TSTP Solution File: SEU238+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU238+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n029.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 17:43:34 EDT 2023
% Result : Theorem 15.00s 2.80s
% Output : Proof 17.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU238+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n029.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 : Wed Aug 23 12:55:37 EDT 2023
% 0.13/0.35 % 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.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.85/1.13 Prover 4: Preprocessing ...
% 2.85/1.13 Prover 1: Preprocessing ...
% 3.38/1.17 Prover 2: Preprocessing ...
% 3.38/1.17 Prover 5: Preprocessing ...
% 3.38/1.17 Prover 6: Preprocessing ...
% 3.38/1.17 Prover 3: Preprocessing ...
% 3.38/1.17 Prover 0: Preprocessing ...
% 7.25/1.75 Prover 2: Proving ...
% 7.25/1.76 Prover 5: Proving ...
% 7.46/1.77 Prover 1: Warning: ignoring some quantifiers
% 7.46/1.79 Prover 3: Warning: ignoring some quantifiers
% 7.46/1.81 Prover 3: Constructing countermodel ...
% 7.46/1.82 Prover 6: Proving ...
% 7.46/1.82 Prover 1: Constructing countermodel ...
% 8.19/1.92 Prover 4: Warning: ignoring some quantifiers
% 8.66/1.95 Prover 4: Constructing countermodel ...
% 9.65/2.11 Prover 0: Proving ...
% 10.63/2.29 Prover 3: gave up
% 10.63/2.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.21/2.33 Prover 7: Preprocessing ...
% 11.72/2.42 Prover 1: gave up
% 11.72/2.43 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.72/2.45 Prover 7: Warning: ignoring some quantifiers
% 12.46/2.47 Prover 7: Constructing countermodel ...
% 12.46/2.47 Prover 8: Preprocessing ...
% 13.51/2.60 Prover 8: Warning: ignoring some quantifiers
% 13.51/2.61 Prover 8: Constructing countermodel ...
% 15.00/2.80 Prover 5: proved (2164ms)
% 15.00/2.80
% 15.00/2.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.00/2.80
% 15.00/2.80 Prover 6: stopped
% 15.00/2.81 Prover 0: stopped
% 15.00/2.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.00/2.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.00/2.83 Prover 2: stopped
% 15.00/2.83 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.00/2.84 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 15.00/2.86 Prover 10: Preprocessing ...
% 15.00/2.88 Prover 11: Preprocessing ...
% 15.00/2.90 Prover 13: Preprocessing ...
% 15.00/2.91 Prover 10: Warning: ignoring some quantifiers
% 15.00/2.92 Prover 10: Constructing countermodel ...
% 15.00/2.92 Prover 16: Preprocessing ...
% 16.13/2.99 Prover 8: gave up
% 16.13/2.99 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 16.13/3.00 Prover 13: Warning: ignoring some quantifiers
% 16.13/3.01 Prover 13: Constructing countermodel ...
% 16.13/3.02 Prover 19: Preprocessing ...
% 16.13/3.03 Prover 7: Found proof (size 46)
% 16.13/3.03 Prover 7: proved (740ms)
% 16.13/3.03 Prover 13: stopped
% 16.13/3.03 Prover 4: stopped
% 16.13/3.03 Prover 10: stopped
% 16.65/3.04 Prover 16: Warning: ignoring some quantifiers
% 16.65/3.04 Prover 16: Constructing countermodel ...
% 16.65/3.05 Prover 16: stopped
% 16.85/3.09 Prover 11: Warning: ignoring some quantifiers
% 16.85/3.10 Prover 11: Constructing countermodel ...
% 16.85/3.11 Prover 11: stopped
% 17.18/3.14 Prover 19: Warning: ignoring some quantifiers
% 17.18/3.15 Prover 19: Constructing countermodel ...
% 17.33/3.16 Prover 19: stopped
% 17.33/3.16
% 17.33/3.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.33/3.16
% 17.33/3.17 % SZS output start Proof for theBenchmark
% 17.33/3.17 Assumptions after simplification:
% 17.33/3.17 ---------------------------------
% 17.33/3.17
% 17.33/3.17 (antisymmetry_r2_hidden)
% 17.33/3.17 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ in(v1, v0) | ~ in(v0,
% 17.33/3.17 v1))
% 17.33/3.18
% 17.33/3.18 (commutativity_k2_xboole_0)
% 17.33/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 17.33/3.19 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 17.33/3.19 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 17.33/3.19 | (set_union2(v1, v0) = v2 & $i(v2)))
% 17.33/3.19
% 17.33/3.19 (d1_ordinal1)
% 17.33/3.20 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 17.33/3.20 (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & $i(v1))) & ! [v0:
% 17.33/3.20 $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 17.33/3.20 (succ(v0) = v2 & set_union2(v0, v1) = v2 & $i(v2)))
% 17.33/3.20
% 17.33/3.20 (d8_xboole_0)
% 17.33/3.20 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ subset(v0,
% 17.33/3.20 v1) | proper_subset(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 17.33/3.20 $i(v0) | ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0: $i] : ( ~
% 17.33/3.20 $i(v0) | ~ proper_subset(v0, v0))
% 17.33/3.20
% 17.33/3.20 (fc3_ordinal1)
% 17.33/3.20 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ~ ordinal(v0) |
% 17.33/3.20 ~ empty(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0)
% 17.33/3.20 | ~ ordinal(v0) | epsilon_connected(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 17.33/3.20 (succ(v0) = v1) | ~ $i(v0) | ~ ordinal(v0) | epsilon_transitive(v1)) & !
% 17.33/3.20 [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ~ ordinal(v0) |
% 17.33/3.20 ordinal(v1))
% 17.33/3.20
% 17.33/3.20 (redefinition_r1_ordinal1)
% 17.33/3.20 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1) | ~
% 17.33/3.20 ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1)) & ! [v0: $i] : !
% 17.33/3.20 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ordinal_subset(v0, v1) | ~ ordinal(v1)
% 17.33/3.20 | ~ ordinal(v0) | subset(v0, v1))
% 17.33/3.20
% 17.33/3.20 (t10_ordinal1)
% 17.33/3.20 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | in(v0, v1))
% 17.33/3.20
% 17.33/3.20 (t21_ordinal1)
% 17.33/3.20 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ epsilon_transitive(v0)
% 17.33/3.20 | ~ ordinal(v1) | ~ proper_subset(v0, v1) | in(v0, v1))
% 17.33/3.20
% 17.33/3.20 (t33_ordinal1)
% 17.33/3.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v1) | ~ $i(v2) | ~
% 17.33/3.21 $i(v0) | ~ ordinal_subset(v1, v2) | ~ ordinal(v2) | ~ ordinal(v0) |
% 17.33/3.21 in(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v1)
% 17.33/3.21 | ~ $i(v2) | ~ $i(v0) | ~ ordinal(v2) | ~ ordinal(v0) | ~ in(v0, v2) |
% 17.33/3.21 ordinal_subset(v1, v2))
% 17.33/3.21
% 17.33/3.21 (t41_ordinal1)
% 17.33/3.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ $i(v1) | ~
% 17.33/3.21 $i(v0) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ ordinal(v0) | ~
% 17.33/3.21 in(v1, v0) | in(v2, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) |
% 17.33/3.21 being_limit_ordinal(v0) | ? [v1: $i] : ? [v2: $i] : (succ(v1) = v2 &
% 17.33/3.21 $i(v2) & $i(v1) & ordinal(v1) & in(v1, v0) & ~ in(v2, v0)))
% 17.33/3.21
% 17.33/3.21 (t42_ordinal1)
% 17.33/3.21 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v1) & $i(v0) & ordinal(v0) &
% 17.33/3.21 ((v2 = v0 & succ(v1) = v0 & being_limit_ordinal(v0) & ordinal(v1)) | ( ~
% 17.33/3.21 being_limit_ordinal(v0) & ! [v3: $i] : ( ~ (succ(v3) = v0) | ~ $i(v3)
% 17.33/3.21 | ~ ordinal(v3)))))
% 17.33/3.21
% 17.33/3.21 Further assumptions not needed in the proof:
% 17.33/3.21 --------------------------------------------
% 17.33/3.21 antisymmetry_r2_xboole_0, cc1_funct_1, cc1_ordinal1, cc1_relat_1, cc2_funct_1,
% 17.33/3.21 cc2_ordinal1, cc3_ordinal1, connectedness_r1_ordinal1, dt_k1_ordinal1,
% 17.33/3.21 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_xboole_0, dt_m1_subset_1,
% 17.33/3.21 existence_m1_subset_1, fc12_relat_1, fc1_ordinal1, fc1_xboole_0, fc2_ordinal1,
% 17.33/3.21 fc2_relat_1, fc2_xboole_0, fc3_xboole_0, fc4_relat_1, idempotence_k2_xboole_0,
% 17.33/3.21 irreflexivity_r2_xboole_0, rc1_funct_1, rc1_ordinal1, rc1_relat_1, rc1_xboole_0,
% 17.33/3.21 rc2_funct_1, rc2_ordinal1, rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_ordinal1,
% 17.33/3.21 rc3_relat_1, rc4_funct_1, reflexivity_r1_ordinal1, reflexivity_r1_tarski,
% 17.33/3.21 t1_boole, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole,
% 17.33/3.21 t7_boole, t8_boole
% 17.33/3.21
% 17.33/3.21 Those formulas are unsatisfiable:
% 17.33/3.21 ---------------------------------
% 17.33/3.21
% 17.33/3.21 Begin of proof
% 17.33/3.21 |
% 17.33/3.21 | ALPHA: (commutativity_k2_xboole_0) implies:
% 17.33/3.21 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 17.33/3.21 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 17.33/3.21 |
% 17.33/3.21 | ALPHA: (d1_ordinal1) implies:
% 17.33/3.21 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2:
% 17.33/3.21 | $i] : (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) &
% 17.33/3.21 | $i(v1)))
% 17.33/3.21 |
% 17.33/3.21 | ALPHA: (d8_xboole_0) implies:
% 17.33/3.21 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 17.33/3.21 | subset(v0, v1) | proper_subset(v0, v1))
% 17.33/3.21 |
% 17.33/3.21 | ALPHA: (fc3_ordinal1) implies:
% 17.33/3.21 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ~
% 17.33/3.21 | ordinal(v0) | ordinal(v1))
% 17.33/3.22 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ~
% 17.33/3.22 | ordinal(v0) | epsilon_transitive(v1))
% 17.33/3.22 |
% 17.33/3.22 | ALPHA: (redefinition_r1_ordinal1) implies:
% 17.33/3.22 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 17.33/3.22 | ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0,
% 17.33/3.22 | v1))
% 17.33/3.22 |
% 17.33/3.22 | ALPHA: (t33_ordinal1) implies:
% 17.33/3.22 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v1) | ~
% 17.33/3.22 | $i(v2) | ~ $i(v0) | ~ ordinal(v2) | ~ ordinal(v0) | ~ in(v0, v2)
% 17.33/3.22 | | ordinal_subset(v1, v2))
% 17.33/3.22 |
% 17.33/3.22 | ALPHA: (t41_ordinal1) implies:
% 17.33/3.22 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | being_limit_ordinal(v0) |
% 17.33/3.22 | ? [v1: $i] : ? [v2: $i] : (succ(v1) = v2 & $i(v2) & $i(v1) &
% 17.33/3.22 | ordinal(v1) & in(v1, v0) & ~ in(v2, v0)))
% 17.33/3.22 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~
% 17.33/3.22 | $i(v1) | ~ $i(v0) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~
% 17.33/3.22 | ordinal(v0) | ~ in(v1, v0) | in(v2, v0))
% 17.33/3.22 |
% 17.33/3.22 | DELTA: instantiating (t42_ordinal1) with fresh symbols all_64_0, all_64_1,
% 17.33/3.22 | all_64_2 gives:
% 17.33/3.22 | (10) $i(all_64_1) & $i(all_64_2) & ordinal(all_64_2) & ((all_64_0 =
% 17.33/3.22 | all_64_2 & succ(all_64_1) = all_64_2 &
% 17.33/3.22 | being_limit_ordinal(all_64_2) & ordinal(all_64_1)) | ( ~
% 17.33/3.22 | being_limit_ordinal(all_64_2) & ! [v0: $i] : ( ~ (succ(v0) =
% 17.33/3.22 | all_64_2) | ~ $i(v0) | ~ ordinal(v0))))
% 17.33/3.22 |
% 17.33/3.22 | ALPHA: (10) implies:
% 17.33/3.22 | (11) ordinal(all_64_2)
% 17.33/3.22 | (12) $i(all_64_2)
% 17.33/3.22 | (13) $i(all_64_1)
% 17.33/3.22 | (14) (all_64_0 = all_64_2 & succ(all_64_1) = all_64_2 &
% 17.33/3.22 | being_limit_ordinal(all_64_2) & ordinal(all_64_1)) | ( ~
% 17.33/3.22 | being_limit_ordinal(all_64_2) & ! [v0: $i] : ( ~ (succ(v0) =
% 17.33/3.22 | all_64_2) | ~ $i(v0) | ~ ordinal(v0)))
% 17.33/3.22 |
% 17.33/3.22 | GROUND_INST: instantiating (8) with all_64_2, simplifying with (11), (12)
% 17.33/3.22 | gives:
% 17.33/3.22 | (15) being_limit_ordinal(all_64_2) | ? [v0: $i] : ? [v1: $i] : (succ(v0)
% 17.33/3.22 | = v1 & $i(v1) & $i(v0) & ordinal(v0) & in(v0, all_64_2) & ~ in(v1,
% 17.33/3.22 | all_64_2))
% 17.33/3.22 |
% 17.33/3.22 | BETA: splitting (14) gives:
% 17.33/3.22 |
% 17.33/3.22 | Case 1:
% 17.33/3.22 | |
% 17.33/3.22 | | (16) all_64_0 = all_64_2 & succ(all_64_1) = all_64_2 &
% 17.33/3.22 | | being_limit_ordinal(all_64_2) & ordinal(all_64_1)
% 17.33/3.22 | |
% 17.33/3.22 | | ALPHA: (16) implies:
% 17.33/3.22 | | (17) ordinal(all_64_1)
% 17.33/3.22 | | (18) being_limit_ordinal(all_64_2)
% 17.33/3.22 | | (19) succ(all_64_1) = all_64_2
% 17.33/3.22 | |
% 17.33/3.22 | | GROUND_INST: instantiating (t10_ordinal1) with all_64_1, all_64_2,
% 17.33/3.23 | | simplifying with (13), (19) gives:
% 17.33/3.23 | | (20) in(all_64_1, all_64_2)
% 17.33/3.23 | |
% 17.33/3.23 | | GROUND_INST: instantiating (2) with all_64_1, all_64_2, simplifying with
% 17.33/3.23 | | (13), (19) gives:
% 17.65/3.23 | | (21) ? [v0: $i] : (singleton(all_64_1) = v0 & set_union2(all_64_1, v0) =
% 17.65/3.23 | | all_64_2 & $i(v0) & $i(all_64_2))
% 17.65/3.23 | |
% 17.65/3.23 | | DELTA: instantiating (21) with fresh symbol all_117_0 gives:
% 17.65/3.23 | | (22) singleton(all_64_1) = all_117_0 & set_union2(all_64_1, all_117_0) =
% 17.65/3.23 | | all_64_2 & $i(all_117_0) & $i(all_64_2)
% 17.65/3.23 | |
% 17.65/3.23 | | ALPHA: (22) implies:
% 17.65/3.23 | | (23) $i(all_117_0)
% 17.65/3.23 | | (24) set_union2(all_64_1, all_117_0) = all_64_2
% 17.65/3.23 | |
% 17.65/3.23 | | GROUND_INST: instantiating (9) with all_64_2, all_64_1, all_64_2,
% 17.65/3.23 | | simplifying with (11), (12), (13), (17), (18), (19), (20)
% 17.65/3.23 | | gives:
% 17.65/3.23 | | (25) in(all_64_2, all_64_2)
% 17.65/3.23 | |
% 17.65/3.23 | | GROUND_INST: instantiating (1) with all_117_0, all_64_1, all_64_2,
% 17.65/3.23 | | simplifying with (13), (23), (24) gives:
% 17.65/3.23 | | (26) set_union2(all_117_0, all_64_1) = all_64_2 & $i(all_64_2)
% 17.65/3.23 | |
% 17.65/3.23 | | GROUND_INST: instantiating (antisymmetry_r2_hidden) with all_64_2, all_64_2,
% 17.65/3.23 | | simplifying with (12), (25) gives:
% 17.65/3.23 | | (27) $false
% 17.65/3.23 | |
% 17.65/3.23 | | CLOSE: (27) is inconsistent.
% 17.65/3.23 | |
% 17.65/3.23 | Case 2:
% 17.65/3.23 | |
% 17.65/3.23 | | (28) ~ being_limit_ordinal(all_64_2) & ! [v0: $i] : ( ~ (succ(v0) =
% 17.65/3.23 | | all_64_2) | ~ $i(v0) | ~ ordinal(v0))
% 17.65/3.23 | |
% 17.65/3.23 | | ALPHA: (28) implies:
% 17.65/3.23 | | (29) ~ being_limit_ordinal(all_64_2)
% 17.65/3.23 | | (30) ! [v0: $i] : ( ~ (succ(v0) = all_64_2) | ~ $i(v0) | ~
% 17.65/3.23 | | ordinal(v0))
% 17.65/3.23 | |
% 17.65/3.23 | | BETA: splitting (15) gives:
% 17.65/3.23 | |
% 17.65/3.23 | | Case 1:
% 17.65/3.23 | | |
% 17.65/3.23 | | | (31) being_limit_ordinal(all_64_2)
% 17.65/3.23 | | |
% 17.65/3.23 | | | PRED_UNIFY: (29), (31) imply:
% 17.65/3.23 | | | (32) $false
% 17.65/3.23 | | |
% 17.65/3.23 | | | CLOSE: (32) is inconsistent.
% 17.65/3.23 | | |
% 17.65/3.23 | | Case 2:
% 17.65/3.23 | | |
% 17.65/3.23 | | | (33) ? [v0: $i] : ? [v1: $i] : (succ(v0) = v1 & $i(v1) & $i(v0) &
% 17.65/3.23 | | | ordinal(v0) & in(v0, all_64_2) & ~ in(v1, all_64_2))
% 17.65/3.23 | | |
% 17.65/3.23 | | | DELTA: instantiating (33) with fresh symbols all_116_0, all_116_1 gives:
% 17.65/3.23 | | | (34) succ(all_116_1) = all_116_0 & $i(all_116_0) & $i(all_116_1) &
% 17.65/3.23 | | | ordinal(all_116_1) & in(all_116_1, all_64_2) & ~ in(all_116_0,
% 17.65/3.23 | | | all_64_2)
% 17.65/3.23 | | |
% 17.65/3.23 | | | ALPHA: (34) implies:
% 17.65/3.23 | | | (35) ~ in(all_116_0, all_64_2)
% 17.65/3.23 | | | (36) in(all_116_1, all_64_2)
% 17.65/3.23 | | | (37) ordinal(all_116_1)
% 17.65/3.23 | | | (38) $i(all_116_1)
% 17.65/3.23 | | | (39) succ(all_116_1) = all_116_0
% 17.65/3.23 | | |
% 17.65/3.23 | | | GROUND_INST: instantiating (7) with all_116_1, all_116_0, all_64_2,
% 17.65/3.23 | | | simplifying with (11), (12), (36), (37), (38), (39) gives:
% 17.65/3.23 | | | (40) ordinal_subset(all_116_0, all_64_2)
% 17.65/3.23 | | |
% 17.65/3.23 | | | GROUND_INST: instantiating (5) with all_116_1, all_116_0, simplifying with
% 17.65/3.24 | | | (37), (38), (39) gives:
% 17.65/3.24 | | | (41) epsilon_transitive(all_116_0)
% 17.65/3.24 | | |
% 17.65/3.24 | | | GROUND_INST: instantiating (4) with all_116_1, all_116_0, simplifying with
% 17.65/3.24 | | | (37), (38), (39) gives:
% 17.65/3.24 | | | (42) ordinal(all_116_0)
% 17.65/3.24 | | |
% 17.65/3.24 | | | GROUND_INST: instantiating (30) with all_116_1, simplifying with (37),
% 17.65/3.24 | | | (38) gives:
% 17.65/3.24 | | | (43) ~ (succ(all_116_1) = all_64_2)
% 17.65/3.24 | | |
% 17.65/3.24 | | | GROUND_INST: instantiating (2) with all_116_1, all_116_0, simplifying with
% 17.65/3.24 | | | (38), (39) gives:
% 17.65/3.24 | | | (44) ? [v0: $i] : (singleton(all_116_1) = v0 & set_union2(all_116_1,
% 17.65/3.24 | | | v0) = all_116_0 & $i(v0) & $i(all_116_0))
% 17.65/3.24 | | |
% 17.65/3.24 | | | DELTA: instantiating (44) with fresh symbol all_128_0 gives:
% 17.65/3.24 | | | (45) singleton(all_116_1) = all_128_0 & set_union2(all_116_1,
% 17.65/3.24 | | | all_128_0) = all_116_0 & $i(all_128_0) & $i(all_116_0)
% 17.65/3.24 | | |
% 17.65/3.24 | | | ALPHA: (45) implies:
% 17.65/3.24 | | | (46) $i(all_116_0)
% 17.65/3.24 | | | (47) $i(all_128_0)
% 17.65/3.24 | | | (48) set_union2(all_116_1, all_128_0) = all_116_0
% 17.65/3.24 | | |
% 17.65/3.24 | | | PRED_UNIFY: (39), (43) imply:
% 17.65/3.24 | | | (49) ~ (all_116_0 = all_64_2)
% 17.65/3.24 | | |
% 17.65/3.24 | | | GROUND_INST: instantiating (6) with all_116_0, all_64_2, simplifying with
% 17.65/3.24 | | | (11), (12), (40), (42), (46) gives:
% 17.65/3.24 | | | (50) subset(all_116_0, all_64_2)
% 17.65/3.24 | | |
% 17.65/3.24 | | | GROUND_INST: instantiating (1) with all_128_0, all_116_1, all_116_0,
% 17.65/3.24 | | | simplifying with (38), (47), (48) gives:
% 17.65/3.24 | | | (51) set_union2(all_128_0, all_116_1) = all_116_0 & $i(all_116_0)
% 17.65/3.24 | | |
% 17.65/3.24 | | | GROUND_INST: instantiating (3) with all_116_0, all_64_2, simplifying with
% 17.65/3.24 | | | (12), (46), (50) gives:
% 17.65/3.24 | | | (52) all_116_0 = all_64_2 | proper_subset(all_116_0, all_64_2)
% 17.65/3.24 | | |
% 17.65/3.24 | | | BETA: splitting (52) gives:
% 17.65/3.24 | | |
% 17.65/3.24 | | | Case 1:
% 17.65/3.24 | | | |
% 17.65/3.24 | | | | (53) proper_subset(all_116_0, all_64_2)
% 17.65/3.24 | | | |
% 17.65/3.24 | | | | GROUND_INST: instantiating (t21_ordinal1) with all_116_0, all_64_2,
% 17.65/3.24 | | | | simplifying with (11), (12), (35), (41), (46), (53) gives:
% 17.65/3.24 | | | | (54) $false
% 17.65/3.24 | | | |
% 17.65/3.24 | | | | CLOSE: (54) is inconsistent.
% 17.65/3.24 | | | |
% 17.65/3.24 | | | Case 2:
% 17.65/3.24 | | | |
% 17.65/3.24 | | | | (55) all_116_0 = all_64_2
% 17.65/3.24 | | | |
% 17.65/3.24 | | | | REDUCE: (49), (55) imply:
% 17.65/3.24 | | | | (56) $false
% 17.65/3.24 | | | |
% 17.65/3.24 | | | | CLOSE: (56) is inconsistent.
% 17.65/3.24 | | | |
% 17.65/3.24 | | | End of split
% 17.65/3.24 | | |
% 17.65/3.24 | | End of split
% 17.65/3.24 | |
% 17.65/3.24 | End of split
% 17.65/3.24 |
% 17.65/3.24 End of proof
% 17.65/3.24 % SZS output end Proof for theBenchmark
% 17.65/3.24
% 17.65/3.24 2630ms
%------------------------------------------------------------------------------