%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI717_1 : TPTP v8.1.2. Released v6.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n015.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 17:48:55 EDT 2023 % Result : Theorem 8.54s 1.91s % Output : Proof 12.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ARI717_1 : TPTP v8.1.2. Released v6.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n015.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Tue Aug 29 18:44:26 EDT 2023 % 0.19/0.34 % CPUTime : % 0.19/0.58 ________ _____ % 0.19/0.58 ___ __ \_________(_)________________________________ % 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.58 (2023-06-19) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2023 % 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.58 Amanda Stjerna. % 0.19/0.58 Free software under BSD-3-Clause. % 0.19/0.58 % 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.59 Running up to 7 provers in parallel. % 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.48/0.89 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.48/0.89 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.48/0.89 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 1.48/0.89 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.48/0.89 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 1.48/0.89 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.48/0.89 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 2.07/0.98 Prover 4: Preprocessing ... % 2.07/0.98 Prover 1: Preprocessing ... % 2.28/1.02 Prover 5: Preprocessing ... % 2.28/1.02 Prover 6: Preprocessing ... % 2.28/1.02 Prover 2: Preprocessing ... % 2.28/1.02 Prover 3: Preprocessing ... % 2.59/1.04 Prover 0: Preprocessing ... % 5.58/1.52 Prover 1: Constructing countermodel ... % 5.58/1.54 Prover 6: Proving ... % 6.08/1.56 Prover 3: Constructing countermodel ... % 6.08/1.57 Prover 4: Constructing countermodel ... % 6.31/1.59 Prover 0: Proving ... % 6.31/1.60 Prover 2: Proving ... % 6.82/1.65 Prover 5: Proving ... % 7.71/1.77 Prover 1: gave up % 7.71/1.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.71/1.78 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 7.71/1.80 Prover 7: Preprocessing ... % 8.54/1.90 Prover 3: proved (1300ms) % 8.54/1.91 % 8.54/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.54/1.91 % 8.54/1.91 Prover 2: stopped % 8.54/1.91 Prover 6: stopped % 8.54/1.92 Prover 5: stopped % 8.89/1.94 Prover 0: stopped % 8.89/1.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.89/1.94 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.89/1.94 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 8.89/1.94 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 8.89/1.94 Prover 7: Warning: ignoring some quantifiers % 8.89/1.94 Prover 8: Preprocessing ... % 8.89/1.94 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.89/1.94 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 8.89/1.94 Prover 7: Constructing countermodel ... % 8.89/1.94 Prover 10: Preprocessing ... % 8.89/1.94 Prover 11: Preprocessing ... % 8.89/1.94 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.89/1.94 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.89/1.94 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 8.89/1.95 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation % 8.89/1.95 Prover 13: Preprocessing ... % 8.89/1.97 Prover 16: Preprocessing ... % 9.51/2.05 Prover 13: Warning: ignoring some quantifiers % 9.51/2.06 Prover 13: Constructing countermodel ... % 9.51/2.08 Prover 8: Warning: ignoring some quantifiers % 9.51/2.08 Prover 10: Warning: ignoring some quantifiers % 9.51/2.08 Prover 10: Constructing countermodel ... % 9.51/2.09 Prover 8: Constructing countermodel ... % 10.22/2.15 Prover 16: Warning: ignoring some quantifiers % 10.22/2.17 Prover 16: Constructing countermodel ... % 10.59/2.18 Prover 11: Constructing countermodel ... % 10.59/2.18 Prover 8: gave up % 10.59/2.20 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 10.59/2.20 Prover 19: Warning: Problem contains reals, using incomplete axiomatisation % 10.59/2.22 Prover 19: Preprocessing ... % 10.59/2.25 Prover 13: gave up % 11.36/2.31 Prover 10: Found proof (size 9) % 11.36/2.31 Prover 10: proved (396ms) % 11.36/2.31 Prover 11: stopped % 11.36/2.31 Prover 4: stopped % 11.36/2.31 Prover 16: stopped % 11.36/2.31 Prover 7: stopped % 11.81/2.39 Prover 19: Warning: ignoring some quantifiers % 11.81/2.39 Prover 19: Constructing countermodel ... % 11.81/2.40 Prover 19: stopped % 11.81/2.40 % 11.81/2.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.81/2.40 % 11.81/2.40 % SZS output start Proof for theBenchmark % 11.81/2.40 Assumptions after simplification: % 11.81/2.40 --------------------------------- % 11.81/2.41 % 11.81/2.41 (prove) % 12.14/2.43 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$sum(v0, real_1/2) = v1) | ? [v2: % 12.14/2.43 $real] : (real_$floor(v1) = v2 & ~ real_$greater(v2, v0))) % 12.14/2.43 % 12.14/2.43 (input) % 12.14/2.46 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_2) & ~ % 12.14/2.46 (real_very_large = real_1/4) & ~ (real_very_large = real_1) & ~ % 12.14/2.46 (real_very_large = real_-1/2) & ~ (real_very_large = real_1/2) & ~ % 12.14/2.46 (real_very_large = real_0) & ~ (real_very_small = real_2) & ~ % 12.14/2.46 (real_very_small = real_1/4) & ~ (real_very_small = real_1) & ~ % 12.14/2.46 (real_very_small = real_-1/2) & ~ (real_very_small = real_1/2) & ~ % 12.14/2.46 (real_very_small = real_0) & ~ (real_2 = real_1/4) & ~ (real_2 = real_1) & % 12.14/2.46 ~ (real_2 = real_-1/2) & ~ (real_2 = real_1/2) & ~ (real_2 = real_0) & ~ % 12.14/2.46 (real_1/4 = real_1) & ~ (real_1/4 = real_-1/2) & ~ (real_1/4 = real_1/2) & % 12.14/2.46 ~ (real_1/4 = real_0) & ~ (real_1 = real_-1/2) & ~ (real_1 = real_1/2) & ~ % 12.14/2.46 (real_1 = real_0) & ~ (real_-1/2 = real_1/2) & ~ (real_-1/2 = real_0) & ~ % 12.14/2.46 (real_1/2 = real_0) & real_$ceiling(real_2) = real_2 & real_$ceiling(real_1/4) % 12.14/2.46 = real_1 & real_$ceiling(real_1) = real_1 & real_$ceiling(real_-1/2) = real_0 % 12.14/2.46 & real_$ceiling(real_1/2) = real_1 & real_$ceiling(real_0) = real_0 & % 12.14/2.46 real_$truncate(real_2) = real_2 & real_$truncate(real_1/4) = real_0 & % 12.14/2.46 real_$truncate(real_1) = real_1 & real_$truncate(real_-1/2) = real_0 & % 12.14/2.46 real_$truncate(real_1/2) = real_0 & real_$truncate(real_0) = real_0 & % 12.14/2.46 real_$round(real_2) = real_2 & real_$round(real_1/4) = real_0 & % 12.14/2.46 real_$round(real_1) = real_1 & real_$round(real_-1/2) = real_0 & % 12.14/2.46 real_$round(real_1/2) = real_1 & real_$round(real_0) = real_0 & % 12.14/2.46 real_$to_int(real_2) = 2 & real_$to_int(real_1/4) = 0 & real_$to_int(real_1) = % 12.14/2.46 1 & real_$to_int(real_-1/2) = -1 & real_$to_int(real_1/2) = 0 & % 12.14/2.46 real_$to_int(real_0) = 0 & real_$to_rat(real_2) = rat_2 & % 12.14/2.46 real_$to_rat(real_1/4) = rat_1/4 & real_$to_rat(real_1) = rat_1 & % 12.14/2.46 real_$to_rat(real_-1/2) = rat_-1/2 & real_$to_rat(real_1/2) = rat_1/2 & % 12.14/2.46 real_$to_rat(real_0) = rat_0 & real_$to_real(real_2) = real_2 & % 12.14/2.46 real_$to_real(real_1/4) = real_1/4 & real_$to_real(real_1) = real_1 & % 12.14/2.46 real_$to_real(real_-1/2) = real_-1/2 & real_$to_real(real_1/2) = real_1/2 & % 12.14/2.46 real_$to_real(real_0) = real_0 & int_$to_real(2) = real_2 & int_$to_real(1) = % 12.14/2.46 real_1 & int_$to_real(0) = real_0 & real_$quotient(real_2, real_2) = real_1 & % 12.14/2.46 real_$quotient(real_2, real_1) = real_2 & real_$quotient(real_1/4, real_1/4) = % 12.14/2.46 real_1 & real_$quotient(real_1/4, real_1) = real_1/4 & % 12.14/2.46 real_$quotient(real_1/4, real_-1/2) = real_-1/2 & real_$quotient(real_1/4, % 12.14/2.46 real_1/2) = real_1/2 & real_$quotient(real_1, real_2) = real_1/2 & % 12.14/2.46 real_$quotient(real_1, real_1) = real_1 & real_$quotient(real_1, real_1/2) = % 12.14/2.46 real_2 & real_$quotient(real_-1/2, real_1) = real_-1/2 & % 12.14/2.46 real_$quotient(real_-1/2, real_-1/2) = real_1 & real_$quotient(real_1/2, % 12.14/2.46 real_2) = real_1/4 & real_$quotient(real_1/2, real_1/4) = real_2 & % 12.14/2.46 real_$quotient(real_1/2, real_1) = real_1/2 & real_$quotient(real_1/2, % 12.14/2.46 real_1/2) = real_1 & real_$quotient(real_0, real_2) = real_0 & % 12.14/2.46 real_$quotient(real_0, real_1/4) = real_0 & real_$quotient(real_0, real_1) = % 12.14/2.46 real_0 & real_$quotient(real_0, real_-1/2) = real_0 & real_$quotient(real_0, % 12.14/2.46 real_1/2) = real_0 & real_$product(real_2, real_1/4) = real_1/2 & % 12.14/2.46 real_$product(real_2, real_1) = real_2 & real_$product(real_2, real_1/2) = % 12.14/2.46 real_1 & real_$product(real_2, real_0) = real_0 & real_$product(real_1/4, % 12.14/2.46 real_2) = real_1/2 & real_$product(real_1/4, real_1) = real_1/4 & % 12.14/2.46 real_$product(real_1/4, real_0) = real_0 & real_$product(real_1, real_2) = % 12.14/2.46 real_2 & real_$product(real_1, real_1/4) = real_1/4 & real_$product(real_1, % 12.14/2.46 real_1) = real_1 & real_$product(real_1, real_-1/2) = real_-1/2 & % 12.14/2.46 real_$product(real_1, real_1/2) = real_1/2 & real_$product(real_1, real_0) = % 12.14/2.46 real_0 & real_$product(real_-1/2, real_1) = real_-1/2 & % 12.14/2.46 real_$product(real_-1/2, real_-1/2) = real_1/4 & real_$product(real_-1/2, % 12.14/2.46 real_0) = real_0 & real_$product(real_1/2, real_2) = real_1 & % 12.14/2.46 real_$product(real_1/2, real_1) = real_1/2 & real_$product(real_1/2, real_1/2) % 12.14/2.46 = real_1/4 & real_$product(real_1/2, real_0) = real_0 & real_$product(real_0, % 12.14/2.46 real_2) = real_0 & real_$product(real_0, real_1/4) = real_0 & % 12.14/2.46 real_$product(real_0, real_1) = real_0 & real_$product(real_0, real_-1/2) = % 12.14/2.46 real_0 & real_$product(real_0, real_1/2) = real_0 & real_$product(real_0, % 12.14/2.46 real_0) = real_0 & real_$difference(real_2, real_2) = real_0 & % 12.14/2.46 real_$difference(real_2, real_1) = real_1 & real_$difference(real_2, real_0) = % 12.14/2.46 real_2 & real_$difference(real_1/4, real_1/4) = real_0 & % 12.14/2.46 real_$difference(real_1/4, real_0) = real_1/4 & real_$difference(real_1, % 12.14/2.46 real_1) = real_0 & real_$difference(real_1, real_1/2) = real_1/2 & % 12.14/2.46 real_$difference(real_1, real_0) = real_1 & real_$difference(real_-1/2, % 12.14/2.46 real_-1/2) = real_0 & real_$difference(real_-1/2, real_0) = real_-1/2 & % 12.14/2.46 real_$difference(real_1/2, real_1/4) = real_1/4 & real_$difference(real_1/2, % 12.14/2.46 real_1) = real_-1/2 & real_$difference(real_1/2, real_-1/2) = real_1 & % 12.14/2.46 real_$difference(real_1/2, real_1/2) = real_0 & real_$difference(real_1/2, % 12.14/2.46 real_0) = real_1/2 & real_$difference(real_0, real_-1/2) = real_1/2 & % 12.14/2.46 real_$difference(real_0, real_1/2) = real_-1/2 & real_$difference(real_0, % 12.14/2.46 real_0) = real_0 & real_$uminus(real_-1/2) = real_1/2 & % 12.14/2.46 real_$uminus(real_1/2) = real_-1/2 & real_$uminus(real_0) = real_0 & % 12.14/2.46 real_$sum(real_2, real_0) = real_2 & real_$sum(real_1/4, real_1/4) = real_1/2 % 12.14/2.46 & real_$sum(real_1/4, real_0) = real_1/4 & real_$sum(real_1, real_1) = real_2 % 12.14/2.46 & real_$sum(real_1, real_-1/2) = real_1/2 & real_$sum(real_1, real_0) = real_1 % 12.14/2.46 & real_$sum(real_-1/2, real_1) = real_1/2 & real_$sum(real_-1/2, real_1/2) = % 12.14/2.46 real_0 & real_$sum(real_-1/2, real_0) = real_-1/2 & real_$sum(real_1/2, % 12.14/2.46 real_-1/2) = real_0 & real_$sum(real_1/2, real_1/2) = real_1 & % 12.14/2.46 real_$sum(real_1/2, real_0) = real_1/2 & real_$sum(real_0, real_2) = real_2 & % 12.14/2.46 real_$sum(real_0, real_1/4) = real_1/4 & real_$sum(real_0, real_1) = real_1 & % 12.14/2.46 real_$sum(real_0, real_-1/2) = real_-1/2 & real_$sum(real_0, real_1/2) = % 12.14/2.46 real_1/2 & real_$sum(real_0, real_0) = real_0 & real_$floor(real_2) = real_2 & % 12.14/2.46 real_$floor(real_1/4) = real_0 & real_$floor(real_1) = real_1 & % 12.14/2.46 real_$floor(real_1/2) = real_0 & real_$floor(real_0) = real_0 & % 12.14/2.46 real_$is_rat(real_2) & real_$is_rat(real_1/4) & real_$is_rat(real_1) & % 12.14/2.46 real_$is_rat(real_-1/2) & real_$is_rat(real_1/2) & real_$is_rat(real_0) & % 12.14/2.46 real_$is_int(real_2) & real_$is_int(real_1) & real_$is_int(real_0) & % 12.14/2.46 real_$greatereq(real_2, real_2) & real_$greatereq(real_2, real_1/4) & % 12.14/2.46 real_$greatereq(real_2, real_1) & real_$greatereq(real_2, real_-1/2) & % 12.14/2.46 real_$greatereq(real_2, real_1/2) & real_$greatereq(real_2, real_0) & % 12.14/2.46 real_$greatereq(real_1/4, real_1/4) & real_$greatereq(real_1/4, real_-1/2) & % 12.14/2.46 real_$greatereq(real_1/4, real_0) & real_$greatereq(real_1, real_1/4) & % 12.14/2.46 real_$greatereq(real_1, real_1) & real_$greatereq(real_1, real_-1/2) & % 12.14/2.47 real_$greatereq(real_1, real_1/2) & real_$greatereq(real_1, real_0) & % 12.14/2.47 real_$greatereq(real_-1/2, real_-1/2) & real_$greatereq(real_1/2, real_1/4) & % 12.14/2.47 real_$greatereq(real_1/2, real_-1/2) & real_$greatereq(real_1/2, real_1/2) & % 12.14/2.47 real_$greatereq(real_1/2, real_0) & real_$greatereq(real_0, real_-1/2) & % 12.14/2.47 real_$greatereq(real_0, real_0) & real_$greater(real_very_large, real_2) & % 12.14/2.47 real_$greater(real_very_large, real_1/4) & real_$greater(real_very_large, % 12.14/2.47 real_1) & real_$greater(real_very_large, real_-1/2) & % 12.14/2.47 real_$greater(real_very_large, real_1/2) & real_$greater(real_very_large, % 12.14/2.47 real_0) & real_$greater(real_2, real_very_small) & real_$greater(real_2, % 12.14/2.47 real_1/4) & real_$greater(real_2, real_1) & real_$greater(real_2, real_-1/2) % 12.14/2.47 & real_$greater(real_2, real_1/2) & real_$greater(real_2, real_0) & % 12.14/2.47 real_$greater(real_1/4, real_very_small) & real_$greater(real_1/4, real_-1/2) % 12.14/2.47 & real_$greater(real_1/4, real_0) & real_$greater(real_1, real_very_small) & % 12.14/2.47 real_$greater(real_1, real_1/4) & real_$greater(real_1, real_-1/2) & % 12.14/2.47 real_$greater(real_1, real_1/2) & real_$greater(real_1, real_0) & % 12.14/2.47 real_$greater(real_-1/2, real_very_small) & real_$greater(real_1/2, % 12.14/2.47 real_very_small) & real_$greater(real_1/2, real_1/4) & % 12.14/2.47 real_$greater(real_1/2, real_-1/2) & real_$greater(real_1/2, real_0) & % 12.14/2.47 real_$greater(real_0, real_very_small) & real_$greater(real_0, real_-1/2) & % 12.14/2.47 real_$lesseq(real_very_small, real_very_large) & real_$lesseq(real_2, real_2) % 12.14/2.47 & real_$lesseq(real_1/4, real_2) & real_$lesseq(real_1/4, real_1/4) & % 12.14/2.47 real_$lesseq(real_1/4, real_1) & real_$lesseq(real_1/4, real_1/2) & % 12.14/2.47 real_$lesseq(real_1, real_2) & real_$lesseq(real_1, real_1) & % 12.14/2.47 real_$lesseq(real_-1/2, real_2) & real_$lesseq(real_-1/2, real_1/4) & % 12.14/2.47 real_$lesseq(real_-1/2, real_1) & real_$lesseq(real_-1/2, real_-1/2) & % 12.14/2.47 real_$lesseq(real_-1/2, real_1/2) & real_$lesseq(real_-1/2, real_0) & % 12.14/2.47 real_$lesseq(real_1/2, real_2) & real_$lesseq(real_1/2, real_1) & % 12.14/2.47 real_$lesseq(real_1/2, real_1/2) & real_$lesseq(real_0, real_2) & % 12.14/2.47 real_$lesseq(real_0, real_1/4) & real_$lesseq(real_0, real_1) & % 12.14/2.47 real_$lesseq(real_0, real_1/2) & real_$lesseq(real_0, real_0) & % 12.14/2.47 real_$less(real_very_small, real_very_large) & real_$less(real_very_small, % 12.14/2.47 real_2) & real_$less(real_very_small, real_1/4) & % 12.14/2.47 real_$less(real_very_small, real_1) & real_$less(real_very_small, real_-1/2) & % 12.14/2.47 real_$less(real_very_small, real_1/2) & real_$less(real_very_small, real_0) & % 12.14/2.47 real_$less(real_2, real_very_large) & real_$less(real_1/4, real_very_large) & % 12.14/2.47 real_$less(real_1/4, real_2) & real_$less(real_1/4, real_1) & % 12.14/2.47 real_$less(real_1/4, real_1/2) & real_$less(real_1, real_very_large) & % 12.14/2.47 real_$less(real_1, real_2) & real_$less(real_-1/2, real_very_large) & % 12.14/2.47 real_$less(real_-1/2, real_2) & real_$less(real_-1/2, real_1/4) & % 12.14/2.47 real_$less(real_-1/2, real_1) & real_$less(real_-1/2, real_1/2) & % 12.14/2.47 real_$less(real_-1/2, real_0) & real_$less(real_1/2, real_very_large) & % 12.14/2.47 real_$less(real_1/2, real_2) & real_$less(real_1/2, real_1) & % 12.14/2.47 real_$less(real_0, real_very_large) & real_$less(real_0, real_2) & % 12.14/2.47 real_$less(real_0, real_1/4) & real_$less(real_0, real_1) & real_$less(real_0, % 12.14/2.47 real_1/2) & ~ real_$is_int(real_1/4) & ~ real_$is_int(real_-1/2) & ~ % 12.14/2.47 real_$is_int(real_1/2) & ~ real_$greatereq(real_very_small, real_very_large) % 12.14/2.47 & ~ real_$greatereq(real_1/4, real_2) & ~ real_$greatereq(real_1/4, real_1) % 12.14/2.47 & ~ real_$greatereq(real_1/4, real_1/2) & ~ real_$greatereq(real_1, real_2) % 12.14/2.47 & ~ real_$greatereq(real_-1/2, real_2) & ~ real_$greatereq(real_-1/2, % 12.14/2.47 real_1/4) & ~ real_$greatereq(real_-1/2, real_1) & ~ % 12.14/2.47 real_$greatereq(real_-1/2, real_1/2) & ~ real_$greatereq(real_-1/2, real_0) & % 12.14/2.47 ~ real_$greatereq(real_1/2, real_2) & ~ real_$greatereq(real_1/2, real_1) & % 12.14/2.47 ~ real_$greatereq(real_0, real_2) & ~ real_$greatereq(real_0, real_1/4) & ~ % 12.14/2.47 real_$greatereq(real_0, real_1) & ~ real_$greatereq(real_0, real_1/2) & ~ % 12.14/2.47 real_$greater(real_very_small, real_very_large) & ~ real_$greater(real_2, % 12.14/2.47 real_2) & ~ real_$greater(real_1/4, real_2) & ~ real_$greater(real_1/4, % 12.14/2.47 real_1/4) & ~ real_$greater(real_1/4, real_1) & ~ real_$greater(real_1/4, % 12.14/2.47 real_1/2) & ~ real_$greater(real_1, real_2) & ~ real_$greater(real_1, % 12.14/2.47 real_1) & ~ real_$greater(real_-1/2, real_2) & ~ real_$greater(real_-1/2, % 12.14/2.47 real_1/4) & ~ real_$greater(real_-1/2, real_1) & ~ % 12.14/2.47 real_$greater(real_-1/2, real_-1/2) & ~ real_$greater(real_-1/2, real_1/2) & % 12.14/2.47 ~ real_$greater(real_-1/2, real_0) & ~ real_$greater(real_1/2, real_2) & ~ % 12.14/2.47 real_$greater(real_1/2, real_1) & ~ real_$greater(real_1/2, real_1/2) & ~ % 12.14/2.47 real_$greater(real_0, real_2) & ~ real_$greater(real_0, real_1/4) & ~ % 12.14/2.47 real_$greater(real_0, real_1) & ~ real_$greater(real_0, real_1/2) & ~ % 12.14/2.47 real_$greater(real_0, real_0) & ~ real_$lesseq(real_2, real_1/4) & ~ % 12.14/2.47 real_$lesseq(real_2, real_1) & ~ real_$lesseq(real_2, real_-1/2) & ~ % 12.14/2.47 real_$lesseq(real_2, real_1/2) & ~ real_$lesseq(real_2, real_0) & ~ % 12.14/2.47 real_$lesseq(real_1/4, real_-1/2) & ~ real_$lesseq(real_1/4, real_0) & ~ % 12.14/2.47 real_$lesseq(real_1, real_1/4) & ~ real_$lesseq(real_1, real_-1/2) & ~ % 12.14/2.47 real_$lesseq(real_1, real_1/2) & ~ real_$lesseq(real_1, real_0) & ~ % 12.14/2.47 real_$lesseq(real_1/2, real_1/4) & ~ real_$lesseq(real_1/2, real_-1/2) & ~ % 12.14/2.47 real_$lesseq(real_1/2, real_0) & ~ real_$lesseq(real_0, real_-1/2) & ~ % 12.14/2.47 real_$less(real_2, real_2) & ~ real_$less(real_2, real_1/4) & ~ % 12.14/2.47 real_$less(real_2, real_1) & ~ real_$less(real_2, real_-1/2) & ~ % 12.14/2.47 real_$less(real_2, real_1/2) & ~ real_$less(real_2, real_0) & ~ % 12.14/2.47 real_$less(real_1/4, real_1/4) & ~ real_$less(real_1/4, real_-1/2) & ~ % 12.14/2.47 real_$less(real_1/4, real_0) & ~ real_$less(real_1, real_1/4) & ~ % 12.14/2.47 real_$less(real_1, real_1) & ~ real_$less(real_1, real_-1/2) & ~ % 12.14/2.47 real_$less(real_1, real_1/2) & ~ real_$less(real_1, real_0) & ~ % 12.14/2.47 real_$less(real_-1/2, real_-1/2) & ~ real_$less(real_1/2, real_1/4) & ~ % 12.14/2.47 real_$less(real_1/2, real_-1/2) & ~ real_$less(real_1/2, real_1/2) & ~ % 12.14/2.47 real_$less(real_1/2, real_0) & ~ real_$less(real_0, real_-1/2) & ~ % 12.14/2.47 real_$less(real_0, real_0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 12.14/2.47 : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ % 12.14/2.47 (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & % 12.14/2.47 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 12.14/2.47 $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~ (real_$quotient(v2, % 12.14/2.47 v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: $real] : ! [v1: % 12.14/2.47 $real] : ! [v2: $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) = v2) | ~ % 12.14/2.47 (real_$sum(v1, v2) = v3) | real_$difference(v1, v0) = v3) & ! [v0: $real] : % 12.14/2.47 ! [v1: $real] : ! [v2: $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | % 12.14/2.47 ~ (real_$sum(v0, v1) = v2)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 12.14/2.47 $real] : ( ~ (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) & ! % 12.14/2.47 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | % 12.40/2.47 real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : % 12.40/2.47 ( ~ real_$lesseq(v2, v1) | ~ real_$lesseq(v1, v0) | real_$lesseq(v2, v0)) & % 12.40/2.47 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ real_$lesseq(v2, v1) | % 12.40/2.47 ~ real_$less(v1, v0) | real_$less(v2, v0)) & ! [v0: $real] : ! [v1: $real] % 12.40/2.47 : ! [v2: $real] : ( ~ real_$lesseq(v1, v0) | ~ real_$less(v2, v1) | % 12.40/2.47 real_$less(v2, v0)) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ % 12.40/2.47 (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | % 12.40/2.47 ~ real_$lesseq(v1, v0) | real_$less(v1, v0)) & ! [v0: $real] : ! [v1: % 12.40/2.47 $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: % 12.40/2.47 $real] : ! [v1: $real] : ( ~ real_$greatereq(v0, v1) | real_$lesseq(v1, % 12.40/2.47 v0)) & ! [v0: $real] : ! [v1: $real] : ( ~ real_$greater(v0, v1) | % 12.40/2.47 real_$less(v1, v0)) & ! [v0: $real] : ! [v1: $real] : ( ~ real_$lesseq(v1, % 12.40/2.47 v0) | real_$greatereq(v0, v1)) & ! [v0: $real] : ! [v1: $real] : ( ~ % 12.40/2.47 real_$less(v1, v0) | real_$greater(v0, v1)) & ! [v0: $real] : ! [v1: % 12.40/2.47 $real] : ( ~ real_$less(v1, v0) | real_$lesseq(v1, v0)) & ! [v0: $real] : % 12.40/2.47 (v0 = real_0 | ~ (real_$uminus(v0) = v0)) & ? [v0: $real] : real_$lesseq(v0, % 12.40/2.47 v0) % 12.40/2.47 % 12.40/2.47 (function-axioms) % 12.40/2.48 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 12.40/2.48 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 12.40/2.48 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 12.40/2.48 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: % 12.40/2.48 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 12.40/2.48 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! % 12.40/2.48 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 12.40/2.48 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: $real] : % 12.40/2.48 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~ % 12.40/2.48 (real_$ceiling(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 12.40/2.48 : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) = v0)) & ! % 12.40/2.48 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$round(v2) % 12.40/2.48 = v1) | ~ (real_$round(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: % 12.40/2.48 $real] : (v1 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0)) % 12.40/2.48 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~ % 12.40/2.48 (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : ! % 12.40/2.48 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~ % 12.40/2.48 (real_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : % 12.40/2.48 (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0: % 12.40/2.48 $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$uminus(v2) = % 12.40/2.48 v1) | ~ (real_$uminus(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! % 12.40/2.48 [v2: $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = % 12.40/2.48 v0)) % 12.40/2.48 % 12.40/2.48 Those formulas are unsatisfiable: % 12.40/2.48 --------------------------------- % 12.40/2.48 % 12.40/2.48 Begin of proof % 12.40/2.48 | % 12.40/2.48 | ALPHA: (function-axioms) implies: % 12.40/2.48 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 12.40/2.48 | (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) % 12.40/2.48 | % 12.40/2.48 | ALPHA: (input) implies: % 12.40/2.48 | (2) real_$greater(real_0, real_-1/2) % 12.40/2.48 | (3) real_$floor(real_0) = real_0 % 12.40/2.48 | (4) real_$sum(real_-1/2, real_1/2) = real_0 % 12.40/2.48 | % 12.40/2.49 | GROUND_INST: instantiating (prove) with real_-1/2, real_0, simplifying with % 12.40/2.49 | (4) gives: % 12.40/2.49 | (5) ? [v0: $real] : (real_$floor(real_0) = v0 & ~ real_$greater(v0, % 12.40/2.49 | real_-1/2)) % 12.40/2.49 | % 12.40/2.49 | DELTA: instantiating (5) with fresh symbol all_30_0 gives: % 12.40/2.49 | (6) real_$floor(real_0) = all_30_0 & ~ real_$greater(all_30_0, real_-1/2) % 12.40/2.49 | % 12.40/2.49 | ALPHA: (6) implies: % 12.40/2.49 | (7) ~ real_$greater(all_30_0, real_-1/2) % 12.40/2.49 | (8) real_$floor(real_0) = all_30_0 % 12.40/2.49 | % 12.40/2.49 | GROUND_INST: instantiating (1) with real_0, all_30_0, real_0, simplifying with % 12.40/2.49 | (3), (8) gives: % 12.40/2.49 | (9) all_30_0 = real_0 % 12.40/2.49 | % 12.40/2.49 | REDUCE: (7), (9) imply: % 12.40/2.49 | (10) ~ real_$greater(real_0, real_-1/2) % 12.40/2.49 | % 12.40/2.49 | PRED_UNIFY: (2), (10) imply: % 12.40/2.49 | (11) $false % 12.40/2.49 | % 12.40/2.49 | CLOSE: (11) is inconsistent. % 12.40/2.49 | % 12.40/2.49 End of proof % 12.40/2.49 % SZS output end Proof for theBenchmark % 12.40/2.49 % 12.40/2.49 1906ms %------------------------------------------------------------------------------