TSTP Solution File: SWV030+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV030+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 : n029.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 22:54:38 EDT 2023
% Result : Theorem 20.22s 3.44s
% Output : Proof 23.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV030+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n029.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 05:52:56 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ________ _____
% 0.18/0.58 ___ __ \_________(_)________________________________
% 0.18/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.58 (2023-06-19)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2023
% 0.18/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.58 Amanda Stjerna.
% 0.18/0.58 Free software under BSD-3-Clause.
% 0.18/0.58
% 0.18/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.58
% 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.62/0.60 Running up to 7 provers in parallel.
% 0.70/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.70/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.70/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.70/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.70/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.70/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.70/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.91/1.42 Prover 4: Preprocessing ...
% 4.91/1.42 Prover 1: Preprocessing ...
% 5.49/1.46 Prover 5: Preprocessing ...
% 5.49/1.46 Prover 6: Preprocessing ...
% 5.49/1.46 Prover 0: Preprocessing ...
% 5.49/1.46 Prover 3: Preprocessing ...
% 5.49/1.46 Prover 2: Preprocessing ...
% 11.19/2.25 Prover 1: Warning: ignoring some quantifiers
% 11.70/2.31 Prover 3: Warning: ignoring some quantifiers
% 11.70/2.33 Prover 1: Constructing countermodel ...
% 11.70/2.34 Prover 3: Constructing countermodel ...
% 11.70/2.36 Prover 6: Proving ...
% 12.36/2.40 Prover 4: Warning: ignoring some quantifiers
% 12.62/2.51 Prover 4: Constructing countermodel ...
% 13.28/2.53 Prover 5: Proving ...
% 13.28/2.54 Prover 0: Proving ...
% 13.28/2.56 Prover 2: Proving ...
% 20.22/3.44 Prover 3: proved (2826ms)
% 20.22/3.44
% 20.22/3.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.22/3.44
% 20.22/3.44 Prover 6: stopped
% 20.22/3.44 Prover 5: stopped
% 20.22/3.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 20.22/3.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 20.22/3.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 20.22/3.45 Prover 0: stopped
% 20.22/3.46 Prover 2: stopped
% 20.22/3.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 20.22/3.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 20.72/3.56 Prover 1: Found proof (size 43)
% 20.72/3.56 Prover 1: proved (2952ms)
% 21.22/3.57 Prover 4: stopped
% 21.94/3.68 Prover 10: Preprocessing ...
% 21.94/3.68 Prover 8: Preprocessing ...
% 22.20/3.71 Prover 11: Preprocessing ...
% 22.20/3.73 Prover 13: Preprocessing ...
% 22.50/3.74 Prover 10: stopped
% 22.50/3.74 Prover 7: Preprocessing ...
% 22.50/3.79 Prover 7: stopped
% 22.96/3.80 Prover 11: stopped
% 22.96/3.82 Prover 13: stopped
% 23.27/3.89 Prover 8: Warning: ignoring some quantifiers
% 23.27/3.90 Prover 8: Constructing countermodel ...
% 23.27/3.92 Prover 8: stopped
% 23.27/3.92
% 23.27/3.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.27/3.92
% 23.27/3.92 % SZS output start Proof for theBenchmark
% 23.27/3.93 Assumptions after simplification:
% 23.27/3.93 ---------------------------------
% 23.27/3.93
% 23.27/3.93 (gauss_init_0033)
% 23.27/3.96 $i(s_values7_init) & $i(simplex7_init) & $i(n330) & $i(n410) & $i(pv1376) &
% 23.27/3.96 $i(pv20) & $i(pv19) & $i(pv7) & $i(init) & $i(n3) & $i(n2) & $i(n1) & $i(n0) &
% 23.27/3.96 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (minus(n330, n1) = v1 & minus(n410,
% 23.27/3.96 n1) = v0 & minus(pv1376, n1) = v2 & leq(pv1376, n3) = 0 & leq(pv20, v1) =
% 23.27/3.96 0 & leq(pv19, v0) = 0 & leq(pv7, v0) = 0 & leq(n0, pv1376) = 0 & leq(n0,
% 23.27/3.96 pv20) = 0 & leq(n0, pv19) = 0 & leq(n0, pv7) = 0 & $i(v2) & $i(v1) &
% 23.27/3.96 $i(v0) & ! [v3: $i] : ( ~ (leq(v3, v2) = 0) | ~ $i(v3) | ? [v4: any] : ?
% 23.27/3.96 [v5: $i] : (a_select2(s_values7_init, v3) = v5 & leq(n0, v3) = v4 & $i(v5)
% 23.27/3.96 & ( ~ (v4 = 0) | v5 = init))) & ! [v3: $i] : ( ~ (leq(v3, n2) = 0) | ~
% 23.27/3.96 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & leq(n0, v3) = v4) | ! [v4: $i] :
% 23.27/3.96 ! [v5: $i] : (v5 = init | ~ (a_select3(simplex7_init, v4, v3) = v5) | ~
% 23.27/3.96 $i(v4) | ? [v6: any] : ? [v7: any] : (leq(v4, n3) = v7 & leq(n0, v4) =
% 23.27/3.96 v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ( ? [v3: $i] : ? [v4: $i] : ( ~
% 23.27/3.97 (v4 = init) & a_select2(s_values7_init, v3) = v4 & leq(v3, v2) = 0 &
% 23.27/3.97 leq(n0, v3) = 0 & $i(v4) & $i(v3)) | ? [v3: $i] : (leq(v3, n2) = 0 &
% 23.27/3.97 leq(n0, v3) = 0 & $i(v3) & ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = init) &
% 23.27/3.97 a_select3(simplex7_init, v4, v3) = v5 & leq(v4, n3) = 0 & leq(n0, v4)
% 23.27/3.97 = 0 & $i(v5) & $i(v4)))))
% 23.27/3.97
% 23.27/3.97 (function-axioms)
% 23.27/3.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 23.27/3.97 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 23.27/3.97 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 23.27/3.97 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 23.27/3.97 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 23.27/3.97 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 23.27/3.97 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 23.27/3.97 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 23.27/3.97 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 23.27/3.97 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 23.27/3.97 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 23.27/3.97 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 23.27/3.97 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 23.27/3.97 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 23.27/3.97 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 23.27/3.97 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 23.27/3.97 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 23.27/3.97 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 23.27/3.97 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 23.27/3.97 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 23.27/3.97 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 23.27/3.97 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 23.27/3.97 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 23.27/3.97 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 23.27/3.97 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.27/3.97 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 23.27/3.97 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 23.27/3.97 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 23.27/3.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 23.27/3.97 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 23.27/3.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 23.27/3.97 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 23.27/3.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 23.27/3.97 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 23.27/3.97 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 23.27/3.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 23.27/3.97 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 23.27/3.97 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 23.27/3.97 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 23.27/3.97
% 23.27/3.97 Further assumptions not needed in the proof:
% 23.27/3.97 --------------------------------------------
% 23.79/3.97 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 23.79/3.97 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 23.79/3.97 finite_domain_5, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1,
% 23.79/3.97 gt_2_tptp_minus_1, gt_330_0, gt_330_1, gt_330_2, gt_330_3, gt_330_4, gt_330_5,
% 23.79/3.97 gt_330_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_410_0,
% 23.79/3.97 gt_410_1, gt_410_2, gt_410_3, gt_410_330, gt_410_4, gt_410_5,
% 23.79/3.97 gt_410_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0,
% 23.79/3.97 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt,
% 23.79/3.97 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt,
% 23.79/3.97 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 23.79/3.97 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 23.79/3.97 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 23.79/3.97 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 23.79/3.97 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 23.79/3.97 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 23.79/3.97 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 23.79/3.97 successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 23.79/3.97 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 23.79/3.97 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 23.79/3.97
% 23.79/3.97 Those formulas are unsatisfiable:
% 23.79/3.97 ---------------------------------
% 23.79/3.97
% 23.79/3.97 Begin of proof
% 23.79/3.97 |
% 23.79/3.98 | ALPHA: (gauss_init_0033) implies:
% 23.79/3.98 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (minus(n330, n1) = v1 &
% 23.79/3.98 | minus(n410, n1) = v0 & minus(pv1376, n1) = v2 & leq(pv1376, n3) = 0 &
% 23.79/3.98 | leq(pv20, v1) = 0 & leq(pv19, v0) = 0 & leq(pv7, v0) = 0 & leq(n0,
% 23.79/3.98 | pv1376) = 0 & leq(n0, pv20) = 0 & leq(n0, pv19) = 0 & leq(n0, pv7)
% 23.79/3.98 | = 0 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ( ~ (leq(v3, v2) = 0)
% 23.79/3.98 | | ~ $i(v3) | ? [v4: any] : ? [v5: $i] :
% 23.79/3.98 | (a_select2(s_values7_init, v3) = v5 & leq(n0, v3) = v4 & $i(v5) & (
% 23.79/3.98 | ~ (v4 = 0) | v5 = init))) & ! [v3: $i] : ( ~ (leq(v3, n2) = 0)
% 23.79/3.98 | | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & leq(n0, v3) = v4) | !
% 23.79/3.98 | [v4: $i] : ! [v5: $i] : (v5 = init | ~ (a_select3(simplex7_init,
% 23.79/3.98 | v4, v3) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] :
% 23.79/3.98 | (leq(v4, n3) = v7 & leq(n0, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 =
% 23.79/3.98 | 0))))) & ( ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = init) &
% 23.79/3.98 | a_select2(s_values7_init, v3) = v4 & leq(v3, v2) = 0 & leq(n0,
% 23.79/3.98 | v3) = 0 & $i(v4) & $i(v3)) | ? [v3: $i] : (leq(v3, n2) = 0 &
% 23.79/3.98 | leq(n0, v3) = 0 & $i(v3) & ? [v4: $i] : ? [v5: $i] : ( ~ (v5 =
% 23.79/3.98 | init) & a_select3(simplex7_init, v4, v3) = v5 & leq(v4, n3) =
% 23.79/3.98 | 0 & leq(n0, v4) = 0 & $i(v5) & $i(v4)))))
% 23.79/3.98 |
% 23.79/3.98 | ALPHA: (function-axioms) implies:
% 23.79/3.98 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 23.79/3.98 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 23.79/3.98 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.79/3.98 | (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0))
% 23.79/3.98 |
% 23.79/3.98 | DELTA: instantiating (1) with fresh symbols all_74_0, all_74_1, all_74_2
% 23.79/3.98 | gives:
% 23.79/3.98 | (4) minus(n330, n1) = all_74_1 & minus(n410, n1) = all_74_2 & minus(pv1376,
% 23.79/3.98 | n1) = all_74_0 & leq(pv1376, n3) = 0 & leq(pv20, all_74_1) = 0 &
% 23.79/3.98 | leq(pv19, all_74_2) = 0 & leq(pv7, all_74_2) = 0 & leq(n0, pv1376) = 0
% 23.79/3.98 | & leq(n0, pv20) = 0 & leq(n0, pv19) = 0 & leq(n0, pv7) = 0 &
% 23.79/3.98 | $i(all_74_0) & $i(all_74_1) & $i(all_74_2) & ! [v0: $i] : ( ~ (leq(v0,
% 23.79/3.98 | all_74_0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] :
% 23.79/3.99 | (a_select2(s_values7_init, v0) = v2 & leq(n0, v0) = v1 & $i(v2) & ( ~
% 23.79/3.99 | (v1 = 0) | v2 = init))) & ! [v0: $i] : ( ~ (leq(v0, n2) = 0) |
% 23.79/3.99 | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) | ! [v1:
% 23.79/3.99 | $i] : ! [v2: $i] : (v2 = init | ~ (a_select3(simplex7_init, v1,
% 23.79/3.99 | v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1,
% 23.79/3.99 | n3) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) &
% 23.79/3.99 | ( ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) &
% 23.79/3.99 | a_select2(s_values7_init, v0) = v1 & leq(v0, all_74_0) = 0 &
% 23.79/3.99 | leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0
% 23.79/3.99 | & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 =
% 23.79/3.99 | init) & a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0
% 23.79/3.99 | & leq(n0, v1) = 0 & $i(v2) & $i(v1))))
% 23.79/3.99 |
% 23.79/3.99 | ALPHA: (4) implies:
% 23.79/3.99 | (5) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(s_values7_init,
% 23.79/3.99 | v0) = v1 & leq(v0, all_74_0) = 0 & leq(n0, v0) = 0 & $i(v1) &
% 23.79/3.99 | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) &
% 23.79/3.99 | ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) &
% 23.79/3.99 | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 & leq(n0,
% 23.79/3.99 | v1) = 0 & $i(v2) & $i(v1)))
% 23.79/3.99 | (6) ! [v0: $i] : ( ~ (leq(v0, n2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 23.79/3.99 | (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 =
% 23.79/3.99 | init | ~ (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ?
% 23.79/3.99 | [v3: any] : ? [v4: any] : (leq(v1, n3) = v4 & leq(n0, v1) = v3 & (
% 23.79/3.99 | ~ (v4 = 0) | ~ (v3 = 0)))))
% 23.79/3.99 | (7) ! [v0: $i] : ( ~ (leq(v0, all_74_0) = 0) | ~ $i(v0) | ? [v1: any] :
% 23.79/3.99 | ? [v2: $i] : (a_select2(s_values7_init, v0) = v2 & leq(n0, v0) = v1 &
% 23.79/3.99 | $i(v2) & ( ~ (v1 = 0) | v2 = init)))
% 23.79/3.99 |
% 23.79/3.99 | BETA: splitting (5) gives:
% 23.79/3.99 |
% 23.79/3.99 | Case 1:
% 23.79/3.99 | |
% 23.79/3.99 | | (8) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) &
% 23.79/3.99 | | a_select2(s_values7_init, v0) = v1 & leq(v0, all_74_0) = 0 &
% 23.79/3.99 | | leq(n0, v0) = 0 & $i(v1) & $i(v0))
% 23.79/3.99 | |
% 23.79/3.99 | | DELTA: instantiating (8) with fresh symbols all_159_0, all_159_1 gives:
% 23.79/3.99 | | (9) ~ (all_159_0 = init) & a_select2(s_values7_init, all_159_1) =
% 23.79/3.99 | | all_159_0 & leq(all_159_1, all_74_0) = 0 & leq(n0, all_159_1) = 0 &
% 23.79/3.99 | | $i(all_159_0) & $i(all_159_1)
% 23.79/3.99 | |
% 23.79/3.99 | | ALPHA: (9) implies:
% 23.79/3.99 | | (10) ~ (all_159_0 = init)
% 23.79/3.99 | | (11) $i(all_159_1)
% 23.79/3.99 | | (12) leq(n0, all_159_1) = 0
% 23.79/3.99 | | (13) leq(all_159_1, all_74_0) = 0
% 23.79/3.99 | | (14) a_select2(s_values7_init, all_159_1) = all_159_0
% 23.79/3.99 | |
% 23.79/3.99 | | GROUND_INST: instantiating (7) with all_159_1, simplifying with (11), (13)
% 23.79/3.99 | | gives:
% 23.79/3.99 | | (15) ? [v0: any] : ? [v1: $i] : (a_select2(s_values7_init, all_159_1) =
% 23.79/3.99 | | v1 & leq(n0, all_159_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = init))
% 23.79/3.99 | |
% 23.79/3.99 | | DELTA: instantiating (15) with fresh symbols all_167_0, all_167_1 gives:
% 23.79/3.99 | | (16) a_select2(s_values7_init, all_159_1) = all_167_0 & leq(n0,
% 23.79/3.99 | | all_159_1) = all_167_1 & $i(all_167_0) & ( ~ (all_167_1 = 0) |
% 23.79/3.99 | | all_167_0 = init)
% 23.79/3.99 | |
% 23.79/3.99 | | ALPHA: (16) implies:
% 23.79/3.99 | | (17) leq(n0, all_159_1) = all_167_1
% 23.79/3.99 | | (18) a_select2(s_values7_init, all_159_1) = all_167_0
% 23.79/3.99 | | (19) ~ (all_167_1 = 0) | all_167_0 = init
% 23.79/3.99 | |
% 23.79/3.99 | | GROUND_INST: instantiating (2) with 0, all_167_1, all_159_1, n0, simplifying
% 23.79/3.99 | | with (12), (17) gives:
% 23.79/3.99 | | (20) all_167_1 = 0
% 23.79/3.99 | |
% 23.79/3.99 | | GROUND_INST: instantiating (3) with all_159_0, all_167_0, all_159_1,
% 23.79/3.99 | | s_values7_init, simplifying with (14), (18) gives:
% 23.79/3.99 | | (21) all_167_0 = all_159_0
% 23.79/3.99 | |
% 23.79/3.99 | | BETA: splitting (19) gives:
% 23.79/3.99 | |
% 23.79/3.99 | | Case 1:
% 23.79/3.99 | | |
% 23.79/3.99 | | | (22) ~ (all_167_1 = 0)
% 23.79/3.99 | | |
% 23.79/3.99 | | | REDUCE: (20), (22) imply:
% 23.79/3.99 | | | (23) $false
% 23.79/4.00 | | |
% 23.79/4.00 | | | CLOSE: (23) is inconsistent.
% 23.79/4.00 | | |
% 23.79/4.00 | | Case 2:
% 23.79/4.00 | | |
% 23.79/4.00 | | | (24) all_167_0 = init
% 23.79/4.00 | | |
% 23.79/4.00 | | | COMBINE_EQS: (21), (24) imply:
% 23.79/4.00 | | | (25) all_159_0 = init
% 23.79/4.00 | | |
% 23.79/4.00 | | | REDUCE: (10), (25) imply:
% 23.79/4.00 | | | (26) $false
% 23.79/4.00 | | |
% 23.79/4.00 | | | CLOSE: (26) is inconsistent.
% 23.79/4.00 | | |
% 23.79/4.00 | | End of split
% 23.79/4.00 | |
% 23.79/4.00 | Case 2:
% 23.79/4.00 | |
% 23.79/4.00 | | (27) ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? [v1:
% 23.79/4.00 | | $i] : ? [v2: $i] : ( ~ (v2 = init) & a_select3(simplex7_init,
% 23.79/4.00 | | v1, v0) = v2 & leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) &
% 23.79/4.00 | | $i(v1)))
% 23.79/4.00 | |
% 23.79/4.00 | | DELTA: instantiating (27) with fresh symbol all_159_0 gives:
% 23.79/4.00 | | (28) leq(all_159_0, n2) = 0 & leq(n0, all_159_0) = 0 & $i(all_159_0) & ?
% 23.79/4.00 | | [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select3(simplex7_init,
% 23.79/4.00 | | v0, all_159_0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1)
% 23.79/4.00 | | & $i(v0))
% 23.79/4.00 | |
% 23.79/4.00 | | ALPHA: (28) implies:
% 23.79/4.00 | | (29) $i(all_159_0)
% 23.79/4.00 | | (30) leq(n0, all_159_0) = 0
% 23.79/4.00 | | (31) leq(all_159_0, n2) = 0
% 23.79/4.00 | | (32) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) &
% 23.79/4.00 | | a_select3(simplex7_init, v0, all_159_0) = v1 & leq(v0, n3) = 0 &
% 23.79/4.00 | | leq(n0, v0) = 0 & $i(v1) & $i(v0))
% 23.79/4.00 | |
% 23.79/4.00 | | DELTA: instantiating (32) with fresh symbols all_161_0, all_161_1 gives:
% 23.79/4.00 | | (33) ~ (all_161_0 = init) & a_select3(simplex7_init, all_161_1,
% 23.79/4.00 | | all_159_0) = all_161_0 & leq(all_161_1, n3) = 0 & leq(n0,
% 23.79/4.00 | | all_161_1) = 0 & $i(all_161_0) & $i(all_161_1)
% 23.79/4.00 | |
% 23.79/4.00 | | ALPHA: (33) implies:
% 23.79/4.00 | | (34) ~ (all_161_0 = init)
% 23.79/4.00 | | (35) $i(all_161_1)
% 23.79/4.00 | | (36) leq(n0, all_161_1) = 0
% 23.79/4.00 | | (37) leq(all_161_1, n3) = 0
% 23.79/4.00 | | (38) a_select3(simplex7_init, all_161_1, all_159_0) = all_161_0
% 23.79/4.00 | |
% 23.79/4.00 | | GROUND_INST: instantiating (6) with all_159_0, simplifying with (29), (31)
% 23.79/4.00 | | gives:
% 23.79/4.00 | | (39) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_159_0) = v0) | ! [v0: $i]
% 23.79/4.00 | | : ! [v1: $i] : (v1 = init | ~ (a_select3(simplex7_init, v0,
% 23.79/4.00 | | all_159_0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 23.79/4.00 | | (leq(v0, n3) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 =
% 23.79/4.00 | | 0))))
% 23.79/4.00 | |
% 23.79/4.00 | | BETA: splitting (39) gives:
% 23.79/4.00 | |
% 23.79/4.00 | | Case 1:
% 23.79/4.00 | | |
% 23.79/4.00 | | | (40) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_159_0) = v0)
% 23.79/4.00 | | |
% 23.79/4.00 | | | DELTA: instantiating (40) with fresh symbol all_172_0 gives:
% 23.79/4.00 | | | (41) ~ (all_172_0 = 0) & leq(n0, all_159_0) = all_172_0
% 23.79/4.00 | | |
% 23.79/4.00 | | | ALPHA: (41) implies:
% 23.79/4.00 | | | (42) ~ (all_172_0 = 0)
% 23.79/4.00 | | | (43) leq(n0, all_159_0) = all_172_0
% 23.79/4.00 | | |
% 23.79/4.00 | | | GROUND_INST: instantiating (2) with 0, all_172_0, all_159_0, n0,
% 23.79/4.00 | | | simplifying with (30), (43) gives:
% 23.79/4.00 | | | (44) all_172_0 = 0
% 23.79/4.00 | | |
% 23.79/4.00 | | | REDUCE: (42), (44) imply:
% 23.79/4.00 | | | (45) $false
% 23.79/4.00 | | |
% 23.79/4.00 | | | CLOSE: (45) is inconsistent.
% 23.79/4.00 | | |
% 23.79/4.00 | | Case 2:
% 23.79/4.00 | | |
% 23.79/4.00 | | | (46) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~
% 23.79/4.00 | | | (a_select3(simplex7_init, v0, all_159_0) = v1) | ~ $i(v0) | ?
% 23.79/4.00 | | | [v2: any] : ? [v3: any] : (leq(v0, n3) = v3 & leq(n0, v0) = v2
% 23.79/4.00 | | | & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.79/4.00 | | |
% 23.79/4.00 | | | GROUND_INST: instantiating (46) with all_161_1, all_161_0, simplifying
% 23.79/4.00 | | | with (35), (38) gives:
% 23.79/4.01 | | | (47) all_161_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_161_1,
% 23.79/4.01 | | | n3) = v1 & leq(n0, all_161_1) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 23.79/4.01 | | | 0)))
% 23.79/4.01 | | |
% 23.79/4.01 | | | BETA: splitting (47) gives:
% 23.79/4.01 | | |
% 23.79/4.01 | | | Case 1:
% 23.79/4.01 | | | |
% 23.79/4.01 | | | | (48) all_161_0 = init
% 23.79/4.01 | | | |
% 23.79/4.01 | | | | REDUCE: (34), (48) imply:
% 23.79/4.01 | | | | (49) $false
% 23.79/4.01 | | | |
% 23.79/4.01 | | | | CLOSE: (49) is inconsistent.
% 23.79/4.01 | | | |
% 23.79/4.01 | | | Case 2:
% 23.79/4.01 | | | |
% 23.79/4.01 | | | | (50) ? [v0: any] : ? [v1: any] : (leq(all_161_1, n3) = v1 & leq(n0,
% 23.79/4.01 | | | | all_161_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 23.79/4.01 | | | |
% 23.79/4.01 | | | | DELTA: instantiating (50) with fresh symbols all_176_0, all_176_1 gives:
% 23.79/4.01 | | | | (51) leq(all_161_1, n3) = all_176_0 & leq(n0, all_161_1) = all_176_1
% 23.79/4.01 | | | | & ( ~ (all_176_0 = 0) | ~ (all_176_1 = 0))
% 23.79/4.01 | | | |
% 23.79/4.01 | | | | ALPHA: (51) implies:
% 23.79/4.01 | | | | (52) leq(n0, all_161_1) = all_176_1
% 23.79/4.01 | | | | (53) leq(all_161_1, n3) = all_176_0
% 23.79/4.01 | | | | (54) ~ (all_176_0 = 0) | ~ (all_176_1 = 0)
% 23.79/4.01 | | | |
% 23.79/4.01 | | | | GROUND_INST: instantiating (2) with 0, all_176_1, all_161_1, n0,
% 23.79/4.01 | | | | simplifying with (36), (52) gives:
% 23.79/4.01 | | | | (55) all_176_1 = 0
% 23.79/4.01 | | | |
% 23.79/4.01 | | | | GROUND_INST: instantiating (2) with 0, all_176_0, n3, all_161_1,
% 23.79/4.01 | | | | simplifying with (37), (53) gives:
% 23.79/4.01 | | | | (56) all_176_0 = 0
% 23.79/4.01 | | | |
% 23.79/4.01 | | | | BETA: splitting (54) gives:
% 23.79/4.01 | | | |
% 23.79/4.01 | | | | Case 1:
% 23.79/4.01 | | | | |
% 23.79/4.01 | | | | | (57) ~ (all_176_0 = 0)
% 23.79/4.01 | | | | |
% 23.79/4.01 | | | | | REDUCE: (56), (57) imply:
% 23.79/4.01 | | | | | (58) $false
% 23.79/4.01 | | | | |
% 23.79/4.01 | | | | | CLOSE: (58) is inconsistent.
% 23.79/4.01 | | | | |
% 23.79/4.01 | | | | Case 2:
% 23.79/4.01 | | | | |
% 23.79/4.01 | | | | | (59) ~ (all_176_1 = 0)
% 23.79/4.01 | | | | |
% 23.97/4.01 | | | | | REDUCE: (55), (59) imply:
% 23.97/4.01 | | | | | (60) $false
% 23.97/4.01 | | | | |
% 23.97/4.01 | | | | | CLOSE: (60) is inconsistent.
% 23.97/4.01 | | | | |
% 23.97/4.01 | | | | End of split
% 23.97/4.01 | | | |
% 23.97/4.01 | | | End of split
% 23.97/4.01 | | |
% 23.97/4.01 | | End of split
% 23.97/4.01 | |
% 23.97/4.01 | End of split
% 23.97/4.01 |
% 23.97/4.01 End of proof
% 23.97/4.01 % SZS output end Proof for theBenchmark
% 23.97/4.01
% 23.97/4.01 3424ms
%------------------------------------------------------------------------------