TSTP Solution File: SEU163+2 by ConnectPP---0.2.2
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- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : SEU163+2 : 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 : n018.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 09:20:25 EST 2024
% Result : Theorem 6.29s 6.48s
% Output : Proof 6.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU163+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Mar 3 11:22:25 EST 2024
% 0.12/0.34 % CPUTime :
% 6.29/6.48 % SZS status Theorem for theBenchmark
% 6.29/6.48 % SZS output start Proof for theBenchmark
% 6.29/6.48
% 6.29/6.48 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 6.29/6.48 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 6.29/6.48
% 6.29/6.48 % Formula: antisymmetry_r2_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(antisymmetry_r2_xboole_0-1, axiom, ( ~proper_subset(_u3, _u2) | ~proper_subset(_u2, _u3) )).
% 6.29/6.48
% 6.29/6.48 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 6.29/6.48 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u5, _u4) = unordered_pair(_u4, _u5)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u7, _u6) = set_union2(_u6, _u7)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: commutativity_k3_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(commutativity_k3_xboole_0-1, axiom, ( ( set_intersection2(_u9, _u8) = set_intersection2(_u8, _u9)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: d10_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(d10_xboole_0-1, axiom, ( ( _u14 != _u12) | subset(_u14, _u12) )).
% 6.29/6.48 cnf(d10_xboole_0-2, axiom, ( ( _u14 != _u12) | subset(_u12, _u14) )).
% 6.29/6.48 cnf(d10_xboole_0-3, axiom, ( ~subset(_u15, _u13) | ~subset(_u13, _u15) | ( _u15 = _u13) )).
% 6.29/6.48
% 6.29/6.48 % Formula: d1_tarski ( axiom ) converted to clauses:
% 6.29/6.48 cnf(d1_tarski-1, axiom, ( ( _u24 != singleton(_u26)) | ~in(_u20, _u24) | ( _u20 = _u26) )).
% 6.29/6.48 cnf(d1_tarski-2, axiom, ( ( _u24 != singleton(_u26)) | ( _u21 != _u26) | in(_u21, _u24) )).
% 6.29/6.48 cnf(d1_tarski-3, axiom, ( ( _u25 = singleton(_u27)) | in(skolem1(_u27, _u25), _u25) | ( skolem2(_u27, _u25) = _u27) )).
% 6.29/6.48 cnf(d1_tarski-4, axiom, ( ( _u25 = singleton(_u27)) | in(skolem1(_u27, _u25), _u25) | ~in(skolem2(_u27, _u25), _u25) )).
% 6.29/6.48 cnf(d1_tarski-5, axiom, ( ( _u25 = singleton(_u27)) | ( skolem1(_u27, _u25) != _u27) | ( skolem2(_u27, _u25) = _u27) )).
% 6.29/6.48 cnf(d1_tarski-6, axiom, ( ( _u25 = singleton(_u27)) | ( skolem1(_u27, _u25) != _u27) | ~in(skolem2(_u27, _u25), _u25) )).
% 6.29/6.48
% 6.29/6.48 % Formula: d1_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(d1_xboole_0-1, axiom, ( ( _u31 != empty_set) | ~in(_u28, _u31) )).
% 6.29/6.48 cnf(d1_xboole_0-2, axiom, ( in(skolem3(_u32), _u32) | ( _u32 = empty_set) )).
% 6.29/6.48
% 6.29/6.48 % Formula: d1_zfmisc_1 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(d1_zfmisc_1-1, axiom, ( ( _u41 != powerset(_u43)) | ~in(_u37, _u41) | subset(_u37, _u43) )).
% 6.29/6.48 cnf(d1_zfmisc_1-2, axiom, ( ( _u41 != powerset(_u43)) | ~subset(_u38, _u43) | in(_u38, _u41) )).
% 6.29/6.48 cnf(d1_zfmisc_1-3, axiom, ( ( _u42 = powerset(_u44)) | in(skolem4(_u44, _u42), _u42) | subset(skolem5(_u44, _u42), _u44) )).
% 6.29/6.48 cnf(d1_zfmisc_1-4, axiom, ( ( _u42 = powerset(_u44)) | in(skolem4(_u44, _u42), _u42) | ~in(skolem5(_u44, _u42), _u42) )).
% 6.29/6.48 cnf(d1_zfmisc_1-5, axiom, ( ( _u42 = powerset(_u44)) | ~subset(skolem4(_u44, _u42), _u44) | subset(skolem5(_u44, _u42), _u44) )).
% 6.29/6.48 cnf(d1_zfmisc_1-6, axiom, ( ( _u42 = powerset(_u44)) | ~subset(skolem4(_u44, _u42), _u44) | ~in(skolem5(_u44, _u42), _u42) )).
% 6.29/6.48
% 6.29/6.48 % Formula: d2_tarski ( axiom ) converted to clauses:
% 6.29/6.48 cnf(d2_tarski-1, axiom, ( ( _u54 != unordered_pair(_u58, _u56)) | ~in(_u50, _u54) | ( _u50 = _u58) | ( _u50 = _u56) )).
% 6.29/6.48 cnf(d2_tarski-2, axiom, ( ( _u54 != unordered_pair(_u58, _u56)) | in(_u51, _u54) | ( _u51 != _u58) )).
% 6.29/6.48 cnf(d2_tarski-3, axiom, ( ( _u54 != unordered_pair(_u58, _u56)) | in(_u51, _u54) | ( _u51 != _u56) )).
% 6.29/6.48 cnf(d2_tarski-4, axiom, ( ( _u55 = unordered_pair(_u59, _u57)) | in(skolem6(_u59, _u57, _u55), _u55) | ( skolem7(_u59, _u57, _u55) = _u59) | ( skolem7(_u59, _u57, _u55) = _u57) )).
% 6.29/6.48 cnf(d2_tarski-5, axiom, ( ( _u55 = unordered_pair(_u59, _u57)) | in(skolem6(_u59, _u57, _u55), _u55) | ~in(skolem7(_u59, _u57, _u55), _u55) )).
% 6.29/6.48 cnf(d2_tarski-6, axiom, ( ( _u55 = unordered_pair(_u59, _u57)) | ( skolem7(_u59, _u57, _u55) = _u59) | ( skolem7(_u59, _u57, _u55) = _u57) | ( skolem6(_u59, _u57, _u55) != _u59) )).
% 6.29/6.48 cnf(d2_tarski-7, axiom, ( ( _u55 = unordered_pair(_u59, _u57)) | ( skolem7(_u59, _u57, _u55) = _u59) | ( skolem7(_u59, _u57, _u55) = _u57) | ( skolem6(_u59, _u57, _u55) != _u57) )).
% 6.29/6.48 cnf(d2_tarski-8, axiom, ( ( _u55 = unordered_pair(_u59, _u57)) | ~in(skolem7(_u59, _u57, _u55), _u55) | ( skolem6(_u59, _u57, _u55) != _u59) )).
% 6.29/6.48 cnf(d2_tarski-9, axiom, ( ( _u55 = unordered_pair(_u59, _u57)) | ~in(skolem7(_u59, _u57, _u55), _u55) | ( skolem6(_u59, _u57, _u55) != _u57) )).
% 6.29/6.48
% 6.29/6.48 % Formula: d2_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(d2_xboole_0-1, axiom, ( ( _u69 != set_union2(_u73, _u71)) | ~in(_u65, _u69) | in(_u65, _u73) | in(_u65, _u71) )).
% 6.29/6.48 cnf(d2_xboole_0-2, axiom, ( ( _u69 != set_union2(_u73, _u71)) | in(_u66, _u69) | ~in(_u66, _u73) )).
% 6.29/6.48 cnf(d2_xboole_0-3, axiom, ( ( _u69 != set_union2(_u73, _u71)) | in(_u66, _u69) | ~in(_u66, _u71) )).
% 6.29/6.48 cnf(d2_xboole_0-4, axiom, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem8(_u74, _u72, _u70), _u70) | in(skolem9(_u74, _u72, _u70), _u74) | in(skolem9(_u74, _u72, _u70), _u72) )).
% 6.29/6.48 cnf(d2_xboole_0-5, axiom, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem8(_u74, _u72, _u70), _u70) | ~in(skolem9(_u74, _u72, _u70), _u70) )).
% 6.29/6.48 cnf(d2_xboole_0-6, axiom, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem9(_u74, _u72, _u70), _u74) | in(skolem9(_u74, _u72, _u70), _u72) | ~in(skolem8(_u74, _u72, _u70), _u74) )).
% 6.29/6.48 cnf(d2_xboole_0-7, axiom, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem9(_u74, _u72, _u70), _u74) | in(skolem9(_u74, _u72, _u70), _u72) | ~in(skolem8(_u74, _u72, _u70), _u72) )).
% 6.29/6.48 cnf(d2_xboole_0-8, axiom, ( ( _u70 = set_union2(_u74, _u72)) | ~in(skolem9(_u74, _u72, _u70), _u70) | ~in(skolem8(_u74, _u72, _u70), _u74) )).
% 6.29/6.48 cnf(d2_xboole_0-9, axiom, ( ( _u70 = set_union2(_u74, _u72)) | ~in(skolem9(_u74, _u72, _u70), _u70) | ~in(skolem8(_u74, _u72, _u70), _u72) )).
% 6.29/6.48
% 6.29/6.48 % Formula: d2_zfmisc_1 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(d2_zfmisc_1-1, axiom, ( ( _u92 != cartesian_product2(_u96, _u94)) | ~in(_u88, _u92) | in(skolem10(_u96, _u94, _u92, _u88), _u96) )).
% 6.29/6.48 cnf(d2_zfmisc_1-2, axiom, ( ( _u92 != cartesian_product2(_u96, _u94)) | ~in(_u88, _u92) | in(skolem11(_u96, _u94, _u92, _u88), _u94) )).
% 6.29/6.48 cnf(d2_zfmisc_1-3, axiom, ( ( _u92 != cartesian_product2(_u96, _u94)) | ~in(_u88, _u92) | ( _u88 = ordered_pair(skolem10(_u96, _u94, _u92, _u88), skolem11(_u96, _u94, _u92, _u88))) )).
% 6.29/6.48 cnf(d2_zfmisc_1-4, axiom, ( ( _u92 != cartesian_product2(_u96, _u94)) | ~in(_u78, _u96) | ~in(_u77, _u94) | ( _u89 != ordered_pair(_u78, _u77)) | in(_u89, _u92) )).
% 6.29/6.48 cnf(d2_zfmisc_1-5, axiom, ( ( _u93 = cartesian_product2(_u97, _u95)) | in(skolem12(_u97, _u95, _u93), _u93) | in(skolem14(_u97, _u95, _u93), _u97) )).
% 6.29/6.48 cnf(d2_zfmisc_1-6, axiom, ( ( _u93 = cartesian_product2(_u97, _u95)) | in(skolem12(_u97, _u95, _u93), _u93) | in(skolem15(_u97, _u95, _u93), _u95) )).
% 6.29/6.48 cnf(d2_zfmisc_1-7, axiom, ( ( _u93 = cartesian_product2(_u97, _u95)) | in(skolem12(_u97, _u95, _u93), _u93) | ( skolem13(_u97, _u95, _u93) = ordered_pair(skolem14(_u97, _u95, _u93), skolem15(_u97, _u95, _u93))) )).
% 6.29/6.48 cnf(d2_zfmisc_1-8, axiom, ( ( _u93 = cartesian_product2(_u97, _u95)) | in(skolem12(_u97, _u95, _u93), _u93) | ~in(skolem13(_u97, _u95, _u93), _u93) )).
% 6.29/6.48 cnf(d2_zfmisc_1-9, axiom, ( ( _u93 = cartesian_product2(_u97, _u95)) | ~in(_u81, _u97) | ~in(_u80, _u95) | ( skolem12(_u97, _u95, _u93) != ordered_pair(_u81, _u80)) | in(skolem14(_u97, _u95, _u93), _u97) )).
% 6.29/6.48 cnf(d2_zfmisc_1-10, axiom, ( ( _u93 = cartesian_product2(_u97, _u95)) | ~in(_u81, _u97) | ~in(_u80, _u95) | ( skolem12(_u97, _u95, _u93) != ordered_pair(_u81, _u80)) | in(skolem15(_u97, _u95, _u93), _u95) )).
% 6.29/6.48 cnf(d2_zfmisc_1-11, axiom, ( ( _u93 = cartesian_product2(_u97, _u95)) | ~in(_u81, _u97) | ~in(_u80, _u95) | ( skolem12(_u97, _u95, _u93) != ordered_pair(_u81, _u80)) | ( skolem13(_u97, _u95, _u93) = ordered_pair(skolem14(_u97, _u95, _u93), skolem15(_u97, _u95, _u93))) )).
% 6.29/6.48 cnf(d2_zfmisc_1-12, axiom, ( ( _u93 = cartesian_product2(_u97, _u95)) | ~in(_u81, _u97) | ~in(_u80, _u95) | ( skolem12(_u97, _u95, _u93) != ordered_pair(_u81, _u80)) | ~in(skolem13(_u97, _u95, _u93), _u93) )).
% 6.29/6.48
% 6.29/6.48 % Formula: d3_tarski ( axiom ) converted to clauses:
% 6.29/6.48 cnf(d3_tarski-1, axiom, ( ~subset(_u104, _u102) | ~in(_u98, _u104) | in(_u98, _u102) )).
% 6.29/6.48 cnf(d3_tarski-2, axiom, ( subset(_u105, _u103) | in(skolem16(_u105, _u103), _u105) )).
% 6.29/6.48 cnf(d3_tarski-3, axiom, ( subset(_u105, _u103) | ~in(skolem16(_u105, _u103), _u103) )).
% 6.29/6.48
% 6.29/6.48 % Formula: d3_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(d3_xboole_0-1, axiom, ( ( _u115 != set_intersection2(_u119, _u117)) | ~in(_u111, _u115) | in(_u111, _u119) )).
% 6.29/6.48 cnf(d3_xboole_0-2, axiom, ( ( _u115 != set_intersection2(_u119, _u117)) | ~in(_u111, _u115) | in(_u111, _u117) )).
% 6.29/6.48 cnf(d3_xboole_0-3, axiom, ( ( _u115 != set_intersection2(_u119, _u117)) | ~in(_u112, _u119) | ~in(_u112, _u117) | in(_u112, _u115) )).
% 6.29/6.48 cnf(d3_xboole_0-4, axiom, ( ( _u116 = set_intersection2(_u120, _u118)) | in(skolem17(_u120, _u118, _u116), _u116) | in(skolem18(_u120, _u118, _u116), _u120) )).
% 6.29/6.48 cnf(d3_xboole_0-5, axiom, ( ( _u116 = set_intersection2(_u120, _u118)) | in(skolem17(_u120, _u118, _u116), _u116) | in(skolem18(_u120, _u118, _u116), _u118) )).
% 6.29/6.48 cnf(d3_xboole_0-6, axiom, ( ( _u116 = set_intersection2(_u120, _u118)) | in(skolem17(_u120, _u118, _u116), _u116) | ~in(skolem18(_u120, _u118, _u116), _u116) )).
% 6.29/6.48 cnf(d3_xboole_0-7, axiom, ( ( _u116 = set_intersection2(_u120, _u118)) | ~in(skolem17(_u120, _u118, _u116), _u120) | ~in(skolem17(_u120, _u118, _u116), _u118) | in(skolem18(_u120, _u118, _u116), _u120) )).
% 6.29/6.48 cnf(d3_xboole_0-8, axiom, ( ( _u116 = set_intersection2(_u120, _u118)) | ~in(skolem17(_u120, _u118, _u116), _u120) | ~in(skolem17(_u120, _u118, _u116), _u118) | in(skolem18(_u120, _u118, _u116), _u118) )).
% 6.29/6.48 cnf(d3_xboole_0-9, axiom, ( ( _u116 = set_intersection2(_u120, _u118)) | ~in(skolem17(_u120, _u118, _u116), _u120) | ~in(skolem17(_u120, _u118, _u116), _u118) | ~in(skolem18(_u120, _u118, _u116), _u116) )).
% 6.29/6.48
% 6.29/6.48 % Formula: d4_tarski ( axiom ) converted to clauses:
% 6.29/6.48 cnf(d4_tarski-1, axiom, ( ( _u133 != union(_u135)) | ~in(_u129, _u133) | in(_u129, skolem19(_u135, _u133, _u129)) )).
% 6.29/6.48 cnf(d4_tarski-2, axiom, ( ( _u133 != union(_u135)) | ~in(_u129, _u133) | in(skolem19(_u135, _u133, _u129), _u135) )).
% 6.29/6.48 cnf(d4_tarski-3, axiom, ( ( _u133 != union(_u135)) | ~in(_u130, _u122) | ~in(_u122, _u135) | in(_u130, _u133) )).
% 6.29/6.48 cnf(d4_tarski-4, axiom, ( ( _u134 = union(_u136)) | in(skolem20(_u136, _u134), _u134) | in(skolem21(_u136, _u134), skolem22(_u136, _u134)) )).
% 6.29/6.48 cnf(d4_tarski-5, axiom, ( ( _u134 = union(_u136)) | in(skolem20(_u136, _u134), _u134) | in(skolem22(_u136, _u134), _u136) )).
% 6.29/6.48 cnf(d4_tarski-6, axiom, ( ( _u134 = union(_u136)) | in(skolem20(_u136, _u134), _u134) | ~in(skolem21(_u136, _u134), _u134) )).
% 6.29/6.48 cnf(d4_tarski-7, axiom, ( ( _u134 = union(_u136)) | ~in(skolem20(_u136, _u134), _u124) | ~in(_u124, _u136) | in(skolem21(_u136, _u134), skolem22(_u136, _u134)) )).
% 6.29/6.48 cnf(d4_tarski-8, axiom, ( ( _u134 = union(_u136)) | ~in(skolem20(_u136, _u134), _u124) | ~in(_u124, _u136) | in(skolem22(_u136, _u134), _u136) )).
% 6.29/6.48 cnf(d4_tarski-9, axiom, ( ( _u134 = union(_u136)) | ~in(skolem20(_u136, _u134), _u124) | ~in(_u124, _u136) | ~in(skolem21(_u136, _u134), _u134) )).
% 6.29/6.48
% 6.29/6.48 % Formula: d4_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(d4_xboole_0-1, axiom, ( ( _u146 != set_difference(_u150, _u148)) | ~in(_u142, _u146) | in(_u142, _u150) )).
% 6.29/6.48 cnf(d4_xboole_0-2, axiom, ( ( _u146 != set_difference(_u150, _u148)) | ~in(_u142, _u146) | ~in(_u142, _u148) )).
% 6.29/6.48 cnf(d4_xboole_0-3, axiom, ( ( _u146 != set_difference(_u150, _u148)) | ~in(_u143, _u150) | in(_u143, _u148) | in(_u143, _u146) )).
% 6.29/6.48 cnf(d4_xboole_0-4, axiom, ( ( _u147 = set_difference(_u151, _u149)) | in(skolem23(_u151, _u149, _u147), _u147) | in(skolem24(_u151, _u149, _u147), _u151) )).
% 6.29/6.48 cnf(d4_xboole_0-5, axiom, ( ( _u147 = set_difference(_u151, _u149)) | in(skolem23(_u151, _u149, _u147), _u147) | ~in(skolem24(_u151, _u149, _u147), _u149) )).
% 6.29/6.48 cnf(d4_xboole_0-6, axiom, ( ( _u147 = set_difference(_u151, _u149)) | in(skolem23(_u151, _u149, _u147), _u147) | ~in(skolem24(_u151, _u149, _u147), _u147) )).
% 6.29/6.48 cnf(d4_xboole_0-7, axiom, ( ( _u147 = set_difference(_u151, _u149)) | ~in(skolem23(_u151, _u149, _u147), _u151) | in(skolem23(_u151, _u149, _u147), _u149) | in(skolem24(_u151, _u149, _u147), _u151) )).
% 6.29/6.48 cnf(d4_xboole_0-8, axiom, ( ( _u147 = set_difference(_u151, _u149)) | ~in(skolem23(_u151, _u149, _u147), _u151) | in(skolem23(_u151, _u149, _u147), _u149) | ~in(skolem24(_u151, _u149, _u147), _u149) )).
% 6.29/6.48 cnf(d4_xboole_0-9, axiom, ( ( _u147 = set_difference(_u151, _u149)) | ~in(skolem23(_u151, _u149, _u147), _u151) | in(skolem23(_u151, _u149, _u147), _u149) | ~in(skolem24(_u151, _u149, _u147), _u147) )).
% 6.29/6.48
% 6.29/6.48 % Formula: d5_tarski ( axiom ) converted to clauses:
% 6.29/6.48 cnf(d5_tarski-1, axiom, ( ( ordered_pair(_u153, _u152) = unordered_pair(unordered_pair(_u153, _u152), singleton(_u153))) )).
% 6.29/6.48
% 6.29/6.48 % Formula: d7_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(d7_xboole_0-1, axiom, ( ~disjoint(_u158, _u156) | ( set_intersection2(_u158, _u156) = empty_set) )).
% 6.29/6.48 cnf(d7_xboole_0-2, axiom, ( ( set_intersection2(_u159, _u157) != empty_set) | disjoint(_u159, _u157) )).
% 6.29/6.48
% 6.29/6.48 % Formula: d8_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(d8_xboole_0-1, axiom, ( ~proper_subset(_u164, _u162) | subset(_u164, _u162) )).
% 6.29/6.48 cnf(d8_xboole_0-2, axiom, ( ~proper_subset(_u164, _u162) | ( _u164 != _u162) )).
% 6.29/6.48 cnf(d8_xboole_0-3, axiom, ( ~subset(_u165, _u163) | ( _u165 = _u163) | proper_subset(_u165, _u163) )).
% 6.29/6.48
% 6.29/6.48 % Formula: dt_k1_tarski ( axiom ) converted to clauses:
% 6.29/6.48
% 6.29/6.48 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48
% 6.29/6.48 % Formula: dt_k1_zfmisc_1 ( axiom ) converted to clauses:
% 6.29/6.48
% 6.29/6.48 % Formula: dt_k2_tarski ( axiom ) converted to clauses:
% 6.29/6.48
% 6.29/6.48 % Formula: dt_k2_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48
% 6.29/6.48 % Formula: dt_k2_zfmisc_1 ( axiom ) converted to clauses:
% 6.29/6.48
% 6.29/6.48 % Formula: dt_k3_tarski ( axiom ) converted to clauses:
% 6.29/6.48
% 6.29/6.48 % Formula: dt_k3_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48
% 6.29/6.48 % Formula: dt_k4_tarski ( axiom ) converted to clauses:
% 6.29/6.48
% 6.29/6.48 % Formula: dt_k4_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48
% 6.29/6.48 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 6.29/6.48
% 6.29/6.48 % Formula: fc1_zfmisc_1 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(fc1_zfmisc_1-1, axiom, ( ~empty(ordered_pair(_u167, _u166)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(fc2_xboole_0-1, axiom, ( empty(_u169) | ~empty(set_union2(_u169, _u168)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(fc3_xboole_0-1, axiom, ( empty(_u171) | ~empty(set_union2(_u170, _u171)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u173, _u173) = _u173) )).
% 6.29/6.48
% 6.29/6.48 % Formula: idempotence_k3_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(idempotence_k3_xboole_0-1, axiom, ( ( set_intersection2(_u175, _u175) = _u175) )).
% 6.29/6.48
% 6.29/6.48 % Formula: irreflexivity_r2_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(irreflexivity_r2_xboole_0-1, axiom, ( ~proper_subset(_u177, _u177) )).
% 6.29/6.48
% 6.29/6.48 % Formula: l1_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(l1_zfmisc_1-1, lemma, ( ( singleton(_u178) != empty_set) )).
% 6.29/6.48
% 6.29/6.48 % Formula: l23_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(l23_zfmisc_1-1, lemma, ( ~in(_u180, _u179) | ( set_union2(singleton(_u180), _u179) = _u179) )).
% 6.29/6.48
% 6.29/6.48 % Formula: l25_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(l25_zfmisc_1-1, lemma, ( ~disjoint(singleton(_u182), _u181) | ~in(_u182, _u181) )).
% 6.29/6.48
% 6.29/6.48 % Formula: l28_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(l28_zfmisc_1-1, lemma, ( in(_u184, _u183) | disjoint(singleton(_u184), _u183) )).
% 6.29/6.48
% 6.29/6.48 % Formula: l2_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(l2_zfmisc_1-1, lemma, ( ~subset(singleton(_u189), _u187) | in(_u189, _u187) )).
% 6.29/6.48 cnf(l2_zfmisc_1-2, lemma, ( ~in(_u190, _u188) | subset(singleton(_u190), _u188) )).
% 6.29/6.48
% 6.29/6.48 % Formula: l32_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(l32_xboole_1-1, lemma, ( ( set_difference(_u195, _u193) != empty_set) | subset(_u195, _u193) )).
% 6.29/6.48 cnf(l32_xboole_1-2, lemma, ( ~subset(_u196, _u194) | ( set_difference(_u196, _u194) = empty_set) )).
% 6.29/6.48
% 6.29/6.48 % Formula: l3_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(l3_zfmisc_1-1, lemma, ( ~subset(_u199, _u198) | in(_u197, _u199) | subset(_u199, set_difference(_u198, singleton(_u197))) )).
% 6.29/6.48
% 6.29/6.48 % Formula: l4_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(l4_zfmisc_1-1, lemma, ( ~subset(_u204, singleton(_u202)) | ( _u204 = empty_set) | ( _u204 = singleton(_u202)) )).
% 6.29/6.48 cnf(l4_zfmisc_1-2, lemma, ( subset(_u205, singleton(_u203)) | ( _u205 != empty_set) )).
% 6.29/6.48 cnf(l4_zfmisc_1-3, lemma, ( subset(_u205, singleton(_u203)) | ( _u205 != singleton(_u203)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: l50_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(l50_zfmisc_1-1, lemma, ( ~in(_u207, _u206) | subset(_u207, union(_u206)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: l55_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(l55_zfmisc_1-1, lemma, ( ~in(ordered_pair(_u218, _u216), cartesian_product2(_u214, _u212)) | in(_u218, _u214) )).
% 6.29/6.48 cnf(l55_zfmisc_1-2, lemma, ( ~in(ordered_pair(_u218, _u216), cartesian_product2(_u214, _u212)) | in(_u216, _u212) )).
% 6.29/6.48 cnf(l55_zfmisc_1-3, lemma, ( ~in(_u219, _u215) | ~in(_u217, _u213) | in(ordered_pair(_u219, _u217), cartesian_product2(_u215, _u213)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(rc1_xboole_0-1, axiom, ( empty(skolem25) )).
% 6.29/6.48
% 6.29/6.48 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem26) )).
% 6.29/6.48
% 6.29/6.48 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 6.29/6.48 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u223, _u223) )).
% 6.29/6.48
% 6.29/6.48 % Formula: symmetry_r1_xboole_0 ( axiom ) converted to clauses:
% 6.29/6.48 cnf(symmetry_r1_xboole_0-1, axiom, ( ~disjoint(_u225, _u224) | disjoint(_u224, _u225) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t10_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t10_zfmisc_1-1, lemma, ( ( _u229 = _u227) | ( unordered_pair(_u229, _u228) != unordered_pair(_u227, _u226)) | ( _u229 = _u226) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t12_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t12_xboole_1-1, lemma, ( ~subset(_u231, _u230) | ( set_union2(_u231, _u230) = _u230) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t17_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t17_xboole_1-1, lemma, ( subset(set_intersection2(_u233, _u232), _u233) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t19_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t19_xboole_1-1, lemma, ( ~subset(_u236, _u235) | ~subset(_u236, _u234) | subset(_u236, set_intersection2(_u235, _u234)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t1_boole ( axiom ) converted to clauses:
% 6.29/6.48 cnf(t1_boole-1, axiom, ( ( set_union2(_u237, empty_set) = _u237) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t1_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t1_xboole_1-1, lemma, ( ~subset(_u240, _u239) | ~subset(_u239, _u238) | subset(_u240, _u238) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t1_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t1_zfmisc_1-1, lemma, ( ( powerset(empty_set) = singleton(empty_set)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t26_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t26_xboole_1-1, lemma, ( ~subset(_u243, _u242) | subset(set_intersection2(_u243, _u241), set_intersection2(_u242, _u241)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t28_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t28_xboole_1-1, lemma, ( ~subset(_u245, _u244) | ( set_intersection2(_u245, _u244) = _u245) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t2_boole ( axiom ) converted to clauses:
% 6.29/6.48 cnf(t2_boole-1, axiom, ( ( set_intersection2(_u246, empty_set) = empty_set) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t2_tarski ( axiom ) converted to clauses:
% 6.29/6.48 cnf(t2_tarski-1, axiom, ( ( _u249 = _u248) | in(skolem27(_u249, _u248), _u249) | in(skolem28(_u249, _u248), _u248) )).
% 6.29/6.48 cnf(t2_tarski-2, axiom, ( ( _u249 = _u248) | in(skolem27(_u249, _u248), _u249) | ~in(skolem28(_u249, _u248), _u249) )).
% 6.29/6.48 cnf(t2_tarski-3, axiom, ( ( _u249 = _u248) | ~in(skolem27(_u249, _u248), _u248) | in(skolem28(_u249, _u248), _u248) )).
% 6.29/6.48 cnf(t2_tarski-4, axiom, ( ( _u249 = _u248) | ~in(skolem27(_u249, _u248), _u248) | ~in(skolem28(_u249, _u248), _u249) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t2_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t2_xboole_1-1, lemma, ( subset(empty_set, _u252) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t33_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t33_xboole_1-1, lemma, ( ~subset(_u255, _u254) | subset(set_difference(_u255, _u253), set_difference(_u254, _u253)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t33_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t33_zfmisc_1-1, lemma, ( ( ordered_pair(_u259, _u258) != ordered_pair(_u257, _u256)) | ( _u259 = _u257) )).
% 6.29/6.48 cnf(t33_zfmisc_1-2, lemma, ( ( ordered_pair(_u259, _u258) != ordered_pair(_u257, _u256)) | ( _u258 = _u256) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t36_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t36_xboole_1-1, lemma, ( subset(set_difference(_u261, _u260), _u261) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t37_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t37_xboole_1-1, lemma, ( ( set_difference(_u266, _u264) != empty_set) | subset(_u266, _u264) )).
% 6.29/6.48 cnf(t37_xboole_1-2, lemma, ( ~subset(_u267, _u265) | ( set_difference(_u267, _u265) = empty_set) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t37_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t37_zfmisc_1-1, lemma, ( ~subset(singleton(_u272), _u270) | in(_u272, _u270) )).
% 6.29/6.48 cnf(t37_zfmisc_1-2, lemma, ( ~in(_u273, _u271) | subset(singleton(_u273), _u271) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t38_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t38_zfmisc_1-1, lemma, ( ~subset(unordered_pair(_u281, _u279), _u277) | in(_u281, _u277) )).
% 6.29/6.48 cnf(t38_zfmisc_1-2, lemma, ( ~subset(unordered_pair(_u281, _u279), _u277) | in(_u279, _u277) )).
% 6.29/6.48 cnf(t38_zfmisc_1-3, lemma, ( ~in(_u282, _u278) | ~in(_u280, _u278) | subset(unordered_pair(_u282, _u280), _u278) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t39_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t39_xboole_1-1, lemma, ( ( set_union2(_u284, set_difference(_u283, _u284)) = set_union2(_u284, _u283)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t39_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t39_zfmisc_1-1, lemma, ( ~subset(_u289, singleton(_u287)) | ( _u289 = empty_set) | ( _u289 = singleton(_u287)) )).
% 6.29/6.48 cnf(t39_zfmisc_1-2, lemma, ( subset(_u290, singleton(_u288)) | ( _u290 != empty_set) )).
% 6.29/6.48 cnf(t39_zfmisc_1-3, lemma, ( subset(_u290, singleton(_u288)) | ( _u290 != singleton(_u288)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t3_boole ( axiom ) converted to clauses:
% 6.29/6.48 cnf(t3_boole-1, axiom, ( ( set_difference(_u291, empty_set) = _u291) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t3_xboole_0 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t3_xboole_0-1, lemma, ( disjoint(_u298, _u296) | in(skolem29(_u298, _u296), _u298) )).
% 6.29/6.48 cnf(t3_xboole_0-2, lemma, ( disjoint(_u298, _u296) | in(skolem29(_u298, _u296), _u296) )).
% 6.29/6.48 cnf(t3_xboole_0-3, lemma, ( ~in(_u293, _u299) | ~in(_u293, _u297) | ~disjoint(_u299, _u297) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t3_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t3_xboole_1-1, lemma, ( ~subset(_u300, empty_set) | ( _u300 = empty_set) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t40_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t40_xboole_1-1, lemma, ( ( set_difference(set_union2(_u302, _u301), _u301) = set_difference(_u302, _u301)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t45_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t45_xboole_1-1, lemma, ( ~subset(_u304, _u303) | ( _u303 = set_union2(_u304, set_difference(_u303, _u304))) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t46_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t46_zfmisc_1-1, lemma, ( ~in(_u306, _u305) | ( set_union2(singleton(_u306), _u305) = _u305) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t48_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t48_xboole_1-1, lemma, ( ( set_difference(_u308, set_difference(_u308, _u307)) = set_intersection2(_u308, _u307)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t4_boole ( axiom ) converted to clauses:
% 6.29/6.48 cnf(t4_boole-1, axiom, ( ( set_difference(empty_set, _u309) = empty_set) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t4_xboole_0 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t4_xboole_0-1, lemma, ( disjoint(_u316, _u314) | in(skolem30(_u316, _u314), set_intersection2(_u316, _u314)) )).
% 6.29/6.48 cnf(t4_xboole_0-2, lemma, ( ~in(_u311, set_intersection2(_u317, _u315)) | ~disjoint(_u317, _u315) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t60_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t60_xboole_1-1, lemma, ( ~subset(_u319, _u318) | ~proper_subset(_u318, _u319) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t63_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t63_xboole_1-1, lemma, ( ~subset(_u322, _u321) | ~disjoint(_u321, _u320) | disjoint(_u322, _u320) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t65_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t65_zfmisc_1-1, lemma, ( ( set_difference(_u327, singleton(_u325)) != _u327) | ~in(_u325, _u327) )).
% 6.29/6.48 cnf(t65_zfmisc_1-2, lemma, ( in(_u326, _u328) | ( set_difference(_u328, singleton(_u326)) = _u328) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t69_enumset1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t69_enumset1-1, lemma, ( ( unordered_pair(_u329, _u329) = singleton(_u329)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t6_boole ( axiom ) converted to clauses:
% 6.29/6.48 cnf(t6_boole-1, axiom, ( ~empty(_u330) | ( _u330 = empty_set) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t6_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t6_zfmisc_1-1, lemma, ( ~subset(singleton(_u332), singleton(_u331)) | ( _u332 = _u331) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t7_boole ( axiom ) converted to clauses:
% 6.29/6.48 cnf(t7_boole-1, axiom, ( ~in(_u334, _u333) | ~empty(_u333) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t7_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t7_xboole_1-1, lemma, ( subset(_u336, set_union2(_u336, _u335)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t83_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t83_xboole_1-1, lemma, ( ~disjoint(_u341, _u339) | ( set_difference(_u341, _u339) = _u341) )).
% 6.29/6.48 cnf(t83_xboole_1-2, lemma, ( ( set_difference(_u342, _u340) != _u342) | disjoint(_u342, _u340) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t8_boole ( axiom ) converted to clauses:
% 6.29/6.48 cnf(t8_boole-1, axiom, ( ~empty(_u344) | ( _u344 = _u343) | ~empty(_u343) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t8_xboole_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t8_xboole_1-1, lemma, ( ~subset(_u347, _u346) | ~subset(_u345, _u346) | subset(set_union2(_u347, _u345), _u346) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t8_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t8_zfmisc_1-1, lemma, ( ( _u350 = _u349) | ( singleton(_u350) != unordered_pair(_u349, _u348)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t92_zfmisc_1 ( conjecture ) converted to clauses:
% 6.29/6.48 cnf(t92_zfmisc_1-1, negated_conjecture, ( in(skolem31, skolem32) )).
% 6.29/6.48 cnf(t92_zfmisc_1-2, negated_conjecture, ( ~subset(skolem31, union(skolem32)) )).
% 6.29/6.48
% 6.29/6.48 % Formula: t9_zfmisc_1 ( lemma ) converted to clauses:
% 6.29/6.48 cnf(t9_zfmisc_1-1, lemma, ( ( singleton(_u355) != unordered_pair(_u354, _u353)) | ( _u354 = _u353) )).
% 6.29/6.48
% 6.29/6.48 % Problem matrix:
% 6.29/6.48 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 6.29/6.48 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 6.29/6.48 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 6.29/6.48 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_intersection2(__eqx_0, __eqx_1) = set_intersection2(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 6.29/6.48 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 6.29/6.48 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( cartesian_product2(__eqx_0, __eqx_1) = cartesian_product2(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( union(__eqx_0) = union(__eqy_0)) )).
% 6.29/6.48 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_difference(__eqx_0, __eqx_1) = set_difference(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( skolem3(__eqx_0) = skolem3(__eqy_0)) )).
% 6.29/6.48 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem5(__eqx_0, __eqx_1) = skolem5(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem6(__eqx_0, __eqx_1, __eqx_2) = skolem6(__eqy_0, __eqy_1, __eqy_2)) )).
% 6.29/6.48 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem7(__eqx_0, __eqx_1, __eqx_2) = skolem7(__eqy_0, __eqy_1, __eqy_2)) )).
% 6.29/6.48 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem8(__eqx_0, __eqx_1, __eqx_2) = skolem8(__eqy_0, __eqy_1, __eqy_2)) )).
% 6.29/6.48 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem9(__eqx_0, __eqx_1, __eqx_2) = skolem9(__eqy_0, __eqy_1, __eqy_2)) )).
% 6.29/6.48 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( skolem10(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = skolem10(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 6.29/6.48 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( skolem11(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = skolem11(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 6.29/6.48 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem12(__eqx_0, __eqx_1, __eqx_2) = skolem12(__eqy_0, __eqy_1, __eqy_2)) )).
% 6.29/6.48 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem13(__eqx_0, __eqx_1, __eqx_2) = skolem13(__eqy_0, __eqy_1, __eqy_2)) )).
% 6.29/6.48 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem14(__eqx_0, __eqx_1, __eqx_2) = skolem14(__eqy_0, __eqy_1, __eqy_2)) )).
% 6.29/6.48 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem15(__eqx_0, __eqx_1, __eqx_2) = skolem15(__eqy_0, __eqy_1, __eqy_2)) )).
% 6.29/6.48 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem16(__eqx_0, __eqx_1) = skolem16(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem17(__eqx_0, __eqx_1, __eqx_2) = skolem17(__eqy_0, __eqy_1, __eqy_2)) )).
% 6.29/6.48 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem18(__eqx_0, __eqx_1, __eqx_2) = skolem18(__eqy_0, __eqy_1, __eqy_2)) )).
% 6.29/6.48 cnf(matrix-30, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem19(__eqx_0, __eqx_1, __eqx_2) = skolem19(__eqy_0, __eqy_1, __eqy_2)) )).
% 6.29/6.48 cnf(matrix-31, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem20(__eqx_0, __eqx_1) = skolem20(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-32, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem21(__eqx_0, __eqx_1) = skolem21(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-33, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem22(__eqx_0, __eqx_1) = skolem22(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-34, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem23(__eqx_0, __eqx_1, __eqx_2) = skolem23(__eqy_0, __eqy_1, __eqy_2)) )).
% 6.29/6.48 cnf(matrix-35, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem24(__eqx_0, __eqx_1, __eqx_2) = skolem24(__eqy_0, __eqy_1, __eqy_2)) )).
% 6.29/6.48 cnf(matrix-36, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem27(__eqx_0, __eqx_1) = skolem27(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-37, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem28(__eqx_0, __eqx_1) = skolem28(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-38, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem29(__eqx_0, __eqx_1) = skolem29(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-39, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem30(__eqx_0, __eqx_1) = skolem30(__eqy_0, __eqy_1)) )).
% 6.29/6.48 cnf(matrix-40, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 6.29/6.48 cnf(matrix-41, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~proper_subset(__eqx_0, __eqx_1) | proper_subset(__eqy_0, __eqy_1) )).
% 6.29/6.48 cnf(matrix-42, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 6.29/6.48 cnf(matrix-43, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~disjoint(__eqx_0, __eqx_1) | disjoint(__eqy_0, __eqy_1) )).
% 6.29/6.48 cnf(matrix-44, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 6.29/6.48 cnf(matrix-45, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 6.29/6.48 cnf(matrix-46, plain, ( ~proper_subset(_u3, _u2) | ~proper_subset(_u2, _u3) )).
% 6.29/6.48 cnf(matrix-47, plain, ( ( unordered_pair(_u5, _u4) = unordered_pair(_u4, _u5)) )).
% 6.29/6.48 cnf(matrix-48, plain, ( ( set_union2(_u7, _u6) = set_union2(_u6, _u7)) )).
% 6.29/6.48 cnf(matrix-49, plain, ( ( set_intersection2(_u9, _u8) = set_intersection2(_u8, _u9)) )).
% 6.29/6.48 cnf(matrix-50, plain, ( ( _u14 != _u12) | subset(_u14, _u12) )).
% 6.29/6.48 cnf(matrix-51, plain, ( ( _u14 != _u12) | subset(_u12, _u14) )).
% 6.29/6.48 cnf(matrix-52, plain, ( ~subset(_u15, _u13) | ~subset(_u13, _u15) | ( _u15 = _u13) )).
% 6.29/6.48 cnf(matrix-53, plain, ( ( _u24 != singleton(_u26)) | ~in(_u20, _u24) | ( _u20 = _u26) )).
% 6.29/6.48 cnf(matrix-54, plain, ( ( _u24 != singleton(_u26)) | ( _u21 != _u26) | in(_u21, _u24) )).
% 6.29/6.48 cnf(matrix-55, plain, ( ( _u25 = singleton(_u27)) | in(skolem1(_u27, _u25), _u25) | ( skolem2(_u27, _u25) = _u27) )).
% 6.29/6.48 cnf(matrix-56, plain, ( ( _u25 = singleton(_u27)) | in(skolem1(_u27, _u25), _u25) | ~in(skolem2(_u27, _u25), _u25) )).
% 6.29/6.48 cnf(matrix-57, plain, ( ( _u25 = singleton(_u27)) | ( skolem1(_u27, _u25) != _u27) | ( skolem2(_u27, _u25) = _u27) )).
% 6.29/6.48 cnf(matrix-58, plain, ( ( _u25 = singleton(_u27)) | ( skolem1(_u27, _u25) != _u27) | ~in(skolem2(_u27, _u25), _u25) )).
% 6.29/6.48 cnf(matrix-59, plain, ( ( _u31 != empty_set) | ~in(_u28, _u31) )).
% 6.29/6.48 cnf(matrix-60, plain, ( in(skolem3(_u32), _u32) | ( _u32 = empty_set) )).
% 6.29/6.48 cnf(matrix-61, plain, ( ( _u41 != powerset(_u43)) | ~in(_u37, _u41) | subset(_u37, _u43) )).
% 6.29/6.48 cnf(matrix-62, plain, ( ( _u41 != powerset(_u43)) | ~subset(_u38, _u43) | in(_u38, _u41) )).
% 6.29/6.48 cnf(matrix-63, plain, ( ( _u42 = powerset(_u44)) | in(skolem4(_u44, _u42), _u42) | subset(skolem5(_u44, _u42), _u44) )).
% 6.29/6.48 cnf(matrix-64, plain, ( ( _u42 = powerset(_u44)) | in(skolem4(_u44, _u42), _u42) | ~in(skolem5(_u44, _u42), _u42) )).
% 6.29/6.48 cnf(matrix-65, plain, ( ( _u42 = powerset(_u44)) | ~subset(skolem4(_u44, _u42), _u44) | subset(skolem5(_u44, _u42), _u44) )).
% 6.29/6.48 cnf(matrix-66, plain, ( ( _u42 = powerset(_u44)) | ~subset(skolem4(_u44, _u42), _u44) | ~in(skolem5(_u44, _u42), _u42) )).
% 6.29/6.48 cnf(matrix-67, plain, ( ( _u54 != unordered_pair(_u58, _u56)) | ~in(_u50, _u54) | ( _u50 = _u58) | ( _u50 = _u56) )).
% 6.29/6.48 cnf(matrix-68, plain, ( ( _u54 != unordered_pair(_u58, _u56)) | in(_u51, _u54) | ( _u51 != _u58) )).
% 6.29/6.48 cnf(matrix-69, plain, ( ( _u54 != unordered_pair(_u58, _u56)) | in(_u51, _u54) | ( _u51 != _u56) )).
% 6.29/6.48 cnf(matrix-70, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | in(skolem6(_u59, _u57, _u55), _u55) | ( skolem7(_u59, _u57, _u55) = _u59) | ( skolem7(_u59, _u57, _u55) = _u57) )).
% 6.29/6.48 cnf(matrix-71, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | in(skolem6(_u59, _u57, _u55), _u55) | ~in(skolem7(_u59, _u57, _u55), _u55) )).
% 6.29/6.48 cnf(matrix-72, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | ( skolem7(_u59, _u57, _u55) = _u59) | ( skolem7(_u59, _u57, _u55) = _u57) | ( skolem6(_u59, _u57, _u55) != _u59) )).
% 6.29/6.48 cnf(matrix-73, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | ( skolem7(_u59, _u57, _u55) = _u59) | ( skolem7(_u59, _u57, _u55) = _u57) | ( skolem6(_u59, _u57, _u55) != _u57) )).
% 6.29/6.48 cnf(matrix-74, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | ~in(skolem7(_u59, _u57, _u55), _u55) | ( skolem6(_u59, _u57, _u55) != _u59) )).
% 6.29/6.48 cnf(matrix-75, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | ~in(skolem7(_u59, _u57, _u55), _u55) | ( skolem6(_u59, _u57, _u55) != _u57) )).
% 6.29/6.48 cnf(matrix-76, plain, ( ( _u69 != set_union2(_u73, _u71)) | ~in(_u65, _u69) | in(_u65, _u73) | in(_u65, _u71) )).
% 6.29/6.48 cnf(matrix-77, plain, ( ( _u69 != set_union2(_u73, _u71)) | in(_u66, _u69) | ~in(_u66, _u73) )).
% 6.29/6.48 cnf(matrix-78, plain, ( ( _u69 != set_union2(_u73, _u71)) | in(_u66, _u69) | ~in(_u66, _u71) )).
% 6.29/6.48 cnf(matrix-79, plain, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem8(_u74, _u72, _u70), _u70) | in(skolem9(_u74, _u72, _u70), _u74) | in(skolem9(_u74, _u72, _u70), _u72) )).
% 6.29/6.48 cnf(matrix-80, plain, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem8(_u74, _u72, _u70), _u70) | ~in(skolem9(_u74, _u72, _u70), _u70) )).
% 6.29/6.48 cnf(matrix-81, plain, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem9(_u74, _u72, _u70), _u74) | in(skolem9(_u74, _u72, _u70), _u72) | ~in(skolem8(_u74, _u72, _u70), _u74) )).
% 6.29/6.48 cnf(matrix-82, plain, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem9(_u74, _u72, _u70), _u74) | in(skolem9(_u74, _u72, _u70), _u72) | ~in(skolem8(_u74, _u72, _u70), _u72) )).
% 6.29/6.48 cnf(matrix-83, plain, ( ( _u70 = set_union2(_u74, _u72)) | ~in(skolem9(_u74, _u72, _u70), _u70) | ~in(skolem8(_u74, _u72, _u70), _u74) )).
% 6.29/6.48 cnf(matrix-84, plain, ( ( _u70 = set_union2(_u74, _u72)) | ~in(skolem9(_u74, _u72, _u70), _u70) | ~in(skolem8(_u74, _u72, _u70), _u72) )).
% 6.29/6.48 cnf(matrix-85, plain, ( ( _u92 != cartesian_product2(_u96, _u94)) | ~in(_u88, _u92) | in(skolem10(_u96, _u94, _u92, _u88), _u96) )).
% 6.29/6.48 cnf(matrix-86, plain, ( ( _u92 != cartesian_product2(_u96, _u94)) | ~in(_u88, _u92) | in(skolem11(_u96, _u94, _u92, _u88), _u94) )).
% 6.29/6.48 cnf(matrix-87, plain, ( ( _u92 != cartesian_product2(_u96, _u94)) | ~in(_u88, _u92) | ( _u88 = ordered_pair(skolem10(_u96, _u94, _u92, _u88), skolem11(_u96, _u94, _u92, _u88))) )).
% 6.29/6.48 cnf(matrix-88, plain, ( ( _u92 != cartesian_product2(_u96, _u94)) | ~in(_u78, _u96) | ~in(_u77, _u94) | ( _u89 != ordered_pair(_u78, _u77)) | in(_u89, _u92) )).
% 6.29/6.48 cnf(matrix-89, plain, ( ( _u93 = cartesian_product2(_u97, _u95)) | in(skolem12(_u97, _u95, _u93), _u93) | in(skolem14(_u97, _u95, _u93), _u97) )).
% 6.29/6.48 cnf(matrix-90, plain, ( ( _u93 = cartesian_product2(_u97, _u95)) | in(skolem12(_u97, _u95, _u93), _u93) | in(skolem15(_u97, _u95, _u93), _u95) )).
% 6.29/6.48 cnf(matrix-91, plain, ( ( _u93 = cartesian_product2(_u97, _u95)) | in(skolem12(_u97, _u95, _u93), _u93) | ( skolem13(_u97, _u95, _u93) = ordered_pair(skolem14(_u97, _u95, _u93), skolem15(_u97, _u95, _u93))) )).
% 6.29/6.48 cnf(matrix-92, plain, ( ( _u93 = cartesian_product2(_u97, _u95)) | in(skolem12(_u97, _u95, _u93), _u93) | ~in(skolem13(_u97, _u95, _u93), _u93) )).
% 6.29/6.48 cnf(matrix-93, plain, ( ( _u93 = cartesian_product2(_u97, _u95)) | ~in(_u81, _u97) | ~in(_u80, _u95) | ( skolem12(_u97, _u95, _u93) != ordered_pair(_u81, _u80)) | in(skolem14(_u97, _u95, _u93), _u97) )).
% 6.29/6.48 cnf(matrix-94, plain, ( ( _u93 = cartesian_product2(_u97, _u95)) | ~in(_u81, _u97) | ~in(_u80, _u95) | ( skolem12(_u97, _u95, _u93) != ordered_pair(_u81, _u80)) | in(skolem15(_u97, _u95, _u93), _u95) )).
% 6.29/6.48 cnf(matrix-95, plain, ( ( _u93 = cartesian_product2(_u97, _u95)) | ~in(_u81, _u97) | ~in(_u80, _u95) | ( skolem12(_u97, _u95, _u93) != ordered_pair(_u81, _u80)) | ( skolem13(_u97, _u95, _u93) = ordered_pair(skolem14(_u97, _u95, _u93), skolem15(_u97, _u95, _u93))) )).
% 6.29/6.48 cnf(matrix-96, plain, ( ( _u93 = cartesian_product2(_u97, _u95)) | ~in(_u81, _u97) | ~in(_u80, _u95) | ( skolem12(_u97, _u95, _u93) != ordered_pair(_u81, _u80)) | ~in(skolem13(_u97, _u95, _u93), _u93) )).
% 6.29/6.48 cnf(matrix-97, plain, ( ~subset(_u104, _u102) | ~in(_u98, _u104) | in(_u98, _u102) )).
% 6.29/6.48 cnf(matrix-98, plain, ( subset(_u105, _u103) | in(skolem16(_u105, _u103), _u105) )).
% 6.29/6.48 cnf(matrix-99, plain, ( subset(_u105, _u103) | ~in(skolem16(_u105, _u103), _u103) )).
% 6.29/6.48 cnf(matrix-100, plain, ( ( _u115 != set_intersection2(_u119, _u117)) | ~in(_u111, _u115) | in(_u111, _u119) )).
% 6.29/6.48 cnf(matrix-101, plain, ( ( _u115 != set_intersection2(_u119, _u117)) | ~in(_u111, _u115) | in(_u111, _u117) )).
% 6.29/6.48 cnf(matrix-102, plain, ( ( _u115 != set_intersection2(_u119, _u117)) | ~in(_u112, _u119) | ~in(_u112, _u117) | in(_u112, _u115) )).
% 6.29/6.48 cnf(matrix-103, plain, ( ( _u116 = set_intersection2(_u120, _u118)) | in(skolem17(_u120, _u118, _u116), _u116) | in(skolem18(_u120, _u118, _u116), _u120) )).
% 6.29/6.48 cnf(matrix-104, plain, ( ( _u116 = set_intersection2(_u120, _u118)) | in(skolem17(_u120, _u118, _u116), _u116) | in(skolem18(_u120, _u118, _u116), _u118) )).
% 6.29/6.48 cnf(matrix-105, plain, ( ( _u116 = set_intersection2(_u120, _u118)) | in(skolem17(_u120, _u118, _u116), _u116) | ~in(skolem18(_u120, _u118, _u116), _u116) )).
% 6.29/6.48 cnf(matrix-106, plain, ( ( _u116 = set_intersection2(_u120, _u118)) | ~in(skolem17(_u120, _u118, _u116), _u120) | ~in(skolem17(_u120, _u118, _u116), _u118) | in(skolem18(_u120, _u118, _u116), _u120) )).
% 6.29/6.48 cnf(matrix-107, plain, ( ( _u116 = set_intersection2(_u120, _u118)) | ~in(skolem17(_u120, _u118, _u116), _u120) | ~in(skolem17(_u120, _u118, _u116), _u118) | in(skolem18(_u120, _u118, _u116), _u118) )).
% 6.29/6.48 cnf(matrix-108, plain, ( ( _u116 = set_intersection2(_u120, _u118)) | ~in(skolem17(_u120, _u118, _u116), _u120) | ~in(skolem17(_u120, _u118, _u116), _u118) | ~in(skolem18(_u120, _u118, _u116), _u116) )).
% 6.29/6.48 cnf(matrix-109, plain, ( ( _u133 != union(_u135)) | ~in(_u129, _u133) | in(_u129, skolem19(_u135, _u133, _u129)) )).
% 6.29/6.48 cnf(matrix-110, plain, ( ( _u133 != union(_u135)) | ~in(_u129, _u133) | in(skolem19(_u135, _u133, _u129), _u135) )).
% 6.29/6.48 cnf(matrix-111, plain, ( ( _u133 != union(_u135)) | ~in(_u130, _u122) | ~in(_u122, _u135) | in(_u130, _u133) )).
% 6.29/6.48 cnf(matrix-112, plain, ( ( _u134 = union(_u136)) | in(skolem20(_u136, _u134), _u134) | in(skolem21(_u136, _u134), skolem22(_u136, _u134)) )).
% 6.29/6.48 cnf(matrix-113, plain, ( ( _u134 = union(_u136)) | in(skolem20(_u136, _u134), _u134) | in(skolem22(_u136, _u134), _u136) )).
% 6.29/6.48 cnf(matrix-114, plain, ( ( _u134 = union(_u136)) | in(skolem20(_u136, _u134), _u134) | ~in(skolem21(_u136, _u134), _u134) )).
% 6.29/6.48 cnf(matrix-115, plain, ( ( _u134 = union(_u136)) | ~in(skolem20(_u136, _u134), _u124) | ~in(_u124, _u136) | in(skolem21(_u136, _u134), skolem22(_u136, _u134)) )).
% 6.29/6.48 cnf(matrix-116, plain, ( ( _u134 = union(_u136)) | ~in(skolem20(_u136, _u134), _u124) | ~in(_u124, _u136) | in(skolem22(_u136, _u134), _u136) )).
% 6.29/6.48 cnf(matrix-117, plain, ( ( _u134 = union(_u136)) | ~in(skolem20(_u136, _u134), _u124) | ~in(_u124, _u136) | ~in(skolem21(_u136, _u134), _u134) )).
% 6.29/6.48 cnf(matrix-118, plain, ( ( _u146 != set_difference(_u150, _u148)) | ~in(_u142, _u146) | in(_u142, _u150) )).
% 6.29/6.48 cnf(matrix-119, plain, ( ( _u146 != set_difference(_u150, _u148)) | ~in(_u142, _u146) | ~in(_u142, _u148) )).
% 6.29/6.48 cnf(matrix-120, plain, ( ( _u146 != set_difference(_u150, _u148)) | ~in(_u143, _u150) | in(_u143, _u148) | in(_u143, _u146) )).
% 6.29/6.48 cnf(matrix-121, plain, ( ( _u147 = set_difference(_u151, _u149)) | in(skolem23(_u151, _u149, _u147), _u147) | in(skolem24(_u151, _u149, _u147), _u151) )).
% 6.29/6.48 cnf(matrix-122, plain, ( ( _u147 = set_difference(_u151, _u149)) | in(skolem23(_u151, _u149, _u147), _u147) | ~in(skolem24(_u151, _u149, _u147), _u149) )).
% 6.29/6.48 cnf(matrix-123, plain, ( ( _u147 = set_difference(_u151, _u149)) | in(skolem23(_u151, _u149, _u147), _u147) | ~in(skolem24(_u151, _u149, _u147), _u147) )).
% 6.29/6.48 cnf(matrix-124, plain, ( ( _u147 = set_difference(_u151, _u149)) | ~in(skolem23(_u151, _u149, _u147), _u151) | in(skolem23(_u151, _u149, _u147), _u149) | in(skolem24(_u151, _u149, _u147), _u151) )).
% 6.29/6.48 cnf(matrix-125, plain, ( ( _u147 = set_difference(_u151, _u149)) | ~in(skolem23(_u151, _u149, _u147), _u151) | in(skolem23(_u151, _u149, _u147), _u149) | ~in(skolem24(_u151, _u149, _u147), _u149) )).
% 6.29/6.48 cnf(matrix-126, plain, ( ( _u147 = set_difference(_u151, _u149)) | ~in(skolem23(_u151, _u149, _u147), _u151) | in(skolem23(_u151, _u149, _u147), _u149) | ~in(skolem24(_u151, _u149, _u147), _u147) )).
% 6.29/6.48 cnf(matrix-127, plain, ( ( ordered_pair(_u153, _u152) = unordered_pair(unordered_pair(_u153, _u152), singleton(_u153))) )).
% 6.29/6.48 cnf(matrix-128, plain, ( ~disjoint(_u158, _u156) | ( set_intersection2(_u158, _u156) = empty_set) )).
% 6.29/6.48 cnf(matrix-129, plain, ( ( set_intersection2(_u159, _u157) != empty_set) | disjoint(_u159, _u157) )).
% 6.29/6.48 cnf(matrix-130, plain, ( ~proper_subset(_u164, _u162) | subset(_u164, _u162) )).
% 6.29/6.48 cnf(matrix-131, plain, ( ~proper_subset(_u164, _u162) | ( _u164 != _u162) )).
% 6.29/6.48 cnf(matrix-132, plain, ( ~subset(_u165, _u163) | ( _u165 = _u163) | proper_subset(_u165, _u163) )).
% 6.29/6.48 cnf(matrix-133, plain, ( empty(empty_set) )).
% 6.29/6.48 cnf(matrix-134, plain, ( ~empty(ordered_pair(_u167, _u166)) )).
% 6.29/6.48 cnf(matrix-135, plain, ( empty(_u169) | ~empty(set_union2(_u169, _u168)) )).
% 6.29/6.48 cnf(matrix-136, plain, ( empty(_u171) | ~empty(set_union2(_u170, _u171)) )).
% 6.29/6.48 cnf(matrix-137, plain, ( ( set_union2(_u173, _u173) = _u173) )).
% 6.29/6.48 cnf(matrix-138, plain, ( ( set_intersection2(_u175, _u175) = _u175) )).
% 6.29/6.48 cnf(matrix-139, plain, ( ~proper_subset(_u177, _u177) )).
% 6.29/6.48 cnf(matrix-140, plain, ( ( singleton(_u178) != empty_set) )).
% 6.29/6.48 cnf(matrix-141, plain, ( ~in(_u180, _u179) | ( set_union2(singleton(_u180), _u179) = _u179) )).
% 6.29/6.48 cnf(matrix-142, plain, ( ~disjoint(singleton(_u182), _u181) | ~in(_u182, _u181) )).
% 6.29/6.48 cnf(matrix-143, plain, ( in(_u184, _u183) | disjoint(singleton(_u184), _u183) )).
% 6.29/6.48 cnf(matrix-144, plain, ( ~subset(singleton(_u189), _u187) | in(_u189, _u187) )).
% 6.29/6.48 cnf(matrix-145, plain, ( ~in(_u190, _u188) | subset(singleton(_u190), _u188) )).
% 6.29/6.48 cnf(matrix-146, plain, ( ( set_difference(_u195, _u193) != empty_set) | subset(_u195, _u193) )).
% 6.29/6.48 cnf(matrix-147, plain, ( ~subset(_u196, _u194) | ( set_difference(_u196, _u194) = empty_set) )).
% 6.29/6.48 cnf(matrix-148, plain, ( ~subset(_u199, _u198) | in(_u197, _u199) | subset(_u199, set_difference(_u198, singleton(_u197))) )).
% 6.29/6.48 cnf(matrix-149, plain, ( ~subset(_u204, singleton(_u202)) | ( _u204 = empty_set) | ( _u204 = singleton(_u202)) )).
% 6.29/6.48 cnf(matrix-150, plain, ( subset(_u205, singleton(_u203)) | ( _u205 != empty_set) )).
% 6.29/6.48 cnf(matrix-151, plain, ( subset(_u205, singleton(_u203)) | ( _u205 != singleton(_u203)) )).
% 6.29/6.48 cnf(matrix-152, plain, ( ~in(_u207, _u206) | subset(_u207, union(_u206)) )).
% 6.29/6.48 cnf(matrix-153, plain, ( ~in(ordered_pair(_u218, _u216), cartesian_product2(_u214, _u212)) | in(_u218, _u214) )).
% 6.29/6.48 cnf(matrix-154, plain, ( ~in(ordered_pair(_u218, _u216), cartesian_product2(_u214, _u212)) | in(_u216, _u212) )).
% 6.29/6.48 cnf(matrix-155, plain, ( ~in(_u219, _u215) | ~in(_u217, _u213) | in(ordered_pair(_u219, _u217), cartesian_product2(_u215, _u213)) )).
% 6.29/6.48 cnf(matrix-156, plain, ( empty(skolem25) )).
% 6.29/6.48 cnf(matrix-157, plain, ( ~empty(skolem26) )).
% 6.29/6.48 cnf(matrix-158, plain, ( subset(_u223, _u223) )).
% 6.29/6.48 cnf(matrix-159, plain, ( ~disjoint(_u225, _u224) | disjoint(_u224, _u225) )).
% 6.29/6.48 cnf(matrix-160, plain, ( ( _u229 = _u227) | ( unordered_pair(_u229, _u228) != unordered_pair(_u227, _u226)) | ( _u229 = _u226) )).
% 6.29/6.48 cnf(matrix-161, plain, ( ~subset(_u231, _u230) | ( set_union2(_u231, _u230) = _u230) )).
% 6.29/6.48 cnf(matrix-162, plain, ( subset(set_intersection2(_u233, _u232), _u233) )).
% 6.29/6.48 cnf(matrix-163, plain, ( ~subset(_u236, _u235) | ~subset(_u236, _u234) | subset(_u236, set_intersection2(_u235, _u234)) )).
% 6.29/6.48 cnf(matrix-164, plain, ( ( set_union2(_u237, empty_set) = _u237) )).
% 6.29/6.48 cnf(matrix-165, plain, ( ~subset(_u240, _u239) | ~subset(_u239, _u238) | subset(_u240, _u238) )).
% 6.29/6.48 cnf(matrix-166, plain, ( ( powerset(empty_set) = singleton(empty_set)) )).
% 6.29/6.48 cnf(matrix-167, plain, ( ~subset(_u243, _u242) | subset(set_intersection2(_u243, _u241), set_intersection2(_u242, _u241)) )).
% 6.29/6.48 cnf(matrix-168, plain, ( ~subset(_u245, _u244) | ( set_intersection2(_u245, _u244) = _u245) )).
% 6.29/6.48 cnf(matrix-169, plain, ( ( set_intersection2(_u246, empty_set) = empty_set) )).
% 6.29/6.48 cnf(matrix-170, plain, ( ( _u249 = _u248) | in(skolem27(_u249, _u248), _u249) | in(skolem28(_u249, _u248), _u248) )).
% 6.29/6.48 cnf(matrix-171, plain, ( ( _u249 = _u248) | in(skolem27(_u249, _u248), _u249) | ~in(skolem28(_u249, _u248), _u249) )).
% 6.29/6.48 cnf(matrix-172, plain, ( ( _u249 = _u248) | ~in(skolem27(_u249, _u248), _u248) | in(skolem28(_u249, _u248), _u248) )).
% 6.29/6.48 cnf(matrix-173, plain, ( ( _u249 = _u248) | ~in(skolem27(_u249, _u248), _u248) | ~in(skolem28(_u249, _u248), _u249) )).
% 6.29/6.48 cnf(matrix-174, plain, ( subset(empty_set, _u252) )).
% 6.29/6.48 cnf(matrix-175, plain, ( ~subset(_u255, _u254) | subset(set_difference(_u255, _u253), set_difference(_u254, _u253)) )).
% 6.29/6.48 cnf(matrix-176, plain, ( ( ordered_pair(_u259, _u258) != ordered_pair(_u257, _u256)) | ( _u259 = _u257) )).
% 6.29/6.48 cnf(matrix-177, plain, ( ( ordered_pair(_u259, _u258) != ordered_pair(_u257, _u256)) | ( _u258 = _u256) )).
% 6.29/6.48 cnf(matrix-178, plain, ( subset(set_difference(_u261, _u260), _u261) )).
% 6.29/6.48 cnf(matrix-179, plain, ( ( set_difference(_u266, _u264) != empty_set) | subset(_u266, _u264) )).
% 6.29/6.48 cnf(matrix-180, plain, ( ~subset(_u267, _u265) | ( set_difference(_u267, _u265) = empty_set) )).
% 6.29/6.48 cnf(matrix-181, plain, ( ~subset(singleton(_u272), _u270) | in(_u272, _u270) )).
% 6.29/6.48 cnf(matrix-182, plain, ( ~in(_u273, _u271) | subset(singleton(_u273), _u271) )).
% 6.29/6.48 cnf(matrix-183, plain, ( ~subset(unordered_pair(_u281, _u279), _u277) | in(_u281, _u277) )).
% 6.29/6.48 cnf(matrix-184, plain, ( ~subset(unordered_pair(_u281, _u279), _u277) | in(_u279, _u277) )).
% 6.29/6.48 cnf(matrix-185, plain, ( ~in(_u282, _u278) | ~in(_u280, _u278) | subset(unordered_pair(_u282, _u280), _u278) )).
% 6.29/6.48 cnf(matrix-186, plain, ( ( set_union2(_u284, set_difference(_u283, _u284)) = set_union2(_u284, _u283)) )).
% 6.29/6.48 cnf(matrix-187, plain, ( ~subset(_u289, singleton(_u287)) | ( _u289 = empty_set) | ( _u289 = singleton(_u287)) )).
% 6.29/6.48 cnf(matrix-188, plain, ( subset(_u290, singleton(_u288)) | ( _u290 != empty_set) )).
% 6.29/6.48 cnf(matrix-189, plain, ( subset(_u290, singleton(_u288)) | ( _u290 != singleton(_u288)) )).
% 6.29/6.48 cnf(matrix-190, plain, ( ( set_difference(_u291, empty_set) = _u291) )).
% 6.29/6.48 cnf(matrix-191, plain, ( disjoint(_u298, _u296) | in(skolem29(_u298, _u296), _u298) )).
% 6.29/6.48 cnf(matrix-192, plain, ( disjoint(_u298, _u296) | in(skolem29(_u298, _u296), _u296) )).
% 6.29/6.48 cnf(matrix-193, plain, ( ~in(_u293, _u299) | ~in(_u293, _u297) | ~disjoint(_u299, _u297) )).
% 6.29/6.48 cnf(matrix-194, plain, ( ~subset(_u300, empty_set) | ( _u300 = empty_set) )).
% 6.29/6.48 cnf(matrix-195, plain, ( ( set_difference(set_union2(_u302, _u301), _u301) = set_difference(_u302, _u301)) )).
% 6.29/6.48 cnf(matrix-196, plain, ( ~subset(_u304, _u303) | ( _u303 = set_union2(_u304, set_difference(_u303, _u304))) )).
% 6.29/6.48 cnf(matrix-197, plain, ( ~in(_u306, _u305) | ( set_union2(singleton(_u306), _u305) = _u305) )).
% 6.29/6.48 cnf(matrix-198, plain, ( ( set_difference(_u308, set_difference(_u308, _u307)) = set_intersection2(_u308, _u307)) )).
% 6.29/6.48 cnf(matrix-199, plain, ( ( set_difference(empty_set, _u309) = empty_set) )).
% 6.29/6.48 cnf(matrix-200, plain, ( disjoint(_u316, _u314) | in(skolem30(_u316, _u314), set_intersection2(_u316, _u314)) )).
% 6.29/6.48 cnf(matrix-201, plain, ( ~in(_u311, set_intersection2(_u317, _u315)) | ~disjoint(_u317, _u315) )).
% 6.29/6.48 cnf(matrix-202, plain, ( ~subset(_u319, _u318) | ~proper_subset(_u318, _u319) )).
% 6.29/6.48 cnf(matrix-203, plain, ( ~subset(_u322, _u321) | ~disjoint(_u321, _u320) | disjoint(_u322, _u320) )).
% 6.29/6.48 cnf(matrix-204, plain, ( ( set_difference(_u327, singleton(_u325)) != _u327) | ~in(_u325, _u327) )).
% 6.29/6.48 cnf(matrix-205, plain, ( in(_u326, _u328) | ( set_difference(_u328, singleton(_u326)) = _u328) )).
% 6.29/6.48 cnf(matrix-206, plain, ( ( unordered_pair(_u329, _u329) = singleton(_u329)) )).
% 6.29/6.48 cnf(matrix-207, plain, ( ~empty(_u330) | ( _u330 = empty_set) )).
% 6.29/6.48 cnf(matrix-208, plain, ( ~subset(singleton(_u332), singleton(_u331)) | ( _u332 = _u331) )).
% 6.29/6.48 cnf(matrix-209, plain, ( ~in(_u334, _u333) | ~empty(_u333) )).
% 6.29/6.48 cnf(matrix-210, plain, ( subset(_u336, set_union2(_u336, _u335)) )).
% 6.29/6.48 cnf(matrix-211, plain, ( ~disjoint(_u341, _u339) | ( set_difference(_u341, _u339) = _u341) )).
% 6.29/6.48 cnf(matrix-212, plain, ( ( set_difference(_u342, _u340) != _u342) | disjoint(_u342, _u340) )).
% 6.29/6.48 cnf(matrix-213, plain, ( ~empty(_u344) | ( _u344 = _u343) | ~empty(_u343) )).
% 6.29/6.48 cnf(matrix-214, plain, ( ~subset(_u347, _u346) | ~subset(_u345, _u346) | subset(set_union2(_u347, _u345), _u346) )).
% 6.29/6.48 cnf(matrix-215, plain, ( ( _u350 = _u349) | ( singleton(_u350) != unordered_pair(_u349, _u348)) )).
% 6.29/6.48 cnf(matrix-216, plain, ( in(skolem31, skolem32) )).
% 6.29/6.48 cnf(matrix-217, plain, ( ~subset(skolem31, union(skolem32)) )).
% 6.29/6.48 cnf(matrix-218, plain, ( ( singleton(_u355) != unordered_pair(_u354, _u353)) | ( _u354 = _u353) )).
% 6.29/6.48
% 6.29/6.48 % Proof stack:
% 6.29/6.48 cnf(proof-stack, plain,
% 6.29/6.48 proof_stack(
% 6.29/6.48 start(217),
% 6.29/6.48 left_branch(0, 152, 1, 2),
% 6.29/6.48 left_branch(0, 216, 0, 3),
% 6.29/6.48 right_branch(3),
% 6.29/6.48 right_branch(2)
% 6.29/6.48 )).
% 6.29/6.48 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------