%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU420+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 : n026.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 17:44:39 EDT 2023 % Result : Theorem 18.60s 3.35s % Output : Proof 19.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU420+1 : TPTP v8.1.2. Released v3.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n026.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Aug 23 19:16:16 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 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 % 2.74/1.11 Prover 4: Preprocessing ... % 2.74/1.11 Prover 1: Preprocessing ... % 2.74/1.15 Prover 5: Preprocessing ... % 2.74/1.15 Prover 0: Preprocessing ... % 2.74/1.15 Prover 2: Preprocessing ... % 2.74/1.15 Prover 3: Preprocessing ... % 2.74/1.15 Prover 6: Preprocessing ... % 6.29/1.71 Prover 1: Warning: ignoring some quantifiers % 6.89/1.74 Prover 5: Proving ... % 6.89/1.76 Prover 3: Warning: ignoring some quantifiers % 6.89/1.77 Prover 4: Warning: ignoring some quantifiers % 6.89/1.77 Prover 1: Constructing countermodel ... % 6.89/1.78 Prover 2: Proving ... % 7.33/1.79 Prover 6: Proving ... % 7.33/1.80 Prover 3: Constructing countermodel ... % 7.33/1.84 Prover 0: Proving ... % 7.33/1.85 Prover 4: Constructing countermodel ... % 12.92/2.59 Prover 3: gave up % 12.92/2.59 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.65/2.67 Prover 7: Preprocessing ... % 14.51/2.79 Prover 7: Warning: ignoring some quantifiers % 14.51/2.82 Prover 7: Constructing countermodel ... % 18.60/3.34 Prover 4: Found proof (size 126) % 18.60/3.34 Prover 4: proved (2721ms) % 18.60/3.34 Prover 7: stopped % 18.60/3.34 Prover 1: stopped % 18.60/3.34 Prover 5: stopped % 18.60/3.34 Prover 6: stopped % 18.60/3.34 Prover 2: stopped % 18.60/3.35 Prover 0: stopped % 18.60/3.35 % 18.60/3.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.60/3.35 % 18.60/3.36 % SZS output start Proof for theBenchmark % 18.60/3.37 Assumptions after simplification: % 18.60/3.37 --------------------------------- % 18.60/3.37 % 18.60/3.37 (commutativity_k3_xboole_0) % 18.90/3.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k3_xboole_0(v1, v0) = v2) | ~ % 18.90/3.40 $i(v1) | ~ $i(v0) | (k3_xboole_0(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 18.90/3.40 [v1: $i] : ! [v2: $i] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ $i(v1) | ~ % 18.90/3.40 $i(v0) | (k3_xboole_0(v1, v0) = v2 & $i(v2))) % 18.90/3.40 % 18.90/3.40 (d13_relat_1) % 18.90/3.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 18.90/3.41 $i] : ! [v6: $i] : (v4 = 0 | ~ (k9_relat_1(v0, v1) = v2) | ~ % 18.90/3.41 (k4_tarski(v5, v3) = v6) | ~ (v1_relat_1(v0) = 0) | ~ (r2_hidden(v3, v2) = % 18.90/3.41 v4) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: % 18.90/3.41 any] : ? [v8: any] : (r2_hidden(v6, v0) = v7 & r2_hidden(v5, v1) = v8 & ( % 18.90/3.41 ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 18.90/3.41 ! [v3: $i] : ! [v4: int] : ! [v5: $i] : (v4 = 0 | ~ (k9_relat_1(v0, v1) = % 18.90/3.41 v2) | ~ (v1_relat_1(v0) = 0) | ~ (r2_hidden(v5, v1) = 0) | ~ % 18.90/3.41 (r2_hidden(v3, v2) = v4) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 18.90/3.41 ~ $i(v0) | ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & k4_tarski(v5, v3) = % 18.90/3.41 v6 & r2_hidden(v6, v0) = v7 & $i(v6))) & ! [v0: $i] : ! [v1: $i] : ! % 18.90/3.41 [v2: $i] : ! [v3: $i] : ( ~ (k9_relat_1(v0, v1) = v2) | ~ (v1_relat_1(v0) = % 18.90/3.41 0) | ~ (r2_hidden(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 18.90/3.41 $i(v0) | ? [v4: $i] : ? [v5: $i] : (k4_tarski(v4, v3) = v5 & r2_hidden(v5, % 18.90/3.41 v0) = 0 & r2_hidden(v4, v1) = 0 & $i(v5) & $i(v4))) & ? [v0: $i] : ! % 18.90/3.41 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (k9_relat_1(v1, v2) = v3) % 18.90/3.41 | ~ (v1_relat_1(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] % 18.90/3.41 : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ? [v9: int] : % 18.90/3.41 (r2_hidden(v4, v0) = v5 & $i(v6) & $i(v4) & ( ~ (v5 = 0) | ( ! [v10: $i] : % 18.90/3.41 ! [v11: $i] : ( ~ (k4_tarski(v10, v4) = v11) | ~ $i(v10) | ? [v12: % 18.90/3.41 any] : ? [v13: any] : (r2_hidden(v11, v1) = v12 & r2_hidden(v10, % 18.90/3.41 v2) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10: $i] : ( ~ % 18.90/3.41 (r2_hidden(v10, v2) = 0) | ~ $i(v10) | ? [v11: $i] : ? [v12: int] % 18.90/3.41 : ( ~ (v12 = 0) & k4_tarski(v10, v4) = v11 & r2_hidden(v11, v1) = % 18.90/3.41 v12 & $i(v11))))) & (v5 = 0 | (v9 = 0 & v8 = 0 & k4_tarski(v6, v4) % 18.90/3.41 = v7 & r2_hidden(v7, v1) = 0 & r2_hidden(v6, v2) = 0 & $i(v7))))) % 18.90/3.41 % 18.90/3.41 (d3_tarski) % 18.90/3.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 18.90/3.41 (r1_tarski(v0, v1) = 0) | ~ (r2_hidden(v2, v1) = v3) | ~ $i(v2) | ~ % 18.90/3.41 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & r2_hidden(v2, v0) = v4)) % 18.90/3.41 & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (r1_tarski(v0, v1) = % 18.90/3.41 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 18.90/3.41 r2_hidden(v3, v1) = v4 & r2_hidden(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : % 18.90/3.41 ! [v1: $i] : ! [v2: $i] : ( ~ (r1_tarski(v0, v1) = 0) | ~ (r2_hidden(v2, v0) % 18.90/3.41 = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | r2_hidden(v2, v1) = 0) % 18.90/3.41 % 18.90/3.41 (d3_xboole_0) % 18.90/3.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 18.90/3.42 | ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v2) = v4) | ~ $i(v3) | % 18.90/3.42 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 18.90/3.42 (r2_hidden(v3, v1) = v6 & r2_hidden(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 18.90/3.42 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 18.90/3.42 [v4: any] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v1) = v4) | ~ % 18.90/3.42 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 18.90/3.42 (r2_hidden(v3, v2) = v5 & r2_hidden(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & % 18.90/3.42 v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 18.90/3.42 ! [v4: any] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v0) = v4) | % 18.90/3.42 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 18.90/3.42 (r2_hidden(v3, v2) = v5 & r2_hidden(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & % 18.90/3.42 v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 18.90/3.42 ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v2) = 0) | ~ $i(v3) | ~ % 18.90/3.42 $i(v2) | ~ $i(v1) | ~ $i(v0) | (r2_hidden(v3, v1) = 0 & r2_hidden(v3, v0) % 18.90/3.42 = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.90/3.42 (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v1) = 0) | ~ $i(v3) | ~ % 18.90/3.42 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 18.90/3.42 (r2_hidden(v3, v2) = v5 & r2_hidden(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) % 18.90/3.42 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k3_xboole_0(v0, % 18.90/3.42 v1) = v2) | ~ (r2_hidden(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 18.90/3.42 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (r2_hidden(v3, v2) = v5 & % 18.90/3.42 r2_hidden(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: % 18.90/3.42 $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (k3_xboole_0(v1, v2) = v3) | % 18.90/3.42 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: % 18.90/3.42 any] : ? [v7: any] : (r2_hidden(v4, v2) = v7 & r2_hidden(v4, v1) = v6 & % 18.90/3.42 r2_hidden(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = % 18.90/3.42 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) % 18.90/3.42 % 18.90/3.42 (fc1_relat_1) % 18.90/3.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ % 18.90/3.42 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 18.90/3.42 (v1_relat_1(v2) = v5 & v1_relat_1(v1) = v4 & v1_relat_1(v0) = v3 & ( ~ (v4 = % 18.90/3.42 0) | ~ (v3 = 0) | v5 = 0))) % 18.90/3.42 % 18.90/3.42 (fc1_subset_1) % 18.90/3.42 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ $i(v0) | ? [v2: % 18.90/3.42 int] : ( ~ (v2 = 0) & v1_xboole_0(v1) = v2)) % 18.90/3.42 % 18.90/3.42 (rc1_subset_1) % 18.90/3.42 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (v1_xboole_0(v0) = v1) | ~ $i(v0) | % 18.90/3.42 ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & k1_zfmisc_1(v0) = % 18.90/3.42 v2 & m1_subset_1(v3, v2) = 0 & v1_xboole_0(v3) = v4 & $i(v3) & $i(v2))) & % 18.90/3.42 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ $i(v0) | ? [v2: % 18.90/3.42 int] : ? [v3: $i] : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ % 18.90/3.42 (v5 = 0) & m1_subset_1(v3, v1) = 0 & v1_xboole_0(v3) = v5) | (v2 = 0 & % 18.90/3.42 v1_xboole_0(v0) = 0)))) % 18.90/3.42 % 18.90/3.42 (rc2_relat_1) % 18.90/3.42 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & v1_relat_1(v0) = 0 & % 18.90/3.42 v1_xboole_0(v0) = v1 & $i(v0)) % 18.90/3.42 % 18.90/3.42 (t13_relset_2) % 18.90/3.42 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 18.90/3.42 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) % 18.90/3.42 & k3_pua2mss1(v0) = v2 & r1_tarski(v6, v8) = v9 & k9_relat_1(v5, v2) = v6 & % 18.90/3.42 k9_relat_1(v4, v2) = v7 & k9_relat_1(v1, v2) = v3 & k3_xboole_0(v3, v7) = v8 % 18.90/3.42 & k3_xboole_0(v1, v4) = v5 & v1_relat_1(v4) = 0 & v1_relat_1(v1) = 0 & % 18.90/3.42 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 18.90/3.42 $i(v0)) % 18.90/3.42 % 18.90/3.42 (t2_subset) % 18.90/3.42 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (r2_hidden(v0, v1) = % 18.90/3.42 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 18.90/3.42 (m1_subset_1(v0, v1) = v3 & v1_xboole_0(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) % 18.90/3.42 & ! [v0: $i] : ! [v1: $i] : ( ~ (m1_subset_1(v0, v1) = 0) | ~ $i(v1) | ~ % 18.90/3.42 $i(v0) | ? [v2: any] : ? [v3: any] : (v1_xboole_0(v1) = v2 & r2_hidden(v0, % 18.90/3.42 v1) = v3 & (v3 = 0 | v2 = 0))) % 18.90/3.42 % 18.90/3.42 (function-axioms) % 18.90/3.43 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 18.90/3.43 [v3: $i] : (v1 = v0 | ~ (m1_subset_1(v3, v2) = v1) | ~ (m1_subset_1(v3, v2) % 18.90/3.43 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 18.90/3.43 $i] : ! [v3: $i] : (v1 = v0 | ~ (m1_eqrel_1(v3, v2) = v1) | ~ % 18.90/3.43 (m1_eqrel_1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.90/3.43 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.90/3.43 (r1_tarski(v3, v2) = v1) | ~ (r1_tarski(v3, v2) = v0)) & ! [v0: $i] : ! % 18.90/3.43 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k9_relat_1(v3, v2) = v1) % 18.90/3.43 | ~ (k9_relat_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 18.90/3.43 ! [v3: $i] : (v1 = v0 | ~ (k4_tarski(v3, v2) = v1) | ~ (k4_tarski(v3, v2) = % 18.90/3.43 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 18.90/3.43 ~ (k3_xboole_0(v3, v2) = v1) | ~ (k3_xboole_0(v3, v2) = v0)) & ! [v0: $i] % 18.90/3.43 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k2_tarski(v3, v2) = % 18.90/3.43 v1) | ~ (k2_tarski(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.90/3.43 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.90/3.43 (r2_hidden(v3, v2) = v1) | ~ (r2_hidden(v3, v2) = v0)) & ! [v0: % 18.90/3.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 18.90/3.43 ~ (v3_relat_1(v2) = v1) | ~ (v3_relat_1(v2) = v0)) & ! [v0: $i] : ! [v1: % 18.90/3.43 $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ % 18.90/3.43 (k1_zfmisc_1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 18.90/3.43 | ~ (k3_pua2mss1(v2) = v1) | ~ (k3_pua2mss1(v2) = v0)) & ! [v0: $i] : ! % 18.90/3.43 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_tarski(v2) = v1) | ~ % 18.90/3.43 (k1_tarski(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.90/3.43 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_relat_1(v2) = v1) | ~ % 18.90/3.43 (v1_relat_1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.90/3.43 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_xboole_0(v2) = v1) | ~ % 18.90/3.43 (v1_xboole_0(v2) = v0)) % 18.90/3.43 % 18.90/3.43 Further assumptions not needed in the proof: % 18.90/3.43 -------------------------------------------- % 18.90/3.43 antisymmetry_r2_hidden, cc1_relat_1, commutativity_k2_tarski, d5_tarski, % 18.90/3.43 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k3_pua2mss1, % 18.90/3.43 dt_k3_xboole_0, dt_k4_tarski, dt_k9_relat_1, dt_m1_eqrel_1, dt_m1_subset_1, % 18.90/3.43 existence_m1_eqrel_1, existence_m1_subset_1, fc12_relat_1, fc2_subset_1, % 18.90/3.43 fc3_subset_1, fc4_relat_1, idempotence_k3_xboole_0, rc1_relat_1, rc2_subset_1, % 18.90/3.43 rc3_relat_1, reflexivity_r1_tarski, t1_subset, t2_boole, t3_subset, t4_subset, % 18.90/3.43 t5_subset, t6_boole, t7_boole, t8_boole % 18.90/3.43 % 18.90/3.43 Those formulas are unsatisfiable: % 18.90/3.43 --------------------------------- % 18.90/3.43 % 18.90/3.43 Begin of proof % 18.90/3.43 | % 18.90/3.43 | ALPHA: (commutativity_k3_xboole_0) implies: % 18.90/3.43 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k3_xboole_0(v1, v0) = % 18.90/3.43 | v2) | ~ $i(v1) | ~ $i(v0) | (k3_xboole_0(v0, v1) = v2 & $i(v2))) % 18.90/3.43 | % 18.90/3.43 | ALPHA: (d13_relat_1) implies: % 18.90/3.43 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.90/3.43 | (k9_relat_1(v0, v1) = v2) | ~ (v1_relat_1(v0) = 0) | ~ % 18.90/3.43 | (r2_hidden(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 18.90/3.43 | $i(v0) | ? [v4: $i] : ? [v5: $i] : (k4_tarski(v4, v3) = v5 & % 18.90/3.43 | r2_hidden(v5, v0) = 0 & r2_hidden(v4, v1) = 0 & $i(v5) & $i(v4))) % 18.90/3.43 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 18.90/3.43 | ! [v5: $i] : ! [v6: $i] : (v4 = 0 | ~ (k9_relat_1(v0, v1) = v2) | ~ % 18.90/3.43 | (k4_tarski(v5, v3) = v6) | ~ (v1_relat_1(v0) = 0) | ~ % 18.90/3.43 | (r2_hidden(v3, v2) = v4) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ % 18.90/3.43 | $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (r2_hidden(v6, v0) % 18.90/3.43 | = v7 & r2_hidden(v5, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) % 18.90/3.43 | % 18.90/3.43 | ALPHA: (d3_tarski) implies: % 18.90/3.43 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (r1_tarski(v0, % 18.90/3.43 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : % 18.90/3.43 | ( ~ (v4 = 0) & r2_hidden(v3, v1) = v4 & r2_hidden(v3, v0) = 0 & % 18.90/3.43 | $i(v3))) % 18.90/3.43 | % 18.90/3.43 | ALPHA: (d3_xboole_0) implies: % 18.90/3.43 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.90/3.43 | (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v2) = 0) | ~ $i(v3) | % 18.90/3.43 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (r2_hidden(v3, v1) = 0 & % 18.90/3.43 | r2_hidden(v3, v0) = 0)) % 18.90/3.43 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 18.90/3.43 | (v4 = 0 | ~ (k3_xboole_0(v0, v1) = v2) | ~ (r2_hidden(v3, v2) = v4) | % 18.90/3.43 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 18.90/3.43 | [v6: any] : (r2_hidden(v3, v1) = v6 & r2_hidden(v3, v0) = v5 & ( ~ % 18.90/3.43 | (v6 = 0) | ~ (v5 = 0)))) % 18.90/3.43 | % 18.90/3.43 | ALPHA: (rc1_subset_1) implies: % 18.90/3.44 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ $i(v0) | ? % 18.90/3.44 | [v2: int] : ? [v3: $i] : ? [v4: int] : ? [v5: int] : ($i(v3) & % 18.90/3.44 | ((v4 = 0 & ~ (v5 = 0) & m1_subset_1(v3, v1) = 0 & v1_xboole_0(v3) % 18.90/3.44 | = v5) | (v2 = 0 & v1_xboole_0(v0) = 0)))) % 18.90/3.44 | (8) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (v1_xboole_0(v0) = v1) | ~ % 18.90/3.44 | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 18.90/3.44 | k1_zfmisc_1(v0) = v2 & m1_subset_1(v3, v2) = 0 & v1_xboole_0(v3) = % 18.90/3.44 | v4 & $i(v3) & $i(v2))) % 18.90/3.44 | % 18.90/3.44 | ALPHA: (t2_subset) implies: % 18.90/3.44 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (m1_subset_1(v0, v1) = 0) | ~ $i(v1) | % 18.90/3.44 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (v1_xboole_0(v1) = v2 & % 18.90/3.44 | r2_hidden(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 18.90/3.44 | % 18.90/3.44 | ALPHA: (function-axioms) implies: % 18.90/3.44 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 18.90/3.44 | : (v1 = v0 | ~ (v1_xboole_0(v2) = v1) | ~ (v1_xboole_0(v2) = v0)) % 18.90/3.44 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 18.90/3.44 | : (v1 = v0 | ~ (v1_relat_1(v2) = v1) | ~ (v1_relat_1(v2) = v0)) % 18.90/3.44 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 18.90/3.44 | : ! [v3: $i] : (v1 = v0 | ~ (r2_hidden(v3, v2) = v1) | ~ % 18.90/3.44 | (r2_hidden(v3, v2) = v0)) % 18.90/3.44 | % 18.90/3.44 | DELTA: instantiating (rc2_relat_1) with fresh symbols all_37_0, all_37_1 % 18.90/3.44 | gives: % 18.90/3.44 | (13) ~ (all_37_0 = 0) & v1_relat_1(all_37_1) = 0 & v1_xboole_0(all_37_1) = % 18.90/3.44 | all_37_0 & $i(all_37_1) % 18.90/3.44 | % 18.90/3.44 | ALPHA: (13) implies: % 18.90/3.44 | (14) ~ (all_37_0 = 0) % 18.90/3.44 | (15) $i(all_37_1) % 18.90/3.44 | (16) v1_xboole_0(all_37_1) = all_37_0 % 18.90/3.44 | % 18.90/3.44 | DELTA: instantiating (t13_relset_2) with fresh symbols all_41_0, all_41_1, % 18.90/3.44 | all_41_2, all_41_3, all_41_4, all_41_5, all_41_6, all_41_7, all_41_8, % 18.90/3.44 | all_41_9 gives: % 18.90/3.44 | (17) ~ (all_41_0 = 0) & k3_pua2mss1(all_41_9) = all_41_7 & % 18.90/3.44 | r1_tarski(all_41_3, all_41_1) = all_41_0 & k9_relat_1(all_41_4, % 18.90/3.44 | all_41_7) = all_41_3 & k9_relat_1(all_41_5, all_41_7) = all_41_2 & % 18.90/3.44 | k9_relat_1(all_41_8, all_41_7) = all_41_6 & k3_xboole_0(all_41_6, % 18.90/3.44 | all_41_2) = all_41_1 & k3_xboole_0(all_41_8, all_41_5) = all_41_4 & % 18.90/3.44 | v1_relat_1(all_41_5) = 0 & v1_relat_1(all_41_8) = 0 & $i(all_41_1) & % 18.90/3.44 | $i(all_41_2) & $i(all_41_3) & $i(all_41_4) & $i(all_41_5) & % 18.90/3.44 | $i(all_41_6) & $i(all_41_7) & $i(all_41_8) & $i(all_41_9) % 18.90/3.44 | % 18.90/3.44 | ALPHA: (17) implies: % 18.90/3.44 | (18) ~ (all_41_0 = 0) % 18.90/3.44 | (19) $i(all_41_8) % 18.90/3.44 | (20) $i(all_41_7) % 18.90/3.44 | (21) $i(all_41_6) % 18.90/3.44 | (22) $i(all_41_5) % 18.90/3.44 | (23) $i(all_41_3) % 18.90/3.44 | (24) $i(all_41_2) % 18.90/3.44 | (25) v1_relat_1(all_41_8) = 0 % 18.90/3.44 | (26) v1_relat_1(all_41_5) = 0 % 18.90/3.44 | (27) k3_xboole_0(all_41_8, all_41_5) = all_41_4 % 18.90/3.44 | (28) k3_xboole_0(all_41_6, all_41_2) = all_41_1 % 18.90/3.44 | (29) k9_relat_1(all_41_8, all_41_7) = all_41_6 % 18.90/3.44 | (30) k9_relat_1(all_41_5, all_41_7) = all_41_2 % 18.90/3.44 | (31) k9_relat_1(all_41_4, all_41_7) = all_41_3 % 18.90/3.44 | (32) r1_tarski(all_41_3, all_41_1) = all_41_0 % 18.90/3.44 | % 18.90/3.44 | GROUND_INST: instantiating (8) with all_37_1, all_37_0, simplifying with (15), % 18.90/3.44 | (16) gives: % 18.90/3.45 | (33) all_37_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 18.90/3.45 | & k1_zfmisc_1(all_37_1) = v0 & m1_subset_1(v1, v0) = 0 & % 18.90/3.45 | v1_xboole_0(v1) = v2 & $i(v1) & $i(v0)) % 18.90/3.45 | % 18.90/3.45 | GROUND_INST: instantiating (1) with all_41_5, all_41_8, all_41_4, simplifying % 18.90/3.45 | with (19), (22), (27) gives: % 18.90/3.45 | (34) k3_xboole_0(all_41_5, all_41_8) = all_41_4 & $i(all_41_4) % 18.90/3.45 | % 18.90/3.45 | ALPHA: (34) implies: % 18.90/3.45 | (35) $i(all_41_4) % 18.90/3.45 | % 18.90/3.45 | GROUND_INST: instantiating (fc1_relat_1) with all_41_8, all_41_5, all_41_4, % 18.90/3.45 | simplifying with (19), (22), (27) gives: % 18.90/3.45 | (36) ? [v0: any] : ? [v1: any] : ? [v2: any] : (v1_relat_1(all_41_4) = % 18.90/3.45 | v2 & v1_relat_1(all_41_5) = v1 & v1_relat_1(all_41_8) = v0 & ( ~ (v1 % 18.90/3.45 | = 0) | ~ (v0 = 0) | v2 = 0)) % 18.90/3.45 | % 18.90/3.45 | GROUND_INST: instantiating (1) with all_41_2, all_41_6, all_41_1, simplifying % 18.90/3.45 | with (21), (24), (28) gives: % 18.90/3.45 | (37) k3_xboole_0(all_41_2, all_41_6) = all_41_1 & $i(all_41_1) % 18.90/3.45 | % 18.90/3.45 | ALPHA: (37) implies: % 18.90/3.45 | (38) $i(all_41_1) % 18.90/3.45 | (39) k3_xboole_0(all_41_2, all_41_6) = all_41_1 % 18.90/3.45 | % 18.90/3.45 | GROUND_INST: instantiating (4) with all_41_3, all_41_1, all_41_0, simplifying % 18.90/3.45 | with (23), (32), (38) gives: % 18.90/3.45 | (40) all_41_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 18.90/3.45 | r2_hidden(v0, all_41_1) = v1 & r2_hidden(v0, all_41_3) = 0 & $i(v0)) % 18.90/3.45 | % 18.90/3.45 | DELTA: instantiating (36) with fresh symbols all_51_0, all_51_1, all_51_2 % 18.90/3.45 | gives: % 18.90/3.45 | (41) v1_relat_1(all_41_4) = all_51_0 & v1_relat_1(all_41_5) = all_51_1 & % 18.90/3.45 | v1_relat_1(all_41_8) = all_51_2 & ( ~ (all_51_1 = 0) | ~ (all_51_2 = % 18.90/3.45 | 0) | all_51_0 = 0) % 18.90/3.45 | % 18.90/3.45 | ALPHA: (41) implies: % 18.90/3.45 | (42) v1_relat_1(all_41_8) = all_51_2 % 18.90/3.45 | (43) v1_relat_1(all_41_5) = all_51_1 % 18.90/3.45 | (44) v1_relat_1(all_41_4) = all_51_0 % 18.90/3.45 | (45) ~ (all_51_1 = 0) | ~ (all_51_2 = 0) | all_51_0 = 0 % 18.90/3.45 | % 18.90/3.45 | BETA: splitting (40) gives: % 18.90/3.45 | % 18.90/3.45 | Case 1: % 18.90/3.45 | | % 18.90/3.45 | | (46) all_41_0 = 0 % 18.90/3.45 | | % 18.90/3.45 | | REDUCE: (18), (46) imply: % 18.90/3.45 | | (47) $false % 18.90/3.45 | | % 18.90/3.45 | | CLOSE: (47) is inconsistent. % 18.90/3.45 | | % 18.90/3.45 | Case 2: % 18.90/3.45 | | % 18.90/3.45 | | (48) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & r2_hidden(v0, all_41_1) % 18.90/3.45 | | = v1 & r2_hidden(v0, all_41_3) = 0 & $i(v0)) % 18.90/3.45 | | % 18.90/3.45 | | DELTA: instantiating (48) with fresh symbols all_59_0, all_59_1 gives: % 19.20/3.46 | | (49) ~ (all_59_0 = 0) & r2_hidden(all_59_1, all_41_1) = all_59_0 & % 19.20/3.46 | | r2_hidden(all_59_1, all_41_3) = 0 & $i(all_59_1) % 19.20/3.46 | | % 19.20/3.46 | | ALPHA: (49) implies: % 19.20/3.46 | | (50) ~ (all_59_0 = 0) % 19.20/3.46 | | (51) $i(all_59_1) % 19.20/3.46 | | (52) r2_hidden(all_59_1, all_41_3) = 0 % 19.20/3.46 | | (53) r2_hidden(all_59_1, all_41_1) = all_59_0 % 19.20/3.46 | | % 19.20/3.46 | | BETA: splitting (33) gives: % 19.20/3.46 | | % 19.20/3.46 | | Case 1: % 19.20/3.46 | | | % 19.20/3.46 | | | (54) all_37_0 = 0 % 19.20/3.46 | | | % 19.20/3.46 | | | REDUCE: (14), (54) imply: % 19.20/3.46 | | | (55) $false % 19.20/3.46 | | | % 19.20/3.46 | | | CLOSE: (55) is inconsistent. % 19.20/3.46 | | | % 19.20/3.46 | | Case 2: % 19.20/3.46 | | | % 19.20/3.46 | | | (56) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 19.20/3.46 | | | k1_zfmisc_1(all_37_1) = v0 & m1_subset_1(v1, v0) = 0 & % 19.20/3.46 | | | v1_xboole_0(v1) = v2 & $i(v1) & $i(v0)) % 19.20/3.46 | | | % 19.20/3.46 | | | DELTA: instantiating (56) with fresh symbols all_69_0, all_69_1, all_69_2 % 19.20/3.46 | | | gives: % 19.20/3.46 | | | (57) ~ (all_69_0 = 0) & k1_zfmisc_1(all_37_1) = all_69_2 & % 19.20/3.46 | | | m1_subset_1(all_69_1, all_69_2) = 0 & v1_xboole_0(all_69_1) = % 19.20/3.46 | | | all_69_0 & $i(all_69_1) & $i(all_69_2) % 19.20/3.46 | | | % 19.20/3.46 | | | ALPHA: (57) implies: % 19.20/3.46 | | | (58) ~ (all_69_0 = 0) % 19.20/3.46 | | | (59) $i(all_69_2) % 19.20/3.46 | | | (60) $i(all_69_1) % 19.20/3.46 | | | (61) v1_xboole_0(all_69_1) = all_69_0 % 19.20/3.46 | | | (62) m1_subset_1(all_69_1, all_69_2) = 0 % 19.20/3.46 | | | (63) k1_zfmisc_1(all_37_1) = all_69_2 % 19.20/3.46 | | | % 19.20/3.46 | | | GROUND_INST: instantiating (11) with 0, all_51_2, all_41_8, simplifying % 19.20/3.46 | | | with (25), (42) gives: % 19.20/3.46 | | | (64) all_51_2 = 0 % 19.20/3.46 | | | % 19.20/3.46 | | | GROUND_INST: instantiating (11) with 0, all_51_1, all_41_5, simplifying % 19.20/3.46 | | | with (26), (43) gives: % 19.20/3.46 | | | (65) all_51_1 = 0 % 19.20/3.46 | | | % 19.20/3.46 | | | BETA: splitting (45) gives: % 19.20/3.46 | | | % 19.20/3.46 | | | Case 1: % 19.20/3.46 | | | | % 19.20/3.46 | | | | (66) ~ (all_51_1 = 0) % 19.20/3.46 | | | | % 19.20/3.46 | | | | REDUCE: (65), (66) imply: % 19.20/3.46 | | | | (67) $false % 19.20/3.46 | | | | % 19.20/3.46 | | | | CLOSE: (67) is inconsistent. % 19.20/3.46 | | | | % 19.20/3.46 | | | Case 2: % 19.20/3.46 | | | | % 19.20/3.46 | | | | (68) ~ (all_51_2 = 0) | all_51_0 = 0 % 19.20/3.46 | | | | % 19.20/3.46 | | | | BETA: splitting (68) gives: % 19.20/3.46 | | | | % 19.20/3.46 | | | | Case 1: % 19.20/3.46 | | | | | % 19.20/3.46 | | | | | (69) ~ (all_51_2 = 0) % 19.20/3.46 | | | | | % 19.20/3.46 | | | | | REDUCE: (64), (69) imply: % 19.20/3.46 | | | | | (70) $false % 19.20/3.46 | | | | | % 19.20/3.46 | | | | | CLOSE: (70) is inconsistent. % 19.20/3.46 | | | | | % 19.20/3.46 | | | | Case 2: % 19.20/3.46 | | | | | % 19.20/3.46 | | | | | (71) all_51_0 = 0 % 19.20/3.46 | | | | | % 19.20/3.46 | | | | | REDUCE: (44), (71) imply: % 19.20/3.46 | | | | | (72) v1_relat_1(all_41_4) = 0 % 19.20/3.46 | | | | | % 19.20/3.46 | | | | | GROUND_INST: instantiating (6) with all_41_6, all_41_2, all_41_1, % 19.20/3.46 | | | | | all_59_1, all_59_0, simplifying with (21), (24), (28), % 19.20/3.46 | | | | | (38), (51), (53) gives: % 19.20/3.46 | | | | | (73) all_59_0 = 0 | ? [v0: any] : ? [v1: any] : % 19.20/3.46 | | | | | (r2_hidden(all_59_1, all_41_2) = v1 & r2_hidden(all_59_1, % 19.20/3.46 | | | | | all_41_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 19.20/3.46 | | | | | % 19.20/3.46 | | | | | GROUND_INST: instantiating (8) with all_69_1, all_69_0, simplifying % 19.20/3.46 | | | | | with (60), (61) gives: % 19.20/3.46 | | | | | (74) all_69_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ % 19.20/3.46 | | | | | (v2 = 0) & k1_zfmisc_1(all_69_1) = v0 & m1_subset_1(v1, v0) % 19.20/3.46 | | | | | = 0 & v1_xboole_0(v1) = v2 & $i(v1) & $i(v0)) % 19.20/3.46 | | | | | % 19.20/3.46 | | | | | GROUND_INST: instantiating (2) with all_41_4, all_41_7, all_41_3, % 19.20/3.46 | | | | | all_59_1, simplifying with (20), (23), (31), (35), (51), % 19.20/3.46 | | | | | (52), (72) gives: % 19.20/3.47 | | | | | (75) ? [v0: $i] : ? [v1: $i] : (k4_tarski(v0, all_59_1) = v1 & % 19.20/3.47 | | | | | r2_hidden(v1, all_41_4) = 0 & r2_hidden(v0, all_41_7) = 0 & % 19.20/3.47 | | | | | $i(v1) & $i(v0)) % 19.20/3.47 | | | | | % 19.20/3.47 | | | | | GROUND_INST: instantiating (6) with all_41_2, all_41_6, all_41_1, % 19.20/3.47 | | | | | all_59_1, all_59_0, simplifying with (21), (24), (38), % 19.20/3.47 | | | | | (39), (51), (53) gives: % 19.20/3.47 | | | | | (76) all_59_0 = 0 | ? [v0: any] : ? [v1: any] : % 19.20/3.47 | | | | | (r2_hidden(all_59_1, all_41_2) = v0 & r2_hidden(all_59_1, % 19.20/3.47 | | | | | all_41_6) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 19.20/3.47 | | | | | % 19.20/3.47 | | | | | GROUND_INST: instantiating (9) with all_69_1, all_69_2, simplifying % 19.20/3.47 | | | | | with (59), (60), (62) gives: % 19.20/3.47 | | | | | (77) ? [v0: any] : ? [v1: any] : (v1_xboole_0(all_69_2) = v0 & % 19.20/3.47 | | | | | r2_hidden(all_69_1, all_69_2) = v1 & (v1 = 0 | v0 = 0)) % 19.20/3.47 | | | | | % 19.20/3.47 | | | | | GROUND_INST: instantiating (fc1_subset_1) with all_37_1, all_69_2, % 19.20/3.47 | | | | | simplifying with (15), (63) gives: % 19.20/3.47 | | | | | (78) ? [v0: int] : ( ~ (v0 = 0) & v1_xboole_0(all_69_2) = v0) % 19.20/3.47 | | | | | % 19.20/3.47 | | | | | DELTA: instantiating (78) with fresh symbol all_93_0 gives: % 19.20/3.47 | | | | | (79) ~ (all_93_0 = 0) & v1_xboole_0(all_69_2) = all_93_0 % 19.20/3.47 | | | | | % 19.20/3.47 | | | | | ALPHA: (79) implies: % 19.20/3.47 | | | | | (80) ~ (all_93_0 = 0) % 19.20/3.47 | | | | | (81) v1_xboole_0(all_69_2) = all_93_0 % 19.20/3.47 | | | | | % 19.20/3.47 | | | | | DELTA: instantiating (77) with fresh symbols all_101_0, all_101_1 % 19.20/3.47 | | | | | gives: % 19.20/3.47 | | | | | (82) v1_xboole_0(all_69_2) = all_101_1 & r2_hidden(all_69_1, % 19.20/3.47 | | | | | all_69_2) = all_101_0 & (all_101_0 = 0 | all_101_1 = 0) % 19.20/3.47 | | | | | % 19.20/3.47 | | | | | ALPHA: (82) implies: % 19.20/3.47 | | | | | (83) v1_xboole_0(all_69_2) = all_101_1 % 19.20/3.47 | | | | | (84) all_101_0 = 0 | all_101_1 = 0 % 19.20/3.47 | | | | | % 19.20/3.47 | | | | | DELTA: instantiating (75) with fresh symbols all_107_0, all_107_1 % 19.20/3.47 | | | | | gives: % 19.20/3.47 | | | | | (85) k4_tarski(all_107_1, all_59_1) = all_107_0 & % 19.20/3.47 | | | | | r2_hidden(all_107_0, all_41_4) = 0 & r2_hidden(all_107_1, % 19.20/3.47 | | | | | all_41_7) = 0 & $i(all_107_0) & $i(all_107_1) % 19.20/3.47 | | | | | % 19.20/3.47 | | | | | ALPHA: (85) implies: % 19.20/3.47 | | | | | (86) $i(all_107_1) % 19.20/3.47 | | | | | (87) $i(all_107_0) % 19.20/3.47 | | | | | (88) r2_hidden(all_107_1, all_41_7) = 0 % 19.20/3.47 | | | | | (89) r2_hidden(all_107_0, all_41_4) = 0 % 19.20/3.47 | | | | | (90) k4_tarski(all_107_1, all_59_1) = all_107_0 % 19.20/3.47 | | | | | % 19.20/3.47 | | | | | BETA: splitting (74) gives: % 19.20/3.47 | | | | | % 19.20/3.47 | | | | | Case 1: % 19.20/3.47 | | | | | | % 19.20/3.47 | | | | | | (91) all_69_0 = 0 % 19.20/3.47 | | | | | | % 19.20/3.47 | | | | | | REDUCE: (58), (91) imply: % 19.20/3.47 | | | | | | (92) $false % 19.20/3.47 | | | | | | % 19.20/3.47 | | | | | | CLOSE: (92) is inconsistent. % 19.20/3.47 | | | | | | % 19.20/3.47 | | | | | Case 2: % 19.20/3.47 | | | | | | % 19.20/3.47 | | | | | | (93) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 19.20/3.47 | | | | | | k1_zfmisc_1(all_69_1) = v0 & m1_subset_1(v1, v0) = 0 & % 19.20/3.47 | | | | | | v1_xboole_0(v1) = v2 & $i(v1) & $i(v0)) % 19.20/3.47 | | | | | | % 19.20/3.47 | | | | | | DELTA: instantiating (93) with fresh symbols all_122_0, all_122_1, % 19.20/3.47 | | | | | | all_122_2 gives: % 19.20/3.47 | | | | | | (94) ~ (all_122_0 = 0) & k1_zfmisc_1(all_69_1) = all_122_2 & % 19.20/3.47 | | | | | | m1_subset_1(all_122_1, all_122_2) = 0 & % 19.20/3.47 | | | | | | v1_xboole_0(all_122_1) = all_122_0 & $i(all_122_1) & % 19.20/3.47 | | | | | | $i(all_122_2) % 19.20/3.47 | | | | | | % 19.20/3.47 | | | | | | ALPHA: (94) implies: % 19.20/3.47 | | | | | | (95) k1_zfmisc_1(all_69_1) = all_122_2 % 19.20/3.47 | | | | | | % 19.20/3.47 | | | | | | BETA: splitting (76) gives: % 19.20/3.47 | | | | | | % 19.20/3.47 | | | | | | Case 1: % 19.20/3.47 | | | | | | | % 19.20/3.47 | | | | | | | (96) all_59_0 = 0 % 19.20/3.47 | | | | | | | % 19.20/3.47 | | | | | | | REDUCE: (50), (96) imply: % 19.20/3.47 | | | | | | | (97) $false % 19.20/3.47 | | | | | | | % 19.20/3.47 | | | | | | | CLOSE: (97) is inconsistent. % 19.20/3.47 | | | | | | | % 19.20/3.47 | | | | | | Case 2: % 19.20/3.47 | | | | | | | % 19.20/3.47 | | | | | | | (98) ? [v0: any] : ? [v1: any] : (r2_hidden(all_59_1, % 19.20/3.47 | | | | | | | all_41_2) = v0 & r2_hidden(all_59_1, all_41_6) = v1 & % 19.20/3.47 | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 19.20/3.47 | | | | | | | % 19.20/3.47 | | | | | | | DELTA: instantiating (98) with fresh symbols all_133_0, all_133_1 % 19.20/3.47 | | | | | | | gives: % 19.20/3.47 | | | | | | | (99) r2_hidden(all_59_1, all_41_2) = all_133_1 & % 19.20/3.47 | | | | | | | r2_hidden(all_59_1, all_41_6) = all_133_0 & ( ~ (all_133_0 % 19.20/3.47 | | | | | | | = 0) | ~ (all_133_1 = 0)) % 19.20/3.47 | | | | | | | % 19.20/3.47 | | | | | | | ALPHA: (99) implies: % 19.20/3.47 | | | | | | | (100) r2_hidden(all_59_1, all_41_6) = all_133_0 % 19.20/3.47 | | | | | | | (101) r2_hidden(all_59_1, all_41_2) = all_133_1 % 19.20/3.47 | | | | | | | (102) ~ (all_133_0 = 0) | ~ (all_133_1 = 0) % 19.20/3.47 | | | | | | | % 19.20/3.47 | | | | | | | BETA: splitting (73) gives: % 19.20/3.47 | | | | | | | % 19.20/3.47 | | | | | | | Case 1: % 19.20/3.47 | | | | | | | | % 19.20/3.47 | | | | | | | | (103) all_59_0 = 0 % 19.20/3.47 | | | | | | | | % 19.20/3.47 | | | | | | | | REDUCE: (50), (103) imply: % 19.20/3.47 | | | | | | | | (104) $false % 19.20/3.47 | | | | | | | | % 19.20/3.47 | | | | | | | | CLOSE: (104) is inconsistent. % 19.20/3.47 | | | | | | | | % 19.20/3.47 | | | | | | | Case 2: % 19.20/3.47 | | | | | | | | % 19.20/3.47 | | | | | | | | (105) ? [v0: any] : ? [v1: any] : (r2_hidden(all_59_1, % 19.20/3.47 | | | | | | | | all_41_2) = v1 & r2_hidden(all_59_1, all_41_6) = v0 % 19.20/3.47 | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 19.20/3.47 | | | | | | | | % 19.20/3.47 | | | | | | | | DELTA: instantiating (105) with fresh symbols all_143_0, % 19.20/3.47 | | | | | | | | all_143_1 gives: % 19.20/3.47 | | | | | | | | (106) r2_hidden(all_59_1, all_41_2) = all_143_0 & % 19.20/3.47 | | | | | | | | r2_hidden(all_59_1, all_41_6) = all_143_1 & ( ~ % 19.20/3.47 | | | | | | | | (all_143_0 = 0) | ~ (all_143_1 = 0)) % 19.20/3.47 | | | | | | | | % 19.20/3.47 | | | | | | | | ALPHA: (106) implies: % 19.20/3.47 | | | | | | | | (107) r2_hidden(all_59_1, all_41_6) = all_143_1 % 19.20/3.47 | | | | | | | | (108) r2_hidden(all_59_1, all_41_2) = all_143_0 % 19.20/3.47 | | | | | | | | % 19.20/3.47 | | | | | | | | GROUND_INST: instantiating (12) with all_133_0, all_143_1, % 19.20/3.47 | | | | | | | | all_41_6, all_59_1, simplifying with (100), (107) % 19.20/3.47 | | | | | | | | gives: % 19.20/3.47 | | | | | | | | (109) all_143_1 = all_133_0 % 19.20/3.47 | | | | | | | | % 19.20/3.47 | | | | | | | | GROUND_INST: instantiating (12) with all_133_1, all_143_0, % 19.20/3.47 | | | | | | | | all_41_2, all_59_1, simplifying with (101), (108) % 19.20/3.47 | | | | | | | | gives: % 19.20/3.47 | | | | | | | | (110) all_143_0 = all_133_1 % 19.20/3.47 | | | | | | | | % 19.20/3.47 | | | | | | | | GROUND_INST: instantiating (10) with all_93_0, all_101_1, % 19.20/3.47 | | | | | | | | all_69_2, simplifying with (81), (83) gives: % 19.20/3.47 | | | | | | | | (111) all_101_1 = all_93_0 % 19.20/3.47 | | | | | | | | % 19.20/3.47 | | | | | | | | BETA: splitting (84) gives: % 19.20/3.47 | | | | | | | | % 19.20/3.47 | | | | | | | | Case 1: % 19.20/3.47 | | | | | | | | | % 19.20/3.47 | | | | | | | | | % 19.20/3.48 | | | | | | | | | GROUND_INST: instantiating (5) with all_41_8, all_41_5, % 19.20/3.48 | | | | | | | | | all_41_4, all_107_0, simplifying with (19), (22), % 19.20/3.48 | | | | | | | | | (27), (35), (87), (89) gives: % 19.20/3.48 | | | | | | | | | (112) r2_hidden(all_107_0, all_41_5) = 0 & % 19.20/3.48 | | | | | | | | | r2_hidden(all_107_0, all_41_8) = 0 % 19.20/3.48 | | | | | | | | | % 19.20/3.48 | | | | | | | | | ALPHA: (112) implies: % 19.20/3.48 | | | | | | | | | (113) r2_hidden(all_107_0, all_41_8) = 0 % 19.20/3.48 | | | | | | | | | (114) r2_hidden(all_107_0, all_41_5) = 0 % 19.20/3.48 | | | | | | | | | % 19.20/3.48 | | | | | | | | | GROUND_INST: instantiating (3) with all_41_5, all_41_7, % 19.20/3.48 | | | | | | | | | all_41_2, all_59_1, all_133_1, all_107_1, % 19.20/3.48 | | | | | | | | | all_107_0, simplifying with (20), (22), (24), % 19.20/3.48 | | | | | | | | | (26), (30), (51), (86), (90), (101) gives: % 19.20/3.48 | | | | | | | | | (115) all_133_1 = 0 | ? [v0: any] : ? [v1: any] : % 19.20/3.48 | | | | | | | | | (r2_hidden(all_107_0, all_41_5) = v0 & % 19.20/3.48 | | | | | | | | | r2_hidden(all_107_1, all_41_7) = v1 & ( ~ (v1 = 0) % 19.20/3.48 | | | | | | | | | | ~ (v0 = 0))) % 19.20/3.48 | | | | | | | | | % 19.20/3.48 | | | | | | | | | GROUND_INST: instantiating (3) with all_41_8, all_41_7, % 19.20/3.48 | | | | | | | | | all_41_6, all_59_1, all_133_0, all_107_1, % 19.20/3.48 | | | | | | | | | all_107_0, simplifying with (19), (20), (21), % 19.20/3.48 | | | | | | | | | (25), (29), (51), (86), (90), (100) gives: % 19.20/3.48 | | | | | | | | | (116) all_133_0 = 0 | ? [v0: any] : ? [v1: any] : % 19.20/3.48 | | | | | | | | | (r2_hidden(all_107_0, all_41_8) = v0 & % 19.20/3.48 | | | | | | | | | r2_hidden(all_107_1, all_41_7) = v1 & ( ~ (v1 = 0) % 19.20/3.48 | | | | | | | | | | ~ (v0 = 0))) % 19.20/3.48 | | | | | | | | | % 19.20/3.48 | | | | | | | | | GROUND_INST: instantiating (7) with all_69_1, all_122_2, % 19.20/3.48 | | | | | | | | | simplifying with (60), (95) gives: % 19.20/3.48 | | | | | | | | | (117) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: % 19.20/3.48 | | | | | | | | | int] : ($i(v1) & ((v2 = 0 & ~ (v3 = 0) & % 19.20/3.48 | | | | | | | | | m1_subset_1(v1, all_122_2) = 0 & % 19.20/3.48 | | | | | | | | | v1_xboole_0(v1) = v3) | (v0 = 0 & % 19.20/3.48 | | | | | | | | | v1_xboole_0(all_69_1) = 0))) % 19.20/3.48 | | | | | | | | | % 19.20/3.48 | | | | | | | | | DELTA: instantiating (117) with fresh symbols all_225_0, % 19.20/3.48 | | | | | | | | | all_225_1, all_225_2, all_225_3 gives: % 19.20/3.48 | | | | | | | | | (118) $i(all_225_2) & ((all_225_1 = 0 & ~ (all_225_0 = 0) % 19.20/3.48 | | | | | | | | | & m1_subset_1(all_225_2, all_122_2) = 0 & % 19.20/3.48 | | | | | | | | | v1_xboole_0(all_225_2) = all_225_0) | (all_225_3 % 19.20/3.48 | | | | | | | | | = 0 & v1_xboole_0(all_69_1) = 0)) % 19.20/3.48 | | | | | | | | | % 19.20/3.48 | | | | | | | | | ALPHA: (118) implies: % 19.20/3.48 | | | | | | | | | (119) (all_225_1 = 0 & ~ (all_225_0 = 0) & % 19.20/3.48 | | | | | | | | | m1_subset_1(all_225_2, all_122_2) = 0 & % 19.20/3.48 | | | | | | | | | v1_xboole_0(all_225_2) = all_225_0) | (all_225_3 = % 19.20/3.48 | | | | | | | | | 0 & v1_xboole_0(all_69_1) = 0) % 19.20/3.48 | | | | | | | | | % 19.20/3.48 | | | | | | | | | BETA: splitting (115) gives: % 19.20/3.48 | | | | | | | | | % 19.20/3.48 | | | | | | | | | Case 1: % 19.20/3.48 | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | (120) all_133_1 = 0 % 19.20/3.48 | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | BETA: splitting (116) gives: % 19.20/3.48 | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | Case 1: % 19.20/3.48 | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | (121) all_133_0 = 0 % 19.20/3.48 | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | BETA: splitting (102) gives: % 19.20/3.48 | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | Case 1: % 19.20/3.48 | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | (122) ~ (all_133_0 = 0) % 19.20/3.48 | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | REDUCE: (121), (122) imply: % 19.20/3.48 | | | | | | | | | | | | (123) $false % 19.20/3.48 | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | CLOSE: (123) is inconsistent. % 19.20/3.48 | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | Case 2: % 19.20/3.48 | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | (124) ~ (all_133_1 = 0) % 19.20/3.48 | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | REDUCE: (120), (124) imply: % 19.20/3.48 | | | | | | | | | | | | (125) $false % 19.20/3.48 | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | CLOSE: (125) is inconsistent. % 19.20/3.48 | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | End of split % 19.20/3.48 | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | Case 2: % 19.20/3.48 | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | (126) ? [v0: any] : ? [v1: any] : % 19.20/3.48 | | | | | | | | | | | (r2_hidden(all_107_0, all_41_8) = v0 & % 19.20/3.48 | | | | | | | | | | | r2_hidden(all_107_1, all_41_7) = v1 & ( ~ (v1 = % 19.20/3.48 | | | | | | | | | | | 0) | ~ (v0 = 0))) % 19.20/3.48 | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | DELTA: instantiating (126) with fresh symbols all_251_0, % 19.20/3.48 | | | | | | | | | | | all_251_1 gives: % 19.20/3.48 | | | | | | | | | | | (127) r2_hidden(all_107_0, all_41_8) = all_251_1 & % 19.20/3.48 | | | | | | | | | | | r2_hidden(all_107_1, all_41_7) = all_251_0 & ( ~ % 19.20/3.48 | | | | | | | | | | | (all_251_0 = 0) | ~ (all_251_1 = 0)) % 19.20/3.48 | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | ALPHA: (127) implies: % 19.20/3.48 | | | | | | | | | | | (128) r2_hidden(all_107_1, all_41_7) = all_251_0 % 19.20/3.48 | | | | | | | | | | | (129) r2_hidden(all_107_0, all_41_8) = all_251_1 % 19.20/3.48 | | | | | | | | | | | (130) ~ (all_251_0 = 0) | ~ (all_251_1 = 0) % 19.20/3.48 | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | BETA: splitting (119) gives: % 19.20/3.48 | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | Case 1: % 19.20/3.48 | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_251_0, all_41_7, % 19.20/3.48 | | | | | | | | | | | | all_107_1, simplifying with (88), (128) gives: % 19.20/3.48 | | | | | | | | | | | | (131) all_251_0 = 0 % 19.20/3.48 | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_251_1, all_41_8, % 19.20/3.48 | | | | | | | | | | | | all_107_0, simplifying with (113), (129) gives: % 19.20/3.48 | | | | | | | | | | | | (132) all_251_1 = 0 % 19.20/3.48 | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | BETA: splitting (130) gives: % 19.20/3.48 | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | Case 1: % 19.20/3.48 | | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | | (133) ~ (all_251_0 = 0) % 19.20/3.48 | | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | | REDUCE: (131), (133) imply: % 19.20/3.48 | | | | | | | | | | | | | (134) $false % 19.20/3.48 | | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | | CLOSE: (134) is inconsistent. % 19.20/3.48 | | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | Case 2: % 19.20/3.48 | | | | | | | | | | | | | % 19.20/3.48 | | | | | | | | | | | | | (135) ~ (all_251_1 = 0) % 19.20/3.49 | | | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | | | REDUCE: (132), (135) imply: % 19.20/3.49 | | | | | | | | | | | | | (136) $false % 19.20/3.49 | | | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | | | CLOSE: (136) is inconsistent. % 19.20/3.49 | | | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | | End of split % 19.20/3.49 | | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | Case 2: % 19.20/3.49 | | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | | (137) all_225_3 = 0 & v1_xboole_0(all_69_1) = 0 % 19.20/3.49 | | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | | ALPHA: (137) implies: % 19.20/3.49 | | | | | | | | | | | | (138) v1_xboole_0(all_69_1) = 0 % 19.20/3.49 | | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_69_0, 0, all_69_1, % 19.20/3.49 | | | | | | | | | | | | simplifying with (61), (138) gives: % 19.20/3.49 | | | | | | | | | | | | (139) all_69_0 = 0 % 19.20/3.49 | | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | | REDUCE: (58), (139) imply: % 19.20/3.49 | | | | | | | | | | | | (140) $false % 19.20/3.49 | | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | | CLOSE: (140) is inconsistent. % 19.20/3.49 | | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | End of split % 19.20/3.49 | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | End of split % 19.20/3.49 | | | | | | | | | | % 19.20/3.49 | | | | | | | | | Case 2: % 19.20/3.49 | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | (141) ? [v0: any] : ? [v1: any] : (r2_hidden(all_107_0, % 19.20/3.49 | | | | | | | | | | all_41_5) = v0 & r2_hidden(all_107_1, all_41_7) % 19.20/3.49 | | | | | | | | | | = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 19.20/3.49 | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | DELTA: instantiating (141) with fresh symbols all_251_0, % 19.20/3.49 | | | | | | | | | | all_251_1 gives: % 19.20/3.49 | | | | | | | | | | (142) r2_hidden(all_107_0, all_41_5) = all_251_1 & % 19.20/3.49 | | | | | | | | | | r2_hidden(all_107_1, all_41_7) = all_251_0 & ( ~ % 19.20/3.49 | | | | | | | | | | (all_251_0 = 0) | ~ (all_251_1 = 0)) % 19.20/3.49 | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | ALPHA: (142) implies: % 19.20/3.49 | | | | | | | | | | (143) r2_hidden(all_107_1, all_41_7) = all_251_0 % 19.20/3.49 | | | | | | | | | | (144) r2_hidden(all_107_0, all_41_5) = all_251_1 % 19.20/3.49 | | | | | | | | | | (145) ~ (all_251_0 = 0) | ~ (all_251_1 = 0) % 19.20/3.49 | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_251_0, all_41_7, % 19.20/3.49 | | | | | | | | | | all_107_1, simplifying with (88), (143) gives: % 19.20/3.49 | | | | | | | | | | (146) all_251_0 = 0 % 19.20/3.49 | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_251_1, all_41_5, % 19.20/3.49 | | | | | | | | | | all_107_0, simplifying with (114), (144) gives: % 19.20/3.49 | | | | | | | | | | (147) all_251_1 = 0 % 19.20/3.49 | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | BETA: splitting (145) gives: % 19.20/3.49 | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | Case 1: % 19.20/3.49 | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | (148) ~ (all_251_0 = 0) % 19.20/3.49 | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | REDUCE: (146), (148) imply: % 19.20/3.49 | | | | | | | | | | | (149) $false % 19.20/3.49 | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | CLOSE: (149) is inconsistent. % 19.20/3.49 | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | Case 2: % 19.20/3.49 | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | (150) ~ (all_251_1 = 0) % 19.20/3.49 | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | REDUCE: (147), (150) imply: % 19.20/3.49 | | | | | | | | | | | (151) $false % 19.20/3.49 | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | | CLOSE: (151) is inconsistent. % 19.20/3.49 | | | | | | | | | | | % 19.20/3.49 | | | | | | | | | | End of split % 19.20/3.49 | | | | | | | | | | % 19.20/3.49 | | | | | | | | | End of split % 19.20/3.49 | | | | | | | | | % 19.20/3.49 | | | | | | | | Case 2: % 19.20/3.49 | | | | | | | | | % 19.20/3.49 | | | | | | | | | (152) all_101_1 = 0 % 19.20/3.49 | | | | | | | | | % 19.20/3.49 | | | | | | | | | COMBINE_EQS: (111), (152) imply: % 19.20/3.49 | | | | | | | | | (153) all_93_0 = 0 % 19.20/3.49 | | | | | | | | | % 19.20/3.49 | | | | | | | | | SIMP: (153) implies: % 19.20/3.49 | | | | | | | | | (154) all_93_0 = 0 % 19.20/3.49 | | | | | | | | | % 19.20/3.49 | | | | | | | | | REDUCE: (80), (154) imply: % 19.20/3.49 | | | | | | | | | (155) $false % 19.20/3.49 | | | | | | | | | % 19.20/3.49 | | | | | | | | | CLOSE: (155) is inconsistent. % 19.20/3.49 | | | | | | | | | % 19.20/3.49 | | | | | | | | End of split % 19.20/3.49 | | | | | | | | % 19.20/3.49 | | | | | | | End of split % 19.20/3.49 | | | | | | | % 19.20/3.49 | | | | | | End of split % 19.20/3.49 | | | | | | % 19.20/3.49 | | | | | End of split % 19.20/3.49 | | | | | % 19.20/3.49 | | | | End of split % 19.20/3.49 | | | | % 19.20/3.49 | | | End of split % 19.20/3.49 | | | % 19.20/3.49 | | End of split % 19.20/3.49 | | % 19.20/3.49 | End of split % 19.20/3.49 | % 19.20/3.49 End of proof % 19.20/3.49 % SZS output end Proof for theBenchmark % 19.20/3.49 % 19.20/3.49 2895ms %------------------------------------------------------------------------------