%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI410_1 : TPTP v8.1.2. Released v5.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n013.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 17:47:56 EDT 2023 % Result : Theorem 12.36s 2.48s % Output : Proof 27.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : ARI410_1 : TPTP v8.1.2. Released v5.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n013.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 18:10:47 EDT 2023 % 0.14/0.35 % CPUTime : % 0.51/0.67 ________ _____ % 0.51/0.67 ___ __ \_________(_)________________________________ % 0.51/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.51/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.51/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.51/0.67 % 0.51/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.51/0.67 (2023-06-19) % 0.51/0.67 % 0.51/0.67 (c) Philipp Rümmer, 2009-2023 % 0.51/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.51/0.67 Amanda Stjerna. % 0.51/0.67 Free software under BSD-3-Clause. % 0.51/0.67 % 0.51/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.51/0.67 % 0.51/0.67 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.74/0.68 Running up to 7 provers in parallel. % 0.74/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.74/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.74/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.74/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.74/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.74/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.74/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.58/0.95 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.95 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.95 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.95 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.95 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.95 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.95 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 2.61/1.08 Prover 1: Preprocessing ... % 2.61/1.08 Prover 4: Preprocessing ... % 2.95/1.13 Prover 0: Preprocessing ... % 2.95/1.13 Prover 6: Preprocessing ... % 3.37/1.27 Prover 5: Preprocessing ... % 4.04/1.30 Prover 2: Preprocessing ... % 4.04/1.30 Prover 3: Preprocessing ... % 6.73/1.70 Prover 6: Constructing countermodel ... % 7.23/1.72 Prover 1: Constructing countermodel ... % 7.23/1.76 Prover 4: Constructing countermodel ... % 7.23/1.79 Prover 0: Proving ... % 11.09/2.26 Prover 6: gave up % 11.09/2.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.09/2.26 Prover 1: gave up % 11.09/2.26 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 11.09/2.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.09/2.27 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 11.09/2.28 Prover 8: Preprocessing ... % 11.85/2.34 Prover 7: Preprocessing ... % 12.36/2.44 Prover 8: Warning: ignoring some quantifiers % 12.36/2.45 Prover 8: Constructing countermodel ... % 12.36/2.48 Prover 0: proved (1786ms) % 12.36/2.48 % 12.36/2.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.36/2.48 % 12.36/2.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.36/2.50 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 13.26/2.55 Prover 10: Preprocessing ... % 15.12/2.78 Prover 8: gave up % 15.12/2.79 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.12/2.79 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 15.59/2.86 Prover 11: Preprocessing ... % 16.49/2.97 Prover 2: Proving ... % 16.49/2.97 Prover 2: stopped % 16.49/2.97 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.79/2.98 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 16.79/2.99 Prover 13: Preprocessing ... % 17.55/3.10 Prover 13: Warning: ignoring some quantifiers % 17.55/3.10 Prover 13: Constructing countermodel ... % 17.85/3.13 Prover 5: Proving ... % 17.85/3.14 Prover 5: stopped % 17.85/3.15 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 17.85/3.15 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation % 17.85/3.15 Prover 3: Constructing countermodel ... % 17.85/3.16 Prover 3: stopped % 17.85/3.18 Prover 4: Found proof (size 35) % 17.85/3.18 Prover 4: proved (2482ms) % 17.85/3.18 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 17.85/3.18 Prover 13: stopped % 17.85/3.18 Prover 19: Warning: Problem contains reals, using incomplete axiomatisation % 18.26/3.19 Prover 16: Preprocessing ... % 18.26/3.21 Prover 19: Preprocessing ... % 18.26/3.25 Prover 10: stopped % 19.42/3.39 Prover 7: Warning: ignoring some quantifiers % 19.42/3.40 Prover 7: Constructing countermodel ... % 20.02/3.44 Prover 7: stopped % 21.00/3.64 Prover 11: stopped % 21.74/3.73 Prover 16: stopped % 25.90/4.71 Prover 19: Warning: ignoring some quantifiers % 25.90/4.72 Prover 19: Constructing countermodel ... % 26.32/4.77 Prover 19: stopped % 26.32/4.77 % 26.32/4.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 26.32/4.77 % 26.32/4.78 % SZS output start Proof for theBenchmark % 26.32/4.79 Assumptions after simplification: % 26.32/4.79 --------------------------------- % 26.32/4.79 % 26.32/4.79 (real_sum_problem_10) % 26.43/4.82 ? [v0: $real] : ( ~ (v0 = real_17/4) & real_$sum(v0, real_23/4) = real_10) % 26.43/4.82 % 26.43/4.83 (input) % 26.43/4.88 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_17/4) & ~ % 26.43/4.88 (real_very_large = real_10) & ~ (real_very_large = real_23/4) & ~ % 26.43/4.88 (real_very_large = real_0) & ~ (real_very_small = real_17/4) & ~ % 26.43/4.88 (real_very_small = real_10) & ~ (real_very_small = real_23/4) & ~ % 26.43/4.88 (real_very_small = real_0) & ~ (real_17/4 = real_10) & ~ (real_17/4 = % 26.43/4.88 real_23/4) & ~ (real_17/4 = real_0) & ~ (real_10 = real_23/4) & ~ % 26.43/4.88 (real_10 = real_0) & ~ (real_23/4 = real_0) & real_$is_int(real_17/4) = 1 & % 26.43/4.89 real_$is_int(real_10) = 0 & real_$is_int(real_23/4) = 1 & real_$is_int(real_0) % 26.43/4.89 = 0 & real_$is_rat(real_17/4) = 0 & real_$is_rat(real_10) = 0 & % 26.43/4.89 real_$is_rat(real_23/4) = 0 & real_$is_rat(real_0) = 0 & real_$floor(real_10) % 26.43/4.89 = real_10 & real_$floor(real_0) = real_0 & real_$ceiling(real_10) = real_10 & % 26.43/4.89 real_$ceiling(real_0) = real_0 & real_$truncate(real_10) = real_10 & % 26.43/4.89 real_$truncate(real_0) = real_0 & real_$round(real_10) = real_10 & % 26.43/4.89 real_$round(real_0) = real_0 & real_$to_int(real_17/4) = 4 & % 26.43/4.89 real_$to_int(real_10) = 10 & real_$to_int(real_23/4) = 5 & % 26.43/4.89 real_$to_int(real_0) = 0 & real_$to_rat(real_17/4) = rat_17/4 & % 26.43/4.89 real_$to_rat(real_10) = rat_10 & real_$to_rat(real_23/4) = rat_23/4 & % 26.43/4.89 real_$to_rat(real_0) = rat_0 & real_$to_real(real_17/4) = real_17/4 & % 26.43/4.89 real_$to_real(real_10) = real_10 & real_$to_real(real_23/4) = real_23/4 & % 26.43/4.89 real_$to_real(real_0) = real_0 & int_$to_real(10) = real_10 & int_$to_real(0) % 26.43/4.89 = real_0 & real_$quotient(real_0, real_17/4) = real_0 & real_$quotient(real_0, % 26.43/4.89 real_10) = real_0 & real_$quotient(real_0, real_23/4) = real_0 & % 26.43/4.89 real_$product(real_17/4, real_0) = real_0 & real_$product(real_10, real_0) = % 26.43/4.89 real_0 & real_$product(real_23/4, real_0) = real_0 & real_$product(real_0, % 26.43/4.89 real_17/4) = real_0 & real_$product(real_0, real_10) = real_0 & % 26.43/4.89 real_$product(real_0, real_23/4) = real_0 & real_$product(real_0, real_0) = % 26.43/4.89 real_0 & real_$difference(real_17/4, real_17/4) = real_0 & % 26.43/4.89 real_$difference(real_17/4, real_0) = real_17/4 & real_$difference(real_10, % 26.43/4.89 real_17/4) = real_23/4 & real_$difference(real_10, real_10) = real_0 & % 26.43/4.89 real_$difference(real_10, real_23/4) = real_17/4 & real_$difference(real_10, % 26.43/4.89 real_0) = real_10 & real_$difference(real_23/4, real_23/4) = real_0 & % 26.43/4.89 real_$difference(real_23/4, real_0) = real_23/4 & real_$difference(real_0, % 26.43/4.89 real_0) = real_0 & real_$uminus(real_0) = real_0 & % 26.43/4.89 real_$greatereq(real_very_small, real_very_large) = 1 & % 26.43/4.89 real_$greatereq(real_17/4, real_17/4) = 0 & real_$greatereq(real_17/4, % 26.43/4.89 real_10) = 1 & real_$greatereq(real_17/4, real_23/4) = 1 & % 26.43/4.89 real_$greatereq(real_17/4, real_0) = 0 & real_$greatereq(real_10, real_17/4) = % 26.43/4.89 0 & real_$greatereq(real_10, real_10) = 0 & real_$greatereq(real_10, % 26.43/4.89 real_23/4) = 0 & real_$greatereq(real_10, real_0) = 0 & % 26.43/4.89 real_$greatereq(real_23/4, real_17/4) = 0 & real_$greatereq(real_23/4, % 26.43/4.89 real_10) = 1 & real_$greatereq(real_23/4, real_23/4) = 0 & % 26.43/4.89 real_$greatereq(real_23/4, real_0) = 0 & real_$greatereq(real_0, real_17/4) = % 26.43/4.89 1 & real_$greatereq(real_0, real_10) = 1 & real_$greatereq(real_0, real_23/4) % 26.43/4.89 = 1 & real_$greatereq(real_0, real_0) = 0 & real_$lesseq(real_very_small, % 26.43/4.89 real_very_large) = 0 & real_$lesseq(real_17/4, real_17/4) = 0 & % 26.43/4.89 real_$lesseq(real_17/4, real_10) = 0 & real_$lesseq(real_17/4, real_23/4) = 0 % 26.43/4.89 & real_$lesseq(real_17/4, real_0) = 1 & real_$lesseq(real_10, real_17/4) = 1 & % 26.43/4.89 real_$lesseq(real_10, real_10) = 0 & real_$lesseq(real_10, real_23/4) = 1 & % 26.43/4.89 real_$lesseq(real_10, real_0) = 1 & real_$lesseq(real_23/4, real_17/4) = 1 & % 26.43/4.89 real_$lesseq(real_23/4, real_10) = 0 & real_$lesseq(real_23/4, real_23/4) = 0 % 26.43/4.89 & real_$lesseq(real_23/4, real_0) = 1 & real_$lesseq(real_0, real_17/4) = 0 & % 26.43/4.89 real_$lesseq(real_0, real_10) = 0 & real_$lesseq(real_0, real_23/4) = 0 & % 26.43/4.89 real_$lesseq(real_0, real_0) = 0 & real_$greater(real_very_large, real_17/4) = % 26.43/4.89 0 & real_$greater(real_very_large, real_10) = 0 & % 26.43/4.89 real_$greater(real_very_large, real_23/4) = 0 & real_$greater(real_very_large, % 26.43/4.89 real_0) = 0 & real_$greater(real_very_small, real_very_large) = 1 & % 26.43/4.89 real_$greater(real_17/4, real_very_small) = 0 & real_$greater(real_17/4, % 26.43/4.89 real_17/4) = 1 & real_$greater(real_17/4, real_10) = 1 & % 26.43/4.89 real_$greater(real_17/4, real_23/4) = 1 & real_$greater(real_17/4, real_0) = 0 % 26.43/4.89 & real_$greater(real_10, real_very_small) = 0 & real_$greater(real_10, % 26.43/4.89 real_17/4) = 0 & real_$greater(real_10, real_10) = 1 & % 26.43/4.89 real_$greater(real_10, real_23/4) = 0 & real_$greater(real_10, real_0) = 0 & % 26.43/4.89 real_$greater(real_23/4, real_very_small) = 0 & real_$greater(real_23/4, % 26.43/4.89 real_17/4) = 0 & real_$greater(real_23/4, real_10) = 1 & % 26.43/4.89 real_$greater(real_23/4, real_23/4) = 1 & real_$greater(real_23/4, real_0) = 0 % 26.43/4.89 & real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0, % 26.43/4.89 real_17/4) = 1 & real_$greater(real_0, real_10) = 1 & real_$greater(real_0, % 26.43/4.89 real_23/4) = 1 & real_$greater(real_0, real_0) = 1 & % 26.43/4.89 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, % 26.43/4.89 real_17/4) = 0 & real_$less(real_very_small, real_10) = 0 & % 26.43/4.89 real_$less(real_very_small, real_23/4) = 0 & real_$less(real_very_small, % 26.43/4.89 real_0) = 0 & real_$less(real_17/4, real_very_large) = 0 & % 26.43/4.89 real_$less(real_17/4, real_17/4) = 1 & real_$less(real_17/4, real_10) = 0 & % 26.43/4.89 real_$less(real_17/4, real_23/4) = 0 & real_$less(real_17/4, real_0) = 1 & % 26.43/4.89 real_$less(real_10, real_very_large) = 0 & real_$less(real_10, real_17/4) = 1 % 26.43/4.89 & real_$less(real_10, real_10) = 1 & real_$less(real_10, real_23/4) = 1 & % 26.43/4.89 real_$less(real_10, real_0) = 1 & real_$less(real_23/4, real_very_large) = 0 & % 26.43/4.89 real_$less(real_23/4, real_17/4) = 1 & real_$less(real_23/4, real_10) = 0 & % 26.43/4.89 real_$less(real_23/4, real_23/4) = 1 & real_$less(real_23/4, real_0) = 1 & % 26.43/4.89 real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_17/4) = 0 & % 26.43/4.89 real_$less(real_0, real_10) = 0 & real_$less(real_0, real_23/4) = 0 & % 26.43/4.89 real_$less(real_0, real_0) = 1 & real_$sum(real_17/4, real_23/4) = real_10 & % 26.43/4.89 real_$sum(real_17/4, real_0) = real_17/4 & real_$sum(real_10, real_0) = % 26.43/4.89 real_10 & real_$sum(real_23/4, real_17/4) = real_10 & real_$sum(real_23/4, % 26.43/4.89 real_0) = real_23/4 & real_$sum(real_0, real_17/4) = real_17/4 & % 26.43/4.89 real_$sum(real_0, real_10) = real_10 & real_$sum(real_0, real_23/4) = % 26.43/4.89 real_23/4 & real_$sum(real_0, real_0) = real_0 & ! [v0: $real] : ! [v1: % 26.43/4.89 $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ % 26.43/4.89 (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] : % 26.43/4.89 (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! % 26.43/4.89 [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ % 26.43/4.90 (real_$sum(v2, v3) = v4) | ~ (real_$sum(v1, v0) = v3) | ? [v5: $real] : % 26.43/4.90 (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) = v5)) & ! [v0: $real] : ! % 26.43/4.90 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, % 26.43/4.90 v1) = 0) | ~ (real_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) % 26.43/4.90 & real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 26.43/4.90 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~ % 26.43/4.90 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0) % 26.43/4.90 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : % 26.43/4.90 (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? % 26.43/4.90 [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! % 26.43/4.90 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, % 26.43/4.90 v0) = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & % 26.43/4.90 real_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 26.43/4.90 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v1) = 0) | ~ % 26.43/4.90 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1, % 26.43/4.90 v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: % 26.43/4.90 int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~ (real_$less(v1, v0) = 0) % 26.43/4.90 | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] % 26.43/4.90 : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) = % 26.43/4.90 v2) | ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, v0) = v3) & ! % 26.43/4.90 [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 26.43/4.90 (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, % 26.43/4.90 v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | % 26.43/4.90 ~ (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 26.43/4.90 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 26.43/4.90 int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = % 26.43/4.90 0) & real_$greatereq(v0, v1) = v3)) & ! [v0: $real] : ! [v1: $real] : % 26.43/4.90 ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ % 26.43/4.90 (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : % 26.43/4.90 ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ % 26.43/4.90 (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : % 26.43/4.90 ! [v2: int] : (v2 = 0 | ~ (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 % 26.43/4.90 = 0) & real_$greater(v0, v1) = v3)) & ! [v0: $real] : ! [v1: $real] : % 26.43/4.90 ! [v2: $real] : (v0 = real_0 | ~ (real_$product(v1, v0) = v2) | % 26.43/4.90 real_$quotient(v2, v0) = v1) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 26.43/4.90 $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) & ! % 26.43/4.90 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = % 26.43/4.90 v2) | real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! % 26.43/4.90 [v2: $real] : ( ~ (real_$difference(v1, v0) = v2) | ? [v3: $real] : % 26.43/4.90 (real_$uminus(v0) = v3 & real_$sum(v1, v3) = v2)) & ! [v0: $real] : ! [v1: % 26.43/4.90 $real] : ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~ % 26.43/4.90 (real_$lesseq(v1, v0) = 0) | real_$lesseq(v2, v0) = 0) & ! [v0: $real] : ! % 26.43/4.90 [v1: $real] : ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~ % 26.43/4.90 (real_$less(v1, v0) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : ! % 26.43/4.90 [v1: $real] : ! [v2: $real] : ( ~ (real_$lesseq(v1, v0) = 0) | ~ % 26.43/4.90 (real_$less(v2, v1) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : ! % 26.43/4.90 [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, % 26.43/4.90 v1) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 26.43/4.90 (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: $real] : ! % 26.43/4.90 [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = % 26.43/4.90 0) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) % 26.43/4.90 = v1)) & ! [v0: $real] : ! [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0, % 26.43/4.90 v0) = v1)) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = % 26.43/4.90 v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 26.43/4.90 (real_$uminus(v0) = v1) | real_$sum(v0, v1) = real_0) & ! [v0: $real] : ! % 26.43/4.90 [v1: $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & % 26.43/4.90 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$lesseq(v1, v0) = 0) | % 26.43/4.90 real_$greatereq(v0, v1) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 26.43/4.90 (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & ! [v0: $real] : ! % 26.43/4.90 [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | real_$lesseq(v1, v0) = 0) & ! % 26.43/4.90 [v0: $real] : ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | % 26.43/4.90 real_$greater(v0, v1) = 0) & ! [v0: $real] : ! [v1: MultipleValueBool] : ( % 26.43/4.90 ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0) = 0) & ! [v0: $real] : % 26.43/4.90 (v0 = real_0 | ~ (real_$uminus(v0) = v0)) % 26.43/4.90 % 26.43/4.90 (function-axioms) % 26.84/4.91 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 26.84/4.91 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 26.84/4.91 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 26.84/4.91 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: % 26.84/4.91 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 26.84/4.91 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! % 26.84/4.91 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! % 26.84/4.91 [v3: $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~ % 26.84/4.91 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.84/4.91 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 26.84/4.91 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0: % 26.84/4.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 26.84/4.91 $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, % 26.84/4.91 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 26.84/4.91 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ % 26.84/4.91 (real_$less(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 26.84/4.91 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$sum(v3, v2) = v1) | ~ % 26.84/4.91 (real_$sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.84/4.91 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1) % 26.84/4.91 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.84/4.91 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) % 26.84/4.91 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 26.84/4.91 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & % 26.84/4.91 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 26.84/4.91 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] : % 26.84/4.91 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ % 26.84/4.91 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 26.84/4.91 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) & % 26.84/4.91 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2) % 26.84/4.91 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 26.84/4.91 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = % 26.84/4.91 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 26.84/4.91 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] : % 26.84/4.91 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ % 26.84/4.91 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 26.84/4.91 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) % 26.84/4.91 % 26.84/4.91 Those formulas are unsatisfiable: % 26.84/4.91 --------------------------------- % 26.84/4.91 % 26.84/4.91 Begin of proof % 26.84/4.91 | % 26.84/4.92 | ALPHA: (function-axioms) implies: % 27.03/4.92 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 27.03/4.92 | (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) % 27.03/4.92 | (2) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 % 27.03/4.92 | = v0 | ~ (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) % 27.03/4.92 | % 27.03/4.92 | ALPHA: (input) implies: % 27.03/4.92 | (3) real_$sum(real_0, real_23/4) = real_23/4 % 27.03/4.92 | (4) real_$sum(real_0, real_10) = real_10 % 27.03/4.92 | (5) real_$difference(real_23/4, real_23/4) = real_0 % 27.03/4.92 | (6) real_$difference(real_10, real_23/4) = real_17/4 % 27.03/4.92 | (7) ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) % 27.03/4.92 | = v1)) % 27.03/4.92 | (8) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 27.03/4.92 | (real_$difference(v1, v0) = v2) | ? [v3: $real] : (real_$uminus(v0) % 27.03/4.92 | = v3 & real_$sum(v1, v3) = v2)) % 27.03/4.92 | (9) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! % 27.03/4.92 | [v4: $real] : ( ~ (real_$sum(v2, v3) = v4) | ~ (real_$sum(v1, v0) = % 27.03/4.92 | v3) | ? [v5: $real] : (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) % 27.03/4.92 | = v5)) % 27.03/4.92 | (10) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! % 27.03/4.92 | [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = % 27.03/4.92 | v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) % 27.03/4.92 | = v5)) % 27.03/4.92 | % 27.03/4.92 | DELTA: instantiating (real_sum_problem_10) with fresh symbol all_5_0 gives: % 27.03/4.92 | (11) ~ (all_5_0 = real_17/4) & real_$sum(all_5_0, real_23/4) = real_10 % 27.03/4.92 | % 27.03/4.92 | ALPHA: (11) implies: % 27.03/4.92 | (12) ~ (all_5_0 = real_17/4) % 27.03/4.92 | (13) real_$sum(all_5_0, real_23/4) = real_10 % 27.03/4.92 | % 27.03/4.93 | GROUND_INST: instantiating (9) with real_23/4, all_5_0, real_0, real_10, % 27.03/4.93 | real_10, simplifying with (4), (13) gives: % 27.03/4.93 | (14) ? [v0: $real] : (real_$sum(v0, real_23/4) = real_10 & % 27.03/4.93 | real_$sum(real_0, all_5_0) = v0) % 27.03/4.93 | % 27.03/4.93 | GROUND_INST: instantiating (9) with real_23/4, real_0, all_5_0, real_23/4, % 27.03/4.93 | real_10, simplifying with (3), (13) gives: % 27.03/4.93 | (15) ? [v0: $real] : (real_$sum(v0, real_23/4) = real_10 & % 27.03/4.93 | real_$sum(all_5_0, real_0) = v0) % 27.03/4.93 | % 27.03/4.93 | GROUND_INST: instantiating (8) with real_23/4, real_23/4, real_0, simplifying % 27.03/4.93 | with (5) gives: % 27.03/4.93 | (16) ? [v0: $real] : (real_$uminus(real_23/4) = v0 & real_$sum(real_23/4, % 27.03/4.93 | v0) = real_0) % 27.03/4.93 | % 27.03/4.93 | GROUND_INST: instantiating (8) with real_23/4, real_10, real_17/4, simplifying % 27.03/4.93 | with (6) gives: % 27.03/4.93 | (17) ? [v0: $real] : (real_$uminus(real_23/4) = v0 & real_$sum(real_10, % 27.03/4.93 | v0) = real_17/4) % 27.03/4.93 | % 27.03/4.93 | DELTA: instantiating (16) with fresh symbol all_23_0 gives: % 27.03/4.93 | (18) real_$uminus(real_23/4) = all_23_0 & real_$sum(real_23/4, all_23_0) = % 27.03/4.93 | real_0 % 27.03/4.93 | % 27.03/4.93 | ALPHA: (18) implies: % 27.03/4.93 | (19) real_$sum(real_23/4, all_23_0) = real_0 % 27.03/4.93 | (20) real_$uminus(real_23/4) = all_23_0 % 27.03/4.93 | % 27.03/4.93 | DELTA: instantiating (17) with fresh symbol all_27_0 gives: % 27.03/4.93 | (21) real_$uminus(real_23/4) = all_27_0 & real_$sum(real_10, all_27_0) = % 27.03/4.93 | real_17/4 % 27.03/4.93 | % 27.03/4.93 | ALPHA: (21) implies: % 27.03/4.93 | (22) real_$sum(real_10, all_27_0) = real_17/4 % 27.03/4.93 | (23) real_$uminus(real_23/4) = all_27_0 % 27.03/4.93 | % 27.03/4.93 | DELTA: instantiating (15) with fresh symbol all_37_0 gives: % 27.03/4.93 | (24) real_$sum(all_37_0, real_23/4) = real_10 & real_$sum(all_5_0, real_0) % 27.03/4.93 | = all_37_0 % 27.03/4.93 | % 27.03/4.93 | ALPHA: (24) implies: % 27.03/4.93 | (25) real_$sum(all_5_0, real_0) = all_37_0 % 27.03/4.93 | (26) real_$sum(all_37_0, real_23/4) = real_10 % 27.03/4.93 | % 27.03/4.93 | DELTA: instantiating (14) with fresh symbol all_39_0 gives: % 27.03/4.93 | (27) real_$sum(all_39_0, real_23/4) = real_10 & real_$sum(real_0, all_5_0) % 27.03/4.93 | = all_39_0 % 27.03/4.93 | % 27.03/4.93 | ALPHA: (27) implies: % 27.03/4.93 | (28) real_$sum(all_39_0, real_23/4) = real_10 % 27.03/4.93 | % 27.03/4.93 | GROUND_INST: instantiating (7) with all_5_0, all_37_0, simplifying with (25) % 27.03/4.93 | gives: % 27.03/4.93 | (29) all_37_0 = all_5_0 % 27.03/4.93 | % 27.03/4.93 | GROUND_INST: instantiating (1) with all_23_0, all_27_0, real_23/4, simplifying % 27.03/4.93 | with (20), (23) gives: % 27.03/4.93 | (30) all_27_0 = all_23_0 % 27.03/4.93 | % 27.03/4.93 | REDUCE: (22), (30) imply: % 27.03/4.93 | (31) real_$sum(real_10, all_23_0) = real_17/4 % 27.03/4.93 | % 27.03/4.93 | GROUND_INST: instantiating (10) with all_23_0, real_23/4, all_5_0, real_10, % 27.03/4.93 | real_17/4, simplifying with (13), (31) gives: % 27.03/4.93 | (32) ? [v0: $real] : (real_$sum(all_5_0, v0) = real_17/4 & % 27.03/4.93 | real_$sum(real_23/4, all_23_0) = v0) % 27.03/4.93 | % 27.03/4.93 | GROUND_INST: instantiating (10) with all_23_0, real_23/4, all_39_0, real_10, % 27.03/4.93 | real_17/4, simplifying with (28), (31) gives: % 27.03/4.94 | (33) ? [v0: $real] : (real_$sum(all_39_0, v0) = real_17/4 & % 27.03/4.94 | real_$sum(real_23/4, all_23_0) = v0) % 27.03/4.94 | % 27.03/4.94 | DELTA: instantiating (32) with fresh symbol all_75_0 gives: % 27.03/4.94 | (34) real_$sum(all_5_0, all_75_0) = real_17/4 & real_$sum(real_23/4, % 27.03/4.94 | all_23_0) = all_75_0 % 27.03/4.94 | % 27.03/4.94 | ALPHA: (34) implies: % 27.03/4.94 | (35) real_$sum(real_23/4, all_23_0) = all_75_0 % 27.03/4.94 | (36) real_$sum(all_5_0, all_75_0) = real_17/4 % 27.03/4.94 | % 27.03/4.94 | DELTA: instantiating (33) with fresh symbol all_165_0 gives: % 27.03/4.94 | (37) real_$sum(all_39_0, all_165_0) = real_17/4 & real_$sum(real_23/4, % 27.03/4.94 | all_23_0) = all_165_0 % 27.03/4.94 | % 27.03/4.94 | ALPHA: (37) implies: % 27.03/4.94 | (38) real_$sum(real_23/4, all_23_0) = all_165_0 % 27.03/4.94 | % 27.03/4.94 | GROUND_INST: instantiating (2) with real_0, all_165_0, all_23_0, real_23/4, % 27.03/4.94 | simplifying with (19), (38) gives: % 27.03/4.94 | (39) all_165_0 = real_0 % 27.03/4.94 | % 27.03/4.94 | GROUND_INST: instantiating (2) with all_75_0, all_165_0, all_23_0, real_23/4, % 27.03/4.94 | simplifying with (35), (38) gives: % 27.03/4.94 | (40) all_165_0 = all_75_0 % 27.03/4.94 | % 27.03/4.94 | COMBINE_EQS: (39), (40) imply: % 27.03/4.94 | (41) all_75_0 = real_0 % 27.03/4.94 | % 27.03/4.94 | SIMP: (41) implies: % 27.03/4.94 | (42) all_75_0 = real_0 % 27.03/4.94 | % 27.03/4.94 | REDUCE: (36), (42) imply: % 27.03/4.94 | (43) real_$sum(all_5_0, real_0) = real_17/4 % 27.03/4.94 | % 27.03/4.94 | GROUND_INST: instantiating (7) with all_5_0, real_17/4, simplifying with (43) % 27.03/4.94 | gives: % 27.03/4.94 | (44) all_5_0 = real_17/4 % 27.03/4.94 | % 27.03/4.94 | REDUCE: (12), (44) imply: % 27.03/4.94 | (45) $false % 27.03/4.94 | % 27.03/4.94 | CLOSE: (45) is inconsistent. % 27.03/4.94 | % 27.03/4.94 End of proof % 27.03/4.94 % SZS output end Proof for theBenchmark % 27.03/4.94 % 27.03/4.94 4270ms %------------------------------------------------------------------------------