TSTP Solution File: SWV157+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV157+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 22:55:08 EDT 2023
% Result : Theorem 17.22s 3.09s
% Output : Proof 21.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV157+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n006.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 07:14:06 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.47/1.39 Prover 4: Preprocessing ...
% 4.47/1.39 Prover 1: Preprocessing ...
% 4.97/1.44 Prover 0: Preprocessing ...
% 4.97/1.44 Prover 5: Preprocessing ...
% 4.97/1.44 Prover 2: Preprocessing ...
% 4.97/1.44 Prover 6: Preprocessing ...
% 4.97/1.44 Prover 3: Preprocessing ...
% 10.91/2.25 Prover 1: Warning: ignoring some quantifiers
% 11.61/2.30 Prover 3: Warning: ignoring some quantifiers
% 11.61/2.35 Prover 1: Constructing countermodel ...
% 11.61/2.36 Prover 3: Constructing countermodel ...
% 11.61/2.37 Prover 6: Proving ...
% 12.42/2.42 Prover 4: Warning: ignoring some quantifiers
% 13.35/2.55 Prover 0: Proving ...
% 13.35/2.56 Prover 4: Constructing countermodel ...
% 13.35/2.57 Prover 5: Proving ...
% 14.10/2.72 Prover 2: Proving ...
% 17.22/3.09 Prover 3: proved (2464ms)
% 17.22/3.09
% 17.22/3.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.22/3.09
% 17.22/3.09 Prover 6: stopped
% 17.22/3.09 Prover 0: stopped
% 17.22/3.09 Prover 2: stopped
% 17.22/3.09 Prover 5: stopped
% 17.69/3.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.69/3.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 17.69/3.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.69/3.13 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 17.69/3.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 19.20/3.30 Prover 8: Preprocessing ...
% 19.20/3.31 Prover 11: Preprocessing ...
% 19.20/3.31 Prover 10: Preprocessing ...
% 19.20/3.32 Prover 7: Preprocessing ...
% 19.20/3.33 Prover 13: Preprocessing ...
% 19.50/3.38 Prover 1: Found proof (size 44)
% 19.50/3.38 Prover 1: proved (2760ms)
% 19.50/3.39 Prover 4: stopped
% 19.50/3.43 Prover 10: stopped
% 19.50/3.43 Prover 7: stopped
% 20.26/3.45 Prover 11: stopped
% 20.26/3.47 Prover 13: stopped
% 20.87/3.56 Prover 8: Warning: ignoring some quantifiers
% 20.87/3.58 Prover 8: Constructing countermodel ...
% 20.87/3.59 Prover 8: stopped
% 20.87/3.59
% 20.87/3.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.87/3.59
% 20.87/3.60 % SZS output start Proof for theBenchmark
% 20.87/3.60 Assumptions after simplification:
% 20.87/3.60 ---------------------------------
% 20.87/3.60
% 20.87/3.60 (cl5_nebula_norm_0007)
% 20.87/3.64 $i(q) & $i(n135299) & $i(pv47) & $i(pv84) & $i(tptp_pi) & $i(rho) & $i(sigma)
% 20.87/3.64 & $i(tptp_minus_2) & $i(tptp_sum_index) & $i(mu) & $i(pv10) & $i(x) & $i(n4) &
% 20.87/3.64 $i(n2) & $i(n1) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 20.87/3.64 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 20.87/3.64 ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ?
% 20.87/3.64 [v14: $i] : ? [v15: $i] : ? [v16: $i] : (sqrt(v11) = v12 & exp(v7) = v8 &
% 20.87/3.64 times(v12, v5) = v13 & times(v8, v9) = v10 & times(v5, v5) = v6 & times(v2,
% 20.87/3.64 v2) = v3 & times(n2, tptp_pi) = v11 & divide(v10, v13) = v14 & divide(v4,
% 20.87/3.64 v6) = v7 & divide(v3, tptp_minus_2) = v4 & minus(v0, v1) = v2 & sum(n0,
% 20.87/3.64 n4, v14) = pv84 & a_select2(rho, tptp_sum_index) = v9 & a_select2(sigma,
% 20.87/3.64 tptp_sum_index) = v5 & a_select2(mu, tptp_sum_index) = v1 & a_select2(x,
% 20.87/3.64 pv10) = v0 & pred(pv47) = v15 & pred(pv10) = v16 & leq(pv47, n4) = 0 &
% 20.87/3.64 leq(pv10, n135299) = 0 & leq(n0, pv47) = 0 & leq(n0, pv10) = 0 & $i(v16) &
% 20.87/3.64 $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8)
% 20.87/3.64 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & !
% 20.87/3.65 [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : !
% 20.87/3.65 [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : !
% 20.87/3.65 [v27: $i] : ! [v28: $i] : ! [v29: $i] : ( ~ (exp(v24) = v25) | ~
% 20.87/3.65 (times(v25, v26) = v27) | ~ (times(v22, v22) = v23) | ~ (times(v19, v19)
% 20.87/3.65 = v20) | ~ (times(v12, v22) = v28) | ~ (divide(v27, v28) = v29) | ~
% 20.87/3.65 (divide(v21, v23) = v24) | ~ (divide(v20, tptp_minus_2) = v21) | ~
% 20.87/3.65 (minus(v0, v18) = v19) | ~ (a_select2(rho, v17) = v26) | ~
% 20.87/3.65 (a_select2(sigma, v17) = v22) | ~ (a_select2(mu, v17) = v18) | ~ $i(v17)
% 20.87/3.65 | ? [v30: any] : ? [v31: any] : ? [v32: $i] : ? [v33: $i] :
% 20.87/3.65 (divide(v29, pv84) = v33 & a_select3(q, pv10, v17) = v32 & leq(v17, v15) =
% 20.87/3.65 v31 & leq(n0, v17) = v30 & $i(v33) & $i(v32) & ( ~ (v31 = 0) | ~ (v30 =
% 20.87/3.65 0) | v33 = v32))) & ! [v17: $i] : ! [v18: $i] : ( ~ (a_select3(q,
% 20.87/3.65 v17, tptp_sum_index) = v18) | ~ $i(v17) | ? [v19: any] : ? [v20:
% 20.87/3.65 any] : ? [v21: $i] : (sum(n0, n4, v18) = v21 & leq(v17, v16) = v20 &
% 20.87/3.65 leq(n0, v17) = v19 & $i(v21) & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 =
% 20.87/3.65 n1))) & ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ?
% 20.87/3.65 [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? [v24: $i] : ? [v25: $i] : ?
% 20.87/3.65 [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ?
% 20.87/3.65 [v31: $i] : ( ~ (v31 = v18) & ~ (v17 = pv47) & exp(v25) = v26 & times(v26,
% 20.87/3.65 v27) = v28 & times(v23, v23) = v24 & times(v20, v20) = v21 & times(v12,
% 20.87/3.65 v23) = v29 & divide(v30, pv84) = v31 & divide(v28, v29) = v30 &
% 20.87/3.65 divide(v22, v24) = v25 & divide(v21, tptp_minus_2) = v22 & minus(v0, v19)
% 20.87/3.65 = v20 & a_select3(q, pv10, v17) = v18 & a_select2(rho, v17) = v27 &
% 20.87/3.65 a_select2(sigma, v17) = v23 & a_select2(mu, v17) = v19 & leq(v17, pv47) =
% 20.87/3.65 0 & leq(n0, v17) = 0 & $i(v31) & $i(v30) & $i(v29) & $i(v28) & $i(v27) &
% 20.87/3.65 $i(v26) & $i(v25) & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) &
% 20.87/3.65 $i(v19) & $i(v18) & $i(v17)))
% 20.87/3.65
% 20.87/3.65 (leq_gt2)
% 20.87/3.65 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (gt(v1, v0)
% 20.87/3.65 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1)
% 20.87/3.65 = v3))
% 20.87/3.65
% 20.87/3.65 (leq_gt_pred)
% 20.87/3.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 20.87/3.65 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 20.87/3.65 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : !
% 20.87/3.65 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)
% 20.87/3.65 | gt(v1, v0) = 0)
% 20.87/3.65
% 20.87/3.65 (function-axioms)
% 20.87/3.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 20.87/3.66 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 20.87/3.66 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 20.87/3.66 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 20.87/3.66 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 20.87/3.66 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 20.87/3.66 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 20.87/3.66 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 20.87/3.66 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 20.87/3.66 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 20.87/3.66 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 20.87/3.66 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (times(v3, v2) = v1) | ~ (times(v3,
% 20.87/3.66 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 20.87/3.66 = v0 | ~ (divide(v3, v2) = v1) | ~ (divide(v3, v2) = v0)) & ! [v0: $i] :
% 20.87/3.66 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) |
% 20.87/3.66 ~ (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 20.87/3.66 $i] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0:
% 20.87/3.66 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3,
% 20.87/3.66 v2) = v1) | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 20.87/3.66 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~
% 20.87/3.66 (tptp_msub(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 20.87/3.66 [v3: $i] : (v1 = v0 | ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) =
% 20.87/3.66 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 20.87/3.66 ~ (dim(v3, v2) = v1) | ~ (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 20.87/3.66 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~
% 20.87/3.66 (tptp_const_array1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 20.87/3.66 : ! [v3: $i] : (v1 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2)
% 20.87/3.66 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 20.87/3.66 | ~ (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) &
% 20.87/3.66 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 20.87/3.66 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 20.87/3.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 20.87/3.66 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 20.87/3.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 20.87/3.66 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 20.87/3.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 20.87/3.66 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 20.87/3.66 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sqrt(v2) = v1) | ~ (sqrt(v2) = v0)) &
% 20.87/3.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (exp(v2) = v1) | ~
% 20.87/3.66 (exp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 20.87/3.66 (inv(v2) = v1) | ~ (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 20.87/3.66 $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] :
% 20.87/3.66 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 20.87/3.66 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~
% 20.87/3.66 (pred(v2) = v0))
% 20.87/3.66
% 20.87/3.66 Further assumptions not needed in the proof:
% 20.87/3.66 --------------------------------------------
% 21.35/3.66 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 21.35/3.66 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 21.35/3.66 finite_domain_5, gt_0_tptp_minus_1, gt_0_tptp_minus_2, gt_135299_0, gt_135299_1,
% 21.35/3.66 gt_135299_2, gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1,
% 21.35/3.66 gt_135299_tptp_minus_2, gt_1_0, gt_1_tptp_minus_1, gt_1_tptp_minus_2, gt_2_0,
% 21.35/3.66 gt_2_1, gt_2_tptp_minus_1, gt_2_tptp_minus_2, gt_3_0, gt_3_1, gt_3_2,
% 21.35/3.66 gt_3_tptp_minus_1, gt_3_tptp_minus_2, gt_4_0, gt_4_1, gt_4_2, gt_4_3,
% 21.35/3.66 gt_4_tptp_minus_1, gt_4_tptp_minus_2, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4,
% 21.35/3.66 gt_5_tptp_minus_1, gt_5_tptp_minus_2, gt_succ, gt_tptp_minus_1_tptp_minus_2,
% 21.35/3.66 irreflexivity_gt, leq_geq, leq_gt1, leq_minus, leq_succ, leq_succ_gt,
% 21.35/3.66 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 21.35/3.66 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 21.35/3.66 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 21.35/3.66 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 21.35/3.66 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 21.35/3.66 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 21.35/3.66 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 21.35/3.66 successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 21.35/3.66 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 21.35/3.66 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 21.35/3.66
% 21.35/3.66 Those formulas are unsatisfiable:
% 21.35/3.66 ---------------------------------
% 21.35/3.66
% 21.35/3.66 Begin of proof
% 21.35/3.66 |
% 21.35/3.66 | ALPHA: (leq_gt_pred) implies:
% 21.35/3.66 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 21.35/3.66 | (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 21.35/3.66 | [v4: int] : ( ~ (v4 = 0) & gt(v1, v0) = v4))
% 21.35/3.66 |
% 21.35/3.66 | ALPHA: (cl5_nebula_norm_0007) implies:
% 21.35/3.66 | (2) $i(pv47)
% 21.35/3.67 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 21.35/3.67 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 21.35/3.67 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 21.35/3.67 | ? [v15: $i] : ? [v16: $i] : (sqrt(v11) = v12 & exp(v7) = v8 &
% 21.35/3.67 | times(v12, v5) = v13 & times(v8, v9) = v10 & times(v5, v5) = v6 &
% 21.35/3.67 | times(v2, v2) = v3 & times(n2, tptp_pi) = v11 & divide(v10, v13) =
% 21.35/3.67 | v14 & divide(v4, v6) = v7 & divide(v3, tptp_minus_2) = v4 & minus(v0,
% 21.35/3.67 | v1) = v2 & sum(n0, n4, v14) = pv84 & a_select2(rho, tptp_sum_index)
% 21.35/3.67 | = v9 & a_select2(sigma, tptp_sum_index) = v5 & a_select2(mu,
% 21.35/3.67 | tptp_sum_index) = v1 & a_select2(x, pv10) = v0 & pred(pv47) = v15 &
% 21.35/3.67 | pred(pv10) = v16 & leq(pv47, n4) = 0 & leq(pv10, n135299) = 0 &
% 21.35/3.67 | leq(n0, pv47) = 0 & leq(n0, pv10) = 0 & $i(v16) & $i(v15) & $i(v14) &
% 21.35/3.67 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 21.35/3.67 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & !
% 21.35/3.67 | [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i]
% 21.35/3.67 | : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : !
% 21.35/3.67 | [v26: $i] : ! [v27: $i] : ! [v28: $i] : ! [v29: $i] : ( ~
% 21.35/3.67 | (exp(v24) = v25) | ~ (times(v25, v26) = v27) | ~ (times(v22, v22)
% 21.35/3.67 | = v23) | ~ (times(v19, v19) = v20) | ~ (times(v12, v22) = v28)
% 21.35/3.67 | | ~ (divide(v27, v28) = v29) | ~ (divide(v21, v23) = v24) | ~
% 21.35/3.67 | (divide(v20, tptp_minus_2) = v21) | ~ (minus(v0, v18) = v19) | ~
% 21.35/3.67 | (a_select2(rho, v17) = v26) | ~ (a_select2(sigma, v17) = v22) | ~
% 21.35/3.67 | (a_select2(mu, v17) = v18) | ~ $i(v17) | ? [v30: any] : ? [v31:
% 21.35/3.67 | any] : ? [v32: $i] : ? [v33: $i] : (divide(v29, pv84) = v33 &
% 21.35/3.67 | a_select3(q, pv10, v17) = v32 & leq(v17, v15) = v31 & leq(n0,
% 21.35/3.67 | v17) = v30 & $i(v33) & $i(v32) & ( ~ (v31 = 0) | ~ (v30 = 0) |
% 21.35/3.67 | v33 = v32))) & ! [v17: $i] : ! [v18: $i] : ( ~ (a_select3(q,
% 21.35/3.67 | v17, tptp_sum_index) = v18) | ~ $i(v17) | ? [v19: any] : ?
% 21.35/3.67 | [v20: any] : ? [v21: $i] : (sum(n0, n4, v18) = v21 & leq(v17, v16)
% 21.35/3.67 | = v20 & leq(n0, v17) = v19 & $i(v21) & ( ~ (v20 = 0) | ~ (v19 =
% 21.35/3.67 | 0) | v21 = n1))) & ? [v17: $i] : ? [v18: $i] : ? [v19: $i]
% 21.35/3.67 | : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ?
% 21.35/3.67 | [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i]
% 21.35/3.67 | : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ( ~ (v31 = v18) & ~
% 21.35/3.67 | (v17 = pv47) & exp(v25) = v26 & times(v26, v27) = v28 & times(v23,
% 21.35/3.67 | v23) = v24 & times(v20, v20) = v21 & times(v12, v23) = v29 &
% 21.35/3.67 | divide(v30, pv84) = v31 & divide(v28, v29) = v30 & divide(v22, v24)
% 21.35/3.67 | = v25 & divide(v21, tptp_minus_2) = v22 & minus(v0, v19) = v20 &
% 21.35/3.67 | a_select3(q, pv10, v17) = v18 & a_select2(rho, v17) = v27 &
% 21.35/3.67 | a_select2(sigma, v17) = v23 & a_select2(mu, v17) = v19 & leq(v17,
% 21.35/3.67 | pv47) = 0 & leq(n0, v17) = 0 & $i(v31) & $i(v30) & $i(v29) &
% 21.35/3.67 | $i(v28) & $i(v27) & $i(v26) & $i(v25) & $i(v24) & $i(v23) & $i(v22)
% 21.35/3.67 | & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17)))
% 21.35/3.67 |
% 21.35/3.67 | ALPHA: (function-axioms) implies:
% 21.35/3.67 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.35/3.67 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 21.35/3.67 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.35/3.67 | (divide(v3, v2) = v1) | ~ (divide(v3, v2) = v0))
% 21.35/3.67 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 21.35/3.67 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2)
% 21.35/3.67 | = v0))
% 21.35/3.67 |
% 21.35/3.67 | DELTA: instantiating (3) with fresh symbols all_76_0, all_76_1, all_76_2,
% 21.35/3.67 | all_76_3, all_76_4, all_76_5, all_76_6, all_76_7, all_76_8, all_76_9,
% 21.35/3.67 | all_76_10, all_76_11, all_76_12, all_76_13, all_76_14, all_76_15,
% 21.35/3.67 | all_76_16 gives:
% 21.35/3.68 | (7) sqrt(all_76_5) = all_76_4 & exp(all_76_9) = all_76_8 & times(all_76_4,
% 21.35/3.68 | all_76_11) = all_76_3 & times(all_76_8, all_76_7) = all_76_6 &
% 21.35/3.68 | times(all_76_11, all_76_11) = all_76_10 & times(all_76_14, all_76_14) =
% 21.35/3.68 | all_76_13 & times(n2, tptp_pi) = all_76_5 & divide(all_76_6, all_76_3)
% 21.35/3.68 | = all_76_2 & divide(all_76_12, all_76_10) = all_76_9 &
% 21.35/3.68 | divide(all_76_13, tptp_minus_2) = all_76_12 & minus(all_76_16,
% 21.35/3.68 | all_76_15) = all_76_14 & sum(n0, n4, all_76_2) = pv84 &
% 21.35/3.68 | a_select2(rho, tptp_sum_index) = all_76_7 & a_select2(sigma,
% 21.35/3.68 | tptp_sum_index) = all_76_11 & a_select2(mu, tptp_sum_index) =
% 21.35/3.68 | all_76_15 & a_select2(x, pv10) = all_76_16 & pred(pv47) = all_76_1 &
% 21.35/3.68 | pred(pv10) = all_76_0 & leq(pv47, n4) = 0 & leq(pv10, n135299) = 0 &
% 21.35/3.68 | leq(n0, pv47) = 0 & leq(n0, pv10) = 0 & $i(all_76_0) & $i(all_76_1) &
% 21.35/3.68 | $i(all_76_2) & $i(all_76_3) & $i(all_76_4) & $i(all_76_5) &
% 21.35/3.68 | $i(all_76_6) & $i(all_76_7) & $i(all_76_8) & $i(all_76_9) &
% 21.35/3.68 | $i(all_76_10) & $i(all_76_11) & $i(all_76_12) & $i(all_76_13) &
% 21.35/3.68 | $i(all_76_14) & $i(all_76_15) & $i(all_76_16) & ! [v0: $i] : ! [v1:
% 21.35/3.68 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 21.35/3.68 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : !
% 21.35/3.68 | [v11: $i] : ! [v12: $i] : ( ~ (exp(v7) = v8) | ~ (times(v8, v9) =
% 21.35/3.68 | v10) | ~ (times(v5, v5) = v6) | ~ (times(v2, v2) = v3) | ~
% 21.35/3.68 | (times(all_76_4, v5) = v11) | ~ (divide(v10, v11) = v12) | ~
% 21.35/3.68 | (divide(v4, v6) = v7) | ~ (divide(v3, tptp_minus_2) = v4) | ~
% 21.35/3.68 | (minus(all_76_16, v1) = v2) | ~ (a_select2(rho, v0) = v9) | ~
% 21.35/3.68 | (a_select2(sigma, v0) = v5) | ~ (a_select2(mu, v0) = v1) | ~ $i(v0)
% 21.35/3.68 | | ? [v13: any] : ? [v14: any] : ? [v15: $i] : ? [v16: $i] :
% 21.35/3.68 | (divide(v12, pv84) = v16 & a_select3(q, pv10, v0) = v15 & leq(v0,
% 21.35/3.68 | all_76_1) = v14 & leq(n0, v0) = v13 & $i(v16) & $i(v15) & ( ~
% 21.35/3.68 | (v14 = 0) | ~ (v13 = 0) | v16 = v15))) & ! [v0: $i] : ! [v1:
% 21.35/3.68 | $i] : ( ~ (a_select3(q, v0, tptp_sum_index) = v1) | ~ $i(v0) | ?
% 21.35/3.68 | [v2: any] : ? [v3: any] : ? [v4: $i] : (sum(n0, n4, v1) = v4 &
% 21.35/3.68 | leq(v0, all_76_0) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) |
% 21.35/3.68 | ~ (v2 = 0) | v4 = n1))) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 21.35/3.68 | $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 21.35/3.68 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ?
% 21.35/3.68 | [v12: $i] : ? [v13: $i] : ? [v14: $i] : ( ~ (v14 = v1) & ~ (v0 =
% 21.35/3.68 | pv47) & exp(v8) = v9 & times(v9, v10) = v11 & times(v6, v6) = v7 &
% 21.35/3.68 | times(v3, v3) = v4 & times(all_76_4, v6) = v12 & divide(v13, pv84) =
% 21.35/3.68 | v14 & divide(v11, v12) = v13 & divide(v5, v7) = v8 & divide(v4,
% 21.35/3.68 | tptp_minus_2) = v5 & minus(all_76_16, v2) = v3 & a_select3(q, pv10,
% 21.35/3.68 | v0) = v1 & a_select2(rho, v0) = v10 & a_select2(sigma, v0) = v6 &
% 21.35/3.68 | a_select2(mu, v0) = v2 & leq(v0, pv47) = 0 & leq(n0, v0) = 0 &
% 21.35/3.68 | $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) &
% 21.35/3.68 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 21.35/3.68 | $i(v0))
% 21.35/3.68 |
% 21.35/3.68 | ALPHA: (7) implies:
% 21.35/3.68 | (8) pred(pv47) = all_76_1
% 21.35/3.68 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 21.35/3.68 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 21.35/3.68 | [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ (exp(v7) = v8) | ~
% 21.35/3.68 | (times(v8, v9) = v10) | ~ (times(v5, v5) = v6) | ~ (times(v2, v2) =
% 21.35/3.68 | v3) | ~ (times(all_76_4, v5) = v11) | ~ (divide(v10, v11) = v12)
% 21.35/3.68 | | ~ (divide(v4, v6) = v7) | ~ (divide(v3, tptp_minus_2) = v4) | ~
% 21.35/3.68 | (minus(all_76_16, v1) = v2) | ~ (a_select2(rho, v0) = v9) | ~
% 21.35/3.68 | (a_select2(sigma, v0) = v5) | ~ (a_select2(mu, v0) = v1) | ~ $i(v0)
% 21.35/3.68 | | ? [v13: any] : ? [v14: any] : ? [v15: $i] : ? [v16: $i] :
% 21.35/3.68 | (divide(v12, pv84) = v16 & a_select3(q, pv10, v0) = v15 & leq(v0,
% 21.35/3.68 | all_76_1) = v14 & leq(n0, v0) = v13 & $i(v16) & $i(v15) & ( ~
% 21.35/3.68 | (v14 = 0) | ~ (v13 = 0) | v16 = v15)))
% 21.35/3.68 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 21.35/3.68 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 21.35/3.68 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 21.35/3.68 | $i] : ( ~ (v14 = v1) & ~ (v0 = pv47) & exp(v8) = v9 & times(v9,
% 21.35/3.68 | v10) = v11 & times(v6, v6) = v7 & times(v3, v3) = v4 &
% 21.35/3.68 | times(all_76_4, v6) = v12 & divide(v13, pv84) = v14 & divide(v11,
% 21.35/3.68 | v12) = v13 & divide(v5, v7) = v8 & divide(v4, tptp_minus_2) = v5 &
% 21.35/3.68 | minus(all_76_16, v2) = v3 & a_select3(q, pv10, v0) = v1 &
% 21.35/3.68 | a_select2(rho, v0) = v10 & a_select2(sigma, v0) = v6 & a_select2(mu,
% 21.35/3.68 | v0) = v2 & leq(v0, pv47) = 0 & leq(n0, v0) = 0 & $i(v14) & $i(v13)
% 21.35/3.68 | & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 21.35/3.68 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 21.35/3.68 |
% 21.35/3.68 | DELTA: instantiating (10) with fresh symbols all_79_0, all_79_1, all_79_2,
% 21.35/3.68 | all_79_3, all_79_4, all_79_5, all_79_6, all_79_7, all_79_8, all_79_9,
% 21.35/3.68 | all_79_10, all_79_11, all_79_12, all_79_13, all_79_14 gives:
% 21.35/3.69 | (11) ~ (all_79_0 = all_79_13) & ~ (all_79_14 = pv47) & exp(all_79_6) =
% 21.35/3.69 | all_79_5 & times(all_79_5, all_79_4) = all_79_3 & times(all_79_8,
% 21.35/3.69 | all_79_8) = all_79_7 & times(all_79_11, all_79_11) = all_79_10 &
% 21.35/3.69 | times(all_76_4, all_79_8) = all_79_2 & divide(all_79_1, pv84) =
% 21.35/3.69 | all_79_0 & divide(all_79_3, all_79_2) = all_79_1 & divide(all_79_9,
% 21.35/3.69 | all_79_7) = all_79_6 & divide(all_79_10, tptp_minus_2) = all_79_9 &
% 21.35/3.69 | minus(all_76_16, all_79_12) = all_79_11 & a_select3(q, pv10,
% 21.35/3.69 | all_79_14) = all_79_13 & a_select2(rho, all_79_14) = all_79_4 &
% 21.35/3.69 | a_select2(sigma, all_79_14) = all_79_8 & a_select2(mu, all_79_14) =
% 21.35/3.69 | all_79_12 & leq(all_79_14, pv47) = 0 & leq(n0, all_79_14) = 0 &
% 21.35/3.69 | $i(all_79_0) & $i(all_79_1) & $i(all_79_2) & $i(all_79_3) &
% 21.35/3.69 | $i(all_79_4) & $i(all_79_5) & $i(all_79_6) & $i(all_79_7) &
% 21.35/3.69 | $i(all_79_8) & $i(all_79_9) & $i(all_79_10) & $i(all_79_11) &
% 21.35/3.69 | $i(all_79_12) & $i(all_79_13) & $i(all_79_14)
% 21.35/3.69 |
% 21.35/3.69 | ALPHA: (11) implies:
% 21.35/3.69 | (12) ~ (all_79_14 = pv47)
% 21.35/3.69 | (13) ~ (all_79_0 = all_79_13)
% 21.35/3.69 | (14) $i(all_79_14)
% 21.35/3.69 | (15) leq(n0, all_79_14) = 0
% 21.35/3.69 | (16) leq(all_79_14, pv47) = 0
% 21.35/3.69 | (17) a_select2(mu, all_79_14) = all_79_12
% 21.35/3.69 | (18) a_select2(sigma, all_79_14) = all_79_8
% 21.35/3.69 | (19) a_select2(rho, all_79_14) = all_79_4
% 21.35/3.69 | (20) a_select3(q, pv10, all_79_14) = all_79_13
% 21.35/3.69 | (21) minus(all_76_16, all_79_12) = all_79_11
% 21.35/3.69 | (22) divide(all_79_10, tptp_minus_2) = all_79_9
% 21.35/3.69 | (23) divide(all_79_9, all_79_7) = all_79_6
% 21.35/3.69 | (24) divide(all_79_3, all_79_2) = all_79_1
% 21.35/3.69 | (25) divide(all_79_1, pv84) = all_79_0
% 21.35/3.69 | (26) times(all_76_4, all_79_8) = all_79_2
% 21.35/3.69 | (27) times(all_79_11, all_79_11) = all_79_10
% 21.35/3.69 | (28) times(all_79_8, all_79_8) = all_79_7
% 21.35/3.69 | (29) times(all_79_5, all_79_4) = all_79_3
% 21.35/3.69 | (30) exp(all_79_6) = all_79_5
% 21.35/3.69 |
% 21.35/3.69 | GROUND_INST: instantiating (9) with all_79_14, all_79_12, all_79_11,
% 21.35/3.69 | all_79_10, all_79_9, all_79_8, all_79_7, all_79_6, all_79_5,
% 21.35/3.69 | all_79_4, all_79_3, all_79_2, all_79_1, simplifying with (14),
% 21.35/3.69 | (17), (18), (19), (21), (22), (23), (24), (26), (27), (28), (29),
% 21.35/3.69 | (30) gives:
% 21.35/3.69 | (31) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 21.35/3.69 | (divide(all_79_1, pv84) = v3 & a_select3(q, pv10, all_79_14) = v2 &
% 21.35/3.69 | leq(all_79_14, all_76_1) = v1 & leq(n0, all_79_14) = v0 & $i(v3) &
% 21.35/3.69 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = v2))
% 21.35/3.69 |
% 21.35/3.69 | DELTA: instantiating (31) with fresh symbols all_103_0, all_103_1, all_103_2,
% 21.35/3.69 | all_103_3 gives:
% 21.35/3.69 | (32) divide(all_79_1, pv84) = all_103_0 & a_select3(q, pv10, all_79_14) =
% 21.35/3.69 | all_103_1 & leq(all_79_14, all_76_1) = all_103_2 & leq(n0, all_79_14)
% 21.35/3.69 | = all_103_3 & $i(all_103_0) & $i(all_103_1) & ( ~ (all_103_2 = 0) | ~
% 21.35/3.69 | (all_103_3 = 0) | all_103_0 = all_103_1)
% 21.35/3.69 |
% 21.35/3.69 | ALPHA: (32) implies:
% 21.35/3.69 | (33) leq(n0, all_79_14) = all_103_3
% 21.35/3.69 | (34) leq(all_79_14, all_76_1) = all_103_2
% 21.35/3.69 | (35) a_select3(q, pv10, all_79_14) = all_103_1
% 21.35/3.69 | (36) divide(all_79_1, pv84) = all_103_0
% 21.35/3.70 | (37) ~ (all_103_2 = 0) | ~ (all_103_3 = 0) | all_103_0 = all_103_1
% 21.35/3.70 |
% 21.35/3.70 | GROUND_INST: instantiating (4) with 0, all_103_3, all_79_14, n0, simplifying
% 21.35/3.70 | with (15), (33) gives:
% 21.35/3.70 | (38) all_103_3 = 0
% 21.35/3.70 |
% 21.54/3.70 | GROUND_INST: instantiating (6) with all_79_13, all_103_1, all_79_14, pv10, q,
% 21.54/3.70 | simplifying with (20), (35) gives:
% 21.54/3.70 | (39) all_103_1 = all_79_13
% 21.54/3.70 |
% 21.54/3.70 | GROUND_INST: instantiating (5) with all_79_0, all_103_0, pv84, all_79_1,
% 21.54/3.70 | simplifying with (25), (36) gives:
% 21.54/3.70 | (40) all_103_0 = all_79_0
% 21.54/3.70 |
% 21.54/3.70 | BETA: splitting (37) gives:
% 21.54/3.70 |
% 21.54/3.70 | Case 1:
% 21.54/3.70 | |
% 21.54/3.70 | | (41) ~ (all_103_2 = 0)
% 21.54/3.70 | |
% 21.54/3.70 | | GROUND_INST: instantiating (1) with all_79_14, pv47, all_76_1, all_103_2,
% 21.54/3.70 | | simplifying with (2), (8), (14), (34) gives:
% 21.54/3.70 | | (42) all_103_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) & gt(pv47, all_79_14) =
% 21.54/3.70 | | v0)
% 21.54/3.70 | |
% 21.54/3.70 | | BETA: splitting (42) gives:
% 21.54/3.70 | |
% 21.54/3.70 | | Case 1:
% 21.54/3.70 | | |
% 21.54/3.70 | | | (43) all_103_2 = 0
% 21.54/3.70 | | |
% 21.54/3.70 | | | REDUCE: (41), (43) imply:
% 21.54/3.70 | | | (44) $false
% 21.54/3.70 | | |
% 21.54/3.70 | | | CLOSE: (44) is inconsistent.
% 21.54/3.70 | | |
% 21.54/3.70 | | Case 2:
% 21.54/3.70 | | |
% 21.54/3.70 | | | (45) ? [v0: int] : ( ~ (v0 = 0) & gt(pv47, all_79_14) = v0)
% 21.54/3.70 | | |
% 21.54/3.70 | | | DELTA: instantiating (45) with fresh symbol all_132_0 gives:
% 21.54/3.70 | | | (46) ~ (all_132_0 = 0) & gt(pv47, all_79_14) = all_132_0
% 21.54/3.70 | | |
% 21.54/3.70 | | | ALPHA: (46) implies:
% 21.54/3.70 | | | (47) ~ (all_132_0 = 0)
% 21.54/3.70 | | | (48) gt(pv47, all_79_14) = all_132_0
% 21.54/3.70 | | |
% 21.54/3.70 | | | GROUND_INST: instantiating (leq_gt2) with all_79_14, pv47, all_132_0,
% 21.54/3.70 | | | simplifying with (2), (14), (48) gives:
% 21.54/3.70 | | | (49) all_132_0 = 0 | all_79_14 = pv47 | ? [v0: int] : ( ~ (v0 = 0) &
% 21.54/3.70 | | | leq(all_79_14, pv47) = v0)
% 21.54/3.70 | | |
% 21.54/3.70 | | | BETA: splitting (49) gives:
% 21.54/3.70 | | |
% 21.54/3.70 | | | Case 1:
% 21.54/3.70 | | | |
% 21.54/3.70 | | | | (50) all_132_0 = 0
% 21.54/3.70 | | | |
% 21.54/3.70 | | | | REDUCE: (47), (50) imply:
% 21.54/3.70 | | | | (51) $false
% 21.54/3.70 | | | |
% 21.54/3.70 | | | | CLOSE: (51) is inconsistent.
% 21.54/3.70 | | | |
% 21.54/3.70 | | | Case 2:
% 21.54/3.70 | | | |
% 21.54/3.70 | | | | (52) all_79_14 = pv47 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_14,
% 21.54/3.70 | | | | pv47) = v0)
% 21.54/3.70 | | | |
% 21.54/3.70 | | | | BETA: splitting (52) gives:
% 21.54/3.70 | | | |
% 21.54/3.70 | | | | Case 1:
% 21.54/3.70 | | | | |
% 21.54/3.70 | | | | | (53) all_79_14 = pv47
% 21.54/3.70 | | | | |
% 21.54/3.70 | | | | | REDUCE: (12), (53) imply:
% 21.54/3.70 | | | | | (54) $false
% 21.54/3.70 | | | | |
% 21.54/3.70 | | | | | CLOSE: (54) is inconsistent.
% 21.54/3.70 | | | | |
% 21.54/3.70 | | | | Case 2:
% 21.54/3.70 | | | | |
% 21.54/3.70 | | | | | (55) ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_14, pv47) = v0)
% 21.54/3.70 | | | | |
% 21.54/3.70 | | | | | DELTA: instantiating (55) with fresh symbol all_167_0 gives:
% 21.54/3.70 | | | | | (56) ~ (all_167_0 = 0) & leq(all_79_14, pv47) = all_167_0
% 21.54/3.70 | | | | |
% 21.54/3.70 | | | | | ALPHA: (56) implies:
% 21.54/3.70 | | | | | (57) ~ (all_167_0 = 0)
% 21.54/3.70 | | | | | (58) leq(all_79_14, pv47) = all_167_0
% 21.54/3.70 | | | | |
% 21.54/3.70 | | | | | GROUND_INST: instantiating (4) with 0, all_167_0, pv47, all_79_14,
% 21.54/3.70 | | | | | simplifying with (16), (58) gives:
% 21.54/3.70 | | | | | (59) all_167_0 = 0
% 21.54/3.70 | | | | |
% 21.54/3.70 | | | | | REDUCE: (57), (59) imply:
% 21.54/3.70 | | | | | (60) $false
% 21.54/3.70 | | | | |
% 21.54/3.70 | | | | | CLOSE: (60) is inconsistent.
% 21.54/3.70 | | | | |
% 21.54/3.70 | | | | End of split
% 21.54/3.70 | | | |
% 21.54/3.70 | | | End of split
% 21.54/3.70 | | |
% 21.54/3.70 | | End of split
% 21.54/3.70 | |
% 21.54/3.70 | Case 2:
% 21.54/3.70 | |
% 21.54/3.70 | | (61) ~ (all_103_3 = 0) | all_103_0 = all_103_1
% 21.54/3.70 | |
% 21.54/3.70 | | BETA: splitting (61) gives:
% 21.54/3.70 | |
% 21.54/3.70 | | Case 1:
% 21.54/3.70 | | |
% 21.54/3.70 | | | (62) ~ (all_103_3 = 0)
% 21.54/3.70 | | |
% 21.54/3.70 | | | REDUCE: (38), (62) imply:
% 21.54/3.70 | | | (63) $false
% 21.54/3.70 | | |
% 21.54/3.70 | | | CLOSE: (63) is inconsistent.
% 21.54/3.70 | | |
% 21.54/3.70 | | Case 2:
% 21.54/3.70 | | |
% 21.54/3.70 | | | (64) all_103_0 = all_103_1
% 21.54/3.70 | | |
% 21.54/3.70 | | | COMBINE_EQS: (40), (64) imply:
% 21.54/3.70 | | | (65) all_103_1 = all_79_0
% 21.54/3.70 | | |
% 21.54/3.70 | | | SIMP: (65) implies:
% 21.54/3.70 | | | (66) all_103_1 = all_79_0
% 21.54/3.70 | | |
% 21.54/3.71 | | | COMBINE_EQS: (39), (66) imply:
% 21.54/3.71 | | | (67) all_79_0 = all_79_13
% 21.54/3.71 | | |
% 21.54/3.71 | | | SIMP: (67) implies:
% 21.54/3.71 | | | (68) all_79_0 = all_79_13
% 21.54/3.71 | | |
% 21.54/3.71 | | | REDUCE: (13), (68) imply:
% 21.54/3.71 | | | (69) $false
% 21.54/3.71 | | |
% 21.54/3.71 | | | CLOSE: (69) is inconsistent.
% 21.54/3.71 | | |
% 21.54/3.71 | | End of split
% 21.54/3.71 | |
% 21.54/3.71 | End of split
% 21.54/3.71 |
% 21.54/3.71 End of proof
% 21.54/3.71 % SZS output end Proof for theBenchmark
% 21.54/3.71
% 21.54/3.71 3106ms
%------------------------------------------------------------------------------