TSTP Solution File: SET676+3 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET676+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 : n019.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 14:32:14 EDT 2024
% Result : Theorem 0.39s 0.61s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET676+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.14/0.33 % Computer : n019.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Mar 20 21:51:03 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.39/0.61 % SZS status Theorem for theBenchmark
% 0.39/0.61 % SZS output start Proof for theBenchmark
% 0.39/0.61
% 0.39/0.61 % Formula: p1 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p1-1, axiom, ( ~ilf_type(_u1, set_type) | ~ilf_type(_u0, set_type) | ilf_type(cross_product(_u1, _u0), relation_type(_u1, _u0)) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p2 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p2-1, axiom, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(_u6, cross_product(_u8, _u7)) | ilf_type(skolem1(_u8, _u7, _u6), set_type) )).
% 0.39/0.61 cnf(p2-2, axiom, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(_u6, cross_product(_u8, _u7)) | member(skolem1(_u8, _u7, _u6), _u8) )).
% 0.39/0.61 cnf(p2-3, axiom, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(_u6, cross_product(_u8, _u7)) | ilf_type(skolem2(_u8, _u7, _u6), set_type) )).
% 0.39/0.61 cnf(p2-4, axiom, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(_u6, cross_product(_u8, _u7)) | member(skolem2(_u8, _u7, _u6), _u7) )).
% 0.39/0.61 cnf(p2-5, axiom, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(_u6, cross_product(_u8, _u7)) | ( _u6 = ordered_pair(skolem1(_u8, _u7, _u6), skolem2(_u8, _u7, _u6))) )).
% 0.39/0.61 cnf(p2-6, axiom, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~ilf_type(_u5, set_type) | ~member(_u5, _u8) | ~ilf_type(_u4, set_type) | ~member(_u4, _u7) | ( _u6 != ordered_pair(_u5, _u4)) | member(_u6, cross_product(_u8, _u7)) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p3 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p3-1, axiom, ( ~ilf_type(_u10, set_type) | ~ilf_type(_u9, set_type) | ilf_type(cross_product(_u10, _u9), set_type) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p4 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p4-1, axiom, ( ~ilf_type(_u12, set_type) | ~ilf_type(_u11, set_type) | ~ilf_type(_u11, identity_relation_of_type(_u12)) | ilf_type(_u11, relation_type(_u12, _u12)) )).
% 0.39/0.61 cnf(p4-2, axiom, ( ~ilf_type(_u12, set_type) | ~ilf_type(_u11, set_type) | ~ilf_type(_u11, relation_type(_u12, _u12)) | ilf_type(_u11, identity_relation_of_type(_u12)) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p5 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p5-1, axiom, ( ~ilf_type(_u14, set_type) | ilf_type(skolem3(_u14), identity_relation_of_type(_u14)) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p6 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p6-1, axiom, ( ~ilf_type(_u16, set_type) | ~ilf_type(_u15, set_type) | ilf_type(ordered_pair(_u16, _u15), set_type) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p7 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p7-1, axiom, ( ~ilf_type(_u20, set_type) | ~ilf_type(_u19, set_type) | ~ilf_type(_u17, subset_type(cross_product(_u20, _u19))) | ilf_type(_u17, relation_type(_u20, _u19)) )).
% 0.39/0.61 cnf(p7-2, axiom, ( ~ilf_type(_u20, set_type) | ~ilf_type(_u19, set_type) | ~ilf_type(_u18, relation_type(_u20, _u19)) | ilf_type(_u18, subset_type(cross_product(_u20, _u19))) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p8 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p8-1, axiom, ( ~ilf_type(_u23, set_type) | ~ilf_type(_u22, set_type) | ilf_type(skolem4(_u23, _u22), relation_type(_u22, _u23)) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p9 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p9-1, axiom, ( ~ilf_type(_u25, set_type) | ~ilf_type(_u24, set_type) | ~ilf_type(_u24, subset_type(_u25)) | ilf_type(_u24, member_type(power_set(_u25))) )).
% 0.39/0.61 cnf(p9-2, axiom, ( ~ilf_type(_u25, set_type) | ~ilf_type(_u24, set_type) | ~ilf_type(_u24, member_type(power_set(_u25))) | ilf_type(_u24, subset_type(_u25)) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p10 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p10-1, axiom, ( ~ilf_type(_u27, set_type) | ilf_type(skolem5(_u27), subset_type(_u27)) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p11 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p11-1, axiom, ( ~ilf_type(_u31, set_type) | ~ilf_type(_u30, set_type) | ~member(_u31, power_set(_u30)) | ~ilf_type(_u28, set_type) | ~member(_u28, _u31) | member(_u28, _u30) )).
% 0.39/0.61 cnf(p11-2, axiom, ( ~ilf_type(_u31, set_type) | ~ilf_type(_u30, set_type) | member(_u31, power_set(_u30)) | ilf_type(skolem6(_u31, _u30), set_type) )).
% 0.39/0.61 cnf(p11-3, axiom, ( ~ilf_type(_u31, set_type) | ~ilf_type(_u30, set_type) | member(_u31, power_set(_u30)) | member(skolem6(_u31, _u30), _u31) )).
% 0.39/0.61 cnf(p11-4, axiom, ( ~ilf_type(_u31, set_type) | ~ilf_type(_u30, set_type) | member(_u31, power_set(_u30)) | ~member(skolem6(_u31, _u30), _u30) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p12 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p12-1, axiom, ( ~ilf_type(_u32, set_type) | ~empty(power_set(_u32)) )).
% 0.39/0.61 cnf(p12-2, axiom, ( ~ilf_type(_u32, set_type) | ilf_type(power_set(_u32), set_type) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p13 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p13-1, axiom, ( ~ilf_type(_u34, set_type) | empty(_u33) | ~ilf_type(_u33, set_type) | ~ilf_type(_u34, member_type(_u33)) | member(_u34, _u33) )).
% 0.39/0.61 cnf(p13-2, axiom, ( ~ilf_type(_u34, set_type) | empty(_u33) | ~ilf_type(_u33, set_type) | ~member(_u34, _u33) | ilf_type(_u34, member_type(_u33)) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p14 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p14-1, axiom, ( empty(_u36) | ~ilf_type(_u36, set_type) | ilf_type(skolem7(_u36), member_type(_u36)) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p15 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p15-1, axiom, ( ~ilf_type(_u39, set_type) | ~empty(_u39) | ~ilf_type(_u37, set_type) | ~member(_u37, _u39) )).
% 0.39/0.61 cnf(p15-2, axiom, ( ~ilf_type(_u39, set_type) | empty(_u39) | ilf_type(skolem8(_u39), set_type) )).
% 0.39/0.61 cnf(p15-3, axiom, ( ~ilf_type(_u39, set_type) | empty(_u39) | member(skolem8(_u39), _u39) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p16 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p16-1, axiom, ( ~ilf_type(_u46, set_type) | ~relation_like(_u46) | ~ilf_type(_u42, set_type) | ~member(_u42, _u46) | ilf_type(skolem9(_u46, _u42), set_type) )).
% 0.39/0.61 cnf(p16-2, axiom, ( ~ilf_type(_u46, set_type) | ~relation_like(_u46) | ~ilf_type(_u42, set_type) | ~member(_u42, _u46) | ilf_type(skolem10(_u46, _u42), set_type) )).
% 0.39/0.61 cnf(p16-3, axiom, ( ~ilf_type(_u46, set_type) | ~relation_like(_u46) | ~ilf_type(_u42, set_type) | ~member(_u42, _u46) | ( _u42 = ordered_pair(skolem9(_u46, _u42), skolem10(_u46, _u42))) )).
% 0.39/0.61 cnf(p16-4, axiom, ( ~ilf_type(_u46, set_type) | relation_like(_u46) | ilf_type(skolem11(_u46), set_type) )).
% 0.39/0.61 cnf(p16-5, axiom, ( ~ilf_type(_u46, set_type) | relation_like(_u46) | member(skolem11(_u46), _u46) )).
% 0.39/0.61 cnf(p16-6, axiom, ( ~ilf_type(_u46, set_type) | relation_like(_u46) | ~ilf_type(_u44, set_type) | ~ilf_type(_u43, set_type) | ( skolem11(_u46) != ordered_pair(_u44, _u43)) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p17 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p17-1, axiom, ( ~empty(_u47) | ~ilf_type(_u47, set_type) | relation_like(_u47) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p18 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p18-1, axiom, ( ~ilf_type(_u50, set_type) | ~ilf_type(_u49, set_type) | ~ilf_type(_u48, subset_type(cross_product(_u50, _u49))) | relation_like(_u48) )).
% 0.39/0.61
% 0.39/0.61 % Formula: p19 ( axiom ) converted to clauses:
% 0.39/0.61 cnf(p19-1, axiom, ( ilf_type(_u51, set_type) )).
% 0.39/0.61
% 0.39/0.61 % Formula: prove_relset_1_41 ( conjecture ) (definitionally) converted to clauses:
% 0.39/0.61 cnf(prove_relset_1_41-1, negated_conjecture, ( ilf_type(skolem12, set_type) )).
% 0.39/0.61 cnf(prove_relset_1_41-2, negated_conjecture, ( ~ilf_type(cross_product(skolem12, skolem12), identity_relation_of_type(skolem12)) )).
% 0.39/0.61
% 0.39/0.61 % Problem matrix:
% 0.39/0.61 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.39/0.61 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.39/0.61 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.39/0.61 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( cross_product(__eqx_0, __eqx_1) = cross_product(__eqy_0, __eqy_1)) )).
% 0.39/0.61 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( relation_type(__eqx_0, __eqx_1) = relation_type(__eqy_0, __eqy_1)) )).
% 0.39/0.61 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 0.39/0.61 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( identity_relation_of_type(__eqx_0) = identity_relation_of_type(__eqy_0)) )).
% 0.39/0.61 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( subset_type(__eqx_0) = subset_type(__eqy_0)) )).
% 0.39/0.61 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( power_set(__eqx_0) = power_set(__eqy_0)) )).
% 0.39/0.61 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( member_type(__eqx_0) = member_type(__eqy_0)) )).
% 0.39/0.61 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem1(__eqx_0, __eqx_1, __eqx_2) = skolem1(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.39/0.61 cnf(matrix-11, 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)) )).
% 0.39/0.61 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( skolem3(__eqx_0) = skolem3(__eqy_0)) )).
% 0.39/0.61 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 0.39/0.61 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( skolem5(__eqx_0) = skolem5(__eqy_0)) )).
% 0.39/0.61 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem6(__eqx_0, __eqx_1) = skolem6(__eqy_0, __eqy_1)) )).
% 0.39/0.61 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( skolem7(__eqx_0) = skolem7(__eqy_0)) )).
% 0.39/0.61 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( skolem8(__eqx_0) = skolem8(__eqy_0)) )).
% 0.39/0.61 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem9(__eqx_0, __eqx_1) = skolem9(__eqy_0, __eqy_1)) )).
% 0.39/0.61 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem10(__eqx_0, __eqx_1) = skolem10(__eqy_0, __eqy_1)) )).
% 0.39/0.61 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( skolem11(__eqx_0) = skolem11(__eqy_0)) )).
% 0.39/0.61 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~ilf_type(__eqx_0, __eqx_1) | ilf_type(__eqy_0, __eqy_1) )).
% 0.39/0.61 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 0.39/0.61 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 0.39/0.61 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ~relation_like(__eqx_0) | relation_like(__eqy_0) )).
% 0.39/0.61 cnf(matrix-25, plain, ( ~ilf_type(_u1, set_type) | ~ilf_type(_u0, set_type) | ilf_type(cross_product(_u1, _u0), relation_type(_u1, _u0)) )).
% 0.39/0.61 cnf(matrix-26, plain, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(_u6, cross_product(_u8, _u7)) | ilf_type(skolem1(_u8, _u7, _u6), set_type) )).
% 0.39/0.61 cnf(matrix-27, plain, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(_u6, cross_product(_u8, _u7)) | member(skolem1(_u8, _u7, _u6), _u8) )).
% 0.39/0.61 cnf(matrix-28, plain, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(_u6, cross_product(_u8, _u7)) | ilf_type(skolem2(_u8, _u7, _u6), set_type) )).
% 0.39/0.61 cnf(matrix-29, plain, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(_u6, cross_product(_u8, _u7)) | member(skolem2(_u8, _u7, _u6), _u7) )).
% 0.39/0.61 cnf(matrix-30, plain, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(_u6, cross_product(_u8, _u7)) | ( _u6 = ordered_pair(skolem1(_u8, _u7, _u6), skolem2(_u8, _u7, _u6))) )).
% 0.39/0.61 cnf(matrix-31, plain, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~ilf_type(_u5, set_type) | ~member(_u5, _u8) | ~ilf_type(_u4, set_type) | ~member(_u4, _u7) | ( _u6 != ordered_pair(_u5, _u4)) | member(_u6, cross_product(_u8, _u7)) )).
% 0.39/0.61 cnf(matrix-32, plain, ( ~ilf_type(_u10, set_type) | ~ilf_type(_u9, set_type) | ilf_type(cross_product(_u10, _u9), set_type) )).
% 0.39/0.61 cnf(matrix-33, plain, ( ~ilf_type(_u12, set_type) | ~ilf_type(_u11, set_type) | ~ilf_type(_u11, identity_relation_of_type(_u12)) | ilf_type(_u11, relation_type(_u12, _u12)) )).
% 0.39/0.61 cnf(matrix-34, plain, ( ~ilf_type(_u12, set_type) | ~ilf_type(_u11, set_type) | ~ilf_type(_u11, relation_type(_u12, _u12)) | ilf_type(_u11, identity_relation_of_type(_u12)) )).
% 0.39/0.61 cnf(matrix-35, plain, ( ~ilf_type(_u14, set_type) | ilf_type(skolem3(_u14), identity_relation_of_type(_u14)) )).
% 0.39/0.61 cnf(matrix-36, plain, ( ~ilf_type(_u16, set_type) | ~ilf_type(_u15, set_type) | ilf_type(ordered_pair(_u16, _u15), set_type) )).
% 0.39/0.61 cnf(matrix-37, plain, ( ~ilf_type(_u20, set_type) | ~ilf_type(_u19, set_type) | ~ilf_type(_u17, subset_type(cross_product(_u20, _u19))) | ilf_type(_u17, relation_type(_u20, _u19)) )).
% 0.39/0.61 cnf(matrix-38, plain, ( ~ilf_type(_u20, set_type) | ~ilf_type(_u19, set_type) | ~ilf_type(_u18, relation_type(_u20, _u19)) | ilf_type(_u18, subset_type(cross_product(_u20, _u19))) )).
% 0.39/0.61 cnf(matrix-39, plain, ( ~ilf_type(_u23, set_type) | ~ilf_type(_u22, set_type) | ilf_type(skolem4(_u23, _u22), relation_type(_u22, _u23)) )).
% 0.39/0.61 cnf(matrix-40, plain, ( ~ilf_type(_u25, set_type) | ~ilf_type(_u24, set_type) | ~ilf_type(_u24, subset_type(_u25)) | ilf_type(_u24, member_type(power_set(_u25))) )).
% 0.39/0.61 cnf(matrix-41, plain, ( ~ilf_type(_u25, set_type) | ~ilf_type(_u24, set_type) | ~ilf_type(_u24, member_type(power_set(_u25))) | ilf_type(_u24, subset_type(_u25)) )).
% 0.39/0.61 cnf(matrix-42, plain, ( ~ilf_type(_u27, set_type) | ilf_type(skolem5(_u27), subset_type(_u27)) )).
% 0.39/0.61 cnf(matrix-43, plain, ( ~ilf_type(_u31, set_type) | ~ilf_type(_u30, set_type) | ~member(_u31, power_set(_u30)) | ~ilf_type(_u28, set_type) | ~member(_u28, _u31) | member(_u28, _u30) )).
% 0.39/0.61 cnf(matrix-44, plain, ( ~ilf_type(_u31, set_type) | ~ilf_type(_u30, set_type) | member(_u31, power_set(_u30)) | ilf_type(skolem6(_u31, _u30), set_type) )).
% 0.39/0.61 cnf(matrix-45, plain, ( ~ilf_type(_u31, set_type) | ~ilf_type(_u30, set_type) | member(_u31, power_set(_u30)) | member(skolem6(_u31, _u30), _u31) )).
% 0.39/0.61 cnf(matrix-46, plain, ( ~ilf_type(_u31, set_type) | ~ilf_type(_u30, set_type) | member(_u31, power_set(_u30)) | ~member(skolem6(_u31, _u30), _u30) )).
% 0.39/0.61 cnf(matrix-47, plain, ( ~ilf_type(_u32, set_type) | ~empty(power_set(_u32)) )).
% 0.39/0.61 cnf(matrix-48, plain, ( ~ilf_type(_u32, set_type) | ilf_type(power_set(_u32), set_type) )).
% 0.39/0.61 cnf(matrix-49, plain, ( ~ilf_type(_u34, set_type) | empty(_u33) | ~ilf_type(_u33, set_type) | ~ilf_type(_u34, member_type(_u33)) | member(_u34, _u33) )).
% 0.39/0.61 cnf(matrix-50, plain, ( ~ilf_type(_u34, set_type) | empty(_u33) | ~ilf_type(_u33, set_type) | ~member(_u34, _u33) | ilf_type(_u34, member_type(_u33)) )).
% 0.39/0.61 cnf(matrix-51, plain, ( empty(_u36) | ~ilf_type(_u36, set_type) | ilf_type(skolem7(_u36), member_type(_u36)) )).
% 0.39/0.61 cnf(matrix-52, plain, ( ~ilf_type(_u39, set_type) | ~empty(_u39) | ~ilf_type(_u37, set_type) | ~member(_u37, _u39) )).
% 0.39/0.61 cnf(matrix-53, plain, ( ~ilf_type(_u39, set_type) | empty(_u39) | ilf_type(skolem8(_u39), set_type) )).
% 0.39/0.61 cnf(matrix-54, plain, ( ~ilf_type(_u39, set_type) | empty(_u39) | member(skolem8(_u39), _u39) )).
% 0.39/0.61 cnf(matrix-55, plain, ( ~ilf_type(_u46, set_type) | ~relation_like(_u46) | ~ilf_type(_u42, set_type) | ~member(_u42, _u46) | ilf_type(skolem9(_u46, _u42), set_type) )).
% 0.39/0.61 cnf(matrix-56, plain, ( ~ilf_type(_u46, set_type) | ~relation_like(_u46) | ~ilf_type(_u42, set_type) | ~member(_u42, _u46) | ilf_type(skolem10(_u46, _u42), set_type) )).
% 0.39/0.61 cnf(matrix-57, plain, ( ~ilf_type(_u46, set_type) | ~relation_like(_u46) | ~ilf_type(_u42, set_type) | ~member(_u42, _u46) | ( _u42 = ordered_pair(skolem9(_u46, _u42), skolem10(_u46, _u42))) )).
% 0.39/0.61 cnf(matrix-58, plain, ( ~ilf_type(_u46, set_type) | relation_like(_u46) | ilf_type(skolem11(_u46), set_type) )).
% 0.39/0.61 cnf(matrix-59, plain, ( ~ilf_type(_u46, set_type) | relation_like(_u46) | member(skolem11(_u46), _u46) )).
% 0.39/0.61 cnf(matrix-60, plain, ( ~ilf_type(_u46, set_type) | relation_like(_u46) | ~ilf_type(_u44, set_type) | ~ilf_type(_u43, set_type) | ( skolem11(_u46) != ordered_pair(_u44, _u43)) )).
% 0.39/0.61 cnf(matrix-61, plain, ( ~empty(_u47) | ~ilf_type(_u47, set_type) | relation_like(_u47) )).
% 0.39/0.61 cnf(matrix-62, plain, ( ~ilf_type(_u50, set_type) | ~ilf_type(_u49, set_type) | ~ilf_type(_u48, subset_type(cross_product(_u50, _u49))) | relation_like(_u48) )).
% 0.39/0.61 cnf(matrix-63, plain, ( ilf_type(_u51, set_type) )).
% 0.39/0.61 cnf(matrix-64, plain, ( ilf_type(skolem12, set_type) )).
% 0.39/0.61 cnf(matrix-65, plain, ( ~ilf_type(cross_product(skolem12, skolem12), identity_relation_of_type(skolem12)) )).
% 0.39/0.61
% 0.39/0.61 % Proof stack:
% 0.39/0.61 cnf(proof-stack, plain,
% 0.39/0.61 proof_stack(
% 0.39/0.61 start(65),
% 0.39/0.61 left_branch(0, 34, 3, 2),
% 0.39/0.61 left_branch(0, 64, 0, 3),
% 0.39/0.61 right_branch(3),
% 0.39/0.61 left_branch(0, 25, 2, 4),
% 0.39/0.61 lemmata(0, 0),
% 0.39/0.61 lemmata(0, 0),
% 0.39/0.61 right_branch(4),
% 0.39/0.61 left_branch(0, 63, 0, 5),
% 0.39/0.61 right_branch(5),
% 0.39/0.61 right_branch(2)
% 0.39/0.61 )).
% 0.39/0.61 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------