%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI268_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 17:47:30 EDT 2023 % Result : Theorem 14.63s 2.69s % Output : Proof 22.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : ARI268_1 : TPTP v8.1.2. Released v5.0.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n009.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 17:56:50 EDT 2023 % 0.13/0.35 % CPUTime : % 0.71/0.68 ________ _____ % 0.71/0.68 ___ __ \_________(_)________________________________ % 0.71/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.71/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.71/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.71/0.68 % 0.71/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.71/0.68 (2023-06-19) % 0.71/0.68 % 0.71/0.68 (c) Philipp Rümmer, 2009-2023 % 0.71/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.71/0.68 Amanda Stjerna. % 0.71/0.68 Free software under BSD-3-Clause. % 0.71/0.68 % 0.71/0.68 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.71/0.68 % 0.71/0.68 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.70 Running up to 7 provers in parallel. % 0.71/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.71/0.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.71/0.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.71/0.71 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.71/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.71/0.71 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.71/0.71 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.56/0.96 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.56/0.96 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 1.56/0.96 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 1.56/0.96 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 1.80/0.96 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 1.80/0.96 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.80/0.97 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 2.22/1.07 Prover 4: Preprocessing ... % 2.22/1.07 Prover 1: Preprocessing ... % 2.53/1.12 Prover 0: Preprocessing ... % 2.53/1.12 Prover 6: Preprocessing ... % 3.30/1.20 Prover 2: Preprocessing ... % 3.30/1.20 Prover 3: Preprocessing ... % 3.30/1.20 Prover 5: Preprocessing ... % 7.01/1.68 Prover 1: Constructing countermodel ... % 7.01/1.72 Prover 4: Constructing countermodel ... % 7.01/1.73 Prover 6: Proving ... % 7.01/1.73 Prover 0: Proving ... % 9.83/2.06 Prover 1: gave up % 10.00/2.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.00/2.10 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation % 10.38/2.14 Prover 7: Preprocessing ... % 10.70/2.20 Prover 2: Proving ... % 11.33/2.25 Prover 3: Constructing countermodel ... % 12.25/2.40 Prover 5: Proving ... % 14.10/2.60 Prover 7: Warning: ignoring some quantifiers % 14.10/2.61 Prover 7: Constructing countermodel ... % 14.63/2.69 Prover 0: proved (1986ms) % 14.63/2.69 % 14.63/2.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.63/2.69 % 14.63/2.69 Prover 2: stopped % 14.63/2.69 Prover 6: stopped % 14.63/2.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.63/2.70 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation % 14.63/2.70 Prover 3: stopped % 14.63/2.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.63/2.70 Prover 8: Preprocessing ... % 14.63/2.70 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation % 14.63/2.70 Prover 5: stopped % 14.63/2.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.63/2.72 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation % 15.15/2.75 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.15/2.75 Prover 16: Warning: Problem contains rationals, using incomplete axiomatisation % 15.15/2.75 Prover 10: Preprocessing ... % 15.15/2.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.15/2.75 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation % 15.15/2.75 Prover 13: Preprocessing ... % 15.15/2.76 Prover 16: Preprocessing ... % 15.45/2.78 Prover 11: Preprocessing ... % 15.45/2.81 Prover 8: Warning: ignoring some quantifiers % 15.45/2.82 Prover 8: Constructing countermodel ... % 16.17/2.88 Prover 13: Warning: ignoring some quantifiers % 16.17/2.89 Prover 13: Constructing countermodel ... % 16.71/2.93 Prover 8: gave up % 16.78/2.95 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 16.78/2.95 Prover 19: Warning: Problem contains rationals, using incomplete axiomatisation % 16.78/3.00 Prover 13: gave up % 16.78/3.00 Prover 19: Preprocessing ... % 17.33/3.02 Prover 10: Warning: ignoring some quantifiers % 17.33/3.03 Prover 10: Constructing countermodel ... % 18.75/3.21 Prover 16: Warning: ignoring some quantifiers % 18.75/3.22 Prover 16: Constructing countermodel ... % 19.22/3.25 Prover 4: Found proof (size 34) % 19.22/3.25 Prover 4: proved (2547ms) % 19.22/3.25 Prover 16: stopped % 19.22/3.27 Prover 10: Found proof (size 3) % 19.22/3.27 Prover 10: proved (570ms) % 19.22/3.31 Prover 11: Constructing countermodel ... % 19.71/3.34 Prover 11: stopped % 20.43/3.47 Prover 7: Found proof (size 3) % 20.43/3.47 Prover 7: proved (1377ms) % 21.36/3.70 Prover 19: Warning: ignoring some quantifiers % 21.36/3.71 Prover 19: Constructing countermodel ... % 21.36/3.73 Prover 19: stopped % 21.36/3.73 % 21.36/3.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.36/3.73 % 21.36/3.73 % SZS output start Proof for theBenchmark % 21.36/3.74 Assumptions after simplification: % 21.36/3.74 --------------------------------- % 21.36/3.74 % 21.36/3.74 (rat_sum_problem_23) % 21.71/3.77 ! [v0: $rat] : ~ (rat_$sum(v0, rat_-7/2) = rat_-11/2) % 21.71/3.77 % 21.71/3.78 (input) % 21.78/3.82 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_-11/2) & ~ % 21.78/3.82 (rat_very_large = rat_-7/2) & ~ (rat_very_large = rat_0) & ~ (rat_very_small % 21.78/3.82 = rat_-11/2) & ~ (rat_very_small = rat_-7/2) & ~ (rat_very_small = rat_0) % 21.78/3.82 & ~ (rat_-11/2 = rat_-7/2) & ~ (rat_-11/2 = rat_0) & ~ (rat_-7/2 = rat_0) & % 21.78/3.82 rat_$is_int(rat_-11/2) = 1 & rat_$is_int(rat_-7/2) = 1 & rat_$is_int(rat_0) = % 21.78/3.82 0 & rat_$is_rat(rat_-11/2) = 0 & rat_$is_rat(rat_-7/2) = 0 & % 21.78/3.82 rat_$is_rat(rat_0) = 0 & rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = % 21.78/3.82 rat_0 & rat_$truncate(rat_0) = rat_0 & rat_$round(rat_0) = rat_0 & % 21.78/3.82 rat_$to_int(rat_-11/2) = -6 & rat_$to_int(rat_-7/2) = -4 & rat_$to_int(rat_0) % 21.78/3.82 = 0 & rat_$to_rat(rat_-11/2) = rat_-11/2 & rat_$to_rat(rat_-7/2) = rat_-7/2 & % 21.78/3.82 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_-11/2) = real_-11/2 & % 21.78/3.82 rat_$to_real(rat_-7/2) = real_-7/2 & rat_$to_real(rat_0) = real_0 & % 21.78/3.82 int_$to_rat(0) = rat_0 & rat_$quotient(rat_0, rat_-11/2) = rat_0 & % 21.78/3.82 rat_$quotient(rat_0, rat_-7/2) = rat_0 & rat_$product(rat_-11/2, rat_0) = % 21.78/3.82 rat_0 & rat_$product(rat_-7/2, rat_0) = rat_0 & rat_$product(rat_0, rat_-11/2) % 21.78/3.82 = rat_0 & rat_$product(rat_0, rat_-7/2) = rat_0 & rat_$product(rat_0, rat_0) = % 21.78/3.82 rat_0 & rat_$difference(rat_-11/2, rat_-11/2) = rat_0 & % 21.78/3.82 rat_$difference(rat_-11/2, rat_0) = rat_-11/2 & rat_$difference(rat_-7/2, % 21.78/3.82 rat_-7/2) = rat_0 & rat_$difference(rat_-7/2, rat_0) = rat_-7/2 & % 21.78/3.82 rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 & % 21.78/3.82 rat_$greatereq(rat_very_small, rat_very_large) = 1 & rat_$greatereq(rat_-11/2, % 21.78/3.82 rat_-11/2) = 0 & rat_$greatereq(rat_-11/2, rat_-7/2) = 1 & % 21.78/3.82 rat_$greatereq(rat_-11/2, rat_0) = 1 & rat_$greatereq(rat_-7/2, rat_-11/2) = 0 % 21.78/3.82 & rat_$greatereq(rat_-7/2, rat_-7/2) = 0 & rat_$greatereq(rat_-7/2, rat_0) = 1 % 21.78/3.82 & rat_$greatereq(rat_0, rat_-11/2) = 0 & rat_$greatereq(rat_0, rat_-7/2) = 0 & % 21.78/3.82 rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large) % 21.78/3.82 = 0 & rat_$lesseq(rat_-11/2, rat_-11/2) = 0 & rat_$lesseq(rat_-11/2, rat_-7/2) % 21.78/3.82 = 0 & rat_$lesseq(rat_-11/2, rat_0) = 0 & rat_$lesseq(rat_-7/2, rat_-11/2) = 1 % 21.78/3.82 & rat_$lesseq(rat_-7/2, rat_-7/2) = 0 & rat_$lesseq(rat_-7/2, rat_0) = 0 & % 21.78/3.82 rat_$lesseq(rat_0, rat_-11/2) = 1 & rat_$lesseq(rat_0, rat_-7/2) = 1 & % 21.78/3.82 rat_$lesseq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_-11/2) = 0 & % 21.78/3.82 rat_$greater(rat_very_large, rat_-7/2) = 0 & rat_$greater(rat_very_large, % 21.78/3.82 rat_0) = 0 & rat_$greater(rat_very_small, rat_very_large) = 1 & % 21.78/3.82 rat_$greater(rat_-11/2, rat_very_small) = 0 & rat_$greater(rat_-11/2, % 21.78/3.82 rat_-11/2) = 1 & rat_$greater(rat_-11/2, rat_-7/2) = 1 & % 21.78/3.82 rat_$greater(rat_-11/2, rat_0) = 1 & rat_$greater(rat_-7/2, rat_very_small) = % 21.78/3.82 0 & rat_$greater(rat_-7/2, rat_-11/2) = 0 & rat_$greater(rat_-7/2, rat_-7/2) = % 21.78/3.82 1 & rat_$greater(rat_-7/2, rat_0) = 1 & rat_$greater(rat_0, rat_very_small) = % 21.78/3.82 0 & rat_$greater(rat_0, rat_-11/2) = 0 & rat_$greater(rat_0, rat_-7/2) = 0 & % 21.78/3.82 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0 % 21.78/3.82 & rat_$less(rat_very_small, rat_-11/2) = 0 & rat_$less(rat_very_small, % 21.78/3.82 rat_-7/2) = 0 & rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_-11/2, % 21.78/3.82 rat_very_large) = 0 & rat_$less(rat_-11/2, rat_-11/2) = 1 & % 21.78/3.82 rat_$less(rat_-11/2, rat_-7/2) = 0 & rat_$less(rat_-11/2, rat_0) = 0 & % 21.78/3.83 rat_$less(rat_-7/2, rat_very_large) = 0 & rat_$less(rat_-7/2, rat_-11/2) = 1 & % 21.78/3.83 rat_$less(rat_-7/2, rat_-7/2) = 1 & rat_$less(rat_-7/2, rat_0) = 0 & % 21.78/3.83 rat_$less(rat_0, rat_very_large) = 0 & rat_$less(rat_0, rat_-11/2) = 1 & % 21.78/3.83 rat_$less(rat_0, rat_-7/2) = 1 & rat_$less(rat_0, rat_0) = 1 & % 21.78/3.83 rat_$sum(rat_-11/2, rat_0) = rat_-11/2 & rat_$sum(rat_-7/2, rat_0) = rat_-7/2 % 21.78/3.83 & rat_$sum(rat_0, rat_-11/2) = rat_-11/2 & rat_$sum(rat_0, rat_-7/2) = % 21.78/3.83 rat_-7/2 & rat_$sum(rat_0, rat_0) = rat_0 & ! [v0: $rat] : ! [v1: $rat] : ! % 21.78/3.83 [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ % 21.78/3.83 (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, v5) = v4 & % 21.78/3.83 rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 21.78/3.83 ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~ (rat_$sum(v1, % 21.78/3.83 v0) = v3) | ? [v5: $rat] : (rat_$sum(v5, v0) = v4 & rat_$sum(v2, v1) = % 21.78/3.83 v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 % 21.78/3.83 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v2, v0) = v3) | ? [v4: % 21.78/3.83 int] : ( ~ (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: % 21.78/3.83 $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = % 21.78/3.83 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & % 21.78/3.83 rat_$less(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 21.78/3.83 ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, % 21.78/3.83 v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! % 21.78/3.83 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 21.78/3.83 (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ % 21.78/3.83 (v4 = 0) & rat_$less(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! % 21.78/3.83 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v1) = 0) | ~ % 21.78/3.83 (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1, v0) % 21.78/3.83 = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : % 21.78/3.83 (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ (rat_$less(v1, v0) = 0) | ? [v4: % 21.78/3.83 int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: % 21.78/3.83 $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) | ~ % 21.78/3.83 (rat_$sum(v1, v2) = v3) | rat_$difference(v1, v0) = v3) & ! [v0: $rat] : ! % 21.78/3.83 [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (rat_$less(v1, v0) = v2) | % 21.78/3.83 ? [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! % 21.78/3.83 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? % 21.78/3.83 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! % 21.78/3.83 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: % 21.78/3.83 int] : ( ~ (v3 = 0) & rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! % 21.78/3.83 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: % 21.78/3.83 int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: % 21.78/3.83 $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: % 21.78/3.83 int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: % 21.78/3.83 $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] % 21.78/3.83 : ( ~ (v3 = 0) & rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] % 21.78/3.83 : ! [v2: $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | % 21.78/3.83 rat_$quotient(v2, v0) = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 21.78/3.83 : ( ~ (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] % 21.78/3.83 : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | % 21.78/3.83 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 21.78/3.83 ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = v3 & % 21.78/3.83 rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 21.78/3.83 ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2, % 21.78/3.83 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 21.78/3.83 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = % 21.78/3.83 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1, % 21.78/3.83 v0) = 0) | ~ (rat_$less(v2, v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: % 21.78/3.83 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) = v2) | % 21.78/3.83 rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 21.78/3.83 (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1: % 21.78/3.83 $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & % 21.78/3.83 ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! % 21.78/3.83 [v0: $rat] : ! [v1: int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & ! [v0: % 21.78/3.83 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & % 21.78/3.83 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1) % 21.78/3.83 = rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) % 21.78/3.83 | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 21.78/3.83 (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & ! [v0: $rat] : ! % 21.78/3.83 [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0: % 21.78/3.83 $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$lesseq(v1, v0) = % 21.78/3.83 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | % 21.78/3.83 rat_$greater(v0, v1) = 0) & ! [v0: $rat] : ! [v1: MultipleValueBool] : ( ~ % 21.78/3.83 (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) = 0) & ! [v0: $rat] : (v0 = % 21.78/3.83 rat_0 | ~ (rat_$uminus(v0) = v0)) % 21.78/3.83 % 21.78/3.83 (function-axioms) % 22.06/3.84 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 22.06/3.84 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0: % 22.06/3.84 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 22.06/3.84 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0: % 22.06/3.84 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 22.06/3.84 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & ! % 22.06/3.84 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 22.06/3.84 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3, % 22.06/3.84 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 22.06/3.84 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ % 22.06/3.84 (rat_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.06/3.84 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 22.06/3.84 (rat_$greater(v3, v2) = v1) | ~ (rat_$greater(v3, v2) = v0)) & ! [v0: % 22.06/3.84 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 22.06/3.84 $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = % 22.06/3.84 v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 % 22.06/3.84 = v0 | ~ (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0: % 22.06/3.84 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = v0 | % 22.06/3.84 ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & ! [v0: % 22.06/3.84 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = v0 | % 22.06/3.84 ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] : ! % 22.06/3.84 [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~ % 22.06/3.84 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 % 22.06/3.84 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0: % 22.06/3.84 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) = % 22.06/3.84 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 22.06/3.84 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) & % 22.06/3.84 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) = % 22.06/3.84 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 22.06/3.84 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) & % 22.06/3.84 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~ % 22.06/3.84 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : ! % 22.06/3.84 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~ % 22.06/3.84 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 22.06/3.84 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0)) % 22.06/3.84 % 22.06/3.84 Those formulas are unsatisfiable: % 22.06/3.84 --------------------------------- % 22.06/3.84 % 22.06/3.84 Begin of proof % 22.06/3.84 | % 22.06/3.84 | ALPHA: (function-axioms) implies: % 22.06/3.84 | (1) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = % 22.06/3.84 | v0 | ~ (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) % 22.06/3.84 | % 22.06/3.84 | ALPHA: (input) implies: % 22.06/3.84 | (2) rat_$sum(rat_0, rat_-7/2) = rat_-7/2 % 22.06/3.84 | (3) rat_$sum(rat_0, rat_-11/2) = rat_-11/2 % 22.06/3.84 | (4) rat_$less(rat_-7/2, rat_-11/2) = 1 % 22.06/3.84 | (5) rat_$less(rat_very_small, rat_-11/2) = 0 % 22.06/3.84 | (6) rat_$difference(rat_-7/2, rat_-7/2) = rat_0 % 22.06/3.84 | (7) rat_$difference(rat_-11/2, rat_-11/2) = rat_0 % 22.06/3.84 | (8) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) = % 22.06/3.84 | v2) | rat_$sum(v0, v1) = v2) % 22.06/3.85 | (9) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 22.06/3.85 | (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = % 22.06/3.85 | v3 & rat_$sum(v1, v3) = v2)) % 22.06/3.85 | (10) ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ % 22.06/3.85 | (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 22.06/3.85 | rat_$greatereq(v0, v1) = v3)) % 22.06/3.85 | (11) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 % 22.06/3.85 | | ~ (rat_$less(v2, v0) = v3) | ~ (rat_$less(v1, v0) = 0) | ? [v4: % 22.06/3.85 | int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) % 22.06/3.85 | (12) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! % 22.06/3.85 | [v4: $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~ (rat_$sum(v1, v0) = v3) % 22.06/3.85 | | ? [v5: $rat] : (rat_$sum(v5, v0) = v4 & rat_$sum(v2, v1) = v5)) % 22.06/3.85 | (13) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! % 22.06/3.85 | [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) % 22.06/3.85 | | ? [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) % 22.06/3.85 | % 22.06/3.85 | GROUND_INST: instantiating (11) with rat_-11/2, rat_very_small, rat_-7/2, 1, % 22.06/3.85 | simplifying with (4), (5) gives: % 22.06/3.85 | (14) ? [v0: int] : ( ~ (v0 = 0) & rat_$lesseq(rat_-7/2, rat_very_small) = % 22.06/3.85 | v0) % 22.06/3.85 | % 22.06/3.85 | GROUND_INST: instantiating (9) with rat_-7/2, rat_-7/2, rat_0, simplifying % 22.06/3.85 | with (6) gives: % 22.06/3.85 | (15) ? [v0: $rat] : (rat_$uminus(rat_-7/2) = v0 & rat_$sum(rat_-7/2, v0) = % 22.06/3.85 | rat_0) % 22.06/3.85 | % 22.06/3.85 | GROUND_INST: instantiating (9) with rat_-11/2, rat_-11/2, rat_0, simplifying % 22.06/3.85 | with (7) gives: % 22.06/3.85 | (16) ? [v0: $rat] : (rat_$uminus(rat_-11/2) = v0 & rat_$sum(rat_-11/2, v0) % 22.06/3.85 | = rat_0) % 22.06/3.85 | % 22.06/3.85 | DELTA: instantiating (16) with fresh symbol all_12_0 gives: % 22.06/3.85 | (17) rat_$uminus(rat_-11/2) = all_12_0 & rat_$sum(rat_-11/2, all_12_0) = % 22.06/3.85 | rat_0 % 22.06/3.85 | % 22.06/3.85 | ALPHA: (17) implies: % 22.06/3.85 | (18) rat_$sum(rat_-11/2, all_12_0) = rat_0 % 22.06/3.85 | % 22.06/3.85 | DELTA: instantiating (15) with fresh symbol all_14_0 gives: % 22.06/3.85 | (19) rat_$uminus(rat_-7/2) = all_14_0 & rat_$sum(rat_-7/2, all_14_0) = % 22.06/3.85 | rat_0 % 22.06/3.85 | % 22.06/3.85 | ALPHA: (19) implies: % 22.06/3.85 | (20) rat_$sum(rat_-7/2, all_14_0) = rat_0 % 22.06/3.85 | % 22.06/3.85 | DELTA: instantiating (14) with fresh symbol all_28_0 gives: % 22.06/3.85 | (21) ~ (all_28_0 = 0) & rat_$lesseq(rat_-7/2, rat_very_small) = all_28_0 % 22.06/3.85 | % 22.06/3.85 | ALPHA: (21) implies: % 22.06/3.85 | (22) ~ (all_28_0 = 0) % 22.06/3.85 | (23) rat_$lesseq(rat_-7/2, rat_very_small) = all_28_0 % 22.06/3.85 | % 22.06/3.85 | GROUND_INST: instantiating (13) with rat_-7/2, all_14_0, rat_-7/2, rat_0, % 22.06/3.85 | rat_-7/2, simplifying with (2), (20) gives: % 22.18/3.85 | (24) ? [v0: $rat] : (rat_$sum(all_14_0, rat_-7/2) = v0 & % 22.18/3.85 | rat_$sum(rat_-7/2, v0) = rat_-7/2) % 22.18/3.85 | % 22.18/3.86 | GROUND_INST: instantiating (8) with all_14_0, rat_-7/2, rat_0, simplifying % 22.18/3.86 | with (20) gives: % 22.18/3.86 | (25) rat_$sum(all_14_0, rat_-7/2) = rat_0 % 22.18/3.86 | % 22.18/3.86 | GROUND_INST: instantiating (13) with rat_-11/2, all_12_0, rat_-11/2, rat_0, % 22.18/3.86 | rat_-11/2, simplifying with (3), (18) gives: % 22.18/3.86 | (26) ? [v0: $rat] : (rat_$sum(all_12_0, rat_-11/2) = v0 & % 22.18/3.86 | rat_$sum(rat_-11/2, v0) = rat_-11/2) % 22.18/3.86 | % 22.18/3.86 | GROUND_INST: instantiating (8) with all_12_0, rat_-11/2, rat_0, simplifying % 22.18/3.86 | with (18) gives: % 22.18/3.86 | (27) rat_$sum(all_12_0, rat_-11/2) = rat_0 % 22.18/3.86 | % 22.18/3.86 | GROUND_INST: instantiating (10) with rat_very_small, rat_-7/2, all_28_0, % 22.18/3.86 | simplifying with (23) gives: % 22.18/3.86 | (28) all_28_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 22.18/3.86 | rat_$greatereq(rat_very_small, rat_-7/2) = v0) % 22.18/3.86 | % 22.18/3.86 | DELTA: instantiating (26) with fresh symbol all_66_0 gives: % 22.18/3.86 | (29) rat_$sum(all_12_0, rat_-11/2) = all_66_0 & rat_$sum(rat_-11/2, % 22.18/3.86 | all_66_0) = rat_-11/2 % 22.18/3.86 | % 22.18/3.86 | ALPHA: (29) implies: % 22.18/3.86 | (30) rat_$sum(rat_-11/2, all_66_0) = rat_-11/2 % 22.18/3.86 | (31) rat_$sum(all_12_0, rat_-11/2) = all_66_0 % 22.18/3.86 | % 22.18/3.86 | DELTA: instantiating (24) with fresh symbol all_72_0 gives: % 22.18/3.86 | (32) rat_$sum(all_14_0, rat_-7/2) = all_72_0 & rat_$sum(rat_-7/2, all_72_0) % 22.18/3.86 | = rat_-7/2 % 22.18/3.86 | % 22.18/3.86 | ALPHA: (32) implies: % 22.18/3.86 | (33) rat_$sum(all_14_0, rat_-7/2) = all_72_0 % 22.18/3.86 | % 22.18/3.86 | BETA: splitting (28) gives: % 22.18/3.86 | % 22.18/3.86 | Case 1: % 22.18/3.86 | | % 22.18/3.86 | | (34) all_28_0 = 0 % 22.18/3.86 | | % 22.18/3.86 | | REDUCE: (22), (34) imply: % 22.18/3.86 | | (35) $false % 22.18/3.86 | | % 22.18/3.86 | | CLOSE: (35) is inconsistent. % 22.18/3.86 | | % 22.18/3.86 | Case 2: % 22.18/3.86 | | % 22.18/3.86 | | % 22.18/3.86 | | GROUND_INST: instantiating (1) with rat_0, all_66_0, rat_-11/2, all_12_0, % 22.18/3.86 | | simplifying with (27), (31) gives: % 22.18/3.86 | | (36) all_66_0 = rat_0 % 22.18/3.86 | | % 22.18/3.86 | | GROUND_INST: instantiating (1) with rat_0, all_72_0, rat_-7/2, all_14_0, % 22.18/3.86 | | simplifying with (25), (33) gives: % 22.18/3.86 | | (37) all_72_0 = rat_0 % 22.18/3.86 | | % 22.18/3.86 | | REDUCE: (30), (36) imply: % 22.18/3.86 | | (38) rat_$sum(rat_-11/2, rat_0) = rat_-11/2 % 22.18/3.86 | | % 22.18/3.86 | | GROUND_INST: instantiating (12) with rat_-7/2, all_14_0, rat_-11/2, rat_0, % 22.18/3.86 | | rat_-11/2, simplifying with (25), (38) gives: % 22.18/3.86 | | (39) ? [v0: $rat] : (rat_$sum(v0, rat_-7/2) = rat_-11/2 & % 22.18/3.86 | | rat_$sum(rat_-11/2, all_14_0) = v0) % 22.18/3.86 | | % 22.18/3.86 | | DELTA: instantiating (39) with fresh symbol all_239_0 gives: % 22.18/3.86 | | (40) rat_$sum(all_239_0, rat_-7/2) = rat_-11/2 & rat_$sum(rat_-11/2, % 22.18/3.86 | | all_14_0) = all_239_0 % 22.18/3.86 | | % 22.18/3.86 | | ALPHA: (40) implies: % 22.18/3.86 | | (41) rat_$sum(all_239_0, rat_-7/2) = rat_-11/2 % 22.18/3.86 | | % 22.18/3.86 | | GROUND_INST: instantiating (rat_sum_problem_23) with all_239_0, simplifying % 22.18/3.86 | | with (41) gives: % 22.18/3.86 | | (42) $false % 22.18/3.86 | | % 22.18/3.86 | | CLOSE: (42) is inconsistent. % 22.18/3.86 | | % 22.18/3.86 | End of split % 22.18/3.86 | % 22.18/3.86 End of proof % 22.18/3.86 % SZS output end Proof for theBenchmark % 22.18/3.86 % 22.18/3.86 3180ms %------------------------------------------------------------------------------