%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI211_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 : n020.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 17:47:17 EDT 2023 % Result : Theorem 6.29s 1.53s % Output : Proof 10.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : ARI211_1 : TPTP v8.1.2. Released v5.0.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n020.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 17:52:28 EDT 2023 % 0.14/0.35 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 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 % 1.81/0.90 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 1.81/0.90 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 1.81/0.90 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 1.81/0.90 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.81/0.90 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 1.81/0.91 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.81/0.91 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 1.97/0.97 Prover 1: Preprocessing ... % 1.97/0.97 Prover 4: Preprocessing ... % 2.64/1.03 Prover 6: Preprocessing ... % 2.64/1.03 Prover 0: Preprocessing ... % 3.20/1.11 Prover 3: Preprocessing ... % 3.20/1.11 Prover 2: Preprocessing ... % 3.20/1.12 Prover 5: Preprocessing ... % 5.71/1.50 Prover 6: Constructing countermodel ... % 6.29/1.53 Prover 6: proved (894ms) % 6.29/1.53 % 6.29/1.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.29/1.53 % 6.29/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.29/1.54 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation % 6.29/1.54 Prover 1: Constructing countermodel ... % 6.64/1.59 Prover 7: Preprocessing ... % 6.64/1.60 Prover 0: Constructing countermodel ... % 6.64/1.60 Prover 0: stopped % 6.64/1.60 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.64/1.60 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation % 6.64/1.60 Prover 2: stopped % 6.64/1.60 Prover 4: Constructing countermodel ... % 6.64/1.61 Prover 8: Preprocessing ... % 6.64/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.64/1.63 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation % 7.29/1.68 Prover 10: Preprocessing ... % 7.68/1.74 Prover 8: Warning: ignoring some quantifiers % 7.91/1.75 Prover 8: Constructing countermodel ... % 8.49/1.85 Prover 4: Found proof (size 7) % 8.49/1.85 Prover 4: proved (1217ms) % 8.49/1.85 Prover 8: stopped % 8.81/1.87 Prover 1: Found proof (size 7) % 8.81/1.87 Prover 1: proved (1242ms) % 9.34/1.99 Prover 5: Constructing countermodel ... % 9.34/1.99 Prover 5: stopped % 9.61/2.05 Prover 3: Constructing countermodel ... % 9.61/2.05 Prover 3: stopped % 9.61/2.07 Prover 10: Warning: ignoring some quantifiers % 10.22/2.08 Prover 7: Warning: ignoring some quantifiers % 10.22/2.08 Prover 10: Constructing countermodel ... % 10.22/2.09 Prover 7: Constructing countermodel ... % 10.40/2.12 Prover 10: stopped % 10.52/2.13 Prover 7: stopped % 10.52/2.13 % 10.52/2.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.52/2.13 % 10.52/2.13 % SZS output start Proof for theBenchmark % 10.52/2.13 Assumptions after simplification: % 10.52/2.13 --------------------------------- % 10.52/2.13 % 10.52/2.13 (rat_lesseq_problem_9) % 10.52/2.16 ? [v0: int] : ( ~ (v0 = 0) & rat_$lesseq(rat_-5/8, rat_-1/4) = v0) % 10.52/2.16 % 10.52/2.16 (input) % 10.52/2.19 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_-1/4) & ~ % 10.52/2.19 (rat_very_large = rat_-5/8) & ~ (rat_very_large = rat_0) & ~ (rat_very_small % 10.52/2.19 = rat_-1/4) & ~ (rat_very_small = rat_-5/8) & ~ (rat_very_small = rat_0) & % 10.52/2.19 ~ (rat_-1/4 = rat_-5/8) & ~ (rat_-1/4 = rat_0) & ~ (rat_-5/8 = rat_0) & % 10.52/2.19 rat_$is_int(rat_-1/4) = 1 & rat_$is_int(rat_-5/8) = 1 & rat_$is_int(rat_0) = 0 % 10.52/2.19 & rat_$is_rat(rat_-1/4) = 0 & rat_$is_rat(rat_-5/8) = 0 & rat_$is_rat(rat_0) = % 10.52/2.19 0 & rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_-1/4) = rat_0 & % 10.52/2.19 rat_$ceiling(rat_-5/8) = rat_0 & rat_$ceiling(rat_0) = rat_0 & % 10.52/2.19 rat_$truncate(rat_-1/4) = rat_0 & rat_$truncate(rat_-5/8) = rat_0 & % 10.52/2.19 rat_$truncate(rat_0) = rat_0 & rat_$round(rat_-1/4) = rat_0 & % 10.52/2.19 rat_$round(rat_0) = rat_0 & rat_$to_int(rat_-1/4) = -1 & rat_$to_int(rat_-5/8) % 10.52/2.19 = -1 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_-1/4) = rat_-1/4 & % 10.52/2.19 rat_$to_rat(rat_-5/8) = rat_-5/8 & rat_$to_rat(rat_0) = rat_0 & % 10.52/2.19 rat_$to_real(rat_-1/4) = real_-1/4 & rat_$to_real(rat_-5/8) = real_-5/8 & % 10.52/2.19 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_0, % 10.52/2.19 rat_-1/4) = rat_0 & rat_$quotient(rat_0, rat_-5/8) = rat_0 & % 10.52/2.19 rat_$product(rat_-1/4, rat_0) = rat_0 & rat_$product(rat_-5/8, rat_0) = rat_0 % 10.52/2.19 & rat_$product(rat_0, rat_-1/4) = rat_0 & rat_$product(rat_0, rat_-5/8) = % 10.52/2.19 rat_0 & rat_$product(rat_0, rat_0) = rat_0 & rat_$difference(rat_-1/4, % 10.52/2.19 rat_-1/4) = rat_0 & rat_$difference(rat_-1/4, rat_0) = rat_-1/4 & % 10.52/2.19 rat_$difference(rat_-5/8, rat_-5/8) = rat_0 & rat_$difference(rat_-5/8, rat_0) % 10.52/2.19 = rat_-5/8 & rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = % 10.52/2.19 rat_0 & rat_$sum(rat_-1/4, rat_0) = rat_-1/4 & rat_$sum(rat_-5/8, rat_0) = % 10.52/2.19 rat_-5/8 & rat_$sum(rat_0, rat_-1/4) = rat_-1/4 & rat_$sum(rat_0, rat_-5/8) = % 10.52/2.19 rat_-5/8 & rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small, % 10.52/2.19 rat_very_large) = 1 & rat_$greatereq(rat_-1/4, rat_-1/4) = 0 & % 10.52/2.19 rat_$greatereq(rat_-1/4, rat_-5/8) = 0 & rat_$greatereq(rat_-1/4, rat_0) = 1 & % 10.52/2.19 rat_$greatereq(rat_-5/8, rat_-1/4) = 1 & rat_$greatereq(rat_-5/8, rat_-5/8) = % 10.52/2.19 0 & rat_$greatereq(rat_-5/8, rat_0) = 1 & rat_$greatereq(rat_0, rat_-1/4) = 0 % 10.52/2.19 & rat_$greatereq(rat_0, rat_-5/8) = 0 & rat_$greatereq(rat_0, rat_0) = 0 & % 10.52/2.19 rat_$greater(rat_very_large, rat_-1/4) = 0 & rat_$greater(rat_very_large, % 10.52/2.19 rat_-5/8) = 0 & rat_$greater(rat_very_large, rat_0) = 0 & % 10.52/2.19 rat_$greater(rat_very_small, rat_very_large) = 1 & rat_$greater(rat_-1/4, % 10.52/2.19 rat_very_small) = 0 & rat_$greater(rat_-1/4, rat_-1/4) = 1 & % 10.52/2.19 rat_$greater(rat_-1/4, rat_-5/8) = 0 & rat_$greater(rat_-1/4, rat_0) = 1 & % 10.52/2.19 rat_$greater(rat_-5/8, rat_very_small) = 0 & rat_$greater(rat_-5/8, rat_-1/4) % 10.52/2.19 = 1 & rat_$greater(rat_-5/8, rat_-5/8) = 1 & rat_$greater(rat_-5/8, rat_0) = 1 % 10.52/2.19 & rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_-1/4) = 0 % 10.52/2.19 & rat_$greater(rat_0, rat_-5/8) = 0 & rat_$greater(rat_0, rat_0) = 1 & % 10.52/2.19 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small, % 10.52/2.19 rat_-1/4) = 0 & rat_$less(rat_very_small, rat_-5/8) = 0 & % 10.52/2.19 rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_-1/4, rat_very_large) = 0 % 10.52/2.19 & rat_$less(rat_-1/4, rat_-1/4) = 1 & rat_$less(rat_-1/4, rat_-5/8) = 1 & % 10.52/2.19 rat_$less(rat_-1/4, rat_0) = 0 & rat_$less(rat_-5/8, rat_very_large) = 0 & % 10.52/2.19 rat_$less(rat_-5/8, rat_-1/4) = 0 & rat_$less(rat_-5/8, rat_-5/8) = 1 & % 10.52/2.19 rat_$less(rat_-5/8, rat_0) = 0 & rat_$less(rat_0, rat_very_large) = 0 & % 10.52/2.19 rat_$less(rat_0, rat_-1/4) = 1 & rat_$less(rat_0, rat_-5/8) = 1 & % 10.52/2.19 rat_$less(rat_0, rat_0) = 1 & rat_$lesseq(rat_very_small, rat_very_large) = 0 % 10.52/2.19 & rat_$lesseq(rat_-1/4, rat_-1/4) = 0 & rat_$lesseq(rat_-1/4, rat_-5/8) = 1 & % 10.52/2.19 rat_$lesseq(rat_-1/4, rat_0) = 0 & rat_$lesseq(rat_-5/8, rat_-1/4) = 0 & % 10.52/2.19 rat_$lesseq(rat_-5/8, rat_-5/8) = 0 & rat_$lesseq(rat_-5/8, rat_0) = 0 & % 10.52/2.19 rat_$lesseq(rat_0, rat_-1/4) = 1 & rat_$lesseq(rat_0, rat_-5/8) = 1 & % 10.52/2.19 rat_$lesseq(rat_0, rat_0) = 0 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 10.52/2.19 : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ % 10.52/2.19 (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, v5) = v4 & % 10.52/2.19 rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 10.52/2.19 ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~ (rat_$sum(v1, % 10.52/2.19 v0) = v3) | ? [v5: $rat] : (rat_$sum(v5, v0) = v4 & rat_$sum(v2, v1) = % 10.52/2.19 v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 % 10.52/2.19 = 0 | ~ (rat_$less(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: % 10.52/2.19 int] : ( ~ (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: % 10.52/2.19 $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) % 10.52/2.19 | ~ (rat_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, % 10.52/2.19 v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: % 10.52/2.19 int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ (rat_$lesseq(v2, v1) = 0) % 10.52/2.19 | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v1, v0) = v4)) & ! [v0: $rat] : % 10.52/2.19 ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) % 10.52/2.19 = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & % 10.52/2.19 rat_$less(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 10.52/2.19 ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v2, % 10.52/2.19 v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & % 10.52/2.19 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 10.52/2.19 (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( % 10.52/2.19 ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : % 10.52/2.19 ! [v2: $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, % 10.52/2.19 v2) = v3) | rat_$difference(v1, v0) = v3) & ! [v0: $rat] : ! [v1: % 10.52/2.19 $rat] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (rat_$less(v1, v0) = v2) | ? % 10.52/2.19 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! % 10.52/2.19 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? % 10.52/2.19 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! % 10.52/2.19 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: % 10.52/2.19 int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: % 10.52/2.19 $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] % 10.52/2.19 : ( ~ (v3 = 0) & rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] % 10.52/2.19 : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ % 10.52/2.19 (v3 = 0) & rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : % 10.52/2.19 ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ % 10.52/2.19 (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! % 10.52/2.19 [v2: $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, % 10.52/2.19 v0) = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 10.52/2.19 (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] : % 10.52/2.19 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | % 10.52/2.19 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 10.52/2.19 ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = v3 & % 10.52/2.19 rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 10.52/2.19 ( ~ (rat_$sum(v1, v0) = v2) | rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1: % 10.52/2.19 $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) % 10.52/2.19 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$less(v2, v1) = 0) % 10.52/2.19 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! % 10.52/2.19 [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$less(v1, v0) = 0) | ~ (rat_$lesseq(v2, % 10.52/2.19 v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! % 10.52/2.19 [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v1, v0) = 0) | % 10.52/2.19 rat_$lesseq(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ % 10.52/2.19 (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ % 10.52/2.19 (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : ! [v1: % 10.52/2.19 int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & ! [v0: $rat] : ! [v1: % 10.52/2.19 $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0: $rat] : % 10.52/2.19 ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1) = rat_0) & ! % 10.52/2.19 [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | % 10.52/2.19 rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 10.52/2.19 (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : ! % 10.52/2.19 [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$greater(v0, v1) = 0) & ! [v0: % 10.52/2.19 $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$lesseq(v1, v0) = % 10.52/2.19 0) & ! [v0: $rat] : ! [v1: MultipleValueBool] : ( ~ (rat_$less(v0, v0) = % 10.52/2.19 v1) | rat_$lesseq(v0, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 10.52/2.20 (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & ! [v0: $rat] : % 10.52/2.20 (v0 = rat_0 | ~ (rat_$uminus(v0) = v0)) % 10.52/2.20 % 10.52/2.20 (function-axioms) % 10.52/2.20 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 10.52/2.20 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0: % 10.52/2.20 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 10.52/2.20 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0: % 10.52/2.20 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 10.52/2.20 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & ! % 10.52/2.20 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 10.52/2.20 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0: % 10.52/2.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 10.52/2.20 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3, % 10.52/2.20 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 10.52/2.20 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$greater(v3, v2) = v1) | ~ % 10.52/2.20 (rat_$greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.52/2.20 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 10.52/2.20 (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = v0)) & ! [v0: % 10.52/2.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 10.52/2.20 $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ (rat_$lesseq(v3, v2) = % 10.52/2.20 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.52/2.20 $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & % 10.52/2.20 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = % 10.52/2.20 v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] % 10.52/2.20 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~ % 10.52/2.20 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 % 10.52/2.20 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0: % 10.52/2.20 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) = % 10.52/2.20 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 10.52/2.20 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) & % 10.52/2.20 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) = % 10.52/2.20 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 10.52/2.20 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) & % 10.52/2.20 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~ % 10.52/2.20 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : ! % 10.52/2.20 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~ % 10.52/2.20 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 10.52/2.20 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0)) % 10.52/2.20 % 10.52/2.20 Those formulas are unsatisfiable: % 10.52/2.20 --------------------------------- % 10.52/2.20 % 10.52/2.20 Begin of proof % 10.52/2.21 | % 10.52/2.21 | ALPHA: (function-axioms) implies: % 10.52/2.21 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] % 10.52/2.21 | : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ % 10.52/2.21 | (rat_$lesseq(v3, v2) = v0)) % 10.52/2.21 | % 10.52/2.21 | ALPHA: (input) implies: % 10.52/2.21 | (2) rat_$lesseq(rat_-5/8, rat_-1/4) = 0 % 10.52/2.21 | % 10.52/2.21 | DELTA: instantiating (rat_lesseq_problem_9) with fresh symbol all_5_0 gives: % 10.52/2.21 | (3) ~ (all_5_0 = 0) & rat_$lesseq(rat_-5/8, rat_-1/4) = all_5_0 % 10.52/2.21 | % 10.52/2.21 | ALPHA: (3) implies: % 10.52/2.21 | (4) ~ (all_5_0 = 0) % 10.52/2.21 | (5) rat_$lesseq(rat_-5/8, rat_-1/4) = all_5_0 % 10.52/2.21 | % 10.52/2.21 | GROUND_INST: instantiating (1) with 0, all_5_0, rat_-1/4, rat_-5/8, % 10.52/2.21 | simplifying with (2), (5) gives: % 10.52/2.21 | (6) all_5_0 = 0 % 10.52/2.21 | % 10.52/2.21 | REDUCE: (4), (6) imply: % 10.52/2.21 | (7) $false % 10.52/2.21 | % 10.52/2.21 | CLOSE: (7) is inconsistent. % 10.52/2.21 | % 10.52/2.22 End of proof % 10.52/2.22 % SZS output end Proof for theBenchmark % 10.52/2.22 % 10.52/2.22 1604ms %------------------------------------------------------------------------------