%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KRS165+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 : n022.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 05:51:30 EDT 2023 % Result : Theorem 4.16s 1.25s % Output : Proof 5.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS165+1 : TPTP v8.1.2. Released v3.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n022.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Aug 28 02:20:39 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.92/0.93 Prover 4: Preprocessing ... % 1.92/0.93 Prover 1: Preprocessing ... % 2.17/0.97 Prover 6: Preprocessing ... % 2.17/0.97 Prover 0: Preprocessing ... % 2.17/0.97 Prover 2: Preprocessing ... % 2.17/0.97 Prover 5: Preprocessing ... % 2.17/0.97 Prover 3: Preprocessing ... % 2.68/1.08 Prover 5: Proving ... % 2.68/1.08 Prover 2: Proving ... % 2.99/1.11 Prover 1: Constructing countermodel ... % 2.99/1.11 Prover 3: Constructing countermodel ... % 2.99/1.11 Prover 6: Constructing countermodel ... % 2.99/1.12 Prover 4: Constructing countermodel ... % 3.44/1.15 Prover 0: Proving ... % 3.89/1.24 Prover 6: proved (607ms) % 4.16/1.25 % 4.16/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.16/1.25 % 4.16/1.25 Prover 3: proved (623ms) % 4.16/1.25 % 4.16/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.16/1.25 % 4.16/1.25 Prover 0: stopped % 4.16/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.16/1.25 Prover 5: proved (630ms) % 4.16/1.25 % 4.16/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.16/1.25 % 4.16/1.25 Prover 2: proved (636ms) % 4.16/1.25 % 4.16/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.16/1.25 % 4.16/1.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.16/1.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.16/1.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.16/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.16/1.27 Prover 7: Preprocessing ... % 4.16/1.27 Prover 8: Preprocessing ... % 4.16/1.27 Prover 10: Preprocessing ... % 4.16/1.27 Prover 11: Preprocessing ... % 4.16/1.28 Prover 13: Preprocessing ... % 4.16/1.29 Prover 7: Warning: ignoring some quantifiers % 4.16/1.29 Prover 10: Warning: ignoring some quantifiers % 4.16/1.30 Prover 7: Constructing countermodel ... % 4.16/1.30 Prover 10: Constructing countermodel ... % 4.16/1.30 Prover 13: Warning: ignoring some quantifiers % 4.16/1.30 Prover 13: Constructing countermodel ... % 4.16/1.32 Prover 10: gave up % 4.16/1.33 Prover 7: gave up % 4.16/1.33 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 4.16/1.34 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 4.74/1.34 Prover 8: Warning: ignoring some quantifiers % 4.74/1.34 Prover 13: gave up % 4.74/1.34 Prover 16: Preprocessing ... % 4.74/1.35 Prover 19: Preprocessing ... % 4.74/1.35 Prover 8: Constructing countermodel ... % 4.74/1.36 Prover 11: Constructing countermodel ... % 4.74/1.36 Prover 16: Warning: ignoring some quantifiers % 4.74/1.37 Prover 16: Constructing countermodel ... % 5.08/1.41 Prover 1: Found proof (size 53) % 5.08/1.41 Prover 1: proved (789ms) % 5.08/1.41 Prover 11: stopped % 5.08/1.41 Prover 16: stopped % 5.08/1.41 Prover 8: stopped % 5.08/1.41 Prover 4: stopped % 5.08/1.42 Prover 19: Warning: ignoring some quantifiers % 5.08/1.43 Prover 19: Constructing countermodel ... % 5.08/1.43 Prover 19: stopped % 5.08/1.43 % 5.08/1.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.08/1.43 % 5.08/1.44 % SZS output start Proof for theBenchmark % 5.08/1.44 Assumptions after simplification: % 5.08/1.44 --------------------------------- % 5.08/1.44 % 5.08/1.44 (axiom_0) % 5.08/1.47 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ $i(v0)) & % 5.08/1.47 ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0)) % 5.08/1.47 % 5.08/1.47 (axiom_1) % 5.08/1.47 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ $i(v0) | % 5.08/1.47 xsd_integer(v0) = 0) & ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | % 5.08/1.47 ? [v1: int] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 5.08/1.47 % 5.08/1.47 (axiom_2) % 5.08/1.48 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cCar(v0) = v1) | ~ $i(v0) | ? % 5.08/1.48 [v2: int] : ( ~ (v2 = 0) & cAutomobile(v0) = v2)) & ! [v0: $i] : ( ~ % 5.08/1.48 (cCar(v0) = 0) | ~ $i(v0) | cAutomobile(v0) = 0) % 5.08/1.48 % 5.08/1.48 (the_axiom) % 5.08/1.48 ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 & % 5.08/1.48 xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = % 5.08/1.48 0)))) | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cowlNothing(v0) = % 5.08/1.48 v2 & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) | ? [v0: $i] : % 5.08/1.48 ? [v1: int] : ( ~ (v1 = 0) & cCar(v0) = v1 & cAutomobile(v0) = 0 & $i(v0)) | % 5.08/1.48 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & cCar(v0) = 0 & cAutomobile(v0) = v1 % 5.08/1.48 & $i(v0)) % 5.08/1.48 % 5.08/1.48 (function-axioms) % 5.08/1.49 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 5.08/1.49 v0 | ~ (cCar(v2) = v1) | ~ (cCar(v2) = v0)) & ! [v0: MultipleValueBool] : % 5.08/1.49 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cAutomobile(v2) = % 5.08/1.49 v1) | ~ (cAutomobile(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 5.08/1.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ % 5.08/1.49 (xsd_string(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 5.08/1.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ % 5.08/1.49 (xsd_integer(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 5.08/1.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ % 5.08/1.49 (cowlNothing(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 5.08/1.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ % 5.08/1.49 (cowlThing(v2) = v0)) % 5.08/1.49 % 5.08/1.49 Those formulas are unsatisfiable: % 5.08/1.49 --------------------------------- % 5.08/1.49 % 5.08/1.49 Begin of proof % 5.08/1.49 | % 5.08/1.49 | ALPHA: (axiom_0) implies: % 5.08/1.49 | (1) ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0)) % 5.08/1.49 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ % 5.08/1.49 | $i(v0)) % 5.08/1.49 | % 5.08/1.49 | ALPHA: (axiom_1) implies: % 5.08/1.49 | (3) ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 5.08/1.49 | (v1 = 0) & xsd_integer(v0) = v1)) % 5.08/1.49 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ % 5.08/1.49 | $i(v0) | xsd_integer(v0) = 0) % 5.08/1.49 | % 5.08/1.49 | ALPHA: (axiom_2) implies: % 5.08/1.49 | (5) ! [v0: $i] : ( ~ (cCar(v0) = 0) | ~ $i(v0) | cAutomobile(v0) = 0) % 5.08/1.50 | (6) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cCar(v0) = v1) | ~ $i(v0) | % 5.08/1.50 | ? [v2: int] : ( ~ (v2 = 0) & cAutomobile(v0) = v2)) % 5.08/1.50 | % 5.08/1.50 | ALPHA: (function-axioms) implies: % 5.08/1.50 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.08/1.50 | (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 5.08/1.50 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.08/1.50 | (v1 = v0 | ~ (cAutomobile(v2) = v1) | ~ (cAutomobile(v2) = v0)) % 5.08/1.50 | % 5.08/1.50 | BETA: splitting (the_axiom) gives: % 5.08/1.50 | % 5.08/1.50 | Case 1: % 5.08/1.50 | | % 5.08/1.50 | | (9) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 & % 5.08/1.50 | | xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & % 5.08/1.50 | | ~ (v1 = 0)))) | ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 5.08/1.50 | | (cowlNothing(v0) = v2 & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | % 5.08/1.50 | | v2 = 0)) % 5.08/1.50 | | % 5.08/1.50 | | BETA: splitting (9) gives: % 5.08/1.50 | | % 5.08/1.50 | | Case 1: % 5.08/1.50 | | | % 5.08/1.50 | | | (10) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 & % 5.08/1.50 | | | xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = % 5.08/1.50 | | | 0) & ~ (v1 = 0)))) % 5.08/1.50 | | | % 5.08/1.50 | | | DELTA: instantiating (10) with fresh symbols all_12_0, all_12_1, all_12_2 % 5.08/1.50 | | | gives: % 5.08/1.50 | | | (11) xsd_string(all_12_2) = all_12_1 & xsd_integer(all_12_2) = all_12_0 % 5.08/1.50 | | | & $i(all_12_2) & ((all_12_0 = 0 & all_12_1 = 0) | ( ~ (all_12_0 = % 5.08/1.50 | | | 0) & ~ (all_12_1 = 0))) % 5.08/1.50 | | | % 5.08/1.50 | | | ALPHA: (11) implies: % 5.08/1.50 | | | (12) $i(all_12_2) % 5.08/1.50 | | | (13) xsd_integer(all_12_2) = all_12_0 % 5.08/1.50 | | | (14) xsd_string(all_12_2) = all_12_1 % 5.08/1.51 | | | (15) (all_12_0 = 0 & all_12_1 = 0) | ( ~ (all_12_0 = 0) & ~ (all_12_1 % 5.08/1.51 | | | = 0)) % 5.08/1.51 | | | % 5.08/1.51 | | | GROUND_INST: instantiating (4) with all_12_2, all_12_1, simplifying with % 5.08/1.51 | | | (12), (14) gives: % 5.08/1.51 | | | (16) all_12_1 = 0 | xsd_integer(all_12_2) = 0 % 5.08/1.51 | | | % 5.08/1.51 | | | BETA: splitting (15) gives: % 5.08/1.51 | | | % 5.08/1.51 | | | Case 1: % 5.08/1.51 | | | | % 5.08/1.51 | | | | (17) all_12_0 = 0 & all_12_1 = 0 % 5.08/1.51 | | | | % 5.08/1.51 | | | | ALPHA: (17) implies: % 5.08/1.51 | | | | (18) all_12_1 = 0 % 5.08/1.51 | | | | (19) all_12_0 = 0 % 5.08/1.51 | | | | % 5.08/1.51 | | | | REDUCE: (14), (18) imply: % 5.08/1.51 | | | | (20) xsd_string(all_12_2) = 0 % 5.08/1.51 | | | | % 5.08/1.51 | | | | REDUCE: (13), (19) imply: % 5.08/1.51 | | | | (21) xsd_integer(all_12_2) = 0 % 5.08/1.51 | | | | % 5.08/1.51 | | | | GROUND_INST: instantiating (3) with all_12_2, simplifying with (12), % 5.08/1.51 | | | | (20) gives: % 5.08/1.51 | | | | (22) ? [v0: int] : ( ~ (v0 = 0) & xsd_integer(all_12_2) = v0) % 5.08/1.51 | | | | % 5.08/1.51 | | | | DELTA: instantiating (22) with fresh symbol all_26_0 gives: % 5.08/1.51 | | | | (23) ~ (all_26_0 = 0) & xsd_integer(all_12_2) = all_26_0 % 5.08/1.51 | | | | % 5.08/1.51 | | | | ALPHA: (23) implies: % 5.08/1.51 | | | | (24) ~ (all_26_0 = 0) % 5.08/1.51 | | | | (25) xsd_integer(all_12_2) = all_26_0 % 5.08/1.51 | | | | % 5.08/1.51 | | | | GROUND_INST: instantiating (7) with 0, all_26_0, all_12_2, simplifying % 5.08/1.51 | | | | with (21), (25) gives: % 5.08/1.51 | | | | (26) all_26_0 = 0 % 5.08/1.51 | | | | % 5.08/1.51 | | | | REDUCE: (24), (26) imply: % 5.08/1.51 | | | | (27) $false % 5.08/1.51 | | | | % 5.08/1.51 | | | | CLOSE: (27) is inconsistent. % 5.08/1.51 | | | | % 5.08/1.51 | | | Case 2: % 5.08/1.51 | | | | % 5.08/1.51 | | | | (28) ~ (all_12_0 = 0) & ~ (all_12_1 = 0) % 5.08/1.51 | | | | % 5.08/1.51 | | | | ALPHA: (28) implies: % 5.08/1.51 | | | | (29) ~ (all_12_1 = 0) % 5.08/1.51 | | | | (30) ~ (all_12_0 = 0) % 5.08/1.51 | | | | % 5.08/1.51 | | | | BETA: splitting (16) gives: % 5.08/1.51 | | | | % 5.08/1.51 | | | | Case 1: % 5.08/1.51 | | | | | % 5.08/1.51 | | | | | (31) xsd_integer(all_12_2) = 0 % 5.08/1.51 | | | | | % 5.08/1.51 | | | | | GROUND_INST: instantiating (7) with all_12_0, 0, all_12_2, simplifying % 5.08/1.51 | | | | | with (13), (31) gives: % 5.08/1.51 | | | | | (32) all_12_0 = 0 % 5.08/1.51 | | | | | % 5.08/1.51 | | | | | REDUCE: (30), (32) imply: % 5.08/1.51 | | | | | (33) $false % 5.08/1.51 | | | | | % 5.08/1.51 | | | | | CLOSE: (33) is inconsistent. % 5.08/1.51 | | | | | % 5.08/1.51 | | | | Case 2: % 5.08/1.51 | | | | | % 5.08/1.51 | | | | | (34) all_12_1 = 0 % 5.08/1.51 | | | | | % 5.08/1.51 | | | | | REDUCE: (29), (34) imply: % 5.08/1.51 | | | | | (35) $false % 5.08/1.51 | | | | | % 5.08/1.51 | | | | | CLOSE: (35) is inconsistent. % 5.08/1.51 | | | | | % 5.08/1.51 | | | | End of split % 5.08/1.51 | | | | % 5.08/1.51 | | | End of split % 5.08/1.51 | | | % 5.08/1.51 | | Case 2: % 5.08/1.51 | | | % 5.08/1.52 | | | (36) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cowlNothing(v0) = v2 % 5.08/1.52 | | | & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 5.08/1.52 | | | % 5.08/1.52 | | | DELTA: instantiating (36) with fresh symbols all_12_0, all_12_1, all_12_2 % 5.08/1.52 | | | gives: % 5.08/1.52 | | | (37) cowlNothing(all_12_2) = all_12_0 & cowlThing(all_12_2) = all_12_1 % 5.08/1.52 | | | & $i(all_12_2) & ( ~ (all_12_1 = 0) | all_12_0 = 0) % 5.08/1.52 | | | % 5.08/1.52 | | | ALPHA: (37) implies: % 5.08/1.52 | | | (38) $i(all_12_2) % 5.08/1.52 | | | (39) cowlThing(all_12_2) = all_12_1 % 5.08/1.52 | | | (40) cowlNothing(all_12_2) = all_12_0 % 5.08/1.52 | | | (41) ~ (all_12_1 = 0) | all_12_0 = 0 % 5.08/1.52 | | | % 5.08/1.52 | | | GROUND_INST: instantiating (2) with all_12_2, all_12_1, simplifying with % 5.08/1.52 | | | (38), (39) gives: % 5.08/1.52 | | | (42) all_12_1 = 0 % 5.08/1.52 | | | % 5.08/1.52 | | | BETA: splitting (41) gives: % 5.08/1.52 | | | % 5.08/1.52 | | | Case 1: % 5.08/1.52 | | | | % 5.08/1.52 | | | | (43) ~ (all_12_1 = 0) % 5.08/1.52 | | | | % 5.08/1.52 | | | | REDUCE: (42), (43) imply: % 5.08/1.52 | | | | (44) $false % 5.08/1.52 | | | | % 5.08/1.52 | | | | CLOSE: (44) is inconsistent. % 5.08/1.52 | | | | % 5.08/1.52 | | | Case 2: % 5.08/1.52 | | | | % 5.08/1.52 | | | | (45) all_12_0 = 0 % 5.08/1.52 | | | | % 5.08/1.52 | | | | REDUCE: (40), (45) imply: % 5.08/1.52 | | | | (46) cowlNothing(all_12_2) = 0 % 5.08/1.52 | | | | % 5.08/1.52 | | | | GROUND_INST: instantiating (1) with all_12_2, simplifying with (38), % 5.08/1.52 | | | | (46) gives: % 5.08/1.52 | | | | (47) $false % 5.08/1.52 | | | | % 5.08/1.52 | | | | CLOSE: (47) is inconsistent. % 5.08/1.52 | | | | % 5.08/1.52 | | | End of split % 5.08/1.52 | | | % 5.08/1.52 | | End of split % 5.08/1.52 | | % 5.08/1.52 | Case 2: % 5.08/1.52 | | % 5.08/1.52 | | (48) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & cCar(v0) = v1 & % 5.08/1.52 | | cAutomobile(v0) = 0 & $i(v0)) | ? [v0: $i] : ? [v1: int] : ( ~ % 5.08/1.52 | | (v1 = 0) & cCar(v0) = 0 & cAutomobile(v0) = v1 & $i(v0)) % 5.08/1.52 | | % 5.08/1.52 | | BETA: splitting (48) gives: % 5.08/1.52 | | % 5.08/1.52 | | Case 1: % 5.08/1.52 | | | % 5.08/1.52 | | | (49) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & cCar(v0) = v1 & % 5.08/1.52 | | | cAutomobile(v0) = 0 & $i(v0)) % 5.08/1.52 | | | % 5.08/1.52 | | | DELTA: instantiating (49) with fresh symbols all_12_0, all_12_1 gives: % 5.08/1.52 | | | (50) ~ (all_12_0 = 0) & cCar(all_12_1) = all_12_0 & % 5.08/1.52 | | | cAutomobile(all_12_1) = 0 & $i(all_12_1) % 5.08/1.52 | | | % 5.08/1.52 | | | ALPHA: (50) implies: % 5.08/1.52 | | | (51) ~ (all_12_0 = 0) % 5.08/1.52 | | | (52) $i(all_12_1) % 5.08/1.52 | | | (53) cAutomobile(all_12_1) = 0 % 5.08/1.52 | | | (54) cCar(all_12_1) = all_12_0 % 5.08/1.52 | | | % 5.08/1.52 | | | GROUND_INST: instantiating (6) with all_12_1, all_12_0, simplifying with % 5.08/1.52 | | | (52), (54) gives: % 5.08/1.52 | | | (55) all_12_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & cAutomobile(all_12_1) % 5.08/1.52 | | | = v0) % 5.08/1.52 | | | % 5.08/1.52 | | | BETA: splitting (55) gives: % 5.08/1.52 | | | % 5.08/1.52 | | | Case 1: % 5.08/1.52 | | | | % 5.08/1.52 | | | | (56) all_12_0 = 0 % 5.08/1.52 | | | | % 5.08/1.52 | | | | REDUCE: (51), (56) imply: % 5.08/1.52 | | | | (57) $false % 5.08/1.52 | | | | % 5.08/1.52 | | | | CLOSE: (57) is inconsistent. % 5.08/1.52 | | | | % 5.08/1.52 | | | Case 2: % 5.08/1.52 | | | | % 5.08/1.52 | | | | (58) ? [v0: int] : ( ~ (v0 = 0) & cAutomobile(all_12_1) = v0) % 5.08/1.52 | | | | % 5.08/1.52 | | | | DELTA: instantiating (58) with fresh symbol all_21_0 gives: % 5.08/1.52 | | | | (59) ~ (all_21_0 = 0) & cAutomobile(all_12_1) = all_21_0 % 5.08/1.52 | | | | % 5.08/1.52 | | | | ALPHA: (59) implies: % 5.08/1.53 | | | | (60) ~ (all_21_0 = 0) % 5.08/1.53 | | | | (61) cAutomobile(all_12_1) = all_21_0 % 5.08/1.53 | | | | % 5.08/1.53 | | | | GROUND_INST: instantiating (8) with 0, all_21_0, all_12_1, simplifying % 5.08/1.53 | | | | with (53), (61) gives: % 5.08/1.53 | | | | (62) all_21_0 = 0 % 5.08/1.53 | | | | % 5.08/1.53 | | | | REDUCE: (60), (62) imply: % 5.08/1.53 | | | | (63) $false % 5.08/1.53 | | | | % 5.08/1.53 | | | | CLOSE: (63) is inconsistent. % 5.08/1.53 | | | | % 5.08/1.53 | | | End of split % 5.08/1.53 | | | % 5.08/1.53 | | Case 2: % 5.08/1.53 | | | % 5.08/1.53 | | | (64) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & cCar(v0) = 0 & % 5.08/1.53 | | | cAutomobile(v0) = v1 & $i(v0)) % 5.08/1.53 | | | % 5.08/1.53 | | | DELTA: instantiating (64) with fresh symbols all_12_0, all_12_1 gives: % 5.08/1.53 | | | (65) ~ (all_12_0 = 0) & cCar(all_12_1) = 0 & cAutomobile(all_12_1) = % 5.08/1.53 | | | all_12_0 & $i(all_12_1) % 5.08/1.53 | | | % 5.08/1.53 | | | ALPHA: (65) implies: % 5.08/1.53 | | | (66) ~ (all_12_0 = 0) % 5.08/1.53 | | | (67) $i(all_12_1) % 5.08/1.53 | | | (68) cAutomobile(all_12_1) = all_12_0 % 5.08/1.53 | | | (69) cCar(all_12_1) = 0 % 5.08/1.53 | | | % 5.08/1.53 | | | GROUND_INST: instantiating (5) with all_12_1, simplifying with (67), (69) % 5.08/1.53 | | | gives: % 5.08/1.53 | | | (70) cAutomobile(all_12_1) = 0 % 5.08/1.53 | | | % 5.08/1.53 | | | GROUND_INST: instantiating (8) with all_12_0, 0, all_12_1, simplifying % 5.08/1.53 | | | with (68), (70) gives: % 5.08/1.53 | | | (71) all_12_0 = 0 % 5.08/1.53 | | | % 5.08/1.53 | | | REDUCE: (66), (71) imply: % 5.08/1.53 | | | (72) $false % 5.08/1.53 | | | % 5.08/1.53 | | | CLOSE: (72) is inconsistent. % 5.08/1.53 | | | % 5.08/1.53 | | End of split % 5.08/1.53 | | % 5.08/1.53 | End of split % 5.08/1.53 | % 5.08/1.53 End of proof % 5.08/1.53 % SZS output end Proof for theBenchmark % 5.08/1.53 % 5.08/1.53 930ms %------------------------------------------------------------------------------