%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI255_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 : n001.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 17:47:27 EDT 2023 % Result : Theorem 10.53s 2.32s % Output : Proof 13.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ARI255_1 : TPTP v8.1.2. Released v5.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n001.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 18:35:38 EDT 2023 % 0.12/0.34 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 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 1: 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 3: Warning: Problem contains rationals, using incomplete axiomatisation % 1.56/0.96 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.56/0.96 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 1.56/0.96 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.56/0.96 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 2.08/1.07 Prover 1: Preprocessing ... % 2.08/1.07 Prover 4: Preprocessing ... % 2.54/1.12 Prover 6: Preprocessing ... % 2.54/1.12 Prover 0: Preprocessing ... % 3.19/1.21 Prover 5: Preprocessing ... % 3.41/1.22 Prover 3: Preprocessing ... % 3.41/1.22 Prover 2: Preprocessing ... % 6.17/1.62 Prover 1: Constructing countermodel ... % 6.40/1.63 Prover 4: Constructing countermodel ... % 6.40/1.64 Prover 6: Proving ... % 6.40/1.65 Prover 0: Proving ... % 9.11/2.02 Prover 1: gave up % 9.11/2.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.11/2.02 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation % 9.28/2.08 Prover 7: Preprocessing ... % 9.98/2.14 Prover 2: Proving ... % 9.98/2.15 Prover 3: Constructing countermodel ... % 10.53/2.32 Prover 0: proved (1680ms) % 10.53/2.32 % 10.53/2.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.53/2.32 % 10.53/2.34 Prover 2: stopped % 10.53/2.34 Prover 6: stopped % 10.53/2.35 Prover 3: stopped % 10.53/2.37 Prover 5: Proving ... % 10.53/2.37 Prover 5: stopped % 10.53/2.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.53/2.37 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation % 10.53/2.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.53/2.37 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation % 10.53/2.37 Prover 8: Preprocessing ... % 10.53/2.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.53/2.37 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation % 10.53/2.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.53/2.37 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation % 10.53/2.37 Prover 13: Preprocessing ... % 10.53/2.38 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 10.53/2.38 Prover 16: Warning: Problem contains rationals, using incomplete axiomatisation % 11.91/2.40 Prover 11: Preprocessing ... % 11.91/2.42 Prover 10: Preprocessing ... % 12.18/2.44 Prover 16: Preprocessing ... % 12.18/2.44 Prover 4: Found proof (size 10) % 12.18/2.44 Prover 4: proved (1800ms) % 12.18/2.45 Prover 13: stopped % 12.18/2.47 Prover 8: Warning: ignoring some quantifiers % 12.18/2.47 Prover 8: Constructing countermodel ... % 12.18/2.49 Prover 8: stopped % 12.73/2.50 Prover 7: Warning: ignoring some quantifiers % 12.73/2.51 Prover 7: Constructing countermodel ... % 12.73/2.53 Prover 7: stopped % 13.23/2.60 Prover 10: stopped % 13.23/2.64 Prover 11: stopped % 13.23/2.65 Prover 16: stopped % 13.23/2.66 % 13.23/2.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.23/2.66 % 13.23/2.66 % SZS output start Proof for theBenchmark % 13.23/2.66 Assumptions after simplification: % 13.23/2.66 --------------------------------- % 13.23/2.66 % 13.23/2.66 (rat_sum_problem_10) % 13.76/2.68 ! [v0: $rat] : ~ (rat_$sum(rat_5/16, v0) = rat_1/2) % 13.76/2.68 % 13.76/2.68 (input) % 13.89/2.71 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_1/2) & ~ % 13.89/2.71 (rat_very_large = rat_5/16) & ~ (rat_very_large = rat_0) & ~ (rat_very_small % 13.89/2.71 = rat_1/2) & ~ (rat_very_small = rat_5/16) & ~ (rat_very_small = rat_0) & % 13.89/2.71 ~ (rat_1/2 = rat_5/16) & ~ (rat_1/2 = rat_0) & ~ (rat_5/16 = rat_0) & % 13.89/2.71 rat_$is_int(rat_1/2) = 1 & rat_$is_int(rat_5/16) = 1 & rat_$is_int(rat_0) = 0 % 13.89/2.71 & rat_$is_rat(rat_1/2) = 0 & rat_$is_rat(rat_5/16) = 0 & rat_$is_rat(rat_0) = % 13.89/2.71 0 & rat_$floor(rat_1/2) = rat_0 & rat_$floor(rat_5/16) = rat_0 & % 13.89/2.71 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 & % 13.89/2.71 rat_$truncate(rat_1/2) = rat_0 & rat_$truncate(rat_5/16) = rat_0 & % 13.89/2.71 rat_$truncate(rat_0) = rat_0 & rat_$round(rat_5/16) = rat_0 & % 13.89/2.71 rat_$round(rat_0) = rat_0 & rat_$to_int(rat_1/2) = 0 & rat_$to_int(rat_5/16) = % 13.89/2.71 0 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_1/2) = rat_1/2 & % 13.89/2.71 rat_$to_rat(rat_5/16) = rat_5/16 & rat_$to_rat(rat_0) = rat_0 & % 13.89/2.71 rat_$to_real(rat_1/2) = real_1/2 & rat_$to_real(rat_5/16) = real_5/16 & % 13.89/2.71 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_0, % 13.89/2.71 rat_1/2) = rat_0 & rat_$quotient(rat_0, rat_5/16) = rat_0 & % 13.89/2.71 rat_$product(rat_1/2, rat_0) = rat_0 & rat_$product(rat_5/16, rat_0) = rat_0 & % 13.89/2.71 rat_$product(rat_0, rat_1/2) = rat_0 & rat_$product(rat_0, rat_5/16) = rat_0 & % 13.89/2.71 rat_$product(rat_0, rat_0) = rat_0 & rat_$difference(rat_1/2, rat_1/2) = rat_0 % 13.89/2.71 & rat_$difference(rat_1/2, rat_0) = rat_1/2 & rat_$difference(rat_5/16, % 13.89/2.71 rat_5/16) = rat_0 & rat_$difference(rat_5/16, rat_0) = rat_5/16 & % 13.89/2.71 rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 & % 13.89/2.71 rat_$greatereq(rat_very_small, rat_very_large) = 1 & rat_$greatereq(rat_1/2, % 13.89/2.71 rat_1/2) = 0 & rat_$greatereq(rat_1/2, rat_5/16) = 0 & % 13.89/2.71 rat_$greatereq(rat_1/2, rat_0) = 0 & rat_$greatereq(rat_5/16, rat_1/2) = 1 & % 13.89/2.71 rat_$greatereq(rat_5/16, rat_5/16) = 0 & rat_$greatereq(rat_5/16, rat_0) = 0 & % 13.89/2.71 rat_$greatereq(rat_0, rat_1/2) = 1 & rat_$greatereq(rat_0, rat_5/16) = 1 & % 13.89/2.71 rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large) % 13.89/2.71 = 0 & rat_$lesseq(rat_1/2, rat_1/2) = 0 & rat_$lesseq(rat_1/2, rat_5/16) = 1 & % 13.89/2.71 rat_$lesseq(rat_1/2, rat_0) = 1 & rat_$lesseq(rat_5/16, rat_1/2) = 0 & % 13.89/2.71 rat_$lesseq(rat_5/16, rat_5/16) = 0 & rat_$lesseq(rat_5/16, rat_0) = 1 & % 13.89/2.71 rat_$lesseq(rat_0, rat_1/2) = 0 & rat_$lesseq(rat_0, rat_5/16) = 0 & % 13.89/2.71 rat_$lesseq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_1/2) = 0 & % 13.89/2.71 rat_$greater(rat_very_large, rat_5/16) = 0 & rat_$greater(rat_very_large, % 13.89/2.71 rat_0) = 0 & rat_$greater(rat_very_small, rat_very_large) = 1 & % 13.89/2.71 rat_$greater(rat_1/2, rat_very_small) = 0 & rat_$greater(rat_1/2, rat_1/2) = 1 % 13.89/2.71 & rat_$greater(rat_1/2, rat_5/16) = 0 & rat_$greater(rat_1/2, rat_0) = 0 & % 13.89/2.71 rat_$greater(rat_5/16, rat_very_small) = 0 & rat_$greater(rat_5/16, rat_1/2) = % 13.89/2.71 1 & rat_$greater(rat_5/16, rat_5/16) = 1 & rat_$greater(rat_5/16, rat_0) = 0 & % 13.89/2.71 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_1/2) = 1 & % 13.89/2.71 rat_$greater(rat_0, rat_5/16) = 1 & rat_$greater(rat_0, rat_0) = 1 & % 13.89/2.71 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small, % 13.89/2.71 rat_1/2) = 0 & rat_$less(rat_very_small, rat_5/16) = 0 & % 13.89/2.71 rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_1/2, rat_very_large) = 0 % 13.89/2.71 & rat_$less(rat_1/2, rat_1/2) = 1 & rat_$less(rat_1/2, rat_5/16) = 1 & % 13.89/2.71 rat_$less(rat_1/2, rat_0) = 1 & rat_$less(rat_5/16, rat_very_large) = 0 & % 13.89/2.71 rat_$less(rat_5/16, rat_1/2) = 0 & rat_$less(rat_5/16, rat_5/16) = 1 & % 13.89/2.71 rat_$less(rat_5/16, rat_0) = 1 & rat_$less(rat_0, rat_very_large) = 0 & % 13.89/2.71 rat_$less(rat_0, rat_1/2) = 0 & rat_$less(rat_0, rat_5/16) = 0 & % 13.89/2.71 rat_$less(rat_0, rat_0) = 1 & rat_$sum(rat_1/2, rat_0) = rat_1/2 & % 13.89/2.71 rat_$sum(rat_5/16, rat_0) = rat_5/16 & rat_$sum(rat_0, rat_1/2) = rat_1/2 & % 13.89/2.71 rat_$sum(rat_0, rat_5/16) = rat_5/16 & rat_$sum(rat_0, rat_0) = rat_0 & ! % 13.89/2.71 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( % 13.89/2.71 ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : % 13.89/2.71 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: % 13.89/2.71 $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2, % 13.89/2.71 v3) = v4) | ~ (rat_$sum(v1, v0) = v3) | ? [v5: $rat] : (rat_$sum(v5, % 13.89/2.71 v0) = v4 & rat_$sum(v2, v1) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! % 13.89/2.71 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ % 13.89/2.71 (rat_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1, % 13.89/2.71 v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: % 13.89/2.71 int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) % 13.89/2.71 | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v1, v0) = v4)) & ! [v0: $rat] : % 13.89/2.71 ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, % 13.89/2.71 v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & % 13.89/2.71 rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 13.89/2.71 : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, % 13.89/2.71 v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & ! % 13.89/2.71 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 13.89/2.71 (rat_$less(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ % 13.89/2.71 (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! % 13.89/2.71 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ % 13.89/2.71 (rat_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) % 13.89/2.71 = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( % 13.89/2.71 ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1, % 13.89/2.71 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 = % 13.89/2.71 v0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 13.89/2.71 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 13.89/2.71 : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 13.89/2.71 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 13.89/2.71 : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 13.89/2.71 rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 13.89/2.71 int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) % 13.89/2.71 & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 13.89/2.71 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 13.89/2.71 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : % 13.89/2.71 (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 13.89/2.71 rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 13.89/2.71 $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0) % 13.89/2.71 = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 13.89/2.71 (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] : % 13.89/2.71 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | % 13.89/2.71 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 13.89/2.71 ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = v3 & % 13.89/2.71 rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 13.89/2.71 ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2, % 13.89/2.71 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 13.89/2.71 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = % 13.89/2.71 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1, % 13.89/2.71 v0) = 0) | ~ (rat_$less(v2, v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: % 13.89/2.71 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) = v2) | % 13.89/2.71 rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 13.89/2.71 (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1: % 13.89/2.71 $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & % 13.89/2.71 ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! % 13.89/2.71 [v0: $rat] : ! [v1: int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & ! [v0: % 13.89/2.71 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & % 13.89/2.71 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1) % 13.89/2.71 = rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) % 13.89/2.71 | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 13.89/2.71 (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & ! [v0: $rat] : ! % 13.89/2.71 [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0: % 13.89/2.71 $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$lesseq(v1, v0) = % 13.89/2.71 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | % 13.89/2.71 rat_$greater(v0, v1) = 0) & ! [v0: $rat] : ! [v1: MultipleValueBool] : ( ~ % 13.89/2.71 (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) = 0) & ! [v0: $rat] : (v0 = % 13.89/2.71 rat_0 | ~ (rat_$uminus(v0) = v0)) % 13.89/2.71 % 13.89/2.71 Those formulas are unsatisfiable: % 13.89/2.71 --------------------------------- % 13.89/2.71 % 13.89/2.71 Begin of proof % 13.89/2.71 | % 13.89/2.71 | ALPHA: (input) implies: % 13.89/2.71 | (1) rat_$sum(rat_0, rat_1/2) = rat_1/2 % 13.89/2.71 | (2) rat_$difference(rat_5/16, rat_5/16) = rat_0 % 13.89/2.71 | (3) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 13.89/2.71 | (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = % 13.89/2.71 | v3 & rat_$sum(v1, v3) = v2)) % 13.89/2.71 | (4) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: % 13.89/2.71 | $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? % 13.89/2.71 | [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) % 13.89/2.71 | % 13.89/2.71 | GROUND_INST: instantiating (3) with rat_5/16, rat_5/16, rat_0, simplifying % 13.89/2.71 | with (2) gives: % 13.89/2.72 | (5) ? [v0: $rat] : (rat_$uminus(rat_5/16) = v0 & rat_$sum(rat_5/16, v0) = % 13.89/2.72 | rat_0) % 13.89/2.72 | % 13.89/2.72 | DELTA: instantiating (5) with fresh symbol all_22_0 gives: % 13.89/2.72 | (6) rat_$uminus(rat_5/16) = all_22_0 & rat_$sum(rat_5/16, all_22_0) = rat_0 % 13.89/2.72 | % 13.89/2.72 | ALPHA: (6) implies: % 13.89/2.72 | (7) rat_$sum(rat_5/16, all_22_0) = rat_0 % 13.89/2.72 | % 13.89/2.72 | GROUND_INST: instantiating (4) with rat_1/2, all_22_0, rat_5/16, rat_0, % 13.89/2.72 | rat_1/2, simplifying with (1), (7) gives: % 13.89/2.72 | (8) ? [v0: $rat] : (rat_$sum(all_22_0, rat_1/2) = v0 & rat_$sum(rat_5/16, % 13.89/2.72 | v0) = rat_1/2) % 13.89/2.72 | % 13.89/2.72 | DELTA: instantiating (8) with fresh symbol all_44_0 gives: % 13.89/2.72 | (9) rat_$sum(all_22_0, rat_1/2) = all_44_0 & rat_$sum(rat_5/16, all_44_0) = % 13.89/2.72 | rat_1/2 % 13.89/2.72 | % 13.89/2.72 | ALPHA: (9) implies: % 13.89/2.72 | (10) rat_$sum(rat_5/16, all_44_0) = rat_1/2 % 13.89/2.72 | % 13.89/2.72 | GROUND_INST: instantiating (rat_sum_problem_10) with all_44_0, simplifying % 13.89/2.72 | with (10) gives: % 13.89/2.72 | (11) $false % 13.89/2.72 | % 13.89/2.72 | CLOSE: (11) is inconsistent. % 13.89/2.72 | % 13.89/2.72 End of proof % 13.89/2.72 % SZS output end Proof for theBenchmark % 13.89/2.72 % 13.89/2.72 2099ms %------------------------------------------------------------------------------