%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KRS145+1 : TPTP v8.1.2. Released v3.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n017.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 05:51:25 EDT 2023 % Result : Theorem 7.69s 1.90s % Output : Proof 9.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS145+1 : TPTP v8.1.2. Released v3.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n017.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Mon Aug 28 01:18:13 EDT 2023 % 0.14/0.34 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.53/1.18 Prover 4: Preprocessing ... % 2.53/1.18 Prover 1: Preprocessing ... % 2.71/1.22 Prover 3: Preprocessing ... % 2.71/1.22 Prover 6: Preprocessing ... % 2.71/1.23 Prover 2: Preprocessing ... % 2.71/1.23 Prover 5: Preprocessing ... % 2.71/1.23 Prover 0: Preprocessing ... % 4.56/1.50 Prover 2: Proving ... % 4.56/1.50 Prover 5: Proving ... % 4.56/1.51 Prover 3: Constructing countermodel ... % 4.56/1.53 Prover 1: Constructing countermodel ... % 4.56/1.54 Prover 6: Proving ... % 4.56/1.55 Prover 4: Constructing countermodel ... % 5.47/1.60 Prover 0: Proving ... % 7.69/1.90 Prover 3: proved (1263ms) % 7.69/1.90 % 7.69/1.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.69/1.90 % 7.69/1.91 Prover 5: stopped % 7.69/1.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.69/1.91 Prover 6: stopped % 7.69/1.91 Prover 2: stopped % 7.69/1.91 Prover 0: stopped % 7.69/1.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.69/1.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.69/1.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.69/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.69/1.96 Prover 8: Preprocessing ... % 7.69/1.97 Prover 7: Preprocessing ... % 7.69/2.01 Prover 7: Warning: ignoring some quantifiers % 7.69/2.01 Prover 11: Preprocessing ... % 7.69/2.01 Prover 10: Preprocessing ... % 7.69/2.01 Prover 7: Constructing countermodel ... % 7.69/2.01 Prover 13: Preprocessing ... % 8.81/2.06 Prover 8: Warning: ignoring some quantifiers % 8.81/2.07 Prover 13: Warning: ignoring some quantifiers % 8.81/2.07 Prover 8: Constructing countermodel ... % 8.81/2.07 Prover 13: Constructing countermodel ... % 8.81/2.09 Prover 10: Warning: ignoring some quantifiers % 8.81/2.09 Prover 4: Found proof (size 61) % 8.81/2.09 Prover 4: proved (1448ms) % 8.81/2.09 Prover 8: stopped % 8.81/2.09 Prover 10: Constructing countermodel ... % 8.81/2.09 Prover 7: stopped % 8.81/2.09 Prover 13: stopped % 8.81/2.09 Prover 1: stopped % 8.81/2.10 Prover 10: stopped % 9.24/2.12 Prover 11: Constructing countermodel ... % 9.24/2.13 Prover 11: stopped % 9.24/2.13 % 9.24/2.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.24/2.13 % 9.24/2.15 % SZS output start Proof for theBenchmark % 9.24/2.15 Assumptions after simplification: % 9.24/2.15 --------------------------------- % 9.24/2.16 % 9.24/2.16 (axiom_0) % 9.45/2.20 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ $i(v0)) & % 9.45/2.20 ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0)) % 9.45/2.20 % 9.45/2.20 (axiom_1) % 9.45/2.21 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ $i(v0) | % 9.45/2.21 xsd_integer(v0) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 9.45/2.21 (xsd_integer(v0) = v1) | ~ $i(v0) | xsd_string(v0) = 0) & ! [v0: $i] : ( ~ % 9.45/2.21 (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 9.45/2.21 xsd_integer(v0) = v1)) & ! [v0: $i] : ( ~ (xsd_integer(v0) = 0) | ~ % 9.45/2.21 $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & xsd_string(v0) = v1)) % 9.45/2.21 % 9.45/2.21 (axiom_2) % 9.45/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v3 = v1 | % 9.45/2.21 v2 = v1 | ~ (rp(v0, v3) = 0) | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | % 9.45/2.21 ~ (cc(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: % 9.45/2.21 $i] : ( ~ (cc(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 9.45/2.22 v1) & rp(v0, v2) = 0 & rp(v0, v1) = 0 & $i(v2) & $i(v1))) % 9.45/2.22 % 9.45/2.22 (the_axiom) % 9.45/2.23 ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 9.45/2.23 int] : ? [v6: int] : ? [v7: int] : ? [v8: $i] : ? [v9: any] : ? [v10: % 9.45/2.23 any] : ? [v11: $i] : ? [v12: any] : ? [v13: any] : ($i(v11) & $i(v8) & % 9.45/2.23 $i(v4) & $i(v3) & $i(v2) & $i(v0) & ((v1 = 0 & cc(v0) = 0 & ( ! [v14: $i] : % 9.45/2.23 ! [v15: $i] : (v15 = v14 | ~ (rp(v0, v15) = 0) | ~ (rp(v0, v14) = 0) % 9.45/2.23 | ~ $i(v15) | ~ $i(v14)) | (v7 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = % 9.45/2.23 v3) & ~ (v4 = v2) & ~ (v3 = v2) & rp(v0, v4) = 0 & rp(v0, v3) = % 9.45/2.23 0 & rp(v0, v2) = 0))) | (xsd_string(v8) = v9 & xsd_integer(v8) = v10 % 9.45/2.23 & ((v10 = 0 & v9 = 0) | ( ~ (v10 = 0) & ~ (v9 = 0)))) | (cowlThing(v11) % 9.45/2.23 = v12 & cowlNothing(v11) = v13 & ( ~ (v12 = 0) | v13 = 0)))) % 9.45/2.23 % 9.45/2.23 (function-axioms) % 9.45/2.23 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.45/2.23 [v3: $i] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [v0: % 9.45/2.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.45/2.23 ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0: % 9.45/2.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.45/2.23 ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0: % 9.45/2.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.45/2.23 ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0: % 9.45/2.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.45/2.23 ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0: % 9.45/2.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.45/2.23 ~ (cc(v2) = v1) | ~ (cc(v2) = v0)) % 9.45/2.23 % 9.45/2.23 Further assumptions not needed in the proof: % 9.45/2.23 -------------------------------------------- % 9.45/2.24 cc_substitution_1, cowlNothing_substitution_1, cowlThing_substitution_1, % 9.45/2.24 rp_substitution_1, rp_substitution_2, xsd_integer_substitution_1, % 9.45/2.24 xsd_string_substitution_1 % 9.45/2.24 % 9.45/2.24 Those formulas are unsatisfiable: % 9.45/2.24 --------------------------------- % 9.45/2.24 % 9.45/2.24 Begin of proof % 9.45/2.24 | % 9.45/2.24 | ALPHA: (axiom_0) implies: % 9.83/2.24 | (1) ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0)) % 9.83/2.24 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ % 9.83/2.24 | $i(v0)) % 9.83/2.24 | % 9.83/2.24 | ALPHA: (axiom_1) implies: % 9.83/2.24 | (3) ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 9.83/2.24 | (v1 = 0) & xsd_integer(v0) = v1)) % 9.83/2.24 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ % 9.83/2.24 | $i(v0) | xsd_string(v0) = 0) % 9.83/2.24 | (5) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ % 9.83/2.24 | $i(v0) | xsd_integer(v0) = 0) % 9.83/2.24 | % 9.83/2.25 | ALPHA: (axiom_2) implies: % 9.83/2.25 | (6) ! [v0: $i] : ( ~ (cc(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] % 9.83/2.25 | : ( ~ (v2 = v1) & rp(v0, v2) = 0 & rp(v0, v1) = 0 & $i(v2) & $i(v1))) % 9.83/2.25 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v3 = % 9.83/2.25 | v1 | v2 = v1 | ~ (rp(v0, v3) = 0) | ~ (rp(v0, v2) = 0) | ~ (rp(v0, % 9.83/2.25 | v1) = 0) | ~ (cc(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 9.83/2.25 | ~ $i(v0)) % 9.83/2.25 | % 9.83/2.25 | ALPHA: (function-axioms) implies: % 9.83/2.25 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.83/2.25 | (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 9.83/2.25 | % 9.83/2.25 | DELTA: instantiating (the_axiom) with fresh symbols all_6_0, all_6_1, all_6_2, % 9.83/2.25 | all_6_3, all_6_4, all_6_5, all_6_6, all_6_7, all_6_8, all_6_9, % 9.83/2.25 | all_6_10, all_6_11, all_6_12, all_6_13 gives: % 9.83/2.26 | (9) $i(all_6_2) & $i(all_6_5) & $i(all_6_9) & $i(all_6_10) & $i(all_6_11) & % 9.83/2.26 | $i(all_6_13) & ((all_6_12 = 0 & cc(all_6_13) = 0 & ( ! [v0: $i] : ! % 9.83/2.26 | [v1: $i] : (v1 = v0 | ~ (rp(all_6_13, v1) = 0) | ~ % 9.83/2.26 | (rp(all_6_13, v0) = 0) | ~ $i(v1) | ~ $i(v0)) | (all_6_6 = 0 % 9.83/2.26 | & all_6_7 = 0 & all_6_8 = 0 & ~ (all_6_9 = all_6_10) & ~ % 9.83/2.26 | (all_6_9 = all_6_11) & ~ (all_6_10 = all_6_11) & rp(all_6_13, % 9.83/2.26 | all_6_9) = 0 & rp(all_6_13, all_6_10) = 0 & rp(all_6_13, % 9.83/2.26 | all_6_11) = 0))) | (xsd_string(all_6_5) = all_6_4 & % 9.83/2.26 | xsd_integer(all_6_5) = all_6_3 & ((all_6_3 = 0 & all_6_4 = 0) | ( ~ % 9.83/2.26 | (all_6_3 = 0) & ~ (all_6_4 = 0)))) | (cowlThing(all_6_2) = % 9.83/2.26 | all_6_1 & cowlNothing(all_6_2) = all_6_0 & ( ~ (all_6_1 = 0) | % 9.83/2.26 | all_6_0 = 0))) % 9.83/2.26 | % 9.83/2.26 | ALPHA: (9) implies: % 9.83/2.26 | (10) $i(all_6_13) % 9.83/2.26 | (11) $i(all_6_11) % 9.83/2.26 | (12) $i(all_6_10) % 9.83/2.26 | (13) $i(all_6_9) % 9.83/2.26 | (14) $i(all_6_5) % 9.83/2.26 | (15) $i(all_6_2) % 9.83/2.27 | (16) (all_6_12 = 0 & cc(all_6_13) = 0 & ( ! [v0: $i] : ! [v1: $i] : (v1 = % 9.83/2.27 | v0 | ~ (rp(all_6_13, v1) = 0) | ~ (rp(all_6_13, v0) = 0) | ~ % 9.83/2.27 | $i(v1) | ~ $i(v0)) | (all_6_6 = 0 & all_6_7 = 0 & all_6_8 = 0 & % 9.83/2.27 | ~ (all_6_9 = all_6_10) & ~ (all_6_9 = all_6_11) & ~ (all_6_10 % 9.83/2.27 | = all_6_11) & rp(all_6_13, all_6_9) = 0 & rp(all_6_13, % 9.83/2.27 | all_6_10) = 0 & rp(all_6_13, all_6_11) = 0))) | % 9.83/2.27 | (xsd_string(all_6_5) = all_6_4 & xsd_integer(all_6_5) = all_6_3 & % 9.83/2.27 | ((all_6_3 = 0 & all_6_4 = 0) | ( ~ (all_6_3 = 0) & ~ (all_6_4 = % 9.83/2.27 | 0)))) | (cowlThing(all_6_2) = all_6_1 & cowlNothing(all_6_2) = % 9.83/2.27 | all_6_0 & ( ~ (all_6_1 = 0) | all_6_0 = 0)) % 9.83/2.27 | % 9.83/2.27 | BETA: splitting (16) gives: % 9.83/2.27 | % 9.83/2.27 | Case 1: % 9.83/2.27 | | % 9.83/2.27 | | (17) all_6_12 = 0 & cc(all_6_13) = 0 & ( ! [v0: $i] : ! [v1: $i] : (v1 = % 9.83/2.27 | | v0 | ~ (rp(all_6_13, v1) = 0) | ~ (rp(all_6_13, v0) = 0) | ~ % 9.83/2.27 | | $i(v1) | ~ $i(v0)) | (all_6_6 = 0 & all_6_7 = 0 & all_6_8 = 0 & % 9.83/2.27 | | ~ (all_6_9 = all_6_10) & ~ (all_6_9 = all_6_11) & ~ (all_6_10 % 9.83/2.27 | | = all_6_11) & rp(all_6_13, all_6_9) = 0 & rp(all_6_13, % 9.83/2.27 | | all_6_10) = 0 & rp(all_6_13, all_6_11) = 0)) % 9.83/2.27 | | % 9.83/2.27 | | ALPHA: (17) implies: % 9.83/2.27 | | (18) cc(all_6_13) = 0 % 9.99/2.27 | | (19) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rp(all_6_13, v1) = 0) | % 9.99/2.27 | | ~ (rp(all_6_13, v0) = 0) | ~ $i(v1) | ~ $i(v0)) | (all_6_6 = 0 & % 9.99/2.27 | | all_6_7 = 0 & all_6_8 = 0 & ~ (all_6_9 = all_6_10) & ~ (all_6_9 % 9.99/2.27 | | = all_6_11) & ~ (all_6_10 = all_6_11) & rp(all_6_13, all_6_9) = % 9.99/2.27 | | 0 & rp(all_6_13, all_6_10) = 0 & rp(all_6_13, all_6_11) = 0) % 9.99/2.27 | | % 9.99/2.28 | | GROUND_INST: instantiating (6) with all_6_13, simplifying with (10), (18) % 9.99/2.28 | | gives: % 9.99/2.28 | | (20) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & rp(all_6_13, v1) = 0 & % 9.99/2.28 | | rp(all_6_13, v0) = 0 & $i(v1) & $i(v0)) % 9.99/2.28 | | % 9.99/2.28 | | DELTA: instantiating (20) with fresh symbols all_20_0, all_20_1 gives: % 9.99/2.28 | | (21) ~ (all_20_0 = all_20_1) & rp(all_6_13, all_20_0) = 0 & rp(all_6_13, % 9.99/2.28 | | all_20_1) = 0 & $i(all_20_0) & $i(all_20_1) % 9.99/2.28 | | % 9.99/2.28 | | ALPHA: (21) implies: % 9.99/2.28 | | (22) ~ (all_20_0 = all_20_1) % 9.99/2.28 | | (23) $i(all_20_1) % 9.99/2.28 | | (24) $i(all_20_0) % 9.99/2.28 | | (25) rp(all_6_13, all_20_1) = 0 % 9.99/2.28 | | (26) rp(all_6_13, all_20_0) = 0 % 9.99/2.28 | | % 9.99/2.28 | | BETA: splitting (19) gives: % 9.99/2.28 | | % 9.99/2.28 | | Case 1: % 9.99/2.28 | | | % 9.99/2.28 | | | (27) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rp(all_6_13, v1) = 0) | % 9.99/2.28 | | | ~ (rp(all_6_13, v0) = 0) | ~ $i(v1) | ~ $i(v0)) % 9.99/2.28 | | | % 9.99/2.28 | | | GROUND_INST: instantiating (27) with all_20_1, all_20_0, simplifying with % 9.99/2.28 | | | (23), (24), (25), (26) gives: % 9.99/2.28 | | | (28) all_20_0 = all_20_1 % 9.99/2.28 | | | % 9.99/2.28 | | | REDUCE: (22), (28) imply: % 9.99/2.28 | | | (29) $false % 9.99/2.28 | | | % 9.99/2.28 | | | CLOSE: (29) is inconsistent. % 9.99/2.28 | | | % 9.99/2.28 | | Case 2: % 9.99/2.28 | | | % 9.99/2.29 | | | (30) all_6_6 = 0 & all_6_7 = 0 & all_6_8 = 0 & ~ (all_6_9 = all_6_10) % 9.99/2.29 | | | & ~ (all_6_9 = all_6_11) & ~ (all_6_10 = all_6_11) & % 9.99/2.29 | | | rp(all_6_13, all_6_9) = 0 & rp(all_6_13, all_6_10) = 0 & % 9.99/2.29 | | | rp(all_6_13, all_6_11) = 0 % 9.99/2.29 | | | % 9.99/2.29 | | | ALPHA: (30) implies: % 9.99/2.29 | | | (31) ~ (all_6_10 = all_6_11) % 9.99/2.29 | | | (32) ~ (all_6_9 = all_6_11) % 9.99/2.29 | | | (33) ~ (all_6_9 = all_6_10) % 9.99/2.29 | | | (34) rp(all_6_13, all_6_11) = 0 % 9.99/2.29 | | | (35) rp(all_6_13, all_6_10) = 0 % 9.99/2.29 | | | (36) rp(all_6_13, all_6_9) = 0 % 9.99/2.29 | | | % 9.99/2.29 | | | GROUND_INST: instantiating (7) with all_6_13, all_6_11, all_6_10, all_6_9, % 9.99/2.29 | | | simplifying with (10), (11), (12), (13), (18), (34), (35), % 9.99/2.29 | | | (36) gives: % 9.99/2.29 | | | (37) all_6_9 = all_6_10 | all_6_9 = all_6_11 | all_6_10 = all_6_11 % 9.99/2.29 | | | % 9.99/2.29 | | | BETA: splitting (37) gives: % 9.99/2.29 | | | % 9.99/2.29 | | | Case 1: % 9.99/2.29 | | | | % 9.99/2.29 | | | | (38) all_6_9 = all_6_10 % 9.99/2.29 | | | | % 9.99/2.29 | | | | REDUCE: (33), (38) imply: % 9.99/2.29 | | | | (39) $false % 9.99/2.29 | | | | % 9.99/2.29 | | | | CLOSE: (39) is inconsistent. % 9.99/2.29 | | | | % 9.99/2.29 | | | Case 2: % 9.99/2.29 | | | | % 9.99/2.29 | | | | (40) all_6_9 = all_6_11 | all_6_10 = all_6_11 % 9.99/2.29 | | | | % 9.99/2.29 | | | | BETA: splitting (40) gives: % 9.99/2.29 | | | | % 9.99/2.29 | | | | Case 1: % 9.99/2.29 | | | | | % 9.99/2.29 | | | | | (41) all_6_9 = all_6_11 % 9.99/2.29 | | | | | % 9.99/2.29 | | | | | REDUCE: (32), (41) imply: % 9.99/2.29 | | | | | (42) $false % 9.99/2.29 | | | | | % 9.99/2.29 | | | | | CLOSE: (42) is inconsistent. % 9.99/2.29 | | | | | % 9.99/2.29 | | | | Case 2: % 9.99/2.29 | | | | | % 9.99/2.29 | | | | | (43) all_6_10 = all_6_11 % 9.99/2.29 | | | | | % 9.99/2.29 | | | | | REDUCE: (31), (43) imply: % 9.99/2.29 | | | | | (44) $false % 9.99/2.29 | | | | | % 9.99/2.29 | | | | | CLOSE: (44) is inconsistent. % 9.99/2.29 | | | | | % 9.99/2.29 | | | | End of split % 9.99/2.29 | | | | % 9.99/2.29 | | | End of split % 9.99/2.29 | | | % 9.99/2.29 | | End of split % 9.99/2.29 | | % 9.99/2.29 | Case 2: % 9.99/2.29 | | % 9.99/2.29 | | (45) (xsd_string(all_6_5) = all_6_4 & xsd_integer(all_6_5) = all_6_3 & % 9.99/2.29 | | ((all_6_3 = 0 & all_6_4 = 0) | ( ~ (all_6_3 = 0) & ~ (all_6_4 = % 9.99/2.29 | | 0)))) | (cowlThing(all_6_2) = all_6_1 & cowlNothing(all_6_2) % 9.99/2.29 | | = all_6_0 & ( ~ (all_6_1 = 0) | all_6_0 = 0)) % 9.99/2.29 | | % 9.99/2.29 | | BETA: splitting (45) gives: % 9.99/2.29 | | % 9.99/2.29 | | Case 1: % 9.99/2.29 | | | % 9.99/2.30 | | | (46) xsd_string(all_6_5) = all_6_4 & xsd_integer(all_6_5) = all_6_3 & % 9.99/2.30 | | | ((all_6_3 = 0 & all_6_4 = 0) | ( ~ (all_6_3 = 0) & ~ (all_6_4 = % 9.99/2.30 | | | 0))) % 9.99/2.30 | | | % 9.99/2.30 | | | ALPHA: (46) implies: % 9.99/2.30 | | | (47) xsd_integer(all_6_5) = all_6_3 % 9.99/2.30 | | | (48) xsd_string(all_6_5) = all_6_4 % 9.99/2.30 | | | (49) (all_6_3 = 0 & all_6_4 = 0) | ( ~ (all_6_3 = 0) & ~ (all_6_4 = % 9.99/2.30 | | | 0)) % 9.99/2.30 | | | % 9.99/2.30 | | | GROUND_INST: instantiating (4) with all_6_5, all_6_3, simplifying with % 9.99/2.30 | | | (14), (47) gives: % 9.99/2.30 | | | (50) all_6_3 = 0 | xsd_string(all_6_5) = 0 % 9.99/2.30 | | | % 9.99/2.30 | | | GROUND_INST: instantiating (5) with all_6_5, all_6_4, simplifying with % 9.99/2.30 | | | (14), (48) gives: % 9.99/2.30 | | | (51) all_6_4 = 0 | xsd_integer(all_6_5) = 0 % 9.99/2.30 | | | % 9.99/2.30 | | | BETA: splitting (49) gives: % 9.99/2.30 | | | % 9.99/2.30 | | | Case 1: % 9.99/2.30 | | | | % 9.99/2.30 | | | | (52) all_6_3 = 0 & all_6_4 = 0 % 9.99/2.30 | | | | % 9.99/2.30 | | | | ALPHA: (52) implies: % 9.99/2.30 | | | | (53) all_6_4 = 0 % 9.99/2.30 | | | | (54) all_6_3 = 0 % 9.99/2.30 | | | | % 9.99/2.30 | | | | REDUCE: (48), (53) imply: % 9.99/2.30 | | | | (55) xsd_string(all_6_5) = 0 % 9.99/2.30 | | | | % 9.99/2.30 | | | | REDUCE: (47), (54) imply: % 9.99/2.30 | | | | (56) xsd_integer(all_6_5) = 0 % 9.99/2.30 | | | | % 9.99/2.30 | | | | REF_CLOSE: (3), (8), (14), (55), (56) are inconsistent by sub-proof #1. % 9.99/2.30 | | | | % 9.99/2.30 | | | Case 2: % 9.99/2.30 | | | | % 9.99/2.30 | | | | (57) ~ (all_6_3 = 0) & ~ (all_6_4 = 0) % 9.99/2.30 | | | | % 9.99/2.30 | | | | ALPHA: (57) implies: % 9.99/2.30 | | | | (58) ~ (all_6_4 = 0) % 9.99/2.30 | | | | (59) ~ (all_6_3 = 0) % 9.99/2.30 | | | | % 9.99/2.30 | | | | BETA: splitting (51) gives: % 9.99/2.30 | | | | % 9.99/2.30 | | | | Case 1: % 9.99/2.30 | | | | | % 9.99/2.30 | | | | | (60) xsd_integer(all_6_5) = 0 % 9.99/2.30 | | | | | % 9.99/2.30 | | | | | BETA: splitting (50) gives: % 9.99/2.30 | | | | | % 9.99/2.30 | | | | | Case 1: % 9.99/2.30 | | | | | | % 9.99/2.30 | | | | | | (61) xsd_string(all_6_5) = 0 % 9.99/2.30 | | | | | | % 9.99/2.30 | | | | | | REF_CLOSE: (3), (8), (14), (60), (61) are inconsistent by sub-proof % 9.99/2.30 | | | | | | #1. % 9.99/2.30 | | | | | | % 9.99/2.30 | | | | | Case 2: % 9.99/2.30 | | | | | | % 9.99/2.31 | | | | | | (62) all_6_3 = 0 % 9.99/2.31 | | | | | | % 9.99/2.31 | | | | | | REDUCE: (59), (62) imply: % 9.99/2.31 | | | | | | (63) $false % 9.99/2.31 | | | | | | % 9.99/2.31 | | | | | | CLOSE: (63) is inconsistent. % 9.99/2.31 | | | | | | % 9.99/2.31 | | | | | End of split % 9.99/2.31 | | | | | % 9.99/2.31 | | | | Case 2: % 9.99/2.31 | | | | | % 9.99/2.31 | | | | | (64) all_6_4 = 0 % 9.99/2.31 | | | | | % 9.99/2.31 | | | | | REDUCE: (58), (64) imply: % 9.99/2.31 | | | | | (65) $false % 9.99/2.31 | | | | | % 9.99/2.31 | | | | | CLOSE: (65) is inconsistent. % 9.99/2.31 | | | | | % 9.99/2.31 | | | | End of split % 9.99/2.31 | | | | % 9.99/2.31 | | | End of split % 9.99/2.31 | | | % 9.99/2.31 | | Case 2: % 9.99/2.31 | | | % 9.99/2.31 | | | (66) cowlThing(all_6_2) = all_6_1 & cowlNothing(all_6_2) = all_6_0 & ( % 9.99/2.31 | | | ~ (all_6_1 = 0) | all_6_0 = 0) % 9.99/2.31 | | | % 9.99/2.31 | | | ALPHA: (66) implies: % 9.99/2.31 | | | (67) cowlNothing(all_6_2) = all_6_0 % 9.99/2.31 | | | (68) cowlThing(all_6_2) = all_6_1 % 9.99/2.31 | | | (69) ~ (all_6_1 = 0) | all_6_0 = 0 % 9.99/2.31 | | | % 9.99/2.31 | | | GROUND_INST: instantiating (2) with all_6_2, all_6_1, simplifying with % 9.99/2.31 | | | (15), (68) gives: % 9.99/2.31 | | | (70) all_6_1 = 0 % 9.99/2.31 | | | % 9.99/2.31 | | | BETA: splitting (69) gives: % 9.99/2.31 | | | % 9.99/2.31 | | | Case 1: % 9.99/2.31 | | | | % 9.99/2.31 | | | | (71) ~ (all_6_1 = 0) % 9.99/2.31 | | | | % 9.99/2.31 | | | | REDUCE: (70), (71) imply: % 9.99/2.31 | | | | (72) $false % 9.99/2.31 | | | | % 9.99/2.31 | | | | CLOSE: (72) is inconsistent. % 9.99/2.31 | | | | % 9.99/2.31 | | | Case 2: % 9.99/2.31 | | | | % 9.99/2.31 | | | | (73) all_6_0 = 0 % 9.99/2.31 | | | | % 9.99/2.31 | | | | REDUCE: (67), (73) imply: % 9.99/2.31 | | | | (74) cowlNothing(all_6_2) = 0 % 9.99/2.31 | | | | % 9.99/2.31 | | | | GROUND_INST: instantiating (1) with all_6_2, simplifying with (15), (74) % 9.99/2.31 | | | | gives: % 9.99/2.31 | | | | (75) $false % 9.99/2.31 | | | | % 9.99/2.31 | | | | CLOSE: (75) is inconsistent. % 9.99/2.31 | | | | % 9.99/2.31 | | | End of split % 9.99/2.31 | | | % 9.99/2.31 | | End of split % 9.99/2.31 | | % 9.99/2.31 | End of split % 9.99/2.31 | % 9.99/2.31 End of proof % 9.99/2.31 % 9.99/2.31 Sub-proof #1 shows that the following formulas are inconsistent: % 9.99/2.31 ---------------------------------------------------------------- % 9.99/2.31 (1) xsd_integer(all_6_5) = 0 % 9.99/2.31 (2) $i(all_6_5) % 9.99/2.31 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.99/2.31 (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 9.99/2.31 (4) xsd_string(all_6_5) = 0 % 9.99/2.32 (5) ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 9.99/2.32 (v1 = 0) & xsd_integer(v0) = v1)) % 9.99/2.32 % 9.99/2.32 Begin of proof % 9.99/2.32 | % 9.99/2.32 | GROUND_INST: instantiating (5) with all_6_5, simplifying with (2), (4) gives: % 9.99/2.32 | (6) ? [v0: int] : ( ~ (v0 = 0) & xsd_integer(all_6_5) = v0) % 9.99/2.32 | % 9.99/2.32 | DELTA: instantiating (6) with fresh symbol all_27_0 gives: % 9.99/2.32 | (7) ~ (all_27_0 = 0) & xsd_integer(all_6_5) = all_27_0 % 9.99/2.32 | % 9.99/2.32 | ALPHA: (7) implies: % 9.99/2.32 | (8) ~ (all_27_0 = 0) % 9.99/2.32 | (9) xsd_integer(all_6_5) = all_27_0 % 9.99/2.32 | % 9.99/2.32 | GROUND_INST: instantiating (3) with 0, all_27_0, all_6_5, simplifying with % 9.99/2.32 | (1), (9) gives: % 9.99/2.32 | (10) all_27_0 = 0 % 9.99/2.32 | % 9.99/2.32 | REDUCE: (8), (10) imply: % 9.99/2.32 | (11) $false % 9.99/2.32 | % 9.99/2.32 | CLOSE: (11) is inconsistent. % 9.99/2.32 | % 9.99/2.32 End of proof % 9.99/2.32 % SZS output end Proof for theBenchmark % 9.99/2.32 % 9.99/2.32 1704ms %------------------------------------------------------------------------------