%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM909_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 : Thu Aug 31 11:50:40 EDT 2023 % Result : Theorem 7.67s 1.87s % Output : Proof 10.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : NUM909_1 : TPTP v8.1.2. Released v5.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n011.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 % 0.20/0.34 % CPULimit : 300 % 0.20/0.34 % WCLimit : 300 % 0.20/0.34 % DateTime : Fri Aug 25 12:07:53 EDT 2023 % 0.20/0.35 % 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. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.33/0.94 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.33/0.94 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.33/0.94 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.33/0.94 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.33/0.94 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.33/0.94 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 1.33/0.94 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 2.22/1.04 Prover 1: Preprocessing ... % 2.22/1.04 Prover 4: Preprocessing ... % 2.22/1.08 Prover 0: Preprocessing ... % 2.22/1.08 Prover 2: Preprocessing ... % 2.22/1.08 Prover 6: Preprocessing ... % 2.22/1.08 Prover 5: Preprocessing ... % 2.22/1.08 Prover 3: Preprocessing ... % 4.90/1.46 Prover 5: Proving ... % 4.90/1.46 Prover 2: Proving ... % 4.90/1.46 Prover 6: Constructing countermodel ... % 4.90/1.46 Prover 1: Constructing countermodel ... % 4.90/1.47 Prover 3: Constructing countermodel ... % 5.52/1.53 Prover 4: Constructing countermodel ... % 5.52/1.58 Prover 0: Proving ... % 6.68/1.69 Prover 1: gave up % 6.68/1.69 Prover 3: gave up % 6.68/1.69 Prover 6: gave up % 6.68/1.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.68/1.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.68/1.70 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 6.68/1.70 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 6.68/1.70 Prover 9: Warning: Problem contains reals, using incomplete axiomatisation % 6.68/1.70 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 6.68/1.71 Prover 9: Preprocessing ... % 6.68/1.71 Prover 8: Preprocessing ... % 6.89/1.72 Prover 7: Preprocessing ... % 7.67/1.82 Prover 7: Warning: ignoring some quantifiers % 7.67/1.82 Prover 8: Warning: ignoring some quantifiers % 7.67/1.82 Prover 7: Constructing countermodel ... % 7.67/1.83 Prover 8: Constructing countermodel ... % 7.67/1.86 Prover 0: proved (1228ms) % 7.67/1.86 % 7.67/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.67/1.87 % 7.67/1.87 Prover 2: stopped % 7.67/1.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.67/1.87 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 7.67/1.87 Prover 5: stopped % 7.67/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.67/1.88 Prover 10: Preprocessing ... % 7.67/1.88 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 7.67/1.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.21/1.88 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 8.21/1.88 Prover 11: Preprocessing ... % 8.21/1.89 Prover 13: Preprocessing ... % 8.21/1.91 Prover 9: Constructing countermodel ... % 8.21/1.92 Prover 9: stopped % 8.21/1.93 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.21/1.94 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation % 8.21/1.94 Prover 16: Preprocessing ... % 8.21/1.95 Prover 10: Warning: ignoring some quantifiers % 8.21/1.95 Prover 10: Constructing countermodel ... % 8.21/1.96 Prover 13: Warning: ignoring some quantifiers % 8.21/1.96 Prover 8: gave up % 8.21/1.96 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 8.21/1.97 Prover 13: Constructing countermodel ... % 8.21/2.01 Prover 19: Warning: Problem contains reals, using incomplete axiomatisation % 8.21/2.01 Prover 16: Warning: ignoring some quantifiers % 8.21/2.01 Prover 19: Preprocessing ... % 8.21/2.01 Prover 16: Constructing countermodel ... % 9.44/2.06 Prover 10: gave up % 9.44/2.07 Prover 11: Constructing countermodel ... % 9.44/2.08 Prover 4: Found proof (size 52) % 9.44/2.08 Prover 4: proved (1433ms) % 9.44/2.08 Prover 7: stopped % 9.44/2.08 Prover 13: stopped % 9.44/2.08 Prover 11: stopped % 9.44/2.08 Prover 16: stopped % 9.66/2.10 Prover 19: Warning: ignoring some quantifiers % 9.66/2.10 Prover 19: Constructing countermodel ... % 9.66/2.10 Prover 19: stopped % 9.66/2.10 % 9.66/2.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.66/2.10 % 9.66/2.12 % SZS output start Proof for theBenchmark % 9.66/2.12 Assumptions after simplification: % 9.66/2.12 --------------------------------- % 9.66/2.12 % 9.66/2.12 (real_difference_problem_13) % 9.93/2.15 ? [v0: $real] : ? [v1: $real] : ( ~ (v1 = v0) & real_$difference(v0, v1) = % 9.93/2.15 real_0) % 9.93/2.15 % 9.93/2.15 (input) % 9.93/2.17 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_0) & ~ % 9.93/2.17 (real_very_small = real_0) & real_$is_int(real_0) = 0 & real_$is_rat(real_0) = % 9.93/2.17 0 & real_$floor(real_0) = real_0 & real_$ceiling(real_0) = real_0 & % 9.93/2.17 real_$truncate(real_0) = real_0 & real_$round(real_0) = real_0 & % 9.93/2.17 real_$to_int(real_0) = 0 & real_$to_rat(real_0) = rat_0 & % 9.93/2.17 real_$to_real(real_0) = real_0 & int_$to_real(0) = real_0 & % 9.93/2.17 real_$product(real_0, real_0) = real_0 & real_$uminus(real_0) = real_0 & % 9.93/2.17 real_$sum(real_0, real_0) = real_0 & real_$greatereq(real_very_small, % 9.93/2.17 real_very_large) = 1 & real_$greatereq(real_0, real_0) = 0 & % 9.93/2.17 real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_0, % 9.93/2.17 real_0) = 0 & real_$greater(real_very_large, real_0) = 0 & % 9.93/2.17 real_$greater(real_very_small, real_very_large) = 1 & real_$greater(real_0, % 9.93/2.17 real_very_small) = 0 & real_$greater(real_0, real_0) = 1 & % 9.93/2.17 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, % 9.93/2.17 real_0) = 0 & real_$less(real_0, real_very_large) = 0 & real_$less(real_0, % 9.93/2.17 real_0) = 1 & real_$difference(real_0, real_0) = real_0 & ! [v0: $real] : % 9.93/2.17 ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ % 9.93/2.17 (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] : % 9.93/2.17 (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! % 9.93/2.17 [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ % 9.93/2.17 (real_$sum(v2, v3) = v4) | ~ (real_$sum(v1, v0) = v3) | ? [v5: $real] : % 9.93/2.17 (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) = v5)) & ! [v0: $real] : ! % 9.93/2.17 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, % 9.93/2.17 v1) = 0) | ~ (real_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) % 9.93/2.17 & real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.93/2.17 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~ % 9.93/2.17 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0) % 9.93/2.17 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : % 9.93/2.17 (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? % 9.93/2.17 [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! % 9.93/2.17 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, % 9.93/2.17 v0) = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & % 9.93/2.17 real_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.93/2.17 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v1) = 0) | ~ % 9.93/2.17 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1, % 9.93/2.17 v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: % 9.93/2.17 int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~ (real_$less(v1, v0) = 0) % 9.93/2.17 | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] % 9.93/2.17 : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) = % 9.93/2.17 v2) | ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, v0) = v3) & ! % 9.93/2.17 [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 9.93/2.17 (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, % 9.93/2.17 v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | % 9.93/2.17 ~ (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 9.93/2.17 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.93/2.17 int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = % 9.93/2.17 0) & real_$greatereq(v0, v1) = v3)) & ! [v0: $real] : ! [v1: $real] : % 9.93/2.17 ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ % 9.93/2.17 (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : % 9.93/2.17 ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ % 9.93/2.17 (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : % 9.93/2.17 ! [v2: int] : (v2 = 0 | ~ (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 % 9.93/2.17 = 0) & real_$greater(v0, v1) = v3)) & ! [v0: $real] : ! [v1: $real] : % 9.93/2.17 ! [v2: $real] : (v0 = real_0 | ~ (real_$product(v1, v0) = v2) | % 9.93/2.17 real_$quotient(v2, v0) = v1) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.93/2.17 $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) & ! % 9.93/2.17 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = % 9.93/2.17 v2) | real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! % 9.93/2.17 [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, v1) = v2) & ! [v0: % 9.93/2.17 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | % 9.93/2.17 real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : % 9.93/2.17 ( ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$lesseq(v1, v0) = 0) | % 9.93/2.17 real_$lesseq(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 9.93/2.17 : ( ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v1, v0) = 0) | % 9.93/2.17 real_$less(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : % 9.93/2.17 ( ~ (real_$lesseq(v1, v0) = 0) | ~ (real_$less(v2, v1) = 0) | real_$less(v2, % 9.93/2.17 v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 9.93/2.17 (real_$difference(v1, v0) = v2) | ? [v3: $real] : (real_$uminus(v0) = v3 & % 9.93/2.17 real_$sum(v1, v3) = v2)) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ % 9.93/2.17 (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | % 9.93/2.17 ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) & ! [v0: $real] : % 9.93/2.17 ! [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0, v0) = v1)) & ! [v0: $real] : ! % 9.93/2.17 [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: % 9.93/2.17 $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$sum(v0, v1) = % 9.93/2.17 real_0) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) = % 9.93/2.17 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 9.93/2.17 (real_$lesseq(v1, v0) = 0) | real_$greatereq(v0, v1) = 0) & ! [v0: $real] : % 9.93/2.17 ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & % 9.93/2.17 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | % 9.93/2.17 real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 9.93/2.17 (real_$less(v1, v0) = 0) | real_$greater(v0, v1) = 0) & ! [v0: $real] : ! % 9.93/2.17 [v1: MultipleValueBool] : ( ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0) % 9.93/2.17 = 0) & ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0)) % 9.93/2.17 % 9.93/2.17 (function-axioms) % 9.93/2.18 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 9.93/2.18 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 9.93/2.18 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 9.93/2.18 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: % 9.93/2.18 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 9.93/2.18 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: % 9.93/2.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 9.93/2.18 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~ % 9.93/2.18 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.93/2.18 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 9.93/2.18 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0: % 9.93/2.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 9.93/2.18 $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, % 9.93/2.18 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 9.93/2.18 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ % 9.93/2.18 (real_$less(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.93/2.18 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$difference(v3, v2) = v1) | ~ % 9.93/2.18 (real_$difference(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.93/2.18 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1) % 9.93/2.18 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.93/2.18 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) % 9.93/2.18 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.93/2.18 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & % 9.93/2.18 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 9.93/2.18 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] : % 9.93/2.18 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ % 9.93/2.18 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.93/2.18 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) & % 9.93/2.18 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2) % 9.93/2.18 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 9.93/2.18 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = % 9.93/2.18 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 9.93/2.18 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] : % 9.93/2.18 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ % 9.93/2.18 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 9.93/2.18 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) % 9.93/2.18 % 9.93/2.18 Those formulas are unsatisfiable: % 9.93/2.18 --------------------------------- % 9.93/2.18 % 9.93/2.18 Begin of proof % 9.93/2.18 | % 9.93/2.18 | ALPHA: (function-axioms) implies: % 9.93/2.19 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 % 9.93/2.19 | = v0 | ~ (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) % 9.93/2.19 | % 9.93/2.19 | ALPHA: (input) implies: % 9.93/2.19 | (2) real_$sum(real_0, real_0) = real_0 % 9.93/2.19 | (3) ! [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | % 9.93/2.19 | real_$sum(v0, v1) = real_0) % 9.93/2.19 | (4) ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) % 9.93/2.19 | = v1)) % 9.93/2.19 | (5) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 9.93/2.19 | (real_$difference(v1, v0) = v2) | ? [v3: $real] : (real_$uminus(v0) % 9.93/2.19 | = v3 & real_$sum(v1, v3) = v2)) % 9.93/2.19 | (6) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v1, % 9.93/2.19 | v0) = v2) | real_$sum(v0, v1) = v2) % 9.93/2.19 | (7) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! % 9.93/2.19 | [v4: $real] : ( ~ (real_$sum(v2, v3) = v4) | ~ (real_$sum(v1, v0) = % 9.93/2.19 | v3) | ? [v5: $real] : (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) % 9.93/2.19 | = v5)) % 9.93/2.19 | (8) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! % 9.93/2.19 | [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = % 9.93/2.19 | v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) % 9.93/2.19 | = v5)) % 9.93/2.19 | % 9.93/2.19 | DELTA: instantiating (real_difference_problem_13) with fresh symbols all_5_0, % 9.93/2.19 | all_5_1 gives: % 9.93/2.19 | (9) ~ (all_5_0 = all_5_1) & real_$difference(all_5_1, all_5_0) = real_0 % 9.93/2.19 | % 9.93/2.19 | ALPHA: (9) implies: % 9.93/2.19 | (10) ~ (all_5_0 = all_5_1) % 9.93/2.19 | (11) real_$difference(all_5_1, all_5_0) = real_0 % 9.93/2.19 | % 9.93/2.19 | GROUND_INST: instantiating (5) with all_5_0, all_5_1, real_0, simplifying with % 9.93/2.19 | (11) gives: % 9.93/2.19 | (12) ? [v0: $real] : (real_$uminus(all_5_0) = v0 & real_$sum(all_5_1, v0) % 9.93/2.19 | = real_0) % 9.93/2.19 | % 9.93/2.19 | DELTA: instantiating (12) with fresh symbol all_17_0 gives: % 9.93/2.19 | (13) real_$uminus(all_5_0) = all_17_0 & real_$sum(all_5_1, all_17_0) = % 9.93/2.19 | real_0 % 9.93/2.19 | % 9.93/2.19 | ALPHA: (13) implies: % 9.93/2.19 | (14) real_$sum(all_5_1, all_17_0) = real_0 % 9.93/2.20 | (15) real_$uminus(all_5_0) = all_17_0 % 9.93/2.20 | % 9.93/2.20 | GROUND_INST: instantiating (8) with real_0, all_17_0, all_5_1, real_0, real_0, % 9.93/2.20 | simplifying with (2), (14) gives: % 9.93/2.20 | (16) ? [v0: $real] : (real_$sum(all_17_0, real_0) = v0 & % 9.93/2.20 | real_$sum(all_5_1, v0) = real_0) % 9.93/2.20 | % 9.93/2.20 | GROUND_INST: instantiating (7) with all_17_0, all_5_1, real_0, real_0, real_0, % 9.93/2.20 | simplifying with (2), (14) gives: % 9.93/2.20 | (17) ? [v0: $real] : (real_$sum(v0, all_17_0) = real_0 & real_$sum(real_0, % 9.93/2.20 | all_5_1) = v0) % 9.93/2.20 | % 9.93/2.20 | GROUND_INST: instantiating (6) with all_17_0, all_5_1, real_0, simplifying % 9.93/2.20 | with (14) gives: % 9.93/2.20 | (18) real_$sum(all_17_0, all_5_1) = real_0 % 9.93/2.20 | % 9.93/2.20 | GROUND_INST: instantiating (3) with all_5_0, all_17_0, simplifying with (15) % 9.93/2.20 | gives: % 9.93/2.20 | (19) real_$sum(all_5_0, all_17_0) = real_0 % 9.93/2.20 | % 9.93/2.20 | DELTA: instantiating (17) with fresh symbol all_29_0 gives: % 9.93/2.20 | (20) real_$sum(all_29_0, all_17_0) = real_0 & real_$sum(real_0, all_5_1) = % 9.93/2.20 | all_29_0 % 9.93/2.20 | % 9.93/2.20 | ALPHA: (20) implies: % 9.93/2.20 | (21) real_$sum(real_0, all_5_1) = all_29_0 % 9.93/2.20 | (22) real_$sum(all_29_0, all_17_0) = real_0 % 9.93/2.20 | % 9.93/2.20 | DELTA: instantiating (16) with fresh symbol all_31_0 gives: % 9.93/2.20 | (23) real_$sum(all_17_0, real_0) = all_31_0 & real_$sum(all_5_1, all_31_0) % 9.93/2.20 | = real_0 % 9.93/2.20 | % 9.93/2.20 | ALPHA: (23) implies: % 9.93/2.20 | (24) real_$sum(all_5_1, all_31_0) = real_0 % 9.93/2.20 | (25) real_$sum(all_17_0, real_0) = all_31_0 % 9.93/2.20 | % 9.93/2.20 | GROUND_INST: instantiating (4) with all_17_0, all_31_0, simplifying with (25) % 9.93/2.20 | gives: % 9.93/2.20 | (26) all_31_0 = all_17_0 % 9.93/2.20 | % 9.93/2.20 | REDUCE: (25), (26) imply: % 9.93/2.20 | (27) real_$sum(all_17_0, real_0) = all_17_0 % 9.93/2.20 | % 9.93/2.20 | GROUND_INST: instantiating (8) with all_5_1, all_17_0, all_5_1, real_0, % 9.93/2.20 | all_29_0, simplifying with (14), (21) gives: % 9.93/2.20 | (28) ? [v0: $real] : (real_$sum(all_17_0, all_5_1) = v0 & % 9.93/2.20 | real_$sum(all_5_1, v0) = all_29_0) % 9.93/2.20 | % 9.93/2.20 | GROUND_INST: instantiating (6) with all_5_1, real_0, all_29_0, simplifying % 9.93/2.20 | with (21) gives: % 9.93/2.20 | (29) real_$sum(all_5_1, real_0) = all_29_0 % 9.93/2.20 | % 9.93/2.20 | GROUND_INST: instantiating (8) with all_5_1, all_17_0, all_5_0, real_0, % 9.93/2.20 | all_29_0, simplifying with (19), (21) gives: % 9.93/2.20 | (30) ? [v0: $real] : (real_$sum(all_17_0, all_5_1) = v0 & % 9.93/2.20 | real_$sum(all_5_0, v0) = all_29_0) % 9.93/2.20 | % 9.93/2.20 | GROUND_INST: instantiating (7) with all_17_0, all_5_1, all_17_0, real_0, % 9.93/2.20 | all_17_0, simplifying with (14), (27) gives: % 9.93/2.20 | (31) ? [v0: $real] : (real_$sum(v0, all_17_0) = all_17_0 & % 9.93/2.20 | real_$sum(all_17_0, all_5_1) = v0) % 9.93/2.20 | % 9.93/2.20 | GROUND_INST: instantiating (8) with real_0, all_5_1, all_17_0, real_0, real_0, % 9.93/2.20 | simplifying with (2), (18) gives: % 9.93/2.21 | (32) ? [v0: $real] : (real_$sum(all_17_0, v0) = real_0 & % 9.93/2.21 | real_$sum(all_5_1, real_0) = v0) % 9.93/2.21 | % 9.93/2.21 | GROUND_INST: instantiating (8) with all_5_1, all_17_0, all_29_0, real_0, % 9.93/2.21 | all_29_0, simplifying with (21), (22) gives: % 9.93/2.21 | (33) ? [v0: $real] : (real_$sum(all_29_0, v0) = all_29_0 & % 9.93/2.21 | real_$sum(all_17_0, all_5_1) = v0) % 9.93/2.21 | % 9.93/2.21 | DELTA: instantiating (32) with fresh symbol all_60_0 gives: % 9.93/2.21 | (34) real_$sum(all_17_0, all_60_0) = real_0 & real_$sum(all_5_1, real_0) = % 9.93/2.21 | all_60_0 % 9.93/2.21 | % 9.93/2.21 | ALPHA: (34) implies: % 9.93/2.21 | (35) real_$sum(all_5_1, real_0) = all_60_0 % 9.93/2.21 | % 9.93/2.21 | DELTA: instantiating (30) with fresh symbol all_62_0 gives: % 9.93/2.21 | (36) real_$sum(all_17_0, all_5_1) = all_62_0 & real_$sum(all_5_0, all_62_0) % 9.93/2.21 | = all_29_0 % 9.93/2.21 | % 9.93/2.21 | ALPHA: (36) implies: % 9.93/2.21 | (37) real_$sum(all_5_0, all_62_0) = all_29_0 % 10.26/2.21 | (38) real_$sum(all_17_0, all_5_1) = all_62_0 % 10.26/2.21 | % 10.26/2.21 | DELTA: instantiating (31) with fresh symbol all_70_0 gives: % 10.26/2.21 | (39) real_$sum(all_70_0, all_17_0) = all_17_0 & real_$sum(all_17_0, % 10.26/2.21 | all_5_1) = all_70_0 % 10.26/2.21 | % 10.26/2.21 | ALPHA: (39) implies: % 10.26/2.21 | (40) real_$sum(all_17_0, all_5_1) = all_70_0 % 10.26/2.21 | % 10.26/2.21 | DELTA: instantiating (33) with fresh symbol all_72_0 gives: % 10.26/2.21 | (41) real_$sum(all_29_0, all_72_0) = all_29_0 & real_$sum(all_17_0, % 10.26/2.21 | all_5_1) = all_72_0 % 10.26/2.21 | % 10.26/2.21 | ALPHA: (41) implies: % 10.26/2.21 | (42) real_$sum(all_17_0, all_5_1) = all_72_0 % 10.26/2.21 | % 10.26/2.21 | DELTA: instantiating (28) with fresh symbol all_74_0 gives: % 10.26/2.21 | (43) real_$sum(all_17_0, all_5_1) = all_74_0 & real_$sum(all_5_1, all_74_0) % 10.26/2.21 | = all_29_0 % 10.26/2.21 | % 10.26/2.21 | ALPHA: (43) implies: % 10.26/2.21 | (44) real_$sum(all_17_0, all_5_1) = all_74_0 % 10.26/2.21 | % 10.26/2.21 | GROUND_INST: instantiating (1) with all_29_0, all_60_0, real_0, all_5_1, % 10.26/2.21 | simplifying with (29), (35) gives: % 10.26/2.21 | (45) all_60_0 = all_29_0 % 10.26/2.21 | % 10.26/2.21 | GROUND_INST: instantiating (4) with all_5_1, all_60_0, simplifying with (35) % 10.26/2.21 | gives: % 10.26/2.21 | (46) all_60_0 = all_5_1 % 10.26/2.21 | % 10.26/2.21 | GROUND_INST: instantiating (1) with all_62_0, all_70_0, all_5_1, all_17_0, % 10.26/2.21 | simplifying with (38), (40) gives: % 10.26/2.21 | (47) all_70_0 = all_62_0 % 10.26/2.21 | % 10.26/2.21 | GROUND_INST: instantiating (1) with all_70_0, all_72_0, all_5_1, all_17_0, % 10.26/2.21 | simplifying with (40), (42) gives: % 10.26/2.21 | (48) all_72_0 = all_70_0 % 10.26/2.21 | % 10.26/2.21 | GROUND_INST: instantiating (1) with real_0, all_74_0, all_5_1, all_17_0, % 10.26/2.21 | simplifying with (18), (44) gives: % 10.26/2.21 | (49) all_74_0 = real_0 % 10.26/2.21 | % 10.26/2.21 | GROUND_INST: instantiating (1) with all_72_0, all_74_0, all_5_1, all_17_0, % 10.26/2.21 | simplifying with (42), (44) gives: % 10.26/2.21 | (50) all_74_0 = all_72_0 % 10.26/2.21 | % 10.26/2.21 | COMBINE_EQS: (49), (50) imply: % 10.26/2.21 | (51) all_72_0 = real_0 % 10.26/2.21 | % 10.26/2.21 | SIMP: (51) implies: % 10.26/2.21 | (52) all_72_0 = real_0 % 10.26/2.21 | % 10.26/2.21 | COMBINE_EQS: (48), (52) imply: % 10.26/2.21 | (53) all_70_0 = real_0 % 10.26/2.21 | % 10.26/2.21 | SIMP: (53) implies: % 10.26/2.21 | (54) all_70_0 = real_0 % 10.26/2.21 | % 10.26/2.21 | COMBINE_EQS: (47), (54) imply: % 10.26/2.21 | (55) all_62_0 = real_0 % 10.26/2.21 | % 10.26/2.21 | COMBINE_EQS: (45), (46) imply: % 10.26/2.21 | (56) all_29_0 = all_5_1 % 10.26/2.22 | % 10.26/2.22 | SIMP: (56) implies: % 10.26/2.22 | (57) all_29_0 = all_5_1 % 10.26/2.22 | % 10.26/2.22 | REDUCE: (37), (55), (57) imply: % 10.26/2.22 | (58) real_$sum(all_5_0, real_0) = all_5_1 % 10.26/2.22 | % 10.26/2.22 | GROUND_INST: instantiating (4) with all_5_0, all_5_1, simplifying with (58) % 10.26/2.22 | gives: % 10.26/2.22 | (59) all_5_0 = all_5_1 % 10.26/2.22 | % 10.26/2.22 | REDUCE: (10), (59) imply: % 10.26/2.22 | (60) $false % 10.26/2.22 | % 10.26/2.22 | CLOSE: (60) is inconsistent. % 10.26/2.22 | % 10.26/2.22 End of proof % 10.26/2.22 % SZS output end Proof for theBenchmark % 10.26/2.22 % 10.26/2.22 1600ms %------------------------------------------------------------------------------