%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI448_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 : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 17:48:05 EDT 2023 % Result : Theorem 8.93s 1.81s % Output : Proof 13.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.07 % Problem : ARI448_1 : TPTP v8.1.2. Released v5.0.0. % 0.04/0.08 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.07/0.26 % Computer : n016.cluster.edu % 0.07/0.26 % Model : x86_64 x86_64 % 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.26 % Memory : 8042.1875MB % 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.26 % CPULimit : 300 % 0.07/0.26 % WCLimit : 300 % 0.07/0.26 % DateTime : Tue Aug 29 19:21:01 EDT 2023 % 0.07/0.27 % CPUTime : % 0.11/0.52 ________ _____ % 0.11/0.52 ___ __ \_________(_)________________________________ % 0.11/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.11/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.11/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.11/0.52 % 0.11/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.11/0.52 (2023-06-19) % 0.11/0.52 % 0.11/0.52 (c) Philipp Rümmer, 2009-2023 % 0.11/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.11/0.52 Amanda Stjerna. % 0.11/0.52 Free software under BSD-3-Clause. % 0.11/0.52 % 0.11/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.11/0.52 % 0.11/0.52 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.11/0.53 Running up to 7 provers in parallel. % 0.61/0.55 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.61/0.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.61/0.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.61/0.55 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.61/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.61/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.61/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.37/0.80 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.37/0.80 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.37/0.80 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.37/0.80 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.37/0.80 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.37/0.80 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 1.37/0.80 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 2.07/0.92 Prover 1: Preprocessing ... % 2.07/0.92 Prover 4: Preprocessing ... % 2.76/0.97 Prover 6: Preprocessing ... % 2.76/0.97 Prover 0: Preprocessing ... % 4.09/1.15 Prover 2: Preprocessing ... % 4.09/1.15 Prover 3: Preprocessing ... % 4.09/1.16 Prover 5: Preprocessing ... % 6.61/1.50 Prover 6: Constructing countermodel ... % 6.61/1.51 Prover 1: Constructing countermodel ... % 6.61/1.51 Prover 4: Constructing countermodel ... % 7.21/1.58 Prover 0: Proving ... % 8.93/1.81 Prover 6: proved (1254ms) % 8.93/1.81 % 8.93/1.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.93/1.81 % 8.93/1.82 Prover 0: stopped % 8.93/1.83 Prover 2: stopped % 9.29/1.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.29/1.83 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 9.29/1.83 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.29/1.83 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 9.29/1.84 Prover 8: Preprocessing ... % 9.29/1.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.42/1.84 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 9.42/1.90 Prover 10: Preprocessing ... % 9.98/1.92 Prover 7: Preprocessing ... % 9.98/1.96 Prover 8: Warning: ignoring some quantifiers % 10.38/1.97 Prover 8: Constructing countermodel ... % 10.38/1.99 Prover 1: Found proof (size 9) % 10.38/1.99 Prover 1: proved (1447ms) % 10.38/1.99 Prover 4: stopped % 10.38/1.99 Prover 8: stopped % 11.27/2.10 Prover 7: stopped % 11.27/2.10 Prover 10: stopped % 12.94/2.38 Prover 3: Constructing countermodel ... % 12.94/2.38 Prover 3: stopped % 13.18/2.43 Prover 5: Proving ... % 13.18/2.43 Prover 5: stopped % 13.18/2.43 % 13.18/2.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.18/2.43 % 13.18/2.44 % SZS output start Proof for theBenchmark % 13.18/2.44 Assumptions after simplification: % 13.18/2.44 --------------------------------- % 13.18/2.44 % 13.18/2.44 (real_product_problem_13) % 13.29/2.46 ? [v0: $real] : ( ~ (v0 = real_29/4) & real_$product(v0, real_4) = real_29) % 13.29/2.46 % 13.29/2.46 (input) % 13.29/2.48 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_29/4) & ~ % 13.29/2.48 (real_very_large = real_29) & ~ (real_very_large = real_4) & ~ % 13.29/2.48 (real_very_large = real_0) & ~ (real_very_small = real_29/4) & ~ % 13.29/2.48 (real_very_small = real_29) & ~ (real_very_small = real_4) & ~ % 13.29/2.48 (real_very_small = real_0) & ~ (real_29/4 = real_29) & ~ (real_29/4 = % 13.29/2.48 real_4) & ~ (real_29/4 = real_0) & ~ (real_29 = real_4) & ~ (real_29 = % 13.29/2.48 real_0) & ~ (real_4 = real_0) & real_$is_int(real_29/4) = 1 & % 13.29/2.48 real_$is_int(real_29) = 0 & real_$is_int(real_4) = 0 & real_$is_int(real_0) = % 13.29/2.48 0 & real_$is_rat(real_29/4) = 0 & real_$is_rat(real_29) = 0 & % 13.29/2.48 real_$is_rat(real_4) = 0 & real_$is_rat(real_0) = 0 & real_$floor(real_29) = % 13.29/2.48 real_29 & real_$floor(real_4) = real_4 & real_$floor(real_0) = real_0 & % 13.29/2.48 real_$ceiling(real_29) = real_29 & real_$ceiling(real_4) = real_4 & % 13.29/2.48 real_$ceiling(real_0) = real_0 & real_$truncate(real_29) = real_29 & % 13.29/2.48 real_$truncate(real_4) = real_4 & real_$truncate(real_0) = real_0 & % 13.29/2.48 real_$round(real_29) = real_29 & real_$round(real_4) = real_4 & % 13.29/2.48 real_$round(real_0) = real_0 & real_$to_int(real_29/4) = 7 & % 13.29/2.48 real_$to_int(real_29) = 29 & real_$to_int(real_4) = 4 & real_$to_int(real_0) = % 13.29/2.48 0 & real_$to_rat(real_29/4) = rat_29/4 & real_$to_rat(real_29) = rat_29 & % 13.29/2.48 real_$to_rat(real_4) = rat_4 & real_$to_rat(real_0) = rat_0 & % 13.29/2.48 real_$to_real(real_29/4) = real_29/4 & real_$to_real(real_29) = real_29 & % 13.29/2.48 real_$to_real(real_4) = real_4 & real_$to_real(real_0) = real_0 & % 13.29/2.48 int_$to_real(29) = real_29 & int_$to_real(4) = real_4 & int_$to_real(0) = % 13.29/2.48 real_0 & real_$quotient(real_29, real_29/4) = real_4 & real_$quotient(real_29, % 13.29/2.48 real_4) = real_29/4 & real_$quotient(real_0, real_29/4) = real_0 & % 13.29/2.48 real_$quotient(real_0, real_29) = real_0 & real_$quotient(real_0, real_4) = % 13.29/2.48 real_0 & real_$difference(real_29/4, real_29/4) = real_0 & % 13.29/2.48 real_$difference(real_29/4, real_0) = real_29/4 & real_$difference(real_29, % 13.29/2.48 real_29) = real_0 & real_$difference(real_29, real_0) = real_29 & % 13.29/2.48 real_$difference(real_4, real_4) = real_0 & real_$difference(real_4, real_0) = % 13.29/2.48 real_4 & real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) = % 13.29/2.48 real_0 & real_$sum(real_29/4, real_0) = real_29/4 & real_$sum(real_29, real_0) % 13.29/2.48 = real_29 & real_$sum(real_4, real_0) = real_4 & real_$sum(real_0, real_29/4) % 13.29/2.48 = real_29/4 & real_$sum(real_0, real_29) = real_29 & real_$sum(real_0, real_4) % 13.29/2.48 = real_4 & real_$sum(real_0, real_0) = real_0 & % 13.29/2.48 real_$greatereq(real_very_small, real_very_large) = 1 & % 13.29/2.48 real_$greatereq(real_29/4, real_29/4) = 0 & real_$greatereq(real_29/4, % 13.29/2.48 real_29) = 1 & real_$greatereq(real_29/4, real_4) = 0 & % 13.29/2.48 real_$greatereq(real_29/4, real_0) = 0 & real_$greatereq(real_29, real_29/4) = % 13.29/2.48 0 & real_$greatereq(real_29, real_29) = 0 & real_$greatereq(real_29, real_4) = % 13.29/2.48 0 & real_$greatereq(real_29, real_0) = 0 & real_$greatereq(real_4, real_29/4) % 13.29/2.48 = 1 & real_$greatereq(real_4, real_29) = 1 & real_$greatereq(real_4, real_4) = % 13.29/2.48 0 & real_$greatereq(real_4, real_0) = 0 & real_$greatereq(real_0, real_29/4) = % 13.29/2.48 1 & real_$greatereq(real_0, real_29) = 1 & real_$greatereq(real_0, real_4) = 1 % 13.29/2.48 & real_$greatereq(real_0, real_0) = 0 & real_$lesseq(real_very_small, % 13.29/2.48 real_very_large) = 0 & real_$lesseq(real_29/4, real_29/4) = 0 & % 13.29/2.49 real_$lesseq(real_29/4, real_29) = 0 & real_$lesseq(real_29/4, real_4) = 1 & % 13.29/2.49 real_$lesseq(real_29/4, real_0) = 1 & real_$lesseq(real_29, real_29/4) = 1 & % 13.29/2.49 real_$lesseq(real_29, real_29) = 0 & real_$lesseq(real_29, real_4) = 1 & % 13.29/2.49 real_$lesseq(real_29, real_0) = 1 & real_$lesseq(real_4, real_29/4) = 0 & % 13.29/2.49 real_$lesseq(real_4, real_29) = 0 & real_$lesseq(real_4, real_4) = 0 & % 13.29/2.49 real_$lesseq(real_4, real_0) = 1 & real_$lesseq(real_0, real_29/4) = 0 & % 13.29/2.49 real_$lesseq(real_0, real_29) = 0 & real_$lesseq(real_0, real_4) = 0 & % 13.29/2.49 real_$lesseq(real_0, real_0) = 0 & real_$greater(real_very_large, real_29/4) = % 13.29/2.49 0 & real_$greater(real_very_large, real_29) = 0 & % 13.29/2.49 real_$greater(real_very_large, real_4) = 0 & real_$greater(real_very_large, % 13.29/2.49 real_0) = 0 & real_$greater(real_very_small, real_very_large) = 1 & % 13.29/2.49 real_$greater(real_29/4, real_very_small) = 0 & real_$greater(real_29/4, % 13.29/2.49 real_29/4) = 1 & real_$greater(real_29/4, real_29) = 1 & % 13.29/2.49 real_$greater(real_29/4, real_4) = 0 & real_$greater(real_29/4, real_0) = 0 & % 13.29/2.49 real_$greater(real_29, real_very_small) = 0 & real_$greater(real_29, % 13.29/2.49 real_29/4) = 0 & real_$greater(real_29, real_29) = 1 & % 13.29/2.49 real_$greater(real_29, real_4) = 0 & real_$greater(real_29, real_0) = 0 & % 13.29/2.49 real_$greater(real_4, real_very_small) = 0 & real_$greater(real_4, real_29/4) % 13.29/2.49 = 1 & real_$greater(real_4, real_29) = 1 & real_$greater(real_4, real_4) = 1 & % 13.29/2.49 real_$greater(real_4, real_0) = 0 & real_$greater(real_0, real_very_small) = 0 % 13.29/2.49 & real_$greater(real_0, real_29/4) = 1 & real_$greater(real_0, real_29) = 1 & % 13.29/2.49 real_$greater(real_0, real_4) = 1 & real_$greater(real_0, real_0) = 1 & % 13.29/2.49 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, % 13.29/2.49 real_29/4) = 0 & real_$less(real_very_small, real_29) = 0 & % 13.29/2.49 real_$less(real_very_small, real_4) = 0 & real_$less(real_very_small, real_0) % 13.29/2.49 = 0 & real_$less(real_29/4, real_very_large) = 0 & real_$less(real_29/4, % 13.29/2.49 real_29/4) = 1 & real_$less(real_29/4, real_29) = 0 & real_$less(real_29/4, % 13.29/2.49 real_4) = 1 & real_$less(real_29/4, real_0) = 1 & real_$less(real_29, % 13.29/2.49 real_very_large) = 0 & real_$less(real_29, real_29/4) = 1 & % 13.29/2.49 real_$less(real_29, real_29) = 1 & real_$less(real_29, real_4) = 1 & % 13.29/2.49 real_$less(real_29, real_0) = 1 & real_$less(real_4, real_very_large) = 0 & % 13.29/2.49 real_$less(real_4, real_29/4) = 0 & real_$less(real_4, real_29) = 0 & % 13.29/2.49 real_$less(real_4, real_4) = 1 & real_$less(real_4, real_0) = 1 & % 13.29/2.49 real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_29/4) = 0 & % 13.29/2.49 real_$less(real_0, real_29) = 0 & real_$less(real_0, real_4) = 0 & % 13.29/2.49 real_$less(real_0, real_0) = 1 & real_$product(real_29/4, real_4) = real_29 & % 13.29/2.49 real_$product(real_29/4, real_0) = real_0 & real_$product(real_29, real_0) = % 13.29/2.49 real_0 & real_$product(real_4, real_29/4) = real_29 & real_$product(real_4, % 13.29/2.49 real_0) = real_0 & real_$product(real_0, real_29/4) = real_0 & % 13.29/2.49 real_$product(real_0, real_29) = real_0 & real_$product(real_0, real_4) = % 13.29/2.49 real_0 & real_$product(real_0, real_0) = real_0 & ! [v0: $real] : ! [v1: % 13.29/2.49 $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ % 13.29/2.49 (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] : % 13.29/2.49 (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! % 13.29/2.49 [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~ % 13.29/2.49 (real_$quotient(v2, v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: % 13.29/2.49 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ % 13.29/2.49 (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] : % 13.29/2.49 ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] % 13.29/2.49 : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0) = 0) | ~ % 13.29/2.49 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1) % 13.29/2.49 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] % 13.29/2.49 : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) | % 13.29/2.49 real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.29/2.49 $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) = % 13.29/2.49 v2)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ % 13.29/2.49 (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 13.29/2.49 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.29/2.49 int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3: % 13.29/2.49 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $real] : ! % 13.29/2.49 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? % 13.29/2.49 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! % 13.29/2.49 [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, % 13.29/2.49 v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 13.29/2.49 (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v1, v0) = 0) | real_$less(v2, % 13.29/2.49 v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 13.29/2.49 (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) & ! [v0: $real] % 13.29/2.49 : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0: % 13.29/2.49 $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | % 13.29/2.49 real_$less(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 13.29/2.49 (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: % 13.29/2.49 $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! % 13.29/2.49 [v0: $real] : ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | % 13.29/2.49 real_$less(v1, v0) = 0) & ! [v0: $real] : (v0 = real_0 | ~ % 13.29/2.49 (real_$uminus(v0) = v0)) % 13.29/2.49 % 13.29/2.49 Those formulas are unsatisfiable: % 13.29/2.49 --------------------------------- % 13.29/2.49 % 13.29/2.49 Begin of proof % 13.29/2.49 | % 13.29/2.49 | ALPHA: (input) implies: % 13.29/2.49 | (1) ~ (real_4 = real_0) % 13.29/2.49 | (2) real_$quotient(real_29, real_4) = real_29/4 % 13.29/2.49 | (3) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v3 % 13.29/2.49 | = v1 | v0 = real_0 | ~ (real_$quotient(v2, v0) = v3) | ~ % 13.29/2.49 | (real_$product(v1, v0) = v2)) % 13.29/2.49 | % 13.29/2.49 | DELTA: instantiating (real_product_problem_13) with fresh symbol all_5_0 % 13.29/2.49 | gives: % 13.29/2.49 | (4) ~ (all_5_0 = real_29/4) & real_$product(all_5_0, real_4) = real_29 % 13.29/2.49 | % 13.29/2.49 | ALPHA: (4) implies: % 13.29/2.50 | (5) ~ (all_5_0 = real_29/4) % 13.29/2.50 | (6) real_$product(all_5_0, real_4) = real_29 % 13.29/2.50 | % 13.29/2.50 | GROUND_INST: instantiating (3) with real_4, all_5_0, real_29, real_29/4, % 13.29/2.50 | simplifying with (2), (6) gives: % 13.29/2.50 | (7) all_5_0 = real_29/4 | real_4 = real_0 % 13.29/2.50 | % 13.29/2.50 | BETA: splitting (7) gives: % 13.29/2.50 | % 13.29/2.50 | Case 1: % 13.29/2.50 | | % 13.29/2.50 | | (8) real_4 = real_0 % 13.29/2.50 | | % 13.29/2.50 | | REDUCE: (1), (8) imply: % 13.29/2.50 | | (9) $false % 13.29/2.50 | | % 13.29/2.50 | | CLOSE: (9) is inconsistent. % 13.29/2.50 | | % 13.29/2.50 | Case 2: % 13.29/2.50 | | % 13.29/2.50 | | (10) all_5_0 = real_29/4 % 13.29/2.50 | | % 13.29/2.50 | | REDUCE: (5), (10) imply: % 13.29/2.50 | | (11) $false % 13.29/2.50 | | % 13.29/2.50 | | CLOSE: (11) is inconsistent. % 13.29/2.50 | | % 13.29/2.50 | End of split % 13.29/2.50 | % 13.29/2.50 End of proof % 13.29/2.50 % SZS output end Proof for theBenchmark % 13.29/2.50 % 13.29/2.50 1977ms %------------------------------------------------------------------------------