%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWW579_2 : TPTP v8.1.2. Released v6.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n006.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 : Fri Sep 1 00:50:47 EDT 2023 % Result : Theorem 9.01s 1.94s % Output : Proof 13.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWW579_2 : TPTP v8.1.2. Released v6.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n006.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sun Aug 27 21:05:22 EDT 2023 % 0.19/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.90/0.97 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.90/0.97 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.90/0.98 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.90/0.98 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.90/0.99 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.90/0.99 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 1.90/0.99 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 2.78/1.13 Prover 1: Preprocessing ... % 2.78/1.13 Prover 0: Preprocessing ... % 2.78/1.13 Prover 6: Preprocessing ... % 2.78/1.13 Prover 5: Preprocessing ... % 2.78/1.13 Prover 3: Preprocessing ... % 2.78/1.14 Prover 4: Preprocessing ... % 2.78/1.14 Prover 2: Preprocessing ... % 6.93/1.65 Prover 1: Warning: ignoring some quantifiers % 6.93/1.71 Prover 6: Proving ... % 6.93/1.71 Prover 1: Constructing countermodel ... % 7.44/1.73 Prover 3: Warning: ignoring some quantifiers % 7.44/1.74 Prover 4: Warning: ignoring some quantifiers % 7.44/1.75 Prover 3: Constructing countermodel ... % 7.44/1.76 Prover 4: Constructing countermodel ... % 7.79/1.81 Prover 0: Proving ... % 7.79/1.84 Prover 5: Proving ... % 8.37/1.86 Prover 2: Proving ... % 9.01/1.94 Prover 6: proved (1305ms) % 9.01/1.94 % 9.01/1.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.01/1.94 % 9.01/1.95 Prover 3: stopped % 9.01/1.96 Prover 2: stopped % 9.01/1.96 Prover 0: stopped % 9.01/1.98 Prover 5: stopped % 9.01/1.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.01/1.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.01/1.99 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.01/1.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.01/1.99 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.01/2.01 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 9.01/2.01 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 9.01/2.02 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 9.01/2.02 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 9.01/2.02 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 9.22/2.08 Prover 11: Preprocessing ... % 9.22/2.09 Prover 8: Preprocessing ... % 9.22/2.10 Prover 13: Preprocessing ... % 9.22/2.10 Prover 10: Preprocessing ... % 9.22/2.10 Prover 7: Preprocessing ... % 10.68/2.20 Prover 8: Warning: ignoring some quantifiers % 10.68/2.22 Prover 8: Constructing countermodel ... % 10.68/2.23 Prover 10: Warning: ignoring some quantifiers % 10.68/2.24 Prover 10: Constructing countermodel ... % 11.19/2.26 Prover 11: Warning: ignoring some quantifiers % 11.32/2.27 Prover 11: Constructing countermodel ... % 11.32/2.27 Prover 13: Warning: ignoring some quantifiers % 11.32/2.30 Prover 13: Constructing countermodel ... % 11.67/2.32 Prover 7: Warning: ignoring some quantifiers % 11.92/2.36 Prover 7: Constructing countermodel ... % 12.98/2.50 Prover 1: Found proof (size 15) % 12.98/2.50 Prover 1: proved (1880ms) % 12.98/2.52 Prover 7: stopped % 12.98/2.52 Prover 4: stopped % 12.98/2.52 Prover 10: stopped % 12.98/2.52 Prover 8: stopped % 12.98/2.52 Prover 11: stopped % 12.98/2.52 Prover 13: stopped % 12.98/2.52 % 12.98/2.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.98/2.52 % 12.98/2.52 % SZS output start Proof for theBenchmark % 12.98/2.53 Assumptions after simplification: % 12.98/2.53 --------------------------------- % 12.98/2.53 % 12.98/2.53 (wP_parameter_sqrt) % 13.40/2.55 ? [v0: $real] : ? [v1: $real] : ? [v2: int] : ? [v3: $real] : ? [v4: % 13.40/2.55 $real] : ? [v5: any] : ? [v6: any] : ? [v7: $real] : ? [v8: $real] : ? % 13.40/2.55 [v9: $real] : ? [v10: $real] : ? [v11: $real] : ? [v12: $real] : ? [v13: % 13.40/2.55 int] : ( ~ (v13 = 0) & $lesseq(1, v2) & int_$to_real(v2) = v4 & % 13.40/2.55 real_$less(v0, v1) = v5 & real_$less(real_1, v1) = v6 & real_$less(real_0, % 13.40/2.55 v8) = 0 & real_$less(real_0, v3) = 0 & max(v0, real_1) = v7 & % 13.40/2.55 real_$lesseq(v11, v12) = 0 & real_$lesseq(v9, v10) = 0 & real_$lesseq(v4, % 13.40/2.55 v12) = v13 & real_$lesseq(v1, v7) = 0 & real_$lesseq(real_0, v0) = 0 & % 13.40/2.55 real_$product(v7, v8) = v10 & real_$product(v4, v3) = v1 & real_$product(v1, % 13.40/2.55 v8) = v9 & real_$quotient(v7, v3) = v12 & real_$quotient(v1, v3) = v11 & % 13.40/2.55 real_$quotient(real_1, v3) = v8 & ( ~ (v6 = 0) | ~ (v5 = 0))) % 13.40/2.55 % 13.40/2.55 (input) % 13.48/2.57 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_1) & ~ % 13.48/2.57 (real_very_large = real_0) & ~ (real_very_small = real_1) & ~ % 13.48/2.57 (real_very_small = real_0) & ~ (real_1 = real_0) & real_$is_int(real_1) = 0 & % 13.48/2.57 real_$is_int(real_0) = 0 & real_$is_rat(real_1) = 0 & real_$is_rat(real_0) = 0 % 13.48/2.57 & real_$floor(real_1) = real_1 & real_$floor(real_0) = real_0 & % 13.48/2.57 real_$ceiling(real_1) = real_1 & real_$ceiling(real_0) = real_0 & % 13.48/2.57 real_$truncate(real_1) = real_1 & real_$truncate(real_0) = real_0 & % 13.48/2.57 real_$round(real_1) = real_1 & real_$round(real_0) = real_0 & % 13.48/2.57 real_$to_int(real_1) = 1 & real_$to_int(real_0) = 0 & real_$to_rat(real_1) = % 13.48/2.57 rat_1 & real_$to_rat(real_0) = rat_0 & real_$to_real(real_1) = real_1 & % 13.48/2.57 real_$to_real(real_0) = real_0 & real_$greatereq(real_very_small, % 13.48/2.57 real_very_large) = 1 & real_$greatereq(real_1, real_1) = 0 & % 13.48/2.57 real_$greatereq(real_1, real_0) = 0 & real_$greatereq(real_0, real_1) = 1 & % 13.48/2.57 real_$greatereq(real_0, real_0) = 0 & real_$greater(real_very_large, real_1) = % 13.48/2.57 0 & real_$greater(real_very_large, real_0) = 0 & % 13.48/2.57 real_$greater(real_very_small, real_very_large) = 1 & real_$greater(real_1, % 13.48/2.57 real_very_small) = 0 & real_$greater(real_1, real_1) = 1 & % 13.48/2.57 real_$greater(real_1, real_0) = 0 & real_$greater(real_0, real_very_small) = 0 % 13.48/2.57 & real_$greater(real_0, real_1) = 1 & real_$greater(real_0, real_0) = 1 & % 13.48/2.57 int_$to_real(1) = real_1 & int_$to_real(0) = real_0 & % 13.48/2.57 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, % 13.48/2.57 real_1) = 0 & real_$less(real_very_small, real_0) = 0 & real_$less(real_1, % 13.48/2.57 real_very_large) = 0 & real_$less(real_1, real_1) = 1 & real_$less(real_1, % 13.48/2.57 real_0) = 1 & real_$less(real_0, real_very_large) = 0 & real_$less(real_0, % 13.48/2.57 real_1) = 0 & real_$less(real_0, real_0) = 1 & real_$lesseq(real_very_small, % 13.48/2.57 real_very_large) = 0 & real_$lesseq(real_1, real_1) = 0 & % 13.48/2.57 real_$lesseq(real_1, real_0) = 1 & real_$lesseq(real_0, real_1) = 0 & % 13.48/2.57 real_$lesseq(real_0, real_0) = 0 & real_$product(real_1, real_1) = real_1 & % 13.48/2.57 real_$product(real_1, real_0) = real_0 & real_$product(real_0, real_1) = % 13.48/2.57 real_0 & real_$product(real_0, real_0) = real_0 & real_$uminus(real_0) = % 13.48/2.57 real_0 & real_$difference(real_1, real_1) = real_0 & real_$difference(real_1, % 13.48/2.57 real_0) = real_1 & real_$difference(real_0, real_0) = real_0 & % 13.48/2.57 real_$sum(real_1, real_0) = real_1 & real_$sum(real_0, real_1) = real_1 & % 13.48/2.57 real_$sum(real_0, real_0) = real_0 & real_$quotient(real_1, real_1) = real_1 & % 13.48/2.57 real_$quotient(real_0, real_1) = real_0 & ! [v0: $real] : ! [v1: $real] : ! % 13.48/2.57 [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | % 13.48/2.57 ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & % 13.48/2.57 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.48/2.57 $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~ (real_$product(v1, v0) % 13.48/2.57 = v2) | ~ (real_$quotient(v2, v0) = v3)) & ! [v0: $real] : ! [v1: % 13.48/2.57 $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v1) = % 13.48/2.57 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & % 13.48/2.57 real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.48/2.57 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~ % 13.48/2.57 (real_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, % 13.48/2.57 v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: % 13.48/2.57 int] : (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = % 13.48/2.57 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: % 13.48/2.57 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ( ~ % 13.48/2.57 (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, % 13.48/2.57 v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v2 = % 13.48/2.57 real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) = v2)) & ! [v0: % 13.48/2.57 $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 13.48/2.57 (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, % 13.48/2.57 v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | % 13.48/2.57 ~ (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 13.48/2.57 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.48/2.57 int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = % 13.48/2.57 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! % 13.48/2.57 [v2: any] : ( ~ (real_$less(v1, v0) = v2) | real_$lesseq(v1, v0) = 0 | ( ~ (v2 % 13.48/2.57 = 0) & ~ (v1 = v0))) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 13.48/2.57 : ( ~ (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) & ! [v0: % 13.48/2.57 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | % 13.48/2.57 real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ % 13.48/2.57 (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : ! [v1: $real] : ( ~ % 13.48/2.57 (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] : % 13.48/2.57 ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & % 13.48/2.57 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | % 13.48/2.57 real_$uminus(v1) = v0) & ! [v0: $real] : (v0 = real_0 | ~ % 13.48/2.57 (real_$uminus(v0) = v0)) % 13.48/2.57 % 13.48/2.57 (function-axioms) % 13.48/2.57 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: bool] : ! % 13.48/2.57 [v5: ty] : (v1 = v0 | ~ (match_bool(v5, v4, v3, v2) = v1) | ~ % 13.48/2.57 (match_bool(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.48/2.57 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 13.48/2.57 (real_$greatereq(v3, v2) = v1) | ~ (real_$greatereq(v3, v2) = v0)) & ! % 13.48/2.57 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! % 13.48/2.57 [v3: $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ % 13.48/2.57 (real_$greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.48/2.57 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 13.48/2.57 (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) = v0)) & ! [v0: $real] : % 13.48/2.57 ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (min(v3, v2) % 13.48/2.57 = v1) | ~ (min(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.48/2.57 $real] : ! [v3: $real] : (v1 = v0 | ~ (max(v3, v2) = v1) | ~ (max(v3, v2) % 13.48/2.57 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.48/2.57 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~ % 13.48/2.57 (real_$lesseq(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.48/2.57 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$product(v3, v2) = v1) | ~ % 13.48/2.57 (real_$product(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.48/2.57 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$difference(v3, v2) = v1) | ~ % 13.48/2.57 (real_$difference(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.48/2.57 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$sum(v3, v2) = v1) | ~ % 13.48/2.57 (real_$sum(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 13.48/2.57 : ! [v3: $real] : (v1 = v0 | ~ (real_$quotient(v3, v2) = v1) | ~ % 13.48/2.57 (real_$quotient(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.48/2.57 MultipleValueBool] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (sort(v3, % 13.48/2.57 v2) = v1) | ~ (sort(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.48/2.57 [v1: MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = % 13.48/2.57 v1) | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.48/2.57 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) % 13.48/2.57 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.48/2.57 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & % 13.48/2.57 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 13.48/2.57 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] : % 13.48/2.57 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ % 13.48/2.57 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.48/2.57 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) & % 13.48/2.57 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2) % 13.48/2.57 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 13.48/2.57 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = % 13.48/2.57 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 13.48/2.57 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] : % 13.48/2.57 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ % 13.48/2.57 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 13.48/2.57 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) & ! % 13.48/2.57 [v0: uni] : ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~ (witness(v2) = v1) | ~ % 13.48/2.57 (witness(v2) = v0)) % 13.48/2.57 % 13.48/2.57 Further assumptions not needed in the proof: % 13.48/2.57 -------------------------------------------- % 13.48/2.58 add_div, assoc_div_div, assoc_div_mul, assoc_mul_div, bool_inversion, % 13.48/2.58 compatOrderMult, compatOrderMult1, match_bool_False, match_bool_True, % 13.48/2.58 match_bool_sort, max_is_ge, max_is_some, min_is_le, min_is_some, neg_div, % 13.48/2.58 sub_div, true_False, tuple0_inversion, witness_sort % 13.48/2.58 % 13.48/2.58 Those formulas are unsatisfiable: % 13.48/2.58 --------------------------------- % 13.48/2.58 % 13.48/2.58 Begin of proof % 13.48/2.58 | % 13.48/2.58 | ALPHA: (function-axioms) implies: % 13.48/2.58 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.48/2.58 | $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | % 13.48/2.58 | ~ (real_$lesseq(v3, v2) = v0)) % 13.48/2.58 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.48/2.58 | $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | % 13.48/2.58 | ~ (real_$less(v3, v2) = v0)) % 13.48/2.58 | % 13.48/2.58 | ALPHA: (input) implies: % 13.48/2.58 | (3) real_$less(real_0, real_0) = 1 % 13.48/2.58 | (4) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v3 % 13.48/2.58 | = v1 | v0 = real_0 | ~ (real_$product(v1, v0) = v2) | ~ % 13.48/2.58 | (real_$quotient(v2, v0) = v3)) % 13.48/2.58 | % 13.48/2.58 | DELTA: instantiating (wP_parameter_sqrt) with fresh symbols all_31_0, % 13.48/2.58 | all_31_1, all_31_2, all_31_3, all_31_4, all_31_5, all_31_6, all_31_7, % 13.48/2.58 | all_31_8, all_31_9, all_31_10, all_31_11, all_31_12, all_31_13 gives: % 13.48/2.58 | (5) ~ (all_31_0 = 0) & $lesseq(1, all_31_11) & int_$to_real(all_31_11) = % 13.48/2.58 | all_31_9 & real_$less(all_31_13, all_31_12) = all_31_8 & % 13.48/2.58 | real_$less(real_1, all_31_12) = all_31_7 & real_$less(real_0, all_31_5) % 13.48/2.58 | = 0 & real_$less(real_0, all_31_10) = 0 & max(all_31_13, real_1) = % 13.48/2.58 | all_31_6 & real_$lesseq(all_31_2, all_31_1) = 0 & % 13.48/2.58 | real_$lesseq(all_31_4, all_31_3) = 0 & real_$lesseq(all_31_9, all_31_1) % 13.48/2.58 | = all_31_0 & real_$lesseq(all_31_12, all_31_6) = 0 & % 13.48/2.58 | real_$lesseq(real_0, all_31_13) = 0 & real_$product(all_31_6, all_31_5) % 13.48/2.58 | = all_31_3 & real_$product(all_31_9, all_31_10) = all_31_12 & % 13.48/2.58 | real_$product(all_31_12, all_31_5) = all_31_4 & % 13.48/2.58 | real_$quotient(all_31_6, all_31_10) = all_31_1 & % 13.48/2.58 | real_$quotient(all_31_12, all_31_10) = all_31_2 & % 13.48/2.58 | real_$quotient(real_1, all_31_10) = all_31_5 & ( ~ (all_31_7 = 0) | ~ % 13.48/2.58 | (all_31_8 = 0)) % 13.48/2.58 | % 13.48/2.58 | ALPHA: (5) implies: % 13.48/2.58 | (6) ~ (all_31_0 = 0) % 13.48/2.58 | (7) real_$quotient(all_31_12, all_31_10) = all_31_2 % 13.48/2.58 | (8) real_$product(all_31_9, all_31_10) = all_31_12 % 13.48/2.58 | (9) real_$lesseq(all_31_9, all_31_1) = all_31_0 % 13.48/2.58 | (10) real_$lesseq(all_31_2, all_31_1) = 0 % 13.48/2.58 | (11) real_$less(real_0, all_31_10) = 0 % 13.48/2.58 | % 13.48/2.58 | GROUND_INST: instantiating (4) with all_31_10, all_31_9, all_31_12, all_31_2, % 13.48/2.58 | simplifying with (7), (8) gives: % 13.48/2.58 | (12) all_31_2 = all_31_9 | all_31_10 = real_0 % 13.48/2.58 | % 13.48/2.58 | BETA: splitting (12) gives: % 13.48/2.58 | % 13.48/2.58 | Case 1: % 13.48/2.58 | | % 13.48/2.58 | | (13) all_31_10 = real_0 % 13.48/2.58 | | % 13.48/2.58 | | REDUCE: (11), (13) imply: % 13.48/2.58 | | (14) real_$less(real_0, real_0) = 0 % 13.48/2.58 | | % 13.48/2.59 | | GROUND_INST: instantiating (2) with 1, 0, real_0, real_0, simplifying with % 13.48/2.59 | | (3), (14) gives: % 13.48/2.59 | | (15) $false % 13.48/2.59 | | % 13.48/2.59 | | CLOSE: (15) is inconsistent. % 13.48/2.59 | | % 13.48/2.59 | Case 2: % 13.48/2.59 | | % 13.48/2.59 | | (16) all_31_2 = all_31_9 % 13.48/2.59 | | % 13.48/2.59 | | REDUCE: (10), (16) imply: % 13.48/2.59 | | (17) real_$lesseq(all_31_9, all_31_1) = 0 % 13.48/2.59 | | % 13.48/2.59 | | GROUND_INST: instantiating (1) with all_31_0, 0, all_31_1, all_31_9, % 13.48/2.59 | | simplifying with (9), (17) gives: % 13.48/2.59 | | (18) all_31_0 = 0 % 13.48/2.59 | | % 13.48/2.59 | | REDUCE: (6), (18) imply: % 13.48/2.59 | | (19) $false % 13.48/2.59 | | % 13.48/2.59 | | CLOSE: (19) is inconsistent. % 13.48/2.59 | | % 13.48/2.59 | End of split % 13.48/2.59 | % 13.48/2.59 End of proof % 13.48/2.59 % SZS output end Proof for theBenchmark % 13.48/2.59 % 13.48/2.59 1981ms %------------------------------------------------------------------------------