TSTP Solution File: SEU114+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU114+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n021.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 17:42:34 EDT 2023
% Result : Theorem 13.01s 2.50s
% Output : Proof 17.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU114+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 22:05:39 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.61 ________ _____
% 0.18/0.61 ___ __ \_________(_)________________________________
% 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.61
% 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.61 (2023-06-19)
% 0.18/0.61
% 0.18/0.61 (c) Philipp Rümmer, 2009-2023
% 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.61 Amanda Stjerna.
% 0.18/0.61 Free software under BSD-3-Clause.
% 0.18/0.61
% 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.61
% 0.18/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.62 Running up to 7 provers in parallel.
% 0.18/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.68/1.06 Prover 1: Preprocessing ...
% 2.68/1.07 Prover 4: Preprocessing ...
% 2.68/1.10 Prover 3: Preprocessing ...
% 2.68/1.10 Prover 0: Preprocessing ...
% 2.68/1.10 Prover 6: Preprocessing ...
% 2.68/1.10 Prover 2: Preprocessing ...
% 2.68/1.11 Prover 5: Preprocessing ...
% 5.70/1.53 Prover 5: Proving ...
% 6.44/1.57 Prover 2: Proving ...
% 6.44/1.59 Prover 1: Warning: ignoring some quantifiers
% 6.77/1.60 Prover 3: Warning: ignoring some quantifiers
% 6.77/1.63 Prover 3: Constructing countermodel ...
% 6.77/1.63 Prover 1: Constructing countermodel ...
% 7.09/1.65 Prover 6: Proving ...
% 7.09/1.65 Prover 4: Warning: ignoring some quantifiers
% 7.09/1.69 Prover 4: Constructing countermodel ...
% 7.09/1.69 Prover 0: Proving ...
% 13.01/2.50 Prover 5: proved (1853ms)
% 13.01/2.50
% 13.01/2.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.01/2.50
% 13.01/2.50 Prover 3: stopped
% 13.01/2.50 Prover 6: stopped
% 13.01/2.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.01/2.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.01/2.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.01/2.51 Prover 0: stopped
% 13.01/2.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.01/2.51 Prover 2: stopped
% 13.01/2.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.71/2.56 Prover 10: Preprocessing ...
% 13.71/2.58 Prover 8: Preprocessing ...
% 13.71/2.59 Prover 7: Preprocessing ...
% 14.02/2.60 Prover 11: Preprocessing ...
% 14.02/2.60 Prover 13: Preprocessing ...
% 14.02/2.64 Prover 10: Warning: ignoring some quantifiers
% 14.02/2.66 Prover 7: Warning: ignoring some quantifiers
% 14.02/2.67 Prover 10: Constructing countermodel ...
% 14.02/2.70 Prover 13: Warning: ignoring some quantifiers
% 14.02/2.71 Prover 7: Constructing countermodel ...
% 14.02/2.71 Prover 13: Constructing countermodel ...
% 14.02/2.74 Prover 8: Warning: ignoring some quantifiers
% 14.02/2.76 Prover 8: Constructing countermodel ...
% 15.39/2.83 Prover 11: Warning: ignoring some quantifiers
% 15.39/2.85 Prover 11: Constructing countermodel ...
% 16.53/2.99 Prover 10: Found proof (size 59)
% 16.53/2.99 Prover 10: proved (484ms)
% 16.53/2.99 Prover 11: stopped
% 16.53/2.99 Prover 7: stopped
% 16.53/2.99 Prover 1: stopped
% 16.53/2.99 Prover 4: stopped
% 16.53/2.99 Prover 13: stopped
% 16.53/2.99 Prover 8: stopped
% 16.53/2.99
% 16.53/2.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.53/2.99
% 16.53/3.00 % SZS output start Proof for theBenchmark
% 16.53/3.01 Assumptions after simplification:
% 16.53/3.01 ---------------------------------
% 16.53/3.01
% 16.53/3.01 (cc2_finset_1)
% 16.53/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v2)
% 16.53/3.03 | ~ $i(v0) | ~ element(v2, v1) | ~ finite(v0) | finite(v2))
% 16.53/3.03
% 16.53/3.03 (d3_tarski)
% 16.53/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 16.53/3.03 ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ? [v0: $i] : ? [v1: $i]
% 16.53/3.03 : ( ~ $i(v1) | ~ $i(v0) | subset(v0, v1) | ? [v2: $i] : ($i(v2) & in(v2, v0)
% 16.53/3.03 & ~ in(v2, v1)))
% 16.53/3.03
% 16.53/3.03 (d5_finsub_1)
% 17.15/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (finite_subsets(v0) =
% 17.15/3.04 v2) | ~ $i(v1) | ~ $i(v0) | ~ preboolean(v1) | ? [v3: $i] : ($i(v3) &
% 17.15/3.04 ( ~ subset(v3, v0) | ~ finite(v3) | ~ in(v3, v1)) & (in(v3, v1) |
% 17.15/3.04 (subset(v3, v0) & finite(v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.15/3.04 $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 17.15/3.04 subset(v2, v0) | ~ preboolean(v1) | ~ finite(v2) | in(v2, v1)) & ! [v0:
% 17.15/3.04 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v2)
% 17.15/3.04 | ~ $i(v1) | ~ $i(v0) | ~ preboolean(v1) | ~ in(v2, v1) | subset(v2,
% 17.15/3.04 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (finite_subsets(v0) =
% 17.15/3.04 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ preboolean(v1) | ~ in(v2,
% 17.15/3.04 v1) | finite(v2))
% 17.15/3.04
% 17.15/3.04 (fc1_finsub_1)
% 17.15/3.04 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ~
% 17.15/3.04 empty(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0)
% 17.15/3.04 | diff_closed(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) |
% 17.15/3.04 ~ $i(v0) | cup_closed(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) =
% 17.15/3.04 v1) | ~ $i(v0) | preboolean(v1))
% 17.15/3.04
% 17.15/3.04 (fc2_finsub_1)
% 17.15/3.04 ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | ~
% 17.15/3.04 empty(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~
% 17.15/3.04 $i(v0) | diff_closed(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 17.15/3.04 (finite_subsets(v0) = v1) | ~ $i(v0) | cup_closed(v1)) & ! [v0: $i] : !
% 17.15/3.04 [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | preboolean(v1))
% 17.15/3.04
% 17.15/3.04 (rc2_finset_1)
% 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i]
% 17.15/3.05 : ($i(v2) & natural(v2) & ordinal(v2) & epsilon_connected(v2) &
% 17.15/3.05 epsilon_transitive(v2) & one_to_one(v2) & function(v2) & relation(v2) &
% 17.15/3.05 element(v2, v1) & finite(v2) & empty(v2)))
% 17.15/3.05
% 17.15/3.05 (rc2_subset_1)
% 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i]
% 17.15/3.05 : ($i(v2) & element(v2, v1) & empty(v2)))
% 17.15/3.05
% 17.15/3.05 (t13_finset_1)
% 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1) | ~
% 17.15/3.05 finite(v1) | finite(v0))
% 17.15/3.05
% 17.15/3.05 (t1_subset)
% 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ in(v0, v1) |
% 17.15/3.05 element(v0, v1))
% 17.15/3.05
% 17.15/3.05 (t26_finsub_1)
% 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | ?
% 17.15/3.05 [v2: $i] : (powerset(v0) = v2 & $i(v2) & subset(v1, v2)))
% 17.15/3.05
% 17.15/3.05 (t27_finsub_1)
% 17.15/3.05 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & finite_subsets(v0) =
% 17.15/3.05 v1 & powerset(v0) = v2 & $i(v2) & $i(v1) & $i(v0) & finite(v0))
% 17.15/3.05
% 17.15/3.05 (t2_subset)
% 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ element(v0, v1) |
% 17.15/3.05 empty(v1) | in(v0, v1))
% 17.15/3.05
% 17.15/3.05 (t3_subset)
% 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ $i(v1)
% 17.15/3.05 | ~ $i(v0) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0: $i] : ! [v1:
% 17.15/3.05 $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 17.15/3.05 element(v0, v2) | subset(v0, v1))
% 17.15/3.05
% 17.15/3.05 (t6_boole)
% 17.15/3.05 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 17.15/3.05
% 17.15/3.05 (t7_boole)
% 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ empty(v1) | ~ in(v0,
% 17.15/3.05 v1))
% 17.15/3.05
% 17.15/3.05 (t8_boole)
% 17.15/3.05 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ empty(v1) |
% 17.15/3.05 ~ empty(v0))
% 17.15/3.05
% 17.15/3.05 (function-axioms)
% 17.15/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (finite_subsets(v2) =
% 17.15/3.06 v1) | ~ (finite_subsets(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.15/3.06 $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 17.15/3.06
% 17.15/3.06 Further assumptions not needed in the proof:
% 17.15/3.06 --------------------------------------------
% 17.15/3.06 antisymmetry_r2_hidden, cc1_finset_1, cc1_finsub_1, cc2_finsub_1, cc3_finsub_1,
% 17.15/3.06 d10_xboole_0, dt_k5_finsub_1, existence_m1_subset_1, fc1_subset_1, fc1_xboole_0,
% 17.15/3.06 rc1_finset_1, rc1_finsub_1, rc1_subset_1, rc1_xboole_0, rc2_xboole_0,
% 17.15/3.06 rc3_finset_1, rc4_finset_1, reflexivity_r1_tarski, t4_subset, t5_subset
% 17.15/3.06
% 17.15/3.06 Those formulas are unsatisfiable:
% 17.15/3.06 ---------------------------------
% 17.15/3.06
% 17.15/3.06 Begin of proof
% 17.15/3.06 |
% 17.15/3.06 | ALPHA: (d3_tarski) implies:
% 17.15/3.06 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 17.15/3.06 | $i(v0) | ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1))
% 17.15/3.06 |
% 17.15/3.06 | ALPHA: (d5_finsub_1) implies:
% 17.15/3.06 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (finite_subsets(v0) = v1)
% 17.15/3.06 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ subset(v2, v0) | ~
% 17.15/3.06 | preboolean(v1) | ~ finite(v2) | in(v2, v1))
% 17.15/3.06 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 17.15/3.06 | (finite_subsets(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ preboolean(v1)
% 17.15/3.06 | | ? [v3: $i] : ($i(v3) & ( ~ subset(v3, v0) | ~ finite(v3) | ~
% 17.15/3.06 | in(v3, v1)) & (in(v3, v1) | (subset(v3, v0) & finite(v3)))))
% 17.15/3.06 |
% 17.15/3.06 | ALPHA: (fc1_finsub_1) implies:
% 17.15/3.06 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) |
% 17.15/3.06 | preboolean(v1))
% 17.15/3.06 |
% 17.15/3.06 | ALPHA: (fc2_finsub_1) implies:
% 17.15/3.06 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) |
% 17.15/3.06 | preboolean(v1))
% 17.15/3.06 |
% 17.15/3.06 | ALPHA: (t3_subset) implies:
% 17.15/3.06 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~
% 17.15/3.06 | $i(v1) | ~ $i(v0) | ~ element(v0, v2) | subset(v0, v1))
% 17.15/3.06 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~
% 17.15/3.06 | $i(v1) | ~ $i(v0) | ~ subset(v0, v1) | element(v0, v2))
% 17.15/3.06 |
% 17.15/3.06 | ALPHA: (t6_boole) implies:
% 17.15/3.06 | (8) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 17.15/3.06 |
% 17.15/3.06 | ALPHA: (function-axioms) implies:
% 17.15/3.06 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) =
% 17.15/3.06 | v1) | ~ (powerset(v2) = v0))
% 17.15/3.06 |
% 17.15/3.06 | DELTA: instantiating (t27_finsub_1) with fresh symbols all_44_0, all_44_1,
% 17.15/3.06 | all_44_2 gives:
% 17.15/3.06 | (10) ~ (all_44_0 = all_44_1) & finite_subsets(all_44_2) = all_44_1 &
% 17.15/3.06 | powerset(all_44_2) = all_44_0 & $i(all_44_0) & $i(all_44_1) &
% 17.15/3.06 | $i(all_44_2) & finite(all_44_2)
% 17.15/3.06 |
% 17.15/3.06 | ALPHA: (10) implies:
% 17.15/3.06 | (11) ~ (all_44_0 = all_44_1)
% 17.15/3.06 | (12) finite(all_44_2)
% 17.15/3.07 | (13) $i(all_44_2)
% 17.15/3.07 | (14) $i(all_44_1)
% 17.15/3.07 | (15) powerset(all_44_2) = all_44_0
% 17.15/3.07 | (16) finite_subsets(all_44_2) = all_44_1
% 17.15/3.07 |
% 17.15/3.07 | GROUND_INST: instantiating (4) with all_44_2, all_44_0, simplifying with (13),
% 17.15/3.07 | (15) gives:
% 17.15/3.07 | (17) preboolean(all_44_0)
% 17.15/3.07 |
% 17.15/3.07 | GROUND_INST: instantiating (rc2_finset_1) with all_44_2, all_44_0, simplifying
% 17.15/3.07 | with (13), (15) gives:
% 17.15/3.07 | (18) ? [v0: $i] : ($i(v0) & natural(v0) & ordinal(v0) &
% 17.15/3.07 | epsilon_connected(v0) & epsilon_transitive(v0) & one_to_one(v0) &
% 17.15/3.07 | function(v0) & relation(v0) & element(v0, all_44_0) & finite(v0) &
% 17.15/3.07 | empty(v0))
% 17.15/3.07 |
% 17.15/3.07 | GROUND_INST: instantiating (rc2_subset_1) with all_44_2, all_44_0, simplifying
% 17.15/3.07 | with (13), (15) gives:
% 17.15/3.07 | (19) ? [v0: $i] : ($i(v0) & element(v0, all_44_0) & empty(v0))
% 17.15/3.07 |
% 17.15/3.07 | GROUND_INST: instantiating (5) with all_44_2, all_44_1, simplifying with (13),
% 17.15/3.07 | (16) gives:
% 17.15/3.07 | (20) preboolean(all_44_1)
% 17.15/3.07 |
% 17.15/3.07 | GROUND_INST: instantiating (t26_finsub_1) with all_44_2, all_44_1, simplifying
% 17.15/3.07 | with (13), (16) gives:
% 17.15/3.07 | (21) ? [v0: $i] : (powerset(all_44_2) = v0 & $i(v0) & subset(all_44_1,
% 17.15/3.07 | v0))
% 17.15/3.07 |
% 17.15/3.07 | DELTA: instantiating (19) with fresh symbol all_52_0 gives:
% 17.15/3.07 | (22) $i(all_52_0) & element(all_52_0, all_44_0) & empty(all_52_0)
% 17.15/3.07 |
% 17.15/3.07 | ALPHA: (22) implies:
% 17.15/3.07 | (23) empty(all_52_0)
% 17.15/3.07 | (24) element(all_52_0, all_44_0)
% 17.15/3.07 | (25) $i(all_52_0)
% 17.15/3.07 |
% 17.15/3.07 | DELTA: instantiating (21) with fresh symbol all_54_0 gives:
% 17.15/3.07 | (26) powerset(all_44_2) = all_54_0 & $i(all_54_0) & subset(all_44_1,
% 17.15/3.07 | all_54_0)
% 17.15/3.07 |
% 17.15/3.07 | ALPHA: (26) implies:
% 17.15/3.07 | (27) subset(all_44_1, all_54_0)
% 17.15/3.07 | (28) $i(all_54_0)
% 17.15/3.07 | (29) powerset(all_44_2) = all_54_0
% 17.15/3.07 |
% 17.15/3.07 | DELTA: instantiating (18) with fresh symbol all_56_0 gives:
% 17.15/3.07 | (30) $i(all_56_0) & natural(all_56_0) & ordinal(all_56_0) &
% 17.15/3.07 | epsilon_connected(all_56_0) & epsilon_transitive(all_56_0) &
% 17.15/3.07 | one_to_one(all_56_0) & function(all_56_0) & relation(all_56_0) &
% 17.15/3.07 | element(all_56_0, all_44_0) & finite(all_56_0) & empty(all_56_0)
% 17.15/3.07 |
% 17.15/3.07 | ALPHA: (30) implies:
% 17.15/3.07 | (31) empty(all_56_0)
% 17.15/3.07 | (32) $i(all_56_0)
% 17.15/3.07 |
% 17.15/3.07 | GROUND_INST: instantiating (9) with all_44_0, all_54_0, all_44_2, simplifying
% 17.15/3.07 | with (15), (29) gives:
% 17.15/3.07 | (33) all_54_0 = all_44_0
% 17.15/3.07 |
% 17.15/3.07 | REDUCE: (28), (33) imply:
% 17.15/3.07 | (34) $i(all_44_0)
% 17.15/3.07 |
% 17.15/3.07 | REDUCE: (27), (33) imply:
% 17.15/3.07 | (35) subset(all_44_1, all_44_0)
% 17.15/3.07 |
% 17.15/3.07 | GROUND_INST: instantiating (t8_boole) with all_52_0, all_56_0, simplifying
% 17.15/3.07 | with (23), (25), (31), (32) gives:
% 17.15/3.07 | (36) all_56_0 = all_52_0
% 17.15/3.07 |
% 17.15/3.07 | GROUND_INST: instantiating (8) with all_56_0, simplifying with (31), (32)
% 17.15/3.07 | gives:
% 17.15/3.07 | (37) all_56_0 = empty_set
% 17.15/3.07 |
% 17.15/3.07 | GROUND_INST: instantiating (3) with all_44_2, all_44_0, all_44_1, simplifying
% 17.15/3.07 | with (13), (16), (17), (34) gives:
% 17.15/3.07 | (38) all_44_0 = all_44_1 | ? [v0: $i] : ($i(v0) & ( ~ subset(v0, all_44_2)
% 17.15/3.07 | | ~ finite(v0) | ~ in(v0, all_44_0)) & (in(v0, all_44_0) |
% 17.15/3.07 | (subset(v0, all_44_2) & finite(v0))))
% 17.15/3.07 |
% 17.15/3.07 | GROUND_INST: instantiating (cc2_finset_1) with all_44_2, all_44_0, all_52_0,
% 17.15/3.07 | simplifying with (12), (13), (15), (24), (25) gives:
% 17.15/3.07 | (39) finite(all_52_0)
% 17.15/3.07 |
% 17.15/3.08 | GROUND_INST: instantiating (6) with all_52_0, all_44_2, all_44_0, simplifying
% 17.15/3.08 | with (13), (15), (24), (25) gives:
% 17.15/3.08 | (40) subset(all_52_0, all_44_2)
% 17.15/3.08 |
% 17.15/3.08 | COMBINE_EQS: (36), (37) imply:
% 17.15/3.08 | (41) all_52_0 = empty_set
% 17.15/3.08 |
% 17.15/3.08 | REDUCE: (25), (41) imply:
% 17.15/3.08 | (42) $i(empty_set)
% 17.15/3.08 |
% 17.15/3.08 | REDUCE: (40), (41) imply:
% 17.15/3.08 | (43) subset(empty_set, all_44_2)
% 17.15/3.08 |
% 17.15/3.08 | REDUCE: (39), (41) imply:
% 17.15/3.08 | (44) finite(empty_set)
% 17.15/3.08 |
% 17.15/3.08 | BETA: splitting (38) gives:
% 17.15/3.08 |
% 17.15/3.08 | Case 1:
% 17.15/3.08 | |
% 17.15/3.08 | | (45) all_44_0 = all_44_1
% 17.15/3.08 | |
% 17.15/3.08 | | REDUCE: (11), (45) imply:
% 17.15/3.08 | | (46) $false
% 17.15/3.08 | |
% 17.15/3.08 | | CLOSE: (46) is inconsistent.
% 17.15/3.08 | |
% 17.15/3.08 | Case 2:
% 17.15/3.08 | |
% 17.15/3.08 | | (47) ? [v0: $i] : ($i(v0) & ( ~ subset(v0, all_44_2) | ~ finite(v0) |
% 17.15/3.08 | | ~ in(v0, all_44_0)) & (in(v0, all_44_0) | (subset(v0, all_44_2)
% 17.15/3.08 | | & finite(v0))))
% 17.15/3.08 | |
% 17.15/3.08 | | DELTA: instantiating (47) with fresh symbol all_72_0 gives:
% 17.15/3.08 | | (48) $i(all_72_0) & ( ~ subset(all_72_0, all_44_2) | ~ finite(all_72_0)
% 17.15/3.08 | | | ~ in(all_72_0, all_44_0)) & (in(all_72_0, all_44_0) |
% 17.15/3.08 | | (subset(all_72_0, all_44_2) & finite(all_72_0)))
% 17.15/3.08 | |
% 17.15/3.08 | | ALPHA: (48) implies:
% 17.15/3.08 | | (49) $i(all_72_0)
% 17.15/3.08 | | (50) in(all_72_0, all_44_0) | (subset(all_72_0, all_44_2) &
% 17.15/3.08 | | finite(all_72_0))
% 17.15/3.08 | | (51) ~ subset(all_72_0, all_44_2) | ~ finite(all_72_0) | ~
% 17.15/3.08 | | in(all_72_0, all_44_0)
% 17.15/3.08 | |
% 17.15/3.08 | | GROUND_INST: instantiating (2) with all_44_2, all_44_1, empty_set,
% 17.15/3.08 | | simplifying with (13), (14), (16), (20), (42), (43), (44)
% 17.15/3.08 | | gives:
% 17.15/3.08 | | (52) in(empty_set, all_44_1)
% 17.15/3.08 | |
% 17.15/3.08 | | GROUND_INST: instantiating (1) with all_44_1, all_44_0, empty_set,
% 17.15/3.08 | | simplifying with (14), (34), (35), (42), (52) gives:
% 17.15/3.08 | | (53) in(empty_set, all_44_0)
% 17.15/3.08 | |
% 17.15/3.08 | | BETA: splitting (51) gives:
% 17.15/3.08 | |
% 17.15/3.08 | | Case 1:
% 17.15/3.08 | | |
% 17.15/3.08 | | | (54) ~ subset(all_72_0, all_44_2)
% 17.15/3.08 | | |
% 17.15/3.08 | | | BETA: splitting (50) gives:
% 17.15/3.08 | | |
% 17.15/3.08 | | | Case 1:
% 17.15/3.08 | | | |
% 17.15/3.08 | | | | (55) in(all_72_0, all_44_0)
% 17.15/3.08 | | | |
% 17.15/3.08 | | | | GROUND_INST: instantiating (t1_subset) with all_72_0, all_44_0,
% 17.15/3.08 | | | | simplifying with (34), (49), (55) gives:
% 17.15/3.08 | | | | (56) element(all_72_0, all_44_0)
% 17.15/3.08 | | | |
% 17.15/3.08 | | | | GROUND_INST: instantiating (6) with all_72_0, all_44_2, all_44_0,
% 17.15/3.08 | | | | simplifying with (13), (15), (49), (54), (56) gives:
% 17.15/3.08 | | | | (57) $false
% 17.15/3.08 | | | |
% 17.15/3.08 | | | | CLOSE: (57) is inconsistent.
% 17.15/3.08 | | | |
% 17.15/3.08 | | | Case 2:
% 17.15/3.08 | | | |
% 17.15/3.08 | | | | (58) subset(all_72_0, all_44_2) & finite(all_72_0)
% 17.15/3.08 | | | |
% 17.15/3.08 | | | | ALPHA: (58) implies:
% 17.15/3.08 | | | | (59) subset(all_72_0, all_44_2)
% 17.15/3.08 | | | |
% 17.15/3.08 | | | | PRED_UNIFY: (54), (59) imply:
% 17.15/3.08 | | | | (60) $false
% 17.15/3.08 | | | |
% 17.15/3.08 | | | | CLOSE: (60) is inconsistent.
% 17.15/3.08 | | | |
% 17.15/3.08 | | | End of split
% 17.15/3.08 | | |
% 17.15/3.08 | | Case 2:
% 17.15/3.08 | | |
% 17.15/3.08 | | | (61) subset(all_72_0, all_44_2)
% 17.15/3.08 | | | (62) ~ finite(all_72_0) | ~ in(all_72_0, all_44_0)
% 17.15/3.08 | | |
% 17.15/3.08 | | | GROUND_INST: instantiating (7) with all_72_0, all_44_2, all_44_0,
% 17.15/3.09 | | | simplifying with (13), (15), (49), (61) gives:
% 17.15/3.09 | | | (63) element(all_72_0, all_44_0)
% 17.15/3.09 | | |
% 17.15/3.09 | | | GROUND_INST: instantiating (t13_finset_1) with all_72_0, all_44_2,
% 17.15/3.09 | | | simplifying with (12), (13), (49), (61) gives:
% 17.15/3.09 | | | (64) finite(all_72_0)
% 17.15/3.09 | | |
% 17.15/3.09 | | | BETA: splitting (62) gives:
% 17.15/3.09 | | |
% 17.15/3.09 | | | Case 1:
% 17.15/3.09 | | | |
% 17.15/3.09 | | | | (65) ~ finite(all_72_0)
% 17.15/3.09 | | | |
% 17.15/3.09 | | | | PRED_UNIFY: (64), (65) imply:
% 17.15/3.09 | | | | (66) $false
% 17.15/3.09 | | | |
% 17.15/3.09 | | | | CLOSE: (66) is inconsistent.
% 17.15/3.09 | | | |
% 17.15/3.09 | | | Case 2:
% 17.15/3.09 | | | |
% 17.15/3.09 | | | | (67) ~ in(all_72_0, all_44_0)
% 17.15/3.09 | | | |
% 17.15/3.09 | | | | GROUND_INST: instantiating (t2_subset) with all_72_0, all_44_0,
% 17.15/3.09 | | | | simplifying with (34), (49), (63), (67) gives:
% 17.15/3.09 | | | | (68) empty(all_44_0)
% 17.15/3.09 | | | |
% 17.15/3.09 | | | | GROUND_INST: instantiating (t7_boole) with empty_set, all_44_0,
% 17.15/3.09 | | | | simplifying with (34), (42), (53), (68) gives:
% 17.15/3.09 | | | | (69) $false
% 17.15/3.09 | | | |
% 17.15/3.09 | | | | CLOSE: (69) is inconsistent.
% 17.15/3.09 | | | |
% 17.15/3.09 | | | End of split
% 17.15/3.09 | | |
% 17.15/3.09 | | End of split
% 17.15/3.09 | |
% 17.15/3.09 | End of split
% 17.15/3.09 |
% 17.15/3.09 End of proof
% 17.15/3.09 % SZS output end Proof for theBenchmark
% 17.15/3.09
% 17.15/3.09 2475ms
%------------------------------------------------------------------------------