%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KRS131+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 : n028.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 05:51:22 EDT 2023 % Result : Theorem 4.21s 1.50s % Output : Proof 6.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : KRS131+1 : TPTP v8.1.2. Released v3.1.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n028.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Mon Aug 28 01:58:54 EDT 2023 % 0.14/0.36 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.13/1.03 Prover 4: Preprocessing ... % 2.13/1.03 Prover 1: Preprocessing ... % 2.13/1.07 Prover 5: Preprocessing ... % 2.13/1.07 Prover 0: Preprocessing ... % 2.13/1.07 Prover 2: Preprocessing ... % 2.13/1.07 Prover 3: Preprocessing ... % 2.13/1.07 Prover 6: Preprocessing ... % 3.53/1.23 Prover 5: Proving ... % 3.53/1.24 Prover 2: Proving ... % 3.53/1.25 Prover 6: Proving ... % 3.53/1.25 Prover 3: Constructing countermodel ... % 3.53/1.26 Prover 1: Constructing countermodel ... % 3.53/1.26 Prover 4: Constructing countermodel ... % 3.53/1.28 Prover 0: Proving ... % 4.21/1.50 Prover 3: proved (847ms) % 4.21/1.50 % 4.21/1.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.21/1.50 % 4.21/1.50 Prover 0: stopped % 4.21/1.50 Prover 5: stopped % 4.21/1.51 Prover 6: stopped % 4.21/1.51 Prover 2: stopped % 5.58/1.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.58/1.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.58/1.52 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.58/1.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.58/1.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.58/1.53 Prover 7: Preprocessing ... % 5.58/1.54 Prover 8: Preprocessing ... % 5.58/1.54 Prover 10: Preprocessing ... % 5.58/1.54 Prover 11: Preprocessing ... % 5.58/1.55 Prover 13: Preprocessing ... % 5.58/1.55 Prover 7: Warning: ignoring some quantifiers % 5.58/1.55 Prover 7: Constructing countermodel ... % 5.58/1.55 Prover 1: Found proof (size 70) % 5.58/1.55 Prover 4: Found proof (size 74) % 5.58/1.55 Prover 10: Warning: ignoring some quantifiers % 5.58/1.55 Prover 1: proved (904ms) % 5.58/1.55 Prover 4: proved (901ms) % 5.58/1.56 Prover 7: stopped % 5.58/1.57 Prover 10: Constructing countermodel ... % 5.58/1.57 Prover 10: stopped % 5.58/1.57 Prover 13: Warning: ignoring some quantifiers % 5.58/1.57 Prover 11: stopped % 5.58/1.57 Prover 13: Constructing countermodel ... % 5.58/1.58 Prover 13: stopped % 6.26/1.63 Prover 8: Warning: ignoring some quantifiers % 6.26/1.63 Prover 8: Constructing countermodel ... % 6.26/1.63 Prover 8: stopped % 6.26/1.64 % 6.26/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.26/1.64 % 6.26/1.65 % SZS output start Proof for theBenchmark % 6.26/1.65 Assumptions after simplification: % 6.26/1.65 --------------------------------- % 6.26/1.65 % 6.26/1.65 (axiom_0) % 6.26/1.68 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ $i(v0)) & % 6.26/1.68 ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0)) % 6.26/1.68 % 6.26/1.68 (axiom_1) % 6.26/1.68 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ $i(v0) | % 6.26/1.68 xsd_integer(v0) = 0) & ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | % 6.26/1.68 ? [v1: int] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 6.26/1.68 % 6.26/1.68 (axiom_2) % 6.26/1.68 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cA(v0) = v1) | ~ $i(v0) | ! [v2: % 6.26/1.68 $i] : ( ~ (rq(v0, v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 6.26/1.68 cowlThing(v2) = v3))) & ! [v0: $i] : ( ~ (cA(v0) = 0) | ~ $i(v0) | ? % 6.26/1.68 [v1: $i] : (rq(v0, v1) = 0 & cowlThing(v1) = 0 & $i(v1))) % 6.26/1.68 % 6.26/1.68 (axiom_3) % 6.26/1.69 ! [v0: $i] : ( ~ (cNothing(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (rp(v0, % 6.26/1.69 v1) = 0) | ~ $i(v1))) % 6.26/1.69 % 6.26/1.69 (axiom_4) % 6.26/1.69 ! [v0: $i] : ( ~ (cNothing(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (rp(v0, v1) = % 6.26/1.69 0 & $i(v1))) % 6.26/1.69 % 6.26/1.69 (axiom_5) % 6.26/1.69 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cnotA(v0) = v1) | ~ $i(v0) | ? % 6.26/1.69 [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & cNothing(v2) = v3 & rq(v0, v2) = 0 % 6.26/1.69 & $i(v2))) & ! [v0: $i] : ( ~ (cnotA(v0) = 0) | ~ $i(v0) | ! [v1: $i] : % 6.26/1.69 ( ~ (rq(v0, v1) = 0) | ~ $i(v1) | cNothing(v1) = 0)) % 6.26/1.69 % 6.26/1.69 (the_axiom) % 6.26/1.69 ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cnotA(v0) = v1 & cA(v0) = v2 & % 6.26/1.70 $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0)))) | ? [v0: $i] : % 6.26/1.70 ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & % 6.26/1.70 $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0)))) | ? [v0: $i] : % 6.26/1.70 ? [v1: any] : ? [v2: any] : (cowlNothing(v0) = v2 & cowlThing(v0) = v1 & % 6.26/1.70 $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 6.26/1.70 % 6.26/1.70 (function-axioms) % 6.66/1.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 6.66/1.70 [v3: $i] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [v0: % 6.66/1.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 6.66/1.70 : (v1 = v0 | ~ (rq(v3, v2) = v1) | ~ (rq(v3, v2) = v0)) & ! [v0: % 6.66/1.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 6.66/1.70 ~ (cnotA(v2) = v1) | ~ (cnotA(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 6.66/1.70 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cNothing(v2) = v1) | ~ % 6.66/1.70 (cNothing(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 6.66/1.70 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2) % 6.66/1.70 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 6.66/1.70 $i] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! % 6.66/1.70 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 6.66/1.70 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0: % 6.66/1.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 6.66/1.70 ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0: % 6.66/1.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 6.66/1.70 ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 6.66/1.70 % 6.66/1.70 Those formulas are unsatisfiable: % 6.66/1.70 --------------------------------- % 6.66/1.70 % 6.66/1.70 Begin of proof % 6.66/1.71 | % 6.66/1.71 | ALPHA: (axiom_0) implies: % 6.66/1.71 | (1) ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0)) % 6.66/1.71 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ % 6.66/1.71 | $i(v0)) % 6.66/1.71 | % 6.66/1.71 | ALPHA: (axiom_1) implies: % 6.66/1.71 | (3) ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 6.66/1.71 | (v1 = 0) & xsd_integer(v0) = v1)) % 6.66/1.71 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ % 6.66/1.71 | $i(v0) | xsd_integer(v0) = 0) % 6.66/1.71 | % 6.66/1.71 | ALPHA: (axiom_2) implies: % 6.66/1.71 | (5) ! [v0: $i] : ( ~ (cA(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (rq(v0, v1) % 6.66/1.71 | = 0 & cowlThing(v1) = 0 & $i(v1))) % 6.66/1.71 | (6) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cA(v0) = v1) | ~ $i(v0) | % 6.66/1.71 | ! [v2: $i] : ( ~ (rq(v0, v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ % 6.66/1.71 | (v3 = 0) & cowlThing(v2) = v3))) % 6.66/1.71 | % 6.66/1.71 | ALPHA: (axiom_5) implies: % 6.66/1.71 | (7) ! [v0: $i] : ( ~ (cnotA(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 6.66/1.71 | (rq(v0, v1) = 0) | ~ $i(v1) | cNothing(v1) = 0)) % 6.66/1.72 | (8) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cnotA(v0) = v1) | ~ $i(v0) % 6.66/1.72 | | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & cNothing(v2) = v3 & % 6.66/1.72 | rq(v0, v2) = 0 & $i(v2))) % 6.66/1.72 | % 6.66/1.72 | ALPHA: (function-axioms) implies: % 6.66/1.72 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 6.66/1.72 | (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 6.66/1.72 | % 6.66/1.72 | BETA: splitting (the_axiom) gives: % 6.66/1.72 | % 6.66/1.72 | Case 1: % 6.66/1.72 | | % 6.66/1.72 | | (10) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cnotA(v0) = v1 & cA(v0) % 6.66/1.72 | | = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0)))) % 6.66/1.72 | | % 6.66/1.72 | | DELTA: instantiating (10) with fresh symbols all_15_0, all_15_1, all_15_2 % 6.66/1.72 | | gives: % 6.66/1.72 | | (11) cnotA(all_15_2) = all_15_1 & cA(all_15_2) = all_15_0 & $i(all_15_2) % 6.66/1.72 | | & ((all_15_0 = 0 & all_15_1 = 0) | ( ~ (all_15_0 = 0) & ~ (all_15_1 % 6.66/1.72 | | = 0))) % 6.66/1.72 | | % 6.66/1.72 | | ALPHA: (11) implies: % 6.66/1.72 | | (12) $i(all_15_2) % 6.66/1.72 | | (13) cA(all_15_2) = all_15_0 % 6.66/1.72 | | (14) cnotA(all_15_2) = all_15_1 % 6.66/1.72 | | (15) (all_15_0 = 0 & all_15_1 = 0) | ( ~ (all_15_0 = 0) & ~ (all_15_1 = % 6.66/1.72 | | 0)) % 6.66/1.72 | | % 6.66/1.72 | | GROUND_INST: instantiating (6) with all_15_2, all_15_0, simplifying with % 6.66/1.72 | | (12), (13) gives: % 6.66/1.72 | | (16) all_15_0 = 0 | ! [v0: $i] : ( ~ (rq(all_15_2, v0) = 0) | ~ $i(v0) % 6.66/1.72 | | | ? [v1: int] : ( ~ (v1 = 0) & cowlThing(v0) = v1)) % 6.66/1.72 | | % 6.66/1.72 | | GROUND_INST: instantiating (8) with all_15_2, all_15_1, simplifying with % 6.66/1.72 | | (12), (14) gives: % 6.66/1.72 | | (17) all_15_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 6.66/1.72 | | cNothing(v0) = v1 & rq(all_15_2, v0) = 0 & $i(v0)) % 6.66/1.72 | | % 6.66/1.72 | | BETA: splitting (15) gives: % 6.66/1.72 | | % 6.66/1.72 | | Case 1: % 6.66/1.72 | | | % 6.66/1.72 | | | (18) all_15_0 = 0 & all_15_1 = 0 % 6.66/1.72 | | | % 6.66/1.72 | | | ALPHA: (18) implies: % 6.66/1.72 | | | (19) all_15_1 = 0 % 6.66/1.72 | | | (20) all_15_0 = 0 % 6.66/1.72 | | | % 6.66/1.73 | | | REDUCE: (14), (19) imply: % 6.66/1.73 | | | (21) cnotA(all_15_2) = 0 % 6.66/1.73 | | | % 6.66/1.73 | | | REDUCE: (13), (20) imply: % 6.66/1.73 | | | (22) cA(all_15_2) = 0 % 6.66/1.73 | | | % 6.66/1.73 | | | GROUND_INST: instantiating (5) with all_15_2, simplifying with (12), (22) % 6.66/1.73 | | | gives: % 6.66/1.73 | | | (23) ? [v0: $i] : (rq(all_15_2, v0) = 0 & cowlThing(v0) = 0 & $i(v0)) % 6.66/1.73 | | | % 6.66/1.73 | | | GROUND_INST: instantiating (7) with all_15_2, simplifying with (12), (21) % 6.66/1.73 | | | gives: % 6.66/1.73 | | | (24) ! [v0: $i] : ( ~ (rq(all_15_2, v0) = 0) | ~ $i(v0) | % 6.66/1.73 | | | cNothing(v0) = 0) % 6.66/1.73 | | | % 6.66/1.73 | | | DELTA: instantiating (23) with fresh symbol all_30_0 gives: % 6.66/1.73 | | | (25) rq(all_15_2, all_30_0) = 0 & cowlThing(all_30_0) = 0 & % 6.66/1.73 | | | $i(all_30_0) % 6.66/1.73 | | | % 6.66/1.73 | | | ALPHA: (25) implies: % 6.66/1.73 | | | (26) $i(all_30_0) % 6.66/1.73 | | | (27) rq(all_15_2, all_30_0) = 0 % 6.66/1.73 | | | % 6.66/1.73 | | | GROUND_INST: instantiating (24) with all_30_0, simplifying with (26), (27) % 6.66/1.73 | | | gives: % 6.66/1.73 | | | (28) cNothing(all_30_0) = 0 % 6.66/1.73 | | | % 6.66/1.73 | | | GROUND_INST: instantiating (axiom_4) with all_30_0, simplifying with (26), % 6.66/1.73 | | | (28) gives: % 6.66/1.73 | | | (29) ? [v0: $i] : (rp(all_30_0, v0) = 0 & $i(v0)) % 6.66/1.73 | | | % 6.66/1.73 | | | GROUND_INST: instantiating (axiom_3) with all_30_0, simplifying with (26), % 6.66/1.73 | | | (28) gives: % 6.66/1.73 | | | (30) ! [v0: $i] : ( ~ (rp(all_30_0, v0) = 0) | ~ $i(v0)) % 6.66/1.73 | | | % 6.66/1.73 | | | DELTA: instantiating (29) with fresh symbol all_44_0 gives: % 6.66/1.73 | | | (31) rp(all_30_0, all_44_0) = 0 & $i(all_44_0) % 6.66/1.73 | | | % 6.66/1.73 | | | ALPHA: (31) implies: % 6.66/1.73 | | | (32) $i(all_44_0) % 6.66/1.73 | | | (33) rp(all_30_0, all_44_0) = 0 % 6.66/1.73 | | | % 6.66/1.73 | | | GROUND_INST: instantiating (30) with all_44_0, simplifying with (32), (33) % 6.66/1.73 | | | gives: % 6.66/1.73 | | | (34) $false % 6.66/1.73 | | | % 6.66/1.73 | | | CLOSE: (34) is inconsistent. % 6.66/1.73 | | | % 6.66/1.73 | | Case 2: % 6.66/1.73 | | | % 6.66/1.73 | | | (35) ~ (all_15_0 = 0) & ~ (all_15_1 = 0) % 6.66/1.73 | | | % 6.66/1.73 | | | ALPHA: (35) implies: % 6.66/1.73 | | | (36) ~ (all_15_1 = 0) % 6.66/1.73 | | | (37) ~ (all_15_0 = 0) % 6.66/1.73 | | | % 6.66/1.73 | | | BETA: splitting (16) gives: % 6.66/1.73 | | | % 6.66/1.73 | | | Case 1: % 6.66/1.73 | | | | % 6.66/1.73 | | | | (38) all_15_0 = 0 % 6.66/1.73 | | | | % 6.66/1.73 | | | | REDUCE: (37), (38) imply: % 6.66/1.73 | | | | (39) $false % 6.66/1.73 | | | | % 6.66/1.73 | | | | CLOSE: (39) is inconsistent. % 6.66/1.73 | | | | % 6.66/1.73 | | | Case 2: % 6.66/1.73 | | | | % 6.66/1.74 | | | | (40) ! [v0: $i] : ( ~ (rq(all_15_2, v0) = 0) | ~ $i(v0) | ? [v1: % 6.66/1.74 | | | | int] : ( ~ (v1 = 0) & cowlThing(v0) = v1)) % 6.66/1.74 | | | | % 6.66/1.74 | | | | BETA: splitting (17) gives: % 6.66/1.74 | | | | % 6.66/1.74 | | | | Case 1: % 6.66/1.74 | | | | | % 6.66/1.74 | | | | | (41) all_15_1 = 0 % 6.66/1.74 | | | | | % 6.66/1.74 | | | | | REDUCE: (36), (41) imply: % 6.66/1.74 | | | | | (42) $false % 6.66/1.74 | | | | | % 6.66/1.74 | | | | | CLOSE: (42) is inconsistent. % 6.66/1.74 | | | | | % 6.66/1.74 | | | | Case 2: % 6.66/1.74 | | | | | % 6.66/1.74 | | | | | (43) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & cNothing(v0) = v1 % 6.66/1.74 | | | | | & rq(all_15_2, v0) = 0 & $i(v0)) % 6.66/1.74 | | | | | % 6.66/1.74 | | | | | DELTA: instantiating (43) with fresh symbols all_32_0, all_32_1 gives: % 6.66/1.74 | | | | | (44) ~ (all_32_0 = 0) & cNothing(all_32_1) = all_32_0 & % 6.66/1.74 | | | | | rq(all_15_2, all_32_1) = 0 & $i(all_32_1) % 6.66/1.74 | | | | | % 6.66/1.74 | | | | | ALPHA: (44) implies: % 6.66/1.74 | | | | | (45) $i(all_32_1) % 6.66/1.74 | | | | | (46) rq(all_15_2, all_32_1) = 0 % 6.66/1.74 | | | | | % 6.66/1.74 | | | | | GROUND_INST: instantiating (40) with all_32_1, simplifying with (45), % 6.66/1.74 | | | | | (46) gives: % 6.66/1.74 | | | | | (47) ? [v0: int] : ( ~ (v0 = 0) & cowlThing(all_32_1) = v0) % 6.66/1.74 | | | | | % 6.66/1.74 | | | | | DELTA: instantiating (47) with fresh symbol all_39_0 gives: % 6.66/1.74 | | | | | (48) ~ (all_39_0 = 0) & cowlThing(all_32_1) = all_39_0 % 6.66/1.74 | | | | | % 6.66/1.74 | | | | | ALPHA: (48) implies: % 6.66/1.74 | | | | | (49) ~ (all_39_0 = 0) % 6.66/1.74 | | | | | (50) cowlThing(all_32_1) = all_39_0 % 6.66/1.74 | | | | | % 6.66/1.74 | | | | | GROUND_INST: instantiating (2) with all_32_1, all_39_0, simplifying % 6.66/1.74 | | | | | with (45), (50) gives: % 6.66/1.74 | | | | | (51) all_39_0 = 0 % 6.66/1.74 | | | | | % 6.66/1.74 | | | | | REDUCE: (49), (51) imply: % 6.66/1.74 | | | | | (52) $false % 6.66/1.74 | | | | | % 6.66/1.74 | | | | | CLOSE: (52) is inconsistent. % 6.66/1.74 | | | | | % 6.66/1.74 | | | | End of split % 6.66/1.74 | | | | % 6.66/1.74 | | | End of split % 6.66/1.74 | | | % 6.66/1.74 | | End of split % 6.66/1.74 | | % 6.66/1.74 | Case 2: % 6.66/1.74 | | % 6.66/1.74 | | (53) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 & % 6.66/1.74 | | xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) % 6.66/1.74 | | & ~ (v1 = 0)))) | ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 6.66/1.74 | | (cowlNothing(v0) = v2 & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | % 6.66/1.74 | | v2 = 0)) % 6.66/1.74 | | % 6.66/1.74 | | BETA: splitting (53) gives: % 6.66/1.74 | | % 6.66/1.74 | | Case 1: % 6.66/1.74 | | | % 6.66/1.74 | | | (54) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 & % 6.66/1.74 | | | xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = % 6.66/1.74 | | | 0) & ~ (v1 = 0)))) % 6.66/1.74 | | | % 6.66/1.74 | | | DELTA: instantiating (54) with fresh symbols all_15_0, all_15_1, all_15_2 % 6.66/1.74 | | | gives: % 6.66/1.74 | | | (55) xsd_string(all_15_2) = all_15_1 & xsd_integer(all_15_2) = all_15_0 % 6.66/1.74 | | | & $i(all_15_2) & ((all_15_0 = 0 & all_15_1 = 0) | ( ~ (all_15_0 = % 6.66/1.74 | | | 0) & ~ (all_15_1 = 0))) % 6.66/1.74 | | | % 6.66/1.74 | | | ALPHA: (55) implies: % 6.66/1.74 | | | (56) $i(all_15_2) % 6.66/1.74 | | | (57) xsd_integer(all_15_2) = all_15_0 % 6.66/1.74 | | | (58) xsd_string(all_15_2) = all_15_1 % 6.66/1.74 | | | (59) (all_15_0 = 0 & all_15_1 = 0) | ( ~ (all_15_0 = 0) & ~ (all_15_1 % 6.66/1.74 | | | = 0)) % 6.66/1.74 | | | % 6.66/1.75 | | | GROUND_INST: instantiating (4) with all_15_2, all_15_1, simplifying with % 6.66/1.75 | | | (56), (58) gives: % 6.66/1.75 | | | (60) all_15_1 = 0 | xsd_integer(all_15_2) = 0 % 6.66/1.75 | | | % 6.66/1.75 | | | BETA: splitting (59) gives: % 6.66/1.75 | | | % 6.66/1.75 | | | Case 1: % 6.66/1.75 | | | | % 6.66/1.75 | | | | (61) all_15_0 = 0 & all_15_1 = 0 % 6.66/1.75 | | | | % 6.66/1.75 | | | | ALPHA: (61) implies: % 6.66/1.75 | | | | (62) all_15_1 = 0 % 6.66/1.75 | | | | (63) all_15_0 = 0 % 6.66/1.75 | | | | % 6.66/1.75 | | | | REDUCE: (58), (62) imply: % 6.66/1.75 | | | | (64) xsd_string(all_15_2) = 0 % 6.66/1.75 | | | | % 6.66/1.75 | | | | REDUCE: (57), (63) imply: % 6.66/1.75 | | | | (65) xsd_integer(all_15_2) = 0 % 6.66/1.75 | | | | % 6.66/1.75 | | | | GROUND_INST: instantiating (3) with all_15_2, simplifying with (56), % 6.66/1.75 | | | | (64) gives: % 6.66/1.75 | | | | (66) ? [v0: int] : ( ~ (v0 = 0) & xsd_integer(all_15_2) = v0) % 6.66/1.75 | | | | % 6.66/1.75 | | | | DELTA: instantiating (66) with fresh symbol all_29_0 gives: % 6.66/1.75 | | | | (67) ~ (all_29_0 = 0) & xsd_integer(all_15_2) = all_29_0 % 6.66/1.75 | | | | % 6.66/1.75 | | | | ALPHA: (67) implies: % 6.66/1.75 | | | | (68) ~ (all_29_0 = 0) % 6.66/1.75 | | | | (69) xsd_integer(all_15_2) = all_29_0 % 6.66/1.75 | | | | % 6.66/1.75 | | | | GROUND_INST: instantiating (9) with 0, all_29_0, all_15_2, simplifying % 6.66/1.75 | | | | with (65), (69) gives: % 6.66/1.75 | | | | (70) all_29_0 = 0 % 6.66/1.75 | | | | % 6.66/1.75 | | | | REDUCE: (68), (70) imply: % 6.66/1.75 | | | | (71) $false % 6.66/1.75 | | | | % 6.66/1.75 | | | | CLOSE: (71) is inconsistent. % 6.66/1.75 | | | | % 6.66/1.75 | | | Case 2: % 6.66/1.75 | | | | % 6.66/1.75 | | | | (72) ~ (all_15_0 = 0) & ~ (all_15_1 = 0) % 6.66/1.75 | | | | % 6.66/1.75 | | | | ALPHA: (72) implies: % 6.66/1.75 | | | | (73) ~ (all_15_1 = 0) % 6.66/1.75 | | | | (74) ~ (all_15_0 = 0) % 6.66/1.75 | | | | % 6.66/1.75 | | | | BETA: splitting (60) gives: % 6.66/1.75 | | | | % 6.66/1.75 | | | | Case 1: % 6.66/1.75 | | | | | % 6.66/1.75 | | | | | (75) xsd_integer(all_15_2) = 0 % 6.66/1.75 | | | | | % 6.66/1.75 | | | | | GROUND_INST: instantiating (9) with all_15_0, 0, all_15_2, simplifying % 6.66/1.75 | | | | | with (57), (75) gives: % 6.66/1.75 | | | | | (76) all_15_0 = 0 % 6.66/1.75 | | | | | % 6.66/1.75 | | | | | REDUCE: (74), (76) imply: % 6.66/1.75 | | | | | (77) $false % 6.66/1.75 | | | | | % 6.66/1.75 | | | | | CLOSE: (77) is inconsistent. % 6.66/1.75 | | | | | % 6.66/1.75 | | | | Case 2: % 6.66/1.75 | | | | | % 6.66/1.75 | | | | | (78) all_15_1 = 0 % 6.66/1.75 | | | | | % 6.66/1.75 | | | | | REDUCE: (73), (78) imply: % 6.66/1.75 | | | | | (79) $false % 6.66/1.75 | | | | | % 6.66/1.75 | | | | | CLOSE: (79) is inconsistent. % 6.66/1.75 | | | | | % 6.66/1.75 | | | | End of split % 6.66/1.75 | | | | % 6.66/1.75 | | | End of split % 6.66/1.75 | | | % 6.66/1.75 | | Case 2: % 6.66/1.75 | | | % 6.66/1.75 | | | (80) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cowlNothing(v0) = v2 % 6.66/1.75 | | | & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 6.66/1.75 | | | % 6.66/1.75 | | | DELTA: instantiating (80) with fresh symbols all_15_0, all_15_1, all_15_2 % 6.66/1.75 | | | gives: % 6.66/1.75 | | | (81) cowlNothing(all_15_2) = all_15_0 & cowlThing(all_15_2) = all_15_1 % 6.66/1.75 | | | & $i(all_15_2) & ( ~ (all_15_1 = 0) | all_15_0 = 0) % 6.66/1.75 | | | % 6.66/1.75 | | | ALPHA: (81) implies: % 6.66/1.75 | | | (82) $i(all_15_2) % 6.66/1.75 | | | (83) cowlThing(all_15_2) = all_15_1 % 6.66/1.75 | | | (84) cowlNothing(all_15_2) = all_15_0 % 6.66/1.75 | | | (85) ~ (all_15_1 = 0) | all_15_0 = 0 % 6.66/1.75 | | | % 6.66/1.75 | | | GROUND_INST: instantiating (2) with all_15_2, all_15_1, simplifying with % 6.66/1.75 | | | (82), (83) gives: % 6.66/1.75 | | | (86) all_15_1 = 0 % 6.66/1.75 | | | % 6.66/1.75 | | | BETA: splitting (85) gives: % 6.66/1.75 | | | % 6.66/1.75 | | | Case 1: % 6.66/1.75 | | | | % 6.66/1.76 | | | | (87) ~ (all_15_1 = 0) % 6.66/1.76 | | | | % 6.66/1.76 | | | | REDUCE: (86), (87) imply: % 6.66/1.76 | | | | (88) $false % 6.66/1.76 | | | | % 6.66/1.76 | | | | CLOSE: (88) is inconsistent. % 6.66/1.76 | | | | % 6.66/1.76 | | | Case 2: % 6.66/1.76 | | | | % 6.66/1.76 | | | | (89) all_15_0 = 0 % 6.66/1.76 | | | | % 6.66/1.76 | | | | REDUCE: (84), (89) imply: % 6.66/1.76 | | | | (90) cowlNothing(all_15_2) = 0 % 6.66/1.76 | | | | % 6.66/1.76 | | | | GROUND_INST: instantiating (1) with all_15_2, simplifying with (82), % 6.66/1.76 | | | | (90) gives: % 6.66/1.76 | | | | (91) $false % 6.66/1.76 | | | | % 6.66/1.76 | | | | CLOSE: (91) is inconsistent. % 6.66/1.76 | | | | % 6.66/1.76 | | | End of split % 6.66/1.76 | | | % 6.66/1.76 | | End of split % 6.66/1.76 | | % 6.66/1.76 | End of split % 6.66/1.76 | % 6.66/1.76 End of proof % 6.66/1.76 % SZS output end Proof for theBenchmark % 6.66/1.76 % 6.66/1.76 1125ms %------------------------------------------------------------------------------