%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI236_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 : n016.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 17:47:23 EDT 2023 % Result : Theorem 5.56s 1.49s % Output : Proof 8.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ARI236_1 : TPTP v8.1.2. Released v5.0.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n016.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Tue Aug 29 18:43:31 EDT 2023 % 0.13/0.33 % CPUTime : % 0.67/0.63 ________ _____ % 0.67/0.63 ___ __ \_________(_)________________________________ % 0.67/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.67/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.67/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.67/0.63 % 0.67/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.67/0.63 (2023-06-19) % 0.67/0.63 % 0.67/0.63 (c) Philipp Rümmer, 2009-2023 % 0.67/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.67/0.63 Amanda Stjerna. % 0.67/0.63 Free software under BSD-3-Clause. % 0.67/0.63 % 0.67/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.67/0.63 % 0.67/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.65 Running up to 7 provers in parallel. % 0.69/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.69/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.69/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.69/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.69/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.69/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.69/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.61/0.99 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 1.61/0.99 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.61/0.99 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 1.61/0.99 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 1.61/0.99 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 1.61/0.99 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.61/0.99 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 2.07/1.04 Prover 1: Preprocessing ... % 2.07/1.05 Prover 4: Preprocessing ... % 2.58/1.09 Prover 0: Preprocessing ... % 2.58/1.09 Prover 2: Preprocessing ... % 2.58/1.09 Prover 6: Preprocessing ... % 2.58/1.09 Prover 5: Preprocessing ... % 2.58/1.09 Prover 3: Preprocessing ... % 5.56/1.47 Prover 6: Constructing countermodel ... % 5.56/1.47 Prover 2: Constructing countermodel ... % 5.56/1.48 Prover 5: Constructing countermodel ... % 5.56/1.49 Prover 1: Constructing countermodel ... % 5.56/1.49 Prover 5: proved (826ms) % 5.56/1.49 Prover 2: proved (830ms) % 5.56/1.49 % 5.56/1.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.56/1.49 % 5.56/1.50 Prover 6: proved (826ms) % 5.56/1.50 % 5.56/1.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.56/1.50 % 5.56/1.51 % 5.56/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.56/1.51 % 5.56/1.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.56/1.52 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation % 5.56/1.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.56/1.52 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.56/1.52 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation % 5.56/1.52 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation % 5.56/1.53 Prover 0: Constructing countermodel ... % 5.56/1.53 Prover 0: stopped % 5.56/1.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.56/1.53 Prover 8: Preprocessing ... % 5.56/1.53 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation % 5.56/1.55 Prover 7: Preprocessing ... % 5.56/1.55 Prover 10: Preprocessing ... % 5.56/1.55 Prover 3: Constructing countermodel ... % 5.56/1.55 Prover 3: stopped % 5.56/1.55 Prover 11: Preprocessing ... % 5.56/1.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.56/1.56 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation % 5.56/1.56 Prover 13: Preprocessing ... % 6.29/1.57 Prover 4: Constructing countermodel ... % 6.68/1.67 Prover 8: Warning: ignoring some quantifiers % 6.68/1.68 Prover 8: Constructing countermodel ... % 6.68/1.70 Prover 13: Warning: ignoring some quantifiers % 6.68/1.70 Prover 13: Constructing countermodel ... % 6.68/1.72 Prover 4: Found proof (size 7) % 6.68/1.72 Prover 4: proved (1053ms) % 6.68/1.72 Prover 1: stopped % 6.68/1.72 Prover 8: stopped % 6.68/1.72 Prover 13: stopped % 6.68/1.72 Prover 10: Warning: ignoring some quantifiers % 7.44/1.73 Prover 7: Warning: ignoring some quantifiers % 7.44/1.74 Prover 10: Constructing countermodel ... % 7.44/1.75 Prover 7: Constructing countermodel ... % 7.44/1.75 Prover 10: stopped % 7.44/1.76 Prover 7: stopped % 7.91/1.84 Prover 11: Constructing countermodel ... % 7.91/1.85 Prover 11: stopped % 7.91/1.85 % 7.91/1.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.91/1.85 % 7.91/1.86 % SZS output start Proof for theBenchmark % 7.91/1.86 Assumptions after simplification: % 7.91/1.86 --------------------------------- % 7.91/1.86 % 7.91/1.86 (rat_greatereq_problem_7) % 8.25/1.88 ? [v0: int] : ( ~ (v0 = 0) & rat_$greatereq(rat_-3/4, rat_-3/4) = v0) % 8.25/1.88 % 8.25/1.88 (input) % 8.36/1.90 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_-3/4) & ~ % 8.36/1.90 (rat_very_large = rat_0) & ~ (rat_very_small = rat_-3/4) & ~ (rat_very_small % 8.36/1.90 = rat_0) & ~ (rat_-3/4 = rat_0) & rat_$is_int(rat_-3/4) = 1 & % 8.36/1.90 rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_-3/4) = 0 & rat_$is_rat(rat_0) = 0 & % 8.36/1.90 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_-3/4) = rat_0 & % 8.36/1.90 rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_-3/4) = rat_0 & % 8.36/1.90 rat_$truncate(rat_0) = rat_0 & rat_$round(rat_0) = rat_0 & % 8.36/1.90 rat_$to_int(rat_-3/4) = -1 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_-3/4) = % 8.36/1.91 rat_-3/4 & rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_-3/4) = real_-3/4 & % 8.36/1.91 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_0, % 8.36/1.91 rat_-3/4) = rat_0 & rat_$product(rat_-3/4, rat_0) = rat_0 & % 8.36/1.91 rat_$product(rat_0, rat_-3/4) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 & % 8.36/1.91 rat_$difference(rat_-3/4, rat_-3/4) = rat_0 & rat_$difference(rat_-3/4, rat_0) % 8.36/1.91 = rat_-3/4 & rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = % 8.36/1.91 rat_0 & rat_$sum(rat_-3/4, rat_0) = rat_-3/4 & rat_$sum(rat_0, rat_-3/4) = % 8.36/1.91 rat_-3/4 & rat_$sum(rat_0, rat_0) = rat_0 & rat_$lesseq(rat_very_small, % 8.36/1.91 rat_very_large) = 0 & rat_$lesseq(rat_-3/4, rat_-3/4) = 0 & % 8.36/1.91 rat_$lesseq(rat_-3/4, rat_0) = 0 & rat_$lesseq(rat_0, rat_-3/4) = 1 & % 8.36/1.91 rat_$lesseq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_-3/4) = 0 & % 8.36/1.91 rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small, % 8.36/1.91 rat_very_large) = 1 & rat_$greater(rat_-3/4, rat_very_small) = 0 & % 8.36/1.91 rat_$greater(rat_-3/4, rat_-3/4) = 1 & rat_$greater(rat_-3/4, rat_0) = 1 & % 8.36/1.91 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_-3/4) = 0 & % 8.36/1.91 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0 % 8.36/1.91 & rat_$less(rat_very_small, rat_-3/4) = 0 & rat_$less(rat_very_small, rat_0) = % 8.36/1.91 0 & rat_$less(rat_-3/4, rat_very_large) = 0 & rat_$less(rat_-3/4, rat_-3/4) = % 8.36/1.91 1 & rat_$less(rat_-3/4, rat_0) = 0 & rat_$less(rat_0, rat_very_large) = 0 & % 8.36/1.91 rat_$less(rat_0, rat_-3/4) = 1 & rat_$less(rat_0, rat_0) = 1 & % 8.36/1.91 rat_$greatereq(rat_very_small, rat_very_large) = 1 & rat_$greatereq(rat_-3/4, % 8.36/1.91 rat_-3/4) = 0 & rat_$greatereq(rat_-3/4, rat_0) = 1 & rat_$greatereq(rat_0, % 8.36/1.91 rat_-3/4) = 0 & rat_$greatereq(rat_0, rat_0) = 0 & ! [v0: $rat] : ! [v1: % 8.36/1.91 $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, % 8.36/1.91 v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, % 8.36/1.91 v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! % 8.36/1.91 [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~ % 8.36/1.91 (rat_$sum(v1, v0) = v3) | ? [v5: $rat] : (rat_$sum(v5, v0) = v4 & % 8.36/1.91 rat_$sum(v2, v1) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 8.36/1.91 ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v2, v0) % 8.36/1.91 = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: % 8.36/1.91 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 8.36/1.91 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ % 8.36/1.91 (v4 = 0) & rat_$less(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! % 8.36/1.91 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v0) = v3) | ~ % 8.36/1.91 (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, % 8.36/1.91 v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: % 8.36/1.91 int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, v0) = v3) % 8.36/1.91 | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & ! [v0: $rat] : % 8.36/1.91 ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v1) % 8.36/1.91 = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & % 8.36/1.91 rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 8.36/1.91 : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ (rat_$less(v1, v0) % 8.36/1.91 = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: % 8.36/1.91 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) % 8.36/1.91 = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1, v0) = v3) & ! % 8.36/1.91 [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 8.36/1.91 (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) % 8.36/1.91 = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ % 8.36/1.91 (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) % 8.36/1.91 = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ % 8.36/1.91 (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 8.36/1.91 rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 8.36/1.91 int] : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = % 8.36/1.91 0) & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 8.36/1.91 int] : (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 8.36/1.91 rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 8.36/1.91 : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 8.36/1.91 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 8.36/1.91 : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0) = v1) & % 8.36/1.91 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v1, v0) = % 8.36/1.91 v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 8.36/1.91 $rat] : ( ~ (rat_$product(v0, v1) = v2) | rat_$product(v1, v0) = v2) & ! % 8.36/1.91 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$difference(v1, v0) = % 8.36/1.91 v2) | ? [v3: $rat] : (rat_$uminus(v0) = v3 & rat_$sum(v1, v3) = v2)) & ! % 8.36/1.91 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) = v2) | % 8.36/1.91 rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 8.36/1.91 (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1: % 8.36/1.91 $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v1, % 8.36/1.91 v0) = 0) | rat_$lesseq(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! % 8.36/1.91 [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1, v0) = 0) | % 8.36/1.91 rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 8.36/1.91 (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, v1) = 0) | rat_$less(v2, v0) = % 8.36/1.91 0) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = % 8.36/1.91 v1)) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) % 8.36/1.91 = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : ! [v1: int] : (v1 = 0 | % 8.36/1.91 ~ (rat_$lesseq(v0, v0) = v1)) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 8.36/1.91 (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0: $rat] : ! [v1: % 8.36/1.91 $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1) = rat_0) & ! [v0: % 8.36/1.91 $rat] : ! [v1: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, % 8.36/1.91 v1) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) % 8.36/1.91 | rat_$less(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 8.36/1.91 (rat_$less(v1, v0) = 0) | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: % 8.36/1.91 $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$greater(v0, v1) = 0) & ! [v0: % 8.36/1.91 $rat] : ! [v1: MultipleValueBool] : ( ~ (rat_$less(v0, v0) = v1) | % 8.36/1.91 rat_$lesseq(v0, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 8.36/1.91 (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : % 8.36/1.91 (v0 = rat_0 | ~ (rat_$uminus(v0) = v0)) % 8.36/1.91 % 8.36/1.91 (function-axioms) % 8.36/1.91 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 8.36/1.91 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0: % 8.36/1.91 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 8.36/1.91 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0: % 8.36/1.91 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 8.36/1.91 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & ! % 8.36/1.91 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 8.36/1.91 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0: % 8.36/1.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 8.36/1.91 $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ (rat_$lesseq(v3, v2) = % 8.36/1.91 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.36/1.91 $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$greater(v3, v2) = v1) | ~ % 8.36/1.91 (rat_$greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.36/1.91 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 8.36/1.91 (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = v0)) & ! [v0: % 8.36/1.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 8.36/1.91 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3, % 8.36/1.91 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 8.36/1.91 ! [v2: $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = % 8.36/1.91 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.36/1.91 $rat] : (v1 = v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & % 8.36/1.91 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = % 8.36/1.91 v1) | ~ (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 8.36/1.91 $rat] : (v1 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) % 8.36/1.91 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ % 8.36/1.91 (rat_$truncate(v2) = v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! % 8.36/1.91 [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ % 8.36/1.91 (rat_$round(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = % 8.36/1.91 v0 | ~ (rat_$to_int(v2) = v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] % 8.36/1.91 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ % 8.36/1.91 (rat_$to_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : % 8.36/1.91 (v1 = v0 | ~ (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: % 8.36/1.91 $rat] : ! [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) % 8.36/1.91 | ~ (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 8.36/1.91 : (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0)) % 8.36/1.91 % 8.36/1.91 Those formulas are unsatisfiable: % 8.36/1.91 --------------------------------- % 8.36/1.91 % 8.36/1.91 Begin of proof % 8.36/1.91 | % 8.36/1.92 | ALPHA: (function-axioms) implies: % 8.46/1.92 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] % 8.46/1.92 | : ! [v3: $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ % 8.46/1.92 | (rat_$greatereq(v3, v2) = v0)) % 8.46/1.92 | % 8.46/1.92 | ALPHA: (input) implies: % 8.46/1.92 | (2) rat_$greatereq(rat_-3/4, rat_-3/4) = 0 % 8.46/1.92 | % 8.46/1.92 | DELTA: instantiating (rat_greatereq_problem_7) with fresh symbol all_5_0 % 8.46/1.92 | gives: % 8.46/1.92 | (3) ~ (all_5_0 = 0) & rat_$greatereq(rat_-3/4, rat_-3/4) = all_5_0 % 8.46/1.92 | % 8.46/1.92 | ALPHA: (3) implies: % 8.46/1.92 | (4) ~ (all_5_0 = 0) % 8.46/1.92 | (5) rat_$greatereq(rat_-3/4, rat_-3/4) = all_5_0 % 8.46/1.92 | % 8.46/1.92 | GROUND_INST: instantiating (1) with 0, all_5_0, rat_-3/4, rat_-3/4, % 8.46/1.92 | simplifying with (2), (5) gives: % 8.46/1.92 | (6) all_5_0 = 0 % 8.46/1.92 | % 8.46/1.92 | REDUCE: (4), (6) imply: % 8.46/1.92 | (7) $false % 8.46/1.92 | % 8.46/1.92 | CLOSE: (7) is inconsistent. % 8.46/1.92 | % 8.46/1.92 End of proof % 8.46/1.92 % SZS output end Proof for theBenchmark % 8.46/1.92 % 8.46/1.92 1293ms %------------------------------------------------------------------------------