%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI269_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 : n013.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 13.90s 2.55s % Output : Proof 21.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : ARI269_1 : TPTP v8.1.2. Released v5.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n013.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 17:46:31 EDT 2023 % 0.13/0.35 % CPUTime : % 0.45/0.63 ________ _____ % 0.45/0.63 ___ __ \_________(_)________________________________ % 0.45/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.45/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.45/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.45/0.63 % 0.45/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.45/0.63 (2023-06-19) % 0.45/0.63 % 0.45/0.63 (c) Philipp Rümmer, 2009-2023 % 0.45/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.45/0.63 Amanda Stjerna. % 0.45/0.63 Free software under BSD-3-Clause. % 0.45/0.63 % 0.45/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.45/0.63 % 0.45/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.45/0.64 Running up to 7 provers in parallel. % 0.45/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.45/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.45/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.45/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.45/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.45/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.45/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.69/0.91 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 1.69/0.91 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.69/0.91 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 1.69/0.91 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.69/0.91 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 1.69/0.91 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 1.69/0.91 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 2.34/1.01 Prover 4: Preprocessing ... % 2.34/1.02 Prover 1: Preprocessing ... % 2.34/1.06 Prover 0: Preprocessing ... % 2.34/1.06 Prover 6: Preprocessing ... % 2.91/1.13 Prover 5: Preprocessing ... % 2.91/1.13 Prover 2: Preprocessing ... % 2.91/1.14 Prover 3: Preprocessing ... % 5.99/1.56 Prover 1: Constructing countermodel ... % 6.56/1.58 Prover 6: Proving ... % 6.56/1.58 Prover 4: Constructing countermodel ... % 6.56/1.62 Prover 0: Proving ... % 8.69/1.91 Prover 1: gave up % 9.24/1.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.24/1.96 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation % 9.51/1.99 Prover 7: Preprocessing ... % 10.00/2.05 Prover 2: Proving ... % 10.20/2.09 Prover 3: Constructing countermodel ... % 11.86/2.28 Prover 5: Proving ... % 12.68/2.46 Prover 7: Warning: ignoring some quantifiers % 13.44/2.48 Prover 7: Constructing countermodel ... % 13.90/2.55 Prover 0: proved (1903ms) % 13.90/2.55 % 13.90/2.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.90/2.55 % 13.90/2.55 Prover 3: stopped % 13.90/2.55 Prover 5: stopped % 13.90/2.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.90/2.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.90/2.56 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation % 13.90/2.56 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation % 13.90/2.56 Prover 6: stopped % 13.90/2.57 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.90/2.57 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation % 13.90/2.57 Prover 8: Preprocessing ... % 13.90/2.57 Prover 2: stopped % 13.90/2.57 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 13.90/2.57 Prover 16: Warning: Problem contains rationals, using incomplete axiomatisation % 13.90/2.58 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.90/2.58 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation % 13.90/2.58 Prover 13: Preprocessing ... % 13.90/2.59 Prover 11: Preprocessing ... % 13.90/2.60 Prover 10: Preprocessing ... % 14.51/2.64 Prover 16: Preprocessing ... % 15.00/2.68 Prover 8: Warning: ignoring some quantifiers % 15.00/2.69 Prover 8: Constructing countermodel ... % 15.00/2.69 Prover 13: Warning: ignoring some quantifiers % 15.00/2.72 Prover 13: Constructing countermodel ... % 15.76/2.80 Prover 8: gave up % 15.76/2.80 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 15.76/2.80 Prover 19: Warning: Problem contains rationals, using incomplete axiomatisation % 16.21/2.84 Prover 19: Preprocessing ... % 16.21/2.87 Prover 13: gave up % 17.47/3.06 Prover 10: Warning: ignoring some quantifiers % 17.47/3.07 Prover 10: Constructing countermodel ... % 18.50/3.17 Prover 16: Warning: ignoring some quantifiers % 18.50/3.18 Prover 16: Constructing countermodel ... % 18.50/3.18 Prover 4: Found proof (size 34) % 18.50/3.18 Prover 4: proved (2528ms) % 18.50/3.18 Prover 10: stopped % 18.50/3.20 Prover 16: stopped % 18.50/3.21 Prover 7: Found proof (size 3) % 18.50/3.21 Prover 7: proved (1257ms) % 19.07/3.23 Prover 11: Constructing countermodel ... % 19.07/3.24 Prover 11: stopped % 20.35/3.57 Prover 19: Warning: ignoring some quantifiers % 20.60/3.58 Prover 19: Constructing countermodel ... % 20.60/3.60 Prover 19: stopped % 20.60/3.60 % 20.60/3.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.60/3.60 % 20.60/3.61 % SZS output start Proof for theBenchmark % 20.60/3.61 Assumptions after simplification: % 20.60/3.61 --------------------------------- % 20.60/3.61 % 20.60/3.61 (rat_sum_problem_24) % 20.60/3.65 ! [v0: $rat] : ~ (rat_$sum(v0, rat_-11/2) = rat_-13/2) % 20.60/3.65 % 20.60/3.65 (input) % 20.60/3.70 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_-13/2) & ~ % 20.60/3.70 (rat_very_large = rat_-11/2) & ~ (rat_very_large = rat_0) & ~ % 20.60/3.70 (rat_very_small = rat_-13/2) & ~ (rat_very_small = rat_-11/2) & ~ % 20.60/3.70 (rat_very_small = rat_0) & ~ (rat_-13/2 = rat_-11/2) & ~ (rat_-13/2 = rat_0) % 20.60/3.70 & ~ (rat_-11/2 = rat_0) & rat_$is_int(rat_-13/2) = 1 & rat_$is_int(rat_-11/2) % 20.60/3.70 = 1 & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_-13/2) = 0 & % 20.60/3.70 rat_$is_rat(rat_-11/2) = 0 & rat_$is_rat(rat_0) = 0 & rat_$floor(rat_0) = % 20.60/3.70 rat_0 & rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_0) = rat_0 & % 20.60/3.70 rat_$round(rat_0) = rat_0 & rat_$to_int(rat_-13/2) = -7 & % 20.60/3.70 rat_$to_int(rat_-11/2) = -6 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_-13/2) % 20.60/3.70 = rat_-13/2 & rat_$to_rat(rat_-11/2) = rat_-11/2 & rat_$to_rat(rat_0) = rat_0 % 20.60/3.70 & rat_$to_real(rat_-13/2) = real_-13/2 & rat_$to_real(rat_-11/2) = real_-11/2 % 20.60/3.70 & rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_0, % 20.60/3.70 rat_-13/2) = rat_0 & rat_$quotient(rat_0, rat_-11/2) = rat_0 & % 20.60/3.70 rat_$product(rat_-13/2, rat_0) = rat_0 & rat_$product(rat_-11/2, rat_0) = % 20.60/3.70 rat_0 & rat_$product(rat_0, rat_-13/2) = rat_0 & rat_$product(rat_0, % 20.60/3.70 rat_-11/2) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 & % 20.60/3.70 rat_$difference(rat_-13/2, rat_-13/2) = rat_0 & rat_$difference(rat_-13/2, % 20.60/3.70 rat_0) = rat_-13/2 & rat_$difference(rat_-11/2, rat_-11/2) = rat_0 & % 20.60/3.70 rat_$difference(rat_-11/2, rat_0) = rat_-11/2 & rat_$difference(rat_0, rat_0) % 20.60/3.70 = rat_0 & rat_$uminus(rat_0) = rat_0 & rat_$greatereq(rat_very_small, % 20.60/3.70 rat_very_large) = 1 & rat_$greatereq(rat_-13/2, rat_-13/2) = 0 & % 20.60/3.70 rat_$greatereq(rat_-13/2, rat_-11/2) = 1 & rat_$greatereq(rat_-13/2, rat_0) = % 20.60/3.70 1 & rat_$greatereq(rat_-11/2, rat_-13/2) = 0 & rat_$greatereq(rat_-11/2, % 20.60/3.70 rat_-11/2) = 0 & rat_$greatereq(rat_-11/2, rat_0) = 1 & % 20.60/3.70 rat_$greatereq(rat_0, rat_-13/2) = 0 & rat_$greatereq(rat_0, rat_-11/2) = 0 & % 20.60/3.70 rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large) % 20.60/3.70 = 0 & rat_$lesseq(rat_-13/2, rat_-13/2) = 0 & rat_$lesseq(rat_-13/2, % 20.60/3.70 rat_-11/2) = 0 & rat_$lesseq(rat_-13/2, rat_0) = 0 & rat_$lesseq(rat_-11/2, % 20.60/3.70 rat_-13/2) = 1 & rat_$lesseq(rat_-11/2, rat_-11/2) = 0 & % 20.60/3.70 rat_$lesseq(rat_-11/2, rat_0) = 0 & rat_$lesseq(rat_0, rat_-13/2) = 1 & % 20.60/3.70 rat_$lesseq(rat_0, rat_-11/2) = 1 & rat_$lesseq(rat_0, rat_0) = 0 & % 20.60/3.70 rat_$greater(rat_very_large, rat_-13/2) = 0 & rat_$greater(rat_very_large, % 20.60/3.70 rat_-11/2) = 0 & rat_$greater(rat_very_large, rat_0) = 0 & % 20.60/3.70 rat_$greater(rat_very_small, rat_very_large) = 1 & rat_$greater(rat_-13/2, % 20.60/3.70 rat_very_small) = 0 & rat_$greater(rat_-13/2, rat_-13/2) = 1 & % 20.60/3.70 rat_$greater(rat_-13/2, rat_-11/2) = 1 & rat_$greater(rat_-13/2, rat_0) = 1 & % 20.60/3.70 rat_$greater(rat_-11/2, rat_very_small) = 0 & rat_$greater(rat_-11/2, % 20.60/3.70 rat_-13/2) = 0 & rat_$greater(rat_-11/2, rat_-11/2) = 1 & % 20.60/3.70 rat_$greater(rat_-11/2, rat_0) = 1 & rat_$greater(rat_0, rat_very_small) = 0 & % 20.60/3.70 rat_$greater(rat_0, rat_-13/2) = 0 & rat_$greater(rat_0, rat_-11/2) = 0 & % 20.60/3.70 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0 % 20.60/3.70 & rat_$less(rat_very_small, rat_-13/2) = 0 & rat_$less(rat_very_small, % 20.60/3.70 rat_-11/2) = 0 & rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_-13/2, % 20.60/3.70 rat_very_large) = 0 & rat_$less(rat_-13/2, rat_-13/2) = 1 & % 20.60/3.70 rat_$less(rat_-13/2, rat_-11/2) = 0 & rat_$less(rat_-13/2, rat_0) = 0 & % 20.60/3.70 rat_$less(rat_-11/2, rat_very_large) = 0 & rat_$less(rat_-11/2, rat_-13/2) = 1 % 20.60/3.70 & rat_$less(rat_-11/2, rat_-11/2) = 1 & rat_$less(rat_-11/2, rat_0) = 0 & % 20.60/3.70 rat_$less(rat_0, rat_very_large) = 0 & rat_$less(rat_0, rat_-13/2) = 1 & % 20.60/3.70 rat_$less(rat_0, rat_-11/2) = 1 & rat_$less(rat_0, rat_0) = 1 & % 20.60/3.70 rat_$sum(rat_-13/2, rat_0) = rat_-13/2 & rat_$sum(rat_-11/2, rat_0) = % 20.60/3.70 rat_-11/2 & rat_$sum(rat_0, rat_-13/2) = rat_-13/2 & rat_$sum(rat_0, % 20.60/3.70 rat_-11/2) = rat_-11/2 & rat_$sum(rat_0, rat_0) = rat_0 & ! [v0: $rat] : ! % 20.60/3.70 [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, % 20.60/3.70 v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, % 20.60/3.70 v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! % 20.60/3.70 [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~ % 20.60/3.70 (rat_$sum(v1, v0) = v3) | ? [v5: $rat] : (rat_$sum(v5, v0) = v4 & % 20.60/3.70 rat_$sum(v2, v1) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 20.60/3.70 ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v2, v0) % 20.60/3.70 = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: % 20.60/3.70 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 20.60/3.70 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ % 20.60/3.70 (v4 = 0) & rat_$less(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! % 20.60/3.70 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v0) = v3) | ~ % 20.60/3.70 (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, % 20.60/3.70 v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: % 20.60/3.70 int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, v0) = v3) % 20.60/3.70 | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & ! [v0: $rat] : % 20.60/3.70 ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v1) % 20.60/3.70 = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & % 20.60/3.71 rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 20.60/3.71 : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ (rat_$less(v1, v0) % 20.60/3.71 = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: % 20.60/3.71 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) % 20.60/3.71 = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1, v0) = v3) & ! % 20.60/3.71 [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 20.60/3.71 (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) % 20.60/3.71 = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ % 20.60/3.71 (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 20.60/3.71 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 20.60/3.71 : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 20.60/3.71 rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 20.60/3.71 int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) % 20.60/3.71 & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 20.60/3.71 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 20.60/3.71 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : % 20.60/3.71 (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 20.60/3.71 rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 20.60/3.71 $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0) % 20.60/3.71 = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 20.60/3.71 (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] : % 20.60/3.71 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | % 20.60/3.71 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 20.60/3.71 ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = v3 & % 20.60/3.71 rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 20.60/3.71 ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2, % 20.60/3.71 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 20.60/3.71 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = % 20.60/3.71 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1, % 20.60/3.71 v0) = 0) | ~ (rat_$less(v2, v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: % 20.60/3.71 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) = v2) | % 20.60/3.71 rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 20.60/3.71 (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1: % 20.60/3.71 $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & % 20.60/3.71 ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! % 20.60/3.71 [v0: $rat] : ! [v1: int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & ! [v0: % 20.60/3.71 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & % 20.60/3.71 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1) % 20.60/3.71 = rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) % 20.60/3.71 | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 20.60/3.71 (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & ! [v0: $rat] : ! % 20.60/3.71 [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0: % 20.60/3.71 $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$lesseq(v1, v0) = % 20.60/3.71 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | % 20.60/3.71 rat_$greater(v0, v1) = 0) & ! [v0: $rat] : ! [v1: MultipleValueBool] : ( ~ % 20.60/3.71 (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) = 0) & ! [v0: $rat] : (v0 = % 20.60/3.71 rat_0 | ~ (rat_$uminus(v0) = v0)) % 20.60/3.71 % 20.60/3.71 (function-axioms) % 21.05/3.72 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 21.05/3.72 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0: % 21.05/3.72 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 21.05/3.72 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0: % 21.05/3.72 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 21.05/3.72 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & ! % 21.05/3.72 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 21.05/3.72 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3, % 21.05/3.72 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 21.05/3.72 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ % 21.05/3.72 (rat_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.05/3.72 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 21.05/3.72 (rat_$greater(v3, v2) = v1) | ~ (rat_$greater(v3, v2) = v0)) & ! [v0: % 21.05/3.72 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 21.05/3.72 $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = % 21.05/3.72 v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 % 21.05/3.72 = v0 | ~ (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0: % 21.05/3.72 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = v0 | % 21.05/3.72 ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & ! [v0: % 21.05/3.72 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = v0 | % 21.05/3.72 ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] : ! % 21.05/3.72 [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~ % 21.05/3.72 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 % 21.05/3.72 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0: % 21.05/3.72 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) = % 21.05/3.72 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 21.05/3.72 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) & % 21.05/3.72 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) = % 21.05/3.72 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 21.05/3.72 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) & % 21.05/3.72 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~ % 21.05/3.72 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : ! % 21.05/3.72 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~ % 21.05/3.72 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 21.05/3.72 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0)) % 21.05/3.72 % 21.05/3.72 Those formulas are unsatisfiable: % 21.05/3.72 --------------------------------- % 21.05/3.72 % 21.05/3.72 Begin of proof % 21.05/3.72 | % 21.05/3.72 | ALPHA: (function-axioms) implies: % 21.05/3.72 | (1) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = % 21.05/3.72 | v0 | ~ (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) % 21.05/3.72 | % 21.05/3.72 | ALPHA: (input) implies: % 21.05/3.73 | (2) rat_$sum(rat_0, rat_-11/2) = rat_-11/2 % 21.05/3.73 | (3) rat_$sum(rat_0, rat_-13/2) = rat_-13/2 % 21.05/3.73 | (4) rat_$less(rat_-11/2, rat_-13/2) = 1 % 21.05/3.73 | (5) rat_$less(rat_very_small, rat_-13/2) = 0 % 21.05/3.73 | (6) rat_$difference(rat_-11/2, rat_-11/2) = rat_0 % 21.05/3.73 | (7) rat_$difference(rat_-13/2, rat_-13/2) = rat_0 % 21.05/3.73 | (8) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) = % 21.05/3.73 | v2) | rat_$sum(v0, v1) = v2) % 21.05/3.73 | (9) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 21.05/3.73 | (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = % 21.05/3.73 | v3 & rat_$sum(v1, v3) = v2)) % 21.05/3.73 | (10) ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ % 21.05/3.73 | (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 21.05/3.73 | rat_$greatereq(v0, v1) = v3)) % 21.05/3.73 | (11) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 % 21.05/3.73 | | ~ (rat_$less(v2, v0) = v3) | ~ (rat_$less(v1, v0) = 0) | ? [v4: % 21.05/3.73 | int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) % 21.05/3.73 | (12) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! % 21.05/3.73 | [v4: $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~ (rat_$sum(v1, v0) = v3) % 21.05/3.73 | | ? [v5: $rat] : (rat_$sum(v5, v0) = v4 & rat_$sum(v2, v1) = v5)) % 21.05/3.73 | (13) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! % 21.05/3.73 | [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) % 21.05/3.73 | | ? [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) % 21.05/3.73 | % 21.05/3.73 | GROUND_INST: instantiating (11) with rat_-13/2, rat_very_small, rat_-11/2, 1, % 21.05/3.73 | simplifying with (4), (5) gives: % 21.05/3.73 | (14) ? [v0: int] : ( ~ (v0 = 0) & rat_$lesseq(rat_-11/2, rat_very_small) = % 21.05/3.73 | v0) % 21.05/3.73 | % 21.05/3.73 | GROUND_INST: instantiating (9) with rat_-11/2, rat_-11/2, rat_0, simplifying % 21.05/3.73 | with (6) gives: % 21.35/3.73 | (15) ? [v0: $rat] : (rat_$uminus(rat_-11/2) = v0 & rat_$sum(rat_-11/2, v0) % 21.35/3.73 | = rat_0) % 21.35/3.73 | % 21.35/3.73 | GROUND_INST: instantiating (9) with rat_-13/2, rat_-13/2, rat_0, simplifying % 21.35/3.73 | with (7) gives: % 21.35/3.73 | (16) ? [v0: $rat] : (rat_$uminus(rat_-13/2) = v0 & rat_$sum(rat_-13/2, v0) % 21.35/3.73 | = rat_0) % 21.35/3.73 | % 21.35/3.73 | DELTA: instantiating (16) with fresh symbol all_12_0 gives: % 21.35/3.73 | (17) rat_$uminus(rat_-13/2) = all_12_0 & rat_$sum(rat_-13/2, all_12_0) = % 21.35/3.73 | rat_0 % 21.35/3.73 | % 21.35/3.73 | ALPHA: (17) implies: % 21.35/3.73 | (18) rat_$sum(rat_-13/2, all_12_0) = rat_0 % 21.35/3.73 | % 21.35/3.73 | DELTA: instantiating (15) with fresh symbol all_14_0 gives: % 21.35/3.73 | (19) rat_$uminus(rat_-11/2) = all_14_0 & rat_$sum(rat_-11/2, all_14_0) = % 21.35/3.73 | rat_0 % 21.35/3.73 | % 21.35/3.73 | ALPHA: (19) implies: % 21.35/3.73 | (20) rat_$sum(rat_-11/2, all_14_0) = rat_0 % 21.35/3.73 | % 21.35/3.73 | DELTA: instantiating (14) with fresh symbol all_28_0 gives: % 21.35/3.73 | (21) ~ (all_28_0 = 0) & rat_$lesseq(rat_-11/2, rat_very_small) = all_28_0 % 21.35/3.74 | % 21.35/3.74 | ALPHA: (21) implies: % 21.35/3.74 | (22) ~ (all_28_0 = 0) % 21.35/3.74 | (23) rat_$lesseq(rat_-11/2, rat_very_small) = all_28_0 % 21.35/3.74 | % 21.35/3.74 | GROUND_INST: instantiating (13) with rat_-11/2, all_14_0, rat_-11/2, rat_0, % 21.35/3.74 | rat_-11/2, simplifying with (2), (20) gives: % 21.35/3.74 | (24) ? [v0: $rat] : (rat_$sum(all_14_0, rat_-11/2) = v0 & % 21.35/3.74 | rat_$sum(rat_-11/2, v0) = rat_-11/2) % 21.35/3.74 | % 21.35/3.74 | GROUND_INST: instantiating (8) with all_14_0, rat_-11/2, rat_0, simplifying % 21.35/3.74 | with (20) gives: % 21.35/3.74 | (25) rat_$sum(all_14_0, rat_-11/2) = rat_0 % 21.35/3.74 | % 21.35/3.74 | GROUND_INST: instantiating (13) with rat_-13/2, all_12_0, rat_-13/2, rat_0, % 21.35/3.74 | rat_-13/2, simplifying with (3), (18) gives: % 21.35/3.74 | (26) ? [v0: $rat] : (rat_$sum(all_12_0, rat_-13/2) = v0 & % 21.35/3.74 | rat_$sum(rat_-13/2, v0) = rat_-13/2) % 21.35/3.74 | % 21.35/3.74 | GROUND_INST: instantiating (8) with all_12_0, rat_-13/2, rat_0, simplifying % 21.35/3.74 | with (18) gives: % 21.35/3.74 | (27) rat_$sum(all_12_0, rat_-13/2) = rat_0 % 21.35/3.74 | % 21.35/3.74 | GROUND_INST: instantiating (10) with rat_very_small, rat_-11/2, all_28_0, % 21.35/3.74 | simplifying with (23) gives: % 21.35/3.74 | (28) all_28_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 21.35/3.74 | rat_$greatereq(rat_very_small, rat_-11/2) = v0) % 21.35/3.74 | % 21.35/3.74 | DELTA: instantiating (26) with fresh symbol all_66_0 gives: % 21.35/3.74 | (29) rat_$sum(all_12_0, rat_-13/2) = all_66_0 & rat_$sum(rat_-13/2, % 21.35/3.74 | all_66_0) = rat_-13/2 % 21.35/3.74 | % 21.35/3.74 | ALPHA: (29) implies: % 21.35/3.74 | (30) rat_$sum(rat_-13/2, all_66_0) = rat_-13/2 % 21.35/3.74 | (31) rat_$sum(all_12_0, rat_-13/2) = all_66_0 % 21.35/3.74 | % 21.35/3.74 | DELTA: instantiating (24) with fresh symbol all_72_0 gives: % 21.35/3.74 | (32) rat_$sum(all_14_0, rat_-11/2) = all_72_0 & rat_$sum(rat_-11/2, % 21.35/3.74 | all_72_0) = rat_-11/2 % 21.35/3.74 | % 21.35/3.74 | ALPHA: (32) implies: % 21.35/3.74 | (33) rat_$sum(all_14_0, rat_-11/2) = all_72_0 % 21.35/3.74 | % 21.35/3.74 | BETA: splitting (28) gives: % 21.35/3.74 | % 21.35/3.74 | Case 1: % 21.35/3.74 | | % 21.35/3.74 | | (34) all_28_0 = 0 % 21.35/3.74 | | % 21.35/3.74 | | REDUCE: (22), (34) imply: % 21.35/3.74 | | (35) $false % 21.35/3.74 | | % 21.35/3.74 | | CLOSE: (35) is inconsistent. % 21.35/3.74 | | % 21.35/3.74 | Case 2: % 21.35/3.74 | | % 21.35/3.74 | | % 21.35/3.74 | | GROUND_INST: instantiating (1) with rat_0, all_66_0, rat_-13/2, all_12_0, % 21.35/3.74 | | simplifying with (27), (31) gives: % 21.35/3.74 | | (36) all_66_0 = rat_0 % 21.35/3.74 | | % 21.35/3.74 | | GROUND_INST: instantiating (1) with rat_0, all_72_0, rat_-11/2, all_14_0, % 21.35/3.74 | | simplifying with (25), (33) gives: % 21.35/3.74 | | (37) all_72_0 = rat_0 % 21.35/3.74 | | % 21.35/3.74 | | REDUCE: (30), (36) imply: % 21.35/3.74 | | (38) rat_$sum(rat_-13/2, rat_0) = rat_-13/2 % 21.35/3.74 | | % 21.35/3.74 | | GROUND_INST: instantiating (12) with rat_-11/2, all_14_0, rat_-13/2, rat_0, % 21.35/3.74 | | rat_-13/2, simplifying with (25), (38) gives: % 21.35/3.74 | | (39) ? [v0: $rat] : (rat_$sum(v0, rat_-11/2) = rat_-13/2 & % 21.35/3.74 | | rat_$sum(rat_-13/2, all_14_0) = v0) % 21.35/3.74 | | % 21.35/3.74 | | DELTA: instantiating (39) with fresh symbol all_239_0 gives: % 21.35/3.74 | | (40) rat_$sum(all_239_0, rat_-11/2) = rat_-13/2 & rat_$sum(rat_-13/2, % 21.35/3.74 | | all_14_0) = all_239_0 % 21.35/3.74 | | % 21.35/3.74 | | ALPHA: (40) implies: % 21.35/3.74 | | (41) rat_$sum(all_239_0, rat_-11/2) = rat_-13/2 % 21.35/3.74 | | % 21.35/3.74 | | GROUND_INST: instantiating (rat_sum_problem_24) with all_239_0, simplifying % 21.35/3.74 | | with (41) gives: % 21.35/3.74 | | (42) $false % 21.35/3.74 | | % 21.35/3.74 | | CLOSE: (42) is inconsistent. % 21.35/3.74 | | % 21.35/3.74 | End of split % 21.35/3.74 | % 21.35/3.74 End of proof % 21.35/3.74 % SZS output end Proof for theBenchmark % 21.35/3.74 % 21.35/3.74 3111ms %------------------------------------------------------------------------------