TSTP Solution File: SEU151+2 by ConnectPP---0.3.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU151+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 : n002.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 57.98s 58.21s
% Output : Proof 57.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU151+2 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.14 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Mar 20 14:54:23 EDT 2024
% 0.13/0.35 % CPUTime :
% 57.98/58.21 % SZS status Theorem for theBenchmark
% 57.98/58.21 % SZS output start Proof for theBenchmark
% 57.98/58.21
% 57.98/58.21 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 57.98/58.21 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 57.98/58.21
% 57.98/58.21 % Formula: antisymmetry_r2_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(antisymmetry_r2_xboole_0-1, axiom, ( ~proper_subset(_u3, _u2) | ~proper_subset(_u2, _u3) )).
% 57.98/58.21
% 57.98/58.21 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 57.98/58.21 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u5, _u4) = unordered_pair(_u4, _u5)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u7, _u6) = set_union2(_u6, _u7)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: commutativity_k3_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(commutativity_k3_xboole_0-1, axiom, ( ( set_intersection2(_u9, _u8) = set_intersection2(_u8, _u9)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: d10_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(d10_xboole_0-1, axiom, ( ( _u14 != _u12) | subset(_u14, _u12) )).
% 57.98/58.21 cnf(d10_xboole_0-2, axiom, ( ( _u14 != _u12) | subset(_u12, _u14) )).
% 57.98/58.21 cnf(d10_xboole_0-3, axiom, ( ~subset(_u15, _u13) | ~subset(_u13, _u15) | ( _u15 = _u13) )).
% 57.98/58.21
% 57.98/58.21 % Formula: d1_tarski ( axiom ) converted to clauses:
% 57.98/58.21 cnf(d1_tarski-1, axiom, ( ( _u24 != singleton(_u26)) | ~in(_u20, _u24) | ( _u20 = _u26) )).
% 57.98/58.21 cnf(d1_tarski-2, axiom, ( ( _u24 != singleton(_u26)) | ( _u21 != _u26) | in(_u21, _u24) )).
% 57.98/58.21 cnf(d1_tarski-3, axiom, ( ( _u25 = singleton(_u27)) | in(skolem1(_u27, _u25), _u25) | ( skolem2(_u27, _u25) = _u27) )).
% 57.98/58.21 cnf(d1_tarski-4, axiom, ( ( _u25 = singleton(_u27)) | in(skolem1(_u27, _u25), _u25) | ~in(skolem2(_u27, _u25), _u25) )).
% 57.98/58.21 cnf(d1_tarski-5, axiom, ( ( _u25 = singleton(_u27)) | ( skolem1(_u27, _u25) != _u27) | ( skolem2(_u27, _u25) = _u27) )).
% 57.98/58.21 cnf(d1_tarski-6, axiom, ( ( _u25 = singleton(_u27)) | ( skolem1(_u27, _u25) != _u27) | ~in(skolem2(_u27, _u25), _u25) )).
% 57.98/58.21
% 57.98/58.21 % Formula: d1_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(d1_xboole_0-1, axiom, ( ( _u31 != empty_set) | ~in(_u28, _u31) )).
% 57.98/58.21 cnf(d1_xboole_0-2, axiom, ( in(skolem3(_u32), _u32) | ( _u32 = empty_set) )).
% 57.98/58.21
% 57.98/58.21 % Formula: d1_zfmisc_1 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(d1_zfmisc_1-1, axiom, ( ( _u41 != powerset(_u43)) | ~in(_u37, _u41) | subset(_u37, _u43) )).
% 57.98/58.21 cnf(d1_zfmisc_1-2, axiom, ( ( _u41 != powerset(_u43)) | ~subset(_u38, _u43) | in(_u38, _u41) )).
% 57.98/58.21 cnf(d1_zfmisc_1-3, axiom, ( ( _u42 = powerset(_u44)) | in(skolem4(_u44, _u42), _u42) | subset(skolem5(_u44, _u42), _u44) )).
% 57.98/58.21 cnf(d1_zfmisc_1-4, axiom, ( ( _u42 = powerset(_u44)) | in(skolem4(_u44, _u42), _u42) | ~in(skolem5(_u44, _u42), _u42) )).
% 57.98/58.21 cnf(d1_zfmisc_1-5, axiom, ( ( _u42 = powerset(_u44)) | ~subset(skolem4(_u44, _u42), _u44) | subset(skolem5(_u44, _u42), _u44) )).
% 57.98/58.21 cnf(d1_zfmisc_1-6, axiom, ( ( _u42 = powerset(_u44)) | ~subset(skolem4(_u44, _u42), _u44) | ~in(skolem5(_u44, _u42), _u42) )).
% 57.98/58.21
% 57.98/58.21 % Formula: d2_tarski ( axiom ) converted to clauses:
% 57.98/58.21 cnf(d2_tarski-1, axiom, ( ( _u54 != unordered_pair(_u58, _u56)) | ~in(_u50, _u54) | ( _u50 = _u58) | ( _u50 = _u56) )).
% 57.98/58.21 cnf(d2_tarski-2, axiom, ( ( _u54 != unordered_pair(_u58, _u56)) | in(_u51, _u54) | ( _u51 != _u58) )).
% 57.98/58.21 cnf(d2_tarski-3, axiom, ( ( _u54 != unordered_pair(_u58, _u56)) | in(_u51, _u54) | ( _u51 != _u56) )).
% 57.98/58.21 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) )).
% 57.98/58.21 cnf(d2_tarski-5, axiom, ( ( _u55 = unordered_pair(_u59, _u57)) | in(skolem6(_u59, _u57, _u55), _u55) | ~in(skolem7(_u59, _u57, _u55), _u55) )).
% 57.98/58.21 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) )).
% 57.98/58.21 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) )).
% 57.98/58.21 cnf(d2_tarski-8, axiom, ( ( _u55 = unordered_pair(_u59, _u57)) | ~in(skolem7(_u59, _u57, _u55), _u55) | ( skolem6(_u59, _u57, _u55) != _u59) )).
% 57.98/58.21 cnf(d2_tarski-9, axiom, ( ( _u55 = unordered_pair(_u59, _u57)) | ~in(skolem7(_u59, _u57, _u55), _u55) | ( skolem6(_u59, _u57, _u55) != _u57) )).
% 57.98/58.21
% 57.98/58.21 % Formula: d2_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(d2_xboole_0-1, axiom, ( ( _u69 != set_union2(_u73, _u71)) | ~in(_u65, _u69) | in(_u65, _u73) | in(_u65, _u71) )).
% 57.98/58.21 cnf(d2_xboole_0-2, axiom, ( ( _u69 != set_union2(_u73, _u71)) | in(_u66, _u69) | ~in(_u66, _u73) )).
% 57.98/58.21 cnf(d2_xboole_0-3, axiom, ( ( _u69 != set_union2(_u73, _u71)) | in(_u66, _u69) | ~in(_u66, _u71) )).
% 57.98/58.21 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) )).
% 57.98/58.21 cnf(d2_xboole_0-5, axiom, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem8(_u74, _u72, _u70), _u70) | ~in(skolem9(_u74, _u72, _u70), _u70) )).
% 57.98/58.21 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) )).
% 57.98/58.21 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) )).
% 57.98/58.21 cnf(d2_xboole_0-8, axiom, ( ( _u70 = set_union2(_u74, _u72)) | ~in(skolem9(_u74, _u72, _u70), _u70) | ~in(skolem8(_u74, _u72, _u70), _u74) )).
% 57.98/58.21 cnf(d2_xboole_0-9, axiom, ( ( _u70 = set_union2(_u74, _u72)) | ~in(skolem9(_u74, _u72, _u70), _u70) | ~in(skolem8(_u74, _u72, _u70), _u72) )).
% 57.98/58.21
% 57.98/58.21 % Formula: d3_tarski ( axiom ) converted to clauses:
% 57.98/58.21 cnf(d3_tarski-1, axiom, ( ~subset(_u81, _u79) | ~in(_u75, _u81) | in(_u75, _u79) )).
% 57.98/58.21 cnf(d3_tarski-2, axiom, ( subset(_u82, _u80) | in(skolem10(_u82, _u80), _u82) )).
% 57.98/58.21 cnf(d3_tarski-3, axiom, ( subset(_u82, _u80) | ~in(skolem10(_u82, _u80), _u80) )).
% 57.98/58.21
% 57.98/58.21 % Formula: d3_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(d3_xboole_0-1, axiom, ( ( _u92 != set_intersection2(_u96, _u94)) | ~in(_u88, _u92) | in(_u88, _u96) )).
% 57.98/58.21 cnf(d3_xboole_0-2, axiom, ( ( _u92 != set_intersection2(_u96, _u94)) | ~in(_u88, _u92) | in(_u88, _u94) )).
% 57.98/58.21 cnf(d3_xboole_0-3, axiom, ( ( _u92 != set_intersection2(_u96, _u94)) | ~in(_u89, _u96) | ~in(_u89, _u94) | in(_u89, _u92) )).
% 57.98/58.21 cnf(d3_xboole_0-4, axiom, ( ( _u93 = set_intersection2(_u97, _u95)) | in(skolem11(_u97, _u95, _u93), _u93) | in(skolem12(_u97, _u95, _u93), _u97) )).
% 57.98/58.21 cnf(d3_xboole_0-5, axiom, ( ( _u93 = set_intersection2(_u97, _u95)) | in(skolem11(_u97, _u95, _u93), _u93) | in(skolem12(_u97, _u95, _u93), _u95) )).
% 57.98/58.21 cnf(d3_xboole_0-6, axiom, ( ( _u93 = set_intersection2(_u97, _u95)) | in(skolem11(_u97, _u95, _u93), _u93) | ~in(skolem12(_u97, _u95, _u93), _u93) )).
% 57.98/58.21 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) )).
% 57.98/58.21 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) )).
% 57.98/58.21 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) )).
% 57.98/58.21
% 57.98/58.21 % Formula: d4_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(d4_xboole_0-1, axiom, ( ( _u107 != set_difference(_u111, _u109)) | ~in(_u103, _u107) | in(_u103, _u111) )).
% 57.98/58.21 cnf(d4_xboole_0-2, axiom, ( ( _u107 != set_difference(_u111, _u109)) | ~in(_u103, _u107) | ~in(_u103, _u109) )).
% 57.98/58.21 cnf(d4_xboole_0-3, axiom, ( ( _u107 != set_difference(_u111, _u109)) | ~in(_u104, _u111) | in(_u104, _u109) | in(_u104, _u107) )).
% 57.98/58.21 cnf(d4_xboole_0-4, axiom, ( ( _u108 = set_difference(_u112, _u110)) | in(skolem13(_u112, _u110, _u108), _u108) | in(skolem14(_u112, _u110, _u108), _u112) )).
% 57.98/58.21 cnf(d4_xboole_0-5, axiom, ( ( _u108 = set_difference(_u112, _u110)) | in(skolem13(_u112, _u110, _u108), _u108) | ~in(skolem14(_u112, _u110, _u108), _u110) )).
% 57.98/58.21 cnf(d4_xboole_0-6, axiom, ( ( _u108 = set_difference(_u112, _u110)) | in(skolem13(_u112, _u110, _u108), _u108) | ~in(skolem14(_u112, _u110, _u108), _u108) )).
% 57.98/58.21 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) )).
% 57.98/58.21 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) )).
% 57.98/58.21 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) )).
% 57.98/58.21
% 57.98/58.21 % Formula: d7_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(d7_xboole_0-1, axiom, ( ~disjoint(_u117, _u115) | ( set_intersection2(_u117, _u115) = empty_set) )).
% 57.98/58.21 cnf(d7_xboole_0-2, axiom, ( ( set_intersection2(_u118, _u116) != empty_set) | disjoint(_u118, _u116) )).
% 57.98/58.21
% 57.98/58.21 % Formula: d8_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(d8_xboole_0-1, axiom, ( ~proper_subset(_u123, _u121) | subset(_u123, _u121) )).
% 57.98/58.21 cnf(d8_xboole_0-2, axiom, ( ~proper_subset(_u123, _u121) | ( _u123 != _u121) )).
% 57.98/58.21 cnf(d8_xboole_0-3, axiom, ( ~subset(_u124, _u122) | ( _u124 = _u122) | proper_subset(_u124, _u122) )).
% 57.98/58.21
% 57.98/58.21 % Formula: dt_k1_tarski ( axiom ) converted to clauses:
% 57.98/58.21 cnf(dt_k1_tarski, axiom, $true).
% 57.98/58.21
% 57.98/58.21 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(dt_k1_xboole_0, axiom, $true).
% 57.98/58.21
% 57.98/58.21 % Formula: dt_k1_zfmisc_1 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(dt_k1_zfmisc_1, axiom, $true).
% 57.98/58.21
% 57.98/58.21 % Formula: dt_k2_tarski ( axiom ) converted to clauses:
% 57.98/58.21 cnf(dt_k2_tarski, axiom, $true).
% 57.98/58.21
% 57.98/58.21 % Formula: dt_k2_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(dt_k2_xboole_0, axiom, $true).
% 57.98/58.21
% 57.98/58.21 % Formula: dt_k3_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(dt_k3_xboole_0, axiom, $true).
% 57.98/58.21
% 57.98/58.21 % Formula: dt_k4_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(dt_k4_xboole_0, axiom, $true).
% 57.98/58.21
% 57.98/58.21 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 57.98/58.21
% 57.98/58.21 % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(fc2_xboole_0-1, axiom, ( empty(_u126) | ~empty(set_union2(_u126, _u125)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(fc3_xboole_0-1, axiom, ( empty(_u128) | ~empty(set_union2(_u127, _u128)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u130, _u130) = _u130) )).
% 57.98/58.21
% 57.98/58.21 % Formula: idempotence_k3_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(idempotence_k3_xboole_0-1, axiom, ( ( set_intersection2(_u132, _u132) = _u132) )).
% 57.98/58.21
% 57.98/58.21 % Formula: irreflexivity_r2_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(irreflexivity_r2_xboole_0-1, axiom, ( ~proper_subset(_u134, _u134) )).
% 57.98/58.21
% 57.98/58.21 % Formula: l1_zfmisc_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(l1_zfmisc_1-1, lemma, ( ( singleton(_u135) != empty_set) )).
% 57.98/58.21
% 57.98/58.21 % Formula: l2_zfmisc_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(l2_zfmisc_1-1, lemma, ( ~subset(singleton(_u140), _u138) | in(_u140, _u138) )).
% 57.98/58.21 cnf(l2_zfmisc_1-2, lemma, ( ~in(_u141, _u139) | subset(singleton(_u141), _u139) )).
% 57.98/58.21
% 57.98/58.21 % Formula: l32_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(l32_xboole_1-1, lemma, ( ( set_difference(_u146, _u144) != empty_set) | subset(_u146, _u144) )).
% 57.98/58.21 cnf(l32_xboole_1-2, lemma, ( ~subset(_u147, _u145) | ( set_difference(_u147, _u145) = empty_set) )).
% 57.98/58.21
% 57.98/58.21 % Formula: l3_zfmisc_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(l3_zfmisc_1-1, lemma, ( ~subset(_u150, _u149) | in(_u148, _u150) | subset(_u150, set_difference(_u149, singleton(_u148))) )).
% 57.98/58.21
% 57.98/58.21 % Formula: l4_zfmisc_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(l4_zfmisc_1-1, lemma, ( ~subset(_u155, singleton(_u153)) | ( _u155 = empty_set) | ( _u155 = singleton(_u153)) )).
% 57.98/58.21 cnf(l4_zfmisc_1-2, lemma, ( subset(_u156, singleton(_u154)) | ( _u156 != empty_set) )).
% 57.98/58.21 cnf(l4_zfmisc_1-3, lemma, ( subset(_u156, singleton(_u154)) | ( _u156 != singleton(_u154)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(rc1_xboole_0-1, axiom, ( empty(skolem15) )).
% 57.98/58.21
% 57.98/58.21 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem16) )).
% 57.98/58.21
% 57.98/58.21 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 57.98/58.21 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u160, _u160) )).
% 57.98/58.21
% 57.98/58.21 % Formula: symmetry_r1_xboole_0 ( axiom ) converted to clauses:
% 57.98/58.21 cnf(symmetry_r1_xboole_0-1, axiom, ( ~disjoint(_u162, _u161) | disjoint(_u161, _u162) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t10_zfmisc_1 ( conjecture ) (definitionally) converted to clauses:
% 57.98/58.21 cnf(t10_zfmisc_1-1, negated_conjecture, ( ( unordered_pair(skolem17, skolem18) = unordered_pair(skolem19, skolem20)) )).
% 57.98/58.21 cnf(t10_zfmisc_1-2, negated_conjecture, ( ( skolem17 != skolem19) )).
% 57.98/58.21 cnf(t10_zfmisc_1-3, negated_conjecture, ( ( skolem17 != skolem20) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t12_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t12_xboole_1-1, lemma, ( ~subset(_u168, _u167) | ( set_union2(_u168, _u167) = _u167) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t17_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t17_xboole_1-1, lemma, ( subset(set_intersection2(_u170, _u169), _u170) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t19_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t19_xboole_1-1, lemma, ( ~subset(_u173, _u172) | ~subset(_u173, _u171) | subset(_u173, set_intersection2(_u172, _u171)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t1_boole ( axiom ) converted to clauses:
% 57.98/58.21 cnf(t1_boole-1, axiom, ( ( set_union2(_u174, empty_set) = _u174) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t1_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t1_xboole_1-1, lemma, ( ~subset(_u177, _u176) | ~subset(_u176, _u175) | subset(_u177, _u175) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t1_zfmisc_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t1_zfmisc_1-1, lemma, ( ( powerset(empty_set) = singleton(empty_set)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t26_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t26_xboole_1-1, lemma, ( ~subset(_u180, _u179) | subset(set_intersection2(_u180, _u178), set_intersection2(_u179, _u178)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t28_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t28_xboole_1-1, lemma, ( ~subset(_u182, _u181) | ( set_intersection2(_u182, _u181) = _u182) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t2_boole ( axiom ) converted to clauses:
% 57.98/58.21 cnf(t2_boole-1, axiom, ( ( set_intersection2(_u183, empty_set) = empty_set) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t2_tarski ( axiom ) converted to clauses:
% 57.98/58.21 cnf(t2_tarski-1, axiom, ( ( _u186 = _u185) | in(skolem21(_u186, _u185), _u186) | in(skolem22(_u186, _u185), _u185) )).
% 57.98/58.21 cnf(t2_tarski-2, axiom, ( ( _u186 = _u185) | in(skolem21(_u186, _u185), _u186) | ~in(skolem22(_u186, _u185), _u186) )).
% 57.98/58.21 cnf(t2_tarski-3, axiom, ( ( _u186 = _u185) | ~in(skolem21(_u186, _u185), _u185) | in(skolem22(_u186, _u185), _u185) )).
% 57.98/58.21 cnf(t2_tarski-4, axiom, ( ( _u186 = _u185) | ~in(skolem21(_u186, _u185), _u185) | ~in(skolem22(_u186, _u185), _u186) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t2_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t2_xboole_1-1, lemma, ( subset(empty_set, _u189) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t33_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t33_xboole_1-1, lemma, ( ~subset(_u192, _u191) | subset(set_difference(_u192, _u190), set_difference(_u191, _u190)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t36_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t36_xboole_1-1, lemma, ( subset(set_difference(_u194, _u193), _u194) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t37_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t37_xboole_1-1, lemma, ( ( set_difference(_u199, _u197) != empty_set) | subset(_u199, _u197) )).
% 57.98/58.21 cnf(t37_xboole_1-2, lemma, ( ~subset(_u200, _u198) | ( set_difference(_u200, _u198) = empty_set) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t39_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t39_xboole_1-1, lemma, ( ( set_union2(_u202, set_difference(_u201, _u202)) = set_union2(_u202, _u201)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t3_boole ( axiom ) converted to clauses:
% 57.98/58.21 cnf(t3_boole-1, axiom, ( ( set_difference(_u203, empty_set) = _u203) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t3_xboole_0 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t3_xboole_0-1, lemma, ( disjoint(_u210, _u208) | in(skolem23(_u210, _u208), _u210) )).
% 57.98/58.21 cnf(t3_xboole_0-2, lemma, ( disjoint(_u210, _u208) | in(skolem23(_u210, _u208), _u208) )).
% 57.98/58.21 cnf(t3_xboole_0-3, lemma, ( ~in(_u205, _u211) | ~in(_u205, _u209) | ~disjoint(_u211, _u209) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t3_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t3_xboole_1-1, lemma, ( ~subset(_u212, empty_set) | ( _u212 = empty_set) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t40_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t40_xboole_1-1, lemma, ( ( set_difference(set_union2(_u214, _u213), _u213) = set_difference(_u214, _u213)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t45_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t45_xboole_1-1, lemma, ( ~subset(_u216, _u215) | ( _u215 = set_union2(_u216, set_difference(_u215, _u216))) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t48_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t48_xboole_1-1, lemma, ( ( set_difference(_u218, set_difference(_u218, _u217)) = set_intersection2(_u218, _u217)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t4_boole ( axiom ) converted to clauses:
% 57.98/58.21 cnf(t4_boole-1, axiom, ( ( set_difference(empty_set, _u219) = empty_set) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t4_xboole_0 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t4_xboole_0-1, lemma, ( disjoint(_u226, _u224) | in(skolem24(_u226, _u224), set_intersection2(_u226, _u224)) )).
% 57.98/58.21 cnf(t4_xboole_0-2, lemma, ( ~in(_u221, set_intersection2(_u227, _u225)) | ~disjoint(_u227, _u225) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t60_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t60_xboole_1-1, lemma, ( ~subset(_u229, _u228) | ~proper_subset(_u228, _u229) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t63_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t63_xboole_1-1, lemma, ( ~subset(_u232, _u231) | ~disjoint(_u231, _u230) | disjoint(_u232, _u230) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t69_enumset1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t69_enumset1-1, lemma, ( ( unordered_pair(_u233, _u233) = singleton(_u233)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t6_boole ( axiom ) converted to clauses:
% 57.98/58.21 cnf(t6_boole-1, axiom, ( ~empty(_u234) | ( _u234 = empty_set) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t6_zfmisc_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t6_zfmisc_1-1, lemma, ( ~subset(singleton(_u236), singleton(_u235)) | ( _u236 = _u235) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t7_boole ( axiom ) converted to clauses:
% 57.98/58.21 cnf(t7_boole-1, axiom, ( ~in(_u238, _u237) | ~empty(_u237) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t7_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t7_xboole_1-1, lemma, ( subset(_u240, set_union2(_u240, _u239)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t83_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t83_xboole_1-1, lemma, ( ~disjoint(_u245, _u243) | ( set_difference(_u245, _u243) = _u245) )).
% 57.98/58.21 cnf(t83_xboole_1-2, lemma, ( ( set_difference(_u246, _u244) != _u246) | disjoint(_u246, _u244) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t8_boole ( axiom ) converted to clauses:
% 57.98/58.21 cnf(t8_boole-1, axiom, ( ~empty(_u248) | ( _u248 = _u247) | ~empty(_u247) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t8_xboole_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t8_xboole_1-1, lemma, ( ~subset(_u251, _u250) | ~subset(_u249, _u250) | subset(set_union2(_u251, _u249), _u250) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t8_zfmisc_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t8_zfmisc_1-1, lemma, ( ( _u254 = _u253) | ( singleton(_u254) != unordered_pair(_u253, _u252)) )).
% 57.98/58.21
% 57.98/58.21 % Formula: t9_zfmisc_1 ( lemma ) converted to clauses:
% 57.98/58.21 cnf(t9_zfmisc_1-1, lemma, ( ( singleton(_u257) != unordered_pair(_u256, _u255)) | ( _u256 = _u255) )).
% 57.98/58.21
% 57.98/58.21 % Problem matrix:
% 57.98/58.21 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 57.98/58.21 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 57.98/58.21 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 57.98/58.21 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 57.98/58.21 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 57.98/58.21 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_intersection2(__eqx_0, __eqx_1) = set_intersection2(__eqy_0, __eqy_1)) )).
% 57.98/58.21 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 57.98/58.21 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 57.98/58.21 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_difference(__eqx_0, __eqx_1) = set_difference(__eqy_0, __eqy_1)) )).
% 57.98/58.21 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 57.98/58.21 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 57.98/58.21 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( skolem3(__eqx_0) = skolem3(__eqy_0)) )).
% 57.98/58.21 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 57.98/58.21 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem5(__eqx_0, __eqx_1) = skolem5(__eqy_0, __eqy_1)) )).
% 57.98/58.21 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)) )).
% 57.98/58.21 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)) )).
% 57.98/58.21 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)) )).
% 57.98/58.21 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)) )).
% 57.98/58.21 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem10(__eqx_0, __eqx_1) = skolem10(__eqy_0, __eqy_1)) )).
% 57.98/58.21 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)) )).
% 57.98/58.21 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)) )).
% 57.98/58.21 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)) )).
% 57.98/58.21 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)) )).
% 57.98/58.21 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem21(__eqx_0, __eqx_1) = skolem21(__eqy_0, __eqy_1)) )).
% 57.98/58.21 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem22(__eqx_0, __eqx_1) = skolem22(__eqy_0, __eqy_1)) )).
% 57.98/58.21 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem23(__eqx_0, __eqx_1) = skolem23(__eqy_0, __eqy_1)) )).
% 57.98/58.21 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem24(__eqx_0, __eqx_1) = skolem24(__eqy_0, __eqy_1)) )).
% 57.98/58.21 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 57.98/58.21 cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~proper_subset(__eqx_0, __eqx_1) | proper_subset(__eqy_0, __eqy_1) )).
% 57.98/58.21 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 57.98/58.21 cnf(matrix-30, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~disjoint(__eqx_0, __eqx_1) | disjoint(__eqy_0, __eqy_1) )).
% 57.98/58.21 cnf(matrix-31, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 57.98/58.21 cnf(matrix-32, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 57.98/58.21 cnf(matrix-33, plain, ( ~proper_subset(_u3, _u2) | ~proper_subset(_u2, _u3) )).
% 57.98/58.21 cnf(matrix-34, plain, ( ( unordered_pair(_u5, _u4) = unordered_pair(_u4, _u5)) )).
% 57.98/58.21 cnf(matrix-35, plain, ( ( set_union2(_u7, _u6) = set_union2(_u6, _u7)) )).
% 57.98/58.21 cnf(matrix-36, plain, ( ( set_intersection2(_u9, _u8) = set_intersection2(_u8, _u9)) )).
% 57.98/58.21 cnf(matrix-37, plain, ( ( _u14 != _u12) | subset(_u14, _u12) )).
% 57.98/58.21 cnf(matrix-38, plain, ( ( _u14 != _u12) | subset(_u12, _u14) )).
% 57.98/58.21 cnf(matrix-39, plain, ( ~subset(_u15, _u13) | ~subset(_u13, _u15) | ( _u15 = _u13) )).
% 57.98/58.21 cnf(matrix-40, plain, ( ( _u24 != singleton(_u26)) | ~in(_u20, _u24) | ( _u20 = _u26) )).
% 57.98/58.21 cnf(matrix-41, plain, ( ( _u24 != singleton(_u26)) | ( _u21 != _u26) | in(_u21, _u24) )).
% 57.98/58.21 cnf(matrix-42, plain, ( ( _u25 = singleton(_u27)) | in(skolem1(_u27, _u25), _u25) | ( skolem2(_u27, _u25) = _u27) )).
% 57.98/58.21 cnf(matrix-43, plain, ( ( _u25 = singleton(_u27)) | in(skolem1(_u27, _u25), _u25) | ~in(skolem2(_u27, _u25), _u25) )).
% 57.98/58.21 cnf(matrix-44, plain, ( ( _u25 = singleton(_u27)) | ( skolem1(_u27, _u25) != _u27) | ( skolem2(_u27, _u25) = _u27) )).
% 57.98/58.21 cnf(matrix-45, plain, ( ( _u25 = singleton(_u27)) | ( skolem1(_u27, _u25) != _u27) | ~in(skolem2(_u27, _u25), _u25) )).
% 57.98/58.21 cnf(matrix-46, plain, ( ( _u31 != empty_set) | ~in(_u28, _u31) )).
% 57.98/58.21 cnf(matrix-47, plain, ( in(skolem3(_u32), _u32) | ( _u32 = empty_set) )).
% 57.98/58.21 cnf(matrix-48, plain, ( ( _u41 != powerset(_u43)) | ~in(_u37, _u41) | subset(_u37, _u43) )).
% 57.98/58.21 cnf(matrix-49, plain, ( ( _u41 != powerset(_u43)) | ~subset(_u38, _u43) | in(_u38, _u41) )).
% 57.98/58.21 cnf(matrix-50, plain, ( ( _u42 = powerset(_u44)) | in(skolem4(_u44, _u42), _u42) | subset(skolem5(_u44, _u42), _u44) )).
% 57.98/58.21 cnf(matrix-51, plain, ( ( _u42 = powerset(_u44)) | in(skolem4(_u44, _u42), _u42) | ~in(skolem5(_u44, _u42), _u42) )).
% 57.98/58.21 cnf(matrix-52, plain, ( ( _u42 = powerset(_u44)) | ~subset(skolem4(_u44, _u42), _u44) | subset(skolem5(_u44, _u42), _u44) )).
% 57.98/58.21 cnf(matrix-53, plain, ( ( _u42 = powerset(_u44)) | ~subset(skolem4(_u44, _u42), _u44) | ~in(skolem5(_u44, _u42), _u42) )).
% 57.98/58.21 cnf(matrix-54, plain, ( ( _u54 != unordered_pair(_u58, _u56)) | ~in(_u50, _u54) | ( _u50 = _u58) | ( _u50 = _u56) )).
% 57.98/58.21 cnf(matrix-55, plain, ( ( _u54 != unordered_pair(_u58, _u56)) | in(_u51, _u54) | ( _u51 != _u58) )).
% 57.98/58.21 cnf(matrix-56, plain, ( ( _u54 != unordered_pair(_u58, _u56)) | in(_u51, _u54) | ( _u51 != _u56) )).
% 57.98/58.21 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) )).
% 57.98/58.21 cnf(matrix-58, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | in(skolem6(_u59, _u57, _u55), _u55) | ~in(skolem7(_u59, _u57, _u55), _u55) )).
% 57.98/58.21 cnf(matrix-59, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | ( skolem7(_u59, _u57, _u55) = _u59) | ( skolem7(_u59, _u57, _u55) = _u57) | ( skolem6(_u59, _u57, _u55) != _u59) )).
% 57.98/58.21 cnf(matrix-60, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | ( skolem7(_u59, _u57, _u55) = _u59) | ( skolem7(_u59, _u57, _u55) = _u57) | ( skolem6(_u59, _u57, _u55) != _u57) )).
% 57.98/58.21 cnf(matrix-61, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | ~in(skolem7(_u59, _u57, _u55), _u55) | ( skolem6(_u59, _u57, _u55) != _u59) )).
% 57.98/58.21 cnf(matrix-62, plain, ( ( _u55 = unordered_pair(_u59, _u57)) | ~in(skolem7(_u59, _u57, _u55), _u55) | ( skolem6(_u59, _u57, _u55) != _u57) )).
% 57.98/58.21 cnf(matrix-63, plain, ( ( _u69 != set_union2(_u73, _u71)) | ~in(_u65, _u69) | in(_u65, _u73) | in(_u65, _u71) )).
% 57.98/58.21 cnf(matrix-64, plain, ( ( _u69 != set_union2(_u73, _u71)) | in(_u66, _u69) | ~in(_u66, _u73) )).
% 57.98/58.21 cnf(matrix-65, plain, ( ( _u69 != set_union2(_u73, _u71)) | in(_u66, _u69) | ~in(_u66, _u71) )).
% 57.98/58.21 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) )).
% 57.98/58.21 cnf(matrix-67, plain, ( ( _u70 = set_union2(_u74, _u72)) | in(skolem8(_u74, _u72, _u70), _u70) | ~in(skolem9(_u74, _u72, _u70), _u70) )).
% 57.98/58.21 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) )).
% 57.98/58.21 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) )).
% 57.98/58.21 cnf(matrix-70, plain, ( ( _u70 = set_union2(_u74, _u72)) | ~in(skolem9(_u74, _u72, _u70), _u70) | ~in(skolem8(_u74, _u72, _u70), _u74) )).
% 57.98/58.21 cnf(matrix-71, plain, ( ( _u70 = set_union2(_u74, _u72)) | ~in(skolem9(_u74, _u72, _u70), _u70) | ~in(skolem8(_u74, _u72, _u70), _u72) )).
% 57.98/58.21 cnf(matrix-72, plain, ( ~subset(_u81, _u79) | ~in(_u75, _u81) | in(_u75, _u79) )).
% 57.98/58.21 cnf(matrix-73, plain, ( subset(_u82, _u80) | in(skolem10(_u82, _u80), _u82) )).
% 57.98/58.21 cnf(matrix-74, plain, ( subset(_u82, _u80) | ~in(skolem10(_u82, _u80), _u80) )).
% 57.98/58.21 cnf(matrix-75, plain, ( ( _u92 != set_intersection2(_u96, _u94)) | ~in(_u88, _u92) | in(_u88, _u96) )).
% 57.98/58.21 cnf(matrix-76, plain, ( ( _u92 != set_intersection2(_u96, _u94)) | ~in(_u88, _u92) | in(_u88, _u94) )).
% 57.98/58.21 cnf(matrix-77, plain, ( ( _u92 != set_intersection2(_u96, _u94)) | ~in(_u89, _u96) | ~in(_u89, _u94) | in(_u89, _u92) )).
% 57.98/58.21 cnf(matrix-78, plain, ( ( _u93 = set_intersection2(_u97, _u95)) | in(skolem11(_u97, _u95, _u93), _u93) | in(skolem12(_u97, _u95, _u93), _u97) )).
% 57.98/58.21 cnf(matrix-79, plain, ( ( _u93 = set_intersection2(_u97, _u95)) | in(skolem11(_u97, _u95, _u93), _u93) | in(skolem12(_u97, _u95, _u93), _u95) )).
% 57.98/58.21 cnf(matrix-80, plain, ( ( _u93 = set_intersection2(_u97, _u95)) | in(skolem11(_u97, _u95, _u93), _u93) | ~in(skolem12(_u97, _u95, _u93), _u93) )).
% 57.98/58.21 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) )).
% 57.98/58.21 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) )).
% 57.98/58.21 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) )).
% 57.98/58.21 cnf(matrix-84, plain, ( ( _u107 != set_difference(_u111, _u109)) | ~in(_u103, _u107) | in(_u103, _u111) )).
% 57.98/58.21 cnf(matrix-85, plain, ( ( _u107 != set_difference(_u111, _u109)) | ~in(_u103, _u107) | ~in(_u103, _u109) )).
% 57.98/58.21 cnf(matrix-86, plain, ( ( _u107 != set_difference(_u111, _u109)) | ~in(_u104, _u111) | in(_u104, _u109) | in(_u104, _u107) )).
% 57.98/58.21 cnf(matrix-87, plain, ( ( _u108 = set_difference(_u112, _u110)) | in(skolem13(_u112, _u110, _u108), _u108) | in(skolem14(_u112, _u110, _u108), _u112) )).
% 57.98/58.21 cnf(matrix-88, plain, ( ( _u108 = set_difference(_u112, _u110)) | in(skolem13(_u112, _u110, _u108), _u108) | ~in(skolem14(_u112, _u110, _u108), _u110) )).
% 57.98/58.21 cnf(matrix-89, plain, ( ( _u108 = set_difference(_u112, _u110)) | in(skolem13(_u112, _u110, _u108), _u108) | ~in(skolem14(_u112, _u110, _u108), _u108) )).
% 57.98/58.21 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) )).
% 57.98/58.21 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) )).
% 57.98/58.21 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) )).
% 57.98/58.21 cnf(matrix-93, plain, ( ~disjoint(_u117, _u115) | ( set_intersection2(_u117, _u115) = empty_set) )).
% 57.98/58.21 cnf(matrix-94, plain, ( ( set_intersection2(_u118, _u116) != empty_set) | disjoint(_u118, _u116) )).
% 57.98/58.21 cnf(matrix-95, plain, ( ~proper_subset(_u123, _u121) | subset(_u123, _u121) )).
% 57.98/58.21 cnf(matrix-96, plain, ( ~proper_subset(_u123, _u121) | ( _u123 != _u121) )).
% 57.98/58.21 cnf(matrix-97, plain, ( ~subset(_u124, _u122) | ( _u124 = _u122) | proper_subset(_u124, _u122) )).
% 57.98/58.21 cnf(matrix-98, plain, ( empty(empty_set) )).
% 57.98/58.21 cnf(matrix-99, plain, ( empty(_u126) | ~empty(set_union2(_u126, _u125)) )).
% 57.98/58.21 cnf(matrix-100, plain, ( empty(_u128) | ~empty(set_union2(_u127, _u128)) )).
% 57.98/58.21 cnf(matrix-101, plain, ( ( set_union2(_u130, _u130) = _u130) )).
% 57.98/58.21 cnf(matrix-102, plain, ( ( set_intersection2(_u132, _u132) = _u132) )).
% 57.98/58.21 cnf(matrix-103, plain, ( ~proper_subset(_u134, _u134) )).
% 57.98/58.21 cnf(matrix-104, plain, ( ( singleton(_u135) != empty_set) )).
% 57.98/58.21 cnf(matrix-105, plain, ( ~subset(singleton(_u140), _u138) | in(_u140, _u138) )).
% 57.98/58.21 cnf(matrix-106, plain, ( ~in(_u141, _u139) | subset(singleton(_u141), _u139) )).
% 57.98/58.21 cnf(matrix-107, plain, ( ( set_difference(_u146, _u144) != empty_set) | subset(_u146, _u144) )).
% 57.98/58.21 cnf(matrix-108, plain, ( ~subset(_u147, _u145) | ( set_difference(_u147, _u145) = empty_set) )).
% 57.98/58.21 cnf(matrix-109, plain, ( ~subset(_u150, _u149) | in(_u148, _u150) | subset(_u150, set_difference(_u149, singleton(_u148))) )).
% 57.98/58.21 cnf(matrix-110, plain, ( ~subset(_u155, singleton(_u153)) | ( _u155 = empty_set) | ( _u155 = singleton(_u153)) )).
% 57.98/58.21 cnf(matrix-111, plain, ( subset(_u156, singleton(_u154)) | ( _u156 != empty_set) )).
% 57.98/58.21 cnf(matrix-112, plain, ( subset(_u156, singleton(_u154)) | ( _u156 != singleton(_u154)) )).
% 57.98/58.21 cnf(matrix-113, plain, ( empty(skolem15) )).
% 57.98/58.21 cnf(matrix-114, plain, ( ~empty(skolem16) )).
% 57.98/58.21 cnf(matrix-115, plain, ( subset(_u160, _u160) )).
% 57.98/58.21 cnf(matrix-116, plain, ( ~disjoint(_u162, _u161) | disjoint(_u161, _u162) )).
% 57.98/58.21 cnf(matrix-117, plain, ( ( unordered_pair(skolem17, skolem18) = unordered_pair(skolem19, skolem20)) )).
% 57.98/58.21 cnf(matrix-118, plain, ( ( skolem17 != skolem19) )).
% 57.98/58.21 cnf(matrix-119, plain, ( ( skolem17 != skolem20) )).
% 57.98/58.21 cnf(matrix-120, plain, ( ~subset(_u168, _u167) | ( set_union2(_u168, _u167) = _u167) )).
% 57.98/58.21 cnf(matrix-121, plain, ( subset(set_intersection2(_u170, _u169), _u170) )).
% 57.98/58.21 cnf(matrix-122, plain, ( ~subset(_u173, _u172) | ~subset(_u173, _u171) | subset(_u173, set_intersection2(_u172, _u171)) )).
% 57.98/58.21 cnf(matrix-123, plain, ( ( set_union2(_u174, empty_set) = _u174) )).
% 57.98/58.21 cnf(matrix-124, plain, ( ~subset(_u177, _u176) | ~subset(_u176, _u175) | subset(_u177, _u175) )).
% 57.98/58.21 cnf(matrix-125, plain, ( ( powerset(empty_set) = singleton(empty_set)) )).
% 57.98/58.21 cnf(matrix-126, plain, ( ~subset(_u180, _u179) | subset(set_intersection2(_u180, _u178), set_intersection2(_u179, _u178)) )).
% 57.98/58.21 cnf(matrix-127, plain, ( ~subset(_u182, _u181) | ( set_intersection2(_u182, _u181) = _u182) )).
% 57.98/58.21 cnf(matrix-128, plain, ( ( set_intersection2(_u183, empty_set) = empty_set) )).
% 57.98/58.21 cnf(matrix-129, plain, ( ( _u186 = _u185) | in(skolem21(_u186, _u185), _u186) | in(skolem22(_u186, _u185), _u185) )).
% 57.98/58.21 cnf(matrix-130, plain, ( ( _u186 = _u185) | in(skolem21(_u186, _u185), _u186) | ~in(skolem22(_u186, _u185), _u186) )).
% 57.98/58.21 cnf(matrix-131, plain, ( ( _u186 = _u185) | ~in(skolem21(_u186, _u185), _u185) | in(skolem22(_u186, _u185), _u185) )).
% 57.98/58.21 cnf(matrix-132, plain, ( ( _u186 = _u185) | ~in(skolem21(_u186, _u185), _u185) | ~in(skolem22(_u186, _u185), _u186) )).
% 57.98/58.21 cnf(matrix-133, plain, ( subset(empty_set, _u189) )).
% 57.98/58.21 cnf(matrix-134, plain, ( ~subset(_u192, _u191) | subset(set_difference(_u192, _u190), set_difference(_u191, _u190)) )).
% 57.98/58.21 cnf(matrix-135, plain, ( subset(set_difference(_u194, _u193), _u194) )).
% 57.98/58.21 cnf(matrix-136, plain, ( ( set_difference(_u199, _u197) != empty_set) | subset(_u199, _u197) )).
% 57.98/58.21 cnf(matrix-137, plain, ( ~subset(_u200, _u198) | ( set_difference(_u200, _u198) = empty_set) )).
% 57.98/58.21 cnf(matrix-138, plain, ( ( set_union2(_u202, set_difference(_u201, _u202)) = set_union2(_u202, _u201)) )).
% 57.98/58.21 cnf(matrix-139, plain, ( ( set_difference(_u203, empty_set) = _u203) )).
% 57.98/58.21 cnf(matrix-140, plain, ( disjoint(_u210, _u208) | in(skolem23(_u210, _u208), _u210) )).
% 57.98/58.21 cnf(matrix-141, plain, ( disjoint(_u210, _u208) | in(skolem23(_u210, _u208), _u208) )).
% 57.98/58.21 cnf(matrix-142, plain, ( ~in(_u205, _u211) | ~in(_u205, _u209) | ~disjoint(_u211, _u209) )).
% 57.98/58.21 cnf(matrix-143, plain, ( ~subset(_u212, empty_set) | ( _u212 = empty_set) )).
% 57.98/58.21 cnf(matrix-144, plain, ( ( set_difference(set_union2(_u214, _u213), _u213) = set_difference(_u214, _u213)) )).
% 57.98/58.21 cnf(matrix-145, plain, ( ~subset(_u216, _u215) | ( _u215 = set_union2(_u216, set_difference(_u215, _u216))) )).
% 57.98/58.21 cnf(matrix-146, plain, ( ( set_difference(_u218, set_difference(_u218, _u217)) = set_intersection2(_u218, _u217)) )).
% 57.98/58.21 cnf(matrix-147, plain, ( ( set_difference(empty_set, _u219) = empty_set) )).
% 57.98/58.21 cnf(matrix-148, plain, ( disjoint(_u226, _u224) | in(skolem24(_u226, _u224), set_intersection2(_u226, _u224)) )).
% 57.98/58.21 cnf(matrix-149, plain, ( ~in(_u221, set_intersection2(_u227, _u225)) | ~disjoint(_u227, _u225) )).
% 57.98/58.21 cnf(matrix-150, plain, ( ~subset(_u229, _u228) | ~proper_subset(_u228, _u229) )).
% 57.98/58.21 cnf(matrix-151, plain, ( ~subset(_u232, _u231) | ~disjoint(_u231, _u230) | disjoint(_u232, _u230) )).
% 57.98/58.21 cnf(matrix-152, plain, ( ( unordered_pair(_u233, _u233) = singleton(_u233)) )).
% 57.98/58.21 cnf(matrix-153, plain, ( ~empty(_u234) | ( _u234 = empty_set) )).
% 57.98/58.21 cnf(matrix-154, plain, ( ~subset(singleton(_u236), singleton(_u235)) | ( _u236 = _u235) )).
% 57.98/58.21 cnf(matrix-155, plain, ( ~in(_u238, _u237) | ~empty(_u237) )).
% 57.98/58.21 cnf(matrix-156, plain, ( subset(_u240, set_union2(_u240, _u239)) )).
% 57.98/58.21 cnf(matrix-157, plain, ( ~disjoint(_u245, _u243) | ( set_difference(_u245, _u243) = _u245) )).
% 57.98/58.21 cnf(matrix-158, plain, ( ( set_difference(_u246, _u244) != _u246) | disjoint(_u246, _u244) )).
% 57.98/58.21 cnf(matrix-159, plain, ( ~empty(_u248) | ( _u248 = _u247) | ~empty(_u247) )).
% 57.98/58.21 cnf(matrix-160, plain, ( ~subset(_u251, _u250) | ~subset(_u249, _u250) | subset(set_union2(_u251, _u249), _u250) )).
% 57.98/58.21 cnf(matrix-161, plain, ( ( _u254 = _u253) | ( singleton(_u254) != unordered_pair(_u253, _u252)) )).
% 57.98/58.21 cnf(matrix-162, plain, ( ( singleton(_u257) != unordered_pair(_u256, _u255)) | ( _u256 = _u255) )).
% 57.98/58.21
% 57.98/58.21 % Proof stack:
% 57.98/58.21 cnf(proof-stack, plain,
% 57.98/58.21 proof_stack(
% 57.98/58.21 start(117),
% 57.98/58.21 left_branch(0, 54, 0, 2),
% 57.98/58.21 left_branch(0, 119, 0, 3),
% 57.98/58.21 right_branch(3),
% 57.98/58.21 left_branch(0, 118, 0, 4),
% 57.98/58.21 right_branch(4),
% 57.98/58.21 left_branch(0, 86, 2, 5),
% 57.98/58.21 left_branch(0, 154, 1, 6),
% 57.98/58.21 left_branch(0, 115, 0, 7),
% 57.98/58.21 right_branch(7),
% 57.98/58.21 right_branch(6),
% 57.98/58.21 left_branch(0, 84, 1, 7),
% 57.98/58.21 left_branch(0, 144, 0, 8),
% 57.98/58.21 right_branch(8),
% 57.98/58.21 reduction(0, 1),
% 57.98/58.21 right_branch(7),
% 57.98/58.21 left_branch(0, 55, 1, 8),
% 57.98/58.21 left_branch(0, 101, 0, 9),
% 57.98/58.21 right_branch(9),
% 57.98/58.21 left_branch(0, 0, 0, 10),
% 57.98/58.21 right_branch(10),
% 57.98/58.21 right_branch(8),
% 57.98/58.21 right_branch(5),
% 57.98/58.21 right_branch(2)
% 57.98/58.21 )).
% 57.98/58.21 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------