TSTP Solution File: KRS113+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS113+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 : n019.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 05:51:18 EDT 2023
% Result : Unsatisfiable 7.77s 1.95s
% Output : Proof 11.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KRS113+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 01:35:58 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.66 ________ _____
% 0.18/0.66 ___ __ \_________(_)________________________________
% 0.18/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.66
% 0.18/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.66 (2023-06-19)
% 0.18/0.66
% 0.18/0.66 (c) Philipp Rümmer, 2009-2023
% 0.18/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.66 Amanda Stjerna.
% 0.18/0.66 Free software under BSD-3-Clause.
% 0.18/0.66
% 0.18/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.66
% 0.18/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.68 Running up to 7 provers in parallel.
% 0.18/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.67/1.18 Prover 4: Preprocessing ...
% 2.67/1.18 Prover 1: Preprocessing ...
% 2.97/1.24 Prover 3: Preprocessing ...
% 2.97/1.24 Prover 0: Preprocessing ...
% 2.97/1.24 Prover 5: Preprocessing ...
% 2.97/1.24 Prover 6: Preprocessing ...
% 2.97/1.24 Prover 2: Preprocessing ...
% 5.76/1.65 Prover 2: Proving ...
% 5.76/1.65 Prover 5: Proving ...
% 6.16/1.73 Prover 6: Proving ...
% 6.66/1.78 Prover 3: Constructing countermodel ...
% 6.92/1.83 Prover 1: Constructing countermodel ...
% 7.15/1.90 Prover 4: Constructing countermodel ...
% 7.77/1.94 Prover 5: proved (1238ms)
% 7.77/1.94
% 7.77/1.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.77/1.95
% 7.77/1.95 Prover 2: proved (1249ms)
% 7.77/1.95
% 7.77/1.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.77/1.95
% 7.77/1.95 Prover 3: stopped
% 7.77/1.96 Prover 6: stopped
% 7.77/1.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.77/1.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.77/1.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.77/1.96 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.13/2.02 Prover 0: Proving ...
% 8.13/2.02 Prover 0: stopped
% 8.13/2.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.60/2.05 Prover 7: Preprocessing ...
% 8.60/2.07 Prover 10: Preprocessing ...
% 8.60/2.09 Prover 11: Preprocessing ...
% 8.60/2.09 Prover 8: Preprocessing ...
% 8.60/2.14 Prover 7: Warning: ignoring some quantifiers
% 8.60/2.15 Prover 1: gave up
% 8.60/2.16 Prover 13: Preprocessing ...
% 8.60/2.17 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.60/2.19 Prover 10: Warning: ignoring some quantifiers
% 8.60/2.19 Prover 7: Constructing countermodel ...
% 8.60/2.20 Prover 10: Constructing countermodel ...
% 9.05/2.22 Prover 16: Preprocessing ...
% 10.00/2.28 Prover 13: Warning: ignoring some quantifiers
% 10.00/2.29 Prover 8: Warning: ignoring some quantifiers
% 10.00/2.29 Prover 10: Found proof (size 24)
% 10.32/2.29 Prover 10: proved (335ms)
% 10.32/2.31 Prover 13: Constructing countermodel ...
% 10.32/2.31 Prover 16: Warning: ignoring some quantifiers
% 10.32/2.31 Prover 8: Constructing countermodel ...
% 10.32/2.31 Prover 7: Found proof (size 27)
% 10.32/2.31 Prover 7: proved (346ms)
% 10.32/2.31 Prover 16: Constructing countermodel ...
% 10.32/2.31 Prover 4: stopped
% 10.32/2.31 Prover 13: stopped
% 10.32/2.31 Prover 8: stopped
% 10.32/2.33 Prover 16: stopped
% 10.87/2.46 Prover 11: Constructing countermodel ...
% 11.15/2.47 Prover 11: stopped
% 11.15/2.47
% 11.15/2.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.15/2.47
% 11.15/2.48 % SZS output start Proof for theBenchmark
% 11.15/2.48 Assumptions after simplification:
% 11.15/2.48 ---------------------------------
% 11.15/2.48
% 11.15/2.48 (axiom_2)
% 11.15/2.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~ $i(v1) |
% 11.15/2.50 ~ $i(v0) | ~ rr(v0, v2) | ~ rr(v0, v1) | ~ cUnsatisfiable(v0)) & ! [v0:
% 11.15/2.50 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 11.15/2.50 rs(v0, v1) | ~ rr(v0, v2) | ~ cpxcomp(v0) | ~ cp(v1) | ~ ca_Vx2(v2) |
% 11.15/2.50 cUnsatisfiable(v0) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) & $i(v4) &
% 11.15/2.50 $i(v3) & rr(v0, v4) & rr(v0, v3))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 11.15/2.50 cUnsatisfiable(v0) | cpxcomp(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 11.15/2.50 cUnsatisfiable(v0) | ? [v1: $i] : ($i(v1) & rs(v0, v1) & cp(v1))) & ! [v0:
% 11.15/2.50 $i] : ( ~ $i(v0) | ~ cUnsatisfiable(v0) | ? [v1: $i] : ($i(v1) & rr(v0,
% 11.15/2.50 v1) & ca_Vx2(v1)))
% 11.15/2.50
% 11.15/2.50 (axiom_3)
% 11.15/2.50 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ra_Px1(v0, v1) | ~
% 11.15/2.50 cp(v0)) & ? [v0: $i] : ( ~ $i(v0) | cp(v0) | ? [v1: $i] : ($i(v1) &
% 11.15/2.50 ra_Px1(v0, v1)))
% 11.15/2.50
% 11.15/2.50 (axiom_4)
% 11.15/2.50 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ra_Px1(v0, v1) |
% 11.15/2.50 cpxcomp(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ cpxcomp(v0) | ? [v1: $i] :
% 11.15/2.50 ($i(v1) & ra_Px1(v0, v1)))
% 11.15/2.50
% 11.15/2.50 (axiom_5)
% 11.15/2.51 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rinvS(v0, v1) | ~
% 11.15/2.51 ca_Vx2(v0) | cp(v1)) & ? [v0: $i] : ( ~ $i(v0) | ca_Vx2(v0) | ? [v1: $i] :
% 11.15/2.51 ($i(v1) & rinvS(v0, v1) & ~ cp(v1)))
% 11.15/2.51
% 11.15/2.51 (axiom_6)
% 11.15/2.51 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rs(v1, v0) | rinvS(v0,
% 11.15/2.51 v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rinvS(v0,
% 11.15/2.51 v1) | rs(v1, v0))
% 11.15/2.51
% 11.15/2.51 (axiom_7)
% 11.15/2.51 $i(i2003_11_14_17_21_22376) & cUnsatisfiable(i2003_11_14_17_21_22376)
% 11.15/2.51
% 11.15/2.51 (axiom_8)
% 11.15/2.51 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rs(v0, v1) | rr(v0,
% 11.15/2.51 v1))
% 11.15/2.51
% 11.15/2.51 Further assumptions not needed in the proof:
% 11.15/2.51 --------------------------------------------
% 11.15/2.51 axiom_0, axiom_1, cUnsatisfiable_substitution_1, ca_Vx2_substitution_1,
% 11.15/2.51 cowlNothing_substitution_1, cowlThing_substitution_1, cp_substitution_1,
% 11.15/2.51 cpxcomp_substitution_1, ra_Px1_substitution_1, ra_Px1_substitution_2,
% 11.15/2.51 rinvS_substitution_1, rinvS_substitution_2, rr_substitution_1,
% 11.15/2.51 rr_substitution_2, rs_substitution_1, rs_substitution_2,
% 11.15/2.51 xsd_integer_substitution_1, xsd_string_substitution_1
% 11.15/2.51
% 11.15/2.51 Those formulas are unsatisfiable:
% 11.15/2.51 ---------------------------------
% 11.15/2.51
% 11.15/2.51 Begin of proof
% 11.15/2.51 |
% 11.15/2.51 | ALPHA: (axiom_7) implies:
% 11.15/2.52 | (1) cUnsatisfiable(i2003_11_14_17_21_22376)
% 11.15/2.52 | (2) $i(i2003_11_14_17_21_22376)
% 11.15/2.52 |
% 11.15/2.52 | ALPHA: (axiom_6) implies:
% 11.15/2.52 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rs(v1, v0) |
% 11.15/2.52 | rinvS(v0, v1))
% 11.15/2.52 |
% 11.15/2.52 | ALPHA: (axiom_5) implies:
% 11.15/2.52 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rinvS(v0, v1) |
% 11.15/2.52 | ~ ca_Vx2(v0) | cp(v1))
% 11.15/2.52 |
% 11.15/2.52 | ALPHA: (axiom_4) implies:
% 11.15/2.52 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ cpxcomp(v0) | ? [v1: $i] : ($i(v1) &
% 11.15/2.52 | ra_Px1(v0, v1)))
% 11.15/2.52 |
% 11.15/2.52 | ALPHA: (axiom_3) implies:
% 11.15/2.52 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ra_Px1(v0, v1)
% 11.15/2.52 | | ~ cp(v0))
% 11.15/2.52 |
% 11.15/2.52 | ALPHA: (axiom_2) implies:
% 11.15/2.52 | (7) ! [v0: $i] : ( ~ $i(v0) | ~ cUnsatisfiable(v0) | ? [v1: $i] :
% 11.15/2.52 | ($i(v1) & rr(v0, v1) & ca_Vx2(v1)))
% 11.15/2.52 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ cUnsatisfiable(v0) | ? [v1: $i] :
% 11.15/2.52 | ($i(v1) & rs(v0, v1) & cp(v1)))
% 11.15/2.52 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ cUnsatisfiable(v0) | cpxcomp(v0))
% 11.15/2.52 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~
% 11.15/2.52 | $i(v1) | ~ $i(v0) | ~ rr(v0, v2) | ~ rr(v0, v1) | ~
% 11.15/2.52 | cUnsatisfiable(v0))
% 11.15/2.52 |
% 11.15/2.53 | GROUND_INST: instantiating (9) with i2003_11_14_17_21_22376, simplifying with
% 11.15/2.53 | (1), (2) gives:
% 11.15/2.53 | (11) cpxcomp(i2003_11_14_17_21_22376)
% 11.15/2.53 |
% 11.15/2.53 | GROUND_INST: instantiating (8) with i2003_11_14_17_21_22376, simplifying with
% 11.15/2.53 | (1), (2) gives:
% 11.15/2.53 | (12) ? [v0: $i] : ($i(v0) & rs(i2003_11_14_17_21_22376, v0) & cp(v0))
% 11.15/2.53 |
% 11.15/2.53 | GROUND_INST: instantiating (7) with i2003_11_14_17_21_22376, simplifying with
% 11.15/2.53 | (1), (2) gives:
% 11.15/2.53 | (13) ? [v0: $i] : ($i(v0) & rr(i2003_11_14_17_21_22376, v0) & ca_Vx2(v0))
% 11.15/2.53 |
% 11.15/2.53 | DELTA: instantiating (12) with fresh symbol all_21_0 gives:
% 11.15/2.53 | (14) $i(all_21_0) & rs(i2003_11_14_17_21_22376, all_21_0) & cp(all_21_0)
% 11.15/2.53 |
% 11.15/2.53 | ALPHA: (14) implies:
% 11.15/2.53 | (15) rs(i2003_11_14_17_21_22376, all_21_0)
% 11.15/2.53 | (16) $i(all_21_0)
% 11.15/2.53 |
% 11.15/2.53 | DELTA: instantiating (13) with fresh symbol all_23_0 gives:
% 11.15/2.53 | (17) $i(all_23_0) & rr(i2003_11_14_17_21_22376, all_23_0) &
% 11.15/2.53 | ca_Vx2(all_23_0)
% 11.15/2.53 |
% 11.15/2.53 | ALPHA: (17) implies:
% 11.15/2.53 | (18) ca_Vx2(all_23_0)
% 11.15/2.53 | (19) rr(i2003_11_14_17_21_22376, all_23_0)
% 11.15/2.53 | (20) $i(all_23_0)
% 11.15/2.53 |
% 11.15/2.53 | GROUND_INST: instantiating (5) with i2003_11_14_17_21_22376, simplifying with
% 11.15/2.54 | (2), (11) gives:
% 11.15/2.54 | (21) ? [v0: $i] : ($i(v0) & ra_Px1(i2003_11_14_17_21_22376, v0))
% 11.15/2.54 |
% 11.15/2.54 | GROUND_INST: instantiating (3) with all_21_0, i2003_11_14_17_21_22376,
% 11.15/2.54 | simplifying with (2), (15), (16) gives:
% 11.15/2.54 | (22) rinvS(all_21_0, i2003_11_14_17_21_22376)
% 11.15/2.54 |
% 11.15/2.54 | GROUND_INST: instantiating (axiom_8) with i2003_11_14_17_21_22376, all_21_0,
% 11.15/2.54 | simplifying with (2), (15), (16) gives:
% 11.15/2.54 | (23) rr(i2003_11_14_17_21_22376, all_21_0)
% 11.15/2.54 |
% 11.15/2.54 | DELTA: instantiating (21) with fresh symbol all_31_0 gives:
% 11.15/2.54 | (24) $i(all_31_0) & ra_Px1(i2003_11_14_17_21_22376, all_31_0)
% 11.15/2.54 |
% 11.15/2.54 | ALPHA: (24) implies:
% 11.15/2.54 | (25) ra_Px1(i2003_11_14_17_21_22376, all_31_0)
% 11.15/2.54 | (26) $i(all_31_0)
% 11.15/2.54 |
% 11.15/2.54 | GROUND_INST: instantiating (10) with i2003_11_14_17_21_22376, all_23_0,
% 11.15/2.54 | all_21_0, simplifying with (1), (2), (16), (19), (20), (23)
% 11.15/2.54 | gives:
% 11.15/2.54 | (27) all_23_0 = all_21_0
% 11.15/2.54 |
% 11.15/2.54 | REDUCE: (18), (27) imply:
% 11.15/2.54 | (28) ca_Vx2(all_21_0)
% 11.15/2.54 |
% 11.15/2.54 | GROUND_INST: instantiating (4) with all_21_0, i2003_11_14_17_21_22376,
% 11.15/2.54 | simplifying with (2), (16), (22), (28) gives:
% 11.15/2.54 | (29) cp(i2003_11_14_17_21_22376)
% 11.15/2.54 |
% 11.15/2.54 | GROUND_INST: instantiating (6) with i2003_11_14_17_21_22376, all_31_0,
% 11.15/2.54 | simplifying with (2), (25), (26), (29) gives:
% 11.15/2.54 | (30) $false
% 11.15/2.55 |
% 11.15/2.55 | CLOSE: (30) is inconsistent.
% 11.15/2.55 |
% 11.15/2.55 End of proof
% 11.15/2.55 % SZS output end Proof for theBenchmark
% 11.15/2.55
% 11.15/2.55 1889ms
%------------------------------------------------------------------------------