TSTP Solution File: ALG227+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG227+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.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 15:37:40 EDT 2022
% Result : Theorem 2.43s 1.23s
% Output : Proof 3.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG227+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n022.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 : Wed Jun 8 09:13:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.58 ____ _
% 0.55/0.58 ___ / __ \_____(_)___ ________ __________
% 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.58
% 0.55/0.58 A Theorem Prover for First-Order Logic
% 0.55/0.58 (ePrincess v.1.0)
% 0.55/0.58
% 0.55/0.58 (c) Philipp Rümmer, 2009-2015
% 0.55/0.58 (c) Peter Backeman, 2014-2015
% 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.58 Bug reports to peter@backeman.se
% 0.55/0.58
% 0.55/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.58
% 0.55/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.62/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.50/0.89 Prover 0: Preprocessing ...
% 1.98/1.08 Prover 0: Warning: ignoring some quantifiers
% 1.98/1.10 Prover 0: Constructing countermodel ...
% 2.43/1.23 Prover 0: proved (603ms)
% 2.43/1.23
% 2.43/1.23 No countermodel exists, formula is valid
% 2.43/1.23 % SZS status Theorem for theBenchmark
% 2.43/1.23
% 2.43/1.23 Generating proof ... Warning: ignoring some quantifiers
% 3.35/1.48 found it (size 6)
% 3.35/1.48
% 3.35/1.48 % SZS output start Proof for theBenchmark
% 3.35/1.48 Assumed formulas after preprocessing and simplification:
% 3.35/1.48 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v4 = k1_xboole_0) & k1_funct_1(v1, v3) = v4 & k1_closure3(v0, v1) = v2 & v2_funct_1(v11) & v2_funct_1(v5) & v1_relat_1(v11) & v1_relat_1(v9) & v1_relat_1(v7) & v1_relat_1(v5) & v1_funct_1(v11) & v1_funct_1(v9) & v1_funct_1(v7) & v1_funct_1(v5) & v1_finset_1(v11) & v1_finset_1(v10) & v1_fraenkel(v11) & m1_subset_1(v3, v0) & m1_pboole(v1, v0) & v1_xboole_0(v11) & v1_xboole_0(v8) & v1_xboole_0(v7) & v1_xboole_0(k1_xboole_0) & ~ r2_hidden(v3, v2) & ~ v1_xboole_0(v10) & ~ v1_xboole_0(v6) & ~ v1_xboole_0(v0) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = k1_xboole_0 | ~ (k1_funct_1(v14, v12) = v16) | ~ (a_2_0_closure3(v13, v14) = v15) | ~ m1_subset_1(v12, v13) | ~ m1_pboole(v14, v13) | r2_hidden(v12, v15) | v1_xboole_0(v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (k1_funct_1(v15, v14) = v13) | ~ (k1_funct_1(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (k1_closure3(v15, v14) = v13) | ~ (k1_closure3(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (a_2_0_closure3(v15, v14) = v13) | ~ (a_2_0_closure3(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (a_2_0_closure3(v13, v14) = v15) | ~ r2_hidden(v12, v15) | ~ m1_pboole(v14, v13) | v1_xboole_0(v13) | ? [v16] : ( ~ (v16 = k1_xboole_0) & k1_funct_1(v14, v12) = v16 & m1_subset_1(v12, v13))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (k1_closure3(v12, v13) = v14) | ~ m1_pboole(v13, v12) | a_2_0_closure3(v12, v13) = v14 | v1_xboole_0(v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (a_2_0_closure3(v12, v13) = v14) | ~ m1_pboole(v13, v12) | k1_closure3(v12, v13) = v14 | v1_xboole_0(v12)) & ! [v12] : ! [v13] : (v13 = v12 | ~ v1_xboole_0(v13) | ~ v1_xboole_0(v12)) & ! [v12] : ! [v13] : ( ~ r2_hidden(v13, v12) | ~ r2_hidden(v12, v13)) & ! [v12] : ! [v13] : ( ~ r2_hidden(v12, v13) | ~ v1_xboole_0(v13)) & ! [v12] : ! [v13] : ( ~ r2_hidden(v12, v13) | m1_subset_1(v12, v13)) & ! [v12] : ! [v13] : ( ~ m1_subset_1(v12, v13) | r2_hidden(v12, v13) | v1_xboole_0(v13)) & ! [v12] : ! [v13] : ( ~ m1_pboole(v13, v12) | v1_relat_1(v13)) & ! [v12] : ! [v13] : ( ~ m1_pboole(v13, v12) | v1_funct_1(v13)) & ! [v12] : (v12 = k1_xboole_0 | ~ v1_xboole_0(v12)) & ! [v12] : ( ~ v1_relat_1(v12) | ~ v1_funct_1(v12) | ~ v1_xboole_0(v12) | v2_funct_1(v12)) & ! [v12] : ( ~ v1_xboole_0(v12) | v1_funct_1(v12)) & ! [v12] : ( ~ v1_xboole_0(v12) | v1_finset_1(v12)) & ! [v12] : ( ~ v1_xboole_0(v12) | v1_fraenkel(v12)) & ? [v12] : ? [v13] : (v13 = v12 | ? [v14] : (( ~ r2_hidden(v14, v13) | ~ r2_hidden(v14, v12)) & (r2_hidden(v14, v13) | r2_hidden(v14, v12)))) & ? [v12] : ? [v13] : m1_subset_1(v13, v12) & ? [v12] : ? [v13] : m1_pboole(v13, v12))
% 3.46/1.52 | 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 yields:
% 3.46/1.52 | (1) ~ (all_0_7_7 = k1_xboole_0) & k1_funct_1(all_0_10_10, all_0_8_8) = all_0_7_7 & k1_closure3(all_0_11_11, all_0_10_10) = all_0_9_9 & v2_funct_1(all_0_0_0) & v2_funct_1(all_0_6_6) & v1_relat_1(all_0_0_0) & v1_relat_1(all_0_2_2) & v1_relat_1(all_0_4_4) & v1_relat_1(all_0_6_6) & v1_funct_1(all_0_0_0) & v1_funct_1(all_0_2_2) & v1_funct_1(all_0_4_4) & v1_funct_1(all_0_6_6) & v1_finset_1(all_0_0_0) & v1_finset_1(all_0_1_1) & v1_fraenkel(all_0_0_0) & m1_subset_1(all_0_8_8, all_0_11_11) & m1_pboole(all_0_10_10, all_0_11_11) & v1_xboole_0(all_0_0_0) & v1_xboole_0(all_0_3_3) & v1_xboole_0(all_0_4_4) & v1_xboole_0(k1_xboole_0) & ~ r2_hidden(all_0_8_8, all_0_9_9) & ~ v1_xboole_0(all_0_1_1) & ~ v1_xboole_0(all_0_5_5) & ~ v1_xboole_0(all_0_11_11) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = k1_xboole_0 | ~ (k1_funct_1(v2, v0) = v4) | ~ (a_2_0_closure3(v1, v2) = v3) | ~ m1_subset_1(v0, v1) | ~ m1_pboole(v2, v1) | r2_hidden(v0, v3) | v1_xboole_0(v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k1_closure3(v3, v2) = v1) | ~ (k1_closure3(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_2_0_closure3(v3, v2) = v1) | ~ (a_2_0_closure3(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (a_2_0_closure3(v1, v2) = v3) | ~ r2_hidden(v0, v3) | ~ m1_pboole(v2, v1) | v1_xboole_0(v1) | ? [v4] : ( ~ (v4 = k1_xboole_0) & k1_funct_1(v2, v0) = v4 & m1_subset_1(v0, v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_closure3(v0, v1) = v2) | ~ m1_pboole(v1, v0) | a_2_0_closure3(v0, v1) = v2 | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (a_2_0_closure3(v0, v1) = v2) | ~ m1_pboole(v1, v0) | k1_closure3(v0, v1) = v2 | v1_xboole_0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | ~ v1_xboole_0(v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1)) & ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | r2_hidden(v0, v1) | v1_xboole_0(v1)) & ! [v0] : ! [v1] : ( ~ m1_pboole(v1, v0) | v1_relat_1(v1)) & ! [v0] : ! [v1] : ( ~ m1_pboole(v1, v0) | v1_funct_1(v1)) & ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) & ! [v0] : ( ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | ~ v1_xboole_0(v0) | v2_funct_1(v0)) & ! [v0] : ( ~ v1_xboole_0(v0) | v1_funct_1(v0)) & ! [v0] : ( ~ v1_xboole_0(v0) | v1_finset_1(v0)) & ! [v0] : ( ~ v1_xboole_0(v0) | v1_fraenkel(v0)) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ r2_hidden(v2, v1) | ~ r2_hidden(v2, v0)) & (r2_hidden(v2, v1) | r2_hidden(v2, v0)))) & ? [v0] : ? [v1] : m1_subset_1(v1, v0) & ? [v0] : ? [v1] : m1_pboole(v1, v0)
% 3.46/1.53 |
% 3.46/1.53 | Applying alpha-rule on (1) yields:
% 3.46/1.53 | (2) ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0))
% 3.46/1.53 | (3) ~ v1_xboole_0(all_0_5_5)
% 3.46/1.53 | (4) ! [v0] : ! [v1] : ( ~ m1_pboole(v1, v0) | v1_funct_1(v1))
% 3.46/1.53 | (5) m1_pboole(all_0_10_10, all_0_11_11)
% 3.46/1.53 | (6) k1_funct_1(all_0_10_10, all_0_8_8) = all_0_7_7
% 3.46/1.53 | (7) v1_relat_1(all_0_0_0)
% 3.46/1.53 | (8) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ r2_hidden(v2, v1) | ~ r2_hidden(v2, v0)) & (r2_hidden(v2, v1) | r2_hidden(v2, v0))))
% 3.46/1.53 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = k1_xboole_0 | ~ (k1_funct_1(v2, v0) = v4) | ~ (a_2_0_closure3(v1, v2) = v3) | ~ m1_subset_1(v0, v1) | ~ m1_pboole(v2, v1) | r2_hidden(v0, v3) | v1_xboole_0(v1))
% 3.46/1.53 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (k1_closure3(v0, v1) = v2) | ~ m1_pboole(v1, v0) | a_2_0_closure3(v0, v1) = v2 | v1_xboole_0(v0))
% 3.46/1.53 | (11) ! [v0] : ( ~ v1_xboole_0(v0) | v1_fraenkel(v0))
% 3.46/1.53 | (12) m1_subset_1(all_0_8_8, all_0_11_11)
% 3.46/1.53 | (13) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1))
% 3.46/1.53 | (14) v1_xboole_0(all_0_3_3)
% 3.46/1.53 | (15) v1_fraenkel(all_0_0_0)
% 3.46/1.53 | (16) ! [v0] : ( ~ v1_xboole_0(v0) | v1_funct_1(v0))
% 3.46/1.53 | (17) v1_finset_1(all_0_1_1)
% 3.46/1.53 | (18) v1_relat_1(all_0_4_4)
% 3.46/1.53 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_2_0_closure3(v3, v2) = v1) | ~ (a_2_0_closure3(v3, v2) = v0))
% 3.46/1.53 | (20) ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1))
% 3.46/1.53 | (21) v1_xboole_0(all_0_4_4)
% 3.46/1.53 | (22) v1_xboole_0(k1_xboole_0)
% 3.46/1.53 | (23) ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | r2_hidden(v0, v1) | v1_xboole_0(v1))
% 3.46/1.53 | (24) k1_closure3(all_0_11_11, all_0_10_10) = all_0_9_9
% 3.46/1.54 | (25) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | ~ v1_xboole_0(v1))
% 3.46/1.54 | (26) v2_funct_1(all_0_0_0)
% 3.46/1.54 | (27) v2_funct_1(all_0_6_6)
% 3.46/1.54 | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0))
% 3.46/1.54 | (29) ~ (all_0_7_7 = k1_xboole_0)
% 3.46/1.54 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = v0))
% 3.46/1.54 | (31) v1_finset_1(all_0_0_0)
% 3.46/1.54 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k1_closure3(v3, v2) = v1) | ~ (k1_closure3(v3, v2) = v0))
% 3.46/1.54 | (33) ? [v0] : ? [v1] : m1_subset_1(v1, v0)
% 3.46/1.54 | (34) v1_funct_1(all_0_2_2)
% 3.46/1.54 | (35) ! [v0] : ! [v1] : ( ~ m1_pboole(v1, v0) | v1_relat_1(v1))
% 3.46/1.54 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (a_2_0_closure3(v0, v1) = v2) | ~ m1_pboole(v1, v0) | k1_closure3(v0, v1) = v2 | v1_xboole_0(v0))
% 3.46/1.54 | (37) v1_relat_1(all_0_6_6)
% 3.46/1.54 | (38) v1_funct_1(all_0_6_6)
% 3.46/1.54 | (39) v1_funct_1(all_0_4_4)
% 3.46/1.54 | (40) v1_funct_1(all_0_0_0)
% 3.46/1.54 | (41) ! [v0] : ( ~ v1_relat_1(v0) | ~ v1_funct_1(v0) | ~ v1_xboole_0(v0) | v2_funct_1(v0))
% 3.46/1.54 | (42) v1_relat_1(all_0_2_2)
% 3.46/1.54 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (a_2_0_closure3(v1, v2) = v3) | ~ r2_hidden(v0, v3) | ~ m1_pboole(v2, v1) | v1_xboole_0(v1) | ? [v4] : ( ~ (v4 = k1_xboole_0) & k1_funct_1(v2, v0) = v4 & m1_subset_1(v0, v1)))
% 3.46/1.54 | (44) v1_xboole_0(all_0_0_0)
% 3.46/1.54 | (45) ~ v1_xboole_0(all_0_1_1)
% 3.46/1.54 | (46) ! [v0] : ( ~ v1_xboole_0(v0) | v1_finset_1(v0))
% 3.46/1.54 | (47) ? [v0] : ? [v1] : m1_pboole(v1, v0)
% 3.46/1.54 | (48) ~ r2_hidden(all_0_8_8, all_0_9_9)
% 3.65/1.54 | (49) ~ v1_xboole_0(all_0_11_11)
% 3.65/1.54 |
% 3.65/1.54 | Instantiating formula (10) with all_0_9_9, all_0_10_10, all_0_11_11 and discharging atoms k1_closure3(all_0_11_11, all_0_10_10) = all_0_9_9, m1_pboole(all_0_10_10, all_0_11_11), ~ v1_xboole_0(all_0_11_11), yields:
% 3.65/1.54 | (50) a_2_0_closure3(all_0_11_11, all_0_10_10) = all_0_9_9
% 3.65/1.54 |
% 3.65/1.54 | Instantiating formula (9) with all_0_7_7, all_0_9_9, all_0_10_10, all_0_11_11, all_0_8_8 and discharging atoms k1_funct_1(all_0_10_10, all_0_8_8) = all_0_7_7, a_2_0_closure3(all_0_11_11, all_0_10_10) = all_0_9_9, m1_subset_1(all_0_8_8, all_0_11_11), m1_pboole(all_0_10_10, all_0_11_11), ~ r2_hidden(all_0_8_8, all_0_9_9), ~ v1_xboole_0(all_0_11_11), yields:
% 3.65/1.54 | (51) all_0_7_7 = k1_xboole_0
% 3.65/1.54 |
% 3.65/1.54 | Equations (51) can reduce 29 to:
% 3.65/1.54 | (52) $false
% 3.65/1.54 |
% 3.65/1.54 |-The branch is then unsatisfiable
% 3.65/1.54 % SZS output end Proof for theBenchmark
% 3.65/1.54
% 3.65/1.55 957ms
%------------------------------------------------------------------------------