TSTP Solution File: KLE076+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE076+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 : n014.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 5.30s 1.53s
% Output : Proof 6.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE076+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n014.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 11:30:45 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.26/1.04 Prover 4: Preprocessing ...
% 2.26/1.04 Prover 1: Preprocessing ...
% 2.26/1.08 Prover 2: Preprocessing ...
% 2.26/1.08 Prover 0: Preprocessing ...
% 2.26/1.08 Prover 6: Preprocessing ...
% 2.26/1.08 Prover 5: Preprocessing ...
% 2.26/1.08 Prover 3: Preprocessing ...
% 4.44/1.37 Prover 1: Constructing countermodel ...
% 4.44/1.37 Prover 3: Constructing countermodel ...
% 4.44/1.37 Prover 6: Constructing countermodel ...
% 4.44/1.41 Prover 4: Constructing countermodel ...
% 4.44/1.45 Prover 5: Proving ...
% 4.44/1.45 Prover 0: Proving ...
% 5.30/1.52 Prover 3: proved (890ms)
% 5.30/1.53
% 5.30/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.30/1.53
% 5.30/1.53 Prover 6: stopped
% 5.30/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.30/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.30/1.53 Prover 0: stopped
% 5.30/1.53 Prover 5: stopped
% 5.30/1.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.30/1.55 Prover 2: Proving ...
% 5.30/1.55 Prover 2: stopped
% 5.30/1.55 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.30/1.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.30/1.55 Prover 8: Preprocessing ...
% 5.30/1.58 Prover 4: Found proof (size 14)
% 5.30/1.58 Prover 4: proved (941ms)
% 5.30/1.58 Prover 1: Found proof (size 16)
% 5.30/1.58 Prover 1: proved (944ms)
% 6.33/1.58 Prover 11: Preprocessing ...
% 6.33/1.59 Prover 10: Preprocessing ...
% 6.33/1.59 Prover 7: Preprocessing ...
% 6.33/1.59 Prover 13: Preprocessing ...
% 6.42/1.60 Prover 11: stopped
% 6.42/1.61 Prover 10: stopped
% 6.53/1.62 Prover 7: stopped
% 6.53/1.62 Prover 8: Warning: ignoring some quantifiers
% 6.53/1.62 Prover 13: stopped
% 6.53/1.63 Prover 8: Constructing countermodel ...
% 6.53/1.64 Prover 8: stopped
% 6.53/1.64
% 6.53/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.53/1.64
% 6.53/1.64 % SZS output start Proof for theBenchmark
% 6.53/1.64 Assumptions after simplification:
% 6.53/1.64 ---------------------------------
% 6.53/1.64
% 6.53/1.64 (domain4)
% 6.53/1.67 domain(zero) = zero & $i(zero)
% 6.53/1.67
% 6.53/1.67 (goals)
% 6.53/1.67 $i(zero) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 6.53/1.67 zero) & domain(v2) = v3 & domain(zero) = v0 & multiplication(v1, v0) = v2
% 6.53/1.67 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 6.53/1.67
% 6.53/1.67 (right_annihilation)
% 6.53/1.67 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(v0,
% 6.53/1.67 zero) = v1) | ~ $i(v0))
% 6.53/1.67
% 6.53/1.67 (function-axioms)
% 6.53/1.68 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.53/1.68 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 6.53/1.68 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.53/1.68 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 6.53/1.68 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 6.53/1.68 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 6.53/1.68 [v2: $i] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0))
% 6.53/1.68
% 6.53/1.68 Further assumptions not needed in the proof:
% 6.53/1.68 --------------------------------------------
% 6.53/1.68 additive_associativity, additive_commutativity, additive_idempotence,
% 6.53/1.68 additive_identity, domain1, domain2, domain3, domain5, left_annihilation,
% 6.53/1.68 left_distributivity, multiplicative_associativity, multiplicative_left_identity,
% 6.53/1.68 multiplicative_right_identity, order, right_distributivity
% 6.53/1.68
% 6.53/1.68 Those formulas are unsatisfiable:
% 6.53/1.68 ---------------------------------
% 6.53/1.68
% 6.53/1.68 Begin of proof
% 6.53/1.68 |
% 6.53/1.68 | ALPHA: (right_annihilation) implies:
% 6.53/1.68 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(v0, zero) =
% 6.53/1.68 | v1) | ~ $i(v0))
% 6.53/1.68 |
% 6.53/1.68 | ALPHA: (domain4) implies:
% 6.53/1.68 | (2) domain(zero) = zero
% 6.53/1.68 |
% 6.53/1.68 | ALPHA: (goals) implies:
% 6.53/1.68 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = zero)
% 6.53/1.68 | & domain(v2) = v3 & domain(zero) = v0 & multiplication(v1, v0) = v2 &
% 6.53/1.68 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 6.53/1.68 |
% 6.53/1.68 | ALPHA: (function-axioms) implies:
% 6.53/1.69 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (domain(v2) =
% 6.53/1.69 | v1) | ~ (domain(v2) = v0))
% 6.53/1.69 |
% 6.53/1.69 | DELTA: instantiating (3) with fresh symbols all_20_0, all_20_1, all_20_2,
% 6.53/1.69 | all_20_3 gives:
% 6.53/1.69 | (5) ~ (all_20_0 = zero) & domain(all_20_1) = all_20_0 & domain(zero) =
% 6.53/1.69 | all_20_3 & multiplication(all_20_2, all_20_3) = all_20_1 & $i(all_20_0)
% 6.53/1.69 | & $i(all_20_1) & $i(all_20_2) & $i(all_20_3)
% 6.53/1.69 |
% 6.53/1.69 | ALPHA: (5) implies:
% 6.53/1.69 | (6) ~ (all_20_0 = zero)
% 6.53/1.69 | (7) $i(all_20_2)
% 6.53/1.69 | (8) multiplication(all_20_2, all_20_3) = all_20_1
% 6.53/1.69 | (9) domain(zero) = all_20_3
% 6.53/1.69 | (10) domain(all_20_1) = all_20_0
% 6.53/1.69 |
% 6.53/1.69 | GROUND_INST: instantiating (4) with zero, all_20_3, zero, simplifying with
% 6.53/1.69 | (2), (9) gives:
% 6.53/1.69 | (11) all_20_3 = zero
% 6.53/1.69 |
% 6.53/1.69 | REDUCE: (8), (11) imply:
% 6.53/1.69 | (12) multiplication(all_20_2, zero) = all_20_1
% 6.53/1.69 |
% 6.53/1.69 | GROUND_INST: instantiating (1) with all_20_2, all_20_1, simplifying with (7),
% 6.53/1.69 | (12) gives:
% 6.53/1.69 | (13) all_20_1 = zero
% 6.53/1.69 |
% 6.53/1.69 | REDUCE: (10), (13) imply:
% 6.53/1.69 | (14) domain(zero) = all_20_0
% 6.53/1.69 |
% 6.53/1.69 | GROUND_INST: instantiating (4) with zero, all_20_0, zero, simplifying with
% 6.53/1.69 | (2), (14) gives:
% 6.53/1.69 | (15) all_20_0 = zero
% 6.53/1.69 |
% 6.53/1.69 | REDUCE: (6), (15) imply:
% 6.53/1.69 | (16) $false
% 6.53/1.70 |
% 6.53/1.70 | CLOSE: (16) is inconsistent.
% 6.53/1.70 |
% 6.53/1.70 End of proof
% 6.53/1.70 % SZS output end Proof for theBenchmark
% 6.53/1.70
% 6.53/1.70 1084ms
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