TSTP Solution File: SWV155+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV155+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 : n025.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 22:55:08 EDT 2023
% Result : Theorem 13.63s 2.76s
% Output : Proof 18.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV155+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 09:44:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.60/1.46 Prover 4: Preprocessing ...
% 4.60/1.46 Prover 1: Preprocessing ...
% 5.26/1.49 Prover 2: Preprocessing ...
% 5.26/1.49 Prover 5: Preprocessing ...
% 5.26/1.49 Prover 3: Preprocessing ...
% 5.26/1.49 Prover 6: Preprocessing ...
% 5.26/1.51 Prover 0: Preprocessing ...
% 11.12/2.26 Prover 1: Warning: ignoring some quantifiers
% 11.48/2.34 Prover 1: Constructing countermodel ...
% 11.74/2.41 Prover 3: Warning: ignoring some quantifiers
% 11.74/2.41 Prover 6: Proving ...
% 11.74/2.43 Prover 4: Warning: ignoring some quantifiers
% 12.38/2.44 Prover 3: Constructing countermodel ...
% 12.76/2.52 Prover 4: Constructing countermodel ...
% 13.26/2.59 Prover 0: Proving ...
% 13.26/2.59 Prover 5: Proving ...
% 13.63/2.63 Prover 2: Proving ...
% 13.63/2.75 Prover 3: proved (2124ms)
% 13.63/2.76
% 13.63/2.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.63/2.76
% 13.63/2.76 Prover 6: stopped
% 13.63/2.76 Prover 0: stopped
% 13.63/2.76 Prover 2: stopped
% 13.63/2.76 Prover 5: stopped
% 13.63/2.76 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.63/2.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.63/2.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.63/2.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.63/2.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 16.17/2.98 Prover 8: Preprocessing ...
% 16.17/2.98 Prover 1: Found proof (size 21)
% 16.17/2.98 Prover 1: proved (2360ms)
% 16.17/3.00 Prover 4: stopped
% 16.61/3.01 Prover 11: Preprocessing ...
% 16.61/3.03 Prover 13: Preprocessing ...
% 16.92/3.06 Prover 7: Preprocessing ...
% 16.92/3.08 Prover 10: Preprocessing ...
% 16.92/3.11 Prover 7: stopped
% 16.92/3.13 Prover 10: stopped
% 17.59/3.15 Prover 11: stopped
% 17.59/3.15 Prover 13: stopped
% 17.59/3.17 Prover 8: Warning: ignoring some quantifiers
% 17.82/3.19 Prover 8: Constructing countermodel ...
% 17.82/3.21 Prover 8: stopped
% 17.82/3.21
% 17.82/3.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.82/3.21
% 17.82/3.21 % SZS output start Proof for theBenchmark
% 17.82/3.22 Assumptions after simplification:
% 17.82/3.22 ---------------------------------
% 17.82/3.22
% 17.82/3.22 (cl5_nebula_norm_0005)
% 18.14/3.25 $i(q) & $i(n135299) & $i(pv12) & $i(pv70) & $i(pv10) & $i(x) &
% 18.14/3.25 $i(tptp_sum_index) & $i(center) & $i(n4) & $i(n1) & $i(n0) & ? [v0: $i] : ?
% 18.14/3.25 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 18.14/3.25 : (times(v2, v2) = v3 & sqrt(v3) = v4 & minus(v0, v1) = v2 & sum(n0, n4, v4) =
% 18.14/3.25 pv70 & a_select3(center, tptp_sum_index, n0) = v0 & a_select2(x, pv10) = v1
% 18.14/3.25 & pred(pv12) = v5 & pred(pv10) = v6 & leq(pv12, n4) = 0 & leq(pv10, n135299)
% 18.14/3.25 = 0 & leq(n0, pv12) = 0 & leq(n0, pv10) = 0 & $i(v6) & $i(v5) & $i(v4) &
% 18.14/3.25 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i]
% 18.14/3.25 : ! [v10: $i] : ( ~ (times(v9, v9) = v10) | ~ (minus(v8, v1) = v9) | ~
% 18.14/3.25 (a_select3(center, v7, n0) = v8) | ~ $i(v7) | ? [v11: any] : ? [v12:
% 18.14/3.25 any] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : (sqrt(v10) = v14 &
% 18.14/3.25 divide(v14, pv70) = v15 & a_select3(q, pv10, v7) = v13 & leq(v7, v5) =
% 18.14/3.25 v12 & leq(n0, v7) = v11 & $i(v15) & $i(v14) & $i(v13) & ( ~ (v12 = 0) |
% 18.14/3.25 ~ (v11 = 0) | v15 = v13))) & ! [v7: $i] : ! [v8: $i] : ( ~
% 18.14/3.25 (a_select3(q, v7, tptp_sum_index) = v8) | ~ $i(v7) | ? [v9: any] : ?
% 18.14/3.25 [v10: any] : ? [v11: $i] : (sum(n0, n4, v8) = v11 & leq(v7, v6) = v10 &
% 18.14/3.25 leq(n0, v7) = v9 & $i(v11) & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = n1))) &
% 18.14/3.25 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ( ~ (v9 = n1) & ~ (v7 = pv10) &
% 18.14/3.25 sum(n0, n4, v8) = v9 & a_select3(q, v7, tptp_sum_index) = v8 & leq(v7, v6)
% 18.14/3.25 = 0 & leq(n0, v7) = 0 & $i(v9) & $i(v8) & $i(v7)))
% 18.14/3.25
% 18.14/3.25 (function-axioms)
% 18.14/3.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.14/3.27 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 18.14/3.27 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 18.14/3.27 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 18.14/3.27 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 18.14/3.27 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 18.14/3.27 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 18.14/3.27 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 18.14/3.27 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 18.14/3.27 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 18.14/3.27 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 18.14/3.27 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (times(v3, v2) = v1) | ~ (times(v3,
% 18.14/3.27 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 18.14/3.27 = v0 | ~ (divide(v3, v2) = v1) | ~ (divide(v3, v2) = v0)) & ! [v0: $i] :
% 18.14/3.27 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) |
% 18.14/3.27 ~ (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 18.14/3.27 $i] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0:
% 18.14/3.27 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3,
% 18.14/3.27 v2) = v1) | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 18.14/3.27 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~
% 18.14/3.27 (tptp_msub(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 18.14/3.27 [v3: $i] : (v1 = v0 | ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) =
% 18.14/3.27 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 18.14/3.27 ~ (dim(v3, v2) = v1) | ~ (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 18.14/3.27 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~
% 18.14/3.27 (tptp_const_array1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 18.14/3.27 : ! [v3: $i] : (v1 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2)
% 18.14/3.27 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 18.14/3.27 | ~ (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) &
% 18.14/3.27 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 18.14/3.27 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 18.14/3.27 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.14/3.27 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 18.14/3.27 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.14/3.27 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 18.14/3.27 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.14/3.27 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 18.14/3.27 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sqrt(v2) = v1) | ~ (sqrt(v2) = v0)) &
% 18.14/3.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~
% 18.14/3.27 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.14/3.27 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 18.14/3.27 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] :
% 18.14/3.27 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) =
% 18.14/3.27 v0))
% 18.14/3.27
% 18.14/3.27 Further assumptions not needed in the proof:
% 18.14/3.27 --------------------------------------------
% 18.14/3.27 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 18.14/3.27 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 18.14/3.27 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2,
% 18.14/3.27 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0,
% 18.14/3.27 gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2,
% 18.14/3.27 gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0,
% 18.14/3.27 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt,
% 18.14/3.27 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt,
% 18.14/3.27 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 18.14/3.27 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 18.14/3.27 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 18.14/3.27 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 18.14/3.27 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 18.14/3.27 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 18.14/3.27 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 18.14/3.27 successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 18.14/3.27 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 18.14/3.27 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 18.14/3.27
% 18.14/3.27 Those formulas are unsatisfiable:
% 18.14/3.27 ---------------------------------
% 18.14/3.27
% 18.14/3.27 Begin of proof
% 18.14/3.27 |
% 18.14/3.27 | ALPHA: (cl5_nebula_norm_0005) implies:
% 18.14/3.27 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 18.14/3.27 | ? [v5: $i] : ? [v6: $i] : (times(v2, v2) = v3 & sqrt(v3) = v4 &
% 18.14/3.27 | minus(v0, v1) = v2 & sum(n0, n4, v4) = pv70 & a_select3(center,
% 18.14/3.27 | tptp_sum_index, n0) = v0 & a_select2(x, pv10) = v1 & pred(pv12) =
% 18.14/3.27 | v5 & pred(pv10) = v6 & leq(pv12, n4) = 0 & leq(pv10, n135299) = 0 &
% 18.14/3.27 | leq(n0, pv12) = 0 & leq(n0, pv10) = 0 & $i(v6) & $i(v5) & $i(v4) &
% 18.14/3.27 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v7: $i] : ! [v8: $i] : !
% 18.14/3.27 | [v9: $i] : ! [v10: $i] : ( ~ (times(v9, v9) = v10) | ~ (minus(v8,
% 18.14/3.27 | v1) = v9) | ~ (a_select3(center, v7, n0) = v8) | ~ $i(v7) |
% 18.14/3.27 | ? [v11: any] : ? [v12: any] : ? [v13: $i] : ? [v14: $i] : ?
% 18.14/3.27 | [v15: $i] : (sqrt(v10) = v14 & divide(v14, pv70) = v15 &
% 18.14/3.27 | a_select3(q, pv10, v7) = v13 & leq(v7, v5) = v12 & leq(n0, v7) =
% 18.14/3.27 | v11 & $i(v15) & $i(v14) & $i(v13) & ( ~ (v12 = 0) | ~ (v11 = 0)
% 18.14/3.27 | | v15 = v13))) & ! [v7: $i] : ! [v8: $i] : ( ~ (a_select3(q,
% 18.14/3.27 | v7, tptp_sum_index) = v8) | ~ $i(v7) | ? [v9: any] : ? [v10:
% 18.14/3.27 | any] : ? [v11: $i] : (sum(n0, n4, v8) = v11 & leq(v7, v6) = v10
% 18.14/3.27 | & leq(n0, v7) = v9 & $i(v11) & ( ~ (v10 = 0) | ~ (v9 = 0) | v11
% 18.14/3.27 | = n1))) & ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ( ~ (v9 =
% 18.14/3.27 | n1) & ~ (v7 = pv10) & sum(n0, n4, v8) = v9 & a_select3(q, v7,
% 18.14/3.27 | tptp_sum_index) = v8 & leq(v7, v6) = 0 & leq(n0, v7) = 0 & $i(v9)
% 18.14/3.27 | & $i(v8) & $i(v7)))
% 18.14/3.27 |
% 18.14/3.27 | ALPHA: (function-axioms) implies:
% 18.14/3.28 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 18.14/3.28 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 18.14/3.28 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 18.14/3.28 | (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | ~ (sum(v4, v3, v2) = v0))
% 18.14/3.28 |
% 18.14/3.28 | DELTA: instantiating (1) with fresh symbols all_74_0, all_74_1, all_74_2,
% 18.14/3.28 | all_74_3, all_74_4, all_74_5, all_74_6 gives:
% 18.14/3.28 | (4) times(all_74_4, all_74_4) = all_74_3 & sqrt(all_74_3) = all_74_2 &
% 18.14/3.28 | minus(all_74_6, all_74_5) = all_74_4 & sum(n0, n4, all_74_2) = pv70 &
% 18.14/3.28 | a_select3(center, tptp_sum_index, n0) = all_74_6 & a_select2(x, pv10) =
% 18.14/3.28 | all_74_5 & pred(pv12) = all_74_1 & pred(pv10) = all_74_0 & leq(pv12,
% 18.14/3.28 | n4) = 0 & leq(pv10, n135299) = 0 & leq(n0, pv12) = 0 & leq(n0, pv10)
% 18.14/3.28 | = 0 & $i(all_74_0) & $i(all_74_1) & $i(all_74_2) & $i(all_74_3) &
% 18.14/3.28 | $i(all_74_4) & $i(all_74_5) & $i(all_74_6) & ! [v0: $i] : ! [v1: $i]
% 18.14/3.28 | : ! [v2: $i] : ! [v3: $i] : ( ~ (times(v2, v2) = v3) | ~ (minus(v1,
% 18.14/3.28 | all_74_5) = v2) | ~ (a_select3(center, v0, n0) = v1) | ~ $i(v0)
% 18.14/3.28 | | ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 18.14/3.28 | $i] : (sqrt(v3) = v7 & divide(v7, pv70) = v8 & a_select3(q, pv10,
% 18.14/3.28 | v0) = v6 & leq(v0, all_74_1) = v5 & leq(n0, v0) = v4 & $i(v8) &
% 18.14/3.28 | $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | v8 = v6))) & ! [v0:
% 18.14/3.28 | $i] : ! [v1: $i] : ( ~ (a_select3(q, v0, tptp_sum_index) = v1) | ~
% 18.14/3.28 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : (sum(n0, n4, v1)
% 18.14/3.28 | = v4 & leq(v0, all_74_0) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3
% 18.14/3.28 | = 0) | ~ (v2 = 0) | v4 = n1))) & ? [v0: $i] : ? [v1: $i] :
% 18.14/3.28 | ? [v2: $i] : ( ~ (v2 = n1) & ~ (v0 = pv10) & sum(n0, n4, v1) = v2 &
% 18.14/3.28 | a_select3(q, v0, tptp_sum_index) = v1 & leq(v0, all_74_0) = 0 &
% 18.14/3.28 | leq(n0, v0) = 0 & $i(v2) & $i(v1) & $i(v0))
% 18.14/3.28 |
% 18.14/3.28 | ALPHA: (4) implies:
% 18.14/3.28 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (a_select3(q, v0, tptp_sum_index) = v1)
% 18.14/3.28 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : (sum(n0,
% 18.14/3.28 | n4, v1) = v4 & leq(v0, all_74_0) = v3 & leq(n0, v0) = v2 & $i(v4)
% 18.14/3.28 | & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = n1)))
% 18.14/3.28 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = n1) & ~ (v0 =
% 18.14/3.28 | pv10) & sum(n0, n4, v1) = v2 & a_select3(q, v0, tptp_sum_index) =
% 18.14/3.28 | v1 & leq(v0, all_74_0) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) &
% 18.14/3.28 | $i(v0))
% 18.14/3.28 |
% 18.14/3.28 | DELTA: instantiating (6) with fresh symbols all_79_0, all_79_1, all_79_2
% 18.14/3.28 | gives:
% 18.14/3.29 | (7) ~ (all_79_0 = n1) & ~ (all_79_2 = pv10) & sum(n0, n4, all_79_1) =
% 18.14/3.29 | all_79_0 & a_select3(q, all_79_2, tptp_sum_index) = all_79_1 &
% 18.14/3.29 | leq(all_79_2, all_74_0) = 0 & leq(n0, all_79_2) = 0 & $i(all_79_0) &
% 18.14/3.29 | $i(all_79_1) & $i(all_79_2)
% 18.14/3.29 |
% 18.14/3.29 | ALPHA: (7) implies:
% 18.14/3.29 | (8) ~ (all_79_0 = n1)
% 18.14/3.29 | (9) $i(all_79_2)
% 18.14/3.29 | (10) leq(n0, all_79_2) = 0
% 18.14/3.29 | (11) leq(all_79_2, all_74_0) = 0
% 18.14/3.29 | (12) a_select3(q, all_79_2, tptp_sum_index) = all_79_1
% 18.14/3.29 | (13) sum(n0, n4, all_79_1) = all_79_0
% 18.14/3.29 |
% 18.14/3.29 | GROUND_INST: instantiating (5) with all_79_2, all_79_1, simplifying with (9),
% 18.14/3.29 | (12) gives:
% 18.14/3.29 | (14) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sum(n0, n4, all_79_1) =
% 18.14/3.29 | v2 & leq(all_79_2, all_74_0) = v1 & leq(n0, all_79_2) = v0 & $i(v2)
% 18.14/3.29 | & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = n1))
% 18.14/3.29 |
% 18.14/3.29 | DELTA: instantiating (14) with fresh symbols all_103_0, all_103_1, all_103_2
% 18.14/3.29 | gives:
% 18.14/3.29 | (15) sum(n0, n4, all_79_1) = all_103_0 & leq(all_79_2, all_74_0) =
% 18.14/3.29 | all_103_1 & leq(n0, all_79_2) = all_103_2 & $i(all_103_0) & ( ~
% 18.14/3.29 | (all_103_1 = 0) | ~ (all_103_2 = 0) | all_103_0 = n1)
% 18.14/3.29 |
% 18.14/3.29 | ALPHA: (15) implies:
% 18.14/3.29 | (16) leq(n0, all_79_2) = all_103_2
% 18.14/3.29 | (17) leq(all_79_2, all_74_0) = all_103_1
% 18.14/3.29 | (18) sum(n0, n4, all_79_1) = all_103_0
% 18.14/3.29 | (19) ~ (all_103_1 = 0) | ~ (all_103_2 = 0) | all_103_0 = n1
% 18.14/3.29 |
% 18.14/3.29 | GROUND_INST: instantiating (2) with 0, all_103_2, all_79_2, n0, simplifying
% 18.14/3.29 | with (10), (16) gives:
% 18.14/3.29 | (20) all_103_2 = 0
% 18.14/3.29 |
% 18.14/3.29 | GROUND_INST: instantiating (2) with 0, all_103_1, all_74_0, all_79_2,
% 18.14/3.29 | simplifying with (11), (17) gives:
% 18.14/3.29 | (21) all_103_1 = 0
% 18.14/3.29 |
% 18.14/3.29 | GROUND_INST: instantiating (3) with all_79_0, all_103_0, all_79_1, n4, n0,
% 18.14/3.29 | simplifying with (13), (18) gives:
% 18.14/3.29 | (22) all_103_0 = all_79_0
% 18.14/3.29 |
% 18.14/3.29 | BETA: splitting (19) gives:
% 18.14/3.29 |
% 18.14/3.29 | Case 1:
% 18.14/3.29 | |
% 18.14/3.29 | | (23) ~ (all_103_1 = 0)
% 18.14/3.29 | |
% 18.14/3.29 | | REDUCE: (21), (23) imply:
% 18.14/3.29 | | (24) $false
% 18.14/3.29 | |
% 18.14/3.29 | | CLOSE: (24) is inconsistent.
% 18.14/3.29 | |
% 18.14/3.29 | Case 2:
% 18.14/3.29 | |
% 18.14/3.29 | | (25) ~ (all_103_2 = 0) | all_103_0 = n1
% 18.14/3.29 | |
% 18.14/3.29 | | BETA: splitting (25) gives:
% 18.14/3.29 | |
% 18.14/3.29 | | Case 1:
% 18.14/3.29 | | |
% 18.14/3.29 | | | (26) ~ (all_103_2 = 0)
% 18.14/3.29 | | |
% 18.14/3.29 | | | REDUCE: (20), (26) imply:
% 18.14/3.29 | | | (27) $false
% 18.14/3.29 | | |
% 18.14/3.29 | | | CLOSE: (27) is inconsistent.
% 18.14/3.29 | | |
% 18.14/3.29 | | Case 2:
% 18.14/3.29 | | |
% 18.14/3.29 | | | (28) all_103_0 = n1
% 18.14/3.29 | | |
% 18.14/3.29 | | | COMBINE_EQS: (22), (28) imply:
% 18.14/3.29 | | | (29) all_79_0 = n1
% 18.14/3.29 | | |
% 18.14/3.29 | | | REDUCE: (8), (29) imply:
% 18.14/3.29 | | | (30) $false
% 18.14/3.29 | | |
% 18.14/3.29 | | | CLOSE: (30) is inconsistent.
% 18.14/3.30 | | |
% 18.14/3.30 | | End of split
% 18.14/3.30 | |
% 18.14/3.30 | End of split
% 18.14/3.30 |
% 18.14/3.30 End of proof
% 18.14/3.30 % SZS output end Proof for theBenchmark
% 18.14/3.30
% 18.14/3.30 2693ms
%------------------------------------------------------------------------------