TSTP Solution File: ALG223+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG223+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n006.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 : Wed Aug 30 16:40:03 EDT 2023
% Result : Theorem 17.49s 3.07s
% Output : Proof 22.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG223+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 02:40:21 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.72/1.09 Prover 1: Preprocessing ...
% 2.72/1.09 Prover 4: Preprocessing ...
% 3.09/1.13 Prover 2: Preprocessing ...
% 3.09/1.13 Prover 0: Preprocessing ...
% 3.09/1.13 Prover 5: Preprocessing ...
% 3.09/1.15 Prover 3: Preprocessing ...
% 3.09/1.15 Prover 6: Preprocessing ...
% 6.35/1.60 Prover 2: Proving ...
% 6.67/1.61 Prover 5: Proving ...
% 6.99/1.66 Prover 1: Warning: ignoring some quantifiers
% 6.99/1.69 Prover 3: Warning: ignoring some quantifiers
% 6.99/1.71 Prover 3: Constructing countermodel ...
% 6.99/1.71 Prover 1: Constructing countermodel ...
% 6.99/1.72 Prover 6: Proving ...
% 7.69/1.76 Prover 4: Warning: ignoring some quantifiers
% 8.08/1.81 Prover 4: Constructing countermodel ...
% 8.52/1.85 Prover 0: Proving ...
% 17.49/3.07 Prover 5: proved (2431ms)
% 17.49/3.07
% 17.49/3.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.49/3.07
% 17.49/3.07 Prover 3: stopped
% 17.49/3.07 Prover 6: stopped
% 17.49/3.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.49/3.08 Prover 2: stopped
% 17.49/3.08 Prover 0: stopped
% 17.49/3.09 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 17.49/3.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.49/3.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 17.49/3.09 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 17.85/3.14 Prover 7: Preprocessing ...
% 17.85/3.14 Prover 11: Preprocessing ...
% 17.85/3.14 Prover 8: Preprocessing ...
% 18.24/3.16 Prover 10: Preprocessing ...
% 18.24/3.17 Prover 13: Preprocessing ...
% 18.24/3.19 Prover 7: Warning: ignoring some quantifiers
% 18.24/3.19 Prover 7: Constructing countermodel ...
% 18.99/3.25 Prover 10: Warning: ignoring some quantifiers
% 18.99/3.25 Prover 10: Constructing countermodel ...
% 18.99/3.27 Prover 13: Warning: ignoring some quantifiers
% 18.99/3.27 Prover 8: Warning: ignoring some quantifiers
% 18.99/3.28 Prover 13: Constructing countermodel ...
% 18.99/3.29 Prover 8: Constructing countermodel ...
% 19.82/3.37 Prover 11: Warning: ignoring some quantifiers
% 20.21/3.40 Prover 11: Constructing countermodel ...
% 20.58/3.65 Prover 10: Found proof (size 77)
% 20.58/3.65 Prover 10: proved (575ms)
% 20.58/3.65 Prover 11: stopped
% 20.58/3.66 Prover 13: stopped
% 20.58/3.66 Prover 4: stopped
% 20.58/3.66 Prover 7: stopped
% 20.58/3.66 Prover 1: stopped
% 20.58/3.66 Prover 8: stopped
% 20.58/3.66
% 20.58/3.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.58/3.66
% 21.69/3.67 % SZS output start Proof for theBenchmark
% 21.69/3.68 Assumptions after simplification:
% 21.69/3.68 ---------------------------------
% 21.69/3.68
% 21.69/3.68 (d1_closure3)
% 21.69/3.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k1_closure2(v0, v1) = v2) | ~
% 21.69/3.72 $i(v1) | ~ $i(v0) | ~ m1_pboole(v1, v0) | ? [v3: $i] : (k1_zfmisc_1(v2) =
% 21.69/3.72 v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~
% 21.69/3.72 $i(v5) | ~ $i(v4) | ~ r2_hidden(v6, v5) | ~ r1_closure3(v0, v1, v4,
% 21.69/3.72 v5) | ~ m1_subset_1(v5, v3) | ~ m1_subset_1(v4, v3) | ? [v7: $i] :
% 21.69/3.72 ($i(v7) & r1_tarski(v6, v7) & r2_hidden(v7, v4))) & ! [v4: $i] : !
% 21.69/3.72 [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~ m1_subset_1(v5, v3) | ~
% 21.69/3.72 m1_subset_1(v4, v3) | r1_closure3(v0, v1, v4, v5) | ? [v6: $i] :
% 21.69/3.72 ($i(v6) & r2_hidden(v6, v5) & ! [v7: $i] : ( ~ $i(v7) | ~
% 21.69/3.72 r1_tarski(v6, v7) | ~ r2_hidden(v7, v4))))))
% 21.69/3.72
% 21.69/3.72 (fc1_subset_1)
% 21.69/3.72 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ $i(v0) | ~
% 21.69/3.72 v1_xboole_0(v1))
% 21.69/3.72
% 22.43/3.72 (fc2_closure2)
% 22.43/3.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k1_closure2(v0, v1) = v2) | ~
% 22.43/3.72 $i(v1) | ~ $i(v0) | ~ v1_xboole_0(v2) | ~ m1_pboole(v1, v0)) & ! [v0:
% 22.43/3.72 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k1_closure2(v0, v1) = v2) | ~ $i(v1)
% 22.43/3.72 | ~ $i(v0) | ~ m1_pboole(v1, v0) | v1_pralg_2(v2)) & ! [v0: $i] : ! [v1:
% 22.43/3.72 $i] : ! [v2: $i] : ( ~ (k1_closure2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 22.43/3.72 ~ m1_pboole(v1, v0) | v1_fraenkel(v2))
% 22.43/3.72
% 22.43/3.72 (rc1_subset_1)
% 22.43/3.72 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ $i(v0) |
% 22.43/3.72 v1_xboole_0(v0) | ? [v2: $i] : ($i(v2) & m1_subset_1(v2, v1) & ~
% 22.43/3.72 v1_xboole_0(v2)))
% 22.43/3.72
% 22.43/3.72 (rc2_closure2)
% 22.43/3.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k1_closure2(v0, v1) = v2) | ~
% 22.43/3.72 $i(v1) | ~ $i(v0) | ~ m1_pboole(v1, v0) | ? [v3: $i] : ? [v4: $i] :
% 22.43/3.72 (k1_zfmisc_1(v2) = v3 & $i(v4) & $i(v3) & v1_pralg_2(v4) & v1_fraenkel(v4) &
% 22.43/3.72 m1_subset_1(v4, v3) & ~ v1_xboole_0(v4)))
% 22.43/3.72
% 22.43/3.72 (rc3_closure2)
% 22.43/3.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k1_closure2(v0, v1) = v2) | ~
% 22.43/3.72 $i(v1) | ~ $i(v0) | ~ m1_pboole(v1, v0) | ? [v3: $i] : ? [v4: $i] :
% 22.43/3.72 (k1_zfmisc_1(v2) = v3 & $i(v4) & $i(v3) & v2_funct_1(v4) & v1_relat_1(v4) &
% 22.43/3.72 v1_funct_1(v4) & v1_finset_1(v4) & v1_fraenkel(v4) & v1_xboole_0(v4) &
% 22.43/3.72 m1_subset_1(v4, v3)))
% 22.43/3.72
% 22.43/3.72 (t1_xboole_1)
% 22.43/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 22.43/3.73 ~ r1_tarski(v1, v2) | ~ r1_tarski(v0, v1) | r1_tarski(v0, v2))
% 22.43/3.73
% 22.43/3.73 (t2_subset)
% 22.43/3.73 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_subset_1(v0, v1) |
% 22.43/3.73 v1_xboole_0(v1) | r2_hidden(v0, v1))
% 22.43/3.73
% 22.43/3.73 (t4_closure3)
% 22.43/3.73 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 22.43/3.73 $i] : ? [v6: $i] : (k1_closure2(v0, v1) = v2 & k1_zfmisc_1(v2) = v3 &
% 22.43/3.73 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 22.43/3.73 r1_closure3(v0, v1, v6, v5) & r1_closure3(v0, v1, v5, v4) & m1_subset_1(v6,
% 22.43/3.73 v3) & m1_subset_1(v5, v3) & m1_subset_1(v4, v3) & m1_pboole(v1, v0) & ~
% 22.43/3.73 r1_closure3(v0, v1, v6, v4))
% 22.43/3.73
% 22.43/3.73 (function-axioms)
% 22.43/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.43/3.73 (k1_closure2(v3, v2) = v1) | ~ (k1_closure2(v3, v2) = v0)) & ! [v0: $i] :
% 22.43/3.73 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~
% 22.43/3.73 (k1_zfmisc_1(v2) = v0))
% 22.43/3.73
% 22.43/3.73 Further assumptions not needed in the proof:
% 22.43/3.73 --------------------------------------------
% 22.43/3.73 antisymmetry_r2_hidden, cc1_closure2, cc1_finset_1, cc1_funct_1, cc2_finset_1,
% 22.43/3.73 cc2_funct_1, dt_k1_closure2, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_m1_pboole,
% 22.43/3.73 dt_m1_subset_1, existence_m1_pboole, existence_m1_subset_1, fc1_xboole_0,
% 22.43/3.73 rc1_closure2, rc1_finset_1, rc1_funct_1, rc1_xboole_0, rc2_funct_1,
% 22.43/3.73 rc2_subset_1, rc2_xboole_0, rc3_finset_1, rc3_funct_1, rc4_finset_1,
% 22.43/3.73 reflexivity_r1_closure3, reflexivity_r1_tarski, t1_subset, t3_subset, t4_subset,
% 22.43/3.73 t5_subset, t6_boole, t7_boole, t8_boole
% 22.43/3.73
% 22.43/3.73 Those formulas are unsatisfiable:
% 22.43/3.73 ---------------------------------
% 22.43/3.73
% 22.43/3.73 Begin of proof
% 22.43/3.73 |
% 22.43/3.73 | ALPHA: (fc2_closure2) implies:
% 22.43/3.73 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k1_closure2(v0, v1) =
% 22.43/3.73 | v2) | ~ $i(v1) | ~ $i(v0) | ~ v1_xboole_0(v2) | ~ m1_pboole(v1,
% 22.43/3.73 | v0))
% 22.43/3.73 |
% 22.43/3.73 | ALPHA: (function-axioms) implies:
% 22.43/3.73 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 22.43/3.73 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 22.43/3.73 |
% 22.43/3.73 | DELTA: instantiating (t4_closure3) with fresh symbols all_48_0, all_48_1,
% 22.43/3.73 | all_48_2, all_48_3, all_48_4, all_48_5, all_48_6 gives:
% 22.43/3.73 | (3) k1_closure2(all_48_6, all_48_5) = all_48_4 & k1_zfmisc_1(all_48_4) =
% 22.43/3.73 | all_48_3 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) & $i(all_48_3) &
% 22.43/3.73 | $i(all_48_4) & $i(all_48_5) & $i(all_48_6) & r1_closure3(all_48_6,
% 22.43/3.73 | all_48_5, all_48_0, all_48_1) & r1_closure3(all_48_6, all_48_5,
% 22.43/3.73 | all_48_1, all_48_2) & m1_subset_1(all_48_0, all_48_3) &
% 22.43/3.73 | m1_subset_1(all_48_1, all_48_3) & m1_subset_1(all_48_2, all_48_3) &
% 22.43/3.73 | m1_pboole(all_48_5, all_48_6) & ~ r1_closure3(all_48_6, all_48_5,
% 22.43/3.73 | all_48_0, all_48_2)
% 22.43/3.73 |
% 22.43/3.73 | ALPHA: (3) implies:
% 22.43/3.73 | (4) ~ r1_closure3(all_48_6, all_48_5, all_48_0, all_48_2)
% 22.43/3.73 | (5) m1_pboole(all_48_5, all_48_6)
% 22.43/3.73 | (6) m1_subset_1(all_48_2, all_48_3)
% 22.43/3.73 | (7) m1_subset_1(all_48_1, all_48_3)
% 22.43/3.73 | (8) m1_subset_1(all_48_0, all_48_3)
% 22.43/3.74 | (9) r1_closure3(all_48_6, all_48_5, all_48_1, all_48_2)
% 22.43/3.74 | (10) r1_closure3(all_48_6, all_48_5, all_48_0, all_48_1)
% 22.43/3.74 | (11) $i(all_48_6)
% 22.43/3.74 | (12) $i(all_48_5)
% 22.43/3.74 | (13) $i(all_48_4)
% 22.43/3.74 | (14) $i(all_48_2)
% 22.43/3.74 | (15) $i(all_48_1)
% 22.43/3.74 | (16) $i(all_48_0)
% 22.43/3.74 | (17) k1_zfmisc_1(all_48_4) = all_48_3
% 22.43/3.74 | (18) k1_closure2(all_48_6, all_48_5) = all_48_4
% 22.43/3.74 |
% 22.43/3.74 | GROUND_INST: instantiating (rc1_subset_1) with all_48_4, all_48_3, simplifying
% 22.43/3.74 | with (13), (17) gives:
% 22.43/3.74 | (19) v1_xboole_0(all_48_4) | ? [v0: $i] : ($i(v0) & m1_subset_1(v0,
% 22.43/3.74 | all_48_3) & ~ v1_xboole_0(v0))
% 22.43/3.74 |
% 22.43/3.74 | GROUND_INST: instantiating (rc2_closure2) with all_48_6, all_48_5, all_48_4,
% 22.43/3.74 | simplifying with (5), (11), (12), (18) gives:
% 22.43/3.74 | (20) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_48_4) = v0 & $i(v1) &
% 22.43/3.74 | $i(v0) & v1_pralg_2(v1) & v1_fraenkel(v1) & m1_subset_1(v1, v0) & ~
% 22.43/3.74 | v1_xboole_0(v1))
% 22.43/3.74 |
% 22.43/3.74 | GROUND_INST: instantiating (rc3_closure2) with all_48_6, all_48_5, all_48_4,
% 22.43/3.74 | simplifying with (5), (11), (12), (18) gives:
% 22.43/3.74 | (21) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_48_4) = v0 & $i(v1) &
% 22.43/3.74 | $i(v0) & v2_funct_1(v1) & v1_relat_1(v1) & v1_funct_1(v1) &
% 22.43/3.74 | v1_finset_1(v1) & v1_fraenkel(v1) & v1_xboole_0(v1) &
% 22.43/3.74 | m1_subset_1(v1, v0))
% 22.43/3.74 |
% 22.43/3.74 | GROUND_INST: instantiating (d1_closure3) with all_48_6, all_48_5, all_48_4,
% 22.43/3.74 | simplifying with (5), (11), (12), (18) gives:
% 22.43/3.74 | (22) ? [v0: $i] : (k1_zfmisc_1(all_48_4) = v0 & $i(v0) & ! [v1: $i] : !
% 22.43/3.74 | [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 22.43/3.74 | r2_hidden(v3, v2) | ~ r1_closure3(all_48_6, all_48_5, v1, v2) |
% 22.43/3.74 | ~ m1_subset_1(v2, v0) | ~ m1_subset_1(v1, v0) | ? [v4: $i] :
% 22.43/3.74 | ($i(v4) & r1_tarski(v3, v4) & r2_hidden(v4, v1))) & ! [v1: $i] :
% 22.43/3.74 | ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ m1_subset_1(v2, v0) | ~
% 22.43/3.74 | m1_subset_1(v1, v0) | r1_closure3(all_48_6, all_48_5, v1, v2) | ?
% 22.43/3.74 | [v3: $i] : ($i(v3) & r2_hidden(v3, v2) & ! [v4: $i] : ( ~ $i(v4)
% 22.43/3.74 | | ~ r1_tarski(v3, v4) | ~ r2_hidden(v4, v1)))))
% 22.43/3.74 |
% 22.43/3.74 | DELTA: instantiating (20) with fresh symbols all_58_0, all_58_1 gives:
% 22.43/3.74 | (23) k1_zfmisc_1(all_48_4) = all_58_1 & $i(all_58_0) & $i(all_58_1) &
% 22.43/3.74 | v1_pralg_2(all_58_0) & v1_fraenkel(all_58_0) & m1_subset_1(all_58_0,
% 22.43/3.74 | all_58_1) & ~ v1_xboole_0(all_58_0)
% 22.43/3.74 |
% 22.43/3.74 | ALPHA: (23) implies:
% 22.43/3.74 | (24) $i(all_58_1)
% 22.43/3.74 | (25) k1_zfmisc_1(all_48_4) = all_58_1
% 22.43/3.74 |
% 22.43/3.74 | DELTA: instantiating (21) with fresh symbols all_60_0, all_60_1 gives:
% 22.43/3.74 | (26) k1_zfmisc_1(all_48_4) = all_60_1 & $i(all_60_0) & $i(all_60_1) &
% 22.43/3.74 | v2_funct_1(all_60_0) & v1_relat_1(all_60_0) & v1_funct_1(all_60_0) &
% 22.43/3.74 | v1_finset_1(all_60_0) & v1_fraenkel(all_60_0) & v1_xboole_0(all_60_0)
% 22.43/3.74 | & m1_subset_1(all_60_0, all_60_1)
% 22.43/3.74 |
% 22.43/3.74 | ALPHA: (26) implies:
% 22.43/3.74 | (27) k1_zfmisc_1(all_48_4) = all_60_1
% 22.43/3.74 |
% 22.43/3.74 | DELTA: instantiating (22) with fresh symbol all_62_0 gives:
% 22.43/3.74 | (28) k1_zfmisc_1(all_48_4) = all_62_0 & $i(all_62_0) & ! [v0: $i] : !
% 22.43/3.74 | [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 22.43/3.74 | r2_hidden(v2, v1) | ~ r1_closure3(all_48_6, all_48_5, v0, v1) | ~
% 22.43/3.74 | m1_subset_1(v1, all_62_0) | ~ m1_subset_1(v0, all_62_0) | ? [v3:
% 22.43/3.74 | $i] : ($i(v3) & r1_tarski(v2, v3) & r2_hidden(v3, v0))) & ! [v0:
% 22.43/3.74 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_subset_1(v1,
% 22.43/3.74 | all_62_0) | ~ m1_subset_1(v0, all_62_0) | r1_closure3(all_48_6,
% 22.43/3.74 | all_48_5, v0, v1) | ? [v2: $i] : ($i(v2) & r2_hidden(v2, v1) & !
% 22.43/3.74 | [v3: $i] : ( ~ $i(v3) | ~ r1_tarski(v2, v3) | ~ r2_hidden(v3,
% 22.43/3.74 | v0))))
% 22.43/3.74 |
% 22.43/3.74 | ALPHA: (28) implies:
% 22.43/3.74 | (29) k1_zfmisc_1(all_48_4) = all_62_0
% 22.43/3.75 | (30) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 22.43/3.75 | m1_subset_1(v1, all_62_0) | ~ m1_subset_1(v0, all_62_0) |
% 22.43/3.75 | r1_closure3(all_48_6, all_48_5, v0, v1) | ? [v2: $i] : ($i(v2) &
% 22.43/3.75 | r2_hidden(v2, v1) & ! [v3: $i] : ( ~ $i(v3) | ~ r1_tarski(v2,
% 22.43/3.75 | v3) | ~ r2_hidden(v3, v0))))
% 22.43/3.75 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 22.43/3.75 | $i(v0) | ~ r2_hidden(v2, v1) | ~ r1_closure3(all_48_6, all_48_5,
% 22.43/3.75 | v0, v1) | ~ m1_subset_1(v1, all_62_0) | ~ m1_subset_1(v0,
% 22.43/3.75 | all_62_0) | ? [v3: $i] : ($i(v3) & r1_tarski(v2, v3) &
% 22.43/3.75 | r2_hidden(v3, v0)))
% 22.43/3.75 |
% 22.43/3.75 | GROUND_INST: instantiating (2) with all_48_3, all_60_1, all_48_4, simplifying
% 22.43/3.75 | with (17), (27) gives:
% 22.43/3.75 | (32) all_60_1 = all_48_3
% 22.43/3.75 |
% 22.43/3.75 | GROUND_INST: instantiating (2) with all_60_1, all_62_0, all_48_4, simplifying
% 22.43/3.75 | with (27), (29) gives:
% 22.43/3.75 | (33) all_62_0 = all_60_1
% 22.43/3.75 |
% 22.43/3.75 | GROUND_INST: instantiating (2) with all_58_1, all_62_0, all_48_4, simplifying
% 22.43/3.75 | with (25), (29) gives:
% 22.43/3.75 | (34) all_62_0 = all_58_1
% 22.43/3.75 |
% 22.43/3.75 | COMBINE_EQS: (33), (34) imply:
% 22.43/3.75 | (35) all_60_1 = all_58_1
% 22.43/3.75 |
% 22.43/3.75 | SIMP: (35) implies:
% 22.43/3.75 | (36) all_60_1 = all_58_1
% 22.43/3.75 |
% 22.43/3.75 | COMBINE_EQS: (32), (36) imply:
% 22.43/3.75 | (37) all_58_1 = all_48_3
% 22.43/3.75 |
% 22.43/3.75 | SIMP: (37) implies:
% 22.43/3.75 | (38) all_58_1 = all_48_3
% 22.43/3.75 |
% 22.43/3.75 | COMBINE_EQS: (34), (38) imply:
% 22.43/3.75 | (39) all_62_0 = all_48_3
% 22.43/3.75 |
% 22.43/3.75 | REDUCE: (24), (38) imply:
% 22.43/3.75 | (40) $i(all_48_3)
% 22.43/3.75 |
% 22.43/3.75 | BETA: splitting (19) gives:
% 22.43/3.75 |
% 22.43/3.75 | Case 1:
% 22.43/3.75 | |
% 22.43/3.75 | | (41) v1_xboole_0(all_48_4)
% 22.43/3.75 | |
% 22.43/3.75 | | GROUND_INST: instantiating (1) with all_48_6, all_48_5, all_48_4,
% 22.43/3.75 | | simplifying with (5), (11), (12), (18), (41) gives:
% 22.43/3.75 | | (42) $false
% 22.43/3.75 | |
% 22.43/3.75 | | CLOSE: (42) is inconsistent.
% 22.43/3.75 | |
% 22.43/3.75 | Case 2:
% 22.43/3.75 | |
% 22.43/3.75 | | (43) ? [v0: $i] : ($i(v0) & m1_subset_1(v0, all_48_3) & ~
% 22.43/3.75 | | v1_xboole_0(v0))
% 22.43/3.75 | |
% 22.43/3.75 | | DELTA: instantiating (43) with fresh symbol all_109_0 gives:
% 22.43/3.75 | | (44) $i(all_109_0) & m1_subset_1(all_109_0, all_48_3) & ~
% 22.43/3.75 | | v1_xboole_0(all_109_0)
% 22.43/3.75 | |
% 22.43/3.75 | | ALPHA: (44) implies:
% 22.43/3.75 | | (45) m1_subset_1(all_109_0, all_48_3)
% 22.43/3.75 | | (46) $i(all_109_0)
% 22.43/3.75 | |
% 22.43/3.75 | | GROUND_INST: instantiating (t2_subset) with all_109_0, all_48_3, simplifying
% 22.43/3.75 | | with (40), (45), (46) gives:
% 22.43/3.75 | | (47) v1_xboole_0(all_48_3) | r2_hidden(all_109_0, all_48_3)
% 22.43/3.75 | |
% 22.43/3.75 | | BETA: splitting (47) gives:
% 22.43/3.75 | |
% 22.43/3.75 | | Case 1:
% 22.43/3.75 | | |
% 22.43/3.75 | | | (48) v1_xboole_0(all_48_3)
% 22.43/3.75 | | |
% 22.43/3.75 | | | GROUND_INST: instantiating (fc1_subset_1) with all_48_4, all_48_3,
% 22.43/3.75 | | | simplifying with (13), (17), (48) gives:
% 22.43/3.75 | | | (49) $false
% 22.43/3.75 | | |
% 22.43/3.75 | | | CLOSE: (49) is inconsistent.
% 22.43/3.75 | | |
% 22.43/3.75 | | Case 2:
% 22.43/3.75 | | |
% 22.43/3.75 | | |
% 22.43/3.75 | | | GROUND_INST: instantiating (30) with all_48_0, all_48_2, simplifying with
% 22.43/3.75 | | | (4), (14), (16) gives:
% 22.43/3.75 | | | (50) ~ m1_subset_1(all_48_0, all_62_0) | ~ m1_subset_1(all_48_2,
% 22.43/3.75 | | | all_62_0) | ? [v0: $i] : ($i(v0) & r2_hidden(v0, all_48_2) & !
% 22.43/3.75 | | | [v1: $i] : ( ~ $i(v1) | ~ r1_tarski(v0, v1) | ~ r2_hidden(v1,
% 22.43/3.75 | | | all_48_0)))
% 22.43/3.75 | | |
% 22.43/3.75 | | | BETA: splitting (50) gives:
% 22.43/3.75 | | |
% 22.43/3.75 | | | Case 1:
% 22.43/3.75 | | | |
% 22.43/3.75 | | | | (51) ~ m1_subset_1(all_48_0, all_62_0)
% 22.43/3.75 | | | |
% 22.43/3.75 | | | | REDUCE: (39), (51) imply:
% 22.43/3.75 | | | | (52) ~ m1_subset_1(all_48_0, all_48_3)
% 22.43/3.76 | | | |
% 22.43/3.76 | | | | PRED_UNIFY: (8), (52) imply:
% 22.43/3.76 | | | | (53) $false
% 22.43/3.76 | | | |
% 22.43/3.76 | | | | CLOSE: (53) is inconsistent.
% 22.43/3.76 | | | |
% 22.43/3.76 | | | Case 2:
% 22.43/3.76 | | | |
% 22.43/3.76 | | | | (54) m1_subset_1(all_48_0, all_62_0)
% 22.43/3.76 | | | | (55) ~ m1_subset_1(all_48_2, all_62_0) | ? [v0: $i] : ($i(v0) &
% 22.43/3.76 | | | | r2_hidden(v0, all_48_2) & ! [v1: $i] : ( ~ $i(v1) | ~
% 22.43/3.76 | | | | r1_tarski(v0, v1) | ~ r2_hidden(v1, all_48_0)))
% 22.43/3.76 | | | |
% 22.43/3.76 | | | | BETA: splitting (55) gives:
% 22.43/3.76 | | | |
% 22.43/3.76 | | | | Case 1:
% 22.43/3.76 | | | | |
% 22.43/3.76 | | | | | (56) ~ m1_subset_1(all_48_2, all_62_0)
% 22.43/3.76 | | | | |
% 22.43/3.76 | | | | | REDUCE: (39), (56) imply:
% 22.43/3.76 | | | | | (57) ~ m1_subset_1(all_48_2, all_48_3)
% 22.43/3.76 | | | | |
% 22.43/3.76 | | | | | PRED_UNIFY: (6), (57) imply:
% 22.43/3.76 | | | | | (58) $false
% 22.43/3.76 | | | | |
% 22.43/3.76 | | | | | CLOSE: (58) is inconsistent.
% 22.43/3.76 | | | | |
% 22.43/3.76 | | | | Case 2:
% 22.43/3.76 | | | | |
% 22.43/3.76 | | | | | (59) m1_subset_1(all_48_2, all_62_0)
% 22.43/3.76 | | | | | (60) ? [v0: $i] : ($i(v0) & r2_hidden(v0, all_48_2) & ! [v1: $i]
% 22.43/3.76 | | | | | : ( ~ $i(v1) | ~ r1_tarski(v0, v1) | ~ r2_hidden(v1,
% 22.43/3.76 | | | | | all_48_0)))
% 22.43/3.76 | | | | |
% 22.43/3.76 | | | | | DELTA: instantiating (60) with fresh symbol all_179_0 gives:
% 22.43/3.76 | | | | | (61) $i(all_179_0) & r2_hidden(all_179_0, all_48_2) & ! [v0: $i] :
% 22.43/3.76 | | | | | ( ~ $i(v0) | ~ r1_tarski(all_179_0, v0) | ~ r2_hidden(v0,
% 22.43/3.76 | | | | | all_48_0))
% 22.43/3.76 | | | | |
% 22.43/3.76 | | | | | ALPHA: (61) implies:
% 22.43/3.76 | | | | | (62) r2_hidden(all_179_0, all_48_2)
% 22.43/3.76 | | | | | (63) $i(all_179_0)
% 22.43/3.76 | | | | | (64) ! [v0: $i] : ( ~ $i(v0) | ~ r1_tarski(all_179_0, v0) | ~
% 22.43/3.76 | | | | | r2_hidden(v0, all_48_0))
% 22.43/3.76 | | | | |
% 22.43/3.76 | | | | | GROUND_INST: instantiating (31) with all_48_1, all_48_2, all_179_0,
% 22.43/3.76 | | | | | simplifying with (9), (14), (15), (62), (63) gives:
% 22.43/3.76 | | | | | (65) ~ m1_subset_1(all_48_1, all_62_0) | ~ m1_subset_1(all_48_2,
% 22.43/3.76 | | | | | all_62_0) | ? [v0: $i] : ($i(v0) & r1_tarski(all_179_0, v0)
% 22.43/3.76 | | | | | & r2_hidden(v0, all_48_1))
% 22.43/3.76 | | | | |
% 22.43/3.76 | | | | | BETA: splitting (65) gives:
% 22.43/3.76 | | | | |
% 22.43/3.76 | | | | | Case 1:
% 22.43/3.76 | | | | | |
% 22.43/3.76 | | | | | | (66) ~ m1_subset_1(all_48_1, all_62_0)
% 22.43/3.76 | | | | | |
% 22.43/3.76 | | | | | | REDUCE: (39), (66) imply:
% 22.43/3.76 | | | | | | (67) ~ m1_subset_1(all_48_1, all_48_3)
% 22.43/3.76 | | | | | |
% 22.43/3.76 | | | | | | PRED_UNIFY: (7), (67) imply:
% 22.43/3.76 | | | | | | (68) $false
% 22.43/3.76 | | | | | |
% 22.43/3.76 | | | | | | CLOSE: (68) is inconsistent.
% 22.43/3.76 | | | | | |
% 22.43/3.76 | | | | | Case 2:
% 22.43/3.76 | | | | | |
% 22.43/3.76 | | | | | | (69) m1_subset_1(all_48_1, all_62_0)
% 22.43/3.76 | | | | | | (70) ~ m1_subset_1(all_48_2, all_62_0) | ? [v0: $i] : ($i(v0) &
% 22.43/3.76 | | | | | | r1_tarski(all_179_0, v0) & r2_hidden(v0, all_48_1))
% 22.43/3.76 | | | | | |
% 22.43/3.76 | | | | | | BETA: splitting (70) gives:
% 22.43/3.76 | | | | | |
% 22.43/3.76 | | | | | | Case 1:
% 22.43/3.76 | | | | | | |
% 22.43/3.76 | | | | | | | (71) ~ m1_subset_1(all_48_2, all_62_0)
% 22.43/3.76 | | | | | | |
% 22.43/3.76 | | | | | | | REDUCE: (39), (71) imply:
% 22.43/3.76 | | | | | | | (72) ~ m1_subset_1(all_48_2, all_48_3)
% 22.43/3.76 | | | | | | |
% 22.43/3.76 | | | | | | | PRED_UNIFY: (6), (72) imply:
% 22.43/3.76 | | | | | | | (73) $false
% 22.43/3.76 | | | | | | |
% 22.43/3.76 | | | | | | | CLOSE: (73) is inconsistent.
% 22.43/3.76 | | | | | | |
% 22.43/3.76 | | | | | | Case 2:
% 22.43/3.76 | | | | | | |
% 22.43/3.76 | | | | | | | (74) ? [v0: $i] : ($i(v0) & r1_tarski(all_179_0, v0) &
% 22.43/3.76 | | | | | | | r2_hidden(v0, all_48_1))
% 22.43/3.76 | | | | | | |
% 22.43/3.76 | | | | | | | DELTA: instantiating (74) with fresh symbol all_196_0 gives:
% 22.43/3.76 | | | | | | | (75) $i(all_196_0) & r1_tarski(all_179_0, all_196_0) &
% 22.43/3.76 | | | | | | | r2_hidden(all_196_0, all_48_1)
% 22.43/3.76 | | | | | | |
% 22.43/3.76 | | | | | | | ALPHA: (75) implies:
% 22.43/3.76 | | | | | | | (76) r2_hidden(all_196_0, all_48_1)
% 22.43/3.76 | | | | | | | (77) r1_tarski(all_179_0, all_196_0)
% 22.43/3.76 | | | | | | | (78) $i(all_196_0)
% 22.43/3.76 | | | | | | |
% 22.43/3.76 | | | | | | | GROUND_INST: instantiating (31) with all_48_0, all_48_1,
% 22.43/3.76 | | | | | | | all_196_0, simplifying with (10), (15), (16), (76),
% 22.43/3.76 | | | | | | | (78) gives:
% 22.43/3.76 | | | | | | | (79) ~ m1_subset_1(all_48_0, all_62_0) | ~
% 22.43/3.76 | | | | | | | m1_subset_1(all_48_1, all_62_0) | ? [v0: $i] : ($i(v0) &
% 22.43/3.76 | | | | | | | r1_tarski(all_196_0, v0) & r2_hidden(v0, all_48_0))
% 22.43/3.76 | | | | | | |
% 22.43/3.76 | | | | | | | BETA: splitting (79) gives:
% 22.43/3.76 | | | | | | |
% 22.43/3.76 | | | | | | | Case 1:
% 22.43/3.76 | | | | | | | |
% 22.43/3.76 | | | | | | | | (80) ~ m1_subset_1(all_48_0, all_62_0)
% 22.43/3.76 | | | | | | | |
% 22.43/3.76 | | | | | | | | REDUCE: (39), (80) imply:
% 22.43/3.76 | | | | | | | | (81) ~ m1_subset_1(all_48_0, all_48_3)
% 22.43/3.76 | | | | | | | |
% 22.43/3.76 | | | | | | | | PRED_UNIFY: (8), (81) imply:
% 22.43/3.76 | | | | | | | | (82) $false
% 22.43/3.76 | | | | | | | |
% 22.43/3.76 | | | | | | | | CLOSE: (82) is inconsistent.
% 22.43/3.76 | | | | | | | |
% 22.43/3.76 | | | | | | | Case 2:
% 22.43/3.76 | | | | | | | |
% 22.43/3.77 | | | | | | | | (83) ~ m1_subset_1(all_48_1, all_62_0) | ? [v0: $i] :
% 22.43/3.77 | | | | | | | | ($i(v0) & r1_tarski(all_196_0, v0) & r2_hidden(v0,
% 22.43/3.77 | | | | | | | | all_48_0))
% 22.43/3.77 | | | | | | | |
% 22.43/3.77 | | | | | | | | BETA: splitting (83) gives:
% 22.43/3.77 | | | | | | | |
% 22.43/3.77 | | | | | | | | Case 1:
% 22.43/3.77 | | | | | | | | |
% 22.43/3.77 | | | | | | | | | (84) ~ m1_subset_1(all_48_1, all_62_0)
% 22.43/3.77 | | | | | | | | |
% 22.43/3.77 | | | | | | | | | REDUCE: (39), (84) imply:
% 22.43/3.77 | | | | | | | | | (85) ~ m1_subset_1(all_48_1, all_48_3)
% 22.43/3.77 | | | | | | | | |
% 22.43/3.77 | | | | | | | | | PRED_UNIFY: (7), (85) imply:
% 22.43/3.77 | | | | | | | | | (86) $false
% 22.43/3.77 | | | | | | | | |
% 22.43/3.77 | | | | | | | | | CLOSE: (86) is inconsistent.
% 22.43/3.77 | | | | | | | | |
% 22.43/3.77 | | | | | | | | Case 2:
% 22.43/3.77 | | | | | | | | |
% 22.43/3.77 | | | | | | | | | (87) ? [v0: $i] : ($i(v0) & r1_tarski(all_196_0, v0) &
% 22.43/3.77 | | | | | | | | | r2_hidden(v0, all_48_0))
% 22.43/3.77 | | | | | | | | |
% 22.43/3.77 | | | | | | | | | DELTA: instantiating (87) with fresh symbol all_212_0 gives:
% 22.43/3.77 | | | | | | | | | (88) $i(all_212_0) & r1_tarski(all_196_0, all_212_0) &
% 22.43/3.77 | | | | | | | | | r2_hidden(all_212_0, all_48_0)
% 22.43/3.77 | | | | | | | | |
% 22.43/3.77 | | | | | | | | | ALPHA: (88) implies:
% 22.43/3.77 | | | | | | | | | (89) r2_hidden(all_212_0, all_48_0)
% 22.43/3.77 | | | | | | | | | (90) r1_tarski(all_196_0, all_212_0)
% 22.43/3.77 | | | | | | | | | (91) $i(all_212_0)
% 22.43/3.77 | | | | | | | | |
% 22.43/3.77 | | | | | | | | | GROUND_INST: instantiating (t1_xboole_1) with all_179_0,
% 22.43/3.77 | | | | | | | | | all_196_0, all_212_0, simplifying with (63), (77),
% 22.43/3.77 | | | | | | | | | (78), (90), (91) gives:
% 22.43/3.77 | | | | | | | | | (92) r1_tarski(all_179_0, all_212_0)
% 22.43/3.77 | | | | | | | | |
% 22.43/3.77 | | | | | | | | | GROUND_INST: instantiating (64) with all_212_0, simplifying
% 22.43/3.77 | | | | | | | | | with (89), (91), (92) gives:
% 22.43/3.77 | | | | | | | | | (93) $false
% 22.43/3.77 | | | | | | | | |
% 22.43/3.77 | | | | | | | | | CLOSE: (93) is inconsistent.
% 22.43/3.77 | | | | | | | | |
% 22.43/3.77 | | | | | | | | End of split
% 22.43/3.77 | | | | | | | |
% 22.43/3.77 | | | | | | | End of split
% 22.43/3.77 | | | | | | |
% 22.43/3.77 | | | | | | End of split
% 22.43/3.77 | | | | | |
% 22.43/3.77 | | | | | End of split
% 22.43/3.77 | | | | |
% 22.43/3.77 | | | | End of split
% 22.43/3.77 | | | |
% 22.43/3.77 | | | End of split
% 22.43/3.77 | | |
% 22.43/3.77 | | End of split
% 22.43/3.77 | |
% 22.43/3.77 | End of split
% 22.43/3.77 |
% 22.43/3.77 End of proof
% 22.43/3.77 % SZS output end Proof for theBenchmark
% 22.43/3.77
% 22.43/3.77 3157ms
%------------------------------------------------------------------------------