TSTP Solution File: SET968+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n014.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 : Tue Jul 19 00:23:30 EDT 2022
% Result : Theorem 2.55s 1.30s
% Output : Proof 4.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n014.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 Jul 11 02:48:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.53/0.57 ____ _
% 0.53/0.57 ___ / __ \_____(_)___ ________ __________
% 0.53/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.57
% 0.53/0.57 A Theorem Prover for First-Order Logic
% 0.53/0.58 (ePrincess v.1.0)
% 0.53/0.58
% 0.53/0.58 (c) Philipp Rümmer, 2009-2015
% 0.53/0.58 (c) Peter Backeman, 2014-2015
% 0.53/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.58 Bug reports to peter@backeman.se
% 0.53/0.58
% 0.53/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.58
% 0.53/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.53/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.29/0.88 Prover 0: Preprocessing ...
% 1.72/1.06 Prover 0: Constructing countermodel ...
% 2.55/1.29 Prover 0: proved (670ms)
% 2.55/1.30
% 2.55/1.30 No countermodel exists, formula is valid
% 2.55/1.30 % SZS status Theorem for theBenchmark
% 2.55/1.30
% 2.55/1.30 Generating proof ... found it (size 65)
% 3.76/1.63
% 3.76/1.63 % SZS output start Proof for theBenchmark
% 3.76/1.63 Assumed formulas after preprocessing and simplification:
% 3.76/1.63 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ( ~ (v13 = v6) & cartesian_product2(v4, v5) = v6 & cartesian_product2(v1, v3) = v12 & cartesian_product2(v1, v2) = v10 & cartesian_product2(v0, v3) = v8 & cartesian_product2(v0, v2) = v7 & set_union2(v11, v12) = v13 & set_union2(v9, v10) = v11 & set_union2(v7, v8) = v9 & set_union2(v2, v3) = v5 & set_union2(v0, v1) = v4 & empty(v15) & ~ empty(v14) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v18, v17) = v20) | ~ (cartesian_product2(v18, v16) = v19) | ~ (set_union2(v19, v20) = v21) | ? [v22] : (cartesian_product2(v18, v22) = v21 & set_union2(v16, v17) = v22)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v17, v18) = v20) | ~ (cartesian_product2(v16, v18) = v19) | ~ (set_union2(v19, v20) = v21) | ? [v22] : (cartesian_product2(v22, v18) = v21 & set_union2(v16, v17) = v22)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v19, v18) = v20) | ~ (set_union2(v16, v17) = v19) | ? [v21] : ? [v22] : (cartesian_product2(v17, v18) = v22 & cartesian_product2(v16, v18) = v21 & set_union2(v21, v22) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v18, v19) = v20) | ~ (set_union2(v16, v17) = v19) | ? [v21] : ? [v22] : (cartesian_product2(v18, v17) = v22 & cartesian_product2(v18, v16) = v21 & set_union2(v21, v22) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_union2(v19, v18) = v20) | ~ (set_union2(v16, v17) = v19) | ? [v21] : (set_union2(v17, v18) = v21 & set_union2(v16, v21) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_union2(v17, v18) = v19) | ~ (set_union2(v16, v19) = v20) | ? [v21] : (set_union2(v21, v18) = v20 & set_union2(v16, v17) = v21)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (cartesian_product2(v19, v18) = v17) | ~ (cartesian_product2(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (set_union2(v19, v18) = v17) | ~ (set_union2(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v17, v16) = v18) | ~ empty(v18) | empty(v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v17, v16) = v18) | set_union2(v16, v17) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v16, v17) = v18) | ~ empty(v18) | empty(v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v16, v17) = v18) | set_union2(v17, v16) = v18) & ! [v16] : ! [v17] : (v17 = v16 | ~ (set_union2(v16, v16) = v17)))
% 4.06/1.66 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15 yields:
% 4.06/1.66 | (1) ~ (all_0_2_2 = all_0_9_9) & cartesian_product2(all_0_11_11, all_0_10_10) = all_0_9_9 & cartesian_product2(all_0_14_14, all_0_12_12) = all_0_3_3 & cartesian_product2(all_0_14_14, all_0_13_13) = all_0_5_5 & cartesian_product2(all_0_15_15, all_0_12_12) = all_0_7_7 & cartesian_product2(all_0_15_15, all_0_13_13) = all_0_8_8 & set_union2(all_0_4_4, all_0_3_3) = all_0_2_2 & set_union2(all_0_6_6, all_0_5_5) = all_0_4_4 & set_union2(all_0_8_8, all_0_7_7) = all_0_6_6 & set_union2(all_0_13_13, all_0_12_12) = all_0_10_10 & set_union2(all_0_15_15, all_0_14_14) = all_0_11_11 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ (set_union2(v3, v4) = v5) | ? [v6] : (cartesian_product2(v2, v6) = v5 & set_union2(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (set_union2(v3, v4) = v5) | ? [v6] : (cartesian_product2(v6, v2) = v5 & set_union2(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v3, v2) = v4) | ~ (set_union2(v0, v1) = v3) | ? [v5] : ? [v6] : (cartesian_product2(v1, v2) = v6 & cartesian_product2(v0, v2) = v5 & set_union2(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v3) = v4) | ~ (set_union2(v0, v1) = v3) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & set_union2(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v3, v2) = v4) | ~ (set_union2(v0, v1) = v3) | ? [v5] : (set_union2(v1, v2) = v5 & set_union2(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v1, v2) = v3) | ~ (set_union2(v0, v3) = v4) | ? [v5] : (set_union2(v5, v2) = v4 & set_union2(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 4.06/1.67 |
% 4.06/1.67 | Applying alpha-rule on (1) yields:
% 4.06/1.67 | (2) cartesian_product2(all_0_11_11, all_0_10_10) = all_0_9_9
% 4.06/1.67 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 4.06/1.67 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 4.06/1.67 | (5) empty(all_0_0_0)
% 4.06/1.67 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v3, v2) = v4) | ~ (set_union2(v0, v1) = v3) | ? [v5] : (set_union2(v1, v2) = v5 & set_union2(v0, v5) = v4))
% 4.06/1.67 | (7) set_union2(all_0_6_6, all_0_5_5) = all_0_4_4
% 4.06/1.67 | (8) set_union2(all_0_15_15, all_0_14_14) = all_0_11_11
% 4.06/1.67 | (9) ~ empty(all_0_1_1)
% 4.06/1.67 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 4.06/1.67 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v3, v2) = v4) | ~ (set_union2(v0, v1) = v3) | ? [v5] : ? [v6] : (cartesian_product2(v1, v2) = v6 & cartesian_product2(v0, v2) = v5 & set_union2(v5, v6) = v4))
% 4.06/1.67 | (12) ~ (all_0_2_2 = all_0_9_9)
% 4.06/1.67 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (set_union2(v3, v4) = v5) | ? [v6] : (cartesian_product2(v6, v2) = v5 & set_union2(v0, v1) = v6))
% 4.06/1.67 | (14) cartesian_product2(all_0_15_15, all_0_12_12) = all_0_7_7
% 4.06/1.67 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ (set_union2(v3, v4) = v5) | ? [v6] : (cartesian_product2(v2, v6) = v5 & set_union2(v0, v1) = v6))
% 4.06/1.67 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 4.06/1.67 | (17) cartesian_product2(all_0_14_14, all_0_12_12) = all_0_3_3
% 4.06/1.67 | (18) set_union2(all_0_8_8, all_0_7_7) = all_0_6_6
% 4.23/1.67 | (19) set_union2(all_0_4_4, all_0_3_3) = all_0_2_2
% 4.23/1.67 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v1, v2) = v3) | ~ (set_union2(v0, v3) = v4) | ? [v5] : (set_union2(v5, v2) = v4 & set_union2(v0, v1) = v5))
% 4.23/1.67 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 4.23/1.67 | (22) cartesian_product2(all_0_14_14, all_0_13_13) = all_0_5_5
% 4.23/1.67 | (23) set_union2(all_0_13_13, all_0_12_12) = all_0_10_10
% 4.23/1.67 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v3) = v4) | ~ (set_union2(v0, v1) = v3) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & set_union2(v5, v6) = v4))
% 4.23/1.67 | (25) cartesian_product2(all_0_15_15, all_0_13_13) = all_0_8_8
% 4.23/1.68 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 4.23/1.68 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 4.23/1.68 |
% 4.23/1.68 | Instantiating formula (6) with all_0_2_2, all_0_4_4, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms set_union2(all_0_4_4, all_0_3_3) = all_0_2_2, set_union2(all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 4.23/1.68 | (28) ? [v0] : (set_union2(all_0_5_5, all_0_3_3) = v0 & set_union2(all_0_6_6, v0) = all_0_2_2)
% 4.23/1.68 |
% 4.23/1.68 | Instantiating formula (15) with all_0_6_6, all_0_7_7, all_0_8_8, all_0_15_15, all_0_12_12, all_0_13_13 and discharging atoms cartesian_product2(all_0_15_15, all_0_12_12) = all_0_7_7, cartesian_product2(all_0_15_15, all_0_13_13) = all_0_8_8, set_union2(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 4.23/1.68 | (29) ? [v0] : (cartesian_product2(all_0_15_15, v0) = all_0_6_6 & set_union2(all_0_13_13, all_0_12_12) = v0)
% 4.23/1.68 |
% 4.23/1.68 | Instantiating formula (24) with all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13 and discharging atoms cartesian_product2(all_0_11_11, all_0_10_10) = all_0_9_9, set_union2(all_0_13_13, all_0_12_12) = all_0_10_10, yields:
% 4.23/1.68 | (30) ? [v0] : ? [v1] : (cartesian_product2(all_0_11_11, all_0_12_12) = v1 & cartesian_product2(all_0_11_11, all_0_13_13) = v0 & set_union2(v0, v1) = all_0_9_9)
% 4.23/1.68 |
% 4.23/1.68 | Instantiating formula (4) with all_0_10_10, all_0_13_13, all_0_12_12 and discharging atoms set_union2(all_0_13_13, all_0_12_12) = all_0_10_10, yields:
% 4.23/1.68 | (31) set_union2(all_0_12_12, all_0_13_13) = all_0_10_10
% 4.23/1.68 |
% 4.23/1.68 | Instantiating formula (11) with all_0_9_9, all_0_11_11, all_0_10_10, all_0_14_14, all_0_15_15 and discharging atoms cartesian_product2(all_0_11_11, all_0_10_10) = all_0_9_9, set_union2(all_0_15_15, all_0_14_14) = all_0_11_11, yields:
% 4.23/1.68 | (32) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_10_10) = v1 & cartesian_product2(all_0_15_15, all_0_10_10) = v0 & set_union2(v0, v1) = all_0_9_9)
% 4.23/1.68 |
% 4.23/1.68 | Instantiating formula (4) with all_0_11_11, all_0_15_15, all_0_14_14 and discharging atoms set_union2(all_0_15_15, all_0_14_14) = all_0_11_11, yields:
% 4.23/1.68 | (33) set_union2(all_0_14_14, all_0_15_15) = all_0_11_11
% 4.23/1.68 |
% 4.23/1.68 | Instantiating (30) with all_9_0_16, all_9_1_17 yields:
% 4.23/1.68 | (34) cartesian_product2(all_0_11_11, all_0_12_12) = all_9_0_16 & cartesian_product2(all_0_11_11, all_0_13_13) = all_9_1_17 & set_union2(all_9_1_17, all_9_0_16) = all_0_9_9
% 4.23/1.68 |
% 4.23/1.68 | Applying alpha-rule on (34) yields:
% 4.23/1.68 | (35) cartesian_product2(all_0_11_11, all_0_12_12) = all_9_0_16
% 4.23/1.68 | (36) cartesian_product2(all_0_11_11, all_0_13_13) = all_9_1_17
% 4.23/1.68 | (37) set_union2(all_9_1_17, all_9_0_16) = all_0_9_9
% 4.23/1.68 |
% 4.23/1.68 | Instantiating (29) with all_11_0_18 yields:
% 4.23/1.68 | (38) cartesian_product2(all_0_15_15, all_11_0_18) = all_0_6_6 & set_union2(all_0_13_13, all_0_12_12) = all_11_0_18
% 4.23/1.68 |
% 4.23/1.68 | Applying alpha-rule on (38) yields:
% 4.23/1.68 | (39) cartesian_product2(all_0_15_15, all_11_0_18) = all_0_6_6
% 4.23/1.68 | (40) set_union2(all_0_13_13, all_0_12_12) = all_11_0_18
% 4.23/1.68 |
% 4.23/1.68 | Instantiating (28) with all_13_0_19 yields:
% 4.23/1.68 | (41) set_union2(all_0_5_5, all_0_3_3) = all_13_0_19 & set_union2(all_0_6_6, all_13_0_19) = all_0_2_2
% 4.23/1.68 |
% 4.23/1.68 | Applying alpha-rule on (41) yields:
% 4.23/1.68 | (42) set_union2(all_0_5_5, all_0_3_3) = all_13_0_19
% 4.23/1.68 | (43) set_union2(all_0_6_6, all_13_0_19) = all_0_2_2
% 4.23/1.68 |
% 4.23/1.68 | Instantiating (32) with all_15_0_20, all_15_1_21 yields:
% 4.23/1.68 | (44) cartesian_product2(all_0_14_14, all_0_10_10) = all_15_0_20 & cartesian_product2(all_0_15_15, all_0_10_10) = all_15_1_21 & set_union2(all_15_1_21, all_15_0_20) = all_0_9_9
% 4.23/1.68 |
% 4.23/1.68 | Applying alpha-rule on (44) yields:
% 4.23/1.68 | (45) cartesian_product2(all_0_14_14, all_0_10_10) = all_15_0_20
% 4.23/1.68 | (46) cartesian_product2(all_0_15_15, all_0_10_10) = all_15_1_21
% 4.23/1.68 | (47) set_union2(all_15_1_21, all_15_0_20) = all_0_9_9
% 4.23/1.68 |
% 4.23/1.68 | Instantiating formula (10) with all_0_13_13, all_0_12_12, all_11_0_18, all_0_10_10 and discharging atoms set_union2(all_0_13_13, all_0_12_12) = all_11_0_18, set_union2(all_0_13_13, all_0_12_12) = all_0_10_10, yields:
% 4.23/1.68 | (48) all_11_0_18 = all_0_10_10
% 4.23/1.68 |
% 4.23/1.68 | From (48) and (39) follows:
% 4.23/1.68 | (49) cartesian_product2(all_0_15_15, all_0_10_10) = all_0_6_6
% 4.23/1.68 |
% 4.23/1.68 | From (48) and (40) follows:
% 4.23/1.68 | (23) set_union2(all_0_13_13, all_0_12_12) = all_0_10_10
% 4.23/1.68 |
% 4.23/1.68 | Instantiating formula (21) with all_0_15_15, all_0_10_10, all_0_6_6, all_15_1_21 and discharging atoms cartesian_product2(all_0_15_15, all_0_10_10) = all_15_1_21, cartesian_product2(all_0_15_15, all_0_10_10) = all_0_6_6, yields:
% 4.23/1.69 | (51) all_15_1_21 = all_0_6_6
% 4.23/1.69 |
% 4.23/1.69 | From (51) and (47) follows:
% 4.23/1.69 | (52) set_union2(all_0_6_6, all_15_0_20) = all_0_9_9
% 4.23/1.69 |
% 4.23/1.69 | Instantiating formula (11) with all_9_0_16, all_0_11_11, all_0_12_12, all_0_14_14, all_0_15_15 and discharging atoms cartesian_product2(all_0_11_11, all_0_12_12) = all_9_0_16, set_union2(all_0_15_15, all_0_14_14) = all_0_11_11, yields:
% 4.23/1.69 | (53) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_12_12) = v1 & cartesian_product2(all_0_15_15, all_0_12_12) = v0 & set_union2(v0, v1) = all_9_0_16)
% 4.23/1.69 |
% 4.23/1.69 | Instantiating formula (11) with all_9_1_17, all_0_11_11, all_0_13_13, all_0_14_14, all_0_15_15 and discharging atoms cartesian_product2(all_0_11_11, all_0_13_13) = all_9_1_17, set_union2(all_0_15_15, all_0_14_14) = all_0_11_11, yields:
% 4.23/1.69 | (54) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_13_13) = v1 & cartesian_product2(all_0_15_15, all_0_13_13) = v0 & set_union2(v0, v1) = all_9_1_17)
% 4.23/1.69 |
% 4.23/1.69 | Instantiating formula (24) with all_15_0_20, all_0_10_10, all_0_14_14, all_0_12_12, all_0_13_13 and discharging atoms cartesian_product2(all_0_14_14, all_0_10_10) = all_15_0_20, set_union2(all_0_13_13, all_0_12_12) = all_0_10_10, yields:
% 4.23/1.69 | (55) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_12_12) = v1 & cartesian_product2(all_0_14_14, all_0_13_13) = v0 & set_union2(v0, v1) = all_15_0_20)
% 4.23/1.69 |
% 4.23/1.69 | Instantiating formula (24) with all_15_0_20, all_0_10_10, all_0_14_14, all_0_13_13, all_0_12_12 and discharging atoms cartesian_product2(all_0_14_14, all_0_10_10) = all_15_0_20, set_union2(all_0_12_12, all_0_13_13) = all_0_10_10, yields:
% 4.23/1.69 | (56) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_12_12) = v0 & cartesian_product2(all_0_14_14, all_0_13_13) = v1 & set_union2(v0, v1) = all_15_0_20)
% 4.23/1.69 |
% 4.23/1.69 | Instantiating formula (11) with all_9_0_16, all_0_11_11, all_0_12_12, all_0_15_15, all_0_14_14 and discharging atoms cartesian_product2(all_0_11_11, all_0_12_12) = all_9_0_16, set_union2(all_0_14_14, all_0_15_15) = all_0_11_11, yields:
% 4.23/1.69 | (57) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_12_12) = v0 & cartesian_product2(all_0_15_15, all_0_12_12) = v1 & set_union2(v0, v1) = all_9_0_16)
% 4.23/1.69 |
% 4.23/1.69 | Instantiating formula (11) with all_9_1_17, all_0_11_11, all_0_13_13, all_0_15_15, all_0_14_14 and discharging atoms cartesian_product2(all_0_11_11, all_0_13_13) = all_9_1_17, set_union2(all_0_14_14, all_0_15_15) = all_0_11_11, yields:
% 4.23/1.69 | (58) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_13_13) = v0 & cartesian_product2(all_0_15_15, all_0_13_13) = v1 & set_union2(v0, v1) = all_9_1_17)
% 4.23/1.69 |
% 4.23/1.69 | Instantiating (55) with all_45_0_29, all_45_1_30 yields:
% 4.23/1.69 | (59) cartesian_product2(all_0_14_14, all_0_12_12) = all_45_0_29 & cartesian_product2(all_0_14_14, all_0_13_13) = all_45_1_30 & set_union2(all_45_1_30, all_45_0_29) = all_15_0_20
% 4.23/1.69 |
% 4.23/1.69 | Applying alpha-rule on (59) yields:
% 4.23/1.69 | (60) cartesian_product2(all_0_14_14, all_0_12_12) = all_45_0_29
% 4.23/1.69 | (61) cartesian_product2(all_0_14_14, all_0_13_13) = all_45_1_30
% 4.23/1.69 | (62) set_union2(all_45_1_30, all_45_0_29) = all_15_0_20
% 4.23/1.69 |
% 4.23/1.69 | Instantiating (54) with all_55_0_35, all_55_1_36 yields:
% 4.23/1.69 | (63) cartesian_product2(all_0_14_14, all_0_13_13) = all_55_0_35 & cartesian_product2(all_0_15_15, all_0_13_13) = all_55_1_36 & set_union2(all_55_1_36, all_55_0_35) = all_9_1_17
% 4.23/1.69 |
% 4.23/1.69 | Applying alpha-rule on (63) yields:
% 4.23/1.69 | (64) cartesian_product2(all_0_14_14, all_0_13_13) = all_55_0_35
% 4.23/1.69 | (65) cartesian_product2(all_0_15_15, all_0_13_13) = all_55_1_36
% 4.23/1.69 | (66) set_union2(all_55_1_36, all_55_0_35) = all_9_1_17
% 4.23/1.69 |
% 4.23/1.69 | Instantiating (58) with all_63_0_40, all_63_1_41 yields:
% 4.23/1.69 | (67) cartesian_product2(all_0_14_14, all_0_13_13) = all_63_1_41 & cartesian_product2(all_0_15_15, all_0_13_13) = all_63_0_40 & set_union2(all_63_1_41, all_63_0_40) = all_9_1_17
% 4.23/1.69 |
% 4.23/1.69 | Applying alpha-rule on (67) yields:
% 4.23/1.69 | (68) cartesian_product2(all_0_14_14, all_0_13_13) = all_63_1_41
% 4.23/1.69 | (69) cartesian_product2(all_0_15_15, all_0_13_13) = all_63_0_40
% 4.23/1.69 | (70) set_union2(all_63_1_41, all_63_0_40) = all_9_1_17
% 4.23/1.69 |
% 4.23/1.69 | Instantiating (57) with all_65_0_42, all_65_1_43 yields:
% 4.23/1.69 | (71) cartesian_product2(all_0_14_14, all_0_12_12) = all_65_1_43 & cartesian_product2(all_0_15_15, all_0_12_12) = all_65_0_42 & set_union2(all_65_1_43, all_65_0_42) = all_9_0_16
% 4.23/1.69 |
% 4.23/1.69 | Applying alpha-rule on (71) yields:
% 4.23/1.69 | (72) cartesian_product2(all_0_14_14, all_0_12_12) = all_65_1_43
% 4.23/1.69 | (73) cartesian_product2(all_0_15_15, all_0_12_12) = all_65_0_42
% 4.23/1.69 | (74) set_union2(all_65_1_43, all_65_0_42) = all_9_0_16
% 4.23/1.69 |
% 4.23/1.69 | Instantiating (53) with all_69_0_46, all_69_1_47 yields:
% 4.23/1.69 | (75) cartesian_product2(all_0_14_14, all_0_12_12) = all_69_0_46 & cartesian_product2(all_0_15_15, all_0_12_12) = all_69_1_47 & set_union2(all_69_1_47, all_69_0_46) = all_9_0_16
% 4.23/1.69 |
% 4.23/1.69 | Applying alpha-rule on (75) yields:
% 4.23/1.69 | (76) cartesian_product2(all_0_14_14, all_0_12_12) = all_69_0_46
% 4.23/1.69 | (77) cartesian_product2(all_0_15_15, all_0_12_12) = all_69_1_47
% 4.23/1.69 | (78) set_union2(all_69_1_47, all_69_0_46) = all_9_0_16
% 4.23/1.69 |
% 4.23/1.69 | Instantiating (56) with all_71_0_48, all_71_1_49 yields:
% 4.23/1.69 | (79) cartesian_product2(all_0_14_14, all_0_12_12) = all_71_1_49 & cartesian_product2(all_0_14_14, all_0_13_13) = all_71_0_48 & set_union2(all_71_1_49, all_71_0_48) = all_15_0_20
% 4.23/1.69 |
% 4.23/1.69 | Applying alpha-rule on (79) yields:
% 4.23/1.69 | (80) cartesian_product2(all_0_14_14, all_0_12_12) = all_71_1_49
% 4.23/1.69 | (81) cartesian_product2(all_0_14_14, all_0_13_13) = all_71_0_48
% 4.23/1.69 | (82) set_union2(all_71_1_49, all_71_0_48) = all_15_0_20
% 4.23/1.69 |
% 4.23/1.69 | Instantiating formula (21) with all_0_14_14, all_0_12_12, all_69_0_46, all_0_3_3 and discharging atoms cartesian_product2(all_0_14_14, all_0_12_12) = all_69_0_46, cartesian_product2(all_0_14_14, all_0_12_12) = all_0_3_3, yields:
% 4.23/1.69 | (83) all_69_0_46 = all_0_3_3
% 4.23/1.69 |
% 4.23/1.70 | Instantiating formula (21) with all_0_14_14, all_0_12_12, all_69_0_46, all_71_1_49 and discharging atoms cartesian_product2(all_0_14_14, all_0_12_12) = all_71_1_49, cartesian_product2(all_0_14_14, all_0_12_12) = all_69_0_46, yields:
% 4.23/1.70 | (84) all_71_1_49 = all_69_0_46
% 4.23/1.70 |
% 4.23/1.70 | Instantiating formula (21) with all_0_14_14, all_0_12_12, all_65_1_43, all_71_1_49 and discharging atoms cartesian_product2(all_0_14_14, all_0_12_12) = all_71_1_49, cartesian_product2(all_0_14_14, all_0_12_12) = all_65_1_43, yields:
% 4.23/1.70 | (85) all_71_1_49 = all_65_1_43
% 4.23/1.70 |
% 4.23/1.70 | Instantiating formula (21) with all_0_14_14, all_0_12_12, all_45_0_29, all_71_1_49 and discharging atoms cartesian_product2(all_0_14_14, all_0_12_12) = all_71_1_49, cartesian_product2(all_0_14_14, all_0_12_12) = all_45_0_29, yields:
% 4.23/1.70 | (86) all_71_1_49 = all_45_0_29
% 4.23/1.70 |
% 4.23/1.70 | Instantiating formula (21) with all_0_14_14, all_0_13_13, all_71_0_48, all_0_5_5 and discharging atoms cartesian_product2(all_0_14_14, all_0_13_13) = all_71_0_48, cartesian_product2(all_0_14_14, all_0_13_13) = all_0_5_5, yields:
% 4.23/1.70 | (87) all_71_0_48 = all_0_5_5
% 4.23/1.70 |
% 4.23/1.70 | Instantiating formula (21) with all_0_14_14, all_0_13_13, all_63_1_41, all_71_0_48 and discharging atoms cartesian_product2(all_0_14_14, all_0_13_13) = all_71_0_48, cartesian_product2(all_0_14_14, all_0_13_13) = all_63_1_41, yields:
% 4.23/1.70 | (88) all_71_0_48 = all_63_1_41
% 4.23/1.70 |
% 4.23/1.70 | Instantiating formula (21) with all_0_14_14, all_0_13_13, all_55_0_35, all_63_1_41 and discharging atoms cartesian_product2(all_0_14_14, all_0_13_13) = all_63_1_41, cartesian_product2(all_0_14_14, all_0_13_13) = all_55_0_35, yields:
% 4.23/1.70 | (89) all_63_1_41 = all_55_0_35
% 4.23/1.70 |
% 4.23/1.70 | Instantiating formula (21) with all_0_14_14, all_0_13_13, all_45_1_30, all_55_0_35 and discharging atoms cartesian_product2(all_0_14_14, all_0_13_13) = all_55_0_35, cartesian_product2(all_0_14_14, all_0_13_13) = all_45_1_30, yields:
% 4.23/1.70 | (90) all_55_0_35 = all_45_1_30
% 4.23/1.70 |
% 4.23/1.70 | Combining equations (88,87) yields a new equation:
% 4.23/1.70 | (91) all_63_1_41 = all_0_5_5
% 4.23/1.70 |
% 4.23/1.70 | Simplifying 91 yields:
% 4.23/1.70 | (92) all_63_1_41 = all_0_5_5
% 4.23/1.70 |
% 4.23/1.70 | Combining equations (84,85) yields a new equation:
% 4.23/1.70 | (93) all_69_0_46 = all_65_1_43
% 4.23/1.70 |
% 4.23/1.70 | Simplifying 93 yields:
% 4.23/1.70 | (94) all_69_0_46 = all_65_1_43
% 4.23/1.70 |
% 4.23/1.70 | Combining equations (86,85) yields a new equation:
% 4.23/1.70 | (95) all_65_1_43 = all_45_0_29
% 4.23/1.70 |
% 4.23/1.70 | Combining equations (94,83) yields a new equation:
% 4.23/1.70 | (96) all_65_1_43 = all_0_3_3
% 4.23/1.70 |
% 4.23/1.70 | Simplifying 96 yields:
% 4.23/1.70 | (97) all_65_1_43 = all_0_3_3
% 4.23/1.70 |
% 4.23/1.70 | Combining equations (97,95) yields a new equation:
% 4.23/1.70 | (98) all_45_0_29 = all_0_3_3
% 4.23/1.70 |
% 4.23/1.70 | Combining equations (89,92) yields a new equation:
% 4.23/1.70 | (99) all_55_0_35 = all_0_5_5
% 4.23/1.70 |
% 4.23/1.70 | Simplifying 99 yields:
% 4.23/1.70 | (100) all_55_0_35 = all_0_5_5
% 4.23/1.70 |
% 4.23/1.70 | Combining equations (90,100) yields a new equation:
% 4.23/1.70 | (101) all_45_1_30 = all_0_5_5
% 4.23/1.70 |
% 4.23/1.70 | Simplifying 101 yields:
% 4.23/1.70 | (102) all_45_1_30 = all_0_5_5
% 4.23/1.70 |
% 4.23/1.70 | From (102)(98) and (62) follows:
% 4.23/1.70 | (103) set_union2(all_0_5_5, all_0_3_3) = all_15_0_20
% 4.23/1.70 |
% 4.23/1.70 | Instantiating formula (10) with all_0_5_5, all_0_3_3, all_15_0_20, all_13_0_19 and discharging atoms set_union2(all_0_5_5, all_0_3_3) = all_15_0_20, set_union2(all_0_5_5, all_0_3_3) = all_13_0_19, yields:
% 4.23/1.70 | (104) all_15_0_20 = all_13_0_19
% 4.23/1.70 |
% 4.23/1.70 | From (104) and (52) follows:
% 4.23/1.70 | (105) set_union2(all_0_6_6, all_13_0_19) = all_0_9_9
% 4.23/1.70 |
% 4.23/1.70 | Instantiating formula (10) with all_0_6_6, all_13_0_19, all_0_9_9, all_0_2_2 and discharging atoms set_union2(all_0_6_6, all_13_0_19) = all_0_2_2, set_union2(all_0_6_6, all_13_0_19) = all_0_9_9, yields:
% 4.23/1.70 | (106) all_0_2_2 = all_0_9_9
% 4.23/1.70 |
% 4.23/1.70 | Equations (106) can reduce 12 to:
% 4.23/1.70 | (107) $false
% 4.23/1.70 |
% 4.23/1.70 |-The branch is then unsatisfiable
% 4.23/1.70 % SZS output end Proof for theBenchmark
% 4.23/1.70
% 4.23/1.70 1118ms
%------------------------------------------------------------------------------