TSTP Solution File: NUM409+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : NUM409+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 : n028.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 16.44s 16.61s
% Output : Proof 16.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM409+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n028.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 20:31:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 16.44/16.61 % SZS status Theorem for theBenchmark
% 16.44/16.61 % SZS output start Proof for theBenchmark
% 16.44/16.61
% 16.44/16.61 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 16.44/16.61 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 16.44/16.61
% 16.44/16.61 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 16.44/16.61 cnf(cc1_funct_1-1, axiom, ( ~empty(_u2) | function(_u2) )).
% 16.44/16.61
% 16.44/16.61 % Formula: cc1_ordinal1 ( axiom ) converted to clauses:
% 16.44/16.61 cnf(cc1_ordinal1-1, axiom, ( ~ordinal(_u3) | epsilon_transitive(_u3) )).
% 16.44/16.61 cnf(cc1_ordinal1-2, axiom, ( ~ordinal(_u3) | epsilon_connected(_u3) )).
% 16.44/16.61
% 16.44/16.61 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 16.44/16.61 cnf(cc1_relat_1-1, axiom, ( ~empty(_u4) | relation(_u4) )).
% 16.44/16.61
% 16.44/16.61 % Formula: cc2_funct_1 ( axiom ) converted to clauses:
% 16.44/16.61 cnf(cc2_funct_1-1, axiom, ( ~relation(_u5) | ~empty(_u5) | ~function(_u5) | one_to_one(_u5) )).
% 16.44/16.61
% 16.44/16.61 % Formula: cc2_ordinal1 ( axiom ) converted to clauses:
% 16.44/16.61 cnf(cc2_ordinal1-1, axiom, ( ~epsilon_transitive(_u6) | ~epsilon_connected(_u6) | ordinal(_u6) )).
% 16.44/16.61
% 16.44/16.61 % Formula: cc3_ordinal1 ( axiom ) converted to clauses:
% 16.44/16.61 cnf(cc3_ordinal1-1, axiom, ( ~empty(_u7) | epsilon_transitive(_u7) )).
% 16.44/16.61 cnf(cc3_ordinal1-2, axiom, ( ~empty(_u7) | epsilon_connected(_u7) )).
% 16.44/16.61 cnf(cc3_ordinal1-3, axiom, ( ~empty(_u7) | ordinal(_u7) )).
% 16.44/16.61
% 16.44/16.61 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 16.44/16.61 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u9, _u8) = unordered_pair(_u8, _u9)) )).
% 16.44/16.61
% 16.44/16.61 % Formula: d4_relat_1 ( axiom ) converted to clauses:
% 16.44/16.61 cnf(d4_relat_1-1, axiom, ( ~relation(_u17) | ( _u22 != relation_dom(_u17)) | ~in(_u18, _u22) | in(ordered_pair(_u18, skolem1(_u17, _u22, _u18)), _u17) )).
% 16.44/16.61 cnf(d4_relat_1-2, axiom, ( ~relation(_u17) | ( _u22 != relation_dom(_u17)) | ~in(ordered_pair(_u19, _u11), _u17) | in(_u19, _u22) )).
% 16.44/16.61 cnf(d4_relat_1-3, axiom, ( ~relation(_u17) | ( _u23 = relation_dom(_u17)) | in(skolem2(_u17, _u23), _u23) | in(ordered_pair(skolem3(_u17, _u23), skolem4(_u17, _u23)), _u17) )).
% 16.44/16.61 cnf(d4_relat_1-4, axiom, ( ~relation(_u17) | ( _u23 = relation_dom(_u17)) | in(skolem2(_u17, _u23), _u23) | ~in(skolem3(_u17, _u23), _u23) )).
% 16.44/16.62 cnf(d4_relat_1-5, axiom, ( ~relation(_u17) | ( _u23 = relation_dom(_u17)) | ~in(ordered_pair(skolem2(_u17, _u23), _u13), _u17) | in(ordered_pair(skolem3(_u17, _u23), skolem4(_u17, _u23)), _u17) )).
% 16.44/16.62 cnf(d4_relat_1-6, axiom, ( ~relation(_u17) | ( _u23 = relation_dom(_u17)) | ~in(ordered_pair(skolem2(_u17, _u23), _u13), _u17) | ~in(skolem3(_u17, _u23), _u23) )).
% 16.44/16.62
% 16.44/16.62 % Formula: d5_tarski ( axiom ) converted to clauses:
% 16.44/16.62 cnf(d5_tarski-1, axiom, ( ( ordered_pair(_u25, _u24) = unordered_pair(unordered_pair(_u25, _u24), singleton(_u25))) )).
% 16.44/16.62
% 16.44/16.62 % Formula: d7_ordinal1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(d7_ordinal1-1, axiom, ( ~relation(_u26) | ~function(_u26) | ~transfinite_sequence(_u26) | ordinal(relation_dom(_u26)) )).
% 16.44/16.62 cnf(d7_ordinal1-2, axiom, ( ~relation(_u26) | ~function(_u26) | ~ordinal(relation_dom(_u26)) | transfinite_sequence(_u26) )).
% 16.44/16.62
% 16.44/16.62 % Formula: d8_ordinal1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(d8_ordinal1-1, axiom, ( ~relation(_u27) | ~function(_u27) | ~transfinite_sequence(_u27) | ~transfinite_sequence_of(_u27, _u28) | subset(relation_rng(_u27), _u28) )).
% 16.44/16.62 cnf(d8_ordinal1-2, axiom, ( ~relation(_u27) | ~function(_u27) | ~transfinite_sequence(_u27) | ~subset(relation_rng(_u27), _u28) | transfinite_sequence_of(_u27, _u28) )).
% 16.44/16.62
% 16.44/16.62 % Formula: dt_m1_ordinal1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(dt_m1_ordinal1-1, axiom, ( ~transfinite_sequence_of(_u29, _u30) | relation(_u29) )).
% 16.44/16.62 cnf(dt_m1_ordinal1-2, axiom, ( ~transfinite_sequence_of(_u29, _u30) | function(_u29) )).
% 16.44/16.62 cnf(dt_m1_ordinal1-3, axiom, ( ~transfinite_sequence_of(_u29, _u30) | transfinite_sequence(_u29) )).
% 16.44/16.62
% 16.44/16.62 % Formula: existence_m1_ordinal1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(existence_m1_ordinal1-1, axiom, ( transfinite_sequence_of(skolem5(_u32), _u32) )).
% 16.44/16.62
% 16.44/16.62 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(existence_m1_subset_1-1, axiom, ( element(skolem6(_u34), _u34) )).
% 16.44/16.62
% 16.44/16.62 % Formula: fc12_relat_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(fc12_relat_1-1, axiom, ( empty(empty_set) )).
% 16.44/16.62 cnf(fc12_relat_1-2, axiom, ( relation(empty_set) )).
% 16.44/16.62 cnf(fc12_relat_1-3, axiom, ( relation_empty_yielding(empty_set) )).
% 16.44/16.62
% 16.44/16.62 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 16.44/16.62
% 16.44/16.62 % Formula: fc1_zfmisc_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(fc1_zfmisc_1-1, axiom, ( ~empty(ordered_pair(_u36, _u35)) )).
% 16.44/16.62
% 16.44/16.62 % Formula: fc2_ordinal1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(fc2_ordinal1-1, axiom, ( relation(empty_set) )).
% 16.44/16.62 cnf(fc2_ordinal1-2, axiom, ( relation_empty_yielding(empty_set) )).
% 16.44/16.62 cnf(fc2_ordinal1-3, axiom, ( function(empty_set) )).
% 16.44/16.62 cnf(fc2_ordinal1-4, axiom, ( one_to_one(empty_set) )).
% 16.44/16.62 cnf(fc2_ordinal1-5, axiom, ( empty(empty_set) )).
% 16.44/16.62 cnf(fc2_ordinal1-6, axiom, ( epsilon_transitive(empty_set) )).
% 16.44/16.62 cnf(fc2_ordinal1-7, axiom, ( epsilon_connected(empty_set) )).
% 16.44/16.62 cnf(fc2_ordinal1-8, axiom, ( ordinal(empty_set) )).
% 16.44/16.62
% 16.44/16.62 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 16.44/16.62 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 16.44/16.62
% 16.44/16.62 % Formula: fc5_relat_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(fc5_relat_1-1, axiom, ( empty(_u37) | ~relation(_u37) | ~empty(relation_dom(_u37)) )).
% 16.44/16.62
% 16.44/16.62 % Formula: fc6_funct_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(fc6_funct_1-1, axiom, ( ~relation(_u38) | ~relation_non_empty(_u38) | ~function(_u38) | with_non_empty_elements(relation_rng(_u38)) )).
% 16.44/16.62
% 16.44/16.62 % Formula: fc6_relat_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(fc6_relat_1-1, axiom, ( empty(_u39) | ~relation(_u39) | ~empty(relation_rng(_u39)) )).
% 16.44/16.62
% 16.44/16.62 % Formula: fc7_relat_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(fc7_relat_1-1, axiom, ( ~empty(_u40) | empty(relation_dom(_u40)) )).
% 16.44/16.62 cnf(fc7_relat_1-2, axiom, ( ~empty(_u40) | relation(relation_dom(_u40)) )).
% 16.44/16.62
% 16.44/16.62 % Formula: fc8_relat_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(fc8_relat_1-1, axiom, ( ~empty(_u41) | empty(relation_rng(_u41)) )).
% 16.44/16.62 cnf(fc8_relat_1-2, axiom, ( ~empty(_u41) | relation(relation_rng(_u41)) )).
% 16.44/16.62
% 16.44/16.62 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(rc1_funct_1-1, axiom, ( relation(skolem7) )).
% 16.44/16.62 cnf(rc1_funct_1-2, axiom, ( function(skolem7) )).
% 16.44/16.62
% 16.44/16.62 % Formula: rc1_ordinal1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(rc1_ordinal1-1, axiom, ( epsilon_transitive(skolem8) )).
% 16.44/16.62 cnf(rc1_ordinal1-2, axiom, ( epsilon_connected(skolem8) )).
% 16.44/16.62 cnf(rc1_ordinal1-3, axiom, ( ordinal(skolem8) )).
% 16.44/16.62
% 16.44/16.62 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(rc1_relat_1-1, axiom, ( empty(skolem9) )).
% 16.44/16.62 cnf(rc1_relat_1-2, axiom, ( relation(skolem9) )).
% 16.44/16.62
% 16.44/16.62 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(rc1_xboole_0-1, axiom, ( empty(skolem10) )).
% 16.44/16.62
% 16.44/16.62 % Formula: rc2_funct_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(rc2_funct_1-1, axiom, ( relation(skolem11) )).
% 16.44/16.62 cnf(rc2_funct_1-2, axiom, ( empty(skolem11) )).
% 16.44/16.62 cnf(rc2_funct_1-3, axiom, ( function(skolem11) )).
% 16.44/16.62
% 16.44/16.62 % Formula: rc2_ordinal1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(rc2_ordinal1-1, axiom, ( relation(skolem12) )).
% 16.44/16.62 cnf(rc2_ordinal1-2, axiom, ( function(skolem12) )).
% 16.44/16.62 cnf(rc2_ordinal1-3, axiom, ( one_to_one(skolem12) )).
% 16.44/16.62 cnf(rc2_ordinal1-4, axiom, ( empty(skolem12) )).
% 16.44/16.62 cnf(rc2_ordinal1-5, axiom, ( epsilon_transitive(skolem12) )).
% 16.44/16.62 cnf(rc2_ordinal1-6, axiom, ( epsilon_connected(skolem12) )).
% 16.44/16.62 cnf(rc2_ordinal1-7, axiom, ( ordinal(skolem12) )).
% 16.44/16.62
% 16.44/16.62 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem13) )).
% 16.44/16.62 cnf(rc2_relat_1-2, axiom, ( relation(skolem13) )).
% 16.44/16.62
% 16.44/16.62 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem14) )).
% 16.44/16.62
% 16.44/16.62 % Formula: rc3_funct_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(rc3_funct_1-1, axiom, ( relation(skolem15) )).
% 16.44/16.62 cnf(rc3_funct_1-2, axiom, ( function(skolem15) )).
% 16.44/16.62 cnf(rc3_funct_1-3, axiom, ( one_to_one(skolem15) )).
% 16.44/16.62
% 16.44/16.62 % Formula: rc3_ordinal1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(rc3_ordinal1-1, axiom, ( ~empty(skolem16) )).
% 16.44/16.62 cnf(rc3_ordinal1-2, axiom, ( epsilon_transitive(skolem16) )).
% 16.44/16.62 cnf(rc3_ordinal1-3, axiom, ( epsilon_connected(skolem16) )).
% 16.44/16.62 cnf(rc3_ordinal1-4, axiom, ( ordinal(skolem16) )).
% 16.44/16.62
% 16.44/16.62 % Formula: rc3_relat_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(rc3_relat_1-1, axiom, ( relation(skolem17) )).
% 16.44/16.62 cnf(rc3_relat_1-2, axiom, ( relation_empty_yielding(skolem17) )).
% 16.44/16.62
% 16.44/16.62 % Formula: rc4_funct_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(rc4_funct_1-1, axiom, ( relation(skolem18) )).
% 16.44/16.62 cnf(rc4_funct_1-2, axiom, ( relation_empty_yielding(skolem18) )).
% 16.44/16.62 cnf(rc4_funct_1-3, axiom, ( function(skolem18) )).
% 16.44/16.62
% 16.44/16.62 % Formula: rc4_ordinal1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(rc4_ordinal1-1, axiom, ( relation(skolem19) )).
% 16.44/16.62 cnf(rc4_ordinal1-2, axiom, ( function(skolem19) )).
% 16.44/16.62 cnf(rc4_ordinal1-3, axiom, ( transfinite_sequence(skolem19) )).
% 16.44/16.62
% 16.44/16.62 % Formula: rc5_funct_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(rc5_funct_1-1, axiom, ( relation(skolem20) )).
% 16.44/16.62 cnf(rc5_funct_1-2, axiom, ( relation_non_empty(skolem20) )).
% 16.44/16.62 cnf(rc5_funct_1-3, axiom, ( function(skolem20) )).
% 16.44/16.62
% 16.44/16.62 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 16.44/16.62 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u57, _u57) )).
% 16.44/16.62
% 16.44/16.62 % Formula: t1_subset ( axiom ) converted to clauses:
% 16.44/16.62 cnf(t1_subset-1, axiom, ( ~in(_u59, _u58) | element(_u59, _u58) )).
% 16.44/16.62
% 16.44/16.62 % Formula: t2_subset ( axiom ) converted to clauses:
% 16.44/16.62 cnf(t2_subset-1, axiom, ( ~element(_u61, _u60) | empty(_u60) | in(_u61, _u60) )).
% 16.44/16.62
% 16.44/16.62 % Formula: t2_xboole_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(t2_xboole_1-1, axiom, ( subset(empty_set, _u62) )).
% 16.44/16.62
% 16.44/16.62 % Formula: t3_subset ( axiom ) converted to clauses:
% 16.44/16.62 cnf(t3_subset-1, axiom, ( ~element(_u67, powerset(_u65)) | subset(_u67, _u65) )).
% 16.44/16.62 cnf(t3_subset-2, axiom, ( ~subset(_u68, _u66) | element(_u68, powerset(_u66)) )).
% 16.44/16.62
% 16.44/16.62 % Formula: t45_ordinal1 ( conjecture ) (definitionally) converted to clauses:
% 16.44/16.62 cnf(t45_ordinal1-1, negated_conjecture, ( ~transfinite_sequence_of(empty_set, skolem21) )).
% 16.44/16.62
% 16.44/16.62 % Formula: t4_subset ( axiom ) converted to clauses:
% 16.44/16.62 cnf(t4_subset-1, axiom, ( ~in(_u72, _u71) | ~element(_u71, powerset(_u70)) | element(_u72, _u70) )).
% 16.44/16.62
% 16.44/16.62 % Formula: t5_subset ( axiom ) converted to clauses:
% 16.44/16.62 cnf(t5_subset-1, axiom, ( ~in(_u75, _u74) | ~element(_u74, powerset(_u73)) | ~empty(_u73) )).
% 16.44/16.62
% 16.44/16.62 % Formula: t65_relat_1 ( axiom ) converted to clauses:
% 16.44/16.62 cnf(t65_relat_1-1, axiom, ( ~relation(_u76) | ( relation_dom(_u76) != empty_set) | ( relation_rng(_u76) = empty_set) )).
% 16.44/16.62 cnf(t65_relat_1-2, axiom, ( ~relation(_u76) | ( relation_rng(_u76) != empty_set) | ( relation_dom(_u76) = empty_set) )).
% 16.44/16.62
% 16.44/16.62 % Formula: t6_boole ( axiom ) converted to clauses:
% 16.44/16.62 cnf(t6_boole-1, axiom, ( ~empty(_u77) | ( _u77 = empty_set) )).
% 16.44/16.62
% 16.44/16.62 % Formula: t7_boole ( axiom ) converted to clauses:
% 16.44/16.62 cnf(t7_boole-1, axiom, ( ~in(_u79, _u78) | ~empty(_u78) )).
% 16.44/16.62
% 16.44/16.62 % Formula: t8_boole ( axiom ) converted to clauses:
% 16.44/16.62 cnf(t8_boole-1, axiom, ( ~empty(_u81) | ( _u81 = _u80) | ~empty(_u80) )).
% 16.44/16.62
% 16.44/16.62 % Problem matrix:
% 16.44/16.62 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 16.44/16.62 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 16.44/16.62 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 16.44/16.62 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 16.44/16.62 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( relation_dom(__eqx_0) = relation_dom(__eqy_0)) )).
% 16.44/16.62 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 16.44/16.62 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 16.44/16.62 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( relation_rng(__eqx_0) = relation_rng(__eqy_0)) )).
% 16.44/16.62 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 16.44/16.62 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem1(__eqx_0, __eqx_1, __eqx_2) = skolem1(__eqy_0, __eqy_1, __eqy_2)) )).
% 16.44/16.62 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 16.44/16.62 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 16.44/16.62 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 16.44/16.62 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( skolem5(__eqx_0) = skolem5(__eqy_0)) )).
% 16.44/16.62 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( skolem6(__eqx_0) = skolem6(__eqy_0)) )).
% 16.44/16.62 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 16.44/16.62 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 16.44/16.62 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 16.44/16.62 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~ordinal(__eqx_0) | ordinal(__eqy_0) )).
% 16.44/16.62 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~epsilon_transitive(__eqx_0) | epsilon_transitive(__eqy_0) )).
% 16.44/16.62 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ~epsilon_connected(__eqx_0) | epsilon_connected(__eqy_0) )).
% 16.44/16.62 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 16.44/16.62 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 16.44/16.62 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ~transfinite_sequence(__eqx_0) | transfinite_sequence(__eqy_0) )).
% 16.44/16.62 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~transfinite_sequence_of(__eqx_0, __eqx_1) | transfinite_sequence_of(__eqy_0, __eqy_1) )).
% 16.44/16.62 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 16.44/16.62 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 16.44/16.62 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ~relation_empty_yielding(__eqx_0) | relation_empty_yielding(__eqy_0) )).
% 16.44/16.62 cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ~relation_non_empty(__eqx_0) | relation_non_empty(__eqy_0) )).
% 16.44/16.62 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ~with_non_empty_elements(__eqx_0) | with_non_empty_elements(__eqy_0) )).
% 16.44/16.62 cnf(matrix-30, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 16.44/16.62 cnf(matrix-31, plain, ( ~empty(_u2) | function(_u2) )).
% 16.44/16.62 cnf(matrix-32, plain, ( ~ordinal(_u3) | epsilon_transitive(_u3) )).
% 16.44/16.62 cnf(matrix-33, plain, ( ~ordinal(_u3) | epsilon_connected(_u3) )).
% 16.44/16.62 cnf(matrix-34, plain, ( ~empty(_u4) | relation(_u4) )).
% 16.44/16.62 cnf(matrix-35, plain, ( ~relation(_u5) | ~empty(_u5) | ~function(_u5) | one_to_one(_u5) )).
% 16.44/16.62 cnf(matrix-36, plain, ( ~epsilon_transitive(_u6) | ~epsilon_connected(_u6) | ordinal(_u6) )).
% 16.44/16.62 cnf(matrix-37, plain, ( ~empty(_u7) | epsilon_transitive(_u7) )).
% 16.44/16.62 cnf(matrix-38, plain, ( ~empty(_u7) | epsilon_connected(_u7) )).
% 16.44/16.62 cnf(matrix-39, plain, ( ~empty(_u7) | ordinal(_u7) )).
% 16.44/16.62 cnf(matrix-40, plain, ( ( unordered_pair(_u9, _u8) = unordered_pair(_u8, _u9)) )).
% 16.44/16.62 cnf(matrix-41, plain, ( ~relation(_u17) | ( _u22 != relation_dom(_u17)) | ~in(_u18, _u22) | in(ordered_pair(_u18, skolem1(_u17, _u22, _u18)), _u17) )).
% 16.44/16.62 cnf(matrix-42, plain, ( ~relation(_u17) | ( _u22 != relation_dom(_u17)) | ~in(ordered_pair(_u19, _u11), _u17) | in(_u19, _u22) )).
% 16.44/16.62 cnf(matrix-43, plain, ( ~relation(_u17) | ( _u23 = relation_dom(_u17)) | in(skolem2(_u17, _u23), _u23) | in(ordered_pair(skolem3(_u17, _u23), skolem4(_u17, _u23)), _u17) )).
% 16.44/16.62 cnf(matrix-44, plain, ( ~relation(_u17) | ( _u23 = relation_dom(_u17)) | in(skolem2(_u17, _u23), _u23) | ~in(skolem3(_u17, _u23), _u23) )).
% 16.44/16.62 cnf(matrix-45, plain, ( ~relation(_u17) | ( _u23 = relation_dom(_u17)) | ~in(ordered_pair(skolem2(_u17, _u23), _u13), _u17) | in(ordered_pair(skolem3(_u17, _u23), skolem4(_u17, _u23)), _u17) )).
% 16.44/16.62 cnf(matrix-46, plain, ( ~relation(_u17) | ( _u23 = relation_dom(_u17)) | ~in(ordered_pair(skolem2(_u17, _u23), _u13), _u17) | ~in(skolem3(_u17, _u23), _u23) )).
% 16.44/16.62 cnf(matrix-47, plain, ( ( ordered_pair(_u25, _u24) = unordered_pair(unordered_pair(_u25, _u24), singleton(_u25))) )).
% 16.44/16.62 cnf(matrix-48, plain, ( ~relation(_u26) | ~function(_u26) | ~transfinite_sequence(_u26) | ordinal(relation_dom(_u26)) )).
% 16.44/16.62 cnf(matrix-49, plain, ( ~relation(_u26) | ~function(_u26) | ~ordinal(relation_dom(_u26)) | transfinite_sequence(_u26) )).
% 16.44/16.62 cnf(matrix-50, plain, ( ~relation(_u27) | ~function(_u27) | ~transfinite_sequence(_u27) | ~transfinite_sequence_of(_u27, _u28) | subset(relation_rng(_u27), _u28) )).
% 16.44/16.62 cnf(matrix-51, plain, ( ~relation(_u27) | ~function(_u27) | ~transfinite_sequence(_u27) | ~subset(relation_rng(_u27), _u28) | transfinite_sequence_of(_u27, _u28) )).
% 16.44/16.62 cnf(matrix-52, plain, ( ~transfinite_sequence_of(_u29, _u30) | relation(_u29) )).
% 16.44/16.62 cnf(matrix-53, plain, ( ~transfinite_sequence_of(_u29, _u30) | function(_u29) )).
% 16.44/16.62 cnf(matrix-54, plain, ( ~transfinite_sequence_of(_u29, _u30) | transfinite_sequence(_u29) )).
% 16.44/16.62 cnf(matrix-55, plain, ( transfinite_sequence_of(skolem5(_u32), _u32) )).
% 16.44/16.62 cnf(matrix-56, plain, ( element(skolem6(_u34), _u34) )).
% 16.44/16.62 cnf(matrix-57, plain, ( empty(empty_set) )).
% 16.44/16.62 cnf(matrix-58, plain, ( relation(empty_set) )).
% 16.44/16.62 cnf(matrix-59, plain, ( relation_empty_yielding(empty_set) )).
% 16.44/16.62 cnf(matrix-60, plain, ( empty(empty_set) )).
% 16.44/16.62 cnf(matrix-61, plain, ( ~empty(ordered_pair(_u36, _u35)) )).
% 16.44/16.62 cnf(matrix-62, plain, ( relation(empty_set) )).
% 16.44/16.62 cnf(matrix-63, plain, ( relation_empty_yielding(empty_set) )).
% 16.44/16.62 cnf(matrix-64, plain, ( function(empty_set) )).
% 16.44/16.62 cnf(matrix-65, plain, ( one_to_one(empty_set) )).
% 16.44/16.62 cnf(matrix-66, plain, ( empty(empty_set) )).
% 16.44/16.62 cnf(matrix-67, plain, ( epsilon_transitive(empty_set) )).
% 16.44/16.62 cnf(matrix-68, plain, ( epsilon_connected(empty_set) )).
% 16.44/16.62 cnf(matrix-69, plain, ( ordinal(empty_set) )).
% 16.44/16.62 cnf(matrix-70, plain, ( empty(empty_set) )).
% 16.44/16.62 cnf(matrix-71, plain, ( relation(empty_set) )).
% 16.44/16.62 cnf(matrix-72, plain, ( empty(_u37) | ~relation(_u37) | ~empty(relation_dom(_u37)) )).
% 16.44/16.62 cnf(matrix-73, plain, ( ~relation(_u38) | ~relation_non_empty(_u38) | ~function(_u38) | with_non_empty_elements(relation_rng(_u38)) )).
% 16.44/16.62 cnf(matrix-74, plain, ( empty(_u39) | ~relation(_u39) | ~empty(relation_rng(_u39)) )).
% 16.44/16.62 cnf(matrix-75, plain, ( ~empty(_u40) | empty(relation_dom(_u40)) )).
% 16.44/16.62 cnf(matrix-76, plain, ( ~empty(_u40) | relation(relation_dom(_u40)) )).
% 16.44/16.62 cnf(matrix-77, plain, ( ~empty(_u41) | empty(relation_rng(_u41)) )).
% 16.44/16.62 cnf(matrix-78, plain, ( ~empty(_u41) | relation(relation_rng(_u41)) )).
% 16.44/16.62 cnf(matrix-79, plain, ( relation(skolem7) )).
% 16.44/16.62 cnf(matrix-80, plain, ( function(skolem7) )).
% 16.44/16.62 cnf(matrix-81, plain, ( epsilon_transitive(skolem8) )).
% 16.44/16.62 cnf(matrix-82, plain, ( epsilon_connected(skolem8) )).
% 16.44/16.62 cnf(matrix-83, plain, ( ordinal(skolem8) )).
% 16.44/16.62 cnf(matrix-84, plain, ( empty(skolem9) )).
% 16.44/16.62 cnf(matrix-85, plain, ( relation(skolem9) )).
% 16.44/16.62 cnf(matrix-86, plain, ( empty(skolem10) )).
% 16.44/16.62 cnf(matrix-87, plain, ( relation(skolem11) )).
% 16.44/16.62 cnf(matrix-88, plain, ( empty(skolem11) )).
% 16.44/16.62 cnf(matrix-89, plain, ( function(skolem11) )).
% 16.44/16.62 cnf(matrix-90, plain, ( relation(skolem12) )).
% 16.44/16.62 cnf(matrix-91, plain, ( function(skolem12) )).
% 16.44/16.62 cnf(matrix-92, plain, ( one_to_one(skolem12) )).
% 16.44/16.62 cnf(matrix-93, plain, ( empty(skolem12) )).
% 16.44/16.62 cnf(matrix-94, plain, ( epsilon_transitive(skolem12) )).
% 16.44/16.62 cnf(matrix-95, plain, ( epsilon_connected(skolem12) )).
% 16.44/16.62 cnf(matrix-96, plain, ( ordinal(skolem12) )).
% 16.44/16.62 cnf(matrix-97, plain, ( ~empty(skolem13) )).
% 16.44/16.62 cnf(matrix-98, plain, ( relation(skolem13) )).
% 16.44/16.62 cnf(matrix-99, plain, ( ~empty(skolem14) )).
% 16.44/16.62 cnf(matrix-100, plain, ( relation(skolem15) )).
% 16.44/16.62 cnf(matrix-101, plain, ( function(skolem15) )).
% 16.44/16.62 cnf(matrix-102, plain, ( one_to_one(skolem15) )).
% 16.44/16.62 cnf(matrix-103, plain, ( ~empty(skolem16) )).
% 16.44/16.62 cnf(matrix-104, plain, ( epsilon_transitive(skolem16) )).
% 16.44/16.62 cnf(matrix-105, plain, ( epsilon_connected(skolem16) )).
% 16.44/16.62 cnf(matrix-106, plain, ( ordinal(skolem16) )).
% 16.44/16.62 cnf(matrix-107, plain, ( relation(skolem17) )).
% 16.44/16.62 cnf(matrix-108, plain, ( relation_empty_yielding(skolem17) )).
% 16.44/16.62 cnf(matrix-109, plain, ( relation(skolem18) )).
% 16.44/16.62 cnf(matrix-110, plain, ( relation_empty_yielding(skolem18) )).
% 16.44/16.62 cnf(matrix-111, plain, ( function(skolem18) )).
% 16.44/16.62 cnf(matrix-112, plain, ( relation(skolem19) )).
% 16.44/16.62 cnf(matrix-113, plain, ( function(skolem19) )).
% 16.44/16.62 cnf(matrix-114, plain, ( transfinite_sequence(skolem19) )).
% 16.44/16.62 cnf(matrix-115, plain, ( relation(skolem20) )).
% 16.44/16.62 cnf(matrix-116, plain, ( relation_non_empty(skolem20) )).
% 16.44/16.62 cnf(matrix-117, plain, ( function(skolem20) )).
% 16.44/16.62 cnf(matrix-118, plain, ( subset(_u57, _u57) )).
% 16.44/16.62 cnf(matrix-119, plain, ( ~in(_u59, _u58) | element(_u59, _u58) )).
% 16.44/16.62 cnf(matrix-120, plain, ( ~element(_u61, _u60) | empty(_u60) | in(_u61, _u60) )).
% 16.44/16.62 cnf(matrix-121, plain, ( subset(empty_set, _u62) )).
% 16.44/16.62 cnf(matrix-122, plain, ( ~element(_u67, powerset(_u65)) | subset(_u67, _u65) )).
% 16.44/16.62 cnf(matrix-123, plain, ( ~subset(_u68, _u66) | element(_u68, powerset(_u66)) )).
% 16.44/16.62 cnf(matrix-124, plain, ( ~transfinite_sequence_of(empty_set, skolem21) )).
% 16.44/16.62 cnf(matrix-125, plain, ( ~in(_u72, _u71) | ~element(_u71, powerset(_u70)) | element(_u72, _u70) )).
% 16.44/16.62 cnf(matrix-126, plain, ( ~in(_u75, _u74) | ~element(_u74, powerset(_u73)) | ~empty(_u73) )).
% 16.44/16.62 cnf(matrix-127, plain, ( ~relation(_u76) | ( relation_dom(_u76) != empty_set) | ( relation_rng(_u76) = empty_set) )).
% 16.44/16.62 cnf(matrix-128, plain, ( ~relation(_u76) | ( relation_rng(_u76) != empty_set) | ( relation_dom(_u76) = empty_set) )).
% 16.44/16.62 cnf(matrix-129, plain, ( ~empty(_u77) | ( _u77 = empty_set) )).
% 16.44/16.62 cnf(matrix-130, plain, ( ~in(_u79, _u78) | ~empty(_u78) )).
% 16.44/16.62 cnf(matrix-131, plain, ( ~empty(_u81) | ( _u81 = _u80) | ~empty(_u80) )).
% 16.44/16.62
% 16.44/16.62 % Proof stack:
% 16.44/16.62 cnf(proof-stack, plain,
% 16.44/16.62 proof_stack(
% 16.44/16.62 start(124),
% 16.44/16.62 left_branch(0, 51, 4, 2),
% 16.44/16.62 left_branch(0, 71, 0, 3),
% 16.44/16.62 right_branch(3),
% 16.44/16.62 left_branch(0, 122, 1, 4),
% 16.44/16.62 left_branch(0, 26, 3, 5),
% 16.44/16.62 left_branch(0, 131, 1, 6),
% 16.44/16.62 left_branch(0, 120, 1, 7),
% 16.44/16.62 left_branch(0, 125, 2, 8),
% 16.44/16.62 left_branch(0, 120, 2, 9),
% 16.44/16.62 left_branch(0, 56, 0, 10),
% 16.44/16.62 right_branch(10),
% 16.44/16.62 reduction(0, 4),
% 16.44/16.62 right_branch(9),
% 16.44/16.62 left_branch(0, 123, 1, 10),
% 16.44/16.62 left_branch(0, 121, 0, 11),
% 16.44/16.62 right_branch(11),
% 16.44/16.62 right_branch(10),
% 16.44/16.62 right_branch(8),
% 16.44/16.62 left_branch(0, 126, 0, 9),
% 16.44/16.62 left_branch(0, 93, 0, 10),
% 16.44/16.62 right_branch(10),
% 16.44/16.62 left_branch(0, 123, 1, 11),
% 16.44/16.62 left_branch(0, 121, 0, 12),
% 16.44/16.62 right_branch(12),
% 16.44/16.62 right_branch(11),
% 16.44/16.62 right_branch(9),
% 16.44/16.62 right_branch(7),
% 16.44/16.62 left_branch(0, 77, 1, 8),
% 16.44/16.62 lemmata(0, 1),
% 16.44/16.62 right_branch(8),
% 16.44/16.62 right_branch(6),
% 16.44/16.62 left_branch(0, 123, 1, 7),
% 16.44/16.62 left_branch(0, 121, 0, 8),
% 16.44/16.62 right_branch(8),
% 16.44/16.62 right_branch(7),
% 16.44/16.62 left_branch(0, 8, 1, 8),
% 16.44/16.62 left_branch(0, 1, 1, 9),
% 16.44/16.62 left_branch(0, 0, 0, 10),
% 16.44/16.62 right_branch(10),
% 16.44/16.62 right_branch(9),
% 16.44/16.62 right_branch(8),
% 16.44/16.62 right_branch(5),
% 16.44/16.62 right_branch(4),
% 16.44/16.62 left_branch(0, 49, 3, 5),
% 16.44/16.62 lemmata(0, 0),
% 16.44/16.62 left_branch(0, 39, 1, 7),
% 16.44/16.62 left_branch(0, 75, 1, 8),
% 16.44/16.62 left_branch(0, 120, 1, 9),
% 16.44/16.62 left_branch(0, 125, 2, 10),
% 16.44/16.62 left_branch(0, 120, 2, 11),
% 16.44/16.62 left_branch(0, 56, 0, 12),
% 16.44/16.62 right_branch(12),
% 16.44/16.62 reduction(0, 4),
% 16.44/16.62 right_branch(11),
% 16.44/16.62 left_branch(0, 123, 1, 12),
% 16.44/16.62 left_branch(0, 121, 0, 13),
% 16.44/16.62 right_branch(13),
% 16.44/16.62 right_branch(12),
% 16.44/16.62 right_branch(10),
% 16.44/16.62 left_branch(0, 126, 0, 11),
% 16.44/16.62 left_branch(0, 93, 0, 12),
% 16.44/16.62 right_branch(12),
% 16.44/16.62 left_branch(0, 123, 1, 13),
% 16.44/16.62 left_branch(0, 121, 0, 14),
% 16.44/16.62 right_branch(14),
% 16.44/16.62 right_branch(13),
% 16.44/16.62 right_branch(11),
% 16.44/16.62 right_branch(9),
% 16.44/16.62 right_branch(8),
% 16.44/16.62 right_branch(7),
% 16.44/16.62 left_branch(0, 64, 0, 8),
% 16.44/16.62 right_branch(8),
% 16.44/16.62 right_branch(5),
% 16.44/16.62 left_branch(0, 64, 0, 6),
% 16.44/16.62 right_branch(6),
% 16.44/16.62 right_branch(2)
% 16.44/16.62 )).
% 16.44/16.62 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------