TSTP Solution File: KRS127+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS127+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n022.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 05:51:21 EDT 2023
% Result : Unsatisfiable 5.52s 1.37s
% Output : Proof 7.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KRS127+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.32 % Computer : n022.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Aug 28 01:21:54 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.56 ________ _____
% 0.18/0.56 ___ __ \_________(_)________________________________
% 0.18/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.56
% 0.18/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.56 (2023-06-19)
% 0.18/0.56
% 0.18/0.56 (c) Philipp Rümmer, 2009-2023
% 0.18/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.56 Amanda Stjerna.
% 0.18/0.56 Free software under BSD-3-Clause.
% 0.18/0.56
% 0.18/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.56
% 0.18/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.57 Running up to 7 provers in parallel.
% 0.18/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.58 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.17/0.94 Prover 4: Preprocessing ...
% 2.17/0.94 Prover 1: Preprocessing ...
% 2.66/0.98 Prover 5: Preprocessing ...
% 2.66/0.98 Prover 0: Preprocessing ...
% 2.66/0.98 Prover 2: Preprocessing ...
% 2.66/0.98 Prover 6: Preprocessing ...
% 2.66/0.98 Prover 3: Preprocessing ...
% 3.77/1.19 Prover 5: Proving ...
% 4.38/1.22 Prover 2: Proving ...
% 4.38/1.27 Prover 1: Constructing countermodel ...
% 4.88/1.30 Prover 3: Constructing countermodel ...
% 4.88/1.31 Prover 6: Proving ...
% 4.88/1.35 Prover 4: Constructing countermodel ...
% 4.88/1.36 Prover 0: Proving ...
% 4.88/1.37 Prover 2: proved (789ms)
% 5.52/1.37
% 5.52/1.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.52/1.37
% 5.52/1.37 Prover 3: stopped
% 5.52/1.38 Prover 5: stopped
% 5.52/1.38 Prover 6: stopped
% 5.52/1.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.52/1.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.52/1.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.52/1.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.52/1.38 Prover 0: stopped
% 5.52/1.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.52/1.42 Prover 7: Preprocessing ...
% 5.52/1.44 Prover 10: Preprocessing ...
% 5.52/1.44 Prover 1: gave up
% 5.52/1.45 Prover 8: Preprocessing ...
% 5.52/1.45 Prover 13: Preprocessing ...
% 5.52/1.45 Prover 11: Preprocessing ...
% 5.52/1.45 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 5.52/1.49 Prover 10: Warning: ignoring some quantifiers
% 5.52/1.49 Prover 13: Warning: ignoring some quantifiers
% 5.52/1.50 Prover 10: Constructing countermodel ...
% 5.52/1.50 Prover 13: Constructing countermodel ...
% 5.52/1.50 Prover 16: Preprocessing ...
% 5.52/1.51 Prover 7: Warning: ignoring some quantifiers
% 6.32/1.52 Prover 4: Found proof (size 20)
% 6.32/1.52 Prover 4: proved (940ms)
% 6.32/1.52 Prover 10: stopped
% 6.32/1.52 Prover 11: stopped
% 6.32/1.52 Prover 13: stopped
% 6.32/1.53 Prover 7: Constructing countermodel ...
% 6.32/1.53 Prover 7: stopped
% 6.67/1.55 Prover 16: Warning: ignoring some quantifiers
% 6.67/1.55 Prover 16: Constructing countermodel ...
% 6.67/1.55 Prover 16: stopped
% 6.72/1.59 Prover 8: Warning: ignoring some quantifiers
% 6.72/1.59 Prover 8: Constructing countermodel ...
% 6.72/1.60 Prover 8: stopped
% 6.72/1.60
% 6.72/1.60 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.72/1.60
% 6.99/1.61 % SZS output start Proof for theBenchmark
% 6.99/1.61 Assumptions after simplification:
% 6.99/1.61 ---------------------------------
% 6.99/1.61
% 6.99/1.61 (axiom_2)
% 6.99/1.65 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~ (rr(v0,
% 6.99/1.65 v3) = 0) | ~ (rr(v0, v2) = 0) | ~ (cUnsatisfiable(v0) = v1) | ~
% 6.99/1.65 $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: int] :
% 6.99/1.65 ? [v7: int] : ? [v8: int] : ? [v9: int] : ($i(v5) & $i(v4) & ((v7 = 0 & v6
% 6.99/1.65 = 0 & ~ (v5 = v4) & rr(v0, v5) = 0 & rr(v0, v4) = 0) | ( ~ (v9 = 0) &
% 6.99/1.65 cc(v3) = v9) | ( ~ (v8 = 0) & cd(v2) = v8)))) & ! [v0: $i] : ! [v1:
% 6.99/1.65 int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~ (rr(v0, v3) = 0) | ~
% 6.99/1.65 (cd(v2) = 0) | ~ (cUnsatisfiable(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~
% 6.99/1.65 $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8:
% 6.99/1.65 int] : ? [v9: int] : ($i(v5) & $i(v4) & ((v7 = 0 & v6 = 0 & ~ (v5 = v4)
% 6.99/1.65 & rr(v0, v5) = 0 & rr(v0, v4) = 0) | ( ~ (v9 = 0) & cc(v3) = v9) | ( ~
% 6.99/1.65 (v8 = 0) & rr(v0, v2) = v8)))) & ! [v0: $i] : ! [v1: int] : ! [v2:
% 6.99/1.65 $i] : ! [v3: $i] : (v1 = 0 | ~ (rr(v0, v2) = 0) | ~ (cc(v3) = 0) | ~
% 6.99/1.65 (cUnsatisfiable(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: $i]
% 6.99/1.65 : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] :
% 6.99/1.65 ($i(v5) & $i(v4) & ((v7 = 0 & v6 = 0 & ~ (v5 = v4) & rr(v0, v5) = 0 &
% 6.99/1.65 rr(v0, v4) = 0) | ( ~ (v9 = 0) & rr(v0, v3) = v9) | ( ~ (v8 = 0) &
% 7.19/1.65 cd(v2) = v8)))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : ! [v3:
% 7.19/1.65 $i] : (v1 = 0 | ~ (cd(v2) = 0) | ~ (cc(v3) = 0) | ~ (cUnsatisfiable(v0) =
% 7.19/1.65 v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ?
% 7.19/1.65 [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ($i(v5) & $i(v4) &
% 7.19/1.65 ((v7 = 0 & v6 = 0 & ~ (v5 = v4) & rr(v0, v5) = 0 & rr(v0, v4) = 0) | ( ~
% 7.19/1.65 (v9 = 0) & rr(v0, v3) = v9) | ( ~ (v8 = 0) & rr(v0, v2) = v8)))) & !
% 7.19/1.65 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (rr(v0, v2) = 0) | ~
% 7.19/1.65 (rr(v0, v1) = 0) | ~ (cUnsatisfiable(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 7.19/1.65 $i(v0)) & ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1:
% 7.19/1.65 $i] : (rr(v0, v1) = 0 & cd(v1) = 0 & $i(v1))) & ! [v0: $i] : ( ~
% 7.19/1.65 (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (rr(v0, v1) = 0 &
% 7.19/1.65 cc(v1) = 0 & $i(v1)))
% 7.19/1.65
% 7.19/1.65 (axiom_3)
% 7.19/1.65 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cdxcomp(v0) = v1) | ~ $i(v0) | ?
% 7.19/1.65 [v2: int] : ( ~ (v2 = 0) & cc(v0) = v2)) & ! [v0: $i] : ( ~ (cc(v0) = 0) |
% 7.19/1.65 ~ $i(v0) | cdxcomp(v0) = 0)
% 7.19/1.65
% 7.19/1.65 (axiom_4)
% 7.19/1.65 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cd(v0) = v1) | ~ $i(v0) | ? [v2:
% 7.19/1.65 $i] : (ra_Px1(v0, v2) = 0 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 7.19/1.65 (ra_Px1(v0, v1) = 0) | ~ (cd(v0) = 0) | ~ $i(v1) | ~ $i(v0))
% 7.19/1.65
% 7.19/1.65 (axiom_5)
% 7.19/1.65 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (ra_Px1(v0, v2) = 0) |
% 7.19/1.65 ~ (cdxcomp(v0) = v1) | ~ $i(v2) | ~ $i(v0)) & ! [v0: $i] : ( ~
% 7.19/1.65 (cdxcomp(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (ra_Px1(v0, v1) = 0 & $i(v1)))
% 7.19/1.65
% 7.19/1.65 (axiom_6)
% 7.19/1.66 cUnsatisfiable(i2003_11_14_17_22_27794) = 0 & $i(i2003_11_14_17_22_27794)
% 7.19/1.66
% 7.19/1.66 Further assumptions not needed in the proof:
% 7.19/1.66 --------------------------------------------
% 7.19/1.66 axiom_0, axiom_1, cUnsatisfiable_substitution_1, cc_substitution_1,
% 7.19/1.66 cd_substitution_1, cdxcomp_substitution_1, cowlNothing_substitution_1,
% 7.19/1.66 cowlThing_substitution_1, ra_Px1_substitution_1, ra_Px1_substitution_2,
% 7.19/1.66 rr_substitution_1, rr_substitution_2, xsd_integer_substitution_1,
% 7.19/1.66 xsd_string_substitution_1
% 7.19/1.66
% 7.19/1.66 Those formulas are unsatisfiable:
% 7.19/1.66 ---------------------------------
% 7.19/1.66
% 7.19/1.66 Begin of proof
% 7.19/1.66 |
% 7.19/1.66 | ALPHA: (axiom_2) implies:
% 7.19/1.66 | (1) ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 7.19/1.66 | (rr(v0, v1) = 0 & cc(v1) = 0 & $i(v1)))
% 7.19/1.66 | (2) ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 7.19/1.66 | (rr(v0, v1) = 0 & cd(v1) = 0 & $i(v1)))
% 7.19/1.66 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (rr(v0, v2) =
% 7.19/1.66 | 0) | ~ (rr(v0, v1) = 0) | ~ (cUnsatisfiable(v0) = 0) | ~ $i(v2)
% 7.19/1.66 | | ~ $i(v1) | ~ $i(v0))
% 7.19/1.66 |
% 7.19/1.66 | ALPHA: (axiom_3) implies:
% 7.19/1.66 | (4) ! [v0: $i] : ( ~ (cc(v0) = 0) | ~ $i(v0) | cdxcomp(v0) = 0)
% 7.19/1.66 |
% 7.19/1.66 | ALPHA: (axiom_4) implies:
% 7.19/1.66 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (ra_Px1(v0, v1) = 0) | ~ (cd(v0) = 0)
% 7.19/1.66 | | ~ $i(v1) | ~ $i(v0))
% 7.19/1.66 |
% 7.19/1.66 | ALPHA: (axiom_5) implies:
% 7.19/1.66 | (6) ! [v0: $i] : ( ~ (cdxcomp(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 7.19/1.66 | (ra_Px1(v0, v1) = 0 & $i(v1)))
% 7.19/1.66 |
% 7.19/1.66 | ALPHA: (axiom_6) implies:
% 7.19/1.66 | (7) $i(i2003_11_14_17_22_27794)
% 7.19/1.66 | (8) cUnsatisfiable(i2003_11_14_17_22_27794) = 0
% 7.19/1.66 |
% 7.19/1.67 | GROUND_INST: instantiating (2) with i2003_11_14_17_22_27794, simplifying with
% 7.19/1.67 | (7), (8) gives:
% 7.19/1.67 | (9) ? [v0: $i] : (rr(i2003_11_14_17_22_27794, v0) = 0 & cd(v0) = 0 &
% 7.19/1.67 | $i(v0))
% 7.19/1.67 |
% 7.19/1.67 | GROUND_INST: instantiating (1) with i2003_11_14_17_22_27794, simplifying with
% 7.19/1.67 | (7), (8) gives:
% 7.19/1.67 | (10) ? [v0: $i] : (rr(i2003_11_14_17_22_27794, v0) = 0 & cc(v0) = 0 &
% 7.19/1.67 | $i(v0))
% 7.19/1.67 |
% 7.19/1.67 | DELTA: instantiating (10) with fresh symbol all_15_0 gives:
% 7.19/1.67 | (11) rr(i2003_11_14_17_22_27794, all_15_0) = 0 & cc(all_15_0) = 0 &
% 7.19/1.67 | $i(all_15_0)
% 7.19/1.67 |
% 7.19/1.67 | ALPHA: (11) implies:
% 7.19/1.67 | (12) $i(all_15_0)
% 7.19/1.67 | (13) cc(all_15_0) = 0
% 7.19/1.67 | (14) rr(i2003_11_14_17_22_27794, all_15_0) = 0
% 7.19/1.67 |
% 7.19/1.67 | DELTA: instantiating (9) with fresh symbol all_17_0 gives:
% 7.19/1.67 | (15) rr(i2003_11_14_17_22_27794, all_17_0) = 0 & cd(all_17_0) = 0 &
% 7.19/1.67 | $i(all_17_0)
% 7.19/1.67 |
% 7.19/1.67 | ALPHA: (15) implies:
% 7.19/1.67 | (16) $i(all_17_0)
% 7.19/1.67 | (17) cd(all_17_0) = 0
% 7.19/1.67 | (18) rr(i2003_11_14_17_22_27794, all_17_0) = 0
% 7.19/1.67 |
% 7.19/1.67 | GROUND_INST: instantiating (4) with all_15_0, simplifying with (12), (13)
% 7.19/1.67 | gives:
% 7.19/1.67 | (19) cdxcomp(all_15_0) = 0
% 7.19/1.67 |
% 7.19/1.67 | GROUND_INST: instantiating (3) with i2003_11_14_17_22_27794, all_15_0,
% 7.19/1.67 | all_17_0, simplifying with (7), (8), (12), (14), (16), (18)
% 7.19/1.67 | gives:
% 7.19/1.67 | (20) all_17_0 = all_15_0
% 7.19/1.67 |
% 7.19/1.67 | REDUCE: (17), (20) imply:
% 7.19/1.67 | (21) cd(all_15_0) = 0
% 7.19/1.67 |
% 7.19/1.67 | GROUND_INST: instantiating (6) with all_15_0, simplifying with (12), (19)
% 7.19/1.67 | gives:
% 7.19/1.67 | (22) ? [v0: $i] : (ra_Px1(all_15_0, v0) = 0 & $i(v0))
% 7.19/1.67 |
% 7.19/1.67 | DELTA: instantiating (22) with fresh symbol all_30_0 gives:
% 7.19/1.67 | (23) ra_Px1(all_15_0, all_30_0) = 0 & $i(all_30_0)
% 7.19/1.67 |
% 7.19/1.67 | ALPHA: (23) implies:
% 7.19/1.67 | (24) $i(all_30_0)
% 7.19/1.67 | (25) ra_Px1(all_15_0, all_30_0) = 0
% 7.19/1.67 |
% 7.19/1.68 | GROUND_INST: instantiating (5) with all_15_0, all_30_0, simplifying with (12),
% 7.19/1.68 | (21), (24), (25) gives:
% 7.19/1.68 | (26) $false
% 7.19/1.68 |
% 7.19/1.68 | CLOSE: (26) is inconsistent.
% 7.19/1.68 |
% 7.19/1.68 End of proof
% 7.19/1.68 % SZS output end Proof for theBenchmark
% 7.19/1.68
% 7.19/1.68 1118ms
%------------------------------------------------------------------------------