%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI406_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 : n009.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 14.43s 2.68s % Output : Proof 22.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.13 % Problem : ARI406_1 : TPTP v8.1.2. Released v5.0.0. % 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % 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 17:56:35 EDT 2023 % 0.13/0.35 % CPUTime : % 0.56/0.62 ________ _____ % 0.56/0.62 ___ __ \_________(_)________________________________ % 0.56/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.56/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.56/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.56/0.62 % 0.56/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.56/0.62 (2023-06-19) % 0.56/0.62 % 0.56/0.62 (c) Philipp Rümmer, 2009-2023 % 0.56/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.56/0.62 Amanda Stjerna. % 0.56/0.62 Free software under BSD-3-Clause. % 0.56/0.62 % 0.56/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.56/0.62 % 0.56/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.65/0.64 Running up to 7 provers in parallel. % 0.65/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.65/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.65/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.65/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.65/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.65/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.65/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.68/0.90 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 1.68/0.90 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.68/0.90 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.68/0.90 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.68/0.90 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 1.68/0.90 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.68/0.90 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 2.38/1.00 Prover 1: Preprocessing ... % 2.38/1.01 Prover 4: Preprocessing ... % 2.96/1.08 Prover 0: Preprocessing ... % 2.96/1.08 Prover 6: Preprocessing ... % 2.96/1.13 Prover 2: Preprocessing ... % 2.96/1.13 Prover 3: Preprocessing ... % 2.96/1.14 Prover 5: Preprocessing ... % 6.18/1.61 Prover 1: Constructing countermodel ... % 6.89/1.64 Prover 6: Proving ... % 6.89/1.66 Prover 4: Constructing countermodel ... % 7.51/1.72 Prover 0: Proving ... % 9.11/1.97 Prover 1: gave up % 9.11/1.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.74/2.00 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 9.74/2.08 Prover 7: Preprocessing ... % 11.47/2.22 Prover 3: Constructing countermodel ... % 11.47/2.27 Prover 2: Proving ... % 11.47/2.28 Prover 5: Proving ... % 13.70/2.56 Prover 7: Warning: ignoring some quantifiers % 13.70/2.57 Prover 7: Constructing countermodel ... % 14.43/2.68 Prover 0: proved (2034ms) % 14.43/2.68 % 14.43/2.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.43/2.68 % 14.43/2.68 Prover 3: stopped % 14.43/2.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.43/2.68 Prover 6: stopped % 14.43/2.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.43/2.68 Prover 2: stopped % 14.43/2.68 Prover 5: stopped % 15.14/2.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.14/2.69 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 15.14/2.69 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 15.14/2.69 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 15.14/2.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.14/2.69 Prover 8: Preprocessing ... % 15.14/2.69 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 15.14/2.69 Prover 13: Preprocessing ... % 15.14/2.71 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.14/2.71 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation % 15.14/2.74 Prover 10: Preprocessing ... % 15.14/2.74 Prover 11: Preprocessing ... % 15.14/2.76 Prover 16: Preprocessing ... % 15.89/2.79 Prover 8: Warning: ignoring some quantifiers % 15.94/2.80 Prover 8: Constructing countermodel ... % 15.94/2.80 Prover 13: Warning: ignoring some quantifiers % 15.94/2.81 Prover 13: Constructing countermodel ... % 16.82/2.95 Prover 8: gave up % 16.82/2.95 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 16.82/2.95 Prover 19: Warning: Problem contains reals, using incomplete axiomatisation % 17.44/2.99 Prover 13: gave up % 17.44/3.00 Prover 19: Preprocessing ... % 18.44/3.15 Prover 10: Warning: ignoring some quantifiers % 18.44/3.17 Prover 10: Constructing countermodel ... % 19.78/3.32 Prover 4: Found proof (size 34) % 19.78/3.32 Prover 4: proved (2669ms) % 19.78/3.32 Prover 10: stopped % 19.78/3.32 Prover 16: Warning: ignoring some quantifiers % 19.78/3.33 Prover 16: Constructing countermodel ... % 19.78/3.35 Prover 16: stopped % 19.78/3.36 Prover 7: Found proof (size 3) % 19.78/3.36 Prover 7: proved (1375ms) % 20.47/3.39 Prover 11: Constructing countermodel ... % 20.47/3.41 Prover 11: stopped % 21.87/3.75 Prover 19: Warning: ignoring some quantifiers % 21.87/3.76 Prover 19: Constructing countermodel ... % 21.87/3.78 Prover 19: stopped % 21.87/3.78 % 21.87/3.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 21.87/3.78 % 21.87/3.79 % SZS output start Proof for theBenchmark % 21.87/3.79 Assumptions after simplification: % 21.87/3.79 --------------------------------- % 21.87/3.79 % 21.87/3.79 (real_sum_problem_6) % 22.24/3.82 ! [v0: $real] : ~ (real_$sum(v0, real_407/100) = real_4769/250) % 22.24/3.82 % 22.24/3.83 (input) % 22.56/3.88 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_4769/250) % 22.56/3.88 & ~ (real_very_large = real_407/100) & ~ (real_very_large = real_0) & ~ % 22.56/3.88 (real_very_small = real_4769/250) & ~ (real_very_small = real_407/100) & ~ % 22.56/3.88 (real_very_small = real_0) & ~ (real_4769/250 = real_407/100) & ~ % 22.56/3.88 (real_4769/250 = real_0) & ~ (real_407/100 = real_0) & % 22.56/3.88 real_$is_int(real_4769/250) = 1 & real_$is_int(real_407/100) = 1 & % 22.56/3.88 real_$is_int(real_0) = 0 & real_$is_rat(real_4769/250) = 0 & % 22.56/3.88 real_$is_rat(real_407/100) = 0 & real_$is_rat(real_0) = 0 & % 22.56/3.88 real_$floor(real_0) = real_0 & real_$ceiling(real_0) = real_0 & % 22.56/3.88 real_$truncate(real_0) = real_0 & real_$round(real_0) = real_0 & % 22.56/3.88 real_$to_int(real_4769/250) = 19 & real_$to_int(real_407/100) = 4 & % 22.56/3.88 real_$to_int(real_0) = 0 & real_$to_rat(real_4769/250) = rat_4769/250 & % 22.56/3.88 real_$to_rat(real_407/100) = rat_407/100 & real_$to_rat(real_0) = rat_0 & % 22.56/3.88 real_$to_real(real_4769/250) = real_4769/250 & real_$to_real(real_407/100) = % 22.56/3.89 real_407/100 & real_$to_real(real_0) = real_0 & int_$to_real(0) = real_0 & % 22.56/3.89 real_$quotient(real_0, real_4769/250) = real_0 & real_$quotient(real_0, % 22.56/3.89 real_407/100) = real_0 & real_$product(real_4769/250, real_0) = real_0 & % 22.56/3.89 real_$product(real_407/100, real_0) = real_0 & real_$product(real_0, % 22.56/3.89 real_4769/250) = real_0 & real_$product(real_0, real_407/100) = real_0 & % 22.56/3.89 real_$product(real_0, real_0) = real_0 & real_$difference(real_4769/250, % 22.56/3.89 real_4769/250) = real_0 & real_$difference(real_4769/250, real_0) = % 22.56/3.89 real_4769/250 & real_$difference(real_407/100, real_407/100) = real_0 & % 22.56/3.89 real_$difference(real_407/100, real_0) = real_407/100 & % 22.56/3.89 real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) = real_0 & % 22.56/3.89 real_$greatereq(real_very_small, real_very_large) = 1 & % 22.56/3.89 real_$greatereq(real_4769/250, real_4769/250) = 0 & % 22.56/3.89 real_$greatereq(real_4769/250, real_407/100) = 0 & % 22.56/3.89 real_$greatereq(real_4769/250, real_0) = 0 & real_$greatereq(real_407/100, % 22.56/3.89 real_4769/250) = 1 & real_$greatereq(real_407/100, real_407/100) = 0 & % 22.56/3.89 real_$greatereq(real_407/100, real_0) = 0 & real_$greatereq(real_0, % 22.56/3.89 real_4769/250) = 1 & real_$greatereq(real_0, real_407/100) = 1 & % 22.56/3.89 real_$greatereq(real_0, real_0) = 0 & real_$lesseq(real_very_small, % 22.56/3.89 real_very_large) = 0 & real_$lesseq(real_4769/250, real_4769/250) = 0 & % 22.56/3.89 real_$lesseq(real_4769/250, real_407/100) = 1 & real_$lesseq(real_4769/250, % 22.56/3.89 real_0) = 1 & real_$lesseq(real_407/100, real_4769/250) = 0 & % 22.56/3.89 real_$lesseq(real_407/100, real_407/100) = 0 & real_$lesseq(real_407/100, % 22.56/3.89 real_0) = 1 & real_$lesseq(real_0, real_4769/250) = 0 & real_$lesseq(real_0, % 22.56/3.89 real_407/100) = 0 & real_$lesseq(real_0, real_0) = 0 & % 22.56/3.89 real_$greater(real_very_large, real_4769/250) = 0 & % 22.56/3.89 real_$greater(real_very_large, real_407/100) = 0 & % 22.56/3.89 real_$greater(real_very_large, real_0) = 0 & real_$greater(real_very_small, % 22.56/3.89 real_very_large) = 1 & real_$greater(real_4769/250, real_very_small) = 0 & % 22.56/3.89 real_$greater(real_4769/250, real_4769/250) = 1 & real_$greater(real_4769/250, % 22.56/3.89 real_407/100) = 0 & real_$greater(real_4769/250, real_0) = 0 & % 22.56/3.89 real_$greater(real_407/100, real_very_small) = 0 & real_$greater(real_407/100, % 22.56/3.89 real_4769/250) = 1 & real_$greater(real_407/100, real_407/100) = 1 & % 22.56/3.89 real_$greater(real_407/100, real_0) = 0 & real_$greater(real_0, % 22.56/3.89 real_very_small) = 0 & real_$greater(real_0, real_4769/250) = 1 & % 22.56/3.89 real_$greater(real_0, real_407/100) = 1 & real_$greater(real_0, real_0) = 1 & % 22.56/3.89 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, % 22.56/3.89 real_4769/250) = 0 & real_$less(real_very_small, real_407/100) = 0 & % 22.56/3.89 real_$less(real_very_small, real_0) = 0 & real_$less(real_4769/250, % 22.56/3.89 real_very_large) = 0 & real_$less(real_4769/250, real_4769/250) = 1 & % 22.56/3.89 real_$less(real_4769/250, real_407/100) = 1 & real_$less(real_4769/250, % 22.56/3.89 real_0) = 1 & real_$less(real_407/100, real_very_large) = 0 & % 22.56/3.89 real_$less(real_407/100, real_4769/250) = 0 & real_$less(real_407/100, % 22.56/3.89 real_407/100) = 1 & real_$less(real_407/100, real_0) = 1 & % 22.56/3.89 real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_4769/250) = % 22.56/3.89 0 & real_$less(real_0, real_407/100) = 0 & real_$less(real_0, real_0) = 1 & % 22.56/3.89 real_$sum(real_4769/250, real_0) = real_4769/250 & real_$sum(real_407/100, % 22.56/3.89 real_0) = real_407/100 & real_$sum(real_0, real_4769/250) = real_4769/250 & % 22.56/3.89 real_$sum(real_0, real_407/100) = real_407/100 & real_$sum(real_0, real_0) = % 22.56/3.89 real_0 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : % 22.56/3.89 ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | % 22.56/3.89 ? [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: % 22.56/3.89 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : % 22.56/3.89 ( ~ (real_$sum(v2, v3) = v4) | ~ (real_$sum(v1, v0) = v3) | ? [v5: $real] : % 22.56/3.89 (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) = v5)) & ! [v0: $real] : ! % 22.56/3.89 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, % 22.56/3.89 v1) = 0) | ~ (real_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) % 22.56/3.89 & real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 22.56/3.89 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~ % 22.56/3.89 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0) % 22.56/3.89 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : % 22.56/3.89 (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? % 22.56/3.89 [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! % 22.56/3.89 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, % 22.56/3.89 v0) = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & % 22.56/3.90 real_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 22.56/3.90 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v1) = 0) | ~ % 22.56/3.90 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1, % 22.56/3.90 v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: % 22.56/3.90 int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~ (real_$less(v1, v0) = 0) % 22.56/3.90 | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] % 22.56/3.90 : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) = % 22.56/3.90 v2) | ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, v0) = v3) & ! % 22.56/3.90 [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 22.56/3.90 (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, % 22.56/3.90 v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | % 22.56/3.90 ~ (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 22.56/3.90 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 22.56/3.90 int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = % 22.56/3.90 0) & real_$greatereq(v0, v1) = v3)) & ! [v0: $real] : ! [v1: $real] : % 22.56/3.90 ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ % 22.56/3.90 (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : % 22.56/3.90 ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ % 22.56/3.90 (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : % 22.56/3.90 ! [v2: int] : (v2 = 0 | ~ (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 % 22.56/3.90 = 0) & real_$greater(v0, v1) = v3)) & ! [v0: $real] : ! [v1: $real] : % 22.56/3.90 ! [v2: $real] : (v0 = real_0 | ~ (real_$product(v1, v0) = v2) | % 22.56/3.90 real_$quotient(v2, v0) = v1) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 22.56/3.90 $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) & ! % 22.56/3.90 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = % 22.56/3.90 v2) | real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! % 22.56/3.90 [v2: $real] : ( ~ (real_$difference(v1, v0) = v2) | ? [v3: $real] : % 22.56/3.90 (real_$uminus(v0) = v3 & real_$sum(v1, v3) = v2)) & ! [v0: $real] : ! [v1: % 22.56/3.90 $real] : ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~ % 22.56/3.90 (real_$lesseq(v1, v0) = 0) | real_$lesseq(v2, v0) = 0) & ! [v0: $real] : ! % 22.56/3.90 [v1: $real] : ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~ % 22.56/3.90 (real_$less(v1, v0) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : ! % 22.56/3.90 [v1: $real] : ! [v2: $real] : ( ~ (real_$lesseq(v1, v0) = 0) | ~ % 22.56/3.90 (real_$less(v2, v1) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : ! % 22.56/3.90 [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, % 22.56/3.90 v1) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 22.56/3.90 (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: $real] : ! % 22.56/3.90 [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = % 22.56/3.90 0) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) % 22.56/3.90 = v1)) & ! [v0: $real] : ! [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0, % 22.56/3.90 v0) = v1)) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = % 22.56/3.90 v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 22.56/3.90 (real_$uminus(v0) = v1) | real_$sum(v0, v1) = real_0) & ! [v0: $real] : ! % 22.56/3.90 [v1: $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & % 22.56/3.90 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$lesseq(v1, v0) = 0) | % 22.56/3.90 real_$greatereq(v0, v1) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 22.56/3.90 (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & ! [v0: $real] : ! % 22.56/3.90 [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | real_$lesseq(v1, v0) = 0) & ! % 22.56/3.90 [v0: $real] : ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | % 22.56/3.90 real_$greater(v0, v1) = 0) & ! [v0: $real] : ! [v1: MultipleValueBool] : ( % 22.56/3.90 ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0) = 0) & ! [v0: $real] : % 22.56/3.90 (v0 = real_0 | ~ (real_$uminus(v0) = v0)) % 22.56/3.90 % 22.56/3.90 (function-axioms) % 22.56/3.91 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 22.56/3.91 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 22.56/3.91 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 22.56/3.91 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: % 22.56/3.91 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 22.56/3.91 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! % 22.56/3.91 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! % 22.56/3.91 [v3: $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~ % 22.56/3.91 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.56/3.91 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 22.56/3.91 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0: % 22.56/3.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 22.56/3.91 $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, % 22.56/3.91 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 22.56/3.91 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ % 22.56/3.91 (real_$less(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 22.56/3.91 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$sum(v3, v2) = v1) | ~ % 22.56/3.91 (real_$sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.56/3.91 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1) % 22.56/3.91 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.56/3.91 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) % 22.56/3.91 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 22.56/3.91 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & % 22.56/3.91 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 22.56/3.91 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] : % 22.56/3.91 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ % 22.56/3.91 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 22.56/3.91 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) & % 22.56/3.91 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2) % 22.56/3.92 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 22.56/3.92 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = % 22.56/3.92 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 22.56/3.92 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] : % 22.56/3.92 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ % 22.56/3.92 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 22.56/3.92 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) % 22.56/3.92 % 22.56/3.92 Those formulas are unsatisfiable: % 22.56/3.92 --------------------------------- % 22.56/3.92 % 22.56/3.92 Begin of proof % 22.56/3.92 | % 22.56/3.92 | ALPHA: (function-axioms) implies: % 22.56/3.92 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 % 22.56/3.92 | = v0 | ~ (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) % 22.56/3.92 | % 22.56/3.92 | ALPHA: (input) implies: % 22.56/3.92 | (2) real_$sum(real_0, real_407/100) = real_407/100 % 22.56/3.92 | (3) real_$sum(real_0, real_4769/250) = real_4769/250 % 22.56/3.92 | (4) real_$less(real_4769/250, real_4769/250) = 1 % 22.56/3.92 | (5) real_$less(real_very_small, real_4769/250) = 0 % 22.56/3.92 | (6) real_$difference(real_407/100, real_407/100) = real_0 % 22.56/3.92 | (7) real_$difference(real_4769/250, real_4769/250) = real_0 % 22.56/3.92 | (8) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v1, % 22.56/3.92 | v0) = v2) | real_$sum(v0, v1) = v2) % 22.56/3.92 | (9) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 22.56/3.92 | (real_$difference(v1, v0) = v2) | ? [v3: $real] : (real_$uminus(v0) % 22.56/3.92 | = v3 & real_$sum(v1, v3) = v2)) % 22.56/3.92 | (10) ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ % 22.56/3.92 | (real_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 22.56/3.92 | real_$greatereq(v0, v1) = v3)) % 22.56/3.92 | (11) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 % 22.56/3.92 | = 0 | ~ (real_$less(v2, v0) = v3) | ~ (real_$less(v1, v0) = 0) | % 22.56/3.92 | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) % 22.56/3.93 | (12) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! % 22.56/3.93 | [v4: $real] : ( ~ (real_$sum(v2, v3) = v4) | ~ (real_$sum(v1, v0) = % 22.56/3.93 | v3) | ? [v5: $real] : (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) % 22.56/3.93 | = v5)) % 22.56/3.93 | (13) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! % 22.56/3.93 | [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = % 22.56/3.93 | v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) % 22.56/3.93 | = v5)) % 22.56/3.93 | % 22.56/3.93 | GROUND_INST: instantiating (11) with real_4769/250, real_very_small, % 22.56/3.93 | real_4769/250, 1, simplifying with (4), (5) gives: % 22.56/3.93 | (14) ? [v0: int] : ( ~ (v0 = 0) & real_$lesseq(real_4769/250, % 22.56/3.93 | real_very_small) = v0) % 22.56/3.93 | % 22.56/3.93 | GROUND_INST: instantiating (9) with real_407/100, real_407/100, real_0, % 22.56/3.93 | simplifying with (6) gives: % 22.56/3.93 | (15) ? [v0: $real] : (real_$uminus(real_407/100) = v0 & % 22.56/3.93 | real_$sum(real_407/100, v0) = real_0) % 22.56/3.93 | % 22.56/3.93 | GROUND_INST: instantiating (9) with real_4769/250, real_4769/250, real_0, % 22.56/3.93 | simplifying with (7) gives: % 22.56/3.93 | (16) ? [v0: $real] : (real_$uminus(real_4769/250) = v0 & % 22.56/3.93 | real_$sum(real_4769/250, v0) = real_0) % 22.56/3.93 | % 22.56/3.93 | DELTA: instantiating (16) with fresh symbol all_20_0 gives: % 22.56/3.93 | (17) real_$uminus(real_4769/250) = all_20_0 & real_$sum(real_4769/250, % 22.56/3.93 | all_20_0) = real_0 % 22.56/3.93 | % 22.56/3.93 | ALPHA: (17) implies: % 22.56/3.93 | (18) real_$sum(real_4769/250, all_20_0) = real_0 % 22.56/3.93 | % 22.56/3.93 | DELTA: instantiating (15) with fresh symbol all_22_0 gives: % 22.56/3.93 | (19) real_$uminus(real_407/100) = all_22_0 & real_$sum(real_407/100, % 22.56/3.93 | all_22_0) = real_0 % 22.56/3.93 | % 22.56/3.93 | ALPHA: (19) implies: % 22.56/3.93 | (20) real_$sum(real_407/100, all_22_0) = real_0 % 22.56/3.93 | % 22.56/3.93 | DELTA: instantiating (14) with fresh symbol all_30_0 gives: % 22.56/3.93 | (21) ~ (all_30_0 = 0) & real_$lesseq(real_4769/250, real_very_small) = % 22.56/3.93 | all_30_0 % 22.56/3.93 | % 22.56/3.93 | ALPHA: (21) implies: % 22.56/3.93 | (22) ~ (all_30_0 = 0) % 22.56/3.93 | (23) real_$lesseq(real_4769/250, real_very_small) = all_30_0 % 22.56/3.93 | % 22.56/3.93 | GROUND_INST: instantiating (13) with real_407/100, all_22_0, real_407/100, % 22.56/3.93 | real_0, real_407/100, simplifying with (2), (20) gives: % 22.56/3.93 | (24) ? [v0: $real] : (real_$sum(all_22_0, real_407/100) = v0 & % 22.56/3.93 | real_$sum(real_407/100, v0) = real_407/100) % 22.56/3.93 | % 22.56/3.93 | GROUND_INST: instantiating (8) with all_22_0, real_407/100, real_0, % 22.56/3.93 | simplifying with (20) gives: % 22.56/3.93 | (25) real_$sum(all_22_0, real_407/100) = real_0 % 22.56/3.93 | % 22.56/3.93 | GROUND_INST: instantiating (13) with real_4769/250, all_20_0, real_4769/250, % 22.56/3.93 | real_0, real_4769/250, simplifying with (3), (18) gives: % 22.56/3.93 | (26) ? [v0: $real] : (real_$sum(all_20_0, real_4769/250) = v0 & % 22.56/3.93 | real_$sum(real_4769/250, v0) = real_4769/250) % 22.56/3.94 | % 22.56/3.94 | GROUND_INST: instantiating (8) with all_20_0, real_4769/250, real_0, % 22.56/3.94 | simplifying with (18) gives: % 22.56/3.94 | (27) real_$sum(all_20_0, real_4769/250) = real_0 % 22.56/3.94 | % 22.56/3.94 | GROUND_INST: instantiating (10) with real_very_small, real_4769/250, all_30_0, % 22.56/3.94 | simplifying with (23) gives: % 22.56/3.94 | (28) all_30_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 22.56/3.94 | real_$greatereq(real_very_small, real_4769/250) = v0) % 22.56/3.94 | % 22.56/3.94 | DELTA: instantiating (24) with fresh symbol all_58_0 gives: % 22.56/3.94 | (29) real_$sum(all_22_0, real_407/100) = all_58_0 & real_$sum(real_407/100, % 22.56/3.94 | all_58_0) = real_407/100 % 22.56/3.94 | % 22.56/3.94 | ALPHA: (29) implies: % 22.56/3.94 | (30) real_$sum(all_22_0, real_407/100) = all_58_0 % 22.56/3.94 | % 22.56/3.94 | DELTA: instantiating (26) with fresh symbol all_72_0 gives: % 22.56/3.94 | (31) real_$sum(all_20_0, real_4769/250) = all_72_0 & % 22.56/3.94 | real_$sum(real_4769/250, all_72_0) = real_4769/250 % 22.56/3.94 | % 22.56/3.94 | ALPHA: (31) implies: % 22.56/3.94 | (32) real_$sum(real_4769/250, all_72_0) = real_4769/250 % 22.56/3.94 | (33) real_$sum(all_20_0, real_4769/250) = all_72_0 % 22.56/3.94 | % 22.56/3.94 | BETA: splitting (28) gives: % 22.56/3.94 | % 22.56/3.94 | Case 1: % 22.56/3.94 | | % 22.56/3.94 | | (34) all_30_0 = 0 % 22.56/3.94 | | % 22.56/3.94 | | REDUCE: (22), (34) imply: % 22.56/3.94 | | (35) $false % 22.56/3.94 | | % 22.56/3.94 | | CLOSE: (35) is inconsistent. % 22.56/3.94 | | % 22.56/3.94 | Case 2: % 22.56/3.94 | | % 22.56/3.94 | | % 22.56/3.94 | | GROUND_INST: instantiating (1) with real_0, all_72_0, real_4769/250, % 22.56/3.94 | | all_20_0, simplifying with (27), (33) gives: % 22.56/3.94 | | (36) all_72_0 = real_0 % 22.56/3.94 | | % 22.56/3.94 | | GROUND_INST: instantiating (1) with real_0, all_58_0, real_407/100, % 22.56/3.94 | | all_22_0, simplifying with (25), (30) gives: % 22.56/3.94 | | (37) all_58_0 = real_0 % 22.56/3.94 | | % 22.56/3.94 | | REDUCE: (32), (36) imply: % 22.56/3.94 | | (38) real_$sum(real_4769/250, real_0) = real_4769/250 % 22.56/3.94 | | % 22.56/3.94 | | GROUND_INST: instantiating (12) with real_407/100, all_22_0, real_4769/250, % 22.56/3.94 | | real_0, real_4769/250, simplifying with (25), (38) gives: % 22.56/3.94 | | (39) ? [v0: $real] : (real_$sum(v0, real_407/100) = real_4769/250 & % 22.56/3.94 | | real_$sum(real_4769/250, all_22_0) = v0) % 22.56/3.94 | | % 22.56/3.94 | | DELTA: instantiating (39) with fresh symbol all_239_0 gives: % 22.56/3.94 | | (40) real_$sum(all_239_0, real_407/100) = real_4769/250 & % 22.56/3.94 | | real_$sum(real_4769/250, all_22_0) = all_239_0 % 22.56/3.94 | | % 22.56/3.94 | | ALPHA: (40) implies: % 22.56/3.94 | | (41) real_$sum(all_239_0, real_407/100) = real_4769/250 % 22.56/3.94 | | % 22.56/3.94 | | GROUND_INST: instantiating (real_sum_problem_6) with all_239_0, simplifying % 22.56/3.94 | | with (41) gives: % 22.56/3.94 | | (42) $false % 22.56/3.94 | | % 22.56/3.94 | | CLOSE: (42) is inconsistent. % 22.56/3.94 | | % 22.56/3.94 | End of split % 22.56/3.94 | % 22.56/3.94 End of proof % 22.56/3.94 % SZS output end Proof for theBenchmark % 22.56/3.94 % 22.56/3.94 3318ms %------------------------------------------------------------------------------