%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM902_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 : 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 11:50:38 EDT 2023 % Result : Theorem 8.75s 1.92s % Output : Proof 10.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM902_1 : TPTP v8.1.2. Released v5.0.0. % 0.13/0.14 % 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 13:57:11 EDT 2023 % 0.14/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.70/0.89 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 1.70/0.89 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 1.70/0.89 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 1.70/0.89 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.70/0.89 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.70/0.89 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 1.70/0.89 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 1.86/0.97 Prover 1: Preprocessing ... % 1.86/0.97 Prover 4: Preprocessing ... % 2.38/1.02 Prover 5: Preprocessing ... % 2.38/1.02 Prover 3: Preprocessing ... % 2.38/1.02 Prover 2: Preprocessing ... % 2.38/1.02 Prover 6: Preprocessing ... % 2.38/1.02 Prover 0: Preprocessing ... % 3.99/1.41 Prover 5: Proving ... % 3.99/1.42 Prover 3: Constructing countermodel ... % 3.99/1.42 Prover 6: Constructing countermodel ... % 4.95/1.42 Prover 1: Constructing countermodel ... % 4.95/1.44 Prover 2: Proving ... % 4.95/1.47 Prover 4: Constructing countermodel ... % 5.85/1.54 Prover 0: Proving ... % 5.85/1.58 Prover 6: gave up % 5.85/1.58 Prover 3: gave up % 5.85/1.59 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.85/1.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.85/1.59 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation % 5.85/1.59 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation % 5.85/1.59 Prover 1: gave up % 5.85/1.59 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.85/1.59 Prover 9: Warning: Problem contains rationals, using incomplete axiomatisation % 5.85/1.59 Prover 7: Preprocessing ... % 5.85/1.60 Prover 8: Preprocessing ... % 6.53/1.60 Prover 9: Preprocessing ... % 6.53/1.69 Prover 7: Warning: ignoring some quantifiers % 7.26/1.69 Prover 7: Constructing countermodel ... % 7.32/1.70 Prover 8: Warning: ignoring some quantifiers % 7.35/1.71 Prover 8: Constructing countermodel ... % 7.35/1.77 Prover 9: Constructing countermodel ... % 8.07/1.88 Prover 8: gave up % 8.07/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.07/1.89 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation % 8.75/1.90 Prover 0: proved (1265ms) % 8.75/1.90 % 8.75/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.75/1.92 % 8.75/1.92 Prover 10: Preprocessing ... % 8.75/1.92 Prover 9: stopped % 8.75/1.93 Prover 2: stopped % 8.75/1.93 Prover 5: stopped % 8.75/1.95 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.75/1.95 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation % 8.75/1.95 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.75/1.95 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation % 8.75/1.95 Prover 11: Preprocessing ... % 8.75/1.95 Prover 13: Preprocessing ... % 8.75/1.95 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.75/1.95 Prover 16: Warning: Problem contains rationals, using incomplete axiomatisation % 8.75/1.95 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 8.75/1.95 Prover 19: Warning: Problem contains rationals, using incomplete axiomatisation % 8.75/1.95 Prover 10: Warning: ignoring some quantifiers % 8.75/1.96 Prover 19: Preprocessing ... % 8.75/1.96 Prover 16: Preprocessing ... % 8.75/1.96 Prover 10: Constructing countermodel ... % 8.75/1.99 Prover 4: Found proof (size 52) % 8.75/1.99 Prover 4: proved (1350ms) % 8.75/1.99 Prover 10: stopped % 8.75/1.99 Prover 13: stopped % 9.47/1.99 Prover 7: stopped % 9.48/1.99 Prover 16: stopped % 9.48/2.04 Prover 19: Warning: ignoring some quantifiers % 9.48/2.04 Prover 19: Constructing countermodel ... % 9.48/2.04 Prover 11: Constructing countermodel ... % 9.48/2.05 Prover 19: stopped % 9.48/2.05 Prover 11: stopped % 9.48/2.05 % 9.48/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.48/2.05 % 9.48/2.06 % SZS output start Proof for theBenchmark % 9.48/2.07 Assumptions after simplification: % 9.48/2.07 --------------------------------- % 9.48/2.07 % 9.48/2.07 (rat_difference_problem_13) % 9.48/2.09 ? [v0: $rat] : ? [v1: $rat] : ( ~ (v1 = v0) & rat_$difference(v0, v1) = % 9.48/2.09 rat_0) % 9.48/2.09 % 9.48/2.09 (input) % 9.86/2.12 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_0) & ~ % 9.86/2.12 (rat_very_small = rat_0) & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_0) = 0 & % 9.86/2.12 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_0) % 9.86/2.12 = rat_0 & rat_$round(rat_0) = rat_0 & rat_$to_int(rat_0) = 0 & % 9.86/2.12 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = % 9.86/2.12 rat_0 & rat_$product(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 & % 9.86/2.12 rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small, % 9.86/2.12 rat_very_large) = 1 & rat_$greatereq(rat_0, rat_0) = 0 & % 9.86/2.12 rat_$lesseq(rat_very_small, rat_very_large) = 0 & rat_$lesseq(rat_0, rat_0) = % 9.86/2.12 0 & rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small, % 9.86/2.12 rat_very_large) = 1 & rat_$greater(rat_0, rat_very_small) = 0 & % 9.86/2.12 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0 % 9.86/2.12 & rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_0, rat_very_large) = 0 % 9.86/2.12 & rat_$less(rat_0, rat_0) = 1 & rat_$difference(rat_0, rat_0) = rat_0 & ! % 9.86/2.12 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( % 9.86/2.12 ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : % 9.86/2.12 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: % 9.86/2.12 $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2, % 9.86/2.12 v3) = v4) | ~ (rat_$sum(v1, v0) = v3) | ? [v5: $rat] : (rat_$sum(v5, % 9.86/2.12 v0) = v4 & rat_$sum(v2, v1) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! % 9.86/2.12 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ % 9.86/2.12 (rat_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1, % 9.86/2.12 v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: % 9.86/2.12 int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) % 9.86/2.12 | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v1, v0) = v4)) & ! [v0: $rat] : % 9.86/2.12 ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, % 9.86/2.12 v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & % 9.86/2.12 rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 9.86/2.12 : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, % 9.86/2.12 v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & ! % 9.86/2.12 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 9.86/2.12 (rat_$less(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ % 9.86/2.12 (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! % 9.86/2.12 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ % 9.86/2.12 (rat_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) % 9.86/2.12 = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( % 9.86/2.12 ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1, % 9.86/2.12 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 = % 9.86/2.12 v0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 9.86/2.12 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 9.86/2.12 : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 9.86/2.12 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 9.86/2.12 : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 9.86/2.12 rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 9.86/2.12 int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) % 9.86/2.12 & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 9.86/2.12 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 9.86/2.12 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : % 9.86/2.12 (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 9.86/2.12 rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 9.86/2.12 $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0) % 9.86/2.12 = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 9.86/2.12 (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] : % 9.86/2.12 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | % 9.86/2.12 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 9.86/2.12 ( ~ (rat_$sum(v1, v0) = v2) | rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1: % 9.86/2.12 $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) % 9.86/2.12 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = % 9.86/2.12 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2, v0) = 0) & ! [v0: % 9.86/2.12 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~ % 9.86/2.12 (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: % 10.18/2.12 $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, % 10.18/2.12 v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! % 10.18/2.12 [v2: $rat] : ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : % 10.18/2.12 (rat_$uminus(v0) = v3 & rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1: % 10.18/2.12 $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1: % 10.18/2.12 $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & % 10.18/2.12 ! [v0: $rat] : ! [v1: int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & ! % 10.18/2.12 [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = % 10.18/2.12 v0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | % 10.18/2.12 rat_$sum(v0, v1) = rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 10.18/2.12 (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! % 10.18/2.12 [v1: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & ! % 10.18/2.12 [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, % 10.18/2.12 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | % 10.18/2.12 rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 10.18/2.12 (rat_$less(v1, v0) = 0) | rat_$greater(v0, v1) = 0) & ! [v0: $rat] : ! % 10.18/2.12 [v1: MultipleValueBool] : ( ~ (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) = % 10.18/2.12 0) & ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0) = v0)) % 10.18/2.12 % 10.18/2.12 (function-axioms) % 10.18/2.13 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 10.18/2.13 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0: % 10.18/2.13 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 10.18/2.13 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0: % 10.18/2.13 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 10.18/2.13 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0: % 10.18/2.13 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 10.18/2.13 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3, % 10.18/2.13 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 10.18/2.13 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ % 10.18/2.13 (rat_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.18/2.13 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ % 10.18/2.13 (rat_$greater(v3, v2) = v1) | ~ (rat_$greater(v3, v2) = v0)) & ! [v0: % 10.18/2.13 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3: % 10.18/2.13 $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = % 10.18/2.13 v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 % 10.18/2.13 = v0 | ~ (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = % 10.18/2.13 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.18/2.13 $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & % 10.18/2.13 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = % 10.18/2.13 v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] % 10.18/2.13 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~ % 10.18/2.13 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 % 10.18/2.13 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0: % 10.18/2.13 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) = % 10.18/2.13 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 10.18/2.13 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) & % 10.18/2.13 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) = % 10.18/2.13 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 10.18/2.13 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) & % 10.18/2.13 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~ % 10.18/2.13 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : ! % 10.18/2.13 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~ % 10.18/2.13 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 10.18/2.13 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0)) % 10.18/2.13 % 10.18/2.13 Those formulas are unsatisfiable: % 10.18/2.13 --------------------------------- % 10.18/2.13 % 10.18/2.13 Begin of proof % 10.18/2.13 | % 10.18/2.13 | ALPHA: (function-axioms) implies: % 10.18/2.13 | (1) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = % 10.18/2.13 | v0 | ~ (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) % 10.18/2.13 | % 10.18/2.14 | ALPHA: (input) implies: % 10.18/2.14 | (2) rat_$sum(rat_0, rat_0) = rat_0 % 10.18/2.14 | (3) ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | % 10.18/2.14 | rat_$sum(v0, v1) = rat_0) % 10.18/2.14 | (4) ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = % 10.18/2.14 | v1)) % 10.18/2.14 | (5) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 10.18/2.14 | (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = % 10.18/2.14 | v3 & rat_$sum(v1, v3) = v2)) % 10.18/2.14 | (6) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) = % 10.18/2.14 | v2) | rat_$sum(v0, v1) = v2) % 10.18/2.14 | (7) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: % 10.18/2.14 | $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~ (rat_$sum(v1, v0) = v3) | ? % 10.18/2.14 | [v5: $rat] : (rat_$sum(v5, v0) = v4 & rat_$sum(v2, v1) = v5)) % 10.18/2.14 | (8) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: % 10.18/2.14 | $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? % 10.18/2.14 | [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) % 10.18/2.14 | % 10.18/2.14 | DELTA: instantiating (rat_difference_problem_13) with fresh symbols all_5_0, % 10.18/2.14 | all_5_1 gives: % 10.18/2.14 | (9) ~ (all_5_0 = all_5_1) & rat_$difference(all_5_1, all_5_0) = rat_0 % 10.18/2.14 | % 10.18/2.14 | ALPHA: (9) implies: % 10.18/2.14 | (10) ~ (all_5_0 = all_5_1) % 10.18/2.14 | (11) rat_$difference(all_5_1, all_5_0) = rat_0 % 10.18/2.14 | % 10.18/2.14 | GROUND_INST: instantiating (5) with all_5_0, all_5_1, rat_0, simplifying with % 10.18/2.14 | (11) gives: % 10.18/2.14 | (12) ? [v0: $rat] : (rat_$uminus(all_5_0) = v0 & rat_$sum(all_5_1, v0) = % 10.18/2.14 | rat_0) % 10.18/2.14 | % 10.18/2.14 | DELTA: instantiating (12) with fresh symbol all_17_0 gives: % 10.18/2.14 | (13) rat_$uminus(all_5_0) = all_17_0 & rat_$sum(all_5_1, all_17_0) = rat_0 % 10.18/2.14 | % 10.18/2.14 | ALPHA: (13) implies: % 10.18/2.14 | (14) rat_$sum(all_5_1, all_17_0) = rat_0 % 10.18/2.14 | (15) rat_$uminus(all_5_0) = all_17_0 % 10.18/2.14 | % 10.18/2.15 | GROUND_INST: instantiating (8) with rat_0, all_17_0, all_5_1, rat_0, rat_0, % 10.18/2.15 | simplifying with (2), (14) gives: % 10.18/2.15 | (16) ? [v0: $rat] : (rat_$sum(all_17_0, rat_0) = v0 & rat_$sum(all_5_1, % 10.18/2.15 | v0) = rat_0) % 10.18/2.15 | % 10.18/2.15 | GROUND_INST: instantiating (7) with all_17_0, all_5_1, rat_0, rat_0, rat_0, % 10.18/2.15 | simplifying with (2), (14) gives: % 10.18/2.15 | (17) ? [v0: $rat] : (rat_$sum(v0, all_17_0) = rat_0 & rat_$sum(rat_0, % 10.18/2.15 | all_5_1) = v0) % 10.18/2.15 | % 10.18/2.15 | GROUND_INST: instantiating (6) with all_17_0, all_5_1, rat_0, simplifying with % 10.18/2.15 | (14) gives: % 10.18/2.15 | (18) rat_$sum(all_17_0, all_5_1) = rat_0 % 10.18/2.15 | % 10.18/2.15 | GROUND_INST: instantiating (3) with all_5_0, all_17_0, simplifying with (15) % 10.18/2.15 | gives: % 10.18/2.15 | (19) rat_$sum(all_5_0, all_17_0) = rat_0 % 10.18/2.15 | % 10.18/2.15 | DELTA: instantiating (17) with fresh symbol all_29_0 gives: % 10.18/2.15 | (20) rat_$sum(all_29_0, all_17_0) = rat_0 & rat_$sum(rat_0, all_5_1) = % 10.18/2.15 | all_29_0 % 10.18/2.15 | % 10.18/2.15 | ALPHA: (20) implies: % 10.18/2.15 | (21) rat_$sum(rat_0, all_5_1) = all_29_0 % 10.18/2.15 | (22) rat_$sum(all_29_0, all_17_0) = rat_0 % 10.18/2.15 | % 10.18/2.15 | DELTA: instantiating (16) with fresh symbol all_31_0 gives: % 10.18/2.15 | (23) rat_$sum(all_17_0, rat_0) = all_31_0 & rat_$sum(all_5_1, all_31_0) = % 10.18/2.15 | rat_0 % 10.18/2.15 | % 10.18/2.15 | ALPHA: (23) implies: % 10.18/2.15 | (24) rat_$sum(all_5_1, all_31_0) = rat_0 % 10.18/2.15 | (25) rat_$sum(all_17_0, rat_0) = all_31_0 % 10.18/2.15 | % 10.18/2.15 | GROUND_INST: instantiating (4) with all_17_0, all_31_0, simplifying with (25) % 10.18/2.15 | gives: % 10.18/2.15 | (26) all_31_0 = all_17_0 % 10.18/2.15 | % 10.18/2.15 | REDUCE: (25), (26) imply: % 10.18/2.15 | (27) rat_$sum(all_17_0, rat_0) = all_17_0 % 10.18/2.15 | % 10.18/2.15 | GROUND_INST: instantiating (8) with all_5_1, all_17_0, all_5_1, rat_0, % 10.18/2.15 | all_29_0, simplifying with (14), (21) gives: % 10.18/2.15 | (28) ? [v0: $rat] : (rat_$sum(all_17_0, all_5_1) = v0 & rat_$sum(all_5_1, % 10.18/2.15 | v0) = all_29_0) % 10.18/2.15 | % 10.18/2.15 | GROUND_INST: instantiating (6) with all_5_1, rat_0, all_29_0, simplifying with % 10.18/2.15 | (21) gives: % 10.18/2.15 | (29) rat_$sum(all_5_1, rat_0) = all_29_0 % 10.18/2.15 | % 10.18/2.15 | GROUND_INST: instantiating (8) with all_5_1, all_17_0, all_5_0, rat_0, % 10.18/2.15 | all_29_0, simplifying with (19), (21) gives: % 10.18/2.15 | (30) ? [v0: $rat] : (rat_$sum(all_17_0, all_5_1) = v0 & rat_$sum(all_5_0, % 10.18/2.15 | v0) = all_29_0) % 10.18/2.15 | % 10.18/2.15 | GROUND_INST: instantiating (7) with all_17_0, all_5_1, all_17_0, rat_0, % 10.18/2.15 | all_17_0, simplifying with (14), (27) gives: % 10.18/2.15 | (31) ? [v0: $rat] : (rat_$sum(v0, all_17_0) = all_17_0 & % 10.18/2.15 | rat_$sum(all_17_0, all_5_1) = v0) % 10.18/2.15 | % 10.18/2.15 | GROUND_INST: instantiating (8) with rat_0, all_5_1, all_17_0, rat_0, rat_0, % 10.18/2.15 | simplifying with (2), (18) gives: % 10.18/2.15 | (32) ? [v0: $rat] : (rat_$sum(all_17_0, v0) = rat_0 & rat_$sum(all_5_1, % 10.18/2.15 | rat_0) = v0) % 10.18/2.15 | % 10.18/2.16 | GROUND_INST: instantiating (8) with all_5_1, all_17_0, all_29_0, rat_0, % 10.18/2.16 | all_29_0, simplifying with (21), (22) gives: % 10.18/2.16 | (33) ? [v0: $rat] : (rat_$sum(all_29_0, v0) = all_29_0 & % 10.18/2.16 | rat_$sum(all_17_0, all_5_1) = v0) % 10.18/2.16 | % 10.18/2.16 | DELTA: instantiating (32) with fresh symbol all_60_0 gives: % 10.18/2.16 | (34) rat_$sum(all_17_0, all_60_0) = rat_0 & rat_$sum(all_5_1, rat_0) = % 10.18/2.16 | all_60_0 % 10.18/2.16 | % 10.18/2.16 | ALPHA: (34) implies: % 10.18/2.16 | (35) rat_$sum(all_5_1, rat_0) = all_60_0 % 10.18/2.16 | % 10.18/2.16 | DELTA: instantiating (30) with fresh symbol all_62_0 gives: % 10.18/2.16 | (36) rat_$sum(all_17_0, all_5_1) = all_62_0 & rat_$sum(all_5_0, all_62_0) = % 10.18/2.16 | all_29_0 % 10.18/2.16 | % 10.18/2.16 | ALPHA: (36) implies: % 10.18/2.16 | (37) rat_$sum(all_5_0, all_62_0) = all_29_0 % 10.18/2.16 | (38) rat_$sum(all_17_0, all_5_1) = all_62_0 % 10.18/2.16 | % 10.18/2.16 | DELTA: instantiating (31) with fresh symbol all_70_0 gives: % 10.18/2.16 | (39) rat_$sum(all_70_0, all_17_0) = all_17_0 & rat_$sum(all_17_0, all_5_1) % 10.18/2.16 | = all_70_0 % 10.18/2.16 | % 10.18/2.16 | ALPHA: (39) implies: % 10.18/2.16 | (40) rat_$sum(all_17_0, all_5_1) = all_70_0 % 10.18/2.16 | % 10.18/2.16 | DELTA: instantiating (33) with fresh symbol all_72_0 gives: % 10.18/2.16 | (41) rat_$sum(all_29_0, all_72_0) = all_29_0 & rat_$sum(all_17_0, all_5_1) % 10.18/2.16 | = all_72_0 % 10.18/2.16 | % 10.18/2.16 | ALPHA: (41) implies: % 10.18/2.16 | (42) rat_$sum(all_17_0, all_5_1) = all_72_0 % 10.18/2.16 | % 10.18/2.16 | DELTA: instantiating (28) with fresh symbol all_74_0 gives: % 10.18/2.16 | (43) rat_$sum(all_17_0, all_5_1) = all_74_0 & rat_$sum(all_5_1, all_74_0) = % 10.18/2.16 | all_29_0 % 10.18/2.16 | % 10.18/2.16 | ALPHA: (43) implies: % 10.18/2.16 | (44) rat_$sum(all_17_0, all_5_1) = all_74_0 % 10.18/2.16 | % 10.18/2.16 | GROUND_INST: instantiating (1) with all_29_0, all_60_0, rat_0, all_5_1, % 10.18/2.16 | simplifying with (29), (35) gives: % 10.18/2.16 | (45) all_60_0 = all_29_0 % 10.18/2.16 | % 10.18/2.16 | GROUND_INST: instantiating (4) with all_5_1, all_60_0, simplifying with (35) % 10.18/2.16 | gives: % 10.18/2.16 | (46) all_60_0 = all_5_1 % 10.18/2.16 | % 10.18/2.16 | GROUND_INST: instantiating (1) with all_62_0, all_70_0, all_5_1, all_17_0, % 10.18/2.16 | simplifying with (38), (40) gives: % 10.18/2.16 | (47) all_70_0 = all_62_0 % 10.18/2.16 | % 10.18/2.16 | GROUND_INST: instantiating (1) with all_70_0, all_72_0, all_5_1, all_17_0, % 10.18/2.16 | simplifying with (40), (42) gives: % 10.18/2.16 | (48) all_72_0 = all_70_0 % 10.18/2.16 | % 10.18/2.16 | GROUND_INST: instantiating (1) with rat_0, all_74_0, all_5_1, all_17_0, % 10.18/2.16 | simplifying with (18), (44) gives: % 10.18/2.16 | (49) all_74_0 = rat_0 % 10.18/2.16 | % 10.18/2.16 | GROUND_INST: instantiating (1) with all_72_0, all_74_0, all_5_1, all_17_0, % 10.18/2.16 | simplifying with (42), (44) gives: % 10.18/2.16 | (50) all_74_0 = all_72_0 % 10.18/2.16 | % 10.18/2.16 | COMBINE_EQS: (49), (50) imply: % 10.18/2.16 | (51) all_72_0 = rat_0 % 10.18/2.16 | % 10.18/2.16 | SIMP: (51) implies: % 10.18/2.16 | (52) all_72_0 = rat_0 % 10.18/2.16 | % 10.18/2.16 | COMBINE_EQS: (48), (52) imply: % 10.18/2.16 | (53) all_70_0 = rat_0 % 10.18/2.16 | % 10.18/2.16 | SIMP: (53) implies: % 10.18/2.16 | (54) all_70_0 = rat_0 % 10.18/2.16 | % 10.18/2.16 | COMBINE_EQS: (47), (54) imply: % 10.18/2.16 | (55) all_62_0 = rat_0 % 10.18/2.16 | % 10.18/2.16 | COMBINE_EQS: (45), (46) imply: % 10.18/2.16 | (56) all_29_0 = all_5_1 % 10.18/2.16 | % 10.18/2.16 | SIMP: (56) implies: % 10.18/2.16 | (57) all_29_0 = all_5_1 % 10.18/2.17 | % 10.18/2.17 | REDUCE: (37), (55), (57) imply: % 10.18/2.17 | (58) rat_$sum(all_5_0, rat_0) = all_5_1 % 10.18/2.17 | % 10.18/2.17 | GROUND_INST: instantiating (4) with all_5_0, all_5_1, simplifying with (58) % 10.18/2.17 | gives: % 10.18/2.17 | (59) all_5_0 = all_5_1 % 10.18/2.17 | % 10.18/2.17 | REDUCE: (10), (59) imply: % 10.18/2.17 | (60) $false % 10.18/2.17 | % 10.18/2.17 | CLOSE: (60) is inconsistent. % 10.18/2.17 | % 10.18/2.17 End of proof % 10.18/2.17 % SZS output end Proof for theBenchmark % 10.18/2.17 % 10.18/2.17 1554ms %------------------------------------------------------------------------------