%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU180+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n015.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:43:05 EDT 2023 % Result : Theorem 12.90s 2.61s % Output : Proof 15.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.14 % Problem : SEU180+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.36 % Computer : n015.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Wed Aug 23 14:59:35 EDT 2023 % 0.15/0.37 % CPUTime : % 0.22/0.64 ________ _____ % 0.22/0.64 ___ __ \_________(_)________________________________ % 0.22/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.64 % 0.22/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.64 (2023-06-19) % 0.22/0.64 % 0.22/0.64 (c) Philipp Rümmer, 2009-2023 % 0.22/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.64 Amanda Stjerna. % 0.22/0.64 Free software under BSD-3-Clause. % 0.22/0.64 % 0.22/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.64 % 0.22/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.65 Running up to 7 provers in parallel. % 0.22/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.58/1.12 Prover 1: Preprocessing ... % 2.58/1.12 Prover 4: Preprocessing ... % 2.99/1.16 Prover 3: Preprocessing ... % 2.99/1.16 Prover 0: Preprocessing ... % 2.99/1.16 Prover 2: Preprocessing ... % 2.99/1.16 Prover 5: Preprocessing ... % 2.99/1.16 Prover 6: Preprocessing ... % 4.60/1.59 Prover 1: Warning: ignoring some quantifiers % 5.99/1.62 Prover 3: Warning: ignoring some quantifiers % 5.99/1.64 Prover 1: Constructing countermodel ... % 6.37/1.65 Prover 3: Constructing countermodel ... % 6.37/1.68 Prover 6: Proving ... % 6.37/1.68 Prover 5: Proving ... % 6.37/1.69 Prover 4: Warning: ignoring some quantifiers % 7.02/1.76 Prover 4: Constructing countermodel ... % 7.02/1.78 Prover 2: Proving ... % 7.38/1.84 Prover 0: Proving ... % 12.90/2.61 Prover 2: proved (1948ms) % 12.90/2.61 % 12.90/2.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.90/2.61 % 12.90/2.61 Prover 3: stopped % 12.90/2.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.90/2.62 Prover 6: stopped % 12.90/2.62 Prover 5: stopped % 12.90/2.63 Prover 0: stopped % 12.90/2.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.90/2.63 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.90/2.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.90/2.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.90/2.65 Prover 7: Preprocessing ... % 13.35/2.65 Prover 10: Preprocessing ... % 13.44/2.66 Prover 8: Preprocessing ... % 13.44/2.67 Prover 13: Preprocessing ... % 13.44/2.68 Prover 11: Preprocessing ... % 13.79/2.73 Prover 7: Warning: ignoring some quantifiers % 14.07/2.75 Prover 7: Constructing countermodel ... % 14.07/2.75 Prover 10: Warning: ignoring some quantifiers % 14.07/2.78 Prover 10: Constructing countermodel ... % 14.07/2.80 Prover 8: Warning: ignoring some quantifiers % 14.07/2.81 Prover 13: Warning: ignoring some quantifiers % 14.07/2.83 Prover 8: Constructing countermodel ... % 14.07/2.83 Prover 13: Constructing countermodel ... % 14.71/2.84 Prover 10: gave up % 14.71/2.87 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 14.71/2.88 Prover 11: Warning: ignoring some quantifiers % 14.71/2.89 Prover 16: Preprocessing ... % 14.71/2.90 Prover 11: Constructing countermodel ... % 14.71/2.94 Prover 7: Found proof (size 21) % 14.71/2.94 Prover 7: proved (324ms) % 14.71/2.94 Prover 13: stopped % 14.71/2.94 Prover 4: stopped % 14.71/2.94 Prover 11: stopped % 14.71/2.94 Prover 1: stopped % 14.71/2.94 Prover 8: stopped % 14.71/2.94 Prover 16: stopped % 14.71/2.94 % 14.71/2.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.71/2.94 % 14.71/2.95 % SZS output start Proof for theBenchmark % 14.71/2.95 Assumptions after simplification: % 14.71/2.95 --------------------------------- % 14.71/2.95 % 14.71/2.96 (commutativity_k2_xboole_0) % 14.71/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 14.71/2.98 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 14.71/2.98 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 14.71/2.98 | (set_union2(v1, v0) = v2 & $i(v2))) % 14.71/2.98 % 14.71/2.98 (d2_xboole_0) % 14.71/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, % 14.71/2.99 v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, % 14.71/2.99 v2) | in(v3, v1) | in(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.71/2.99 ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 14.71/2.99 $i(v1) | ~ $i(v0) | ~ in(v3, v1) | in(v3, v2)) & ! [v0: $i] : ! [v1: $i] % 14.71/2.99 : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ % 14.71/2.99 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2)) & ? [v0: $i] : % 14.71/2.99 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_union2(v1, v2) = % 14.71/2.99 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ($i(v4) & ( ~ % 14.71/2.99 in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) % 14.71/2.99 | in(v4, v0)))) % 14.71/2.99 % 14.71/2.99 (d4_relat_1) % 14.71/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 14.71/2.99 (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 14.71/2.99 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v2, % 14.71/2.99 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) = % 14.71/2.99 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) % 14.71/2.99 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & % 14.71/2.99 in(v4, v0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 14.71/2.99 (relation_dom(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3: % 14.71/2.99 $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ in(v3, v0) | ! % 14.71/2.99 [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v3, v6) = v7) | ~ $i(v6) | % 14.71/2.99 ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & $i(v5) & % 14.71/2.99 in(v5, v1))))) % 14.71/2.99 % 14.71/3.00 (d5_relat_1) % 14.71/3.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 14.71/3.00 (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ $i(v3) | ~ % 14.71/3.00 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v2, % 14.71/3.00 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0) = % 14.71/3.00 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) % 14.71/3.00 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v3, v2) = v4 & $i(v4) & $i(v3) & % 14.71/3.00 in(v4, v0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 14.71/3.00 (relation_rng(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3: % 14.71/3.00 $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ in(v3, v0) | ! % 14.71/3.00 [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v3) = v7) | ~ $i(v6) | % 14.71/3.00 ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & $i(v5) & % 14.71/3.00 in(v5, v1))))) % 14.71/3.00 % 14.71/3.00 (d6_relat_1) % 14.71/3.00 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ~ % 14.71/3.00 relation(v0) | ? [v2: $i] : ? [v3: $i] : (relation_rng(v0) = v3 & % 14.71/3.00 relation_dom(v0) = v2 & set_union2(v2, v3) = v1 & $i(v3) & $i(v2) & % 14.71/3.00 $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ % 14.71/3.00 $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: $i] : (relation_field(v0) = % 14.71/3.00 v2 & relation_dom(v0) = v3 & set_union2(v3, v1) = v2 & $i(v3) & $i(v2))) & % 14.71/3.00 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ % 14.71/3.00 relation(v0) | ? [v2: $i] : ? [v3: $i] : (relation_field(v0) = v2 & % 14.71/3.00 relation_rng(v0) = v3 & set_union2(v1, v3) = v2 & $i(v3) & $i(v2))) % 14.71/3.00 % 14.71/3.00 (t30_relat_1) % 14.71/3.00 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 14.71/3.00 (relation_field(v2) = v4 & ordered_pair(v0, v1) = v3 & $i(v4) & $i(v3) & % 14.71/3.00 $i(v2) & $i(v1) & $i(v0) & relation(v2) & in(v3, v2) & ( ~ in(v1, v4) | ~ % 14.71/3.00 in(v0, v4))) % 14.71/3.00 % 14.71/3.00 Further assumptions not needed in the proof: % 14.71/3.00 -------------------------------------------- % 14.71/3.00 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, dt_k1_relat_1, % 14.71/3.00 dt_k1_tarski, dt_k1_xboole_0, dt_k2_relat_1, dt_k2_tarski, dt_k2_xboole_0, % 14.71/3.00 dt_k3_relat_1, dt_k4_tarski, dt_m1_subset_1, existence_m1_subset_1, % 14.71/3.00 fc1_xboole_0, fc1_zfmisc_1, fc2_relat_1, fc2_subset_1, fc2_xboole_0, % 14.71/3.00 fc3_subset_1, fc3_xboole_0, idempotence_k2_xboole_0, rc1_relat_1, rc1_xboole_0, % 14.71/3.00 rc2_xboole_0, t1_boole, t1_subset, t2_subset, t6_boole, t7_boole, t8_boole % 14.71/3.00 % 14.71/3.00 Those formulas are unsatisfiable: % 14.71/3.00 --------------------------------- % 14.71/3.00 % 14.71/3.00 Begin of proof % 14.71/3.01 | % 14.71/3.01 | ALPHA: (commutativity_k2_xboole_0) implies: % 14.71/3.01 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 14.71/3.01 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 14.71/3.01 | % 14.71/3.01 | ALPHA: (d2_xboole_0) implies: % 14.71/3.01 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 14.71/3.01 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 14.71/3.01 | $i(v0) | ~ in(v3, v0) | in(v3, v2)) % 14.71/3.01 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 14.71/3.01 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 14.71/3.01 | $i(v0) | ~ in(v3, v1) | in(v3, v2)) % 14.71/3.01 | % 14.71/3.01 | ALPHA: (d4_relat_1) implies: % 14.71/3.01 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 14.71/3.01 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ % 14.71/3.01 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ % 14.71/3.01 | in(v4, v0) | in(v2, v1)) % 14.71/3.01 | % 14.71/3.01 | ALPHA: (d5_relat_1) implies: % 15.58/3.01 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 15.58/3.01 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ % 15.58/3.01 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ % 15.58/3.01 | in(v4, v0) | in(v2, v1)) % 15.58/3.01 | % 15.58/3.01 | ALPHA: (d6_relat_1) implies: % 15.58/3.01 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | % 15.58/3.01 | ~ relation(v0) | ? [v2: $i] : ? [v3: $i] : (relation_rng(v0) = v3 % 15.58/3.01 | & relation_dom(v0) = v2 & set_union2(v2, v3) = v1 & $i(v3) & $i(v2) % 15.58/3.01 | & $i(v1))) % 15.58/3.01 | % 15.58/3.01 | DELTA: instantiating (t30_relat_1) with fresh symbols all_32_0, all_32_1, % 15.58/3.01 | all_32_2, all_32_3, all_32_4 gives: % 15.58/3.01 | (7) relation_field(all_32_2) = all_32_0 & ordered_pair(all_32_4, all_32_3) % 15.58/3.01 | = all_32_1 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) % 15.58/3.01 | & $i(all_32_4) & relation(all_32_2) & in(all_32_1, all_32_2) & ( ~ % 15.58/3.01 | in(all_32_3, all_32_0) | ~ in(all_32_4, all_32_0)) % 15.58/3.01 | % 15.58/3.01 | ALPHA: (7) implies: % 15.58/3.01 | (8) in(all_32_1, all_32_2) % 15.58/3.01 | (9) relation(all_32_2) % 15.58/3.01 | (10) $i(all_32_4) % 15.58/3.01 | (11) $i(all_32_3) % 15.58/3.01 | (12) $i(all_32_2) % 15.58/3.01 | (13) ordered_pair(all_32_4, all_32_3) = all_32_1 % 15.58/3.01 | (14) relation_field(all_32_2) = all_32_0 % 15.58/3.01 | (15) ~ in(all_32_3, all_32_0) | ~ in(all_32_4, all_32_0) % 15.58/3.01 | % 15.58/3.01 | GROUND_INST: instantiating (6) with all_32_2, all_32_0, simplifying with (9), % 15.58/3.01 | (12), (14) gives: % 15.58/3.02 | (16) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_32_2) = v1 & % 15.58/3.02 | relation_dom(all_32_2) = v0 & set_union2(v0, v1) = all_32_0 & $i(v1) % 15.58/3.02 | & $i(v0) & $i(all_32_0)) % 15.58/3.02 | % 15.58/3.02 | DELTA: instantiating (16) with fresh symbols all_50_0, all_50_1 gives: % 15.58/3.02 | (17) relation_rng(all_32_2) = all_50_0 & relation_dom(all_32_2) = all_50_1 % 15.58/3.02 | & set_union2(all_50_1, all_50_0) = all_32_0 & $i(all_50_0) & % 15.58/3.02 | $i(all_50_1) & $i(all_32_0) % 15.58/3.02 | % 15.58/3.02 | ALPHA: (17) implies: % 15.58/3.02 | (18) $i(all_50_1) % 15.58/3.02 | (19) $i(all_50_0) % 15.58/3.02 | (20) set_union2(all_50_1, all_50_0) = all_32_0 % 15.58/3.02 | (21) relation_dom(all_32_2) = all_50_1 % 15.58/3.02 | (22) relation_rng(all_32_2) = all_50_0 % 15.58/3.02 | % 15.58/3.02 | GROUND_INST: instantiating (1) with all_50_0, all_50_1, all_32_0, simplifying % 15.58/3.02 | with (18), (19), (20) gives: % 15.58/3.02 | (23) set_union2(all_50_0, all_50_1) = all_32_0 & $i(all_32_0) % 15.58/3.02 | % 15.58/3.02 | ALPHA: (23) implies: % 15.58/3.02 | (24) $i(all_32_0) % 15.58/3.02 | (25) set_union2(all_50_0, all_50_1) = all_32_0 % 15.58/3.02 | % 15.58/3.02 | GROUND_INST: instantiating (4) with all_32_2, all_50_1, all_32_4, all_32_3, % 15.58/3.02 | all_32_1, simplifying with (8), (9), (10), (11), (12), (13), % 15.58/3.02 | (18), (21) gives: % 15.58/3.02 | (26) in(all_32_4, all_50_1) % 15.58/3.02 | % 15.58/3.02 | GROUND_INST: instantiating (5) with all_32_2, all_50_0, all_32_3, all_32_4, % 15.58/3.02 | all_32_1, simplifying with (8), (9), (10), (11), (12), (13), % 15.58/3.02 | (19), (22) gives: % 15.58/3.02 | (27) in(all_32_3, all_50_0) % 15.58/3.02 | % 15.58/3.02 | GROUND_INST: instantiating (2) with all_50_0, all_50_1, all_32_0, all_32_3, % 15.58/3.02 | simplifying with (11), (18), (19), (24), (25), (27) gives: % 15.58/3.02 | (28) in(all_32_3, all_32_0) % 15.58/3.02 | % 15.58/3.02 | GROUND_INST: instantiating (3) with all_50_0, all_50_1, all_32_0, all_32_4, % 15.58/3.02 | simplifying with (10), (18), (19), (24), (25), (26) gives: % 15.58/3.02 | (29) in(all_32_4, all_32_0) % 15.58/3.02 | % 15.58/3.02 | BETA: splitting (15) gives: % 15.58/3.02 | % 15.58/3.02 | Case 1: % 15.58/3.02 | | % 15.58/3.02 | | (30) ~ in(all_32_3, all_32_0) % 15.58/3.02 | | % 15.58/3.02 | | PRED_UNIFY: (28), (30) imply: % 15.58/3.02 | | (31) $false % 15.58/3.02 | | % 15.58/3.02 | | CLOSE: (31) is inconsistent. % 15.58/3.02 | | % 15.58/3.02 | Case 2: % 15.58/3.02 | | % 15.58/3.02 | | (32) ~ in(all_32_4, all_32_0) % 15.58/3.02 | | % 15.58/3.02 | | PRED_UNIFY: (29), (32) imply: % 15.58/3.02 | | (33) $false % 15.58/3.02 | | % 15.58/3.02 | | CLOSE: (33) is inconsistent. % 15.58/3.02 | | % 15.58/3.02 | End of split % 15.58/3.02 | % 15.58/3.02 End of proof % 15.58/3.02 % SZS output end Proof for theBenchmark % 15.58/3.03 % 15.58/3.03 2387ms %------------------------------------------------------------------------------