TSTP Solution File: SWV025+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV025+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 : n031.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 153.62s 20.99s
% Output : Proof 154.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV025+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34 % Computer : n031.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Aug 29 06:44:55 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.95/1.41 Prover 4: Preprocessing ...
% 4.95/1.41 Prover 1: Preprocessing ...
% 4.95/1.45 Prover 6: Preprocessing ...
% 4.95/1.45 Prover 2: Preprocessing ...
% 4.95/1.45 Prover 5: Preprocessing ...
% 4.95/1.45 Prover 0: Preprocessing ...
% 4.95/1.47 Prover 3: Preprocessing ...
% 11.83/2.33 Prover 1: Warning: ignoring some quantifiers
% 11.94/2.38 Prover 3: Warning: ignoring some quantifiers
% 12.50/2.42 Prover 1: Constructing countermodel ...
% 12.50/2.42 Prover 6: Proving ...
% 12.50/2.45 Prover 3: Constructing countermodel ...
% 12.96/2.52 Prover 4: Warning: ignoring some quantifiers
% 13.75/2.61 Prover 0: Proving ...
% 13.75/2.62 Prover 4: Constructing countermodel ...
% 13.75/2.63 Prover 5: Proving ...
% 13.75/2.67 Prover 2: Proving ...
% 72.48/10.31 Prover 2: stopped
% 72.48/10.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.13/10.50 Prover 7: Preprocessing ...
% 75.62/10.69 Prover 7: Warning: ignoring some quantifiers
% 75.99/10.74 Prover 7: Constructing countermodel ...
% 101.22/13.97 Prover 5: stopped
% 101.22/13.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 102.00/14.09 Prover 8: Preprocessing ...
% 103.22/14.29 Prover 8: Warning: ignoring some quantifiers
% 103.22/14.31 Prover 8: Constructing countermodel ...
% 116.02/15.97 Prover 1: stopped
% 116.02/15.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 117.24/16.09 Prover 9: Preprocessing ...
% 118.93/16.38 Prover 9: Warning: ignoring some quantifiers
% 119.52/16.40 Prover 9: Constructing countermodel ...
% 130.68/17.88 Prover 6: stopped
% 130.68/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 131.49/18.02 Prover 10: Preprocessing ...
% 132.59/18.13 Prover 10: Warning: ignoring some quantifiers
% 132.59/18.14 Prover 10: Constructing countermodel ...
% 153.62/20.96 Prover 10: Found proof (size 316)
% 153.62/20.96 Prover 10: proved (3077ms)
% 153.62/20.96 Prover 9: stopped
% 153.62/20.96 Prover 0: stopped
% 153.62/20.97 Prover 3: stopped
% 153.62/20.97 Prover 4: stopped
% 153.62/20.97 Prover 8: stopped
% 153.62/20.99 Prover 7: stopped
% 153.62/20.99
% 153.62/20.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 153.62/20.99
% 153.62/21.01 % SZS output start Proof for theBenchmark
% 153.62/21.01 Assumptions after simplification:
% 153.62/21.01 ---------------------------------
% 153.62/21.01
% 153.62/21.01 (finite_domain_1)
% 154.05/21.02 $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0,
% 154.05/21.02 n1) | ~ leq(n0, v0))
% 154.05/21.02
% 154.05/21.02 (finite_domain_2)
% 154.05/21.02 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~
% 154.05/21.02 $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0))
% 154.05/21.02
% 154.05/21.02 (finite_domain_3)
% 154.05/21.02 $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n3 | v0 = n2 | v0 = n1
% 154.05/21.02 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n3) | ~ leq(n0, v0))
% 154.05/21.02
% 154.05/21.02 (gauss_init_0013)
% 154.05/21.05 $i(pvar1402_init) & $i(pvar1401_init) & $i(pvar1400_init) & $i(loopcounter) &
% 154.05/21.05 $i(s_try7_init) & $i(s_center7_init) & $i(s_values7_init) & $i(simplex7_init)
% 154.05/21.05 & $i(n330) & $i(n410) & $i(pv20) & $i(pv19) & $i(pv7) & $i(s_worst7) &
% 154.05/21.05 $i(s_sworst7) & $i(s_best7) & $i(s_worst7_init) & $i(s_sworst7_init) &
% 154.05/21.05 $i(s_best7_init) & $i(init) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ? [v0: $i]
% 154.05/21.05 : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 154.05/21.05 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11:
% 154.05/21.05 $i] : (s_worst7_init = init & s_sworst7_init = init & s_best7_init = init &
% 154.05/21.05 minus(n330, n1) = v1 & minus(n410, n1) = v0 & minus(n3, n1) = v2 & $i(v10) &
% 154.05/21.05 $i(v9) & $i(v7) & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & leq(pv20, v1)
% 154.05/21.05 & leq(pv19, v0) & leq(pv7, v0) & leq(s_worst7, n3) & leq(s_sworst7, n3) &
% 154.05/21.05 leq(s_best7, n3) & leq(n0, pv20) & leq(n0, pv19) & leq(n0, pv7) & leq(n0,
% 154.05/21.05 s_worst7) & leq(n0, s_sworst7) & leq(n0, s_best7) & ! [v12: $i] : !
% 154.05/21.05 [v13: $i] : ! [v14: $i] : (v14 = init | ~ (a_select3(simplex7_init, v13,
% 154.05/21.05 v12) = v14) | ~ $i(v13) | ~ $i(v12) | ~ leq(v13, n3) | ~ leq(v12,
% 154.05/21.05 n2) | ~ leq(n0, v13) | ~ leq(n0, v12)) & ! [v12: $i] : ! [v13: $i] :
% 154.05/21.05 (v13 = init | ~ (a_select2(s_try7_init, v12) = v13) | ~ $i(v12) | ~
% 154.05/21.05 leq(v12, v2) | ~ leq(n0, v12)) & ! [v12: $i] : ! [v13: $i] : (v13 =
% 154.05/21.05 init | ~ (a_select2(s_center7_init, v12) = v13) | ~ $i(v12) | ~
% 154.05/21.06 leq(v12, n2) | ~ leq(n0, v12)) & ! [v12: $i] : ! [v13: $i] : (v13 =
% 154.05/21.06 init | ~ (a_select2(s_values7_init, v12) = v13) | ~ $i(v12) | ~
% 154.05/21.06 leq(v12, n3) | ~ leq(n0, v12)) & ( ~ gt(loopcounter, n1) | (pvar1402_init
% 154.05/21.06 = init & pvar1401_init = init & pvar1400_init = init)) & (( ~ (v11 =
% 154.05/21.06 init) & a_select3(simplex7_init, v10, v9) = v11 & $i(v11) & leq(v10,
% 154.05/21.06 n3) & leq(v9, n2) & leq(n0, v10) & leq(n0, v9)) | ( ~ (v8 = init) &
% 154.05/21.06 a_select2(s_values7_init, v7) = v8 & $i(v8) & leq(v7, n3) & leq(n0, v7))
% 154.05/21.06 | ( ~ (v6 = init) & a_select2(s_center7_init, v5) = v6 & $i(v6) & leq(v5,
% 154.05/21.06 n2) & leq(n0, v5)) | ( ~ (v4 = init) & a_select2(s_try7_init, v3) = v4
% 154.05/21.06 & $i(v4) & leq(v3, v2) & leq(n0, v3)) | (gt(loopcounter, n1) & ( ~
% 154.05/21.06 (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ (pvar1400_init
% 154.05/21.06 = init)))))
% 154.05/21.06
% 154.05/21.06 (gt_4_2)
% 154.05/21.06 $i(n4) & $i(n2) & gt(n4, n2)
% 154.05/21.06
% 154.05/21.06 (irreflexivity_gt)
% 154.05/21.06 ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0))
% 154.05/21.06
% 154.05/21.06 (leq_gt2)
% 154.05/21.06 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1)
% 154.05/21.06 | gt(v1, v0))
% 154.05/21.06
% 154.05/21.06 (leq_gt_pred)
% 154.05/21.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~
% 154.05/21.06 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 154.05/21.06 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0,
% 154.05/21.06 v2))
% 154.05/21.06
% 154.05/21.06 (leq_succ_gt_equiv)
% 154.05/21.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ $i(v1) | ~
% 154.05/21.06 $i(v0) | ~ leq(v0, v1) | gt(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 154.05/21.06 $i] : ( ~ (succ(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v2, v0) | leq(v0,
% 154.05/21.06 v1))
% 154.05/21.06
% 154.05/21.06 (pred_minus_1)
% 154.05/21.06 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 154.05/21.06 (pred(v0) = v1 & $i(v1)))
% 154.05/21.06
% 154.05/21.06 (pred_succ)
% 154.05/21.06 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0)
% 154.05/21.06
% 154.05/21.06 (successor_1)
% 154.05/21.06 succ(n0) = n1 & $i(n1) & $i(n0)
% 154.05/21.06
% 154.05/21.06 (successor_2)
% 154.05/21.06 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 154.05/21.06
% 154.05/21.06 (successor_3)
% 154.05/21.06 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 &
% 154.05/21.06 succ(n0) = v0 & $i(v1) & $i(v0))
% 154.05/21.06
% 154.05/21.06 (successor_4)
% 154.05/21.06 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 &
% 154.05/21.06 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 154.05/21.06
% 154.05/21.06 (successor_5)
% 154.05/21.06 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 154.05/21.06 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0
% 154.05/21.06 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 154.05/21.06
% 154.05/21.06 (transitivity_leq)
% 154.05/21.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 154.05/21.07 ~ leq(v1, v2) | ~ leq(v0, v1) | leq(v0, v2))
% 154.05/21.07
% 154.05/21.07 (function-axioms)
% 154.05/21.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 154.05/21.07 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 154.05/21.07 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 154.05/21.07 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 154.34/21.07 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 154.34/21.07 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 154.34/21.07 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 154.34/21.07 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 154.34/21.07 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 154.34/21.07 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 154.34/21.07 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 154.34/21.07 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 154.34/21.07 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 154.34/21.07 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 154.34/21.07 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 154.34/21.07 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 154.34/21.07 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 154.34/21.07 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 154.34/21.07 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 154.34/21.07 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 154.34/21.07 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 154.34/21.07 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 154.34/21.07 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 154.34/21.07 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 154.34/21.07 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.34/21.07 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 154.34/21.07 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~
% 154.34/21.07 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 154.34/21.07 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 154.34/21.07 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] :
% 154.34/21.07 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) =
% 154.34/21.07 v0))
% 154.34/21.07
% 154.34/21.07 Further assumptions not needed in the proof:
% 154.34/21.07 --------------------------------------------
% 154.34/21.07 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 154.34/21.07 finite_domain_4, finite_domain_5, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1,
% 154.34/21.07 gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_330_0, gt_330_1, gt_330_2, gt_330_3,
% 154.34/21.07 gt_330_4, gt_330_5, gt_330_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2,
% 154.34/21.07 gt_3_tptp_minus_1, gt_410_0, gt_410_1, gt_410_2, gt_410_3, gt_410_330, gt_410_4,
% 154.34/21.07 gt_410_5, gt_410_tptp_minus_1, gt_4_0, gt_4_1, gt_4_3, gt_4_tptp_minus_1,
% 154.34/21.07 gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, leq_geq,
% 154.34/21.07 leq_gt1, leq_minus, leq_succ, leq_succ_gt, leq_succ_succ, lt_gt,
% 154.34/21.07 matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv,
% 154.34/21.07 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 154.34/21.07 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2,
% 154.34/21.07 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l,
% 154.34/21.07 succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r,
% 154.34/21.07 succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred,
% 154.34/21.07 succ_tptp_minus_1, sum_plus_base, sum_plus_base_float, totality,
% 154.34/21.07 transitivity_gt, ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 154.34/21.07
% 154.34/21.07 Those formulas are unsatisfiable:
% 154.34/21.07 ---------------------------------
% 154.34/21.07
% 154.34/21.07 Begin of proof
% 154.34/21.08 |
% 154.34/21.08 | ALPHA: (leq_gt_pred) implies:
% 154.34/21.08 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 154.34/21.08 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 154.34/21.08 |
% 154.34/21.08 | ALPHA: (leq_succ_gt_equiv) implies:
% 154.34/21.08 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~
% 154.34/21.08 | $i(v1) | ~ $i(v0) | ~ gt(v2, v0) | leq(v0, v1))
% 154.34/21.08 |
% 154.34/21.08 | ALPHA: (pred_minus_1) implies:
% 154.34/21.08 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 154.34/21.08 | (pred(v0) = v1 & $i(v1)))
% 154.34/21.08 |
% 154.34/21.08 | ALPHA: (gt_4_2) implies:
% 154.34/21.08 | (4) gt(n4, n2)
% 154.34/21.08 |
% 154.34/21.08 | ALPHA: (finite_domain_1) implies:
% 154.34/21.08 | (5) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 154.34/21.08 | leq(n0, v0))
% 154.34/21.08 |
% 154.34/21.08 | ALPHA: (finite_domain_2) implies:
% 154.34/21.08 | (6) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2)
% 154.34/21.08 | | ~ leq(n0, v0))
% 154.34/21.08 |
% 154.34/21.08 | ALPHA: (finite_domain_3) implies:
% 154.34/21.08 | (7) ! [v0: $i] : (v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~
% 154.34/21.08 | leq(v0, n3) | ~ leq(n0, v0))
% 154.34/21.08 |
% 154.34/21.08 | ALPHA: (successor_4) implies:
% 154.34/21.08 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) =
% 154.34/21.08 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 154.34/21.08 |
% 154.34/21.08 | ALPHA: (successor_5) implies:
% 154.34/21.08 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5
% 154.34/21.08 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 &
% 154.34/21.08 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 154.34/21.08 |
% 154.34/21.08 | ALPHA: (successor_1) implies:
% 154.34/21.08 | (10) succ(n0) = n1
% 154.34/21.08 |
% 154.34/21.08 | ALPHA: (successor_2) implies:
% 154.34/21.08 | (11) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 154.34/21.08 |
% 154.34/21.08 | ALPHA: (successor_3) implies:
% 154.34/21.08 | (12) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0)
% 154.34/21.08 | = v0 & $i(v1) & $i(v0))
% 154.34/21.08 |
% 154.34/21.08 | ALPHA: (gauss_init_0013) implies:
% 154.34/21.08 | (13) $i(n0)
% 154.34/21.09 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 154.34/21.09 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 154.34/21.09 | ? [v10: $i] : ? [v11: $i] : (s_worst7_init = init & s_sworst7_init =
% 154.34/21.09 | init & s_best7_init = init & minus(n330, n1) = v1 & minus(n410, n1)
% 154.34/21.09 | = v0 & minus(n3, n1) = v2 & $i(v10) & $i(v9) & $i(v7) & $i(v5) &
% 154.34/21.09 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & leq(pv20, v1) & leq(pv19, v0) &
% 154.34/21.09 | leq(pv7, v0) & leq(s_worst7, n3) & leq(s_sworst7, n3) & leq(s_best7,
% 154.34/21.09 | n3) & leq(n0, pv20) & leq(n0, pv19) & leq(n0, pv7) & leq(n0,
% 154.34/21.09 | s_worst7) & leq(n0, s_sworst7) & leq(n0, s_best7) & ! [v12: $i] :
% 154.34/21.09 | ! [v13: $i] : ! [v14: $i] : (v14 = init | ~
% 154.34/21.09 | (a_select3(simplex7_init, v13, v12) = v14) | ~ $i(v13) | ~
% 154.34/21.09 | $i(v12) | ~ leq(v13, n3) | ~ leq(v12, n2) | ~ leq(n0, v13) | ~
% 154.34/21.09 | leq(n0, v12)) & ! [v12: $i] : ! [v13: $i] : (v13 = init | ~
% 154.34/21.09 | (a_select2(s_try7_init, v12) = v13) | ~ $i(v12) | ~ leq(v12, v2)
% 154.34/21.09 | | ~ leq(n0, v12)) & ! [v12: $i] : ! [v13: $i] : (v13 = init |
% 154.34/21.09 | ~ (a_select2(s_center7_init, v12) = v13) | ~ $i(v12) | ~
% 154.34/21.09 | leq(v12, n2) | ~ leq(n0, v12)) & ! [v12: $i] : ! [v13: $i] :
% 154.34/21.09 | (v13 = init | ~ (a_select2(s_values7_init, v12) = v13) | ~ $i(v12)
% 154.34/21.09 | | ~ leq(v12, n3) | ~ leq(n0, v12)) & ( ~ gt(loopcounter, n1) |
% 154.34/21.09 | (pvar1402_init = init & pvar1401_init = init & pvar1400_init =
% 154.34/21.09 | init)) & (( ~ (v11 = init) & a_select3(simplex7_init, v10, v9) =
% 154.34/21.09 | v11 & $i(v11) & leq(v10, n3) & leq(v9, n2) & leq(n0, v10) &
% 154.34/21.09 | leq(n0, v9)) | ( ~ (v8 = init) & a_select2(s_values7_init, v7) =
% 154.34/21.09 | v8 & $i(v8) & leq(v7, n3) & leq(n0, v7)) | ( ~ (v6 = init) &
% 154.34/21.09 | a_select2(s_center7_init, v5) = v6 & $i(v6) & leq(v5, n2) &
% 154.34/21.09 | leq(n0, v5)) | ( ~ (v4 = init) & a_select2(s_try7_init, v3) = v4
% 154.34/21.09 | & $i(v4) & leq(v3, v2) & leq(n0, v3)) | (gt(loopcounter, n1) & (
% 154.34/21.09 | ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~
% 154.34/21.09 | (pvar1400_init = init)))))
% 154.34/21.09 |
% 154.34/21.09 | ALPHA: (function-axioms) implies:
% 154.34/21.09 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) =
% 154.34/21.09 | v1) | ~ (pred(v2) = v0))
% 154.34/21.09 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) =
% 154.34/21.09 | v1) | ~ (succ(v2) = v0))
% 154.34/21.09 |
% 154.34/21.09 | DELTA: instantiating (11) with fresh symbol all_54_0 gives:
% 154.34/21.09 | (17) succ(all_54_0) = n2 & succ(n0) = all_54_0 & $i(all_54_0)
% 154.34/21.09 |
% 154.34/21.09 | ALPHA: (17) implies:
% 154.34/21.09 | (18) $i(all_54_0)
% 154.34/21.09 | (19) succ(n0) = all_54_0
% 154.34/21.09 | (20) succ(all_54_0) = n2
% 154.34/21.09 |
% 154.34/21.09 | DELTA: instantiating (12) with fresh symbols all_57_0, all_57_1 gives:
% 154.34/21.09 | (21) succ(all_57_0) = n3 & succ(all_57_1) = all_57_0 & succ(n0) = all_57_1
% 154.34/21.09 | & $i(all_57_0) & $i(all_57_1)
% 154.34/21.09 |
% 154.34/21.09 | ALPHA: (21) implies:
% 154.34/21.09 | (22) $i(all_57_0)
% 154.34/21.09 | (23) succ(n0) = all_57_1
% 154.34/21.10 | (24) succ(all_57_1) = all_57_0
% 154.34/21.10 | (25) succ(all_57_0) = n3
% 154.34/21.10 |
% 154.34/21.10 | DELTA: instantiating (8) with fresh symbols all_59_0, all_59_1, all_59_2
% 154.34/21.10 | gives:
% 154.34/21.10 | (26) succ(all_59_0) = n4 & succ(all_59_1) = all_59_0 & succ(all_59_2) =
% 154.34/21.10 | all_59_1 & succ(n0) = all_59_2 & $i(all_59_0) & $i(all_59_1) &
% 154.34/21.10 | $i(all_59_2)
% 154.34/21.10 |
% 154.34/21.10 | ALPHA: (26) implies:
% 154.34/21.10 | (27) $i(all_59_0)
% 154.34/21.10 | (28) succ(n0) = all_59_2
% 154.34/21.10 | (29) succ(all_59_2) = all_59_1
% 154.34/21.10 | (30) succ(all_59_1) = all_59_0
% 154.34/21.10 | (31) succ(all_59_0) = n4
% 154.34/21.10 |
% 154.34/21.10 | DELTA: instantiating (9) with fresh symbols all_61_0, all_61_1, all_61_2,
% 154.34/21.10 | all_61_3 gives:
% 154.34/21.10 | (32) succ(all_61_0) = n5 & succ(all_61_1) = all_61_0 & succ(all_61_2) =
% 154.34/21.10 | all_61_1 & succ(all_61_3) = all_61_2 & succ(n0) = all_61_3 &
% 154.34/21.10 | $i(all_61_0) & $i(all_61_1) & $i(all_61_2) & $i(all_61_3)
% 154.34/21.10 |
% 154.34/21.10 | ALPHA: (32) implies:
% 154.34/21.10 | (33) succ(n0) = all_61_3
% 154.34/21.10 | (34) succ(all_61_3) = all_61_2
% 154.34/21.10 | (35) succ(all_61_2) = all_61_1
% 154.34/21.10 | (36) succ(all_61_1) = all_61_0
% 154.34/21.10 |
% 154.34/21.10 | DELTA: instantiating (14) with fresh symbols all_71_0, all_71_1, all_71_2,
% 154.34/21.10 | all_71_3, all_71_4, all_71_5, all_71_6, all_71_7, all_71_8, all_71_9,
% 154.34/21.10 | all_71_10, all_71_11 gives:
% 154.34/21.10 | (37) s_worst7_init = init & s_sworst7_init = init & s_best7_init = init &
% 154.34/21.10 | minus(n330, n1) = all_71_10 & minus(n410, n1) = all_71_11 & minus(n3,
% 154.34/21.10 | n1) = all_71_9 & $i(all_71_1) & $i(all_71_2) & $i(all_71_4) &
% 154.34/21.10 | $i(all_71_6) & $i(all_71_8) & $i(all_71_9) & $i(all_71_10) &
% 154.34/21.10 | $i(all_71_11) & leq(pv20, all_71_10) & leq(pv19, all_71_11) & leq(pv7,
% 154.34/21.10 | all_71_11) & leq(s_worst7, n3) & leq(s_sworst7, n3) & leq(s_best7,
% 154.34/21.10 | n3) & leq(n0, pv20) & leq(n0, pv19) & leq(n0, pv7) & leq(n0,
% 154.34/21.10 | s_worst7) & leq(n0, s_sworst7) & leq(n0, s_best7) & ! [v0: $i] : !
% 154.34/21.10 | [v1: $i] : ! [v2: $i] : (v2 = init | ~ (a_select3(simplex7_init, v1,
% 154.34/21.10 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, n3) | ~ leq(v0,
% 154.34/21.10 | n2) | ~ leq(n0, v1) | ~ leq(n0, v0)) & ! [v0: $i] : ! [v1: $i]
% 154.34/21.10 | : (v1 = init | ~ (a_select2(s_try7_init, v0) = v1) | ~ $i(v0) | ~
% 154.34/21.10 | leq(v0, all_71_9) | ~ leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] :
% 154.34/21.10 | (v1 = init | ~ (a_select2(s_center7_init, v0) = v1) | ~ $i(v0) | ~
% 154.34/21.10 | leq(v0, n2) | ~ leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 154.34/21.10 | init | ~ (a_select2(s_values7_init, v0) = v1) | ~ $i(v0) | ~
% 154.34/21.10 | leq(v0, n3) | ~ leq(n0, v0)) & ( ~ gt(loopcounter, n1) |
% 154.34/21.10 | (pvar1402_init = init & pvar1401_init = init & pvar1400_init =
% 154.34/21.10 | init)) & (( ~ (all_71_0 = init) & a_select3(simplex7_init,
% 154.34/21.10 | all_71_1, all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1,
% 154.34/21.10 | n3) & leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2))
% 154.34/21.10 | | ( ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 154.34/21.11 | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0, all_71_4)) |
% 154.34/21.11 | ( ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) =
% 154.34/21.11 | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0, all_71_6)) |
% 154.34/21.11 | ( ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) = all_71_7
% 154.34/21.11 | & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0, all_71_8)) |
% 154.34/21.11 | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~
% 154.34/21.11 | (pvar1401_init = init) | ~ (pvar1400_init = init))))
% 154.34/21.11 |
% 154.34/21.11 | ALPHA: (37) implies:
% 154.34/21.11 | (38) $i(all_71_8)
% 154.34/21.11 | (39) $i(all_71_6)
% 154.34/21.11 | (40) $i(all_71_4)
% 154.34/21.11 | (41) $i(all_71_2)
% 154.34/21.11 | (42) $i(all_71_1)
% 154.34/21.11 | (43) minus(n3, n1) = all_71_9
% 154.34/21.11 | (44) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1, all_71_2) =
% 154.34/21.11 | all_71_0 & $i(all_71_0) & leq(all_71_1, n3) & leq(all_71_2, n2) &
% 154.34/21.11 | leq(n0, all_71_1) & leq(n0, all_71_2)) | ( ~ (all_71_3 = init) &
% 154.34/21.11 | a_select2(s_values7_init, all_71_4) = all_71_3 & $i(all_71_3) &
% 154.34/21.11 | leq(all_71_4, n3) & leq(n0, all_71_4)) | ( ~ (all_71_5 = init) &
% 154.34/21.11 | a_select2(s_center7_init, all_71_6) = all_71_5 & $i(all_71_5) &
% 154.34/21.11 | leq(all_71_6, n2) & leq(n0, all_71_6)) | ( ~ (all_71_7 = init) &
% 154.34/21.11 | a_select2(s_try7_init, all_71_8) = all_71_7 & $i(all_71_7) &
% 154.34/21.11 | leq(all_71_8, all_71_9) & leq(n0, all_71_8)) | (gt(loopcounter, n1)
% 154.34/21.11 | & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~
% 154.34/21.11 | (pvar1400_init = init)))
% 154.34/21.11 | (45) ~ gt(loopcounter, n1) | (pvar1402_init = init & pvar1401_init = init
% 154.34/21.11 | & pvar1400_init = init)
% 154.34/21.11 | (46) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_values7_init,
% 154.34/21.11 | v0) = v1) | ~ $i(v0) | ~ leq(v0, n3) | ~ leq(n0, v0))
% 154.34/21.11 | (47) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_center7_init,
% 154.34/21.11 | v0) = v1) | ~ $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0))
% 154.34/21.11 | (48) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init,
% 154.34/21.11 | v0) = v1) | ~ $i(v0) | ~ leq(v0, all_71_9) | ~ leq(n0, v0))
% 154.34/21.11 | (49) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~
% 154.34/21.11 | (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 154.34/21.11 | leq(v1, n3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0))
% 154.34/21.11 |
% 154.34/21.11 | GROUND_INST: instantiating (16) with all_54_0, all_57_1, n0, simplifying with
% 154.34/21.11 | (19), (23) gives:
% 154.34/21.11 | (50) all_57_1 = all_54_0
% 154.34/21.11 |
% 154.34/21.11 | GROUND_INST: instantiating (16) with all_57_1, all_59_2, n0, simplifying with
% 154.34/21.11 | (23), (28) gives:
% 154.34/21.11 | (51) all_59_2 = all_57_1
% 154.34/21.11 |
% 154.34/21.11 | GROUND_INST: instantiating (16) with all_59_2, all_61_3, n0, simplifying with
% 154.34/21.11 | (28), (33) gives:
% 154.34/21.11 | (52) all_61_3 = all_59_2
% 154.34/21.11 |
% 154.34/21.11 | GROUND_INST: instantiating (16) with n1, all_61_3, n0, simplifying with (10),
% 154.34/21.11 | (33) gives:
% 154.34/21.11 | (53) all_61_3 = n1
% 154.34/21.11 |
% 154.34/21.11 | COMBINE_EQS: (52), (53) imply:
% 154.34/21.11 | (54) all_59_2 = n1
% 154.34/21.11 |
% 154.34/21.11 | SIMP: (54) implies:
% 154.34/21.11 | (55) all_59_2 = n1
% 154.34/21.11 |
% 154.34/21.11 | COMBINE_EQS: (51), (55) imply:
% 154.34/21.12 | (56) all_57_1 = n1
% 154.34/21.12 |
% 154.34/21.12 | SIMP: (56) implies:
% 154.34/21.12 | (57) all_57_1 = n1
% 154.34/21.12 |
% 154.34/21.12 | COMBINE_EQS: (50), (57) imply:
% 154.34/21.12 | (58) all_54_0 = n1
% 154.34/21.12 |
% 154.34/21.12 | SIMP: (58) implies:
% 154.34/21.12 | (59) all_54_0 = n1
% 154.34/21.12 |
% 154.34/21.12 | REDUCE: (34), (53) imply:
% 154.34/21.12 | (60) succ(n1) = all_61_2
% 154.34/21.12 |
% 154.34/21.12 | REDUCE: (29), (55) imply:
% 154.34/21.12 | (61) succ(n1) = all_59_1
% 154.34/21.12 |
% 154.34/21.12 | REDUCE: (24), (57) imply:
% 154.34/21.12 | (62) succ(n1) = all_57_0
% 154.34/21.12 |
% 154.34/21.12 | REDUCE: (20), (59) imply:
% 154.34/21.12 | (63) succ(n1) = n2
% 154.34/21.12 |
% 154.34/21.12 | REDUCE: (18), (59) imply:
% 154.34/21.12 | (64) $i(n1)
% 154.34/21.12 |
% 154.34/21.12 | GROUND_INST: instantiating (16) with all_57_0, all_59_1, n1, simplifying with
% 154.34/21.12 | (61), (62) gives:
% 154.34/21.12 | (65) all_59_1 = all_57_0
% 154.34/21.12 |
% 154.34/21.12 | GROUND_INST: instantiating (16) with all_59_1, all_61_2, n1, simplifying with
% 154.34/21.12 | (60), (61) gives:
% 154.34/21.12 | (66) all_61_2 = all_59_1
% 154.34/21.12 |
% 154.34/21.12 | GROUND_INST: instantiating (16) with n2, all_61_2, n1, simplifying with (60),
% 154.34/21.12 | (63) gives:
% 154.34/21.12 | (67) all_61_2 = n2
% 154.34/21.12 |
% 154.34/21.12 | COMBINE_EQS: (66), (67) imply:
% 154.34/21.12 | (68) all_59_1 = n2
% 154.34/21.12 |
% 154.34/21.12 | SIMP: (68) implies:
% 154.34/21.12 | (69) all_59_1 = n2
% 154.34/21.12 |
% 154.34/21.12 | COMBINE_EQS: (65), (69) imply:
% 154.34/21.12 | (70) all_57_0 = n2
% 154.34/21.12 |
% 154.34/21.12 | REDUCE: (35), (67) imply:
% 154.34/21.12 | (71) succ(n2) = all_61_1
% 154.34/21.12 |
% 154.34/21.12 | REDUCE: (30), (69) imply:
% 154.34/21.12 | (72) succ(n2) = all_59_0
% 154.34/21.12 |
% 154.34/21.12 | REDUCE: (25), (70) imply:
% 154.34/21.12 | (73) succ(n2) = n3
% 154.34/21.12 |
% 154.34/21.12 | REDUCE: (22), (70) imply:
% 154.34/21.12 | (74) $i(n2)
% 154.34/21.12 |
% 154.34/21.12 | GROUND_INST: instantiating (16) with all_59_0, all_61_1, n2, simplifying with
% 154.34/21.12 | (71), (72) gives:
% 154.34/21.12 | (75) all_61_1 = all_59_0
% 154.34/21.12 |
% 154.34/21.12 | GROUND_INST: instantiating (16) with n3, all_61_1, n2, simplifying with (71),
% 154.34/21.12 | (73) gives:
% 154.34/21.12 | (76) all_61_1 = n3
% 154.34/21.12 |
% 154.34/21.12 | COMBINE_EQS: (75), (76) imply:
% 154.34/21.12 | (77) all_59_0 = n3
% 154.34/21.12 |
% 154.34/21.12 | SIMP: (77) implies:
% 154.34/21.12 | (78) all_59_0 = n3
% 154.34/21.12 |
% 154.34/21.12 | REDUCE: (36), (76) imply:
% 154.34/21.12 | (79) succ(n3) = all_61_0
% 154.34/21.12 |
% 154.34/21.12 | REDUCE: (31), (78) imply:
% 154.34/21.12 | (80) succ(n3) = n4
% 154.34/21.12 |
% 154.34/21.12 | REDUCE: (27), (78) imply:
% 154.34/21.12 | (81) $i(n3)
% 154.34/21.12 |
% 154.34/21.12 | GROUND_INST: instantiating (16) with n4, all_61_0, n3, simplifying with (79),
% 154.34/21.12 | (80) gives:
% 154.34/21.12 | (82) all_61_0 = n4
% 154.34/21.12 |
% 154.34/21.12 | GROUND_INST: instantiating (pred_succ) with n1, n2, simplifying with (63),
% 154.34/21.12 | (64) gives:
% 154.34/21.12 | (83) pred(n2) = n1
% 154.34/21.12 |
% 154.34/21.12 | GROUND_INST: instantiating (pred_succ) with n2, n3, simplifying with (73),
% 154.34/21.12 | (74) gives:
% 154.34/21.12 | (84) pred(n3) = n2
% 154.34/21.12 |
% 154.34/21.12 | GROUND_INST: instantiating (2) with n2, n3, n4, simplifying with (4), (74),
% 154.34/21.12 | (80), (81) gives:
% 154.34/21.12 | (85) leq(n2, n3)
% 154.34/21.12 |
% 154.34/21.12 | GROUND_INST: instantiating (3) with n3, all_71_9, simplifying with (43), (81)
% 154.34/21.12 | gives:
% 154.34/21.12 | (86) pred(n3) = all_71_9 & $i(all_71_9)
% 154.34/21.12 |
% 154.34/21.12 | ALPHA: (86) implies:
% 154.34/21.12 | (87) $i(all_71_9)
% 154.34/21.12 | (88) pred(n3) = all_71_9
% 154.34/21.12 |
% 154.34/21.13 | GROUND_INST: instantiating (15) with n2, all_71_9, n3, simplifying with (84),
% 154.34/21.13 | (88) gives:
% 154.34/21.13 | (89) all_71_9 = n2
% 154.34/21.13 |
% 154.34/21.13 | BETA: splitting (45) gives:
% 154.34/21.13 |
% 154.34/21.13 | Case 1:
% 154.34/21.13 | |
% 154.34/21.13 | | (90) ~ gt(loopcounter, n1)
% 154.34/21.13 | |
% 154.34/21.13 | | BETA: splitting (44) gives:
% 154.34/21.13 | |
% 154.34/21.13 | | Case 1:
% 154.34/21.13 | | |
% 154.34/21.13 | | | (91) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 154.34/21.13 | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 154.34/21.13 | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)) | ( ~
% 154.34/21.13 | | | (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 154.34/21.13 | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0, all_71_4))
% 154.34/21.13 | | |
% 154.34/21.13 | | | BETA: splitting (91) gives:
% 154.34/21.13 | | |
% 154.34/21.13 | | | Case 1:
% 154.34/21.13 | | | |
% 154.34/21.13 | | | | (92) ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 154.34/21.13 | | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 154.34/21.13 | | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)
% 154.34/21.13 | | | |
% 154.34/21.13 | | | | ALPHA: (92) implies:
% 154.34/21.13 | | | | (93) ~ (all_71_0 = init)
% 154.34/21.13 | | | | (94) leq(n0, all_71_2)
% 154.34/21.13 | | | | (95) leq(n0, all_71_1)
% 154.34/21.13 | | | | (96) leq(all_71_2, n2)
% 154.34/21.13 | | | | (97) leq(all_71_1, n3)
% 154.34/21.13 | | | | (98) a_select3(simplex7_init, all_71_1, all_71_2) = all_71_0
% 154.34/21.13 | | | |
% 154.34/21.13 | | | | GROUND_INST: instantiating (49) with all_71_2, all_71_1, all_71_0,
% 154.34/21.13 | | | | simplifying with (41), (42), (94), (95), (96), (97), (98)
% 154.34/21.13 | | | | gives:
% 154.34/21.13 | | | | (99) all_71_0 = init
% 154.34/21.13 | | | |
% 154.34/21.13 | | | | REDUCE: (93), (99) imply:
% 154.34/21.13 | | | | (100) $false
% 154.34/21.13 | | | |
% 154.34/21.13 | | | | CLOSE: (100) is inconsistent.
% 154.34/21.13 | | | |
% 154.34/21.13 | | | Case 2:
% 154.34/21.13 | | | |
% 154.34/21.13 | | | | (101) ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 154.34/21.13 | | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0, all_71_4)
% 154.34/21.13 | | | |
% 154.34/21.13 | | | | ALPHA: (101) implies:
% 154.34/21.13 | | | | (102) ~ (all_71_3 = init)
% 154.34/21.13 | | | | (103) leq(n0, all_71_4)
% 154.34/21.13 | | | | (104) leq(all_71_4, n3)
% 154.34/21.13 | | | | (105) a_select2(s_values7_init, all_71_4) = all_71_3
% 154.34/21.13 | | | |
% 154.34/21.13 | | | | GROUND_INST: instantiating (46) with all_71_4, all_71_3, simplifying
% 154.34/21.13 | | | | with (40), (103), (104), (105) gives:
% 154.34/21.13 | | | | (106) all_71_3 = init
% 154.34/21.13 | | | |
% 154.34/21.13 | | | | REDUCE: (102), (106) imply:
% 154.34/21.13 | | | | (107) $false
% 154.34/21.13 | | | |
% 154.34/21.13 | | | | CLOSE: (107) is inconsistent.
% 154.34/21.13 | | | |
% 154.34/21.13 | | | End of split
% 154.34/21.13 | | |
% 154.34/21.13 | | Case 2:
% 154.34/21.13 | | |
% 154.34/21.13 | | | (108) ( ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) =
% 154.34/21.13 | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0,
% 154.34/21.13 | | | all_71_6)) | ( ~ (all_71_7 = init) & a_select2(s_try7_init,
% 154.34/21.13 | | | all_71_8) = all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9)
% 154.34/21.13 | | | & leq(n0, all_71_8)) | (gt(loopcounter, n1) & ( ~
% 154.34/21.13 | | | (pvar1402_init = init) | ~ (pvar1401_init = init) | ~
% 154.34/21.13 | | | (pvar1400_init = init)))
% 154.34/21.13 | | |
% 154.34/21.13 | | | BETA: splitting (108) gives:
% 154.34/21.13 | | |
% 154.34/21.13 | | | Case 1:
% 154.34/21.13 | | | |
% 154.34/21.14 | | | | (109) ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) =
% 154.34/21.14 | | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0, all_71_6)
% 154.34/21.14 | | | |
% 154.34/21.14 | | | | ALPHA: (109) implies:
% 154.34/21.14 | | | | (110) ~ (all_71_5 = init)
% 154.34/21.14 | | | | (111) leq(n0, all_71_6)
% 154.34/21.14 | | | | (112) leq(all_71_6, n2)
% 154.34/21.14 | | | | (113) a_select2(s_center7_init, all_71_6) = all_71_5
% 154.34/21.14 | | | |
% 154.34/21.14 | | | | GROUND_INST: instantiating (47) with all_71_6, all_71_5, simplifying
% 154.34/21.14 | | | | with (39), (111), (112), (113) gives:
% 154.34/21.14 | | | | (114) all_71_5 = init
% 154.34/21.14 | | | |
% 154.34/21.14 | | | | REDUCE: (110), (114) imply:
% 154.34/21.14 | | | | (115) $false
% 154.34/21.14 | | | |
% 154.34/21.14 | | | | CLOSE: (115) is inconsistent.
% 154.34/21.14 | | | |
% 154.34/21.14 | | | Case 2:
% 154.34/21.14 | | | |
% 154.34/21.14 | | | | (116) ( ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) =
% 154.34/21.14 | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0,
% 154.34/21.14 | | | | all_71_8)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init =
% 154.34/21.14 | | | | init) | ~ (pvar1401_init = init) | ~ (pvar1400_init =
% 154.34/21.14 | | | | init)))
% 154.34/21.14 | | | |
% 154.34/21.14 | | | | BETA: splitting (116) gives:
% 154.34/21.14 | | | |
% 154.34/21.14 | | | | Case 1:
% 154.34/21.14 | | | | |
% 154.34/21.14 | | | | | (117) ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) =
% 154.34/21.14 | | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0,
% 154.34/21.14 | | | | | all_71_8)
% 154.34/21.14 | | | | |
% 154.34/21.14 | | | | | REF_CLOSE: (1), (5), (6), (7), (13), (38), (48), (74), (81), (83),
% 154.34/21.14 | | | | | (85), (89), (117), (irreflexivity_gt), (leq_gt2),
% 154.34/21.14 | | | | | (transitivity_leq) are inconsistent by sub-proof #1.
% 154.34/21.14 | | | | |
% 154.34/21.14 | | | | Case 2:
% 154.34/21.14 | | | | |
% 154.34/21.14 | | | | | (118) gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~
% 154.34/21.14 | | | | | (pvar1401_init = init) | ~ (pvar1400_init = init))
% 154.34/21.14 | | | | |
% 154.34/21.14 | | | | | ALPHA: (118) implies:
% 154.34/21.14 | | | | | (119) gt(loopcounter, n1)
% 154.34/21.14 | | | | |
% 154.34/21.14 | | | | | PRED_UNIFY: (90), (119) imply:
% 154.34/21.14 | | | | | (120) $false
% 154.34/21.14 | | | | |
% 154.34/21.14 | | | | | CLOSE: (120) is inconsistent.
% 154.34/21.14 | | | | |
% 154.34/21.14 | | | | End of split
% 154.34/21.14 | | | |
% 154.34/21.14 | | | End of split
% 154.34/21.14 | | |
% 154.34/21.14 | | End of split
% 154.34/21.14 | |
% 154.34/21.14 | Case 2:
% 154.34/21.14 | |
% 154.34/21.14 | | (121) pvar1402_init = init & pvar1401_init = init & pvar1400_init = init
% 154.34/21.14 | |
% 154.34/21.14 | | ALPHA: (121) implies:
% 154.34/21.14 | | (122) pvar1400_init = init
% 154.34/21.14 | | (123) pvar1401_init = init
% 154.34/21.14 | | (124) pvar1402_init = init
% 154.34/21.14 | |
% 154.34/21.14 | | BETA: splitting (44) gives:
% 154.34/21.14 | |
% 154.34/21.14 | | Case 1:
% 154.34/21.14 | | |
% 154.34/21.14 | | | (125) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 154.34/21.14 | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 154.34/21.14 | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)) | (
% 154.34/21.14 | | | ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 154.34/21.14 | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0,
% 154.34/21.14 | | | all_71_4))
% 154.34/21.14 | | |
% 154.34/21.14 | | | BETA: splitting (125) gives:
% 154.34/21.14 | | |
% 154.34/21.14 | | | Case 1:
% 154.34/21.14 | | | |
% 154.34/21.14 | | | | (126) ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1,
% 154.34/21.14 | | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) &
% 154.34/21.14 | | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)
% 154.34/21.14 | | | |
% 154.34/21.14 | | | | ALPHA: (126) implies:
% 154.34/21.14 | | | | (127) ~ (all_71_0 = init)
% 154.34/21.14 | | | | (128) leq(n0, all_71_2)
% 154.34/21.14 | | | | (129) leq(n0, all_71_1)
% 154.34/21.14 | | | | (130) leq(all_71_2, n2)
% 154.34/21.14 | | | | (131) leq(all_71_1, n3)
% 154.34/21.14 | | | | (132) a_select3(simplex7_init, all_71_1, all_71_2) = all_71_0
% 154.34/21.14 | | | |
% 154.34/21.15 | | | | GROUND_INST: instantiating (49) with all_71_2, all_71_1, all_71_0,
% 154.34/21.15 | | | | simplifying with (41), (42), (128), (129), (130), (131),
% 154.34/21.15 | | | | (132) gives:
% 154.34/21.15 | | | | (133) all_71_0 = init
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | REDUCE: (127), (133) imply:
% 154.34/21.15 | | | | (134) $false
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | CLOSE: (134) is inconsistent.
% 154.34/21.15 | | | |
% 154.34/21.15 | | | Case 2:
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | (135) ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) =
% 154.34/21.15 | | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0, all_71_4)
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | ALPHA: (135) implies:
% 154.34/21.15 | | | | (136) ~ (all_71_3 = init)
% 154.34/21.15 | | | | (137) leq(n0, all_71_4)
% 154.34/21.15 | | | | (138) leq(all_71_4, n3)
% 154.34/21.15 | | | | (139) a_select2(s_values7_init, all_71_4) = all_71_3
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | GROUND_INST: instantiating (46) with all_71_4, all_71_3, simplifying
% 154.34/21.15 | | | | with (40), (137), (138), (139) gives:
% 154.34/21.15 | | | | (140) all_71_3 = init
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | REDUCE: (136), (140) imply:
% 154.34/21.15 | | | | (141) $false
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | CLOSE: (141) is inconsistent.
% 154.34/21.15 | | | |
% 154.34/21.15 | | | End of split
% 154.34/21.15 | | |
% 154.34/21.15 | | Case 2:
% 154.34/21.15 | | |
% 154.34/21.15 | | | (142) ( ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) =
% 154.34/21.15 | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0,
% 154.34/21.15 | | | all_71_6)) | ( ~ (all_71_7 = init) & a_select2(s_try7_init,
% 154.34/21.15 | | | all_71_8) = all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9)
% 154.34/21.15 | | | & leq(n0, all_71_8)) | (gt(loopcounter, n1) & ( ~
% 154.34/21.15 | | | (pvar1402_init = init) | ~ (pvar1401_init = init) | ~
% 154.34/21.15 | | | (pvar1400_init = init)))
% 154.34/21.15 | | |
% 154.34/21.15 | | | BETA: splitting (142) gives:
% 154.34/21.15 | | |
% 154.34/21.15 | | | Case 1:
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | (143) ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) =
% 154.34/21.15 | | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0, all_71_6)
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | ALPHA: (143) implies:
% 154.34/21.15 | | | | (144) ~ (all_71_5 = init)
% 154.34/21.15 | | | | (145) leq(n0, all_71_6)
% 154.34/21.15 | | | | (146) leq(all_71_6, n2)
% 154.34/21.15 | | | | (147) a_select2(s_center7_init, all_71_6) = all_71_5
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | GROUND_INST: instantiating (47) with all_71_6, all_71_5, simplifying
% 154.34/21.15 | | | | with (39), (145), (146), (147) gives:
% 154.34/21.15 | | | | (148) all_71_5 = init
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | REDUCE: (144), (148) imply:
% 154.34/21.15 | | | | (149) $false
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | CLOSE: (149) is inconsistent.
% 154.34/21.15 | | | |
% 154.34/21.15 | | | Case 2:
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | (150) ( ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) =
% 154.34/21.15 | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0,
% 154.34/21.15 | | | | all_71_8)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init =
% 154.34/21.15 | | | | init) | ~ (pvar1401_init = init) | ~ (pvar1400_init =
% 154.34/21.15 | | | | init)))
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | BETA: splitting (150) gives:
% 154.34/21.15 | | | |
% 154.34/21.15 | | | | Case 1:
% 154.34/21.15 | | | | |
% 154.34/21.15 | | | | | (151) ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) =
% 154.34/21.15 | | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0,
% 154.34/21.15 | | | | | all_71_8)
% 154.34/21.15 | | | | |
% 154.34/21.15 | | | | | REF_CLOSE: (1), (5), (6), (7), (13), (38), (48), (74), (81), (83),
% 154.34/21.15 | | | | | (85), (89), (151), (irreflexivity_gt), (leq_gt2),
% 154.34/21.15 | | | | | (transitivity_leq) are inconsistent by sub-proof #1.
% 154.34/21.15 | | | | |
% 154.34/21.15 | | | | Case 2:
% 154.34/21.15 | | | | |
% 154.34/21.15 | | | | | (152) gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~
% 154.34/21.15 | | | | | (pvar1401_init = init) | ~ (pvar1400_init = init))
% 154.34/21.15 | | | | |
% 154.34/21.15 | | | | | ALPHA: (152) implies:
% 154.34/21.15 | | | | | (153) ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~
% 154.34/21.15 | | | | | (pvar1400_init = init)
% 154.34/21.15 | | | | |
% 154.34/21.15 | | | | | BETA: splitting (153) gives:
% 154.34/21.15 | | | | |
% 154.34/21.15 | | | | | Case 1:
% 154.34/21.15 | | | | | |
% 154.75/21.15 | | | | | | (154) ~ (pvar1402_init = init)
% 154.75/21.15 | | | | | |
% 154.75/21.15 | | | | | | REDUCE: (124), (154) imply:
% 154.75/21.15 | | | | | | (155) $false
% 154.75/21.15 | | | | | |
% 154.75/21.15 | | | | | | CLOSE: (155) is inconsistent.
% 154.75/21.15 | | | | | |
% 154.75/21.15 | | | | | Case 2:
% 154.75/21.15 | | | | | |
% 154.75/21.15 | | | | | | (156) ~ (pvar1401_init = init) | ~ (pvar1400_init = init)
% 154.75/21.15 | | | | | |
% 154.75/21.15 | | | | | | BETA: splitting (156) gives:
% 154.75/21.15 | | | | | |
% 154.75/21.15 | | | | | | Case 1:
% 154.75/21.15 | | | | | | |
% 154.75/21.15 | | | | | | | (157) ~ (pvar1401_init = init)
% 154.75/21.15 | | | | | | |
% 154.75/21.15 | | | | | | | REDUCE: (123), (157) imply:
% 154.75/21.15 | | | | | | | (158) $false
% 154.75/21.15 | | | | | | |
% 154.75/21.15 | | | | | | | CLOSE: (158) is inconsistent.
% 154.75/21.15 | | | | | | |
% 154.75/21.15 | | | | | | Case 2:
% 154.75/21.15 | | | | | | |
% 154.75/21.16 | | | | | | | (159) ~ (pvar1400_init = init)
% 154.75/21.16 | | | | | | |
% 154.75/21.16 | | | | | | | REDUCE: (122), (159) imply:
% 154.75/21.16 | | | | | | | (160) $false
% 154.75/21.16 | | | | | | |
% 154.75/21.16 | | | | | | | CLOSE: (160) is inconsistent.
% 154.75/21.16 | | | | | | |
% 154.75/21.16 | | | | | | End of split
% 154.75/21.16 | | | | | |
% 154.75/21.16 | | | | | End of split
% 154.75/21.16 | | | | |
% 154.75/21.16 | | | | End of split
% 154.75/21.16 | | | |
% 154.75/21.16 | | | End of split
% 154.75/21.16 | | |
% 154.75/21.16 | | End of split
% 154.75/21.16 | |
% 154.75/21.16 | End of split
% 154.75/21.16 |
% 154.75/21.16 End of proof
% 154.75/21.16
% 154.75/21.16 Sub-proof #1 shows that the following formulas are inconsistent:
% 154.75/21.16 ----------------------------------------------------------------
% 154.75/21.16 (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0,
% 154.75/21.16 v1) | gt(v1, v0))
% 154.75/21.16 (2) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2) |
% 154.75/21.16 ~ leq(n0, v0))
% 154.75/21.16 (3) $i(n3)
% 154.75/21.16 (4) leq(n2, n3)
% 154.75/21.16 (5) ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) = all_71_7 &
% 154.75/21.16 $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0, all_71_8)
% 154.75/21.16 (6) $i(all_71_8)
% 154.75/21.16 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1)
% 154.75/21.16 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 154.75/21.16 (8) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 154.75/21.16 leq(n0, v0))
% 154.75/21.16 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 154.75/21.16 $i(v0) | ~ leq(v1, v2) | ~ leq(v0, v1) | leq(v0, v2))
% 154.75/21.16 (10) all_71_9 = n2
% 154.75/21.16 (11) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0))
% 154.75/21.16 (12) $i(n0)
% 154.75/21.16 (13) ! [v0: $i] : (v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~
% 154.75/21.16 leq(v0, n3) | ~ leq(n0, v0))
% 154.75/21.16 (14) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0)
% 154.75/21.16 = v1) | ~ $i(v0) | ~ leq(v0, all_71_9) | ~ leq(n0, v0))
% 154.75/21.16 (15) pred(n2) = n1
% 154.75/21.16 (16) $i(n2)
% 154.75/21.16
% 154.75/21.16 Begin of proof
% 154.75/21.16 |
% 154.75/21.16 | ALPHA: (5) implies:
% 154.75/21.16 | (17) ~ (all_71_7 = init)
% 154.75/21.16 | (18) leq(n0, all_71_8)
% 154.75/21.16 | (19) leq(all_71_8, all_71_9)
% 154.75/21.16 | (20) a_select2(s_try7_init, all_71_8) = all_71_7
% 154.75/21.16 |
% 154.75/21.16 | REDUCE: (10), (19) imply:
% 154.75/21.16 | (21) leq(all_71_8, n2)
% 154.75/21.16 |
% 154.75/21.16 | GROUND_INST: instantiating (1) with n0, all_71_8, simplifying with (6), (12),
% 154.75/21.16 | (18) gives:
% 154.75/21.16 | (22) all_71_8 = n0 | gt(all_71_8, n0)
% 154.75/21.16 |
% 154.75/21.16 | GROUND_INST: instantiating (9) with all_71_8, n2, n3, simplifying with (3),
% 154.75/21.16 | (4), (6), (16), (21) gives:
% 154.75/21.16 | (23) leq(all_71_8, n3)
% 154.75/21.16 |
% 154.75/21.16 | GROUND_INST: instantiating (2) with all_71_8, simplifying with (6), (18), (21)
% 154.75/21.16 | gives:
% 154.75/21.16 | (24) all_71_8 = n2 | all_71_8 = n1 | all_71_8 = n0
% 154.75/21.16 |
% 154.75/21.16 | GROUND_INST: instantiating (1) with all_71_8, n2, simplifying with (6), (16),
% 154.75/21.16 | (21) gives:
% 154.75/21.16 | (25) all_71_8 = n2 | gt(n2, all_71_8)
% 154.75/21.16 |
% 154.75/21.16 | GROUND_INST: instantiating (13) with all_71_8, simplifying with (6), (18),
% 154.75/21.16 | (23) gives:
% 154.75/21.16 | (26) all_71_8 = n3 | all_71_8 = n2 | all_71_8 = n1 | all_71_8 = n0
% 154.75/21.16 |
% 154.75/21.16 | BETA: splitting (22) gives:
% 154.75/21.16 |
% 154.75/21.16 | Case 1:
% 154.75/21.16 | |
% 154.75/21.16 | | (27) gt(all_71_8, n0)
% 154.75/21.16 | |
% 154.75/21.16 | | BETA: splitting (25) gives:
% 154.75/21.16 | |
% 154.75/21.16 | | Case 1:
% 154.75/21.16 | | |
% 154.75/21.16 | | | (28) gt(n2, all_71_8)
% 154.75/21.16 | | |
% 154.75/21.16 | | | BETA: splitting (24) gives:
% 154.75/21.16 | | |
% 154.75/21.16 | | | Case 1:
% 154.75/21.16 | | | |
% 154.75/21.16 | | | | (29) all_71_8 = n0
% 154.75/21.16 | | | |
% 154.75/21.16 | | | | REDUCE: (27), (29) imply:
% 154.75/21.16 | | | | (30) gt(n0, n0)
% 154.75/21.16 | | | |
% 154.75/21.16 | | | | GROUND_INST: instantiating (11) with n0, simplifying with (12), (30)
% 154.75/21.16 | | | | gives:
% 154.75/21.16 | | | | (31) $false
% 154.75/21.16 | | | |
% 154.75/21.16 | | | | CLOSE: (31) is inconsistent.
% 154.75/21.16 | | | |
% 154.75/21.16 | | | Case 2:
% 154.75/21.16 | | | |
% 154.75/21.16 | | | | (32) ~ (all_71_8 = n0)
% 154.75/21.16 | | | |
% 154.75/21.16 | | | | BETA: splitting (26) gives:
% 154.75/21.16 | | | |
% 154.75/21.16 | | | | Case 1:
% 154.75/21.16 | | | | |
% 154.75/21.16 | | | | | (33) all_71_8 = n0
% 154.75/21.17 | | | | |
% 154.75/21.17 | | | | | REDUCE: (32), (33) imply:
% 154.75/21.17 | | | | | (34) $false
% 154.75/21.17 | | | | |
% 154.75/21.17 | | | | | CLOSE: (34) is inconsistent.
% 154.75/21.17 | | | | |
% 154.75/21.17 | | | | Case 2:
% 154.75/21.17 | | | | |
% 154.75/21.17 | | | | |
% 154.75/21.17 | | | | | REF_CLOSE: (6), (7), (8), (10), (14), (15), (16), (17), (18), (20),
% 154.75/21.17 | | | | | (21), (28), (32) are inconsistent by sub-proof #3.
% 154.75/21.17 | | | | |
% 154.75/21.17 | | | | End of split
% 154.75/21.17 | | | |
% 154.75/21.17 | | | End of split
% 154.75/21.17 | | |
% 154.75/21.17 | | Case 2:
% 154.75/21.17 | | |
% 154.75/21.17 | | | (35) all_71_8 = n2
% 154.75/21.17 | | |
% 154.75/21.17 | | | REF_CLOSE: (6), (10), (14), (17), (18), (20), (21), (35) are inconsistent
% 154.75/21.17 | | | by sub-proof #2.
% 154.75/21.17 | | |
% 154.75/21.17 | | End of split
% 154.75/21.17 | |
% 154.75/21.17 | Case 2:
% 154.75/21.17 | |
% 154.75/21.17 | | (36) all_71_8 = n0
% 154.75/21.17 | | (37) ~ gt(all_71_8, n0)
% 154.75/21.17 | |
% 154.75/21.17 | | REDUCE: (36), (37) imply:
% 154.75/21.17 | | (38) ~ gt(n0, n0)
% 154.75/21.17 | |
% 154.75/21.17 | | BETA: splitting (22) gives:
% 154.75/21.17 | |
% 154.75/21.17 | | Case 1:
% 154.75/21.17 | | |
% 154.75/21.17 | | | (39) gt(all_71_8, n0)
% 154.75/21.17 | | |
% 154.75/21.17 | | | BETA: splitting (25) gives:
% 154.75/21.17 | | |
% 154.75/21.17 | | | Case 1:
% 154.75/21.17 | | | |
% 154.75/21.17 | | | | (40) gt(n2, all_71_8)
% 154.75/21.17 | | | |
% 154.75/21.17 | | | | BETA: splitting (24) gives:
% 154.75/21.17 | | | |
% 154.75/21.17 | | | | Case 1:
% 154.75/21.17 | | | | |
% 154.75/21.17 | | | | |
% 154.75/21.17 | | | | | REDUCE: (36), (39) imply:
% 154.75/21.17 | | | | | (41) gt(n0, n0)
% 154.75/21.17 | | | | |
% 154.75/21.17 | | | | | PRED_UNIFY: (38), (41) imply:
% 154.75/21.17 | | | | | (42) $false
% 154.75/21.17 | | | | |
% 154.75/21.17 | | | | | CLOSE: (42) is inconsistent.
% 154.75/21.17 | | | | |
% 154.75/21.17 | | | | Case 2:
% 154.75/21.17 | | | | |
% 154.75/21.17 | | | | | (43) ~ (all_71_8 = n0)
% 154.75/21.17 | | | | |
% 154.75/21.17 | | | | | REF_CLOSE: (6), (7), (8), (10), (14), (15), (16), (17), (18), (20),
% 154.75/21.17 | | | | | (21), (40), (43) are inconsistent by sub-proof #3.
% 154.75/21.17 | | | | |
% 154.75/21.17 | | | | End of split
% 154.75/21.17 | | | |
% 154.75/21.17 | | | Case 2:
% 154.75/21.17 | | | |
% 154.75/21.17 | | | | (44) all_71_8 = n2
% 154.75/21.17 | | | |
% 154.75/21.17 | | | | REF_CLOSE: (6), (10), (14), (17), (18), (20), (21), (44) are
% 154.75/21.17 | | | | inconsistent by sub-proof #2.
% 154.75/21.17 | | | |
% 154.75/21.17 | | | End of split
% 154.75/21.17 | | |
% 154.75/21.17 | | Case 2:
% 154.75/21.17 | | |
% 154.75/21.17 | | |
% 154.75/21.17 | | | REDUCE: (20), (36) imply:
% 154.75/21.17 | | | (45) a_select2(s_try7_init, n0) = all_71_7
% 154.75/21.17 | | |
% 154.75/21.17 | | | REDUCE: (21), (36) imply:
% 154.75/21.17 | | | (46) leq(n0, n2)
% 154.75/21.17 | | |
% 154.75/21.17 | | | REDUCE: (18), (36) imply:
% 154.75/21.17 | | | (47) leq(n0, n0)
% 154.75/21.17 | | |
% 154.75/21.17 | | | GROUND_INST: instantiating (14) with n0, all_71_7, simplifying with (12),
% 154.75/21.17 | | | (45), (47) gives:
% 154.75/21.17 | | | (48) all_71_7 = init | ~ leq(n0, all_71_9)
% 154.75/21.17 | | |
% 154.75/21.17 | | | BETA: splitting (48) gives:
% 154.75/21.17 | | |
% 154.75/21.17 | | | Case 1:
% 154.75/21.17 | | | |
% 154.75/21.17 | | | | (49) ~ leq(n0, all_71_9)
% 154.75/21.17 | | | |
% 154.75/21.17 | | | | REDUCE: (10), (49) imply:
% 154.75/21.17 | | | | (50) ~ leq(n0, n2)
% 154.75/21.17 | | | |
% 154.75/21.17 | | | | PRED_UNIFY: (46), (50) imply:
% 154.75/21.17 | | | | (51) $false
% 154.75/21.17 | | | |
% 154.75/21.17 | | | | CLOSE: (51) is inconsistent.
% 154.75/21.17 | | | |
% 154.75/21.17 | | | Case 2:
% 154.75/21.17 | | | |
% 154.75/21.17 | | | | (52) all_71_7 = init
% 154.75/21.17 | | | |
% 154.75/21.17 | | | | REDUCE: (17), (52) imply:
% 154.75/21.17 | | | | (53) $false
% 154.75/21.17 | | | |
% 154.75/21.17 | | | | CLOSE: (53) is inconsistent.
% 154.75/21.17 | | | |
% 154.75/21.17 | | | End of split
% 154.75/21.17 | | |
% 154.75/21.17 | | End of split
% 154.75/21.17 | |
% 154.75/21.17 | End of split
% 154.75/21.17 |
% 154.75/21.17 End of proof
% 154.75/21.17
% 154.75/21.17 Sub-proof #2 shows that the following formulas are inconsistent:
% 154.75/21.17 ----------------------------------------------------------------
% 154.75/21.17 (1) $i(all_71_8)
% 154.75/21.17 (2) all_71_8 = n2
% 154.75/21.17 (3) a_select2(s_try7_init, all_71_8) = all_71_7
% 154.75/21.17 (4) all_71_9 = n2
% 154.75/21.17 (5) leq(n0, all_71_8)
% 154.75/21.17 (6) ~ (all_71_7 = init)
% 154.75/21.17 (7) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0) =
% 154.75/21.17 v1) | ~ $i(v0) | ~ leq(v0, all_71_9) | ~ leq(n0, v0))
% 154.75/21.17 (8) leq(all_71_8, n2)
% 154.75/21.17
% 154.75/21.17 Begin of proof
% 154.75/21.17 |
% 154.75/21.17 | REDUCE: (2), (3) imply:
% 154.75/21.17 | (9) a_select2(s_try7_init, n2) = all_71_7
% 154.75/21.17 |
% 154.75/21.17 | REDUCE: (1), (2) imply:
% 154.75/21.17 | (10) $i(n2)
% 154.75/21.17 |
% 154.75/21.17 | REDUCE: (2), (8) imply:
% 154.75/21.17 | (11) leq(n2, n2)
% 154.75/21.17 |
% 154.75/21.17 | REDUCE: (2), (5) imply:
% 154.75/21.17 | (12) leq(n0, n2)
% 154.75/21.17 |
% 154.75/21.17 | GROUND_INST: instantiating (7) with n2, all_71_7, simplifying with (9), (10),
% 154.75/21.17 | (12) gives:
% 154.75/21.17 | (13) all_71_7 = init | ~ leq(n2, all_71_9)
% 154.75/21.17 |
% 154.75/21.17 | BETA: splitting (13) gives:
% 154.75/21.17 |
% 154.75/21.17 | Case 1:
% 154.75/21.17 | |
% 154.75/21.17 | | (14) ~ leq(n2, all_71_9)
% 154.75/21.17 | |
% 154.75/21.17 | | REDUCE: (4), (14) imply:
% 154.75/21.17 | | (15) ~ leq(n2, n2)
% 154.75/21.17 | |
% 154.75/21.17 | | PRED_UNIFY: (11), (15) imply:
% 154.75/21.17 | | (16) $false
% 154.75/21.17 | |
% 154.75/21.17 | | CLOSE: (16) is inconsistent.
% 154.75/21.17 | |
% 154.75/21.17 | Case 2:
% 154.75/21.17 | |
% 154.75/21.17 | | (17) all_71_7 = init
% 154.75/21.17 | |
% 154.75/21.17 | | REDUCE: (6), (17) imply:
% 154.75/21.17 | | (18) $false
% 154.75/21.17 | |
% 154.75/21.17 | | CLOSE: (18) is inconsistent.
% 154.75/21.17 | |
% 154.75/21.17 | End of split
% 154.75/21.17 |
% 154.75/21.17 End of proof
% 154.75/21.17
% 154.75/21.17 Sub-proof #3 shows that the following formulas are inconsistent:
% 154.75/21.17 ----------------------------------------------------------------
% 154.75/21.17 (1) $i(all_71_8)
% 154.75/21.17 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1)
% 154.75/21.17 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 154.75/21.17 (3) a_select2(s_try7_init, all_71_8) = all_71_7
% 154.75/21.17 (4) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 154.75/21.17 leq(n0, v0))
% 154.75/21.17 (5) ~ (all_71_8 = n0)
% 154.75/21.17 (6) all_71_9 = n2
% 154.75/21.17 (7) leq(n0, all_71_8)
% 154.75/21.17 (8) ~ (all_71_7 = init)
% 154.75/21.17 (9) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0) =
% 154.75/21.17 v1) | ~ $i(v0) | ~ leq(v0, all_71_9) | ~ leq(n0, v0))
% 154.75/21.17 (10) gt(n2, all_71_8)
% 154.75/21.18 (11) leq(all_71_8, n2)
% 154.75/21.18 (12) pred(n2) = n1
% 154.75/21.18 (13) $i(n2)
% 154.75/21.18
% 154.75/21.18 Begin of proof
% 154.75/21.18 |
% 154.75/21.18 | GROUND_INST: instantiating (2) with all_71_8, n2, n1, simplifying with (1),
% 154.75/21.18 | (10), (12), (13) gives:
% 154.75/21.18 | (14) leq(all_71_8, n1)
% 154.75/21.18 |
% 154.75/21.18 | GROUND_INST: instantiating (4) with all_71_8, simplifying with (1), (7), (14)
% 154.75/21.18 | gives:
% 154.75/21.18 | (15) all_71_8 = n1 | all_71_8 = n0
% 154.75/21.18 |
% 154.75/21.18 | BETA: splitting (15) gives:
% 154.75/21.18 |
% 154.75/21.18 | Case 1:
% 154.75/21.18 | |
% 154.75/21.18 | | (16) all_71_8 = n0
% 154.75/21.18 | |
% 154.75/21.18 | | REDUCE: (5), (16) imply:
% 154.75/21.18 | | (17) $false
% 154.75/21.18 | |
% 154.75/21.18 | | CLOSE: (17) is inconsistent.
% 154.75/21.18 | |
% 154.75/21.18 | Case 2:
% 154.75/21.18 | |
% 154.75/21.18 | | (18) all_71_8 = n1
% 154.75/21.18 | |
% 154.75/21.18 | | REDUCE: (3), (18) imply:
% 154.75/21.18 | | (19) a_select2(s_try7_init, n1) = all_71_7
% 154.75/21.18 | |
% 154.75/21.18 | | REDUCE: (1), (18) imply:
% 154.75/21.18 | | (20) $i(n1)
% 154.75/21.18 | |
% 154.75/21.18 | | REDUCE: (11), (18) imply:
% 154.75/21.18 | | (21) leq(n1, n2)
% 154.75/21.18 | |
% 154.75/21.18 | | REDUCE: (7), (18) imply:
% 154.75/21.18 | | (22) leq(n0, n1)
% 154.75/21.18 | |
% 154.75/21.18 | | GROUND_INST: instantiating (9) with n1, all_71_7, simplifying with (19),
% 154.75/21.18 | | (20), (22) gives:
% 154.75/21.18 | | (23) all_71_7 = init | ~ leq(n1, all_71_9)
% 154.75/21.18 | |
% 154.75/21.18 | | BETA: splitting (23) gives:
% 154.75/21.18 | |
% 154.75/21.18 | | Case 1:
% 154.75/21.18 | | |
% 154.75/21.18 | | | (24) ~ leq(n1, all_71_9)
% 154.75/21.18 | | |
% 154.75/21.18 | | | REDUCE: (6), (24) imply:
% 154.75/21.18 | | | (25) ~ leq(n1, n2)
% 154.75/21.18 | | |
% 154.75/21.18 | | | PRED_UNIFY: (21), (25) imply:
% 154.75/21.18 | | | (26) $false
% 154.75/21.18 | | |
% 154.75/21.18 | | | CLOSE: (26) is inconsistent.
% 154.75/21.18 | | |
% 154.75/21.18 | | Case 2:
% 154.75/21.18 | | |
% 154.75/21.18 | | | (27) all_71_7 = init
% 154.75/21.18 | | |
% 154.75/21.18 | | | REDUCE: (8), (27) imply:
% 154.75/21.18 | | | (28) $false
% 154.75/21.18 | | |
% 154.75/21.18 | | | CLOSE: (28) is inconsistent.
% 154.75/21.18 | | |
% 154.75/21.18 | | End of split
% 154.75/21.18 | |
% 154.75/21.18 | End of split
% 154.75/21.18 |
% 154.75/21.18 End of proof
% 154.75/21.18 % SZS output end Proof for theBenchmark
% 154.86/21.18
% 154.86/21.18 20572ms
%------------------------------------------------------------------------------