TSTP Solution File: SWV024+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV024+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 : n003.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 22:54:37 EDT 2023
% Result : Theorem 171.13s 23.29s
% Output : Proof 172.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV024+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 03:41:55 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.03/1.41 Prover 1: Preprocessing ...
% 5.03/1.41 Prover 4: Preprocessing ...
% 5.62/1.46 Prover 3: Preprocessing ...
% 5.62/1.46 Prover 6: Preprocessing ...
% 5.62/1.46 Prover 2: Preprocessing ...
% 5.62/1.46 Prover 5: Preprocessing ...
% 5.62/1.46 Prover 0: Preprocessing ...
% 11.31/2.25 Prover 1: Warning: ignoring some quantifiers
% 11.83/2.33 Prover 1: Constructing countermodel ...
% 11.83/2.36 Prover 3: Warning: ignoring some quantifiers
% 12.53/2.39 Prover 3: Constructing countermodel ...
% 12.71/2.39 Prover 6: Proving ...
% 13.28/2.49 Prover 4: Warning: ignoring some quantifiers
% 14.03/2.61 Prover 4: Constructing countermodel ...
% 14.03/2.61 Prover 2: Proving ...
% 14.40/2.64 Prover 5: Proving ...
% 14.56/2.66 Prover 0: Proving ...
% 73.68/10.36 Prover 2: stopped
% 73.68/10.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 75.84/10.57 Prover 7: Preprocessing ...
% 77.37/10.79 Prover 7: Warning: ignoring some quantifiers
% 77.37/10.82 Prover 7: Constructing countermodel ...
% 101.98/13.97 Prover 5: stopped
% 101.98/13.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 102.78/14.10 Prover 8: Preprocessing ...
% 104.12/14.27 Prover 8: Warning: ignoring some quantifiers
% 104.59/14.32 Prover 8: Constructing countermodel ...
% 117.14/15.98 Prover 1: stopped
% 117.14/15.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 117.82/16.06 Prover 9: Preprocessing ...
% 120.19/16.35 Prover 9: Warning: ignoring some quantifiers
% 120.19/16.36 Prover 9: Constructing countermodel ...
% 131.40/17.89 Prover 6: stopped
% 131.40/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 132.30/18.03 Prover 10: Preprocessing ...
% 133.64/18.14 Prover 10: Warning: ignoring some quantifiers
% 133.64/18.15 Prover 10: Constructing countermodel ...
% 171.13/23.28 Prover 10: Found proof (size 604)
% 171.13/23.28 Prover 10: proved (5388ms)
% 171.13/23.29 Prover 9: stopped
% 171.13/23.29 Prover 0: stopped
% 171.13/23.29 Prover 3: stopped
% 171.13/23.29 Prover 7: stopped
% 171.13/23.29 Prover 8: stopped
% 171.13/23.29 Prover 4: stopped
% 171.13/23.29
% 171.13/23.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 171.13/23.29
% 171.48/23.32 % SZS output start Proof for theBenchmark
% 171.48/23.33 Assumptions after simplification:
% 171.48/23.33 ---------------------------------
% 171.48/23.33
% 171.48/23.33 (finite_domain_1)
% 171.48/23.34 $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0,
% 171.48/23.34 n1) | ~ leq(n0, v0))
% 171.48/23.34
% 171.48/23.34 (finite_domain_2)
% 171.48/23.34 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~
% 171.48/23.34 $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0))
% 171.48/23.34
% 171.48/23.34 (finite_domain_3)
% 171.48/23.34 $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n3 | v0 = n2 | v0 = n1
% 171.48/23.34 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n3) | ~ leq(n0, v0))
% 171.48/23.34
% 171.48/23.34 (finite_domain_5)
% 171.48/23.34 $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n5 |
% 171.48/23.34 v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n5)
% 171.48/23.34 | ~ leq(n0, v0))
% 171.48/23.34
% 171.48/23.34 (gauss_init_0009)
% 171.68/23.37 $i(pvar1402_init) & $i(pvar1401_init) & $i(pvar1400_init) & $i(loopcounter) &
% 171.68/23.37 $i(s_try7_init) & $i(s_center7_init) & $i(s_values7_init) & $i(simplex7_init)
% 171.68/23.37 & $i(n330) & $i(n410) & $i(pv20) & $i(pv19) & $i(pv8) & $i(pv7) & $i(s_worst7)
% 171.68/23.38 & $i(s_sworst7) & $i(s_best7) & $i(s_worst7_init) & $i(s_sworst7_init) &
% 171.68/23.38 $i(s_best7_init) & $i(init) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ? [v0: $i]
% 171.68/23.38 : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 171.68/23.38 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11:
% 171.68/23.38 $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : (s_worst7_init = init &
% 171.68/23.38 s_sworst7_init = init & s_best7_init = init & minus(n330, n1) = v1 &
% 171.68/23.38 minus(n410, n1) = v0 & minus(n3, n1) = v2 & $i(v13) & $i(v12) & $i(v10) &
% 171.68/23.38 $i(v8) & $i(v6) & $i(v2) & $i(v1) & $i(v0) & leq(pv20, v1) & leq(pv19, v0) &
% 171.68/23.38 leq(pv8, v1) & leq(pv7, v0) & leq(s_worst7, n3) & leq(s_sworst7, n3) &
% 171.68/23.38 leq(s_best7, n3) & leq(n0, pv20) & leq(n0, pv19) & leq(n0, pv8) & leq(n0,
% 171.68/23.38 pv7) & leq(n0, s_worst7) & leq(n0, s_sworst7) & leq(n0, s_best7) & !
% 171.68/23.38 [v15: $i] : ! [v16: $i] : ! [v17: $i] : (v17 = init | ~
% 171.68/23.38 (a_select3(simplex7_init, v16, v15) = v17) | ~ $i(v16) | ~ $i(v15) | ~
% 171.68/23.38 leq(v16, n3) | ~ leq(v15, n2) | ~ leq(n0, v16) | ~ leq(n0, v15)) & !
% 171.68/23.38 [v15: $i] : ! [v16: $i] : (v16 = init | ~ (a_select2(s_try7_init, v15) =
% 171.68/23.38 v16) | ~ $i(v15) | ~ leq(v15, v2) | ~ leq(n0, v15)) & ! [v15: $i] :
% 171.68/23.38 ! [v16: $i] : (v16 = init | ~ (a_select2(s_center7_init, v15) = v16) | ~
% 171.68/23.38 $i(v15) | ~ leq(v15, n2) | ~ leq(n0, v15)) & ! [v15: $i] : ! [v16: $i]
% 171.68/23.38 : (v16 = init | ~ (a_select2(s_values7_init, v15) = v16) | ~ $i(v15) | ~
% 171.68/23.38 leq(v15, n3) | ~ leq(n0, v15)) & ( ~ gt(loopcounter, n1) | (pvar1402_init
% 171.68/23.38 = init & pvar1401_init = init & pvar1400_init = init)) & (( ~ (v14 =
% 171.68/23.38 init) & a_select3(simplex7_init, v13, v12) = v14 & $i(v14) & leq(v13,
% 171.68/23.38 n3) & leq(v12, n2) & leq(n0, v13) & leq(n0, v12)) | ( ~ (v11 = init) &
% 171.68/23.38 a_select2(s_values7_init, v10) = v11 & $i(v11) & leq(v10, n3) & leq(n0,
% 171.68/23.38 v10)) | ( ~ (v9 = init) & a_select2(s_center7_init, v8) = v9 & $i(v9)
% 171.68/23.38 & leq(v8, n2) & leq(n0, v8)) | ( ~ (v7 = init) & a_select2(s_try7_init,
% 171.68/23.38 v6) = v7 & $i(v7) & leq(v6, v2) & leq(n0, v6)) | ( ~ (v5 = init) &
% 171.68/23.38 a_select2(s_try7_init, n2) = v5 & $i(v5)) | ( ~ (v4 = init) &
% 171.68/23.38 a_select2(s_try7_init, n1) = v4 & $i(v4)) | ( ~ (v3 = init) &
% 171.68/23.38 a_select2(s_try7_init, n0) = v3 & $i(v3)) | (gt(loopcounter, n1) & ( ~
% 171.68/23.38 (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ (pvar1400_init
% 171.68/23.38 = init)))))
% 171.68/23.38
% 171.68/23.38 (gt_1_0)
% 171.68/23.38 $i(n1) & $i(n0) & gt(n1, n0)
% 171.68/23.38
% 171.68/23.38 (gt_2_0)
% 171.68/23.38 $i(n2) & $i(n0) & gt(n2, n0)
% 171.68/23.38
% 171.68/23.38 (gt_330_5)
% 171.68/23.38 $i(n330) & $i(n5) & gt(n330, n5)
% 171.68/23.38
% 171.68/23.38 (gt_3_0)
% 171.68/23.38 $i(n3) & $i(n0) & gt(n3, n0)
% 171.68/23.38
% 171.68/23.38 (gt_3_1)
% 171.68/23.38 $i(n3) & $i(n1) & gt(n3, n1)
% 171.68/23.38
% 171.68/23.38 (gt_3_2)
% 171.68/23.38 $i(n3) & $i(n2) & gt(n3, n2)
% 171.68/23.38
% 171.68/23.38 (gt_410_330)
% 171.68/23.38 $i(n330) & $i(n410) & gt(n410, n330)
% 171.68/23.38
% 171.68/23.38 (gt_410_5)
% 171.68/23.38 $i(n410) & $i(n5) & gt(n410, n5)
% 171.68/23.38
% 171.68/23.38 (gt_5_4)
% 171.68/23.38 $i(n5) & $i(n4) & gt(n5, n4)
% 171.68/23.38
% 171.68/23.38 (irreflexivity_gt)
% 171.68/23.38 ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0))
% 171.68/23.38
% 171.68/23.38 (leq_gt1)
% 171.68/23.38 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0,
% 171.68/23.38 v1))
% 171.68/23.38
% 171.68/23.38 (leq_gt2)
% 171.68/23.38 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1)
% 171.68/23.38 | gt(v1, v0))
% 171.68/23.38
% 171.68/23.38 (leq_gt_pred)
% 171.68/23.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~
% 171.68/23.38 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 171.68/23.38 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0,
% 171.68/23.38 v2))
% 171.68/23.38
% 171.68/23.38 (leq_succ)
% 171.68/23.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ $i(v1) | ~
% 171.68/23.38 $i(v0) | ~ leq(v0, v1) | leq(v0, v2))
% 171.68/23.38
% 171.68/23.38 (leq_succ_gt)
% 171.68/23.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v2) | ~ $i(v1) | ~
% 171.68/23.38 $i(v0) | ~ leq(v2, v1) | gt(v1, v0))
% 171.68/23.38
% 171.68/23.38 (leq_succ_gt_equiv)
% 171.68/23.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ $i(v1) | ~
% 171.68/23.39 $i(v0) | ~ leq(v0, v1) | gt(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 171.68/23.39 $i] : ( ~ (succ(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v2, v0) | leq(v0,
% 171.68/23.39 v1))
% 171.68/23.39
% 171.68/23.39 (pred_minus_1)
% 171.68/23.39 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 171.68/23.39 (pred(v0) = v1 & $i(v1)))
% 171.68/23.39
% 171.68/23.39 (pred_succ)
% 171.68/23.39 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0)
% 171.68/23.39
% 171.68/23.39 (succ_pred)
% 171.68/23.39 ! [v0: $i] : ! [v1: $i] : ( ~ (pred(v0) = v1) | ~ $i(v0) | succ(v1) = v0)
% 171.68/23.39
% 171.68/23.39 (successor_1)
% 171.68/23.39 succ(n0) = n1 & $i(n1) & $i(n0)
% 171.68/23.39
% 171.68/23.39 (successor_2)
% 171.68/23.39 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 171.68/23.39
% 171.68/23.39 (successor_3)
% 171.68/23.39 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 &
% 171.68/23.39 succ(n0) = v0 & $i(v1) & $i(v0))
% 171.68/23.39
% 171.68/23.39 (successor_4)
% 171.68/23.39 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 &
% 171.68/23.39 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 171.68/23.39
% 171.68/23.39 (successor_5)
% 171.68/23.39 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 171.68/23.39 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0
% 171.68/23.39 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 171.68/23.39
% 171.68/23.39 (transitivity_gt)
% 171.68/23.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 171.68/23.39 ~ gt(v1, v2) | ~ gt(v0, v1) | gt(v0, v2))
% 171.68/23.39
% 171.68/23.39 (transitivity_leq)
% 171.68/23.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 171.68/23.39 ~ leq(v1, v2) | ~ leq(v0, v1) | leq(v0, v2))
% 171.68/23.39
% 171.68/23.39 (function-axioms)
% 171.68/23.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 171.68/23.40 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 171.68/23.40 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 171.68/23.40 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 171.68/23.40 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 171.68/23.40 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 171.68/23.40 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 171.68/23.40 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 171.68/23.40 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 171.68/23.40 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 171.68/23.40 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 171.68/23.40 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 171.68/23.40 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 171.68/23.40 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 171.68/23.40 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 171.68/23.40 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 171.68/23.40 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 171.68/23.40 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 171.68/23.40 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 171.68/23.40 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 171.68/23.40 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 171.68/23.40 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 171.68/23.40 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 171.68/23.40 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 171.68/23.40 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.68/23.40 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 171.68/23.40 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~
% 171.68/23.40 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 171.68/23.40 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 171.68/23.40 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] :
% 171.68/23.40 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) =
% 171.68/23.40 v0))
% 171.68/23.40
% 171.68/23.40 Further assumptions not needed in the proof:
% 171.68/23.40 --------------------------------------------
% 171.68/23.40 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 171.68/23.40 finite_domain_4, gt_0_tptp_minus_1, gt_1_tptp_minus_1, gt_2_1,
% 171.68/23.40 gt_2_tptp_minus_1, gt_330_0, gt_330_1, gt_330_2, gt_330_3, gt_330_4,
% 171.68/23.40 gt_330_tptp_minus_1, gt_3_tptp_minus_1, gt_410_0, gt_410_1, gt_410_2, gt_410_3,
% 171.68/23.40 gt_410_4, gt_410_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3,
% 171.68/23.40 gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_tptp_minus_1, gt_succ,
% 171.68/23.40 leq_geq, leq_minus, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 171.68/23.40 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 171.68/23.40 matrix_symm_trans, matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1,
% 171.68/23.40 sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3,
% 171.68/23.40 succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l,
% 171.68/23.40 succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r,
% 171.68/23.40 succ_tptp_minus_1, sum_plus_base, sum_plus_base_float, totality, ttrue,
% 171.68/23.40 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 171.68/23.40
% 171.68/23.40 Those formulas are unsatisfiable:
% 171.68/23.40 ---------------------------------
% 171.68/23.40
% 171.68/23.40 Begin of proof
% 171.68/23.40 |
% 171.68/23.40 | ALPHA: (leq_gt_pred) implies:
% 171.68/23.41 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 171.68/23.41 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (leq_succ_gt_equiv) implies:
% 171.68/23.41 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~
% 171.68/23.41 | $i(v1) | ~ $i(v0) | ~ gt(v2, v0) | leq(v0, v1))
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (pred_minus_1) implies:
% 171.68/23.41 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 171.68/23.41 | (pred(v0) = v1 & $i(v1)))
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (gt_5_4) implies:
% 171.68/23.41 | (4) gt(n5, n4)
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (gt_330_5) implies:
% 171.68/23.41 | (5) gt(n330, n5)
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (gt_410_5) implies:
% 171.68/23.41 | (6) gt(n410, n5)
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (gt_410_330) implies:
% 171.68/23.41 | (7) gt(n410, n330)
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (gt_1_0) implies:
% 171.68/23.41 | (8) gt(n1, n0)
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (gt_2_0) implies:
% 171.68/23.41 | (9) gt(n2, n0)
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (gt_3_0) implies:
% 171.68/23.41 | (10) gt(n3, n0)
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (gt_3_1) implies:
% 171.68/23.41 | (11) gt(n3, n1)
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (gt_3_2) implies:
% 171.68/23.41 | (12) gt(n3, n2)
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (finite_domain_5) implies:
% 171.68/23.41 | (13) ! [v0: $i] : (v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 =
% 171.68/23.41 | n0 | ~ $i(v0) | ~ leq(v0, n5) | ~ leq(n0, v0))
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (finite_domain_1) implies:
% 171.68/23.41 | (14) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 171.68/23.41 | leq(n0, v0))
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (finite_domain_2) implies:
% 171.68/23.41 | (15) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0,
% 171.68/23.41 | n2) | ~ leq(n0, v0))
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (finite_domain_3) implies:
% 171.68/23.41 | (16) ! [v0: $i] : (v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~
% 171.68/23.41 | leq(v0, n3) | ~ leq(n0, v0))
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (successor_4) implies:
% 171.68/23.41 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) =
% 171.68/23.41 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (successor_5) implies:
% 171.68/23.41 | (18) $i(n5)
% 171.68/23.41 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5
% 171.68/23.41 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 &
% 171.68/23.41 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (successor_1) implies:
% 171.68/23.41 | (20) succ(n0) = n1
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (successor_2) implies:
% 171.68/23.41 | (21) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (successor_3) implies:
% 171.68/23.41 | (22) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0)
% 171.68/23.41 | = v0 & $i(v1) & $i(v0))
% 171.68/23.41 |
% 171.68/23.41 | ALPHA: (gauss_init_0009) implies:
% 171.68/23.41 | (23) $i(n0)
% 171.68/23.41 | (24) $i(s_sworst7)
% 171.68/23.41 | (25) $i(n410)
% 171.68/23.41 | (26) $i(n330)
% 171.68/23.42 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 171.68/23.42 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 171.68/23.42 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 171.68/23.42 | $i] : (s_worst7_init = init & s_sworst7_init = init & s_best7_init =
% 171.68/23.42 | init & minus(n330, n1) = v1 & minus(n410, n1) = v0 & minus(n3, n1) =
% 171.68/23.42 | v2 & $i(v13) & $i(v12) & $i(v10) & $i(v8) & $i(v6) & $i(v2) & $i(v1)
% 171.68/23.42 | & $i(v0) & leq(pv20, v1) & leq(pv19, v0) & leq(pv8, v1) & leq(pv7,
% 171.68/23.42 | v0) & leq(s_worst7, n3) & leq(s_sworst7, n3) & leq(s_best7, n3) &
% 171.68/23.42 | leq(n0, pv20) & leq(n0, pv19) & leq(n0, pv8) & leq(n0, pv7) &
% 171.68/23.42 | leq(n0, s_worst7) & leq(n0, s_sworst7) & leq(n0, s_best7) & ! [v15:
% 171.68/23.42 | $i] : ! [v16: $i] : ! [v17: $i] : (v17 = init | ~
% 171.68/23.42 | (a_select3(simplex7_init, v16, v15) = v17) | ~ $i(v16) | ~
% 171.68/23.42 | $i(v15) | ~ leq(v16, n3) | ~ leq(v15, n2) | ~ leq(n0, v16) | ~
% 171.68/23.42 | leq(n0, v15)) & ! [v15: $i] : ! [v16: $i] : (v16 = init | ~
% 171.68/23.42 | (a_select2(s_try7_init, v15) = v16) | ~ $i(v15) | ~ leq(v15, v2)
% 171.68/23.42 | | ~ leq(n0, v15)) & ! [v15: $i] : ! [v16: $i] : (v16 = init |
% 171.68/23.42 | ~ (a_select2(s_center7_init, v15) = v16) | ~ $i(v15) | ~
% 171.68/23.42 | leq(v15, n2) | ~ leq(n0, v15)) & ! [v15: $i] : ! [v16: $i] :
% 171.68/23.42 | (v16 = init | ~ (a_select2(s_values7_init, v15) = v16) | ~ $i(v15)
% 171.68/23.42 | | ~ leq(v15, n3) | ~ leq(n0, v15)) & ( ~ gt(loopcounter, n1) |
% 171.68/23.42 | (pvar1402_init = init & pvar1401_init = init & pvar1400_init =
% 171.68/23.42 | init)) & (( ~ (v14 = init) & a_select3(simplex7_init, v13, v12)
% 171.68/23.42 | = v14 & $i(v14) & leq(v13, n3) & leq(v12, n2) & leq(n0, v13) &
% 171.68/23.42 | leq(n0, v12)) | ( ~ (v11 = init) & a_select2(s_values7_init,
% 171.68/23.42 | v10) = v11 & $i(v11) & leq(v10, n3) & leq(n0, v10)) | ( ~ (v9
% 171.68/23.42 | = init) & a_select2(s_center7_init, v8) = v9 & $i(v9) &
% 171.68/23.42 | leq(v8, n2) & leq(n0, v8)) | ( ~ (v7 = init) &
% 171.68/23.42 | a_select2(s_try7_init, v6) = v7 & $i(v7) & leq(v6, v2) & leq(n0,
% 171.68/23.42 | v6)) | ( ~ (v5 = init) & a_select2(s_try7_init, n2) = v5 &
% 171.68/23.42 | $i(v5)) | ( ~ (v4 = init) & a_select2(s_try7_init, n1) = v4 &
% 171.68/23.42 | $i(v4)) | ( ~ (v3 = init) & a_select2(s_try7_init, n0) = v3 &
% 171.68/23.42 | $i(v3)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~
% 171.68/23.42 | (pvar1401_init = init) | ~ (pvar1400_init = init)))))
% 171.68/23.42 |
% 171.68/23.42 | ALPHA: (function-axioms) implies:
% 171.68/23.42 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) =
% 171.68/23.42 | v1) | ~ (pred(v2) = v0))
% 171.68/23.42 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) =
% 171.68/23.42 | v1) | ~ (succ(v2) = v0))
% 171.68/23.42 |
% 171.68/23.42 | DELTA: instantiating (21) with fresh symbol all_54_0 gives:
% 171.68/23.42 | (30) succ(all_54_0) = n2 & succ(n0) = all_54_0 & $i(all_54_0)
% 171.68/23.42 |
% 171.68/23.42 | ALPHA: (30) implies:
% 171.68/23.42 | (31) $i(all_54_0)
% 171.68/23.42 | (32) succ(n0) = all_54_0
% 171.68/23.42 | (33) succ(all_54_0) = n2
% 171.68/23.42 |
% 171.68/23.42 | DELTA: instantiating (22) with fresh symbols all_57_0, all_57_1 gives:
% 171.68/23.42 | (34) succ(all_57_0) = n3 & succ(all_57_1) = all_57_0 & succ(n0) = all_57_1
% 171.68/23.42 | & $i(all_57_0) & $i(all_57_1)
% 171.68/23.42 |
% 171.68/23.42 | ALPHA: (34) implies:
% 171.68/23.43 | (35) $i(all_57_0)
% 171.68/23.43 | (36) succ(n0) = all_57_1
% 171.68/23.43 | (37) succ(all_57_1) = all_57_0
% 171.68/23.43 | (38) succ(all_57_0) = n3
% 171.68/23.43 |
% 171.68/23.43 | DELTA: instantiating (17) with fresh symbols all_59_0, all_59_1, all_59_2
% 171.68/23.43 | gives:
% 171.68/23.43 | (39) succ(all_59_0) = n4 & succ(all_59_1) = all_59_0 & succ(all_59_2) =
% 171.68/23.43 | all_59_1 & succ(n0) = all_59_2 & $i(all_59_0) & $i(all_59_1) &
% 171.68/23.43 | $i(all_59_2)
% 171.68/23.43 |
% 171.68/23.43 | ALPHA: (39) implies:
% 171.68/23.43 | (40) $i(all_59_0)
% 171.68/23.43 | (41) succ(n0) = all_59_2
% 171.68/23.43 | (42) succ(all_59_2) = all_59_1
% 171.68/23.43 | (43) succ(all_59_1) = all_59_0
% 171.68/23.43 | (44) succ(all_59_0) = n4
% 171.68/23.43 |
% 171.68/23.43 | DELTA: instantiating (19) with fresh symbols all_61_0, all_61_1, all_61_2,
% 171.68/23.43 | all_61_3 gives:
% 171.68/23.43 | (45) succ(all_61_0) = n5 & succ(all_61_1) = all_61_0 & succ(all_61_2) =
% 171.68/23.43 | all_61_1 & succ(all_61_3) = all_61_2 & succ(n0) = all_61_3 &
% 171.68/23.43 | $i(all_61_0) & $i(all_61_1) & $i(all_61_2) & $i(all_61_3)
% 171.68/23.43 |
% 171.68/23.43 | ALPHA: (45) implies:
% 171.68/23.43 | (46) $i(all_61_0)
% 171.68/23.43 | (47) succ(n0) = all_61_3
% 171.68/23.43 | (48) succ(all_61_3) = all_61_2
% 171.68/23.43 | (49) succ(all_61_2) = all_61_1
% 171.68/23.43 | (50) succ(all_61_1) = all_61_0
% 171.68/23.43 |
% 171.68/23.43 | DELTA: instantiating (27) with fresh symbols all_71_0, all_71_1, all_71_2,
% 171.68/23.43 | all_71_3, all_71_4, all_71_5, all_71_6, all_71_7, all_71_8, all_71_9,
% 171.68/23.43 | all_71_10, all_71_11, all_71_12, all_71_13, all_71_14 gives:
% 171.68/23.43 | (51) s_worst7_init = init & s_sworst7_init = init & s_best7_init = init &
% 171.68/23.43 | minus(n330, n1) = all_71_13 & minus(n410, n1) = all_71_14 & minus(n3,
% 171.68/23.43 | n1) = all_71_12 & $i(all_71_1) & $i(all_71_2) & $i(all_71_4) &
% 171.68/23.43 | $i(all_71_6) & $i(all_71_8) & $i(all_71_12) & $i(all_71_13) &
% 171.68/23.43 | $i(all_71_14) & leq(pv20, all_71_13) & leq(pv19, all_71_14) & leq(pv8,
% 171.68/23.43 | all_71_13) & leq(pv7, all_71_14) & leq(s_worst7, n3) &
% 171.68/23.43 | leq(s_sworst7, n3) & leq(s_best7, n3) & leq(n0, pv20) & leq(n0, pv19)
% 171.68/23.43 | & leq(n0, pv8) & leq(n0, pv7) & leq(n0, s_worst7) & leq(n0, s_sworst7)
% 171.68/23.43 | & leq(n0, s_best7) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 =
% 171.68/23.43 | init | ~ (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ~
% 171.68/23.43 | $i(v0) | ~ leq(v1, n3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~
% 171.68/23.43 | leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~
% 171.68/23.43 | (a_select2(s_try7_init, v0) = v1) | ~ $i(v0) | ~ leq(v0,
% 171.68/23.43 | all_71_12) | ~ leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 171.68/23.43 | init | ~ (a_select2(s_center7_init, v0) = v1) | ~ $i(v0) | ~
% 171.68/23.43 | leq(v0, n2) | ~ leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 171.68/23.43 | init | ~ (a_select2(s_values7_init, v0) = v1) | ~ $i(v0) | ~
% 171.68/23.43 | leq(v0, n3) | ~ leq(n0, v0)) & ( ~ gt(loopcounter, n1) |
% 171.68/23.43 | (pvar1402_init = init & pvar1401_init = init & pvar1400_init =
% 171.68/23.43 | init)) & (( ~ (all_71_0 = init) & a_select3(simplex7_init,
% 171.68/23.43 | all_71_1, all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1,
% 171.68/23.43 | n3) & leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2))
% 171.68/23.43 | | ( ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 171.68/23.43 | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0, all_71_4)) |
% 171.68/23.43 | ( ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) =
% 171.68/23.43 | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0, all_71_6)) |
% 171.68/23.43 | ( ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) = all_71_7
% 171.68/23.43 | & $i(all_71_7) & leq(all_71_8, all_71_12) & leq(n0, all_71_8)) | (
% 171.68/23.43 | ~ (all_71_9 = init) & a_select2(s_try7_init, n2) = all_71_9 &
% 171.68/23.43 | $i(all_71_9)) | ( ~ (all_71_10 = init) & a_select2(s_try7_init,
% 171.68/23.43 | n1) = all_71_10 & $i(all_71_10)) | ( ~ (all_71_11 = init) &
% 171.68/23.43 | a_select2(s_try7_init, n0) = all_71_11 & $i(all_71_11)) |
% 171.68/23.43 | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~
% 171.68/23.43 | (pvar1401_init = init) | ~ (pvar1400_init = init))))
% 171.68/23.43 |
% 171.68/23.43 | ALPHA: (51) implies:
% 171.68/23.44 | (52) leq(n0, s_sworst7)
% 171.68/23.44 | (53) leq(s_sworst7, n3)
% 171.68/23.44 | (54) $i(all_71_8)
% 171.68/23.44 | (55) $i(all_71_6)
% 171.68/23.44 | (56) $i(all_71_4)
% 171.68/23.44 | (57) $i(all_71_2)
% 171.68/23.44 | (58) $i(all_71_1)
% 171.68/23.44 | (59) minus(n3, n1) = all_71_12
% 171.68/23.44 | (60) minus(n410, n1) = all_71_14
% 171.68/23.44 | (61) minus(n330, n1) = all_71_13
% 171.68/23.44 | (62) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1, all_71_2) =
% 171.68/23.44 | all_71_0 & $i(all_71_0) & leq(all_71_1, n3) & leq(all_71_2, n2) &
% 171.68/23.44 | leq(n0, all_71_1) & leq(n0, all_71_2)) | ( ~ (all_71_3 = init) &
% 171.68/23.44 | a_select2(s_values7_init, all_71_4) = all_71_3 & $i(all_71_3) &
% 171.68/23.44 | leq(all_71_4, n3) & leq(n0, all_71_4)) | ( ~ (all_71_5 = init) &
% 171.68/23.44 | a_select2(s_center7_init, all_71_6) = all_71_5 & $i(all_71_5) &
% 171.68/23.44 | leq(all_71_6, n2) & leq(n0, all_71_6)) | ( ~ (all_71_7 = init) &
% 171.68/23.44 | a_select2(s_try7_init, all_71_8) = all_71_7 & $i(all_71_7) &
% 171.68/23.44 | leq(all_71_8, all_71_12) & leq(n0, all_71_8)) | ( ~ (all_71_9 =
% 171.68/23.44 | init) & a_select2(s_try7_init, n2) = all_71_9 & $i(all_71_9)) | (
% 171.68/23.44 | ~ (all_71_10 = init) & a_select2(s_try7_init, n1) = all_71_10 &
% 171.68/23.44 | $i(all_71_10)) | ( ~ (all_71_11 = init) & a_select2(s_try7_init, n0)
% 171.68/23.44 | = all_71_11 & $i(all_71_11)) | (gt(loopcounter, n1) & ( ~
% 171.68/23.44 | (pvar1402_init = init) | ~ (pvar1401_init = init) | ~
% 171.68/23.44 | (pvar1400_init = init)))
% 171.68/23.44 | (63) ~ gt(loopcounter, n1) | (pvar1402_init = init & pvar1401_init = init
% 171.68/23.44 | & pvar1400_init = init)
% 171.68/23.44 | (64) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_values7_init,
% 171.68/23.44 | v0) = v1) | ~ $i(v0) | ~ leq(v0, n3) | ~ leq(n0, v0))
% 171.68/23.44 | (65) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_center7_init,
% 171.68/23.44 | v0) = v1) | ~ $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0))
% 171.68/23.44 | (66) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init,
% 171.68/23.44 | v0) = v1) | ~ $i(v0) | ~ leq(v0, all_71_12) | ~ leq(n0, v0))
% 171.68/23.44 | (67) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~
% 171.68/23.44 | (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 171.68/23.44 | leq(v1, n3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0))
% 171.68/23.44 |
% 171.68/23.44 | GROUND_INST: instantiating (29) with all_54_0, all_57_1, n0, simplifying with
% 171.68/23.44 | (32), (36) gives:
% 171.68/23.44 | (68) all_57_1 = all_54_0
% 171.68/23.44 |
% 172.13/23.44 | GROUND_INST: instantiating (29) with all_57_1, all_59_2, n0, simplifying with
% 172.13/23.44 | (36), (41) gives:
% 172.13/23.44 | (69) all_59_2 = all_57_1
% 172.13/23.44 |
% 172.13/23.44 | GROUND_INST: instantiating (29) with all_59_2, all_61_3, n0, simplifying with
% 172.13/23.45 | (41), (47) gives:
% 172.13/23.45 | (70) all_61_3 = all_59_2
% 172.13/23.45 |
% 172.13/23.45 | GROUND_INST: instantiating (29) with n1, all_61_3, n0, simplifying with (20),
% 172.13/23.45 | (47) gives:
% 172.13/23.45 | (71) all_61_3 = n1
% 172.13/23.45 |
% 172.13/23.45 | COMBINE_EQS: (70), (71) imply:
% 172.13/23.45 | (72) all_59_2 = n1
% 172.13/23.45 |
% 172.13/23.45 | SIMP: (72) implies:
% 172.13/23.45 | (73) all_59_2 = n1
% 172.13/23.45 |
% 172.13/23.45 | COMBINE_EQS: (69), (73) imply:
% 172.13/23.45 | (74) all_57_1 = n1
% 172.13/23.45 |
% 172.13/23.45 | SIMP: (74) implies:
% 172.13/23.45 | (75) all_57_1 = n1
% 172.13/23.45 |
% 172.13/23.45 | COMBINE_EQS: (68), (75) imply:
% 172.13/23.45 | (76) all_54_0 = n1
% 172.13/23.45 |
% 172.13/23.45 | SIMP: (76) implies:
% 172.13/23.45 | (77) all_54_0 = n1
% 172.13/23.45 |
% 172.13/23.45 | REDUCE: (48), (71) imply:
% 172.13/23.45 | (78) succ(n1) = all_61_2
% 172.13/23.45 |
% 172.13/23.45 | REDUCE: (42), (73) imply:
% 172.13/23.45 | (79) succ(n1) = all_59_1
% 172.13/23.45 |
% 172.13/23.45 | REDUCE: (37), (75) imply:
% 172.13/23.45 | (80) succ(n1) = all_57_0
% 172.13/23.45 |
% 172.13/23.45 | REDUCE: (33), (77) imply:
% 172.13/23.45 | (81) succ(n1) = n2
% 172.13/23.45 |
% 172.13/23.45 | REDUCE: (31), (77) imply:
% 172.13/23.45 | (82) $i(n1)
% 172.13/23.45 |
% 172.13/23.45 | GROUND_INST: instantiating (29) with all_57_0, all_59_1, n1, simplifying with
% 172.13/23.45 | (79), (80) gives:
% 172.13/23.45 | (83) all_59_1 = all_57_0
% 172.13/23.45 |
% 172.13/23.45 | GROUND_INST: instantiating (29) with all_59_1, all_61_2, n1, simplifying with
% 172.13/23.45 | (78), (79) gives:
% 172.13/23.45 | (84) all_61_2 = all_59_1
% 172.13/23.45 |
% 172.13/23.45 | GROUND_INST: instantiating (29) with n2, all_61_2, n1, simplifying with (78),
% 172.13/23.45 | (81) gives:
% 172.13/23.45 | (85) all_61_2 = n2
% 172.13/23.45 |
% 172.13/23.45 | COMBINE_EQS: (84), (85) imply:
% 172.13/23.45 | (86) all_59_1 = n2
% 172.13/23.45 |
% 172.13/23.45 | SIMP: (86) implies:
% 172.13/23.45 | (87) all_59_1 = n2
% 172.13/23.45 |
% 172.13/23.45 | COMBINE_EQS: (83), (87) imply:
% 172.13/23.45 | (88) all_57_0 = n2
% 172.13/23.45 |
% 172.13/23.45 | REDUCE: (49), (85) imply:
% 172.13/23.45 | (89) succ(n2) = all_61_1
% 172.13/23.45 |
% 172.13/23.45 | REDUCE: (43), (87) imply:
% 172.13/23.45 | (90) succ(n2) = all_59_0
% 172.13/23.45 |
% 172.13/23.45 | REDUCE: (38), (88) imply:
% 172.13/23.45 | (91) succ(n2) = n3
% 172.13/23.45 |
% 172.13/23.45 | REDUCE: (35), (88) imply:
% 172.13/23.45 | (92) $i(n2)
% 172.13/23.45 |
% 172.13/23.45 | GROUND_INST: instantiating (29) with all_59_0, all_61_1, n2, simplifying with
% 172.13/23.45 | (89), (90) gives:
% 172.13/23.45 | (93) all_61_1 = all_59_0
% 172.13/23.45 |
% 172.13/23.45 | GROUND_INST: instantiating (29) with n3, all_61_1, n2, simplifying with (89),
% 172.13/23.45 | (91) gives:
% 172.13/23.45 | (94) all_61_1 = n3
% 172.13/23.45 |
% 172.13/23.45 | COMBINE_EQS: (93), (94) imply:
% 172.13/23.45 | (95) all_59_0 = n3
% 172.13/23.45 |
% 172.13/23.45 | SIMP: (95) implies:
% 172.13/23.45 | (96) all_59_0 = n3
% 172.13/23.45 |
% 172.13/23.45 | REDUCE: (50), (94) imply:
% 172.13/23.45 | (97) succ(n3) = all_61_0
% 172.13/23.45 |
% 172.13/23.45 | REDUCE: (44), (96) imply:
% 172.13/23.45 | (98) succ(n3) = n4
% 172.13/23.45 |
% 172.13/23.45 | REDUCE: (40), (96) imply:
% 172.13/23.45 | (99) $i(n3)
% 172.13/23.45 |
% 172.13/23.45 | GROUND_INST: instantiating (29) with n4, all_61_0, n3, simplifying with (97),
% 172.13/23.45 | (98) gives:
% 172.13/23.45 | (100) all_61_0 = n4
% 172.13/23.45 |
% 172.13/23.45 | REDUCE: (46), (100) imply:
% 172.13/23.45 | (101) $i(n4)
% 172.13/23.45 |
% 172.13/23.45 | GROUND_INST: instantiating (leq_gt1) with n4, n5, simplifying with (4), (18),
% 172.13/23.45 | (101) gives:
% 172.13/23.45 | (102) leq(n4, n5)
% 172.13/23.45 |
% 172.13/23.45 | GROUND_INST: instantiating (leq_gt2) with n0, s_sworst7, simplifying with
% 172.13/23.45 | (23), (24), (52) gives:
% 172.13/23.45 | (103) s_sworst7 = n0 | gt(s_sworst7, n0)
% 172.13/23.45 |
% 172.13/23.45 | GROUND_INST: instantiating (16) with s_sworst7, simplifying with (24), (52),
% 172.13/23.46 | (53) gives:
% 172.13/23.46 | (104) s_sworst7 = n3 | s_sworst7 = n2 | s_sworst7 = n1 | s_sworst7 = n0
% 172.13/23.46 |
% 172.13/23.46 | GROUND_INST: instantiating (2) with n0, n0, n1, simplifying with (8), (20),
% 172.13/23.46 | (23) gives:
% 172.13/23.46 | (105) leq(n0, n0)
% 172.13/23.46 |
% 172.13/23.46 | GROUND_INST: instantiating (2) with n0, n1, n2, simplifying with (9), (23),
% 172.13/23.46 | (81), (82) gives:
% 172.13/23.46 | (106) leq(n0, n1)
% 172.13/23.46 |
% 172.13/23.46 | GROUND_INST: instantiating (pred_succ) with n1, n2, simplifying with (81),
% 172.13/23.46 | (82) gives:
% 172.13/23.46 | (107) pred(n2) = n1
% 172.13/23.46 |
% 172.13/23.46 | GROUND_INST: instantiating (2) with n2, n2, n3, simplifying with (12), (91),
% 172.13/23.46 | (92) gives:
% 172.13/23.46 | (108) leq(n2, n2)
% 172.13/23.46 |
% 172.13/23.46 | GROUND_INST: instantiating (2) with n1, n2, n3, simplifying with (11), (82),
% 172.13/23.46 | (91), (92) gives:
% 172.13/23.46 | (109) leq(n1, n2)
% 172.13/23.46 |
% 172.13/23.46 | GROUND_INST: instantiating (2) with n0, n2, n3, simplifying with (10), (23),
% 172.13/23.46 | (91), (92) gives:
% 172.13/23.46 | (110) leq(n0, n2)
% 172.13/23.46 |
% 172.13/23.46 | GROUND_INST: instantiating (pred_succ) with n2, n3, simplifying with (91),
% 172.13/23.46 | (92) gives:
% 172.13/23.46 | (111) pred(n3) = n2
% 172.13/23.46 |
% 172.13/23.46 | GROUND_INST: instantiating (leq_succ) with s_sworst7, n3, n4, simplifying with
% 172.13/23.46 | (24), (53), (98), (99) gives:
% 172.13/23.46 | (112) leq(s_sworst7, n4)
% 172.13/23.46 |
% 172.13/23.46 | GROUND_INST: instantiating (3) with n3, all_71_12, simplifying with (59), (99)
% 172.13/23.46 | gives:
% 172.13/23.46 | (113) pred(n3) = all_71_12 & $i(all_71_12)
% 172.13/23.46 |
% 172.13/23.46 | ALPHA: (113) implies:
% 172.13/23.46 | (114) $i(all_71_12)
% 172.13/23.46 | (115) pred(n3) = all_71_12
% 172.13/23.46 |
% 172.13/23.46 | GROUND_INST: instantiating (3) with n410, all_71_14, simplifying with (25),
% 172.13/23.47 | (60) gives:
% 172.13/23.47 | (116) pred(n410) = all_71_14 & $i(all_71_14)
% 172.13/23.47 |
% 172.13/23.47 | ALPHA: (116) implies:
% 172.13/23.47 | (117) $i(all_71_14)
% 172.13/23.47 | (118) pred(n410) = all_71_14
% 172.13/23.47 |
% 172.13/23.47 | GROUND_INST: instantiating (3) with n330, all_71_13, simplifying with (26),
% 172.13/23.47 | (61) gives:
% 172.13/23.47 | (119) pred(n330) = all_71_13 & $i(all_71_13)
% 172.13/23.47 |
% 172.13/23.47 | ALPHA: (119) implies:
% 172.13/23.47 | (120) $i(all_71_13)
% 172.13/23.47 | (121) pred(n330) = all_71_13
% 172.13/23.47 |
% 172.13/23.47 | GROUND_INST: instantiating (28) with n2, all_71_12, n3, simplifying with
% 172.13/23.47 | (111), (115) gives:
% 172.13/23.47 | (122) all_71_12 = n2
% 172.13/23.47 |
% 172.13/23.47 | GROUND_INST: instantiating (transitivity_leq) with s_sworst7, n4, n5,
% 172.13/23.47 | simplifying with (18), (24), (101), (102), (112) gives:
% 172.13/23.47 | (123) leq(s_sworst7, n5)
% 172.13/23.47 |
% 172.13/23.47 | GROUND_INST: instantiating (1) with n330, n410, all_71_14, simplifying with
% 172.13/23.47 | (7), (25), (26), (118) gives:
% 172.13/23.47 | (124) leq(n330, all_71_14)
% 172.13/23.47 |
% 172.13/23.47 | GROUND_INST: instantiating (1) with n5, n410, all_71_14, simplifying with (6),
% 172.13/23.47 | (18), (25), (118) gives:
% 172.13/23.47 | (125) leq(n5, all_71_14)
% 172.13/23.47 |
% 172.13/23.47 | GROUND_INST: instantiating (1) with n5, n330, all_71_13, simplifying with (5),
% 172.13/23.47 | (18), (26), (121) gives:
% 172.13/23.47 | (126) leq(n5, all_71_13)
% 172.13/23.47 |
% 172.13/23.47 | GROUND_INST: instantiating (succ_pred) with n330, all_71_13, simplifying with
% 172.13/23.47 | (26), (121) gives:
% 172.13/23.47 | (127) succ(all_71_13) = n330
% 172.13/23.47 |
% 172.13/23.47 | GROUND_INST: instantiating (leq_gt2) with n5, all_71_14, simplifying with
% 172.13/23.47 | (18), (117), (125) gives:
% 172.13/23.47 | (128) all_71_14 = n5 | gt(all_71_14, n5)
% 172.13/23.47 |
% 172.13/23.47 | GROUND_INST: instantiating (leq_gt2) with n5, all_71_13, simplifying with
% 172.13/23.47 | (18), (120), (126) gives:
% 172.13/23.47 | (129) all_71_13 = n5 | gt(all_71_13, n5)
% 172.13/23.47 |
% 172.13/23.47 | GROUND_INST: instantiating (13) with s_sworst7, simplifying with (24), (52),
% 172.13/23.47 | (123) gives:
% 172.13/23.47 | (130) s_sworst7 = n5 | s_sworst7 = n4 | s_sworst7 = n3 | s_sworst7 = n2 |
% 172.13/23.47 | s_sworst7 = n1 | s_sworst7 = n0
% 172.13/23.47 |
% 172.13/23.47 | GROUND_INST: instantiating (leq_succ_gt) with all_71_13, all_71_14, n330,
% 172.13/23.47 | simplifying with (117), (120), (124), (127) gives:
% 172.13/23.47 | (131) gt(all_71_14, all_71_13)
% 172.13/23.47 |
% 172.13/23.47 | BETA: splitting (63) gives:
% 172.13/23.47 |
% 172.13/23.47 | Case 1:
% 172.13/23.47 | |
% 172.13/23.47 | | (132) ~ gt(loopcounter, n1)
% 172.13/23.47 | |
% 172.13/23.47 | | BETA: splitting (103) gives:
% 172.13/23.47 | |
% 172.13/23.47 | | Case 1:
% 172.13/23.47 | | |
% 172.13/23.47 | | | (133) gt(s_sworst7, n0)
% 172.13/23.47 | | |
% 172.13/23.47 | | | BETA: splitting (62) gives:
% 172.13/23.47 | | |
% 172.13/23.47 | | | Case 1:
% 172.13/23.47 | | | |
% 172.13/23.47 | | | | (134) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 172.13/23.47 | | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 172.13/23.47 | | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)) |
% 172.13/23.47 | | | | ( ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 172.13/23.47 | | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0,
% 172.13/23.47 | | | | all_71_4)) | ( ~ (all_71_5 = init) &
% 172.13/23.47 | | | | a_select2(s_center7_init, all_71_6) = all_71_5 & $i(all_71_5)
% 172.13/23.47 | | | | & leq(all_71_6, n2) & leq(n0, all_71_6)) | ( ~ (all_71_7 =
% 172.13/23.47 | | | | init) & a_select2(s_try7_init, all_71_8) = all_71_7 &
% 172.13/23.47 | | | | $i(all_71_7) & leq(all_71_8, all_71_12) & leq(n0, all_71_8))
% 172.13/23.47 | | | |
% 172.13/23.47 | | | | BETA: splitting (134) gives:
% 172.13/23.47 | | | |
% 172.13/23.47 | | | | Case 1:
% 172.13/23.47 | | | | |
% 172.13/23.48 | | | | | (135) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 172.13/23.48 | | | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 172.13/23.48 | | | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2))
% 172.13/23.48 | | | | | | ( ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4)
% 172.13/23.48 | | | | | = all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0,
% 172.13/23.48 | | | | | all_71_4))
% 172.13/23.48 | | | | |
% 172.13/23.48 | | | | | REF_CLOSE: (56), (57), (58), (64), (67), (135) are inconsistent by
% 172.13/23.48 | | | | | sub-proof #10.
% 172.13/23.48 | | | | |
% 172.13/23.48 | | | | Case 2:
% 172.13/23.48 | | | | |
% 172.13/23.48 | | | | | (136) ( ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) =
% 172.13/23.48 | | | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0,
% 172.13/23.48 | | | | | all_71_6)) | ( ~ (all_71_7 = init) &
% 172.13/23.48 | | | | | a_select2(s_try7_init, all_71_8) = all_71_7 & $i(all_71_7)
% 172.13/23.48 | | | | | & leq(all_71_8, all_71_12) & leq(n0, all_71_8))
% 172.13/23.48 | | | | |
% 172.13/23.48 | | | | | BETA: splitting (136) gives:
% 172.13/23.48 | | | | |
% 172.13/23.48 | | | | | Case 1:
% 172.13/23.48 | | | | | |
% 172.13/23.48 | | | | | | (137) ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6)
% 172.13/23.48 | | | | | | = all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0,
% 172.13/23.48 | | | | | | all_71_6)
% 172.13/23.48 | | | | | |
% 172.13/23.48 | | | | | | REF_CLOSE: (55), (65), (137) are inconsistent by sub-proof #9.
% 172.13/23.48 | | | | | |
% 172.13/23.48 | | | | | Case 2:
% 172.13/23.48 | | | | | |
% 172.13/23.48 | | | | | | (138) ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) =
% 172.13/23.48 | | | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_12) &
% 172.13/23.48 | | | | | | leq(n0, all_71_8)
% 172.13/23.48 | | | | | |
% 172.13/23.48 | | | | | | ALPHA: (138) implies:
% 172.13/23.48 | | | | | | (139) ~ (all_71_7 = init)
% 172.13/23.48 | | | | | | (140) leq(n0, all_71_8)
% 172.13/23.48 | | | | | | (141) leq(all_71_8, all_71_12)
% 172.13/23.48 | | | | | | (142) a_select2(s_try7_init, all_71_8) = all_71_7
% 172.13/23.48 | | | | | |
% 172.13/23.48 | | | | | | REDUCE: (122), (141) imply:
% 172.13/23.48 | | | | | | (143) leq(all_71_8, n2)
% 172.13/23.48 | | | | | |
% 172.13/23.48 | | | | | | BETA: splitting (104) gives:
% 172.13/23.48 | | | | | |
% 172.13/23.48 | | | | | | Case 1:
% 172.13/23.48 | | | | | | |
% 172.13/23.48 | | | | | | | (144) s_sworst7 = n0
% 172.13/23.48 | | | | | | |
% 172.13/23.48 | | | | | | | REDUCE: (133), (144) imply:
% 172.13/23.48 | | | | | | | (145) gt(n0, n0)
% 172.13/23.48 | | | | | | |
% 172.13/23.48 | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n0, simplifying
% 172.13/23.48 | | | | | | | with (23), (145) gives:
% 172.13/23.48 | | | | | | | (146) $false
% 172.13/23.48 | | | | | | |
% 172.13/23.48 | | | | | | | CLOSE: (146) is inconsistent.
% 172.13/23.48 | | | | | | |
% 172.13/23.48 | | | | | | Case 2:
% 172.13/23.48 | | | | | | |
% 172.13/23.48 | | | | | | | (147) ~ (s_sworst7 = n0)
% 172.13/23.48 | | | | | | |
% 172.13/23.48 | | | | | | | BETA: splitting (130) gives:
% 172.13/23.48 | | | | | | |
% 172.13/23.48 | | | | | | | Case 1:
% 172.13/23.48 | | | | | | | |
% 172.13/23.48 | | | | | | | | (148) s_sworst7 = n0
% 172.13/23.48 | | | | | | | |
% 172.13/23.48 | | | | | | | | REDUCE: (147), (148) imply:
% 172.13/23.48 | | | | | | | | (149) $false
% 172.13/23.48 | | | | | | | |
% 172.13/23.48 | | | | | | | | CLOSE: (149) is inconsistent.
% 172.13/23.48 | | | | | | | |
% 172.13/23.48 | | | | | | | Case 2:
% 172.13/23.48 | | | | | | | |
% 172.13/23.48 | | | | | | | |
% 172.13/23.48 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n0, all_71_8,
% 172.13/23.48 | | | | | | | | simplifying with (23), (54), (140) gives:
% 172.13/23.48 | | | | | | | | (150) all_71_8 = n0 | gt(all_71_8, n0)
% 172.13/23.48 | | | | | | | |
% 172.13/23.48 | | | | | | | | REF_CLOSE: (1), (14), (15), (54), (66), (92), (107), (122),
% 172.13/23.48 | | | | | | | | (139), (140), (142), (143), (150),
% 172.13/23.48 | | | | | | | | (irreflexivity_gt), (leq_gt2) are inconsistent by
% 172.13/23.48 | | | | | | | | sub-proof #5.
% 172.13/23.48 | | | | | | | |
% 172.13/23.48 | | | | | | | End of split
% 172.13/23.48 | | | | | | |
% 172.13/23.48 | | | | | | End of split
% 172.13/23.48 | | | | | |
% 172.13/23.48 | | | | | End of split
% 172.13/23.48 | | | | |
% 172.13/23.48 | | | | End of split
% 172.13/23.48 | | | |
% 172.13/23.48 | | | Case 2:
% 172.13/23.48 | | | |
% 172.13/23.48 | | | | (151) ( ~ (all_71_9 = init) & a_select2(s_try7_init, n2) = all_71_9 &
% 172.13/23.48 | | | | $i(all_71_9)) | ( ~ (all_71_10 = init) &
% 172.13/23.48 | | | | a_select2(s_try7_init, n1) = all_71_10 & $i(all_71_10)) | ( ~
% 172.13/23.48 | | | | (all_71_11 = init) & a_select2(s_try7_init, n0) = all_71_11 &
% 172.13/23.48 | | | | $i(all_71_11)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init =
% 172.13/23.48 | | | | init) | ~ (pvar1401_init = init) | ~ (pvar1400_init =
% 172.13/23.48 | | | | init)))
% 172.13/23.48 | | | |
% 172.13/23.48 | | | | REF_CLOSE: (23), (66), (82), (92), (105), (106), (108), (109), (110),
% 172.13/23.48 | | | | (117), (120), (122), (128), (129), (131), (132), (151),
% 172.13/23.48 | | | | (transitivity_gt) are inconsistent by sub-proof #1.
% 172.13/23.48 | | | |
% 172.13/23.48 | | | End of split
% 172.13/23.48 | | |
% 172.13/23.48 | | Case 2:
% 172.13/23.48 | | |
% 172.13/23.48 | | | (152) s_sworst7 = n0
% 172.13/23.48 | | | (153) ~ gt(s_sworst7, n0)
% 172.13/23.48 | | |
% 172.13/23.48 | | | REDUCE: (152), (153) imply:
% 172.13/23.48 | | | (154) ~ gt(n0, n0)
% 172.13/23.48 | | |
% 172.13/23.48 | | | BETA: splitting (62) gives:
% 172.13/23.48 | | |
% 172.13/23.48 | | | Case 1:
% 172.13/23.48 | | | |
% 172.13/23.48 | | | | (155) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 172.13/23.48 | | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 172.13/23.48 | | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)) |
% 172.13/23.48 | | | | ( ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 172.13/23.48 | | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0,
% 172.13/23.48 | | | | all_71_4)) | ( ~ (all_71_5 = init) &
% 172.13/23.48 | | | | a_select2(s_center7_init, all_71_6) = all_71_5 & $i(all_71_5)
% 172.13/23.48 | | | | & leq(all_71_6, n2) & leq(n0, all_71_6)) | ( ~ (all_71_7 =
% 172.13/23.48 | | | | init) & a_select2(s_try7_init, all_71_8) = all_71_7 &
% 172.13/23.48 | | | | $i(all_71_7) & leq(all_71_8, all_71_12) & leq(n0, all_71_8))
% 172.13/23.48 | | | |
% 172.13/23.48 | | | | BETA: splitting (155) gives:
% 172.13/23.48 | | | |
% 172.13/23.48 | | | | Case 1:
% 172.13/23.48 | | | | |
% 172.13/23.49 | | | | | (156) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 172.13/23.49 | | | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 172.13/23.49 | | | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2))
% 172.13/23.49 | | | | | | ( ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4)
% 172.13/23.49 | | | | | = all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0,
% 172.13/23.49 | | | | | all_71_4))
% 172.13/23.49 | | | | |
% 172.13/23.49 | | | | | REF_CLOSE: (56), (57), (58), (64), (67), (156) are inconsistent by
% 172.13/23.49 | | | | | sub-proof #10.
% 172.13/23.49 | | | | |
% 172.13/23.49 | | | | Case 2:
% 172.13/23.49 | | | | |
% 172.13/23.49 | | | | | (157) ( ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) =
% 172.13/23.49 | | | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0,
% 172.13/23.49 | | | | | all_71_6)) | ( ~ (all_71_7 = init) &
% 172.13/23.49 | | | | | a_select2(s_try7_init, all_71_8) = all_71_7 & $i(all_71_7)
% 172.13/23.49 | | | | | & leq(all_71_8, all_71_12) & leq(n0, all_71_8))
% 172.13/23.49 | | | | |
% 172.13/23.49 | | | | | BETA: splitting (157) gives:
% 172.13/23.49 | | | | |
% 172.13/23.49 | | | | | Case 1:
% 172.13/23.49 | | | | | |
% 172.13/23.49 | | | | | | (158) ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6)
% 172.13/23.49 | | | | | | = all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0,
% 172.13/23.49 | | | | | | all_71_6)
% 172.13/23.49 | | | | | |
% 172.13/23.49 | | | | | | REF_CLOSE: (55), (65), (158) are inconsistent by sub-proof #9.
% 172.13/23.49 | | | | | |
% 172.13/23.49 | | | | | Case 2:
% 172.13/23.49 | | | | | |
% 172.13/23.49 | | | | | | (159) ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) =
% 172.13/23.49 | | | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_12) &
% 172.13/23.49 | | | | | | leq(n0, all_71_8)
% 172.13/23.49 | | | | | |
% 172.13/23.49 | | | | | | ALPHA: (159) implies:
% 172.13/23.49 | | | | | | (160) ~ (all_71_7 = init)
% 172.13/23.49 | | | | | | (161) leq(n0, all_71_8)
% 172.13/23.49 | | | | | | (162) leq(all_71_8, all_71_12)
% 172.13/23.49 | | | | | | (163) a_select2(s_try7_init, all_71_8) = all_71_7
% 172.13/23.49 | | | | | |
% 172.13/23.49 | | | | | | REDUCE: (122), (162) imply:
% 172.13/23.49 | | | | | | (164) leq(all_71_8, n2)
% 172.13/23.49 | | | | | |
% 172.13/23.49 | | | | | | GROUND_INST: instantiating (leq_gt2) with n0, all_71_8, simplifying
% 172.13/23.49 | | | | | | with (23), (54), (161) gives:
% 172.13/23.49 | | | | | | (165) all_71_8 = n0 | gt(all_71_8, n0)
% 172.13/23.49 | | | | | |
% 172.13/23.49 | | | | | | GROUND_INST: instantiating (15) with all_71_8, simplifying with
% 172.13/23.49 | | | | | | (54), (161), (164) gives:
% 172.13/23.49 | | | | | | (166) all_71_8 = n2 | all_71_8 = n1 | all_71_8 = n0
% 172.13/23.49 | | | | | |
% 172.13/23.49 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_71_8, n2, simplifying
% 172.13/23.49 | | | | | | with (54), (92), (164) gives:
% 172.13/23.49 | | | | | | (167) all_71_8 = n2 | gt(n2, all_71_8)
% 172.13/23.49 | | | | | |
% 172.13/23.49 | | | | | | REF_CLOSE: (1), (14), (54), (66), (92), (107), (122), (154), (160),
% 172.13/23.49 | | | | | | (161), (163), (164), (165), (166), (167) are inconsistent
% 172.13/23.49 | | | | | | by sub-proof #6.
% 172.13/23.49 | | | | | |
% 172.13/23.49 | | | | | End of split
% 172.13/23.49 | | | | |
% 172.13/23.49 | | | | End of split
% 172.13/23.49 | | | |
% 172.13/23.49 | | | Case 2:
% 172.13/23.49 | | | |
% 172.13/23.49 | | | | (168) ( ~ (all_71_9 = init) & a_select2(s_try7_init, n2) = all_71_9 &
% 172.13/23.49 | | | | $i(all_71_9)) | ( ~ (all_71_10 = init) &
% 172.13/23.49 | | | | a_select2(s_try7_init, n1) = all_71_10 & $i(all_71_10)) | ( ~
% 172.13/23.49 | | | | (all_71_11 = init) & a_select2(s_try7_init, n0) = all_71_11 &
% 172.13/23.49 | | | | $i(all_71_11)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init =
% 172.13/23.49 | | | | init) | ~ (pvar1401_init = init) | ~ (pvar1400_init =
% 172.13/23.49 | | | | init)))
% 172.13/23.49 | | | |
% 172.13/23.49 | | | | REF_CLOSE: (23), (66), (82), (92), (105), (106), (108), (109), (110),
% 172.13/23.49 | | | | (117), (120), (122), (128), (129), (131), (132), (168),
% 172.13/23.49 | | | | (transitivity_gt) are inconsistent by sub-proof #1.
% 172.13/23.49 | | | |
% 172.13/23.49 | | | End of split
% 172.13/23.49 | | |
% 172.13/23.49 | | End of split
% 172.13/23.49 | |
% 172.13/23.49 | Case 2:
% 172.13/23.49 | |
% 172.13/23.49 | | (169) pvar1402_init = init & pvar1401_init = init & pvar1400_init = init
% 172.13/23.49 | |
% 172.35/23.49 | | ALPHA: (169) implies:
% 172.35/23.49 | | (170) pvar1400_init = init
% 172.35/23.49 | | (171) pvar1401_init = init
% 172.35/23.49 | | (172) pvar1402_init = init
% 172.35/23.49 | |
% 172.35/23.49 | | BETA: splitting (62) gives:
% 172.35/23.49 | |
% 172.35/23.49 | | Case 1:
% 172.35/23.49 | | |
% 172.35/23.49 | | | (173) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 172.35/23.49 | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 172.35/23.49 | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)) | (
% 172.35/23.49 | | | ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 172.35/23.49 | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0,
% 172.35/23.49 | | | all_71_4)) | ( ~ (all_71_5 = init) &
% 172.35/23.49 | | | a_select2(s_center7_init, all_71_6) = all_71_5 & $i(all_71_5) &
% 172.35/23.49 | | | leq(all_71_6, n2) & leq(n0, all_71_6)) | ( ~ (all_71_7 = init)
% 172.35/23.49 | | | & a_select2(s_try7_init, all_71_8) = all_71_7 & $i(all_71_7) &
% 172.35/23.49 | | | leq(all_71_8, all_71_12) & leq(n0, all_71_8))
% 172.35/23.49 | | |
% 172.35/23.49 | | | BETA: splitting (173) gives:
% 172.35/23.49 | | |
% 172.35/23.49 | | | Case 1:
% 172.35/23.49 | | | |
% 172.35/23.49 | | | | (174) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 172.35/23.49 | | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 172.35/23.49 | | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)) |
% 172.35/23.49 | | | | ( ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 172.35/23.49 | | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0,
% 172.35/23.49 | | | | all_71_4))
% 172.35/23.49 | | | |
% 172.35/23.49 | | | | REF_CLOSE: (56), (57), (58), (64), (67), (174) are inconsistent by
% 172.35/23.49 | | | | sub-proof #10.
% 172.35/23.49 | | | |
% 172.35/23.49 | | | Case 2:
% 172.35/23.49 | | | |
% 172.35/23.49 | | | | (175) ( ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) =
% 172.35/23.49 | | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0,
% 172.35/23.49 | | | | all_71_6)) | ( ~ (all_71_7 = init) & a_select2(s_try7_init,
% 172.35/23.49 | | | | all_71_8) = all_71_7 & $i(all_71_7) & leq(all_71_8,
% 172.35/23.49 | | | | all_71_12) & leq(n0, all_71_8))
% 172.35/23.49 | | | |
% 172.35/23.49 | | | | BETA: splitting (175) gives:
% 172.35/23.49 | | | |
% 172.35/23.49 | | | | Case 1:
% 172.35/23.49 | | | | |
% 172.35/23.49 | | | | | (176) ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) =
% 172.35/23.49 | | | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0,
% 172.35/23.49 | | | | | all_71_6)
% 172.35/23.49 | | | | |
% 172.35/23.49 | | | | | REF_CLOSE: (55), (65), (176) are inconsistent by sub-proof #9.
% 172.35/23.49 | | | | |
% 172.35/23.49 | | | | Case 2:
% 172.35/23.49 | | | | |
% 172.35/23.49 | | | | | (177) ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) =
% 172.35/23.49 | | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_12) & leq(n0,
% 172.35/23.49 | | | | | all_71_8)
% 172.35/23.49 | | | | |
% 172.35/23.49 | | | | | ALPHA: (177) implies:
% 172.35/23.49 | | | | | (178) ~ (all_71_7 = init)
% 172.35/23.49 | | | | | (179) leq(n0, all_71_8)
% 172.35/23.49 | | | | | (180) leq(all_71_8, all_71_12)
% 172.35/23.49 | | | | | (181) a_select2(s_try7_init, all_71_8) = all_71_7
% 172.35/23.49 | | | | |
% 172.35/23.49 | | | | | REDUCE: (122), (180) imply:
% 172.35/23.49 | | | | | (182) leq(all_71_8, n2)
% 172.35/23.49 | | | | |
% 172.35/23.50 | | | | | GROUND_INST: instantiating (leq_gt2) with n0, all_71_8, simplifying
% 172.35/23.50 | | | | | with (23), (54), (179) gives:
% 172.35/23.50 | | | | | (183) all_71_8 = n0 | gt(all_71_8, n0)
% 172.35/23.50 | | | | |
% 172.35/23.50 | | | | | REF_CLOSE: (1), (14), (15), (54), (66), (92), (107), (122), (178),
% 172.35/23.50 | | | | | (179), (181), (182), (183), (irreflexivity_gt), (leq_gt2)
% 172.35/23.50 | | | | | are inconsistent by sub-proof #5.
% 172.35/23.50 | | | | |
% 172.35/23.50 | | | | End of split
% 172.35/23.50 | | | |
% 172.35/23.50 | | | End of split
% 172.35/23.50 | | |
% 172.35/23.50 | | Case 2:
% 172.35/23.50 | | |
% 172.35/23.50 | | | (184) ( ~ (all_71_9 = init) & a_select2(s_try7_init, n2) = all_71_9 &
% 172.35/23.50 | | | $i(all_71_9)) | ( ~ (all_71_10 = init) & a_select2(s_try7_init,
% 172.35/23.50 | | | n1) = all_71_10 & $i(all_71_10)) | ( ~ (all_71_11 = init) &
% 172.35/23.50 | | | a_select2(s_try7_init, n0) = all_71_11 & $i(all_71_11)) |
% 172.35/23.50 | | | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~
% 172.35/23.50 | | | (pvar1401_init = init) | ~ (pvar1400_init = init)))
% 172.35/23.50 | | |
% 172.35/23.50 | | | BETA: splitting (184) gives:
% 172.35/23.50 | | |
% 172.35/23.50 | | | Case 1:
% 172.35/23.50 | | | |
% 172.35/23.50 | | | | (185) ( ~ (all_71_9 = init) & a_select2(s_try7_init, n2) = all_71_9 &
% 172.35/23.50 | | | | $i(all_71_9)) | ( ~ (all_71_10 = init) &
% 172.35/23.50 | | | | a_select2(s_try7_init, n1) = all_71_10 & $i(all_71_10))
% 172.35/23.50 | | | |
% 172.35/23.50 | | | | REF_CLOSE: (66), (82), (92), (106), (108), (109), (110), (117), (120),
% 172.35/23.50 | | | | (122), (128), (129), (131), (185), (transitivity_gt) are
% 172.35/23.50 | | | | inconsistent by sub-proof #3.
% 172.35/23.50 | | | |
% 172.35/23.50 | | | Case 2:
% 172.35/23.50 | | | |
% 172.35/23.50 | | | | (186) ( ~ (all_71_11 = init) & a_select2(s_try7_init, n0) = all_71_11
% 172.35/23.50 | | | | & $i(all_71_11)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init
% 172.35/23.50 | | | | = init) | ~ (pvar1401_init = init) | ~ (pvar1400_init =
% 172.35/23.50 | | | | init)))
% 172.35/23.50 | | | |
% 172.35/23.50 | | | | BETA: splitting (186) gives:
% 172.35/23.50 | | | |
% 172.35/23.50 | | | | Case 1:
% 172.35/23.50 | | | | |
% 172.35/23.50 | | | | | (187) ~ (all_71_11 = init) & a_select2(s_try7_init, n0) =
% 172.35/23.50 | | | | | all_71_11 & $i(all_71_11)
% 172.35/23.50 | | | | |
% 172.35/23.50 | | | | | REF_CLOSE: (23), (66), (105), (110), (117), (120), (122), (128),
% 172.35/23.50 | | | | | (129), (131), (187), (transitivity_gt) are inconsistent by
% 172.35/23.50 | | | | | sub-proof #2.
% 172.35/23.50 | | | | |
% 172.35/23.50 | | | | Case 2:
% 172.35/23.50 | | | | |
% 172.35/23.50 | | | | | (188) gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~
% 172.35/23.50 | | | | | (pvar1401_init = init) | ~ (pvar1400_init = init))
% 172.35/23.50 | | | | |
% 172.35/23.50 | | | | | ALPHA: (188) implies:
% 172.35/23.50 | | | | | (189) ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~
% 172.35/23.50 | | | | | (pvar1400_init = init)
% 172.35/23.50 | | | | |
% 172.35/23.50 | | | | | BETA: splitting (189) gives:
% 172.35/23.50 | | | | |
% 172.35/23.50 | | | | | Case 1:
% 172.35/23.50 | | | | | |
% 172.35/23.50 | | | | | | (190) ~ (pvar1402_init = init)
% 172.35/23.50 | | | | | |
% 172.35/23.50 | | | | | | REDUCE: (172), (190) imply:
% 172.35/23.50 | | | | | | (191) $false
% 172.35/23.50 | | | | | |
% 172.35/23.50 | | | | | | CLOSE: (191) is inconsistent.
% 172.35/23.50 | | | | | |
% 172.35/23.50 | | | | | Case 2:
% 172.35/23.50 | | | | | |
% 172.35/23.50 | | | | | | (192) ~ (pvar1401_init = init) | ~ (pvar1400_init = init)
% 172.35/23.50 | | | | | |
% 172.35/23.50 | | | | | | BETA: splitting (192) gives:
% 172.35/23.50 | | | | | |
% 172.35/23.50 | | | | | | Case 1:
% 172.35/23.50 | | | | | | |
% 172.35/23.50 | | | | | | | (193) ~ (pvar1401_init = init)
% 172.35/23.50 | | | | | | |
% 172.35/23.50 | | | | | | | REDUCE: (171), (193) imply:
% 172.35/23.50 | | | | | | | (194) $false
% 172.35/23.50 | | | | | | |
% 172.35/23.50 | | | | | | | CLOSE: (194) is inconsistent.
% 172.35/23.50 | | | | | | |
% 172.35/23.50 | | | | | | Case 2:
% 172.35/23.50 | | | | | | |
% 172.35/23.50 | | | | | | | (195) ~ (pvar1400_init = init)
% 172.35/23.50 | | | | | | |
% 172.35/23.50 | | | | | | | REDUCE: (170), (195) imply:
% 172.35/23.50 | | | | | | | (196) $false
% 172.35/23.50 | | | | | | |
% 172.35/23.50 | | | | | | | CLOSE: (196) is inconsistent.
% 172.35/23.50 | | | | | | |
% 172.35/23.50 | | | | | | End of split
% 172.35/23.50 | | | | | |
% 172.35/23.50 | | | | | End of split
% 172.35/23.50 | | | | |
% 172.35/23.50 | | | | End of split
% 172.35/23.50 | | | |
% 172.35/23.50 | | | End of split
% 172.35/23.50 | | |
% 172.35/23.50 | | End of split
% 172.35/23.50 | |
% 172.35/23.50 | End of split
% 172.35/23.50 |
% 172.35/23.50 End of proof
% 172.35/23.50
% 172.35/23.50 Sub-proof #1 shows that the following formulas are inconsistent:
% 172.35/23.50 ----------------------------------------------------------------
% 172.35/23.50 (1) all_71_14 = n5 | gt(all_71_14, n5)
% 172.35/23.50 (2) $i(all_71_13)
% 172.35/23.50 (3) leq(n0, n1)
% 172.35/23.50 (4) $i(n2)
% 172.35/23.50 (5) leq(n0, n2)
% 172.35/23.50 (6) ~ gt(loopcounter, n1)
% 172.35/23.50 (7) gt(all_71_14, all_71_13)
% 172.35/23.50 (8) $i(n1)
% 172.35/23.50 (9) all_71_13 = n5 | gt(all_71_13, n5)
% 172.35/23.50 (10) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0)
% 172.35/23.50 = v1) | ~ $i(v0) | ~ leq(v0, all_71_12) | ~ leq(n0, v0))
% 172.35/23.50 (11) leq(n0, n0)
% 172.35/23.50 (12) $i(all_71_14)
% 172.35/23.50 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 172.35/23.50 $i(v0) | ~ gt(v1, v2) | ~ gt(v0, v1) | gt(v0, v2))
% 172.35/23.50 (14) leq(n2, n2)
% 172.35/23.50 (15) $i(n0)
% 172.35/23.50 (16) all_71_12 = n2
% 172.35/23.50 (17) ( ~ (all_71_9 = init) & a_select2(s_try7_init, n2) = all_71_9 &
% 172.35/23.50 $i(all_71_9)) | ( ~ (all_71_10 = init) & a_select2(s_try7_init, n1) =
% 172.35/23.50 all_71_10 & $i(all_71_10)) | ( ~ (all_71_11 = init) &
% 172.35/23.50 a_select2(s_try7_init, n0) = all_71_11 & $i(all_71_11)) |
% 172.35/23.50 (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~ (pvar1401_init =
% 172.35/23.50 init) | ~ (pvar1400_init = init)))
% 172.35/23.50 (18) leq(n1, n2)
% 172.35/23.50
% 172.35/23.50 Begin of proof
% 172.35/23.50 |
% 172.35/23.50 | BETA: splitting (17) gives:
% 172.35/23.50 |
% 172.35/23.50 | Case 1:
% 172.35/23.50 | |
% 172.35/23.50 | | (19) ( ~ (all_71_9 = init) & a_select2(s_try7_init, n2) = all_71_9 &
% 172.35/23.50 | | $i(all_71_9)) | ( ~ (all_71_10 = init) & a_select2(s_try7_init,
% 172.35/23.50 | | n1) = all_71_10 & $i(all_71_10))
% 172.35/23.50 | |
% 172.35/23.50 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 172.35/23.50 | | (16), (18), (19) are inconsistent by sub-proof #3.
% 172.35/23.50 | |
% 172.35/23.50 | Case 2:
% 172.35/23.50 | |
% 172.35/23.50 | | (20) ( ~ (all_71_11 = init) & a_select2(s_try7_init, n0) = all_71_11 &
% 172.35/23.50 | | $i(all_71_11)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init)
% 172.35/23.50 | | | ~ (pvar1401_init = init) | ~ (pvar1400_init = init)))
% 172.35/23.50 | |
% 172.35/23.50 | | BETA: splitting (20) gives:
% 172.35/23.50 | |
% 172.35/23.50 | | Case 1:
% 172.35/23.50 | | |
% 172.35/23.50 | | | (21) ~ (all_71_11 = init) & a_select2(s_try7_init, n0) = all_71_11 &
% 172.35/23.50 | | | $i(all_71_11)
% 172.35/23.50 | | |
% 172.35/23.50 | | | REF_CLOSE: (1), (2), (5), (7), (9), (10), (11), (12), (13), (15), (16),
% 172.35/23.50 | | | (21) are inconsistent by sub-proof #2.
% 172.35/23.50 | | |
% 172.35/23.50 | | Case 2:
% 172.35/23.50 | | |
% 172.35/23.50 | | | (22) gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~
% 172.35/23.50 | | | (pvar1401_init = init) | ~ (pvar1400_init = init))
% 172.35/23.50 | | |
% 172.35/23.51 | | | ALPHA: (22) implies:
% 172.35/23.51 | | | (23) gt(loopcounter, n1)
% 172.35/23.51 | | |
% 172.35/23.51 | | | PRED_UNIFY: (6), (23) imply:
% 172.35/23.51 | | | (24) $false
% 172.35/23.51 | | |
% 172.35/23.51 | | | CLOSE: (24) is inconsistent.
% 172.35/23.51 | | |
% 172.35/23.51 | | End of split
% 172.35/23.51 | |
% 172.35/23.51 | End of split
% 172.35/23.51 |
% 172.35/23.51 End of proof
% 172.35/23.51
% 172.35/23.51 Sub-proof #2 shows that the following formulas are inconsistent:
% 172.35/23.51 ----------------------------------------------------------------
% 172.35/23.51 (1) all_71_14 = n5 | gt(all_71_14, n5)
% 172.35/23.51 (2) $i(all_71_13)
% 172.35/23.51 (3) leq(n0, n2)
% 172.35/23.51 (4) gt(all_71_14, all_71_13)
% 172.35/23.51 (5) all_71_13 = n5 | gt(all_71_13, n5)
% 172.35/23.51 (6) ~ (all_71_11 = init) & a_select2(s_try7_init, n0) = all_71_11 &
% 172.35/23.51 $i(all_71_11)
% 172.35/23.51 (7) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0) =
% 172.35/23.51 v1) | ~ $i(v0) | ~ leq(v0, all_71_12) | ~ leq(n0, v0))
% 172.35/23.51 (8) leq(n0, n0)
% 172.35/23.51 (9) $i(all_71_14)
% 172.35/23.51 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 172.35/23.51 $i(v0) | ~ gt(v1, v2) | ~ gt(v0, v1) | gt(v0, v2))
% 172.35/23.51 (11) $i(n0)
% 172.35/23.51 (12) all_71_12 = n2
% 172.35/23.51
% 172.35/23.51 Begin of proof
% 172.35/23.51 |
% 172.35/23.51 | ALPHA: (6) implies:
% 172.35/23.51 | (13) ~ (all_71_11 = init)
% 172.35/23.51 | (14) a_select2(s_try7_init, n0) = all_71_11
% 172.35/23.51 |
% 172.35/23.51 | BETA: splitting (1) gives:
% 172.35/23.51 |
% 172.35/23.51 | Case 1:
% 172.35/23.51 | |
% 172.35/23.51 | |
% 172.35/23.51 | | GROUND_INST: instantiating (7) with n0, all_71_11, simplifying with (8),
% 172.35/23.51 | | (11), (14) gives:
% 172.35/23.51 | | (15) all_71_11 = init | ~ leq(n0, all_71_12)
% 172.35/23.51 | |
% 172.35/23.51 | | BETA: splitting (15) gives:
% 172.35/23.51 | |
% 172.35/23.51 | | Case 1:
% 172.35/23.51 | | |
% 172.35/23.51 | | | (16) ~ leq(n0, all_71_12)
% 172.35/23.51 | | |
% 172.35/23.51 | | | REDUCE: (12), (16) imply:
% 172.35/23.51 | | | (17) ~ leq(n0, n2)
% 172.35/23.51 | | |
% 172.35/23.51 | | | PRED_UNIFY: (3), (17) imply:
% 172.35/23.51 | | | (18) $false
% 172.35/23.51 | | |
% 172.35/23.51 | | | CLOSE: (18) is inconsistent.
% 172.35/23.51 | | |
% 172.35/23.51 | | Case 2:
% 172.35/23.51 | | |
% 172.35/23.51 | | | (19) all_71_11 = init
% 172.35/23.51 | | |
% 172.35/23.51 | | | REDUCE: (13), (19) imply:
% 172.35/23.51 | | | (20) $false
% 172.35/23.51 | | |
% 172.35/23.51 | | | CLOSE: (20) is inconsistent.
% 172.35/23.51 | | |
% 172.35/23.51 | | End of split
% 172.35/23.51 | |
% 172.35/23.51 | Case 2:
% 172.35/23.51 | |
% 172.35/23.51 | | (21) all_71_14 = n5
% 172.35/23.51 | | (22) ~ gt(all_71_14, n5)
% 172.35/23.51 | |
% 172.35/23.51 | | REDUCE: (9), (21) imply:
% 172.35/23.51 | | (23) $i(n5)
% 172.35/23.51 | |
% 172.35/23.51 | | REDUCE: (4), (21) imply:
% 172.35/23.51 | | (24) gt(n5, all_71_13)
% 172.35/23.51 | |
% 172.35/23.51 | | REDUCE: (21), (22) imply:
% 172.35/23.51 | | (25) ~ gt(n5, n5)
% 172.35/23.51 | |
% 172.35/23.51 | | REF_CLOSE: (2), (5), (10), (23), (24), (25) are inconsistent by sub-proof
% 172.35/23.51 | | #4.
% 172.35/23.51 | |
% 172.35/23.51 | End of split
% 172.35/23.51 |
% 172.35/23.51 End of proof
% 172.35/23.51
% 172.35/23.51 Sub-proof #3 shows that the following formulas are inconsistent:
% 172.35/23.51 ----------------------------------------------------------------
% 172.35/23.51 (1) all_71_14 = n5 | gt(all_71_14, n5)
% 172.35/23.51 (2) $i(all_71_13)
% 172.35/23.51 (3) leq(n0, n1)
% 172.35/23.51 (4) $i(n2)
% 172.35/23.51 (5) leq(n0, n2)
% 172.35/23.51 (6) gt(all_71_14, all_71_13)
% 172.35/23.51 (7) $i(n1)
% 172.35/23.51 (8) all_71_13 = n5 | gt(all_71_13, n5)
% 172.35/23.51 (9) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0) =
% 172.35/23.51 v1) | ~ $i(v0) | ~ leq(v0, all_71_12) | ~ leq(n0, v0))
% 172.35/23.51 (10) $i(all_71_14)
% 172.35/23.51 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 172.35/23.51 $i(v0) | ~ gt(v1, v2) | ~ gt(v0, v1) | gt(v0, v2))
% 172.35/23.51 (12) leq(n2, n2)
% 172.35/23.51 (13) all_71_12 = n2
% 172.35/23.51 (14) leq(n1, n2)
% 172.35/23.51 (15) ( ~ (all_71_9 = init) & a_select2(s_try7_init, n2) = all_71_9 &
% 172.35/23.51 $i(all_71_9)) | ( ~ (all_71_10 = init) & a_select2(s_try7_init, n1) =
% 172.35/23.51 all_71_10 & $i(all_71_10))
% 172.35/23.51
% 172.35/23.51 Begin of proof
% 172.35/23.51 |
% 172.35/23.51 | BETA: splitting (15) gives:
% 172.35/23.51 |
% 172.35/23.51 | Case 1:
% 172.35/23.51 | |
% 172.35/23.51 | | (16) ~ (all_71_9 = init) & a_select2(s_try7_init, n2) = all_71_9 &
% 172.35/23.51 | | $i(all_71_9)
% 172.35/23.51 | |
% 172.35/23.51 | | ALPHA: (16) implies:
% 172.35/23.51 | | (17) ~ (all_71_9 = init)
% 172.35/23.51 | | (18) a_select2(s_try7_init, n2) = all_71_9
% 172.35/23.51 | |
% 172.35/23.51 | | BETA: splitting (1) gives:
% 172.35/23.51 | |
% 172.35/23.51 | | Case 1:
% 172.35/23.51 | | |
% 172.35/23.51 | | |
% 172.35/23.51 | | | GROUND_INST: instantiating (9) with n2, all_71_9, simplifying with (4),
% 172.35/23.51 | | | (5), (18) gives:
% 172.35/23.51 | | | (19) all_71_9 = init | ~ leq(n2, all_71_12)
% 172.35/23.51 | | |
% 172.35/23.51 | | | BETA: splitting (19) gives:
% 172.35/23.51 | | |
% 172.35/23.51 | | | Case 1:
% 172.35/23.51 | | | |
% 172.35/23.51 | | | | (20) ~ leq(n2, all_71_12)
% 172.35/23.51 | | | |
% 172.35/23.51 | | | | REDUCE: (13), (20) imply:
% 172.35/23.51 | | | | (21) ~ leq(n2, n2)
% 172.35/23.51 | | | |
% 172.35/23.51 | | | | PRED_UNIFY: (12), (21) imply:
% 172.35/23.51 | | | | (22) $false
% 172.35/23.51 | | | |
% 172.35/23.51 | | | | CLOSE: (22) is inconsistent.
% 172.35/23.51 | | | |
% 172.35/23.51 | | | Case 2:
% 172.35/23.51 | | | |
% 172.35/23.51 | | | | (23) all_71_9 = init
% 172.35/23.51 | | | |
% 172.35/23.51 | | | | REDUCE: (17), (23) imply:
% 172.35/23.51 | | | | (24) $false
% 172.35/23.51 | | | |
% 172.35/23.51 | | | | CLOSE: (24) is inconsistent.
% 172.35/23.51 | | | |
% 172.35/23.51 | | | End of split
% 172.35/23.51 | | |
% 172.35/23.51 | | Case 2:
% 172.35/23.51 | | |
% 172.35/23.51 | | | (25) all_71_14 = n5
% 172.35/23.51 | | | (26) ~ gt(all_71_14, n5)
% 172.35/23.51 | | |
% 172.35/23.51 | | | REDUCE: (10), (25) imply:
% 172.35/23.51 | | | (27) $i(n5)
% 172.35/23.51 | | |
% 172.35/23.51 | | | REDUCE: (6), (25) imply:
% 172.35/23.51 | | | (28) gt(n5, all_71_13)
% 172.35/23.51 | | |
% 172.35/23.51 | | | REDUCE: (25), (26) imply:
% 172.35/23.51 | | | (29) ~ gt(n5, n5)
% 172.35/23.51 | | |
% 172.35/23.51 | | | REF_CLOSE: (2), (8), (11), (27), (28), (29) are inconsistent by sub-proof
% 172.35/23.51 | | | #4.
% 172.35/23.51 | | |
% 172.35/23.51 | | End of split
% 172.35/23.51 | |
% 172.35/23.51 | Case 2:
% 172.35/23.51 | |
% 172.35/23.51 | | (30) ~ (all_71_10 = init) & a_select2(s_try7_init, n1) = all_71_10 &
% 172.35/23.51 | | $i(all_71_10)
% 172.35/23.51 | |
% 172.35/23.51 | | ALPHA: (30) implies:
% 172.35/23.51 | | (31) ~ (all_71_10 = init)
% 172.35/23.51 | | (32) a_select2(s_try7_init, n1) = all_71_10
% 172.35/23.51 | |
% 172.35/23.51 | | GROUND_INST: instantiating (9) with n1, all_71_10, simplifying with (3),
% 172.35/23.51 | | (7), (32) gives:
% 172.35/23.52 | | (33) all_71_10 = init | ~ leq(n1, all_71_12)
% 172.35/23.52 | |
% 172.35/23.52 | | BETA: splitting (33) gives:
% 172.35/23.52 | |
% 172.35/23.52 | | Case 1:
% 172.35/23.52 | | |
% 172.35/23.52 | | | (34) ~ leq(n1, all_71_12)
% 172.35/23.52 | | |
% 172.35/23.52 | | | REDUCE: (13), (34) imply:
% 172.35/23.52 | | | (35) ~ leq(n1, n2)
% 172.35/23.52 | | |
% 172.35/23.52 | | | PRED_UNIFY: (14), (35) imply:
% 172.35/23.52 | | | (36) $false
% 172.35/23.52 | | |
% 172.35/23.52 | | | CLOSE: (36) is inconsistent.
% 172.35/23.52 | | |
% 172.35/23.52 | | Case 2:
% 172.35/23.52 | | |
% 172.35/23.52 | | | (37) all_71_10 = init
% 172.35/23.52 | | |
% 172.35/23.52 | | | REDUCE: (31), (37) imply:
% 172.35/23.52 | | | (38) $false
% 172.35/23.52 | | |
% 172.35/23.52 | | | CLOSE: (38) is inconsistent.
% 172.35/23.52 | | |
% 172.35/23.52 | | End of split
% 172.35/23.52 | |
% 172.35/23.52 | End of split
% 172.35/23.52 |
% 172.35/23.52 End of proof
% 172.35/23.52
% 172.35/23.52 Sub-proof #4 shows that the following formulas are inconsistent:
% 172.35/23.52 ----------------------------------------------------------------
% 172.35/23.52 (1) $i(all_71_13)
% 172.35/23.52 (2) ~ gt(n5, n5)
% 172.35/23.52 (3) $i(n5)
% 172.35/23.52 (4) gt(n5, all_71_13)
% 172.35/23.52 (5) all_71_13 = n5 | gt(all_71_13, n5)
% 172.35/23.52 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 172.35/23.52 $i(v0) | ~ gt(v1, v2) | ~ gt(v0, v1) | gt(v0, v2))
% 172.35/23.52
% 172.35/23.52 Begin of proof
% 172.35/23.52 |
% 172.35/23.52 | BETA: splitting (5) gives:
% 172.35/23.52 |
% 172.35/23.52 | Case 1:
% 172.35/23.52 | |
% 172.35/23.52 | | (7) gt(all_71_13, n5)
% 172.35/23.52 | |
% 172.35/23.52 | | GROUND_INST: instantiating (6) with n5, all_71_13, n5, simplifying with (1),
% 172.35/23.52 | | (2), (3), (4), (7) gives:
% 172.35/23.52 | | (8) $false
% 172.35/23.52 | |
% 172.35/23.52 | | CLOSE: (8) is inconsistent.
% 172.35/23.52 | |
% 172.35/23.52 | Case 2:
% 172.35/23.52 | |
% 172.35/23.52 | | (9) all_71_13 = n5
% 172.35/23.52 | | (10) ~ gt(all_71_13, n5)
% 172.35/23.52 | |
% 172.35/23.52 | | REDUCE: (4), (9) imply:
% 172.35/23.52 | | (11) gt(n5, n5)
% 172.35/23.52 | |
% 172.35/23.52 | | PRED_UNIFY: (2), (11) imply:
% 172.35/23.52 | | (12) $false
% 172.35/23.52 | |
% 172.35/23.52 | | CLOSE: (12) is inconsistent.
% 172.35/23.52 | |
% 172.35/23.52 | End of split
% 172.35/23.52 |
% 172.35/23.52 End of proof
% 172.35/23.52
% 172.35/23.52 Sub-proof #5 shows that the following formulas are inconsistent:
% 172.35/23.52 ----------------------------------------------------------------
% 172.35/23.52 (1) all_71_8 = n0 | gt(all_71_8, n0)
% 172.35/23.52 (2) $i(n2)
% 172.35/23.52 (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0,
% 172.35/23.52 v1) | gt(v1, v0))
% 172.35/23.52 (4) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 172.35/23.52 leq(n0, v0))
% 172.35/23.52 (5) pred(n2) = n1
% 172.35/23.52 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1)
% 172.35/23.52 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 172.35/23.52 (7) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0) =
% 172.35/23.52 v1) | ~ $i(v0) | ~ leq(v0, all_71_12) | ~ leq(n0, v0))
% 172.35/23.52 (8) leq(n0, all_71_8)
% 172.35/23.52 (9) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0))
% 172.35/23.52 (10) ~ (all_71_7 = init)
% 172.35/23.52 (11) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2)
% 172.35/23.52 | ~ leq(n0, v0))
% 172.35/23.52 (12) leq(all_71_8, n2)
% 172.35/23.52 (13) all_71_12 = n2
% 172.35/23.52 (14) $i(all_71_8)
% 172.35/23.52 (15) a_select2(s_try7_init, all_71_8) = all_71_7
% 172.35/23.52
% 172.35/23.52 Begin of proof
% 172.35/23.52 |
% 172.35/23.52 | GROUND_INST: instantiating (11) with all_71_8, simplifying with (8), (12),
% 172.35/23.52 | (14) gives:
% 172.35/23.52 | (16) all_71_8 = n2 | all_71_8 = n1 | all_71_8 = n0
% 172.35/23.52 |
% 172.35/23.52 | GROUND_INST: instantiating (3) with all_71_8, n2, simplifying with (2), (12),
% 172.35/23.52 | (14) gives:
% 172.35/23.52 | (17) all_71_8 = n2 | gt(n2, all_71_8)
% 172.35/23.52 |
% 172.35/23.52 | BETA: splitting (1) gives:
% 172.35/23.52 |
% 172.35/23.52 | Case 1:
% 172.35/23.52 | |
% 172.35/23.52 | | (18) gt(all_71_8, n0)
% 172.35/23.52 | |
% 172.35/23.52 | | BETA: splitting (17) gives:
% 172.35/23.52 | |
% 172.35/23.52 | | Case 1:
% 172.35/23.52 | | |
% 172.35/23.52 | | | (19) gt(n2, all_71_8)
% 172.35/23.52 | | |
% 172.35/23.52 | | | GROUND_INST: instantiating (6) with all_71_8, n2, n1, simplifying with
% 172.35/23.52 | | | (2), (5), (14), (19) gives:
% 172.35/23.52 | | | (20) leq(all_71_8, n1)
% 172.35/23.52 | | |
% 172.35/23.52 | | | GROUND_INST: instantiating (4) with all_71_8, simplifying with (8), (14),
% 172.35/23.52 | | | (20) gives:
% 172.35/23.52 | | | (21) all_71_8 = n1 | all_71_8 = n0
% 172.35/23.52 | | |
% 172.35/23.52 | | | BETA: splitting (16) gives:
% 172.35/23.52 | | |
% 172.35/23.52 | | | Case 1:
% 172.35/23.52 | | | |
% 172.35/23.52 | | | | (22) all_71_8 = n0
% 172.35/23.52 | | | |
% 172.35/23.52 | | | | REDUCE: (14), (22) imply:
% 172.35/23.52 | | | | (23) $i(n0)
% 172.35/23.52 | | | |
% 172.35/23.52 | | | | REDUCE: (18), (22) imply:
% 172.35/23.52 | | | | (24) gt(n0, n0)
% 172.35/23.52 | | | |
% 172.35/23.52 | | | | GROUND_INST: instantiating (9) with n0, simplifying with (23), (24)
% 172.35/23.52 | | | | gives:
% 172.35/23.52 | | | | (25) $false
% 172.35/23.52 | | | |
% 172.35/23.52 | | | | CLOSE: (25) is inconsistent.
% 172.35/23.52 | | | |
% 172.35/23.52 | | | Case 2:
% 172.35/23.52 | | | |
% 172.35/23.52 | | | | (26) ~ (all_71_8 = n0)
% 172.35/23.52 | | | |
% 172.35/23.52 | | | | REF_CLOSE: (7), (8), (10), (12), (13), (14), (15), (21), (26) are
% 172.35/23.52 | | | | inconsistent by sub-proof #8.
% 172.35/23.52 | | | |
% 172.35/23.52 | | | End of split
% 172.35/23.52 | | |
% 172.35/23.52 | | Case 2:
% 172.35/23.52 | | |
% 172.35/23.52 | | | (27) all_71_8 = n2
% 172.35/23.52 | | |
% 172.35/23.52 | | | REF_CLOSE: (7), (8), (10), (12), (13), (14), (15), (27) are inconsistent
% 172.35/23.52 | | | by sub-proof #7.
% 172.35/23.52 | | |
% 172.35/23.52 | | End of split
% 172.35/23.52 | |
% 172.35/23.52 | Case 2:
% 172.35/23.52 | |
% 172.35/23.52 | | (28) all_71_8 = n0
% 172.35/23.52 | | (29) ~ gt(all_71_8, n0)
% 172.35/23.52 | |
% 172.35/23.52 | | REDUCE: (28), (29) imply:
% 172.35/23.52 | | (30) ~ gt(n0, n0)
% 172.35/23.52 | |
% 172.35/23.52 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (12), (13), (14), (15),
% 172.35/23.52 | | (16), (17), (30) are inconsistent by sub-proof #6.
% 172.35/23.52 | |
% 172.35/23.52 | End of split
% 172.35/23.52 |
% 172.35/23.52 End of proof
% 172.35/23.52
% 172.35/23.52 Sub-proof #6 shows that the following formulas are inconsistent:
% 172.35/23.52 ----------------------------------------------------------------
% 172.35/23.52 (1) all_71_8 = n0 | gt(all_71_8, n0)
% 172.35/23.52 (2) all_71_8 = n2 | gt(n2, all_71_8)
% 172.35/23.52 (3) $i(n2)
% 172.35/23.52 (4) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 172.35/23.52 leq(n0, v0))
% 172.35/23.53 (5) pred(n2) = n1
% 172.35/23.53 (6) all_71_8 = n2 | all_71_8 = n1 | all_71_8 = n0
% 172.35/23.53 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1)
% 172.35/23.53 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 172.35/23.53 (8) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0) =
% 172.35/23.53 v1) | ~ $i(v0) | ~ leq(v0, all_71_12) | ~ leq(n0, v0))
% 172.35/23.53 (9) leq(n0, all_71_8)
% 172.35/23.53 (10) ~ (all_71_7 = init)
% 172.35/23.53 (11) ~ gt(n0, n0)
% 172.35/23.53 (12) leq(all_71_8, n2)
% 172.35/23.53 (13) all_71_12 = n2
% 172.35/23.53 (14) $i(all_71_8)
% 172.35/23.53 (15) a_select2(s_try7_init, all_71_8) = all_71_7
% 172.35/23.53
% 172.35/23.53 Begin of proof
% 172.35/23.53 |
% 172.35/23.53 | BETA: splitting (1) gives:
% 172.35/23.53 |
% 172.35/23.53 | Case 1:
% 172.35/23.53 | |
% 172.35/23.53 | | (16) gt(all_71_8, n0)
% 172.35/23.53 | |
% 172.35/23.53 | | BETA: splitting (2) gives:
% 172.35/23.53 | |
% 172.35/23.53 | | Case 1:
% 172.35/23.53 | | |
% 172.35/23.53 | | | (17) gt(n2, all_71_8)
% 172.35/23.53 | | |
% 172.35/23.53 | | | GROUND_INST: instantiating (7) with all_71_8, n2, n1, simplifying with
% 172.35/23.53 | | | (3), (5), (14), (17) gives:
% 172.35/23.53 | | | (18) leq(all_71_8, n1)
% 172.35/23.53 | | |
% 172.35/23.53 | | | GROUND_INST: instantiating (4) with all_71_8, simplifying with (9), (14),
% 172.35/23.53 | | | (18) gives:
% 172.35/23.53 | | | (19) all_71_8 = n1 | all_71_8 = n0
% 172.35/23.53 | | |
% 172.35/23.53 | | | BETA: splitting (6) gives:
% 172.35/23.53 | | |
% 172.35/23.53 | | | Case 1:
% 172.35/23.53 | | | |
% 172.35/23.53 | | | | (20) all_71_8 = n0
% 172.35/23.53 | | | |
% 172.35/23.53 | | | | REDUCE: (16), (20) imply:
% 172.35/23.53 | | | | (21) gt(n0, n0)
% 172.35/23.53 | | | |
% 172.35/23.53 | | | | PRED_UNIFY: (11), (21) imply:
% 172.35/23.53 | | | | (22) $false
% 172.35/23.53 | | | |
% 172.35/23.53 | | | | CLOSE: (22) is inconsistent.
% 172.35/23.53 | | | |
% 172.35/23.53 | | | Case 2:
% 172.35/23.53 | | | |
% 172.35/23.53 | | | | (23) ~ (all_71_8 = n0)
% 172.35/23.53 | | | |
% 172.35/23.53 | | | | REF_CLOSE: (8), (9), (10), (12), (13), (14), (15), (19), (23) are
% 172.35/23.53 | | | | inconsistent by sub-proof #8.
% 172.35/23.53 | | | |
% 172.35/23.53 | | | End of split
% 172.35/23.53 | | |
% 172.35/23.53 | | Case 2:
% 172.35/23.53 | | |
% 172.35/23.53 | | | (24) all_71_8 = n2
% 172.35/23.53 | | |
% 172.35/23.53 | | | REF_CLOSE: (8), (9), (10), (12), (13), (14), (15), (24) are inconsistent
% 172.35/23.53 | | | by sub-proof #7.
% 172.35/23.53 | | |
% 172.35/23.53 | | End of split
% 172.35/23.53 | |
% 172.35/23.53 | Case 2:
% 172.35/23.53 | |
% 172.35/23.53 | | (25) all_71_8 = n0
% 172.35/23.53 | |
% 172.35/23.53 | | REDUCE: (15), (25) imply:
% 172.35/23.53 | | (26) a_select2(s_try7_init, n0) = all_71_7
% 172.35/23.53 | |
% 172.35/23.53 | | REDUCE: (14), (25) imply:
% 172.35/23.53 | | (27) $i(n0)
% 172.35/23.53 | |
% 172.35/23.53 | | REDUCE: (12), (25) imply:
% 172.35/23.53 | | (28) leq(n0, n2)
% 172.35/23.53 | |
% 172.35/23.53 | | REDUCE: (9), (25) imply:
% 172.35/23.53 | | (29) leq(n0, n0)
% 172.35/23.53 | |
% 172.35/23.53 | | GROUND_INST: instantiating (8) with n0, all_71_7, simplifying with (26),
% 172.35/23.53 | | (27), (29) gives:
% 172.35/23.53 | | (30) all_71_7 = init | ~ leq(n0, all_71_12)
% 172.35/23.53 | |
% 172.35/23.53 | | BETA: splitting (30) gives:
% 172.35/23.53 | |
% 172.35/23.53 | | Case 1:
% 172.35/23.53 | | |
% 172.35/23.53 | | | (31) ~ leq(n0, all_71_12)
% 172.35/23.53 | | |
% 172.35/23.53 | | | REDUCE: (13), (31) imply:
% 172.35/23.53 | | | (32) ~ leq(n0, n2)
% 172.35/23.53 | | |
% 172.35/23.53 | | | PRED_UNIFY: (28), (32) imply:
% 172.35/23.53 | | | (33) $false
% 172.35/23.53 | | |
% 172.35/23.53 | | | CLOSE: (33) is inconsistent.
% 172.35/23.53 | | |
% 172.35/23.53 | | Case 2:
% 172.35/23.53 | | |
% 172.35/23.53 | | | (34) all_71_7 = init
% 172.35/23.53 | | |
% 172.35/23.53 | | | REDUCE: (10), (34) imply:
% 172.35/23.53 | | | (35) $false
% 172.35/23.53 | | |
% 172.35/23.53 | | | CLOSE: (35) is inconsistent.
% 172.35/23.53 | | |
% 172.35/23.53 | | End of split
% 172.35/23.53 | |
% 172.35/23.53 | End of split
% 172.35/23.53 |
% 172.35/23.53 End of proof
% 172.35/23.53
% 172.35/23.53 Sub-proof #7 shows that the following formulas are inconsistent:
% 172.35/23.53 ----------------------------------------------------------------
% 172.35/23.53 (1) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0) =
% 172.35/23.53 v1) | ~ $i(v0) | ~ leq(v0, all_71_12) | ~ leq(n0, v0))
% 172.35/23.53 (2) leq(n0, all_71_8)
% 172.35/23.53 (3) ~ (all_71_7 = init)
% 172.35/23.53 (4) leq(all_71_8, n2)
% 172.35/23.53 (5) all_71_12 = n2
% 172.35/23.53 (6) $i(all_71_8)
% 172.35/23.53 (7) a_select2(s_try7_init, all_71_8) = all_71_7
% 172.35/23.53 (8) all_71_8 = n2
% 172.35/23.53
% 172.35/23.53 Begin of proof
% 172.35/23.53 |
% 172.35/23.53 | REDUCE: (7), (8) imply:
% 172.35/23.53 | (9) a_select2(s_try7_init, n2) = all_71_7
% 172.35/23.53 |
% 172.35/23.53 | REDUCE: (6), (8) imply:
% 172.35/23.53 | (10) $i(n2)
% 172.35/23.53 |
% 172.35/23.53 | REDUCE: (4), (8) imply:
% 172.35/23.53 | (11) leq(n2, n2)
% 172.35/23.53 |
% 172.35/23.53 | REDUCE: (2), (8) imply:
% 172.35/23.53 | (12) leq(n0, n2)
% 172.35/23.53 |
% 172.35/23.53 | GROUND_INST: instantiating (1) with n2, all_71_7, simplifying with (9), (10),
% 172.35/23.53 | (12) gives:
% 172.35/23.53 | (13) all_71_7 = init | ~ leq(n2, all_71_12)
% 172.35/23.53 |
% 172.35/23.53 | BETA: splitting (13) gives:
% 172.35/23.53 |
% 172.35/23.53 | Case 1:
% 172.35/23.53 | |
% 172.35/23.53 | | (14) ~ leq(n2, all_71_12)
% 172.35/23.53 | |
% 172.35/23.53 | | REDUCE: (5), (14) imply:
% 172.35/23.53 | | (15) ~ leq(n2, n2)
% 172.35/23.53 | |
% 172.35/23.53 | | PRED_UNIFY: (11), (15) imply:
% 172.35/23.53 | | (16) $false
% 172.35/23.53 | |
% 172.35/23.53 | | CLOSE: (16) is inconsistent.
% 172.35/23.53 | |
% 172.35/23.53 | Case 2:
% 172.35/23.53 | |
% 172.35/23.53 | | (17) all_71_7 = init
% 172.35/23.53 | |
% 172.35/23.53 | | REDUCE: (3), (17) imply:
% 172.35/23.53 | | (18) $false
% 172.35/23.53 | |
% 172.35/23.53 | | CLOSE: (18) is inconsistent.
% 172.35/23.53 | |
% 172.35/23.53 | End of split
% 172.35/23.53 |
% 172.35/23.53 End of proof
% 172.35/23.53
% 172.35/23.53 Sub-proof #8 shows that the following formulas are inconsistent:
% 172.35/23.53 ----------------------------------------------------------------
% 172.35/23.53 (1) ~ (all_71_8 = n0)
% 172.35/23.53 (2) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0) =
% 172.35/23.53 v1) | ~ $i(v0) | ~ leq(v0, all_71_12) | ~ leq(n0, v0))
% 172.35/23.53 (3) leq(n0, all_71_8)
% 172.35/23.53 (4) ~ (all_71_7 = init)
% 172.35/23.53 (5) leq(all_71_8, n2)
% 172.35/23.53 (6) all_71_8 = n1 | all_71_8 = n0
% 172.35/23.53 (7) all_71_12 = n2
% 172.35/23.53 (8) $i(all_71_8)
% 172.35/23.53 (9) a_select2(s_try7_init, all_71_8) = all_71_7
% 172.35/23.53
% 172.35/23.53 Begin of proof
% 172.35/23.53 |
% 172.35/23.53 | BETA: splitting (6) gives:
% 172.35/23.53 |
% 172.35/23.53 | Case 1:
% 172.35/23.53 | |
% 172.35/23.53 | | (10) all_71_8 = n0
% 172.35/23.53 | |
% 172.35/23.53 | | REDUCE: (1), (10) imply:
% 172.35/23.53 | | (11) $false
% 172.35/23.53 | |
% 172.35/23.53 | | CLOSE: (11) is inconsistent.
% 172.35/23.53 | |
% 172.35/23.53 | Case 2:
% 172.35/23.53 | |
% 172.35/23.53 | | (12) all_71_8 = n1
% 172.35/23.53 | |
% 172.35/23.53 | | REDUCE: (9), (12) imply:
% 172.35/23.53 | | (13) a_select2(s_try7_init, n1) = all_71_7
% 172.35/23.53 | |
% 172.35/23.53 | | REDUCE: (8), (12) imply:
% 172.35/23.53 | | (14) $i(n1)
% 172.35/23.53 | |
% 172.35/23.53 | | REDUCE: (5), (12) imply:
% 172.35/23.53 | | (15) leq(n1, n2)
% 172.35/23.53 | |
% 172.35/23.53 | | REDUCE: (3), (12) imply:
% 172.35/23.53 | | (16) leq(n0, n1)
% 172.35/23.53 | |
% 172.35/23.53 | | GROUND_INST: instantiating (2) with n1, all_71_7, simplifying with (13),
% 172.35/23.53 | | (14), (16) gives:
% 172.35/23.53 | | (17) all_71_7 = init | ~ leq(n1, all_71_12)
% 172.35/23.53 | |
% 172.35/23.53 | | BETA: splitting (17) gives:
% 172.35/23.53 | |
% 172.35/23.53 | | Case 1:
% 172.35/23.53 | | |
% 172.35/23.53 | | | (18) ~ leq(n1, all_71_12)
% 172.35/23.53 | | |
% 172.35/23.53 | | | REDUCE: (7), (18) imply:
% 172.35/23.53 | | | (19) ~ leq(n1, n2)
% 172.35/23.53 | | |
% 172.35/23.53 | | | PRED_UNIFY: (15), (19) imply:
% 172.35/23.53 | | | (20) $false
% 172.35/23.53 | | |
% 172.35/23.53 | | | CLOSE: (20) is inconsistent.
% 172.35/23.53 | | |
% 172.35/23.53 | | Case 2:
% 172.35/23.53 | | |
% 172.35/23.54 | | | (21) all_71_7 = init
% 172.35/23.54 | | |
% 172.35/23.54 | | | REDUCE: (4), (21) imply:
% 172.35/23.54 | | | (22) $false
% 172.35/23.54 | | |
% 172.35/23.54 | | | CLOSE: (22) is inconsistent.
% 172.35/23.54 | | |
% 172.35/23.54 | | End of split
% 172.35/23.54 | |
% 172.35/23.54 | End of split
% 172.35/23.54 |
% 172.35/23.54 End of proof
% 172.35/23.54
% 172.35/23.54 Sub-proof #9 shows that the following formulas are inconsistent:
% 172.35/23.54 ----------------------------------------------------------------
% 172.35/23.54 (1) ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) = all_71_5 &
% 172.35/23.54 $i(all_71_5) & leq(all_71_6, n2) & leq(n0, all_71_6)
% 172.35/23.54 (2) $i(all_71_6)
% 172.35/23.54 (3) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_center7_init,
% 172.35/23.54 v0) = v1) | ~ $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0))
% 172.35/23.54
% 172.35/23.54 Begin of proof
% 172.35/23.54 |
% 172.35/23.54 | ALPHA: (1) implies:
% 172.35/23.54 | (4) ~ (all_71_5 = init)
% 172.35/23.54 | (5) leq(n0, all_71_6)
% 172.35/23.54 | (6) leq(all_71_6, n2)
% 172.35/23.54 | (7) a_select2(s_center7_init, all_71_6) = all_71_5
% 172.35/23.54 |
% 172.35/23.54 | GROUND_INST: instantiating (3) with all_71_6, all_71_5, simplifying with (2),
% 172.35/23.54 | (5), (6), (7) gives:
% 172.35/23.54 | (8) all_71_5 = init
% 172.35/23.54 |
% 172.35/23.54 | REDUCE: (4), (8) imply:
% 172.35/23.54 | (9) $false
% 172.35/23.54 |
% 172.35/23.54 | CLOSE: (9) is inconsistent.
% 172.35/23.54 |
% 172.35/23.54 End of proof
% 172.35/23.54
% 172.35/23.54 Sub-proof #10 shows that the following formulas are inconsistent:
% 172.35/23.54 ----------------------------------------------------------------
% 172.35/23.54 (1) $i(all_71_2)
% 172.35/23.54 (2) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1, all_71_2) =
% 172.35/23.54 all_71_0 & $i(all_71_0) & leq(all_71_1, n3) & leq(all_71_2, n2) &
% 172.35/23.54 leq(n0, all_71_1) & leq(n0, all_71_2)) | ( ~ (all_71_3 = init) &
% 172.35/23.54 a_select2(s_values7_init, all_71_4) = all_71_3 & $i(all_71_3) &
% 172.35/23.54 leq(all_71_4, n3) & leq(n0, all_71_4))
% 172.35/23.54 (3) $i(all_71_4)
% 172.35/23.54 (4) $i(all_71_1)
% 172.35/23.54 (5) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_values7_init,
% 172.35/23.54 v0) = v1) | ~ $i(v0) | ~ leq(v0, n3) | ~ leq(n0, v0))
% 172.35/23.54 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~
% 172.35/23.54 (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 172.35/23.54 leq(v1, n3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0))
% 172.35/23.54
% 172.35/23.54 Begin of proof
% 172.35/23.54 |
% 172.35/23.54 | BETA: splitting (2) gives:
% 172.35/23.54 |
% 172.35/23.54 | Case 1:
% 172.35/23.54 | |
% 172.35/23.54 | | (7) ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1, all_71_2) =
% 172.35/23.54 | | all_71_0 & $i(all_71_0) & leq(all_71_1, n3) & leq(all_71_2, n2) &
% 172.35/23.54 | | leq(n0, all_71_1) & leq(n0, all_71_2)
% 172.35/23.54 | |
% 172.35/23.54 | | ALPHA: (7) implies:
% 172.35/23.54 | | (8) ~ (all_71_0 = init)
% 172.35/23.54 | | (9) leq(n0, all_71_2)
% 172.35/23.54 | | (10) leq(n0, all_71_1)
% 172.35/23.54 | | (11) leq(all_71_2, n2)
% 172.35/23.54 | | (12) leq(all_71_1, n3)
% 172.35/23.54 | | (13) a_select3(simplex7_init, all_71_1, all_71_2) = all_71_0
% 172.35/23.54 | |
% 172.35/23.54 | | GROUND_INST: instantiating (6) with all_71_2, all_71_1, all_71_0,
% 172.35/23.54 | | simplifying with (1), (4), (9), (10), (11), (12), (13) gives:
% 172.35/23.54 | | (14) all_71_0 = init
% 172.35/23.54 | |
% 172.35/23.54 | | REDUCE: (8), (14) imply:
% 172.35/23.54 | | (15) $false
% 172.35/23.54 | |
% 172.35/23.54 | | CLOSE: (15) is inconsistent.
% 172.35/23.54 | |
% 172.35/23.54 | Case 2:
% 172.35/23.54 | |
% 172.35/23.54 | | (16) ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 172.35/23.54 | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0, all_71_4)
% 172.35/23.54 | |
% 172.35/23.54 | | ALPHA: (16) implies:
% 172.35/23.54 | | (17) ~ (all_71_3 = init)
% 172.35/23.54 | | (18) leq(n0, all_71_4)
% 172.35/23.54 | | (19) leq(all_71_4, n3)
% 172.35/23.54 | | (20) a_select2(s_values7_init, all_71_4) = all_71_3
% 172.35/23.54 | |
% 172.35/23.54 | | GROUND_INST: instantiating (5) with all_71_4, all_71_3, simplifying with
% 172.35/23.54 | | (3), (18), (19), (20) gives:
% 172.35/23.54 | | (21) all_71_3 = init
% 172.35/23.54 | |
% 172.35/23.54 | | REDUCE: (17), (21) imply:
% 172.35/23.54 | | (22) $false
% 172.35/23.54 | |
% 172.35/23.54 | | CLOSE: (22) is inconsistent.
% 172.35/23.54 | |
% 172.35/23.54 | End of split
% 172.35/23.54 |
% 172.35/23.54 End of proof
% 172.35/23.54 % SZS output end Proof for theBenchmark
% 172.35/23.54
% 172.35/23.54 22927ms
%------------------------------------------------------------------------------