%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU062+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 : n023.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 17:42:26 EDT 2023 % Result : Theorem 9.07s 2.04s % Output : Proof 15.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU062+1 : TPTP v8.1.2. Released v3.2.0. % 0.04/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n023.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Wed Aug 23 20:12:27 EDT 2023 % 0.13/0.33 % CPUTime : % 0.65/0.66 ________ _____ % 0.65/0.66 ___ __ \_________(_)________________________________ % 0.65/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.65/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.65/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.65/0.66 % 0.65/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.65/0.66 (2023-06-19) % 0.65/0.66 % 0.65/0.66 (c) Philipp Rümmer, 2009-2023 % 0.65/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.65/0.66 Amanda Stjerna. % 0.65/0.66 Free software under BSD-3-Clause. % 0.65/0.66 % 0.65/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.65/0.66 % 0.65/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.65/0.67 Running up to 7 provers in parallel. % 0.74/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.74/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.74/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.74/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.74/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.74/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.74/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.95/1.14 Prover 4: Preprocessing ... % 2.95/1.14 Prover 1: Preprocessing ... % 3.13/1.18 Prover 5: Preprocessing ... % 3.13/1.18 Prover 6: Preprocessing ... % 3.13/1.18 Prover 0: Preprocessing ... % 3.13/1.18 Prover 2: Preprocessing ... % 3.13/1.18 Prover 3: Preprocessing ... % 5.27/1.51 Prover 2: Proving ... % 5.73/1.54 Prover 1: Warning: ignoring some quantifiers % 5.73/1.54 Prover 5: Proving ... % 5.73/1.56 Prover 1: Constructing countermodel ... % 5.99/1.58 Prover 3: Warning: ignoring some quantifiers % 5.99/1.59 Prover 3: Constructing countermodel ... % 5.99/1.60 Prover 4: Warning: ignoring some quantifiers % 5.99/1.63 Prover 4: Constructing countermodel ... % 5.99/1.64 Prover 6: Proving ... % 6.84/1.73 Prover 0: Proving ... % 8.09/1.88 Prover 3: gave up % 8.09/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.09/1.93 Prover 7: Preprocessing ... % 8.71/1.95 Prover 1: gave up % 8.71/1.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.07/1.98 Prover 8: Preprocessing ... % 9.07/1.99 Prover 7: Warning: ignoring some quantifiers % 9.07/2.00 Prover 7: Constructing countermodel ... % 9.07/2.04 Prover 0: proved (1358ms) % 9.07/2.04 % 9.07/2.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.07/2.04 % 9.53/2.06 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.53/2.06 Prover 2: stopped % 9.62/2.07 Prover 6: stopped % 9.62/2.07 Prover 5: stopped % 9.62/2.08 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.62/2.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.62/2.08 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.62/2.09 Prover 10: Preprocessing ... % 9.62/2.11 Prover 16: Preprocessing ... % 10.02/2.12 Prover 11: Preprocessing ... % 10.02/2.13 Prover 13: Preprocessing ... % 10.02/2.13 Prover 8: Warning: ignoring some quantifiers % 10.02/2.14 Prover 8: Constructing countermodel ... % 10.37/2.16 Prover 16: Warning: ignoring some quantifiers % 10.37/2.17 Prover 10: Warning: ignoring some quantifiers % 10.37/2.18 Prover 16: Constructing countermodel ... % 10.37/2.18 Prover 10: Constructing countermodel ... % 10.37/2.21 Prover 13: Warning: ignoring some quantifiers % 10.37/2.23 Prover 13: Constructing countermodel ... % 11.02/2.24 Prover 10: gave up % 11.02/2.26 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.02/2.26 Prover 7: gave up % 11.02/2.28 Prover 11: Warning: ignoring some quantifiers % 11.02/2.28 Prover 11: Constructing countermodel ... % 11.02/2.29 Prover 19: Preprocessing ... % 11.83/2.39 Prover 19: Warning: ignoring some quantifiers % 12.23/2.41 Prover 19: Constructing countermodel ... % 12.23/2.45 Prover 8: gave up % 14.95/2.77 Prover 19: gave up % 14.95/2.77 Prover 13: gave up % 14.95/2.78 Prover 4: Found proof (size 66) % 14.95/2.78 Prover 4: proved (2102ms) % 14.95/2.78 Prover 16: stopped % 14.95/2.78 Prover 11: stopped % 14.95/2.78 % 14.95/2.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.95/2.78 % 14.95/2.79 % SZS output start Proof for theBenchmark % 14.95/2.80 Assumptions after simplification: % 14.95/2.80 --------------------------------- % 14.95/2.80 % 14.95/2.80 (d3_tarski) % 14.95/2.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 14.95/2.82 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 14.95/2.82 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 14.95/2.82 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 14.95/2.82 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 14.95/2.82 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 14.95/2.82 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 14.95/2.82 $i(v0) | in(v2, v1) = 0) % 14.95/2.82 % 14.95/2.82 (fc6_relat_1) % 14.95/2.83 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 14.95/2.83 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_rng(v0) = v3 & % 14.95/2.83 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = % 14.95/2.83 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ % 14.95/2.83 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & % 14.95/2.83 empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & % 14.95/2.83 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] % 14.95/2.83 : ? [v3: any] : (relation_rng(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & % 14.95/2.83 $i(v2) & ( ~ (v3 = 0) | v1 = 0))) % 14.95/2.83 % 14.95/2.83 (rc1_subset_1) % 14.95/2.83 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 14.95/2.83 [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v0) = v2 & % 14.95/2.83 element(v3, v2) = 0 & empty(v3) = v4 & $i(v3) & $i(v2))) & ! [v0: $i] : % 14.95/2.83 ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] % 14.95/2.83 : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & % 14.95/2.83 element(v3, v1) = 0 & empty(v3) = v5) | (v2 = 0 & empty(v0) = 0)))) % 14.95/2.83 % 14.95/2.83 (rc2_relat_1) % 14.95/2.83 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & relation(v0) = 0 & empty(v0) = v1 % 14.95/2.83 & $i(v0)) % 14.95/2.83 % 14.95/2.83 (rc2_xboole_0) % 14.95/2.83 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0)) % 14.95/2.83 % 14.95/2.83 (t142_funct_1) % 14.95/2.83 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 14.95/2.83 (relation_inverse_image(v1, v2) = v3) | ~ (singleton(v0) = v2) | ~ $i(v1) % 14.95/2.83 | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : (relation_rng(v1) % 14.95/2.83 = v5 & relation(v1) = v4 & in(v0, v5) = v6 & $i(v5) & ( ~ (v4 = 0) | (( ~ % 14.95/2.83 (v6 = 0) | ~ (v3 = empty_set)) & (v6 = 0 | v3 = empty_set))))) & ! % 14.95/2.83 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (relation_rng(v1) = % 14.95/2.83 v2) | ~ (in(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 14.95/2.83 [v5: $i] : ? [v6: $i] : (relation_inverse_image(v1, v5) = v6 & % 14.95/2.83 singleton(v0) = v5 & relation(v1) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | % 14.95/2.83 (( ~ (v6 = empty_set) | ~ (v3 = 0)) & (v6 = empty_set | v3 = 0))))) % 14.95/2.83 % 14.95/2.83 (t143_funct_1) % 14.95/2.83 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ % 14.95/2.83 (v3 = 0) & relation_rng(v1) = v2 & subset(v0, v2) = v3 & relation(v1) = 0 & % 14.95/2.83 $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ( ~ (singleton(v4) = % 14.95/2.83 v5) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : % 14.95/2.83 (relation_inverse_image(v1, v5) = v7 & in(v4, v0) = v6 & $i(v7) & ( ~ (v7 % 14.95/2.83 = empty_set) | ~ (v6 = 0)))) & ! [v4: $i] : ( ~ (in(v4, v0) = 0) | % 14.95/2.83 ~ $i(v4) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = empty_set) & % 14.95/2.83 relation_inverse_image(v1, v5) = v6 & singleton(v4) = v5 & $i(v6) & % 14.95/2.83 $i(v5)))) % 14.95/2.83 % 14.95/2.84 (function-axioms) % 14.95/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.95/2.84 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = % 14.95/2.84 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.95/2.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, % 14.95/2.84 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 14.95/2.84 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ % 14.95/2.84 (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.95/2.84 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = % 14.95/2.84 v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.95/2.84 (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: % 14.95/2.84 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 14.95/2.84 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 14.95/2.84 ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: % 14.95/2.84 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 14.95/2.84 ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = % 14.95/2.84 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.95/2.84 $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! % 14.95/2.84 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 14.95/2.84 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: % 14.95/2.84 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 14.95/2.84 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] % 14.95/2.84 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | % 14.95/2.84 ~ (empty(v2) = v0)) % 14.95/2.84 % 14.95/2.84 Further assumptions not needed in the proof: % 14.95/2.84 -------------------------------------------- % 14.95/2.84 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, % 14.95/2.84 existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc2_subset_1, % 14.95/2.84 fc4_relat_1, fc8_relat_1, rc1_funct_1, rc1_relat_1, rc1_xboole_0, rc2_funct_1, % 14.95/2.84 rc2_subset_1, rc3_funct_1, rc3_relat_1, reflexivity_r1_tarski, t1_subset, % 14.95/2.84 t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 14.95/2.84 % 14.95/2.84 Those formulas are unsatisfiable: % 14.95/2.84 --------------------------------- % 14.95/2.84 % 14.95/2.84 Begin of proof % 14.95/2.84 | % 14.95/2.84 | ALPHA: (d3_tarski) implies: % 14.95/2.84 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 14.95/2.84 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 14.95/2.84 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 14.95/2.84 | % 14.95/2.84 | ALPHA: (fc6_relat_1) implies: % 14.95/2.84 | (2) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 14.95/2.84 | [v2: $i] : ? [v3: any] : (relation_rng(v0) = v2 & empty(v2) = v3 & % 14.95/2.84 | empty(v0) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0))) % 14.95/2.84 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 14.95/2.84 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & % 14.95/2.84 | empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = % 14.95/2.84 | 0))) % 14.95/2.85 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) % 14.95/2.85 | | ? [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_rng(v0) = v3 % 14.95/2.85 | & relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ % 14.95/2.85 | (v2 = 0)))) % 14.95/2.85 | % 14.95/2.85 | ALPHA: (rc1_subset_1) implies: % 14.95/2.85 | (5) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) % 14.95/2.85 | | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 14.95/2.85 | powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3) & % 14.95/2.85 | $i(v2))) % 14.95/2.85 | % 14.95/2.85 | ALPHA: (t142_funct_1) implies: % 14.95/2.85 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 14.95/2.85 | (relation_rng(v1) = v2) | ~ (in(v0, v2) = v3) | ~ $i(v1) | ~ % 14.95/2.85 | $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 14.95/2.85 | (relation_inverse_image(v1, v5) = v6 & singleton(v0) = v5 & % 14.95/2.85 | relation(v1) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | (( ~ (v6 = % 14.95/2.85 | empty_set) | ~ (v3 = 0)) & (v6 = empty_set | v3 = 0))))) % 14.95/2.85 | % 14.95/2.85 | ALPHA: (t143_funct_1) implies: % 14.95/2.85 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 14.95/2.85 | relation_rng(v1) = v2 & subset(v0, v2) = v3 & relation(v1) = 0 & % 14.95/2.85 | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ( ~ % 14.95/2.85 | (singleton(v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : % 14.95/2.85 | (relation_inverse_image(v1, v5) = v7 & in(v4, v0) = v6 & $i(v7) & ( % 14.95/2.85 | ~ (v7 = empty_set) | ~ (v6 = 0)))) & ! [v4: $i] : ( ~ (in(v4, % 14.95/2.85 | v0) = 0) | ~ $i(v4) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = % 14.95/2.85 | empty_set) & relation_inverse_image(v1, v5) = v6 & % 14.95/2.85 | singleton(v4) = v5 & $i(v6) & $i(v5)))) % 14.95/2.85 | % 14.95/2.85 | ALPHA: (function-axioms) implies: % 14.95/2.85 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.95/2.85 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 14.95/2.85 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) % 14.95/2.85 | = v1) | ~ (singleton(v2) = v0)) % 14.95/2.85 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.95/2.85 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 14.95/2.85 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.95/2.85 | (relation_inverse_image(v3, v2) = v1) | ~ % 14.95/2.85 | (relation_inverse_image(v3, v2) = v0)) % 14.95/2.85 | % 14.95/2.85 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_27_0, all_27_1 % 14.95/2.85 | gives: % 14.95/2.85 | (12) ~ (all_27_0 = 0) & empty(all_27_1) = all_27_0 & $i(all_27_1) % 14.95/2.85 | % 14.95/2.85 | ALPHA: (12) implies: % 14.95/2.85 | (13) ~ (all_27_0 = 0) % 14.95/2.85 | (14) $i(all_27_1) % 14.95/2.85 | (15) empty(all_27_1) = all_27_0 % 14.95/2.85 | % 14.95/2.85 | DELTA: instantiating (rc2_relat_1) with fresh symbols all_40_0, all_40_1 % 14.95/2.85 | gives: % 15.47/2.85 | (16) ~ (all_40_0 = 0) & relation(all_40_1) = 0 & empty(all_40_1) = % 15.47/2.85 | all_40_0 & $i(all_40_1) % 15.47/2.85 | % 15.47/2.85 | ALPHA: (16) implies: % 15.47/2.85 | (17) ~ (all_40_0 = 0) % 15.47/2.85 | (18) $i(all_40_1) % 15.47/2.85 | (19) empty(all_40_1) = all_40_0 % 15.47/2.85 | (20) relation(all_40_1) = 0 % 15.47/2.85 | % 15.47/2.85 | DELTA: instantiating (7) with fresh symbols all_42_0, all_42_1, all_42_2, % 15.47/2.85 | all_42_3 gives: % 15.47/2.86 | (21) ~ (all_42_0 = 0) & relation_rng(all_42_2) = all_42_1 & % 15.47/2.86 | subset(all_42_3, all_42_1) = all_42_0 & relation(all_42_2) = 0 & % 15.47/2.86 | $i(all_42_1) & $i(all_42_2) & $i(all_42_3) & ! [v0: $i] : ! [v1: $i] % 15.47/2.86 | : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 15.47/2.86 | (relation_inverse_image(all_42_2, v1) = v3 & in(v0, all_42_3) = v2 & % 15.47/2.86 | $i(v3) & ( ~ (v3 = empty_set) | ~ (v2 = 0)))) & ! [v0: $i] : ( ~ % 15.47/2.86 | (in(v0, all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ( ~ % 15.47/2.86 | (v2 = empty_set) & relation_inverse_image(all_42_2, v1) = v2 & % 15.47/2.86 | singleton(v0) = v1 & $i(v2) & $i(v1))) % 15.47/2.86 | % 15.47/2.86 | ALPHA: (21) implies: % 15.47/2.86 | (22) ~ (all_42_0 = 0) % 15.47/2.86 | (23) $i(all_42_3) % 15.47/2.86 | (24) $i(all_42_2) % 15.47/2.86 | (25) $i(all_42_1) % 15.47/2.86 | (26) relation(all_42_2) = 0 % 15.47/2.86 | (27) subset(all_42_3, all_42_1) = all_42_0 % 15.47/2.86 | (28) relation_rng(all_42_2) = all_42_1 % 15.47/2.86 | (29) ! [v0: $i] : ( ~ (in(v0, all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] : % 15.47/2.86 | ? [v2: $i] : ( ~ (v2 = empty_set) & relation_inverse_image(all_42_2, % 15.47/2.86 | v1) = v2 & singleton(v0) = v1 & $i(v2) & $i(v1))) % 15.47/2.86 | % 15.47/2.86 | GROUND_INST: instantiating (5) with all_27_1, all_27_0, simplifying with (14), % 15.47/2.86 | (15) gives: % 15.47/2.86 | (30) all_27_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 15.47/2.86 | & powerset(all_27_1) = v0 & element(v1, v0) = 0 & empty(v1) = v2 & % 15.47/2.86 | $i(v1) & $i(v0)) % 15.47/2.86 | % 15.47/2.86 | GROUND_INST: instantiating (4) with all_40_1, all_40_0, simplifying with (18), % 15.47/2.86 | (19) gives: % 15.47/2.86 | (31) all_40_0 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 15.47/2.86 | (relation_rng(all_40_1) = v1 & relation(all_40_1) = v0 & empty(v1) = % 15.47/2.86 | v2 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0))) % 15.47/2.86 | % 15.47/2.86 | GROUND_INST: instantiating (2) with all_42_2, simplifying with (24), (26) % 15.47/2.86 | gives: % 15.47/2.86 | (32) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_rng(all_42_2) = % 15.47/2.86 | v1 & empty(v1) = v2 & empty(all_42_2) = v0 & $i(v1) & ( ~ (v2 = 0) | % 15.47/2.86 | v0 = 0)) % 15.47/2.86 | % 15.47/2.86 | GROUND_INST: instantiating (1) with all_42_3, all_42_1, all_42_0, simplifying % 15.47/2.86 | with (23), (25), (27) gives: % 15.47/2.86 | (33) all_42_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 15.47/2.86 | all_42_1) = v1 & in(v0, all_42_3) = 0 & $i(v0)) % 15.47/2.86 | % 15.47/2.86 | GROUND_INST: instantiating (3) with all_42_2, all_42_1, simplifying with (24), % 15.47/2.86 | (28) gives: % 15.47/2.86 | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_42_2) = v1 % 15.47/2.86 | & empty(all_42_1) = v2 & empty(all_42_2) = v0 & ( ~ (v2 = 0) | ~ % 15.47/2.86 | (v1 = 0) | v0 = 0)) % 15.47/2.86 | % 15.47/2.86 | DELTA: instantiating (34) with fresh symbols all_63_0, all_63_1, all_63_2 % 15.47/2.86 | gives: % 15.47/2.86 | (35) relation(all_42_2) = all_63_1 & empty(all_42_1) = all_63_0 & % 15.47/2.86 | empty(all_42_2) = all_63_2 & ( ~ (all_63_0 = 0) | ~ (all_63_1 = 0) | % 15.47/2.86 | all_63_2 = 0) % 15.47/2.86 | % 15.47/2.86 | ALPHA: (35) implies: % 15.47/2.86 | (36) relation(all_42_2) = all_63_1 % 15.47/2.86 | % 15.47/2.86 | DELTA: instantiating (32) with fresh symbols all_85_0, all_85_1, all_85_2 % 15.47/2.86 | gives: % 15.47/2.86 | (37) relation_rng(all_42_2) = all_85_1 & empty(all_85_1) = all_85_0 & % 15.47/2.86 | empty(all_42_2) = all_85_2 & $i(all_85_1) & ( ~ (all_85_0 = 0) | % 15.47/2.86 | all_85_2 = 0) % 15.47/2.86 | % 15.47/2.86 | ALPHA: (37) implies: % 15.47/2.86 | (38) relation_rng(all_42_2) = all_85_1 % 15.47/2.86 | % 15.47/2.86 | BETA: splitting (31) gives: % 15.47/2.86 | % 15.47/2.86 | Case 1: % 15.47/2.86 | | % 15.47/2.86 | | (39) all_40_0 = 0 % 15.47/2.86 | | % 15.47/2.87 | | REDUCE: (17), (39) imply: % 15.47/2.87 | | (40) $false % 15.47/2.87 | | % 15.47/2.87 | | CLOSE: (40) is inconsistent. % 15.47/2.87 | | % 15.47/2.87 | Case 2: % 15.47/2.87 | | % 15.47/2.87 | | (41) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_rng(all_40_1) % 15.47/2.87 | | = v1 & relation(all_40_1) = v0 & empty(v1) = v2 & $i(v1) & ( ~ (v2 % 15.47/2.87 | | = 0) | ~ (v0 = 0))) % 15.47/2.87 | | % 15.47/2.87 | | DELTA: instantiating (41) with fresh symbols all_115_0, all_115_1, all_115_2 % 15.47/2.87 | | gives: % 15.47/2.87 | | (42) relation_rng(all_40_1) = all_115_1 & relation(all_40_1) = all_115_2 % 15.47/2.87 | | & empty(all_115_1) = all_115_0 & $i(all_115_1) & ( ~ (all_115_0 = 0) % 15.47/2.87 | | | ~ (all_115_2 = 0)) % 15.47/2.87 | | % 15.47/2.87 | | ALPHA: (42) implies: % 15.47/2.87 | | (43) relation(all_40_1) = all_115_2 % 15.47/2.87 | | (44) ~ (all_115_0 = 0) | ~ (all_115_2 = 0) % 15.47/2.87 | | % 15.47/2.87 | | BETA: splitting (33) gives: % 15.47/2.87 | | % 15.47/2.87 | | Case 1: % 15.47/2.87 | | | % 15.47/2.87 | | | (45) all_42_0 = 0 % 15.47/2.87 | | | % 15.47/2.87 | | | REDUCE: (22), (45) imply: % 15.47/2.87 | | | (46) $false % 15.47/2.87 | | | % 15.47/2.87 | | | CLOSE: (46) is inconsistent. % 15.47/2.87 | | | % 15.47/2.87 | | Case 2: % 15.47/2.87 | | | % 15.47/2.87 | | | (47) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_42_1) = v1 % 15.47/2.87 | | | & in(v0, all_42_3) = 0 & $i(v0)) % 15.47/2.87 | | | % 15.47/2.87 | | | DELTA: instantiating (47) with fresh symbols all_120_0, all_120_1 gives: % 15.47/2.87 | | | (48) ~ (all_120_0 = 0) & in(all_120_1, all_42_1) = all_120_0 & % 15.47/2.87 | | | in(all_120_1, all_42_3) = 0 & $i(all_120_1) % 15.47/2.87 | | | % 15.47/2.87 | | | ALPHA: (48) implies: % 15.47/2.87 | | | (49) ~ (all_120_0 = 0) % 15.47/2.87 | | | (50) $i(all_120_1) % 15.47/2.87 | | | (51) in(all_120_1, all_42_3) = 0 % 15.47/2.87 | | | (52) in(all_120_1, all_42_1) = all_120_0 % 15.47/2.87 | | | % 15.47/2.87 | | | BETA: splitting (30) gives: % 15.47/2.87 | | | % 15.47/2.87 | | | Case 1: % 15.47/2.87 | | | | % 15.47/2.87 | | | | (53) all_27_0 = 0 % 15.47/2.87 | | | | % 15.47/2.87 | | | | REDUCE: (13), (53) imply: % 15.47/2.87 | | | | (54) $false % 15.47/2.87 | | | | % 15.47/2.87 | | | | CLOSE: (54) is inconsistent. % 15.47/2.87 | | | | % 15.47/2.87 | | | Case 2: % 15.47/2.87 | | | | % 15.47/2.87 | | | | % 15.47/2.87 | | | | GROUND_INST: instantiating (8) with 0, all_115_2, all_40_1, simplifying % 15.47/2.87 | | | | with (20), (43) gives: % 15.47/2.87 | | | | (55) all_115_2 = 0 % 15.47/2.87 | | | | % 15.47/2.87 | | | | GROUND_INST: instantiating (8) with 0, all_63_1, all_42_2, simplifying % 15.47/2.87 | | | | with (26), (36) gives: % 15.47/2.87 | | | | (56) all_63_1 = 0 % 15.47/2.87 | | | | % 15.47/2.87 | | | | GROUND_INST: instantiating (10) with all_42_1, all_85_1, all_42_2, % 15.47/2.87 | | | | simplifying with (28), (38) gives: % 15.47/2.87 | | | | (57) all_85_1 = all_42_1 % 15.47/2.87 | | | | % 15.47/2.87 | | | | BETA: splitting (44) gives: % 15.47/2.87 | | | | % 15.47/2.87 | | | | Case 1: % 15.47/2.87 | | | | | % 15.47/2.87 | | | | | % 15.47/2.87 | | | | | GROUND_INST: instantiating (29) with all_120_1, simplifying with (50), % 15.47/2.87 | | | | | (51) gives: % 15.47/2.87 | | | | | (58) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = empty_set) & % 15.47/2.87 | | | | | relation_inverse_image(all_42_2, v0) = v1 & % 15.47/2.87 | | | | | singleton(all_120_1) = v0 & $i(v1) & $i(v0)) % 15.47/2.87 | | | | | % 15.47/2.87 | | | | | GROUND_INST: instantiating (6) with all_120_1, all_42_2, all_42_1, % 15.47/2.87 | | | | | all_120_0, simplifying with (24), (28), (50), (52) gives: % 15.47/2.87 | | | | | (59) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 15.47/2.87 | | | | | (relation_inverse_image(all_42_2, v1) = v2 & % 15.47/2.87 | | | | | singleton(all_120_1) = v1 & relation(all_42_2) = v0 & $i(v2) % 15.47/2.87 | | | | | & $i(v1) & ( ~ (v0 = 0) | (( ~ (v2 = empty_set) | ~ % 15.47/2.87 | | | | | (all_120_0 = 0)) & (v2 = empty_set | all_120_0 = 0)))) % 15.47/2.87 | | | | | % 15.47/2.87 | | | | | DELTA: instantiating (58) with fresh symbols all_207_0, all_207_1 % 15.47/2.87 | | | | | gives: % 15.47/2.87 | | | | | (60) ~ (all_207_0 = empty_set) & relation_inverse_image(all_42_2, % 15.47/2.87 | | | | | all_207_1) = all_207_0 & singleton(all_120_1) = all_207_1 & % 15.47/2.87 | | | | | $i(all_207_0) & $i(all_207_1) % 15.47/2.87 | | | | | % 15.47/2.88 | | | | | ALPHA: (60) implies: % 15.47/2.88 | | | | | (61) ~ (all_207_0 = empty_set) % 15.47/2.88 | | | | | (62) singleton(all_120_1) = all_207_1 % 15.47/2.88 | | | | | (63) relation_inverse_image(all_42_2, all_207_1) = all_207_0 % 15.47/2.88 | | | | | % 15.47/2.88 | | | | | DELTA: instantiating (59) with fresh symbols all_245_0, all_245_1, % 15.47/2.88 | | | | | all_245_2 gives: % 15.47/2.88 | | | | | (64) relation_inverse_image(all_42_2, all_245_1) = all_245_0 & % 15.47/2.88 | | | | | singleton(all_120_1) = all_245_1 & relation(all_42_2) = % 15.47/2.88 | | | | | all_245_2 & $i(all_245_0) & $i(all_245_1) & ( ~ (all_245_2 = % 15.47/2.88 | | | | | 0) | (( ~ (all_245_0 = empty_set) | ~ (all_120_0 = 0)) & % 15.47/2.88 | | | | | (all_245_0 = empty_set | all_120_0 = 0))) % 15.47/2.88 | | | | | % 15.47/2.88 | | | | | ALPHA: (64) implies: % 15.47/2.88 | | | | | (65) relation(all_42_2) = all_245_2 % 15.47/2.88 | | | | | (66) singleton(all_120_1) = all_245_1 % 15.47/2.88 | | | | | (67) relation_inverse_image(all_42_2, all_245_1) = all_245_0 % 15.47/2.88 | | | | | (68) ~ (all_245_2 = 0) | (( ~ (all_245_0 = empty_set) | ~ % 15.47/2.88 | | | | | (all_120_0 = 0)) & (all_245_0 = empty_set | all_120_0 = % 15.47/2.88 | | | | | 0)) % 15.47/2.88 | | | | | % 15.47/2.88 | | | | | GROUND_INST: instantiating (8) with 0, all_245_2, all_42_2, % 15.47/2.88 | | | | | simplifying with (26), (65) gives: % 15.47/2.88 | | | | | (69) all_245_2 = 0 % 15.47/2.88 | | | | | % 15.47/2.88 | | | | | GROUND_INST: instantiating (9) with all_207_1, all_245_1, all_120_1, % 15.47/2.88 | | | | | simplifying with (62), (66) gives: % 15.47/2.88 | | | | | (70) all_245_1 = all_207_1 % 15.47/2.88 | | | | | % 15.47/2.88 | | | | | REDUCE: (67), (70) imply: % 15.47/2.88 | | | | | (71) relation_inverse_image(all_42_2, all_207_1) = all_245_0 % 15.47/2.88 | | | | | % 15.47/2.88 | | | | | BETA: splitting (68) gives: % 15.47/2.88 | | | | | % 15.47/2.88 | | | | | Case 1: % 15.47/2.88 | | | | | | % 15.47/2.88 | | | | | | (72) ~ (all_245_2 = 0) % 15.47/2.88 | | | | | | % 15.47/2.88 | | | | | | REDUCE: (69), (72) imply: % 15.47/2.88 | | | | | | (73) $false % 15.47/2.88 | | | | | | % 15.47/2.88 | | | | | | CLOSE: (73) is inconsistent. % 15.47/2.88 | | | | | | % 15.47/2.88 | | | | | Case 2: % 15.47/2.88 | | | | | | % 15.47/2.88 | | | | | | (74) ( ~ (all_245_0 = empty_set) | ~ (all_120_0 = 0)) & % 15.47/2.88 | | | | | | (all_245_0 = empty_set | all_120_0 = 0) % 15.47/2.88 | | | | | | % 15.47/2.88 | | | | | | ALPHA: (74) implies: % 15.47/2.88 | | | | | | (75) all_245_0 = empty_set | all_120_0 = 0 % 15.47/2.88 | | | | | | % 15.47/2.88 | | | | | | BETA: splitting (75) gives: % 15.47/2.88 | | | | | | % 15.47/2.88 | | | | | | Case 1: % 15.47/2.88 | | | | | | | % 15.47/2.88 | | | | | | | (76) all_245_0 = empty_set % 15.47/2.88 | | | | | | | % 15.47/2.88 | | | | | | | REDUCE: (71), (76) imply: % 15.47/2.88 | | | | | | | (77) relation_inverse_image(all_42_2, all_207_1) = empty_set % 15.47/2.88 | | | | | | | % 15.47/2.88 | | | | | | | GROUND_INST: instantiating (11) with all_207_0, empty_set, % 15.47/2.88 | | | | | | | all_207_1, all_42_2, simplifying with (63), (77) % 15.47/2.88 | | | | | | | gives: % 15.47/2.88 | | | | | | | (78) all_207_0 = empty_set % 15.47/2.88 | | | | | | | % 15.47/2.88 | | | | | | | REDUCE: (61), (78) imply: % 15.47/2.88 | | | | | | | (79) $false % 15.47/2.88 | | | | | | | % 15.47/2.88 | | | | | | | CLOSE: (79) is inconsistent. % 15.47/2.88 | | | | | | | % 15.47/2.88 | | | | | | Case 2: % 15.47/2.88 | | | | | | | % 15.47/2.88 | | | | | | | (80) all_120_0 = 0 % 15.47/2.88 | | | | | | | % 15.47/2.88 | | | | | | | REDUCE: (49), (80) imply: % 15.47/2.88 | | | | | | | (81) $false % 15.47/2.88 | | | | | | | % 15.47/2.88 | | | | | | | CLOSE: (81) is inconsistent. % 15.47/2.88 | | | | | | | % 15.47/2.88 | | | | | | End of split % 15.47/2.88 | | | | | | % 15.47/2.88 | | | | | End of split % 15.47/2.88 | | | | | % 15.47/2.88 | | | | Case 2: % 15.47/2.88 | | | | | % 15.47/2.88 | | | | | (82) ~ (all_115_2 = 0) % 15.47/2.88 | | | | | % 15.47/2.88 | | | | | REDUCE: (55), (82) imply: % 15.47/2.88 | | | | | (83) $false % 15.47/2.88 | | | | | % 15.47/2.88 | | | | | CLOSE: (83) is inconsistent. % 15.47/2.88 | | | | | % 15.47/2.88 | | | | End of split % 15.47/2.88 | | | | % 15.47/2.88 | | | End of split % 15.47/2.88 | | | % 15.47/2.88 | | End of split % 15.47/2.88 | | % 15.47/2.88 | End of split % 15.47/2.88 | % 15.47/2.88 End of proof % 15.47/2.88 % SZS output end Proof for theBenchmark % 15.47/2.88 % 15.47/2.88 2223ms %------------------------------------------------------------------------------