TSTP Solution File: KLE002+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE002+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : Thu Aug 31 05:34:08 EDT 2023
% Result : Theorem 6.23s 1.72s
% Output : Proof 7.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE002+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 : Tue Aug 29 12:33:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.68 ________ _____
% 0.19/0.68 ___ __ \_________(_)________________________________
% 0.19/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.68
% 0.19/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.68 (2023-06-19)
% 0.19/0.68
% 0.19/0.68 (c) Philipp Rümmer, 2009-2023
% 0.19/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.68 Amanda Stjerna.
% 0.19/0.68 Free software under BSD-3-Clause.
% 0.19/0.68
% 0.19/0.68 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.68
% 0.19/0.68 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.70 Running up to 7 provers in parallel.
% 0.19/0.73 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.73 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.73 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.73 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.73 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.73 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.73 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.50/1.19 Prover 1: Preprocessing ...
% 2.50/1.20 Prover 4: Preprocessing ...
% 2.50/1.26 Prover 5: Preprocessing ...
% 2.50/1.26 Prover 2: Preprocessing ...
% 2.50/1.26 Prover 6: Preprocessing ...
% 2.50/1.26 Prover 3: Preprocessing ...
% 2.50/1.26 Prover 0: Preprocessing ...
% 4.11/1.54 Prover 3: Constructing countermodel ...
% 4.11/1.56 Prover 6: Constructing countermodel ...
% 4.11/1.56 Prover 1: Constructing countermodel ...
% 4.11/1.57 Prover 4: Constructing countermodel ...
% 5.24/1.59 Prover 0: Proving ...
% 5.24/1.59 Prover 5: Proving ...
% 5.84/1.69 Prover 2: Proving ...
% 6.23/1.72 Prover 3: proved (993ms)
% 6.23/1.72
% 6.23/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.23/1.72
% 6.23/1.72 Prover 6: stopped
% 6.23/1.73 Prover 5: stopped
% 6.23/1.73 Prover 2: stopped
% 6.23/1.73 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.23/1.73 Prover 0: stopped
% 6.23/1.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.23/1.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.23/1.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.23/1.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.23/1.74 Prover 7: Preprocessing ...
% 6.48/1.76 Prover 8: Preprocessing ...
% 6.48/1.76 Prover 10: Preprocessing ...
% 6.48/1.77 Prover 11: Preprocessing ...
% 6.48/1.78 Prover 13: Preprocessing ...
% 6.48/1.78 Prover 1: Found proof (size 19)
% 6.48/1.78 Prover 1: proved (1073ms)
% 6.48/1.79 Prover 4: stopped
% 6.48/1.80 Prover 11: stopped
% 6.48/1.80 Prover 10: stopped
% 6.48/1.81 Prover 13: stopped
% 6.48/1.82 Prover 7: Constructing countermodel ...
% 7.03/1.83 Prover 8: Warning: ignoring some quantifiers
% 7.03/1.83 Prover 7: stopped
% 7.03/1.84 Prover 8: Constructing countermodel ...
% 7.03/1.85 Prover 8: stopped
% 7.03/1.85
% 7.03/1.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.03/1.85
% 7.03/1.85 % SZS output start Proof for theBenchmark
% 7.03/1.86 Assumptions after simplification:
% 7.03/1.86 ---------------------------------
% 7.03/1.86
% 7.03/1.86 (goals)
% 7.26/1.89 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.26/1.89 int] : ( ~ (v5 = 0) & leq(v3, v4) = v5 & leq(v0, v1) = 0 &
% 7.26/1.89 multiplication(v1, v2) = v4 & multiplication(v0, v2) = v3 & $i(v4) & $i(v3)
% 7.26/1.89 & $i(v2) & $i(v1) & $i(v0))
% 7.26/1.89
% 7.26/1.89 (left_distributivity)
% 7.26/1.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 7.26/1.90 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) |
% 7.26/1.90 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 7.26/1.90 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5)))
% 7.26/1.90
% 7.26/1.90 (order)
% 7.26/1.90 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) = v2) |
% 7.26/1.90 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) & addition(v0, v1) = v3 &
% 7.26/1.90 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v0, v1) = 0) | ~ $i(v1) |
% 7.26/1.90 ~ $i(v0) | addition(v0, v1) = v1)
% 7.26/1.90
% 7.26/1.90 (function-axioms)
% 7.26/1.91 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.26/1.91 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 7.26/1.91 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.26/1.91 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 7.26/1.91 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 7.26/1.91 v2) = v1) | ~ (addition(v3, v2) = v0))
% 7.26/1.91
% 7.26/1.91 Further assumptions not needed in the proof:
% 7.26/1.91 --------------------------------------------
% 7.26/1.91 additive_associativity, additive_commutativity, additive_idempotence,
% 7.26/1.91 additive_identity, left_annihilation, multiplicative_associativity,
% 7.26/1.91 multiplicative_left_identity, multiplicative_right_identity, right_annihilation,
% 7.26/1.91 right_distributivity
% 7.26/1.91
% 7.26/1.91 Those formulas are unsatisfiable:
% 7.26/1.91 ---------------------------------
% 7.26/1.91
% 7.26/1.91 Begin of proof
% 7.26/1.91 |
% 7.26/1.91 | ALPHA: (order) implies:
% 7.26/1.92 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v0, v1) = 0) | ~ $i(v1) | ~
% 7.26/1.92 | $i(v0) | addition(v0, v1) = v1)
% 7.26/1.92 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) =
% 7.26/1.92 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 7.26/1.92 | addition(v0, v1) = v3 & $i(v3)))
% 7.26/1.92 |
% 7.26/1.92 | ALPHA: (function-axioms) implies:
% 7.26/1.92 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.26/1.92 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 7.26/1.92 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.26/1.92 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 7.26/1.92 |
% 7.26/1.92 | DELTA: instantiating (goals) with fresh symbols all_16_0, all_16_1, all_16_2,
% 7.26/1.92 | all_16_3, all_16_4, all_16_5 gives:
% 7.26/1.93 | (5) ~ (all_16_0 = 0) & leq(all_16_2, all_16_1) = all_16_0 & leq(all_16_5,
% 7.26/1.93 | all_16_4) = 0 & multiplication(all_16_4, all_16_3) = all_16_1 &
% 7.26/1.93 | multiplication(all_16_5, all_16_3) = all_16_2 & $i(all_16_1) &
% 7.26/1.93 | $i(all_16_2) & $i(all_16_3) & $i(all_16_4) & $i(all_16_5)
% 7.26/1.93 |
% 7.26/1.93 | ALPHA: (5) implies:
% 7.26/1.93 | (6) ~ (all_16_0 = 0)
% 7.26/1.93 | (7) $i(all_16_5)
% 7.26/1.93 | (8) $i(all_16_4)
% 7.26/1.93 | (9) $i(all_16_3)
% 7.26/1.93 | (10) $i(all_16_2)
% 7.26/1.93 | (11) $i(all_16_1)
% 7.26/1.93 | (12) multiplication(all_16_5, all_16_3) = all_16_2
% 7.26/1.93 | (13) multiplication(all_16_4, all_16_3) = all_16_1
% 7.26/1.93 | (14) leq(all_16_5, all_16_4) = 0
% 7.26/1.93 | (15) leq(all_16_2, all_16_1) = all_16_0
% 7.26/1.93 |
% 7.26/1.93 | GROUND_INST: instantiating (1) with all_16_5, all_16_4, simplifying with (7),
% 7.26/1.93 | (8), (14) gives:
% 7.26/1.93 | (16) addition(all_16_5, all_16_4) = all_16_4
% 7.26/1.93 |
% 7.26/1.93 | GROUND_INST: instantiating (2) with all_16_2, all_16_1, all_16_0, simplifying
% 7.26/1.93 | with (10), (11), (15) gives:
% 7.26/1.94 | (17) all_16_0 = 0 | ? [v0: any] : ( ~ (v0 = all_16_1) & addition(all_16_2,
% 7.26/1.94 | all_16_1) = v0 & $i(v0))
% 7.26/1.94 |
% 7.26/1.94 | BETA: splitting (17) gives:
% 7.26/1.94 |
% 7.26/1.94 | Case 1:
% 7.26/1.94 | |
% 7.26/1.94 | | (18) all_16_0 = 0
% 7.26/1.94 | |
% 7.26/1.94 | | REDUCE: (6), (18) imply:
% 7.26/1.94 | | (19) $false
% 7.26/1.94 | |
% 7.26/1.94 | | CLOSE: (19) is inconsistent.
% 7.26/1.94 | |
% 7.26/1.94 | Case 2:
% 7.26/1.94 | |
% 7.26/1.94 | | (20) ? [v0: any] : ( ~ (v0 = all_16_1) & addition(all_16_2, all_16_1) =
% 7.26/1.94 | | v0 & $i(v0))
% 7.26/1.94 | |
% 7.26/1.94 | | DELTA: instantiating (20) with fresh symbol all_28_0 gives:
% 7.26/1.94 | | (21) ~ (all_28_0 = all_16_1) & addition(all_16_2, all_16_1) = all_28_0 &
% 7.26/1.94 | | $i(all_28_0)
% 7.26/1.94 | |
% 7.26/1.94 | | ALPHA: (21) implies:
% 7.58/1.94 | | (22) ~ (all_28_0 = all_16_1)
% 7.58/1.94 | | (23) addition(all_16_2, all_16_1) = all_28_0
% 7.58/1.94 | |
% 7.58/1.95 | | GROUND_INST: instantiating (left_distributivity) with all_16_5, all_16_4,
% 7.58/1.95 | | all_16_3, all_16_2, all_16_1, all_28_0, simplifying with (7),
% 7.58/1.95 | | (8), (9), (12), (13), (23) gives:
% 7.58/1.95 | | (24) ? [v0: $i] : (multiplication(v0, all_16_3) = all_28_0 &
% 7.58/1.95 | | addition(all_16_5, all_16_4) = v0 & $i(v0) & $i(all_28_0))
% 7.58/1.95 | |
% 7.58/1.95 | | DELTA: instantiating (24) with fresh symbol all_36_0 gives:
% 7.58/1.95 | | (25) multiplication(all_36_0, all_16_3) = all_28_0 & addition(all_16_5,
% 7.58/1.95 | | all_16_4) = all_36_0 & $i(all_36_0) & $i(all_28_0)
% 7.58/1.95 | |
% 7.58/1.95 | | ALPHA: (25) implies:
% 7.58/1.95 | | (26) addition(all_16_5, all_16_4) = all_36_0
% 7.58/1.95 | | (27) multiplication(all_36_0, all_16_3) = all_28_0
% 7.58/1.95 | |
% 7.58/1.95 | | GROUND_INST: instantiating (3) with all_16_4, all_36_0, all_16_4, all_16_5,
% 7.58/1.95 | | simplifying with (16), (26) gives:
% 7.58/1.95 | | (28) all_36_0 = all_16_4
% 7.58/1.95 | |
% 7.58/1.95 | | REDUCE: (27), (28) imply:
% 7.58/1.95 | | (29) multiplication(all_16_4, all_16_3) = all_28_0
% 7.58/1.95 | |
% 7.58/1.95 | | GROUND_INST: instantiating (4) with all_16_1, all_28_0, all_16_3, all_16_4,
% 7.58/1.95 | | simplifying with (13), (29) gives:
% 7.58/1.95 | | (30) all_28_0 = all_16_1
% 7.58/1.95 | |
% 7.58/1.95 | | REDUCE: (22), (30) imply:
% 7.58/1.95 | | (31) $false
% 7.58/1.95 | |
% 7.58/1.95 | | CLOSE: (31) is inconsistent.
% 7.58/1.95 | |
% 7.58/1.95 | End of split
% 7.58/1.95 |
% 7.58/1.95 End of proof
% 7.58/1.95 % SZS output end Proof for theBenchmark
% 7.58/1.95
% 7.58/1.95 1273ms
%------------------------------------------------------------------------------