TSTP Solution File: SET790+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET790+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 : n011.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 6.85s 1.64s
% Output : Proof 9.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET790+4 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 11:42:54 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.95/1.10 Prover 1: Preprocessing ...
% 2.95/1.10 Prover 4: Preprocessing ...
% 3.10/1.14 Prover 6: Preprocessing ...
% 3.10/1.14 Prover 5: Preprocessing ...
% 3.10/1.14 Prover 3: Preprocessing ...
% 3.10/1.14 Prover 2: Preprocessing ...
% 3.10/1.14 Prover 0: Preprocessing ...
% 5.39/1.44 Prover 5: Proving ...
% 5.58/1.49 Prover 2: Proving ...
% 6.28/1.61 Prover 6: Proving ...
% 6.28/1.63 Prover 3: Constructing countermodel ...
% 6.85/1.63 Prover 1: Constructing countermodel ...
% 6.85/1.64 Prover 2: proved (1007ms)
% 6.85/1.64
% 6.85/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.85/1.64
% 6.85/1.64 Prover 5: proved (1006ms)
% 6.85/1.64
% 6.85/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.85/1.64
% 6.85/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.85/1.64 Prover 6: stopped
% 6.85/1.65 Prover 3: stopped
% 6.85/1.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.85/1.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.85/1.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.17/1.70 Prover 4: Constructing countermodel ...
% 7.17/1.72 Prover 7: Preprocessing ...
% 7.17/1.72 Prover 8: Preprocessing ...
% 7.17/1.73 Prover 10: Preprocessing ...
% 7.17/1.74 Prover 11: Preprocessing ...
% 7.68/1.76 Prover 0: Proving ...
% 7.83/1.77 Prover 0: stopped
% 7.83/1.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.83/1.78 Prover 1: gave up
% 7.83/1.79 Prover 7: Warning: ignoring some quantifiers
% 7.83/1.80 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.83/1.81 Prover 10: Warning: ignoring some quantifiers
% 8.23/1.83 Prover 7: Constructing countermodel ...
% 8.23/1.84 Prover 10: Constructing countermodel ...
% 8.50/1.86 Prover 13: Preprocessing ...
% 8.50/1.86 Prover 16: Preprocessing ...
% 8.50/1.90 Prover 13: Warning: ignoring some quantifiers
% 8.50/1.92 Prover 8: Warning: ignoring some quantifiers
% 8.50/1.92 Prover 13: Constructing countermodel ...
% 8.50/1.92 Prover 16: Warning: ignoring some quantifiers
% 8.50/1.93 Prover 8: Constructing countermodel ...
% 8.50/1.94 Prover 16: Constructing countermodel ...
% 8.50/1.97 Prover 7: Found proof (size 11)
% 8.50/1.97 Prover 7: proved (327ms)
% 8.50/1.97 Prover 8: stopped
% 8.50/1.97 Prover 10: Found proof (size 11)
% 8.50/1.97 Prover 10: proved (312ms)
% 8.50/1.97 Prover 13: stopped
% 8.50/1.97 Prover 4: stopped
% 8.50/1.98 Prover 16: stopped
% 9.39/2.03 Prover 11: Constructing countermodel ...
% 9.39/2.04 Prover 11: stopped
% 9.39/2.04
% 9.39/2.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.39/2.04
% 9.39/2.04 % SZS output start Proof for theBenchmark
% 9.75/2.04 Assumptions after simplification:
% 9.75/2.05 ---------------------------------
% 9.75/2.05
% 9.75/2.05 (least)
% 9.75/2.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 9.75/2.05 | ~ $i(v1) | ~ $i(v0) | ~ least(v2, v0, v1) | ~ member(v3, v1) |
% 9.75/2.05 apply(v0, v2, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) |
% 9.75/2.05 ~ $i(v1) | ~ $i(v0) | ~ least(v2, v0, v1) | member(v2, v1)) & ? [v0: $i]
% 9.75/2.05 : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 9.75/2.05 member(v2, v1) | least(v2, v0, v1) | ? [v3: $i] : ($i(v3) & member(v3, v1)
% 9.75/2.05 & ~ apply(v0, v2, v3)))
% 9.75/2.05
% 9.75/2.05 (order)
% 9.75/2.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 9.75/2.06 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ apply(v0, v3,
% 9.75/2.06 v4) | ~ apply(v0, v2, v3) | ~ member(v4, v1) | ~ member(v3, v1) | ~
% 9.75/2.06 member(v2, v1) | ~ order(v0, v1) | apply(v0, v2, v4)) & ! [v0: $i] : !
% 9.75/2.06 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ $i(v3) | ~ $i(v2) | ~
% 9.75/2.06 $i(v1) | ~ $i(v0) | ~ apply(v0, v3, v2) | ~ apply(v0, v2, v3) | ~
% 9.75/2.06 member(v3, v1) | ~ member(v2, v1) | ~ order(v0, v1)) & ! [v0: $i] : !
% 9.75/2.06 [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v2,
% 9.75/2.06 v1) | ~ order(v0, v1) | apply(v0, v2, v2)) & ? [v0: $i] : ? [v1: $i] :
% 9.75/2.06 ( ~ $i(v1) | ~ $i(v0) | order(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 9.75/2.06 $i] : ($i(v4) & $i(v3) & $i(v2) & (( ~ (v3 = v2) & apply(v0, v3, v2) &
% 9.75/2.06 apply(v0, v2, v3) & member(v3, v1) & member(v2, v1)) | (apply(v0, v3,
% 9.75/2.06 v4) & apply(v0, v2, v3) & member(v4, v1) & member(v3, v1) &
% 9.75/2.06 member(v2, v1) & ~ apply(v0, v2, v4)) | (member(v2, v1) & ~
% 9.75/2.06 apply(v0, v2, v2)))))
% 9.75/2.06
% 9.75/2.06 (thIV2)
% 9.75/2.06 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & $i(v3)
% 9.75/2.06 & $i(v2) & $i(v1) & $i(v0) & least(v3, v0, v1) & least(v2, v0, v1) &
% 9.75/2.06 order(v0, v1))
% 9.75/2.06
% 9.75/2.06 Further assumptions not needed in the proof:
% 9.75/2.06 --------------------------------------------
% 9.75/2.06 greatest, greatest_lower_bound, least_upper_bound, lower_bound, max, min,
% 9.75/2.06 total_order, upper_bound
% 9.75/2.06
% 9.75/2.06 Those formulas are unsatisfiable:
% 9.75/2.06 ---------------------------------
% 9.75/2.06
% 9.75/2.06 Begin of proof
% 9.75/2.06 |
% 9.75/2.07 | ALPHA: (least) implies:
% 9.75/2.07 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 9.75/2.07 | $i(v0) | ~ least(v2, v0, v1) | member(v2, v1))
% 9.75/2.07 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 9.75/2.07 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ least(v2, v0, v1) | ~ member(v3,
% 9.75/2.07 | v1) | apply(v0, v2, v3))
% 9.75/2.07 |
% 9.75/2.07 | ALPHA: (order) implies:
% 9.75/2.07 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 9.75/2.07 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ apply(v0, v3, v2) |
% 9.75/2.07 | ~ apply(v0, v2, v3) | ~ member(v3, v1) | ~ member(v2, v1) | ~
% 9.75/2.07 | order(v0, v1))
% 9.75/2.07 |
% 9.75/2.07 | DELTA: instantiating (thIV2) with fresh symbols all_18_0, all_18_1, all_18_2,
% 9.75/2.07 | all_18_3 gives:
% 9.75/2.07 | (4) ~ (all_18_0 = all_18_1) & $i(all_18_0) & $i(all_18_1) & $i(all_18_2) &
% 9.75/2.07 | $i(all_18_3) & least(all_18_0, all_18_3, all_18_2) & least(all_18_1,
% 9.75/2.07 | all_18_3, all_18_2) & order(all_18_3, all_18_2)
% 9.75/2.07 |
% 9.75/2.07 | ALPHA: (4) implies:
% 9.75/2.07 | (5) ~ (all_18_0 = all_18_1)
% 9.75/2.07 | (6) order(all_18_3, all_18_2)
% 9.75/2.07 | (7) least(all_18_1, all_18_3, all_18_2)
% 9.75/2.07 | (8) least(all_18_0, all_18_3, all_18_2)
% 9.75/2.07 | (9) $i(all_18_3)
% 9.75/2.07 | (10) $i(all_18_2)
% 9.75/2.07 | (11) $i(all_18_1)
% 9.75/2.07 | (12) $i(all_18_0)
% 9.75/2.07 |
% 9.75/2.08 | GROUND_INST: instantiating (1) with all_18_3, all_18_2, all_18_1, simplifying
% 9.75/2.08 | with (7), (9), (10), (11) gives:
% 9.75/2.08 | (13) member(all_18_1, all_18_2)
% 9.75/2.08 |
% 9.75/2.08 | GROUND_INST: instantiating (1) with all_18_3, all_18_2, all_18_0, simplifying
% 9.75/2.08 | with (8), (9), (10), (12) gives:
% 9.75/2.08 | (14) member(all_18_0, all_18_2)
% 9.75/2.08 |
% 9.75/2.08 | GROUND_INST: instantiating (2) with all_18_3, all_18_2, all_18_0, all_18_1,
% 9.75/2.08 | simplifying with (8), (9), (10), (11), (12), (13) gives:
% 9.75/2.08 | (15) apply(all_18_3, all_18_0, all_18_1)
% 9.75/2.08 |
% 9.75/2.08 | GROUND_INST: instantiating (2) with all_18_3, all_18_2, all_18_1, all_18_0,
% 9.75/2.08 | simplifying with (7), (9), (10), (11), (12), (14) gives:
% 9.75/2.08 | (16) apply(all_18_3, all_18_1, all_18_0)
% 9.75/2.08 |
% 9.75/2.08 | GROUND_INST: instantiating (3) with all_18_3, all_18_2, all_18_1, all_18_0,
% 9.75/2.08 | simplifying with (6), (9), (10), (11), (12), (13), (14), (15),
% 9.75/2.08 | (16) gives:
% 9.75/2.08 | (17) all_18_0 = all_18_1
% 9.75/2.08 |
% 9.75/2.08 | REDUCE: (5), (17) imply:
% 9.75/2.08 | (18) $false
% 9.75/2.08 |
% 9.75/2.08 | CLOSE: (18) is inconsistent.
% 9.75/2.08 |
% 9.75/2.08 End of proof
% 9.75/2.08 % SZS output end Proof for theBenchmark
% 9.75/2.08
% 9.75/2.08 1467ms
%------------------------------------------------------------------------------