%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU037+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n032.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 17:42:21 EDT 2023 % Result : Theorem 88.22s 12.82s % Output : Proof 90.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU037+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.32 % Computer : n032.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Wed Aug 23 13:19:25 EDT 2023 % 0.12/0.32 % CPUTime : % 0.17/0.56 ________ _____ % 0.17/0.56 ___ __ \_________(_)________________________________ % 0.17/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.56 % 0.17/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.56 (2023-06-19) % 0.17/0.56 % 0.17/0.56 (c) Philipp Rümmer, 2009-2023 % 0.17/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.56 Amanda Stjerna. % 0.17/0.56 Free software under BSD-3-Clause. % 0.17/0.56 % 0.17/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.56 % 0.17/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.17/0.57 Running up to 7 provers in parallel. % 0.17/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.54/1.06 Prover 1: Preprocessing ... % 2.54/1.07 Prover 4: Preprocessing ... % 3.04/1.11 Prover 3: Preprocessing ... % 3.04/1.11 Prover 2: Preprocessing ... % 3.04/1.11 Prover 0: Preprocessing ... % 3.04/1.11 Prover 5: Preprocessing ... % 3.04/1.11 Prover 6: Preprocessing ... % 6.51/1.64 Prover 1: Warning: ignoring some quantifiers % 6.51/1.66 Prover 5: Proving ... % 6.51/1.68 Prover 1: Constructing countermodel ... % 6.51/1.70 Prover 3: Warning: ignoring some quantifiers % 7.11/1.72 Prover 3: Constructing countermodel ... % 7.11/1.76 Prover 6: Proving ... % 7.56/1.80 Prover 2: Proving ... % 8.52/2.08 Prover 4: Warning: ignoring some quantifiers % 9.29/2.14 Prover 4: Constructing countermodel ... % 10.62/2.22 Prover 3: gave up % 10.62/2.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.01/2.35 Prover 7: Preprocessing ... % 11.63/2.38 Prover 0: Proving ... % 12.03/2.49 Prover 7: Warning: ignoring some quantifiers % 12.03/2.51 Prover 7: Constructing countermodel ... % 12.67/2.52 Prover 1: gave up % 12.67/2.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.67/2.58 Prover 8: Preprocessing ... % 13.82/2.78 Prover 8: Warning: ignoring some quantifiers % 13.82/2.82 Prover 8: Constructing countermodel ... % 16.17/3.00 Prover 7: gave up % 16.17/3.02 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 16.83/3.11 Prover 9: Preprocessing ... % 18.45/3.35 Prover 8: gave up % 18.45/3.36 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 19.13/3.42 Prover 10: Preprocessing ... % 19.13/3.47 Prover 9: Warning: ignoring some quantifiers % 19.13/3.48 Prover 9: Constructing countermodel ... % 19.83/3.52 Prover 10: Warning: ignoring some quantifiers % 19.83/3.53 Prover 10: Constructing countermodel ... % 21.32/3.74 Prover 10: gave up % 21.32/3.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 21.32/3.79 Prover 11: Preprocessing ... % 24.37/4.13 Prover 11: Warning: ignoring some quantifiers % 24.37/4.15 Prover 11: Constructing countermodel ... % 57.12/8.47 Prover 2: stopped % 57.12/8.48 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 57.56/8.54 Prover 12: Preprocessing ... % 57.97/8.70 Prover 12: Proving ... % 70.67/10.35 Prover 12: stopped % 70.67/10.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 70.67/10.43 Prover 13: Preprocessing ... % 71.64/10.50 Prover 13: Warning: ignoring some quantifiers % 71.64/10.51 Prover 13: Constructing countermodel ... % 88.22/12.80 Prover 13: Found proof (size 154) % 88.22/12.81 Prover 13: proved (2437ms) % 88.22/12.81 Prover 9: stopped % 88.22/12.81 Prover 0: stopped % 88.22/12.81 Prover 5: stopped % 88.22/12.81 Prover 6: stopped % 88.22/12.81 Prover 4: stopped % 88.22/12.82 Prover 11: stopped % 88.22/12.82 % 88.22/12.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 88.22/12.82 % 88.22/12.83 % SZS output start Proof for theBenchmark % 88.22/12.84 Assumptions after simplification: % 88.22/12.84 --------------------------------- % 88.22/12.84 % 88.22/12.84 (cc1_funct_1) % 88.22/12.84 ! [v0: $i] : ( ~ $i(v0) | ~ empty(v0) | function(v0)) % 88.22/12.84 % 88.22/12.84 (cc1_relat_1) % 88.22/12.84 ! [v0: $i] : ( ~ $i(v0) | ~ empty(v0) | relation(v0)) % 88.22/12.84 % 88.22/12.84 (commutativity_k3_xboole_0) % 89.60/12.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 89.60/12.87 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) & ? % 89.60/12.87 [v0: $i] : ? [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : % 89.60/12.87 (set_intersection2(v1, v0) = v2 & set_intersection2(v0, v1) = v2 & $i(v2))) % 89.60/12.87 % 90.12/12.87 (dt_k7_relat_1) % 90.12/12.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0, % 90.12/12.87 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | relation(v2)) & ? % 90.12/12.87 [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v2: % 90.12/12.87 $i] : (relation_dom_restriction(v1, v0) = v2 & $i(v2) & relation(v2))) % 90.12/12.87 % 90.12/12.87 (fc4_funct_1) % 90.12/12.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0, % 90.12/12.87 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) | % 90.12/12.87 relation(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 90.12/12.87 (relation_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 90.12/12.87 relation(v0) | ~ function(v0) | function(v2)) & ? [v0: $i] : ! [v1: $i] : % 90.12/12.87 ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ? [v2: $i] : % 90.12/12.87 (relation_dom_restriction(v1, v0) = v2 & $i(v2) & relation(v2) & % 90.12/12.87 function(v2))) % 90.12/12.87 % 90.12/12.87 (fc4_relat_1) % 90.12/12.87 $i(empty_set) & relation(empty_set) & empty(empty_set) % 90.12/12.87 % 90.12/12.87 (fc5_relat_1) % 90.12/12.88 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ % 90.12/12.88 relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 90.12/12.88 relation(v0) | empty(v0) | ? [v1: $i] : (relation_dom(v0) = v1 & $i(v1) & % 90.12/12.88 ~ empty(v1))) % 90.12/12.88 % 90.12/12.88 (fc7_relat_1) % 90.12/12.88 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ % 90.12/12.88 empty(v0) | relation(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 90.12/12.88 (relation_dom(v0) = v1) | ~ $i(v0) | ~ empty(v0) | empty(v1)) & ! [v0: % 90.12/12.88 $i] : ( ~ $i(v0) | ~ empty(v0) | ? [v1: $i] : (relation_dom(v0) = v1 & % 90.12/12.88 $i(v1) & relation(v1) & empty(v1))) % 90.12/12.88 % 90.12/12.88 (rc1_funct_1) % 90.12/12.88 ? [v0: $i] : ($i(v0) & relation(v0) & function(v0)) % 90.12/12.88 % 90.12/12.88 (rc1_relat_1) % 90.12/12.88 ? [v0: $i] : ($i(v0) & relation(v0) & empty(v0)) % 90.12/12.88 % 90.12/12.88 (rc1_xboole_0) % 90.12/12.88 ? [v0: $i] : ($i(v0) & empty(v0)) % 90.12/12.88 % 90.12/12.88 (rc2_funct_1) % 90.12/12.88 ? [v0: $i] : ($i(v0) & relation(v0) & function(v0) & empty(v0)) % 90.12/12.88 % 90.12/12.88 (t68_funct_1) % 90.12/12.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 90.12/12.88 $i] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ % 90.12/12.88 (set_intersection2(v4, v0) = v5) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 90.12/12.88 relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v6: % 90.12/12.88 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 90.12/12.88 (relation_dom_restriction(v3, v0) = v6 & $i(v7) & $i(v6) & ( ~ (v6 = v1) | % 90.12/12.88 (v5 = v2 & ! [v10: $i] : ! [v11: $i] : ( ~ (apply(v1, v10) = v11) | ~ % 90.12/12.88 $i(v10) | ~ in(v10, v2) | (apply(v3, v10) = v11 & $i(v11))))) & ( ~ % 90.12/12.88 (v5 = v2) | v6 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) % 90.12/12.88 = v8 & $i(v9) & $i(v8) & in(v7, v2))))) & ? [v0: $i] : ! [v1: $i] : % 90.12/12.88 ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ? [v2: $i] : % 90.12/12.88 (relation_dom(v1) = v2 & $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ relation(v3) % 90.12/12.89 | ~ function(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 90.12/12.89 $i] : ? [v8: $i] : ? [v9: $i] : (relation_dom(v3) = v5 & % 90.12/12.89 relation_dom_restriction(v3, v0) = v4 & set_intersection2(v5, v0) = v6 % 90.12/12.89 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~ (v6 = v2) | v4 = v1 | ( ~ % 90.12/12.89 (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & $i(v9) & % 90.12/12.89 $i(v8) & in(v7, v2))) & ( ~ (v4 = v1) | (v6 = v2 & ! [v10: $i] : % 90.12/12.89 ( ~ $i(v10) | ~ in(v10, v2) | ? [v11: $i] : (apply(v3, v10) = % 90.12/12.89 v11 & apply(v1, v10) = v11 & $i(v11))))))))) % 90.12/12.89 % 90.12/12.89 (t6_boole) % 90.12/12.89 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0)) % 90.12/12.89 % 90.12/12.89 (t71_funct_1) % 90.12/12.89 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 90.12/12.89 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & apply(v5, v1) = v6 & % 90.12/12.89 apply(v2, v1) = v7 & relation_dom(v2) = v3 & relation_dom_restriction(v2, % 90.12/12.89 v0) = v5 & set_intersection2(v3, v0) = v4 & $i(v7) & $i(v6) & $i(v5) & % 90.12/12.89 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & relation(v2) & function(v2) & % 90.12/12.89 in(v1, v4)) % 90.12/12.89 % 90.12/12.89 (t7_boole) % 90.12/12.89 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ empty(v1) | ~ in(v0, % 90.12/12.89 v1)) % 90.12/12.89 % 90.12/12.89 (t8_boole) % 90.12/12.89 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ empty(v1) | % 90.12/12.89 ~ empty(v0)) % 90.12/12.89 % 90.12/12.89 (function-axioms) % 90.12/12.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 90.12/12.89 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 90.12/12.89 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) % 90.12/12.89 = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : ! % 90.12/12.89 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, % 90.12/12.89 v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 90.12/12.89 $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 90.12/12.89 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 90.12/12.89 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 90.12/12.89 % 90.12/12.89 Further assumptions not needed in the proof: % 90.12/12.89 -------------------------------------------- % 90.12/12.89 antisymmetry_r2_hidden, cc2_funct_1, existence_m1_subset_1, fc12_relat_1, % 90.12/12.89 fc13_relat_1, fc1_relat_1, fc1_subset_1, fc1_xboole_0, idempotence_k3_xboole_0, % 90.12/12.89 rc1_subset_1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, % 90.12/12.89 reflexivity_r1_tarski, t1_subset, t2_boole, t2_subset, t3_subset, t4_subset, % 90.12/12.89 t5_subset % 90.12/12.89 % 90.12/12.89 Those formulas are unsatisfiable: % 90.12/12.89 --------------------------------- % 90.12/12.89 % 90.12/12.89 Begin of proof % 90.12/12.89 | % 90.12/12.89 | ALPHA: (commutativity_k3_xboole_0) implies: % 90.12/12.89 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, % 90.12/12.89 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = % 90.12/12.89 | v2 & $i(v2))) % 90.12/12.89 | % 90.12/12.89 | ALPHA: (dt_k7_relat_1) implies: % 90.12/12.89 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 90.12/12.89 | (relation_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 90.12/12.89 | relation(v0) | relation(v2)) % 90.12/12.89 | % 90.12/12.89 | ALPHA: (fc4_funct_1) implies: % 90.12/12.90 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 90.12/12.90 | (relation_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 90.12/12.90 | relation(v0) | ~ function(v0) | function(v2)) % 90.12/12.90 | % 90.12/12.90 | ALPHA: (fc4_relat_1) implies: % 90.12/12.90 | (4) empty(empty_set) % 90.12/12.90 | % 90.12/12.90 | ALPHA: (fc5_relat_1) implies: % 90.12/12.90 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ relation(v0) | empty(v0) | ? [v1: $i] : % 90.12/12.90 | (relation_dom(v0) = v1 & $i(v1) & ~ empty(v1))) % 90.12/12.90 | % 90.12/12.90 | ALPHA: (fc7_relat_1) implies: % 90.12/12.90 | (6) ! [v0: $i] : ( ~ $i(v0) | ~ empty(v0) | ? [v1: $i] : % 90.12/12.90 | (relation_dom(v0) = v1 & $i(v1) & relation(v1) & empty(v1))) % 90.12/12.90 | % 90.12/12.90 | ALPHA: (t68_funct_1) implies: % 90.12/12.90 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 90.12/12.90 | ! [v5: $i] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | % 90.12/12.90 | ~ (set_intersection2(v4, v0) = v5) | ~ $i(v3) | ~ $i(v1) | ~ % 90.12/12.90 | $i(v0) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ % 90.12/12.90 | function(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 90.12/12.90 | : (relation_dom_restriction(v3, v0) = v6 & $i(v7) & $i(v6) & ( ~ (v6 % 90.12/12.90 | = v1) | (v5 = v2 & ! [v10: $i] : ! [v11: $i] : ( ~ (apply(v1, % 90.12/12.90 | v10) = v11) | ~ $i(v10) | ~ in(v10, v2) | (apply(v3, % 90.12/12.90 | v10) = v11 & $i(v11))))) & ( ~ (v5 = v2) | v6 = v1 | ( ~ % 90.12/12.90 | (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & $i(v9) & % 90.12/12.90 | $i(v8) & in(v7, v2))))) % 90.12/12.90 | % 90.12/12.90 | ALPHA: (t6_boole) implies: % 90.12/12.90 | (8) $i(empty_set) % 90.12/12.90 | (9) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0)) % 90.12/12.90 | % 90.12/12.90 | ALPHA: (function-axioms) implies: % 90.12/12.90 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 90.12/12.90 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 90.12/12.90 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 90.12/12.90 | (relation_dom_restriction(v3, v2) = v1) | ~ % 90.12/12.90 | (relation_dom_restriction(v3, v2) = v0)) % 90.12/12.90 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 90.12/12.90 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 90.12/12.90 | % 90.12/12.90 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_31_0 gives: % 90.12/12.90 | (13) $i(all_31_0) & empty(all_31_0) % 90.12/12.90 | % 90.12/12.90 | ALPHA: (13) implies: % 90.12/12.90 | (14) empty(all_31_0) % 90.12/12.90 | (15) $i(all_31_0) % 90.12/12.90 | % 90.12/12.90 | DELTA: instantiating (rc1_funct_1) with fresh symbol all_38_0 gives: % 90.12/12.90 | (16) $i(all_38_0) & relation(all_38_0) & function(all_38_0) % 90.12/12.90 | % 90.12/12.90 | ALPHA: (16) implies: % 90.12/12.90 | (17) function(all_38_0) % 90.12/12.90 | (18) relation(all_38_0) % 90.12/12.90 | (19) $i(all_38_0) % 90.12/12.90 | % 90.12/12.90 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_41_0 gives: % 90.12/12.90 | (20) $i(all_41_0) & relation(all_41_0) & empty(all_41_0) % 90.12/12.90 | % 90.12/12.90 | ALPHA: (20) implies: % 90.12/12.90 | (21) empty(all_41_0) % 90.12/12.90 | (22) $i(all_41_0) % 90.12/12.90 | % 90.12/12.90 | DELTA: instantiating (rc2_funct_1) with fresh symbol all_43_0 gives: % 90.12/12.90 | (23) $i(all_43_0) & relation(all_43_0) & function(all_43_0) & % 90.12/12.90 | empty(all_43_0) % 90.12/12.90 | % 90.12/12.91 | ALPHA: (23) implies: % 90.12/12.91 | (24) empty(all_43_0) % 90.12/12.91 | (25) $i(all_43_0) % 90.12/12.91 | % 90.12/12.91 | DELTA: instantiating (t71_funct_1) with fresh symbols all_55_0, all_55_1, % 90.12/12.91 | all_55_2, all_55_3, all_55_4, all_55_5, all_55_6, all_55_7 gives: % 90.12/12.91 | (26) ~ (all_55_0 = all_55_1) & apply(all_55_2, all_55_6) = all_55_1 & % 90.12/12.91 | apply(all_55_5, all_55_6) = all_55_0 & relation_dom(all_55_5) = % 90.12/12.91 | all_55_4 & relation_dom_restriction(all_55_5, all_55_7) = all_55_2 & % 90.12/12.91 | set_intersection2(all_55_4, all_55_7) = all_55_3 & $i(all_55_0) & % 90.12/12.91 | $i(all_55_1) & $i(all_55_2) & $i(all_55_3) & $i(all_55_4) & % 90.12/12.91 | $i(all_55_5) & $i(all_55_6) & $i(all_55_7) & relation(all_55_5) & % 90.12/12.91 | function(all_55_5) & in(all_55_6, all_55_3) % 90.12/12.91 | % 90.12/12.91 | ALPHA: (26) implies: % 90.12/12.91 | (27) ~ (all_55_0 = all_55_1) % 90.12/12.91 | (28) in(all_55_6, all_55_3) % 90.12/12.91 | (29) function(all_55_5) % 90.12/12.91 | (30) relation(all_55_5) % 90.12/12.91 | (31) $i(all_55_7) % 90.12/12.91 | (32) $i(all_55_6) % 90.12/12.91 | (33) $i(all_55_5) % 90.12/12.91 | (34) $i(all_55_4) % 90.12/12.91 | (35) set_intersection2(all_55_4, all_55_7) = all_55_3 % 90.12/12.91 | (36) relation_dom_restriction(all_55_5, all_55_7) = all_55_2 % 90.12/12.91 | (37) relation_dom(all_55_5) = all_55_4 % 90.12/12.91 | (38) apply(all_55_5, all_55_6) = all_55_0 % 90.12/12.91 | (39) apply(all_55_2, all_55_6) = all_55_1 % 90.12/12.91 | % 90.12/12.91 | GROUND_INST: instantiating (6) with empty_set, simplifying with (4), (8) % 90.12/12.91 | gives: % 90.12/12.91 | (40) ? [v0: $i] : (relation_dom(empty_set) = v0 & $i(v0) & relation(v0) & % 90.12/12.91 | empty(v0)) % 90.12/12.91 | % 90.12/12.91 | GROUND_INST: instantiating (cc1_relat_1) with all_31_0, simplifying with (14), % 90.12/12.91 | (15) gives: % 90.12/12.91 | (41) relation(all_31_0) % 90.12/12.91 | % 90.12/12.91 | GROUND_INST: instantiating (cc1_funct_1) with all_31_0, simplifying with (14), % 90.12/12.91 | (15) gives: % 90.12/12.91 | (42) function(all_31_0) % 90.12/12.91 | % 90.12/12.91 | GROUND_INST: instantiating (6) with all_31_0, simplifying with (14), (15) % 90.12/12.91 | gives: % 90.12/12.91 | (43) ? [v0: $i] : (relation_dom(all_31_0) = v0 & $i(v0) & relation(v0) & % 90.12/12.91 | empty(v0)) % 90.12/12.91 | % 90.12/12.91 | GROUND_INST: instantiating (t8_boole) with all_31_0, all_41_0, simplifying % 90.12/12.91 | with (14), (15), (21), (22) gives: % 90.12/12.91 | (44) all_41_0 = all_31_0 % 90.12/12.91 | % 90.12/12.91 | GROUND_INST: instantiating (6) with all_41_0, simplifying with (21), (22) % 90.12/12.91 | gives: % 90.12/12.91 | (45) ? [v0: $i] : (relation_dom(all_41_0) = v0 & $i(v0) & relation(v0) & % 90.12/12.91 | empty(v0)) % 90.12/12.91 | % 90.12/12.91 | GROUND_INST: instantiating (t8_boole) with all_41_0, all_43_0, simplifying % 90.12/12.91 | with (21), (22), (24), (25) gives: % 90.12/12.91 | (46) all_43_0 = all_41_0 % 90.12/12.91 | % 90.12/12.91 | GROUND_INST: instantiating (9) with all_43_0, simplifying with (24), (25) % 90.12/12.91 | gives: % 90.12/12.91 | (47) all_43_0 = empty_set % 90.12/12.91 | % 90.12/12.91 | GROUND_INST: instantiating (6) with all_43_0, simplifying with (24), (25) % 90.12/12.91 | gives: % 90.12/12.92 | (48) ? [v0: $i] : (relation_dom(all_43_0) = v0 & $i(v0) & relation(v0) & % 90.12/12.92 | empty(v0)) % 90.12/12.92 | % 90.12/12.92 | GROUND_INST: instantiating (5) with all_38_0, simplifying with (18), (19) % 90.12/12.92 | gives: % 90.12/12.92 | (49) empty(all_38_0) | ? [v0: $i] : (relation_dom(all_38_0) = v0 & $i(v0) % 90.12/12.92 | & ~ empty(v0)) % 90.12/12.92 | % 90.12/12.92 | GROUND_INST: instantiating (1) with all_55_4, all_55_7, all_55_3, simplifying % 90.12/12.92 | with (31), (34), (35) gives: % 90.12/12.92 | (50) set_intersection2(all_55_7, all_55_4) = all_55_3 & $i(all_55_3) % 90.12/12.92 | % 90.12/12.92 | ALPHA: (50) implies: % 90.12/12.92 | (51) $i(all_55_3) % 90.12/12.92 | % 90.12/12.92 | GROUND_INST: instantiating (3) with all_55_5, all_55_7, all_55_2, simplifying % 90.12/12.92 | with (29), (30), (31), (33), (36) gives: % 90.12/12.92 | (52) function(all_55_2) % 90.12/12.92 | % 90.12/12.92 | GROUND_INST: instantiating (2) with all_55_5, all_55_7, all_55_2, simplifying % 90.12/12.92 | with (30), (31), (33), (36) gives: % 90.12/12.92 | (53) relation(all_55_2) % 90.12/12.92 | % 90.12/12.92 | GROUND_INST: instantiating (7) with all_55_7, all_55_5, all_55_4, all_55_5, % 90.12/12.92 | all_55_4, all_55_3, simplifying with (29), (30), (31), (33), % 90.12/12.92 | (35), (37) gives: % 90.12/12.92 | (54) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 90.12/12.92 | (relation_dom_restriction(all_55_5, all_55_7) = v0 & $i(v1) & $i(v0) & % 90.12/12.92 | ( ~ (v0 = all_55_5) | (all_55_3 = all_55_4 & ! [v4: $i] : ! [v5: % 90.12/12.92 | $i] : ( ~ (apply(all_55_5, v4) = v5) | ~ $i(v4) | ~ in(v4, % 90.12/12.92 | all_55_4) | $i(v5)))) & ( ~ (all_55_3 = all_55_4) | v0 = % 90.12/12.92 | all_55_5 | ( ~ (v3 = v2) & apply(all_55_5, v1) = v3 & % 90.12/12.92 | apply(all_55_5, v1) = v2 & $i(v3) & $i(v2) & in(v1, all_55_4)))) % 90.12/12.92 | % 90.12/12.92 | COMBINE_EQS: (46), (47) imply: % 90.12/12.92 | (55) all_41_0 = empty_set % 90.12/12.92 | % 90.12/12.92 | SIMP: (55) implies: % 90.12/12.92 | (56) all_41_0 = empty_set % 90.12/12.92 | % 90.12/12.92 | COMBINE_EQS: (44), (56) imply: % 90.12/12.92 | (57) all_31_0 = empty_set % 90.12/12.92 | % 90.12/12.92 | SIMP: (57) implies: % 90.12/12.92 | (58) all_31_0 = empty_set % 90.12/12.92 | % 90.12/12.92 | DELTA: instantiating (48) with fresh symbol all_67_0 gives: % 90.12/12.92 | (59) relation_dom(all_43_0) = all_67_0 & $i(all_67_0) & relation(all_67_0) % 90.12/12.92 | & empty(all_67_0) % 90.12/12.92 | % 90.12/12.92 | ALPHA: (59) implies: % 90.12/12.92 | (60) relation_dom(all_43_0) = all_67_0 % 90.12/12.92 | % 90.12/12.92 | DELTA: instantiating (40) with fresh symbol all_69_0 gives: % 90.12/12.92 | (61) relation_dom(empty_set) = all_69_0 & $i(all_69_0) & relation(all_69_0) % 90.12/12.92 | & empty(all_69_0) % 90.12/12.92 | % 90.12/12.92 | ALPHA: (61) implies: % 90.12/12.92 | (62) empty(all_69_0) % 90.12/12.92 | (63) $i(all_69_0) % 90.12/12.92 | (64) relation_dom(empty_set) = all_69_0 % 90.12/12.92 | % 90.12/12.92 | DELTA: instantiating (45) with fresh symbol all_71_0 gives: % 90.12/12.92 | (65) relation_dom(all_41_0) = all_71_0 & $i(all_71_0) & relation(all_71_0) % 90.12/12.92 | & empty(all_71_0) % 90.12/12.92 | % 90.12/12.92 | ALPHA: (65) implies: % 90.12/12.92 | (66) relation_dom(all_41_0) = all_71_0 % 90.12/12.92 | % 90.12/12.92 | DELTA: instantiating (43) with fresh symbol all_73_0 gives: % 90.12/12.92 | (67) relation_dom(all_31_0) = all_73_0 & $i(all_73_0) & relation(all_73_0) % 90.12/12.92 | & empty(all_73_0) % 90.12/12.92 | % 90.12/12.92 | ALPHA: (67) implies: % 90.12/12.92 | (68) relation_dom(all_31_0) = all_73_0 % 90.12/12.92 | % 90.12/12.92 | DELTA: instantiating (54) with fresh symbols all_75_0, all_75_1, all_75_2, % 90.12/12.92 | all_75_3 gives: % 90.12/12.93 | (69) relation_dom_restriction(all_55_5, all_55_7) = all_75_3 & $i(all_75_2) % 90.12/12.93 | & $i(all_75_3) & ( ~ (all_75_3 = all_55_5) | (all_55_3 = all_55_4 & ! % 90.12/12.93 | [v0: $i] : ! [v1: $i] : ( ~ (apply(all_55_5, v0) = v1) | ~ % 90.12/12.93 | $i(v0) | ~ in(v0, all_55_4) | $i(v1)))) & ( ~ (all_55_3 = % 90.12/12.93 | all_55_4) | all_75_3 = all_55_5 | ( ~ (all_75_0 = all_75_1) & % 90.12/12.93 | apply(all_55_5, all_75_2) = all_75_0 & apply(all_55_5, all_75_2) = % 90.12/12.93 | all_75_1 & $i(all_75_0) & $i(all_75_1) & in(all_75_2, all_55_4))) % 90.12/12.93 | % 90.12/12.93 | ALPHA: (69) implies: % 90.12/12.93 | (70) $i(all_75_3) % 90.12/12.93 | (71) relation_dom_restriction(all_55_5, all_55_7) = all_75_3 % 90.12/12.93 | % 90.12/12.93 | REDUCE: (47), (60) imply: % 90.12/12.93 | (72) relation_dom(empty_set) = all_67_0 % 90.12/12.93 | % 90.12/12.93 | REDUCE: (56), (66) imply: % 90.12/12.93 | (73) relation_dom(empty_set) = all_71_0 % 90.12/12.93 | % 90.12/12.93 | REDUCE: (58), (68) imply: % 90.12/12.93 | (74) relation_dom(empty_set) = all_73_0 % 90.12/12.93 | % 90.12/12.93 | REDUCE: (41), (58) imply: % 90.12/12.93 | (75) relation(empty_set) % 90.12/12.93 | % 90.40/12.93 | REDUCE: (42), (58) imply: % 90.40/12.93 | (76) function(empty_set) % 90.40/12.93 | % 90.40/12.93 | GROUND_INST: instantiating (11) with all_55_2, all_75_3, all_55_7, all_55_5, % 90.40/12.93 | simplifying with (36), (71) gives: % 90.40/12.93 | (77) all_75_3 = all_55_2 % 90.40/12.93 | % 90.40/12.93 | GROUND_INST: instantiating (10) with all_69_0, all_71_0, empty_set, % 90.40/12.93 | simplifying with (64), (73) gives: % 90.40/12.93 | (78) all_71_0 = all_69_0 % 90.40/12.93 | % 90.40/12.93 | GROUND_INST: instantiating (10) with all_71_0, all_73_0, empty_set, % 90.40/12.93 | simplifying with (73), (74) gives: % 90.40/12.93 | (79) all_73_0 = all_71_0 % 90.40/12.93 | % 90.40/12.93 | GROUND_INST: instantiating (10) with all_67_0, all_73_0, empty_set, % 90.40/12.93 | simplifying with (72), (74) gives: % 90.40/12.93 | (80) all_73_0 = all_67_0 % 90.40/12.93 | % 90.40/12.93 | COMBINE_EQS: (79), (80) imply: % 90.40/12.93 | (81) all_71_0 = all_67_0 % 90.40/12.93 | % 90.40/12.93 | SIMP: (81) implies: % 90.40/12.93 | (82) all_71_0 = all_67_0 % 90.40/12.93 | % 90.40/12.93 | COMBINE_EQS: (78), (82) imply: % 90.40/12.93 | (83) all_69_0 = all_67_0 % 90.40/12.93 | % 90.40/12.93 | REDUCE: (70), (77) imply: % 90.40/12.93 | (84) $i(all_55_2) % 90.40/12.93 | % 90.40/12.93 | REDUCE: (63), (83) imply: % 90.40/12.93 | (85) $i(all_67_0) % 90.40/12.93 | % 90.40/12.93 | REDUCE: (62), (83) imply: % 90.40/12.93 | (86) empty(all_67_0) % 90.40/12.93 | % 90.40/12.93 | GROUND_INST: instantiating (9) with all_67_0, simplifying with (85), (86) % 90.40/12.93 | gives: % 90.40/12.93 | (87) all_67_0 = empty_set % 90.40/12.93 | % 90.40/12.93 | GROUND_INST: instantiating (5) with all_55_2, simplifying with (53), (84) % 90.40/12.93 | gives: % 90.40/12.93 | (88) empty(all_55_2) | ? [v0: $i] : (relation_dom(all_55_2) = v0 & $i(v0) % 90.40/12.93 | & ~ empty(v0)) % 90.40/12.93 | % 90.40/12.93 | GROUND_INST: instantiating (7) with all_55_7, empty_set, all_67_0, all_55_5, % 90.40/12.93 | all_55_4, all_55_3, simplifying with (8), (29), (30), (31), (33), % 90.40/12.93 | (35), (37), (72), (75), (76) gives: % 90.40/12.94 | (89) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 90.40/12.94 | (relation_dom_restriction(all_55_5, all_55_7) = v0 & $i(v1) & $i(v0) & % 90.40/12.94 | ( ~ (v0 = empty_set) | (all_67_0 = all_55_3 & ! [v4: $i] : ! [v5: % 90.40/12.94 | $i] : ( ~ (apply(empty_set, v4) = v5) | ~ $i(v4) | ~ in(v4, % 90.40/12.94 | all_55_3) | (apply(all_55_5, v4) = v5 & $i(v5))))) & ( ~ % 90.40/12.94 | (all_67_0 = all_55_3) | v0 = empty_set | ( ~ (v3 = v2) & % 90.40/12.94 | apply(all_55_5, v1) = v3 & apply(empty_set, v1) = v2 & $i(v3) & % 90.40/12.94 | $i(v2) & in(v1, all_55_3)))) % 90.40/12.94 | % 90.40/12.94 | DELTA: instantiating (89) with fresh symbols all_89_0, all_89_1, all_89_2, % 90.40/12.94 | all_89_3 gives: % 90.40/12.94 | (90) relation_dom_restriction(all_55_5, all_55_7) = all_89_3 & $i(all_89_2) % 90.40/12.94 | & $i(all_89_3) & ( ~ (all_89_3 = empty_set) | (all_67_0 = all_55_3 & % 90.40/12.94 | ! [v0: $i] : ! [v1: $i] : ( ~ (apply(empty_set, v0) = v1) | ~ % 90.40/12.94 | $i(v0) | ~ in(v0, all_55_3) | (apply(all_55_5, v0) = v1 & % 90.40/12.94 | $i(v1))))) & ( ~ (all_67_0 = all_55_3) | all_89_3 = empty_set % 90.40/12.94 | | ( ~ (all_89_0 = all_89_1) & apply(all_55_5, all_89_2) = all_89_0 & % 90.40/12.94 | apply(empty_set, all_89_2) = all_89_1 & $i(all_89_0) & % 90.40/12.94 | $i(all_89_1) & in(all_89_2, all_55_3))) % 90.40/12.94 | % 90.40/12.94 | ALPHA: (90) implies: % 90.40/12.94 | (91) $i(all_89_3) % 90.40/12.94 | (92) relation_dom_restriction(all_55_5, all_55_7) = all_89_3 % 90.40/12.94 | (93) ~ (all_89_3 = empty_set) | (all_67_0 = all_55_3 & ! [v0: $i] : ! % 90.40/12.94 | [v1: $i] : ( ~ (apply(empty_set, v0) = v1) | ~ $i(v0) | ~ in(v0, % 90.40/12.94 | all_55_3) | (apply(all_55_5, v0) = v1 & $i(v1)))) % 90.40/12.94 | % 90.40/12.94 | GROUND_INST: instantiating (11) with all_55_2, all_89_3, all_55_7, all_55_5, % 90.40/12.94 | simplifying with (36), (92) gives: % 90.40/12.94 | (94) all_89_3 = all_55_2 % 90.40/12.94 | % 90.40/12.94 | BETA: splitting (49) gives: % 90.40/12.94 | % 90.40/12.94 | Case 1: % 90.40/12.94 | | % 90.40/12.94 | | (95) empty(all_38_0) % 90.40/12.94 | | % 90.40/12.94 | | BETA: splitting (88) gives: % 90.40/12.94 | | % 90.40/12.94 | | Case 1: % 90.40/12.94 | | | % 90.40/12.94 | | | (96) empty(all_55_2) % 90.40/12.94 | | | % 90.40/12.94 | | | BETA: splitting (93) gives: % 90.40/12.94 | | | % 90.40/12.94 | | | Case 1: % 90.40/12.94 | | | | % 90.40/12.94 | | | | (97) ~ (all_89_3 = empty_set) % 90.40/12.94 | | | | % 90.40/12.94 | | | | REDUCE: (94), (97) imply: % 90.40/12.94 | | | | (98) ~ (all_55_2 = empty_set) % 90.40/12.94 | | | | % 90.40/12.94 | | | | GROUND_INST: instantiating (t8_boole) with all_38_0, all_55_2, % 90.40/12.94 | | | | simplifying with (19), (84), (95), (96) gives: % 90.40/12.94 | | | | (99) all_55_2 = all_38_0 % 90.40/12.94 | | | | % 90.40/12.94 | | | | GROUND_INST: instantiating (9) with all_55_2, simplifying with (84), % 90.40/12.94 | | | | (96) gives: % 90.40/12.94 | | | | (100) all_55_2 = empty_set % 90.40/12.94 | | | | % 90.40/12.94 | | | | COMBINE_EQS: (99), (100) imply: % 90.40/12.94 | | | | (101) all_38_0 = empty_set % 90.40/12.94 | | | | % 90.40/12.94 | | | | REDUCE: (98), (100) imply: % 90.40/12.94 | | | | (102) $false % 90.40/12.94 | | | | % 90.40/12.94 | | | | CLOSE: (102) is inconsistent. % 90.40/12.94 | | | | % 90.40/12.94 | | | Case 2: % 90.40/12.94 | | | | % 90.40/12.94 | | | | (103) all_89_3 = empty_set % 90.40/12.94 | | | | (104) all_67_0 = all_55_3 & ! [v0: $i] : ! [v1: $i] : ( ~ % 90.40/12.94 | | | | (apply(empty_set, v0) = v1) | ~ $i(v0) | ~ in(v0, all_55_3) % 90.40/12.94 | | | | | (apply(all_55_5, v0) = v1 & $i(v1))) % 90.40/12.94 | | | | % 90.40/12.94 | | | | ALPHA: (104) implies: % 90.40/12.94 | | | | (105) all_67_0 = all_55_3 % 90.40/12.94 | | | | % 90.40/12.94 | | | | COMBINE_EQS: (94), (103) imply: % 90.40/12.94 | | | | (106) all_55_2 = empty_set % 90.40/12.94 | | | | % 90.40/12.94 | | | | COMBINE_EQS: (87), (105) imply: % 90.40/12.94 | | | | (107) all_55_3 = empty_set % 90.40/12.94 | | | | % 90.40/12.95 | | | | REDUCE: (28), (107) imply: % 90.40/12.95 | | | | (108) in(all_55_6, empty_set) % 90.40/12.95 | | | | % 90.40/12.95 | | | | GROUND_INST: instantiating (t7_boole) with all_55_6, empty_set, % 90.40/12.95 | | | | simplifying with (4), (8), (32), (108) gives: % 90.40/12.95 | | | | (109) $false % 90.40/12.95 | | | | % 90.40/12.95 | | | | CLOSE: (109) is inconsistent. % 90.40/12.95 | | | | % 90.40/12.95 | | | End of split % 90.40/12.95 | | | % 90.40/12.95 | | Case 2: % 90.40/12.95 | | | % 90.40/12.95 | | | (110) ? [v0: $i] : (relation_dom(all_55_2) = v0 & $i(v0) & ~ % 90.40/12.95 | | | empty(v0)) % 90.40/12.95 | | | % 90.40/12.95 | | | DELTA: instantiating (110) with fresh symbol all_365_0 gives: % 90.40/12.95 | | | (111) relation_dom(all_55_2) = all_365_0 & $i(all_365_0) & ~ % 90.40/12.95 | | | empty(all_365_0) % 90.40/12.95 | | | % 90.40/12.95 | | | ALPHA: (111) implies: % 90.40/12.95 | | | (112) relation_dom(all_55_2) = all_365_0 % 90.40/12.95 | | | % 90.40/12.95 | | | GROUND_INST: instantiating (7) with all_55_7, all_55_2, all_365_0, % 90.40/12.95 | | | all_55_5, all_55_4, all_55_3, simplifying with (29), (30), % 90.40/12.95 | | | (31), (33), (35), (37), (52), (53), (84), (112) gives: % 90.40/12.95 | | | (113) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 90.40/12.95 | | | (relation_dom_restriction(all_55_5, all_55_7) = v0 & $i(v1) & % 90.40/12.95 | | | $i(v0) & ( ~ (v0 = all_55_2) | (all_365_0 = all_55_3 & ! [v4: % 90.40/12.95 | | | $i] : ! [v5: $i] : ( ~ (apply(all_55_2, v4) = v5) | ~ % 90.40/12.95 | | | $i(v4) | ~ in(v4, all_55_3) | (apply(all_55_5, v4) = v5 % 90.40/12.95 | | | & $i(v5))))) & ( ~ (all_365_0 = all_55_3) | v0 = % 90.40/12.95 | | | all_55_2 | ( ~ (v3 = v2) & apply(all_55_2, v1) = v2 & % 90.40/12.95 | | | apply(all_55_5, v1) = v3 & $i(v3) & $i(v2) & in(v1, % 90.40/12.95 | | | all_55_3)))) % 90.40/12.95 | | | % 90.40/12.95 | | | DELTA: instantiating (113) with fresh symbols all_483_0, all_483_1, % 90.40/12.95 | | | all_483_2, all_483_3 gives: % 90.40/12.95 | | | (114) relation_dom_restriction(all_55_5, all_55_7) = all_483_3 & % 90.40/12.95 | | | $i(all_483_2) & $i(all_483_3) & ( ~ (all_483_3 = all_55_2) | % 90.40/12.95 | | | (all_365_0 = all_55_3 & ! [v0: $i] : ! [v1: $i] : ( ~ % 90.40/12.95 | | | (apply(all_55_2, v0) = v1) | ~ $i(v0) | ~ in(v0, % 90.40/12.95 | | | all_55_3) | (apply(all_55_5, v0) = v1 & $i(v1))))) & ( ~ % 90.40/12.95 | | | (all_365_0 = all_55_3) | all_483_3 = all_55_2 | ( ~ (all_483_0 % 90.40/12.95 | | | = all_483_1) & apply(all_55_2, all_483_2) = all_483_1 & % 90.40/12.95 | | | apply(all_55_5, all_483_2) = all_483_0 & $i(all_483_0) & % 90.40/12.95 | | | $i(all_483_1) & in(all_483_2, all_55_3))) % 90.40/12.95 | | | % 90.40/12.95 | | | ALPHA: (114) implies: % 90.40/12.95 | | | (115) relation_dom_restriction(all_55_5, all_55_7) = all_483_3 % 90.40/12.95 | | | (116) ~ (all_483_3 = all_55_2) | (all_365_0 = all_55_3 & ! [v0: $i] : % 90.40/12.95 | | | ! [v1: $i] : ( ~ (apply(all_55_2, v0) = v1) | ~ $i(v0) | ~ % 90.40/12.95 | | | in(v0, all_55_3) | (apply(all_55_5, v0) = v1 & $i(v1)))) % 90.40/12.95 | | | % 90.40/12.95 | | | GROUND_INST: instantiating (11) with all_55_2, all_483_3, all_55_7, % 90.40/12.95 | | | all_55_5, simplifying with (36), (115) gives: % 90.40/12.95 | | | (117) all_483_3 = all_55_2 % 90.40/12.95 | | | % 90.40/12.95 | | | BETA: splitting (116) gives: % 90.40/12.95 | | | % 90.40/12.95 | | | Case 1: % 90.40/12.95 | | | | % 90.40/12.95 | | | | (118) ~ (all_483_3 = all_55_2) % 90.40/12.95 | | | | % 90.40/12.95 | | | | REDUCE: (117), (118) imply: % 90.40/12.95 | | | | (119) $false % 90.40/12.95 | | | | % 90.40/12.95 | | | | CLOSE: (119) is inconsistent. % 90.40/12.95 | | | | % 90.40/12.95 | | | Case 2: % 90.40/12.95 | | | | % 90.40/12.95 | | | | (120) all_365_0 = all_55_3 & ! [v0: $i] : ! [v1: $i] : ( ~ % 90.40/12.95 | | | | (apply(all_55_2, v0) = v1) | ~ $i(v0) | ~ in(v0, all_55_3) % 90.40/12.95 | | | | | (apply(all_55_5, v0) = v1 & $i(v1))) % 90.40/12.95 | | | | % 90.40/12.95 | | | | ALPHA: (120) implies: % 90.40/12.95 | | | | (121) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_55_2, v0) = v1) | ~ % 90.40/12.95 | | | | $i(v0) | ~ in(v0, all_55_3) | (apply(all_55_5, v0) = v1 & % 90.40/12.95 | | | | $i(v1))) % 90.40/12.95 | | | | % 90.40/12.95 | | | | REF_CLOSE: (12), (27), (28), (32), (38), (39), (121) are inconsistent by % 90.40/12.95 | | | | sub-proof #1. % 90.40/12.95 | | | | % 90.40/12.95 | | | End of split % 90.40/12.95 | | | % 90.40/12.95 | | End of split % 90.40/12.95 | | % 90.40/12.95 | Case 2: % 90.40/12.95 | | % 90.40/12.95 | | (122) ? [v0: $i] : (relation_dom(all_38_0) = v0 & $i(v0) & ~ empty(v0)) % 90.40/12.95 | | % 90.40/12.95 | | DELTA: instantiating (122) with fresh symbol all_339_0 gives: % 90.40/12.95 | | (123) relation_dom(all_38_0) = all_339_0 & $i(all_339_0) & ~ % 90.40/12.95 | | empty(all_339_0) % 90.40/12.95 | | % 90.40/12.95 | | ALPHA: (123) implies: % 90.40/12.95 | | (124) relation_dom(all_38_0) = all_339_0 % 90.40/12.95 | | % 90.40/12.95 | | BETA: splitting (88) gives: % 90.40/12.95 | | % 90.40/12.95 | | Case 1: % 90.40/12.95 | | | % 90.40/12.95 | | | (125) empty(all_55_2) % 90.40/12.95 | | | % 90.40/12.95 | | | BETA: splitting (93) gives: % 90.40/12.95 | | | % 90.40/12.95 | | | Case 1: % 90.40/12.95 | | | | % 90.40/12.95 | | | | (126) ~ (all_89_3 = empty_set) % 90.40/12.95 | | | | % 90.40/12.95 | | | | REDUCE: (94), (126) imply: % 90.40/12.95 | | | | (127) ~ (all_55_2 = empty_set) % 90.40/12.95 | | | | % 90.40/12.95 | | | | GROUND_INST: instantiating (9) with all_55_2, simplifying with (84), % 90.40/12.95 | | | | (125) gives: % 90.40/12.95 | | | | (128) all_55_2 = empty_set % 90.40/12.95 | | | | % 90.40/12.95 | | | | REDUCE: (127), (128) imply: % 90.40/12.95 | | | | (129) $false % 90.40/12.95 | | | | % 90.40/12.95 | | | | CLOSE: (129) is inconsistent. % 90.40/12.95 | | | | % 90.40/12.95 | | | Case 2: % 90.40/12.95 | | | | % 90.40/12.95 | | | | (130) all_89_3 = empty_set % 90.40/12.95 | | | | (131) all_67_0 = all_55_3 & ! [v0: $i] : ! [v1: $i] : ( ~ % 90.40/12.95 | | | | (apply(empty_set, v0) = v1) | ~ $i(v0) | ~ in(v0, all_55_3) % 90.40/12.95 | | | | | (apply(all_55_5, v0) = v1 & $i(v1))) % 90.40/12.95 | | | | % 90.40/12.95 | | | | ALPHA: (131) implies: % 90.40/12.95 | | | | (132) all_67_0 = all_55_3 % 90.40/12.95 | | | | % 90.40/12.95 | | | | COMBINE_EQS: (94), (130) imply: % 90.40/12.95 | | | | (133) all_55_2 = empty_set % 90.40/12.95 | | | | % 90.40/12.95 | | | | COMBINE_EQS: (87), (132) imply: % 90.40/12.95 | | | | (134) all_55_3 = empty_set % 90.40/12.95 | | | | % 90.40/12.95 | | | | REDUCE: (28), (134) imply: % 90.40/12.95 | | | | (135) in(all_55_6, empty_set) % 90.40/12.95 | | | | % 90.40/12.95 | | | | GROUND_INST: instantiating (t7_boole) with all_55_6, empty_set, % 90.40/12.95 | | | | simplifying with (4), (8), (32), (135) gives: % 90.40/12.95 | | | | (136) $false % 90.40/12.95 | | | | % 90.40/12.95 | | | | CLOSE: (136) is inconsistent. % 90.40/12.95 | | | | % 90.40/12.95 | | | End of split % 90.40/12.95 | | | % 90.40/12.95 | | Case 2: % 90.40/12.95 | | | % 90.40/12.95 | | | (137) ? [v0: $i] : (relation_dom(all_55_2) = v0 & $i(v0) & ~ % 90.40/12.95 | | | empty(v0)) % 90.40/12.95 | | | % 90.40/12.95 | | | DELTA: instantiating (137) with fresh symbol all_369_0 gives: % 90.40/12.95 | | | (138) relation_dom(all_55_2) = all_369_0 & $i(all_369_0) & ~ % 90.40/12.95 | | | empty(all_369_0) % 90.40/12.95 | | | % 90.40/12.95 | | | ALPHA: (138) implies: % 90.40/12.95 | | | (139) relation_dom(all_55_2) = all_369_0 % 90.40/12.95 | | | % 90.53/12.96 | | | GROUND_INST: instantiating (7) with all_55_7, all_38_0, all_339_0, % 90.53/12.96 | | | all_55_5, all_55_4, all_55_3, simplifying with (17), (18), % 90.53/12.96 | | | (19), (29), (30), (31), (33), (35), (37), (124) gives: % 90.53/12.96 | | | (140) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 90.53/12.96 | | | (relation_dom_restriction(all_55_5, all_55_7) = v0 & $i(v1) & % 90.53/12.96 | | | $i(v0) & ( ~ (v0 = all_38_0) | (all_339_0 = all_55_3 & ! [v4: % 90.53/12.96 | | | $i] : ! [v5: $i] : ( ~ (apply(all_38_0, v4) = v5) | ~ % 90.53/12.96 | | | $i(v4) | ~ in(v4, all_55_3) | (apply(all_55_5, v4) = v5 % 90.53/12.96 | | | & $i(v5))))) & ( ~ (all_339_0 = all_55_3) | v0 = % 90.53/12.96 | | | all_38_0 | ( ~ (v3 = v2) & apply(all_55_5, v1) = v3 & % 90.53/12.96 | | | apply(all_38_0, v1) = v2 & $i(v3) & $i(v2) & in(v1, % 90.53/12.96 | | | all_55_3)))) % 90.53/12.96 | | | % 90.53/12.96 | | | GROUND_INST: instantiating (7) with all_55_7, all_55_2, all_369_0, % 90.53/12.96 | | | all_55_5, all_55_4, all_55_3, simplifying with (29), (30), % 90.53/12.96 | | | (31), (33), (35), (37), (52), (53), (84), (139) gives: % 90.53/12.96 | | | (141) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 90.53/12.96 | | | (relation_dom_restriction(all_55_5, all_55_7) = v0 & $i(v1) & % 90.53/12.96 | | | $i(v0) & ( ~ (v0 = all_55_2) | (all_369_0 = all_55_3 & ! [v4: % 90.53/12.96 | | | $i] : ! [v5: $i] : ( ~ (apply(all_55_2, v4) = v5) | ~ % 90.53/12.96 | | | $i(v4) | ~ in(v4, all_55_3) | (apply(all_55_5, v4) = v5 % 90.53/12.96 | | | & $i(v5))))) & ( ~ (all_369_0 = all_55_3) | v0 = % 90.53/12.96 | | | all_55_2 | ( ~ (v3 = v2) & apply(all_55_2, v1) = v2 & % 90.53/12.96 | | | apply(all_55_5, v1) = v3 & $i(v3) & $i(v2) & in(v1, % 90.53/12.96 | | | all_55_3)))) % 90.53/12.96 | | | % 90.53/12.96 | | | DELTA: instantiating (141) with fresh symbols all_463_0, all_463_1, % 90.53/12.96 | | | all_463_2, all_463_3 gives: % 90.53/12.96 | | | (142) relation_dom_restriction(all_55_5, all_55_7) = all_463_3 & % 90.53/12.96 | | | $i(all_463_2) & $i(all_463_3) & ( ~ (all_463_3 = all_55_2) | % 90.53/12.96 | | | (all_369_0 = all_55_3 & ! [v0: $i] : ! [v1: $i] : ( ~ % 90.53/12.96 | | | (apply(all_55_2, v0) = v1) | ~ $i(v0) | ~ in(v0, % 90.53/12.96 | | | all_55_3) | (apply(all_55_5, v0) = v1 & $i(v1))))) & ( ~ % 90.53/12.96 | | | (all_369_0 = all_55_3) | all_463_3 = all_55_2 | ( ~ (all_463_0 % 90.53/12.96 | | | = all_463_1) & apply(all_55_2, all_463_2) = all_463_1 & % 90.53/12.96 | | | apply(all_55_5, all_463_2) = all_463_0 & $i(all_463_0) & % 90.53/12.96 | | | $i(all_463_1) & in(all_463_2, all_55_3))) % 90.53/12.96 | | | % 90.53/12.96 | | | ALPHA: (142) implies: % 90.53/12.96 | | | (143) relation_dom_restriction(all_55_5, all_55_7) = all_463_3 % 90.53/12.96 | | | (144) ~ (all_463_3 = all_55_2) | (all_369_0 = all_55_3 & ! [v0: $i] : % 90.53/12.96 | | | ! [v1: $i] : ( ~ (apply(all_55_2, v0) = v1) | ~ $i(v0) | ~ % 90.53/12.96 | | | in(v0, all_55_3) | (apply(all_55_5, v0) = v1 & $i(v1)))) % 90.53/12.96 | | | % 90.53/12.96 | | | DELTA: instantiating (140) with fresh symbols all_465_0, all_465_1, % 90.53/12.96 | | | all_465_2, all_465_3 gives: % 90.53/12.96 | | | (145) relation_dom_restriction(all_55_5, all_55_7) = all_465_3 & % 90.53/12.96 | | | $i(all_465_2) & $i(all_465_3) & ( ~ (all_465_3 = all_38_0) | % 90.53/12.96 | | | (all_339_0 = all_55_3 & ! [v0: $i] : ! [v1: $i] : ( ~ % 90.53/12.96 | | | (apply(all_38_0, v0) = v1) | ~ $i(v0) | ~ in(v0, % 90.53/12.96 | | | all_55_3) | (apply(all_55_5, v0) = v1 & $i(v1))))) & ( ~ % 90.53/12.96 | | | (all_339_0 = all_55_3) | all_465_3 = all_38_0 | ( ~ (all_465_0 % 90.53/12.96 | | | = all_465_1) & apply(all_55_5, all_465_2) = all_465_0 & % 90.53/12.96 | | | apply(all_38_0, all_465_2) = all_465_1 & $i(all_465_0) & % 90.53/12.96 | | | $i(all_465_1) & in(all_465_2, all_55_3))) % 90.53/12.96 | | | % 90.53/12.96 | | | ALPHA: (145) implies: % 90.53/12.96 | | | (146) relation_dom_restriction(all_55_5, all_55_7) = all_465_3 % 90.53/12.96 | | | % 90.53/12.96 | | | GROUND_INST: instantiating (11) with all_55_2, all_465_3, all_55_7, % 90.53/12.96 | | | all_55_5, simplifying with (36), (146) gives: % 90.53/12.96 | | | (147) all_465_3 = all_55_2 % 90.53/12.96 | | | % 90.53/12.96 | | | GROUND_INST: instantiating (11) with all_463_3, all_465_3, all_55_7, % 90.53/12.96 | | | all_55_5, simplifying with (143), (146) gives: % 90.53/12.96 | | | (148) all_465_3 = all_463_3 % 90.53/12.96 | | | % 90.53/12.96 | | | COMBINE_EQS: (147), (148) imply: % 90.53/12.96 | | | (149) all_463_3 = all_55_2 % 90.53/12.96 | | | % 90.53/12.96 | | | BETA: splitting (144) gives: % 90.53/12.96 | | | % 90.53/12.96 | | | Case 1: % 90.53/12.96 | | | | % 90.53/12.96 | | | | (150) ~ (all_463_3 = all_55_2) % 90.53/12.96 | | | | % 90.53/12.96 | | | | REDUCE: (149), (150) imply: % 90.53/12.96 | | | | (151) $false % 90.53/12.96 | | | | % 90.53/12.96 | | | | CLOSE: (151) is inconsistent. % 90.53/12.96 | | | | % 90.53/12.96 | | | Case 2: % 90.53/12.96 | | | | % 90.53/12.96 | | | | (152) all_369_0 = all_55_3 & ! [v0: $i] : ! [v1: $i] : ( ~ % 90.53/12.96 | | | | (apply(all_55_2, v0) = v1) | ~ $i(v0) | ~ in(v0, all_55_3) % 90.53/12.96 | | | | | (apply(all_55_5, v0) = v1 & $i(v1))) % 90.53/12.96 | | | | % 90.53/12.96 | | | | ALPHA: (152) implies: % 90.53/12.96 | | | | (153) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_55_2, v0) = v1) | ~ % 90.53/12.96 | | | | $i(v0) | ~ in(v0, all_55_3) | (apply(all_55_5, v0) = v1 & % 90.53/12.96 | | | | $i(v1))) % 90.53/12.96 | | | | % 90.53/12.96 | | | | REF_CLOSE: (12), (27), (28), (32), (38), (39), (153) are inconsistent by % 90.53/12.96 | | | | sub-proof #1. % 90.53/12.96 | | | | % 90.53/12.96 | | | End of split % 90.53/12.96 | | | % 90.53/12.96 | | End of split % 90.53/12.96 | | % 90.53/12.96 | End of split % 90.53/12.96 | % 90.53/12.96 End of proof % 90.53/12.96 % 90.53/12.96 Sub-proof #1 shows that the following formulas are inconsistent: % 90.53/12.96 ---------------------------------------------------------------- % 90.53/12.96 (1) ~ (all_55_0 = all_55_1) % 90.53/12.96 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 90.53/12.96 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 90.53/12.96 (3) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_55_2, v0) = v1) | ~ $i(v0) | % 90.53/12.96 ~ in(v0, all_55_3) | (apply(all_55_5, v0) = v1 & $i(v1))) % 90.53/12.96 (4) apply(all_55_5, all_55_6) = all_55_0 % 90.53/12.96 (5) in(all_55_6, all_55_3) % 90.53/12.96 (6) apply(all_55_2, all_55_6) = all_55_1 % 90.53/12.96 (7) $i(all_55_6) % 90.53/12.96 % 90.53/12.96 Begin of proof % 90.53/12.96 | % 90.53/12.96 | GROUND_INST: instantiating (3) with all_55_6, all_55_1, simplifying with (5), % 90.53/12.96 | (6), (7) gives: % 90.53/12.96 | (8) apply(all_55_5, all_55_6) = all_55_1 & $i(all_55_1) % 90.53/12.96 | % 90.53/12.96 | ALPHA: (8) implies: % 90.53/12.96 | (9) apply(all_55_5, all_55_6) = all_55_1 % 90.53/12.96 | % 90.53/12.96 | GROUND_INST: instantiating (2) with all_55_0, all_55_1, all_55_6, all_55_5, % 90.53/12.96 | simplifying with (4), (9) gives: % 90.53/12.96 | (10) all_55_0 = all_55_1 % 90.53/12.96 | % 90.53/12.96 | REDUCE: (1), (10) imply: % 90.53/12.96 | (11) $false % 90.53/12.96 | % 90.53/12.96 | CLOSE: (11) is inconsistent. % 90.53/12.96 | % 90.53/12.96 End of proof % 90.53/12.96 % SZS output end Proof for theBenchmark % 90.53/12.96 % 90.53/12.96 12404ms %------------------------------------------------------------------------------