TSTP Solution File: SEU203+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU203+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n014.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 17:43:15 EDT 2023
% Result : Theorem 59.66s 8.74s
% Output : Proof 83.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU203+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Wed Aug 23 18:51:49 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.59 ________ _____
% 0.20/0.59 ___ __ \_________(_)________________________________
% 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59 (2023-06-19)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2023
% 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59 Amanda Stjerna.
% 0.20/0.59 Free software under BSD-3-Clause.
% 0.20/0.59
% 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.60 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.83/1.58 Prover 1: Preprocessing ...
% 5.83/1.58 Prover 4: Preprocessing ...
% 6.25/1.62 Prover 2: Preprocessing ...
% 6.25/1.62 Prover 3: Preprocessing ...
% 6.25/1.62 Prover 6: Preprocessing ...
% 6.25/1.62 Prover 0: Preprocessing ...
% 6.25/1.63 Prover 5: Preprocessing ...
% 18.08/3.21 Prover 1: Warning: ignoring some quantifiers
% 18.08/3.26 Prover 3: Warning: ignoring some quantifiers
% 18.99/3.31 Prover 3: Constructing countermodel ...
% 19.05/3.32 Prover 6: Proving ...
% 19.05/3.32 Prover 5: Proving ...
% 19.05/3.33 Prover 1: Constructing countermodel ...
% 20.23/3.54 Prover 4: Warning: ignoring some quantifiers
% 20.23/3.62 Prover 2: Proving ...
% 20.23/3.67 Prover 4: Constructing countermodel ...
% 20.23/3.68 Prover 0: Proving ...
% 59.66/8.74 Prover 0: proved (7998ms)
% 59.66/8.74
% 59.66/8.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 59.66/8.74
% 59.66/8.74 Prover 5: stopped
% 59.66/8.74 Prover 6: stopped
% 59.66/8.75 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 59.66/8.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 59.66/8.75 Prover 3: stopped
% 59.66/8.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 59.66/8.75 Prover 2: stopped
% 59.66/8.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 59.66/8.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 61.23/9.04 Prover 7: Preprocessing ...
% 61.23/9.05 Prover 10: Preprocessing ...
% 61.23/9.05 Prover 11: Preprocessing ...
% 61.23/9.09 Prover 13: Preprocessing ...
% 62.84/9.15 Prover 8: Preprocessing ...
% 64.19/9.33 Prover 10: Warning: ignoring some quantifiers
% 64.19/9.38 Prover 7: Warning: ignoring some quantifiers
% 64.19/9.38 Prover 10: Constructing countermodel ...
% 64.76/9.43 Prover 7: Constructing countermodel ...
% 64.76/9.44 Prover 8: Warning: ignoring some quantifiers
% 64.76/9.47 Prover 8: Constructing countermodel ...
% 65.90/9.56 Prover 13: Warning: ignoring some quantifiers
% 66.54/9.63 Prover 13: Constructing countermodel ...
% 67.04/9.69 Prover 11: Warning: ignoring some quantifiers
% 67.04/9.73 Prover 11: Constructing countermodel ...
% 82.87/11.80 Prover 10: Found proof (size 69)
% 82.87/11.80 Prover 10: proved (3058ms)
% 82.87/11.81 Prover 8: stopped
% 82.87/11.81 Prover 13: stopped
% 82.87/11.81 Prover 11: stopped
% 82.87/11.81 Prover 7: stopped
% 82.87/11.81 Prover 4: stopped
% 82.87/11.81 Prover 1: stopped
% 82.87/11.81
% 82.87/11.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 82.87/11.81
% 83.28/11.82 % SZS output start Proof for theBenchmark
% 83.28/11.83 Assumptions after simplification:
% 83.28/11.83 ---------------------------------
% 83.28/11.83
% 83.28/11.83 (d13_relat_1)
% 83.44/11.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 83.44/11.86 $i] : ( ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v4, v3) = v5) |
% 83.44/11.86 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) |
% 83.44/11.86 ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [v0: $i] : ! [v1: $i] : !
% 83.44/11.86 [v2: $i] : ! [v3: $i] : ( ~ (relation_image(v0, v1) = v2) | ~ $i(v3) | ~
% 83.44/11.86 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v3, v2) | ? [v4:
% 83.44/11.86 $i] : ? [v5: $i] : (ordered_pair(v4, v3) = v5 & $i(v5) & $i(v4) & in(v5,
% 83.44/11.86 v0) & in(v4, v1))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 83.44/11.86 $i] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 83.44/11.86 ~ $i(v0) | ~ relation(v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 83.44/11.86 ($i(v5) & $i(v4) & ( ~ in(v4, v0) | ! [v7: $i] : ! [v8: $i] : ( ~
% 83.44/11.86 (ordered_pair(v7, v4) = v8) | ~ $i(v7) | ~ in(v8, v1) | ~ in(v7,
% 83.44/11.86 v2))) & (in(v4, v0) | (ordered_pair(v5, v4) = v6 & $i(v6) & in(v6,
% 83.44/11.86 v1) & in(v5, v2)))))
% 83.44/11.86
% 83.44/11.86 (d1_xboole_0)
% 83.44/11.86 $i(empty_set) & ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) & ? [v0: $i]
% 83.44/11.86 : (v0 = empty_set | ~ $i(v0) | ? [v1: $i] : ($i(v1) & in(v1, v0)))
% 83.44/11.86
% 83.44/11.86 (d2_relat_1)
% 83.44/11.86 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ relation(v1)
% 83.44/11.86 | ~ relation(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 83.44/11.86 (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & ( ~ in(v4, v1) | ~
% 83.44/11.86 in(v4, v0)) & (in(v4, v1) | in(v4, v0))))
% 83.44/11.86
% 83.44/11.86 (d3_relat_1)
% 83.44/11.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 83.44/11.87 (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 83.44/11.87 | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) |
% 83.44/11.87 in(v4, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 83.44/11.87 relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i]
% 83.44/11.87 : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) &
% 83.44/11.87 in(v4, v0) & ~ in(v4, v1)))
% 83.44/11.87
% 83.44/11.87 (d4_relat_1)
% 83.44/11.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 83.44/11.88 (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~
% 83.44/11.88 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v2,
% 83.44/11.88 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) =
% 83.44/11.88 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1)
% 83.44/11.88 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) &
% 83.44/11.88 in(v4, v0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 83.44/11.88 (relation_dom(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3:
% 83.44/11.88 $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ in(v3, v0) | !
% 83.44/11.88 [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v3, v6) = v7) | ~ $i(v6) |
% 83.44/11.88 ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & $i(v5) &
% 83.44/11.88 in(v5, v1)))))
% 83.44/11.88
% 83.44/11.88 (d8_xboole_0)
% 83.44/11.88 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ subset(v0,
% 83.44/11.88 v1) | proper_subset(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 83.44/11.88 $i(v0) | ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0: $i] : ( ~
% 83.44/11.88 $i(v0) | ~ proper_subset(v0, v0))
% 83.44/11.88
% 83.44/11.88 (fc4_relat_1)
% 83.44/11.88 $i(empty_set) & relation(empty_set) & empty(empty_set)
% 83.44/11.88
% 83.44/11.88 (rc1_relat_1)
% 83.44/11.88 ? [v0: $i] : ($i(v0) & relation(v0) & empty(v0))
% 83.44/11.88
% 83.44/11.88 (rc1_xboole_0)
% 83.44/11.88 ? [v0: $i] : ($i(v0) & empty(v0))
% 83.44/11.88
% 83.44/11.88 (rc2_relat_1)
% 83.44/11.88 ? [v0: $i] : ($i(v0) & relation(v0) & ~ empty(v0))
% 83.44/11.88
% 83.44/11.88 (rc2_subset_1)
% 83.44/11.88 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i]
% 83.44/11.88 : ($i(v2) & element(v2, v1) & empty(v2)))
% 83.44/11.88
% 83.44/11.88 (t143_relat_1)
% 83.44/11.89 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 83.44/11.89 $i] : ? [v6: $i] : (relation_dom(v2) = v4 & relation_image(v2, v1) = v3 &
% 83.44/11.89 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & relation(v2) &
% 83.44/11.89 ((ordered_pair(v5, v0) = v6 & $i(v6) & in(v6, v2) & in(v5, v4) & in(v5, v1)
% 83.44/11.89 & ~ in(v0, v3)) | (in(v0, v3) & ! [v7: $i] : ! [v8: $i] : ( ~
% 83.44/11.89 (ordered_pair(v7, v0) = v8) | ~ $i(v7) | ~ in(v8, v2) | ~ in(v7,
% 83.44/11.89 v4) | ~ in(v7, v1)))))
% 83.44/11.89
% 83.44/11.89 (t1_zfmisc_1)
% 83.44/11.89 $i(empty_set) & ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set)
% 83.44/11.89 = v0 & $i(v0))
% 83.44/11.89
% 83.44/11.89 (t6_boole)
% 83.44/11.89 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 83.44/11.89
% 83.44/11.89 (t8_boole)
% 83.44/11.89 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ empty(v1) |
% 83.44/11.89 ~ empty(v0))
% 83.44/11.89
% 83.44/11.89 Further assumptions not needed in the proof:
% 83.44/11.89 --------------------------------------------
% 83.44/11.89 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_relat_1,
% 83.44/11.89 commutativity_k2_tarski, commutativity_k2_xboole_0, commutativity_k3_xboole_0,
% 83.44/11.89 d10_relat_1, d10_xboole_0, d11_relat_1, d12_relat_1, d1_relat_1, d1_setfam_1,
% 83.44/11.89 d1_tarski, d1_zfmisc_1, d2_subset_1, d2_tarski, d2_xboole_0, d2_zfmisc_1,
% 83.44/11.89 d3_tarski, d3_xboole_0, d4_subset_1, d4_tarski, d4_xboole_0, d5_relat_1,
% 83.44/11.89 d5_subset_1, d5_tarski, d6_relat_1, d7_relat_1, d7_xboole_0, d8_relat_1,
% 83.44/11.89 d8_setfam_1, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0,
% 83.44/11.89 dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0,
% 83.44/11.89 dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0,
% 83.44/11.89 dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1,
% 83.44/11.89 dt_k6_relat_1, dt_k6_setfam_1, dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1,
% 83.44/11.89 dt_k8_relat_1, dt_k9_relat_1, dt_m1_subset_1, existence_m1_subset_1,
% 83.44/11.89 fc10_relat_1, fc1_relat_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1,
% 83.44/11.89 fc2_relat_1, fc2_subset_1, fc2_xboole_0, fc3_subset_1, fc3_xboole_0,
% 83.44/11.89 fc4_subset_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1, fc9_relat_1,
% 83.44/11.89 idempotence_k2_xboole_0, idempotence_k3_xboole_0, involutiveness_k3_subset_1,
% 83.44/11.89 involutiveness_k4_relat_1, involutiveness_k7_setfam_1,
% 83.44/11.89 irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1,
% 83.44/11.89 l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_zfmisc_1, l4_zfmisc_1,
% 83.44/11.89 l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, rc1_subset_1, rc2_xboole_0,
% 83.44/11.89 redefinition_k5_setfam_1, redefinition_k6_setfam_1, redefinition_k6_subset_1,
% 83.44/11.89 reflexivity_r1_tarski, symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1,
% 83.44/11.89 t115_relat_1, t116_relat_1, t117_relat_1, t118_relat_1, t118_zfmisc_1,
% 83.44/11.89 t119_relat_1, t119_zfmisc_1, t12_xboole_1, t136_zfmisc_1, t140_relat_1,
% 83.44/11.89 t17_xboole_1, t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, t20_relat_1,
% 83.44/11.89 t21_relat_1, t25_relat_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_subset,
% 83.44/11.89 t2_tarski, t2_xboole_1, t30_relat_1, t33_xboole_1, t33_zfmisc_1, t36_xboole_1,
% 83.44/11.89 t37_relat_1, t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1,
% 83.44/11.89 t39_zfmisc_1, t3_boole, t3_subset, t3_xboole_0, t3_xboole_1, t40_xboole_1,
% 83.44/11.89 t43_subset_1, t44_relat_1, t45_relat_1, t45_xboole_1, t46_relat_1, t46_setfam_1,
% 83.44/11.89 t46_zfmisc_1, t47_relat_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole,
% 83.44/11.89 t4_subset, t4_xboole_0, t50_subset_1, t54_subset_1, t56_relat_1, t5_subset,
% 83.44/11.89 t60_relat_1, t60_xboole_1, t63_xboole_1, t64_relat_1, t65_relat_1, t65_zfmisc_1,
% 83.44/11.89 t69_enumset1, t6_zfmisc_1, t71_relat_1, t74_relat_1, t7_boole, t7_xboole_1,
% 83.44/11.89 t83_xboole_1, t86_relat_1, t88_relat_1, t8_xboole_1, t8_zfmisc_1, t90_relat_1,
% 83.44/11.89 t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1, t9_tarski, t9_zfmisc_1
% 83.44/11.89
% 83.44/11.89 Those formulas are unsatisfiable:
% 83.44/11.89 ---------------------------------
% 83.44/11.89
% 83.44/11.89 Begin of proof
% 83.44/11.89 |
% 83.44/11.90 | ALPHA: (d13_relat_1) implies:
% 83.44/11.90 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 83.44/11.90 | (relation_image(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 83.44/11.90 | ~ $i(v0) | ~ relation(v0) | ~ in(v3, v2) | ? [v4: $i] : ? [v5:
% 83.44/11.90 | $i] : (ordered_pair(v4, v3) = v5 & $i(v5) & $i(v4) & in(v5, v0) &
% 83.44/11.90 | in(v4, v1)))
% 83.44/11.90 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 83.44/11.90 | ! [v5: $i] : ( ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v4,
% 83.44/11.90 | v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 83.44/11.90 | $i(v0) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3,
% 83.44/11.90 | v2))
% 83.44/11.90 |
% 83.44/11.90 | ALPHA: (d1_xboole_0) implies:
% 83.44/11.90 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set))
% 83.44/11.90 |
% 83.44/11.90 | ALPHA: (d3_relat_1) implies:
% 83.44/11.90 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) |
% 83.44/11.90 | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 83.44/11.90 | $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) &
% 83.44/11.90 | in(v4, v0) & ~ in(v4, v1)))
% 83.44/11.90 |
% 83.44/11.90 | ALPHA: (d4_relat_1) implies:
% 83.44/11.91 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 83.44/11.91 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~
% 83.44/11.91 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~
% 83.44/11.91 | in(v4, v0) | in(v2, v1))
% 83.44/11.91 |
% 83.44/11.91 | ALPHA: (d8_xboole_0) implies:
% 83.44/11.91 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 83.44/11.91 | subset(v0, v1) | proper_subset(v0, v1))
% 83.44/11.91 |
% 83.44/11.91 | ALPHA: (fc4_relat_1) implies:
% 83.44/11.91 | (7) relation(empty_set)
% 83.44/11.91 |
% 83.44/11.91 | ALPHA: (t1_zfmisc_1) implies:
% 83.44/11.91 | (8) ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) = v0 &
% 83.44/11.91 | $i(v0))
% 83.44/11.91 |
% 83.44/11.91 | ALPHA: (t6_boole) implies:
% 83.44/11.91 | (9) $i(empty_set)
% 83.44/11.91 | (10) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 83.44/11.91 |
% 83.44/11.91 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_170_0 gives:
% 83.44/11.91 | (11) $i(all_170_0) & empty(all_170_0)
% 83.44/11.91 |
% 83.44/11.91 | ALPHA: (11) implies:
% 83.44/11.91 | (12) empty(all_170_0)
% 83.44/11.91 | (13) $i(all_170_0)
% 83.44/11.91 |
% 83.44/11.91 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_175_0 gives:
% 83.44/11.91 | (14) $i(all_175_0) & relation(all_175_0) & empty(all_175_0)
% 83.44/11.91 |
% 83.44/11.91 | ALPHA: (14) implies:
% 83.44/11.91 | (15) empty(all_175_0)
% 83.44/11.91 | (16) relation(all_175_0)
% 83.44/11.91 | (17) $i(all_175_0)
% 83.44/11.91 |
% 83.44/11.91 | DELTA: instantiating (8) with fresh symbol all_177_0 gives:
% 83.44/11.91 | (18) powerset(empty_set) = all_177_0 & singleton(empty_set) = all_177_0 &
% 83.44/11.91 | $i(all_177_0)
% 83.44/11.91 |
% 83.44/11.91 | ALPHA: (18) implies:
% 83.44/11.91 | (19) powerset(empty_set) = all_177_0
% 83.44/11.91 |
% 83.44/11.91 | DELTA: instantiating (rc2_relat_1) with fresh symbol all_179_0 gives:
% 83.44/11.91 | (20) $i(all_179_0) & relation(all_179_0) & ~ empty(all_179_0)
% 83.44/11.91 |
% 83.44/11.91 | ALPHA: (20) implies:
% 83.44/11.91 | (21) ~ empty(all_179_0)
% 83.44/11.91 | (22) relation(all_179_0)
% 83.44/11.92 | (23) $i(all_179_0)
% 83.44/11.92 |
% 83.44/11.92 | DELTA: instantiating (t143_relat_1) with fresh symbols all_222_0, all_222_1,
% 83.44/11.92 | all_222_2, all_222_3, all_222_4, all_222_5, all_222_6 gives:
% 83.44/11.92 | (24) relation_dom(all_222_4) = all_222_2 & relation_image(all_222_4,
% 83.44/11.92 | all_222_5) = all_222_3 & $i(all_222_1) & $i(all_222_2) &
% 83.44/11.92 | $i(all_222_3) & $i(all_222_4) & $i(all_222_5) & $i(all_222_6) &
% 83.44/11.92 | relation(all_222_4) & ((ordered_pair(all_222_1, all_222_6) = all_222_0
% 83.44/11.92 | & $i(all_222_0) & in(all_222_0, all_222_4) & in(all_222_1,
% 83.44/11.92 | all_222_2) & in(all_222_1, all_222_5) & ~ in(all_222_6,
% 83.44/11.92 | all_222_3)) | (in(all_222_6, all_222_3) & ! [v0: $i] : ! [v1:
% 83.44/11.92 | $i] : ( ~ (ordered_pair(v0, all_222_6) = v1) | ~ $i(v0) | ~
% 83.44/11.92 | in(v1, all_222_4) | ~ in(v0, all_222_2) | ~ in(v0,
% 83.44/11.92 | all_222_5))))
% 83.44/11.92 |
% 83.44/11.92 | ALPHA: (24) implies:
% 83.44/11.92 | (25) relation(all_222_4)
% 83.44/11.92 | (26) $i(all_222_6)
% 83.44/11.92 | (27) $i(all_222_5)
% 83.44/11.92 | (28) $i(all_222_4)
% 83.44/11.92 | (29) $i(all_222_3)
% 83.44/11.92 | (30) $i(all_222_2)
% 83.44/11.92 | (31) $i(all_222_1)
% 83.44/11.92 | (32) relation_image(all_222_4, all_222_5) = all_222_3
% 83.44/11.92 | (33) relation_dom(all_222_4) = all_222_2
% 83.44/11.92 | (34) (ordered_pair(all_222_1, all_222_6) = all_222_0 & $i(all_222_0) &
% 83.44/11.92 | in(all_222_0, all_222_4) & in(all_222_1, all_222_2) & in(all_222_1,
% 83.44/11.92 | all_222_5) & ~ in(all_222_6, all_222_3)) | (in(all_222_6,
% 83.44/11.92 | all_222_3) & ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0,
% 83.44/11.92 | all_222_6) = v1) | ~ $i(v0) | ~ in(v1, all_222_4) | ~
% 83.44/11.92 | in(v0, all_222_2) | ~ in(v0, all_222_5)))
% 83.44/11.92 |
% 83.44/11.92 | GROUND_INST: instantiating (t8_boole) with all_170_0, all_175_0, simplifying
% 83.44/11.92 | with (12), (13), (15), (17) gives:
% 83.44/11.92 | (35) all_175_0 = all_170_0
% 83.44/11.92 |
% 83.44/11.92 | GROUND_INST: instantiating (10) with all_175_0, simplifying with (15), (17)
% 83.44/11.92 | gives:
% 83.44/11.92 | (36) all_175_0 = empty_set
% 83.44/11.92 |
% 83.44/11.92 | GROUND_INST: instantiating (4) with all_175_0, all_179_0, simplifying with
% 83.44/11.92 | (16), (17), (22), (23) gives:
% 83.44/11.92 | (37) subset(all_175_0, all_179_0) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 83.44/11.92 | : (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2,
% 83.44/11.92 | all_175_0) & ~ in(v2, all_179_0))
% 83.44/11.93 |
% 83.44/11.93 | GROUND_INST: instantiating (d2_relat_1) with empty_set, all_179_0, simplifying
% 83.44/11.93 | with (7), (9), (22), (23) gives:
% 83.44/11.93 | (38) all_179_0 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 83.44/11.93 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2,
% 83.44/11.93 | all_179_0) | ~ in(v2, empty_set)) & (in(v2, all_179_0) | in(v2,
% 83.44/11.93 | empty_set)))
% 83.44/11.93 |
% 83.44/11.93 | GROUND_INST: instantiating (4) with empty_set, all_179_0, simplifying with
% 83.44/11.93 | (7), (9), (22), (23) gives:
% 83.44/11.93 | (39) subset(empty_set, all_179_0) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 83.44/11.93 | : (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2,
% 83.44/11.93 | empty_set) & ~ in(v2, all_179_0))
% 83.44/11.93 |
% 83.44/11.93 | GROUND_INST: instantiating (rc2_subset_1) with empty_set, all_177_0,
% 83.44/11.93 | simplifying with (9), (19) gives:
% 83.44/11.93 | (40) ? [v0: $i] : ($i(v0) & element(v0, all_177_0) & empty(v0))
% 83.44/11.93 |
% 83.44/11.93 | COMBINE_EQS: (35), (36) imply:
% 83.44/11.93 | (41) all_170_0 = empty_set
% 83.44/11.93 |
% 83.44/11.93 | DELTA: instantiating (40) with fresh symbol all_230_0 gives:
% 83.44/11.93 | (42) $i(all_230_0) & element(all_230_0, all_177_0) & empty(all_230_0)
% 83.44/11.93 |
% 83.44/11.93 | ALPHA: (42) implies:
% 83.44/11.93 | (43) empty(all_230_0)
% 83.44/11.93 | (44) $i(all_230_0)
% 83.44/11.93 |
% 83.44/11.93 | GROUND_INST: instantiating (10) with all_230_0, simplifying with (43), (44)
% 83.44/11.93 | gives:
% 83.44/11.93 | (45) all_230_0 = empty_set
% 83.44/11.93 |
% 83.44/11.93 | REDUCE: (43), (45) imply:
% 83.44/11.93 | (46) empty(empty_set)
% 83.44/11.93 |
% 83.44/11.93 | BETA: splitting (34) gives:
% 83.44/11.93 |
% 83.83/11.93 | Case 1:
% 83.83/11.93 | |
% 83.83/11.93 | | (47) ordered_pair(all_222_1, all_222_6) = all_222_0 & $i(all_222_0) &
% 83.83/11.93 | | in(all_222_0, all_222_4) & in(all_222_1, all_222_2) & in(all_222_1,
% 83.83/11.93 | | all_222_5) & ~ in(all_222_6, all_222_3)
% 83.83/11.93 | |
% 83.83/11.93 | | ALPHA: (47) implies:
% 83.83/11.93 | | (48) ~ in(all_222_6, all_222_3)
% 83.83/11.93 | | (49) in(all_222_1, all_222_5)
% 83.83/11.93 | | (50) in(all_222_0, all_222_4)
% 83.83/11.93 | | (51) ordered_pair(all_222_1, all_222_6) = all_222_0
% 83.83/11.93 | |
% 83.83/11.93 | | GROUND_INST: instantiating (2) with all_222_4, all_222_5, all_222_3,
% 83.83/11.93 | | all_222_6, all_222_1, all_222_0, simplifying with (25), (26),
% 83.83/11.93 | | (27), (28), (29), (31), (32), (48), (49), (50), (51) gives:
% 83.83/11.93 | | (52) $false
% 83.83/11.93 | |
% 83.83/11.93 | | CLOSE: (52) is inconsistent.
% 83.83/11.93 | |
% 83.83/11.93 | Case 2:
% 83.83/11.93 | |
% 83.83/11.94 | | (53) in(all_222_6, all_222_3) & ! [v0: $i] : ! [v1: $i] : ( ~
% 83.83/11.94 | | (ordered_pair(v0, all_222_6) = v1) | ~ $i(v0) | ~ in(v1,
% 83.83/11.94 | | all_222_4) | ~ in(v0, all_222_2) | ~ in(v0, all_222_5))
% 83.83/11.94 | |
% 83.83/11.94 | | ALPHA: (53) implies:
% 83.83/11.94 | | (54) in(all_222_6, all_222_3)
% 83.83/11.94 | | (55) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, all_222_6) = v1) |
% 83.83/11.94 | | ~ $i(v0) | ~ in(v1, all_222_4) | ~ in(v0, all_222_2) | ~
% 83.83/11.94 | | in(v0, all_222_5))
% 83.83/11.94 | |
% 83.83/11.94 | | BETA: splitting (37) gives:
% 83.83/11.94 | |
% 83.83/11.94 | | Case 1:
% 83.83/11.94 | | |
% 83.83/11.94 | | | (56) subset(all_175_0, all_179_0)
% 83.83/11.94 | | |
% 83.83/11.94 | | | REDUCE: (36), (56) imply:
% 83.83/11.94 | | | (57) subset(empty_set, all_179_0)
% 83.83/11.94 | | |
% 83.83/11.94 | | | BETA: splitting (38) gives:
% 83.83/11.94 | | |
% 83.83/11.94 | | | Case 1:
% 83.83/11.94 | | | |
% 83.83/11.94 | | | | (58) all_179_0 = empty_set
% 83.83/11.94 | | | |
% 83.83/11.94 | | | | REDUCE: (21), (58) imply:
% 83.83/11.94 | | | | (59) ~ empty(empty_set)
% 83.83/11.94 | | | |
% 83.83/11.94 | | | | PRED_UNIFY: (46), (59) imply:
% 83.83/11.94 | | | | (60) $false
% 83.83/11.94 | | | |
% 83.83/11.94 | | | | CLOSE: (60) is inconsistent.
% 83.83/11.94 | | | |
% 83.83/11.94 | | | Case 2:
% 83.83/11.94 | | | |
% 83.83/11.94 | | | | (61) ~ (all_179_0 = empty_set)
% 83.83/11.94 | | | |
% 83.83/11.94 | | | | GROUND_INST: instantiating (1) with all_222_4, all_222_5, all_222_3,
% 83.83/11.94 | | | | all_222_6, simplifying with (25), (26), (27), (28), (29),
% 83.83/11.94 | | | | (32), (54) gives:
% 83.83/11.94 | | | | (62) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, all_222_6) = v1 &
% 83.83/11.94 | | | | $i(v1) & $i(v0) & in(v1, all_222_4) & in(v0, all_222_5))
% 83.83/11.94 | | | |
% 83.83/11.94 | | | | GROUND_INST: instantiating (6) with empty_set, all_179_0, simplifying
% 83.83/11.94 | | | | with (9), (23), (57) gives:
% 83.83/11.94 | | | | (63) all_179_0 = empty_set | proper_subset(empty_set, all_179_0)
% 83.83/11.94 | | | |
% 83.83/11.94 | | | | DELTA: instantiating (62) with fresh symbols all_548_0, all_548_1 gives:
% 83.83/11.94 | | | | (64) ordered_pair(all_548_1, all_222_6) = all_548_0 & $i(all_548_0) &
% 83.83/11.94 | | | | $i(all_548_1) & in(all_548_0, all_222_4) & in(all_548_1,
% 83.83/11.94 | | | | all_222_5)
% 83.83/11.94 | | | |
% 83.83/11.94 | | | | ALPHA: (64) implies:
% 83.83/11.94 | | | | (65) in(all_548_1, all_222_5)
% 83.83/11.94 | | | | (66) in(all_548_0, all_222_4)
% 83.83/11.94 | | | | (67) $i(all_548_1)
% 83.83/11.94 | | | | (68) ordered_pair(all_548_1, all_222_6) = all_548_0
% 83.83/11.94 | | | |
% 83.83/11.94 | | | | BETA: splitting (63) gives:
% 83.83/11.94 | | | |
% 83.83/11.94 | | | | Case 1:
% 83.83/11.94 | | | | |
% 83.83/11.94 | | | | |
% 83.83/11.94 | | | | | GROUND_INST: instantiating (5) with all_222_4, all_222_2, all_548_1,
% 83.83/11.94 | | | | | all_222_6, all_548_0, simplifying with (25), (26), (28),
% 83.83/11.94 | | | | | (30), (33), (66), (67), (68) gives:
% 83.83/11.94 | | | | | (69) in(all_548_1, all_222_2)
% 83.83/11.94 | | | | |
% 83.83/11.94 | | | | | GROUND_INST: instantiating (55) with all_548_1, all_548_0, simplifying
% 83.83/11.94 | | | | | with (65), (66), (67), (68), (69) gives:
% 83.83/11.94 | | | | | (70) $false
% 83.83/11.94 | | | | |
% 83.83/11.94 | | | | | CLOSE: (70) is inconsistent.
% 83.83/11.94 | | | | |
% 83.83/11.94 | | | | Case 2:
% 83.83/11.94 | | | | |
% 83.83/11.94 | | | | | (71) all_179_0 = empty_set
% 83.83/11.94 | | | | |
% 83.83/11.94 | | | | | REDUCE: (61), (71) imply:
% 83.83/11.94 | | | | | (72) $false
% 83.83/11.94 | | | | |
% 83.83/11.94 | | | | | CLOSE: (72) is inconsistent.
% 83.83/11.94 | | | | |
% 83.83/11.94 | | | | End of split
% 83.83/11.94 | | | |
% 83.83/11.94 | | | End of split
% 83.83/11.94 | | |
% 83.83/11.94 | | Case 2:
% 83.83/11.94 | | |
% 83.83/11.94 | | | (73) ~ subset(all_175_0, all_179_0)
% 83.83/11.94 | | |
% 83.83/11.94 | | | REDUCE: (36), (73) imply:
% 83.83/11.94 | | | (74) ~ subset(empty_set, all_179_0)
% 83.83/11.94 | | |
% 83.83/11.94 | | | BETA: splitting (39) gives:
% 83.83/11.94 | | |
% 83.83/11.94 | | | Case 1:
% 83.83/11.94 | | | |
% 83.83/11.94 | | | | (75) subset(empty_set, all_179_0)
% 83.83/11.94 | | | |
% 83.83/11.94 | | | | PRED_UNIFY: (74), (75) imply:
% 83.83/11.94 | | | | (76) $false
% 83.83/11.94 | | | |
% 83.83/11.94 | | | | CLOSE: (76) is inconsistent.
% 83.83/11.94 | | | |
% 83.83/11.94 | | | Case 2:
% 83.83/11.94 | | | |
% 83.83/11.95 | | | | (77) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1)
% 83.83/11.95 | | | | = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, empty_set) & ~
% 83.83/11.95 | | | | in(v2, all_179_0))
% 83.83/11.95 | | | |
% 83.83/11.95 | | | | DELTA: instantiating (77) with fresh symbols all_401_0, all_401_1,
% 83.83/11.95 | | | | all_401_2 gives:
% 83.83/11.95 | | | | (78) ordered_pair(all_401_2, all_401_1) = all_401_0 & $i(all_401_0) &
% 83.83/11.95 | | | | $i(all_401_1) & $i(all_401_2) & in(all_401_0, empty_set) & ~
% 83.83/11.95 | | | | in(all_401_0, all_179_0)
% 83.83/11.95 | | | |
% 83.83/11.95 | | | | ALPHA: (78) implies:
% 83.83/11.95 | | | | (79) in(all_401_0, empty_set)
% 83.83/11.95 | | | | (80) $i(all_401_0)
% 83.83/11.95 | | | |
% 83.83/11.95 | | | | GROUND_INST: instantiating (3) with all_401_0, simplifying with (79),
% 83.83/11.95 | | | | (80) gives:
% 83.83/11.95 | | | | (81) $false
% 83.83/11.95 | | | |
% 83.83/11.95 | | | | CLOSE: (81) is inconsistent.
% 83.83/11.95 | | | |
% 83.83/11.95 | | | End of split
% 83.83/11.95 | | |
% 83.83/11.95 | | End of split
% 83.83/11.95 | |
% 83.83/11.95 | End of split
% 83.83/11.95 |
% 83.83/11.95 End of proof
% 83.83/11.95 % SZS output end Proof for theBenchmark
% 83.83/11.95
% 83.83/11.95 11354ms
%------------------------------------------------------------------------------