%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI279_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 17:47:33 EDT 2023 % Result : Theorem 14.26s 2.63s % Output : Proof 21.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : ARI279_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 18:35:01 EDT 2023 % 0.14/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.56/0.90 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 1.56/0.90 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 1.56/0.90 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 1.56/0.90 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.56/0.90 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 1.56/0.90 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.56/0.90 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 2.35/1.01 Prover 4: Preprocessing ... % 2.35/1.01 Prover 1: Preprocessing ... % 2.52/1.08 Prover 6: Preprocessing ... % 2.52/1.08 Prover 0: Preprocessing ... % 3.72/1.19 Prover 5: Preprocessing ... % 3.72/1.20 Prover 2: Preprocessing ... % 3.72/1.21 Prover 3: Preprocessing ... % 6.77/1.61 Prover 6: Constructing countermodel ... % 6.77/1.63 Prover 1: Constructing countermodel ... % 7.40/1.70 Prover 4: Constructing countermodel ... % 7.72/1.72 Prover 0: Proving ... % 10.35/2.09 Prover 6: gave up % 10.35/2.09 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.35/2.09 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation % 10.35/2.09 Prover 1: gave up % 10.35/2.10 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.35/2.11 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation % 10.70/2.12 Prover 8: Preprocessing ... % 10.87/2.14 Prover 7: Preprocessing ... % 11.47/2.25 Prover 8: Warning: ignoring some quantifiers % 11.47/2.26 Prover 8: Constructing countermodel ... % 13.05/2.46 Prover 8: gave up % 13.05/2.47 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 13.05/2.47 Prover 9: Warning: Problem contains rationals, using incomplete axiomatisation % 13.31/2.56 Prover 9: Preprocessing ... % 14.26/2.62 Prover 0: proved (1990ms) % 14.26/2.63 % 14.26/2.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.26/2.63 % 14.68/2.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.68/2.64 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation % 14.77/2.67 Prover 10: Preprocessing ... % 14.77/2.71 Prover 3: Constructing countermodel ... % 15.23/2.71 Prover 3: stopped % 15.23/2.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.23/2.73 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation % 15.23/2.73 Prover 2: Proving ... % 15.23/2.73 Prover 2: stopped % 15.23/2.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.23/2.74 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation % 15.23/2.74 Prover 13: Preprocessing ... % 15.58/2.77 Prover 11: Preprocessing ... % 16.27/2.87 Prover 13: Warning: ignoring some quantifiers % 16.27/2.88 Prover 13: Constructing countermodel ... % 16.59/2.92 Prover 5: Proving ... % 16.59/2.92 Prover 5: stopped % 16.59/2.93 Prover 4: Found proof (size 40) % 16.59/2.93 Prover 4: proved (2287ms) % 16.59/2.93 Prover 13: stopped % 16.59/2.93 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 16.59/2.93 Prover 16: Warning: Problem contains rationals, using incomplete axiomatisation % 17.11/2.95 Prover 7: Warning: ignoring some quantifiers % 17.11/2.96 Prover 7: Constructing countermodel ... % 17.11/2.98 Prover 16: Preprocessing ... % 17.55/3.01 Prover 7: stopped % 17.98/3.17 Prover 10: stopped % 19.98/3.43 Prover 11: stopped % 19.98/3.44 Prover 16: stopped % 20.63/3.53 Prover 9: Constructing countermodel ... % 20.63/3.54 Prover 9: stopped % 20.63/3.54 % 20.63/3.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.63/3.54 % 20.83/3.56 % SZS output start Proof for theBenchmark % 20.83/3.57 Assumptions after simplification: % 20.83/3.57 --------------------------------- % 20.83/3.57 % 20.83/3.57 (rat_difference_problem_7) % 20.83/3.61 ? [v0: $rat] : ( ~ (v0 = rat_1/2) & rat_$difference(v0, rat_3/16) = rat_5/16) % 20.83/3.61 % 20.83/3.61 (input) % 21.26/3.65 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_1/2) & ~ % 21.26/3.65 (rat_very_large = rat_5/16) & ~ (rat_very_large = rat_3/16) & ~ % 21.26/3.65 (rat_very_large = rat_0) & ~ (rat_very_small = rat_1/2) & ~ (rat_very_small % 21.26/3.65 = rat_5/16) & ~ (rat_very_small = rat_3/16) & ~ (rat_very_small = rat_0) & % 21.26/3.65 ~ (rat_1/2 = rat_5/16) & ~ (rat_1/2 = rat_3/16) & ~ (rat_1/2 = rat_0) & ~ % 21.26/3.65 (rat_5/16 = rat_3/16) & ~ (rat_5/16 = rat_0) & ~ (rat_3/16 = rat_0) & % 21.26/3.65 rat_$is_int(rat_1/2) = 1 & rat_$is_int(rat_5/16) = 1 & rat_$is_int(rat_3/16) = % 21.26/3.65 1 & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_1/2) = 0 & rat_$is_rat(rat_5/16) % 21.26/3.65 = 0 & rat_$is_rat(rat_3/16) = 0 & rat_$is_rat(rat_0) = 0 & rat_$floor(rat_1/2) % 21.26/3.65 = rat_0 & rat_$floor(rat_5/16) = rat_0 & rat_$floor(rat_3/16) = rat_0 & % 21.26/3.65 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 & % 21.26/3.65 rat_$truncate(rat_1/2) = rat_0 & rat_$truncate(rat_5/16) = rat_0 & % 21.26/3.65 rat_$truncate(rat_3/16) = rat_0 & rat_$truncate(rat_0) = rat_0 & % 21.26/3.65 rat_$round(rat_5/16) = rat_0 & rat_$round(rat_3/16) = rat_0 & % 21.26/3.65 rat_$round(rat_0) = rat_0 & rat_$to_int(rat_1/2) = 0 & rat_$to_int(rat_5/16) = % 21.26/3.65 0 & rat_$to_int(rat_3/16) = 0 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_1/2) % 21.26/3.65 = rat_1/2 & rat_$to_rat(rat_5/16) = rat_5/16 & rat_$to_rat(rat_3/16) = % 21.26/3.65 rat_3/16 & rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_1/2) = real_1/2 & % 21.26/3.65 rat_$to_real(rat_5/16) = real_5/16 & rat_$to_real(rat_3/16) = real_3/16 & % 21.26/3.65 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_0, % 21.26/3.65 rat_1/2) = rat_0 & rat_$quotient(rat_0, rat_5/16) = rat_0 & % 21.26/3.65 rat_$quotient(rat_0, rat_3/16) = rat_0 & rat_$product(rat_1/2, rat_0) = rat_0 % 21.26/3.65 & rat_$product(rat_5/16, rat_0) = rat_0 & rat_$product(rat_3/16, rat_0) = % 21.26/3.65 rat_0 & rat_$product(rat_0, rat_1/2) = rat_0 & rat_$product(rat_0, rat_5/16) = % 21.26/3.65 rat_0 & rat_$product(rat_0, rat_3/16) = rat_0 & rat_$product(rat_0, rat_0) = % 21.26/3.65 rat_0 & rat_$uminus(rat_0) = rat_0 & rat_$sum(rat_1/2, rat_0) = rat_1/2 & % 21.26/3.65 rat_$sum(rat_5/16, rat_3/16) = rat_1/2 & rat_$sum(rat_5/16, rat_0) = rat_5/16 % 21.26/3.65 & rat_$sum(rat_3/16, rat_5/16) = rat_1/2 & rat_$sum(rat_3/16, rat_0) = % 21.26/3.65 rat_3/16 & rat_$sum(rat_0, rat_1/2) = rat_1/2 & rat_$sum(rat_0, rat_5/16) = % 21.26/3.65 rat_5/16 & rat_$sum(rat_0, rat_3/16) = rat_3/16 & rat_$sum(rat_0, rat_0) = % 21.26/3.65 rat_0 & rat_$greatereq(rat_very_small, rat_very_large) = 1 & % 21.26/3.65 rat_$greatereq(rat_1/2, rat_1/2) = 0 & rat_$greatereq(rat_1/2, rat_5/16) = 0 & % 21.26/3.65 rat_$greatereq(rat_1/2, rat_3/16) = 0 & rat_$greatereq(rat_1/2, rat_0) = 0 & % 21.26/3.65 rat_$greatereq(rat_5/16, rat_1/2) = 1 & rat_$greatereq(rat_5/16, rat_5/16) = 0 % 21.26/3.65 & rat_$greatereq(rat_5/16, rat_3/16) = 0 & rat_$greatereq(rat_5/16, rat_0) = 0 % 21.26/3.65 & rat_$greatereq(rat_3/16, rat_1/2) = 1 & rat_$greatereq(rat_3/16, rat_5/16) = % 21.26/3.65 1 & rat_$greatereq(rat_3/16, rat_3/16) = 0 & rat_$greatereq(rat_3/16, rat_0) = % 21.26/3.65 0 & rat_$greatereq(rat_0, rat_1/2) = 1 & rat_$greatereq(rat_0, rat_5/16) = 1 & % 21.26/3.65 rat_$greatereq(rat_0, rat_3/16) = 1 & rat_$greatereq(rat_0, rat_0) = 0 & % 21.26/3.65 rat_$lesseq(rat_very_small, rat_very_large) = 0 & rat_$lesseq(rat_1/2, % 21.26/3.65 rat_1/2) = 0 & rat_$lesseq(rat_1/2, rat_5/16) = 1 & rat_$lesseq(rat_1/2, % 21.26/3.65 rat_3/16) = 1 & rat_$lesseq(rat_1/2, rat_0) = 1 & rat_$lesseq(rat_5/16, % 21.26/3.65 rat_1/2) = 0 & rat_$lesseq(rat_5/16, rat_5/16) = 0 & rat_$lesseq(rat_5/16, % 21.26/3.65 rat_3/16) = 1 & rat_$lesseq(rat_5/16, rat_0) = 1 & rat_$lesseq(rat_3/16, % 21.26/3.65 rat_1/2) = 0 & rat_$lesseq(rat_3/16, rat_5/16) = 0 & rat_$lesseq(rat_3/16, % 21.26/3.65 rat_3/16) = 0 & rat_$lesseq(rat_3/16, rat_0) = 1 & rat_$lesseq(rat_0, % 21.26/3.65 rat_1/2) = 0 & rat_$lesseq(rat_0, rat_5/16) = 0 & rat_$lesseq(rat_0, % 21.26/3.65 rat_3/16) = 0 & rat_$lesseq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, % 21.26/3.65 rat_1/2) = 0 & rat_$greater(rat_very_large, rat_5/16) = 0 & % 21.26/3.65 rat_$greater(rat_very_large, rat_3/16) = 0 & rat_$greater(rat_very_large, % 21.26/3.65 rat_0) = 0 & rat_$greater(rat_very_small, rat_very_large) = 1 & % 21.26/3.65 rat_$greater(rat_1/2, rat_very_small) = 0 & rat_$greater(rat_1/2, rat_1/2) = 1 % 21.26/3.65 & rat_$greater(rat_1/2, rat_5/16) = 0 & rat_$greater(rat_1/2, rat_3/16) = 0 & % 21.26/3.65 rat_$greater(rat_1/2, rat_0) = 0 & rat_$greater(rat_5/16, rat_very_small) = 0 % 21.26/3.65 & rat_$greater(rat_5/16, rat_1/2) = 1 & rat_$greater(rat_5/16, rat_5/16) = 1 & % 21.26/3.66 rat_$greater(rat_5/16, rat_3/16) = 0 & rat_$greater(rat_5/16, rat_0) = 0 & % 21.26/3.66 rat_$greater(rat_3/16, rat_very_small) = 0 & rat_$greater(rat_3/16, rat_1/2) = % 21.26/3.66 1 & rat_$greater(rat_3/16, rat_5/16) = 1 & rat_$greater(rat_3/16, rat_3/16) = % 21.26/3.66 1 & rat_$greater(rat_3/16, rat_0) = 0 & rat_$greater(rat_0, rat_very_small) = % 21.26/3.66 0 & rat_$greater(rat_0, rat_1/2) = 1 & rat_$greater(rat_0, rat_5/16) = 1 & % 21.26/3.66 rat_$greater(rat_0, rat_3/16) = 1 & rat_$greater(rat_0, rat_0) = 1 & % 21.26/3.66 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small, % 21.26/3.66 rat_1/2) = 0 & rat_$less(rat_very_small, rat_5/16) = 0 & % 21.26/3.66 rat_$less(rat_very_small, rat_3/16) = 0 & rat_$less(rat_very_small, rat_0) = 0 % 21.26/3.66 & rat_$less(rat_1/2, rat_very_large) = 0 & rat_$less(rat_1/2, rat_1/2) = 1 & % 21.26/3.66 rat_$less(rat_1/2, rat_5/16) = 1 & rat_$less(rat_1/2, rat_3/16) = 1 & % 21.26/3.66 rat_$less(rat_1/2, rat_0) = 1 & rat_$less(rat_5/16, rat_very_large) = 0 & % 21.26/3.66 rat_$less(rat_5/16, rat_1/2) = 0 & rat_$less(rat_5/16, rat_5/16) = 1 & % 21.26/3.66 rat_$less(rat_5/16, rat_3/16) = 1 & rat_$less(rat_5/16, rat_0) = 1 & % 21.26/3.66 rat_$less(rat_3/16, rat_very_large) = 0 & rat_$less(rat_3/16, rat_1/2) = 0 & % 21.26/3.66 rat_$less(rat_3/16, rat_5/16) = 0 & rat_$less(rat_3/16, rat_3/16) = 1 & % 21.26/3.66 rat_$less(rat_3/16, rat_0) = 1 & rat_$less(rat_0, rat_very_large) = 0 & % 21.26/3.66 rat_$less(rat_0, rat_1/2) = 0 & rat_$less(rat_0, rat_5/16) = 0 & % 21.26/3.66 rat_$less(rat_0, rat_3/16) = 0 & rat_$less(rat_0, rat_0) = 1 & % 21.26/3.66 rat_$difference(rat_1/2, rat_1/2) = rat_0 & rat_$difference(rat_1/2, rat_5/16) % 21.26/3.66 = rat_3/16 & rat_$difference(rat_1/2, rat_3/16) = rat_5/16 & % 21.26/3.66 rat_$difference(rat_1/2, rat_0) = rat_1/2 & rat_$difference(rat_5/16, % 21.26/3.66 rat_5/16) = rat_0 & rat_$difference(rat_5/16, rat_0) = rat_5/16 & % 21.26/3.66 rat_$difference(rat_3/16, rat_3/16) = rat_0 & rat_$difference(rat_3/16, rat_0) % 21.26/3.66 = rat_3/16 & rat_$difference(rat_0, rat_0) = rat_0 & ! [v0: $rat] : ! [v1: % 21.26/3.66 $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, % 21.26/3.66 v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, % 21.26/3.66 v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! % 21.26/3.66 [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~ % 21.26/3.66 (rat_$sum(v1, v0) = v3) | ? [v5: $rat] : (rat_$sum(v5, v0) = v4 & % 21.26/3.66 rat_$sum(v2, v1) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 21.26/3.66 ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v2, v0) % 21.26/3.66 = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: % 21.26/3.66 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 21.26/3.66 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ % 21.26/3.66 (v4 = 0) & rat_$less(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! % 21.26/3.66 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v0) = v3) | ~ % 21.26/3.66 (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, % 21.26/3.66 v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: % 21.26/3.66 int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, v0) = v3) % 21.26/3.66 | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & ! [v0: $rat] : % 21.26/3.66 ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v1) % 21.26/3.66 = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & % 21.26/3.66 rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 21.26/3.66 : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ (rat_$less(v1, v0) % 21.26/3.66 = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: % 21.26/3.66 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) % 21.26/3.66 = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1, v0) = v3) & ! % 21.26/3.66 [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 21.26/3.66 (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) % 21.26/3.66 = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ % 21.26/3.66 (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 21.26/3.66 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 21.26/3.66 : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 21.26/3.66 rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 21.26/3.66 int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) % 21.26/3.66 & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 21.26/3.66 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 21.26/3.66 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : % 21.26/3.66 (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 21.26/3.66 rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 21.26/3.66 $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0) % 21.26/3.66 = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 21.26/3.66 (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] : % 21.26/3.66 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | % 21.26/3.66 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 21.26/3.66 ( ~ (rat_$sum(v1, v0) = v2) | rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1: % 21.26/3.66 $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) % 21.26/3.66 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = % 21.26/3.66 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2, v0) = 0) & ! [v0: % 21.26/3.66 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~ % 21.26/3.66 (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: % 21.26/3.66 $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, % 21.26/3.66 v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! % 21.26/3.66 [v2: $rat] : ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : % 21.26/3.66 (rat_$uminus(v0) = v3 & rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1: % 21.26/3.66 $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1: % 21.26/3.66 $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & % 21.26/3.66 ! [v0: $rat] : ! [v1: int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & ! % 21.26/3.66 [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = % 21.26/3.66 v0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | % 21.26/3.66 rat_$sum(v0, v1) = rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 21.26/3.66 (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! % 21.26/3.66 [v1: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & ! % 21.26/3.66 [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, % 21.26/3.66 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | % 21.26/3.66 rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 21.26/3.66 (rat_$less(v1, v0) = 0) | rat_$greater(v0, v1) = 0) & ! [v0: $rat] : ! % 21.26/3.66 [v1: MultipleValueBool] : ( ~ (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) = % 21.26/3.66 0) & ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0) = v0)) % 21.26/3.66 % 21.26/3.66 (function-axioms) % 21.26/3.67 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 21.26/3.67 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0: % 21.26/3.67 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 21.26/3.67 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0: % 21.26/3.67 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 21.26/3.67 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0: % 21.26/3.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 21.26/3.67 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3, % 21.26/3.67 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 21.26/3.67 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ % 21.26/3.67 (rat_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.26/3.67 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 21.26/3.67 (rat_$greater(v3, v2) = v1) | ~ (rat_$greater(v3, v2) = v0)) & ! [v0: % 21.26/3.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 21.26/3.67 $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = % 21.26/3.67 v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 % 21.26/3.67 = v0 | ~ (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = % 21.26/3.67 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.26/3.67 $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & % 21.26/3.67 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = % 21.26/3.67 v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] % 21.26/3.67 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~ % 21.26/3.67 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 % 21.26/3.67 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0: % 21.26/3.67 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) = % 21.26/3.67 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 21.26/3.67 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) & % 21.26/3.67 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) = % 21.26/3.67 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 21.26/3.67 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) & % 21.26/3.67 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~ % 21.26/3.67 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : ! % 21.26/3.67 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~ % 21.26/3.67 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 21.26/3.67 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0)) % 21.26/3.67 % 21.26/3.67 Those formulas are unsatisfiable: % 21.26/3.67 --------------------------------- % 21.26/3.67 % 21.26/3.67 Begin of proof % 21.26/3.67 | % 21.26/3.67 | ALPHA: (function-axioms) implies: % 21.26/3.67 | (1) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ % 21.26/3.67 | (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0)) % 21.26/3.67 | (2) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = % 21.26/3.68 | v0 | ~ (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) % 21.26/3.68 | % 21.26/3.68 | ALPHA: (input) implies: % 21.26/3.68 | (3) rat_$difference(rat_3/16, rat_3/16) = rat_0 % 21.26/3.68 | (4) rat_$difference(rat_1/2, rat_3/16) = rat_5/16 % 21.26/3.68 | (5) rat_$sum(rat_0, rat_3/16) = rat_3/16 % 21.26/3.68 | (6) rat_$sum(rat_5/16, rat_3/16) = rat_1/2 % 21.26/3.68 | (7) ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = % 21.26/3.68 | v1)) % 21.26/3.68 | (8) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 21.26/3.68 | (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = % 21.26/3.68 | v3 & rat_$sum(v1, v3) = v2)) % 21.26/3.68 | (9) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) = % 21.26/3.68 | v2) | rat_$sum(v0, v1) = v2) % 21.26/3.68 | (10) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! % 21.26/3.68 | [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) % 21.26/3.68 | | ? [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) % 21.26/3.68 | % 21.26/3.68 | DELTA: instantiating (rat_difference_problem_7) with fresh symbol all_5_0 % 21.26/3.68 | gives: % 21.26/3.68 | (11) ~ (all_5_0 = rat_1/2) & rat_$difference(all_5_0, rat_3/16) = rat_5/16 % 21.26/3.68 | % 21.26/3.68 | ALPHA: (11) implies: % 21.26/3.68 | (12) ~ (all_5_0 = rat_1/2) % 21.26/3.68 | (13) rat_$difference(all_5_0, rat_3/16) = rat_5/16 % 21.26/3.68 | % 21.26/3.68 | GROUND_INST: instantiating (8) with rat_3/16, rat_3/16, rat_0, simplifying % 21.26/3.68 | with (3) gives: % 21.26/3.68 | (14) ? [v0: $rat] : (rat_$uminus(rat_3/16) = v0 & rat_$sum(rat_3/16, v0) = % 21.26/3.68 | rat_0) % 21.26/3.68 | % 21.26/3.68 | GROUND_INST: instantiating (8) with rat_3/16, rat_1/2, rat_5/16, simplifying % 21.26/3.68 | with (4) gives: % 21.26/3.68 | (15) ? [v0: $rat] : (rat_$uminus(rat_3/16) = v0 & rat_$sum(rat_1/2, v0) = % 21.26/3.68 | rat_5/16) % 21.26/3.68 | % 21.26/3.68 | GROUND_INST: instantiating (8) with rat_3/16, all_5_0, rat_5/16, simplifying % 21.26/3.68 | with (13) gives: % 21.26/3.68 | (16) ? [v0: $rat] : (rat_$uminus(rat_3/16) = v0 & rat_$sum(all_5_0, v0) = % 21.26/3.68 | rat_5/16) % 21.26/3.68 | % 21.26/3.68 | DELTA: instantiating (16) with fresh symbol all_29_0 gives: % 21.26/3.68 | (17) rat_$uminus(rat_3/16) = all_29_0 & rat_$sum(all_5_0, all_29_0) = % 21.26/3.68 | rat_5/16 % 21.26/3.68 | % 21.26/3.68 | ALPHA: (17) implies: % 21.26/3.68 | (18) rat_$sum(all_5_0, all_29_0) = rat_5/16 % 21.49/3.68 | (19) rat_$uminus(rat_3/16) = all_29_0 % 21.49/3.68 | % 21.49/3.68 | DELTA: instantiating (14) with fresh symbol all_37_0 gives: % 21.49/3.68 | (20) rat_$uminus(rat_3/16) = all_37_0 & rat_$sum(rat_3/16, all_37_0) = % 21.49/3.68 | rat_0 % 21.49/3.68 | % 21.49/3.68 | ALPHA: (20) implies: % 21.49/3.69 | (21) rat_$sum(rat_3/16, all_37_0) = rat_0 % 21.49/3.69 | (22) rat_$uminus(rat_3/16) = all_37_0 % 21.49/3.69 | % 21.49/3.69 | DELTA: instantiating (15) with fresh symbol all_41_0 gives: % 21.49/3.69 | (23) rat_$uminus(rat_3/16) = all_41_0 & rat_$sum(rat_1/2, all_41_0) = % 21.49/3.69 | rat_5/16 % 21.49/3.69 | % 21.49/3.69 | ALPHA: (23) implies: % 21.49/3.69 | (24) rat_$sum(rat_1/2, all_41_0) = rat_5/16 % 21.49/3.69 | (25) rat_$uminus(rat_3/16) = all_41_0 % 21.49/3.69 | % 21.49/3.69 | GROUND_INST: instantiating (1) with all_37_0, all_41_0, rat_3/16, simplifying % 21.49/3.69 | with (22), (25) gives: % 21.49/3.69 | (26) all_41_0 = all_37_0 % 21.49/3.69 | % 21.49/3.69 | GROUND_INST: instantiating (1) with all_29_0, all_41_0, rat_3/16, simplifying % 21.49/3.69 | with (19), (25) gives: % 21.49/3.69 | (27) all_41_0 = all_29_0 % 21.49/3.69 | % 21.49/3.69 | COMBINE_EQS: (26), (27) imply: % 21.49/3.69 | (28) all_37_0 = all_29_0 % 21.49/3.69 | % 21.49/3.69 | SIMP: (28) implies: % 21.49/3.69 | (29) all_37_0 = all_29_0 % 21.49/3.69 | % 21.49/3.69 | REDUCE: (24), (27) imply: % 21.49/3.69 | (30) rat_$sum(rat_1/2, all_29_0) = rat_5/16 % 21.49/3.69 | % 21.49/3.69 | REDUCE: (21), (29) imply: % 21.49/3.69 | (31) rat_$sum(rat_3/16, all_29_0) = rat_0 % 21.49/3.69 | % 21.49/3.69 | GROUND_INST: instantiating (10) with rat_3/16, all_29_0, rat_3/16, rat_0, % 21.49/3.69 | rat_3/16, simplifying with (5), (31) gives: % 21.49/3.69 | (32) ? [v0: $rat] : (rat_$sum(all_29_0, rat_3/16) = v0 & % 21.49/3.69 | rat_$sum(rat_3/16, v0) = rat_3/16) % 21.49/3.69 | % 21.49/3.69 | GROUND_INST: instantiating (9) with all_29_0, rat_3/16, rat_0, simplifying % 21.49/3.69 | with (31) gives: % 21.49/3.69 | (33) rat_$sum(all_29_0, rat_3/16) = rat_0 % 21.49/3.69 | % 21.49/3.69 | GROUND_INST: instantiating (10) with rat_3/16, all_29_0, rat_1/2, rat_5/16, % 21.49/3.69 | rat_1/2, simplifying with (6), (30) gives: % 21.49/3.69 | (34) ? [v0: $rat] : (rat_$sum(all_29_0, rat_3/16) = v0 & rat_$sum(rat_1/2, % 21.49/3.69 | v0) = rat_1/2) % 21.49/3.69 | % 21.49/3.69 | GROUND_INST: instantiating (10) with rat_3/16, all_29_0, all_5_0, rat_5/16, % 21.49/3.69 | rat_1/2, simplifying with (6), (18) gives: % 21.49/3.69 | (35) ? [v0: $rat] : (rat_$sum(all_29_0, rat_3/16) = v0 & rat_$sum(all_5_0, % 21.49/3.69 | v0) = rat_1/2) % 21.49/3.69 | % 21.49/3.69 | DELTA: instantiating (35) with fresh symbol all_65_0 gives: % 21.49/3.69 | (36) rat_$sum(all_29_0, rat_3/16) = all_65_0 & rat_$sum(all_5_0, all_65_0) % 21.49/3.69 | = rat_1/2 % 21.49/3.69 | % 21.49/3.69 | ALPHA: (36) implies: % 21.49/3.69 | (37) rat_$sum(all_5_0, all_65_0) = rat_1/2 % 21.49/3.69 | (38) rat_$sum(all_29_0, rat_3/16) = all_65_0 % 21.49/3.69 | % 21.49/3.69 | DELTA: instantiating (32) with fresh symbol all_77_0 gives: % 21.49/3.69 | (39) rat_$sum(all_29_0, rat_3/16) = all_77_0 & rat_$sum(rat_3/16, all_77_0) % 21.49/3.69 | = rat_3/16 % 21.49/3.69 | % 21.49/3.69 | ALPHA: (39) implies: % 21.49/3.69 | (40) rat_$sum(all_29_0, rat_3/16) = all_77_0 % 21.49/3.69 | % 21.49/3.69 | DELTA: instantiating (34) with fresh symbol all_149_0 gives: % 21.49/3.69 | (41) rat_$sum(all_29_0, rat_3/16) = all_149_0 & rat_$sum(rat_1/2, % 21.49/3.69 | all_149_0) = rat_1/2 % 21.49/3.69 | % 21.49/3.69 | ALPHA: (41) implies: % 21.49/3.69 | (42) rat_$sum(all_29_0, rat_3/16) = all_149_0 % 21.49/3.69 | % 21.49/3.69 | GROUND_INST: instantiating (2) with all_65_0, all_77_0, rat_3/16, all_29_0, % 21.49/3.69 | simplifying with (38), (40) gives: % 21.49/3.69 | (43) all_77_0 = all_65_0 % 21.49/3.69 | % 21.49/3.69 | GROUND_INST: instantiating (2) with all_77_0, all_149_0, rat_3/16, all_29_0, % 21.49/3.69 | simplifying with (40), (42) gives: % 21.49/3.69 | (44) all_149_0 = all_77_0 % 21.49/3.69 | % 21.49/3.70 | GROUND_INST: instantiating (2) with rat_0, all_149_0, rat_3/16, all_29_0, % 21.49/3.70 | simplifying with (33), (42) gives: % 21.49/3.70 | (45) all_149_0 = rat_0 % 21.49/3.70 | % 21.49/3.70 | COMBINE_EQS: (44), (45) imply: % 21.49/3.70 | (46) all_77_0 = rat_0 % 21.49/3.70 | % 21.49/3.70 | SIMP: (46) implies: % 21.49/3.70 | (47) all_77_0 = rat_0 % 21.49/3.70 | % 21.49/3.70 | COMBINE_EQS: (43), (47) imply: % 21.49/3.70 | (48) all_65_0 = rat_0 % 21.49/3.70 | % 21.49/3.70 | REDUCE: (37), (48) imply: % 21.49/3.70 | (49) rat_$sum(all_5_0, rat_0) = rat_1/2 % 21.49/3.70 | % 21.49/3.70 | GROUND_INST: instantiating (7) with all_5_0, rat_1/2, simplifying with (49) % 21.49/3.70 | gives: % 21.49/3.70 | (50) all_5_0 = rat_1/2 % 21.49/3.70 | % 21.49/3.70 | REDUCE: (12), (50) imply: % 21.49/3.70 | (51) $false % 21.49/3.70 | % 21.49/3.70 | CLOSE: (51) is inconsistent. % 21.49/3.70 | % 21.49/3.70 End of proof % 21.49/3.70 % SZS output end Proof for theBenchmark % 21.49/3.70 % 21.49/3.70 3084ms %------------------------------------------------------------------------------