%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : ALG029+1 : TPTP v8.1.0. Released v2.7.0.
% 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 : Thu Jul 14 15:33:49 EDT 2022

% Result   : Theorem 2.54s 1.29s
% Output   : Proof 4.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : ALG029+1 : TPTP v8.1.0. Released v2.7.0.
% 0.10/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun  9 03:30:10 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.59/0.59          ____       _                          
% 0.59/0.59    ___  / __ \_____(_)___  ________  __________
% 0.59/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.59/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.59/0.59  
% 0.59/0.59  A Theorem Prover for First-Order Logic
% 0.59/0.59  (ePrincess v.1.0)
% 0.59/0.59  
% 0.59/0.59  (c) Philipp Rümmer, 2009-2015
% 0.59/0.59  (c) Peter Backeman, 2014-2015
% 0.59/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.60  Bug reports to peter@backeman.se
% 0.59/0.60  
% 0.59/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.60  
% 0.59/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.46/0.90  Prover 0: Preprocessing ...
% 1.81/1.08  Prover 0: Constructing countermodel ...
% 2.54/1.28  Prover 0: proved (639ms)
% 2.54/1.29  
% 2.54/1.29  No countermodel exists, formula is valid
% 2.54/1.29  % SZS status Theorem for theBenchmark
% 2.54/1.29  
% 2.54/1.29  Generating proof ... found it (size 150)
% 4.52/1.79  
% 4.52/1.79  % SZS output start Proof for theBenchmark
% 4.52/1.79  Assumed formulas after preprocessing and simplification: 
% 4.52/1.79  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : ( ~ (v3 = v2) & op2(v1, v0) = v3 & op2(v0, v1) = v2 & sorti2(v1) & sorti2(v0) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (op2(v7, v6) = v5) |  ~ (op2(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (op1(v7, v6) = v5) |  ~ (op1(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (j(v6) = v5) |  ~ (j(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (h(v6) = v5) |  ~ (h(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (op2(v4, v5) = v6) |  ~ sorti2(v5) |  ~ sorti2(v4) | sorti2(v6)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (op1(v5, v4) = v6) |  ~ sorti1(v5) |  ~ sorti1(v4) | op1(v4, v5) = v6) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (op1(v4, v5) = v6) |  ~ sorti1(v5) |  ~ sorti1(v4) | op1(v5, v4) = v6) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (op1(v4, v5) = v6) |  ~ sorti1(v5) |  ~ sorti1(v4) | sorti1(v6)) &  ! [v4] : ( ~ sorti2(v4) |  ? [v5] : (j(v4) = v5 & h(v5) = v4)) &  ! [v4] : ( ~ sorti2(v4) |  ? [v5] : (j(v4) = v5 & sorti1(v5))) &  ! [v4] : ( ~ sorti2(v4) |  ? [v5] : (j(v4) = v5 &  ! [v6] : ( ~ sorti2(v6) |  ? [v7] :  ? [v8] :  ? [v9] : (j(v7) = v8 & j(v6) = v9 & op2(v4, v6) = v7 & op1(v5, v9) = v8)))) &  ! [v4] : ( ~ sorti1(v4) |  ? [v5] : (j(v5) = v4 & h(v4) = v5)) &  ! [v4] : ( ~ sorti1(v4) |  ? [v5] : (h(v4) = v5 & sorti2(v5))) &  ! [v4] : ( ~ sorti1(v4) |  ? [v5] : (h(v4) = v5 &  ! [v6] : ( ~ sorti1(v6) |  ? [v7] :  ? [v8] :  ? [v9] : (h(v7) = v8 & h(v6) = v9 & op2(v5, v9) = v8 & op1(v4, v6) = v7)))))
% 4.70/1.82  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 4.70/1.82  | (1)  ~ (all_0_0_0 = all_0_1_1) & op2(all_0_2_2, all_0_3_3) = all_0_0_0 & op2(all_0_3_3, all_0_2_2) = all_0_1_1 & sorti2(all_0_2_2) & sorti2(all_0_3_3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (op2(v3, v2) = v1) |  ~ (op2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (op1(v3, v2) = v1) |  ~ (op1(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (j(v2) = v1) |  ~ (j(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (h(v2) = v1) |  ~ (h(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (op2(v0, v1) = v2) |  ~ sorti2(v1) |  ~ sorti2(v0) | sorti2(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (op1(v1, v0) = v2) |  ~ sorti1(v1) |  ~ sorti1(v0) | op1(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (op1(v0, v1) = v2) |  ~ sorti1(v1) |  ~ sorti1(v0) | op1(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (op1(v0, v1) = v2) |  ~ sorti1(v1) |  ~ sorti1(v0) | sorti1(v2)) &  ! [v0] : ( ~ sorti2(v0) |  ? [v1] : (j(v0) = v1 & h(v1) = v0)) &  ! [v0] : ( ~ sorti2(v0) |  ? [v1] : (j(v0) = v1 & sorti1(v1))) &  ! [v0] : ( ~ sorti2(v0) |  ? [v1] : (j(v0) = v1 &  ! [v2] : ( ~ sorti2(v2) |  ? [v3] :  ? [v4] :  ? [v5] : (j(v3) = v4 & j(v2) = v5 & op2(v0, v2) = v3 & op1(v1, v5) = v4)))) &  ! [v0] : ( ~ sorti1(v0) |  ? [v1] : (j(v1) = v0 & h(v0) = v1)) &  ! [v0] : ( ~ sorti1(v0) |  ? [v1] : (h(v0) = v1 & sorti2(v1))) &  ! [v0] : ( ~ sorti1(v0) |  ? [v1] : (h(v0) = v1 &  ! [v2] : ( ~ sorti1(v2) |  ? [v3] :  ? [v4] :  ? [v5] : (h(v3) = v4 & h(v2) = v5 & op2(v1, v5) = v4 & op1(v0, v2) = v3))))
% 4.70/1.83  |
% 4.70/1.83  | Applying alpha-rule on (1) yields:
% 4.70/1.83  | (2)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (op2(v0, v1) = v2) |  ~ sorti2(v1) |  ~ sorti2(v0) | sorti2(v2))
% 4.70/1.83  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (op2(v3, v2) = v1) |  ~ (op2(v3, v2) = v0))
% 4.70/1.83  | (4)  ! [v0] : ( ~ sorti2(v0) |  ? [v1] : (j(v0) = v1 & h(v1) = v0))
% 4.70/1.83  | (5)  ! [v0] : ( ~ sorti2(v0) |  ? [v1] : (j(v0) = v1 &  ! [v2] : ( ~ sorti2(v2) |  ? [v3] :  ? [v4] :  ? [v5] : (j(v3) = v4 & j(v2) = v5 & op2(v0, v2) = v3 & op1(v1, v5) = v4))))
% 4.70/1.83  | (6) sorti2(all_0_3_3)
% 4.70/1.83  | (7) op2(all_0_3_3, all_0_2_2) = all_0_1_1
% 4.70/1.83  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (op1(v1, v0) = v2) |  ~ sorti1(v1) |  ~ sorti1(v0) | op1(v0, v1) = v2)
% 4.70/1.83  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (op1(v0, v1) = v2) |  ~ sorti1(v1) |  ~ sorti1(v0) | op1(v1, v0) = v2)
% 4.70/1.83  | (10)  ! [v0] : ( ~ sorti2(v0) |  ? [v1] : (j(v0) = v1 & sorti1(v1)))
% 4.70/1.83  | (11) sorti2(all_0_2_2)
% 4.70/1.83  | (12)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (j(v2) = v1) |  ~ (j(v2) = v0))
% 4.70/1.83  | (13)  ! [v0] : ( ~ sorti1(v0) |  ? [v1] : (j(v1) = v0 & h(v0) = v1))
% 4.70/1.83  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (op1(v0, v1) = v2) |  ~ sorti1(v1) |  ~ sorti1(v0) | sorti1(v2))
% 4.70/1.83  | (15)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (h(v2) = v1) |  ~ (h(v2) = v0))
% 4.70/1.83  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (op1(v3, v2) = v1) |  ~ (op1(v3, v2) = v0))
% 4.70/1.83  | (17)  ! [v0] : ( ~ sorti1(v0) |  ? [v1] : (h(v0) = v1 & sorti2(v1)))
% 4.70/1.83  | (18) op2(all_0_2_2, all_0_3_3) = all_0_0_0
% 4.70/1.83  | (19)  ~ (all_0_0_0 = all_0_1_1)
% 4.70/1.83  | (20)  ! [v0] : ( ~ sorti1(v0) |  ? [v1] : (h(v0) = v1 &  ! [v2] : ( ~ sorti1(v2) |  ? [v3] :  ? [v4] :  ? [v5] : (h(v3) = v4 & h(v2) = v5 & op2(v1, v5) = v4 & op1(v0, v2) = v3))))
% 4.70/1.83  |
% 4.70/1.83  | Instantiating formula (10) with all_0_2_2 and discharging atoms sorti2(all_0_2_2), yields:
% 4.70/1.83  | (21)  ? [v0] : (j(all_0_2_2) = v0 & sorti1(v0))
% 4.70/1.83  |
% 4.70/1.83  | Instantiating formula (5) with all_0_2_2 and discharging atoms sorti2(all_0_2_2), yields:
% 4.70/1.84  | (22)  ? [v0] : (j(all_0_2_2) = v0 &  ! [v1] : ( ~ sorti2(v1) |  ? [v2] :  ? [v3] :  ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_0_2_2, v1) = v2 & op1(v0, v4) = v3)))
% 4.70/1.84  |
% 4.70/1.84  | Instantiating formula (2) with all_0_0_0, all_0_3_3, all_0_2_2 and discharging atoms op2(all_0_2_2, all_0_3_3) = all_0_0_0, sorti2(all_0_2_2), sorti2(all_0_3_3), yields:
% 4.70/1.84  | (23) sorti2(all_0_0_0)
% 4.70/1.84  |
% 4.70/1.84  | Instantiating formula (2) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms op2(all_0_3_3, all_0_2_2) = all_0_1_1, sorti2(all_0_2_2), sorti2(all_0_3_3), yields:
% 4.70/1.84  | (24) sorti2(all_0_1_1)
% 4.70/1.84  |
% 4.70/1.84  | Instantiating formula (4) with all_0_3_3 and discharging atoms sorti2(all_0_3_3), yields:
% 4.70/1.84  | (25)  ? [v0] : (j(all_0_3_3) = v0 & h(v0) = all_0_3_3)
% 4.70/1.84  |
% 4.70/1.84  | Instantiating formula (10) with all_0_3_3 and discharging atoms sorti2(all_0_3_3), yields:
% 4.70/1.84  | (26)  ? [v0] : (j(all_0_3_3) = v0 & sorti1(v0))
% 4.70/1.84  |
% 4.70/1.84  | Instantiating formula (5) with all_0_3_3 and discharging atoms sorti2(all_0_3_3), yields:
% 4.70/1.84  | (27)  ? [v0] : (j(all_0_3_3) = v0 &  ! [v1] : ( ~ sorti2(v1) |  ? [v2] :  ? [v3] :  ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_0_3_3, v1) = v2 & op1(v0, v4) = v3)))
% 4.70/1.84  |
% 4.70/1.84  | Instantiating (21) with all_9_0_4 yields:
% 4.70/1.84  | (28) j(all_0_2_2) = all_9_0_4 & sorti1(all_9_0_4)
% 4.70/1.84  |
% 4.70/1.84  | Applying alpha-rule on (28) yields:
% 4.70/1.84  | (29) j(all_0_2_2) = all_9_0_4
% 4.70/1.84  | (30) sorti1(all_9_0_4)
% 4.70/1.84  |
% 4.70/1.84  | Instantiating (27) with all_11_0_5 yields:
% 4.70/1.84  | (31) j(all_0_3_3) = all_11_0_5 &  ! [v0] : ( ~ sorti2(v0) |  ? [v1] :  ? [v2] :  ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_0_3_3, v0) = v1 & op1(all_11_0_5, v3) = v2))
% 4.70/1.84  |
% 4.70/1.84  | Applying alpha-rule on (31) yields:
% 4.70/1.84  | (32) j(all_0_3_3) = all_11_0_5
% 4.70/1.84  | (33)  ! [v0] : ( ~ sorti2(v0) |  ? [v1] :  ? [v2] :  ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_0_3_3, v0) = v1 & op1(all_11_0_5, v3) = v2))
% 4.70/1.84  |
% 4.70/1.84  | Instantiating formula (33) with all_0_2_2 and discharging atoms sorti2(all_0_2_2), yields:
% 4.70/1.84  | (34)  ? [v0] :  ? [v1] :  ? [v2] : (j(v0) = v1 & j(all_0_2_2) = v2 & op2(all_0_3_3, all_0_2_2) = v0 & op1(all_11_0_5, v2) = v1)
% 4.70/1.84  |
% 4.70/1.84  | Instantiating formula (33) with all_0_3_3 and discharging atoms sorti2(all_0_3_3), yields:
% 4.70/1.84  | (35)  ? [v0] :  ? [v1] :  ? [v2] : (j(v0) = v1 & j(all_0_3_3) = v2 & op2(all_0_3_3, all_0_3_3) = v0 & op1(all_11_0_5, v2) = v1)
% 4.70/1.84  |
% 4.70/1.84  | Instantiating (26) with all_14_0_6 yields:
% 4.70/1.84  | (36) j(all_0_3_3) = all_14_0_6 & sorti1(all_14_0_6)
% 4.70/1.84  |
% 4.70/1.84  | Applying alpha-rule on (36) yields:
% 4.70/1.84  | (37) j(all_0_3_3) = all_14_0_6
% 4.70/1.84  | (38) sorti1(all_14_0_6)
% 4.70/1.84  |
% 4.70/1.84  | Instantiating (25) with all_18_0_8 yields:
% 4.70/1.84  | (39) j(all_0_3_3) = all_18_0_8 & h(all_18_0_8) = all_0_3_3
% 4.70/1.84  |
% 4.70/1.84  | Applying alpha-rule on (39) yields:
% 4.70/1.84  | (40) j(all_0_3_3) = all_18_0_8
% 4.70/1.84  | (41) h(all_18_0_8) = all_0_3_3
% 4.70/1.84  |
% 4.70/1.84  | Instantiating (22) with all_20_0_9 yields:
% 4.70/1.84  | (42) j(all_0_2_2) = all_20_0_9 &  ! [v0] : ( ~ sorti2(v0) |  ? [v1] :  ? [v2] :  ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_0_2_2, v0) = v1 & op1(all_20_0_9, v3) = v2))
% 4.70/1.84  |
% 4.70/1.84  | Applying alpha-rule on (42) yields:
% 4.70/1.84  | (43) j(all_0_2_2) = all_20_0_9
% 4.70/1.84  | (44)  ! [v0] : ( ~ sorti2(v0) |  ? [v1] :  ? [v2] :  ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_0_2_2, v0) = v1 & op1(all_20_0_9, v3) = v2))
% 4.70/1.84  |
% 4.70/1.84  | Instantiating formula (44) with all_0_2_2 and discharging atoms sorti2(all_0_2_2), yields:
% 4.70/1.84  | (45)  ? [v0] :  ? [v1] :  ? [v2] : (j(v0) = v1 & j(all_0_2_2) = v2 & op2(all_0_2_2, all_0_2_2) = v0 & op1(all_20_0_9, v2) = v1)
% 4.70/1.84  |
% 4.70/1.84  | Instantiating formula (44) with all_0_3_3 and discharging atoms sorti2(all_0_3_3), yields:
% 4.70/1.84  | (46)  ? [v0] :  ? [v1] :  ? [v2] : (j(v0) = v1 & j(all_0_3_3) = v2 & op2(all_0_2_2, all_0_3_3) = v0 & op1(all_20_0_9, v2) = v1)
% 4.70/1.84  |
% 4.70/1.84  | Instantiating (35) with all_23_0_10, all_23_1_11, all_23_2_12 yields:
% 4.70/1.84  | (47) j(all_23_2_12) = all_23_1_11 & j(all_0_3_3) = all_23_0_10 & op2(all_0_3_3, all_0_3_3) = all_23_2_12 & op1(all_11_0_5, all_23_0_10) = all_23_1_11
% 4.70/1.84  |
% 4.70/1.84  | Applying alpha-rule on (47) yields:
% 4.70/1.84  | (48) j(all_23_2_12) = all_23_1_11
% 4.70/1.84  | (49) j(all_0_3_3) = all_23_0_10
% 4.70/1.84  | (50) op2(all_0_3_3, all_0_3_3) = all_23_2_12
% 4.70/1.84  | (51) op1(all_11_0_5, all_23_0_10) = all_23_1_11
% 4.70/1.84  |
% 4.70/1.84  | Instantiating (34) with all_25_0_13, all_25_1_14, all_25_2_15 yields:
% 4.70/1.84  | (52) j(all_25_2_15) = all_25_1_14 & j(all_0_2_2) = all_25_0_13 & op2(all_0_3_3, all_0_2_2) = all_25_2_15 & op1(all_11_0_5, all_25_0_13) = all_25_1_14
% 4.70/1.85  |
% 4.70/1.85  | Applying alpha-rule on (52) yields:
% 4.70/1.85  | (53) j(all_25_2_15) = all_25_1_14
% 4.70/1.85  | (54) j(all_0_2_2) = all_25_0_13
% 4.70/1.85  | (55) op2(all_0_3_3, all_0_2_2) = all_25_2_15
% 4.70/1.85  | (56) op1(all_11_0_5, all_25_0_13) = all_25_1_14
% 4.70/1.85  |
% 4.70/1.85  | Instantiating (46) with all_27_0_16, all_27_1_17, all_27_2_18 yields:
% 4.70/1.85  | (57) j(all_27_2_18) = all_27_1_17 & j(all_0_3_3) = all_27_0_16 & op2(all_0_2_2, all_0_3_3) = all_27_2_18 & op1(all_20_0_9, all_27_0_16) = all_27_1_17
% 4.70/1.85  |
% 4.70/1.85  | Applying alpha-rule on (57) yields:
% 4.70/1.85  | (58) j(all_27_2_18) = all_27_1_17
% 4.70/1.85  | (59) j(all_0_3_3) = all_27_0_16
% 4.70/1.85  | (60) op2(all_0_2_2, all_0_3_3) = all_27_2_18
% 4.70/1.85  | (61) op1(all_20_0_9, all_27_0_16) = all_27_1_17
% 4.70/1.85  |
% 4.70/1.85  | Instantiating (45) with all_29_0_19, all_29_1_20, all_29_2_21 yields:
% 4.70/1.85  | (62) j(all_29_2_21) = all_29_1_20 & j(all_0_2_2) = all_29_0_19 & op2(all_0_2_2, all_0_2_2) = all_29_2_21 & op1(all_20_0_9, all_29_0_19) = all_29_1_20
% 4.70/1.85  |
% 4.70/1.85  | Applying alpha-rule on (62) yields:
% 4.70/1.85  | (63) j(all_29_2_21) = all_29_1_20
% 4.70/1.85  | (64) j(all_0_2_2) = all_29_0_19
% 4.70/1.85  | (65) op2(all_0_2_2, all_0_2_2) = all_29_2_21
% 4.70/1.85  | (66) op1(all_20_0_9, all_29_0_19) = all_29_1_20
% 4.70/1.85  |
% 4.70/1.85  | Instantiating formula (12) with all_0_2_2, all_25_0_13, all_29_0_19 and discharging atoms j(all_0_2_2) = all_29_0_19, j(all_0_2_2) = all_25_0_13, yields:
% 4.70/1.85  | (67) all_29_0_19 = all_25_0_13
% 4.70/1.85  |
% 4.70/1.85  | Instantiating formula (12) with all_0_2_2, all_20_0_9, all_25_0_13 and discharging atoms j(all_0_2_2) = all_25_0_13, j(all_0_2_2) = all_20_0_9, yields:
% 4.70/1.85  | (68) all_25_0_13 = all_20_0_9
% 4.70/1.85  |
% 4.70/1.85  | Instantiating formula (12) with all_0_2_2, all_9_0_4, all_29_0_19 and discharging atoms j(all_0_2_2) = all_29_0_19, j(all_0_2_2) = all_9_0_4, yields:
% 4.70/1.85  | (69) all_29_0_19 = all_9_0_4
% 4.70/1.85  |
% 4.70/1.85  | Instantiating formula (12) with all_0_3_3, all_23_0_10, all_27_0_16 and discharging atoms j(all_0_3_3) = all_27_0_16, j(all_0_3_3) = all_23_0_10, yields:
% 4.70/1.85  | (70) all_27_0_16 = all_23_0_10
% 4.70/1.85  |
% 4.70/1.85  | Instantiating formula (12) with all_0_3_3, all_18_0_8, all_27_0_16 and discharging atoms j(all_0_3_3) = all_27_0_16, j(all_0_3_3) = all_18_0_8, yields:
% 4.70/1.85  | (71) all_27_0_16 = all_18_0_8
% 4.70/1.85  |
% 4.70/1.85  | Instantiating formula (12) with all_0_3_3, all_14_0_6, all_27_0_16 and discharging atoms j(all_0_3_3) = all_27_0_16, j(all_0_3_3) = all_14_0_6, yields:
% 4.70/1.85  | (72) all_27_0_16 = all_14_0_6
% 4.70/1.85  |
% 4.70/1.85  | Instantiating formula (12) with all_0_3_3, all_11_0_5, all_27_0_16 and discharging atoms j(all_0_3_3) = all_27_0_16, j(all_0_3_3) = all_11_0_5, yields:
% 4.70/1.85  | (73) all_27_0_16 = all_11_0_5
% 4.70/1.85  |
% 4.70/1.85  | Instantiating formula (3) with all_0_2_2, all_0_3_3, all_27_2_18, all_0_0_0 and discharging atoms op2(all_0_2_2, all_0_3_3) = all_27_2_18, op2(all_0_2_2, all_0_3_3) = all_0_0_0, yields:
% 4.70/1.85  | (74) all_27_2_18 = all_0_0_0
% 4.70/1.85  |
% 4.70/1.85  | Instantiating formula (3) with all_0_3_3, all_0_2_2, all_25_2_15, all_0_1_1 and discharging atoms op2(all_0_3_3, all_0_2_2) = all_25_2_15, op2(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 4.70/1.85  | (75) all_25_2_15 = all_0_1_1
% 4.70/1.85  |
% 4.70/1.85  | Combining equations (67,69) yields a new equation:
% 4.70/1.85  | (76) all_25_0_13 = all_9_0_4
% 4.70/1.85  |
% 4.70/1.85  | Simplifying 76 yields:
% 4.70/1.85  | (77) all_25_0_13 = all_9_0_4
% 4.70/1.85  |
% 4.70/1.85  | Combining equations (72,70) yields a new equation:
% 4.70/1.85  | (78) all_23_0_10 = all_14_0_6
% 4.70/1.85  |
% 4.70/1.85  | Combining equations (71,70) yields a new equation:
% 4.70/1.85  | (79) all_23_0_10 = all_18_0_8
% 4.70/1.85  |
% 4.70/1.85  | Combining equations (73,70) yields a new equation:
% 4.70/1.85  | (80) all_23_0_10 = all_11_0_5
% 4.70/1.85  |
% 4.70/1.85  | Combining equations (68,77) yields a new equation:
% 4.70/1.85  | (81) all_20_0_9 = all_9_0_4
% 4.70/1.85  |
% 4.70/1.85  | Simplifying 81 yields:
% 4.70/1.85  | (82) all_20_0_9 = all_9_0_4
% 4.70/1.85  |
% 4.70/1.85  | Combining equations (80,79) yields a new equation:
% 4.70/1.85  | (83) all_18_0_8 = all_11_0_5
% 4.70/1.85  |
% 4.70/1.85  | Combining equations (78,79) yields a new equation:
% 4.70/1.85  | (84) all_18_0_8 = all_14_0_6
% 4.70/1.85  |
% 4.70/1.85  | Combining equations (84,83) yields a new equation:
% 4.70/1.85  | (85) all_14_0_6 = all_11_0_5
% 4.70/1.85  |
% 4.70/1.85  | Simplifying 85 yields:
% 4.70/1.85  | (86) all_14_0_6 = all_11_0_5
% 4.70/1.85  |
% 4.70/1.85  | Combining equations (83,79) yields a new equation:
% 4.70/1.85  | (80) all_23_0_10 = all_11_0_5
% 4.70/1.85  |
% 4.70/1.85  | Combining equations (80,70) yields a new equation:
% 4.70/1.85  | (73) all_27_0_16 = all_11_0_5
% 4.70/1.85  |
% 4.70/1.85  | From (74) and (58) follows:
% 4.70/1.85  | (89) j(all_0_0_0) = all_27_1_17
% 4.70/1.85  |
% 4.70/1.85  | From (75) and (53) follows:
% 4.70/1.85  | (90) j(all_0_1_1) = all_25_1_14
% 4.70/1.86  |
% 4.70/1.86  | From (82)(73) and (61) follows:
% 4.70/1.86  | (91) op1(all_9_0_4, all_11_0_5) = all_27_1_17
% 4.70/1.86  |
% 4.70/1.86  | From (77) and (56) follows:
% 4.70/1.86  | (92) op1(all_11_0_5, all_9_0_4) = all_25_1_14
% 4.70/1.86  |
% 4.70/1.86  | From (86) and (38) follows:
% 4.70/1.86  | (93) sorti1(all_11_0_5)
% 4.70/1.86  |
% 4.70/1.86  | Instantiating formula (44) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields:
% 4.70/1.86  | (94)  ? [v0] :  ? [v1] :  ? [v2] : (j(v0) = v1 & j(all_0_0_0) = v2 & op2(all_0_2_2, all_0_0_0) = v0 & op1(all_20_0_9, v2) = v1)
% 4.70/1.86  |
% 4.70/1.86  | Instantiating formula (4) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields:
% 4.70/1.86  | (95)  ? [v0] : (j(all_0_0_0) = v0 & h(v0) = all_0_0_0)
% 4.70/1.86  |
% 4.70/1.86  | Instantiating formula (10) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields:
% 4.70/1.86  | (96)  ? [v0] : (j(all_0_0_0) = v0 & sorti1(v0))
% 4.70/1.86  |
% 4.70/1.86  | Instantiating formula (5) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields:
% 4.70/1.86  | (97)  ? [v0] : (j(all_0_0_0) = v0 &  ! [v1] : ( ~ sorti2(v1) |  ? [v2] :  ? [v3] :  ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_0_0_0, v1) = v2 & op1(v0, v4) = v3)))
% 4.70/1.86  |
% 4.70/1.86  | Instantiating formula (33) with all_0_1_1 and discharging atoms sorti2(all_0_1_1), yields:
% 4.70/1.86  | (98)  ? [v0] :  ? [v1] :  ? [v2] : (j(v0) = v1 & j(all_0_1_1) = v2 & op2(all_0_3_3, all_0_1_1) = v0 & op1(all_11_0_5, v2) = v1)
% 4.70/1.86  |
% 4.70/1.86  | Instantiating formula (4) with all_0_1_1 and discharging atoms sorti2(all_0_1_1), yields:
% 4.70/1.86  | (99)  ? [v0] : (j(all_0_1_1) = v0 & h(v0) = all_0_1_1)
% 4.70/1.86  |
% 4.70/1.86  | Instantiating formula (10) with all_0_1_1 and discharging atoms sorti2(all_0_1_1), yields:
% 4.70/1.86  | (100)  ? [v0] : (j(all_0_1_1) = v0 & sorti1(v0))
% 4.70/1.86  |
% 4.70/1.86  | Instantiating formula (5) with all_0_1_1 and discharging atoms sorti2(all_0_1_1), yields:
% 4.70/1.86  | (101)  ? [v0] : (j(all_0_1_1) = v0 &  ! [v1] : ( ~ sorti2(v1) |  ? [v2] :  ? [v3] :  ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_0_1_1, v1) = v2 & op1(v0, v4) = v3)))
% 4.70/1.86  |
% 4.70/1.86  | Instantiating formula (20) with all_11_0_5 and discharging atoms sorti1(all_11_0_5), yields:
% 4.70/1.86  | (102)  ? [v0] : (h(all_11_0_5) = v0 &  ! [v1] : ( ~ sorti1(v1) |  ? [v2] :  ? [v3] :  ? [v4] : (h(v2) = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_11_0_5, v1) = v2)))
% 4.70/1.86  |
% 4.70/1.86  | Instantiating formula (8) with all_25_1_14, all_11_0_5, all_9_0_4 and discharging atoms op1(all_11_0_5, all_9_0_4) = all_25_1_14, sorti1(all_11_0_5), sorti1(all_9_0_4), yields:
% 4.70/1.86  | (103) op1(all_9_0_4, all_11_0_5) = all_25_1_14
% 4.70/1.86  |
% 4.70/1.86  | Instantiating formula (20) with all_9_0_4 and discharging atoms sorti1(all_9_0_4), yields:
% 4.70/1.86  | (104)  ? [v0] : (h(all_9_0_4) = v0 &  ! [v1] : ( ~ sorti1(v1) |  ? [v2] :  ? [v3] :  ? [v4] : (h(v2) = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_9_0_4, v1) = v2)))
% 4.70/1.86  |
% 4.70/1.86  | Instantiating (104) with all_43_0_25 yields:
% 4.70/1.86  | (105) h(all_9_0_4) = all_43_0_25 &  ! [v0] : ( ~ sorti1(v0) |  ? [v1] :  ? [v2] :  ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_43_0_25, v3) = v2 & op1(all_9_0_4, v0) = v1))
% 4.70/1.86  |
% 4.70/1.86  | Applying alpha-rule on (105) yields:
% 4.70/1.86  | (106) h(all_9_0_4) = all_43_0_25
% 4.70/1.86  | (107)  ! [v0] : ( ~ sorti1(v0) |  ? [v1] :  ? [v2] :  ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_43_0_25, v3) = v2 & op1(all_9_0_4, v0) = v1))
% 4.70/1.86  |
% 4.70/1.86  | Instantiating formula (107) with all_11_0_5 and discharging atoms sorti1(all_11_0_5), yields:
% 4.70/1.86  | (108)  ? [v0] :  ? [v1] :  ? [v2] : (h(v0) = v1 & h(all_11_0_5) = v2 & op2(all_43_0_25, v2) = v1 & op1(all_9_0_4, all_11_0_5) = v0)
% 4.70/1.86  |
% 4.70/1.86  | Instantiating (94) with all_46_0_26, all_46_1_27, all_46_2_28 yields:
% 4.70/1.86  | (109) j(all_46_2_28) = all_46_1_27 & j(all_0_0_0) = all_46_0_26 & op2(all_0_2_2, all_0_0_0) = all_46_2_28 & op1(all_20_0_9, all_46_0_26) = all_46_1_27
% 4.70/1.86  |
% 4.70/1.86  | Applying alpha-rule on (109) yields:
% 4.70/1.86  | (110) j(all_46_2_28) = all_46_1_27
% 4.70/1.86  | (111) j(all_0_0_0) = all_46_0_26
% 4.70/1.86  | (112) op2(all_0_2_2, all_0_0_0) = all_46_2_28
% 4.70/1.86  | (113) op1(all_20_0_9, all_46_0_26) = all_46_1_27
% 4.70/1.86  |
% 4.70/1.86  | Instantiating (102) with all_48_0_29 yields:
% 4.70/1.86  | (114) h(all_11_0_5) = all_48_0_29 &  ! [v0] : ( ~ sorti1(v0) |  ? [v1] :  ? [v2] :  ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_48_0_29, v3) = v2 & op1(all_11_0_5, v0) = v1))
% 4.70/1.87  |
% 4.70/1.87  | Applying alpha-rule on (114) yields:
% 4.70/1.87  | (115) h(all_11_0_5) = all_48_0_29
% 4.70/1.87  | (116)  ! [v0] : ( ~ sorti1(v0) |  ? [v1] :  ? [v2] :  ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_48_0_29, v3) = v2 & op1(all_11_0_5, v0) = v1))
% 4.70/1.87  |
% 4.70/1.87  | Instantiating formula (116) with all_9_0_4 and discharging atoms sorti1(all_9_0_4), yields:
% 4.70/1.87  | (117)  ? [v0] :  ? [v1] :  ? [v2] : (h(v0) = v1 & h(all_9_0_4) = v2 & op2(all_48_0_29, v2) = v1 & op1(all_11_0_5, all_9_0_4) = v0)
% 4.70/1.87  |
% 4.70/1.87  | Instantiating (97) with all_53_0_33 yields:
% 4.70/1.87  | (118) j(all_0_0_0) = all_53_0_33 &  ! [v0] : ( ~ sorti2(v0) |  ? [v1] :  ? [v2] :  ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_0_0_0, v0) = v1 & op1(all_53_0_33, v3) = v2))
% 4.70/1.87  |
% 4.70/1.87  | Applying alpha-rule on (118) yields:
% 4.70/1.87  | (119) j(all_0_0_0) = all_53_0_33
% 4.70/1.87  | (120)  ! [v0] : ( ~ sorti2(v0) |  ? [v1] :  ? [v2] :  ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_0_0_0, v0) = v1 & op1(all_53_0_33, v3) = v2))
% 4.70/1.87  |
% 4.70/1.87  | Instantiating formula (120) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields:
% 4.70/1.87  | (121)  ? [v0] :  ? [v1] :  ? [v2] : (j(v0) = v1 & j(all_0_0_0) = v2 & op2(all_0_0_0, all_0_0_0) = v0 & op1(all_53_0_33, v2) = v1)
% 4.70/1.87  |
% 4.70/1.87  | Instantiating formula (120) with all_0_1_1 and discharging atoms sorti2(all_0_1_1), yields:
% 4.70/1.87  | (122)  ? [v0] :  ? [v1] :  ? [v2] : (j(v0) = v1 & j(all_0_1_1) = v2 & op2(all_0_0_0, all_0_1_1) = v0 & op1(all_53_0_33, v2) = v1)
% 4.70/1.87  |
% 4.70/1.87  | Instantiating (96) with all_56_0_34 yields:
% 4.70/1.87  | (123) j(all_0_0_0) = all_56_0_34 & sorti1(all_56_0_34)
% 4.70/1.87  |
% 4.70/1.87  | Applying alpha-rule on (123) yields:
% 4.70/1.87  | (124) j(all_0_0_0) = all_56_0_34
% 4.70/1.87  | (125) sorti1(all_56_0_34)
% 4.70/1.87  |
% 4.70/1.87  | Instantiating (95) with all_58_0_35 yields:
% 4.70/1.87  | (126) j(all_0_0_0) = all_58_0_35 & h(all_58_0_35) = all_0_0_0
% 4.70/1.87  |
% 4.70/1.87  | Applying alpha-rule on (126) yields:
% 4.70/1.87  | (127) j(all_0_0_0) = all_58_0_35
% 4.70/1.87  | (128) h(all_58_0_35) = all_0_0_0
% 4.70/1.87  |
% 4.70/1.87  | Instantiating (101) with all_60_0_36 yields:
% 4.70/1.87  | (129) j(all_0_1_1) = all_60_0_36 &  ! [v0] : ( ~ sorti2(v0) |  ? [v1] :  ? [v2] :  ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_0_1_1, v0) = v1 & op1(all_60_0_36, v3) = v2))
% 4.70/1.87  |
% 4.70/1.87  | Applying alpha-rule on (129) yields:
% 4.70/1.87  | (130) j(all_0_1_1) = all_60_0_36
% 4.70/1.87  | (131)  ! [v0] : ( ~ sorti2(v0) |  ? [v1] :  ? [v2] :  ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_0_1_1, v0) = v1 & op1(all_60_0_36, v3) = v2))
% 4.70/1.87  |
% 4.70/1.87  | Instantiating formula (131) with all_0_1_1 and discharging atoms sorti2(all_0_1_1), yields:
% 4.70/1.87  | (132)  ? [v0] :  ? [v1] :  ? [v2] : (j(v0) = v1 & j(all_0_1_1) = v2 & op2(all_0_1_1, all_0_1_1) = v0 & op1(all_60_0_36, v2) = v1)
% 4.70/1.87  |
% 4.70/1.87  | Instantiating (100) with all_63_0_37 yields:
% 4.70/1.87  | (133) j(all_0_1_1) = all_63_0_37 & sorti1(all_63_0_37)
% 4.70/1.87  |
% 4.70/1.87  | Applying alpha-rule on (133) yields:
% 4.70/1.87  | (134) j(all_0_1_1) = all_63_0_37
% 4.70/1.87  | (135) sorti1(all_63_0_37)
% 4.70/1.87  |
% 4.70/1.87  | Instantiating (99) with all_65_0_38 yields:
% 4.70/1.87  | (136) j(all_0_1_1) = all_65_0_38 & h(all_65_0_38) = all_0_1_1
% 4.70/1.87  |
% 4.70/1.87  | Applying alpha-rule on (136) yields:
% 4.70/1.87  | (137) j(all_0_1_1) = all_65_0_38
% 4.70/1.87  | (138) h(all_65_0_38) = all_0_1_1
% 4.70/1.87  |
% 4.70/1.87  | Instantiating (98) with all_67_0_39, all_67_1_40, all_67_2_41 yields:
% 4.70/1.87  | (139) j(all_67_2_41) = all_67_1_40 & j(all_0_1_1) = all_67_0_39 & op2(all_0_3_3, all_0_1_1) = all_67_2_41 & op1(all_11_0_5, all_67_0_39) = all_67_1_40
% 4.70/1.87  |
% 4.70/1.87  | Applying alpha-rule on (139) yields:
% 4.70/1.87  | (140) j(all_67_2_41) = all_67_1_40
% 4.70/1.87  | (141) j(all_0_1_1) = all_67_0_39
% 4.70/1.87  | (142) op2(all_0_3_3, all_0_1_1) = all_67_2_41
% 4.70/1.87  | (143) op1(all_11_0_5, all_67_0_39) = all_67_1_40
% 4.70/1.88  |
% 4.70/1.88  | Instantiating (108) with all_71_0_45, all_71_1_46, all_71_2_47 yields:
% 4.70/1.88  | (144) h(all_71_2_47) = all_71_1_46 & h(all_11_0_5) = all_71_0_45 & op2(all_43_0_25, all_71_0_45) = all_71_1_46 & op1(all_9_0_4, all_11_0_5) = all_71_2_47
% 4.70/1.88  |
% 4.70/1.88  | Applying alpha-rule on (144) yields:
% 4.70/1.88  | (145) h(all_71_2_47) = all_71_1_46
% 4.70/1.88  | (146) h(all_11_0_5) = all_71_0_45
% 4.70/1.88  | (147) op2(all_43_0_25, all_71_0_45) = all_71_1_46
% 4.70/1.88  | (148) op1(all_9_0_4, all_11_0_5) = all_71_2_47
% 4.70/1.88  |
% 4.70/1.88  | Instantiating (117) with all_73_0_48, all_73_1_49, all_73_2_50 yields:
% 4.70/1.88  | (149) h(all_73_2_50) = all_73_1_49 & h(all_9_0_4) = all_73_0_48 & op2(all_48_0_29, all_73_0_48) = all_73_1_49 & op1(all_11_0_5, all_9_0_4) = all_73_2_50
% 4.70/1.88  |
% 4.70/1.88  | Applying alpha-rule on (149) yields:
% 4.70/1.88  | (150) h(all_73_2_50) = all_73_1_49
% 4.70/1.88  | (151) h(all_9_0_4) = all_73_0_48
% 4.70/1.88  | (152) op2(all_48_0_29, all_73_0_48) = all_73_1_49
% 4.70/1.88  | (153) op1(all_11_0_5, all_9_0_4) = all_73_2_50
% 4.70/1.88  |
% 4.70/1.88  | Instantiating (122) with all_81_0_60, all_81_1_61, all_81_2_62 yields:
% 4.70/1.88  | (154) j(all_81_2_62) = all_81_1_61 & j(all_0_1_1) = all_81_0_60 & op2(all_0_0_0, all_0_1_1) = all_81_2_62 & op1(all_53_0_33, all_81_0_60) = all_81_1_61
% 4.70/1.88  |
% 4.70/1.88  | Applying alpha-rule on (154) yields:
% 4.70/1.88  | (155) j(all_81_2_62) = all_81_1_61
% 4.70/1.88  | (156) j(all_0_1_1) = all_81_0_60
% 4.70/1.88  | (157) op2(all_0_0_0, all_0_1_1) = all_81_2_62
% 4.70/1.88  | (158) op1(all_53_0_33, all_81_0_60) = all_81_1_61
% 4.70/1.88  |
% 4.70/1.88  | Instantiating (121) with all_83_0_63, all_83_1_64, all_83_2_65 yields:
% 4.70/1.88  | (159) j(all_83_2_65) = all_83_1_64 & j(all_0_0_0) = all_83_0_63 & op2(all_0_0_0, all_0_0_0) = all_83_2_65 & op1(all_53_0_33, all_83_0_63) = all_83_1_64
% 4.70/1.88  |
% 4.70/1.88  | Applying alpha-rule on (159) yields:
% 4.70/1.88  | (160) j(all_83_2_65) = all_83_1_64
% 4.70/1.88  | (161) j(all_0_0_0) = all_83_0_63
% 4.70/1.88  | (162) op2(all_0_0_0, all_0_0_0) = all_83_2_65
% 4.70/1.88  | (163) op1(all_53_0_33, all_83_0_63) = all_83_1_64
% 4.70/1.88  |
% 4.70/1.88  | Instantiating (132) with all_89_0_72, all_89_1_73, all_89_2_74 yields:
% 4.70/1.88  | (164) j(all_89_2_74) = all_89_1_73 & j(all_0_1_1) = all_89_0_72 & op2(all_0_1_1, all_0_1_1) = all_89_2_74 & op1(all_60_0_36, all_89_0_72) = all_89_1_73
% 4.70/1.88  |
% 4.70/1.88  | Applying alpha-rule on (164) yields:
% 4.70/1.88  | (165) j(all_89_2_74) = all_89_1_73
% 4.70/1.88  | (166) j(all_0_1_1) = all_89_0_72
% 4.70/1.88  | (167) op2(all_0_1_1, all_0_1_1) = all_89_2_74
% 4.70/1.88  | (168) op1(all_60_0_36, all_89_0_72) = all_89_1_73
% 4.70/1.88  |
% 4.70/1.88  | Instantiating formula (12) with all_0_0_0, all_56_0_34, all_27_1_17 and discharging atoms j(all_0_0_0) = all_56_0_34, j(all_0_0_0) = all_27_1_17, yields:
% 4.70/1.88  | (169) all_56_0_34 = all_27_1_17
% 4.70/1.88  |
% 4.70/1.88  | Instantiating formula (12) with all_0_0_0, all_56_0_34, all_83_0_63 and discharging atoms j(all_0_0_0) = all_83_0_63, j(all_0_0_0) = all_56_0_34, yields:
% 4.70/1.88  | (170) all_83_0_63 = all_56_0_34
% 4.70/1.88  |
% 4.70/1.88  | Instantiating formula (12) with all_0_0_0, all_56_0_34, all_58_0_35 and discharging atoms j(all_0_0_0) = all_58_0_35, j(all_0_0_0) = all_56_0_34, yields:
% 4.70/1.88  | (171) all_58_0_35 = all_56_0_34
% 4.70/1.88  |
% 4.70/1.88  | Instantiating formula (12) with all_0_0_0, all_53_0_33, all_83_0_63 and discharging atoms j(all_0_0_0) = all_83_0_63, j(all_0_0_0) = all_53_0_33, yields:
% 4.70/1.88  | (172) all_83_0_63 = all_53_0_33
% 4.70/1.88  |
% 4.70/1.88  | Instantiating formula (12) with all_0_0_0, all_46_0_26, all_58_0_35 and discharging atoms j(all_0_0_0) = all_58_0_35, j(all_0_0_0) = all_46_0_26, yields:
% 4.70/1.88  | (173) all_58_0_35 = all_46_0_26
% 4.70/1.88  |
% 4.70/1.88  | Instantiating formula (12) with all_0_1_1, all_89_0_72, all_25_1_14 and discharging atoms j(all_0_1_1) = all_89_0_72, j(all_0_1_1) = all_25_1_14, yields:
% 4.70/1.88  | (174) all_89_0_72 = all_25_1_14
% 4.70/1.88  |
% 4.70/1.88  | Instantiating formula (12) with all_0_1_1, all_81_0_60, all_89_0_72 and discharging atoms j(all_0_1_1) = all_89_0_72, j(all_0_1_1) = all_81_0_60, yields:
% 4.70/1.89  | (175) all_89_0_72 = all_81_0_60
% 4.70/1.89  |
% 4.70/1.89  | Instantiating formula (12) with all_0_1_1, all_67_0_39, all_81_0_60 and discharging atoms j(all_0_1_1) = all_81_0_60, j(all_0_1_1) = all_67_0_39, yields:
% 4.70/1.89  | (176) all_81_0_60 = all_67_0_39
% 4.70/1.89  |
% 4.70/1.89  | Instantiating formula (12) with all_0_1_1, all_65_0_38, all_81_0_60 and discharging atoms j(all_0_1_1) = all_81_0_60, j(all_0_1_1) = all_65_0_38, yields:
% 4.70/1.89  | (177) all_81_0_60 = all_65_0_38
% 4.70/1.89  |
% 4.70/1.89  | Instantiating formula (12) with all_0_1_1, all_63_0_37, all_65_0_38 and discharging atoms j(all_0_1_1) = all_65_0_38, j(all_0_1_1) = all_63_0_37, yields:
% 4.70/1.89  | (178) all_65_0_38 = all_63_0_37
% 4.70/1.89  |
% 4.70/1.89  | Instantiating formula (16) with all_11_0_5, all_9_0_4, all_73_2_50, all_25_1_14 and discharging atoms op1(all_11_0_5, all_9_0_4) = all_73_2_50, op1(all_11_0_5, all_9_0_4) = all_25_1_14, yields:
% 4.70/1.89  | (179) all_73_2_50 = all_25_1_14
% 4.70/1.89  |
% 4.70/1.89  | Instantiating formula (16) with all_9_0_4, all_11_0_5, all_71_2_47, all_27_1_17 and discharging atoms op1(all_9_0_4, all_11_0_5) = all_71_2_47, op1(all_9_0_4, all_11_0_5) = all_27_1_17, yields:
% 4.70/1.89  | (180) all_71_2_47 = all_27_1_17
% 4.70/1.89  |
% 4.70/1.89  | Instantiating formula (16) with all_9_0_4, all_11_0_5, all_25_1_14, all_71_2_47 and discharging atoms op1(all_9_0_4, all_11_0_5) = all_71_2_47, op1(all_9_0_4, all_11_0_5) = all_25_1_14, yields:
% 4.70/1.89  | (181) all_71_2_47 = all_25_1_14
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (175,174) yields a new equation:
% 4.70/1.89  | (182) all_81_0_60 = all_25_1_14
% 4.70/1.89  |
% 4.70/1.89  | Simplifying 182 yields:
% 4.70/1.89  | (183) all_81_0_60 = all_25_1_14
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (170,172) yields a new equation:
% 4.70/1.89  | (184) all_56_0_34 = all_53_0_33
% 4.70/1.89  |
% 4.70/1.89  | Simplifying 184 yields:
% 4.70/1.89  | (185) all_56_0_34 = all_53_0_33
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (177,176) yields a new equation:
% 4.70/1.89  | (186) all_67_0_39 = all_65_0_38
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (183,176) yields a new equation:
% 4.70/1.89  | (187) all_67_0_39 = all_25_1_14
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (181,180) yields a new equation:
% 4.70/1.89  | (188) all_27_1_17 = all_25_1_14
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (186,187) yields a new equation:
% 4.70/1.89  | (189) all_65_0_38 = all_25_1_14
% 4.70/1.89  |
% 4.70/1.89  | Simplifying 189 yields:
% 4.70/1.89  | (190) all_65_0_38 = all_25_1_14
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (190,178) yields a new equation:
% 4.70/1.89  | (191) all_63_0_37 = all_25_1_14
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (171,173) yields a new equation:
% 4.70/1.89  | (192) all_56_0_34 = all_46_0_26
% 4.70/1.89  |
% 4.70/1.89  | Simplifying 192 yields:
% 4.70/1.89  | (193) all_56_0_34 = all_46_0_26
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (193,185) yields a new equation:
% 4.70/1.89  | (194) all_53_0_33 = all_46_0_26
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (169,185) yields a new equation:
% 4.70/1.89  | (195) all_53_0_33 = all_27_1_17
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (194,195) yields a new equation:
% 4.70/1.89  | (196) all_46_0_26 = all_27_1_17
% 4.70/1.89  |
% 4.70/1.89  | Simplifying 196 yields:
% 4.70/1.89  | (197) all_46_0_26 = all_27_1_17
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (188,197) yields a new equation:
% 4.70/1.89  | (198) all_46_0_26 = all_25_1_14
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (198,173) yields a new equation:
% 4.70/1.89  | (199) all_58_0_35 = all_25_1_14
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (191,178) yields a new equation:
% 4.70/1.89  | (190) all_65_0_38 = all_25_1_14
% 4.70/1.89  |
% 4.70/1.89  | Combining equations (188,180) yields a new equation:
% 4.70/1.89  | (181) all_71_2_47 = all_25_1_14
% 4.70/1.89  |
% 4.70/1.89  | From (179) and (150) follows:
% 4.70/1.89  | (202) h(all_25_1_14) = all_73_1_49
% 4.70/1.89  |
% 4.70/1.89  | From (181) and (145) follows:
% 4.70/1.89  | (203) h(all_25_1_14) = all_71_1_46
% 4.70/1.89  |
% 4.70/1.89  | From (190) and (138) follows:
% 4.70/1.89  | (204) h(all_25_1_14) = all_0_1_1
% 4.70/1.89  |
% 4.70/1.89  | From (199) and (128) follows:
% 4.70/1.89  | (205) h(all_25_1_14) = all_0_0_0
% 4.70/1.89  |
% 4.70/1.89  | Instantiating formula (15) with all_25_1_14, all_71_1_46, all_73_1_49 and discharging atoms h(all_25_1_14) = all_73_1_49, h(all_25_1_14) = all_71_1_46, yields:
% 4.70/1.89  | (206) all_73_1_49 = all_71_1_46
% 4.70/1.90  |
% 4.70/1.90  | Instantiating formula (15) with all_25_1_14, all_0_0_0, all_73_1_49 and discharging atoms h(all_25_1_14) = all_73_1_49, h(all_25_1_14) = all_0_0_0, yields:
% 4.70/1.90  | (207) all_73_1_49 = all_0_0_0
% 4.70/1.90  |
% 4.70/1.90  | Instantiating formula (15) with all_25_1_14, all_0_1_1, all_71_1_46 and discharging atoms h(all_25_1_14) = all_71_1_46, h(all_25_1_14) = all_0_1_1, yields:
% 4.70/1.90  | (208) all_71_1_46 = all_0_1_1
% 4.70/1.90  |
% 4.70/1.90  | Combining equations (206,207) yields a new equation:
% 4.70/1.90  | (209) all_71_1_46 = all_0_0_0
% 4.70/1.90  |
% 4.70/1.90  | Simplifying 209 yields:
% 4.70/1.90  | (210) all_71_1_46 = all_0_0_0
% 4.70/1.90  |
% 4.70/1.90  | Combining equations (210,208) yields a new equation:
% 4.70/1.90  | (211) all_0_0_0 = all_0_1_1
% 4.70/1.90  |
% 4.70/1.90  | Simplifying 211 yields:
% 4.70/1.90  | (212) all_0_0_0 = all_0_1_1
% 4.70/1.90  |
% 4.70/1.90  | Equations (212) can reduce 19 to:
% 4.70/1.90  | (213) $false
% 4.70/1.90  |
% 4.70/1.90  |-The branch is then unsatisfiable
% 4.70/1.90  % SZS output end Proof for theBenchmark
% 4.70/1.90  
% 4.70/1.90  1292ms
%------------------------------------------------------------------------------