%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI431_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 : n026.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 17:48:01 EDT 2023 % Result : Theorem 22.40s 4.00s % Output : Proof 35.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : ARI431_1 : TPTP v8.1.2. Released v5.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n026.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 18:19:50 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.65 ________ _____ % 0.21/0.65 ___ __ \_________(_)________________________________ % 0.21/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.65 % 0.21/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.65 (2023-06-19) % 0.21/0.65 % 0.21/0.65 (c) Philipp Rümmer, 2009-2023 % 0.21/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.65 Amanda Stjerna. % 0.21/0.65 Free software under BSD-3-Clause. % 0.21/0.65 % 0.21/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.65 % 0.21/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.67 Running up to 7 provers in parallel. % 0.21/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.78/0.99 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 1.78/0.99 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.78/0.99 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.78/0.99 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.78/0.99 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.78/0.99 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.78/0.99 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 2.85/1.17 Prover 1: Preprocessing ... % 2.85/1.17 Prover 4: Preprocessing ... % 2.85/1.20 Prover 0: Preprocessing ... % 2.85/1.20 Prover 6: Preprocessing ... % 5.05/1.59 Prover 2: Preprocessing ... % 5.62/1.60 Prover 5: Preprocessing ... % 5.62/1.63 Prover 3: Preprocessing ... % 9.05/2.14 Prover 6: Constructing countermodel ... % 9.05/2.15 Prover 1: Constructing countermodel ... % 9.05/2.23 Prover 4: Constructing countermodel ... % 10.87/2.40 Prover 0: Proving ... % 15.82/3.07 Prover 1: gave up % 15.82/3.09 Prover 6: gave up % 15.82/3.12 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.82/3.12 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 15.82/3.12 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.23/3.13 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 16.50/3.16 Prover 8: Preprocessing ... % 17.01/3.25 Prover 7: Preprocessing ... % 17.99/3.42 Prover 8: Warning: ignoring some quantifiers % 18.39/3.43 Prover 8: Constructing countermodel ... % 20.53/3.83 Prover 3: Constructing countermodel ... % 21.54/3.89 Prover 2: Proving ... % 22.40/3.99 Prover 0: proved (3310ms) % 22.40/3.99 % 22.40/4.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.40/4.00 % 22.40/4.00 Prover 3: stopped % 22.40/4.01 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.40/4.01 Prover 8: gave up % 22.40/4.01 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 22.40/4.02 Prover 2: stopped % 22.40/4.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 22.40/4.03 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 22.40/4.03 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 22.40/4.03 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 22.40/4.03 Prover 13: Preprocessing ... % 22.40/4.03 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 22.40/4.03 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation % 23.27/4.09 Prover 10: Preprocessing ... % 23.27/4.11 Prover 11: Preprocessing ... % 23.27/4.13 Prover 13: Warning: ignoring some quantifiers % 23.71/4.13 Prover 13: Constructing countermodel ... % 23.71/4.15 Prover 16: Preprocessing ... % 24.73/4.29 Prover 7: Warning: ignoring some quantifiers % 24.73/4.31 Prover 7: Constructing countermodel ... % 24.73/4.42 Prover 5: Proving ... % 24.73/4.43 Prover 5: stopped % 24.73/4.44 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 24.73/4.44 Prover 19: Warning: Problem contains reals, using incomplete axiomatisation % 25.97/4.48 Prover 13: gave up % 26.42/4.52 Prover 19: Preprocessing ... % 26.42/4.57 Prover 4: Found proof (size 40) % 26.88/4.57 Prover 4: proved (3875ms) % 26.88/4.57 Prover 7: stopped % 26.88/4.58 Prover 16: stopped % 26.88/4.65 Prover 11: stopped % 28.12/4.82 Prover 10: Warning: ignoring some quantifiers % 28.12/4.83 Prover 10: Constructing countermodel ... % 28.42/4.91 Prover 10: stopped % 34.91/6.52 Prover 19: Warning: ignoring some quantifiers % 34.91/6.54 Prover 19: Constructing countermodel ... % 35.37/6.59 Prover 19: stopped % 35.37/6.59 % 35.37/6.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 35.37/6.59 % 35.43/6.60 % SZS output start Proof for theBenchmark % 35.43/6.61 Assumptions after simplification: % 35.43/6.61 --------------------------------- % 35.43/6.61 % 35.43/6.61 (real_difference_problem_7) % 35.48/6.64 ? [v0: $real] : ( ~ (v0 = real_321/20) & real_$difference(v0, real_241/20) = % 35.48/6.64 real_4) % 35.48/6.64 % 35.48/6.64 (input) % 35.48/6.69 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_321/20) & % 35.48/6.69 ~ (real_very_large = real_4) & ~ (real_very_large = real_241/20) & ~ % 35.48/6.69 (real_very_large = real_0) & ~ (real_very_small = real_321/20) & ~ % 35.48/6.69 (real_very_small = real_4) & ~ (real_very_small = real_241/20) & ~ % 35.48/6.69 (real_very_small = real_0) & ~ (real_321/20 = real_4) & ~ (real_321/20 = % 35.48/6.69 real_241/20) & ~ (real_321/20 = real_0) & ~ (real_4 = real_241/20) & ~ % 35.48/6.69 (real_4 = real_0) & ~ (real_241/20 = real_0) & real_$is_int(real_321/20) = 1 % 35.48/6.69 & real_$is_int(real_4) = 0 & real_$is_int(real_241/20) = 1 & % 35.48/6.69 real_$is_int(real_0) = 0 & real_$is_rat(real_321/20) = 0 & % 35.48/6.69 real_$is_rat(real_4) = 0 & real_$is_rat(real_241/20) = 0 & % 35.48/6.69 real_$is_rat(real_0) = 0 & real_$floor(real_4) = real_4 & real_$floor(real_0) % 35.48/6.69 = real_0 & real_$ceiling(real_4) = real_4 & real_$ceiling(real_0) = real_0 & % 35.48/6.69 real_$truncate(real_4) = real_4 & real_$truncate(real_0) = real_0 & % 35.48/6.69 real_$round(real_4) = real_4 & real_$round(real_0) = real_0 & % 35.48/6.69 real_$to_int(real_321/20) = 16 & real_$to_int(real_4) = 4 & % 35.48/6.70 real_$to_int(real_241/20) = 12 & real_$to_int(real_0) = 0 & % 35.48/6.70 real_$to_rat(real_321/20) = rat_321/20 & real_$to_rat(real_4) = rat_4 & % 35.48/6.70 real_$to_rat(real_241/20) = rat_241/20 & real_$to_rat(real_0) = rat_0 & % 35.48/6.70 real_$to_real(real_321/20) = real_321/20 & real_$to_real(real_4) = real_4 & % 35.48/6.70 real_$to_real(real_241/20) = real_241/20 & real_$to_real(real_0) = real_0 & % 35.48/6.70 int_$to_real(4) = real_4 & int_$to_real(0) = real_0 & real_$quotient(real_0, % 35.48/6.70 real_321/20) = real_0 & real_$quotient(real_0, real_4) = real_0 & % 35.48/6.70 real_$quotient(real_0, real_241/20) = real_0 & real_$product(real_321/20, % 35.48/6.70 real_0) = real_0 & real_$product(real_4, real_0) = real_0 & % 35.48/6.70 real_$product(real_241/20, real_0) = real_0 & real_$product(real_0, % 35.48/6.70 real_321/20) = real_0 & real_$product(real_0, real_4) = real_0 & % 35.48/6.70 real_$product(real_0, real_241/20) = real_0 & real_$product(real_0, real_0) = % 35.48/6.70 real_0 & real_$uminus(real_0) = real_0 & real_$sum(real_321/20, real_0) = % 35.48/6.70 real_321/20 & real_$sum(real_4, real_241/20) = real_321/20 & real_$sum(real_4, % 35.48/6.70 real_0) = real_4 & real_$sum(real_241/20, real_4) = real_321/20 & % 35.48/6.70 real_$sum(real_241/20, real_0) = real_241/20 & real_$sum(real_0, real_321/20) % 35.48/6.70 = real_321/20 & real_$sum(real_0, real_4) = real_4 & real_$sum(real_0, % 35.48/6.70 real_241/20) = real_241/20 & real_$sum(real_0, real_0) = real_0 & % 35.48/6.70 real_$greatereq(real_very_small, real_very_large) = 1 & % 35.48/6.70 real_$greatereq(real_321/20, real_321/20) = 0 & real_$greatereq(real_321/20, % 35.48/6.70 real_4) = 0 & real_$greatereq(real_321/20, real_241/20) = 0 & % 35.48/6.70 real_$greatereq(real_321/20, real_0) = 0 & real_$greatereq(real_4, % 35.48/6.70 real_321/20) = 1 & real_$greatereq(real_4, real_4) = 0 & % 35.48/6.70 real_$greatereq(real_4, real_241/20) = 1 & real_$greatereq(real_4, real_0) = 0 % 35.48/6.70 & real_$greatereq(real_241/20, real_321/20) = 1 & real_$greatereq(real_241/20, % 35.48/6.70 real_4) = 0 & real_$greatereq(real_241/20, real_241/20) = 0 & % 35.48/6.70 real_$greatereq(real_241/20, real_0) = 0 & real_$greatereq(real_0, % 35.48/6.70 real_321/20) = 1 & real_$greatereq(real_0, real_4) = 1 & % 35.48/6.70 real_$greatereq(real_0, real_241/20) = 1 & real_$greatereq(real_0, real_0) = 0 % 35.48/6.70 & real_$lesseq(real_very_small, real_very_large) = 0 & % 35.48/6.70 real_$lesseq(real_321/20, real_321/20) = 0 & real_$lesseq(real_321/20, real_4) % 35.48/6.70 = 1 & real_$lesseq(real_321/20, real_241/20) = 1 & real_$lesseq(real_321/20, % 35.48/6.70 real_0) = 1 & real_$lesseq(real_4, real_321/20) = 0 & real_$lesseq(real_4, % 35.48/6.70 real_4) = 0 & real_$lesseq(real_4, real_241/20) = 0 & real_$lesseq(real_4, % 35.48/6.70 real_0) = 1 & real_$lesseq(real_241/20, real_321/20) = 0 & % 35.48/6.70 real_$lesseq(real_241/20, real_4) = 1 & real_$lesseq(real_241/20, real_241/20) % 35.48/6.70 = 0 & real_$lesseq(real_241/20, real_0) = 1 & real_$lesseq(real_0, % 35.48/6.70 real_321/20) = 0 & real_$lesseq(real_0, real_4) = 0 & real_$lesseq(real_0, % 35.48/6.70 real_241/20) = 0 & real_$lesseq(real_0, real_0) = 0 & % 35.48/6.70 real_$greater(real_very_large, real_321/20) = 0 & % 35.48/6.70 real_$greater(real_very_large, real_4) = 0 & real_$greater(real_very_large, % 35.48/6.70 real_241/20) = 0 & real_$greater(real_very_large, real_0) = 0 & % 35.48/6.70 real_$greater(real_very_small, real_very_large) = 1 & % 35.48/6.70 real_$greater(real_321/20, real_very_small) = 0 & real_$greater(real_321/20, % 35.48/6.70 real_321/20) = 1 & real_$greater(real_321/20, real_4) = 0 & % 35.48/6.70 real_$greater(real_321/20, real_241/20) = 0 & real_$greater(real_321/20, % 35.48/6.70 real_0) = 0 & real_$greater(real_4, real_very_small) = 0 & % 35.48/6.70 real_$greater(real_4, real_321/20) = 1 & real_$greater(real_4, real_4) = 1 & % 35.48/6.70 real_$greater(real_4, real_241/20) = 1 & real_$greater(real_4, real_0) = 0 & % 35.48/6.70 real_$greater(real_241/20, real_very_small) = 0 & real_$greater(real_241/20, % 35.48/6.70 real_321/20) = 1 & real_$greater(real_241/20, real_4) = 0 & % 35.48/6.70 real_$greater(real_241/20, real_241/20) = 1 & real_$greater(real_241/20, % 35.48/6.70 real_0) = 0 & real_$greater(real_0, real_very_small) = 0 & % 35.48/6.70 real_$greater(real_0, real_321/20) = 1 & real_$greater(real_0, real_4) = 1 & % 35.48/6.70 real_$greater(real_0, real_241/20) = 1 & real_$greater(real_0, real_0) = 1 & % 35.48/6.70 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, % 35.48/6.70 real_321/20) = 0 & real_$less(real_very_small, real_4) = 0 & % 35.48/6.70 real_$less(real_very_small, real_241/20) = 0 & real_$less(real_very_small, % 35.48/6.70 real_0) = 0 & real_$less(real_321/20, real_very_large) = 0 & % 35.48/6.70 real_$less(real_321/20, real_321/20) = 1 & real_$less(real_321/20, real_4) = 1 % 35.48/6.70 & real_$less(real_321/20, real_241/20) = 1 & real_$less(real_321/20, real_0) = % 35.48/6.70 1 & real_$less(real_4, real_very_large) = 0 & real_$less(real_4, real_321/20) % 35.48/6.70 = 0 & real_$less(real_4, real_4) = 1 & real_$less(real_4, real_241/20) = 0 & % 35.48/6.70 real_$less(real_4, real_0) = 1 & real_$less(real_241/20, real_very_large) = 0 % 35.48/6.70 & real_$less(real_241/20, real_321/20) = 0 & real_$less(real_241/20, real_4) = % 35.48/6.70 1 & real_$less(real_241/20, real_241/20) = 1 & real_$less(real_241/20, real_0) % 35.48/6.70 = 1 & real_$less(real_0, real_very_large) = 0 & real_$less(real_0, % 35.48/6.70 real_321/20) = 0 & real_$less(real_0, real_4) = 0 & real_$less(real_0, % 35.48/6.70 real_241/20) = 0 & real_$less(real_0, real_0) = 1 & % 35.48/6.70 real_$difference(real_321/20, real_321/20) = real_0 & % 35.48/6.70 real_$difference(real_321/20, real_4) = real_241/20 & % 35.48/6.70 real_$difference(real_321/20, real_241/20) = real_4 & % 35.48/6.70 real_$difference(real_321/20, real_0) = real_321/20 & real_$difference(real_4, % 35.48/6.70 real_4) = real_0 & real_$difference(real_4, real_0) = real_4 & % 35.48/6.70 real_$difference(real_241/20, real_241/20) = real_0 & % 35.48/6.70 real_$difference(real_241/20, real_0) = real_241/20 & real_$difference(real_0, % 35.48/6.70 real_0) = real_0 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! % 35.48/6.70 [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ % 35.48/6.70 (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & % 35.48/6.70 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 35.48/6.70 $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v2, v3) = v4) | ~ % 35.48/6.70 (real_$sum(v1, v0) = v3) | ? [v5: $real] : (real_$sum(v5, v0) = v4 & % 35.48/6.70 real_$sum(v2, v1) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 35.48/6.70 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~ % 35.48/6.70 (real_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1, % 35.48/6.70 v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: % 35.48/6.70 int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v2, v0) = % 35.48/6.70 v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0) = v4)) & ! [v0: % 35.48/6.70 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ % 35.48/6.70 (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] : % 35.48/6.71 ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] % 35.48/6.71 : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0) = 0) | ~ % 35.48/6.71 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1) % 35.48/6.71 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : % 35.48/6.71 (v3 = 0 | ~ (real_$less(v2, v1) = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: % 35.48/6.71 int] : ( ~ (v4 = 0) & real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : ! % 35.48/6.71 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0) % 35.48/6.71 = v3) | ~ (real_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & % 35.48/6.71 real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 35.48/6.71 $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, % 35.48/6.71 v2) = v3) | real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: % 35.48/6.71 $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (real_$less(v1, v0) = v2) | % 35.48/6.71 ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : % 35.48/6.71 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greatereq(v0, v1) = v2) | % 35.48/6.71 ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : % 35.48/6.71 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? % 35.48/6.71 [v3: int] : ( ~ (v3 = 0) & real_$greatereq(v0, v1) = v3)) & ! [v0: $real] : % 35.48/6.71 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? % 35.48/6.71 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! % 35.48/6.71 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? % 35.48/6.71 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! % 35.48/6.71 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$less(v1, v0) = v2) | ? [v3: % 35.48/6.71 int] : ( ~ (v3 = 0) & real_$greater(v0, v1) = v3)) & ! [v0: $real] : ! % 35.48/6.71 [v1: $real] : ! [v2: $real] : (v0 = real_0 | ~ (real_$product(v1, v0) = v2) % 35.48/6.71 | real_$quotient(v2, v0) = v1) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 35.48/6.71 $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) & ! % 35.48/6.71 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = % 35.48/6.71 v2) | real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! % 35.48/6.71 [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, v1) = v2) & ! [v0: % 35.48/6.71 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | % 35.97/6.71 real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : % 35.97/6.71 ( ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$lesseq(v1, v0) = 0) | % 35.97/6.71 real_$lesseq(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 35.97/6.71 : ( ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v1, v0) = 0) | % 35.97/6.71 real_$less(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : % 35.97/6.71 ( ~ (real_$lesseq(v1, v0) = 0) | ~ (real_$less(v2, v1) = 0) | real_$less(v2, % 35.97/6.71 v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 35.97/6.71 (real_$difference(v1, v0) = v2) | ? [v3: $real] : (real_$uminus(v0) = v3 & % 35.97/6.71 real_$sum(v1, v3) = v2)) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ % 35.97/6.71 (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | % 35.97/6.71 ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) & ! [v0: $real] : % 35.97/6.71 ! [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0, v0) = v1)) & ! [v0: $real] : ! % 35.97/6.71 [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: % 35.97/6.71 $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$sum(v0, v1) = % 35.97/6.71 real_0) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) = % 35.97/6.71 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 35.97/6.71 (real_$lesseq(v1, v0) = 0) | real_$greatereq(v0, v1) = 0) & ! [v0: $real] : % 35.97/6.71 ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & % 35.97/6.71 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | % 35.97/6.71 real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 35.97/6.71 (real_$less(v1, v0) = 0) | real_$greater(v0, v1) = 0) & ! [v0: $real] : ! % 35.97/6.71 [v1: MultipleValueBool] : ( ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0) % 35.97/6.71 = 0) & ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0)) % 35.97/6.71 % 35.97/6.71 (function-axioms) % 35.97/6.72 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 35.97/6.72 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 35.97/6.72 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 35.97/6.72 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: % 35.97/6.72 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 35.97/6.72 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: % 35.97/6.72 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 35.97/6.72 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~ % 35.97/6.72 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 35.97/6.72 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 35.97/6.72 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0: % 35.97/6.72 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 35.97/6.72 $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, % 35.97/6.72 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 35.97/6.72 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ % 35.97/6.72 (real_$less(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 35.97/6.72 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$difference(v3, v2) = v1) | ~ % 35.97/6.72 (real_$difference(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 35.97/6.72 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1) % 35.97/6.72 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 35.97/6.72 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) % 35.97/6.72 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 35.97/6.72 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & % 35.97/6.72 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 35.97/6.72 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] : % 35.97/6.72 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ % 35.97/6.72 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 35.97/6.72 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) & % 35.97/6.72 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2) % 35.97/6.72 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 35.97/6.72 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = % 35.97/6.72 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 35.97/6.73 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] : % 35.97/6.73 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ % 35.97/6.73 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 35.97/6.73 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) % 35.97/6.73 % 35.97/6.73 Those formulas are unsatisfiable: % 35.97/6.73 --------------------------------- % 35.97/6.73 % 35.97/6.73 Begin of proof % 35.97/6.73 | % 35.97/6.73 | ALPHA: (function-axioms) implies: % 35.97/6.73 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 35.97/6.73 | (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) % 35.97/6.73 | (2) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 % 35.97/6.73 | = v0 | ~ (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) % 35.97/6.73 | % 35.97/6.73 | ALPHA: (input) implies: % 35.97/6.73 | (3) real_$difference(real_241/20, real_241/20) = real_0 % 35.97/6.73 | (4) real_$difference(real_321/20, real_241/20) = real_4 % 35.97/6.73 | (5) real_$sum(real_0, real_241/20) = real_241/20 % 35.97/6.74 | (6) real_$sum(real_4, real_241/20) = real_321/20 % 35.97/6.74 | (7) ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) % 35.97/6.74 | = v1)) % 35.97/6.74 | (8) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 35.97/6.74 | (real_$difference(v1, v0) = v2) | ? [v3: $real] : (real_$uminus(v0) % 35.97/6.74 | = v3 & real_$sum(v1, v3) = v2)) % 35.97/6.74 | (9) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v1, % 35.97/6.74 | v0) = v2) | real_$sum(v0, v1) = v2) % 35.97/6.74 | (10) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! % 35.97/6.74 | [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = % 35.97/6.74 | v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) % 35.97/6.74 | = v5)) % 35.97/6.74 | % 35.97/6.74 | DELTA: instantiating (real_difference_problem_7) with fresh symbol all_5_0 % 35.97/6.74 | gives: % 35.97/6.74 | (11) ~ (all_5_0 = real_321/20) & real_$difference(all_5_0, real_241/20) = % 35.97/6.74 | real_4 % 35.97/6.74 | % 35.97/6.74 | ALPHA: (11) implies: % 35.97/6.74 | (12) ~ (all_5_0 = real_321/20) % 35.97/6.74 | (13) real_$difference(all_5_0, real_241/20) = real_4 % 35.97/6.74 | % 35.97/6.74 | GROUND_INST: instantiating (8) with real_241/20, real_241/20, real_0, % 35.97/6.74 | simplifying with (3) gives: % 35.97/6.74 | (14) ? [v0: $real] : (real_$uminus(real_241/20) = v0 & % 35.97/6.74 | real_$sum(real_241/20, v0) = real_0) % 35.97/6.74 | % 35.97/6.74 | GROUND_INST: instantiating (8) with real_241/20, real_321/20, real_4, % 35.97/6.74 | simplifying with (4) gives: % 35.97/6.74 | (15) ? [v0: $real] : (real_$uminus(real_241/20) = v0 & % 35.97/6.74 | real_$sum(real_321/20, v0) = real_4) % 35.97/6.74 | % 35.97/6.74 | GROUND_INST: instantiating (8) with real_241/20, all_5_0, real_4, simplifying % 35.97/6.74 | with (13) gives: % 35.97/6.74 | (16) ? [v0: $real] : (real_$uminus(real_241/20) = v0 & real_$sum(all_5_0, % 35.97/6.74 | v0) = real_4) % 35.97/6.74 | % 35.97/6.74 | DELTA: instantiating (16) with fresh symbol all_15_0 gives: % 35.97/6.74 | (17) real_$uminus(real_241/20) = all_15_0 & real_$sum(all_5_0, all_15_0) = % 35.97/6.74 | real_4 % 35.97/6.74 | % 35.97/6.74 | ALPHA: (17) implies: % 35.97/6.75 | (18) real_$sum(all_5_0, all_15_0) = real_4 % 35.97/6.75 | (19) real_$uminus(real_241/20) = all_15_0 % 35.97/6.75 | % 35.97/6.75 | DELTA: instantiating (15) with fresh symbol all_37_0 gives: % 35.97/6.75 | (20) real_$uminus(real_241/20) = all_37_0 & real_$sum(real_321/20, % 35.97/6.75 | all_37_0) = real_4 % 35.97/6.75 | % 35.97/6.75 | ALPHA: (20) implies: % 35.97/6.75 | (21) real_$sum(real_321/20, all_37_0) = real_4 % 35.97/6.75 | (22) real_$uminus(real_241/20) = all_37_0 % 35.97/6.75 | % 35.97/6.75 | DELTA: instantiating (14) with fresh symbol all_43_0 gives: % 35.97/6.75 | (23) real_$uminus(real_241/20) = all_43_0 & real_$sum(real_241/20, % 35.97/6.75 | all_43_0) = real_0 % 35.97/6.75 | % 35.97/6.75 | ALPHA: (23) implies: % 35.97/6.75 | (24) real_$sum(real_241/20, all_43_0) = real_0 % 35.97/6.75 | (25) real_$uminus(real_241/20) = all_43_0 % 35.97/6.75 | % 35.97/6.75 | GROUND_INST: instantiating (1) with all_37_0, all_43_0, real_241/20, % 35.97/6.75 | simplifying with (22), (25) gives: % 35.97/6.75 | (26) all_43_0 = all_37_0 % 35.97/6.75 | % 35.97/6.75 | GROUND_INST: instantiating (1) with all_15_0, all_43_0, real_241/20, % 35.97/6.75 | simplifying with (19), (25) gives: % 35.97/6.75 | (27) all_43_0 = all_15_0 % 35.97/6.75 | % 35.97/6.75 | COMBINE_EQS: (26), (27) imply: % 35.97/6.75 | (28) all_37_0 = all_15_0 % 35.97/6.75 | % 35.97/6.75 | SIMP: (28) implies: % 35.97/6.75 | (29) all_37_0 = all_15_0 % 35.97/6.75 | % 35.97/6.75 | REDUCE: (21), (29) imply: % 35.97/6.75 | (30) real_$sum(real_321/20, all_15_0) = real_4 % 35.97/6.75 | % 35.97/6.75 | REDUCE: (24), (27) imply: % 35.97/6.75 | (31) real_$sum(real_241/20, all_15_0) = real_0 % 35.97/6.75 | % 35.97/6.75 | GROUND_INST: instantiating (10) with real_241/20, all_15_0, real_241/20, % 35.97/6.75 | real_0, real_241/20, simplifying with (5), (31) gives: % 35.97/6.75 | (32) ? [v0: $real] : (real_$sum(all_15_0, real_241/20) = v0 & % 35.97/6.75 | real_$sum(real_241/20, v0) = real_241/20) % 35.97/6.75 | % 35.97/6.75 | GROUND_INST: instantiating (9) with all_15_0, real_241/20, real_0, simplifying % 35.97/6.75 | with (31) gives: % 35.97/6.75 | (33) real_$sum(all_15_0, real_241/20) = real_0 % 35.97/6.75 | % 35.97/6.75 | GROUND_INST: instantiating (10) with real_241/20, all_15_0, real_321/20, % 35.97/6.75 | real_4, real_321/20, simplifying with (6), (30) gives: % 35.97/6.75 | (34) ? [v0: $real] : (real_$sum(all_15_0, real_241/20) = v0 & % 35.97/6.75 | real_$sum(real_321/20, v0) = real_321/20) % 35.97/6.75 | % 35.97/6.76 | GROUND_INST: instantiating (10) with real_241/20, all_15_0, all_5_0, real_4, % 35.97/6.76 | real_321/20, simplifying with (6), (18) gives: % 35.97/6.76 | (35) ? [v0: $real] : (real_$sum(all_15_0, real_241/20) = v0 & % 35.97/6.76 | real_$sum(all_5_0, v0) = real_321/20) % 35.97/6.76 | % 35.97/6.76 | DELTA: instantiating (35) with fresh symbol all_73_0 gives: % 35.97/6.76 | (36) real_$sum(all_15_0, real_241/20) = all_73_0 & real_$sum(all_5_0, % 35.97/6.76 | all_73_0) = real_321/20 % 35.97/6.76 | % 35.97/6.76 | ALPHA: (36) implies: % 35.97/6.76 | (37) real_$sum(all_5_0, all_73_0) = real_321/20 % 35.97/6.76 | (38) real_$sum(all_15_0, real_241/20) = all_73_0 % 35.97/6.76 | % 35.97/6.76 | DELTA: instantiating (32) with fresh symbol all_83_0 gives: % 35.97/6.76 | (39) real_$sum(all_15_0, real_241/20) = all_83_0 & real_$sum(real_241/20, % 35.97/6.76 | all_83_0) = real_241/20 % 35.97/6.76 | % 35.97/6.76 | ALPHA: (39) implies: % 35.97/6.76 | (40) real_$sum(all_15_0, real_241/20) = all_83_0 % 35.97/6.76 | % 35.97/6.76 | DELTA: instantiating (34) with fresh symbol all_147_0 gives: % 35.97/6.76 | (41) real_$sum(all_15_0, real_241/20) = all_147_0 & real_$sum(real_321/20, % 35.97/6.76 | all_147_0) = real_321/20 % 35.97/6.76 | % 35.97/6.76 | ALPHA: (41) implies: % 35.97/6.76 | (42) real_$sum(all_15_0, real_241/20) = all_147_0 % 35.97/6.76 | % 35.97/6.76 | GROUND_INST: instantiating (2) with all_83_0, all_147_0, real_241/20, % 35.97/6.76 | all_15_0, simplifying with (40), (42) gives: % 35.97/6.76 | (43) all_147_0 = all_83_0 % 35.97/6.76 | % 35.97/6.76 | GROUND_INST: instantiating (2) with all_73_0, all_147_0, real_241/20, % 35.97/6.76 | all_15_0, simplifying with (38), (42) gives: % 35.97/6.76 | (44) all_147_0 = all_73_0 % 35.97/6.76 | % 35.97/6.76 | GROUND_INST: instantiating (2) with real_0, all_147_0, real_241/20, all_15_0, % 35.97/6.76 | simplifying with (33), (42) gives: % 35.97/6.76 | (45) all_147_0 = real_0 % 35.97/6.76 | % 35.97/6.76 | COMBINE_EQS: (43), (44) imply: % 35.97/6.76 | (46) all_83_0 = all_73_0 % 35.97/6.76 | % 35.97/6.76 | COMBINE_EQS: (43), (45) imply: % 35.97/6.76 | (47) all_83_0 = real_0 % 35.97/6.76 | % 35.97/6.76 | COMBINE_EQS: (46), (47) imply: % 35.97/6.76 | (48) all_73_0 = real_0 % 35.97/6.76 | % 35.97/6.76 | REDUCE: (37), (48) imply: % 35.97/6.76 | (49) real_$sum(all_5_0, real_0) = real_321/20 % 35.97/6.76 | % 35.97/6.76 | GROUND_INST: instantiating (7) with all_5_0, real_321/20, simplifying with % 35.97/6.76 | (49) gives: % 35.97/6.76 | (50) all_5_0 = real_321/20 % 35.97/6.76 | % 35.97/6.76 | REDUCE: (12), (50) imply: % 35.97/6.76 | (51) $false % 35.97/6.76 | % 35.97/6.76 | CLOSE: (51) is inconsistent. % 35.97/6.76 | % 35.97/6.76 End of proof % 35.97/6.76 % SZS output end Proof for theBenchmark % 35.97/6.76 % 35.97/6.76 6109ms %------------------------------------------------------------------------------