%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU250+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 : n024.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 17:43:39 EDT 2023 % Result : Theorem 7.68s 1.83s % Output : Proof 10.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU250+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n024.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Aug 24 01:01:55 EDT 2023 % 0.12/0.33 % CPUTime : % 0.18/0.59 ________ _____ % 0.18/0.59 ___ __ \_________(_)________________________________ % 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.59 % 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.59 (2023-06-19) % 0.18/0.59 % 0.18/0.59 (c) Philipp Rümmer, 2009-2023 % 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.59 Amanda Stjerna. % 0.18/0.59 Free software under BSD-3-Clause. % 0.18/0.59 % 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.59 % 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.18/0.60 Running up to 7 provers in parallel. % 0.18/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.67/1.03 Prover 4: Preprocessing ... % 2.67/1.04 Prover 1: Preprocessing ... % 2.67/1.08 Prover 2: Preprocessing ... % 2.67/1.08 Prover 0: Preprocessing ... % 2.67/1.08 Prover 5: Preprocessing ... % 2.67/1.08 Prover 3: Preprocessing ... % 2.67/1.08 Prover 6: Preprocessing ... % 5.48/1.46 Prover 1: Warning: ignoring some quantifiers % 6.17/1.51 Prover 1: Constructing countermodel ... % 6.17/1.52 Prover 5: Proving ... % 6.17/1.52 Prover 2: Proving ... % 6.17/1.54 Prover 3: Warning: ignoring some quantifiers % 6.17/1.55 Prover 4: Warning: ignoring some quantifiers % 6.17/1.56 Prover 3: Constructing countermodel ... % 6.17/1.57 Prover 6: Proving ... % 6.17/1.58 Prover 4: Constructing countermodel ... % 6.76/1.60 Prover 0: Proving ... % 7.68/1.83 Prover 6: proved (1213ms) % 7.68/1.83 % 7.68/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.68/1.83 % 7.68/1.84 Prover 3: stopped % 7.68/1.84 Prover 2: stopped % 7.68/1.84 Prover 0: stopped % 7.68/1.84 Prover 5: stopped % 7.68/1.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.68/1.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.68/1.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.68/1.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.68/1.84 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.52/1.89 Prover 8: Preprocessing ... % 8.52/1.89 Prover 10: Preprocessing ... % 8.52/1.89 Prover 7: Preprocessing ... % 8.52/1.90 Prover 13: Preprocessing ... % 8.52/1.90 Prover 11: Preprocessing ... % 9.42/1.96 Prover 1: Found proof (size 49) % 9.42/1.97 Prover 1: proved (1355ms) % 9.42/1.97 Prover 4: stopped % 9.42/1.98 Prover 10: Warning: ignoring some quantifiers % 9.42/1.98 Prover 7: Warning: ignoring some quantifiers % 9.42/1.98 Prover 10: Constructing countermodel ... % 9.42/1.99 Prover 11: stopped % 9.42/1.99 Prover 10: stopped % 9.42/2.00 Prover 7: Constructing countermodel ... % 9.42/2.00 Prover 13: Warning: ignoring some quantifiers % 9.42/2.00 Prover 8: Warning: ignoring some quantifiers % 9.42/2.00 Prover 7: stopped % 9.42/2.01 Prover 13: Constructing countermodel ... % 9.42/2.01 Prover 8: Constructing countermodel ... % 9.42/2.02 Prover 13: stopped % 9.42/2.02 Prover 8: stopped % 9.42/2.02 % 9.42/2.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.42/2.02 % 9.42/2.03 % SZS output start Proof for theBenchmark % 9.42/2.04 Assumptions after simplification: % 9.42/2.04 --------------------------------- % 9.42/2.04 % 9.42/2.04 (d3_tarski) % 9.98/2.06 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 9.98/2.06 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 9.98/2.06 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 9.98/2.06 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 9.98/2.06 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 9.98/2.06 % 9.98/2.06 (dt_k2_wellord1) % 9.98/2.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) = % 9.98/2.06 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (relation(v2) % 9.98/2.06 = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 9.98/2.06 % 9.98/2.06 (t19_wellord1) % 9.98/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 9.98/2.07 (relation_restriction(v2, v1) = v3) | ~ (relation_field(v3) = v4) | ~ % 9.98/2.07 (in(v0, v4) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 9.98/2.07 [v6: $i] : ? [v7: any] : ? [v8: any] : (relation_field(v2) = v6 & % 9.98/2.07 relation(v2) = v5 & in(v0, v6) = v7 & in(v0, v1) = v8 & $i(v6) & ( ~ (v5 = % 9.98/2.07 0) | (v8 = 0 & v7 = 0)))) % 9.98/2.07 % 9.98/2.07 (t20_wellord1) % 9.98/2.07 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 9.98/2.07 any] : ? [v6: any] : (relation_restriction(v1, v0) = v2 & % 9.98/2.07 relation_field(v2) = v3 & relation_field(v1) = v4 & subset(v3, v4) = v5 & % 9.98/2.07 subset(v3, v0) = v6 & relation(v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 9.98/2.07 $i(v0) & ( ~ (v6 = 0) | ~ (v5 = 0))) % 9.98/2.07 % 9.98/2.07 (function-axioms) % 9.98/2.08 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.98/2.08 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 9.98/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.98/2.08 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 9.98/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.98/2.08 (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = % 9.98/2.08 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.98/2.08 $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) % 9.98/2.08 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 9.98/2.08 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 9.98/2.08 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.98/2.08 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: % 9.98/2.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.98/2.08 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 9.98/2.08 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) % 9.98/2.08 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 9.98/2.08 (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i] : ! % 9.98/2.08 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ % 9.98/2.08 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 9.98/2.08 v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0: % 9.98/2.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.98/2.08 ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0: % 9.98/2.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.98/2.08 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] % 9.98/2.08 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) % 9.98/2.08 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.98/2.08 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 9.98/2.08 (empty(v2) = v0)) % 9.98/2.08 % 9.98/2.08 Further assumptions not needed in the proof: % 9.98/2.08 -------------------------------------------- % 9.98/2.08 antisymmetry_r2_hidden, cc1_funct_1, cc2_funct_1, commutativity_k2_xboole_0, % 9.98/2.08 commutativity_k3_xboole_0, d6_relat_1, d6_wellord1, dt_k1_relat_1, % 9.98/2.08 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_xboole_0, dt_k2_zfmisc_1, % 9.98/2.08 dt_k3_relat_1, dt_k3_xboole_0, dt_m1_subset_1, existence_m1_subset_1, % 9.98/2.08 fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 9.98/2.08 idempotence_k3_xboole_0, rc1_funct_1, rc1_xboole_0, rc2_funct_1, rc2_xboole_0, % 9.98/2.08 rc3_funct_1, reflexivity_r1_tarski, t1_boole, t1_subset, t2_boole, t2_subset, % 9.98/2.08 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 9.98/2.08 % 9.98/2.08 Those formulas are unsatisfiable: % 9.98/2.08 --------------------------------- % 9.98/2.08 % 9.98/2.08 Begin of proof % 9.98/2.08 | % 9.98/2.08 | ALPHA: (d3_tarski) implies: % 9.98/2.08 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 9.98/2.08 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 9.98/2.08 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 9.98/2.08 | % 9.98/2.09 | ALPHA: (function-axioms) implies: % 9.98/2.09 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.98/2.09 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 9.98/2.09 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 9.98/2.09 | (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 9.98/2.09 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.98/2.09 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 9.98/2.09 | % 9.98/2.09 | DELTA: instantiating (t20_wellord1) with fresh symbols all_43_0, all_43_1, % 9.98/2.09 | all_43_2, all_43_3, all_43_4, all_43_5, all_43_6 gives: % 10.15/2.09 | (5) relation_restriction(all_43_5, all_43_6) = all_43_4 & % 10.15/2.09 | relation_field(all_43_4) = all_43_3 & relation_field(all_43_5) = % 10.15/2.09 | all_43_2 & subset(all_43_3, all_43_2) = all_43_1 & subset(all_43_3, % 10.15/2.09 | all_43_6) = all_43_0 & relation(all_43_5) = 0 & $i(all_43_2) & % 10.15/2.09 | $i(all_43_3) & $i(all_43_4) & $i(all_43_5) & $i(all_43_6) & ( ~ % 10.15/2.09 | (all_43_0 = 0) | ~ (all_43_1 = 0)) % 10.15/2.09 | % 10.15/2.09 | ALPHA: (5) implies: % 10.15/2.09 | (6) $i(all_43_6) % 10.15/2.09 | (7) $i(all_43_5) % 10.15/2.09 | (8) $i(all_43_3) % 10.15/2.09 | (9) $i(all_43_2) % 10.15/2.09 | (10) relation(all_43_5) = 0 % 10.15/2.09 | (11) subset(all_43_3, all_43_6) = all_43_0 % 10.15/2.09 | (12) subset(all_43_3, all_43_2) = all_43_1 % 10.15/2.09 | (13) relation_field(all_43_5) = all_43_2 % 10.15/2.09 | (14) relation_field(all_43_4) = all_43_3 % 10.15/2.09 | (15) relation_restriction(all_43_5, all_43_6) = all_43_4 % 10.15/2.09 | (16) ~ (all_43_0 = 0) | ~ (all_43_1 = 0) % 10.15/2.09 | % 10.15/2.09 | GROUND_INST: instantiating (1) with all_43_3, all_43_6, all_43_0, simplifying % 10.15/2.09 | with (6), (8), (11) gives: % 10.15/2.09 | (17) all_43_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 10.15/2.09 | all_43_3) = 0 & in(v0, all_43_6) = v1 & $i(v0)) % 10.15/2.09 | % 10.15/2.09 | GROUND_INST: instantiating (1) with all_43_3, all_43_2, all_43_1, simplifying % 10.15/2.09 | with (8), (9), (12) gives: % 10.15/2.09 | (18) all_43_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 10.15/2.09 | all_43_2) = v1 & in(v0, all_43_3) = 0 & $i(v0)) % 10.15/2.09 | % 10.15/2.09 | GROUND_INST: instantiating (dt_k2_wellord1) with all_43_5, all_43_6, all_43_4, % 10.15/2.09 | simplifying with (6), (7), (15) gives: % 10.15/2.10 | (19) ? [v0: any] : ? [v1: any] : (relation(all_43_4) = v1 & % 10.15/2.10 | relation(all_43_5) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 10.15/2.10 | % 10.15/2.10 | DELTA: instantiating (19) with fresh symbols all_57_0, all_57_1 gives: % 10.15/2.10 | (20) relation(all_43_4) = all_57_0 & relation(all_43_5) = all_57_1 & ( ~ % 10.15/2.10 | (all_57_1 = 0) | all_57_0 = 0) % 10.15/2.10 | % 10.15/2.10 | ALPHA: (20) implies: % 10.15/2.10 | (21) relation(all_43_5) = all_57_1 % 10.15/2.10 | % 10.15/2.10 | GROUND_INST: instantiating (2) with 0, all_57_1, all_43_5, simplifying with % 10.15/2.10 | (10), (21) gives: % 10.15/2.10 | (22) all_57_1 = 0 % 10.15/2.10 | % 10.15/2.10 | BETA: splitting (16) gives: % 10.15/2.10 | % 10.15/2.10 | Case 1: % 10.15/2.10 | | % 10.15/2.10 | | (23) ~ (all_43_0 = 0) % 10.15/2.10 | | % 10.15/2.10 | | BETA: splitting (17) gives: % 10.15/2.10 | | % 10.15/2.10 | | Case 1: % 10.15/2.10 | | | % 10.15/2.10 | | | (24) all_43_0 = 0 % 10.15/2.10 | | | % 10.15/2.10 | | | REDUCE: (23), (24) imply: % 10.15/2.10 | | | (25) $false % 10.15/2.10 | | | % 10.15/2.10 | | | CLOSE: (25) is inconsistent. % 10.15/2.10 | | | % 10.15/2.10 | | Case 2: % 10.15/2.10 | | | % 10.15/2.10 | | | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_43_3) = 0 & % 10.15/2.10 | | | in(v0, all_43_6) = v1 & $i(v0)) % 10.15/2.10 | | | % 10.15/2.10 | | | DELTA: instantiating (26) with fresh symbols all_88_0, all_88_1 gives: % 10.15/2.10 | | | (27) ~ (all_88_0 = 0) & in(all_88_1, all_43_3) = 0 & in(all_88_1, % 10.15/2.10 | | | all_43_6) = all_88_0 & $i(all_88_1) % 10.15/2.10 | | | % 10.15/2.10 | | | ALPHA: (27) implies: % 10.15/2.10 | | | (28) ~ (all_88_0 = 0) % 10.15/2.10 | | | (29) $i(all_88_1) % 10.15/2.10 | | | (30) in(all_88_1, all_43_6) = all_88_0 % 10.15/2.10 | | | (31) in(all_88_1, all_43_3) = 0 % 10.15/2.10 | | | % 10.15/2.10 | | | GROUND_INST: instantiating (t19_wellord1) with all_88_1, all_43_6, % 10.15/2.10 | | | all_43_5, all_43_4, all_43_3, simplifying with (6), (7), % 10.15/2.10 | | | (14), (15), (29), (31) gives: % 10.15/2.10 | | | (32) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 10.15/2.10 | | | (relation_field(all_43_5) = v1 & relation(all_43_5) = v0 & % 10.15/2.10 | | | in(all_88_1, v1) = v2 & in(all_88_1, all_43_6) = v3 & $i(v1) & ( % 10.15/2.10 | | | ~ (v0 = 0) | (v3 = 0 & v2 = 0))) % 10.15/2.10 | | | % 10.15/2.10 | | | DELTA: instantiating (32) with fresh symbols all_99_0, all_99_1, all_99_2, % 10.15/2.10 | | | all_99_3 gives: % 10.15/2.10 | | | (33) relation_field(all_43_5) = all_99_2 & relation(all_43_5) = % 10.15/2.10 | | | all_99_3 & in(all_88_1, all_99_2) = all_99_1 & in(all_88_1, % 10.15/2.10 | | | all_43_6) = all_99_0 & $i(all_99_2) & ( ~ (all_99_3 = 0) | % 10.15/2.10 | | | (all_99_0 = 0 & all_99_1 = 0)) % 10.15/2.10 | | | % 10.15/2.10 | | | ALPHA: (33) implies: % 10.15/2.10 | | | (34) in(all_88_1, all_43_6) = all_99_0 % 10.15/2.10 | | | (35) relation(all_43_5) = all_99_3 % 10.15/2.10 | | | (36) ~ (all_99_3 = 0) | (all_99_0 = 0 & all_99_1 = 0) % 10.15/2.10 | | | % 10.15/2.10 | | | GROUND_INST: instantiating (4) with all_88_0, all_99_0, all_43_6, % 10.15/2.10 | | | all_88_1, simplifying with (30), (34) gives: % 10.15/2.10 | | | (37) all_99_0 = all_88_0 % 10.15/2.10 | | | % 10.15/2.10 | | | GROUND_INST: instantiating (2) with 0, all_99_3, all_43_5, simplifying % 10.15/2.10 | | | with (10), (35) gives: % 10.15/2.10 | | | (38) all_99_3 = 0 % 10.15/2.10 | | | % 10.15/2.10 | | | BETA: splitting (36) gives: % 10.15/2.10 | | | % 10.15/2.10 | | | Case 1: % 10.15/2.10 | | | | % 10.15/2.10 | | | | (39) ~ (all_99_3 = 0) % 10.15/2.10 | | | | % 10.15/2.10 | | | | REDUCE: (38), (39) imply: % 10.15/2.10 | | | | (40) $false % 10.15/2.10 | | | | % 10.15/2.11 | | | | CLOSE: (40) is inconsistent. % 10.15/2.11 | | | | % 10.15/2.11 | | | Case 2: % 10.15/2.11 | | | | % 10.15/2.11 | | | | (41) all_99_0 = 0 & all_99_1 = 0 % 10.15/2.11 | | | | % 10.15/2.11 | | | | ALPHA: (41) implies: % 10.15/2.11 | | | | (42) all_99_0 = 0 % 10.15/2.11 | | | | % 10.15/2.11 | | | | COMBINE_EQS: (37), (42) imply: % 10.15/2.11 | | | | (43) all_88_0 = 0 % 10.15/2.11 | | | | % 10.15/2.11 | | | | REDUCE: (28), (43) imply: % 10.15/2.11 | | | | (44) $false % 10.15/2.11 | | | | % 10.15/2.11 | | | | CLOSE: (44) is inconsistent. % 10.15/2.11 | | | | % 10.15/2.11 | | | End of split % 10.15/2.11 | | | % 10.15/2.11 | | End of split % 10.15/2.11 | | % 10.15/2.11 | Case 2: % 10.15/2.11 | | % 10.15/2.11 | | (45) ~ (all_43_1 = 0) % 10.15/2.11 | | % 10.15/2.11 | | BETA: splitting (18) gives: % 10.15/2.11 | | % 10.15/2.11 | | Case 1: % 10.15/2.11 | | | % 10.15/2.11 | | | (46) all_43_1 = 0 % 10.15/2.11 | | | % 10.15/2.11 | | | REDUCE: (45), (46) imply: % 10.15/2.11 | | | (47) $false % 10.15/2.11 | | | % 10.15/2.11 | | | CLOSE: (47) is inconsistent. % 10.15/2.11 | | | % 10.15/2.11 | | Case 2: % 10.15/2.11 | | | % 10.15/2.11 | | | (48) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_43_2) = v1 % 10.15/2.11 | | | & in(v0, all_43_3) = 0 & $i(v0)) % 10.15/2.11 | | | % 10.15/2.11 | | | DELTA: instantiating (48) with fresh symbols all_88_0, all_88_1 gives: % 10.15/2.11 | | | (49) ~ (all_88_0 = 0) & in(all_88_1, all_43_2) = all_88_0 & % 10.15/2.11 | | | in(all_88_1, all_43_3) = 0 & $i(all_88_1) % 10.15/2.11 | | | % 10.15/2.11 | | | ALPHA: (49) implies: % 10.15/2.11 | | | (50) ~ (all_88_0 = 0) % 10.15/2.11 | | | (51) $i(all_88_1) % 10.15/2.11 | | | (52) in(all_88_1, all_43_3) = 0 % 10.15/2.11 | | | (53) in(all_88_1, all_43_2) = all_88_0 % 10.15/2.11 | | | % 10.15/2.11 | | | GROUND_INST: instantiating (t19_wellord1) with all_88_1, all_43_6, % 10.15/2.11 | | | all_43_5, all_43_4, all_43_3, simplifying with (6), (7), % 10.15/2.11 | | | (14), (15), (51), (52) gives: % 10.15/2.11 | | | (54) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 10.15/2.11 | | | (relation_field(all_43_5) = v1 & relation(all_43_5) = v0 & % 10.15/2.11 | | | in(all_88_1, v1) = v2 & in(all_88_1, all_43_6) = v3 & $i(v1) & ( % 10.15/2.11 | | | ~ (v0 = 0) | (v3 = 0 & v2 = 0))) % 10.15/2.11 | | | % 10.15/2.11 | | | DELTA: instantiating (54) with fresh symbols all_101_0, all_101_1, % 10.15/2.11 | | | all_101_2, all_101_3 gives: % 10.15/2.11 | | | (55) relation_field(all_43_5) = all_101_2 & relation(all_43_5) = % 10.15/2.11 | | | all_101_3 & in(all_88_1, all_101_2) = all_101_1 & in(all_88_1, % 10.15/2.11 | | | all_43_6) = all_101_0 & $i(all_101_2) & ( ~ (all_101_3 = 0) | % 10.15/2.11 | | | (all_101_0 = 0 & all_101_1 = 0)) % 10.15/2.11 | | | % 10.15/2.11 | | | ALPHA: (55) implies: % 10.15/2.11 | | | (56) in(all_88_1, all_101_2) = all_101_1 % 10.15/2.11 | | | (57) relation(all_43_5) = all_101_3 % 10.15/2.11 | | | (58) relation_field(all_43_5) = all_101_2 % 10.15/2.11 | | | (59) ~ (all_101_3 = 0) | (all_101_0 = 0 & all_101_1 = 0) % 10.15/2.11 | | | % 10.15/2.11 | | | GROUND_INST: instantiating (2) with 0, all_101_3, all_43_5, simplifying % 10.15/2.11 | | | with (10), (57) gives: % 10.15/2.11 | | | (60) all_101_3 = 0 % 10.15/2.11 | | | % 10.15/2.11 | | | GROUND_INST: instantiating (3) with all_43_2, all_101_2, all_43_5, % 10.15/2.11 | | | simplifying with (13), (58) gives: % 10.15/2.11 | | | (61) all_101_2 = all_43_2 % 10.15/2.11 | | | % 10.15/2.11 | | | REDUCE: (56), (61) imply: % 10.15/2.11 | | | (62) in(all_88_1, all_43_2) = all_101_1 % 10.15/2.11 | | | % 10.15/2.11 | | | BETA: splitting (59) gives: % 10.15/2.11 | | | % 10.15/2.11 | | | Case 1: % 10.15/2.11 | | | | % 10.15/2.11 | | | | (63) ~ (all_101_3 = 0) % 10.15/2.11 | | | | % 10.15/2.11 | | | | REDUCE: (60), (63) imply: % 10.15/2.11 | | | | (64) $false % 10.15/2.11 | | | | % 10.15/2.11 | | | | CLOSE: (64) is inconsistent. % 10.15/2.11 | | | | % 10.15/2.11 | | | Case 2: % 10.15/2.11 | | | | % 10.15/2.11 | | | | (65) all_101_0 = 0 & all_101_1 = 0 % 10.15/2.11 | | | | % 10.15/2.11 | | | | ALPHA: (65) implies: % 10.15/2.11 | | | | (66) all_101_1 = 0 % 10.15/2.11 | | | | % 10.15/2.11 | | | | REDUCE: (62), (66) imply: % 10.15/2.11 | | | | (67) in(all_88_1, all_43_2) = 0 % 10.15/2.11 | | | | % 10.15/2.11 | | | | GROUND_INST: instantiating (4) with all_88_0, 0, all_43_2, all_88_1, % 10.15/2.11 | | | | simplifying with (53), (67) gives: % 10.15/2.11 | | | | (68) all_88_0 = 0 % 10.15/2.11 | | | | % 10.15/2.11 | | | | REDUCE: (50), (68) imply: % 10.15/2.11 | | | | (69) $false % 10.15/2.11 | | | | % 10.15/2.11 | | | | CLOSE: (69) is inconsistent. % 10.15/2.11 | | | | % 10.15/2.11 | | | End of split % 10.15/2.11 | | | % 10.15/2.11 | | End of split % 10.15/2.11 | | % 10.15/2.11 | End of split % 10.15/2.11 | % 10.15/2.11 End of proof % 10.15/2.11 % SZS output end Proof for theBenchmark % 10.15/2.11 % 10.15/2.11 1522ms %------------------------------------------------------------------------------