%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI297_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 : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 17:47:37 EDT 2023 % Result : Theorem 10.42s 2.43s % Output : Proof 19.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : ARI297_1 : TPTP v8.1.2. Released v5.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.33 % Computer : n008.cluster.edu % 0.09/0.33 % Model : x86_64 x86_64 % 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.33 % Memory : 8042.1875MB % 0.09/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.33 % CPULimit : 300 % 0.09/0.33 % WCLimit : 300 % 0.09/0.33 % DateTime : Tue Aug 29 18:17:17 EDT 2023 % 0.09/0.33 % CPUTime : % 0.14/0.58 ________ _____ % 0.14/0.58 ___ __ \_________(_)________________________________ % 0.14/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.14/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.14/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.14/0.58 % 0.14/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.14/0.58 (2023-06-19) % 0.14/0.58 % 0.14/0.58 (c) Philipp Rümmer, 2009-2023 % 0.14/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.14/0.58 Amanda Stjerna. % 0.14/0.58 Free software under BSD-3-Clause. % 0.14/0.58 % 0.14/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.14/0.58 % 0.14/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.14/0.60 Running up to 7 provers in parallel. % 0.14/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.14/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.14/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.14/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.14/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.14/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.14/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.13/0.89 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 1.13/0.89 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.13/0.89 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 1.13/0.89 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 1.13/0.89 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 1.13/0.89 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.13/0.89 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 2.08/1.03 Prover 4: Preprocessing ... % 2.08/1.04 Prover 1: Preprocessing ... % 2.43/1.10 Prover 6: Preprocessing ... % 2.43/1.10 Prover 0: Preprocessing ... % 4.47/1.39 Prover 5: Preprocessing ... % 4.92/1.40 Prover 3: Preprocessing ... % 4.92/1.42 Prover 2: Preprocessing ... % 8.66/1.93 Prover 1: Constructing countermodel ... % 8.66/1.93 Prover 6: Constructing countermodel ... % 8.89/1.96 Prover 4: Constructing countermodel ... % 8.89/2.02 Prover 0: Proving ... % 10.42/2.43 Prover 6: proved (1811ms) % 10.42/2.43 % 10.42/2.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.42/2.43 % 11.27/2.45 Prover 0: stopped % 11.27/2.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.27/2.46 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation % 11.27/2.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.27/2.47 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation % 11.27/2.48 Prover 2: stopped % 11.27/2.48 Prover 8: Preprocessing ... % 12.68/2.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.68/2.50 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation % 13.43/2.59 Prover 7: Preprocessing ... % 13.43/2.61 Prover 10: Preprocessing ... % 13.87/2.71 Prover 1: Found proof (size 9) % 13.87/2.71 Prover 1: proved (2106ms) % 13.87/2.72 Prover 4: stopped % 14.53/2.77 Prover 8: Warning: ignoring some quantifiers % 15.01/2.80 Prover 8: Constructing countermodel ... % 15.01/2.82 Prover 8: stopped % 15.91/2.97 Prover 7: stopped % 15.91/3.02 Prover 10: stopped % 17.95/3.31 Prover 3: Constructing countermodel ... % 17.95/3.32 Prover 3: stopped % 19.34/3.62 Prover 5: Proving ... % 19.34/3.62 Prover 5: stopped % 19.34/3.62 % 19.34/3.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.34/3.62 % 19.34/3.63 % SZS output start Proof for theBenchmark % 19.34/3.63 Assumptions after simplification: % 19.34/3.63 --------------------------------- % 19.34/3.63 % 19.34/3.63 (rat_product_problem_14) % 19.70/3.67 ? [v0: $rat] : ( ~ (v0 = rat_5/8) & rat_$product(v0, rat_2/5) = rat_1/4) % 19.70/3.67 % 19.70/3.67 (input) % 19.70/3.71 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_5/8) & ~ % 19.70/3.71 (rat_very_large = rat_1/4) & ~ (rat_very_large = rat_2/5) & ~ % 19.70/3.71 (rat_very_large = rat_0) & ~ (rat_very_small = rat_5/8) & ~ (rat_very_small % 19.70/3.71 = rat_1/4) & ~ (rat_very_small = rat_2/5) & ~ (rat_very_small = rat_0) & % 19.70/3.71 ~ (rat_5/8 = rat_1/4) & ~ (rat_5/8 = rat_2/5) & ~ (rat_5/8 = rat_0) & ~ % 19.70/3.71 (rat_1/4 = rat_2/5) & ~ (rat_1/4 = rat_0) & ~ (rat_2/5 = rat_0) & % 19.70/3.71 rat_$is_int(rat_5/8) = 1 & rat_$is_int(rat_1/4) = 1 & rat_$is_int(rat_2/5) = 1 % 19.70/3.71 & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_5/8) = 0 & rat_$is_rat(rat_1/4) = 0 % 19.70/3.71 & rat_$is_rat(rat_2/5) = 0 & rat_$is_rat(rat_0) = 0 & rat_$floor(rat_5/8) = % 19.70/3.71 rat_0 & rat_$floor(rat_1/4) = rat_0 & rat_$floor(rat_2/5) = rat_0 & % 19.70/3.71 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 & % 19.70/3.71 rat_$truncate(rat_5/8) = rat_0 & rat_$truncate(rat_1/4) = rat_0 & % 19.70/3.71 rat_$truncate(rat_2/5) = rat_0 & rat_$truncate(rat_0) = rat_0 & % 19.70/3.71 rat_$round(rat_1/4) = rat_0 & rat_$round(rat_2/5) = rat_0 & rat_$round(rat_0) % 19.70/3.71 = rat_0 & rat_$to_int(rat_5/8) = 0 & rat_$to_int(rat_1/4) = 0 & % 19.70/3.71 rat_$to_int(rat_2/5) = 0 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_5/8) = % 19.70/3.71 rat_5/8 & rat_$to_rat(rat_1/4) = rat_1/4 & rat_$to_rat(rat_2/5) = rat_2/5 & % 19.70/3.71 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_5/8) = real_5/8 & % 19.70/3.71 rat_$to_real(rat_1/4) = real_1/4 & rat_$to_real(rat_2/5) = real_2/5 & % 19.70/3.71 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_1/4, % 19.70/3.71 rat_5/8) = rat_2/5 & rat_$quotient(rat_1/4, rat_2/5) = rat_5/8 & % 19.70/3.71 rat_$quotient(rat_0, rat_5/8) = rat_0 & rat_$quotient(rat_0, rat_1/4) = rat_0 % 19.70/3.71 & rat_$quotient(rat_0, rat_2/5) = rat_0 & rat_$difference(rat_5/8, rat_5/8) = % 19.70/3.71 rat_0 & rat_$difference(rat_5/8, rat_0) = rat_5/8 & rat_$difference(rat_1/4, % 19.70/3.71 rat_1/4) = rat_0 & rat_$difference(rat_1/4, rat_0) = rat_1/4 & % 19.70/3.71 rat_$difference(rat_2/5, rat_2/5) = rat_0 & rat_$difference(rat_2/5, rat_0) = % 19.70/3.71 rat_2/5 & rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 & % 19.70/3.71 rat_$sum(rat_5/8, rat_0) = rat_5/8 & rat_$sum(rat_1/4, rat_0) = rat_1/4 & % 19.70/3.71 rat_$sum(rat_2/5, rat_0) = rat_2/5 & rat_$sum(rat_0, rat_5/8) = rat_5/8 & % 19.70/3.71 rat_$sum(rat_0, rat_1/4) = rat_1/4 & rat_$sum(rat_0, rat_2/5) = rat_2/5 & % 19.70/3.71 rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small, % 19.70/3.71 rat_very_large) = 1 & rat_$greatereq(rat_5/8, rat_5/8) = 0 & % 19.70/3.71 rat_$greatereq(rat_5/8, rat_1/4) = 0 & rat_$greatereq(rat_5/8, rat_2/5) = 0 & % 19.70/3.71 rat_$greatereq(rat_5/8, rat_0) = 0 & rat_$greatereq(rat_1/4, rat_5/8) = 1 & % 19.70/3.71 rat_$greatereq(rat_1/4, rat_1/4) = 0 & rat_$greatereq(rat_1/4, rat_2/5) = 1 & % 19.70/3.71 rat_$greatereq(rat_1/4, rat_0) = 0 & rat_$greatereq(rat_2/5, rat_5/8) = 1 & % 19.70/3.71 rat_$greatereq(rat_2/5, rat_1/4) = 0 & rat_$greatereq(rat_2/5, rat_2/5) = 0 & % 19.70/3.71 rat_$greatereq(rat_2/5, rat_0) = 0 & rat_$greatereq(rat_0, rat_5/8) = 1 & % 19.70/3.71 rat_$greatereq(rat_0, rat_1/4) = 1 & rat_$greatereq(rat_0, rat_2/5) = 1 & % 19.70/3.71 rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large) % 19.70/3.71 = 0 & rat_$lesseq(rat_5/8, rat_5/8) = 0 & rat_$lesseq(rat_5/8, rat_1/4) = 1 & % 19.70/3.71 rat_$lesseq(rat_5/8, rat_2/5) = 1 & rat_$lesseq(rat_5/8, rat_0) = 1 & % 19.70/3.71 rat_$lesseq(rat_1/4, rat_5/8) = 0 & rat_$lesseq(rat_1/4, rat_1/4) = 0 & % 19.70/3.71 rat_$lesseq(rat_1/4, rat_2/5) = 0 & rat_$lesseq(rat_1/4, rat_0) = 1 & % 19.70/3.71 rat_$lesseq(rat_2/5, rat_5/8) = 0 & rat_$lesseq(rat_2/5, rat_1/4) = 1 & % 19.70/3.71 rat_$lesseq(rat_2/5, rat_2/5) = 0 & rat_$lesseq(rat_2/5, rat_0) = 1 & % 19.70/3.71 rat_$lesseq(rat_0, rat_5/8) = 0 & rat_$lesseq(rat_0, rat_1/4) = 0 & % 19.70/3.71 rat_$lesseq(rat_0, rat_2/5) = 0 & rat_$lesseq(rat_0, rat_0) = 0 & % 19.70/3.71 rat_$greater(rat_very_large, rat_5/8) = 0 & rat_$greater(rat_very_large, % 19.70/3.71 rat_1/4) = 0 & rat_$greater(rat_very_large, rat_2/5) = 0 & % 19.70/3.71 rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small, % 19.70/3.71 rat_very_large) = 1 & rat_$greater(rat_5/8, rat_very_small) = 0 & % 19.70/3.71 rat_$greater(rat_5/8, rat_5/8) = 1 & rat_$greater(rat_5/8, rat_1/4) = 0 & % 19.70/3.71 rat_$greater(rat_5/8, rat_2/5) = 0 & rat_$greater(rat_5/8, rat_0) = 0 & % 19.70/3.71 rat_$greater(rat_1/4, rat_very_small) = 0 & rat_$greater(rat_1/4, rat_5/8) = 1 % 19.70/3.71 & rat_$greater(rat_1/4, rat_1/4) = 1 & rat_$greater(rat_1/4, rat_2/5) = 1 & % 19.70/3.71 rat_$greater(rat_1/4, rat_0) = 0 & rat_$greater(rat_2/5, rat_very_small) = 0 & % 19.70/3.71 rat_$greater(rat_2/5, rat_5/8) = 1 & rat_$greater(rat_2/5, rat_1/4) = 0 & % 19.70/3.71 rat_$greater(rat_2/5, rat_2/5) = 1 & rat_$greater(rat_2/5, rat_0) = 0 & % 19.70/3.71 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_5/8) = 1 & % 19.70/3.71 rat_$greater(rat_0, rat_1/4) = 1 & rat_$greater(rat_0, rat_2/5) = 1 & % 19.70/3.71 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0 % 19.70/3.71 & rat_$less(rat_very_small, rat_5/8) = 0 & rat_$less(rat_very_small, rat_1/4) % 19.70/3.71 = 0 & rat_$less(rat_very_small, rat_2/5) = 0 & rat_$less(rat_very_small, % 19.70/3.72 rat_0) = 0 & rat_$less(rat_5/8, rat_very_large) = 0 & rat_$less(rat_5/8, % 19.70/3.72 rat_5/8) = 1 & rat_$less(rat_5/8, rat_1/4) = 1 & rat_$less(rat_5/8, rat_2/5) % 19.70/3.72 = 1 & rat_$less(rat_5/8, rat_0) = 1 & rat_$less(rat_1/4, rat_very_large) = 0 & % 19.70/3.72 rat_$less(rat_1/4, rat_5/8) = 0 & rat_$less(rat_1/4, rat_1/4) = 1 & % 19.70/3.72 rat_$less(rat_1/4, rat_2/5) = 0 & rat_$less(rat_1/4, rat_0) = 1 & % 19.70/3.72 rat_$less(rat_2/5, rat_very_large) = 0 & rat_$less(rat_2/5, rat_5/8) = 0 & % 19.70/3.72 rat_$less(rat_2/5, rat_1/4) = 1 & rat_$less(rat_2/5, rat_2/5) = 1 & % 19.70/3.72 rat_$less(rat_2/5, rat_0) = 1 & rat_$less(rat_0, rat_very_large) = 0 & % 19.70/3.72 rat_$less(rat_0, rat_5/8) = 0 & rat_$less(rat_0, rat_1/4) = 0 & % 19.70/3.72 rat_$less(rat_0, rat_2/5) = 0 & rat_$less(rat_0, rat_0) = 1 & % 19.70/3.72 rat_$product(rat_5/8, rat_2/5) = rat_1/4 & rat_$product(rat_5/8, rat_0) = % 19.70/3.72 rat_0 & rat_$product(rat_1/4, rat_0) = rat_0 & rat_$product(rat_2/5, rat_5/8) % 19.70/3.72 = rat_1/4 & rat_$product(rat_2/5, rat_0) = rat_0 & rat_$product(rat_0, % 19.70/3.72 rat_5/8) = rat_0 & rat_$product(rat_0, rat_1/4) = rat_0 & % 19.70/3.72 rat_$product(rat_0, rat_2/5) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 & ! % 19.70/3.72 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( % 19.70/3.72 ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : % 19.70/3.72 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: % 19.70/3.72 $rat] : ! [v2: $rat] : ! [v3: $rat] : (v3 = v1 | v0 = rat_0 | ~ % 19.70/3.72 (rat_$quotient(v2, v0) = v3) | ~ (rat_$product(v1, v0) = v2)) & ! [v0: % 19.70/3.72 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 19.70/3.72 (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( % 19.70/3.72 ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : % 19.70/3.72 ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~ % 19.70/3.72 (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = % 19.70/3.72 v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~ % 19.70/3.72 (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1, % 19.70/3.72 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v2 = rat_0 | % 19.70/3.72 ~ (rat_$uminus(v0) = v1) | ~ (rat_$sum(v0, v1) = v2)) & ! [v0: $rat] : ! % 19.70/3.72 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? % 19.70/3.72 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! % 19.70/3.72 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1 % 19.70/3.72 = v0) & ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3))) & ! % 19.70/3.72 [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1) % 19.70/3.72 = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0: % 19.70/3.72 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | % 19.70/3.72 rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 19.70/3.72 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = % 19.70/3.72 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, % 19.70/3.72 v1) = v2) | rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : % 19.70/3.72 (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] : % 19.70/3.72 (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0: % 19.70/3.72 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & % 19.70/3.72 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | % 19.70/3.72 rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 19.70/3.72 (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : (v0 = % 19.70/3.72 rat_0 | ~ (rat_$uminus(v0) = v0)) % 19.70/3.72 % 19.70/3.72 Those formulas are unsatisfiable: % 19.70/3.72 --------------------------------- % 19.70/3.72 % 19.70/3.72 Begin of proof % 19.70/3.72 | % 19.70/3.72 | ALPHA: (input) implies: % 19.70/3.73 | (1) ~ (rat_2/5 = rat_0) % 19.70/3.73 | (2) rat_$quotient(rat_1/4, rat_2/5) = rat_5/8 % 19.70/3.73 | (3) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v3 = % 19.70/3.73 | v1 | v0 = rat_0 | ~ (rat_$quotient(v2, v0) = v3) | ~ % 19.70/3.73 | (rat_$product(v1, v0) = v2)) % 19.70/3.73 | % 19.70/3.73 | DELTA: instantiating (rat_product_problem_14) with fresh symbol all_5_0 gives: % 19.70/3.73 | (4) ~ (all_5_0 = rat_5/8) & rat_$product(all_5_0, rat_2/5) = rat_1/4 % 19.70/3.73 | % 19.70/3.73 | ALPHA: (4) implies: % 19.70/3.73 | (5) ~ (all_5_0 = rat_5/8) % 19.70/3.73 | (6) rat_$product(all_5_0, rat_2/5) = rat_1/4 % 19.70/3.73 | % 19.70/3.73 | GROUND_INST: instantiating (3) with rat_2/5, all_5_0, rat_1/4, rat_5/8, % 19.70/3.73 | simplifying with (2), (6) gives: % 19.70/3.73 | (7) all_5_0 = rat_5/8 | rat_2/5 = rat_0 % 19.70/3.73 | % 19.70/3.73 | BETA: splitting (7) gives: % 19.70/3.73 | % 19.70/3.73 | Case 1: % 19.70/3.73 | | % 19.70/3.73 | | (8) rat_2/5 = rat_0 % 19.70/3.73 | | % 19.70/3.73 | | REDUCE: (1), (8) imply: % 19.70/3.73 | | (9) $false % 19.70/3.74 | | % 19.70/3.74 | | CLOSE: (9) is inconsistent. % 19.70/3.74 | | % 19.70/3.74 | Case 2: % 19.70/3.74 | | % 19.70/3.74 | | (10) all_5_0 = rat_5/8 % 19.70/3.74 | | % 19.70/3.74 | | REDUCE: (5), (10) imply: % 19.70/3.74 | | (11) $false % 19.70/3.74 | | % 19.70/3.74 | | CLOSE: (11) is inconsistent. % 19.70/3.74 | | % 19.70/3.74 | End of split % 19.70/3.74 | % 19.70/3.74 End of proof % 19.70/3.74 % SZS output end Proof for theBenchmark % 19.70/3.74 % 19.70/3.74 3153ms %------------------------------------------------------------------------------