%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KRS167+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 : n005.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 05:51:31 EDT 2023 % Result : Theorem 5.96s 1.53s % Output : Proof 7.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : KRS167+1 : TPTP v8.1.2. Released v3.1.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n005.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 : Mon Aug 28 01:09:38 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/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 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 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 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.32/0.99 Prover 1: Preprocessing ... % 2.32/0.99 Prover 4: Preprocessing ... % 2.32/1.03 Prover 3: Preprocessing ... % 2.32/1.03 Prover 6: Preprocessing ... % 2.32/1.03 Prover 2: Preprocessing ... % 2.32/1.03 Prover 5: Preprocessing ... % 2.32/1.03 Prover 0: Preprocessing ... % 4.07/1.26 Prover 2: Proving ... % 4.07/1.28 Prover 5: Proving ... % 4.07/1.28 Prover 3: Constructing countermodel ... % 4.07/1.29 Prover 6: Proving ... % 4.07/1.30 Prover 4: Constructing countermodel ... % 4.07/1.30 Prover 1: Constructing countermodel ... % 4.07/1.31 Prover 0: Proving ... % 5.96/1.52 Prover 3: proved (896ms) % 5.96/1.53 % 5.96/1.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.96/1.53 % 5.96/1.53 Prover 6: stopped % 5.96/1.53 Prover 5: stopped % 5.96/1.53 Prover 0: stopped % 5.96/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.96/1.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.96/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.96/1.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.96/1.53 Prover 2: proved (910ms) % 5.96/1.53 % 5.96/1.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.96/1.53 % 5.96/1.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.41/1.58 Prover 11: Preprocessing ... % 6.41/1.58 Prover 7: Preprocessing ... % 6.41/1.58 Prover 10: Preprocessing ... % 6.41/1.58 Prover 8: Preprocessing ... % 6.41/1.60 Prover 13: Preprocessing ... % 6.41/1.60 Prover 7: Warning: ignoring some quantifiers % 6.41/1.61 Prover 7: Constructing countermodel ... % 6.41/1.61 Prover 10: Warning: ignoring some quantifiers % 6.41/1.62 Prover 1: Found proof (size 81) % 6.41/1.62 Prover 1: proved (995ms) % 6.41/1.62 Prover 10: Constructing countermodel ... % 6.41/1.62 Prover 7: stopped % 6.41/1.62 Prover 13: stopped % 6.41/1.62 Prover 10: stopped % 6.41/1.62 Prover 4: Found proof (size 80) % 6.41/1.62 Prover 4: proved (997ms) % 6.41/1.66 Prover 11: Constructing countermodel ... % 7.02/1.66 Prover 11: stopped % 7.02/1.66 Prover 8: Warning: ignoring some quantifiers % 7.02/1.67 Prover 8: Constructing countermodel ... % 7.02/1.67 Prover 8: stopped % 7.02/1.67 % 7.02/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.02/1.67 % 7.13/1.68 % SZS output start Proof for theBenchmark % 7.13/1.69 Assumptions after simplification: % 7.13/1.69 --------------------------------- % 7.13/1.69 % 7.13/1.69 (axiom_0) % 7.13/1.71 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ $i(v0)) & % 7.13/1.71 ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0)) % 7.13/1.71 % 7.13/1.71 (axiom_1) % 7.13/1.71 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ $i(v0) | % 7.13/1.71 xsd_integer(v0) = 0) & ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | % 7.13/1.71 ? [v1: int] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 7.13/1.71 % 7.13/1.71 (axiom_2) % 7.33/1.72 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cc1(v0) = v1) | ~ $i(v0) | ? [v2: % 7.33/1.72 $i] : ? [v3: $i] : ( ~ (v3 = v2) & rp(v0, v3) = 0 & rp(v0, v2) = 0 & % 7.33/1.72 $i(v3) & $i(v2)) | ! [v2: $i] : ( ~ (rp(v0, v2) = 0) | ~ $i(v2))) & ! % 7.33/1.72 [v0: $i] : ( ~ (cc1(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: $i] : (v2 = % 7.33/1.72 v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1)) % 7.33/1.72 & ? [v1: $i] : (rp(v0, v1) = 0 & $i(v1)))) % 7.33/1.72 % 7.33/1.72 (axiom_3) % 7.33/1.73 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cc2(v0) = v1) | ~ $i(v0) | ? [v2: % 7.33/1.73 $i] : ? [v3: $i] : ( ~ (v3 = v2) & rp(v0, v3) = 0 & rp(v0, v2) = 0 & % 7.33/1.73 $i(v3) & $i(v2)) | ! [v2: $i] : ( ~ (rp(v0, v2) = 0) | ~ $i(v2))) & ! % 7.33/1.73 [v0: $i] : ( ~ (cc2(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: $i] : (v2 = % 7.33/1.73 v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1)) % 7.33/1.73 & ? [v1: $i] : (rp(v0, v1) = 0 & $i(v1)))) % 7.33/1.73 % 7.33/1.73 (the_axiom) % 7.33/1.73 ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 & % 7.33/1.73 xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = % 7.33/1.73 0)))) | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cowlThing(v0) = % 7.33/1.73 v1 & cowlNothing(v0) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) | ? [v0: $i] : % 7.33/1.73 ? [v1: any] : ? [v2: any] : (cc2(v0) = v2 & cc1(v0) = v1 & $i(v0) & ((v2 = 0 % 7.33/1.73 & ~ (v1 = 0)) | (v1 = 0 & ~ (v2 = 0)))) % 7.33/1.73 % 7.33/1.73 (function-axioms) % 7.40/1.74 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 7.40/1.74 [v3: $i] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [v0: % 7.40/1.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.40/1.74 ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0: % 7.40/1.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.40/1.74 ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0: % 7.40/1.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.40/1.74 ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0: % 7.40/1.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.40/1.74 ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0: % 7.40/1.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.40/1.74 ~ (cc2(v2) = v1) | ~ (cc2(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 7.40/1.74 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cc1(v2) = v1) | ~ % 7.40/1.74 (cc1(v2) = v0)) % 7.40/1.74 % 7.40/1.74 Further assumptions not needed in the proof: % 7.40/1.74 -------------------------------------------- % 7.40/1.74 cc1_substitution_1, cc2_substitution_1, cowlNothing_substitution_1, % 7.40/1.74 cowlThing_substitution_1, rp_substitution_1, rp_substitution_2, % 7.40/1.74 xsd_integer_substitution_1, xsd_string_substitution_1 % 7.40/1.74 % 7.40/1.74 Those formulas are unsatisfiable: % 7.40/1.74 --------------------------------- % 7.40/1.74 % 7.40/1.74 Begin of proof % 7.40/1.74 | % 7.40/1.74 | ALPHA: (axiom_0) implies: % 7.40/1.74 | (1) ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0)) % 7.40/1.74 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ % 7.40/1.74 | $i(v0)) % 7.40/1.74 | % 7.40/1.74 | ALPHA: (axiom_1) implies: % 7.40/1.74 | (3) ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 7.40/1.74 | (v1 = 0) & xsd_integer(v0) = v1)) % 7.40/1.74 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ % 7.40/1.74 | $i(v0) | xsd_integer(v0) = 0) % 7.40/1.74 | % 7.40/1.74 | ALPHA: (axiom_2) implies: % 7.40/1.75 | (5) ! [v0: $i] : ( ~ (cc1(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: % 7.40/1.75 | $i] : (v2 = v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ % 7.40/1.75 | $i(v2) | ~ $i(v1)) & ? [v1: $i] : (rp(v0, v1) = 0 & $i(v1)))) % 7.40/1.75 | (6) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cc1(v0) = v1) | ~ $i(v0) | % 7.40/1.75 | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & rp(v0, v3) = 0 & rp(v0, % 7.40/1.75 | v2) = 0 & $i(v3) & $i(v2)) | ! [v2: $i] : ( ~ (rp(v0, v2) = 0) | % 7.40/1.75 | ~ $i(v2))) % 7.40/1.75 | % 7.40/1.75 | ALPHA: (axiom_3) implies: % 7.40/1.75 | (7) ! [v0: $i] : ( ~ (cc2(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: % 7.40/1.75 | $i] : (v2 = v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ % 7.40/1.75 | $i(v2) | ~ $i(v1)) & ? [v1: $i] : (rp(v0, v1) = 0 & $i(v1)))) % 7.40/1.75 | (8) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cc2(v0) = v1) | ~ $i(v0) | % 7.40/1.75 | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & rp(v0, v3) = 0 & rp(v0, % 7.40/1.75 | v2) = 0 & $i(v3) & $i(v2)) | ! [v2: $i] : ( ~ (rp(v0, v2) = 0) | % 7.40/1.75 | ~ $i(v2))) % 7.40/1.75 | % 7.40/1.75 | ALPHA: (function-axioms) implies: % 7.40/1.75 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.40/1.75 | (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 7.40/1.75 | % 7.40/1.75 | BETA: splitting (the_axiom) gives: % 7.40/1.75 | % 7.40/1.76 | Case 1: % 7.40/1.76 | | % 7.40/1.76 | | (10) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 & % 7.40/1.76 | | xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) % 7.40/1.76 | | & ~ (v1 = 0)))) % 7.40/1.76 | | % 7.40/1.76 | | DELTA: instantiating (10) with fresh symbols all_13_0, all_13_1, all_13_2 % 7.40/1.76 | | gives: % 7.40/1.76 | | (11) xsd_string(all_13_2) = all_13_1 & xsd_integer(all_13_2) = all_13_0 & % 7.40/1.76 | | $i(all_13_2) & ((all_13_0 = 0 & all_13_1 = 0) | ( ~ (all_13_0 = 0) & % 7.40/1.76 | | ~ (all_13_1 = 0))) % 7.40/1.76 | | % 7.40/1.76 | | ALPHA: (11) implies: % 7.40/1.76 | | (12) $i(all_13_2) % 7.40/1.76 | | (13) xsd_integer(all_13_2) = all_13_0 % 7.40/1.76 | | (14) xsd_string(all_13_2) = all_13_1 % 7.40/1.76 | | (15) (all_13_0 = 0 & all_13_1 = 0) | ( ~ (all_13_0 = 0) & ~ (all_13_1 = % 7.40/1.76 | | 0)) % 7.40/1.76 | | % 7.40/1.76 | | GROUND_INST: instantiating (4) with all_13_2, all_13_1, simplifying with % 7.40/1.76 | | (12), (14) gives: % 7.40/1.76 | | (16) all_13_1 = 0 | xsd_integer(all_13_2) = 0 % 7.40/1.76 | | % 7.40/1.76 | | BETA: splitting (15) gives: % 7.40/1.76 | | % 7.40/1.76 | | Case 1: % 7.40/1.76 | | | % 7.40/1.76 | | | (17) all_13_0 = 0 & all_13_1 = 0 % 7.40/1.76 | | | % 7.40/1.76 | | | ALPHA: (17) implies: % 7.40/1.76 | | | (18) all_13_1 = 0 % 7.40/1.76 | | | (19) all_13_0 = 0 % 7.40/1.76 | | | % 7.40/1.76 | | | REDUCE: (14), (18) imply: % 7.40/1.76 | | | (20) xsd_string(all_13_2) = 0 % 7.40/1.76 | | | % 7.40/1.76 | | | REDUCE: (13), (19) imply: % 7.40/1.76 | | | (21) xsd_integer(all_13_2) = 0 % 7.40/1.76 | | | % 7.40/1.76 | | | GROUND_INST: instantiating (3) with all_13_2, simplifying with (12), (20) % 7.40/1.76 | | | gives: % 7.40/1.76 | | | (22) ? [v0: int] : ( ~ (v0 = 0) & xsd_integer(all_13_2) = v0) % 7.40/1.76 | | | % 7.40/1.76 | | | DELTA: instantiating (22) with fresh symbol all_27_0 gives: % 7.40/1.76 | | | (23) ~ (all_27_0 = 0) & xsd_integer(all_13_2) = all_27_0 % 7.40/1.76 | | | % 7.40/1.76 | | | ALPHA: (23) implies: % 7.40/1.76 | | | (24) ~ (all_27_0 = 0) % 7.40/1.76 | | | (25) xsd_integer(all_13_2) = all_27_0 % 7.40/1.76 | | | % 7.40/1.76 | | | GROUND_INST: instantiating (9) with 0, all_27_0, all_13_2, simplifying % 7.40/1.76 | | | with (21), (25) gives: % 7.40/1.76 | | | (26) all_27_0 = 0 % 7.40/1.76 | | | % 7.40/1.76 | | | REDUCE: (24), (26) imply: % 7.40/1.76 | | | (27) $false % 7.40/1.77 | | | % 7.40/1.77 | | | CLOSE: (27) is inconsistent. % 7.40/1.77 | | | % 7.40/1.77 | | Case 2: % 7.40/1.77 | | | % 7.40/1.77 | | | (28) ~ (all_13_0 = 0) & ~ (all_13_1 = 0) % 7.40/1.77 | | | % 7.40/1.77 | | | ALPHA: (28) implies: % 7.40/1.77 | | | (29) ~ (all_13_1 = 0) % 7.40/1.77 | | | (30) ~ (all_13_0 = 0) % 7.40/1.77 | | | % 7.40/1.77 | | | BETA: splitting (16) gives: % 7.40/1.77 | | | % 7.40/1.77 | | | Case 1: % 7.40/1.77 | | | | % 7.40/1.77 | | | | (31) xsd_integer(all_13_2) = 0 % 7.40/1.77 | | | | % 7.40/1.77 | | | | GROUND_INST: instantiating (9) with all_13_0, 0, all_13_2, simplifying % 7.40/1.77 | | | | with (13), (31) gives: % 7.40/1.77 | | | | (32) all_13_0 = 0 % 7.40/1.77 | | | | % 7.40/1.77 | | | | REDUCE: (30), (32) imply: % 7.40/1.77 | | | | (33) $false % 7.40/1.77 | | | | % 7.40/1.77 | | | | CLOSE: (33) is inconsistent. % 7.40/1.77 | | | | % 7.40/1.77 | | | Case 2: % 7.40/1.77 | | | | % 7.40/1.77 | | | | (34) all_13_1 = 0 % 7.40/1.77 | | | | % 7.40/1.77 | | | | REDUCE: (29), (34) imply: % 7.40/1.77 | | | | (35) $false % 7.40/1.77 | | | | % 7.40/1.77 | | | | CLOSE: (35) is inconsistent. % 7.40/1.77 | | | | % 7.40/1.77 | | | End of split % 7.40/1.77 | | | % 7.40/1.77 | | End of split % 7.40/1.77 | | % 7.40/1.77 | Case 2: % 7.40/1.77 | | % 7.40/1.77 | | (36) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cowlThing(v0) = v1 & % 7.40/1.77 | | cowlNothing(v0) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) | ? [v0: % 7.40/1.77 | | $i] : ? [v1: any] : ? [v2: any] : (cc2(v0) = v2 & cc1(v0) = v1 & % 7.40/1.77 | | $i(v0) & ((v2 = 0 & ~ (v1 = 0)) | (v1 = 0 & ~ (v2 = 0)))) % 7.40/1.77 | | % 7.40/1.77 | | BETA: splitting (36) gives: % 7.40/1.77 | | % 7.40/1.77 | | Case 1: % 7.40/1.77 | | | % 7.40/1.77 | | | (37) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cowlThing(v0) = v1 & % 7.40/1.77 | | | cowlNothing(v0) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 7.40/1.77 | | | % 7.40/1.77 | | | DELTA: instantiating (37) with fresh symbols all_13_0, all_13_1, all_13_2 % 7.40/1.77 | | | gives: % 7.40/1.77 | | | (38) cowlThing(all_13_2) = all_13_1 & cowlNothing(all_13_2) = all_13_0 % 7.40/1.77 | | | & $i(all_13_2) & ( ~ (all_13_1 = 0) | all_13_0 = 0) % 7.40/1.77 | | | % 7.40/1.77 | | | ALPHA: (38) implies: % 7.40/1.77 | | | (39) $i(all_13_2) % 7.40/1.77 | | | (40) cowlNothing(all_13_2) = all_13_0 % 7.40/1.77 | | | (41) cowlThing(all_13_2) = all_13_1 % 7.40/1.77 | | | (42) ~ (all_13_1 = 0) | all_13_0 = 0 % 7.40/1.77 | | | % 7.40/1.77 | | | GROUND_INST: instantiating (2) with all_13_2, all_13_1, simplifying with % 7.40/1.77 | | | (39), (41) gives: % 7.40/1.77 | | | (43) all_13_1 = 0 % 7.40/1.77 | | | % 7.40/1.77 | | | BETA: splitting (42) gives: % 7.40/1.77 | | | % 7.40/1.77 | | | Case 1: % 7.40/1.77 | | | | % 7.40/1.77 | | | | (44) ~ (all_13_1 = 0) % 7.40/1.77 | | | | % 7.40/1.77 | | | | REDUCE: (43), (44) imply: % 7.40/1.77 | | | | (45) $false % 7.40/1.77 | | | | % 7.40/1.77 | | | | CLOSE: (45) is inconsistent. % 7.40/1.77 | | | | % 7.40/1.77 | | | Case 2: % 7.40/1.77 | | | | % 7.40/1.77 | | | | (46) all_13_0 = 0 % 7.40/1.77 | | | | % 7.40/1.77 | | | | REDUCE: (40), (46) imply: % 7.40/1.77 | | | | (47) cowlNothing(all_13_2) = 0 % 7.40/1.77 | | | | % 7.40/1.77 | | | | GROUND_INST: instantiating (1) with all_13_2, simplifying with (39), % 7.40/1.77 | | | | (47) gives: % 7.40/1.77 | | | | (48) $false % 7.40/1.77 | | | | % 7.40/1.77 | | | | CLOSE: (48) is inconsistent. % 7.40/1.77 | | | | % 7.40/1.77 | | | End of split % 7.40/1.77 | | | % 7.40/1.77 | | Case 2: % 7.40/1.77 | | | % 7.40/1.77 | | | (49) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cc2(v0) = v2 & % 7.40/1.77 | | | cc1(v0) = v1 & $i(v0) & ((v2 = 0 & ~ (v1 = 0)) | (v1 = 0 & ~ % 7.40/1.77 | | | (v2 = 0)))) % 7.40/1.77 | | | % 7.40/1.77 | | | DELTA: instantiating (49) with fresh symbols all_13_0, all_13_1, all_13_2 % 7.40/1.77 | | | gives: % 7.40/1.78 | | | (50) cc2(all_13_2) = all_13_0 & cc1(all_13_2) = all_13_1 & $i(all_13_2) % 7.40/1.78 | | | & ((all_13_0 = 0 & ~ (all_13_1 = 0)) | (all_13_1 = 0 & ~ % 7.40/1.78 | | | (all_13_0 = 0))) % 7.40/1.78 | | | % 7.40/1.78 | | | ALPHA: (50) implies: % 7.40/1.78 | | | (51) $i(all_13_2) % 7.40/1.78 | | | (52) cc1(all_13_2) = all_13_1 % 7.40/1.78 | | | (53) cc2(all_13_2) = all_13_0 % 7.40/1.78 | | | (54) (all_13_0 = 0 & ~ (all_13_1 = 0)) | (all_13_1 = 0 & ~ (all_13_0 % 7.40/1.78 | | | = 0)) % 7.40/1.78 | | | % 7.40/1.78 | | | GROUND_INST: instantiating (6) with all_13_2, all_13_1, simplifying with % 7.40/1.78 | | | (51), (52) gives: % 7.40/1.78 | | | (55) all_13_1 = 0 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 7.40/1.78 | | | rp(all_13_2, v1) = 0 & rp(all_13_2, v0) = 0 & $i(v1) & $i(v0)) | % 7.40/1.78 | | | ! [v0: $i] : ( ~ (rp(all_13_2, v0) = 0) | ~ $i(v0)) % 7.40/1.78 | | | % 7.40/1.78 | | | GROUND_INST: instantiating (8) with all_13_2, all_13_0, simplifying with % 7.40/1.78 | | | (51), (53) gives: % 7.40/1.78 | | | (56) all_13_0 = 0 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 7.40/1.78 | | | rp(all_13_2, v1) = 0 & rp(all_13_2, v0) = 0 & $i(v1) & $i(v0)) | % 7.40/1.78 | | | ! [v0: $i] : ( ~ (rp(all_13_2, v0) = 0) | ~ $i(v0)) % 7.40/1.78 | | | % 7.40/1.78 | | | BETA: splitting (54) gives: % 7.40/1.78 | | | % 7.40/1.78 | | | Case 1: % 7.40/1.78 | | | | % 7.40/1.78 | | | | (57) all_13_0 = 0 & ~ (all_13_1 = 0) % 7.40/1.78 | | | | % 7.40/1.78 | | | | ALPHA: (57) implies: % 7.40/1.78 | | | | (58) all_13_0 = 0 % 7.40/1.78 | | | | (59) ~ (all_13_1 = 0) % 7.40/1.78 | | | | % 7.40/1.78 | | | | REDUCE: (53), (58) imply: % 7.40/1.78 | | | | (60) cc2(all_13_2) = 0 % 7.40/1.78 | | | | % 7.40/1.78 | | | | GROUND_INST: instantiating (7) with all_13_2, simplifying with (51), % 7.40/1.78 | | | | (60) gives: % 7.40/1.78 | | | | (61) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rp(all_13_2, v1) = 0) % 7.40/1.78 | | | | | ~ (rp(all_13_2, v0) = 0) | ~ $i(v1) | ~ $i(v0)) & ? [v0: % 7.40/1.78 | | | | $i] : (rp(all_13_2, v0) = 0 & $i(v0)) % 7.40/1.78 | | | | % 7.40/1.78 | | | | ALPHA: (61) implies: % 7.40/1.78 | | | | (62) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rp(all_13_2, v1) = 0) % 7.40/1.78 | | | | | ~ (rp(all_13_2, v0) = 0) | ~ $i(v1) | ~ $i(v0)) % 7.40/1.78 | | | | (63) ? [v0: $i] : (rp(all_13_2, v0) = 0 & $i(v0)) % 7.40/1.78 | | | | % 7.40/1.78 | | | | DELTA: instantiating (63) with fresh symbol all_28_0 gives: % 7.40/1.78 | | | | (64) rp(all_13_2, all_28_0) = 0 & $i(all_28_0) % 7.40/1.78 | | | | % 7.40/1.78 | | | | ALPHA: (64) implies: % 7.40/1.78 | | | | (65) $i(all_28_0) % 7.40/1.78 | | | | (66) rp(all_13_2, all_28_0) = 0 % 7.40/1.78 | | | | % 7.40/1.78 | | | | BETA: splitting (55) gives: % 7.40/1.78 | | | | % 7.40/1.78 | | | | Case 1: % 7.40/1.78 | | | | | % 7.40/1.78 | | | | | (67) all_13_1 = 0 % 7.40/1.79 | | | | | % 7.40/1.79 | | | | | REDUCE: (59), (67) imply: % 7.40/1.79 | | | | | (68) $false % 7.40/1.79 | | | | | % 7.40/1.79 | | | | | CLOSE: (68) is inconsistent. % 7.40/1.79 | | | | | % 7.40/1.79 | | | | Case 2: % 7.40/1.79 | | | | | % 7.40/1.79 | | | | | (69) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & rp(all_13_2, v1) = % 7.40/1.79 | | | | | 0 & rp(all_13_2, v0) = 0 & $i(v1) & $i(v0)) | ! [v0: $i] : % 7.40/1.79 | | | | | ( ~ (rp(all_13_2, v0) = 0) | ~ $i(v0)) % 7.40/1.79 | | | | | % 7.40/1.79 | | | | | BETA: splitting (69) gives: % 7.40/1.79 | | | | | % 7.40/1.79 | | | | | Case 1: % 7.40/1.79 | | | | | | % 7.40/1.79 | | | | | | (70) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & rp(all_13_2, v1) % 7.40/1.79 | | | | | | = 0 & rp(all_13_2, v0) = 0 & $i(v1) & $i(v0)) % 7.40/1.79 | | | | | | % 7.40/1.79 | | | | | | DELTA: instantiating (70) with fresh symbols all_43_0, all_43_1 % 7.40/1.79 | | | | | | gives: % 7.40/1.79 | | | | | | (71) ~ (all_43_0 = all_43_1) & rp(all_13_2, all_43_0) = 0 & % 7.40/1.79 | | | | | | rp(all_13_2, all_43_1) = 0 & $i(all_43_0) & $i(all_43_1) % 7.40/1.79 | | | | | | % 7.40/1.79 | | | | | | ALPHA: (71) implies: % 7.40/1.79 | | | | | | (72) ~ (all_43_0 = all_43_1) % 7.40/1.79 | | | | | | (73) $i(all_43_1) % 7.40/1.79 | | | | | | (74) $i(all_43_0) % 7.40/1.79 | | | | | | (75) rp(all_13_2, all_43_1) = 0 % 7.40/1.79 | | | | | | (76) rp(all_13_2, all_43_0) = 0 % 7.40/1.79 | | | | | | % 7.40/1.79 | | | | | | GROUND_INST: instantiating (62) with all_28_0, all_43_0, simplifying % 7.40/1.79 | | | | | | with (65), (66), (74), (76) gives: % 7.40/1.79 | | | | | | (77) all_43_0 = all_28_0 % 7.40/1.79 | | | | | | % 7.40/1.79 | | | | | | GROUND_INST: instantiating (62) with all_43_1, all_43_0, simplifying % 7.40/1.79 | | | | | | with (73), (74), (75), (76) gives: % 7.40/1.79 | | | | | | (78) all_43_0 = all_43_1 % 7.40/1.79 | | | | | | % 7.40/1.79 | | | | | | COMBINE_EQS: (77), (78) imply: % 7.40/1.79 | | | | | | (79) all_43_1 = all_28_0 % 7.40/1.79 | | | | | | % 7.40/1.79 | | | | | | REDUCE: (72), (77), (79) imply: % 7.40/1.79 | | | | | | (80) $false % 7.40/1.79 | | | | | | % 7.40/1.79 | | | | | | CLOSE: (80) is inconsistent. % 7.40/1.79 | | | | | | % 7.40/1.79 | | | | | Case 2: % 7.40/1.79 | | | | | | % 7.40/1.79 | | | | | | (81) ! [v0: $i] : ( ~ (rp(all_13_2, v0) = 0) | ~ $i(v0)) % 7.40/1.79 | | | | | | % 7.40/1.79 | | | | | | GROUND_INST: instantiating (81) with all_28_0, simplifying with % 7.40/1.79 | | | | | | (65), (66) gives: % 7.40/1.79 | | | | | | (82) $false % 7.40/1.79 | | | | | | % 7.40/1.79 | | | | | | CLOSE: (82) is inconsistent. % 7.40/1.79 | | | | | | % 7.40/1.79 | | | | | End of split % 7.40/1.79 | | | | | % 7.40/1.79 | | | | End of split % 7.40/1.79 | | | | % 7.40/1.79 | | | Case 2: % 7.40/1.79 | | | | % 7.40/1.79 | | | | (83) all_13_1 = 0 & ~ (all_13_0 = 0) % 7.40/1.79 | | | | % 7.40/1.79 | | | | ALPHA: (83) implies: % 7.40/1.79 | | | | (84) all_13_1 = 0 % 7.40/1.79 | | | | (85) ~ (all_13_0 = 0) % 7.40/1.79 | | | | % 7.40/1.79 | | | | REDUCE: (52), (84) imply: % 7.40/1.79 | | | | (86) cc1(all_13_2) = 0 % 7.40/1.79 | | | | % 7.40/1.79 | | | | GROUND_INST: instantiating (5) with all_13_2, simplifying with (51), % 7.40/1.79 | | | | (86) gives: % 7.40/1.79 | | | | (87) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rp(all_13_2, v1) = 0) % 7.40/1.79 | | | | | ~ (rp(all_13_2, v0) = 0) | ~ $i(v1) | ~ $i(v0)) & ? [v0: % 7.40/1.79 | | | | $i] : (rp(all_13_2, v0) = 0 & $i(v0)) % 7.40/1.79 | | | | % 7.40/1.79 | | | | ALPHA: (87) implies: % 7.40/1.80 | | | | (88) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rp(all_13_2, v1) = 0) % 7.40/1.80 | | | | | ~ (rp(all_13_2, v0) = 0) | ~ $i(v1) | ~ $i(v0)) % 7.40/1.80 | | | | (89) ? [v0: $i] : (rp(all_13_2, v0) = 0 & $i(v0)) % 7.40/1.80 | | | | % 7.40/1.80 | | | | DELTA: instantiating (89) with fresh symbol all_28_0 gives: % 7.40/1.80 | | | | (90) rp(all_13_2, all_28_0) = 0 & $i(all_28_0) % 7.40/1.80 | | | | % 7.40/1.80 | | | | ALPHA: (90) implies: % 7.40/1.80 | | | | (91) $i(all_28_0) % 7.40/1.80 | | | | (92) rp(all_13_2, all_28_0) = 0 % 7.40/1.80 | | | | % 7.40/1.80 | | | | BETA: splitting (56) gives: % 7.40/1.80 | | | | % 7.40/1.80 | | | | Case 1: % 7.40/1.80 | | | | | % 7.40/1.80 | | | | | (93) all_13_0 = 0 % 7.40/1.80 | | | | | % 7.40/1.80 | | | | | REDUCE: (85), (93) imply: % 7.40/1.80 | | | | | (94) $false % 7.40/1.80 | | | | | % 7.40/1.80 | | | | | CLOSE: (94) is inconsistent. % 7.40/1.80 | | | | | % 7.40/1.80 | | | | Case 2: % 7.40/1.80 | | | | | % 7.40/1.80 | | | | | (95) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & rp(all_13_2, v1) = % 7.40/1.80 | | | | | 0 & rp(all_13_2, v0) = 0 & $i(v1) & $i(v0)) | ! [v0: $i] : % 7.40/1.80 | | | | | ( ~ (rp(all_13_2, v0) = 0) | ~ $i(v0)) % 7.40/1.80 | | | | | % 7.40/1.80 | | | | | BETA: splitting (95) gives: % 7.40/1.80 | | | | | % 7.40/1.80 | | | | | Case 1: % 7.40/1.80 | | | | | | % 7.40/1.80 | | | | | | (96) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & rp(all_13_2, v1) % 7.40/1.80 | | | | | | = 0 & rp(all_13_2, v0) = 0 & $i(v1) & $i(v0)) % 7.40/1.80 | | | | | | % 7.40/1.80 | | | | | | DELTA: instantiating (96) with fresh symbols all_43_0, all_43_1 % 7.40/1.80 | | | | | | gives: % 7.40/1.80 | | | | | | (97) ~ (all_43_0 = all_43_1) & rp(all_13_2, all_43_0) = 0 & % 7.40/1.80 | | | | | | rp(all_13_2, all_43_1) = 0 & $i(all_43_0) & $i(all_43_1) % 7.40/1.80 | | | | | | % 7.40/1.80 | | | | | | ALPHA: (97) implies: % 7.40/1.80 | | | | | | (98) ~ (all_43_0 = all_43_1) % 7.40/1.80 | | | | | | (99) $i(all_43_1) % 7.40/1.80 | | | | | | (100) $i(all_43_0) % 7.40/1.80 | | | | | | (101) rp(all_13_2, all_43_1) = 0 % 7.40/1.80 | | | | | | (102) rp(all_13_2, all_43_0) = 0 % 7.40/1.80 | | | | | | % 7.40/1.80 | | | | | | GROUND_INST: instantiating (88) with all_28_0, all_43_0, simplifying % 7.40/1.80 | | | | | | with (91), (92), (100), (102) gives: % 7.40/1.80 | | | | | | (103) all_43_0 = all_28_0 % 7.40/1.80 | | | | | | % 7.40/1.80 | | | | | | GROUND_INST: instantiating (88) with all_43_1, all_43_0, simplifying % 7.40/1.80 | | | | | | with (99), (100), (101), (102) gives: % 7.40/1.80 | | | | | | (104) all_43_0 = all_43_1 % 7.40/1.80 | | | | | | % 7.40/1.80 | | | | | | COMBINE_EQS: (103), (104) imply: % 7.40/1.80 | | | | | | (105) all_43_1 = all_28_0 % 7.40/1.80 | | | | | | % 7.40/1.80 | | | | | | REDUCE: (98), (103), (105) imply: % 7.40/1.80 | | | | | | (106) $false % 7.40/1.80 | | | | | | % 7.40/1.80 | | | | | | CLOSE: (106) is inconsistent. % 7.40/1.80 | | | | | | % 7.40/1.80 | | | | | Case 2: % 7.40/1.80 | | | | | | % 7.40/1.80 | | | | | | (107) ! [v0: $i] : ( ~ (rp(all_13_2, v0) = 0) | ~ $i(v0)) % 7.40/1.80 | | | | | | % 7.40/1.80 | | | | | | GROUND_INST: instantiating (107) with all_28_0, simplifying with % 7.40/1.80 | | | | | | (91), (92) gives: % 7.40/1.80 | | | | | | (108) $false % 7.40/1.80 | | | | | | % 7.40/1.80 | | | | | | CLOSE: (108) is inconsistent. % 7.40/1.80 | | | | | | % 7.40/1.80 | | | | | End of split % 7.40/1.80 | | | | | % 7.40/1.80 | | | | End of split % 7.40/1.80 | | | | % 7.40/1.80 | | | End of split % 7.40/1.80 | | | % 7.40/1.80 | | End of split % 7.40/1.80 | | % 7.40/1.80 | End of split % 7.40/1.80 | % 7.40/1.80 End of proof % 7.40/1.81 % SZS output end Proof for theBenchmark % 7.40/1.81 % 7.40/1.81 1202ms %------------------------------------------------------------------------------