TSTP Solution File: ALG040+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG040+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 15:33:52 EDT 2022
% Result : Theorem 2.55s 1.28s
% Output : Proof 4.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ALG040+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.13 % 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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 8 01:45:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.53/0.60 ____ _
% 0.53/0.60 ___ / __ \_____(_)___ ________ __________
% 0.53/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.60
% 0.53/0.60 A Theorem Prover for First-Order Logic
% 0.53/0.60 (ePrincess v.1.0)
% 0.53/0.60
% 0.53/0.60 (c) Philipp Rümmer, 2009-2015
% 0.53/0.60 (c) Peter Backeman, 2014-2015
% 0.53/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.60 Bug reports to peter@backeman.se
% 0.53/0.60
% 0.53/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.60
% 0.53/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.44/0.90 Prover 0: Preprocessing ...
% 1.82/1.05 Prover 0: Constructing countermodel ...
% 2.55/1.28 Prover 0: proved (630ms)
% 2.55/1.28
% 2.55/1.28 No countermodel exists, formula is valid
% 2.55/1.28 % SZS status Theorem for theBenchmark
% 2.55/1.28
% 2.55/1.28 Generating proof ... found it (size 81)
% 4.10/1.76
% 4.10/1.76 % SZS output start Proof for theBenchmark
% 4.10/1.76 Assumed formulas after preprocessing and simplification:
% 4.10/1.76 | (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] : ! [v2] : (v2 = v0 | ~ (op1(v1, v1) = v2) | ~ sorti1(v1)) & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ( ~ (v3 = v1) & op2(v2, v2) = v3 & sorti2(v2))) & ! [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] : ( ~ 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)))))
% 4.47/1.79 | Instantiating (0) with all_0_0_0 yields:
% 4.47/1.79 | (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] : ! [v1] : (v1 = all_0_0_0 | ~ (op1(v0, v0) = v1) | ~ sorti1(v0)) & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ( ~ (v2 = v0) & op2(v1, v1) = v2 & sorti2(v1))) & ! [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))))
% 4.47/1.80 |
% 4.47/1.80 | Applying alpha-rule on (1) yields:
% 4.47/1.80 | (2) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & h(v1) = v0))
% 4.47/1.80 | (3) ! [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))))
% 4.47/1.80 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 4.47/1.80 | (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))))
% 4.47/1.80 | (6) sorti1(all_0_0_0)
% 4.47/1.80 | (7) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & sorti2(v1)))
% 4.47/1.80 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 4.47/1.80 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 4.47/1.80 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (op1(v0, v1) = v2) | ~ sorti1(v1) | ~ sorti1(v0) | sorti1(v2))
% 4.47/1.80 | (11) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & sorti1(v1)))
% 4.47/1.80 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 4.47/1.80 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (op2(v0, v1) = v2) | ~ sorti2(v1) | ~ sorti2(v0) | sorti2(v2))
% 4.47/1.80 | (14) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ( ~ (v2 = v0) & op2(v1, v1) = v2 & sorti2(v1)))
% 4.47/1.80 | (15) ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (op1(v0, v0) = v1) | ~ sorti1(v0))
% 4.47/1.80 | (16) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (j(v1) = v0 & h(v0) = v1))
% 4.47/1.80 |
% 4.47/1.80 | Instantiating formula (16) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields:
% 4.47/1.81 | (17) ? [v0] : (j(v0) = all_0_0_0 & h(all_0_0_0) = v0)
% 4.47/1.81 |
% 4.47/1.81 | Instantiating formula (7) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields:
% 4.47/1.81 | (18) ? [v0] : (h(all_0_0_0) = v0 & sorti2(v0))
% 4.47/1.81 |
% 4.47/1.81 | Instantiating formula (3) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields:
% 4.47/1.81 | (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)))
% 4.63/1.81 |
% 4.63/1.81 | Instantiating (19) with all_8_0_1 yields:
% 4.63/1.81 | (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))
% 4.63/1.81 |
% 4.63/1.81 | Applying alpha-rule on (20) yields:
% 4.63/1.81 | (21) h(all_0_0_0) = all_8_0_1
% 4.63/1.81 | (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))
% 4.63/1.81 |
% 4.63/1.81 | Instantiating formula (22) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields:
% 4.63/1.81 | (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)
% 4.63/1.81 |
% 4.63/1.81 | Instantiating (18) with all_11_0_2 yields:
% 4.63/1.81 | (24) h(all_0_0_0) = all_11_0_2 & sorti2(all_11_0_2)
% 4.63/1.81 |
% 4.63/1.81 | Applying alpha-rule on (24) yields:
% 4.63/1.81 | (25) h(all_0_0_0) = all_11_0_2
% 4.63/1.81 | (26) sorti2(all_11_0_2)
% 4.63/1.81 |
% 4.63/1.81 | Instantiating (17) with all_13_0_3 yields:
% 4.63/1.81 | (27) j(all_13_0_3) = all_0_0_0 & h(all_0_0_0) = all_13_0_3
% 4.63/1.81 |
% 4.63/1.81 | Applying alpha-rule on (27) yields:
% 4.63/1.81 | (28) j(all_13_0_3) = all_0_0_0
% 4.63/1.81 | (29) h(all_0_0_0) = all_13_0_3
% 4.63/1.81 |
% 4.63/1.81 | Instantiating (23) with all_15_0_4, all_15_1_5, all_15_2_6 yields:
% 4.63/1.81 | (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
% 4.63/1.81 |
% 4.63/1.81 | Applying alpha-rule on (30) yields:
% 4.63/1.81 | (31) h(all_15_2_6) = all_15_1_5
% 4.63/1.81 | (32) h(all_0_0_0) = all_15_0_4
% 4.63/1.81 | (33) op2(all_8_0_1, all_15_0_4) = all_15_1_5
% 4.63/1.81 | (34) op1(all_0_0_0, all_0_0_0) = all_15_2_6
% 4.63/1.81 |
% 4.63/1.81 | Instantiating formula (12) 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:
% 4.63/1.81 | (35) all_15_0_4 = all_13_0_3
% 4.63/1.81 |
% 4.63/1.81 | Instantiating formula (12) 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:
% 4.63/1.81 | (36) all_15_0_4 = all_11_0_2
% 4.63/1.81 |
% 4.63/1.81 | Instantiating formula (12) 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:
% 4.63/1.81 | (37) all_13_0_3 = all_8_0_1
% 4.63/1.81 |
% 4.63/1.81 | Instantiating formula (15) with all_15_2_6, all_0_0_0 and discharging atoms op1(all_0_0_0, all_0_0_0) = all_15_2_6, sorti1(all_0_0_0), yields:
% 4.63/1.81 | (38) all_15_2_6 = all_0_0_0
% 4.63/1.81 |
% 4.63/1.81 | Combining equations (35,36) yields a new equation:
% 4.63/1.81 | (39) all_13_0_3 = all_11_0_2
% 4.63/1.81 |
% 4.63/1.81 | Simplifying 39 yields:
% 4.63/1.81 | (40) all_13_0_3 = all_11_0_2
% 4.63/1.81 |
% 4.63/1.81 | Combining equations (37,40) yields a new equation:
% 4.63/1.81 | (41) all_11_0_2 = all_8_0_1
% 4.63/1.81 |
% 4.63/1.81 | From (38) and (31) follows:
% 4.63/1.81 | (42) h(all_0_0_0) = all_15_1_5
% 4.63/1.81 |
% 4.63/1.81 | From (41) and (25) follows:
% 4.63/1.81 | (21) h(all_0_0_0) = all_8_0_1
% 4.63/1.81 |
% 4.63/1.81 | From (41) and (26) follows:
% 4.63/1.81 | (44) sorti2(all_8_0_1)
% 4.63/1.81 |
% 4.63/1.81 | Instantiating formula (12) with all_0_0_0, all_15_1_5, all_8_0_1 and discharging atoms h(all_0_0_0) = all_15_1_5, h(all_0_0_0) = all_8_0_1, yields:
% 4.63/1.81 | (45) all_15_1_5 = all_8_0_1
% 4.63/1.81 |
% 4.63/1.81 | From (45) and (42) follows:
% 4.63/1.81 | (21) h(all_0_0_0) = all_8_0_1
% 4.63/1.81 |
% 4.63/1.81 | Instantiating formula (14) with all_8_0_1 and discharging atoms sorti2(all_8_0_1), yields:
% 4.63/1.81 | (47) ? [v0] : ? [v1] : ( ~ (v1 = all_8_0_1) & op2(v0, v0) = v1 & sorti2(v0))
% 4.63/1.82 |
% 4.63/1.82 | Instantiating (47) with all_33_0_8, all_33_1_9 yields:
% 4.63/1.82 | (48) ~ (all_33_0_8 = all_8_0_1) & op2(all_33_1_9, all_33_1_9) = all_33_0_8 & sorti2(all_33_1_9)
% 4.63/1.82 |
% 4.63/1.82 | Applying alpha-rule on (48) yields:
% 4.63/1.82 | (49) ~ (all_33_0_8 = all_8_0_1)
% 4.63/1.82 | (50) op2(all_33_1_9, all_33_1_9) = all_33_0_8
% 4.63/1.82 | (51) sorti2(all_33_1_9)
% 4.63/1.82 |
% 4.63/1.82 | Instantiating formula (2) with all_33_1_9 and discharging atoms sorti2(all_33_1_9), yields:
% 4.63/1.82 | (52) ? [v0] : (j(all_33_1_9) = v0 & h(v0) = all_33_1_9)
% 4.63/1.82 |
% 4.63/1.82 | Instantiating formula (11) with all_33_1_9 and discharging atoms sorti2(all_33_1_9), yields:
% 4.63/1.82 | (53) ? [v0] : (j(all_33_1_9) = v0 & sorti1(v0))
% 4.63/1.82 |
% 4.63/1.82 | Instantiating formula (5) with all_33_1_9 and discharging atoms sorti2(all_33_1_9), yields:
% 4.63/1.82 | (54) ? [v0] : (j(all_33_1_9) = v0 & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_33_1_9, v1) = v2 & op1(v0, v4) = v3)))
% 4.63/1.82 |
% 4.63/1.82 | Instantiating (54) with all_51_0_13 yields:
% 4.63/1.82 | (55) j(all_33_1_9) = all_51_0_13 & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_33_1_9, v0) = v1 & op1(all_51_0_13, v3) = v2))
% 4.63/1.82 |
% 4.63/1.82 | Applying alpha-rule on (55) yields:
% 4.63/1.82 | (56) j(all_33_1_9) = all_51_0_13
% 4.63/1.82 | (57) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_33_1_9, v0) = v1 & op1(all_51_0_13, v3) = v2))
% 4.63/1.82 |
% 4.63/1.82 | Instantiating formula (57) with all_33_1_9 and discharging atoms sorti2(all_33_1_9), yields:
% 4.63/1.82 | (58) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_33_1_9) = v2 & op2(all_33_1_9, all_33_1_9) = v0 & op1(all_51_0_13, v2) = v1)
% 4.63/1.82 |
% 4.63/1.82 | Instantiating (53) with all_56_0_17 yields:
% 4.63/1.82 | (59) j(all_33_1_9) = all_56_0_17 & sorti1(all_56_0_17)
% 4.63/1.82 |
% 4.63/1.82 | Applying alpha-rule on (59) yields:
% 4.63/1.82 | (60) j(all_33_1_9) = all_56_0_17
% 4.63/1.82 | (61) sorti1(all_56_0_17)
% 4.63/1.82 |
% 4.63/1.82 | Instantiating (52) with all_58_0_18 yields:
% 4.63/1.82 | (62) j(all_33_1_9) = all_58_0_18 & h(all_58_0_18) = all_33_1_9
% 4.63/1.82 |
% 4.63/1.82 | Applying alpha-rule on (62) yields:
% 4.63/1.82 | (63) j(all_33_1_9) = all_58_0_18
% 4.63/1.82 | (64) h(all_58_0_18) = all_33_1_9
% 4.63/1.82 |
% 4.63/1.82 | Instantiating (58) with all_64_0_24, all_64_1_25, all_64_2_26 yields:
% 4.63/1.82 | (65) j(all_64_2_26) = all_64_1_25 & j(all_33_1_9) = all_64_0_24 & op2(all_33_1_9, all_33_1_9) = all_64_2_26 & op1(all_51_0_13, all_64_0_24) = all_64_1_25
% 4.63/1.82 |
% 4.63/1.82 | Applying alpha-rule on (65) yields:
% 4.63/1.82 | (66) j(all_64_2_26) = all_64_1_25
% 4.63/1.82 | (67) j(all_33_1_9) = all_64_0_24
% 4.63/1.82 | (68) op2(all_33_1_9, all_33_1_9) = all_64_2_26
% 4.63/1.82 | (69) op1(all_51_0_13, all_64_0_24) = all_64_1_25
% 4.63/1.82 |
% 4.63/1.82 | Instantiating formula (4) with all_33_1_9, all_58_0_18, all_64_0_24 and discharging atoms j(all_33_1_9) = all_64_0_24, j(all_33_1_9) = all_58_0_18, yields:
% 4.63/1.82 | (70) all_64_0_24 = all_58_0_18
% 4.63/1.82 |
% 4.63/1.82 | Instantiating formula (4) with all_33_1_9, all_56_0_17, all_58_0_18 and discharging atoms j(all_33_1_9) = all_58_0_18, j(all_33_1_9) = all_56_0_17, yields:
% 4.63/1.82 | (71) all_58_0_18 = all_56_0_17
% 4.63/1.82 |
% 4.63/1.82 | Instantiating formula (4) with all_33_1_9, all_51_0_13, all_64_0_24 and discharging atoms j(all_33_1_9) = all_64_0_24, j(all_33_1_9) = all_51_0_13, yields:
% 4.63/1.82 | (72) all_64_0_24 = all_51_0_13
% 4.63/1.82 |
% 4.63/1.82 | Instantiating formula (9) with all_33_1_9, all_33_1_9, all_64_2_26, all_33_0_8 and discharging atoms op2(all_33_1_9, all_33_1_9) = all_64_2_26, op2(all_33_1_9, all_33_1_9) = all_33_0_8, yields:
% 4.63/1.82 | (73) all_64_2_26 = all_33_0_8
% 4.63/1.82 |
% 4.63/1.82 | Combining equations (70,72) yields a new equation:
% 4.63/1.82 | (74) all_58_0_18 = all_51_0_13
% 4.63/1.82 |
% 4.63/1.82 | Simplifying 74 yields:
% 4.63/1.82 | (75) all_58_0_18 = all_51_0_13
% 4.63/1.82 |
% 4.63/1.82 | Combining equations (71,75) yields a new equation:
% 4.63/1.82 | (76) all_56_0_17 = all_51_0_13
% 4.63/1.82 |
% 4.63/1.82 | Simplifying 76 yields:
% 4.63/1.82 | (77) all_56_0_17 = all_51_0_13
% 4.63/1.82 |
% 4.63/1.82 | From (75) and (64) follows:
% 4.63/1.82 | (78) h(all_51_0_13) = all_33_1_9
% 4.63/1.82 |
% 4.63/1.82 | From (73) and (68) follows:
% 4.63/1.82 | (50) op2(all_33_1_9, all_33_1_9) = all_33_0_8
% 4.63/1.82 |
% 4.63/1.82 | From (77) and (61) follows:
% 4.63/1.82 | (80) sorti1(all_51_0_13)
% 4.63/1.82 |
% 4.63/1.82 | Instantiating formula (22) with all_51_0_13 and discharging atoms sorti1(all_51_0_13), yields:
% 4.63/1.82 | (81) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_51_0_13) = v2 & op2(all_8_0_1, v2) = v1 & op1(all_0_0_0, all_51_0_13) = v0)
% 4.63/1.82 |
% 4.63/1.83 | Instantiating formula (3) with all_51_0_13 and discharging atoms sorti1(all_51_0_13), yields:
% 4.63/1.83 | (82) ? [v0] : (h(all_51_0_13) = v0 & ! [v1] : ( ~ sorti1(v1) | ? [v2] : ? [v3] : ? [v4] : (h(v2) = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_51_0_13, v1) = v2)))
% 4.63/1.83 |
% 4.63/1.83 | Instantiating (82) with all_89_0_32 yields:
% 4.63/1.83 | (83) h(all_51_0_13) = all_89_0_32 & ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_89_0_32, v3) = v2 & op1(all_51_0_13, v0) = v1))
% 4.63/1.83 |
% 4.63/1.83 | Applying alpha-rule on (83) yields:
% 4.63/1.83 | (84) h(all_51_0_13) = all_89_0_32
% 4.63/1.83 | (85) ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_89_0_32, v3) = v2 & op1(all_51_0_13, v0) = v1))
% 4.63/1.83 |
% 4.63/1.83 | Instantiating formula (85) with all_51_0_13 and discharging atoms sorti1(all_51_0_13), yields:
% 4.63/1.83 | (86) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_51_0_13) = v2 & op2(all_89_0_32, v2) = v1 & op1(all_51_0_13, all_51_0_13) = v0)
% 4.63/1.83 |
% 4.63/1.83 | Instantiating formula (85) with all_0_0_0 and discharging atoms sorti1(all_0_0_0), yields:
% 4.63/1.83 | (87) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_0_0_0) = v2 & op2(all_89_0_32, v2) = v1 & op1(all_51_0_13, all_0_0_0) = v0)
% 4.63/1.83 |
% 4.73/1.83 | Instantiating (81) with all_96_0_37, all_96_1_38, all_96_2_39 yields:
% 4.73/1.83 | (88) h(all_96_2_39) = all_96_1_38 & h(all_51_0_13) = all_96_0_37 & op2(all_8_0_1, all_96_0_37) = all_96_1_38 & op1(all_0_0_0, all_51_0_13) = all_96_2_39
% 4.73/1.83 |
% 4.73/1.83 | Applying alpha-rule on (88) yields:
% 4.73/1.83 | (89) h(all_96_2_39) = all_96_1_38
% 4.73/1.83 | (90) h(all_51_0_13) = all_96_0_37
% 4.73/1.83 | (91) op2(all_8_0_1, all_96_0_37) = all_96_1_38
% 4.73/1.83 | (92) op1(all_0_0_0, all_51_0_13) = all_96_2_39
% 4.73/1.83 |
% 4.73/1.83 | Instantiating (87) with all_117_0_64, all_117_1_65, all_117_2_66 yields:
% 4.73/1.83 | (93) h(all_117_2_66) = all_117_1_65 & h(all_0_0_0) = all_117_0_64 & op2(all_89_0_32, all_117_0_64) = all_117_1_65 & op1(all_51_0_13, all_0_0_0) = all_117_2_66
% 4.73/1.83 |
% 4.73/1.83 | Applying alpha-rule on (93) yields:
% 4.73/1.83 | (94) h(all_117_2_66) = all_117_1_65
% 4.73/1.83 | (95) h(all_0_0_0) = all_117_0_64
% 4.73/1.83 | (96) op2(all_89_0_32, all_117_0_64) = all_117_1_65
% 4.73/1.83 | (97) op1(all_51_0_13, all_0_0_0) = all_117_2_66
% 4.73/1.83 |
% 4.73/1.83 | Instantiating (86) with all_119_0_67, all_119_1_68, all_119_2_69 yields:
% 4.73/1.83 | (98) h(all_119_2_69) = all_119_1_68 & h(all_51_0_13) = all_119_0_67 & op2(all_89_0_32, all_119_0_67) = all_119_1_68 & op1(all_51_0_13, all_51_0_13) = all_119_2_69
% 4.73/1.83 |
% 4.73/1.83 | Applying alpha-rule on (98) yields:
% 4.73/1.83 | (99) h(all_119_2_69) = all_119_1_68
% 4.73/1.83 | (100) h(all_51_0_13) = all_119_0_67
% 4.73/1.83 | (101) op2(all_89_0_32, all_119_0_67) = all_119_1_68
% 4.73/1.83 | (102) op1(all_51_0_13, all_51_0_13) = all_119_2_69
% 4.73/1.83 |
% 4.73/1.83 | Instantiating formula (12) with all_51_0_13, all_119_0_67, all_33_1_9 and discharging atoms h(all_51_0_13) = all_119_0_67, h(all_51_0_13) = all_33_1_9, yields:
% 4.73/1.83 | (103) all_119_0_67 = all_33_1_9
% 4.73/1.83 |
% 4.73/1.83 | Instantiating formula (12) with all_51_0_13, all_96_0_37, all_119_0_67 and discharging atoms h(all_51_0_13) = all_119_0_67, h(all_51_0_13) = all_96_0_37, yields:
% 4.73/1.83 | (104) all_119_0_67 = all_96_0_37
% 4.73/1.83 |
% 4.73/1.83 | Instantiating formula (12) with all_51_0_13, all_89_0_32, all_96_0_37 and discharging atoms h(all_51_0_13) = all_96_0_37, h(all_51_0_13) = all_89_0_32, yields:
% 4.73/1.83 | (105) all_96_0_37 = all_89_0_32
% 4.73/1.83 |
% 4.73/1.83 | Instantiating formula (12) with all_0_0_0, all_117_0_64, all_8_0_1 and discharging atoms h(all_0_0_0) = all_117_0_64, h(all_0_0_0) = all_8_0_1, yields:
% 4.73/1.83 | (106) all_117_0_64 = all_8_0_1
% 4.73/1.83 |
% 4.73/1.83 | Instantiating formula (15) with all_119_2_69, all_51_0_13 and discharging atoms op1(all_51_0_13, all_51_0_13) = all_119_2_69, sorti1(all_51_0_13), yields:
% 4.73/1.83 | (107) all_119_2_69 = all_0_0_0
% 4.73/1.83 |
% 4.73/1.83 | Combining equations (104,103) yields a new equation:
% 4.73/1.83 | (108) all_96_0_37 = all_33_1_9
% 4.73/1.83 |
% 4.73/1.83 | Simplifying 108 yields:
% 4.73/1.83 | (109) all_96_0_37 = all_33_1_9
% 4.73/1.83 |
% 4.73/1.83 | Combining equations (105,109) yields a new equation:
% 4.73/1.83 | (110) all_89_0_32 = all_33_1_9
% 4.73/1.83 |
% 4.73/1.83 | Simplifying 110 yields:
% 4.73/1.83 | (111) all_89_0_32 = all_33_1_9
% 4.73/1.84 |
% 4.73/1.84 | From (107) and (99) follows:
% 4.73/1.84 | (112) h(all_0_0_0) = all_119_1_68
% 4.73/1.84 |
% 4.73/1.84 | From (106) and (95) follows:
% 4.73/1.84 | (21) h(all_0_0_0) = all_8_0_1
% 4.73/1.84 |
% 4.73/1.84 | From (111)(103) and (101) follows:
% 4.73/1.84 | (114) op2(all_33_1_9, all_33_1_9) = all_119_1_68
% 4.73/1.84 |
% 4.73/1.84 | Instantiating formula (12) with all_0_0_0, all_119_1_68, all_8_0_1 and discharging atoms h(all_0_0_0) = all_119_1_68, h(all_0_0_0) = all_8_0_1, yields:
% 4.73/1.84 | (115) all_119_1_68 = all_8_0_1
% 4.73/1.84 |
% 4.73/1.84 | Instantiating formula (9) with all_33_1_9, all_33_1_9, all_119_1_68, all_33_0_8 and discharging atoms op2(all_33_1_9, all_33_1_9) = all_119_1_68, op2(all_33_1_9, all_33_1_9) = all_33_0_8, yields:
% 4.73/1.84 | (116) all_119_1_68 = all_33_0_8
% 4.73/1.84 |
% 4.73/1.84 | Combining equations (115,116) yields a new equation:
% 4.73/1.84 | (117) all_33_0_8 = all_8_0_1
% 4.73/1.84 |
% 4.73/1.84 | Equations (117) can reduce 49 to:
% 4.73/1.84 | (118) $false
% 4.73/1.84 |
% 4.73/1.84 |-The branch is then unsatisfiable
% 4.73/1.84 % SZS output end Proof for theBenchmark
% 4.73/1.84
% 4.73/1.84 1229ms
%------------------------------------------------------------------------------