TSTP Solution File: KLE022+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE022+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 : n022.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 05:34:15 EDT 2023
% Result : Theorem 8.16s 1.83s
% Output : Proof 10.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE022+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n022.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 12:32:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.49/1.03 Prover 1: Preprocessing ...
% 2.49/1.03 Prover 4: Preprocessing ...
% 2.49/1.07 Prover 3: Preprocessing ...
% 2.49/1.07 Prover 6: Preprocessing ...
% 2.49/1.07 Prover 5: Preprocessing ...
% 2.49/1.07 Prover 0: Preprocessing ...
% 2.49/1.07 Prover 2: Preprocessing ...
% 4.22/1.36 Prover 3: Constructing countermodel ...
% 5.11/1.41 Prover 1: Constructing countermodel ...
% 5.11/1.42 Prover 6: Proving ...
% 5.11/1.48 Prover 5: Proving ...
% 5.11/1.48 Prover 4: Constructing countermodel ...
% 5.80/1.52 Prover 0: Proving ...
% 5.80/1.55 Prover 2: Proving ...
% 6.51/1.60 Prover 3: gave up
% 6.51/1.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.51/1.62 Prover 7: Preprocessing ...
% 7.40/1.76 Prover 7: Constructing countermodel ...
% 8.16/1.82 Prover 1: gave up
% 8.16/1.83 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.16/1.83 Prover 0: proved (1188ms)
% 8.16/1.83
% 8.16/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.16/1.83
% 8.16/1.83 Prover 6: stopped
% 8.16/1.83 Prover 5: stopped
% 8.16/1.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.16/1.84 Prover 2: stopped
% 8.16/1.85 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.16/1.85 Prover 8: Preprocessing ...
% 8.16/1.85 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.16/1.85 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.16/1.85 Prover 10: Preprocessing ...
% 8.16/1.87 Prover 11: Preprocessing ...
% 8.16/1.88 Prover 16: Preprocessing ...
% 8.16/1.89 Prover 13: Preprocessing ...
% 8.84/1.92 Prover 8: Warning: ignoring some quantifiers
% 8.84/1.92 Prover 8: Constructing countermodel ...
% 8.84/1.96 Prover 10: Constructing countermodel ...
% 9.47/1.99 Prover 11: Constructing countermodel ...
% 9.47/2.01 Prover 16: Warning: ignoring some quantifiers
% 9.47/2.01 Prover 13: Warning: ignoring some quantifiers
% 9.47/2.02 Prover 13: Constructing countermodel ...
% 9.47/2.03 Prover 16: Constructing countermodel ...
% 9.47/2.08 Prover 10: Found proof (size 25)
% 9.47/2.08 Prover 10: proved (247ms)
% 9.47/2.08 Prover 16: stopped
% 9.47/2.08 Prover 4: stopped
% 9.47/2.08 Prover 11: stopped
% 9.47/2.08 Prover 7: stopped
% 9.47/2.08 Prover 13: stopped
% 9.47/2.08 Prover 8: stopped
% 9.47/2.08
% 9.47/2.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.47/2.08
% 9.47/2.09 % SZS output start Proof for theBenchmark
% 9.47/2.10 Assumptions after simplification:
% 9.47/2.10 ---------------------------------
% 9.47/2.10
% 9.47/2.10 (additive_commutativity)
% 9.47/2.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~
% 9.47/2.12 $i(v1) | ~ $i(v0) | (addition(v1, v0) = v2 & $i(v2)))
% 9.47/2.12
% 9.47/2.12 (goals)
% 9.47/2.13 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 9.47/2.13 $i] : ( ~ (v5 = v0) & c(v1) = v3 & multiplication(v0, v3) = v4 &
% 9.47/2.13 multiplication(v0, v1) = v2 & addition(v2, v4) = v5 & $i(v5) & $i(v4) &
% 9.47/2.13 $i(v3) & $i(v2) & $i(v1) & $i(v0) & test(v1))
% 9.47/2.13
% 9.47/2.13 (multiplicative_right_identity)
% 9.47/2.13 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 9.47/2.13 v1) | ~ $i(v0))
% 9.47/2.13
% 9.47/2.13 (right_distributivity)
% 9.47/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 9.47/2.13 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) |
% 9.47/2.13 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 9.47/2.13 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5)))
% 9.47/2.13
% 9.47/2.13 (test_2)
% 9.47/2.13 $i(one) & $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = one | ~
% 9.47/2.13 (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0)) &
% 9.47/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~
% 9.47/2.13 $i(v1) | ~ $i(v0) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero
% 9.47/2.13 & multiplication(v0, v1) = zero)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 9.47/2.14 (addition(v0, v1) = one) | ~ $i(v1) | ~ $i(v0) | complement(v1, v0) | ?
% 9.47/2.14 [v2: $i] : ? [v3: $i] : (( ~ (v3 = zero) & multiplication(v1, v0) = v3 &
% 9.47/2.14 $i(v3)) | ( ~ (v2 = zero) & multiplication(v0, v1) = v2 & $i(v2))))
% 9.47/2.14
% 9.47/2.14 (test_3)
% 9.47/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (c(v0) = v2) | ~
% 9.47/2.14 $i(v1) | ~ $i(v0) | ~ complement(v0, v1) | ~ test(v0)) & ! [v0: $i] : !
% 9.47/2.14 [v1: $i] : ( ~ (c(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ test(v0) |
% 9.47/2.14 complement(v0, v1))
% 9.47/2.14
% 9.47/2.14 (function-axioms)
% 9.47/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.47/2.14 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 9.47/2.14 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 9.47/2.14 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 9.47/2.14 [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0))
% 9.47/2.14
% 9.47/2.14 Further assumptions not needed in the proof:
% 9.47/2.14 --------------------------------------------
% 9.47/2.14 additive_associativity, additive_idempotence, additive_identity,
% 9.47/2.14 left_annihilation, left_distributivity, multiplicative_associativity,
% 9.47/2.14 multiplicative_left_identity, order, right_annihilation, test_1, test_4
% 9.47/2.14
% 9.47/2.14 Those formulas are unsatisfiable:
% 9.47/2.14 ---------------------------------
% 9.47/2.14
% 9.47/2.14 Begin of proof
% 9.47/2.14 |
% 9.47/2.14 | ALPHA: (multiplicative_right_identity) implies:
% 9.47/2.14 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 9.47/2.14 | v1) | ~ $i(v0))
% 9.47/2.14 |
% 9.47/2.14 | ALPHA: (test_2) implies:
% 9.47/2.15 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = one | ~ (addition(v0,
% 9.47/2.15 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0))
% 9.47/2.15 |
% 9.47/2.15 | ALPHA: (test_3) implies:
% 9.47/2.15 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (c(v0) = v1) | ~ $i(v1) | ~ $i(v0) |
% 9.47/2.15 | ~ test(v0) | complement(v0, v1))
% 9.47/2.15 |
% 9.47/2.15 | ALPHA: (function-axioms) implies:
% 9.47/2.15 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.47/2.15 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 9.47/2.15 |
% 9.47/2.15 | DELTA: instantiating (goals) with fresh symbols all_20_0, all_20_1, all_20_2,
% 9.47/2.15 | all_20_3, all_20_4, all_20_5 gives:
% 9.47/2.15 | (5) ~ (all_20_0 = all_20_5) & c(all_20_4) = all_20_2 &
% 9.47/2.15 | multiplication(all_20_5, all_20_2) = all_20_1 &
% 9.47/2.15 | multiplication(all_20_5, all_20_4) = all_20_3 & addition(all_20_3,
% 9.47/2.15 | all_20_1) = all_20_0 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) &
% 9.47/2.15 | $i(all_20_3) & $i(all_20_4) & $i(all_20_5) & test(all_20_4)
% 9.47/2.15 |
% 9.47/2.15 | ALPHA: (5) implies:
% 10.55/2.15 | (6) ~ (all_20_0 = all_20_5)
% 10.55/2.15 | (7) test(all_20_4)
% 10.55/2.15 | (8) $i(all_20_5)
% 10.55/2.15 | (9) $i(all_20_4)
% 10.55/2.15 | (10) $i(all_20_3)
% 10.55/2.15 | (11) $i(all_20_2)
% 10.55/2.15 | (12) $i(all_20_1)
% 10.55/2.15 | (13) addition(all_20_3, all_20_1) = all_20_0
% 10.55/2.15 | (14) multiplication(all_20_5, all_20_4) = all_20_3
% 10.55/2.15 | (15) multiplication(all_20_5, all_20_2) = all_20_1
% 10.55/2.15 | (16) c(all_20_4) = all_20_2
% 10.55/2.15 |
% 10.55/2.15 | GROUND_INST: instantiating (additive_commutativity) with all_20_3, all_20_1,
% 10.55/2.15 | all_20_0, simplifying with (10), (12), (13) gives:
% 10.55/2.15 | (17) addition(all_20_1, all_20_3) = all_20_0 & $i(all_20_0)
% 10.55/2.15 |
% 10.55/2.15 | ALPHA: (17) implies:
% 10.55/2.15 | (18) addition(all_20_1, all_20_3) = all_20_0
% 10.55/2.15 |
% 10.55/2.16 | GROUND_INST: instantiating (right_distributivity) with all_20_5, all_20_4,
% 10.55/2.16 | all_20_2, all_20_3, all_20_1, all_20_0, simplifying with (8),
% 10.55/2.16 | (9), (11), (13), (14), (15) gives:
% 10.55/2.16 | (19) ? [v0: $i] : (multiplication(all_20_5, v0) = all_20_0 &
% 10.55/2.16 | addition(all_20_4, all_20_2) = v0 & $i(v0) & $i(all_20_0))
% 10.55/2.16 |
% 10.55/2.16 | GROUND_INST: instantiating (3) with all_20_4, all_20_2, simplifying with (7),
% 10.55/2.16 | (9), (11), (16) gives:
% 10.55/2.16 | (20) complement(all_20_4, all_20_2)
% 10.55/2.16 |
% 10.55/2.16 | DELTA: instantiating (19) with fresh symbol all_30_0 gives:
% 10.55/2.16 | (21) multiplication(all_20_5, all_30_0) = all_20_0 & addition(all_20_4,
% 10.55/2.16 | all_20_2) = all_30_0 & $i(all_30_0) & $i(all_20_0)
% 10.55/2.16 |
% 10.55/2.16 | ALPHA: (21) implies:
% 10.55/2.16 | (22) addition(all_20_4, all_20_2) = all_30_0
% 10.55/2.16 |
% 10.55/2.16 | GROUND_INST: instantiating (additive_commutativity) with all_20_4, all_20_2,
% 10.55/2.16 | all_30_0, simplifying with (9), (11), (22) gives:
% 10.55/2.16 | (23) addition(all_20_2, all_20_4) = all_30_0 & $i(all_30_0)
% 10.55/2.16 |
% 10.55/2.16 | ALPHA: (23) implies:
% 10.55/2.16 | (24) addition(all_20_2, all_20_4) = all_30_0
% 10.55/2.16 |
% 10.55/2.16 | GROUND_INST: instantiating (right_distributivity) with all_20_5, all_20_2,
% 10.55/2.16 | all_20_4, all_20_1, all_20_3, all_20_0, simplifying with (8),
% 10.55/2.16 | (9), (11), (14), (15), (18) gives:
% 10.55/2.16 | (25) ? [v0: $i] : (multiplication(all_20_5, v0) = all_20_0 &
% 10.55/2.16 | addition(all_20_2, all_20_4) = v0 & $i(v0) & $i(all_20_0))
% 10.55/2.16 |
% 10.55/2.16 | DELTA: instantiating (25) with fresh symbol all_38_0 gives:
% 10.55/2.16 | (26) multiplication(all_20_5, all_38_0) = all_20_0 & addition(all_20_2,
% 10.55/2.16 | all_20_4) = all_38_0 & $i(all_38_0) & $i(all_20_0)
% 10.55/2.16 |
% 10.55/2.16 | ALPHA: (26) implies:
% 10.55/2.16 | (27) addition(all_20_2, all_20_4) = all_38_0
% 10.55/2.16 | (28) multiplication(all_20_5, all_38_0) = all_20_0
% 10.55/2.16 |
% 10.55/2.16 | GROUND_INST: instantiating (4) with all_30_0, all_38_0, all_20_4, all_20_2,
% 10.55/2.16 | simplifying with (24), (27) gives:
% 10.55/2.16 | (29) all_38_0 = all_30_0
% 10.55/2.16 |
% 10.55/2.16 | REDUCE: (28), (29) imply:
% 10.55/2.16 | (30) multiplication(all_20_5, all_30_0) = all_20_0
% 10.55/2.16 |
% 10.65/2.16 | GROUND_INST: instantiating (2) with all_20_2, all_20_4, all_30_0, simplifying
% 10.65/2.16 | with (9), (11), (20), (24) gives:
% 10.65/2.16 | (31) all_30_0 = one
% 10.65/2.16 |
% 10.65/2.16 | REDUCE: (30), (31) imply:
% 10.65/2.16 | (32) multiplication(all_20_5, one) = all_20_0
% 10.65/2.16 |
% 10.65/2.16 | GROUND_INST: instantiating (1) with all_20_5, all_20_0, simplifying with (8),
% 10.65/2.16 | (32) gives:
% 10.65/2.17 | (33) all_20_0 = all_20_5
% 10.65/2.17 |
% 10.65/2.17 | REDUCE: (6), (33) imply:
% 10.65/2.17 | (34) $false
% 10.65/2.17 |
% 10.65/2.17 | CLOSE: (34) is inconsistent.
% 10.65/2.17 |
% 10.65/2.17 End of proof
% 10.65/2.17 % SZS output end Proof for theBenchmark
% 10.65/2.17
% 10.65/2.17 1542ms
%------------------------------------------------------------------------------