TSTP Solution File: NUM410+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : NUM410+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 : n025.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 14:26:41 EDT 2024
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% 0.04/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.14/0.33 % Computer : n025.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
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Mar 20 19:21:38 EDT 2024
% 0.14/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem for theBenchmark
% 0.19/0.37 % SZS output start Proof for theBenchmark
% 0.19/0.37
% 0.19/0.37 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 0.19/0.37 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.19/0.37
% 0.19/0.37 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(cc1_funct_1-1, axiom, ( ~empty(_u2) | function(_u2) )).
% 0.19/0.37
% 0.19/0.37 % Formula: cc1_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(cc1_ordinal1-1, axiom, ( ~ordinal(_u3) | epsilon_transitive(_u3) )).
% 0.19/0.37 cnf(cc1_ordinal1-2, axiom, ( ~ordinal(_u3) | epsilon_connected(_u3) )).
% 0.19/0.37
% 0.19/0.37 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(cc1_relat_1-1, axiom, ( ~empty(_u4) | relation(_u4) )).
% 0.19/0.37
% 0.19/0.37 % Formula: cc2_funct_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(cc2_funct_1-1, axiom, ( ~relation(_u5) | ~empty(_u5) | ~function(_u5) | one_to_one(_u5) )).
% 0.19/0.37
% 0.19/0.37 % Formula: cc2_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(cc2_ordinal1-1, axiom, ( ~epsilon_transitive(_u6) | ~epsilon_connected(_u6) | ordinal(_u6) )).
% 0.19/0.37
% 0.19/0.37 % Formula: cc3_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(cc3_ordinal1-1, axiom, ( ~empty(_u7) | epsilon_transitive(_u7) )).
% 0.19/0.37 cnf(cc3_ordinal1-2, axiom, ( ~empty(_u7) | epsilon_connected(_u7) )).
% 0.19/0.37 cnf(cc3_ordinal1-3, axiom, ( ~empty(_u7) | ordinal(_u7) )).
% 0.19/0.37
% 0.19/0.37 % Formula: d7_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(d7_ordinal1-1, axiom, ( ~relation(_u8) | ~function(_u8) | ~transfinite_sequence(_u8) | ordinal(relation_dom(_u8)) )).
% 0.19/0.37 cnf(d7_ordinal1-2, axiom, ( ~relation(_u8) | ~function(_u8) | ~ordinal(relation_dom(_u8)) | transfinite_sequence(_u8) )).
% 0.19/0.37
% 0.19/0.37 % Formula: d8_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(d8_ordinal1-1, axiom, ( ~relation(_u9) | ~function(_u9) | ~transfinite_sequence(_u9) | ~transfinite_sequence_of(_u9, _u10) | subset(relation_rng(_u9), _u10) )).
% 0.19/0.37 cnf(d8_ordinal1-2, axiom, ( ~relation(_u9) | ~function(_u9) | ~transfinite_sequence(_u9) | ~subset(relation_rng(_u9), _u10) | transfinite_sequence_of(_u9, _u10) )).
% 0.19/0.37
% 0.19/0.37 % Formula: dt_m1_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(dt_m1_ordinal1-1, axiom, ( ~transfinite_sequence_of(_u11, _u12) | relation(_u11) )).
% 0.19/0.37 cnf(dt_m1_ordinal1-2, axiom, ( ~transfinite_sequence_of(_u11, _u12) | function(_u11) )).
% 0.19/0.37 cnf(dt_m1_ordinal1-3, axiom, ( ~transfinite_sequence_of(_u11, _u12) | transfinite_sequence(_u11) )).
% 0.19/0.37
% 0.19/0.37 % Formula: existence_m1_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(existence_m1_ordinal1-1, axiom, ( transfinite_sequence_of(skolem1(_u14), _u14) )).
% 0.19/0.37
% 0.19/0.37 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(existence_m1_subset_1-1, axiom, ( element(skolem2(_u16), _u16) )).
% 0.19/0.37
% 0.19/0.37 % Formula: fc12_relat_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(fc12_relat_1-1, axiom, ( empty(empty_set) )).
% 0.19/0.37 cnf(fc12_relat_1-2, axiom, ( relation(empty_set) )).
% 0.19/0.37 cnf(fc12_relat_1-3, axiom, ( relation_empty_yielding(empty_set) )).
% 0.19/0.37
% 0.19/0.37 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 0.19/0.37
% 0.19/0.37 % Formula: fc2_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(fc2_ordinal1-1, axiom, ( relation(empty_set) )).
% 0.19/0.37 cnf(fc2_ordinal1-2, axiom, ( relation_empty_yielding(empty_set) )).
% 0.19/0.37 cnf(fc2_ordinal1-3, axiom, ( function(empty_set) )).
% 0.19/0.37 cnf(fc2_ordinal1-4, axiom, ( one_to_one(empty_set) )).
% 0.19/0.37 cnf(fc2_ordinal1-5, axiom, ( empty(empty_set) )).
% 0.19/0.37 cnf(fc2_ordinal1-6, axiom, ( epsilon_transitive(empty_set) )).
% 0.19/0.37 cnf(fc2_ordinal1-7, axiom, ( epsilon_connected(empty_set) )).
% 0.19/0.37 cnf(fc2_ordinal1-8, axiom, ( ordinal(empty_set) )).
% 0.19/0.37
% 0.19/0.37 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 0.19/0.37 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 0.19/0.37
% 0.19/0.37 % Formula: fc5_relat_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(fc5_relat_1-1, axiom, ( empty(_u17) | ~relation(_u17) | ~empty(relation_dom(_u17)) )).
% 0.19/0.37
% 0.19/0.37 % Formula: fc6_funct_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(fc6_funct_1-1, axiom, ( ~relation(_u18) | ~relation_non_empty(_u18) | ~function(_u18) | with_non_empty_elements(relation_rng(_u18)) )).
% 0.19/0.37
% 0.19/0.37 % Formula: fc6_relat_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(fc6_relat_1-1, axiom, ( empty(_u19) | ~relation(_u19) | ~empty(relation_rng(_u19)) )).
% 0.19/0.37
% 0.19/0.37 % Formula: fc7_relat_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(fc7_relat_1-1, axiom, ( ~empty(_u20) | empty(relation_dom(_u20)) )).
% 0.19/0.37 cnf(fc7_relat_1-2, axiom, ( ~empty(_u20) | relation(relation_dom(_u20)) )).
% 0.19/0.37
% 0.19/0.37 % Formula: fc8_relat_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(fc8_relat_1-1, axiom, ( ~empty(_u21) | empty(relation_rng(_u21)) )).
% 0.19/0.37 cnf(fc8_relat_1-2, axiom, ( ~empty(_u21) | relation(relation_rng(_u21)) )).
% 0.19/0.37
% 0.19/0.37 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(rc1_funct_1-1, axiom, ( relation(skolem3) )).
% 0.19/0.37 cnf(rc1_funct_1-2, axiom, ( function(skolem3) )).
% 0.19/0.37
% 0.19/0.37 % Formula: rc1_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(rc1_ordinal1-1, axiom, ( epsilon_transitive(skolem4) )).
% 0.19/0.37 cnf(rc1_ordinal1-2, axiom, ( epsilon_connected(skolem4) )).
% 0.19/0.37 cnf(rc1_ordinal1-3, axiom, ( ordinal(skolem4) )).
% 0.19/0.37
% 0.19/0.37 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(rc1_relat_1-1, axiom, ( empty(skolem5) )).
% 0.19/0.37 cnf(rc1_relat_1-2, axiom, ( relation(skolem5) )).
% 0.19/0.37
% 0.19/0.37 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(rc1_xboole_0-1, axiom, ( empty(skolem6) )).
% 0.19/0.37
% 0.19/0.37 % Formula: rc2_funct_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(rc2_funct_1-1, axiom, ( relation(skolem7) )).
% 0.19/0.37 cnf(rc2_funct_1-2, axiom, ( empty(skolem7) )).
% 0.19/0.37 cnf(rc2_funct_1-3, axiom, ( function(skolem7) )).
% 0.19/0.37
% 0.19/0.37 % Formula: rc2_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(rc2_ordinal1-1, axiom, ( relation(skolem8) )).
% 0.19/0.37 cnf(rc2_ordinal1-2, axiom, ( function(skolem8) )).
% 0.19/0.37 cnf(rc2_ordinal1-3, axiom, ( one_to_one(skolem8) )).
% 0.19/0.37 cnf(rc2_ordinal1-4, axiom, ( empty(skolem8) )).
% 0.19/0.37 cnf(rc2_ordinal1-5, axiom, ( epsilon_transitive(skolem8) )).
% 0.19/0.37 cnf(rc2_ordinal1-6, axiom, ( epsilon_connected(skolem8) )).
% 0.19/0.37 cnf(rc2_ordinal1-7, axiom, ( ordinal(skolem8) )).
% 0.19/0.37
% 0.19/0.37 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem9) )).
% 0.19/0.37 cnf(rc2_relat_1-2, axiom, ( relation(skolem9) )).
% 0.19/0.37
% 0.19/0.37 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem10) )).
% 0.19/0.37
% 0.19/0.37 % Formula: rc3_funct_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(rc3_funct_1-1, axiom, ( relation(skolem11) )).
% 0.19/0.37 cnf(rc3_funct_1-2, axiom, ( function(skolem11) )).
% 0.19/0.37 cnf(rc3_funct_1-3, axiom, ( one_to_one(skolem11) )).
% 0.19/0.37
% 0.19/0.37 % Formula: rc3_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(rc3_ordinal1-1, axiom, ( ~empty(skolem12) )).
% 0.19/0.37 cnf(rc3_ordinal1-2, axiom, ( epsilon_transitive(skolem12) )).
% 0.19/0.37 cnf(rc3_ordinal1-3, axiom, ( epsilon_connected(skolem12) )).
% 0.19/0.37 cnf(rc3_ordinal1-4, axiom, ( ordinal(skolem12) )).
% 0.19/0.37
% 0.19/0.37 % Formula: rc3_relat_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(rc3_relat_1-1, axiom, ( relation(skolem13) )).
% 0.19/0.37 cnf(rc3_relat_1-2, axiom, ( relation_empty_yielding(skolem13) )).
% 0.19/0.37
% 0.19/0.37 % Formula: rc4_funct_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(rc4_funct_1-1, axiom, ( relation(skolem14) )).
% 0.19/0.37 cnf(rc4_funct_1-2, axiom, ( relation_empty_yielding(skolem14) )).
% 0.19/0.37 cnf(rc4_funct_1-3, axiom, ( function(skolem14) )).
% 0.19/0.37
% 0.19/0.37 % Formula: rc4_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(rc4_ordinal1-1, axiom, ( relation(skolem15) )).
% 0.19/0.37 cnf(rc4_ordinal1-2, axiom, ( function(skolem15) )).
% 0.19/0.37 cnf(rc4_ordinal1-3, axiom, ( transfinite_sequence(skolem15) )).
% 0.19/0.37
% 0.19/0.37 % Formula: rc5_funct_1 ( axiom ) converted to clauses:
% 0.19/0.37 cnf(rc5_funct_1-1, axiom, ( relation(skolem16) )).
% 0.19/0.37 cnf(rc5_funct_1-2, axiom, ( relation_non_empty(skolem16) )).
% 0.19/0.37 cnf(rc5_funct_1-3, axiom, ( function(skolem16) )).
% 0.19/0.37
% 0.19/0.37 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 0.19/0.37 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u37, _u37) )).
% 0.19/0.37
% 0.19/0.37 % Formula: t1_subset ( axiom ) converted to clauses:
% 0.19/0.37 cnf(t1_subset-1, axiom, ( ~in(_u39, _u38) | element(_u39, _u38) )).
% 0.19/0.37
% 0.19/0.37 % Formula: t2_subset ( axiom ) converted to clauses:
% 0.19/0.37 cnf(t2_subset-1, axiom, ( ~element(_u41, _u40) | empty(_u40) | in(_u41, _u40) )).
% 0.19/0.37
% 0.19/0.37 % Formula: t3_subset ( axiom ) converted to clauses:
% 0.19/0.37 cnf(t3_subset-1, axiom, ( ~element(_u46, powerset(_u44)) | subset(_u46, _u44) )).
% 0.19/0.37 cnf(t3_subset-2, axiom, ( ~subset(_u47, _u45) | element(_u47, powerset(_u45)) )).
% 0.19/0.37
% 0.19/0.37 % Formula: t46_ordinal1 ( conjecture ) (definitionally) converted to clauses:
% 0.19/0.37 cnf(t46_ordinal1-1, negated_conjecture, ( relation(skolem17) )).
% 0.19/0.37 cnf(t46_ordinal1-2, negated_conjecture, ( function(skolem17) )).
% 0.19/0.37 cnf(t46_ordinal1-3, negated_conjecture, ( ordinal(relation_dom(skolem17)) )).
% 0.19/0.37 cnf(t46_ordinal1-4, negated_conjecture, ( ~transfinite_sequence_of(skolem17, relation_rng(skolem17)) )).
% 0.19/0.37
% 0.19/0.37 % Formula: t4_subset ( axiom ) converted to clauses:
% 0.19/0.37 cnf(t4_subset-1, axiom, ( ~in(_u51, _u50) | ~element(_u50, powerset(_u49)) | element(_u51, _u49) )).
% 0.19/0.37
% 0.19/0.37 % Formula: t5_subset ( axiom ) converted to clauses:
% 0.19/0.37 cnf(t5_subset-1, axiom, ( ~in(_u54, _u53) | ~element(_u53, powerset(_u52)) | ~empty(_u52) )).
% 0.19/0.37
% 0.19/0.37 % Formula: t6_boole ( axiom ) converted to clauses:
% 0.19/0.37 cnf(t6_boole-1, axiom, ( ~empty(_u55) | ( _u55 = empty_set) )).
% 0.19/0.37
% 0.19/0.37 % Formula: t7_boole ( axiom ) converted to clauses:
% 0.19/0.37 cnf(t7_boole-1, axiom, ( ~in(_u57, _u56) | ~empty(_u56) )).
% 0.19/0.37
% 0.19/0.37 % Formula: t8_boole ( axiom ) converted to clauses:
% 0.19/0.37 cnf(t8_boole-1, axiom, ( ~empty(_u59) | ( _u59 = _u58) | ~empty(_u58) )).
% 0.19/0.37
% 0.19/0.37 % Problem matrix:
% 0.19/0.37 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.19/0.37 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.19/0.37 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.19/0.37 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( relation_dom(__eqx_0) = relation_dom(__eqy_0)) )).
% 0.19/0.37 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( relation_rng(__eqx_0) = relation_rng(__eqy_0)) )).
% 0.19/0.37 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 0.19/0.37 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 0.19/0.37 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( skolem2(__eqx_0) = skolem2(__eqy_0)) )).
% 0.19/0.37 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 0.19/0.37 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 0.19/0.37 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 0.19/0.37 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ~ordinal(__eqx_0) | ordinal(__eqy_0) )).
% 0.19/0.37 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ~epsilon_transitive(__eqx_0) | epsilon_transitive(__eqy_0) )).
% 0.19/0.37 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ~epsilon_connected(__eqx_0) | epsilon_connected(__eqy_0) )).
% 0.19/0.37 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 0.19/0.37 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 0.19/0.37 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~transfinite_sequence(__eqx_0) | transfinite_sequence(__eqy_0) )).
% 0.19/0.37 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~transfinite_sequence_of(__eqx_0, __eqx_1) | transfinite_sequence_of(__eqy_0, __eqy_1) )).
% 0.19/0.37 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 0.19/0.37 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 0.19/0.37 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ~relation_empty_yielding(__eqx_0) | relation_empty_yielding(__eqy_0) )).
% 0.19/0.37 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ~relation_non_empty(__eqx_0) | relation_non_empty(__eqy_0) )).
% 0.19/0.37 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ~with_non_empty_elements(__eqx_0) | with_non_empty_elements(__eqy_0) )).
% 0.19/0.37 cnf(matrix-23, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.19/0.37 cnf(matrix-24, plain, ( ~empty(_u2) | function(_u2) )).
% 0.19/0.37 cnf(matrix-25, plain, ( ~ordinal(_u3) | epsilon_transitive(_u3) )).
% 0.19/0.37 cnf(matrix-26, plain, ( ~ordinal(_u3) | epsilon_connected(_u3) )).
% 0.19/0.37 cnf(matrix-27, plain, ( ~empty(_u4) | relation(_u4) )).
% 0.19/0.37 cnf(matrix-28, plain, ( ~relation(_u5) | ~empty(_u5) | ~function(_u5) | one_to_one(_u5) )).
% 0.19/0.37 cnf(matrix-29, plain, ( ~epsilon_transitive(_u6) | ~epsilon_connected(_u6) | ordinal(_u6) )).
% 0.19/0.37 cnf(matrix-30, plain, ( ~empty(_u7) | epsilon_transitive(_u7) )).
% 0.19/0.37 cnf(matrix-31, plain, ( ~empty(_u7) | epsilon_connected(_u7) )).
% 0.19/0.37 cnf(matrix-32, plain, ( ~empty(_u7) | ordinal(_u7) )).
% 0.19/0.37 cnf(matrix-33, plain, ( ~relation(_u8) | ~function(_u8) | ~transfinite_sequence(_u8) | ordinal(relation_dom(_u8)) )).
% 0.19/0.37 cnf(matrix-34, plain, ( ~relation(_u8) | ~function(_u8) | ~ordinal(relation_dom(_u8)) | transfinite_sequence(_u8) )).
% 0.19/0.37 cnf(matrix-35, plain, ( ~relation(_u9) | ~function(_u9) | ~transfinite_sequence(_u9) | ~transfinite_sequence_of(_u9, _u10) | subset(relation_rng(_u9), _u10) )).
% 0.19/0.37 cnf(matrix-36, plain, ( ~relation(_u9) | ~function(_u9) | ~transfinite_sequence(_u9) | ~subset(relation_rng(_u9), _u10) | transfinite_sequence_of(_u9, _u10) )).
% 0.19/0.37 cnf(matrix-37, plain, ( ~transfinite_sequence_of(_u11, _u12) | relation(_u11) )).
% 0.19/0.37 cnf(matrix-38, plain, ( ~transfinite_sequence_of(_u11, _u12) | function(_u11) )).
% 0.19/0.37 cnf(matrix-39, plain, ( ~transfinite_sequence_of(_u11, _u12) | transfinite_sequence(_u11) )).
% 0.19/0.37 cnf(matrix-40, plain, ( transfinite_sequence_of(skolem1(_u14), _u14) )).
% 0.19/0.37 cnf(matrix-41, plain, ( element(skolem2(_u16), _u16) )).
% 0.19/0.37 cnf(matrix-42, plain, ( empty(empty_set) )).
% 0.19/0.37 cnf(matrix-43, plain, ( relation(empty_set) )).
% 0.19/0.37 cnf(matrix-44, plain, ( relation_empty_yielding(empty_set) )).
% 0.19/0.37 cnf(matrix-45, plain, ( empty(empty_set) )).
% 0.19/0.37 cnf(matrix-46, plain, ( relation(empty_set) )).
% 0.19/0.37 cnf(matrix-47, plain, ( relation_empty_yielding(empty_set) )).
% 0.19/0.37 cnf(matrix-48, plain, ( function(empty_set) )).
% 0.19/0.37 cnf(matrix-49, plain, ( one_to_one(empty_set) )).
% 0.19/0.37 cnf(matrix-50, plain, ( empty(empty_set) )).
% 0.19/0.37 cnf(matrix-51, plain, ( epsilon_transitive(empty_set) )).
% 0.19/0.37 cnf(matrix-52, plain, ( epsilon_connected(empty_set) )).
% 0.19/0.37 cnf(matrix-53, plain, ( ordinal(empty_set) )).
% 0.19/0.37 cnf(matrix-54, plain, ( empty(empty_set) )).
% 0.19/0.37 cnf(matrix-55, plain, ( relation(empty_set) )).
% 0.19/0.37 cnf(matrix-56, plain, ( empty(_u17) | ~relation(_u17) | ~empty(relation_dom(_u17)) )).
% 0.19/0.37 cnf(matrix-57, plain, ( ~relation(_u18) | ~relation_non_empty(_u18) | ~function(_u18) | with_non_empty_elements(relation_rng(_u18)) )).
% 0.19/0.37 cnf(matrix-58, plain, ( empty(_u19) | ~relation(_u19) | ~empty(relation_rng(_u19)) )).
% 0.19/0.37 cnf(matrix-59, plain, ( ~empty(_u20) | empty(relation_dom(_u20)) )).
% 0.19/0.37 cnf(matrix-60, plain, ( ~empty(_u20) | relation(relation_dom(_u20)) )).
% 0.19/0.37 cnf(matrix-61, plain, ( ~empty(_u21) | empty(relation_rng(_u21)) )).
% 0.19/0.37 cnf(matrix-62, plain, ( ~empty(_u21) | relation(relation_rng(_u21)) )).
% 0.19/0.37 cnf(matrix-63, plain, ( relation(skolem3) )).
% 0.19/0.37 cnf(matrix-64, plain, ( function(skolem3) )).
% 0.19/0.37 cnf(matrix-65, plain, ( epsilon_transitive(skolem4) )).
% 0.19/0.37 cnf(matrix-66, plain, ( epsilon_connected(skolem4) )).
% 0.19/0.37 cnf(matrix-67, plain, ( ordinal(skolem4) )).
% 0.19/0.37 cnf(matrix-68, plain, ( empty(skolem5) )).
% 0.19/0.37 cnf(matrix-69, plain, ( relation(skolem5) )).
% 0.19/0.37 cnf(matrix-70, plain, ( empty(skolem6) )).
% 0.19/0.37 cnf(matrix-71, plain, ( relation(skolem7) )).
% 0.19/0.37 cnf(matrix-72, plain, ( empty(skolem7) )).
% 0.19/0.37 cnf(matrix-73, plain, ( function(skolem7) )).
% 0.19/0.37 cnf(matrix-74, plain, ( relation(skolem8) )).
% 0.19/0.37 cnf(matrix-75, plain, ( function(skolem8) )).
% 0.19/0.37 cnf(matrix-76, plain, ( one_to_one(skolem8) )).
% 0.19/0.37 cnf(matrix-77, plain, ( empty(skolem8) )).
% 0.19/0.37 cnf(matrix-78, plain, ( epsilon_transitive(skolem8) )).
% 0.19/0.37 cnf(matrix-79, plain, ( epsilon_connected(skolem8) )).
% 0.19/0.37 cnf(matrix-80, plain, ( ordinal(skolem8) )).
% 0.19/0.37 cnf(matrix-81, plain, ( ~empty(skolem9) )).
% 0.19/0.37 cnf(matrix-82, plain, ( relation(skolem9) )).
% 0.19/0.37 cnf(matrix-83, plain, ( ~empty(skolem10) )).
% 0.19/0.37 cnf(matrix-84, plain, ( relation(skolem11) )).
% 0.19/0.37 cnf(matrix-85, plain, ( function(skolem11) )).
% 0.19/0.37 cnf(matrix-86, plain, ( one_to_one(skolem11) )).
% 0.19/0.37 cnf(matrix-87, plain, ( ~empty(skolem12) )).
% 0.19/0.37 cnf(matrix-88, plain, ( epsilon_transitive(skolem12) )).
% 0.19/0.37 cnf(matrix-89, plain, ( epsilon_connected(skolem12) )).
% 0.19/0.37 cnf(matrix-90, plain, ( ordinal(skolem12) )).
% 0.19/0.37 cnf(matrix-91, plain, ( relation(skolem13) )).
% 0.19/0.37 cnf(matrix-92, plain, ( relation_empty_yielding(skolem13) )).
% 0.19/0.37 cnf(matrix-93, plain, ( relation(skolem14) )).
% 0.19/0.37 cnf(matrix-94, plain, ( relation_empty_yielding(skolem14) )).
% 0.19/0.37 cnf(matrix-95, plain, ( function(skolem14) )).
% 0.19/0.37 cnf(matrix-96, plain, ( relation(skolem15) )).
% 0.19/0.37 cnf(matrix-97, plain, ( function(skolem15) )).
% 0.19/0.37 cnf(matrix-98, plain, ( transfinite_sequence(skolem15) )).
% 0.19/0.37 cnf(matrix-99, plain, ( relation(skolem16) )).
% 0.19/0.37 cnf(matrix-100, plain, ( relation_non_empty(skolem16) )).
% 0.19/0.37 cnf(matrix-101, plain, ( function(skolem16) )).
% 0.19/0.37 cnf(matrix-102, plain, ( subset(_u37, _u37) )).
% 0.19/0.37 cnf(matrix-103, plain, ( ~in(_u39, _u38) | element(_u39, _u38) )).
% 0.19/0.37 cnf(matrix-104, plain, ( ~element(_u41, _u40) | empty(_u40) | in(_u41, _u40) )).
% 0.19/0.37 cnf(matrix-105, plain, ( ~element(_u46, powerset(_u44)) | subset(_u46, _u44) )).
% 0.19/0.37 cnf(matrix-106, plain, ( ~subset(_u47, _u45) | element(_u47, powerset(_u45)) )).
% 0.19/0.37 cnf(matrix-107, plain, ( relation(skolem17) )).
% 0.19/0.37 cnf(matrix-108, plain, ( function(skolem17) )).
% 0.19/0.37 cnf(matrix-109, plain, ( ordinal(relation_dom(skolem17)) )).
% 0.19/0.37 cnf(matrix-110, plain, ( ~transfinite_sequence_of(skolem17, relation_rng(skolem17)) )).
% 0.19/0.37 cnf(matrix-111, plain, ( ~in(_u51, _u50) | ~element(_u50, powerset(_u49)) | element(_u51, _u49) )).
% 0.19/0.37 cnf(matrix-112, plain, ( ~in(_u54, _u53) | ~element(_u53, powerset(_u52)) | ~empty(_u52) )).
% 0.19/0.37 cnf(matrix-113, plain, ( ~empty(_u55) | ( _u55 = empty_set) )).
% 0.19/0.37 cnf(matrix-114, plain, ( ~in(_u57, _u56) | ~empty(_u56) )).
% 0.19/0.37 cnf(matrix-115, plain, ( ~empty(_u59) | ( _u59 = _u58) | ~empty(_u58) )).
% 0.19/0.37
% 0.19/0.37 % Proof stack:
% 0.19/0.37 cnf(proof-stack, plain,
% 0.19/0.37 proof_stack(
% 0.19/0.37 start(110),
% 0.19/0.37 left_branch(0, 36, 4, 2),
% 0.19/0.37 left_branch(0, 107, 0, 3),
% 0.19/0.37 right_branch(3),
% 0.19/0.37 left_branch(0, 102, 0, 4),
% 0.19/0.37 right_branch(4),
% 0.19/0.37 left_branch(0, 34, 3, 5),
% 0.19/0.37 lemmata(0, 0),
% 0.19/0.37 left_branch(0, 109, 0, 7),
% 0.19/0.37 right_branch(7),
% 0.19/0.37 left_branch(0, 108, 0, 8),
% 0.19/0.37 right_branch(8),
% 0.19/0.37 right_branch(5),
% 0.19/0.37 left_branch(0, 108, 0, 6),
% 0.19/0.37 right_branch(6),
% 0.19/0.37 right_branch(2)
% 0.19/0.37 )).
% 0.19/0.37 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------