%------------------------------------------------------------------------------
% File     : ConnectPP---0.3.0
% Problem  : SET658+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s

% Computer : n013.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 14:32:12 EDT 2024

% Result   : Theorem 0.62s 0.79s
% Output   : Proof 0.62s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET658+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command  : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33  % Computer : n013.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Mar 20 21:15:48 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.62/0.79  % SZS status Theorem for theBenchmark
% 0.62/0.79  % SZS output start Proof for theBenchmark
% 0.62/0.79  
% 0.62/0.79  % Formula: p1 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p1-1, axiom, ( ~ilf_type(_u1, set_type) | ~ilf_type(_u0, binary_relation_type) | ~subset(domain_of(_u0), _u1) | ilf_type(_u0, relation_type(_u1, range_of(_u0))) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p2 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p2-1, axiom, ( ~ilf_type(_u5, binary_relation_type) | ~ilf_type(_u4, set_type) | ~member(_u4, domain_of(_u5)) | ilf_type(skolem1(_u5, _u4), set_type) )).
% 0.62/0.79  cnf(p2-2, axiom, ( ~ilf_type(_u5, binary_relation_type) | ~ilf_type(_u4, set_type) | ~member(_u4, domain_of(_u5)) | member(ordered_pair(_u4, skolem1(_u5, _u4)), _u5) )).
% 0.62/0.79  cnf(p2-3, axiom, ( ~ilf_type(_u5, binary_relation_type) | ~ilf_type(_u4, set_type) | ~ilf_type(_u3, set_type) | ~member(ordered_pair(_u4, _u3), _u5) | member(_u4, domain_of(_u5)) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p3 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p3-1, axiom, ( ~ilf_type(_u6, binary_relation_type) | ilf_type(domain_of(_u6), set_type) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p4 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p4-1, axiom, ( ~ilf_type(_u10, binary_relation_type) | ~ilf_type(_u9, set_type) | ~member(_u9, range_of(_u10)) | ilf_type(skolem2(_u10, _u9), set_type) )).
% 0.62/0.79  cnf(p4-2, axiom, ( ~ilf_type(_u10, binary_relation_type) | ~ilf_type(_u9, set_type) | ~member(_u9, range_of(_u10)) | member(ordered_pair(skolem2(_u10, _u9), _u9), _u10) )).
% 0.62/0.79  cnf(p4-3, axiom, ( ~ilf_type(_u10, binary_relation_type) | ~ilf_type(_u9, set_type) | ~ilf_type(_u8, set_type) | ~member(ordered_pair(_u8, _u9), _u10) | member(_u9, range_of(_u10)) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p5 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p5-1, axiom, ( ~ilf_type(_u11, binary_relation_type) | ilf_type(range_of(_u11), set_type) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p6 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p6-1, axiom, ( ~ilf_type(_u12, set_type) | ~ilf_type(_u12, binary_relation_type) | relation_like(_u12) )).
% 0.62/0.79  cnf(p6-2, axiom, ( ~ilf_type(_u12, set_type) | ~relation_like(_u12) | ilf_type(_u12, binary_relation_type) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p7 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p7-1, axiom, ( ilf_type(skolem3, binary_relation_type) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p8 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p8-1, axiom, ( ~ilf_type(_u17, set_type) | ~ilf_type(_u16, set_type) | ~ilf_type(_u14, subset_type(cross_product(_u17, _u16))) | ilf_type(_u14, relation_type(_u17, _u16)) )).
% 0.62/0.79  cnf(p8-2, axiom, ( ~ilf_type(_u17, set_type) | ~ilf_type(_u16, set_type) | ~ilf_type(_u15, relation_type(_u17, _u16)) | ilf_type(_u15, subset_type(cross_product(_u17, _u16))) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p9 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p9-1, axiom, ( ~ilf_type(_u20, set_type) | ~ilf_type(_u19, set_type) | ilf_type(skolem4(_u20, _u19), relation_type(_u19, _u20)) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p10 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p10-1, axiom, ( ~ilf_type(_u22, set_type) | ~ilf_type(_u21, set_type) | ilf_type(cross_product(_u22, _u21), set_type) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p11 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p11-1, axiom, ( ~ilf_type(_u24, set_type) | ~ilf_type(_u23, set_type) | ilf_type(ordered_pair(_u24, _u23), set_type) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p12 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p12-1, axiom, ( ~ilf_type(_u26, set_type) | ~ilf_type(_u25, set_type) | ~ilf_type(_u25, subset_type(_u26)) | ilf_type(_u25, member_type(power_set(_u26))) )).
% 0.62/0.79  cnf(p12-2, axiom, ( ~ilf_type(_u26, set_type) | ~ilf_type(_u25, set_type) | ~ilf_type(_u25, member_type(power_set(_u26))) | ilf_type(_u25, subset_type(_u26)) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p13 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p13-1, axiom, ( ~ilf_type(_u28, set_type) | ilf_type(skolem5(_u28), subset_type(_u28)) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p14 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p14-1, axiom, ( ~ilf_type(_u32, set_type) | ~ilf_type(_u31, set_type) | ~subset(_u32, _u31) | ~ilf_type(_u29, set_type) | ~member(_u29, _u32) | member(_u29, _u31) )).
% 0.62/0.79  cnf(p14-2, axiom, ( ~ilf_type(_u32, set_type) | ~ilf_type(_u31, set_type) | subset(_u32, _u31) | ilf_type(skolem6(_u32, _u31), set_type) )).
% 0.62/0.79  cnf(p14-3, axiom, ( ~ilf_type(_u32, set_type) | ~ilf_type(_u31, set_type) | subset(_u32, _u31) | member(skolem6(_u32, _u31), _u32) )).
% 0.62/0.79  cnf(p14-4, axiom, ( ~ilf_type(_u32, set_type) | ~ilf_type(_u31, set_type) | subset(_u32, _u31) | ~member(skolem6(_u32, _u31), _u31) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p15 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p15-1, axiom, ( ~ilf_type(_u33, set_type) | subset(_u33, _u33) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p16 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p16-1, axiom, ( ~ilf_type(_u40, set_type) | ~relation_like(_u40) | ~ilf_type(_u36, set_type) | ~member(_u36, _u40) | ilf_type(skolem7(_u40, _u36), set_type) )).
% 0.62/0.79  cnf(p16-2, axiom, ( ~ilf_type(_u40, set_type) | ~relation_like(_u40) | ~ilf_type(_u36, set_type) | ~member(_u36, _u40) | ilf_type(skolem8(_u40, _u36), set_type) )).
% 0.62/0.79  cnf(p16-3, axiom, ( ~ilf_type(_u40, set_type) | ~relation_like(_u40) | ~ilf_type(_u36, set_type) | ~member(_u36, _u40) | ( _u36 = ordered_pair(skolem7(_u40, _u36), skolem8(_u40, _u36))) )).
% 0.62/0.79  cnf(p16-4, axiom, ( ~ilf_type(_u40, set_type) | relation_like(_u40) | ilf_type(skolem9(_u40), set_type) )).
% 0.62/0.79  cnf(p16-5, axiom, ( ~ilf_type(_u40, set_type) | relation_like(_u40) | member(skolem9(_u40), _u40) )).
% 0.62/0.79  cnf(p16-6, axiom, ( ~ilf_type(_u40, set_type) | relation_like(_u40) | ~ilf_type(_u38, set_type) | ~ilf_type(_u37, set_type) | ( skolem9(_u40) != ordered_pair(_u38, _u37)) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p17 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p17-1, axiom, ( ~ilf_type(_u43, set_type) | ~ilf_type(_u42, set_type) | ~ilf_type(_u41, subset_type(cross_product(_u43, _u42))) | relation_like(_u41) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p18 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p18-1, axiom, ( ~ilf_type(_u47, set_type) | ~ilf_type(_u46, set_type) | ~member(_u47, power_set(_u46)) | ~ilf_type(_u44, set_type) | ~member(_u44, _u47) | member(_u44, _u46) )).
% 0.62/0.79  cnf(p18-2, axiom, ( ~ilf_type(_u47, set_type) | ~ilf_type(_u46, set_type) | member(_u47, power_set(_u46)) | ilf_type(skolem10(_u47, _u46), set_type) )).
% 0.62/0.79  cnf(p18-3, axiom, ( ~ilf_type(_u47, set_type) | ~ilf_type(_u46, set_type) | member(_u47, power_set(_u46)) | member(skolem10(_u47, _u46), _u47) )).
% 0.62/0.79  cnf(p18-4, axiom, ( ~ilf_type(_u47, set_type) | ~ilf_type(_u46, set_type) | member(_u47, power_set(_u46)) | ~member(skolem10(_u47, _u46), _u46) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p19 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p19-1, axiom, ( ~ilf_type(_u48, set_type) | ~empty(power_set(_u48)) )).
% 0.62/0.79  cnf(p19-2, axiom, ( ~ilf_type(_u48, set_type) | ilf_type(power_set(_u48), set_type) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p20 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p20-1, axiom, ( ~ilf_type(_u50, set_type) | empty(_u49) | ~ilf_type(_u49, set_type) | ~ilf_type(_u50, member_type(_u49)) | member(_u50, _u49) )).
% 0.62/0.79  cnf(p20-2, axiom, ( ~ilf_type(_u50, set_type) | empty(_u49) | ~ilf_type(_u49, set_type) | ~member(_u50, _u49) | ilf_type(_u50, member_type(_u49)) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p21 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p21-1, axiom, ( empty(_u52) | ~ilf_type(_u52, set_type) | ilf_type(skolem11(_u52), member_type(_u52)) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p22 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p22-1, axiom, ( ~ilf_type(_u55, set_type) | ~empty(_u55) | ~ilf_type(_u53, set_type) | ~member(_u53, _u55) )).
% 0.62/0.79  cnf(p22-2, axiom, ( ~ilf_type(_u55, set_type) | empty(_u55) | ilf_type(skolem12(_u55), set_type) )).
% 0.62/0.79  cnf(p22-3, axiom, ( ~ilf_type(_u55, set_type) | empty(_u55) | member(skolem12(_u55), _u55) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p23 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p23-1, axiom, ( ~empty(_u56) | ~ilf_type(_u56, set_type) | relation_like(_u56) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p24 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p24-1, axiom, ( ~ilf_type(_u59, set_type) | ~ilf_type(_u58, set_type) | ~ilf_type(_u57, relation_type(_u59, _u58)) | ( domain(_u59, _u58, _u57) = domain_of(_u57)) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p25 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p25-1, axiom, ( ~ilf_type(_u62, set_type) | ~ilf_type(_u61, set_type) | ~ilf_type(_u60, relation_type(_u62, _u61)) | ilf_type(domain(_u62, _u61, _u60), subset_type(_u62)) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p26 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p26-1, axiom, ( ~ilf_type(_u65, set_type) | ~ilf_type(_u64, set_type) | ~ilf_type(_u63, relation_type(_u65, _u64)) | ( range(_u65, _u64, _u63) = range_of(_u63)) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p27 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p27-1, axiom, ( ~ilf_type(_u68, set_type) | ~ilf_type(_u67, set_type) | ~ilf_type(_u66, relation_type(_u68, _u67)) | ilf_type(range(_u68, _u67, _u66), subset_type(_u67)) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: p28 ( axiom ) converted to clauses:
% 0.62/0.79  cnf(p28-1, axiom, ( ilf_type(_u69, set_type) )).
% 0.62/0.79  
% 0.62/0.79  % Formula: prove_relset_1_20 ( conjecture ) (definitionally) converted to clauses:
% 0.62/0.79  cnf(prove_relset_1_20-1, negated_conjecture, ( ilf_type(skolem13, binary_relation_type) )).
% 0.62/0.79  cnf(prove_relset_1_20-2, negated_conjecture, ( ~ilf_type(skolem13, relation_type(domain_of(skolem13), range_of(skolem13))) )).
% 0.62/0.79  
% 0.62/0.79  % Problem matrix:
% 0.62/0.79  cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.62/0.79  cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.62/0.79  cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.62/0.79  cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( domain_of(__eqx_0) = domain_of(__eqy_0)) )).
% 0.62/0.79  cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( range_of(__eqx_0) = range_of(__eqy_0)) )).
% 0.62/0.79  cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( relation_type(__eqx_0, __eqx_1) = relation_type(__eqy_0, __eqy_1)) )).
% 0.62/0.79  cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 0.62/0.79  cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( cross_product(__eqx_0, __eqx_1) = cross_product(__eqy_0, __eqy_1)) )).
% 0.62/0.79  cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( subset_type(__eqx_0) = subset_type(__eqy_0)) )).
% 0.62/0.79  cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( power_set(__eqx_0) = power_set(__eqy_0)) )).
% 0.62/0.79  cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( member_type(__eqx_0) = member_type(__eqy_0)) )).
% 0.62/0.79  cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( domain(__eqx_0, __eqx_1, __eqx_2) = domain(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.62/0.79  cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( range(__eqx_0, __eqx_1, __eqx_2) = range(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.62/0.79  cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 0.62/0.79  cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 0.62/0.79  cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 0.62/0.79  cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( skolem5(__eqx_0) = skolem5(__eqy_0)) )).
% 0.62/0.79  cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem6(__eqx_0, __eqx_1) = skolem6(__eqy_0, __eqy_1)) )).
% 0.62/0.79  cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem7(__eqx_0, __eqx_1) = skolem7(__eqy_0, __eqy_1)) )).
% 0.62/0.79  cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem8(__eqx_0, __eqx_1) = skolem8(__eqy_0, __eqy_1)) )).
% 0.62/0.79  cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( skolem9(__eqx_0) = skolem9(__eqy_0)) )).
% 0.62/0.79  cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem10(__eqx_0, __eqx_1) = skolem10(__eqy_0, __eqy_1)) )).
% 0.62/0.79  cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( skolem11(__eqx_0) = skolem11(__eqy_0)) )).
% 0.62/0.79  cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( skolem12(__eqx_0) = skolem12(__eqy_0)) )).
% 0.62/0.79  cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~ilf_type(__eqx_0, __eqx_1) | ilf_type(__eqy_0, __eqy_1) )).
% 0.62/0.79  cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 0.62/0.79  cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 0.62/0.79  cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ~relation_like(__eqx_0) | relation_like(__eqy_0) )).
% 0.62/0.79  cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 0.62/0.79  cnf(matrix-29, plain, ( ~ilf_type(_u1, set_type) | ~ilf_type(_u0, binary_relation_type) | ~subset(domain_of(_u0), _u1) | ilf_type(_u0, relation_type(_u1, range_of(_u0))) )).
% 0.62/0.79  cnf(matrix-30, plain, ( ~ilf_type(_u5, binary_relation_type) | ~ilf_type(_u4, set_type) | ~member(_u4, domain_of(_u5)) | ilf_type(skolem1(_u5, _u4), set_type) )).
% 0.62/0.79  cnf(matrix-31, plain, ( ~ilf_type(_u5, binary_relation_type) | ~ilf_type(_u4, set_type) | ~member(_u4, domain_of(_u5)) | member(ordered_pair(_u4, skolem1(_u5, _u4)), _u5) )).
% 0.62/0.79  cnf(matrix-32, plain, ( ~ilf_type(_u5, binary_relation_type) | ~ilf_type(_u4, set_type) | ~ilf_type(_u3, set_type) | ~member(ordered_pair(_u4, _u3), _u5) | member(_u4, domain_of(_u5)) )).
% 0.62/0.79  cnf(matrix-33, plain, ( ~ilf_type(_u6, binary_relation_type) | ilf_type(domain_of(_u6), set_type) )).
% 0.62/0.79  cnf(matrix-34, plain, ( ~ilf_type(_u10, binary_relation_type) | ~ilf_type(_u9, set_type) | ~member(_u9, range_of(_u10)) | ilf_type(skolem2(_u10, _u9), set_type) )).
% 0.62/0.79  cnf(matrix-35, plain, ( ~ilf_type(_u10, binary_relation_type) | ~ilf_type(_u9, set_type) | ~member(_u9, range_of(_u10)) | member(ordered_pair(skolem2(_u10, _u9), _u9), _u10) )).
% 0.62/0.79  cnf(matrix-36, plain, ( ~ilf_type(_u10, binary_relation_type) | ~ilf_type(_u9, set_type) | ~ilf_type(_u8, set_type) | ~member(ordered_pair(_u8, _u9), _u10) | member(_u9, range_of(_u10)) )).
% 0.62/0.79  cnf(matrix-37, plain, ( ~ilf_type(_u11, binary_relation_type) | ilf_type(range_of(_u11), set_type) )).
% 0.62/0.79  cnf(matrix-38, plain, ( ~ilf_type(_u12, set_type) | ~ilf_type(_u12, binary_relation_type) | relation_like(_u12) )).
% 0.62/0.79  cnf(matrix-39, plain, ( ~ilf_type(_u12, set_type) | ~relation_like(_u12) | ilf_type(_u12, binary_relation_type) )).
% 0.62/0.79  cnf(matrix-40, plain, ( ilf_type(skolem3, binary_relation_type) )).
% 0.62/0.79  cnf(matrix-41, plain, ( ~ilf_type(_u17, set_type) | ~ilf_type(_u16, set_type) | ~ilf_type(_u14, subset_type(cross_product(_u17, _u16))) | ilf_type(_u14, relation_type(_u17, _u16)) )).
% 0.62/0.79  cnf(matrix-42, plain, ( ~ilf_type(_u17, set_type) | ~ilf_type(_u16, set_type) | ~ilf_type(_u15, relation_type(_u17, _u16)) | ilf_type(_u15, subset_type(cross_product(_u17, _u16))) )).
% 0.62/0.79  cnf(matrix-43, plain, ( ~ilf_type(_u20, set_type) | ~ilf_type(_u19, set_type) | ilf_type(skolem4(_u20, _u19), relation_type(_u19, _u20)) )).
% 0.62/0.79  cnf(matrix-44, plain, ( ~ilf_type(_u22, set_type) | ~ilf_type(_u21, set_type) | ilf_type(cross_product(_u22, _u21), set_type) )).
% 0.62/0.79  cnf(matrix-45, plain, ( ~ilf_type(_u24, set_type) | ~ilf_type(_u23, set_type) | ilf_type(ordered_pair(_u24, _u23), set_type) )).
% 0.62/0.79  cnf(matrix-46, plain, ( ~ilf_type(_u26, set_type) | ~ilf_type(_u25, set_type) | ~ilf_type(_u25, subset_type(_u26)) | ilf_type(_u25, member_type(power_set(_u26))) )).
% 0.62/0.79  cnf(matrix-47, plain, ( ~ilf_type(_u26, set_type) | ~ilf_type(_u25, set_type) | ~ilf_type(_u25, member_type(power_set(_u26))) | ilf_type(_u25, subset_type(_u26)) )).
% 0.62/0.79  cnf(matrix-48, plain, ( ~ilf_type(_u28, set_type) | ilf_type(skolem5(_u28), subset_type(_u28)) )).
% 0.62/0.79  cnf(matrix-49, plain, ( ~ilf_type(_u32, set_type) | ~ilf_type(_u31, set_type) | ~subset(_u32, _u31) | ~ilf_type(_u29, set_type) | ~member(_u29, _u32) | member(_u29, _u31) )).
% 0.62/0.79  cnf(matrix-50, plain, ( ~ilf_type(_u32, set_type) | ~ilf_type(_u31, set_type) | subset(_u32, _u31) | ilf_type(skolem6(_u32, _u31), set_type) )).
% 0.62/0.79  cnf(matrix-51, plain, ( ~ilf_type(_u32, set_type) | ~ilf_type(_u31, set_type) | subset(_u32, _u31) | member(skolem6(_u32, _u31), _u32) )).
% 0.62/0.79  cnf(matrix-52, plain, ( ~ilf_type(_u32, set_type) | ~ilf_type(_u31, set_type) | subset(_u32, _u31) | ~member(skolem6(_u32, _u31), _u31) )).
% 0.62/0.79  cnf(matrix-53, plain, ( ~ilf_type(_u33, set_type) | subset(_u33, _u33) )).
% 0.62/0.79  cnf(matrix-54, plain, ( ~ilf_type(_u40, set_type) | ~relation_like(_u40) | ~ilf_type(_u36, set_type) | ~member(_u36, _u40) | ilf_type(skolem7(_u40, _u36), set_type) )).
% 0.62/0.79  cnf(matrix-55, plain, ( ~ilf_type(_u40, set_type) | ~relation_like(_u40) | ~ilf_type(_u36, set_type) | ~member(_u36, _u40) | ilf_type(skolem8(_u40, _u36), set_type) )).
% 0.62/0.79  cnf(matrix-56, plain, ( ~ilf_type(_u40, set_type) | ~relation_like(_u40) | ~ilf_type(_u36, set_type) | ~member(_u36, _u40) | ( _u36 = ordered_pair(skolem7(_u40, _u36), skolem8(_u40, _u36))) )).
% 0.62/0.79  cnf(matrix-57, plain, ( ~ilf_type(_u40, set_type) | relation_like(_u40) | ilf_type(skolem9(_u40), set_type) )).
% 0.62/0.79  cnf(matrix-58, plain, ( ~ilf_type(_u40, set_type) | relation_like(_u40) | member(skolem9(_u40), _u40) )).
% 0.62/0.79  cnf(matrix-59, plain, ( ~ilf_type(_u40, set_type) | relation_like(_u40) | ~ilf_type(_u38, set_type) | ~ilf_type(_u37, set_type) | ( skolem9(_u40) != ordered_pair(_u38, _u37)) )).
% 0.62/0.79  cnf(matrix-60, plain, ( ~ilf_type(_u43, set_type) | ~ilf_type(_u42, set_type) | ~ilf_type(_u41, subset_type(cross_product(_u43, _u42))) | relation_like(_u41) )).
% 0.62/0.79  cnf(matrix-61, plain, ( ~ilf_type(_u47, set_type) | ~ilf_type(_u46, set_type) | ~member(_u47, power_set(_u46)) | ~ilf_type(_u44, set_type) | ~member(_u44, _u47) | member(_u44, _u46) )).
% 0.62/0.79  cnf(matrix-62, plain, ( ~ilf_type(_u47, set_type) | ~ilf_type(_u46, set_type) | member(_u47, power_set(_u46)) | ilf_type(skolem10(_u47, _u46), set_type) )).
% 0.62/0.79  cnf(matrix-63, plain, ( ~ilf_type(_u47, set_type) | ~ilf_type(_u46, set_type) | member(_u47, power_set(_u46)) | member(skolem10(_u47, _u46), _u47) )).
% 0.62/0.79  cnf(matrix-64, plain, ( ~ilf_type(_u47, set_type) | ~ilf_type(_u46, set_type) | member(_u47, power_set(_u46)) | ~member(skolem10(_u47, _u46), _u46) )).
% 0.62/0.79  cnf(matrix-65, plain, ( ~ilf_type(_u48, set_type) | ~empty(power_set(_u48)) )).
% 0.62/0.79  cnf(matrix-66, plain, ( ~ilf_type(_u48, set_type) | ilf_type(power_set(_u48), set_type) )).
% 0.62/0.79  cnf(matrix-67, plain, ( ~ilf_type(_u50, set_type) | empty(_u49) | ~ilf_type(_u49, set_type) | ~ilf_type(_u50, member_type(_u49)) | member(_u50, _u49) )).
% 0.62/0.79  cnf(matrix-68, plain, ( ~ilf_type(_u50, set_type) | empty(_u49) | ~ilf_type(_u49, set_type) | ~member(_u50, _u49) | ilf_type(_u50, member_type(_u49)) )).
% 0.62/0.79  cnf(matrix-69, plain, ( empty(_u52) | ~ilf_type(_u52, set_type) | ilf_type(skolem11(_u52), member_type(_u52)) )).
% 0.62/0.79  cnf(matrix-70, plain, ( ~ilf_type(_u55, set_type) | ~empty(_u55) | ~ilf_type(_u53, set_type) | ~member(_u53, _u55) )).
% 0.62/0.79  cnf(matrix-71, plain, ( ~ilf_type(_u55, set_type) | empty(_u55) | ilf_type(skolem12(_u55), set_type) )).
% 0.62/0.79  cnf(matrix-72, plain, ( ~ilf_type(_u55, set_type) | empty(_u55) | member(skolem12(_u55), _u55) )).
% 0.62/0.79  cnf(matrix-73, plain, ( ~empty(_u56) | ~ilf_type(_u56, set_type) | relation_like(_u56) )).
% 0.62/0.79  cnf(matrix-74, plain, ( ~ilf_type(_u59, set_type) | ~ilf_type(_u58, set_type) | ~ilf_type(_u57, relation_type(_u59, _u58)) | ( domain(_u59, _u58, _u57) = domain_of(_u57)) )).
% 0.62/0.79  cnf(matrix-75, plain, ( ~ilf_type(_u62, set_type) | ~ilf_type(_u61, set_type) | ~ilf_type(_u60, relation_type(_u62, _u61)) | ilf_type(domain(_u62, _u61, _u60), subset_type(_u62)) )).
% 0.62/0.79  cnf(matrix-76, plain, ( ~ilf_type(_u65, set_type) | ~ilf_type(_u64, set_type) | ~ilf_type(_u63, relation_type(_u65, _u64)) | ( range(_u65, _u64, _u63) = range_of(_u63)) )).
% 0.62/0.79  cnf(matrix-77, plain, ( ~ilf_type(_u68, set_type) | ~ilf_type(_u67, set_type) | ~ilf_type(_u66, relation_type(_u68, _u67)) | ilf_type(range(_u68, _u67, _u66), subset_type(_u67)) )).
% 0.62/0.79  cnf(matrix-78, plain, ( ilf_type(_u69, set_type) )).
% 0.62/0.79  cnf(matrix-79, plain, ( ilf_type(skolem13, binary_relation_type) )).
% 0.62/0.79  cnf(matrix-80, plain, ( ~ilf_type(skolem13, relation_type(domain_of(skolem13), range_of(skolem13))) )).
% 0.62/0.79  
% 0.62/0.79  % Proof stack:
% 0.62/0.79  cnf(proof-stack, plain, 
% 0.62/0.79  proof_stack(
% 0.62/0.79  start(80), 
% 0.62/0.79  left_branch(0, 29, 3, 2), 
% 0.62/0.79  left_branch(0, 78, 0, 3), 
% 0.62/0.79  right_branch(3), 
% 0.62/0.79  left_branch(0, 53, 1, 4), 
% 0.62/0.79  lemmata(0, 0), 
% 0.62/0.79  right_branch(4), 
% 0.62/0.79  left_branch(0, 79, 0, 5), 
% 0.62/0.79  right_branch(5), 
% 0.62/0.79  right_branch(2)
% 0.62/0.79  )).
% 0.62/0.79  % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------