%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI298_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 : n032.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 15.06s 2.91s % Output : Proof 22.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : ARI298_1 : TPTP v8.1.2. Released v5.0.0. % 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.32 % Computer : n032.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Tue Aug 29 18:49:02 EDT 2023 % 0.11/0.32 % CPUTime : % 0.57/0.61 ________ _____ % 0.57/0.61 ___ __ \_________(_)________________________________ % 0.57/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.57/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.57/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.57/0.61 % 0.57/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.57/0.62 (2023-06-19) % 0.57/0.62 % 0.57/0.62 (c) Philipp Rümmer, 2009-2023 % 0.57/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.57/0.62 Amanda Stjerna. % 0.57/0.62 Free software under BSD-3-Clause. % 0.57/0.62 % 0.57/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.57/0.62 % 0.57/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.57/0.63 Running up to 7 provers in parallel. % 0.57/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.57/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.57/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.57/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.57/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.57/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.57/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.26/0.98 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 1.26/0.98 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 1.26/0.98 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.26/0.98 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.26/0.98 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 1.26/0.98 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 1.26/0.98 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 2.21/1.14 Prover 4: Preprocessing ... % 2.21/1.14 Prover 1: Preprocessing ... % 2.83/1.23 Prover 0: Preprocessing ... % 2.83/1.23 Prover 6: Preprocessing ... % 4.92/1.50 Prover 3: Preprocessing ... % 4.92/1.51 Prover 5: Preprocessing ... % 4.92/1.51 Prover 2: Preprocessing ... % 9.51/2.17 Prover 1: Constructing countermodel ... % 9.51/2.18 Prover 6: Constructing countermodel ... % 10.02/2.23 Prover 4: Constructing countermodel ... % 10.02/2.25 Prover 0: Proving ... % 15.06/2.91 Prover 6: proved (2260ms) % 15.06/2.91 % 15.06/2.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.06/2.91 % 15.06/2.93 Prover 0: stopped % 15.58/2.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.58/2.94 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation % 15.58/2.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.58/2.94 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation % 15.76/2.97 Prover 8: Preprocessing ... % 15.76/2.97 Prover 1: Found proof (size 10) % 15.76/2.97 Prover 1: proved (2332ms) % 15.76/2.97 Prover 4: stopped % 16.47/3.11 Prover 8: Warning: ignoring some quantifiers % 16.47/3.12 Prover 8: Constructing countermodel ... % 16.47/3.12 Prover 7: Preprocessing ... % 17.06/3.14 Prover 8: stopped % 19.30/3.47 Prover 7: stopped % 21.30/3.78 Prover 3: Constructing countermodel ... % 21.30/3.79 Prover 3: stopped % 21.91/3.89 Prover 2: Proving ... % 21.91/3.89 Prover 2: stopped % 22.48/4.04 Prover 5: Proving ... % 22.48/4.04 Prover 5: stopped % 22.48/4.04 % 22.48/4.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.48/4.04 % 22.48/4.05 % SZS output start Proof for theBenchmark % 22.48/4.05 Assumptions after simplification: % 22.48/4.05 --------------------------------- % 22.48/4.05 % 22.48/4.05 (rat_product_problem_15) % 22.91/4.09 ? [v0: $rat] : ( ~ (v0 = rat_2/5) & rat_$product(rat_5/8, v0) = rat_1/4) % 22.91/4.09 % 22.91/4.09 (input) % 22.91/4.14 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_2/5) & ~ % 22.91/4.14 (rat_very_large = rat_1/4) & ~ (rat_very_large = rat_5/8) & ~ % 22.91/4.14 (rat_very_large = rat_0) & ~ (rat_very_small = rat_2/5) & ~ (rat_very_small % 22.91/4.14 = rat_1/4) & ~ (rat_very_small = rat_5/8) & ~ (rat_very_small = rat_0) & % 22.91/4.14 ~ (rat_2/5 = rat_1/4) & ~ (rat_2/5 = rat_5/8) & ~ (rat_2/5 = rat_0) & ~ % 22.91/4.14 (rat_1/4 = rat_5/8) & ~ (rat_1/4 = rat_0) & ~ (rat_5/8 = rat_0) & % 22.91/4.14 rat_$is_int(rat_2/5) = 1 & rat_$is_int(rat_1/4) = 1 & rat_$is_int(rat_5/8) = 1 % 22.91/4.14 & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_2/5) = 0 & rat_$is_rat(rat_1/4) = 0 % 22.91/4.14 & rat_$is_rat(rat_5/8) = 0 & rat_$is_rat(rat_0) = 0 & rat_$floor(rat_2/5) = % 22.91/4.14 rat_0 & rat_$floor(rat_1/4) = rat_0 & rat_$floor(rat_5/8) = rat_0 & % 22.91/4.14 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 & % 22.91/4.14 rat_$truncate(rat_2/5) = rat_0 & rat_$truncate(rat_1/4) = rat_0 & % 22.91/4.14 rat_$truncate(rat_5/8) = rat_0 & rat_$truncate(rat_0) = rat_0 & % 22.91/4.14 rat_$round(rat_2/5) = rat_0 & rat_$round(rat_1/4) = rat_0 & rat_$round(rat_0) % 22.91/4.14 = rat_0 & rat_$to_int(rat_2/5) = 0 & rat_$to_int(rat_1/4) = 0 & % 22.91/4.14 rat_$to_int(rat_5/8) = 0 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_2/5) = % 22.91/4.14 rat_2/5 & rat_$to_rat(rat_1/4) = rat_1/4 & rat_$to_rat(rat_5/8) = rat_5/8 & % 22.91/4.14 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_2/5) = real_2/5 & % 22.91/4.14 rat_$to_real(rat_1/4) = real_1/4 & rat_$to_real(rat_5/8) = real_5/8 & % 22.91/4.14 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_1/4, % 22.91/4.14 rat_2/5) = rat_5/8 & rat_$quotient(rat_1/4, rat_5/8) = rat_2/5 & % 22.91/4.14 rat_$quotient(rat_0, rat_2/5) = rat_0 & rat_$quotient(rat_0, rat_1/4) = rat_0 % 22.91/4.14 & rat_$quotient(rat_0, rat_5/8) = rat_0 & rat_$difference(rat_2/5, rat_2/5) = % 22.91/4.14 rat_0 & rat_$difference(rat_2/5, rat_0) = rat_2/5 & rat_$difference(rat_1/4, % 22.91/4.14 rat_1/4) = rat_0 & rat_$difference(rat_1/4, rat_0) = rat_1/4 & % 22.91/4.14 rat_$difference(rat_5/8, rat_5/8) = rat_0 & rat_$difference(rat_5/8, rat_0) = % 22.91/4.14 rat_5/8 & rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 & % 22.91/4.14 rat_$sum(rat_2/5, rat_0) = rat_2/5 & rat_$sum(rat_1/4, rat_0) = rat_1/4 & % 22.91/4.14 rat_$sum(rat_5/8, rat_0) = rat_5/8 & rat_$sum(rat_0, rat_2/5) = rat_2/5 & % 22.91/4.14 rat_$sum(rat_0, rat_1/4) = rat_1/4 & rat_$sum(rat_0, rat_5/8) = rat_5/8 & % 22.91/4.14 rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small, % 22.91/4.14 rat_very_large) = 1 & rat_$greatereq(rat_2/5, rat_2/5) = 0 & % 22.91/4.14 rat_$greatereq(rat_2/5, rat_1/4) = 0 & rat_$greatereq(rat_2/5, rat_5/8) = 1 & % 22.91/4.14 rat_$greatereq(rat_2/5, rat_0) = 0 & rat_$greatereq(rat_1/4, rat_2/5) = 1 & % 22.91/4.14 rat_$greatereq(rat_1/4, rat_1/4) = 0 & rat_$greatereq(rat_1/4, rat_5/8) = 1 & % 22.91/4.14 rat_$greatereq(rat_1/4, rat_0) = 0 & rat_$greatereq(rat_5/8, rat_2/5) = 0 & % 22.91/4.14 rat_$greatereq(rat_5/8, rat_1/4) = 0 & rat_$greatereq(rat_5/8, rat_5/8) = 0 & % 22.91/4.14 rat_$greatereq(rat_5/8, rat_0) = 0 & rat_$greatereq(rat_0, rat_2/5) = 1 & % 22.91/4.14 rat_$greatereq(rat_0, rat_1/4) = 1 & rat_$greatereq(rat_0, rat_5/8) = 1 & % 22.91/4.14 rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large) % 22.91/4.14 = 0 & rat_$lesseq(rat_2/5, rat_2/5) = 0 & rat_$lesseq(rat_2/5, rat_1/4) = 1 & % 22.91/4.14 rat_$lesseq(rat_2/5, rat_5/8) = 0 & rat_$lesseq(rat_2/5, rat_0) = 1 & % 22.91/4.14 rat_$lesseq(rat_1/4, rat_2/5) = 0 & rat_$lesseq(rat_1/4, rat_1/4) = 0 & % 22.91/4.14 rat_$lesseq(rat_1/4, rat_5/8) = 0 & rat_$lesseq(rat_1/4, rat_0) = 1 & % 22.91/4.14 rat_$lesseq(rat_5/8, rat_2/5) = 1 & rat_$lesseq(rat_5/8, rat_1/4) = 1 & % 22.91/4.14 rat_$lesseq(rat_5/8, rat_5/8) = 0 & rat_$lesseq(rat_5/8, rat_0) = 1 & % 22.91/4.14 rat_$lesseq(rat_0, rat_2/5) = 0 & rat_$lesseq(rat_0, rat_1/4) = 0 & % 22.91/4.14 rat_$lesseq(rat_0, rat_5/8) = 0 & rat_$lesseq(rat_0, rat_0) = 0 & % 22.91/4.14 rat_$greater(rat_very_large, rat_2/5) = 0 & rat_$greater(rat_very_large, % 22.91/4.14 rat_1/4) = 0 & rat_$greater(rat_very_large, rat_5/8) = 0 & % 22.91/4.14 rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small, % 22.91/4.14 rat_very_large) = 1 & rat_$greater(rat_2/5, rat_very_small) = 0 & % 22.91/4.14 rat_$greater(rat_2/5, rat_2/5) = 1 & rat_$greater(rat_2/5, rat_1/4) = 0 & % 22.91/4.14 rat_$greater(rat_2/5, rat_5/8) = 1 & rat_$greater(rat_2/5, rat_0) = 0 & % 22.91/4.14 rat_$greater(rat_1/4, rat_very_small) = 0 & rat_$greater(rat_1/4, rat_2/5) = 1 % 22.91/4.14 & rat_$greater(rat_1/4, rat_1/4) = 1 & rat_$greater(rat_1/4, rat_5/8) = 1 & % 22.91/4.14 rat_$greater(rat_1/4, rat_0) = 0 & rat_$greater(rat_5/8, rat_very_small) = 0 & % 22.91/4.14 rat_$greater(rat_5/8, rat_2/5) = 0 & rat_$greater(rat_5/8, rat_1/4) = 0 & % 22.91/4.14 rat_$greater(rat_5/8, rat_5/8) = 1 & rat_$greater(rat_5/8, rat_0) = 0 & % 22.91/4.14 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_2/5) = 1 & % 22.91/4.14 rat_$greater(rat_0, rat_1/4) = 1 & rat_$greater(rat_0, rat_5/8) = 1 & % 22.91/4.14 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0 % 22.91/4.15 & rat_$less(rat_very_small, rat_2/5) = 0 & rat_$less(rat_very_small, rat_1/4) % 22.91/4.15 = 0 & rat_$less(rat_very_small, rat_5/8) = 0 & rat_$less(rat_very_small, % 22.91/4.15 rat_0) = 0 & rat_$less(rat_2/5, rat_very_large) = 0 & rat_$less(rat_2/5, % 22.91/4.15 rat_2/5) = 1 & rat_$less(rat_2/5, rat_1/4) = 1 & rat_$less(rat_2/5, rat_5/8) % 22.91/4.15 = 0 & rat_$less(rat_2/5, rat_0) = 1 & rat_$less(rat_1/4, rat_very_large) = 0 & % 22.91/4.15 rat_$less(rat_1/4, rat_2/5) = 0 & rat_$less(rat_1/4, rat_1/4) = 1 & % 22.91/4.15 rat_$less(rat_1/4, rat_5/8) = 0 & rat_$less(rat_1/4, rat_0) = 1 & % 22.91/4.15 rat_$less(rat_5/8, rat_very_large) = 0 & rat_$less(rat_5/8, rat_2/5) = 1 & % 22.91/4.15 rat_$less(rat_5/8, rat_1/4) = 1 & rat_$less(rat_5/8, rat_5/8) = 1 & % 22.91/4.15 rat_$less(rat_5/8, rat_0) = 1 & rat_$less(rat_0, rat_very_large) = 0 & % 22.91/4.15 rat_$less(rat_0, rat_2/5) = 0 & rat_$less(rat_0, rat_1/4) = 0 & % 22.91/4.15 rat_$less(rat_0, rat_5/8) = 0 & rat_$less(rat_0, rat_0) = 1 & % 22.91/4.15 rat_$product(rat_2/5, rat_5/8) = rat_1/4 & rat_$product(rat_2/5, rat_0) = % 22.91/4.15 rat_0 & rat_$product(rat_1/4, rat_0) = rat_0 & rat_$product(rat_5/8, rat_2/5) % 22.91/4.15 = rat_1/4 & rat_$product(rat_5/8, rat_0) = rat_0 & rat_$product(rat_0, % 22.91/4.15 rat_2/5) = rat_0 & rat_$product(rat_0, rat_1/4) = rat_0 & % 22.91/4.15 rat_$product(rat_0, rat_5/8) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 & ! % 22.91/4.15 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( % 22.91/4.15 ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : % 22.91/4.15 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: % 22.91/4.15 $rat] : ! [v2: $rat] : ! [v3: $rat] : (v3 = v1 | v0 = rat_0 | ~ % 22.91/4.15 (rat_$quotient(v2, v0) = v3) | ~ (rat_$product(v1, v0) = v2)) & ! [v0: % 22.91/4.15 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 22.91/4.15 (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( % 22.91/4.15 ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : % 22.91/4.15 ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~ % 22.91/4.15 (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = % 22.91/4.15 v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~ % 22.91/4.15 (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1, % 22.91/4.15 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v2 = rat_0 | % 22.91/4.15 ~ (rat_$uminus(v0) = v1) | ~ (rat_$sum(v0, v1) = v2)) & ! [v0: $rat] : ! % 22.91/4.15 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? % 22.91/4.15 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! % 22.91/4.15 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1 % 22.91/4.15 = v0) & ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3))) & ! % 22.91/4.15 [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1) % 22.91/4.15 = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0: % 22.91/4.15 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | % 22.91/4.15 rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 22.91/4.15 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = % 22.91/4.15 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, % 22.91/4.15 v1) = v2) | rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : % 22.91/4.15 (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] : % 22.91/4.15 (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0: % 22.91/4.15 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & % 22.91/4.15 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | % 22.91/4.15 rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 22.91/4.15 (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : (v0 = % 22.91/4.15 rat_0 | ~ (rat_$uminus(v0) = v0)) % 22.91/4.15 % 22.91/4.15 Those formulas are unsatisfiable: % 22.91/4.15 --------------------------------- % 22.91/4.15 % 22.91/4.15 Begin of proof % 22.91/4.15 | % 22.91/4.15 | ALPHA: (input) implies: % 22.91/4.16 | (1) ~ (rat_5/8 = rat_0) % 22.91/4.16 | (2) rat_$quotient(rat_1/4, rat_5/8) = rat_2/5 % 22.91/4.16 | (3) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, % 22.91/4.16 | v1) = v2) | rat_$product(v1, v0) = v2) % 22.91/4.16 | (4) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v3 = % 22.91/4.16 | v1 | v0 = rat_0 | ~ (rat_$quotient(v2, v0) = v3) | ~ % 22.91/4.16 | (rat_$product(v1, v0) = v2)) % 22.91/4.16 | % 22.91/4.16 | DELTA: instantiating (rat_product_problem_15) with fresh symbol all_5_0 gives: % 22.91/4.16 | (5) ~ (all_5_0 = rat_2/5) & rat_$product(rat_5/8, all_5_0) = rat_1/4 % 22.91/4.16 | % 22.91/4.16 | ALPHA: (5) implies: % 22.91/4.16 | (6) ~ (all_5_0 = rat_2/5) % 22.91/4.16 | (7) rat_$product(rat_5/8, all_5_0) = rat_1/4 % 22.91/4.16 | % 22.91/4.16 | GROUND_INST: instantiating (3) with rat_5/8, all_5_0, rat_1/4, simplifying % 22.91/4.16 | with (7) gives: % 22.91/4.16 | (8) rat_$product(all_5_0, rat_5/8) = rat_1/4 % 22.91/4.16 | % 22.91/4.17 | GROUND_INST: instantiating (4) with rat_5/8, all_5_0, rat_1/4, rat_2/5, % 22.91/4.17 | simplifying with (2), (8) gives: % 22.91/4.17 | (9) all_5_0 = rat_2/5 | rat_5/8 = rat_0 % 22.91/4.17 | % 22.91/4.17 | BETA: splitting (9) gives: % 22.91/4.17 | % 22.91/4.17 | Case 1: % 22.91/4.17 | | % 22.91/4.17 | | (10) rat_5/8 = rat_0 % 22.91/4.17 | | % 22.91/4.17 | | REDUCE: (1), (10) imply: % 22.91/4.17 | | (11) $false % 22.91/4.17 | | % 22.91/4.17 | | CLOSE: (11) is inconsistent. % 22.91/4.17 | | % 22.91/4.17 | Case 2: % 22.91/4.17 | | % 22.91/4.17 | | (12) all_5_0 = rat_2/5 % 22.91/4.17 | | % 22.91/4.17 | | REDUCE: (6), (12) imply: % 22.91/4.17 | | (13) $false % 22.91/4.17 | | % 22.91/4.17 | | CLOSE: (13) is inconsistent. % 22.91/4.17 | | % 22.91/4.17 | End of split % 22.91/4.17 | % 22.91/4.17 End of proof % 22.91/4.17 % SZS output end Proof for theBenchmark % 22.91/4.17 % 22.91/4.17 3552ms %------------------------------------------------------------------------------