TSTP Solution File: SET804+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET804+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 : n012.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 15:26:31 EDT 2023
% Result : Theorem 7.46s 1.72s
% Output : Proof 9.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET804+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 12:14:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.67/1.06 Prover 4: Preprocessing ...
% 2.67/1.06 Prover 1: Preprocessing ...
% 3.14/1.10 Prover 2: Preprocessing ...
% 3.14/1.10 Prover 3: Preprocessing ...
% 3.14/1.10 Prover 6: Preprocessing ...
% 3.14/1.10 Prover 0: Preprocessing ...
% 3.14/1.11 Prover 5: Preprocessing ...
% 5.31/1.44 Prover 5: Proving ...
% 5.31/1.48 Prover 2: Proving ...
% 5.31/1.55 Prover 6: Proving ...
% 6.05/1.58 Prover 1: Constructing countermodel ...
% 6.05/1.59 Prover 3: Constructing countermodel ...
% 7.21/1.69 Prover 1: gave up
% 7.21/1.69 Prover 3: gave up
% 7.21/1.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.21/1.70 Prover 0: Proving ...
% 7.21/1.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.46/1.72 Prover 4: Constructing countermodel ...
% 7.46/1.72 Prover 5: proved (1081ms)
% 7.46/1.72
% 7.46/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.46/1.72
% 7.46/1.73 Prover 0: stopped
% 7.46/1.73 Prover 2: stopped
% 7.65/1.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.65/1.73 Prover 6: stopped
% 7.65/1.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.65/1.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.65/1.75 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.65/1.75 Prover 7: Preprocessing ...
% 7.65/1.75 Prover 8: Preprocessing ...
% 7.65/1.79 Prover 16: Preprocessing ...
% 7.65/1.79 Prover 11: Preprocessing ...
% 7.65/1.80 Prover 10: Preprocessing ...
% 7.65/1.80 Prover 13: Preprocessing ...
% 8.29/1.83 Prover 7: Warning: ignoring some quantifiers
% 8.29/1.84 Prover 16: Warning: ignoring some quantifiers
% 8.29/1.84 Prover 7: Constructing countermodel ...
% 8.29/1.85 Prover 13: Warning: ignoring some quantifiers
% 8.29/1.85 Prover 16: Constructing countermodel ...
% 8.29/1.85 Prover 10: Warning: ignoring some quantifiers
% 8.29/1.86 Prover 10: Constructing countermodel ...
% 8.29/1.87 Prover 13: Constructing countermodel ...
% 8.83/1.91 Prover 8: Warning: ignoring some quantifiers
% 8.83/1.92 Prover 8: Constructing countermodel ...
% 9.45/2.00 Prover 10: Found proof (size 14)
% 9.45/2.00 Prover 10: proved (269ms)
% 9.45/2.00 Prover 7: stopped
% 9.45/2.00 Prover 16: stopped
% 9.45/2.00 Prover 13: Found proof (size 14)
% 9.45/2.00 Prover 13: proved (254ms)
% 9.45/2.00 Prover 8: stopped
% 9.69/2.00 Prover 4: stopped
% 9.80/2.05 Prover 11: Constructing countermodel ...
% 9.80/2.06 Prover 11: stopped
% 9.80/2.06
% 9.80/2.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.80/2.06
% 9.80/2.06 % SZS output start Proof for theBenchmark
% 9.80/2.06 Assumptions after simplification:
% 9.80/2.06 ---------------------------------
% 9.80/2.06
% 9.80/2.06 (least)
% 9.80/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 9.80/2.07 | ~ $i(v1) | ~ $i(v0) | ~ least(v2, v0, v1) | ~ member(v3, v1) |
% 9.80/2.07 apply(v0, v2, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) |
% 9.80/2.07 ~ $i(v1) | ~ $i(v0) | ~ least(v2, v0, v1) | member(v2, v1)) & ? [v0: $i]
% 9.80/2.07 : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 9.80/2.07 member(v2, v1) | least(v2, v0, v1) | ? [v3: $i] : ($i(v3) & member(v3, v1)
% 9.80/2.07 & ~ apply(v0, v2, v3)))
% 9.80/2.07
% 9.80/2.07 (min)
% 9.80/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ $i(v3) |
% 9.80/2.08 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ min(v2, v0, v1) | ~ apply(v0, v3,
% 9.80/2.08 v2) | ~ member(v3, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 9.80/2.08 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ min(v2, v0, v1) | member(v2, v1)) & ?
% 9.80/2.08 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 9.80/2.08 member(v2, v1) | min(v2, v0, v1) | ? [v3: $i] : ( ~ (v3 = v2) & $i(v3) &
% 9.80/2.08 apply(v0, v3, v2) & member(v3, v1)))
% 9.80/2.08
% 9.80/2.08 (thIV16)
% 9.80/2.08 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v3
% 9.80/2.08 = v2) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & min(v3, v0, v1) &
% 9.80/2.08 min(v2, v0, v1) & least(v4, v0, v1) & order(v0, v1))
% 9.80/2.08
% 9.80/2.08 Further assumptions not needed in the proof:
% 9.80/2.08 --------------------------------------------
% 9.80/2.08 greatest, greatest_lower_bound, least_upper_bound, lower_bound, max, order,
% 9.80/2.08 total_order, upper_bound
% 9.80/2.08
% 9.80/2.08 Those formulas are unsatisfiable:
% 9.80/2.08 ---------------------------------
% 9.80/2.08
% 9.80/2.08 Begin of proof
% 9.80/2.08 |
% 9.80/2.08 | ALPHA: (min) implies:
% 9.80/2.08 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 9.80/2.08 | $i(v0) | ~ min(v2, v0, v1) | member(v2, v1))
% 9.80/2.09 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 9.80/2.09 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ min(v2, v0, v1) | ~
% 9.80/2.09 | apply(v0, v3, v2) | ~ member(v3, v1))
% 9.80/2.09 |
% 9.80/2.09 | ALPHA: (least) implies:
% 9.80/2.09 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 9.80/2.09 | $i(v0) | ~ least(v2, v0, v1) | member(v2, v1))
% 9.80/2.09 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 9.80/2.09 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ least(v2, v0, v1) | ~ member(v3,
% 9.80/2.09 | v1) | apply(v0, v2, v3))
% 9.80/2.09 |
% 9.80/2.09 | DELTA: instantiating (thIV16) with fresh symbols all_22_0, all_22_1, all_22_2,
% 9.80/2.09 | all_22_3, all_22_4 gives:
% 9.80/2.09 | (5) ~ (all_22_1 = all_22_2) & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) &
% 9.80/2.09 | $i(all_22_3) & $i(all_22_4) & min(all_22_1, all_22_4, all_22_3) &
% 9.80/2.09 | min(all_22_2, all_22_4, all_22_3) & least(all_22_0, all_22_4, all_22_3)
% 9.80/2.09 | & order(all_22_4, all_22_3)
% 9.80/2.09 |
% 9.80/2.09 | ALPHA: (5) implies:
% 9.80/2.09 | (6) ~ (all_22_1 = all_22_2)
% 9.80/2.09 | (7) least(all_22_0, all_22_4, all_22_3)
% 9.80/2.09 | (8) min(all_22_2, all_22_4, all_22_3)
% 9.80/2.09 | (9) min(all_22_1, all_22_4, all_22_3)
% 9.80/2.09 | (10) $i(all_22_4)
% 9.80/2.09 | (11) $i(all_22_3)
% 9.80/2.09 | (12) $i(all_22_2)
% 9.80/2.09 | (13) $i(all_22_1)
% 9.80/2.09 | (14) $i(all_22_0)
% 9.80/2.09 |
% 9.80/2.09 | GROUND_INST: instantiating (3) with all_22_4, all_22_3, all_22_0, simplifying
% 9.80/2.09 | with (7), (10), (11), (14) gives:
% 9.80/2.09 | (15) member(all_22_0, all_22_3)
% 9.80/2.09 |
% 9.80/2.09 | GROUND_INST: instantiating (1) with all_22_4, all_22_3, all_22_2, simplifying
% 9.80/2.09 | with (8), (10), (11), (12) gives:
% 9.80/2.10 | (16) member(all_22_2, all_22_3)
% 9.80/2.10 |
% 9.80/2.10 | GROUND_INST: instantiating (1) with all_22_4, all_22_3, all_22_1, simplifying
% 9.80/2.10 | with (9), (10), (11), (13) gives:
% 9.80/2.10 | (17) member(all_22_1, all_22_3)
% 9.80/2.10 |
% 9.80/2.10 | GROUND_INST: instantiating (4) with all_22_4, all_22_3, all_22_0, all_22_2,
% 9.80/2.10 | simplifying with (7), (10), (11), (12), (14), (16) gives:
% 9.80/2.10 | (18) apply(all_22_4, all_22_0, all_22_2)
% 9.80/2.10 |
% 9.80/2.10 | GROUND_INST: instantiating (4) with all_22_4, all_22_3, all_22_0, all_22_1,
% 9.80/2.10 | simplifying with (7), (10), (11), (13), (14), (17) gives:
% 9.80/2.10 | (19) apply(all_22_4, all_22_0, all_22_1)
% 9.80/2.10 |
% 9.80/2.10 | GROUND_INST: instantiating (2) with all_22_4, all_22_3, all_22_2, all_22_0,
% 9.80/2.10 | simplifying with (8), (10), (11), (12), (14), (15), (18) gives:
% 9.80/2.10 | (20) all_22_0 = all_22_2
% 9.80/2.10 |
% 9.80/2.10 | GROUND_INST: instantiating (2) with all_22_4, all_22_3, all_22_1, all_22_0,
% 9.80/2.10 | simplifying with (9), (10), (11), (13), (14), (15), (19) gives:
% 9.80/2.10 | (21) all_22_0 = all_22_1
% 9.80/2.10 |
% 9.80/2.10 | COMBINE_EQS: (20), (21) imply:
% 9.80/2.10 | (22) all_22_1 = all_22_2
% 9.80/2.10 |
% 9.80/2.10 | REDUCE: (6), (22) imply:
% 9.80/2.10 | (23) $false
% 9.80/2.10 |
% 9.80/2.10 | CLOSE: (23) is inconsistent.
% 9.80/2.10 |
% 9.80/2.10 End of proof
% 9.80/2.10 % SZS output end Proof for theBenchmark
% 9.80/2.10
% 9.80/2.10 1487ms
%------------------------------------------------------------------------------