%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI558_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 : n023.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 17:48:23 EDT 2023 % Result : Theorem 10.69s 2.18s % Output : Proof 11.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : ARI558_1 : TPTP v8.1.2. Released v5.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n023.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 19:05:40 EDT 2023 % 0.14/0.34 % CPUTime : % 0.62/0.61 ________ _____ % 0.62/0.61 ___ __ \_________(_)________________________________ % 0.62/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.62/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.62/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.62/0.61 % 0.62/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.62/0.61 (2023-06-19) % 0.62/0.61 % 0.62/0.61 (c) Philipp Rümmer, 2009-2023 % 0.62/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.62/0.61 Amanda Stjerna. % 0.62/0.61 Free software under BSD-3-Clause. % 0.62/0.61 % 0.62/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.62/0.61 % 0.62/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.62/0.62 Running up to 7 provers in parallel. % 0.72/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.72/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.72/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.72/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.72/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.72/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.72/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.48/0.89 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.48/0.89 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 1.48/0.89 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 1.48/0.89 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 1.48/0.89 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 1.48/0.89 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.48/0.89 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 2.04/0.99 Prover 1: Preprocessing ... % 2.48/1.00 Prover 4: Preprocessing ... % 2.48/1.07 Prover 0: Preprocessing ... % 2.48/1.07 Prover 6: Preprocessing ... % 2.94/1.10 Prover 2: Preprocessing ... % 2.94/1.10 Prover 3: Preprocessing ... % 2.94/1.10 Prover 5: Preprocessing ... % 6.39/1.58 Prover 1: Constructing countermodel ... % 6.39/1.62 Prover 4: Constructing countermodel ... % 7.08/1.63 Prover 6: Proving ... % 7.08/1.67 Prover 0: Proving ... % 9.90/2.02 Prover 1: Found proof (size 10) % 9.90/2.02 Prover 1: proved (1387ms) % 9.90/2.03 Prover 4: stopped % 9.90/2.03 Prover 6: stopped % 9.90/2.03 Prover 0: stopped % 9.90/2.07 Prover 3: Constructing countermodel ... % 9.90/2.07 Prover 3: stopped % 10.60/2.10 Prover 2: Proving ... % 10.60/2.10 Prover 2: stopped % 10.69/2.18 Prover 5: Proving ... % 10.69/2.18 Prover 5: stopped % 10.69/2.18 % 10.69/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.69/2.18 % 10.69/2.18 % SZS output start Proof for theBenchmark % 10.69/2.18 Assumptions after simplification: % 10.69/2.18 --------------------------------- % 10.69/2.18 % 10.69/2.18 (rat_combined_problem_18) % 10.69/2.21 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$product(v0, rat_-1/20) = v1) | ? % 10.69/2.21 [v2: $rat] : ? [v3: int] : ( ~ (v3 = 0) & rat_$difference(rat_-1/4, v1) = % 10.69/2.21 v2 & rat_$lesseq(v2, rat_0) = v3)) % 10.69/2.21 % 10.69/2.21 (input) % 11.18/2.23 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_-1/20) & ~ % 11.18/2.23 (rat_very_large = rat_-1/4) & ~ (rat_very_large = rat_0) & ~ (rat_very_small % 11.18/2.23 = rat_-1/20) & ~ (rat_very_small = rat_-1/4) & ~ (rat_very_small = rat_0) % 11.18/2.23 & ~ (rat_-1/20 = rat_-1/4) & ~ (rat_-1/20 = rat_0) & ~ (rat_-1/4 = rat_0) & % 11.18/2.23 rat_$is_int(rat_-1/20) = 1 & rat_$is_int(rat_-1/4) = 1 & rat_$is_int(rat_0) = % 11.18/2.23 0 & rat_$is_rat(rat_-1/20) = 0 & rat_$is_rat(rat_-1/4) = 0 & % 11.18/2.23 rat_$is_rat(rat_0) = 0 & rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_-1/20) = % 11.18/2.23 rat_0 & rat_$ceiling(rat_-1/4) = rat_0 & rat_$ceiling(rat_0) = rat_0 & % 11.18/2.23 rat_$truncate(rat_-1/20) = rat_0 & rat_$truncate(rat_-1/4) = rat_0 & % 11.18/2.23 rat_$truncate(rat_0) = rat_0 & rat_$round(rat_-1/20) = rat_0 & % 11.18/2.23 rat_$round(rat_-1/4) = rat_0 & rat_$round(rat_0) = rat_0 & % 11.18/2.23 rat_$to_int(rat_-1/20) = -1 & rat_$to_int(rat_-1/4) = -1 & rat_$to_int(rat_0) % 11.18/2.23 = 0 & rat_$to_rat(rat_-1/20) = rat_-1/20 & rat_$to_rat(rat_-1/4) = rat_-1/4 & % 11.18/2.23 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_-1/20) = real_-1/20 & % 11.18/2.23 rat_$to_real(rat_-1/4) = real_-1/4 & rat_$to_real(rat_0) = real_0 & % 11.18/2.23 int_$to_rat(0) = rat_0 & rat_$quotient(rat_0, rat_-1/20) = rat_0 & % 11.18/2.23 rat_$quotient(rat_0, rat_-1/4) = rat_0 & rat_$uminus(rat_0) = rat_0 & % 11.18/2.23 rat_$sum(rat_-1/20, rat_0) = rat_-1/20 & rat_$sum(rat_-1/4, rat_0) = rat_-1/4 % 11.18/2.23 & rat_$sum(rat_0, rat_-1/20) = rat_-1/20 & rat_$sum(rat_0, rat_-1/4) = % 11.18/2.23 rat_-1/4 & rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small, % 11.18/2.23 rat_very_large) = 1 & rat_$greatereq(rat_-1/20, rat_-1/20) = 0 & % 11.18/2.23 rat_$greatereq(rat_-1/20, rat_-1/4) = 0 & rat_$greatereq(rat_-1/20, rat_0) = 1 % 11.18/2.23 & rat_$greatereq(rat_-1/4, rat_-1/20) = 1 & rat_$greatereq(rat_-1/4, rat_-1/4) % 11.18/2.23 = 0 & rat_$greatereq(rat_-1/4, rat_0) = 1 & rat_$greatereq(rat_0, rat_-1/20) = % 11.18/2.23 0 & rat_$greatereq(rat_0, rat_-1/4) = 0 & rat_$greatereq(rat_0, rat_0) = 0 & % 11.18/2.23 rat_$greater(rat_very_large, rat_-1/20) = 0 & rat_$greater(rat_very_large, % 11.18/2.23 rat_-1/4) = 0 & rat_$greater(rat_very_large, rat_0) = 0 & % 11.18/2.23 rat_$greater(rat_very_small, rat_very_large) = 1 & rat_$greater(rat_-1/20, % 11.18/2.23 rat_very_small) = 0 & rat_$greater(rat_-1/20, rat_-1/20) = 1 & % 11.18/2.23 rat_$greater(rat_-1/20, rat_-1/4) = 0 & rat_$greater(rat_-1/20, rat_0) = 1 & % 11.18/2.23 rat_$greater(rat_-1/4, rat_very_small) = 0 & rat_$greater(rat_-1/4, rat_-1/20) % 11.18/2.23 = 1 & rat_$greater(rat_-1/4, rat_-1/4) = 1 & rat_$greater(rat_-1/4, rat_0) = 1 % 11.18/2.23 & rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_-1/20) = 0 % 11.18/2.23 & rat_$greater(rat_0, rat_-1/4) = 0 & rat_$greater(rat_0, rat_0) = 1 & % 11.18/2.23 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small, % 11.18/2.23 rat_-1/20) = 0 & rat_$less(rat_very_small, rat_-1/4) = 0 & % 11.18/2.23 rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_-1/20, rat_very_large) = % 11.18/2.23 0 & rat_$less(rat_-1/20, rat_-1/20) = 1 & rat_$less(rat_-1/20, rat_-1/4) = 1 & % 11.18/2.23 rat_$less(rat_-1/20, rat_0) = 0 & rat_$less(rat_-1/4, rat_very_large) = 0 & % 11.18/2.23 rat_$less(rat_-1/4, rat_-1/20) = 0 & rat_$less(rat_-1/4, rat_-1/4) = 1 & % 11.18/2.23 rat_$less(rat_-1/4, rat_0) = 0 & rat_$less(rat_0, rat_very_large) = 0 & % 11.18/2.23 rat_$less(rat_0, rat_-1/20) = 1 & rat_$less(rat_0, rat_-1/4) = 1 & % 11.18/2.23 rat_$less(rat_0, rat_0) = 1 & rat_$product(rat_-1/20, rat_0) = rat_0 & % 11.18/2.23 rat_$product(rat_-1/4, rat_0) = rat_0 & rat_$product(rat_0, rat_-1/20) = rat_0 % 11.18/2.23 & rat_$product(rat_0, rat_-1/4) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 & % 11.18/2.23 rat_$difference(rat_-1/20, rat_-1/20) = rat_0 & rat_$difference(rat_-1/20, % 11.18/2.23 rat_0) = rat_-1/20 & rat_$difference(rat_-1/4, rat_-1/4) = rat_0 & % 11.18/2.23 rat_$difference(rat_-1/4, rat_0) = rat_-1/4 & rat_$difference(rat_0, rat_0) = % 11.18/2.23 rat_0 & rat_$lesseq(rat_very_small, rat_very_large) = 0 & % 11.18/2.23 rat_$lesseq(rat_-1/20, rat_-1/20) = 0 & rat_$lesseq(rat_-1/20, rat_-1/4) = 1 & % 11.18/2.23 rat_$lesseq(rat_-1/20, rat_0) = 0 & rat_$lesseq(rat_-1/4, rat_-1/20) = 0 & % 11.18/2.23 rat_$lesseq(rat_-1/4, rat_-1/4) = 0 & rat_$lesseq(rat_-1/4, rat_0) = 0 & % 11.18/2.23 rat_$lesseq(rat_0, rat_-1/20) = 1 & rat_$lesseq(rat_0, rat_-1/4) = 1 & % 11.18/2.23 rat_$lesseq(rat_0, rat_0) = 0 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 11.18/2.23 : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ % 11.18/2.23 (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, v5) = v4 & % 11.18/2.23 rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 11.18/2.23 ! [v3: $rat] : (v3 = v1 | v0 = rat_0 | ~ (rat_$quotient(v2, v0) = v3) | ~ % 11.18/2.23 (rat_$product(v1, v0) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 11.18/2.23 : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ (rat_$lesseq(v1, % 11.18/2.23 v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & ! % 11.18/2.23 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 11.18/2.23 (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( % 11.18/2.23 ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : % 11.18/2.23 ! [v2: $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, % 11.18/2.23 v2) = v3) | rat_$difference(v1, v0) = v3) & ! [v0: $rat] : ! [v1: % 11.18/2.23 $rat] : ! [v2: $rat] : (v2 = rat_0 | ~ (rat_$uminus(v0) = v1) | ~ % 11.18/2.23 (rat_$sum(v0, v1) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : % 11.18/2.23 (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 11.18/2.23 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 11.18/2.23 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 11.18/2.23 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : % 11.18/2.23 (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3: int] : ( ~ % 11.18/2.23 (v3 = 0) & rat_$less(v1, v0) = v3))) & ! [v0: $rat] : ! [v1: $rat] : % 11.18/2.23 ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0: % 11.18/2.23 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$less(v1, v0) = 0) | ~ % 11.18/2.23 (rat_$lesseq(v2, v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: % 11.18/2.23 $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | rat_$product(v1, % 11.18/2.23 v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, % 11.18/2.23 rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ % 11.18/2.23 (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : ! [v1: % 11.18/2.23 $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0: $rat] : % 11.18/2.23 ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1, v0) = 0) & % 11.18/2.23 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, % 11.18/2.23 v0) = 0) & ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0) = v0)) % 11.18/2.23 % 11.18/2.24 (function-axioms) % 11.18/2.24 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 11.18/2.24 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0: % 11.18/2.24 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 11.18/2.24 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0: % 11.18/2.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 11.18/2.24 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3, % 11.18/2.24 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 11.18/2.24 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$greater(v3, v2) = v1) | ~ % 11.18/2.24 (rat_$greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.18/2.24 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 11.18/2.24 (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = v0)) & ! [v0: $rat] : ! % 11.18/2.24 [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$product(v3, % 11.18/2.24 v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0: $rat] : ! [v1: % 11.18/2.24 $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$difference(v3, % 11.18/2.24 v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & ! [v0: % 11.18/2.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 11.18/2.24 $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ (rat_$lesseq(v3, v2) = % 11.18/2.24 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.18/2.24 $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & % 11.18/2.24 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = % 11.18/2.24 v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] % 11.18/2.24 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~ % 11.18/2.24 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 % 11.18/2.24 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0: % 11.18/2.24 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) = % 11.18/2.24 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 11.18/2.24 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) & % 11.18/2.24 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) = % 11.18/2.24 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 11.18/2.24 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) & % 11.18/2.24 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~ % 11.18/2.24 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : ! % 11.18/2.24 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~ % 11.18/2.24 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 11.18/2.24 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0)) % 11.18/2.24 % 11.18/2.24 Those formulas are unsatisfiable: % 11.18/2.24 --------------------------------- % 11.18/2.24 % 11.18/2.24 Begin of proof % 11.18/2.24 | % 11.18/2.24 | ALPHA: (function-axioms) implies: % 11.18/2.25 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] % 11.18/2.25 | : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ % 11.18/2.25 | (rat_$lesseq(v3, v2) = v0)) % 11.18/2.25 | (2) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = % 11.18/2.25 | v0 | ~ (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) % 11.18/2.25 | = v0)) % 11.18/2.25 | % 11.18/2.25 | ALPHA: (input) implies: % 11.18/2.25 | (3) rat_$lesseq(rat_-1/4, rat_0) = 0 % 11.18/2.25 | (4) rat_$difference(rat_-1/4, rat_0) = rat_-1/4 % 11.18/2.25 | (5) rat_$product(rat_0, rat_-1/20) = rat_0 % 11.18/2.25 | % 11.18/2.25 | GROUND_INST: instantiating (rat_combined_problem_18) with rat_0, rat_0, % 11.18/2.25 | simplifying with (5) gives: % 11.18/2.25 | (6) ? [v0: $rat] : ? [v1: int] : ( ~ (v1 = 0) & rat_$difference(rat_-1/4, % 11.18/2.25 | rat_0) = v0 & rat_$lesseq(v0, rat_0) = v1) % 11.18/2.25 | % 11.18/2.25 | DELTA: instantiating (6) with fresh symbols all_15_0, all_15_1 gives: % 11.18/2.25 | (7) ~ (all_15_0 = 0) & rat_$difference(rat_-1/4, rat_0) = all_15_1 & % 11.18/2.25 | rat_$lesseq(all_15_1, rat_0) = all_15_0 % 11.18/2.25 | % 11.18/2.25 | ALPHA: (7) implies: % 11.18/2.25 | (8) ~ (all_15_0 = 0) % 11.18/2.25 | (9) rat_$lesseq(all_15_1, rat_0) = all_15_0 % 11.18/2.25 | (10) rat_$difference(rat_-1/4, rat_0) = all_15_1 % 11.18/2.25 | % 11.18/2.25 | GROUND_INST: instantiating (2) with rat_-1/4, all_15_1, rat_0, rat_-1/4, % 11.18/2.25 | simplifying with (4), (10) gives: % 11.18/2.25 | (11) all_15_1 = rat_-1/4 % 11.18/2.25 | % 11.18/2.25 | REDUCE: (9), (11) imply: % 11.18/2.25 | (12) rat_$lesseq(rat_-1/4, rat_0) = all_15_0 % 11.18/2.25 | % 11.18/2.25 | GROUND_INST: instantiating (1) with 0, all_15_0, rat_0, rat_-1/4, simplifying % 11.18/2.25 | with (3), (12) gives: % 11.18/2.25 | (13) all_15_0 = 0 % 11.18/2.25 | % 11.18/2.25 | REDUCE: (8), (13) imply: % 11.18/2.25 | (14) $false % 11.18/2.26 | % 11.18/2.26 | CLOSE: (14) is inconsistent. % 11.18/2.26 | % 11.18/2.26 End of proof % 11.18/2.26 % SZS output end Proof for theBenchmark % 11.18/2.26 % 11.18/2.26 1646ms %------------------------------------------------------------------------------