%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM411+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 11:47:36 EDT 2023 % Result : Theorem 11.58s 2.32s % Output : Proof 19.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : NUM411+1 : TPTP v8.1.2. Released v3.2.0. % 0.06/0.12 % 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 : Fri Aug 25 08:25:57 EDT 2023 % 0.13/0.33 % CPUTime : % 0.52/0.60 ________ _____ % 0.52/0.60 ___ __ \_________(_)________________________________ % 0.52/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.52/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.52/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.52/0.60 % 0.52/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.52/0.60 (2023-06-19) % 0.52/0.60 % 0.52/0.60 (c) Philipp Rümmer, 2009-2023 % 0.52/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.52/0.60 Amanda Stjerna. % 0.52/0.60 Free software under BSD-3-Clause. % 0.52/0.60 % 0.52/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.52/0.60 % 0.52/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.52/0.61 Running up to 7 provers in parallel. % 0.52/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.52/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.52/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.52/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.52/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.52/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.52/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.84/1.10 Prover 4: Preprocessing ... % 2.84/1.10 Prover 1: Preprocessing ... % 3.21/1.14 Prover 3: Preprocessing ... % 3.21/1.14 Prover 0: Preprocessing ... % 3.21/1.14 Prover 2: Preprocessing ... % 3.21/1.14 Prover 6: Preprocessing ... % 3.21/1.14 Prover 5: Preprocessing ... % 6.01/1.53 Prover 1: Warning: ignoring some quantifiers % 6.01/1.56 Prover 2: Proving ... % 6.01/1.56 Prover 5: Proving ... % 6.29/1.58 Prover 1: Constructing countermodel ... % 6.29/1.61 Prover 6: Proving ... % 6.29/1.63 Prover 3: Warning: ignoring some quantifiers % 6.29/1.64 Prover 4: Warning: ignoring some quantifiers % 6.85/1.65 Prover 3: Constructing countermodel ... % 7.08/1.69 Prover 4: Constructing countermodel ... % 7.08/1.71 Prover 0: Proving ... % 9.30/2.00 Prover 3: gave up % 9.30/2.01 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.96/2.06 Prover 7: Preprocessing ... % 10.37/2.12 Prover 1: gave up % 10.37/2.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.37/2.17 Prover 8: Preprocessing ... % 10.68/2.19 Prover 7: Warning: ignoring some quantifiers % 10.68/2.20 Prover 7: Constructing countermodel ... % 11.58/2.31 Prover 8: Warning: ignoring some quantifiers % 11.58/2.32 Prover 0: proved (1703ms) % 11.58/2.32 % 11.58/2.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.58/2.32 % 11.58/2.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.58/2.33 Prover 2: stopped % 11.58/2.33 Prover 6: stopped % 11.58/2.33 Prover 5: stopped % 11.58/2.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.58/2.33 Prover 8: Constructing countermodel ... % 11.58/2.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.58/2.33 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 12.13/2.38 Prover 13: Preprocessing ... % 12.13/2.38 Prover 10: Preprocessing ... % 12.13/2.39 Prover 16: Preprocessing ... % 12.13/2.39 Prover 11: Preprocessing ... % 12.13/2.40 Prover 7: gave up % 12.13/2.40 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 12.60/2.43 Prover 19: Preprocessing ... % 12.60/2.44 Prover 10: Warning: ignoring some quantifiers % 12.60/2.44 Prover 10: Constructing countermodel ... % 12.93/2.46 Prover 13: Warning: ignoring some quantifiers % 12.93/2.47 Prover 13: Constructing countermodel ... % 12.93/2.48 Prover 16: Warning: ignoring some quantifiers % 12.93/2.49 Prover 16: Constructing countermodel ... % 12.93/2.53 Prover 10: gave up % 13.87/2.60 Prover 19: Warning: ignoring some quantifiers % 13.87/2.61 Prover 19: Constructing countermodel ... % 13.87/2.62 Prover 8: gave up % 13.87/2.63 Prover 11: Warning: ignoring some quantifiers % 14.29/2.64 Prover 11: Constructing countermodel ... % 15.26/2.82 Prover 19: gave up % 19.47/3.34 Prover 4: Found proof (size 60) % 19.47/3.34 Prover 4: proved (2716ms) % 19.47/3.34 Prover 13: stopped % 19.47/3.34 Prover 16: stopped % 19.47/3.34 Prover 11: stopped % 19.47/3.34 % 19.47/3.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.47/3.34 % 19.47/3.35 % SZS output start Proof for theBenchmark % 19.47/3.35 Assumptions after simplification: % 19.47/3.35 --------------------------------- % 19.47/3.35 % 19.47/3.35 (d8_ordinal1) % 19.78/3.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (relation_rng(v1) % 19.78/3.38 = v2) | ~ (subset(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : % 19.78/3.38 ? [v5: any] : ? [v6: any] : ? [v7: any] : (transfinite_sequence(v1) = v6 & % 19.78/3.38 transfinite_sequence_of(v1, v0) = v7 & relation(v1) = v4 & function(v1) = % 19.78/3.38 v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v7 = 0) | v3 = 0) & % 19.78/3.38 ( ~ (v3 = 0) | v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] % 19.78/3.38 : ( ~ (transfinite_sequence_of(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 19.78/3.38 any] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : % 19.78/3.38 (relation_rng(v1) = v6 & subset(v6, v0) = v7 & transfinite_sequence(v1) = v5 % 19.78/3.38 & relation(v1) = v3 & function(v1) = v4 & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = % 19.78/3.38 0) | ~ (v3 = 0) | (( ~ (v7 = 0) | v2 = 0) & ( ~ (v2 = 0) | v7 = % 19.78/3.38 0))))) % 19.78/3.38 % 19.78/3.38 (dt_m1_ordinal1) % 19.78/3.38 ! [v0: $i] : ! [v1: $i] : ( ~ (transfinite_sequence_of(v1, v0) = 0) | ~ % 19.78/3.38 $i(v1) | ~ $i(v0) | (transfinite_sequence(v1) = 0 & relation(v1) = 0 & % 19.78/3.38 function(v1) = 0)) % 19.78/3.38 % 19.78/3.38 (t1_xboole_1) % 19.78/3.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 19.78/3.38 (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 19.78/3.38 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : % 19.78/3.39 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (subset(v0, v2) = v3) % 19.78/3.39 | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] % 19.78/3.39 : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.78/3.39 $i] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ % 19.78/3.39 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0) % 19.78/3.39 % 19.78/3.39 (t47_ordinal1) % 19.78/3.39 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 19.78/3.39 subset(v0, v1) = 0 & transfinite_sequence_of(v2, v1) = v3 & % 19.78/3.39 transfinite_sequence_of(v2, v0) = 0 & $i(v2) & $i(v1) & $i(v0)) % 19.78/3.39 % 19.78/3.39 (function-axioms) % 19.78/3.39 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 19.78/3.39 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 19.78/3.39 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 19.78/3.39 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 19.78/3.39 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 19.78/3.39 $i] : (v1 = v0 | ~ (transfinite_sequence_of(v3, v2) = v1) | ~ % 19.78/3.39 (transfinite_sequence_of(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 19.78/3.39 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, % 19.78/3.39 v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.78/3.39 $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: % 19.78/3.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 19.78/3.39 ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0)) & ! % 19.78/3.39 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 19.78/3.39 | ~ (with_non_empty_elements(v2) = v1) | ~ (with_non_empty_elements(v2) = % 19.78/3.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 19.78/3.39 $i] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ % 19.78/3.39 (relation_empty_yielding(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.78/3.39 $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & % 19.78/3.39 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 19.78/3.39 v0 | ~ (transfinite_sequence(v2) = v1) | ~ (transfinite_sequence(v2) = % 19.78/3.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 19.78/3.39 $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! % 19.78/3.39 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 19.78/3.39 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: % 19.78/3.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 19.78/3.39 ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! % 19.78/3.39 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 19.78/3.39 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0: % 19.78/3.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 19.78/3.39 ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: % 19.78/3.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 19.78/3.39 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] % 19.78/3.39 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | % 19.78/3.39 ~ (empty(v2) = v0)) % 19.78/3.39 % 19.78/3.39 Further assumptions not needed in the proof: % 19.78/3.39 -------------------------------------------- % 19.78/3.40 antisymmetry_r2_hidden, cc1_funct_1, cc1_ordinal1, cc1_relat_1, cc2_funct_1, % 19.78/3.40 cc2_ordinal1, cc3_ordinal1, existence_m1_ordinal1, existence_m1_subset_1, % 19.78/3.40 fc12_relat_1, fc1_xboole_0, fc2_ordinal1, fc4_relat_1, fc6_funct_1, fc6_relat_1, % 19.78/3.40 fc8_relat_1, rc1_funct_1, rc1_ordinal1, rc1_relat_1, rc1_xboole_0, rc2_funct_1, % 19.78/3.40 rc2_ordinal1, rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_ordinal1, rc3_relat_1, % 19.78/3.40 rc4_funct_1, rc4_ordinal1, rc5_funct_1, reflexivity_r1_tarski, t1_subset, % 19.78/3.40 t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 19.78/3.40 % 19.78/3.40 Those formulas are unsatisfiable: % 19.78/3.40 --------------------------------- % 19.78/3.40 % 19.78/3.40 Begin of proof % 19.78/3.40 | % 19.78/3.40 | ALPHA: (d8_ordinal1) implies: % 19.78/3.40 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 19.78/3.40 | (transfinite_sequence_of(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 19.78/3.40 | [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] % 19.78/3.40 | : (relation_rng(v1) = v6 & subset(v6, v0) = v7 & % 19.78/3.40 | transfinite_sequence(v1) = v5 & relation(v1) = v3 & function(v1) = % 19.78/3.40 | v4 & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v7 = % 19.78/3.40 | 0) | v2 = 0) & ( ~ (v2 = 0) | v7 = 0))))) % 19.78/3.40 | % 19.78/3.40 | ALPHA: (t1_xboole_1) implies: % 19.78/3.40 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v1, v2) = 0) | ~ % 19.78/3.40 | (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | subset(v0, % 19.78/3.40 | v2) = 0) % 19.78/3.40 | % 19.78/3.40 | ALPHA: (function-axioms) implies: % 19.78/3.40 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 19.78/3.40 | (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 19.78/3.40 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 19.78/3.40 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 19.78/3.40 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 19.78/3.40 | (v1 = v0 | ~ (transfinite_sequence(v2) = v1) | ~ % 19.78/3.40 | (transfinite_sequence(v2) = v0)) % 19.78/3.40 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.78/3.40 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 19.78/3.40 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 19.78/3.40 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) % 19.78/3.40 | = v0)) % 19.78/3.40 | % 19.78/3.40 | DELTA: instantiating (t47_ordinal1) with fresh symbols all_54_0, all_54_1, % 19.78/3.40 | all_54_2, all_54_3 gives: % 19.78/3.40 | (8) ~ (all_54_0 = 0) & subset(all_54_3, all_54_2) = 0 & % 19.78/3.40 | transfinite_sequence_of(all_54_1, all_54_2) = all_54_0 & % 19.78/3.40 | transfinite_sequence_of(all_54_1, all_54_3) = 0 & $i(all_54_1) & % 19.78/3.40 | $i(all_54_2) & $i(all_54_3) % 19.78/3.40 | % 19.78/3.40 | ALPHA: (8) implies: % 19.78/3.40 | (9) ~ (all_54_0 = 0) % 19.78/3.40 | (10) $i(all_54_3) % 19.78/3.40 | (11) $i(all_54_2) % 19.78/3.40 | (12) $i(all_54_1) % 19.78/3.40 | (13) transfinite_sequence_of(all_54_1, all_54_3) = 0 % 19.78/3.40 | (14) transfinite_sequence_of(all_54_1, all_54_2) = all_54_0 % 19.78/3.40 | (15) subset(all_54_3, all_54_2) = 0 % 19.78/3.40 | % 19.78/3.41 | GROUND_INST: instantiating (dt_m1_ordinal1) with all_54_3, all_54_1, % 19.78/3.41 | simplifying with (10), (12), (13) gives: % 19.78/3.41 | (16) transfinite_sequence(all_54_1) = 0 & relation(all_54_1) = 0 & % 19.78/3.41 | function(all_54_1) = 0 % 19.78/3.41 | % 19.78/3.41 | ALPHA: (16) implies: % 19.78/3.41 | (17) function(all_54_1) = 0 % 19.78/3.41 | (18) relation(all_54_1) = 0 % 19.78/3.41 | (19) transfinite_sequence(all_54_1) = 0 % 19.78/3.41 | % 19.78/3.41 | GROUND_INST: instantiating (1) with all_54_3, all_54_1, 0, simplifying with % 19.78/3.41 | (10), (12), (13) gives: % 19.78/3.41 | (20) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 19.78/3.41 | any] : (relation_rng(all_54_1) = v3 & subset(v3, all_54_3) = v4 & % 19.78/3.41 | transfinite_sequence(all_54_1) = v2 & relation(all_54_1) = v0 & % 19.78/3.41 | function(all_54_1) = v1 & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 19.78/3.41 | (v0 = 0) | v4 = 0)) % 19.78/3.41 | % 19.78/3.41 | GROUND_INST: instantiating (1) with all_54_2, all_54_1, all_54_0, simplifying % 19.78/3.41 | with (11), (12), (14) gives: % 19.78/3.41 | (21) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 19.78/3.41 | any] : (relation_rng(all_54_1) = v3 & subset(v3, all_54_2) = v4 & % 19.78/3.41 | transfinite_sequence(all_54_1) = v2 & relation(all_54_1) = v0 & % 19.78/3.41 | function(all_54_1) = v1 & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 19.78/3.41 | (v0 = 0) | (( ~ (v4 = 0) | all_54_0 = 0) & ( ~ (all_54_0 = 0) | v4 % 19.78/3.41 | = 0)))) % 19.78/3.41 | % 19.78/3.41 | DELTA: instantiating (20) with fresh symbols all_182_0, all_182_1, all_182_2, % 19.78/3.41 | all_182_3, all_182_4 gives: % 19.78/3.41 | (22) relation_rng(all_54_1) = all_182_1 & subset(all_182_1, all_54_3) = % 19.78/3.41 | all_182_0 & transfinite_sequence(all_54_1) = all_182_2 & % 19.78/3.41 | relation(all_54_1) = all_182_4 & function(all_54_1) = all_182_3 & % 19.78/3.41 | $i(all_182_1) & ( ~ (all_182_2 = 0) | ~ (all_182_3 = 0) | ~ % 19.78/3.41 | (all_182_4 = 0) | all_182_0 = 0) % 19.78/3.41 | % 19.78/3.41 | ALPHA: (22) implies: % 19.78/3.41 | (23) function(all_54_1) = all_182_3 % 19.78/3.41 | (24) relation(all_54_1) = all_182_4 % 19.78/3.41 | (25) transfinite_sequence(all_54_1) = all_182_2 % 19.78/3.41 | (26) subset(all_182_1, all_54_3) = all_182_0 % 19.78/3.41 | (27) relation_rng(all_54_1) = all_182_1 % 19.78/3.41 | (28) ~ (all_182_2 = 0) | ~ (all_182_3 = 0) | ~ (all_182_4 = 0) | % 19.78/3.41 | all_182_0 = 0 % 19.78/3.41 | % 19.78/3.41 | DELTA: instantiating (21) with fresh symbols all_184_0, all_184_1, all_184_2, % 19.78/3.41 | all_184_3, all_184_4 gives: % 19.78/3.41 | (29) relation_rng(all_54_1) = all_184_1 & subset(all_184_1, all_54_2) = % 19.78/3.41 | all_184_0 & transfinite_sequence(all_54_1) = all_184_2 & % 19.78/3.41 | relation(all_54_1) = all_184_4 & function(all_54_1) = all_184_3 & % 19.78/3.41 | $i(all_184_1) & ( ~ (all_184_2 = 0) | ~ (all_184_3 = 0) | ~ % 19.78/3.41 | (all_184_4 = 0) | (( ~ (all_184_0 = 0) | all_54_0 = 0) & ( ~ % 19.78/3.41 | (all_54_0 = 0) | all_184_0 = 0))) % 19.78/3.41 | % 19.78/3.41 | ALPHA: (29) implies: % 19.78/3.41 | (30) $i(all_184_1) % 19.78/3.41 | (31) function(all_54_1) = all_184_3 % 19.78/3.41 | (32) relation(all_54_1) = all_184_4 % 19.78/3.41 | (33) transfinite_sequence(all_54_1) = all_184_2 % 19.78/3.41 | (34) subset(all_184_1, all_54_2) = all_184_0 % 19.78/3.41 | (35) relation_rng(all_54_1) = all_184_1 % 19.78/3.41 | (36) ~ (all_184_2 = 0) | ~ (all_184_3 = 0) | ~ (all_184_4 = 0) | (( ~ % 19.78/3.41 | (all_184_0 = 0) | all_54_0 = 0) & ( ~ (all_54_0 = 0) | all_184_0 = % 19.78/3.41 | 0)) % 19.78/3.41 | % 19.78/3.41 | GROUND_INST: instantiating (3) with all_182_3, all_184_3, all_54_1, % 19.78/3.41 | simplifying with (23), (31) gives: % 19.78/3.41 | (37) all_184_3 = all_182_3 % 19.78/3.41 | % 19.78/3.41 | GROUND_INST: instantiating (3) with 0, all_184_3, all_54_1, simplifying with % 19.78/3.41 | (17), (31) gives: % 19.78/3.41 | (38) all_184_3 = 0 % 19.78/3.41 | % 19.78/3.41 | GROUND_INST: instantiating (4) with all_182_4, all_184_4, all_54_1, % 19.78/3.41 | simplifying with (24), (32) gives: % 19.78/3.41 | (39) all_184_4 = all_182_4 % 19.78/3.41 | % 19.78/3.41 | GROUND_INST: instantiating (4) with 0, all_184_4, all_54_1, simplifying with % 19.78/3.41 | (18), (32) gives: % 19.78/3.41 | (40) all_184_4 = 0 % 19.78/3.41 | % 19.78/3.42 | GROUND_INST: instantiating (5) with all_182_2, all_184_2, all_54_1, % 19.78/3.42 | simplifying with (25), (33) gives: % 19.78/3.42 | (41) all_184_2 = all_182_2 % 19.78/3.42 | % 19.78/3.42 | GROUND_INST: instantiating (5) with 0, all_184_2, all_54_1, simplifying with % 19.78/3.42 | (19), (33) gives: % 19.78/3.42 | (42) all_184_2 = 0 % 19.78/3.42 | % 19.78/3.42 | GROUND_INST: instantiating (6) with all_182_1, all_184_1, all_54_1, % 19.78/3.42 | simplifying with (27), (35) gives: % 19.78/3.42 | (43) all_184_1 = all_182_1 % 19.78/3.42 | % 19.78/3.42 | COMBINE_EQS: (41), (42) imply: % 19.78/3.42 | (44) all_182_2 = 0 % 19.78/3.42 | % 19.78/3.42 | SIMP: (44) implies: % 19.78/3.42 | (45) all_182_2 = 0 % 19.78/3.42 | % 19.78/3.42 | COMBINE_EQS: (37), (38) imply: % 19.78/3.42 | (46) all_182_3 = 0 % 19.78/3.42 | % 19.78/3.42 | SIMP: (46) implies: % 19.78/3.42 | (47) all_182_3 = 0 % 19.78/3.42 | % 19.78/3.42 | COMBINE_EQS: (39), (40) imply: % 19.78/3.42 | (48) all_182_4 = 0 % 19.78/3.42 | % 19.78/3.42 | SIMP: (48) implies: % 19.78/3.42 | (49) all_182_4 = 0 % 19.78/3.42 | % 19.78/3.42 | REDUCE: (34), (43) imply: % 19.78/3.42 | (50) subset(all_182_1, all_54_2) = all_184_0 % 19.78/3.42 | % 19.78/3.42 | REDUCE: (30), (43) imply: % 19.78/3.42 | (51) $i(all_182_1) % 19.78/3.42 | % 19.78/3.42 | BETA: splitting (36) gives: % 19.78/3.42 | % 19.78/3.42 | Case 1: % 19.78/3.42 | | % 19.78/3.42 | | (52) ~ (all_184_2 = 0) % 19.78/3.42 | | % 19.78/3.42 | | REDUCE: (42), (52) imply: % 19.78/3.42 | | (53) $false % 19.78/3.42 | | % 19.78/3.42 | | CLOSE: (53) is inconsistent. % 19.78/3.42 | | % 19.78/3.42 | Case 2: % 19.78/3.42 | | % 19.78/3.42 | | (54) ~ (all_184_3 = 0) | ~ (all_184_4 = 0) | (( ~ (all_184_0 = 0) | % 19.78/3.42 | | all_54_0 = 0) & ( ~ (all_54_0 = 0) | all_184_0 = 0)) % 19.78/3.42 | | % 19.78/3.42 | | BETA: splitting (28) gives: % 19.78/3.42 | | % 19.78/3.42 | | Case 1: % 19.78/3.42 | | | % 19.78/3.42 | | | (55) ~ (all_182_2 = 0) % 19.78/3.42 | | | % 19.78/3.42 | | | REDUCE: (45), (55) imply: % 19.78/3.42 | | | (56) $false % 19.78/3.42 | | | % 19.78/3.42 | | | CLOSE: (56) is inconsistent. % 19.78/3.42 | | | % 19.78/3.42 | | Case 2: % 19.78/3.42 | | | % 19.78/3.42 | | | (57) ~ (all_182_3 = 0) | ~ (all_182_4 = 0) | all_182_0 = 0 % 19.78/3.42 | | | % 19.78/3.42 | | | BETA: splitting (54) gives: % 19.78/3.42 | | | % 19.78/3.42 | | | Case 1: % 19.78/3.42 | | | | % 19.78/3.42 | | | | (58) ~ (all_184_3 = 0) % 19.78/3.42 | | | | % 19.78/3.42 | | | | REDUCE: (38), (58) imply: % 19.78/3.42 | | | | (59) $false % 19.78/3.42 | | | | % 19.78/3.42 | | | | CLOSE: (59) is inconsistent. % 19.78/3.42 | | | | % 19.78/3.42 | | | Case 2: % 19.78/3.42 | | | | % 19.78/3.42 | | | | (60) ~ (all_184_4 = 0) | (( ~ (all_184_0 = 0) | all_54_0 = 0) & ( ~ % 19.78/3.42 | | | | (all_54_0 = 0) | all_184_0 = 0)) % 19.78/3.42 | | | | % 19.78/3.42 | | | | BETA: splitting (60) gives: % 19.78/3.42 | | | | % 19.78/3.42 | | | | Case 1: % 19.78/3.42 | | | | | % 19.78/3.42 | | | | | (61) ~ (all_184_4 = 0) % 19.78/3.42 | | | | | % 19.78/3.42 | | | | | REDUCE: (40), (61) imply: % 19.78/3.42 | | | | | (62) $false % 19.78/3.42 | | | | | % 19.78/3.42 | | | | | CLOSE: (62) is inconsistent. % 19.78/3.42 | | | | | % 19.78/3.42 | | | | Case 2: % 19.78/3.42 | | | | | % 19.78/3.42 | | | | | (63) ( ~ (all_184_0 = 0) | all_54_0 = 0) & ( ~ (all_54_0 = 0) | % 19.78/3.42 | | | | | all_184_0 = 0) % 19.78/3.42 | | | | | % 19.78/3.42 | | | | | ALPHA: (63) implies: % 19.78/3.42 | | | | | (64) ~ (all_184_0 = 0) | all_54_0 = 0 % 19.78/3.42 | | | | | % 19.78/3.42 | | | | | BETA: splitting (64) gives: % 19.78/3.42 | | | | | % 19.78/3.42 | | | | | Case 1: % 19.78/3.42 | | | | | | % 19.78/3.42 | | | | | | (65) ~ (all_184_0 = 0) % 19.78/3.42 | | | | | | % 19.78/3.42 | | | | | | BETA: splitting (57) gives: % 19.78/3.42 | | | | | | % 19.78/3.42 | | | | | | Case 1: % 19.78/3.42 | | | | | | | % 19.78/3.42 | | | | | | | (66) ~ (all_182_3 = 0) % 19.78/3.42 | | | | | | | % 19.78/3.42 | | | | | | | REDUCE: (47), (66) imply: % 19.78/3.42 | | | | | | | (67) $false % 19.78/3.42 | | | | | | | % 19.78/3.42 | | | | | | | CLOSE: (67) is inconsistent. % 19.78/3.42 | | | | | | | % 19.78/3.42 | | | | | | Case 2: % 19.78/3.42 | | | | | | | % 19.78/3.42 | | | | | | | (68) ~ (all_182_4 = 0) | all_182_0 = 0 % 19.78/3.42 | | | | | | | % 19.78/3.42 | | | | | | | BETA: splitting (68) gives: % 19.78/3.42 | | | | | | | % 19.78/3.42 | | | | | | | Case 1: % 19.78/3.42 | | | | | | | | % 19.78/3.42 | | | | | | | | (69) ~ (all_182_4 = 0) % 19.78/3.42 | | | | | | | | % 19.78/3.42 | | | | | | | | REDUCE: (49), (69) imply: % 19.78/3.42 | | | | | | | | (70) $false % 19.78/3.42 | | | | | | | | % 19.78/3.42 | | | | | | | | CLOSE: (70) is inconsistent. % 19.78/3.42 | | | | | | | | % 19.78/3.42 | | | | | | | Case 2: % 19.78/3.42 | | | | | | | | % 19.78/3.42 | | | | | | | | (71) all_182_0 = 0 % 19.78/3.42 | | | | | | | | % 19.78/3.42 | | | | | | | | REDUCE: (26), (71) imply: % 19.78/3.42 | | | | | | | | (72) subset(all_182_1, all_54_3) = 0 % 19.78/3.42 | | | | | | | | % 19.78/3.42 | | | | | | | | GROUND_INST: instantiating (2) with all_182_1, all_54_3, % 19.78/3.42 | | | | | | | | all_54_2, simplifying with (10), (11), (15), (51), % 19.78/3.42 | | | | | | | | (72) gives: % 19.78/3.42 | | | | | | | | (73) subset(all_182_1, all_54_2) = 0 % 19.78/3.42 | | | | | | | | % 19.78/3.42 | | | | | | | | GROUND_INST: instantiating (7) with all_184_0, 0, all_54_2, % 19.78/3.42 | | | | | | | | all_182_1, simplifying with (50), (73) gives: % 19.78/3.43 | | | | | | | | (74) all_184_0 = 0 % 19.78/3.43 | | | | | | | | % 19.78/3.43 | | | | | | | | REDUCE: (65), (74) imply: % 19.78/3.43 | | | | | | | | (75) $false % 19.78/3.43 | | | | | | | | % 19.78/3.43 | | | | | | | | CLOSE: (75) is inconsistent. % 19.78/3.43 | | | | | | | | % 19.78/3.43 | | | | | | | End of split % 19.78/3.43 | | | | | | | % 19.78/3.43 | | | | | | End of split % 19.78/3.43 | | | | | | % 19.78/3.43 | | | | | Case 2: % 19.78/3.43 | | | | | | % 19.78/3.43 | | | | | | (76) all_54_0 = 0 % 19.78/3.43 | | | | | | % 19.78/3.43 | | | | | | REDUCE: (9), (76) imply: % 19.78/3.43 | | | | | | (77) $false % 19.78/3.43 | | | | | | % 19.78/3.43 | | | | | | CLOSE: (77) is inconsistent. % 19.78/3.43 | | | | | | % 19.78/3.43 | | | | | End of split % 19.78/3.43 | | | | | % 19.78/3.43 | | | | End of split % 19.78/3.43 | | | | % 19.78/3.43 | | | End of split % 19.78/3.43 | | | % 19.78/3.43 | | End of split % 19.78/3.43 | | % 19.78/3.43 | End of split % 19.78/3.43 | % 19.78/3.43 End of proof % 19.78/3.43 % SZS output end Proof for theBenchmark % 19.78/3.43 % 19.78/3.43 2826ms %------------------------------------------------------------------------------