TSTP Solution File: SWV093+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV093+1 : TPTP v8.1.2. Bugfixed 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 22:54:53 EDT 2023
% Result : Theorem 19.02s 3.25s
% Output : Proof 23.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV093+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 09:39:30 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.40/1.39 Prover 1: Preprocessing ...
% 4.40/1.39 Prover 4: Preprocessing ...
% 5.22/1.43 Prover 5: Preprocessing ...
% 5.22/1.43 Prover 6: Preprocessing ...
% 5.22/1.43 Prover 2: Preprocessing ...
% 5.22/1.43 Prover 0: Preprocessing ...
% 5.22/1.43 Prover 3: Preprocessing ...
% 11.26/2.26 Prover 3: Warning: ignoring some quantifiers
% 11.67/2.29 Prover 1: Warning: ignoring some quantifiers
% 11.67/2.32 Prover 3: Constructing countermodel ...
% 11.67/2.35 Prover 6: Proving ...
% 12.30/2.35 Prover 1: Constructing countermodel ...
% 12.82/2.44 Prover 4: Warning: ignoring some quantifiers
% 13.53/2.53 Prover 5: Proving ...
% 13.53/2.53 Prover 4: Constructing countermodel ...
% 13.53/2.53 Prover 0: Proving ...
% 13.53/2.54 Prover 2: Proving ...
% 19.02/3.25 Prover 3: proved (2605ms)
% 19.02/3.25
% 19.02/3.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.02/3.25
% 19.02/3.25 Prover 6: stopped
% 19.02/3.25 Prover 0: stopped
% 19.02/3.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 19.02/3.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 19.02/3.27 Prover 5: stopped
% 19.02/3.27 Prover 2: stopped
% 19.02/3.27 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 19.02/3.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 19.02/3.27 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 19.29/3.42 Prover 8: Preprocessing ...
% 20.25/3.46 Prover 7: Preprocessing ...
% 20.25/3.46 Prover 13: Preprocessing ...
% 20.62/3.47 Prover 10: Preprocessing ...
% 20.62/3.48 Prover 11: Preprocessing ...
% 22.17/3.68 Prover 10: Warning: ignoring some quantifiers
% 22.17/3.69 Prover 8: Warning: ignoring some quantifiers
% 22.17/3.71 Prover 7: Warning: ignoring some quantifiers
% 22.17/3.71 Prover 1: Found proof (size 217)
% 22.17/3.71 Prover 1: proved (3071ms)
% 22.17/3.71 Prover 4: stopped
% 22.17/3.71 Prover 10: Constructing countermodel ...
% 22.17/3.72 Prover 13: Warning: ignoring some quantifiers
% 22.17/3.72 Prover 8: Constructing countermodel ...
% 22.66/3.73 Prover 10: stopped
% 22.66/3.74 Prover 7: Constructing countermodel ...
% 22.66/3.76 Prover 13: Constructing countermodel ...
% 22.66/3.76 Prover 7: stopped
% 22.89/3.77 Prover 8: stopped
% 22.89/3.78 Prover 11: Warning: ignoring some quantifiers
% 22.89/3.79 Prover 13: stopped
% 22.89/3.80 Prover 11: Constructing countermodel ...
% 22.89/3.82 Prover 11: stopped
% 22.89/3.82
% 22.89/3.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.89/3.82
% 23.33/3.87 % SZS output start Proof for theBenchmark
% 23.33/3.88 Assumptions after simplification:
% 23.33/3.88 ---------------------------------
% 23.33/3.88
% 23.33/3.88 (gt_3_0)
% 23.33/3.90 gt(n3, n0) = 0 & $i(n3) & $i(n0)
% 23.33/3.90
% 23.33/3.90 (gt_3_1)
% 23.33/3.90 gt(n3, n1) = 0 & $i(n3) & $i(n1)
% 23.33/3.90
% 23.33/3.90 (gt_3_2)
% 23.33/3.90 gt(n3, n2) = 0 & $i(n3) & $i(n2)
% 23.33/3.90
% 23.33/3.90 (gt_3_tptp_minus_1)
% 23.33/3.90 gt(n3, tptp_minus_1) = 0 & $i(n3) & $i(tptp_minus_1)
% 23.33/3.90
% 23.33/3.90 (leq_succ_gt)
% 23.33/3.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v2) | ~ (leq(v2,
% 23.33/3.90 v1) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0)
% 23.33/3.90
% 23.33/3.90 (leq_succ_gt_equiv)
% 23.33/3.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 23.33/3.90 (succ(v1) = v2) | ~ (gt(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 23.33/3.90 int] : ( ~ (v4 = 0) & leq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : !
% 23.33/3.90 [v2: $i] : ( ~ (succ(v1) = v2) | ~ (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 23.33/3.90 leq(v0, v1) = 0)
% 23.33/3.90
% 23.33/3.91 (pred_minus_1)
% 23.33/3.91 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 23.33/3.91 (pred(v0) = v1 & $i(v1)))
% 23.33/3.91
% 23.33/3.91 (quaternion_ds1_inuse_0005)
% 23.33/3.92 $i(z_defuse) & $i(n6) & $i(n999) & $i(pv41) & $i(pv5) & $i(xinit_noise_defuse)
% 23.33/3.92 & $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) &
% 23.33/3.92 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0)
% 23.33/3.92 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (minus(n6, n1) = v1 & minus(n999,
% 23.33/3.92 n1) = v0 & minus(pv5, n1) = v2 & a_select3(u_defuse, n2, n0) = use &
% 23.33/3.92 a_select3(u_defuse, n1, n0) = use & a_select3(u_defuse, n0, n0) = use &
% 23.33/3.92 a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4)
% 23.33/3.92 = use & a_select2(xinit_noise_defuse, n3) = use &
% 23.33/3.92 a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1)
% 23.33/3.92 = use & a_select2(xinit_noise_defuse, n0) = use &
% 23.33/3.92 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) =
% 23.33/3.92 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 23.33/3.92 n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 23.33/3.92 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use &
% 23.33/3.92 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use &
% 23.33/3.92 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use &
% 23.33/3.92 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use &
% 23.33/3.92 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use &
% 23.33/3.92 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 23.33/3.92 a_select2(rho_defuse, n0) = use & leq(pv41, v1) = 0 & leq(pv5, v0) = 0 &
% 23.33/3.92 leq(n0, pv41) = 0 & leq(n0, pv5) = 0 & $i(v2) & $i(v1) & $i(v0) & ! [v3:
% 23.33/3.92 $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (a_select3(z_defuse, v3, v4) = v5) |
% 23.33/3.92 ~ $i(v4) | ~ $i(v3) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 23.33/3.92 [v9: any] : ? [v10: $i] : (a_select3(u_defuse, v3, v4) = v10 & leq(v4,
% 23.33/3.92 pv5) = v9 & leq(v3, n2) = v8 & leq(n0, v4) = v7 & leq(n0, v3) = v6 &
% 23.33/3.92 $i(v10) & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v10
% 23.33/3.92 = use & v5 = use)))) & ! [v3: $i] : ! [v4: $i] : ( ~ (leq(v4, v2)
% 23.33/3.92 = 0) | ~ (leq(v3, n2) = 0) | ~ $i(v4) | ~ $i(v3) | ? [v5: any] : ?
% 23.33/3.92 [v6: any] : ? [v7: $i] : ? [v8: $i] : (a_select3(z_defuse, v3, v4) = v8
% 23.33/3.92 & a_select3(u_defuse, v3, v4) = v7 & leq(n0, v4) = v6 & leq(n0, v3) = v5
% 23.33/3.92 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = use & v7 =
% 23.33/3.92 use)))) & ( ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 23.33/3.92 (a_select3(z_defuse, v3, v4) = v6 & a_select3(u_defuse, v3, v4) = v5 &
% 23.33/3.92 leq(v4, v2) = 0 & leq(v3, n2) = 0 & leq(n0, v4) = 0 & leq(n0, v3) = 0 &
% 23.33/3.92 $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v6 = use) | ~ (v5 = use))) |
% 23.33/3.92 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 23.33/3.92 (a_select3(z_defuse, v3, v4) = v6 & a_select3(u_defuse, v3, v4) = v5 &
% 23.33/3.92 leq(v4, pv5) = 0 & leq(v3, n2) = 0 & leq(n0, v4) = 0 & leq(n0, v3) = 0 &
% 23.33/3.92 $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v6 = use) | ~ (v5 = use)))))
% 23.33/3.92
% 23.33/3.92 (succ_pred)
% 23.33/3.92 ! [v0: $i] : ! [v1: $i] : ( ~ (pred(v0) = v1) | ~ $i(v0) | succ(v1) = v0)
% 23.33/3.92
% 23.33/3.92 (succ_tptp_minus_1)
% 23.33/3.92 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0)
% 23.33/3.92
% 23.33/3.92 (successor_1)
% 23.33/3.92 succ(n0) = n1 & $i(n1) & $i(n0)
% 23.33/3.92
% 23.33/3.92 (successor_2)
% 23.33/3.92 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 23.33/3.92
% 23.33/3.92 (successor_3)
% 23.33/3.92 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 &
% 23.33/3.92 succ(n0) = v0 & $i(v1) & $i(v0))
% 23.33/3.92
% 23.33/3.92 (successor_4)
% 23.33/3.92 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 &
% 23.33/3.92 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 23.33/3.92
% 23.33/3.92 (successor_5)
% 23.33/3.92 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 23.33/3.92 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0
% 23.33/3.92 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 23.33/3.92
% 23.33/3.92 (successor_6)
% 23.33/3.93 $i(n6) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 23.33/3.93 [v4: $i] : (succ(v4) = n6 & succ(v3) = v4 & succ(v2) = v3 & succ(v1) = v2 &
% 23.33/3.93 succ(v0) = v1 & succ(n0) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 23.33/3.93
% 23.33/3.93 (function-axioms)
% 23.64/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 23.64/3.93 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 23.64/3.93 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 23.64/3.93 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 23.64/3.93 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 23.64/3.93 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 23.64/3.93 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 23.64/3.93 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 23.64/3.93 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 23.64/3.93 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 23.64/3.93 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 23.64/3.93 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 23.64/3.93 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 23.64/3.93 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 23.64/3.93 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 23.64/3.93 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 23.64/3.93 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 23.64/3.93 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 23.64/3.93 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 23.64/3.93 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 23.64/3.93 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 23.64/3.93 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 23.64/3.93 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 23.64/3.93 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 23.64/3.93 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.64/3.93 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 23.64/3.93 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 23.64/3.93 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 23.64/3.93 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 23.64/3.93 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 23.64/3.93 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 23.64/3.93 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 23.64/3.93 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 23.64/3.93 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 23.64/3.93 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 23.64/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 23.64/3.93 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 23.64/3.93 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 23.64/3.93 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 23.64/3.93
% 23.64/3.93 Further assumptions not needed in the proof:
% 23.64/3.93 --------------------------------------------
% 23.64/3.94 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 23.64/3.94 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 23.64/3.94 finite_domain_5, finite_domain_6, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1,
% 23.64/3.94 gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3,
% 23.64/3.94 gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1,
% 23.64/3.94 gt_6_0, gt_6_1, gt_6_2, gt_6_3, gt_6_4, gt_6_5, gt_6_tptp_minus_1, gt_999_0,
% 23.64/3.94 gt_999_1, gt_999_2, gt_999_3, gt_999_4, gt_999_5, gt_999_6, gt_999_tptp_minus_1,
% 23.64/3.94 gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus,
% 23.64/3.94 leq_succ, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 23.64/3.94 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 23.64/3.94 matrix_symm_trans, matrix_symm_update_diagonal, pred_succ, reflexivity_leq,
% 23.64/3.94 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2,
% 23.64/3.94 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r,
% 23.64/3.94 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l,
% 23.64/3.94 succ_plus_5_r, sum_plus_base, sum_plus_base_float, totality, transitivity_gt,
% 23.64/3.94 transitivity_leq, ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 23.64/3.94
% 23.64/3.94 Those formulas are unsatisfiable:
% 23.64/3.94 ---------------------------------
% 23.64/3.94
% 23.64/3.94 Begin of proof
% 23.64/3.94 |
% 23.64/3.94 | ALPHA: (leq_succ_gt_equiv) implies:
% 23.64/3.94 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~
% 23.64/3.94 | (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | leq(v0, v1) = 0)
% 23.64/3.94 |
% 23.64/3.94 | ALPHA: (succ_tptp_minus_1) implies:
% 23.64/3.94 | (2) succ(tptp_minus_1) = n0
% 23.64/3.94 |
% 23.64/3.94 | ALPHA: (pred_minus_1) implies:
% 23.64/3.94 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 23.64/3.94 | (pred(v0) = v1 & $i(v1)))
% 23.64/3.94 |
% 23.64/3.94 | ALPHA: (gt_3_tptp_minus_1) implies:
% 23.64/3.94 | (4) $i(tptp_minus_1)
% 23.64/3.94 | (5) gt(n3, tptp_minus_1) = 0
% 23.64/3.94 |
% 23.64/3.94 | ALPHA: (gt_3_0) implies:
% 23.64/3.94 | (6) gt(n3, n0) = 0
% 23.64/3.94 |
% 23.64/3.94 | ALPHA: (gt_3_1) implies:
% 23.64/3.94 | (7) gt(n3, n1) = 0
% 23.64/3.94 |
% 23.64/3.94 | ALPHA: (gt_3_2) implies:
% 23.64/3.94 | (8) gt(n3, n2) = 0
% 23.64/3.94 |
% 23.64/3.94 | ALPHA: (successor_4) implies:
% 23.64/3.94 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) =
% 23.64/3.94 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 23.64/3.94 |
% 23.64/3.94 | ALPHA: (successor_5) implies:
% 23.64/3.94 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5
% 23.64/3.94 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 &
% 23.64/3.94 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 23.64/3.94 |
% 23.64/3.94 | ALPHA: (successor_6) implies:
% 23.64/3.94 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 23.64/3.94 | (succ(v4) = n6 & succ(v3) = v4 & succ(v2) = v3 & succ(v1) = v2 &
% 23.64/3.94 | succ(v0) = v1 & succ(n0) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 23.64/3.94 | $i(v0))
% 23.64/3.94 |
% 23.64/3.94 | ALPHA: (successor_1) implies:
% 23.64/3.94 | (12) succ(n0) = n1
% 23.64/3.94 |
% 23.64/3.94 | ALPHA: (successor_2) implies:
% 23.64/3.95 | (13) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 23.64/3.95 |
% 23.64/3.95 | ALPHA: (successor_3) implies:
% 23.64/3.95 | (14) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0)
% 23.64/3.95 | = v0 & $i(v1) & $i(v0))
% 23.64/3.95 |
% 23.64/3.95 | ALPHA: (quaternion_ds1_inuse_0005) implies:
% 23.64/3.95 | (15) $i(n0)
% 23.64/3.95 | (16) $i(pv5)
% 23.64/3.95 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (minus(n6, n1) = v1 &
% 23.64/3.95 | minus(n999, n1) = v0 & minus(pv5, n1) = v2 & a_select3(u_defuse, n2,
% 23.64/3.95 | n0) = use & a_select3(u_defuse, n1, n0) = use &
% 23.64/3.95 | a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse,
% 23.64/3.95 | n5) = use & a_select2(xinit_noise_defuse, n4) = use &
% 23.64/3.95 | a_select2(xinit_noise_defuse, n3) = use &
% 23.64/3.95 | a_select2(xinit_noise_defuse, n2) = use &
% 23.64/3.95 | a_select2(xinit_noise_defuse, n1) = use &
% 23.64/3.95 | a_select2(xinit_noise_defuse, n0) = use &
% 23.64/3.95 | a_select2(xinit_mean_defuse, n5) = use &
% 23.64/3.95 | a_select2(xinit_mean_defuse, n4) = use &
% 23.64/3.95 | a_select2(xinit_mean_defuse, n3) = use &
% 23.64/3.95 | a_select2(xinit_mean_defuse, n2) = use &
% 23.64/3.95 | a_select2(xinit_mean_defuse, n1) = use &
% 23.64/3.95 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5)
% 23.64/3.95 | = use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse,
% 23.64/3.95 | n3) = use & a_select2(sigma_defuse, n5) = use &
% 23.64/3.95 | a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) =
% 23.64/3.95 | use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse,
% 23.64/3.95 | n1) = use & a_select2(sigma_defuse, n0) = use &
% 23.64/3.95 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 23.64/3.95 | a_select2(rho_defuse, n0) = use & leq(pv41, v1) = 0 & leq(pv5, v0) =
% 23.64/3.95 | 0 & leq(n0, pv41) = 0 & leq(n0, pv5) = 0 & $i(v2) & $i(v1) & $i(v0)
% 23.64/3.95 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (a_select3(z_defuse,
% 23.64/3.95 | v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: any] : ? [v7:
% 23.64/3.95 | any] : ? [v8: any] : ? [v9: any] : ? [v10: $i] :
% 23.64/3.95 | (a_select3(u_defuse, v3, v4) = v10 & leq(v4, pv5) = v9 & leq(v3,
% 23.64/3.95 | n2) = v8 & leq(n0, v4) = v7 & leq(n0, v3) = v6 & $i(v10) & ( ~
% 23.64/3.95 | (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v10 =
% 23.64/3.95 | use & v5 = use)))) & ! [v3: $i] : ! [v4: $i] : ( ~
% 23.64/3.95 | (leq(v4, v2) = 0) | ~ (leq(v3, n2) = 0) | ~ $i(v4) | ~ $i(v3) |
% 23.64/3.95 | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] :
% 23.64/3.95 | (a_select3(z_defuse, v3, v4) = v8 & a_select3(u_defuse, v3, v4) =
% 23.64/3.95 | v7 & leq(n0, v4) = v6 & leq(n0, v3) = v5 & $i(v8) & $i(v7) & ( ~
% 23.64/3.95 | (v6 = 0) | ~ (v5 = 0) | (v8 = use & v7 = use)))) & ( ? [v3:
% 23.64/3.95 | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 23.64/3.95 | (a_select3(z_defuse, v3, v4) = v6 & a_select3(u_defuse, v3, v4) =
% 23.64/3.95 | v5 & leq(v4, v2) = 0 & leq(v3, n2) = 0 & leq(n0, v4) = 0 &
% 23.64/3.95 | leq(n0, v3) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v6 =
% 23.64/3.95 | use) | ~ (v5 = use))) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 23.64/3.95 | $i] : ? [v6: $i] : (a_select3(z_defuse, v3, v4) = v6 &
% 23.64/3.95 | a_select3(u_defuse, v3, v4) = v5 & leq(v4, pv5) = 0 & leq(v3,
% 23.64/3.95 | n2) = 0 & leq(n0, v4) = 0 & leq(n0, v3) = 0 & $i(v6) & $i(v5)
% 23.64/3.95 | & $i(v4) & $i(v3) & ( ~ (v6 = use) | ~ (v5 = use)))))
% 23.64/3.95 |
% 23.64/3.95 | ALPHA: (function-axioms) implies:
% 23.64/3.95 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) =
% 23.64/3.95 | v1) | ~ (succ(v2) = v0))
% 23.64/3.96 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 23.64/3.96 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) =
% 23.64/3.96 | v0))
% 23.64/3.96 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 23.64/3.96 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2)
% 23.64/3.96 | = v0))
% 23.64/3.96 |
% 23.64/3.96 | DELTA: instantiating (13) with fresh symbol all_50_0 gives:
% 23.64/3.96 | (21) succ(all_50_0) = n2 & succ(n0) = all_50_0 & $i(all_50_0)
% 23.64/3.96 |
% 23.64/3.96 | ALPHA: (21) implies:
% 23.64/3.96 | (22) $i(all_50_0)
% 23.64/3.96 | (23) succ(n0) = all_50_0
% 23.64/3.96 | (24) succ(all_50_0) = n2
% 23.64/3.96 |
% 23.64/3.96 | DELTA: instantiating (14) with fresh symbols all_52_0, all_52_1 gives:
% 23.64/3.96 | (25) succ(all_52_0) = n3 & succ(all_52_1) = all_52_0 & succ(n0) = all_52_1
% 23.64/3.96 | & $i(all_52_0) & $i(all_52_1)
% 23.64/3.96 |
% 23.64/3.96 | ALPHA: (25) implies:
% 23.64/3.96 | (26) $i(all_52_0)
% 23.64/3.96 | (27) succ(n0) = all_52_1
% 23.64/3.96 | (28) succ(all_52_1) = all_52_0
% 23.64/3.96 | (29) succ(all_52_0) = n3
% 23.64/3.96 |
% 23.64/3.96 | DELTA: instantiating (9) with fresh symbols all_54_0, all_54_1, all_54_2
% 23.64/3.96 | gives:
% 23.64/3.96 | (30) succ(all_54_0) = n4 & succ(all_54_1) = all_54_0 & succ(all_54_2) =
% 23.64/3.96 | all_54_1 & succ(n0) = all_54_2 & $i(all_54_0) & $i(all_54_1) &
% 23.64/3.96 | $i(all_54_2)
% 23.64/3.96 |
% 23.64/3.96 | ALPHA: (30) implies:
% 23.64/3.96 | (31) succ(n0) = all_54_2
% 23.64/3.96 | (32) succ(all_54_2) = all_54_1
% 23.64/3.96 | (33) succ(all_54_1) = all_54_0
% 23.64/3.96 |
% 23.64/3.96 | DELTA: instantiating (10) with fresh symbols all_56_0, all_56_1, all_56_2,
% 23.64/3.96 | all_56_3 gives:
% 23.64/3.96 | (34) succ(all_56_0) = n5 & succ(all_56_1) = all_56_0 & succ(all_56_2) =
% 23.64/3.96 | all_56_1 & succ(all_56_3) = all_56_2 & succ(n0) = all_56_3 &
% 23.64/3.96 | $i(all_56_0) & $i(all_56_1) & $i(all_56_2) & $i(all_56_3)
% 23.64/3.96 |
% 23.64/3.96 | ALPHA: (34) implies:
% 23.64/3.96 | (35) succ(n0) = all_56_3
% 23.64/3.96 | (36) succ(all_56_3) = all_56_2
% 23.64/3.96 | (37) succ(all_56_2) = all_56_1
% 23.64/3.96 |
% 23.64/3.96 | DELTA: instantiating (11) with fresh symbols all_58_0, all_58_1, all_58_2,
% 23.64/3.96 | all_58_3, all_58_4 gives:
% 23.64/3.96 | (38) succ(all_58_0) = n6 & succ(all_58_1) = all_58_0 & succ(all_58_2) =
% 23.64/3.96 | all_58_1 & succ(all_58_3) = all_58_2 & succ(all_58_4) = all_58_3 &
% 23.64/3.96 | succ(n0) = all_58_4 & $i(all_58_0) & $i(all_58_1) & $i(all_58_2) &
% 23.64/3.96 | $i(all_58_3) & $i(all_58_4)
% 23.64/3.96 |
% 23.64/3.96 | ALPHA: (38) implies:
% 23.64/3.96 | (39) succ(n0) = all_58_4
% 23.64/3.96 | (40) succ(all_58_4) = all_58_3
% 23.64/3.96 | (41) succ(all_58_3) = all_58_2
% 23.64/3.96 |
% 23.64/3.96 | DELTA: instantiating (17) with fresh symbols all_79_0, all_79_1, all_79_2
% 23.64/3.96 | gives:
% 23.64/3.97 | (42) minus(n6, n1) = all_79_1 & minus(n999, n1) = all_79_2 & minus(pv5, n1)
% 23.64/3.97 | = all_79_0 & a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse,
% 23.64/3.97 | n1, n0) = use & a_select3(u_defuse, n0, n0) = use &
% 23.64/3.97 | a_select2(xinit_noise_defuse, n5) = use &
% 23.64/3.97 | a_select2(xinit_noise_defuse, n4) = use &
% 23.64/3.97 | a_select2(xinit_noise_defuse, n3) = use &
% 23.64/3.97 | a_select2(xinit_noise_defuse, n2) = use &
% 23.64/3.97 | a_select2(xinit_noise_defuse, n1) = use &
% 23.64/3.97 | a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse,
% 23.64/3.97 | n5) = use & a_select2(xinit_mean_defuse, n4) = use &
% 23.64/3.97 | a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 23.64/3.97 | n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 23.64/3.97 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) =
% 23.64/3.97 | use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3)
% 23.64/3.97 | = use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse,
% 23.64/3.97 | n4) = use & a_select2(sigma_defuse, n3) = use &
% 23.64/3.97 | a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use
% 23.64/3.97 | & a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use
% 23.64/3.97 | & a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use &
% 23.64/3.97 | leq(pv41, all_79_1) = 0 & leq(pv5, all_79_2) = 0 & leq(n0, pv41) = 0 &
% 23.64/3.97 | leq(n0, pv5) = 0 & $i(all_79_0) & $i(all_79_1) & $i(all_79_2) & !
% 23.64/3.97 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(z_defuse, v0,
% 23.64/3.97 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any]
% 23.64/3.97 | : ? [v5: any] : ? [v6: any] : ? [v7: $i] : (a_select3(u_defuse,
% 23.64/3.97 | v0, v1) = v7 & leq(v1, pv5) = v6 & leq(v0, n2) = v5 & leq(n0,
% 23.64/3.97 | v1) = v4 & leq(n0, v0) = v3 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 =
% 23.64/3.97 | 0) | ~ (v4 = 0) | ~ (v3 = 0) | (v7 = use & v2 = use)))) & !
% 23.64/3.97 | [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_79_0) = 0) | ~ (leq(v0, n2)
% 23.64/3.97 | = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ?
% 23.64/3.97 | [v4: $i] : ? [v5: $i] : (a_select3(z_defuse, v0, v1) = v5 &
% 23.64/3.97 | a_select3(u_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & leq(n0, v0)
% 23.64/3.97 | = v2 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = use &
% 23.64/3.97 | v4 = use)))) & ( ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 23.64/3.97 | [v3: $i] : (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse,
% 23.64/3.97 | v0, v1) = v2 & leq(v1, all_79_0) = 0 & leq(v0, n2) = 0 & leq(n0,
% 23.64/3.97 | v1) = 0 & leq(n0, v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 23.64/3.97 | ( ~ (v3 = use) | ~ (v2 = use))) | ? [v0: $i] : ? [v1: $i] : ?
% 23.64/3.97 | [v2: $i] : ? [v3: $i] : (a_select3(z_defuse, v0, v1) = v3 &
% 23.64/3.97 | a_select3(u_defuse, v0, v1) = v2 & leq(v1, pv5) = 0 & leq(v0, n2)
% 23.64/3.97 | = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v3) & $i(v2) & $i(v1)
% 23.64/3.97 | & $i(v0) & ( ~ (v3 = use) | ~ (v2 = use))))
% 23.64/3.97 |
% 23.64/3.97 | ALPHA: (42) implies:
% 23.64/3.97 | (43) leq(n0, pv5) = 0
% 23.64/3.97 | (44) minus(pv5, n1) = all_79_0
% 23.64/3.97 | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 23.64/3.97 | (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1) = v2 &
% 23.64/3.97 | leq(v1, all_79_0) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0,
% 23.64/3.97 | v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = use) | ~
% 23.64/3.97 | (v2 = use))) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 23.64/3.97 | $i] : (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0,
% 23.64/3.97 | v1) = v2 & leq(v1, pv5) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 &
% 23.64/3.97 | leq(n0, v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = use)
% 23.64/3.97 | | ~ (v2 = use)))
% 23.64/3.98 | (46) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_79_0) = 0) | ~ (leq(v0,
% 23.64/3.98 | n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 23.64/3.98 | ? [v4: $i] : ? [v5: $i] : (a_select3(z_defuse, v0, v1) = v5 &
% 23.64/3.98 | a_select3(u_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & leq(n0, v0)
% 23.64/3.98 | = v2 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = use &
% 23.64/3.98 | v4 = use))))
% 23.64/3.98 | (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(z_defuse, v0,
% 23.64/3.98 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any]
% 23.64/3.98 | : ? [v5: any] : ? [v6: any] : ? [v7: $i] : (a_select3(u_defuse,
% 23.64/3.98 | v0, v1) = v7 & leq(v1, pv5) = v6 & leq(v0, n2) = v5 & leq(n0,
% 23.64/3.98 | v1) = v4 & leq(n0, v0) = v3 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 =
% 23.64/3.98 | 0) | ~ (v4 = 0) | ~ (v3 = 0) | (v7 = use & v2 = use))))
% 23.64/3.98 |
% 23.64/3.98 | GROUND_INST: instantiating (18) with all_54_2, all_56_3, n0, simplifying with
% 23.64/3.98 | (31), (35) gives:
% 23.64/3.98 | (48) all_56_3 = all_54_2
% 23.64/3.98 |
% 23.64/3.98 | GROUND_INST: instantiating (18) with all_52_1, all_56_3, n0, simplifying with
% 23.64/3.98 | (27), (35) gives:
% 23.64/3.98 | (49) all_56_3 = all_52_1
% 23.64/3.98 |
% 23.64/3.98 | GROUND_INST: instantiating (18) with all_50_0, all_56_3, n0, simplifying with
% 23.64/3.98 | (23), (35) gives:
% 23.64/3.98 | (50) all_56_3 = all_50_0
% 23.64/3.98 |
% 23.64/3.98 | GROUND_INST: instantiating (18) with all_52_1, all_58_4, n0, simplifying with
% 23.64/3.98 | (27), (39) gives:
% 23.64/3.98 | (51) all_58_4 = all_52_1
% 23.64/3.98 |
% 23.64/3.98 | GROUND_INST: instantiating (18) with n1, all_58_4, n0, simplifying with (12),
% 23.64/3.98 | (39) gives:
% 23.64/3.98 | (52) all_58_4 = n1
% 23.64/3.98 |
% 23.64/3.98 | COMBINE_EQS: (51), (52) imply:
% 23.64/3.98 | (53) all_52_1 = n1
% 23.64/3.98 |
% 23.64/3.98 | SIMP: (53) implies:
% 23.64/3.98 | (54) all_52_1 = n1
% 23.64/3.98 |
% 23.64/3.98 | COMBINE_EQS: (48), (50) imply:
% 23.64/3.98 | (55) all_54_2 = all_50_0
% 23.64/3.98 |
% 23.64/3.98 | COMBINE_EQS: (48), (49) imply:
% 23.64/3.98 | (56) all_54_2 = all_52_1
% 23.64/3.98 |
% 23.64/3.98 | COMBINE_EQS: (55), (56) imply:
% 23.64/3.98 | (57) all_52_1 = all_50_0
% 23.64/3.98 |
% 23.64/3.98 | SIMP: (57) implies:
% 23.64/3.98 | (58) all_52_1 = all_50_0
% 23.64/3.98 |
% 23.64/3.98 | COMBINE_EQS: (54), (58) imply:
% 23.64/3.98 | (59) all_50_0 = n1
% 23.64/3.98 |
% 23.64/3.98 | COMBINE_EQS: (55), (59) imply:
% 23.64/3.98 | (60) all_54_2 = n1
% 23.64/3.98 |
% 23.64/3.98 | COMBINE_EQS: (48), (60) imply:
% 23.64/3.98 | (61) all_56_3 = n1
% 23.64/3.98 |
% 23.64/3.98 | REDUCE: (40), (52) imply:
% 23.64/3.98 | (62) succ(n1) = all_58_3
% 23.64/3.98 |
% 23.64/3.98 | REDUCE: (36), (61) imply:
% 23.64/3.98 | (63) succ(n1) = all_56_2
% 23.64/3.98 |
% 23.64/3.98 | REDUCE: (32), (60) imply:
% 23.64/3.98 | (64) succ(n1) = all_54_1
% 23.64/3.98 |
% 23.64/3.98 | REDUCE: (28), (54) imply:
% 23.64/3.98 | (65) succ(n1) = all_52_0
% 23.64/3.98 |
% 23.64/3.98 | REDUCE: (24), (59) imply:
% 23.64/3.98 | (66) succ(n1) = n2
% 23.64/3.98 |
% 23.64/3.98 | REDUCE: (22), (59) imply:
% 23.64/3.98 | (67) $i(n1)
% 23.64/3.98 |
% 23.64/3.98 | GROUND_INST: instantiating (18) with all_54_1, all_56_2, n1, simplifying with
% 23.64/3.98 | (63), (64) gives:
% 23.64/3.98 | (68) all_56_2 = all_54_1
% 23.64/3.98 |
% 23.64/3.98 | GROUND_INST: instantiating (18) with all_52_0, all_56_2, n1, simplifying with
% 23.64/3.98 | (63), (65) gives:
% 23.64/3.98 | (69) all_56_2 = all_52_0
% 23.64/3.98 |
% 23.64/3.98 | GROUND_INST: instantiating (18) with all_54_1, all_58_3, n1, simplifying with
% 23.64/3.98 | (62), (64) gives:
% 23.64/3.98 | (70) all_58_3 = all_54_1
% 23.64/3.98 |
% 23.64/3.98 | GROUND_INST: instantiating (18) with n2, all_58_3, n1, simplifying with (62),
% 23.64/3.98 | (66) gives:
% 23.64/3.98 | (71) all_58_3 = n2
% 23.64/3.98 |
% 23.64/3.98 | COMBINE_EQS: (70), (71) imply:
% 23.64/3.98 | (72) all_54_1 = n2
% 23.64/3.98 |
% 23.64/3.98 | SIMP: (72) implies:
% 23.64/3.98 | (73) all_54_1 = n2
% 23.64/3.98 |
% 23.64/3.98 | COMBINE_EQS: (68), (69) imply:
% 23.64/3.98 | (74) all_54_1 = all_52_0
% 23.64/3.98 |
% 23.64/3.98 | SIMP: (74) implies:
% 23.64/3.98 | (75) all_54_1 = all_52_0
% 23.64/3.98 |
% 23.64/3.98 | COMBINE_EQS: (73), (75) imply:
% 23.64/3.98 | (76) all_52_0 = n2
% 23.64/3.98 |
% 23.64/3.98 | SIMP: (76) implies:
% 23.64/3.98 | (77) all_52_0 = n2
% 23.64/3.98 |
% 23.64/3.98 | COMBINE_EQS: (69), (77) imply:
% 23.64/3.98 | (78) all_56_2 = n2
% 23.64/3.98 |
% 23.64/3.98 | REDUCE: (41), (71) imply:
% 23.64/3.98 | (79) succ(n2) = all_58_2
% 23.64/3.98 |
% 23.64/3.98 | REDUCE: (37), (78) imply:
% 23.64/3.98 | (80) succ(n2) = all_56_1
% 23.64/3.98 |
% 23.64/3.98 | REDUCE: (33), (73) imply:
% 23.64/3.98 | (81) succ(n2) = all_54_0
% 23.64/3.98 |
% 23.64/3.98 | REDUCE: (29), (77) imply:
% 23.64/3.98 | (82) succ(n2) = n3
% 23.64/3.98 |
% 23.64/3.98 | REDUCE: (26), (77) imply:
% 23.64/3.98 | (83) $i(n2)
% 23.64/3.98 |
% 23.64/3.99 | GROUND_INST: instantiating (18) with all_54_0, all_56_1, n2, simplifying with
% 23.64/3.99 | (80), (81) gives:
% 23.64/3.99 | (84) all_56_1 = all_54_0
% 23.64/3.99 |
% 23.64/3.99 | GROUND_INST: instantiating (18) with all_56_1, all_58_2, n2, simplifying with
% 23.64/3.99 | (79), (80) gives:
% 23.64/3.99 | (85) all_58_2 = all_56_1
% 23.64/3.99 |
% 23.64/3.99 | GROUND_INST: instantiating (18) with n3, all_58_2, n2, simplifying with (79),
% 23.64/3.99 | (82) gives:
% 23.64/3.99 | (86) all_58_2 = n3
% 23.64/3.99 |
% 23.64/3.99 | COMBINE_EQS: (85), (86) imply:
% 23.64/3.99 | (87) all_56_1 = n3
% 23.64/3.99 |
% 23.64/3.99 | SIMP: (87) implies:
% 23.64/3.99 | (88) all_56_1 = n3
% 23.64/3.99 |
% 23.64/3.99 | COMBINE_EQS: (84), (88) imply:
% 23.64/3.99 | (89) all_54_0 = n3
% 23.64/3.99 |
% 23.64/3.99 | SIMP: (89) implies:
% 23.64/3.99 | (90) all_54_0 = n3
% 23.64/3.99 |
% 23.64/3.99 | GROUND_INST: instantiating (leq_succ_gt) with tptp_minus_1, pv5, n0,
% 23.64/3.99 | simplifying with (2), (4), (16), (43) gives:
% 23.64/3.99 | (91) gt(pv5, tptp_minus_1) = 0
% 23.64/3.99 |
% 23.64/3.99 | GROUND_INST: instantiating (1) with n2, n2, n3, simplifying with (8), (82),
% 23.64/3.99 | (83) gives:
% 23.64/3.99 | (92) leq(n2, n2) = 0
% 23.64/3.99 |
% 23.64/3.99 | GROUND_INST: instantiating (1) with n1, n2, n3, simplifying with (7), (67),
% 23.64/3.99 | (82), (83) gives:
% 23.64/3.99 | (93) leq(n1, n2) = 0
% 23.64/3.99 |
% 23.64/3.99 | GROUND_INST: instantiating (1) with tptp_minus_1, n2, n3, simplifying with
% 23.64/3.99 | (4), (5), (82), (83) gives:
% 23.64/3.99 | (94) leq(tptp_minus_1, n2) = 0
% 23.64/3.99 |
% 23.64/3.99 | GROUND_INST: instantiating (1) with n0, n2, n3, simplifying with (6), (15),
% 23.64/3.99 | (82), (83) gives:
% 23.64/3.99 | (95) leq(n0, n2) = 0
% 23.64/3.99 |
% 23.64/3.99 | GROUND_INST: instantiating (3) with pv5, all_79_0, simplifying with (16), (44)
% 23.64/3.99 | gives:
% 23.64/3.99 | (96) pred(pv5) = all_79_0 & $i(all_79_0)
% 23.64/3.99 |
% 23.64/3.99 | ALPHA: (96) implies:
% 23.64/3.99 | (97) $i(all_79_0)
% 23.64/3.99 | (98) pred(pv5) = all_79_0
% 23.64/3.99 |
% 23.64/3.99 | GROUND_INST: instantiating (succ_pred) with pv5, all_79_0, simplifying with
% 23.64/3.99 | (16), (98) gives:
% 23.64/3.99 | (99) succ(all_79_0) = pv5
% 23.64/3.99 |
% 23.64/3.99 | GROUND_INST: instantiating (1) with tptp_minus_1, all_79_0, pv5, simplifying
% 23.64/3.99 | with (4), (91), (97), (99) gives:
% 23.64/3.99 | (100) leq(tptp_minus_1, all_79_0) = 0
% 23.64/3.99 |
% 23.64/3.99 | GROUND_INST: instantiating (46) with n2, tptp_minus_1, simplifying with (4),
% 23.64/3.99 | (83), (92), (100) gives:
% 23.64/3.99 | (101) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 23.64/3.99 | (a_select3(z_defuse, n2, tptp_minus_1) = v3 & a_select3(u_defuse, n2,
% 23.64/3.99 | tptp_minus_1) = v2 & leq(n0, n2) = v0 & leq(n0, tptp_minus_1) =
% 23.64/3.99 | v1 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2
% 23.64/3.99 | = use)))
% 23.64/3.99 |
% 23.64/3.99 | GROUND_INST: instantiating (46) with n1, tptp_minus_1, simplifying with (4),
% 23.64/3.99 | (67), (93), (100) gives:
% 23.64/3.99 | (102) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 23.64/3.99 | (a_select3(z_defuse, n1, tptp_minus_1) = v3 & a_select3(u_defuse, n1,
% 23.64/3.99 | tptp_minus_1) = v2 & leq(n0, n1) = v0 & leq(n0, tptp_minus_1) =
% 23.64/3.99 | v1 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2
% 23.64/3.99 | = use)))
% 23.64/3.99 |
% 23.64/3.99 | GROUND_INST: instantiating (46) with tptp_minus_1, tptp_minus_1, simplifying
% 23.64/3.99 | with (4), (94), (100) gives:
% 23.64/3.99 | (103) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 23.64/3.99 | (a_select3(z_defuse, tptp_minus_1, tptp_minus_1) = v3 &
% 23.64/3.99 | a_select3(u_defuse, tptp_minus_1, tptp_minus_1) = v2 & leq(n0,
% 23.64/3.99 | tptp_minus_1) = v1 & leq(n0, tptp_minus_1) = v0 & $i(v3) & $i(v2)
% 23.64/3.99 | & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = use)))
% 23.64/3.99 |
% 23.64/3.99 | GROUND_INST: instantiating (46) with n0, tptp_minus_1, simplifying with (4),
% 23.64/3.99 | (15), (95), (100) gives:
% 23.64/3.99 | (104) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 23.64/3.99 | (a_select3(z_defuse, n0, tptp_minus_1) = v3 & a_select3(u_defuse, n0,
% 23.64/3.99 | tptp_minus_1) = v2 & leq(n0, tptp_minus_1) = v1 & leq(n0, n0) =
% 23.64/3.99 | v0 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2
% 23.64/3.99 | = use)))
% 23.64/3.99 |
% 23.64/3.99 | DELTA: instantiating (103) with fresh symbols all_130_0, all_130_1, all_130_2,
% 23.64/3.99 | all_130_3 gives:
% 23.64/3.99 | (105) a_select3(z_defuse, tptp_minus_1, tptp_minus_1) = all_130_0 &
% 23.64/3.99 | a_select3(u_defuse, tptp_minus_1, tptp_minus_1) = all_130_1 & leq(n0,
% 23.64/3.99 | tptp_minus_1) = all_130_2 & leq(n0, tptp_minus_1) = all_130_3 &
% 23.64/3.99 | $i(all_130_0) & $i(all_130_1) & ( ~ (all_130_2 = 0) | ~ (all_130_3 =
% 23.64/3.99 | 0) | (all_130_0 = use & all_130_1 = use))
% 23.64/3.99 |
% 23.64/3.99 | ALPHA: (105) implies:
% 23.64/3.99 | (106) a_select3(z_defuse, tptp_minus_1, tptp_minus_1) = all_130_0
% 23.64/3.99 |
% 23.64/3.99 | DELTA: instantiating (102) with fresh symbols all_132_0, all_132_1, all_132_2,
% 23.64/3.99 | all_132_3 gives:
% 23.64/3.99 | (107) a_select3(z_defuse, n1, tptp_minus_1) = all_132_0 &
% 23.64/3.99 | a_select3(u_defuse, n1, tptp_minus_1) = all_132_1 & leq(n0, n1) =
% 23.64/3.99 | all_132_3 & leq(n0, tptp_minus_1) = all_132_2 & $i(all_132_0) &
% 23.64/3.99 | $i(all_132_1) & ( ~ (all_132_2 = 0) | ~ (all_132_3 = 0) | (all_132_0
% 23.64/3.99 | = use & all_132_1 = use))
% 23.64/4.00 |
% 23.64/4.00 | ALPHA: (107) implies:
% 23.64/4.00 | (108) a_select3(z_defuse, n1, tptp_minus_1) = all_132_0
% 23.64/4.00 |
% 23.64/4.00 | DELTA: instantiating (101) with fresh symbols all_134_0, all_134_1, all_134_2,
% 23.64/4.00 | all_134_3 gives:
% 23.64/4.00 | (109) a_select3(z_defuse, n2, tptp_minus_1) = all_134_0 &
% 23.64/4.00 | a_select3(u_defuse, n2, tptp_minus_1) = all_134_1 & leq(n0, n2) =
% 23.64/4.00 | all_134_3 & leq(n0, tptp_minus_1) = all_134_2 & $i(all_134_0) &
% 23.64/4.00 | $i(all_134_1) & ( ~ (all_134_2 = 0) | ~ (all_134_3 = 0) | (all_134_0
% 23.64/4.00 | = use & all_134_1 = use))
% 23.64/4.00 |
% 23.64/4.00 | ALPHA: (109) implies:
% 23.64/4.00 | (110) leq(n0, n2) = all_134_3
% 23.64/4.00 | (111) a_select3(z_defuse, n2, tptp_minus_1) = all_134_0
% 23.64/4.00 |
% 23.64/4.00 | DELTA: instantiating (104) with fresh symbols all_136_0, all_136_1, all_136_2,
% 23.64/4.00 | all_136_3 gives:
% 23.64/4.00 | (112) a_select3(z_defuse, n0, tptp_minus_1) = all_136_0 &
% 23.64/4.00 | a_select3(u_defuse, n0, tptp_minus_1) = all_136_1 & leq(n0,
% 23.64/4.00 | tptp_minus_1) = all_136_2 & leq(n0, n0) = all_136_3 & $i(all_136_0)
% 23.64/4.00 | & $i(all_136_1) & ( ~ (all_136_2 = 0) | ~ (all_136_3 = 0) |
% 23.64/4.00 | (all_136_0 = use & all_136_1 = use))
% 23.64/4.00 |
% 23.64/4.00 | ALPHA: (112) implies:
% 23.64/4.00 | (113) a_select3(z_defuse, n0, tptp_minus_1) = all_136_0
% 23.64/4.00 |
% 23.64/4.00 | GROUND_INST: instantiating (19) with 0, all_134_3, n2, n0, simplifying with
% 23.64/4.00 | (95), (110) gives:
% 23.64/4.00 | (114) all_134_3 = 0
% 23.64/4.00 |
% 23.64/4.00 | GROUND_INST: instantiating (47) with n0, tptp_minus_1, all_136_0, simplifying
% 23.64/4.00 | with (4), (15), (113) gives:
% 23.64/4.00 | (115) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 23.64/4.00 | $i] : (a_select3(u_defuse, n0, tptp_minus_1) = v4 &
% 23.64/4.00 | leq(tptp_minus_1, pv5) = v3 & leq(n0, n2) = v2 & leq(n0,
% 23.64/4.00 | tptp_minus_1) = v1 & leq(n0, n0) = v0 & $i(v4) & ( ~ (v3 = 0) |
% 23.64/4.00 | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v4 = use & all_136_0 =
% 23.64/4.00 | use)))
% 23.64/4.00 |
% 23.64/4.00 | GROUND_INST: instantiating (47) with tptp_minus_1, tptp_minus_1, all_130_0,
% 23.64/4.00 | simplifying with (4), (106) gives:
% 23.64/4.00 | (116) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 23.64/4.00 | $i] : (a_select3(u_defuse, tptp_minus_1, tptp_minus_1) = v4 &
% 23.64/4.00 | leq(tptp_minus_1, pv5) = v3 & leq(tptp_minus_1, n2) = v2 & leq(n0,
% 23.64/4.00 | tptp_minus_1) = v1 & leq(n0, tptp_minus_1) = v0 & $i(v4) & ( ~
% 23.64/4.00 | (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v4 = use &
% 23.64/4.00 | all_130_0 = use)))
% 23.64/4.00 |
% 23.64/4.00 | GROUND_INST: instantiating (47) with n1, tptp_minus_1, all_132_0, simplifying
% 23.64/4.00 | with (4), (67), (108) gives:
% 23.64/4.00 | (117) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 23.64/4.00 | $i] : (a_select3(u_defuse, n1, tptp_minus_1) = v4 & leq(n1, n2) =
% 23.64/4.00 | v2 & leq(tptp_minus_1, pv5) = v3 & leq(n0, n1) = v0 & leq(n0,
% 23.64/4.00 | tptp_minus_1) = v1 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1
% 23.64/4.00 | = 0) | ~ (v0 = 0) | (v4 = use & all_132_0 = use)))
% 23.64/4.00 |
% 23.64/4.00 | GROUND_INST: instantiating (47) with n2, tptp_minus_1, all_134_0, simplifying
% 23.64/4.00 | with (4), (83), (111) gives:
% 23.64/4.00 | (118) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 23.64/4.00 | $i] : (a_select3(u_defuse, n2, tptp_minus_1) = v4 & leq(n2, n2) =
% 23.64/4.00 | v2 & leq(tptp_minus_1, pv5) = v3 & leq(n0, n2) = v0 & leq(n0,
% 23.64/4.00 | tptp_minus_1) = v1 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1
% 23.64/4.00 | = 0) | ~ (v0 = 0) | (v4 = use & all_134_0 = use)))
% 23.64/4.00 |
% 23.64/4.00 | DELTA: instantiating (118) with fresh symbols all_148_0, all_148_1, all_148_2,
% 23.64/4.00 | all_148_3, all_148_4 gives:
% 23.64/4.00 | (119) a_select3(u_defuse, n2, tptp_minus_1) = all_148_0 & leq(n2, n2) =
% 23.64/4.00 | all_148_2 & leq(tptp_minus_1, pv5) = all_148_1 & leq(n0, n2) =
% 23.64/4.00 | all_148_4 & leq(n0, tptp_minus_1) = all_148_3 & $i(all_148_0) & ( ~
% 23.64/4.00 | (all_148_1 = 0) | ~ (all_148_2 = 0) | ~ (all_148_3 = 0) | ~
% 23.64/4.00 | (all_148_4 = 0) | (all_148_0 = use & all_134_0 = use))
% 23.64/4.00 |
% 23.64/4.00 | ALPHA: (119) implies:
% 23.64/4.00 | (120) leq(n0, n2) = all_148_4
% 23.64/4.00 | (121) leq(n2, n2) = all_148_2
% 23.64/4.00 |
% 23.64/4.00 | DELTA: instantiating (117) with fresh symbols all_150_0, all_150_1, all_150_2,
% 23.64/4.00 | all_150_3, all_150_4 gives:
% 23.64/4.00 | (122) a_select3(u_defuse, n1, tptp_minus_1) = all_150_0 & leq(n1, n2) =
% 23.64/4.00 | all_150_2 & leq(tptp_minus_1, pv5) = all_150_1 & leq(n0, n1) =
% 23.64/4.00 | all_150_4 & leq(n0, tptp_minus_1) = all_150_3 & $i(all_150_0) & ( ~
% 23.64/4.00 | (all_150_1 = 0) | ~ (all_150_2 = 0) | ~ (all_150_3 = 0) | ~
% 23.64/4.00 | (all_150_4 = 0) | (all_150_0 = use & all_132_0 = use))
% 23.64/4.00 |
% 23.64/4.00 | ALPHA: (122) implies:
% 23.64/4.00 | (123) leq(n1, n2) = all_150_2
% 23.64/4.00 |
% 23.64/4.00 | DELTA: instantiating (116) with fresh symbols all_152_0, all_152_1, all_152_2,
% 23.64/4.00 | all_152_3, all_152_4 gives:
% 23.64/4.00 | (124) a_select3(u_defuse, tptp_minus_1, tptp_minus_1) = all_152_0 &
% 23.64/4.00 | leq(tptp_minus_1, pv5) = all_152_1 & leq(tptp_minus_1, n2) =
% 23.64/4.00 | all_152_2 & leq(n0, tptp_minus_1) = all_152_3 & leq(n0, tptp_minus_1)
% 23.64/4.00 | = all_152_4 & $i(all_152_0) & ( ~ (all_152_1 = 0) | ~ (all_152_2 =
% 23.64/4.00 | 0) | ~ (all_152_3 = 0) | ~ (all_152_4 = 0) | (all_152_0 = use &
% 23.64/4.00 | all_130_0 = use))
% 23.64/4.00 |
% 23.64/4.00 | ALPHA: (124) implies:
% 23.64/4.00 | (125) leq(tptp_minus_1, n2) = all_152_2
% 23.64/4.00 |
% 23.64/4.00 | DELTA: instantiating (115) with fresh symbols all_154_0, all_154_1, all_154_2,
% 23.64/4.00 | all_154_3, all_154_4 gives:
% 23.64/4.00 | (126) a_select3(u_defuse, n0, tptp_minus_1) = all_154_0 & leq(tptp_minus_1,
% 23.64/4.00 | pv5) = all_154_1 & leq(n0, n2) = all_154_2 & leq(n0, tptp_minus_1)
% 23.64/4.00 | = all_154_3 & leq(n0, n0) = all_154_4 & $i(all_154_0) & ( ~
% 23.64/4.00 | (all_154_1 = 0) | ~ (all_154_2 = 0) | ~ (all_154_3 = 0) | ~
% 23.64/4.00 | (all_154_4 = 0) | (all_154_0 = use & all_136_0 = use))
% 23.64/4.00 |
% 23.64/4.00 | ALPHA: (126) implies:
% 23.64/4.00 | (127) leq(n0, n2) = all_154_2
% 23.64/4.00 |
% 23.64/4.00 | GROUND_INST: instantiating (19) with 0, all_154_2, n2, n0, simplifying with
% 23.64/4.00 | (95), (127) gives:
% 23.64/4.00 | (128) all_154_2 = 0
% 23.64/4.00 |
% 23.64/4.00 | GROUND_INST: instantiating (19) with all_148_4, all_154_2, n2, n0, simplifying
% 23.64/4.00 | with (120), (127) gives:
% 23.64/4.00 | (129) all_154_2 = all_148_4
% 23.64/4.00 |
% 23.64/4.01 | GROUND_INST: instantiating (19) with 0, all_152_2, n2, tptp_minus_1,
% 23.64/4.01 | simplifying with (94), (125) gives:
% 23.64/4.01 | (130) all_152_2 = 0
% 23.64/4.01 |
% 23.64/4.01 | GROUND_INST: instantiating (19) with 0, all_150_2, n2, n1, simplifying with
% 23.64/4.01 | (93), (123) gives:
% 23.64/4.01 | (131) all_150_2 = 0
% 23.64/4.01 |
% 23.64/4.01 | GROUND_INST: instantiating (19) with 0, all_148_2, n2, n2, simplifying with
% 23.64/4.01 | (92), (121) gives:
% 23.64/4.01 | (132) all_148_2 = 0
% 23.64/4.01 |
% 23.64/4.01 | COMBINE_EQS: (128), (129) imply:
% 23.64/4.01 | (133) all_148_4 = 0
% 23.64/4.01 |
% 23.64/4.01 | BETA: splitting (45) gives:
% 23.64/4.01 |
% 23.64/4.01 | Case 1:
% 23.64/4.01 | |
% 23.64/4.01 | | (134) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 23.64/4.01 | | (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1) =
% 23.64/4.01 | | v2 & leq(v1, all_79_0) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 &
% 23.64/4.01 | | leq(n0, v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 =
% 23.64/4.01 | | use) | ~ (v2 = use)))
% 23.64/4.01 | |
% 23.64/4.01 | | DELTA: instantiating (134) with fresh symbols all_173_0, all_173_1,
% 23.64/4.01 | | all_173_2, all_173_3 gives:
% 23.64/4.01 | | (135) a_select3(z_defuse, all_173_3, all_173_2) = all_173_0 &
% 23.64/4.01 | | a_select3(u_defuse, all_173_3, all_173_2) = all_173_1 &
% 23.64/4.01 | | leq(all_173_2, all_79_0) = 0 & leq(all_173_3, n2) = 0 & leq(n0,
% 23.64/4.01 | | all_173_2) = 0 & leq(n0, all_173_3) = 0 & $i(all_173_0) &
% 23.64/4.01 | | $i(all_173_1) & $i(all_173_2) & $i(all_173_3) & ( ~ (all_173_0 =
% 23.64/4.01 | | use) | ~ (all_173_1 = use))
% 23.64/4.01 | |
% 23.64/4.01 | | ALPHA: (135) implies:
% 23.64/4.01 | | (136) $i(all_173_3)
% 23.64/4.01 | | (137) $i(all_173_2)
% 23.64/4.01 | | (138) leq(n0, all_173_3) = 0
% 23.64/4.01 | | (139) leq(n0, all_173_2) = 0
% 23.64/4.01 | | (140) leq(all_173_3, n2) = 0
% 23.64/4.01 | | (141) leq(all_173_2, all_79_0) = 0
% 23.64/4.01 | | (142) a_select3(u_defuse, all_173_3, all_173_2) = all_173_1
% 23.64/4.01 | | (143) a_select3(z_defuse, all_173_3, all_173_2) = all_173_0
% 23.64/4.01 | | (144) ~ (all_173_0 = use) | ~ (all_173_1 = use)
% 23.64/4.01 | |
% 23.64/4.01 | | GROUND_INST: instantiating (46) with all_173_3, tptp_minus_1, simplifying
% 23.64/4.01 | | with (4), (100), (136), (140) gives:
% 23.64/4.01 | | (145) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 23.64/4.01 | | (a_select3(z_defuse, all_173_3, tptp_minus_1) = v3 &
% 23.64/4.01 | | a_select3(u_defuse, all_173_3, tptp_minus_1) = v2 & leq(n0,
% 23.64/4.01 | | all_173_3) = v0 & leq(n0, tptp_minus_1) = v1 & $i(v3) & $i(v2)
% 23.64/4.01 | | & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = use)))
% 23.64/4.01 | |
% 23.64/4.01 | | GROUND_INST: instantiating (46) with n2, all_173_2, simplifying with (83),
% 23.64/4.01 | | (92), (137), (141) gives:
% 23.64/4.01 | | (146) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 23.64/4.01 | | (a_select3(z_defuse, n2, all_173_2) = v3 & a_select3(u_defuse, n2,
% 23.64/4.01 | | all_173_2) = v2 & leq(n0, all_173_2) = v1 & leq(n0, n2) = v0 &
% 23.64/4.01 | | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 =
% 23.64/4.01 | | use)))
% 23.64/4.01 | |
% 23.64/4.01 | | GROUND_INST: instantiating (46) with n1, all_173_2, simplifying with (67),
% 23.64/4.01 | | (93), (137), (141) gives:
% 23.64/4.01 | | (147) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 23.64/4.01 | | (a_select3(z_defuse, n1, all_173_2) = v3 & a_select3(u_defuse, n1,
% 23.64/4.01 | | all_173_2) = v2 & leq(n0, all_173_2) = v1 & leq(n0, n1) = v0 &
% 23.64/4.01 | | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 =
% 23.64/4.01 | | use)))
% 23.64/4.01 | |
% 23.64/4.01 | | GROUND_INST: instantiating (46) with tptp_minus_1, all_173_2, simplifying
% 23.64/4.01 | | with (4), (94), (137), (141) gives:
% 23.64/4.01 | | (148) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 23.64/4.01 | | (a_select3(z_defuse, tptp_minus_1, all_173_2) = v3 &
% 23.64/4.01 | | a_select3(u_defuse, tptp_minus_1, all_173_2) = v2 & leq(n0,
% 23.64/4.01 | | all_173_2) = v1 & leq(n0, tptp_minus_1) = v0 & $i(v3) & $i(v2)
% 23.64/4.01 | | & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = use)))
% 23.64/4.01 | |
% 23.64/4.01 | | GROUND_INST: instantiating (46) with n0, all_173_2, simplifying with (15),
% 23.64/4.01 | | (95), (137), (141) gives:
% 23.64/4.01 | | (149) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 23.64/4.01 | | (a_select3(z_defuse, n0, all_173_2) = v3 & a_select3(u_defuse, n0,
% 23.64/4.01 | | all_173_2) = v2 & leq(n0, all_173_2) = v1 & leq(n0, n0) = v0 &
% 23.64/4.01 | | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 =
% 23.64/4.01 | | use)))
% 23.64/4.01 | |
% 23.64/4.01 | | GROUND_INST: instantiating (46) with all_173_3, all_173_2, simplifying with
% 23.64/4.01 | | (136), (137), (140), (141) gives:
% 23.64/4.01 | | (150) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 23.64/4.01 | | (a_select3(z_defuse, all_173_3, all_173_2) = v3 &
% 23.64/4.01 | | a_select3(u_defuse, all_173_3, all_173_2) = v2 & leq(n0,
% 23.64/4.01 | | all_173_2) = v1 & leq(n0, all_173_3) = v0 & $i(v3) & $i(v2) & (
% 23.64/4.01 | | ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = use)))
% 23.64/4.01 | |
% 23.64/4.02 | | GROUND_INST: instantiating (47) with all_173_3, all_173_2, all_173_0,
% 23.64/4.02 | | simplifying with (136), (137), (143) gives:
% 23.64/4.02 | | (151) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 23.64/4.02 | | $i] : (a_select3(u_defuse, all_173_3, all_173_2) = v4 &
% 23.64/4.02 | | leq(all_173_2, pv5) = v3 & leq(all_173_3, n2) = v2 & leq(n0,
% 23.64/4.02 | | all_173_2) = v1 & leq(n0, all_173_3) = v0 & $i(v4) & ( ~ (v3 =
% 23.64/4.02 | | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v4 = use &
% 23.64/4.02 | | all_173_0 = use)))
% 23.64/4.02 | |
% 23.64/4.02 | | DELTA: instantiating (150) with fresh symbols all_181_0, all_181_1,
% 23.64/4.02 | | all_181_2, all_181_3 gives:
% 23.64/4.02 | | (152) a_select3(z_defuse, all_173_3, all_173_2) = all_181_0 &
% 23.64/4.02 | | a_select3(u_defuse, all_173_3, all_173_2) = all_181_1 & leq(n0,
% 23.64/4.02 | | all_173_2) = all_181_2 & leq(n0, all_173_3) = all_181_3 &
% 23.64/4.02 | | $i(all_181_0) & $i(all_181_1) & ( ~ (all_181_2 = 0) | ~ (all_181_3
% 23.64/4.02 | | = 0) | (all_181_0 = use & all_181_1 = use))
% 23.64/4.02 | |
% 23.64/4.02 | | ALPHA: (152) implies:
% 23.64/4.02 | | (153) leq(n0, all_173_3) = all_181_3
% 23.64/4.02 | | (154) leq(n0, all_173_2) = all_181_2
% 23.64/4.02 | | (155) a_select3(u_defuse, all_173_3, all_173_2) = all_181_1
% 23.64/4.02 | | (156) a_select3(z_defuse, all_173_3, all_173_2) = all_181_0
% 23.64/4.02 | | (157) ~ (all_181_2 = 0) | ~ (all_181_3 = 0) | (all_181_0 = use &
% 23.64/4.02 | | all_181_1 = use)
% 23.64/4.02 | |
% 23.64/4.02 | | DELTA: instantiating (149) with fresh symbols all_183_0, all_183_1,
% 23.64/4.02 | | all_183_2, all_183_3 gives:
% 23.64/4.02 | | (158) a_select3(z_defuse, n0, all_173_2) = all_183_0 &
% 23.64/4.02 | | a_select3(u_defuse, n0, all_173_2) = all_183_1 & leq(n0, all_173_2)
% 23.64/4.02 | | = all_183_2 & leq(n0, n0) = all_183_3 & $i(all_183_0) &
% 23.64/4.02 | | $i(all_183_1) & ( ~ (all_183_2 = 0) | ~ (all_183_3 = 0) |
% 23.64/4.02 | | (all_183_0 = use & all_183_1 = use))
% 23.64/4.02 | |
% 23.64/4.02 | | ALPHA: (158) implies:
% 23.64/4.02 | | (159) leq(n0, all_173_2) = all_183_2
% 23.64/4.02 | |
% 23.64/4.02 | | DELTA: instantiating (148) with fresh symbols all_185_0, all_185_1,
% 23.64/4.02 | | all_185_2, all_185_3 gives:
% 23.64/4.02 | | (160) a_select3(z_defuse, tptp_minus_1, all_173_2) = all_185_0 &
% 23.64/4.02 | | a_select3(u_defuse, tptp_minus_1, all_173_2) = all_185_1 & leq(n0,
% 23.64/4.02 | | all_173_2) = all_185_2 & leq(n0, tptp_minus_1) = all_185_3 &
% 23.64/4.02 | | $i(all_185_0) & $i(all_185_1) & ( ~ (all_185_2 = 0) | ~ (all_185_3
% 23.64/4.02 | | = 0) | (all_185_0 = use & all_185_1 = use))
% 23.64/4.02 | |
% 23.64/4.02 | | ALPHA: (160) implies:
% 23.64/4.02 | | (161) leq(n0, all_173_2) = all_185_2
% 23.64/4.02 | |
% 23.64/4.02 | | DELTA: instantiating (147) with fresh symbols all_187_0, all_187_1,
% 23.64/4.02 | | all_187_2, all_187_3 gives:
% 23.64/4.02 | | (162) a_select3(z_defuse, n1, all_173_2) = all_187_0 &
% 23.64/4.02 | | a_select3(u_defuse, n1, all_173_2) = all_187_1 & leq(n0, all_173_2)
% 23.64/4.02 | | = all_187_2 & leq(n0, n1) = all_187_3 & $i(all_187_0) &
% 23.64/4.02 | | $i(all_187_1) & ( ~ (all_187_2 = 0) | ~ (all_187_3 = 0) |
% 23.64/4.02 | | (all_187_0 = use & all_187_1 = use))
% 23.64/4.02 | |
% 23.64/4.02 | | ALPHA: (162) implies:
% 23.64/4.02 | | (163) leq(n0, all_173_2) = all_187_2
% 23.64/4.02 | |
% 23.64/4.02 | | DELTA: instantiating (145) with fresh symbols all_189_0, all_189_1,
% 23.64/4.02 | | all_189_2, all_189_3 gives:
% 23.64/4.02 | | (164) a_select3(z_defuse, all_173_3, tptp_minus_1) = all_189_0 &
% 23.64/4.02 | | a_select3(u_defuse, all_173_3, tptp_minus_1) = all_189_1 & leq(n0,
% 23.64/4.02 | | all_173_3) = all_189_3 & leq(n0, tptp_minus_1) = all_189_2 &
% 23.64/4.02 | | $i(all_189_0) & $i(all_189_1) & ( ~ (all_189_2 = 0) | ~ (all_189_3
% 23.64/4.02 | | = 0) | (all_189_0 = use & all_189_1 = use))
% 23.64/4.02 | |
% 23.64/4.02 | | ALPHA: (164) implies:
% 23.64/4.02 | | (165) leq(n0, all_173_3) = all_189_3
% 23.64/4.02 | |
% 23.64/4.02 | | DELTA: instantiating (146) with fresh symbols all_191_0, all_191_1,
% 23.64/4.02 | | all_191_2, all_191_3 gives:
% 23.64/4.02 | | (166) a_select3(z_defuse, n2, all_173_2) = all_191_0 &
% 23.64/4.02 | | a_select3(u_defuse, n2, all_173_2) = all_191_1 & leq(n0, all_173_2)
% 23.64/4.02 | | = all_191_2 & leq(n0, n2) = all_191_3 & $i(all_191_0) &
% 23.64/4.02 | | $i(all_191_1) & ( ~ (all_191_2 = 0) | ~ (all_191_3 = 0) |
% 23.64/4.02 | | (all_191_0 = use & all_191_1 = use))
% 23.64/4.02 | |
% 23.64/4.02 | | ALPHA: (166) implies:
% 23.64/4.02 | | (167) leq(n0, all_173_2) = all_191_2
% 23.64/4.02 | |
% 23.64/4.02 | | DELTA: instantiating (151) with fresh symbols all_193_0, all_193_1,
% 23.64/4.02 | | all_193_2, all_193_3, all_193_4 gives:
% 23.64/4.02 | | (168) a_select3(u_defuse, all_173_3, all_173_2) = all_193_0 &
% 23.64/4.02 | | leq(all_173_2, pv5) = all_193_1 & leq(all_173_3, n2) = all_193_2 &
% 23.64/4.02 | | leq(n0, all_173_2) = all_193_3 & leq(n0, all_173_3) = all_193_4 &
% 23.64/4.02 | | $i(all_193_0) & ( ~ (all_193_1 = 0) | ~ (all_193_2 = 0) | ~
% 23.64/4.02 | | (all_193_3 = 0) | ~ (all_193_4 = 0) | (all_193_0 = use &
% 23.64/4.02 | | all_173_0 = use))
% 23.64/4.02 | |
% 23.64/4.02 | | ALPHA: (168) implies:
% 23.64/4.02 | | (169) leq(n0, all_173_3) = all_193_4
% 23.64/4.02 | | (170) leq(n0, all_173_2) = all_193_3
% 23.64/4.02 | | (171) a_select3(u_defuse, all_173_3, all_173_2) = all_193_0
% 23.64/4.02 | |
% 23.64/4.02 | | GROUND_INST: instantiating (19) with 0, all_189_3, all_173_3, n0,
% 23.64/4.02 | | simplifying with (138), (165) gives:
% 23.64/4.02 | | (172) all_189_3 = 0
% 23.64/4.02 | |
% 23.64/4.02 | | GROUND_INST: instantiating (19) with all_189_3, all_193_4, all_173_3, n0,
% 23.64/4.02 | | simplifying with (165), (169) gives:
% 23.64/4.02 | | (173) all_193_4 = all_189_3
% 23.64/4.02 | |
% 23.64/4.02 | | GROUND_INST: instantiating (19) with all_181_3, all_193_4, all_173_3, n0,
% 23.64/4.02 | | simplifying with (153), (169) gives:
% 23.64/4.02 | | (174) all_193_4 = all_181_3
% 23.64/4.02 | |
% 23.64/4.02 | | GROUND_INST: instantiating (19) with all_183_2, all_185_2, all_173_2, n0,
% 23.64/4.02 | | simplifying with (159), (161) gives:
% 23.64/4.02 | | (175) all_185_2 = all_183_2
% 23.64/4.02 | |
% 23.64/4.02 | | GROUND_INST: instantiating (19) with all_183_2, all_191_2, all_173_2, n0,
% 23.64/4.02 | | simplifying with (159), (167) gives:
% 23.64/4.02 | | (176) all_191_2 = all_183_2
% 23.64/4.02 | |
% 23.64/4.02 | | GROUND_INST: instantiating (19) with all_181_2, all_191_2, all_173_2, n0,
% 23.64/4.02 | | simplifying with (154), (167) gives:
% 23.64/4.02 | | (177) all_191_2 = all_181_2
% 23.64/4.02 | |
% 23.64/4.02 | | GROUND_INST: instantiating (19) with 0, all_193_3, all_173_2, n0,
% 23.64/4.02 | | simplifying with (139), (170) gives:
% 23.64/4.02 | | (178) all_193_3 = 0
% 23.64/4.02 | |
% 23.64/4.02 | | GROUND_INST: instantiating (19) with all_187_2, all_193_3, all_173_2, n0,
% 23.64/4.02 | | simplifying with (163), (170) gives:
% 23.64/4.02 | | (179) all_193_3 = all_187_2
% 23.64/4.02 | |
% 23.64/4.02 | | GROUND_INST: instantiating (19) with all_185_2, all_193_3, all_173_2, n0,
% 23.64/4.02 | | simplifying with (161), (170) gives:
% 23.64/4.02 | | (180) all_193_3 = all_185_2
% 23.64/4.02 | |
% 23.64/4.02 | | GROUND_INST: instantiating (20) with all_173_1, all_193_0, all_173_2,
% 23.64/4.02 | | all_173_3, u_defuse, simplifying with (142), (171) gives:
% 23.64/4.02 | | (181) all_193_0 = all_173_1
% 23.64/4.02 | |
% 23.64/4.02 | | GROUND_INST: instantiating (20) with all_181_1, all_193_0, all_173_2,
% 23.64/4.02 | | all_173_3, u_defuse, simplifying with (155), (171) gives:
% 23.64/4.02 | | (182) all_193_0 = all_181_1
% 23.64/4.02 | |
% 23.64/4.02 | | GROUND_INST: instantiating (20) with all_173_0, all_181_0, all_173_2,
% 23.64/4.02 | | all_173_3, z_defuse, simplifying with (143), (156) gives:
% 23.64/4.02 | | (183) all_181_0 = all_173_0
% 23.64/4.02 | |
% 23.64/4.02 | | COMBINE_EQS: (181), (182) imply:
% 23.64/4.02 | | (184) all_181_1 = all_173_1
% 23.64/4.02 | |
% 23.64/4.02 | | COMBINE_EQS: (178), (179) imply:
% 23.64/4.03 | | (185) all_187_2 = 0
% 23.64/4.03 | |
% 23.64/4.03 | | COMBINE_EQS: (179), (180) imply:
% 23.64/4.03 | | (186) all_187_2 = all_185_2
% 23.64/4.03 | |
% 23.64/4.03 | | COMBINE_EQS: (173), (174) imply:
% 23.64/4.03 | | (187) all_189_3 = all_181_3
% 23.64/4.03 | |
% 23.64/4.03 | | SIMP: (187) implies:
% 23.64/4.03 | | (188) all_189_3 = all_181_3
% 23.64/4.03 | |
% 23.64/4.03 | | COMBINE_EQS: (176), (177) imply:
% 23.64/4.03 | | (189) all_183_2 = all_181_2
% 23.64/4.03 | |
% 23.64/4.03 | | SIMP: (189) implies:
% 23.64/4.03 | | (190) all_183_2 = all_181_2
% 23.64/4.03 | |
% 23.64/4.03 | | COMBINE_EQS: (172), (188) imply:
% 23.64/4.03 | | (191) all_181_3 = 0
% 23.64/4.03 | |
% 23.64/4.03 | | COMBINE_EQS: (185), (186) imply:
% 23.64/4.03 | | (192) all_185_2 = 0
% 23.64/4.03 | |
% 23.64/4.03 | | SIMP: (192) implies:
% 23.64/4.03 | | (193) all_185_2 = 0
% 23.64/4.03 | |
% 23.64/4.03 | | COMBINE_EQS: (175), (193) imply:
% 23.64/4.03 | | (194) all_183_2 = 0
% 23.64/4.03 | |
% 23.64/4.03 | | SIMP: (194) implies:
% 23.64/4.03 | | (195) all_183_2 = 0
% 23.64/4.03 | |
% 23.64/4.03 | | COMBINE_EQS: (190), (195) imply:
% 23.64/4.03 | | (196) all_181_2 = 0
% 23.64/4.03 | |
% 23.64/4.03 | | BETA: splitting (157) gives:
% 23.64/4.03 | |
% 23.64/4.03 | | Case 1:
% 23.64/4.03 | | |
% 23.64/4.03 | | | (197) ~ (all_181_2 = 0)
% 23.64/4.03 | | |
% 23.64/4.03 | | | REDUCE: (196), (197) imply:
% 23.64/4.03 | | | (198) $false
% 23.64/4.03 | | |
% 23.64/4.03 | | | CLOSE: (198) is inconsistent.
% 23.64/4.03 | | |
% 23.64/4.03 | | Case 2:
% 23.64/4.03 | | |
% 23.64/4.03 | | | (199) ~ (all_181_3 = 0) | (all_181_0 = use & all_181_1 = use)
% 23.64/4.03 | | |
% 23.64/4.03 | | | BETA: splitting (199) gives:
% 23.64/4.03 | | |
% 23.64/4.03 | | | Case 1:
% 23.64/4.03 | | | |
% 23.64/4.03 | | | | (200) ~ (all_181_3 = 0)
% 23.64/4.03 | | | |
% 23.64/4.03 | | | | REDUCE: (191), (200) imply:
% 23.64/4.03 | | | | (201) $false
% 23.64/4.03 | | | |
% 23.64/4.03 | | | | CLOSE: (201) is inconsistent.
% 23.64/4.03 | | | |
% 23.64/4.03 | | | Case 2:
% 23.64/4.03 | | | |
% 23.64/4.03 | | | | (202) all_181_0 = use & all_181_1 = use
% 23.64/4.03 | | | |
% 23.64/4.03 | | | | ALPHA: (202) implies:
% 23.64/4.03 | | | | (203) all_181_1 = use
% 23.64/4.03 | | | | (204) all_181_0 = use
% 23.64/4.03 | | | |
% 23.64/4.03 | | | | COMBINE_EQS: (183), (204) imply:
% 23.64/4.03 | | | | (205) all_173_0 = use
% 23.64/4.03 | | | |
% 23.64/4.03 | | | | COMBINE_EQS: (184), (203) imply:
% 23.64/4.03 | | | | (206) all_173_1 = use
% 23.64/4.03 | | | |
% 23.64/4.03 | | | | BETA: splitting (144) gives:
% 23.64/4.03 | | | |
% 23.64/4.03 | | | | Case 1:
% 23.64/4.03 | | | | |
% 23.64/4.03 | | | | | (207) ~ (all_173_0 = use)
% 23.64/4.03 | | | | |
% 23.64/4.03 | | | | | REDUCE: (205), (207) imply:
% 23.64/4.03 | | | | | (208) $false
% 23.64/4.03 | | | | |
% 23.64/4.03 | | | | | CLOSE: (208) is inconsistent.
% 23.64/4.03 | | | | |
% 23.64/4.03 | | | | Case 2:
% 23.64/4.03 | | | | |
% 23.64/4.03 | | | | | (209) ~ (all_173_1 = use)
% 23.64/4.03 | | | | |
% 23.64/4.03 | | | | | REDUCE: (206), (209) imply:
% 23.64/4.03 | | | | | (210) $false
% 23.64/4.03 | | | | |
% 23.64/4.03 | | | | | CLOSE: (210) is inconsistent.
% 23.64/4.03 | | | | |
% 23.64/4.03 | | | | End of split
% 23.64/4.03 | | | |
% 23.64/4.03 | | | End of split
% 23.64/4.03 | | |
% 23.64/4.03 | | End of split
% 23.64/4.03 | |
% 23.64/4.03 | Case 2:
% 23.64/4.03 | |
% 23.64/4.03 | | (211) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 23.64/4.03 | | (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1) =
% 23.64/4.03 | | v2 & leq(v1, pv5) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 &
% 23.64/4.03 | | leq(n0, v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 =
% 23.64/4.03 | | use) | ~ (v2 = use)))
% 23.64/4.03 | |
% 23.64/4.03 | | DELTA: instantiating (211) with fresh symbols all_173_0, all_173_1,
% 23.64/4.03 | | all_173_2, all_173_3 gives:
% 23.64/4.03 | | (212) a_select3(z_defuse, all_173_3, all_173_2) = all_173_0 &
% 23.64/4.03 | | a_select3(u_defuse, all_173_3, all_173_2) = all_173_1 &
% 23.64/4.03 | | leq(all_173_2, pv5) = 0 & leq(all_173_3, n2) = 0 & leq(n0,
% 23.64/4.03 | | all_173_2) = 0 & leq(n0, all_173_3) = 0 & $i(all_173_0) &
% 23.64/4.03 | | $i(all_173_1) & $i(all_173_2) & $i(all_173_3) & ( ~ (all_173_0 =
% 23.64/4.03 | | use) | ~ (all_173_1 = use))
% 23.64/4.03 | |
% 23.64/4.03 | | ALPHA: (212) implies:
% 23.64/4.03 | | (213) $i(all_173_3)
% 23.64/4.03 | | (214) $i(all_173_2)
% 23.64/4.03 | | (215) leq(n0, all_173_3) = 0
% 23.64/4.03 | | (216) leq(n0, all_173_2) = 0
% 23.64/4.03 | | (217) leq(all_173_3, n2) = 0
% 23.64/4.03 | | (218) leq(all_173_2, pv5) = 0
% 23.64/4.03 | | (219) a_select3(u_defuse, all_173_3, all_173_2) = all_173_1
% 23.64/4.03 | | (220) a_select3(z_defuse, all_173_3, all_173_2) = all_173_0
% 23.64/4.03 | | (221) ~ (all_173_0 = use) | ~ (all_173_1 = use)
% 23.64/4.03 | |
% 23.64/4.03 | | GROUND_INST: instantiating (46) with all_173_3, tptp_minus_1, simplifying
% 23.64/4.03 | | with (4), (100), (213), (217) gives:
% 23.64/4.03 | | (222) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 23.64/4.03 | | (a_select3(z_defuse, all_173_3, tptp_minus_1) = v3 &
% 23.64/4.03 | | a_select3(u_defuse, all_173_3, tptp_minus_1) = v2 & leq(n0,
% 23.64/4.03 | | all_173_3) = v0 & leq(n0, tptp_minus_1) = v1 & $i(v3) & $i(v2)
% 23.64/4.03 | | & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = use)))
% 23.64/4.03 | |
% 23.64/4.03 | | GROUND_INST: instantiating (47) with all_173_3, all_173_2, all_173_0,
% 23.64/4.03 | | simplifying with (213), (214), (220) gives:
% 23.64/4.03 | | (223) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 23.64/4.03 | | $i] : (a_select3(u_defuse, all_173_3, all_173_2) = v4 &
% 23.64/4.03 | | leq(all_173_2, pv5) = v3 & leq(all_173_3, n2) = v2 & leq(n0,
% 23.64/4.03 | | all_173_2) = v1 & leq(n0, all_173_3) = v0 & $i(v4) & ( ~ (v3 =
% 23.64/4.03 | | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v4 = use &
% 23.64/4.03 | | all_173_0 = use)))
% 23.64/4.03 | |
% 23.64/4.03 | | DELTA: instantiating (222) with fresh symbols all_181_0, all_181_1,
% 23.64/4.03 | | all_181_2, all_181_3 gives:
% 23.64/4.04 | | (224) a_select3(z_defuse, all_173_3, tptp_minus_1) = all_181_0 &
% 23.64/4.04 | | a_select3(u_defuse, all_173_3, tptp_minus_1) = all_181_1 & leq(n0,
% 23.64/4.04 | | all_173_3) = all_181_3 & leq(n0, tptp_minus_1) = all_181_2 &
% 23.64/4.04 | | $i(all_181_0) & $i(all_181_1) & ( ~ (all_181_2 = 0) | ~ (all_181_3
% 23.64/4.04 | | = 0) | (all_181_0 = use & all_181_1 = use))
% 23.64/4.04 | |
% 23.64/4.04 | | ALPHA: (224) implies:
% 23.64/4.04 | | (225) leq(n0, all_173_3) = all_181_3
% 23.64/4.04 | |
% 23.64/4.04 | | DELTA: instantiating (223) with fresh symbols all_183_0, all_183_1,
% 23.64/4.04 | | all_183_2, all_183_3, all_183_4 gives:
% 23.64/4.04 | | (226) a_select3(u_defuse, all_173_3, all_173_2) = all_183_0 &
% 23.64/4.04 | | leq(all_173_2, pv5) = all_183_1 & leq(all_173_3, n2) = all_183_2 &
% 23.64/4.04 | | leq(n0, all_173_2) = all_183_3 & leq(n0, all_173_3) = all_183_4 &
% 23.64/4.04 | | $i(all_183_0) & ( ~ (all_183_1 = 0) | ~ (all_183_2 = 0) | ~
% 23.64/4.04 | | (all_183_3 = 0) | ~ (all_183_4 = 0) | (all_183_0 = use &
% 23.64/4.04 | | all_173_0 = use))
% 23.64/4.04 | |
% 23.64/4.04 | | ALPHA: (226) implies:
% 23.64/4.04 | | (227) leq(n0, all_173_3) = all_183_4
% 23.64/4.04 | | (228) leq(n0, all_173_2) = all_183_3
% 23.64/4.04 | | (229) leq(all_173_3, n2) = all_183_2
% 23.64/4.04 | | (230) leq(all_173_2, pv5) = all_183_1
% 23.64/4.04 | | (231) a_select3(u_defuse, all_173_3, all_173_2) = all_183_0
% 23.64/4.04 | | (232) ~ (all_183_1 = 0) | ~ (all_183_2 = 0) | ~ (all_183_3 = 0) | ~
% 23.64/4.04 | | (all_183_4 = 0) | (all_183_0 = use & all_173_0 = use)
% 23.64/4.04 | |
% 23.64/4.04 | | GROUND_INST: instantiating (19) with 0, all_183_4, all_173_3, n0,
% 23.64/4.04 | | simplifying with (215), (227) gives:
% 23.64/4.04 | | (233) all_183_4 = 0
% 23.64/4.04 | |
% 23.64/4.04 | | GROUND_INST: instantiating (19) with all_181_3, all_183_4, all_173_3, n0,
% 23.64/4.04 | | simplifying with (225), (227) gives:
% 23.64/4.04 | | (234) all_183_4 = all_181_3
% 23.64/4.04 | |
% 23.64/4.04 | | GROUND_INST: instantiating (19) with 0, all_183_3, all_173_2, n0,
% 23.64/4.04 | | simplifying with (216), (228) gives:
% 23.64/4.04 | | (235) all_183_3 = 0
% 23.64/4.04 | |
% 23.64/4.04 | | GROUND_INST: instantiating (19) with 0, all_183_2, n2, all_173_3,
% 23.64/4.04 | | simplifying with (217), (229) gives:
% 23.64/4.04 | | (236) all_183_2 = 0
% 23.64/4.04 | |
% 23.64/4.04 | | GROUND_INST: instantiating (19) with 0, all_183_1, pv5, all_173_2,
% 23.64/4.04 | | simplifying with (218), (230) gives:
% 23.64/4.04 | | (237) all_183_1 = 0
% 23.64/4.04 | |
% 23.64/4.04 | | GROUND_INST: instantiating (20) with all_173_1, all_183_0, all_173_2,
% 23.64/4.04 | | all_173_3, u_defuse, simplifying with (219), (231) gives:
% 23.64/4.04 | | (238) all_183_0 = all_173_1
% 23.64/4.04 | |
% 23.64/4.04 | | COMBINE_EQS: (233), (234) imply:
% 23.64/4.04 | | (239) all_181_3 = 0
% 23.64/4.04 | |
% 23.64/4.04 | | BETA: splitting (232) gives:
% 23.64/4.04 | |
% 23.64/4.04 | | Case 1:
% 23.64/4.04 | | |
% 23.64/4.04 | | | (240) ~ (all_183_1 = 0)
% 23.64/4.04 | | |
% 23.64/4.04 | | | REDUCE: (237), (240) imply:
% 23.64/4.04 | | | (241) $false
% 23.64/4.04 | | |
% 23.64/4.04 | | | CLOSE: (241) is inconsistent.
% 23.64/4.04 | | |
% 23.64/4.04 | | Case 2:
% 23.64/4.04 | | |
% 23.64/4.04 | | | (242) ~ (all_183_2 = 0) | ~ (all_183_3 = 0) | ~ (all_183_4 = 0) |
% 23.64/4.04 | | | (all_183_0 = use & all_173_0 = use)
% 23.64/4.04 | | |
% 23.64/4.04 | | | BETA: splitting (242) gives:
% 23.64/4.04 | | |
% 23.64/4.04 | | | Case 1:
% 23.64/4.04 | | | |
% 23.64/4.04 | | | | (243) ~ (all_183_2 = 0)
% 23.64/4.04 | | | |
% 23.64/4.04 | | | | REDUCE: (236), (243) imply:
% 23.64/4.04 | | | | (244) $false
% 23.64/4.04 | | | |
% 23.64/4.04 | | | | CLOSE: (244) is inconsistent.
% 23.64/4.04 | | | |
% 23.64/4.04 | | | Case 2:
% 23.64/4.04 | | | |
% 23.64/4.04 | | | | (245) ~ (all_183_3 = 0) | ~ (all_183_4 = 0) | (all_183_0 = use &
% 23.64/4.04 | | | | all_173_0 = use)
% 23.64/4.04 | | | |
% 23.64/4.04 | | | | BETA: splitting (245) gives:
% 23.64/4.04 | | | |
% 23.64/4.04 | | | | Case 1:
% 23.64/4.04 | | | | |
% 23.64/4.04 | | | | | (246) ~ (all_183_3 = 0)
% 23.64/4.04 | | | | |
% 23.64/4.04 | | | | | REDUCE: (235), (246) imply:
% 23.64/4.04 | | | | | (247) $false
% 23.64/4.04 | | | | |
% 23.64/4.04 | | | | | CLOSE: (247) is inconsistent.
% 23.64/4.04 | | | | |
% 23.64/4.04 | | | | Case 2:
% 23.64/4.04 | | | | |
% 23.64/4.04 | | | | | (248) ~ (all_183_4 = 0) | (all_183_0 = use & all_173_0 = use)
% 23.64/4.04 | | | | |
% 23.64/4.04 | | | | | BETA: splitting (248) gives:
% 23.64/4.04 | | | | |
% 23.64/4.04 | | | | | Case 1:
% 23.64/4.04 | | | | | |
% 23.64/4.04 | | | | | | (249) ~ (all_183_4 = 0)
% 23.64/4.04 | | | | | |
% 23.64/4.04 | | | | | | REDUCE: (233), (249) imply:
% 23.64/4.04 | | | | | | (250) $false
% 23.64/4.04 | | | | | |
% 23.64/4.04 | | | | | | CLOSE: (250) is inconsistent.
% 23.64/4.04 | | | | | |
% 23.64/4.04 | | | | | Case 2:
% 23.64/4.04 | | | | | |
% 23.64/4.04 | | | | | | (251) all_183_0 = use & all_173_0 = use
% 23.64/4.04 | | | | | |
% 23.64/4.04 | | | | | | ALPHA: (251) implies:
% 23.64/4.04 | | | | | | (252) all_173_0 = use
% 23.64/4.04 | | | | | | (253) all_183_0 = use
% 23.64/4.04 | | | | | |
% 23.64/4.04 | | | | | | COMBINE_EQS: (238), (253) imply:
% 23.64/4.04 | | | | | | (254) all_173_1 = use
% 23.64/4.04 | | | | | |
% 23.64/4.04 | | | | | | BETA: splitting (221) gives:
% 23.64/4.04 | | | | | |
% 23.64/4.04 | | | | | | Case 1:
% 23.64/4.04 | | | | | | |
% 23.64/4.04 | | | | | | | (255) ~ (all_173_0 = use)
% 23.64/4.04 | | | | | | |
% 23.64/4.04 | | | | | | | REDUCE: (252), (255) imply:
% 23.64/4.04 | | | | | | | (256) $false
% 23.64/4.04 | | | | | | |
% 23.64/4.04 | | | | | | | CLOSE: (256) is inconsistent.
% 23.64/4.04 | | | | | | |
% 23.64/4.04 | | | | | | Case 2:
% 23.64/4.04 | | | | | | |
% 23.64/4.04 | | | | | | | (257) ~ (all_173_1 = use)
% 23.64/4.04 | | | | | | |
% 23.64/4.04 | | | | | | | REDUCE: (254), (257) imply:
% 23.64/4.04 | | | | | | | (258) $false
% 23.64/4.04 | | | | | | |
% 23.64/4.04 | | | | | | | CLOSE: (258) is inconsistent.
% 23.64/4.04 | | | | | | |
% 23.64/4.04 | | | | | | End of split
% 23.64/4.04 | | | | | |
% 23.64/4.04 | | | | | End of split
% 23.64/4.04 | | | | |
% 23.64/4.04 | | | | End of split
% 23.64/4.04 | | | |
% 23.64/4.04 | | | End of split
% 23.64/4.04 | | |
% 23.64/4.04 | | End of split
% 23.64/4.04 | |
% 23.64/4.04 | End of split
% 23.64/4.04 |
% 23.64/4.04 End of proof
% 23.64/4.04 % SZS output end Proof for theBenchmark
% 23.64/4.04
% 23.64/4.04 3423ms
%------------------------------------------------------------------------------