TSTP Solution File: SET789+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET789+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n023.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 15:26:27 EDT 2023
% Result : Theorem 7.01s 1.68s
% Output : Proof 10.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET789+4 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 15:43:41 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.59/0.60 ________ _____
% 0.59/0.60 ___ __ \_________(_)________________________________
% 0.59/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.59/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.59/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.59/0.60
% 0.59/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.59/0.60 (2023-06-19)
% 0.59/0.60
% 0.59/0.60 (c) Philipp Rümmer, 2009-2023
% 0.59/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.59/0.60 Amanda Stjerna.
% 0.59/0.60 Free software under BSD-3-Clause.
% 0.59/0.60
% 0.59/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.59/0.60
% 0.59/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.63/0.61 Running up to 7 provers in parallel.
% 0.63/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.63/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.63/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.63/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.63/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.63/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.63/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.65/1.07 Prover 1: Preprocessing ...
% 2.65/1.07 Prover 4: Preprocessing ...
% 3.10/1.12 Prover 0: Preprocessing ...
% 3.10/1.12 Prover 5: Preprocessing ...
% 3.10/1.12 Prover 3: Preprocessing ...
% 3.10/1.12 Prover 6: Preprocessing ...
% 3.10/1.12 Prover 2: Preprocessing ...
% 5.25/1.43 Prover 5: Proving ...
% 5.25/1.44 Prover 2: Proving ...
% 6.39/1.56 Prover 6: Proving ...
% 6.39/1.59 Prover 3: Constructing countermodel ...
% 7.01/1.64 Prover 1: Constructing countermodel ...
% 7.01/1.68 Prover 5: proved (1060ms)
% 7.01/1.68
% 7.01/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.01/1.68
% 7.54/1.69 Prover 6: stopped
% 7.54/1.70 Prover 2: stopped
% 7.54/1.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.54/1.70 Prover 3: stopped
% 7.54/1.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.54/1.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.54/1.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.54/1.71 Prover 0: Proving ...
% 7.54/1.73 Prover 0: stopped
% 7.54/1.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.54/1.74 Prover 4: Constructing countermodel ...
% 7.54/1.76 Prover 11: Preprocessing ...
% 8.16/1.77 Prover 7: Preprocessing ...
% 8.16/1.77 Prover 1: gave up
% 8.16/1.78 Prover 13: Preprocessing ...
% 8.16/1.78 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.16/1.78 Prover 10: Preprocessing ...
% 8.16/1.78 Prover 8: Preprocessing ...
% 8.47/1.82 Prover 16: Preprocessing ...
% 8.51/1.85 Prover 7: Warning: ignoring some quantifiers
% 8.51/1.85 Prover 10: Warning: ignoring some quantifiers
% 8.51/1.86 Prover 13: Warning: ignoring some quantifiers
% 8.51/1.87 Prover 13: Constructing countermodel ...
% 8.51/1.87 Prover 16: Warning: ignoring some quantifiers
% 8.51/1.88 Prover 10: Constructing countermodel ...
% 8.51/1.89 Prover 7: Constructing countermodel ...
% 8.51/1.89 Prover 16: Constructing countermodel ...
% 9.68/1.99 Prover 7: Found proof (size 11)
% 9.68/1.99 Prover 7: proved (295ms)
% 9.68/1.99 Prover 10: stopped
% 9.68/1.99 Prover 16: stopped
% 9.68/1.99 Prover 4: stopped
% 9.68/2.00 Prover 13: stopped
% 9.68/2.00 Prover 8: Warning: ignoring some quantifiers
% 9.68/2.01 Prover 8: Constructing countermodel ...
% 9.68/2.02 Prover 8: stopped
% 9.68/2.06 Prover 11: Constructing countermodel ...
% 9.68/2.06 Prover 11: stopped
% 9.68/2.06
% 9.68/2.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.68/2.06
% 9.68/2.07 % SZS output start Proof for theBenchmark
% 9.68/2.07 Assumptions after simplification:
% 9.68/2.07 ---------------------------------
% 9.68/2.07
% 9.68/2.07 (greatest)
% 10.22/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 10.22/2.08 | ~ $i(v1) | ~ $i(v0) | ~ greatest(v2, v0, v1) | ~ member(v3, v1) |
% 10.22/2.08 apply(v0, v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) |
% 10.22/2.08 ~ $i(v1) | ~ $i(v0) | ~ greatest(v2, v0, v1) | member(v2, v1)) & ? [v0:
% 10.22/2.08 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 10.22/2.08 member(v2, v1) | greatest(v2, v0, v1) | ? [v3: $i] : ($i(v3) & member(v3,
% 10.22/2.08 v1) & ~ apply(v0, v3, v2)))
% 10.22/2.08
% 10.22/2.08 (order)
% 10.22/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 10.22/2.08 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ apply(v0, v3,
% 10.22/2.08 v4) | ~ apply(v0, v2, v3) | ~ member(v4, v1) | ~ member(v3, v1) | ~
% 10.22/2.08 member(v2, v1) | ~ order(v0, v1) | apply(v0, v2, v4)) & ! [v0: $i] : !
% 10.22/2.08 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ $i(v3) | ~ $i(v2) | ~
% 10.22/2.08 $i(v1) | ~ $i(v0) | ~ apply(v0, v3, v2) | ~ apply(v0, v2, v3) | ~
% 10.22/2.09 member(v3, v1) | ~ member(v2, v1) | ~ order(v0, v1)) & ! [v0: $i] : !
% 10.22/2.09 [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v2,
% 10.22/2.09 v1) | ~ order(v0, v1) | apply(v0, v2, v2)) & ? [v0: $i] : ? [v1: $i] :
% 10.22/2.09 ( ~ $i(v1) | ~ $i(v0) | order(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 10.22/2.09 $i] : ($i(v4) & $i(v3) & $i(v2) & (( ~ (v3 = v2) & apply(v0, v3, v2) &
% 10.22/2.09 apply(v0, v2, v3) & member(v3, v1) & member(v2, v1)) | (apply(v0, v3,
% 10.22/2.09 v4) & apply(v0, v2, v3) & member(v4, v1) & member(v3, v1) &
% 10.22/2.09 member(v2, v1) & ~ apply(v0, v2, v4)) | (member(v2, v1) & ~
% 10.22/2.09 apply(v0, v2, v2)))))
% 10.22/2.09
% 10.22/2.09 (thIV1)
% 10.22/2.09 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & $i(v3)
% 10.22/2.09 & $i(v2) & $i(v1) & $i(v0) & greatest(v3, v0, v1) & greatest(v2, v0, v1) &
% 10.22/2.09 order(v0, v1))
% 10.22/2.09
% 10.22/2.09 Further assumptions not needed in the proof:
% 10.22/2.09 --------------------------------------------
% 10.22/2.09 greatest_lower_bound, least, least_upper_bound, lower_bound, max, min,
% 10.22/2.09 total_order, upper_bound
% 10.22/2.09
% 10.22/2.09 Those formulas are unsatisfiable:
% 10.22/2.09 ---------------------------------
% 10.22/2.09
% 10.22/2.09 Begin of proof
% 10.22/2.09 |
% 10.22/2.09 | ALPHA: (greatest) implies:
% 10.31/2.09 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 10.31/2.09 | $i(v0) | ~ greatest(v2, v0, v1) | member(v2, v1))
% 10.31/2.09 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 10.31/2.09 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ greatest(v2, v0, v1) | ~
% 10.31/2.09 | member(v3, v1) | apply(v0, v3, v2))
% 10.31/2.09 |
% 10.31/2.09 | ALPHA: (order) implies:
% 10.31/2.09 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 10.31/2.09 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ apply(v0, v3, v2) |
% 10.31/2.09 | ~ apply(v0, v2, v3) | ~ member(v3, v1) | ~ member(v2, v1) | ~
% 10.31/2.09 | order(v0, v1))
% 10.31/2.09 |
% 10.31/2.10 | DELTA: instantiating (thIV1) with fresh symbols all_18_0, all_18_1, all_18_2,
% 10.31/2.10 | all_18_3 gives:
% 10.31/2.10 | (4) ~ (all_18_0 = all_18_1) & $i(all_18_0) & $i(all_18_1) & $i(all_18_2) &
% 10.31/2.10 | $i(all_18_3) & greatest(all_18_0, all_18_3, all_18_2) &
% 10.31/2.10 | greatest(all_18_1, all_18_3, all_18_2) & order(all_18_3, all_18_2)
% 10.31/2.10 |
% 10.31/2.10 | ALPHA: (4) implies:
% 10.31/2.10 | (5) ~ (all_18_0 = all_18_1)
% 10.31/2.10 | (6) order(all_18_3, all_18_2)
% 10.31/2.10 | (7) greatest(all_18_1, all_18_3, all_18_2)
% 10.31/2.10 | (8) greatest(all_18_0, all_18_3, all_18_2)
% 10.31/2.10 | (9) $i(all_18_3)
% 10.31/2.10 | (10) $i(all_18_2)
% 10.31/2.10 | (11) $i(all_18_1)
% 10.31/2.10 | (12) $i(all_18_0)
% 10.31/2.10 |
% 10.31/2.10 | GROUND_INST: instantiating (1) with all_18_3, all_18_2, all_18_1, simplifying
% 10.31/2.10 | with (7), (9), (10), (11) gives:
% 10.31/2.10 | (13) member(all_18_1, all_18_2)
% 10.31/2.10 |
% 10.31/2.10 | GROUND_INST: instantiating (1) with all_18_3, all_18_2, all_18_0, simplifying
% 10.31/2.10 | with (8), (9), (10), (12) gives:
% 10.31/2.10 | (14) member(all_18_0, all_18_2)
% 10.31/2.10 |
% 10.31/2.10 | GROUND_INST: instantiating (2) with all_18_3, all_18_2, all_18_0, all_18_1,
% 10.31/2.10 | simplifying with (8), (9), (10), (11), (12), (13) gives:
% 10.31/2.10 | (15) apply(all_18_3, all_18_1, all_18_0)
% 10.31/2.10 |
% 10.31/2.10 | GROUND_INST: instantiating (2) with all_18_3, all_18_2, all_18_1, all_18_0,
% 10.31/2.10 | simplifying with (7), (9), (10), (11), (12), (14) gives:
% 10.31/2.10 | (16) apply(all_18_3, all_18_0, all_18_1)
% 10.31/2.10 |
% 10.31/2.10 | GROUND_INST: instantiating (3) with all_18_3, all_18_2, all_18_1, all_18_0,
% 10.31/2.10 | simplifying with (6), (9), (10), (11), (12), (13), (14), (15),
% 10.31/2.10 | (16) gives:
% 10.31/2.10 | (17) all_18_0 = all_18_1
% 10.31/2.10 |
% 10.31/2.10 | REDUCE: (5), (17) imply:
% 10.31/2.10 | (18) $false
% 10.31/2.10 |
% 10.31/2.10 | CLOSE: (18) is inconsistent.
% 10.31/2.10 |
% 10.31/2.10 End of proof
% 10.31/2.10 % SZS output end Proof for theBenchmark
% 10.31/2.10
% 10.31/2.10 1506ms
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