%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KRS138+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 : n018.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 05:51:23 EDT 2023 % Result : Theorem 5.74s 1.60s % Output : Proof 8.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS138+1 : TPTP v8.1.2. Released v3.1.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n018.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % 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 01:41:31 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.30/1.02 Prover 4: Preprocessing ... % 2.30/1.03 Prover 1: Preprocessing ... % 2.30/1.06 Prover 5: Preprocessing ... % 2.30/1.06 Prover 6: Preprocessing ... % 2.30/1.06 Prover 0: Preprocessing ... % 2.30/1.06 Prover 3: Preprocessing ... % 2.30/1.06 Prover 2: Preprocessing ... % 3.69/1.27 Prover 5: Proving ... % 3.69/1.28 Prover 2: Proving ... % 4.23/1.31 Prover 3: Constructing countermodel ... % 4.23/1.31 Prover 6: Constructing countermodel ... % 4.23/1.32 Prover 1: Constructing countermodel ... % 4.23/1.32 Prover 4: Constructing countermodel ... % 4.23/1.36 Prover 0: Proving ... % 5.74/1.59 Prover 2: proved (964ms) % 5.74/1.60 % 5.74/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.74/1.60 % 5.74/1.60 Prover 6: stopped % 5.74/1.60 Prover 0: stopped % 5.74/1.61 Prover 5: stopped % 6.34/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.34/1.61 Prover 3: stopped % 6.34/1.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.34/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.34/1.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.34/1.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.34/1.66 Prover 8: Preprocessing ... % 6.34/1.67 Prover 7: Preprocessing ... % 6.34/1.67 Prover 13: Preprocessing ... % 6.34/1.68 Prover 11: Preprocessing ... % 6.34/1.68 Prover 10: Preprocessing ... % 6.88/1.71 Prover 10: Warning: ignoring some quantifiers % 6.88/1.71 Prover 10: Constructing countermodel ... % 6.88/1.74 Prover 7: Warning: ignoring some quantifiers % 6.88/1.74 Prover 13: Warning: ignoring some quantifiers % 6.88/1.74 Prover 13: Constructing countermodel ... % 6.88/1.74 Prover 4: Found proof (size 103) % 6.88/1.74 Prover 4: proved (1095ms) % 6.88/1.74 Prover 1: stopped % 6.88/1.74 Prover 13: stopped % 6.88/1.74 Prover 11: stopped % 6.88/1.74 Prover 7: Constructing countermodel ... % 6.88/1.74 Prover 10: stopped % 6.88/1.74 Prover 7: stopped % 6.88/1.76 Prover 8: Warning: ignoring some quantifiers % 6.88/1.77 Prover 8: Constructing countermodel ... % 7.46/1.78 Prover 8: stopped % 7.46/1.78 % 7.46/1.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.46/1.78 % 7.51/1.80 % SZS output start Proof for theBenchmark % 7.51/1.80 Assumptions after simplification: % 7.51/1.80 --------------------------------- % 7.51/1.80 % 7.51/1.80 (axiom_0) % 7.68/1.83 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ $i(v0)) & % 7.68/1.83 ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0)) % 7.68/1.83 % 7.68/1.83 (axiom_1) % 7.68/1.83 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ $i(v0) | % 7.68/1.83 xsd_integer(v0) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 7.68/1.83 (xsd_integer(v0) = v1) | ~ $i(v0) | xsd_string(v0) = 0) & ! [v0: $i] : ( ~ % 7.68/1.83 (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 7.68/1.83 xsd_integer(v0) = v1)) & ! [v0: $i] : ( ~ (xsd_integer(v0) = 0) | ~ % 7.68/1.83 $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & xsd_string(v0) = v1)) % 7.68/1.83 % 7.68/1.83 (axiom_2) % 7.68/1.83 $i(ia) & $i(ib) & ! [v0: $i] : (v0 = ia | v0 = ib | ~ (cA(v0) = 0) | ~ % 7.68/1.83 $i(v0)) & ! [v0: int] : (v0 = 0 | ~ (cA(ia) = v0)) & ! [v0: int] : (v0 = % 7.68/1.83 0 | ~ (cA(ib) = v0)) % 7.68/1.83 % 7.68/1.83 (axiom_3) % 7.68/1.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (requalityOnA(v2, v0) % 7.68/1.84 = 0) | ~ (requalityOnA(v1, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 7.68/1.84 % 7.68/1.84 (axiom_4) % 7.68/1.84 ! [v0: $i] : ! [v1: $i] : ( ~ (requalityOnA(v0, v1) = 0) | ~ $i(v1) | ~ % 7.68/1.84 $i(v0) | cA(v1) = 0) % 7.68/1.84 % 7.68/1.84 (axiom_5) % 7.68/1.84 cowlThing(ia) = 0 & $i(ia) % 7.68/1.84 % 7.68/1.84 (axiom_6) % 7.68/1.84 requalityOnA(ia, ia) = 0 & $i(ia) % 7.68/1.84 % 7.68/1.84 (axiom_7) % 7.68/1.84 cowlThing(ib) = 0 & $i(ib) % 7.68/1.84 % 7.68/1.84 (axiom_8) % 7.68/1.84 requalityOnA(ib, ib) = 0 & $i(ib) % 7.68/1.84 % 7.68/1.84 (axiom_9) % 7.68/1.84 cowlThing(ic) = 0 & $i(ic) % 7.68/1.84 % 7.68/1.84 (the_axiom) % 7.68/1.85 $i(ic) & $i(ia) & $i(ib) & ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 7.68/1.85 [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: % 7.68/1.85 $i] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: any] : ? [v13: % 7.68/1.85 any] : ? [v14: $i] : ? [v15: any] : ? [v16: any] : (requalityOnA(ia, ia) % 7.68/1.85 = v1 & cowlThing(ic) = v3 & cowlThing(ia) = v0 & cowlThing(ib) = v2 & % 7.68/1.85 $i(v14) & $i(v11) & $i(v9) & $i(v8) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | ~ % 7.68/1.85 (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v10 = 0 & ~ (v8 = ic) & ~ (v8 = % 7.68/1.85 ia) & ~ (v8 = ib) & requalityOnA(v8, v9) = 0) | (v6 = 0 & ~ (v7 = 0) % 7.68/1.85 & requalityOnA(v5, v4) = v7 & requalityOnA(v4, v5) = 0) | % 7.68/1.85 (xsd_string(v11) = v12 & xsd_integer(v11) = v13 & ((v13 = 0 & v12 = 0) | ( % 7.68/1.85 ~ (v13 = 0) & ~ (v12 = 0)))) | (cowlThing(v14) = v15 & % 7.68/1.85 cowlNothing(v14) = v16 & ( ~ (v15 = 0) | v16 = 0)))) % 7.68/1.85 % 7.68/1.85 (function-axioms) % 7.68/1.85 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 7.68/1.85 [v3: $i] : (v1 = v0 | ~ (requalityOnA(v3, v2) = v1) | ~ (requalityOnA(v3, % 7.68/1.85 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 7.68/1.85 ! [v2: $i] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & % 7.68/1.85 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 7.68/1.86 v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0: % 7.68/1.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.68/1.86 ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0: % 7.68/1.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.68/1.86 ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0: % 7.68/1.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.68/1.86 ~ (cA(v2) = v1) | ~ (cA(v2) = v0)) % 7.68/1.86 % 7.68/1.86 Further assumptions not needed in the proof: % 7.68/1.86 -------------------------------------------- % 7.68/1.86 cA_substitution_1, cowlNothing_substitution_1, cowlThing_substitution_1, % 7.68/1.86 requalityOnA_substitution_1, requalityOnA_substitution_2, % 7.68/1.86 xsd_integer_substitution_1, xsd_string_substitution_1 % 7.68/1.86 % 7.68/1.86 Those formulas are unsatisfiable: % 7.68/1.86 --------------------------------- % 7.68/1.86 % 7.68/1.86 Begin of proof % 7.68/1.86 | % 7.68/1.86 | ALPHA: (axiom_0) implies: % 7.68/1.86 | (1) ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0)) % 7.68/1.86 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ % 7.68/1.86 | $i(v0)) % 7.68/1.86 | % 7.68/1.86 | ALPHA: (axiom_1) implies: % 7.68/1.86 | (3) ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 7.68/1.86 | (v1 = 0) & xsd_integer(v0) = v1)) % 7.68/1.86 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ % 7.68/1.86 | $i(v0) | xsd_string(v0) = 0) % 7.68/1.86 | (5) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ % 7.68/1.86 | $i(v0) | xsd_integer(v0) = 0) % 7.68/1.86 | % 7.68/1.86 | ALPHA: (axiom_2) implies: % 7.68/1.87 | (6) ! [v0: $i] : (v0 = ia | v0 = ib | ~ (cA(v0) = 0) | ~ $i(v0)) % 7.68/1.87 | % 7.68/1.87 | ALPHA: (axiom_5) implies: % 7.68/1.87 | (7) cowlThing(ia) = 0 % 7.68/1.87 | % 7.68/1.87 | ALPHA: (axiom_6) implies: % 7.68/1.87 | (8) requalityOnA(ia, ia) = 0 % 7.68/1.87 | % 7.68/1.87 | ALPHA: (axiom_7) implies: % 7.68/1.87 | (9) cowlThing(ib) = 0 % 7.68/1.87 | % 7.68/1.87 | ALPHA: (axiom_8) implies: % 7.68/1.87 | (10) requalityOnA(ib, ib) = 0 % 7.68/1.87 | % 7.68/1.87 | ALPHA: (axiom_9) implies: % 7.68/1.87 | (11) cowlThing(ic) = 0 % 7.68/1.87 | % 7.68/1.87 | ALPHA: (the_axiom) implies: % 7.68/1.87 | (12) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 7.68/1.87 | $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: $i] : ? % 7.68/1.87 | [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: any] : ? [v13: % 7.68/1.87 | any] : ? [v14: $i] : ? [v15: any] : ? [v16: any] : % 7.68/1.87 | (requalityOnA(ia, ia) = v1 & cowlThing(ic) = v3 & cowlThing(ia) = v0 & % 7.68/1.87 | cowlThing(ib) = v2 & $i(v14) & $i(v11) & $i(v9) & $i(v8) & $i(v5) & % 7.68/1.87 | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | % 7.68/1.87 | (v10 = 0 & ~ (v8 = ic) & ~ (v8 = ia) & ~ (v8 = ib) & % 7.68/1.87 | requalityOnA(v8, v9) = 0) | (v6 = 0 & ~ (v7 = 0) & % 7.68/1.87 | requalityOnA(v5, v4) = v7 & requalityOnA(v4, v5) = 0) | % 7.68/1.87 | (xsd_string(v11) = v12 & xsd_integer(v11) = v13 & ((v13 = 0 & v12 % 7.68/1.87 | = 0) | ( ~ (v13 = 0) & ~ (v12 = 0)))) | (cowlThing(v14) = % 7.68/1.87 | v15 & cowlNothing(v14) = v16 & ( ~ (v15 = 0) | v16 = 0)))) % 7.68/1.87 | % 7.68/1.87 | ALPHA: (function-axioms) implies: % 7.68/1.87 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 7.68/1.87 | : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 7.68/1.88 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 7.68/1.88 | : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 7.68/1.88 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 7.68/1.88 | : ! [v3: $i] : (v1 = v0 | ~ (requalityOnA(v3, v2) = v1) | ~ % 7.68/1.88 | (requalityOnA(v3, v2) = v0)) % 7.68/1.88 | % 7.68/1.88 | DELTA: instantiating (12) with fresh symbols all_9_0, all_9_1, all_9_2, % 7.68/1.88 | all_9_3, all_9_4, all_9_5, all_9_6, all_9_7, all_9_8, all_9_9, % 7.68/1.88 | all_9_10, all_9_11, all_9_12, all_9_13, all_9_14, all_9_15, all_9_16 % 7.68/1.88 | gives: % 7.68/1.88 | (16) requalityOnA(ia, ia) = all_9_15 & cowlThing(ic) = all_9_13 & % 7.68/1.88 | cowlThing(ia) = all_9_16 & cowlThing(ib) = all_9_14 & $i(all_9_2) & % 7.68/1.88 | $i(all_9_5) & $i(all_9_7) & $i(all_9_8) & $i(all_9_11) & $i(all_9_12) % 7.68/1.88 | & ( ~ (all_9_13 = 0) | ~ (all_9_14 = 0) | ~ (all_9_15 = 0) | ~ % 7.68/1.88 | (all_9_16 = 0) | (all_9_6 = 0 & ~ (all_9_8 = ic) & ~ (all_9_8 = % 7.68/1.88 | ia) & ~ (all_9_8 = ib) & requalityOnA(all_9_8, all_9_7) = 0) | % 7.68/1.88 | (all_9_10 = 0 & ~ (all_9_9 = 0) & requalityOnA(all_9_11, all_9_12) % 7.68/1.88 | = all_9_9 & requalityOnA(all_9_12, all_9_11) = 0) | % 7.68/1.88 | (xsd_string(all_9_5) = all_9_4 & xsd_integer(all_9_5) = all_9_3 & % 7.68/1.88 | ((all_9_3 = 0 & all_9_4 = 0) | ( ~ (all_9_3 = 0) & ~ (all_9_4 = % 7.68/1.88 | 0)))) | (cowlThing(all_9_2) = all_9_1 & cowlNothing(all_9_2) % 7.68/1.88 | = all_9_0 & ( ~ (all_9_1 = 0) | all_9_0 = 0))) % 7.68/1.88 | % 7.68/1.88 | ALPHA: (16) implies: % 7.68/1.88 | (17) $i(all_9_12) % 7.68/1.88 | (18) $i(all_9_11) % 7.68/1.88 | (19) $i(all_9_8) % 7.68/1.88 | (20) $i(all_9_7) % 7.68/1.88 | (21) $i(all_9_5) % 7.68/1.88 | (22) $i(all_9_2) % 7.68/1.88 | (23) cowlThing(ib) = all_9_14 % 7.68/1.88 | (24) cowlThing(ia) = all_9_16 % 7.68/1.88 | (25) cowlThing(ic) = all_9_13 % 7.68/1.88 | (26) requalityOnA(ia, ia) = all_9_15 % 7.68/1.89 | (27) ~ (all_9_13 = 0) | ~ (all_9_14 = 0) | ~ (all_9_15 = 0) | ~ % 7.68/1.89 | (all_9_16 = 0) | (all_9_6 = 0 & ~ (all_9_8 = ic) & ~ (all_9_8 = ia) % 7.68/1.89 | & ~ (all_9_8 = ib) & requalityOnA(all_9_8, all_9_7) = 0) | % 7.68/1.89 | (all_9_10 = 0 & ~ (all_9_9 = 0) & requalityOnA(all_9_11, all_9_12) = % 7.68/1.89 | all_9_9 & requalityOnA(all_9_12, all_9_11) = 0) | % 7.68/1.89 | (xsd_string(all_9_5) = all_9_4 & xsd_integer(all_9_5) = all_9_3 & % 7.68/1.89 | ((all_9_3 = 0 & all_9_4 = 0) | ( ~ (all_9_3 = 0) & ~ (all_9_4 = % 7.68/1.89 | 0)))) | (cowlThing(all_9_2) = all_9_1 & cowlNothing(all_9_2) = % 7.68/1.89 | all_9_0 & ( ~ (all_9_1 = 0) | all_9_0 = 0)) % 7.68/1.89 | % 7.68/1.89 | GROUND_INST: instantiating (13) with 0, all_9_14, ib, simplifying with (9), % 7.68/1.89 | (23) gives: % 7.68/1.89 | (28) all_9_14 = 0 % 7.68/1.89 | % 7.68/1.89 | GROUND_INST: instantiating (13) with 0, all_9_16, ia, simplifying with (7), % 7.68/1.89 | (24) gives: % 7.68/1.89 | (29) all_9_16 = 0 % 7.68/1.89 | % 7.68/1.89 | GROUND_INST: instantiating (13) with 0, all_9_13, ic, simplifying with (11), % 7.68/1.89 | (25) gives: % 7.68/1.89 | (30) all_9_13 = 0 % 7.68/1.89 | % 7.68/1.89 | GROUND_INST: instantiating (15) with 0, all_9_15, ia, ia, simplifying with % 7.68/1.89 | (8), (26) gives: % 7.68/1.89 | (31) all_9_15 = 0 % 7.68/1.89 | % 7.68/1.89 | BETA: splitting (27) gives: % 7.68/1.89 | % 7.68/1.89 | Case 1: % 7.68/1.89 | | % 7.68/1.89 | | (32) ~ (all_9_13 = 0) % 7.68/1.89 | | % 7.68/1.89 | | REDUCE: (30), (32) imply: % 7.68/1.89 | | (33) $false % 7.68/1.89 | | % 7.68/1.89 | | CLOSE: (33) is inconsistent. % 7.68/1.89 | | % 7.68/1.89 | Case 2: % 7.68/1.89 | | % 7.68/1.89 | | (34) ~ (all_9_14 = 0) | ~ (all_9_15 = 0) | ~ (all_9_16 = 0) | (all_9_6 % 7.68/1.89 | | = 0 & ~ (all_9_8 = ic) & ~ (all_9_8 = ia) & ~ (all_9_8 = ib) & % 7.68/1.89 | | requalityOnA(all_9_8, all_9_7) = 0) | (all_9_10 = 0 & ~ (all_9_9 % 7.68/1.89 | | = 0) & requalityOnA(all_9_11, all_9_12) = all_9_9 & % 7.68/1.89 | | requalityOnA(all_9_12, all_9_11) = 0) | (xsd_string(all_9_5) = % 7.68/1.89 | | all_9_4 & xsd_integer(all_9_5) = all_9_3 & ((all_9_3 = 0 & all_9_4 % 7.68/1.89 | | = 0) | ( ~ (all_9_3 = 0) & ~ (all_9_4 = 0)))) | % 7.68/1.89 | | (cowlThing(all_9_2) = all_9_1 & cowlNothing(all_9_2) = all_9_0 & ( ~ % 7.68/1.89 | | (all_9_1 = 0) | all_9_0 = 0)) % 7.68/1.89 | | % 7.68/1.89 | | BETA: splitting (34) gives: % 7.68/1.89 | | % 7.68/1.89 | | Case 1: % 7.68/1.89 | | | % 7.68/1.89 | | | (35) ~ (all_9_14 = 0) % 7.68/1.89 | | | % 7.68/1.89 | | | REDUCE: (28), (35) imply: % 7.68/1.89 | | | (36) $false % 7.68/1.89 | | | % 7.68/1.89 | | | CLOSE: (36) is inconsistent. % 7.68/1.89 | | | % 7.68/1.89 | | Case 2: % 7.68/1.89 | | | % 7.68/1.90 | | | (37) ~ (all_9_15 = 0) | ~ (all_9_16 = 0) | (all_9_6 = 0 & ~ (all_9_8 % 7.68/1.90 | | | = ic) & ~ (all_9_8 = ia) & ~ (all_9_8 = ib) & % 7.68/1.90 | | | requalityOnA(all_9_8, all_9_7) = 0) | (all_9_10 = 0 & ~ % 7.68/1.90 | | | (all_9_9 = 0) & requalityOnA(all_9_11, all_9_12) = all_9_9 & % 7.68/1.90 | | | requalityOnA(all_9_12, all_9_11) = 0) | (xsd_string(all_9_5) = % 7.68/1.90 | | | all_9_4 & xsd_integer(all_9_5) = all_9_3 & ((all_9_3 = 0 & % 7.68/1.90 | | | all_9_4 = 0) | ( ~ (all_9_3 = 0) & ~ (all_9_4 = 0)))) | % 7.68/1.90 | | | (cowlThing(all_9_2) = all_9_1 & cowlNothing(all_9_2) = all_9_0 & ( % 7.68/1.90 | | | ~ (all_9_1 = 0) | all_9_0 = 0)) % 7.68/1.90 | | | % 7.68/1.90 | | | BETA: splitting (37) gives: % 7.68/1.90 | | | % 7.68/1.90 | | | Case 1: % 7.68/1.90 | | | | % 7.68/1.90 | | | | (38) ~ (all_9_15 = 0) % 7.68/1.90 | | | | % 7.68/1.90 | | | | REDUCE: (31), (38) imply: % 7.68/1.90 | | | | (39) $false % 7.68/1.90 | | | | % 7.68/1.90 | | | | CLOSE: (39) is inconsistent. % 7.68/1.90 | | | | % 7.68/1.90 | | | Case 2: % 7.68/1.90 | | | | % 7.68/1.90 | | | | (40) ~ (all_9_16 = 0) | (all_9_6 = 0 & ~ (all_9_8 = ic) & ~ % 7.68/1.90 | | | | (all_9_8 = ia) & ~ (all_9_8 = ib) & requalityOnA(all_9_8, % 7.68/1.90 | | | | all_9_7) = 0) | (all_9_10 = 0 & ~ (all_9_9 = 0) & % 7.68/1.90 | | | | requalityOnA(all_9_11, all_9_12) = all_9_9 & % 7.68/1.90 | | | | requalityOnA(all_9_12, all_9_11) = 0) | (xsd_string(all_9_5) = % 7.68/1.90 | | | | all_9_4 & xsd_integer(all_9_5) = all_9_3 & ((all_9_3 = 0 & % 7.68/1.90 | | | | all_9_4 = 0) | ( ~ (all_9_3 = 0) & ~ (all_9_4 = 0)))) | % 7.68/1.90 | | | | (cowlThing(all_9_2) = all_9_1 & cowlNothing(all_9_2) = all_9_0 & % 7.68/1.90 | | | | ( ~ (all_9_1 = 0) | all_9_0 = 0)) % 7.68/1.90 | | | | % 7.68/1.90 | | | | BETA: splitting (40) gives: % 7.68/1.90 | | | | % 7.68/1.90 | | | | Case 1: % 7.68/1.90 | | | | | % 7.68/1.90 | | | | | (41) ~ (all_9_16 = 0) % 7.68/1.90 | | | | | % 7.68/1.90 | | | | | REDUCE: (29), (41) imply: % 7.68/1.90 | | | | | (42) $false % 7.68/1.90 | | | | | % 7.68/1.90 | | | | | CLOSE: (42) is inconsistent. % 7.68/1.90 | | | | | % 7.68/1.90 | | | | Case 2: % 7.68/1.90 | | | | | % 7.68/1.90 | | | | | (43) (all_9_6 = 0 & ~ (all_9_8 = ic) & ~ (all_9_8 = ia) & ~ % 7.68/1.90 | | | | | (all_9_8 = ib) & requalityOnA(all_9_8, all_9_7) = 0) | % 7.68/1.90 | | | | | (all_9_10 = 0 & ~ (all_9_9 = 0) & requalityOnA(all_9_11, % 7.68/1.90 | | | | | all_9_12) = all_9_9 & requalityOnA(all_9_12, all_9_11) = % 7.68/1.90 | | | | | 0) | (xsd_string(all_9_5) = all_9_4 & xsd_integer(all_9_5) = % 7.68/1.90 | | | | | all_9_3 & ((all_9_3 = 0 & all_9_4 = 0) | ( ~ (all_9_3 = 0) & % 7.68/1.90 | | | | | ~ (all_9_4 = 0)))) | (cowlThing(all_9_2) = all_9_1 & % 7.68/1.90 | | | | | cowlNothing(all_9_2) = all_9_0 & ( ~ (all_9_1 = 0) | all_9_0 % 7.68/1.90 | | | | | = 0)) % 7.68/1.90 | | | | | % 7.68/1.90 | | | | | BETA: splitting (43) gives: % 7.68/1.90 | | | | | % 7.68/1.90 | | | | | Case 1: % 7.68/1.90 | | | | | | % 7.68/1.90 | | | | | | (44) (all_9_6 = 0 & ~ (all_9_8 = ic) & ~ (all_9_8 = ia) & ~ % 7.68/1.90 | | | | | | (all_9_8 = ib) & requalityOnA(all_9_8, all_9_7) = 0) | % 7.68/1.90 | | | | | | (all_9_10 = 0 & ~ (all_9_9 = 0) & requalityOnA(all_9_11, % 7.68/1.90 | | | | | | all_9_12) = all_9_9 & requalityOnA(all_9_12, all_9_11) = % 7.68/1.90 | | | | | | 0) % 7.68/1.90 | | | | | | % 7.68/1.90 | | | | | | BETA: splitting (44) gives: % 7.68/1.90 | | | | | | % 7.68/1.90 | | | | | | Case 1: % 7.68/1.90 | | | | | | | % 7.68/1.90 | | | | | | | (45) all_9_6 = 0 & ~ (all_9_8 = ic) & ~ (all_9_8 = ia) & ~ % 7.68/1.90 | | | | | | | (all_9_8 = ib) & requalityOnA(all_9_8, all_9_7) = 0 % 7.68/1.90 | | | | | | | % 7.68/1.90 | | | | | | | ALPHA: (45) implies: % 7.68/1.90 | | | | | | | (46) ~ (all_9_8 = ib) % 7.68/1.90 | | | | | | | (47) ~ (all_9_8 = ia) % 7.68/1.90 | | | | | | | (48) requalityOnA(all_9_8, all_9_7) = 0 % 7.68/1.90 | | | | | | | % 7.68/1.90 | | | | | | | GROUND_INST: instantiating (axiom_4) with all_9_8, all_9_7, % 7.68/1.90 | | | | | | | simplifying with (19), (20), (48) gives: % 7.68/1.90 | | | | | | | (49) cA(all_9_7) = 0 % 7.68/1.90 | | | | | | | % 7.68/1.90 | | | | | | | GROUND_INST: instantiating (6) with all_9_7, simplifying with % 7.68/1.90 | | | | | | | (20), (49) gives: % 7.68/1.90 | | | | | | | (50) all_9_7 = ia | all_9_7 = ib % 7.68/1.90 | | | | | | | % 7.68/1.90 | | | | | | | BETA: splitting (50) gives: % 7.68/1.90 | | | | | | | % 7.68/1.90 | | | | | | | Case 1: % 7.68/1.91 | | | | | | | | % 7.68/1.91 | | | | | | | | (51) all_9_7 = ia % 7.68/1.91 | | | | | | | | % 7.68/1.91 | | | | | | | | REDUCE: (48), (51) imply: % 7.68/1.91 | | | | | | | | (52) requalityOnA(all_9_8, ia) = 0 % 7.68/1.91 | | | | | | | | % 7.68/1.91 | | | | | | | | REDUCE: (20), (51) imply: % 7.68/1.91 | | | | | | | | (53) $i(ia) % 7.68/1.91 | | | | | | | | % 7.68/1.91 | | | | | | | | GROUND_INST: instantiating (axiom_3) with ia, ia, all_9_8, % 7.68/1.91 | | | | | | | | simplifying with (8), (19), (52), (53) gives: % 7.68/1.91 | | | | | | | | (54) all_9_8 = ia % 7.68/1.91 | | | | | | | | % 7.68/1.91 | | | | | | | | REDUCE: (47), (54) imply: % 7.68/1.91 | | | | | | | | (55) $false % 7.68/1.91 | | | | | | | | % 7.68/1.91 | | | | | | | | CLOSE: (55) is inconsistent. % 7.68/1.91 | | | | | | | | % 7.68/1.91 | | | | | | | Case 2: % 7.68/1.91 | | | | | | | | % 7.68/1.91 | | | | | | | | (56) all_9_7 = ib % 7.68/1.91 | | | | | | | | % 7.68/1.91 | | | | | | | | REDUCE: (48), (56) imply: % 7.68/1.91 | | | | | | | | (57) requalityOnA(all_9_8, ib) = 0 % 7.68/1.91 | | | | | | | | % 7.68/1.91 | | | | | | | | REDUCE: (20), (56) imply: % 7.68/1.91 | | | | | | | | (58) $i(ib) % 7.68/1.91 | | | | | | | | % 7.68/1.91 | | | | | | | | GROUND_INST: instantiating (axiom_3) with ib, ib, all_9_8, % 7.68/1.91 | | | | | | | | simplifying with (10), (19), (57), (58) gives: % 7.68/1.91 | | | | | | | | (59) all_9_8 = ib % 7.68/1.91 | | | | | | | | % 7.68/1.91 | | | | | | | | REDUCE: (46), (59) imply: % 7.68/1.91 | | | | | | | | (60) $false % 7.68/1.91 | | | | | | | | % 7.68/1.91 | | | | | | | | CLOSE: (60) is inconsistent. % 7.68/1.91 | | | | | | | | % 7.68/1.91 | | | | | | | End of split % 7.68/1.91 | | | | | | | % 7.68/1.91 | | | | | | Case 2: % 7.68/1.91 | | | | | | | % 8.13/1.91 | | | | | | | (61) all_9_10 = 0 & ~ (all_9_9 = 0) & requalityOnA(all_9_11, % 8.13/1.91 | | | | | | | all_9_12) = all_9_9 & requalityOnA(all_9_12, all_9_11) = % 8.13/1.91 | | | | | | | 0 % 8.13/1.91 | | | | | | | % 8.13/1.91 | | | | | | | ALPHA: (61) implies: % 8.13/1.91 | | | | | | | (62) ~ (all_9_9 = 0) % 8.13/1.91 | | | | | | | (63) requalityOnA(all_9_12, all_9_11) = 0 % 8.13/1.91 | | | | | | | (64) requalityOnA(all_9_11, all_9_12) = all_9_9 % 8.13/1.91 | | | | | | | % 8.13/1.91 | | | | | | | GROUND_INST: instantiating (axiom_4) with all_9_12, all_9_11, % 8.13/1.91 | | | | | | | simplifying with (17), (18), (63) gives: % 8.13/1.91 | | | | | | | (65) cA(all_9_11) = 0 % 8.13/1.91 | | | | | | | % 8.13/1.91 | | | | | | | GROUND_INST: instantiating (6) with all_9_11, simplifying with % 8.13/1.91 | | | | | | | (18), (65) gives: % 8.13/1.91 | | | | | | | (66) all_9_11 = ia | all_9_11 = ib % 8.13/1.91 | | | | | | | % 8.13/1.91 | | | | | | | BETA: splitting (66) gives: % 8.13/1.91 | | | | | | | % 8.13/1.91 | | | | | | | Case 1: % 8.13/1.91 | | | | | | | | % 8.13/1.91 | | | | | | | | (67) all_9_11 = ia % 8.13/1.91 | | | | | | | | % 8.13/1.91 | | | | | | | | REDUCE: (64), (67) imply: % 8.13/1.91 | | | | | | | | (68) requalityOnA(ia, all_9_12) = all_9_9 % 8.13/1.91 | | | | | | | | % 8.13/1.91 | | | | | | | | REDUCE: (63), (67) imply: % 8.13/1.91 | | | | | | | | (69) requalityOnA(all_9_12, ia) = 0 % 8.13/1.91 | | | | | | | | % 8.13/1.91 | | | | | | | | REDUCE: (18), (67) imply: % 8.13/1.91 | | | | | | | | (70) $i(ia) % 8.13/1.91 | | | | | | | | % 8.13/1.91 | | | | | | | | GROUND_INST: instantiating (axiom_3) with ia, ia, all_9_12, % 8.13/1.91 | | | | | | | | simplifying with (8), (17), (69), (70) gives: % 8.13/1.91 | | | | | | | | (71) all_9_12 = ia % 8.13/1.91 | | | | | | | | % 8.13/1.91 | | | | | | | | REDUCE: (68), (71) imply: % 8.13/1.91 | | | | | | | | (72) requalityOnA(ia, ia) = all_9_9 % 8.13/1.91 | | | | | | | | % 8.13/1.91 | | | | | | | | GROUND_INST: instantiating (15) with 0, all_9_9, ia, ia, % 8.13/1.91 | | | | | | | | simplifying with (8), (72) gives: % 8.13/1.91 | | | | | | | | (73) all_9_9 = 0 % 8.13/1.91 | | | | | | | | % 8.13/1.91 | | | | | | | | REDUCE: (62), (73) imply: % 8.13/1.92 | | | | | | | | (74) $false % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | | CLOSE: (74) is inconsistent. % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | Case 2: % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | | (75) all_9_11 = ib % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | | REDUCE: (64), (75) imply: % 8.13/1.92 | | | | | | | | (76) requalityOnA(ib, all_9_12) = all_9_9 % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | | REDUCE: (63), (75) imply: % 8.13/1.92 | | | | | | | | (77) requalityOnA(all_9_12, ib) = 0 % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | | REDUCE: (18), (75) imply: % 8.13/1.92 | | | | | | | | (78) $i(ib) % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | | GROUND_INST: instantiating (axiom_3) with ib, ib, all_9_12, % 8.13/1.92 | | | | | | | | simplifying with (10), (17), (77), (78) gives: % 8.13/1.92 | | | | | | | | (79) all_9_12 = ib % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | | REDUCE: (76), (79) imply: % 8.13/1.92 | | | | | | | | (80) requalityOnA(ib, ib) = all_9_9 % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | | GROUND_INST: instantiating (15) with 0, all_9_9, ib, ib, % 8.13/1.92 | | | | | | | | simplifying with (10), (80) gives: % 8.13/1.92 | | | | | | | | (81) all_9_9 = 0 % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | | REDUCE: (62), (81) imply: % 8.13/1.92 | | | | | | | | (82) $false % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | | CLOSE: (82) is inconsistent. % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | End of split % 8.13/1.92 | | | | | | | % 8.13/1.92 | | | | | | End of split % 8.13/1.92 | | | | | | % 8.13/1.92 | | | | | Case 2: % 8.13/1.92 | | | | | | % 8.13/1.92 | | | | | | (83) (xsd_string(all_9_5) = all_9_4 & xsd_integer(all_9_5) = % 8.13/1.92 | | | | | | all_9_3 & ((all_9_3 = 0 & all_9_4 = 0) | ( ~ (all_9_3 = 0) % 8.13/1.92 | | | | | | & ~ (all_9_4 = 0)))) | (cowlThing(all_9_2) = all_9_1 % 8.13/1.92 | | | | | | & cowlNothing(all_9_2) = all_9_0 & ( ~ (all_9_1 = 0) | % 8.13/1.92 | | | | | | all_9_0 = 0)) % 8.13/1.92 | | | | | | % 8.13/1.92 | | | | | | BETA: splitting (83) gives: % 8.13/1.92 | | | | | | % 8.13/1.92 | | | | | | Case 1: % 8.13/1.92 | | | | | | | % 8.13/1.92 | | | | | | | (84) xsd_string(all_9_5) = all_9_4 & xsd_integer(all_9_5) = % 8.13/1.92 | | | | | | | all_9_3 & ((all_9_3 = 0 & all_9_4 = 0) | ( ~ (all_9_3 = 0) % 8.13/1.92 | | | | | | | & ~ (all_9_4 = 0))) % 8.13/1.92 | | | | | | | % 8.13/1.92 | | | | | | | ALPHA: (84) implies: % 8.13/1.92 | | | | | | | (85) xsd_integer(all_9_5) = all_9_3 % 8.13/1.92 | | | | | | | (86) xsd_string(all_9_5) = all_9_4 % 8.13/1.92 | | | | | | | (87) (all_9_3 = 0 & all_9_4 = 0) | ( ~ (all_9_3 = 0) & ~ % 8.13/1.92 | | | | | | | (all_9_4 = 0)) % 8.13/1.92 | | | | | | | % 8.13/1.92 | | | | | | | GROUND_INST: instantiating (4) with all_9_5, all_9_3, simplifying % 8.13/1.92 | | | | | | | with (21), (85) gives: % 8.13/1.92 | | | | | | | (88) all_9_3 = 0 | xsd_string(all_9_5) = 0 % 8.13/1.92 | | | | | | | % 8.13/1.92 | | | | | | | GROUND_INST: instantiating (5) with all_9_5, all_9_4, simplifying % 8.13/1.92 | | | | | | | with (21), (86) gives: % 8.13/1.92 | | | | | | | (89) all_9_4 = 0 | xsd_integer(all_9_5) = 0 % 8.13/1.92 | | | | | | | % 8.13/1.92 | | | | | | | BETA: splitting (87) gives: % 8.13/1.92 | | | | | | | % 8.13/1.92 | | | | | | | Case 1: % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | | (90) all_9_3 = 0 & all_9_4 = 0 % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | | ALPHA: (90) implies: % 8.13/1.92 | | | | | | | | (91) all_9_4 = 0 % 8.13/1.92 | | | | | | | | (92) all_9_3 = 0 % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | | REDUCE: (86), (91) imply: % 8.13/1.92 | | | | | | | | (93) xsd_string(all_9_5) = 0 % 8.13/1.92 | | | | | | | | % 8.13/1.92 | | | | | | | | REDUCE: (85), (92) imply: % 8.13/1.92 | | | | | | | | (94) xsd_integer(all_9_5) = 0 % 8.13/1.92 | | | | | | | | % 8.13/1.93 | | | | | | | | REF_CLOSE: (3), (14), (21), (93), (94) are inconsistent by % 8.13/1.93 | | | | | | | | sub-proof #1. % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | Case 2: % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | | (95) ~ (all_9_3 = 0) & ~ (all_9_4 = 0) % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | | ALPHA: (95) implies: % 8.13/1.93 | | | | | | | | (96) ~ (all_9_4 = 0) % 8.13/1.93 | | | | | | | | (97) ~ (all_9_3 = 0) % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | | BETA: splitting (89) gives: % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | | Case 1: % 8.13/1.93 | | | | | | | | | % 8.13/1.93 | | | | | | | | | (98) xsd_integer(all_9_5) = 0 % 8.13/1.93 | | | | | | | | | % 8.13/1.93 | | | | | | | | | BETA: splitting (88) gives: % 8.13/1.93 | | | | | | | | | % 8.13/1.93 | | | | | | | | | Case 1: % 8.13/1.93 | | | | | | | | | | % 8.13/1.93 | | | | | | | | | | (99) xsd_string(all_9_5) = 0 % 8.13/1.93 | | | | | | | | | | % 8.13/1.93 | | | | | | | | | | REF_CLOSE: (3), (14), (21), (98), (99) are inconsistent by % 8.13/1.93 | | | | | | | | | | sub-proof #1. % 8.13/1.93 | | | | | | | | | | % 8.13/1.93 | | | | | | | | | Case 2: % 8.13/1.93 | | | | | | | | | | % 8.13/1.93 | | | | | | | | | | (100) all_9_3 = 0 % 8.13/1.93 | | | | | | | | | | % 8.13/1.93 | | | | | | | | | | REDUCE: (97), (100) imply: % 8.13/1.93 | | | | | | | | | | (101) $false % 8.13/1.93 | | | | | | | | | | % 8.13/1.93 | | | | | | | | | | CLOSE: (101) is inconsistent. % 8.13/1.93 | | | | | | | | | | % 8.13/1.93 | | | | | | | | | End of split % 8.13/1.93 | | | | | | | | | % 8.13/1.93 | | | | | | | | Case 2: % 8.13/1.93 | | | | | | | | | % 8.13/1.93 | | | | | | | | | (102) all_9_4 = 0 % 8.13/1.93 | | | | | | | | | % 8.13/1.93 | | | | | | | | | REDUCE: (96), (102) imply: % 8.13/1.93 | | | | | | | | | (103) $false % 8.13/1.93 | | | | | | | | | % 8.13/1.93 | | | | | | | | | CLOSE: (103) is inconsistent. % 8.13/1.93 | | | | | | | | | % 8.13/1.93 | | | | | | | | End of split % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | End of split % 8.13/1.93 | | | | | | | % 8.13/1.93 | | | | | | Case 2: % 8.13/1.93 | | | | | | | % 8.13/1.93 | | | | | | | (104) cowlThing(all_9_2) = all_9_1 & cowlNothing(all_9_2) = % 8.13/1.93 | | | | | | | all_9_0 & ( ~ (all_9_1 = 0) | all_9_0 = 0) % 8.13/1.93 | | | | | | | % 8.13/1.93 | | | | | | | ALPHA: (104) implies: % 8.13/1.93 | | | | | | | (105) cowlNothing(all_9_2) = all_9_0 % 8.13/1.93 | | | | | | | (106) cowlThing(all_9_2) = all_9_1 % 8.13/1.93 | | | | | | | (107) ~ (all_9_1 = 0) | all_9_0 = 0 % 8.13/1.93 | | | | | | | % 8.13/1.93 | | | | | | | GROUND_INST: instantiating (2) with all_9_2, all_9_1, simplifying % 8.13/1.93 | | | | | | | with (22), (106) gives: % 8.13/1.93 | | | | | | | (108) all_9_1 = 0 % 8.13/1.93 | | | | | | | % 8.13/1.93 | | | | | | | BETA: splitting (107) gives: % 8.13/1.93 | | | | | | | % 8.13/1.93 | | | | | | | Case 1: % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | | (109) ~ (all_9_1 = 0) % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | | REDUCE: (108), (109) imply: % 8.13/1.93 | | | | | | | | (110) $false % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | | CLOSE: (110) is inconsistent. % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | Case 2: % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | | (111) all_9_0 = 0 % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | | REDUCE: (105), (111) imply: % 8.13/1.93 | | | | | | | | (112) cowlNothing(all_9_2) = 0 % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | | GROUND_INST: instantiating (1) with all_9_2, simplifying with % 8.13/1.93 | | | | | | | | (22), (112) gives: % 8.13/1.93 | | | | | | | | (113) $false % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | | CLOSE: (113) is inconsistent. % 8.13/1.93 | | | | | | | | % 8.13/1.93 | | | | | | | End of split % 8.13/1.93 | | | | | | | % 8.13/1.93 | | | | | | End of split % 8.13/1.93 | | | | | | % 8.13/1.93 | | | | | End of split % 8.13/1.93 | | | | | % 8.13/1.93 | | | | End of split % 8.13/1.93 | | | | % 8.13/1.93 | | | End of split % 8.13/1.93 | | | % 8.13/1.93 | | End of split % 8.13/1.93 | | % 8.13/1.93 | End of split % 8.13/1.93 | % 8.13/1.93 End of proof % 8.13/1.93 % 8.13/1.93 Sub-proof #1 shows that the following formulas are inconsistent: % 8.13/1.93 ---------------------------------------------------------------- % 8.13/1.93 (1) xsd_string(all_9_5) = 0 % 8.13/1.93 (2) xsd_integer(all_9_5) = 0 % 8.13/1.93 (3) ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 8.13/1.93 (v1 = 0) & xsd_integer(v0) = v1)) % 8.13/1.93 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.13/1.93 (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 8.13/1.93 (5) $i(all_9_5) % 8.13/1.93 % 8.13/1.93 Begin of proof % 8.13/1.93 | % 8.13/1.93 | GROUND_INST: instantiating (3) with all_9_5, simplifying with (1), (5) gives: % 8.13/1.94 | (6) ? [v0: int] : ( ~ (v0 = 0) & xsd_integer(all_9_5) = v0) % 8.13/1.94 | % 8.13/1.94 | DELTA: instantiating (6) with fresh symbol all_68_0 gives: % 8.13/1.94 | (7) ~ (all_68_0 = 0) & xsd_integer(all_9_5) = all_68_0 % 8.13/1.94 | % 8.13/1.94 | ALPHA: (7) implies: % 8.13/1.94 | (8) ~ (all_68_0 = 0) % 8.13/1.94 | (9) xsd_integer(all_9_5) = all_68_0 % 8.13/1.94 | % 8.13/1.94 | GROUND_INST: instantiating (4) with 0, all_68_0, all_9_5, simplifying with % 8.13/1.94 | (2), (9) gives: % 8.13/1.94 | (10) all_68_0 = 0 % 8.13/1.94 | % 8.13/1.94 | REDUCE: (8), (10) imply: % 8.13/1.94 | (11) $false % 8.13/1.94 | % 8.13/1.94 | CLOSE: (11) is inconsistent. % 8.13/1.94 | % 8.13/1.94 End of proof % 8.13/1.94 % SZS output end Proof for theBenchmark % 8.13/1.94 % 8.13/1.94 1330ms %------------------------------------------------------------------------------