TSTP Solution File: SEU230+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU230+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.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 08:47:55 EDT 2022
% Result : Theorem 2.90s 1.45s
% Output : Proof 4.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU230+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jun 18 20:01:08 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.65/0.66 ____ _
% 0.65/0.66 ___ / __ \_____(_)___ ________ __________
% 0.65/0.66 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.65/0.66 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.65/0.66 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.65/0.66
% 0.65/0.66 A Theorem Prover for First-Order Logic
% 0.65/0.66 (ePrincess v.1.0)
% 0.65/0.66
% 0.65/0.66 (c) Philipp Rümmer, 2009-2015
% 0.65/0.66 (c) Peter Backeman, 2014-2015
% 0.65/0.66 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.65/0.66 Free software under GNU Lesser General Public License (LGPL).
% 0.65/0.66 Bug reports to peter@backeman.se
% 0.65/0.66
% 0.65/0.66 For more information, visit http://user.uu.se/~petba168/breu/
% 0.65/0.66
% 0.65/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.79/0.71 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.69/1.02 Prover 0: Preprocessing ...
% 2.21/1.26 Prover 0: Warning: ignoring some quantifiers
% 2.34/1.28 Prover 0: Constructing countermodel ...
% 2.90/1.45 Prover 0: proved (739ms)
% 2.90/1.45
% 2.90/1.45 No countermodel exists, formula is valid
% 2.90/1.45 % SZS status Theorem for theBenchmark
% 2.90/1.45
% 2.90/1.45 Generating proof ... Warning: ignoring some quantifiers
% 4.07/1.69 found it (size 9)
% 4.07/1.69
% 4.07/1.69 % SZS output start Proof for theBenchmark
% 4.07/1.69 Assumed formulas after preprocessing and simplification:
% 4.07/1.69 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (succ(v0) = v1 & relation_empty_yielding(v3) & relation_empty_yielding(v2) & relation_empty_yielding(empty_set) & one_to_one(v4) & relation(v10) & relation(v9) & relation(v7) & relation(v6) & relation(v4) & relation(v3) & relation(v2) & relation(empty_set) & function(v10) & function(v7) & function(v4) & function(v2) & empty(v9) & empty(v8) & empty(v7) & empty(empty_set) & ~ empty(v6) & ~ empty(v5) & ~ in(v0, v1) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (set_union2(v14, v13) = v12) | ~ (set_union2(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v11, v12) = v13) | ~ in(v14, v13) | in(v14, v12) | in(v14, v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v11, v12) = v13) | ~ in(v14, v12) | in(v14, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v11, v12) = v13) | ~ in(v14, v11) | in(v14, v13)) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_union2(v12, v13) = v14) | ? [v15] : (( ~ in(v15, v11) | ( ~ in(v15, v13) & ~ in(v15, v12))) & (in(v15, v13) | in(v15, v12) | in(v15, v11)))) & ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (singleton(v11) = v12) | ~ in(v13, v12)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v13) = v12) | ~ (singleton(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (succ(v13) = v12) | ~ (succ(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v11) = v12) | ~ (set_union2(v11, v12) = v13) | succ(v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v12, v11) = v13) | ~ empty(v13) | empty(v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v12, v11) = v13) | set_union2(v11, v12) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | ~ empty(v13) | empty(v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | set_union2(v12, v11) = v13) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (singleton(v12) = v13) | ? [v14] : (( ~ (v14 = v12) | ~ in(v12, v11)) & (v14 = v12 | in(v14, v11)))) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_union2(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_union2(v11, empty_set) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ empty(v12) | ~ empty(v11)) & ! [v11] : ! [v12] : ( ~ (singleton(v11) = v12) | in(v11, v12)) & ! [v11] : ! [v12] : ( ~ (succ(v11) = v12) | ~ empty(v12)) & ! [v11] : ! [v12] : ( ~ (succ(v11) = v12) | ? [v13] : (singleton(v11) = v13 & set_union2(v11, v13) = v12)) & ! [v11] : ! [v12] : ( ~ element(v11, v12) | empty(v12) | in(v11, v12)) & ! [v11] : ! [v12] : ( ~ empty(v12) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v12, v11) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v11, v12) | element(v11, v12)) & ! [v11] : (v11 = empty_set | ~ empty(v11)) & ! [v11] : ( ~ relation(v11) | ~ function(v11) | ~ empty(v11) | one_to_one(v11)) & ! [v11] : ( ~ empty(v11) | relation(v11)) & ! [v11] : ( ~ empty(v11) | function(v11)) & ? [v11] : ? [v12] : element(v12, v11))
% 4.07/1.73 | 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 yields:
% 4.07/1.73 | (1) succ(all_0_10_10) = all_0_9_9 & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(all_0_8_8) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_6_6) & relation(all_0_7_7) & relation(all_0_8_8) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_8_8) & empty(all_0_1_1) & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & ~ empty(all_0_4_4) & ~ empty(all_0_5_5) & ~ in(all_0_10_10, all_0_9_9) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2) & ! [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) | ~ relation(v1) | ~ relation(v0) | relation(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] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ? [v0] : ? [v1] : element(v1, v0)
% 4.07/1.74 |
% 4.07/1.74 | Applying alpha-rule on (1) yields:
% 4.29/1.74 | (2) function(all_0_6_6)
% 4.29/1.74 | (3) relation(all_0_7_7)
% 4.29/1.74 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 4.29/1.74 | (5) relation_empty_yielding(all_0_8_8)
% 4.29/1.74 | (6) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 4.29/1.74 | (7) function(all_0_3_3)
% 4.29/1.74 | (8) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 4.29/1.74 | (9) relation(all_0_4_4)
% 4.29/1.74 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2)
% 4.29/1.74 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 4.29/1.74 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 4.29/1.74 | (13) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 4.29/1.74 | (14) function(all_0_8_8)
% 4.29/1.74 | (15) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1))
% 4.29/1.74 | (16) ! [v0] : ( ~ empty(v0) | function(v0))
% 4.29/1.74 | (17) empty(all_0_3_3)
% 4.29/1.74 | (18) one_to_one(all_0_6_6)
% 4.29/1.74 | (19) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.29/1.74 | (20) ~ empty(all_0_5_5)
% 4.29/1.74 | (21) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0))))
% 4.29/1.74 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2))
% 4.29/1.74 | (23) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 4.29/1.74 | (24) relation(all_0_3_3)
% 4.29/1.74 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 4.29/1.74 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2))
% 4.29/1.74 | (27) relation(all_0_8_8)
% 4.29/1.74 | (28) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 4.29/1.74 | (29) empty(empty_set)
% 4.29/1.74 | (30) ? [v0] : ? [v1] : element(v1, v0)
% 4.29/1.74 | (31) empty(all_0_2_2)
% 4.29/1.74 | (32) relation_empty_yielding(all_0_7_7)
% 4.29/1.74 | (33) succ(all_0_10_10) = all_0_9_9
% 4.29/1.74 | (34) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 4.29/1.74 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 4.29/1.74 | (36) empty(all_0_1_1)
% 4.29/1.74 | (37) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 4.29/1.74 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 4.29/1.75 | (39) ~ in(all_0_10_10, all_0_9_9)
% 4.29/1.75 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 4.29/1.75 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 4.29/1.75 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 4.29/1.75 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 4.29/1.75 | (44) relation(all_0_0_0)
% 4.29/1.75 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 4.29/1.75 | (46) relation_empty_yielding(empty_set)
% 4.29/1.75 | (47) ! [v0] : ( ~ empty(v0) | relation(v0))
% 4.29/1.75 | (48) ~ empty(all_0_4_4)
% 4.29/1.75 | (49) relation(all_0_6_6)
% 4.29/1.75 | (50) relation(all_0_1_1)
% 4.29/1.75 | (51) function(all_0_0_0)
% 4.29/1.75 | (52) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 4.29/1.75 | (53) relation(empty_set)
% 4.29/1.75 | (54) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1))
% 4.29/1.75 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 4.29/1.75 |
% 4.29/1.75 | Instantiating formula (15) with all_0_9_9, all_0_10_10 and discharging atoms succ(all_0_10_10) = all_0_9_9, yields:
% 4.29/1.75 | (56) ? [v0] : (singleton(all_0_10_10) = v0 & set_union2(all_0_10_10, v0) = all_0_9_9)
% 4.29/1.75 |
% 4.29/1.75 | Instantiating (56) with all_19_0_15 yields:
% 4.29/1.75 | (57) singleton(all_0_10_10) = all_19_0_15 & set_union2(all_0_10_10, all_19_0_15) = all_0_9_9
% 4.29/1.75 |
% 4.29/1.75 | Applying alpha-rule on (57) yields:
% 4.29/1.75 | (58) singleton(all_0_10_10) = all_19_0_15
% 4.29/1.75 | (59) set_union2(all_0_10_10, all_19_0_15) = all_0_9_9
% 4.29/1.75 |
% 4.29/1.75 | Instantiating formula (13) with all_19_0_15, all_0_10_10 and discharging atoms singleton(all_0_10_10) = all_19_0_15, yields:
% 4.29/1.75 | (60) in(all_0_10_10, all_19_0_15)
% 4.29/1.75 |
% 4.29/1.75 | Instantiating formula (43) with all_0_9_9, all_0_10_10, all_19_0_15 and discharging atoms set_union2(all_0_10_10, all_19_0_15) = all_0_9_9, yields:
% 4.35/1.75 | (61) set_union2(all_19_0_15, all_0_10_10) = all_0_9_9
% 4.35/1.75 |
% 4.35/1.75 | Instantiating formula (22) with all_0_10_10, all_0_9_9, all_0_10_10, all_19_0_15 and discharging atoms set_union2(all_19_0_15, all_0_10_10) = all_0_9_9, in(all_0_10_10, all_19_0_15), ~ in(all_0_10_10, all_0_9_9), yields:
% 4.35/1.75 | (62) $false
% 4.35/1.75 |
% 4.35/1.75 |-The branch is then unsatisfiable
% 4.35/1.75 % SZS output end Proof for theBenchmark
% 4.35/1.75
% 4.35/1.75 1085ms
%------------------------------------------------------------------------------