TSTP Solution File: KLE057+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE057+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 05:34:24 EDT 2023
% Result : Theorem 4.27s 1.37s
% Output : Proof 6.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : KLE057+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 11:25:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.11/1.05 Prover 4: Preprocessing ...
% 2.11/1.05 Prover 1: Preprocessing ...
% 2.78/1.08 Prover 6: Preprocessing ...
% 2.78/1.08 Prover 5: Preprocessing ...
% 2.78/1.08 Prover 0: Preprocessing ...
% 2.78/1.08 Prover 2: Preprocessing ...
% 2.78/1.08 Prover 3: Preprocessing ...
% 4.27/1.31 Prover 6: Constructing countermodel ...
% 4.27/1.32 Prover 3: Constructing countermodel ...
% 4.27/1.34 Prover 5: Constructing countermodel ...
% 4.27/1.36 Prover 6: proved (725ms)
% 4.27/1.37
% 4.27/1.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.27/1.37
% 4.27/1.38 Prover 1: Constructing countermodel ...
% 4.27/1.38 Prover 5: proved (727ms)
% 4.27/1.38
% 4.27/1.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.27/1.38
% 4.27/1.38 Prover 3: proved (730ms)
% 4.27/1.38
% 4.27/1.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.27/1.38
% 4.27/1.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.27/1.39 Prover 0: Constructing countermodel ...
% 4.27/1.39 Prover 0: stopped
% 4.27/1.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.27/1.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.27/1.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.27/1.42 Prover 8: Preprocessing ...
% 4.27/1.42 Prover 4: Constructing countermodel ...
% 4.27/1.43 Prover 10: Preprocessing ...
% 4.27/1.43 Prover 11: Preprocessing ...
% 4.27/1.45 Prover 7: Preprocessing ...
% 5.66/1.50 Prover 2: Constructing countermodel ...
% 5.66/1.50 Prover 2: stopped
% 5.66/1.50 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.89/1.52 Prover 13: Preprocessing ...
% 5.89/1.54 Prover 8: Warning: ignoring some quantifiers
% 5.89/1.54 Prover 4: Found proof (size 8)
% 5.89/1.54 Prover 1: Found proof (size 8)
% 5.89/1.54 Prover 1: proved (916ms)
% 5.89/1.54 Prover 4: proved (912ms)
% 5.89/1.55 Prover 8: Constructing countermodel ...
% 5.89/1.56 Prover 13: stopped
% 5.89/1.57 Prover 10: Constructing countermodel ...
% 5.89/1.57 Prover 8: stopped
% 5.89/1.58 Prover 10: stopped
% 5.89/1.59 Prover 11: Constructing countermodel ...
% 5.89/1.59 Prover 7: Constructing countermodel ...
% 5.89/1.60 Prover 7: stopped
% 5.89/1.60 Prover 11: stopped
% 5.89/1.60
% 5.89/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.89/1.60
% 5.89/1.60 % SZS output start Proof for theBenchmark
% 5.89/1.60 Assumptions after simplification:
% 5.89/1.60 ---------------------------------
% 5.89/1.60
% 5.89/1.60 (domain4)
% 6.49/1.63 domain(zero) = zero & $i(zero)
% 6.49/1.63
% 6.49/1.63 (goals)
% 6.49/1.63 $i(zero) & ? [v0: $i] : ( ~ (v0 = zero) & domain(zero) = v0 & $i(v0))
% 6.49/1.63
% 6.49/1.63 (function-axioms)
% 6.49/1.64 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.49/1.64 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 6.49/1.64 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.49/1.64 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 6.49/1.64 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 6.49/1.64 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 6.49/1.64 [v2: $i] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0))
% 6.49/1.64
% 6.49/1.64 Further assumptions not needed in the proof:
% 6.49/1.64 --------------------------------------------
% 6.49/1.64 additive_associativity, additive_commutativity, additive_idempotence,
% 6.49/1.64 additive_identity, domain1, domain2, domain3, domain5, left_annihilation,
% 6.49/1.64 left_distributivity, multiplicative_associativity, multiplicative_left_identity,
% 6.49/1.64 multiplicative_right_identity, order, right_annihilation, right_distributivity
% 6.49/1.64
% 6.49/1.64 Those formulas are unsatisfiable:
% 6.49/1.64 ---------------------------------
% 6.49/1.64
% 6.49/1.64 Begin of proof
% 6.49/1.64 |
% 6.49/1.64 | ALPHA: (domain4) implies:
% 6.49/1.64 | (1) domain(zero) = zero
% 6.49/1.64 |
% 6.49/1.64 | ALPHA: (goals) implies:
% 6.49/1.64 | (2) ? [v0: $i] : ( ~ (v0 = zero) & domain(zero) = v0 & $i(v0))
% 6.49/1.64 |
% 6.49/1.64 | ALPHA: (function-axioms) implies:
% 6.49/1.64 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (domain(v2) =
% 6.49/1.64 | v1) | ~ (domain(v2) = v0))
% 6.49/1.64 |
% 6.49/1.64 | DELTA: instantiating (2) with fresh symbol all_20_0 gives:
% 6.49/1.65 | (4) ~ (all_20_0 = zero) & domain(zero) = all_20_0 & $i(all_20_0)
% 6.49/1.65 |
% 6.49/1.65 | ALPHA: (4) implies:
% 6.49/1.65 | (5) ~ (all_20_0 = zero)
% 6.49/1.65 | (6) domain(zero) = all_20_0
% 6.49/1.65 |
% 6.49/1.65 | GROUND_INST: instantiating (3) with zero, all_20_0, zero, simplifying with
% 6.49/1.65 | (1), (6) gives:
% 6.49/1.65 | (7) all_20_0 = zero
% 6.49/1.65 |
% 6.49/1.65 | REDUCE: (5), (7) imply:
% 6.49/1.65 | (8) $false
% 6.49/1.65 |
% 6.49/1.65 | CLOSE: (8) is inconsistent.
% 6.49/1.65 |
% 6.49/1.65 End of proof
% 6.49/1.65 % SZS output end Proof for theBenchmark
% 6.49/1.65
% 6.49/1.65 1040ms
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