%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI365_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 : n018.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 17:47:46 EDT 2023 % Result : Theorem 5.92s 1.56s % Output : Proof 9.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : ARI365_1 : TPTP v8.1.2. Released v5.0.0. % 0.11/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n018.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 18:12:33 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.62/0.92 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.62/0.92 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 1.62/0.92 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.62/0.92 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.62/0.92 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.62/0.92 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 1.62/0.93 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 2.20/0.98 Prover 1: Preprocessing ... % 2.20/0.98 Prover 4: Preprocessing ... % 2.48/1.03 Prover 0: Preprocessing ... % 2.48/1.05 Prover 6: Preprocessing ... % 2.48/1.05 Prover 5: Preprocessing ... % 2.48/1.05 Prover 3: Preprocessing ... % 2.48/1.06 Prover 2: Preprocessing ... % 5.26/1.51 Prover 6: Constructing countermodel ... % 5.92/1.55 Prover 6: proved (894ms) % 5.92/1.55 % 5.92/1.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.92/1.56 % 5.92/1.57 Prover 1: Constructing countermodel ... % 5.92/1.57 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.92/1.57 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 5.92/1.58 Prover 0: Constructing countermodel ... % 5.92/1.58 Prover 0: stopped % 6.43/1.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.43/1.59 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 6.43/1.60 Prover 8: Preprocessing ... % 6.43/1.62 Prover 7: Preprocessing ... % 6.43/1.62 Prover 4: Constructing countermodel ... % 6.43/1.65 Prover 2: Constructing countermodel ... % 6.43/1.65 Prover 2: stopped % 6.43/1.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.43/1.67 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 7.26/1.71 Prover 5: Constructing countermodel ... % 7.26/1.71 Prover 5: stopped % 7.26/1.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.26/1.72 Prover 10: Preprocessing ... % 7.26/1.72 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 7.41/1.78 Prover 11: Preprocessing ... % 7.41/1.80 Prover 3: Constructing countermodel ... % 7.41/1.80 Prover 3: stopped % 7.41/1.81 Prover 8: Warning: ignoring some quantifiers % 7.41/1.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.41/1.81 Prover 8: Constructing countermodel ... % 7.41/1.81 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 7.41/1.82 Prover 13: Preprocessing ... % 8.47/1.88 Prover 1: Found proof (size 7) % 8.47/1.88 Prover 1: proved (1223ms) % 8.47/1.88 Prover 4: Found proof (size 7) % 8.47/1.88 Prover 4: proved (1223ms) % 8.47/1.88 Prover 8: stopped % 8.47/1.89 Prover 13: stopped % 8.47/1.89 Prover 10: stopped % 8.95/1.96 Prover 11: stopped % 8.95/1.98 Prover 7: Warning: ignoring some quantifiers % 8.95/1.99 Prover 7: Constructing countermodel ... % 8.95/2.01 Prover 7: stopped % 8.95/2.01 % 8.95/2.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.95/2.01 % 8.95/2.01 % SZS output start Proof for theBenchmark % 8.95/2.01 Assumptions after simplification: % 8.95/2.01 --------------------------------- % 8.95/2.01 % 8.95/2.01 (real_lesseq_problem_8) % 9.37/2.03 ? [v0: int] : ( ~ (v0 = 0) & real_$lesseq(real_-13/4, real_13/4) = v0) % 9.37/2.03 % 9.37/2.03 (input) % 9.37/2.06 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_13/4) & ~ % 9.37/2.06 (real_very_large = real_-13/4) & ~ (real_very_large = real_0) & ~ % 9.37/2.06 (real_very_small = real_13/4) & ~ (real_very_small = real_-13/4) & ~ % 9.37/2.06 (real_very_small = real_0) & ~ (real_13/4 = real_-13/4) & ~ (real_13/4 = % 9.37/2.06 real_0) & ~ (real_-13/4 = real_0) & real_$is_int(real_13/4) = 1 & % 9.37/2.06 real_$is_int(real_-13/4) = 1 & real_$is_int(real_0) = 0 & % 9.37/2.06 real_$is_rat(real_13/4) = 0 & real_$is_rat(real_-13/4) = 0 & % 9.37/2.06 real_$is_rat(real_0) = 0 & real_$floor(real_0) = real_0 & % 9.37/2.06 real_$ceiling(real_0) = real_0 & real_$truncate(real_0) = real_0 & % 9.37/2.06 real_$round(real_0) = real_0 & real_$to_int(real_13/4) = 3 & % 9.37/2.06 real_$to_int(real_-13/4) = -4 & real_$to_int(real_0) = 0 & % 9.37/2.06 real_$to_rat(real_13/4) = rat_13/4 & real_$to_rat(real_-13/4) = rat_-13/4 & % 9.37/2.06 real_$to_rat(real_0) = rat_0 & real_$to_real(real_13/4) = real_13/4 & % 9.37/2.06 real_$to_real(real_-13/4) = real_-13/4 & real_$to_real(real_0) = real_0 & % 9.37/2.06 int_$to_real(0) = real_0 & real_$quotient(real_0, real_13/4) = real_0 & % 9.37/2.06 real_$quotient(real_0, real_-13/4) = real_0 & real_$product(real_13/4, real_0) % 9.37/2.06 = real_0 & real_$product(real_-13/4, real_0) = real_0 & real_$product(real_0, % 9.37/2.06 real_13/4) = real_0 & real_$product(real_0, real_-13/4) = real_0 & % 9.37/2.06 real_$product(real_0, real_0) = real_0 & real_$difference(real_13/4, % 9.37/2.06 real_13/4) = real_0 & real_$difference(real_13/4, real_0) = real_13/4 & % 9.37/2.06 real_$difference(real_-13/4, real_-13/4) = real_0 & % 9.37/2.06 real_$difference(real_-13/4, real_0) = real_-13/4 & real_$difference(real_0, % 9.37/2.06 real_13/4) = real_-13/4 & real_$difference(real_0, real_-13/4) = real_13/4 & % 9.37/2.06 real_$difference(real_0, real_0) = real_0 & real_$uminus(real_13/4) = % 9.37/2.06 real_-13/4 & real_$uminus(real_-13/4) = real_13/4 & real_$uminus(real_0) = % 9.37/2.06 real_0 & real_$sum(real_13/4, real_-13/4) = real_0 & real_$sum(real_13/4, % 9.37/2.06 real_0) = real_13/4 & real_$sum(real_-13/4, real_13/4) = real_0 & % 9.37/2.06 real_$sum(real_-13/4, real_0) = real_-13/4 & real_$sum(real_0, real_13/4) = % 9.37/2.06 real_13/4 & real_$sum(real_0, real_-13/4) = real_-13/4 & real_$sum(real_0, % 9.37/2.06 real_0) = real_0 & real_$greatereq(real_very_small, real_very_large) = 1 & % 9.37/2.06 real_$greatereq(real_13/4, real_13/4) = 0 & real_$greatereq(real_13/4, % 9.37/2.06 real_-13/4) = 0 & real_$greatereq(real_13/4, real_0) = 0 & % 9.37/2.06 real_$greatereq(real_-13/4, real_13/4) = 1 & real_$greatereq(real_-13/4, % 9.37/2.06 real_-13/4) = 0 & real_$greatereq(real_-13/4, real_0) = 1 & % 9.37/2.06 real_$greatereq(real_0, real_13/4) = 1 & real_$greatereq(real_0, real_-13/4) = % 9.37/2.06 0 & real_$greatereq(real_0, real_0) = 0 & real_$greater(real_very_large, % 9.37/2.06 real_13/4) = 0 & real_$greater(real_very_large, real_-13/4) = 0 & % 9.37/2.06 real_$greater(real_very_large, real_0) = 0 & real_$greater(real_very_small, % 9.37/2.06 real_very_large) = 1 & real_$greater(real_13/4, real_very_small) = 0 & % 9.37/2.06 real_$greater(real_13/4, real_13/4) = 1 & real_$greater(real_13/4, real_-13/4) % 9.37/2.06 = 0 & real_$greater(real_13/4, real_0) = 0 & real_$greater(real_-13/4, % 9.37/2.06 real_very_small) = 0 & real_$greater(real_-13/4, real_13/4) = 1 & % 9.37/2.06 real_$greater(real_-13/4, real_-13/4) = 1 & real_$greater(real_-13/4, real_0) % 9.37/2.06 = 1 & real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0, % 9.37/2.06 real_13/4) = 1 & real_$greater(real_0, real_-13/4) = 0 & % 9.37/2.06 real_$greater(real_0, real_0) = 1 & real_$less(real_very_small, % 9.37/2.06 real_very_large) = 0 & real_$less(real_very_small, real_13/4) = 0 & % 9.37/2.06 real_$less(real_very_small, real_-13/4) = 0 & real_$less(real_very_small, % 9.37/2.06 real_0) = 0 & real_$less(real_13/4, real_very_large) = 0 & % 9.37/2.06 real_$less(real_13/4, real_13/4) = 1 & real_$less(real_13/4, real_-13/4) = 1 & % 9.37/2.06 real_$less(real_13/4, real_0) = 1 & real_$less(real_-13/4, real_very_large) = % 9.37/2.06 0 & real_$less(real_-13/4, real_13/4) = 0 & real_$less(real_-13/4, real_-13/4) % 9.37/2.06 = 1 & real_$less(real_-13/4, real_0) = 0 & real_$less(real_0, real_very_large) % 9.37/2.06 = 0 & real_$less(real_0, real_13/4) = 0 & real_$less(real_0, real_-13/4) = 1 & % 9.37/2.06 real_$less(real_0, real_0) = 1 & real_$lesseq(real_very_small, % 9.37/2.06 real_very_large) = 0 & real_$lesseq(real_13/4, real_13/4) = 0 & % 9.37/2.06 real_$lesseq(real_13/4, real_-13/4) = 1 & real_$lesseq(real_13/4, real_0) = 1 % 9.37/2.06 & real_$lesseq(real_-13/4, real_13/4) = 0 & real_$lesseq(real_-13/4, % 9.37/2.06 real_-13/4) = 0 & real_$lesseq(real_-13/4, real_0) = 0 & % 9.37/2.06 real_$lesseq(real_0, real_13/4) = 0 & real_$lesseq(real_0, real_-13/4) = 1 & % 9.37/2.06 real_$lesseq(real_0, real_0) = 0 & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.37/2.06 $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ % 9.37/2.06 (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & % 9.37/2.06 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.37/2.06 $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~ (real_$quotient(v2, % 9.37/2.06 v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: $real] : ! [v1: % 9.37/2.06 $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0) = % 9.37/2.06 v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & % 9.37/2.06 real_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.37/2.06 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ % 9.37/2.06 (real_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, % 9.37/2.06 v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: % 9.37/2.06 $real] : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) | % 9.37/2.06 real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.37/2.06 $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) = % 9.37/2.06 v2)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ % 9.37/2.06 (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 9.37/2.06 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.37/2.06 int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = % 9.37/2.06 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! % 9.37/2.06 [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3: % 9.37/2.06 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $real] : ! % 9.37/2.06 [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = v2) | % 9.37/2.06 real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.37/2.06 $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: % 9.37/2.06 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$less(v1, v0) = 0) | ~ % 9.37/2.06 (real_$lesseq(v2, v1) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : ! % 9.37/2.06 [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : % 9.37/2.06 ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) % 9.37/2.06 = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | % 9.37/2.06 real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 9.37/2.06 (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] : % 9.37/2.06 ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & % 9.37/2.06 ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0)) % 9.37/2.06 % 9.37/2.06 (function-axioms) % 9.37/2.07 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 9.37/2.07 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 9.37/2.07 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 9.37/2.07 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: % 9.37/2.07 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 9.37/2.07 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! % 9.37/2.07 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 9.37/2.07 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: % 9.37/2.07 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 9.37/2.07 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~ % 9.37/2.07 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.37/2.07 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 9.37/2.07 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0: % 9.37/2.07 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 9.37/2.07 $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) = % 9.37/2.07 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.37/2.07 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~ % 9.37/2.07 (real_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.37/2.07 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1) % 9.37/2.07 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.37/2.07 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) % 9.37/2.07 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.37/2.07 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & % 9.37/2.07 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 9.37/2.07 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] : % 9.37/2.07 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ % 9.37/2.07 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.37/2.07 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) & % 9.37/2.07 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2) % 9.37/2.07 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 9.37/2.07 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = % 9.37/2.07 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 9.37/2.07 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] : % 9.37/2.07 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ % 9.37/2.07 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 9.37/2.07 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) % 9.37/2.07 % 9.37/2.07 Those formulas are unsatisfiable: % 9.37/2.07 --------------------------------- % 9.37/2.07 % 9.37/2.07 Begin of proof % 9.37/2.07 | % 9.37/2.07 | ALPHA: (function-axioms) implies: % 9.37/2.07 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.37/2.07 | $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | % 9.37/2.07 | ~ (real_$lesseq(v3, v2) = v0)) % 9.37/2.07 | % 9.37/2.07 | ALPHA: (input) implies: % 9.37/2.07 | (2) real_$lesseq(real_-13/4, real_13/4) = 0 % 9.37/2.07 | % 9.37/2.07 | DELTA: instantiating (real_lesseq_problem_8) with fresh symbol all_5_0 gives: % 9.37/2.07 | (3) ~ (all_5_0 = 0) & real_$lesseq(real_-13/4, real_13/4) = all_5_0 % 9.37/2.07 | % 9.37/2.07 | ALPHA: (3) implies: % 9.37/2.08 | (4) ~ (all_5_0 = 0) % 9.37/2.08 | (5) real_$lesseq(real_-13/4, real_13/4) = all_5_0 % 9.37/2.08 | % 9.37/2.08 | GROUND_INST: instantiating (1) with 0, all_5_0, real_13/4, real_-13/4, % 9.37/2.08 | simplifying with (2), (5) gives: % 9.37/2.08 | (6) all_5_0 = 0 % 9.37/2.08 | % 9.37/2.08 | REDUCE: (4), (6) imply: % 9.37/2.08 | (7) $false % 9.62/2.08 | % 9.62/2.08 | CLOSE: (7) is inconsistent. % 9.62/2.08 | % 9.62/2.08 End of proof % 9.62/2.08 % SZS output end Proof for theBenchmark % 9.62/2.08 % 9.62/2.08 1453ms %------------------------------------------------------------------------------