TSTP Solution File: SEU097+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU097+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 08:46:35 EDT 2022
% Result : Theorem 3.36s 1.44s
% Output : Proof 5.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU097+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n026.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 Jun 18 23:27:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.57 ____ _
% 0.54/0.57 ___ / __ \_____(_)___ ________ __________
% 0.54/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.57
% 0.54/0.57 A Theorem Prover for First-Order Logic
% 0.54/0.57 (ePrincess v.1.0)
% 0.54/0.57
% 0.54/0.57 (c) Philipp Rümmer, 2009-2015
% 0.54/0.57 (c) Peter Backeman, 2014-2015
% 0.54/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.57 Bug reports to peter@backeman.se
% 0.54/0.57
% 0.54/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.57
% 0.59/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.59/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.83/0.96 Prover 0: Preprocessing ...
% 2.63/1.22 Prover 0: Warning: ignoring some quantifiers
% 2.80/1.25 Prover 0: Constructing countermodel ...
% 3.36/1.44 Prover 0: proved (817ms)
% 3.36/1.44
% 3.36/1.44 No countermodel exists, formula is valid
% 3.36/1.44 % SZS status Theorem for theBenchmark
% 3.36/1.44
% 3.36/1.44 Generating proof ... Warning: ignoring some quantifiers
% 5.32/1.79 found it (size 16)
% 5.32/1.79
% 5.32/1.79 % SZS output start Proof for theBenchmark
% 5.32/1.79 Assumed formulas after preprocessing and simplification:
% 5.32/1.79 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (symmetric_difference(v0, v1) = v2 & relation_non_empty(v3) & ordinal_yielding(v12) & transfinite_sequence(v12) & transfinite_sequence(v4) & being_limit_ordinal(v18) & function_yielding(v21) & relation_empty_yielding(v6) & relation_empty_yielding(v5) & relation_empty_yielding(empty_set) & one_to_one(v13) & one_to_one(v8) & one_to_one(empty_set) & natural(v23) & natural(v9) & relation(v21) & relation(v20) & relation(v17) & relation(v14) & relation(v13) & relation(v12) & relation(v11) & relation(v8) & relation(v6) & relation(v5) & relation(v4) & relation(v3) & relation(empty_set) & function(v21) & function(v20) & function(v14) & function(v13) & function(v12) & function(v8) & function(v5) & function(v4) & function(v3) & function(empty_set) & finite(v22) & finite(v1) & finite(v0) & empty(v17) & empty(v16) & empty(v14) & empty(v13) & empty(v9) & empty(empty_set) & epsilon_connected(v23) & epsilon_connected(v19) & epsilon_connected(v18) & epsilon_connected(v15) & epsilon_connected(v13) & epsilon_connected(v9) & epsilon_connected(v7) & epsilon_connected(empty_set) & epsilon_transitive(v23) & epsilon_transitive(v19) & epsilon_transitive(v18) & epsilon_transitive(v15) & epsilon_transitive(v13) & epsilon_transitive(v9) & epsilon_transitive(v7) & epsilon_transitive(empty_set) & element(v15, positive_rationals) & element(v9, positive_rationals) & ordinal(v23) & ordinal(v19) & ordinal(v18) & ordinal(v15) & ordinal(v13) & ordinal(v9) & ordinal(v7) & ordinal(empty_set) & ~ finite(v2) & ~ empty(v23) & ~ empty(v22) & ~ empty(v15) & ~ empty(v11) & ~ empty(v10) & ~ empty(v7) & ~ empty(positive_rationals) & ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : ( ~ (set_difference(v25, v24) = v27) | ~ (set_difference(v24, v25) = v26) | ~ (set_union2(v26, v27) = v28) | symmetric_difference(v24, v25) = v28) & ! [v24] : ! [v25] : ! [v26] : ! [v27] : (v25 = v24 | ~ (set_difference(v27, v26) = v25) | ~ (set_difference(v27, v26) = v24)) & ! [v24] : ! [v25] : ! [v26] : ! [v27] : (v25 = v24 | ~ (symmetric_difference(v27, v26) = v25) | ~ (symmetric_difference(v27, v26) = v24)) & ! [v24] : ! [v25] : ! [v26] : ! [v27] : (v25 = v24 | ~ (set_union2(v27, v26) = v25) | ~ (set_union2(v27, v26) = v24)) & ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (powerset(v26) = v27) | ~ empty(v26) | ~ element(v25, v27) | ~ in(v24, v25)) & ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (powerset(v26) = v27) | ~ element(v25, v27) | ~ in(v24, v25) | element(v24, v26)) & ! [v24] : ! [v25] : ! [v26] : (v25 = v24 | ~ (powerset(v26) = v25) | ~ (powerset(v26) = v24)) & ! [v24] : ! [v25] : ! [v26] : ( ~ (set_difference(v24, v25) = v26) | ~ relation(v25) | ~ relation(v24) | relation(v26)) & ! [v24] : ! [v25] : ! [v26] : ( ~ (set_difference(v24, v25) = v26) | ~ finite(v24) | finite(v26)) & ! [v24] : ! [v25] : ! [v26] : ( ~ (symmetric_difference(v25, v24) = v26) | symmetric_difference(v24, v25) = v26) & ! [v24] : ! [v25] : ! [v26] : ( ~ (symmetric_difference(v24, v25) = v26) | symmetric_difference(v25, v24) = v26) & ! [v24] : ! [v25] : ! [v26] : ( ~ (symmetric_difference(v24, v25) = v26) | ? [v27] : ? [v28] : (set_difference(v25, v24) = v28 & set_difference(v24, v25) = v27 & set_union2(v27, v28) = v26)) & ! [v24] : ! [v25] : ! [v26] : ( ~ (set_union2(v25, v24) = v26) | ~ empty(v26) | empty(v24)) & ! [v24] : ! [v25] : ! [v26] : ( ~ (set_union2(v25, v24) = v26) | set_union2(v24, v25) = v26) & ! [v24] : ! [v25] : ! [v26] : ( ~ (set_union2(v24, v25) = v26) | ~ relation(v25) | ~ relation(v24) | relation(v26)) & ! [v24] : ! [v25] : ! [v26] : ( ~ (set_union2(v24, v25) = v26) | ~ finite(v25) | ~ finite(v24) | finite(v26)) & ! [v24] : ! [v25] : ! [v26] : ( ~ (set_union2(v24, v25) = v26) | ~ empty(v26) | empty(v24)) & ! [v24] : ! [v25] : ! [v26] : ( ~ (set_union2(v24, v25) = v26) | set_union2(v25, v24) = v26) & ! [v24] : ! [v25] : ! [v26] : ( ~ (powerset(v25) = v26) | ~ subset(v24, v25) | element(v24, v26)) & ! [v24] : ! [v25] : ! [v26] : ( ~ (powerset(v25) = v26) | ~ element(v24, v26) | subset(v24, v25)) & ! [v24] : ! [v25] : ! [v26] : ( ~ (powerset(v24) = v25) | ~ finite(v24) | ~ element(v26, v25) | finite(v26)) & ! [v24] : ! [v25] : (v25 = v24 | ~ (set_difference(v24, empty_set) = v25)) & ! [v24] : ! [v25] : (v25 = v24 | ~ (symmetric_difference(v24, empty_set) = v25)) & ! [v24] : ! [v25] : (v25 = v24 | ~ (set_union2(v24, v24) = v25)) & ! [v24] : ! [v25] : (v25 = v24 | ~ (set_union2(v24, empty_set) = v25)) & ! [v24] : ! [v25] : (v25 = v24 | ~ empty(v25) | ~ empty(v24)) & ! [v24] : ! [v25] : (v25 = empty_set | ~ (set_difference(empty_set, v24) = v25)) & ! [v24] : ! [v25] : ( ~ (powerset(v24) = v25) | ~ empty(v25)) & ! [v24] : ! [v25] : ( ~ (powerset(v24) = v25) | empty(v24) | ? [v26] : (finite(v26) & element(v26, v25) & ~ empty(v26))) & ! [v24] : ! [v25] : ( ~ (powerset(v24) = v25) | empty(v24) | ? [v26] : (element(v26, v25) & ~ empty(v26))) & ! [v24] : ! [v25] : ( ~ (powerset(v24) = v25) | ? [v26] : (one_to_one(v26) & natural(v26) & relation(v26) & function(v26) & finite(v26) & empty(v26) & epsilon_connected(v26) & epsilon_transitive(v26) & element(v26, v25) & ordinal(v26))) & ! [v24] : ! [v25] : ( ~ (powerset(v24) = v25) | ? [v26] : (empty(v26) & element(v26, v25))) & ! [v24] : ! [v25] : ( ~ empty(v25) | ~ in(v24, v25)) & ! [v24] : ! [v25] : ( ~ element(v25, v24) | ~ ordinal(v24) | epsilon_connected(v25)) & ! [v24] : ! [v25] : ( ~ element(v25, v24) | ~ ordinal(v24) | epsilon_transitive(v25)) & ! [v24] : ! [v25] : ( ~ element(v25, v24) | ~ ordinal(v24) | ordinal(v25)) & ! [v24] : ! [v25] : ( ~ element(v24, v25) | empty(v25) | in(v24, v25)) & ! [v24] : ! [v25] : ( ~ in(v25, v24) | ~ in(v24, v25)) & ! [v24] : ! [v25] : ( ~ in(v24, v25) | element(v24, v25)) & ! [v24] : (v24 = empty_set | ~ empty(v24)) & ! [v24] : ( ~ relation(v24) | ~ function(v24) | ~ empty(v24) | one_to_one(v24)) & ! [v24] : ( ~ empty(v24) | ~ ordinal(v24) | natural(v24)) & ! [v24] : ( ~ empty(v24) | ~ ordinal(v24) | epsilon_connected(v24)) & ! [v24] : ( ~ empty(v24) | ~ ordinal(v24) | epsilon_transitive(v24)) & ! [v24] : ( ~ empty(v24) | relation(v24)) & ! [v24] : ( ~ empty(v24) | function(v24)) & ! [v24] : ( ~ empty(v24) | finite(v24)) & ! [v24] : ( ~ empty(v24) | epsilon_connected(v24)) & ! [v24] : ( ~ empty(v24) | epsilon_transitive(v24)) & ! [v24] : ( ~ empty(v24) | ordinal(v24)) & ! [v24] : ( ~ epsilon_connected(v24) | ~ epsilon_transitive(v24) | ordinal(v24)) & ! [v24] : ( ~ element(v24, positive_rationals) | ~ ordinal(v24) | natural(v24)) & ! [v24] : ( ~ element(v24, positive_rationals) | ~ ordinal(v24) | epsilon_connected(v24)) & ! [v24] : ( ~ element(v24, positive_rationals) | ~ ordinal(v24) | epsilon_transitive(v24)) & ! [v24] : ( ~ ordinal(v24) | epsilon_connected(v24)) & ! [v24] : ( ~ ordinal(v24) | epsilon_transitive(v24)) & ? [v24] : ? [v25] : element(v25, v24) & ? [v24] : subset(v24, v24))
% 5.46/1.84 | 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, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20, all_0_21_21, all_0_22_22, all_0_23_23 yields:
% 5.46/1.84 | (1) symmetric_difference(all_0_23_23, all_0_22_22) = all_0_21_21 & relation_non_empty(all_0_20_20) & ordinal_yielding(all_0_11_11) & transfinite_sequence(all_0_11_11) & transfinite_sequence(all_0_19_19) & being_limit_ordinal(all_0_5_5) & function_yielding(all_0_2_2) & relation_empty_yielding(all_0_17_17) & relation_empty_yielding(all_0_18_18) & relation_empty_yielding(empty_set) & one_to_one(all_0_10_10) & one_to_one(all_0_15_15) & one_to_one(empty_set) & natural(all_0_0_0) & natural(all_0_14_14) & relation(all_0_2_2) & relation(all_0_3_3) & relation(all_0_6_6) & relation(all_0_9_9) & relation(all_0_10_10) & relation(all_0_11_11) & relation(all_0_12_12) & relation(all_0_15_15) & relation(all_0_17_17) & relation(all_0_18_18) & relation(all_0_19_19) & relation(all_0_20_20) & relation(empty_set) & function(all_0_2_2) & function(all_0_3_3) & function(all_0_9_9) & function(all_0_10_10) & function(all_0_11_11) & function(all_0_15_15) & function(all_0_18_18) & function(all_0_19_19) & function(all_0_20_20) & function(empty_set) & finite(all_0_1_1) & finite(all_0_22_22) & finite(all_0_23_23) & empty(all_0_6_6) & empty(all_0_7_7) & empty(all_0_9_9) & empty(all_0_10_10) & empty(all_0_14_14) & empty(empty_set) & epsilon_connected(all_0_0_0) & epsilon_connected(all_0_4_4) & epsilon_connected(all_0_5_5) & epsilon_connected(all_0_8_8) & epsilon_connected(all_0_10_10) & epsilon_connected(all_0_14_14) & epsilon_connected(all_0_16_16) & epsilon_connected(empty_set) & epsilon_transitive(all_0_0_0) & epsilon_transitive(all_0_4_4) & epsilon_transitive(all_0_5_5) & epsilon_transitive(all_0_8_8) & epsilon_transitive(all_0_10_10) & epsilon_transitive(all_0_14_14) & epsilon_transitive(all_0_16_16) & epsilon_transitive(empty_set) & element(all_0_8_8, positive_rationals) & element(all_0_14_14, positive_rationals) & ordinal(all_0_0_0) & ordinal(all_0_4_4) & ordinal(all_0_5_5) & ordinal(all_0_8_8) & ordinal(all_0_10_10) & ordinal(all_0_14_14) & ordinal(all_0_16_16) & ordinal(empty_set) & ~ finite(all_0_21_21) & ~ empty(all_0_0_0) & ~ empty(all_0_1_1) & ~ empty(all_0_8_8) & ~ empty(all_0_12_12) & ~ empty(all_0_13_13) & ~ empty(all_0_16_16) & ~ empty(positive_rationals) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v0) = v3) | ~ (set_difference(v0, v1) = v2) | ~ (set_union2(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ 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] : ( ~ (set_difference(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ finite(v0) | finite(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v1, v0) = v4 & set_difference(v0, v1) = v3 & set_union2(v3, v4) = 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) | ~ finite(v1) | ~ finite(v0) | finite(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] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | ~ element(v2, v1) | finite(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (symmetric_difference(v0, empty_set) = v1)) & ! [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] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (finite(v2) & element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (one_to_one(v2) & natural(v2) & relation(v2) & function(v2) & finite(v2) & empty(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & element(v2, v1) & ordinal(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | epsilon_connected(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | epsilon_transitive(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | ordinal(v1)) & ! [v0] : ! [v1] : ( ~ element(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) | ~ ordinal(v0) | natural(v0)) & ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ! [v0] : ( ~ empty(v0) | finite(v0)) & ! [v0] : ( ~ empty(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ empty(v0) | ordinal(v0)) & ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0)) & ! [v0] : ( ~ element(v0, positive_rationals) | ~ ordinal(v0) | natural(v0)) & ! [v0] : ( ~ element(v0, positive_rationals) | ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ element(v0, positive_rationals) | ~ ordinal(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0)
% 5.46/1.85 |
% 5.46/1.85 | Applying alpha-rule on (1) yields:
% 5.46/1.86 | (2) relation(all_0_19_19)
% 5.46/1.86 | (3) ~ empty(all_0_13_13)
% 5.46/1.86 | (4) ordinal(all_0_16_16)
% 5.46/1.86 | (5) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 5.46/1.86 | (6) ordinal(all_0_0_0)
% 5.46/1.86 | (7) epsilon_transitive(all_0_0_0)
% 5.46/1.86 | (8) transfinite_sequence(all_0_11_11)
% 5.46/1.86 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 5.46/1.86 | (10) ~ empty(all_0_16_16)
% 5.46/1.86 | (11) function(empty_set)
% 5.46/1.86 | (12) relation_non_empty(all_0_20_20)
% 5.46/1.86 | (13) natural(all_0_14_14)
% 5.46/1.86 | (14) finite(all_0_1_1)
% 5.46/1.86 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (symmetric_difference(v0, empty_set) = v1))
% 5.46/1.86 | (16) function(all_0_20_20)
% 5.46/1.86 | (17) function(all_0_19_19)
% 5.46/1.86 | (18) relation(all_0_18_18)
% 5.46/1.86 | (19) relation(all_0_2_2)
% 5.46/1.86 | (20) epsilon_transitive(all_0_14_14)
% 5.46/1.86 | (21) ! [v0] : ( ~ empty(v0) | relation(v0))
% 5.46/1.86 | (22) being_limit_ordinal(all_0_5_5)
% 5.46/1.86 | (23) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | epsilon_transitive(v1))
% 5.46/1.86 | (24) ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0))
% 5.46/1.86 | (25) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 5.46/1.86 | (26) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 5.46/1.86 | (27) ! [v0] : ( ~ element(v0, positive_rationals) | ~ ordinal(v0) | natural(v0))
% 5.46/1.86 | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 5.46/1.86 | (29) epsilon_connected(all_0_8_8)
% 5.46/1.86 | (30) natural(all_0_0_0)
% 5.46/1.86 | (31) ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | epsilon_connected(v0))
% 5.46/1.86 | (32) function(all_0_2_2)
% 5.46/1.86 | (33) function(all_0_3_3)
% 5.46/1.86 | (34) ! [v0] : ( ~ empty(v0) | ordinal(v0))
% 5.46/1.86 | (35) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 5.46/1.86 | (36) epsilon_transitive(all_0_4_4)
% 5.46/1.86 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ finite(v0) | finite(v2))
% 5.46/1.86 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 5.46/1.86 | (39) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 5.46/1.86 | (40) ordinal(all_0_14_14)
% 5.46/1.86 | (41) element(all_0_8_8, positive_rationals)
% 5.46/1.86 | (42) function(all_0_15_15)
% 5.46/1.86 | (43) epsilon_connected(all_0_4_4)
% 5.46/1.86 | (44) empty(all_0_6_6)
% 5.46/1.86 | (45) ~ empty(all_0_12_12)
% 5.46/1.86 | (46) symmetric_difference(all_0_23_23, all_0_22_22) = all_0_21_21
% 5.46/1.86 | (47) function(all_0_10_10)
% 5.46/1.86 | (48) ~ empty(positive_rationals)
% 5.46/1.86 | (49) relation_empty_yielding(all_0_18_18)
% 5.46/1.86 | (50) relation_empty_yielding(all_0_17_17)
% 5.46/1.86 | (51) function(all_0_18_18)
% 5.46/1.86 | (52) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 5.46/1.86 | (53) empty(empty_set)
% 5.46/1.86 | (54) ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0))
% 5.46/1.86 | (55) ! [v0] : ( ~ empty(v0) | epsilon_connected(v0))
% 5.46/1.86 | (56) ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0))
% 5.46/1.86 | (57) ~ finite(all_0_21_21)
% 5.46/1.87 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1))
% 5.46/1.87 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 5.46/1.87 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 5.46/1.87 | (61) ordinal(all_0_8_8)
% 5.46/1.87 | (62) ~ empty(all_0_0_0)
% 5.46/1.87 | (63) epsilon_transitive(all_0_5_5)
% 5.46/1.87 | (64) epsilon_transitive(all_0_16_16)
% 5.46/1.87 | (65) ! [v0] : ( ~ empty(v0) | function(v0))
% 5.46/1.87 | (66) ! [v0] : ( ~ element(v0, positive_rationals) | ~ ordinal(v0) | epsilon_transitive(v0))
% 5.46/1.87 | (67) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | epsilon_connected(v1))
% 5.46/1.87 | (68) relation(all_0_6_6)
% 5.46/1.87 | (69) ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0))
% 5.46/1.87 | (70) relation(all_0_20_20)
% 5.46/1.87 | (71) epsilon_connected(all_0_14_14)
% 5.46/1.87 | (72) finite(all_0_23_23)
% 5.46/1.87 | (73) ! [v0] : ( ~ empty(v0) | finite(v0))
% 5.46/1.87 | (74) one_to_one(empty_set)
% 5.46/1.87 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0))
% 5.46/1.87 | (76) transfinite_sequence(all_0_19_19)
% 5.46/1.87 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | ~ element(v2, v1) | finite(v2))
% 5.46/1.87 | (78) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | ordinal(v1))
% 5.46/1.87 | (79) epsilon_transitive(all_0_10_10)
% 5.46/1.87 | (80) ~ empty(all_0_1_1)
% 5.46/1.87 | (81) epsilon_connected(all_0_16_16)
% 5.46/1.87 | (82) empty(all_0_14_14)
% 5.46/1.87 | (83) epsilon_connected(all_0_10_10)
% 5.46/1.87 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 5.46/1.87 | (85) ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | natural(v0))
% 5.46/1.87 | (86) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 5.46/1.87 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 5.46/1.87 | (88) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 5.46/1.87 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ finite(v1) | ~ finite(v0) | finite(v2))
% 5.46/1.87 | (90) ordinal(all_0_10_10)
% 5.46/1.87 | (91) empty(all_0_9_9)
% 5.46/1.87 | (92) relation(all_0_15_15)
% 5.46/1.87 | (93) relation_empty_yielding(empty_set)
% 5.46/1.87 | (94) relation(all_0_11_11)
% 5.46/1.87 | (95) ordinal_yielding(all_0_11_11)
% 5.46/1.87 | (96) epsilon_connected(empty_set)
% 5.46/1.87 | (97) relation(all_0_17_17)
% 5.46/1.87 | (98) epsilon_transitive(all_0_8_8)
% 5.46/1.87 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v0) = v3) | ~ (set_difference(v0, v1) = v2) | ~ (set_union2(v2, v3) = v4) | symmetric_difference(v0, v1) = v4)
% 5.46/1.88 | (100) relation(all_0_3_3)
% 5.46/1.88 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 5.46/1.88 | (102) function(all_0_9_9)
% 5.46/1.88 | (103) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 5.46/1.88 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 5.46/1.88 | (105) ~ empty(all_0_8_8)
% 5.46/1.88 | (106) function(all_0_11_11)
% 5.46/1.88 | (107) ordinal(empty_set)
% 5.46/1.88 | (108) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (finite(v2) & element(v2, v1) & ~ empty(v2)))
% 5.46/1.88 | (109) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 5.46/1.88 | (110) ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | epsilon_transitive(v0))
% 5.46/1.88 | (111) one_to_one(all_0_15_15)
% 5.46/1.88 | (112) finite(all_0_22_22)
% 5.46/1.88 | (113) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 5.46/1.88 | (114) relation(all_0_10_10)
% 5.46/1.88 | (115) empty(all_0_10_10)
% 5.46/1.88 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2)
% 5.46/1.88 | (117) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2)
% 5.46/1.88 | (118) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 5.46/1.88 | (119) relation(all_0_9_9)
% 5.46/1.88 | (120) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 5.46/1.88 | (121) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 5.46/1.88 | (122) ? [v0] : subset(v0, v0)
% 5.46/1.88 | (123) epsilon_connected(all_0_0_0)
% 5.46/1.88 | (124) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1)))
% 5.46/1.89 | (125) empty(all_0_7_7)
% 5.46/1.89 | (126) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 5.46/1.89 | (127) relation(all_0_12_12)
% 5.46/1.89 | (128) relation(empty_set)
% 5.46/1.89 | (129) one_to_one(all_0_10_10)
% 5.46/1.89 | (130) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (one_to_one(v2) & natural(v2) & relation(v2) & function(v2) & finite(v2) & empty(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & element(v2, v1) & ordinal(v2)))
% 5.46/1.89 | (131) ordinal(all_0_5_5)
% 5.46/1.89 | (132) element(all_0_14_14, positive_rationals)
% 5.46/1.89 | (133) epsilon_transitive(empty_set)
% 5.46/1.89 | (134) function_yielding(all_0_2_2)
% 5.46/1.89 | (135) ? [v0] : ? [v1] : element(v1, v0)
% 5.46/1.89 | (136) epsilon_connected(all_0_5_5)
% 5.46/1.89 | (137) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 5.46/1.89 | (138) ordinal(all_0_4_4)
% 5.46/1.89 | (139) ! [v0] : ( ~ element(v0, positive_rationals) | ~ ordinal(v0) | epsilon_connected(v0))
% 5.46/1.89 | (140) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v1, v0) = v4 & set_difference(v0, v1) = v3 & set_union2(v3, v4) = v2))
% 5.46/1.89 |
% 5.46/1.89 | Instantiating formula (117) with all_0_21_21, all_0_23_23, all_0_22_22 and discharging atoms symmetric_difference(all_0_23_23, all_0_22_22) = all_0_21_21, yields:
% 5.46/1.89 | (141) symmetric_difference(all_0_22_22, all_0_23_23) = all_0_21_21
% 5.46/1.89 |
% 5.46/1.89 | Instantiating formula (140) with all_0_21_21, all_0_22_22, all_0_23_23 and discharging atoms symmetric_difference(all_0_23_23, all_0_22_22) = all_0_21_21, yields:
% 5.46/1.89 | (142) ? [v0] : ? [v1] : (set_difference(all_0_22_22, all_0_23_23) = v1 & set_difference(all_0_23_23, all_0_22_22) = v0 & set_union2(v0, v1) = all_0_21_21)
% 5.46/1.89 |
% 5.46/1.89 | Instantiating (142) with all_17_0_27, all_17_1_28 yields:
% 5.46/1.89 | (143) set_difference(all_0_22_22, all_0_23_23) = all_17_0_27 & set_difference(all_0_23_23, all_0_22_22) = all_17_1_28 & set_union2(all_17_1_28, all_17_0_27) = all_0_21_21
% 5.46/1.89 |
% 5.46/1.89 | Applying alpha-rule on (143) yields:
% 5.46/1.89 | (144) set_difference(all_0_22_22, all_0_23_23) = all_17_0_27
% 5.46/1.89 | (145) set_difference(all_0_23_23, all_0_22_22) = all_17_1_28
% 5.46/1.89 | (146) set_union2(all_17_1_28, all_17_0_27) = all_0_21_21
% 5.46/1.89 |
% 5.46/1.89 | Instantiating formula (37) with all_17_0_27, all_0_23_23, all_0_22_22 and discharging atoms set_difference(all_0_22_22, all_0_23_23) = all_17_0_27, finite(all_0_22_22), yields:
% 5.46/1.89 | (147) finite(all_17_0_27)
% 5.46/1.89 |
% 5.46/1.89 | Instantiating formula (37) with all_17_1_28, all_0_22_22, all_0_23_23 and discharging atoms set_difference(all_0_23_23, all_0_22_22) = all_17_1_28, finite(all_0_23_23), yields:
% 5.46/1.89 | (148) finite(all_17_1_28)
% 5.46/1.89 |
% 5.46/1.89 | Instantiating formula (140) with all_0_21_21, all_0_23_23, all_0_22_22 and discharging atoms symmetric_difference(all_0_22_22, all_0_23_23) = all_0_21_21, yields:
% 5.46/1.89 | (149) ? [v0] : ? [v1] : (set_difference(all_0_22_22, all_0_23_23) = v0 & set_difference(all_0_23_23, all_0_22_22) = v1 & set_union2(v0, v1) = all_0_21_21)
% 5.46/1.89 |
% 5.46/1.89 | Instantiating (149) with all_25_0_29, all_25_1_30 yields:
% 5.46/1.89 | (150) set_difference(all_0_22_22, all_0_23_23) = all_25_1_30 & set_difference(all_0_23_23, all_0_22_22) = all_25_0_29 & set_union2(all_25_1_30, all_25_0_29) = all_0_21_21
% 5.46/1.89 |
% 5.46/1.89 | Applying alpha-rule on (150) yields:
% 5.46/1.89 | (151) set_difference(all_0_22_22, all_0_23_23) = all_25_1_30
% 5.46/1.89 | (152) set_difference(all_0_23_23, all_0_22_22) = all_25_0_29
% 5.46/1.89 | (153) set_union2(all_25_1_30, all_25_0_29) = all_0_21_21
% 5.46/1.89 |
% 5.46/1.89 | Instantiating formula (104) with all_0_22_22, all_0_23_23, all_25_1_30, all_17_0_27 and discharging atoms set_difference(all_0_22_22, all_0_23_23) = all_25_1_30, set_difference(all_0_22_22, all_0_23_23) = all_17_0_27, yields:
% 5.46/1.89 | (154) all_25_1_30 = all_17_0_27
% 5.46/1.89 |
% 5.46/1.89 | Instantiating formula (104) with all_0_23_23, all_0_22_22, all_25_0_29, all_17_1_28 and discharging atoms set_difference(all_0_23_23, all_0_22_22) = all_25_0_29, set_difference(all_0_23_23, all_0_22_22) = all_17_1_28, yields:
% 5.46/1.89 | (155) all_25_0_29 = all_17_1_28
% 5.46/1.89 |
% 5.46/1.90 | From (154)(155) and (153) follows:
% 5.46/1.90 | (156) set_union2(all_17_0_27, all_17_1_28) = all_0_21_21
% 5.46/1.90 |
% 5.46/1.90 | Instantiating formula (89) with all_0_21_21, all_17_1_28, all_17_0_27 and discharging atoms set_union2(all_17_0_27, all_17_1_28) = all_0_21_21, finite(all_17_0_27), finite(all_17_1_28), ~ finite(all_0_21_21), yields:
% 5.46/1.90 | (157) $false
% 5.46/1.90 |
% 5.46/1.90 |-The branch is then unsatisfiable
% 5.46/1.90 % SZS output end Proof for theBenchmark
% 5.46/1.90
% 5.46/1.90 1315ms
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