TSTP Solution File: GRP715+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GRP715+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 : Sat Jul 16 08:43:45 EDT 2022
% Result : Theorem 16.53s 4.62s
% Output : Proof 19.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP715+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 11:02:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.45/0.61 ____ _
% 0.45/0.61 ___ / __ \_____(_)___ ________ __________
% 0.45/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.45/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.45/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.45/0.61
% 0.45/0.61 A Theorem Prover for First-Order Logic
% 0.45/0.61 (ePrincess v.1.0)
% 0.45/0.61
% 0.45/0.61 (c) Philipp Rümmer, 2009-2015
% 0.45/0.61 (c) Peter Backeman, 2014-2015
% 0.45/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.45/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.45/0.61 Bug reports to peter@backeman.se
% 0.45/0.61
% 0.45/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.45/0.61
% 0.45/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.41/0.93 Prover 0: Preprocessing ...
% 1.97/1.15 Prover 0: Constructing countermodel ...
% 4.97/1.89 Prover 0: gave up
% 4.97/1.89 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.97/1.90 Prover 1: Preprocessing ...
% 4.97/1.94 Prover 1: Constructing countermodel ...
% 6.36/2.21 Prover 1: gave up
% 6.36/2.21 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.36/2.22 Prover 2: Preprocessing ...
% 6.36/2.26 Prover 2: Warning: ignoring some quantifiers
% 6.36/2.26 Prover 2: Constructing countermodel ...
% 15.18/4.37 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 15.18/4.39 Prover 3: Preprocessing ...
% 15.50/4.43 Prover 3: Constructing countermodel ...
% 15.95/4.51 Prover 3: gave up
% 15.95/4.51 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 16.06/4.52 Prover 4: Preprocessing ...
% 16.16/4.55 Prover 4: Warning: ignoring some quantifiers
% 16.16/4.55 Prover 4: Constructing countermodel ...
% 16.53/4.62 Prover 4: proved (112ms)
% 16.53/4.62 Prover 2: stopped
% 16.53/4.62
% 16.53/4.62 No countermodel exists, formula is valid
% 16.53/4.62 % SZS status Theorem for theBenchmark
% 16.53/4.62
% 16.53/4.62 Generating proof ... Warning: ignoring some quantifiers
% 18.62/5.10 found it (size 152)
% 18.62/5.10
% 18.62/5.10 % SZS output start Proof for theBenchmark
% 18.62/5.10 Assumed formulas after preprocessing and simplification:
% 18.62/5.10 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (mult(v3, op_a) = v4 & mult(v1, op_b) = v2 & mult(v0, op_b) = v3 & mult(v0, op_a) = v1 & mult(op_b, op_a) = unit & mult(op_a, op_b) = unit & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (mult(v8, v6) = v9) | ~ (mult(v7, v9) = v10) | ~ (mult(v6, v5) = v8) | ? [v11] : ? [v12] : (mult(v12, v6) = v10 & mult(v11, v5) = v12 & mult(v7, v6) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (mult(v7, v6) = v8) | ~ (mult(v7, v5) = v9) | ~ (plus(v8, v9) = v10) | ? [v11] : (mult(v7, v11) = v10 & plus(v6, v5) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (mult(v8, v5) = v9) | ~ (mult(v7, v6) = v8) | ? [v10] : ? [v11] : ? [v12] : (mult(v11, v6) = v12 & mult(v9, v6) = v10 & mult(v7, v12) = v10 & mult(v6, v5) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (mult(v7, v8) = v9) | ~ (plus(v6, v5) = v8) | ? [v10] : ? [v11] : (mult(v7, v6) = v10 & mult(v7, v5) = v11 & plus(v10, v11) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (plus(v8, v5) = v9) | ~ (plus(v7, v6) = v8) | ? [v10] : (plus(v7, v10) = v9 & plus(v6, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (plus(v7, v8) = v9) | ~ (plus(v6, v5) = v8) | ? [v10] : (plus(v10, v5) = v9 & plus(v7, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (mult(v8, v7) = v6) | ~ (mult(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (plus(v8, v7) = v6) | ~ (plus(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (mult(v6, v7) = v8) | ~ (mult(v5, v5) = v7) | ? [v9] : (mult(v9, v5) = v8 & mult(v6, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (minus(v7) = v6) | ~ (minus(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (mult(v6, v5) = v7) | ? [v8] : ? [v9] : (mult(v7, v5) = v9 & mult(v6, v8) = v9 & mult(v5, v5) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (plus(v6, v5) = v7) | plus(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (plus(v5, v6) = v7) | plus(v6, v5) = v7) & ! [v5] : ! [v6] : (v6 = v5 | ~ (mult(v5, unit) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (mult(unit, v5) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (plus(v5, op_0) = v6)) & ! [v5] : ! [v6] : ( ~ (minus(v5) = v6) | plus(v5, v6) = op_0) & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (mult(v7, v8) = v9 & mult(v7, v6) = v10 & mult(v7, v5) = v11 & plus(v10, v11) = v9 & plus(v6, v5) = v8) & ? [v5] : ? [v6] : (minus(v5) = v6 & plus(v5, v6) = op_0) & ( ~ (v4 = v0) | ~ (v2 = v0)))
% 18.81/5.13 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 18.81/5.13 | (1) mult(all_0_1_1, op_a) = all_0_0_0 & mult(all_0_3_3, op_b) = all_0_2_2 & mult(all_0_4_4, op_b) = all_0_1_1 & mult(all_0_4_4, op_a) = all_0_3_3 & mult(op_b, op_a) = unit & mult(op_a, op_b) = unit & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (mult(v3, v1) = v4) | ~ (mult(v2, v4) = v5) | ~ (mult(v1, v0) = v3) | ? [v6] : ? [v7] : (mult(v7, v1) = v5 & mult(v6, v0) = v7 & mult(v2, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (mult(v2, v1) = v3) | ~ (mult(v2, v0) = v4) | ~ (plus(v3, v4) = v5) | ? [v6] : (mult(v2, v6) = v5 & plus(v1, v0) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (mult(v3, v0) = v4) | ~ (mult(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (mult(v6, v1) = v7 & mult(v4, v1) = v5 & mult(v2, v7) = v5 & mult(v1, v0) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (mult(v2, v3) = v4) | ~ (plus(v1, v0) = v3) | ? [v5] : ? [v6] : (mult(v2, v1) = v5 & mult(v2, v0) = v6 & plus(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus(v3, v0) = v4) | ~ (plus(v2, v1) = v3) | ? [v5] : (plus(v2, v5) = v4 & plus(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus(v2, v3) = v4) | ~ (plus(v1, v0) = v3) | ? [v5] : (plus(v5, v0) = v4 & plus(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (mult(v3, v2) = v1) | ~ (mult(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (mult(v1, v2) = v3) | ~ (mult(v0, v0) = v2) | ? [v4] : (mult(v4, v0) = v3 & mult(v1, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (minus(v2) = v1) | ~ (minus(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (mult(v1, v0) = v2) | ? [v3] : ? [v4] : (mult(v2, v0) = v4 & mult(v1, v3) = v4 & mult(v0, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, v0) = v2) | plus(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v0, v1) = v2) | plus(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (mult(v0, unit) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (mult(unit, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (plus(v0, op_0) = v1)) & ! [v0] : ! [v1] : ( ~ (minus(v0) = v1) | plus(v0, v1) = op_0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (mult(v2, v3) = v4 & mult(v2, v1) = v5 & mult(v2, v0) = v6 & plus(v5, v6) = v4 & plus(v1, v0) = v3) & ? [v0] : ? [v1] : (minus(v0) = v1 & plus(v0, v1) = op_0) & ( ~ (all_0_0_0 = all_0_4_4) | ~ (all_0_2_2 = all_0_4_4))
% 18.81/5.14 |
% 18.81/5.14 | Applying alpha-rule on (1) yields:
% 18.81/5.14 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (mult(unit, v0) = v1))
% 18.81/5.14 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v0, v1) = v2) | plus(v1, v0) = v2)
% 18.81/5.14 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, v0) = v2) | plus(v0, v1) = v2)
% 18.81/5.14 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (mult(v1, v2) = v3) | ~ (mult(v0, v0) = v2) | ? [v4] : (mult(v4, v0) = v3 & mult(v1, v0) = v4))
% 18.81/5.14 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus(v3, v0) = v4) | ~ (plus(v2, v1) = v3) | ? [v5] : (plus(v2, v5) = v4 & plus(v1, v0) = v5))
% 18.81/5.14 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (mult(v2, v1) = v3) | ~ (mult(v2, v0) = v4) | ~ (plus(v3, v4) = v5) | ? [v6] : (mult(v2, v6) = v5 & plus(v1, v0) = v6))
% 18.81/5.14 | (8) mult(all_0_4_4, op_a) = all_0_3_3
% 18.81/5.15 | (9) mult(all_0_1_1, op_a) = all_0_0_0
% 18.81/5.15 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (mult(v3, v0) = v4) | ~ (mult(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (mult(v6, v1) = v7 & mult(v4, v1) = v5 & mult(v2, v7) = v5 & mult(v1, v0) = v6))
% 18.81/5.15 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (mult(v3, v2) = v1) | ~ (mult(v3, v2) = v0))
% 18.81/5.15 | (12) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (mult(v2, v3) = v4 & mult(v2, v1) = v5 & mult(v2, v0) = v6 & plus(v5, v6) = v4 & plus(v1, v0) = v3)
% 18.81/5.15 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0))
% 18.81/5.15 | (14) mult(op_a, op_b) = unit
% 18.81/5.15 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (minus(v2) = v1) | ~ (minus(v2) = v0))
% 18.81/5.15 | (16) mult(op_b, op_a) = unit
% 18.81/5.15 | (17) ? [v0] : ? [v1] : (minus(v0) = v1 & plus(v0, v1) = op_0)
% 18.81/5.15 | (18) ! [v0] : ! [v1] : ( ~ (minus(v0) = v1) | plus(v0, v1) = op_0)
% 18.81/5.15 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (mult(v1, v0) = v2) | ? [v3] : ? [v4] : (mult(v2, v0) = v4 & mult(v1, v3) = v4 & mult(v0, v0) = v3))
% 18.81/5.15 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ (mult(v0, unit) = v1))
% 18.81/5.15 | (21) ~ (all_0_0_0 = all_0_4_4) | ~ (all_0_2_2 = all_0_4_4)
% 18.81/5.15 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (plus(v0, op_0) = v1))
% 18.81/5.15 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus(v2, v3) = v4) | ~ (plus(v1, v0) = v3) | ? [v5] : (plus(v5, v0) = v4 & plus(v2, v1) = v5))
% 18.81/5.15 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (mult(v2, v3) = v4) | ~ (plus(v1, v0) = v3) | ? [v5] : ? [v6] : (mult(v2, v1) = v5 & mult(v2, v0) = v6 & plus(v5, v6) = v4))
% 18.81/5.15 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (mult(v3, v1) = v4) | ~ (mult(v2, v4) = v5) | ~ (mult(v1, v0) = v3) | ? [v6] : ? [v7] : (mult(v7, v1) = v5 & mult(v6, v0) = v7 & mult(v2, v1) = v6))
% 18.81/5.15 | (26) mult(all_0_4_4, op_b) = all_0_1_1
% 18.81/5.15 | (27) mult(all_0_3_3, op_b) = all_0_2_2
% 18.81/5.15 |
% 18.81/5.15 | Instantiating formula (19) with all_0_0_0, all_0_1_1, op_a and discharging atoms mult(all_0_1_1, op_a) = all_0_0_0, yields:
% 18.81/5.15 | (28) ? [v0] : ? [v1] : (mult(all_0_0_0, op_a) = v1 & mult(all_0_1_1, v0) = v1 & mult(op_a, op_a) = v0)
% 18.81/5.15 |
% 18.81/5.15 | Instantiating formula (19) with all_0_2_2, all_0_3_3, op_b and discharging atoms mult(all_0_3_3, op_b) = all_0_2_2, yields:
% 18.81/5.15 | (29) ? [v0] : ? [v1] : (mult(all_0_2_2, op_b) = v1 & mult(all_0_3_3, v0) = v1 & mult(op_b, op_b) = v0)
% 18.81/5.15 |
% 18.81/5.15 | Instantiating formula (10) with all_0_0_0, all_0_1_1, all_0_4_4, op_b, op_a and discharging atoms mult(all_0_1_1, op_a) = all_0_0_0, mult(all_0_4_4, op_b) = all_0_1_1, yields:
% 18.81/5.15 | (30) ? [v0] : ? [v1] : ? [v2] : (mult(v1, op_b) = v2 & mult(all_0_0_0, op_b) = v0 & mult(all_0_4_4, v2) = v0 & mult(op_b, op_a) = v1)
% 18.81/5.15 |
% 18.81/5.15 | Instantiating formula (19) with all_0_1_1, all_0_4_4, op_b and discharging atoms mult(all_0_4_4, op_b) = all_0_1_1, yields:
% 18.81/5.15 | (31) ? [v0] : ? [v1] : (mult(all_0_1_1, op_b) = v1 & mult(all_0_4_4, v0) = v1 & mult(op_b, op_b) = v0)
% 18.81/5.15 |
% 18.81/5.15 | Instantiating formula (10) with all_0_2_2, all_0_3_3, all_0_4_4, op_a, op_b and discharging atoms mult(all_0_3_3, op_b) = all_0_2_2, mult(all_0_4_4, op_a) = all_0_3_3, yields:
% 18.81/5.15 | (32) ? [v0] : ? [v1] : ? [v2] : (mult(v1, op_a) = v2 & mult(all_0_2_2, op_a) = v0 & mult(all_0_4_4, v2) = v0 & mult(op_a, op_b) = v1)
% 18.81/5.15 |
% 18.81/5.15 | Instantiating formula (19) with unit, op_b, op_a and discharging atoms mult(op_b, op_a) = unit, yields:
% 18.81/5.15 | (33) ? [v0] : ? [v1] : (mult(op_b, v0) = v1 & mult(op_a, op_a) = v0 & mult(unit, op_a) = v1)
% 18.81/5.15 |
% 18.81/5.15 | Instantiating formula (19) with unit, op_a, op_b and discharging atoms mult(op_a, op_b) = unit, yields:
% 18.81/5.15 | (34) ? [v0] : ? [v1] : (mult(op_b, op_b) = v0 & mult(op_a, v0) = v1 & mult(unit, op_b) = v1)
% 18.81/5.15 |
% 18.81/5.15 | Instantiating (31) with all_13_0_14, all_13_1_15 yields:
% 18.81/5.15 | (35) mult(all_0_1_1, op_b) = all_13_0_14 & mult(all_0_4_4, all_13_1_15) = all_13_0_14 & mult(op_b, op_b) = all_13_1_15
% 18.81/5.15 |
% 18.81/5.15 | Applying alpha-rule on (35) yields:
% 18.81/5.16 | (36) mult(all_0_1_1, op_b) = all_13_0_14
% 18.81/5.16 | (37) mult(all_0_4_4, all_13_1_15) = all_13_0_14
% 18.81/5.16 | (38) mult(op_b, op_b) = all_13_1_15
% 18.81/5.16 |
% 18.81/5.16 | Instantiating (30) with all_15_0_16, all_15_1_17, all_15_2_18 yields:
% 18.81/5.16 | (39) mult(all_15_1_17, op_b) = all_15_0_16 & mult(all_0_0_0, op_b) = all_15_2_18 & mult(all_0_4_4, all_15_0_16) = all_15_2_18 & mult(op_b, op_a) = all_15_1_17
% 18.81/5.16 |
% 18.81/5.16 | Applying alpha-rule on (39) yields:
% 18.81/5.16 | (40) mult(all_15_1_17, op_b) = all_15_0_16
% 18.81/5.16 | (41) mult(all_0_0_0, op_b) = all_15_2_18
% 18.81/5.16 | (42) mult(all_0_4_4, all_15_0_16) = all_15_2_18
% 18.81/5.16 | (43) mult(op_b, op_a) = all_15_1_17
% 18.81/5.16 |
% 18.81/5.16 | Instantiating (29) with all_17_0_19, all_17_1_20 yields:
% 18.81/5.16 | (44) mult(all_0_2_2, op_b) = all_17_0_19 & mult(all_0_3_3, all_17_1_20) = all_17_0_19 & mult(op_b, op_b) = all_17_1_20
% 18.81/5.16 |
% 18.81/5.16 | Applying alpha-rule on (44) yields:
% 18.81/5.16 | (45) mult(all_0_2_2, op_b) = all_17_0_19
% 18.81/5.16 | (46) mult(all_0_3_3, all_17_1_20) = all_17_0_19
% 18.81/5.16 | (47) mult(op_b, op_b) = all_17_1_20
% 18.81/5.16 |
% 18.81/5.16 | Instantiating (28) with all_19_0_21, all_19_1_22 yields:
% 18.81/5.16 | (48) mult(all_0_0_0, op_a) = all_19_0_21 & mult(all_0_1_1, all_19_1_22) = all_19_0_21 & mult(op_a, op_a) = all_19_1_22
% 18.81/5.16 |
% 18.81/5.16 | Applying alpha-rule on (48) yields:
% 18.81/5.16 | (49) mult(all_0_0_0, op_a) = all_19_0_21
% 18.81/5.16 | (50) mult(all_0_1_1, all_19_1_22) = all_19_0_21
% 18.81/5.16 | (51) mult(op_a, op_a) = all_19_1_22
% 18.81/5.16 |
% 18.81/5.16 | Instantiating (34) with all_21_0_23, all_21_1_24 yields:
% 18.81/5.16 | (52) mult(op_b, op_b) = all_21_1_24 & mult(op_a, all_21_1_24) = all_21_0_23 & mult(unit, op_b) = all_21_0_23
% 18.81/5.16 |
% 18.81/5.16 | Applying alpha-rule on (52) yields:
% 18.81/5.16 | (53) mult(op_b, op_b) = all_21_1_24
% 18.81/5.16 | (54) mult(op_a, all_21_1_24) = all_21_0_23
% 18.81/5.16 | (55) mult(unit, op_b) = all_21_0_23
% 18.81/5.16 |
% 18.81/5.16 | Instantiating (32) with all_31_0_33, all_31_1_34, all_31_2_35 yields:
% 18.81/5.16 | (56) mult(all_31_1_34, op_a) = all_31_0_33 & mult(all_0_2_2, op_a) = all_31_2_35 & mult(all_0_4_4, all_31_0_33) = all_31_2_35 & mult(op_a, op_b) = all_31_1_34
% 18.81/5.16 |
% 18.81/5.16 | Applying alpha-rule on (56) yields:
% 18.81/5.16 | (57) mult(all_31_1_34, op_a) = all_31_0_33
% 18.81/5.16 | (58) mult(all_0_2_2, op_a) = all_31_2_35
% 18.81/5.16 | (59) mult(all_0_4_4, all_31_0_33) = all_31_2_35
% 18.81/5.16 | (60) mult(op_a, op_b) = all_31_1_34
% 18.81/5.16 |
% 18.81/5.16 | Instantiating (33) with all_33_0_36, all_33_1_37 yields:
% 18.81/5.16 | (61) mult(op_b, all_33_1_37) = all_33_0_36 & mult(op_a, op_a) = all_33_1_37 & mult(unit, op_a) = all_33_0_36
% 18.81/5.16 |
% 18.81/5.16 | Applying alpha-rule on (61) yields:
% 18.81/5.16 | (62) mult(op_b, all_33_1_37) = all_33_0_36
% 18.81/5.16 | (63) mult(op_a, op_a) = all_33_1_37
% 18.81/5.16 | (64) mult(unit, op_a) = all_33_0_36
% 18.81/5.16 |
% 18.81/5.16 | Instantiating formula (11) with op_b, op_b, all_17_1_20, all_21_1_24 and discharging atoms mult(op_b, op_b) = all_21_1_24, mult(op_b, op_b) = all_17_1_20, yields:
% 18.81/5.16 | (65) all_21_1_24 = all_17_1_20
% 18.81/5.16 |
% 18.81/5.16 | Instantiating formula (11) with op_b, op_b, all_13_1_15, all_21_1_24 and discharging atoms mult(op_b, op_b) = all_21_1_24, mult(op_b, op_b) = all_13_1_15, yields:
% 18.81/5.16 | (66) all_21_1_24 = all_13_1_15
% 18.81/5.16 |
% 18.81/5.16 | Instantiating formula (11) with op_b, op_a, all_15_1_17, unit and discharging atoms mult(op_b, op_a) = all_15_1_17, mult(op_b, op_a) = unit, yields:
% 18.81/5.16 | (67) all_15_1_17 = unit
% 18.81/5.16 |
% 18.81/5.16 | Instantiating formula (11) with op_a, op_b, all_31_1_34, unit and discharging atoms mult(op_a, op_b) = all_31_1_34, mult(op_a, op_b) = unit, yields:
% 18.81/5.16 | (68) all_31_1_34 = unit
% 18.81/5.16 |
% 18.81/5.16 | Instantiating formula (11) with op_a, op_a, all_19_1_22, all_33_1_37 and discharging atoms mult(op_a, op_a) = all_33_1_37, mult(op_a, op_a) = all_19_1_22, yields:
% 18.81/5.16 | (69) all_33_1_37 = all_19_1_22
% 18.81/5.16 |
% 18.81/5.16 | Instantiating formula (2) with all_21_0_23, op_b and discharging atoms mult(unit, op_b) = all_21_0_23, yields:
% 18.81/5.16 | (70) all_21_0_23 = op_b
% 18.81/5.16 |
% 18.81/5.16 | Instantiating formula (2) with all_33_0_36, op_a and discharging atoms mult(unit, op_a) = all_33_0_36, yields:
% 18.81/5.16 | (71) all_33_0_36 = op_a
% 18.81/5.16 |
% 18.81/5.16 | Combining equations (65,66) yields a new equation:
% 18.81/5.16 | (72) all_17_1_20 = all_13_1_15
% 18.81/5.16 |
% 18.81/5.16 | Simplifying 72 yields:
% 18.81/5.16 | (73) all_17_1_20 = all_13_1_15
% 18.81/5.16 |
% 18.81/5.16 | From (68) and (57) follows:
% 18.81/5.16 | (74) mult(unit, op_a) = all_31_0_33
% 18.81/5.16 |
% 18.81/5.16 | From (67) and (40) follows:
% 18.81/5.16 | (75) mult(unit, op_b) = all_15_0_16
% 18.81/5.16 |
% 18.81/5.16 | From (73) and (46) follows:
% 18.81/5.16 | (76) mult(all_0_3_3, all_13_1_15) = all_17_0_19
% 18.81/5.16 |
% 18.81/5.16 | From (69)(71) and (62) follows:
% 18.81/5.16 | (77) mult(op_b, all_19_1_22) = op_a
% 18.81/5.16 |
% 18.81/5.16 | From (67) and (43) follows:
% 18.81/5.16 | (16) mult(op_b, op_a) = unit
% 18.81/5.16 |
% 18.81/5.16 | From (66)(70) and (54) follows:
% 18.81/5.16 | (79) mult(op_a, all_13_1_15) = op_b
% 18.81/5.16 |
% 18.81/5.16 | From (68) and (60) follows:
% 18.81/5.16 | (14) mult(op_a, op_b) = unit
% 18.81/5.16 |
% 18.81/5.16 | From (70) and (55) follows:
% 18.81/5.16 | (81) mult(unit, op_b) = op_b
% 18.81/5.16 |
% 18.81/5.16 | From (71) and (64) follows:
% 18.81/5.16 | (82) mult(unit, op_a) = op_a
% 18.81/5.16 |
% 18.81/5.16 | Instantiating formula (11) with unit, op_b, op_b, all_15_0_16 and discharging atoms mult(unit, op_b) = all_15_0_16, mult(unit, op_b) = op_b, yields:
% 18.81/5.16 | (83) all_15_0_16 = op_b
% 18.81/5.16 |
% 18.81/5.17 | Instantiating formula (11) with unit, op_a, op_a, all_31_0_33 and discharging atoms mult(unit, op_a) = all_31_0_33, mult(unit, op_a) = op_a, yields:
% 18.81/5.17 | (84) all_31_0_33 = op_a
% 18.81/5.17 |
% 18.81/5.17 | From (84) and (59) follows:
% 18.81/5.17 | (85) mult(all_0_4_4, op_a) = all_31_2_35
% 18.81/5.17 |
% 18.81/5.17 | From (83) and (42) follows:
% 18.81/5.17 | (86) mult(all_0_4_4, op_b) = all_15_2_18
% 18.81/5.17 |
% 18.81/5.17 | From (83) and (75) follows:
% 18.81/5.17 | (81) mult(unit, op_b) = op_b
% 18.81/5.17 |
% 18.81/5.17 | From (84) and (74) follows:
% 18.81/5.17 | (82) mult(unit, op_a) = op_a
% 18.81/5.17 |
% 18.81/5.17 | Instantiating formula (11) with all_0_4_4, op_b, all_15_2_18, all_0_1_1 and discharging atoms mult(all_0_4_4, op_b) = all_15_2_18, mult(all_0_4_4, op_b) = all_0_1_1, yields:
% 18.81/5.17 | (89) all_15_2_18 = all_0_1_1
% 18.81/5.17 |
% 18.81/5.17 | Instantiating formula (11) with all_0_4_4, op_a, all_31_2_35, all_0_3_3 and discharging atoms mult(all_0_4_4, op_a) = all_31_2_35, mult(all_0_4_4, op_a) = all_0_3_3, yields:
% 18.81/5.17 | (90) all_31_2_35 = all_0_3_3
% 18.81/5.17 |
% 18.81/5.17 | From (89) and (41) follows:
% 18.81/5.17 | (91) mult(all_0_0_0, op_b) = all_0_1_1
% 18.81/5.17 |
% 18.81/5.17 | From (90) and (58) follows:
% 18.81/5.17 | (92) mult(all_0_2_2, op_a) = all_0_3_3
% 18.81/5.17 |
% 18.81/5.17 | From (89) and (86) follows:
% 18.81/5.17 | (26) mult(all_0_4_4, op_b) = all_0_1_1
% 18.81/5.17 |
% 18.81/5.17 | From (90) and (85) follows:
% 18.81/5.17 | (8) mult(all_0_4_4, op_a) = all_0_3_3
% 18.81/5.17 |
% 18.81/5.17 | Instantiating formula (10) with all_19_0_21, all_0_1_1, all_0_4_4, op_b, all_19_1_22 and discharging atoms mult(all_0_1_1, all_19_1_22) = all_19_0_21, mult(all_0_4_4, op_b) = all_0_1_1, yields:
% 18.81/5.17 | (95) ? [v0] : ? [v1] : ? [v2] : (mult(v1, op_b) = v2 & mult(all_19_0_21, op_b) = v0 & mult(all_0_4_4, v2) = v0 & mult(op_b, all_19_1_22) = v1)
% 18.81/5.17 |
% 18.81/5.17 | Instantiating formula (10) with all_19_0_21, all_0_1_1, all_0_0_0, op_b, all_19_1_22 and discharging atoms mult(all_0_0_0, op_b) = all_0_1_1, mult(all_0_1_1, all_19_1_22) = all_19_0_21, yields:
% 18.81/5.17 | (96) ? [v0] : ? [v1] : ? [v2] : (mult(v1, op_b) = v2 & mult(all_19_0_21, op_b) = v0 & mult(all_0_0_0, v2) = v0 & mult(op_b, all_19_1_22) = v1)
% 18.81/5.17 |
% 18.81/5.17 | Instantiating formula (10) with all_17_0_19, all_0_3_3, all_0_4_4, op_a, all_13_1_15 and discharging atoms mult(all_0_3_3, all_13_1_15) = all_17_0_19, mult(all_0_4_4, op_a) = all_0_3_3, yields:
% 18.81/5.17 | (97) ? [v0] : ? [v1] : ? [v2] : (mult(v1, op_a) = v2 & mult(all_17_0_19, op_a) = v0 & mult(all_0_4_4, v2) = v0 & mult(op_a, all_13_1_15) = v1)
% 18.81/5.17 |
% 18.81/5.17 | Instantiating formula (10) with all_17_0_19, all_0_3_3, all_0_2_2, op_a, all_13_1_15 and discharging atoms mult(all_0_2_2, op_a) = all_0_3_3, mult(all_0_3_3, all_13_1_15) = all_17_0_19, yields:
% 18.81/5.17 | (98) ? [v0] : ? [v1] : ? [v2] : (mult(v1, op_a) = v2 & mult(all_17_0_19, op_a) = v0 & mult(all_0_2_2, v2) = v0 & mult(op_a, all_13_1_15) = v1)
% 18.81/5.17 |
% 18.81/5.17 | Instantiating formula (10) with op_a, op_b, op_a, all_13_1_15, all_19_1_22 and discharging atoms mult(op_b, all_19_1_22) = op_a, mult(op_a, all_13_1_15) = op_b, yields:
% 18.81/5.17 | (99) ? [v0] : ? [v1] : ? [v2] : (mult(v1, all_13_1_15) = v2 & mult(all_13_1_15, all_19_1_22) = v1 & mult(op_a, v2) = v0 & mult(op_a, all_13_1_15) = v0)
% 18.81/5.17 |
% 18.81/5.17 | Instantiating formula (10) with op_b, op_a, op_b, all_19_1_22, all_13_1_15 and discharging atoms mult(op_b, all_19_1_22) = op_a, mult(op_a, all_13_1_15) = op_b, yields:
% 18.81/5.17 | (100) ? [v0] : ? [v1] : ? [v2] : (mult(v1, all_19_1_22) = v2 & mult(all_19_1_22, all_13_1_15) = v1 & mult(op_b, v2) = v0 & mult(op_b, all_19_1_22) = v0)
% 18.81/5.17 |
% 18.81/5.17 | Instantiating formula (25) with all_17_0_19, op_b, unit, all_0_2_2, op_b, op_a and discharging atoms mult(all_0_2_2, op_b) = all_17_0_19, mult(op_b, op_a) = unit, mult(unit, op_b) = op_b, yields:
% 18.81/5.17 | (101) ? [v0] : ? [v1] : (mult(v1, op_b) = all_17_0_19 & mult(v0, op_a) = v1 & mult(all_0_2_2, op_b) = v0)
% 18.81/5.17 |
% 18.81/5.17 | Instantiating formula (10) with op_a, op_b, unit, op_b, all_19_1_22 and discharging atoms mult(op_b, all_19_1_22) = op_a, mult(unit, op_b) = op_b, yields:
% 18.81/5.17 | (102) ? [v0] : ? [v1] : ? [v2] : (mult(v1, op_b) = v2 & mult(op_b, all_19_1_22) = v1 & mult(op_a, op_b) = v0 & mult(unit, v2) = v0)
% 18.81/5.17 |
% 18.81/5.17 | Instantiating formula (25) with all_19_0_21, op_a, unit, all_0_0_0, op_a, op_b and discharging atoms mult(all_0_0_0, op_a) = all_19_0_21, mult(op_a, op_b) = unit, mult(unit, op_a) = op_a, yields:
% 18.81/5.17 | (103) ? [v0] : ? [v1] : (mult(v1, op_a) = all_19_0_21 & mult(v0, op_b) = v1 & mult(all_0_0_0, op_a) = v0)
% 18.81/5.17 |
% 18.81/5.17 | Instantiating formula (10) with op_b, op_a, unit, op_a, all_13_1_15 and discharging atoms mult(op_a, all_13_1_15) = op_b, mult(unit, op_a) = op_a, yields:
% 18.81/5.17 | (104) ? [v0] : ? [v1] : ? [v2] : (mult(v1, op_a) = v2 & mult(op_b, op_a) = v0 & mult(op_a, all_13_1_15) = v1 & mult(unit, v2) = v0)
% 18.81/5.17 |
% 18.81/5.17 | Instantiating (104) with all_54_0_40, all_54_1_41, all_54_2_42 yields:
% 18.81/5.17 | (105) mult(all_54_1_41, op_a) = all_54_0_40 & mult(op_b, op_a) = all_54_2_42 & mult(op_a, all_13_1_15) = all_54_1_41 & mult(unit, all_54_0_40) = all_54_2_42
% 18.81/5.17 |
% 18.81/5.17 | Applying alpha-rule on (105) yields:
% 18.81/5.17 | (106) mult(all_54_1_41, op_a) = all_54_0_40
% 18.81/5.17 | (107) mult(op_b, op_a) = all_54_2_42
% 18.81/5.17 | (108) mult(op_a, all_13_1_15) = all_54_1_41
% 18.81/5.17 | (109) mult(unit, all_54_0_40) = all_54_2_42
% 18.81/5.17 |
% 18.81/5.17 | Instantiating (102) with all_68_0_57, all_68_1_58, all_68_2_59 yields:
% 18.81/5.17 | (110) mult(all_68_1_58, op_b) = all_68_0_57 & mult(op_b, all_19_1_22) = all_68_1_58 & mult(op_a, op_b) = all_68_2_59 & mult(unit, all_68_0_57) = all_68_2_59
% 18.81/5.17 |
% 18.81/5.17 | Applying alpha-rule on (110) yields:
% 18.81/5.17 | (111) mult(all_68_1_58, op_b) = all_68_0_57
% 18.81/5.17 | (112) mult(op_b, all_19_1_22) = all_68_1_58
% 18.81/5.17 | (113) mult(op_a, op_b) = all_68_2_59
% 18.81/5.17 | (114) mult(unit, all_68_0_57) = all_68_2_59
% 18.81/5.17 |
% 18.81/5.17 | Instantiating (101) with all_72_0_62, all_72_1_63 yields:
% 18.81/5.17 | (115) mult(all_72_0_62, op_b) = all_17_0_19 & mult(all_72_1_63, op_a) = all_72_0_62 & mult(all_0_2_2, op_b) = all_72_1_63
% 18.81/5.17 |
% 18.81/5.17 | Applying alpha-rule on (115) yields:
% 18.81/5.17 | (116) mult(all_72_0_62, op_b) = all_17_0_19
% 18.81/5.17 | (117) mult(all_72_1_63, op_a) = all_72_0_62
% 18.81/5.18 | (118) mult(all_0_2_2, op_b) = all_72_1_63
% 18.81/5.18 |
% 18.81/5.18 | Instantiating (103) with all_78_0_68, all_78_1_69 yields:
% 18.81/5.18 | (119) mult(all_78_0_68, op_a) = all_19_0_21 & mult(all_78_1_69, op_b) = all_78_0_68 & mult(all_0_0_0, op_a) = all_78_1_69
% 18.81/5.18 |
% 18.81/5.18 | Applying alpha-rule on (119) yields:
% 18.81/5.18 | (120) mult(all_78_0_68, op_a) = all_19_0_21
% 18.81/5.18 | (121) mult(all_78_1_69, op_b) = all_78_0_68
% 18.81/5.18 | (122) mult(all_0_0_0, op_a) = all_78_1_69
% 18.81/5.18 |
% 18.81/5.18 | Instantiating (99) with all_90_0_84, all_90_1_85, all_90_2_86 yields:
% 18.81/5.18 | (123) mult(all_90_1_85, all_13_1_15) = all_90_0_84 & mult(all_13_1_15, all_19_1_22) = all_90_1_85 & mult(op_a, all_90_0_84) = all_90_2_86 & mult(op_a, all_13_1_15) = all_90_2_86
% 18.81/5.18 |
% 18.81/5.18 | Applying alpha-rule on (123) yields:
% 18.81/5.18 | (124) mult(all_90_1_85, all_13_1_15) = all_90_0_84
% 18.81/5.18 | (125) mult(all_13_1_15, all_19_1_22) = all_90_1_85
% 18.81/5.18 | (126) mult(op_a, all_90_0_84) = all_90_2_86
% 18.81/5.18 | (127) mult(op_a, all_13_1_15) = all_90_2_86
% 18.81/5.18 |
% 18.81/5.18 | Instantiating (100) with all_94_0_90, all_94_1_91, all_94_2_92 yields:
% 18.81/5.18 | (128) mult(all_94_1_91, all_19_1_22) = all_94_0_90 & mult(all_19_1_22, all_13_1_15) = all_94_1_91 & mult(op_b, all_94_0_90) = all_94_2_92 & mult(op_b, all_19_1_22) = all_94_2_92
% 18.81/5.18 |
% 18.81/5.18 | Applying alpha-rule on (128) yields:
% 18.81/5.18 | (129) mult(all_94_1_91, all_19_1_22) = all_94_0_90
% 18.81/5.18 | (130) mult(all_19_1_22, all_13_1_15) = all_94_1_91
% 18.81/5.18 | (131) mult(op_b, all_94_0_90) = all_94_2_92
% 18.81/5.18 | (132) mult(op_b, all_19_1_22) = all_94_2_92
% 18.81/5.18 |
% 18.81/5.18 | Instantiating (97) with all_102_0_101, all_102_1_102, all_102_2_103 yields:
% 18.81/5.18 | (133) mult(all_102_1_102, op_a) = all_102_0_101 & mult(all_17_0_19, op_a) = all_102_2_103 & mult(all_0_4_4, all_102_0_101) = all_102_2_103 & mult(op_a, all_13_1_15) = all_102_1_102
% 18.81/5.18 |
% 18.81/5.18 | Applying alpha-rule on (133) yields:
% 18.81/5.18 | (134) mult(all_102_1_102, op_a) = all_102_0_101
% 18.81/5.18 | (135) mult(all_17_0_19, op_a) = all_102_2_103
% 18.81/5.18 | (136) mult(all_0_4_4, all_102_0_101) = all_102_2_103
% 18.81/5.18 | (137) mult(op_a, all_13_1_15) = all_102_1_102
% 18.81/5.18 |
% 18.81/5.18 | Instantiating (98) with all_116_0_117, all_116_1_118, all_116_2_119 yields:
% 18.81/5.18 | (138) mult(all_116_1_118, op_a) = all_116_0_117 & mult(all_17_0_19, op_a) = all_116_2_119 & mult(all_0_2_2, all_116_0_117) = all_116_2_119 & mult(op_a, all_13_1_15) = all_116_1_118
% 18.81/5.18 |
% 18.81/5.18 | Applying alpha-rule on (138) yields:
% 18.81/5.18 | (139) mult(all_116_1_118, op_a) = all_116_0_117
% 18.81/5.18 | (140) mult(all_17_0_19, op_a) = all_116_2_119
% 18.81/5.18 | (141) mult(all_0_2_2, all_116_0_117) = all_116_2_119
% 18.81/5.18 | (142) mult(op_a, all_13_1_15) = all_116_1_118
% 18.81/5.18 |
% 18.81/5.18 | Instantiating (96) with all_160_0_168, all_160_1_169, all_160_2_170 yields:
% 18.81/5.18 | (143) mult(all_160_1_169, op_b) = all_160_0_168 & mult(all_19_0_21, op_b) = all_160_2_170 & mult(all_0_0_0, all_160_0_168) = all_160_2_170 & mult(op_b, all_19_1_22) = all_160_1_169
% 18.81/5.18 |
% 18.81/5.18 | Applying alpha-rule on (143) yields:
% 18.81/5.18 | (144) mult(all_160_1_169, op_b) = all_160_0_168
% 18.81/5.18 | (145) mult(all_19_0_21, op_b) = all_160_2_170
% 18.81/5.18 | (146) mult(all_0_0_0, all_160_0_168) = all_160_2_170
% 18.81/5.18 | (147) mult(op_b, all_19_1_22) = all_160_1_169
% 18.81/5.18 |
% 18.81/5.18 | Instantiating (95) with all_162_0_171, all_162_1_172, all_162_2_173 yields:
% 18.81/5.18 | (148) mult(all_162_1_172, op_b) = all_162_0_171 & mult(all_19_0_21, op_b) = all_162_2_173 & mult(all_0_4_4, all_162_0_171) = all_162_2_173 & mult(op_b, all_19_1_22) = all_162_1_172
% 18.81/5.18 |
% 18.81/5.18 | Applying alpha-rule on (148) yields:
% 18.81/5.18 | (149) mult(all_162_1_172, op_b) = all_162_0_171
% 18.81/5.18 | (150) mult(all_19_0_21, op_b) = all_162_2_173
% 18.81/5.18 | (151) mult(all_0_4_4, all_162_0_171) = all_162_2_173
% 18.81/5.18 | (152) mult(op_b, all_19_1_22) = all_162_1_172
% 18.81/5.18 |
% 18.81/5.18 | Instantiating formula (11) with all_19_0_21, op_b, all_160_2_170, all_162_2_173 and discharging atoms mult(all_19_0_21, op_b) = all_162_2_173, mult(all_19_0_21, op_b) = all_160_2_170, yields:
% 18.81/5.18 | (153) all_162_2_173 = all_160_2_170
% 18.81/5.18 |
% 18.81/5.18 | Instantiating formula (11) with all_17_0_19, op_a, all_102_2_103, all_116_2_119 and discharging atoms mult(all_17_0_19, op_a) = all_116_2_119, mult(all_17_0_19, op_a) = all_102_2_103, yields:
% 18.81/5.18 | (154) all_116_2_119 = all_102_2_103
% 18.81/5.18 |
% 18.81/5.18 | Instantiating formula (11) with all_0_0_0, op_a, all_78_1_69, all_19_0_21 and discharging atoms mult(all_0_0_0, op_a) = all_78_1_69, mult(all_0_0_0, op_a) = all_19_0_21, yields:
% 18.81/5.18 | (155) all_78_1_69 = all_19_0_21
% 18.81/5.18 |
% 18.81/5.18 | Instantiating formula (11) with all_0_2_2, op_b, all_72_1_63, all_17_0_19 and discharging atoms mult(all_0_2_2, op_b) = all_72_1_63, mult(all_0_2_2, op_b) = all_17_0_19, yields:
% 18.81/5.18 | (156) all_72_1_63 = all_17_0_19
% 18.81/5.18 |
% 18.81/5.18 | Instantiating formula (11) with op_b, all_19_1_22, all_160_1_169, all_162_1_172 and discharging atoms mult(op_b, all_19_1_22) = all_162_1_172, mult(op_b, all_19_1_22) = all_160_1_169, yields:
% 18.81/5.18 | (157) all_162_1_172 = all_160_1_169
% 18.81/5.18 |
% 18.81/5.18 | Instantiating formula (11) with op_b, all_19_1_22, all_94_2_92, op_a and discharging atoms mult(op_b, all_19_1_22) = all_94_2_92, mult(op_b, all_19_1_22) = op_a, yields:
% 18.81/5.18 | (158) all_94_2_92 = op_a
% 18.81/5.18 |
% 18.81/5.18 | Instantiating formula (11) with op_b, all_19_1_22, all_94_2_92, all_160_1_169 and discharging atoms mult(op_b, all_19_1_22) = all_160_1_169, mult(op_b, all_19_1_22) = all_94_2_92, yields:
% 18.81/5.18 | (159) all_160_1_169 = all_94_2_92
% 18.81/5.18 |
% 18.81/5.18 | Instantiating formula (11) with op_b, all_19_1_22, all_68_1_58, all_162_1_172 and discharging atoms mult(op_b, all_19_1_22) = all_162_1_172, mult(op_b, all_19_1_22) = all_68_1_58, yields:
% 18.81/5.18 | (160) all_162_1_172 = all_68_1_58
% 18.81/5.18 |
% 18.81/5.18 | Instantiating formula (11) with op_b, op_a, all_54_2_42, unit and discharging atoms mult(op_b, op_a) = all_54_2_42, mult(op_b, op_a) = unit, yields:
% 18.81/5.19 | (161) all_54_2_42 = unit
% 18.81/5.19 |
% 18.81/5.19 | Instantiating formula (11) with op_a, all_13_1_15, all_102_1_102, op_b and discharging atoms mult(op_a, all_13_1_15) = all_102_1_102, mult(op_a, all_13_1_15) = op_b, yields:
% 18.81/5.19 | (162) all_102_1_102 = op_b
% 18.81/5.19 |
% 18.81/5.19 | Instantiating formula (11) with op_a, all_13_1_15, all_102_1_102, all_116_1_118 and discharging atoms mult(op_a, all_13_1_15) = all_116_1_118, mult(op_a, all_13_1_15) = all_102_1_102, yields:
% 18.81/5.19 | (163) all_116_1_118 = all_102_1_102
% 18.81/5.19 |
% 18.81/5.19 | Instantiating formula (11) with op_a, all_13_1_15, all_90_2_86, all_102_1_102 and discharging atoms mult(op_a, all_13_1_15) = all_102_1_102, mult(op_a, all_13_1_15) = all_90_2_86, yields:
% 18.81/5.19 | (164) all_102_1_102 = all_90_2_86
% 18.81/5.19 |
% 18.81/5.19 | Instantiating formula (11) with op_a, all_13_1_15, all_54_1_41, all_116_1_118 and discharging atoms mult(op_a, all_13_1_15) = all_116_1_118, mult(op_a, all_13_1_15) = all_54_1_41, yields:
% 18.81/5.19 | (165) all_116_1_118 = all_54_1_41
% 18.81/5.19 |
% 18.81/5.19 | Instantiating formula (11) with op_a, op_b, all_68_2_59, unit and discharging atoms mult(op_a, op_b) = all_68_2_59, mult(op_a, op_b) = unit, yields:
% 18.81/5.19 | (166) all_68_2_59 = unit
% 18.81/5.19 |
% 18.81/5.19 | Combining equations (157,160) yields a new equation:
% 18.81/5.19 | (167) all_160_1_169 = all_68_1_58
% 18.81/5.19 |
% 18.81/5.19 | Simplifying 167 yields:
% 18.81/5.19 | (168) all_160_1_169 = all_68_1_58
% 18.81/5.19 |
% 18.81/5.19 | Combining equations (159,168) yields a new equation:
% 18.81/5.19 | (169) all_94_2_92 = all_68_1_58
% 18.81/5.19 |
% 18.81/5.19 | Simplifying 169 yields:
% 18.81/5.19 | (170) all_94_2_92 = all_68_1_58
% 18.81/5.19 |
% 18.81/5.19 | Combining equations (163,165) yields a new equation:
% 18.81/5.19 | (171) all_102_1_102 = all_54_1_41
% 18.81/5.19 |
% 18.81/5.19 | Simplifying 171 yields:
% 18.81/5.19 | (172) all_102_1_102 = all_54_1_41
% 18.81/5.19 |
% 18.81/5.19 | Combining equations (162,164) yields a new equation:
% 18.81/5.19 | (173) all_90_2_86 = op_b
% 18.81/5.19 |
% 18.81/5.19 | Combining equations (172,164) yields a new equation:
% 18.81/5.19 | (174) all_90_2_86 = all_54_1_41
% 18.81/5.19 |
% 18.81/5.19 | Combining equations (158,170) yields a new equation:
% 18.81/5.19 | (175) all_68_1_58 = op_a
% 18.81/5.19 |
% 18.81/5.19 | Combining equations (173,174) yields a new equation:
% 18.81/5.19 | (176) all_54_1_41 = op_b
% 18.81/5.19 |
% 18.81/5.19 | Combining equations (176,174) yields a new equation:
% 18.81/5.19 | (173) all_90_2_86 = op_b
% 18.81/5.19 |
% 18.81/5.19 | Combining equations (173,164) yields a new equation:
% 18.81/5.19 | (162) all_102_1_102 = op_b
% 18.81/5.19 |
% 18.81/5.19 | Combining equations (176,165) yields a new equation:
% 18.81/5.19 | (179) all_116_1_118 = op_b
% 18.81/5.19 |
% 18.81/5.19 | Combining equations (175,168) yields a new equation:
% 18.81/5.19 | (180) all_160_1_169 = op_a
% 18.81/5.19 |
% 18.81/5.19 | Combining equations (175,160) yields a new equation:
% 18.81/5.19 | (181) all_162_1_172 = op_a
% 18.81/5.19 |
% 18.81/5.19 | From (181) and (149) follows:
% 18.81/5.19 | (182) mult(op_a, op_b) = all_162_0_171
% 18.81/5.19 |
% 18.81/5.19 | From (180) and (144) follows:
% 18.81/5.19 | (183) mult(op_a, op_b) = all_160_0_168
% 18.81/5.19 |
% 18.81/5.19 | From (179) and (139) follows:
% 18.81/5.19 | (184) mult(op_b, op_a) = all_116_0_117
% 18.81/5.19 |
% 18.81/5.19 | From (162) and (134) follows:
% 18.81/5.19 | (185) mult(op_b, op_a) = all_102_0_101
% 18.81/5.19 |
% 18.81/5.19 | From (155) and (121) follows:
% 18.81/5.19 | (186) mult(all_19_0_21, op_b) = all_78_0_68
% 18.81/5.19 |
% 18.81/5.19 | From (156) and (117) follows:
% 18.81/5.19 | (187) mult(all_17_0_19, op_a) = all_72_0_62
% 18.81/5.19 |
% 18.81/5.19 | From (153) and (150) follows:
% 18.81/5.19 | (145) mult(all_19_0_21, op_b) = all_160_2_170
% 18.81/5.19 |
% 18.81/5.19 | From (154) and (140) follows:
% 18.81/5.19 | (135) mult(all_17_0_19, op_a) = all_102_2_103
% 18.81/5.19 |
% 18.81/5.19 | From (154) and (141) follows:
% 18.81/5.19 | (190) mult(all_0_2_2, all_116_0_117) = all_102_2_103
% 18.81/5.19 |
% 18.81/5.19 | From (153) and (151) follows:
% 18.81/5.19 | (191) mult(all_0_4_4, all_162_0_171) = all_160_2_170
% 18.81/5.19 |
% 18.81/5.19 | From (161) and (107) follows:
% 18.81/5.19 | (16) mult(op_b, op_a) = unit
% 18.81/5.19 |
% 18.81/5.19 | From (166) and (113) follows:
% 18.81/5.19 | (14) mult(op_a, op_b) = unit
% 18.81/5.19 |
% 18.81/5.19 | Instantiating formula (11) with all_19_0_21, op_b, all_78_0_68, all_160_2_170 and discharging atoms mult(all_19_0_21, op_b) = all_160_2_170, mult(all_19_0_21, op_b) = all_78_0_68, yields:
% 18.81/5.20 | (194) all_160_2_170 = all_78_0_68
% 18.81/5.20 |
% 18.81/5.20 | Instantiating formula (11) with all_17_0_19, op_a, all_72_0_62, all_102_2_103 and discharging atoms mult(all_17_0_19, op_a) = all_102_2_103, mult(all_17_0_19, op_a) = all_72_0_62, yields:
% 18.81/5.20 | (195) all_102_2_103 = all_72_0_62
% 18.81/5.20 |
% 18.81/5.20 | Instantiating formula (11) with op_b, op_a, all_116_0_117, unit and discharging atoms mult(op_b, op_a) = all_116_0_117, mult(op_b, op_a) = unit, yields:
% 18.81/5.20 | (196) all_116_0_117 = unit
% 18.81/5.20 |
% 18.81/5.20 | Instantiating formula (11) with op_b, op_a, all_102_0_101, all_116_0_117 and discharging atoms mult(op_b, op_a) = all_116_0_117, mult(op_b, op_a) = all_102_0_101, yields:
% 18.81/5.20 | (197) all_116_0_117 = all_102_0_101
% 18.81/5.20 |
% 18.81/5.20 | Instantiating formula (11) with op_a, op_b, all_162_0_171, unit and discharging atoms mult(op_a, op_b) = all_162_0_171, mult(op_a, op_b) = unit, yields:
% 18.81/5.20 | (198) all_162_0_171 = unit
% 18.81/5.20 |
% 18.81/5.20 | Instantiating formula (11) with op_a, op_b, all_160_0_168, all_162_0_171 and discharging atoms mult(op_a, op_b) = all_162_0_171, mult(op_a, op_b) = all_160_0_168, yields:
% 18.81/5.20 | (199) all_162_0_171 = all_160_0_168
% 18.81/5.20 |
% 18.81/5.20 | Combining equations (198,199) yields a new equation:
% 18.81/5.20 | (200) all_160_0_168 = unit
% 18.81/5.20 |
% 18.81/5.20 | Combining equations (197,196) yields a new equation:
% 18.81/5.20 | (201) all_102_0_101 = unit
% 18.81/5.20 |
% 18.81/5.20 | Simplifying 201 yields:
% 18.81/5.20 | (202) all_102_0_101 = unit
% 18.81/5.20 |
% 18.81/5.20 | Combining equations (200,199) yields a new equation:
% 18.81/5.20 | (198) all_162_0_171 = unit
% 18.81/5.20 |
% 18.81/5.20 | From (200)(194) and (146) follows:
% 18.81/5.20 | (204) mult(all_0_0_0, unit) = all_78_0_68
% 18.81/5.20 |
% 18.81/5.20 | From (196)(195) and (190) follows:
% 18.81/5.20 | (205) mult(all_0_2_2, unit) = all_72_0_62
% 18.81/5.20 |
% 18.81/5.20 | From (198)(194) and (191) follows:
% 18.81/5.20 | (206) mult(all_0_4_4, unit) = all_78_0_68
% 18.81/5.20 |
% 18.81/5.20 | From (202)(195) and (136) follows:
% 18.81/5.20 | (207) mult(all_0_4_4, unit) = all_72_0_62
% 18.81/5.20 |
% 18.81/5.20 | Instantiating formula (20) with all_78_0_68, all_0_0_0 and discharging atoms mult(all_0_0_0, unit) = all_78_0_68, yields:
% 18.81/5.20 | (208) all_78_0_68 = all_0_0_0
% 18.81/5.20 |
% 19.14/5.20 | Instantiating formula (20) with all_72_0_62, all_0_2_2 and discharging atoms mult(all_0_2_2, unit) = all_72_0_62, yields:
% 19.14/5.20 | (209) all_72_0_62 = all_0_2_2
% 19.14/5.20 |
% 19.14/5.20 | Instantiating formula (20) with all_78_0_68, all_0_4_4 and discharging atoms mult(all_0_4_4, unit) = all_78_0_68, yields:
% 19.14/5.20 | (210) all_78_0_68 = all_0_4_4
% 19.14/5.20 |
% 19.14/5.20 | Instantiating formula (11) with all_0_4_4, unit, all_72_0_62, all_78_0_68 and discharging atoms mult(all_0_4_4, unit) = all_78_0_68, mult(all_0_4_4, unit) = all_72_0_62, yields:
% 19.14/5.20 | (211) all_78_0_68 = all_72_0_62
% 19.14/5.20 |
% 19.14/5.20 | Combining equations (211,210) yields a new equation:
% 19.14/5.20 | (212) all_72_0_62 = all_0_4_4
% 19.14/5.20 |
% 19.14/5.20 | Simplifying 212 yields:
% 19.14/5.20 | (213) all_72_0_62 = all_0_4_4
% 19.14/5.20 |
% 19.14/5.20 | Combining equations (208,210) yields a new equation:
% 19.14/5.20 | (214) all_0_0_0 = all_0_4_4
% 19.14/5.20 |
% 19.14/5.20 | Simplifying 214 yields:
% 19.14/5.20 | (215) all_0_0_0 = all_0_4_4
% 19.14/5.20 |
% 19.14/5.20 | Combining equations (213,209) yields a new equation:
% 19.14/5.20 | (216) all_0_2_2 = all_0_4_4
% 19.14/5.20 |
% 19.14/5.20 +-Applying beta-rule and splitting (21), into two cases.
% 19.14/5.20 |-Branch one:
% 19.14/5.20 | (217) ~ (all_0_0_0 = all_0_4_4)
% 19.14/5.20 |
% 19.14/5.20 | Equations (215) can reduce 217 to:
% 19.14/5.20 | (218) $false
% 19.14/5.20 |
% 19.14/5.20 |-The branch is then unsatisfiable
% 19.14/5.20 |-Branch two:
% 19.14/5.20 | (215) all_0_0_0 = all_0_4_4
% 19.14/5.20 | (220) ~ (all_0_2_2 = all_0_4_4)
% 19.14/5.20 |
% 19.14/5.20 | Equations (216) can reduce 220 to:
% 19.14/5.20 | (218) $false
% 19.14/5.20 |
% 19.14/5.20 |-The branch is then unsatisfiable
% 19.14/5.20 % SZS output end Proof for theBenchmark
% 19.14/5.20
% 19.14/5.20 4581ms
%------------------------------------------------------------------------------