TSTP Solution File: LCL664+1.001 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL664+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n008.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 08:12:14 EDT 2023
% Result : Theorem 3.97s 1.25s
% Output : Proof 4.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL664+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n008.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 : Fri Aug 25 05:07:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.65 Running up to 7 provers in parallel.
% 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.93/0.98 Prover 4: Preprocessing ...
% 1.93/0.98 Prover 1: Preprocessing ...
% 2.31/1.03 Prover 6: Preprocessing ...
% 2.31/1.03 Prover 5: Preprocessing ...
% 2.31/1.03 Prover 3: Preprocessing ...
% 2.31/1.03 Prover 0: Preprocessing ...
% 2.31/1.03 Prover 2: Preprocessing ...
% 2.67/1.13 Prover 5: Proving ...
% 2.67/1.13 Prover 2: Proving ...
% 3.36/1.16 Prover 1: Constructing countermodel ...
% 3.36/1.17 Prover 6: Proving ...
% 3.36/1.17 Prover 0: Proving ...
% 3.36/1.18 Prover 4: Constructing countermodel ...
% 3.36/1.19 Prover 3: Constructing countermodel ...
% 3.97/1.25 Prover 3: proved (589ms)
% 3.97/1.25
% 3.97/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.97/1.25
% 3.97/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.97/1.25 Prover 6: stopped
% 3.97/1.26 Prover 5: stopped
% 3.97/1.27 Prover 2: stopped
% 3.97/1.27 Prover 0: stopped
% 3.97/1.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.97/1.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.97/1.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.97/1.28 Prover 7: Preprocessing ...
% 3.97/1.29 Prover 7: Warning: ignoring some quantifiers
% 3.97/1.29 Prover 10: Preprocessing ...
% 3.97/1.29 Prover 7: Constructing countermodel ...
% 3.97/1.29 Prover 11: Preprocessing ...
% 3.97/1.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.97/1.30 Prover 8: Preprocessing ...
% 3.97/1.30 Prover 13: Preprocessing ...
% 3.97/1.32 Prover 10: Warning: ignoring some quantifiers
% 3.97/1.33 Prover 13: Warning: ignoring some quantifiers
% 3.97/1.33 Prover 13: Constructing countermodel ...
% 3.97/1.33 Prover 1: Found proof (size 14)
% 3.97/1.33 Prover 1: proved (670ms)
% 3.97/1.33 Prover 4: stopped
% 3.97/1.33 Prover 7: Found proof (size 4)
% 3.97/1.33 Prover 7: proved (80ms)
% 3.97/1.33 Prover 13: stopped
% 3.97/1.33 Prover 10: Constructing countermodel ...
% 3.97/1.34 Prover 10: stopped
% 3.97/1.36 Prover 8: Warning: ignoring some quantifiers
% 3.97/1.37 Prover 8: Constructing countermodel ...
% 3.97/1.37 Prover 8: stopped
% 3.97/1.38 Prover 11: Constructing countermodel ...
% 3.97/1.39 Prover 11: stopped
% 3.97/1.39
% 3.97/1.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.97/1.39
% 3.97/1.39 % SZS output start Proof for theBenchmark
% 3.97/1.40 Assumptions after simplification:
% 3.97/1.40 ---------------------------------
% 3.97/1.40
% 3.97/1.40 (main)
% 3.97/1.43 ? [v0: $i] : ($i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (p14(v1) =
% 3.97/1.43 v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) = v3)) & !
% 3.97/1.43 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (p12(v1) = v2) | ~ $i(v1) | ? [v3:
% 3.97/1.43 int] : ( ~ (v3 = 0) & r1(v0, v1) = v3)) & ! [v1: $i] : ! [v2: int] :
% 3.97/1.43 (v2 = 0 | ~ (p16(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 3.97/1.44 r1(v0, v1) = v3)) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & p11(v1)
% 3.97/1.44 = v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 =
% 3.97/1.44 0) & p13(v1) = v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1: $i] : ? [v2:
% 3.97/1.44 int] : ( ~ (v2 = 0) & p15(v1) = v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1:
% 3.97/1.44 $i] : ? [v2: int] : ( ~ (v2 = 0) & p12(v1) = v2 & r1(v0, v1) = 0 &
% 3.97/1.44 $i(v1)))
% 3.97/1.44
% 3.97/1.44 (function-axioms)
% 3.97/1.44 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 3.97/1.44 [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) & ! [v0:
% 3.97/1.44 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 3.97/1.44 ~ (p11(v2) = v1) | ~ (p11(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 3.97/1.44 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (p13(v2) = v1) | ~
% 3.97/1.44 (p13(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 3.97/1.44 ! [v2: $i] : (v1 = v0 | ~ (p15(v2) = v1) | ~ (p15(v2) = v0)) & ! [v0:
% 3.97/1.44 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 3.97/1.44 ~ (p14(v2) = v1) | ~ (p14(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 4.72/1.44 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (p12(v2) = v1) | ~
% 4.72/1.44 (p12(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 4.72/1.44 ! [v2: $i] : (v1 = v0 | ~ (p16(v2) = v1) | ~ (p16(v2) = v0))
% 4.72/1.44
% 4.72/1.44 Further assumptions not needed in the proof:
% 4.72/1.44 --------------------------------------------
% 4.72/1.44 reflexivity
% 4.72/1.44
% 4.72/1.44 Those formulas are unsatisfiable:
% 4.72/1.44 ---------------------------------
% 4.72/1.44
% 4.72/1.44 Begin of proof
% 4.72/1.44 |
% 4.72/1.44 | ALPHA: (function-axioms) implies:
% 4.72/1.45 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.72/1.45 | ! [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0))
% 4.72/1.45 |
% 4.72/1.45 | DELTA: instantiating (main) with fresh symbol all_4_0 gives:
% 4.72/1.45 | (2) $i(all_4_0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p14(v0) = v1)
% 4.72/1.45 | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_4_0, v0) = v2)) &
% 4.72/1.45 | ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p12(v0) = v1) | ~ $i(v0) |
% 4.72/1.45 | ? [v2: int] : ( ~ (v2 = 0) & r1(all_4_0, v0) = v2)) & ! [v0: $i] :
% 4.72/1.45 | ! [v1: int] : (v1 = 0 | ~ (p16(v0) = v1) | ~ $i(v0) | ? [v2: int] :
% 4.72/1.45 | ( ~ (v2 = 0) & r1(all_4_0, v0) = v2)) & ? [v0: $i] : ? [v1: int] :
% 4.72/1.45 | ( ~ (v1 = 0) & p11(v0) = v1 & r1(all_4_0, v0) = 0 & $i(v0)) & ? [v0:
% 4.72/1.45 | $i] : ? [v1: int] : ( ~ (v1 = 0) & p13(v0) = v1 & r1(all_4_0, v0) =
% 4.72/1.45 | 0 & $i(v0)) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p15(v0) =
% 4.72/1.45 | v1 & r1(all_4_0, v0) = 0 & $i(v0)) & ? [v0: $i] : ? [v1: int] : ( ~
% 4.72/1.45 | (v1 = 0) & p12(v0) = v1 & r1(all_4_0, v0) = 0 & $i(v0))
% 4.72/1.45 |
% 4.72/1.45 | ALPHA: (2) implies:
% 4.72/1.45 | (3) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p12(v0) = v1) | ~ $i(v0) |
% 4.72/1.45 | ? [v2: int] : ( ~ (v2 = 0) & r1(all_4_0, v0) = v2))
% 4.72/1.46 | (4) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p12(v0) = v1 & r1(all_4_0,
% 4.72/1.46 | v0) = 0 & $i(v0))
% 4.72/1.46 |
% 4.72/1.46 | DELTA: instantiating (4) with fresh symbols all_13_0, all_13_1 gives:
% 4.72/1.46 | (5) ~ (all_13_0 = 0) & p12(all_13_1) = all_13_0 & r1(all_4_0, all_13_1) =
% 4.72/1.46 | 0 & $i(all_13_1)
% 4.72/1.46 |
% 4.72/1.46 | ALPHA: (5) implies:
% 4.72/1.46 | (6) ~ (all_13_0 = 0)
% 4.72/1.46 | (7) $i(all_13_1)
% 4.72/1.46 | (8) r1(all_4_0, all_13_1) = 0
% 4.72/1.46 | (9) p12(all_13_1) = all_13_0
% 4.72/1.46 |
% 4.72/1.46 | GROUND_INST: instantiating (3) with all_13_1, all_13_0, simplifying with (7),
% 4.72/1.46 | (9) gives:
% 4.72/1.46 | (10) all_13_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_4_0, all_13_1) =
% 4.72/1.46 | v0)
% 4.72/1.46 |
% 4.72/1.46 | BETA: splitting (10) gives:
% 4.72/1.46 |
% 4.72/1.46 | Case 1:
% 4.72/1.46 | |
% 4.72/1.46 | | (11) all_13_0 = 0
% 4.72/1.46 | |
% 4.72/1.46 | | REDUCE: (6), (11) imply:
% 4.72/1.46 | | (12) $false
% 4.72/1.46 | |
% 4.72/1.46 | | CLOSE: (12) is inconsistent.
% 4.72/1.46 | |
% 4.72/1.46 | Case 2:
% 4.72/1.46 | |
% 4.72/1.46 | | (13) ? [v0: int] : ( ~ (v0 = 0) & r1(all_4_0, all_13_1) = v0)
% 4.72/1.46 | |
% 4.72/1.46 | | DELTA: instantiating (13) with fresh symbol all_22_0 gives:
% 4.72/1.46 | | (14) ~ (all_22_0 = 0) & r1(all_4_0, all_13_1) = all_22_0
% 4.72/1.46 | |
% 4.72/1.46 | | ALPHA: (14) implies:
% 4.72/1.46 | | (15) ~ (all_22_0 = 0)
% 4.72/1.46 | | (16) r1(all_4_0, all_13_1) = all_22_0
% 4.72/1.46 | |
% 4.72/1.46 | | GROUND_INST: instantiating (1) with 0, all_22_0, all_13_1, all_4_0,
% 4.72/1.46 | | simplifying with (8), (16) gives:
% 4.72/1.47 | | (17) all_22_0 = 0
% 4.72/1.47 | |
% 4.72/1.47 | | REDUCE: (15), (17) imply:
% 4.72/1.47 | | (18) $false
% 4.72/1.47 | |
% 4.72/1.47 | | CLOSE: (18) is inconsistent.
% 4.72/1.47 | |
% 4.72/1.47 | End of split
% 4.72/1.47 |
% 4.72/1.47 End of proof
% 4.72/1.47 % SZS output end Proof for theBenchmark
% 4.72/1.47
% 4.72/1.47 834ms
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