TSTP Solution File: SWV038+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV038+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 : n007.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 22:54:40 EDT 2023
% Result : Theorem 140.98s 18.94s
% Output : Proof 141.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV038+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.04/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 08:44:28 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.58/0.60 ________ _____
% 0.58/0.60 ___ __ \_________(_)________________________________
% 0.58/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.58/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.58/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.58/0.60
% 0.58/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.58/0.60 (2023-06-19)
% 0.58/0.60
% 0.58/0.60 (c) Philipp Rümmer, 2009-2023
% 0.58/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.58/0.60 Amanda Stjerna.
% 0.58/0.60 Free software under BSD-3-Clause.
% 0.58/0.60
% 0.58/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.58/0.60
% 0.58/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.58/0.61 Running up to 7 provers in parallel.
% 0.58/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.58/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.58/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.58/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.58/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.58/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.58/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.00/1.36 Prover 4: Preprocessing ...
% 5.00/1.37 Prover 1: Preprocessing ...
% 5.00/1.40 Prover 2: Preprocessing ...
% 5.00/1.40 Prover 6: Preprocessing ...
% 5.00/1.40 Prover 5: Preprocessing ...
% 5.00/1.40 Prover 3: Preprocessing ...
% 5.00/1.40 Prover 0: Preprocessing ...
% 10.88/2.18 Prover 1: Warning: ignoring some quantifiers
% 10.88/2.21 Prover 3: Warning: ignoring some quantifiers
% 11.45/2.27 Prover 3: Constructing countermodel ...
% 11.45/2.27 Prover 1: Constructing countermodel ...
% 11.97/2.31 Prover 4: Warning: ignoring some quantifiers
% 11.97/2.36 Prover 6: Proving ...
% 12.64/2.40 Prover 4: Constructing countermodel ...
% 13.06/2.48 Prover 5: Proving ...
% 13.71/2.53 Prover 0: Proving ...
% 13.71/2.57 Prover 2: Proving ...
% 74.03/10.30 Prover 2: stopped
% 74.03/10.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.97/10.41 Prover 7: Preprocessing ...
% 76.37/10.59 Prover 7: Warning: ignoring some quantifiers
% 76.37/10.61 Prover 7: Constructing countermodel ...
% 102.73/13.95 Prover 5: stopped
% 102.73/13.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 103.80/14.07 Prover 8: Preprocessing ...
% 105.11/14.24 Prover 8: Warning: ignoring some quantifiers
% 105.11/14.27 Prover 8: Constructing countermodel ...
% 118.53/15.97 Prover 1: stopped
% 118.53/15.97 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 118.53/16.03 Prover 9: Preprocessing ...
% 120.41/16.24 Prover 9: Warning: ignoring some quantifiers
% 120.87/16.26 Prover 9: Constructing countermodel ...
% 132.80/17.87 Prover 6: stopped
% 132.80/17.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 133.45/17.94 Prover 10: Preprocessing ...
% 134.07/18.02 Prover 10: Warning: ignoring some quantifiers
% 134.07/18.02 Prover 10: Constructing countermodel ...
% 140.98/18.93 Prover 10: Found proof (size 314)
% 140.98/18.94 Prover 10: proved (1065ms)
% 140.98/18.94 Prover 0: stopped
% 140.98/18.94 Prover 9: stopped
% 140.98/18.94 Prover 3: stopped
% 140.98/18.94 Prover 7: stopped
% 140.98/18.94 Prover 4: stopped
% 140.98/18.94 Prover 8: stopped
% 140.98/18.94
% 140.98/18.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 140.98/18.94
% 140.98/18.95 % SZS output start Proof for theBenchmark
% 140.98/18.96 Assumptions after simplification:
% 140.98/18.96 ---------------------------------
% 140.98/18.96
% 140.98/18.96 (finite_domain_1)
% 141.16/18.96 $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0,
% 141.16/18.96 n1) | ~ leq(n0, v0))
% 141.16/18.96
% 141.16/18.96 (finite_domain_2)
% 141.16/18.97 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~
% 141.16/18.97 $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0))
% 141.16/18.97
% 141.16/18.97 (finite_domain_5)
% 141.16/18.97 $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n5 |
% 141.16/18.97 v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n5)
% 141.16/18.97 | ~ leq(n0, v0))
% 141.16/18.97
% 141.16/18.97 (gauss_init_0065)
% 141.16/19.00 $i(pv1413) & $i(pvar1402_init) & $i(pvar1401_init) & $i(pvar1400_init) &
% 141.16/19.00 $i(loopcounter) & $i(s_try7_init) & $i(s_center7_init) & $i(s_values7_init) &
% 141.16/19.00 $i(simplex7_init) & $i(s_worst7) & $i(s_sworst7) & $i(s_best7) &
% 141.16/19.00 $i(s_worst7_init) & $i(s_sworst7_init) & $i(s_best7_init) & $i(init) & $i(n3)
% 141.16/19.00 & $i(n2) & $i(n1) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 141.16/19.00 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 141.16/19.00 ? [v9: $i] : (s_worst7_init = init & s_sworst7_init = init & s_best7_init =
% 141.16/19.00 init & minus(n3, n1) = v0 & $i(v8) & $i(v7) & $i(v5) & $i(v3) & $i(v1) &
% 141.16/19.00 $i(v0) & leq(s_worst7, n3) & leq(s_sworst7, n3) & leq(s_best7, n3) & leq(n0,
% 141.16/19.00 s_worst7) & leq(n0, s_sworst7) & leq(n0, s_best7) & ! [v10: $i] : !
% 141.16/19.00 [v11: $i] : ! [v12: $i] : (v12 = init | ~ (a_select3(simplex7_init, v11,
% 141.16/19.00 v10) = v12) | ~ $i(v11) | ~ $i(v10) | ~ leq(v11, n3) | ~ leq(v10,
% 141.16/19.00 n2) | ~ leq(n0, v11) | ~ leq(n0, v10)) & ! [v10: $i] : ! [v11: $i] :
% 141.16/19.00 (v11 = init | ~ (a_select2(s_try7_init, v10) = v11) | ~ $i(v10) | ~
% 141.16/19.00 leq(v10, v0) | ~ leq(n0, v10)) & ! [v10: $i] : ! [v11: $i] : (v11 =
% 141.16/19.00 init | ~ (a_select2(s_center7_init, v10) = v11) | ~ $i(v10) | ~
% 141.16/19.00 leq(v10, n2) | ~ leq(n0, v10)) & ! [v10: $i] : ! [v11: $i] : (v11 =
% 141.16/19.00 init | ~ (a_select2(s_values7_init, v10) = v11) | ~ $i(v10) | ~
% 141.16/19.00 leq(v10, n3) | ~ leq(n0, v10)) & ( ~ gt(loopcounter, n1) | (pvar1402_init
% 141.16/19.00 = init & pvar1401_init = init & pvar1400_init = init)) & ((pv1413 = n0 &
% 141.16/19.00 ~ true) | ( ~ (pv1413 = n0) & (( ~ (v9 = init) &
% 141.16/19.00 a_select3(simplex7_init, v8, v7) = v9 & $i(v9) & leq(v8, n3) &
% 141.16/19.00 leq(v7, n2) & leq(n0, v8) & leq(n0, v7)) | ( ~ (v6 = init) &
% 141.16/19.00 a_select2(s_values7_init, v5) = v6 & $i(v6) & leq(v5, n3) & leq(n0,
% 141.16/19.00 v5)) | ( ~ (v4 = init) & a_select2(s_center7_init, v3) = v4 &
% 141.16/19.00 $i(v4) & leq(v3, n2) & leq(n0, v3)) | ( ~ (v2 = init) &
% 141.16/19.00 a_select2(s_try7_init, v1) = v2 & $i(v2) & leq(v1, v0) & leq(n0,
% 141.16/19.00 v1)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~
% 141.16/19.00 (pvar1401_init = init) | ~ (pvar1400_init = init)))))))
% 141.16/19.00
% 141.16/19.00 (gt_5_2)
% 141.16/19.00 $i(n5) & $i(n2) & gt(n5, n2)
% 141.16/19.00
% 141.16/19.00 (irreflexivity_gt)
% 141.16/19.00 ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0))
% 141.16/19.00
% 141.16/19.00 (leq_gt1)
% 141.16/19.00 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0,
% 141.16/19.00 v1))
% 141.16/19.00
% 141.16/19.00 (leq_gt2)
% 141.16/19.01 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1)
% 141.16/19.01 | gt(v1, v0))
% 141.16/19.01
% 141.16/19.01 (leq_gt_pred)
% 141.16/19.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~
% 141.16/19.01 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 141.16/19.01 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0,
% 141.16/19.01 v2))
% 141.16/19.01
% 141.16/19.01 (pred_minus_1)
% 141.16/19.01 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 141.16/19.01 (pred(v0) = v1 & $i(v1)))
% 141.16/19.01
% 141.16/19.01 (pred_succ)
% 141.16/19.01 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0)
% 141.16/19.01
% 141.16/19.01 (successor_1)
% 141.16/19.01 succ(n0) = n1 & $i(n1) & $i(n0)
% 141.16/19.01
% 141.16/19.01 (successor_2)
% 141.16/19.01 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 141.16/19.01
% 141.16/19.01 (successor_3)
% 141.16/19.01 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 &
% 141.16/19.01 succ(n0) = v0 & $i(v1) & $i(v0))
% 141.16/19.01
% 141.16/19.01 (successor_4)
% 141.16/19.01 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 &
% 141.16/19.01 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 141.16/19.01
% 141.16/19.01 (successor_5)
% 141.16/19.01 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 141.16/19.01 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0
% 141.16/19.01 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 141.16/19.01
% 141.16/19.01 (transitivity_leq)
% 141.16/19.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 141.16/19.02 ~ leq(v1, v2) | ~ leq(v0, v1) | leq(v0, v2))
% 141.16/19.02
% 141.16/19.02 (ttrue)
% 141.16/19.02 true
% 141.16/19.02
% 141.16/19.02 (function-axioms)
% 141.16/19.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 141.16/19.02 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 141.16/19.02 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 141.16/19.02 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 141.16/19.02 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 141.16/19.02 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 141.16/19.02 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 141.16/19.02 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 141.16/19.02 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 141.16/19.02 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 141.16/19.02 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 141.16/19.02 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 141.16/19.02 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 141.16/19.02 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 141.16/19.02 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 141.16/19.02 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 141.16/19.02 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 141.16/19.03 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 141.16/19.03 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 141.16/19.03 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 141.16/19.03 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 141.16/19.03 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 141.16/19.03 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 141.16/19.03 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 141.16/19.03 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.16/19.03 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 141.16/19.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~
% 141.16/19.03 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 141.16/19.03 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 141.16/19.03 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] :
% 141.16/19.03 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) =
% 141.16/19.03 v0))
% 141.16/19.03
% 141.16/19.03 Further assumptions not needed in the proof:
% 141.16/19.03 --------------------------------------------
% 141.16/19.03 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 141.16/19.03 finite_domain_3, finite_domain_4, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1,
% 141.16/19.03 gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1,
% 141.16/19.03 gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_3,
% 141.16/19.03 gt_5_4, gt_5_tptp_minus_1, gt_succ, leq_geq, leq_minus, leq_succ, leq_succ_gt,
% 141.16/19.03 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 141.16/19.03 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 141.16/19.03 matrix_symm_trans, matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1,
% 141.16/19.03 sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3,
% 141.16/19.03 succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l,
% 141.16/19.03 succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r,
% 141.16/19.03 succ_pred, succ_tptp_minus_1, sum_plus_base, sum_plus_base_float, totality,
% 141.16/19.03 transitivity_gt, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 141.16/19.03
% 141.16/19.03 Those formulas are unsatisfiable:
% 141.16/19.03 ---------------------------------
% 141.16/19.03
% 141.16/19.03 Begin of proof
% 141.16/19.03 |
% 141.16/19.03 | ALPHA: (leq_gt_pred) implies:
% 141.16/19.03 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 141.16/19.03 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 141.16/19.03 |
% 141.16/19.03 | ALPHA: (pred_minus_1) implies:
% 141.16/19.03 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 141.48/19.03 | (pred(v0) = v1 & $i(v1)))
% 141.48/19.03 |
% 141.48/19.03 | ALPHA: (gt_5_2) implies:
% 141.48/19.03 | (3) gt(n5, n2)
% 141.48/19.03 |
% 141.48/19.03 | ALPHA: (finite_domain_5) implies:
% 141.48/19.03 | (4) ! [v0: $i] : (v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 =
% 141.48/19.03 | n0 | ~ $i(v0) | ~ leq(v0, n5) | ~ leq(n0, v0))
% 141.48/19.03 |
% 141.48/19.03 | ALPHA: (finite_domain_1) implies:
% 141.48/19.03 | (5) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 141.48/19.03 | leq(n0, v0))
% 141.48/19.03 |
% 141.48/19.03 | ALPHA: (finite_domain_2) implies:
% 141.48/19.03 | (6) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2)
% 141.48/19.03 | | ~ leq(n0, v0))
% 141.48/19.03 |
% 141.48/19.03 | ALPHA: (successor_4) implies:
% 141.48/19.03 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) =
% 141.48/19.03 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 141.48/19.03 |
% 141.48/19.03 | ALPHA: (successor_5) implies:
% 141.48/19.03 | (8) $i(n5)
% 141.48/19.03 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5
% 141.48/19.03 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 &
% 141.48/19.03 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 141.48/19.03 |
% 141.48/19.03 | ALPHA: (successor_1) implies:
% 141.48/19.03 | (10) succ(n0) = n1
% 141.48/19.03 |
% 141.48/19.03 | ALPHA: (successor_2) implies:
% 141.48/19.04 | (11) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 141.48/19.04 |
% 141.48/19.04 | ALPHA: (successor_3) implies:
% 141.48/19.04 | (12) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0)
% 141.48/19.04 | = v0 & $i(v1) & $i(v0))
% 141.48/19.04 |
% 141.48/19.04 | ALPHA: (gauss_init_0065) implies:
% 141.48/19.04 | (13) $i(n0)
% 141.48/19.04 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 141.48/19.04 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 141.48/19.04 | (s_worst7_init = init & s_sworst7_init = init & s_best7_init = init &
% 141.48/19.04 | minus(n3, n1) = v0 & $i(v8) & $i(v7) & $i(v5) & $i(v3) & $i(v1) &
% 141.48/19.04 | $i(v0) & leq(s_worst7, n3) & leq(s_sworst7, n3) & leq(s_best7, n3) &
% 141.48/19.04 | leq(n0, s_worst7) & leq(n0, s_sworst7) & leq(n0, s_best7) & ! [v10:
% 141.48/19.04 | $i] : ! [v11: $i] : ! [v12: $i] : (v12 = init | ~
% 141.48/19.04 | (a_select3(simplex7_init, v11, v10) = v12) | ~ $i(v11) | ~
% 141.48/19.04 | $i(v10) | ~ leq(v11, n3) | ~ leq(v10, n2) | ~ leq(n0, v11) | ~
% 141.48/19.04 | leq(n0, v10)) & ! [v10: $i] : ! [v11: $i] : (v11 = init | ~
% 141.48/19.04 | (a_select2(s_try7_init, v10) = v11) | ~ $i(v10) | ~ leq(v10, v0)
% 141.48/19.04 | | ~ leq(n0, v10)) & ! [v10: $i] : ! [v11: $i] : (v11 = init |
% 141.48/19.04 | ~ (a_select2(s_center7_init, v10) = v11) | ~ $i(v10) | ~
% 141.48/19.04 | leq(v10, n2) | ~ leq(n0, v10)) & ! [v10: $i] : ! [v11: $i] :
% 141.48/19.04 | (v11 = init | ~ (a_select2(s_values7_init, v10) = v11) | ~ $i(v10)
% 141.48/19.04 | | ~ leq(v10, n3) | ~ leq(n0, v10)) & ( ~ gt(loopcounter, n1) |
% 141.48/19.04 | (pvar1402_init = init & pvar1401_init = init & pvar1400_init =
% 141.48/19.04 | init)) & ((pv1413 = n0 & ~ true) | ( ~ (pv1413 = n0) & (( ~ (v9
% 141.48/19.04 | = init) & a_select3(simplex7_init, v8, v7) = v9 & $i(v9) &
% 141.48/19.04 | leq(v8, n3) & leq(v7, n2) & leq(n0, v8) & leq(n0, v7)) | ( ~
% 141.48/19.04 | (v6 = init) & a_select2(s_values7_init, v5) = v6 & $i(v6) &
% 141.48/19.04 | leq(v5, n3) & leq(n0, v5)) | ( ~ (v4 = init) &
% 141.48/19.04 | a_select2(s_center7_init, v3) = v4 & $i(v4) & leq(v3, n2) &
% 141.48/19.04 | leq(n0, v3)) | ( ~ (v2 = init) & a_select2(s_try7_init, v1)
% 141.48/19.04 | = v2 & $i(v2) & leq(v1, v0) & leq(n0, v1)) |
% 141.48/19.04 | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~
% 141.48/19.04 | (pvar1401_init = init) | ~ (pvar1400_init = init)))))))
% 141.48/19.04 |
% 141.48/19.04 | ALPHA: (function-axioms) implies:
% 141.48/19.04 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) =
% 141.48/19.04 | v1) | ~ (pred(v2) = v0))
% 141.48/19.04 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) =
% 141.48/19.04 | v1) | ~ (succ(v2) = v0))
% 141.48/19.04 |
% 141.48/19.04 | DELTA: instantiating (11) with fresh symbol all_54_0 gives:
% 141.48/19.04 | (17) succ(all_54_0) = n2 & succ(n0) = all_54_0 & $i(all_54_0)
% 141.48/19.04 |
% 141.48/19.04 | ALPHA: (17) implies:
% 141.48/19.04 | (18) $i(all_54_0)
% 141.48/19.05 | (19) succ(n0) = all_54_0
% 141.48/19.05 | (20) succ(all_54_0) = n2
% 141.48/19.05 |
% 141.48/19.05 | DELTA: instantiating (12) with fresh symbols all_56_0, all_56_1 gives:
% 141.48/19.05 | (21) succ(all_56_0) = n3 & succ(all_56_1) = all_56_0 & succ(n0) = all_56_1
% 141.48/19.05 | & $i(all_56_0) & $i(all_56_1)
% 141.48/19.05 |
% 141.48/19.05 | ALPHA: (21) implies:
% 141.48/19.05 | (22) $i(all_56_0)
% 141.48/19.05 | (23) succ(n0) = all_56_1
% 141.48/19.05 | (24) succ(all_56_1) = all_56_0
% 141.48/19.05 | (25) succ(all_56_0) = n3
% 141.48/19.05 |
% 141.48/19.05 | DELTA: instantiating (7) with fresh symbols all_59_0, all_59_1, all_59_2
% 141.48/19.05 | gives:
% 141.48/19.05 | (26) succ(all_59_0) = n4 & succ(all_59_1) = all_59_0 & succ(all_59_2) =
% 141.48/19.05 | all_59_1 & succ(n0) = all_59_2 & $i(all_59_0) & $i(all_59_1) &
% 141.48/19.05 | $i(all_59_2)
% 141.48/19.05 |
% 141.48/19.05 | ALPHA: (26) implies:
% 141.48/19.05 | (27) $i(all_59_0)
% 141.48/19.05 | (28) succ(n0) = all_59_2
% 141.48/19.05 | (29) succ(all_59_2) = all_59_1
% 141.48/19.05 | (30) succ(all_59_1) = all_59_0
% 141.48/19.05 |
% 141.48/19.05 | DELTA: instantiating (9) with fresh symbols all_61_0, all_61_1, all_61_2,
% 141.48/19.05 | all_61_3 gives:
% 141.48/19.05 | (31) succ(all_61_0) = n5 & succ(all_61_1) = all_61_0 & succ(all_61_2) =
% 141.48/19.05 | all_61_1 & succ(all_61_3) = all_61_2 & succ(n0) = all_61_3 &
% 141.48/19.05 | $i(all_61_0) & $i(all_61_1) & $i(all_61_2) & $i(all_61_3)
% 141.48/19.05 |
% 141.48/19.05 | ALPHA: (31) implies:
% 141.48/19.05 | (32) succ(n0) = all_61_3
% 141.48/19.05 | (33) succ(all_61_3) = all_61_2
% 141.48/19.05 | (34) succ(all_61_2) = all_61_1
% 141.48/19.05 |
% 141.48/19.05 | DELTA: instantiating (14) with fresh symbols all_71_0, all_71_1, all_71_2,
% 141.48/19.05 | all_71_3, all_71_4, all_71_5, all_71_6, all_71_7, all_71_8, all_71_9
% 141.48/19.05 | gives:
% 141.48/19.05 | (35) s_worst7_init = init & s_sworst7_init = init & s_best7_init = init &
% 141.48/19.05 | minus(n3, n1) = all_71_9 & $i(all_71_1) & $i(all_71_2) & $i(all_71_4)
% 141.48/19.05 | & $i(all_71_6) & $i(all_71_8) & $i(all_71_9) & leq(s_worst7, n3) &
% 141.48/19.05 | leq(s_sworst7, n3) & leq(s_best7, n3) & leq(n0, s_worst7) & leq(n0,
% 141.48/19.05 | s_sworst7) & leq(n0, s_best7) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 141.48/19.05 | $i] : (v2 = init | ~ (a_select3(simplex7_init, v1, v0) = v2) | ~
% 141.48/19.05 | $i(v1) | ~ $i(v0) | ~ leq(v1, n3) | ~ leq(v0, n2) | ~ leq(n0,
% 141.48/19.05 | v1) | ~ leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = init |
% 141.48/19.05 | ~ (a_select2(s_try7_init, v0) = v1) | ~ $i(v0) | ~ leq(v0,
% 141.48/19.05 | all_71_9) | ~ leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 141.48/19.05 | init | ~ (a_select2(s_center7_init, v0) = v1) | ~ $i(v0) | ~
% 141.48/19.05 | leq(v0, n2) | ~ leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 141.48/19.05 | init | ~ (a_select2(s_values7_init, v0) = v1) | ~ $i(v0) | ~
% 141.48/19.05 | leq(v0, n3) | ~ leq(n0, v0)) & ( ~ gt(loopcounter, n1) |
% 141.48/19.05 | (pvar1402_init = init & pvar1401_init = init & pvar1400_init =
% 141.48/19.05 | init)) & ((pv1413 = n0 & ~ true) | ( ~ (pv1413 = n0) & (( ~
% 141.48/19.05 | (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 141.48/19.05 | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 141.48/19.05 | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)) | (
% 141.48/19.05 | ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 141.48/19.05 | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0,
% 141.48/19.05 | all_71_4)) | ( ~ (all_71_5 = init) &
% 141.48/19.05 | a_select2(s_center7_init, all_71_6) = all_71_5 & $i(all_71_5)
% 141.48/19.06 | & leq(all_71_6, n2) & leq(n0, all_71_6)) | ( ~ (all_71_7 =
% 141.48/19.06 | init) & a_select2(s_try7_init, all_71_8) = all_71_7 &
% 141.48/19.06 | $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0, all_71_8)) |
% 141.48/19.06 | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~
% 141.48/19.06 | (pvar1401_init = init) | ~ (pvar1400_init = init))))))
% 141.48/19.06 |
% 141.48/19.06 | ALPHA: (35) implies:
% 141.48/19.06 | (36) $i(all_71_8)
% 141.48/19.06 | (37) $i(all_71_6)
% 141.48/19.06 | (38) $i(all_71_4)
% 141.48/19.06 | (39) $i(all_71_2)
% 141.48/19.06 | (40) $i(all_71_1)
% 141.48/19.06 | (41) minus(n3, n1) = all_71_9
% 141.48/19.06 | (42) (pv1413 = n0 & ~ true) | ( ~ (pv1413 = n0) & (( ~ (all_71_0 = init) &
% 141.48/19.06 | a_select3(simplex7_init, all_71_1, all_71_2) = all_71_0 &
% 141.48/19.06 | $i(all_71_0) & leq(all_71_1, n3) & leq(all_71_2, n2) & leq(n0,
% 141.48/19.06 | all_71_1) & leq(n0, all_71_2)) | ( ~ (all_71_3 = init) &
% 141.48/19.06 | a_select2(s_values7_init, all_71_4) = all_71_3 & $i(all_71_3) &
% 141.48/19.06 | leq(all_71_4, n3) & leq(n0, all_71_4)) | ( ~ (all_71_5 = init) &
% 141.48/19.06 | a_select2(s_center7_init, all_71_6) = all_71_5 & $i(all_71_5) &
% 141.48/19.06 | leq(all_71_6, n2) & leq(n0, all_71_6)) | ( ~ (all_71_7 = init) &
% 141.48/19.06 | a_select2(s_try7_init, all_71_8) = all_71_7 & $i(all_71_7) &
% 141.48/19.06 | leq(all_71_8, all_71_9) & leq(n0, all_71_8)) | (gt(loopcounter,
% 141.48/19.06 | n1) & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = init) |
% 141.48/19.06 | ~ (pvar1400_init = init)))))
% 141.48/19.06 | (43) ~ gt(loopcounter, n1) | (pvar1402_init = init & pvar1401_init = init
% 141.48/19.06 | & pvar1400_init = init)
% 141.48/19.06 | (44) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_values7_init,
% 141.48/19.06 | v0) = v1) | ~ $i(v0) | ~ leq(v0, n3) | ~ leq(n0, v0))
% 141.48/19.06 | (45) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_center7_init,
% 141.48/19.06 | v0) = v1) | ~ $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0))
% 141.48/19.06 | (46) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init,
% 141.48/19.06 | v0) = v1) | ~ $i(v0) | ~ leq(v0, all_71_9) | ~ leq(n0, v0))
% 141.48/19.06 | (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~
% 141.48/19.06 | (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 141.48/19.06 | leq(v1, n3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0))
% 141.48/19.06 |
% 141.48/19.06 | BETA: splitting (42) gives:
% 141.48/19.06 |
% 141.48/19.06 | Case 1:
% 141.48/19.06 | |
% 141.48/19.06 | | (48) pv1413 = n0 & ~ true
% 141.48/19.06 | |
% 141.48/19.06 | | ALPHA: (48) implies:
% 141.64/19.06 | | (49) ~ true
% 141.64/19.06 | |
% 141.64/19.06 | | PRED_UNIFY: (49), (ttrue) imply:
% 141.64/19.06 | | (50) $false
% 141.64/19.06 | |
% 141.64/19.06 | | CLOSE: (50) is inconsistent.
% 141.64/19.06 | |
% 141.64/19.06 | Case 2:
% 141.64/19.06 | |
% 141.64/19.07 | | (51) ~ (pv1413 = n0) & (( ~ (all_71_0 = init) & a_select3(simplex7_init,
% 141.64/19.07 | | all_71_1, all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1,
% 141.64/19.07 | | n3) & leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0,
% 141.64/19.07 | | all_71_2)) | ( ~ (all_71_3 = init) & a_select2(s_values7_init,
% 141.64/19.07 | | all_71_4) = all_71_3 & $i(all_71_3) & leq(all_71_4, n3) &
% 141.64/19.07 | | leq(n0, all_71_4)) | ( ~ (all_71_5 = init) &
% 141.64/19.07 | | a_select2(s_center7_init, all_71_6) = all_71_5 & $i(all_71_5) &
% 141.64/19.07 | | leq(all_71_6, n2) & leq(n0, all_71_6)) | ( ~ (all_71_7 = init) &
% 141.64/19.07 | | a_select2(s_try7_init, all_71_8) = all_71_7 & $i(all_71_7) &
% 141.64/19.07 | | leq(all_71_8, all_71_9) & leq(n0, all_71_8)) | (gt(loopcounter,
% 141.64/19.07 | | n1) & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = init) |
% 141.64/19.07 | | ~ (pvar1400_init = init))))
% 141.64/19.07 | |
% 141.64/19.07 | | ALPHA: (51) implies:
% 141.64/19.07 | | (52) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1, all_71_2)
% 141.64/19.07 | | = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) & leq(all_71_2, n2)
% 141.64/19.07 | | & leq(n0, all_71_1) & leq(n0, all_71_2)) | ( ~ (all_71_3 = init) &
% 141.64/19.07 | | a_select2(s_values7_init, all_71_4) = all_71_3 & $i(all_71_3) &
% 141.64/19.07 | | leq(all_71_4, n3) & leq(n0, all_71_4)) | ( ~ (all_71_5 = init) &
% 141.64/19.07 | | a_select2(s_center7_init, all_71_6) = all_71_5 & $i(all_71_5) &
% 141.64/19.07 | | leq(all_71_6, n2) & leq(n0, all_71_6)) | ( ~ (all_71_7 = init) &
% 141.64/19.07 | | a_select2(s_try7_init, all_71_8) = all_71_7 & $i(all_71_7) &
% 141.64/19.07 | | leq(all_71_8, all_71_9) & leq(n0, all_71_8)) | (gt(loopcounter,
% 141.64/19.07 | | n1) & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = init) |
% 141.64/19.07 | | ~ (pvar1400_init = init)))
% 141.64/19.07 | |
% 141.64/19.07 | | GROUND_INST: instantiating (16) with all_54_0, all_56_1, n0, simplifying
% 141.64/19.07 | | with (19), (23) gives:
% 141.64/19.07 | | (53) all_56_1 = all_54_0
% 141.64/19.07 | |
% 141.64/19.07 | | GROUND_INST: instantiating (16) with all_56_1, all_59_2, n0, simplifying
% 141.64/19.07 | | with (23), (28) gives:
% 141.64/19.07 | | (54) all_59_2 = all_56_1
% 141.64/19.07 | |
% 141.64/19.07 | | GROUND_INST: instantiating (16) with all_59_2, all_61_3, n0, simplifying
% 141.64/19.07 | | with (28), (32) gives:
% 141.64/19.07 | | (55) all_61_3 = all_59_2
% 141.64/19.07 | |
% 141.64/19.07 | | GROUND_INST: instantiating (16) with n1, all_61_3, n0, simplifying with
% 141.64/19.07 | | (10), (32) gives:
% 141.64/19.07 | | (56) all_61_3 = n1
% 141.64/19.07 | |
% 141.64/19.07 | | COMBINE_EQS: (55), (56) imply:
% 141.64/19.07 | | (57) all_59_2 = n1
% 141.64/19.07 | |
% 141.64/19.07 | | SIMP: (57) implies:
% 141.64/19.07 | | (58) all_59_2 = n1
% 141.64/19.07 | |
% 141.64/19.07 | | COMBINE_EQS: (54), (58) imply:
% 141.64/19.07 | | (59) all_56_1 = n1
% 141.64/19.07 | |
% 141.64/19.07 | | SIMP: (59) implies:
% 141.64/19.07 | | (60) all_56_1 = n1
% 141.64/19.07 | |
% 141.64/19.07 | | COMBINE_EQS: (53), (60) imply:
% 141.64/19.07 | | (61) all_54_0 = n1
% 141.64/19.07 | |
% 141.64/19.07 | | SIMP: (61) implies:
% 141.64/19.07 | | (62) all_54_0 = n1
% 141.64/19.07 | |
% 141.64/19.07 | | REDUCE: (33), (56) imply:
% 141.64/19.07 | | (63) succ(n1) = all_61_2
% 141.64/19.07 | |
% 141.64/19.07 | | REDUCE: (29), (58) imply:
% 141.64/19.07 | | (64) succ(n1) = all_59_1
% 141.64/19.07 | |
% 141.64/19.07 | | REDUCE: (24), (60) imply:
% 141.64/19.07 | | (65) succ(n1) = all_56_0
% 141.64/19.07 | |
% 141.64/19.07 | | REDUCE: (20), (62) imply:
% 141.64/19.07 | | (66) succ(n1) = n2
% 141.64/19.07 | |
% 141.64/19.07 | | REDUCE: (18), (62) imply:
% 141.64/19.07 | | (67) $i(n1)
% 141.64/19.07 | |
% 141.64/19.07 | | GROUND_INST: instantiating (16) with all_56_0, all_59_1, n1, simplifying
% 141.64/19.07 | | with (64), (65) gives:
% 141.64/19.07 | | (68) all_59_1 = all_56_0
% 141.64/19.07 | |
% 141.64/19.07 | | GROUND_INST: instantiating (16) with all_59_1, all_61_2, n1, simplifying
% 141.64/19.07 | | with (63), (64) gives:
% 141.64/19.07 | | (69) all_61_2 = all_59_1
% 141.64/19.07 | |
% 141.64/19.08 | | GROUND_INST: instantiating (16) with n2, all_61_2, n1, simplifying with
% 141.64/19.08 | | (63), (66) gives:
% 141.64/19.08 | | (70) all_61_2 = n2
% 141.64/19.08 | |
% 141.64/19.08 | | COMBINE_EQS: (69), (70) imply:
% 141.64/19.08 | | (71) all_59_1 = n2
% 141.64/19.08 | |
% 141.64/19.08 | | SIMP: (71) implies:
% 141.64/19.08 | | (72) all_59_1 = n2
% 141.64/19.08 | |
% 141.64/19.08 | | COMBINE_EQS: (68), (72) imply:
% 141.64/19.08 | | (73) all_56_0 = n2
% 141.64/19.08 | |
% 141.64/19.08 | | REDUCE: (34), (70) imply:
% 141.64/19.08 | | (74) succ(n2) = all_61_1
% 141.64/19.08 | |
% 141.64/19.08 | | REDUCE: (30), (72) imply:
% 141.64/19.08 | | (75) succ(n2) = all_59_0
% 141.64/19.08 | |
% 141.64/19.08 | | REDUCE: (25), (73) imply:
% 141.64/19.08 | | (76) succ(n2) = n3
% 141.64/19.08 | |
% 141.64/19.08 | | REDUCE: (22), (73) imply:
% 141.64/19.08 | | (77) $i(n2)
% 141.64/19.08 | |
% 141.64/19.08 | | GROUND_INST: instantiating (16) with all_59_0, all_61_1, n2, simplifying
% 141.64/19.08 | | with (74), (75) gives:
% 141.64/19.08 | | (78) all_61_1 = all_59_0
% 141.64/19.08 | |
% 141.64/19.08 | | GROUND_INST: instantiating (16) with n3, all_61_1, n2, simplifying with
% 141.64/19.08 | | (74), (76) gives:
% 141.64/19.08 | | (79) all_61_1 = n3
% 141.64/19.08 | |
% 141.64/19.08 | | COMBINE_EQS: (78), (79) imply:
% 141.64/19.08 | | (80) all_59_0 = n3
% 141.64/19.08 | |
% 141.64/19.08 | | SIMP: (80) implies:
% 141.64/19.08 | | (81) all_59_0 = n3
% 141.64/19.08 | |
% 141.64/19.08 | | REDUCE: (27), (81) imply:
% 141.64/19.08 | | (82) $i(n3)
% 141.64/19.08 | |
% 141.64/19.08 | | GROUND_INST: instantiating (leq_gt1) with n2, n5, simplifying with (3), (8),
% 141.64/19.08 | | (77) gives:
% 141.64/19.08 | | (83) leq(n2, n5)
% 141.64/19.08 | |
% 141.64/19.08 | | GROUND_INST: instantiating (pred_succ) with n1, n2, simplifying with (66),
% 141.64/19.08 | | (67) gives:
% 141.64/19.08 | | (84) pred(n2) = n1
% 141.64/19.08 | |
% 141.64/19.08 | | GROUND_INST: instantiating (pred_succ) with n2, n3, simplifying with (76),
% 141.64/19.08 | | (77) gives:
% 141.64/19.08 | | (85) pred(n3) = n2
% 141.64/19.08 | |
% 141.64/19.08 | | GROUND_INST: instantiating (2) with n3, all_71_9, simplifying with (41),
% 141.64/19.08 | | (82) gives:
% 141.64/19.08 | | (86) pred(n3) = all_71_9 & $i(all_71_9)
% 141.64/19.08 | |
% 141.64/19.08 | | ALPHA: (86) implies:
% 141.64/19.08 | | (87) $i(all_71_9)
% 141.64/19.08 | | (88) pred(n3) = all_71_9
% 141.64/19.08 | |
% 141.64/19.08 | | GROUND_INST: instantiating (15) with n2, all_71_9, n3, simplifying with
% 141.64/19.08 | | (85), (88) gives:
% 141.64/19.08 | | (89) all_71_9 = n2
% 141.64/19.08 | |
% 141.64/19.08 | | BETA: splitting (43) gives:
% 141.64/19.08 | |
% 141.64/19.08 | | Case 1:
% 141.64/19.08 | | |
% 141.64/19.08 | | | (90) ~ gt(loopcounter, n1)
% 141.64/19.08 | | |
% 141.64/19.08 | | | BETA: splitting (52) gives:
% 141.64/19.08 | | |
% 141.64/19.08 | | | Case 1:
% 141.64/19.08 | | | |
% 141.64/19.08 | | | | (91) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 141.64/19.08 | | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 141.64/19.08 | | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)) | (
% 141.64/19.08 | | | | ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 141.64/19.08 | | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0,
% 141.64/19.08 | | | | all_71_4))
% 141.64/19.08 | | | |
% 141.64/19.08 | | | | BETA: splitting (91) gives:
% 141.64/19.08 | | | |
% 141.64/19.08 | | | | Case 1:
% 141.64/19.08 | | | | |
% 141.64/19.08 | | | | | (92) ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 141.64/19.08 | | | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 141.64/19.08 | | | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)
% 141.64/19.08 | | | | |
% 141.64/19.08 | | | | | ALPHA: (92) implies:
% 141.64/19.08 | | | | | (93) ~ (all_71_0 = init)
% 141.64/19.08 | | | | | (94) leq(n0, all_71_2)
% 141.64/19.08 | | | | | (95) leq(n0, all_71_1)
% 141.64/19.08 | | | | | (96) leq(all_71_2, n2)
% 141.64/19.08 | | | | | (97) leq(all_71_1, n3)
% 141.64/19.08 | | | | | (98) a_select3(simplex7_init, all_71_1, all_71_2) = all_71_0
% 141.64/19.08 | | | | |
% 141.64/19.08 | | | | | GROUND_INST: instantiating (47) with all_71_2, all_71_1, all_71_0,
% 141.64/19.08 | | | | | simplifying with (39), (40), (94), (95), (96), (97), (98)
% 141.64/19.08 | | | | | gives:
% 141.64/19.08 | | | | | (99) all_71_0 = init
% 141.64/19.08 | | | | |
% 141.64/19.08 | | | | | REDUCE: (93), (99) imply:
% 141.64/19.08 | | | | | (100) $false
% 141.64/19.08 | | | | |
% 141.64/19.08 | | | | | CLOSE: (100) is inconsistent.
% 141.64/19.08 | | | | |
% 141.64/19.09 | | | | Case 2:
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | | (101) ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 141.64/19.09 | | | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0,
% 141.64/19.09 | | | | | all_71_4)
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | | ALPHA: (101) implies:
% 141.64/19.09 | | | | | (102) ~ (all_71_3 = init)
% 141.64/19.09 | | | | | (103) leq(n0, all_71_4)
% 141.64/19.09 | | | | | (104) leq(all_71_4, n3)
% 141.64/19.09 | | | | | (105) a_select2(s_values7_init, all_71_4) = all_71_3
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | | GROUND_INST: instantiating (44) with all_71_4, all_71_3, simplifying
% 141.64/19.09 | | | | | with (38), (103), (104), (105) gives:
% 141.64/19.09 | | | | | (106) all_71_3 = init
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | | REDUCE: (102), (106) imply:
% 141.64/19.09 | | | | | (107) $false
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | | CLOSE: (107) is inconsistent.
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | End of split
% 141.64/19.09 | | | |
% 141.64/19.09 | | | Case 2:
% 141.64/19.09 | | | |
% 141.64/19.09 | | | | (108) ( ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) =
% 141.64/19.09 | | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0,
% 141.64/19.09 | | | | all_71_6)) | ( ~ (all_71_7 = init) & a_select2(s_try7_init,
% 141.64/19.09 | | | | all_71_8) = all_71_7 & $i(all_71_7) & leq(all_71_8,
% 141.64/19.09 | | | | all_71_9) & leq(n0, all_71_8)) | (gt(loopcounter, n1) & ( ~
% 141.64/19.09 | | | | (pvar1402_init = init) | ~ (pvar1401_init = init) | ~
% 141.64/19.09 | | | | (pvar1400_init = init)))
% 141.64/19.09 | | | |
% 141.64/19.09 | | | | BETA: splitting (108) gives:
% 141.64/19.09 | | | |
% 141.64/19.09 | | | | Case 1:
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | | (109) ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) =
% 141.64/19.09 | | | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0,
% 141.64/19.09 | | | | | all_71_6)
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | | ALPHA: (109) implies:
% 141.64/19.09 | | | | | (110) ~ (all_71_5 = init)
% 141.64/19.09 | | | | | (111) leq(n0, all_71_6)
% 141.64/19.09 | | | | | (112) leq(all_71_6, n2)
% 141.64/19.09 | | | | | (113) a_select2(s_center7_init, all_71_6) = all_71_5
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | | GROUND_INST: instantiating (45) with all_71_6, all_71_5, simplifying
% 141.64/19.09 | | | | | with (37), (111), (112), (113) gives:
% 141.64/19.09 | | | | | (114) all_71_5 = init
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | | REDUCE: (110), (114) imply:
% 141.64/19.09 | | | | | (115) $false
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | | CLOSE: (115) is inconsistent.
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | Case 2:
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | | (116) ( ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) =
% 141.64/19.09 | | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0,
% 141.64/19.09 | | | | | all_71_8)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init =
% 141.64/19.09 | | | | | init) | ~ (pvar1401_init = init) | ~ (pvar1400_init =
% 141.64/19.09 | | | | | init)))
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | | BETA: splitting (116) gives:
% 141.64/19.09 | | | | |
% 141.64/19.09 | | | | | Case 1:
% 141.64/19.09 | | | | | |
% 141.64/19.09 | | | | | | (117) ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) =
% 141.64/19.09 | | | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0,
% 141.64/19.09 | | | | | | all_71_8)
% 141.64/19.09 | | | | | |
% 141.64/19.09 | | | | | | REF_CLOSE: (1), (4), (5), (6), (8), (13), (36), (46), (77), (83),
% 141.64/19.10 | | | | | | (84), (89), (117), (irreflexivity_gt), (leq_gt2),
% 141.64/19.10 | | | | | | (transitivity_leq) are inconsistent by sub-proof #1.
% 141.64/19.10 | | | | | |
% 141.64/19.10 | | | | | Case 2:
% 141.64/19.10 | | | | | |
% 141.64/19.10 | | | | | | (118) gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~
% 141.64/19.10 | | | | | | (pvar1401_init = init) | ~ (pvar1400_init = init))
% 141.64/19.10 | | | | | |
% 141.64/19.10 | | | | | | ALPHA: (118) implies:
% 141.64/19.10 | | | | | | (119) gt(loopcounter, n1)
% 141.64/19.10 | | | | | |
% 141.64/19.10 | | | | | | PRED_UNIFY: (90), (119) imply:
% 141.64/19.10 | | | | | | (120) $false
% 141.64/19.10 | | | | | |
% 141.64/19.10 | | | | | | CLOSE: (120) is inconsistent.
% 141.64/19.10 | | | | | |
% 141.64/19.10 | | | | | End of split
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | End of split
% 141.64/19.10 | | | |
% 141.64/19.10 | | | End of split
% 141.64/19.10 | | |
% 141.64/19.10 | | Case 2:
% 141.64/19.10 | | |
% 141.64/19.10 | | | (121) pvar1402_init = init & pvar1401_init = init & pvar1400_init =
% 141.64/19.10 | | | init
% 141.64/19.10 | | |
% 141.64/19.10 | | | ALPHA: (121) implies:
% 141.64/19.10 | | | (122) pvar1400_init = init
% 141.64/19.10 | | | (123) pvar1401_init = init
% 141.64/19.10 | | | (124) pvar1402_init = init
% 141.64/19.10 | | |
% 141.64/19.10 | | | BETA: splitting (52) gives:
% 141.64/19.10 | | |
% 141.64/19.10 | | | Case 1:
% 141.64/19.10 | | | |
% 141.64/19.10 | | | | (125) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 141.64/19.10 | | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 141.64/19.10 | | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)) |
% 141.64/19.10 | | | | ( ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 141.64/19.10 | | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0,
% 141.64/19.10 | | | | all_71_4))
% 141.64/19.10 | | | |
% 141.64/19.10 | | | | BETA: splitting (125) gives:
% 141.64/19.10 | | | |
% 141.64/19.10 | | | | Case 1:
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | | (126) ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 141.64/19.10 | | | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 141.64/19.10 | | | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | | ALPHA: (126) implies:
% 141.64/19.10 | | | | | (127) ~ (all_71_0 = init)
% 141.64/19.10 | | | | | (128) leq(n0, all_71_2)
% 141.64/19.10 | | | | | (129) leq(n0, all_71_1)
% 141.64/19.10 | | | | | (130) leq(all_71_2, n2)
% 141.64/19.10 | | | | | (131) leq(all_71_1, n3)
% 141.64/19.10 | | | | | (132) a_select3(simplex7_init, all_71_1, all_71_2) = all_71_0
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | | GROUND_INST: instantiating (47) with all_71_2, all_71_1, all_71_0,
% 141.64/19.10 | | | | | simplifying with (39), (40), (128), (129), (130), (131),
% 141.64/19.10 | | | | | (132) gives:
% 141.64/19.10 | | | | | (133) all_71_0 = init
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | | REDUCE: (127), (133) imply:
% 141.64/19.10 | | | | | (134) $false
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | | CLOSE: (134) is inconsistent.
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | Case 2:
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | | (135) ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 141.64/19.10 | | | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0,
% 141.64/19.10 | | | | | all_71_4)
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | | ALPHA: (135) implies:
% 141.64/19.10 | | | | | (136) ~ (all_71_3 = init)
% 141.64/19.10 | | | | | (137) leq(n0, all_71_4)
% 141.64/19.10 | | | | | (138) leq(all_71_4, n3)
% 141.64/19.10 | | | | | (139) a_select2(s_values7_init, all_71_4) = all_71_3
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | | GROUND_INST: instantiating (44) with all_71_4, all_71_3, simplifying
% 141.64/19.10 | | | | | with (38), (137), (138), (139) gives:
% 141.64/19.10 | | | | | (140) all_71_3 = init
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | | REDUCE: (136), (140) imply:
% 141.64/19.10 | | | | | (141) $false
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | | CLOSE: (141) is inconsistent.
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | End of split
% 141.64/19.10 | | | |
% 141.64/19.10 | | | Case 2:
% 141.64/19.10 | | | |
% 141.64/19.10 | | | | (142) ( ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) =
% 141.64/19.10 | | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0,
% 141.64/19.10 | | | | all_71_6)) | ( ~ (all_71_7 = init) & a_select2(s_try7_init,
% 141.64/19.10 | | | | all_71_8) = all_71_7 & $i(all_71_7) & leq(all_71_8,
% 141.64/19.10 | | | | all_71_9) & leq(n0, all_71_8)) | (gt(loopcounter, n1) & ( ~
% 141.64/19.10 | | | | (pvar1402_init = init) | ~ (pvar1401_init = init) | ~
% 141.64/19.10 | | | | (pvar1400_init = init)))
% 141.64/19.10 | | | |
% 141.64/19.10 | | | | BETA: splitting (142) gives:
% 141.64/19.10 | | | |
% 141.64/19.10 | | | | Case 1:
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | | (143) ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) =
% 141.64/19.10 | | | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0,
% 141.64/19.10 | | | | | all_71_6)
% 141.64/19.10 | | | | |
% 141.64/19.10 | | | | | ALPHA: (143) implies:
% 141.64/19.11 | | | | | (144) ~ (all_71_5 = init)
% 141.64/19.11 | | | | | (145) leq(n0, all_71_6)
% 141.64/19.11 | | | | | (146) leq(all_71_6, n2)
% 141.64/19.11 | | | | | (147) a_select2(s_center7_init, all_71_6) = all_71_5
% 141.64/19.11 | | | | |
% 141.64/19.11 | | | | | GROUND_INST: instantiating (45) with all_71_6, all_71_5, simplifying
% 141.64/19.11 | | | | | with (37), (145), (146), (147) gives:
% 141.64/19.11 | | | | | (148) all_71_5 = init
% 141.64/19.11 | | | | |
% 141.64/19.11 | | | | | REDUCE: (144), (148) imply:
% 141.64/19.11 | | | | | (149) $false
% 141.64/19.11 | | | | |
% 141.64/19.11 | | | | | CLOSE: (149) is inconsistent.
% 141.64/19.11 | | | | |
% 141.64/19.11 | | | | Case 2:
% 141.64/19.11 | | | | |
% 141.64/19.11 | | | | | (150) ( ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) =
% 141.64/19.11 | | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0,
% 141.64/19.11 | | | | | all_71_8)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init =
% 141.64/19.11 | | | | | init) | ~ (pvar1401_init = init) | ~ (pvar1400_init =
% 141.64/19.11 | | | | | init)))
% 141.64/19.11 | | | | |
% 141.64/19.11 | | | | | BETA: splitting (150) gives:
% 141.64/19.11 | | | | |
% 141.64/19.11 | | | | | Case 1:
% 141.64/19.11 | | | | | |
% 141.64/19.11 | | | | | | (151) ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) =
% 141.64/19.11 | | | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0,
% 141.64/19.11 | | | | | | all_71_8)
% 141.64/19.11 | | | | | |
% 141.64/19.11 | | | | | | REF_CLOSE: (1), (4), (5), (6), (8), (13), (36), (46), (77), (83),
% 141.64/19.11 | | | | | | (84), (89), (151), (irreflexivity_gt), (leq_gt2),
% 141.64/19.11 | | | | | | (transitivity_leq) are inconsistent by sub-proof #1.
% 141.64/19.11 | | | | | |
% 141.64/19.11 | | | | | Case 2:
% 141.64/19.11 | | | | | |
% 141.64/19.11 | | | | | | (152) gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~
% 141.64/19.11 | | | | | | (pvar1401_init = init) | ~ (pvar1400_init = init))
% 141.64/19.11 | | | | | |
% 141.64/19.11 | | | | | | ALPHA: (152) implies:
% 141.64/19.11 | | | | | | (153) ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~
% 141.64/19.11 | | | | | | (pvar1400_init = init)
% 141.64/19.11 | | | | | |
% 141.64/19.11 | | | | | | BETA: splitting (153) gives:
% 141.64/19.11 | | | | | |
% 141.64/19.11 | | | | | | Case 1:
% 141.64/19.11 | | | | | | |
% 141.64/19.11 | | | | | | | (154) ~ (pvar1402_init = init)
% 141.64/19.11 | | | | | | |
% 141.64/19.11 | | | | | | | REDUCE: (124), (154) imply:
% 141.64/19.11 | | | | | | | (155) $false
% 141.64/19.11 | | | | | | |
% 141.64/19.11 | | | | | | | CLOSE: (155) is inconsistent.
% 141.64/19.11 | | | | | | |
% 141.64/19.11 | | | | | | Case 2:
% 141.64/19.11 | | | | | | |
% 141.64/19.11 | | | | | | | (156) ~ (pvar1401_init = init) | ~ (pvar1400_init = init)
% 141.64/19.11 | | | | | | |
% 141.64/19.11 | | | | | | | BETA: splitting (156) gives:
% 141.64/19.11 | | | | | | |
% 141.64/19.11 | | | | | | | Case 1:
% 141.64/19.11 | | | | | | | |
% 141.64/19.11 | | | | | | | | (157) ~ (pvar1401_init = init)
% 141.64/19.11 | | | | | | | |
% 141.64/19.11 | | | | | | | | REDUCE: (123), (157) imply:
% 141.64/19.11 | | | | | | | | (158) $false
% 141.64/19.11 | | | | | | | |
% 141.64/19.11 | | | | | | | | CLOSE: (158) is inconsistent.
% 141.64/19.11 | | | | | | | |
% 141.64/19.11 | | | | | | | Case 2:
% 141.64/19.11 | | | | | | | |
% 141.64/19.11 | | | | | | | | (159) ~ (pvar1400_init = init)
% 141.64/19.11 | | | | | | | |
% 141.64/19.11 | | | | | | | | REDUCE: (122), (159) imply:
% 141.64/19.11 | | | | | | | | (160) $false
% 141.64/19.11 | | | | | | | |
% 141.64/19.11 | | | | | | | | CLOSE: (160) is inconsistent.
% 141.64/19.11 | | | | | | | |
% 141.64/19.11 | | | | | | | End of split
% 141.64/19.11 | | | | | | |
% 141.64/19.11 | | | | | | End of split
% 141.64/19.11 | | | | | |
% 141.64/19.11 | | | | | End of split
% 141.64/19.11 | | | | |
% 141.64/19.11 | | | | End of split
% 141.64/19.11 | | | |
% 141.64/19.11 | | | End of split
% 141.64/19.11 | | |
% 141.64/19.11 | | End of split
% 141.64/19.11 | |
% 141.64/19.11 | End of split
% 141.64/19.11 |
% 141.64/19.11 End of proof
% 141.64/19.11
% 141.64/19.11 Sub-proof #1 shows that the following formulas are inconsistent:
% 141.64/19.11 ----------------------------------------------------------------
% 141.64/19.11 (1) pred(n2) = n1
% 141.64/19.11 (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0,
% 141.64/19.11 v1) | gt(v1, v0))
% 141.64/19.11 (3) $i(n0)
% 141.64/19.11 (4) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0) =
% 141.64/19.11 v1) | ~ $i(v0) | ~ leq(v0, all_71_9) | ~ leq(n0, v0))
% 141.64/19.11 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 141.64/19.11 $i(v0) | ~ leq(v1, v2) | ~ leq(v0, v1) | leq(v0, v2))
% 141.64/19.11 (6) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2) |
% 141.64/19.11 ~ leq(n0, v0))
% 141.64/19.11 (7) $i(all_71_8)
% 141.64/19.11 (8) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 141.64/19.11 leq(n0, v0))
% 141.64/19.11 (9) leq(n2, n5)
% 141.64/19.12 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 141.64/19.12 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 141.64/19.12 (11) all_71_9 = n2
% 141.64/19.12 (12) $i(n5)
% 141.64/19.12 (13) $i(n2)
% 141.64/19.12 (14) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0))
% 141.64/19.12 (15) ! [v0: $i] : (v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0
% 141.64/19.12 | ~ $i(v0) | ~ leq(v0, n5) | ~ leq(n0, v0))
% 141.64/19.12 (16) ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) = all_71_7 &
% 141.64/19.12 $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0, all_71_8)
% 141.64/19.12
% 141.64/19.12 Begin of proof
% 141.64/19.12 |
% 141.64/19.12 | ALPHA: (16) implies:
% 141.64/19.12 | (17) ~ (all_71_7 = init)
% 141.64/19.12 | (18) leq(n0, all_71_8)
% 141.64/19.12 | (19) leq(all_71_8, all_71_9)
% 141.64/19.12 | (20) a_select2(s_try7_init, all_71_8) = all_71_7
% 141.64/19.12 |
% 141.64/19.12 | REDUCE: (11), (19) imply:
% 141.64/19.12 | (21) leq(all_71_8, n2)
% 141.64/19.12 |
% 141.64/19.12 | GROUND_INST: instantiating (2) with n0, all_71_8, simplifying with (3), (7),
% 141.64/19.12 | (18) gives:
% 141.64/19.12 | (22) all_71_8 = n0 | gt(all_71_8, n0)
% 141.64/19.12 |
% 141.64/19.12 | GROUND_INST: instantiating (5) with all_71_8, n2, n5, simplifying with (7),
% 141.64/19.12 | (9), (12), (13), (21) gives:
% 141.64/19.12 | (23) leq(all_71_8, n5)
% 141.64/19.12 |
% 141.64/19.12 | GROUND_INST: instantiating (6) with all_71_8, simplifying with (7), (18), (21)
% 141.64/19.12 | gives:
% 141.64/19.12 | (24) all_71_8 = n2 | all_71_8 = n1 | all_71_8 = n0
% 141.64/19.12 |
% 141.64/19.12 | GROUND_INST: instantiating (2) with all_71_8, n2, simplifying with (7), (13),
% 141.64/19.12 | (21) gives:
% 141.64/19.12 | (25) all_71_8 = n2 | gt(n2, all_71_8)
% 141.64/19.12 |
% 141.64/19.12 | GROUND_INST: instantiating (15) with all_71_8, simplifying with (7), (18),
% 141.64/19.12 | (23) gives:
% 141.64/19.12 | (26) all_71_8 = n5 | all_71_8 = n4 | all_71_8 = n3 | all_71_8 = n2 |
% 141.64/19.12 | all_71_8 = n1 | all_71_8 = n0
% 141.64/19.12 |
% 141.64/19.12 | BETA: splitting (22) gives:
% 141.64/19.12 |
% 141.64/19.12 | Case 1:
% 141.64/19.12 | |
% 141.64/19.12 | | (27) gt(all_71_8, n0)
% 141.64/19.12 | |
% 141.64/19.12 | | BETA: splitting (25) gives:
% 141.64/19.12 | |
% 141.64/19.12 | | Case 1:
% 141.64/19.12 | | |
% 141.64/19.12 | | | (28) gt(n2, all_71_8)
% 141.64/19.12 | | |
% 141.64/19.12 | | | BETA: splitting (24) gives:
% 141.64/19.12 | | |
% 141.64/19.12 | | | Case 1:
% 141.64/19.12 | | | |
% 141.64/19.12 | | | | (29) all_71_8 = n0
% 141.64/19.12 | | | |
% 141.64/19.12 | | | | REDUCE: (27), (29) imply:
% 141.64/19.12 | | | | (30) gt(n0, n0)
% 141.64/19.12 | | | |
% 141.64/19.12 | | | | GROUND_INST: instantiating (14) with n0, simplifying with (3), (30)
% 141.64/19.12 | | | | gives:
% 141.64/19.12 | | | | (31) $false
% 141.64/19.12 | | | |
% 141.64/19.12 | | | | CLOSE: (31) is inconsistent.
% 141.64/19.12 | | | |
% 141.64/19.12 | | | Case 2:
% 141.64/19.12 | | | |
% 141.64/19.12 | | | | (32) ~ (all_71_8 = n0)
% 141.64/19.12 | | | |
% 141.64/19.12 | | | | BETA: splitting (26) gives:
% 141.64/19.12 | | | |
% 141.64/19.12 | | | | Case 1:
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | | (33) all_71_8 = n0
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | | REDUCE: (32), (33) imply:
% 141.64/19.12 | | | | | (34) $false
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | | CLOSE: (34) is inconsistent.
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | Case 2:
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | | GROUND_INST: instantiating (10) with all_71_8, n2, n1, simplifying
% 141.64/19.12 | | | | | with (1), (7), (13), (28) gives:
% 141.64/19.12 | | | | | (35) leq(all_71_8, n1)
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | | GROUND_INST: instantiating (8) with all_71_8, simplifying with (7),
% 141.64/19.12 | | | | | (18), (35) gives:
% 141.64/19.12 | | | | | (36) all_71_8 = n1 | all_71_8 = n0
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | | REF_CLOSE: (4), (7), (11), (17), (18), (20), (21), (32), (36) are
% 141.64/19.12 | | | | | inconsistent by sub-proof #3.
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | End of split
% 141.64/19.12 | | | |
% 141.64/19.12 | | | End of split
% 141.64/19.12 | | |
% 141.64/19.12 | | Case 2:
% 141.64/19.12 | | |
% 141.64/19.12 | | | (37) all_71_8 = n2
% 141.64/19.12 | | |
% 141.64/19.12 | | | REF_CLOSE: (4), (7), (11), (17), (18), (20), (21), (37) are inconsistent
% 141.64/19.12 | | | by sub-proof #2.
% 141.64/19.12 | | |
% 141.64/19.12 | | End of split
% 141.64/19.12 | |
% 141.64/19.12 | Case 2:
% 141.64/19.12 | |
% 141.64/19.12 | | (38) all_71_8 = n0
% 141.64/19.12 | | (39) ~ gt(all_71_8, n0)
% 141.64/19.12 | |
% 141.64/19.12 | | REDUCE: (38), (39) imply:
% 141.64/19.12 | | (40) ~ gt(n0, n0)
% 141.64/19.12 | |
% 141.64/19.12 | | BETA: splitting (22) gives:
% 141.64/19.12 | |
% 141.64/19.12 | | Case 1:
% 141.64/19.12 | | |
% 141.64/19.12 | | | (41) gt(all_71_8, n0)
% 141.64/19.12 | | |
% 141.64/19.12 | | | BETA: splitting (25) gives:
% 141.64/19.12 | | |
% 141.64/19.12 | | | Case 1:
% 141.64/19.12 | | | |
% 141.64/19.12 | | | | (42) gt(n2, all_71_8)
% 141.64/19.12 | | | |
% 141.64/19.12 | | | | GROUND_INST: instantiating (10) with all_71_8, n2, n1, simplifying with
% 141.64/19.12 | | | | (1), (7), (13), (42) gives:
% 141.64/19.12 | | | | (43) leq(all_71_8, n1)
% 141.64/19.12 | | | |
% 141.64/19.12 | | | | GROUND_INST: instantiating (8) with all_71_8, simplifying with (7),
% 141.64/19.12 | | | | (18), (43) gives:
% 141.64/19.12 | | | | (44) all_71_8 = n1 | all_71_8 = n0
% 141.64/19.12 | | | |
% 141.64/19.12 | | | | BETA: splitting (24) gives:
% 141.64/19.12 | | | |
% 141.64/19.12 | | | | Case 1:
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | | REDUCE: (38), (41) imply:
% 141.64/19.12 | | | | | (45) gt(n0, n0)
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | | PRED_UNIFY: (40), (45) imply:
% 141.64/19.12 | | | | | (46) $false
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | | CLOSE: (46) is inconsistent.
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | Case 2:
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | | (47) ~ (all_71_8 = n0)
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | | REF_CLOSE: (4), (7), (11), (17), (18), (20), (21), (44), (47) are
% 141.64/19.12 | | | | | inconsistent by sub-proof #3.
% 141.64/19.12 | | | | |
% 141.64/19.12 | | | | End of split
% 141.64/19.12 | | | |
% 141.64/19.12 | | | Case 2:
% 141.64/19.12 | | | |
% 141.64/19.12 | | | | (48) all_71_8 = n2
% 141.64/19.12 | | | |
% 141.64/19.13 | | | | REF_CLOSE: (4), (7), (11), (17), (18), (20), (21), (48) are inconsistent
% 141.64/19.13 | | | | by sub-proof #2.
% 141.64/19.13 | | | |
% 141.64/19.13 | | | End of split
% 141.64/19.13 | | |
% 141.64/19.13 | | Case 2:
% 141.64/19.13 | | |
% 141.64/19.13 | | |
% 141.64/19.13 | | | REDUCE: (20), (38) imply:
% 141.64/19.13 | | | (49) a_select2(s_try7_init, n0) = all_71_7
% 141.64/19.13 | | |
% 141.64/19.13 | | | REDUCE: (21), (38) imply:
% 141.64/19.13 | | | (50) leq(n0, n2)
% 141.64/19.13 | | |
% 141.64/19.13 | | | REDUCE: (18), (38) imply:
% 141.64/19.13 | | | (51) leq(n0, n0)
% 141.64/19.13 | | |
% 141.64/19.13 | | | GROUND_INST: instantiating (4) with n0, all_71_7, simplifying with (3),
% 141.64/19.13 | | | (49), (51) gives:
% 141.64/19.13 | | | (52) all_71_7 = init | ~ leq(n0, all_71_9)
% 141.64/19.13 | | |
% 141.64/19.13 | | | BETA: splitting (52) gives:
% 141.64/19.13 | | |
% 141.64/19.13 | | | Case 1:
% 141.64/19.13 | | | |
% 141.64/19.13 | | | | (53) ~ leq(n0, all_71_9)
% 141.64/19.13 | | | |
% 141.64/19.13 | | | | REDUCE: (11), (53) imply:
% 141.64/19.13 | | | | (54) ~ leq(n0, n2)
% 141.64/19.13 | | | |
% 141.64/19.13 | | | | PRED_UNIFY: (50), (54) imply:
% 141.64/19.13 | | | | (55) $false
% 141.64/19.13 | | | |
% 141.64/19.13 | | | | CLOSE: (55) is inconsistent.
% 141.64/19.13 | | | |
% 141.64/19.13 | | | Case 2:
% 141.64/19.13 | | | |
% 141.64/19.13 | | | | (56) all_71_7 = init
% 141.64/19.13 | | | |
% 141.64/19.13 | | | | REDUCE: (17), (56) imply:
% 141.64/19.13 | | | | (57) $false
% 141.64/19.13 | | | |
% 141.64/19.13 | | | | CLOSE: (57) is inconsistent.
% 141.64/19.13 | | | |
% 141.64/19.13 | | | End of split
% 141.64/19.13 | | |
% 141.64/19.13 | | End of split
% 141.64/19.13 | |
% 141.64/19.13 | End of split
% 141.64/19.13 |
% 141.64/19.13 End of proof
% 141.64/19.13
% 141.64/19.13 Sub-proof #2 shows that the following formulas are inconsistent:
% 141.64/19.13 ----------------------------------------------------------------
% 141.64/19.13 (1) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0) =
% 141.64/19.13 v1) | ~ $i(v0) | ~ leq(v0, all_71_9) | ~ leq(n0, v0))
% 141.64/19.13 (2) $i(all_71_8)
% 141.64/19.13 (3) leq(all_71_8, n2)
% 141.64/19.13 (4) ~ (all_71_7 = init)
% 141.64/19.13 (5) all_71_8 = n2
% 141.64/19.13 (6) all_71_9 = n2
% 141.64/19.13 (7) a_select2(s_try7_init, all_71_8) = all_71_7
% 141.64/19.13 (8) leq(n0, all_71_8)
% 141.64/19.13
% 141.64/19.13 Begin of proof
% 141.64/19.13 |
% 141.64/19.13 | REDUCE: (5), (7) imply:
% 141.64/19.13 | (9) a_select2(s_try7_init, n2) = all_71_7
% 141.64/19.13 |
% 141.64/19.13 | REDUCE: (2), (5) imply:
% 141.64/19.13 | (10) $i(n2)
% 141.64/19.13 |
% 141.64/19.13 | REDUCE: (3), (5) imply:
% 141.64/19.13 | (11) leq(n2, n2)
% 141.96/19.13 |
% 141.96/19.13 | REDUCE: (5), (8) imply:
% 141.96/19.13 | (12) leq(n0, n2)
% 141.96/19.13 |
% 141.96/19.13 | GROUND_INST: instantiating (1) with n2, all_71_7, simplifying with (9), (10),
% 141.96/19.13 | (12) gives:
% 141.96/19.13 | (13) all_71_7 = init | ~ leq(n2, all_71_9)
% 141.96/19.13 |
% 141.96/19.13 | BETA: splitting (13) gives:
% 141.96/19.13 |
% 141.96/19.13 | Case 1:
% 141.96/19.13 | |
% 141.96/19.13 | | (14) ~ leq(n2, all_71_9)
% 141.96/19.13 | |
% 141.96/19.13 | | REDUCE: (6), (14) imply:
% 141.96/19.13 | | (15) ~ leq(n2, n2)
% 141.96/19.13 | |
% 141.96/19.13 | | PRED_UNIFY: (11), (15) imply:
% 141.96/19.13 | | (16) $false
% 141.96/19.13 | |
% 141.96/19.13 | | CLOSE: (16) is inconsistent.
% 141.96/19.13 | |
% 141.96/19.13 | Case 2:
% 141.96/19.13 | |
% 141.96/19.13 | | (17) all_71_7 = init
% 141.96/19.13 | |
% 141.96/19.13 | | REDUCE: (4), (17) imply:
% 141.96/19.13 | | (18) $false
% 141.96/19.13 | |
% 141.96/19.13 | | CLOSE: (18) is inconsistent.
% 141.96/19.13 | |
% 141.96/19.13 | End of split
% 141.96/19.13 |
% 141.96/19.13 End of proof
% 141.96/19.13
% 141.96/19.13 Sub-proof #3 shows that the following formulas are inconsistent:
% 141.96/19.13 ----------------------------------------------------------------
% 141.96/19.13 (1) ~ (all_71_8 = n0)
% 141.96/19.13 (2) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0) =
% 141.96/19.13 v1) | ~ $i(v0) | ~ leq(v0, all_71_9) | ~ leq(n0, v0))
% 141.96/19.13 (3) $i(all_71_8)
% 141.96/19.13 (4) leq(all_71_8, n2)
% 141.96/19.13 (5) ~ (all_71_7 = init)
% 141.96/19.13 (6) all_71_8 = n1 | all_71_8 = n0
% 141.96/19.13 (7) all_71_9 = n2
% 141.96/19.13 (8) a_select2(s_try7_init, all_71_8) = all_71_7
% 141.96/19.13 (9) leq(n0, all_71_8)
% 141.96/19.13
% 141.96/19.13 Begin of proof
% 141.96/19.13 |
% 141.96/19.13 | BETA: splitting (6) gives:
% 141.96/19.13 |
% 141.96/19.13 | Case 1:
% 141.96/19.13 | |
% 141.96/19.13 | | (10) all_71_8 = n0
% 141.96/19.13 | |
% 141.96/19.13 | | REDUCE: (1), (10) imply:
% 141.96/19.13 | | (11) $false
% 141.96/19.13 | |
% 141.96/19.13 | | CLOSE: (11) is inconsistent.
% 141.96/19.13 | |
% 141.96/19.13 | Case 2:
% 141.96/19.13 | |
% 141.96/19.13 | | (12) all_71_8 = n1
% 141.96/19.13 | |
% 141.96/19.13 | | REDUCE: (8), (12) imply:
% 141.96/19.13 | | (13) a_select2(s_try7_init, n1) = all_71_7
% 141.96/19.13 | |
% 141.96/19.13 | | REDUCE: (3), (12) imply:
% 141.96/19.13 | | (14) $i(n1)
% 141.96/19.13 | |
% 141.96/19.13 | | REDUCE: (4), (12) imply:
% 141.96/19.13 | | (15) leq(n1, n2)
% 141.96/19.13 | |
% 141.96/19.13 | | REDUCE: (9), (12) imply:
% 141.96/19.13 | | (16) leq(n0, n1)
% 141.96/19.13 | |
% 141.96/19.13 | | GROUND_INST: instantiating (2) with n1, all_71_7, simplifying with (13),
% 141.96/19.13 | | (14), (16) gives:
% 141.96/19.13 | | (17) all_71_7 = init | ~ leq(n1, all_71_9)
% 141.96/19.13 | |
% 141.96/19.13 | | BETA: splitting (17) gives:
% 141.96/19.13 | |
% 141.96/19.13 | | Case 1:
% 141.96/19.13 | | |
% 141.96/19.13 | | | (18) ~ leq(n1, all_71_9)
% 141.96/19.13 | | |
% 141.96/19.13 | | | REDUCE: (7), (18) imply:
% 141.96/19.13 | | | (19) ~ leq(n1, n2)
% 141.96/19.13 | | |
% 141.96/19.13 | | | PRED_UNIFY: (15), (19) imply:
% 141.96/19.13 | | | (20) $false
% 141.96/19.13 | | |
% 141.96/19.13 | | | CLOSE: (20) is inconsistent.
% 141.96/19.13 | | |
% 141.96/19.13 | | Case 2:
% 141.96/19.13 | | |
% 141.96/19.13 | | | (21) all_71_7 = init
% 141.96/19.13 | | |
% 141.96/19.13 | | | REDUCE: (5), (21) imply:
% 141.96/19.13 | | | (22) $false
% 141.96/19.13 | | |
% 141.96/19.13 | | | CLOSE: (22) is inconsistent.
% 141.96/19.13 | | |
% 141.96/19.13 | | End of split
% 141.96/19.13 | |
% 141.96/19.13 | End of split
% 141.96/19.13 |
% 141.96/19.13 End of proof
% 141.96/19.13 % SZS output end Proof for theBenchmark
% 141.96/19.13
% 141.96/19.13 18532ms
%------------------------------------------------------------------------------