TSTP Solution File: PUZ133_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : PUZ133_2 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n021.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 13:23:14 EDT 2023
% Result : Theorem 4.65s 1.47s
% Output : Proof 6.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : PUZ133_2 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.19/0.37 % Computer : n021.cluster.edu
% 0.19/0.37 % Model : x86_64 x86_64
% 0.19/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.37 % Memory : 8042.1875MB
% 0.19/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.37 % CPULimit : 300
% 0.19/0.37 % WCLimit : 300
% 0.19/0.37 % DateTime : Sat Aug 26 22:40:57 EDT 2023
% 0.19/0.37 % CPUTime :
% 0.22/0.62 ________ _____
% 0.22/0.62 ___ __ \_________(_)________________________________
% 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.62
% 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.62 (2023-06-19)
% 0.22/0.62
% 0.22/0.62 (c) Philipp Rümmer, 2009-2023
% 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.62 Amanda Stjerna.
% 0.22/0.62 Free software under BSD-3-Clause.
% 0.22/0.62
% 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.62
% 0.22/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.63 Running up to 7 provers in parallel.
% 0.22/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.44/1.07 Prover 1: Preprocessing ...
% 2.44/1.07 Prover 4: Preprocessing ...
% 2.44/1.11 Prover 2: Preprocessing ...
% 2.44/1.11 Prover 0: Preprocessing ...
% 2.44/1.11 Prover 6: Preprocessing ...
% 2.44/1.11 Prover 3: Preprocessing ...
% 2.44/1.11 Prover 5: Preprocessing ...
% 3.70/1.28 Prover 1: Constructing countermodel ...
% 3.70/1.28 Prover 3: Constructing countermodel ...
% 3.70/1.29 Prover 6: Proving ...
% 3.70/1.29 Prover 5: Proving ...
% 3.70/1.29 Prover 4: Constructing countermodel ...
% 4.18/1.31 Prover 0: Proving ...
% 4.18/1.32 Prover 2: Proving ...
% 4.65/1.47 Prover 2: proved (827ms)
% 4.65/1.47
% 4.65/1.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.65/1.47
% 4.65/1.47 Prover 0: stopped
% 4.65/1.47 Prover 6: stopped
% 4.65/1.48 Prover 5: stopped
% 4.65/1.49 Prover 3: stopped
% 4.65/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.65/1.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.65/1.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.65/1.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.65/1.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.65/1.52 Prover 7: Preprocessing ...
% 4.65/1.52 Prover 8: Preprocessing ...
% 4.65/1.53 Prover 10: Preprocessing ...
% 4.65/1.54 Prover 11: Preprocessing ...
% 4.65/1.55 Prover 13: Preprocessing ...
% 4.65/1.60 Prover 1: Found proof (size 49)
% 4.65/1.60 Prover 1: proved (964ms)
% 4.65/1.60 Prover 4: stopped
% 4.65/1.60 Prover 8: Warning: ignoring some quantifiers
% 4.65/1.60 Prover 8: Constructing countermodel ...
% 4.65/1.60 Prover 7: Constructing countermodel ...
% 4.65/1.61 Prover 8: stopped
% 6.28/1.61 Prover 7: stopped
% 6.28/1.61 Prover 11: Constructing countermodel ...
% 6.28/1.61 Prover 13: Warning: ignoring some quantifiers
% 6.28/1.62 Prover 11: stopped
% 6.28/1.62 Prover 10: Constructing countermodel ...
% 6.28/1.62 Prover 13: Constructing countermodel ...
% 6.28/1.62 Prover 10: stopped
% 6.28/1.62 Prover 13: stopped
% 6.28/1.62
% 6.28/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.28/1.62
% 6.28/1.64 % SZS output start Proof for theBenchmark
% 6.28/1.64 Assumptions after simplification:
% 6.28/1.64 ---------------------------------
% 6.28/1.64
% 6.28/1.64 (permutation)
% 6.58/1.66 ! [v0: int] : ! [v1: int] : ($difference($sum(v1, v0), n) = 1 | ~ (perm(v0)
% 6.58/1.66 = v1))
% 6.58/1.66
% 6.58/1.66 (permutation_another_one)
% 6.58/1.66 ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] :
% 6.58/1.66 ($sum($difference(v3, v2), v1) = v0 | ~ (perm(v1) = v3) | ~ (perm(v0) = v2))
% 6.58/1.66
% 6.58/1.66 (queens_p)
% 6.58/1.66 ~ queens_p | ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ( ~
% 6.58/1.66 ($lesseq(v1, n)) | ~ ($lesseq(1, $difference(v1, v0))) | ~ ($lesseq(1,
% 6.58/1.66 v0)) | ~ (p(v1) = v3) | ~ (p(v0) = v2) | ( ~
% 6.58/1.66 ($sum($difference($difference(v3, v2), v1), v0) = 0) & ~
% 6.58/1.66 ($sum($difference(v3, v2), v1) = v0) & ~ (v3 = v2)))
% 6.58/1.66
% 6.58/1.66 (queens_q)
% 6.58/1.66 queens_q | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4:
% 6.58/1.66 int] : ? [v5: int] : ($lesseq(1, $difference(v2, v3)) & $lesseq(v1, n) &
% 6.58/1.66 $lesseq(1, $difference(v1, v0)) & $lesseq(1, v0) & q(v1) = v5 & q(v0) = v4 &
% 6.58/1.67 perm(v1) = v3 & perm(v0) = v2 & ($sum($difference($difference(v5, v4), v1),
% 6.58/1.67 v0) = 0 | $sum($difference(v5, v4), v1) = v0 | v5 = v4))
% 6.58/1.67
% 6.58/1.67 (queens_sym)
% 6.58/1.67 queens_p & ~ queens_q & ! [v0: int] : ! [v1: int] : ( ~ (q(v0) = v1) | ?
% 6.58/1.67 [v2: int] : (perm(v0) = v2 & p(v2) = v1))
% 6.58/1.67
% 6.58/1.67 Further assumptions not needed in the proof:
% 6.58/1.67 --------------------------------------------
% 6.58/1.67 permutation_range
% 6.58/1.67
% 6.58/1.67 Those formulas are unsatisfiable:
% 6.58/1.67 ---------------------------------
% 6.58/1.67
% 6.58/1.67 Begin of proof
% 6.58/1.67 |
% 6.58/1.67 | ALPHA: (queens_sym) implies:
% 6.58/1.67 | (1) ~ queens_q
% 6.58/1.67 | (2) queens_p
% 6.58/1.67 | (3) ! [v0: int] : ! [v1: int] : ( ~ (q(v0) = v1) | ? [v2: int] :
% 6.58/1.67 | (perm(v0) = v2 & p(v2) = v1))
% 6.58/1.67 |
% 6.58/1.67 | BETA: splitting (queens_p) gives:
% 6.58/1.67 |
% 6.58/1.67 | Case 1:
% 6.58/1.67 | |
% 6.58/1.67 | | (4) ~ queens_p
% 6.58/1.67 | |
% 6.58/1.67 | | PRED_UNIFY: (2), (4) imply:
% 6.58/1.67 | | (5) $false
% 6.58/1.67 | |
% 6.58/1.67 | | CLOSE: (5) is inconsistent.
% 6.58/1.67 | |
% 6.58/1.67 | Case 2:
% 6.58/1.67 | |
% 6.58/1.68 | | (6) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ( ~
% 6.58/1.68 | | ($lesseq(v1, n)) | ~ ($lesseq(1, $difference(v1, v0))) | ~
% 6.58/1.68 | | ($lesseq(1, v0)) | ~ (p(v1) = v3) | ~ (p(v0) = v2) | ( ~
% 6.58/1.68 | | ($sum($difference($difference(v3, v2), v1), v0) = 0) & ~
% 6.58/1.68 | | ($sum($difference(v3, v2), v1) = v0) & ~ (v3 = v2)))
% 6.58/1.68 | |
% 6.58/1.68 | | BETA: splitting (queens_q) gives:
% 6.58/1.68 | |
% 6.58/1.68 | | Case 1:
% 6.58/1.68 | | |
% 6.58/1.68 | | | (7) queens_q
% 6.58/1.68 | | |
% 6.58/1.68 | | | PRED_UNIFY: (1), (7) imply:
% 6.58/1.68 | | | (8) $false
% 6.58/1.68 | | |
% 6.58/1.68 | | | CLOSE: (8) is inconsistent.
% 6.58/1.68 | | |
% 6.58/1.68 | | Case 2:
% 6.58/1.68 | | |
% 6.58/1.68 | | | (9) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4:
% 6.58/1.68 | | | int] : ? [v5: int] : ($lesseq(1, $difference(v2, v3)) &
% 6.58/1.68 | | | $lesseq(v1, n) & $lesseq(1, $difference(v1, v0)) & $lesseq(1, v0)
% 6.58/1.68 | | | & q(v1) = v5 & q(v0) = v4 & perm(v1) = v3 & perm(v0) = v2 &
% 6.58/1.68 | | | ($sum($difference($difference(v5, v4), v1), v0) = 0 |
% 6.58/1.68 | | | $sum($difference(v5, v4), v1) = v0 | v5 = v4))
% 6.58/1.68 | | |
% 6.58/1.68 | | | DELTA: instantiating (9) with fresh symbols all_16_0, all_16_1, all_16_2,
% 6.58/1.68 | | | all_16_3, all_16_4, all_16_5 gives:
% 6.58/1.68 | | | (10) $lesseq(1, $difference(all_16_3, all_16_2)) & $lesseq(all_16_4, n)
% 6.78/1.68 | | | & $lesseq(1, $difference(all_16_4, all_16_5)) & $lesseq(1,
% 6.78/1.68 | | | all_16_5) & q(all_16_4) = all_16_0 & q(all_16_5) = all_16_1 &
% 6.78/1.68 | | | perm(all_16_4) = all_16_2 & perm(all_16_5) = all_16_3 &
% 6.78/1.68 | | | ($sum($difference($difference(all_16_0, all_16_1), all_16_4),
% 6.78/1.68 | | | all_16_5) = 0 | $sum($difference(all_16_0, all_16_1),
% 6.78/1.68 | | | all_16_4) = all_16_5 | all_16_0 = all_16_1)
% 6.78/1.68 | | |
% 6.78/1.68 | | | ALPHA: (10) implies:
% 6.78/1.69 | | | (11) $lesseq(1, all_16_5)
% 6.78/1.69 | | | (12) $lesseq(all_16_4, n)
% 6.78/1.69 | | | (13) $lesseq(1, $difference(all_16_3, all_16_2))
% 6.78/1.69 | | | (14) perm(all_16_5) = all_16_3
% 6.78/1.69 | | | (15) perm(all_16_4) = all_16_2
% 6.78/1.69 | | | (16) q(all_16_5) = all_16_1
% 6.78/1.69 | | | (17) q(all_16_4) = all_16_0
% 6.78/1.69 | | | (18) $sum($difference($difference(all_16_0, all_16_1), all_16_4),
% 6.78/1.69 | | | all_16_5) = 0 | $sum($difference(all_16_0, all_16_1), all_16_4)
% 6.78/1.69 | | | = all_16_5 | all_16_0 = all_16_1
% 6.78/1.69 | | |
% 6.78/1.69 | | | GROUND_INST: instantiating (permutation_another_one) with all_16_5,
% 6.78/1.69 | | | all_16_4, all_16_3, all_16_2, simplifying with (14), (15)
% 6.78/1.69 | | | gives:
% 6.78/1.69 | | | (19) $sum($difference(all_16_2, all_16_3), all_16_4) = all_16_5
% 6.78/1.69 | | |
% 6.78/1.69 | | | GROUND_INST: instantiating (permutation) with all_16_4, all_16_2,
% 6.78/1.69 | | | simplifying with (15) gives:
% 6.78/1.69 | | | (20) $difference($sum(all_16_2, all_16_4), n) = 1
% 6.78/1.69 | | |
% 6.78/1.69 | | | COMBINE_EQS: (19), (20) imply:
% 6.78/1.69 | | | (21) $difference($sum(all_16_3, all_16_5), n) = 1
% 6.78/1.69 | | |
% 6.78/1.69 | | | SIMP: (21) implies:
% 6.78/1.69 | | | (22) $difference($sum(all_16_3, all_16_5), n) = 1
% 6.78/1.69 | | |
% 6.78/1.69 | | | REDUCE: (13), (20), (22) imply:
% 6.78/1.69 | | | (23) $lesseq(1, $difference(all_16_4, all_16_5))
% 6.78/1.69 | | |
% 6.78/1.69 | | | GROUND_INST: instantiating (3) with all_16_5, all_16_1, simplifying with
% 6.78/1.69 | | | (16) gives:
% 6.78/1.69 | | | (24) ? [v0: int] : (perm(all_16_5) = v0 & p(v0) = all_16_1)
% 6.78/1.69 | | |
% 6.78/1.69 | | | GROUND_INST: instantiating (3) with all_16_4, all_16_0, simplifying with
% 6.78/1.69 | | | (17) gives:
% 6.78/1.69 | | | (25) ? [v0: int] : (perm(all_16_4) = v0 & p(v0) = all_16_0)
% 6.78/1.70 | | |
% 6.78/1.70 | | | DELTA: instantiating (25) with fresh symbol all_34_0 gives:
% 6.78/1.70 | | | (26) perm(all_16_4) = all_34_0 & p(all_34_0) = all_16_0
% 6.78/1.70 | | |
% 6.78/1.70 | | | ALPHA: (26) implies:
% 6.78/1.70 | | | (27) p(all_34_0) = all_16_0
% 6.78/1.70 | | | (28) perm(all_16_4) = all_34_0
% 6.78/1.70 | | |
% 6.78/1.70 | | | DELTA: instantiating (24) with fresh symbol all_36_0 gives:
% 6.78/1.70 | | | (29) perm(all_16_5) = all_36_0 & p(all_36_0) = all_16_1
% 6.78/1.70 | | |
% 6.78/1.70 | | | ALPHA: (29) implies:
% 6.78/1.70 | | | (30) p(all_36_0) = all_16_1
% 6.78/1.70 | | | (31) perm(all_16_5) = all_36_0
% 6.78/1.70 | | |
% 6.78/1.70 | | | GROUND_INST: instantiating (6) with all_34_0, all_36_0, all_16_0,
% 6.78/1.70 | | | all_16_1, simplifying with (27), (30) gives:
% 6.78/1.70 | | | (32) ~ ($lesseq(all_36_0, n)) | ~ ($lesseq(1, $difference(all_36_0,
% 6.78/1.70 | | | all_34_0))) | ~ ($lesseq(1, all_34_0)) | ( ~
% 6.78/1.70 | | | ($sum($difference($difference(all_36_0, all_34_0), all_16_0),
% 6.78/1.70 | | | all_16_1) = 0) & ~ ($sum($difference(all_36_0, all_34_0),
% 6.78/1.70 | | | all_16_0) = all_16_1) & ~ (all_16_0 = all_16_1))
% 6.78/1.70 | | |
% 6.78/1.70 | | | GROUND_INST: instantiating (permutation) with all_16_5, all_36_0,
% 6.78/1.70 | | | simplifying with (31) gives:
% 6.78/1.70 | | | (33) $difference($sum(all_36_0, all_16_5), n) = 1
% 6.78/1.70 | | |
% 6.78/1.70 | | | GROUND_INST: instantiating (permutation_another_one) with all_16_5,
% 6.78/1.70 | | | all_16_4, all_36_0, all_34_0, simplifying with (28), (31)
% 6.78/1.70 | | | gives:
% 6.78/1.70 | | | (34) $sum($difference($difference(all_36_0, all_34_0), all_16_4),
% 6.78/1.70 | | | all_16_5) = 0
% 6.78/1.70 | | |
% 6.78/1.70 | | | COMBINE_EQS: (33), (34) imply:
% 6.78/1.70 | | | (35) $difference($sum(all_34_0, all_16_4), n) = 1
% 6.78/1.70 | | |
% 6.78/1.70 | | | BETA: splitting (32) gives:
% 6.78/1.70 | | |
% 6.78/1.70 | | | Case 1:
% 6.78/1.70 | | | |
% 6.78/1.70 | | | | (36) $lesseq(1, $difference(all_36_0, n))
% 6.78/1.70 | | | |
% 6.78/1.70 | | | | REDUCE: (33), (36) imply:
% 6.78/1.70 | | | | (37) $lesseq(all_16_5, 0)
% 6.78/1.70 | | | |
% 6.78/1.70 | | | | COMBINE_INEQS: (11), (37) imply:
% 6.78/1.70 | | | | (38) $false
% 6.78/1.70 | | | |
% 6.78/1.70 | | | | CLOSE: (38) is inconsistent.
% 6.78/1.70 | | | |
% 6.78/1.70 | | | Case 2:
% 6.78/1.70 | | | |
% 6.78/1.70 | | | | (39) ~ ($lesseq(1, $difference(all_36_0, all_34_0))) | ~
% 6.78/1.70 | | | | ($lesseq(1, all_34_0)) | ( ~
% 6.78/1.70 | | | | ($sum($difference($difference(all_36_0, all_34_0), all_16_0),
% 6.78/1.70 | | | | all_16_1) = 0) & ~ ($sum($difference(all_36_0, all_34_0),
% 6.78/1.70 | | | | all_16_0) = all_16_1) & ~ (all_16_0 = all_16_1))
% 6.78/1.70 | | | |
% 6.78/1.70 | | | | BETA: splitting (39) gives:
% 6.78/1.70 | | | |
% 6.78/1.71 | | | | Case 1:
% 6.78/1.71 | | | | |
% 6.78/1.71 | | | | | (40) $lesseq(all_34_0, 0)
% 6.78/1.71 | | | | |
% 6.78/1.71 | | | | | REDUCE: (35), (40) imply:
% 6.78/1.71 | | | | | (41) $lesseq(1, $difference(all_16_4, n))
% 6.78/1.71 | | | | |
% 6.78/1.71 | | | | | COMBINE_INEQS: (12), (41) imply:
% 6.78/1.71 | | | | | (42) $false
% 6.78/1.71 | | | | |
% 6.78/1.71 | | | | | CLOSE: (42) is inconsistent.
% 6.78/1.71 | | | | |
% 6.78/1.71 | | | | Case 2:
% 6.78/1.71 | | | | |
% 6.78/1.71 | | | | | (43) ~ ($lesseq(1, $difference(all_36_0, all_34_0))) | ( ~
% 6.78/1.71 | | | | | ($sum($difference($difference(all_36_0, all_34_0),
% 6.78/1.71 | | | | | all_16_0), all_16_1) = 0) & ~
% 6.78/1.71 | | | | | ($sum($difference(all_36_0, all_34_0), all_16_0) = all_16_1)
% 6.78/1.71 | | | | | & ~ (all_16_0 = all_16_1))
% 6.78/1.71 | | | | |
% 6.78/1.71 | | | | | BETA: splitting (43) gives:
% 6.78/1.71 | | | | |
% 6.78/1.71 | | | | | Case 1:
% 6.78/1.71 | | | | | |
% 6.78/1.71 | | | | | | (44) $lesseq(all_36_0, all_34_0)
% 6.78/1.71 | | | | | |
% 6.78/1.71 | | | | | | REDUCE: (33), (35), (44) imply:
% 6.78/1.71 | | | | | | (45) $lesseq(all_16_4, all_16_5)
% 6.78/1.71 | | | | | |
% 6.78/1.71 | | | | | | COMBINE_INEQS: (23), (45) imply:
% 6.78/1.71 | | | | | | (46) $false
% 6.78/1.71 | | | | | |
% 6.78/1.71 | | | | | | CLOSE: (46) is inconsistent.
% 6.78/1.71 | | | | | |
% 6.78/1.71 | | | | | Case 2:
% 6.78/1.71 | | | | | |
% 6.78/1.71 | | | | | | (47) ~ ($sum($difference($difference(all_36_0, all_34_0),
% 6.78/1.71 | | | | | | all_16_0), all_16_1) = 0) & ~
% 6.78/1.71 | | | | | | ($sum($difference(all_36_0, all_34_0), all_16_0) = all_16_1)
% 6.78/1.71 | | | | | | & ~ (all_16_0 = all_16_1)
% 6.78/1.71 | | | | | |
% 6.78/1.71 | | | | | | ALPHA: (47) implies:
% 6.78/1.71 | | | | | | (48) ~ (all_16_0 = all_16_1)
% 6.78/1.71 | | | | | | (49) ~ ($sum($difference(all_36_0, all_34_0), all_16_0) =
% 6.78/1.71 | | | | | | all_16_1)
% 6.78/1.71 | | | | | | (50) ~ ($sum($difference($difference(all_36_0, all_34_0),
% 6.78/1.71 | | | | | | all_16_0), all_16_1) = 0)
% 6.78/1.71 | | | | | |
% 6.78/1.71 | | | | | | REDUCE: (33), (35), (50) imply:
% 6.78/1.71 | | | | | | (51) ~ ($sum($difference($difference(all_16_0, all_16_1),
% 6.78/1.71 | | | | | | all_16_4), all_16_5) = 0)
% 6.78/1.71 | | | | | |
% 6.78/1.71 | | | | | | SIMP: (51) implies:
% 6.78/1.71 | | | | | | (52) ~ ($sum($difference($difference(all_16_0, all_16_1),
% 6.78/1.71 | | | | | | all_16_4), all_16_5) = 0)
% 6.78/1.71 | | | | | |
% 6.78/1.71 | | | | | | REDUCE: (33), (35), (49) imply:
% 6.78/1.71 | | | | | | (53) ~ ($sum($difference(all_16_0, all_16_1), all_16_4) =
% 6.78/1.71 | | | | | | all_16_5)
% 6.78/1.71 | | | | | |
% 6.78/1.71 | | | | | | BETA: splitting (18) gives:
% 6.78/1.71 | | | | | |
% 6.78/1.71 | | | | | | Case 1:
% 6.78/1.71 | | | | | | |
% 6.78/1.71 | | | | | | | (54) all_16_0 = all_16_1
% 6.78/1.71 | | | | | | |
% 6.78/1.71 | | | | | | | REDUCE: (48), (54) imply:
% 6.78/1.71 | | | | | | | (55) $false
% 6.78/1.71 | | | | | | |
% 6.78/1.71 | | | | | | | CLOSE: (55) is inconsistent.
% 6.78/1.71 | | | | | | |
% 6.78/1.71 | | | | | | Case 2:
% 6.78/1.71 | | | | | | |
% 6.78/1.71 | | | | | | | (56) $sum($difference($difference(all_16_0, all_16_1),
% 6.78/1.71 | | | | | | | all_16_4), all_16_5) = 0 | $sum($difference(all_16_0,
% 6.78/1.71 | | | | | | | all_16_1), all_16_4) = all_16_5
% 6.78/1.71 | | | | | | |
% 6.78/1.71 | | | | | | | BETA: splitting (56) gives:
% 6.78/1.71 | | | | | | |
% 6.78/1.71 | | | | | | | Case 1:
% 6.78/1.71 | | | | | | | |
% 6.78/1.71 | | | | | | | | (57) $sum($difference($difference(all_16_0, all_16_1),
% 6.78/1.71 | | | | | | | | all_16_4), all_16_5) = 0
% 6.78/1.71 | | | | | | | |
% 6.78/1.71 | | | | | | | | REDUCE: (52), (57) imply:
% 6.78/1.71 | | | | | | | | (58) $false
% 6.78/1.71 | | | | | | | |
% 6.78/1.71 | | | | | | | | CLOSE: (58) is inconsistent.
% 6.78/1.71 | | | | | | | |
% 6.78/1.71 | | | | | | | Case 2:
% 6.78/1.71 | | | | | | | |
% 6.78/1.71 | | | | | | | | (59) $sum($difference(all_16_0, all_16_1), all_16_4) =
% 6.78/1.71 | | | | | | | | all_16_5
% 6.78/1.71 | | | | | | | |
% 6.78/1.71 | | | | | | | | REDUCE: (53), (59) imply:
% 6.78/1.71 | | | | | | | | (60) $false
% 6.78/1.71 | | | | | | | |
% 6.78/1.71 | | | | | | | | CLOSE: (60) is inconsistent.
% 6.78/1.71 | | | | | | | |
% 6.78/1.71 | | | | | | | End of split
% 6.78/1.71 | | | | | | |
% 6.78/1.71 | | | | | | End of split
% 6.78/1.71 | | | | | |
% 6.78/1.71 | | | | | End of split
% 6.78/1.71 | | | | |
% 6.78/1.71 | | | | End of split
% 6.78/1.71 | | | |
% 6.78/1.71 | | | End of split
% 6.78/1.71 | | |
% 6.78/1.71 | | End of split
% 6.78/1.71 | |
% 6.78/1.71 | End of split
% 6.78/1.71 |
% 6.78/1.71 End of proof
% 6.78/1.71 % SZS output end Proof for theBenchmark
% 6.78/1.72
% 6.78/1.72 1098ms
%------------------------------------------------------------------------------