TSTP Solution File: SET653+3 by ConnectPP---0.2.2
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%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : SET653+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 : n024.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 09:19:32 EST 2024
% Result : Theorem 31.63s 31.79s
% Output : Proof 31.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET653+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Mar 3 19:47:36 EST 2024
% 0.13/0.34 % CPUTime :
% 31.63/31.79 % SZS status Theorem for theBenchmark
% 31.63/31.79 % SZS output start Proof for theBenchmark
% 31.63/31.79
% 31.63/31.79 % Formula: p1 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p1-1, axiom, ( ~ilf_type(_u2, set_type) | ~ilf_type(_u1, set_type) | ~ilf_type(_u0, set_type) | ~subset(_u2, _u1) | ~subset(_u1, _u0) | subset(_u2, _u0) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p2 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p2-1, axiom, ( ~ilf_type(_u5, set_type) | ~ilf_type(_u4, set_type) | ~ilf_type(_u3, relation_type(_u5, _u4)) | subset(domain_of(_u3), _u5) )).
% 31.63/31.79 cnf(p2-2, axiom, ( ~ilf_type(_u5, set_type) | ~ilf_type(_u4, set_type) | ~ilf_type(_u3, relation_type(_u5, _u4)) | subset(range_of(_u3), _u4) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p3 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p3-1, axiom, ( ~ilf_type(_u9, set_type) | ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, relation_type(_u9, _u7)) | ~subset(domain_of(_u6), _u8) | ilf_type(_u6, relation_type(_u8, _u7)) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p4 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p4-1, axiom, ( ~ilf_type(_u13, set_type) | ~ilf_type(_u12, set_type) | ~ilf_type(_u10, subset_type(cross_product(_u13, _u12))) | ilf_type(_u10, relation_type(_u13, _u12)) )).
% 31.63/31.79 cnf(p4-2, axiom, ( ~ilf_type(_u13, set_type) | ~ilf_type(_u12, set_type) | ~ilf_type(_u11, relation_type(_u13, _u12)) | ilf_type(_u11, subset_type(cross_product(_u13, _u12))) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p5 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p5-1, axiom, ( ~ilf_type(_u16, set_type) | ~ilf_type(_u15, set_type) | ilf_type(skolem1(_u16, _u15), relation_type(_u15, _u16)) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p6 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p6-1, axiom, ( ~ilf_type(_u20, set_type) | ~ilf_type(_u19, set_type) | ~subset(_u20, _u19) | ~ilf_type(_u17, set_type) | ~member(_u17, _u20) | member(_u17, _u19) )).
% 31.63/31.79 cnf(p6-2, axiom, ( ~ilf_type(_u20, set_type) | ~ilf_type(_u19, set_type) | subset(_u20, _u19) | ilf_type(skolem2(_u20, _u19), set_type) )).
% 31.63/31.79 cnf(p6-3, axiom, ( ~ilf_type(_u20, set_type) | ~ilf_type(_u19, set_type) | subset(_u20, _u19) | member(skolem2(_u20, _u19), _u20) )).
% 31.63/31.79 cnf(p6-4, axiom, ( ~ilf_type(_u20, set_type) | ~ilf_type(_u19, set_type) | subset(_u20, _u19) | ~member(skolem2(_u20, _u19), _u19) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p7 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p7-1, axiom, ( ~ilf_type(_u21, binary_relation_type) | ilf_type(domain_of(_u21), set_type) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p8 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p8-1, axiom, ( ~ilf_type(_u23, set_type) | ~ilf_type(_u22, set_type) | ilf_type(cross_product(_u23, _u22), set_type) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p9 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p9-1, axiom, ( ~ilf_type(_u24, binary_relation_type) | ilf_type(range_of(_u24), set_type) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p10 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p10-1, 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))) )).
% 31.63/31.79 cnf(p10-2, 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)) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p11 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p11-1, axiom, ( ~ilf_type(_u28, set_type) | ilf_type(skolem3(_u28), subset_type(_u28)) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p12 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p12-1, axiom, ( ~ilf_type(_u29, set_type) | subset(_u29, _u29) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p13 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p13-1, axiom, ( ~ilf_type(_u33, set_type) | ~ilf_type(_u32, set_type) | ~member(_u33, power_set(_u32)) | ~ilf_type(_u30, set_type) | ~member(_u30, _u33) | member(_u30, _u32) )).
% 31.63/31.79 cnf(p13-2, axiom, ( ~ilf_type(_u33, set_type) | ~ilf_type(_u32, set_type) | member(_u33, power_set(_u32)) | ilf_type(skolem4(_u33, _u32), set_type) )).
% 31.63/31.79 cnf(p13-3, axiom, ( ~ilf_type(_u33, set_type) | ~ilf_type(_u32, set_type) | member(_u33, power_set(_u32)) | member(skolem4(_u33, _u32), _u33) )).
% 31.63/31.79 cnf(p13-4, axiom, ( ~ilf_type(_u33, set_type) | ~ilf_type(_u32, set_type) | member(_u33, power_set(_u32)) | ~member(skolem4(_u33, _u32), _u32) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p14 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p14-1, axiom, ( ~ilf_type(_u34, set_type) | ~empty(power_set(_u34)) )).
% 31.63/31.79 cnf(p14-2, axiom, ( ~ilf_type(_u34, set_type) | ilf_type(power_set(_u34), set_type) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p15 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p15-1, axiom, ( ~ilf_type(_u36, set_type) | empty(_u35) | ~ilf_type(_u35, set_type) | ~ilf_type(_u36, member_type(_u35)) | member(_u36, _u35) )).
% 31.63/31.79 cnf(p15-2, axiom, ( ~ilf_type(_u36, set_type) | empty(_u35) | ~ilf_type(_u35, set_type) | ~member(_u36, _u35) | ilf_type(_u36, member_type(_u35)) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p16 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p16-1, axiom, ( empty(_u38) | ~ilf_type(_u38, set_type) | ilf_type(skolem5(_u38), member_type(_u38)) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p17 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p17-1, axiom, ( ~ilf_type(_u41, set_type) | ~empty(_u41) | ~ilf_type(_u39, set_type) | ~member(_u39, _u41) )).
% 31.63/31.79 cnf(p17-2, axiom, ( ~ilf_type(_u41, set_type) | empty(_u41) | ilf_type(skolem6(_u41), set_type) )).
% 31.63/31.79 cnf(p17-3, axiom, ( ~ilf_type(_u41, set_type) | empty(_u41) | member(skolem6(_u41), _u41) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p18 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p18-1, axiom, ( ~ilf_type(_u48, set_type) | ~relation_like(_u48) | ~ilf_type(_u44, set_type) | ~member(_u44, _u48) | ilf_type(skolem7(_u48, _u44), set_type) )).
% 31.63/31.79 cnf(p18-2, axiom, ( ~ilf_type(_u48, set_type) | ~relation_like(_u48) | ~ilf_type(_u44, set_type) | ~member(_u44, _u48) | ilf_type(skolem8(_u48, _u44), set_type) )).
% 31.63/31.79 cnf(p18-3, axiom, ( ~ilf_type(_u48, set_type) | ~relation_like(_u48) | ~ilf_type(_u44, set_type) | ~member(_u44, _u48) | ( _u44 = ordered_pair(skolem7(_u48, _u44), skolem8(_u48, _u44))) )).
% 31.63/31.79 cnf(p18-4, axiom, ( ~ilf_type(_u48, set_type) | relation_like(_u48) | ilf_type(skolem9(_u48), set_type) )).
% 31.63/31.79 cnf(p18-5, axiom, ( ~ilf_type(_u48, set_type) | relation_like(_u48) | member(skolem9(_u48), _u48) )).
% 31.63/31.79 cnf(p18-6, axiom, ( ~ilf_type(_u48, set_type) | relation_like(_u48) | ~ilf_type(_u46, set_type) | ~ilf_type(_u45, set_type) | ( skolem9(_u48) != ordered_pair(_u46, _u45)) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p19 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p19-1, axiom, ( ~empty(_u49) | ~ilf_type(_u49, set_type) | relation_like(_u49) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p20 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p20-1, axiom, ( ~ilf_type(_u52, set_type) | ~ilf_type(_u51, set_type) | ~ilf_type(_u50, subset_type(cross_product(_u52, _u51))) | relation_like(_u50) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p21 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p21-1, axiom, ( ~ilf_type(_u54, set_type) | ~ilf_type(_u53, set_type) | ilf_type(ordered_pair(_u54, _u53), set_type) )).
% 31.63/31.79
% 31.63/31.79 % Formula: p22 ( axiom ) converted to clauses:
% 31.63/31.79 cnf(p22-1, axiom, ( ilf_type(_u55, set_type) )).
% 31.63/31.79
% 31.63/31.79 % Formula: prove_relset_1_15 ( conjecture ) converted to clauses:
% 31.63/31.79 cnf(prove_relset_1_15-1, negated_conjecture, ( ilf_type(skolem10, set_type) )).
% 31.63/31.79 cnf(prove_relset_1_15-2, negated_conjecture, ( ilf_type(skolem11, set_type) )).
% 31.63/31.79 cnf(prove_relset_1_15-3, negated_conjecture, ( ilf_type(skolem12, set_type) )).
% 31.63/31.79 cnf(prove_relset_1_15-4, negated_conjecture, ( ilf_type(skolem13, relation_type(skolem10, skolem12)) )).
% 31.63/31.79 cnf(prove_relset_1_15-5, negated_conjecture, ( subset(skolem10, skolem11) )).
% 31.63/31.79 cnf(prove_relset_1_15-6, negated_conjecture, ( ~ilf_type(skolem13, relation_type(skolem11, skolem12)) )).
% 31.63/31.79
% 31.63/31.79 % Problem matrix:
% 31.63/31.79 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 31.63/31.79 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 31.63/31.79 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 31.63/31.79 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( relation_type(__eqx_0, __eqx_1) = relation_type(__eqy_0, __eqy_1)) )).
% 31.63/31.79 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( domain_of(__eqx_0) = domain_of(__eqy_0)) )).
% 31.63/31.79 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( range_of(__eqx_0) = range_of(__eqy_0)) )).
% 31.63/31.79 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( cross_product(__eqx_0, __eqx_1) = cross_product(__eqy_0, __eqy_1)) )).
% 31.63/31.79 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( subset_type(__eqx_0) = subset_type(__eqy_0)) )).
% 31.63/31.79 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( power_set(__eqx_0) = power_set(__eqy_0)) )).
% 31.63/31.79 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( member_type(__eqx_0) = member_type(__eqy_0)) )).
% 31.63/31.79 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 31.63/31.80 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 31.63/31.80 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 31.63/31.80 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( skolem3(__eqx_0) = skolem3(__eqy_0)) )).
% 31.63/31.80 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 31.63/31.80 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( skolem5(__eqx_0) = skolem5(__eqy_0)) )).
% 31.63/31.80 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( skolem6(__eqx_0) = skolem6(__eqy_0)) )).
% 31.63/31.80 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem7(__eqx_0, __eqx_1) = skolem7(__eqy_0, __eqy_1)) )).
% 31.63/31.80 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem8(__eqx_0, __eqx_1) = skolem8(__eqy_0, __eqy_1)) )).
% 31.63/31.80 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( skolem9(__eqx_0) = skolem9(__eqy_0)) )).
% 31.63/31.80 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~ilf_type(__eqx_0, __eqx_1) | ilf_type(__eqy_0, __eqy_1) )).
% 31.63/31.80 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 31.63/31.80 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 31.63/31.80 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 31.63/31.80 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ~relation_like(__eqx_0) | relation_like(__eqy_0) )).
% 31.63/31.80 cnf(matrix-25, plain, ( ~ilf_type(_u2, set_type) | ~ilf_type(_u1, set_type) | ~ilf_type(_u0, set_type) | ~subset(_u2, _u1) | ~subset(_u1, _u0) | subset(_u2, _u0) )).
% 31.63/31.80 cnf(matrix-26, plain, ( ~ilf_type(_u5, set_type) | ~ilf_type(_u4, set_type) | ~ilf_type(_u3, relation_type(_u5, _u4)) | subset(domain_of(_u3), _u5) )).
% 31.63/31.80 cnf(matrix-27, plain, ( ~ilf_type(_u5, set_type) | ~ilf_type(_u4, set_type) | ~ilf_type(_u3, relation_type(_u5, _u4)) | subset(range_of(_u3), _u4) )).
% 31.63/31.80 cnf(matrix-28, plain, ( ~ilf_type(_u9, set_type) | ~ilf_type(_u8, set_type) | ~ilf_type(_u7, set_type) | ~ilf_type(_u6, relation_type(_u9, _u7)) | ~subset(domain_of(_u6), _u8) | ilf_type(_u6, relation_type(_u8, _u7)) )).
% 31.63/31.80 cnf(matrix-29, plain, ( ~ilf_type(_u13, set_type) | ~ilf_type(_u12, set_type) | ~ilf_type(_u10, subset_type(cross_product(_u13, _u12))) | ilf_type(_u10, relation_type(_u13, _u12)) )).
% 31.63/31.80 cnf(matrix-30, plain, ( ~ilf_type(_u13, set_type) | ~ilf_type(_u12, set_type) | ~ilf_type(_u11, relation_type(_u13, _u12)) | ilf_type(_u11, subset_type(cross_product(_u13, _u12))) )).
% 31.63/31.80 cnf(matrix-31, plain, ( ~ilf_type(_u16, set_type) | ~ilf_type(_u15, set_type) | ilf_type(skolem1(_u16, _u15), relation_type(_u15, _u16)) )).
% 31.63/31.80 cnf(matrix-32, plain, ( ~ilf_type(_u20, set_type) | ~ilf_type(_u19, set_type) | ~subset(_u20, _u19) | ~ilf_type(_u17, set_type) | ~member(_u17, _u20) | member(_u17, _u19) )).
% 31.63/31.80 cnf(matrix-33, plain, ( ~ilf_type(_u20, set_type) | ~ilf_type(_u19, set_type) | subset(_u20, _u19) | ilf_type(skolem2(_u20, _u19), set_type) )).
% 31.63/31.80 cnf(matrix-34, plain, ( ~ilf_type(_u20, set_type) | ~ilf_type(_u19, set_type) | subset(_u20, _u19) | member(skolem2(_u20, _u19), _u20) )).
% 31.63/31.80 cnf(matrix-35, plain, ( ~ilf_type(_u20, set_type) | ~ilf_type(_u19, set_type) | subset(_u20, _u19) | ~member(skolem2(_u20, _u19), _u19) )).
% 31.63/31.80 cnf(matrix-36, plain, ( ~ilf_type(_u21, binary_relation_type) | ilf_type(domain_of(_u21), set_type) )).
% 31.63/31.80 cnf(matrix-37, plain, ( ~ilf_type(_u23, set_type) | ~ilf_type(_u22, set_type) | ilf_type(cross_product(_u23, _u22), set_type) )).
% 31.63/31.80 cnf(matrix-38, plain, ( ~ilf_type(_u24, binary_relation_type) | ilf_type(range_of(_u24), set_type) )).
% 31.63/31.80 cnf(matrix-39, 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))) )).
% 31.63/31.80 cnf(matrix-40, 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)) )).
% 31.63/31.80 cnf(matrix-41, plain, ( ~ilf_type(_u28, set_type) | ilf_type(skolem3(_u28), subset_type(_u28)) )).
% 31.63/31.80 cnf(matrix-42, plain, ( ~ilf_type(_u29, set_type) | subset(_u29, _u29) )).
% 31.63/31.80 cnf(matrix-43, plain, ( ~ilf_type(_u33, set_type) | ~ilf_type(_u32, set_type) | ~member(_u33, power_set(_u32)) | ~ilf_type(_u30, set_type) | ~member(_u30, _u33) | member(_u30, _u32) )).
% 31.63/31.80 cnf(matrix-44, plain, ( ~ilf_type(_u33, set_type) | ~ilf_type(_u32, set_type) | member(_u33, power_set(_u32)) | ilf_type(skolem4(_u33, _u32), set_type) )).
% 31.63/31.80 cnf(matrix-45, plain, ( ~ilf_type(_u33, set_type) | ~ilf_type(_u32, set_type) | member(_u33, power_set(_u32)) | member(skolem4(_u33, _u32), _u33) )).
% 31.63/31.80 cnf(matrix-46, plain, ( ~ilf_type(_u33, set_type) | ~ilf_type(_u32, set_type) | member(_u33, power_set(_u32)) | ~member(skolem4(_u33, _u32), _u32) )).
% 31.63/31.80 cnf(matrix-47, plain, ( ~ilf_type(_u34, set_type) | ~empty(power_set(_u34)) )).
% 31.63/31.80 cnf(matrix-48, plain, ( ~ilf_type(_u34, set_type) | ilf_type(power_set(_u34), set_type) )).
% 31.63/31.80 cnf(matrix-49, plain, ( ~ilf_type(_u36, set_type) | empty(_u35) | ~ilf_type(_u35, set_type) | ~ilf_type(_u36, member_type(_u35)) | member(_u36, _u35) )).
% 31.63/31.80 cnf(matrix-50, plain, ( ~ilf_type(_u36, set_type) | empty(_u35) | ~ilf_type(_u35, set_type) | ~member(_u36, _u35) | ilf_type(_u36, member_type(_u35)) )).
% 31.63/31.80 cnf(matrix-51, plain, ( empty(_u38) | ~ilf_type(_u38, set_type) | ilf_type(skolem5(_u38), member_type(_u38)) )).
% 31.63/31.80 cnf(matrix-52, plain, ( ~ilf_type(_u41, set_type) | ~empty(_u41) | ~ilf_type(_u39, set_type) | ~member(_u39, _u41) )).
% 31.63/31.80 cnf(matrix-53, plain, ( ~ilf_type(_u41, set_type) | empty(_u41) | ilf_type(skolem6(_u41), set_type) )).
% 31.63/31.80 cnf(matrix-54, plain, ( ~ilf_type(_u41, set_type) | empty(_u41) | member(skolem6(_u41), _u41) )).
% 31.63/31.80 cnf(matrix-55, plain, ( ~ilf_type(_u48, set_type) | ~relation_like(_u48) | ~ilf_type(_u44, set_type) | ~member(_u44, _u48) | ilf_type(skolem7(_u48, _u44), set_type) )).
% 31.63/31.80 cnf(matrix-56, plain, ( ~ilf_type(_u48, set_type) | ~relation_like(_u48) | ~ilf_type(_u44, set_type) | ~member(_u44, _u48) | ilf_type(skolem8(_u48, _u44), set_type) )).
% 31.63/31.80 cnf(matrix-57, plain, ( ~ilf_type(_u48, set_type) | ~relation_like(_u48) | ~ilf_type(_u44, set_type) | ~member(_u44, _u48) | ( _u44 = ordered_pair(skolem7(_u48, _u44), skolem8(_u48, _u44))) )).
% 31.63/31.80 cnf(matrix-58, plain, ( ~ilf_type(_u48, set_type) | relation_like(_u48) | ilf_type(skolem9(_u48), set_type) )).
% 31.63/31.80 cnf(matrix-59, plain, ( ~ilf_type(_u48, set_type) | relation_like(_u48) | member(skolem9(_u48), _u48) )).
% 31.63/31.80 cnf(matrix-60, plain, ( ~ilf_type(_u48, set_type) | relation_like(_u48) | ~ilf_type(_u46, set_type) | ~ilf_type(_u45, set_type) | ( skolem9(_u48) != ordered_pair(_u46, _u45)) )).
% 31.63/31.80 cnf(matrix-61, plain, ( ~empty(_u49) | ~ilf_type(_u49, set_type) | relation_like(_u49) )).
% 31.63/31.80 cnf(matrix-62, plain, ( ~ilf_type(_u52, set_type) | ~ilf_type(_u51, set_type) | ~ilf_type(_u50, subset_type(cross_product(_u52, _u51))) | relation_like(_u50) )).
% 31.63/31.80 cnf(matrix-63, plain, ( ~ilf_type(_u54, set_type) | ~ilf_type(_u53, set_type) | ilf_type(ordered_pair(_u54, _u53), set_type) )).
% 31.63/31.80 cnf(matrix-64, plain, ( ilf_type(_u55, set_type) )).
% 31.63/31.80 cnf(matrix-65, plain, ( ilf_type(skolem10, set_type) )).
% 31.63/31.80 cnf(matrix-66, plain, ( ilf_type(skolem11, set_type) )).
% 31.63/31.80 cnf(matrix-67, plain, ( ilf_type(skolem12, set_type) )).
% 31.63/31.80 cnf(matrix-68, plain, ( ilf_type(skolem13, relation_type(skolem10, skolem12)) )).
% 31.63/31.80 cnf(matrix-69, plain, ( subset(skolem10, skolem11) )).
% 31.63/31.80 cnf(matrix-70, plain, ( ~ilf_type(skolem13, relation_type(skolem11, skolem12)) )).
% 31.63/31.80
% 31.63/31.80 % Proof stack:
% 31.63/31.80 cnf(proof-stack, plain,
% 31.63/31.80 proof_stack(
% 31.63/31.80 start(65),
% 31.63/31.80 left_branch(0, 28, 0, 2),
% 31.63/31.80 left_branch(0, 70, 0, 3),
% 31.63/31.80 right_branch(3),
% 31.63/31.80 left_branch(0, 25, 5, 4),
% 31.63/31.80 left_branch(0, 64, 0, 5),
% 31.63/31.80 right_branch(5),
% 31.63/31.80 left_branch(0, 69, 0, 6),
% 31.63/31.80 right_branch(6),
% 31.63/31.80 left_branch(0, 26, 3, 7),
% 31.63/31.80 reduction(0, 0),
% 31.63/31.80 left_branch(0, 68, 0, 9),
% 31.63/31.80 right_branch(9),
% 31.63/31.80 left_branch(0, 67, 0, 10),
% 31.63/31.80 right_branch(10),
% 31.63/31.80 right_branch(7),
% 31.63/31.80 left_branch(0, 66, 0, 8),
% 31.63/31.80 right_branch(8),
% 31.63/31.80 reduction(0, 0),
% 31.63/31.80 right_branch(4),
% 31.63/31.80 left_branch(0, 68, 0, 5),
% 31.63/31.80 right_branch(5),
% 31.63/31.80 left_branch(0, 67, 0, 6),
% 31.63/31.80 right_branch(6),
% 31.63/31.80 left_branch(0, 66, 0, 7),
% 31.63/31.80 right_branch(7),
% 31.63/31.80 right_branch(2)
% 31.63/31.80 )).
% 31.63/31.80 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------