TSTP Solution File: SET200+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n029.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 15:24:17 EDT 2023
% Result : Theorem 4.46s 1.69s
% Output : Proof 6.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n029.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 : Sat Aug 26 14:34:40 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
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.48/0.98 Prover 4: Preprocessing ...
% 1.48/0.98 Prover 1: Preprocessing ...
% 1.88/1.03 Prover 3: Preprocessing ...
% 1.88/1.03 Prover 6: Preprocessing ...
% 1.88/1.03 Prover 0: Preprocessing ...
% 1.88/1.04 Prover 5: Preprocessing ...
% 1.88/1.04 Prover 2: Preprocessing ...
% 2.78/1.29 Prover 1: Warning: ignoring some quantifiers
% 2.78/1.31 Prover 4: Warning: ignoring some quantifiers
% 2.78/1.31 Prover 3: Warning: ignoring some quantifiers
% 2.78/1.33 Prover 4: Constructing countermodel ...
% 2.78/1.33 Prover 6: Proving ...
% 2.78/1.33 Prover 5: Proving ...
% 2.78/1.33 Prover 0: Proving ...
% 2.78/1.33 Prover 2: Proving ...
% 2.78/1.33 Prover 3: Constructing countermodel ...
% 2.78/1.33 Prover 1: Constructing countermodel ...
% 4.46/1.65 Prover 0: proved (1017ms)
% 4.46/1.67
% 4.46/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.46/1.69
% 4.74/1.70 Prover 3: stopped
% 4.74/1.71 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.74/1.71 Prover 6: stopped
% 4.74/1.73 Prover 2: stopped
% 4.74/1.74 Prover 5: stopped
% 4.74/1.75 Prover 7: Preprocessing ...
% 4.74/1.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.74/1.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.74/1.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.74/1.77 Prover 8: Preprocessing ...
% 4.74/1.77 Prover 10: Preprocessing ...
% 4.74/1.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.74/1.77 Prover 7: Warning: ignoring some quantifiers
% 4.74/1.78 Prover 11: Preprocessing ...
% 4.74/1.78 Prover 7: Constructing countermodel ...
% 4.74/1.78 Prover 13: Preprocessing ...
% 5.29/1.81 Prover 10: Warning: ignoring some quantifiers
% 5.29/1.82 Prover 8: Warning: ignoring some quantifiers
% 5.29/1.82 Prover 10: Constructing countermodel ...
% 5.29/1.85 Prover 8: Constructing countermodel ...
% 5.29/1.86 Prover 13: Warning: ignoring some quantifiers
% 5.29/1.86 Prover 13: Constructing countermodel ...
% 5.29/1.88 Prover 11: Warning: ignoring some quantifiers
% 5.29/1.89 Prover 1: Found proof (size 38)
% 5.29/1.89 Prover 4: Found proof (size 69)
% 5.29/1.89 Prover 11: Constructing countermodel ...
% 5.29/1.90 Prover 4: proved (1217ms)
% 5.29/1.90 Prover 1: proved (1251ms)
% 5.29/1.90 Prover 13: stopped
% 5.29/1.90 Prover 8: stopped
% 5.29/1.90 Prover 7: stopped
% 5.29/1.90 Prover 10: gave up
% 5.29/1.90 Prover 11: stopped
% 5.29/1.90
% 5.29/1.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.29/1.90
% 5.74/1.92 % SZS output start Proof for theBenchmark
% 5.74/1.92 Assumptions after simplification:
% 5.74/1.92 ---------------------------------
% 5.74/1.92
% 5.74/1.92 (commutativity_of_union)
% 5.74/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~ $i(v1)
% 5.74/1.96 | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] :
% 5.74/1.96 ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (union(v1, v0)
% 5.74/1.96 = v2 & $i(v2)))
% 5.74/1.96
% 5.74/1.96 (prove_th34)
% 5.74/1.96 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 5.74/1.96 $i] : ? [v6: int] : ( ~ (v6 = 0) & subset(v4, v5) = v6 & subset(v2, v3) = 0
% 5.74/1.96 & subset(v0, v1) = 0 & union(v1, v3) = v5 & union(v0, v2) = v4 & $i(v5) &
% 5.74/1.96 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 5.74/1.96
% 5.74/1.96 (subset_defn)
% 5.74/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 5.74/1.97 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 5.74/1.97 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] :
% 5.74/1.97 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) |
% 5.74/1.97 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 &
% 5.74/1.97 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 5.74/1.97 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 5.74/1.97 ~ $i(v0) | member(v2, v1) = 0)
% 5.74/1.97
% 5.74/1.97 (union_defn)
% 5.74/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 5.74/1.97 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 5.74/1.97 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 5.74/1.97 member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 5.74/1.97 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0)
% 5.74/1.97 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 5.74/1.97 (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0)))
% 5.74/1.97
% 5.74/1.97 (function-axioms)
% 5.74/1.98 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 5.74/1.98 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 5.74/1.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.74/1.98 (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 5.74/1.98 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.74/1.98 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 5.74/1.98
% 5.74/1.98 Further assumptions not needed in the proof:
% 5.74/1.98 --------------------------------------------
% 5.74/1.98 equal_member_defn, reflexivity_of_subset
% 5.74/1.98
% 5.74/1.98 Those formulas are unsatisfiable:
% 5.74/1.98 ---------------------------------
% 5.74/1.98
% 5.74/1.98 Begin of proof
% 5.74/1.98 |
% 5.74/1.98 | ALPHA: (union_defn) implies:
% 6.05/1.99 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0,
% 6.05/1.99 | v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 6.05/1.99 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v2, v1) = v5 &
% 6.05/1.99 | member(v2, v0) = v4 & (v5 = 0 | v4 = 0)))
% 6.05/1.99 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 6.05/1.99 | (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~
% 6.05/1.99 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 6.05/1.99 | (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) =
% 6.05/1.99 | v5))
% 6.05/2.00 |
% 6.05/2.00 | ALPHA: (subset_defn) implies:
% 6.05/2.00 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 6.05/2.00 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 6.05/2.00 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 6.05/2.00 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 6.05/2.00 | (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~
% 6.05/2.00 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) =
% 6.05/2.00 | v4))
% 6.05/2.00 |
% 6.05/2.00 | ALPHA: (commutativity_of_union) implies:
% 6.05/2.00 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~
% 6.05/2.00 | $i(v1) | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2)))
% 6.05/2.00 |
% 6.05/2.00 | ALPHA: (function-axioms) implies:
% 6.05/2.00 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.05/2.00 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 6.05/2.00 | = v0))
% 6.05/2.00 |
% 6.05/2.00 | DELTA: instantiating (prove_th34) with fresh symbols all_8_0, all_8_1,
% 6.05/2.00 | all_8_2, all_8_3, all_8_4, all_8_5, all_8_6 gives:
% 6.05/2.01 | (7) ~ (all_8_0 = 0) & subset(all_8_2, all_8_1) = all_8_0 & subset(all_8_4,
% 6.05/2.01 | all_8_3) = 0 & subset(all_8_6, all_8_5) = 0 & union(all_8_5, all_8_3)
% 6.05/2.01 | = all_8_1 & union(all_8_6, all_8_4) = all_8_2 & $i(all_8_1) &
% 6.05/2.01 | $i(all_8_2) & $i(all_8_3) & $i(all_8_4) & $i(all_8_5) & $i(all_8_6)
% 6.05/2.01 |
% 6.05/2.01 | ALPHA: (7) implies:
% 6.05/2.01 | (8) ~ (all_8_0 = 0)
% 6.05/2.01 | (9) $i(all_8_6)
% 6.05/2.01 | (10) $i(all_8_5)
% 6.05/2.01 | (11) $i(all_8_4)
% 6.05/2.01 | (12) $i(all_8_3)
% 6.05/2.01 | (13) union(all_8_6, all_8_4) = all_8_2
% 6.05/2.01 | (14) union(all_8_5, all_8_3) = all_8_1
% 6.05/2.01 | (15) subset(all_8_6, all_8_5) = 0
% 6.05/2.01 | (16) subset(all_8_4, all_8_3) = 0
% 6.05/2.01 | (17) subset(all_8_2, all_8_1) = all_8_0
% 6.05/2.01 |
% 6.05/2.01 | GROUND_INST: instantiating (5) with all_8_4, all_8_6, all_8_2, simplifying
% 6.05/2.01 | with (9), (11), (13) gives:
% 6.05/2.01 | (18) union(all_8_4, all_8_6) = all_8_2 & $i(all_8_2)
% 6.05/2.01 |
% 6.05/2.01 | ALPHA: (18) implies:
% 6.05/2.01 | (19) $i(all_8_2)
% 6.05/2.01 | (20) union(all_8_4, all_8_6) = all_8_2
% 6.05/2.01 |
% 6.05/2.01 | GROUND_INST: instantiating (5) with all_8_3, all_8_5, all_8_1, simplifying
% 6.05/2.01 | with (10), (12), (14) gives:
% 6.05/2.01 | (21) union(all_8_3, all_8_5) = all_8_1 & $i(all_8_1)
% 6.05/2.01 |
% 6.05/2.01 | ALPHA: (21) implies:
% 6.05/2.01 | (22) $i(all_8_1)
% 6.05/2.02 | (23) union(all_8_3, all_8_5) = all_8_1
% 6.05/2.02 |
% 6.05/2.02 | GROUND_INST: instantiating (3) with all_8_2, all_8_1, all_8_0, simplifying
% 6.05/2.02 | with (17), (19), (22) gives:
% 6.05/2.02 | (24) all_8_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 6.05/2.02 | all_8_1) = v1 & member(v0, all_8_2) = 0 & $i(v0))
% 6.05/2.02 |
% 6.05/2.02 | BETA: splitting (24) gives:
% 6.05/2.02 |
% 6.05/2.02 | Case 1:
% 6.05/2.02 | |
% 6.05/2.02 | | (25) all_8_0 = 0
% 6.05/2.02 | |
% 6.05/2.02 | | REDUCE: (8), (25) imply:
% 6.05/2.02 | | (26) $false
% 6.05/2.02 | |
% 6.05/2.02 | | CLOSE: (26) is inconsistent.
% 6.05/2.02 | |
% 6.05/2.02 | Case 2:
% 6.05/2.02 | |
% 6.05/2.02 | | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_8_1) = v1
% 6.05/2.02 | | & member(v0, all_8_2) = 0 & $i(v0))
% 6.05/2.02 | |
% 6.05/2.02 | | DELTA: instantiating (27) with fresh symbols all_20_0, all_20_1 gives:
% 6.05/2.02 | | (28) ~ (all_20_0 = 0) & member(all_20_1, all_8_1) = all_20_0 &
% 6.05/2.02 | | member(all_20_1, all_8_2) = 0 & $i(all_20_1)
% 6.05/2.02 | |
% 6.05/2.02 | | ALPHA: (28) implies:
% 6.05/2.02 | | (29) ~ (all_20_0 = 0)
% 6.05/2.02 | | (30) $i(all_20_1)
% 6.05/2.02 | | (31) member(all_20_1, all_8_2) = 0
% 6.05/2.02 | | (32) member(all_20_1, all_8_1) = all_20_0
% 6.05/2.02 | |
% 6.05/2.02 | | GROUND_INST: instantiating (1) with all_8_6, all_8_4, all_20_1, all_8_2,
% 6.05/2.02 | | simplifying with (9), (11), (13), (30), (31) gives:
% 6.05/2.03 | | (33) ? [v0: any] : ? [v1: any] : (member(all_20_1, all_8_4) = v1 &
% 6.05/2.03 | | member(all_20_1, all_8_6) = v0 & (v1 = 0 | v0 = 0))
% 6.05/2.03 | |
% 6.05/2.03 | | GROUND_INST: instantiating (2) with all_8_5, all_8_3, all_20_1, all_8_1,
% 6.05/2.03 | | all_20_0, simplifying with (10), (12), (14), (30), (32) gives:
% 6.05/2.03 | | (34) all_20_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 =
% 6.05/2.03 | | 0) & member(all_20_1, all_8_3) = v1 & member(all_20_1, all_8_5)
% 6.05/2.03 | | = v0)
% 6.05/2.03 | |
% 6.05/2.03 | | GROUND_INST: instantiating (1) with all_8_4, all_8_6, all_20_1, all_8_2,
% 6.05/2.03 | | simplifying with (9), (11), (20), (30), (31) gives:
% 6.05/2.03 | | (35) ? [v0: any] : ? [v1: any] : (member(all_20_1, all_8_4) = v0 &
% 6.05/2.03 | | member(all_20_1, all_8_6) = v1 & (v1 = 0 | v0 = 0))
% 6.05/2.03 | |
% 6.05/2.03 | | GROUND_INST: instantiating (2) with all_8_3, all_8_5, all_20_1, all_8_1,
% 6.05/2.03 | | all_20_0, simplifying with (10), (12), (23), (30), (32) gives:
% 6.05/2.03 | | (36) all_20_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 =
% 6.05/2.03 | | 0) & member(all_20_1, all_8_3) = v0 & member(all_20_1, all_8_5)
% 6.05/2.03 | | = v1)
% 6.05/2.03 | |
% 6.05/2.03 | | DELTA: instantiating (35) with fresh symbols all_27_0, all_27_1 gives:
% 6.05/2.03 | | (37) member(all_20_1, all_8_4) = all_27_1 & member(all_20_1, all_8_6) =
% 6.05/2.03 | | all_27_0 & (all_27_0 = 0 | all_27_1 = 0)
% 6.05/2.03 | |
% 6.05/2.03 | | ALPHA: (37) implies:
% 6.05/2.03 | | (38) member(all_20_1, all_8_6) = all_27_0
% 6.05/2.03 | | (39) member(all_20_1, all_8_4) = all_27_1
% 6.05/2.03 | |
% 6.05/2.03 | | DELTA: instantiating (33) with fresh symbols all_29_0, all_29_1 gives:
% 6.05/2.03 | | (40) member(all_20_1, all_8_4) = all_29_0 & member(all_20_1, all_8_6) =
% 6.05/2.03 | | all_29_1 & (all_29_0 = 0 | all_29_1 = 0)
% 6.05/2.03 | |
% 6.05/2.03 | | ALPHA: (40) implies:
% 6.05/2.03 | | (41) member(all_20_1, all_8_6) = all_29_1
% 6.05/2.03 | | (42) member(all_20_1, all_8_4) = all_29_0
% 6.05/2.03 | | (43) all_29_0 = 0 | all_29_1 = 0
% 6.05/2.03 | |
% 6.05/2.03 | | BETA: splitting (36) gives:
% 6.05/2.03 | |
% 6.05/2.03 | | Case 1:
% 6.05/2.03 | | |
% 6.05/2.03 | | | (44) all_20_0 = 0
% 6.05/2.03 | | |
% 6.05/2.04 | | | REDUCE: (29), (44) imply:
% 6.05/2.04 | | | (45) $false
% 6.05/2.04 | | |
% 6.05/2.04 | | | CLOSE: (45) is inconsistent.
% 6.05/2.04 | | |
% 6.05/2.04 | | Case 2:
% 6.05/2.04 | | |
% 6.05/2.04 | | | (46) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 6.05/2.04 | | | member(all_20_1, all_8_3) = v0 & member(all_20_1, all_8_5) = v1)
% 6.05/2.04 | | |
% 6.05/2.04 | | | DELTA: instantiating (46) with fresh symbols all_35_0, all_35_1 gives:
% 6.05/2.04 | | | (47) ~ (all_35_0 = 0) & ~ (all_35_1 = 0) & member(all_20_1, all_8_3)
% 6.05/2.04 | | | = all_35_1 & member(all_20_1, all_8_5) = all_35_0
% 6.05/2.04 | | |
% 6.05/2.04 | | | ALPHA: (47) implies:
% 6.05/2.04 | | | (48) member(all_20_1, all_8_5) = all_35_0
% 6.05/2.04 | | | (49) member(all_20_1, all_8_3) = all_35_1
% 6.05/2.04 | | |
% 6.05/2.04 | | | BETA: splitting (34) gives:
% 6.05/2.04 | | |
% 6.05/2.04 | | | Case 1:
% 6.05/2.04 | | | |
% 6.05/2.04 | | | | (50) all_20_0 = 0
% 6.05/2.04 | | | |
% 6.05/2.04 | | | | REDUCE: (29), (50) imply:
% 6.05/2.04 | | | | (51) $false
% 6.05/2.04 | | | |
% 6.05/2.04 | | | | CLOSE: (51) is inconsistent.
% 6.05/2.04 | | | |
% 6.05/2.04 | | | Case 2:
% 6.05/2.04 | | | |
% 6.05/2.04 | | | | (52) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 6.05/2.04 | | | | member(all_20_1, all_8_3) = v1 & member(all_20_1, all_8_5) =
% 6.05/2.04 | | | | v0)
% 6.05/2.04 | | | |
% 6.05/2.04 | | | | DELTA: instantiating (52) with fresh symbols all_40_0, all_40_1 gives:
% 6.05/2.06 | | | | (53) ~ (all_40_0 = 0) & ~ (all_40_1 = 0) & member(all_20_1,
% 6.05/2.06 | | | | all_8_3) = all_40_0 & member(all_20_1, all_8_5) = all_40_1
% 6.05/2.06 | | | |
% 6.05/2.06 | | | | ALPHA: (53) implies:
% 6.05/2.06 | | | | (54) ~ (all_40_1 = 0)
% 6.05/2.06 | | | | (55) ~ (all_40_0 = 0)
% 6.05/2.06 | | | | (56) member(all_20_1, all_8_5) = all_40_1
% 6.05/2.06 | | | | (57) member(all_20_1, all_8_3) = all_40_0
% 6.05/2.06 | | | |
% 6.05/2.06 | | | | GROUND_INST: instantiating (6) with all_27_0, all_29_1, all_8_6,
% 6.05/2.06 | | | | all_20_1, simplifying with (38), (41) gives:
% 6.05/2.06 | | | | (58) all_29_1 = all_27_0
% 6.05/2.06 | | | |
% 6.05/2.06 | | | | GROUND_INST: instantiating (6) with all_35_0, all_40_1, all_8_5,
% 6.05/2.06 | | | | all_20_1, simplifying with (48), (56) gives:
% 6.05/2.06 | | | | (59) all_40_1 = all_35_0
% 6.05/2.06 | | | |
% 6.05/2.06 | | | | GROUND_INST: instantiating (6) with all_27_1, all_29_0, all_8_4,
% 6.05/2.06 | | | | all_20_1, simplifying with (39), (42) gives:
% 6.05/2.06 | | | | (60) all_29_0 = all_27_1
% 6.05/2.06 | | | |
% 6.05/2.06 | | | | GROUND_INST: instantiating (6) with all_35_1, all_40_0, all_8_3,
% 6.05/2.06 | | | | all_20_1, simplifying with (49), (57) gives:
% 6.05/2.06 | | | | (61) all_40_0 = all_35_1
% 6.05/2.06 | | | |
% 6.05/2.06 | | | | REDUCE: (55), (61) imply:
% 6.05/2.06 | | | | (62) ~ (all_35_1 = 0)
% 6.05/2.06 | | | |
% 6.05/2.06 | | | | REDUCE: (54), (59) imply:
% 6.05/2.06 | | | | (63) ~ (all_35_0 = 0)
% 6.05/2.06 | | | |
% 6.05/2.06 | | | | GROUND_INST: instantiating (4) with all_8_6, all_8_5, all_20_1,
% 6.05/2.06 | | | | all_35_0, simplifying with (9), (10), (15), (30), (48)
% 6.05/2.06 | | | | gives:
% 6.05/2.06 | | | | (64) all_35_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_20_1,
% 6.05/2.06 | | | | all_8_6) = v0)
% 6.05/2.06 | | | |
% 6.05/2.06 | | | | GROUND_INST: instantiating (4) with all_8_4, all_8_3, all_20_1,
% 6.05/2.06 | | | | all_35_1, simplifying with (11), (12), (16), (30), (49)
% 6.05/2.06 | | | | gives:
% 6.05/2.06 | | | | (65) all_35_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_20_1,
% 6.05/2.06 | | | | all_8_4) = v0)
% 6.05/2.06 | | | |
% 6.05/2.06 | | | | BETA: splitting (65) gives:
% 6.05/2.06 | | | |
% 6.05/2.06 | | | | Case 1:
% 6.05/2.06 | | | | |
% 6.05/2.06 | | | | | (66) all_35_1 = 0
% 6.05/2.06 | | | | |
% 6.05/2.06 | | | | | REDUCE: (62), (66) imply:
% 6.05/2.06 | | | | | (67) $false
% 6.05/2.06 | | | | |
% 6.05/2.06 | | | | | CLOSE: (67) is inconsistent.
% 6.05/2.06 | | | | |
% 6.05/2.06 | | | | Case 2:
% 6.05/2.06 | | | | |
% 6.05/2.07 | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & member(all_20_1, all_8_4) = v0)
% 6.05/2.07 | | | | |
% 6.05/2.07 | | | | | DELTA: instantiating (68) with fresh symbol all_57_0 gives:
% 6.05/2.07 | | | | | (69) ~ (all_57_0 = 0) & member(all_20_1, all_8_4) = all_57_0
% 6.05/2.07 | | | | |
% 6.05/2.07 | | | | | ALPHA: (69) implies:
% 6.05/2.07 | | | | | (70) ~ (all_57_0 = 0)
% 6.05/2.07 | | | | | (71) member(all_20_1, all_8_4) = all_57_0
% 6.05/2.07 | | | | |
% 6.05/2.07 | | | | | BETA: splitting (64) gives:
% 6.05/2.07 | | | | |
% 6.05/2.07 | | | | | Case 1:
% 6.05/2.07 | | | | | |
% 6.05/2.07 | | | | | | (72) all_35_0 = 0
% 6.05/2.07 | | | | | |
% 6.05/2.07 | | | | | | REDUCE: (63), (72) imply:
% 6.05/2.07 | | | | | | (73) $false
% 6.05/2.07 | | | | | |
% 6.05/2.07 | | | | | | CLOSE: (73) is inconsistent.
% 6.05/2.07 | | | | | |
% 6.05/2.07 | | | | | Case 2:
% 6.05/2.07 | | | | | |
% 6.05/2.07 | | | | | | (74) ? [v0: int] : ( ~ (v0 = 0) & member(all_20_1, all_8_6) =
% 6.05/2.07 | | | | | | v0)
% 6.05/2.07 | | | | | |
% 6.05/2.07 | | | | | | DELTA: instantiating (74) with fresh symbol all_63_0 gives:
% 6.05/2.07 | | | | | | (75) ~ (all_63_0 = 0) & member(all_20_1, all_8_6) = all_63_0
% 6.05/2.07 | | | | | |
% 6.05/2.07 | | | | | | ALPHA: (75) implies:
% 6.05/2.07 | | | | | | (76) ~ (all_63_0 = 0)
% 6.05/2.07 | | | | | | (77) member(all_20_1, all_8_6) = all_63_0
% 6.05/2.07 | | | | | |
% 6.05/2.07 | | | | | | GROUND_INST: instantiating (6) with all_27_0, all_63_0, all_8_6,
% 6.05/2.07 | | | | | | all_20_1, simplifying with (38), (77) gives:
% 6.05/2.07 | | | | | | (78) all_63_0 = all_27_0
% 6.05/2.07 | | | | | |
% 6.05/2.07 | | | | | | GROUND_INST: instantiating (6) with all_27_1, all_57_0, all_8_4,
% 6.05/2.07 | | | | | | all_20_1, simplifying with (39), (71) gives:
% 6.05/2.07 | | | | | | (79) all_57_0 = all_27_1
% 6.05/2.07 | | | | | |
% 6.05/2.07 | | | | | | REDUCE: (76), (78) imply:
% 6.05/2.07 | | | | | | (80) ~ (all_27_0 = 0)
% 6.05/2.07 | | | | | |
% 6.05/2.07 | | | | | | REDUCE: (70), (79) imply:
% 6.05/2.07 | | | | | | (81) ~ (all_27_1 = 0)
% 6.05/2.07 | | | | | |
% 6.05/2.07 | | | | | | BETA: splitting (43) gives:
% 6.05/2.07 | | | | | |
% 6.05/2.07 | | | | | | Case 1:
% 6.05/2.07 | | | | | | |
% 6.05/2.07 | | | | | | | (82) all_29_0 = 0
% 6.05/2.07 | | | | | | |
% 6.05/2.07 | | | | | | | COMBINE_EQS: (60), (82) imply:
% 6.05/2.07 | | | | | | | (83) all_27_1 = 0
% 6.05/2.07 | | | | | | |
% 6.05/2.07 | | | | | | | SIMP: (83) implies:
% 6.05/2.07 | | | | | | | (84) all_27_1 = 0
% 6.05/2.07 | | | | | | |
% 6.05/2.07 | | | | | | | REDUCE: (81), (84) imply:
% 6.05/2.07 | | | | | | | (85) $false
% 6.05/2.07 | | | | | | |
% 6.05/2.07 | | | | | | | CLOSE: (85) is inconsistent.
% 6.05/2.07 | | | | | | |
% 6.05/2.07 | | | | | | Case 2:
% 6.05/2.07 | | | | | | |
% 6.05/2.07 | | | | | | | (86) all_29_1 = 0
% 6.05/2.07 | | | | | | |
% 6.05/2.07 | | | | | | | COMBINE_EQS: (58), (86) imply:
% 6.05/2.07 | | | | | | | (87) all_27_0 = 0
% 6.05/2.07 | | | | | | |
% 6.05/2.07 | | | | | | | REDUCE: (80), (87) imply:
% 6.05/2.07 | | | | | | | (88) $false
% 6.05/2.07 | | | | | | |
% 6.05/2.07 | | | | | | | CLOSE: (88) is inconsistent.
% 6.05/2.08 | | | | | | |
% 6.05/2.08 | | | | | | End of split
% 6.05/2.08 | | | | | |
% 6.05/2.08 | | | | | End of split
% 6.05/2.08 | | | | |
% 6.05/2.08 | | | | End of split
% 6.05/2.08 | | | |
% 6.05/2.08 | | | End of split
% 6.05/2.08 | | |
% 6.05/2.08 | | End of split
% 6.05/2.08 | |
% 6.05/2.08 | End of split
% 6.05/2.08 |
% 6.05/2.08 End of proof
% 6.05/2.08 % SZS output end Proof for theBenchmark
% 6.05/2.08
% 6.05/2.08 1460ms
%------------------------------------------------------------------------------