%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI407_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 : n011.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 17:47:56 EDT 2023 % Result : Theorem 10.93s 2.27s % Output : Proof 14.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : ARI407_1 : TPTP v8.1.2. Released v5.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n011.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 18:19:41 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.64/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.64/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.64/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.64/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.64/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.64/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.64/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.45/0.95 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.45/0.95 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.45/0.95 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.45/0.95 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.45/0.95 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 1.45/0.95 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 1.45/0.95 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 2.41/1.05 Prover 1: Preprocessing ... % 2.41/1.05 Prover 4: Preprocessing ... % 2.73/1.11 Prover 0: Preprocessing ... % 2.73/1.11 Prover 6: Preprocessing ... % 3.15/1.17 Prover 2: Preprocessing ... % 3.15/1.17 Prover 5: Preprocessing ... % 3.15/1.17 Prover 3: Preprocessing ... % 6.38/1.60 Prover 1: Constructing countermodel ... % 6.38/1.60 Prover 6: Proving ... % 6.73/1.65 Prover 4: Constructing countermodel ... % 6.73/1.66 Prover 0: Proving ... % 9.62/2.06 Prover 1: gave up % 9.62/2.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.62/2.07 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 10.31/2.13 Prover 7: Preprocessing ... % 10.31/2.16 Prover 3: Constructing countermodel ... % 10.31/2.18 Prover 2: Proving ... % 10.93/2.26 Prover 0: proved (1612ms) % 10.93/2.26 % 10.93/2.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.93/2.27 % 10.93/2.28 Prover 2: stopped % 10.93/2.28 Prover 6: stopped % 11.58/2.29 Prover 3: stopped % 11.58/2.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.58/2.29 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.58/2.29 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 11.58/2.29 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 11.58/2.29 Prover 8: Preprocessing ... % 11.58/2.29 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.58/2.29 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 11.58/2.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.58/2.30 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 11.74/2.30 Prover 13: Preprocessing ... % 11.74/2.31 Prover 10: Preprocessing ... % 11.86/2.32 Prover 11: Preprocessing ... % 11.86/2.34 Prover 5: Proving ... % 11.86/2.35 Prover 5: stopped % 11.86/2.36 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.86/2.36 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation % 11.86/2.38 Prover 16: Preprocessing ... % 12.60/2.41 Prover 8: Warning: ignoring some quantifiers % 12.60/2.42 Prover 13: Warning: ignoring some quantifiers % 12.60/2.42 Prover 8: Constructing countermodel ... % 12.60/2.42 Prover 13: Constructing countermodel ... % 12.60/2.45 Prover 4: Found proof (size 10) % 12.60/2.45 Prover 4: proved (1797ms) % 12.60/2.45 Prover 13: stopped % 12.60/2.45 Prover 8: stopped % 12.60/2.54 Prover 10: stopped % 12.60/2.56 Prover 7: Warning: ignoring some quantifiers % 13.54/2.57 Prover 7: Constructing countermodel ... % 13.54/2.59 Prover 7: stopped % 13.54/2.60 Prover 16: stopped % 13.54/2.62 Prover 11: stopped % 13.54/2.62 % 13.54/2.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.54/2.62 % 13.54/2.62 % SZS output start Proof for theBenchmark % 13.54/2.62 Assumptions after simplification: % 13.54/2.62 --------------------------------- % 13.54/2.62 % 13.54/2.62 (real_sum_problem_7) % 13.54/2.64 ! [v0: $real] : ~ (real_$sum(real_17/4, v0) = real_10) % 13.54/2.64 % 13.54/2.64 (input) % 14.17/2.67 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_10) & ~ % 14.17/2.67 (real_very_large = real_17/4) & ~ (real_very_large = real_0) & ~ % 14.17/2.67 (real_very_small = real_10) & ~ (real_very_small = real_17/4) & ~ % 14.17/2.67 (real_very_small = real_0) & ~ (real_10 = real_17/4) & ~ (real_10 = real_0) % 14.17/2.67 & ~ (real_17/4 = real_0) & real_$is_int(real_10) = 0 & % 14.17/2.67 real_$is_int(real_17/4) = 1 & real_$is_int(real_0) = 0 & real_$is_rat(real_10) % 14.17/2.67 = 0 & real_$is_rat(real_17/4) = 0 & real_$is_rat(real_0) = 0 & % 14.17/2.67 real_$floor(real_10) = real_10 & real_$floor(real_0) = real_0 & % 14.17/2.67 real_$ceiling(real_10) = real_10 & real_$ceiling(real_0) = real_0 & % 14.17/2.67 real_$truncate(real_10) = real_10 & real_$truncate(real_0) = real_0 & % 14.17/2.67 real_$round(real_10) = real_10 & real_$round(real_0) = real_0 & % 14.17/2.67 real_$to_int(real_10) = 10 & real_$to_int(real_17/4) = 4 & % 14.17/2.67 real_$to_int(real_0) = 0 & real_$to_rat(real_10) = rat_10 & % 14.17/2.67 real_$to_rat(real_17/4) = rat_17/4 & real_$to_rat(real_0) = rat_0 & % 14.17/2.67 real_$to_real(real_10) = real_10 & real_$to_real(real_17/4) = real_17/4 & % 14.17/2.67 real_$to_real(real_0) = real_0 & int_$to_real(10) = real_10 & int_$to_real(0) % 14.17/2.67 = real_0 & real_$quotient(real_0, real_10) = real_0 & real_$quotient(real_0, % 14.17/2.67 real_17/4) = real_0 & real_$product(real_10, real_0) = real_0 & % 14.17/2.67 real_$product(real_17/4, real_0) = real_0 & real_$product(real_0, real_10) = % 14.17/2.67 real_0 & real_$product(real_0, real_17/4) = real_0 & real_$product(real_0, % 14.17/2.67 real_0) = real_0 & real_$difference(real_10, real_10) = real_0 & % 14.17/2.67 real_$difference(real_10, real_0) = real_10 & real_$difference(real_17/4, % 14.17/2.67 real_17/4) = real_0 & real_$difference(real_17/4, real_0) = real_17/4 & % 14.17/2.67 real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) = real_0 & % 14.17/2.67 real_$greatereq(real_very_small, real_very_large) = 1 & % 14.17/2.67 real_$greatereq(real_10, real_10) = 0 & real_$greatereq(real_10, real_17/4) = % 14.17/2.67 0 & real_$greatereq(real_10, real_0) = 0 & real_$greatereq(real_17/4, real_10) % 14.17/2.67 = 1 & real_$greatereq(real_17/4, real_17/4) = 0 & real_$greatereq(real_17/4, % 14.17/2.67 real_0) = 0 & real_$greatereq(real_0, real_10) = 1 & real_$greatereq(real_0, % 14.17/2.67 real_17/4) = 1 & real_$greatereq(real_0, real_0) = 0 & % 14.17/2.67 real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_10, % 14.17/2.67 real_10) = 0 & real_$lesseq(real_10, real_17/4) = 1 & real_$lesseq(real_10, % 14.17/2.67 real_0) = 1 & real_$lesseq(real_17/4, real_10) = 0 & real_$lesseq(real_17/4, % 14.17/2.67 real_17/4) = 0 & real_$lesseq(real_17/4, real_0) = 1 & real_$lesseq(real_0, % 14.17/2.67 real_10) = 0 & real_$lesseq(real_0, real_17/4) = 0 & real_$lesseq(real_0, % 14.17/2.67 real_0) = 0 & real_$greater(real_very_large, real_10) = 0 & % 14.17/2.67 real_$greater(real_very_large, real_17/4) = 0 & real_$greater(real_very_large, % 14.17/2.67 real_0) = 0 & real_$greater(real_very_small, real_very_large) = 1 & % 14.17/2.67 real_$greater(real_10, real_very_small) = 0 & real_$greater(real_10, real_10) % 14.17/2.67 = 1 & real_$greater(real_10, real_17/4) = 0 & real_$greater(real_10, real_0) = % 14.17/2.67 0 & real_$greater(real_17/4, real_very_small) = 0 & real_$greater(real_17/4, % 14.17/2.67 real_10) = 1 & real_$greater(real_17/4, real_17/4) = 1 & % 14.17/2.67 real_$greater(real_17/4, real_0) = 0 & real_$greater(real_0, real_very_small) % 14.17/2.67 = 0 & real_$greater(real_0, real_10) = 1 & real_$greater(real_0, real_17/4) = % 14.17/2.67 1 & real_$greater(real_0, real_0) = 1 & real_$less(real_very_small, % 14.17/2.67 real_very_large) = 0 & real_$less(real_very_small, real_10) = 0 & % 14.17/2.67 real_$less(real_very_small, real_17/4) = 0 & real_$less(real_very_small, % 14.17/2.67 real_0) = 0 & real_$less(real_10, real_very_large) = 0 & real_$less(real_10, % 14.17/2.67 real_10) = 1 & real_$less(real_10, real_17/4) = 1 & real_$less(real_10, % 14.17/2.67 real_0) = 1 & real_$less(real_17/4, real_very_large) = 0 & % 14.17/2.67 real_$less(real_17/4, real_10) = 0 & real_$less(real_17/4, real_17/4) = 1 & % 14.17/2.67 real_$less(real_17/4, real_0) = 1 & real_$less(real_0, real_very_large) = 0 & % 14.17/2.67 real_$less(real_0, real_10) = 0 & real_$less(real_0, real_17/4) = 0 & % 14.17/2.67 real_$less(real_0, real_0) = 1 & real_$sum(real_10, real_0) = real_10 & % 14.17/2.67 real_$sum(real_17/4, real_0) = real_17/4 & real_$sum(real_0, real_10) = % 14.17/2.67 real_10 & real_$sum(real_0, real_17/4) = real_17/4 & real_$sum(real_0, real_0) % 14.17/2.67 = real_0 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : % 14.17/2.67 ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | % 14.17/2.67 ? [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: % 14.17/2.67 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : % 14.17/2.67 ( ~ (real_$sum(v2, v3) = v4) | ~ (real_$sum(v1, v0) = v3) | ? [v5: $real] : % 14.17/2.67 (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) = v5)) & ! [v0: $real] : ! % 14.17/2.67 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, % 14.17/2.67 v1) = 0) | ~ (real_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) % 14.17/2.67 & real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 14.17/2.67 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~ % 14.17/2.67 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0) % 14.17/2.67 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : % 14.17/2.67 (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? % 14.17/2.67 [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! % 14.17/2.67 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, % 14.17/2.67 v0) = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & % 14.17/2.67 real_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 14.17/2.67 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v1) = 0) | ~ % 14.17/2.67 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1, % 14.17/2.67 v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: % 14.17/2.67 int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~ (real_$less(v1, v0) = 0) % 14.17/2.67 | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] % 14.17/2.67 : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) = % 14.17/2.67 v2) | ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, v0) = v3) & ! % 14.17/2.67 [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 14.17/2.67 (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, % 14.17/2.67 v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | % 14.17/2.67 ~ (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 14.17/2.68 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 14.17/2.68 int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = % 14.17/2.68 0) & real_$greatereq(v0, v1) = v3)) & ! [v0: $real] : ! [v1: $real] : % 14.17/2.68 ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ % 14.17/2.68 (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : % 14.17/2.68 ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ % 14.17/2.68 (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : % 14.17/2.68 ! [v2: int] : (v2 = 0 | ~ (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 % 14.17/2.68 = 0) & real_$greater(v0, v1) = v3)) & ! [v0: $real] : ! [v1: $real] : % 14.17/2.68 ! [v2: $real] : (v0 = real_0 | ~ (real_$product(v1, v0) = v2) | % 14.17/2.68 real_$quotient(v2, v0) = v1) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 14.17/2.68 $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) & ! % 14.17/2.68 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = % 14.17/2.68 v2) | real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! % 14.17/2.68 [v2: $real] : ( ~ (real_$difference(v1, v0) = v2) | ? [v3: $real] : % 14.17/2.68 (real_$uminus(v0) = v3 & real_$sum(v1, v3) = v2)) & ! [v0: $real] : ! [v1: % 14.17/2.68 $real] : ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~ % 14.17/2.68 (real_$lesseq(v1, v0) = 0) | real_$lesseq(v2, v0) = 0) & ! [v0: $real] : ! % 14.17/2.68 [v1: $real] : ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~ % 14.17/2.68 (real_$less(v1, v0) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : ! % 14.17/2.68 [v1: $real] : ! [v2: $real] : ( ~ (real_$lesseq(v1, v0) = 0) | ~ % 14.17/2.68 (real_$less(v2, v1) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : ! % 14.17/2.68 [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, % 14.17/2.68 v1) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 14.17/2.68 (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: $real] : ! % 14.17/2.68 [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = % 14.17/2.68 0) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) % 14.17/2.68 = v1)) & ! [v0: $real] : ! [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0, % 14.17/2.68 v0) = v1)) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = % 14.17/2.68 v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 14.17/2.68 (real_$uminus(v0) = v1) | real_$sum(v0, v1) = real_0) & ! [v0: $real] : ! % 14.17/2.68 [v1: $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & % 14.17/2.68 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$lesseq(v1, v0) = 0) | % 14.17/2.68 real_$greatereq(v0, v1) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 14.17/2.68 (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & ! [v0: $real] : ! % 14.17/2.68 [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | real_$lesseq(v1, v0) = 0) & ! % 14.17/2.68 [v0: $real] : ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | % 14.17/2.68 real_$greater(v0, v1) = 0) & ! [v0: $real] : ! [v1: MultipleValueBool] : ( % 14.17/2.68 ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0) = 0) & ! [v0: $real] : % 14.17/2.68 (v0 = real_0 | ~ (real_$uminus(v0) = v0)) % 14.17/2.68 % 14.17/2.68 Those formulas are unsatisfiable: % 14.17/2.68 --------------------------------- % 14.17/2.68 % 14.17/2.68 Begin of proof % 14.17/2.68 | % 14.17/2.68 | ALPHA: (input) implies: % 14.17/2.68 | (1) real_$sum(real_0, real_10) = real_10 % 14.17/2.68 | (2) real_$difference(real_17/4, real_17/4) = real_0 % 14.17/2.68 | (3) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 14.17/2.68 | (real_$difference(v1, v0) = v2) | ? [v3: $real] : (real_$uminus(v0) % 14.17/2.68 | = v3 & real_$sum(v1, v3) = v2)) % 14.17/2.68 | (4) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! % 14.17/2.68 | [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = % 14.17/2.68 | v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) % 14.17/2.68 | = v5)) % 14.17/2.68 | % 14.17/2.68 | GROUND_INST: instantiating (3) with real_17/4, real_17/4, real_0, simplifying % 14.17/2.68 | with (2) gives: % 14.17/2.68 | (5) ? [v0: $real] : (real_$uminus(real_17/4) = v0 & real_$sum(real_17/4, % 14.17/2.68 | v0) = real_0) % 14.17/2.68 | % 14.17/2.68 | DELTA: instantiating (5) with fresh symbol all_22_0 gives: % 14.17/2.68 | (6) real_$uminus(real_17/4) = all_22_0 & real_$sum(real_17/4, all_22_0) = % 14.17/2.68 | real_0 % 14.17/2.68 | % 14.17/2.68 | ALPHA: (6) implies: % 14.17/2.68 | (7) real_$sum(real_17/4, all_22_0) = real_0 % 14.17/2.69 | % 14.17/2.69 | GROUND_INST: instantiating (4) with real_10, all_22_0, real_17/4, real_0, % 14.17/2.69 | real_10, simplifying with (1), (7) gives: % 14.17/2.69 | (8) ? [v0: $real] : (real_$sum(all_22_0, real_10) = v0 & % 14.17/2.69 | real_$sum(real_17/4, v0) = real_10) % 14.17/2.69 | % 14.17/2.69 | DELTA: instantiating (8) with fresh symbol all_44_0 gives: % 14.17/2.69 | (9) real_$sum(all_22_0, real_10) = all_44_0 & real_$sum(real_17/4, % 14.17/2.69 | all_44_0) = real_10 % 14.17/2.69 | % 14.17/2.69 | ALPHA: (9) implies: % 14.17/2.69 | (10) real_$sum(real_17/4, all_44_0) = real_10 % 14.17/2.69 | % 14.17/2.69 | GROUND_INST: instantiating (real_sum_problem_7) with all_44_0, simplifying % 14.17/2.69 | with (10) gives: % 14.17/2.69 | (11) $false % 14.17/2.69 | % 14.17/2.69 | CLOSE: (11) is inconsistent. % 14.17/2.69 | % 14.17/2.69 End of proof % 14.17/2.69 % SZS output end Proof for theBenchmark % 14.17/2.69 % 14.17/2.69 2056ms %------------------------------------------------------------------------------