TSTP Solution File: ITP018_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ITP018_1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.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 04:08:52 EDT 2023
% Result : Theorem 13.04s 2.58s
% Output : Proof 16.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP018_1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n001.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 : Sun Aug 27 16:29:03 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.77/1.30 Prover 1: Preprocessing ...
% 3.77/1.30 Prover 4: Preprocessing ...
% 4.19/1.33 Prover 6: Preprocessing ...
% 4.19/1.33 Prover 3: Preprocessing ...
% 4.19/1.33 Prover 5: Preprocessing ...
% 4.19/1.33 Prover 0: Preprocessing ...
% 4.19/1.33 Prover 2: Preprocessing ...
% 9.43/2.22 Prover 4: Warning: ignoring some quantifiers
% 10.78/2.24 Prover 3: Warning: ignoring some quantifiers
% 10.78/2.26 Prover 1: Warning: ignoring some quantifiers
% 10.78/2.29 Prover 0: Proving ...
% 10.78/2.29 Prover 4: Constructing countermodel ...
% 10.78/2.29 Prover 3: Constructing countermodel ...
% 10.78/2.30 Prover 1: Constructing countermodel ...
% 10.78/2.32 Prover 6: Proving ...
% 12.05/2.41 Prover 5: Proving ...
% 12.05/2.42 Prover 2: Proving ...
% 13.04/2.58 Prover 3: proved (1919ms)
% 13.04/2.58
% 13.04/2.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.04/2.58
% 13.04/2.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.04/2.58 Prover 0: stopped
% 13.04/2.58 Prover 6: stopped
% 13.04/2.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.04/2.58 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.04/2.58 Prover 2: stopped
% 13.04/2.59 Prover 5: stopped
% 13.04/2.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.04/2.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.19/2.72 Prover 11: Preprocessing ...
% 14.19/2.72 Prover 7: Preprocessing ...
% 14.19/2.73 Prover 10: Preprocessing ...
% 14.19/2.74 Prover 8: Preprocessing ...
% 14.76/2.77 Prover 13: Preprocessing ...
% 14.76/2.78 Prover 1: Found proof (size 43)
% 14.76/2.78 Prover 1: proved (2144ms)
% 14.76/2.80 Prover 4: stopped
% 14.76/2.84 Prover 7: stopped
% 14.76/2.86 Prover 11: stopped
% 14.76/2.87 Prover 10: stopped
% 15.74/2.94 Prover 13: stopped
% 15.90/2.97 Prover 8: Warning: ignoring some quantifiers
% 15.90/2.99 Prover 8: Constructing countermodel ...
% 15.90/3.00 Prover 8: stopped
% 15.90/3.00
% 15.90/3.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.90/3.00
% 15.90/3.01 % SZS output start Proof for theBenchmark
% 15.90/3.01 Assumptions after simplification:
% 15.90/3.01 ---------------------------------
% 15.90/3.01
% 15.90/3.01 (ij_2Emono_2Etyop_2Erealax_2Ereal)
% 16.27/3.04 d(tyop_2Erealax_2Ereal) & ! [v0: u] : ! [v1: du] : ( ~
% 16.27/3.04 (s(tyop_2Erealax_2Ereal, v0) = v1) | ~ u(v0) | ? [v2:
% 16.27/3.04 mono_2Etyop_2Erealax_2Ereal] : ? [v3: u] :
% 16.27/3.04 (j_mono_2Etyop_2Erealax_2Ereal(v1) = v2 & i_mono_2Etyop_2Erealax_2Ereal(v2)
% 16.27/3.04 = v3 & s(tyop_2Erealax_2Ereal, v3) = v1 & mono_2Etyop_2Erealax_2Ereal(v2)
% 16.27/3.04 & du(v1) & u(v3)))
% 16.27/3.04
% 16.27/3.04 (thm_2Ebinary__ieee_2Efloat__to__real__negate)
% 16.27/3.04 d(tyop_2Erealax_2Ereal) & ! [v0: d] : ! [v1: d] : ! [v2: u] : ! [v3: d] :
% 16.27/3.04 ! [v4: du] : ! [v5: u] : ! [v6: du] : ( ~ (tyop_2Ebinary__ieee_2Efloat(v0,
% 16.27/3.04 v1) = v3) | ~ (c_2Ebinary__ieee_2Efloat__negate_2E1(v4) = v5) | ~
% 16.27/3.04 (s(v3, v5) = v6) | ~ (s(v3, v2) = v4) | ~ d(v1) | ~ d(v0) | ~ u(v2) | ?
% 16.27/3.04 [v7: u] : ? [v8: du] : ? [v9: mono_2Etyop_2Erealax_2Ereal] : ? [v10: u] :
% 16.27/3.04 ? [v11: du] : ? [v12: mono_2Etyop_2Erealax_2Ereal] :
% 16.27/3.04 (mono_2Ec_2Erealax_2Ereal__neg_2E1(v12) = v9 &
% 16.27/3.04 c_2Ebinary__ieee_2Efloat__to__real_2E1(v6) = v7 &
% 16.27/3.04 c_2Ebinary__ieee_2Efloat__to__real_2E1(v4) = v10 &
% 16.27/3.04 j_mono_2Etyop_2Erealax_2Ereal(v11) = v12 &
% 16.27/3.04 j_mono_2Etyop_2Erealax_2Ereal(v8) = v9 & s(tyop_2Erealax_2Ereal, v10) =
% 16.27/3.04 v11 & s(tyop_2Erealax_2Ereal, v7) = v8 & mono_2Etyop_2Erealax_2Ereal(v12)
% 16.27/3.04 & mono_2Etyop_2Erealax_2Ereal(v9) & du(v11) & du(v8) & u(v10) & u(v7)))
% 16.27/3.04
% 16.27/3.04 (thm_2Ebinary__ieee_2Eneg__ulp)
% 16.27/3.05 d(tyop_2Erealax_2Ereal) & u(c_2Ebool_2Ethe__value_2E0) & ? [v0: d] : ? [v1:
% 16.27/3.05 d] : ? [v2: d] : ? [v3: d] : ? [v4: du] : ? [v5: u] : ? [v6: du] : ?
% 16.27/3.05 [v7: mono_2Etyop_2Erealax_2Ereal] : ? [v8: mono_2Etyop_2Erealax_2Ereal] : ?
% 16.27/3.05 [v9: d] : ? [v10: u] : ? [v11: du] : ? [v12: u] : ? [v13: du] : ? [v14:
% 16.27/3.05 u] : ? [v15: du] : ? [v16: mono_2Etyop_2Erealax_2Ereal] : ( ~ (v16 = v8) &
% 16.27/3.05 c_2Ebinary__ieee_2Eulp_2E1(v4) = v5 & mono_2Ec_2Erealax_2Ereal__neg_2E1(v7)
% 16.27/3.05 = v8 & c_2Ebinary__ieee_2Efloat__to__real_2E1(v13) = v14 &
% 16.27/3.05 tyop_2Epair_2Eprod(v0, v1) = v2 & tyop_2Ebool_2Eitself(v2) = v3 &
% 16.27/3.05 c_2Ebinary__ieee_2Efloat__plus__min_2E1(v4) = v10 &
% 16.27/3.05 tyop_2Ebinary__ieee_2Efloat(v0, v1) = v9 &
% 16.27/3.05 c_2Ebinary__ieee_2Efloat__negate_2E1(v11) = v12 &
% 16.27/3.05 j_mono_2Etyop_2Erealax_2Ereal(v15) = v16 & j_mono_2Etyop_2Erealax_2Ereal(v6)
% 16.27/3.05 = v7 & s(v9, v12) = v13 & s(v9, v10) = v11 & s(v3,
% 16.27/3.05 c_2Ebool_2Ethe__value_2E0) = v4 & s(tyop_2Erealax_2Ereal, v14) = v15 &
% 16.27/3.05 s(tyop_2Erealax_2Ereal, v5) = v6 & mono_2Etyop_2Erealax_2Ereal(v16) &
% 16.27/3.05 mono_2Etyop_2Erealax_2Ereal(v8) & mono_2Etyop_2Erealax_2Ereal(v7) & du(v15)
% 16.27/3.05 & du(v13) & du(v11) & du(v6) & du(v4) & d(v9) & d(v3) & d(v2) & d(v1) &
% 16.27/3.05 d(v0) & u(v14) & u(v12) & u(v10) & u(v5))
% 16.27/3.05
% 16.27/3.05 (thm_2Ebinary__ieee_2Eulp)
% 16.27/3.05 d(tyop_2Erealax_2Ereal) & u(c_2Ebool_2Ethe__value_2E0) & ! [v0: d] : ! [v1:
% 16.27/3.05 d] : ! [v2: d] : ! [v3: d] : ! [v4: du] : ! [v5: d] : ! [v6: u] : !
% 16.27/3.05 [v7: du] : ( ~ (tyop_2Epair_2Eprod(v0, v1) = v2) | ~
% 16.27/3.05 (tyop_2Ebool_2Eitself(v2) = v3) | ~
% 16.27/3.05 (c_2Ebinary__ieee_2Efloat__plus__min_2E1(v4) = v6) | ~
% 16.27/3.05 (tyop_2Ebinary__ieee_2Efloat(v0, v1) = v5) | ~ (s(v5, v6) = v7) | ~ (s(v3,
% 16.27/3.05 c_2Ebool_2Ethe__value_2E0) = v4) | ~ d(v1) | ~ d(v0) | ? [v8: u] : ?
% 16.27/3.05 [v9: du] : ? [v10: mono_2Etyop_2Erealax_2Ereal] : ? [v11: u] : ? [v12:
% 16.27/3.05 du] : (c_2Ebinary__ieee_2Eulp_2E1(v4) = v8 &
% 16.27/3.05 c_2Ebinary__ieee_2Efloat__to__real_2E1(v7) = v11 &
% 16.27/3.05 j_mono_2Etyop_2Erealax_2Ereal(v12) = v10 &
% 16.27/3.05 j_mono_2Etyop_2Erealax_2Ereal(v9) = v10 & s(tyop_2Erealax_2Ereal, v11) =
% 16.27/3.05 v12 & s(tyop_2Erealax_2Ereal, v8) = v9 & mono_2Etyop_2Erealax_2Ereal(v10)
% 16.27/3.05 & du(v12) & du(v9) & u(v11) & u(v8)))
% 16.27/3.05
% 16.27/3.05 (function-axioms)
% 16.27/3.06 ! [v0: mono_2Etyop_2Erealax_2Ereal] : ! [v1: mono_2Etyop_2Erealax_2Ereal] :
% 16.27/3.06 ! [v2: mono_2Etyop_2Erealax_2Ereal] : ! [v3:
% 16.27/3.06 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 16.27/3.06 (v1 = v0 | ~
% 16.27/3.06 (mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(v3,
% 16.27/3.06 v2) = v1) | ~
% 16.27/3.06 (mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(v3,
% 16.27/3.06 v2) = v0)) & ! [v0: d] : ! [v1: d] : ! [v2: d] : ! [v3: d] : (v1 =
% 16.27/3.06 v0 | ~ (tyop_2Epair_2Eprod(v3, v2) = v1) | ~ (tyop_2Epair_2Eprod(v3, v2) =
% 16.27/3.06 v0)) & ! [v0: d] : ! [v1: d] : ! [v2: d] : ! [v3: d] : (v1 = v0 | ~
% 16.27/3.06 (tyop_2Ebinary__ieee_2Efloat(v3, v2) = v1) | ~
% 16.27/3.06 (tyop_2Ebinary__ieee_2Efloat(v3, v2) = v0)) & ! [v0:
% 16.27/3.06 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : !
% 16.27/3.06 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : !
% 16.27/3.06 [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3:
% 16.27/3.06 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29]
% 16.27/3.06 : (v1 = v0 | ~
% 16.27/3.06 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v3,
% 16.27/3.06 v2) = v1) | ~
% 16.27/3.06 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v3,
% 16.27/3.06 v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1:
% 16.27/3.06 mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3:
% 16.27/3.06 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : (v1 =
% 16.27/3.06 v0 | ~
% 16.27/3.06 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3,
% 16.27/3.06 v2) = v1) | ~
% 16.27/3.06 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3,
% 16.27/3.06 v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : ! [v3: du] : (v1 =
% 16.27/3.06 v0 | ~ (c_2Emin_2E_3D_2E2(v3, v2) = v1) | ~ (c_2Emin_2E_3D_2E2(v3, v2) =
% 16.27/3.06 v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1:
% 16.27/3.06 mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3:
% 16.27/3.06 mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~
% 16.27/3.06 (mono_2Ec_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v1) | ~
% 16.27/3.06 (mono_2Ec_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v0)) & ! [v0:
% 16.27/3.06 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2:
% 16.27/3.06 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 |
% 16.27/3.06 ~ (mono_2Ec_2Ebool_2E_5C_2F_2E2(v3, v2) = v1) | ~
% 16.27/3.06 (mono_2Ec_2Ebool_2E_5C_2F_2E2(v3, v2) = v0)) & ! [v0:
% 16.27/3.06 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2:
% 16.27/3.06 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 |
% 16.27/3.06 ~ (mono_2Ec_2Ebool_2E_2F_5C_2E2(v3, v2) = v1) | ~
% 16.27/3.06 (mono_2Ec_2Ebool_2E_2F_5C_2E2(v3, v2) = v0)) & ! [v0: d] : ! [v1: d] : !
% 16.27/3.06 [v2: d] : ! [v3: d] : (v1 = v0 | ~ (tyop_2Emin_2Efun(v3, v2) = v1) | ~
% 16.27/3.06 (tyop_2Emin_2Efun(v3, v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] :
% 16.27/3.06 ! [v3: du] : (v1 = v0 | ~ (app_2E2(v3, v2) = v1) | ~ (app_2E2(v3, v2) = v0))
% 16.27/3.06 & ! [v0: du] : ! [v1: du] : ! [v2: u] : ! [v3: d] : (v1 = v0 | ~ (s(v3,
% 16.27/3.06 v2) = v1) | ~ (s(v3, v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du]
% 16.27/3.06 : (v1 = v0 | ~ (c_2Ebinary__ieee_2Eulp_2E1(v2) = v1) | ~
% 16.27/3.06 (c_2Ebinary__ieee_2Eulp_2E1(v2) = v0)) & ! [v0:
% 16.27/3.06 mono_2Etyop_2Erealax_2Ereal] : ! [v1: mono_2Etyop_2Erealax_2Ereal] : !
% 16.27/3.06 [v2: mono_2Etyop_2Erealax_2Ereal] : (v1 = v0 | ~
% 16.27/3.06 (mono_2Ec_2Erealax_2Ereal__neg_2E1(v2) = v1) | ~
% 16.27/3.06 (mono_2Ec_2Erealax_2Ereal__neg_2E1(v2) = v0)) & ! [v0: u] : ! [v1: u] : !
% 16.27/3.06 [v2: du] : (v1 = v0 | ~ (c_2Ebinary__ieee_2Efloat__to__real_2E1(v2) = v1) |
% 16.27/3.06 ~ (c_2Ebinary__ieee_2Efloat__to__real_2E1(v2) = v0)) & ! [v0: d] : ! [v1:
% 16.27/3.06 d] : ! [v2: d] : (v1 = v0 | ~ (tyop_2Ebool_2Eitself(v2) = v1) | ~
% 16.27/3.06 (tyop_2Ebool_2Eitself(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] :
% 16.27/3.06 (v1 = v0 | ~ (c_2Ebinary__ieee_2Efloat__plus__min_2E1(v2) = v1) | ~
% 16.27/3.06 (c_2Ebinary__ieee_2Efloat__plus__min_2E1(v2) = v0)) & ! [v0: u] : ! [v1:
% 16.27/3.06 u] : ! [v2: du] : (v1 = v0 | ~ (c_2Ebinary__ieee_2Efloat__negate_2E1(v2) =
% 16.27/3.06 v1) | ~ (c_2Ebinary__ieee_2Efloat__negate_2E1(v2) = v0)) & ! [v0:
% 16.27/3.06 mono_2Etyop_2Erealax_2Ereal] : ! [v1: mono_2Etyop_2Erealax_2Ereal] : !
% 16.27/3.06 [v2: du] : (v1 = v0 | ~ (j_mono_2Etyop_2Erealax_2Ereal(v2) = v1) | ~
% 16.27/3.06 (j_mono_2Etyop_2Erealax_2Ereal(v2) = v0)) & ! [v0: u] : ! [v1: u] : !
% 16.27/3.06 [v2: mono_2Etyop_2Erealax_2Ereal] : (v1 = v0 | ~
% 16.27/3.06 (i_mono_2Etyop_2Erealax_2Ereal(v2) = v1) | ~
% 16.27/3.06 (i_mono_2Etyop_2Erealax_2Ereal(v2) = v0)) & ! [v0:
% 16.27/3.06 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 16.27/3.06 ! [v1:
% 16.27/3.06 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 16.27/3.06 ! [v2: du] : (v1 = v0 | ~
% 16.27/3.06 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2)
% 16.27/3.06 = v1) | ~
% 16.27/3.06 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2)
% 16.27/3.06 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2:
% 16.27/3.06 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 16.27/3.06 (v1 = v0 | ~
% 16.27/3.06 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2)
% 16.27/3.06 = v1) | ~
% 16.27/3.06 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2)
% 16.27/3.06 = v0)) & ! [v0:
% 16.27/3.06 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29]
% 16.27/3.06 : ! [v1:
% 16.27/3.06 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29]
% 16.27/3.06 : ! [v2: du] : (v1 = v0 | ~
% 16.27/3.06 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2)
% 16.27/3.06 = v1) | ~
% 16.27/3.06 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2)
% 16.27/3.06 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2:
% 16.27/3.06 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29]
% 16.27/3.06 : (v1 = v0 | ~
% 16.27/3.06 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2)
% 16.27/3.06 = v1) | ~
% 16.27/3.06 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2)
% 16.27/3.06 = v0)) & ! [v0:
% 16.27/3.06 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : !
% 16.27/3.06 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : !
% 16.27/3.06 [v2: du] : (v1 = v0 | ~
% 16.27/3.06 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) =
% 16.27/3.06 v1) | ~
% 16.27/3.06 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) =
% 16.27/3.06 v0)) & ! [v0: u] : ! [v1: u] : ! [v2:
% 16.27/3.06 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : (v1 =
% 16.27/3.06 v0 | ~
% 16.27/3.06 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) =
% 16.27/3.06 v1) | ~
% 16.27/3.06 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) =
% 16.27/3.06 v0)) & ! [v0: u] : ! [v1: u] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 =
% 16.27/3.06 v0 | ~ (i_mono_2Etyop_2Emin_2Ebool(v2) = v1) | ~
% 16.27/3.06 (i_mono_2Etyop_2Emin_2Ebool(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2:
% 16.27/3.06 du] : (v1 = v0 | ~ (c_2Ebool_2E_3F_2E1(v2) = v1) | ~
% 16.27/3.06 (c_2Ebool_2E_3F_2E1(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : (v1
% 16.27/3.06 = v0 | ~ (c_2Ebool_2E_21_2E1(v2) = v1) | ~ (c_2Ebool_2E_21_2E1(v2) = v0))
% 16.27/3.06 & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : !
% 16.27/3.06 [v2: du] : (v1 = v0 | ~ (j_mono_2Etyop_2Emin_2Ebool(v2) = v1) | ~
% 16.27/3.06 (j_mono_2Etyop_2Emin_2Ebool(v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] :
% 16.27/3.06 ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 =
% 16.27/3.06 v0 | ~ (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v1) | ~
% 16.27/3.06 (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.27/3.06 MultipleValueBool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~
% 16.27/3.06 (p(v2) = v1) | ~ (p(v2) = v0))
% 16.27/3.06
% 16.27/3.06 Further assumptions not needed in the proof:
% 16.27/3.06 --------------------------------------------
% 16.27/3.06 arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27a_20mono_2EA_27b,
% 16.27/3.06 arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27t_20mono_2EA_27w,
% 16.27/3.06 arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w,
% 16.27/3.06 arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b,
% 16.27/3.06 arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w,
% 16.27/3.06 arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w,
% 16.27/3.06 arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,
% 16.27/3.06 arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Ebool_2E_7E_2E1,
% 16.27/3.06 arityeq1_2Ec_2Erealax_2Ereal__neg_2E1, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,
% 16.27/3.06 arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,
% 16.27/3.06 arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, ij_2Emono_2Etyop_2Emin_2Ebool,
% 16.27/3.06 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,
% 16.27/3.06 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,
% 16.27/3.06 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,
% 16.27/3.06 ji_2Emono_2Etyop_2Emin_2Ebool,
% 16.27/3.06 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,
% 16.27/3.06 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,
% 16.27/3.06 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,
% 16.27/3.06 ji_2Emono_2Etyop_2Erealax_2Ereal,
% 16.27/3.06 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,
% 16.27/3.06 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,
% 16.27/3.06 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,
% 16.27/3.06 reserved_2Eho_2Ebool__cases__ax, reserved_2Eho_2Eboolext,
% 16.27/3.06 reserved_2Eho_2Eeq__ext, reserved_2Eho_2Ei__thm, reserved_2Eho_2Ek__thm,
% 16.27/3.06 reserved_2Eho_2Enotfalse, reserved_2Eho_2Es__thm, reserved_2Eho_2Etruth,
% 16.27/3.06 reserved_2Elogic_2E_2F_5C, reserved_2Elogic_2E_3D, reserved_2Elogic_2E_3D_3D_3E,
% 16.27/3.06 reserved_2Elogic_2E_5C_2F, reserved_2Elogic_2E_7E, reserved_2Equant_2E_21,
% 16.27/3.06 reserved_2Equant_2E_3F, thm_2Ebool_2EREFL__CLAUSE, thm_2Ebool_2ETRUTH
% 16.27/3.06
% 16.27/3.06 Those formulas are unsatisfiable:
% 16.27/3.06 ---------------------------------
% 16.27/3.06
% 16.27/3.06 Begin of proof
% 16.27/3.07 |
% 16.27/3.07 | ALPHA: (ij_2Emono_2Etyop_2Erealax_2Ereal) implies:
% 16.27/3.07 | (1) ! [v0: u] : ! [v1: du] : ( ~ (s(tyop_2Erealax_2Ereal, v0) = v1) | ~
% 16.27/3.07 | u(v0) | ? [v2: mono_2Etyop_2Erealax_2Ereal] : ? [v3: u] :
% 16.27/3.07 | (j_mono_2Etyop_2Erealax_2Ereal(v1) = v2 &
% 16.27/3.07 | i_mono_2Etyop_2Erealax_2Ereal(v2) = v3 & s(tyop_2Erealax_2Ereal,
% 16.27/3.07 | v3) = v1 & mono_2Etyop_2Erealax_2Ereal(v2) & du(v1) & u(v3)))
% 16.27/3.07 |
% 16.27/3.07 | ALPHA: (thm_2Ebinary__ieee_2Efloat__to__real__negate) implies:
% 16.27/3.07 | (2) ! [v0: d] : ! [v1: d] : ! [v2: u] : ! [v3: d] : ! [v4: du] : !
% 16.27/3.07 | [v5: u] : ! [v6: du] : ( ~ (tyop_2Ebinary__ieee_2Efloat(v0, v1) = v3)
% 16.27/3.07 | | ~ (c_2Ebinary__ieee_2Efloat__negate_2E1(v4) = v5) | ~ (s(v3, v5)
% 16.27/3.07 | = v6) | ~ (s(v3, v2) = v4) | ~ d(v1) | ~ d(v0) | ~ u(v2) | ?
% 16.27/3.07 | [v7: u] : ? [v8: du] : ? [v9: mono_2Etyop_2Erealax_2Ereal] : ?
% 16.27/3.07 | [v10: u] : ? [v11: du] : ? [v12: mono_2Etyop_2Erealax_2Ereal] :
% 16.27/3.07 | (mono_2Ec_2Erealax_2Ereal__neg_2E1(v12) = v9 &
% 16.27/3.07 | c_2Ebinary__ieee_2Efloat__to__real_2E1(v6) = v7 &
% 16.27/3.07 | c_2Ebinary__ieee_2Efloat__to__real_2E1(v4) = v10 &
% 16.27/3.07 | j_mono_2Etyop_2Erealax_2Ereal(v11) = v12 &
% 16.27/3.07 | j_mono_2Etyop_2Erealax_2Ereal(v8) = v9 & s(tyop_2Erealax_2Ereal,
% 16.27/3.07 | v10) = v11 & s(tyop_2Erealax_2Ereal, v7) = v8 &
% 16.27/3.07 | mono_2Etyop_2Erealax_2Ereal(v12) & mono_2Etyop_2Erealax_2Ereal(v9)
% 16.27/3.07 | & du(v11) & du(v8) & u(v10) & u(v7)))
% 16.27/3.07 |
% 16.27/3.07 | ALPHA: (thm_2Ebinary__ieee_2Eulp) implies:
% 16.27/3.07 | (3) ! [v0: d] : ! [v1: d] : ! [v2: d] : ! [v3: d] : ! [v4: du] : !
% 16.27/3.07 | [v5: d] : ! [v6: u] : ! [v7: du] : ( ~ (tyop_2Epair_2Eprod(v0, v1) =
% 16.27/3.07 | v2) | ~ (tyop_2Ebool_2Eitself(v2) = v3) | ~
% 16.27/3.07 | (c_2Ebinary__ieee_2Efloat__plus__min_2E1(v4) = v6) | ~
% 16.27/3.07 | (tyop_2Ebinary__ieee_2Efloat(v0, v1) = v5) | ~ (s(v5, v6) = v7) | ~
% 16.27/3.07 | (s(v3, c_2Ebool_2Ethe__value_2E0) = v4) | ~ d(v1) | ~ d(v0) | ?
% 16.27/3.07 | [v8: u] : ? [v9: du] : ? [v10: mono_2Etyop_2Erealax_2Ereal] : ?
% 16.27/3.07 | [v11: u] : ? [v12: du] : (c_2Ebinary__ieee_2Eulp_2E1(v4) = v8 &
% 16.27/3.07 | c_2Ebinary__ieee_2Efloat__to__real_2E1(v7) = v11 &
% 16.27/3.07 | j_mono_2Etyop_2Erealax_2Ereal(v12) = v10 &
% 16.27/3.07 | j_mono_2Etyop_2Erealax_2Ereal(v9) = v10 & s(tyop_2Erealax_2Ereal,
% 16.27/3.07 | v11) = v12 & s(tyop_2Erealax_2Ereal, v8) = v9 &
% 16.27/3.07 | mono_2Etyop_2Erealax_2Ereal(v10) & du(v12) & du(v9) & u(v11) &
% 16.27/3.07 | u(v8)))
% 16.27/3.07 |
% 16.27/3.07 | ALPHA: (thm_2Ebinary__ieee_2Eneg__ulp) implies:
% 16.51/3.08 | (4) ? [v0: d] : ? [v1: d] : ? [v2: d] : ? [v3: d] : ? [v4: du] : ?
% 16.51/3.08 | [v5: u] : ? [v6: du] : ? [v7: mono_2Etyop_2Erealax_2Ereal] : ? [v8:
% 16.51/3.08 | mono_2Etyop_2Erealax_2Ereal] : ? [v9: d] : ? [v10: u] : ? [v11:
% 16.51/3.08 | du] : ? [v12: u] : ? [v13: du] : ? [v14: u] : ? [v15: du] : ?
% 16.51/3.08 | [v16: mono_2Etyop_2Erealax_2Ereal] : ( ~ (v16 = v8) &
% 16.51/3.08 | c_2Ebinary__ieee_2Eulp_2E1(v4) = v5 &
% 16.51/3.08 | mono_2Ec_2Erealax_2Ereal__neg_2E1(v7) = v8 &
% 16.51/3.08 | c_2Ebinary__ieee_2Efloat__to__real_2E1(v13) = v14 &
% 16.51/3.08 | tyop_2Epair_2Eprod(v0, v1) = v2 & tyop_2Ebool_2Eitself(v2) = v3 &
% 16.51/3.08 | c_2Ebinary__ieee_2Efloat__plus__min_2E1(v4) = v10 &
% 16.51/3.08 | tyop_2Ebinary__ieee_2Efloat(v0, v1) = v9 &
% 16.51/3.08 | c_2Ebinary__ieee_2Efloat__negate_2E1(v11) = v12 &
% 16.51/3.08 | j_mono_2Etyop_2Erealax_2Ereal(v15) = v16 &
% 16.51/3.08 | j_mono_2Etyop_2Erealax_2Ereal(v6) = v7 & s(v9, v12) = v13 & s(v9,
% 16.51/3.08 | v10) = v11 & s(v3, c_2Ebool_2Ethe__value_2E0) = v4 &
% 16.51/3.08 | s(tyop_2Erealax_2Ereal, v14) = v15 & s(tyop_2Erealax_2Ereal, v5) = v6
% 16.51/3.08 | & mono_2Etyop_2Erealax_2Ereal(v16) & mono_2Etyop_2Erealax_2Ereal(v8)
% 16.51/3.08 | & mono_2Etyop_2Erealax_2Ereal(v7) & du(v15) & du(v13) & du(v11) &
% 16.51/3.08 | du(v6) & du(v4) & d(v9) & d(v3) & d(v2) & d(v1) & d(v0) & u(v14) &
% 16.51/3.08 | u(v12) & u(v10) & u(v5))
% 16.51/3.08 |
% 16.51/3.08 | ALPHA: (function-axioms) implies:
% 16.51/3.08 | (5) ! [v0: mono_2Etyop_2Erealax_2Ereal] : ! [v1:
% 16.51/3.08 | mono_2Etyop_2Erealax_2Ereal] : ! [v2: du] : (v1 = v0 | ~
% 16.51/3.08 | (j_mono_2Etyop_2Erealax_2Ereal(v2) = v1) | ~
% 16.51/3.08 | (j_mono_2Etyop_2Erealax_2Ereal(v2) = v0))
% 16.51/3.08 | (6) ! [v0: u] : ! [v1: u] : ! [v2: du] : (v1 = v0 | ~
% 16.51/3.08 | (c_2Ebinary__ieee_2Efloat__to__real_2E1(v2) = v1) | ~
% 16.51/3.08 | (c_2Ebinary__ieee_2Efloat__to__real_2E1(v2) = v0))
% 16.51/3.08 | (7) ! [v0: mono_2Etyop_2Erealax_2Ereal] : ! [v1:
% 16.51/3.08 | mono_2Etyop_2Erealax_2Ereal] : ! [v2: mono_2Etyop_2Erealax_2Ereal] :
% 16.51/3.08 | (v1 = v0 | ~ (mono_2Ec_2Erealax_2Ereal__neg_2E1(v2) = v1) | ~
% 16.51/3.08 | (mono_2Ec_2Erealax_2Ereal__neg_2E1(v2) = v0))
% 16.51/3.08 | (8) ! [v0: u] : ! [v1: u] : ! [v2: du] : (v1 = v0 | ~
% 16.51/3.08 | (c_2Ebinary__ieee_2Eulp_2E1(v2) = v1) | ~
% 16.51/3.08 | (c_2Ebinary__ieee_2Eulp_2E1(v2) = v0))
% 16.51/3.08 | (9) ! [v0: du] : ! [v1: du] : ! [v2: u] : ! [v3: d] : (v1 = v0 | ~
% 16.51/3.08 | (s(v3, v2) = v1) | ~ (s(v3, v2) = v0))
% 16.51/3.08 |
% 16.51/3.08 | DELTA: instantiating (4) with fresh symbols all_85_0, all_85_1, all_85_2,
% 16.51/3.08 | all_85_3, all_85_4, all_85_5, all_85_6, all_85_7, all_85_8, all_85_9,
% 16.51/3.08 | all_85_10, all_85_11, all_85_12, all_85_13, all_85_14, all_85_15,
% 16.51/3.08 | all_85_16 gives:
% 16.51/3.09 | (10) ~ (all_85_0 = all_85_8) & c_2Ebinary__ieee_2Eulp_2E1(all_85_12) =
% 16.51/3.09 | all_85_11 & mono_2Ec_2Erealax_2Ereal__neg_2E1(all_85_9) = all_85_8 &
% 16.51/3.09 | c_2Ebinary__ieee_2Efloat__to__real_2E1(all_85_3) = all_85_2 &
% 16.51/3.09 | tyop_2Epair_2Eprod(all_85_16, all_85_15) = all_85_14 &
% 16.51/3.09 | tyop_2Ebool_2Eitself(all_85_14) = all_85_13 &
% 16.51/3.09 | c_2Ebinary__ieee_2Efloat__plus__min_2E1(all_85_12) = all_85_6 &
% 16.51/3.09 | tyop_2Ebinary__ieee_2Efloat(all_85_16, all_85_15) = all_85_7 &
% 16.51/3.09 | c_2Ebinary__ieee_2Efloat__negate_2E1(all_85_5) = all_85_4 &
% 16.51/3.09 | j_mono_2Etyop_2Erealax_2Ereal(all_85_1) = all_85_0 &
% 16.51/3.09 | j_mono_2Etyop_2Erealax_2Ereal(all_85_10) = all_85_9 & s(all_85_7,
% 16.51/3.09 | all_85_4) = all_85_3 & s(all_85_7, all_85_6) = all_85_5 &
% 16.51/3.09 | s(all_85_13, c_2Ebool_2Ethe__value_2E0) = all_85_12 &
% 16.51/3.09 | s(tyop_2Erealax_2Ereal, all_85_2) = all_85_1 & s(tyop_2Erealax_2Ereal,
% 16.51/3.09 | all_85_11) = all_85_10 & mono_2Etyop_2Erealax_2Ereal(all_85_0) &
% 16.51/3.09 | mono_2Etyop_2Erealax_2Ereal(all_85_8) &
% 16.51/3.09 | mono_2Etyop_2Erealax_2Ereal(all_85_9) & du(all_85_1) & du(all_85_3) &
% 16.51/3.09 | du(all_85_5) & du(all_85_10) & du(all_85_12) & d(all_85_7) &
% 16.51/3.09 | d(all_85_13) & d(all_85_14) & d(all_85_15) & d(all_85_16) &
% 16.51/3.09 | u(all_85_2) & u(all_85_4) & u(all_85_6) & u(all_85_11)
% 16.51/3.09 |
% 16.51/3.09 | ALPHA: (10) implies:
% 16.51/3.09 | (11) ~ (all_85_0 = all_85_8)
% 16.51/3.09 | (12) u(all_85_11)
% 16.51/3.09 | (13) u(all_85_6)
% 16.51/3.09 | (14) u(all_85_2)
% 16.51/3.09 | (15) d(all_85_16)
% 16.51/3.09 | (16) d(all_85_15)
% 16.51/3.09 | (17) s(tyop_2Erealax_2Ereal, all_85_11) = all_85_10
% 16.51/3.09 | (18) s(tyop_2Erealax_2Ereal, all_85_2) = all_85_1
% 16.51/3.09 | (19) s(all_85_13, c_2Ebool_2Ethe__value_2E0) = all_85_12
% 16.51/3.09 | (20) s(all_85_7, all_85_6) = all_85_5
% 16.51/3.09 | (21) s(all_85_7, all_85_4) = all_85_3
% 16.51/3.09 | (22) j_mono_2Etyop_2Erealax_2Ereal(all_85_10) = all_85_9
% 16.51/3.09 | (23) j_mono_2Etyop_2Erealax_2Ereal(all_85_1) = all_85_0
% 16.51/3.09 | (24) c_2Ebinary__ieee_2Efloat__negate_2E1(all_85_5) = all_85_4
% 16.51/3.09 | (25) tyop_2Ebinary__ieee_2Efloat(all_85_16, all_85_15) = all_85_7
% 16.51/3.09 | (26) c_2Ebinary__ieee_2Efloat__plus__min_2E1(all_85_12) = all_85_6
% 16.51/3.09 | (27) tyop_2Ebool_2Eitself(all_85_14) = all_85_13
% 16.51/3.09 | (28) tyop_2Epair_2Eprod(all_85_16, all_85_15) = all_85_14
% 16.51/3.09 | (29) c_2Ebinary__ieee_2Efloat__to__real_2E1(all_85_3) = all_85_2
% 16.51/3.09 | (30) mono_2Ec_2Erealax_2Ereal__neg_2E1(all_85_9) = all_85_8
% 16.51/3.09 | (31) c_2Ebinary__ieee_2Eulp_2E1(all_85_12) = all_85_11
% 16.51/3.09 |
% 16.51/3.10 | GROUND_INST: instantiating (1) with all_85_11, all_85_10, simplifying with
% 16.51/3.10 | (12), (17) gives:
% 16.51/3.10 | (32) ? [v0: mono_2Etyop_2Erealax_2Ereal] : ? [v1: u] :
% 16.51/3.10 | (j_mono_2Etyop_2Erealax_2Ereal(all_85_10) = v0 &
% 16.51/3.10 | i_mono_2Etyop_2Erealax_2Ereal(v0) = v1 & s(tyop_2Erealax_2Ereal, v1)
% 16.51/3.10 | = all_85_10 & mono_2Etyop_2Erealax_2Ereal(v0) & du(all_85_10) &
% 16.51/3.10 | u(v1))
% 16.51/3.10 |
% 16.51/3.10 | GROUND_INST: instantiating (1) with all_85_2, all_85_1, simplifying with (14),
% 16.51/3.10 | (18) gives:
% 16.51/3.10 | (33) ? [v0: mono_2Etyop_2Erealax_2Ereal] : ? [v1: u] :
% 16.51/3.10 | (j_mono_2Etyop_2Erealax_2Ereal(all_85_1) = v0 &
% 16.51/3.10 | i_mono_2Etyop_2Erealax_2Ereal(v0) = v1 & s(tyop_2Erealax_2Ereal, v1)
% 16.51/3.10 | = all_85_1 & mono_2Etyop_2Erealax_2Ereal(v0) & du(all_85_1) & u(v1))
% 16.51/3.10 |
% 16.51/3.10 | GROUND_INST: instantiating (2) with all_85_16, all_85_15, all_85_6, all_85_7,
% 16.51/3.10 | all_85_5, all_85_4, all_85_3, simplifying with (13), (15), (16),
% 16.51/3.10 | (20), (21), (24), (25) gives:
% 16.51/3.10 | (34) ? [v0: u] : ? [v1: du] : ? [v2: mono_2Etyop_2Erealax_2Ereal] : ?
% 16.51/3.10 | [v3: u] : ? [v4: du] : ? [v5: mono_2Etyop_2Erealax_2Ereal] :
% 16.51/3.10 | (mono_2Ec_2Erealax_2Ereal__neg_2E1(v5) = v2 &
% 16.51/3.10 | c_2Ebinary__ieee_2Efloat__to__real_2E1(all_85_3) = v0 &
% 16.51/3.10 | c_2Ebinary__ieee_2Efloat__to__real_2E1(all_85_5) = v3 &
% 16.51/3.10 | j_mono_2Etyop_2Erealax_2Ereal(v4) = v5 &
% 16.51/3.10 | j_mono_2Etyop_2Erealax_2Ereal(v1) = v2 & s(tyop_2Erealax_2Ereal, v3)
% 16.51/3.10 | = v4 & s(tyop_2Erealax_2Ereal, v0) = v1 &
% 16.51/3.10 | mono_2Etyop_2Erealax_2Ereal(v5) & mono_2Etyop_2Erealax_2Ereal(v2) &
% 16.51/3.10 | du(v4) & du(v1) & u(v3) & u(v0))
% 16.51/3.10 |
% 16.51/3.10 | GROUND_INST: instantiating (3) with all_85_16, all_85_15, all_85_14,
% 16.51/3.10 | all_85_13, all_85_12, all_85_7, all_85_6, all_85_5, simplifying
% 16.51/3.10 | with (15), (16), (19), (20), (25), (26), (27), (28) gives:
% 16.51/3.10 | (35) ? [v0: u] : ? [v1: du] : ? [v2: mono_2Etyop_2Erealax_2Ereal] : ?
% 16.51/3.10 | [v3: u] : ? [v4: du] : (c_2Ebinary__ieee_2Eulp_2E1(all_85_12) = v0 &
% 16.51/3.10 | c_2Ebinary__ieee_2Efloat__to__real_2E1(all_85_5) = v3 &
% 16.51/3.10 | j_mono_2Etyop_2Erealax_2Ereal(v4) = v2 &
% 16.51/3.10 | j_mono_2Etyop_2Erealax_2Ereal(v1) = v2 & s(tyop_2Erealax_2Ereal, v3)
% 16.51/3.10 | = v4 & s(tyop_2Erealax_2Ereal, v0) = v1 &
% 16.51/3.10 | mono_2Etyop_2Erealax_2Ereal(v2) & du(v4) & du(v1) & u(v3) & u(v0))
% 16.51/3.10 |
% 16.51/3.10 | DELTA: instantiating (33) with fresh symbols all_100_0, all_100_1 gives:
% 16.51/3.11 | (36) j_mono_2Etyop_2Erealax_2Ereal(all_85_1) = all_100_1 &
% 16.51/3.11 | i_mono_2Etyop_2Erealax_2Ereal(all_100_1) = all_100_0 &
% 16.51/3.11 | s(tyop_2Erealax_2Ereal, all_100_0) = all_85_1 &
% 16.51/3.11 | mono_2Etyop_2Erealax_2Ereal(all_100_1) & du(all_85_1) & u(all_100_0)
% 16.51/3.11 |
% 16.51/3.11 | ALPHA: (36) implies:
% 16.51/3.11 | (37) j_mono_2Etyop_2Erealax_2Ereal(all_85_1) = all_100_1
% 16.51/3.11 |
% 16.51/3.11 | DELTA: instantiating (32) with fresh symbols all_102_0, all_102_1 gives:
% 16.51/3.11 | (38) j_mono_2Etyop_2Erealax_2Ereal(all_85_10) = all_102_1 &
% 16.51/3.11 | i_mono_2Etyop_2Erealax_2Ereal(all_102_1) = all_102_0 &
% 16.51/3.11 | s(tyop_2Erealax_2Ereal, all_102_0) = all_85_10 &
% 16.51/3.11 | mono_2Etyop_2Erealax_2Ereal(all_102_1) & du(all_85_10) & u(all_102_0)
% 16.51/3.11 |
% 16.51/3.11 | ALPHA: (38) implies:
% 16.51/3.11 | (39) j_mono_2Etyop_2Erealax_2Ereal(all_85_10) = all_102_1
% 16.51/3.11 |
% 16.51/3.11 | DELTA: instantiating (35) with fresh symbols all_104_0, all_104_1, all_104_2,
% 16.51/3.11 | all_104_3, all_104_4 gives:
% 16.51/3.11 | (40) c_2Ebinary__ieee_2Eulp_2E1(all_85_12) = all_104_4 &
% 16.51/3.11 | c_2Ebinary__ieee_2Efloat__to__real_2E1(all_85_5) = all_104_1 &
% 16.51/3.11 | j_mono_2Etyop_2Erealax_2Ereal(all_104_0) = all_104_2 &
% 16.51/3.11 | j_mono_2Etyop_2Erealax_2Ereal(all_104_3) = all_104_2 &
% 16.51/3.11 | s(tyop_2Erealax_2Ereal, all_104_1) = all_104_0 &
% 16.51/3.11 | s(tyop_2Erealax_2Ereal, all_104_4) = all_104_3 &
% 16.51/3.11 | mono_2Etyop_2Erealax_2Ereal(all_104_2) & du(all_104_0) & du(all_104_3)
% 16.51/3.11 | & u(all_104_1) & u(all_104_4)
% 16.51/3.11 |
% 16.51/3.11 | ALPHA: (40) implies:
% 16.51/3.11 | (41) s(tyop_2Erealax_2Ereal, all_104_4) = all_104_3
% 16.51/3.11 | (42) s(tyop_2Erealax_2Ereal, all_104_1) = all_104_0
% 16.51/3.11 | (43) j_mono_2Etyop_2Erealax_2Ereal(all_104_3) = all_104_2
% 16.51/3.11 | (44) j_mono_2Etyop_2Erealax_2Ereal(all_104_0) = all_104_2
% 16.51/3.11 | (45) c_2Ebinary__ieee_2Efloat__to__real_2E1(all_85_5) = all_104_1
% 16.51/3.11 | (46) c_2Ebinary__ieee_2Eulp_2E1(all_85_12) = all_104_4
% 16.51/3.11 |
% 16.51/3.11 | DELTA: instantiating (34) with fresh symbols all_106_0, all_106_1, all_106_2,
% 16.51/3.11 | all_106_3, all_106_4, all_106_5 gives:
% 16.51/3.11 | (47) mono_2Ec_2Erealax_2Ereal__neg_2E1(all_106_0) = all_106_3 &
% 16.51/3.11 | c_2Ebinary__ieee_2Efloat__to__real_2E1(all_85_3) = all_106_5 &
% 16.51/3.11 | c_2Ebinary__ieee_2Efloat__to__real_2E1(all_85_5) = all_106_2 &
% 16.51/3.11 | j_mono_2Etyop_2Erealax_2Ereal(all_106_1) = all_106_0 &
% 16.51/3.11 | j_mono_2Etyop_2Erealax_2Ereal(all_106_4) = all_106_3 &
% 16.51/3.11 | s(tyop_2Erealax_2Ereal, all_106_2) = all_106_1 &
% 16.51/3.11 | s(tyop_2Erealax_2Ereal, all_106_5) = all_106_4 &
% 16.51/3.11 | mono_2Etyop_2Erealax_2Ereal(all_106_0) &
% 16.51/3.11 | mono_2Etyop_2Erealax_2Ereal(all_106_3) & du(all_106_1) & du(all_106_4)
% 16.51/3.11 | & u(all_106_2) & u(all_106_5)
% 16.51/3.11 |
% 16.51/3.11 | ALPHA: (47) implies:
% 16.51/3.11 | (48) s(tyop_2Erealax_2Ereal, all_106_5) = all_106_4
% 16.51/3.11 | (49) s(tyop_2Erealax_2Ereal, all_106_2) = all_106_1
% 16.51/3.11 | (50) j_mono_2Etyop_2Erealax_2Ereal(all_106_4) = all_106_3
% 16.51/3.11 | (51) j_mono_2Etyop_2Erealax_2Ereal(all_106_1) = all_106_0
% 16.51/3.11 | (52) c_2Ebinary__ieee_2Efloat__to__real_2E1(all_85_5) = all_106_2
% 16.51/3.11 | (53) c_2Ebinary__ieee_2Efloat__to__real_2E1(all_85_3) = all_106_5
% 16.51/3.11 | (54) mono_2Ec_2Erealax_2Ereal__neg_2E1(all_106_0) = all_106_3
% 16.51/3.11 |
% 16.51/3.11 | GROUND_INST: instantiating (5) with all_85_9, all_102_1, all_85_10,
% 16.51/3.11 | simplifying with (22), (39) gives:
% 16.51/3.11 | (55) all_102_1 = all_85_9
% 16.51/3.11 |
% 16.51/3.11 | GROUND_INST: instantiating (5) with all_85_0, all_100_1, all_85_1, simplifying
% 16.51/3.11 | with (23), (37) gives:
% 16.51/3.11 | (56) all_100_1 = all_85_0
% 16.51/3.11 |
% 16.51/3.12 | GROUND_INST: instantiating (6) with all_104_1, all_106_2, all_85_5,
% 16.51/3.12 | simplifying with (45), (52) gives:
% 16.51/3.12 | (57) all_106_2 = all_104_1
% 16.51/3.12 |
% 16.51/3.12 | GROUND_INST: instantiating (6) with all_85_2, all_106_5, all_85_3, simplifying
% 16.51/3.12 | with (29), (53) gives:
% 16.51/3.12 | (58) all_106_5 = all_85_2
% 16.51/3.12 |
% 16.51/3.12 | GROUND_INST: instantiating (8) with all_85_11, all_104_4, all_85_12,
% 16.51/3.12 | simplifying with (31), (46) gives:
% 16.51/3.12 | (59) all_104_4 = all_85_11
% 16.51/3.12 |
% 16.51/3.12 | REDUCE: (49), (57) imply:
% 16.51/3.12 | (60) s(tyop_2Erealax_2Ereal, all_104_1) = all_106_1
% 16.51/3.12 |
% 16.51/3.12 | REDUCE: (48), (58) imply:
% 16.51/3.12 | (61) s(tyop_2Erealax_2Ereal, all_85_2) = all_106_4
% 16.51/3.12 |
% 16.51/3.12 | REDUCE: (41), (59) imply:
% 16.51/3.12 | (62) s(tyop_2Erealax_2Ereal, all_85_11) = all_104_3
% 16.51/3.12 |
% 16.51/3.12 | GROUND_INST: instantiating (9) with all_85_10, all_104_3, all_85_11,
% 16.51/3.12 | tyop_2Erealax_2Ereal, simplifying with (17), (62) gives:
% 16.51/3.12 | (63) all_104_3 = all_85_10
% 16.51/3.12 |
% 16.51/3.12 | GROUND_INST: instantiating (9) with all_85_1, all_106_4, all_85_2,
% 16.51/3.12 | tyop_2Erealax_2Ereal, simplifying with (18), (61) gives:
% 16.51/3.12 | (64) all_106_4 = all_85_1
% 16.51/3.12 |
% 16.51/3.12 | GROUND_INST: instantiating (9) with all_104_0, all_106_1, all_104_1,
% 16.51/3.12 | tyop_2Erealax_2Ereal, simplifying with (42), (60) gives:
% 16.51/3.12 | (65) all_106_1 = all_104_0
% 16.51/3.12 |
% 16.51/3.12 | REDUCE: (51), (65) imply:
% 16.51/3.12 | (66) j_mono_2Etyop_2Erealax_2Ereal(all_104_0) = all_106_0
% 16.51/3.12 |
% 16.51/3.12 | REDUCE: (50), (64) imply:
% 16.51/3.12 | (67) j_mono_2Etyop_2Erealax_2Ereal(all_85_1) = all_106_3
% 16.51/3.12 |
% 16.51/3.12 | REDUCE: (43), (63) imply:
% 16.51/3.12 | (68) j_mono_2Etyop_2Erealax_2Ereal(all_85_10) = all_104_2
% 16.51/3.12 |
% 16.51/3.12 | GROUND_INST: instantiating (5) with all_85_9, all_104_2, all_85_10,
% 16.51/3.12 | simplifying with (22), (68) gives:
% 16.51/3.12 | (69) all_104_2 = all_85_9
% 16.51/3.12 |
% 16.51/3.12 | GROUND_INST: instantiating (5) with all_85_0, all_106_3, all_85_1, simplifying
% 16.51/3.12 | with (23), (67) gives:
% 16.51/3.12 | (70) all_106_3 = all_85_0
% 16.51/3.12 |
% 16.51/3.12 | GROUND_INST: instantiating (5) with all_104_2, all_106_0, all_104_0,
% 16.51/3.12 | simplifying with (44), (66) gives:
% 16.51/3.12 | (71) all_106_0 = all_104_2
% 16.51/3.12 |
% 16.51/3.12 | COMBINE_EQS: (69), (71) imply:
% 16.51/3.12 | (72) all_106_0 = all_85_9
% 16.51/3.12 |
% 16.51/3.12 | REDUCE: (54), (70), (72) imply:
% 16.51/3.12 | (73) mono_2Ec_2Erealax_2Ereal__neg_2E1(all_85_9) = all_85_0
% 16.51/3.12 |
% 16.51/3.12 | GROUND_INST: instantiating (7) with all_85_8, all_85_0, all_85_9, simplifying
% 16.51/3.12 | with (30), (73) gives:
% 16.51/3.12 | (74) all_85_0 = all_85_8
% 16.51/3.12 |
% 16.51/3.12 | REDUCE: (11), (74) imply:
% 16.51/3.12 | (75) $false
% 16.51/3.13 |
% 16.51/3.13 | CLOSE: (75) is inconsistent.
% 16.51/3.13 |
% 16.51/3.13 End of proof
% 16.51/3.13 % SZS output end Proof for theBenchmark
% 16.51/3.13
% 16.51/3.13 2506ms
%------------------------------------------------------------------------------