TSTP Solution File: SWV159+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV159+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 : n032.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 22:55:09 EDT 2023
% Result : Theorem 14.06s 2.57s
% Output : Proof 18.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV159+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.06/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.31 % Computer : n032.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Aug 29 10:22:31 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.17/0.56 ________ _____
% 0.17/0.56 ___ __ \_________(_)________________________________
% 0.17/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.56
% 0.17/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.56 (2023-06-19)
% 0.17/0.56
% 0.17/0.56 (c) Philipp Rümmer, 2009-2023
% 0.17/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.56 Amanda Stjerna.
% 0.17/0.56 Free software under BSD-3-Clause.
% 0.17/0.56
% 0.17/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.56
% 0.17/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.58 Running up to 7 provers in parallel.
% 0.17/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.17/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 4.14/1.30 Prover 1: Preprocessing ...
% 4.14/1.30 Prover 4: Preprocessing ...
% 4.89/1.34 Prover 5: Preprocessing ...
% 4.89/1.34 Prover 6: Preprocessing ...
% 4.89/1.34 Prover 0: Preprocessing ...
% 4.89/1.34 Prover 3: Preprocessing ...
% 4.89/1.34 Prover 2: Preprocessing ...
% 10.97/2.11 Prover 1: Warning: ignoring some quantifiers
% 11.23/2.13 Prover 3: Warning: ignoring some quantifiers
% 11.23/2.17 Prover 6: Proving ...
% 11.23/2.18 Prover 1: Constructing countermodel ...
% 11.23/2.18 Prover 3: Constructing countermodel ...
% 12.00/2.25 Prover 4: Warning: ignoring some quantifiers
% 12.00/2.29 Prover 5: Proving ...
% 12.50/2.31 Prover 4: Constructing countermodel ...
% 13.01/2.38 Prover 2: Proving ...
% 13.01/2.38 Prover 0: Proving ...
% 14.06/2.57 Prover 3: proved (1980ms)
% 14.06/2.57
% 14.06/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.06/2.57
% 14.06/2.57 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.06/2.57 Prover 5: stopped
% 14.06/2.59 Prover 6: stopped
% 14.06/2.59 Prover 2: stopped
% 14.62/2.59 Prover 0: stopped
% 14.62/2.60 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.62/2.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.62/2.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.62/2.60 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.54/2.74 Prover 1: Found proof (size 21)
% 15.54/2.74 Prover 1: proved (2160ms)
% 16.06/2.76 Prover 4: stopped
% 16.09/2.77 Prover 11: Preprocessing ...
% 16.09/2.78 Prover 7: Preprocessing ...
% 16.09/2.79 Prover 8: Preprocessing ...
% 16.41/2.81 Prover 10: Preprocessing ...
% 16.41/2.81 Prover 13: Preprocessing ...
% 16.69/2.86 Prover 7: stopped
% 16.69/2.87 Prover 10: stopped
% 16.69/2.87 Prover 11: stopped
% 16.69/2.91 Prover 13: stopped
% 17.26/2.97 Prover 8: Warning: ignoring some quantifiers
% 17.26/2.99 Prover 8: Constructing countermodel ...
% 17.55/2.99 Prover 8: stopped
% 17.55/2.99
% 17.55/2.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.55/2.99
% 17.55/3.00 % SZS output start Proof for theBenchmark
% 17.55/3.01 Assumptions after simplification:
% 17.55/3.01 ---------------------------------
% 17.55/3.01
% 17.55/3.01 (cl5_nebula_norm_0009)
% 17.87/3.07 $i(q) & $i(n135299) & $i(pv47) & $i(pv84) & $i(tptp_pi) & $i(rho) & $i(sigma)
% 17.87/3.07 & $i(tptp_minus_2) & $i(tptp_sum_index) & $i(mu) & $i(pv10) & $i(x) & $i(n4) &
% 17.87/3.07 $i(n2) & $i(n1) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 17.87/3.07 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 17.87/3.07 ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ?
% 17.87/3.07 [v14: $i] : ? [v15: $i] : ? [v16: $i] : (sqrt(v11) = v12 & exp(v7) = v8 &
% 17.87/3.07 times(v12, v5) = v13 & times(v8, v9) = v10 & times(v5, v5) = v6 & times(v2,
% 17.87/3.07 v2) = v3 & times(n2, tptp_pi) = v11 & divide(v10, v13) = v14 & divide(v4,
% 17.87/3.07 v6) = v7 & divide(v3, tptp_minus_2) = v4 & minus(v0, v1) = v2 & sum(n0,
% 17.87/3.07 n4, v14) = pv84 & a_select2(rho, tptp_sum_index) = v9 & a_select2(sigma,
% 17.87/3.07 tptp_sum_index) = v5 & a_select2(mu, tptp_sum_index) = v1 & a_select2(x,
% 17.87/3.07 pv10) = v0 & pred(pv47) = v15 & pred(pv10) = v16 & leq(pv47, n4) = 0 &
% 17.87/3.07 leq(pv10, n135299) = 0 & leq(n0, pv47) = 0 & leq(n0, pv10) = 0 & $i(v16) &
% 17.87/3.07 $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8)
% 17.87/3.07 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & !
% 17.87/3.07 [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : !
% 17.87/3.07 [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : !
% 17.87/3.07 [v27: $i] : ! [v28: $i] : ! [v29: $i] : ( ~ (exp(v24) = v25) | ~
% 17.87/3.07 (times(v25, v26) = v27) | ~ (times(v22, v22) = v23) | ~ (times(v19, v19)
% 17.87/3.07 = v20) | ~ (times(v12, v22) = v28) | ~ (divide(v27, v28) = v29) | ~
% 17.87/3.07 (divide(v21, v23) = v24) | ~ (divide(v20, tptp_minus_2) = v21) | ~
% 17.87/3.07 (minus(v0, v18) = v19) | ~ (a_select2(rho, v17) = v26) | ~
% 17.87/3.07 (a_select2(sigma, v17) = v22) | ~ (a_select2(mu, v17) = v18) | ~ $i(v17)
% 17.87/3.07 | ? [v30: any] : ? [v31: any] : ? [v32: $i] : ? [v33: $i] :
% 17.87/3.07 (divide(v29, pv84) = v33 & a_select3(q, pv10, v17) = v32 & leq(v17, v15) =
% 17.87/3.07 v31 & leq(n0, v17) = v30 & $i(v33) & $i(v32) & ( ~ (v31 = 0) | ~ (v30 =
% 17.87/3.07 0) | v33 = v32))) & ! [v17: $i] : ! [v18: $i] : ( ~ (a_select3(q,
% 17.87/3.07 v17, tptp_sum_index) = v18) | ~ $i(v17) | ? [v19: any] : ? [v20:
% 17.87/3.07 any] : ? [v21: $i] : (sum(n0, n4, v18) = v21 & leq(v17, v16) = v20 &
% 17.87/3.07 leq(n0, v17) = v19 & $i(v21) & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 =
% 17.87/3.07 n1))) & ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ( ~ (v19 = n1) &
% 17.87/3.07 ~ (v17 = pv10) & sum(n0, n4, v18) = v19 & a_select3(q, v17,
% 17.87/3.07 tptp_sum_index) = v18 & leq(v17, v16) = 0 & leq(n0, v17) = 0 & $i(v19) &
% 17.87/3.07 $i(v18) & $i(v17)))
% 17.87/3.07
% 17.87/3.07 (function-axioms)
% 17.87/3.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.87/3.08 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 17.87/3.08 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.87/3.08 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 17.87/3.08 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.87/3.08 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 17.87/3.08 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.87/3.08 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 17.87/3.08 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.87/3.08 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 17.87/3.08 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.87/3.08 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (times(v3, v2) = v1) | ~ (times(v3,
% 17.87/3.08 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.87/3.08 = v0 | ~ (divide(v3, v2) = v1) | ~ (divide(v3, v2) = v0)) & ! [v0: $i] :
% 17.87/3.08 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) |
% 17.87/3.08 ~ (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 17.87/3.08 $i] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0:
% 17.87/3.08 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3,
% 17.87/3.08 v2) = v1) | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 17.87/3.08 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~
% 17.87/3.08 (tptp_msub(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.87/3.08 [v3: $i] : (v1 = v0 | ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) =
% 17.87/3.08 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 17.87/3.08 ~ (dim(v3, v2) = v1) | ~ (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 17.87/3.08 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~
% 17.87/3.08 (tptp_const_array1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 17.87/3.08 : ! [v3: $i] : (v1 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2)
% 17.87/3.08 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 17.87/3.08 | ~ (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) &
% 17.87/3.08 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.87/3.08 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 17.87/3.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.87/3.08 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 17.87/3.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.87/3.08 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 17.87/3.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.87/3.08 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 17.87/3.08 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sqrt(v2) = v1) | ~ (sqrt(v2) = v0)) &
% 17.87/3.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (exp(v2) = v1) | ~
% 17.87/3.08 (exp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.87/3.08 (inv(v2) = v1) | ~ (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.87/3.08 $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] :
% 17.87/3.08 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 17.87/3.08 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~
% 17.87/3.08 (pred(v2) = v0))
% 17.87/3.08
% 17.87/3.08 Further assumptions not needed in the proof:
% 17.87/3.08 --------------------------------------------
% 17.87/3.08 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 17.87/3.08 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 17.87/3.08 finite_domain_5, gt_0_tptp_minus_1, gt_0_tptp_minus_2, gt_135299_0, gt_135299_1,
% 17.87/3.08 gt_135299_2, gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1,
% 17.87/3.08 gt_135299_tptp_minus_2, gt_1_0, gt_1_tptp_minus_1, gt_1_tptp_minus_2, gt_2_0,
% 17.87/3.08 gt_2_1, gt_2_tptp_minus_1, gt_2_tptp_minus_2, gt_3_0, gt_3_1, gt_3_2,
% 17.87/3.08 gt_3_tptp_minus_1, gt_3_tptp_minus_2, gt_4_0, gt_4_1, gt_4_2, gt_4_3,
% 17.87/3.08 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,
% 17.87/3.08 gt_5_tptp_minus_1, gt_5_tptp_minus_2, gt_succ, gt_tptp_minus_1_tptp_minus_2,
% 17.87/3.08 irreflexivity_gt, leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ,
% 17.87/3.08 leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1,
% 17.87/3.08 matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update,
% 17.87/3.08 matrix_symm_sub, matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1,
% 17.87/3.08 pred_succ, reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3,
% 17.87/3.08 sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r,
% 17.87/3.08 succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l,
% 17.87/3.08 succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1,
% 17.87/3.08 successor_1, successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 17.87/3.08 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 17.87/3.08 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 17.87/3.08
% 17.87/3.08 Those formulas are unsatisfiable:
% 17.87/3.08 ---------------------------------
% 17.87/3.08
% 17.87/3.08 Begin of proof
% 17.87/3.08 |
% 17.87/3.08 | ALPHA: (cl5_nebula_norm_0009) implies:
% 17.87/3.09 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 17.87/3.09 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 17.87/3.09 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 17.87/3.09 | ? [v15: $i] : ? [v16: $i] : (sqrt(v11) = v12 & exp(v7) = v8 &
% 17.87/3.09 | times(v12, v5) = v13 & times(v8, v9) = v10 & times(v5, v5) = v6 &
% 17.87/3.09 | times(v2, v2) = v3 & times(n2, tptp_pi) = v11 & divide(v10, v13) =
% 17.87/3.09 | v14 & divide(v4, v6) = v7 & divide(v3, tptp_minus_2) = v4 & minus(v0,
% 17.87/3.09 | v1) = v2 & sum(n0, n4, v14) = pv84 & a_select2(rho, tptp_sum_index)
% 17.87/3.09 | = v9 & a_select2(sigma, tptp_sum_index) = v5 & a_select2(mu,
% 17.87/3.09 | tptp_sum_index) = v1 & a_select2(x, pv10) = v0 & pred(pv47) = v15 &
% 17.87/3.09 | pred(pv10) = v16 & leq(pv47, n4) = 0 & leq(pv10, n135299) = 0 &
% 17.87/3.09 | leq(n0, pv47) = 0 & leq(n0, pv10) = 0 & $i(v16) & $i(v15) & $i(v14) &
% 17.87/3.09 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 17.87/3.09 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & !
% 17.87/3.09 | [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i]
% 17.87/3.09 | : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : !
% 17.87/3.09 | [v26: $i] : ! [v27: $i] : ! [v28: $i] : ! [v29: $i] : ( ~
% 17.87/3.09 | (exp(v24) = v25) | ~ (times(v25, v26) = v27) | ~ (times(v22, v22)
% 17.87/3.09 | = v23) | ~ (times(v19, v19) = v20) | ~ (times(v12, v22) = v28)
% 17.87/3.09 | | ~ (divide(v27, v28) = v29) | ~ (divide(v21, v23) = v24) | ~
% 17.87/3.09 | (divide(v20, tptp_minus_2) = v21) | ~ (minus(v0, v18) = v19) | ~
% 17.87/3.09 | (a_select2(rho, v17) = v26) | ~ (a_select2(sigma, v17) = v22) | ~
% 17.87/3.09 | (a_select2(mu, v17) = v18) | ~ $i(v17) | ? [v30: any] : ? [v31:
% 17.87/3.09 | any] : ? [v32: $i] : ? [v33: $i] : (divide(v29, pv84) = v33 &
% 17.87/3.09 | a_select3(q, pv10, v17) = v32 & leq(v17, v15) = v31 & leq(n0,
% 17.87/3.09 | v17) = v30 & $i(v33) & $i(v32) & ( ~ (v31 = 0) | ~ (v30 = 0) |
% 17.87/3.09 | v33 = v32))) & ! [v17: $i] : ! [v18: $i] : ( ~ (a_select3(q,
% 17.87/3.09 | v17, tptp_sum_index) = v18) | ~ $i(v17) | ? [v19: any] : ?
% 17.87/3.09 | [v20: any] : ? [v21: $i] : (sum(n0, n4, v18) = v21 & leq(v17, v16)
% 17.87/3.09 | = v20 & leq(n0, v17) = v19 & $i(v21) & ( ~ (v20 = 0) | ~ (v19 =
% 17.87/3.09 | 0) | v21 = n1))) & ? [v17: $i] : ? [v18: $i] : ? [v19: $i]
% 17.87/3.09 | : ( ~ (v19 = n1) & ~ (v17 = pv10) & sum(n0, n4, v18) = v19 &
% 17.87/3.09 | a_select3(q, v17, tptp_sum_index) = v18 & leq(v17, v16) = 0 &
% 17.87/3.09 | leq(n0, v17) = 0 & $i(v19) & $i(v18) & $i(v17)))
% 17.87/3.09 |
% 17.87/3.09 | ALPHA: (function-axioms) implies:
% 17.87/3.09 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.87/3.09 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 17.87/3.09 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.87/3.09 | (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | ~ (sum(v4, v3, v2) = v0))
% 17.87/3.09 |
% 17.87/3.09 | DELTA: instantiating (1) with fresh symbols all_76_0, all_76_1, all_76_2,
% 17.87/3.09 | all_76_3, all_76_4, all_76_5, all_76_6, all_76_7, all_76_8, all_76_9,
% 17.87/3.09 | all_76_10, all_76_11, all_76_12, all_76_13, all_76_14, all_76_15,
% 17.87/3.09 | all_76_16 gives:
% 17.87/3.10 | (4) sqrt(all_76_5) = all_76_4 & exp(all_76_9) = all_76_8 & times(all_76_4,
% 17.87/3.10 | all_76_11) = all_76_3 & times(all_76_8, all_76_7) = all_76_6 &
% 17.87/3.10 | times(all_76_11, all_76_11) = all_76_10 & times(all_76_14, all_76_14) =
% 17.87/3.10 | all_76_13 & times(n2, tptp_pi) = all_76_5 & divide(all_76_6, all_76_3)
% 17.87/3.10 | = all_76_2 & divide(all_76_12, all_76_10) = all_76_9 &
% 17.87/3.10 | divide(all_76_13, tptp_minus_2) = all_76_12 & minus(all_76_16,
% 17.87/3.10 | all_76_15) = all_76_14 & sum(n0, n4, all_76_2) = pv84 &
% 17.87/3.10 | a_select2(rho, tptp_sum_index) = all_76_7 & a_select2(sigma,
% 17.87/3.10 | tptp_sum_index) = all_76_11 & a_select2(mu, tptp_sum_index) =
% 17.87/3.10 | all_76_15 & a_select2(x, pv10) = all_76_16 & pred(pv47) = all_76_1 &
% 17.87/3.10 | pred(pv10) = all_76_0 & leq(pv47, n4) = 0 & leq(pv10, n135299) = 0 &
% 17.87/3.10 | leq(n0, pv47) = 0 & leq(n0, pv10) = 0 & $i(all_76_0) & $i(all_76_1) &
% 17.87/3.10 | $i(all_76_2) & $i(all_76_3) & $i(all_76_4) & $i(all_76_5) &
% 17.87/3.10 | $i(all_76_6) & $i(all_76_7) & $i(all_76_8) & $i(all_76_9) &
% 17.87/3.10 | $i(all_76_10) & $i(all_76_11) & $i(all_76_12) & $i(all_76_13) &
% 17.87/3.10 | $i(all_76_14) & $i(all_76_15) & $i(all_76_16) & ! [v0: $i] : ! [v1:
% 17.87/3.10 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 17.87/3.10 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : !
% 17.87/3.10 | [v11: $i] : ! [v12: $i] : ( ~ (exp(v7) = v8) | ~ (times(v8, v9) =
% 17.87/3.10 | v10) | ~ (times(v5, v5) = v6) | ~ (times(v2, v2) = v3) | ~
% 17.87/3.10 | (times(all_76_4, v5) = v11) | ~ (divide(v10, v11) = v12) | ~
% 17.87/3.10 | (divide(v4, v6) = v7) | ~ (divide(v3, tptp_minus_2) = v4) | ~
% 17.87/3.10 | (minus(all_76_16, v1) = v2) | ~ (a_select2(rho, v0) = v9) | ~
% 17.87/3.10 | (a_select2(sigma, v0) = v5) | ~ (a_select2(mu, v0) = v1) | ~ $i(v0)
% 17.87/3.10 | | ? [v13: any] : ? [v14: any] : ? [v15: $i] : ? [v16: $i] :
% 17.87/3.10 | (divide(v12, pv84) = v16 & a_select3(q, pv10, v0) = v15 & leq(v0,
% 17.87/3.10 | all_76_1) = v14 & leq(n0, v0) = v13 & $i(v16) & $i(v15) & ( ~
% 17.87/3.10 | (v14 = 0) | ~ (v13 = 0) | v16 = v15))) & ! [v0: $i] : ! [v1:
% 17.87/3.10 | $i] : ( ~ (a_select3(q, v0, tptp_sum_index) = v1) | ~ $i(v0) | ?
% 17.87/3.10 | [v2: any] : ? [v3: any] : ? [v4: $i] : (sum(n0, n4, v1) = v4 &
% 17.87/3.10 | leq(v0, all_76_0) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) |
% 17.87/3.10 | ~ (v2 = 0) | v4 = n1))) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 17.87/3.10 | $i] : ( ~ (v2 = n1) & ~ (v0 = pv10) & sum(n0, n4, v1) = v2 &
% 17.87/3.10 | a_select3(q, v0, tptp_sum_index) = v1 & leq(v0, all_76_0) = 0 &
% 17.87/3.10 | leq(n0, v0) = 0 & $i(v2) & $i(v1) & $i(v0))
% 17.87/3.10 |
% 17.87/3.10 | ALPHA: (4) implies:
% 17.87/3.10 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (a_select3(q, v0, tptp_sum_index) = v1)
% 17.87/3.10 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : (sum(n0,
% 17.87/3.10 | n4, v1) = v4 & leq(v0, all_76_0) = v3 & leq(n0, v0) = v2 & $i(v4)
% 17.87/3.10 | & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = n1)))
% 17.87/3.10 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = n1) & ~ (v0 =
% 17.87/3.10 | pv10) & sum(n0, n4, v1) = v2 & a_select3(q, v0, tptp_sum_index) =
% 17.87/3.10 | v1 & leq(v0, all_76_0) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) &
% 17.87/3.10 | $i(v0))
% 17.87/3.10 |
% 17.87/3.10 | DELTA: instantiating (6) with fresh symbols all_79_0, all_79_1, all_79_2
% 17.87/3.10 | gives:
% 17.87/3.10 | (7) ~ (all_79_0 = n1) & ~ (all_79_2 = pv10) & sum(n0, n4, all_79_1) =
% 17.87/3.10 | all_79_0 & a_select3(q, all_79_2, tptp_sum_index) = all_79_1 &
% 17.87/3.10 | leq(all_79_2, all_76_0) = 0 & leq(n0, all_79_2) = 0 & $i(all_79_0) &
% 17.87/3.10 | $i(all_79_1) & $i(all_79_2)
% 17.87/3.10 |
% 17.87/3.10 | ALPHA: (7) implies:
% 17.87/3.10 | (8) ~ (all_79_0 = n1)
% 17.87/3.10 | (9) $i(all_79_2)
% 17.87/3.10 | (10) leq(n0, all_79_2) = 0
% 17.87/3.10 | (11) leq(all_79_2, all_76_0) = 0
% 17.87/3.10 | (12) a_select3(q, all_79_2, tptp_sum_index) = all_79_1
% 17.87/3.10 | (13) sum(n0, n4, all_79_1) = all_79_0
% 17.87/3.10 |
% 17.87/3.10 | GROUND_INST: instantiating (5) with all_79_2, all_79_1, simplifying with (9),
% 17.87/3.10 | (12) gives:
% 17.87/3.10 | (14) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sum(n0, n4, all_79_1) =
% 17.87/3.10 | v2 & leq(all_79_2, all_76_0) = v1 & leq(n0, all_79_2) = v0 & $i(v2)
% 17.87/3.10 | & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = n1))
% 17.87/3.10 |
% 17.87/3.10 | DELTA: instantiating (14) with fresh symbols all_103_0, all_103_1, all_103_2
% 17.87/3.10 | gives:
% 17.87/3.10 | (15) sum(n0, n4, all_79_1) = all_103_0 & leq(all_79_2, all_76_0) =
% 17.87/3.10 | all_103_1 & leq(n0, all_79_2) = all_103_2 & $i(all_103_0) & ( ~
% 17.87/3.10 | (all_103_1 = 0) | ~ (all_103_2 = 0) | all_103_0 = n1)
% 17.87/3.10 |
% 17.87/3.10 | ALPHA: (15) implies:
% 17.87/3.10 | (16) leq(n0, all_79_2) = all_103_2
% 18.07/3.10 | (17) leq(all_79_2, all_76_0) = all_103_1
% 18.07/3.10 | (18) sum(n0, n4, all_79_1) = all_103_0
% 18.07/3.10 | (19) ~ (all_103_1 = 0) | ~ (all_103_2 = 0) | all_103_0 = n1
% 18.07/3.10 |
% 18.07/3.10 | GROUND_INST: instantiating (2) with 0, all_103_2, all_79_2, n0, simplifying
% 18.07/3.11 | with (10), (16) gives:
% 18.07/3.11 | (20) all_103_2 = 0
% 18.07/3.11 |
% 18.07/3.11 | GROUND_INST: instantiating (2) with 0, all_103_1, all_76_0, all_79_2,
% 18.07/3.11 | simplifying with (11), (17) gives:
% 18.07/3.11 | (21) all_103_1 = 0
% 18.07/3.11 |
% 18.07/3.11 | GROUND_INST: instantiating (3) with all_79_0, all_103_0, all_79_1, n4, n0,
% 18.07/3.11 | simplifying with (13), (18) gives:
% 18.07/3.11 | (22) all_103_0 = all_79_0
% 18.07/3.11 |
% 18.07/3.11 | BETA: splitting (19) gives:
% 18.07/3.11 |
% 18.07/3.11 | Case 1:
% 18.07/3.11 | |
% 18.07/3.11 | | (23) ~ (all_103_1 = 0)
% 18.07/3.11 | |
% 18.07/3.11 | | REDUCE: (21), (23) imply:
% 18.07/3.11 | | (24) $false
% 18.07/3.11 | |
% 18.07/3.11 | | CLOSE: (24) is inconsistent.
% 18.07/3.11 | |
% 18.07/3.11 | Case 2:
% 18.07/3.11 | |
% 18.07/3.11 | | (25) ~ (all_103_2 = 0) | all_103_0 = n1
% 18.07/3.11 | |
% 18.07/3.11 | | BETA: splitting (25) gives:
% 18.07/3.11 | |
% 18.07/3.11 | | Case 1:
% 18.07/3.11 | | |
% 18.07/3.11 | | | (26) ~ (all_103_2 = 0)
% 18.07/3.11 | | |
% 18.07/3.11 | | | REDUCE: (20), (26) imply:
% 18.07/3.11 | | | (27) $false
% 18.07/3.11 | | |
% 18.07/3.11 | | | CLOSE: (27) is inconsistent.
% 18.07/3.11 | | |
% 18.07/3.11 | | Case 2:
% 18.07/3.11 | | |
% 18.07/3.11 | | | (28) all_103_0 = n1
% 18.07/3.11 | | |
% 18.07/3.11 | | | COMBINE_EQS: (22), (28) imply:
% 18.07/3.11 | | | (29) all_79_0 = n1
% 18.07/3.11 | | |
% 18.07/3.11 | | | REDUCE: (8), (29) imply:
% 18.07/3.11 | | | (30) $false
% 18.07/3.11 | | |
% 18.07/3.11 | | | CLOSE: (30) is inconsistent.
% 18.07/3.11 | | |
% 18.07/3.11 | | End of split
% 18.07/3.11 | |
% 18.07/3.11 | End of split
% 18.07/3.11 |
% 18.07/3.11 End of proof
% 18.07/3.11 % SZS output end Proof for theBenchmark
% 18.07/3.11
% 18.07/3.11 2544ms
%------------------------------------------------------------------------------