TSTP Solution File: DAT021_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT021_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.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 : Wed Aug 30 22:18:54 EDT 2023
% Result : Theorem 6.30s 1.64s
% Output : Proof 7.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT021_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n001.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 15:15:41 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.41/1.09 Prover 1: Preprocessing ...
% 2.41/1.09 Prover 4: Preprocessing ...
% 2.63/1.12 Prover 5: Preprocessing ...
% 2.63/1.12 Prover 3: Preprocessing ...
% 2.63/1.12 Prover 2: Preprocessing ...
% 2.63/1.12 Prover 6: Preprocessing ...
% 2.63/1.12 Prover 0: Preprocessing ...
% 3.96/1.31 Prover 4: Constructing countermodel ...
% 3.96/1.31 Prover 1: Constructing countermodel ...
% 3.96/1.31 Prover 5: Proving ...
% 3.96/1.31 Prover 2: Proving ...
% 3.96/1.31 Prover 6: Constructing countermodel ...
% 3.96/1.32 Prover 3: Constructing countermodel ...
% 3.96/1.33 Prover 0: Proving ...
% 6.30/1.63 Prover 3: proved (973ms)
% 6.30/1.63
% 6.30/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.30/1.64
% 6.30/1.64 Prover 6: stopped
% 6.30/1.64 Prover 2: stopped
% 6.30/1.64 Prover 5: stopped
% 6.30/1.64 Prover 0: stopped
% 6.30/1.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.30/1.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.30/1.65 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.30/1.65 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.30/1.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.30/1.66 Prover 1: Found proof (size 71)
% 6.30/1.66 Prover 1: proved (1002ms)
% 6.30/1.67 Prover 4: Found proof (size 69)
% 6.30/1.67 Prover 4: proved (999ms)
% 6.30/1.68 Prover 13: Preprocessing ...
% 6.30/1.68 Prover 8: Preprocessing ...
% 6.64/1.68 Prover 10: Preprocessing ...
% 6.64/1.69 Prover 11: Preprocessing ...
% 6.64/1.69 Prover 7: Preprocessing ...
% 6.64/1.70 Prover 7: stopped
% 6.64/1.70 Prover 10: stopped
% 6.64/1.71 Prover 13: stopped
% 6.64/1.71 Prover 11: stopped
% 6.64/1.73 Prover 8: Warning: ignoring some quantifiers
% 6.64/1.73 Prover 8: Constructing countermodel ...
% 6.64/1.73 Prover 8: stopped
% 6.64/1.73
% 6.64/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.64/1.73
% 6.64/1.74 % SZS output start Proof for theBenchmark
% 6.64/1.75 Assumptions after simplification:
% 6.64/1.75 ---------------------------------
% 6.64/1.75
% 6.64/1.75 (ax1)
% 7.11/1.77 collection(empty) & ! [v0: int] : ~ (in(v0, empty) = 0)
% 7.11/1.77
% 7.11/1.77 (ax4)
% 7.11/1.77 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : !
% 7.11/1.77 [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~
% 7.11/1.77 collection(v1) | ( ~ (v2 = v0) & ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) =
% 7.11/1.77 v5))) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3:
% 7.11/1.77 collection] : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~
% 7.11/1.77 collection(v1) | in(v0, v1) = 0)
% 7.11/1.77
% 7.11/1.77 (co1)
% 7.11/1.77 collection(empty) & ? [v0: collection] : ? [v1: collection] : ? [v2:
% 7.11/1.77 collection] : (add(5, v1) = v2 & add(3, v0) = v1 & add(1, empty) = v0 &
% 7.11/1.78 collection(v2) & collection(v1) & collection(v0) & ? [v3: int] : ? [v4:
% 7.11/1.78 int] : ( ~ (v4 = v3) & $lesseq(9, $sum(v4, v3)) & in(v4, v2) = 0 & in(v3,
% 7.11/1.78 v2) = 0))
% 7.11/1.78
% 7.11/1.78 Further assumptions not needed in the proof:
% 7.11/1.78 --------------------------------------------
% 7.11/1.78 ax2, ax3, ax5
% 7.11/1.78
% 7.11/1.78 Those formulas are unsatisfiable:
% 7.11/1.78 ---------------------------------
% 7.11/1.78
% 7.11/1.78 Begin of proof
% 7.11/1.78 |
% 7.11/1.78 | ALPHA: (ax1) implies:
% 7.11/1.78 | (1) ! [v0: int] : ~ (in(v0, empty) = 0)
% 7.11/1.78 |
% 7.11/1.78 | ALPHA: (ax4) implies:
% 7.11/1.78 | (2) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection]
% 7.11/1.78 | : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~
% 7.11/1.78 | collection(v1) | in(v0, v1) = 0)
% 7.11/1.78 |
% 7.11/1.78 | ALPHA: (co1) implies:
% 7.11/1.78 | (3) collection(empty)
% 7.11/1.78 | (4) ? [v0: collection] : ? [v1: collection] : ? [v2: collection] :
% 7.11/1.78 | (add(5, v1) = v2 & add(3, v0) = v1 & add(1, empty) = v0 &
% 7.11/1.78 | collection(v2) & collection(v1) & collection(v0) & ? [v3: int] : ?
% 7.11/1.78 | [v4: int] : ( ~ (v4 = v3) & $lesseq(9, $sum(v4, v3)) & in(v4, v2) = 0
% 7.11/1.78 | & in(v3, v2) = 0))
% 7.11/1.78 |
% 7.11/1.78 | DELTA: instantiating (4) with fresh symbols all_11_0, all_11_1, all_11_2
% 7.11/1.78 | gives:
% 7.11/1.79 | (5) add(5, all_11_1) = all_11_0 & add(3, all_11_2) = all_11_1 & add(1,
% 7.11/1.79 | empty) = all_11_2 & collection(all_11_0) & collection(all_11_1) &
% 7.11/1.79 | collection(all_11_2) & ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) &
% 7.11/1.79 | $lesseq(9, $sum(v1, v0)) & in(v1, all_11_0) = 0 & in(v0, all_11_0) =
% 7.11/1.79 | 0)
% 7.11/1.79 |
% 7.11/1.79 | ALPHA: (5) implies:
% 7.11/1.79 | (6) collection(all_11_2)
% 7.11/1.79 | (7) collection(all_11_1)
% 7.11/1.79 | (8) add(1, empty) = all_11_2
% 7.11/1.79 | (9) add(3, all_11_2) = all_11_1
% 7.11/1.79 | (10) add(5, all_11_1) = all_11_0
% 7.11/1.79 | (11) ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & $lesseq(9, $sum(v1, v0))
% 7.11/1.79 | & in(v1, all_11_0) = 0 & in(v0, all_11_0) = 0)
% 7.11/1.79 |
% 7.11/1.79 | DELTA: instantiating (11) with fresh symbols all_13_0, all_13_1 gives:
% 7.11/1.79 | (12) ~ (all_13_0 = all_13_1) & $lesseq(9, $sum(all_13_0, all_13_1)) &
% 7.11/1.79 | in(all_13_0, all_11_0) = 0 & in(all_13_1, all_11_0) = 0
% 7.11/1.79 |
% 7.11/1.79 | ALPHA: (12) implies:
% 7.11/1.79 | (13) ~ (all_13_0 = all_13_1)
% 7.11/1.79 | (14) $lesseq(9, $sum(all_13_0, all_13_1))
% 7.11/1.79 | (15) in(all_13_1, all_11_0) = 0
% 7.11/1.79 | (16) in(all_13_0, all_11_0) = 0
% 7.11/1.79 |
% 7.11/1.79 | GROUND_INST: instantiating (2) with all_13_0, all_11_1, 5, all_11_0,
% 7.11/1.79 | simplifying with (7), (10), (16) gives:
% 7.11/1.80 | (17) all_13_0 = 5 | in(all_13_0, all_11_1) = 0
% 7.11/1.80 |
% 7.11/1.80 | GROUND_INST: instantiating (2) with all_13_1, all_11_1, 5, all_11_0,
% 7.11/1.80 | simplifying with (7), (10), (15) gives:
% 7.11/1.80 | (18) all_13_1 = 5 | in(all_13_1, all_11_1) = 0
% 7.11/1.80 |
% 7.11/1.80 | BETA: splitting (18) gives:
% 7.11/1.80 |
% 7.11/1.80 | Case 1:
% 7.11/1.80 | |
% 7.11/1.80 | | (19) in(all_13_1, all_11_1) = 0
% 7.11/1.80 | |
% 7.11/1.80 | | GROUND_INST: instantiating (2) with all_13_1, all_11_2, 3, all_11_1,
% 7.11/1.80 | | simplifying with (6), (9), (19) gives:
% 7.11/1.80 | | (20) all_13_1 = 3 | in(all_13_1, all_11_2) = 0
% 7.11/1.80 | |
% 7.11/1.80 | | BETA: splitting (17) gives:
% 7.11/1.80 | |
% 7.11/1.80 | | Case 1:
% 7.11/1.80 | | |
% 7.11/1.80 | | | (21) in(all_13_0, all_11_1) = 0
% 7.11/1.80 | | |
% 7.11/1.80 | | | GROUND_INST: instantiating (2) with all_13_0, all_11_2, 3, all_11_1,
% 7.11/1.80 | | | simplifying with (6), (9), (21) gives:
% 7.11/1.80 | | | (22) all_13_0 = 3 | in(all_13_0, all_11_2) = 0
% 7.11/1.80 | | |
% 7.11/1.80 | | | BETA: splitting (20) gives:
% 7.11/1.80 | | |
% 7.11/1.80 | | | Case 1:
% 7.11/1.80 | | | |
% 7.11/1.80 | | | | (23) in(all_13_1, all_11_2) = 0
% 7.11/1.80 | | | |
% 7.11/1.80 | | | | GROUND_INST: instantiating (2) with all_13_1, empty, 1, all_11_2,
% 7.11/1.80 | | | | simplifying with (3), (8), (23) gives:
% 7.11/1.80 | | | | (24) all_13_1 = 1 | in(all_13_1, empty) = 0
% 7.11/1.80 | | | |
% 7.11/1.80 | | | | BETA: splitting (22) gives:
% 7.11/1.80 | | | |
% 7.11/1.80 | | | | Case 1:
% 7.11/1.80 | | | | |
% 7.11/1.80 | | | | | (25) in(all_13_0, all_11_2) = 0
% 7.11/1.80 | | | | |
% 7.11/1.80 | | | | | GROUND_INST: instantiating (2) with all_13_0, empty, 1, all_11_2,
% 7.11/1.80 | | | | | simplifying with (3), (8), (25) gives:
% 7.11/1.80 | | | | | (26) all_13_0 = 1 | in(all_13_0, empty) = 0
% 7.11/1.80 | | | | |
% 7.11/1.80 | | | | | BETA: splitting (24) gives:
% 7.11/1.80 | | | | |
% 7.11/1.80 | | | | | Case 1:
% 7.11/1.80 | | | | | |
% 7.11/1.80 | | | | | | (27) in(all_13_1, empty) = 0
% 7.11/1.80 | | | | | |
% 7.11/1.80 | | | | | | GROUND_INST: instantiating (1) with all_13_1, simplifying with (27)
% 7.11/1.80 | | | | | | gives:
% 7.11/1.80 | | | | | | (28) $false
% 7.11/1.80 | | | | | |
% 7.11/1.80 | | | | | | CLOSE: (28) is inconsistent.
% 7.11/1.80 | | | | | |
% 7.11/1.80 | | | | | Case 2:
% 7.11/1.80 | | | | | |
% 7.11/1.80 | | | | | | (29) all_13_1 = 1
% 7.11/1.80 | | | | | |
% 7.11/1.80 | | | | | | REDUCE: (14), (29) imply:
% 7.11/1.80 | | | | | | (30) $lesseq(8, all_13_0)
% 7.11/1.80 | | | | | |
% 7.11/1.80 | | | | | | BETA: splitting (26) gives:
% 7.11/1.80 | | | | | |
% 7.11/1.80 | | | | | | Case 1:
% 7.11/1.80 | | | | | | |
% 7.11/1.81 | | | | | | | (31) in(all_13_0, empty) = 0
% 7.11/1.81 | | | | | | |
% 7.11/1.81 | | | | | | | GROUND_INST: instantiating (1) with all_13_0, simplifying with
% 7.11/1.81 | | | | | | | (31) gives:
% 7.11/1.81 | | | | | | | (32) $false
% 7.11/1.81 | | | | | | |
% 7.11/1.81 | | | | | | | CLOSE: (32) is inconsistent.
% 7.11/1.81 | | | | | | |
% 7.11/1.81 | | | | | | Case 2:
% 7.11/1.81 | | | | | | |
% 7.11/1.81 | | | | | | | (33) all_13_0 = 1
% 7.11/1.81 | | | | | | |
% 7.11/1.81 | | | | | | | REDUCE: (30), (33) imply:
% 7.11/1.81 | | | | | | | (34) $false
% 7.11/1.81 | | | | | | |
% 7.11/1.81 | | | | | | | CLOSE: (34) is inconsistent.
% 7.11/1.81 | | | | | | |
% 7.11/1.81 | | | | | | End of split
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | End of split
% 7.11/1.81 | | | | |
% 7.11/1.81 | | | | Case 2:
% 7.11/1.81 | | | | |
% 7.11/1.81 | | | | | (35) all_13_0 = 3
% 7.11/1.81 | | | | |
% 7.11/1.81 | | | | | REDUCE: (14), (35) imply:
% 7.11/1.81 | | | | | (36) $lesseq(6, all_13_1)
% 7.11/1.81 | | | | |
% 7.11/1.81 | | | | | BETA: splitting (24) gives:
% 7.11/1.81 | | | | |
% 7.11/1.81 | | | | | Case 1:
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | | (37) in(all_13_1, empty) = 0
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | | GROUND_INST: instantiating (1) with all_13_1, simplifying with (37)
% 7.11/1.81 | | | | | | gives:
% 7.11/1.81 | | | | | | (38) $false
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | | CLOSE: (38) is inconsistent.
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | Case 2:
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | | (39) all_13_1 = 1
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | | REDUCE: (36), (39) imply:
% 7.11/1.81 | | | | | | (40) $false
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | | CLOSE: (40) is inconsistent.
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | End of split
% 7.11/1.81 | | | | |
% 7.11/1.81 | | | | End of split
% 7.11/1.81 | | | |
% 7.11/1.81 | | | Case 2:
% 7.11/1.81 | | | |
% 7.11/1.81 | | | | (41) all_13_1 = 3
% 7.11/1.81 | | | |
% 7.11/1.81 | | | | REDUCE: (14), (41) imply:
% 7.11/1.81 | | | | (42) $lesseq(6, all_13_0)
% 7.11/1.81 | | | |
% 7.11/1.81 | | | | BETA: splitting (22) gives:
% 7.11/1.81 | | | |
% 7.11/1.81 | | | | Case 1:
% 7.11/1.81 | | | | |
% 7.11/1.81 | | | | | (43) in(all_13_0, all_11_2) = 0
% 7.11/1.81 | | | | |
% 7.11/1.81 | | | | | GROUND_INST: instantiating (2) with all_13_0, empty, 1, all_11_2,
% 7.11/1.81 | | | | | simplifying with (3), (8), (43) gives:
% 7.11/1.81 | | | | | (44) all_13_0 = 1 | in(all_13_0, empty) = 0
% 7.11/1.81 | | | | |
% 7.11/1.81 | | | | | BETA: splitting (44) gives:
% 7.11/1.81 | | | | |
% 7.11/1.81 | | | | | Case 1:
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | | (45) in(all_13_0, empty) = 0
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | | GROUND_INST: instantiating (1) with all_13_0, simplifying with (45)
% 7.11/1.81 | | | | | | gives:
% 7.11/1.81 | | | | | | (46) $false
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | | CLOSE: (46) is inconsistent.
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | Case 2:
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | | (47) all_13_0 = 1
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | | REDUCE: (42), (47) imply:
% 7.11/1.81 | | | | | | (48) $false
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | | CLOSE: (48) is inconsistent.
% 7.11/1.81 | | | | | |
% 7.11/1.81 | | | | | End of split
% 7.11/1.81 | | | | |
% 7.11/1.81 | | | | Case 2:
% 7.11/1.81 | | | | |
% 7.34/1.81 | | | | | (49) all_13_0 = 3
% 7.34/1.81 | | | | |
% 7.34/1.81 | | | | | REDUCE: (42), (49) imply:
% 7.34/1.81 | | | | | (50) $false
% 7.34/1.81 | | | | |
% 7.34/1.81 | | | | | CLOSE: (50) is inconsistent.
% 7.34/1.81 | | | | |
% 7.34/1.81 | | | | End of split
% 7.34/1.81 | | | |
% 7.34/1.81 | | | End of split
% 7.34/1.81 | | |
% 7.34/1.81 | | Case 2:
% 7.34/1.81 | | |
% 7.34/1.81 | | | (51) all_13_0 = 5
% 7.34/1.81 | | |
% 7.34/1.81 | | | REDUCE: (14), (51) imply:
% 7.34/1.81 | | | (52) $lesseq(4, all_13_1)
% 7.34/1.81 | | |
% 7.34/1.81 | | | BETA: splitting (20) gives:
% 7.34/1.81 | | |
% 7.34/1.81 | | | Case 1:
% 7.34/1.81 | | | |
% 7.34/1.81 | | | | (53) in(all_13_1, all_11_2) = 0
% 7.34/1.81 | | | |
% 7.34/1.81 | | | | GROUND_INST: instantiating (2) with all_13_1, empty, 1, all_11_2,
% 7.34/1.81 | | | | simplifying with (3), (8), (53) gives:
% 7.34/1.82 | | | | (54) all_13_1 = 1 | in(all_13_1, empty) = 0
% 7.34/1.82 | | | |
% 7.34/1.82 | | | | BETA: splitting (54) gives:
% 7.34/1.82 | | | |
% 7.34/1.82 | | | | Case 1:
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | | (55) in(all_13_1, empty) = 0
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | | GROUND_INST: instantiating (1) with all_13_1, simplifying with (55)
% 7.34/1.82 | | | | | gives:
% 7.34/1.82 | | | | | (56) $false
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | | CLOSE: (56) is inconsistent.
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | Case 2:
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | | (57) all_13_1 = 1
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | | REDUCE: (52), (57) imply:
% 7.34/1.82 | | | | | (58) $false
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | | CLOSE: (58) is inconsistent.
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | End of split
% 7.34/1.82 | | | |
% 7.34/1.82 | | | Case 2:
% 7.34/1.82 | | | |
% 7.34/1.82 | | | | (59) all_13_1 = 3
% 7.34/1.82 | | | |
% 7.34/1.82 | | | | REDUCE: (52), (59) imply:
% 7.34/1.82 | | | | (60) $false
% 7.34/1.82 | | | |
% 7.34/1.82 | | | | CLOSE: (60) is inconsistent.
% 7.34/1.82 | | | |
% 7.34/1.82 | | | End of split
% 7.34/1.82 | | |
% 7.34/1.82 | | End of split
% 7.34/1.82 | |
% 7.34/1.82 | Case 2:
% 7.34/1.82 | |
% 7.34/1.82 | | (61) all_13_1 = 5
% 7.34/1.82 | |
% 7.34/1.82 | | REDUCE: (14), (61) imply:
% 7.34/1.82 | | (62) $lesseq(4, all_13_0)
% 7.34/1.82 | |
% 7.34/1.82 | | REDUCE: (13), (61) imply:
% 7.34/1.82 | | (63) ~ (all_13_0 = 5)
% 7.34/1.82 | |
% 7.34/1.82 | | BETA: splitting (17) gives:
% 7.34/1.82 | |
% 7.34/1.82 | | Case 1:
% 7.34/1.82 | | |
% 7.34/1.82 | | | (64) in(all_13_0, all_11_1) = 0
% 7.34/1.82 | | |
% 7.34/1.82 | | | GROUND_INST: instantiating (2) with all_13_0, all_11_2, 3, all_11_1,
% 7.34/1.82 | | | simplifying with (6), (9), (64) gives:
% 7.34/1.82 | | | (65) all_13_0 = 3 | in(all_13_0, all_11_2) = 0
% 7.34/1.82 | | |
% 7.34/1.82 | | | BETA: splitting (65) gives:
% 7.34/1.82 | | |
% 7.34/1.82 | | | Case 1:
% 7.34/1.82 | | | |
% 7.34/1.82 | | | | (66) in(all_13_0, all_11_2) = 0
% 7.34/1.82 | | | |
% 7.34/1.82 | | | | GROUND_INST: instantiating (2) with all_13_0, empty, 1, all_11_2,
% 7.34/1.82 | | | | simplifying with (3), (8), (66) gives:
% 7.34/1.82 | | | | (67) all_13_0 = 1 | in(all_13_0, empty) = 0
% 7.34/1.82 | | | |
% 7.34/1.82 | | | | BETA: splitting (67) gives:
% 7.34/1.82 | | | |
% 7.34/1.82 | | | | Case 1:
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | | (68) in(all_13_0, empty) = 0
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | | GROUND_INST: instantiating (1) with all_13_0, simplifying with (68)
% 7.34/1.82 | | | | | gives:
% 7.34/1.82 | | | | | (69) $false
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | | CLOSE: (69) is inconsistent.
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | Case 2:
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | | (70) all_13_0 = 1
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | | REDUCE: (62), (70) imply:
% 7.34/1.82 | | | | | (71) $false
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | | CLOSE: (71) is inconsistent.
% 7.34/1.82 | | | | |
% 7.34/1.82 | | | | End of split
% 7.34/1.82 | | | |
% 7.34/1.82 | | | Case 2:
% 7.34/1.82 | | | |
% 7.34/1.82 | | | | (72) all_13_0 = 3
% 7.34/1.82 | | | |
% 7.34/1.82 | | | | REDUCE: (62), (72) imply:
% 7.34/1.82 | | | | (73) $false
% 7.34/1.82 | | | |
% 7.34/1.82 | | | | CLOSE: (73) is inconsistent.
% 7.34/1.82 | | | |
% 7.34/1.82 | | | End of split
% 7.34/1.82 | | |
% 7.34/1.82 | | Case 2:
% 7.34/1.82 | | |
% 7.34/1.82 | | | (74) all_13_0 = 5
% 7.34/1.82 | | |
% 7.34/1.82 | | | REDUCE: (63), (74) imply:
% 7.34/1.82 | | | (75) $false
% 7.34/1.82 | | |
% 7.34/1.82 | | | CLOSE: (75) is inconsistent.
% 7.34/1.82 | | |
% 7.34/1.82 | | End of split
% 7.34/1.82 | |
% 7.34/1.82 | End of split
% 7.34/1.82 |
% 7.34/1.82 End of proof
% 7.34/1.82 % SZS output end Proof for theBenchmark
% 7.34/1.82
% 7.34/1.82 1188ms
%------------------------------------------------------------------------------