%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM907_1 : TPTP v8.1.2. Bugfixed v5.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.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 : Thu Aug 31 11:50:39 EDT 2023 % Result : Theorem 9.20s 2.07s % Output : Proof 13.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM907_1 : TPTP v8.1.2. Bugfixed v5.4.0. % 0.14/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n012.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Aug 25 08:41:56 EDT 2023 % 0.14/0.36 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.61/0.91 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.61/0.91 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 1.61/0.91 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.61/0.91 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 1.61/0.91 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 1.61/0.91 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 1.61/0.91 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 2.28/1.01 Prover 1: Preprocessing ... % 2.28/1.01 Prover 4: Preprocessing ... % 2.46/1.05 Prover 5: Preprocessing ... % 2.46/1.05 Prover 3: Preprocessing ... % 2.46/1.05 Prover 0: Preprocessing ... % 2.46/1.05 Prover 6: Preprocessing ... % 2.46/1.05 Prover 2: Preprocessing ... % 4.02/1.46 Prover 5: Proving ... % 4.02/1.47 Prover 6: Constructing countermodel ... % 4.96/1.47 Prover 3: Constructing countermodel ... % 4.96/1.48 Prover 1: Constructing countermodel ... % 4.96/1.50 Prover 2: Proving ... % 5.65/1.56 Prover 4: Constructing countermodel ... % 5.65/1.56 Prover 0: Proving ... % 6.28/1.68 Prover 1: gave up % 6.28/1.69 Prover 3: gave up % 6.28/1.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.28/1.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.28/1.69 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation % 6.98/1.69 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation % 6.98/1.70 Prover 8: Preprocessing ... % 6.98/1.70 Prover 7: Preprocessing ... % 6.98/1.71 Prover 6: gave up % 6.98/1.73 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 6.98/1.73 Prover 9: Warning: Problem contains rationals, using incomplete axiomatisation % 6.98/1.74 Prover 9: Preprocessing ... % 7.82/1.81 Prover 8: Warning: ignoring some quantifiers % 7.82/1.81 Prover 8: Constructing countermodel ... % 7.82/1.83 Prover 7: Warning: ignoring some quantifiers % 7.82/1.84 Prover 7: Constructing countermodel ... % 8.53/1.90 Prover 9: Constructing countermodel ... % 8.53/1.98 Prover 8: gave up % 8.53/1.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.53/1.98 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation % 9.20/1.99 Prover 10: Preprocessing ... % 9.20/2.07 Prover 0: proved (1425ms) % 9.20/2.07 Prover 5: proved (1417ms) % 9.20/2.07 % 9.20/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.20/2.07 % 9.20/2.08 % 9.20/2.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.20/2.08 % 9.20/2.09 Prover 2: stopped % 9.96/2.09 Prover 9: stopped % 9.96/2.11 Prover 10: Warning: ignoring some quantifiers % 9.96/2.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.96/2.11 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation % 9.96/2.11 Prover 10: Constructing countermodel ... % 9.96/2.11 Prover 11: Preprocessing ... % 9.96/2.11 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.96/2.11 Prover 16: Warning: Problem contains rationals, using incomplete axiomatisation % 9.96/2.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.96/2.11 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation % 9.96/2.11 Prover 16: Preprocessing ... % 9.96/2.11 Prover 13: Preprocessing ... % 9.96/2.11 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 9.96/2.11 Prover 19: Warning: Problem contains rationals, using incomplete axiomatisation % 9.96/2.11 Prover 19: Preprocessing ... % 9.96/2.14 Prover 10: gave up % 9.96/2.21 Prover 16: Warning: ignoring some quantifiers % 9.96/2.21 Prover 16: Constructing countermodel ... % 9.96/2.21 Prover 11: Constructing countermodel ... % 9.96/2.21 Prover 13: Warning: ignoring some quantifiers % 9.96/2.22 Prover 13: Constructing countermodel ... % 11.01/2.26 Prover 19: Warning: ignoring some quantifiers % 11.01/2.27 Prover 19: Constructing countermodel ... % 11.55/2.36 Prover 13: gave up % 11.93/2.42 Prover 19: gave up % 12.83/2.50 Prover 11: Found proof (size 59) % 12.83/2.50 Prover 11: proved (420ms) % 12.83/2.50 Prover 16: gave up % 12.83/2.50 Prover 7: stopped % 12.83/2.50 Prover 4: stopped % 12.83/2.50 % 12.83/2.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.83/2.50 % 12.83/2.50 % SZS output start Proof for theBenchmark % 12.83/2.51 Assumptions after simplification: % 12.83/2.51 --------------------------------- % 12.83/2.51 % 12.83/2.51 (rat_combined_problem_2) % 13.13/2.53 ? [v0: $rat] : ? [v1: $rat] : ? [v2: $rat] : ? [v3: $rat] : ? [v4: $rat] % 13.13/2.53 : ? [v5: $rat] : (rat_$sum(v0, v1) = v3 & ((v5 = v1 & v4 = v0 & ~ (v3 = v2) % 13.13/2.53 & rat_$difference(v2, v1) = v0 & rat_$difference(v2, v0) = v1) | (v3 = % 13.13/2.53 v2 & (( ~ (v5 = v1) & rat_$difference(v2, v0) = v5) | ( ~ (v4 = v0) & % 13.13/2.53 rat_$difference(v2, v1) = v4))))) % 13.13/2.53 % 13.13/2.53 (input) % 13.21/2.55 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_0) & ~ % 13.21/2.55 (rat_very_small = rat_0) & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_0) = 0 & % 13.21/2.55 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_0) % 13.21/2.55 = rat_0 & rat_$round(rat_0) = rat_0 & rat_$to_int(rat_0) = 0 & % 13.21/2.55 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = % 13.21/2.55 rat_0 & rat_$product(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 & % 13.21/2.55 rat_$greatereq(rat_very_small, rat_very_large) = 1 & rat_$greatereq(rat_0, % 13.21/2.55 rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large) = 0 & % 13.21/2.55 rat_$lesseq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_0) = 0 & % 13.21/2.55 rat_$greater(rat_very_small, rat_very_large) = 1 & rat_$greater(rat_0, % 13.21/2.55 rat_very_small) = 0 & rat_$greater(rat_0, rat_0) = 1 & % 13.21/2.55 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small, % 13.21/2.55 rat_0) = 0 & rat_$less(rat_0, rat_very_large) = 0 & rat_$less(rat_0, rat_0) % 13.21/2.55 = 1 & rat_$sum(rat_0, rat_0) = rat_0 & rat_$difference(rat_0, rat_0) = rat_0 & % 13.21/2.55 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] % 13.21/2.55 : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : % 13.21/2.55 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: % 13.21/2.55 $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2, % 13.21/2.55 v3) = v4) | ~ (rat_$sum(v1, v0) = v3) | ? [v5: $rat] : (rat_$sum(v5, % 13.21/2.55 v0) = v4 & rat_$sum(v2, v1) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! % 13.21/2.55 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ % 13.21/2.55 (rat_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1, % 13.21/2.55 v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: % 13.21/2.55 int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) % 13.21/2.55 | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v1, v0) = v4)) & ! [v0: $rat] : % 13.21/2.55 ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, % 13.21/2.55 v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & % 13.21/2.55 rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 13.21/2.55 : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, % 13.21/2.55 v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & ! % 13.21/2.55 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 13.21/2.55 (rat_$less(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ % 13.21/2.55 (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! % 13.21/2.55 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ % 13.21/2.55 (rat_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) % 13.21/2.55 = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( % 13.21/2.55 ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1, % 13.21/2.55 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 = % 13.21/2.55 v0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 13.21/2.55 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 13.21/2.55 : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 13.21/2.55 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 13.21/2.55 : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 13.21/2.55 rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 13.21/2.55 int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) % 13.21/2.55 & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 13.21/2.55 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 13.21/2.55 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : % 13.21/2.55 (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 13.21/2.55 rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 13.21/2.55 $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0) % 13.21/2.55 = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 13.21/2.55 (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] : % 13.21/2.55 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | % 13.21/2.55 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 13.21/2.55 ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2, % 13.21/2.55 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 13.21/2.55 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = % 13.21/2.55 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1, % 13.21/2.55 v0) = 0) | ~ (rat_$less(v2, v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: % 13.21/2.55 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) = v2) | % 13.21/2.55 rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 13.21/2.55 (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1: % 13.21/2.55 $rat] : ! [v2: $rat] : ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : % 13.21/2.55 (rat_$uminus(v0) = v3 & rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1: % 13.21/2.55 $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & % 13.21/2.55 ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! % 13.21/2.55 [v0: $rat] : ! [v1: int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & ! [v0: % 13.21/2.55 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & % 13.21/2.55 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1) % 13.21/2.55 = rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) % 13.21/2.55 | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 13.21/2.55 (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & ! [v0: $rat] : ! % 13.21/2.56 [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0: % 13.21/2.56 $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$lesseq(v1, v0) = % 13.21/2.56 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | % 13.21/2.56 rat_$greater(v0, v1) = 0) & ! [v0: $rat] : ! [v1: MultipleValueBool] : ( ~ % 13.21/2.56 (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) = 0) & ! [v0: $rat] : (v0 = % 13.21/2.56 rat_0 | ~ (rat_$uminus(v0) = v0)) % 13.21/2.56 % 13.21/2.56 (function-axioms) % 13.21/2.56 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 13.21/2.56 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0: % 13.21/2.56 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 13.21/2.56 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0: % 13.21/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 13.21/2.56 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3, % 13.21/2.56 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 13.21/2.56 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ % 13.21/2.56 (rat_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.21/2.56 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 13.21/2.56 (rat_$greater(v3, v2) = v1) | ~ (rat_$greater(v3, v2) = v0)) & ! [v0: % 13.21/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 13.21/2.56 $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = % 13.21/2.56 v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 % 13.21/2.56 = v0 | ~ (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0: % 13.21/2.56 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 13.21/2.56 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & ! % 13.21/2.56 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = % 13.21/2.56 v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & ! [v0: % 13.21/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = v0 | % 13.21/2.56 ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] : ! % 13.21/2.56 [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~ % 13.21/2.56 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 % 13.21/2.56 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0: % 13.21/2.56 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) = % 13.21/2.56 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 13.21/2.56 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) & % 13.21/2.56 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) = % 13.21/2.56 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 13.21/2.56 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) & % 13.21/2.56 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~ % 13.21/2.56 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : ! % 13.21/2.56 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~ % 13.21/2.56 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 13.21/2.56 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0)) % 13.21/2.56 % 13.21/2.56 Those formulas are unsatisfiable: % 13.21/2.56 --------------------------------- % 13.21/2.56 % 13.21/2.56 Begin of proof % 13.21/2.56 | % 13.21/2.56 | ALPHA: (function-axioms) implies: % 13.21/2.57 | (1) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = % 13.21/2.57 | v0 | ~ (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) % 13.21/2.57 | % 13.21/2.57 | ALPHA: (input) implies: % 13.21/2.57 | (2) ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | % 13.21/2.57 | rat_$sum(v0, v1) = rat_0) % 13.21/2.57 | (3) ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = % 13.21/2.57 | v1)) % 13.21/2.57 | (4) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 13.21/2.57 | (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = % 13.21/2.57 | v3 & rat_$sum(v1, v3) = v2)) % 13.21/2.57 | (5) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) = % 13.21/2.57 | v2) | rat_$sum(v0, v1) = v2) % 13.21/2.57 | (6) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: % 13.21/2.57 | $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~ (rat_$sum(v1, v0) = v3) | ? % 13.21/2.57 | [v5: $rat] : (rat_$sum(v5, v0) = v4 & rat_$sum(v2, v1) = v5)) % 13.21/2.57 | (7) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: % 13.21/2.57 | $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? % 13.21/2.57 | [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) % 13.21/2.57 | % 13.21/2.57 | DELTA: instantiating (rat_combined_problem_2) with fresh symbols all_5_0, % 13.21/2.57 | all_5_1, all_5_2, all_5_3, all_5_4, all_5_5 gives: % 13.21/2.57 | (8) rat_$sum(all_5_5, all_5_4) = all_5_2 & ((all_5_0 = all_5_4 & all_5_1 = % 13.21/2.57 | all_5_5 & ~ (all_5_2 = all_5_3) & rat_$difference(all_5_3, % 13.21/2.57 | all_5_4) = all_5_5 & rat_$difference(all_5_3, all_5_5) = all_5_4) % 13.21/2.57 | | (all_5_2 = all_5_3 & (( ~ (all_5_0 = all_5_4) & % 13.21/2.57 | rat_$difference(all_5_3, all_5_5) = all_5_0) | ( ~ (all_5_1 = % 13.21/2.57 | all_5_5) & rat_$difference(all_5_3, all_5_4) = all_5_1)))) % 13.21/2.57 | % 13.21/2.57 | ALPHA: (8) implies: % 13.21/2.57 | (9) rat_$sum(all_5_5, all_5_4) = all_5_2 % 13.21/2.57 | (10) (all_5_0 = all_5_4 & all_5_1 = all_5_5 & ~ (all_5_2 = all_5_3) & % 13.21/2.57 | rat_$difference(all_5_3, all_5_4) = all_5_5 & % 13.21/2.57 | rat_$difference(all_5_3, all_5_5) = all_5_4) | (all_5_2 = all_5_3 & % 13.21/2.57 | (( ~ (all_5_0 = all_5_4) & rat_$difference(all_5_3, all_5_5) = % 13.21/2.57 | all_5_0) | ( ~ (all_5_1 = all_5_5) & rat_$difference(all_5_3, % 13.21/2.57 | all_5_4) = all_5_1))) % 13.21/2.57 | % 13.21/2.57 | GROUND_INST: instantiating (5) with all_5_4, all_5_5, all_5_2, simplifying % 13.21/2.57 | with (9) gives: % 13.21/2.57 | (11) rat_$sum(all_5_4, all_5_5) = all_5_2 % 13.21/2.57 | % 13.21/2.57 | BETA: splitting (10) gives: % 13.21/2.57 | % 13.21/2.57 | Case 1: % 13.21/2.57 | | % 13.21/2.58 | | (12) all_5_0 = all_5_4 & all_5_1 = all_5_5 & ~ (all_5_2 = all_5_3) & % 13.21/2.58 | | rat_$difference(all_5_3, all_5_4) = all_5_5 & % 13.21/2.58 | | rat_$difference(all_5_3, all_5_5) = all_5_4 % 13.21/2.58 | | % 13.21/2.58 | | ALPHA: (12) implies: % 13.21/2.58 | | (13) ~ (all_5_2 = all_5_3) % 13.21/2.58 | | (14) rat_$difference(all_5_3, all_5_4) = all_5_5 % 13.21/2.58 | | % 13.21/2.58 | | GROUND_INST: instantiating (4) with all_5_4, all_5_3, all_5_5, simplifying % 13.21/2.58 | | with (14) gives: % 13.21/2.58 | | (15) ? [v0: $rat] : (rat_$uminus(all_5_4) = v0 & rat_$sum(all_5_3, v0) = % 13.21/2.58 | | all_5_5) % 13.21/2.58 | | % 13.21/2.58 | | DELTA: instantiating (15) with fresh symbol all_65_0 gives: % 13.21/2.58 | | (16) rat_$uminus(all_5_4) = all_65_0 & rat_$sum(all_5_3, all_65_0) = % 13.21/2.58 | | all_5_5 % 13.21/2.58 | | % 13.21/2.58 | | ALPHA: (16) implies: % 13.21/2.58 | | (17) rat_$sum(all_5_3, all_65_0) = all_5_5 % 13.21/2.58 | | (18) rat_$uminus(all_5_4) = all_65_0 % 13.21/2.58 | | % 13.21/2.58 | | GROUND_INST: instantiating (7) with all_5_4, all_65_0, all_5_3, all_5_5, % 13.21/2.58 | | all_5_2, simplifying with (9), (17) gives: % 13.21/2.58 | | (19) ? [v0: $rat] : (rat_$sum(all_65_0, all_5_4) = v0 & % 13.21/2.58 | | rat_$sum(all_5_3, v0) = all_5_2) % 13.21/2.58 | | % 13.21/2.58 | | GROUND_INST: instantiating (5) with all_65_0, all_5_3, all_5_5, simplifying % 13.21/2.58 | | with (17) gives: % 13.21/2.58 | | (20) rat_$sum(all_65_0, all_5_3) = all_5_5 % 13.21/2.58 | | % 13.21/2.58 | | GROUND_INST: instantiating (2) with all_5_4, all_65_0, simplifying with (18) % 13.21/2.58 | | gives: % 13.21/2.58 | | (21) rat_$sum(all_5_4, all_65_0) = rat_0 % 13.21/2.58 | | % 13.21/2.58 | | DELTA: instantiating (19) with fresh symbol all_77_0 gives: % 13.21/2.58 | | (22) rat_$sum(all_65_0, all_5_4) = all_77_0 & rat_$sum(all_5_3, all_77_0) % 13.21/2.58 | | = all_5_2 % 13.21/2.58 | | % 13.21/2.58 | | ALPHA: (22) implies: % 13.21/2.58 | | (23) rat_$sum(all_5_3, all_77_0) = all_5_2 % 13.21/2.58 | | (24) rat_$sum(all_65_0, all_5_4) = all_77_0 % 13.21/2.58 | | % 13.21/2.58 | | GROUND_INST: instantiating (5) with all_5_4, all_65_0, all_77_0, simplifying % 13.21/2.58 | | with (24) gives: % 13.21/2.58 | | (25) rat_$sum(all_5_4, all_65_0) = all_77_0 % 13.21/2.58 | | % 13.21/2.58 | | GROUND_INST: instantiating (6) with all_5_3, all_65_0, all_5_4, all_5_5, % 13.21/2.58 | | all_5_2, simplifying with (11), (20) gives: % 13.21/2.58 | | (26) ? [v0: $rat] : (rat_$sum(v0, all_5_3) = all_5_2 & rat_$sum(all_5_4, % 13.21/2.58 | | all_65_0) = v0) % 13.21/2.58 | | % 13.21/2.58 | | DELTA: instantiating (26) with fresh symbol all_105_0 gives: % 13.21/2.58 | | (27) rat_$sum(all_105_0, all_5_3) = all_5_2 & rat_$sum(all_5_4, all_65_0) % 13.21/2.58 | | = all_105_0 % 13.21/2.58 | | % 13.21/2.58 | | ALPHA: (27) implies: % 13.21/2.58 | | (28) rat_$sum(all_5_4, all_65_0) = all_105_0 % 13.21/2.58 | | % 13.21/2.58 | | GROUND_INST: instantiating (1) with rat_0, all_105_0, all_65_0, all_5_4, % 13.21/2.58 | | simplifying with (21), (28) gives: % 13.21/2.58 | | (29) all_105_0 = rat_0 % 13.21/2.58 | | % 13.21/2.58 | | GROUND_INST: instantiating (1) with all_77_0, all_105_0, all_65_0, all_5_4, % 13.21/2.58 | | simplifying with (25), (28) gives: % 13.21/2.58 | | (30) all_105_0 = all_77_0 % 13.21/2.58 | | % 13.21/2.58 | | COMBINE_EQS: (29), (30) imply: % 13.21/2.58 | | (31) all_77_0 = rat_0 % 13.21/2.58 | | % 13.21/2.58 | | REDUCE: (23), (31) imply: % 13.21/2.58 | | (32) rat_$sum(all_5_3, rat_0) = all_5_2 % 13.21/2.58 | | % 13.21/2.58 | | GROUND_INST: instantiating (3) with all_5_3, all_5_2, simplifying with (32) % 13.21/2.58 | | gives: % 13.21/2.58 | | (33) all_5_2 = all_5_3 % 13.21/2.58 | | % 13.21/2.58 | | REDUCE: (13), (33) imply: % 13.21/2.58 | | (34) $false % 13.21/2.58 | | % 13.21/2.58 | | CLOSE: (34) is inconsistent. % 13.21/2.58 | | % 13.21/2.59 | Case 2: % 13.21/2.59 | | % 13.21/2.59 | | (35) all_5_2 = all_5_3 & (( ~ (all_5_0 = all_5_4) & % 13.21/2.59 | | rat_$difference(all_5_3, all_5_5) = all_5_0) | ( ~ (all_5_1 = % 13.21/2.59 | | all_5_5) & rat_$difference(all_5_3, all_5_4) = all_5_1)) % 13.21/2.59 | | % 13.21/2.59 | | ALPHA: (35) implies: % 13.21/2.59 | | (36) all_5_2 = all_5_3 % 13.21/2.59 | | (37) ( ~ (all_5_0 = all_5_4) & rat_$difference(all_5_3, all_5_5) = % 13.21/2.59 | | all_5_0) | ( ~ (all_5_1 = all_5_5) & rat_$difference(all_5_3, % 13.21/2.59 | | all_5_4) = all_5_1) % 13.21/2.59 | | % 13.21/2.59 | | REDUCE: (11), (36) imply: % 13.21/2.59 | | (38) rat_$sum(all_5_4, all_5_5) = all_5_3 % 13.21/2.59 | | % 13.21/2.59 | | REDUCE: (9), (36) imply: % 13.21/2.59 | | (39) rat_$sum(all_5_5, all_5_4) = all_5_3 % 13.21/2.59 | | % 13.21/2.59 | | BETA: splitting (37) gives: % 13.21/2.59 | | % 13.21/2.59 | | Case 1: % 13.21/2.59 | | | % 13.21/2.59 | | | (40) ~ (all_5_0 = all_5_4) & rat_$difference(all_5_3, all_5_5) = % 13.21/2.59 | | | all_5_0 % 13.21/2.59 | | | % 13.21/2.59 | | | ALPHA: (40) implies: % 13.21/2.59 | | | (41) ~ (all_5_0 = all_5_4) % 13.21/2.59 | | | (42) rat_$difference(all_5_3, all_5_5) = all_5_0 % 13.21/2.59 | | | % 13.21/2.59 | | | GROUND_INST: instantiating (4) with all_5_5, all_5_3, all_5_0, simplifying % 13.21/2.59 | | | with (42) gives: % 13.21/2.59 | | | (43) ? [v0: $rat] : (rat_$uminus(all_5_5) = v0 & rat_$sum(all_5_3, v0) % 13.21/2.59 | | | = all_5_0) % 13.21/2.59 | | | % 13.21/2.59 | | | DELTA: instantiating (43) with fresh symbol all_72_0 gives: % 13.21/2.59 | | | (44) rat_$uminus(all_5_5) = all_72_0 & rat_$sum(all_5_3, all_72_0) = % 13.21/2.59 | | | all_5_0 % 13.21/2.59 | | | % 13.21/2.59 | | | ALPHA: (44) implies: % 13.21/2.59 | | | (45) rat_$sum(all_5_3, all_72_0) = all_5_0 % 13.21/2.59 | | | (46) rat_$uminus(all_5_5) = all_72_0 % 13.21/2.59 | | | % 13.21/2.59 | | | GROUND_INST: instantiating (7) with all_72_0, all_5_5, all_5_4, all_5_3, % 13.21/2.59 | | | all_5_0, simplifying with (38), (45) gives: % 13.21/2.59 | | | (47) ? [v0: $rat] : (rat_$sum(all_5_4, v0) = all_5_0 & % 13.21/2.59 | | | rat_$sum(all_5_5, all_72_0) = v0) % 13.21/2.59 | | | % 13.21/2.59 | | | GROUND_INST: instantiating (2) with all_5_5, all_72_0, simplifying with % 13.21/2.59 | | | (46) gives: % 13.21/2.59 | | | (48) rat_$sum(all_5_5, all_72_0) = rat_0 % 13.21/2.59 | | | % 13.21/2.59 | | | DELTA: instantiating (47) with fresh symbol all_82_0 gives: % 13.21/2.59 | | | (49) rat_$sum(all_5_4, all_82_0) = all_5_0 & rat_$sum(all_5_5, % 13.21/2.59 | | | all_72_0) = all_82_0 % 13.21/2.59 | | | % 13.21/2.59 | | | ALPHA: (49) implies: % 13.21/2.59 | | | (50) rat_$sum(all_5_5, all_72_0) = all_82_0 % 13.21/2.59 | | | (51) rat_$sum(all_5_4, all_82_0) = all_5_0 % 13.21/2.59 | | | % 13.21/2.59 | | | GROUND_INST: instantiating (1) with rat_0, all_82_0, all_72_0, all_5_5, % 13.21/2.59 | | | simplifying with (48), (50) gives: % 13.21/2.59 | | | (52) all_82_0 = rat_0 % 13.21/2.59 | | | % 13.21/2.59 | | | REDUCE: (51), (52) imply: % 13.21/2.59 | | | (53) rat_$sum(all_5_4, rat_0) = all_5_0 % 13.21/2.59 | | | % 13.21/2.59 | | | GROUND_INST: instantiating (3) with all_5_4, all_5_0, simplifying with % 13.21/2.59 | | | (53) gives: % 13.21/2.59 | | | (54) all_5_0 = all_5_4 % 13.21/2.59 | | | % 13.21/2.59 | | | REDUCE: (41), (54) imply: % 13.21/2.59 | | | (55) $false % 13.21/2.59 | | | % 13.21/2.59 | | | CLOSE: (55) is inconsistent. % 13.21/2.59 | | | % 13.21/2.59 | | Case 2: % 13.21/2.59 | | | % 13.21/2.59 | | | (56) ~ (all_5_1 = all_5_5) & rat_$difference(all_5_3, all_5_4) = % 13.21/2.59 | | | all_5_1 % 13.21/2.59 | | | % 13.21/2.59 | | | ALPHA: (56) implies: % 13.21/2.59 | | | (57) ~ (all_5_1 = all_5_5) % 13.21/2.59 | | | (58) rat_$difference(all_5_3, all_5_4) = all_5_1 % 13.21/2.59 | | | % 13.21/2.59 | | | GROUND_INST: instantiating (4) with all_5_4, all_5_3, all_5_1, simplifying % 13.21/2.59 | | | with (58) gives: % 13.21/2.60 | | | (59) ? [v0: $rat] : (rat_$uminus(all_5_4) = v0 & rat_$sum(all_5_3, v0) % 13.21/2.60 | | | = all_5_1) % 13.21/2.60 | | | % 13.21/2.60 | | | DELTA: instantiating (59) with fresh symbol all_72_0 gives: % 13.21/2.60 | | | (60) rat_$uminus(all_5_4) = all_72_0 & rat_$sum(all_5_3, all_72_0) = % 13.21/2.60 | | | all_5_1 % 13.21/2.60 | | | % 13.21/2.60 | | | ALPHA: (60) implies: % 13.21/2.60 | | | (61) rat_$sum(all_5_3, all_72_0) = all_5_1 % 13.21/2.60 | | | (62) rat_$uminus(all_5_4) = all_72_0 % 13.21/2.60 | | | % 13.21/2.60 | | | GROUND_INST: instantiating (7) with all_72_0, all_5_4, all_5_5, all_5_3, % 13.21/2.60 | | | all_5_1, simplifying with (39), (61) gives: % 13.21/2.60 | | | (63) ? [v0: $rat] : (rat_$sum(all_5_4, all_72_0) = v0 & % 13.21/2.60 | | | rat_$sum(all_5_5, v0) = all_5_1) % 13.21/2.60 | | | % 13.21/2.60 | | | GROUND_INST: instantiating (2) with all_5_4, all_72_0, simplifying with % 13.21/2.60 | | | (62) gives: % 13.21/2.60 | | | (64) rat_$sum(all_5_4, all_72_0) = rat_0 % 13.21/2.60 | | | % 13.21/2.60 | | | DELTA: instantiating (63) with fresh symbol all_80_0 gives: % 13.21/2.60 | | | (65) rat_$sum(all_5_4, all_72_0) = all_80_0 & rat_$sum(all_5_5, % 13.21/2.60 | | | all_80_0) = all_5_1 % 13.21/2.60 | | | % 13.21/2.60 | | | ALPHA: (65) implies: % 13.21/2.60 | | | (66) rat_$sum(all_5_5, all_80_0) = all_5_1 % 13.21/2.60 | | | (67) rat_$sum(all_5_4, all_72_0) = all_80_0 % 13.21/2.60 | | | % 13.21/2.60 | | | GROUND_INST: instantiating (1) with rat_0, all_80_0, all_72_0, all_5_4, % 13.21/2.60 | | | simplifying with (64), (67) gives: % 13.21/2.60 | | | (68) all_80_0 = rat_0 % 13.21/2.60 | | | % 13.21/2.60 | | | REDUCE: (66), (68) imply: % 13.21/2.60 | | | (69) rat_$sum(all_5_5, rat_0) = all_5_1 % 13.21/2.60 | | | % 13.21/2.60 | | | GROUND_INST: instantiating (3) with all_5_5, all_5_1, simplifying with % 13.21/2.60 | | | (69) gives: % 13.21/2.60 | | | (70) all_5_1 = all_5_5 % 13.21/2.60 | | | % 13.21/2.60 | | | REDUCE: (57), (70) imply: % 13.21/2.60 | | | (71) $false % 13.21/2.60 | | | % 13.21/2.60 | | | CLOSE: (71) is inconsistent. % 13.21/2.60 | | | % 13.21/2.60 | | End of split % 13.21/2.60 | | % 13.21/2.60 | End of split % 13.21/2.60 | % 13.21/2.60 End of proof % 13.21/2.60 % SZS output end Proof for theBenchmark % 13.21/2.60 % 13.21/2.60 1973ms %------------------------------------------------------------------------------