%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI528_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 : n024.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 17:48:16 EDT 2023 % Result : Theorem 7.12s 1.75s % Output : Proof 12.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : ARI528_1 : TPTP v8.1.2. Released v5.0.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n024.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 17:51:22 EDT 2023 % 0.14/0.35 % CPUTime : % 0.20/0.67 ________ _____ % 0.20/0.67 ___ __ \_________(_)________________________________ % 0.20/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.67 % 0.20/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.67 (2023-06-19) % 0.20/0.67 % 0.20/0.67 (c) Philipp Rümmer, 2009-2023 % 0.20/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.67 Amanda Stjerna. % 0.20/0.67 Free software under BSD-3-Clause. % 0.20/0.67 % 0.20/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.67 % 0.20/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.68 Running up to 7 provers in parallel. % 0.20/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.58/0.98 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.98 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.98 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.98 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.98 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.98 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.98 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.99 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 1.58/0.99 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 1.58/0.99 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.58/0.99 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 1.58/0.99 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.58/1.00 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 1.58/1.00 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 2.50/1.12 Prover 1: Preprocessing ... % 2.50/1.12 Prover 4: Preprocessing ... % 2.50/1.12 Prover 0: Preprocessing ... % 2.50/1.13 Prover 6: Preprocessing ... % 3.46/1.28 Prover 2: Preprocessing ... % 3.46/1.28 Prover 5: Preprocessing ... % 3.90/1.29 Prover 3: Preprocessing ... % 6.99/1.70 Prover 6: Constructing countermodel ... % 7.12/1.74 Prover 6: proved (1041ms) % 7.12/1.74 % 7.12/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.12/1.75 % 7.12/1.75 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.12/1.76 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 7.12/1.76 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation % 7.12/1.79 Prover 1: Constructing countermodel ... % 7.12/1.80 Prover 2: stopped % 7.12/1.81 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.32/1.82 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 7.32/1.82 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation % 7.32/1.83 Prover 8: Preprocessing ... % 7.32/1.84 Prover 0: Constructing countermodel ... % 7.32/1.84 Prover 0: stopped % 7.32/1.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.32/1.88 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 7.32/1.88 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation % 7.32/1.88 Prover 7: Preprocessing ... % 7.32/1.90 Prover 4: Constructing countermodel ... % 8.54/1.97 Prover 10: Preprocessing ... % 10.10/2.11 Prover 8: Warning: ignoring some quantifiers % 10.16/2.12 Prover 8: Constructing countermodel ... % 10.16/2.13 Prover 1: Found proof (size 8) % 10.16/2.13 Prover 1: proved (1435ms) % 10.16/2.13 Prover 4: stopped % 10.16/2.13 Prover 8: stopped % 10.85/2.26 Prover 7: stopped % 11.49/2.33 Prover 3: Constructing countermodel ... % 11.49/2.33 Prover 3: stopped % 11.49/2.34 Prover 10: stopped % 12.02/2.39 Prover 5: Constructing countermodel ... % 12.02/2.39 Prover 5: stopped % 12.02/2.39 % 12.02/2.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.02/2.39 % 12.02/2.39 % SZS output start Proof for theBenchmark % 12.06/2.39 Assumptions after simplification: % 12.06/2.39 --------------------------------- % 12.06/2.39 % 12.06/2.39 (mixed_types_problem_33) % 12.06/2.41 ? [v0: int] : ? [v1: int] : ( ~ ($sum($product(10, v1), v0) = 100) & % 12.06/2.41 real_$to_int(real_2549/50) = v0 & rat_$to_int(rat_11/2) = v1) % 12.06/2.41 % 12.06/2.41 (input) % 12.06/2.45 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_11/2) & ~ % 12.06/2.45 (real_very_large = real_2549/50) & ~ (real_very_large = real_0) & ~ % 12.06/2.45 (real_very_small = real_11/2) & ~ (real_very_small = real_2549/50) & ~ % 12.06/2.45 (real_very_small = real_0) & ~ (rat_very_large = rat_very_small) & ~ % 12.06/2.45 (rat_very_large = rat_11/2) & ~ (rat_very_large = rat_2549/50) & ~ % 12.06/2.45 (rat_very_large = rat_0) & ~ (rat_very_small = rat_11/2) & ~ (rat_very_small % 12.06/2.46 = rat_2549/50) & ~ (rat_very_small = rat_0) & ~ (real_11/2 = real_2549/50) % 12.06/2.46 & ~ (real_11/2 = real_0) & ~ (rat_11/2 = rat_2549/50) & ~ (rat_11/2 = % 12.06/2.46 rat_0) & ~ (real_2549/50 = real_0) & ~ (rat_2549/50 = rat_0) & % 12.06/2.46 rat_$is_int(rat_11/2) = 1 & rat_$is_int(rat_2549/50) = 1 & rat_$is_int(rat_0) % 12.06/2.46 = 0 & rat_$is_rat(rat_11/2) = 0 & rat_$is_rat(rat_2549/50) = 0 & % 12.06/2.46 rat_$is_rat(rat_0) = 0 & rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = % 12.06/2.46 rat_0 & rat_$truncate(rat_0) = rat_0 & rat_$round(rat_0) = rat_0 & % 12.06/2.46 rat_$to_rat(rat_11/2) = rat_11/2 & rat_$to_rat(rat_2549/50) = rat_2549/50 & % 12.06/2.46 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_11/2) = real_11/2 & % 12.06/2.46 rat_$to_real(rat_2549/50) = real_2549/50 & rat_$to_real(rat_0) = real_0 & % 12.06/2.46 int_$to_rat(0) = rat_0 & real_$is_int(real_11/2) = 1 & % 12.06/2.46 real_$is_int(real_2549/50) = 1 & real_$is_int(real_0) = 0 & % 12.06/2.46 real_$is_rat(real_11/2) = 0 & real_$is_rat(real_2549/50) = 0 & % 12.06/2.46 real_$is_rat(real_0) = 0 & real_$floor(real_0) = real_0 & % 12.06/2.46 real_$ceiling(real_0) = real_0 & real_$truncate(real_0) = real_0 & % 12.06/2.46 real_$round(real_0) = real_0 & real_$to_rat(real_11/2) = rat_11/2 & % 12.06/2.46 real_$to_rat(real_2549/50) = rat_2549/50 & real_$to_rat(real_0) = rat_0 & % 12.06/2.46 real_$to_real(real_11/2) = real_11/2 & real_$to_real(real_2549/50) = % 12.06/2.46 real_2549/50 & real_$to_real(real_0) = real_0 & int_$to_real(0) = real_0 & % 12.06/2.46 real_$quotient(real_0, real_11/2) = real_0 & real_$quotient(real_0, % 12.06/2.46 real_2549/50) = real_0 & real_$product(real_11/2, real_0) = real_0 & % 12.06/2.46 real_$product(real_2549/50, real_0) = real_0 & real_$product(real_0, % 12.06/2.46 real_11/2) = real_0 & real_$product(real_0, real_2549/50) = real_0 & % 12.06/2.46 real_$product(real_0, real_0) = real_0 & real_$difference(real_11/2, % 12.06/2.46 real_11/2) = real_0 & real_$difference(real_11/2, real_0) = real_11/2 & % 12.06/2.46 real_$difference(real_2549/50, real_2549/50) = real_0 & % 12.06/2.46 real_$difference(real_2549/50, real_0) = real_2549/50 & % 12.06/2.46 real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) = real_0 & % 12.06/2.46 real_$sum(real_11/2, real_0) = real_11/2 & real_$sum(real_2549/50, real_0) = % 12.06/2.46 real_2549/50 & real_$sum(real_0, real_11/2) = real_11/2 & real_$sum(real_0, % 12.06/2.46 real_2549/50) = real_2549/50 & real_$sum(real_0, real_0) = real_0 & % 12.06/2.46 real_$greatereq(real_very_small, real_very_large) = 1 & % 12.06/2.46 real_$greatereq(real_11/2, real_11/2) = 0 & real_$greatereq(real_11/2, % 12.06/2.46 real_2549/50) = 1 & real_$greatereq(real_11/2, real_0) = 0 & % 12.06/2.46 real_$greatereq(real_2549/50, real_11/2) = 0 & real_$greatereq(real_2549/50, % 12.06/2.46 real_2549/50) = 0 & real_$greatereq(real_2549/50, real_0) = 0 & % 12.06/2.46 real_$greatereq(real_0, real_11/2) = 1 & real_$greatereq(real_0, real_2549/50) % 12.06/2.46 = 1 & real_$greatereq(real_0, real_0) = 0 & real_$lesseq(real_very_small, % 12.06/2.46 real_very_large) = 0 & real_$lesseq(real_11/2, real_11/2) = 0 & % 12.06/2.46 real_$lesseq(real_11/2, real_2549/50) = 0 & real_$lesseq(real_11/2, real_0) = % 12.06/2.46 1 & real_$lesseq(real_2549/50, real_11/2) = 1 & real_$lesseq(real_2549/50, % 12.06/2.46 real_2549/50) = 0 & real_$lesseq(real_2549/50, real_0) = 1 & % 12.06/2.46 real_$lesseq(real_0, real_11/2) = 0 & real_$lesseq(real_0, real_2549/50) = 0 & % 12.06/2.46 real_$lesseq(real_0, real_0) = 0 & real_$greater(real_very_large, real_11/2) = % 12.06/2.46 0 & real_$greater(real_very_large, real_2549/50) = 0 & % 12.06/2.46 real_$greater(real_very_large, real_0) = 0 & real_$greater(real_very_small, % 12.06/2.46 real_very_large) = 1 & real_$greater(real_11/2, real_very_small) = 0 & % 12.06/2.46 real_$greater(real_11/2, real_11/2) = 1 & real_$greater(real_11/2, % 12.06/2.46 real_2549/50) = 1 & real_$greater(real_11/2, real_0) = 0 & % 12.06/2.46 real_$greater(real_2549/50, real_very_small) = 0 & real_$greater(real_2549/50, % 12.06/2.46 real_11/2) = 0 & real_$greater(real_2549/50, real_2549/50) = 1 & % 12.06/2.46 real_$greater(real_2549/50, real_0) = 0 & real_$greater(real_0, % 12.06/2.46 real_very_small) = 0 & real_$greater(real_0, real_11/2) = 1 & % 12.06/2.46 real_$greater(real_0, real_2549/50) = 1 & real_$greater(real_0, real_0) = 1 & % 12.06/2.46 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, % 12.06/2.46 real_11/2) = 0 & real_$less(real_very_small, real_2549/50) = 0 & % 12.06/2.46 real_$less(real_very_small, real_0) = 0 & real_$less(real_11/2, % 12.06/2.46 real_very_large) = 0 & real_$less(real_11/2, real_11/2) = 1 & % 12.06/2.46 real_$less(real_11/2, real_2549/50) = 0 & real_$less(real_11/2, real_0) = 1 & % 12.06/2.46 real_$less(real_2549/50, real_very_large) = 0 & real_$less(real_2549/50, % 12.06/2.46 real_11/2) = 1 & real_$less(real_2549/50, real_2549/50) = 1 & % 12.06/2.46 real_$less(real_2549/50, real_0) = 1 & real_$less(real_0, real_very_large) = 0 % 12.06/2.46 & real_$less(real_0, real_11/2) = 0 & real_$less(real_0, real_2549/50) = 0 & % 12.06/2.46 real_$less(real_0, real_0) = 1 & rat_$quotient(rat_0, rat_11/2) = rat_0 & % 12.06/2.46 rat_$quotient(rat_0, rat_2549/50) = rat_0 & rat_$product(rat_11/2, rat_0) = % 12.06/2.46 rat_0 & rat_$product(rat_2549/50, rat_0) = rat_0 & rat_$product(rat_0, % 12.06/2.46 rat_11/2) = rat_0 & rat_$product(rat_0, rat_2549/50) = rat_0 & % 12.06/2.46 rat_$product(rat_0, rat_0) = rat_0 & rat_$difference(rat_11/2, rat_11/2) = % 12.06/2.46 rat_0 & rat_$difference(rat_11/2, rat_0) = rat_11/2 & % 12.06/2.46 rat_$difference(rat_2549/50, rat_2549/50) = rat_0 & % 12.06/2.46 rat_$difference(rat_2549/50, rat_0) = rat_2549/50 & rat_$difference(rat_0, % 12.06/2.46 rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 & rat_$sum(rat_11/2, rat_0) = % 12.06/2.46 rat_11/2 & rat_$sum(rat_2549/50, rat_0) = rat_2549/50 & rat_$sum(rat_0, % 12.06/2.46 rat_11/2) = rat_11/2 & rat_$sum(rat_0, rat_2549/50) = rat_2549/50 & % 12.06/2.46 rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small, % 12.06/2.46 rat_very_large) = 1 & rat_$greatereq(rat_11/2, rat_11/2) = 0 & % 12.06/2.46 rat_$greatereq(rat_11/2, rat_2549/50) = 1 & rat_$greatereq(rat_11/2, rat_0) = % 12.06/2.46 0 & rat_$greatereq(rat_2549/50, rat_11/2) = 0 & rat_$greatereq(rat_2549/50, % 12.06/2.46 rat_2549/50) = 0 & rat_$greatereq(rat_2549/50, rat_0) = 0 & % 12.06/2.46 rat_$greatereq(rat_0, rat_11/2) = 1 & rat_$greatereq(rat_0, rat_2549/50) = 1 & % 12.06/2.46 rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large) % 12.06/2.46 = 0 & rat_$lesseq(rat_11/2, rat_11/2) = 0 & rat_$lesseq(rat_11/2, rat_2549/50) % 12.06/2.46 = 0 & rat_$lesseq(rat_11/2, rat_0) = 1 & rat_$lesseq(rat_2549/50, rat_11/2) = % 12.06/2.46 1 & rat_$lesseq(rat_2549/50, rat_2549/50) = 0 & rat_$lesseq(rat_2549/50, % 12.06/2.46 rat_0) = 1 & rat_$lesseq(rat_0, rat_11/2) = 0 & rat_$lesseq(rat_0, % 12.06/2.46 rat_2549/50) = 0 & rat_$lesseq(rat_0, rat_0) = 0 & % 12.06/2.46 rat_$greater(rat_very_large, rat_11/2) = 0 & rat_$greater(rat_very_large, % 12.06/2.46 rat_2549/50) = 0 & rat_$greater(rat_very_large, rat_0) = 0 & % 12.06/2.46 rat_$greater(rat_very_small, rat_very_large) = 1 & rat_$greater(rat_11/2, % 12.06/2.46 rat_very_small) = 0 & rat_$greater(rat_11/2, rat_11/2) = 1 & % 12.06/2.46 rat_$greater(rat_11/2, rat_2549/50) = 1 & rat_$greater(rat_11/2, rat_0) = 0 & % 12.06/2.46 rat_$greater(rat_2549/50, rat_very_small) = 0 & rat_$greater(rat_2549/50, % 12.06/2.46 rat_11/2) = 0 & rat_$greater(rat_2549/50, rat_2549/50) = 1 & % 12.06/2.46 rat_$greater(rat_2549/50, rat_0) = 0 & rat_$greater(rat_0, rat_very_small) = 0 % 12.06/2.46 & rat_$greater(rat_0, rat_11/2) = 1 & rat_$greater(rat_0, rat_2549/50) = 1 & % 12.06/2.46 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0 % 12.06/2.46 & rat_$less(rat_very_small, rat_11/2) = 0 & rat_$less(rat_very_small, % 12.06/2.46 rat_2549/50) = 0 & rat_$less(rat_very_small, rat_0) = 0 & % 12.06/2.46 rat_$less(rat_11/2, rat_very_large) = 0 & rat_$less(rat_11/2, rat_11/2) = 1 & % 12.06/2.46 rat_$less(rat_11/2, rat_2549/50) = 0 & rat_$less(rat_11/2, rat_0) = 1 & % 12.06/2.46 rat_$less(rat_2549/50, rat_very_large) = 0 & rat_$less(rat_2549/50, rat_11/2) % 12.06/2.46 = 1 & rat_$less(rat_2549/50, rat_2549/50) = 1 & rat_$less(rat_2549/50, rat_0) % 12.06/2.46 = 1 & rat_$less(rat_0, rat_very_large) = 0 & rat_$less(rat_0, rat_11/2) = 0 & % 12.06/2.46 rat_$less(rat_0, rat_2549/50) = 0 & rat_$less(rat_0, rat_0) = 1 & % 12.06/2.46 real_$to_int(real_11/2) = 5 & real_$to_int(real_2549/50) = 50 & % 12.06/2.46 real_$to_int(real_0) = 0 & rat_$to_int(rat_11/2) = 5 & % 12.06/2.46 rat_$to_int(rat_2549/50) = 50 & rat_$to_int(rat_0) = 0 & ! [v0: $real] : ! % 12.06/2.46 [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ % 12.06/2.46 (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] : % 12.06/2.46 (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: % 12.06/2.46 $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, % 12.06/2.46 v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, % 12.06/2.46 v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : % 12.06/2.46 ! [v2: $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~ % 12.06/2.46 (real_$quotient(v2, v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: % 12.06/2.46 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v3 = v1 | v0 = % 12.06/2.46 rat_0 | ~ (rat_$quotient(v2, v0) = v3) | ~ (rat_$product(v1, v0) = v2)) & % 12.06/2.46 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ % 12.06/2.46 (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] : % 12.06/2.46 ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] % 12.06/2.46 : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0) = 0) | ~ % 12.06/2.46 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1) % 12.06/2.46 = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : % 12.06/2.46 (v3 = 0 | ~ (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? % 12.06/2.46 [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! % 12.06/2.46 [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) % 12.06/2.46 = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & % 12.06/2.46 rat_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 12.06/2.46 $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, % 12.06/2.46 v2) = v3) | real_$difference(v1, v0) = v3) & ! [v0: $rat] : ! [v1: % 12.06/2.46 $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) | ~ % 12.06/2.46 (rat_$sum(v1, v2) = v3) | rat_$difference(v1, v0) = v3) & ! [v0: $real] : % 12.06/2.46 ! [v1: $real] : ! [v2: $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | % 12.06/2.46 ~ (real_$sum(v0, v1) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 12.06/2.46 : (v2 = rat_0 | ~ (rat_$uminus(v0) = v1) | ~ (rat_$sum(v0, v1) = v2)) & ! % 12.06/2.46 [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ % 12.06/2.46 (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 12.06/2.46 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 12.06/2.46 int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3: % 12.06/2.46 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $real] : ! % 12.06/2.46 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? % 12.06/2.46 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $rat] : ! % 12.06/2.46 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? % 12.06/2.46 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! % 12.06/2.46 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1 % 12.06/2.46 = v0) & ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3))) & ! % 12.06/2.46 [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1) % 12.06/2.46 = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0: % 12.06/2.46 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = v2) % 12.06/2.46 | real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 12.06/2.46 $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: % 12.06/2.46 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | % 12.06/2.46 ~ (real_$less(v1, v0) = 0) | real_$less(v2, v0) = 0) & ! [v0: $rat] : ! % 12.06/2.46 [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | % 12.21/2.46 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 12.21/2.46 ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1: % 12.21/2.46 $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1, % 12.21/2.46 v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : % 12.21/2.46 (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : ! [v1: $real] % 12.21/2.46 : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) & ! [v0: % 12.21/2.46 $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: % 12.21/2.46 $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | % 12.21/2.46 rat_$less(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 12.21/2.46 (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: % 12.21/2.46 $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! % 12.21/2.46 [v0: $real] : ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | % 12.21/2.46 real_$less(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 12.21/2.46 (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0: $rat] : ! [v1: % 12.21/2.46 $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1, v0) = 0) & ! % 12.21/2.46 [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, % 12.21/2.46 v0) = 0) & ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0)) & % 12.21/2.46 ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0) = v0)) % 12.21/2.46 % 12.21/2.46 (function-axioms) % 12.45/2.48 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 12.45/2.48 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 12.45/2.48 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 12.45/2.48 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: % 12.45/2.48 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 12.45/2.48 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! % 12.45/2.48 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 12.45/2.48 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: % 12.45/2.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 12.45/2.48 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~ % 12.45/2.48 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.48 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 12.45/2.48 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0: % 12.45/2.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 12.45/2.48 $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, % 12.45/2.48 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 12.45/2.48 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ % 12.45/2.48 (real_$less(v3, v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 12.45/2.48 ! [v3: $rat] : (v1 = v0 | ~ (rat_$quotient(v3, v2) = v1) | ~ % 12.45/2.48 (rat_$quotient(v3, v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 12.45/2.48 $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$product(v3, v2) = v1) | ~ % 12.45/2.48 (rat_$product(v3, v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 12.45/2.48 : ! [v3: $rat] : (v1 = v0 | ~ (rat_$difference(v3, v2) = v1) | ~ % 12.45/2.48 (rat_$difference(v3, v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 12.45/2.48 $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$sum(v3, v2) = v1) | ~ % 12.45/2.48 (rat_$sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.48 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 12.45/2.48 (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3, v2) = v0)) & ! [v0: % 12.45/2.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 12.45/2.48 $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ (rat_$lesseq(v3, v2) = % 12.45/2.48 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.45/2.48 $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$greater(v3, v2) = v1) | ~ % 12.45/2.48 (rat_$greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.48 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 12.45/2.48 (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = v0)) & ! [v0: % 12.45/2.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = v0 | % 12.45/2.48 ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & ! [v0: % 12.45/2.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = v0 | % 12.45/2.48 ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] : ! % 12.45/2.48 [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~ % 12.45/2.48 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 % 12.45/2.48 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0: % 12.45/2.48 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) = % 12.45/2.48 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 12.45/2.48 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) & % 12.45/2.48 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) % 12.45/2.48 = v1) | ~ (rat_$to_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! % 12.45/2.48 [v2: $rat] : (v1 = v0 | ~ (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = % 12.45/2.48 v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ % 12.45/2.48 (int_$to_rat(v2) = v1) | ~ (int_$to_rat(v2) = v0)) & ! [v0: % 12.45/2.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : (v1 = v0 % 12.45/2.48 | ~ (real_$is_int(v2) = v1) | ~ (real_$is_int(v2) = v0)) & ! [v0: % 12.45/2.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : (v1 = v0 % 12.45/2.48 | ~ (real_$is_rat(v2) = v1) | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] % 12.45/2.48 : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ % 12.45/2.48 (real_$floor(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : % 12.45/2.48 (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! % 12.45/2.48 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 12.45/2.48 (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) = v0)) & ! [v0: $real] : % 12.45/2.48 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ % 12.45/2.48 (real_$round(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $real] : % 12.45/2.48 (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: % 12.45/2.48 $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) % 12.45/2.48 = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : % 12.45/2.48 ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = % 12.45/2.48 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 12.45/2.48 (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) & ! [v0: $rat] : ! % 12.45/2.48 [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ % 12.45/2.48 (rat_$uminus(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 % 12.45/2.48 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: % 12.45/2.48 int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) = v1) | % 12.45/2.48 ~ (rat_$to_int(v2) = v0)) % 12.45/2.48 % 12.45/2.48 Those formulas are unsatisfiable: % 12.45/2.48 --------------------------------- % 12.45/2.48 % 12.45/2.48 Begin of proof % 12.45/2.48 | % 12.45/2.48 | ALPHA: (function-axioms) implies: % 12.45/2.48 | (1) ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ % 12.45/2.48 | (rat_$to_int(v2) = v1) | ~ (rat_$to_int(v2) = v0)) % 12.45/2.48 | (2) ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ % 12.45/2.48 | (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0)) % 12.45/2.49 | % 12.45/2.49 | ALPHA: (input) implies: % 12.45/2.49 | (3) rat_$to_int(rat_11/2) = 5 % 12.45/2.49 | (4) real_$to_int(real_2549/50) = 50 % 12.45/2.49 | % 12.45/2.49 | DELTA: instantiating (mixed_types_problem_33) with fresh symbols all_5_0, % 12.45/2.49 | all_5_1 gives: % 12.45/2.49 | (5) ~ ($sum($product(10, all_5_0), all_5_1) = 100) & % 12.45/2.49 | real_$to_int(real_2549/50) = all_5_1 & rat_$to_int(rat_11/2) = all_5_0 % 12.45/2.49 | % 12.45/2.49 | ALPHA: (5) implies: % 12.45/2.49 | (6) ~ ($sum($product(10, all_5_0), all_5_1) = 100) % 12.45/2.49 | (7) rat_$to_int(rat_11/2) = all_5_0 % 12.45/2.49 | (8) real_$to_int(real_2549/50) = all_5_1 % 12.45/2.49 | % 12.45/2.49 | GROUND_INST: instantiating (1) with 5, all_5_0, rat_11/2, simplifying with % 12.45/2.49 | (3), (7) gives: % 12.45/2.49 | (9) all_5_0 = 5 % 12.45/2.49 | % 12.45/2.49 | GROUND_INST: instantiating (2) with 50, all_5_1, real_2549/50, simplifying % 12.45/2.49 | with (4), (8) gives: % 12.45/2.49 | (10) all_5_1 = 50 % 12.45/2.49 | % 12.45/2.49 | REDUCE: (6), (9), (10) imply: % 12.45/2.49 | (11) $false % 12.45/2.49 | % 12.45/2.49 | CLOSE: (11) is inconsistent. % 12.45/2.49 | % 12.45/2.49 End of proof % 12.45/2.49 % SZS output end Proof for theBenchmark % 12.45/2.49 % 12.45/2.49 1823ms %------------------------------------------------------------------------------