%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KRS142+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 05:51:24 EDT 2023 % Result : Theorem 4.66s 1.52s % Output : Proof 6.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.15 % Problem : KRS142+1 : TPTP v8.1.2. Released v3.1.0. % 0.15/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.37 % Computer : n028.cluster.edu % 0.15/0.37 % Model : x86_64 x86_64 % 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.37 % Memory : 8042.1875MB % 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.37 % CPULimit : 300 % 0.15/0.37 % WCLimit : 300 % 0.15/0.37 % DateTime : Mon Aug 28 01:26:39 EDT 2023 % 0.15/0.37 % CPUTime : % 0.23/0.66 ________ _____ % 0.23/0.66 ___ __ \_________(_)________________________________ % 0.23/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.23/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.23/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.23/0.66 % 0.23/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.23/0.66 (2023-06-19) % 0.23/0.66 % 0.23/0.66 (c) Philipp Rümmer, 2009-2023 % 0.23/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.23/0.66 Amanda Stjerna. % 0.23/0.66 Free software under BSD-3-Clause. % 0.23/0.66 % 0.23/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.23/0.66 % 0.23/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.23/0.67 Running up to 7 provers in parallel. % 0.23/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.23/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.23/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.23/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.23/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.23/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.23/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.15/1.04 Prover 4: Preprocessing ... % 2.15/1.04 Prover 1: Preprocessing ... % 2.57/1.08 Prover 2: Preprocessing ... % 2.57/1.08 Prover 0: Preprocessing ... % 2.57/1.08 Prover 3: Preprocessing ... % 2.57/1.08 Prover 5: Preprocessing ... % 2.57/1.08 Prover 6: Preprocessing ... % 3.48/1.24 Prover 2: Proving ... % 3.48/1.25 Prover 5: Proving ... % 4.04/1.33 Prover 4: Constructing countermodel ... % 4.04/1.33 Prover 0: Proving ... % 4.04/1.34 Prover 6: Proving ... % 4.04/1.36 Prover 3: Constructing countermodel ... % 4.04/1.36 Prover 1: Constructing countermodel ... % 4.66/1.51 Prover 5: proved (828ms) % 4.66/1.52 % 4.66/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.66/1.52 % 4.66/1.52 Prover 2: proved (830ms) % 4.66/1.52 % 4.66/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.66/1.52 % 4.66/1.52 Prover 3: stopped % 4.66/1.52 Prover 6: stopped % 4.66/1.52 Prover 0: stopped % 4.66/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.66/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.66/1.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.66/1.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.66/1.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.66/1.57 Prover 11: Preprocessing ... % 4.66/1.57 Prover 7: Preprocessing ... % 4.66/1.57 Prover 10: Preprocessing ... % 4.66/1.58 Prover 8: Preprocessing ... % 5.67/1.60 Prover 13: Preprocessing ... % 5.79/1.62 Prover 7: Warning: ignoring some quantifiers % 5.79/1.64 Prover 10: Warning: ignoring some quantifiers % 5.79/1.64 Prover 7: Constructing countermodel ... % 5.79/1.64 Prover 10: Constructing countermodel ... % 5.79/1.64 Prover 1: Found proof (size 52) % 5.79/1.64 Prover 13: Warning: ignoring some quantifiers % 5.79/1.64 Prover 1: proved (963ms) % 5.79/1.64 Prover 4: stopped % 5.79/1.65 Prover 10: stopped % 5.79/1.65 Prover 7: stopped % 5.79/1.65 Prover 13: Constructing countermodel ... % 5.79/1.65 Prover 13: stopped % 5.79/1.65 Prover 8: Warning: ignoring some quantifiers % 5.79/1.66 Prover 8: Constructing countermodel ... % 5.79/1.66 Prover 8: stopped % 5.79/1.67 Prover 11: Constructing countermodel ... % 5.79/1.68 Prover 11: stopped % 5.79/1.68 % 5.79/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.79/1.68 % 5.79/1.69 % SZS output start Proof for theBenchmark % 5.79/1.69 Assumptions after simplification: % 5.79/1.69 --------------------------------- % 5.79/1.69 % 5.79/1.69 (axiom_0) % 6.34/1.72 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ $i(v0)) & % 6.34/1.72 ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0)) % 6.34/1.72 % 6.34/1.72 (axiom_1) % 6.34/1.72 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ $i(v0) | % 6.34/1.72 xsd_integer(v0) = 0) & ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | % 6.34/1.72 ? [v1: int] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 6.34/1.72 % 6.34/1.72 (axiom_2) % 6.34/1.73 ! [v0: $i] : ( ~ (cc(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: $i] : (v2 % 6.34/1.73 = v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ $i(v2) | ~ % 6.34/1.73 $i(v1)) & ? [v1: $i] : (rp(v0, v1) = 0 & $i(v1)))) % 6.34/1.73 % 6.34/1.73 (the_axiom) % 6.34/1.73 ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 & % 6.34/1.73 xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = % 6.34/1.73 0)))) | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cowlThing(v0) = % 6.34/1.73 v1 & cowlNothing(v0) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) | ? [v0: $i] : % 6.34/1.73 (cc(v0) = 0 & $i(v0) & ! [v1: $i] : ( ~ (rp(v0, v1) = 0) | ~ $i(v1))) | ? % 6.34/1.73 [v0: $i] : (cc(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & % 6.34/1.73 rp(v0, v2) = 0 & rp(v0, v1) = 0 & $i(v2) & $i(v1))) % 6.34/1.73 % 6.34/1.73 (function-axioms) % 6.34/1.74 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 6.34/1.74 [v3: $i] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [v0: % 6.34/1.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 6.34/1.74 ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0: % 6.34/1.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 6.34/1.74 ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0: % 6.34/1.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 6.34/1.74 ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0: % 6.34/1.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 6.34/1.74 ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0: % 6.34/1.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 6.34/1.74 ~ (cc(v2) = v1) | ~ (cc(v2) = v0)) % 6.34/1.74 % 6.34/1.74 Further assumptions not needed in the proof: % 6.34/1.74 -------------------------------------------- % 6.34/1.74 cc_substitution_1, cowlNothing_substitution_1, cowlThing_substitution_1, % 6.34/1.74 rp_substitution_1, rp_substitution_2, xsd_integer_substitution_1, % 6.34/1.74 xsd_string_substitution_1 % 6.34/1.74 % 6.34/1.74 Those formulas are unsatisfiable: % 6.34/1.74 --------------------------------- % 6.34/1.74 % 6.34/1.74 Begin of proof % 6.34/1.74 | % 6.34/1.74 | ALPHA: (axiom_0) implies: % 6.34/1.74 | (1) ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0)) % 6.34/1.74 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ % 6.34/1.74 | $i(v0)) % 6.34/1.74 | % 6.34/1.74 | ALPHA: (axiom_1) implies: % 6.34/1.74 | (3) ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 6.34/1.74 | (v1 = 0) & xsd_integer(v0) = v1)) % 6.34/1.74 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ % 6.34/1.74 | $i(v0) | xsd_integer(v0) = 0) % 6.34/1.74 | % 6.34/1.74 | ALPHA: (function-axioms) implies: % 6.34/1.75 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 6.34/1.75 | (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 6.34/1.75 | % 6.34/1.75 | BETA: splitting (the_axiom) gives: % 6.34/1.75 | % 6.34/1.75 | Case 1: % 6.34/1.75 | | % 6.34/1.75 | | (6) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 & % 6.34/1.75 | | xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & % 6.34/1.75 | | ~ (v1 = 0)))) | ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 6.34/1.75 | | (cowlThing(v0) = v1 & cowlNothing(v0) = v2 & $i(v0) & ( ~ (v1 = 0) | % 6.34/1.75 | | v2 = 0)) % 6.34/1.75 | | % 6.34/1.75 | | BETA: splitting (6) gives: % 6.34/1.75 | | % 6.34/1.75 | | Case 1: % 6.34/1.75 | | | % 6.34/1.75 | | | (7) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 & % 6.34/1.75 | | | xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) % 6.34/1.75 | | | & ~ (v1 = 0)))) % 6.34/1.75 | | | % 6.34/1.75 | | | DELTA: instantiating (7) with fresh symbols all_12_0, all_12_1, all_12_2 % 6.34/1.75 | | | gives: % 6.34/1.75 | | | (8) xsd_string(all_12_2) = all_12_1 & xsd_integer(all_12_2) = all_12_0 % 6.34/1.75 | | | & $i(all_12_2) & ((all_12_0 = 0 & all_12_1 = 0) | ( ~ (all_12_0 = % 6.34/1.75 | | | 0) & ~ (all_12_1 = 0))) % 6.34/1.75 | | | % 6.34/1.75 | | | ALPHA: (8) implies: % 6.34/1.75 | | | (9) $i(all_12_2) % 6.34/1.75 | | | (10) xsd_integer(all_12_2) = all_12_0 % 6.34/1.75 | | | (11) xsd_string(all_12_2) = all_12_1 % 6.34/1.76 | | | (12) (all_12_0 = 0 & all_12_1 = 0) | ( ~ (all_12_0 = 0) & ~ (all_12_1 % 6.34/1.76 | | | = 0)) % 6.34/1.76 | | | % 6.34/1.76 | | | GROUND_INST: instantiating (4) with all_12_2, all_12_1, simplifying with % 6.34/1.76 | | | (9), (11) gives: % 6.34/1.76 | | | (13) all_12_1 = 0 | xsd_integer(all_12_2) = 0 % 6.34/1.76 | | | % 6.34/1.76 | | | BETA: splitting (12) gives: % 6.34/1.76 | | | % 6.34/1.76 | | | Case 1: % 6.34/1.76 | | | | % 6.34/1.76 | | | | (14) all_12_0 = 0 & all_12_1 = 0 % 6.34/1.76 | | | | % 6.34/1.76 | | | | ALPHA: (14) implies: % 6.34/1.76 | | | | (15) all_12_1 = 0 % 6.34/1.76 | | | | (16) all_12_0 = 0 % 6.34/1.76 | | | | % 6.34/1.76 | | | | REDUCE: (11), (15) imply: % 6.34/1.76 | | | | (17) xsd_string(all_12_2) = 0 % 6.34/1.76 | | | | % 6.34/1.76 | | | | REDUCE: (10), (16) imply: % 6.34/1.76 | | | | (18) xsd_integer(all_12_2) = 0 % 6.34/1.76 | | | | % 6.34/1.76 | | | | GROUND_INST: instantiating (3) with all_12_2, simplifying with (9), (17) % 6.34/1.76 | | | | gives: % 6.34/1.76 | | | | (19) ? [v0: int] : ( ~ (v0 = 0) & xsd_integer(all_12_2) = v0) % 6.34/1.76 | | | | % 6.34/1.76 | | | | DELTA: instantiating (19) with fresh symbol all_26_0 gives: % 6.34/1.76 | | | | (20) ~ (all_26_0 = 0) & xsd_integer(all_12_2) = all_26_0 % 6.34/1.76 | | | | % 6.34/1.76 | | | | ALPHA: (20) implies: % 6.34/1.76 | | | | (21) ~ (all_26_0 = 0) % 6.34/1.76 | | | | (22) xsd_integer(all_12_2) = all_26_0 % 6.34/1.76 | | | | % 6.34/1.76 | | | | GROUND_INST: instantiating (5) with 0, all_26_0, all_12_2, simplifying % 6.34/1.76 | | | | with (18), (22) gives: % 6.34/1.76 | | | | (23) all_26_0 = 0 % 6.34/1.76 | | | | % 6.34/1.76 | | | | REDUCE: (21), (23) imply: % 6.34/1.76 | | | | (24) $false % 6.34/1.76 | | | | % 6.34/1.76 | | | | CLOSE: (24) is inconsistent. % 6.34/1.76 | | | | % 6.34/1.76 | | | Case 2: % 6.34/1.76 | | | | % 6.34/1.76 | | | | (25) ~ (all_12_0 = 0) & ~ (all_12_1 = 0) % 6.34/1.76 | | | | % 6.34/1.76 | | | | ALPHA: (25) implies: % 6.34/1.76 | | | | (26) ~ (all_12_1 = 0) % 6.34/1.76 | | | | (27) ~ (all_12_0 = 0) % 6.34/1.76 | | | | % 6.34/1.76 | | | | BETA: splitting (13) gives: % 6.34/1.76 | | | | % 6.34/1.76 | | | | Case 1: % 6.34/1.76 | | | | | % 6.34/1.76 | | | | | (28) xsd_integer(all_12_2) = 0 % 6.34/1.76 | | | | | % 6.34/1.77 | | | | | GROUND_INST: instantiating (5) with all_12_0, 0, all_12_2, simplifying % 6.34/1.77 | | | | | with (10), (28) gives: % 6.34/1.77 | | | | | (29) all_12_0 = 0 % 6.34/1.77 | | | | | % 6.34/1.77 | | | | | REDUCE: (27), (29) imply: % 6.34/1.77 | | | | | (30) $false % 6.34/1.77 | | | | | % 6.34/1.77 | | | | | CLOSE: (30) is inconsistent. % 6.34/1.77 | | | | | % 6.34/1.77 | | | | Case 2: % 6.34/1.77 | | | | | % 6.34/1.77 | | | | | (31) all_12_1 = 0 % 6.34/1.77 | | | | | % 6.34/1.77 | | | | | REDUCE: (26), (31) imply: % 6.34/1.77 | | | | | (32) $false % 6.34/1.77 | | | | | % 6.34/1.77 | | | | | CLOSE: (32) is inconsistent. % 6.34/1.77 | | | | | % 6.34/1.77 | | | | End of split % 6.34/1.77 | | | | % 6.34/1.77 | | | End of split % 6.34/1.77 | | | % 6.34/1.77 | | Case 2: % 6.34/1.77 | | | % 6.34/1.77 | | | (33) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cowlThing(v0) = v1 & % 6.34/1.77 | | | cowlNothing(v0) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 6.34/1.77 | | | % 6.34/1.77 | | | DELTA: instantiating (33) with fresh symbols all_12_0, all_12_1, all_12_2 % 6.34/1.77 | | | gives: % 6.34/1.77 | | | (34) cowlThing(all_12_2) = all_12_1 & cowlNothing(all_12_2) = all_12_0 % 6.34/1.77 | | | & $i(all_12_2) & ( ~ (all_12_1 = 0) | all_12_0 = 0) % 6.34/1.77 | | | % 6.34/1.77 | | | ALPHA: (34) implies: % 6.34/1.77 | | | (35) $i(all_12_2) % 6.34/1.77 | | | (36) cowlNothing(all_12_2) = all_12_0 % 6.34/1.77 | | | (37) cowlThing(all_12_2) = all_12_1 % 6.34/1.77 | | | (38) ~ (all_12_1 = 0) | all_12_0 = 0 % 6.34/1.77 | | | % 6.34/1.77 | | | GROUND_INST: instantiating (2) with all_12_2, all_12_1, simplifying with % 6.34/1.77 | | | (35), (37) gives: % 6.34/1.77 | | | (39) all_12_1 = 0 % 6.34/1.77 | | | % 6.34/1.77 | | | BETA: splitting (38) gives: % 6.34/1.77 | | | % 6.34/1.77 | | | Case 1: % 6.34/1.77 | | | | % 6.34/1.77 | | | | (40) ~ (all_12_1 = 0) % 6.34/1.77 | | | | % 6.34/1.77 | | | | REDUCE: (39), (40) imply: % 6.34/1.77 | | | | (41) $false % 6.34/1.77 | | | | % 6.34/1.77 | | | | CLOSE: (41) is inconsistent. % 6.34/1.77 | | | | % 6.34/1.77 | | | Case 2: % 6.34/1.77 | | | | % 6.34/1.77 | | | | (42) all_12_0 = 0 % 6.34/1.77 | | | | % 6.34/1.77 | | | | REDUCE: (36), (42) imply: % 6.34/1.77 | | | | (43) cowlNothing(all_12_2) = 0 % 6.34/1.77 | | | | % 6.34/1.77 | | | | GROUND_INST: instantiating (1) with all_12_2, simplifying with (35), % 6.34/1.77 | | | | (43) gives: % 6.34/1.77 | | | | (44) $false % 6.34/1.77 | | | | % 6.34/1.77 | | | | CLOSE: (44) is inconsistent. % 6.34/1.77 | | | | % 6.34/1.77 | | | End of split % 6.34/1.77 | | | % 6.34/1.77 | | End of split % 6.34/1.77 | | % 6.34/1.77 | Case 2: % 6.34/1.77 | | % 6.34/1.77 | | (45) ? [v0: $i] : (cc(v0) = 0 & $i(v0) & ! [v1: $i] : ( ~ (rp(v0, v1) = % 6.34/1.77 | | 0) | ~ $i(v1))) | ? [v0: $i] : (cc(v0) = 0 & $i(v0) & ? % 6.34/1.77 | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & rp(v0, v2) = 0 & rp(v0, % 6.34/1.77 | | v1) = 0 & $i(v2) & $i(v1))) % 6.34/1.77 | | % 6.34/1.77 | | BETA: splitting (45) gives: % 6.34/1.77 | | % 6.34/1.77 | | Case 1: % 6.34/1.77 | | | % 6.34/1.77 | | | (46) ? [v0: $i] : (cc(v0) = 0 & $i(v0) & ! [v1: $i] : ( ~ (rp(v0, v1) % 6.34/1.77 | | | = 0) | ~ $i(v1))) % 6.34/1.77 | | | % 6.34/1.77 | | | DELTA: instantiating (46) with fresh symbol all_12_0 gives: % 6.34/1.77 | | | (47) cc(all_12_0) = 0 & $i(all_12_0) & ! [v0: $i] : ( ~ (rp(all_12_0, % 6.34/1.77 | | | v0) = 0) | ~ $i(v0)) % 6.34/1.77 | | | % 6.34/1.77 | | | ALPHA: (47) implies: % 6.34/1.78 | | | (48) $i(all_12_0) % 6.34/1.78 | | | (49) cc(all_12_0) = 0 % 6.34/1.78 | | | (50) ! [v0: $i] : ( ~ (rp(all_12_0, v0) = 0) | ~ $i(v0)) % 6.34/1.78 | | | % 6.34/1.78 | | | GROUND_INST: instantiating (axiom_2) with all_12_0, simplifying with (48), % 6.34/1.78 | | | (49) gives: % 6.34/1.78 | | | (51) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rp(all_12_0, v1) = 0) | % 6.34/1.78 | | | ~ (rp(all_12_0, v0) = 0) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] % 6.34/1.78 | | | : (rp(all_12_0, v0) = 0 & $i(v0)) % 6.34/1.78 | | | % 6.34/1.78 | | | ALPHA: (51) implies: % 6.34/1.78 | | | (52) ? [v0: $i] : (rp(all_12_0, v0) = 0 & $i(v0)) % 6.34/1.78 | | | % 6.34/1.78 | | | DELTA: instantiating (52) with fresh symbol all_21_0 gives: % 6.34/1.78 | | | (53) rp(all_12_0, all_21_0) = 0 & $i(all_21_0) % 6.34/1.78 | | | % 6.34/1.78 | | | ALPHA: (53) implies: % 6.34/1.78 | | | (54) $i(all_21_0) % 6.34/1.78 | | | (55) rp(all_12_0, all_21_0) = 0 % 6.34/1.78 | | | % 6.34/1.78 | | | GROUND_INST: instantiating (50) with all_21_0, simplifying with (54), (55) % 6.34/1.78 | | | gives: % 6.34/1.78 | | | (56) $false % 6.34/1.78 | | | % 6.34/1.78 | | | CLOSE: (56) is inconsistent. % 6.34/1.78 | | | % 6.34/1.78 | | Case 2: % 6.34/1.78 | | | % 6.34/1.78 | | | (57) ? [v0: $i] : (cc(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( % 6.34/1.78 | | | ~ (v2 = v1) & rp(v0, v2) = 0 & rp(v0, v1) = 0 & $i(v2) & % 6.34/1.78 | | | $i(v1))) % 6.34/1.78 | | | % 6.34/1.78 | | | DELTA: instantiating (57) with fresh symbol all_12_0 gives: % 6.34/1.78 | | | (58) cc(all_12_0) = 0 & $i(all_12_0) & ? [v0: $i] : ? [v1: $i] : ( ~ % 6.34/1.78 | | | (v1 = v0) & rp(all_12_0, v1) = 0 & rp(all_12_0, v0) = 0 & $i(v1) % 6.34/1.78 | | | & $i(v0)) % 6.34/1.78 | | | % 6.34/1.78 | | | ALPHA: (58) implies: % 6.34/1.78 | | | (59) $i(all_12_0) % 6.34/1.78 | | | (60) cc(all_12_0) = 0 % 6.34/1.78 | | | (61) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & rp(all_12_0, v1) = 0 & % 6.34/1.78 | | | rp(all_12_0, v0) = 0 & $i(v1) & $i(v0)) % 6.34/1.78 | | | % 6.34/1.78 | | | DELTA: instantiating (61) with fresh symbols all_14_0, all_14_1 gives: % 6.34/1.78 | | | (62) ~ (all_14_0 = all_14_1) & rp(all_12_0, all_14_0) = 0 & % 6.34/1.78 | | | rp(all_12_0, all_14_1) = 0 & $i(all_14_0) & $i(all_14_1) % 6.34/1.78 | | | % 6.34/1.78 | | | ALPHA: (62) implies: % 6.34/1.78 | | | (63) ~ (all_14_0 = all_14_1) % 6.34/1.78 | | | (64) $i(all_14_1) % 6.34/1.78 | | | (65) $i(all_14_0) % 6.34/1.79 | | | (66) rp(all_12_0, all_14_1) = 0 % 6.34/1.79 | | | (67) rp(all_12_0, all_14_0) = 0 % 6.34/1.79 | | | % 6.34/1.79 | | | GROUND_INST: instantiating (axiom_2) with all_12_0, simplifying with (59), % 6.34/1.79 | | | (60) gives: % 6.34/1.79 | | | (68) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rp(all_12_0, v1) = 0) | % 6.34/1.79 | | | ~ (rp(all_12_0, v0) = 0) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] % 6.34/1.79 | | | : (rp(all_12_0, v0) = 0 & $i(v0)) % 6.34/1.79 | | | % 6.34/1.79 | | | ALPHA: (68) implies: % 6.34/1.79 | | | (69) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rp(all_12_0, v1) = 0) | % 6.34/1.79 | | | ~ (rp(all_12_0, v0) = 0) | ~ $i(v1) | ~ $i(v0)) % 6.34/1.79 | | | % 6.34/1.79 | | | GROUND_INST: instantiating (69) with all_14_1, all_14_0, simplifying with % 6.34/1.79 | | | (64), (65), (66), (67) gives: % 6.34/1.79 | | | (70) all_14_0 = all_14_1 % 6.34/1.79 | | | % 6.34/1.79 | | | REDUCE: (63), (70) imply: % 6.34/1.79 | | | (71) $false % 6.34/1.79 | | | % 6.34/1.79 | | | CLOSE: (71) is inconsistent. % 6.34/1.79 | | | % 6.34/1.79 | | End of split % 6.34/1.79 | | % 6.34/1.79 | End of split % 6.34/1.79 | % 6.34/1.79 End of proof % 6.34/1.79 % SZS output end Proof for theBenchmark % 6.34/1.79 % 6.34/1.79 1130ms %------------------------------------------------------------------------------