (61) gives: % 15.77/3.12 | (84) all_70_2 = all_64_2 % 15.77/3.12 | % 15.77/3.13 | GROUND_INST: instantiating (1) with 0, all_72_2, all_41_2, simplifying with % 15.77/3.13 | (11), (66) gives: % 15.77/3.13 | (85) all_72_2 = 0 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (1) with all_68_2, all_72_2, all_41_2, simplifying % 15.77/3.13 | with (54), (66) gives: % 15.77/3.13 | (86) all_72_2 = all_68_2 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (1) with all_66_2, all_72_2, all_41_2, simplifying % 15.77/3.13 | with (48), (66) gives: % 15.77/3.13 | (87) all_72_2 = all_66_2 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (1) with all_70_2, all_74_2, all_41_2, simplifying % 15.77/3.13 | with (61), (72) gives: % 15.77/3.13 | (88) all_74_2 = all_70_2 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (1) with all_60_2, all_74_2, all_41_2, simplifying % 15.77/3.13 | with (36), (72) gives: % 15.77/3.13 | (89) all_74_2 = all_60_2 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (2) with all_66_3, all_68_3, all_41_2, simplifying % 15.77/3.13 | with (49), (55) gives: % 15.77/3.13 | (90) all_68_3 = all_66_3 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (2) with 0, all_70_3, all_41_2, simplifying with % 15.77/3.13 | (12), (62) gives: % 15.77/3.13 | (91) all_70_3 = 0 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (2) with all_68_3, all_70_3, all_41_2, simplifying % 15.77/3.13 | with (55), (62) gives: % 15.77/3.13 | (92) all_70_3 = all_68_3 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (2) with all_72_3, all_74_3, all_41_2, simplifying % 15.77/3.13 | with (67), (73) gives: % 15.77/3.13 | (93) all_74_3 = all_72_3 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (2) with all_66_3, all_74_3, all_41_2, simplifying % 15.77/3.13 | with (49), (73) gives: % 15.77/3.13 | (94) all_74_3 = all_66_3 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (2) with all_64_3, all_74_3, all_41_2, simplifying % 15.77/3.13 | with (43), (73) gives: % 15.77/3.13 | (95) all_74_3 = all_64_3 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (3) with all_41_1, all_64_4, all_41_2, simplifying % 15.77/3.13 | with (13), (44) gives: % 15.77/3.13 | (96) all_64_4 = all_41_1 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (3) with all_66_4, all_68_4, all_41_2, simplifying % 15.77/3.13 | with (50), (56) gives: % 15.77/3.13 | (97) all_68_4 = all_66_4 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (3) with all_64_4, all_68_4, all_41_2, simplifying % 15.77/3.13 | with (44), (56) gives: % 15.77/3.13 | (98) all_68_4 = all_64_4 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (3) with all_64_4, all_70_4, all_41_2, simplifying % 15.77/3.13 | with (44), (63) gives: % 15.77/3.13 | (99) all_70_4 = all_64_4 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (3) with all_60_4, all_70_4, all_41_2, simplifying % 15.77/3.13 | with (37), (63) gives: % 15.77/3.13 | (100) all_70_4 = all_60_4 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (3) with all_68_4, all_72_4, all_41_2, simplifying % 15.77/3.13 | with (56), (68) gives: % 15.77/3.13 | (101) all_72_4 = all_68_4 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (3) with all_72_4, all_74_4, all_41_2, simplifying % 15.77/3.13 | with (68), (74) gives: % 15.77/3.13 | (102) all_74_4 = all_72_4 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (3) with all_74_4, all_76_1, all_41_2, simplifying % 15.77/3.13 | with (74), (76) gives: % 15.77/3.13 | (103) all_76_1 = all_74_4 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (3) with all_62_4, all_76_1, all_41_2, simplifying % 15.77/3.13 | with (40), (76) gives: % 15.77/3.13 | (104) all_76_1 = all_62_4 % 15.77/3.13 | % 15.77/3.13 | GROUND_INST: instantiating (4) with all_41_0, all_76_0, all_41_2, simplifying % 15.77/3.13 | with (14), (77) gives: % 15.77/3.13 | (105) all_76_0 = all_41_0 % 15.77/3.13 | % 15.77/3.13 | COMBINE_EQS: (103), (104) imply: % 15.77/3.13 | (106) all_74_4 = all_62_4 % 15.77/3.13 | % 15.77/3.13 | SIMP: (106) implies: % 15.77/3.13 | (107) all_74_4 = all_62_4 % 15.77/3.13 | % 15.77/3.13 | COMBINE_EQS: (88), (89) imply: % 15.77/3.13 | (108) all_70_2 = all_60_2 % 15.77/3.13 | % 15.77/3.13 | SIMP: (108) implies: % 15.77/3.13 | (109) all_70_2 = all_60_2 % 15.77/3.13 | % 15.77/3.13 | COMBINE_EQS: (93), (94) imply: % 15.77/3.13 | (110) all_72_3 = all_66_3 % 15.77/3.13 | % 15.77/3.13 | COMBINE_EQS: (93), (95) imply: % 15.77/3.13 | (111) all_72_3 = all_64_3 % 15.77/3.13 | % 15.77/3.13 | COMBINE_EQS: (102), (107) imply: % 15.77/3.13 | (112) all_72_4 = all_62_4 % 15.77/3.13 | % 15.77/3.13 | SIMP: (112) implies: % 15.77/3.13 | (113) all_72_4 = all_62_4 % 15.77/3.13 | % 15.77/3.13 | COMBINE_EQS: (85), (87) imply: % 15.77/3.13 | (114) all_66_2 = 0 % 15.77/3.13 | % 15.77/3.13 | COMBINE_EQS: (86), (87) imply: % 15.77/3.13 | (115) all_68_2 = all_66_2 % 15.77/3.13 | % 15.77/3.13 | SIMP: (115) implies: % 15.77/3.13 | (116) all_68_2 = all_66_2 % 15.77/3.13 | % 15.77/3.13 | COMBINE_EQS: (110), (111) imply: % 15.77/3.13 | (117) all_66_3 = all_64_3 % 15.77/3.13 | % 15.77/3.13 | SIMP: (117) implies: % 15.77/3.13 | (118) all_66_3 = all_64_3 % 15.77/3.13 | % 15.77/3.13 | COMBINE_EQS: (101), (113) imply: % 15.77/3.14 | (119) all_68_4 = all_62_4 % 15.77/3.14 | % 15.77/3.14 | SIMP: (119) implies: % 15.77/3.14 | (120) all_68_4 = all_62_4 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (80), (81) imply: % 15.77/3.14 | (121) all_68_1 = all_66_1 % 15.77/3.14 | % 15.77/3.14 | SIMP: (121) implies: % 15.77/3.14 | (122) all_68_1 = all_66_1 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (84), (109) imply: % 15.77/3.14 | (123) all_64_2 = all_60_2 % 15.77/3.14 | % 15.77/3.14 | SIMP: (123) implies: % 15.77/3.14 | (124) all_64_2 = all_60_2 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (91), (92) imply: % 15.77/3.14 | (125) all_68_3 = 0 % 15.77/3.14 | % 15.77/3.14 | SIMP: (125) implies: % 15.77/3.14 | (126) all_68_3 = 0 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (99), (100) imply: % 15.77/3.14 | (127) all_64_4 = all_60_4 % 15.77/3.14 | % 15.77/3.14 | SIMP: (127) implies: % 15.77/3.14 | (128) all_64_4 = all_60_4 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (82), (83) imply: % 15.77/3.14 | (129) all_64_2 = all_62_2 % 15.77/3.14 | % 15.77/3.14 | SIMP: (129) implies: % 15.77/3.14 | (130) all_64_2 = all_62_2 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (83), (116) imply: % 15.77/3.14 | (131) all_66_2 = all_62_2 % 15.77/3.14 | % 15.77/3.14 | SIMP: (131) implies: % 15.77/3.14 | (132) all_66_2 = all_62_2 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (90), (126) imply: % 15.77/3.14 | (133) all_66_3 = 0 % 15.77/3.14 | % 15.77/3.14 | SIMP: (133) implies: % 15.77/3.14 | (134) all_66_3 = 0 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (97), (98) imply: % 15.77/3.14 | (135) all_66_4 = all_64_4 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (97), (120) imply: % 15.77/3.14 | (136) all_66_4 = all_62_4 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (114), (132) imply: % 15.77/3.14 | (137) all_62_2 = 0 % 15.77/3.14 | % 15.77/3.14 | SIMP: (137) implies: % 15.77/3.14 | (138) all_62_2 = 0 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (118), (134) imply: % 15.77/3.14 | (139) all_64_3 = 0 % 15.77/3.14 | % 15.77/3.14 | SIMP: (139) implies: % 15.77/3.14 | (140) all_64_3 = 0 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (135), (136) imply: % 15.77/3.14 | (141) all_64_4 = all_62_4 % 15.77/3.14 | % 15.77/3.14 | SIMP: (141) implies: % 15.77/3.14 | (142) all_64_4 = all_62_4 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (124), (130) imply: % 15.77/3.14 | (143) all_62_2 = all_60_2 % 15.77/3.14 | % 15.77/3.14 | SIMP: (143) implies: % 15.77/3.14 | (144) all_62_2 = all_60_2 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (96), (142) imply: % 15.77/3.14 | (145) all_62_4 = all_41_1 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (128), (142) imply: % 15.77/3.14 | (146) all_62_4 = all_60_4 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (138), (144) imply: % 15.77/3.14 | (147) all_60_2 = 0 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (145), (146) imply: % 15.77/3.14 | (148) all_60_4 = all_41_1 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (136), (145) imply: % 15.77/3.14 | (149) all_66_4 = all_41_1 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (97), (149) imply: % 15.77/3.14 | (150) all_68_4 = all_41_1 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (83), (138) imply: % 15.77/3.14 | (151) all_68_2 = 0 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (113), (145) imply: % 15.77/3.14 | (152) all_72_4 = all_41_1 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (111), (140) imply: % 15.77/3.14 | (153) all_72_3 = 0 % 15.77/3.14 | % 15.77/3.14 | COMBINE_EQS: (104), (145) imply: % 15.77/3.14 | (154) all_76_1 = all_41_1 % 15.77/3.14 | % 15.77/3.14 | BETA: splitting (51) gives: % 15.77/3.14 | % 15.77/3.14 | Case 1: % 15.77/3.14 | | % 15.77/3.14 | | (155) ~ (all_66_2 = 0) % 15.77/3.14 | | % 15.77/3.14 | | REDUCE: (114), (155) imply: % 15.77/3.14 | | (156) $false % 15.77/3.14 | | % 15.77/3.14 | | CLOSE: (156) is inconsistent. % 15.77/3.14 | | % 15.77/3.14 | Case 2: % 15.77/3.14 | | % 15.77/3.14 | | (157) ~ (all_66_3 = 0) | all_66_0 = all_66_1 | all_66_4 = 0 % 15.77/3.14 | | % 15.77/3.14 | | BETA: splitting (70) gives: % 15.77/3.14 | | % 15.77/3.14 | | Case 1: % 15.77/3.14 | | | % 15.77/3.14 | | | (158) ~ (all_72_2 = 0) % 15.77/3.14 | | | % 15.77/3.14 | | | REDUCE: (85), (158) imply: % 15.77/3.14 | | | (159) $false % 15.77/3.14 | | | % 15.77/3.14 | | | CLOSE: (159) is inconsistent. % 15.77/3.14 | | | % 15.77/3.14 | | Case 2: % 15.77/3.14 | | | % 15.77/3.14 | | | (160) ~ (all_72_3 = 0) | all_72_0 = all_72_1 | all_72_4 = 0 % 15.77/3.14 | | | % 15.77/3.14 | | | BETA: splitting (160) gives: % 15.77/3.14 | | | % 15.77/3.14 | | | Case 1: % 15.77/3.14 | | | | % 15.77/3.14 | | | | (161) ~ (all_72_3 = 0) % 15.77/3.14 | | | | % 15.77/3.14 | | | | REDUCE: (153), (161) imply: % 15.77/3.14 | | | | (162) $false % 15.77/3.14 | | | | % 15.77/3.14 | | | | CLOSE: (162) is inconsistent. % 15.77/3.14 | | | | % 16.30/3.14 | | | Case 2: % 16.30/3.14 | | | | % 16.30/3.14 | | | | (163) all_72_0 = all_72_1 | all_72_4 = 0 % 16.30/3.14 | | | | % 16.30/3.14 | | | | BETA: splitting (58) gives: % 16.30/3.14 | | | | % 16.30/3.14 | | | | Case 1: % 16.30/3.14 | | | | | % 16.30/3.14 | | | | | (164) ~ (all_68_2 = 0) % 16.30/3.14 | | | | | % 16.30/3.15 | | | | | REDUCE: (151), (164) imply: % 16.30/3.15 | | | | | (165) $false % 16.30/3.15 | | | | | % 16.30/3.15 | | | | | CLOSE: (165) is inconsistent. % 16.30/3.15 | | | | | % 16.30/3.15 | | | | Case 2: % 16.30/3.15 | | | | | % 16.30/3.15 | | | | | (166) ~ (all_68_3 = 0) | all_68_0 = all_68_1 | all_68_4 = 0 % 16.30/3.15 | | | | | % 16.30/3.15 | | | | | BETA: splitting (78) gives: % 16.30/3.15 | | | | | % 16.30/3.15 | | | | | Case 1: % 16.30/3.15 | | | | | | % 16.30/3.15 | | | | | | (167) all_76_1 = 0 % 16.30/3.15 | | | | | | % 16.30/3.15 | | | | | | COMBINE_EQS: (154), (167) imply: % 16.30/3.15 | | | | | | (168) all_41_1 = 0 % 16.30/3.15 | | | | | | % 16.30/3.15 | | | | | | REDUCE: (9), (168) imply: % 16.30/3.15 | | | | | | (169) $false % 16.30/3.15 | | | | | | % 16.30/3.15 | | | | | | CLOSE: (169) is inconsistent. % 16.30/3.15 | | | | | | % 16.30/3.15 | | | | | Case 2: % 16.30/3.15 | | | | | | % 16.30/3.15 | | | | | | (170) ~ (all_76_1 = 0) % 16.30/3.15 | | | | | | (171) ! [v0: $i] : ( ~ (element(v0, all_76_0) = 0) | ~ $i(v0) | % 16.30/3.15 | | | | | | ! [v1: $i] : ( ~ (element(v1, all_76_0) = 0) | ~ $i(v1) % 16.30/3.15 | | | | | | | ? [v2: any] : ? [v3: $i] : (below(all_41_2, v0, v1) % 16.30/3.15 | | | | | | = v2 & join(all_41_2, v0, v1) = v3 & $i(v3) & ( ~ (v3 % 16.30/3.15 | | | | | | = v1) | v2 = 0) & ( ~ (v2 = 0) | v3 = v1)))) % 16.30/3.15 | | | | | | % 16.30/3.15 | | | | | | BETA: splitting (157) gives: % 16.30/3.15 | | | | | | % 16.30/3.15 | | | | | | Case 1: % 16.30/3.15 | | | | | | | % 16.30/3.15 | | | | | | | (172) ~ (all_66_3 = 0) % 16.30/3.15 | | | | | | | % 16.30/3.15 | | | | | | | REDUCE: (134), (172) imply: % 16.30/3.15 | | | | | | | (173) $false % 16.30/3.15 | | | | | | | % 16.30/3.15 | | | | | | | CLOSE: (173) is inconsistent. % 16.30/3.15 | | | | | | | % 16.30/3.15 | | | | | | Case 2: % 16.30/3.15 | | | | | | | % 16.30/3.15 | | | | | | | (174) all_66_0 = all_66_1 | all_66_4 = 0 % 16.30/3.15 | | | | | | | % 16.30/3.15 | | | | | | | BETA: splitting (163) gives: % 16.30/3.15 | | | | | | | % 16.30/3.15 | | | | | | | Case 1: % 16.30/3.15 | | | | | | | | % 16.30/3.15 | | | | | | | | (175) all_72_4 = 0 % 16.30/3.15 | | | | | | | | % 16.30/3.15 | | | | | | | | COMBINE_EQS: (152), (175) imply: % 16.30/3.15 | | | | | | | | (176) all_41_1 = 0 % 16.30/3.15 | | | | | | | | % 16.30/3.15 | | | | | | | | REDUCE: (9), (176) imply: % 16.30/3.15 | | | | | | | | (177) $false % 16.30/3.15 | | | | | | | | % 16.30/3.15 | | | | | | | | CLOSE: (177) is inconsistent. % 16.30/3.15 | | | | | | | | % 16.30/3.15 | | | | | | | Case 2: % 16.30/3.15 | | | | | | | | % 16.30/3.15 | | | | | | | | (178) all_72_0 = all_72_1 % 16.30/3.15 | | | | | | | | (179) ~ (all_72_4 = 0) % 16.30/3.15 | | | | | | | | % 16.30/3.15 | | | | | | | | COMBINE_EQS: (79), (178) imply: % 16.30/3.15 | | | | | | | | (180) all_72_0 = all_66_0 % 16.30/3.15 | | | | | | | | % 16.30/3.15 | | | | | | | | REDUCE: (69), (180) imply: % 16.30/3.15 | | | | | | | | (181) join(all_41_2, all_43_0, all_45_0) = all_66_0 % 16.30/3.15 | | | | | | | | % 16.30/3.15 | | | | | | | | BETA: splitting (174) gives: % 16.30/3.15 | | | | | | | | % 16.30/3.15 | | | | | | | | Case 1: % 16.30/3.15 | | | | | | | | | % 16.30/3.15 | | | | | | | | | (182) all_66_4 = 0 % 16.30/3.15 | | | | | | | | | % 16.30/3.15 | | | | | | | | | COMBINE_EQS: (149), (182) imply: % 16.30/3.15 | | | | | | | | | (183) all_41_1 = 0 % 16.30/3.15 | | | | | | | | | % 16.30/3.15 | | | | | | | | | SIMP: (183) implies: % 16.30/3.15 | | | | | | | | | (184) all_41_1 = 0 % 16.30/3.15 | | | | | | | | | % 16.30/3.15 | | | | | | | | | REDUCE: (9), (184) imply: % 16.30/3.15 | | | | | | | | | (185) $false % 16.30/3.15 | | | | | | | | | % 16.30/3.15 | | | | | | | | | CLOSE: (185) is inconsistent. % 16.30/3.15 | | | | | | | | | % 16.30/3.15 | | | | | | | | Case 2: % 16.30/3.15 | | | | | | | | | % 16.30/3.15 | | | | | | | | | (186) all_66_0 = all_66_1 % 16.30/3.15 | | | | | | | | | (187) ~ (all_66_4 = 0) % 16.30/3.15 | | | | | | | | | % 16.30/3.15 | | | | | | | | | REDUCE: (181), (186) imply: % 16.30/3.15 | | | | | | | | | (188) join(all_41_2, all_43_0, all_45_0) = all_66_1 % 16.30/3.15 | | | | | | | | | % 16.30/3.15 | | | | | | | | | BETA: splitting (166) gives: % 16.30/3.15 | | | | | | | | | % 16.30/3.15 | | | | | | | | | Case 1: % 16.30/3.15 | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | (189) ~ (all_68_3 = 0) % 16.30/3.15 | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | REDUCE: (126), (189) imply: % 16.30/3.15 | | | | | | | | | | (190) $false % 16.30/3.15 | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | CLOSE: (190) is inconsistent. % 16.30/3.15 | | | | | | | | | | % 16.30/3.15 | | | | | | | | | Case 2: % 16.30/3.15 | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | (191) all_68_0 = all_68_1 | all_68_4 = 0 % 16.30/3.15 | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | BETA: splitting (191) gives: % 16.30/3.15 | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | Case 1: % 16.30/3.15 | | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | | (192) all_68_4 = 0 % 16.30/3.15 | | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | | COMBINE_EQS: (150), (192) imply: % 16.30/3.15 | | | | | | | | | | | (193) all_41_1 = 0 % 16.30/3.15 | | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | | REDUCE: (9), (193) imply: % 16.30/3.15 | | | | | | | | | | | (194) $false % 16.30/3.15 | | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | | CLOSE: (194) is inconsistent. % 16.30/3.15 | | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | Case 2: % 16.30/3.15 | | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | | (195) all_68_0 = all_68_1 % 16.30/3.15 | | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | | COMBINE_EQS: (122), (195) imply: % 16.30/3.15 | | | | | | | | | | | (196) all_68_0 = all_66_1 % 16.30/3.15 | | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | | REDUCE: (57), (196) imply: % 16.30/3.15 | | | | | | | | | | | (197) join(all_41_2, all_45_0, all_43_0) = all_66_1 % 16.30/3.15 | | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | | GROUND_INST: instantiating (171) with all_43_0, simplifying % 16.30/3.15 | | | | | | | | | | | with (17) gives: % 16.30/3.15 | | | | | | | | | | | (198) ~ (element(all_43_0, all_76_0) = 0) | ! [v0: $i] % 16.30/3.15 | | | | | | | | | | | : ( ~ (element(v0, all_76_0) = 0) | ~ $i(v0) | ? % 16.30/3.15 | | | | | | | | | | | [v1: any] : ? [v2: $i] : (below(all_41_2, % 16.30/3.15 | | | | | | | | | | | all_43_0, v0) = v1 & join(all_41_2, % 16.30/3.15 | | | | | | | | | | | all_43_0, v0) = v2 & $i(v2) & ( ~ (v2 = v0) % 16.30/3.15 | | | | | | | | | | | | v1 = 0) & ( ~ (v1 = 0) | v2 = v0))) % 16.30/3.15 | | | | | | | | | | | % 16.30/3.15 | | | | | | | | | | | GROUND_INST: instantiating (171) with all_45_0, simplifying % 16.30/3.15 | | | | | | | | | | | with (22) gives: % 16.30/3.16 | | | | | | | | | | | (199) ~ (element(all_45_0, all_76_0) = 0) | ! [v0: $i] % 16.30/3.16 | | | | | | | | | | | : ( ~ (element(v0, all_76_0) = 0) | ~ $i(v0) | ? % 16.30/3.16 | | | | | | | | | | | [v1: any] : ? [v2: $i] : (below(all_41_2, % 16.30/3.16 | | | | | | | | | | | all_45_0, v0) = v1 & join(all_41_2, % 16.30/3.16 | | | | | | | | | | | all_45_0, v0) = v2 & $i(v2) & ( ~ (v2 = v0) % 16.30/3.16 | | | | | | | | | | | | v1 = 0) & ( ~ (v1 = 0) | v2 = v0))) % 16.30/3.16 | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | BETA: splitting (199) gives: % 16.30/3.16 | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | Case 1: % 16.30/3.16 | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | (200) ~ (element(all_45_0, all_76_0) = 0) % 16.30/3.16 | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | REDUCE: (105), (200) imply: % 16.30/3.16 | | | | | | | | | | | | (201) ~ (element(all_45_0, all_41_0) = 0) % 16.30/3.16 | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | PRED_UNIFY: (23), (201) imply: % 16.30/3.16 | | | | | | | | | | | | (202) $false % 16.30/3.16 | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | CLOSE: (202) is inconsistent. % 16.30/3.16 | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | Case 2: % 16.30/3.16 | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | (203) element(all_45_0, all_76_0) = 0 % 16.30/3.16 | | | | | | | | | | | | (204) ! [v0: $i] : ( ~ (element(v0, all_76_0) = 0) | ~ % 16.30/3.16 | | | | | | | | | | | | $i(v0) | ? [v1: any] : ? [v2: $i] : % 16.30/3.16 | | | | | | | | | | | | (below(all_41_2, all_45_0, v0) = v1 & % 16.30/3.16 | | | | | | | | | | | | join(all_41_2, all_45_0, v0) = v2 & $i(v2) & ( % 16.30/3.16 | | | | | | | | | | | | ~ (v2 = v0) | v1 = 0) & ( ~ (v1 = 0) | v2 = % 16.30/3.16 | | | | | | | | | | | | v0))) % 16.30/3.16 | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | GROUND_INST: instantiating (204) with all_43_0, simplifying % 16.30/3.16 | | | | | | | | | | | | with (17) gives: % 16.30/3.16 | | | | | | | | | | | | (205) ~ (element(all_43_0, all_76_0) = 0) | ? [v0: % 16.30/3.16 | | | | | | | | | | | | any] : ? [v1: $i] : (below(all_41_2, all_45_0, % 16.30/3.16 | | | | | | | | | | | | all_43_0) = v0 & join(all_41_2, all_45_0, % 16.30/3.16 | | | | | | | | | | | | all_43_0) = v1 & $i(v1) & ( ~ (v1 = all_43_0) % 16.30/3.16 | | | | | | | | | | | | | v0 = 0) & ( ~ (v0 = 0) | v1 = all_43_0)) % 16.30/3.16 | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | BETA: splitting (205) gives: % 16.30/3.16 | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | Case 1: % 16.30/3.16 | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | (206) ~ (element(all_43_0, all_76_0) = 0) % 16.30/3.16 | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | REDUCE: (105), (206) imply: % 16.30/3.16 | | | | | | | | | | | | | (207) ~ (element(all_43_0, all_41_0) = 0) % 16.30/3.16 | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | PRED_UNIFY: (18), (207) imply: % 16.30/3.16 | | | | | | | | | | | | | (208) $false % 16.30/3.16 | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | CLOSE: (208) is inconsistent. % 16.30/3.16 | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | Case 2: % 16.30/3.16 | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | (209) element(all_43_0, all_76_0) = 0 % 16.30/3.16 | | | | | | | | | | | | | (210) ? [v0: any] : ? [v1: $i] : (below(all_41_2, % 16.30/3.16 | | | | | | | | | | | | | all_45_0, all_43_0) = v0 & join(all_41_2, % 16.30/3.16 | | | | | | | | | | | | | all_45_0, all_43_0) = v1 & $i(v1) & ( ~ (v1 = % 16.30/3.16 | | | | | | | | | | | | | all_43_0) | v0 = 0) & ( ~ (v0 = 0) | v1 = % 16.30/3.16 | | | | | | | | | | | | | all_43_0)) % 16.30/3.16 | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | DELTA: instantiating (210) with fresh symbols all_264_0, % 16.30/3.16 | | | | | | | | | | | | | all_264_1 gives: % 16.30/3.16 | | | | | | | | | | | | | (211) below(all_41_2, all_45_0, all_43_0) = all_264_1 & % 16.30/3.16 | | | | | | | | | | | | | join(all_41_2, all_45_0, all_43_0) = all_264_0 & % 16.30/3.16 | | | | | | | | | | | | | $i(all_264_0) & ( ~ (all_264_0 = all_43_0) | % 16.30/3.16 | | | | | | | | | | | | | all_264_1 = 0) & ( ~ (all_264_1 = 0) | all_264_0 % 16.30/3.16 | | | | | | | | | | | | | = all_43_0) % 16.30/3.16 | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | ALPHA: (211) implies: % 16.30/3.16 | | | | | | | | | | | | | (212) join(all_41_2, all_45_0, all_43_0) = all_264_0 % 16.30/3.16 | | | | | | | | | | | | | (213) below(all_41_2, all_45_0, all_43_0) = all_264_1 % 16.30/3.16 | | | | | | | | | | | | | (214) ~ (all_264_1 = 0) | all_264_0 = all_43_0 % 16.30/3.16 | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | BETA: splitting (198) gives: % 16.30/3.16 | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | Case 1: % 16.30/3.16 | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | (215) ~ (element(all_43_0, all_76_0) = 0) % 16.30/3.16 | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | REDUCE: (105), (215) imply: % 16.30/3.16 | | | | | | | | | | | | | | (216) ~ (element(all_43_0, all_41_0) = 0) % 16.30/3.16 | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | PRED_UNIFY: (18), (216) imply: % 16.30/3.16 | | | | | | | | | | | | | | (217) $false % 16.30/3.16 | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | CLOSE: (217) is inconsistent. % 16.30/3.16 | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | Case 2: % 16.30/3.16 | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | (218) ! [v0: $i] : ( ~ (element(v0, all_76_0) = 0) | ~ % 16.30/3.16 | | | | | | | | | | | | | | $i(v0) | ? [v1: any] : ? [v2: $i] : % 16.30/3.16 | | | | | | | | | | | | | | (below(all_41_2, all_43_0, v0) = v1 & % 16.30/3.16 | | | | | | | | | | | | | | join(all_41_2, all_43_0, v0) = v2 & $i(v2) & ( % 16.30/3.16 | | | | | | | | | | | | | | ~ (v2 = v0) | v1 = 0) & ( ~ (v1 = 0) | v2 = % 16.30/3.16 | | | | | | | | | | | | | | v0))) % 16.30/3.16 | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (218) with all_45_0, simplifying % 16.30/3.16 | | | | | | | | | | | | | | with (22) gives: % 16.30/3.16 | | | | | | | | | | | | | | (219) ~ (element(all_45_0, all_76_0) = 0) | ? [v0: % 16.30/3.16 | | | | | | | | | | | | | | any] : ? [v1: $i] : (below(all_41_2, all_43_0, % 16.30/3.16 | | | | | | | | | | | | | | all_45_0) = v0 & join(all_41_2, all_43_0, % 16.30/3.16 | | | | | | | | | | | | | | all_45_0) = v1 & $i(v1) & ( ~ (v1 = all_45_0) % 16.30/3.16 | | | | | | | | | | | | | | | v0 = 0) & ( ~ (v0 = 0) | v1 = all_45_0)) % 16.30/3.16 | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | BETA: splitting (219) gives: % 16.30/3.16 | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | Case 1: % 16.30/3.16 | | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | | (220) ~ (element(all_45_0, all_76_0) = 0) % 16.30/3.16 | | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | | REDUCE: (105), (220) imply: % 16.30/3.16 | | | | | | | | | | | | | | | (221) ~ (element(all_45_0, all_41_0) = 0) % 16.30/3.16 | | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | | PRED_UNIFY: (23), (221) imply: % 16.30/3.16 | | | | | | | | | | | | | | | (222) $false % 16.30/3.16 | | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | | CLOSE: (222) is inconsistent. % 16.30/3.16 | | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | Case 2: % 16.30/3.16 | | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | | (223) ? [v0: any] : ? [v1: $i] : (below(all_41_2, % 16.30/3.16 | | | | | | | | | | | | | | | all_43_0, all_45_0) = v0 & join(all_41_2, % 16.30/3.16 | | | | | | | | | | | | | | | all_43_0, all_45_0) = v1 & $i(v1) & ( ~ (v1 = % 16.30/3.16 | | | | | | | | | | | | | | | all_45_0) | v0 = 0) & ( ~ (v0 = 0) | v1 = % 16.30/3.16 | | | | | | | | | | | | | | | all_45_0)) % 16.30/3.16 | | | | | | | | | | | | | | | % 16.30/3.16 | | | | | | | | | | | | | | | DELTA: instantiating (223) with fresh symbols all_280_0, % 16.30/3.16 | | | | | | | | | | | | | | | all_280_1 gives: % 16.67/3.17 | | | | | | | | | | | | | | | (224) below(all_41_2, all_43_0, all_45_0) = all_280_1 & % 16.67/3.17 | | | | | | | | | | | | | | | join(all_41_2, all_43_0, all_45_0) = all_280_0 & % 16.67/3.17 | | | | | | | | | | | | | | | $i(all_280_0) & ( ~ (all_280_0 = all_45_0) | % 16.67/3.17 | | | | | | | | | | | | | | | all_280_1 = 0) & ( ~ (all_280_1 = 0) | all_280_0 % 16.67/3.17 | | | | | | | | | | | | | | | = all_45_0) % 16.67/3.17 | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | ALPHA: (224) implies: % 16.67/3.17 | | | | | | | | | | | | | | | (225) join(all_41_2, all_43_0, all_45_0) = all_280_0 % 16.67/3.17 | | | | | | | | | | | | | | | (226) below(all_41_2, all_43_0, all_45_0) = all_280_1 % 16.67/3.17 | | | | | | | | | | | | | | | (227) ~ (all_280_1 = 0) | all_280_0 = all_45_0 % 16.67/3.17 | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_66_1, all_280_0, % 16.67/3.17 | | | | | | | | | | | | | | | all_45_0, all_43_0, all_41_2, simplifying with % 16.67/3.17 | | | | | | | | | | | | | | | (188), (225) gives: % 16.67/3.17 | | | | | | | | | | | | | | | (228) all_280_0 = all_66_1 % 16.67/3.17 | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_66_1, all_264_0, % 16.67/3.17 | | | | | | | | | | | | | | | all_43_0, all_45_0, all_41_2, simplifying with % 16.67/3.17 | | | | | | | | | | | | | | | (197), (212) gives: % 16.67/3.17 | | | | | | | | | | | | | | | (229) all_264_0 = all_66_1 % 16.67/3.17 | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_280_1, all_45_0, % 16.67/3.17 | | | | | | | | | | | | | | | all_43_0, all_41_2, simplifying with (24), (226) % 16.67/3.17 | | | | | | | | | | | | | | | gives: % 16.67/3.17 | | | | | | | | | | | | | | | (230) all_280_1 = 0 % 16.67/3.17 | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_264_1, all_43_0, % 16.67/3.17 | | | | | | | | | | | | | | | all_45_0, all_41_2, simplifying with (25), (213) % 16.67/3.17 | | | | | | | | | | | | | | | gives: % 16.67/3.17 | | | | | | | | | | | | | | | (231) all_264_1 = 0 % 16.67/3.17 | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 16.67/3.17 | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | Case 1: % 16.67/3.17 | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | (232) ~ (all_280_1 = 0) % 16.67/3.17 | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | REDUCE: (230), (232) imply: % 16.67/3.17 | | | | | | | | | | | | | | | | (233) $false % 16.67/3.17 | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | CLOSE: (233) is inconsistent. % 16.67/3.17 | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | Case 2: % 16.67/3.17 | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | (234) all_280_0 = all_45_0 % 16.67/3.17 | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | COMBINE_EQS: (228), (234) imply: % 16.67/3.17 | | | | | | | | | | | | | | | | (235) all_66_1 = all_45_0 % 16.67/3.17 | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | COMBINE_EQS: (229), (235) imply: % 16.67/3.17 | | | | | | | | | | | | | | | | (236) all_264_0 = all_45_0 % 16.67/3.17 | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 16.67/3.17 | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | Case 1: % 16.67/3.17 | | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | | (237) ~ (all_264_1 = 0) % 16.67/3.17 | | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | | REDUCE: (231), (237) imply: % 16.67/3.17 | | | | | | | | | | | | | | | | | (238) $false % 16.67/3.17 | | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | | CLOSE: (238) is inconsistent. % 16.67/3.17 | | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | Case 2: % 16.67/3.17 | | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | | (239) all_264_0 = all_43_0 % 16.67/3.17 | | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | | COMBINE_EQS: (236), (239) imply: % 16.67/3.17 | | | | | | | | | | | | | | | | | (240) all_45_0 = all_43_0 % 16.67/3.17 | | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | | SIMP: (240) implies: % 16.67/3.17 | | | | | | | | | | | | | | | | | (241) all_45_0 = all_43_0 % 16.67/3.17 | | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | | REDUCE: (21), (241) imply: % 16.67/3.17 | | | | | | | | | | | | | | | | | (242) $false % 16.67/3.17 | | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | | CLOSE: (242) is inconsistent. % 16.67/3.17 | | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | | End of split % 16.67/3.17 | | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | | End of split % 16.67/3.17 | | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | | End of split % 16.67/3.17 | | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | | End of split % 16.67/3.17 | | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | | End of split % 16.67/3.17 | | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | | End of split % 16.67/3.17 | | | | | | | | | | | % 16.67/3.17 | | | | | | | | | | End of split % 16.67/3.17 | | | | | | | | | | % 16.67/3.17 | | | | | | | | | End of split % 16.67/3.17 | | | | | | | | | % 16.67/3.17 | | | | | | | | End of split % 16.67/3.17 | | | | | | | | % 16.67/3.17 | | | | | | | End of split % 16.67/3.17 | | | | | | | % 16.67/3.17 | | | | | | End of split % 16.67/3.17 | | | | | | % 16.67/3.17 | | | | | End of split % 16.67/3.17 | | | | | % 16.67/3.17 | | | | End of split % 16.67/3.17 | | | | % 16.67/3.17 | | | End of split % 16.67/3.17 | | | % 16.67/3.17 | | End of split % 16.67/3.17 | | % 16.67/3.17 | End of split % 16.67/3.17 | % 16.67/3.17 End of proof % 16.67/3.17 % SZS output end Proof for theBenchmark % 16.67/3.17 % 16.67/3.17 2552ms %------------------------------------------------------------------------------