%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU110+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 : n009.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 17:42:33 EDT 2023 % Result : Theorem 11.85s 2.37s % Output : Proof 20.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU110+1 : TPTP v8.1.2. Released v3.2.0. % 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n009.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Wed Aug 23 18:29:36 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.90/1.13 Prover 1: Preprocessing ... % 2.90/1.13 Prover 4: Preprocessing ... % 2.90/1.17 Prover 6: Preprocessing ... % 2.90/1.17 Prover 2: Preprocessing ... % 2.90/1.17 Prover 5: Preprocessing ... % 2.90/1.17 Prover 3: Preprocessing ... % 2.90/1.17 Prover 0: Preprocessing ... % 5.56/1.54 Prover 5: Proving ... % 5.56/1.56 Prover 1: Warning: ignoring some quantifiers % 5.56/1.59 Prover 2: Proving ... % 5.56/1.60 Prover 1: Constructing countermodel ... % 6.65/1.67 Prover 3: Warning: ignoring some quantifiers % 6.65/1.69 Prover 3: Constructing countermodel ... % 6.65/1.70 Prover 6: Proving ... % 6.65/1.71 Prover 4: Warning: ignoring some quantifiers % 7.30/1.75 Prover 4: Constructing countermodel ... % 7.30/1.78 Prover 0: Proving ... % 11.85/2.37 Prover 3: proved (1726ms) % 11.85/2.37 % 11.85/2.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.85/2.37 % 11.85/2.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.85/2.37 Prover 0: stopped % 11.85/2.37 Prover 2: stopped % 11.85/2.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.85/2.38 Prover 6: stopped % 11.85/2.38 Prover 5: stopped % 12.07/2.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.07/2.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.07/2.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.07/2.42 Prover 8: Preprocessing ... % 12.47/2.44 Prover 7: Preprocessing ... % 12.47/2.45 Prover 10: Preprocessing ... % 12.47/2.46 Prover 11: Preprocessing ... % 12.47/2.46 Prover 13: Preprocessing ... % 12.47/2.50 Prover 10: Warning: ignoring some quantifiers % 13.02/2.51 Prover 10: Constructing countermodel ... % 13.02/2.53 Prover 7: Warning: ignoring some quantifiers % 13.02/2.54 Prover 7: Constructing countermodel ... % 13.02/2.55 Prover 13: Warning: ignoring some quantifiers % 13.02/2.56 Prover 13: Constructing countermodel ... % 13.47/2.59 Prover 8: Warning: ignoring some quantifiers % 13.47/2.63 Prover 8: Constructing countermodel ... % 14.11/2.67 Prover 11: Warning: ignoring some quantifiers % 14.11/2.67 Prover 11: Constructing countermodel ... % 14.77/2.80 Prover 10: gave up % 14.77/2.81 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 14.77/2.84 Prover 16: Preprocessing ... % 14.77/2.88 Prover 7: gave up % 14.77/2.89 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 15.74/2.93 Prover 19: Preprocessing ... % 15.74/2.94 Prover 16: Warning: ignoring some quantifiers % 15.74/2.94 Prover 16: Constructing countermodel ... % 16.50/3.05 Prover 13: gave up % 17.30/3.09 Prover 19: Warning: ignoring some quantifiers % 17.30/3.09 Prover 19: Constructing countermodel ... % 19.82/3.47 Prover 1: Found proof (size 74) % 19.82/3.47 Prover 1: proved (2837ms) % 19.82/3.47 Prover 19: stopped % 19.82/3.47 Prover 16: stopped % 19.82/3.47 Prover 11: stopped % 19.82/3.47 Prover 4: stopped % 19.82/3.48 Prover 8: stopped % 19.82/3.48 % 19.82/3.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.82/3.48 % 19.82/3.49 % SZS output start Proof for theBenchmark % 19.82/3.49 Assumptions after simplification: % 19.82/3.49 --------------------------------- % 19.82/3.49 % 19.82/3.49 (cc2_finset_1) % 19.82/3.52 ! [v0: $i] : ( ~ (finite(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (powerset(v0) = % 19.82/3.52 v1 & $i(v1) & ! [v2: $i] : ( ~ (element(v2, v1) = 0) | ~ $i(v2) | % 19.82/3.52 finite(v2) = 0))) % 19.82/3.52 % 19.82/3.52 (cc3_finsub_1) % 19.82/3.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (finite_subsets(v0) = v2) | ~ % 19.82/3.52 (element(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | finite(v1) = 0) % 19.82/3.52 % 19.82/3.52 (d3_tarski) % 19.82/3.52 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 19.82/3.52 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 19.82/3.52 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 19.82/3.52 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 19.82/3.52 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 19.82/3.52 % 19.82/3.52 (d5_finsub_1) % 19.82/3.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (finite_subsets(v0) = v2) | ~ % 19.82/3.53 (preboolean(v1) = 0) | ~ $i(v1) | ~ $i(v0) | (( ~ (v2 = v1) | ( ! [v3: $i] % 19.82/3.53 : ! [v4: any] : ( ~ (finite(v3) = v4) | ~ $i(v3) | ? [v5: any] : ? % 19.82/3.53 [v6: any] : (subset(v3, v0) = v6 & in(v3, v1) = v5 & ( ~ (v5 = 0) | % 19.82/3.53 (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (finite(v3) = 0) | ~ % 19.82/3.53 $i(v3) | ? [v4: any] : ? [v5: any] : (subset(v3, v0) = v4 & in(v3, % 19.82/3.53 v1) = v5 & ( ~ (v4 = 0) | v5 = 0))))) & (v2 = v1 | ? [v3: $i] : % 19.82/3.53 ? [v4: any] : ? [v5: any] : ? [v6: any] : (subset(v3, v0) = v5 & % 19.82/3.53 finite(v3) = v6 & in(v3, v1) = v4 & $i(v3) & ( ~ (v6 = 0) | ~ (v5 = % 19.82/3.53 0) | ~ (v4 = 0)) & (v4 = 0 | (v6 = 0 & v5 = 0)))))) % 19.82/3.53 % 19.82/3.53 (fc2_finsub_1) % 19.82/3.53 ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | % 19.82/3.53 diff_closed(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = % 19.82/3.53 v1) | ~ $i(v0) | preboolean(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 19.82/3.53 (finite_subsets(v0) = v1) | ~ $i(v0) | cup_closed(v1) = 0) & ! [v0: $i] : % 19.82/3.53 ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 19.82/3.53 (v2 = 0) & empty(v1) = v2)) % 19.82/3.53 % 19.82/3.53 (rc1_finset_1) % 20.30/3.53 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & finite(v0) = 0 & empty(v0) = v1 & % 20.30/3.53 $i(v0)) % 20.30/3.53 % 20.30/3.53 (rc1_subset_1) % 20.30/3.53 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | empty(v0) = % 20.30/3.53 0 | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & element(v2, v1) = 0 & % 20.30/3.53 empty(v2) = v3 & $i(v2))) % 20.30/3.53 % 20.30/3.53 (t1_subset) % 20.30/3.53 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 20.30/3.53 element(v0, v1) = 0) % 20.30/3.53 % 20.30/3.53 (t1_xboole_1) % 20.30/3.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.30/3.53 (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 20.30/3.53 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 20.30/3.53 % 20.30/3.53 (t23_finsub_1) % 20.30/3.54 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 20.30/3.54 = 0) & subset(v2, v3) = v4 & subset(v0, v1) = 0 & finite_subsets(v1) = v3 % 20.30/3.54 & finite_subsets(v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 20.30/3.54 % 20.30/3.54 (function-axioms) % 20.30/3.54 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 20.30/3.54 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 20.30/3.54 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 20.30/3.54 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! % 20.30/3.54 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 20.30/3.54 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 20.30/3.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 20.30/3.54 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] % 20.30/3.54 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) % 20.30/3.54 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.30/3.54 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ % 20.30/3.54 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.30/3.54 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_transitive(v2) = % 20.30/3.54 v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 20.30/3.54 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_connected(v2) = % 20.30/3.54 v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 20.30/3.54 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ % 20.30/3.54 (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.30/3.54 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (natural(v2) = v1) | ~ % 20.30/3.54 (natural(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.30/3.54 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cap_closed(v2) = v1) | ~ % 20.30/3.54 (cap_closed(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 20.30/3.54 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0)) & ! [v0: $i] % 20.30/3.54 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 20.30/3.54 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.30/3.54 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (diff_closed(v2) = v1) | ~ % 20.30/3.54 (diff_closed(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.30/3.54 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (preboolean(v2) = v1) | ~ % 20.30/3.54 (preboolean(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.30/3.54 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cup_closed(v2) = v1) | ~ % 20.30/3.54 (cup_closed(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.30/3.54 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (finite(v2) = v1) | ~ % 20.30/3.54 (finite(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 20.30/3.54 : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 20.30/3.54 % 20.30/3.54 Further assumptions not needed in the proof: % 20.30/3.54 -------------------------------------------- % 20.30/3.54 antisymmetry_r2_hidden, cc1_finset_1, cc1_finsub_1, cc2_finsub_1, % 20.30/3.54 dt_k5_finsub_1, existence_m1_subset_1, fc1_finsub_1, fc1_subset_1, fc1_xboole_0, % 20.30/3.54 rc1_finsub_1, rc1_xboole_0, rc2_finset_1, rc2_subset_1, rc2_xboole_0, % 20.30/3.54 rc3_finset_1, rc4_finset_1, reflexivity_r1_tarski, t2_subset, t3_subset, % 20.30/3.54 t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 20.30/3.54 % 20.30/3.54 Those formulas are unsatisfiable: % 20.30/3.54 --------------------------------- % 20.30/3.54 % 20.30/3.54 Begin of proof % 20.30/3.54 | % 20.30/3.54 | ALPHA: (d3_tarski) implies: % 20.30/3.54 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 20.30/3.54 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 20.30/3.54 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 20.30/3.54 | % 20.30/3.54 | ALPHA: (fc2_finsub_1) implies: % 20.30/3.54 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | % 20.30/3.54 | preboolean(v1) = 0) % 20.30/3.54 | % 20.30/3.54 | ALPHA: (function-axioms) implies: % 20.30/3.54 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.30/3.54 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 20.30/3.55 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.30/3.55 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 20.30/3.55 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.30/3.55 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) % 20.30/3.55 | = v0)) % 20.30/3.55 | % 20.30/3.55 | DELTA: instantiating (rc1_finset_1) with fresh symbols all_37_0, all_37_1 % 20.30/3.55 | gives: % 20.30/3.55 | (6) ~ (all_37_0 = 0) & finite(all_37_1) = 0 & empty(all_37_1) = all_37_0 & % 20.30/3.55 | $i(all_37_1) % 20.30/3.55 | % 20.30/3.55 | ALPHA: (6) implies: % 20.30/3.55 | (7) ~ (all_37_0 = 0) % 20.30/3.55 | (8) $i(all_37_1) % 20.30/3.55 | (9) empty(all_37_1) = all_37_0 % 20.30/3.55 | (10) finite(all_37_1) = 0 % 20.30/3.55 | % 20.30/3.55 | DELTA: instantiating (t23_finsub_1) with fresh symbols all_41_0, all_41_1, % 20.30/3.55 | all_41_2, all_41_3, all_41_4 gives: % 20.30/3.55 | (11) ~ (all_41_0 = 0) & subset(all_41_2, all_41_1) = all_41_0 & % 20.30/3.55 | subset(all_41_4, all_41_3) = 0 & finite_subsets(all_41_3) = all_41_1 & % 20.30/3.55 | finite_subsets(all_41_4) = all_41_2 & $i(all_41_1) & $i(all_41_2) & % 20.30/3.55 | $i(all_41_3) & $i(all_41_4) % 20.30/3.55 | % 20.30/3.55 | ALPHA: (11) implies: % 20.30/3.55 | (12) ~ (all_41_0 = 0) % 20.30/3.55 | (13) $i(all_41_4) % 20.30/3.55 | (14) $i(all_41_3) % 20.30/3.55 | (15) $i(all_41_2) % 20.30/3.55 | (16) $i(all_41_1) % 20.30/3.55 | (17) finite_subsets(all_41_4) = all_41_2 % 20.30/3.55 | (18) finite_subsets(all_41_3) = all_41_1 % 20.30/3.55 | (19) subset(all_41_4, all_41_3) = 0 % 20.30/3.55 | (20) subset(all_41_2, all_41_1) = all_41_0 % 20.30/3.55 | % 20.30/3.55 | GROUND_INST: instantiating (cc2_finset_1) with all_37_1, simplifying with (8), % 20.30/3.55 | (10) gives: % 20.30/3.55 | (21) ? [v0: $i] : (powerset(all_37_1) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 20.30/3.55 | (element(v1, v0) = 0) | ~ $i(v1) | finite(v1) = 0)) % 20.30/3.55 | % 20.30/3.55 | GROUND_INST: instantiating (2) with all_41_4, all_41_2, simplifying with (13), % 20.30/3.55 | (17) gives: % 20.30/3.55 | (22) preboolean(all_41_2) = 0 % 20.30/3.55 | % 20.30/3.55 | GROUND_INST: instantiating (2) with all_41_3, all_41_1, simplifying with (14), % 20.30/3.55 | (18) gives: % 20.30/3.55 | (23) preboolean(all_41_1) = 0 % 20.30/3.55 | % 20.30/3.55 | GROUND_INST: instantiating (1) with all_41_2, all_41_1, all_41_0, simplifying % 20.30/3.55 | with (15), (16), (20) gives: % 20.30/3.55 | (24) all_41_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 20.30/3.55 | all_41_1) = v1 & in(v0, all_41_2) = 0 & $i(v0)) % 20.30/3.55 | % 20.30/3.55 | DELTA: instantiating (21) with fresh symbol all_54_0 gives: % 20.30/3.55 | (25) powerset(all_37_1) = all_54_0 & $i(all_54_0) & ! [v0: $i] : ( ~ % 20.30/3.55 | (element(v0, all_54_0) = 0) | ~ $i(v0) | finite(v0) = 0) % 20.30/3.55 | % 20.30/3.55 | ALPHA: (25) implies: % 20.30/3.55 | (26) powerset(all_37_1) = all_54_0 % 20.30/3.55 | % 20.30/3.55 | BETA: splitting (24) gives: % 20.30/3.55 | % 20.30/3.55 | Case 1: % 20.30/3.55 | | % 20.30/3.55 | | (27) all_41_0 = 0 % 20.30/3.55 | | % 20.30/3.55 | | REDUCE: (12), (27) imply: % 20.30/3.55 | | (28) $false % 20.30/3.55 | | % 20.30/3.55 | | CLOSE: (28) is inconsistent. % 20.30/3.55 | | % 20.30/3.55 | Case 2: % 20.30/3.55 | | % 20.30/3.55 | | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_41_1) = v1 & % 20.30/3.55 | | in(v0, all_41_2) = 0 & $i(v0)) % 20.30/3.55 | | % 20.30/3.55 | | DELTA: instantiating (29) with fresh symbols all_61_0, all_61_1 gives: % 20.30/3.56 | | (30) ~ (all_61_0 = 0) & in(all_61_1, all_41_1) = all_61_0 & in(all_61_1, % 20.30/3.56 | | all_41_2) = 0 & $i(all_61_1) % 20.30/3.56 | | % 20.30/3.56 | | ALPHA: (30) implies: % 20.30/3.56 | | (31) ~ (all_61_0 = 0) % 20.30/3.56 | | (32) $i(all_61_1) % 20.30/3.56 | | (33) in(all_61_1, all_41_2) = 0 % 20.30/3.56 | | (34) in(all_61_1, all_41_1) = all_61_0 % 20.30/3.56 | | % 20.30/3.56 | | GROUND_INST: instantiating (t1_subset) with all_61_1, all_41_2, simplifying % 20.30/3.56 | | with (15), (32), (33) gives: % 20.30/3.56 | | (35) element(all_61_1, all_41_2) = 0 % 20.30/3.56 | | % 20.30/3.56 | | GROUND_INST: instantiating (d5_finsub_1) with all_41_4, all_41_2, all_41_2, % 20.30/3.56 | | simplifying with (13), (15), (17), (22) gives: % 20.30/3.56 | | (36) ! [v0: $i] : ! [v1: any] : ( ~ (finite(v0) = v1) | ~ $i(v0) | ? % 20.30/3.56 | | [v2: any] : ? [v3: any] : (subset(v0, all_41_4) = v3 & in(v0, % 20.30/3.56 | | all_41_2) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: % 20.30/3.56 | | $i] : ( ~ (finite(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 20.30/3.56 | | any] : (subset(v0, all_41_4) = v1 & in(v0, all_41_2) = v2 & ( ~ % 20.30/3.56 | | (v1 = 0) | v2 = 0))) % 20.30/3.56 | | % 20.30/3.56 | | ALPHA: (36) implies: % 20.30/3.56 | | (37) ! [v0: $i] : ( ~ (finite(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 20.30/3.56 | | [v2: any] : (subset(v0, all_41_4) = v1 & in(v0, all_41_2) = v2 & ( % 20.30/3.56 | | ~ (v1 = 0) | v2 = 0))) % 20.30/3.56 | | (38) ! [v0: $i] : ! [v1: any] : ( ~ (finite(v0) = v1) | ~ $i(v0) | ? % 20.30/3.56 | | [v2: any] : ? [v3: any] : (subset(v0, all_41_4) = v3 & in(v0, % 20.30/3.56 | | all_41_2) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 20.30/3.56 | | % 20.30/3.56 | | GROUND_INST: instantiating (d5_finsub_1) with all_41_3, all_41_1, all_41_1, % 20.30/3.56 | | simplifying with (14), (16), (18), (23) gives: % 20.30/3.56 | | (39) ! [v0: $i] : ! [v1: any] : ( ~ (finite(v0) = v1) | ~ $i(v0) | ? % 20.30/3.56 | | [v2: any] : ? [v3: any] : (subset(v0, all_41_3) = v3 & in(v0, % 20.30/3.56 | | all_41_1) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: % 20.30/3.56 | | $i] : ( ~ (finite(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 20.30/3.56 | | any] : (subset(v0, all_41_3) = v1 & in(v0, all_41_1) = v2 & ( ~ % 20.30/3.56 | | (v1 = 0) | v2 = 0))) % 20.30/3.56 | | % 20.30/3.56 | | ALPHA: (39) implies: % 20.30/3.56 | | (40) ! [v0: $i] : ( ~ (finite(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 20.30/3.56 | | [v2: any] : (subset(v0, all_41_3) = v1 & in(v0, all_41_1) = v2 & ( % 20.30/3.56 | | ~ (v1 = 0) | v2 = 0))) % 20.30/3.56 | | (41) ! [v0: $i] : ! [v1: any] : ( ~ (finite(v0) = v1) | ~ $i(v0) | ? % 20.30/3.56 | | [v2: any] : ? [v3: any] : (subset(v0, all_41_3) = v3 & in(v0, % 20.30/3.56 | | all_41_1) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 20.30/3.56 | | % 20.30/3.56 | | GROUND_INST: instantiating (rc1_subset_1) with all_37_1, all_54_0, % 20.30/3.56 | | simplifying with (8), (26) gives: % 20.30/3.56 | | (42) empty(all_37_1) = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 20.30/3.56 | | element(v0, all_54_0) = 0 & empty(v0) = v1 & $i(v0)) % 20.30/3.56 | | % 20.30/3.56 | | BETA: splitting (42) gives: % 20.30/3.56 | | % 20.30/3.56 | | Case 1: % 20.30/3.56 | | | % 20.30/3.56 | | | (43) empty(all_37_1) = 0 % 20.30/3.56 | | | % 20.30/3.56 | | | GROUND_INST: instantiating (3) with all_37_0, 0, all_37_1, simplifying % 20.30/3.56 | | | with (9), (43) gives: % 20.30/3.56 | | | (44) all_37_0 = 0 % 20.30/3.56 | | | % 20.30/3.56 | | | REDUCE: (7), (44) imply: % 20.30/3.56 | | | (45) $false % 20.30/3.56 | | | % 20.30/3.56 | | | CLOSE: (45) is inconsistent. % 20.30/3.56 | | | % 20.30/3.56 | | Case 2: % 20.30/3.56 | | | % 20.30/3.56 | | | % 20.30/3.56 | | | GROUND_INST: instantiating (cc3_finsub_1) with all_41_4, all_61_1, % 20.30/3.56 | | | all_41_2, simplifying with (13), (17), (32), (35) gives: % 20.30/3.57 | | | (46) finite(all_61_1) = 0 % 20.30/3.57 | | | % 20.30/3.57 | | | GROUND_INST: instantiating (40) with all_61_1, simplifying with (32), (46) % 20.30/3.57 | | | gives: % 20.30/3.57 | | | (47) ? [v0: any] : ? [v1: any] : (subset(all_61_1, all_41_3) = v0 & % 20.30/3.57 | | | in(all_61_1, all_41_1) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 20.30/3.57 | | | % 20.30/3.57 | | | GROUND_INST: instantiating (37) with all_61_1, simplifying with (32), (46) % 20.30/3.57 | | | gives: % 20.30/3.57 | | | (48) ? [v0: any] : ? [v1: any] : (subset(all_61_1, all_41_4) = v0 & % 20.30/3.57 | | | in(all_61_1, all_41_2) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 20.30/3.57 | | | % 20.30/3.57 | | | GROUND_INST: instantiating (41) with all_61_1, 0, simplifying with (32), % 20.30/3.57 | | | (46) gives: % 20.30/3.57 | | | (49) ? [v0: any] : ? [v1: any] : (subset(all_61_1, all_41_3) = v1 & % 20.30/3.57 | | | in(all_61_1, all_41_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 20.30/3.57 | | | % 20.30/3.57 | | | GROUND_INST: instantiating (38) with all_61_1, 0, simplifying with (32), % 20.30/3.57 | | | (46) gives: % 20.30/3.57 | | | (50) ? [v0: any] : ? [v1: any] : (subset(all_61_1, all_41_4) = v1 & % 20.30/3.57 | | | in(all_61_1, all_41_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 20.30/3.57 | | | % 20.30/3.57 | | | DELTA: instantiating (50) with fresh symbols all_172_0, all_172_1 gives: % 20.30/3.57 | | | (51) subset(all_61_1, all_41_4) = all_172_0 & in(all_61_1, all_41_2) = % 20.30/3.57 | | | all_172_1 & ( ~ (all_172_1 = 0) | all_172_0 = 0) % 20.30/3.57 | | | % 20.30/3.57 | | | ALPHA: (51) implies: % 20.30/3.57 | | | (52) in(all_61_1, all_41_2) = all_172_1 % 20.30/3.57 | | | (53) subset(all_61_1, all_41_4) = all_172_0 % 20.30/3.57 | | | (54) ~ (all_172_1 = 0) | all_172_0 = 0 % 20.30/3.57 | | | % 20.30/3.57 | | | DELTA: instantiating (49) with fresh symbols all_174_0, all_174_1 gives: % 20.30/3.57 | | | (55) subset(all_61_1, all_41_3) = all_174_0 & in(all_61_1, all_41_1) = % 20.30/3.57 | | | all_174_1 & ( ~ (all_174_1 = 0) | all_174_0 = 0) % 20.30/3.57 | | | % 20.30/3.57 | | | ALPHA: (55) implies: % 20.30/3.57 | | | (56) in(all_61_1, all_41_1) = all_174_1 % 20.30/3.57 | | | (57) subset(all_61_1, all_41_3) = all_174_0 % 20.30/3.57 | | | % 20.30/3.57 | | | DELTA: instantiating (48) with fresh symbols all_184_0, all_184_1 gives: % 20.30/3.57 | | | (58) subset(all_61_1, all_41_4) = all_184_1 & in(all_61_1, all_41_2) = % 20.30/3.57 | | | all_184_0 & ( ~ (all_184_1 = 0) | all_184_0 = 0) % 20.30/3.57 | | | % 20.30/3.57 | | | ALPHA: (58) implies: % 20.30/3.57 | | | (59) in(all_61_1, all_41_2) = all_184_0 % 20.30/3.57 | | | (60) subset(all_61_1, all_41_4) = all_184_1 % 20.30/3.57 | | | % 20.30/3.57 | | | DELTA: instantiating (47) with fresh symbols all_186_0, all_186_1 gives: % 20.30/3.57 | | | (61) subset(all_61_1, all_41_3) = all_186_1 & in(all_61_1, all_41_1) = % 20.30/3.57 | | | all_186_0 & ( ~ (all_186_1 = 0) | all_186_0 = 0) % 20.30/3.57 | | | % 20.30/3.57 | | | ALPHA: (61) implies: % 20.30/3.57 | | | (62) in(all_61_1, all_41_1) = all_186_0 % 20.30/3.57 | | | (63) subset(all_61_1, all_41_3) = all_186_1 % 20.30/3.57 | | | (64) ~ (all_186_1 = 0) | all_186_0 = 0 % 20.30/3.57 | | | % 20.30/3.57 | | | GROUND_INST: instantiating (4) with 0, all_184_0, all_41_2, all_61_1, % 20.30/3.57 | | | simplifying with (33), (59) gives: % 20.30/3.57 | | | (65) all_184_0 = 0 % 20.30/3.57 | | | % 20.30/3.57 | | | GROUND_INST: instantiating (4) with all_172_1, all_184_0, all_41_2, % 20.30/3.57 | | | all_61_1, simplifying with (52), (59) gives: % 20.30/3.57 | | | (66) all_184_0 = all_172_1 % 20.30/3.57 | | | % 20.30/3.57 | | | GROUND_INST: instantiating (4) with all_61_0, all_186_0, all_41_1, % 20.30/3.57 | | | all_61_1, simplifying with (34), (62) gives: % 20.30/3.57 | | | (67) all_186_0 = all_61_0 % 20.30/3.57 | | | % 20.30/3.57 | | | GROUND_INST: instantiating (4) with all_174_1, all_186_0, all_41_1, % 20.30/3.57 | | | all_61_1, simplifying with (56), (62) gives: % 20.30/3.57 | | | (68) all_186_0 = all_174_1 % 20.30/3.57 | | | % 20.30/3.57 | | | GROUND_INST: instantiating (5) with all_172_0, all_184_1, all_41_4, % 20.30/3.57 | | | all_61_1, simplifying with (53), (60) gives: % 20.30/3.57 | | | (69) all_184_1 = all_172_0 % 20.30/3.57 | | | % 20.30/3.57 | | | GROUND_INST: instantiating (5) with all_174_0, all_186_1, all_41_3, % 20.30/3.57 | | | all_61_1, simplifying with (57), (63) gives: % 20.30/3.57 | | | (70) all_186_1 = all_174_0 % 20.30/3.57 | | | % 20.30/3.57 | | | COMBINE_EQS: (67), (68) imply: % 20.30/3.57 | | | (71) all_174_1 = all_61_0 % 20.30/3.57 | | | % 20.30/3.57 | | | COMBINE_EQS: (65), (66) imply: % 20.30/3.57 | | | (72) all_172_1 = 0 % 20.30/3.57 | | | % 20.30/3.57 | | | BETA: splitting (54) gives: % 20.30/3.57 | | | % 20.30/3.57 | | | Case 1: % 20.30/3.57 | | | | % 20.30/3.57 | | | | (73) ~ (all_172_1 = 0) % 20.30/3.57 | | | | % 20.30/3.57 | | | | REDUCE: (72), (73) imply: % 20.30/3.57 | | | | (74) $false % 20.30/3.58 | | | | % 20.30/3.58 | | | | CLOSE: (74) is inconsistent. % 20.30/3.58 | | | | % 20.30/3.58 | | | Case 2: % 20.30/3.58 | | | | % 20.30/3.58 | | | | (75) all_172_0 = 0 % 20.30/3.58 | | | | % 20.30/3.58 | | | | REDUCE: (53), (75) imply: % 20.30/3.58 | | | | (76) subset(all_61_1, all_41_4) = 0 % 20.30/3.58 | | | | % 20.30/3.58 | | | | BETA: splitting (64) gives: % 20.30/3.58 | | | | % 20.30/3.58 | | | | Case 1: % 20.30/3.58 | | | | | % 20.30/3.58 | | | | | (77) ~ (all_186_1 = 0) % 20.30/3.58 | | | | | % 20.30/3.58 | | | | | REDUCE: (70), (77) imply: % 20.30/3.58 | | | | | (78) ~ (all_174_0 = 0) % 20.30/3.58 | | | | | % 20.30/3.58 | | | | | GROUND_INST: instantiating (t1_xboole_1) with all_61_1, all_41_4, % 20.30/3.58 | | | | | all_41_3, all_174_0, simplifying with (13), (14), (32), % 20.30/3.58 | | | | | (57), (76) gives: % 20.30/3.58 | | | | | (79) all_174_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_41_4, % 20.30/3.58 | | | | | all_41_3) = v0) % 20.30/3.58 | | | | | % 20.30/3.58 | | | | | BETA: splitting (79) gives: % 20.30/3.58 | | | | | % 20.30/3.58 | | | | | Case 1: % 20.30/3.58 | | | | | | % 20.30/3.58 | | | | | | (80) all_174_0 = 0 % 20.30/3.58 | | | | | | % 20.30/3.58 | | | | | | REDUCE: (78), (80) imply: % 20.30/3.58 | | | | | | (81) $false % 20.30/3.58 | | | | | | % 20.30/3.58 | | | | | | CLOSE: (81) is inconsistent. % 20.30/3.58 | | | | | | % 20.30/3.58 | | | | | Case 2: % 20.30/3.58 | | | | | | % 20.30/3.58 | | | | | | (82) ? [v0: int] : ( ~ (v0 = 0) & subset(all_41_4, all_41_3) = % 20.30/3.58 | | | | | | v0) % 20.30/3.58 | | | | | | % 20.30/3.58 | | | | | | DELTA: instantiating (82) with fresh symbol all_371_0 gives: % 20.30/3.58 | | | | | | (83) ~ (all_371_0 = 0) & subset(all_41_4, all_41_3) = all_371_0 % 20.30/3.58 | | | | | | % 20.30/3.58 | | | | | | ALPHA: (83) implies: % 20.30/3.58 | | | | | | (84) ~ (all_371_0 = 0) % 20.30/3.58 | | | | | | (85) subset(all_41_4, all_41_3) = all_371_0 % 20.30/3.58 | | | | | | % 20.30/3.58 | | | | | | GROUND_INST: instantiating (5) with 0, all_371_0, all_41_3, % 20.30/3.58 | | | | | | all_41_4, simplifying with (19), (85) gives: % 20.30/3.58 | | | | | | (86) all_371_0 = 0 % 20.30/3.58 | | | | | | % 20.30/3.58 | | | | | | REDUCE: (84), (86) imply: % 20.30/3.58 | | | | | | (87) $false % 20.30/3.58 | | | | | | % 20.30/3.58 | | | | | | CLOSE: (87) is inconsistent. % 20.30/3.58 | | | | | | % 20.30/3.58 | | | | | End of split % 20.30/3.58 | | | | | % 20.30/3.58 | | | | Case 2: % 20.30/3.58 | | | | | % 20.30/3.58 | | | | | (88) all_186_0 = 0 % 20.30/3.58 | | | | | % 20.30/3.58 | | | | | COMBINE_EQS: (67), (88) imply: % 20.30/3.58 | | | | | (89) all_61_0 = 0 % 20.30/3.58 | | | | | % 20.30/3.58 | | | | | REDUCE: (31), (89) imply: % 20.30/3.58 | | | | | (90) $false % 20.30/3.58 | | | | | % 20.30/3.58 | | | | | CLOSE: (90) is inconsistent. % 20.30/3.58 | | | | | % 20.30/3.58 | | | | End of split % 20.30/3.58 | | | | % 20.30/3.58 | | | End of split % 20.30/3.58 | | | % 20.30/3.58 | | End of split % 20.30/3.58 | | % 20.30/3.58 | End of split % 20.30/3.58 | % 20.30/3.58 End of proof % 20.30/3.58 % SZS output end Proof for theBenchmark % 20.30/3.58 % 20.30/3.58 2963ms %------------------------------------------------------------------------------