TSTP Solution File: SYN415+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN415+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n026.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 : Fri Sep 1 03:27:36 EDT 2023
% Result : Theorem 3.50s 1.19s
% Output : Proof 4.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN415+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n026.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 21:07:03 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.56/0.94 Prover 4: Preprocessing ...
% 1.56/0.95 Prover 1: Preprocessing ...
% 2.18/0.99 Prover 3: Preprocessing ...
% 2.18/0.99 Prover 5: Preprocessing ...
% 2.18/0.99 Prover 0: Preprocessing ...
% 2.18/0.99 Prover 2: Preprocessing ...
% 2.18/0.99 Prover 6: Preprocessing ...
% 2.49/1.09 Prover 3: Constructing countermodel ...
% 2.49/1.09 Prover 1: Constructing countermodel ...
% 2.49/1.09 Prover 5: Constructing countermodel ...
% 2.49/1.09 Prover 0: Proving ...
% 2.49/1.09 Prover 4: Constructing countermodel ...
% 2.49/1.09 Prover 2: Constructing countermodel ...
% 2.49/1.09 Prover 6: Proving ...
% 3.50/1.19 Prover 5: proved (561ms)
% 3.50/1.19
% 3.50/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.50/1.19
% 3.50/1.19 Prover 2: stopped
% 3.50/1.19 Prover 3: stopped
% 3.50/1.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.50/1.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.50/1.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.50/1.19 Prover 6: stopped
% 3.50/1.19 Prover 0: stopped
% 3.50/1.20 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.50/1.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.50/1.20 Prover 7: Preprocessing ...
% 3.50/1.21 Prover 10: Preprocessing ...
% 3.50/1.21 Prover 8: Preprocessing ...
% 3.50/1.21 Prover 11: Preprocessing ...
% 3.50/1.22 Prover 13: Preprocessing ...
% 3.50/1.23 Prover 10: Constructing countermodel ...
% 3.50/1.24 Prover 8: Warning: ignoring some quantifiers
% 3.50/1.24 Prover 7: Constructing countermodel ...
% 3.50/1.24 Prover 13: Constructing countermodel ...
% 3.50/1.24 Prover 8: Constructing countermodel ...
% 3.50/1.24 Prover 1: Found proof (size 22)
% 3.50/1.24 Prover 1: proved (617ms)
% 3.50/1.25 Prover 8: stopped
% 3.50/1.25 Prover 4: stopped
% 3.50/1.25 Prover 10: stopped
% 3.50/1.25 Prover 13: stopped
% 3.50/1.25 Prover 7: stopped
% 3.50/1.26 Prover 11: Constructing countermodel ...
% 3.50/1.27 Prover 11: stopped
% 3.50/1.27
% 3.50/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.50/1.27
% 4.12/1.27 % SZS output start Proof for theBenchmark
% 4.12/1.27 Assumptions after simplification:
% 4.12/1.27 ---------------------------------
% 4.12/1.27
% 4.12/1.27 (kalish317)
% 4.18/1.31 ( ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (f(v1) = 0) | ~ (f(v0) = 0) | ~
% 4.18/1.31 $i(v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ (f(v0) = 0) | ~ $i(v0) | ? [v1:
% 4.18/1.31 $i] : ( ~ (v1 = v0) & f(v1) = 0 & $i(v1))) & ? [v0: $i] : (f(v0) = 0 &
% 4.18/1.31 $i(v0))) | ( ? [v0: $i] : (f(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = v0 |
% 4.18/1.31 ~ (f(v1) = 0) | ~ $i(v1))) & ( ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0)
% 4.18/1.31 & f(v1) = 0 & f(v0) = 0 & $i(v1) & $i(v0)) | ! [v0: $i] : ( ~ (f(v0) =
% 4.18/1.31 0) | ~ $i(v0))))
% 4.18/1.31
% 4.18/1.31 Those formulas are unsatisfiable:
% 4.18/1.31 ---------------------------------
% 4.18/1.31
% 4.18/1.31 Begin of proof
% 4.18/1.31 |
% 4.18/1.31 | BETA: splitting (kalish317) gives:
% 4.18/1.31 |
% 4.18/1.31 | Case 1:
% 4.18/1.31 | |
% 4.18/1.32 | | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (f(v1) = 0) | ~ (f(v0) =
% 4.18/1.32 | | 0) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ (f(v0) = 0) | ~
% 4.18/1.32 | | $i(v0) | ? [v1: $i] : ( ~ (v1 = v0) & f(v1) = 0 & $i(v1))) & ?
% 4.18/1.32 | | [v0: $i] : (f(v0) = 0 & $i(v0))
% 4.30/1.32 | |
% 4.30/1.32 | | ALPHA: (1) implies:
% 4.30/1.32 | | (2) ! [v0: $i] : ( ~ (f(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ( ~ (v1 =
% 4.30/1.32 | | v0) & f(v1) = 0 & $i(v1)))
% 4.30/1.32 | | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (f(v1) = 0) | ~ (f(v0) =
% 4.30/1.32 | | 0) | ~ $i(v1) | ~ $i(v0))
% 4.30/1.32 | | (4) ? [v0: $i] : (f(v0) = 0 & $i(v0))
% 4.30/1.32 | |
% 4.30/1.32 | | DELTA: instantiating (4) with fresh symbol all_10_0 gives:
% 4.30/1.32 | | (5) f(all_10_0) = 0 & $i(all_10_0)
% 4.30/1.32 | |
% 4.30/1.32 | | ALPHA: (5) implies:
% 4.30/1.32 | | (6) $i(all_10_0)
% 4.30/1.33 | | (7) f(all_10_0) = 0
% 4.30/1.33 | |
% 4.30/1.33 | | GROUND_INST: instantiating (2) with all_10_0, simplifying with (6), (7)
% 4.30/1.33 | | gives:
% 4.30/1.33 | | (8) ? [v0: any] : ( ~ (v0 = all_10_0) & f(v0) = 0 & $i(v0))
% 4.30/1.33 | |
% 4.30/1.33 | | DELTA: instantiating (8) with fresh symbol all_17_0 gives:
% 4.30/1.33 | | (9) ~ (all_17_0 = all_10_0) & f(all_17_0) = 0 & $i(all_17_0)
% 4.30/1.33 | |
% 4.30/1.33 | | ALPHA: (9) implies:
% 4.30/1.33 | | (10) ~ (all_17_0 = all_10_0)
% 4.30/1.33 | | (11) $i(all_17_0)
% 4.30/1.33 | | (12) f(all_17_0) = 0
% 4.30/1.33 | |
% 4.30/1.33 | | GROUND_INST: instantiating (3) with all_10_0, all_17_0, simplifying with
% 4.30/1.33 | | (6), (7), (11), (12) gives:
% 4.30/1.33 | | (13) all_17_0 = all_10_0
% 4.30/1.33 | |
% 4.30/1.33 | | REDUCE: (10), (13) imply:
% 4.30/1.33 | | (14) $false
% 4.30/1.33 | |
% 4.30/1.33 | | CLOSE: (14) is inconsistent.
% 4.30/1.33 | |
% 4.30/1.33 | Case 2:
% 4.30/1.33 | |
% 4.30/1.33 | | (15) ? [v0: $i] : (f(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = v0 | ~
% 4.30/1.33 | | (f(v1) = 0) | ~ $i(v1))) & ( ? [v0: $i] : ? [v1: $i] : ( ~ (v1
% 4.30/1.33 | | = v0) & f(v1) = 0 & f(v0) = 0 & $i(v1) & $i(v0)) | ! [v0: $i]
% 4.30/1.33 | | : ( ~ (f(v0) = 0) | ~ $i(v0)))
% 4.30/1.33 | |
% 4.30/1.33 | | ALPHA: (15) implies:
% 4.30/1.34 | | (16) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & f(v1) = 0 & f(v0) = 0 &
% 4.30/1.34 | | $i(v1) & $i(v0)) | ! [v0: $i] : ( ~ (f(v0) = 0) | ~ $i(v0))
% 4.30/1.34 | | (17) ? [v0: $i] : (f(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = v0 | ~
% 4.30/1.34 | | (f(v1) = 0) | ~ $i(v1)))
% 4.30/1.34 | |
% 4.30/1.34 | | DELTA: instantiating (17) with fresh symbol all_9_0 gives:
% 4.30/1.34 | | (18) f(all_9_0) = 0 & $i(all_9_0) & ! [v0: any] : (v0 = all_9_0 | ~
% 4.30/1.34 | | (f(v0) = 0) | ~ $i(v0))
% 4.30/1.34 | |
% 4.30/1.34 | | ALPHA: (18) implies:
% 4.30/1.34 | | (19) $i(all_9_0)
% 4.30/1.34 | | (20) f(all_9_0) = 0
% 4.30/1.34 | | (21) ! [v0: any] : (v0 = all_9_0 | ~ (f(v0) = 0) | ~ $i(v0))
% 4.30/1.34 | |
% 4.30/1.34 | | BETA: splitting (16) gives:
% 4.30/1.34 | |
% 4.30/1.34 | | Case 1:
% 4.30/1.34 | | |
% 4.30/1.34 | | | (22) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & f(v1) = 0 & f(v0) = 0
% 4.30/1.34 | | | & $i(v1) & $i(v0))
% 4.30/1.34 | | |
% 4.30/1.34 | | | DELTA: instantiating (22) with fresh symbols all_18_0, all_18_1 gives:
% 4.30/1.34 | | | (23) ~ (all_18_0 = all_18_1) & f(all_18_0) = 0 & f(all_18_1) = 0 &
% 4.30/1.34 | | | $i(all_18_0) & $i(all_18_1)
% 4.30/1.34 | | |
% 4.30/1.34 | | | ALPHA: (23) implies:
% 4.30/1.34 | | | (24) ~ (all_18_0 = all_18_1)
% 4.30/1.34 | | | (25) $i(all_18_1)
% 4.30/1.34 | | | (26) $i(all_18_0)
% 4.30/1.34 | | | (27) f(all_18_1) = 0
% 4.30/1.34 | | | (28) f(all_18_0) = 0
% 4.30/1.34 | | |
% 4.30/1.34 | | | GROUND_INST: instantiating (21) with all_18_1, simplifying with (25), (27)
% 4.30/1.34 | | | gives:
% 4.30/1.34 | | | (29) all_18_1 = all_9_0
% 4.30/1.34 | | |
% 4.30/1.34 | | | GROUND_INST: instantiating (21) with all_18_0, simplifying with (26), (28)
% 4.30/1.34 | | | gives:
% 4.30/1.34 | | | (30) all_18_0 = all_9_0
% 4.30/1.34 | | |
% 4.30/1.35 | | | REDUCE: (24), (29), (30) imply:
% 4.30/1.35 | | | (31) $false
% 4.30/1.35 | | |
% 4.30/1.35 | | | CLOSE: (31) is inconsistent.
% 4.30/1.35 | | |
% 4.30/1.35 | | Case 2:
% 4.30/1.35 | | |
% 4.30/1.35 | | | (32) ! [v0: $i] : ( ~ (f(v0) = 0) | ~ $i(v0))
% 4.30/1.35 | | |
% 4.30/1.35 | | | GROUND_INST: instantiating (32) with all_9_0, simplifying with (19), (20)
% 4.30/1.35 | | | gives:
% 4.30/1.35 | | | (33) $false
% 4.30/1.35 | | |
% 4.30/1.35 | | | CLOSE: (33) is inconsistent.
% 4.30/1.35 | | |
% 4.30/1.35 | | End of split
% 4.30/1.35 | |
% 4.30/1.35 | End of split
% 4.30/1.35 |
% 4.30/1.35 End of proof
% 4.30/1.35 % SZS output end Proof for theBenchmark
% 4.30/1.35
% 4.30/1.35 741ms
%------------------------------------------------------------------------------