TSTP Solution File: KLE003+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE003+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 : n031.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 05:34:09 EDT 2023
% Result : Theorem 5.29s 1.39s
% Output : Proof 6.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE003+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n031.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 12:19:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.14/0.99 Prover 4: Preprocessing ...
% 2.14/0.99 Prover 1: Preprocessing ...
% 2.54/1.03 Prover 6: Preprocessing ...
% 2.54/1.03 Prover 2: Preprocessing ...
% 2.54/1.03 Prover 3: Preprocessing ...
% 2.54/1.03 Prover 0: Preprocessing ...
% 2.54/1.03 Prover 5: Preprocessing ...
% 4.29/1.26 Prover 4: Constructing countermodel ...
% 4.29/1.26 Prover 1: Constructing countermodel ...
% 4.29/1.27 Prover 3: Constructing countermodel ...
% 4.29/1.27 Prover 5: Proving ...
% 4.29/1.27 Prover 6: Proving ...
% 4.29/1.28 Prover 0: Proving ...
% 4.50/1.35 Prover 2: Proving ...
% 4.50/1.39 Prover 3: proved (750ms)
% 4.50/1.39
% 5.29/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.29/1.39
% 5.29/1.39 Prover 5: stopped
% 5.29/1.39 Prover 0: stopped
% 5.29/1.39 Prover 2: stopped
% 5.29/1.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.29/1.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.29/1.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.29/1.39 Prover 6: stopped
% 5.29/1.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.29/1.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.29/1.41 Prover 7: Preprocessing ...
% 5.29/1.42 Prover 13: Preprocessing ...
% 5.29/1.42 Prover 8: Preprocessing ...
% 5.29/1.43 Prover 11: Preprocessing ...
% 5.59/1.43 Prover 10: Preprocessing ...
% 5.59/1.43 Prover 4: Found proof (size 12)
% 5.59/1.43 Prover 4: proved (796ms)
% 5.59/1.44 Prover 1: Found proof (size 14)
% 5.59/1.44 Prover 1: proved (804ms)
% 5.66/1.45 Prover 11: stopped
% 5.66/1.45 Prover 13: stopped
% 5.66/1.46 Prover 10: stopped
% 5.66/1.47 Prover 8: Warning: ignoring some quantifiers
% 5.66/1.48 Prover 8: Constructing countermodel ...
% 5.66/1.48 Prover 8: stopped
% 5.66/1.48 Prover 7: Constructing countermodel ...
% 5.66/1.49 Prover 7: stopped
% 5.66/1.49
% 5.66/1.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.66/1.49
% 5.66/1.50 % SZS output start Proof for theBenchmark
% 5.66/1.50 Assumptions after simplification:
% 5.66/1.50 ---------------------------------
% 5.66/1.50
% 5.66/1.50 (additive_idempotence)
% 6.07/1.53 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~ $i(v0))
% 6.07/1.53
% 6.07/1.53 (goals)
% 6.07/1.53 $i(one) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (addition(one, one) = v0 &
% 6.07/1.53 $i(v1) & $i(v0) & ((v0 = one & ~ (v2 = v1) & addition(v1, v1) = v2 &
% 6.07/1.53 $i(v2)) | ( ~ (v0 = one) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~
% 6.07/1.53 (addition(v3, v3) = v4) | ~ $i(v3)))))
% 6.07/1.53
% 6.07/1.53 Further assumptions not needed in the proof:
% 6.07/1.53 --------------------------------------------
% 6.07/1.53 additive_associativity, additive_commutativity, additive_identity,
% 6.07/1.53 left_annihilation, left_distributivity, multiplicative_associativity,
% 6.07/1.53 multiplicative_left_identity, multiplicative_right_identity, order,
% 6.07/1.53 right_annihilation, right_distributivity
% 6.07/1.53
% 6.07/1.53 Those formulas are unsatisfiable:
% 6.07/1.53 ---------------------------------
% 6.07/1.53
% 6.07/1.53 Begin of proof
% 6.07/1.53 |
% 6.07/1.53 | ALPHA: (goals) implies:
% 6.07/1.54 | (1) $i(one)
% 6.07/1.54 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (addition(one, one) = v0 &
% 6.07/1.54 | $i(v1) & $i(v0) & ((v0 = one & ~ (v2 = v1) & addition(v1, v1) = v2 &
% 6.07/1.54 | $i(v2)) | ( ~ (v0 = one) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 |
% 6.07/1.54 | ~ (addition(v3, v3) = v4) | ~ $i(v3)))))
% 6.07/1.54 |
% 6.07/1.54 | DELTA: instantiating (2) with fresh symbols all_16_0, all_16_1, all_16_2
% 6.07/1.54 | gives:
% 6.07/1.54 | (3) addition(one, one) = all_16_2 & $i(all_16_1) & $i(all_16_2) &
% 6.07/1.54 | ((all_16_2 = one & ~ (all_16_0 = all_16_1) & addition(all_16_1,
% 6.07/1.54 | all_16_1) = all_16_0 & $i(all_16_0)) | ( ~ (all_16_2 = one) & !
% 6.07/1.54 | [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~
% 6.07/1.54 | $i(v0))))
% 6.07/1.54 |
% 6.07/1.54 | ALPHA: (3) implies:
% 6.07/1.54 | (4) $i(all_16_1)
% 6.07/1.54 | (5) addition(one, one) = all_16_2
% 6.07/1.54 | (6) (all_16_2 = one & ~ (all_16_0 = all_16_1) & addition(all_16_1,
% 6.07/1.54 | all_16_1) = all_16_0 & $i(all_16_0)) | ( ~ (all_16_2 = one) & !
% 6.07/1.54 | [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~
% 6.07/1.54 | $i(v0)))
% 6.07/1.54 |
% 6.07/1.55 | GROUND_INST: instantiating (additive_idempotence) with one, all_16_2,
% 6.07/1.55 | simplifying with (1), (5) gives:
% 6.07/1.55 | (7) all_16_2 = one
% 6.07/1.55 |
% 6.07/1.55 | BETA: splitting (6) gives:
% 6.07/1.55 |
% 6.07/1.55 | Case 1:
% 6.07/1.55 | |
% 6.07/1.55 | | (8) all_16_2 = one & ~ (all_16_0 = all_16_1) & addition(all_16_1,
% 6.07/1.55 | | all_16_1) = all_16_0 & $i(all_16_0)
% 6.07/1.55 | |
% 6.07/1.55 | | ALPHA: (8) implies:
% 6.07/1.55 | | (9) ~ (all_16_0 = all_16_1)
% 6.07/1.55 | | (10) addition(all_16_1, all_16_1) = all_16_0
% 6.07/1.55 | |
% 6.07/1.55 | | GROUND_INST: instantiating (additive_idempotence) with all_16_1, all_16_0,
% 6.07/1.55 | | simplifying with (4), (10) gives:
% 6.07/1.55 | | (11) all_16_0 = all_16_1
% 6.07/1.55 | |
% 6.07/1.55 | | REDUCE: (9), (11) imply:
% 6.07/1.55 | | (12) $false
% 6.07/1.55 | |
% 6.07/1.55 | | CLOSE: (12) is inconsistent.
% 6.07/1.55 | |
% 6.07/1.55 | Case 2:
% 6.07/1.55 | |
% 6.07/1.55 | | (13) ~ (all_16_2 = one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 6.07/1.55 | | (addition(v0, v0) = v1) | ~ $i(v0))
% 6.07/1.55 | |
% 6.07/1.55 | | ALPHA: (13) implies:
% 6.07/1.55 | | (14) ~ (all_16_2 = one)
% 6.07/1.55 | |
% 6.07/1.55 | | REDUCE: (7), (14) imply:
% 6.07/1.55 | | (15) $false
% 6.07/1.55 | |
% 6.07/1.55 | | CLOSE: (15) is inconsistent.
% 6.07/1.55 | |
% 6.07/1.55 | End of split
% 6.07/1.55 |
% 6.07/1.55 End of proof
% 6.07/1.55 % SZS output end Proof for theBenchmark
% 6.07/1.55
% 6.07/1.55 938ms
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