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 0.02/0.23 % Computer : n173.star.cs.uiowa.edu 0.02/0.23 % Model : x86_64 x86_64 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.23 % Memory : 32218.625MB 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.23 % CPULimit : 300 0.02/0.23 % DateTime : Sat Jul 14 04:39:10 CDT 2018 0.02/0.23 % CPUTime : 0.06/0.44 ________ _____ 0.06/0.44 ___ __ \_________(_)________________________________ 0.06/0.44 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ 0.06/0.44 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) 0.06/0.44 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ 0.06/0.44 0.06/0.44 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic 0.06/0.44 (CASC 2017-07-17) 0.06/0.44 0.06/0.44 (c) Philipp Rümmer, 2009-2017 0.06/0.44 (contributions by Peter Backeman, Peter Baumgartner, 0.06/0.44 Angelo Brillout, Aleksandar Zeljic) 0.06/0.44 Free software under GNU Lesser General Public License (LGPL). 0.06/0.44 Bug reports to ph_r@gmx.net 0.06/0.44 0.06/0.44 For more information, visit http://www.philipp.ruemmer.org/princess.shtml 0.06/0.44 0.06/0.44 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... 0.06/0.47 Prover 0: Options: +triggersInConjecture -genTotalityAxioms=ctors +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=off 0.75/0.66 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation 1.06/0.85 Prover 0: Preprocessing ... 2.96/1.44 Prover 0: Constructing countermodel ... 4.40/1.91 Prover 0: proved (1436ms) 4.40/1.91 4.40/1.91 VALID 4.40/1.91 % SZS status Theorem for theBenchmark 4.40/1.91 4.40/1.91 Prover 1: Options: +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off 4.40/1.91 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation 4.68/1.95 Prover 1: Preprocessing ... 5.31/2.09 Prover 1: Constructing countermodel ... 6.03/2.32 Prover 1: Found proof (size 22) 6.03/2.32 Prover 1: proved (411ms) 6.03/2.32 6.03/2.32 6.03/2.33 % SZS output start Proof for theBenchmark 6.03/2.33 Assumptions after simplification: 6.03/2.33 --------------------------------- 6.03/2.33 6.03/2.33 (sqrt_four) 6.03/2.36 ? [v0: $int] : ( ~ (v0 = real_2) & sqrt(real_4) = v0) 6.03/2.36 6.03/2.36 (sqrt_positive) 6.03/2.36 ! [v0: $int] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $int] : 6.03/2.36 (real_$lesseq(real_0, v1) = 0 & sqrt(v0) = v1)) 6.03/2.36 6.03/2.36 (sqrt_square) 6.03/2.36 ! [v0: $int] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $int] : (sqr(v1) 6.03/2.36 = v0 & sqrt(v0) = v1)) 6.03/2.36 6.03/2.36 (square_sqrt) 6.03/2.36 ! [v0: $int] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $int] : 6.03/2.36 (real_$product(v0, v0) = v1 & sqrt(v1) = v0)) 6.03/2.36 6.03/2.36 (axioms) 6.31/2.40 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_4) & ~ 6.31/2.40 (real_very_large = real_2) & ~ (real_very_large = real_1) & ~ 6.31/2.40 (real_very_large = real_0) & ~ (real_very_small = real_4) & ~ 6.31/2.40 (real_very_small = real_2) & ~ (real_very_small = real_1) & ~ 6.31/2.40 (real_very_small = real_0) & ~ (real_4 = real_2) & ~ (real_4 = real_1) & ~ 6.31/2.40 (real_4 = real_0) & ~ (real_2 = real_1) & ~ (real_2 = real_0) & ~ (real_1 = 6.31/2.40 real_0) & real_$is_int(real_4) = 0 & real_$is_int(real_2) = 0 & 6.31/2.40 real_$is_int(real_1) = 0 & real_$is_int(real_0) = 0 & real_$is_rat(real_4) = 0 6.31/2.41 & real_$is_rat(real_2) = 0 & real_$is_rat(real_1) = 0 & real_$is_rat(real_0) = 6.31/2.41 0 & real_$floor(real_4) = real_4 & real_$floor(real_2) = real_2 & 6.31/2.41 real_$floor(real_1) = real_1 & real_$floor(real_0) = real_0 & 6.31/2.41 real_$ceiling(real_4) = real_4 & real_$ceiling(real_2) = real_2 & 6.31/2.41 real_$ceiling(real_1) = real_1 & real_$ceiling(real_0) = real_0 & 6.31/2.41 real_$truncate(real_4) = real_4 & real_$truncate(real_2) = real_2 & 6.31/2.41 real_$truncate(real_1) = real_1 & real_$truncate(real_0) = real_0 & 6.31/2.41 real_$round(real_4) = real_4 & real_$round(real_2) = real_2 & 6.31/2.41 real_$round(real_1) = real_1 & real_$round(real_0) = real_0 & 6.31/2.41 real_$to_int(real_4) = 4 & real_$to_int(real_2) = 2 & real_$to_int(real_1) = 1 6.31/2.41 & real_$to_int(real_0) = 0 & real_$to_rat(real_4) = rat_4 & 6.31/2.41 real_$to_rat(real_2) = rat_2 & real_$to_rat(real_1) = rat_1 & 6.31/2.41 real_$to_rat(real_0) = rat_0 & real_$to_real(real_4) = real_4 & 6.31/2.41 real_$to_real(real_2) = real_2 & real_$to_real(real_1) = real_1 & 6.31/2.41 real_$to_real(real_0) = real_0 & int_$to_real(4) = real_4 & int_$to_real(2) = 6.31/2.41 real_2 & int_$to_real(1) = real_1 & int_$to_real(0) = real_0 & 6.31/2.41 real_$quotient(real_4, real_4) = real_1 & real_$quotient(real_4, real_2) = 6.31/2.41 real_2 & real_$quotient(real_4, real_1) = real_4 & real_$quotient(real_2, 6.31/2.41 real_2) = real_1 & real_$quotient(real_2, real_1) = real_2 & 6.31/2.41 real_$quotient(real_1, real_1) = real_1 & real_$quotient(real_0, real_4) = 6.31/2.41 real_0 & real_$quotient(real_0, real_2) = real_0 & real_$quotient(real_0, 6.31/2.41 real_1) = real_0 & real_$difference(real_4, real_4) = real_0 & 6.31/2.41 real_$difference(real_4, real_2) = real_2 & real_$difference(real_4, real_0) = 6.31/2.41 real_4 & real_$difference(real_2, real_2) = real_0 & real_$difference(real_2, 6.31/2.41 real_1) = real_1 & real_$difference(real_2, real_0) = real_2 & 6.31/2.41 real_$difference(real_1, real_1) = real_0 & real_$difference(real_1, real_0) = 6.31/2.41 real_1 & real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) = 6.31/2.41 real_0 & real_$sum(real_4, real_0) = real_4 & real_$sum(real_2, real_2) = 6.31/2.41 real_4 & real_$sum(real_2, real_0) = real_2 & real_$sum(real_1, real_1) = 6.31/2.41 real_2 & real_$sum(real_1, real_0) = real_1 & real_$sum(real_0, real_4) = 6.31/2.41 real_4 & real_$sum(real_0, real_2) = real_2 & real_$sum(real_0, real_1) = 6.31/2.41 real_1 & real_$sum(real_0, real_0) = real_0 & real_$greatereq(real_very_small, 6.31/2.41 real_very_large) = 1 & real_$greatereq(real_4, real_4) = 0 & 6.31/2.41 real_$greatereq(real_4, real_2) = 0 & real_$greatereq(real_4, real_1) = 0 & 6.31/2.41 real_$greatereq(real_4, real_0) = 0 & real_$greatereq(real_2, real_4) = 1 & 6.31/2.41 real_$greatereq(real_2, real_2) = 0 & real_$greatereq(real_2, real_1) = 0 & 6.31/2.41 real_$greatereq(real_2, real_0) = 0 & real_$greatereq(real_1, real_4) = 1 & 6.31/2.41 real_$greatereq(real_1, real_2) = 1 & real_$greatereq(real_1, real_1) = 0 & 6.31/2.41 real_$greatereq(real_1, real_0) = 0 & real_$greatereq(real_0, real_4) = 1 & 6.31/2.41 real_$greatereq(real_0, real_2) = 1 & real_$greatereq(real_0, real_1) = 1 & 6.31/2.41 real_$greatereq(real_0, real_0) = 0 & real_$greater(real_very_large, real_4) = 6.31/2.41 0 & real_$greater(real_very_large, real_2) = 0 & 6.31/2.41 real_$greater(real_very_large, real_1) = 0 & real_$greater(real_very_large, 6.31/2.41 real_0) = 0 & real_$greater(real_very_small, real_very_large) = 1 & 6.31/2.41 real_$greater(real_4, real_very_small) = 0 & real_$greater(real_4, real_4) = 1 6.31/2.41 & real_$greater(real_4, real_2) = 0 & real_$greater(real_4, real_1) = 0 & 6.31/2.41 real_$greater(real_4, real_0) = 0 & real_$greater(real_2, real_very_small) = 0 6.31/2.41 & real_$greater(real_2, real_4) = 1 & real_$greater(real_2, real_2) = 1 & 6.31/2.41 real_$greater(real_2, real_1) = 0 & real_$greater(real_2, real_0) = 0 & 6.31/2.41 real_$greater(real_1, real_very_small) = 0 & real_$greater(real_1, real_4) = 1 6.31/2.41 & real_$greater(real_1, real_2) = 1 & real_$greater(real_1, real_1) = 1 & 6.31/2.41 real_$greater(real_1, real_0) = 0 & real_$greater(real_0, real_very_small) = 0 6.31/2.41 & real_$greater(real_0, real_4) = 1 & real_$greater(real_0, real_2) = 1 & 6.31/2.41 real_$greater(real_0, real_1) = 1 & real_$greater(real_0, real_0) = 1 & 6.31/2.41 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, 6.31/2.41 real_4) = 0 & real_$less(real_very_small, real_2) = 0 & 6.31/2.41 real_$less(real_very_small, real_1) = 0 & real_$less(real_very_small, real_0) 6.31/2.41 = 0 & real_$less(real_4, real_very_large) = 0 & real_$less(real_4, real_4) = 1 6.31/2.41 & real_$less(real_4, real_2) = 1 & real_$less(real_4, real_1) = 1 & 6.31/2.41 real_$less(real_4, real_0) = 1 & real_$less(real_2, real_very_large) = 0 & 6.31/2.41 real_$less(real_2, real_4) = 0 & real_$less(real_2, real_2) = 1 & 6.31/2.41 real_$less(real_2, real_1) = 1 & real_$less(real_2, real_0) = 1 & 6.31/2.41 real_$less(real_1, real_very_large) = 0 & real_$less(real_1, real_4) = 0 & 6.31/2.41 real_$less(real_1, real_2) = 0 & real_$less(real_1, real_1) = 1 & 6.31/2.41 real_$less(real_1, real_0) = 1 & real_$less(real_0, real_very_large) = 0 & 6.31/2.41 real_$less(real_0, real_4) = 0 & real_$less(real_0, real_2) = 0 & 6.31/2.41 real_$less(real_0, real_1) = 0 & real_$less(real_0, real_0) = 1 & 6.31/2.41 real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_4, 6.31/2.41 real_4) = 0 & real_$lesseq(real_4, real_2) = 1 & real_$lesseq(real_4, 6.31/2.41 real_1) = 1 & real_$lesseq(real_4, real_0) = 1 & real_$lesseq(real_2, 6.31/2.41 real_4) = 0 & real_$lesseq(real_2, real_2) = 0 & real_$lesseq(real_2, 6.31/2.41 real_1) = 1 & real_$lesseq(real_2, real_0) = 1 & real_$lesseq(real_1, 6.31/2.41 real_4) = 0 & real_$lesseq(real_1, real_2) = 0 & real_$lesseq(real_1, 6.31/2.41 real_1) = 0 & real_$lesseq(real_1, real_0) = 1 & real_$lesseq(real_0, 6.31/2.41 real_4) = 0 & real_$lesseq(real_0, real_2) = 0 & real_$lesseq(real_0, 6.31/2.41 real_1) = 0 & real_$lesseq(real_0, real_0) = 0 & real_$product(real_4, 6.31/2.41 real_1) = real_4 & real_$product(real_4, real_0) = real_0 & 6.31/2.41 real_$product(real_2, real_2) = real_4 & real_$product(real_2, real_1) = 6.31/2.41 real_2 & real_$product(real_2, real_0) = real_0 & real_$product(real_1, 6.31/2.41 real_4) = real_4 & real_$product(real_1, real_2) = real_2 & 6.31/2.41 real_$product(real_1, real_1) = real_1 & real_$product(real_1, real_0) = 6.31/2.41 real_0 & real_$product(real_0, real_4) = real_0 & real_$product(real_0, 6.31/2.41 real_2) = real_0 & real_$product(real_0, real_1) = real_0 & 6.31/2.41 real_$product(real_0, real_0) = real_0 & ! [v0: $int] : ! [v1: $int] : ! 6.31/2.41 [v2: $int] : ! [v3: $int] : ! [v4: $int] : ( ~ (real_$sum(v3, v0) = v4) | ~ 6.31/2.41 (real_$sum(v2, v1) = v3) | ? [v5: $int] : (real_$sum(v2, v5) = v4 & 6.31/2.41 real_$sum(v1, v0) = v5)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 6.31/2.41 ! [v3: $int] : (v3 = v1 | v0 = real_0 | ~ (real_$quotient(v2, v0) = v3) | ~ 6.31/2.41 (real_$product(v1, v0) = v2)) & ! [v0: $int] : ! [v1: $int] : ! [v2: 6.31/2.41 $int] : ! [v3: $int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~ 6.31/2.41 (real_$lesseq(v1, v0) = 0) | ? [v4: $int] : ( ~ (v4 = 0) & real_$less(v2, 6.31/2.41 v1) = v4)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: 6.31/2.41 $int] : (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) 6.31/2.41 = 0) | ? [v4: $int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! 6.31/2.41 [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 6.31/2.41 (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! [v0: 6.31/2.41 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 6.31/2.42 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! 6.31/2.42 [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 6.31/2.42 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: $int] : ! 6.31/2.42 [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 6.31/2.42 (real_$greatereq(v3, v2) = v1) | ~ (real_$greatereq(v3, v2) = v0)) & ! 6.31/2.42 [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 6.31/2.42 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0: 6.31/2.42 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 6.31/2.42 (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) = v0)) & ! [v0: $int] : 6.31/2.42 ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ (real_$lesseq(v3, 6.31/2.42 v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0: $int] : ! [v1: 6.31/2.42 $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ (real_$product(v3, v2) 6.31/2.42 = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : 6.31/2.42 ! [v2: $int] : ! [v3: $int] : ( ~ (real_$uminus(v0) = v2) | ~ 6.31/2.42 (real_$sum(v1, v2) = v3) | real_$difference(v1, v0) = v3) & ! [v0: $int] : 6.31/2.42 ! [v1: $int] : ! [v2: $int] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~ 6.31/2.42 (real_$sum(v0, v1) = v2)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 6.31/2.42 (v2 = 0 | ~ (real_$greatereq(v0, v1) = v2) | ? [v3: $int] : ( ~ (v3 = 0) & 6.31/2.42 real_$lesseq(v1, v0) = v3)) & ! [v0: $int] : ! [v1: $int] : ! [v2: 6.31/2.42 $int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: $int] : ( ~ (v3 6.31/2.42 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $int] : ! [v1: $int] : ! 6.31/2.42 [v2: $int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? 6.31/2.42 [v3: $int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $int] : 6.31/2.42 ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (real_$is_int(v2) = v1) | ~ 6.31/2.42 (real_$is_int(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 6.31/2.42 (v1 = v0 | ~ (real_$is_rat(v2) = v1) | ~ (real_$is_rat(v2) = v0)) & ! [v0: 6.31/2.42 $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (real_$floor(v2) = v1) 6.31/2.42 | ~ (real_$floor(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] 6.31/2.42 : (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! 6.31/2.42 [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (real_$truncate(v2) 6.31/2.42 = v1) | ~ (real_$truncate(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! 6.31/2.42 [v2: $int] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) 6.31/2.42 & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 6.31/2.42 (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $int] : ! 6.31/2.42 [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ 6.31/2.42 (real_$to_rat(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 6.31/2.42 (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! 6.31/2.42 [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (int_$to_real(v2) = 6.31/2.42 v1) | ~ (int_$to_real(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! 6.31/2.42 [v2: $int] : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = 6.31/2.42 v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 6.31/2.42 (sqr(v2) = v1) | ~ (sqr(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! 6.31/2.42 [v2: $int] : (v1 = v0 | ~ (sqrt(v2) = v1) | ~ (sqrt(v2) = v0)) & ! [v0: 6.31/2.42 $int] : ! [v1: $int] : ! [v2: $int] : ( ~ (real_$sum(v0, v1) = v2) | 6.31/2.42 real_$sum(v1, v0) = v2) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( 6.31/2.42 ~ (real_$less(v1, v0) = 0) | ~ (real_$lesseq(v2, v1) = 0) | real_$less(v2, 6.31/2.42 v0) = 0) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ 6.31/2.42 (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) & ! [v0: $int] : 6.31/2.42 ! [v1: $int] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0: $int] : 6.31/2.42 ! [v1: $int] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 6.31/2.42 0) & ! [v0: $int] : ! [v1: $int] : ( ~ (real_$uminus(v0) = v1) | 6.31/2.42 real_$uminus(v1) = v0) & ! [v0: $int] : ! [v1: $int] : ( ~ 6.31/2.42 (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $int] : 6.31/2.42 ! [v1: $int] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & ! 6.31/2.42 [v0: $int] : (v0 = real_0 | ~ (real_$uminus(v0) = v0)) 6.31/2.42 6.31/2.42 Further assumptions not needed in the proof: 6.31/2.42 -------------------------------------------- 6.31/2.42 sqr_def, sqrt_le, sqrt_mul, sqrt_one, sqrt_zero 6.31/2.42 6.31/2.42 Those formulas are unsatisfiable: 6.31/2.42 --------------------------------- 6.31/2.42 6.31/2.42 Begin of proof 6.31/2.42 | 6.31/2.42 | ALPHA: (axioms) implies: 6.31/2.43 | (1) real_$product(real_2, real_2) = real_4 6.31/2.43 | (2) real_$lesseq(real_0, real_2) = 0 6.31/2.43 | (3) real_$lesseq(real_0, real_4) = 0 6.31/2.43 | (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (sqrt(v2) 6.31/2.43 | = v1) | ~ (sqrt(v2) = v0)) 6.31/2.43 | (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = 6.31/2.43 | v0 | ~ (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = 6.31/2.43 | v0)) 6.31/2.43 | 6.31/2.43 | DELTA: instantiating (sqrt_four) with fresh symbol all_8_0 gives: 6.31/2.43 | (6) ~ (all_8_0 = real_2) & sqrt(real_4) = all_8_0 6.31/2.43 | 6.31/2.43 | ALPHA: (6) implies: 6.31/2.43 | (7) ~ (all_8_0 = real_2) 6.31/2.43 | (8) sqrt(real_4) = all_8_0 6.31/2.44 | 6.31/2.44 | GROUND_INST: instantiating (sqrt_square) with real_4, simplifying with (3) 6.31/2.44 | gives: 6.31/2.44 | (9) ? [v0: $int] : (sqr(v0) = real_4 & sqrt(real_4) = v0) 6.31/2.44 | 6.31/2.44 | GROUND_INST: instantiating (sqrt_positive) with real_4, simplifying with (3) 6.31/2.44 | gives: 6.31/2.44 | (10) ? [v0: $int] : (real_$lesseq(real_0, v0) = 0 & sqrt(real_4) = v0) 6.31/2.44 | 6.31/2.44 | GROUND_INST: instantiating (square_sqrt) with real_2, simplifying with (2) 6.31/2.44 | gives: 6.31/2.44 | (11) ? [v0: $int] : (real_$product(real_2, real_2) = v0 & sqrt(v0) = 6.31/2.44 | real_2) 6.31/2.44 | 6.31/2.44 | DELTA: instantiating (9) with fresh symbol all_25_0 gives: 6.31/2.44 | (12) sqr(all_25_0) = real_4 & sqrt(real_4) = all_25_0 6.31/2.44 | 6.31/2.44 | ALPHA: (12) implies: 6.31/2.44 | (13) sqrt(real_4) = all_25_0 6.31/2.44 | 6.31/2.44 | DELTA: instantiating (11) with fresh symbol all_31_0 gives: 6.31/2.44 | (14) real_$product(real_2, real_2) = all_31_0 & sqrt(all_31_0) = real_2 6.31/2.44 | 6.31/2.44 | ALPHA: (14) implies: 6.31/2.44 | (15) sqrt(all_31_0) = real_2 6.31/2.44 | (16) real_$product(real_2, real_2) = all_31_0 6.31/2.44 | 6.31/2.44 | DELTA: instantiating (10) with fresh symbol all_35_0 gives: 6.31/2.44 | (17) real_$lesseq(real_0, all_35_0) = 0 & sqrt(real_4) = all_35_0 6.31/2.44 | 6.31/2.44 | ALPHA: (17) implies: 6.31/2.44 | (18) sqrt(real_4) = all_35_0 6.31/2.44 | 6.31/2.44 | GROUND_INST: instantiating (5) with real_4, all_31_0, real_2, real_2, 6.31/2.44 | simplifying with (1), (16) gives: 6.31/2.44 | (19) all_31_0 = real_4 6.31/2.44 | 6.31/2.44 | GROUND_INST: instantiating (4) with all_8_0, all_35_0, real_4, simplifying 6.31/2.44 | with (8), (18) gives: 6.31/2.44 | (20) all_35_0 = all_8_0 6.31/2.44 | 6.31/2.44 | GROUND_INST: instantiating (4) with all_35_0, all_25_0, real_4, simplifying 6.31/2.44 | with (13), (18) gives: 6.31/2.44 | (21) all_35_0 = all_25_0 6.31/2.44 | 6.31/2.44 | COMBINE_EQS: (20), (21) imply: 6.31/2.44 | (22) all_25_0 = all_8_0 6.31/2.44 | 6.31/2.44 | SIMP: (22) implies: 6.31/2.44 | (23) all_25_0 = all_8_0 6.31/2.44 | 6.31/2.44 | REDUCE: (15), (19) imply: 6.31/2.44 | (24) sqrt(real_4) = real_2 6.31/2.44 | 6.31/2.44 | GROUND_INST: instantiating (4) with all_8_0, real_2, real_4, simplifying with 6.31/2.44 | (8), (24) gives: 6.31/2.44 | (25) all_8_0 = real_2 6.31/2.44 | 6.31/2.44 | REDUCE: (7), (25) imply: 6.31/2.44 | (26) ~ (0 = 0) 6.31/2.44 | 6.31/2.44 | CLOSE: (26) is inconsistent. 6.31/2.44 | 6.31/2.44 End of proof 6.31/2.44 % SZS output end Proof for theBenchmark 6.31/2.44 6.31/2.44 1989ms 6.59/2.50 EOF