TSTP Solution File: SEU306+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU306+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 08:48:42 EDT 2022
% Result : Theorem 2.88s 1.35s
% Output : Proof 4.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU306+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 07:42:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.53/0.59 ____ _
% 0.53/0.59 ___ / __ \_____(_)___ ________ __________
% 0.53/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.59
% 0.53/0.59 A Theorem Prover for First-Order Logic
% 0.53/0.59 (ePrincess v.1.0)
% 0.53/0.59
% 0.53/0.59 (c) Philipp Rümmer, 2009-2015
% 0.53/0.59 (c) Peter Backeman, 2014-2015
% 0.53/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.59 Bug reports to peter@backeman.se
% 0.53/0.59
% 0.53/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.59
% 0.53/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.74/0.95 Prover 0: Preprocessing ...
% 2.40/1.19 Prover 0: Warning: ignoring some quantifiers
% 2.40/1.22 Prover 0: Constructing countermodel ...
% 2.88/1.34 Prover 0: proved (705ms)
% 2.88/1.35
% 2.88/1.35 No countermodel exists, formula is valid
% 2.88/1.35 % SZS status Theorem for theBenchmark
% 2.88/1.35
% 2.88/1.35 Generating proof ... Warning: ignoring some quantifiers
% 3.96/1.63 found it (size 12)
% 3.96/1.63
% 3.96/1.63 % SZS output start Proof for theBenchmark
% 3.96/1.63 Assumed formulas after preprocessing and simplification:
% 3.96/1.63 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v2 = v1) & the_carrier(v0) = v2 & cast_as_carrier_subset(v0) = v1 & one_sorted_str(v3) & one_sorted_str(v0) & empty(empty_set) & v1_membered(v4) & v1_membered(empty_set) & v2_membered(v4) & v2_membered(empty_set) & v3_membered(v4) & v3_membered(empty_set) & v4_membered(v4) & v4_membered(empty_set) & v5_membered(v4) & v5_membered(empty_set) & ~ empty(v4) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ~ element(v6, v8) | ~ empty(v7) | ~ in(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ~ element(v6, v8) | ~ in(v5, v6) | element(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (the_carrier(v7) = v6) | ~ (the_carrier(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cast_as_carrier_subset(v7) = v6) | ~ (cast_as_carrier_subset(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (powerset(v7) = v6) | ~ (powerset(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | ~ subset(v5, v6) | element(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | ~ element(v5, v7) | subset(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v1_membered(v5) | v1_membered(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v2_membered(v5) | v1_membered(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v2_membered(v5) | v2_membered(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v3_membered(v5) | v1_membered(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v3_membered(v5) | v2_membered(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v3_membered(v5) | v3_membered(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v4_membered(v5) | v1_membered(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v4_membered(v5) | v2_membered(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v4_membered(v5) | v3_membered(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v4_membered(v5) | v4_membered(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v5_membered(v5) | v1_membered(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v5_membered(v5) | v2_membered(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v5_membered(v5) | v3_membered(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v5_membered(v5) | v4_membered(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v5) = v6) | ~ element(v7, v6) | ~ v5_membered(v5) | v5_membered(v7)) & ! [v5] : ! [v6] : (v6 = v5 | ~ empty(v6) | ~ empty(v5)) & ! [v5] : ! [v6] : ( ~ (the_carrier(v5) = v6) | ~ one_sorted_str(v5) | cast_as_carrier_subset(v5) = v6) & ! [v5] : ! [v6] : ( ~ (the_carrier(v5) = v6) | ~ one_sorted_str(v5) | ? [v7] : ? [v8] : (cast_as_carrier_subset(v5) = v7 & powerset(v6) = v8 & element(v7, v8))) & ! [v5] : ! [v6] : ( ~ (cast_as_carrier_subset(v5) = v6) | ~ one_sorted_str(v5) | the_carrier(v5) = v6) & ! [v5] : ! [v6] : ( ~ (cast_as_carrier_subset(v5) = v6) | ~ one_sorted_str(v5) | ? [v7] : ? [v8] : (the_carrier(v5) = v7 & powerset(v7) = v8 & element(v6, v8))) & ! [v5] : ! [v6] : ( ~ (powerset(v5) = v6) | ~ empty(v6)) & ! [v5] : ! [v6] : ( ~ (powerset(v5) = v6) | empty(v5) | ? [v7] : (element(v7, v6) & ~ empty(v7))) & ! [v5] : ! [v6] : ( ~ (powerset(v5) = v6) | ? [v7] : (element(v7, v6) & empty(v7))) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v1_membered(v5) | v1_xcmplx_0(v6)) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v2_membered(v5) | v1_xreal_0(v6)) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v2_membered(v5) | v1_xcmplx_0(v6)) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v3_membered(v5) | v1_rat_1(v6)) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v3_membered(v5) | v1_xreal_0(v6)) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v3_membered(v5) | v1_xcmplx_0(v6)) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v4_membered(v5) | v1_int_1(v6)) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v4_membered(v5) | v1_rat_1(v6)) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v4_membered(v5) | v1_xreal_0(v6)) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v4_membered(v5) | v1_xcmplx_0(v6)) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v5_membered(v5) | natural(v6)) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v5_membered(v5) | v1_int_1(v6)) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v5_membered(v5) | v1_rat_1(v6)) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v5_membered(v5) | v1_xreal_0(v6)) & ! [v5] : ! [v6] : ( ~ element(v6, v5) | ~ v5_membered(v5) | v1_xcmplx_0(v6)) & ! [v5] : ! [v6] : ( ~ element(v5, v6) | empty(v6) | in(v5, v6)) & ! [v5] : ! [v6] : ( ~ empty(v6) | ~ in(v5, v6)) & ! [v5] : ! [v6] : ( ~ in(v6, v5) | ~ in(v5, v6)) & ! [v5] : ! [v6] : ( ~ in(v5, v6) | element(v5, v6)) & ! [v5] : (v5 = empty_set | ~ empty(v5)) & ! [v5] : ( ~ empty(v5) | v1_membered(v5)) & ! [v5] : ( ~ empty(v5) | v2_membered(v5)) & ! [v5] : ( ~ empty(v5) | v3_membered(v5)) & ! [v5] : ( ~ empty(v5) | v4_membered(v5)) & ! [v5] : ( ~ empty(v5) | v5_membered(v5)) & ! [v5] : ( ~ v2_membered(v5) | v1_membered(v5)) & ! [v5] : ( ~ v3_membered(v5) | v2_membered(v5)) & ! [v5] : ( ~ v4_membered(v5) | v3_membered(v5)) & ! [v5] : ( ~ v5_membered(v5) | v4_membered(v5)) & ? [v5] : ? [v6] : element(v6, v5) & ? [v5] : subset(v5, v5))
% 4.33/1.68 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 4.33/1.68 | (1) ~ (all_0_2_2 = all_0_3_3) & the_carrier(all_0_4_4) = all_0_2_2 & cast_as_carrier_subset(all_0_4_4) = all_0_3_3 & one_sorted_str(all_0_1_1) & one_sorted_str(all_0_4_4) & empty(empty_set) & v1_membered(all_0_0_0) & v1_membered(empty_set) & v2_membered(all_0_0_0) & v2_membered(empty_set) & v3_membered(all_0_0_0) & v3_membered(empty_set) & v4_membered(all_0_0_0) & v4_membered(empty_set) & v5_membered(all_0_0_0) & v5_membered(empty_set) & ~ empty(all_0_0_0) & ! [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 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [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) | ~ element(v2, v1) | ~ v1_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v2_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v2_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v3_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v3_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v3_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v5_membered(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | cast_as_carrier_subset(v0) = v1) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v2 & powerset(v1) = v3 & element(v2, v3))) & ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | the_carrier(v0) = v1) & ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & element(v1, v3))) & ! [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(v1, v0) | ~ v1_membered(v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v2_membered(v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v2_membered(v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v3_membered(v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v3_membered(v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v3_membered(v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_int_1(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | natural(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_int_1(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_xcmplx_0(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] : ( ~ empty(v0) | v1_membered(v0)) & ! [v0] : ( ~ empty(v0) | v2_membered(v0)) & ! [v0] : ( ~ empty(v0) | v3_membered(v0)) & ! [v0] : ( ~ empty(v0) | v4_membered(v0)) & ! [v0] : ( ~ empty(v0) | v5_membered(v0)) & ! [v0] : ( ~ v2_membered(v0) | v1_membered(v0)) & ! [v0] : ( ~ v3_membered(v0) | v2_membered(v0)) & ! [v0] : ( ~ v4_membered(v0) | v3_membered(v0)) & ! [v0] : ( ~ v5_membered(v0) | v4_membered(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0)
% 4.58/1.69 |
% 4.58/1.69 | Applying alpha-rule on (1) yields:
% 4.58/1.69 | (2) v1_membered(empty_set)
% 4.58/1.69 | (3) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_int_1(v1))
% 4.58/1.69 | (4) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | natural(v1))
% 4.58/1.69 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 4.58/1.69 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 4.58/1.69 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 4.58/1.69 | (8) v5_membered(all_0_0_0)
% 4.58/1.69 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v2_membered(v0) | v1_membered(v2))
% 4.58/1.69 | (10) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v3_membered(v0) | v1_rat_1(v1))
% 4.58/1.69 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v2_membered(v0) | v2_membered(v2))
% 4.58/1.69 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v4_membered(v2))
% 4.58/1.69 | (13) ? [v0] : subset(v0, v0)
% 4.58/1.69 | (14) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 4.58/1.69 | (15) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | cast_as_carrier_subset(v0) = v1)
% 4.58/1.69 | (16) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | the_carrier(v0) = v1)
% 4.58/1.69 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v4_membered(v2))
% 4.58/1.69 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v2_membered(v2))
% 4.58/1.69 | (19) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.58/1.69 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v1_membered(v2))
% 4.58/1.69 | (21) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_int_1(v1))
% 4.58/1.69 | (22) v4_membered(all_0_0_0)
% 4.58/1.69 | (23) one_sorted_str(all_0_1_1)
% 4.58/1.69 | (24) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 4.58/1.69 | (25) ! [v0] : ( ~ empty(v0) | v3_membered(v0))
% 4.58/1.70 | (26) v1_membered(all_0_0_0)
% 4.58/1.70 | (27) ! [v0] : ( ~ v5_membered(v0) | v4_membered(v0))
% 4.58/1.70 | (28) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_xreal_0(v1))
% 4.58/1.70 | (29) ~ (all_0_2_2 = all_0_3_3)
% 4.58/1.70 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v5_membered(v2))
% 4.58/1.70 | (31) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 4.58/1.70 | (32) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v3_membered(v0) | v1_xreal_0(v1))
% 4.58/1.70 | (33) ! [v0] : ( ~ empty(v0) | v2_membered(v0))
% 4.58/1.70 | (34) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v2_membered(v0) | v1_xcmplx_0(v1))
% 4.58/1.70 | (35) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_xcmplx_0(v1))
% 4.58/1.70 | (36) empty(empty_set)
% 4.58/1.70 | (37) ! [v0] : ( ~ v2_membered(v0) | v1_membered(v0))
% 4.58/1.70 | (38) ? [v0] : ? [v1] : element(v1, v0)
% 4.58/1.70 | (39) ! [v0] : ( ~ empty(v0) | v1_membered(v0))
% 4.58/1.70 | (40) v3_membered(all_0_0_0)
% 4.58/1.70 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v2_membered(v2))
% 4.58/1.70 | (42) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 4.58/1.70 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v3_membered(v0) | v3_membered(v2))
% 4.58/1.70 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v3_membered(v2))
% 4.58/1.70 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v3_membered(v2))
% 4.58/1.70 | (46) the_carrier(all_0_4_4) = all_0_2_2
% 4.58/1.70 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 4.58/1.70 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 4.58/1.70 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 4.58/1.70 | (50) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 4.58/1.70 | (51) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_xreal_0(v1))
% 4.58/1.70 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v3_membered(v0) | v1_membered(v2))
% 4.58/1.70 | (53) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 4.58/1.70 | (54) v2_membered(empty_set)
% 4.58/1.70 | (55) ! [v0] : ( ~ empty(v0) | v4_membered(v0))
% 4.58/1.70 | (56) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 4.58/1.70 | (57) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v1_membered(v0) | v1_xcmplx_0(v1))
% 4.58/1.70 | (58) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_rat_1(v1))
% 4.58/1.70 | (59) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v2_membered(v0) | v1_xreal_0(v1))
% 4.58/1.70 | (60) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_xcmplx_0(v1))
% 4.58/1.70 | (61) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 4.58/1.70 | (62) ~ empty(all_0_0_0)
% 4.58/1.70 | (63) ! [v0] : ( ~ v4_membered(v0) | v3_membered(v0))
% 4.58/1.70 | (64) v3_membered(empty_set)
% 4.58/1.70 | (65) v4_membered(empty_set)
% 4.58/1.70 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v1_membered(v0) | v1_membered(v2))
% 4.58/1.71 | (67) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & element(v1, v3)))
% 4.58/1.71 | (68) cast_as_carrier_subset(all_0_4_4) = all_0_3_3
% 4.58/1.71 | (69) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = v0))
% 4.58/1.71 | (70) v2_membered(all_0_0_0)
% 4.58/1.71 | (71) one_sorted_str(all_0_4_4)
% 4.58/1.71 | (72) ! [v0] : ( ~ v3_membered(v0) | v2_membered(v0))
% 4.58/1.71 | (73) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v3_membered(v0) | v1_xcmplx_0(v1))
% 4.58/1.71 | (74) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v2 & powerset(v1) = v3 & element(v2, v3)))
% 4.58/1.71 | (75) v5_membered(empty_set)
% 4.58/1.71 | (76) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_rat_1(v1))
% 4.58/1.71 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v1_membered(v2))
% 4.58/1.71 | (78) ! [v0] : ( ~ empty(v0) | v5_membered(v0))
% 4.58/1.71 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v3_membered(v0) | v2_membered(v2))
% 4.58/1.71 |
% 4.58/1.71 | Instantiating formula (16) with all_0_3_3, all_0_4_4 and discharging atoms cast_as_carrier_subset(all_0_4_4) = all_0_3_3, one_sorted_str(all_0_4_4), yields:
% 4.58/1.71 | (80) the_carrier(all_0_4_4) = all_0_3_3
% 4.58/1.71 |
% 4.58/1.71 | Instantiating formula (67) with all_0_3_3, all_0_4_4 and discharging atoms cast_as_carrier_subset(all_0_4_4) = all_0_3_3, one_sorted_str(all_0_4_4), yields:
% 4.58/1.71 | (81) ? [v0] : ? [v1] : (the_carrier(all_0_4_4) = v0 & powerset(v0) = v1 & element(all_0_3_3, v1))
% 4.58/1.71 |
% 4.58/1.71 | Instantiating (81) with all_13_0_8, all_13_1_9 yields:
% 4.58/1.71 | (82) the_carrier(all_0_4_4) = all_13_1_9 & powerset(all_13_1_9) = all_13_0_8 & element(all_0_3_3, all_13_0_8)
% 4.58/1.71 |
% 4.58/1.71 | Applying alpha-rule on (82) yields:
% 4.58/1.71 | (83) the_carrier(all_0_4_4) = all_13_1_9
% 4.58/1.71 | (84) powerset(all_13_1_9) = all_13_0_8
% 4.58/1.71 | (85) element(all_0_3_3, all_13_0_8)
% 4.58/1.71 |
% 4.58/1.71 | Instantiating formula (48) with all_0_4_4, all_13_1_9, all_0_2_2 and discharging atoms the_carrier(all_0_4_4) = all_13_1_9, the_carrier(all_0_4_4) = all_0_2_2, yields:
% 4.58/1.71 | (86) all_13_1_9 = all_0_2_2
% 4.58/1.71 |
% 4.58/1.71 | Instantiating formula (48) with all_0_4_4, all_0_3_3, all_13_1_9 and discharging atoms the_carrier(all_0_4_4) = all_13_1_9, the_carrier(all_0_4_4) = all_0_3_3, yields:
% 4.58/1.71 | (87) all_13_1_9 = all_0_3_3
% 4.58/1.71 |
% 4.58/1.71 | Combining equations (86,87) yields a new equation:
% 4.58/1.71 | (88) all_0_2_2 = all_0_3_3
% 4.58/1.71 |
% 4.58/1.71 | Simplifying 88 yields:
% 4.58/1.71 | (89) all_0_2_2 = all_0_3_3
% 4.58/1.71 |
% 4.58/1.71 | Equations (89) can reduce 29 to:
% 4.58/1.71 | (90) $false
% 4.58/1.71 |
% 4.58/1.71 |-The branch is then unsatisfiable
% 4.58/1.71 % SZS output end Proof for theBenchmark
% 4.58/1.71
% 4.58/1.71 1114ms
%------------------------------------------------------------------------------