TSTP Solution File: SWV153+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV153+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 : n006.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 22:55:07 EDT 2023
% Result : Theorem 15.83s 2.88s
% Output : Proof 19.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWV153+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n006.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 05:34:21 EDT 2023
% 0.12/0.33 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.62/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.62/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.62/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.62/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.62/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.62/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.62/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.66/1.36 Prover 4: Preprocessing ...
% 4.66/1.36 Prover 1: Preprocessing ...
% 5.17/1.38 Prover 5: Preprocessing ...
% 5.17/1.38 Prover 0: Preprocessing ...
% 5.17/1.38 Prover 2: Preprocessing ...
% 5.17/1.38 Prover 3: Preprocessing ...
% 5.17/1.38 Prover 6: Preprocessing ...
% 10.59/2.18 Prover 1: Warning: ignoring some quantifiers
% 11.24/2.21 Prover 6: Proving ...
% 11.24/2.27 Prover 1: Constructing countermodel ...
% 11.24/2.27 Prover 3: Warning: ignoring some quantifiers
% 11.91/2.30 Prover 3: Constructing countermodel ...
% 11.91/2.32 Prover 4: Warning: ignoring some quantifiers
% 12.65/2.38 Prover 4: Constructing countermodel ...
% 13.04/2.50 Prover 0: Proving ...
% 13.04/2.50 Prover 5: Proving ...
% 13.04/2.52 Prover 2: Proving ...
% 15.83/2.87 Prover 3: proved (2243ms)
% 15.83/2.88
% 15.83/2.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.83/2.88
% 15.83/2.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.83/2.88 Prover 2: stopped
% 15.83/2.88 Prover 0: stopped
% 15.83/2.88 Prover 5: stopped
% 15.83/2.88 Prover 6: stopped
% 16.39/2.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 16.39/2.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 16.39/2.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 16.39/2.91 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 17.32/3.05 Prover 7: Preprocessing ...
% 17.32/3.05 Prover 11: Preprocessing ...
% 17.32/3.05 Prover 13: Preprocessing ...
% 17.32/3.06 Prover 10: Preprocessing ...
% 17.32/3.08 Prover 8: Preprocessing ...
% 17.73/3.11 Prover 1: Found proof (size 46)
% 17.73/3.11 Prover 1: proved (2482ms)
% 17.73/3.13 Prover 4: stopped
% 17.73/3.13 Prover 7: stopped
% 17.73/3.15 Prover 10: stopped
% 17.73/3.16 Prover 11: stopped
% 18.53/3.18 Prover 13: stopped
% 18.98/3.27 Prover 8: Warning: ignoring some quantifiers
% 18.98/3.29 Prover 8: Constructing countermodel ...
% 18.98/3.31 Prover 8: stopped
% 18.98/3.31
% 18.98/3.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.98/3.31
% 18.98/3.32 % SZS output start Proof for theBenchmark
% 19.21/3.32 Assumptions after simplification:
% 19.21/3.32 ---------------------------------
% 19.21/3.32
% 19.21/3.32 (cl5_nebula_norm_0003)
% 19.33/3.36 $i(q) & $i(n135299) & $i(pv12) & $i(pv70) & $i(pv10) & $i(x) &
% 19.33/3.36 $i(tptp_sum_index) & $i(center) & $i(n4) & $i(n1) & $i(n0) & ? [v0: $i] : ?
% 19.33/3.36 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 19.33/3.36 : (times(v2, v2) = v3 & sqrt(v3) = v4 & minus(v0, v1) = v2 & sum(n0, n4, v4) =
% 19.33/3.36 pv70 & a_select3(center, tptp_sum_index, n0) = v0 & a_select2(x, pv10) = v1
% 19.33/3.36 & pred(pv12) = v5 & pred(pv10) = v6 & leq(pv12, n4) = 0 & leq(pv10, n135299)
% 19.33/3.36 = 0 & leq(n0, pv12) = 0 & leq(n0, pv10) = 0 & $i(v6) & $i(v5) & $i(v4) &
% 19.33/3.36 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i]
% 19.33/3.36 : ! [v10: $i] : ( ~ (times(v9, v9) = v10) | ~ (minus(v8, v1) = v9) | ~
% 19.33/3.36 (a_select3(center, v7, n0) = v8) | ~ $i(v7) | ? [v11: any] : ? [v12:
% 19.33/3.36 any] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : (sqrt(v10) = v14 &
% 19.33/3.36 divide(v14, pv70) = v15 & a_select3(q, pv10, v7) = v13 & leq(v7, v5) =
% 19.33/3.36 v12 & leq(n0, v7) = v11 & $i(v15) & $i(v14) & $i(v13) & ( ~ (v12 = 0) |
% 19.33/3.36 ~ (v11 = 0) | v15 = v13))) & ! [v7: $i] : ! [v8: $i] : ( ~
% 19.33/3.36 (a_select3(q, v7, tptp_sum_index) = v8) | ~ $i(v7) | ? [v9: any] : ?
% 19.33/3.36 [v10: any] : ? [v11: $i] : (sum(n0, n4, v8) = v11 & leq(v7, v6) = v10 &
% 19.33/3.36 leq(n0, v7) = v9 & $i(v11) & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = n1))) &
% 19.33/3.36 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ?
% 19.33/3.36 [v12: $i] : ? [v13: $i] : ( ~ (v13 = v8) & ~ (v7 = pv12) & times(v10, v10)
% 19.33/3.36 = v11 & sqrt(v11) = v12 & divide(v12, pv70) = v13 & minus(v9, v1) = v10 &
% 19.33/3.36 a_select3(q, pv10, v7) = v8 & a_select3(center, v7, n0) = v9 & leq(v7,
% 19.33/3.36 pv12) = 0 & leq(n0, v7) = 0 & $i(v13) & $i(v12) & $i(v11) & $i(v10) &
% 19.33/3.36 $i(v9) & $i(v8) & $i(v7)))
% 19.33/3.36
% 19.33/3.36 (leq_gt2)
% 19.33/3.37 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (gt(v1, v0)
% 19.33/3.37 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1)
% 19.33/3.37 = v3))
% 19.33/3.37
% 19.33/3.37 (leq_gt_pred)
% 19.33/3.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 19.33/3.37 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 19.33/3.37 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : !
% 19.33/3.37 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)
% 19.33/3.37 | gt(v1, v0) = 0)
% 19.33/3.37
% 19.33/3.37 (function-axioms)
% 19.33/3.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 19.33/3.37 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 19.33/3.37 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 19.33/3.37 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 19.33/3.37 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.33/3.37 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 19.33/3.37 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 19.33/3.37 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 19.33/3.37 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.33/3.37 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 19.33/3.37 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.33/3.37 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (times(v3, v2) = v1) | ~ (times(v3,
% 19.33/3.37 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 19.33/3.37 = v0 | ~ (divide(v3, v2) = v1) | ~ (divide(v3, v2) = v0)) & ! [v0: $i] :
% 19.33/3.37 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) |
% 19.33/3.37 ~ (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 19.33/3.37 $i] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0:
% 19.33/3.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3,
% 19.33/3.37 v2) = v1) | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 19.33/3.37 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~
% 19.33/3.37 (tptp_msub(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 19.33/3.37 [v3: $i] : (v1 = v0 | ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) =
% 19.33/3.37 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 19.33/3.37 ~ (dim(v3, v2) = v1) | ~ (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 19.33/3.37 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~
% 19.33/3.37 (tptp_const_array1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 19.33/3.37 : ! [v3: $i] : (v1 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2)
% 19.33/3.37 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 19.33/3.37 | ~ (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) &
% 19.33/3.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 19.33/3.37 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 19.33/3.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.33/3.37 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 19.33/3.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.33/3.37 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 19.33/3.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.33/3.37 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 19.33/3.37 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sqrt(v2) = v1) | ~ (sqrt(v2) = v0)) &
% 19.33/3.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~
% 19.33/3.37 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 19.33/3.37 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.33/3.37 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] :
% 19.33/3.37 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) =
% 19.33/3.37 v0))
% 19.33/3.37
% 19.33/3.37 Further assumptions not needed in the proof:
% 19.33/3.37 --------------------------------------------
% 19.33/3.37 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 19.33/3.37 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 19.33/3.37 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2,
% 19.33/3.37 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0,
% 19.33/3.37 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,
% 19.33/3.37 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,
% 19.33/3.37 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt,
% 19.33/3.37 leq_geq, leq_gt1, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv,
% 19.33/3.37 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add,
% 19.33/3.37 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 19.33/3.37 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq,
% 19.33/3.37 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2,
% 19.33/3.37 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r,
% 19.33/3.37 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l,
% 19.33/3.37 succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, successor_2,
% 19.33/3.37 successor_3, successor_4, successor_5, sum_plus_base, sum_plus_base_float,
% 19.33/3.37 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi,
% 19.33/3.37 uniform_int_rand_ranges_lo
% 19.33/3.37
% 19.33/3.37 Those formulas are unsatisfiable:
% 19.33/3.37 ---------------------------------
% 19.33/3.37
% 19.33/3.37 Begin of proof
% 19.33/3.38 |
% 19.33/3.38 | ALPHA: (leq_gt_pred) implies:
% 19.33/3.38 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 19.33/3.38 | (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 19.33/3.38 | [v4: int] : ( ~ (v4 = 0) & gt(v1, v0) = v4))
% 19.33/3.38 |
% 19.33/3.38 | ALPHA: (cl5_nebula_norm_0003) implies:
% 19.33/3.38 | (2) $i(pv12)
% 19.33/3.38 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 19.33/3.38 | ? [v5: $i] : ? [v6: $i] : (times(v2, v2) = v3 & sqrt(v3) = v4 &
% 19.33/3.38 | minus(v0, v1) = v2 & sum(n0, n4, v4) = pv70 & a_select3(center,
% 19.33/3.38 | tptp_sum_index, n0) = v0 & a_select2(x, pv10) = v1 & pred(pv12) =
% 19.33/3.38 | v5 & pred(pv10) = v6 & leq(pv12, n4) = 0 & leq(pv10, n135299) = 0 &
% 19.33/3.38 | leq(n0, pv12) = 0 & leq(n0, pv10) = 0 & $i(v6) & $i(v5) & $i(v4) &
% 19.33/3.38 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v7: $i] : ! [v8: $i] : !
% 19.33/3.38 | [v9: $i] : ! [v10: $i] : ( ~ (times(v9, v9) = v10) | ~ (minus(v8,
% 19.33/3.38 | v1) = v9) | ~ (a_select3(center, v7, n0) = v8) | ~ $i(v7) |
% 19.33/3.38 | ? [v11: any] : ? [v12: any] : ? [v13: $i] : ? [v14: $i] : ?
% 19.33/3.38 | [v15: $i] : (sqrt(v10) = v14 & divide(v14, pv70) = v15 &
% 19.33/3.38 | a_select3(q, pv10, v7) = v13 & leq(v7, v5) = v12 & leq(n0, v7) =
% 19.33/3.38 | v11 & $i(v15) & $i(v14) & $i(v13) & ( ~ (v12 = 0) | ~ (v11 = 0)
% 19.33/3.38 | | v15 = v13))) & ! [v7: $i] : ! [v8: $i] : ( ~ (a_select3(q,
% 19.33/3.38 | v7, tptp_sum_index) = v8) | ~ $i(v7) | ? [v9: any] : ? [v10:
% 19.33/3.38 | any] : ? [v11: $i] : (sum(n0, n4, v8) = v11 & leq(v7, v6) = v10
% 19.33/3.38 | & leq(n0, v7) = v9 & $i(v11) & ( ~ (v10 = 0) | ~ (v9 = 0) | v11
% 19.33/3.38 | = n1))) & ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10:
% 19.33/3.38 | $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ( ~ (v13 = v8) &
% 19.33/3.38 | ~ (v7 = pv12) & times(v10, v10) = v11 & sqrt(v11) = v12 &
% 19.33/3.38 | divide(v12, pv70) = v13 & minus(v9, v1) = v10 & a_select3(q, pv10,
% 19.33/3.38 | v7) = v8 & a_select3(center, v7, n0) = v9 & leq(v7, pv12) = 0 &
% 19.33/3.38 | leq(n0, v7) = 0 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) &
% 19.33/3.38 | $i(v8) & $i(v7)))
% 19.33/3.38 |
% 19.33/3.38 | ALPHA: (function-axioms) implies:
% 19.33/3.38 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sqrt(v2) = v1)
% 19.33/3.38 | | ~ (sqrt(v2) = v0))
% 19.33/3.38 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 19.33/3.38 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 19.33/3.38 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.33/3.38 | (divide(v3, v2) = v1) | ~ (divide(v3, v2) = v0))
% 19.33/3.38 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 19.33/3.38 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2)
% 19.33/3.38 | = v0))
% 19.33/3.38 |
% 19.33/3.38 | DELTA: instantiating (3) with fresh symbols all_74_0, all_74_1, all_74_2,
% 19.33/3.38 | all_74_3, all_74_4, all_74_5, all_74_6 gives:
% 19.33/3.39 | (8) times(all_74_4, all_74_4) = all_74_3 & sqrt(all_74_3) = all_74_2 &
% 19.33/3.39 | minus(all_74_6, all_74_5) = all_74_4 & sum(n0, n4, all_74_2) = pv70 &
% 19.33/3.39 | a_select3(center, tptp_sum_index, n0) = all_74_6 & a_select2(x, pv10) =
% 19.33/3.39 | all_74_5 & pred(pv12) = all_74_1 & pred(pv10) = all_74_0 & leq(pv12,
% 19.33/3.39 | n4) = 0 & leq(pv10, n135299) = 0 & leq(n0, pv12) = 0 & leq(n0, pv10)
% 19.33/3.39 | = 0 & $i(all_74_0) & $i(all_74_1) & $i(all_74_2) & $i(all_74_3) &
% 19.33/3.39 | $i(all_74_4) & $i(all_74_5) & $i(all_74_6) & ! [v0: $i] : ! [v1: $i]
% 19.33/3.39 | : ! [v2: $i] : ! [v3: $i] : ( ~ (times(v2, v2) = v3) | ~ (minus(v1,
% 19.33/3.39 | all_74_5) = v2) | ~ (a_select3(center, v0, n0) = v1) | ~ $i(v0)
% 19.33/3.39 | | ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 19.33/3.39 | $i] : (sqrt(v3) = v7 & divide(v7, pv70) = v8 & a_select3(q, pv10,
% 19.33/3.39 | v0) = v6 & leq(v0, all_74_1) = v5 & leq(n0, v0) = v4 & $i(v8) &
% 19.33/3.39 | $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | v8 = v6))) & ! [v0:
% 19.33/3.39 | $i] : ! [v1: $i] : ( ~ (a_select3(q, v0, tptp_sum_index) = v1) | ~
% 19.33/3.39 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : (sum(n0, n4, v1)
% 19.33/3.39 | = v4 & leq(v0, all_74_0) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3
% 19.33/3.39 | = 0) | ~ (v2 = 0) | v4 = n1))) & ? [v0: $i] : ? [v1: $i] :
% 19.33/3.39 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (
% 19.33/3.39 | ~ (v6 = v1) & ~ (v0 = pv12) & times(v3, v3) = v4 & sqrt(v4) = v5 &
% 19.33/3.39 | divide(v5, pv70) = v6 & minus(v2, all_74_5) = v3 & a_select3(q, pv10,
% 19.33/3.39 | v0) = v1 & a_select3(center, v0, n0) = v2 & leq(v0, pv12) = 0 &
% 19.33/3.39 | leq(n0, v0) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1)
% 19.33/3.39 | & $i(v0))
% 19.33/3.39 |
% 19.33/3.39 | ALPHA: (8) implies:
% 19.33/3.39 | (9) pred(pv12) = all_74_1
% 19.33/3.39 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (times(v2,
% 19.33/3.39 | v2) = v3) | ~ (minus(v1, all_74_5) = v2) | ~
% 19.33/3.39 | (a_select3(center, v0, n0) = v1) | ~ $i(v0) | ? [v4: any] : ?
% 19.33/3.39 | [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sqrt(v3) = v7
% 19.33/3.39 | & divide(v7, pv70) = v8 & a_select3(q, pv10, v0) = v6 & leq(v0,
% 19.33/3.39 | all_74_1) = v5 & leq(n0, v0) = v4 & $i(v8) & $i(v7) & $i(v6) & (
% 19.33/3.39 | ~ (v5 = 0) | ~ (v4 = 0) | v8 = v6)))
% 19.33/3.39 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 19.33/3.39 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v1) & ~ (v0 = pv12) & times(v3,
% 19.33/3.39 | v3) = v4 & sqrt(v4) = v5 & divide(v5, pv70) = v6 & minus(v2,
% 19.33/3.39 | all_74_5) = v3 & a_select3(q, pv10, v0) = v1 & a_select3(center,
% 19.33/3.39 | v0, n0) = v2 & leq(v0, pv12) = 0 & leq(n0, v0) = 0 & $i(v6) &
% 19.33/3.39 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 19.33/3.39 |
% 19.33/3.39 | DELTA: instantiating (11) with fresh symbols all_79_0, all_79_1, all_79_2,
% 19.33/3.39 | all_79_3, all_79_4, all_79_5, all_79_6 gives:
% 19.33/3.39 | (12) ~ (all_79_0 = all_79_5) & ~ (all_79_6 = pv12) & times(all_79_3,
% 19.33/3.39 | all_79_3) = all_79_2 & sqrt(all_79_2) = all_79_1 & divide(all_79_1,
% 19.33/3.39 | pv70) = all_79_0 & minus(all_79_4, all_74_5) = all_79_3 &
% 19.33/3.39 | a_select3(q, pv10, all_79_6) = all_79_5 & a_select3(center, all_79_6,
% 19.33/3.39 | n0) = all_79_4 & leq(all_79_6, pv12) = 0 & leq(n0, all_79_6) = 0 &
% 19.33/3.39 | $i(all_79_0) & $i(all_79_1) & $i(all_79_2) & $i(all_79_3) &
% 19.33/3.39 | $i(all_79_4) & $i(all_79_5) & $i(all_79_6)
% 19.33/3.39 |
% 19.33/3.39 | ALPHA: (12) implies:
% 19.33/3.39 | (13) ~ (all_79_6 = pv12)
% 19.33/3.39 | (14) ~ (all_79_0 = all_79_5)
% 19.33/3.39 | (15) $i(all_79_6)
% 19.33/3.39 | (16) leq(n0, all_79_6) = 0
% 19.33/3.39 | (17) leq(all_79_6, pv12) = 0
% 19.33/3.39 | (18) a_select3(center, all_79_6, n0) = all_79_4
% 19.33/3.39 | (19) a_select3(q, pv10, all_79_6) = all_79_5
% 19.33/3.39 | (20) minus(all_79_4, all_74_5) = all_79_3
% 19.33/3.39 | (21) divide(all_79_1, pv70) = all_79_0
% 19.33/3.39 | (22) sqrt(all_79_2) = all_79_1
% 19.33/3.39 | (23) times(all_79_3, all_79_3) = all_79_2
% 19.33/3.39 |
% 19.33/3.39 | GROUND_INST: instantiating (10) with all_79_6, all_79_4, all_79_3, all_79_2,
% 19.33/3.39 | simplifying with (15), (18), (20), (23) gives:
% 19.33/3.40 | (24) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 19.33/3.40 | : (sqrt(all_79_2) = v3 & divide(v3, pv70) = v4 & a_select3(q, pv10,
% 19.33/3.40 | all_79_6) = v2 & leq(all_79_6, all_74_1) = v1 & leq(n0, all_79_6)
% 19.33/3.40 | = v0 & $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 =
% 19.33/3.40 | v2))
% 19.33/3.40 |
% 19.33/3.40 | DELTA: instantiating (24) with fresh symbols all_103_0, all_103_1, all_103_2,
% 19.33/3.40 | all_103_3, all_103_4 gives:
% 19.33/3.40 | (25) sqrt(all_79_2) = all_103_1 & divide(all_103_1, pv70) = all_103_0 &
% 19.33/3.40 | a_select3(q, pv10, all_79_6) = all_103_2 & leq(all_79_6, all_74_1) =
% 19.33/3.40 | all_103_3 & leq(n0, all_79_6) = all_103_4 & $i(all_103_0) &
% 19.33/3.40 | $i(all_103_1) & $i(all_103_2) & ( ~ (all_103_3 = 0) | ~ (all_103_4 =
% 19.33/3.40 | 0) | all_103_0 = all_103_2)
% 19.33/3.40 |
% 19.33/3.40 | ALPHA: (25) implies:
% 19.33/3.40 | (26) leq(n0, all_79_6) = all_103_4
% 19.33/3.40 | (27) leq(all_79_6, all_74_1) = all_103_3
% 19.33/3.40 | (28) a_select3(q, pv10, all_79_6) = all_103_2
% 19.33/3.40 | (29) divide(all_103_1, pv70) = all_103_0
% 19.33/3.40 | (30) sqrt(all_79_2) = all_103_1
% 19.33/3.40 | (31) ~ (all_103_3 = 0) | ~ (all_103_4 = 0) | all_103_0 = all_103_2
% 19.33/3.40 |
% 19.33/3.40 | GROUND_INST: instantiating (5) with 0, all_103_4, all_79_6, n0, simplifying
% 19.33/3.40 | with (16), (26) gives:
% 19.33/3.40 | (32) all_103_4 = 0
% 19.33/3.40 |
% 19.33/3.40 | GROUND_INST: instantiating (7) with all_79_5, all_103_2, all_79_6, pv10, q,
% 19.33/3.40 | simplifying with (19), (28) gives:
% 19.33/3.40 | (33) all_103_2 = all_79_5
% 19.33/3.40 |
% 19.33/3.40 | GROUND_INST: instantiating (4) with all_79_1, all_103_1, all_79_2, simplifying
% 19.33/3.40 | with (22), (30) gives:
% 19.33/3.40 | (34) all_103_1 = all_79_1
% 19.33/3.40 |
% 19.33/3.40 | REDUCE: (29), (34) imply:
% 19.33/3.40 | (35) divide(all_79_1, pv70) = all_103_0
% 19.33/3.40 |
% 19.33/3.40 | GROUND_INST: instantiating (6) with all_79_0, all_103_0, pv70, all_79_1,
% 19.33/3.40 | simplifying with (21), (35) gives:
% 19.33/3.40 | (36) all_103_0 = all_79_0
% 19.33/3.40 |
% 19.33/3.40 | BETA: splitting (31) gives:
% 19.33/3.40 |
% 19.33/3.40 | Case 1:
% 19.33/3.40 | |
% 19.33/3.40 | | (37) ~ (all_103_3 = 0)
% 19.33/3.40 | |
% 19.33/3.40 | | GROUND_INST: instantiating (1) with all_79_6, pv12, all_74_1, all_103_3,
% 19.33/3.40 | | simplifying with (2), (9), (15), (27) gives:
% 19.33/3.40 | | (38) all_103_3 = 0 | ? [v0: int] : ( ~ (v0 = 0) & gt(pv12, all_79_6) =
% 19.33/3.40 | | v0)
% 19.33/3.40 | |
% 19.33/3.40 | | BETA: splitting (38) gives:
% 19.33/3.40 | |
% 19.33/3.40 | | Case 1:
% 19.33/3.40 | | |
% 19.33/3.40 | | | (39) all_103_3 = 0
% 19.33/3.40 | | |
% 19.33/3.40 | | | REDUCE: (37), (39) imply:
% 19.33/3.40 | | | (40) $false
% 19.33/3.40 | | |
% 19.33/3.40 | | | CLOSE: (40) is inconsistent.
% 19.33/3.40 | | |
% 19.33/3.40 | | Case 2:
% 19.33/3.40 | | |
% 19.33/3.40 | | | (41) ? [v0: int] : ( ~ (v0 = 0) & gt(pv12, all_79_6) = v0)
% 19.33/3.40 | | |
% 19.33/3.40 | | | DELTA: instantiating (41) with fresh symbol all_136_0 gives:
% 19.33/3.40 | | | (42) ~ (all_136_0 = 0) & gt(pv12, all_79_6) = all_136_0
% 19.33/3.40 | | |
% 19.33/3.40 | | | ALPHA: (42) implies:
% 19.33/3.40 | | | (43) ~ (all_136_0 = 0)
% 19.33/3.40 | | | (44) gt(pv12, all_79_6) = all_136_0
% 19.33/3.40 | | |
% 19.33/3.40 | | | GROUND_INST: instantiating (leq_gt2) with all_79_6, pv12, all_136_0,
% 19.33/3.40 | | | simplifying with (2), (15), (44) gives:
% 19.33/3.40 | | | (45) all_136_0 = 0 | all_79_6 = pv12 | ? [v0: int] : ( ~ (v0 = 0) &
% 19.33/3.40 | | | leq(all_79_6, pv12) = v0)
% 19.33/3.40 | | |
% 19.33/3.40 | | | BETA: splitting (45) gives:
% 19.33/3.40 | | |
% 19.33/3.40 | | | Case 1:
% 19.33/3.40 | | | |
% 19.33/3.40 | | | | (46) all_136_0 = 0
% 19.33/3.40 | | | |
% 19.33/3.40 | | | | REDUCE: (43), (46) imply:
% 19.33/3.40 | | | | (47) $false
% 19.33/3.40 | | | |
% 19.33/3.40 | | | | CLOSE: (47) is inconsistent.
% 19.33/3.40 | | | |
% 19.33/3.40 | | | Case 2:
% 19.33/3.40 | | | |
% 19.33/3.40 | | | | (48) all_79_6 = pv12 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_6,
% 19.33/3.40 | | | | pv12) = v0)
% 19.33/3.40 | | | |
% 19.33/3.40 | | | | BETA: splitting (48) gives:
% 19.33/3.40 | | | |
% 19.33/3.40 | | | | Case 1:
% 19.33/3.40 | | | | |
% 19.33/3.40 | | | | | (49) all_79_6 = pv12
% 19.33/3.40 | | | | |
% 19.33/3.40 | | | | | REDUCE: (13), (49) imply:
% 19.33/3.41 | | | | | (50) $false
% 19.33/3.41 | | | | |
% 19.33/3.41 | | | | | CLOSE: (50) is inconsistent.
% 19.33/3.41 | | | | |
% 19.33/3.41 | | | | Case 2:
% 19.33/3.41 | | | | |
% 19.33/3.41 | | | | | (51) ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_6, pv12) = v0)
% 19.33/3.41 | | | | |
% 19.33/3.41 | | | | | DELTA: instantiating (51) with fresh symbol all_175_0 gives:
% 19.33/3.41 | | | | | (52) ~ (all_175_0 = 0) & leq(all_79_6, pv12) = all_175_0
% 19.33/3.41 | | | | |
% 19.33/3.41 | | | | | ALPHA: (52) implies:
% 19.33/3.41 | | | | | (53) ~ (all_175_0 = 0)
% 19.33/3.41 | | | | | (54) leq(all_79_6, pv12) = all_175_0
% 19.33/3.41 | | | | |
% 19.33/3.41 | | | | | GROUND_INST: instantiating (5) with 0, all_175_0, pv12, all_79_6,
% 19.33/3.41 | | | | | simplifying with (17), (54) gives:
% 19.33/3.41 | | | | | (55) all_175_0 = 0
% 19.33/3.41 | | | | |
% 19.33/3.41 | | | | | REDUCE: (53), (55) imply:
% 19.33/3.41 | | | | | (56) $false
% 19.33/3.41 | | | | |
% 19.33/3.41 | | | | | CLOSE: (56) is inconsistent.
% 19.33/3.41 | | | | |
% 19.33/3.41 | | | | End of split
% 19.33/3.41 | | | |
% 19.33/3.41 | | | End of split
% 19.33/3.41 | | |
% 19.33/3.41 | | End of split
% 19.33/3.41 | |
% 19.33/3.41 | Case 2:
% 19.33/3.41 | |
% 19.33/3.41 | | (57) ~ (all_103_4 = 0) | all_103_0 = all_103_2
% 19.33/3.41 | |
% 19.33/3.41 | | BETA: splitting (57) gives:
% 19.33/3.41 | |
% 19.33/3.41 | | Case 1:
% 19.33/3.41 | | |
% 19.33/3.41 | | | (58) ~ (all_103_4 = 0)
% 19.33/3.41 | | |
% 19.33/3.41 | | | REDUCE: (32), (58) imply:
% 19.33/3.41 | | | (59) $false
% 19.33/3.41 | | |
% 19.33/3.41 | | | CLOSE: (59) is inconsistent.
% 19.33/3.41 | | |
% 19.33/3.41 | | Case 2:
% 19.33/3.41 | | |
% 19.33/3.41 | | | (60) all_103_0 = all_103_2
% 19.33/3.41 | | |
% 19.33/3.41 | | | COMBINE_EQS: (36), (60) imply:
% 19.33/3.41 | | | (61) all_103_2 = all_79_0
% 19.33/3.41 | | |
% 19.33/3.41 | | | SIMP: (61) implies:
% 19.33/3.41 | | | (62) all_103_2 = all_79_0
% 19.33/3.41 | | |
% 19.33/3.41 | | | COMBINE_EQS: (33), (62) imply:
% 19.33/3.41 | | | (63) all_79_0 = all_79_5
% 19.33/3.41 | | |
% 19.33/3.41 | | | SIMP: (63) implies:
% 19.33/3.41 | | | (64) all_79_0 = all_79_5
% 19.33/3.41 | | |
% 19.33/3.41 | | | REDUCE: (14), (64) imply:
% 19.33/3.41 | | | (65) $false
% 19.33/3.41 | | |
% 19.33/3.41 | | | CLOSE: (65) is inconsistent.
% 19.33/3.41 | | |
% 19.33/3.41 | | End of split
% 19.33/3.41 | |
% 19.33/3.41 | End of split
% 19.33/3.41 |
% 19.33/3.41 End of proof
% 19.33/3.41 % SZS output end Proof for theBenchmark
% 19.33/3.41
% 19.33/3.41 2799ms
%------------------------------------------------------------------------------