TSTP Solution File: SWV209+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV209+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 : n010.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 22:55:21 EDT 2023
% Result : Theorem 16.68s 2.93s
% Output : Proof 25.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV209+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 03:24:49 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.43/1.40 Prover 4: Preprocessing ...
% 4.43/1.40 Prover 1: Preprocessing ...
% 5.34/1.44 Prover 2: Preprocessing ...
% 5.34/1.44 Prover 6: Preprocessing ...
% 5.34/1.44 Prover 0: Preprocessing ...
% 5.34/1.44 Prover 3: Preprocessing ...
% 5.34/1.44 Prover 5: Preprocessing ...
% 10.96/2.20 Prover 1: Warning: ignoring some quantifiers
% 11.31/2.23 Prover 3: Warning: ignoring some quantifiers
% 11.55/2.29 Prover 4: Warning: ignoring some quantifiers
% 11.55/2.29 Prover 3: Constructing countermodel ...
% 11.55/2.30 Prover 1: Constructing countermodel ...
% 11.55/2.31 Prover 6: Proving ...
% 12.25/2.35 Prover 4: Constructing countermodel ...
% 12.64/2.42 Prover 5: Proving ...
% 13.59/2.52 Prover 0: Proving ...
% 13.59/2.52 Prover 2: Proving ...
% 16.68/2.93 Prover 6: proved (2287ms)
% 16.68/2.93
% 16.68/2.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.68/2.93
% 16.83/2.94 Prover 3: stopped
% 16.83/2.96 Prover 2: stopped
% 16.83/2.96 Prover 0: stopped
% 16.83/2.96 Prover 5: stopped
% 16.83/2.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 16.83/2.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 16.83/2.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 16.83/2.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 16.83/2.98 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.62/3.21 Prover 7: Preprocessing ...
% 18.62/3.21 Prover 13: Preprocessing ...
% 18.62/3.24 Prover 10: Preprocessing ...
% 18.62/3.26 Prover 8: Preprocessing ...
% 18.62/3.27 Prover 11: Preprocessing ...
% 19.92/3.43 Prover 7: Warning: ignoring some quantifiers
% 19.92/3.43 Prover 10: Warning: ignoring some quantifiers
% 20.51/3.46 Prover 7: Constructing countermodel ...
% 20.51/3.46 Prover 10: Constructing countermodel ...
% 20.82/3.52 Prover 8: Warning: ignoring some quantifiers
% 21.29/3.56 Prover 8: Constructing countermodel ...
% 21.48/3.56 Prover 13: Warning: ignoring some quantifiers
% 21.48/3.60 Prover 11: Warning: ignoring some quantifiers
% 21.48/3.61 Prover 13: Constructing countermodel ...
% 21.48/3.62 Prover 11: Constructing countermodel ...
% 24.20/4.03 Prover 10: Found proof (size 110)
% 24.20/4.03 Prover 10: proved (1072ms)
% 24.20/4.03 Prover 7: stopped
% 24.20/4.03 Prover 11: stopped
% 24.20/4.03 Prover 4: stopped
% 24.20/4.03 Prover 8: stopped
% 24.20/4.03 Prover 13: stopped
% 24.20/4.03 Prover 1: stopped
% 24.20/4.03
% 24.20/4.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.20/4.03
% 24.20/4.05 % SZS output start Proof for theBenchmark
% 25.16/4.06 Assumptions after simplification:
% 25.16/4.06 ---------------------------------
% 25.16/4.06
% 25.16/4.06 (finite_domain_1)
% 25.16/4.06 $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0,
% 25.16/4.06 n1) | ~ leq(n0, v0))
% 25.16/4.06
% 25.16/4.06 (finite_domain_5)
% 25.16/4.06 $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n5 |
% 25.16/4.06 v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n5)
% 25.16/4.06 | ~ leq(n0, v0))
% 25.16/4.06
% 25.16/4.06 (leq_gt2)
% 25.16/4.06 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1)
% 25.16/4.06 | gt(v1, v0))
% 25.16/4.06
% 25.16/4.06 (leq_gt_pred)
% 25.16/4.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~
% 25.16/4.09 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 25.16/4.09 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0,
% 25.16/4.09 v2))
% 25.16/4.09
% 25.16/4.09 (pred_succ)
% 25.16/4.09 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0)
% 25.16/4.09
% 25.16/4.09 (quaternion_ds1_inuse_0020)
% 25.33/4.09 $i(z_defuse) & $i(n998) & $i(xinit_noise_defuse) & $i(xinit_mean_defuse) &
% 25.33/4.09 $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) & $i(rho_defuse) & $i(use)
% 25.33/4.09 & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ? [v0: $i] : ? [v1:
% 25.33/4.09 $i] : ( ~ (v1 = use) & a_select3(u_defuse, n2, n0) = use &
% 25.33/4.09 a_select3(u_defuse, n1, n0) = use & a_select3(u_defuse, n0, n0) = use &
% 25.33/4.09 a_select2(xinit_noise_defuse, v0) = v1 & a_select2(xinit_noise_defuse, n5) =
% 25.33/4.09 use & a_select2(xinit_noise_defuse, n4) = use &
% 25.33/4.09 a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse, n2)
% 25.33/4.09 = use & a_select2(xinit_noise_defuse, n1) = use &
% 25.33/4.09 a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse, n5) =
% 25.33/4.09 use & a_select2(xinit_mean_defuse, n4) = use & a_select2(xinit_mean_defuse,
% 25.33/4.09 n3) = use & a_select2(xinit_mean_defuse, n2) = use &
% 25.33/4.09 a_select2(xinit_mean_defuse, n1) = use & a_select2(xinit_mean_defuse, n0) =
% 25.33/4.09 use & a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use
% 25.33/4.09 & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = use &
% 25.33/4.09 a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) = use &
% 25.33/4.09 a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use &
% 25.33/4.09 a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use &
% 25.33/4.09 a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use & $i(v1) &
% 25.33/4.09 $i(v0) & leq(v0, n5) & leq(n0, v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 25.33/4.09 : (v4 = use | ~ (a_select3(z_defuse, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2)
% 25.33/4.09 | ~ leq(v3, n998) | ~ leq(v2, n2) | ~ leq(n0, v3) | ~ leq(n0, v2)) &
% 25.33/4.09 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = use | ~ (a_select3(u_defuse,
% 25.33/4.09 v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ leq(v3, n998) | ~ leq(v2,
% 25.33/4.09 n2) | ~ leq(n0, v3) | ~ leq(n0, v2)))
% 25.33/4.09
% 25.33/4.09 (successor_1)
% 25.33/4.09 succ(n0) = n1 & $i(n1) & $i(n0)
% 25.33/4.09
% 25.33/4.09 (successor_2)
% 25.33/4.09 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 25.33/4.09
% 25.33/4.09 (successor_3)
% 25.33/4.10 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 &
% 25.33/4.10 succ(n0) = v0 & $i(v1) & $i(v0))
% 25.33/4.10
% 25.33/4.10 (successor_4)
% 25.33/4.10 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 &
% 25.33/4.10 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 25.33/4.10
% 25.33/4.10 (successor_5)
% 25.33/4.10 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 25.33/4.10 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0
% 25.33/4.10 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 25.33/4.10
% 25.33/4.10 (function-axioms)
% 25.33/4.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 25.33/4.10 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 25.33/4.10 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 25.33/4.10 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 25.33/4.10 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 25.33/4.10 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 25.33/4.10 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 25.33/4.10 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 25.33/4.10 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 25.33/4.10 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 25.33/4.10 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 25.33/4.10 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 25.33/4.10 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 25.33/4.10 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 25.33/4.10 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 25.33/4.10 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 25.33/4.10 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 25.33/4.10 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 25.33/4.10 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 25.33/4.10 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 25.33/4.10 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 25.33/4.10 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 25.33/4.10 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 25.33/4.10 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 25.33/4.10 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.33/4.10 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 25.33/4.10 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~
% 25.33/4.10 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 25.33/4.10 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 25.33/4.10 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] :
% 25.33/4.10 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) =
% 25.33/4.10 v0))
% 25.33/4.10
% 25.33/4.10 Further assumptions not needed in the proof:
% 25.33/4.10 --------------------------------------------
% 25.33/4.10 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 25.33/4.10 finite_domain_2, finite_domain_3, finite_domain_4, gt_0_tptp_minus_1, gt_1_0,
% 25.33/4.10 gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2,
% 25.33/4.10 gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0,
% 25.33/4.10 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_998_0, gt_998_1, gt_998_2,
% 25.33/4.10 gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1, gt_succ, irreflexivity_gt,
% 25.33/4.10 leq_geq, leq_gt1, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv,
% 25.33/4.10 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add,
% 25.33/4.10 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 25.33/4.10 matrix_symm_update_diagonal, pred_minus_1, reflexivity_leq, sel2_update_1,
% 25.33/4.10 sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3,
% 25.33/4.10 succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l,
% 25.33/4.10 succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r,
% 25.33/4.10 succ_pred, succ_tptp_minus_1, sum_plus_base, sum_plus_base_float, totality,
% 25.33/4.10 transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi,
% 25.33/4.10 uniform_int_rand_ranges_lo
% 25.33/4.10
% 25.33/4.10 Those formulas are unsatisfiable:
% 25.33/4.10 ---------------------------------
% 25.33/4.10
% 25.33/4.10 Begin of proof
% 25.33/4.10 |
% 25.33/4.11 | ALPHA: (leq_gt_pred) implies:
% 25.33/4.11 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 25.33/4.11 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 25.33/4.11 |
% 25.33/4.11 | ALPHA: (finite_domain_5) implies:
% 25.33/4.11 | (2) ! [v0: $i] : (v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 =
% 25.33/4.11 | n0 | ~ $i(v0) | ~ leq(v0, n5) | ~ leq(n0, v0))
% 25.33/4.11 |
% 25.33/4.11 | ALPHA: (finite_domain_1) implies:
% 25.33/4.11 | (3) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 25.33/4.11 | leq(n0, v0))
% 25.33/4.11 |
% 25.33/4.11 | ALPHA: (successor_4) implies:
% 25.33/4.11 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) =
% 25.33/4.11 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 25.33/4.11 |
% 25.33/4.11 | ALPHA: (successor_5) implies:
% 25.33/4.11 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5
% 25.33/4.11 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 &
% 25.33/4.11 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 25.33/4.11 |
% 25.33/4.11 | ALPHA: (successor_1) implies:
% 25.33/4.11 | (6) succ(n0) = n1
% 25.33/4.11 |
% 25.33/4.11 | ALPHA: (successor_2) implies:
% 25.33/4.11 | (7) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 25.33/4.11 |
% 25.33/4.11 | ALPHA: (successor_3) implies:
% 25.33/4.11 | (8) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) =
% 25.33/4.11 | v0 & $i(v1) & $i(v0))
% 25.33/4.11 |
% 25.33/4.11 | ALPHA: (quaternion_ds1_inuse_0020) implies:
% 25.33/4.11 | (9) $i(n5)
% 25.33/4.11 | (10) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = use) & a_select3(u_defuse, n2,
% 25.33/4.11 | n0) = use & a_select3(u_defuse, n1, n0) = use &
% 25.33/4.11 | a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse,
% 25.33/4.11 | v0) = v1 & a_select2(xinit_noise_defuse, n5) = use &
% 25.33/4.11 | a_select2(xinit_noise_defuse, n4) = use &
% 25.33/4.11 | a_select2(xinit_noise_defuse, n3) = use &
% 25.33/4.11 | a_select2(xinit_noise_defuse, n2) = use &
% 25.33/4.11 | a_select2(xinit_noise_defuse, n1) = use &
% 25.33/4.11 | a_select2(xinit_noise_defuse, n0) = use &
% 25.33/4.11 | a_select2(xinit_mean_defuse, n5) = use &
% 25.33/4.11 | a_select2(xinit_mean_defuse, n4) = use &
% 25.33/4.11 | a_select2(xinit_mean_defuse, n3) = use &
% 25.33/4.11 | a_select2(xinit_mean_defuse, n2) = use &
% 25.33/4.11 | a_select2(xinit_mean_defuse, n1) = use &
% 25.33/4.11 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5)
% 25.33/4.11 | = use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse,
% 25.33/4.11 | n3) = use & a_select2(sigma_defuse, n5) = use &
% 25.33/4.11 | a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) =
% 25.33/4.11 | use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse,
% 25.33/4.11 | n1) = use & a_select2(sigma_defuse, n0) = use &
% 25.33/4.11 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 25.33/4.11 | a_select2(rho_defuse, n0) = use & $i(v1) & $i(v0) & leq(v0, n5) &
% 25.33/4.11 | leq(n0, v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = use |
% 25.33/4.11 | ~ (a_select3(z_defuse, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 25.33/4.11 | leq(v3, n998) | ~ leq(v2, n2) | ~ leq(n0, v3) | ~ leq(n0, v2))
% 25.33/4.11 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = use | ~
% 25.33/4.11 | (a_select3(u_defuse, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 25.33/4.11 | leq(v3, n998) | ~ leq(v2, n2) | ~ leq(n0, v3) | ~ leq(n0, v2)))
% 25.33/4.11 |
% 25.33/4.11 | ALPHA: (function-axioms) implies:
% 25.33/4.11 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) =
% 25.33/4.11 | v1) | ~ (succ(v2) = v0))
% 25.33/4.12 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.33/4.12 | (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0))
% 25.33/4.12 |
% 25.33/4.12 | DELTA: instantiating (7) with fresh symbol all_54_0 gives:
% 25.33/4.12 | (13) succ(all_54_0) = n2 & succ(n0) = all_54_0 & $i(all_54_0)
% 25.33/4.12 |
% 25.33/4.12 | ALPHA: (13) implies:
% 25.33/4.12 | (14) $i(all_54_0)
% 25.33/4.12 | (15) succ(n0) = all_54_0
% 25.33/4.12 | (16) succ(all_54_0) = n2
% 25.33/4.12 |
% 25.33/4.12 | DELTA: instantiating (8) with fresh symbols all_56_0, all_56_1 gives:
% 25.33/4.12 | (17) succ(all_56_0) = n3 & succ(all_56_1) = all_56_0 & succ(n0) = all_56_1
% 25.33/4.12 | & $i(all_56_0) & $i(all_56_1)
% 25.33/4.12 |
% 25.33/4.12 | ALPHA: (17) implies:
% 25.33/4.12 | (18) $i(all_56_0)
% 25.33/4.12 | (19) succ(n0) = all_56_1
% 25.33/4.12 | (20) succ(all_56_1) = all_56_0
% 25.33/4.12 | (21) succ(all_56_0) = n3
% 25.33/4.12 |
% 25.33/4.12 | DELTA: instantiating (4) with fresh symbols all_59_0, all_59_1, all_59_2
% 25.33/4.12 | gives:
% 25.33/4.12 | (22) succ(all_59_0) = n4 & succ(all_59_1) = all_59_0 & succ(all_59_2) =
% 25.33/4.12 | all_59_1 & succ(n0) = all_59_2 & $i(all_59_0) & $i(all_59_1) &
% 25.33/4.12 | $i(all_59_2)
% 25.33/4.12 |
% 25.33/4.12 | ALPHA: (22) implies:
% 25.33/4.12 | (23) $i(all_59_0)
% 25.33/4.12 | (24) succ(n0) = all_59_2
% 25.33/4.12 | (25) succ(all_59_2) = all_59_1
% 25.33/4.12 | (26) succ(all_59_1) = all_59_0
% 25.33/4.12 | (27) succ(all_59_0) = n4
% 25.33/4.12 |
% 25.33/4.12 | DELTA: instantiating (5) with fresh symbols all_61_0, all_61_1, all_61_2,
% 25.33/4.12 | all_61_3 gives:
% 25.33/4.12 | (28) succ(all_61_0) = n5 & succ(all_61_1) = all_61_0 & succ(all_61_2) =
% 25.33/4.12 | all_61_1 & succ(all_61_3) = all_61_2 & succ(n0) = all_61_3 &
% 25.33/4.12 | $i(all_61_0) & $i(all_61_1) & $i(all_61_2) & $i(all_61_3)
% 25.33/4.12 |
% 25.33/4.12 | ALPHA: (28) implies:
% 25.33/4.12 | (29) $i(all_61_0)
% 25.33/4.12 | (30) succ(n0) = all_61_3
% 25.33/4.12 | (31) succ(all_61_3) = all_61_2
% 25.33/4.12 | (32) succ(all_61_2) = all_61_1
% 25.33/4.12 | (33) succ(all_61_1) = all_61_0
% 25.33/4.12 | (34) succ(all_61_0) = n5
% 25.33/4.12 |
% 25.33/4.12 | DELTA: instantiating (10) with fresh symbols all_69_0, all_69_1 gives:
% 25.33/4.12 | (35) ~ (all_69_0 = use) & a_select3(u_defuse, n2, n0) = use &
% 25.33/4.12 | a_select3(u_defuse, n1, n0) = use & a_select3(u_defuse, n0, n0) = use
% 25.33/4.12 | & a_select2(xinit_noise_defuse, all_69_1) = all_69_0 &
% 25.33/4.12 | a_select2(xinit_noise_defuse, n5) = use &
% 25.33/4.12 | a_select2(xinit_noise_defuse, n4) = use &
% 25.33/4.12 | a_select2(xinit_noise_defuse, n3) = use &
% 25.33/4.12 | a_select2(xinit_noise_defuse, n2) = use &
% 25.33/4.12 | a_select2(xinit_noise_defuse, n1) = use &
% 25.33/4.12 | a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse,
% 25.33/4.12 | n5) = use & a_select2(xinit_mean_defuse, n4) = use &
% 25.33/4.12 | a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 25.33/4.12 | n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 25.33/4.12 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) =
% 25.33/4.12 | use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3)
% 25.33/4.12 | = use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse,
% 25.33/4.12 | n4) = use & a_select2(sigma_defuse, n3) = use &
% 25.33/4.12 | a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use
% 25.33/4.12 | & a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use
% 25.33/4.12 | & a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use &
% 25.33/4.12 | $i(all_69_0) & $i(all_69_1) & leq(all_69_1, n5) & leq(n0, all_69_1) &
% 25.33/4.12 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = use | ~
% 25.33/4.12 | (a_select3(z_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 25.33/4.12 | leq(v1, n998) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0)) &
% 25.33/4.12 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = use | ~
% 25.33/4.12 | (a_select3(u_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 25.33/4.12 | leq(v1, n998) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0))
% 25.33/4.12 |
% 25.33/4.12 | ALPHA: (35) implies:
% 25.33/4.12 | (36) ~ (all_69_0 = use)
% 25.33/4.12 | (37) leq(n0, all_69_1)
% 25.33/4.12 | (38) leq(all_69_1, n5)
% 25.33/4.12 | (39) $i(all_69_1)
% 25.33/4.13 | (40) a_select2(xinit_noise_defuse, n0) = use
% 25.33/4.13 | (41) a_select2(xinit_noise_defuse, n1) = use
% 25.33/4.13 | (42) a_select2(xinit_noise_defuse, n2) = use
% 25.33/4.13 | (43) a_select2(xinit_noise_defuse, n3) = use
% 25.33/4.13 | (44) a_select2(xinit_noise_defuse, n4) = use
% 25.33/4.13 | (45) a_select2(xinit_noise_defuse, n5) = use
% 25.33/4.13 | (46) a_select2(xinit_noise_defuse, all_69_1) = all_69_0
% 25.33/4.13 |
% 25.33/4.13 | GROUND_INST: instantiating (11) with all_56_1, all_59_2, n0, simplifying with
% 25.33/4.13 | (19), (24) gives:
% 25.33/4.13 | (47) all_59_2 = all_56_1
% 25.33/4.13 |
% 25.33/4.13 | GROUND_INST: instantiating (11) with all_54_0, all_59_2, n0, simplifying with
% 25.33/4.13 | (15), (24) gives:
% 25.33/4.13 | (48) all_59_2 = all_54_0
% 25.33/4.13 |
% 25.33/4.13 | GROUND_INST: instantiating (11) with all_56_1, all_61_3, n0, simplifying with
% 25.33/4.13 | (19), (30) gives:
% 25.33/4.13 | (49) all_61_3 = all_56_1
% 25.33/4.13 |
% 25.33/4.13 | GROUND_INST: instantiating (11) with n1, all_61_3, n0, simplifying with (6),
% 25.33/4.13 | (30) gives:
% 25.33/4.13 | (50) all_61_3 = n1
% 25.33/4.13 |
% 25.33/4.13 | COMBINE_EQS: (49), (50) imply:
% 25.33/4.13 | (51) all_56_1 = n1
% 25.33/4.13 |
% 25.33/4.13 | SIMP: (51) implies:
% 25.33/4.13 | (52) all_56_1 = n1
% 25.33/4.13 |
% 25.33/4.13 | COMBINE_EQS: (47), (48) imply:
% 25.33/4.13 | (53) all_56_1 = all_54_0
% 25.33/4.13 |
% 25.33/4.13 | SIMP: (53) implies:
% 25.33/4.13 | (54) all_56_1 = all_54_0
% 25.33/4.13 |
% 25.33/4.13 | COMBINE_EQS: (52), (54) imply:
% 25.33/4.13 | (55) all_54_0 = n1
% 25.33/4.13 |
% 25.33/4.13 | COMBINE_EQS: (48), (55) imply:
% 25.33/4.13 | (56) all_59_2 = n1
% 25.33/4.13 |
% 25.33/4.13 | REDUCE: (31), (50) imply:
% 25.33/4.13 | (57) succ(n1) = all_61_2
% 25.33/4.13 |
% 25.33/4.13 | REDUCE: (25), (56) imply:
% 25.33/4.13 | (58) succ(n1) = all_59_1
% 25.33/4.13 |
% 25.33/4.13 | REDUCE: (20), (52) imply:
% 25.33/4.13 | (59) succ(n1) = all_56_0
% 25.33/4.13 |
% 25.33/4.13 | REDUCE: (16), (55) imply:
% 25.33/4.13 | (60) succ(n1) = n2
% 25.33/4.13 |
% 25.33/4.13 | REDUCE: (14), (55) imply:
% 25.33/4.13 | (61) $i(n1)
% 25.33/4.13 |
% 25.33/4.13 | GROUND_INST: instantiating (11) with all_56_0, all_59_1, n1, simplifying with
% 25.33/4.13 | (58), (59) gives:
% 25.33/4.13 | (62) all_59_1 = all_56_0
% 25.33/4.13 |
% 25.33/4.13 | GROUND_INST: instantiating (11) with all_59_1, all_61_2, n1, simplifying with
% 25.33/4.13 | (57), (58) gives:
% 25.33/4.13 | (63) all_61_2 = all_59_1
% 25.33/4.13 |
% 25.33/4.13 | GROUND_INST: instantiating (11) with n2, all_61_2, n1, simplifying with (57),
% 25.33/4.13 | (60) gives:
% 25.33/4.13 | (64) all_61_2 = n2
% 25.33/4.13 |
% 25.33/4.13 | COMBINE_EQS: (63), (64) imply:
% 25.33/4.13 | (65) all_59_1 = n2
% 25.33/4.13 |
% 25.33/4.13 | SIMP: (65) implies:
% 25.33/4.13 | (66) all_59_1 = n2
% 25.33/4.13 |
% 25.33/4.13 | COMBINE_EQS: (62), (66) imply:
% 25.33/4.13 | (67) all_56_0 = n2
% 25.33/4.13 |
% 25.33/4.13 | SIMP: (67) implies:
% 25.33/4.13 | (68) all_56_0 = n2
% 25.33/4.13 |
% 25.55/4.13 | REDUCE: (32), (64) imply:
% 25.55/4.13 | (69) succ(n2) = all_61_1
% 25.55/4.13 |
% 25.55/4.13 | REDUCE: (26), (66) imply:
% 25.55/4.13 | (70) succ(n2) = all_59_0
% 25.55/4.13 |
% 25.55/4.13 | REDUCE: (21), (68) imply:
% 25.55/4.13 | (71) succ(n2) = n3
% 25.55/4.13 |
% 25.55/4.13 | REDUCE: (18), (68) imply:
% 25.55/4.13 | (72) $i(n2)
% 25.55/4.13 |
% 25.55/4.13 | GROUND_INST: instantiating (11) with all_59_0, all_61_1, n2, simplifying with
% 25.55/4.13 | (69), (70) gives:
% 25.55/4.13 | (73) all_61_1 = all_59_0
% 25.55/4.13 |
% 25.55/4.13 | GROUND_INST: instantiating (11) with n3, all_61_1, n2, simplifying with (69),
% 25.55/4.13 | (71) gives:
% 25.55/4.13 | (74) all_61_1 = n3
% 25.55/4.13 |
% 25.55/4.13 | COMBINE_EQS: (73), (74) imply:
% 25.55/4.13 | (75) all_59_0 = n3
% 25.55/4.13 |
% 25.55/4.13 | SIMP: (75) implies:
% 25.55/4.13 | (76) all_59_0 = n3
% 25.55/4.13 |
% 25.55/4.13 | REDUCE: (33), (74) imply:
% 25.55/4.13 | (77) succ(n3) = all_61_0
% 25.55/4.13 |
% 25.55/4.13 | REDUCE: (27), (76) imply:
% 25.55/4.13 | (78) succ(n3) = n4
% 25.55/4.13 |
% 25.55/4.13 | REDUCE: (23), (76) imply:
% 25.55/4.14 | (79) $i(n3)
% 25.55/4.14 |
% 25.55/4.14 | GROUND_INST: instantiating (11) with n4, all_61_0, n3, simplifying with (77),
% 25.55/4.14 | (78) gives:
% 25.55/4.14 | (80) all_61_0 = n4
% 25.55/4.14 |
% 25.55/4.14 | REDUCE: (34), (80) imply:
% 25.55/4.14 | (81) succ(n4) = n5
% 25.55/4.14 |
% 25.55/4.14 | REDUCE: (29), (80) imply:
% 25.55/4.14 | (82) $i(n4)
% 25.55/4.14 |
% 25.55/4.14 | GROUND_INST: instantiating (2) with all_69_1, simplifying with (37), (38),
% 25.55/4.14 | (39) gives:
% 25.55/4.14 | (83) all_69_1 = n5 | all_69_1 = n4 | all_69_1 = n3 | all_69_1 = n2 |
% 25.55/4.14 | all_69_1 = n1 | all_69_1 = n0
% 25.55/4.14 |
% 25.55/4.14 | GROUND_INST: instantiating (leq_gt2) with all_69_1, n5, simplifying with (9),
% 25.55/4.14 | (38), (39) gives:
% 25.55/4.14 | (84) all_69_1 = n5 | gt(n5, all_69_1)
% 25.55/4.14 |
% 25.55/4.14 | GROUND_INST: instantiating (pred_succ) with n1, n2, simplifying with (60),
% 25.55/4.14 | (61) gives:
% 25.55/4.14 | (85) pred(n2) = n1
% 25.55/4.14 |
% 25.55/4.14 | GROUND_INST: instantiating (pred_succ) with n2, n3, simplifying with (71),
% 25.55/4.14 | (72) gives:
% 25.55/4.14 | (86) pred(n3) = n2
% 25.55/4.14 |
% 25.55/4.14 | GROUND_INST: instantiating (pred_succ) with n3, n4, simplifying with (78),
% 25.55/4.14 | (79) gives:
% 25.55/4.14 | (87) pred(n4) = n3
% 25.55/4.14 |
% 25.55/4.14 | GROUND_INST: instantiating (pred_succ) with n4, n5, simplifying with (81),
% 25.55/4.14 | (82) gives:
% 25.55/4.14 | (88) pred(n5) = n4
% 25.55/4.14 |
% 25.55/4.14 | BETA: splitting (84) gives:
% 25.55/4.14 |
% 25.55/4.14 | Case 1:
% 25.55/4.14 | |
% 25.55/4.14 | | (89) gt(n5, all_69_1)
% 25.55/4.14 | |
% 25.55/4.14 | | GROUND_INST: instantiating (1) with all_69_1, n5, n4, simplifying with (9),
% 25.55/4.14 | | (39), (88), (89) gives:
% 25.55/4.14 | | (90) leq(all_69_1, n4)
% 25.55/4.14 | |
% 25.55/4.14 | | GROUND_INST: instantiating (leq_gt2) with all_69_1, n4, simplifying with
% 25.55/4.14 | | (39), (82), (90) gives:
% 25.55/4.14 | | (91) all_69_1 = n4 | gt(n4, all_69_1)
% 25.55/4.14 | |
% 25.55/4.14 | | BETA: splitting (83) gives:
% 25.55/4.14 | |
% 25.55/4.14 | | Case 1:
% 25.55/4.14 | | |
% 25.55/4.14 | | | (92) all_69_1 = n0
% 25.55/4.14 | | |
% 25.55/4.14 | | | REDUCE: (46), (92) imply:
% 25.55/4.14 | | | (93) a_select2(xinit_noise_defuse, n0) = all_69_0
% 25.55/4.14 | | |
% 25.55/4.14 | | | GROUND_INST: instantiating (12) with use, all_69_0, n0,
% 25.55/4.14 | | | xinit_noise_defuse, simplifying with (40), (93) gives:
% 25.55/4.14 | | | (94) all_69_0 = use
% 25.55/4.14 | | |
% 25.60/4.14 | | | REDUCE: (36), (94) imply:
% 25.60/4.14 | | | (95) $false
% 25.60/4.14 | | |
% 25.60/4.14 | | | CLOSE: (95) is inconsistent.
% 25.60/4.14 | | |
% 25.60/4.14 | | Case 2:
% 25.60/4.14 | | |
% 25.60/4.14 | | | (96) ~ (all_69_1 = n0)
% 25.60/4.14 | | |
% 25.60/4.14 | | | BETA: splitting (91) gives:
% 25.60/4.14 | | |
% 25.60/4.14 | | | Case 1:
% 25.60/4.14 | | | |
% 25.60/4.14 | | | | (97) gt(n4, all_69_1)
% 25.60/4.14 | | | |
% 25.60/4.14 | | | | GROUND_INST: instantiating (1) with all_69_1, n4, n3, simplifying with
% 25.60/4.14 | | | | (39), (82), (87), (97) gives:
% 25.60/4.14 | | | | (98) leq(all_69_1, n3)
% 25.60/4.14 | | | |
% 25.60/4.14 | | | | GROUND_INST: instantiating (leq_gt2) with all_69_1, n3, simplifying with
% 25.60/4.14 | | | | (39), (79), (98) gives:
% 25.60/4.14 | | | | (99) all_69_1 = n3 | gt(n3, all_69_1)
% 25.60/4.14 | | | |
% 25.60/4.14 | | | | BETA: splitting (99) gives:
% 25.60/4.14 | | | |
% 25.60/4.14 | | | | Case 1:
% 25.60/4.14 | | | | |
% 25.60/4.14 | | | | | (100) gt(n3, all_69_1)
% 25.60/4.14 | | | | |
% 25.60/4.15 | | | | | GROUND_INST: instantiating (1) with all_69_1, n3, n2, simplifying with
% 25.60/4.15 | | | | | (39), (79), (86), (100) gives:
% 25.60/4.15 | | | | | (101) leq(all_69_1, n2)
% 25.60/4.15 | | | | |
% 25.60/4.15 | | | | | GROUND_INST: instantiating (leq_gt2) with all_69_1, n2, simplifying
% 25.60/4.15 | | | | | with (39), (72), (101) gives:
% 25.60/4.15 | | | | | (102) all_69_1 = n2 | gt(n2, all_69_1)
% 25.60/4.15 | | | | |
% 25.60/4.15 | | | | | BETA: splitting (102) gives:
% 25.60/4.15 | | | | |
% 25.60/4.15 | | | | | Case 1:
% 25.60/4.15 | | | | | |
% 25.60/4.15 | | | | | | (103) gt(n2, all_69_1)
% 25.60/4.15 | | | | | |
% 25.60/4.15 | | | | | | GROUND_INST: instantiating (1) with all_69_1, n2, n1, simplifying
% 25.60/4.15 | | | | | | with (39), (72), (85), (103) gives:
% 25.60/4.15 | | | | | | (104) leq(all_69_1, n1)
% 25.60/4.15 | | | | | |
% 25.60/4.15 | | | | | | GROUND_INST: instantiating (3) with all_69_1, simplifying with (37),
% 25.60/4.15 | | | | | | (39), (104) gives:
% 25.60/4.15 | | | | | | (105) all_69_1 = n1 | all_69_1 = n0
% 25.60/4.15 | | | | | |
% 25.60/4.15 | | | | | | BETA: splitting (105) gives:
% 25.60/4.15 | | | | | |
% 25.60/4.15 | | | | | | Case 1:
% 25.60/4.15 | | | | | | |
% 25.60/4.15 | | | | | | | (106) all_69_1 = n0
% 25.60/4.15 | | | | | | |
% 25.60/4.15 | | | | | | | REDUCE: (96), (106) imply:
% 25.60/4.15 | | | | | | | (107) $false
% 25.60/4.15 | | | | | | |
% 25.60/4.15 | | | | | | | CLOSE: (107) is inconsistent.
% 25.60/4.15 | | | | | | |
% 25.60/4.15 | | | | | | Case 2:
% 25.60/4.15 | | | | | | |
% 25.60/4.15 | | | | | | | (108) all_69_1 = n1
% 25.60/4.15 | | | | | | |
% 25.60/4.15 | | | | | | | REDUCE: (46), (108) imply:
% 25.60/4.15 | | | | | | | (109) a_select2(xinit_noise_defuse, n1) = all_69_0
% 25.60/4.15 | | | | | | |
% 25.60/4.15 | | | | | | | GROUND_INST: instantiating (12) with use, all_69_0, n1,
% 25.60/4.15 | | | | | | | xinit_noise_defuse, simplifying with (41), (109)
% 25.60/4.15 | | | | | | | gives:
% 25.60/4.15 | | | | | | | (110) all_69_0 = use
% 25.60/4.15 | | | | | | |
% 25.60/4.15 | | | | | | | REDUCE: (36), (110) imply:
% 25.60/4.15 | | | | | | | (111) $false
% 25.60/4.15 | | | | | | |
% 25.60/4.15 | | | | | | | CLOSE: (111) is inconsistent.
% 25.60/4.15 | | | | | | |
% 25.60/4.15 | | | | | | End of split
% 25.60/4.15 | | | | | |
% 25.60/4.15 | | | | | Case 2:
% 25.60/4.15 | | | | | |
% 25.60/4.15 | | | | | | (112) all_69_1 = n2
% 25.60/4.15 | | | | | |
% 25.60/4.15 | | | | | | REDUCE: (46), (112) imply:
% 25.60/4.15 | | | | | | (113) a_select2(xinit_noise_defuse, n2) = all_69_0
% 25.60/4.15 | | | | | |
% 25.60/4.15 | | | | | | GROUND_INST: instantiating (12) with use, all_69_0, n2,
% 25.60/4.15 | | | | | | xinit_noise_defuse, simplifying with (42), (113) gives:
% 25.60/4.15 | | | | | | (114) all_69_0 = use
% 25.60/4.15 | | | | | |
% 25.60/4.15 | | | | | | REDUCE: (36), (114) imply:
% 25.60/4.15 | | | | | | (115) $false
% 25.60/4.15 | | | | | |
% 25.60/4.15 | | | | | | CLOSE: (115) is inconsistent.
% 25.60/4.15 | | | | | |
% 25.60/4.15 | | | | | End of split
% 25.60/4.15 | | | | |
% 25.60/4.15 | | | | Case 2:
% 25.60/4.15 | | | | |
% 25.60/4.15 | | | | | (116) all_69_1 = n3
% 25.60/4.15 | | | | |
% 25.60/4.15 | | | | | REDUCE: (46), (116) imply:
% 25.60/4.15 | | | | | (117) a_select2(xinit_noise_defuse, n3) = all_69_0
% 25.60/4.15 | | | | |
% 25.60/4.15 | | | | | GROUND_INST: instantiating (12) with use, all_69_0, n3,
% 25.60/4.15 | | | | | xinit_noise_defuse, simplifying with (43), (117) gives:
% 25.60/4.15 | | | | | (118) all_69_0 = use
% 25.60/4.15 | | | | |
% 25.60/4.15 | | | | | REDUCE: (36), (118) imply:
% 25.60/4.15 | | | | | (119) $false
% 25.60/4.15 | | | | |
% 25.60/4.15 | | | | | CLOSE: (119) is inconsistent.
% 25.60/4.15 | | | | |
% 25.60/4.15 | | | | End of split
% 25.60/4.15 | | | |
% 25.60/4.15 | | | Case 2:
% 25.60/4.15 | | | |
% 25.60/4.15 | | | | (120) all_69_1 = n4
% 25.60/4.15 | | | |
% 25.60/4.15 | | | | REDUCE: (46), (120) imply:
% 25.60/4.15 | | | | (121) a_select2(xinit_noise_defuse, n4) = all_69_0
% 25.60/4.15 | | | |
% 25.60/4.15 | | | | GROUND_INST: instantiating (12) with use, all_69_0, n4,
% 25.60/4.15 | | | | xinit_noise_defuse, simplifying with (44), (121) gives:
% 25.60/4.15 | | | | (122) all_69_0 = use
% 25.60/4.15 | | | |
% 25.60/4.15 | | | | REDUCE: (36), (122) imply:
% 25.60/4.15 | | | | (123) $false
% 25.60/4.15 | | | |
% 25.60/4.15 | | | | CLOSE: (123) is inconsistent.
% 25.60/4.15 | | | |
% 25.60/4.15 | | | End of split
% 25.60/4.15 | | |
% 25.60/4.15 | | End of split
% 25.60/4.15 | |
% 25.60/4.15 | Case 2:
% 25.60/4.15 | |
% 25.60/4.15 | | (124) all_69_1 = n5
% 25.60/4.15 | |
% 25.60/4.15 | | REDUCE: (46), (124) imply:
% 25.60/4.15 | | (125) a_select2(xinit_noise_defuse, n5) = all_69_0
% 25.60/4.15 | |
% 25.60/4.15 | | GROUND_INST: instantiating (12) with use, all_69_0, n5, xinit_noise_defuse,
% 25.60/4.15 | | simplifying with (45), (125) gives:
% 25.60/4.15 | | (126) all_69_0 = use
% 25.60/4.15 | |
% 25.60/4.15 | | REDUCE: (36), (126) imply:
% 25.60/4.15 | | (127) $false
% 25.60/4.15 | |
% 25.60/4.15 | | CLOSE: (127) is inconsistent.
% 25.60/4.15 | |
% 25.60/4.15 | End of split
% 25.60/4.15 |
% 25.60/4.15 End of proof
% 25.60/4.15 % SZS output end Proof for theBenchmark
% 25.60/4.15
% 25.60/4.15 3535ms
%------------------------------------------------------------------------------