%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI191_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 : n013.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 17:47:13 EDT 2023 % Result : Theorem 6.06s 1.60s % Output : Proof 9.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ARI191_1 : TPTP v8.1.2. Released v5.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n013.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 18:38:16 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.53/0.96 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 1.53/0.96 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.53/0.96 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 1.53/0.96 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 1.53/0.96 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 1.53/0.96 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 1.53/0.96 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 2.05/1.04 Prover 4: Preprocessing ... % 2.05/1.05 Prover 1: Preprocessing ... % 2.84/1.10 Prover 6: Preprocessing ... % 2.84/1.11 Prover 0: Preprocessing ... % 2.92/1.14 Prover 5: Preprocessing ... % 2.92/1.14 Prover 3: Preprocessing ... % 2.92/1.14 Prover 2: Preprocessing ... % 6.06/1.57 Prover 6: Constructing countermodel ... % 6.06/1.59 Prover 6: proved (940ms) % 6.06/1.60 % 6.06/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.06/1.60 % 6.06/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.06/1.61 Prover 0: Constructing countermodel ... % 6.49/1.61 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation % 6.49/1.61 Prover 0: stopped % 6.49/1.62 Prover 1: Constructing countermodel ... % 6.49/1.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.49/1.62 Prover 2: stopped % 6.49/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.49/1.62 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation % 6.49/1.62 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation % 6.49/1.62 Prover 8: Preprocessing ... % 6.83/1.66 Prover 4: Constructing countermodel ... % 6.83/1.66 Prover 7: Preprocessing ... % 6.83/1.68 Prover 10: Preprocessing ... % 7.51/1.77 Prover 8: Warning: ignoring some quantifiers % 7.85/1.79 Prover 8: Constructing countermodel ... % 8.58/1.92 Prover 4: Found proof (size 4) % 8.58/1.92 Prover 4: proved (1272ms) % 8.58/1.92 Prover 1: stopped % 8.58/1.92 Prover 8: stopped % 8.58/1.93 Prover 10: stopped % 8.58/1.94 Prover 7: stopped % 8.58/1.95 Prover 5: Constructing countermodel ... % 8.58/1.95 Prover 5: stopped % 9.04/1.98 Prover 3: Constructing countermodel ... % 9.04/1.98 Prover 3: stopped % 9.04/1.98 % 9.04/1.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.04/1.98 % 9.04/1.98 % SZS output start Proof for theBenchmark % 9.04/1.98 Assumptions after simplification: % 9.04/1.98 --------------------------------- % 9.04/1.98 % 9.04/1.98 (rat_less_problem_2) % 9.04/2.00 rat_$less(rat_1/2, rat_1/21) = 0 % 9.04/2.00 % 9.04/2.00 (input) % 9.27/2.03 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_1/21) & ~ % 9.27/2.03 (rat_very_large = rat_1/2) & ~ (rat_very_large = rat_0) & ~ (rat_very_small % 9.27/2.03 = rat_1/21) & ~ (rat_very_small = rat_1/2) & ~ (rat_very_small = rat_0) & % 9.27/2.04 ~ (rat_1/21 = rat_1/2) & ~ (rat_1/21 = rat_0) & ~ (rat_1/2 = rat_0) & % 9.27/2.04 rat_$is_int(rat_1/21) = 1 & rat_$is_int(rat_1/2) = 1 & rat_$is_int(rat_0) = 0 % 9.27/2.04 & rat_$is_rat(rat_1/21) = 0 & rat_$is_rat(rat_1/2) = 0 & rat_$is_rat(rat_0) = % 9.27/2.04 0 & rat_$floor(rat_1/21) = rat_0 & rat_$floor(rat_1/2) = rat_0 & % 9.27/2.04 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 & % 9.27/2.04 rat_$truncate(rat_1/21) = rat_0 & rat_$truncate(rat_1/2) = rat_0 & % 9.27/2.04 rat_$truncate(rat_0) = rat_0 & rat_$round(rat_1/21) = rat_0 & % 9.27/2.04 rat_$round(rat_0) = rat_0 & rat_$to_int(rat_1/21) = 0 & rat_$to_int(rat_1/2) = % 9.27/2.04 0 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_1/21) = rat_1/21 & % 9.27/2.04 rat_$to_rat(rat_1/2) = rat_1/2 & rat_$to_rat(rat_0) = rat_0 & % 9.27/2.04 rat_$to_real(rat_1/21) = real_1/21 & rat_$to_real(rat_1/2) = real_1/2 & % 9.27/2.04 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_0, % 9.27/2.04 rat_1/21) = rat_0 & rat_$quotient(rat_0, rat_1/2) = rat_0 & % 9.27/2.04 rat_$product(rat_1/21, rat_0) = rat_0 & rat_$product(rat_1/2, rat_0) = rat_0 & % 9.27/2.04 rat_$product(rat_0, rat_1/21) = rat_0 & rat_$product(rat_0, rat_1/2) = rat_0 & % 9.27/2.04 rat_$product(rat_0, rat_0) = rat_0 & rat_$difference(rat_1/21, rat_1/21) = % 9.27/2.04 rat_0 & rat_$difference(rat_1/21, rat_0) = rat_1/21 & rat_$difference(rat_1/2, % 9.27/2.04 rat_1/2) = rat_0 & rat_$difference(rat_1/2, rat_0) = rat_1/2 & % 9.27/2.04 rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 & % 9.27/2.04 rat_$sum(rat_1/21, rat_0) = rat_1/21 & rat_$sum(rat_1/2, rat_0) = rat_1/2 & % 9.27/2.04 rat_$sum(rat_0, rat_1/21) = rat_1/21 & rat_$sum(rat_0, rat_1/2) = rat_1/2 & % 9.27/2.04 rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small, % 9.27/2.04 rat_very_large) = 1 & rat_$greatereq(rat_1/21, rat_1/21) = 0 & % 9.27/2.04 rat_$greatereq(rat_1/21, rat_1/2) = 1 & rat_$greatereq(rat_1/21, rat_0) = 0 & % 9.27/2.04 rat_$greatereq(rat_1/2, rat_1/21) = 0 & rat_$greatereq(rat_1/2, rat_1/2) = 0 & % 9.27/2.04 rat_$greatereq(rat_1/2, rat_0) = 0 & rat_$greatereq(rat_0, rat_1/21) = 1 & % 9.27/2.04 rat_$greatereq(rat_0, rat_1/2) = 1 & rat_$greatereq(rat_0, rat_0) = 0 & % 9.27/2.04 rat_$lesseq(rat_very_small, rat_very_large) = 0 & rat_$lesseq(rat_1/21, % 9.27/2.04 rat_1/21) = 0 & rat_$lesseq(rat_1/21, rat_1/2) = 0 & rat_$lesseq(rat_1/21, % 9.27/2.04 rat_0) = 1 & rat_$lesseq(rat_1/2, rat_1/21) = 1 & rat_$lesseq(rat_1/2, % 9.27/2.04 rat_1/2) = 0 & rat_$lesseq(rat_1/2, rat_0) = 1 & rat_$lesseq(rat_0, % 9.27/2.04 rat_1/21) = 0 & rat_$lesseq(rat_0, rat_1/2) = 0 & rat_$lesseq(rat_0, rat_0) % 9.27/2.04 = 0 & rat_$greater(rat_very_large, rat_1/21) = 0 & % 9.27/2.04 rat_$greater(rat_very_large, rat_1/2) = 0 & rat_$greater(rat_very_large, % 9.27/2.04 rat_0) = 0 & rat_$greater(rat_very_small, rat_very_large) = 1 & % 9.27/2.04 rat_$greater(rat_1/21, rat_very_small) = 0 & rat_$greater(rat_1/21, rat_1/21) % 9.27/2.04 = 1 & rat_$greater(rat_1/21, rat_1/2) = 1 & rat_$greater(rat_1/21, rat_0) = 0 % 9.27/2.04 & rat_$greater(rat_1/2, rat_very_small) = 0 & rat_$greater(rat_1/2, rat_1/21) % 9.27/2.04 = 0 & rat_$greater(rat_1/2, rat_1/2) = 1 & rat_$greater(rat_1/2, rat_0) = 0 & % 9.27/2.04 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_1/21) = 1 & % 9.27/2.04 rat_$greater(rat_0, rat_1/2) = 1 & rat_$greater(rat_0, rat_0) = 1 & % 9.27/2.04 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small, % 9.27/2.04 rat_1/21) = 0 & rat_$less(rat_very_small, rat_1/2) = 0 & % 9.27/2.04 rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_1/21, rat_very_large) = 0 % 9.27/2.04 & rat_$less(rat_1/21, rat_1/21) = 1 & rat_$less(rat_1/21, rat_1/2) = 0 & % 9.27/2.04 rat_$less(rat_1/21, rat_0) = 1 & rat_$less(rat_1/2, rat_very_large) = 0 & % 9.27/2.04 rat_$less(rat_1/2, rat_1/21) = 1 & rat_$less(rat_1/2, rat_1/2) = 1 & % 9.27/2.04 rat_$less(rat_1/2, rat_0) = 1 & rat_$less(rat_0, rat_very_large) = 0 & % 9.27/2.04 rat_$less(rat_0, rat_1/21) = 0 & rat_$less(rat_0, rat_1/2) = 0 & % 9.27/2.04 rat_$less(rat_0, rat_0) = 1 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 9.27/2.04 ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, % 9.27/2.04 v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = % 9.27/2.04 v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! % 9.27/2.04 [v4: $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~ (rat_$sum(v1, v0) = v3) | ? % 9.27/2.04 [v5: $rat] : (rat_$sum(v5, v0) = v4 & rat_$sum(v2, v1) = v5)) & ! [v0: % 9.27/2.04 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 9.27/2.04 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v2, v0) = v3) | ? [v4: int] : ( % 9.27/2.04 ~ (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : % 9.27/2.04 ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ % 9.27/2.04 (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v1, v0) = % 9.27/2.04 v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 % 9.27/2.04 = 0 | ~ (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: % 9.27/2.04 int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: % 9.27/2.04 $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = % 9.27/2.04 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & % 9.27/2.04 rat_$less(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 9.27/2.04 ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v1) = 0) | ~ (rat_$less(v2, v0) = % 9.27/2.04 v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: % 9.27/2.04 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 9.27/2.04 (rat_$less(v2, v0) = v3) | ~ (rat_$less(v1, v0) = 0) | ? [v4: int] : ( ~ % 9.27/2.04 (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! % 9.27/2.04 [v2: $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) % 9.27/2.04 = v3) | rat_$difference(v1, v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! % 9.27/2.04 [v2: int] : (v2 = 0 | v1 = v0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( % 9.27/2.04 ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : % 9.27/2.04 ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ % 9.27/2.04 (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! % 9.27/2.04 [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = % 9.27/2.04 0) & rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! % 9.27/2.04 [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = % 9.27/2.04 0) & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 9.27/2.04 int] : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = % 9.27/2.04 0) & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 9.27/2.04 int] : (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 9.27/2.04 rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 9.27/2.04 $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0) % 9.27/2.04 = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 9.27/2.04 (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] : % 9.27/2.04 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | % 9.27/2.04 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 9.43/2.04 ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = v3 & % 9.43/2.04 rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 9.43/2.04 ( ~ (rat_$sum(v1, v0) = v2) | rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1: % 9.43/2.04 $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) % 9.43/2.04 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = % 9.43/2.04 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2, v0) = 0) & ! [v0: % 9.43/2.04 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~ % 9.43/2.04 (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: % 9.43/2.04 $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, % 9.43/2.04 v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : (v1 % 9.43/2.04 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] : (v1 % 9.43/2.04 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] % 9.43/2.04 : ! [v1: int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & ! [v0: $rat] : ! % 9.43/2.04 [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0: % 9.43/2.04 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1) = % 9.43/2.04 rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | % 9.43/2.04 rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 9.43/2.04 (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & ! [v0: $rat] : ! % 9.43/2.04 [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0: % 9.43/2.04 $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$lesseq(v1, v0) = % 9.43/2.04 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | % 9.43/2.04 rat_$greater(v0, v1) = 0) & ! [v0: $rat] : ! [v1: MultipleValueBool] : ( ~ % 9.43/2.04 (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) = 0) & ! [v0: $rat] : (v0 = % 9.43/2.04 rat_0 | ~ (rat_$uminus(v0) = v0)) % 9.43/2.04 % 9.43/2.04 (function-axioms) % 9.43/2.05 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 9.43/2.05 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0: % 9.43/2.05 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 9.43/2.05 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0: % 9.43/2.05 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 9.43/2.05 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & ! % 9.43/2.05 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 9.43/2.05 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0: % 9.43/2.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 9.43/2.05 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3, % 9.43/2.05 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 9.43/2.05 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ % 9.43/2.05 (rat_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.43/2.05 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 9.43/2.05 (rat_$greater(v3, v2) = v1) | ~ (rat_$greater(v3, v2) = v0)) & ! [v0: % 9.43/2.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 9.43/2.05 $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = % 9.43/2.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.43/2.05 $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & % 9.43/2.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = % 9.43/2.05 v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] % 9.43/2.05 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~ % 9.43/2.05 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 % 9.43/2.05 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0: % 9.43/2.05 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) = % 9.43/2.05 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 9.43/2.05 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) & % 9.43/2.05 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) = % 9.43/2.05 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 9.43/2.05 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) & % 9.43/2.05 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~ % 9.43/2.05 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : ! % 9.43/2.05 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~ % 9.43/2.05 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 9.43/2.05 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0)) % 9.43/2.05 % 9.43/2.05 Those formulas are unsatisfiable: % 9.43/2.05 --------------------------------- % 9.43/2.05 % 9.43/2.05 Begin of proof % 9.43/2.05 | % 9.43/2.05 | ALPHA: (function-axioms) implies: % 9.43/2.06 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] % 9.43/2.06 | : ! [v3: $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ % 9.43/2.06 | (rat_$less(v3, v2) = v0)) % 9.43/2.06 | % 9.43/2.06 | ALPHA: (input) implies: % 9.43/2.06 | (2) rat_$less(rat_1/2, rat_1/21) = 1 % 9.43/2.06 | % 9.43/2.06 | GROUND_INST: instantiating (1) with 0, 1, rat_1/21, rat_1/2, simplifying with % 9.43/2.06 | (2), (rat_less_problem_2) gives: % 9.43/2.06 | (3) $false % 9.43/2.06 | % 9.43/2.06 | CLOSE: (3) is inconsistent. % 9.43/2.06 | % 9.43/2.06 End of proof % 9.43/2.06 % SZS output end Proof for theBenchmark % 9.43/2.06 % 9.43/2.06 1439ms %------------------------------------------------------------------------------