TSTP Solution File: SEU009+1 by ConnectPP---0.2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : SEU009+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Mar 6 09:20:07 EST 2024
% Result : Theorem 3.53s 3.69s
% Output : Proof 3.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU009+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n029.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 10:23:35 EST 2024
% 0.13/0.34 % CPUTime :
% 3.53/3.69 % SZS status Theorem for theBenchmark
% 3.53/3.69 % SZS output start Proof for theBenchmark
% 3.53/3.69
% 3.53/3.69 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 3.53/3.69 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 3.53/3.69
% 3.53/3.69 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(cc1_funct_1-1, axiom, ( ~empty(_u2) | function(_u2) )).
% 3.53/3.69
% 3.53/3.69 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(cc1_relat_1-1, axiom, ( ~empty(_u3) | relation(_u3) )).
% 3.53/3.69
% 3.53/3.69 % Formula: dt_k5_relat_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(dt_k5_relat_1-1, axiom, ( ~relation(_u5) | ~relation(_u4) | relation(relation_composition(_u5, _u4)) )).
% 3.53/3.69
% 3.53/3.69 % Formula: dt_k6_relat_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(dt_k6_relat_1-1, axiom, ( relation(identity_relation(_u6)) )).
% 3.53/3.69
% 3.53/3.69 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(existence_m1_subset_1-1, axiom, ( element(skolem1(_u8), _u8) )).
% 3.53/3.69
% 3.53/3.69 % Formula: fc10_relat_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(fc10_relat_1-1, axiom, ( ~empty(_u10) | ~relation(_u9) | empty(relation_composition(_u9, _u10)) )).
% 3.53/3.69 cnf(fc10_relat_1-2, axiom, ( ~empty(_u10) | ~relation(_u9) | relation(relation_composition(_u9, _u10)) )).
% 3.53/3.69
% 3.53/3.69 % Formula: fc12_relat_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(fc12_relat_1-1, axiom, ( empty(empty_set) )).
% 3.53/3.69 cnf(fc12_relat_1-2, axiom, ( relation(empty_set) )).
% 3.53/3.69 cnf(fc12_relat_1-3, axiom, ( relation_empty_yielding(empty_set) )).
% 3.53/3.69
% 3.53/3.69 % Formula: fc1_funct_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(fc1_funct_1-1, axiom, ( ~relation(_u12) | ~function(_u12) | ~relation(_u11) | ~function(_u11) | relation(relation_composition(_u12, _u11)) )).
% 3.53/3.69 cnf(fc1_funct_1-2, axiom, ( ~relation(_u12) | ~function(_u12) | ~relation(_u11) | ~function(_u11) | function(relation_composition(_u12, _u11)) )).
% 3.53/3.69
% 3.53/3.69 % Formula: fc1_subset_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(fc1_subset_1-1, axiom, ( ~empty(powerset(_u13)) )).
% 3.53/3.69
% 3.53/3.69 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 3.53/3.69
% 3.53/3.69 % Formula: fc2_funct_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(fc2_funct_1-1, axiom, ( relation(identity_relation(_u15)) )).
% 3.53/3.69 cnf(fc2_funct_1-2, axiom, ( function(identity_relation(_u16)) )).
% 3.53/3.69
% 3.53/3.69 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 3.53/3.69 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 3.53/3.69
% 3.53/3.69 % Formula: fc5_relat_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(fc5_relat_1-1, axiom, ( empty(_u17) | ~relation(_u17) | ~empty(relation_dom(_u17)) )).
% 3.53/3.69
% 3.53/3.69 % Formula: fc7_relat_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(fc7_relat_1-1, axiom, ( ~empty(_u18) | empty(relation_dom(_u18)) )).
% 3.53/3.69 cnf(fc7_relat_1-2, axiom, ( ~empty(_u18) | relation(relation_dom(_u18)) )).
% 3.53/3.69
% 3.53/3.69 % Formula: fc9_relat_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(fc9_relat_1-1, axiom, ( ~empty(_u20) | ~relation(_u19) | empty(relation_composition(_u20, _u19)) )).
% 3.53/3.69 cnf(fc9_relat_1-2, axiom, ( ~empty(_u20) | ~relation(_u19) | relation(relation_composition(_u20, _u19)) )).
% 3.53/3.69
% 3.53/3.69 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(rc1_funct_1-1, axiom, ( relation(skolem2) )).
% 3.53/3.69 cnf(rc1_funct_1-2, axiom, ( function(skolem2) )).
% 3.53/3.69
% 3.53/3.69 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(rc1_relat_1-1, axiom, ( empty(skolem3) )).
% 3.53/3.69 cnf(rc1_relat_1-2, axiom, ( relation(skolem3) )).
% 3.53/3.69
% 3.53/3.69 % Formula: rc1_subset_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(rc1_subset_1-1, axiom, ( empty(_u24) | element(skolem4(_u24), powerset(_u24)) )).
% 3.53/3.69 cnf(rc1_subset_1-2, axiom, ( empty(_u24) | ~empty(skolem4(_u24)) )).
% 3.53/3.69
% 3.53/3.69 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(rc1_xboole_0-1, axiom, ( empty(skolem5) )).
% 3.53/3.69
% 3.53/3.69 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem6) )).
% 3.53/3.69 cnf(rc2_relat_1-2, axiom, ( relation(skolem6) )).
% 3.53/3.69
% 3.53/3.69 % Formula: rc2_subset_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(rc2_subset_1-1, axiom, ( element(skolem7(_u28), powerset(_u28)) )).
% 3.53/3.69 cnf(rc2_subset_1-2, axiom, ( empty(skolem7(_u28)) )).
% 3.53/3.69
% 3.53/3.69 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem8) )).
% 3.53/3.69
% 3.53/3.69 % Formula: rc3_relat_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(rc3_relat_1-1, axiom, ( relation(skolem9) )).
% 3.53/3.69 cnf(rc3_relat_1-2, axiom, ( relation_empty_yielding(skolem9) )).
% 3.53/3.69
% 3.53/3.69 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 3.53/3.69 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u32, _u32) )).
% 3.53/3.69
% 3.53/3.69 % Formula: t1_subset ( axiom ) converted to clauses:
% 3.53/3.69 cnf(t1_subset-1, axiom, ( ~in(_u34, _u33) | element(_u34, _u33) )).
% 3.53/3.69
% 3.53/3.69 % Formula: t21_funct_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(t21_funct_1-1, axiom, ( ~relation(_u36) | ~function(_u36) | ~relation(_u35) | ~function(_u35) | ~in(_u37, relation_dom(relation_composition(_u35, _u36))) | in(_u37, relation_dom(_u35)) )).
% 3.53/3.69 cnf(t21_funct_1-2, axiom, ( ~relation(_u36) | ~function(_u36) | ~relation(_u35) | ~function(_u35) | ~in(_u37, relation_dom(relation_composition(_u35, _u36))) | in(apply(_u35, _u37), relation_dom(_u36)) )).
% 3.53/3.69 cnf(t21_funct_1-3, axiom, ( ~relation(_u36) | ~function(_u36) | ~relation(_u35) | ~function(_u35) | ~in(_u37, relation_dom(_u35)) | ~in(apply(_u35, _u37), relation_dom(_u36)) | in(_u37, relation_dom(relation_composition(_u35, _u36))) )).
% 3.53/3.69
% 3.53/3.69 % Formula: t2_subset ( axiom ) converted to clauses:
% 3.53/3.69 cnf(t2_subset-1, axiom, ( ~element(_u39, _u38) | empty(_u38) | in(_u39, _u38) )).
% 3.53/3.69
% 3.53/3.69 % Formula: t34_funct_1 ( axiom ) converted to clauses:
% 3.53/3.69 cnf(t34_funct_1-1, axiom, ( ~relation(_u42) | ~function(_u42) | ( _u42 != identity_relation(_u43)) | ( relation_dom(_u42) = _u43) )).
% 3.53/3.69 cnf(t34_funct_1-2, axiom, ( ~relation(_u42) | ~function(_u42) | ( _u42 != identity_relation(_u43)) | ~in(_u40, _u43) | ( apply(_u42, _u40) = _u40) )).
% 3.53/3.69 cnf(t34_funct_1-3, axiom, ( ~relation(_u42) | ~function(_u42) | ( _u42 = identity_relation(_u43)) | ( relation_dom(_u42) != _u43) | in(skolem10(_u43, _u42), _u43) )).
% 3.53/3.69 cnf(t34_funct_1-4, axiom, ( ~relation(_u42) | ~function(_u42) | ( _u42 = identity_relation(_u43)) | ( relation_dom(_u42) != _u43) | ( apply(_u42, skolem10(_u43, _u42)) != skolem10(_u43, _u42)) )).
% 3.53/3.69
% 3.53/3.69 % Formula: t3_subset ( axiom ) converted to clauses:
% 3.53/3.69 cnf(t3_subset-1, axiom, ( ~element(_u48, powerset(_u46)) | subset(_u48, _u46) )).
% 3.53/3.69 cnf(t3_subset-2, axiom, ( ~subset(_u49, _u47) | element(_u49, powerset(_u47)) )).
% 3.53/3.69
% 3.53/3.69 % Formula: t40_funct_1 ( conjecture ) converted to clauses:
% 3.53/3.69 cnf(t40_funct_1-1, negated_conjecture, ( relation(skolem13) )).
% 3.53/3.69 cnf(t40_funct_1-2, negated_conjecture, ( function(skolem13) )).
% 3.53/3.69 cnf(t40_funct_1-3, negated_conjecture, ( in(skolem12, relation_dom(relation_composition(skolem13, identity_relation(skolem11)))) | in(skolem12, relation_dom(skolem13)) )).
% 3.53/3.69 cnf(t40_funct_1-4, negated_conjecture, ( in(skolem12, relation_dom(relation_composition(skolem13, identity_relation(skolem11)))) | in(apply(skolem13, skolem12), skolem11) )).
% 3.53/3.69 cnf(t40_funct_1-5, negated_conjecture, ( ~in(skolem12, relation_dom(skolem13)) | ~in(apply(skolem13, skolem12), skolem11) | ~in(skolem12, relation_dom(relation_composition(skolem13, identity_relation(skolem11)))) )).
% 3.53/3.69
% 3.53/3.69 % Formula: t4_subset ( axiom ) converted to clauses:
% 3.53/3.69 cnf(t4_subset-1, axiom, ( ~in(_u55, _u54) | ~element(_u54, powerset(_u53)) | element(_u55, _u53) )).
% 3.53/3.69
% 3.53/3.69 % Formula: t5_subset ( axiom ) converted to clauses:
% 3.53/3.69 cnf(t5_subset-1, axiom, ( ~in(_u58, _u57) | ~element(_u57, powerset(_u56)) | ~empty(_u56) )).
% 3.53/3.69
% 3.53/3.69 % Formula: t6_boole ( axiom ) converted to clauses:
% 3.53/3.69 cnf(t6_boole-1, axiom, ( ~empty(_u59) | ( _u59 = empty_set) )).
% 3.53/3.69
% 3.53/3.69 % Formula: t7_boole ( axiom ) converted to clauses:
% 3.53/3.69 cnf(t7_boole-1, axiom, ( ~in(_u61, _u60) | ~empty(_u60) )).
% 3.53/3.69
% 3.53/3.69 % Formula: t8_boole ( axiom ) converted to clauses:
% 3.53/3.69 cnf(t8_boole-1, axiom, ( ~empty(_u63) | ( _u63 = _u62) | ~empty(_u62) )).
% 3.53/3.69
% 3.53/3.69 % Problem matrix:
% 3.53/3.69 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 3.53/3.69 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 3.53/3.69 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 3.53/3.69 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( relation_composition(__eqx_0, __eqx_1) = relation_composition(__eqy_0, __eqy_1)) )).
% 3.53/3.69 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( identity_relation(__eqx_0) = identity_relation(__eqy_0)) )).
% 3.53/3.69 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 3.53/3.69 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( relation_dom(__eqx_0) = relation_dom(__eqy_0)) )).
% 3.53/3.69 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( apply(__eqx_0, __eqx_1) = apply(__eqy_0, __eqy_1)) )).
% 3.53/3.69 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 3.53/3.69 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( skolem4(__eqx_0) = skolem4(__eqy_0)) )).
% 3.53/3.69 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( skolem7(__eqx_0) = skolem7(__eqy_0)) )).
% 3.53/3.69 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem10(__eqx_0, __eqx_1) = skolem10(__eqy_0, __eqy_1)) )).
% 3.53/3.69 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 3.53/3.69 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 3.53/3.69 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 3.53/3.69 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 3.53/3.69 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 3.53/3.69 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~relation_empty_yielding(__eqx_0) | relation_empty_yielding(__eqy_0) )).
% 3.53/3.69 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 3.53/3.69 cnf(matrix-19, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 3.53/3.69 cnf(matrix-20, plain, ( ~empty(_u2) | function(_u2) )).
% 3.53/3.69 cnf(matrix-21, plain, ( ~empty(_u3) | relation(_u3) )).
% 3.53/3.69 cnf(matrix-22, plain, ( ~relation(_u5) | ~relation(_u4) | relation(relation_composition(_u5, _u4)) )).
% 3.53/3.69 cnf(matrix-23, plain, ( relation(identity_relation(_u6)) )).
% 3.53/3.69 cnf(matrix-24, plain, ( element(skolem1(_u8), _u8) )).
% 3.53/3.69 cnf(matrix-25, plain, ( ~empty(_u10) | ~relation(_u9) | empty(relation_composition(_u9, _u10)) )).
% 3.53/3.69 cnf(matrix-26, plain, ( ~empty(_u10) | ~relation(_u9) | relation(relation_composition(_u9, _u10)) )).
% 3.53/3.69 cnf(matrix-27, plain, ( empty(empty_set) )).
% 3.53/3.69 cnf(matrix-28, plain, ( relation(empty_set) )).
% 3.53/3.69 cnf(matrix-29, plain, ( relation_empty_yielding(empty_set) )).
% 3.53/3.69 cnf(matrix-30, plain, ( ~relation(_u12) | ~function(_u12) | ~relation(_u11) | ~function(_u11) | relation(relation_composition(_u12, _u11)) )).
% 3.53/3.69 cnf(matrix-31, plain, ( ~relation(_u12) | ~function(_u12) | ~relation(_u11) | ~function(_u11) | function(relation_composition(_u12, _u11)) )).
% 3.53/3.69 cnf(matrix-32, plain, ( ~empty(powerset(_u13)) )).
% 3.53/3.69 cnf(matrix-33, plain, ( empty(empty_set) )).
% 3.53/3.69 cnf(matrix-34, plain, ( relation(identity_relation(_u15)) )).
% 3.53/3.69 cnf(matrix-35, plain, ( function(identity_relation(_u16)) )).
% 3.53/3.69 cnf(matrix-36, plain, ( empty(empty_set) )).
% 3.53/3.69 cnf(matrix-37, plain, ( relation(empty_set) )).
% 3.53/3.69 cnf(matrix-38, plain, ( empty(_u17) | ~relation(_u17) | ~empty(relation_dom(_u17)) )).
% 3.53/3.69 cnf(matrix-39, plain, ( ~empty(_u18) | empty(relation_dom(_u18)) )).
% 3.53/3.69 cnf(matrix-40, plain, ( ~empty(_u18) | relation(relation_dom(_u18)) )).
% 3.53/3.69 cnf(matrix-41, plain, ( ~empty(_u20) | ~relation(_u19) | empty(relation_composition(_u20, _u19)) )).
% 3.53/3.69 cnf(matrix-42, plain, ( ~empty(_u20) | ~relation(_u19) | relation(relation_composition(_u20, _u19)) )).
% 3.53/3.69 cnf(matrix-43, plain, ( relation(skolem2) )).
% 3.53/3.69 cnf(matrix-44, plain, ( function(skolem2) )).
% 3.53/3.69 cnf(matrix-45, plain, ( empty(skolem3) )).
% 3.53/3.69 cnf(matrix-46, plain, ( relation(skolem3) )).
% 3.53/3.69 cnf(matrix-47, plain, ( empty(_u24) | element(skolem4(_u24), powerset(_u24)) )).
% 3.53/3.69 cnf(matrix-48, plain, ( empty(_u24) | ~empty(skolem4(_u24)) )).
% 3.53/3.69 cnf(matrix-49, plain, ( empty(skolem5) )).
% 3.53/3.69 cnf(matrix-50, plain, ( ~empty(skolem6) )).
% 3.53/3.69 cnf(matrix-51, plain, ( relation(skolem6) )).
% 3.53/3.69 cnf(matrix-52, plain, ( element(skolem7(_u28), powerset(_u28)) )).
% 3.53/3.69 cnf(matrix-53, plain, ( empty(skolem7(_u28)) )).
% 3.53/3.69 cnf(matrix-54, plain, ( ~empty(skolem8) )).
% 3.53/3.69 cnf(matrix-55, plain, ( relation(skolem9) )).
% 3.53/3.69 cnf(matrix-56, plain, ( relation_empty_yielding(skolem9) )).
% 3.53/3.69 cnf(matrix-57, plain, ( subset(_u32, _u32) )).
% 3.53/3.69 cnf(matrix-58, plain, ( ~in(_u34, _u33) | element(_u34, _u33) )).
% 3.53/3.69 cnf(matrix-59, plain, ( ~relation(_u36) | ~function(_u36) | ~relation(_u35) | ~function(_u35) | ~in(_u37, relation_dom(relation_composition(_u35, _u36))) | in(_u37, relation_dom(_u35)) )).
% 3.53/3.69 cnf(matrix-60, plain, ( ~relation(_u36) | ~function(_u36) | ~relation(_u35) | ~function(_u35) | ~in(_u37, relation_dom(relation_composition(_u35, _u36))) | in(apply(_u35, _u37), relation_dom(_u36)) )).
% 3.53/3.69 cnf(matrix-61, plain, ( ~relation(_u36) | ~function(_u36) | ~relation(_u35) | ~function(_u35) | ~in(_u37, relation_dom(_u35)) | ~in(apply(_u35, _u37), relation_dom(_u36)) | in(_u37, relation_dom(relation_composition(_u35, _u36))) )).
% 3.53/3.69 cnf(matrix-62, plain, ( ~element(_u39, _u38) | empty(_u38) | in(_u39, _u38) )).
% 3.53/3.69 cnf(matrix-63, plain, ( ~relation(_u42) | ~function(_u42) | ( _u42 != identity_relation(_u43)) | ( relation_dom(_u42) = _u43) )).
% 3.53/3.69 cnf(matrix-64, plain, ( ~relation(_u42) | ~function(_u42) | ( _u42 != identity_relation(_u43)) | ~in(_u40, _u43) | ( apply(_u42, _u40) = _u40) )).
% 3.53/3.69 cnf(matrix-65, plain, ( ~relation(_u42) | ~function(_u42) | ( _u42 = identity_relation(_u43)) | ( relation_dom(_u42) != _u43) | in(skolem10(_u43, _u42), _u43) )).
% 3.53/3.69 cnf(matrix-66, plain, ( ~relation(_u42) | ~function(_u42) | ( _u42 = identity_relation(_u43)) | ( relation_dom(_u42) != _u43) | ( apply(_u42, skolem10(_u43, _u42)) != skolem10(_u43, _u42)) )).
% 3.53/3.69 cnf(matrix-67, plain, ( ~element(_u48, powerset(_u46)) | subset(_u48, _u46) )).
% 3.53/3.69 cnf(matrix-68, plain, ( ~subset(_u49, _u47) | element(_u49, powerset(_u47)) )).
% 3.53/3.69 cnf(matrix-69, plain, ( relation(skolem13) )).
% 3.53/3.69 cnf(matrix-70, plain, ( function(skolem13) )).
% 3.53/3.69 cnf(matrix-71, plain, ( in(skolem12, relation_dom(relation_composition(skolem13, identity_relation(skolem11)))) | in(skolem12, relation_dom(skolem13)) )).
% 3.53/3.69 cnf(matrix-72, plain, ( in(skolem12, relation_dom(relation_composition(skolem13, identity_relation(skolem11)))) | in(apply(skolem13, skolem12), skolem11) )).
% 3.53/3.69 cnf(matrix-73, plain, ( ~in(skolem12, relation_dom(skolem13)) | ~in(apply(skolem13, skolem12), skolem11) | ~in(skolem12, relation_dom(relation_composition(skolem13, identity_relation(skolem11)))) )).
% 3.53/3.69 cnf(matrix-74, plain, ( ~in(_u55, _u54) | ~element(_u54, powerset(_u53)) | element(_u55, _u53) )).
% 3.53/3.69 cnf(matrix-75, plain, ( ~in(_u58, _u57) | ~element(_u57, powerset(_u56)) | ~empty(_u56) )).
% 3.53/3.69 cnf(matrix-76, plain, ( ~empty(_u59) | ( _u59 = empty_set) )).
% 3.53/3.69 cnf(matrix-77, plain, ( ~in(_u61, _u60) | ~empty(_u60) )).
% 3.53/3.69 cnf(matrix-78, plain, ( ~empty(_u63) | ( _u63 = _u62) | ~empty(_u62) )).
% 3.53/3.69
% 3.53/3.69 % Proof stack:
% 3.53/3.69 cnf(proof-stack, plain,
% 3.53/3.69 proof_stack(
% 3.53/3.69 start(73),
% 3.53/3.69 left_branch(0, 71, 1, 2),
% 3.53/3.69 left_branch(0, 59, 4, 3),
% 3.53/3.69 left_branch(0, 34, 0, 4),
% 3.53/3.69 right_branch(4),
% 3.53/3.69 reduction(0, 0),
% 3.53/3.69 left_branch(0, 70, 0, 6),
% 3.53/3.69 right_branch(6),
% 3.53/3.69 left_branch(0, 69, 0, 7),
% 3.53/3.69 right_branch(7),
% 3.53/3.69 left_branch(0, 35, 0, 8),
% 3.53/3.69 right_branch(8),
% 3.53/3.69 right_branch(3),
% 3.53/3.69 right_branch(2),
% 3.53/3.69 left_branch(0, 61, 6, 3),
% 3.53/3.69 left_branch(0, 34, 0, 4),
% 3.53/3.69 right_branch(4),
% 3.53/3.69 left_branch(0, 12, 3, 5),
% 3.53/3.69 left_branch(0, 7, 2, 6),
% 3.53/3.69 left_branch(0, 1, 1, 7),
% 3.53/3.69 left_branch(0, 0, 0, 8),
% 3.53/3.69 right_branch(8),
% 3.53/3.69 right_branch(7),
% 3.53/3.69 left_branch(0, 1, 1, 8),
% 3.53/3.69 left_branch(0, 0, 0, 9),
% 3.53/3.69 right_branch(9),
% 3.53/3.69 right_branch(8),
% 3.53/3.69 right_branch(6),
% 3.53/3.69 left_branch(0, 72, 1, 7),
% 3.53/3.69 reduction(0, 0),
% 3.53/3.69 right_branch(7),
% 3.53/3.69 left_branch(0, 1, 1, 8),
% 3.53/3.69 left_branch(0, 63, 3, 9),
% 3.53/3.69 lemmata(0, 1),
% 3.53/3.69 left_branch(0, 0, 0, 11),
% 3.53/3.69 right_branch(11),
% 3.53/3.69 left_branch(0, 35, 0, 12),
% 3.53/3.69 right_branch(12),
% 3.53/3.69 right_branch(9),
% 3.53/3.69 right_branch(8),
% 3.53/3.69 right_branch(5),
% 3.53/3.69 lemmata(0, 0),
% 3.53/3.69 left_branch(0, 70, 0, 7),
% 3.53/3.69 right_branch(7),
% 3.53/3.69 left_branch(0, 69, 0, 8),
% 3.53/3.69 right_branch(8),
% 3.53/3.69 left_branch(0, 35, 0, 9),
% 3.53/3.69 right_branch(9),
% 3.53/3.69 right_branch(3),
% 3.53/3.69 left_branch(0, 72, 1, 4),
% 3.53/3.69 left_branch(0, 60, 4, 5),
% 3.53/3.69 left_branch(0, 34, 0, 6),
% 3.53/3.69 right_branch(6),
% 3.53/3.69 left_branch(0, 12, 2, 7),
% 3.53/3.69 left_branch(0, 7, 2, 8),
% 3.53/3.69 left_branch(0, 0, 0, 9),
% 3.53/3.69 right_branch(9),
% 3.53/3.69 left_branch(0, 0, 0, 10),
% 3.53/3.69 right_branch(10),
% 3.53/3.69 right_branch(8),
% 3.53/3.69 reduction(0, 0),
% 3.53/3.69 left_branch(0, 63, 3, 10),
% 3.53/3.69 lemmata(0, 2),
% 3.53/3.69 left_branch(0, 0, 0, 12),
% 3.53/3.69 right_branch(12),
% 3.53/3.69 left_branch(0, 35, 0, 13),
% 3.53/3.69 right_branch(13),
% 3.53/3.69 right_branch(10),
% 3.53/3.69 right_branch(7),
% 3.53/3.69 left_branch(0, 70, 0, 8),
% 3.53/3.69 right_branch(8),
% 3.53/3.69 left_branch(0, 69, 0, 9),
% 3.53/3.69 right_branch(9),
% 3.53/3.69 left_branch(0, 35, 0, 10),
% 3.53/3.69 right_branch(10),
% 3.53/3.69 right_branch(5),
% 3.53/3.69 right_branch(4)
% 3.53/3.69 )).
% 3.53/3.69 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------