TSTP Solution File: KRS110+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS110+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 : n020.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 05:51:17 EDT 2023
% Result : Unsatisfiable 6.72s 1.61s
% Output : Proof 8.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS110+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34 % Computer : n020.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon Aug 28 01:10:29 EDT 2023
% 0.16/0.34 % 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/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.58/1.05 Prover 1: Preprocessing ...
% 2.58/1.05 Prover 4: Preprocessing ...
% 2.58/1.09 Prover 6: Preprocessing ...
% 2.58/1.09 Prover 5: Preprocessing ...
% 2.58/1.09 Prover 2: Preprocessing ...
% 2.58/1.09 Prover 3: Preprocessing ...
% 2.58/1.09 Prover 0: Preprocessing ...
% 4.71/1.38 Prover 5: Proving ...
% 4.71/1.39 Prover 2: Proving ...
% 5.39/1.44 Prover 6: Proving ...
% 5.39/1.48 Prover 3: Constructing countermodel ...
% 5.39/1.48 Prover 1: Constructing countermodel ...
% 5.39/1.55 Prover 4: Constructing countermodel ...
% 5.39/1.56 Prover 0: Proving ...
% 6.64/1.61 Prover 2: proved (981ms)
% 6.72/1.61
% 6.72/1.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.72/1.61
% 6.72/1.61 Prover 3: stopped
% 6.72/1.61 Prover 6: stopped
% 6.72/1.61 Prover 0: stopped
% 6.72/1.61 Prover 5: stopped
% 6.72/1.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.72/1.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.72/1.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.72/1.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.72/1.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.72/1.68 Prover 1: gave up
% 6.72/1.69 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.72/1.70 Prover 7: Preprocessing ...
% 7.44/1.72 Prover 13: Preprocessing ...
% 7.44/1.72 Prover 10: Preprocessing ...
% 7.44/1.72 Prover 8: Preprocessing ...
% 7.44/1.74 Prover 11: Preprocessing ...
% 7.44/1.77 Prover 16: Preprocessing ...
% 7.44/1.77 Prover 7: Warning: ignoring some quantifiers
% 7.44/1.78 Prover 7: Constructing countermodel ...
% 7.44/1.79 Prover 10: Warning: ignoring some quantifiers
% 8.10/1.80 Prover 10: Constructing countermodel ...
% 8.10/1.81 Prover 4: Found proof (size 16)
% 8.10/1.81 Prover 4: proved (1185ms)
% 8.10/1.82 Prover 7: stopped
% 8.10/1.82 Prover 10: stopped
% 8.10/1.82 Prover 11: stopped
% 8.10/1.82 Prover 13: Warning: ignoring some quantifiers
% 8.10/1.83 Prover 13: Constructing countermodel ...
% 8.10/1.83 Prover 16: Warning: ignoring some quantifiers
% 8.10/1.84 Prover 13: stopped
% 8.10/1.84 Prover 16: Constructing countermodel ...
% 8.10/1.85 Prover 16: stopped
% 8.10/1.86 Prover 8: Warning: ignoring some quantifiers
% 8.10/1.87 Prover 8: Constructing countermodel ...
% 8.10/1.88 Prover 8: stopped
% 8.10/1.88
% 8.10/1.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.10/1.88
% 8.10/1.88 % SZS output start Proof for theBenchmark
% 8.10/1.88 Assumptions after simplification:
% 8.10/1.88 ---------------------------------
% 8.10/1.88
% 8.10/1.88 (axiom_12)
% 8.73/1.90 cUnsatisfiable(i2003_11_14_17_21_12565) = 0 & $i(i2003_11_14_17_21_12565)
% 8.73/1.90
% 8.73/1.90 (axiom_2)
% 8.77/1.91 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (cpxcomp(v1) = v2) |
% 8.77/1.91 ~ (cUnsatisfiable(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3
% 8.77/1.91 = 0) & rs(v0, v1) = v3)) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] :
% 8.77/1.91 (v1 = 0 | ~ (rs(v0, v2) = 0) | ~ (cUnsatisfiable(v0) = v1) | ~ $i(v2) | ~
% 8.77/1.91 $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: int] : ? [v6: int] : ($i(v3)
% 8.77/1.91 & ((v4 = 0 & ~ (v5 = 0) & rs(v0, v3) = 0 & cpxcomp(v3) = v5) | ( ~ (v6 =
% 8.77/1.91 0) & ca_Ax2(v2) = v6)))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i]
% 8.77/1.91 : (v1 = 0 | ~ (ca_Ax2(v2) = 0) | ~ (cUnsatisfiable(v0) = v1) | ~ $i(v2) |
% 8.77/1.91 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 8.77/1.91 ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & rs(v0, v3) = 0 & cpxcomp(v3) = v5) | ( ~
% 8.77/1.91 (v6 = 0) & rs(v0, v2) = v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.77/1.91 (rs(v0, v1) = 0) | ~ (cUnsatisfiable(v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 8.77/1.91 cpxcomp(v1) = 0) & ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) |
% 8.77/1.91 ? [v1: $i] : (rs(v0, v1) = 0 & ca_Ax2(v1) = 0 & $i(v1)))
% 8.77/1.91
% 8.77/1.91 (axiom_3)
% 8.77/1.91 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cp(v0) = v1) | ~ $i(v0) | ? [v2:
% 8.77/1.91 $i] : (ra_Px1(v0, v2) = 0 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.77/1.91 (ra_Px1(v0, v1) = 0) | ~ (cp(v0) = 0) | ~ $i(v1) | ~ $i(v0))
% 8.77/1.91
% 8.77/1.91 (axiom_4)
% 8.77/1.92 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (ra_Px1(v0, v2) = 0) |
% 8.77/1.92 ~ (cpxcomp(v0) = v1) | ~ $i(v2) | ~ $i(v0)) & ! [v0: $i] : ( ~
% 8.77/1.92 (cpxcomp(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (ra_Px1(v0, v1) = 0 & $i(v1)))
% 8.77/1.92
% 8.77/1.92 (axiom_5)
% 8.77/1.92 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (rinvS(v0, v2) = 0) |
% 8.77/1.92 ~ (ca_Ax2(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : (( ~ (v3 = 0) &
% 8.77/1.92 cp(v2) = v3) | ( ~ (v3 = 0) & cp(v0) = v3))) & ! [v0: $i] : ! [v1:
% 8.77/1.92 int] : ! [v2: $i] : (v1 = 0 | ~ (cp(v2) = 0) | ~ (ca_Ax2(v0) = v1) | ~
% 8.77/1.92 $i(v2) | ~ $i(v0) | ? [v3: int] : (( ~ (v3 = 0) & rinvS(v0, v2) = v3) | (
% 8.77/1.92 ~ (v3 = 0) & cp(v0) = v3))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 8.77/1.92 (cp(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ca_Ax2(v0) = v2))
% 8.77/1.92 & ! [v0: $i] : ! [v1: $i] : ( ~ (rinvS(v0, v1) = 0) | ~ (cp(v0) = 0) | ~
% 8.77/1.92 $i(v1) | ~ $i(v0) | ? [v2: int] : ((v2 = 0 & ca_Ax2(v0) = 0) | ( ~ (v2 =
% 8.77/1.92 0) & cp(v1) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (cp(v1) = 0) |
% 8.77/1.92 ~ (cp(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ((v2 = 0 &
% 8.77/1.92 ca_Ax2(v0) = 0) | ( ~ (v2 = 0) & rinvS(v0, v1) = v2))) & ! [v0: $i] :
% 8.77/1.92 ! [v1: MultipleValueBool] : ( ~ (cp(v0) = v1) | ~ $i(v0) | ? [v2: int] : ?
% 8.77/1.92 [v3: $i] : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v5 = 0 & v4 = 0 &
% 8.77/1.92 rinvS(v0, v3) = 0 & cp(v3) = 0) | ( ~ (v2 = 0) & ca_Ax2(v0) = v2)))) &
% 8.77/1.92 ! [v0: $i] : ( ~ (ca_Ax2(v0) = 0) | ~ $i(v0) | cp(v0) = 0) & ! [v0: $i] : (
% 8.77/1.92 ~ (ca_Ax2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (rinvS(v0, v1) = 0 & cp(v1) =
% 8.77/1.92 0 & $i(v1)))
% 8.77/1.92
% 8.77/1.92 Further assumptions not needed in the proof:
% 8.77/1.92 --------------------------------------------
% 8.77/1.92 axiom_0, axiom_1, axiom_10, axiom_11, axiom_13, axiom_14, axiom_6, axiom_7,
% 8.77/1.92 axiom_8, axiom_9, cUnsatisfiable_substitution_1, ca_Ax2_substitution_1,
% 8.77/1.92 cowlNothing_substitution_1, cowlThing_substitution_1, cp_substitution_1,
% 8.77/1.92 cpxcomp_substitution_1, ra_Px1_substitution_1, ra_Px1_substitution_2,
% 8.77/1.92 rf1_substitution_1, rf1_substitution_2, rf_substitution_1, rf_substitution_2,
% 8.77/1.92 rinvF1_substitution_1, rinvF1_substitution_2, rinvF_substitution_1,
% 8.77/1.92 rinvF_substitution_2, rinvS_substitution_1, rinvS_substitution_2,
% 8.77/1.92 rs_substitution_1, rs_substitution_2, xsd_integer_substitution_1,
% 8.77/1.92 xsd_string_substitution_1
% 8.77/1.92
% 8.77/1.92 Those formulas are unsatisfiable:
% 8.77/1.92 ---------------------------------
% 8.77/1.92
% 8.77/1.92 Begin of proof
% 8.77/1.93 |
% 8.77/1.93 | ALPHA: (axiom_2) implies:
% 8.77/1.93 | (1) ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 8.77/1.93 | (rs(v0, v1) = 0 & ca_Ax2(v1) = 0 & $i(v1)))
% 8.77/1.93 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (rs(v0, v1) = 0) | ~
% 8.77/1.93 | (cUnsatisfiable(v0) = 0) | ~ $i(v1) | ~ $i(v0) | cpxcomp(v1) = 0)
% 8.77/1.93 |
% 8.77/1.93 | ALPHA: (axiom_3) implies:
% 8.77/1.93 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (ra_Px1(v0, v1) = 0) | ~ (cp(v0) = 0)
% 8.77/1.93 | | ~ $i(v1) | ~ $i(v0))
% 8.77/1.93 |
% 8.77/1.93 | ALPHA: (axiom_4) implies:
% 8.77/1.93 | (4) ! [v0: $i] : ( ~ (cpxcomp(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 8.77/1.93 | (ra_Px1(v0, v1) = 0 & $i(v1)))
% 8.77/1.93 |
% 8.77/1.93 | ALPHA: (axiom_5) implies:
% 8.77/1.93 | (5) ! [v0: $i] : ( ~ (ca_Ax2(v0) = 0) | ~ $i(v0) | cp(v0) = 0)
% 8.77/1.93 |
% 8.77/1.93 | ALPHA: (axiom_12) implies:
% 8.77/1.93 | (6) $i(i2003_11_14_17_21_12565)
% 8.77/1.93 | (7) cUnsatisfiable(i2003_11_14_17_21_12565) = 0
% 8.77/1.93 |
% 8.77/1.93 | GROUND_INST: instantiating (1) with i2003_11_14_17_21_12565, simplifying with
% 8.77/1.93 | (6), (7) gives:
% 8.77/1.93 | (8) ? [v0: $i] : (rs(i2003_11_14_17_21_12565, v0) = 0 & ca_Ax2(v0) = 0 &
% 8.77/1.93 | $i(v0))
% 8.77/1.93 |
% 8.77/1.93 | DELTA: instantiating (8) with fresh symbol all_23_0 gives:
% 8.77/1.93 | (9) rs(i2003_11_14_17_21_12565, all_23_0) = 0 & ca_Ax2(all_23_0) = 0 &
% 8.77/1.93 | $i(all_23_0)
% 8.77/1.93 |
% 8.77/1.93 | ALPHA: (9) implies:
% 8.77/1.93 | (10) $i(all_23_0)
% 8.77/1.93 | (11) ca_Ax2(all_23_0) = 0
% 8.77/1.93 | (12) rs(i2003_11_14_17_21_12565, all_23_0) = 0
% 8.77/1.93 |
% 8.77/1.93 | GROUND_INST: instantiating (5) with all_23_0, simplifying with (10), (11)
% 8.77/1.93 | gives:
% 8.77/1.93 | (13) cp(all_23_0) = 0
% 8.77/1.93 |
% 8.77/1.94 | GROUND_INST: instantiating (2) with i2003_11_14_17_21_12565, all_23_0,
% 8.77/1.94 | simplifying with (6), (7), (10), (12) gives:
% 8.77/1.94 | (14) cpxcomp(all_23_0) = 0
% 8.77/1.94 |
% 8.77/1.94 | GROUND_INST: instantiating (4) with all_23_0, simplifying with (10), (14)
% 8.77/1.94 | gives:
% 8.77/1.94 | (15) ? [v0: $i] : (ra_Px1(all_23_0, v0) = 0 & $i(v0))
% 8.77/1.94 |
% 8.77/1.94 | DELTA: instantiating (15) with fresh symbol all_39_0 gives:
% 8.77/1.94 | (16) ra_Px1(all_23_0, all_39_0) = 0 & $i(all_39_0)
% 8.77/1.94 |
% 8.77/1.94 | ALPHA: (16) implies:
% 8.77/1.94 | (17) $i(all_39_0)
% 8.77/1.94 | (18) ra_Px1(all_23_0, all_39_0) = 0
% 8.77/1.94 |
% 8.77/1.94 | GROUND_INST: instantiating (3) with all_23_0, all_39_0, simplifying with (10),
% 8.77/1.94 | (13), (17), (18) gives:
% 8.77/1.94 | (19) $false
% 8.77/1.94 |
% 8.77/1.94 | CLOSE: (19) is inconsistent.
% 8.77/1.94 |
% 8.77/1.94 End of proof
% 8.77/1.94 % SZS output end Proof for theBenchmark
% 8.77/1.94
% 8.77/1.94 1330ms
%------------------------------------------------------------------------------