TSTP Solution File: KLE075+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE075+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 : n015.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 05:34:28 EDT 2023
% Result : Theorem 7.15s 1.87s
% Output : Proof 8.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : KLE075+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n015.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 : Tue Aug 29 11:57:41 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.65 ________ _____
% 0.22/0.65 ___ __ \_________(_)________________________________
% 0.22/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.65
% 0.22/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.65 (2023-06-19)
% 0.22/0.65
% 0.22/0.65 (c) Philipp Rümmer, 2009-2023
% 0.22/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.65 Amanda Stjerna.
% 0.22/0.65 Free software under BSD-3-Clause.
% 0.22/0.65
% 0.22/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.65
% 0.22/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.67 Running up to 7 provers in parallel.
% 0.22/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.42/1.15 Prover 1: Preprocessing ...
% 2.42/1.15 Prover 4: Preprocessing ...
% 2.75/1.21 Prover 2: Preprocessing ...
% 2.75/1.21 Prover 5: Preprocessing ...
% 2.75/1.21 Prover 3: Preprocessing ...
% 2.75/1.21 Prover 0: Preprocessing ...
% 2.75/1.21 Prover 6: Preprocessing ...
% 4.32/1.63 Prover 1: Constructing countermodel ...
% 5.65/1.65 Prover 6: Constructing countermodel ...
% 5.65/1.67 Prover 3: Constructing countermodel ...
% 6.04/1.70 Prover 4: Constructing countermodel ...
% 6.04/1.72 Prover 0: Proving ...
% 6.04/1.72 Prover 5: Proving ...
% 7.15/1.85 Prover 2: Proving ...
% 7.15/1.87 Prover 3: proved (1186ms)
% 7.15/1.87
% 7.15/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.15/1.87
% 7.15/1.87 Prover 6: stopped
% 7.15/1.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.15/1.87 Prover 2: stopped
% 7.15/1.88 Prover 5: stopped
% 7.15/1.88 Prover 0: stopped
% 7.15/1.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.15/1.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.15/1.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.15/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.15/1.91 Prover 10: Preprocessing ...
% 7.15/1.92 Prover 13: Preprocessing ...
% 7.15/1.92 Prover 11: Preprocessing ...
% 7.15/1.92 Prover 1: Found proof (size 18)
% 7.15/1.92 Prover 1: proved (1247ms)
% 7.79/1.93 Prover 4: stopped
% 7.79/1.94 Prover 7: Preprocessing ...
% 7.79/1.95 Prover 8: Preprocessing ...
% 7.79/1.95 Prover 10: stopped
% 7.79/1.96 Prover 11: stopped
% 7.79/1.97 Prover 13: stopped
% 7.79/1.98 Prover 7: stopped
% 8.14/2.03 Prover 8: Warning: ignoring some quantifiers
% 8.14/2.04 Prover 8: Constructing countermodel ...
% 8.44/2.05 Prover 8: stopped
% 8.44/2.05
% 8.44/2.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.44/2.05
% 8.44/2.06 % SZS output start Proof for theBenchmark
% 8.50/2.06 Assumptions after simplification:
% 8.50/2.06 ---------------------------------
% 8.50/2.06
% 8.50/2.06 (domain2)
% 8.50/2.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (domain(v1) = v2)
% 8.50/2.12 | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 8.50/2.12 ? [v5: $i] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) =
% 8.50/2.12 v4 & $i(v5) & $i(v4)))
% 8.50/2.12
% 8.50/2.12 (goals)
% 8.50/2.12 $i(one) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 8.50/2.12 v1) & domain(v2) = v3 & domain(v0) = v1 & multiplication(one, v1) = v2 &
% 8.50/2.12 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.50/2.12
% 8.50/2.12 (multiplicative_left_identity)
% 8.50/2.12 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(one, v0) =
% 8.50/2.12 v1) | ~ $i(v0))
% 8.50/2.12
% 8.50/2.12 (function-axioms)
% 8.50/2.13 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.50/2.13 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 8.50/2.13 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.50/2.13 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 8.50/2.13 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 8.50/2.13 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 8.50/2.13 [v2: $i] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0))
% 8.50/2.13
% 8.50/2.13 Further assumptions not needed in the proof:
% 8.50/2.13 --------------------------------------------
% 8.50/2.13 additive_associativity, additive_commutativity, additive_idempotence,
% 8.50/2.13 additive_identity, domain1, domain3, domain4, domain5, left_annihilation,
% 8.50/2.13 left_distributivity, multiplicative_associativity,
% 8.50/2.13 multiplicative_right_identity, order, right_annihilation, right_distributivity
% 8.50/2.13
% 8.50/2.13 Those formulas are unsatisfiable:
% 8.50/2.13 ---------------------------------
% 8.50/2.13
% 8.50/2.13 Begin of proof
% 8.50/2.13 |
% 8.50/2.13 | ALPHA: (multiplicative_left_identity) implies:
% 8.50/2.13 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(one, v0) =
% 8.50/2.13 | v1) | ~ $i(v0))
% 8.50/2.13 |
% 8.50/2.13 | ALPHA: (goals) implies:
% 8.50/2.14 | (2) $i(one)
% 8.50/2.14 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v1) &
% 8.50/2.14 | domain(v2) = v3 & domain(v0) = v1 & multiplication(one, v1) = v2 &
% 8.50/2.14 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.50/2.14 |
% 8.50/2.14 | ALPHA: (function-axioms) implies:
% 8.50/2.14 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (domain(v2) =
% 8.50/2.14 | v1) | ~ (domain(v2) = v0))
% 8.50/2.14 |
% 8.50/2.14 | DELTA: instantiating (3) with fresh symbols all_20_0, all_20_1, all_20_2,
% 8.50/2.14 | all_20_3 gives:
% 8.50/2.14 | (5) ~ (all_20_0 = all_20_2) & domain(all_20_1) = all_20_0 &
% 8.50/2.14 | domain(all_20_3) = all_20_2 & multiplication(one, all_20_2) = all_20_1
% 8.50/2.14 | & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & $i(all_20_3)
% 8.50/2.14 |
% 8.50/2.14 | ALPHA: (5) implies:
% 8.50/2.15 | (6) ~ (all_20_0 = all_20_2)
% 8.50/2.15 | (7) $i(all_20_3)
% 8.50/2.15 | (8) $i(all_20_2)
% 8.50/2.15 | (9) multiplication(one, all_20_2) = all_20_1
% 8.50/2.15 | (10) domain(all_20_3) = all_20_2
% 8.50/2.15 | (11) domain(all_20_1) = all_20_0
% 8.50/2.15 |
% 8.50/2.15 | GROUND_INST: instantiating (1) with all_20_2, all_20_1, simplifying with (8),
% 8.50/2.15 | (9) gives:
% 8.50/2.15 | (12) all_20_1 = all_20_2
% 8.50/2.15 |
% 8.50/2.15 | GROUND_INST: instantiating (domain2) with one, all_20_3, all_20_2, all_20_1,
% 8.50/2.15 | simplifying with (2), (7), (9), (10) gives:
% 8.50/2.15 | (13) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_20_1) = v1 &
% 8.50/2.15 | multiplication(one, all_20_3) = v0 & $i(v1) & $i(v0))
% 8.50/2.15 |
% 8.50/2.15 | DELTA: instantiating (13) with fresh symbols all_28_0, all_28_1 gives:
% 8.50/2.15 | (14) domain(all_28_1) = all_28_0 & domain(all_20_1) = all_28_0 &
% 8.50/2.15 | multiplication(one, all_20_3) = all_28_1 & $i(all_28_0) & $i(all_28_1)
% 8.50/2.15 |
% 8.50/2.15 | ALPHA: (14) implies:
% 8.50/2.15 | (15) multiplication(one, all_20_3) = all_28_1
% 8.50/2.15 | (16) domain(all_20_1) = all_28_0
% 8.50/2.16 | (17) domain(all_28_1) = all_28_0
% 8.50/2.16 |
% 8.50/2.16 | REDUCE: (12), (16) imply:
% 8.50/2.16 | (18) domain(all_20_2) = all_28_0
% 8.50/2.16 |
% 8.50/2.16 | REDUCE: (11), (12) imply:
% 8.50/2.16 | (19) domain(all_20_2) = all_20_0
% 8.50/2.16 |
% 8.50/2.16 | GROUND_INST: instantiating (4) with all_20_0, all_28_0, all_20_2, simplifying
% 8.50/2.16 | with (18), (19) gives:
% 8.50/2.16 | (20) all_28_0 = all_20_0
% 8.50/2.16 |
% 8.50/2.16 | REDUCE: (17), (20) imply:
% 8.50/2.16 | (21) domain(all_28_1) = all_20_0
% 8.50/2.16 |
% 8.50/2.16 | GROUND_INST: instantiating (1) with all_20_3, all_28_1, simplifying with (7),
% 8.50/2.16 | (15) gives:
% 8.50/2.16 | (22) all_28_1 = all_20_3
% 8.50/2.16 |
% 8.50/2.16 | REDUCE: (21), (22) imply:
% 8.50/2.16 | (23) domain(all_20_3) = all_20_0
% 8.50/2.16 |
% 8.50/2.16 | GROUND_INST: instantiating (4) with all_20_2, all_20_0, all_20_3, simplifying
% 8.50/2.16 | with (10), (23) gives:
% 8.50/2.16 | (24) all_20_0 = all_20_2
% 8.50/2.16 |
% 8.50/2.16 | REDUCE: (6), (24) imply:
% 8.50/2.16 | (25) $false
% 8.50/2.16 |
% 8.50/2.16 | CLOSE: (25) is inconsistent.
% 8.50/2.16 |
% 8.50/2.16 End of proof
% 8.50/2.16 % SZS output end Proof for theBenchmark
% 8.50/2.16
% 8.50/2.16 1508ms
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