TSTP Solution File: ARI741_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI741_1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n009.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 : Wed Aug 30 17:48:59 EDT 2023
% Result : Theorem 14.35s 2.70s
% Output : Proof 22.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ARI741_1 : TPTP v8.1.2. Released v7.0.0.
% 0.11/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 18:30:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.60/0.63 ________ _____
% 0.60/0.63 ___ __ \_________(_)________________________________
% 0.60/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.60/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.60/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.60/0.63
% 0.60/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.60/0.63 (2023-06-19)
% 0.60/0.63
% 0.60/0.63 (c) Philipp Rümmer, 2009-2023
% 0.60/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.60/0.63 Amanda Stjerna.
% 0.60/0.63 Free software under BSD-3-Clause.
% 0.60/0.63
% 0.60/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.60/0.63
% 0.60/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.64 Running up to 7 provers in parallel.
% 0.69/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.69/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.69/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.69/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.69/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.69/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.69/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.17/0.94 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.17/0.94 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.17/0.94 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.17/0.94 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.17/0.94 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.17/0.94 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.17/0.94 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 3.03/1.19 Prover 4: Preprocessing ...
% 3.03/1.19 Prover 1: Preprocessing ...
% 3.47/1.27 Prover 0: Preprocessing ...
% 3.47/1.27 Prover 6: Preprocessing ...
% 5.24/1.50 Prover 5: Preprocessing ...
% 5.24/1.50 Prover 2: Preprocessing ...
% 5.24/1.50 Prover 3: Preprocessing ...
% 8.72/1.93 Prover 1: Constructing countermodel ...
% 8.72/1.93 Prover 6: Constructing countermodel ...
% 9.44/2.01 Prover 4: Constructing countermodel ...
% 9.66/2.02 Prover 0: Proving ...
% 14.35/2.70 Prover 6: proved (2047ms)
% 14.35/2.70
% 14.35/2.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.35/2.70
% 14.35/2.70 Prover 0: stopped
% 14.35/2.71 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.35/2.71 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 15.09/2.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.09/2.72 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 15.09/2.79 Prover 8: Preprocessing ...
% 16.57/2.91 Prover 8: Warning: ignoring some quantifiers
% 16.72/2.93 Prover 8: Constructing countermodel ...
% 16.72/2.96 Prover 7: Preprocessing ...
% 16.72/2.96 Prover 1: Found proof (size 37)
% 16.72/2.96 Prover 1: proved (2314ms)
% 16.72/2.96 Prover 4: stopped
% 16.72/2.96 Prover 8: stopped
% 19.44/3.29 Prover 7: stopped
% 19.54/3.37 Prover 2: Proving ...
% 19.54/3.38 Prover 2: stopped
% 20.58/3.51 Prover 3: Constructing countermodel ...
% 20.58/3.51 Prover 3: stopped
% 21.47/3.74 Prover 5: Proving ...
% 21.47/3.74 Prover 5: stopped
% 21.47/3.74
% 21.47/3.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.47/3.74
% 21.47/3.76 % SZS output start Proof for theBenchmark
% 21.47/3.76 Assumptions after simplification:
% 21.47/3.76 ---------------------------------
% 21.47/3.76
% 21.47/3.76 (pow_2_21)
% 21.81/3.81 ? [v0: $real] : ( ~ (v0 = real_4) & pow(real_2, real_2) = v0)
% 21.81/3.81
% 21.81/3.81 (pow_pos)
% 21.81/3.81 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (pow(v0, v1) = v2) | ?
% 21.81/3.81 [v3: any] : ? [v4: any] : (real_$less(real_0, v2) = v4 & real_$less(real_0,
% 21.81/3.81 v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 21.81/3.81
% 21.81/3.81 (pow_x_two)
% 21.81/3.81 ! [v0: $real] : ! [v1: $real] : ( ~ (pow(v0, real_2) = v1) | ? [v2: any] :
% 21.81/3.81 ? [v3: $real] : (sqr(v0) = v3 & real_$less(real_0, v0) = v2 & ( ~ (v2 = 0) |
% 21.81/3.81 v3 = v1)))
% 21.81/3.81
% 21.81/3.81 (sqrt_positive)
% 21.81/3.81 ! [v0: $real] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $real] :
% 21.81/3.81 (sqrt(v0) = v1 & real_$lesseq(real_0, v1) = 0))
% 21.81/3.81
% 21.81/3.82 (sqrt_square)
% 21.81/3.82 ! [v0: $real] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $real] :
% 21.81/3.82 (sqrt(v0) = v1 & sqr(v1) = v0))
% 21.81/3.82
% 21.81/3.82 (square_sqrt)
% 21.81/3.82 ! [v0: $real] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $real] :
% 21.81/3.82 (sqrt(v1) = v0 & real_$product(v0, v0) = v1))
% 21.81/3.82
% 21.81/3.82 (input)
% 21.81/3.86 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_4) & ~
% 21.81/3.86 (real_very_large = real_1/2) & ~ (real_very_large = real_10) & ~
% 21.81/3.86 (real_very_large = real_2) & ~ (real_very_large = real_1) & ~
% 21.81/3.86 (real_very_large = real_0) & ~ (real_very_small = real_4) & ~
% 21.81/3.86 (real_very_small = real_1/2) & ~ (real_very_small = real_10) & ~
% 21.81/3.86 (real_very_small = real_2) & ~ (real_very_small = real_1) & ~
% 21.81/3.86 (real_very_small = real_0) & ~ (real_4 = real_1/2) & ~ (real_4 = real_10) &
% 21.81/3.86 ~ (real_4 = real_2) & ~ (real_4 = real_1) & ~ (real_4 = real_0) & ~
% 21.81/3.86 (real_1/2 = real_10) & ~ (real_1/2 = real_2) & ~ (real_1/2 = real_1) & ~
% 21.81/3.86 (real_1/2 = real_0) & ~ (real_10 = real_2) & ~ (real_10 = real_1) & ~
% 21.81/3.86 (real_10 = real_0) & ~ (real_2 = real_1) & ~ (real_2 = real_0) & ~ (real_1
% 21.81/3.86 = real_0) & real_$is_int(real_4) = 0 & real_$is_int(real_1/2) = 1 &
% 21.81/3.86 real_$is_int(real_10) = 0 & real_$is_int(real_2) = 0 & real_$is_int(real_1) =
% 21.81/3.86 0 & real_$is_int(real_0) = 0 & real_$is_rat(real_4) = 0 &
% 21.81/3.86 real_$is_rat(real_1/2) = 0 & real_$is_rat(real_10) = 0 & real_$is_rat(real_2)
% 21.81/3.86 = 0 & real_$is_rat(real_1) = 0 & real_$is_rat(real_0) = 0 &
% 21.81/3.86 real_$floor(real_4) = real_4 & real_$floor(real_1/2) = real_0 &
% 21.81/3.86 real_$floor(real_10) = real_10 & real_$floor(real_2) = real_2 &
% 21.81/3.86 real_$floor(real_1) = real_1 & real_$floor(real_0) = real_0 &
% 21.81/3.86 real_$ceiling(real_4) = real_4 & real_$ceiling(real_1/2) = real_1 &
% 21.81/3.86 real_$ceiling(real_10) = real_10 & real_$ceiling(real_2) = real_2 &
% 21.81/3.86 real_$ceiling(real_1) = real_1 & real_$ceiling(real_0) = real_0 &
% 21.81/3.86 real_$truncate(real_4) = real_4 & real_$truncate(real_1/2) = real_0 &
% 21.81/3.86 real_$truncate(real_10) = real_10 & real_$truncate(real_2) = real_2 &
% 21.81/3.86 real_$truncate(real_1) = real_1 & real_$truncate(real_0) = real_0 &
% 21.81/3.86 real_$round(real_4) = real_4 & real_$round(real_1/2) = real_1 &
% 21.81/3.86 real_$round(real_10) = real_10 & real_$round(real_2) = real_2 &
% 21.81/3.86 real_$round(real_1) = real_1 & real_$round(real_0) = real_0 &
% 21.81/3.86 real_$to_int(real_4) = 4 & real_$to_int(real_1/2) = 0 & real_$to_int(real_10)
% 21.81/3.86 = 10 & real_$to_int(real_2) = 2 & real_$to_int(real_1) = 1 &
% 21.81/3.86 real_$to_int(real_0) = 0 & real_$to_rat(real_4) = rat_4 &
% 21.81/3.86 real_$to_rat(real_1/2) = rat_1/2 & real_$to_rat(real_10) = rat_10 &
% 21.81/3.86 real_$to_rat(real_2) = rat_2 & real_$to_rat(real_1) = rat_1 &
% 21.81/3.86 real_$to_rat(real_0) = rat_0 & real_$to_real(real_4) = real_4 &
% 21.81/3.86 real_$to_real(real_1/2) = real_1/2 & real_$to_real(real_10) = real_10 &
% 21.81/3.86 real_$to_real(real_2) = real_2 & real_$to_real(real_1) = real_1 &
% 21.81/3.86 real_$to_real(real_0) = real_0 & int_$to_real(10) = real_10 & int_$to_real(4)
% 21.81/3.86 = real_4 & int_$to_real(2) = real_2 & int_$to_real(1) = real_1 &
% 21.81/3.86 int_$to_real(0) = real_0 & real_$difference(real_4, real_4) = real_0 &
% 21.81/3.86 real_$difference(real_4, real_2) = real_2 & real_$difference(real_4, real_0) =
% 21.81/3.86 real_4 & real_$difference(real_1/2, real_1/2) = real_0 &
% 21.81/3.86 real_$difference(real_1/2, real_0) = real_1/2 & real_$difference(real_10,
% 21.81/3.86 real_10) = real_0 & real_$difference(real_10, real_0) = real_10 &
% 21.81/3.86 real_$difference(real_2, real_2) = real_0 & real_$difference(real_2, real_1) =
% 21.81/3.86 real_1 & real_$difference(real_2, real_0) = real_2 & real_$difference(real_1,
% 21.81/3.86 real_1/2) = real_1/2 & real_$difference(real_1, real_1) = real_0 &
% 21.81/3.86 real_$difference(real_1, real_0) = real_1 & real_$difference(real_0, real_0) =
% 21.81/3.86 real_0 & real_$uminus(real_0) = real_0 & real_$greatereq(real_very_small,
% 21.81/3.86 real_very_large) = 1 & real_$greatereq(real_4, real_4) = 0 &
% 21.81/3.86 real_$greatereq(real_4, real_1/2) = 0 & real_$greatereq(real_4, real_10) = 1 &
% 21.81/3.86 real_$greatereq(real_4, real_2) = 0 & real_$greatereq(real_4, real_1) = 0 &
% 21.81/3.86 real_$greatereq(real_4, real_0) = 0 & real_$greatereq(real_1/2, real_4) = 1 &
% 21.81/3.86 real_$greatereq(real_1/2, real_1/2) = 0 & real_$greatereq(real_1/2, real_10) =
% 21.81/3.86 1 & real_$greatereq(real_1/2, real_2) = 1 & real_$greatereq(real_1/2, real_1)
% 21.81/3.86 = 1 & real_$greatereq(real_1/2, real_0) = 0 & real_$greatereq(real_10, real_4)
% 21.81/3.86 = 0 & real_$greatereq(real_10, real_1/2) = 0 & real_$greatereq(real_10,
% 21.81/3.86 real_10) = 0 & real_$greatereq(real_10, real_2) = 0 &
% 21.81/3.86 real_$greatereq(real_10, real_1) = 0 & real_$greatereq(real_10, real_0) = 0 &
% 21.81/3.86 real_$greatereq(real_2, real_4) = 1 & real_$greatereq(real_2, real_1/2) = 0 &
% 21.81/3.86 real_$greatereq(real_2, real_10) = 1 & real_$greatereq(real_2, real_2) = 0 &
% 21.81/3.86 real_$greatereq(real_2, real_1) = 0 & real_$greatereq(real_2, real_0) = 0 &
% 21.81/3.86 real_$greatereq(real_1, real_4) = 1 & real_$greatereq(real_1, real_1/2) = 0 &
% 21.81/3.86 real_$greatereq(real_1, real_10) = 1 & real_$greatereq(real_1, real_2) = 1 &
% 21.81/3.86 real_$greatereq(real_1, real_1) = 0 & real_$greatereq(real_1, real_0) = 0 &
% 21.81/3.86 real_$greatereq(real_0, real_4) = 1 & real_$greatereq(real_0, real_1/2) = 1 &
% 21.81/3.86 real_$greatereq(real_0, real_10) = 1 & real_$greatereq(real_0, real_2) = 1 &
% 21.81/3.87 real_$greatereq(real_0, real_1) = 1 & real_$greatereq(real_0, real_0) = 0 &
% 21.81/3.87 real_$greater(real_very_large, real_4) = 0 & real_$greater(real_very_large,
% 21.81/3.87 real_1/2) = 0 & real_$greater(real_very_large, real_10) = 0 &
% 21.81/3.87 real_$greater(real_very_large, real_2) = 0 & real_$greater(real_very_large,
% 21.81/3.87 real_1) = 0 & real_$greater(real_very_large, real_0) = 0 &
% 21.81/3.87 real_$greater(real_very_small, real_very_large) = 1 & real_$greater(real_4,
% 21.81/3.87 real_very_small) = 0 & real_$greater(real_4, real_4) = 1 &
% 21.81/3.87 real_$greater(real_4, real_1/2) = 0 & real_$greater(real_4, real_10) = 1 &
% 21.81/3.87 real_$greater(real_4, real_2) = 0 & real_$greater(real_4, real_1) = 0 &
% 21.81/3.87 real_$greater(real_4, real_0) = 0 & real_$greater(real_1/2, real_very_small) =
% 21.81/3.87 0 & real_$greater(real_1/2, real_4) = 1 & real_$greater(real_1/2, real_1/2) =
% 21.81/3.87 1 & real_$greater(real_1/2, real_10) = 1 & real_$greater(real_1/2, real_2) = 1
% 21.81/3.87 & real_$greater(real_1/2, real_1) = 1 & real_$greater(real_1/2, real_0) = 0 &
% 21.81/3.87 real_$greater(real_10, real_very_small) = 0 & real_$greater(real_10, real_4) =
% 21.81/3.87 0 & real_$greater(real_10, real_1/2) = 0 & real_$greater(real_10, real_10) = 1
% 21.81/3.87 & real_$greater(real_10, real_2) = 0 & real_$greater(real_10, real_1) = 0 &
% 21.81/3.87 real_$greater(real_10, real_0) = 0 & real_$greater(real_2, real_very_small) =
% 21.81/3.87 0 & real_$greater(real_2, real_4) = 1 & real_$greater(real_2, real_1/2) = 0 &
% 21.81/3.87 real_$greater(real_2, real_10) = 1 & real_$greater(real_2, real_2) = 1 &
% 21.81/3.87 real_$greater(real_2, real_1) = 0 & real_$greater(real_2, real_0) = 0 &
% 21.81/3.87 real_$greater(real_1, real_very_small) = 0 & real_$greater(real_1, real_4) = 1
% 21.81/3.87 & real_$greater(real_1, real_1/2) = 0 & real_$greater(real_1, real_10) = 1 &
% 21.81/3.87 real_$greater(real_1, real_2) = 1 & real_$greater(real_1, real_1) = 1 &
% 21.81/3.87 real_$greater(real_1, real_0) = 0 & real_$greater(real_0, real_very_small) = 0
% 21.81/3.87 & real_$greater(real_0, real_4) = 1 & real_$greater(real_0, real_1/2) = 1 &
% 21.81/3.87 real_$greater(real_0, real_10) = 1 & real_$greater(real_0, real_2) = 1 &
% 21.81/3.87 real_$greater(real_0, real_1) = 1 & real_$greater(real_0, real_0) = 1 &
% 21.81/3.87 real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_4,
% 21.81/3.87 real_4) = 0 & real_$lesseq(real_4, real_1/2) = 1 & real_$lesseq(real_4,
% 21.81/3.87 real_10) = 0 & real_$lesseq(real_4, real_2) = 1 & real_$lesseq(real_4,
% 21.81/3.87 real_1) = 1 & real_$lesseq(real_4, real_0) = 1 & real_$lesseq(real_1/2,
% 21.81/3.87 real_4) = 0 & real_$lesseq(real_1/2, real_1/2) = 0 & real_$lesseq(real_1/2,
% 21.81/3.87 real_10) = 0 & real_$lesseq(real_1/2, real_2) = 0 & real_$lesseq(real_1/2,
% 21.81/3.87 real_1) = 0 & real_$lesseq(real_1/2, real_0) = 1 & real_$lesseq(real_10,
% 21.81/3.87 real_4) = 1 & real_$lesseq(real_10, real_1/2) = 1 & real_$lesseq(real_10,
% 21.81/3.87 real_10) = 0 & real_$lesseq(real_10, real_2) = 1 & real_$lesseq(real_10,
% 21.81/3.87 real_1) = 1 & real_$lesseq(real_10, real_0) = 1 & real_$lesseq(real_2,
% 21.81/3.87 real_4) = 0 & real_$lesseq(real_2, real_1/2) = 1 & real_$lesseq(real_2,
% 21.81/3.87 real_10) = 0 & real_$lesseq(real_2, real_2) = 0 & real_$lesseq(real_2,
% 21.81/3.87 real_1) = 1 & real_$lesseq(real_2, real_0) = 1 & real_$lesseq(real_1,
% 21.81/3.87 real_4) = 0 & real_$lesseq(real_1, real_1/2) = 1 & real_$lesseq(real_1,
% 21.81/3.87 real_10) = 0 & real_$lesseq(real_1, real_2) = 0 & real_$lesseq(real_1,
% 21.81/3.87 real_1) = 0 & real_$lesseq(real_1, real_0) = 1 & real_$lesseq(real_0,
% 21.81/3.87 real_4) = 0 & real_$lesseq(real_0, real_1/2) = 0 & real_$lesseq(real_0,
% 21.81/3.87 real_10) = 0 & real_$lesseq(real_0, real_2) = 0 & real_$lesseq(real_0,
% 21.81/3.87 real_1) = 0 & real_$lesseq(real_0, real_0) = 0 & real_$quotient(real_4,
% 21.81/3.87 real_4) = real_1 & real_$quotient(real_4, real_2) = real_2 &
% 21.81/3.87 real_$quotient(real_4, real_1) = real_4 & real_$quotient(real_1/2, real_1/2) =
% 21.81/3.87 real_1 & real_$quotient(real_1/2, real_1) = real_1/2 & real_$quotient(real_10,
% 21.81/3.87 real_10) = real_1 & real_$quotient(real_10, real_1) = real_10 &
% 21.81/3.87 real_$quotient(real_2, real_4) = real_1/2 & real_$quotient(real_2, real_1/2) =
% 21.81/3.87 real_4 & real_$quotient(real_2, real_2) = real_1 & real_$quotient(real_2,
% 21.81/3.87 real_1) = real_2 & real_$quotient(real_1, real_1/2) = real_2 &
% 21.81/3.87 real_$quotient(real_1, real_2) = real_1/2 & real_$quotient(real_1, real_1) =
% 21.81/3.87 real_1 & real_$quotient(real_0, real_4) = real_0 & real_$quotient(real_0,
% 21.81/3.87 real_1/2) = real_0 & real_$quotient(real_0, real_10) = real_0 &
% 21.81/3.87 real_$quotient(real_0, real_2) = real_0 & real_$quotient(real_0, real_1) =
% 21.81/3.87 real_0 & real_$less(real_very_small, real_very_large) = 0 &
% 21.81/3.87 real_$less(real_very_small, real_4) = 0 & real_$less(real_very_small,
% 21.81/3.87 real_1/2) = 0 & real_$less(real_very_small, real_10) = 0 &
% 21.81/3.87 real_$less(real_very_small, real_2) = 0 & real_$less(real_very_small, real_1)
% 21.81/3.87 = 0 & real_$less(real_very_small, real_0) = 0 & real_$less(real_4,
% 21.81/3.87 real_very_large) = 0 & real_$less(real_4, real_4) = 1 & real_$less(real_4,
% 21.81/3.87 real_1/2) = 1 & real_$less(real_4, real_10) = 0 & real_$less(real_4, real_2)
% 21.81/3.87 = 1 & real_$less(real_4, real_1) = 1 & real_$less(real_4, real_0) = 1 &
% 21.81/3.87 real_$less(real_1/2, real_very_large) = 0 & real_$less(real_1/2, real_4) = 0 &
% 21.81/3.87 real_$less(real_1/2, real_1/2) = 1 & real_$less(real_1/2, real_10) = 0 &
% 21.81/3.87 real_$less(real_1/2, real_2) = 0 & real_$less(real_1/2, real_1) = 0 &
% 21.81/3.87 real_$less(real_1/2, real_0) = 1 & real_$less(real_10, real_very_large) = 0 &
% 21.81/3.87 real_$less(real_10, real_4) = 1 & real_$less(real_10, real_1/2) = 1 &
% 21.81/3.87 real_$less(real_10, real_10) = 1 & real_$less(real_10, real_2) = 1 &
% 21.81/3.87 real_$less(real_10, real_1) = 1 & real_$less(real_10, real_0) = 1 &
% 21.81/3.87 real_$less(real_2, real_very_large) = 0 & real_$less(real_2, real_4) = 0 &
% 21.81/3.87 real_$less(real_2, real_1/2) = 1 & real_$less(real_2, real_10) = 0 &
% 21.81/3.87 real_$less(real_2, real_2) = 1 & real_$less(real_2, real_1) = 1 &
% 21.81/3.87 real_$less(real_2, real_0) = 1 & real_$less(real_1, real_very_large) = 0 &
% 21.81/3.87 real_$less(real_1, real_4) = 0 & real_$less(real_1, real_1/2) = 1 &
% 21.81/3.87 real_$less(real_1, real_10) = 0 & real_$less(real_1, real_2) = 0 &
% 21.81/3.87 real_$less(real_1, real_1) = 1 & real_$less(real_1, real_0) = 1 &
% 21.81/3.87 real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_4) = 0 &
% 21.81/3.87 real_$less(real_0, real_1/2) = 0 & real_$less(real_0, real_10) = 0 &
% 21.81/3.87 real_$less(real_0, real_2) = 0 & real_$less(real_0, real_1) = 0 &
% 21.81/3.87 real_$less(real_0, real_0) = 1 & real_$product(real_4, real_1/2) = real_2 &
% 21.81/3.87 real_$product(real_4, real_1) = real_4 & real_$product(real_4, real_0) =
% 21.81/3.87 real_0 & real_$product(real_1/2, real_4) = real_2 & real_$product(real_1/2,
% 21.81/3.87 real_2) = real_1 & real_$product(real_1/2, real_1) = real_1/2 &
% 21.81/3.87 real_$product(real_1/2, real_0) = real_0 & real_$product(real_10, real_1) =
% 21.81/3.87 real_10 & real_$product(real_10, real_0) = real_0 & real_$product(real_2,
% 21.81/3.87 real_1/2) = real_1 & real_$product(real_2, real_2) = real_4 &
% 21.81/3.87 real_$product(real_2, real_1) = real_2 & real_$product(real_2, real_0) =
% 21.81/3.87 real_0 & real_$product(real_1, real_4) = real_4 & real_$product(real_1,
% 21.81/3.87 real_1/2) = real_1/2 & real_$product(real_1, real_10) = real_10 &
% 21.81/3.87 real_$product(real_1, real_2) = real_2 & real_$product(real_1, real_1) =
% 21.81/3.87 real_1 & real_$product(real_1, real_0) = real_0 & real_$product(real_0,
% 21.81/3.87 real_4) = real_0 & real_$product(real_0, real_1/2) = real_0 &
% 21.81/3.87 real_$product(real_0, real_10) = real_0 & real_$product(real_0, real_2) =
% 21.81/3.87 real_0 & real_$product(real_0, real_1) = real_0 & real_$product(real_0,
% 21.81/3.87 real_0) = real_0 & real_$sum(real_4, real_0) = real_4 & real_$sum(real_1/2,
% 21.81/3.87 real_1/2) = real_1 & real_$sum(real_1/2, real_0) = real_1/2 &
% 21.81/3.87 real_$sum(real_10, real_0) = real_10 & real_$sum(real_2, real_2) = real_4 &
% 21.81/3.87 real_$sum(real_2, real_0) = real_2 & real_$sum(real_1, real_1) = real_2 &
% 21.81/3.87 real_$sum(real_1, real_0) = real_1 & real_$sum(real_0, real_4) = real_4 &
% 21.81/3.87 real_$sum(real_0, real_1/2) = real_1/2 & real_$sum(real_0, real_10) = real_10
% 21.81/3.87 & real_$sum(real_0, real_2) = real_2 & real_$sum(real_0, real_1) = real_1 &
% 21.81/3.87 real_$sum(real_0, real_0) = real_0 & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 21.81/3.87 $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~
% 21.81/3.87 (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 &
% 21.81/3.87 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 21.81/3.87 $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~ (real_$quotient(v2,
% 21.81/3.87 v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: $real] : ! [v1:
% 21.81/3.87 $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v0)
% 21.81/3.87 = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) &
% 21.81/3.87 real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 21.81/3.87 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0) = 0) | ~
% 21.81/3.87 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1)
% 21.81/3.87 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real]
% 21.81/3.87 : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) |
% 21.81/3.87 real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 21.81/3.87 $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) =
% 21.81/3.87 v2)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~
% 21.81/3.87 (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 21.81/3.87 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 21.81/3.87 int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 =
% 21.81/3.87 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : !
% 21.81/3.87 [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3:
% 21.81/3.87 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $real] : !
% 21.81/3.87 [v1: $real] : ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~
% 21.81/3.87 (real_$less(v1, v0) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : !
% 21.81/3.87 [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = v2) |
% 21.81/3.87 real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 21.81/3.87 $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0:
% 21.81/3.87 $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) |
% 21.81/3.87 real_$less(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~
% 21.81/3.87 (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : ! [v1: $real] : ( ~
% 21.81/3.87 (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1:
% 21.81/3.87 $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & !
% 21.81/3.87 [v0: $real] : ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) |
% 21.81/3.87 real_$less(v1, v0) = 0) & ! [v0: $real] : (v0 = real_0 | ~
% 21.81/3.87 (real_$uminus(v0) = v0))
% 21.81/3.87
% 21.81/3.87 (function-axioms)
% 21.81/3.87 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 |
% 21.81/3.87 ~ (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) &
% 21.81/3.87 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : !
% 21.81/3.87 [v3: $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~
% 21.81/3.87 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 21.81/3.87 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 21.81/3.87 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0:
% 21.81/3.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 21.81/3.87 $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3,
% 21.81/3.87 v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 21.81/3.88 $real] : (v1 = v0 | ~ (pow(v3, v2) = v1) | ~ (pow(v3, v2) = v0)) & ! [v0:
% 21.81/3.88 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 21.81/3.88 (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! [v0:
% 21.81/3.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 21.81/3.88 $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) =
% 21.81/3.88 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] :
% 21.81/3.88 (v1 = v0 | ~ (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0))
% 21.81/3.88 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0
% 21.81/3.88 | ~ (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0:
% 21.81/3.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : (v1 = v0
% 21.81/3.88 | ~ (real_$is_int(v2) = v1) | ~ (real_$is_int(v2) = v0)) & ! [v0:
% 21.81/3.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : (v1 = v0
% 21.81/3.88 | ~ (real_$is_rat(v2) = v1) | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real]
% 21.81/3.88 : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~
% 21.81/3.88 (real_$floor(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 21.81/3.88 (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & !
% 21.81/3.88 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 21.81/3.88 (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) = v0)) & ! [v0: $real] :
% 21.81/3.88 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~
% 21.81/3.88 (real_$round(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1
% 21.81/3.88 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0:
% 21.81/3.88 $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) =
% 21.81/3.88 v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : !
% 21.81/3.88 [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) =
% 21.81/3.88 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~
% 21.81/3.88 (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0: $real] : !
% 21.81/3.88 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~
% 21.81/3.88 (real_$uminus(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real]
% 21.81/3.88 : (v1 = v0 | ~ (sqrt(v2) = v1) | ~ (sqrt(v2) = v0)) & ! [v0: $real] : !
% 21.81/3.88 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (sqr(v2) = v1) | ~ (sqr(v2) =
% 21.81/3.88 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 21.81/3.88 (log10(v2) = v1) | ~ (log10(v2) = v0)) & ! [v0: $real] : ! [v1: $real] :
% 21.81/3.88 ! [v2: $real] : (v1 = v0 | ~ (log2(v2) = v1) | ~ (log2(v2) = v0)) & ! [v0:
% 21.81/3.88 $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (log(v2) = v1) | ~
% 21.81/3.88 (log(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 =
% 21.81/3.88 v0 | ~ (exp(v2) = v1) | ~ (exp(v2) = v0))
% 21.81/3.88
% 21.81/3.88 Further assumptions not needed in the proof:
% 21.81/3.88 --------------------------------------------
% 22.27/3.88 exp_log, exp_sum, exp_zero, log10_def, log2_def, log_exp, log_mul, log_one,
% 22.27/3.88 pow_def, pow_half, pow_mult, pow_one_y, pow_plus, pow_x_one, pow_x_zero,
% 22.27/3.88 sqr_def, sqrt_le, sqrt_mul
% 22.27/3.88
% 22.27/3.88 Those formulas are unsatisfiable:
% 22.27/3.88 ---------------------------------
% 22.27/3.88
% 22.27/3.88 Begin of proof
% 22.27/3.88 |
% 22.27/3.88 | ALPHA: (function-axioms) implies:
% 22.27/3.88 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 22.27/3.88 | (sqr(v2) = v1) | ~ (sqr(v2) = v0))
% 22.27/3.88 | (2) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 22.27/3.88 | (sqrt(v2) = v1) | ~ (sqrt(v2) = v0))
% 22.27/3.88 | (3) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1
% 22.27/3.88 | = v0 | ~ (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) =
% 22.27/3.88 | v0))
% 22.27/3.88 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 22.27/3.88 | $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) |
% 22.27/3.88 | ~ (real_$less(v3, v2) = v0))
% 22.27/3.88 |
% 22.27/3.88 | ALPHA: (input) implies:
% 22.27/3.88 | (5) real_$product(real_2, real_2) = real_4
% 22.27/3.88 | (6) real_$less(real_0, real_2) = 0
% 22.27/3.88 | (7) real_$lesseq(real_0, real_2) = 0
% 22.27/3.88 | (8) real_$lesseq(real_0, real_4) = 0
% 22.27/3.88 |
% 22.27/3.88 | DELTA: instantiating (pow_2_21) with fresh symbol all_24_0 gives:
% 22.27/3.88 | (9) ~ (all_24_0 = real_4) & pow(real_2, real_2) = all_24_0
% 22.27/3.88 |
% 22.27/3.88 | ALPHA: (9) implies:
% 22.27/3.88 | (10) ~ (all_24_0 = real_4)
% 22.27/3.88 | (11) pow(real_2, real_2) = all_24_0
% 22.27/3.88 |
% 22.27/3.88 | GROUND_INST: instantiating (pow_x_two) with real_2, all_24_0, simplifying with
% 22.27/3.88 | (11) gives:
% 22.27/3.89 | (12) ? [v0: any] : ? [v1: $real] : (sqr(real_2) = v1 & real_$less(real_0,
% 22.27/3.89 | real_2) = v0 & ( ~ (v0 = 0) | v1 = all_24_0))
% 22.27/3.89 |
% 22.27/3.89 | GROUND_INST: instantiating (pow_pos) with real_2, real_2, all_24_0,
% 22.27/3.89 | simplifying with (11) gives:
% 22.27/3.89 | (13) ? [v0: any] : ? [v1: any] : (real_$less(real_0, all_24_0) = v1 &
% 22.27/3.89 | real_$less(real_0, real_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 22.27/3.89 |
% 22.27/3.89 | GROUND_INST: instantiating (square_sqrt) with real_2, simplifying with (7)
% 22.27/3.89 | gives:
% 22.27/3.89 | (14) ? [v0: $real] : (sqrt(v0) = real_2 & real_$product(real_2, real_2) =
% 22.27/3.89 | v0)
% 22.27/3.89 |
% 22.27/3.89 | GROUND_INST: instantiating (sqrt_positive) with real_4, simplifying with (8)
% 22.27/3.89 | gives:
% 22.27/3.89 | (15) ? [v0: $real] : (sqrt(real_4) = v0 & real_$lesseq(real_0, v0) = 0)
% 22.27/3.89 |
% 22.27/3.89 | GROUND_INST: instantiating (sqrt_square) with real_4, simplifying with (8)
% 22.27/3.89 | gives:
% 22.27/3.89 | (16) ? [v0: $real] : (sqrt(real_4) = v0 & sqr(v0) = real_4)
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (15) with fresh symbol all_39_0 gives:
% 22.27/3.89 | (17) sqrt(real_4) = all_39_0 & real_$lesseq(real_0, all_39_0) = 0
% 22.27/3.89 |
% 22.27/3.89 | ALPHA: (17) implies:
% 22.27/3.89 | (18) sqrt(real_4) = all_39_0
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (16) with fresh symbol all_55_0 gives:
% 22.27/3.89 | (19) sqrt(real_4) = all_55_0 & sqr(all_55_0) = real_4
% 22.27/3.89 |
% 22.27/3.89 | ALPHA: (19) implies:
% 22.27/3.89 | (20) sqr(all_55_0) = real_4
% 22.27/3.89 | (21) sqrt(real_4) = all_55_0
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (14) with fresh symbol all_61_0 gives:
% 22.27/3.89 | (22) sqrt(all_61_0) = real_2 & real_$product(real_2, real_2) = all_61_0
% 22.27/3.89 |
% 22.27/3.89 | ALPHA: (22) implies:
% 22.27/3.89 | (23) real_$product(real_2, real_2) = all_61_0
% 22.27/3.89 | (24) sqrt(all_61_0) = real_2
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (12) with fresh symbols all_91_0, all_91_1 gives:
% 22.27/3.89 | (25) sqr(real_2) = all_91_0 & real_$less(real_0, real_2) = all_91_1 & ( ~
% 22.27/3.89 | (all_91_1 = 0) | all_91_0 = all_24_0)
% 22.27/3.89 |
% 22.27/3.89 | ALPHA: (25) implies:
% 22.27/3.89 | (26) real_$less(real_0, real_2) = all_91_1
% 22.27/3.89 | (27) sqr(real_2) = all_91_0
% 22.27/3.89 | (28) ~ (all_91_1 = 0) | all_91_0 = all_24_0
% 22.27/3.89 |
% 22.27/3.89 | DELTA: instantiating (13) with fresh symbols all_93_0, all_93_1 gives:
% 22.27/3.89 | (29) real_$less(real_0, all_24_0) = all_93_0 & real_$less(real_0, real_2) =
% 22.27/3.89 | all_93_1 & ( ~ (all_93_1 = 0) | all_93_0 = 0)
% 22.27/3.89 |
% 22.27/3.89 | ALPHA: (29) implies:
% 22.27/3.89 | (30) real_$less(real_0, real_2) = all_93_1
% 22.27/3.89 |
% 22.27/3.89 | GROUND_INST: instantiating (3) with real_4, all_61_0, real_2, real_2,
% 22.27/3.89 | simplifying with (5), (23) gives:
% 22.27/3.89 | (31) all_61_0 = real_4
% 22.27/3.89 |
% 22.27/3.89 | GROUND_INST: instantiating (4) with 0, all_93_1, real_2, real_0, simplifying
% 22.27/3.89 | with (6), (30) gives:
% 22.27/3.89 | (32) all_93_1 = 0
% 22.27/3.89 |
% 22.35/3.89 | GROUND_INST: instantiating (4) with all_91_1, all_93_1, real_2, real_0,
% 22.35/3.89 | simplifying with (26), (30) gives:
% 22.35/3.89 | (33) all_93_1 = all_91_1
% 22.35/3.89 |
% 22.35/3.89 | GROUND_INST: instantiating (2) with all_39_0, all_55_0, real_4, simplifying
% 22.35/3.89 | with (18), (21) gives:
% 22.35/3.89 | (34) all_55_0 = all_39_0
% 22.35/3.89 |
% 22.35/3.89 | COMBINE_EQS: (32), (33) imply:
% 22.35/3.89 | (35) all_91_1 = 0
% 22.35/3.89 |
% 22.35/3.89 | REDUCE: (24), (31) imply:
% 22.35/3.89 | (36) sqrt(real_4) = real_2
% 22.35/3.89 |
% 22.35/3.89 | REDUCE: (20), (34) imply:
% 22.35/3.89 | (37) sqr(all_39_0) = real_4
% 22.35/3.89 |
% 22.35/3.89 | BETA: splitting (28) gives:
% 22.35/3.89 |
% 22.35/3.89 | Case 1:
% 22.35/3.89 | |
% 22.35/3.89 | | (38) ~ (all_91_1 = 0)
% 22.35/3.89 | |
% 22.35/3.89 | | REDUCE: (35), (38) imply:
% 22.35/3.90 | | (39) $false
% 22.35/3.90 | |
% 22.35/3.90 | | CLOSE: (39) is inconsistent.
% 22.35/3.90 | |
% 22.35/3.90 | Case 2:
% 22.35/3.90 | |
% 22.35/3.90 | | (40) all_91_0 = all_24_0
% 22.35/3.90 | |
% 22.35/3.90 | | REDUCE: (27), (40) imply:
% 22.35/3.90 | | (41) sqr(real_2) = all_24_0
% 22.35/3.90 | |
% 22.35/3.90 | | GROUND_INST: instantiating (2) with all_39_0, real_2, real_4, simplifying
% 22.35/3.90 | | with (18), (36) gives:
% 22.35/3.90 | | (42) all_39_0 = real_2
% 22.35/3.90 | |
% 22.35/3.90 | | REDUCE: (37), (42) imply:
% 22.35/3.90 | | (43) sqr(real_2) = real_4
% 22.35/3.90 | |
% 22.35/3.90 | | GROUND_INST: instantiating (1) with all_24_0, real_4, real_2, simplifying
% 22.35/3.90 | | with (41), (43) gives:
% 22.35/3.90 | | (44) all_24_0 = real_4
% 22.35/3.90 | |
% 22.35/3.90 | | REDUCE: (10), (44) imply:
% 22.35/3.90 | | (45) $false
% 22.35/3.90 | |
% 22.35/3.90 | | CLOSE: (45) is inconsistent.
% 22.35/3.90 | |
% 22.35/3.90 | End of split
% 22.35/3.90 |
% 22.35/3.90 End of proof
% 22.35/3.90 % SZS output end Proof for theBenchmark
% 22.35/3.90
% 22.35/3.90 3271ms
%------------------------------------------------------------------------------