%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG227+1 : TPTP v8.1.2. Released v3.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n004.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 : Wed Aug 30 16:40:05 EDT 2023 % Result : Theorem 7.01s 1.71s % Output : Proof 9.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : ALG227+1 : TPTP v8.1.2. Released v3.4.0. % 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n004.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon Aug 28 03:42:22 EDT 2023 % 0.12/0.33 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.56/1.05 Prover 4: Preprocessing ... % 2.56/1.05 Prover 1: Preprocessing ... % 2.56/1.09 Prover 0: Preprocessing ... % 2.56/1.09 Prover 3: Preprocessing ... % 2.56/1.10 Prover 2: Preprocessing ... % 2.56/1.10 Prover 5: Preprocessing ... % 2.56/1.10 Prover 6: Preprocessing ... % 5.17/1.47 Prover 1: Warning: ignoring some quantifiers % 5.17/1.49 Prover 2: Proving ... % 5.17/1.49 Prover 5: Proving ... % 5.17/1.50 Prover 3: Warning: ignoring some quantifiers % 5.66/1.51 Prover 1: Constructing countermodel ... % 5.66/1.53 Prover 3: Constructing countermodel ... % 5.66/1.53 Prover 4: Warning: ignoring some quantifiers % 5.66/1.53 Prover 6: Proving ... % 5.66/1.56 Prover 4: Constructing countermodel ... % 6.15/1.61 Prover 0: Proving ... % 7.01/1.71 Prover 3: proved (1092ms) % 7.01/1.71 % 7.01/1.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.01/1.71 % 7.01/1.72 Prover 5: stopped % 7.01/1.72 Prover 0: stopped % 7.01/1.72 Prover 6: stopped % 7.29/1.74 Prover 2: stopped % 7.29/1.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.29/1.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.29/1.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.29/1.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.29/1.76 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.29/1.78 Prover 7: Preprocessing ... % 7.29/1.80 Prover 8: Preprocessing ... % 7.75/1.81 Prover 11: Preprocessing ... % 7.75/1.82 Prover 10: Preprocessing ... % 7.75/1.82 Prover 13: Preprocessing ... % 8.27/1.89 Prover 7: Warning: ignoring some quantifiers % 8.27/1.89 Prover 10: Warning: ignoring some quantifiers % 8.27/1.90 Prover 7: Constructing countermodel ... % 8.27/1.90 Prover 10: Constructing countermodel ... % 8.27/1.91 Prover 1: Found proof (size 60) % 8.27/1.91 Prover 1: proved (1301ms) % 8.27/1.91 Prover 7: stopped % 8.27/1.91 Prover 4: stopped % 8.27/1.92 Prover 10: stopped % 8.27/1.93 Prover 13: Warning: ignoring some quantifiers % 8.27/1.94 Prover 13: Constructing countermodel ... % 8.27/1.95 Prover 13: stopped % 8.27/1.96 Prover 8: Warning: ignoring some quantifiers % 8.94/1.97 Prover 8: Constructing countermodel ... % 8.94/1.98 Prover 8: stopped % 8.94/1.98 Prover 11: Warning: ignoring some quantifiers % 8.94/1.99 Prover 11: Constructing countermodel ... % 8.94/2.01 Prover 11: stopped % 8.94/2.01 % 8.94/2.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.94/2.01 % 8.94/2.02 % SZS output start Proof for theBenchmark % 8.94/2.03 Assumptions after simplification: % 8.94/2.03 --------------------------------- % 8.94/2.03 % 8.94/2.03 (d3_closure3) % 8.94/2.07 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (v1_xboole_0(v0) = v1) | ~ $i(v0) | % 8.94/2.07 ! [v2: $i] : ! [v3: $i] : ( ~ (k1_closure3(v0, v2) = v3) | ~ $i(v2) | ? % 8.94/2.07 [v4: any] : ? [v5: $i] : (m1_pboole(v2, v0) = v4 & a_2_0_closure3(v0, v2) % 8.94/2.07 = v5 & $i(v5) & ( ~ (v4 = 0) | v5 = v3)))) % 8.94/2.07 % 8.94/2.07 (fraenkel_a_2_0_closure3) % 9.35/2.07 $i(k1_xboole_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 9.35/2.07 [v4: any] : ( ~ (a_2_0_closure3(v1, v2) = v3) | ~ (r2_hidden(v0, v3) = v4) | % 9.35/2.07 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 9.35/2.07 (m1_pboole(v2, v1) = v6 & v1_xboole_0(v1) = v5 & ( ~ (v6 = 0) | v5 = 0)) | % 9.35/2.07 (( ~ (v4 = 0) | ? [v5: $i] : ( ~ (v5 = k1_xboole_0) & k1_funct_1(v2, v0) = % 9.35/2.07 v5 & m1_subset_1(v0, v1) = 0 & $i(v5))) & (v4 = 0 | ! [v5: $i] : (v5 % 9.35/2.07 = k1_xboole_0 | ~ (k1_funct_1(v2, v0) = v5) | ? [v6: int] : ( ~ (v6 % 9.35/2.07 = 0) & m1_subset_1(v0, v1) = v6))))) % 9.35/2.07 % 9.35/2.07 (rc1_finset_1) % 9.35/2.07 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & v1_finset_1(v0) = 0 & % 9.35/2.07 v1_xboole_0(v0) = v1 & $i(v0)) % 9.35/2.07 % 9.35/2.07 (t2_subset) % 9.35/2.07 ! [v0: $i] : ! [v1: $i] : ( ~ (m1_subset_1(v0, v1) = 0) | ~ $i(v1) | ~ % 9.35/2.07 $i(v0) | ? [v2: any] : ? [v3: any] : (v1_xboole_0(v1) = v2 & r2_hidden(v0, % 9.35/2.07 v1) = v3 & (v3 = 0 | v2 = 0))) % 9.35/2.07 % 9.35/2.07 (t8_closure3) % 9.35/2.08 $i(k1_xboole_0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & v1_xboole_0(v0) % 9.35/2.08 = v1 & $i(v0) & ? [v2: $i] : ? [v3: $i] : (k1_closure3(v0, v2) = v3 & % 9.35/2.08 m1_pboole(v2, v0) = 0 & $i(v3) & $i(v2) & ? [v4: $i] : ? [v5: int] : ? % 9.35/2.08 [v6: $i] : ( ~ (v6 = k1_xboole_0) & ~ (v5 = 0) & k1_funct_1(v2, v4) = v6 % 9.35/2.08 & m1_subset_1(v4, v0) = 0 & r2_hidden(v4, v3) = v5 & $i(v6) & $i(v4)))) % 9.35/2.08 % 9.35/2.08 (function-axioms) % 9.35/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.35/2.09 (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = v0)) & ! [v0: % 9.35/2.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.35/2.09 : (v1 = v0 | ~ (m1_subset_1(v3, v2) = v1) | ~ (m1_subset_1(v3, v2) = v0)) & % 9.35/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.35/2.09 (k1_closure3(v3, v2) = v1) | ~ (k1_closure3(v3, v2) = v0)) & ! [v0: % 9.35/2.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.35/2.09 : (v1 = v0 | ~ (m1_pboole(v3, v2) = v1) | ~ (m1_pboole(v3, v2) = v0)) & ! % 9.35/2.09 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.35/2.09 (a_2_0_closure3(v3, v2) = v1) | ~ (a_2_0_closure3(v3, v2) = v0)) & ! [v0: % 9.35/2.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.35/2.09 : (v1 = v0 | ~ (r2_hidden(v3, v2) = v1) | ~ (r2_hidden(v3, v2) = v0)) & ! % 9.35/2.09 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 9.35/2.09 | ~ (v2_funct_1(v2) = v1) | ~ (v2_funct_1(v2) = v0)) & ! [v0: % 9.35/2.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.35/2.09 ~ (v1_relat_1(v2) = v1) | ~ (v1_relat_1(v2) = v0)) & ! [v0: % 9.35/2.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.35/2.09 ~ (v1_funct_1(v2) = v1) | ~ (v1_funct_1(v2) = v0)) & ! [v0: % 9.35/2.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.35/2.09 ~ (v1_finset_1(v2) = v1) | ~ (v1_finset_1(v2) = v0)) & ! [v0: % 9.35/2.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.35/2.09 ~ (v1_fraenkel(v2) = v1) | ~ (v1_fraenkel(v2) = v0)) & ! [v0: % 9.35/2.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.35/2.09 ~ (v1_xboole_0(v2) = v1) | ~ (v1_xboole_0(v2) = v0)) % 9.35/2.09 % 9.35/2.09 Further assumptions not needed in the proof: % 9.35/2.09 -------------------------------------------- % 9.35/2.09 antisymmetry_r2_hidden, cc1_closure2, cc1_finset_1, cc1_funct_1, cc2_funct_1, % 9.35/2.09 dt_k1_closure3, dt_k1_funct_1, dt_k1_xboole_0, dt_m1_pboole, dt_m1_subset_1, % 9.35/2.09 existence_m1_pboole, existence_m1_subset_1, fc1_xboole_0, rc1_closure2, % 9.35/2.09 rc1_funct_1, rc1_xboole_0, rc2_funct_1, rc2_xboole_0, rc3_funct_1, t1_subset, % 9.35/2.09 t2_tarski, t6_boole, t7_boole, t8_boole % 9.35/2.09 % 9.35/2.09 Those formulas are unsatisfiable: % 9.35/2.09 --------------------------------- % 9.35/2.09 % 9.35/2.09 Begin of proof % 9.35/2.09 | % 9.35/2.09 | ALPHA: (fraenkel_a_2_0_closure3) implies: % 9.35/2.09 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 9.35/2.09 | ( ~ (a_2_0_closure3(v1, v2) = v3) | ~ (r2_hidden(v0, v3) = v4) | ~ % 9.35/2.09 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 9.35/2.09 | (m1_pboole(v2, v1) = v6 & v1_xboole_0(v1) = v5 & ( ~ (v6 = 0) | v5 = % 9.35/2.09 | 0)) | (( ~ (v4 = 0) | ? [v5: $i] : ( ~ (v5 = k1_xboole_0) & % 9.35/2.09 | k1_funct_1(v2, v0) = v5 & m1_subset_1(v0, v1) = 0 & $i(v5))) & % 9.35/2.09 | (v4 = 0 | ! [v5: $i] : (v5 = k1_xboole_0 | ~ (k1_funct_1(v2, v0) % 9.35/2.09 | = v5) | ? [v6: int] : ( ~ (v6 = 0) & m1_subset_1(v0, v1) = % 9.35/2.09 | v6))))) % 9.35/2.09 | % 9.35/2.09 | ALPHA: (t8_closure3) implies: % 9.35/2.09 | (2) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & v1_xboole_0(v0) = v1 & % 9.35/2.09 | $i(v0) & ? [v2: $i] : ? [v3: $i] : (k1_closure3(v0, v2) = v3 & % 9.35/2.09 | m1_pboole(v2, v0) = 0 & $i(v3) & $i(v2) & ? [v4: $i] : ? [v5: % 9.35/2.09 | int] : ? [v6: $i] : ( ~ (v6 = k1_xboole_0) & ~ (v5 = 0) & % 9.35/2.09 | k1_funct_1(v2, v4) = v6 & m1_subset_1(v4, v0) = 0 & r2_hidden(v4, % 9.35/2.09 | v3) = v5 & $i(v6) & $i(v4)))) % 9.35/2.09 | % 9.35/2.09 | ALPHA: (function-axioms) implies: % 9.35/2.10 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.35/2.10 | (v1 = v0 | ~ (v1_xboole_0(v2) = v1) | ~ (v1_xboole_0(v2) = v0)) % 9.35/2.10 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.35/2.10 | ! [v3: $i] : (v1 = v0 | ~ (m1_pboole(v3, v2) = v1) | ~ % 9.35/2.10 | (m1_pboole(v3, v2) = v0)) % 9.35/2.10 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.35/2.10 | ! [v3: $i] : (v1 = v0 | ~ (m1_subset_1(v3, v2) = v1) | ~ % 9.35/2.10 | (m1_subset_1(v3, v2) = v0)) % 9.35/2.10 | % 9.35/2.10 | DELTA: instantiating (rc1_finset_1) with fresh symbols all_25_0, all_25_1 % 9.35/2.10 | gives: % 9.35/2.10 | (6) ~ (all_25_0 = 0) & v1_finset_1(all_25_1) = 0 & v1_xboole_0(all_25_1) = % 9.35/2.10 | all_25_0 & $i(all_25_1) % 9.35/2.10 | % 9.35/2.10 | ALPHA: (6) implies: % 9.35/2.10 | (7) ~ (all_25_0 = 0) % 9.35/2.10 | (8) $i(all_25_1) % 9.35/2.10 | (9) v1_xboole_0(all_25_1) = all_25_0 % 9.35/2.10 | % 9.35/2.10 | DELTA: instantiating (2) with fresh symbols all_34_0, all_34_1 gives: % 9.35/2.10 | (10) ~ (all_34_0 = 0) & v1_xboole_0(all_34_1) = all_34_0 & $i(all_34_1) & % 9.35/2.10 | ? [v0: $i] : ? [v1: $i] : (k1_closure3(all_34_1, v0) = v1 & % 9.35/2.10 | m1_pboole(v0, all_34_1) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : ? % 9.35/2.10 | [v3: int] : ? [v4: $i] : ( ~ (v4 = k1_xboole_0) & ~ (v3 = 0) & % 9.35/2.10 | k1_funct_1(v0, v2) = v4 & m1_subset_1(v2, all_34_1) = 0 & % 9.35/2.10 | r2_hidden(v2, v1) = v3 & $i(v4) & $i(v2))) % 9.35/2.10 | % 9.35/2.10 | ALPHA: (10) implies: % 9.35/2.10 | (11) ~ (all_34_0 = 0) % 9.35/2.10 | (12) $i(all_34_1) % 9.35/2.10 | (13) v1_xboole_0(all_34_1) = all_34_0 % 9.35/2.10 | (14) ? [v0: $i] : ? [v1: $i] : (k1_closure3(all_34_1, v0) = v1 & % 9.35/2.10 | m1_pboole(v0, all_34_1) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : ? % 9.35/2.10 | [v3: int] : ? [v4: $i] : ( ~ (v4 = k1_xboole_0) & ~ (v3 = 0) & % 9.35/2.10 | k1_funct_1(v0, v2) = v4 & m1_subset_1(v2, all_34_1) = 0 & % 9.35/2.10 | r2_hidden(v2, v1) = v3 & $i(v4) & $i(v2))) % 9.35/2.10 | % 9.35/2.10 | DELTA: instantiating (14) with fresh symbols all_36_0, all_36_1 gives: % 9.63/2.11 | (15) k1_closure3(all_34_1, all_36_1) = all_36_0 & m1_pboole(all_36_1, % 9.63/2.11 | all_34_1) = 0 & $i(all_36_0) & $i(all_36_1) & ? [v0: $i] : ? [v1: % 9.63/2.11 | int] : ? [v2: $i] : ( ~ (v2 = k1_xboole_0) & ~ (v1 = 0) & % 9.63/2.11 | k1_funct_1(all_36_1, v0) = v2 & m1_subset_1(v0, all_34_1) = 0 & % 9.63/2.11 | r2_hidden(v0, all_36_0) = v1 & $i(v2) & $i(v0)) % 9.63/2.11 | % 9.63/2.11 | ALPHA: (15) implies: % 9.63/2.11 | (16) $i(all_36_1) % 9.63/2.11 | (17) m1_pboole(all_36_1, all_34_1) = 0 % 9.63/2.11 | (18) k1_closure3(all_34_1, all_36_1) = all_36_0 % 9.63/2.11 | (19) ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ( ~ (v2 = k1_xboole_0) & ~ % 9.63/2.11 | (v1 = 0) & k1_funct_1(all_36_1, v0) = v2 & m1_subset_1(v0, all_34_1) % 9.63/2.11 | = 0 & r2_hidden(v0, all_36_0) = v1 & $i(v2) & $i(v0)) % 9.63/2.11 | % 9.63/2.11 | DELTA: instantiating (19) with fresh symbols all_38_0, all_38_1, all_38_2 % 9.63/2.11 | gives: % 9.63/2.11 | (20) ~ (all_38_0 = k1_xboole_0) & ~ (all_38_1 = 0) & k1_funct_1(all_36_1, % 9.63/2.11 | all_38_2) = all_38_0 & m1_subset_1(all_38_2, all_34_1) = 0 & % 9.63/2.11 | r2_hidden(all_38_2, all_36_0) = all_38_1 & $i(all_38_0) & $i(all_38_2) % 9.63/2.11 | % 9.63/2.11 | ALPHA: (20) implies: % 9.63/2.11 | (21) ~ (all_38_1 = 0) % 9.63/2.11 | (22) ~ (all_38_0 = k1_xboole_0) % 9.63/2.11 | (23) $i(all_38_2) % 9.63/2.11 | (24) r2_hidden(all_38_2, all_36_0) = all_38_1 % 9.63/2.11 | (25) m1_subset_1(all_38_2, all_34_1) = 0 % 9.63/2.11 | (26) k1_funct_1(all_36_1, all_38_2) = all_38_0 % 9.63/2.11 | % 9.63/2.11 | GROUND_INST: instantiating (d3_closure3) with all_25_1, all_25_0, simplifying % 9.63/2.11 | with (8), (9) gives: % 9.66/2.11 | (27) all_25_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (k1_closure3(all_25_1, % 9.66/2.11 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 9.66/2.11 | (m1_pboole(v0, all_25_1) = v2 & a_2_0_closure3(all_25_1, v0) = v3 & % 9.66/2.11 | $i(v3) & ( ~ (v2 = 0) | v3 = v1))) % 9.66/2.11 | % 9.66/2.11 | GROUND_INST: instantiating (d3_closure3) with all_34_1, all_34_0, simplifying % 9.66/2.11 | with (12), (13) gives: % 9.66/2.11 | (28) all_34_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (k1_closure3(all_34_1, % 9.66/2.11 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 9.66/2.11 | (m1_pboole(v0, all_34_1) = v2 & a_2_0_closure3(all_34_1, v0) = v3 & % 9.66/2.11 | $i(v3) & ( ~ (v2 = 0) | v3 = v1))) % 9.66/2.11 | % 9.66/2.11 | GROUND_INST: instantiating (t2_subset) with all_38_2, all_34_1, simplifying % 9.66/2.11 | with (12), (23), (25) gives: % 9.66/2.12 | (29) ? [v0: any] : ? [v1: any] : (v1_xboole_0(all_34_1) = v0 & % 9.66/2.12 | r2_hidden(all_38_2, all_34_1) = v1 & (v1 = 0 | v0 = 0)) % 9.66/2.12 | % 9.66/2.12 | DELTA: instantiating (29) with fresh symbols all_48_0, all_48_1 gives: % 9.66/2.12 | (30) v1_xboole_0(all_34_1) = all_48_1 & r2_hidden(all_38_2, all_34_1) = % 9.66/2.12 | all_48_0 & (all_48_0 = 0 | all_48_1 = 0) % 9.66/2.12 | % 9.66/2.12 | ALPHA: (30) implies: % 9.66/2.12 | (31) v1_xboole_0(all_34_1) = all_48_1 % 9.66/2.12 | % 9.66/2.12 | BETA: splitting (28) gives: % 9.66/2.12 | % 9.66/2.12 | Case 1: % 9.66/2.12 | | % 9.66/2.12 | | (32) all_34_0 = 0 % 9.66/2.12 | | % 9.66/2.12 | | REDUCE: (11), (32) imply: % 9.66/2.12 | | (33) $false % 9.66/2.12 | | % 9.66/2.12 | | CLOSE: (33) is inconsistent. % 9.66/2.12 | | % 9.66/2.12 | Case 2: % 9.66/2.12 | | % 9.66/2.12 | | (34) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_closure3(all_34_1, v0) = v1) | % 9.66/2.12 | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (m1_pboole(v0, all_34_1) = % 9.66/2.12 | | v2 & a_2_0_closure3(all_34_1, v0) = v3 & $i(v3) & ( ~ (v2 = 0) | % 9.66/2.12 | | v3 = v1))) % 9.66/2.12 | | % 9.66/2.12 | | GROUND_INST: instantiating (34) with all_36_1, all_36_0, simplifying with % 9.66/2.12 | | (16), (18) gives: % 9.66/2.12 | | (35) ? [v0: any] : ? [v1: $i] : (m1_pboole(all_36_1, all_34_1) = v0 & % 9.66/2.12 | | a_2_0_closure3(all_34_1, all_36_1) = v1 & $i(v1) & ( ~ (v0 = 0) | % 9.66/2.12 | | v1 = all_36_0)) % 9.66/2.12 | | % 9.66/2.12 | | BETA: splitting (27) gives: % 9.66/2.12 | | % 9.66/2.12 | | Case 1: % 9.66/2.12 | | | % 9.66/2.12 | | | (36) all_25_0 = 0 % 9.66/2.12 | | | % 9.66/2.12 | | | REDUCE: (7), (36) imply: % 9.66/2.12 | | | (37) $false % 9.66/2.12 | | | % 9.66/2.12 | | | CLOSE: (37) is inconsistent. % 9.66/2.12 | | | % 9.66/2.12 | | Case 2: % 9.66/2.12 | | | % 9.66/2.12 | | | % 9.66/2.12 | | | DELTA: instantiating (35) with fresh symbols all_63_0, all_63_1 gives: % 9.66/2.12 | | | (38) m1_pboole(all_36_1, all_34_1) = all_63_1 & % 9.66/2.12 | | | a_2_0_closure3(all_34_1, all_36_1) = all_63_0 & $i(all_63_0) & ( ~ % 9.66/2.12 | | | (all_63_1 = 0) | all_63_0 = all_36_0) % 9.66/2.12 | | | % 9.66/2.12 | | | ALPHA: (38) implies: % 9.66/2.12 | | | (39) a_2_0_closure3(all_34_1, all_36_1) = all_63_0 % 9.66/2.12 | | | (40) m1_pboole(all_36_1, all_34_1) = all_63_1 % 9.66/2.12 | | | (41) ~ (all_63_1 = 0) | all_63_0 = all_36_0 % 9.66/2.12 | | | % 9.66/2.12 | | | GROUND_INST: instantiating (3) with all_34_0, all_48_1, all_34_1, % 9.66/2.12 | | | simplifying with (13), (31) gives: % 9.66/2.12 | | | (42) all_48_1 = all_34_0 % 9.66/2.12 | | | % 9.66/2.12 | | | GROUND_INST: instantiating (4) with 0, all_63_1, all_34_1, all_36_1, % 9.66/2.12 | | | simplifying with (17), (40) gives: % 9.66/2.12 | | | (43) all_63_1 = 0 % 9.66/2.12 | | | % 9.66/2.12 | | | BETA: splitting (41) gives: % 9.66/2.12 | | | % 9.66/2.12 | | | Case 1: % 9.66/2.12 | | | | % 9.66/2.12 | | | | (44) ~ (all_63_1 = 0) % 9.66/2.12 | | | | % 9.66/2.12 | | | | REDUCE: (43), (44) imply: % 9.66/2.12 | | | | (45) $false % 9.66/2.12 | | | | % 9.66/2.12 | | | | CLOSE: (45) is inconsistent. % 9.66/2.12 | | | | % 9.66/2.12 | | | Case 2: % 9.66/2.12 | | | | % 9.66/2.12 | | | | (46) all_63_0 = all_36_0 % 9.66/2.12 | | | | % 9.66/2.12 | | | | REDUCE: (39), (46) imply: % 9.66/2.12 | | | | (47) a_2_0_closure3(all_34_1, all_36_1) = all_36_0 % 9.66/2.12 | | | | % 9.66/2.13 | | | | GROUND_INST: instantiating (1) with all_38_2, all_34_1, all_36_1, % 9.66/2.13 | | | | all_36_0, all_38_1, simplifying with (12), (16), (23), % 9.66/2.13 | | | | (24), (47) gives: % 9.66/2.13 | | | | (48) ? [v0: any] : ? [v1: any] : (m1_pboole(all_36_1, all_34_1) = % 9.66/2.13 | | | | v1 & v1_xboole_0(all_34_1) = v0 & ( ~ (v1 = 0) | v0 = 0)) | (( % 9.66/2.13 | | | | ~ (all_38_1 = 0) | ? [v0: $i] : ( ~ (v0 = k1_xboole_0) & % 9.66/2.13 | | | | k1_funct_1(all_36_1, all_38_2) = v0 & % 9.66/2.13 | | | | m1_subset_1(all_38_2, all_34_1) = 0 & $i(v0))) & (all_38_1 % 9.66/2.13 | | | | = 0 | ! [v0: $i] : (v0 = k1_xboole_0 | ~ % 9.66/2.13 | | | | (k1_funct_1(all_36_1, all_38_2) = v0) | ? [v1: int] : ( ~ % 9.66/2.13 | | | | (v1 = 0) & m1_subset_1(all_38_2, all_34_1) = v1)))) % 9.66/2.13 | | | | % 9.66/2.13 | | | | BETA: splitting (48) gives: % 9.66/2.13 | | | | % 9.66/2.13 | | | | Case 1: % 9.66/2.13 | | | | | % 9.66/2.13 | | | | | (49) ? [v0: any] : ? [v1: any] : (m1_pboole(all_36_1, all_34_1) = % 9.66/2.13 | | | | | v1 & v1_xboole_0(all_34_1) = v0 & ( ~ (v1 = 0) | v0 = 0)) % 9.66/2.13 | | | | | % 9.66/2.13 | | | | | DELTA: instantiating (49) with fresh symbols all_87_0, all_87_1 gives: % 9.66/2.13 | | | | | (50) m1_pboole(all_36_1, all_34_1) = all_87_0 & % 9.66/2.13 | | | | | v1_xboole_0(all_34_1) = all_87_1 & ( ~ (all_87_0 = 0) | % 9.66/2.13 | | | | | all_87_1 = 0) % 9.66/2.13 | | | | | % 9.66/2.13 | | | | | ALPHA: (50) implies: % 9.66/2.13 | | | | | (51) v1_xboole_0(all_34_1) = all_87_1 % 9.66/2.13 | | | | | (52) m1_pboole(all_36_1, all_34_1) = all_87_0 % 9.66/2.13 | | | | | (53) ~ (all_87_0 = 0) | all_87_1 = 0 % 9.66/2.13 | | | | | % 9.66/2.13 | | | | | GROUND_INST: instantiating (3) with all_34_0, all_87_1, all_34_1, % 9.66/2.13 | | | | | simplifying with (13), (51) gives: % 9.66/2.13 | | | | | (54) all_87_1 = all_34_0 % 9.66/2.13 | | | | | % 9.66/2.13 | | | | | GROUND_INST: instantiating (4) with 0, all_87_0, all_34_1, all_36_1, % 9.66/2.13 | | | | | simplifying with (17), (52) gives: % 9.66/2.13 | | | | | (55) all_87_0 = 0 % 9.66/2.13 | | | | | % 9.66/2.13 | | | | | BETA: splitting (53) gives: % 9.66/2.13 | | | | | % 9.66/2.13 | | | | | Case 1: % 9.66/2.13 | | | | | | % 9.66/2.13 | | | | | | (56) ~ (all_87_0 = 0) % 9.66/2.13 | | | | | | % 9.66/2.13 | | | | | | REDUCE: (55), (56) imply: % 9.66/2.13 | | | | | | (57) $false % 9.66/2.13 | | | | | | % 9.66/2.13 | | | | | | CLOSE: (57) is inconsistent. % 9.66/2.13 | | | | | | % 9.66/2.13 | | | | | Case 2: % 9.66/2.13 | | | | | | % 9.66/2.13 | | | | | | (58) all_87_1 = 0 % 9.66/2.13 | | | | | | % 9.66/2.13 | | | | | | COMBINE_EQS: (54), (58) imply: % 9.66/2.13 | | | | | | (59) all_34_0 = 0 % 9.66/2.13 | | | | | | % 9.66/2.13 | | | | | | SIMP: (59) implies: % 9.66/2.13 | | | | | | (60) all_34_0 = 0 % 9.66/2.13 | | | | | | % 9.66/2.13 | | | | | | REDUCE: (11), (60) imply: % 9.66/2.13 | | | | | | (61) $false % 9.66/2.13 | | | | | | % 9.66/2.13 | | | | | | CLOSE: (61) is inconsistent. % 9.66/2.13 | | | | | | % 9.66/2.13 | | | | | End of split % 9.66/2.13 | | | | | % 9.66/2.13 | | | | Case 2: % 9.66/2.13 | | | | | % 9.66/2.13 | | | | | (62) ( ~ (all_38_1 = 0) | ? [v0: $i] : ( ~ (v0 = k1_xboole_0) & % 9.66/2.13 | | | | | k1_funct_1(all_36_1, all_38_2) = v0 & % 9.66/2.13 | | | | | m1_subset_1(all_38_2, all_34_1) = 0 & $i(v0))) & (all_38_1 % 9.66/2.13 | | | | | = 0 | ! [v0: $i] : (v0 = k1_xboole_0 | ~ % 9.66/2.13 | | | | | (k1_funct_1(all_36_1, all_38_2) = v0) | ? [v1: int] : ( ~ % 9.66/2.13 | | | | | (v1 = 0) & m1_subset_1(all_38_2, all_34_1) = v1))) % 9.66/2.13 | | | | | % 9.66/2.13 | | | | | ALPHA: (62) implies: % 9.66/2.13 | | | | | (63) all_38_1 = 0 | ! [v0: $i] : (v0 = k1_xboole_0 | ~ % 9.66/2.13 | | | | | (k1_funct_1(all_36_1, all_38_2) = v0) | ? [v1: int] : ( ~ % 9.66/2.13 | | | | | (v1 = 0) & m1_subset_1(all_38_2, all_34_1) = v1)) % 9.66/2.13 | | | | | % 9.66/2.13 | | | | | BETA: splitting (63) gives: % 9.66/2.13 | | | | | % 9.66/2.13 | | | | | Case 1: % 9.66/2.13 | | | | | | % 9.66/2.13 | | | | | | (64) all_38_1 = 0 % 9.66/2.13 | | | | | | % 9.66/2.14 | | | | | | REDUCE: (21), (64) imply: % 9.66/2.14 | | | | | | (65) $false % 9.66/2.14 | | | | | | % 9.66/2.14 | | | | | | CLOSE: (65) is inconsistent. % 9.66/2.14 | | | | | | % 9.66/2.14 | | | | | Case 2: % 9.66/2.14 | | | | | | % 9.66/2.14 | | | | | | (66) ! [v0: $i] : (v0 = k1_xboole_0 | ~ (k1_funct_1(all_36_1, % 9.66/2.14 | | | | | | all_38_2) = v0) | ? [v1: int] : ( ~ (v1 = 0) & % 9.66/2.14 | | | | | | m1_subset_1(all_38_2, all_34_1) = v1)) % 9.66/2.14 | | | | | | % 9.66/2.14 | | | | | | GROUND_INST: instantiating (66) with all_38_0, simplifying with (26) % 9.66/2.14 | | | | | | gives: % 9.66/2.14 | | | | | | (67) all_38_0 = k1_xboole_0 | ? [v0: int] : ( ~ (v0 = 0) & % 9.66/2.14 | | | | | | m1_subset_1(all_38_2, all_34_1) = v0) % 9.66/2.14 | | | | | | % 9.66/2.14 | | | | | | BETA: splitting (67) gives: % 9.66/2.14 | | | | | | % 9.66/2.14 | | | | | | Case 1: % 9.66/2.14 | | | | | | | % 9.66/2.14 | | | | | | | (68) all_38_0 = k1_xboole_0 % 9.66/2.14 | | | | | | | % 9.66/2.14 | | | | | | | REDUCE: (22), (68) imply: % 9.66/2.14 | | | | | | | (69) $false % 9.66/2.14 | | | | | | | % 9.66/2.14 | | | | | | | CLOSE: (69) is inconsistent. % 9.66/2.14 | | | | | | | % 9.66/2.14 | | | | | | Case 2: % 9.66/2.14 | | | | | | | % 9.66/2.14 | | | | | | | (70) ? [v0: int] : ( ~ (v0 = 0) & m1_subset_1(all_38_2, % 9.66/2.14 | | | | | | | all_34_1) = v0) % 9.66/2.14 | | | | | | | % 9.66/2.14 | | | | | | | DELTA: instantiating (70) with fresh symbol all_95_0 gives: % 9.66/2.14 | | | | | | | (71) ~ (all_95_0 = 0) & m1_subset_1(all_38_2, all_34_1) = % 9.66/2.14 | | | | | | | all_95_0 % 9.66/2.14 | | | | | | | % 9.66/2.14 | | | | | | | ALPHA: (71) implies: % 9.66/2.14 | | | | | | | (72) ~ (all_95_0 = 0) % 9.66/2.14 | | | | | | | (73) m1_subset_1(all_38_2, all_34_1) = all_95_0 % 9.66/2.14 | | | | | | | % 9.66/2.14 | | | | | | | GROUND_INST: instantiating (5) with 0, all_95_0, all_34_1, % 9.66/2.14 | | | | | | | all_38_2, simplifying with (25), (73) gives: % 9.66/2.14 | | | | | | | (74) all_95_0 = 0 % 9.66/2.14 | | | | | | | % 9.66/2.14 | | | | | | | REDUCE: (72), (74) imply: % 9.66/2.14 | | | | | | | (75) $false % 9.66/2.14 | | | | | | | % 9.66/2.14 | | | | | | | CLOSE: (75) is inconsistent. % 9.66/2.14 | | | | | | | % 9.66/2.14 | | | | | | End of split % 9.66/2.14 | | | | | | % 9.66/2.14 | | | | | End of split % 9.66/2.14 | | | | | % 9.66/2.14 | | | | End of split % 9.66/2.14 | | | | % 9.66/2.14 | | | End of split % 9.66/2.14 | | | % 9.66/2.14 | | End of split % 9.66/2.14 | | % 9.66/2.14 | End of split % 9.66/2.14 | % 9.66/2.14 End of proof % 9.66/2.14 % SZS output end Proof for theBenchmark % 9.66/2.14 % 9.66/2.14 1547ms %------------------------------------------------------------------------------