%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI203_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 : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 17:47:16 EDT 2023 % Result : Theorem 5.25s 1.43s % Output : Proof 8.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ARI203_1 : TPTP v8.1.2. Released v5.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n008.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Aug 29 18:05:02 EDT 2023 % 0.14/0.34 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.85/0.91 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 1.85/0.91 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 1.85/0.91 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 1.85/0.91 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 1.85/0.91 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.85/0.91 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 1.85/0.91 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 2.05/0.98 Prover 4: Preprocessing ... % 2.05/0.98 Prover 1: Preprocessing ... % 2.58/1.03 Prover 5: Preprocessing ... % 2.58/1.03 Prover 3: Preprocessing ... % 2.58/1.03 Prover 0: Preprocessing ... % 2.58/1.03 Prover 2: Preprocessing ... % 2.58/1.03 Prover 6: Preprocessing ... % 5.25/1.40 Prover 6: Constructing countermodel ... % 5.25/1.43 Prover 2: Constructing countermodel ... % 5.25/1.43 Prover 6: proved (793ms) % 5.25/1.43 % 5.25/1.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.25/1.43 % 5.25/1.44 Prover 2: stopped % 5.25/1.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.25/1.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.25/1.44 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation % 5.25/1.44 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation % 5.25/1.45 Prover 1: Constructing countermodel ... % 5.25/1.45 Prover 8: Preprocessing ... % 5.25/1.47 Prover 5: Constructing countermodel ... % 5.25/1.47 Prover 5: stopped % 5.25/1.48 Prover 7: Preprocessing ... % 5.25/1.48 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.25/1.48 Prover 0: Constructing countermodel ... % 5.25/1.48 Prover 0: stopped % 5.25/1.48 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.25/1.48 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation % 5.25/1.49 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation % 5.25/1.49 Prover 4: Constructing countermodel ... % 5.25/1.50 Prover 3: Constructing countermodel ... % 5.25/1.50 Prover 3: stopped % 5.25/1.52 Prover 10: Preprocessing ... % 5.25/1.52 Prover 11: Preprocessing ... % 5.25/1.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.25/1.52 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation % 5.25/1.52 Prover 13: Preprocessing ... % 5.95/1.60 Prover 8: Warning: ignoring some quantifiers % 6.83/1.65 Prover 8: Constructing countermodel ... % 7.11/1.68 Prover 13: Warning: ignoring some quantifiers % 7.11/1.69 Prover 13: Constructing countermodel ... % 7.11/1.69 Prover 1: Found proof (size 7) % 7.11/1.69 Prover 4: Found proof (size 6) % 7.11/1.69 Prover 4: proved (1058ms) % 7.11/1.69 Prover 1: proved (1064ms) % 7.11/1.69 Prover 8: stopped % 7.11/1.70 Prover 10: Warning: ignoring some quantifiers % 7.11/1.70 Prover 13: stopped % 7.11/1.70 Prover 10: Constructing countermodel ... % 7.11/1.71 Prover 7: Warning: ignoring some quantifiers % 7.11/1.71 Prover 10: stopped % 7.11/1.72 Prover 7: Constructing countermodel ... % 7.11/1.73 Prover 7: stopped % 7.70/1.78 Prover 11: Constructing countermodel ... % 7.92/1.79 Prover 11: stopped % 7.92/1.79 % 7.92/1.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.92/1.79 % 7.92/1.80 % SZS output start Proof for theBenchmark % 7.92/1.80 Assumptions after simplification: % 7.92/1.80 --------------------------------- % 7.92/1.80 % 7.92/1.80 (rat_lesseq_problem_1) % 7.92/1.82 ? [v0: int] : ( ~ (v0 = 0) & rat_$lesseq(rat_5/12, rat_5/12) = v0) % 7.92/1.82 % 7.92/1.82 (input) % 8.21/1.85 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_5/12) & ~ % 8.21/1.85 (rat_very_large = rat_0) & ~ (rat_very_small = rat_5/12) & ~ (rat_very_small % 8.21/1.85 = rat_0) & ~ (rat_5/12 = rat_0) & rat_$is_int(rat_5/12) = 1 & % 8.21/1.85 rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_5/12) = 0 & rat_$is_rat(rat_0) = 0 & % 8.21/1.85 rat_$floor(rat_5/12) = rat_0 & rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) % 8.21/1.85 = rat_0 & rat_$truncate(rat_5/12) = rat_0 & rat_$truncate(rat_0) = rat_0 & % 8.21/1.85 rat_$round(rat_5/12) = rat_0 & rat_$round(rat_0) = rat_0 & % 8.21/1.85 rat_$to_int(rat_5/12) = 0 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_5/12) = % 8.21/1.85 rat_5/12 & rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_5/12) = real_5/12 & % 8.21/1.85 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_0, % 8.21/1.85 rat_5/12) = rat_0 & rat_$product(rat_5/12, rat_0) = rat_0 & % 8.21/1.85 rat_$product(rat_0, rat_5/12) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 & % 8.21/1.85 rat_$difference(rat_5/12, rat_5/12) = rat_0 & rat_$difference(rat_5/12, rat_0) % 8.21/1.85 = rat_5/12 & rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = % 8.21/1.85 rat_0 & rat_$sum(rat_5/12, rat_0) = rat_5/12 & rat_$sum(rat_0, rat_5/12) = % 8.21/1.85 rat_5/12 & rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small, % 8.21/1.85 rat_very_large) = 1 & rat_$greatereq(rat_5/12, rat_5/12) = 0 & % 8.21/1.85 rat_$greatereq(rat_5/12, rat_0) = 0 & rat_$greatereq(rat_0, rat_5/12) = 1 & % 8.21/1.85 rat_$greatereq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_5/12) = 0 % 8.21/1.85 & rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small, % 8.21/1.85 rat_very_large) = 1 & rat_$greater(rat_5/12, rat_very_small) = 0 & % 8.21/1.85 rat_$greater(rat_5/12, rat_5/12) = 1 & rat_$greater(rat_5/12, rat_0) = 0 & % 8.21/1.85 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_5/12) = 1 & % 8.21/1.85 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0 % 8.21/1.85 & rat_$less(rat_very_small, rat_5/12) = 0 & rat_$less(rat_very_small, rat_0) = % 8.21/1.85 0 & rat_$less(rat_5/12, rat_very_large) = 0 & rat_$less(rat_5/12, rat_5/12) = % 8.21/1.85 1 & rat_$less(rat_5/12, rat_0) = 1 & rat_$less(rat_0, rat_very_large) = 0 & % 8.21/1.85 rat_$less(rat_0, rat_5/12) = 0 & rat_$less(rat_0, rat_0) = 1 & % 8.21/1.85 rat_$lesseq(rat_very_small, rat_very_large) = 0 & rat_$lesseq(rat_5/12, % 8.21/1.85 rat_5/12) = 0 & rat_$lesseq(rat_5/12, rat_0) = 1 & rat_$lesseq(rat_0, % 8.21/1.85 rat_5/12) = 0 & rat_$lesseq(rat_0, rat_0) = 0 & ! [v0: $rat] : ! [v1: % 8.21/1.85 $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, % 8.21/1.85 v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, % 8.21/1.85 v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! % 8.21/1.85 [v2: $rat] : ! [v3: $rat] : (v3 = v1 | v0 = rat_0 | ~ (rat_$quotient(v2, v0) % 8.21/1.85 = v3) | ~ (rat_$product(v1, v0) = v2)) & ! [v0: $rat] : ! [v1: $rat] : % 8.21/1.85 ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ % 8.21/1.85 (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) % 8.21/1.85 = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : % 8.21/1.85 (v3 = 0 | ~ (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? % 8.21/1.85 [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! % 8.21/1.85 [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) | ~ % 8.21/1.85 (rat_$sum(v1, v2) = v3) | rat_$difference(v1, v0) = v3) & ! [v0: $rat] : ! % 8.21/1.85 [v1: $rat] : ! [v2: $rat] : (v2 = rat_0 | ~ (rat_$uminus(v0) = v1) | ~ % 8.21/1.85 (rat_$sum(v0, v1) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : % 8.21/1.85 (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 8.21/1.85 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 8.21/1.85 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 8.21/1.85 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : % 8.21/1.85 (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3: int] : ( ~ % 8.21/1.85 (v3 = 0) & rat_$less(v1, v0) = v3))) & ! [v0: $rat] : ! [v1: $rat] : % 8.21/1.85 ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | rat_$product(v1, v0) = v2) & % 8.21/1.85 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | % 8.21/1.85 rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 8.21/1.85 (rat_$less(v1, v0) = 0) | ~ (rat_$lesseq(v2, v1) = 0) | rat_$less(v2, v0) = % 8.21/1.85 0) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = % 8.21/1.85 v1)) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) % 8.21/1.85 = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 8.21/1.85 (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0: $rat] : ! [v1: % 8.21/1.85 $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1, v0) = 0) & ! % 8.21/1.85 [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, % 8.21/1.85 v0) = 0) & ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0) = v0)) % 8.21/1.85 % 8.21/1.85 (function-axioms) % 8.27/1.86 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 8.27/1.86 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0: % 8.27/1.86 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 8.27/1.86 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0: % 8.27/1.86 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 8.27/1.86 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & ! % 8.27/1.86 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 8.27/1.86 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0: % 8.27/1.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 8.27/1.86 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3, % 8.27/1.86 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 8.27/1.86 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$greater(v3, v2) = v1) | ~ % 8.27/1.86 (rat_$greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.27/1.86 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 8.27/1.86 (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = v0)) & ! [v0: % 8.27/1.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 8.27/1.86 $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ (rat_$lesseq(v3, v2) = % 8.27/1.86 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.27/1.86 $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & % 8.27/1.86 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = % 8.27/1.86 v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] % 8.27/1.86 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~ % 8.27/1.86 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 % 8.27/1.86 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0: % 8.27/1.86 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) = % 8.27/1.86 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 8.27/1.86 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) & % 8.27/1.86 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) = % 8.27/1.86 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 8.27/1.86 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) & % 8.27/1.86 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~ % 8.27/1.86 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : ! % 8.27/1.86 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~ % 8.27/1.86 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 8.27/1.86 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0)) % 8.27/1.86 % 8.27/1.86 Those formulas are unsatisfiable: % 8.27/1.86 --------------------------------- % 8.27/1.86 % 8.27/1.86 Begin of proof % 8.27/1.86 | % 8.27/1.86 | ALPHA: (function-axioms) implies: % 8.27/1.86 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] % 8.27/1.86 | : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ % 8.27/1.86 | (rat_$lesseq(v3, v2) = v0)) % 8.27/1.86 | % 8.27/1.86 | ALPHA: (input) implies: % 8.27/1.86 | (2) rat_$lesseq(rat_5/12, rat_5/12) = 0 % 8.27/1.86 | % 8.27/1.86 | DELTA: instantiating (rat_lesseq_problem_1) with fresh symbol all_5_0 gives: % 8.27/1.86 | (3) ~ (all_5_0 = 0) & rat_$lesseq(rat_5/12, rat_5/12) = all_5_0 % 8.27/1.87 | % 8.27/1.87 | ALPHA: (3) implies: % 8.27/1.87 | (4) ~ (all_5_0 = 0) % 8.27/1.87 | (5) rat_$lesseq(rat_5/12, rat_5/12) = all_5_0 % 8.27/1.87 | % 8.27/1.87 | GROUND_INST: instantiating (1) with 0, all_5_0, rat_5/12, rat_5/12, % 8.27/1.87 | simplifying with (2), (5) gives: % 8.27/1.87 | (6) all_5_0 = 0 % 8.27/1.87 | % 8.27/1.87 | REDUCE: (4), (6) imply: % 8.27/1.87 | (7) $false % 8.27/1.87 | % 8.27/1.87 | CLOSE: (7) is inconsistent. % 8.27/1.87 | % 8.27/1.87 End of proof % 8.27/1.87 % SZS output end Proof for theBenchmark % 8.27/1.87 % 8.27/1.87 1260ms %------------------------------------------------------------------------------