%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI554_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 : n017.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 17:48:22 EDT 2023 % Result : Theorem 7.64s 1.76s % Output : Proof 18.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : ARI554_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 : n017.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 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 17:57:14 EDT 2023 % 0.13/0.34 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.52/0.97 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 1.52/0.97 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.52/0.97 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 1.52/0.97 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.52/0.97 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 1.52/0.97 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 1.52/0.97 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 2.07/1.05 Prover 1: Preprocessing ... % 2.07/1.05 Prover 4: Preprocessing ... % 3.00/1.12 Prover 6: Preprocessing ... % 3.00/1.12 Prover 0: Preprocessing ... % 4.38/1.40 Prover 5: Preprocessing ... % 4.38/1.41 Prover 2: Preprocessing ... % 4.38/1.42 Prover 3: Preprocessing ... % 7.09/1.72 Prover 6: Constructing countermodel ... % 7.09/1.72 Prover 0: Constructing countermodel ... % 7.54/1.75 Prover 1: Constructing countermodel ... % 7.54/1.76 Prover 6: proved (1121ms) % 7.54/1.76 % 7.64/1.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.64/1.76 % 7.64/1.76 Prover 0: proved (1123ms) % 7.64/1.76 % 7.64/1.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.64/1.76 % 7.64/1.77 Prover 4: Constructing countermodel ... % 7.64/1.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.64/1.77 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.64/1.77 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation % 7.64/1.77 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation % 7.64/1.78 Prover 8: Preprocessing ... % 8.24/1.92 Prover 8: Warning: ignoring some quantifiers % 8.24/1.95 Prover 8: Constructing countermodel ... % 8.24/1.98 Prover 7: Preprocessing ... % 9.12/2.02 Prover 1: Found proof (size 7) % 9.12/2.02 Prover 1: proved (1388ms) % 9.12/2.02 Prover 4: stopped % 9.12/2.03 Prover 8: stopped % 11.45/2.30 Prover 2: stopped % 13.13/2.64 Prover 7: stopped % 15.63/3.01 Prover 5: Constructing countermodel ... % 15.63/3.01 Prover 5: stopped % 18.03/3.73 Prover 3: Constructing countermodel ... % 18.03/3.73 Prover 3: stopped % 18.03/3.73 % 18.03/3.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.03/3.73 % 18.03/3.74 % SZS output start Proof for theBenchmark % 18.03/3.74 Assumptions after simplification: % 18.03/3.74 --------------------------------- % 18.03/3.74 % 18.03/3.74 (rat_combined_problem_14) % 18.03/3.79 ? [v0: int] : ( ~ (v0 = 0) & rat_$lesseq(rat_21/80, rat_23/80) = v0) % 18.03/3.79 % 18.03/3.79 (input) % 18.42/3.86 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_23/80) & ~ % 18.42/3.86 (rat_very_large = rat_21/80) & ~ (rat_very_large = rat_7/10) & ~ % 18.42/3.86 (rat_very_large = rat_3/8) & ~ (rat_very_large = rat_0) & ~ (rat_very_small % 18.42/3.86 = rat_23/80) & ~ (rat_very_small = rat_21/80) & ~ (rat_very_small = % 18.42/3.86 rat_7/10) & ~ (rat_very_small = rat_3/8) & ~ (rat_very_small = rat_0) & ~ % 18.42/3.86 (rat_23/80 = rat_21/80) & ~ (rat_23/80 = rat_7/10) & ~ (rat_23/80 = rat_3/8) % 18.42/3.86 & ~ (rat_23/80 = rat_0) & ~ (rat_21/80 = rat_7/10) & ~ (rat_21/80 = % 18.42/3.86 rat_3/8) & ~ (rat_21/80 = rat_0) & ~ (rat_7/10 = rat_3/8) & ~ (rat_7/10 = % 18.42/3.86 rat_0) & ~ (rat_3/8 = rat_0) & rat_$is_int(rat_23/80) = 1 & % 18.42/3.86 rat_$is_int(rat_21/80) = 1 & rat_$is_int(rat_7/10) = 1 & rat_$is_int(rat_3/8) % 18.42/3.86 = 1 & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_23/80) = 0 & % 18.42/3.86 rat_$is_rat(rat_21/80) = 0 & rat_$is_rat(rat_7/10) = 0 & rat_$is_rat(rat_3/8) % 18.42/3.86 = 0 & rat_$is_rat(rat_0) = 0 & rat_$floor(rat_23/80) = rat_0 & % 18.42/3.86 rat_$floor(rat_21/80) = rat_0 & rat_$floor(rat_7/10) = rat_0 & % 18.42/3.86 rat_$floor(rat_3/8) = rat_0 & rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) % 18.42/3.86 = rat_0 & rat_$truncate(rat_23/80) = rat_0 & rat_$truncate(rat_21/80) = rat_0 % 18.42/3.86 & rat_$truncate(rat_7/10) = rat_0 & rat_$truncate(rat_3/8) = rat_0 & % 18.42/3.86 rat_$truncate(rat_0) = rat_0 & rat_$round(rat_23/80) = rat_0 & % 18.42/3.86 rat_$round(rat_21/80) = rat_0 & rat_$round(rat_3/8) = rat_0 & % 18.42/3.86 rat_$round(rat_0) = rat_0 & rat_$to_int(rat_23/80) = 0 & % 18.42/3.86 rat_$to_int(rat_21/80) = 0 & rat_$to_int(rat_7/10) = 0 & rat_$to_int(rat_3/8) % 18.42/3.86 = 0 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_23/80) = rat_23/80 & % 18.42/3.86 rat_$to_rat(rat_21/80) = rat_21/80 & rat_$to_rat(rat_7/10) = rat_7/10 & % 18.42/3.86 rat_$to_rat(rat_3/8) = rat_3/8 & rat_$to_rat(rat_0) = rat_0 & % 18.42/3.86 rat_$to_real(rat_23/80) = real_23/80 & rat_$to_real(rat_21/80) = real_21/80 & % 18.42/3.86 rat_$to_real(rat_7/10) = real_7/10 & rat_$to_real(rat_3/8) = real_3/8 & % 18.42/3.86 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & % 18.42/3.86 rat_$quotient(rat_21/80, rat_7/10) = rat_3/8 & rat_$quotient(rat_21/80, % 18.42/3.86 rat_3/8) = rat_7/10 & rat_$quotient(rat_0, rat_23/80) = rat_0 & % 18.42/3.86 rat_$quotient(rat_0, rat_21/80) = rat_0 & rat_$quotient(rat_0, rat_7/10) = % 18.42/3.86 rat_0 & rat_$quotient(rat_0, rat_3/8) = rat_0 & rat_$product(rat_23/80, rat_0) % 18.42/3.86 = rat_0 & rat_$product(rat_21/80, rat_0) = rat_0 & rat_$product(rat_7/10, % 18.42/3.86 rat_3/8) = rat_21/80 & rat_$product(rat_7/10, rat_0) = rat_0 & % 18.42/3.86 rat_$product(rat_3/8, rat_7/10) = rat_21/80 & rat_$product(rat_3/8, rat_0) = % 18.42/3.86 rat_0 & rat_$product(rat_0, rat_23/80) = rat_0 & rat_$product(rat_0, % 18.42/3.86 rat_21/80) = rat_0 & rat_$product(rat_0, rat_7/10) = rat_0 & % 18.42/3.86 rat_$product(rat_0, rat_3/8) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 & % 18.42/3.86 rat_$difference(rat_23/80, rat_23/80) = rat_0 & rat_$difference(rat_23/80, % 18.42/3.86 rat_0) = rat_23/80 & rat_$difference(rat_21/80, rat_21/80) = rat_0 & % 18.42/3.86 rat_$difference(rat_21/80, rat_0) = rat_21/80 & rat_$difference(rat_7/10, % 18.42/3.86 rat_7/10) = rat_0 & rat_$difference(rat_7/10, rat_0) = rat_7/10 & % 18.42/3.86 rat_$difference(rat_3/8, rat_3/8) = rat_0 & rat_$difference(rat_3/8, rat_0) = % 18.42/3.86 rat_3/8 & rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 & % 18.42/3.86 rat_$sum(rat_23/80, rat_0) = rat_23/80 & rat_$sum(rat_21/80, rat_0) = % 18.42/3.86 rat_21/80 & rat_$sum(rat_7/10, rat_0) = rat_7/10 & rat_$sum(rat_3/8, rat_0) = % 18.42/3.86 rat_3/8 & rat_$sum(rat_0, rat_23/80) = rat_23/80 & rat_$sum(rat_0, rat_21/80) % 18.42/3.86 = rat_21/80 & rat_$sum(rat_0, rat_7/10) = rat_7/10 & rat_$sum(rat_0, rat_3/8) % 18.42/3.86 = rat_3/8 & rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small, % 18.42/3.86 rat_very_large) = 1 & rat_$greatereq(rat_23/80, rat_23/80) = 0 & % 18.42/3.86 rat_$greatereq(rat_23/80, rat_21/80) = 0 & rat_$greatereq(rat_23/80, rat_7/10) % 18.42/3.86 = 1 & rat_$greatereq(rat_23/80, rat_3/8) = 1 & rat_$greatereq(rat_23/80, % 18.42/3.86 rat_0) = 0 & rat_$greatereq(rat_21/80, rat_23/80) = 1 & % 18.42/3.86 rat_$greatereq(rat_21/80, rat_21/80) = 0 & rat_$greatereq(rat_21/80, rat_7/10) % 18.42/3.86 = 1 & rat_$greatereq(rat_21/80, rat_3/8) = 1 & rat_$greatereq(rat_21/80, % 18.42/3.86 rat_0) = 0 & rat_$greatereq(rat_7/10, rat_23/80) = 0 & % 18.42/3.86 rat_$greatereq(rat_7/10, rat_21/80) = 0 & rat_$greatereq(rat_7/10, rat_7/10) = % 18.42/3.86 0 & rat_$greatereq(rat_7/10, rat_3/8) = 0 & rat_$greatereq(rat_7/10, rat_0) = % 18.42/3.86 0 & rat_$greatereq(rat_3/8, rat_23/80) = 0 & rat_$greatereq(rat_3/8, % 18.42/3.86 rat_21/80) = 0 & rat_$greatereq(rat_3/8, rat_7/10) = 1 & % 18.42/3.86 rat_$greatereq(rat_3/8, rat_3/8) = 0 & rat_$greatereq(rat_3/8, rat_0) = 0 & % 18.42/3.86 rat_$greatereq(rat_0, rat_23/80) = 1 & rat_$greatereq(rat_0, rat_21/80) = 1 & % 18.42/3.86 rat_$greatereq(rat_0, rat_7/10) = 1 & rat_$greatereq(rat_0, rat_3/8) = 1 & % 18.42/3.86 rat_$greatereq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_23/80) = 0 % 18.42/3.86 & rat_$greater(rat_very_large, rat_21/80) = 0 & rat_$greater(rat_very_large, % 18.42/3.86 rat_7/10) = 0 & rat_$greater(rat_very_large, rat_3/8) = 0 & % 18.42/3.86 rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small, % 18.42/3.86 rat_very_large) = 1 & rat_$greater(rat_23/80, rat_very_small) = 0 & % 18.42/3.86 rat_$greater(rat_23/80, rat_23/80) = 1 & rat_$greater(rat_23/80, rat_21/80) = % 18.42/3.86 0 & rat_$greater(rat_23/80, rat_7/10) = 1 & rat_$greater(rat_23/80, rat_3/8) = % 18.42/3.86 1 & rat_$greater(rat_23/80, rat_0) = 0 & rat_$greater(rat_21/80, % 18.42/3.86 rat_very_small) = 0 & rat_$greater(rat_21/80, rat_23/80) = 1 & % 18.42/3.86 rat_$greater(rat_21/80, rat_21/80) = 1 & rat_$greater(rat_21/80, rat_7/10) = 1 % 18.42/3.86 & rat_$greater(rat_21/80, rat_3/8) = 1 & rat_$greater(rat_21/80, rat_0) = 0 & % 18.42/3.86 rat_$greater(rat_7/10, rat_very_small) = 0 & rat_$greater(rat_7/10, rat_23/80) % 18.42/3.86 = 0 & rat_$greater(rat_7/10, rat_21/80) = 0 & rat_$greater(rat_7/10, rat_7/10) % 18.42/3.86 = 1 & rat_$greater(rat_7/10, rat_3/8) = 0 & rat_$greater(rat_7/10, rat_0) = 0 % 18.42/3.86 & rat_$greater(rat_3/8, rat_very_small) = 0 & rat_$greater(rat_3/8, rat_23/80) % 18.42/3.86 = 0 & rat_$greater(rat_3/8, rat_21/80) = 0 & rat_$greater(rat_3/8, rat_7/10) = % 18.42/3.86 1 & rat_$greater(rat_3/8, rat_3/8) = 1 & rat_$greater(rat_3/8, rat_0) = 0 & % 18.42/3.86 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_23/80) = 1 & % 18.42/3.86 rat_$greater(rat_0, rat_21/80) = 1 & rat_$greater(rat_0, rat_7/10) = 1 & % 18.42/3.86 rat_$greater(rat_0, rat_3/8) = 1 & rat_$greater(rat_0, rat_0) = 1 & % 18.42/3.86 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small, % 18.42/3.86 rat_23/80) = 0 & rat_$less(rat_very_small, rat_21/80) = 0 & % 18.42/3.86 rat_$less(rat_very_small, rat_7/10) = 0 & rat_$less(rat_very_small, rat_3/8) = % 18.42/3.86 0 & rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_23/80, % 18.42/3.86 rat_very_large) = 0 & rat_$less(rat_23/80, rat_23/80) = 1 & % 18.42/3.86 rat_$less(rat_23/80, rat_21/80) = 1 & rat_$less(rat_23/80, rat_7/10) = 0 & % 18.42/3.86 rat_$less(rat_23/80, rat_3/8) = 0 & rat_$less(rat_23/80, rat_0) = 1 & % 18.42/3.86 rat_$less(rat_21/80, rat_very_large) = 0 & rat_$less(rat_21/80, rat_23/80) = 0 % 18.42/3.86 & rat_$less(rat_21/80, rat_21/80) = 1 & rat_$less(rat_21/80, rat_7/10) = 0 & % 18.42/3.86 rat_$less(rat_21/80, rat_3/8) = 0 & rat_$less(rat_21/80, rat_0) = 1 & % 18.42/3.87 rat_$less(rat_7/10, rat_very_large) = 0 & rat_$less(rat_7/10, rat_23/80) = 1 & % 18.42/3.87 rat_$less(rat_7/10, rat_21/80) = 1 & rat_$less(rat_7/10, rat_7/10) = 1 & % 18.42/3.87 rat_$less(rat_7/10, rat_3/8) = 1 & rat_$less(rat_7/10, rat_0) = 1 & % 18.42/3.87 rat_$less(rat_3/8, rat_very_large) = 0 & rat_$less(rat_3/8, rat_23/80) = 1 & % 18.42/3.87 rat_$less(rat_3/8, rat_21/80) = 1 & rat_$less(rat_3/8, rat_7/10) = 0 & % 18.42/3.87 rat_$less(rat_3/8, rat_3/8) = 1 & rat_$less(rat_3/8, rat_0) = 1 & % 18.42/3.87 rat_$less(rat_0, rat_very_large) = 0 & rat_$less(rat_0, rat_23/80) = 0 & % 18.42/3.87 rat_$less(rat_0, rat_21/80) = 0 & rat_$less(rat_0, rat_7/10) = 0 & % 18.42/3.87 rat_$less(rat_0, rat_3/8) = 0 & rat_$less(rat_0, rat_0) = 1 & % 18.42/3.87 rat_$lesseq(rat_very_small, rat_very_large) = 0 & rat_$lesseq(rat_23/80, % 18.42/3.87 rat_23/80) = 0 & rat_$lesseq(rat_23/80, rat_21/80) = 1 & % 18.42/3.87 rat_$lesseq(rat_23/80, rat_7/10) = 0 & rat_$lesseq(rat_23/80, rat_3/8) = 0 & % 18.42/3.87 rat_$lesseq(rat_23/80, rat_0) = 1 & rat_$lesseq(rat_21/80, rat_23/80) = 0 & % 18.42/3.87 rat_$lesseq(rat_21/80, rat_21/80) = 0 & rat_$lesseq(rat_21/80, rat_7/10) = 0 & % 18.42/3.87 rat_$lesseq(rat_21/80, rat_3/8) = 0 & rat_$lesseq(rat_21/80, rat_0) = 1 & % 18.42/3.87 rat_$lesseq(rat_7/10, rat_23/80) = 1 & rat_$lesseq(rat_7/10, rat_21/80) = 1 & % 18.42/3.87 rat_$lesseq(rat_7/10, rat_7/10) = 0 & rat_$lesseq(rat_7/10, rat_3/8) = 1 & % 18.42/3.87 rat_$lesseq(rat_7/10, rat_0) = 1 & rat_$lesseq(rat_3/8, rat_23/80) = 1 & % 18.42/3.87 rat_$lesseq(rat_3/8, rat_21/80) = 1 & rat_$lesseq(rat_3/8, rat_7/10) = 0 & % 18.42/3.87 rat_$lesseq(rat_3/8, rat_3/8) = 0 & rat_$lesseq(rat_3/8, rat_0) = 1 & % 18.42/3.87 rat_$lesseq(rat_0, rat_23/80) = 0 & rat_$lesseq(rat_0, rat_21/80) = 0 & % 18.42/3.87 rat_$lesseq(rat_0, rat_7/10) = 0 & rat_$lesseq(rat_0, rat_3/8) = 0 & % 18.42/3.87 rat_$lesseq(rat_0, rat_0) = 0 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 18.42/3.87 : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ % 18.42/3.87 (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, v5) = v4 & % 18.42/3.87 rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 18.42/3.87 ! [v3: $rat] : (v3 = v1 | v0 = rat_0 | ~ (rat_$quotient(v2, v0) = v3) | ~ % 18.42/3.87 (rat_$product(v1, v0) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 18.42/3.87 : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ (rat_$lesseq(v1, % 18.42/3.87 v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & ! % 18.42/3.87 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 18.42/3.87 (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( % 18.42/3.87 ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : % 18.42/3.87 ! [v2: $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, % 18.42/3.87 v2) = v3) | rat_$difference(v1, v0) = v3) & ! [v0: $rat] : ! [v1: % 18.42/3.87 $rat] : ! [v2: $rat] : (v2 = rat_0 | ~ (rat_$uminus(v0) = v1) | ~ % 18.42/3.87 (rat_$sum(v0, v1) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : % 18.42/3.87 (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 18.42/3.87 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 18.42/3.87 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 18.42/3.87 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : % 18.42/3.87 (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3: int] : ( ~ % 18.42/3.87 (v3 = 0) & rat_$less(v1, v0) = v3))) & ! [v0: $rat] : ! [v1: $rat] : % 18.42/3.87 ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | rat_$product(v1, v0) = v2) & % 18.42/3.87 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | % 18.42/3.87 rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 18.42/3.87 (rat_$less(v1, v0) = 0) | ~ (rat_$lesseq(v2, v1) = 0) | rat_$less(v2, v0) = % 18.42/3.87 0) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = % 18.42/3.87 v1)) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) % 18.42/3.87 = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 18.42/3.87 (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0: $rat] : ! [v1: % 18.42/3.87 $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1, v0) = 0) & ! % 18.42/3.87 [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, % 18.42/3.87 v0) = 0) & ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0) = v0)) % 18.42/3.87 % 18.42/3.87 (function-axioms) % 18.42/3.88 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 18.42/3.88 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0: % 18.42/3.88 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 18.42/3.88 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0: % 18.42/3.88 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 18.42/3.88 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & ! % 18.42/3.88 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 18.42/3.88 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0: % 18.42/3.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 18.42/3.88 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3, % 18.42/3.88 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 18.42/3.88 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$greater(v3, v2) = v1) | ~ % 18.42/3.88 (rat_$greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.42/3.88 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 18.42/3.88 (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = v0)) & ! [v0: % 18.42/3.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 18.42/3.88 $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ (rat_$lesseq(v3, v2) = % 18.42/3.88 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 18.42/3.88 $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & % 18.42/3.88 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = % 18.42/3.88 v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] % 18.42/3.88 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~ % 18.42/3.88 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 % 18.42/3.88 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0: % 18.42/3.88 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) = % 18.42/3.88 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 18.42/3.88 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) & % 18.42/3.88 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) = % 18.42/3.88 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 18.42/3.88 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) & % 18.42/3.88 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~ % 18.42/3.88 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : ! % 18.42/3.88 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~ % 18.42/3.88 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 18.42/3.88 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0)) % 18.42/3.88 % 18.42/3.88 Those formulas are unsatisfiable: % 18.42/3.88 --------------------------------- % 18.42/3.88 % 18.42/3.88 Begin of proof % 18.42/3.88 | % 18.42/3.88 | ALPHA: (function-axioms) implies: % 18.42/3.88 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] % 18.42/3.89 | : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ % 18.42/3.89 | (rat_$lesseq(v3, v2) = v0)) % 18.42/3.89 | % 18.42/3.89 | ALPHA: (input) implies: % 18.42/3.89 | (2) rat_$lesseq(rat_21/80, rat_23/80) = 0 % 18.42/3.89 | % 18.42/3.89 | DELTA: instantiating (rat_combined_problem_14) with fresh symbol all_5_0 % 18.42/3.89 | gives: % 18.42/3.89 | (3) ~ (all_5_0 = 0) & rat_$lesseq(rat_21/80, rat_23/80) = all_5_0 % 18.42/3.89 | % 18.42/3.89 | ALPHA: (3) implies: % 18.42/3.89 | (4) ~ (all_5_0 = 0) % 18.42/3.89 | (5) rat_$lesseq(rat_21/80, rat_23/80) = all_5_0 % 18.42/3.89 | % 18.42/3.89 | GROUND_INST: instantiating (1) with 0, all_5_0, rat_23/80, rat_21/80, % 18.42/3.89 | simplifying with (2), (5) gives: % 18.42/3.89 | (6) all_5_0 = 0 % 18.42/3.89 | % 18.42/3.89 | REDUCE: (4), (6) imply: % 18.42/3.89 | (7) $false % 18.42/3.89 | % 18.42/3.89 | CLOSE: (7) is inconsistent. % 18.42/3.89 | % 18.42/3.89 End of proof % 18.42/3.89 % SZS output end Proof for theBenchmark % 18.42/3.89 % 18.42/3.89 3281ms %------------------------------------------------------------------------------