TSTP Solution File: KLE074+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE074+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 : n005.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 05:34:27 EDT 2023
% Result : Theorem 7.02s 1.84s
% Output : Proof 9.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE074+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 11:20:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.64 ________ _____
% 0.20/0.64 ___ __ \_________(_)________________________________
% 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.64
% 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.64 (2023-06-19)
% 0.20/0.64
% 0.20/0.64 (c) Philipp Rümmer, 2009-2023
% 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.64 Amanda Stjerna.
% 0.20/0.64 Free software under BSD-3-Clause.
% 0.20/0.64
% 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.64
% 0.20/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.66 Running up to 7 provers in parallel.
% 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.31/1.20 Prover 4: Preprocessing ...
% 2.31/1.21 Prover 1: Preprocessing ...
% 2.96/1.26 Prover 5: Preprocessing ...
% 2.96/1.26 Prover 2: Preprocessing ...
% 2.96/1.26 Prover 0: Preprocessing ...
% 2.96/1.26 Prover 6: Preprocessing ...
% 2.96/1.26 Prover 3: Preprocessing ...
% 5.69/1.64 Prover 1: Constructing countermodel ...
% 5.69/1.64 Prover 6: Constructing countermodel ...
% 5.69/1.65 Prover 3: Constructing countermodel ...
% 5.69/1.69 Prover 4: Constructing countermodel ...
% 6.20/1.72 Prover 5: Proving ...
% 6.71/1.78 Prover 0: Proving ...
% 7.02/1.83 Prover 3: proved (1157ms)
% 7.02/1.84
% 7.02/1.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.02/1.84
% 7.02/1.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.02/1.85 Prover 5: stopped
% 7.02/1.86 Prover 0: stopped
% 7.02/1.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.02/1.87 Prover 6: stopped
% 7.02/1.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.02/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.02/1.88 Prover 7: Preprocessing ...
% 7.02/1.88 Prover 8: Preprocessing ...
% 7.02/1.90 Prover 10: Preprocessing ...
% 7.02/1.90 Prover 11: Preprocessing ...
% 7.71/1.94 Prover 2: Proving ...
% 7.71/1.94 Prover 2: stopped
% 7.71/1.96 Prover 1: Found proof (size 23)
% 7.71/1.96 Prover 1: proved (1286ms)
% 7.71/1.96 Prover 4: stopped
% 7.71/1.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.71/1.98 Prover 8: Warning: ignoring some quantifiers
% 7.71/1.99 Prover 13: Preprocessing ...
% 7.71/1.99 Prover 8: Constructing countermodel ...
% 8.22/2.00 Prover 8: stopped
% 8.22/2.01 Prover 10: Constructing countermodel ...
% 8.22/2.01 Prover 13: stopped
% 8.22/2.02 Prover 10: stopped
% 8.22/2.04 Prover 7: Constructing countermodel ...
% 8.22/2.05 Prover 7: stopped
% 8.22/2.05 Prover 11: Constructing countermodel ...
% 8.22/2.06 Prover 11: stopped
% 8.22/2.07
% 8.22/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.22/2.07
% 8.22/2.07 % SZS output start Proof for theBenchmark
% 8.22/2.08 Assumptions after simplification:
% 8.22/2.08 ---------------------------------
% 8.22/2.08
% 8.22/2.08 (domain2)
% 8.22/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (domain(v1) = v2)
% 8.22/2.13 | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 8.22/2.13 ? [v5: $i] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) =
% 8.22/2.13 v4 & $i(v5) & $i(v4)))
% 8.22/2.13
% 8.22/2.13 (goals)
% 8.22/2.14 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 8.22/2.14 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 8.22/2.14 ( ~ (v10 = v6) & domain(v9) = v10 & domain(v7) = v8 & domain(v5) = v6 &
% 8.22/2.14 domain(v2) = v4 & multiplication(v3, v4) = v5 & multiplication(v1, v4) = v7
% 8.22/2.14 & multiplication(v0, v8) = v9 & multiplication(v0, v1) = v3 & $i(v10) &
% 8.22/2.14 $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 8.22/2.14 $i(v1) & $i(v0))
% 8.22/2.14
% 8.22/2.14 (multiplicative_associativity)
% 8.22/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 8.22/2.14 (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ $i(v2)
% 8.22/2.14 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1, v2) = v5 &
% 8.22/2.14 multiplication(v0, v5) = v4 & $i(v5) & $i(v4)))
% 8.22/2.14
% 8.22/2.14 (function-axioms)
% 8.22/2.15 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.22/2.15 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 8.22/2.15 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.22/2.15 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 8.22/2.15 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 8.22/2.15 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 8.22/2.15 [v2: $i] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0))
% 8.22/2.15
% 8.22/2.15 Further assumptions not needed in the proof:
% 8.22/2.15 --------------------------------------------
% 8.22/2.15 additive_associativity, additive_commutativity, additive_idempotence,
% 8.22/2.15 additive_identity, domain1, domain3, domain4, domain5, left_annihilation,
% 8.22/2.15 left_distributivity, multiplicative_left_identity,
% 8.22/2.15 multiplicative_right_identity, order, right_annihilation, right_distributivity
% 8.22/2.15
% 8.22/2.15 Those formulas are unsatisfiable:
% 8.22/2.15 ---------------------------------
% 8.22/2.15
% 8.22/2.15 Begin of proof
% 8.22/2.15 |
% 8.22/2.15 | ALPHA: (function-axioms) implies:
% 8.22/2.16 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (domain(v2) =
% 8.22/2.16 | v1) | ~ (domain(v2) = v0))
% 8.22/2.16 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.22/2.16 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 8.22/2.16 |
% 8.22/2.16 | DELTA: instantiating (goals) with fresh symbols all_20_0, all_20_1, all_20_2,
% 8.22/2.16 | all_20_3, all_20_4, all_20_5, all_20_6, all_20_7, all_20_8, all_20_9,
% 8.22/2.16 | all_20_10 gives:
% 8.22/2.17 | (3) ~ (all_20_0 = all_20_4) & domain(all_20_1) = all_20_0 &
% 8.22/2.17 | domain(all_20_3) = all_20_2 & domain(all_20_5) = all_20_4 &
% 8.22/2.17 | domain(all_20_8) = all_20_6 & multiplication(all_20_7, all_20_6) =
% 8.22/2.17 | all_20_5 & multiplication(all_20_9, all_20_6) = all_20_3 &
% 8.22/2.17 | multiplication(all_20_10, all_20_2) = all_20_1 &
% 8.22/2.17 | multiplication(all_20_10, all_20_9) = all_20_7 & $i(all_20_0) &
% 8.87/2.17 | $i(all_20_1) & $i(all_20_2) & $i(all_20_3) & $i(all_20_4) &
% 8.87/2.17 | $i(all_20_5) & $i(all_20_6) & $i(all_20_7) & $i(all_20_8) &
% 8.87/2.17 | $i(all_20_9) & $i(all_20_10)
% 8.87/2.17 |
% 8.87/2.17 | ALPHA: (3) implies:
% 9.14/2.17 | (4) ~ (all_20_0 = all_20_4)
% 9.14/2.17 | (5) $i(all_20_10)
% 9.14/2.17 | (6) $i(all_20_9)
% 9.14/2.17 | (7) $i(all_20_8)
% 9.14/2.17 | (8) $i(all_20_7)
% 9.14/2.17 | (9) $i(all_20_6)
% 9.14/2.17 | (10) $i(all_20_3)
% 9.14/2.17 | (11) multiplication(all_20_10, all_20_9) = all_20_7
% 9.14/2.17 | (12) multiplication(all_20_10, all_20_2) = all_20_1
% 9.14/2.17 | (13) multiplication(all_20_9, all_20_6) = all_20_3
% 9.14/2.17 | (14) multiplication(all_20_7, all_20_6) = all_20_5
% 9.14/2.17 | (15) domain(all_20_8) = all_20_6
% 9.14/2.17 | (16) domain(all_20_5) = all_20_4
% 9.14/2.18 | (17) domain(all_20_3) = all_20_2
% 9.14/2.18 | (18) domain(all_20_1) = all_20_0
% 9.14/2.18 |
% 9.14/2.18 | GROUND_INST: instantiating (multiplicative_associativity) with all_20_10,
% 9.14/2.18 | all_20_9, all_20_6, all_20_7, all_20_5, simplifying with (5),
% 9.14/2.18 | (6), (9), (11), (14) gives:
% 9.14/2.18 | (19) ? [v0: $i] : (multiplication(all_20_9, all_20_6) = v0 &
% 9.14/2.18 | multiplication(all_20_10, v0) = all_20_5 & $i(v0) & $i(all_20_5))
% 9.14/2.18 |
% 9.14/2.18 | GROUND_INST: instantiating (domain2) with all_20_7, all_20_8, all_20_6,
% 9.14/2.18 | all_20_5, simplifying with (7), (8), (14), (15) gives:
% 9.14/2.18 | (20) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_20_5) = v1 &
% 9.14/2.18 | multiplication(all_20_7, all_20_8) = v0 & $i(v1) & $i(v0))
% 9.14/2.18 |
% 9.14/2.18 | GROUND_INST: instantiating (domain2) with all_20_10, all_20_3, all_20_2,
% 9.14/2.18 | all_20_1, simplifying with (5), (10), (12), (17) gives:
% 9.14/2.19 | (21) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_20_1) = v1 &
% 9.14/2.19 | multiplication(all_20_10, all_20_3) = v0 & $i(v1) & $i(v0))
% 9.14/2.19 |
% 9.14/2.19 | DELTA: instantiating (19) with fresh symbol all_28_0 gives:
% 9.14/2.19 | (22) multiplication(all_20_9, all_20_6) = all_28_0 &
% 9.14/2.19 | multiplication(all_20_10, all_28_0) = all_20_5 & $i(all_28_0) &
% 9.14/2.19 | $i(all_20_5)
% 9.14/2.19 |
% 9.14/2.19 | ALPHA: (22) implies:
% 9.14/2.19 | (23) multiplication(all_20_10, all_28_0) = all_20_5
% 9.14/2.19 | (24) multiplication(all_20_9, all_20_6) = all_28_0
% 9.14/2.19 |
% 9.14/2.19 | DELTA: instantiating (21) with fresh symbols all_30_0, all_30_1 gives:
% 9.14/2.19 | (25) domain(all_30_1) = all_30_0 & domain(all_20_1) = all_30_0 &
% 9.14/2.19 | multiplication(all_20_10, all_20_3) = all_30_1 & $i(all_30_0) &
% 9.14/2.19 | $i(all_30_1)
% 9.14/2.19 |
% 9.14/2.19 | ALPHA: (25) implies:
% 9.14/2.19 | (26) multiplication(all_20_10, all_20_3) = all_30_1
% 9.14/2.19 | (27) domain(all_20_1) = all_30_0
% 9.14/2.19 | (28) domain(all_30_1) = all_30_0
% 9.14/2.19 |
% 9.14/2.19 | DELTA: instantiating (20) with fresh symbols all_34_0, all_34_1 gives:
% 9.26/2.19 | (29) domain(all_34_1) = all_34_0 & domain(all_20_5) = all_34_0 &
% 9.26/2.19 | multiplication(all_20_7, all_20_8) = all_34_1 & $i(all_34_0) &
% 9.26/2.19 | $i(all_34_1)
% 9.26/2.19 |
% 9.26/2.19 | ALPHA: (29) implies:
% 9.26/2.19 | (30) domain(all_20_5) = all_34_0
% 9.26/2.19 |
% 9.26/2.19 | GROUND_INST: instantiating (2) with all_20_3, all_28_0, all_20_6, all_20_9,
% 9.26/2.19 | simplifying with (13), (24) gives:
% 9.26/2.20 | (31) all_28_0 = all_20_3
% 9.26/2.20 |
% 9.26/2.20 | GROUND_INST: instantiating (1) with all_20_4, all_34_0, all_20_5, simplifying
% 9.26/2.20 | with (16), (30) gives:
% 9.26/2.20 | (32) all_34_0 = all_20_4
% 9.26/2.20 |
% 9.26/2.20 | GROUND_INST: instantiating (1) with all_20_0, all_30_0, all_20_1, simplifying
% 9.26/2.20 | with (18), (27) gives:
% 9.26/2.20 | (33) all_30_0 = all_20_0
% 9.26/2.20 |
% 9.26/2.20 | REDUCE: (28), (33) imply:
% 9.26/2.20 | (34) domain(all_30_1) = all_20_0
% 9.26/2.20 |
% 9.26/2.20 | REDUCE: (23), (31) imply:
% 9.26/2.20 | (35) multiplication(all_20_10, all_20_3) = all_20_5
% 9.26/2.20 |
% 9.26/2.20 | GROUND_INST: instantiating (2) with all_30_1, all_20_5, all_20_3, all_20_10,
% 9.26/2.20 | simplifying with (26), (35) gives:
% 9.26/2.20 | (36) all_30_1 = all_20_5
% 9.26/2.20 |
% 9.26/2.20 | REDUCE: (34), (36) imply:
% 9.26/2.20 | (37) domain(all_20_5) = all_20_0
% 9.26/2.20 |
% 9.26/2.20 | GROUND_INST: instantiating (1) with all_20_4, all_20_0, all_20_5, simplifying
% 9.26/2.20 | with (16), (37) gives:
% 9.26/2.20 | (38) all_20_0 = all_20_4
% 9.26/2.20 |
% 9.26/2.20 | REDUCE: (4), (38) imply:
% 9.26/2.20 | (39) $false
% 9.26/2.20 |
% 9.26/2.20 | CLOSE: (39) is inconsistent.
% 9.26/2.20 |
% 9.26/2.20 End of proof
% 9.26/2.20 % SZS output end Proof for theBenchmark
% 9.26/2.20
% 9.26/2.20 1564ms
%------------------------------------------------------------------------------