%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN067+1 : TPTP v8.1.2. Released v2.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n002.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 : Fri Sep 1 03:26:27 EDT 2023 % Result : Theorem 6.10s 1.54s % Output : Proof 9.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SYN067+1 : TPTP v8.1.2. Released v2.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n002.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 17:50:18 EDT 2023 % 0.12/0.34 % 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/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 1.71/0.97 Prover 1: Preprocessing ... % 1.71/0.97 Prover 4: Preprocessing ... % 2.28/1.02 Prover 6: Preprocessing ... % 2.28/1.02 Prover 2: Preprocessing ... % 2.28/1.02 Prover 0: Preprocessing ... % 2.28/1.02 Prover 3: Preprocessing ... % 2.28/1.02 Prover 5: Preprocessing ... % 3.19/1.15 Prover 5: Proving ... % 3.19/1.15 Prover 2: Proving ... % 3.19/1.16 Prover 6: Proving ... % 3.19/1.19 Prover 3: Warning: ignoring some quantifiers % 3.19/1.20 Prover 1: Warning: ignoring some quantifiers % 3.19/1.20 Prover 3: Constructing countermodel ... % 3.19/1.20 Prover 1: Constructing countermodel ... % 3.80/1.21 Prover 4: Warning: ignoring some quantifiers % 3.80/1.22 Prover 4: Constructing countermodel ... % 3.80/1.23 Prover 0: Proving ... % 6.10/1.54 Prover 2: proved (917ms) % 6.10/1.54 % 6.10/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.10/1.54 % 6.10/1.54 Prover 3: stopped % 6.10/1.54 Prover 6: stopped % 6.37/1.55 Prover 5: stopped % 6.37/1.55 Prover 0: stopped % 6.37/1.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.37/1.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.37/1.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.37/1.55 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.37/1.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.37/1.57 Prover 8: Preprocessing ... % 6.37/1.58 Prover 10: Preprocessing ... % 6.37/1.58 Prover 13: Preprocessing ... % 6.37/1.58 Prover 11: Preprocessing ... % 6.37/1.58 Prover 7: Preprocessing ... % 6.37/1.60 Prover 13: Warning: ignoring some quantifiers % 6.37/1.60 Prover 13: Constructing countermodel ... % 6.37/1.61 Prover 10: Warning: ignoring some quantifiers % 6.37/1.61 Prover 10: Constructing countermodel ... % 6.37/1.62 Prover 7: Warning: ignoring some quantifiers % 6.37/1.62 Prover 7: Constructing countermodel ... % 6.37/1.62 Prover 10: gave up % 6.37/1.62 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.02/1.64 Prover 13: gave up % 7.02/1.64 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.02/1.64 Prover 7: gave up % 7.02/1.64 Prover 16: Preprocessing ... % 7.02/1.65 Prover 1: gave up % 7.02/1.66 Prover 19: Preprocessing ... % 7.02/1.66 Prover 8: Warning: ignoring some quantifiers % 7.02/1.66 Prover 16: Warning: ignoring some quantifiers % 7.02/1.66 Prover 16: Constructing countermodel ... % 7.02/1.66 Prover 8: Constructing countermodel ... % 7.02/1.67 Prover 11: Warning: ignoring some quantifiers % 7.02/1.67 Prover 11: Constructing countermodel ... % 7.39/1.73 Prover 19: Warning: ignoring some quantifiers % 7.39/1.73 Prover 19: Constructing countermodel ... % 7.89/1.75 Prover 16: gave up % 7.89/1.75 Prover 8: gave up % 7.99/1.79 Prover 19: gave up % 8.53/1.87 Prover 4: Found proof (size 90) % 8.53/1.87 Prover 4: proved (1237ms) % 8.53/1.87 Prover 11: stopped % 8.53/1.87 % 8.53/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.53/1.87 % 8.53/1.88 % SZS output start Proof for theBenchmark % 8.53/1.88 Assumptions after simplification: % 8.53/1.88 --------------------------------- % 8.53/1.88 % 8.53/1.88 (pel38) % 8.53/1.93 $i(a) & ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: int] % 8.53/1.93 : ? [v5: int] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: int] : ? % 8.53/1.93 [v10: int] : (big_p(a) = v0 & $i(v8) & $i(v6) & $i(v3) & $i(v1) & ((v0 = 0 & % 8.53/1.93 big_p(v6) = v7 & ! [v11: $i] : ! [v12: MultipleValueBool] : ! [v13: % 8.53/1.93 $i] : ( ~ (big_r(v11, v13) = 0) | ~ (big_p(v11) = v12) | ~ $i(v13) | % 8.53/1.93 ~ $i(v11) | ? [v14: $i] : ? [v15: $i] : ? [v16: int] : ? [v17: % 8.53/1.93 int] : ? [v18: int] : ? [v19: int] : ($i(v15) & $i(v14) & ((v18 = % 8.53/1.93 0 & v17 = 0 & v16 = 0 & big_r(v15, v14) = 0 & big_r(v11, v15) = % 8.53/1.93 0 & big_p(v14) = 0) | ( ~ (v19 = 0) & big_p(v13) = v19)))) & ! % 8.53/1.93 [v11: $i] : ! [v12: MultipleValueBool] : ! [v13: $i] : ( ~ (big_p(v13) % 8.53/1.93 = 0) | ~ (big_p(v11) = v12) | ~ $i(v13) | ~ $i(v11) | ? [v14: % 8.53/1.93 $i] : ? [v15: $i] : ? [v16: int] : ? [v17: int] : ? [v18: int] : % 8.53/1.93 ? [v19: int] : ($i(v15) & $i(v14) & ((v18 = 0 & v17 = 0 & v16 = 0 & % 8.53/1.93 big_r(v15, v14) = 0 & big_r(v11, v15) = 0 & big_p(v14) = 0) | ( % 8.53/1.93 ~ (v19 = 0) & big_r(v11, v13) = v19)))) & ! [v11: $i] : ! % 8.53/1.93 [v12: int] : (v12 = 0 | ~ (big_p(v11) = v12) | ~ $i(v11) | ? [v13: % 8.53/1.93 $i] : ? [v14: $i] : (big_r(v14, v13) = 0 & big_r(v11, v14) = 0 & % 8.53/1.93 big_p(v13) = 0 & $i(v14) & $i(v13))) & ! [v11: $i] : ! [v12: $i] : % 8.53/1.93 ( ~ (big_r(v12, v11) = 0) | ~ $i(v12) | ~ $i(v11) | ? [v13: any] : ? % 8.53/1.93 [v14: any] : (big_r(v6, v12) = v14 & big_p(v11) = v13 & ( ~ (v14 = 0) % 8.53/1.93 | ~ (v13 = 0)))) & ( ~ (v7 = 0) | (v10 = 0 & v9 = 0 & big_r(v6, % 8.53/1.93 v8) = 0 & big_p(v8) = 0))) | (v0 = 0 & big_p(v1) = v2 & ! [v11: % 8.53/1.93 $i] : ! [v12: int] : (v12 = 0 | ~ (big_p(v11) = v12) | ~ $i(v11) | % 8.53/1.93 ? [v13: $i] : ? [v14: $i] : (big_r(v14, v13) = 0 & big_r(v11, v14) = % 8.53/1.93 0 & big_p(v13) = 0 & $i(v14) & $i(v13))) & ! [v11: $i] : ! [v12: % 8.53/1.93 $i] : ( ~ (big_r(v12, v11) = 0) | ~ $i(v12) | ~ $i(v11) | ? [v13: % 8.53/1.93 any] : ? [v14: any] : (big_r(v1, v12) = v14 & big_p(v11) = v13 & ( % 8.53/1.93 ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v11: $i] : ! [v12: $i] : ( ~ % 8.53/1.93 (big_r(v11, v12) = 0) | ~ $i(v12) | ~ $i(v11) | ? [v13: $i] : ? % 8.53/1.93 [v14: $i] : ? [v15: int] : ? [v16: int] : ? [v17: int] : ? [v18: % 8.53/1.93 int] : ($i(v14) & $i(v13) & ((v17 = 0 & v16 = 0 & v15 = 0 & % 8.53/1.93 big_r(v14, v13) = 0 & big_r(v11, v14) = 0 & big_p(v13) = 0) | ( % 8.53/1.93 ~ (v18 = 0) & big_p(v12) = v18)))) & ? [v11: $i] : ! [v12: $i] % 8.53/1.93 : ( ~ (big_p(v12) = 0) | ~ $i(v12) | ~ $i(v11) | ? [v13: $i] : ? % 8.53/1.93 [v14: $i] : ? [v15: int] : ? [v16: int] : ? [v17: int] : ? [v18: % 8.53/1.93 int] : ($i(v14) & $i(v13) & ((v17 = 0 & v16 = 0 & v15 = 0 & % 8.53/1.93 big_r(v14, v13) = 0 & big_r(v11, v14) = 0 & big_p(v13) = 0) | ( % 8.53/1.93 ~ (v18 = 0) & big_r(v11, v12) = v18)))) & ( ~ (v2 = 0) | (v5 = 0 % 8.53/1.93 & v4 = 0 & big_r(v1, v3) = 0 & big_p(v3) = 0))))) % 8.53/1.93 % 8.53/1.93 (function-axioms) % 8.53/1.93 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.53/1.93 [v3: $i] : (v1 = v0 | ~ (big_r(v3, v2) = v1) | ~ (big_r(v3, v2) = v0)) & ! % 8.53/1.93 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 8.53/1.93 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) % 8.53/1.93 % 8.53/1.93 Those formulas are unsatisfiable: % 8.53/1.93 --------------------------------- % 8.53/1.93 % 8.53/1.93 Begin of proof % 8.53/1.93 | % 8.53/1.94 | ALPHA: (pel38) implies: % 8.53/1.95 | (1) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: int] % 8.53/1.95 | : ? [v5: int] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: % 8.53/1.95 | int] : ? [v10: int] : (big_p(a) = v0 & $i(v8) & $i(v6) & $i(v3) & % 8.53/1.95 | $i(v1) & ((v0 = 0 & big_p(v6) = v7 & ! [v11: $i] : ! [v12: % 8.53/1.95 | MultipleValueBool] : ! [v13: $i] : ( ~ (big_r(v11, v13) = 0) | % 8.53/1.95 | ~ (big_p(v11) = v12) | ~ $i(v13) | ~ $i(v11) | ? [v14: $i] % 8.53/1.95 | : ? [v15: $i] : ? [v16: int] : ? [v17: int] : ? [v18: int] % 8.53/1.95 | : ? [v19: int] : ($i(v15) & $i(v14) & ((v18 = 0 & v17 = 0 & % 8.53/1.95 | v16 = 0 & big_r(v15, v14) = 0 & big_r(v11, v15) = 0 & % 8.53/1.95 | big_p(v14) = 0) | ( ~ (v19 = 0) & big_p(v13) = v19)))) & % 8.53/1.95 | ! [v11: $i] : ! [v12: MultipleValueBool] : ! [v13: $i] : ( ~ % 8.53/1.95 | (big_p(v13) = 0) | ~ (big_p(v11) = v12) | ~ $i(v13) | ~ % 8.53/1.95 | $i(v11) | ? [v14: $i] : ? [v15: $i] : ? [v16: int] : ? % 8.53/1.95 | [v17: int] : ? [v18: int] : ? [v19: int] : ($i(v15) & $i(v14) % 8.53/1.95 | & ((v18 = 0 & v17 = 0 & v16 = 0 & big_r(v15, v14) = 0 & % 8.53/1.95 | big_r(v11, v15) = 0 & big_p(v14) = 0) | ( ~ (v19 = 0) & % 8.53/1.95 | big_r(v11, v13) = v19)))) & ! [v11: $i] : ! [v12: int] % 8.53/1.95 | : (v12 = 0 | ~ (big_p(v11) = v12) | ~ $i(v11) | ? [v13: $i] : % 8.53/1.95 | ? [v14: $i] : (big_r(v14, v13) = 0 & big_r(v11, v14) = 0 & % 8.53/1.95 | big_p(v13) = 0 & $i(v14) & $i(v13))) & ! [v11: $i] : ! % 8.53/1.95 | [v12: $i] : ( ~ (big_r(v12, v11) = 0) | ~ $i(v12) | ~ $i(v11) | % 8.53/1.95 | ? [v13: any] : ? [v14: any] : (big_r(v6, v12) = v14 & % 8.53/1.95 | big_p(v11) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ( ~ (v7 % 8.53/1.95 | = 0) | (v10 = 0 & v9 = 0 & big_r(v6, v8) = 0 & big_p(v8) = % 8.53/1.95 | 0))) | (v0 = 0 & big_p(v1) = v2 & ! [v11: $i] : ! [v12: % 8.53/1.95 | int] : (v12 = 0 | ~ (big_p(v11) = v12) | ~ $i(v11) | ? [v13: % 8.53/1.95 | $i] : ? [v14: $i] : (big_r(v14, v13) = 0 & big_r(v11, v14) = % 8.53/1.95 | 0 & big_p(v13) = 0 & $i(v14) & $i(v13))) & ! [v11: $i] : ! % 8.53/1.95 | [v12: $i] : ( ~ (big_r(v12, v11) = 0) | ~ $i(v12) | ~ $i(v11) | % 8.53/1.95 | ? [v13: any] : ? [v14: any] : (big_r(v1, v12) = v14 & % 8.53/1.95 | big_p(v11) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v11: % 8.53/1.95 | $i] : ! [v12: $i] : ( ~ (big_r(v11, v12) = 0) | ~ $i(v12) | % 8.53/1.95 | ~ $i(v11) | ? [v13: $i] : ? [v14: $i] : ? [v15: int] : ? % 8.53/1.95 | [v16: int] : ? [v17: int] : ? [v18: int] : ($i(v14) & $i(v13) % 8.53/1.95 | & ((v17 = 0 & v16 = 0 & v15 = 0 & big_r(v14, v13) = 0 & % 8.53/1.95 | big_r(v11, v14) = 0 & big_p(v13) = 0) | ( ~ (v18 = 0) & % 8.53/1.95 | big_p(v12) = v18)))) & ? [v11: $i] : ! [v12: $i] : ( ~ % 8.53/1.95 | (big_p(v12) = 0) | ~ $i(v12) | ~ $i(v11) | ? [v13: $i] : ? % 8.53/1.95 | [v14: $i] : ? [v15: int] : ? [v16: int] : ? [v17: int] : ? % 8.53/1.95 | [v18: int] : ($i(v14) & $i(v13) & ((v17 = 0 & v16 = 0 & v15 = 0 % 8.53/1.95 | & big_r(v14, v13) = 0 & big_r(v11, v14) = 0 & big_p(v13) % 8.53/1.95 | = 0) | ( ~ (v18 = 0) & big_r(v11, v12) = v18)))) & ( ~ % 8.53/1.95 | (v2 = 0) | (v5 = 0 & v4 = 0 & big_r(v1, v3) = 0 & big_p(v3) = % 8.53/1.95 | 0))))) % 8.53/1.95 | % 8.53/1.95 | ALPHA: (function-axioms) implies: % 8.53/1.95 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.53/1.95 | (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) % 8.53/1.95 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.53/1.95 | ! [v3: $i] : (v1 = v0 | ~ (big_r(v3, v2) = v1) | ~ (big_r(v3, v2) = % 8.53/1.95 | v0)) % 8.53/1.95 | % 8.53/1.95 | DELTA: instantiating (1) with fresh symbols all_4_0, all_4_1, all_4_2, % 8.53/1.95 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9, all_4_10 % 8.53/1.95 | gives: % 8.53/1.96 | (4) big_p(a) = all_4_10 & $i(all_4_2) & $i(all_4_4) & $i(all_4_7) & % 8.53/1.96 | $i(all_4_9) & ((all_4_10 = 0 & big_p(all_4_4) = all_4_3 & ! [v0: $i] : % 8.53/1.96 | ! [v1: MultipleValueBool] : ! [v2: $i] : ( ~ (big_r(v0, v2) = 0) % 8.53/1.96 | | ~ (big_p(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ? % 8.53/1.96 | [v4: $i] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: % 8.53/1.96 | int] : ($i(v4) & $i(v3) & ((v7 = 0 & v6 = 0 & v5 = 0 & % 8.53/1.96 | big_r(v4, v3) = 0 & big_r(v0, v4) = 0 & big_p(v3) = 0) | ( % 8.53/1.96 | ~ (v8 = 0) & big_p(v2) = v8)))) & ! [v0: $i] : ! [v1: % 8.53/1.96 | MultipleValueBool] : ! [v2: $i] : ( ~ (big_p(v2) = 0) | ~ % 8.53/1.96 | (big_p(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 8.53/1.96 | $i] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] % 8.53/1.96 | : ($i(v4) & $i(v3) & ((v7 = 0 & v6 = 0 & v5 = 0 & big_r(v4, v3) = % 8.53/1.96 | 0 & big_r(v0, v4) = 0 & big_p(v3) = 0) | ( ~ (v8 = 0) & % 8.53/1.96 | big_r(v0, v2) = v8)))) & ! [v0: $i] : ! [v1: int] : (v1 = % 8.53/1.96 | 0 | ~ (big_p(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : % 8.53/1.96 | (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0 & $i(v3) & % 8.53/1.96 | $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (big_r(v1, v0) = 0) % 8.53/1.96 | | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 8.53/1.96 | (big_r(all_4_4, v1) = v3 & big_p(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 % 8.53/1.96 | = 0)))) & ( ~ (all_4_3 = 0) | (all_4_0 = 0 & all_4_1 = 0 & % 8.53/1.96 | big_r(all_4_4, all_4_2) = 0 & big_p(all_4_2) = 0))) | (all_4_10 % 8.53/1.96 | = 0 & big_p(all_4_9) = all_4_8 & ! [v0: $i] : ! [v1: int] : (v1 = % 8.53/1.96 | 0 | ~ (big_p(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : % 8.53/1.96 | (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0 & $i(v3) & % 8.53/1.96 | $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (big_r(v1, v0) = 0) % 8.53/1.96 | | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 8.53/1.96 | (big_r(all_4_9, v1) = v3 & big_p(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 % 8.53/1.96 | = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (big_r(v0, v1) = % 8.53/1.96 | 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? % 8.53/1.96 | [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ($i(v3) % 8.53/1.96 | & $i(v2) & ((v6 = 0 & v5 = 0 & v4 = 0 & big_r(v3, v2) = 0 & % 8.53/1.96 | big_r(v0, v3) = 0 & big_p(v2) = 0) | ( ~ (v7 = 0) & % 8.53/1.96 | big_p(v1) = v7)))) & ? [v0: $i] : ! [v1: $i] : ( ~ % 8.53/1.96 | (big_p(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 8.53/1.96 | $i] : ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] % 8.53/1.96 | : ($i(v3) & $i(v2) & ((v6 = 0 & v5 = 0 & v4 = 0 & big_r(v3, v2) = % 8.53/1.96 | 0 & big_r(v0, v3) = 0 & big_p(v2) = 0) | ( ~ (v7 = 0) & % 8.53/1.96 | big_r(v0, v1) = v7)))) & ( ~ (all_4_8 = 0) | (all_4_5 = 0 & % 8.53/1.96 | all_4_6 = 0 & big_r(all_4_9, all_4_7) = 0 & big_p(all_4_7) = % 8.53/1.96 | 0)))) % 8.53/1.96 | % 8.53/1.96 | ALPHA: (4) implies: % 8.53/1.96 | (5) $i(all_4_9) % 8.53/1.96 | (6) $i(all_4_7) % 8.53/1.96 | (7) $i(all_4_4) % 8.53/1.96 | (8) $i(all_4_2) % 8.53/1.97 | (9) (all_4_10 = 0 & big_p(all_4_4) = all_4_3 & ! [v0: $i] : ! [v1: % 8.53/1.97 | MultipleValueBool] : ! [v2: $i] : ( ~ (big_r(v0, v2) = 0) | ~ % 8.53/1.97 | (big_p(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 8.53/1.97 | $i] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : % 8.53/1.97 | ($i(v4) & $i(v3) & ((v7 = 0 & v6 = 0 & v5 = 0 & big_r(v4, v3) = 0 & % 8.53/1.97 | big_r(v0, v4) = 0 & big_p(v3) = 0) | ( ~ (v8 = 0) & big_p(v2) % 8.53/1.97 | = v8)))) & ! [v0: $i] : ! [v1: MultipleValueBool] : ! [v2: % 8.53/1.97 | $i] : ( ~ (big_p(v2) = 0) | ~ (big_p(v0) = v1) | ~ $i(v2) | ~ % 8.53/1.97 | $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : % 8.53/1.97 | ? [v7: int] : ? [v8: int] : ($i(v4) & $i(v3) & ((v7 = 0 & v6 = 0 & % 8.53/1.97 | v5 = 0 & big_r(v4, v3) = 0 & big_r(v0, v4) = 0 & big_p(v3) = % 8.53/1.97 | 0) | ( ~ (v8 = 0) & big_r(v0, v2) = v8)))) & ! [v0: $i] : ! % 8.53/1.97 | [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 8.53/1.97 | ? [v3: $i] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = % 8.53/1.97 | 0 & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 8.53/1.97 | (big_r(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? % 8.53/1.97 | [v3: any] : (big_r(all_4_4, v1) = v3 & big_p(v0) = v2 & ( ~ (v3 = % 8.53/1.97 | 0) | ~ (v2 = 0)))) & ( ~ (all_4_3 = 0) | (all_4_0 = 0 & % 8.53/1.97 | all_4_1 = 0 & big_r(all_4_4, all_4_2) = 0 & big_p(all_4_2) = 0))) % 8.53/1.97 | | (all_4_10 = 0 & big_p(all_4_9) = all_4_8 & ! [v0: $i] : ! [v1: int] % 8.53/1.97 | : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 8.53/1.97 | $i] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0 & % 8.53/1.97 | $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (big_r(v1, % 8.53/1.97 | v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] % 8.53/1.97 | : (big_r(all_4_9, v1) = v3 & big_p(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 % 8.53/1.97 | = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (big_r(v0, v1) = 0) % 8.53/1.97 | | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] % 8.53/1.97 | : ? [v5: int] : ? [v6: int] : ? [v7: int] : ($i(v3) & $i(v2) & % 8.53/1.97 | ((v6 = 0 & v5 = 0 & v4 = 0 & big_r(v3, v2) = 0 & big_r(v0, v3) = % 8.53/1.97 | 0 & big_p(v2) = 0) | ( ~ (v7 = 0) & big_p(v1) = v7)))) & ? % 8.53/1.97 | [v0: $i] : ! [v1: $i] : ( ~ (big_p(v1) = 0) | ~ $i(v1) | ~ $i(v0) % 8.53/1.97 | | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: int] : ? [v6: % 8.53/1.97 | int] : ? [v7: int] : ($i(v3) & $i(v2) & ((v6 = 0 & v5 = 0 & v4 = % 8.53/1.97 | 0 & big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0) | % 8.53/1.97 | ( ~ (v7 = 0) & big_r(v0, v1) = v7)))) & ( ~ (all_4_8 = 0) | % 8.53/1.97 | (all_4_5 = 0 & all_4_6 = 0 & big_r(all_4_9, all_4_7) = 0 & % 8.53/1.97 | big_p(all_4_7) = 0))) % 8.53/1.97 | % 8.53/1.97 | BETA: splitting (9) gives: % 8.53/1.97 | % 8.53/1.97 | Case 1: % 8.53/1.97 | | % 8.53/1.97 | | (10) all_4_10 = 0 & big_p(all_4_4) = all_4_3 & ! [v0: $i] : ! [v1: % 8.53/1.97 | | MultipleValueBool] : ! [v2: $i] : ( ~ (big_r(v0, v2) = 0) | ~ % 8.53/1.97 | | (big_p(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 8.53/1.97 | | $i] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] % 8.53/1.97 | | : ($i(v4) & $i(v3) & ((v7 = 0 & v6 = 0 & v5 = 0 & big_r(v4, v3) = % 8.53/1.97 | | 0 & big_r(v0, v4) = 0 & big_p(v3) = 0) | ( ~ (v8 = 0) & % 8.53/1.97 | | big_p(v2) = v8)))) & ! [v0: $i] : ! [v1: % 8.53/1.97 | | MultipleValueBool] : ! [v2: $i] : ( ~ (big_p(v2) = 0) | ~ % 8.53/1.97 | | (big_p(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 8.53/1.97 | | $i] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] % 8.53/1.97 | | : ($i(v4) & $i(v3) & ((v7 = 0 & v6 = 0 & v5 = 0 & big_r(v4, v3) = % 8.53/1.97 | | 0 & big_r(v0, v4) = 0 & big_p(v3) = 0) | ( ~ (v8 = 0) & % 8.53/1.97 | | big_r(v0, v2) = v8)))) & ! [v0: $i] : ! [v1: int] : (v1 = % 8.53/1.97 | | 0 | ~ (big_p(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : % 8.53/1.97 | | (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0 & $i(v3) & % 8.53/1.97 | | $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (big_r(v1, v0) = 0) | % 8.53/1.97 | | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 8.53/1.97 | | (big_r(all_4_4, v1) = v3 & big_p(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 % 8.53/1.97 | | = 0)))) & ( ~ (all_4_3 = 0) | (all_4_0 = 0 & all_4_1 = 0 & % 8.53/1.97 | | big_r(all_4_4, all_4_2) = 0 & big_p(all_4_2) = 0)) % 8.53/1.97 | | % 8.53/1.97 | | ALPHA: (10) implies: % 8.53/1.97 | | (11) big_p(all_4_4) = all_4_3 % 8.53/1.97 | | (12) ~ (all_4_3 = 0) | (all_4_0 = 0 & all_4_1 = 0 & big_r(all_4_4, % 8.53/1.97 | | all_4_2) = 0 & big_p(all_4_2) = 0) % 8.53/1.98 | | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (big_r(v1, v0) = 0) | ~ $i(v1) | ~ % 8.53/1.98 | | $i(v0) | ? [v2: any] : ? [v3: any] : (big_r(all_4_4, v1) = v3 & % 8.53/1.98 | | big_p(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 8.53/1.98 | | (14) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 8.53/1.98 | | $i(v0) | ? [v2: $i] : ? [v3: $i] : (big_r(v3, v2) = 0 & % 8.53/1.98 | | big_r(v0, v3) = 0 & big_p(v2) = 0 & $i(v3) & $i(v2))) % 8.53/1.98 | | (15) ! [v0: $i] : ! [v1: MultipleValueBool] : ! [v2: $i] : ( ~ % 8.53/1.98 | | (big_p(v2) = 0) | ~ (big_p(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? % 8.53/1.98 | | [v3: $i] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : ? [v7: % 8.53/1.98 | | int] : ? [v8: int] : ($i(v4) & $i(v3) & ((v7 = 0 & v6 = 0 & v5 % 8.53/1.98 | | = 0 & big_r(v4, v3) = 0 & big_r(v0, v4) = 0 & big_p(v3) = 0) % 8.53/1.98 | | | ( ~ (v8 = 0) & big_r(v0, v2) = v8)))) % 8.53/1.98 | | % 8.53/1.98 | | GROUND_INST: instantiating (14) with all_4_4, all_4_3, simplifying with (7), % 8.53/1.98 | | (11) gives: % 8.53/1.98 | | (16) all_4_3 = 0 | ? [v0: $i] : ? [v1: $i] : (big_r(v1, v0) = 0 & % 8.53/1.98 | | big_r(all_4_4, v1) = 0 & big_p(v0) = 0 & $i(v1) & $i(v0)) % 8.53/1.98 | | % 8.53/1.98 | | BETA: splitting (12) gives: % 8.53/1.98 | | % 8.53/1.98 | | Case 1: % 8.53/1.98 | | | % 8.53/1.98 | | | (17) ~ (all_4_3 = 0) % 8.53/1.98 | | | % 8.53/1.98 | | | BETA: splitting (16) gives: % 8.53/1.98 | | | % 8.53/1.98 | | | Case 1: % 8.53/1.98 | | | | % 8.53/1.98 | | | | (18) all_4_3 = 0 % 8.53/1.98 | | | | % 8.53/1.98 | | | | REDUCE: (17), (18) imply: % 8.53/1.98 | | | | (19) $false % 8.53/1.98 | | | | % 8.53/1.98 | | | | CLOSE: (19) is inconsistent. % 8.53/1.98 | | | | % 8.53/1.98 | | | Case 2: % 8.53/1.98 | | | | % 8.53/1.98 | | | | (20) ? [v0: $i] : ? [v1: $i] : (big_r(v1, v0) = 0 & big_r(all_4_4, % 8.53/1.98 | | | | v1) = 0 & big_p(v0) = 0 & $i(v1) & $i(v0)) % 8.53/1.98 | | | | % 8.53/1.98 | | | | DELTA: instantiating (20) with fresh symbols all_34_0, all_34_1 gives: % 8.53/1.98 | | | | (21) big_r(all_34_0, all_34_1) = 0 & big_r(all_4_4, all_34_0) = 0 & % 8.53/1.98 | | | | big_p(all_34_1) = 0 & $i(all_34_0) & $i(all_34_1) % 8.53/1.98 | | | | % 8.53/1.98 | | | | ALPHA: (21) implies: % 8.53/1.98 | | | | (22) $i(all_34_1) % 8.53/1.98 | | | | (23) $i(all_34_0) % 8.53/1.98 | | | | (24) big_p(all_34_1) = 0 % 8.53/1.98 | | | | (25) big_r(all_4_4, all_34_0) = 0 % 8.53/1.98 | | | | (26) big_r(all_34_0, all_34_1) = 0 % 8.53/1.98 | | | | % 8.53/1.98 | | | | GROUND_INST: instantiating (13) with all_34_1, all_34_0, simplifying % 8.53/1.98 | | | | with (22), (23), (26) gives: % 8.53/1.98 | | | | (27) ? [v0: any] : ? [v1: any] : (big_r(all_4_4, all_34_0) = v1 & % 8.53/1.98 | | | | big_p(all_34_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.53/1.98 | | | | % 8.53/1.98 | | | | DELTA: instantiating (27) with fresh symbols all_41_0, all_41_1 gives: % 8.53/1.99 | | | | (28) big_r(all_4_4, all_34_0) = all_41_0 & big_p(all_34_1) = all_41_1 % 8.53/1.99 | | | | & ( ~ (all_41_0 = 0) | ~ (all_41_1 = 0)) % 8.53/1.99 | | | | % 8.53/1.99 | | | | ALPHA: (28) implies: % 8.53/1.99 | | | | (29) big_p(all_34_1) = all_41_1 % 8.53/1.99 | | | | (30) big_r(all_4_4, all_34_0) = all_41_0 % 8.53/1.99 | | | | (31) ~ (all_41_0 = 0) | ~ (all_41_1 = 0) % 8.53/1.99 | | | | % 8.53/1.99 | | | | GROUND_INST: instantiating (2) with 0, all_41_1, all_34_1, simplifying % 8.53/1.99 | | | | with (24), (29) gives: % 8.53/1.99 | | | | (32) all_41_1 = 0 % 8.53/1.99 | | | | % 8.53/1.99 | | | | GROUND_INST: instantiating (3) with 0, all_41_0, all_34_0, all_4_4, % 8.53/1.99 | | | | simplifying with (25), (30) gives: % 8.53/1.99 | | | | (33) all_41_0 = 0 % 8.53/1.99 | | | | % 8.53/1.99 | | | | BETA: splitting (31) gives: % 8.53/1.99 | | | | % 8.53/1.99 | | | | Case 1: % 8.53/1.99 | | | | | % 8.53/1.99 | | | | | (34) ~ (all_41_0 = 0) % 8.53/1.99 | | | | | % 8.53/1.99 | | | | | REDUCE: (33), (34) imply: % 8.53/1.99 | | | | | (35) $false % 8.53/1.99 | | | | | % 8.53/1.99 | | | | | CLOSE: (35) is inconsistent. % 8.53/1.99 | | | | | % 8.53/1.99 | | | | Case 2: % 8.53/1.99 | | | | | % 8.53/1.99 | | | | | (36) ~ (all_41_1 = 0) % 8.53/1.99 | | | | | % 8.53/1.99 | | | | | REDUCE: (32), (36) imply: % 8.53/1.99 | | | | | (37) $false % 8.53/1.99 | | | | | % 8.53/1.99 | | | | | CLOSE: (37) is inconsistent. % 8.53/1.99 | | | | | % 8.53/1.99 | | | | End of split % 8.53/1.99 | | | | % 8.53/1.99 | | | End of split % 8.53/1.99 | | | % 8.53/1.99 | | Case 2: % 8.53/1.99 | | | % 8.53/1.99 | | | (38) all_4_3 = 0 % 8.53/1.99 | | | (39) all_4_0 = 0 & all_4_1 = 0 & big_r(all_4_4, all_4_2) = 0 & % 8.53/1.99 | | | big_p(all_4_2) = 0 % 8.53/1.99 | | | % 8.53/1.99 | | | ALPHA: (39) implies: % 8.53/1.99 | | | (40) big_p(all_4_2) = 0 % 8.53/1.99 | | | (41) big_r(all_4_4, all_4_2) = 0 % 8.53/1.99 | | | % 8.53/1.99 | | | REDUCE: (11), (38) imply: % 8.53/1.99 | | | (42) big_p(all_4_4) = 0 % 8.53/1.99 | | | % 8.53/1.99 | | | GROUND_INST: instantiating (15) with all_4_4, 0, all_4_2, simplifying with % 8.53/1.99 | | | (7), (8), (40), (42) gives: % 8.53/1.99 | | | (43) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ? [v4: % 8.53/1.99 | | | int] : ? [v5: int] : ($i(v1) & $i(v0) & ((v4 = 0 & v3 = 0 & v2 % 8.53/1.99 | | | = 0 & big_r(v1, v0) = 0 & big_r(all_4_4, v1) = 0 & big_p(v0) % 8.53/1.99 | | | = 0) | ( ~ (v5 = 0) & big_r(all_4_4, all_4_2) = v5))) % 8.53/1.99 | | | % 8.53/1.99 | | | DELTA: instantiating (43) with fresh symbols all_43_0, all_43_1, all_43_2, % 8.53/1.99 | | | all_43_3, all_43_4, all_43_5 gives: % 8.53/1.99 | | | (44) $i(all_43_4) & $i(all_43_5) & ((all_43_1 = 0 & all_43_2 = 0 & % 8.53/1.99 | | | all_43_3 = 0 & big_r(all_43_4, all_43_5) = 0 & big_r(all_4_4, % 8.53/1.99 | | | all_43_4) = 0 & big_p(all_43_5) = 0) | ( ~ (all_43_0 = 0) & % 8.53/1.99 | | | big_r(all_4_4, all_4_2) = all_43_0)) % 8.53/1.99 | | | % 8.53/1.99 | | | ALPHA: (44) implies: % 8.53/1.99 | | | (45) $i(all_43_5) % 8.53/1.99 | | | (46) $i(all_43_4) % 8.53/1.99 | | | (47) (all_43_1 = 0 & all_43_2 = 0 & all_43_3 = 0 & big_r(all_43_4, % 8.53/1.99 | | | all_43_5) = 0 & big_r(all_4_4, all_43_4) = 0 & big_p(all_43_5) % 8.53/1.99 | | | = 0) | ( ~ (all_43_0 = 0) & big_r(all_4_4, all_4_2) = all_43_0) % 8.53/1.99 | | | % 8.53/1.99 | | | BETA: splitting (47) gives: % 8.53/1.99 | | | % 8.53/1.99 | | | Case 1: % 8.53/1.99 | | | | % 8.53/1.99 | | | | (48) all_43_1 = 0 & all_43_2 = 0 & all_43_3 = 0 & big_r(all_43_4, % 8.53/1.99 | | | | all_43_5) = 0 & big_r(all_4_4, all_43_4) = 0 & big_p(all_43_5) % 8.53/1.99 | | | | = 0 % 8.53/1.99 | | | | % 8.53/1.99 | | | | ALPHA: (48) implies: % 8.53/1.99 | | | | (49) big_p(all_43_5) = 0 % 8.53/1.99 | | | | (50) big_r(all_4_4, all_43_4) = 0 % 8.53/1.99 | | | | (51) big_r(all_43_4, all_43_5) = 0 % 8.53/1.99 | | | | % 8.53/2.00 | | | | GROUND_INST: instantiating (13) with all_43_5, all_43_4, simplifying % 8.53/2.00 | | | | with (45), (46), (51) gives: % 8.53/2.00 | | | | (52) ? [v0: any] : ? [v1: any] : (big_r(all_4_4, all_43_4) = v1 & % 8.53/2.00 | | | | big_p(all_43_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.53/2.00 | | | | % 8.53/2.00 | | | | DELTA: instantiating (52) with fresh symbols all_76_0, all_76_1 gives: % 8.53/2.00 | | | | (53) big_r(all_4_4, all_43_4) = all_76_0 & big_p(all_43_5) = all_76_1 % 8.53/2.00 | | | | & ( ~ (all_76_0 = 0) | ~ (all_76_1 = 0)) % 8.53/2.00 | | | | % 8.53/2.00 | | | | ALPHA: (53) implies: % 8.53/2.00 | | | | (54) big_p(all_43_5) = all_76_1 % 8.53/2.00 | | | | (55) big_r(all_4_4, all_43_4) = all_76_0 % 8.53/2.00 | | | | (56) ~ (all_76_0 = 0) | ~ (all_76_1 = 0) % 8.53/2.00 | | | | % 8.53/2.00 | | | | GROUND_INST: instantiating (2) with 0, all_76_1, all_43_5, simplifying % 8.53/2.00 | | | | with (49), (54) gives: % 8.53/2.00 | | | | (57) all_76_1 = 0 % 8.53/2.00 | | | | % 8.53/2.00 | | | | GROUND_INST: instantiating (3) with 0, all_76_0, all_43_4, all_4_4, % 8.53/2.00 | | | | simplifying with (50), (55) gives: % 8.53/2.00 | | | | (58) all_76_0 = 0 % 8.53/2.00 | | | | % 8.53/2.00 | | | | BETA: splitting (56) gives: % 8.53/2.00 | | | | % 8.53/2.00 | | | | Case 1: % 8.53/2.00 | | | | | % 8.53/2.00 | | | | | (59) ~ (all_76_0 = 0) % 8.53/2.00 | | | | | % 8.53/2.00 | | | | | REDUCE: (58), (59) imply: % 9.30/2.00 | | | | | (60) $false % 9.30/2.00 | | | | | % 9.30/2.00 | | | | | CLOSE: (60) is inconsistent. % 9.30/2.00 | | | | | % 9.30/2.00 | | | | Case 2: % 9.30/2.00 | | | | | % 9.30/2.00 | | | | | (61) ~ (all_76_1 = 0) % 9.30/2.00 | | | | | % 9.30/2.00 | | | | | REDUCE: (57), (61) imply: % 9.30/2.00 | | | | | (62) $false % 9.30/2.00 | | | | | % 9.30/2.00 | | | | | CLOSE: (62) is inconsistent. % 9.30/2.00 | | | | | % 9.30/2.00 | | | | End of split % 9.30/2.00 | | | | % 9.30/2.00 | | | Case 2: % 9.30/2.00 | | | | % 9.30/2.00 | | | | (63) ~ (all_43_0 = 0) & big_r(all_4_4, all_4_2) = all_43_0 % 9.30/2.00 | | | | % 9.30/2.00 | | | | ALPHA: (63) implies: % 9.30/2.00 | | | | (64) ~ (all_43_0 = 0) % 9.30/2.00 | | | | (65) big_r(all_4_4, all_4_2) = all_43_0 % 9.30/2.00 | | | | % 9.30/2.00 | | | | GROUND_INST: instantiating (3) with 0, all_43_0, all_4_2, all_4_4, % 9.30/2.00 | | | | simplifying with (41), (65) gives: % 9.30/2.00 | | | | (66) all_43_0 = 0 % 9.30/2.00 | | | | % 9.30/2.00 | | | | REDUCE: (64), (66) imply: % 9.30/2.00 | | | | (67) $false % 9.30/2.00 | | | | % 9.30/2.00 | | | | CLOSE: (67) is inconsistent. % 9.30/2.00 | | | | % 9.30/2.00 | | | End of split % 9.30/2.00 | | | % 9.30/2.00 | | End of split % 9.30/2.00 | | % 9.30/2.00 | Case 2: % 9.30/2.00 | | % 9.30/2.00 | | (68) all_4_10 = 0 & big_p(all_4_9) = all_4_8 & ! [v0: $i] : ! [v1: int] % 9.30/2.00 | | : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 9.30/2.00 | | $i] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0 & % 9.30/2.00 | | $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (big_r(v1, % 9.30/2.00 | | v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] % 9.30/2.00 | | : (big_r(all_4_9, v1) = v3 & big_p(v0) = v2 & ( ~ (v3 = 0) | ~ % 9.30/2.00 | | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (big_r(v0, v1) = % 9.30/2.00 | | 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 9.30/2.00 | | int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ($i(v3) & % 9.30/2.00 | | $i(v2) & ((v6 = 0 & v5 = 0 & v4 = 0 & big_r(v3, v2) = 0 & % 9.30/2.00 | | big_r(v0, v3) = 0 & big_p(v2) = 0) | ( ~ (v7 = 0) & % 9.30/2.00 | | big_p(v1) = v7)))) & ? [v0: $i] : ! [v1: $i] : ( ~ % 9.30/2.00 | | (big_p(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 9.30/2.00 | | $i] : ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] % 9.30/2.00 | | : ($i(v3) & $i(v2) & ((v6 = 0 & v5 = 0 & v4 = 0 & big_r(v3, v2) = % 9.30/2.00 | | 0 & big_r(v0, v3) = 0 & big_p(v2) = 0) | ( ~ (v7 = 0) & % 9.30/2.00 | | big_r(v0, v1) = v7)))) & ( ~ (all_4_8 = 0) | (all_4_5 = 0 & % 9.30/2.00 | | all_4_6 = 0 & big_r(all_4_9, all_4_7) = 0 & big_p(all_4_7) = 0)) % 9.30/2.00 | | % 9.30/2.00 | | ALPHA: (68) implies: % 9.30/2.01 | | (69) big_p(all_4_9) = all_4_8 % 9.30/2.01 | | (70) ~ (all_4_8 = 0) | (all_4_5 = 0 & all_4_6 = 0 & big_r(all_4_9, % 9.30/2.01 | | all_4_7) = 0 & big_p(all_4_7) = 0) % 9.30/2.01 | | (71) ! [v0: $i] : ! [v1: $i] : ( ~ (big_r(v0, v1) = 0) | ~ $i(v1) | ~ % 9.30/2.01 | | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: int] : % 9.30/2.01 | | ? [v6: int] : ? [v7: int] : ($i(v3) & $i(v2) & ((v6 = 0 & v5 = 0 % 9.30/2.01 | | & v4 = 0 & big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) % 9.30/2.01 | | = 0) | ( ~ (v7 = 0) & big_p(v1) = v7)))) % 9.30/2.01 | | (72) ! [v0: $i] : ! [v1: $i] : ( ~ (big_r(v1, v0) = 0) | ~ $i(v1) | ~ % 9.30/2.01 | | $i(v0) | ? [v2: any] : ? [v3: any] : (big_r(all_4_9, v1) = v3 & % 9.30/2.01 | | big_p(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 9.30/2.01 | | (73) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 9.30/2.01 | | $i(v0) | ? [v2: $i] : ? [v3: $i] : (big_r(v3, v2) = 0 & % 9.30/2.01 | | big_r(v0, v3) = 0 & big_p(v2) = 0 & $i(v3) & $i(v2))) % 9.30/2.01 | | % 9.30/2.01 | | GROUND_INST: instantiating (73) with all_4_9, all_4_8, simplifying with (5), % 9.30/2.01 | | (69) gives: % 9.30/2.01 | | (74) all_4_8 = 0 | ? [v0: $i] : ? [v1: $i] : (big_r(v1, v0) = 0 & % 9.30/2.01 | | big_r(all_4_9, v1) = 0 & big_p(v0) = 0 & $i(v1) & $i(v0)) % 9.30/2.01 | | % 9.30/2.01 | | BETA: splitting (70) gives: % 9.30/2.01 | | % 9.30/2.01 | | Case 1: % 9.30/2.01 | | | % 9.30/2.01 | | | (75) ~ (all_4_8 = 0) % 9.30/2.01 | | | % 9.30/2.01 | | | BETA: splitting (74) gives: % 9.30/2.01 | | | % 9.30/2.01 | | | Case 1: % 9.30/2.01 | | | | % 9.30/2.01 | | | | (76) all_4_8 = 0 % 9.30/2.01 | | | | % 9.30/2.01 | | | | REDUCE: (75), (76) imply: % 9.30/2.01 | | | | (77) $false % 9.30/2.01 | | | | % 9.30/2.01 | | | | CLOSE: (77) is inconsistent. % 9.30/2.01 | | | | % 9.30/2.01 | | | Case 2: % 9.30/2.01 | | | | % 9.30/2.01 | | | | (78) ? [v0: $i] : ? [v1: $i] : (big_r(v1, v0) = 0 & big_r(all_4_9, % 9.30/2.01 | | | | v1) = 0 & big_p(v0) = 0 & $i(v1) & $i(v0)) % 9.30/2.01 | | | | % 9.30/2.01 | | | | DELTA: instantiating (78) with fresh symbols all_27_0, all_27_1 gives: % 9.30/2.01 | | | | (79) big_r(all_27_0, all_27_1) = 0 & big_r(all_4_9, all_27_0) = 0 & % 9.30/2.01 | | | | big_p(all_27_1) = 0 & $i(all_27_0) & $i(all_27_1) % 9.30/2.01 | | | | % 9.30/2.01 | | | | ALPHA: (79) implies: % 9.30/2.01 | | | | (80) $i(all_27_1) % 9.30/2.01 | | | | (81) $i(all_27_0) % 9.30/2.01 | | | | (82) big_p(all_27_1) = 0 % 9.30/2.01 | | | | (83) big_r(all_4_9, all_27_0) = 0 % 9.30/2.01 | | | | (84) big_r(all_27_0, all_27_1) = 0 % 9.30/2.01 | | | | % 9.30/2.01 | | | | GROUND_INST: instantiating (72) with all_27_1, all_27_0, simplifying % 9.30/2.01 | | | | with (80), (81), (84) gives: % 9.30/2.01 | | | | (85) ? [v0: any] : ? [v1: any] : (big_r(all_4_9, all_27_0) = v1 & % 9.30/2.01 | | | | big_p(all_27_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 9.30/2.01 | | | | % 9.30/2.01 | | | | DELTA: instantiating (85) with fresh symbols all_34_0, all_34_1 gives: % 9.30/2.01 | | | | (86) big_r(all_4_9, all_27_0) = all_34_0 & big_p(all_27_1) = all_34_1 % 9.30/2.01 | | | | & ( ~ (all_34_0 = 0) | ~ (all_34_1 = 0)) % 9.30/2.01 | | | | % 9.30/2.01 | | | | ALPHA: (86) implies: % 9.30/2.01 | | | | (87) big_p(all_27_1) = all_34_1 % 9.30/2.01 | | | | (88) big_r(all_4_9, all_27_0) = all_34_0 % 9.30/2.01 | | | | (89) ~ (all_34_0 = 0) | ~ (all_34_1 = 0) % 9.30/2.01 | | | | % 9.30/2.01 | | | | GROUND_INST: instantiating (2) with 0, all_34_1, all_27_1, simplifying % 9.30/2.01 | | | | with (82), (87) gives: % 9.30/2.01 | | | | (90) all_34_1 = 0 % 9.30/2.01 | | | | % 9.30/2.01 | | | | GROUND_INST: instantiating (3) with 0, all_34_0, all_27_0, all_4_9, % 9.30/2.01 | | | | simplifying with (83), (88) gives: % 9.30/2.02 | | | | (91) all_34_0 = 0 % 9.30/2.02 | | | | % 9.30/2.02 | | | | BETA: splitting (89) gives: % 9.30/2.02 | | | | % 9.30/2.02 | | | | Case 1: % 9.30/2.02 | | | | | % 9.30/2.02 | | | | | (92) ~ (all_34_0 = 0) % 9.30/2.02 | | | | | % 9.30/2.02 | | | | | REDUCE: (91), (92) imply: % 9.30/2.02 | | | | | (93) $false % 9.30/2.02 | | | | | % 9.30/2.02 | | | | | CLOSE: (93) is inconsistent. % 9.30/2.02 | | | | | % 9.30/2.02 | | | | Case 2: % 9.30/2.02 | | | | | % 9.30/2.02 | | | | | (94) ~ (all_34_1 = 0) % 9.30/2.02 | | | | | % 9.30/2.02 | | | | | REDUCE: (90), (94) imply: % 9.30/2.02 | | | | | (95) $false % 9.30/2.02 | | | | | % 9.30/2.02 | | | | | CLOSE: (95) is inconsistent. % 9.30/2.02 | | | | | % 9.30/2.02 | | | | End of split % 9.30/2.02 | | | | % 9.30/2.02 | | | End of split % 9.30/2.02 | | | % 9.30/2.02 | | Case 2: % 9.30/2.02 | | | % 9.30/2.02 | | | (96) all_4_5 = 0 & all_4_6 = 0 & big_r(all_4_9, all_4_7) = 0 & % 9.30/2.02 | | | big_p(all_4_7) = 0 % 9.30/2.02 | | | % 9.30/2.02 | | | ALPHA: (96) implies: % 9.30/2.02 | | | (97) big_p(all_4_7) = 0 % 9.30/2.02 | | | (98) big_r(all_4_9, all_4_7) = 0 % 9.30/2.02 | | | % 9.30/2.02 | | | GROUND_INST: instantiating (72) with all_4_7, all_4_9, simplifying with % 9.30/2.02 | | | (5), (6), (98) gives: % 9.30/2.02 | | | (99) ? [v0: any] : ? [v1: any] : (big_r(all_4_9, all_4_9) = v1 & % 9.30/2.02 | | | big_p(all_4_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 9.30/2.02 | | | % 9.30/2.02 | | | GROUND_INST: instantiating (71) with all_4_9, all_4_7, simplifying with % 9.30/2.02 | | | (5), (6), (98) gives: % 9.30/2.02 | | | (100) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ? [v4: % 9.30/2.02 | | | int] : ? [v5: int] : ($i(v1) & $i(v0) & ((v4 = 0 & v3 = 0 & v2 % 9.30/2.02 | | | = 0 & big_r(v1, v0) = 0 & big_r(all_4_9, v1) = 0 & % 9.30/2.02 | | | big_p(v0) = 0) | ( ~ (v5 = 0) & big_p(all_4_7) = v5))) % 9.30/2.02 | | | % 9.30/2.02 | | | DELTA: instantiating (99) with fresh symbols all_28_0, all_28_1 gives: % 9.30/2.02 | | | (101) big_r(all_4_9, all_4_9) = all_28_0 & big_p(all_4_7) = all_28_1 & % 9.30/2.02 | | | ( ~ (all_28_0 = 0) | ~ (all_28_1 = 0)) % 9.30/2.02 | | | % 9.30/2.02 | | | ALPHA: (101) implies: % 9.30/2.02 | | | (102) big_p(all_4_7) = all_28_1 % 9.30/2.02 | | | % 9.30/2.02 | | | DELTA: instantiating (100) with fresh symbols all_30_0, all_30_1, % 9.30/2.02 | | | all_30_2, all_30_3, all_30_4, all_30_5 gives: % 9.30/2.02 | | | (103) $i(all_30_4) & $i(all_30_5) & ((all_30_1 = 0 & all_30_2 = 0 & % 9.30/2.02 | | | all_30_3 = 0 & big_r(all_30_4, all_30_5) = 0 & big_r(all_4_9, % 9.30/2.02 | | | all_30_4) = 0 & big_p(all_30_5) = 0) | ( ~ (all_30_0 = 0) & % 9.30/2.02 | | | big_p(all_4_7) = all_30_0)) % 9.30/2.02 | | | % 9.30/2.02 | | | ALPHA: (103) implies: % 9.30/2.02 | | | (104) $i(all_30_5) % 9.30/2.02 | | | (105) $i(all_30_4) % 9.30/2.02 | | | (106) (all_30_1 = 0 & all_30_2 = 0 & all_30_3 = 0 & big_r(all_30_4, % 9.30/2.02 | | | all_30_5) = 0 & big_r(all_4_9, all_30_4) = 0 & % 9.30/2.02 | | | big_p(all_30_5) = 0) | ( ~ (all_30_0 = 0) & big_p(all_4_7) = % 9.30/2.02 | | | all_30_0) % 9.30/2.02 | | | % 9.30/2.02 | | | GROUND_INST: instantiating (2) with 0, all_28_1, all_4_7, simplifying with % 9.30/2.02 | | | (97), (102) gives: % 9.30/2.02 | | | (107) all_28_1 = 0 % 9.30/2.02 | | | % 9.30/2.02 | | | BETA: splitting (106) gives: % 9.30/2.02 | | | % 9.30/2.02 | | | Case 1: % 9.30/2.02 | | | | % 9.30/2.02 | | | | (108) all_30_1 = 0 & all_30_2 = 0 & all_30_3 = 0 & big_r(all_30_4, % 9.30/2.02 | | | | all_30_5) = 0 & big_r(all_4_9, all_30_4) = 0 & % 9.30/2.02 | | | | big_p(all_30_5) = 0 % 9.30/2.02 | | | | % 9.30/2.02 | | | | ALPHA: (108) implies: % 9.30/2.02 | | | | (109) big_p(all_30_5) = 0 % 9.30/2.03 | | | | (110) big_r(all_4_9, all_30_4) = 0 % 9.30/2.03 | | | | (111) big_r(all_30_4, all_30_5) = 0 % 9.30/2.03 | | | | % 9.30/2.03 | | | | GROUND_INST: instantiating (72) with all_30_5, all_30_4, simplifying % 9.30/2.03 | | | | with (104), (105), (111) gives: % 9.30/2.03 | | | | (112) ? [v0: any] : ? [v1: any] : (big_r(all_4_9, all_30_4) = v1 & % 9.30/2.03 | | | | big_p(all_30_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 9.30/2.03 | | | | % 9.30/2.03 | | | | DELTA: instantiating (112) with fresh symbols all_49_0, all_49_1 gives: % 9.30/2.03 | | | | (113) big_r(all_4_9, all_30_4) = all_49_0 & big_p(all_30_5) = % 9.30/2.03 | | | | all_49_1 & ( ~ (all_49_0 = 0) | ~ (all_49_1 = 0)) % 9.30/2.03 | | | | % 9.30/2.03 | | | | ALPHA: (113) implies: % 9.30/2.03 | | | | (114) big_p(all_30_5) = all_49_1 % 9.30/2.03 | | | | (115) big_r(all_4_9, all_30_4) = all_49_0 % 9.30/2.03 | | | | (116) ~ (all_49_0 = 0) | ~ (all_49_1 = 0) % 9.30/2.03 | | | | % 9.30/2.03 | | | | GROUND_INST: instantiating (2) with 0, all_49_1, all_30_5, simplifying % 9.30/2.03 | | | | with (109), (114) gives: % 9.30/2.03 | | | | (117) all_49_1 = 0 % 9.30/2.03 | | | | % 9.30/2.03 | | | | GROUND_INST: instantiating (3) with 0, all_49_0, all_30_4, all_4_9, % 9.30/2.03 | | | | simplifying with (110), (115) gives: % 9.30/2.03 | | | | (118) all_49_0 = 0 % 9.30/2.03 | | | | % 9.30/2.03 | | | | BETA: splitting (116) gives: % 9.30/2.03 | | | | % 9.30/2.03 | | | | Case 1: % 9.30/2.03 | | | | | % 9.30/2.03 | | | | | (119) ~ (all_49_0 = 0) % 9.30/2.03 | | | | | % 9.30/2.03 | | | | | REDUCE: (118), (119) imply: % 9.30/2.03 | | | | | (120) $false % 9.30/2.03 | | | | | % 9.30/2.03 | | | | | CLOSE: (120) is inconsistent. % 9.30/2.03 | | | | | % 9.30/2.03 | | | | Case 2: % 9.30/2.03 | | | | | % 9.30/2.03 | | | | | (121) ~ (all_49_1 = 0) % 9.30/2.03 | | | | | % 9.30/2.03 | | | | | REDUCE: (117), (121) imply: % 9.30/2.03 | | | | | (122) $false % 9.30/2.03 | | | | | % 9.30/2.03 | | | | | CLOSE: (122) is inconsistent. % 9.30/2.03 | | | | | % 9.30/2.03 | | | | End of split % 9.30/2.03 | | | | % 9.30/2.03 | | | Case 2: % 9.30/2.03 | | | | % 9.30/2.03 | | | | (123) ~ (all_30_0 = 0) & big_p(all_4_7) = all_30_0 % 9.30/2.03 | | | | % 9.30/2.03 | | | | ALPHA: (123) implies: % 9.30/2.03 | | | | (124) ~ (all_30_0 = 0) % 9.30/2.03 | | | | (125) big_p(all_4_7) = all_30_0 % 9.30/2.03 | | | | % 9.30/2.03 | | | | GROUND_INST: instantiating (2) with 0, all_30_0, all_4_7, simplifying % 9.30/2.03 | | | | with (97), (125) gives: % 9.30/2.03 | | | | (126) all_30_0 = 0 % 9.30/2.03 | | | | % 9.30/2.03 | | | | REDUCE: (124), (126) imply: % 9.30/2.03 | | | | (127) $false % 9.30/2.03 | | | | % 9.30/2.03 | | | | CLOSE: (127) is inconsistent. % 9.30/2.03 | | | | % 9.30/2.03 | | | End of split % 9.30/2.03 | | | % 9.30/2.03 | | End of split % 9.30/2.03 | | % 9.30/2.03 | End of split % 9.30/2.03 | % 9.30/2.03 End of proof % 9.30/2.03 % SZS output end Proof for theBenchmark % 9.30/2.03 % 9.30/2.03 1428ms %------------------------------------------------------------------------------