TSTP Solution File: SEU047+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU047+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n003.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 08:46:22 EDT 2022
% Result : Theorem 2.61s 1.33s
% Output : Proof 3.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU047+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n003.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 : Mon Jun 20 06:40:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.62/0.59 ____ _
% 0.62/0.59 ___ / __ \_____(_)___ ________ __________
% 0.62/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.62/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.62/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.62/0.59
% 0.62/0.59 A Theorem Prover for First-Order Logic
% 0.62/0.59 (ePrincess v.1.0)
% 0.62/0.59
% 0.62/0.59 (c) Philipp Rümmer, 2009-2015
% 0.62/0.59 (c) Peter Backeman, 2014-2015
% 0.62/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.59 Bug reports to peter@backeman.se
% 0.62/0.59
% 0.62/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.59
% 0.62/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.54/1.00 Prover 0: Preprocessing ...
% 1.91/1.17 Prover 0: Warning: ignoring some quantifiers
% 2.17/1.19 Prover 0: Constructing countermodel ...
% 2.61/1.32 Prover 0: proved (656ms)
% 2.61/1.33
% 2.61/1.33 No countermodel exists, formula is valid
% 2.61/1.33 % SZS status Theorem for theBenchmark
% 2.61/1.33
% 2.61/1.33 Generating proof ... Warning: ignoring some quantifiers
% 3.53/1.58 found it (size 10)
% 3.53/1.58
% 3.53/1.58 % SZS output start Proof for theBenchmark
% 3.53/1.58 Assumed formulas after preprocessing and simplification:
% 3.53/1.58 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (relation_rng_restriction(v1, v3) = v4 & relation_rng_restriction(v1, v2) = v5 & relation_rng_restriction(v0, v5) = v6 & relation_rng_restriction(v0, v2) = v3 & subset(v0, v1) & one_to_one(v12) & function(v14) & function(v13) & function(v12) & function(v2) & relation_empty_yielding(v9) & relation_empty_yielding(empty_set) & relation(v14) & relation(v13) & relation(v12) & relation(v11) & relation(v10) & relation(v9) & relation(v2) & relation(empty_set) & empty(v13) & empty(v11) & empty(v8) & empty(empty_set) & ~ empty(v10) & ~ empty(v7) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (relation_rng_restriction(v16, v18) = v19) | ~ (relation_rng_restriction(v15, v17) = v18) | ~ subset(v15, v16) | ~ relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v16, v17) = v18) | ~ (relation_rng_restriction(v15, v18) = v19) | ~ subset(v15, v16) | ~ relation(v17) | relation_rng_restriction(v15, v17) = v19) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_rng_restriction(v18, v17) = v16) | ~ (relation_rng_restriction(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | ~ empty(v17) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | ~ in(v15, v16) | element(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (powerset(v17) = v16) | ~ (powerset(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ function(v16) | ~ relation(v16) | function(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ function(v16) | ~ relation(v16) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ subset(v15, v16) | element(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | subset(v15, v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ empty(v16) | ~ empty(v15)) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ empty(v16)) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | empty(v15) | ? [v17] : (element(v17, v16) & ~ empty(v17))) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ? [v17] : (element(v17, v16) & empty(v17))) & ! [v15] : ! [v16] : ( ~ element(v15, v16) | empty(v16) | in(v15, v16)) & ! [v15] : ! [v16] : ( ~ empty(v16) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ( ~ in(v16, v15) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ( ~ in(v15, v16) | element(v15, v16)) & ! [v15] : (v15 = empty_set | ~ empty(v15)) & ! [v15] : ( ~ function(v15) | ~ relation(v15) | ~ empty(v15) | one_to_one(v15)) & ! [v15] : ( ~ empty(v15) | function(v15)) & ! [v15] : ( ~ empty(v15) | relation(v15)) & ? [v15] : ? [v16] : element(v16, v15) & ? [v15] : subset(v15, v15) & ( ~ (v6 = v3) | ~ (v4 = v3)))
% 3.84/1.62 | 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 yields:
% 3.84/1.62 | (1) relation_rng_restriction(all_0_13_13, all_0_11_11) = all_0_10_10 & relation_rng_restriction(all_0_13_13, all_0_12_12) = all_0_9_9 & relation_rng_restriction(all_0_14_14, all_0_9_9) = all_0_8_8 & relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11 & subset(all_0_14_14, all_0_13_13) & one_to_one(all_0_2_2) & function(all_0_0_0) & function(all_0_1_1) & function(all_0_2_2) & function(all_0_12_12) & relation_empty_yielding(all_0_5_5) & relation_empty_yielding(empty_set) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_2_2) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_5_5) & relation(all_0_12_12) & relation(empty_set) & empty(all_0_1_1) & empty(all_0_3_3) & empty(all_0_6_6) & empty(empty_set) & ~ empty(all_0_4_4) & ~ empty(all_0_7_7) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (relation_rng_restriction(v1, v3) = v4) | ~ (relation_rng_restriction(v0, v2) = v3) | ~ subset(v0, v1) | ~ relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v1, v2) = v3) | ~ (relation_rng_restriction(v0, v3) = v4) | ~ subset(v0, v1) | ~ relation(v2) | relation_rng_restriction(v0, v2) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ function(v1) | ~ relation(v1) | function(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ function(v1) | ~ relation(v1) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [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] : ( ~ function(v0) | ~ relation(v0) | ~ empty(v0) | one_to_one(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) & ( ~ (all_0_8_8 = all_0_11_11) | ~ (all_0_10_10 = all_0_11_11))
% 3.84/1.63 |
% 3.84/1.63 | Applying alpha-rule on (1) yields:
% 3.84/1.63 | (2) ~ (all_0_8_8 = all_0_11_11) | ~ (all_0_10_10 = all_0_11_11)
% 3.84/1.63 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 3.84/1.63 | (4) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 3.84/1.63 | (5) relation(all_0_12_12)
% 3.84/1.63 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (relation_rng_restriction(v1, v3) = v4) | ~ (relation_rng_restriction(v0, v2) = v3) | ~ subset(v0, v1) | ~ relation(v2))
% 3.84/1.64 | (7) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 3.84/1.64 | (8) function(all_0_2_2)
% 3.84/1.64 | (9) one_to_one(all_0_2_2)
% 3.84/1.64 | (10) function(all_0_0_0)
% 3.84/1.64 | (11) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 3.84/1.64 | (12) ! [v0] : ( ~ empty(v0) | function(v0))
% 3.84/1.64 | (13) ? [v0] : subset(v0, v0)
% 3.84/1.64 | (14) relation_empty_yielding(empty_set)
% 3.84/1.64 | (15) function(all_0_12_12)
% 3.84/1.64 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 3.84/1.64 | (17) relation_rng_restriction(all_0_13_13, all_0_12_12) = all_0_9_9
% 3.84/1.64 | (18) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 3.84/1.64 | (19) empty(all_0_1_1)
% 3.84/1.64 | (20) relation_empty_yielding(all_0_5_5)
% 3.84/1.64 | (21) relation(all_0_3_3)
% 3.84/1.64 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v1, v2) = v3) | ~ (relation_rng_restriction(v0, v3) = v4) | ~ subset(v0, v1) | ~ relation(v2) | relation_rng_restriction(v0, v2) = v4)
% 3.84/1.64 | (23) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 3.84/1.64 | (24) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 3.84/1.64 | (25) relation(all_0_1_1)
% 3.84/1.64 | (26) relation_rng_restriction(all_0_13_13, all_0_11_11) = all_0_10_10
% 3.84/1.64 | (27) relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11
% 3.84/1.64 | (28) ! [v0] : ( ~ function(v0) | ~ relation(v0) | ~ empty(v0) | one_to_one(v0))
% 3.84/1.64 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2))
% 3.84/1.64 | (30) ? [v0] : ? [v1] : element(v1, v0)
% 3.84/1.64 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ function(v1) | ~ relation(v1) | relation(v2))
% 3.84/1.64 | (32) ~ empty(all_0_4_4)
% 3.84/1.64 | (33) relation(empty_set)
% 3.84/1.64 | (34) relation_rng_restriction(all_0_14_14, all_0_9_9) = all_0_8_8
% 3.84/1.64 | (35) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 3.84/1.64 | (36) relation(all_0_4_4)
% 3.84/1.64 | (37) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 3.84/1.64 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 3.84/1.64 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 3.84/1.64 | (40) ~ empty(all_0_7_7)
% 3.84/1.64 | (41) relation(all_0_0_0)
% 3.84/1.64 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ function(v1) | ~ relation(v1) | function(v2))
% 3.84/1.64 | (43) relation(all_0_5_5)
% 3.84/1.64 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 3.84/1.65 | (45) subset(all_0_14_14, all_0_13_13)
% 3.84/1.65 | (46) function(all_0_1_1)
% 3.84/1.65 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0))
% 3.84/1.65 | (48) ! [v0] : ( ~ empty(v0) | relation(v0))
% 3.84/1.65 | (49) empty(all_0_3_3)
% 3.84/1.65 | (50) relation(all_0_2_2)
% 3.84/1.65 | (51) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 3.84/1.65 | (52) empty(all_0_6_6)
% 3.84/1.65 | (53) empty(empty_set)
% 3.84/1.65 |
% 3.84/1.65 | Instantiating formula (6) with all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14 and discharging atoms relation_rng_restriction(all_0_13_13, all_0_11_11) = all_0_10_10, relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11, subset(all_0_14_14, all_0_13_13), relation(all_0_12_12), yields:
% 3.84/1.65 | (54) all_0_10_10 = all_0_11_11
% 3.84/1.65 |
% 3.84/1.65 +-Applying beta-rule and splitting (2), into two cases.
% 3.84/1.65 |-Branch one:
% 3.84/1.65 | (55) ~ (all_0_8_8 = all_0_11_11)
% 3.84/1.65 |
% 3.84/1.65 | Instantiating formula (22) with all_0_8_8, all_0_9_9, all_0_12_12, all_0_13_13, all_0_14_14 and discharging atoms relation_rng_restriction(all_0_13_13, all_0_12_12) = all_0_9_9, relation_rng_restriction(all_0_14_14, all_0_9_9) = all_0_8_8, subset(all_0_14_14, all_0_13_13), relation(all_0_12_12), yields:
% 3.84/1.65 | (56) relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_8_8
% 3.84/1.65 |
% 3.84/1.65 | Instantiating formula (47) with all_0_14_14, all_0_12_12, all_0_8_8, all_0_11_11 and discharging atoms relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_8_8, relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11, yields:
% 3.84/1.65 | (57) all_0_8_8 = all_0_11_11
% 3.84/1.65 |
% 3.84/1.65 | Equations (57) can reduce 55 to:
% 3.84/1.65 | (58) $false
% 3.84/1.65 |
% 3.84/1.65 |-The branch is then unsatisfiable
% 3.84/1.65 |-Branch two:
% 3.84/1.65 | (57) all_0_8_8 = all_0_11_11
% 3.84/1.65 | (60) ~ (all_0_10_10 = all_0_11_11)
% 3.84/1.65 |
% 3.84/1.65 | Equations (54) can reduce 60 to:
% 3.84/1.65 | (58) $false
% 3.84/1.65 |
% 3.84/1.65 |-The branch is then unsatisfiable
% 3.84/1.65 % SZS output end Proof for theBenchmark
% 3.84/1.65
% 3.84/1.65 1044ms
%------------------------------------------------------------------------------