TSTP Solution File: KLE035+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE035+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 : 600s
% DateTime : Sun Jul 17 01:51:02 EDT 2022
% Result : Theorem 23.77s 6.67s
% Output : Proof 34.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE035+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 12:29:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.53/0.62 ____ _
% 0.53/0.62 ___ / __ \_____(_)___ ________ __________
% 0.53/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.62
% 0.53/0.62 A Theorem Prover for First-Order Logic
% 0.53/0.62 (ePrincess v.1.0)
% 0.53/0.62
% 0.53/0.62 (c) Philipp Rümmer, 2009-2015
% 0.53/0.62 (c) Peter Backeman, 2014-2015
% 0.53/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.62 Bug reports to peter@backeman.se
% 0.53/0.62
% 0.53/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.62
% 0.53/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.63/0.98 Prover 0: Preprocessing ...
% 2.47/1.24 Prover 0: Constructing countermodel ...
% 20.63/5.98 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.89/6.01 Prover 1: Preprocessing ...
% 21.27/6.10 Prover 1: Constructing countermodel ...
% 23.77/6.66 Prover 1: proved (683ms)
% 23.77/6.67 Prover 0: stopped
% 23.77/6.67
% 23.77/6.67 No countermodel exists, formula is valid
% 23.77/6.67 % SZS status Theorem for theBenchmark
% 23.77/6.67
% 23.77/6.67 Generating proof ... found it (size 69)
% 34.05/9.15
% 34.05/9.15 % SZS output start Proof for theBenchmark
% 34.05/9.15 Assumed formulas after preprocessing and simplification:
% 34.05/9.15 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = 0) & c(v3) = v5 & test(v3) = 0 & test(v2) = 0 & leq(v11, zero) = v12 & leq(v8, zero) = 0 & leq(v6, zero) = 0 & multiplication(v10, v5) = v11 & multiplication(v7, v5) = v8 & multiplication(v4, v5) = v6 & multiplication(v2, v9) = v10 & multiplication(v2, v1) = v7 & multiplication(v2, v0) = v4 & addition(v0, v1) = v9 & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (multiplication(v14, v15) = v17) | ~ (multiplication(v13, v15) = v16) | ~ (addition(v16, v17) = v18) | ? [v19] : (multiplication(v19, v15) = v18 & addition(v13, v14) = v19)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (multiplication(v13, v15) = v17) | ~ (multiplication(v13, v14) = v16) | ~ (addition(v16, v17) = v18) | ? [v19] : (multiplication(v13, v19) = v18 & addition(v14, v15) = v19)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (multiplication(v16, v15) = v17) | ~ (multiplication(v13, v14) = v16) | ? [v18] : (multiplication(v14, v15) = v18 & multiplication(v13, v18) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (addition(v16, v13) = v17) | ~ (addition(v15, v14) = v16) | ? [v18] : (addition(v15, v18) = v17 & addition(v14, v13) = v18)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (complement(v16, v15) = v14) | ~ (complement(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (leq(v16, v15) = v14) | ~ (leq(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (multiplication(v16, v15) = v14) | ~ (multiplication(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (addition(v16, v15) = v14) | ~ (addition(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (complement(v14, v13) = v15) | ? [v16] : ? [v17] : ? [v18] : (multiplication(v14, v13) = v17 & multiplication(v13, v14) = v16 & addition(v13, v14) = v18 & ( ~ (v18 = one) | ~ (v17 = zero) | ~ (v16 = zero)))) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (leq(v13, v14) = v15) | ? [v16] : ( ~ (v16 = v14) & addition(v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (c(v15) = v14) | ~ (c(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (test(v15) = v14) | ~ (test(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (test(v13) = v14) | ~ (complement(v15, v13) = 0)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (complement(v13, v14) = v15) | ? [v16] : ? [v17] : (c(v13) = v17 & test(v13) = v16 & ( ~ (v16 = 0) | (( ~ (v17 = v14) | v15 = 0) & ( ~ (v15 = 0) | v17 = v14))))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (addition(v13, v14) = v15) | addition(v14, v13) = v15) & ! [v13] : ! [v14] : (v14 = v13 | ~ (multiplication(v13, one) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (multiplication(one, v13) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (addition(v13, v13) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (addition(v13, zero) = v14)) & ! [v13] : ! [v14] : (v14 = zero | ~ (multiplication(v13, zero) = v14)) & ! [v13] : ! [v14] : (v14 = zero | ~ (multiplication(zero, v13) = v14)) & ! [v13] : ! [v14] : (v14 = 0 | ~ (test(v13) = v14) | c(v13) = zero) & ! [v13] : ! [v14] : ( ~ (complement(v14, v13) = 0) | (multiplication(v14, v13) = zero & multiplication(v13, v14) = zero & addition(v13, v14) = one)) & ! [v13] : ! [v14] : ( ~ (leq(v13, v14) = 0) | addition(v13, v14) = v14) & ! [v13] : ( ~ (test(v13) = 0) | ? [v14] : complement(v14, v13) = 0))
% 34.05/9.19 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12 yields:
% 34.05/9.19 | (1) ~ (all_0_0_0 = 0) & c(all_0_9_9) = all_0_7_7 & test(all_0_9_9) = 0 & test(all_0_10_10) = 0 & leq(all_0_1_1, zero) = all_0_0_0 & leq(all_0_4_4, zero) = 0 & leq(all_0_6_6, zero) = 0 & multiplication(all_0_2_2, all_0_7_7) = all_0_1_1 & multiplication(all_0_5_5, all_0_7_7) = all_0_4_4 & multiplication(all_0_8_8, all_0_7_7) = all_0_6_6 & multiplication(all_0_10_10, all_0_3_3) = all_0_2_2 & multiplication(all_0_10_10, all_0_11_11) = all_0_5_5 & multiplication(all_0_10_10, all_0_12_12) = all_0_8_8 & addition(all_0_12_12, all_0_11_11) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (complement(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : (multiplication(v1, v0) = v4 & multiplication(v0, v1) = v3 & addition(v0, v1) = v5 & ( ~ (v5 = one) | ~ (v4 = zero) | ~ (v3 = zero)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (test(v2) = v1) | ~ (test(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (test(v0) = v1) | ~ (complement(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0, v1) = v2) | ? [v3] : ? [v4] : (c(v0) = v4 & test(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = v1) | v2 = 0) & ( ~ (v2 = 0) | v4 = v1))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (test(v0) = v1) | c(v0) = zero) & ! [v0] : ! [v1] : ( ~ (complement(v1, v0) = 0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero & addition(v0, v1) = one)) & ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) & ! [v0] : ( ~ (test(v0) = 0) | ? [v1] : complement(v1, v0) = 0)
% 34.05/9.20 |
% 34.05/9.20 | Applying alpha-rule on (1) yields:
% 34.05/9.20 | (2) leq(all_0_6_6, zero) = 0
% 34.05/9.20 | (3) ! [v0] : ! [v1] : ( ~ (complement(v1, v0) = 0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero & addition(v0, v1) = one))
% 34.05/9.20 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 34.05/9.20 | (5) ~ (all_0_0_0 = 0)
% 34.05/9.20 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 34.05/9.20 | (7) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 34.05/9.20 | (8) ! [v0] : ! [v1] : (v1 = 0 | ~ (test(v0) = v1) | c(v0) = zero)
% 34.05/9.20 | (9) multiplication(all_0_10_10, all_0_3_3) = all_0_2_2
% 34.05/9.20 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0, v1) = v2) | ? [v3] : ? [v4] : (c(v0) = v4 & test(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = v1) | v2 = 0) & ( ~ (v2 = 0) | v4 = v1)))))
% 34.05/9.20 | (11) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1))
% 34.05/9.20 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 34.05/9.20 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (complement(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : (multiplication(v1, v0) = v4 & multiplication(v0, v1) = v3 & addition(v0, v1) = v5 & ( ~ (v5 = one) | ~ (v4 = zero) | ~ (v3 = zero))))
% 34.05/9.20 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 34.05/9.20 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 34.05/9.20 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (test(v2) = v1) | ~ (test(v2) = v0))
% 34.05/9.20 | (17) multiplication(all_0_10_10, all_0_11_11) = all_0_5_5
% 34.05/9.20 | (18) multiplication(all_0_8_8, all_0_7_7) = all_0_6_6
% 34.05/9.20 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 34.05/9.20 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (test(v0) = v1) | ~ (complement(v2, v0) = 0))
% 34.05/9.20 | (21) addition(all_0_12_12, all_0_11_11) = all_0_3_3
% 34.05/9.20 | (22) test(all_0_9_9) = 0
% 34.05/9.20 | (23) multiplication(all_0_2_2, all_0_7_7) = all_0_1_1
% 34.05/9.20 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 34.05/9.20 | (25) multiplication(all_0_10_10, all_0_12_12) = all_0_8_8
% 34.05/9.21 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 34.05/9.21 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 34.05/9.21 | (28) test(all_0_10_10) = 0
% 34.05/9.21 | (29) ! [v0] : ( ~ (test(v0) = 0) | ? [v1] : complement(v1, v0) = 0)
% 34.05/9.21 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6))
% 34.05/9.21 | (31) c(all_0_9_9) = all_0_7_7
% 34.05/9.21 | (32) leq(all_0_4_4, zero) = 0
% 34.05/9.21 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 34.05/9.21 | (34) multiplication(all_0_5_5, all_0_7_7) = all_0_4_4
% 34.05/9.21 | (35) leq(all_0_1_1, zero) = all_0_0_0
% 34.05/9.21 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3, v2) = v0))
% 34.05/9.21 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 34.05/9.21 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0))
% 34.05/9.21 | (39) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 34.05/9.21 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6))
% 34.05/9.21 |
% 34.05/9.21 | Instantiating formula (33) with all_0_0_0, zero, all_0_1_1 and discharging atoms leq(all_0_1_1, zero) = all_0_0_0, yields:
% 34.05/9.21 | (41) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = zero) & addition(all_0_1_1, zero) = v0)
% 34.05/9.21 |
% 34.05/9.21 | Instantiating formula (39) with zero, all_0_4_4 and discharging atoms leq(all_0_4_4, zero) = 0, yields:
% 34.05/9.21 | (42) addition(all_0_4_4, zero) = zero
% 34.05/9.21 |
% 34.05/9.21 | Instantiating formula (39) with zero, all_0_6_6 and discharging atoms leq(all_0_6_6, zero) = 0, yields:
% 34.05/9.21 | (43) addition(all_0_6_6, zero) = zero
% 34.05/9.21 |
% 34.05/9.21 | Instantiating formula (37) with all_0_4_4, all_0_5_5, all_0_7_7, all_0_11_11, all_0_10_10 and discharging atoms multiplication(all_0_5_5, all_0_7_7) = all_0_4_4, multiplication(all_0_10_10, all_0_11_11) = all_0_5_5, yields:
% 34.05/9.21 | (44) ? [v0] : (multiplication(all_0_10_10, v0) = all_0_4_4 & multiplication(all_0_11_11, all_0_7_7) = v0)
% 34.05/9.21 |
% 34.05/9.21 | Instantiating formula (37) with all_0_6_6, all_0_8_8, all_0_7_7, all_0_12_12, all_0_10_10 and discharging atoms multiplication(all_0_8_8, all_0_7_7) = all_0_6_6, multiplication(all_0_10_10, all_0_12_12) = all_0_8_8, yields:
% 34.05/9.21 | (45) ? [v0] : (multiplication(all_0_10_10, v0) = all_0_6_6 & multiplication(all_0_12_12, all_0_7_7) = v0)
% 34.05/9.21 |
% 34.05/9.21 | Instantiating (44) with all_9_0_13 yields:
% 34.05/9.21 | (46) multiplication(all_0_10_10, all_9_0_13) = all_0_4_4 & multiplication(all_0_11_11, all_0_7_7) = all_9_0_13
% 34.05/9.21 |
% 34.05/9.21 | Applying alpha-rule on (46) yields:
% 34.05/9.21 | (47) multiplication(all_0_10_10, all_9_0_13) = all_0_4_4
% 34.05/9.21 | (48) multiplication(all_0_11_11, all_0_7_7) = all_9_0_13
% 34.05/9.21 |
% 34.05/9.21 | Instantiating (45) with all_17_0_17 yields:
% 34.05/9.21 | (49) multiplication(all_0_10_10, all_17_0_17) = all_0_6_6 & multiplication(all_0_12_12, all_0_7_7) = all_17_0_17
% 34.05/9.21 |
% 34.05/9.21 | Applying alpha-rule on (49) yields:
% 34.05/9.21 | (50) multiplication(all_0_10_10, all_17_0_17) = all_0_6_6
% 34.05/9.21 | (51) multiplication(all_0_12_12, all_0_7_7) = all_17_0_17
% 34.05/9.21 |
% 34.05/9.21 +-Applying beta-rule and splitting (41), into two cases.
% 34.05/9.21 |-Branch one:
% 34.05/9.21 | (52) all_0_0_0 = 0
% 34.05/9.21 |
% 34.05/9.21 | Equations (52) can reduce 5 to:
% 34.05/9.21 | (53) $false
% 34.05/9.21 |
% 34.05/9.21 |-The branch is then unsatisfiable
% 34.05/9.21 |-Branch two:
% 34.05/9.21 | (5) ~ (all_0_0_0 = 0)
% 34.05/9.21 | (55) ? [v0] : ( ~ (v0 = zero) & addition(all_0_1_1, zero) = v0)
% 34.05/9.22 |
% 34.05/9.22 | Instantiating (55) with all_23_0_18 yields:
% 34.05/9.22 | (56) ~ (all_23_0_18 = zero) & addition(all_0_1_1, zero) = all_23_0_18
% 34.05/9.22 |
% 34.05/9.22 | Applying alpha-rule on (56) yields:
% 34.05/9.22 | (57) ~ (all_23_0_18 = zero)
% 34.05/9.22 | (58) addition(all_0_1_1, zero) = all_23_0_18
% 34.05/9.22 |
% 34.05/9.22 | Instantiating formula (6) with all_23_0_18, all_0_1_1 and discharging atoms addition(all_0_1_1, zero) = all_23_0_18, yields:
% 34.05/9.22 | (59) all_23_0_18 = all_0_1_1
% 34.05/9.22 |
% 34.05/9.22 | Instantiating formula (6) with zero, all_0_4_4 and discharging atoms addition(all_0_4_4, zero) = zero, yields:
% 34.05/9.22 | (60) all_0_4_4 = zero
% 34.05/9.22 |
% 34.05/9.22 | Instantiating formula (6) with zero, all_0_6_6 and discharging atoms addition(all_0_6_6, zero) = zero, yields:
% 34.05/9.22 | (61) all_0_6_6 = zero
% 34.05/9.22 |
% 34.05/9.22 | Equations (59) can reduce 57 to:
% 34.05/9.22 | (62) ~ (all_0_1_1 = zero)
% 34.05/9.22 |
% 34.05/9.22 | From (60) and (34) follows:
% 34.05/9.22 | (63) multiplication(all_0_5_5, all_0_7_7) = zero
% 34.05/9.22 |
% 34.05/9.22 | From (61) and (18) follows:
% 34.05/9.22 | (64) multiplication(all_0_8_8, all_0_7_7) = zero
% 34.05/9.22 |
% 34.05/9.22 | From (61) and (50) follows:
% 34.05/9.22 | (65) multiplication(all_0_10_10, all_17_0_17) = zero
% 34.05/9.22 |
% 34.05/9.22 | From (60) and (47) follows:
% 34.05/9.22 | (66) multiplication(all_0_10_10, all_9_0_13) = zero
% 34.05/9.22 |
% 34.05/9.22 | From (61) and (43) follows:
% 34.05/9.22 | (67) addition(zero, zero) = zero
% 34.05/9.22 |
% 34.05/9.22 | Instantiating formula (30) with zero, zero, zero, all_0_7_7, all_0_5_5, all_0_8_8 and discharging atoms multiplication(all_0_5_5, all_0_7_7) = zero, multiplication(all_0_8_8, all_0_7_7) = zero, addition(zero, zero) = zero, yields:
% 34.05/9.22 | (68) ? [v0] : (multiplication(v0, all_0_7_7) = zero & addition(all_0_8_8, all_0_5_5) = v0)
% 34.05/9.22 |
% 34.05/9.22 | Instantiating formula (30) with zero, zero, zero, all_0_7_7, all_0_8_8, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_7_7) = zero, multiplication(all_0_8_8, all_0_7_7) = zero, addition(zero, zero) = zero, yields:
% 34.05/9.22 | (69) ? [v0] : (multiplication(v0, all_0_7_7) = zero & addition(all_0_5_5, all_0_8_8) = v0)
% 34.05/9.22 |
% 34.05/9.22 | Instantiating formula (30) with zero, zero, zero, all_0_7_7, all_0_8_8, all_0_8_8 and discharging atoms multiplication(all_0_8_8, all_0_7_7) = zero, addition(zero, zero) = zero, yields:
% 34.05/9.22 | (70) ? [v0] : (multiplication(v0, all_0_7_7) = zero & addition(all_0_8_8, all_0_8_8) = v0)
% 34.05/9.22 |
% 34.05/9.22 | Instantiating formula (40) with zero, zero, zero, all_9_0_13, all_17_0_17, all_0_10_10 and discharging atoms multiplication(all_0_10_10, all_17_0_17) = zero, multiplication(all_0_10_10, all_9_0_13) = zero, addition(zero, zero) = zero, yields:
% 34.05/9.22 | (71) ? [v0] : (multiplication(all_0_10_10, v0) = zero & addition(all_17_0_17, all_9_0_13) = v0)
% 34.05/9.22 |
% 34.05/9.22 | Instantiating (70) with all_103_0_19 yields:
% 34.05/9.22 | (72) multiplication(all_103_0_19, all_0_7_7) = zero & addition(all_0_8_8, all_0_8_8) = all_103_0_19
% 34.05/9.22 |
% 34.05/9.22 | Applying alpha-rule on (72) yields:
% 34.05/9.22 | (73) multiplication(all_103_0_19, all_0_7_7) = zero
% 34.05/9.22 | (74) addition(all_0_8_8, all_0_8_8) = all_103_0_19
% 34.05/9.22 |
% 34.05/9.22 | Instantiating (69) with all_105_0_20 yields:
% 34.05/9.22 | (75) multiplication(all_105_0_20, all_0_7_7) = zero & addition(all_0_5_5, all_0_8_8) = all_105_0_20
% 34.05/9.22 |
% 34.05/9.22 | Applying alpha-rule on (75) yields:
% 34.05/9.22 | (76) multiplication(all_105_0_20, all_0_7_7) = zero
% 34.05/9.22 | (77) addition(all_0_5_5, all_0_8_8) = all_105_0_20
% 34.05/9.22 |
% 34.05/9.22 | Instantiating (68) with all_113_0_25 yields:
% 34.05/9.22 | (78) multiplication(all_113_0_25, all_0_7_7) = zero & addition(all_0_8_8, all_0_5_5) = all_113_0_25
% 34.05/9.22 |
% 34.05/9.22 | Applying alpha-rule on (78) yields:
% 34.05/9.22 | (79) multiplication(all_113_0_25, all_0_7_7) = zero
% 34.05/9.22 | (80) addition(all_0_8_8, all_0_5_5) = all_113_0_25
% 34.05/9.22 |
% 34.05/9.22 | Instantiating (71) with all_125_0_32 yields:
% 34.05/9.22 | (81) multiplication(all_0_10_10, all_125_0_32) = zero & addition(all_17_0_17, all_9_0_13) = all_125_0_32
% 34.05/9.22 |
% 34.05/9.22 | Applying alpha-rule on (81) yields:
% 34.05/9.22 | (82) multiplication(all_0_10_10, all_125_0_32) = zero
% 34.05/9.22 | (83) addition(all_17_0_17, all_9_0_13) = all_125_0_32
% 34.49/9.22 |
% 34.49/9.22 | Instantiating formula (24) with all_105_0_20, all_0_7_7, zero, all_0_1_1 and discharging atoms multiplication(all_105_0_20, all_0_7_7) = zero, yields:
% 34.49/9.22 | (84) all_0_1_1 = zero | ~ (multiplication(all_105_0_20, all_0_7_7) = all_0_1_1)
% 34.49/9.22 |
% 34.49/9.22 | Instantiating formula (15) with all_103_0_19, all_0_8_8 and discharging atoms addition(all_0_8_8, all_0_8_8) = all_103_0_19, yields:
% 34.49/9.22 | (85) all_103_0_19 = all_0_8_8
% 34.49/9.22 |
% 34.49/9.22 | From (85) and (74) follows:
% 34.49/9.22 | (86) addition(all_0_8_8, all_0_8_8) = all_0_8_8
% 34.49/9.22 |
% 34.49/9.22 | Instantiating formula (30) with all_125_0_32, all_9_0_13, all_17_0_17, all_0_7_7, all_0_11_11, all_0_12_12 and discharging atoms multiplication(all_0_11_11, all_0_7_7) = all_9_0_13, multiplication(all_0_12_12, all_0_7_7) = all_17_0_17, addition(all_17_0_17, all_9_0_13) = all_125_0_32, yields:
% 34.49/9.22 | (87) ? [v0] : (multiplication(v0, all_0_7_7) = all_125_0_32 & addition(all_0_12_12, all_0_11_11) = v0)
% 34.49/9.22 |
% 34.49/9.22 | Instantiating formula (12) with all_105_0_20, all_0_8_8, all_0_5_5 and discharging atoms addition(all_0_5_5, all_0_8_8) = all_105_0_20, yields:
% 34.49/9.22 | (88) addition(all_0_8_8, all_0_5_5) = all_105_0_20
% 34.49/9.22 |
% 34.49/9.22 | Instantiating formula (40) with all_113_0_25, all_0_5_5, all_0_8_8, all_0_11_11, all_0_12_12, all_0_10_10 and discharging atoms multiplication(all_0_10_10, all_0_11_11) = all_0_5_5, multiplication(all_0_10_10, all_0_12_12) = all_0_8_8, addition(all_0_8_8, all_0_5_5) = all_113_0_25, yields:
% 34.49/9.22 | (89) ? [v0] : (multiplication(all_0_10_10, v0) = all_113_0_25 & addition(all_0_12_12, all_0_11_11) = v0)
% 34.49/9.22 |
% 34.49/9.22 | Instantiating formula (27) with all_113_0_25, all_0_8_8, all_0_8_8, all_0_8_8, all_0_5_5 and discharging atoms addition(all_0_8_8, all_0_5_5) = all_113_0_25, addition(all_0_8_8, all_0_8_8) = all_0_8_8, yields:
% 34.49/9.22 | (90) ? [v0] : (addition(all_0_8_8, v0) = all_113_0_25 & addition(all_0_8_8, all_0_5_5) = v0)
% 34.49/9.22 |
% 34.49/9.22 | Instantiating (90) with all_377_0_41 yields:
% 34.49/9.22 | (91) addition(all_0_8_8, all_377_0_41) = all_113_0_25 & addition(all_0_8_8, all_0_5_5) = all_377_0_41
% 34.49/9.22 |
% 34.49/9.22 | Applying alpha-rule on (91) yields:
% 34.49/9.22 | (92) addition(all_0_8_8, all_377_0_41) = all_113_0_25
% 34.49/9.22 | (93) addition(all_0_8_8, all_0_5_5) = all_377_0_41
% 34.49/9.22 |
% 34.49/9.22 | Instantiating (89) with all_445_0_75 yields:
% 34.49/9.22 | (94) multiplication(all_0_10_10, all_445_0_75) = all_113_0_25 & addition(all_0_12_12, all_0_11_11) = all_445_0_75
% 34.49/9.22 |
% 34.49/9.22 | Applying alpha-rule on (94) yields:
% 34.49/9.22 | (95) multiplication(all_0_10_10, all_445_0_75) = all_113_0_25
% 34.49/9.22 | (96) addition(all_0_12_12, all_0_11_11) = all_445_0_75
% 34.49/9.22 |
% 34.49/9.22 | Instantiating (87) with all_555_0_130 yields:
% 34.49/9.22 | (97) multiplication(all_555_0_130, all_0_7_7) = all_125_0_32 & addition(all_0_12_12, all_0_11_11) = all_555_0_130
% 34.49/9.22 |
% 34.49/9.22 | Applying alpha-rule on (97) yields:
% 34.49/9.22 | (98) multiplication(all_555_0_130, all_0_7_7) = all_125_0_32
% 34.49/9.22 | (99) addition(all_0_12_12, all_0_11_11) = all_555_0_130
% 34.49/9.22 |
% 34.49/9.22 | Instantiating formula (24) with all_0_10_10, all_0_3_3, all_105_0_20, all_0_2_2 and discharging atoms multiplication(all_0_10_10, all_0_3_3) = all_0_2_2, yields:
% 34.49/9.22 | (100) all_105_0_20 = all_0_2_2 | ~ (multiplication(all_0_10_10, all_0_3_3) = all_105_0_20)
% 34.49/9.22 |
% 34.49/9.22 | Instantiating formula (26) with all_0_8_8, all_0_5_5, all_377_0_41, all_113_0_25 and discharging atoms addition(all_0_8_8, all_0_5_5) = all_377_0_41, addition(all_0_8_8, all_0_5_5) = all_113_0_25, yields:
% 34.49/9.23 | (101) all_377_0_41 = all_113_0_25
% 34.49/9.23 |
% 34.49/9.23 | Instantiating formula (26) with all_0_8_8, all_0_5_5, all_105_0_20, all_377_0_41 and discharging atoms addition(all_0_8_8, all_0_5_5) = all_377_0_41, addition(all_0_8_8, all_0_5_5) = all_105_0_20, yields:
% 34.49/9.23 | (102) all_377_0_41 = all_105_0_20
% 34.49/9.23 |
% 34.49/9.23 | Instantiating formula (26) with all_0_12_12, all_0_11_11, all_555_0_130, all_0_3_3 and discharging atoms addition(all_0_12_12, all_0_11_11) = all_555_0_130, addition(all_0_12_12, all_0_11_11) = all_0_3_3, yields:
% 34.49/9.23 | (103) all_555_0_130 = all_0_3_3
% 34.49/9.23 |
% 34.49/9.23 | Instantiating formula (26) with all_0_12_12, all_0_11_11, all_445_0_75, all_555_0_130 and discharging atoms addition(all_0_12_12, all_0_11_11) = all_555_0_130, addition(all_0_12_12, all_0_11_11) = all_445_0_75, yields:
% 34.49/9.23 | (104) all_555_0_130 = all_445_0_75
% 34.49/9.23 |
% 34.49/9.23 | Combining equations (104,103) yields a new equation:
% 34.49/9.23 | (105) all_445_0_75 = all_0_3_3
% 34.49/9.23 |
% 34.49/9.23 | Simplifying 105 yields:
% 34.49/9.23 | (106) all_445_0_75 = all_0_3_3
% 34.49/9.23 |
% 34.49/9.23 | Combining equations (101,102) yields a new equation:
% 34.49/9.23 | (107) all_113_0_25 = all_105_0_20
% 34.49/9.23 |
% 34.49/9.23 | Simplifying 107 yields:
% 34.49/9.23 | (108) all_113_0_25 = all_105_0_20
% 34.49/9.23 |
% 34.49/9.23 | From (106)(108) and (95) follows:
% 34.49/9.23 | (109) multiplication(all_0_10_10, all_0_3_3) = all_105_0_20
% 34.49/9.23 |
% 34.49/9.23 +-Applying beta-rule and splitting (100), into two cases.
% 34.49/9.23 |-Branch one:
% 34.49/9.23 | (110) ~ (multiplication(all_0_10_10, all_0_3_3) = all_105_0_20)
% 34.49/9.23 |
% 34.49/9.23 | Using (109) and (110) yields:
% 34.49/9.23 | (111) $false
% 34.49/9.23 |
% 34.49/9.23 |-The branch is then unsatisfiable
% 34.49/9.23 |-Branch two:
% 34.49/9.23 | (109) multiplication(all_0_10_10, all_0_3_3) = all_105_0_20
% 34.49/9.23 | (113) all_105_0_20 = all_0_2_2
% 34.49/9.23 |
% 34.49/9.23 +-Applying beta-rule and splitting (84), into two cases.
% 34.49/9.23 |-Branch one:
% 34.49/9.23 | (114) ~ (multiplication(all_105_0_20, all_0_7_7) = all_0_1_1)
% 34.49/9.23 |
% 34.49/9.23 | From (113) and (114) follows:
% 34.49/9.23 | (115) ~ (multiplication(all_0_2_2, all_0_7_7) = all_0_1_1)
% 34.49/9.23 |
% 34.49/9.23 | Using (23) and (115) yields:
% 34.49/9.23 | (111) $false
% 34.49/9.23 |
% 34.49/9.23 |-The branch is then unsatisfiable
% 34.49/9.23 |-Branch two:
% 34.49/9.23 | (117) multiplication(all_105_0_20, all_0_7_7) = all_0_1_1
% 34.49/9.23 | (118) all_0_1_1 = zero
% 34.49/9.23 |
% 34.49/9.23 | Equations (118) can reduce 62 to:
% 34.49/9.23 | (53) $false
% 34.49/9.23 |
% 34.49/9.23 |-The branch is then unsatisfiable
% 34.49/9.23 % SZS output end Proof for theBenchmark
% 34.49/9.23
% 34.49/9.23 8591ms
%------------------------------------------------------------------------------