%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KRS144+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 : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 05:51:25 EDT 2023 % Result : Theorem 6.40s 1.69s % Output : Proof 8.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : KRS144+1 : TPTP v8.1.2. Released v3.1.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n008.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 01:36:32 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.64 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.93/1.03 Prover 1: Preprocessing ... % 1.93/1.04 Prover 4: Preprocessing ... % 2.72/1.09 Prover 2: Preprocessing ... % 2.72/1.09 Prover 5: Preprocessing ... % 2.72/1.09 Prover 0: Preprocessing ... % 2.72/1.09 Prover 6: Preprocessing ... % 2.72/1.09 Prover 3: Preprocessing ... % 4.07/1.32 Prover 2: Proving ... % 4.07/1.32 Prover 5: Proving ... % 4.07/1.35 Prover 6: Proving ... % 4.64/1.36 Prover 1: Constructing countermodel ... % 4.64/1.36 Prover 4: Constructing countermodel ... % 4.64/1.36 Prover 3: Constructing countermodel ... % 4.64/1.38 Prover 0: Proving ... % 6.40/1.68 Prover 3: proved (1036ms) % 6.40/1.69 % 6.40/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.40/1.69 % 6.40/1.69 Prover 2: proved (1043ms) % 6.40/1.69 % 6.40/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.40/1.69 % 6.40/1.69 Prover 0: stopped % 6.40/1.70 Prover 5: stopped % 6.40/1.71 Prover 6: stopped % 7.01/1.71 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.01/1.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.01/1.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.01/1.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.01/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.01/1.75 Prover 8: Preprocessing ... % 7.01/1.76 Prover 7: Preprocessing ... % 7.01/1.76 Prover 11: Preprocessing ... % 7.01/1.76 Prover 10: Preprocessing ... % 7.01/1.77 Prover 1: Found proof (size 59) % 7.01/1.77 Prover 1: proved (1124ms) % 7.01/1.77 Prover 7: stopped % 7.01/1.77 Prover 4: stopped % 7.01/1.77 Prover 10: stopped % 7.01/1.78 Prover 13: Preprocessing ... % 7.53/1.79 Prover 11: stopped % 7.53/1.80 Prover 13: stopped % 7.53/1.84 Prover 8: Warning: ignoring some quantifiers % 7.53/1.84 Prover 8: Constructing countermodel ... % 7.53/1.85 Prover 8: stopped % 7.53/1.85 % 7.53/1.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.53/1.85 % 7.53/1.86 % SZS output start Proof for theBenchmark % 7.53/1.86 Assumptions after simplification: % 7.53/1.86 --------------------------------- % 7.53/1.87 % 7.53/1.87 (axiom_0) % 8.02/1.90 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ $i(v0)) & % 8.02/1.90 ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0)) % 8.02/1.90 % 8.02/1.90 (axiom_1) % 8.02/1.90 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ $i(v0) | % 8.02/1.90 xsd_integer(v0) = 0) & ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | % 8.02/1.90 ? [v1: int] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 8.02/1.90 % 8.02/1.90 (axiom_2) % 8.02/1.91 ! [v0: $i] : ( ~ (cc(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: $i] : ! % 8.02/1.91 [v3: $i] : (v3 = v2 | v3 = v1 | v2 = v1 | ~ (rp(v0, v3) = 0) | ~ (rp(v0, % 8.02/1.91 v2) = 0) | ~ (rp(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)) % 8.02/1.91 & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & rp(v0, v2) = 0 & rp(v0, v1) % 8.02/1.91 = 0 & $i(v2) & $i(v1)))) % 8.02/1.91 % 8.02/1.91 (the_axiom) % 8.13/1.91 ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 & % 8.13/1.91 xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = % 8.13/1.91 0)))) | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cowlThing(v0) = % 8.13/1.91 v1 & cowlNothing(v0) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) | ? [v0: $i] : % 8.13/1.91 (cc(v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (rp(v0, v2) = % 8.13/1.91 0) | ~ (rp(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1))) | ? [v0: $i] : % 8.13/1.91 (cc(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) % 8.13/1.91 & ~ (v3 = v1) & ~ (v2 = v1) & rp(v0, v3) = 0 & rp(v0, v2) = 0 & rp(v0, % 8.13/1.91 v1) = 0 & $i(v3) & $i(v2) & $i(v1))) % 8.13/1.91 % 8.13/1.91 (function-axioms) % 8.18/1.92 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.18/1.92 [v3: $i] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [v0: % 8.18/1.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.18/1.92 ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0: % 8.18/1.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.18/1.92 ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0: % 8.18/1.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.18/1.92 ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0: % 8.18/1.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.18/1.92 ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0: % 8.18/1.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.18/1.92 ~ (cc(v2) = v1) | ~ (cc(v2) = v0)) % 8.18/1.92 % 8.18/1.92 Further assumptions not needed in the proof: % 8.18/1.92 -------------------------------------------- % 8.18/1.92 cc_substitution_1, cowlNothing_substitution_1, cowlThing_substitution_1, % 8.18/1.92 rp_substitution_1, rp_substitution_2, xsd_integer_substitution_1, % 8.18/1.92 xsd_string_substitution_1 % 8.18/1.92 % 8.18/1.92 Those formulas are unsatisfiable: % 8.18/1.92 --------------------------------- % 8.18/1.92 % 8.18/1.92 Begin of proof % 8.18/1.92 | % 8.18/1.92 | ALPHA: (axiom_0) implies: % 8.18/1.92 | (1) ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0)) % 8.18/1.92 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ % 8.18/1.92 | $i(v0)) % 8.18/1.92 | % 8.18/1.92 | ALPHA: (axiom_1) implies: % 8.18/1.93 | (3) ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 8.18/1.93 | (v1 = 0) & xsd_integer(v0) = v1)) % 8.18/1.93 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ % 8.18/1.93 | $i(v0) | xsd_integer(v0) = 0) % 8.18/1.93 | % 8.18/1.93 | ALPHA: (function-axioms) implies: % 8.18/1.93 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.18/1.93 | (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 8.18/1.93 | % 8.18/1.93 | BETA: splitting (the_axiom) gives: % 8.18/1.93 | % 8.18/1.93 | Case 1: % 8.18/1.93 | | % 8.18/1.93 | | (6) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 & % 8.18/1.93 | | xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & % 8.18/1.93 | | ~ (v1 = 0)))) | ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 8.18/1.93 | | (cowlThing(v0) = v1 & cowlNothing(v0) = v2 & $i(v0) & ( ~ (v1 = 0) | % 8.18/1.93 | | v2 = 0)) % 8.18/1.93 | | % 8.18/1.93 | | BETA: splitting (6) gives: % 8.18/1.93 | | % 8.18/1.93 | | Case 1: % 8.18/1.93 | | | % 8.18/1.93 | | | (7) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 & % 8.18/1.93 | | | xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) % 8.18/1.93 | | | & ~ (v1 = 0)))) % 8.18/1.93 | | | % 8.18/1.93 | | | DELTA: instantiating (7) with fresh symbols all_12_0, all_12_1, all_12_2 % 8.18/1.93 | | | gives: % 8.18/1.93 | | | (8) xsd_string(all_12_2) = all_12_1 & xsd_integer(all_12_2) = all_12_0 % 8.18/1.93 | | | & $i(all_12_2) & ((all_12_0 = 0 & all_12_1 = 0) | ( ~ (all_12_0 = % 8.18/1.94 | | | 0) & ~ (all_12_1 = 0))) % 8.18/1.94 | | | % 8.18/1.94 | | | ALPHA: (8) implies: % 8.18/1.94 | | | (9) $i(all_12_2) % 8.18/1.94 | | | (10) xsd_integer(all_12_2) = all_12_0 % 8.18/1.94 | | | (11) xsd_string(all_12_2) = all_12_1 % 8.18/1.94 | | | (12) (all_12_0 = 0 & all_12_1 = 0) | ( ~ (all_12_0 = 0) & ~ (all_12_1 % 8.18/1.94 | | | = 0)) % 8.18/1.94 | | | % 8.18/1.94 | | | GROUND_INST: instantiating (4) with all_12_2, all_12_1, simplifying with % 8.18/1.94 | | | (9), (11) gives: % 8.18/1.94 | | | (13) all_12_1 = 0 | xsd_integer(all_12_2) = 0 % 8.18/1.94 | | | % 8.18/1.94 | | | BETA: splitting (12) gives: % 8.18/1.94 | | | % 8.18/1.94 | | | Case 1: % 8.18/1.94 | | | | % 8.18/1.94 | | | | (14) all_12_0 = 0 & all_12_1 = 0 % 8.18/1.94 | | | | % 8.18/1.94 | | | | ALPHA: (14) implies: % 8.18/1.94 | | | | (15) all_12_1 = 0 % 8.18/1.94 | | | | (16) all_12_0 = 0 % 8.18/1.94 | | | | % 8.18/1.94 | | | | REDUCE: (11), (15) imply: % 8.18/1.94 | | | | (17) xsd_string(all_12_2) = 0 % 8.18/1.94 | | | | % 8.18/1.94 | | | | REDUCE: (10), (16) imply: % 8.18/1.94 | | | | (18) xsd_integer(all_12_2) = 0 % 8.18/1.94 | | | | % 8.18/1.94 | | | | GROUND_INST: instantiating (3) with all_12_2, simplifying with (9), (17) % 8.18/1.94 | | | | gives: % 8.18/1.94 | | | | (19) ? [v0: int] : ( ~ (v0 = 0) & xsd_integer(all_12_2) = v0) % 8.18/1.94 | | | | % 8.18/1.94 | | | | DELTA: instantiating (19) with fresh symbol all_26_0 gives: % 8.18/1.94 | | | | (20) ~ (all_26_0 = 0) & xsd_integer(all_12_2) = all_26_0 % 8.18/1.94 | | | | % 8.18/1.94 | | | | ALPHA: (20) implies: % 8.18/1.94 | | | | (21) ~ (all_26_0 = 0) % 8.18/1.94 | | | | (22) xsd_integer(all_12_2) = all_26_0 % 8.18/1.94 | | | | % 8.18/1.94 | | | | GROUND_INST: instantiating (5) with 0, all_26_0, all_12_2, simplifying % 8.18/1.94 | | | | with (18), (22) gives: % 8.18/1.94 | | | | (23) all_26_0 = 0 % 8.18/1.94 | | | | % 8.18/1.94 | | | | REDUCE: (21), (23) imply: % 8.18/1.94 | | | | (24) $false % 8.18/1.94 | | | | % 8.18/1.94 | | | | CLOSE: (24) is inconsistent. % 8.18/1.94 | | | | % 8.18/1.94 | | | Case 2: % 8.18/1.94 | | | | % 8.18/1.94 | | | | (25) ~ (all_12_0 = 0) & ~ (all_12_1 = 0) % 8.18/1.94 | | | | % 8.18/1.94 | | | | ALPHA: (25) implies: % 8.18/1.94 | | | | (26) ~ (all_12_1 = 0) % 8.18/1.94 | | | | (27) ~ (all_12_0 = 0) % 8.18/1.94 | | | | % 8.18/1.94 | | | | BETA: splitting (13) gives: % 8.18/1.94 | | | | % 8.18/1.94 | | | | Case 1: % 8.18/1.94 | | | | | % 8.18/1.94 | | | | | (28) xsd_integer(all_12_2) = 0 % 8.18/1.94 | | | | | % 8.18/1.95 | | | | | GROUND_INST: instantiating (5) with all_12_0, 0, all_12_2, simplifying % 8.18/1.95 | | | | | with (10), (28) gives: % 8.18/1.95 | | | | | (29) all_12_0 = 0 % 8.18/1.95 | | | | | % 8.18/1.95 | | | | | REDUCE: (27), (29) imply: % 8.18/1.95 | | | | | (30) $false % 8.18/1.95 | | | | | % 8.18/1.95 | | | | | CLOSE: (30) is inconsistent. % 8.18/1.95 | | | | | % 8.18/1.95 | | | | Case 2: % 8.18/1.95 | | | | | % 8.18/1.95 | | | | | (31) all_12_1 = 0 % 8.18/1.95 | | | | | % 8.18/1.95 | | | | | REDUCE: (26), (31) imply: % 8.18/1.95 | | | | | (32) $false % 8.18/1.95 | | | | | % 8.18/1.95 | | | | | CLOSE: (32) is inconsistent. % 8.18/1.95 | | | | | % 8.18/1.95 | | | | End of split % 8.18/1.95 | | | | % 8.18/1.95 | | | End of split % 8.18/1.95 | | | % 8.18/1.95 | | Case 2: % 8.18/1.95 | | | % 8.18/1.95 | | | (33) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cowlThing(v0) = v1 & % 8.18/1.95 | | | cowlNothing(v0) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 8.18/1.95 | | | % 8.18/1.95 | | | DELTA: instantiating (33) with fresh symbols all_12_0, all_12_1, all_12_2 % 8.18/1.95 | | | gives: % 8.18/1.95 | | | (34) cowlThing(all_12_2) = all_12_1 & cowlNothing(all_12_2) = all_12_0 % 8.18/1.95 | | | & $i(all_12_2) & ( ~ (all_12_1 = 0) | all_12_0 = 0) % 8.18/1.95 | | | % 8.18/1.95 | | | ALPHA: (34) implies: % 8.18/1.95 | | | (35) $i(all_12_2) % 8.18/1.95 | | | (36) cowlNothing(all_12_2) = all_12_0 % 8.18/1.95 | | | (37) cowlThing(all_12_2) = all_12_1 % 8.18/1.95 | | | (38) ~ (all_12_1 = 0) | all_12_0 = 0 % 8.18/1.95 | | | % 8.18/1.95 | | | GROUND_INST: instantiating (2) with all_12_2, all_12_1, simplifying with % 8.18/1.95 | | | (35), (37) gives: % 8.18/1.95 | | | (39) all_12_1 = 0 % 8.18/1.95 | | | % 8.18/1.95 | | | BETA: splitting (38) gives: % 8.18/1.95 | | | % 8.18/1.95 | | | Case 1: % 8.18/1.95 | | | | % 8.18/1.95 | | | | (40) ~ (all_12_1 = 0) % 8.18/1.95 | | | | % 8.18/1.95 | | | | REDUCE: (39), (40) imply: % 8.18/1.95 | | | | (41) $false % 8.18/1.95 | | | | % 8.18/1.95 | | | | CLOSE: (41) is inconsistent. % 8.18/1.95 | | | | % 8.18/1.95 | | | Case 2: % 8.18/1.95 | | | | % 8.18/1.95 | | | | (42) all_12_0 = 0 % 8.18/1.95 | | | | % 8.18/1.95 | | | | REDUCE: (36), (42) imply: % 8.18/1.95 | | | | (43) cowlNothing(all_12_2) = 0 % 8.18/1.95 | | | | % 8.18/1.95 | | | | GROUND_INST: instantiating (1) with all_12_2, simplifying with (35), % 8.18/1.95 | | | | (43) gives: % 8.18/1.95 | | | | (44) $false % 8.18/1.95 | | | | % 8.18/1.95 | | | | CLOSE: (44) is inconsistent. % 8.18/1.95 | | | | % 8.18/1.95 | | | End of split % 8.18/1.95 | | | % 8.18/1.95 | | End of split % 8.18/1.95 | | % 8.18/1.95 | Case 2: % 8.18/1.95 | | % 8.18/1.95 | | (45) ? [v0: $i] : (cc(v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 % 8.18/1.95 | | = v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ $i(v2) | % 8.18/1.95 | | ~ $i(v1))) | ? [v0: $i] : (cc(v0) = 0 & $i(v0) & ? [v1: $i] : % 8.18/1.95 | | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & ~ (v3 = v1) & ~ (v2 = % 8.18/1.95 | | v1) & rp(v0, v3) = 0 & rp(v0, v2) = 0 & rp(v0, v1) = 0 & % 8.18/1.95 | | $i(v3) & $i(v2) & $i(v1))) % 8.18/1.95 | | % 8.18/1.95 | | BETA: splitting (45) gives: % 8.18/1.95 | | % 8.18/1.95 | | Case 1: % 8.18/1.95 | | | % 8.18/1.96 | | | (46) ? [v0: $i] : (cc(v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 8.18/1.96 | | | (v2 = v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ $i(v2) % 8.18/1.96 | | | | ~ $i(v1))) % 8.18/1.96 | | | % 8.18/1.96 | | | DELTA: instantiating (46) with fresh symbol all_12_0 gives: % 8.18/1.96 | | | (47) cc(all_12_0) = 0 & $i(all_12_0) & ! [v0: $i] : ! [v1: $i] : (v1 % 8.18/1.96 | | | = v0 | ~ (rp(all_12_0, v1) = 0) | ~ (rp(all_12_0, v0) = 0) | % 8.18/1.96 | | | ~ $i(v1) | ~ $i(v0)) % 8.18/1.96 | | | % 8.18/1.96 | | | ALPHA: (47) implies: % 8.18/1.96 | | | (48) $i(all_12_0) % 8.18/1.96 | | | (49) cc(all_12_0) = 0 % 8.18/1.96 | | | (50) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rp(all_12_0, v1) = 0) | % 8.18/1.96 | | | ~ (rp(all_12_0, v0) = 0) | ~ $i(v1) | ~ $i(v0)) % 8.18/1.96 | | | % 8.18/1.96 | | | GROUND_INST: instantiating (axiom_2) with all_12_0, simplifying with (48), % 8.18/1.96 | | | (49) gives: % 8.18/1.96 | | | (51) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | v2 = v0 | v1 % 8.18/1.96 | | | = v0 | ~ (rp(all_12_0, v2) = 0) | ~ (rp(all_12_0, v1) = 0) | % 8.18/1.96 | | | ~ (rp(all_12_0, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & % 8.18/1.96 | | | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & rp(all_12_0, v1) = 0 & % 8.18/1.96 | | | rp(all_12_0, v0) = 0 & $i(v1) & $i(v0)) % 8.18/1.96 | | | % 8.18/1.96 | | | ALPHA: (51) implies: % 8.18/1.96 | | | (52) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & rp(all_12_0, v1) = 0 & % 8.18/1.96 | | | rp(all_12_0, v0) = 0 & $i(v1) & $i(v0)) % 8.18/1.96 | | | % 8.18/1.96 | | | DELTA: instantiating (52) with fresh symbols all_21_0, all_21_1 gives: % 8.18/1.96 | | | (53) ~ (all_21_0 = all_21_1) & rp(all_12_0, all_21_0) = 0 & % 8.18/1.96 | | | rp(all_12_0, all_21_1) = 0 & $i(all_21_0) & $i(all_21_1) % 8.18/1.96 | | | % 8.18/1.96 | | | ALPHA: (53) implies: % 8.18/1.96 | | | (54) ~ (all_21_0 = all_21_1) % 8.18/1.96 | | | (55) $i(all_21_1) % 8.18/1.96 | | | (56) $i(all_21_0) % 8.18/1.96 | | | (57) rp(all_12_0, all_21_1) = 0 % 8.18/1.96 | | | (58) rp(all_12_0, all_21_0) = 0 % 8.18/1.96 | | | % 8.18/1.96 | | | GROUND_INST: instantiating (50) with all_21_1, all_21_0, simplifying with % 8.18/1.96 | | | (55), (56), (57), (58) gives: % 8.18/1.96 | | | (59) all_21_0 = all_21_1 % 8.18/1.96 | | | % 8.18/1.96 | | | REDUCE: (54), (59) imply: % 8.18/1.96 | | | (60) $false % 8.18/1.96 | | | % 8.18/1.96 | | | CLOSE: (60) is inconsistent. % 8.18/1.96 | | | % 8.18/1.96 | | Case 2: % 8.18/1.96 | | | % 8.18/1.97 | | | (61) ? [v0: $i] : (cc(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : % 8.18/1.97 | | | ? [v3: $i] : ( ~ (v3 = v2) & ~ (v3 = v1) & ~ (v2 = v1) & % 8.18/1.97 | | | rp(v0, v3) = 0 & rp(v0, v2) = 0 & rp(v0, v1) = 0 & $i(v3) & % 8.18/1.97 | | | $i(v2) & $i(v1))) % 8.18/1.97 | | | % 8.18/1.97 | | | DELTA: instantiating (61) with fresh symbol all_12_0 gives: % 8.18/1.97 | | | (62) cc(all_12_0) = 0 & $i(all_12_0) & ? [v0: $i] : ? [v1: $i] : ? % 8.18/1.97 | | | [v2: $i] : ( ~ (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & % 8.18/1.97 | | | rp(all_12_0, v2) = 0 & rp(all_12_0, v1) = 0 & rp(all_12_0, v0) = % 8.18/1.97 | | | 0 & $i(v2) & $i(v1) & $i(v0)) % 8.18/1.97 | | | % 8.18/1.97 | | | ALPHA: (62) implies: % 8.18/1.97 | | | (63) $i(all_12_0) % 8.18/1.97 | | | (64) cc(all_12_0) = 0 % 8.18/1.97 | | | (65) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & ~ (v2 = % 8.18/1.97 | | | v0) & ~ (v1 = v0) & rp(all_12_0, v2) = 0 & rp(all_12_0, v1) = % 8.18/1.97 | | | 0 & rp(all_12_0, v0) = 0 & $i(v2) & $i(v1) & $i(v0)) % 8.18/1.97 | | | % 8.18/1.97 | | | DELTA: instantiating (65) with fresh symbols all_14_0, all_14_1, all_14_2 % 8.18/1.97 | | | gives: % 8.18/1.97 | | | (66) ~ (all_14_0 = all_14_1) & ~ (all_14_0 = all_14_2) & ~ (all_14_1 % 8.18/1.97 | | | = all_14_2) & rp(all_12_0, all_14_0) = 0 & rp(all_12_0, % 8.18/1.97 | | | all_14_1) = 0 & rp(all_12_0, all_14_2) = 0 & $i(all_14_0) & % 8.18/1.97 | | | $i(all_14_1) & $i(all_14_2) % 8.18/1.97 | | | % 8.18/1.97 | | | ALPHA: (66) implies: % 8.18/1.97 | | | (67) ~ (all_14_1 = all_14_2) % 8.18/1.97 | | | (68) ~ (all_14_0 = all_14_2) % 8.18/1.97 | | | (69) ~ (all_14_0 = all_14_1) % 8.18/1.97 | | | (70) $i(all_14_2) % 8.18/1.97 | | | (71) $i(all_14_1) % 8.18/1.97 | | | (72) $i(all_14_0) % 8.18/1.97 | | | (73) rp(all_12_0, all_14_2) = 0 % 8.18/1.97 | | | (74) rp(all_12_0, all_14_1) = 0 % 8.18/1.97 | | | (75) rp(all_12_0, all_14_0) = 0 % 8.18/1.97 | | | % 8.18/1.97 | | | GROUND_INST: instantiating (axiom_2) with all_12_0, simplifying with (63), % 8.18/1.97 | | | (64) gives: % 8.18/1.97 | | | (76) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | v2 = v0 | v1 % 8.18/1.97 | | | = v0 | ~ (rp(all_12_0, v2) = 0) | ~ (rp(all_12_0, v1) = 0) | % 8.18/1.97 | | | ~ (rp(all_12_0, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & % 8.18/1.97 | | | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & rp(all_12_0, v1) = 0 & % 8.18/1.97 | | | rp(all_12_0, v0) = 0 & $i(v1) & $i(v0)) % 8.18/1.97 | | | % 8.18/1.97 | | | ALPHA: (76) implies: % 8.18/1.98 | | | (77) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | v2 = v0 | v1 % 8.18/1.98 | | | = v0 | ~ (rp(all_12_0, v2) = 0) | ~ (rp(all_12_0, v1) = 0) | % 8.18/1.98 | | | ~ (rp(all_12_0, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 8.18/1.98 | | | % 8.18/1.98 | | | GROUND_INST: instantiating (77) with all_14_2, all_14_1, all_14_0, % 8.18/1.98 | | | simplifying with (70), (71), (72), (73), (74), (75) gives: % 8.18/1.98 | | | (78) all_14_0 = all_14_1 | all_14_0 = all_14_2 | all_14_1 = all_14_2 % 8.18/1.98 | | | % 8.18/1.98 | | | BETA: splitting (78) gives: % 8.18/1.98 | | | % 8.18/1.98 | | | Case 1: % 8.18/1.98 | | | | % 8.18/1.98 | | | | (79) all_14_0 = all_14_1 % 8.18/1.98 | | | | % 8.18/1.98 | | | | REDUCE: (69), (79) imply: % 8.18/1.98 | | | | (80) $false % 8.18/1.98 | | | | % 8.18/1.98 | | | | CLOSE: (80) is inconsistent. % 8.18/1.98 | | | | % 8.18/1.98 | | | Case 2: % 8.18/1.98 | | | | % 8.18/1.98 | | | | (81) all_14_0 = all_14_2 | all_14_1 = all_14_2 % 8.18/1.98 | | | | % 8.18/1.98 | | | | BETA: splitting (81) gives: % 8.18/1.98 | | | | % 8.18/1.98 | | | | Case 1: % 8.18/1.98 | | | | | % 8.18/1.98 | | | | | (82) all_14_0 = all_14_2 % 8.18/1.98 | | | | | % 8.18/1.98 | | | | | REDUCE: (68), (82) imply: % 8.18/1.98 | | | | | (83) $false % 8.18/1.98 | | | | | % 8.18/1.98 | | | | | CLOSE: (83) is inconsistent. % 8.18/1.98 | | | | | % 8.18/1.98 | | | | Case 2: % 8.18/1.98 | | | | | % 8.18/1.98 | | | | | (84) all_14_1 = all_14_2 % 8.18/1.98 | | | | | % 8.18/1.98 | | | | | REDUCE: (67), (84) imply: % 8.18/1.98 | | | | | (85) $false % 8.18/1.98 | | | | | % 8.18/1.98 | | | | | CLOSE: (85) is inconsistent. % 8.18/1.98 | | | | | % 8.18/1.98 | | | | End of split % 8.18/1.98 | | | | % 8.18/1.98 | | | End of split % 8.18/1.98 | | | % 8.18/1.98 | | End of split % 8.18/1.98 | | % 8.18/1.98 | End of split % 8.18/1.98 | % 8.18/1.98 End of proof % 8.18/1.98 % SZS output end Proof for theBenchmark % 8.18/1.98 % 8.18/1.98 1353ms %------------------------------------------------------------------------------