0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : princess-casc +printProof -timeout=%d %s 0.03/0.23 % Computer : n175.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 04:20:10 CDT 2018 0.03/0.23 % CPUTime : 0.07/0.44 ________ _____ 0.07/0.44 ___ __ \_________(_)________________________________ 0.07/0.44 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ 0.07/0.44 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) 0.07/0.44 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ 0.07/0.44 0.07/0.44 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic 0.07/0.44 (CASC 2017-07-17) 0.07/0.44 0.07/0.44 (c) Philipp Rümmer, 2009-2017 0.07/0.44 (contributions by Peter Backeman, Peter Baumgartner, 0.07/0.44 Angelo Brillout, Aleksandar Zeljic) 0.07/0.44 Free software under GNU Lesser General Public License (LGPL). 0.07/0.44 Bug reports to ph_r@gmx.net 0.07/0.44 0.07/0.44 For more information, visit http://www.philipp.ruemmer.org/princess.shtml 0.07/0.44 0.07/0.44 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... 0.07/0.47 Prover 0: Options: +triggersInConjecture -genTotalityAxioms=ctors +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=off 0.74/0.67 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation 1.43/0.91 Prover 0: Preprocessing ... 3.84/1.64 Prover 0: Constructing countermodel ... 6.40/2.47 Prover 0: proved (1999ms) 6.40/2.47 6.40/2.47 VALID 6.40/2.47 % SZS status Theorem for theBenchmark 6.40/2.47 6.40/2.48 Prover 1: Options: +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off 6.40/2.48 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation 6.72/2.54 Prover 1: Preprocessing ... 7.18/2.71 Prover 1: Constructing countermodel ... 9.15/3.28 Prover 1: Found proof (size 31) 9.15/3.28 Prover 1: proved (801ms) 9.15/3.28 9.15/3.28 9.15/3.29 % SZS output start Proof for theBenchmark 9.15/3.29 Assumptions after simplification: 9.15/3.29 --------------------------------- 9.15/3.29 9.15/3.29 (pow_2_21) 9.27/3.32 ? [v0: $int] : ( ~ (v0 = real_4) & pow(real_2, real_2) = v0) 9.27/3.32 9.27/3.33 (pow_x_two) 9.27/3.33 ! [v0: $int] : ! [v1: $int] : ( ~ (pow(v0, real_2) = v1) | ? [v2: $int] : 9.27/3.33 ? [v3: $int] : (sqr(v0) = v3 & real_$less(real_0, v0) = v2 & ( ~ (v2 = 0) | 9.27/3.33 v3 = v1))) 9.27/3.33 9.27/3.33 (sqrt_positive) 9.27/3.33 ! [v0: $int] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $int] : 9.27/3.33 (real_$lesseq(real_0, v1) = 0 & sqrt(v0) = v1)) 9.27/3.33 9.27/3.33 (sqrt_square) 9.27/3.33 ! [v0: $int] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $int] : (sqr(v1) 9.27/3.33 = v0 & sqrt(v0) = v1)) 9.27/3.33 9.27/3.33 (square_sqrt) 9.27/3.33 ! [v0: $int] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $int] : 9.27/3.33 (real_$product(v0, v0) = v1 & sqrt(v1) = v0)) 9.27/3.33 9.27/3.33 (axioms) 9.40/3.37 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_4) & ~ 9.40/3.37 (real_very_large = real_1/2) & ~ (real_very_large = real_10) & ~ 9.40/3.37 (real_very_large = real_2) & ~ (real_very_large = real_1) & ~ 9.40/3.38 (real_very_large = real_0) & ~ (real_very_small = real_4) & ~ 9.40/3.38 (real_very_small = real_1/2) & ~ (real_very_small = real_10) & ~ 9.40/3.38 (real_very_small = real_2) & ~ (real_very_small = real_1) & ~ 9.40/3.38 (real_very_small = real_0) & ~ (real_4 = real_1/2) & ~ (real_4 = real_10) & 9.40/3.38 ~ (real_4 = real_2) & ~ (real_4 = real_1) & ~ (real_4 = real_0) & ~ 9.40/3.38 (real_1/2 = real_10) & ~ (real_1/2 = real_2) & ~ (real_1/2 = real_1) & ~ 9.40/3.38 (real_1/2 = real_0) & ~ (real_10 = real_2) & ~ (real_10 = real_1) & ~ 9.40/3.38 (real_10 = real_0) & ~ (real_2 = real_1) & ~ (real_2 = real_0) & ~ (real_1 9.40/3.38 = real_0) & real_$is_int(real_4) = 0 & real_$is_int(real_1/2) = 1 & 9.40/3.38 real_$is_int(real_10) = 0 & real_$is_int(real_2) = 0 & real_$is_int(real_1) = 9.40/3.38 0 & real_$is_int(real_0) = 0 & real_$is_rat(real_4) = 0 & 9.40/3.38 real_$is_rat(real_1/2) = 0 & real_$is_rat(real_10) = 0 & real_$is_rat(real_2) 9.40/3.38 = 0 & real_$is_rat(real_1) = 0 & real_$is_rat(real_0) = 0 & 9.40/3.38 real_$floor(real_4) = real_4 & real_$floor(real_1/2) = real_0 & 9.40/3.38 real_$floor(real_10) = real_10 & real_$floor(real_2) = real_2 & 9.40/3.38 real_$floor(real_1) = real_1 & real_$floor(real_0) = real_0 & 9.40/3.38 real_$ceiling(real_4) = real_4 & real_$ceiling(real_1/2) = real_1 & 9.40/3.38 real_$ceiling(real_10) = real_10 & real_$ceiling(real_2) = real_2 & 9.40/3.38 real_$ceiling(real_1) = real_1 & real_$ceiling(real_0) = real_0 & 9.40/3.38 real_$truncate(real_4) = real_4 & real_$truncate(real_1/2) = real_0 & 9.40/3.38 real_$truncate(real_10) = real_10 & real_$truncate(real_2) = real_2 & 9.40/3.38 real_$truncate(real_1) = real_1 & real_$truncate(real_0) = real_0 & 9.40/3.38 real_$round(real_4) = real_4 & real_$round(real_1/2) = real_1 & 9.40/3.38 real_$round(real_10) = real_10 & real_$round(real_2) = real_2 & 9.40/3.38 real_$round(real_1) = real_1 & real_$round(real_0) = real_0 & 9.40/3.38 real_$to_int(real_4) = 4 & real_$to_int(real_1/2) = 0 & real_$to_int(real_10) 9.40/3.38 = 10 & real_$to_int(real_2) = 2 & real_$to_int(real_1) = 1 & 9.40/3.38 real_$to_int(real_0) = 0 & real_$to_rat(real_4) = rat_4 & 9.40/3.38 real_$to_rat(real_1/2) = rat_1/2 & real_$to_rat(real_10) = rat_10 & 9.40/3.38 real_$to_rat(real_2) = rat_2 & real_$to_rat(real_1) = rat_1 & 9.40/3.38 real_$to_rat(real_0) = rat_0 & real_$to_real(real_4) = real_4 & 9.40/3.38 real_$to_real(real_1/2) = real_1/2 & real_$to_real(real_10) = real_10 & 9.40/3.38 real_$to_real(real_2) = real_2 & real_$to_real(real_1) = real_1 & 9.40/3.38 real_$to_real(real_0) = real_0 & int_$to_real(10) = real_10 & int_$to_real(4) 9.40/3.38 = real_4 & int_$to_real(2) = real_2 & int_$to_real(1) = real_1 & 9.40/3.38 int_$to_real(0) = real_0 & real_$difference(real_4, real_4) = real_0 & 9.40/3.38 real_$difference(real_4, real_2) = real_2 & real_$difference(real_4, real_0) = 9.40/3.38 real_4 & real_$difference(real_1/2, real_1/2) = real_0 & 9.40/3.38 real_$difference(real_1/2, real_0) = real_1/2 & real_$difference(real_10, 9.40/3.38 real_10) = real_0 & real_$difference(real_10, real_0) = real_10 & 9.40/3.38 real_$difference(real_2, real_2) = real_0 & real_$difference(real_2, real_1) = 9.40/3.38 real_1 & real_$difference(real_2, real_0) = real_2 & real_$difference(real_1, 9.40/3.38 real_1/2) = real_1/2 & real_$difference(real_1, real_1) = real_0 & 9.40/3.38 real_$difference(real_1, real_0) = real_1 & real_$difference(real_0, real_0) = 9.40/3.38 real_0 & real_$uminus(real_0) = real_0 & real_$greatereq(real_very_small, 9.40/3.38 real_very_large) = 1 & real_$greatereq(real_4, real_4) = 0 & 9.40/3.38 real_$greatereq(real_4, real_1/2) = 0 & real_$greatereq(real_4, real_10) = 1 & 9.40/3.38 real_$greatereq(real_4, real_2) = 0 & real_$greatereq(real_4, real_1) = 0 & 9.40/3.38 real_$greatereq(real_4, real_0) = 0 & real_$greatereq(real_1/2, real_4) = 1 & 9.40/3.38 real_$greatereq(real_1/2, real_1/2) = 0 & real_$greatereq(real_1/2, real_10) = 9.40/3.38 1 & real_$greatereq(real_1/2, real_2) = 1 & real_$greatereq(real_1/2, real_1) 9.40/3.38 = 1 & real_$greatereq(real_1/2, real_0) = 0 & real_$greatereq(real_10, real_4) 9.40/3.38 = 0 & real_$greatereq(real_10, real_1/2) = 0 & real_$greatereq(real_10, 9.40/3.38 real_10) = 0 & real_$greatereq(real_10, real_2) = 0 & 9.40/3.38 real_$greatereq(real_10, real_1) = 0 & real_$greatereq(real_10, real_0) = 0 & 9.40/3.38 real_$greatereq(real_2, real_4) = 1 & real_$greatereq(real_2, real_1/2) = 0 & 9.40/3.38 real_$greatereq(real_2, real_10) = 1 & real_$greatereq(real_2, real_2) = 0 & 9.40/3.38 real_$greatereq(real_2, real_1) = 0 & real_$greatereq(real_2, real_0) = 0 & 9.40/3.38 real_$greatereq(real_1, real_4) = 1 & real_$greatereq(real_1, real_1/2) = 0 & 9.40/3.38 real_$greatereq(real_1, real_10) = 1 & real_$greatereq(real_1, real_2) = 1 & 9.40/3.38 real_$greatereq(real_1, real_1) = 0 & real_$greatereq(real_1, real_0) = 0 & 9.40/3.38 real_$greatereq(real_0, real_4) = 1 & real_$greatereq(real_0, real_1/2) = 1 & 9.40/3.38 real_$greatereq(real_0, real_10) = 1 & real_$greatereq(real_0, real_2) = 1 & 9.40/3.38 real_$greatereq(real_0, real_1) = 1 & real_$greatereq(real_0, real_0) = 0 & 9.40/3.38 real_$greater(real_very_large, real_4) = 0 & real_$greater(real_very_large, 9.40/3.38 real_1/2) = 0 & real_$greater(real_very_large, real_10) = 0 & 9.40/3.38 real_$greater(real_very_large, real_2) = 0 & real_$greater(real_very_large, 9.40/3.38 real_1) = 0 & real_$greater(real_very_large, real_0) = 0 & 9.40/3.38 real_$greater(real_very_small, real_very_large) = 1 & real_$greater(real_4, 9.40/3.38 real_very_small) = 0 & real_$greater(real_4, real_4) = 1 & 9.40/3.38 real_$greater(real_4, real_1/2) = 0 & real_$greater(real_4, real_10) = 1 & 9.40/3.38 real_$greater(real_4, real_2) = 0 & real_$greater(real_4, real_1) = 0 & 9.40/3.38 real_$greater(real_4, real_0) = 0 & real_$greater(real_1/2, real_very_small) = 9.40/3.38 0 & real_$greater(real_1/2, real_4) = 1 & real_$greater(real_1/2, real_1/2) = 9.40/3.38 1 & real_$greater(real_1/2, real_10) = 1 & real_$greater(real_1/2, real_2) = 1 9.40/3.38 & real_$greater(real_1/2, real_1) = 1 & real_$greater(real_1/2, real_0) = 0 & 9.40/3.38 real_$greater(real_10, real_very_small) = 0 & real_$greater(real_10, real_4) = 9.40/3.38 0 & real_$greater(real_10, real_1/2) = 0 & real_$greater(real_10, real_10) = 1 9.40/3.38 & real_$greater(real_10, real_2) = 0 & real_$greater(real_10, real_1) = 0 & 9.40/3.38 real_$greater(real_10, real_0) = 0 & real_$greater(real_2, real_very_small) = 9.40/3.38 0 & real_$greater(real_2, real_4) = 1 & real_$greater(real_2, real_1/2) = 0 & 9.40/3.38 real_$greater(real_2, real_10) = 1 & real_$greater(real_2, real_2) = 1 & 9.40/3.38 real_$greater(real_2, real_1) = 0 & real_$greater(real_2, real_0) = 0 & 9.40/3.38 real_$greater(real_1, real_very_small) = 0 & real_$greater(real_1, real_4) = 1 9.40/3.38 & real_$greater(real_1, real_1/2) = 0 & real_$greater(real_1, real_10) = 1 & 9.40/3.38 real_$greater(real_1, real_2) = 1 & real_$greater(real_1, real_1) = 1 & 9.40/3.38 real_$greater(real_1, real_0) = 0 & real_$greater(real_0, real_very_small) = 0 9.40/3.38 & real_$greater(real_0, real_4) = 1 & real_$greater(real_0, real_1/2) = 1 & 9.40/3.38 real_$greater(real_0, real_10) = 1 & real_$greater(real_0, real_2) = 1 & 9.40/3.38 real_$greater(real_0, real_1) = 1 & real_$greater(real_0, real_0) = 1 & 9.40/3.38 real_$sum(real_4, real_0) = real_4 & real_$sum(real_1/2, real_1/2) = real_1 & 9.40/3.38 real_$sum(real_1/2, real_0) = real_1/2 & real_$sum(real_10, real_0) = real_10 9.40/3.38 & real_$sum(real_2, real_2) = real_4 & real_$sum(real_2, real_0) = real_2 & 9.40/3.38 real_$sum(real_1, real_1) = real_2 & real_$sum(real_1, real_0) = real_1 & 9.40/3.38 real_$sum(real_0, real_4) = real_4 & real_$sum(real_0, real_1/2) = real_1/2 & 9.40/3.38 real_$sum(real_0, real_10) = real_10 & real_$sum(real_0, real_2) = real_2 & 9.40/3.38 real_$sum(real_0, real_1) = real_1 & real_$sum(real_0, real_0) = real_0 & 9.40/3.38 real_$quotient(real_4, real_4) = real_1 & real_$quotient(real_4, real_2) = 9.40/3.38 real_2 & real_$quotient(real_4, real_1) = real_4 & real_$quotient(real_1/2, 9.40/3.38 real_1/2) = real_1 & real_$quotient(real_1/2, real_1) = real_1/2 & 9.40/3.38 real_$quotient(real_10, real_10) = real_1 & real_$quotient(real_10, real_1) = 9.40/3.38 real_10 & real_$quotient(real_2, real_4) = real_1/2 & real_$quotient(real_2, 9.40/3.38 real_1/2) = real_4 & real_$quotient(real_2, real_2) = real_1 & 9.40/3.38 real_$quotient(real_2, real_1) = real_2 & real_$quotient(real_1, real_1/2) = 9.40/3.38 real_2 & real_$quotient(real_1, real_2) = real_1/2 & real_$quotient(real_1, 9.40/3.38 real_1) = real_1 & real_$quotient(real_0, real_4) = real_0 & 9.40/3.38 real_$quotient(real_0, real_1/2) = real_0 & real_$quotient(real_0, real_10) = 9.40/3.38 real_0 & real_$quotient(real_0, real_2) = real_0 & real_$quotient(real_0, 9.40/3.38 real_1) = real_0 & real_$lesseq(real_very_small, real_very_large) = 0 & 9.40/3.38 real_$lesseq(real_4, real_4) = 0 & real_$lesseq(real_4, real_1/2) = 1 & 9.40/3.38 real_$lesseq(real_4, real_10) = 0 & real_$lesseq(real_4, real_2) = 1 & 9.40/3.38 real_$lesseq(real_4, real_1) = 1 & real_$lesseq(real_4, real_0) = 1 & 9.40/3.38 real_$lesseq(real_1/2, real_4) = 0 & real_$lesseq(real_1/2, real_1/2) = 0 & 9.40/3.38 real_$lesseq(real_1/2, real_10) = 0 & real_$lesseq(real_1/2, real_2) = 0 & 9.40/3.38 real_$lesseq(real_1/2, real_1) = 0 & real_$lesseq(real_1/2, real_0) = 1 & 9.40/3.38 real_$lesseq(real_10, real_4) = 1 & real_$lesseq(real_10, real_1/2) = 1 & 9.40/3.38 real_$lesseq(real_10, real_10) = 0 & real_$lesseq(real_10, real_2) = 1 & 9.40/3.38 real_$lesseq(real_10, real_1) = 1 & real_$lesseq(real_10, real_0) = 1 & 9.40/3.38 real_$lesseq(real_2, real_4) = 0 & real_$lesseq(real_2, real_1/2) = 1 & 9.40/3.38 real_$lesseq(real_2, real_10) = 0 & real_$lesseq(real_2, real_2) = 0 & 9.40/3.38 real_$lesseq(real_2, real_1) = 1 & real_$lesseq(real_2, real_0) = 1 & 9.40/3.38 real_$lesseq(real_1, real_4) = 0 & real_$lesseq(real_1, real_1/2) = 1 & 9.40/3.38 real_$lesseq(real_1, real_10) = 0 & real_$lesseq(real_1, real_2) = 0 & 9.40/3.38 real_$lesseq(real_1, real_1) = 0 & real_$lesseq(real_1, real_0) = 1 & 9.40/3.38 real_$lesseq(real_0, real_4) = 0 & real_$lesseq(real_0, real_1/2) = 0 & 9.40/3.38 real_$lesseq(real_0, real_10) = 0 & real_$lesseq(real_0, real_2) = 0 & 9.40/3.38 real_$lesseq(real_0, real_1) = 0 & real_$lesseq(real_0, real_0) = 0 & 9.40/3.38 real_$product(real_4, real_1/2) = real_2 & real_$product(real_4, real_1) = 9.40/3.38 real_4 & real_$product(real_4, real_0) = real_0 & real_$product(real_1/2, 9.40/3.38 real_4) = real_2 & real_$product(real_1/2, real_2) = real_1 & 9.40/3.38 real_$product(real_1/2, real_1) = real_1/2 & real_$product(real_1/2, real_0) = 9.40/3.38 real_0 & real_$product(real_10, real_1) = real_10 & real_$product(real_10, 9.40/3.38 real_0) = real_0 & real_$product(real_2, real_1/2) = real_1 & 9.40/3.38 real_$product(real_2, real_2) = real_4 & real_$product(real_2, real_1) = 9.40/3.38 real_2 & real_$product(real_2, real_0) = real_0 & real_$product(real_1, 9.40/3.38 real_4) = real_4 & real_$product(real_1, real_1/2) = real_1/2 & 9.40/3.38 real_$product(real_1, real_10) = real_10 & real_$product(real_1, real_2) = 9.40/3.38 real_2 & real_$product(real_1, real_1) = real_1 & real_$product(real_1, 9.40/3.38 real_0) = real_0 & real_$product(real_0, real_4) = real_0 & 9.40/3.38 real_$product(real_0, real_1/2) = real_0 & real_$product(real_0, real_10) = 9.40/3.38 real_0 & real_$product(real_0, real_2) = real_0 & real_$product(real_0, 9.40/3.38 real_1) = real_0 & real_$product(real_0, real_0) = real_0 & 9.40/3.38 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, 9.40/3.38 real_4) = 0 & real_$less(real_very_small, real_1/2) = 0 & 9.40/3.38 real_$less(real_very_small, real_10) = 0 & real_$less(real_very_small, real_2) 9.40/3.38 = 0 & real_$less(real_very_small, real_1) = 0 & real_$less(real_very_small, 9.40/3.38 real_0) = 0 & real_$less(real_4, real_very_large) = 0 & real_$less(real_4, 9.40/3.38 real_4) = 1 & real_$less(real_4, real_1/2) = 1 & real_$less(real_4, real_10) 9.40/3.38 = 0 & real_$less(real_4, real_2) = 1 & real_$less(real_4, real_1) = 1 & 9.40/3.38 real_$less(real_4, real_0) = 1 & real_$less(real_1/2, real_very_large) = 0 & 9.40/3.38 real_$less(real_1/2, real_4) = 0 & real_$less(real_1/2, real_1/2) = 1 & 9.40/3.38 real_$less(real_1/2, real_10) = 0 & real_$less(real_1/2, real_2) = 0 & 9.40/3.38 real_$less(real_1/2, real_1) = 0 & real_$less(real_1/2, real_0) = 1 & 9.40/3.38 real_$less(real_10, real_very_large) = 0 & real_$less(real_10, real_4) = 1 & 9.40/3.38 real_$less(real_10, real_1/2) = 1 & real_$less(real_10, real_10) = 1 & 9.40/3.38 real_$less(real_10, real_2) = 1 & real_$less(real_10, real_1) = 1 & 9.40/3.38 real_$less(real_10, real_0) = 1 & real_$less(real_2, real_very_large) = 0 & 9.40/3.38 real_$less(real_2, real_4) = 0 & real_$less(real_2, real_1/2) = 1 & 9.40/3.38 real_$less(real_2, real_10) = 0 & real_$less(real_2, real_2) = 1 & 9.40/3.38 real_$less(real_2, real_1) = 1 & real_$less(real_2, real_0) = 1 & 9.40/3.38 real_$less(real_1, real_very_large) = 0 & real_$less(real_1, real_4) = 0 & 9.40/3.38 real_$less(real_1, real_1/2) = 1 & real_$less(real_1, real_10) = 0 & 9.40/3.38 real_$less(real_1, real_2) = 0 & real_$less(real_1, real_1) = 1 & 9.40/3.39 real_$less(real_1, real_0) = 1 & real_$less(real_0, real_very_large) = 0 & 9.40/3.39 real_$less(real_0, real_4) = 0 & real_$less(real_0, real_1/2) = 0 & 9.40/3.39 real_$less(real_0, real_10) = 0 & real_$less(real_0, real_2) = 0 & 9.40/3.39 real_$less(real_0, real_1) = 0 & real_$less(real_0, real_0) = 1 & ! [v0: 9.40/3.39 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ( ~ 9.40/3.39 (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ? [v5: $int] : 9.40/3.39 (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: $int] : ! [v1: 9.40/3.39 $int] : ! [v2: $int] : ! [v3: $int] : (v3 = v1 | v0 = real_0 | ~ 9.40/3.39 (real_$quotient(v2, v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: 9.40/3.39 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v3 = 0 | ~ 9.40/3.39 (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: $int] 9.40/3.39 : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $int] : ! [v1: $int] 9.40/3.39 : ! [v2: $int] : ! [v3: $int] : (v3 = 0 | ~ (real_$lesseq(v1, v0) = 0) | ~ 9.40/3.39 (real_$less(v2, v0) = v3) | ? [v4: $int] : ( ~ (v4 = 0) & real_$less(v2, 9.40/3.39 v1) = v4)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: 9.40/3.39 $int] : (v1 = v0 | ~ (real_$difference(v3, v2) = v1) | ~ 9.40/3.39 (real_$difference(v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: 9.40/3.39 $int] : ! [v3: $int] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~ 9.40/3.39 (real_$greatereq(v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: 9.40/3.39 $int] : ! [v3: $int] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ 9.40/3.39 (real_$greater(v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: 9.40/3.39 $int] : ! [v3: $int] : (v1 = v0 | ~ (real_$sum(v3, v2) = v1) | ~ 9.40/3.39 (real_$sum(v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 9.40/3.39 ! [v3: $int] : (v1 = v0 | ~ (real_$quotient(v3, v2) = v1) | ~ 9.40/3.39 (real_$quotient(v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: 9.40/3.39 $int] : ! [v3: $int] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~ 9.40/3.39 (real_$lesseq(v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] 9.40/3.39 : ! [v3: $int] : (v1 = v0 | ~ (real_$product(v3, v2) = v1) | ~ 9.40/3.39 (real_$product(v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: 9.40/3.39 $int] : ! [v3: $int] : (v1 = v0 | ~ (pow(v3, v2) = v1) | ~ (pow(v3, v2) = 9.40/3.39 v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 9.40/3.39 = v0 | ~ (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) = v0)) & ! 9.40/3.39 [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 9.40/3.39 (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, 9.40/3.39 v0) = v3) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v2 = real_0 | 9.40/3.39 ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) = v2)) & ! [v0: $int] : 9.40/3.39 ! [v1: $int] : ! [v2: $int] : (v2 = 0 | ~ (real_$greatereq(v0, v1) = v2) | 9.40/3.39 ? [v3: $int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $int] : 9.40/3.39 ! [v1: $int] : ! [v2: $int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? 9.40/3.39 [v3: $int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $int] : ! 9.40/3.39 [v1: $int] : ! [v2: $int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ 9.40/3.39 (v1 = v0) & ? [v3: $int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! 9.40/3.39 [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (real_$is_int(v2) = 9.40/3.39 v1) | ~ (real_$is_int(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! 9.40/3.39 [v2: $int] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) | ~ (real_$is_rat(v2) = 9.40/3.39 v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 9.40/3.39 (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & ! [v0: $int] : ! 9.40/3.39 [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~ 9.40/3.39 (real_$ceiling(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 9.40/3.39 (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) = v0)) & ! 9.40/3.39 [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (real_$round(v2) = 9.40/3.39 v1) | ~ (real_$round(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: 9.40/3.39 $int] : (v1 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0)) 9.40/3.39 & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 9.40/3.39 (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $int] : ! 9.40/3.39 [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~ 9.40/3.39 (real_$to_real(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 9.40/3.39 (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0: 9.40/3.39 $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (real_$uminus(v2) = 9.40/3.39 v1) | ~ (real_$uminus(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! 9.40/3.39 [v2: $int] : (v1 = v0 | ~ (exp(v2) = v1) | ~ (exp(v2) = v0)) & ! [v0: $int] 9.40/3.39 : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (log10(v2) = v1) | ~ 9.40/3.39 (log10(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 9.40/3.39 | ~ (log2(v2) = v1) | ~ (log2(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : 9.40/3.39 ! [v2: $int] : (v1 = v0 | ~ (sqr(v2) = v1) | ~ (sqr(v2) = v0)) & ! [v0: 9.40/3.39 $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (log(v2) = v1) | ~ 9.40/3.39 (log(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | 9.40/3.39 ~ (sqrt(v2) = v1) | ~ (sqrt(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : 9.40/3.39 ! [v2: $int] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! 9.40/3.39 [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ (real_$lesseq(v2, v1) = 0) | 9.40/3.39 ~ (real_$less(v1, v0) = 0) | real_$less(v2, v0) = 0) & ! [v0: $int] : ! 9.40/3.39 [v1: $int] : ! [v2: $int] : ( ~ (real_$product(v0, v1) = v2) | 9.40/3.39 real_$product(v1, v0) = v2) & ! [v0: $int] : ! [v1: $int] : (v1 = v0 | ~ 9.40/3.39 (real_$sum(v0, real_0) = v1)) & ! [v0: $int] : ! [v1: $int] : (v1 = v0 | 9.40/3.39 ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) & ! [v0: $int] : ! 9.40/3.39 [v1: $int] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: 9.40/3.39 $int] : ! [v1: $int] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, 9.40/3.39 v0) = 0) & ! [v0: $int] : ! [v1: $int] : ( ~ (real_$greater(v0, v1) = 0) 9.40/3.39 | real_$less(v1, v0) = 0) & ! [v0: $int] : (v0 = real_0 | ~ 9.40/3.39 (real_$uminus(v0) = v0)) 9.40/3.39 9.40/3.39 Further assumptions not needed in the proof: 9.40/3.39 -------------------------------------------- 9.40/3.39 exp_log, exp_sum, exp_zero, log10_def, log2_def, log_exp, log_mul, log_one, 9.40/3.39 pow_def, pow_half, pow_mult, pow_one_y, pow_plus, pow_pos, pow_x_one, 9.40/3.39 pow_x_zero, sqr_def, sqrt_le, sqrt_mul 9.40/3.39 9.40/3.39 Those formulas are unsatisfiable: 9.40/3.39 --------------------------------- 9.40/3.39 9.40/3.39 Begin of proof 9.40/3.39 | 9.40/3.39 | ALPHA: (axioms) implies: 9.40/3.40 | (1) real_$less(real_0, real_2) = 0 9.40/3.40 | (2) real_$product(real_2, real_2) = real_4 9.40/3.40 | (3) real_$lesseq(real_0, real_2) = 0 9.40/3.40 | (4) real_$lesseq(real_0, real_4) = 0 9.40/3.40 | (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (sqrt(v2) 9.40/3.40 | = v1) | ~ (sqrt(v2) = v0)) 9.40/3.40 | (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (sqr(v2) 9.40/3.40 | = v1) | ~ (sqr(v2) = v0)) 9.40/3.40 | (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = 9.40/3.40 | v0 | ~ (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) = v0)) 9.40/3.40 | (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = 9.40/3.40 | v0 | ~ (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = 9.40/3.40 | v0)) 9.40/3.40 | 9.40/3.40 | DELTA: instantiating (pow_2_21) with fresh symbol all_27_0 gives: 9.40/3.40 | (9) ~ (all_27_0 = real_4) & pow(real_2, real_2) = all_27_0 9.40/3.40 | 9.40/3.40 | ALPHA: (9) implies: 9.40/3.40 | (10) ~ (all_27_0 = real_4) 9.40/3.40 | (11) pow(real_2, real_2) = all_27_0 9.40/3.40 | 9.40/3.40 | GROUND_INST: instantiating (sqrt_square) with real_4, simplifying with (4) 9.40/3.40 | gives: 9.40/3.40 | (12) ? [v0: $int] : (sqr(v0) = real_4 & sqrt(real_4) = v0) 9.40/3.40 | 9.40/3.40 | GROUND_INST: instantiating (sqrt_positive) with real_4, simplifying with (4) 9.40/3.40 | gives: 9.40/3.40 | (13) ? [v0: $int] : (real_$lesseq(real_0, v0) = 0 & sqrt(real_4) = v0) 9.40/3.40 | 9.40/3.40 | GROUND_INST: instantiating (square_sqrt) with real_2, simplifying with (3) 9.40/3.40 | gives: 9.40/3.40 | (14) ? [v0: $int] : (real_$product(real_2, real_2) = v0 & sqrt(v0) = 9.40/3.40 | real_2) 9.40/3.40 | 9.40/3.40 | GROUND_INST: instantiating (pow_x_two) with real_2, all_27_0, simplifying with 9.40/3.40 | (11) gives: 9.40/3.40 | (15) ? [v0: $int] : ? [v1: $int] : (sqr(real_2) = v1 & real_$less(real_0, 9.40/3.40 | real_2) = v0 & ( ~ (v0 = 0) | v1 = all_27_0)) 9.40/3.40 | 9.40/3.40 | DELTA: instantiating (15) with fresh symbols all_44_0, all_44_1 gives: 9.40/3.41 | (16) sqr(real_2) = all_44_0 & real_$less(real_0, real_2) = all_44_1 & ( ~ 9.40/3.41 | (all_44_1 = 0) | all_44_0 = all_27_0) 9.40/3.41 | 9.40/3.41 | ALPHA: (16) implies: 9.40/3.41 | (17) real_$less(real_0, real_2) = all_44_1 9.40/3.41 | (18) sqr(real_2) = all_44_0 9.40/3.41 | (19) ~ (all_44_1 = 0) | all_44_0 = all_27_0 9.40/3.41 | 9.40/3.41 | DELTA: instantiating (14) with fresh symbol all_68_0 gives: 9.40/3.41 | (20) real_$product(real_2, real_2) = all_68_0 & sqrt(all_68_0) = real_2 9.40/3.41 | 9.40/3.41 | ALPHA: (20) implies: 9.40/3.41 | (21) sqrt(all_68_0) = real_2 9.40/3.41 | (22) real_$product(real_2, real_2) = all_68_0 9.40/3.41 | 9.40/3.41 | DELTA: instantiating (13) with fresh symbol all_92_0 gives: 9.40/3.41 | (23) real_$lesseq(real_0, all_92_0) = 0 & sqrt(real_4) = all_92_0 9.40/3.41 | 9.40/3.41 | ALPHA: (23) implies: 9.40/3.41 | (24) sqrt(real_4) = all_92_0 9.40/3.41 | 9.40/3.41 | DELTA: instantiating (12) with fresh symbol all_100_0 gives: 9.40/3.41 | (25) sqr(all_100_0) = real_4 & sqrt(real_4) = all_100_0 9.40/3.41 | 9.40/3.41 | ALPHA: (25) implies: 9.40/3.41 | (26) sqrt(real_4) = all_100_0 9.40/3.41 | (27) sqr(all_100_0) = real_4 9.40/3.41 | 9.40/3.41 | GROUND_INST: instantiating (8) with real_4, all_68_0, real_2, real_2, 9.40/3.41 | simplifying with (2), (22) gives: 9.40/3.41 | (28) all_68_0 = real_4 9.40/3.41 | 9.40/3.41 | GROUND_INST: instantiating (5) with all_100_0, all_92_0, real_4, simplifying 9.40/3.41 | with (24), (26) gives: 9.40/3.41 | (29) all_100_0 = all_92_0 9.40/3.41 | 9.40/3.41 | GROUND_INST: instantiating (7) with 0, all_44_1, real_2, real_0, simplifying 9.40/3.41 | with (1), (17) gives: 9.40/3.41 | (30) all_44_1 = 0 9.40/3.41 | 9.40/3.41 | REDUCE: (27), (29) imply: 9.40/3.41 | (31) sqr(all_92_0) = real_4 9.40/3.41 | 9.40/3.41 | REDUCE: (21), (28) imply: 9.40/3.41 | (32) sqrt(real_4) = real_2 9.40/3.41 | 9.40/3.41 | BETA: splitting (19) gives: 9.40/3.41 | 9.40/3.41 | Case 1: 9.40/3.41 | | 9.40/3.41 | | (33) ~ (all_44_1 = 0) 9.40/3.41 | | 9.40/3.41 | | REDUCE: (30), (33) imply: 9.40/3.41 | | (34) ~ (0 = 0) 9.40/3.41 | | 9.40/3.41 | | CLOSE: (34) is inconsistent. 9.40/3.41 | | 9.40/3.41 | Case 2: 9.40/3.41 | | 9.40/3.41 | | (35) all_44_0 = all_27_0 9.40/3.41 | | 9.40/3.41 | | REDUCE: (18), (35) imply: 9.40/3.41 | | (36) sqr(real_2) = all_27_0 9.40/3.41 | | 9.40/3.41 | | GROUND_INST: instantiating (5) with all_92_0, real_2, real_4, simplifying 9.40/3.41 | | with (24), (32) gives: 9.40/3.41 | | (37) all_92_0 = real_2 9.40/3.41 | | 9.40/3.41 | | REDUCE: (31), (37) imply: 9.40/3.41 | | (38) sqr(real_2) = real_4 9.40/3.41 | | 9.40/3.41 | | GROUND_INST: instantiating (6) with all_27_0, real_4, real_2, simplifying 9.40/3.41 | | with (36), (38) gives: 9.40/3.41 | | (39) all_27_0 = real_4 9.40/3.41 | | 9.40/3.41 | | REDUCE: (10), (39) imply: 9.40/3.41 | | (40) ~ (0 = 0) 9.40/3.41 | | 9.40/3.41 | | CLOSE: (40) is inconsistent. 9.40/3.41 | | 9.40/3.41 | End of split 9.40/3.41 | 9.40/3.41 End of proof 9.40/3.41 % SZS output end Proof for theBenchmark 9.40/3.41 9.40/3.41 2957ms 9.75/3.55 EOF