%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM913_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 : n015.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 11:50:41 EDT 2023 % Result : Theorem 6.60s 1.61s % Output : Proof 8.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : NUM913_1 : TPTP v8.1.2. Released v5.0.0. % 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.35 % Computer : n015.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Aug 25 14:40:22 EDT 2023 % 0.15/0.35 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.61/0.89 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.61/0.89 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.61/0.89 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.61/0.89 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.61/0.89 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 1.61/0.89 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.61/0.89 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 2.07/0.98 Prover 4: Preprocessing ... % 2.07/0.98 Prover 1: Preprocessing ... % 2.47/1.02 Prover 0: Preprocessing ... % 2.47/1.02 Prover 3: Preprocessing ... % 2.47/1.02 Prover 5: Preprocessing ... % 2.47/1.02 Prover 6: Preprocessing ... % 2.47/1.02 Prover 2: Preprocessing ... % 4.27/1.37 Prover 1: Constructing countermodel ... % 4.27/1.39 Prover 5: Proving ... % 4.27/1.39 Prover 6: Constructing countermodel ... % 4.27/1.43 Prover 3: Constructing countermodel ... % 4.27/1.45 Prover 2: Proving ... % 5.66/1.46 Prover 4: Constructing countermodel ... % 6.02/1.50 Prover 0: Proving ... % 6.60/1.61 Prover 3: proved (979ms) % 6.60/1.61 % 6.60/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.60/1.61 % 6.60/1.61 Prover 6: stopped % 6.60/1.61 Prover 0: stopped % 6.60/1.61 Prover 5: stopped % 6.60/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.60/1.61 Prover 2: stopped % 6.60/1.62 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 6.60/1.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.60/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.60/1.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.60/1.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.60/1.62 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 6.60/1.62 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 6.60/1.62 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 6.60/1.63 Prover 8: Preprocessing ... % 6.60/1.63 Prover 10: Preprocessing ... % 6.60/1.63 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 6.60/1.63 Prover 13: Preprocessing ... % 6.60/1.63 Prover 7: Preprocessing ... % 6.60/1.64 Prover 11: Preprocessing ... % 7.27/1.69 Prover 1: Found proof (size 30) % 7.27/1.69 Prover 1: proved (1068ms) % 7.36/1.69 Prover 4: stopped % 7.36/1.70 Prover 11: stopped % 7.51/1.71 Prover 10: Warning: ignoring some quantifiers % 7.56/1.72 Prover 10: Constructing countermodel ... % 7.56/1.72 Prover 10: stopped % 7.56/1.72 Prover 7: Warning: ignoring some quantifiers % 7.56/1.73 Prover 8: Warning: ignoring some quantifiers % 7.56/1.73 Prover 7: Constructing countermodel ... % 7.56/1.73 Prover 8: Constructing countermodel ... % 7.56/1.74 Prover 13: Warning: ignoring some quantifiers % 7.56/1.74 Prover 7: stopped % 7.56/1.74 Prover 13: Constructing countermodel ... % 7.56/1.74 Prover 8: stopped % 7.56/1.75 Prover 13: stopped % 7.56/1.75 % 7.56/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.56/1.75 % 7.56/1.75 % SZS output start Proof for theBenchmark % 7.56/1.75 Assumptions after simplification: % 7.56/1.75 --------------------------------- % 7.56/1.75 % 7.56/1.75 (real_combined_problem_1) % 7.56/1.78 ? [v0: $real] : ? [v1: $real] : ? [v2: any] : ? [v3: any] : % 7.56/1.78 (real_$lesseq(v0, v1) = v2 & real_$less(v0, v1) = v3 & ((v2 = 0 & ~ (v3 = 0) % 7.56/1.78 & ~ (v1 = v0)) | ( ~ (v2 = 0) & (v3 = 0 | v1 = v0)))) % 7.56/1.78 % 7.56/1.78 (input) % 7.56/1.80 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_0) & ~ % 7.56/1.80 (real_very_small = real_0) & real_$is_int(real_0) = 0 & real_$is_rat(real_0) = % 7.56/1.80 0 & real_$floor(real_0) = real_0 & real_$ceiling(real_0) = real_0 & % 8.04/1.80 real_$truncate(real_0) = real_0 & real_$round(real_0) = real_0 & % 8.04/1.80 real_$to_int(real_0) = 0 & real_$to_rat(real_0) = rat_0 & % 8.04/1.80 real_$to_real(real_0) = real_0 & int_$to_real(0) = real_0 & % 8.04/1.80 real_$product(real_0, real_0) = real_0 & real_$difference(real_0, real_0) = % 8.04/1.80 real_0 & real_$uminus(real_0) = real_0 & real_$sum(real_0, real_0) = real_0 & % 8.04/1.80 real_$greatereq(real_very_small, real_very_large) = 1 & % 8.04/1.80 real_$greatereq(real_0, real_0) = 0 & real_$greater(real_very_large, real_0) = % 8.04/1.80 0 & real_$greater(real_very_small, real_very_large) = 1 & % 8.04/1.80 real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0, real_0) = 1 % 8.04/1.80 & real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_0, % 8.04/1.80 real_0) = 0 & real_$less(real_very_small, real_very_large) = 0 & % 8.04/1.80 real_$less(real_very_small, real_0) = 0 & real_$less(real_0, real_very_large) % 8.04/1.80 = 0 & real_$less(real_0, real_0) = 1 & ! [v0: $real] : ! [v1: $real] : ! % 8.04/1.80 [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | % 8.04/1.81 ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & % 8.04/1.81 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 8.04/1.81 $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~ (real_$quotient(v2, % 8.04/1.81 v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: $real] : ! [v1: % 8.04/1.81 $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v0) % 8.04/1.81 = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & % 8.04/1.81 real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 8.04/1.81 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0) = 0) | ~ % 8.04/1.81 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1) % 8.04/1.81 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] % 8.04/1.81 : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) | % 8.04/1.81 real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 8.04/1.81 $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) = % 8.04/1.81 v2)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ % 8.04/1.81 (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 8.04/1.81 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 8.04/1.81 int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = % 8.04/1.81 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! % 8.04/1.81 [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3: % 8.04/1.81 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $real] : ! % 8.04/1.81 [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = v2) | % 8.04/1.81 real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 8.04/1.81 $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: % 8.04/1.81 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | % 8.04/1.81 ~ (real_$less(v1, v0) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : ! % 8.04/1.81 [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : % 8.04/1.81 ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) % 8.04/1.81 = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | % 8.04/1.81 real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 8.04/1.81 (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] : % 8.04/1.81 ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & % 8.04/1.81 ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0)) % 8.04/1.81 % 8.04/1.81 (function-axioms) % 8.04/1.82 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 8.04/1.82 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 8.04/1.82 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 8.04/1.82 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: % 8.04/1.82 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 8.04/1.82 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! % 8.04/1.82 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 8.04/1.82 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: % 8.04/1.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 8.04/1.82 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~ % 8.04/1.82 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.04/1.82 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 8.04/1.82 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0: % 8.04/1.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 8.04/1.82 $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, % 8.04/1.82 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 8.04/1.82 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ % 8.04/1.82 (real_$less(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.04/1.82 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1) % 8.04/1.82 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.04/1.82 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) % 8.04/1.82 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 8.04/1.82 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & % 8.04/1.82 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 8.04/1.82 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] : % 8.04/1.82 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ % 8.04/1.82 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 8.04/1.82 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) & % 8.04/1.82 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2) % 8.04/1.82 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 8.04/1.82 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = % 8.04/1.82 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 8.04/1.82 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] : % 8.04/1.82 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ % 8.04/1.82 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 8.04/1.82 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) % 8.04/1.82 % 8.04/1.82 Those formulas are unsatisfiable: % 8.04/1.82 --------------------------------- % 8.04/1.82 % 8.04/1.82 Begin of proof % 8.04/1.82 | % 8.04/1.82 | ALPHA: (function-axioms) implies: % 8.04/1.82 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.04/1.82 | $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | % 8.04/1.82 | ~ (real_$less(v3, v2) = v0)) % 8.04/1.82 | % 8.04/1.82 | ALPHA: (input) implies: % 8.04/1.82 | (2) ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = % 8.04/1.82 | 0) | real_$less(v1, v0) = 0) % 8.04/1.82 | (3) ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ % 8.04/1.82 | (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3: int] : ( ~ (v3 % 8.04/1.82 | = 0) & real_$less(v1, v0) = v3))) % 8.04/1.82 | % 8.04/1.82 | DELTA: instantiating (real_combined_problem_1) with fresh symbols all_5_0, % 8.04/1.82 | all_5_1, all_5_2, all_5_3 gives: % 8.04/1.82 | (4) real_$lesseq(all_5_3, all_5_2) = all_5_1 & real_$less(all_5_3, all_5_2) % 8.04/1.82 | = all_5_0 & ((all_5_1 = 0 & ~ (all_5_0 = 0) & ~ (all_5_2 = all_5_3)) % 8.04/1.82 | | ( ~ (all_5_1 = 0) & (all_5_0 = 0 | all_5_2 = all_5_3))) % 8.04/1.82 | % 8.04/1.82 | ALPHA: (4) implies: % 8.04/1.83 | (5) real_$less(all_5_3, all_5_2) = all_5_0 % 8.04/1.83 | (6) real_$lesseq(all_5_3, all_5_2) = all_5_1 % 8.04/1.83 | (7) (all_5_1 = 0 & ~ (all_5_0 = 0) & ~ (all_5_2 = all_5_3)) | ( ~ % 8.04/1.83 | (all_5_1 = 0) & (all_5_0 = 0 | all_5_2 = all_5_3)) % 8.04/1.83 | % 8.04/1.83 | GROUND_INST: instantiating (3) with all_5_2, all_5_3, all_5_1, simplifying % 8.04/1.83 | with (6) gives: % 8.04/1.83 | (8) all_5_1 = 0 | ( ~ (all_5_2 = all_5_3) & ? [v0: int] : ( ~ (v0 = 0) & % 8.04/1.83 | real_$less(all_5_3, all_5_2) = v0)) % 8.04/1.83 | % 8.04/1.83 | BETA: splitting (7) gives: % 8.04/1.83 | % 8.04/1.83 | Case 1: % 8.04/1.83 | | % 8.04/1.83 | | (9) all_5_1 = 0 & ~ (all_5_0 = 0) & ~ (all_5_2 = all_5_3) % 8.04/1.83 | | % 8.04/1.83 | | ALPHA: (9) implies: % 8.04/1.83 | | (10) all_5_1 = 0 % 8.04/1.83 | | (11) ~ (all_5_2 = all_5_3) % 8.04/1.83 | | (12) ~ (all_5_0 = 0) % 8.04/1.83 | | % 8.04/1.83 | | REDUCE: (6), (10) imply: % 8.04/1.83 | | (13) real_$lesseq(all_5_3, all_5_2) = 0 % 8.04/1.83 | | % 8.04/1.83 | | GROUND_INST: instantiating (2) with all_5_2, all_5_3, simplifying with (13) % 8.04/1.83 | | gives: % 8.04/1.83 | | (14) all_5_2 = all_5_3 | real_$less(all_5_3, all_5_2) = 0 % 8.04/1.83 | | % 8.04/1.83 | | BETA: splitting (14) gives: % 8.04/1.83 | | % 8.04/1.83 | | Case 1: % 8.04/1.83 | | | % 8.04/1.83 | | | (15) real_$less(all_5_3, all_5_2) = 0 % 8.04/1.83 | | | % 8.04/1.83 | | | GROUND_INST: instantiating (1) with all_5_0, 0, all_5_2, all_5_3, % 8.04/1.83 | | | simplifying with (5), (15) gives: % 8.04/1.83 | | | (16) all_5_0 = 0 % 8.04/1.83 | | | % 8.04/1.83 | | | REDUCE: (12), (16) imply: % 8.04/1.83 | | | (17) $false % 8.04/1.83 | | | % 8.04/1.83 | | | CLOSE: (17) is inconsistent. % 8.04/1.83 | | | % 8.04/1.83 | | Case 2: % 8.04/1.83 | | | % 8.04/1.83 | | | (18) all_5_2 = all_5_3 % 8.04/1.83 | | | % 8.04/1.83 | | | REDUCE: (11), (18) imply: % 8.04/1.83 | | | (19) $false % 8.04/1.83 | | | % 8.04/1.83 | | | CLOSE: (19) is inconsistent. % 8.04/1.83 | | | % 8.04/1.83 | | End of split % 8.04/1.83 | | % 8.04/1.83 | Case 2: % 8.04/1.83 | | % 8.04/1.83 | | (20) ~ (all_5_1 = 0) & (all_5_0 = 0 | all_5_2 = all_5_3) % 8.04/1.83 | | % 8.04/1.83 | | ALPHA: (20) implies: % 8.04/1.83 | | (21) ~ (all_5_1 = 0) % 8.04/1.83 | | (22) all_5_0 = 0 | all_5_2 = all_5_3 % 8.04/1.83 | | % 8.04/1.83 | | BETA: splitting (8) gives: % 8.04/1.83 | | % 8.04/1.83 | | Case 1: % 8.04/1.83 | | | % 8.04/1.83 | | | (23) all_5_1 = 0 % 8.04/1.83 | | | % 8.04/1.83 | | | REDUCE: (21), (23) imply: % 8.04/1.83 | | | (24) $false % 8.04/1.83 | | | % 8.04/1.83 | | | CLOSE: (24) is inconsistent. % 8.04/1.83 | | | % 8.04/1.83 | | Case 2: % 8.04/1.83 | | | % 8.04/1.83 | | | (25) ~ (all_5_2 = all_5_3) & ? [v0: int] : ( ~ (v0 = 0) & % 8.04/1.83 | | | real_$less(all_5_3, all_5_2) = v0) % 8.04/1.83 | | | % 8.04/1.83 | | | ALPHA: (25) implies: % 8.04/1.83 | | | (26) ~ (all_5_2 = all_5_3) % 8.04/1.84 | | | (27) ? [v0: int] : ( ~ (v0 = 0) & real_$less(all_5_3, all_5_2) = v0) % 8.04/1.84 | | | % 8.04/1.84 | | | DELTA: instantiating (27) with fresh symbol all_27_0 gives: % 8.04/1.84 | | | (28) ~ (all_27_0 = 0) & real_$less(all_5_3, all_5_2) = all_27_0 % 8.04/1.84 | | | % 8.04/1.84 | | | ALPHA: (28) implies: % 8.04/1.84 | | | (29) ~ (all_27_0 = 0) % 8.04/1.84 | | | (30) real_$less(all_5_3, all_5_2) = all_27_0 % 8.04/1.84 | | | % 8.04/1.84 | | | BETA: splitting (22) gives: % 8.04/1.84 | | | % 8.04/1.84 | | | Case 1: % 8.04/1.84 | | | | % 8.04/1.84 | | | | (31) all_5_0 = 0 % 8.04/1.84 | | | | % 8.04/1.84 | | | | REDUCE: (5), (31) imply: % 8.04/1.84 | | | | (32) real_$less(all_5_3, all_5_2) = 0 % 8.04/1.84 | | | | % 8.04/1.84 | | | | GROUND_INST: instantiating (1) with 0, all_27_0, all_5_2, all_5_3, % 8.04/1.84 | | | | simplifying with (30), (32) gives: % 8.04/1.84 | | | | (33) all_27_0 = 0 % 8.04/1.84 | | | | % 8.04/1.84 | | | | REDUCE: (29), (33) imply: % 8.04/1.84 | | | | (34) $false % 8.04/1.84 | | | | % 8.04/1.84 | | | | CLOSE: (34) is inconsistent. % 8.04/1.84 | | | | % 8.04/1.84 | | | Case 2: % 8.04/1.84 | | | | % 8.04/1.84 | | | | (35) all_5_2 = all_5_3 % 8.04/1.84 | | | | % 8.04/1.84 | | | | REDUCE: (26), (35) imply: % 8.04/1.84 | | | | (36) $false % 8.04/1.84 | | | | % 8.04/1.84 | | | | CLOSE: (36) is inconsistent. % 8.04/1.84 | | | | % 8.04/1.84 | | | End of split % 8.04/1.84 | | | % 8.04/1.84 | | End of split % 8.04/1.84 | | % 8.04/1.84 | End of split % 8.04/1.84 | % 8.04/1.84 End of proof % 8.04/1.84 % SZS output end Proof for theBenchmark % 8.04/1.84 % 8.04/1.84 1235ms %------------------------------------------------------------------------------