TSTP Solution File: SET677+3 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET677+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 : n008.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 0.63s 0.83s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET677+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n008.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 : Wed Mar 20 21:31:43 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.63/0.83 % SZS status Theorem for theBenchmark
% 0.63/0.83 % SZS output start Proof for theBenchmark
% 0.63/0.83
% 0.63/0.83 % Formula: p1 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p1-1, axiom, ( ~ilf_type(_u2, set_type) | ~ilf_type(_u1, set_type) | ~ilf_type(_u0, relation_type(_u1, _u2)) | ~subset(identity_relation_of(_u1), _u0) | ( _u1 = domain(_u1, _u2, _u0)) )).
% 0.63/0.83 cnf(p1-2, axiom, ( ~ilf_type(_u2, set_type) | ~ilf_type(_u1, set_type) | ~ilf_type(_u0, relation_type(_u1, _u2)) | ~subset(identity_relation_of(_u1), _u0) | subset(_u1, range(_u1, _u2, _u0)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p2 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p2-1, axiom, ( ~ilf_type(_u5, set_type) | ~ilf_type(_u4, set_type) | ~ilf_type(_u3, relation_type(_u5, _u4)) | ~subset(identity_relation_of(_u4), _u3) | subset(_u4, domain(_u5, _u4, _u3)) )).
% 0.63/0.83 cnf(p2-2, axiom, ( ~ilf_type(_u5, set_type) | ~ilf_type(_u4, set_type) | ~ilf_type(_u3, relation_type(_u5, _u4)) | ~subset(identity_relation_of(_u4), _u3) | ( _u4 = range(_u5, _u4, _u3)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p3 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p3-1, axiom, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(ordered_pair(_u7, _u6), identity_relation_of(_u8)) | member(_u7, _u8) )).
% 0.63/0.83 cnf(p3-2, axiom, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(ordered_pair(_u7, _u6), identity_relation_of(_u8)) | ( _u7 = _u6) )).
% 0.63/0.83 cnf(p3-3, axiom, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(_u7, _u8) | ( _u7 != _u6) | member(ordered_pair(_u7, _u6), identity_relation_of(_u8)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p4 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p4-1, axiom, ( ~ilf_type(_u9, set_type) | ilf_type(identity_relation_of(_u9), binary_relation_type) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p5 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p5-1, axiom, ( ~ilf_type(_u11, set_type) | ~ilf_type(_u10, set_type) | ~ilf_type(_u10, identity_relation_of_type(_u11)) | ilf_type(_u10, relation_type(_u11, _u11)) )).
% 0.63/0.83 cnf(p5-2, axiom, ( ~ilf_type(_u11, set_type) | ~ilf_type(_u10, set_type) | ~ilf_type(_u10, relation_type(_u11, _u11)) | ilf_type(_u10, identity_relation_of_type(_u11)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p6 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p6-1, axiom, ( ~ilf_type(_u13, set_type) | ilf_type(skolem1(_u13), identity_relation_of_type(_u13)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p7 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p7-1, axiom, ( ~ilf_type(_u19, binary_relation_type) | ~ilf_type(_u18, binary_relation_type) | ~subset(_u19, _u18) | ~ilf_type(_u15, set_type) | ~ilf_type(_u14, set_type) | ~member(ordered_pair(_u15, _u14), _u19) | member(ordered_pair(_u15, _u14), _u18) )).
% 0.63/0.83 cnf(p7-2, axiom, ( ~ilf_type(_u19, binary_relation_type) | ~ilf_type(_u18, binary_relation_type) | subset(_u19, _u18) | ilf_type(skolem2(_u19, _u18), set_type) )).
% 0.63/0.83 cnf(p7-3, axiom, ( ~ilf_type(_u19, binary_relation_type) | ~ilf_type(_u18, binary_relation_type) | subset(_u19, _u18) | ilf_type(skolem3(_u19, _u18), set_type) )).
% 0.63/0.83 cnf(p7-4, axiom, ( ~ilf_type(_u19, binary_relation_type) | ~ilf_type(_u18, binary_relation_type) | subset(_u19, _u18) | member(ordered_pair(skolem2(_u19, _u18), skolem3(_u19, _u18)), _u19) )).
% 0.63/0.83 cnf(p7-5, axiom, ( ~ilf_type(_u19, binary_relation_type) | ~ilf_type(_u18, binary_relation_type) | subset(_u19, _u18) | ~member(ordered_pair(skolem2(_u19, _u18), skolem3(_u19, _u18)), _u18) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p8 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p8-1, axiom, ( ~ilf_type(_u21, set_type) | ~ilf_type(_u20, set_type) | ( _u21 != _u20) | subset(_u21, _u20) )).
% 0.63/0.83 cnf(p8-2, axiom, ( ~ilf_type(_u21, set_type) | ~ilf_type(_u20, set_type) | ( _u21 != _u20) | subset(_u20, _u21) )).
% 0.63/0.83 cnf(p8-3, axiom, ( ~ilf_type(_u21, set_type) | ~ilf_type(_u20, set_type) | ~subset(_u21, _u20) | ~subset(_u20, _u21) | ( _u21 = _u20) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p9 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p9-1, axiom, ( ~ilf_type(_u22, binary_relation_type) | ilf_type(domain_of(_u22), set_type) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p10 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p10-1, axiom, ( ~ilf_type(_u23, binary_relation_type) | ilf_type(range_of(_u23), set_type) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p11 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p11-1, axiom, ( ~ilf_type(_u25, set_type) | ~ilf_type(_u24, set_type) | ilf_type(ordered_pair(_u25, _u24), set_type) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p12 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p12-1, axiom, ( ~ilf_type(_u26, set_type) | ~ilf_type(_u26, binary_relation_type) | relation_like(_u26) )).
% 0.63/0.83 cnf(p12-2, axiom, ( ~ilf_type(_u26, set_type) | ~relation_like(_u26) | ilf_type(_u26, binary_relation_type) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p13 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p13-1, axiom, ( ilf_type(skolem4, binary_relation_type) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p14 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p14-1, axiom, ( ~ilf_type(_u31, set_type) | ~ilf_type(_u30, set_type) | ~ilf_type(_u28, subset_type(cross_product(_u31, _u30))) | ilf_type(_u28, relation_type(_u31, _u30)) )).
% 0.63/0.83 cnf(p14-2, axiom, ( ~ilf_type(_u31, set_type) | ~ilf_type(_u30, set_type) | ~ilf_type(_u29, relation_type(_u31, _u30)) | ilf_type(_u29, subset_type(cross_product(_u31, _u30))) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p15 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p15-1, axiom, ( ~ilf_type(_u34, set_type) | ~ilf_type(_u33, set_type) | ilf_type(skolem5(_u34, _u33), relation_type(_u33, _u34)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p16 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p16-1, axiom, ( ~ilf_type(_u36, set_type) | ~ilf_type(_u35, set_type) | ~ilf_type(_u35, subset_type(_u36)) | ilf_type(_u35, member_type(power_set(_u36))) )).
% 0.63/0.83 cnf(p16-2, axiom, ( ~ilf_type(_u36, set_type) | ~ilf_type(_u35, set_type) | ~ilf_type(_u35, member_type(power_set(_u36))) | ilf_type(_u35, subset_type(_u36)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p17 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p17-1, axiom, ( ~ilf_type(_u38, set_type) | ilf_type(skolem6(_u38), subset_type(_u38)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p18 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p18-1, axiom, ( ~ilf_type(_u42, set_type) | ~ilf_type(_u41, set_type) | ~subset(_u42, _u41) | ~ilf_type(_u39, set_type) | ~member(_u39, _u42) | member(_u39, _u41) )).
% 0.63/0.83 cnf(p18-2, axiom, ( ~ilf_type(_u42, set_type) | ~ilf_type(_u41, set_type) | subset(_u42, _u41) | ilf_type(skolem7(_u42, _u41), set_type) )).
% 0.63/0.83 cnf(p18-3, axiom, ( ~ilf_type(_u42, set_type) | ~ilf_type(_u41, set_type) | subset(_u42, _u41) | member(skolem7(_u42, _u41), _u42) )).
% 0.63/0.83 cnf(p18-4, axiom, ( ~ilf_type(_u42, set_type) | ~ilf_type(_u41, set_type) | subset(_u42, _u41) | ~member(skolem7(_u42, _u41), _u41) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p19 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p19-1, axiom, ( ~ilf_type(_u43, set_type) | subset(_u43, _u43) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p20 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p20-1, axiom, ( ~ilf_type(_u44, binary_relation_type) | subset(_u44, _u44) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p21 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p21-1, axiom, ( ~ilf_type(_u46, set_type) | ~ilf_type(_u45, set_type) | ilf_type(cross_product(_u46, _u45), set_type) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p22 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p22-1, axiom, ( ~ilf_type(_u50, set_type) | ~ilf_type(_u49, set_type) | ~member(_u50, power_set(_u49)) | ~ilf_type(_u47, set_type) | ~member(_u47, _u50) | member(_u47, _u49) )).
% 0.63/0.83 cnf(p22-2, axiom, ( ~ilf_type(_u50, set_type) | ~ilf_type(_u49, set_type) | member(_u50, power_set(_u49)) | ilf_type(skolem8(_u50, _u49), set_type) )).
% 0.63/0.83 cnf(p22-3, axiom, ( ~ilf_type(_u50, set_type) | ~ilf_type(_u49, set_type) | member(_u50, power_set(_u49)) | member(skolem8(_u50, _u49), _u50) )).
% 0.63/0.83 cnf(p22-4, axiom, ( ~ilf_type(_u50, set_type) | ~ilf_type(_u49, set_type) | member(_u50, power_set(_u49)) | ~member(skolem8(_u50, _u49), _u49) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p23 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p23-1, axiom, ( ~ilf_type(_u51, set_type) | ~empty(power_set(_u51)) )).
% 0.63/0.83 cnf(p23-2, axiom, ( ~ilf_type(_u51, set_type) | ilf_type(power_set(_u51), set_type) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p24 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p24-1, axiom, ( ~ilf_type(_u53, set_type) | empty(_u52) | ~ilf_type(_u52, set_type) | ~ilf_type(_u53, member_type(_u52)) | member(_u53, _u52) )).
% 0.63/0.83 cnf(p24-2, axiom, ( ~ilf_type(_u53, set_type) | empty(_u52) | ~ilf_type(_u52, set_type) | ~member(_u53, _u52) | ilf_type(_u53, member_type(_u52)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p25 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p25-1, axiom, ( empty(_u55) | ~ilf_type(_u55, set_type) | ilf_type(skolem9(_u55), member_type(_u55)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p26 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p26-1, axiom, ( ~ilf_type(_u62, set_type) | ~relation_like(_u62) | ~ilf_type(_u58, set_type) | ~member(_u58, _u62) | ilf_type(skolem10(_u62, _u58), set_type) )).
% 0.63/0.83 cnf(p26-2, axiom, ( ~ilf_type(_u62, set_type) | ~relation_like(_u62) | ~ilf_type(_u58, set_type) | ~member(_u58, _u62) | ilf_type(skolem11(_u62, _u58), set_type) )).
% 0.63/0.83 cnf(p26-3, axiom, ( ~ilf_type(_u62, set_type) | ~relation_like(_u62) | ~ilf_type(_u58, set_type) | ~member(_u58, _u62) | ( _u58 = ordered_pair(skolem10(_u62, _u58), skolem11(_u62, _u58))) )).
% 0.63/0.83 cnf(p26-4, axiom, ( ~ilf_type(_u62, set_type) | relation_like(_u62) | ilf_type(skolem12(_u62), set_type) )).
% 0.63/0.83 cnf(p26-5, axiom, ( ~ilf_type(_u62, set_type) | relation_like(_u62) | member(skolem12(_u62), _u62) )).
% 0.63/0.83 cnf(p26-6, axiom, ( ~ilf_type(_u62, set_type) | relation_like(_u62) | ~ilf_type(_u60, set_type) | ~ilf_type(_u59, set_type) | ( skolem12(_u62) != ordered_pair(_u60, _u59)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p27 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p27-1, axiom, ( ~ilf_type(_u65, set_type) | ~ilf_type(_u64, set_type) | ~ilf_type(_u63, subset_type(cross_product(_u65, _u64))) | relation_like(_u63) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p28 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p28-1, axiom, ( ~ilf_type(_u68, set_type) | ~empty(_u68) | ~ilf_type(_u66, set_type) | ~member(_u66, _u68) )).
% 0.63/0.83 cnf(p28-2, axiom, ( ~ilf_type(_u68, set_type) | empty(_u68) | ilf_type(skolem13(_u68), set_type) )).
% 0.63/0.83 cnf(p28-3, axiom, ( ~ilf_type(_u68, set_type) | empty(_u68) | member(skolem13(_u68), _u68) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p29 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p29-1, axiom, ( ~empty(_u69) | ~ilf_type(_u69, set_type) | relation_like(_u69) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p30 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p30-1, axiom, ( ~ilf_type(_u72, set_type) | ~ilf_type(_u71, set_type) | ~ilf_type(_u70, relation_type(_u72, _u71)) | ( domain(_u72, _u71, _u70) = domain_of(_u70)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p31 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p31-1, axiom, ( ~ilf_type(_u75, set_type) | ~ilf_type(_u74, set_type) | ~ilf_type(_u73, relation_type(_u75, _u74)) | ilf_type(domain(_u75, _u74, _u73), subset_type(_u75)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p32 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p32-1, axiom, ( ~ilf_type(_u78, set_type) | ~ilf_type(_u77, set_type) | ~ilf_type(_u76, relation_type(_u78, _u77)) | ( range(_u78, _u77, _u76) = range_of(_u76)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p33 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p33-1, axiom, ( ~ilf_type(_u81, set_type) | ~ilf_type(_u80, set_type) | ~ilf_type(_u79, relation_type(_u81, _u80)) | ilf_type(range(_u81, _u80, _u79), subset_type(_u80)) )).
% 0.63/0.83
% 0.63/0.83 % Formula: p34 ( axiom ) converted to clauses:
% 0.63/0.83 cnf(p34-1, axiom, ( ilf_type(_u82, set_type) )).
% 0.63/0.83
% 0.63/0.83 % Formula: prove_relset_1_44 ( conjecture ) (definitionally) converted to clauses:
% 0.63/0.83 cnf(prove_relset_1_44-1, negated_conjecture, ( ilf_type(skolem14, set_type) )).
% 0.63/0.83 cnf(prove_relset_1_44-2, negated_conjecture, ( ilf_type(skolem15, identity_relation_of_type(skolem14)) )).
% 0.63/0.83 cnf(prove_relset_1_44-3, negated_conjecture, ( subset(identity_relation_of(skolem14), skolem15) )).
% 0.63/0.83 cnf(prove_relset_1_44-4, negated_conjecture, ( ( skolem14 != domain(skolem14, skolem14, skolem15)) | ( skolem14 != range(skolem14, skolem14, skolem15)) )).
% 0.63/0.83
% 0.63/0.83 % Problem matrix:
% 0.63/0.83 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.63/0.83 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.63/0.83 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.63/0.83 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( relation_type(__eqx_0, __eqx_1) = relation_type(__eqy_0, __eqy_1)) )).
% 0.63/0.83 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( identity_relation_of(__eqx_0) = identity_relation_of(__eqy_0)) )).
% 0.63/0.83 cnf(matrix-5, 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)) )).
% 0.63/0.83 cnf(matrix-6, 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)) )).
% 0.63/0.83 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 0.63/0.83 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( identity_relation_of_type(__eqx_0) = identity_relation_of_type(__eqy_0)) )).
% 0.63/0.83 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( domain_of(__eqx_0) = domain_of(__eqy_0)) )).
% 0.63/0.83 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( range_of(__eqx_0) = range_of(__eqy_0)) )).
% 0.63/0.83 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( cross_product(__eqx_0, __eqx_1) = cross_product(__eqy_0, __eqy_1)) )).
% 0.63/0.83 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( subset_type(__eqx_0) = subset_type(__eqy_0)) )).
% 0.63/0.83 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( power_set(__eqx_0) = power_set(__eqy_0)) )).
% 0.63/0.83 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( member_type(__eqx_0) = member_type(__eqy_0)) )).
% 0.63/0.83 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 0.63/0.83 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 0.63/0.83 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 0.63/0.83 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem5(__eqx_0, __eqx_1) = skolem5(__eqy_0, __eqy_1)) )).
% 0.63/0.83 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( skolem6(__eqx_0) = skolem6(__eqy_0)) )).
% 0.63/0.83 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem7(__eqx_0, __eqx_1) = skolem7(__eqy_0, __eqy_1)) )).
% 0.63/0.83 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem8(__eqx_0, __eqx_1) = skolem8(__eqy_0, __eqy_1)) )).
% 0.63/0.83 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( skolem9(__eqx_0) = skolem9(__eqy_0)) )).
% 0.63/0.83 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem10(__eqx_0, __eqx_1) = skolem10(__eqy_0, __eqy_1)) )).
% 0.63/0.83 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem11(__eqx_0, __eqx_1) = skolem11(__eqy_0, __eqy_1)) )).
% 0.63/0.83 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( skolem12(__eqx_0) = skolem12(__eqy_0)) )).
% 0.63/0.83 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( skolem13(__eqx_0) = skolem13(__eqy_0)) )).
% 0.63/0.83 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~ilf_type(__eqx_0, __eqx_1) | ilf_type(__eqy_0, __eqy_1) )).
% 0.63/0.83 cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 0.63/0.83 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 0.63/0.83 cnf(matrix-30, plain, ( ( __eqx_0 != __eqy_0) | ~relation_like(__eqx_0) | relation_like(__eqy_0) )).
% 0.63/0.83 cnf(matrix-31, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 0.63/0.83 cnf(matrix-32, plain, ( ~ilf_type(_u2, set_type) | ~ilf_type(_u1, set_type) | ~ilf_type(_u0, relation_type(_u1, _u2)) | ~subset(identity_relation_of(_u1), _u0) | ( _u1 = domain(_u1, _u2, _u0)) )).
% 0.63/0.83 cnf(matrix-33, plain, ( ~ilf_type(_u2, set_type) | ~ilf_type(_u1, set_type) | ~ilf_type(_u0, relation_type(_u1, _u2)) | ~subset(identity_relation_of(_u1), _u0) | subset(_u1, range(_u1, _u2, _u0)) )).
% 0.63/0.83 cnf(matrix-34, plain, ( ~ilf_type(_u5, set_type) | ~ilf_type(_u4, set_type) | ~ilf_type(_u3, relation_type(_u5, _u4)) | ~subset(identity_relation_of(_u4), _u3) | subset(_u4, domain(_u5, _u4, _u3)) )).
% 0.63/0.83 cnf(matrix-35, plain, ( ~ilf_type(_u5, set_type) | ~ilf_type(_u4, set_type) | ~ilf_type(_u3, relation_type(_u5, _u4)) | ~subset(identity_relation_of(_u4), _u3) | ( _u4 = range(_u5, _u4, _u3)) )).
% 0.63/0.83 cnf(matrix-36, plain, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(ordered_pair(_u7, _u6), identity_relation_of(_u8)) | member(_u7, _u8) )).
% 0.63/0.83 cnf(matrix-37, plain, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(ordered_pair(_u7, _u6), identity_relation_of(_u8)) | ( _u7 = _u6) )).
% 0.63/0.83 cnf(matrix-38, plain, ( ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, set_type) | ~member(_u7, _u8) | ( _u7 != _u6) | member(ordered_pair(_u7, _u6), identity_relation_of(_u8)) )).
% 0.63/0.83 cnf(matrix-39, plain, ( ~ilf_type(_u9, set_type) | ilf_type(identity_relation_of(_u9), binary_relation_type) )).
% 0.63/0.83 cnf(matrix-40, plain, ( ~ilf_type(_u11, set_type) | ~ilf_type(_u10, set_type) | ~ilf_type(_u10, identity_relation_of_type(_u11)) | ilf_type(_u10, relation_type(_u11, _u11)) )).
% 0.63/0.83 cnf(matrix-41, plain, ( ~ilf_type(_u11, set_type) | ~ilf_type(_u10, set_type) | ~ilf_type(_u10, relation_type(_u11, _u11)) | ilf_type(_u10, identity_relation_of_type(_u11)) )).
% 0.63/0.83 cnf(matrix-42, plain, ( ~ilf_type(_u13, set_type) | ilf_type(skolem1(_u13), identity_relation_of_type(_u13)) )).
% 0.63/0.83 cnf(matrix-43, plain, ( ~ilf_type(_u19, binary_relation_type) | ~ilf_type(_u18, binary_relation_type) | ~subset(_u19, _u18) | ~ilf_type(_u15, set_type) | ~ilf_type(_u14, set_type) | ~member(ordered_pair(_u15, _u14), _u19) | member(ordered_pair(_u15, _u14), _u18) )).
% 0.63/0.83 cnf(matrix-44, plain, ( ~ilf_type(_u19, binary_relation_type) | ~ilf_type(_u18, binary_relation_type) | subset(_u19, _u18) | ilf_type(skolem2(_u19, _u18), set_type) )).
% 0.63/0.83 cnf(matrix-45, plain, ( ~ilf_type(_u19, binary_relation_type) | ~ilf_type(_u18, binary_relation_type) | subset(_u19, _u18) | ilf_type(skolem3(_u19, _u18), set_type) )).
% 0.63/0.83 cnf(matrix-46, plain, ( ~ilf_type(_u19, binary_relation_type) | ~ilf_type(_u18, binary_relation_type) | subset(_u19, _u18) | member(ordered_pair(skolem2(_u19, _u18), skolem3(_u19, _u18)), _u19) )).
% 0.63/0.83 cnf(matrix-47, plain, ( ~ilf_type(_u19, binary_relation_type) | ~ilf_type(_u18, binary_relation_type) | subset(_u19, _u18) | ~member(ordered_pair(skolem2(_u19, _u18), skolem3(_u19, _u18)), _u18) )).
% 0.63/0.83 cnf(matrix-48, plain, ( ~ilf_type(_u21, set_type) | ~ilf_type(_u20, set_type) | ( _u21 != _u20) | subset(_u21, _u20) )).
% 0.63/0.83 cnf(matrix-49, plain, ( ~ilf_type(_u21, set_type) | ~ilf_type(_u20, set_type) | ( _u21 != _u20) | subset(_u20, _u21) )).
% 0.63/0.83 cnf(matrix-50, plain, ( ~ilf_type(_u21, set_type) | ~ilf_type(_u20, set_type) | ~subset(_u21, _u20) | ~subset(_u20, _u21) | ( _u21 = _u20) )).
% 0.63/0.83 cnf(matrix-51, plain, ( ~ilf_type(_u22, binary_relation_type) | ilf_type(domain_of(_u22), set_type) )).
% 0.63/0.83 cnf(matrix-52, plain, ( ~ilf_type(_u23, binary_relation_type) | ilf_type(range_of(_u23), set_type) )).
% 0.63/0.83 cnf(matrix-53, plain, ( ~ilf_type(_u25, set_type) | ~ilf_type(_u24, set_type) | ilf_type(ordered_pair(_u25, _u24), set_type) )).
% 0.63/0.83 cnf(matrix-54, plain, ( ~ilf_type(_u26, set_type) | ~ilf_type(_u26, binary_relation_type) | relation_like(_u26) )).
% 0.63/0.83 cnf(matrix-55, plain, ( ~ilf_type(_u26, set_type) | ~relation_like(_u26) | ilf_type(_u26, binary_relation_type) )).
% 0.63/0.83 cnf(matrix-56, plain, ( ilf_type(skolem4, binary_relation_type) )).
% 0.63/0.83 cnf(matrix-57, plain, ( ~ilf_type(_u31, set_type) | ~ilf_type(_u30, set_type) | ~ilf_type(_u28, subset_type(cross_product(_u31, _u30))) | ilf_type(_u28, relation_type(_u31, _u30)) )).
% 0.63/0.83 cnf(matrix-58, plain, ( ~ilf_type(_u31, set_type) | ~ilf_type(_u30, set_type) | ~ilf_type(_u29, relation_type(_u31, _u30)) | ilf_type(_u29, subset_type(cross_product(_u31, _u30))) )).
% 0.63/0.83 cnf(matrix-59, plain, ( ~ilf_type(_u34, set_type) | ~ilf_type(_u33, set_type) | ilf_type(skolem5(_u34, _u33), relation_type(_u33, _u34)) )).
% 0.63/0.83 cnf(matrix-60, plain, ( ~ilf_type(_u36, set_type) | ~ilf_type(_u35, set_type) | ~ilf_type(_u35, subset_type(_u36)) | ilf_type(_u35, member_type(power_set(_u36))) )).
% 0.63/0.83 cnf(matrix-61, plain, ( ~ilf_type(_u36, set_type) | ~ilf_type(_u35, set_type) | ~ilf_type(_u35, member_type(power_set(_u36))) | ilf_type(_u35, subset_type(_u36)) )).
% 0.63/0.83 cnf(matrix-62, plain, ( ~ilf_type(_u38, set_type) | ilf_type(skolem6(_u38), subset_type(_u38)) )).
% 0.63/0.83 cnf(matrix-63, plain, ( ~ilf_type(_u42, set_type) | ~ilf_type(_u41, set_type) | ~subset(_u42, _u41) | ~ilf_type(_u39, set_type) | ~member(_u39, _u42) | member(_u39, _u41) )).
% 0.63/0.83 cnf(matrix-64, plain, ( ~ilf_type(_u42, set_type) | ~ilf_type(_u41, set_type) | subset(_u42, _u41) | ilf_type(skolem7(_u42, _u41), set_type) )).
% 0.63/0.83 cnf(matrix-65, plain, ( ~ilf_type(_u42, set_type) | ~ilf_type(_u41, set_type) | subset(_u42, _u41) | member(skolem7(_u42, _u41), _u42) )).
% 0.63/0.83 cnf(matrix-66, plain, ( ~ilf_type(_u42, set_type) | ~ilf_type(_u41, set_type) | subset(_u42, _u41) | ~member(skolem7(_u42, _u41), _u41) )).
% 0.63/0.83 cnf(matrix-67, plain, ( ~ilf_type(_u43, set_type) | subset(_u43, _u43) )).
% 0.63/0.83 cnf(matrix-68, plain, ( ~ilf_type(_u44, binary_relation_type) | subset(_u44, _u44) )).
% 0.63/0.83 cnf(matrix-69, plain, ( ~ilf_type(_u46, set_type) | ~ilf_type(_u45, set_type) | ilf_type(cross_product(_u46, _u45), set_type) )).
% 0.63/0.83 cnf(matrix-70, plain, ( ~ilf_type(_u50, set_type) | ~ilf_type(_u49, set_type) | ~member(_u50, power_set(_u49)) | ~ilf_type(_u47, set_type) | ~member(_u47, _u50) | member(_u47, _u49) )).
% 0.63/0.83 cnf(matrix-71, plain, ( ~ilf_type(_u50, set_type) | ~ilf_type(_u49, set_type) | member(_u50, power_set(_u49)) | ilf_type(skolem8(_u50, _u49), set_type) )).
% 0.63/0.83 cnf(matrix-72, plain, ( ~ilf_type(_u50, set_type) | ~ilf_type(_u49, set_type) | member(_u50, power_set(_u49)) | member(skolem8(_u50, _u49), _u50) )).
% 0.63/0.83 cnf(matrix-73, plain, ( ~ilf_type(_u50, set_type) | ~ilf_type(_u49, set_type) | member(_u50, power_set(_u49)) | ~member(skolem8(_u50, _u49), _u49) )).
% 0.63/0.83 cnf(matrix-74, plain, ( ~ilf_type(_u51, set_type) | ~empty(power_set(_u51)) )).
% 0.63/0.83 cnf(matrix-75, plain, ( ~ilf_type(_u51, set_type) | ilf_type(power_set(_u51), set_type) )).
% 0.63/0.83 cnf(matrix-76, plain, ( ~ilf_type(_u53, set_type) | empty(_u52) | ~ilf_type(_u52, set_type) | ~ilf_type(_u53, member_type(_u52)) | member(_u53, _u52) )).
% 0.63/0.83 cnf(matrix-77, plain, ( ~ilf_type(_u53, set_type) | empty(_u52) | ~ilf_type(_u52, set_type) | ~member(_u53, _u52) | ilf_type(_u53, member_type(_u52)) )).
% 0.63/0.83 cnf(matrix-78, plain, ( empty(_u55) | ~ilf_type(_u55, set_type) | ilf_type(skolem9(_u55), member_type(_u55)) )).
% 0.63/0.83 cnf(matrix-79, plain, ( ~ilf_type(_u62, set_type) | ~relation_like(_u62) | ~ilf_type(_u58, set_type) | ~member(_u58, _u62) | ilf_type(skolem10(_u62, _u58), set_type) )).
% 0.63/0.83 cnf(matrix-80, plain, ( ~ilf_type(_u62, set_type) | ~relation_like(_u62) | ~ilf_type(_u58, set_type) | ~member(_u58, _u62) | ilf_type(skolem11(_u62, _u58), set_type) )).
% 0.63/0.83 cnf(matrix-81, plain, ( ~ilf_type(_u62, set_type) | ~relation_like(_u62) | ~ilf_type(_u58, set_type) | ~member(_u58, _u62) | ( _u58 = ordered_pair(skolem10(_u62, _u58), skolem11(_u62, _u58))) )).
% 0.63/0.83 cnf(matrix-82, plain, ( ~ilf_type(_u62, set_type) | relation_like(_u62) | ilf_type(skolem12(_u62), set_type) )).
% 0.63/0.83 cnf(matrix-83, plain, ( ~ilf_type(_u62, set_type) | relation_like(_u62) | member(skolem12(_u62), _u62) )).
% 0.63/0.83 cnf(matrix-84, plain, ( ~ilf_type(_u62, set_type) | relation_like(_u62) | ~ilf_type(_u60, set_type) | ~ilf_type(_u59, set_type) | ( skolem12(_u62) != ordered_pair(_u60, _u59)) )).
% 0.63/0.83 cnf(matrix-85, plain, ( ~ilf_type(_u65, set_type) | ~ilf_type(_u64, set_type) | ~ilf_type(_u63, subset_type(cross_product(_u65, _u64))) | relation_like(_u63) )).
% 0.63/0.83 cnf(matrix-86, plain, ( ~ilf_type(_u68, set_type) | ~empty(_u68) | ~ilf_type(_u66, set_type) | ~member(_u66, _u68) )).
% 0.63/0.83 cnf(matrix-87, plain, ( ~ilf_type(_u68, set_type) | empty(_u68) | ilf_type(skolem13(_u68), set_type) )).
% 0.63/0.83 cnf(matrix-88, plain, ( ~ilf_type(_u68, set_type) | empty(_u68) | member(skolem13(_u68), _u68) )).
% 0.63/0.83 cnf(matrix-89, plain, ( ~empty(_u69) | ~ilf_type(_u69, set_type) | relation_like(_u69) )).
% 0.63/0.83 cnf(matrix-90, plain, ( ~ilf_type(_u72, set_type) | ~ilf_type(_u71, set_type) | ~ilf_type(_u70, relation_type(_u72, _u71)) | ( domain(_u72, _u71, _u70) = domain_of(_u70)) )).
% 0.63/0.83 cnf(matrix-91, plain, ( ~ilf_type(_u75, set_type) | ~ilf_type(_u74, set_type) | ~ilf_type(_u73, relation_type(_u75, _u74)) | ilf_type(domain(_u75, _u74, _u73), subset_type(_u75)) )).
% 0.63/0.83 cnf(matrix-92, plain, ( ~ilf_type(_u78, set_type) | ~ilf_type(_u77, set_type) | ~ilf_type(_u76, relation_type(_u78, _u77)) | ( range(_u78, _u77, _u76) = range_of(_u76)) )).
% 0.63/0.83 cnf(matrix-93, plain, ( ~ilf_type(_u81, set_type) | ~ilf_type(_u80, set_type) | ~ilf_type(_u79, relation_type(_u81, _u80)) | ilf_type(range(_u81, _u80, _u79), subset_type(_u80)) )).
% 0.63/0.83 cnf(matrix-94, plain, ( ilf_type(_u82, set_type) )).
% 0.63/0.83 cnf(matrix-95, plain, ( ilf_type(skolem14, set_type) )).
% 0.63/0.83 cnf(matrix-96, plain, ( ilf_type(skolem15, identity_relation_of_type(skolem14)) )).
% 0.63/0.83 cnf(matrix-97, plain, ( subset(identity_relation_of(skolem14), skolem15) )).
% 0.63/0.83 cnf(matrix-98, plain, ( ( skolem14 != domain(skolem14, skolem14, skolem15)) | ( skolem14 != range(skolem14, skolem14, skolem15)) )).
% 0.63/0.83
% 0.63/0.83 % Proof stack:
% 0.63/0.83 cnf(proof-stack, plain,
% 0.63/0.83 proof_stack(
% 0.63/0.83 start(98),
% 0.63/0.83 left_branch(0, 32, 4, 2),
% 0.63/0.83 left_branch(0, 95, 0, 3),
% 0.63/0.83 right_branch(3),
% 0.63/0.83 left_branch(0, 97, 0, 4),
% 0.63/0.83 right_branch(4),
% 0.63/0.83 left_branch(0, 40, 3, 5),
% 0.63/0.83 lemmata(0, 0),
% 0.63/0.83 left_branch(0, 96, 0, 7),
% 0.63/0.83 right_branch(7),
% 0.63/0.83 left_branch(0, 94, 0, 8),
% 0.63/0.83 right_branch(8),
% 0.63/0.83 right_branch(5),
% 0.63/0.83 lemmata(0, 0),
% 0.63/0.83 right_branch(2),
% 0.63/0.83 left_branch(0, 35, 4, 3),
% 0.63/0.83 left_branch(0, 95, 0, 4),
% 0.63/0.83 right_branch(4),
% 0.63/0.83 left_branch(0, 97, 0, 5),
% 0.63/0.83 right_branch(5),
% 0.63/0.83 left_branch(0, 40, 3, 6),
% 0.63/0.83 lemmata(0, 1),
% 0.63/0.83 left_branch(0, 96, 0, 8),
% 0.63/0.83 right_branch(8),
% 0.63/0.83 left_branch(0, 94, 0, 9),
% 0.63/0.83 right_branch(9),
% 0.63/0.83 right_branch(6),
% 0.63/0.83 lemmata(0, 1),
% 0.63/0.83 right_branch(3)
% 0.63/0.83 )).
% 0.63/0.83 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------