TSTP Solution File: SET941+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET941+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n013.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 00:23:20 EDT 2022
% Result : Theorem 3.61s 1.56s
% Output : Proof 4.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET941+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n013.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 : Sat Jul 9 19:07:29 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.18/0.57 ____ _
% 0.18/0.57 ___ / __ \_____(_)___ ________ __________
% 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic
% 0.18/0.57 (ePrincess v.1.0)
% 0.18/0.57
% 0.18/0.57 (c) Philipp Rümmer, 2009-2015
% 0.18/0.57 (c) Peter Backeman, 2014-2015
% 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.57 Bug reports to peter@backeman.se
% 0.18/0.57
% 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.57
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.63/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.34/0.88 Prover 0: Preprocessing ...
% 1.52/0.99 Prover 0: Warning: ignoring some quantifiers
% 1.65/1.01 Prover 0: Constructing countermodel ...
% 1.89/1.14 Prover 0: gave up
% 1.89/1.14 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.89/1.15 Prover 1: Preprocessing ...
% 2.33/1.23 Prover 1: Warning: ignoring some quantifiers
% 2.40/1.23 Prover 1: Constructing countermodel ...
% 2.94/1.42 Prover 1: gave up
% 2.94/1.42 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.94/1.43 Prover 2: Preprocessing ...
% 3.33/1.49 Prover 2: Warning: ignoring some quantifiers
% 3.33/1.50 Prover 2: Constructing countermodel ...
% 3.61/1.56 Prover 2: proved (141ms)
% 3.61/1.56
% 3.61/1.56 No countermodel exists, formula is valid
% 3.61/1.56 % SZS status Theorem for theBenchmark
% 3.61/1.56
% 3.61/1.56 Generating proof ... Warning: ignoring some quantifiers
% 4.26/1.75 found it (size 20)
% 4.26/1.75
% 4.26/1.75 % SZS output start Proof for theBenchmark
% 4.26/1.75 Assumed formulas after preprocessing and simplification:
% 4.26/1.75 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & ~ (v3 = 0) & empty(v6) = 0 & empty(v4) = v5 & union(v0) = v2 & subset(v2, v1) = v3 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (union(v7) = v8) | ~ (in(v11, v7) = 0) | ~ (in(v9, v8) = v10) | ? [v12] : ( ~ (v12 = 0) & in(v9, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (union(v7) = v8) | ~ (in(v9, v11) = 0) | ~ (in(v9, v8) = v10) | ? [v12] : ( ~ (v12 = 0) & in(v11, v7) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v7, v8) = 0) | ~ (in(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & in(v9, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (in(v10, v9) = v8) | ~ (in(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (empty(v9) = v8) | ~ (empty(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (union(v9) = v8) | ~ (union(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (union(v7) = v8) | ~ (in(v9, v8) = 0) | ? [v10] : (in(v10, v7) = 0 & in(v9, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (in(v9, v7) = 0) | in(v9, v8) = 0) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (union(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (((v14 = 0 & v13 = 0 & in(v12, v8) = 0 & in(v10, v12) = 0) | (v11 = 0 & in(v10, v7) = 0)) & (( ~ (v11 = 0) & in(v10, v7) = v11) | ( ! [v15] : ( ~ (in(v15, v8) = 0) | ? [v16] : ( ~ (v16 = 0) & in(v10, v15) = v16)) & ! [v15] : ( ~ (in(v10, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & in(v15, v8) = v16)))))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v1) = v8) | ? [v9] : ( ~ (v9 = 0) & in(v7, v0) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) & ! [v7] : ( ~ (in(v7, v0) = 0) | subset(v7, v1) = 0) & ? [v7] : ? [v8] : ? [v9] : subset(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : in(v8, v7) = v9 & ? [v7] : ? [v8] : empty(v7) = v8 & ? [v7] : ? [v8] : union(v7) = v8)
% 4.59/1.78 | 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 yields:
% 4.59/1.78 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & union(all_0_6_6) = all_0_4_4 & subset(all_0_4_4, all_0_5_5) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v2, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v4 = 0) & in(v3, v0) = v4) | ( ! [v8] : ( ~ (in(v8, v1) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v3, v8) = v9)) & ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9)))))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, all_0_5_5) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_6_6) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : ( ~ (in(v0, all_0_6_6) = 0) | subset(v0, all_0_5_5) = 0) & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : ? [v1] : union(v0) = v1
% 4.59/1.79 |
% 4.59/1.79 | Applying alpha-rule on (1) yields:
% 4.59/1.79 | (2) union(all_0_6_6) = all_0_4_4
% 4.59/1.79 | (3) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 4.59/1.79 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0))
% 4.59/1.79 | (5) ~ (all_0_3_3 = 0)
% 4.59/1.79 | (6) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 4.59/1.79 | (7) ~ (all_0_1_1 = 0)
% 4.59/1.79 | (8) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 4.59/1.79 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, all_0_5_5) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_6_6) = v2))
% 4.59/1.80 | (10) ? [v0] : ? [v1] : empty(v0) = v1
% 4.59/1.80 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5))
% 4.59/1.80 | (12) ? [v0] : ? [v1] : union(v0) = v1
% 4.59/1.80 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 4.59/1.80 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 4.59/1.80 | (15) ! [v0] : ( ~ (in(v0, all_0_6_6) = 0) | subset(v0, all_0_5_5) = 0)
% 4.59/1.80 | (16) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 4.59/1.80 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 4.59/1.80 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 4.59/1.80 | (19) empty(all_0_2_2) = all_0_1_1
% 4.59/1.80 | (20) subset(all_0_4_4, all_0_5_5) = all_0_3_3
% 4.59/1.80 | (21) empty(all_0_0_0) = 0
% 4.59/1.80 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v2, v4) = v5))
% 4.59/1.80 | (23) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v4 = 0) & in(v3, v0) = v4) | ( ! [v8] : ( ~ (in(v8, v1) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v3, v8) = v9)) & ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9))))))
% 4.59/1.80 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 4.59/1.80 | (25) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 4.59/1.80 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 4.59/1.80 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 4.59/1.80 |
% 4.59/1.80 | Instantiating formula (24) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_5_5) = all_0_3_3, yields:
% 4.59/1.80 | (28) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_5_5) = v1)
% 4.59/1.80 |
% 4.59/1.80 +-Applying beta-rule and splitting (28), into two cases.
% 4.59/1.80 |-Branch one:
% 4.59/1.80 | (29) all_0_3_3 = 0
% 4.59/1.80 |
% 4.59/1.80 | Equations (29) can reduce 5 to:
% 4.59/1.80 | (30) $false
% 4.59/1.80 |
% 4.59/1.80 |-The branch is then unsatisfiable
% 4.59/1.80 |-Branch two:
% 4.59/1.80 | (5) ~ (all_0_3_3 = 0)
% 4.59/1.81 | (32) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_5_5) = v1)
% 4.59/1.81 |
% 4.59/1.81 | Instantiating (32) with all_20_0_18, all_20_1_19 yields:
% 4.59/1.81 | (33) ~ (all_20_0_18 = 0) & in(all_20_1_19, all_0_4_4) = 0 & in(all_20_1_19, all_0_5_5) = all_20_0_18
% 4.59/1.81 |
% 4.59/1.81 | Applying alpha-rule on (33) yields:
% 4.59/1.81 | (34) ~ (all_20_0_18 = 0)
% 4.59/1.81 | (35) in(all_20_1_19, all_0_4_4) = 0
% 4.59/1.81 | (36) in(all_20_1_19, all_0_5_5) = all_20_0_18
% 4.59/1.81 |
% 4.59/1.81 | Instantiating formula (4) with all_20_1_19, all_0_4_4, all_0_6_6 and discharging atoms union(all_0_6_6) = all_0_4_4, in(all_20_1_19, all_0_4_4) = 0, yields:
% 4.59/1.81 | (37) ? [v0] : (in(v0, all_0_6_6) = 0 & in(all_20_1_19, v0) = 0)
% 4.71/1.81 |
% 4.71/1.81 | Instantiating (37) with all_35_0_22 yields:
% 4.71/1.81 | (38) in(all_35_0_22, all_0_6_6) = 0 & in(all_20_1_19, all_35_0_22) = 0
% 4.71/1.81 |
% 4.71/1.81 | Applying alpha-rule on (38) yields:
% 4.71/1.81 | (39) in(all_35_0_22, all_0_6_6) = 0
% 4.71/1.81 | (40) in(all_20_1_19, all_35_0_22) = 0
% 4.71/1.81 |
% 4.71/1.81 | Instantiating formula (15) with all_35_0_22 and discharging atoms in(all_35_0_22, all_0_6_6) = 0, yields:
% 4.71/1.81 | (41) subset(all_35_0_22, all_0_5_5) = 0
% 4.71/1.81 |
% 4.71/1.81 | Instantiating formula (27) with all_20_1_19, all_0_5_5, all_35_0_22 and discharging atoms subset(all_35_0_22, all_0_5_5) = 0, in(all_20_1_19, all_35_0_22) = 0, yields:
% 4.71/1.81 | (42) in(all_20_1_19, all_0_5_5) = 0
% 4.71/1.81 |
% 4.71/1.81 | Instantiating formula (14) with all_20_0_18, all_20_1_19, all_0_5_5, all_35_0_22 and discharging atoms subset(all_35_0_22, all_0_5_5) = 0, in(all_20_1_19, all_0_5_5) = all_20_0_18, yields:
% 4.71/1.81 | (43) all_20_0_18 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_20_1_19, all_35_0_22) = v0)
% 4.71/1.81 |
% 4.71/1.81 +-Applying beta-rule and splitting (43), into two cases.
% 4.71/1.81 |-Branch one:
% 4.71/1.81 | (44) all_20_0_18 = 0
% 4.71/1.81 |
% 4.71/1.81 | Equations (44) can reduce 34 to:
% 4.71/1.81 | (30) $false
% 4.71/1.81 |
% 4.71/1.81 |-The branch is then unsatisfiable
% 4.71/1.81 |-Branch two:
% 4.71/1.81 | (34) ~ (all_20_0_18 = 0)
% 4.71/1.81 | (47) ? [v0] : ( ~ (v0 = 0) & in(all_20_1_19, all_35_0_22) = v0)
% 4.71/1.81 |
% 4.71/1.81 | Instantiating formula (26) with all_20_1_19, all_0_5_5, 0, all_20_0_18 and discharging atoms in(all_20_1_19, all_0_5_5) = all_20_0_18, in(all_20_1_19, all_0_5_5) = 0, yields:
% 4.71/1.81 | (44) all_20_0_18 = 0
% 4.71/1.81 |
% 4.71/1.81 | Equations (44) can reduce 34 to:
% 4.71/1.81 | (30) $false
% 4.71/1.81 |
% 4.71/1.81 |-The branch is then unsatisfiable
% 4.71/1.81 % SZS output end Proof for theBenchmark
% 4.71/1.81
% 4.71/1.81 1226ms
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