%------------------------------------------------------------------------------
% File     : ConnectPP---0.2.2
% Problem  : SEU130+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 : n026.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 09:20:17 EST 2024

% Result   : Theorem 3.33s 3.49s
% Output   : Proof 3.33s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU130+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.12  % Command  : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Mar  3 10:18:22 EST 2024
% 0.12/0.33  % CPUTime  : 
% 3.33/3.49  % SZS status Theorem for theBenchmark
% 3.33/3.49  % SZS output start Proof for theBenchmark
% 3.33/3.49  
% 3.33/3.49  % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 3.33/3.49  cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u3, _u2) = set_union2(_u2, _u3)) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: commutativity_k3_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(commutativity_k3_xboole_0-1, axiom, ( ( set_intersection2(_u5, _u4) = set_intersection2(_u4, _u5)) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: d10_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(d10_xboole_0-1, axiom, ( ( _u10 != _u8) | subset(_u10, _u8) )).
% 3.33/3.49  cnf(d10_xboole_0-2, axiom, ( ( _u10 != _u8) | subset(_u8, _u10) )).
% 3.33/3.49  cnf(d10_xboole_0-3, axiom, ( ~subset(_u11, _u9) | ~subset(_u9, _u11) | ( _u11 = _u9) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: d1_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(d1_xboole_0-1, axiom, ( ( _u15 != empty_set) | ~in(_u12, _u15) )).
% 3.33/3.49  cnf(d1_xboole_0-2, axiom, ( in(skolem1(_u16), _u16) | ( _u16 = empty_set) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: d2_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(d2_xboole_0-1, axiom, ( ( _u26 != set_union2(_u30, _u28)) | ~in(_u22, _u26) | in(_u22, _u30) | in(_u22, _u28) )).
% 3.33/3.49  cnf(d2_xboole_0-2, axiom, ( ( _u26 != set_union2(_u30, _u28)) | in(_u23, _u26) | ~in(_u23, _u30) )).
% 3.33/3.49  cnf(d2_xboole_0-3, axiom, ( ( _u26 != set_union2(_u30, _u28)) | in(_u23, _u26) | ~in(_u23, _u28) )).
% 3.33/3.49  cnf(d2_xboole_0-4, axiom, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem2(_u31, _u29, _u27), _u27) | in(skolem3(_u31, _u29, _u27), _u31) | in(skolem3(_u31, _u29, _u27), _u29) )).
% 3.33/3.49  cnf(d2_xboole_0-5, axiom, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem2(_u31, _u29, _u27), _u27) | ~in(skolem3(_u31, _u29, _u27), _u27) )).
% 3.33/3.49  cnf(d2_xboole_0-6, axiom, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem3(_u31, _u29, _u27), _u31) | in(skolem3(_u31, _u29, _u27), _u29) | ~in(skolem2(_u31, _u29, _u27), _u31) )).
% 3.33/3.49  cnf(d2_xboole_0-7, axiom, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem3(_u31, _u29, _u27), _u31) | in(skolem3(_u31, _u29, _u27), _u29) | ~in(skolem2(_u31, _u29, _u27), _u29) )).
% 3.33/3.49  cnf(d2_xboole_0-8, axiom, ( ( _u27 = set_union2(_u31, _u29)) | ~in(skolem3(_u31, _u29, _u27), _u27) | ~in(skolem2(_u31, _u29, _u27), _u31) )).
% 3.33/3.49  cnf(d2_xboole_0-9, axiom, ( ( _u27 = set_union2(_u31, _u29)) | ~in(skolem3(_u31, _u29, _u27), _u27) | ~in(skolem2(_u31, _u29, _u27), _u29) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: d3_tarski ( axiom ) converted to clauses:
% 3.33/3.49  cnf(d3_tarski-1, axiom, ( ~subset(_u38, _u36) | ~in(_u32, _u38) | in(_u32, _u36) )).
% 3.33/3.49  cnf(d3_tarski-2, axiom, ( subset(_u39, _u37) | in(skolem4(_u39, _u37), _u39) )).
% 3.33/3.49  cnf(d3_tarski-3, axiom, ( subset(_u39, _u37) | ~in(skolem4(_u39, _u37), _u37) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: d3_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(d3_xboole_0-1, axiom, ( ( _u49 != set_intersection2(_u53, _u51)) | ~in(_u45, _u49) | in(_u45, _u53) )).
% 3.33/3.49  cnf(d3_xboole_0-2, axiom, ( ( _u49 != set_intersection2(_u53, _u51)) | ~in(_u45, _u49) | in(_u45, _u51) )).
% 3.33/3.49  cnf(d3_xboole_0-3, axiom, ( ( _u49 != set_intersection2(_u53, _u51)) | ~in(_u46, _u53) | ~in(_u46, _u51) | in(_u46, _u49) )).
% 3.33/3.49  cnf(d3_xboole_0-4, axiom, ( ( _u50 = set_intersection2(_u54, _u52)) | in(skolem5(_u54, _u52, _u50), _u50) | in(skolem6(_u54, _u52, _u50), _u54) )).
% 3.33/3.49  cnf(d3_xboole_0-5, axiom, ( ( _u50 = set_intersection2(_u54, _u52)) | in(skolem5(_u54, _u52, _u50), _u50) | in(skolem6(_u54, _u52, _u50), _u52) )).
% 3.33/3.49  cnf(d3_xboole_0-6, axiom, ( ( _u50 = set_intersection2(_u54, _u52)) | in(skolem5(_u54, _u52, _u50), _u50) | ~in(skolem6(_u54, _u52, _u50), _u50) )).
% 3.33/3.49  cnf(d3_xboole_0-7, axiom, ( ( _u50 = set_intersection2(_u54, _u52)) | ~in(skolem5(_u54, _u52, _u50), _u54) | ~in(skolem5(_u54, _u52, _u50), _u52) | in(skolem6(_u54, _u52, _u50), _u54) )).
% 3.33/3.49  cnf(d3_xboole_0-8, axiom, ( ( _u50 = set_intersection2(_u54, _u52)) | ~in(skolem5(_u54, _u52, _u50), _u54) | ~in(skolem5(_u54, _u52, _u50), _u52) | in(skolem6(_u54, _u52, _u50), _u52) )).
% 3.33/3.49  cnf(d3_xboole_0-9, axiom, ( ( _u50 = set_intersection2(_u54, _u52)) | ~in(skolem5(_u54, _u52, _u50), _u54) | ~in(skolem5(_u54, _u52, _u50), _u52) | ~in(skolem6(_u54, _u52, _u50), _u50) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: d7_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(d7_xboole_0-1, axiom, ( ~disjoint(_u59, _u57) | ( set_intersection2(_u59, _u57) = empty_set) )).
% 3.33/3.49  cnf(d7_xboole_0-2, axiom, ( ( set_intersection2(_u60, _u58) != empty_set) | disjoint(_u60, _u58) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  
% 3.33/3.49  % Formula: dt_k2_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  
% 3.33/3.49  % Formula: dt_k3_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  
% 3.33/3.49  % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(fc2_xboole_0-1, axiom, ( empty(_u62) | ~empty(set_union2(_u62, _u61)) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(fc3_xboole_0-1, axiom, ( empty(_u64) | ~empty(set_union2(_u63, _u64)) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u66, _u66) = _u66) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: idempotence_k3_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(idempotence_k3_xboole_0-1, axiom, ( ( set_intersection2(_u68, _u68) = _u68) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(rc1_xboole_0-1, axiom, ( empty(skolem7) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem8) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 3.33/3.49  cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u72, _u72) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: symmetry_r1_xboole_0 ( axiom ) converted to clauses:
% 3.33/3.49  cnf(symmetry_r1_xboole_0-1, axiom, ( ~disjoint(_u74, _u73) | disjoint(_u73, _u74) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t12_xboole_1 ( lemma ) converted to clauses:
% 3.33/3.49  cnf(t12_xboole_1-1, lemma, ( ~subset(_u76, _u75) | ( set_union2(_u76, _u75) = _u75) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t17_xboole_1 ( lemma ) converted to clauses:
% 3.33/3.49  cnf(t17_xboole_1-1, lemma, ( subset(set_intersection2(_u78, _u77), _u78) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t19_xboole_1 ( lemma ) converted to clauses:
% 3.33/3.49  cnf(t19_xboole_1-1, lemma, ( ~subset(_u81, _u80) | ~subset(_u81, _u79) | subset(_u81, set_intersection2(_u80, _u79)) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t1_boole ( axiom ) converted to clauses:
% 3.33/3.49  cnf(t1_boole-1, axiom, ( ( set_union2(_u82, empty_set) = _u82) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t1_xboole_1 ( lemma ) converted to clauses:
% 3.33/3.49  cnf(t1_xboole_1-1, lemma, ( ~subset(_u85, _u84) | ~subset(_u84, _u83) | subset(_u85, _u83) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t26_xboole_1 ( lemma ) converted to clauses:
% 3.33/3.49  cnf(t26_xboole_1-1, lemma, ( ~subset(_u88, _u87) | subset(set_intersection2(_u88, _u86), set_intersection2(_u87, _u86)) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t28_xboole_1 ( conjecture ) converted to clauses:
% 3.33/3.49  cnf(t28_xboole_1-1, negated_conjecture, ( subset(skolem9, skolem10) )).
% 3.33/3.49  cnf(t28_xboole_1-2, negated_conjecture, ( ( set_intersection2(skolem9, skolem10) != skolem9) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t2_boole ( axiom ) converted to clauses:
% 3.33/3.49  cnf(t2_boole-1, axiom, ( ( set_intersection2(_u91, empty_set) = empty_set) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t2_xboole_1 ( lemma ) converted to clauses:
% 3.33/3.49  cnf(t2_xboole_1-1, lemma, ( subset(empty_set, _u92) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t3_xboole_0 ( lemma ) converted to clauses:
% 3.33/3.49  cnf(t3_xboole_0-1, lemma, ( disjoint(_u99, _u97) | in(skolem11(_u99, _u97), _u99) )).
% 3.33/3.49  cnf(t3_xboole_0-2, lemma, ( disjoint(_u99, _u97) | in(skolem11(_u99, _u97), _u97) )).
% 3.33/3.49  cnf(t3_xboole_0-3, lemma, ( ~in(_u94, _u100) | ~in(_u94, _u98) | ~disjoint(_u100, _u98) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t3_xboole_1 ( lemma ) converted to clauses:
% 3.33/3.49  cnf(t3_xboole_1-1, lemma, ( ~subset(_u101, empty_set) | ( _u101 = empty_set) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t4_xboole_0 ( lemma ) converted to clauses:
% 3.33/3.49  cnf(t4_xboole_0-1, lemma, ( disjoint(_u108, _u106) | in(skolem12(_u108, _u106), set_intersection2(_u108, _u106)) )).
% 3.33/3.49  cnf(t4_xboole_0-2, lemma, ( ~in(_u103, set_intersection2(_u109, _u107)) | ~disjoint(_u109, _u107) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t6_boole ( axiom ) converted to clauses:
% 3.33/3.49  cnf(t6_boole-1, axiom, ( ~empty(_u110) | ( _u110 = empty_set) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t7_boole ( axiom ) converted to clauses:
% 3.33/3.49  cnf(t7_boole-1, axiom, ( ~in(_u112, _u111) | ~empty(_u111) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t7_xboole_1 ( lemma ) converted to clauses:
% 3.33/3.49  cnf(t7_xboole_1-1, lemma, ( subset(_u114, set_union2(_u114, _u113)) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t8_boole ( axiom ) converted to clauses:
% 3.33/3.49  cnf(t8_boole-1, axiom, ( ~empty(_u116) | ( _u116 = _u115) | ~empty(_u115) )).
% 3.33/3.49  
% 3.33/3.49  % Formula: t8_xboole_1 ( lemma ) converted to clauses:
% 3.33/3.49  cnf(t8_xboole_1-1, lemma, ( ~subset(_u119, _u118) | ~subset(_u117, _u118) | subset(set_union2(_u119, _u117), _u118) )).
% 3.33/3.49  
% 3.33/3.49  % Problem matrix:
% 3.33/3.49  cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 3.33/3.49  cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 3.33/3.49  cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 3.33/3.49  cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 3.33/3.49  cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_intersection2(__eqx_0, __eqx_1) = set_intersection2(__eqy_0, __eqy_1)) )).
% 3.33/3.49  cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 3.33/3.49  cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem2(__eqx_0, __eqx_1, __eqx_2) = skolem2(__eqy_0, __eqy_1, __eqy_2)) )).
% 3.33/3.49  cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem3(__eqx_0, __eqx_1, __eqx_2) = skolem3(__eqy_0, __eqy_1, __eqy_2)) )).
% 3.33/3.49  cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 3.33/3.49  cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem5(__eqx_0, __eqx_1, __eqx_2) = skolem5(__eqy_0, __eqy_1, __eqy_2)) )).
% 3.33/3.49  cnf(matrix-10, 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)) )).
% 3.33/3.49  cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem11(__eqx_0, __eqx_1) = skolem11(__eqy_0, __eqy_1)) )).
% 3.33/3.49  cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem12(__eqx_0, __eqx_1) = skolem12(__eqy_0, __eqy_1)) )).
% 3.33/3.49  cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 3.33/3.49  cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 3.33/3.49  cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~disjoint(__eqx_0, __eqx_1) | disjoint(__eqy_0, __eqy_1) )).
% 3.33/3.49  cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 3.33/3.49  cnf(matrix-17, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 3.33/3.49  cnf(matrix-18, plain, ( ( set_union2(_u3, _u2) = set_union2(_u2, _u3)) )).
% 3.33/3.49  cnf(matrix-19, plain, ( ( set_intersection2(_u5, _u4) = set_intersection2(_u4, _u5)) )).
% 3.33/3.49  cnf(matrix-20, plain, ( ( _u10 != _u8) | subset(_u10, _u8) )).
% 3.33/3.49  cnf(matrix-21, plain, ( ( _u10 != _u8) | subset(_u8, _u10) )).
% 3.33/3.49  cnf(matrix-22, plain, ( ~subset(_u11, _u9) | ~subset(_u9, _u11) | ( _u11 = _u9) )).
% 3.33/3.49  cnf(matrix-23, plain, ( ( _u15 != empty_set) | ~in(_u12, _u15) )).
% 3.33/3.49  cnf(matrix-24, plain, ( in(skolem1(_u16), _u16) | ( _u16 = empty_set) )).
% 3.33/3.49  cnf(matrix-25, plain, ( ( _u26 != set_union2(_u30, _u28)) | ~in(_u22, _u26) | in(_u22, _u30) | in(_u22, _u28) )).
% 3.33/3.49  cnf(matrix-26, plain, ( ( _u26 != set_union2(_u30, _u28)) | in(_u23, _u26) | ~in(_u23, _u30) )).
% 3.33/3.49  cnf(matrix-27, plain, ( ( _u26 != set_union2(_u30, _u28)) | in(_u23, _u26) | ~in(_u23, _u28) )).
% 3.33/3.49  cnf(matrix-28, plain, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem2(_u31, _u29, _u27), _u27) | in(skolem3(_u31, _u29, _u27), _u31) | in(skolem3(_u31, _u29, _u27), _u29) )).
% 3.33/3.49  cnf(matrix-29, plain, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem2(_u31, _u29, _u27), _u27) | ~in(skolem3(_u31, _u29, _u27), _u27) )).
% 3.33/3.49  cnf(matrix-30, plain, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem3(_u31, _u29, _u27), _u31) | in(skolem3(_u31, _u29, _u27), _u29) | ~in(skolem2(_u31, _u29, _u27), _u31) )).
% 3.33/3.49  cnf(matrix-31, plain, ( ( _u27 = set_union2(_u31, _u29)) | in(skolem3(_u31, _u29, _u27), _u31) | in(skolem3(_u31, _u29, _u27), _u29) | ~in(skolem2(_u31, _u29, _u27), _u29) )).
% 3.33/3.49  cnf(matrix-32, plain, ( ( _u27 = set_union2(_u31, _u29)) | ~in(skolem3(_u31, _u29, _u27), _u27) | ~in(skolem2(_u31, _u29, _u27), _u31) )).
% 3.33/3.49  cnf(matrix-33, plain, ( ( _u27 = set_union2(_u31, _u29)) | ~in(skolem3(_u31, _u29, _u27), _u27) | ~in(skolem2(_u31, _u29, _u27), _u29) )).
% 3.33/3.49  cnf(matrix-34, plain, ( ~subset(_u38, _u36) | ~in(_u32, _u38) | in(_u32, _u36) )).
% 3.33/3.49  cnf(matrix-35, plain, ( subset(_u39, _u37) | in(skolem4(_u39, _u37), _u39) )).
% 3.33/3.49  cnf(matrix-36, plain, ( subset(_u39, _u37) | ~in(skolem4(_u39, _u37), _u37) )).
% 3.33/3.49  cnf(matrix-37, plain, ( ( _u49 != set_intersection2(_u53, _u51)) | ~in(_u45, _u49) | in(_u45, _u53) )).
% 3.33/3.49  cnf(matrix-38, plain, ( ( _u49 != set_intersection2(_u53, _u51)) | ~in(_u45, _u49) | in(_u45, _u51) )).
% 3.33/3.49  cnf(matrix-39, plain, ( ( _u49 != set_intersection2(_u53, _u51)) | ~in(_u46, _u53) | ~in(_u46, _u51) | in(_u46, _u49) )).
% 3.33/3.49  cnf(matrix-40, plain, ( ( _u50 = set_intersection2(_u54, _u52)) | in(skolem5(_u54, _u52, _u50), _u50) | in(skolem6(_u54, _u52, _u50), _u54) )).
% 3.33/3.49  cnf(matrix-41, plain, ( ( _u50 = set_intersection2(_u54, _u52)) | in(skolem5(_u54, _u52, _u50), _u50) | in(skolem6(_u54, _u52, _u50), _u52) )).
% 3.33/3.49  cnf(matrix-42, plain, ( ( _u50 = set_intersection2(_u54, _u52)) | in(skolem5(_u54, _u52, _u50), _u50) | ~in(skolem6(_u54, _u52, _u50), _u50) )).
% 3.33/3.49  cnf(matrix-43, plain, ( ( _u50 = set_intersection2(_u54, _u52)) | ~in(skolem5(_u54, _u52, _u50), _u54) | ~in(skolem5(_u54, _u52, _u50), _u52) | in(skolem6(_u54, _u52, _u50), _u54) )).
% 3.33/3.49  cnf(matrix-44, plain, ( ( _u50 = set_intersection2(_u54, _u52)) | ~in(skolem5(_u54, _u52, _u50), _u54) | ~in(skolem5(_u54, _u52, _u50), _u52) | in(skolem6(_u54, _u52, _u50), _u52) )).
% 3.33/3.49  cnf(matrix-45, plain, ( ( _u50 = set_intersection2(_u54, _u52)) | ~in(skolem5(_u54, _u52, _u50), _u54) | ~in(skolem5(_u54, _u52, _u50), _u52) | ~in(skolem6(_u54, _u52, _u50), _u50) )).
% 3.33/3.49  cnf(matrix-46, plain, ( ~disjoint(_u59, _u57) | ( set_intersection2(_u59, _u57) = empty_set) )).
% 3.33/3.49  cnf(matrix-47, plain, ( ( set_intersection2(_u60, _u58) != empty_set) | disjoint(_u60, _u58) )).
% 3.33/3.49  cnf(matrix-48, plain, ( empty(empty_set) )).
% 3.33/3.49  cnf(matrix-49, plain, ( empty(_u62) | ~empty(set_union2(_u62, _u61)) )).
% 3.33/3.49  cnf(matrix-50, plain, ( empty(_u64) | ~empty(set_union2(_u63, _u64)) )).
% 3.33/3.49  cnf(matrix-51, plain, ( ( set_union2(_u66, _u66) = _u66) )).
% 3.33/3.49  cnf(matrix-52, plain, ( ( set_intersection2(_u68, _u68) = _u68) )).
% 3.33/3.49  cnf(matrix-53, plain, ( empty(skolem7) )).
% 3.33/3.49  cnf(matrix-54, plain, ( ~empty(skolem8) )).
% 3.33/3.49  cnf(matrix-55, plain, ( subset(_u72, _u72) )).
% 3.33/3.49  cnf(matrix-56, plain, ( ~disjoint(_u74, _u73) | disjoint(_u73, _u74) )).
% 3.33/3.49  cnf(matrix-57, plain, ( ~subset(_u76, _u75) | ( set_union2(_u76, _u75) = _u75) )).
% 3.33/3.49  cnf(matrix-58, plain, ( subset(set_intersection2(_u78, _u77), _u78) )).
% 3.33/3.49  cnf(matrix-59, plain, ( ~subset(_u81, _u80) | ~subset(_u81, _u79) | subset(_u81, set_intersection2(_u80, _u79)) )).
% 3.33/3.49  cnf(matrix-60, plain, ( ( set_union2(_u82, empty_set) = _u82) )).
% 3.33/3.49  cnf(matrix-61, plain, ( ~subset(_u85, _u84) | ~subset(_u84, _u83) | subset(_u85, _u83) )).
% 3.33/3.49  cnf(matrix-62, plain, ( ~subset(_u88, _u87) | subset(set_intersection2(_u88, _u86), set_intersection2(_u87, _u86)) )).
% 3.33/3.49  cnf(matrix-63, plain, ( subset(skolem9, skolem10) )).
% 3.33/3.49  cnf(matrix-64, plain, ( ( set_intersection2(skolem9, skolem10) != skolem9) )).
% 3.33/3.49  cnf(matrix-65, plain, ( ( set_intersection2(_u91, empty_set) = empty_set) )).
% 3.33/3.49  cnf(matrix-66, plain, ( subset(empty_set, _u92) )).
% 3.33/3.49  cnf(matrix-67, plain, ( disjoint(_u99, _u97) | in(skolem11(_u99, _u97), _u99) )).
% 3.33/3.49  cnf(matrix-68, plain, ( disjoint(_u99, _u97) | in(skolem11(_u99, _u97), _u97) )).
% 3.33/3.49  cnf(matrix-69, plain, ( ~in(_u94, _u100) | ~in(_u94, _u98) | ~disjoint(_u100, _u98) )).
% 3.33/3.49  cnf(matrix-70, plain, ( ~subset(_u101, empty_set) | ( _u101 = empty_set) )).
% 3.33/3.49  cnf(matrix-71, plain, ( disjoint(_u108, _u106) | in(skolem12(_u108, _u106), set_intersection2(_u108, _u106)) )).
% 3.33/3.49  cnf(matrix-72, plain, ( ~in(_u103, set_intersection2(_u109, _u107)) | ~disjoint(_u109, _u107) )).
% 3.33/3.49  cnf(matrix-73, plain, ( ~empty(_u110) | ( _u110 = empty_set) )).
% 3.33/3.49  cnf(matrix-74, plain, ( ~in(_u112, _u111) | ~empty(_u111) )).
% 3.33/3.49  cnf(matrix-75, plain, ( subset(_u114, set_union2(_u114, _u113)) )).
% 3.33/3.49  cnf(matrix-76, plain, ( ~empty(_u116) | ( _u116 = _u115) | ~empty(_u115) )).
% 3.33/3.49  cnf(matrix-77, plain, ( ~subset(_u119, _u118) | ~subset(_u117, _u118) | subset(set_union2(_u119, _u117), _u118) )).
% 3.33/3.49  
% 3.33/3.49  % Proof stack:
% 3.33/3.49  cnf(proof-stack, plain, 
% 3.33/3.49  proof_stack(
% 3.33/3.49  start(64), 
% 3.33/3.49  left_branch(0, 22, 2, 2), 
% 3.33/3.49  left_branch(0, 58, 0, 3), 
% 3.33/3.49  right_branch(3), 
% 3.33/3.49  left_branch(0, 59, 2, 4), 
% 3.33/3.49  left_branch(0, 55, 0, 5), 
% 3.33/3.49  right_branch(5), 
% 3.33/3.49  left_branch(0, 63, 0, 6), 
% 3.33/3.49  right_branch(6), 
% 3.33/3.49  right_branch(4), 
% 3.33/3.49  right_branch(2)
% 3.33/3.49  )).
% 3.33/3.49  % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------