TSTP Solution File: KLE056+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE056+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 05:34:24 EDT 2023
% Result : Theorem 8.46s 1.87s
% Output : Proof 10.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE056+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n015.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 12:25:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.51/1.03 Prover 1: Preprocessing ...
% 2.51/1.04 Prover 4: Preprocessing ...
% 2.82/1.10 Prover 5: Preprocessing ...
% 2.82/1.10 Prover 6: Preprocessing ...
% 2.82/1.10 Prover 0: Preprocessing ...
% 2.82/1.10 Prover 3: Preprocessing ...
% 2.82/1.10 Prover 2: Preprocessing ...
% 4.57/1.38 Prover 3: Constructing countermodel ...
% 4.57/1.38 Prover 6: Constructing countermodel ...
% 4.57/1.39 Prover 1: Constructing countermodel ...
% 4.57/1.40 Prover 4: Constructing countermodel ...
% 4.57/1.48 Prover 5: Proving ...
% 4.57/1.49 Prover 0: Proving ...
% 6.21/1.57 Prover 2: Proving ...
% 7.34/1.72 Prover 3: gave up
% 7.34/1.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.34/1.76 Prover 7: Preprocessing ...
% 8.46/1.87 Prover 0: proved (1220ms)
% 8.46/1.87
% 8.46/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.46/1.87
% 8.46/1.87 Prover 6: stopped
% 8.46/1.87 Prover 2: stopped
% 8.56/1.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.56/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.56/1.89 Prover 7: Constructing countermodel ...
% 8.56/1.89 Prover 5: stopped
% 8.56/1.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.56/1.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.56/1.90 Prover 8: Preprocessing ...
% 8.78/1.92 Prover 10: Preprocessing ...
% 8.78/1.92 Prover 11: Preprocessing ...
% 8.78/1.93 Prover 13: Preprocessing ...
% 8.99/1.98 Prover 8: Warning: ignoring some quantifiers
% 8.99/1.98 Prover 8: Constructing countermodel ...
% 8.99/2.00 Prover 10: Constructing countermodel ...
% 8.99/2.00 Prover 13: Warning: ignoring some quantifiers
% 8.99/2.01 Prover 11: Constructing countermodel ...
% 8.99/2.02 Prover 13: Constructing countermodel ...
% 8.99/2.07 Prover 1: gave up
% 8.99/2.09 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.99/2.11 Prover 16: Preprocessing ...
% 9.80/2.15 Prover 7: Found proof (size 17)
% 9.80/2.15 Prover 7: proved (412ms)
% 9.80/2.15 Prover 10: stopped
% 9.80/2.15 Prover 8: stopped
% 9.80/2.15 Prover 13: stopped
% 9.80/2.15 Prover 4: stopped
% 9.80/2.15 Prover 16: stopped
% 9.80/2.16 Prover 11: stopped
% 9.80/2.16
% 9.80/2.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.80/2.16
% 9.80/2.16 % SZS output start Proof for theBenchmark
% 9.80/2.16 Assumptions after simplification:
% 9.80/2.16 ---------------------------------
% 9.80/2.16
% 9.80/2.16 (additive_identity)
% 9.80/2.19 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1)
% 9.80/2.19 | ~ $i(v0))
% 9.80/2.19
% 9.80/2.19 (domain1)
% 9.80/2.19 ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 9.80/2.19 (multiplication(v1, v0) = v2 & addition(v0, v2) = v2 & $i(v2)))
% 9.80/2.19
% 9.80/2.19 (goals)
% 9.80/2.19 $i(zero) & ? [v0: $i] : ( ~ (v0 = zero) & domain(v0) = zero & $i(v0))
% 9.80/2.19
% 9.80/2.19 (left_annihilation)
% 9.80/2.19 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero,
% 9.80/2.19 v0) = v1) | ~ $i(v0))
% 10.68/2.19
% 10.68/2.19 Further assumptions not needed in the proof:
% 10.68/2.19 --------------------------------------------
% 10.68/2.19 additive_associativity, additive_commutativity, additive_idempotence, domain2,
% 10.68/2.19 domain3, domain4, domain5, left_distributivity, multiplicative_associativity,
% 10.68/2.19 multiplicative_left_identity, multiplicative_right_identity, order,
% 10.68/2.19 right_annihilation, right_distributivity
% 10.68/2.19
% 10.68/2.19 Those formulas are unsatisfiable:
% 10.68/2.19 ---------------------------------
% 10.68/2.19
% 10.68/2.19 Begin of proof
% 10.68/2.19 |
% 10.68/2.19 | ALPHA: (additive_identity) implies:
% 10.68/2.19 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) |
% 10.68/2.19 | ~ $i(v0))
% 10.68/2.19 |
% 10.68/2.20 | ALPHA: (left_annihilation) implies:
% 10.68/2.20 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero, v0) =
% 10.68/2.20 | v1) | ~ $i(v0))
% 10.68/2.20 |
% 10.68/2.20 | ALPHA: (goals) implies:
% 10.68/2.20 | (3) ? [v0: $i] : ( ~ (v0 = zero) & domain(v0) = zero & $i(v0))
% 10.68/2.20 |
% 10.68/2.20 | DELTA: instantiating (3) with fresh symbol all_20_0 gives:
% 10.68/2.20 | (4) ~ (all_20_0 = zero) & domain(all_20_0) = zero & $i(all_20_0)
% 10.68/2.20 |
% 10.68/2.20 | ALPHA: (4) implies:
% 10.68/2.20 | (5) ~ (all_20_0 = zero)
% 10.68/2.20 | (6) $i(all_20_0)
% 10.68/2.20 | (7) domain(all_20_0) = zero
% 10.68/2.20 |
% 10.68/2.20 | GROUND_INST: instantiating (domain1) with all_20_0, zero, simplifying with
% 10.68/2.20 | (6), (7) gives:
% 10.68/2.20 | (8) ? [v0: $i] : (multiplication(zero, all_20_0) = v0 & addition(all_20_0,
% 10.68/2.20 | v0) = v0 & $i(v0))
% 10.68/2.20 |
% 10.68/2.20 | DELTA: instantiating (8) with fresh symbol all_28_0 gives:
% 10.68/2.20 | (9) multiplication(zero, all_20_0) = all_28_0 & addition(all_20_0,
% 10.68/2.20 | all_28_0) = all_28_0 & $i(all_28_0)
% 10.68/2.20 |
% 10.68/2.20 | ALPHA: (9) implies:
% 10.68/2.20 | (10) addition(all_20_0, all_28_0) = all_28_0
% 10.68/2.20 | (11) multiplication(zero, all_20_0) = all_28_0
% 10.68/2.20 |
% 10.68/2.20 | GROUND_INST: instantiating (1) with all_20_0, zero, simplifying with (6)
% 10.68/2.20 | gives:
% 10.68/2.20 | (12) all_20_0 = zero | ~ (addition(all_20_0, zero) = zero)
% 10.68/2.20 |
% 10.68/2.20 | GROUND_INST: instantiating (2) with all_20_0, all_28_0, simplifying with (6),
% 10.68/2.20 | (11) gives:
% 10.68/2.20 | (13) all_28_0 = zero
% 10.68/2.20 |
% 10.68/2.20 | REDUCE: (10), (13) imply:
% 10.68/2.20 | (14) addition(all_20_0, zero) = zero
% 10.68/2.20 |
% 10.68/2.20 | BETA: splitting (12) gives:
% 10.68/2.21 |
% 10.68/2.21 | Case 1:
% 10.68/2.21 | |
% 10.68/2.21 | | (15) ~ (addition(all_20_0, zero) = zero)
% 10.68/2.21 | |
% 10.68/2.21 | | PRED_UNIFY: (14), (15) imply:
% 10.68/2.21 | | (16) $false
% 10.68/2.21 | |
% 10.68/2.21 | | CLOSE: (16) is inconsistent.
% 10.68/2.21 | |
% 10.68/2.21 | Case 2:
% 10.68/2.21 | |
% 10.68/2.21 | | (17) all_20_0 = zero
% 10.68/2.21 | |
% 10.68/2.21 | | REDUCE: (5), (17) imply:
% 10.68/2.21 | | (18) $false
% 10.68/2.21 | |
% 10.68/2.21 | | CLOSE: (18) is inconsistent.
% 10.68/2.21 | |
% 10.68/2.21 | End of split
% 10.68/2.21 |
% 10.68/2.21 End of proof
% 10.68/2.21 % SZS output end Proof for theBenchmark
% 10.68/2.21
% 10.68/2.21 1579ms
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