TSTP Solution File: SEU230+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU230+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.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 17:43:30 EDT 2023
% Result : Theorem 12.09s 2.66s
% Output : Proof 14.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU230+3 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.08/0.31 % Computer : n004.cluster.edu
% 0.08/0.31 % Model : x86_64 x86_64
% 0.08/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.31 % Memory : 8042.1875MB
% 0.08/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.31 % CPULimit : 300
% 0.08/0.31 % WCLimit : 300
% 0.08/0.31 % DateTime : Wed Aug 23 15:12:53 EDT 2023
% 0.08/0.31 % CPUTime :
% 0.13/0.55 ________ _____
% 0.13/0.55 ___ __ \_________(_)________________________________
% 0.13/0.55 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.13/0.55 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.13/0.55 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.13/0.55
% 0.13/0.55 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.13/0.55 (2023-06-19)
% 0.13/0.55
% 0.13/0.55 (c) Philipp Rümmer, 2009-2023
% 0.13/0.55 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.13/0.55 Amanda Stjerna.
% 0.13/0.55 Free software under BSD-3-Clause.
% 0.13/0.55
% 0.13/0.55 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.13/0.55
% 0.13/0.55 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.13/0.58 Running up to 7 provers in parallel.
% 0.13/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.13/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.13/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.13/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.13/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.13/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.13/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.61/1.15 Prover 4: Preprocessing ...
% 2.61/1.15 Prover 1: Preprocessing ...
% 3.06/1.22 Prover 3: Preprocessing ...
% 3.06/1.22 Prover 6: Preprocessing ...
% 3.06/1.22 Prover 2: Preprocessing ...
% 3.06/1.22 Prover 5: Preprocessing ...
% 3.06/1.22 Prover 0: Preprocessing ...
% 6.69/1.80 Prover 5: Proving ...
% 6.69/1.81 Prover 3: Warning: ignoring some quantifiers
% 6.69/1.82 Prover 1: Warning: ignoring some quantifiers
% 7.01/1.85 Prover 2: Proving ...
% 7.01/1.85 Prover 3: Constructing countermodel ...
% 7.01/1.86 Prover 1: Constructing countermodel ...
% 7.01/1.86 Prover 4: Warning: ignoring some quantifiers
% 7.01/1.87 Prover 6: Proving ...
% 7.46/1.91 Prover 4: Constructing countermodel ...
% 7.46/1.96 Prover 0: Proving ...
% 10.06/2.33 Prover 3: gave up
% 10.06/2.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.20/2.38 Prover 1: gave up
% 10.20/2.41 Prover 7: Preprocessing ...
% 10.20/2.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.68/2.46 Prover 8: Preprocessing ...
% 11.72/2.58 Prover 7: Warning: ignoring some quantifiers
% 11.94/2.61 Prover 7: Constructing countermodel ...
% 12.09/2.63 Prover 8: Warning: ignoring some quantifiers
% 12.09/2.66 Prover 0: proved (2070ms)
% 12.09/2.66
% 12.09/2.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.09/2.66
% 12.09/2.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.09/2.66 Prover 5: stopped
% 12.09/2.66 Prover 2: stopped
% 12.09/2.68 Prover 6: stopped
% 12.09/2.68 Prover 8: Constructing countermodel ...
% 12.09/2.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.09/2.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.09/2.69 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 12.54/2.74 Prover 10: Preprocessing ...
% 12.54/2.77 Prover 13: Preprocessing ...
% 12.54/2.77 Prover 11: Preprocessing ...
% 12.54/2.81 Prover 16: Preprocessing ...
% 12.54/2.82 Prover 10: Warning: ignoring some quantifiers
% 12.54/2.83 Prover 10: Constructing countermodel ...
% 12.54/2.92 Prover 10: gave up
% 13.21/2.93 Prover 7: Found proof (size 14)
% 13.21/2.93 Prover 7: proved (590ms)
% 13.21/2.93 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 13.21/2.93 Prover 4: stopped
% 13.21/2.93 Prover 8: stopped
% 13.21/2.95 Prover 19: Preprocessing ...
% 13.21/2.95 Prover 13: Warning: ignoring some quantifiers
% 13.21/2.95 Prover 16: Warning: ignoring some quantifiers
% 13.21/2.96 Prover 13: Constructing countermodel ...
% 13.21/2.96 Prover 16: Constructing countermodel ...
% 13.21/2.97 Prover 13: stopped
% 13.21/2.97 Prover 16: stopped
% 13.21/2.98 Prover 11: Warning: ignoring some quantifiers
% 13.21/3.00 Prover 11: Constructing countermodel ...
% 14.30/3.02 Prover 11: stopped
% 14.38/3.05 Prover 19: Warning: ignoring some quantifiers
% 14.38/3.06 Prover 19: Constructing countermodel ...
% 14.38/3.07 Prover 19: stopped
% 14.38/3.08
% 14.38/3.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.38/3.08
% 14.38/3.08 % SZS output start Proof for theBenchmark
% 14.38/3.09 Assumptions after simplification:
% 14.38/3.09 ---------------------------------
% 14.38/3.09
% 14.38/3.09 (commutativity_k2_xboole_0)
% 14.81/3.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 14.81/3.13 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 14.81/3.13 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 14.81/3.13 | (set_union2(v1, v0) = v2 & $i(v2)))
% 14.81/3.13
% 14.81/3.13 (d1_ordinal1)
% 14.81/3.13 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 14.81/3.13 (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & $i(v1))) & ! [v0:
% 14.81/3.13 $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 14.81/3.13 (succ(v0) = v2 & set_union2(v0, v1) = v2 & $i(v2)))
% 14.81/3.13
% 14.81/3.13 (d1_tarski)
% 14.81/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 14.81/3.14 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1:
% 14.81/3.14 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~
% 14.81/3.14 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 |
% 14.81/3.14 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) |
% 14.81/3.14 ~ $i(v1) | ~ $i(v0) | in(v0, v1))
% 14.81/3.14
% 14.81/3.14 (d2_xboole_0)
% 14.81/3.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0,
% 14.81/3.15 v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3,
% 14.81/3.15 v2) | in(v3, v1) | in(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.81/3.15 ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 14.81/3.15 $i(v1) | ~ $i(v0) | ~ in(v3, v1) | in(v3, v2)) & ! [v0: $i] : ! [v1: $i]
% 14.81/3.15 : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~
% 14.81/3.15 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2)) & ? [v0: $i] :
% 14.81/3.15 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_union2(v1, v2) =
% 14.81/3.15 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ($i(v4) & ( ~
% 14.81/3.15 in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1)
% 14.81/3.15 | in(v4, v0))))
% 14.81/3.15
% 14.81/3.15 (t10_ordinal1)
% 14.81/3.15 ? [v0: $i] : ? [v1: $i] : (succ(v0) = v1 & $i(v1) & $i(v0) & ~ in(v0, v1))
% 14.81/3.15
% 14.81/3.15 Further assumptions not needed in the proof:
% 14.81/3.15 --------------------------------------------
% 14.81/3.15 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1,
% 14.81/3.15 existence_m1_subset_1, fc12_relat_1, fc1_ordinal1, fc1_xboole_0, fc2_relat_1,
% 14.81/3.15 fc2_xboole_0, fc3_xboole_0, fc4_relat_1, idempotence_k2_xboole_0, rc1_funct_1,
% 14.81/3.15 rc1_relat_1, rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_xboole_0, rc3_funct_1,
% 14.81/3.15 rc3_relat_1, rc4_funct_1, rc5_funct_1, t1_boole, t1_subset, t2_subset, t6_boole,
% 14.81/3.15 t7_boole, t8_boole
% 14.81/3.15
% 14.81/3.15 Those formulas are unsatisfiable:
% 14.81/3.15 ---------------------------------
% 14.81/3.15
% 14.81/3.15 Begin of proof
% 14.81/3.15 |
% 14.81/3.15 | ALPHA: (commutativity_k2_xboole_0) implies:
% 14.81/3.15 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 14.81/3.15 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 14.81/3.15 |
% 14.81/3.15 | ALPHA: (d1_ordinal1) implies:
% 14.81/3.15 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2:
% 14.81/3.15 | $i] : (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) &
% 14.81/3.15 | $i(v1)))
% 14.81/3.15 |
% 14.81/3.15 | ALPHA: (d1_tarski) implies:
% 14.81/3.16 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~
% 14.81/3.16 | $i(v0) | in(v0, v1))
% 14.81/3.16 |
% 14.81/3.16 | ALPHA: (d2_xboole_0) implies:
% 14.81/3.16 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 14.81/3.16 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 14.81/3.16 | $i(v0) | ~ in(v3, v0) | in(v3, v2))
% 14.81/3.16 |
% 14.81/3.16 | DELTA: instantiating (t10_ordinal1) with fresh symbols all_36_0, all_36_1
% 14.81/3.16 | gives:
% 14.81/3.16 | (5) succ(all_36_1) = all_36_0 & $i(all_36_0) & $i(all_36_1) & ~
% 14.81/3.16 | in(all_36_1, all_36_0)
% 14.81/3.16 |
% 14.81/3.16 | ALPHA: (5) implies:
% 14.81/3.16 | (6) ~ in(all_36_1, all_36_0)
% 14.81/3.16 | (7) $i(all_36_1)
% 14.81/3.16 | (8) succ(all_36_1) = all_36_0
% 14.81/3.16 |
% 14.81/3.16 | GROUND_INST: instantiating (2) with all_36_1, all_36_0, simplifying with (7),
% 14.81/3.16 | (8) gives:
% 14.81/3.16 | (9) ? [v0: $i] : (singleton(all_36_1) = v0 & set_union2(all_36_1, v0) =
% 14.81/3.16 | all_36_0 & $i(v0) & $i(all_36_0))
% 14.81/3.16 |
% 14.81/3.16 | DELTA: instantiating (9) with fresh symbol all_60_0 gives:
% 14.81/3.16 | (10) singleton(all_36_1) = all_60_0 & set_union2(all_36_1, all_60_0) =
% 14.81/3.16 | all_36_0 & $i(all_60_0) & $i(all_36_0)
% 14.81/3.16 |
% 14.81/3.16 | ALPHA: (10) implies:
% 14.81/3.16 | (11) $i(all_60_0)
% 14.81/3.17 | (12) set_union2(all_36_1, all_60_0) = all_36_0
% 14.81/3.17 | (13) singleton(all_36_1) = all_60_0
% 14.81/3.17 |
% 14.81/3.17 | GROUND_INST: instantiating (1) with all_60_0, all_36_1, all_36_0, simplifying
% 14.81/3.17 | with (7), (11), (12) gives:
% 14.81/3.17 | (14) set_union2(all_60_0, all_36_1) = all_36_0 & $i(all_36_0)
% 14.81/3.17 |
% 14.81/3.17 | ALPHA: (14) implies:
% 14.81/3.17 | (15) $i(all_36_0)
% 14.81/3.17 | (16) set_union2(all_60_0, all_36_1) = all_36_0
% 14.81/3.17 |
% 14.81/3.17 | GROUND_INST: instantiating (3) with all_36_1, all_60_0, simplifying with (7),
% 14.81/3.17 | (11), (13) gives:
% 14.81/3.17 | (17) in(all_36_1, all_60_0)
% 14.81/3.17 |
% 14.81/3.17 | GROUND_INST: instantiating (4) with all_60_0, all_36_1, all_36_0, all_36_1,
% 14.81/3.17 | simplifying with (6), (7), (11), (15), (16), (17) gives:
% 14.81/3.17 | (18) $false
% 14.81/3.17 |
% 14.81/3.17 | CLOSE: (18) is inconsistent.
% 14.81/3.17 |
% 14.81/3.17 End of proof
% 14.81/3.17 % SZS output end Proof for theBenchmark
% 14.81/3.17
% 14.81/3.17 2618ms
%------------------------------------------------------------------------------