%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI743_1 : TPTP v8.1.2. Released v7.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.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 17:48:59 EDT 2023 % Result : Theorem 8.54s 1.91s % Output : Proof 9.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : ARI743_1 : TPTP v8.1.2. Released v7.0.0. % 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n012.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 : Tue Aug 29 18:30:23 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.34/0.91 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 1.34/0.91 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.34/0.91 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.34/0.91 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.34/0.91 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.34/0.91 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.34/0.91 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 2.39/1.05 Prover 4: Preprocessing ... % 2.39/1.05 Prover 1: Preprocessing ... % 2.68/1.10 Prover 3: Preprocessing ... % 2.68/1.10 Prover 2: Preprocessing ... % 2.68/1.10 Prover 5: Preprocessing ... % 2.68/1.10 Prover 6: Preprocessing ... % 2.68/1.11 Prover 0: Preprocessing ... % 5.99/1.57 Prover 6: Constructing countermodel ... % 5.99/1.59 Prover 1: Constructing countermodel ... % 6.63/1.62 Prover 3: Constructing countermodel ... % 6.63/1.65 Prover 4: Constructing countermodel ... % 6.63/1.67 Prover 2: Proving ... % 7.12/1.68 Prover 5: Proving ... % 7.12/1.69 Prover 0: Proving ... % 7.88/1.91 Prover 6: proved (1275ms) % 7.88/1.91 % 8.54/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.54/1.91 % 8.54/1.91 Prover 3: stopped % 8.54/1.91 Prover 2: stopped % 8.54/1.91 Prover 5: stopped % 8.90/1.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.90/1.92 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 8.90/1.92 Prover 0: stopped % 8.90/1.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.90/1.93 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 8.90/1.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.90/1.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.90/1.93 Prover 7: Preprocessing ... % 8.90/1.93 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 8.90/1.93 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 8.90/1.93 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.90/1.94 Prover 10: Preprocessing ... % 8.90/1.94 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 8.90/1.95 Prover 8: Preprocessing ... % 8.90/1.96 Prover 13: Preprocessing ... % 8.90/1.97 Prover 11: Preprocessing ... % 8.90/2.00 Prover 1: Found proof (size 22) % 8.90/2.00 Prover 1: proved (1378ms) % 8.90/2.00 Prover 10: stopped % 8.90/2.00 Prover 4: stopped % 8.90/2.00 Prover 7: stopped % 9.54/2.01 Prover 13: stopped % 9.54/2.02 Prover 11: stopped % 9.54/2.05 Prover 8: Warning: ignoring some quantifiers % 9.54/2.06 Prover 8: Constructing countermodel ... % 9.54/2.07 Prover 8: stopped % 9.54/2.07 % 9.54/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.54/2.07 % 9.54/2.08 % SZS output start Proof for theBenchmark % 9.92/2.08 Assumptions after simplification: % 9.92/2.08 --------------------------------- % 9.92/2.08 % 9.92/2.08 (sqrt_one) % 9.92/2.11 ? [v0: $real] : ( ~ (v0 = real_1) & sqrt(real_1) = v0) % 9.92/2.11 % 9.92/2.11 (sqrt_positive) % 9.92/2.11 ! [v0: $real] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $real] : % 9.92/2.11 (sqrt(v0) = v1 & real_$lesseq(real_0, v1) = 0)) % 9.92/2.11 % 9.92/2.11 (sqrt_square) % 9.92/2.11 ! [v0: $real] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $real] : % 9.92/2.11 (sqrt(v0) = v1 & sqr(v1) = v0)) % 9.92/2.11 % 9.92/2.11 (square_sqrt) % 9.92/2.11 ! [v0: $real] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $real] : % 9.92/2.11 (sqrt(v1) = v0 & real_$product(v0, v0) = v1)) % 9.92/2.11 % 9.92/2.11 (input) % 9.92/2.13 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_1) & ~ % 9.92/2.13 (real_very_large = real_0) & ~ (real_very_small = real_1) & ~ % 9.92/2.13 (real_very_small = real_0) & ~ (real_1 = real_0) & real_$is_int(real_1) = 0 & % 9.92/2.13 real_$is_int(real_0) = 0 & real_$is_rat(real_1) = 0 & real_$is_rat(real_0) = 0 % 9.92/2.13 & real_$floor(real_1) = real_1 & real_$floor(real_0) = real_0 & % 9.92/2.13 real_$ceiling(real_1) = real_1 & real_$ceiling(real_0) = real_0 & % 9.92/2.13 real_$truncate(real_1) = real_1 & real_$truncate(real_0) = real_0 & % 9.92/2.13 real_$round(real_1) = real_1 & real_$round(real_0) = real_0 & % 9.92/2.13 real_$to_int(real_1) = 1 & real_$to_int(real_0) = 0 & real_$to_rat(real_1) = % 9.92/2.13 rat_1 & real_$to_rat(real_0) = rat_0 & real_$to_real(real_1) = real_1 & % 9.92/2.13 real_$to_real(real_0) = real_0 & int_$to_real(1) = real_1 & int_$to_real(0) = % 9.92/2.13 real_0 & real_$quotient(real_1, real_1) = real_1 & real_$quotient(real_0, % 9.92/2.13 real_1) = real_0 & real_$difference(real_1, real_1) = real_0 & % 9.92/2.13 real_$difference(real_1, real_0) = real_1 & real_$difference(real_0, real_0) = % 9.92/2.13 real_0 & real_$uminus(real_0) = real_0 & real_$sum(real_1, real_0) = real_1 & % 9.92/2.13 real_$sum(real_0, real_1) = real_1 & real_$sum(real_0, real_0) = real_0 & % 9.92/2.13 real_$greatereq(real_very_small, real_very_large) = 1 & % 9.92/2.13 real_$greatereq(real_1, real_1) = 0 & real_$greatereq(real_1, real_0) = 0 & % 9.92/2.13 real_$greatereq(real_0, real_1) = 1 & real_$greatereq(real_0, real_0) = 0 & % 9.92/2.13 real_$greater(real_very_large, real_1) = 0 & real_$greater(real_very_large, % 9.92/2.13 real_0) = 0 & real_$greater(real_very_small, real_very_large) = 1 & % 9.92/2.13 real_$greater(real_1, real_very_small) = 0 & real_$greater(real_1, real_1) = 1 % 9.92/2.13 & real_$greater(real_1, real_0) = 0 & real_$greater(real_0, real_very_small) = % 9.92/2.13 0 & real_$greater(real_0, real_1) = 1 & real_$greater(real_0, real_0) = 1 & % 9.92/2.13 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, % 9.92/2.13 real_1) = 0 & real_$less(real_very_small, real_0) = 0 & real_$less(real_1, % 9.92/2.13 real_very_large) = 0 & real_$less(real_1, real_1) = 1 & real_$less(real_1, % 9.92/2.13 real_0) = 1 & real_$less(real_0, real_very_large) = 0 & real_$less(real_0, % 9.92/2.13 real_1) = 0 & real_$less(real_0, real_0) = 1 & real_$lesseq(real_very_small, % 9.92/2.13 real_very_large) = 0 & real_$lesseq(real_1, real_1) = 0 & % 9.92/2.13 real_$lesseq(real_1, real_0) = 1 & real_$lesseq(real_0, real_1) = 0 & % 9.92/2.13 real_$lesseq(real_0, real_0) = 0 & real_$product(real_1, real_1) = real_1 & % 9.92/2.13 real_$product(real_1, real_0) = real_0 & real_$product(real_0, real_1) = % 9.92/2.13 real_0 & real_$product(real_0, real_0) = real_0 & ! [v0: $real] : ! [v1: % 9.92/2.13 $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ % 9.92/2.13 (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] : % 9.92/2.13 (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! % 9.92/2.13 [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~ % 9.92/2.13 (real_$quotient(v2, v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: % 9.92/2.13 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ % 9.92/2.13 (real_$less(v2, v1) = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ % 9.92/2.13 (v4 = 0) & real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : ! [v1: $real] : % 9.92/2.13 ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~ % 9.92/2.13 (real_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, % 9.92/2.13 v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: % 9.92/2.13 int] : (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = % 9.92/2.13 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: % 9.92/2.13 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ( ~ % 9.92/2.13 (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, % 9.92/2.13 v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v2 = % 9.92/2.13 real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) = v2)) & ! [v0: % 9.92/2.13 $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 9.92/2.13 (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, % 9.92/2.13 v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | % 9.92/2.13 ~ (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 9.92/2.13 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.92/2.13 int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = % 9.92/2.13 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! % 9.92/2.13 [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: % 9.92/2.13 $real] : ! [v1: $real] : ! [v2: any] : ( ~ (real_$less(v1, v0) = v2) | % 9.92/2.13 real_$lesseq(v1, v0) = 0 | ( ~ (v2 = 0) & ~ (v1 = v0))) & ! [v0: $real] : % 9.92/2.13 ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = v2) | % 9.92/2.13 real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | % 9.92/2.13 ~ (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : ! [v1: $real] : ( ~ % 9.92/2.13 (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: % 9.92/2.13 $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! % 9.92/2.13 [v0: $real] : ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | % 9.92/2.13 real_$less(v1, v0) = 0) & ! [v0: $real] : (v0 = real_0 | ~ % 9.92/2.13 (real_$uminus(v0) = v0)) % 9.92/2.13 % 9.92/2.13 (function-axioms) % 9.92/2.14 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 9.92/2.14 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 9.92/2.14 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 9.92/2.14 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! % 9.92/2.14 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 9.92/2.14 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: % 9.92/2.14 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 9.92/2.14 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~ % 9.92/2.14 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.92/2.14 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 9.92/2.14 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0: % 9.92/2.14 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 9.92/2.14 $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) = % 9.92/2.14 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.92/2.14 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~ % 9.92/2.14 (real_$lesseq(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.92/2.14 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$product(v3, v2) = v1) | ~ % 9.92/2.14 (real_$product(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.92/2.14 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1) % 9.92/2.14 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.92/2.14 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) % 9.92/2.14 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.92/2.14 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & % 9.92/2.14 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 9.92/2.14 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] : % 9.92/2.14 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ % 9.92/2.14 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 9.92/2.14 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) & % 9.92/2.14 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2) % 9.92/2.14 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 9.92/2.14 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = % 9.92/2.14 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 9.92/2.14 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] : % 9.92/2.14 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ % 9.92/2.14 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 9.92/2.14 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) & ! % 9.92/2.14 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (sqrt(v2) = v1) % 9.92/2.14 | ~ (sqrt(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : % 9.92/2.14 (v1 = v0 | ~ (sqr(v2) = v1) | ~ (sqr(v2) = v0)) % 9.92/2.14 % 9.92/2.14 Further assumptions not needed in the proof: % 9.92/2.14 -------------------------------------------- % 9.92/2.14 sqr_def, sqrt_le, sqrt_mul, sqrt_zero % 9.92/2.14 % 9.92/2.14 Those formulas are unsatisfiable: % 9.92/2.14 --------------------------------- % 9.92/2.14 % 9.92/2.14 Begin of proof % 9.92/2.14 | % 9.92/2.14 | ALPHA: (function-axioms) implies: % 9.92/2.14 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 9.92/2.14 | (sqrt(v2) = v1) | ~ (sqrt(v2) = v0)) % 9.92/2.14 | (2) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 % 9.92/2.14 | = v0 | ~ (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = % 9.92/2.14 | v0)) % 9.92/2.15 | % 9.92/2.15 | ALPHA: (input) implies: % 9.92/2.15 | (3) real_$product(real_1, real_1) = real_1 % 9.92/2.15 | (4) real_$lesseq(real_0, real_1) = 0 % 9.92/2.15 | % 9.92/2.15 | DELTA: instantiating (sqrt_one) with fresh symbol all_11_0 gives: % 9.92/2.15 | (5) ~ (all_11_0 = real_1) & sqrt(real_1) = all_11_0 % 9.92/2.15 | % 9.92/2.15 | ALPHA: (5) implies: % 9.92/2.15 | (6) ~ (all_11_0 = real_1) % 9.92/2.15 | (7) sqrt(real_1) = all_11_0 % 9.92/2.15 | % 9.92/2.15 | GROUND_INST: instantiating (square_sqrt) with real_1, simplifying with (4) % 9.92/2.15 | gives: % 9.92/2.15 | (8) ? [v0: $real] : (sqrt(v0) = real_1 & real_$product(real_1, real_1) = % 9.92/2.15 | v0) % 9.92/2.15 | % 9.92/2.15 | GROUND_INST: instantiating (sqrt_positive) with real_1, simplifying with (4) % 9.92/2.15 | gives: % 9.92/2.15 | (9) ? [v0: $real] : (sqrt(real_1) = v0 & real_$lesseq(real_0, v0) = 0) % 9.92/2.15 | % 9.92/2.15 | GROUND_INST: instantiating (sqrt_square) with real_1, simplifying with (4) % 9.92/2.15 | gives: % 9.92/2.15 | (10) ? [v0: $real] : (sqrt(real_1) = v0 & sqr(v0) = real_1) % 9.92/2.15 | % 9.92/2.15 | DELTA: instantiating (10) with fresh symbol all_25_0 gives: % 9.92/2.15 | (11) sqrt(real_1) = all_25_0 & sqr(all_25_0) = real_1 % 9.92/2.15 | % 9.92/2.15 | ALPHA: (11) implies: % 9.92/2.15 | (12) sqrt(real_1) = all_25_0 % 9.92/2.15 | % 9.92/2.15 | DELTA: instantiating (8) with fresh symbol all_27_0 gives: % 9.92/2.15 | (13) sqrt(all_27_0) = real_1 & real_$product(real_1, real_1) = all_27_0 % 9.92/2.15 | % 9.92/2.15 | ALPHA: (13) implies: % 9.92/2.15 | (14) real_$product(real_1, real_1) = all_27_0 % 9.92/2.15 | (15) sqrt(all_27_0) = real_1 % 9.92/2.15 | % 9.92/2.15 | DELTA: instantiating (9) with fresh symbol all_37_0 gives: % 9.92/2.15 | (16) sqrt(real_1) = all_37_0 & real_$lesseq(real_0, all_37_0) = 0 % 9.92/2.15 | % 9.92/2.15 | ALPHA: (16) implies: % 9.92/2.15 | (17) sqrt(real_1) = all_37_0 % 9.92/2.15 | % 9.92/2.15 | GROUND_INST: instantiating (2) with real_1, all_27_0, real_1, real_1, % 9.92/2.15 | simplifying with (3), (14) gives: % 9.92/2.15 | (18) all_27_0 = real_1 % 9.92/2.15 | % 9.92/2.15 | GROUND_INST: instantiating (1) with all_11_0, all_37_0, real_1, simplifying % 9.92/2.15 | with (7), (17) gives: % 9.92/2.15 | (19) all_37_0 = all_11_0 % 9.92/2.15 | % 9.92/2.15 | GROUND_INST: instantiating (1) with all_25_0, all_37_0, real_1, simplifying % 9.92/2.15 | with (12), (17) gives: % 9.92/2.15 | (20) all_37_0 = all_25_0 % 9.92/2.15 | % 9.92/2.15 | COMBINE_EQS: (19), (20) imply: % 9.92/2.15 | (21) all_25_0 = all_11_0 % 9.92/2.15 | % 9.92/2.15 | REDUCE: (15), (18) imply: % 9.92/2.15 | (22) sqrt(real_1) = real_1 % 9.92/2.15 | % 9.92/2.15 | GROUND_INST: instantiating (1) with all_11_0, real_1, real_1, simplifying with % 9.92/2.15 | (7), (22) gives: % 9.92/2.16 | (23) all_11_0 = real_1 % 9.92/2.16 | % 9.92/2.16 | REDUCE: (6), (23) imply: % 9.92/2.16 | (24) $false % 9.92/2.16 | % 9.92/2.16 | CLOSE: (24) is inconsistent. % 9.92/2.16 | % 9.92/2.16 End of proof % 9.92/2.16 % SZS output end Proof for theBenchmark % 9.92/2.16 % 9.92/2.16 1552ms %------------------------------------------------------------------------------