%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI567_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 : n018.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 17:48:25 EDT 2023 % Result : Theorem 10.40s 2.11s % Output : Proof 10.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : ARI567_1 : TPTP v8.1.2. Released v5.0.0. % 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.31 % Computer : n018.cluster.edu % 0.12/0.31 % Model : x86_64 x86_64 % 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.31 % Memory : 8042.1875MB % 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.31 % CPULimit : 300 % 0.12/0.31 % WCLimit : 300 % 0.12/0.31 % DateTime : Tue Aug 29 18:09:18 EDT 2023 % 0.12/0.31 % CPUTime : % 0.16/0.58 ________ _____ % 0.16/0.58 ___ __ \_________(_)________________________________ % 0.16/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.58 % 0.16/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.58 (2023-06-19) % 0.16/0.58 % 0.16/0.58 (c) Philipp Rümmer, 2009-2023 % 0.16/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.58 Amanda Stjerna. % 0.16/0.58 Free software under BSD-3-Clause. % 0.16/0.58 % 0.16/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.58 % 0.16/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.16/0.60 Running up to 7 provers in parallel. % 0.16/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.62/0.88 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.62/0.88 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.62/0.88 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.62/0.88 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.62/0.88 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.62/0.88 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 1.62/0.88 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 2.29/0.99 Prover 1: Preprocessing ... % 2.29/0.99 Prover 4: Preprocessing ... % 2.99/1.06 Prover 0: Preprocessing ... % 2.99/1.06 Prover 6: Preprocessing ... % 2.99/1.10 Prover 2: Preprocessing ... % 2.99/1.10 Prover 5: Preprocessing ... % 2.99/1.12 Prover 3: Preprocessing ... % 5.92/1.51 Prover 1: Constructing countermodel ... % 5.92/1.52 Prover 6: Proving ... % 6.59/1.56 Prover 4: Constructing countermodel ... % 7.25/1.64 Prover 0: Proving ... % 9.36/1.95 Prover 3: Constructing countermodel ... % 9.36/1.98 Prover 1: Found proof (size 10) % 9.36/1.98 Prover 1: proved (1370ms) % 9.36/1.98 Prover 4: stopped % 9.36/1.98 Prover 6: stopped % 9.36/1.98 Prover 0: stopped % 9.36/1.99 Prover 3: stopped % 9.96/2.01 Prover 2: Proving ... % 9.96/2.01 Prover 2: stopped % 10.40/2.11 Prover 5: Proving ... % 10.40/2.11 Prover 5: stopped % 10.40/2.11 % 10.40/2.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.40/2.11 % 10.40/2.12 % SZS output start Proof for theBenchmark % 10.40/2.12 Assumptions after simplification: % 10.40/2.12 --------------------------------- % 10.40/2.12 % 10.40/2.12 (real_combined_problem_18) % 10.40/2.14 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$product(v0, real_-1/20) = v1) | % 10.40/2.14 ? [v2: $real] : ? [v3: int] : ( ~ (v3 = 0) & real_$difference(real_-1/4, % 10.40/2.14 v1) = v2 & real_$lesseq(v2, real_0) = v3)) % 10.40/2.14 % 10.40/2.14 (input) % 10.40/2.17 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_-1/20) & % 10.40/2.17 ~ (real_very_large = real_-1/4) & ~ (real_very_large = real_0) & ~ % 10.40/2.17 (real_very_small = real_-1/20) & ~ (real_very_small = real_-1/4) & ~ % 10.40/2.17 (real_very_small = real_0) & ~ (real_-1/20 = real_-1/4) & ~ (real_-1/20 = % 10.40/2.17 real_0) & ~ (real_-1/4 = real_0) & real_$is_int(real_-1/20) = 1 & % 10.40/2.17 real_$is_int(real_-1/4) = 1 & real_$is_int(real_0) = 0 & % 10.40/2.17 real_$is_rat(real_-1/20) = 0 & real_$is_rat(real_-1/4) = 0 & % 10.40/2.17 real_$is_rat(real_0) = 0 & real_$floor(real_0) = real_0 & % 10.40/2.17 real_$ceiling(real_-1/20) = real_0 & real_$ceiling(real_-1/4) = real_0 & % 10.40/2.17 real_$ceiling(real_0) = real_0 & real_$truncate(real_-1/20) = real_0 & % 10.40/2.17 real_$truncate(real_-1/4) = real_0 & real_$truncate(real_0) = real_0 & % 10.40/2.17 real_$round(real_-1/20) = real_0 & real_$round(real_-1/4) = real_0 & % 10.40/2.17 real_$round(real_0) = real_0 & real_$to_int(real_-1/20) = -1 & % 10.40/2.17 real_$to_int(real_-1/4) = -1 & real_$to_int(real_0) = 0 & % 10.40/2.17 real_$to_rat(real_-1/20) = rat_-1/20 & real_$to_rat(real_-1/4) = rat_-1/4 & % 10.40/2.17 real_$to_rat(real_0) = rat_0 & real_$to_real(real_-1/20) = real_-1/20 & % 10.40/2.17 real_$to_real(real_-1/4) = real_-1/4 & real_$to_real(real_0) = real_0 & % 10.40/2.17 int_$to_real(0) = real_0 & real_$quotient(real_0, real_-1/20) = real_0 & % 10.40/2.17 real_$quotient(real_0, real_-1/4) = real_0 & real_$uminus(real_0) = real_0 & % 10.40/2.17 real_$sum(real_-1/20, real_0) = real_-1/20 & real_$sum(real_-1/4, real_0) = % 10.40/2.17 real_-1/4 & real_$sum(real_0, real_-1/20) = real_-1/20 & real_$sum(real_0, % 10.40/2.17 real_-1/4) = real_-1/4 & real_$sum(real_0, real_0) = real_0 & % 10.40/2.17 real_$greatereq(real_very_small, real_very_large) = 1 & % 10.40/2.17 real_$greatereq(real_-1/20, real_-1/20) = 0 & real_$greatereq(real_-1/20, % 10.40/2.17 real_-1/4) = 0 & real_$greatereq(real_-1/20, real_0) = 1 & % 10.40/2.17 real_$greatereq(real_-1/4, real_-1/20) = 1 & real_$greatereq(real_-1/4, % 10.40/2.17 real_-1/4) = 0 & real_$greatereq(real_-1/4, real_0) = 1 & % 10.40/2.17 real_$greatereq(real_0, real_-1/20) = 0 & real_$greatereq(real_0, real_-1/4) = % 10.40/2.17 0 & real_$greatereq(real_0, real_0) = 0 & real_$greater(real_very_large, % 10.40/2.17 real_-1/20) = 0 & real_$greater(real_very_large, real_-1/4) = 0 & % 10.40/2.17 real_$greater(real_very_large, real_0) = 0 & real_$greater(real_very_small, % 10.40/2.17 real_very_large) = 1 & real_$greater(real_-1/20, real_very_small) = 0 & % 10.40/2.17 real_$greater(real_-1/20, real_-1/20) = 1 & real_$greater(real_-1/20, % 10.40/2.17 real_-1/4) = 0 & real_$greater(real_-1/20, real_0) = 1 & % 10.40/2.17 real_$greater(real_-1/4, real_very_small) = 0 & real_$greater(real_-1/4, % 10.40/2.17 real_-1/20) = 1 & real_$greater(real_-1/4, real_-1/4) = 1 & % 10.40/2.17 real_$greater(real_-1/4, real_0) = 1 & real_$greater(real_0, real_very_small) % 10.40/2.17 = 0 & real_$greater(real_0, real_-1/20) = 0 & real_$greater(real_0, real_-1/4) % 10.40/2.17 = 0 & real_$greater(real_0, real_0) = 1 & real_$less(real_very_small, % 10.40/2.17 real_very_large) = 0 & real_$less(real_very_small, real_-1/20) = 0 & % 10.40/2.17 real_$less(real_very_small, real_-1/4) = 0 & real_$less(real_very_small, % 10.40/2.17 real_0) = 0 & real_$less(real_-1/20, real_very_large) = 0 & % 10.40/2.17 real_$less(real_-1/20, real_-1/20) = 1 & real_$less(real_-1/20, real_-1/4) = 1 % 10.40/2.17 & real_$less(real_-1/20, real_0) = 0 & real_$less(real_-1/4, real_very_large) % 10.40/2.17 = 0 & real_$less(real_-1/4, real_-1/20) = 0 & real_$less(real_-1/4, real_-1/4) % 10.40/2.17 = 1 & real_$less(real_-1/4, real_0) = 0 & real_$less(real_0, real_very_large) % 10.40/2.17 = 0 & real_$less(real_0, real_-1/20) = 1 & real_$less(real_0, real_-1/4) = 1 & % 10.40/2.17 real_$less(real_0, real_0) = 1 & real_$product(real_-1/20, real_0) = real_0 & % 10.40/2.17 real_$product(real_-1/4, real_0) = real_0 & real_$product(real_0, real_-1/20) % 10.40/2.17 = real_0 & real_$product(real_0, real_-1/4) = real_0 & real_$product(real_0, % 10.40/2.17 real_0) = real_0 & real_$difference(real_-1/20, real_-1/20) = real_0 & % 10.40/2.17 real_$difference(real_-1/20, real_0) = real_-1/20 & % 10.40/2.17 real_$difference(real_-1/4, real_-1/4) = real_0 & real_$difference(real_-1/4, % 10.40/2.17 real_0) = real_-1/4 & real_$difference(real_0, real_0) = real_0 & % 10.40/2.17 real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_-1/20, % 10.40/2.17 real_-1/20) = 0 & real_$lesseq(real_-1/20, real_-1/4) = 1 & % 10.40/2.17 real_$lesseq(real_-1/20, real_0) = 0 & real_$lesseq(real_-1/4, real_-1/20) = 0 % 10.40/2.17 & real_$lesseq(real_-1/4, real_-1/4) = 0 & real_$lesseq(real_-1/4, real_0) = 0 % 10.40/2.17 & real_$lesseq(real_0, real_-1/20) = 1 & real_$lesseq(real_0, real_-1/4) = 1 & % 10.40/2.17 real_$lesseq(real_0, real_0) = 0 & ! [v0: $real] : ! [v1: $real] : ! [v2: % 10.40/2.17 $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ % 10.40/2.17 (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & % 10.40/2.17 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 10.40/2.17 $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~ (real_$quotient(v2, % 10.40/2.17 v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: $real] : ! [v1: % 10.40/2.17 $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0) = % 10.40/2.17 v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & % 10.40/2.17 real_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 10.40/2.17 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ % 10.40/2.17 (real_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, % 10.40/2.17 v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: % 10.40/2.17 $real] : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) | % 10.40/2.17 real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 10.40/2.17 $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) = % 10.40/2.17 v2)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ % 10.40/2.17 (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 10.40/2.17 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 10.40/2.17 int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = % 10.40/2.17 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! % 10.40/2.17 [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3: % 10.40/2.17 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $real] : ! % 10.40/2.17 [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, % 10.40/2.17 v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 10.40/2.17 (real_$less(v1, v0) = 0) | ~ (real_$lesseq(v2, v1) = 0) | real_$less(v2, % 10.40/2.17 v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 10.40/2.17 (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) & ! [v0: $real] % 10.40/2.17 : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0: % 10.40/2.17 $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | % 10.40/2.17 real_$less(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 10.40/2.17 (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: % 10.40/2.17 $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! % 10.40/2.17 [v0: $real] : ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | % 10.40/2.17 real_$less(v1, v0) = 0) & ! [v0: $real] : (v0 = real_0 | ~ % 10.40/2.17 (real_$uminus(v0) = v0)) % 10.40/2.17 % 10.40/2.17 (function-axioms) % 10.40/2.18 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 10.40/2.18 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 10.40/2.18 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 10.40/2.18 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: % 10.40/2.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 10.40/2.18 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~ % 10.40/2.18 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.40/2.18 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 10.40/2.18 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0: % 10.40/2.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 10.40/2.18 $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) = % 10.40/2.18 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : % 10.40/2.18 (v1 = v0 | ~ (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) % 10.40/2.18 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 % 10.40/2.18 | ~ (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & % 10.40/2.18 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! % 10.40/2.18 [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, % 10.40/2.18 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 10.40/2.18 ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1) | ~ (real_$is_int(v2) = % 10.40/2.18 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.40/2.18 $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) | ~ (real_$is_rat(v2) = v0)) % 10.40/2.18 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 10.40/2.18 (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & ! [v0: $real] : ! % 10.40/2.18 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~ % 10.40/2.18 (real_$ceiling(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 10.40/2.18 : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) = v0)) & ! % 10.40/2.18 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$round(v2) % 10.40/2.18 = v1) | ~ (real_$round(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: % 10.40/2.18 $real] : (v1 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0)) % 10.40/2.18 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~ % 10.40/2.18 (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : ! % 10.40/2.18 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~ % 10.40/2.18 (real_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : % 10.40/2.18 (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0: % 10.40/2.18 $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$uminus(v2) = % 10.40/2.18 v1) | ~ (real_$uminus(v2) = v0)) % 10.40/2.18 % 10.40/2.18 Those formulas are unsatisfiable: % 10.40/2.18 --------------------------------- % 10.40/2.18 % 10.40/2.18 Begin of proof % 10.40/2.18 | % 10.40/2.19 | ALPHA: (function-axioms) implies: % 10.40/2.19 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.40/2.19 | $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | % 10.82/2.19 | ~ (real_$lesseq(v3, v2) = v0)) % 10.82/2.19 | (2) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 % 10.82/2.19 | = v0 | ~ (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, % 10.82/2.19 | v2) = v0)) % 10.82/2.19 | % 10.82/2.19 | ALPHA: (input) implies: % 10.82/2.19 | (3) real_$lesseq(real_-1/4, real_0) = 0 % 10.82/2.19 | (4) real_$difference(real_-1/4, real_0) = real_-1/4 % 10.82/2.19 | (5) real_$product(real_0, real_-1/20) = real_0 % 10.82/2.19 | % 10.82/2.19 | GROUND_INST: instantiating (real_combined_problem_18) with real_0, real_0, % 10.82/2.19 | simplifying with (5) gives: % 10.82/2.19 | (6) ? [v0: $real] : ? [v1: int] : ( ~ (v1 = 0) & % 10.82/2.19 | real_$difference(real_-1/4, real_0) = v0 & real_$lesseq(v0, real_0) = % 10.82/2.19 | v1) % 10.82/2.19 | % 10.82/2.19 | DELTA: instantiating (6) with fresh symbols all_15_0, all_15_1 gives: % 10.82/2.19 | (7) ~ (all_15_0 = 0) & real_$difference(real_-1/4, real_0) = all_15_1 & % 10.82/2.19 | real_$lesseq(all_15_1, real_0) = all_15_0 % 10.82/2.19 | % 10.82/2.19 | ALPHA: (7) implies: % 10.82/2.19 | (8) ~ (all_15_0 = 0) % 10.82/2.19 | (9) real_$lesseq(all_15_1, real_0) = all_15_0 % 10.82/2.19 | (10) real_$difference(real_-1/4, real_0) = all_15_1 % 10.82/2.19 | % 10.82/2.19 | GROUND_INST: instantiating (2) with real_-1/4, all_15_1, real_0, real_-1/4, % 10.82/2.19 | simplifying with (4), (10) gives: % 10.82/2.19 | (11) all_15_1 = real_-1/4 % 10.82/2.19 | % 10.82/2.19 | REDUCE: (9), (11) imply: % 10.82/2.20 | (12) real_$lesseq(real_-1/4, real_0) = all_15_0 % 10.82/2.20 | % 10.82/2.20 | GROUND_INST: instantiating (1) with 0, all_15_0, real_0, real_-1/4, % 10.82/2.20 | simplifying with (3), (12) gives: % 10.82/2.20 | (13) all_15_0 = 0 % 10.82/2.20 | % 10.82/2.20 | REDUCE: (8), (13) imply: % 10.82/2.20 | (14) $false % 10.82/2.20 | % 10.82/2.20 | CLOSE: (14) is inconsistent. % 10.82/2.20 | % 10.82/2.20 End of proof % 10.82/2.20 % SZS output end Proof for theBenchmark % 10.82/2.20 % 10.82/2.20 1613ms %------------------------------------------------------------------------------