TSTP Solution File: SEU208+2 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU208+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 : n026.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 17:43:16 EDT 2023
% Result : Theorem 65.45s 9.56s
% Output : Proof 87.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU208+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34 % Computer : n026.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 14:50:01 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 4.61/1.47 Prover 1: Preprocessing ...
% 4.61/1.48 Prover 4: Preprocessing ...
% 5.62/1.55 Prover 5: Preprocessing ...
% 5.62/1.55 Prover 3: Preprocessing ...
% 5.62/1.55 Prover 6: Preprocessing ...
% 5.62/1.55 Prover 2: Preprocessing ...
% 5.62/1.55 Prover 0: Preprocessing ...
% 16.24/3.06 Prover 1: Warning: ignoring some quantifiers
% 17.86/3.22 Prover 3: Warning: ignoring some quantifiers
% 17.86/3.23 Prover 6: Proving ...
% 17.86/3.23 Prover 5: Proving ...
% 17.86/3.27 Prover 1: Constructing countermodel ...
% 17.86/3.27 Prover 3: Constructing countermodel ...
% 18.45/3.34 Prover 4: Warning: ignoring some quantifiers
% 19.19/3.49 Prover 4: Constructing countermodel ...
% 20.47/3.58 Prover 2: Proving ...
% 21.18/3.67 Prover 0: Proving ...
% 65.45/9.56 Prover 0: proved (8862ms)
% 65.45/9.56
% 65.45/9.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 65.45/9.56
% 65.45/9.57 Prover 3: stopped
% 65.45/9.57 Prover 5: stopped
% 65.45/9.58 Prover 2: stopped
% 65.45/9.59 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 65.45/9.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 65.45/9.59 Prover 6: stopped
% 65.45/9.59 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 65.45/9.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 65.45/9.60 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 67.74/9.87 Prover 10: Preprocessing ...
% 67.74/9.88 Prover 7: Preprocessing ...
% 67.74/9.88 Prover 8: Preprocessing ...
% 67.74/9.89 Prover 13: Preprocessing ...
% 67.74/9.92 Prover 11: Preprocessing ...
% 71.68/10.38 Prover 10: Warning: ignoring some quantifiers
% 71.90/10.41 Prover 10: Constructing countermodel ...
% 72.27/10.47 Prover 8: Warning: ignoring some quantifiers
% 72.27/10.49 Prover 8: Constructing countermodel ...
% 72.85/10.51 Prover 7: Warning: ignoring some quantifiers
% 72.85/10.57 Prover 7: Constructing countermodel ...
% 73.35/10.58 Prover 13: Warning: ignoring some quantifiers
% 73.35/10.65 Prover 13: Constructing countermodel ...
% 75.74/10.89 Prover 11: Warning: ignoring some quantifiers
% 75.90/10.94 Prover 11: Constructing countermodel ...
% 87.00/12.40 Prover 10: Found proof (size 66)
% 87.00/12.40 Prover 10: proved (2816ms)
% 87.00/12.40 Prover 11: stopped
% 87.00/12.40 Prover 13: stopped
% 87.00/12.40 Prover 8: stopped
% 87.00/12.40 Prover 7: stopped
% 87.00/12.40 Prover 4: stopped
% 87.00/12.40 Prover 1: stopped
% 87.00/12.40
% 87.00/12.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 87.00/12.40
% 87.00/12.41 % SZS output start Proof for theBenchmark
% 87.00/12.42 Assumptions after simplification:
% 87.00/12.42 ---------------------------------
% 87.00/12.42
% 87.00/12.42 (d14_relat_1)
% 87.51/12.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 87.51/12.45 $i] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v4) =
% 87.51/12.45 v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 87.51/12.45 relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [v0: $i] :
% 87.51/12.45 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (relation_inverse_image(v0, v1) =
% 87.51/12.45 v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~
% 87.51/12.45 in(v3, v2) | ? [v4: $i] : ? [v5: $i] : (ordered_pair(v3, v4) = v5 & $i(v5)
% 87.51/12.45 & $i(v4) & in(v5, v0) & in(v4, v1))) & ? [v0: $i] : ! [v1: $i] : ! [v2:
% 87.51/12.45 $i] : ! [v3: $i] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~
% 87.51/12.45 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v4: $i] : ? [v5: $i]
% 87.51/12.45 : ? [v6: $i] : ($i(v5) & $i(v4) & ( ~ in(v4, v0) | ! [v7: $i] : ! [v8:
% 87.51/12.45 $i] : ( ~ (ordered_pair(v4, v7) = v8) | ~ $i(v7) | ~ in(v8, v1) | ~
% 87.51/12.45 in(v7, v2))) & (in(v4, v0) | (ordered_pair(v4, v5) = v6 & $i(v6) &
% 87.51/12.45 in(v6, v1) & in(v5, v2)))))
% 87.51/12.45
% 87.51/12.45 (d3_relat_1)
% 87.51/12.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 87.51/12.45 (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 87.51/12.45 | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) |
% 87.51/12.45 in(v4, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 87.51/12.45 relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i]
% 87.51/12.45 : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) &
% 87.51/12.45 in(v4, v0) & ~ in(v4, v1)))
% 87.51/12.45
% 87.51/12.45 (d5_relat_1)
% 87.51/12.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 87.51/12.46 (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ $i(v3) | ~
% 87.51/12.46 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v2,
% 87.51/12.46 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0) =
% 87.51/12.46 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1)
% 87.51/12.46 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v3, v2) = v4 & $i(v4) & $i(v3) &
% 87.51/12.46 in(v4, v0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 87.51/12.46 (relation_rng(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3:
% 87.51/12.46 $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ in(v3, v0) | !
% 87.51/12.46 [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v3) = v7) | ~ $i(v6) |
% 87.51/12.46 ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & $i(v5) &
% 87.51/12.46 in(v5, v1)))))
% 87.51/12.46
% 87.51/12.46 (fc4_relat_1)
% 87.51/12.46 $i(empty_set) & relation(empty_set) & empty(empty_set)
% 87.51/12.46
% 87.51/12.46 (rc1_relat_1)
% 87.51/12.46 ? [v0: $i] : ($i(v0) & relation(v0) & empty(v0))
% 87.51/12.46
% 87.51/12.46 (rc1_xboole_0)
% 87.51/12.46 ? [v0: $i] : ($i(v0) & empty(v0))
% 87.51/12.46
% 87.51/12.46 (rc2_relat_1)
% 87.51/12.46 ? [v0: $i] : ($i(v0) & relation(v0) & ~ empty(v0))
% 87.51/12.46
% 87.51/12.46 (rc2_subset_1)
% 87.51/12.46 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i]
% 87.51/12.46 : ($i(v2) & element(v2, v1) & empty(v2)))
% 87.51/12.46
% 87.51/12.46 (t166_relat_1)
% 87.51/12.46 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 87.51/12.46 $i] : ? [v6: $i] : (relation_rng(v2) = v4 & relation_inverse_image(v2, v1)
% 87.51/12.46 = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & relation(v2) &
% 87.51/12.46 ((ordered_pair(v0, v5) = v6 & $i(v6) & in(v6, v2) & in(v5, v4) & in(v5, v1)
% 87.51/12.46 & ~ in(v0, v3)) | (in(v0, v3) & ! [v7: $i] : ! [v8: $i] : ( ~
% 87.51/12.46 (ordered_pair(v0, v7) = v8) | ~ $i(v7) | ~ in(v8, v2) | ~ in(v7,
% 87.51/12.46 v4) | ~ in(v7, v1)))))
% 87.51/12.46
% 87.51/12.46 (t1_zfmisc_1)
% 87.51/12.46 $i(empty_set) & ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set)
% 87.51/12.46 = v0 & $i(v0))
% 87.51/12.46
% 87.51/12.46 (t3_xboole_1)
% 87.51/12.46 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ subset(v0,
% 87.51/12.46 empty_set))
% 87.51/12.46
% 87.51/12.46 (t60_relat_1)
% 87.51/12.46 relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set &
% 87.51/12.46 $i(empty_set)
% 87.51/12.46
% 87.51/12.46 (t6_boole)
% 87.51/12.46 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 87.51/12.46
% 87.51/12.46 (t8_boole)
% 87.51/12.46 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ empty(v1) |
% 87.51/12.46 ~ empty(v0))
% 87.51/12.46
% 87.51/12.46 Further assumptions not needed in the proof:
% 87.51/12.46 --------------------------------------------
% 87.51/12.46 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_relat_1,
% 87.51/12.46 commutativity_k2_tarski, commutativity_k2_xboole_0, commutativity_k3_xboole_0,
% 87.51/12.46 d10_relat_1, d10_xboole_0, d11_relat_1, d12_relat_1, d13_relat_1, d1_relat_1,
% 87.51/12.46 d1_setfam_1, d1_tarski, d1_xboole_0, d1_zfmisc_1, d2_relat_1, d2_subset_1,
% 87.51/12.46 d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_tarski, d3_xboole_0, d4_relat_1,
% 87.51/12.46 d4_subset_1, d4_tarski, d4_xboole_0, d5_subset_1, d5_tarski, d6_relat_1,
% 87.51/12.46 d7_relat_1, d7_xboole_0, d8_relat_1, d8_setfam_1, d8_xboole_0, dt_k10_relat_1,
% 87.51/12.46 dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1,
% 87.51/12.46 dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1,
% 87.51/12.46 dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_relat_1,
% 87.51/12.46 dt_k4_tarski, dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1, dt_k6_relat_1,
% 87.51/12.46 dt_k6_setfam_1, dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1, dt_k8_relat_1,
% 87.51/12.46 dt_k9_relat_1, dt_m1_subset_1, existence_m1_subset_1, fc10_relat_1, fc1_relat_1,
% 87.51/12.46 fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_relat_1, fc2_subset_1,
% 87.51/12.46 fc2_xboole_0, fc3_subset_1, fc3_xboole_0, fc4_subset_1, fc5_relat_1,
% 87.51/12.46 fc6_relat_1, fc7_relat_1, fc8_relat_1, fc9_relat_1, idempotence_k2_xboole_0,
% 87.51/12.46 idempotence_k3_xboole_0, involutiveness_k3_subset_1, involutiveness_k4_relat_1,
% 87.51/12.46 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_zfmisc_1,
% 87.51/12.46 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1,
% 87.51/12.46 l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1,
% 87.51/12.46 rc1_subset_1, rc2_xboole_0, redefinition_k5_setfam_1, redefinition_k6_setfam_1,
% 87.51/12.46 redefinition_k6_subset_1, reflexivity_r1_tarski, symmetry_r1_xboole_0,
% 87.51/12.46 t106_zfmisc_1, t10_zfmisc_1, t115_relat_1, t116_relat_1, t117_relat_1,
% 87.51/12.46 t118_relat_1, t118_zfmisc_1, t119_relat_1, t119_zfmisc_1, t12_xboole_1,
% 87.51/12.46 t136_zfmisc_1, t140_relat_1, t143_relat_1, t144_relat_1, t145_relat_1,
% 87.51/12.46 t146_relat_1, t160_relat_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset,
% 87.51/12.46 t1_xboole_1, t20_relat_1, t21_relat_1, t25_relat_1, t26_xboole_1, t28_xboole_1,
% 87.51/12.46 t2_boole, t2_subset, t2_tarski, t2_xboole_1, t30_relat_1, t33_xboole_1,
% 87.51/12.46 t33_zfmisc_1, t36_xboole_1, t37_relat_1, t37_xboole_1, t37_zfmisc_1,
% 87.51/12.46 t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_subset, t3_xboole_0,
% 87.51/12.46 t40_xboole_1, t43_subset_1, t44_relat_1, t45_relat_1, t45_xboole_1, t46_relat_1,
% 87.51/12.46 t46_setfam_1, t46_zfmisc_1, t47_relat_1, t47_setfam_1, t48_setfam_1,
% 87.51/12.46 t48_xboole_1, t4_boole, t4_subset, t4_xboole_0, t50_subset_1, t54_subset_1,
% 87.51/12.47 t56_relat_1, t5_subset, t60_xboole_1, t63_xboole_1, t64_relat_1, t65_relat_1,
% 87.51/12.47 t65_zfmisc_1, t69_enumset1, t6_zfmisc_1, t71_relat_1, t74_relat_1, t7_boole,
% 87.51/12.47 t7_xboole_1, t83_xboole_1, t86_relat_1, t88_relat_1, t8_xboole_1, t8_zfmisc_1,
% 87.51/12.47 t90_relat_1, t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1, t9_tarski,
% 87.51/12.47 t9_zfmisc_1
% 87.51/12.47
% 87.51/12.47 Those formulas are unsatisfiable:
% 87.51/12.47 ---------------------------------
% 87.51/12.47
% 87.51/12.47 Begin of proof
% 87.51/12.47 |
% 87.51/12.47 | ALPHA: (d14_relat_1) implies:
% 87.51/12.47 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 87.51/12.47 | (relation_inverse_image(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 87.51/12.47 | $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v3, v2) | ? [v4: $i] :
% 87.51/12.47 | ? [v5: $i] : (ordered_pair(v3, v4) = v5 & $i(v5) & $i(v4) & in(v5,
% 87.51/12.47 | v0) & in(v4, v1)))
% 87.51/12.47 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 87.51/12.47 | ! [v5: $i] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~
% 87.51/12.47 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 87.51/12.47 | $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1)
% 87.51/12.47 | | in(v3, v2))
% 87.51/12.47 |
% 87.51/12.47 | ALPHA: (d3_relat_1) implies:
% 87.51/12.47 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) |
% 87.51/12.47 | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 87.51/12.47 | $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) &
% 87.51/12.47 | in(v4, v0) & ~ in(v4, v1)))
% 87.51/12.47 |
% 87.51/12.47 | ALPHA: (d5_relat_1) implies:
% 87.51/12.47 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 87.51/12.47 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~
% 87.51/12.47 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~
% 87.51/12.47 | in(v4, v0) | in(v2, v1))
% 87.51/12.47 | (5) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 87.51/12.47 | (relation_rng(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) |
% 87.51/12.47 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~
% 87.51/12.47 | in(v3, v0) | ! [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v6,
% 87.51/12.47 | v3) = v7) | ~ $i(v6) | ~ in(v7, v1))) & (in(v3, v0) |
% 87.51/12.47 | (ordered_pair(v4, v3) = v5 & $i(v5) & in(v5, v1)))))
% 87.51/12.47 |
% 87.51/12.47 | ALPHA: (fc4_relat_1) implies:
% 87.51/12.47 | (6) relation(empty_set)
% 87.51/12.47 |
% 87.51/12.47 | ALPHA: (t1_zfmisc_1) implies:
% 87.51/12.47 | (7) ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) = v0 &
% 87.51/12.47 | $i(v0))
% 87.51/12.47 |
% 87.51/12.47 | ALPHA: (t3_xboole_1) implies:
% 87.51/12.47 | (8) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ subset(v0, empty_set))
% 87.51/12.47 |
% 87.51/12.47 | ALPHA: (t60_relat_1) implies:
% 87.51/12.47 | (9) relation_rng(empty_set) = empty_set
% 87.51/12.47 |
% 87.51/12.47 | ALPHA: (t6_boole) implies:
% 87.72/12.47 | (10) $i(empty_set)
% 87.72/12.47 | (11) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 87.72/12.47 |
% 87.72/12.48 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_172_0 gives:
% 87.72/12.48 | (12) $i(all_172_0) & empty(all_172_0)
% 87.72/12.48 |
% 87.72/12.48 | ALPHA: (12) implies:
% 87.72/12.48 | (13) empty(all_172_0)
% 87.72/12.48 | (14) $i(all_172_0)
% 87.72/12.48 |
% 87.72/12.48 | DELTA: instantiating (7) with fresh symbol all_179_0 gives:
% 87.72/12.48 | (15) powerset(empty_set) = all_179_0 & singleton(empty_set) = all_179_0 &
% 87.72/12.48 | $i(all_179_0)
% 87.72/12.48 |
% 87.72/12.48 | ALPHA: (15) implies:
% 87.72/12.48 | (16) powerset(empty_set) = all_179_0
% 87.72/12.48 |
% 87.72/12.48 | DELTA: instantiating (rc2_relat_1) with fresh symbol all_181_0 gives:
% 87.72/12.48 | (17) $i(all_181_0) & relation(all_181_0) & ~ empty(all_181_0)
% 87.72/12.48 |
% 87.72/12.48 | ALPHA: (17) implies:
% 87.72/12.48 | (18) ~ empty(all_181_0)
% 87.72/12.48 | (19) relation(all_181_0)
% 87.72/12.48 | (20) $i(all_181_0)
% 87.72/12.48 |
% 87.72/12.48 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_183_0 gives:
% 87.72/12.48 | (21) $i(all_183_0) & relation(all_183_0) & empty(all_183_0)
% 87.72/12.48 |
% 87.72/12.48 | ALPHA: (21) implies:
% 87.72/12.48 | (22) empty(all_183_0)
% 87.72/12.48 | (23) relation(all_183_0)
% 87.72/12.48 | (24) $i(all_183_0)
% 87.72/12.48 |
% 87.72/12.48 | DELTA: instantiating (5) with fresh symbol all_215_0 gives:
% 87.72/12.48 | (25) ! [v0: $i] : ! [v1: int] : (v1 = all_215_0 | ~ (relation_rng(v0) =
% 87.72/12.48 | v1) | ~ $i(v0) | ~ $i(all_215_0) | ~ relation(v0) | ? [v2: $i]
% 87.72/12.48 | : ? [v3: $i] : ? [v4: $i] : ($i(v3) & $i(v2) & ( ~ in(v2,
% 87.72/12.48 | all_215_0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5,
% 87.72/12.48 | v2) = v6) | ~ $i(v5) | ~ in(v6, v0))) & (in(v2,
% 87.72/12.48 | all_215_0) | (ordered_pair(v3, v2) = v4 & $i(v4) & in(v4,
% 87.72/12.48 | v0)))))
% 87.72/12.48 |
% 87.72/12.48 | DELTA: instantiating (t166_relat_1) with fresh symbols all_229_0, all_229_1,
% 87.72/12.48 | all_229_2, all_229_3, all_229_4, all_229_5, all_229_6 gives:
% 87.72/12.48 | (26) relation_rng(all_229_4) = all_229_2 &
% 87.72/12.48 | relation_inverse_image(all_229_4, all_229_5) = all_229_3 &
% 87.72/12.48 | $i(all_229_1) & $i(all_229_2) & $i(all_229_3) & $i(all_229_4) &
% 87.72/12.48 | $i(all_229_5) & $i(all_229_6) & relation(all_229_4) &
% 87.72/12.48 | ((ordered_pair(all_229_6, all_229_1) = all_229_0 & $i(all_229_0) &
% 87.72/12.48 | in(all_229_0, all_229_4) & in(all_229_1, all_229_2) &
% 87.72/12.48 | in(all_229_1, all_229_5) & ~ in(all_229_6, all_229_3)) |
% 87.72/12.48 | (in(all_229_6, all_229_3) & ! [v0: $i] : ! [v1: $i] : ( ~
% 87.72/12.48 | (ordered_pair(all_229_6, v0) = v1) | ~ $i(v0) | ~ in(v1,
% 87.72/12.48 | all_229_4) | ~ in(v0, all_229_2) | ~ in(v0, all_229_5))))
% 87.72/12.48 |
% 87.72/12.48 | ALPHA: (26) implies:
% 87.72/12.48 | (27) relation(all_229_4)
% 87.72/12.48 | (28) $i(all_229_6)
% 87.72/12.48 | (29) $i(all_229_5)
% 87.72/12.48 | (30) $i(all_229_4)
% 87.72/12.48 | (31) $i(all_229_3)
% 87.72/12.48 | (32) $i(all_229_2)
% 87.72/12.48 | (33) $i(all_229_1)
% 87.72/12.48 | (34) relation_inverse_image(all_229_4, all_229_5) = all_229_3
% 87.72/12.48 | (35) relation_rng(all_229_4) = all_229_2
% 87.72/12.48 | (36) (ordered_pair(all_229_6, all_229_1) = all_229_0 & $i(all_229_0) &
% 87.72/12.48 | in(all_229_0, all_229_4) & in(all_229_1, all_229_2) & in(all_229_1,
% 87.72/12.48 | all_229_5) & ~ in(all_229_6, all_229_3)) | (in(all_229_6,
% 87.72/12.48 | all_229_3) & ! [v0: $i] : ! [v1: $i] : ( ~
% 87.72/12.48 | (ordered_pair(all_229_6, v0) = v1) | ~ $i(v0) | ~ in(v1,
% 87.72/12.48 | all_229_4) | ~ in(v0, all_229_2) | ~ in(v0, all_229_5)))
% 87.72/12.48 |
% 87.72/12.48 | GROUND_INST: instantiating (t8_boole) with all_172_0, all_183_0, simplifying
% 87.72/12.48 | with (13), (14), (22), (24) gives:
% 87.72/12.48 | (37) all_183_0 = all_172_0
% 87.72/12.48 |
% 87.72/12.48 | GROUND_INST: instantiating (11) with all_183_0, simplifying with (22), (24)
% 87.72/12.48 | gives:
% 87.72/12.48 | (38) all_183_0 = empty_set
% 87.72/12.48 |
% 87.72/12.49 | GROUND_INST: instantiating (3) with all_181_0, empty_set, simplifying with
% 87.72/12.49 | (6), (10), (19), (20) gives:
% 87.72/12.49 | (39) subset(all_181_0, empty_set) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 87.72/12.49 | : (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2,
% 87.72/12.49 | all_181_0) & ~ in(v2, empty_set))
% 87.72/12.49 |
% 87.72/12.49 | GROUND_INST: instantiating (3) with all_181_0, all_183_0, simplifying with
% 87.72/12.49 | (19), (20), (23), (24) gives:
% 87.72/12.49 | (40) subset(all_181_0, all_183_0) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 87.72/12.49 | : (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2,
% 87.72/12.49 | all_181_0) & ~ in(v2, all_183_0))
% 87.72/12.49 |
% 87.72/12.49 | GROUND_INST: instantiating (rc2_subset_1) with empty_set, all_179_0,
% 87.72/12.49 | simplifying with (10), (16) gives:
% 87.72/12.49 | (41) ? [v0: $i] : ($i(v0) & element(v0, all_179_0) & empty(v0))
% 87.72/12.49 |
% 87.72/12.49 | GROUND_INST: instantiating (25) with empty_set, empty_set, simplifying with
% 87.72/12.49 | (6), (9), (10) gives:
% 87.72/12.49 | (42) all_215_0 = empty_set | ~ $i(all_215_0) | ? [v0: $i] : ? [v1: $i] :
% 87.72/12.49 | ? [v2: $i] : ($i(v1) & $i(v0) & ( ~ in(v0, all_215_0) | ! [v3: $i] :
% 87.72/12.49 | ! [v4: $i] : ( ~ (ordered_pair(v3, v0) = v4) | ~ $i(v3) | ~
% 87.72/12.49 | in(v4, empty_set))) & (in(v0, all_215_0) | (ordered_pair(v1, v0)
% 87.72/12.49 | = v2 & $i(v2) & in(v2, empty_set))))
% 87.72/12.49 |
% 87.72/12.49 | GROUND_INST: instantiating (25) with all_229_4, all_229_2, simplifying with
% 87.72/12.49 | (27), (30), (35) gives:
% 87.72/12.49 | (43) all_229_2 = all_215_0 | ~ $i(all_215_0) | ? [v0: $i] : ? [v1: $i] :
% 87.72/12.49 | ? [v2: $i] : ($i(v1) & $i(v0) & ( ~ in(v0, all_215_0) | ! [v3: $i] :
% 87.72/12.49 | ! [v4: $i] : ( ~ (ordered_pair(v3, v0) = v4) | ~ $i(v3) | ~
% 87.72/12.49 | in(v4, all_229_4))) & (in(v0, all_215_0) | (ordered_pair(v1, v0)
% 87.72/12.49 | = v2 & $i(v2) & in(v2, all_229_4))))
% 87.72/12.49 |
% 87.72/12.49 | COMBINE_EQS: (37), (38) imply:
% 87.72/12.49 | (44) all_172_0 = empty_set
% 87.72/12.49 |
% 87.72/12.49 | DELTA: instantiating (41) with fresh symbol all_239_0 gives:
% 87.72/12.49 | (45) $i(all_239_0) & element(all_239_0, all_179_0) & empty(all_239_0)
% 87.72/12.49 |
% 87.72/12.49 | ALPHA: (45) implies:
% 87.72/12.49 | (46) empty(all_239_0)
% 87.72/12.49 | (47) $i(all_239_0)
% 87.72/12.49 |
% 87.72/12.49 | GROUND_INST: instantiating (11) with all_239_0, simplifying with (46), (47)
% 87.72/12.49 | gives:
% 87.72/12.49 | (48) all_239_0 = empty_set
% 87.72/12.49 |
% 87.72/12.49 | REDUCE: (46), (48) imply:
% 87.72/12.49 | (49) empty(empty_set)
% 87.72/12.49 |
% 87.72/12.49 | BETA: splitting (36) gives:
% 87.72/12.49 |
% 87.72/12.49 | Case 1:
% 87.72/12.49 | |
% 87.72/12.49 | | (50) ordered_pair(all_229_6, all_229_1) = all_229_0 & $i(all_229_0) &
% 87.72/12.49 | | in(all_229_0, all_229_4) & in(all_229_1, all_229_2) & in(all_229_1,
% 87.72/12.49 | | all_229_5) & ~ in(all_229_6, all_229_3)
% 87.72/12.49 | |
% 87.72/12.49 | | ALPHA: (50) implies:
% 87.72/12.49 | | (51) ~ in(all_229_6, all_229_3)
% 87.72/12.49 | | (52) in(all_229_1, all_229_5)
% 87.72/12.49 | | (53) in(all_229_0, all_229_4)
% 87.72/12.49 | | (54) ordered_pair(all_229_6, all_229_1) = all_229_0
% 87.72/12.49 | |
% 87.72/12.50 | | GROUND_INST: instantiating (2) with all_229_4, all_229_5, all_229_3,
% 87.72/12.50 | | all_229_6, all_229_1, all_229_0, simplifying with (27), (28),
% 87.72/12.50 | | (29), (30), (31), (33), (34), (51), (52), (53), (54) gives:
% 87.72/12.50 | | (55) $false
% 87.72/12.50 | |
% 87.72/12.50 | | CLOSE: (55) is inconsistent.
% 87.72/12.50 | |
% 87.72/12.50 | Case 2:
% 87.72/12.50 | |
% 87.72/12.50 | | (56) in(all_229_6, all_229_3) & ! [v0: $i] : ! [v1: $i] : ( ~
% 87.72/12.50 | | (ordered_pair(all_229_6, v0) = v1) | ~ $i(v0) | ~ in(v1,
% 87.72/12.50 | | all_229_4) | ~ in(v0, all_229_2) | ~ in(v0, all_229_5))
% 87.72/12.50 | |
% 87.72/12.50 | | ALPHA: (56) implies:
% 87.72/12.50 | | (57) in(all_229_6, all_229_3)
% 87.72/12.50 | | (58) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(all_229_6, v0) = v1) |
% 87.72/12.50 | | ~ $i(v0) | ~ in(v1, all_229_4) | ~ in(v0, all_229_2) | ~
% 87.72/12.50 | | in(v0, all_229_5))
% 87.72/12.50 | |
% 87.72/12.50 | | BETA: splitting (39) gives:
% 87.72/12.50 | |
% 87.72/12.50 | | Case 1:
% 87.72/12.50 | | |
% 87.72/12.50 | | | (59) subset(all_181_0, empty_set)
% 87.72/12.50 | | |
% 87.72/12.50 | | | GROUND_INST: instantiating (8) with all_181_0, simplifying with (20), (59)
% 87.72/12.50 | | | gives:
% 87.72/12.50 | | | (60) all_181_0 = empty_set
% 87.72/12.50 | | |
% 87.72/12.50 | | | REDUCE: (18), (60) imply:
% 87.72/12.50 | | | (61) ~ empty(empty_set)
% 87.72/12.50 | | |
% 87.72/12.50 | | | PRED_UNIFY: (49), (61) imply:
% 87.72/12.50 | | | (62) $false
% 87.72/12.50 | | |
% 87.72/12.50 | | | CLOSE: (62) is inconsistent.
% 87.72/12.50 | | |
% 87.72/12.50 | | Case 2:
% 87.72/12.50 | | |
% 87.72/12.50 | | | (63) ~ subset(all_181_0, empty_set)
% 87.72/12.50 | | |
% 87.72/12.50 | | | BETA: splitting (40) gives:
% 87.72/12.50 | | |
% 87.72/12.50 | | | Case 1:
% 87.72/12.50 | | | |
% 87.72/12.50 | | | | (64) subset(all_181_0, all_183_0)
% 87.72/12.50 | | | |
% 87.72/12.50 | | | | REDUCE: (38), (64) imply:
% 87.72/12.50 | | | | (65) subset(all_181_0, empty_set)
% 87.72/12.50 | | | |
% 87.72/12.50 | | | | PRED_UNIFY: (63), (65) imply:
% 87.72/12.50 | | | | (66) $false
% 87.72/12.50 | | | |
% 87.72/12.50 | | | | CLOSE: (66) is inconsistent.
% 87.72/12.50 | | | |
% 87.72/12.50 | | | Case 2:
% 87.72/12.50 | | | |
% 87.72/12.50 | | | |
% 87.72/12.50 | | | | GROUND_INST: instantiating (1) with all_229_4, all_229_5, all_229_3,
% 87.72/12.50 | | | | all_229_6, simplifying with (27), (28), (29), (30), (31),
% 87.72/12.50 | | | | (34), (57) gives:
% 87.72/12.50 | | | | (67) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_229_6, v0) = v1 &
% 87.72/12.50 | | | | $i(v1) & $i(v0) & in(v1, all_229_4) & in(v0, all_229_5))
% 87.72/12.50 | | | |
% 87.72/12.50 | | | | DELTA: instantiating (67) with fresh symbols all_401_0, all_401_1 gives:
% 87.72/12.50 | | | | (68) ordered_pair(all_229_6, all_401_1) = all_401_0 & $i(all_401_0) &
% 87.72/12.50 | | | | $i(all_401_1) & in(all_401_0, all_229_4) & in(all_401_1,
% 87.72/12.50 | | | | all_229_5)
% 87.72/12.50 | | | |
% 87.72/12.50 | | | | ALPHA: (68) implies:
% 87.72/12.50 | | | | (69) in(all_401_1, all_229_5)
% 87.72/12.50 | | | | (70) in(all_401_0, all_229_4)
% 87.72/12.50 | | | | (71) $i(all_401_1)
% 87.72/12.50 | | | | (72) ordered_pair(all_229_6, all_401_1) = all_401_0
% 87.72/12.50 | | | |
% 87.72/12.50 | | | | BETA: splitting (43) gives:
% 87.72/12.50 | | | |
% 87.72/12.50 | | | | Case 1:
% 87.72/12.50 | | | | |
% 87.72/12.50 | | | | |
% 87.72/12.50 | | | | | GROUND_INST: instantiating (4) with all_229_4, all_229_2, all_401_1,
% 87.72/12.50 | | | | | all_229_6, all_401_0, simplifying with (27), (28), (30),
% 87.72/12.50 | | | | | (32), (35), (70), (71), (72) gives:
% 87.72/12.50 | | | | | (73) in(all_401_1, all_229_2)
% 87.72/12.50 | | | | |
% 87.72/12.50 | | | | | GROUND_INST: instantiating (58) with all_401_1, all_401_0, simplifying
% 87.72/12.50 | | | | | with (69), (70), (71), (72), (73) gives:
% 87.72/12.50 | | | | | (74) $false
% 87.72/12.50 | | | | |
% 87.72/12.50 | | | | | CLOSE: (74) is inconsistent.
% 87.72/12.50 | | | | |
% 87.72/12.50 | | | | Case 2:
% 87.72/12.50 | | | | |
% 87.72/12.50 | | | | | (75) $i(all_215_0)
% 87.72/12.50 | | | | |
% 87.72/12.50 | | | | | BETA: splitting (42) gives:
% 87.72/12.50 | | | | |
% 87.72/12.50 | | | | | Case 1:
% 87.72/12.50 | | | | | |
% 87.72/12.51 | | | | | | (76) ~ $i(all_215_0)
% 87.72/12.51 | | | | | |
% 87.72/12.51 | | | | | | PRED_UNIFY: (75), (76) imply:
% 87.72/12.51 | | | | | | (77) $false
% 87.72/12.51 | | | | | |
% 87.72/12.51 | | | | | | CLOSE: (77) is inconsistent.
% 87.72/12.51 | | | | | |
% 87.72/12.51 | | | | | Case 2:
% 87.72/12.51 | | | | | |
% 87.72/12.51 | | | | | |
% 87.72/12.51 | | | | | | GROUND_INST: instantiating (4) with all_229_4, all_229_2, all_401_1,
% 87.72/12.51 | | | | | | all_229_6, all_401_0, simplifying with (27), (28),
% 87.72/12.51 | | | | | | (30), (32), (35), (70), (71), (72) gives:
% 87.72/12.51 | | | | | | (78) in(all_401_1, all_229_2)
% 87.72/12.51 | | | | | |
% 87.72/12.51 | | | | | | GROUND_INST: instantiating (58) with all_401_1, all_401_0,
% 87.72/12.51 | | | | | | simplifying with (69), (70), (71), (72), (78) gives:
% 87.72/12.51 | | | | | | (79) $false
% 87.72/12.51 | | | | | |
% 87.72/12.51 | | | | | | CLOSE: (79) is inconsistent.
% 87.72/12.51 | | | | | |
% 87.72/12.51 | | | | | End of split
% 87.72/12.51 | | | | |
% 87.72/12.51 | | | | End of split
% 87.72/12.51 | | | |
% 87.72/12.51 | | | End of split
% 87.72/12.51 | | |
% 87.72/12.51 | | End of split
% 87.72/12.51 | |
% 87.72/12.51 | End of split
% 87.72/12.51 |
% 87.72/12.51 End of proof
% 87.72/12.51 % SZS output end Proof for theBenchmark
% 87.72/12.51
% 87.72/12.51 11891ms
%------------------------------------------------------------------------------