TSTP Solution File: ALG176+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG176+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 15:37:05 EDT 2022
% Result : Theorem 2.73s 1.37s
% Output : Proof 4.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG176+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n025.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 : Wed Jun 8 08:20:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.58/0.59 ____ _
% 0.58/0.59 ___ / __ \_____(_)___ ________ __________
% 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.59
% 0.58/0.59 A Theorem Prover for First-Order Logic
% 0.58/0.60 (ePrincess v.1.0)
% 0.58/0.60
% 0.58/0.60 (c) Philipp Rümmer, 2009-2015
% 0.58/0.60 (c) Peter Backeman, 2014-2015
% 0.58/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.60 Bug reports to peter@backeman.se
% 0.58/0.60
% 0.58/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.60
% 0.58/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.54/0.94 Prover 0: Preprocessing ...
% 1.95/1.12 Prover 0: Constructing countermodel ...
% 2.73/1.36 Prover 0: proved (718ms)
% 2.73/1.37
% 2.73/1.37 No countermodel exists, formula is valid
% 2.73/1.37 % SZS status Theorem for theBenchmark
% 2.73/1.37
% 2.73/1.37 Generating proof ... found it (size 88)
% 4.10/1.73
% 4.10/1.73 % SZS output start Proof for theBenchmark
% 4.10/1.73 Assumed formulas after preprocessing and simplification:
% 4.10/1.73 | (0) ? [v0] : (sorti1(v0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (op2(v4, v3) = v2) | ~ (op2(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (op1(v4, v3) = v2) | ~ (op1(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (j(v3) = v2) | ~ (j(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (h(v3) = v2) | ~ (h(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (op2(v1, v2) = v3) | ~ sorti2(v2) | ~ sorti2(v1) | sorti2(v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (op1(v1, v2) = v3) | ~ sorti1(v2) | ~ sorti1(v1) | sorti1(v3)) & ! [v1] : ( ~ (op1(v1, v0) = v1) | ~ sorti1(v1)) & ! [v1] : ( ~ sorti2(v1) | ? [v2] : (j(v1) = v2 & h(v2) = v1)) & ! [v1] : ( ~ sorti2(v1) | ? [v2] : (j(v1) = v2 & sorti1(v2))) & ! [v1] : ( ~ sorti2(v1) | ? [v2] : (j(v1) = v2 & ! [v3] : ( ~ sorti2(v3) | ? [v4] : ? [v5] : ? [v6] : (j(v4) = v5 & j(v3) = v6 & op2(v1, v3) = v4 & op1(v2, v6) = v5)))) & ! [v1] : ( ~ sorti2(v1) | ? [v2] : (op2(v2, v1) = v2 & sorti2(v2))) & ! [v1] : ( ~ sorti1(v1) | ? [v2] : (j(v2) = v1 & h(v1) = v2)) & ! [v1] : ( ~ sorti1(v1) | ? [v2] : (h(v1) = v2 & sorti2(v2))) & ! [v1] : ( ~ sorti1(v1) | ? [v2] : (h(v1) = v2 & ! [v3] : ( ~ sorti1(v3) | ? [v4] : ? [v5] : ? [v6] : (h(v4) = v5 & h(v3) = v6 & op2(v2, v6) = v5 & op1(v1, v3) = v4)))))
% 4.10/1.76 | Instantiating (0) with all_0_0_0 yields:
% 4.10/1.76 | (1) sorti1(all_0_0_0) & ! [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(v0, v1) = v2) | ~ sorti1(v1) | ~ sorti1(v0) | sorti1(v2)) & ! [v0] : ( ~ (op1(v0, all_0_0_0) = v0) | ~ sorti1(v0)) & ! [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] : ( ~ sorti2(v0) | ? [v1] : (op2(v1, v0) = v1 & sorti2(v1))) & ! [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))))
% 4.10/1.77 |
% 4.10/1.77 | Applying alpha-rule on (1) yields:
% 4.10/1.77 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (op2(v0, v1) = v2) | ~ sorti2(v1) | ~ sorti2(v0) | sorti2(v2))
% 4.10/1.77 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 4.10/1.77 | (4) ! [v0] : ( ~ (op1(v0, all_0_0_0) = v0) | ~ sorti1(v0))
% 4.10/1.77 | (5) sorti1(all_0_0_0)
% 4.10/1.77 | (6) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & h(v1) = v0))
% 4.10/1.77 | (7) ! [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))))
% 4.10/1.77 | (8) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & sorti1(v1)))
% 4.10/1.77 | (9) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (op2(v1, v0) = v1 & sorti2(v1)))
% 4.10/1.77 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 4.10/1.77 | (11) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (j(v1) = v0 & h(v0) = v1))
% 4.10/1.77 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (op1(v0, v1) = v2) | ~ sorti1(v1) | ~ sorti1(v0) | sorti1(v2))
% 4.10/1.77 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 4.10/1.77 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 4.10/1.77 | (15) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & sorti2(v1)))
% 4.10/1.77 | (16) ! [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))))
% 4.10/1.77 |
% 4.10/1.77 | Instantiating formula (11) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields:
% 4.10/1.77 | (17) ? [v0] : (j(v0) = all_0_0_0 & h(all_0_0_0) = v0)
% 4.10/1.77 |
% 4.10/1.77 | Instantiating formula (15) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields:
% 4.10/1.78 | (18) ? [v0] : (h(all_0_0_0) = v0 & sorti2(v0))
% 4.10/1.78 |
% 4.10/1.78 | Instantiating formula (16) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields:
% 4.10/1.78 | (19) ? [v0] : (h(all_0_0_0) = v0 & ! [v1] : ( ~ sorti1(v1) | ? [v2] : ? [v3] : ? [v4] : (h(v2) = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_0_0_0, v1) = v2)))
% 4.10/1.78 |
% 4.10/1.78 | Instantiating (19) with all_8_0_1 yields:
% 4.10/1.78 | (20) h(all_0_0_0) = all_8_0_1 & ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_8_0_1, v3) = v2 & op1(all_0_0_0, v0) = v1))
% 4.10/1.78 |
% 4.10/1.78 | Applying alpha-rule on (20) yields:
% 4.10/1.78 | (21) h(all_0_0_0) = all_8_0_1
% 4.10/1.78 | (22) ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_8_0_1, v3) = v2 & op1(all_0_0_0, v0) = v1))
% 4.10/1.78 |
% 4.10/1.78 | Instantiating formula (22) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields:
% 4.10/1.78 | (23) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_0_0_0) = v2 & op2(all_8_0_1, v2) = v1 & op1(all_0_0_0, all_0_0_0) = v0)
% 4.10/1.78 |
% 4.10/1.78 | Instantiating (18) with all_11_0_2 yields:
% 4.10/1.78 | (24) h(all_0_0_0) = all_11_0_2 & sorti2(all_11_0_2)
% 4.10/1.78 |
% 4.10/1.78 | Applying alpha-rule on (24) yields:
% 4.10/1.78 | (25) h(all_0_0_0) = all_11_0_2
% 4.10/1.78 | (26) sorti2(all_11_0_2)
% 4.10/1.78 |
% 4.10/1.78 | Instantiating (17) with all_13_0_3 yields:
% 4.10/1.78 | (27) j(all_13_0_3) = all_0_0_0 & h(all_0_0_0) = all_13_0_3
% 4.10/1.78 |
% 4.10/1.78 | Applying alpha-rule on (27) yields:
% 4.10/1.78 | (28) j(all_13_0_3) = all_0_0_0
% 4.10/1.78 | (29) h(all_0_0_0) = all_13_0_3
% 4.10/1.78 |
% 4.10/1.78 | Instantiating (23) with all_15_0_4, all_15_1_5, all_15_2_6 yields:
% 4.10/1.78 | (30) h(all_15_2_6) = all_15_1_5 & h(all_0_0_0) = all_15_0_4 & op2(all_8_0_1, all_15_0_4) = all_15_1_5 & op1(all_0_0_0, all_0_0_0) = all_15_2_6
% 4.10/1.78 |
% 4.10/1.78 | Applying alpha-rule on (30) yields:
% 4.10/1.78 | (31) h(all_15_2_6) = all_15_1_5
% 4.10/1.78 | (32) h(all_0_0_0) = all_15_0_4
% 4.10/1.78 | (33) op2(all_8_0_1, all_15_0_4) = all_15_1_5
% 4.10/1.78 | (34) op1(all_0_0_0, all_0_0_0) = all_15_2_6
% 4.10/1.78 |
% 4.10/1.78 | Instantiating formula (13) with all_0_0_0, all_13_0_3, all_15_0_4 and discharging atoms h(all_0_0_0) = all_15_0_4, h(all_0_0_0) = all_13_0_3, yields:
% 4.10/1.78 | (35) all_15_0_4 = all_13_0_3
% 4.36/1.78 |
% 4.36/1.78 | Instantiating formula (13) with all_0_0_0, all_11_0_2, all_15_0_4 and discharging atoms h(all_0_0_0) = all_15_0_4, h(all_0_0_0) = all_11_0_2, yields:
% 4.36/1.78 | (36) all_15_0_4 = all_11_0_2
% 4.36/1.78 |
% 4.36/1.78 | Instantiating formula (13) with all_0_0_0, all_8_0_1, all_13_0_3 and discharging atoms h(all_0_0_0) = all_13_0_3, h(all_0_0_0) = all_8_0_1, yields:
% 4.36/1.78 | (37) all_13_0_3 = all_8_0_1
% 4.36/1.78 |
% 4.36/1.78 | Combining equations (35,36) yields a new equation:
% 4.36/1.78 | (38) all_13_0_3 = all_11_0_2
% 4.36/1.78 |
% 4.36/1.78 | Simplifying 38 yields:
% 4.36/1.78 | (39) all_13_0_3 = all_11_0_2
% 4.36/1.78 |
% 4.36/1.78 | Combining equations (37,39) yields a new equation:
% 4.36/1.78 | (40) all_11_0_2 = all_8_0_1
% 4.36/1.78 |
% 4.36/1.78 | Combining equations (40,39) yields a new equation:
% 4.36/1.78 | (37) all_13_0_3 = all_8_0_1
% 4.36/1.78 |
% 4.36/1.78 | Combining equations (40,36) yields a new equation:
% 4.36/1.78 | (42) all_15_0_4 = all_8_0_1
% 4.36/1.78 |
% 4.36/1.78 | From (37) and (28) follows:
% 4.36/1.78 | (43) j(all_8_0_1) = all_0_0_0
% 4.36/1.78 |
% 4.36/1.78 | From (42) and (33) follows:
% 4.36/1.78 | (44) op2(all_8_0_1, all_8_0_1) = all_15_1_5
% 4.36/1.78 |
% 4.36/1.78 | From (40) and (26) follows:
% 4.36/1.78 | (45) sorti2(all_8_0_1)
% 4.36/1.78 |
% 4.36/1.78 | Instantiating formula (2) with all_15_1_5, all_8_0_1, all_8_0_1 and discharging atoms op2(all_8_0_1, all_8_0_1) = all_15_1_5, sorti2(all_8_0_1), yields:
% 4.36/1.78 | (46) sorti2(all_15_1_5)
% 4.36/1.78 |
% 4.36/1.78 | Instantiating formula (7) with all_8_0_1 and discharging atoms sorti2(all_8_0_1), yields:
% 4.36/1.78 | (47) ? [v0] : (j(all_8_0_1) = v0 & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_8_0_1, v1) = v2 & op1(v0, v4) = v3)))
% 4.36/1.79 |
% 4.36/1.79 | Instantiating formula (9) with all_8_0_1 and discharging atoms sorti2(all_8_0_1), yields:
% 4.36/1.79 | (48) ? [v0] : (op2(v0, all_8_0_1) = v0 & sorti2(v0))
% 4.36/1.79 |
% 4.36/1.79 | Instantiating (48) with all_27_0_7 yields:
% 4.36/1.79 | (49) op2(all_27_0_7, all_8_0_1) = all_27_0_7 & sorti2(all_27_0_7)
% 4.36/1.79 |
% 4.36/1.79 | Applying alpha-rule on (49) yields:
% 4.36/1.79 | (50) op2(all_27_0_7, all_8_0_1) = all_27_0_7
% 4.36/1.79 | (51) sorti2(all_27_0_7)
% 4.36/1.79 |
% 4.36/1.79 | Instantiating (47) with all_29_0_8 yields:
% 4.36/1.79 | (52) j(all_8_0_1) = all_29_0_8 & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_8_0_1, v0) = v1 & op1(all_29_0_8, v3) = v2))
% 4.36/1.79 |
% 4.36/1.79 | Applying alpha-rule on (52) yields:
% 4.36/1.79 | (53) j(all_8_0_1) = all_29_0_8
% 4.36/1.79 | (54) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_8_0_1, v0) = v1 & op1(all_29_0_8, v3) = v2))
% 4.36/1.79 |
% 4.36/1.79 | Instantiating formula (54) with all_8_0_1 and discharging atoms sorti2(all_8_0_1), yields:
% 4.36/1.79 | (55) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_8_0_1) = v2 & op2(all_8_0_1, all_8_0_1) = v0 & op1(all_29_0_8, v2) = v1)
% 4.36/1.79 |
% 4.36/1.79 | Instantiating (55) with all_32_0_9, all_32_1_10, all_32_2_11 yields:
% 4.36/1.79 | (56) j(all_32_2_11) = all_32_1_10 & j(all_8_0_1) = all_32_0_9 & op2(all_8_0_1, all_8_0_1) = all_32_2_11 & op1(all_29_0_8, all_32_0_9) = all_32_1_10
% 4.36/1.79 |
% 4.36/1.79 | Applying alpha-rule on (56) yields:
% 4.36/1.79 | (57) j(all_32_2_11) = all_32_1_10
% 4.36/1.79 | (58) j(all_8_0_1) = all_32_0_9
% 4.36/1.79 | (59) op2(all_8_0_1, all_8_0_1) = all_32_2_11
% 4.36/1.79 | (60) op1(all_29_0_8, all_32_0_9) = all_32_1_10
% 4.36/1.79 |
% 4.36/1.79 | Instantiating formula (10) with all_8_0_1, all_32_0_9, all_0_0_0 and discharging atoms j(all_8_0_1) = all_32_0_9, j(all_8_0_1) = all_0_0_0, yields:
% 4.36/1.79 | (61) all_32_0_9 = all_0_0_0
% 4.36/1.79 |
% 4.36/1.79 | Instantiating formula (10) with all_8_0_1, all_29_0_8, all_32_0_9 and discharging atoms j(all_8_0_1) = all_32_0_9, j(all_8_0_1) = all_29_0_8, yields:
% 4.36/1.79 | (62) all_32_0_9 = all_29_0_8
% 4.36/1.79 |
% 4.36/1.79 | Combining equations (61,62) yields a new equation:
% 4.36/1.79 | (63) all_29_0_8 = all_0_0_0
% 4.36/1.79 |
% 4.36/1.79 | From (63) and (53) follows:
% 4.36/1.79 | (43) j(all_8_0_1) = all_0_0_0
% 4.36/1.79 |
% 4.36/1.79 | Instantiating formula (54) with all_27_0_7 and discharging atoms sorti2(all_27_0_7), yields:
% 4.36/1.79 | (65) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_27_0_7) = v2 & op2(all_8_0_1, all_27_0_7) = v0 & op1(all_29_0_8, v2) = v1)
% 4.36/1.79 |
% 4.36/1.79 | Instantiating formula (6) with all_27_0_7 and discharging atoms sorti2(all_27_0_7), yields:
% 4.36/1.79 | (66) ? [v0] : (j(all_27_0_7) = v0 & h(v0) = all_27_0_7)
% 4.36/1.79 |
% 4.36/1.79 | Instantiating formula (8) with all_27_0_7 and discharging atoms sorti2(all_27_0_7), yields:
% 4.36/1.79 | (67) ? [v0] : (j(all_27_0_7) = v0 & sorti1(v0))
% 4.36/1.79 |
% 4.36/1.79 | Instantiating formula (7) with all_27_0_7 and discharging atoms sorti2(all_27_0_7), yields:
% 4.36/1.79 | (68) ? [v0] : (j(all_27_0_7) = v0 & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_27_0_7, v1) = v2 & op1(v0, v4) = v3)))
% 4.36/1.79 |
% 4.36/1.79 | Instantiating formula (7) with all_15_1_5 and discharging atoms sorti2(all_15_1_5), yields:
% 4.36/1.79 | (69) ? [v0] : (j(all_15_1_5) = v0 & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_15_1_5, v1) = v2 & op1(v0, v4) = v3)))
% 4.36/1.79 |
% 4.36/1.79 | Instantiating (69) with all_56_0_20 yields:
% 4.36/1.79 | (70) j(all_15_1_5) = all_56_0_20 & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_15_1_5, v0) = v1 & op1(all_56_0_20, v3) = v2))
% 4.36/1.79 |
% 4.36/1.79 | Applying alpha-rule on (70) yields:
% 4.36/1.79 | (71) j(all_15_1_5) = all_56_0_20
% 4.36/1.79 | (72) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_15_1_5, v0) = v1 & op1(all_56_0_20, v3) = v2))
% 4.36/1.79 |
% 4.36/1.79 | Instantiating formula (72) with all_27_0_7 and discharging atoms sorti2(all_27_0_7), yields:
% 4.36/1.80 | (73) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_27_0_7) = v2 & op2(all_15_1_5, all_27_0_7) = v0 & op1(all_56_0_20, v2) = v1)
% 4.36/1.80 |
% 4.36/1.80 | Instantiating (68) with all_61_0_22 yields:
% 4.36/1.80 | (74) j(all_27_0_7) = all_61_0_22 & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_27_0_7, v0) = v1 & op1(all_61_0_22, v3) = v2))
% 4.36/1.80 |
% 4.36/1.80 | Applying alpha-rule on (74) yields:
% 4.36/1.80 | (75) j(all_27_0_7) = all_61_0_22
% 4.36/1.80 | (76) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_27_0_7, v0) = v1 & op1(all_61_0_22, v3) = v2))
% 4.36/1.80 |
% 4.36/1.80 | Instantiating formula (76) with all_27_0_7 and discharging atoms sorti2(all_27_0_7), yields:
% 4.36/1.80 | (77) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_27_0_7) = v2 & op2(all_27_0_7, all_27_0_7) = v0 & op1(all_61_0_22, v2) = v1)
% 4.36/1.80 |
% 4.36/1.80 | Instantiating formula (76) with all_8_0_1 and discharging atoms sorti2(all_8_0_1), yields:
% 4.36/1.80 | (78) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_8_0_1) = v2 & op2(all_27_0_7, all_8_0_1) = v0 & op1(all_61_0_22, v2) = v1)
% 4.36/1.80 |
% 4.36/1.80 | Instantiating (66) with all_64_0_23 yields:
% 4.36/1.80 | (79) j(all_27_0_7) = all_64_0_23 & h(all_64_0_23) = all_27_0_7
% 4.36/1.80 |
% 4.36/1.80 | Applying alpha-rule on (79) yields:
% 4.36/1.80 | (80) j(all_27_0_7) = all_64_0_23
% 4.36/1.80 | (81) h(all_64_0_23) = all_27_0_7
% 4.36/1.80 |
% 4.36/1.80 | Instantiating (65) with all_66_0_24, all_66_1_25, all_66_2_26 yields:
% 4.36/1.80 | (82) j(all_66_2_26) = all_66_1_25 & j(all_27_0_7) = all_66_0_24 & op2(all_8_0_1, all_27_0_7) = all_66_2_26 & op1(all_29_0_8, all_66_0_24) = all_66_1_25
% 4.36/1.80 |
% 4.36/1.80 | Applying alpha-rule on (82) yields:
% 4.36/1.80 | (83) j(all_66_2_26) = all_66_1_25
% 4.36/1.80 | (84) j(all_27_0_7) = all_66_0_24
% 4.42/1.80 | (85) op2(all_8_0_1, all_27_0_7) = all_66_2_26
% 4.42/1.80 | (86) op1(all_29_0_8, all_66_0_24) = all_66_1_25
% 4.42/1.80 |
% 4.42/1.80 | Instantiating (67) with all_68_0_27 yields:
% 4.42/1.80 | (87) j(all_27_0_7) = all_68_0_27 & sorti1(all_68_0_27)
% 4.42/1.80 |
% 4.42/1.80 | Applying alpha-rule on (87) yields:
% 4.42/1.80 | (88) j(all_27_0_7) = all_68_0_27
% 4.42/1.80 | (89) sorti1(all_68_0_27)
% 4.42/1.80 |
% 4.42/1.80 | Instantiating (73) with all_78_0_40, all_78_1_41, all_78_2_42 yields:
% 4.42/1.80 | (90) j(all_78_2_42) = all_78_1_41 & j(all_27_0_7) = all_78_0_40 & op2(all_15_1_5, all_27_0_7) = all_78_2_42 & op1(all_56_0_20, all_78_0_40) = all_78_1_41
% 4.42/1.80 |
% 4.42/1.80 | Applying alpha-rule on (90) yields:
% 4.42/1.80 | (91) j(all_78_2_42) = all_78_1_41
% 4.42/1.80 | (92) j(all_27_0_7) = all_78_0_40
% 4.42/1.80 | (93) op2(all_15_1_5, all_27_0_7) = all_78_2_42
% 4.42/1.80 | (94) op1(all_56_0_20, all_78_0_40) = all_78_1_41
% 4.42/1.80 |
% 4.42/1.80 | Instantiating (78) with all_80_0_43, all_80_1_44, all_80_2_45 yields:
% 4.42/1.80 | (95) j(all_80_2_45) = all_80_1_44 & j(all_8_0_1) = all_80_0_43 & op2(all_27_0_7, all_8_0_1) = all_80_2_45 & op1(all_61_0_22, all_80_0_43) = all_80_1_44
% 4.42/1.80 |
% 4.42/1.80 | Applying alpha-rule on (95) yields:
% 4.42/1.80 | (96) j(all_80_2_45) = all_80_1_44
% 4.42/1.80 | (97) j(all_8_0_1) = all_80_0_43
% 4.42/1.80 | (98) op2(all_27_0_7, all_8_0_1) = all_80_2_45
% 4.42/1.80 | (99) op1(all_61_0_22, all_80_0_43) = all_80_1_44
% 4.42/1.80 |
% 4.42/1.80 | Instantiating (77) with all_84_0_49, all_84_1_50, all_84_2_51 yields:
% 4.42/1.80 | (100) j(all_84_2_51) = all_84_1_50 & j(all_27_0_7) = all_84_0_49 & op2(all_27_0_7, all_27_0_7) = all_84_2_51 & op1(all_61_0_22, all_84_0_49) = all_84_1_50
% 4.42/1.80 |
% 4.42/1.80 | Applying alpha-rule on (100) yields:
% 4.42/1.80 | (101) j(all_84_2_51) = all_84_1_50
% 4.42/1.80 | (102) j(all_27_0_7) = all_84_0_49
% 4.42/1.80 | (103) op2(all_27_0_7, all_27_0_7) = all_84_2_51
% 4.42/1.80 | (104) op1(all_61_0_22, all_84_0_49) = all_84_1_50
% 4.42/1.80 |
% 4.42/1.80 | Instantiating formula (10) with all_27_0_7, all_68_0_27, all_84_0_49 and discharging atoms j(all_27_0_7) = all_84_0_49, j(all_27_0_7) = all_68_0_27, yields:
% 4.42/1.80 | (105) all_84_0_49 = all_68_0_27
% 4.42/1.80 |
% 4.42/1.80 | Instantiating formula (10) with all_27_0_7, all_68_0_27, all_78_0_40 and discharging atoms j(all_27_0_7) = all_78_0_40, j(all_27_0_7) = all_68_0_27, yields:
% 4.42/1.80 | (106) all_78_0_40 = all_68_0_27
% 4.42/1.80 |
% 4.42/1.80 | Instantiating formula (10) with all_27_0_7, all_66_0_24, all_78_0_40 and discharging atoms j(all_27_0_7) = all_78_0_40, j(all_27_0_7) = all_66_0_24, yields:
% 4.42/1.81 | (107) all_78_0_40 = all_66_0_24
% 4.42/1.81 |
% 4.42/1.81 | Instantiating formula (10) with all_27_0_7, all_64_0_23, all_84_0_49 and discharging atoms j(all_27_0_7) = all_84_0_49, j(all_27_0_7) = all_64_0_23, yields:
% 4.42/1.81 | (108) all_84_0_49 = all_64_0_23
% 4.42/1.81 |
% 4.42/1.81 | Instantiating formula (10) with all_27_0_7, all_61_0_22, all_78_0_40 and discharging atoms j(all_27_0_7) = all_78_0_40, j(all_27_0_7) = all_61_0_22, yields:
% 4.42/1.81 | (109) all_78_0_40 = all_61_0_22
% 4.42/1.81 |
% 4.42/1.81 | Instantiating formula (10) with all_8_0_1, all_80_0_43, all_0_0_0 and discharging atoms j(all_8_0_1) = all_80_0_43, j(all_8_0_1) = all_0_0_0, yields:
% 4.42/1.81 | (110) all_80_0_43 = all_0_0_0
% 4.42/1.81 |
% 4.42/1.81 | Instantiating formula (3) with all_27_0_7, all_8_0_1, all_80_2_45, all_27_0_7 and discharging atoms op2(all_27_0_7, all_8_0_1) = all_80_2_45, op2(all_27_0_7, all_8_0_1) = all_27_0_7, yields:
% 4.42/1.81 | (111) all_80_2_45 = all_27_0_7
% 4.42/1.81 |
% 4.42/1.81 | Combining equations (105,108) yields a new equation:
% 4.42/1.81 | (112) all_68_0_27 = all_64_0_23
% 4.42/1.81 |
% 4.42/1.81 | Simplifying 112 yields:
% 4.42/1.81 | (113) all_68_0_27 = all_64_0_23
% 4.42/1.81 |
% 4.42/1.81 | Combining equations (109,107) yields a new equation:
% 4.42/1.81 | (114) all_66_0_24 = all_61_0_22
% 4.42/1.81 |
% 4.42/1.81 | Combining equations (106,107) yields a new equation:
% 4.42/1.81 | (115) all_68_0_27 = all_66_0_24
% 4.42/1.81 |
% 4.42/1.81 | Simplifying 115 yields:
% 4.42/1.81 | (116) all_68_0_27 = all_66_0_24
% 4.42/1.81 |
% 4.42/1.81 | Combining equations (116,113) yields a new equation:
% 4.42/1.81 | (117) all_66_0_24 = all_64_0_23
% 4.42/1.81 |
% 4.42/1.81 | Simplifying 117 yields:
% 4.42/1.81 | (118) all_66_0_24 = all_64_0_23
% 4.42/1.81 |
% 4.42/1.81 | Combining equations (118,114) yields a new equation:
% 4.42/1.81 | (119) all_64_0_23 = all_61_0_22
% 4.42/1.81 |
% 4.42/1.81 | Simplifying 119 yields:
% 4.42/1.81 | (120) all_64_0_23 = all_61_0_22
% 4.42/1.81 |
% 4.42/1.81 | Combining equations (120,113) yields a new equation:
% 4.42/1.81 | (121) all_68_0_27 = all_61_0_22
% 4.42/1.81 |
% 4.42/1.81 | From (111) and (96) follows:
% 4.42/1.81 | (122) j(all_27_0_7) = all_80_1_44
% 4.42/1.81 |
% 4.42/1.81 | From (120) and (80) follows:
% 4.42/1.81 | (75) j(all_27_0_7) = all_61_0_22
% 4.42/1.81 |
% 4.42/1.81 | From (110) and (99) follows:
% 4.42/1.81 | (124) op1(all_61_0_22, all_0_0_0) = all_80_1_44
% 4.42/1.81 |
% 4.42/1.81 | From (121) and (89) follows:
% 4.42/1.81 | (125) sorti1(all_61_0_22)
% 4.42/1.81 |
% 4.42/1.81 | Instantiating formula (10) with all_27_0_7, all_80_1_44, all_61_0_22 and discharging atoms j(all_27_0_7) = all_80_1_44, j(all_27_0_7) = all_61_0_22, yields:
% 4.42/1.81 | (126) all_80_1_44 = all_61_0_22
% 4.42/1.81 |
% 4.42/1.81 | From (126) and (124) follows:
% 4.42/1.81 | (127) op1(all_61_0_22, all_0_0_0) = all_61_0_22
% 4.42/1.81 |
% 4.42/1.81 | Instantiating formula (4) with all_61_0_22 and discharging atoms op1(all_61_0_22, all_0_0_0) = all_61_0_22, sorti1(all_61_0_22), yields:
% 4.42/1.81 | (128) $false
% 4.42/1.81 |
% 4.42/1.81 |-The branch is then unsatisfiable
% 4.42/1.81 % SZS output end Proof for theBenchmark
% 4.42/1.81
% 4.42/1.81 1206ms
%------------------------------------------------------------------------------