TSTP Solution File: SEU341+1 by ConnectPP---0.2.2
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%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : SEU341+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n005.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 : 300s
% DateTime : Wed Mar 6 09:20:53 EST 2024
% Result : Theorem 1.53s 1.75s
% Output : Proof 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU341+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Mar 3 10:13:48 EST 2024
% 0.13/0.34 % CPUTime :
% 1.53/1.75 % SZS status Theorem for theBenchmark
% 1.53/1.75 % SZS output start Proof for theBenchmark
% 1.53/1.75
% 1.53/1.75 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 1.53/1.75 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc10_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc10_membered-1, axiom, ( ~v1_membered(_u3) | ~element(_u2, _u3) | v1_xcmplx_0(_u2) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc11_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc11_membered-1, axiom, ( ~v2_membered(_u5) | ~element(_u4, _u5) | v1_xcmplx_0(_u4) )).
% 1.53/1.75 cnf(cc11_membered-2, axiom, ( ~v2_membered(_u5) | ~element(_u4, _u5) | v1_xreal_0(_u4) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc12_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc12_membered-1, axiom, ( ~v3_membered(_u7) | ~element(_u6, _u7) | v1_xcmplx_0(_u6) )).
% 1.53/1.75 cnf(cc12_membered-2, axiom, ( ~v3_membered(_u7) | ~element(_u6, _u7) | v1_xreal_0(_u6) )).
% 1.53/1.75 cnf(cc12_membered-3, axiom, ( ~v3_membered(_u7) | ~element(_u6, _u7) | v1_rat_1(_u6) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc13_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc13_membered-1, axiom, ( ~v4_membered(_u9) | ~element(_u8, _u9) | v1_xcmplx_0(_u8) )).
% 1.53/1.75 cnf(cc13_membered-2, axiom, ( ~v4_membered(_u9) | ~element(_u8, _u9) | v1_xreal_0(_u8) )).
% 1.53/1.75 cnf(cc13_membered-3, axiom, ( ~v4_membered(_u9) | ~element(_u8, _u9) | v1_int_1(_u8) )).
% 1.53/1.75 cnf(cc13_membered-4, axiom, ( ~v4_membered(_u9) | ~element(_u8, _u9) | v1_rat_1(_u8) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc14_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc14_membered-1, axiom, ( ~v5_membered(_u11) | ~element(_u10, _u11) | v1_xcmplx_0(_u10) )).
% 1.53/1.75 cnf(cc14_membered-2, axiom, ( ~v5_membered(_u11) | ~element(_u10, _u11) | natural(_u10) )).
% 1.53/1.75 cnf(cc14_membered-3, axiom, ( ~v5_membered(_u11) | ~element(_u10, _u11) | v1_xreal_0(_u10) )).
% 1.53/1.75 cnf(cc14_membered-4, axiom, ( ~v5_membered(_u11) | ~element(_u10, _u11) | v1_int_1(_u10) )).
% 1.53/1.75 cnf(cc14_membered-5, axiom, ( ~v5_membered(_u11) | ~element(_u10, _u11) | v1_rat_1(_u10) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc15_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc15_membered-1, axiom, ( ~empty(_u12) | v1_membered(_u12) )).
% 1.53/1.75 cnf(cc15_membered-2, axiom, ( ~empty(_u12) | v2_membered(_u12) )).
% 1.53/1.75 cnf(cc15_membered-3, axiom, ( ~empty(_u12) | v3_membered(_u12) )).
% 1.53/1.75 cnf(cc15_membered-4, axiom, ( ~empty(_u12) | v4_membered(_u12) )).
% 1.53/1.75 cnf(cc15_membered-5, axiom, ( ~empty(_u12) | v5_membered(_u12) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc16_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc16_membered-1, axiom, ( ~v1_membered(_u14) | ~element(_u13, powerset(_u14)) | v1_membered(_u13) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc17_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc17_membered-1, axiom, ( ~v2_membered(_u16) | ~element(_u15, powerset(_u16)) | v1_membered(_u15) )).
% 1.53/1.75 cnf(cc17_membered-2, axiom, ( ~v2_membered(_u16) | ~element(_u15, powerset(_u16)) | v2_membered(_u15) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc18_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc18_membered-1, axiom, ( ~v3_membered(_u18) | ~element(_u17, powerset(_u18)) | v1_membered(_u17) )).
% 1.53/1.75 cnf(cc18_membered-2, axiom, ( ~v3_membered(_u18) | ~element(_u17, powerset(_u18)) | v2_membered(_u17) )).
% 1.53/1.75 cnf(cc18_membered-3, axiom, ( ~v3_membered(_u18) | ~element(_u17, powerset(_u18)) | v3_membered(_u17) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc19_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc19_membered-1, axiom, ( ~v4_membered(_u20) | ~element(_u19, powerset(_u20)) | v1_membered(_u19) )).
% 1.53/1.75 cnf(cc19_membered-2, axiom, ( ~v4_membered(_u20) | ~element(_u19, powerset(_u20)) | v2_membered(_u19) )).
% 1.53/1.75 cnf(cc19_membered-3, axiom, ( ~v4_membered(_u20) | ~element(_u19, powerset(_u20)) | v3_membered(_u19) )).
% 1.53/1.75 cnf(cc19_membered-4, axiom, ( ~v4_membered(_u20) | ~element(_u19, powerset(_u20)) | v4_membered(_u19) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc1_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc1_membered-1, axiom, ( ~v5_membered(_u21) | v4_membered(_u21) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc20_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc20_membered-1, axiom, ( ~v5_membered(_u23) | ~element(_u22, powerset(_u23)) | v1_membered(_u22) )).
% 1.53/1.75 cnf(cc20_membered-2, axiom, ( ~v5_membered(_u23) | ~element(_u22, powerset(_u23)) | v2_membered(_u22) )).
% 1.53/1.75 cnf(cc20_membered-3, axiom, ( ~v5_membered(_u23) | ~element(_u22, powerset(_u23)) | v3_membered(_u22) )).
% 1.53/1.75 cnf(cc20_membered-4, axiom, ( ~v5_membered(_u23) | ~element(_u22, powerset(_u23)) | v4_membered(_u22) )).
% 1.53/1.75 cnf(cc20_membered-5, axiom, ( ~v5_membered(_u23) | ~element(_u22, powerset(_u23)) | v5_membered(_u22) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc2_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc2_membered-1, axiom, ( ~v4_membered(_u24) | v3_membered(_u24) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc3_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc3_membered-1, axiom, ( ~v3_membered(_u25) | v2_membered(_u25) )).
% 1.53/1.75
% 1.53/1.75 % Formula: cc4_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(cc4_membered-1, axiom, ( ~v2_membered(_u26) | v1_membered(_u26) )).
% 1.53/1.75
% 1.53/1.75 % Formula: d1_connsp_2 ( axiom ) converted to clauses:
% 1.53/1.75 cnf(d1_connsp_2-1, axiom, ( empty_carrier(_u29) | ~topological_space(_u29) | ~top_str(_u29) | ~element(_u28, the_carrier(_u29)) | ~element(_u27, powerset(the_carrier(_u29))) | ~point_neighbourhood(_u27, _u29, _u28) | in(_u28, interior(_u29, _u27)) )).
% 1.53/1.75 cnf(d1_connsp_2-2, axiom, ( empty_carrier(_u29) | ~topological_space(_u29) | ~top_str(_u29) | ~element(_u28, the_carrier(_u29)) | ~element(_u27, powerset(the_carrier(_u29))) | ~in(_u28, interior(_u29, _u27)) | point_neighbourhood(_u27, _u29, _u28) )).
% 1.53/1.75
% 1.53/1.75 % Formula: dt_k1_tops_1 ( axiom ) converted to clauses:
% 1.53/1.75 cnf(dt_k1_tops_1-1, axiom, ( ~top_str(_u31) | ~element(_u30, powerset(the_carrier(_u31))) | element(interior(_u31, _u30), powerset(the_carrier(_u31))) )).
% 1.53/1.75
% 1.53/1.75 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 1.53/1.75
% 1.53/1.75 % Formula: dt_k1_zfmisc_1 ( axiom ) converted to clauses:
% 1.53/1.75
% 1.53/1.75 % Formula: dt_l1_pre_topc ( axiom ) converted to clauses:
% 1.53/1.75 cnf(dt_l1_pre_topc-1, axiom, ( ~top_str(_u32) | one_sorted_str(_u32) )).
% 1.53/1.75
% 1.53/1.75 % Formula: dt_l1_struct_0 ( axiom ) converted to clauses:
% 1.53/1.75
% 1.53/1.75 % Formula: dt_m1_connsp_2 ( axiom ) converted to clauses:
% 1.53/1.75 cnf(dt_m1_connsp_2-1, axiom, ( empty_carrier(_u35) | ~topological_space(_u35) | ~top_str(_u35) | ~element(_u34, the_carrier(_u35)) | ~point_neighbourhood(_u33, _u35, _u34) | element(_u33, powerset(the_carrier(_u35))) )).
% 1.53/1.75
% 1.53/1.75 % Formula: dt_m1_subset_1 ( axiom ) converted to clauses:
% 1.53/1.75
% 1.53/1.75 % Formula: dt_u1_struct_0 ( axiom ) converted to clauses:
% 1.53/1.75
% 1.53/1.75 % Formula: existence_l1_pre_topc ( axiom ) converted to clauses:
% 1.53/1.75 cnf(existence_l1_pre_topc-1, axiom, ( top_str(skolem1) )).
% 1.53/1.75
% 1.53/1.75 % Formula: existence_l1_struct_0 ( axiom ) converted to clauses:
% 1.53/1.75 cnf(existence_l1_struct_0-1, axiom, ( one_sorted_str(skolem2) )).
% 1.53/1.75
% 1.53/1.75 % Formula: existence_m1_connsp_2 ( axiom ) converted to clauses:
% 1.53/1.75 cnf(existence_m1_connsp_2-1, axiom, ( empty_carrier(_u40) | ~topological_space(_u40) | ~top_str(_u40) | ~element(_u39, the_carrier(_u40)) | point_neighbourhood(skolem3(_u40, _u39), _u40, _u39) )).
% 1.53/1.75
% 1.53/1.75 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 1.53/1.75 cnf(existence_m1_subset_1-1, axiom, ( element(skolem4(_u42), _u42) )).
% 1.53/1.75
% 1.53/1.75 % Formula: fc1_subset_1 ( axiom ) converted to clauses:
% 1.53/1.75 cnf(fc1_subset_1-1, axiom, ( ~empty(powerset(_u43)) )).
% 1.53/1.75
% 1.53/1.75 % Formula: fc6_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(fc6_membered-1, axiom, ( empty(empty_set) )).
% 1.53/1.75 cnf(fc6_membered-2, axiom, ( v1_membered(empty_set) )).
% 1.53/1.75 cnf(fc6_membered-3, axiom, ( v2_membered(empty_set) )).
% 1.53/1.75 cnf(fc6_membered-4, axiom, ( v3_membered(empty_set) )).
% 1.53/1.75 cnf(fc6_membered-5, axiom, ( v4_membered(empty_set) )).
% 1.53/1.75 cnf(fc6_membered-6, axiom, ( v5_membered(empty_set) )).
% 1.53/1.75
% 1.53/1.75 % Formula: rc1_membered ( axiom ) converted to clauses:
% 1.53/1.75 cnf(rc1_membered-1, axiom, ( ~empty(skolem5) )).
% 1.53/1.75 cnf(rc1_membered-2, axiom, ( v1_membered(skolem5) )).
% 1.53/1.75 cnf(rc1_membered-3, axiom, ( v2_membered(skolem5) )).
% 1.53/1.75 cnf(rc1_membered-4, axiom, ( v3_membered(skolem5) )).
% 1.53/1.75 cnf(rc1_membered-5, axiom, ( v4_membered(skolem5) )).
% 1.53/1.75 cnf(rc1_membered-6, axiom, ( v5_membered(skolem5) )).
% 1.53/1.75
% 1.53/1.75 % Formula: rc1_subset_1 ( axiom ) converted to clauses:
% 1.53/1.75 cnf(rc1_subset_1-1, axiom, ( empty(_u46) | element(skolem6(_u46), powerset(_u46)) )).
% 1.53/1.75 cnf(rc1_subset_1-2, axiom, ( empty(_u46) | ~empty(skolem6(_u46)) )).
% 1.53/1.75
% 1.53/1.75 % Formula: rc2_subset_1 ( axiom ) converted to clauses:
% 1.53/1.75 cnf(rc2_subset_1-1, axiom, ( element(skolem7(_u48), powerset(_u48)) )).
% 1.53/1.75 cnf(rc2_subset_1-2, axiom, ( empty(skolem7(_u48)) )).
% 1.53/1.75
% 1.53/1.75 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 1.53/1.75 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u50, _u50) )).
% 1.53/1.75
% 1.53/1.75 % Formula: t1_subset ( axiom ) converted to clauses:
% 1.53/1.75 cnf(t1_subset-1, axiom, ( ~in(_u52, _u51) | element(_u52, _u51) )).
% 1.53/1.75
% 1.53/1.75 % Formula: t2_subset ( axiom ) converted to clauses:
% 1.53/1.75 cnf(t2_subset-1, axiom, ( ~element(_u54, _u53) | empty(_u53) | in(_u54, _u53) )).
% 1.53/1.75
% 1.53/1.75 % Formula: t3_subset ( axiom ) converted to clauses:
% 1.53/1.75 cnf(t3_subset-1, axiom, ( ~element(_u59, powerset(_u57)) | subset(_u59, _u57) )).
% 1.53/1.75 cnf(t3_subset-2, axiom, ( ~subset(_u60, _u58) | element(_u60, powerset(_u58)) )).
% 1.53/1.75
% 1.53/1.75 % Formula: t4_subset ( axiom ) converted to clauses:
% 1.53/1.75 cnf(t4_subset-1, axiom, ( ~in(_u63, _u62) | ~element(_u62, powerset(_u61)) | element(_u63, _u61) )).
% 1.53/1.75
% 1.53/1.75 % Formula: t55_tops_1 ( axiom ) converted to clauses:
% 1.53/1.75 cnf(t55_tops_1-1, axiom, ( ~topological_space(_u67) | ~top_str(_u67) | ~top_str(_u66) | ~element(_u65, powerset(the_carrier(_u67))) | ~element(_u64, powerset(the_carrier(_u66))) | ~open_subset(_u64, _u66) | ( interior(_u66, _u64) = _u64) )).
% 1.53/1.75 cnf(t55_tops_1-2, axiom, ( ~topological_space(_u67) | ~top_str(_u67) | ~top_str(_u66) | ~element(_u65, powerset(the_carrier(_u67))) | ~element(_u64, powerset(the_carrier(_u66))) | ( interior(_u67, _u65) != _u65) | open_subset(_u65, _u67) )).
% 1.53/1.75
% 1.53/1.75 % Formula: t5_connsp_2 ( conjecture ) converted to clauses:
% 1.53/1.75 cnf(t5_connsp_2-1, negated_conjecture, ( ~empty_carrier(skolem8) )).
% 1.53/1.75 cnf(t5_connsp_2-2, negated_conjecture, ( topological_space(skolem8) )).
% 1.53/1.75 cnf(t5_connsp_2-3, negated_conjecture, ( top_str(skolem8) )).
% 1.53/1.75 cnf(t5_connsp_2-4, negated_conjecture, ( element(skolem9, powerset(the_carrier(skolem8))) )).
% 1.53/1.75 cnf(t5_connsp_2-5, negated_conjecture, ( element(skolem10, the_carrier(skolem8)) )).
% 1.53/1.75 cnf(t5_connsp_2-6, negated_conjecture, ( open_subset(skolem9, skolem8) )).
% 1.53/1.75 cnf(t5_connsp_2-7, negated_conjecture, ( in(skolem10, skolem9) )).
% 1.53/1.75 cnf(t5_connsp_2-8, negated_conjecture, ( ~point_neighbourhood(skolem9, skolem8, skolem10) )).
% 1.53/1.75
% 1.53/1.75 % Formula: t5_subset ( axiom ) converted to clauses:
% 1.53/1.75 cnf(t5_subset-1, axiom, ( ~in(_u73, _u72) | ~element(_u72, powerset(_u71)) | ~empty(_u71) )).
% 1.53/1.75
% 1.53/1.75 % Formula: t6_boole ( axiom ) converted to clauses:
% 1.53/1.75 cnf(t6_boole-1, axiom, ( ~empty(_u74) | ( _u74 = empty_set) )).
% 1.53/1.75
% 1.53/1.75 % Formula: t7_boole ( axiom ) converted to clauses:
% 1.53/1.75 cnf(t7_boole-1, axiom, ( ~in(_u76, _u75) | ~empty(_u75) )).
% 1.53/1.75
% 1.53/1.75 % Formula: t8_boole ( axiom ) converted to clauses:
% 1.53/1.75 cnf(t8_boole-1, axiom, ( ~empty(_u78) | ( _u78 = _u77) | ~empty(_u77) )).
% 1.53/1.75
% 1.53/1.75 % Problem matrix:
% 1.53/1.75 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 1.53/1.75 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 1.53/1.75 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 1.53/1.75 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 1.53/1.75 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( the_carrier(__eqx_0) = the_carrier(__eqy_0)) )).
% 1.53/1.75 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( interior(__eqx_0, __eqx_1) = interior(__eqy_0, __eqy_1)) )).
% 1.53/1.75 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 1.53/1.75 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( skolem4(__eqx_0) = skolem4(__eqy_0)) )).
% 1.53/1.75 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( skolem6(__eqx_0) = skolem6(__eqy_0)) )).
% 1.53/1.75 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( skolem7(__eqx_0) = skolem7(__eqy_0)) )).
% 1.53/1.75 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 1.53/1.75 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ~v1_membered(__eqx_0) | v1_membered(__eqy_0) )).
% 1.53/1.75 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 1.53/1.75 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ~v1_xcmplx_0(__eqx_0) | v1_xcmplx_0(__eqy_0) )).
% 1.53/1.75 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~v2_membered(__eqx_0) | v2_membered(__eqy_0) )).
% 1.53/1.75 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~v1_xreal_0(__eqx_0) | v1_xreal_0(__eqy_0) )).
% 1.53/1.75 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~v3_membered(__eqx_0) | v3_membered(__eqy_0) )).
% 1.53/1.75 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~v1_rat_1(__eqx_0) | v1_rat_1(__eqy_0) )).
% 1.53/1.75 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~v4_membered(__eqx_0) | v4_membered(__eqy_0) )).
% 1.53/1.75 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~v1_int_1(__eqx_0) | v1_int_1(__eqy_0) )).
% 1.53/1.75 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ~v5_membered(__eqx_0) | v5_membered(__eqy_0) )).
% 1.53/1.75 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ~natural(__eqx_0) | natural(__eqy_0) )).
% 1.53/1.75 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 1.53/1.75 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ~empty_carrier(__eqx_0) | empty_carrier(__eqy_0) )).
% 1.53/1.75 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ~topological_space(__eqx_0) | topological_space(__eqy_0) )).
% 1.53/1.75 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ~top_str(__eqx_0) | top_str(__eqy_0) )).
% 1.53/1.75 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~point_neighbourhood(__eqx_0, __eqx_1, __eqx_2) | point_neighbourhood(__eqy_0, __eqy_1, __eqy_2) )).
% 1.53/1.75 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ~one_sorted_str(__eqx_0) | one_sorted_str(__eqy_0) )).
% 1.53/1.75 cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 1.53/1.75 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~open_subset(__eqx_0, __eqx_1) | open_subset(__eqy_0, __eqy_1) )).
% 1.53/1.75 cnf(matrix-30, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 1.53/1.75 cnf(matrix-31, plain, ( ~v1_membered(_u3) | ~element(_u2, _u3) | v1_xcmplx_0(_u2) )).
% 1.53/1.75 cnf(matrix-32, plain, ( ~v2_membered(_u5) | ~element(_u4, _u5) | v1_xcmplx_0(_u4) )).
% 1.53/1.75 cnf(matrix-33, plain, ( ~v2_membered(_u5) | ~element(_u4, _u5) | v1_xreal_0(_u4) )).
% 1.53/1.75 cnf(matrix-34, plain, ( ~v3_membered(_u7) | ~element(_u6, _u7) | v1_xcmplx_0(_u6) )).
% 1.53/1.75 cnf(matrix-35, plain, ( ~v3_membered(_u7) | ~element(_u6, _u7) | v1_xreal_0(_u6) )).
% 1.53/1.75 cnf(matrix-36, plain, ( ~v3_membered(_u7) | ~element(_u6, _u7) | v1_rat_1(_u6) )).
% 1.53/1.75 cnf(matrix-37, plain, ( ~v4_membered(_u9) | ~element(_u8, _u9) | v1_xcmplx_0(_u8) )).
% 1.53/1.75 cnf(matrix-38, plain, ( ~v4_membered(_u9) | ~element(_u8, _u9) | v1_xreal_0(_u8) )).
% 1.53/1.75 cnf(matrix-39, plain, ( ~v4_membered(_u9) | ~element(_u8, _u9) | v1_int_1(_u8) )).
% 1.53/1.75 cnf(matrix-40, plain, ( ~v4_membered(_u9) | ~element(_u8, _u9) | v1_rat_1(_u8) )).
% 1.53/1.75 cnf(matrix-41, plain, ( ~v5_membered(_u11) | ~element(_u10, _u11) | v1_xcmplx_0(_u10) )).
% 1.53/1.75 cnf(matrix-42, plain, ( ~v5_membered(_u11) | ~element(_u10, _u11) | natural(_u10) )).
% 1.53/1.75 cnf(matrix-43, plain, ( ~v5_membered(_u11) | ~element(_u10, _u11) | v1_xreal_0(_u10) )).
% 1.53/1.75 cnf(matrix-44, plain, ( ~v5_membered(_u11) | ~element(_u10, _u11) | v1_int_1(_u10) )).
% 1.53/1.75 cnf(matrix-45, plain, ( ~v5_membered(_u11) | ~element(_u10, _u11) | v1_rat_1(_u10) )).
% 1.53/1.75 cnf(matrix-46, plain, ( ~empty(_u12) | v1_membered(_u12) )).
% 1.53/1.75 cnf(matrix-47, plain, ( ~empty(_u12) | v2_membered(_u12) )).
% 1.53/1.75 cnf(matrix-48, plain, ( ~empty(_u12) | v3_membered(_u12) )).
% 1.53/1.75 cnf(matrix-49, plain, ( ~empty(_u12) | v4_membered(_u12) )).
% 1.53/1.75 cnf(matrix-50, plain, ( ~empty(_u12) | v5_membered(_u12) )).
% 1.53/1.75 cnf(matrix-51, plain, ( ~v1_membered(_u14) | ~element(_u13, powerset(_u14)) | v1_membered(_u13) )).
% 1.53/1.75 cnf(matrix-52, plain, ( ~v2_membered(_u16) | ~element(_u15, powerset(_u16)) | v1_membered(_u15) )).
% 1.53/1.75 cnf(matrix-53, plain, ( ~v2_membered(_u16) | ~element(_u15, powerset(_u16)) | v2_membered(_u15) )).
% 1.53/1.75 cnf(matrix-54, plain, ( ~v3_membered(_u18) | ~element(_u17, powerset(_u18)) | v1_membered(_u17) )).
% 1.53/1.75 cnf(matrix-55, plain, ( ~v3_membered(_u18) | ~element(_u17, powerset(_u18)) | v2_membered(_u17) )).
% 1.53/1.75 cnf(matrix-56, plain, ( ~v3_membered(_u18) | ~element(_u17, powerset(_u18)) | v3_membered(_u17) )).
% 1.53/1.75 cnf(matrix-57, plain, ( ~v4_membered(_u20) | ~element(_u19, powerset(_u20)) | v1_membered(_u19) )).
% 1.53/1.75 cnf(matrix-58, plain, ( ~v4_membered(_u20) | ~element(_u19, powerset(_u20)) | v2_membered(_u19) )).
% 1.53/1.75 cnf(matrix-59, plain, ( ~v4_membered(_u20) | ~element(_u19, powerset(_u20)) | v3_membered(_u19) )).
% 1.53/1.75 cnf(matrix-60, plain, ( ~v4_membered(_u20) | ~element(_u19, powerset(_u20)) | v4_membered(_u19) )).
% 1.53/1.75 cnf(matrix-61, plain, ( ~v5_membered(_u21) | v4_membered(_u21) )).
% 1.53/1.75 cnf(matrix-62, plain, ( ~v5_membered(_u23) | ~element(_u22, powerset(_u23)) | v1_membered(_u22) )).
% 1.53/1.75 cnf(matrix-63, plain, ( ~v5_membered(_u23) | ~element(_u22, powerset(_u23)) | v2_membered(_u22) )).
% 1.53/1.75 cnf(matrix-64, plain, ( ~v5_membered(_u23) | ~element(_u22, powerset(_u23)) | v3_membered(_u22) )).
% 1.53/1.75 cnf(matrix-65, plain, ( ~v5_membered(_u23) | ~element(_u22, powerset(_u23)) | v4_membered(_u22) )).
% 1.53/1.75 cnf(matrix-66, plain, ( ~v5_membered(_u23) | ~element(_u22, powerset(_u23)) | v5_membered(_u22) )).
% 1.53/1.75 cnf(matrix-67, plain, ( ~v4_membered(_u24) | v3_membered(_u24) )).
% 1.53/1.75 cnf(matrix-68, plain, ( ~v3_membered(_u25) | v2_membered(_u25) )).
% 1.53/1.75 cnf(matrix-69, plain, ( ~v2_membered(_u26) | v1_membered(_u26) )).
% 1.53/1.75 cnf(matrix-70, plain, ( empty_carrier(_u29) | ~topological_space(_u29) | ~top_str(_u29) | ~element(_u28, the_carrier(_u29)) | ~element(_u27, powerset(the_carrier(_u29))) | ~point_neighbourhood(_u27, _u29, _u28) | in(_u28, interior(_u29, _u27)) )).
% 1.53/1.75 cnf(matrix-71, plain, ( empty_carrier(_u29) | ~topological_space(_u29) | ~top_str(_u29) | ~element(_u28, the_carrier(_u29)) | ~element(_u27, powerset(the_carrier(_u29))) | ~in(_u28, interior(_u29, _u27)) | point_neighbourhood(_u27, _u29, _u28) )).
% 1.53/1.75 cnf(matrix-72, plain, ( ~top_str(_u31) | ~element(_u30, powerset(the_carrier(_u31))) | element(interior(_u31, _u30), powerset(the_carrier(_u31))) )).
% 1.53/1.75 cnf(matrix-73, plain, ( ~top_str(_u32) | one_sorted_str(_u32) )).
% 1.53/1.75 cnf(matrix-74, plain, ( empty_carrier(_u35) | ~topological_space(_u35) | ~top_str(_u35) | ~element(_u34, the_carrier(_u35)) | ~point_neighbourhood(_u33, _u35, _u34) | element(_u33, powerset(the_carrier(_u35))) )).
% 1.53/1.75 cnf(matrix-75, plain, ( top_str(skolem1) )).
% 1.53/1.75 cnf(matrix-76, plain, ( one_sorted_str(skolem2) )).
% 1.53/1.75 cnf(matrix-77, plain, ( empty_carrier(_u40) | ~topological_space(_u40) | ~top_str(_u40) | ~element(_u39, the_carrier(_u40)) | point_neighbourhood(skolem3(_u40, _u39), _u40, _u39) )).
% 1.53/1.75 cnf(matrix-78, plain, ( element(skolem4(_u42), _u42) )).
% 1.53/1.75 cnf(matrix-79, plain, ( ~empty(powerset(_u43)) )).
% 1.53/1.75 cnf(matrix-80, plain, ( empty(empty_set) )).
% 1.53/1.75 cnf(matrix-81, plain, ( v1_membered(empty_set) )).
% 1.53/1.75 cnf(matrix-82, plain, ( v2_membered(empty_set) )).
% 1.53/1.75 cnf(matrix-83, plain, ( v3_membered(empty_set) )).
% 1.53/1.75 cnf(matrix-84, plain, ( v4_membered(empty_set) )).
% 1.53/1.75 cnf(matrix-85, plain, ( v5_membered(empty_set) )).
% 1.53/1.75 cnf(matrix-86, plain, ( ~empty(skolem5) )).
% 1.53/1.75 cnf(matrix-87, plain, ( v1_membered(skolem5) )).
% 1.53/1.75 cnf(matrix-88, plain, ( v2_membered(skolem5) )).
% 1.53/1.75 cnf(matrix-89, plain, ( v3_membered(skolem5) )).
% 1.53/1.75 cnf(matrix-90, plain, ( v4_membered(skolem5) )).
% 1.53/1.75 cnf(matrix-91, plain, ( v5_membered(skolem5) )).
% 1.53/1.75 cnf(matrix-92, plain, ( empty(_u46) | element(skolem6(_u46), powerset(_u46)) )).
% 1.53/1.75 cnf(matrix-93, plain, ( empty(_u46) | ~empty(skolem6(_u46)) )).
% 1.53/1.75 cnf(matrix-94, plain, ( element(skolem7(_u48), powerset(_u48)) )).
% 1.53/1.75 cnf(matrix-95, plain, ( empty(skolem7(_u48)) )).
% 1.53/1.75 cnf(matrix-96, plain, ( subset(_u50, _u50) )).
% 1.53/1.75 cnf(matrix-97, plain, ( ~in(_u52, _u51) | element(_u52, _u51) )).
% 1.53/1.75 cnf(matrix-98, plain, ( ~element(_u54, _u53) | empty(_u53) | in(_u54, _u53) )).
% 1.53/1.75 cnf(matrix-99, plain, ( ~element(_u59, powerset(_u57)) | subset(_u59, _u57) )).
% 1.53/1.75 cnf(matrix-100, plain, ( ~subset(_u60, _u58) | element(_u60, powerset(_u58)) )).
% 1.53/1.75 cnf(matrix-101, plain, ( ~in(_u63, _u62) | ~element(_u62, powerset(_u61)) | element(_u63, _u61) )).
% 1.53/1.75 cnf(matrix-102, plain, ( ~topological_space(_u67) | ~top_str(_u67) | ~top_str(_u66) | ~element(_u65, powerset(the_carrier(_u67))) | ~element(_u64, powerset(the_carrier(_u66))) | ~open_subset(_u64, _u66) | ( interior(_u66, _u64) = _u64) )).
% 1.53/1.75 cnf(matrix-103, plain, ( ~topological_space(_u67) | ~top_str(_u67) | ~top_str(_u66) | ~element(_u65, powerset(the_carrier(_u67))) | ~element(_u64, powerset(the_carrier(_u66))) | ( interior(_u67, _u65) != _u65) | open_subset(_u65, _u67) )).
% 1.53/1.75 cnf(matrix-104, plain, ( ~empty_carrier(skolem8) )).
% 1.53/1.75 cnf(matrix-105, plain, ( topological_space(skolem8) )).
% 1.53/1.75 cnf(matrix-106, plain, ( top_str(skolem8) )).
% 1.53/1.75 cnf(matrix-107, plain, ( element(skolem9, powerset(the_carrier(skolem8))) )).
% 1.53/1.75 cnf(matrix-108, plain, ( element(skolem10, the_carrier(skolem8)) )).
% 1.53/1.75 cnf(matrix-109, plain, ( open_subset(skolem9, skolem8) )).
% 1.53/1.75 cnf(matrix-110, plain, ( in(skolem10, skolem9) )).
% 1.53/1.75 cnf(matrix-111, plain, ( ~point_neighbourhood(skolem9, skolem8, skolem10) )).
% 1.53/1.75 cnf(matrix-112, plain, ( ~in(_u73, _u72) | ~element(_u72, powerset(_u71)) | ~empty(_u71) )).
% 1.53/1.75 cnf(matrix-113, plain, ( ~empty(_u74) | ( _u74 = empty_set) )).
% 1.53/1.75 cnf(matrix-114, plain, ( ~in(_u76, _u75) | ~empty(_u75) )).
% 1.53/1.75 cnf(matrix-115, plain, ( ~empty(_u78) | ( _u78 = _u77) | ~empty(_u77) )).
% 1.53/1.75
% 1.53/1.75 % Proof stack:
% 1.53/1.75 cnf(proof-stack, plain,
% 1.53/1.75 proof_stack(
% 1.53/1.75 start(104),
% 1.53/1.75 left_branch(0, 71, 0, 2),
% 1.53/1.75 left_branch(0, 111, 0, 3),
% 1.53/1.75 right_branch(3),
% 1.53/1.75 left_branch(0, 10, 3, 4),
% 1.53/1.75 left_branch(0, 1, 1, 5),
% 1.53/1.75 left_branch(0, 0, 0, 6),
% 1.53/1.75 right_branch(6),
% 1.53/1.75 right_branch(5),
% 1.53/1.75 left_branch(0, 110, 0, 6),
% 1.53/1.75 right_branch(6),
% 1.53/1.75 left_branch(0, 1, 1, 7),
% 1.53/1.75 left_branch(0, 102, 6, 8),
% 1.53/1.75 left_branch(0, 105, 0, 9),
% 1.53/1.75 right_branch(9),
% 1.53/1.75 left_branch(0, 109, 0, 10),
% 1.53/1.75 right_branch(10),
% 1.53/1.75 left_branch(0, 107, 0, 11),
% 1.53/1.75 right_branch(11),
% 1.53/1.75 left_branch(0, 107, 0, 12),
% 1.53/1.75 right_branch(12),
% 1.53/1.76 left_branch(0, 106, 0, 13),
% 1.53/1.76 right_branch(13),
% 1.53/1.76 lemmata(0, 7),
% 1.53/1.76 right_branch(8),
% 1.53/1.76 right_branch(7),
% 1.53/1.76 right_branch(4),
% 1.53/1.76 left_branch(0, 107, 0, 5),
% 1.53/1.76 right_branch(5),
% 1.53/1.76 left_branch(0, 108, 0, 6),
% 1.53/1.76 right_branch(6),
% 1.53/1.76 left_branch(0, 106, 0, 7),
% 1.53/1.76 right_branch(7),
% 1.53/1.76 left_branch(0, 105, 0, 8),
% 1.53/1.76 right_branch(8),
% 1.53/1.76 right_branch(2)
% 1.53/1.76 )).
% 1.53/1.76 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------