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 : n013.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 04:23:10 CDT 2018 0.03/0.24 % CPUTime : 0.07/0.45 ________ _____ 0.07/0.45 ___ __ \_________(_)________________________________ 0.07/0.45 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ 0.07/0.45 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) 0.07/0.45 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ 0.07/0.45 0.07/0.45 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic 0.07/0.45 (CASC 2017-07-17) 0.07/0.45 0.07/0.45 (c) Philipp Rümmer, 2009-2017 0.07/0.45 (contributions by Peter Backeman, Peter Baumgartner, 0.07/0.45 Angelo Brillout, Aleksandar Zeljic) 0.07/0.45 Free software under GNU Lesser General Public License (LGPL). 0.07/0.45 Bug reports to ph_r@gmx.net 0.07/0.45 0.07/0.45 For more information, visit http://www.philipp.ruemmer.org/princess.shtml 0.07/0.45 0.07/0.45 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... 0.07/0.48 Prover 0: Options: +triggersInConjecture -genTotalityAxioms=ctors +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=off 0.76/0.67 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation 1.06/0.84 Prover 0: Preprocessing ... 2.88/1.37 Prover 0: Constructing countermodel ... 3.87/1.63 Prover 0: proved (1149ms) 3.87/1.63 3.87/1.63 VALID 3.87/1.63 % SZS status Theorem for theBenchmark 3.87/1.63 3.87/1.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off 3.87/1.64 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation 3.87/1.68 Prover 1: Preprocessing ... 4.46/1.80 Prover 1: Constructing countermodel ... 4.96/1.97 Prover 1: Found proof (size 22) 4.96/1.97 Prover 1: proved (336ms) 4.96/1.97 4.96/1.97 4.96/1.98 % SZS output start Proof for theBenchmark 4.96/1.98 Assumptions after simplification: 4.96/1.98 --------------------------------- 4.96/1.98 4.96/1.98 (sqrt_one) 4.96/2.01 ? [v0: $int] : ( ~ (v0 = real_1) & sqrt(real_1) = v0) 4.96/2.01 4.96/2.01 (sqrt_positive) 5.19/2.01 ! [v0: $int] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $int] : (sqrt(v0) 5.19/2.01 = v1 & real_$lesseq(real_0, v1) = 0)) 5.19/2.01 5.19/2.01 (sqrt_square) 5.19/2.01 ! [v0: $int] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $int] : (sqr(v1) 5.19/2.01 = v0 & sqrt(v0) = v1)) 5.19/2.01 5.19/2.01 (square_sqrt) 5.19/2.01 ! [v0: $int] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $int] : 5.19/2.01 (real_$product(v0, v0) = v1 & sqrt(v1) = v0)) 5.19/2.01 5.19/2.01 (axioms) 5.19/2.04 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_1) & ~ 5.19/2.04 (real_very_large = real_0) & ~ (real_very_small = real_1) & ~ 5.19/2.04 (real_very_small = real_0) & ~ (real_1 = real_0) & real_$is_int(real_1) = 0 & 5.19/2.04 real_$is_int(real_0) = 0 & real_$is_rat(real_1) = 0 & real_$is_rat(real_0) = 0 5.19/2.04 & real_$floor(real_1) = real_1 & real_$floor(real_0) = real_0 & 5.19/2.04 real_$ceiling(real_1) = real_1 & real_$ceiling(real_0) = real_0 & 5.19/2.04 real_$truncate(real_1) = real_1 & real_$truncate(real_0) = real_0 & 5.19/2.04 real_$round(real_1) = real_1 & real_$round(real_0) = real_0 & 5.19/2.04 real_$to_int(real_1) = 1 & real_$to_int(real_0) = 0 & real_$to_rat(real_1) = 5.19/2.04 rat_1 & real_$to_rat(real_0) = rat_0 & real_$to_real(real_1) = real_1 & 5.19/2.04 real_$to_real(real_0) = real_0 & int_$to_real(1) = real_1 & int_$to_real(0) = 5.19/2.04 real_0 & real_$quotient(real_1, real_1) = real_1 & real_$quotient(real_0, 5.19/2.04 real_1) = real_0 & real_$difference(real_1, real_1) = real_0 & 5.19/2.04 real_$difference(real_1, real_0) = real_1 & real_$difference(real_0, real_0) = 5.19/2.04 real_0 & real_$uminus(real_0) = real_0 & real_$sum(real_1, real_0) = real_1 & 5.19/2.04 real_$sum(real_0, real_1) = real_1 & real_$sum(real_0, real_0) = real_0 & 5.19/2.04 real_$greatereq(real_very_small, real_very_large) = 1 & 5.19/2.04 real_$greatereq(real_1, real_1) = 0 & real_$greatereq(real_1, real_0) = 0 & 5.19/2.04 real_$greatereq(real_0, real_1) = 1 & real_$greatereq(real_0, real_0) = 0 & 5.19/2.04 real_$greater(real_very_large, real_1) = 0 & real_$greater(real_very_large, 5.19/2.04 real_0) = 0 & real_$greater(real_very_small, real_very_large) = 1 & 5.19/2.04 real_$greater(real_1, real_very_small) = 0 & real_$greater(real_1, real_1) = 1 5.19/2.04 & real_$greater(real_1, real_0) = 0 & real_$greater(real_0, real_very_small) = 5.19/2.05 0 & real_$greater(real_0, real_1) = 1 & real_$greater(real_0, real_0) = 1 & 5.19/2.05 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, 5.19/2.05 real_1) = 0 & real_$less(real_very_small, real_0) = 0 & real_$less(real_1, 5.19/2.05 real_very_large) = 0 & real_$less(real_1, real_1) = 1 & real_$less(real_1, 5.19/2.05 real_0) = 1 & real_$less(real_0, real_very_large) = 0 & real_$less(real_0, 5.19/2.05 real_1) = 0 & real_$less(real_0, real_0) = 1 & real_$product(real_1, real_1) 5.19/2.05 = real_1 & real_$product(real_1, real_0) = real_0 & real_$product(real_0, 5.19/2.05 real_1) = real_0 & real_$product(real_0, real_0) = real_0 & 5.19/2.05 real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_1, 5.19/2.05 real_1) = 0 & real_$lesseq(real_1, real_0) = 1 & real_$lesseq(real_0, 5.19/2.05 real_1) = 0 & real_$lesseq(real_0, real_0) = 0 & ! [v0: $int] : ! [v1: 5.19/2.05 $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ( ~ (real_$sum(v3, 5.19/2.05 v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ? [v5: $int] : (real_$sum(v2, 5.19/2.05 v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: $int] : ! [v1: $int] : ! 5.19/2.05 [v2: $int] : ! [v3: $int] : (v3 = v1 | v0 = real_0 | ~ (real_$quotient(v2, 5.19/2.05 v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: $int] : ! [v1: 5.19/2.05 $int] : ! [v2: $int] : ! [v3: $int] : (v3 = 0 | ~ (real_$less(v2, v1) = 5.19/2.05 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: $int] : ( ~ (v4 = 0) & 5.19/2.05 real_$lesseq(v1, v0) = v4)) & ! [v0: $int] : ! [v1: $int] : ! [v2: 5.19/2.05 $int] : ! [v3: $int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~ 5.19/2.05 (real_$less(v1, v0) = 0) | ? [v4: $int] : ( ~ (v4 = 0) & real_$lesseq(v2, 5.19/2.05 v1) = v4)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: 5.19/2.05 $int] : (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) 5.19/2.05 = 0) | ? [v4: $int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! 5.19/2.05 [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 5.19/2.05 (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! [v0: 5.19/2.05 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 5.19/2.05 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! 5.19/2.05 [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 5.19/2.05 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: $int] : ! 5.19/2.05 [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 5.19/2.05 (real_$greatereq(v3, v2) = v1) | ~ (real_$greatereq(v3, v2) = v0)) & ! 5.19/2.05 [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 5.19/2.05 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0: 5.19/2.05 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 5.19/2.05 (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) = v0)) & ! [v0: $int] : 5.19/2.05 ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 5.19/2.05 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: 5.19/2.05 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 5.19/2.05 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0: 5.19/2.05 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 5.19/2.05 (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, 5.19/2.05 v0) = v3) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v2 = real_0 | 5.19/2.05 ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) = v2)) & ! [v0: $int] : 5.19/2.05 ! [v1: $int] : ! [v2: $int] : (v2 = 0 | v1 = v0 | ~ (real_$less(v1, v0) = 5.19/2.05 v2) | ? [v3: $int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: 5.19/2.05 $int] : ! [v1: $int] : ! [v2: $int] : (v2 = 0 | ~ (real_$greatereq(v0, 5.19/2.05 v1) = v2) | ? [v3: $int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & 5.19/2.05 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v2 = 0 | ~ 5.19/2.05 (real_$greater(v0, v1) = v2) | ? [v3: $int] : ( ~ (v3 = 0) & real_$less(v1, 5.19/2.05 v0) = v3)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | 5.19/2.05 ~ (real_$is_int(v2) = v1) | ~ (real_$is_int(v2) = v0)) & ! [v0: $int] : ! 5.19/2.05 [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) | ~ 5.19/2.05 (real_$is_rat(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 5.19/2.05 (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & ! [v0: 5.19/2.05 $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (real_$ceiling(v2) = 5.19/2.05 v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! 5.19/2.05 [v2: $int] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) 5.19/2.05 = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 5.19/2.05 (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) & ! [v0: $int] : ! 5.19/2.05 [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (real_$to_int(v2) = v1) | ~ 5.19/2.05 (real_$to_int(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 5.19/2.05 (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: 5.19/2.05 $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (real_$to_real(v2) = 5.19/2.05 v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! 5.19/2.05 [v2: $int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = 5.19/2.05 v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 5.19/2.05 (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) & ! [v0: $int] : ! 5.19/2.05 [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (sqr(v2) = v1) | ~ (sqr(v2) = v0)) 5.19/2.05 & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (sqrt(v2) = 5.19/2.05 v1) | ~ (sqrt(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] 5.19/2.05 : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: $int] : ! 5.19/2.05 [v1: $int] : ! [v2: $int] : ( ~ (real_$less(v1, v0) = v2) | real_$lesseq(v1, 5.19/2.05 v0) = 0 | ( ~ (v2 = 0) & ~ (v1 = v0))) & ! [v0: $int] : ! [v1: $int] : 5.19/2.05 ! [v2: $int] : ( ~ (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) 5.19/2.05 & ! [v0: $int] : ! [v1: $int] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) 5.19/2.05 & ! [v0: $int] : ! [v1: $int] : ( ~ (real_$uminus(v0) = v1) | 5.19/2.05 real_$uminus(v1) = v0) & ! [v0: $int] : ! [v1: $int] : ( ~ 5.19/2.05 (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $int] : 5.19/2.05 ! [v1: $int] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & ! 5.19/2.05 [v0: $int] : (v0 = real_0 | ~ (real_$uminus(v0) = v0)) 5.19/2.05 5.19/2.05 Further assumptions not needed in the proof: 5.19/2.05 -------------------------------------------- 5.19/2.05 sqr_def, sqrt_le, sqrt_mul, sqrt_zero 5.19/2.05 5.19/2.05 Those formulas are unsatisfiable: 5.19/2.05 --------------------------------- 5.19/2.05 5.19/2.05 Begin of proof 5.19/2.05 | 5.19/2.05 | ALPHA: (axioms) implies: 5.19/2.06 | (1) real_$lesseq(real_0, real_1) = 0 5.19/2.06 | (2) real_$product(real_1, real_1) = real_1 5.19/2.06 | (3) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (sqrt(v2) 5.19/2.06 | = v1) | ~ (sqrt(v2) = v0)) 5.19/2.06 | (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = 5.19/2.06 | v0 | ~ (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = 5.19/2.06 | v0)) 5.19/2.06 | 5.19/2.06 | DELTA: instantiating (sqrt_one) with fresh symbol all_8_0 gives: 5.19/2.06 | (5) ~ (all_8_0 = real_1) & sqrt(real_1) = all_8_0 5.19/2.06 | 5.19/2.06 | ALPHA: (5) implies: 5.19/2.06 | (6) ~ (all_8_0 = real_1) 5.19/2.06 | (7) sqrt(real_1) = all_8_0 5.19/2.06 | 5.19/2.06 | GROUND_INST: instantiating (sqrt_square) with real_1, simplifying with (1) 5.19/2.06 | gives: 5.19/2.06 | (8) ? [v0: $int] : (sqr(v0) = real_1 & sqrt(real_1) = v0) 5.19/2.06 | 5.19/2.06 | GROUND_INST: instantiating (square_sqrt) with real_1, simplifying with (1) 5.19/2.06 | gives: 5.19/2.06 | (9) ? [v0: $int] : (real_$product(real_1, real_1) = v0 & sqrt(v0) = 5.19/2.06 | real_1) 5.19/2.06 | 5.19/2.06 | GROUND_INST: instantiating (sqrt_positive) with real_1, simplifying with (1) 5.19/2.06 | gives: 5.19/2.06 | (10) ? [v0: $int] : (sqrt(real_1) = v0 & real_$lesseq(real_0, v0) = 0) 5.19/2.06 | 5.19/2.06 | DELTA: instantiating (9) with fresh symbol all_16_0 gives: 5.19/2.06 | (11) real_$product(real_1, real_1) = all_16_0 & sqrt(all_16_0) = real_1 5.19/2.06 | 5.19/2.06 | ALPHA: (11) implies: 5.19/2.06 | (12) sqrt(all_16_0) = real_1 5.19/2.06 | (13) real_$product(real_1, real_1) = all_16_0 5.19/2.06 | 5.19/2.06 | DELTA: instantiating (8) with fresh symbol all_22_0 gives: 5.19/2.06 | (14) sqr(all_22_0) = real_1 & sqrt(real_1) = all_22_0 5.19/2.06 | 5.19/2.06 | ALPHA: (14) implies: 5.19/2.07 | (15) sqrt(real_1) = all_22_0 5.19/2.07 | 5.19/2.07 | DELTA: instantiating (10) with fresh symbol all_30_0 gives: 5.19/2.07 | (16) sqrt(real_1) = all_30_0 & real_$lesseq(real_0, all_30_0) = 0 5.19/2.07 | 5.19/2.07 | ALPHA: (16) implies: 5.19/2.07 | (17) sqrt(real_1) = all_30_0 5.19/2.07 | 5.19/2.07 | GROUND_INST: instantiating (4) with real_1, all_16_0, real_1, real_1, 5.19/2.07 | simplifying with (2), (13) gives: 5.19/2.07 | (18) all_16_0 = real_1 5.19/2.07 | 5.19/2.07 | GROUND_INST: instantiating (3) with all_8_0, all_30_0, real_1, simplifying 5.19/2.07 | with (7), (17) gives: 5.19/2.07 | (19) all_30_0 = all_8_0 5.19/2.07 | 5.19/2.07 | GROUND_INST: instantiating (3) with all_30_0, all_22_0, real_1, simplifying 5.19/2.07 | with (15), (17) gives: 5.19/2.07 | (20) all_30_0 = all_22_0 5.19/2.07 | 5.19/2.07 | COMBINE_EQS: (19), (20) imply: 5.19/2.07 | (21) all_22_0 = all_8_0 5.19/2.07 | 5.19/2.07 | SIMP: (21) implies: 5.19/2.07 | (22) all_22_0 = all_8_0 5.19/2.07 | 5.19/2.07 | REDUCE: (12), (18) imply: 5.19/2.07 | (23) sqrt(real_1) = real_1 5.19/2.07 | 5.19/2.07 | GROUND_INST: instantiating (3) with all_8_0, real_1, real_1, simplifying with 5.19/2.07 | (7), (23) gives: 5.19/2.07 | (24) all_8_0 = real_1 5.19/2.07 | 5.19/2.07 | REDUCE: (6), (24) imply: 5.19/2.07 | (25) ~ (0 = 0) 5.44/2.07 | 5.44/2.07 | CLOSE: (25) is inconsistent. 5.44/2.07 | 5.44/2.07 End of proof 5.44/2.07 % SZS output end Proof for theBenchmark 5.44/2.07 5.44/2.07 1615ms 5.75/2.39 EOF