TSTP Solution File: SET803+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET803+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 : n016.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 15:26:30 EDT 2023
% Result : Theorem 7.63s 1.79s
% Output : Proof 10.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET803+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 15:44:57 EDT 2023
% 0.14/0.35 % 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 ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.48/1.11 Prover 1: Preprocessing ...
% 2.48/1.11 Prover 4: Preprocessing ...
% 3.10/1.14 Prover 5: Preprocessing ...
% 3.10/1.14 Prover 2: Preprocessing ...
% 3.10/1.14 Prover 3: Preprocessing ...
% 3.10/1.14 Prover 6: Preprocessing ...
% 3.10/1.14 Prover 0: Preprocessing ...
% 4.42/1.48 Prover 5: Proving ...
% 5.01/1.51 Prover 2: Proving ...
% 6.83/1.66 Prover 3: Constructing countermodel ...
% 6.83/1.66 Prover 6: Proving ...
% 6.83/1.67 Prover 1: Constructing countermodel ...
% 7.31/1.76 Prover 4: Constructing countermodel ...
% 7.31/1.76 Prover 3: gave up
% 7.31/1.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.63/1.78 Prover 1: gave up
% 7.63/1.79 Prover 5: proved (1140ms)
% 7.63/1.79
% 7.63/1.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.63/1.79
% 7.63/1.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.63/1.80 Prover 2: proved (1151ms)
% 7.63/1.80
% 7.63/1.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.63/1.80
% 7.63/1.82 Prover 7: Preprocessing ...
% 7.63/1.82 Prover 6: stopped
% 7.63/1.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.63/1.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.63/1.83 Prover 0: Proving ...
% 7.63/1.83 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.19/1.86 Prover 0: stopped
% 8.19/1.87 Prover 8: Preprocessing ...
% 8.40/1.88 Prover 7: Warning: ignoring some quantifiers
% 8.40/1.88 Prover 10: Preprocessing ...
% 8.40/1.88 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.40/1.89 Prover 7: Constructing countermodel ...
% 8.40/1.91 Prover 13: Preprocessing ...
% 8.40/1.91 Prover 11: Preprocessing ...
% 8.40/1.93 Prover 16: Preprocessing ...
% 8.82/1.95 Prover 10: Warning: ignoring some quantifiers
% 8.98/1.96 Prover 10: Constructing countermodel ...
% 8.98/1.97 Prover 13: Warning: ignoring some quantifiers
% 8.98/1.99 Prover 13: Constructing countermodel ...
% 8.98/1.99 Prover 16: Warning: ignoring some quantifiers
% 8.98/2.01 Prover 8: Warning: ignoring some quantifiers
% 8.98/2.01 Prover 16: Constructing countermodel ...
% 9.49/2.02 Prover 8: Constructing countermodel ...
% 9.49/2.09 Prover 7: Found proof (size 14)
% 9.49/2.09 Prover 7: proved (331ms)
% 9.49/2.09 Prover 8: stopped
% 9.49/2.09 Prover 13: stopped
% 9.49/2.09 Prover 4: stopped
% 9.49/2.09 Prover 10: Found proof (size 14)
% 9.49/2.09 Prover 10: proved (292ms)
% 9.49/2.10 Prover 16: stopped
% 9.49/2.15 Prover 11: Constructing countermodel ...
% 9.49/2.16 Prover 11: stopped
% 9.49/2.16
% 9.49/2.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.49/2.16
% 9.49/2.17 % SZS output start Proof for theBenchmark
% 9.49/2.17 Assumptions after simplification:
% 9.49/2.17 ---------------------------------
% 9.49/2.17
% 9.49/2.17 (greatest)
% 10.09/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 10.09/2.18 | ~ $i(v1) | ~ $i(v0) | ~ greatest(v2, v0, v1) | ~ member(v3, v1) |
% 10.09/2.18 apply(v0, v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) |
% 10.09/2.18 ~ $i(v1) | ~ $i(v0) | ~ greatest(v2, v0, v1) | member(v2, v1)) & ? [v0:
% 10.09/2.18 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 10.09/2.18 member(v2, v1) | greatest(v2, v0, v1) | ? [v3: $i] : ($i(v3) & member(v3,
% 10.09/2.18 v1) & ~ apply(v0, v3, v2)))
% 10.09/2.18
% 10.09/2.18 (max)
% 10.09/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ $i(v3) |
% 10.09/2.19 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ max(v2, v0, v1) | ~ apply(v0, v2,
% 10.09/2.19 v3) | ~ member(v3, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 10.09/2.19 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ max(v2, v0, v1) | member(v2, v1)) & ?
% 10.09/2.19 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 10.09/2.19 member(v2, v1) | max(v2, v0, v1) | ? [v3: $i] : ( ~ (v3 = v2) & $i(v3) &
% 10.09/2.19 apply(v0, v2, v3) & member(v3, v1)))
% 10.09/2.19
% 10.09/2.19 (thIV15)
% 10.09/2.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v3
% 10.09/2.19 = v2) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & max(v3, v0, v1) &
% 10.09/2.19 max(v2, v0, v1) & greatest(v4, v0, v1) & order(v0, v1))
% 10.09/2.19
% 10.09/2.19 Further assumptions not needed in the proof:
% 10.09/2.19 --------------------------------------------
% 10.09/2.19 greatest_lower_bound, least, least_upper_bound, lower_bound, min, order,
% 10.09/2.19 total_order, upper_bound
% 10.09/2.19
% 10.09/2.19 Those formulas are unsatisfiable:
% 10.09/2.19 ---------------------------------
% 10.09/2.19
% 10.09/2.19 Begin of proof
% 10.09/2.19 |
% 10.09/2.19 | ALPHA: (max) implies:
% 10.09/2.20 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 10.09/2.20 | $i(v0) | ~ max(v2, v0, v1) | member(v2, v1))
% 10.09/2.20 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 10.09/2.20 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ max(v2, v0, v1) | ~
% 10.09/2.20 | apply(v0, v2, v3) | ~ member(v3, v1))
% 10.09/2.20 |
% 10.09/2.20 | ALPHA: (greatest) implies:
% 10.09/2.20 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 10.09/2.20 | $i(v0) | ~ greatest(v2, v0, v1) | member(v2, v1))
% 10.09/2.20 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 10.09/2.20 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ greatest(v2, v0, v1) | ~
% 10.09/2.20 | member(v3, v1) | apply(v0, v3, v2))
% 10.09/2.20 |
% 10.09/2.20 | DELTA: instantiating (thIV15) with fresh symbols all_22_0, all_22_1, all_22_2,
% 10.09/2.20 | all_22_3, all_22_4 gives:
% 10.09/2.20 | (5) ~ (all_22_1 = all_22_2) & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) &
% 10.09/2.20 | $i(all_22_3) & $i(all_22_4) & max(all_22_1, all_22_4, all_22_3) &
% 10.09/2.20 | max(all_22_2, all_22_4, all_22_3) & greatest(all_22_0, all_22_4,
% 10.09/2.20 | all_22_3) & order(all_22_4, all_22_3)
% 10.09/2.20 |
% 10.09/2.20 | ALPHA: (5) implies:
% 10.09/2.21 | (6) ~ (all_22_1 = all_22_2)
% 10.09/2.21 | (7) greatest(all_22_0, all_22_4, all_22_3)
% 10.09/2.21 | (8) max(all_22_2, all_22_4, all_22_3)
% 10.09/2.21 | (9) max(all_22_1, all_22_4, all_22_3)
% 10.09/2.21 | (10) $i(all_22_4)
% 10.09/2.21 | (11) $i(all_22_3)
% 10.09/2.21 | (12) $i(all_22_2)
% 10.09/2.21 | (13) $i(all_22_1)
% 10.09/2.21 | (14) $i(all_22_0)
% 10.09/2.21 |
% 10.09/2.21 | GROUND_INST: instantiating (3) with all_22_4, all_22_3, all_22_0, simplifying
% 10.09/2.21 | with (7), (10), (11), (14) gives:
% 10.09/2.21 | (15) member(all_22_0, all_22_3)
% 10.09/2.21 |
% 10.09/2.21 | GROUND_INST: instantiating (1) with all_22_4, all_22_3, all_22_2, simplifying
% 10.09/2.21 | with (8), (10), (11), (12) gives:
% 10.09/2.21 | (16) member(all_22_2, all_22_3)
% 10.09/2.21 |
% 10.09/2.21 | GROUND_INST: instantiating (1) with all_22_4, all_22_3, all_22_1, simplifying
% 10.09/2.21 | with (9), (10), (11), (13) gives:
% 10.09/2.21 | (17) member(all_22_1, all_22_3)
% 10.09/2.21 |
% 10.09/2.21 | GROUND_INST: instantiating (4) with all_22_4, all_22_3, all_22_0, all_22_2,
% 10.09/2.21 | simplifying with (7), (10), (11), (12), (14), (16) gives:
% 10.09/2.21 | (18) apply(all_22_4, all_22_2, all_22_0)
% 10.09/2.21 |
% 10.09/2.21 | GROUND_INST: instantiating (4) with all_22_4, all_22_3, all_22_0, all_22_1,
% 10.09/2.21 | simplifying with (7), (10), (11), (13), (14), (17) gives:
% 10.09/2.21 | (19) apply(all_22_4, all_22_1, all_22_0)
% 10.09/2.21 |
% 10.09/2.21 | GROUND_INST: instantiating (2) with all_22_4, all_22_3, all_22_2, all_22_0,
% 10.09/2.21 | simplifying with (8), (10), (11), (12), (14), (15), (18) gives:
% 10.09/2.22 | (20) all_22_0 = all_22_2
% 10.09/2.22 |
% 10.09/2.22 | GROUND_INST: instantiating (2) with all_22_4, all_22_3, all_22_1, all_22_0,
% 10.09/2.22 | simplifying with (9), (10), (11), (13), (14), (15), (19) gives:
% 10.09/2.22 | (21) all_22_0 = all_22_1
% 10.09/2.22 |
% 10.09/2.22 | COMBINE_EQS: (20), (21) imply:
% 10.09/2.22 | (22) all_22_1 = all_22_2
% 10.09/2.22 |
% 10.09/2.22 | REDUCE: (6), (22) imply:
% 10.09/2.22 | (23) $false
% 10.09/2.22 |
% 10.09/2.22 | CLOSE: (23) is inconsistent.
% 10.09/2.22 |
% 10.09/2.22 End of proof
% 10.09/2.22 % SZS output end Proof for theBenchmark
% 10.09/2.22
% 10.09/2.22 1601ms
%------------------------------------------------------------------------------