TSTP Solution File: SWV205+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV205+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 : n008.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 22:55:20 EDT 2023
% Result : Theorem 17.09s 3.05s
% Output : Proof 25.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV205+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n008.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 09:28:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 ________ _____
% 0.20/0.58 ___ __ \_________(_)________________________________
% 0.20/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.58 (2023-06-19)
% 0.20/0.58
% 0.20/0.58 (c) Philipp Rümmer, 2009-2023
% 0.20/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.58 Amanda Stjerna.
% 0.20/0.58 Free software under BSD-3-Clause.
% 0.20/0.58
% 0.20/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.58
% 0.20/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.59 Running up to 7 provers in parallel.
% 0.20/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.62/1.37 Prover 4: Preprocessing ...
% 4.62/1.37 Prover 1: Preprocessing ...
% 5.04/1.42 Prover 0: Preprocessing ...
% 5.04/1.42 Prover 2: Preprocessing ...
% 5.04/1.42 Prover 5: Preprocessing ...
% 5.04/1.42 Prover 6: Preprocessing ...
% 5.04/1.42 Prover 3: Preprocessing ...
% 9.92/2.15 Prover 1: Warning: ignoring some quantifiers
% 9.92/2.23 Prover 1: Constructing countermodel ...
% 10.83/2.27 Prover 3: Warning: ignoring some quantifiers
% 11.47/2.30 Prover 3: Constructing countermodel ...
% 11.47/2.31 Prover 6: Proving ...
% 11.89/2.36 Prover 4: Warning: ignoring some quantifiers
% 12.56/2.46 Prover 4: Constructing countermodel ...
% 12.56/2.49 Prover 0: Proving ...
% 12.56/2.53 Prover 5: Proving ...
% 13.24/2.58 Prover 2: Proving ...
% 16.82/3.05 Prover 6: proved (2442ms)
% 16.82/3.05
% 17.09/3.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.09/3.05
% 17.09/3.05 Prover 3: stopped
% 17.09/3.06 Prover 0: stopped
% 17.09/3.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.09/3.06 Prover 5: stopped
% 17.09/3.07 Prover 2: stopped
% 17.09/3.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.09/3.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 17.09/3.08 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 17.09/3.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.55/3.29 Prover 7: Preprocessing ...
% 18.55/3.29 Prover 11: Preprocessing ...
% 18.55/3.30 Prover 8: Preprocessing ...
% 18.55/3.30 Prover 10: Preprocessing ...
% 18.98/3.32 Prover 13: Preprocessing ...
% 19.95/3.46 Prover 7: Warning: ignoring some quantifiers
% 19.95/3.47 Prover 10: Warning: ignoring some quantifiers
% 19.95/3.49 Prover 7: Constructing countermodel ...
% 19.95/3.51 Prover 10: Constructing countermodel ...
% 19.95/3.57 Prover 8: Warning: ignoring some quantifiers
% 19.95/3.57 Prover 11: Warning: ignoring some quantifiers
% 20.69/3.62 Prover 8: Constructing countermodel ...
% 20.69/3.64 Prover 11: Constructing countermodel ...
% 21.60/3.68 Prover 13: Warning: ignoring some quantifiers
% 21.73/3.70 Prover 13: Constructing countermodel ...
% 24.40/4.09 Prover 1: Found proof (size 98)
% 24.40/4.09 Prover 1: proved (3492ms)
% 24.40/4.09 Prover 7: stopped
% 24.40/4.09 Prover 13: stopped
% 24.40/4.09 Prover 8: stopped
% 24.40/4.10 Prover 11: stopped
% 24.40/4.10 Prover 10: stopped
% 24.40/4.10 Prover 4: stopped
% 24.40/4.10
% 24.40/4.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.40/4.10
% 24.40/4.11 % SZS output start Proof for theBenchmark
% 24.40/4.11 Assumptions after simplification:
% 24.40/4.11 ---------------------------------
% 24.40/4.12
% 24.40/4.12 (finite_domain_0)
% 24.40/4.14 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 24.40/4.14 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 24.40/4.14
% 24.40/4.14 (finite_domain_5)
% 24.40/4.14 $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n5 |
% 24.40/4.14 v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n5) = 0) | ~
% 24.40/4.14 $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1))
% 24.40/4.14
% 24.40/4.14 (leq_gt2)
% 24.40/4.14 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (gt(v1, v0)
% 24.40/4.14 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1)
% 24.40/4.14 = v3))
% 24.40/4.14
% 24.40/4.14 (leq_gt_pred)
% 24.40/4.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 24.40/4.15 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 24.40/4.15 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : !
% 24.40/4.15 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)
% 24.40/4.15 | gt(v1, v0) = 0)
% 24.40/4.15
% 24.40/4.15 (pred_succ)
% 24.40/4.15 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0)
% 24.40/4.15
% 24.40/4.15 (quaternion_ds1_inuse_0016)
% 24.40/4.16 a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 24.40/4.16 a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = use &
% 24.40/4.16 a_select2(xinit_noise_defuse, n4) = use & a_select2(xinit_noise_defuse, n3) =
% 24.40/4.16 use & a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse,
% 24.40/4.16 n1) = use & a_select2(xinit_noise_defuse, n0) = use &
% 24.40/4.16 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) =
% 24.40/4.16 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 24.40/4.16 n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 24.40/4.16 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use &
% 24.40/4.16 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use &
% 24.40/4.16 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use &
% 24.40/4.16 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use &
% 24.40/4.16 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use &
% 24.40/4.16 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 24.40/4.16 a_select2(rho_defuse, n0) = use & $i(z_defuse) & $i(n998) &
% 24.40/4.16 $i(xinit_noise_defuse) & $i(xinit_mean_defuse) & $i(xinit_defuse) &
% 24.40/4.16 $i(u_defuse) & $i(sigma_defuse) & $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) &
% 24.40/4.16 $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 24.40/4.16 (v2 = use | ~ (a_select3(z_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.40/4.16 [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] : (leq(v1, n998) = v6
% 24.40/4.16 & leq(v0, n2) = v5 & leq(n0, v1) = v4 & leq(n0, v0) = v3 & ( ~ (v6 = 0) |
% 24.40/4.16 ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] :
% 24.40/4.16 ! [v2: $i] : (v2 = use | ~ (a_select3(u_defuse, v0, v1) = v2) | ~ $i(v1) |
% 24.40/4.16 ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 24.40/4.16 (leq(v1, n998) = v6 & leq(v0, n2) = v5 & leq(n0, v1) = v4 & leq(n0, v0) = v3
% 24.40/4.16 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0)))) & ? [v0: $i]
% 24.40/4.16 : ? [v1: $i] : ( ~ (v1 = use) & a_select2(sigma_defuse, v0) = v1 & leq(v0,
% 24.40/4.16 n5) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0))
% 24.40/4.16
% 24.40/4.16 (successor_1)
% 24.40/4.16 succ(n0) = n1 & $i(n1) & $i(n0)
% 24.40/4.16
% 24.40/4.16 (successor_2)
% 24.40/4.16 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 24.40/4.16
% 24.40/4.16 (successor_3)
% 24.40/4.17 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 &
% 24.40/4.17 succ(n0) = v0 & $i(v1) & $i(v0))
% 24.40/4.17
% 24.40/4.17 (successor_4)
% 24.40/4.17 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 &
% 24.40/4.17 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 24.40/4.17
% 24.40/4.17 (successor_5)
% 24.40/4.17 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 24.40/4.17 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0
% 24.40/4.17 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 24.40/4.17
% 24.40/4.17 (function-axioms)
% 24.40/4.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 24.40/4.18 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 24.40/4.18 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 24.40/4.18 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 24.40/4.18 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 24.40/4.18 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 24.40/4.18 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 24.40/4.18 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 24.40/4.18 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 24.40/4.18 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 24.40/4.18 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 24.40/4.18 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 24.40/4.18 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 24.40/4.18 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 24.40/4.18 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 24.40/4.18 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 24.40/4.18 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 24.40/4.18 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 24.40/4.18 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 24.40/4.18 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 24.40/4.18 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 24.40/4.18 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 24.40/4.18 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 24.40/4.18 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 24.40/4.18 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.40/4.18 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 24.40/4.18 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 24.40/4.18 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 24.40/4.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.40/4.18 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 24.40/4.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.40/4.18 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 24.40/4.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.40/4.18 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 24.40/4.18 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 24.40/4.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 24.40/4.18 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 24.40/4.18 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 24.40/4.18 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 24.40/4.18
% 24.40/4.18 Further assumptions not needed in the proof:
% 24.40/4.18 --------------------------------------------
% 24.40/4.18 const_array1_select, const_array2_select, defuse, finite_domain_1,
% 24.40/4.18 finite_domain_2, finite_domain_3, finite_domain_4, gt_0_tptp_minus_1, gt_1_0,
% 24.40/4.18 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,
% 24.40/4.18 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,
% 24.40/4.18 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,
% 24.40/4.18 gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1, gt_succ, irreflexivity_gt,
% 24.40/4.18 leq_geq, leq_gt1, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv,
% 24.40/4.18 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add,
% 24.40/4.18 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 24.40/4.18 matrix_symm_update_diagonal, pred_minus_1, reflexivity_leq, sel2_update_1,
% 24.40/4.18 sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3,
% 24.40/4.18 succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l,
% 24.40/4.18 succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r,
% 24.40/4.18 succ_pred, succ_tptp_minus_1, sum_plus_base, sum_plus_base_float, totality,
% 24.40/4.18 transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi,
% 24.40/4.18 uniform_int_rand_ranges_lo
% 24.40/4.18
% 24.40/4.18 Those formulas are unsatisfiable:
% 24.40/4.18 ---------------------------------
% 24.40/4.18
% 24.40/4.18 Begin of proof
% 24.40/4.18 |
% 24.40/4.19 | ALPHA: (leq_gt_pred) implies:
% 24.40/4.19 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 24.40/4.19 | (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 24.40/4.19 | [v4: int] : ( ~ (v4 = 0) & gt(v1, v0) = v4))
% 24.40/4.19 |
% 24.40/4.19 | ALPHA: (finite_domain_5) implies:
% 24.40/4.19 | (2) ! [v0: $i] : (v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 =
% 24.40/4.19 | n0 | ~ (leq(v0, n5) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 24.40/4.19 | leq(n0, v0) = v1))
% 24.40/4.19 |
% 24.40/4.19 | ALPHA: (finite_domain_0) implies:
% 24.40/4.19 | (3) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 24.40/4.19 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 24.40/4.19 |
% 24.40/4.19 | ALPHA: (successor_4) implies:
% 24.40/4.19 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) =
% 24.40/4.19 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 24.40/4.19 |
% 24.40/4.19 | ALPHA: (successor_5) implies:
% 24.40/4.19 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5
% 24.40/4.19 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 &
% 24.40/4.19 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 24.40/4.19 |
% 24.40/4.19 | ALPHA: (successor_1) implies:
% 24.40/4.19 | (6) succ(n0) = n1
% 24.40/4.19 |
% 24.40/4.19 | ALPHA: (successor_2) implies:
% 24.40/4.19 | (7) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 24.40/4.19 |
% 24.40/4.19 | ALPHA: (successor_3) implies:
% 24.40/4.19 | (8) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) =
% 24.40/4.19 | v0 & $i(v1) & $i(v0))
% 24.40/4.19 |
% 24.40/4.19 | ALPHA: (quaternion_ds1_inuse_0016) implies:
% 24.40/4.20 | (9) $i(n0)
% 24.40/4.20 | (10) a_select2(sigma_defuse, n0) = use
% 24.40/4.20 | (11) a_select2(sigma_defuse, n1) = use
% 24.40/4.20 | (12) a_select2(sigma_defuse, n2) = use
% 24.40/4.20 | (13) a_select2(sigma_defuse, n3) = use
% 24.40/4.20 | (14) a_select2(sigma_defuse, n4) = use
% 24.40/4.20 | (15) a_select2(sigma_defuse, n5) = use
% 24.40/4.21 | (16) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = use) & a_select2(sigma_defuse,
% 24.40/4.21 | v0) = v1 & leq(v0, n5) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0))
% 24.40/4.21 |
% 24.40/4.21 | ALPHA: (function-axioms) implies:
% 24.40/4.21 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) =
% 24.40/4.21 | v1) | ~ (succ(v2) = v0))
% 24.40/4.21 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.40/4.21 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) =
% 24.40/4.21 | v0))
% 24.40/4.21 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.40/4.21 | (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0))
% 24.40/4.21 |
% 24.40/4.21 | DELTA: instantiating (7) with fresh symbol all_50_0 gives:
% 24.40/4.21 | (20) succ(all_50_0) = n2 & succ(n0) = all_50_0 & $i(all_50_0)
% 24.40/4.21 |
% 24.40/4.21 | ALPHA: (20) implies:
% 24.40/4.21 | (21) $i(all_50_0)
% 24.40/4.21 | (22) succ(n0) = all_50_0
% 24.40/4.21 |
% 24.40/4.21 | DELTA: instantiating (8) with fresh symbols all_52_0, all_52_1 gives:
% 24.40/4.21 | (23) succ(all_52_0) = n3 & succ(all_52_1) = all_52_0 & succ(n0) = all_52_1
% 24.40/4.21 | & $i(all_52_0) & $i(all_52_1)
% 24.40/4.21 |
% 24.40/4.21 | ALPHA: (23) implies:
% 24.40/4.21 | (24) succ(n0) = all_52_1
% 24.40/4.21 |
% 24.40/4.21 | DELTA: instantiating (16) with fresh symbols all_54_0, all_54_1 gives:
% 24.40/4.21 | (25) ~ (all_54_0 = use) & a_select2(sigma_defuse, all_54_1) = all_54_0 &
% 24.40/4.21 | leq(all_54_1, n5) = 0 & leq(n0, all_54_1) = 0 & $i(all_54_0) &
% 24.40/4.21 | $i(all_54_1)
% 24.40/4.21 |
% 24.40/4.21 | ALPHA: (25) implies:
% 24.40/4.21 | (26) ~ (all_54_0 = use)
% 24.40/4.21 | (27) $i(all_54_1)
% 24.40/4.21 | (28) leq(n0, all_54_1) = 0
% 24.40/4.21 | (29) leq(all_54_1, n5) = 0
% 24.40/4.21 | (30) a_select2(sigma_defuse, all_54_1) = all_54_0
% 24.40/4.21 |
% 24.40/4.21 | DELTA: instantiating (4) with fresh symbols all_56_0, all_56_1, all_56_2
% 24.40/4.21 | gives:
% 24.40/4.21 | (31) succ(all_56_0) = n4 & succ(all_56_1) = all_56_0 & succ(all_56_2) =
% 24.40/4.21 | all_56_1 & succ(n0) = all_56_2 & $i(all_56_0) & $i(all_56_1) &
% 24.40/4.21 | $i(all_56_2)
% 24.40/4.21 |
% 24.40/4.21 | ALPHA: (31) implies:
% 24.40/4.21 | (32) succ(n0) = all_56_2
% 24.40/4.21 |
% 24.40/4.21 | DELTA: instantiating (5) with fresh symbols all_58_0, all_58_1, all_58_2,
% 24.40/4.21 | all_58_3 gives:
% 24.40/4.21 | (33) succ(all_58_0) = n5 & succ(all_58_1) = all_58_0 & succ(all_58_2) =
% 24.40/4.21 | all_58_1 & succ(all_58_3) = all_58_2 & succ(n0) = all_58_3 &
% 24.40/4.21 | $i(all_58_0) & $i(all_58_1) & $i(all_58_2) & $i(all_58_3)
% 24.40/4.21 |
% 24.40/4.21 | ALPHA: (33) implies:
% 24.40/4.21 | (34) succ(n0) = all_58_3
% 24.40/4.21 |
% 24.40/4.22 | GROUND_INST: instantiating (17) with all_52_1, all_56_2, n0, simplifying with
% 24.40/4.22 | (24), (32) gives:
% 24.40/4.22 | (35) all_56_2 = all_52_1
% 24.40/4.22 |
% 24.40/4.22 | GROUND_INST: instantiating (17) with all_50_0, all_56_2, n0, simplifying with
% 24.40/4.22 | (22), (32) gives:
% 24.40/4.22 | (36) all_56_2 = all_50_0
% 24.40/4.22 |
% 24.40/4.22 | GROUND_INST: instantiating (17) with all_52_1, all_58_3, n0, simplifying with
% 24.40/4.22 | (24), (34) gives:
% 24.40/4.22 | (37) all_58_3 = all_52_1
% 24.40/4.22 |
% 24.40/4.22 | GROUND_INST: instantiating (17) with n1, all_58_3, n0, simplifying with (6),
% 24.40/4.22 | (34) gives:
% 24.40/4.22 | (38) all_58_3 = n1
% 24.40/4.22 |
% 24.40/4.22 | COMBINE_EQS: (37), (38) imply:
% 24.40/4.22 | (39) all_52_1 = n1
% 24.40/4.22 |
% 24.40/4.22 | SIMP: (39) implies:
% 24.40/4.22 | (40) all_52_1 = n1
% 24.40/4.22 |
% 24.40/4.22 | COMBINE_EQS: (35), (36) imply:
% 24.40/4.22 | (41) all_52_1 = all_50_0
% 24.40/4.22 |
% 24.40/4.22 | SIMP: (41) implies:
% 24.40/4.22 | (42) all_52_1 = all_50_0
% 24.40/4.22 |
% 24.40/4.22 | COMBINE_EQS: (40), (42) imply:
% 24.40/4.22 | (43) all_50_0 = n1
% 24.40/4.22 |
% 24.40/4.22 | REDUCE: (21), (43) imply:
% 24.40/4.22 | (44) $i(n1)
% 24.40/4.22 |
% 24.40/4.22 | GROUND_INST: instantiating (3) with all_54_1, simplifying with (27), (28)
% 24.40/4.22 | gives:
% 24.40/4.22 | (45) all_54_1 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_54_1, n0) = v0)
% 24.40/4.22 |
% 24.40/4.22 | GROUND_INST: instantiating (2) with all_54_1, simplifying with (27), (29)
% 24.40/4.22 | gives:
% 24.40/4.22 | (46) all_54_1 = n5 | all_54_1 = n4 | all_54_1 = n3 | all_54_1 = n2 |
% 24.40/4.22 | all_54_1 = n1 | all_54_1 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(n0,
% 24.40/4.22 | all_54_1) = v0)
% 24.40/4.22 |
% 24.40/4.22 | GROUND_INST: instantiating (pred_succ) with n0, n1, simplifying with (6), (9)
% 24.40/4.22 | gives:
% 24.40/4.22 | (47) pred(n1) = n0
% 24.40/4.22 |
% 24.40/4.22 | BETA: splitting (45) gives:
% 24.40/4.22 |
% 24.40/4.22 | Case 1:
% 24.40/4.22 | |
% 24.40/4.22 | | (48) all_54_1 = n0
% 24.40/4.22 | |
% 24.40/4.22 | | REDUCE: (30), (48) imply:
% 24.40/4.22 | | (49) a_select2(sigma_defuse, n0) = all_54_0
% 24.40/4.22 | |
% 24.40/4.22 | | GROUND_INST: instantiating (19) with use, all_54_0, n0, sigma_defuse,
% 24.40/4.22 | | simplifying with (10), (49) gives:
% 24.40/4.22 | | (50) all_54_0 = use
% 24.40/4.22 | |
% 24.40/4.22 | | REDUCE: (26), (50) imply:
% 24.40/4.22 | | (51) $false
% 24.40/4.22 | |
% 24.40/4.22 | | CLOSE: (51) is inconsistent.
% 24.40/4.22 | |
% 24.40/4.22 | Case 2:
% 24.40/4.22 | |
% 24.40/4.22 | | (52) ~ (all_54_1 = n0)
% 24.40/4.22 | | (53) ? [v0: int] : ( ~ (v0 = 0) & leq(all_54_1, n0) = v0)
% 24.40/4.22 | |
% 24.40/4.22 | | DELTA: instantiating (53) with fresh symbol all_121_0 gives:
% 24.40/4.22 | | (54) ~ (all_121_0 = 0) & leq(all_54_1, n0) = all_121_0
% 24.40/4.22 | |
% 24.40/4.22 | | ALPHA: (54) implies:
% 24.40/4.22 | | (55) ~ (all_121_0 = 0)
% 24.40/4.22 | | (56) leq(all_54_1, n0) = all_121_0
% 24.40/4.22 | |
% 24.40/4.22 | | GROUND_INST: instantiating (1) with all_54_1, n1, n0, all_121_0, simplifying
% 24.40/4.22 | | with (27), (44), (47), (56) gives:
% 24.40/4.22 | | (57) all_121_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & gt(n1, all_54_1) = v0)
% 24.40/4.22 | |
% 24.40/4.22 | | BETA: splitting (57) gives:
% 24.40/4.22 | |
% 24.40/4.22 | | Case 1:
% 24.40/4.22 | | |
% 24.40/4.22 | | | (58) all_121_0 = 0
% 24.40/4.22 | | |
% 24.40/4.22 | | | REDUCE: (55), (58) imply:
% 24.40/4.22 | | | (59) $false
% 24.40/4.22 | | |
% 24.40/4.22 | | | CLOSE: (59) is inconsistent.
% 24.40/4.22 | | |
% 24.40/4.22 | | Case 2:
% 24.40/4.22 | | |
% 24.40/4.22 | | | (60) ? [v0: int] : ( ~ (v0 = 0) & gt(n1, all_54_1) = v0)
% 24.40/4.22 | | |
% 24.40/4.22 | | | DELTA: instantiating (60) with fresh symbol all_141_0 gives:
% 24.40/4.23 | | | (61) ~ (all_141_0 = 0) & gt(n1, all_54_1) = all_141_0
% 24.40/4.23 | | |
% 24.40/4.23 | | | ALPHA: (61) implies:
% 24.40/4.23 | | | (62) ~ (all_141_0 = 0)
% 24.40/4.23 | | | (63) gt(n1, all_54_1) = all_141_0
% 24.40/4.23 | | |
% 24.40/4.23 | | | GROUND_INST: instantiating (leq_gt2) with all_54_1, n1, all_141_0,
% 24.40/4.23 | | | simplifying with (27), (44), (63) gives:
% 24.40/4.23 | | | (64) all_141_0 = 0 | all_54_1 = n1 | ? [v0: int] : ( ~ (v0 = 0) &
% 24.40/4.23 | | | leq(all_54_1, n1) = v0)
% 24.40/4.23 | | |
% 24.40/4.23 | | | BETA: splitting (46) gives:
% 24.40/4.23 | | |
% 24.40/4.23 | | | Case 1:
% 24.40/4.23 | | | |
% 24.40/4.23 | | | | (65) all_54_1 = n0
% 24.40/4.23 | | | |
% 24.40/4.23 | | | | REDUCE: (52), (65) imply:
% 24.40/4.23 | | | | (66) $false
% 24.40/4.23 | | | |
% 24.40/4.23 | | | | CLOSE: (66) is inconsistent.
% 24.40/4.23 | | | |
% 24.40/4.23 | | | Case 2:
% 24.40/4.23 | | | |
% 24.40/4.23 | | | | (67) all_54_1 = n5 | all_54_1 = n4 | all_54_1 = n3 | all_54_1 = n2 |
% 24.40/4.23 | | | | all_54_1 = n1 | ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_54_1)
% 24.40/4.23 | | | | = v0)
% 24.40/4.23 | | | |
% 24.40/4.23 | | | | BETA: splitting (64) gives:
% 24.40/4.23 | | | |
% 24.40/4.23 | | | | Case 1:
% 24.40/4.23 | | | | |
% 24.40/4.23 | | | | | (68) all_141_0 = 0
% 24.40/4.23 | | | | |
% 24.40/4.23 | | | | | REDUCE: (62), (68) imply:
% 24.40/4.23 | | | | | (69) $false
% 24.40/4.23 | | | | |
% 24.40/4.23 | | | | | CLOSE: (69) is inconsistent.
% 24.40/4.23 | | | | |
% 24.40/4.23 | | | | Case 2:
% 24.40/4.23 | | | | |
% 24.40/4.23 | | | | | (70) all_54_1 = n1 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_54_1,
% 25.25/4.23 | | | | | n1) = v0)
% 25.25/4.23 | | | | |
% 25.25/4.23 | | | | | BETA: splitting (67) gives:
% 25.25/4.23 | | | | |
% 25.25/4.23 | | | | | Case 1:
% 25.25/4.23 | | | | | |
% 25.25/4.23 | | | | | | (71) all_54_1 = n5
% 25.25/4.23 | | | | | |
% 25.25/4.23 | | | | | | REDUCE: (30), (71) imply:
% 25.25/4.23 | | | | | | (72) a_select2(sigma_defuse, n5) = all_54_0
% 25.25/4.23 | | | | | |
% 25.25/4.23 | | | | | | GROUND_INST: instantiating (19) with use, all_54_0, n5,
% 25.25/4.23 | | | | | | sigma_defuse, simplifying with (15), (72) gives:
% 25.25/4.23 | | | | | | (73) all_54_0 = use
% 25.25/4.23 | | | | | |
% 25.25/4.23 | | | | | | REDUCE: (26), (73) imply:
% 25.25/4.23 | | | | | | (74) $false
% 25.25/4.23 | | | | | |
% 25.25/4.23 | | | | | | CLOSE: (74) is inconsistent.
% 25.25/4.23 | | | | | |
% 25.25/4.23 | | | | | Case 2:
% 25.25/4.23 | | | | | |
% 25.25/4.23 | | | | | | (75) all_54_1 = n4 | all_54_1 = n3 | all_54_1 = n2 | all_54_1 =
% 25.25/4.23 | | | | | | n1 | ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_54_1) = v0)
% 25.25/4.23 | | | | | |
% 25.25/4.23 | | | | | | BETA: splitting (70) gives:
% 25.25/4.23 | | | | | |
% 25.25/4.23 | | | | | | Case 1:
% 25.25/4.23 | | | | | | |
% 25.25/4.23 | | | | | | | (76) all_54_1 = n1
% 25.25/4.23 | | | | | | |
% 25.25/4.23 | | | | | | | REDUCE: (30), (76) imply:
% 25.25/4.23 | | | | | | | (77) a_select2(sigma_defuse, n1) = all_54_0
% 25.25/4.23 | | | | | | |
% 25.25/4.23 | | | | | | | GROUND_INST: instantiating (19) with use, all_54_0, n1,
% 25.25/4.23 | | | | | | | sigma_defuse, simplifying with (11), (77) gives:
% 25.25/4.23 | | | | | | | (78) all_54_0 = use
% 25.25/4.23 | | | | | | |
% 25.25/4.23 | | | | | | | REDUCE: (26), (78) imply:
% 25.25/4.23 | | | | | | | (79) $false
% 25.25/4.23 | | | | | | |
% 25.25/4.23 | | | | | | | CLOSE: (79) is inconsistent.
% 25.25/4.23 | | | | | | |
% 25.25/4.23 | | | | | | Case 2:
% 25.25/4.23 | | | | | | |
% 25.25/4.23 | | | | | | | (80) ~ (all_54_1 = n1)
% 25.25/4.23 | | | | | | |
% 25.25/4.23 | | | | | | | BETA: splitting (75) gives:
% 25.25/4.23 | | | | | | |
% 25.25/4.23 | | | | | | | Case 1:
% 25.25/4.23 | | | | | | | |
% 25.25/4.23 | | | | | | | | (81) all_54_1 = n4
% 25.25/4.23 | | | | | | | |
% 25.25/4.23 | | | | | | | | REDUCE: (30), (81) imply:
% 25.25/4.23 | | | | | | | | (82) a_select2(sigma_defuse, n4) = all_54_0
% 25.25/4.23 | | | | | | | |
% 25.25/4.23 | | | | | | | | GROUND_INST: instantiating (19) with use, all_54_0, n4,
% 25.25/4.23 | | | | | | | | sigma_defuse, simplifying with (14), (82) gives:
% 25.25/4.23 | | | | | | | | (83) all_54_0 = use
% 25.25/4.23 | | | | | | | |
% 25.25/4.23 | | | | | | | | REDUCE: (26), (83) imply:
% 25.25/4.23 | | | | | | | | (84) $false
% 25.25/4.23 | | | | | | | |
% 25.25/4.23 | | | | | | | | CLOSE: (84) is inconsistent.
% 25.25/4.23 | | | | | | | |
% 25.25/4.23 | | | | | | | Case 2:
% 25.25/4.23 | | | | | | | |
% 25.25/4.23 | | | | | | | | (85) all_54_1 = n3 | all_54_1 = n2 | all_54_1 = n1 | ? [v0:
% 25.25/4.23 | | | | | | | | int] : ( ~ (v0 = 0) & leq(n0, all_54_1) = v0)
% 25.25/4.23 | | | | | | | |
% 25.25/4.23 | | | | | | | | BETA: splitting (85) gives:
% 25.25/4.23 | | | | | | | |
% 25.25/4.23 | | | | | | | | Case 1:
% 25.25/4.23 | | | | | | | | |
% 25.25/4.23 | | | | | | | | | (86) all_54_1 = n3
% 25.25/4.23 | | | | | | | | |
% 25.25/4.23 | | | | | | | | | REDUCE: (30), (86) imply:
% 25.25/4.23 | | | | | | | | | (87) a_select2(sigma_defuse, n3) = all_54_0
% 25.25/4.23 | | | | | | | | |
% 25.25/4.23 | | | | | | | | | GROUND_INST: instantiating (19) with use, all_54_0, n3,
% 25.25/4.23 | | | | | | | | | sigma_defuse, simplifying with (13), (87) gives:
% 25.25/4.23 | | | | | | | | | (88) all_54_0 = use
% 25.25/4.23 | | | | | | | | |
% 25.25/4.23 | | | | | | | | | REDUCE: (26), (88) imply:
% 25.25/4.23 | | | | | | | | | (89) $false
% 25.25/4.23 | | | | | | | | |
% 25.25/4.23 | | | | | | | | | CLOSE: (89) is inconsistent.
% 25.25/4.23 | | | | | | | | |
% 25.25/4.23 | | | | | | | | Case 2:
% 25.25/4.23 | | | | | | | | |
% 25.25/4.23 | | | | | | | | | (90) all_54_1 = n2 | all_54_1 = n1 | ? [v0: int] : ( ~ (v0
% 25.25/4.23 | | | | | | | | | = 0) & leq(n0, all_54_1) = v0)
% 25.25/4.23 | | | | | | | | |
% 25.25/4.23 | | | | | | | | | BETA: splitting (90) gives:
% 25.25/4.23 | | | | | | | | |
% 25.25/4.23 | | | | | | | | | Case 1:
% 25.25/4.23 | | | | | | | | | |
% 25.25/4.23 | | | | | | | | | | (91) all_54_1 = n2
% 25.25/4.23 | | | | | | | | | |
% 25.25/4.23 | | | | | | | | | | REDUCE: (30), (91) imply:
% 25.25/4.24 | | | | | | | | | | (92) a_select2(sigma_defuse, n2) = all_54_0
% 25.25/4.24 | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | GROUND_INST: instantiating (19) with use, all_54_0, n2,
% 25.25/4.24 | | | | | | | | | | sigma_defuse, simplifying with (12), (92) gives:
% 25.25/4.24 | | | | | | | | | | (93) all_54_0 = use
% 25.25/4.24 | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | REDUCE: (26), (93) imply:
% 25.25/4.24 | | | | | | | | | | (94) $false
% 25.25/4.24 | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | CLOSE: (94) is inconsistent.
% 25.25/4.24 | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | Case 2:
% 25.25/4.24 | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | (95) all_54_1 = n1 | ? [v0: int] : ( ~ (v0 = 0) &
% 25.25/4.24 | | | | | | | | | | leq(n0, all_54_1) = v0)
% 25.25/4.24 | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | BETA: splitting (95) gives:
% 25.25/4.24 | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | Case 1:
% 25.25/4.24 | | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | | (96) all_54_1 = n1
% 25.25/4.24 | | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | | REDUCE: (80), (96) imply:
% 25.25/4.24 | | | | | | | | | | | (97) $false
% 25.25/4.24 | | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | | CLOSE: (97) is inconsistent.
% 25.25/4.24 | | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | Case 2:
% 25.25/4.24 | | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | | (98) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_54_1) =
% 25.25/4.24 | | | | | | | | | | | v0)
% 25.25/4.24 | | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | | DELTA: instantiating (98) with fresh symbol all_613_0
% 25.25/4.24 | | | | | | | | | | | gives:
% 25.25/4.24 | | | | | | | | | | | (99) ~ (all_613_0 = 0) & leq(n0, all_54_1) = all_613_0
% 25.25/4.24 | | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | | ALPHA: (99) implies:
% 25.25/4.24 | | | | | | | | | | | (100) ~ (all_613_0 = 0)
% 25.25/4.24 | | | | | | | | | | | (101) leq(n0, all_54_1) = all_613_0
% 25.25/4.24 | | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_613_0, all_54_1,
% 25.25/4.24 | | | | | | | | | | | n0, simplifying with (28), (101) gives:
% 25.25/4.24 | | | | | | | | | | | (102) all_613_0 = 0
% 25.25/4.24 | | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | | REDUCE: (100), (102) imply:
% 25.25/4.24 | | | | | | | | | | | (103) $false
% 25.25/4.24 | | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | | CLOSE: (103) is inconsistent.
% 25.25/4.24 | | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | | End of split
% 25.25/4.24 | | | | | | | | | |
% 25.25/4.24 | | | | | | | | | End of split
% 25.25/4.24 | | | | | | | | |
% 25.25/4.24 | | | | | | | | End of split
% 25.25/4.24 | | | | | | | |
% 25.25/4.24 | | | | | | | End of split
% 25.25/4.24 | | | | | | |
% 25.25/4.24 | | | | | | End of split
% 25.25/4.24 | | | | | |
% 25.25/4.24 | | | | | End of split
% 25.25/4.24 | | | | |
% 25.25/4.24 | | | | End of split
% 25.25/4.24 | | | |
% 25.25/4.24 | | | End of split
% 25.25/4.24 | | |
% 25.25/4.24 | | End of split
% 25.25/4.24 | |
% 25.25/4.24 | End of split
% 25.25/4.24 |
% 25.25/4.24 End of proof
% 25.25/4.24 % SZS output end Proof for theBenchmark
% 25.25/4.24
% 25.25/4.24 3658ms
%------------------------------------------------------------------------------