%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI725_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 : 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 : Wed Aug 30 17:48:56 EDT 2023 % Result : Theorem 8.63s 1.97s % Output : Proof 13.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ARI725_1 : TPTP v8.1.2. Released v6.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n001.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Aug 29 18:50:08 EDT 2023 % 0.17/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.60/0.93 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.60/0.93 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.60/0.93 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 1.60/0.93 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.60/0.93 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 1.60/0.94 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.60/0.94 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 2.16/1.03 Prover 1: Preprocessing ... % 2.16/1.03 Prover 4: Preprocessing ... % 2.16/1.08 Prover 6: Preprocessing ... % 2.16/1.08 Prover 3: Preprocessing ... % 2.16/1.08 Prover 2: Preprocessing ... % 2.16/1.08 Prover 0: Preprocessing ... % 2.16/1.08 Prover 5: Preprocessing ... % 4.84/1.55 Prover 6: Proving ... % 4.84/1.58 Prover 1: Constructing countermodel ... % 4.84/1.58 Prover 4: Constructing countermodel ... % 6.33/1.62 Prover 0: Proving ... % 6.46/1.66 Prover 3: Constructing countermodel ... % 6.46/1.68 Prover 2: Proving ... % 6.46/1.69 Prover 5: Proving ... % 8.15/1.87 Prover 1: gave up % 8.24/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.24/1.89 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 8.24/1.90 Prover 7: Preprocessing ... % 8.63/1.97 Prover 3: proved (1349ms) % 8.63/1.97 % 8.63/1.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.63/1.97 % 8.63/1.97 Prover 0: stopped % 8.63/1.97 Prover 5: stopped % 8.63/1.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.63/1.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.63/1.98 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 8.63/1.98 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 8.63/1.98 Prover 2: stopped % 8.63/1.98 Prover 8: Preprocessing ... % 8.63/1.98 Prover 6: stopped % 8.63/1.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.63/1.99 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.63/1.99 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 8.63/1.99 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 8.63/1.99 Prover 10: Preprocessing ... % 8.63/1.99 Prover 13: Preprocessing ... % 8.63/1.99 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.63/2.00 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation % 8.63/2.01 Prover 11: Preprocessing ... % 8.63/2.01 Prover 16: Preprocessing ... % 9.82/2.09 Prover 7: Warning: ignoring some quantifiers % 9.82/2.10 Prover 7: Constructing countermodel ... % 9.82/2.13 Prover 8: Warning: ignoring some quantifiers % 9.82/2.14 Prover 8: Constructing countermodel ... % 9.82/2.16 Prover 13: Warning: ignoring some quantifiers % 9.82/2.18 Prover 10: Warning: ignoring some quantifiers % 9.82/2.18 Prover 13: Constructing countermodel ... % 9.82/2.19 Prover 10: Constructing countermodel ... % 9.82/2.20 Prover 16: Warning: ignoring some quantifiers % 9.82/2.21 Prover 16: Constructing countermodel ... % 9.82/2.25 Prover 11: Constructing countermodel ... % 11.48/2.34 Prover 8: gave up % 11.48/2.34 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.48/2.34 Prover 19: Warning: Problem contains reals, using incomplete axiomatisation % 11.73/2.36 Prover 19: Preprocessing ... % 12.34/2.45 Prover 10: Found proof (size 13) % 12.34/2.45 Prover 10: proved (482ms) % 12.34/2.45 Prover 7: stopped % 12.34/2.45 Prover 16: stopped % 12.34/2.45 Prover 11: stopped % 12.34/2.45 Prover 4: stopped % 12.34/2.45 Prover 13: stopped % 12.94/2.55 Prover 19: Warning: ignoring some quantifiers % 12.94/2.55 Prover 19: Constructing countermodel ... % 12.94/2.56 Prover 19: stopped % 12.94/2.56 % 12.94/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.94/2.56 % 13.04/2.56 % SZS output start Proof for theBenchmark % 13.04/2.57 Assumptions after simplification: % 13.04/2.57 --------------------------------- % 13.04/2.57 % 13.04/2.57 (prove) % 13.04/2.59 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$product(real_2, v0) = v1) | ? % 13.04/2.59 [v2: $real] : ? [v3: $real] : ? [v4: $real] : (real_$floor(v1) = v2 & % 13.04/2.59 real_$floor(v0) = v3 & real_$product(real_2, v3) = v4 & ~ % 13.04/2.59 real_$greater(v2, v4))) % 13.04/2.59 % 13.04/2.59 (input) % 13.04/2.62 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_1) & ~ % 13.04/2.62 (real_very_large = real_1/2) & ~ (real_very_large = real_4) & ~ % 13.32/2.62 (real_very_large = real_-2) & ~ (real_very_large = real_2) & ~ % 13.32/2.62 (real_very_large = real_0) & ~ (real_very_small = real_1) & ~ % 13.32/2.62 (real_very_small = real_1/2) & ~ (real_very_small = real_4) & ~ % 13.32/2.62 (real_very_small = real_-2) & ~ (real_very_small = real_2) & ~ % 13.32/2.62 (real_very_small = real_0) & ~ (real_1 = real_1/2) & ~ (real_1 = real_4) & % 13.32/2.62 ~ (real_1 = real_-2) & ~ (real_1 = real_2) & ~ (real_1 = real_0) & ~ % 13.32/2.62 (real_1/2 = real_4) & ~ (real_1/2 = real_-2) & ~ (real_1/2 = real_2) & ~ % 13.32/2.62 (real_1/2 = real_0) & ~ (real_4 = real_-2) & ~ (real_4 = real_2) & ~ % 13.32/2.62 (real_4 = real_0) & ~ (real_-2 = real_2) & ~ (real_-2 = real_0) & ~ (real_2 % 13.32/2.62 = real_0) & real_$ceiling(real_1) = real_1 & real_$ceiling(real_1/2) = % 13.32/2.62 real_1 & real_$ceiling(real_4) = real_4 & real_$ceiling(real_-2) = real_-2 & % 13.32/2.62 real_$ceiling(real_2) = real_2 & real_$ceiling(real_0) = real_0 & % 13.32/2.62 real_$truncate(real_1) = real_1 & real_$truncate(real_1/2) = real_0 & % 13.32/2.62 real_$truncate(real_4) = real_4 & real_$truncate(real_-2) = real_-2 & % 13.32/2.62 real_$truncate(real_2) = real_2 & real_$truncate(real_0) = real_0 & % 13.32/2.62 real_$round(real_1) = real_1 & real_$round(real_1/2) = real_1 & % 13.32/2.62 real_$round(real_4) = real_4 & real_$round(real_-2) = real_-2 & % 13.32/2.62 real_$round(real_2) = real_2 & real_$round(real_0) = real_0 & % 13.32/2.62 real_$to_int(real_1) = 1 & real_$to_int(real_1/2) = 0 & real_$to_int(real_4) = % 13.32/2.62 4 & real_$to_int(real_-2) = -2 & real_$to_int(real_2) = 2 & % 13.32/2.62 real_$to_int(real_0) = 0 & real_$to_rat(real_1) = rat_1 & % 13.32/2.62 real_$to_rat(real_1/2) = rat_1/2 & real_$to_rat(real_4) = rat_4 & % 13.32/2.62 real_$to_rat(real_-2) = rat_-2 & real_$to_rat(real_2) = rat_2 & % 13.32/2.62 real_$to_rat(real_0) = rat_0 & real_$to_real(real_1) = real_1 & % 13.32/2.62 real_$to_real(real_1/2) = real_1/2 & real_$to_real(real_4) = real_4 & % 13.32/2.62 real_$to_real(real_-2) = real_-2 & real_$to_real(real_2) = real_2 & % 13.32/2.62 real_$to_real(real_0) = real_0 & int_$to_real(4) = real_4 & int_$to_real(-2) = % 13.32/2.62 real_-2 & int_$to_real(2) = real_2 & int_$to_real(1) = real_1 & % 13.32/2.62 int_$to_real(0) = real_0 & real_$quotient(real_1, real_1) = real_1 & % 13.32/2.62 real_$quotient(real_1, real_1/2) = real_2 & real_$quotient(real_1, real_2) = % 13.32/2.62 real_1/2 & real_$quotient(real_1/2, real_1) = real_1/2 & % 13.32/2.62 real_$quotient(real_1/2, real_1/2) = real_1 & real_$quotient(real_4, real_1) = % 13.32/2.62 real_4 & real_$quotient(real_4, real_4) = real_1 & real_$quotient(real_4, % 13.32/2.62 real_-2) = real_-2 & real_$quotient(real_4, real_2) = real_2 & % 13.32/2.62 real_$quotient(real_-2, real_1) = real_-2 & real_$quotient(real_-2, real_-2) = % 13.32/2.62 real_1 & real_$quotient(real_2, real_1) = real_2 & real_$quotient(real_2, % 13.32/2.62 real_1/2) = real_4 & real_$quotient(real_2, real_4) = real_1/2 & % 13.32/2.62 real_$quotient(real_2, real_2) = real_1 & real_$quotient(real_0, real_1) = % 13.32/2.62 real_0 & real_$quotient(real_0, real_1/2) = real_0 & real_$quotient(real_0, % 13.32/2.62 real_4) = real_0 & real_$quotient(real_0, real_-2) = real_0 & % 13.32/2.62 real_$quotient(real_0, real_2) = real_0 & real_$difference(real_1, real_1) = % 13.32/2.62 real_0 & real_$difference(real_1, real_1/2) = real_1/2 & % 13.32/2.62 real_$difference(real_1, real_0) = real_1 & real_$difference(real_1/2, % 13.32/2.62 real_1/2) = real_0 & real_$difference(real_1/2, real_0) = real_1/2 & % 13.32/2.62 real_$difference(real_4, real_4) = real_0 & real_$difference(real_4, real_2) = % 13.32/2.62 real_2 & real_$difference(real_4, real_0) = real_4 & real_$difference(real_-2, % 13.32/2.62 real_-2) = real_0 & real_$difference(real_-2, real_0) = real_-2 & % 13.32/2.62 real_$difference(real_2, real_1) = real_1 & real_$difference(real_2, real_4) = % 13.32/2.62 real_-2 & real_$difference(real_2, real_-2) = real_4 & % 13.32/2.62 real_$difference(real_2, real_2) = real_0 & real_$difference(real_2, real_0) = % 13.32/2.62 real_2 & real_$difference(real_0, real_-2) = real_2 & real_$difference(real_0, % 13.32/2.62 real_2) = real_-2 & real_$difference(real_0, real_0) = real_0 & % 13.32/2.62 real_$uminus(real_-2) = real_2 & real_$uminus(real_2) = real_-2 & % 13.32/2.62 real_$uminus(real_0) = real_0 & real_$sum(real_1, real_1) = real_2 & % 13.32/2.62 real_$sum(real_1, real_0) = real_1 & real_$sum(real_1/2, real_1/2) = real_1 & % 13.32/2.62 real_$sum(real_1/2, real_0) = real_1/2 & real_$sum(real_4, real_-2) = real_2 & % 13.32/2.62 real_$sum(real_4, real_0) = real_4 & real_$sum(real_-2, real_4) = real_2 & % 13.32/2.62 real_$sum(real_-2, real_2) = real_0 & real_$sum(real_-2, real_0) = real_-2 & % 13.32/2.62 real_$sum(real_2, real_-2) = real_0 & real_$sum(real_2, real_2) = real_4 & % 13.32/2.62 real_$sum(real_2, real_0) = real_2 & real_$sum(real_0, real_1) = real_1 & % 13.32/2.62 real_$sum(real_0, real_1/2) = real_1/2 & real_$sum(real_0, real_4) = real_4 & % 13.32/2.62 real_$sum(real_0, real_-2) = real_-2 & real_$sum(real_0, real_2) = real_2 & % 13.32/2.62 real_$sum(real_0, real_0) = real_0 & real_$floor(real_1) = real_1 & % 13.32/2.62 real_$floor(real_1/2) = real_0 & real_$floor(real_4) = real_4 & % 13.32/2.62 real_$floor(real_-2) = real_-2 & real_$floor(real_2) = real_2 & % 13.32/2.62 real_$floor(real_0) = real_0 & real_$product(real_1, real_1) = real_1 & % 13.32/2.62 real_$product(real_1, real_1/2) = real_1/2 & real_$product(real_1, real_4) = % 13.32/2.62 real_4 & real_$product(real_1, real_-2) = real_-2 & real_$product(real_1, % 13.32/2.62 real_2) = real_2 & real_$product(real_1, real_0) = real_0 & % 13.32/2.62 real_$product(real_1/2, real_1) = real_1/2 & real_$product(real_1/2, real_4) = % 13.32/2.62 real_2 & real_$product(real_1/2, real_2) = real_1 & real_$product(real_1/2, % 13.32/2.62 real_0) = real_0 & real_$product(real_4, real_1) = real_4 & % 13.32/2.62 real_$product(real_4, real_1/2) = real_2 & real_$product(real_4, real_0) = % 13.32/2.62 real_0 & real_$product(real_-2, real_1) = real_-2 & real_$product(real_-2, % 13.32/2.62 real_-2) = real_4 & real_$product(real_-2, real_0) = real_0 & % 13.32/2.62 real_$product(real_2, real_1) = real_2 & real_$product(real_2, real_1/2) = % 13.32/2.62 real_1 & real_$product(real_2, real_2) = real_4 & real_$product(real_2, % 13.32/2.62 real_0) = real_0 & real_$product(real_0, real_1) = real_0 & % 13.32/2.62 real_$product(real_0, real_1/2) = real_0 & real_$product(real_0, real_4) = % 13.32/2.62 real_0 & real_$product(real_0, real_-2) = real_0 & real_$product(real_0, % 13.32/2.62 real_2) = real_0 & real_$product(real_0, real_0) = real_0 & % 13.32/2.62 real_$is_rat(real_1) & real_$is_rat(real_1/2) & real_$is_rat(real_4) & % 13.32/2.62 real_$is_rat(real_-2) & real_$is_rat(real_2) & real_$is_rat(real_0) & % 13.32/2.62 real_$is_int(real_1) & real_$is_int(real_4) & real_$is_int(real_-2) & % 13.32/2.62 real_$is_int(real_2) & real_$is_int(real_0) & real_$greatereq(real_1, real_1) % 13.32/2.62 & real_$greatereq(real_1, real_1/2) & real_$greatereq(real_1, real_-2) & % 13.32/2.62 real_$greatereq(real_1, real_0) & real_$greatereq(real_1/2, real_1/2) & % 13.32/2.62 real_$greatereq(real_1/2, real_-2) & real_$greatereq(real_1/2, real_0) & % 13.32/2.62 real_$greatereq(real_4, real_1) & real_$greatereq(real_4, real_1/2) & % 13.32/2.62 real_$greatereq(real_4, real_4) & real_$greatereq(real_4, real_-2) & % 13.32/2.62 real_$greatereq(real_4, real_2) & real_$greatereq(real_4, real_0) & % 13.32/2.62 real_$greatereq(real_-2, real_-2) & real_$greatereq(real_2, real_1) & % 13.32/2.62 real_$greatereq(real_2, real_1/2) & real_$greatereq(real_2, real_-2) & % 13.32/2.62 real_$greatereq(real_2, real_2) & real_$greatereq(real_2, real_0) & % 13.32/2.62 real_$greatereq(real_0, real_-2) & real_$greatereq(real_0, real_0) & % 13.32/2.62 real_$greater(real_very_large, real_1) & real_$greater(real_very_large, % 13.32/2.62 real_1/2) & real_$greater(real_very_large, real_4) & % 13.32/2.62 real_$greater(real_very_large, real_-2) & real_$greater(real_very_large, % 13.32/2.62 real_2) & real_$greater(real_very_large, real_0) & real_$greater(real_1, % 13.32/2.63 real_very_small) & real_$greater(real_1, real_1/2) & real_$greater(real_1, % 13.32/2.63 real_-2) & real_$greater(real_1, real_0) & real_$greater(real_1/2, % 13.32/2.63 real_very_small) & real_$greater(real_1/2, real_-2) & % 13.32/2.63 real_$greater(real_1/2, real_0) & real_$greater(real_4, real_very_small) & % 13.32/2.63 real_$greater(real_4, real_1) & real_$greater(real_4, real_1/2) & % 13.32/2.63 real_$greater(real_4, real_-2) & real_$greater(real_4, real_2) & % 13.32/2.63 real_$greater(real_4, real_0) & real_$greater(real_-2, real_very_small) & % 13.32/2.63 real_$greater(real_2, real_very_small) & real_$greater(real_2, real_1) & % 13.32/2.63 real_$greater(real_2, real_1/2) & real_$greater(real_2, real_-2) & % 13.32/2.63 real_$greater(real_2, real_0) & real_$greater(real_0, real_very_small) & % 13.32/2.63 real_$greater(real_0, real_-2) & real_$lesseq(real_very_small, % 13.32/2.63 real_very_large) & real_$lesseq(real_1, real_1) & real_$lesseq(real_1, % 13.32/2.63 real_4) & real_$lesseq(real_1, real_2) & real_$lesseq(real_1/2, real_1) & % 13.32/2.63 real_$lesseq(real_1/2, real_1/2) & real_$lesseq(real_1/2, real_4) & % 13.32/2.63 real_$lesseq(real_1/2, real_2) & real_$lesseq(real_4, real_4) & % 13.32/2.63 real_$lesseq(real_-2, real_1) & real_$lesseq(real_-2, real_1/2) & % 13.32/2.63 real_$lesseq(real_-2, real_4) & real_$lesseq(real_-2, real_-2) & % 13.32/2.63 real_$lesseq(real_-2, real_2) & real_$lesseq(real_-2, real_0) & % 13.32/2.63 real_$lesseq(real_2, real_4) & real_$lesseq(real_2, real_2) & % 13.32/2.63 real_$lesseq(real_0, real_1) & real_$lesseq(real_0, real_1/2) & % 13.32/2.63 real_$lesseq(real_0, real_4) & real_$lesseq(real_0, real_2) & % 13.32/2.63 real_$lesseq(real_0, real_0) & real_$less(real_very_small, real_very_large) & % 13.32/2.63 real_$less(real_very_small, real_1) & real_$less(real_very_small, real_1/2) & % 13.32/2.63 real_$less(real_very_small, real_4) & real_$less(real_very_small, real_-2) & % 13.32/2.63 real_$less(real_very_small, real_2) & real_$less(real_very_small, real_0) & % 13.32/2.63 real_$less(real_1, real_very_large) & real_$less(real_1, real_4) & % 13.32/2.63 real_$less(real_1, real_2) & real_$less(real_1/2, real_very_large) & % 13.32/2.63 real_$less(real_1/2, real_1) & real_$less(real_1/2, real_4) & % 13.32/2.63 real_$less(real_1/2, real_2) & real_$less(real_4, real_very_large) & % 13.32/2.63 real_$less(real_-2, real_very_large) & real_$less(real_-2, real_1) & % 13.32/2.63 real_$less(real_-2, real_1/2) & real_$less(real_-2, real_4) & % 13.32/2.63 real_$less(real_-2, real_2) & real_$less(real_-2, real_0) & real_$less(real_2, % 13.32/2.63 real_very_large) & real_$less(real_2, real_4) & real_$less(real_0, % 13.32/2.63 real_very_large) & real_$less(real_0, real_1) & real_$less(real_0, real_1/2) % 13.32/2.63 & real_$less(real_0, real_4) & real_$less(real_0, real_2) & ~ % 13.32/2.63 real_$is_int(real_1/2) & ~ real_$greatereq(real_very_small, real_very_large) % 13.32/2.63 & ~ real_$greatereq(real_1, real_4) & ~ real_$greatereq(real_1, real_2) & ~ % 13.32/2.63 real_$greatereq(real_1/2, real_1) & ~ real_$greatereq(real_1/2, real_4) & ~ % 13.32/2.63 real_$greatereq(real_1/2, real_2) & ~ real_$greatereq(real_-2, real_1) & ~ % 13.32/2.63 real_$greatereq(real_-2, real_1/2) & ~ real_$greatereq(real_-2, real_4) & ~ % 13.32/2.63 real_$greatereq(real_-2, real_2) & ~ real_$greatereq(real_-2, real_0) & ~ % 13.32/2.63 real_$greatereq(real_2, real_4) & ~ real_$greatereq(real_0, real_1) & ~ % 13.32/2.63 real_$greatereq(real_0, real_1/2) & ~ real_$greatereq(real_0, real_4) & ~ % 13.32/2.63 real_$greatereq(real_0, real_2) & ~ real_$greater(real_very_small, % 13.32/2.63 real_very_large) & ~ real_$greater(real_1, real_1) & ~ % 13.32/2.63 real_$greater(real_1, real_4) & ~ real_$greater(real_1, real_2) & ~ % 13.32/2.63 real_$greater(real_1/2, real_1) & ~ real_$greater(real_1/2, real_1/2) & ~ % 13.32/2.63 real_$greater(real_1/2, real_4) & ~ real_$greater(real_1/2, real_2) & ~ % 13.32/2.63 real_$greater(real_4, real_4) & ~ real_$greater(real_-2, real_1) & ~ % 13.32/2.63 real_$greater(real_-2, real_1/2) & ~ real_$greater(real_-2, real_4) & ~ % 13.32/2.63 real_$greater(real_-2, real_-2) & ~ real_$greater(real_-2, real_2) & ~ % 13.32/2.63 real_$greater(real_-2, real_0) & ~ real_$greater(real_2, real_4) & ~ % 13.32/2.63 real_$greater(real_2, real_2) & ~ real_$greater(real_0, real_1) & ~ % 13.32/2.63 real_$greater(real_0, real_1/2) & ~ real_$greater(real_0, real_4) & ~ % 13.32/2.63 real_$greater(real_0, real_2) & ~ real_$greater(real_0, real_0) & ~ % 13.32/2.63 real_$lesseq(real_1, real_1/2) & ~ real_$lesseq(real_1, real_-2) & ~ % 13.32/2.63 real_$lesseq(real_1, real_0) & ~ real_$lesseq(real_1/2, real_-2) & ~ % 13.32/2.63 real_$lesseq(real_1/2, real_0) & ~ real_$lesseq(real_4, real_1) & ~ % 13.32/2.63 real_$lesseq(real_4, real_1/2) & ~ real_$lesseq(real_4, real_-2) & ~ % 13.32/2.63 real_$lesseq(real_4, real_2) & ~ real_$lesseq(real_4, real_0) & ~ % 13.32/2.63 real_$lesseq(real_2, real_1) & ~ real_$lesseq(real_2, real_1/2) & ~ % 13.32/2.63 real_$lesseq(real_2, real_-2) & ~ real_$lesseq(real_2, real_0) & ~ % 13.32/2.63 real_$lesseq(real_0, real_-2) & ~ real_$less(real_1, real_1) & ~ % 13.32/2.63 real_$less(real_1, real_1/2) & ~ real_$less(real_1, real_-2) & ~ % 13.32/2.63 real_$less(real_1, real_0) & ~ real_$less(real_1/2, real_1/2) & ~ % 13.32/2.63 real_$less(real_1/2, real_-2) & ~ real_$less(real_1/2, real_0) & ~ % 13.32/2.63 real_$less(real_4, real_1) & ~ real_$less(real_4, real_1/2) & ~ % 13.32/2.63 real_$less(real_4, real_4) & ~ real_$less(real_4, real_-2) & ~ % 13.32/2.63 real_$less(real_4, real_2) & ~ real_$less(real_4, real_0) & ~ % 13.32/2.63 real_$less(real_-2, real_-2) & ~ real_$less(real_2, real_1) & ~ % 13.32/2.63 real_$less(real_2, real_1/2) & ~ real_$less(real_2, real_-2) & ~ % 13.32/2.63 real_$less(real_2, real_2) & ~ real_$less(real_2, real_0) & ~ % 13.32/2.63 real_$less(real_0, real_-2) & ~ real_$less(real_0, real_0) & ! [v0: $real] : % 13.32/2.63 ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ % 13.32/2.63 (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] : % 13.32/2.63 (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! % 13.32/2.63 [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~ % 13.32/2.63 (real_$quotient(v2, v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: % 13.32/2.63 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ( ~ % 13.32/2.63 (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, % 13.32/2.63 v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v2 = % 13.32/2.63 real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) = v2)) & ! [v0: % 13.32/2.63 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | % 13.32/2.63 real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : % 13.32/2.63 ( ~ (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) & ! [v0: % 13.32/2.63 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ real_$lesseq(v2, v1) | ~ % 13.32/2.63 real_$lesseq(v1, v0) | real_$lesseq(v2, v0)) & ! [v0: $real] : ! [v1: % 13.32/2.63 $real] : ! [v2: $real] : ( ~ real_$lesseq(v2, v1) | ~ real_$less(v1, v0) | % 13.32/2.63 real_$less(v2, v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 13.32/2.63 real_$lesseq(v1, v0) | ~ real_$less(v2, v1) | real_$less(v2, v0)) & ! [v0: % 13.32/2.63 $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! % 13.32/2.63 [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ real_$lesseq(v1, v0) | % 13.32/2.63 real_$less(v1, v0)) & ! [v0: $real] : ! [v1: $real] : ( ~ % 13.32/2.63 (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: % 13.32/2.63 $real] : ( ~ real_$greatereq(v0, v1) | real_$lesseq(v1, v0)) & ! [v0: % 13.32/2.63 $real] : ! [v1: $real] : ( ~ real_$greater(v0, v1) | real_$less(v1, v0)) & % 13.32/2.63 ! [v0: $real] : ! [v1: $real] : ( ~ real_$lesseq(v1, v0) | % 13.32/2.63 real_$greatereq(v0, v1)) & ! [v0: $real] : ! [v1: $real] : ( ~ % 13.32/2.63 real_$less(v1, v0) | real_$greater(v0, v1)) & ! [v0: $real] : ! [v1: % 13.32/2.63 $real] : ( ~ real_$less(v1, v0) | real_$lesseq(v1, v0)) & ! [v0: $real] : % 13.32/2.63 (v0 = real_0 | ~ (real_$uminus(v0) = v0)) & ? [v0: $real] : real_$lesseq(v0, % 13.32/2.63 v0) % 13.32/2.63 % 13.32/2.63 (function-axioms) % 13.32/2.64 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 13.32/2.64 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 13.32/2.64 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 13.32/2.64 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! % 13.32/2.64 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 13.32/2.64 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: $real] : % 13.32/2.64 ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 13.32/2.64 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: % 13.32/2.64 $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$ceiling(v2) % 13.32/2.64 = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : % 13.32/2.64 ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ % 13.32/2.64 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.32/2.64 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) & % 13.32/2.64 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2) % 13.32/2.64 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 13.32/2.64 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = % 13.32/2.64 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 13.32/2.64 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] : % 13.32/2.64 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ % 13.32/2.64 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 13.32/2.64 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) & ! % 13.32/2.64 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$floor(v2) % 13.32/2.64 = v1) | ~ (real_$floor(v2) = v0)) % 13.32/2.64 % 13.32/2.64 Those formulas are unsatisfiable: % 13.32/2.64 --------------------------------- % 13.32/2.64 % 13.32/2.64 Begin of proof % 13.32/2.64 | % 13.32/2.64 | ALPHA: (function-axioms) implies: % 13.32/2.64 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 13.32/2.64 | (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) % 13.32/2.64 | (2) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 % 13.32/2.64 | = v0 | ~ (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = % 13.32/2.64 | v0)) % 13.32/2.64 | % 13.32/2.64 | ALPHA: (input) implies: % 13.32/2.64 | (3) real_$greater(real_1, real_0) % 13.32/2.64 | (4) real_$product(real_2, real_0) = real_0 % 13.32/2.64 | (5) real_$product(real_2, real_1/2) = real_1 % 13.32/2.64 | (6) real_$floor(real_1/2) = real_0 % 13.32/2.64 | (7) real_$floor(real_1) = real_1 % 13.32/2.64 | % 13.32/2.65 | GROUND_INST: instantiating (prove) with real_1/2, real_1, simplifying with (5) % 13.32/2.65 | gives: % 13.32/2.65 | (8) ? [v0: $real] : ? [v1: $real] : ? [v2: $real] : (real_$floor(real_1) % 13.32/2.65 | = v0 & real_$floor(real_1/2) = v1 & real_$product(real_2, v1) = v2 & % 13.32/2.65 | ~ real_$greater(v0, v2)) % 13.32/2.65 | % 13.32/2.65 | DELTA: instantiating (8) with fresh symbols all_36_0, all_36_1, all_36_2 % 13.32/2.65 | gives: % 13.32/2.65 | (9) real_$floor(real_1) = all_36_2 & real_$floor(real_1/2) = all_36_1 & % 13.32/2.65 | real_$product(real_2, all_36_1) = all_36_0 & ~ real_$greater(all_36_2, % 13.32/2.65 | all_36_0) % 13.32/2.65 | % 13.32/2.65 | ALPHA: (9) implies: % 13.32/2.65 | (10) ~ real_$greater(all_36_2, all_36_0) % 13.32/2.65 | (11) real_$product(real_2, all_36_1) = all_36_0 % 13.32/2.65 | (12) real_$floor(real_1/2) = all_36_1 % 13.32/2.65 | (13) real_$floor(real_1) = all_36_2 % 13.32/2.65 | % 13.32/2.65 | GROUND_INST: instantiating (1) with real_0, all_36_1, real_1/2, simplifying % 13.32/2.65 | with (6), (12) gives: % 13.32/2.65 | (14) all_36_1 = real_0 % 13.32/2.65 | % 13.32/2.65 | GROUND_INST: instantiating (1) with real_1, all_36_2, real_1, simplifying with % 13.32/2.65 | (7), (13) gives: % 13.32/2.65 | (15) all_36_2 = real_1 % 13.32/2.65 | % 13.32/2.65 | REDUCE: (11), (14) imply: % 13.32/2.65 | (16) real_$product(real_2, real_0) = all_36_0 % 13.32/2.65 | % 13.32/2.65 | REDUCE: (10), (15) imply: % 13.32/2.65 | (17) ~ real_$greater(real_1, all_36_0) % 13.32/2.65 | % 13.32/2.65 | GROUND_INST: instantiating (2) with real_0, all_36_0, real_0, real_2, % 13.32/2.65 | simplifying with (4), (16) gives: % 13.32/2.65 | (18) all_36_0 = real_0 % 13.32/2.65 | % 13.32/2.65 | REDUCE: (17), (18) imply: % 13.32/2.65 | (19) ~ real_$greater(real_1, real_0) % 13.32/2.65 | % 13.32/2.65 | PRED_UNIFY: (3), (19) imply: % 13.32/2.65 | (20) $false % 13.49/2.65 | % 13.49/2.65 | CLOSE: (20) is inconsistent. % 13.49/2.65 | % 13.49/2.65 End of proof % 13.49/2.65 % SZS output end Proof for theBenchmark % 13.49/2.65 % 13.49/2.65 2055ms %------------------------------------------------------------------------------