TSTP Solution File: SWV137+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV137+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 : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 22:55:04 EDT 2023
% Result : Theorem 18.43s 3.25s
% Output : Proof 23.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV137+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.31 % Computer : n023.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.31 % CPULimit : 300
% 0.15/0.31 % WCLimit : 300
% 0.15/0.31 % DateTime : Tue Aug 29 09:21:25 EDT 2023
% 0.15/0.32 % CPUTime :
% 0.16/0.59 ________ _____
% 0.16/0.59 ___ __ \_________(_)________________________________
% 0.16/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.59
% 0.16/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.59 (2023-06-19)
% 0.16/0.59
% 0.16/0.59 (c) Philipp Rümmer, 2009-2023
% 0.16/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.59 Amanda Stjerna.
% 0.16/0.59 Free software under BSD-3-Clause.
% 0.16/0.59
% 0.16/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.59
% 0.16/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.61/0.61 Running up to 7 provers in parallel.
% 0.61/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.61/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.61/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.61/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.61/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.61/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.61/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.36/1.34 Prover 4: Preprocessing ...
% 4.36/1.34 Prover 1: Preprocessing ...
% 4.52/1.40 Prover 3: Preprocessing ...
% 4.52/1.40 Prover 6: Preprocessing ...
% 4.52/1.40 Prover 2: Preprocessing ...
% 4.52/1.40 Prover 5: Preprocessing ...
% 4.52/1.42 Prover 0: Preprocessing ...
% 13.16/2.50 Prover 1: Warning: ignoring some quantifiers
% 13.43/2.55 Prover 3: Warning: ignoring some quantifiers
% 13.43/2.59 Prover 4: Warning: ignoring some quantifiers
% 13.88/2.62 Prover 3: Constructing countermodel ...
% 13.88/2.62 Prover 1: Constructing countermodel ...
% 13.88/2.63 Prover 6: Proving ...
% 14.35/2.71 Prover 4: Constructing countermodel ...
% 15.05/2.77 Prover 0: Proving ...
% 15.05/2.77 Prover 5: Proving ...
% 15.34/2.83 Prover 2: Proving ...
% 18.43/3.24 Prover 3: proved (2617ms)
% 18.43/3.24
% 18.43/3.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.43/3.25
% 18.43/3.25 Prover 2: stopped
% 18.43/3.25 Prover 6: stopped
% 18.43/3.25 Prover 5: stopped
% 18.43/3.26 Prover 0: stopped
% 18.99/3.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 18.99/3.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 18.99/3.27 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 18.99/3.27 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 18.99/3.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 20.26/3.44 Prover 10: Preprocessing ...
% 20.26/3.46 Prover 8: Preprocessing ...
% 20.86/3.53 Prover 11: Preprocessing ...
% 20.86/3.53 Prover 13: Preprocessing ...
% 20.86/3.56 Prover 7: Preprocessing ...
% 21.44/3.64 Prover 1: Found proof (size 57)
% 21.44/3.64 Prover 1: proved (3021ms)
% 21.44/3.64 Prover 4: stopped
% 21.44/3.65 Prover 10: stopped
% 22.13/3.71 Prover 11: stopped
% 22.13/3.71 Prover 7: stopped
% 22.42/3.74 Prover 13: stopped
% 22.42/3.79 Prover 8: Warning: ignoring some quantifiers
% 22.42/3.80 Prover 8: Constructing countermodel ...
% 22.85/3.82 Prover 8: stopped
% 22.85/3.82
% 22.85/3.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.85/3.82
% 22.85/3.84 % SZS output start Proof for theBenchmark
% 22.85/3.85 Assumptions after simplification:
% 22.85/3.85 ---------------------------------
% 22.85/3.85
% 22.85/3.85 (gauss_array_0007)
% 22.85/3.87 $i(s_values7) & $i(pv1325) & $i(s_worst7) & $i(s_sworst7) & $i(s_best7) &
% 22.85/3.87 $i(n3) & $i(n2) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 22.85/3.87 int] : ( ~ (v3 = 0) & a_select2(s_values7, pv1325) = v0 &
% 22.85/3.87 a_select2(s_values7, s_worst7) = v2 & a_select2(s_values7, s_best7) = v1 &
% 22.85/3.87 leq(v0, v2) = 0 & leq(v0, v1) = 0 & leq(pv1325, n3) = 0 & leq(s_worst7, n3)
% 22.85/3.87 = 0 & leq(s_sworst7, n3) = 0 & leq(s_best7, n3) = 0 & leq(n2, pv1325) = 0 &
% 22.85/3.88 leq(n0, pv1325) = v3 & leq(n0, s_worst7) = 0 & leq(n0, s_sworst7) = 0 &
% 22.85/3.88 leq(n0, s_best7) = 0 & $i(v2) & $i(v1) & $i(v0))
% 22.85/3.88
% 22.85/3.88 (gt_2_0)
% 22.85/3.88 gt(n2, n0) = 0 & $i(n2) & $i(n0)
% 22.85/3.88
% 22.85/3.88 (leq_gt1)
% 22.85/3.88 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 22.85/3.88 leq(v0, v1) = 0)
% 22.85/3.88
% 22.85/3.88 (leq_succ_gt)
% 22.85/3.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v2) | ~ (leq(v2,
% 22.85/3.88 v1) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0)
% 22.85/3.88
% 22.85/3.88 (leq_succ_gt_equiv)
% 22.85/3.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 22.85/3.88 (succ(v1) = v2) | ~ (gt(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 22.85/3.88 int] : ( ~ (v4 = 0) & leq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : !
% 22.85/3.88 [v2: $i] : ( ~ (succ(v1) = v2) | ~ (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 22.85/3.88 leq(v0, v1) = 0)
% 22.85/3.88
% 22.85/3.88 (successor_1)
% 23.21/3.88 succ(n0) = n1 & $i(n1) & $i(n0)
% 23.21/3.88
% 23.21/3.88 (successor_2)
% 23.21/3.88 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 23.21/3.88
% 23.21/3.88 (successor_3)
% 23.21/3.88 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 &
% 23.21/3.88 succ(n0) = v0 & $i(v1) & $i(v0))
% 23.21/3.88
% 23.21/3.88 (successor_4)
% 23.21/3.89 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 &
% 23.21/3.89 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 23.21/3.89
% 23.21/3.89 (successor_5)
% 23.21/3.89 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 23.21/3.89 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0
% 23.21/3.89 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 23.21/3.89
% 23.21/3.89 (transitivity_leq)
% 23.21/3.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (leq(v0,
% 23.21/3.89 v2) = v3) | ~ (leq(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 23.21/3.89 ? [v4: int] : ( ~ (v4 = 0) & leq(v1, v2) = v4))
% 23.21/3.89
% 23.21/3.89 (function-axioms)
% 23.21/3.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 23.21/3.90 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 23.21/3.90 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 23.21/3.90 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 23.21/3.90 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 23.21/3.90 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 23.21/3.90 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 23.21/3.90 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 23.21/3.90 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 23.21/3.90 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 23.21/3.90 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 23.21/3.90 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 23.21/3.90 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 23.21/3.90 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 23.21/3.90 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 23.21/3.90 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 23.21/3.90 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 23.21/3.90 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 23.21/3.90 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 23.21/3.90 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 23.21/3.90 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 23.21/3.90 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 23.21/3.90 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 23.21/3.90 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 23.21/3.90 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.21/3.90 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 23.21/3.90 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 23.21/3.90 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 23.21/3.90 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 23.21/3.90 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 23.21/3.90 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 23.21/3.90 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 23.21/3.90 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 23.21/3.90 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 23.21/3.90 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 23.21/3.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 23.21/3.90 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 23.21/3.90 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 23.21/3.90 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 23.21/3.90
% 23.21/3.90 Further assumptions not needed in the proof:
% 23.21/3.90 --------------------------------------------
% 23.21/3.90 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 23.21/3.90 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 23.21/3.90 finite_domain_5, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_1,
% 23.21/3.90 gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_4_0, gt_4_1,
% 23.21/3.90 gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4,
% 23.21/3.90 gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, leq_gt2, leq_gt_pred,
% 23.21/3.90 leq_minus, leq_succ, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 23.21/3.90 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 23.21/3.90 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 23.21/3.90 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 23.21/3.90 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 23.21/3.90 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 23.21/3.90 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, sum_plus_base,
% 23.21/3.90 sum_plus_base_float, totality, transitivity_gt, ttrue,
% 23.21/3.90 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 23.21/3.90
% 23.21/3.90 Those formulas are unsatisfiable:
% 23.21/3.90 ---------------------------------
% 23.21/3.90
% 23.21/3.90 Begin of proof
% 23.21/3.90 |
% 23.21/3.90 | ALPHA: (leq_succ_gt_equiv) implies:
% 23.21/3.91 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~
% 23.21/3.91 | (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | leq(v0, v1) = 0)
% 23.21/3.91 |
% 23.21/3.91 | ALPHA: (gt_2_0) implies:
% 23.21/3.91 | (2) gt(n2, n0) = 0
% 23.21/3.91 |
% 23.21/3.91 | ALPHA: (successor_4) implies:
% 23.21/3.91 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) =
% 23.21/3.91 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 23.21/3.91 |
% 23.21/3.91 | ALPHA: (successor_5) implies:
% 23.21/3.91 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5
% 23.21/3.91 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 &
% 23.21/3.91 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 23.21/3.91 |
% 23.21/3.91 | ALPHA: (successor_1) implies:
% 23.21/3.91 | (5) succ(n0) = n1
% 23.21/3.91 |
% 23.21/3.91 | ALPHA: (successor_2) implies:
% 23.21/3.91 | (6) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 23.21/3.91 |
% 23.21/3.91 | ALPHA: (successor_3) implies:
% 23.21/3.91 | (7) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) =
% 23.21/3.91 | v0 & $i(v1) & $i(v0))
% 23.21/3.91 |
% 23.21/3.91 | ALPHA: (gauss_array_0007) implies:
% 23.21/3.91 | (8) $i(n0)
% 23.21/3.91 | (9) $i(pv1325)
% 23.21/3.91 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0)
% 23.21/3.91 | & a_select2(s_values7, pv1325) = v0 & a_select2(s_values7, s_worst7)
% 23.21/3.91 | = v2 & a_select2(s_values7, s_best7) = v1 & leq(v0, v2) = 0 &
% 23.21/3.91 | leq(v0, v1) = 0 & leq(pv1325, n3) = 0 & leq(s_worst7, n3) = 0 &
% 23.21/3.91 | leq(s_sworst7, n3) = 0 & leq(s_best7, n3) = 0 & leq(n2, pv1325) = 0
% 23.21/3.91 | & leq(n0, pv1325) = v3 & leq(n0, s_worst7) = 0 & leq(n0, s_sworst7)
% 23.21/3.91 | = 0 & leq(n0, s_best7) = 0 & $i(v2) & $i(v1) & $i(v0))
% 23.21/3.91 |
% 23.21/3.91 | ALPHA: (function-axioms) implies:
% 23.21/3.92 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) =
% 23.21/3.92 | v1) | ~ (succ(v2) = v0))
% 23.21/3.92 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 23.21/3.92 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) =
% 23.21/3.92 | v0))
% 23.21/3.92 |
% 23.21/3.92 | DELTA: instantiating (6) with fresh symbol all_49_0 gives:
% 23.21/3.92 | (13) succ(all_49_0) = n2 & succ(n0) = all_49_0 & $i(all_49_0)
% 23.21/3.92 |
% 23.21/3.92 | ALPHA: (13) implies:
% 23.21/3.92 | (14) $i(all_49_0)
% 23.21/3.92 | (15) succ(n0) = all_49_0
% 23.21/3.92 | (16) succ(all_49_0) = n2
% 23.21/3.92 |
% 23.21/3.92 | DELTA: instantiating (7) with fresh symbols all_51_0, all_51_1 gives:
% 23.21/3.92 | (17) succ(all_51_0) = n3 & succ(all_51_1) = all_51_0 & succ(n0) = all_51_1
% 23.21/3.92 | & $i(all_51_0) & $i(all_51_1)
% 23.21/3.92 |
% 23.21/3.92 | ALPHA: (17) implies:
% 23.21/3.92 | (18) succ(n0) = all_51_1
% 23.21/3.92 | (19) succ(all_51_1) = all_51_0
% 23.21/3.92 |
% 23.21/3.92 | DELTA: instantiating (3) with fresh symbols all_53_0, all_53_1, all_53_2
% 23.21/3.92 | gives:
% 23.21/3.92 | (20) succ(all_53_0) = n4 & succ(all_53_1) = all_53_0 & succ(all_53_2) =
% 23.21/3.92 | all_53_1 & succ(n0) = all_53_2 & $i(all_53_0) & $i(all_53_1) &
% 23.21/3.92 | $i(all_53_2)
% 23.21/3.92 |
% 23.21/3.92 | ALPHA: (20) implies:
% 23.21/3.92 | (21) succ(n0) = all_53_2
% 23.21/3.92 | (22) succ(all_53_2) = all_53_1
% 23.21/3.92 |
% 23.21/3.92 | DELTA: instantiating (4) with fresh symbols all_55_0, all_55_1, all_55_2,
% 23.21/3.92 | all_55_3 gives:
% 23.21/3.92 | (23) succ(all_55_0) = n5 & succ(all_55_1) = all_55_0 & succ(all_55_2) =
% 23.21/3.92 | all_55_1 & succ(all_55_3) = all_55_2 & succ(n0) = all_55_3 &
% 23.21/3.92 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3)
% 23.21/3.92 |
% 23.21/3.92 | ALPHA: (23) implies:
% 23.21/3.92 | (24) succ(n0) = all_55_3
% 23.21/3.92 | (25) succ(all_55_3) = all_55_2
% 23.21/3.92 |
% 23.21/3.92 | DELTA: instantiating (10) with fresh symbols all_61_0, all_61_1, all_61_2,
% 23.21/3.92 | all_61_3 gives:
% 23.21/3.92 | (26) ~ (all_61_0 = 0) & a_select2(s_values7, pv1325) = all_61_3 &
% 23.21/3.92 | a_select2(s_values7, s_worst7) = all_61_1 & a_select2(s_values7,
% 23.21/3.92 | s_best7) = all_61_2 & leq(all_61_3, all_61_1) = 0 & leq(all_61_3,
% 23.21/3.92 | all_61_2) = 0 & leq(pv1325, n3) = 0 & leq(s_worst7, n3) = 0 &
% 23.21/3.92 | leq(s_sworst7, n3) = 0 & leq(s_best7, n3) = 0 & leq(n2, pv1325) = 0 &
% 23.21/3.92 | leq(n0, pv1325) = all_61_0 & leq(n0, s_worst7) = 0 & leq(n0,
% 23.21/3.92 | s_sworst7) = 0 & leq(n0, s_best7) = 0 & $i(all_61_1) & $i(all_61_2)
% 23.21/3.92 | & $i(all_61_3)
% 23.21/3.92 |
% 23.21/3.92 | ALPHA: (26) implies:
% 23.21/3.93 | (27) ~ (all_61_0 = 0)
% 23.21/3.93 | (28) leq(n0, pv1325) = all_61_0
% 23.21/3.93 | (29) leq(n2, pv1325) = 0
% 23.21/3.93 |
% 23.21/3.93 | GROUND_INST: instantiating (11) with all_51_1, all_53_2, n0, simplifying with
% 23.21/3.93 | (18), (21) gives:
% 23.21/3.93 | (30) all_53_2 = all_51_1
% 23.21/3.93 |
% 23.21/3.93 | GROUND_INST: instantiating (11) with all_49_0, all_53_2, n0, simplifying with
% 23.21/3.93 | (15), (21) gives:
% 23.21/3.93 | (31) all_53_2 = all_49_0
% 23.21/3.93 |
% 23.21/3.93 | GROUND_INST: instantiating (11) with all_51_1, all_55_3, n0, simplifying with
% 23.21/3.93 | (18), (24) gives:
% 23.21/3.93 | (32) all_55_3 = all_51_1
% 23.21/3.93 |
% 23.21/3.93 | GROUND_INST: instantiating (11) with n1, all_55_3, n0, simplifying with (5),
% 23.21/3.93 | (24) gives:
% 23.21/3.93 | (33) all_55_3 = n1
% 23.21/3.93 |
% 23.21/3.93 | COMBINE_EQS: (32), (33) imply:
% 23.21/3.93 | (34) all_51_1 = n1
% 23.21/3.93 |
% 23.21/3.93 | SIMP: (34) implies:
% 23.21/3.93 | (35) all_51_1 = n1
% 23.21/3.93 |
% 23.21/3.93 | COMBINE_EQS: (30), (31) imply:
% 23.21/3.93 | (36) all_51_1 = all_49_0
% 23.21/3.93 |
% 23.21/3.93 | SIMP: (36) implies:
% 23.21/3.93 | (37) all_51_1 = all_49_0
% 23.21/3.93 |
% 23.21/3.93 | COMBINE_EQS: (35), (37) imply:
% 23.21/3.93 | (38) all_49_0 = n1
% 23.21/3.93 |
% 23.21/3.93 | COMBINE_EQS: (31), (38) imply:
% 23.21/3.93 | (39) all_53_2 = n1
% 23.21/3.93 |
% 23.21/3.93 | REDUCE: (25), (33) imply:
% 23.21/3.93 | (40) succ(n1) = all_55_2
% 23.21/3.93 |
% 23.21/3.93 | REDUCE: (22), (39) imply:
% 23.21/3.93 | (41) succ(n1) = all_53_1
% 23.21/3.93 |
% 23.21/3.93 | REDUCE: (19), (35) imply:
% 23.21/3.93 | (42) succ(n1) = all_51_0
% 23.21/3.93 |
% 23.21/3.93 | REDUCE: (16), (38) imply:
% 23.21/3.93 | (43) succ(n1) = n2
% 23.21/3.93 |
% 23.21/3.93 | REDUCE: (14), (38) imply:
% 23.21/3.93 | (44) $i(n1)
% 23.21/3.93 |
% 23.21/3.93 | GROUND_INST: instantiating (11) with all_51_0, all_53_1, n1, simplifying with
% 23.21/3.93 | (41), (42) gives:
% 23.21/3.93 | (45) all_53_1 = all_51_0
% 23.21/3.93 |
% 23.21/3.93 | GROUND_INST: instantiating (11) with all_53_1, all_55_2, n1, simplifying with
% 23.21/3.93 | (40), (41) gives:
% 23.21/3.93 | (46) all_55_2 = all_53_1
% 23.21/3.93 |
% 23.21/3.93 | GROUND_INST: instantiating (11) with n2, all_55_2, n1, simplifying with (40),
% 23.21/3.93 | (43) gives:
% 23.21/3.93 | (47) all_55_2 = n2
% 23.21/3.93 |
% 23.21/3.93 | COMBINE_EQS: (46), (47) imply:
% 23.21/3.94 | (48) all_53_1 = n2
% 23.21/3.94 |
% 23.21/3.94 | SIMP: (48) implies:
% 23.21/3.94 | (49) all_53_1 = n2
% 23.21/3.94 |
% 23.21/3.94 | COMBINE_EQS: (45), (49) imply:
% 23.21/3.94 | (50) all_51_0 = n2
% 23.21/3.94 |
% 23.21/3.94 | SIMP: (50) implies:
% 23.21/3.94 | (51) all_51_0 = n2
% 23.21/3.94 |
% 23.21/3.94 | GROUND_INST: instantiating (leq_succ_gt) with n1, pv1325, n2, simplifying with
% 23.21/3.94 | (9), (29), (43), (44) gives:
% 23.21/3.94 | (52) gt(pv1325, n1) = 0
% 23.21/3.94 |
% 23.21/3.94 | GROUND_INST: instantiating (1) with n0, n1, n2, simplifying with (2), (8),
% 23.21/3.94 | (43), (44) gives:
% 23.21/3.94 | (53) leq(n0, n1) = 0
% 23.21/3.94 |
% 23.21/3.94 | GROUND_INST: instantiating (leq_gt1) with n1, pv1325, simplifying with (9),
% 23.21/3.94 | (44), (52) gives:
% 23.21/3.94 | (54) leq(n1, pv1325) = 0
% 23.21/3.94 |
% 23.21/3.94 | GROUND_INST: instantiating (transitivity_leq) with n0, n1, pv1325, all_61_0,
% 23.21/3.94 | simplifying with (8), (9), (28), (44), (53) gives:
% 23.21/3.94 | (55) all_61_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & leq(n1, pv1325) = v0)
% 23.21/3.94 |
% 23.21/3.94 | BETA: splitting (55) gives:
% 23.21/3.94 |
% 23.21/3.94 | Case 1:
% 23.21/3.94 | |
% 23.21/3.94 | | (56) all_61_0 = 0
% 23.21/3.94 | |
% 23.21/3.94 | | REDUCE: (27), (56) imply:
% 23.21/3.94 | | (57) $false
% 23.21/3.94 | |
% 23.21/3.94 | | CLOSE: (57) is inconsistent.
% 23.21/3.94 | |
% 23.21/3.94 | Case 2:
% 23.21/3.94 | |
% 23.21/3.94 | | (58) ? [v0: int] : ( ~ (v0 = 0) & leq(n1, pv1325) = v0)
% 23.21/3.94 | |
% 23.21/3.94 | | DELTA: instantiating (58) with fresh symbol all_126_0 gives:
% 23.21/3.94 | | (59) ~ (all_126_0 = 0) & leq(n1, pv1325) = all_126_0
% 23.21/3.94 | |
% 23.21/3.94 | | ALPHA: (59) implies:
% 23.21/3.94 | | (60) ~ (all_126_0 = 0)
% 23.21/3.94 | | (61) leq(n1, pv1325) = all_126_0
% 23.21/3.94 | |
% 23.21/3.95 | | GROUND_INST: instantiating (12) with 0, all_126_0, pv1325, n1, simplifying
% 23.21/3.95 | | with (54), (61) gives:
% 23.21/3.95 | | (62) all_126_0 = 0
% 23.21/3.95 | |
% 23.21/3.95 | | REDUCE: (60), (62) imply:
% 23.21/3.95 | | (63) $false
% 23.21/3.95 | |
% 23.21/3.95 | | CLOSE: (63) is inconsistent.
% 23.21/3.95 | |
% 23.21/3.95 | End of split
% 23.21/3.95 |
% 23.21/3.95 End of proof
% 23.21/3.95 % SZS output end Proof for theBenchmark
% 23.21/3.95
% 23.21/3.95 3357ms
%------------------------------------------------------------------------------