%------------------------------------------------------------------------------
% File     : ConnectPP---0.3.0
% Problem  : SEU152+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 : n021.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 : Mon Mar 25 14:33:19 EDT 2024

% Result   : Theorem 12.41s 12.60s
% Output   : Proof 12.41s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14  % Problem  : SEU152+2 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.15  % Command  : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.15/0.37  % Computer : n021.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Wed Mar 20 14:40:18 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 12.41/12.60  % SZS status Theorem for theBenchmark
% 12.41/12.60  % SZS output start Proof for theBenchmark
% 12.41/12.60  
% 12.41/12.60  % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 12.41/12.60  cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: antisymmetry_r2_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(antisymmetry_r2_xboole_0-1, axiom, ( ~proper_subset(_u3, _u2) | ~proper_subset(_u2, _u3) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 12.41/12.60  cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u5, _u4) = unordered_pair(_u4, _u5)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u7, _u6) = set_union2(_u6, _u7)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: commutativity_k3_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(commutativity_k3_xboole_0-1, axiom, ( ( set_intersection2(_u9, _u8) = set_intersection2(_u8, _u9)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: d10_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(d10_xboole_0-1, axiom, ( ( _u14 != _u12) | subset(_u14, _u12) )).
% 12.41/12.60  cnf(d10_xboole_0-2, axiom, ( ( _u14 != _u12) | subset(_u12, _u14) )).
% 12.41/12.60  cnf(d10_xboole_0-3, axiom, ( ~subset(_u15, _u13) | ~subset(_u13, _u15) | ( _u15 = _u13) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: d1_tarski ( axiom ) converted to clauses:
% 12.41/12.60  cnf(d1_tarski-1, axiom, ( ( _u24 != singleton(_u26)) | ~in(_u20, _u24) | ( _u20 = _u26) )).
% 12.41/12.60  cnf(d1_tarski-2, axiom, ( ( _u24 != singleton(_u26)) | ( _u21 != _u26) | in(_u21, _u24) )).
% 12.41/12.60  cnf(d1_tarski-3, axiom, ( ( _u25 = singleton(_u27)) | in(skolem1(_u27, _u25), _u25) | ( skolem2(_u27, _u25) = _u27) )).
% 12.41/12.60  cnf(d1_tarski-4, axiom, ( ( _u25 = singleton(_u27)) | in(skolem1(_u27, _u25), _u25) | ~in(skolem2(_u27, _u25), _u25) )).
% 12.41/12.60  cnf(d1_tarski-5, axiom, ( ( _u25 = singleton(_u27)) | ( skolem1(_u27, _u25) != _u27) | ( skolem2(_u27, _u25) = _u27) )).
% 12.41/12.60  cnf(d1_tarski-6, axiom, ( ( _u25 = singleton(_u27)) | ( skolem1(_u27, _u25) != _u27) | ~in(skolem2(_u27, _u25), _u25) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: d1_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(d1_xboole_0-1, axiom, ( ( _u31 != empty_set) | ~in(_u28, _u31) )).
% 12.41/12.60  cnf(d1_xboole_0-2, axiom, ( in(skolem3(_u32), _u32) | ( _u32 = empty_set) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: d1_zfmisc_1 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(d1_zfmisc_1-1, axiom, ( ( _u41 != powerset(_u43)) | ~in(_u37, _u41) | subset(_u37, _u43) )).
% 12.41/12.60  cnf(d1_zfmisc_1-2, axiom, ( ( _u41 != powerset(_u43)) | ~subset(_u38, _u43) | in(_u38, _u41) )).
% 12.41/12.60  cnf(d1_zfmisc_1-3, axiom, ( ( _u42 = powerset(_u44)) | in(skolem4(_u44, _u42), _u42) | subset(skolem5(_u44, _u42), _u44) )).
% 12.41/12.60  cnf(d1_zfmisc_1-4, axiom, ( ( _u42 = powerset(_u44)) | in(skolem4(_u44, _u42), _u42) | ~in(skolem5(_u44, _u42), _u42) )).
% 12.41/12.60  cnf(d1_zfmisc_1-5, axiom, ( ( _u42 = powerset(_u44)) | ~subset(skolem4(_u44, _u42), _u44) | subset(skolem5(_u44, _u42), _u44) )).
% 12.41/12.60  cnf(d1_zfmisc_1-6, axiom, ( ( _u42 = powerset(_u44)) | ~subset(skolem4(_u44, _u42), _u44) | ~in(skolem5(_u44, _u42), _u42) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: d2_tarski ( axiom ) converted to clauses:
% 12.41/12.60  cnf(d2_tarski-1, axiom, ( ( _u54 != unordered_pair(_u58, _u56)) | ~in(_u50, _u54) | ( _u50 = _u58) | ( _u50 = _u56) )).
% 12.41/12.60  cnf(d2_tarski-2, axiom, ( ( _u54 != unordered_pair(_u58, _u56)) | in(_u51, _u54) | ( _u51 != _u58) )).
% 12.41/12.60  cnf(d2_tarski-3, axiom, ( ( _u54 != unordered_pair(_u58, _u56)) | in(_u51, _u54) | ( _u51 != _u56) )).
% 12.41/12.60  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) )).
% 12.41/12.60  cnf(d2_tarski-5, axiom, ( ( _u55 = unordered_pair(_u59, _u57)) | in(skolem6(_u59, _u57, _u55), _u55) | ~in(skolem7(_u59, _u57, _u55), _u55) )).
% 12.41/12.60  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) )).
% 12.41/12.60  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) )).
% 12.41/12.60  cnf(d2_tarski-8, axiom, ( ( _u55 = unordered_pair(_u59, _u57)) | ~in(skolem7(_u59, _u57, _u55), _u55) | ( skolem6(_u59, _u57, _u55) != _u59) )).
% 12.41/12.60  cnf(d2_tarski-9, axiom, ( ( _u55 = unordered_pair(_u59, _u57)) | ~in(skolem7(_u59, _u57, _u55), _u55) | ( skolem6(_u59, _u57, _u55) != _u57) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: d2_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(d2_xboole_0-1, axiom, ( ( _u69 != set_union2(_u73, _u71)) | ~in(_u65, _u69) | in(_u65, _u73) | in(_u65, _u71) )).
% 12.41/12.60  cnf(d2_xboole_0-2, axiom, ( ( _u69 != set_union2(_u73, _u71)) | in(_u66, _u69) | ~in(_u66, _u73) )).
% 12.41/12.60  cnf(d2_xboole_0-3, axiom, ( ( _u69 != set_union2(_u73, _u71)) | in(_u66, _u69) | ~in(_u66, _u71) )).
% 12.41/12.60  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) )).
% 12.41/12.60  cnf(d2_xboole_0-5, axiom, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem8(_u74, _u72, _u70), _u70) | ~in(skolem9(_u74, _u72, _u70), _u70) )).
% 12.41/12.60  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) )).
% 12.41/12.60  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) )).
% 12.41/12.60  cnf(d2_xboole_0-8, axiom, ( ( _u70 = set_union2(_u74, _u72)) | ~in(skolem9(_u74, _u72, _u70), _u70) | ~in(skolem8(_u74, _u72, _u70), _u74) )).
% 12.41/12.60  cnf(d2_xboole_0-9, axiom, ( ( _u70 = set_union2(_u74, _u72)) | ~in(skolem9(_u74, _u72, _u70), _u70) | ~in(skolem8(_u74, _u72, _u70), _u72) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: d3_tarski ( axiom ) converted to clauses:
% 12.41/12.60  cnf(d3_tarski-1, axiom, ( ~subset(_u81, _u79) | ~in(_u75, _u81) | in(_u75, _u79) )).
% 12.41/12.60  cnf(d3_tarski-2, axiom, ( subset(_u82, _u80) | in(skolem10(_u82, _u80), _u82) )).
% 12.41/12.60  cnf(d3_tarski-3, axiom, ( subset(_u82, _u80) | ~in(skolem10(_u82, _u80), _u80) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: d3_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(d3_xboole_0-1, axiom, ( ( _u92 != set_intersection2(_u96, _u94)) | ~in(_u88, _u92) | in(_u88, _u96) )).
% 12.41/12.60  cnf(d3_xboole_0-2, axiom, ( ( _u92 != set_intersection2(_u96, _u94)) | ~in(_u88, _u92) | in(_u88, _u94) )).
% 12.41/12.60  cnf(d3_xboole_0-3, axiom, ( ( _u92 != set_intersection2(_u96, _u94)) | ~in(_u89, _u96) | ~in(_u89, _u94) | in(_u89, _u92) )).
% 12.41/12.60  cnf(d3_xboole_0-4, axiom, ( ( _u93 = set_intersection2(_u97, _u95)) | in(skolem11(_u97, _u95, _u93), _u93) | in(skolem12(_u97, _u95, _u93), _u97) )).
% 12.41/12.60  cnf(d3_xboole_0-5, axiom, ( ( _u93 = set_intersection2(_u97, _u95)) | in(skolem11(_u97, _u95, _u93), _u93) | in(skolem12(_u97, _u95, _u93), _u95) )).
% 12.41/12.60  cnf(d3_xboole_0-6, axiom, ( ( _u93 = set_intersection2(_u97, _u95)) | in(skolem11(_u97, _u95, _u93), _u93) | ~in(skolem12(_u97, _u95, _u93), _u93) )).
% 12.41/12.60  cnf(d3_xboole_0-7, axiom, ( ( _u93 = set_intersection2(_u97, _u95)) | ~in(skolem11(_u97, _u95, _u93), _u97) | ~in(skolem11(_u97, _u95, _u93), _u95) | in(skolem12(_u97, _u95, _u93), _u97) )).
% 12.41/12.60  cnf(d3_xboole_0-8, axiom, ( ( _u93 = set_intersection2(_u97, _u95)) | ~in(skolem11(_u97, _u95, _u93), _u97) | ~in(skolem11(_u97, _u95, _u93), _u95) | in(skolem12(_u97, _u95, _u93), _u95) )).
% 12.41/12.60  cnf(d3_xboole_0-9, axiom, ( ( _u93 = set_intersection2(_u97, _u95)) | ~in(skolem11(_u97, _u95, _u93), _u97) | ~in(skolem11(_u97, _u95, _u93), _u95) | ~in(skolem12(_u97, _u95, _u93), _u93) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: d4_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(d4_xboole_0-1, axiom, ( ( _u107 != set_difference(_u111, _u109)) | ~in(_u103, _u107) | in(_u103, _u111) )).
% 12.41/12.60  cnf(d4_xboole_0-2, axiom, ( ( _u107 != set_difference(_u111, _u109)) | ~in(_u103, _u107) | ~in(_u103, _u109) )).
% 12.41/12.60  cnf(d4_xboole_0-3, axiom, ( ( _u107 != set_difference(_u111, _u109)) | ~in(_u104, _u111) | in(_u104, _u109) | in(_u104, _u107) )).
% 12.41/12.60  cnf(d4_xboole_0-4, axiom, ( ( _u108 = set_difference(_u112, _u110)) | in(skolem13(_u112, _u110, _u108), _u108) | in(skolem14(_u112, _u110, _u108), _u112) )).
% 12.41/12.60  cnf(d4_xboole_0-5, axiom, ( ( _u108 = set_difference(_u112, _u110)) | in(skolem13(_u112, _u110, _u108), _u108) | ~in(skolem14(_u112, _u110, _u108), _u110) )).
% 12.41/12.60  cnf(d4_xboole_0-6, axiom, ( ( _u108 = set_difference(_u112, _u110)) | in(skolem13(_u112, _u110, _u108), _u108) | ~in(skolem14(_u112, _u110, _u108), _u108) )).
% 12.41/12.60  cnf(d4_xboole_0-7, axiom, ( ( _u108 = set_difference(_u112, _u110)) | ~in(skolem13(_u112, _u110, _u108), _u112) | in(skolem13(_u112, _u110, _u108), _u110) | in(skolem14(_u112, _u110, _u108), _u112) )).
% 12.41/12.60  cnf(d4_xboole_0-8, axiom, ( ( _u108 = set_difference(_u112, _u110)) | ~in(skolem13(_u112, _u110, _u108), _u112) | in(skolem13(_u112, _u110, _u108), _u110) | ~in(skolem14(_u112, _u110, _u108), _u110) )).
% 12.41/12.60  cnf(d4_xboole_0-9, axiom, ( ( _u108 = set_difference(_u112, _u110)) | ~in(skolem13(_u112, _u110, _u108), _u112) | in(skolem13(_u112, _u110, _u108), _u110) | ~in(skolem14(_u112, _u110, _u108), _u108) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: d7_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(d7_xboole_0-1, axiom, ( ~disjoint(_u117, _u115) | ( set_intersection2(_u117, _u115) = empty_set) )).
% 12.41/12.60  cnf(d7_xboole_0-2, axiom, ( ( set_intersection2(_u118, _u116) != empty_set) | disjoint(_u118, _u116) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: d8_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(d8_xboole_0-1, axiom, ( ~proper_subset(_u123, _u121) | subset(_u123, _u121) )).
% 12.41/12.60  cnf(d8_xboole_0-2, axiom, ( ~proper_subset(_u123, _u121) | ( _u123 != _u121) )).
% 12.41/12.60  cnf(d8_xboole_0-3, axiom, ( ~subset(_u124, _u122) | ( _u124 = _u122) | proper_subset(_u124, _u122) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: dt_k1_tarski ( axiom ) converted to clauses:
% 12.41/12.60  cnf(dt_k1_tarski, axiom, $true).
% 12.41/12.60  
% 12.41/12.60  % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(dt_k1_xboole_0, axiom, $true).
% 12.41/12.60  
% 12.41/12.60  % Formula: dt_k1_zfmisc_1 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(dt_k1_zfmisc_1, axiom, $true).
% 12.41/12.60  
% 12.41/12.60  % Formula: dt_k2_tarski ( axiom ) converted to clauses:
% 12.41/12.60  cnf(dt_k2_tarski, axiom, $true).
% 12.41/12.60  
% 12.41/12.60  % Formula: dt_k2_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(dt_k2_xboole_0, axiom, $true).
% 12.41/12.60  
% 12.41/12.60  % Formula: dt_k3_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(dt_k3_xboole_0, axiom, $true).
% 12.41/12.60  
% 12.41/12.60  % Formula: dt_k4_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(dt_k4_xboole_0, axiom, $true).
% 12.41/12.60  
% 12.41/12.60  % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(fc2_xboole_0-1, axiom, ( empty(_u126) | ~empty(set_union2(_u126, _u125)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(fc3_xboole_0-1, axiom, ( empty(_u128) | ~empty(set_union2(_u127, _u128)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u130, _u130) = _u130) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: idempotence_k3_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(idempotence_k3_xboole_0-1, axiom, ( ( set_intersection2(_u132, _u132) = _u132) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: irreflexivity_r2_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(irreflexivity_r2_xboole_0-1, axiom, ( ~proper_subset(_u134, _u134) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: l1_zfmisc_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(l1_zfmisc_1-1, lemma, ( ( singleton(_u135) != empty_set) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: l23_zfmisc_1 ( conjecture ) (definitionally) converted to clauses:
% 12.41/12.60  cnf(l23_zfmisc_1-1, negated_conjecture, ( in(skolem15, skolem16) )).
% 12.41/12.60  cnf(l23_zfmisc_1-2, negated_conjecture, ( ( set_union2(singleton(skolem15), skolem16) != skolem16) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: l2_zfmisc_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(l2_zfmisc_1-1, lemma, ( ~subset(singleton(_u142), _u140) | in(_u142, _u140) )).
% 12.41/12.60  cnf(l2_zfmisc_1-2, lemma, ( ~in(_u143, _u141) | subset(singleton(_u143), _u141) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: l32_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(l32_xboole_1-1, lemma, ( ( set_difference(_u148, _u146) != empty_set) | subset(_u148, _u146) )).
% 12.41/12.60  cnf(l32_xboole_1-2, lemma, ( ~subset(_u149, _u147) | ( set_difference(_u149, _u147) = empty_set) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: l3_zfmisc_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(l3_zfmisc_1-1, lemma, ( ~subset(_u152, _u151) | in(_u150, _u152) | subset(_u152, set_difference(_u151, singleton(_u150))) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: l4_zfmisc_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(l4_zfmisc_1-1, lemma, ( ~subset(_u157, singleton(_u155)) | ( _u157 = empty_set) | ( _u157 = singleton(_u155)) )).
% 12.41/12.60  cnf(l4_zfmisc_1-2, lemma, ( subset(_u158, singleton(_u156)) | ( _u158 != empty_set) )).
% 12.41/12.60  cnf(l4_zfmisc_1-3, lemma, ( subset(_u158, singleton(_u156)) | ( _u158 != singleton(_u156)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(rc1_xboole_0-1, axiom, ( empty(skolem17) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem18) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 12.41/12.60  cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u162, _u162) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: symmetry_r1_xboole_0 ( axiom ) converted to clauses:
% 12.41/12.60  cnf(symmetry_r1_xboole_0-1, axiom, ( ~disjoint(_u164, _u163) | disjoint(_u163, _u164) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t10_zfmisc_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t10_zfmisc_1-1, lemma, ( ( _u168 = _u166) | ( unordered_pair(_u168, _u167) != unordered_pair(_u166, _u165)) | ( _u168 = _u165) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t12_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t12_xboole_1-1, lemma, ( ~subset(_u170, _u169) | ( set_union2(_u170, _u169) = _u169) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t17_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t17_xboole_1-1, lemma, ( subset(set_intersection2(_u172, _u171), _u172) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t19_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t19_xboole_1-1, lemma, ( ~subset(_u175, _u174) | ~subset(_u175, _u173) | subset(_u175, set_intersection2(_u174, _u173)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t1_boole ( axiom ) converted to clauses:
% 12.41/12.60  cnf(t1_boole-1, axiom, ( ( set_union2(_u176, empty_set) = _u176) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t1_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t1_xboole_1-1, lemma, ( ~subset(_u179, _u178) | ~subset(_u178, _u177) | subset(_u179, _u177) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t1_zfmisc_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t1_zfmisc_1-1, lemma, ( ( powerset(empty_set) = singleton(empty_set)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t26_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t26_xboole_1-1, lemma, ( ~subset(_u182, _u181) | subset(set_intersection2(_u182, _u180), set_intersection2(_u181, _u180)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t28_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t28_xboole_1-1, lemma, ( ~subset(_u184, _u183) | ( set_intersection2(_u184, _u183) = _u184) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t2_boole ( axiom ) converted to clauses:
% 12.41/12.60  cnf(t2_boole-1, axiom, ( ( set_intersection2(_u185, empty_set) = empty_set) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t2_tarski ( axiom ) converted to clauses:
% 12.41/12.60  cnf(t2_tarski-1, axiom, ( ( _u188 = _u187) | in(skolem19(_u188, _u187), _u188) | in(skolem20(_u188, _u187), _u187) )).
% 12.41/12.60  cnf(t2_tarski-2, axiom, ( ( _u188 = _u187) | in(skolem19(_u188, _u187), _u188) | ~in(skolem20(_u188, _u187), _u188) )).
% 12.41/12.60  cnf(t2_tarski-3, axiom, ( ( _u188 = _u187) | ~in(skolem19(_u188, _u187), _u187) | in(skolem20(_u188, _u187), _u187) )).
% 12.41/12.60  cnf(t2_tarski-4, axiom, ( ( _u188 = _u187) | ~in(skolem19(_u188, _u187), _u187) | ~in(skolem20(_u188, _u187), _u188) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t2_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t2_xboole_1-1, lemma, ( subset(empty_set, _u191) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t33_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t33_xboole_1-1, lemma, ( ~subset(_u194, _u193) | subset(set_difference(_u194, _u192), set_difference(_u193, _u192)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t36_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t36_xboole_1-1, lemma, ( subset(set_difference(_u196, _u195), _u196) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t37_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t37_xboole_1-1, lemma, ( ( set_difference(_u201, _u199) != empty_set) | subset(_u201, _u199) )).
% 12.41/12.60  cnf(t37_xboole_1-2, lemma, ( ~subset(_u202, _u200) | ( set_difference(_u202, _u200) = empty_set) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t39_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t39_xboole_1-1, lemma, ( ( set_union2(_u204, set_difference(_u203, _u204)) = set_union2(_u204, _u203)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t3_boole ( axiom ) converted to clauses:
% 12.41/12.60  cnf(t3_boole-1, axiom, ( ( set_difference(_u205, empty_set) = _u205) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t3_xboole_0 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t3_xboole_0-1, lemma, ( disjoint(_u212, _u210) | in(skolem21(_u212, _u210), _u212) )).
% 12.41/12.60  cnf(t3_xboole_0-2, lemma, ( disjoint(_u212, _u210) | in(skolem21(_u212, _u210), _u210) )).
% 12.41/12.60  cnf(t3_xboole_0-3, lemma, ( ~in(_u207, _u213) | ~in(_u207, _u211) | ~disjoint(_u213, _u211) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t3_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t3_xboole_1-1, lemma, ( ~subset(_u214, empty_set) | ( _u214 = empty_set) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t40_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t40_xboole_1-1, lemma, ( ( set_difference(set_union2(_u216, _u215), _u215) = set_difference(_u216, _u215)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t45_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t45_xboole_1-1, lemma, ( ~subset(_u218, _u217) | ( _u217 = set_union2(_u218, set_difference(_u217, _u218))) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t48_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t48_xboole_1-1, lemma, ( ( set_difference(_u220, set_difference(_u220, _u219)) = set_intersection2(_u220, _u219)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t4_boole ( axiom ) converted to clauses:
% 12.41/12.60  cnf(t4_boole-1, axiom, ( ( set_difference(empty_set, _u221) = empty_set) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t4_xboole_0 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t4_xboole_0-1, lemma, ( disjoint(_u228, _u226) | in(skolem22(_u228, _u226), set_intersection2(_u228, _u226)) )).
% 12.41/12.60  cnf(t4_xboole_0-2, lemma, ( ~in(_u223, set_intersection2(_u229, _u227)) | ~disjoint(_u229, _u227) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t60_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t60_xboole_1-1, lemma, ( ~subset(_u231, _u230) | ~proper_subset(_u230, _u231) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t63_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t63_xboole_1-1, lemma, ( ~subset(_u234, _u233) | ~disjoint(_u233, _u232) | disjoint(_u234, _u232) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t69_enumset1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t69_enumset1-1, lemma, ( ( unordered_pair(_u235, _u235) = singleton(_u235)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t6_boole ( axiom ) converted to clauses:
% 12.41/12.60  cnf(t6_boole-1, axiom, ( ~empty(_u236) | ( _u236 = empty_set) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t6_zfmisc_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t6_zfmisc_1-1, lemma, ( ~subset(singleton(_u238), singleton(_u237)) | ( _u238 = _u237) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t7_boole ( axiom ) converted to clauses:
% 12.41/12.60  cnf(t7_boole-1, axiom, ( ~in(_u240, _u239) | ~empty(_u239) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t7_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t7_xboole_1-1, lemma, ( subset(_u242, set_union2(_u242, _u241)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t83_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t83_xboole_1-1, lemma, ( ~disjoint(_u247, _u245) | ( set_difference(_u247, _u245) = _u247) )).
% 12.41/12.60  cnf(t83_xboole_1-2, lemma, ( ( set_difference(_u248, _u246) != _u248) | disjoint(_u248, _u246) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t8_boole ( axiom ) converted to clauses:
% 12.41/12.60  cnf(t8_boole-1, axiom, ( ~empty(_u250) | ( _u250 = _u249) | ~empty(_u249) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t8_xboole_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t8_xboole_1-1, lemma, ( ~subset(_u253, _u252) | ~subset(_u251, _u252) | subset(set_union2(_u253, _u251), _u252) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t8_zfmisc_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t8_zfmisc_1-1, lemma, ( ( _u256 = _u255) | ( singleton(_u256) != unordered_pair(_u255, _u254)) )).
% 12.41/12.60  
% 12.41/12.60  % Formula: t9_zfmisc_1 ( lemma ) converted to clauses:
% 12.41/12.60  cnf(t9_zfmisc_1-1, lemma, ( ( singleton(_u259) != unordered_pair(_u258, _u257)) | ( _u258 = _u257) )).
% 12.41/12.60  
% 12.41/12.60  % Problem matrix:
% 12.41/12.60  cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 12.41/12.60  cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 12.41/12.60  cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 12.41/12.60  cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 12.41/12.60  cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 12.41/12.60  cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_intersection2(__eqx_0, __eqx_1) = set_intersection2(__eqy_0, __eqy_1)) )).
% 12.41/12.60  cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 12.41/12.60  cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 12.41/12.60  cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_difference(__eqx_0, __eqx_1) = set_difference(__eqy_0, __eqy_1)) )).
% 12.41/12.60  cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 12.41/12.60  cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 12.41/12.60  cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( skolem3(__eqx_0) = skolem3(__eqy_0)) )).
% 12.41/12.60  cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 12.41/12.60  cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem5(__eqx_0, __eqx_1) = skolem5(__eqy_0, __eqy_1)) )).
% 12.41/12.60  cnf(matrix-14, 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)) )).
% 12.41/12.60  cnf(matrix-15, 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)) )).
% 12.41/12.60  cnf(matrix-16, 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)) )).
% 12.41/12.60  cnf(matrix-17, 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)) )).
% 12.41/12.60  cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem10(__eqx_0, __eqx_1) = skolem10(__eqy_0, __eqy_1)) )).
% 12.41/12.60  cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem11(__eqx_0, __eqx_1, __eqx_2) = skolem11(__eqy_0, __eqy_1, __eqy_2)) )).
% 12.41/12.60  cnf(matrix-20, 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)) )).
% 12.41/12.60  cnf(matrix-21, 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)) )).
% 12.41/12.60  cnf(matrix-22, 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)) )).
% 12.41/12.60  cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem19(__eqx_0, __eqx_1) = skolem19(__eqy_0, __eqy_1)) )).
% 12.41/12.60  cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem20(__eqx_0, __eqx_1) = skolem20(__eqy_0, __eqy_1)) )).
% 12.41/12.60  cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem21(__eqx_0, __eqx_1) = skolem21(__eqy_0, __eqy_1)) )).
% 12.41/12.60  cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem22(__eqx_0, __eqx_1) = skolem22(__eqy_0, __eqy_1)) )).
% 12.41/12.60  cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 12.41/12.60  cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~proper_subset(__eqx_0, __eqx_1) | proper_subset(__eqy_0, __eqy_1) )).
% 12.41/12.60  cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 12.41/12.60  cnf(matrix-30, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~disjoint(__eqx_0, __eqx_1) | disjoint(__eqy_0, __eqy_1) )).
% 12.41/12.60  cnf(matrix-31, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 12.41/12.60  cnf(matrix-32, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 12.41/12.60  cnf(matrix-33, plain, ( ~proper_subset(_u3, _u2) | ~proper_subset(_u2, _u3) )).
% 12.41/12.60  cnf(matrix-34, plain, ( ( unordered_pair(_u5, _u4) = unordered_pair(_u4, _u5)) )).
% 12.41/12.60  cnf(matrix-35, plain, ( ( set_union2(_u7, _u6) = set_union2(_u6, _u7)) )).
% 12.41/12.60  cnf(matrix-36, plain, ( ( set_intersection2(_u9, _u8) = set_intersection2(_u8, _u9)) )).
% 12.41/12.60  cnf(matrix-37, plain, ( ( _u14 != _u12) | subset(_u14, _u12) )).
% 12.41/12.60  cnf(matrix-38, plain, ( ( _u14 != _u12) | subset(_u12, _u14) )).
% 12.41/12.60  cnf(matrix-39, plain, ( ~subset(_u15, _u13) | ~subset(_u13, _u15) | ( _u15 = _u13) )).
% 12.41/12.60  cnf(matrix-40, plain, ( ( _u24 != singleton(_u26)) | ~in(_u20, _u24) | ( _u20 = _u26) )).
% 12.41/12.60  cnf(matrix-41, plain, ( ( _u24 != singleton(_u26)) | ( _u21 != _u26) | in(_u21, _u24) )).
% 12.41/12.60  cnf(matrix-42, plain, ( ( _u25 = singleton(_u27)) | in(skolem1(_u27, _u25), _u25) | ( skolem2(_u27, _u25) = _u27) )).
% 12.41/12.60  cnf(matrix-43, plain, ( ( _u25 = singleton(_u27)) | in(skolem1(_u27, _u25), _u25) | ~in(skolem2(_u27, _u25), _u25) )).
% 12.41/12.60  cnf(matrix-44, plain, ( ( _u25 = singleton(_u27)) | ( skolem1(_u27, _u25) != _u27) | ( skolem2(_u27, _u25) = _u27) )).
% 12.41/12.60  cnf(matrix-45, plain, ( ( _u25 = singleton(_u27)) | ( skolem1(_u27, _u25) != _u27) | ~in(skolem2(_u27, _u25), _u25) )).
% 12.41/12.60  cnf(matrix-46, plain, ( ( _u31 != empty_set) | ~in(_u28, _u31) )).
% 12.41/12.60  cnf(matrix-47, plain, ( in(skolem3(_u32), _u32) | ( _u32 = empty_set) )).
% 12.41/12.60  cnf(matrix-48, plain, ( ( _u41 != powerset(_u43)) | ~in(_u37, _u41) | subset(_u37, _u43) )).
% 12.41/12.60  cnf(matrix-49, plain, ( ( _u41 != powerset(_u43)) | ~subset(_u38, _u43) | in(_u38, _u41) )).
% 12.41/12.60  cnf(matrix-50, plain, ( ( _u42 = powerset(_u44)) | in(skolem4(_u44, _u42), _u42) | subset(skolem5(_u44, _u42), _u44) )).
% 12.41/12.60  cnf(matrix-51, plain, ( ( _u42 = powerset(_u44)) | in(skolem4(_u44, _u42), _u42) | ~in(skolem5(_u44, _u42), _u42) )).
% 12.41/12.60  cnf(matrix-52, plain, ( ( _u42 = powerset(_u44)) | ~subset(skolem4(_u44, _u42), _u44) | subset(skolem5(_u44, _u42), _u44) )).
% 12.41/12.60  cnf(matrix-53, plain, ( ( _u42 = powerset(_u44)) | ~subset(skolem4(_u44, _u42), _u44) | ~in(skolem5(_u44, _u42), _u42) )).
% 12.41/12.60  cnf(matrix-54, plain, ( ( _u54 != unordered_pair(_u58, _u56)) | ~in(_u50, _u54) | ( _u50 = _u58) | ( _u50 = _u56) )).
% 12.41/12.60  cnf(matrix-55, plain, ( ( _u54 != unordered_pair(_u58, _u56)) | in(_u51, _u54) | ( _u51 != _u58) )).
% 12.41/12.60  cnf(matrix-56, plain, ( ( _u54 != unordered_pair(_u58, _u56)) | in(_u51, _u54) | ( _u51 != _u56) )).
% 12.41/12.60  cnf(matrix-57, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | in(skolem6(_u59, _u57, _u55), _u55) | ( skolem7(_u59, _u57, _u55) = _u59) | ( skolem7(_u59, _u57, _u55) = _u57) )).
% 12.41/12.60  cnf(matrix-58, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | in(skolem6(_u59, _u57, _u55), _u55) | ~in(skolem7(_u59, _u57, _u55), _u55) )).
% 12.41/12.60  cnf(matrix-59, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | ( skolem7(_u59, _u57, _u55) = _u59) | ( skolem7(_u59, _u57, _u55) = _u57) | ( skolem6(_u59, _u57, _u55) != _u59) )).
% 12.41/12.60  cnf(matrix-60, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | ( skolem7(_u59, _u57, _u55) = _u59) | ( skolem7(_u59, _u57, _u55) = _u57) | ( skolem6(_u59, _u57, _u55) != _u57) )).
% 12.41/12.60  cnf(matrix-61, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | ~in(skolem7(_u59, _u57, _u55), _u55) | ( skolem6(_u59, _u57, _u55) != _u59) )).
% 12.41/12.60  cnf(matrix-62, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | ~in(skolem7(_u59, _u57, _u55), _u55) | ( skolem6(_u59, _u57, _u55) != _u57) )).
% 12.41/12.60  cnf(matrix-63, plain, ( ( _u69 != set_union2(_u73, _u71)) | ~in(_u65, _u69) | in(_u65, _u73) | in(_u65, _u71) )).
% 12.41/12.60  cnf(matrix-64, plain, ( ( _u69 != set_union2(_u73, _u71)) | in(_u66, _u69) | ~in(_u66, _u73) )).
% 12.41/12.60  cnf(matrix-65, plain, ( ( _u69 != set_union2(_u73, _u71)) | in(_u66, _u69) | ~in(_u66, _u71) )).
% 12.41/12.60  cnf(matrix-66, plain, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem8(_u74, _u72, _u70), _u70) | in(skolem9(_u74, _u72, _u70), _u74) | in(skolem9(_u74, _u72, _u70), _u72) )).
% 12.41/12.60  cnf(matrix-67, plain, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem8(_u74, _u72, _u70), _u70) | ~in(skolem9(_u74, _u72, _u70), _u70) )).
% 12.41/12.60  cnf(matrix-68, plain, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem9(_u74, _u72, _u70), _u74) | in(skolem9(_u74, _u72, _u70), _u72) | ~in(skolem8(_u74, _u72, _u70), _u74) )).
% 12.41/12.60  cnf(matrix-69, plain, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem9(_u74, _u72, _u70), _u74) | in(skolem9(_u74, _u72, _u70), _u72) | ~in(skolem8(_u74, _u72, _u70), _u72) )).
% 12.41/12.60  cnf(matrix-70, plain, ( ( _u70 = set_union2(_u74, _u72)) | ~in(skolem9(_u74, _u72, _u70), _u70) | ~in(skolem8(_u74, _u72, _u70), _u74) )).
% 12.41/12.60  cnf(matrix-71, plain, ( ( _u70 = set_union2(_u74, _u72)) | ~in(skolem9(_u74, _u72, _u70), _u70) | ~in(skolem8(_u74, _u72, _u70), _u72) )).
% 12.41/12.60  cnf(matrix-72, plain, ( ~subset(_u81, _u79) | ~in(_u75, _u81) | in(_u75, _u79) )).
% 12.41/12.60  cnf(matrix-73, plain, ( subset(_u82, _u80) | in(skolem10(_u82, _u80), _u82) )).
% 12.41/12.60  cnf(matrix-74, plain, ( subset(_u82, _u80) | ~in(skolem10(_u82, _u80), _u80) )).
% 12.41/12.60  cnf(matrix-75, plain, ( ( _u92 != set_intersection2(_u96, _u94)) | ~in(_u88, _u92) | in(_u88, _u96) )).
% 12.41/12.60  cnf(matrix-76, plain, ( ( _u92 != set_intersection2(_u96, _u94)) | ~in(_u88, _u92) | in(_u88, _u94) )).
% 12.41/12.60  cnf(matrix-77, plain, ( ( _u92 != set_intersection2(_u96, _u94)) | ~in(_u89, _u96) | ~in(_u89, _u94) | in(_u89, _u92) )).
% 12.41/12.60  cnf(matrix-78, plain, ( ( _u93 = set_intersection2(_u97, _u95)) | in(skolem11(_u97, _u95, _u93), _u93) | in(skolem12(_u97, _u95, _u93), _u97) )).
% 12.41/12.60  cnf(matrix-79, plain, ( ( _u93 = set_intersection2(_u97, _u95)) | in(skolem11(_u97, _u95, _u93), _u93) | in(skolem12(_u97, _u95, _u93), _u95) )).
% 12.41/12.60  cnf(matrix-80, plain, ( ( _u93 = set_intersection2(_u97, _u95)) | in(skolem11(_u97, _u95, _u93), _u93) | ~in(skolem12(_u97, _u95, _u93), _u93) )).
% 12.41/12.60  cnf(matrix-81, plain, ( ( _u93 = set_intersection2(_u97, _u95)) | ~in(skolem11(_u97, _u95, _u93), _u97) | ~in(skolem11(_u97, _u95, _u93), _u95) | in(skolem12(_u97, _u95, _u93), _u97) )).
% 12.41/12.60  cnf(matrix-82, plain, ( ( _u93 = set_intersection2(_u97, _u95)) | ~in(skolem11(_u97, _u95, _u93), _u97) | ~in(skolem11(_u97, _u95, _u93), _u95) | in(skolem12(_u97, _u95, _u93), _u95) )).
% 12.41/12.60  cnf(matrix-83, plain, ( ( _u93 = set_intersection2(_u97, _u95)) | ~in(skolem11(_u97, _u95, _u93), _u97) | ~in(skolem11(_u97, _u95, _u93), _u95) | ~in(skolem12(_u97, _u95, _u93), _u93) )).
% 12.41/12.60  cnf(matrix-84, plain, ( ( _u107 != set_difference(_u111, _u109)) | ~in(_u103, _u107) | in(_u103, _u111) )).
% 12.41/12.60  cnf(matrix-85, plain, ( ( _u107 != set_difference(_u111, _u109)) | ~in(_u103, _u107) | ~in(_u103, _u109) )).
% 12.41/12.60  cnf(matrix-86, plain, ( ( _u107 != set_difference(_u111, _u109)) | ~in(_u104, _u111) | in(_u104, _u109) | in(_u104, _u107) )).
% 12.41/12.60  cnf(matrix-87, plain, ( ( _u108 = set_difference(_u112, _u110)) | in(skolem13(_u112, _u110, _u108), _u108) | in(skolem14(_u112, _u110, _u108), _u112) )).
% 12.41/12.60  cnf(matrix-88, plain, ( ( _u108 = set_difference(_u112, _u110)) | in(skolem13(_u112, _u110, _u108), _u108) | ~in(skolem14(_u112, _u110, _u108), _u110) )).
% 12.41/12.60  cnf(matrix-89, plain, ( ( _u108 = set_difference(_u112, _u110)) | in(skolem13(_u112, _u110, _u108), _u108) | ~in(skolem14(_u112, _u110, _u108), _u108) )).
% 12.41/12.60  cnf(matrix-90, plain, ( ( _u108 = set_difference(_u112, _u110)) | ~in(skolem13(_u112, _u110, _u108), _u112) | in(skolem13(_u112, _u110, _u108), _u110) | in(skolem14(_u112, _u110, _u108), _u112) )).
% 12.41/12.60  cnf(matrix-91, plain, ( ( _u108 = set_difference(_u112, _u110)) | ~in(skolem13(_u112, _u110, _u108), _u112) | in(skolem13(_u112, _u110, _u108), _u110) | ~in(skolem14(_u112, _u110, _u108), _u110) )).
% 12.41/12.60  cnf(matrix-92, plain, ( ( _u108 = set_difference(_u112, _u110)) | ~in(skolem13(_u112, _u110, _u108), _u112) | in(skolem13(_u112, _u110, _u108), _u110) | ~in(skolem14(_u112, _u110, _u108), _u108) )).
% 12.41/12.60  cnf(matrix-93, plain, ( ~disjoint(_u117, _u115) | ( set_intersection2(_u117, _u115) = empty_set) )).
% 12.41/12.60  cnf(matrix-94, plain, ( ( set_intersection2(_u118, _u116) != empty_set) | disjoint(_u118, _u116) )).
% 12.41/12.60  cnf(matrix-95, plain, ( ~proper_subset(_u123, _u121) | subset(_u123, _u121) )).
% 12.41/12.60  cnf(matrix-96, plain, ( ~proper_subset(_u123, _u121) | ( _u123 != _u121) )).
% 12.41/12.60  cnf(matrix-97, plain, ( ~subset(_u124, _u122) | ( _u124 = _u122) | proper_subset(_u124, _u122) )).
% 12.41/12.60  cnf(matrix-98, plain, ( empty(empty_set) )).
% 12.41/12.60  cnf(matrix-99, plain, ( empty(_u126) | ~empty(set_union2(_u126, _u125)) )).
% 12.41/12.60  cnf(matrix-100, plain, ( empty(_u128) | ~empty(set_union2(_u127, _u128)) )).
% 12.41/12.60  cnf(matrix-101, plain, ( ( set_union2(_u130, _u130) = _u130) )).
% 12.41/12.60  cnf(matrix-102, plain, ( ( set_intersection2(_u132, _u132) = _u132) )).
% 12.41/12.60  cnf(matrix-103, plain, ( ~proper_subset(_u134, _u134) )).
% 12.41/12.60  cnf(matrix-104, plain, ( ( singleton(_u135) != empty_set) )).
% 12.41/12.60  cnf(matrix-105, plain, ( in(skolem15, skolem16) )).
% 12.41/12.60  cnf(matrix-106, plain, ( ( set_union2(singleton(skolem15), skolem16) != skolem16) )).
% 12.41/12.60  cnf(matrix-107, plain, ( ~subset(singleton(_u142), _u140) | in(_u142, _u140) )).
% 12.41/12.60  cnf(matrix-108, plain, ( ~in(_u143, _u141) | subset(singleton(_u143), _u141) )).
% 12.41/12.60  cnf(matrix-109, plain, ( ( set_difference(_u148, _u146) != empty_set) | subset(_u148, _u146) )).
% 12.41/12.60  cnf(matrix-110, plain, ( ~subset(_u149, _u147) | ( set_difference(_u149, _u147) = empty_set) )).
% 12.41/12.60  cnf(matrix-111, plain, ( ~subset(_u152, _u151) | in(_u150, _u152) | subset(_u152, set_difference(_u151, singleton(_u150))) )).
% 12.41/12.60  cnf(matrix-112, plain, ( ~subset(_u157, singleton(_u155)) | ( _u157 = empty_set) | ( _u157 = singleton(_u155)) )).
% 12.41/12.60  cnf(matrix-113, plain, ( subset(_u158, singleton(_u156)) | ( _u158 != empty_set) )).
% 12.41/12.60  cnf(matrix-114, plain, ( subset(_u158, singleton(_u156)) | ( _u158 != singleton(_u156)) )).
% 12.41/12.60  cnf(matrix-115, plain, ( empty(skolem17) )).
% 12.41/12.60  cnf(matrix-116, plain, ( ~empty(skolem18) )).
% 12.41/12.60  cnf(matrix-117, plain, ( subset(_u162, _u162) )).
% 12.41/12.60  cnf(matrix-118, plain, ( ~disjoint(_u164, _u163) | disjoint(_u163, _u164) )).
% 12.41/12.60  cnf(matrix-119, plain, ( ( _u168 = _u166) | ( unordered_pair(_u168, _u167) != unordered_pair(_u166, _u165)) | ( _u168 = _u165) )).
% 12.41/12.60  cnf(matrix-120, plain, ( ~subset(_u170, _u169) | ( set_union2(_u170, _u169) = _u169) )).
% 12.41/12.60  cnf(matrix-121, plain, ( subset(set_intersection2(_u172, _u171), _u172) )).
% 12.41/12.60  cnf(matrix-122, plain, ( ~subset(_u175, _u174) | ~subset(_u175, _u173) | subset(_u175, set_intersection2(_u174, _u173)) )).
% 12.41/12.60  cnf(matrix-123, plain, ( ( set_union2(_u176, empty_set) = _u176) )).
% 12.41/12.60  cnf(matrix-124, plain, ( ~subset(_u179, _u178) | ~subset(_u178, _u177) | subset(_u179, _u177) )).
% 12.41/12.60  cnf(matrix-125, plain, ( ( powerset(empty_set) = singleton(empty_set)) )).
% 12.41/12.60  cnf(matrix-126, plain, ( ~subset(_u182, _u181) | subset(set_intersection2(_u182, _u180), set_intersection2(_u181, _u180)) )).
% 12.41/12.60  cnf(matrix-127, plain, ( ~subset(_u184, _u183) | ( set_intersection2(_u184, _u183) = _u184) )).
% 12.41/12.60  cnf(matrix-128, plain, ( ( set_intersection2(_u185, empty_set) = empty_set) )).
% 12.41/12.60  cnf(matrix-129, plain, ( ( _u188 = _u187) | in(skolem19(_u188, _u187), _u188) | in(skolem20(_u188, _u187), _u187) )).
% 12.41/12.60  cnf(matrix-130, plain, ( ( _u188 = _u187) | in(skolem19(_u188, _u187), _u188) | ~in(skolem20(_u188, _u187), _u188) )).
% 12.41/12.60  cnf(matrix-131, plain, ( ( _u188 = _u187) | ~in(skolem19(_u188, _u187), _u187) | in(skolem20(_u188, _u187), _u187) )).
% 12.41/12.60  cnf(matrix-132, plain, ( ( _u188 = _u187) | ~in(skolem19(_u188, _u187), _u187) | ~in(skolem20(_u188, _u187), _u188) )).
% 12.41/12.60  cnf(matrix-133, plain, ( subset(empty_set, _u191) )).
% 12.41/12.60  cnf(matrix-134, plain, ( ~subset(_u194, _u193) | subset(set_difference(_u194, _u192), set_difference(_u193, _u192)) )).
% 12.41/12.60  cnf(matrix-135, plain, ( subset(set_difference(_u196, _u195), _u196) )).
% 12.41/12.60  cnf(matrix-136, plain, ( ( set_difference(_u201, _u199) != empty_set) | subset(_u201, _u199) )).
% 12.41/12.60  cnf(matrix-137, plain, ( ~subset(_u202, _u200) | ( set_difference(_u202, _u200) = empty_set) )).
% 12.41/12.60  cnf(matrix-138, plain, ( ( set_union2(_u204, set_difference(_u203, _u204)) = set_union2(_u204, _u203)) )).
% 12.41/12.60  cnf(matrix-139, plain, ( ( set_difference(_u205, empty_set) = _u205) )).
% 12.41/12.60  cnf(matrix-140, plain, ( disjoint(_u212, _u210) | in(skolem21(_u212, _u210), _u212) )).
% 12.41/12.60  cnf(matrix-141, plain, ( disjoint(_u212, _u210) | in(skolem21(_u212, _u210), _u210) )).
% 12.41/12.60  cnf(matrix-142, plain, ( ~in(_u207, _u213) | ~in(_u207, _u211) | ~disjoint(_u213, _u211) )).
% 12.41/12.60  cnf(matrix-143, plain, ( ~subset(_u214, empty_set) | ( _u214 = empty_set) )).
% 12.41/12.60  cnf(matrix-144, plain, ( ( set_difference(set_union2(_u216, _u215), _u215) = set_difference(_u216, _u215)) )).
% 12.41/12.60  cnf(matrix-145, plain, ( ~subset(_u218, _u217) | ( _u217 = set_union2(_u218, set_difference(_u217, _u218))) )).
% 12.41/12.60  cnf(matrix-146, plain, ( ( set_difference(_u220, set_difference(_u220, _u219)) = set_intersection2(_u220, _u219)) )).
% 12.41/12.60  cnf(matrix-147, plain, ( ( set_difference(empty_set, _u221) = empty_set) )).
% 12.41/12.60  cnf(matrix-148, plain, ( disjoint(_u228, _u226) | in(skolem22(_u228, _u226), set_intersection2(_u228, _u226)) )).
% 12.41/12.60  cnf(matrix-149, plain, ( ~in(_u223, set_intersection2(_u229, _u227)) | ~disjoint(_u229, _u227) )).
% 12.41/12.60  cnf(matrix-150, plain, ( ~subset(_u231, _u230) | ~proper_subset(_u230, _u231) )).
% 12.41/12.60  cnf(matrix-151, plain, ( ~subset(_u234, _u233) | ~disjoint(_u233, _u232) | disjoint(_u234, _u232) )).
% 12.41/12.60  cnf(matrix-152, plain, ( ( unordered_pair(_u235, _u235) = singleton(_u235)) )).
% 12.41/12.60  cnf(matrix-153, plain, ( ~empty(_u236) | ( _u236 = empty_set) )).
% 12.41/12.60  cnf(matrix-154, plain, ( ~subset(singleton(_u238), singleton(_u237)) | ( _u238 = _u237) )).
% 12.41/12.60  cnf(matrix-155, plain, ( ~in(_u240, _u239) | ~empty(_u239) )).
% 12.41/12.60  cnf(matrix-156, plain, ( subset(_u242, set_union2(_u242, _u241)) )).
% 12.41/12.60  cnf(matrix-157, plain, ( ~disjoint(_u247, _u245) | ( set_difference(_u247, _u245) = _u247) )).
% 12.41/12.60  cnf(matrix-158, plain, ( ( set_difference(_u248, _u246) != _u248) | disjoint(_u248, _u246) )).
% 12.41/12.60  cnf(matrix-159, plain, ( ~empty(_u250) | ( _u250 = _u249) | ~empty(_u249) )).
% 12.41/12.60  cnf(matrix-160, plain, ( ~subset(_u253, _u252) | ~subset(_u251, _u252) | subset(set_union2(_u253, _u251), _u252) )).
% 12.41/12.60  cnf(matrix-161, plain, ( ( _u256 = _u255) | ( singleton(_u256) != unordered_pair(_u255, _u254)) )).
% 12.41/12.60  cnf(matrix-162, plain, ( ( singleton(_u259) != unordered_pair(_u258, _u257)) | ( _u258 = _u257) )).
% 12.41/12.60  
% 12.41/12.60  % Proof stack:
% 12.41/12.60  cnf(proof-stack, plain, 
% 12.41/12.60  proof_stack(
% 12.41/12.60  start(105), 
% 12.41/12.60  left_branch(0, 108, 0, 2), 
% 12.41/12.60  left_branch(0, 120, 0, 3), 
% 12.41/12.60  left_branch(0, 106, 0, 4), 
% 12.41/12.60  right_branch(4), 
% 12.41/12.60  right_branch(3), 
% 12.41/12.60  right_branch(2)
% 12.41/12.60  )).
% 12.41/12.60  % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------