TSTP Solution File: SEU242+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU242+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n021.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 14:33:43 EDT 2024
% Result : Theorem 0.90s 1.06s
% Output : Proof 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU242+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n021.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 : Wed Mar 20 14:51:03 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.90/1.06 % SZS status Theorem for theBenchmark
% 0.90/1.06 % SZS output start Proof for theBenchmark
% 0.90/1.06
% 0.90/1.06 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 0.90/1.06 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.90/1.06
% 0.90/1.06 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(cc1_funct_1-1, axiom, ( ~empty(_u2) | function(_u2) )).
% 0.90/1.06
% 0.90/1.06 % Formula: cc2_funct_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(cc2_funct_1-1, axiom, ( ~relation(_u3) | ~empty(_u3) | ~function(_u3) | one_to_one(_u3) )).
% 0.90/1.06
% 0.90/1.06 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 0.90/1.06 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u5, _u4) = unordered_pair(_u4, _u5)) )).
% 0.90/1.06
% 0.90/1.06 % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u7, _u6) = set_union2(_u6, _u7)) )).
% 0.90/1.06
% 0.90/1.06 % Formula: d14_relat_2 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(d14_relat_2-1, axiom, ( ~relation(_u8) | ~connected(_u8) | is_connected_in(_u8, relation_field(_u8)) )).
% 0.90/1.06 cnf(d14_relat_2-2, axiom, ( ~relation(_u8) | ~is_connected_in(_u8, relation_field(_u8)) | connected(_u8) )).
% 0.90/1.06
% 0.90/1.06 % Formula: d5_tarski ( axiom ) converted to clauses:
% 0.90/1.06 cnf(d5_tarski-1, axiom, ( ( ordered_pair(_u10, _u9) = unordered_pair(unordered_pair(_u10, _u9), singleton(_u10))) )).
% 0.90/1.06
% 0.90/1.06 % Formula: d6_relat_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(d6_relat_1-1, axiom, ( ~relation(_u11) | ( relation_field(_u11) = set_union2(relation_dom(_u11), relation_rng(_u11))) )).
% 0.90/1.06
% 0.90/1.06 % Formula: d6_relat_2 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(d6_relat_2-1, axiom, ( ~relation(_u17) | ~is_connected_in(_u17, _u18) | ~in(_u13, _u18) | ~in(_u12, _u18) | ( _u13 = _u12) | in(ordered_pair(_u13, _u12), _u17) | in(ordered_pair(_u12, _u13), _u17) )).
% 0.90/1.06 cnf(d6_relat_2-2, axiom, ( ~relation(_u17) | is_connected_in(_u17, _u19) | in(skolem1(_u17, _u19), _u19) )).
% 0.90/1.06 cnf(d6_relat_2-3, axiom, ( ~relation(_u17) | is_connected_in(_u17, _u19) | in(skolem2(_u17, _u19), _u19) )).
% 0.90/1.06 cnf(d6_relat_2-4, axiom, ( ~relation(_u17) | is_connected_in(_u17, _u19) | ( skolem1(_u17, _u19) != skolem2(_u17, _u19)) )).
% 0.90/1.06 cnf(d6_relat_2-5, axiom, ( ~relation(_u17) | is_connected_in(_u17, _u19) | ~in(ordered_pair(skolem1(_u17, _u19), skolem2(_u17, _u19)), _u17) )).
% 0.90/1.06 cnf(d6_relat_2-6, axiom, ( ~relation(_u17) | is_connected_in(_u17, _u19) | ~in(ordered_pair(skolem2(_u17, _u19), skolem1(_u17, _u19)), _u17) )).
% 0.90/1.06
% 0.90/1.06 % Formula: dt_k1_relat_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(dt_k1_relat_1, axiom, $true).
% 0.90/1.06
% 0.90/1.06 % Formula: dt_k1_tarski ( axiom ) converted to clauses:
% 0.90/1.06 cnf(dt_k1_tarski, axiom, $true).
% 0.90/1.06
% 0.90/1.06 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(dt_k1_xboole_0, axiom, $true).
% 0.90/1.06
% 0.90/1.06 % Formula: dt_k2_relat_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(dt_k2_relat_1, axiom, $true).
% 0.90/1.06
% 0.90/1.06 % Formula: dt_k2_tarski ( axiom ) converted to clauses:
% 0.90/1.06 cnf(dt_k2_tarski, axiom, $true).
% 0.90/1.06
% 0.90/1.06 % Formula: dt_k2_xboole_0 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(dt_k2_xboole_0, axiom, $true).
% 0.90/1.06
% 0.90/1.06 % Formula: dt_k3_relat_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(dt_k3_relat_1, axiom, $true).
% 0.90/1.06
% 0.90/1.06 % Formula: dt_k4_tarski ( axiom ) converted to clauses:
% 0.90/1.06 cnf(dt_k4_tarski, axiom, $true).
% 0.90/1.06
% 0.90/1.06 % Formula: dt_m1_subset_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(dt_m1_subset_1, axiom, $true).
% 0.90/1.06
% 0.90/1.06 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(existence_m1_subset_1-1, axiom, ( element(skolem3(_u21), _u21) )).
% 0.90/1.06
% 0.90/1.06 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 0.90/1.06
% 0.90/1.06 % Formula: fc1_zfmisc_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(fc1_zfmisc_1-1, axiom, ( ~empty(ordered_pair(_u23, _u22)) )).
% 0.90/1.06
% 0.90/1.06 % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(fc2_xboole_0-1, axiom, ( empty(_u25) | ~empty(set_union2(_u25, _u24)) )).
% 0.90/1.06
% 0.90/1.06 % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(fc3_xboole_0-1, axiom, ( empty(_u27) | ~empty(set_union2(_u26, _u27)) )).
% 0.90/1.06
% 0.90/1.06 % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u29, _u29) = _u29) )).
% 0.90/1.06
% 0.90/1.06 % Formula: l4_wellord1 ( conjecture ) (definitionally) converted to clauses:
% 0.90/1.06 cnf(l4_wellord1-1, negated_conjecture, ( relation(skolem4) )).
% 0.90/1.06 cnf(l4_wellord1-2, negated_conjecture, ( ~_def0 | ~_def1(_u32, _u33) )).
% 0.90/1.06 cnf(l4_wellord1-3, negated_conjecture, ( _def0 | connected(skolem4) )).
% 0.90/1.06 cnf(l4_wellord1-4, negated_conjecture, ( _def0 | in(skolem5, relation_field(skolem4)) )).
% 0.90/1.06 cnf(l4_wellord1-5, negated_conjecture, ( _def0 | in(skolem6, relation_field(skolem4)) )).
% 0.90/1.06 cnf(l4_wellord1-6, negated_conjecture, ( _def0 | ( skolem5 != skolem6) )).
% 0.90/1.06 cnf(l4_wellord1-7, negated_conjecture, ( _def0 | ~in(ordered_pair(skolem5, skolem6), skolem4) )).
% 0.90/1.06 cnf(l4_wellord1-8, negated_conjecture, ( _def0 | ~in(ordered_pair(skolem6, skolem5), skolem4) )).
% 0.90/1.06 cnf(l4_wellord1-9, negated_conjecture, ( _def1(_u32, _u33) | ~in(_u33, relation_field(skolem4)) | ~in(_u32, relation_field(skolem4)) | ( _u33 = _u32) | in(ordered_pair(_u33, _u32), skolem4) | in(ordered_pair(_u32, _u33), skolem4) )).
% 0.90/1.06 cnf(l4_wellord1-10, negated_conjecture, ( _def1(_u32, _u33) | ~connected(skolem4) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc1_funct_1-1, axiom, ( relation(skolem7) )).
% 0.90/1.06 cnf(rc1_funct_1-2, axiom, ( function(skolem7) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc1_xboole_0-1, axiom, ( empty(skolem8) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc2_funct_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc2_funct_1-1, axiom, ( relation(skolem9) )).
% 0.90/1.06 cnf(rc2_funct_1-2, axiom, ( empty(skolem9) )).
% 0.90/1.06 cnf(rc2_funct_1-3, axiom, ( function(skolem9) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem10) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc3_funct_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc3_funct_1-1, axiom, ( relation(skolem11) )).
% 0.90/1.06 cnf(rc3_funct_1-2, axiom, ( function(skolem11) )).
% 0.90/1.06 cnf(rc3_funct_1-3, axiom, ( one_to_one(skolem11) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t1_boole ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t1_boole-1, axiom, ( ( set_union2(_u40, empty_set) = _u40) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t1_subset ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t1_subset-1, axiom, ( ~in(_u42, _u41) | element(_u42, _u41) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t2_subset ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t2_subset-1, axiom, ( ~element(_u44, _u43) | empty(_u43) | in(_u44, _u43) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t6_boole ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t6_boole-1, axiom, ( ~empty(_u45) | ( _u45 = empty_set) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t7_boole ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t7_boole-1, axiom, ( ~in(_u47, _u46) | ~empty(_u46) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t8_boole ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t8_boole-1, axiom, ( ~empty(_u49) | ( _u49 = _u48) | ~empty(_u48) )).
% 0.90/1.06
% 0.90/1.06 % Problem matrix:
% 0.90/1.06 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.90/1.06 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.90/1.06 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.90/1.06 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 0.90/1.06 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 0.90/1.06 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( relation_field(__eqx_0) = relation_field(__eqy_0)) )).
% 0.90/1.06 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 0.90/1.06 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 0.90/1.06 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( relation_dom(__eqx_0) = relation_dom(__eqy_0)) )).
% 0.90/1.06 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( relation_rng(__eqx_0) = relation_rng(__eqy_0)) )).
% 0.90/1.06 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 0.90/1.06 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 0.90/1.06 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( skolem3(__eqx_0) = skolem3(__eqy_0)) )).
% 0.90/1.06 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 0.90/1.06 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 0.90/1.06 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 0.90/1.06 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 0.90/1.06 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 0.90/1.06 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~connected(__eqx_0) | connected(__eqy_0) )).
% 0.90/1.06 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~is_connected_in(__eqx_0, __eqx_1) | is_connected_in(__eqy_0, __eqy_1) )).
% 0.90/1.06 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 0.90/1.06 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~_def1(__eqx_0, __eqx_1) | _def1(__eqy_0, __eqy_1) )).
% 0.90/1.06 cnf(matrix-22, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.90/1.06 cnf(matrix-23, plain, ( ~empty(_u2) | function(_u2) )).
% 0.90/1.06 cnf(matrix-24, plain, ( ~relation(_u3) | ~empty(_u3) | ~function(_u3) | one_to_one(_u3) )).
% 0.90/1.06 cnf(matrix-25, plain, ( ( unordered_pair(_u5, _u4) = unordered_pair(_u4, _u5)) )).
% 0.90/1.06 cnf(matrix-26, plain, ( ( set_union2(_u7, _u6) = set_union2(_u6, _u7)) )).
% 0.90/1.06 cnf(matrix-27, plain, ( ~relation(_u8) | ~connected(_u8) | is_connected_in(_u8, relation_field(_u8)) )).
% 0.90/1.06 cnf(matrix-28, plain, ( ~relation(_u8) | ~is_connected_in(_u8, relation_field(_u8)) | connected(_u8) )).
% 0.90/1.06 cnf(matrix-29, plain, ( ( ordered_pair(_u10, _u9) = unordered_pair(unordered_pair(_u10, _u9), singleton(_u10))) )).
% 0.90/1.06 cnf(matrix-30, plain, ( ~relation(_u11) | ( relation_field(_u11) = set_union2(relation_dom(_u11), relation_rng(_u11))) )).
% 0.90/1.06 cnf(matrix-31, plain, ( ~relation(_u17) | ~is_connected_in(_u17, _u18) | ~in(_u13, _u18) | ~in(_u12, _u18) | ( _u13 = _u12) | in(ordered_pair(_u13, _u12), _u17) | in(ordered_pair(_u12, _u13), _u17) )).
% 0.90/1.06 cnf(matrix-32, plain, ( ~relation(_u17) | is_connected_in(_u17, _u19) | in(skolem1(_u17, _u19), _u19) )).
% 0.90/1.06 cnf(matrix-33, plain, ( ~relation(_u17) | is_connected_in(_u17, _u19) | in(skolem2(_u17, _u19), _u19) )).
% 0.90/1.06 cnf(matrix-34, plain, ( ~relation(_u17) | is_connected_in(_u17, _u19) | ( skolem1(_u17, _u19) != skolem2(_u17, _u19)) )).
% 0.90/1.06 cnf(matrix-35, plain, ( ~relation(_u17) | is_connected_in(_u17, _u19) | ~in(ordered_pair(skolem1(_u17, _u19), skolem2(_u17, _u19)), _u17) )).
% 0.90/1.06 cnf(matrix-36, plain, ( ~relation(_u17) | is_connected_in(_u17, _u19) | ~in(ordered_pair(skolem2(_u17, _u19), skolem1(_u17, _u19)), _u17) )).
% 0.90/1.06 cnf(matrix-37, plain, ( element(skolem3(_u21), _u21) )).
% 0.90/1.06 cnf(matrix-38, plain, ( empty(empty_set) )).
% 0.90/1.06 cnf(matrix-39, plain, ( ~empty(ordered_pair(_u23, _u22)) )).
% 0.90/1.06 cnf(matrix-40, plain, ( empty(_u25) | ~empty(set_union2(_u25, _u24)) )).
% 0.90/1.06 cnf(matrix-41, plain, ( empty(_u27) | ~empty(set_union2(_u26, _u27)) )).
% 0.90/1.06 cnf(matrix-42, plain, ( ( set_union2(_u29, _u29) = _u29) )).
% 0.90/1.06 cnf(matrix-43, plain, ( relation(skolem4) )).
% 0.90/1.06 cnf(matrix-44, plain, ( ~_def0 | ~_def1(_u32, _u33) )).
% 0.90/1.06 cnf(matrix-45, plain, ( _def0 | connected(skolem4) )).
% 0.90/1.06 cnf(matrix-46, plain, ( _def0 | in(skolem5, relation_field(skolem4)) )).
% 0.90/1.06 cnf(matrix-47, plain, ( _def0 | in(skolem6, relation_field(skolem4)) )).
% 0.90/1.06 cnf(matrix-48, plain, ( _def0 | ( skolem5 != skolem6) )).
% 0.90/1.06 cnf(matrix-49, plain, ( _def0 | ~in(ordered_pair(skolem5, skolem6), skolem4) )).
% 0.90/1.06 cnf(matrix-50, plain, ( _def0 | ~in(ordered_pair(skolem6, skolem5), skolem4) )).
% 0.90/1.06 cnf(matrix-51, plain, ( _def1(_u32, _u33) | ~in(_u33, relation_field(skolem4)) | ~in(_u32, relation_field(skolem4)) | ( _u33 = _u32) | in(ordered_pair(_u33, _u32), skolem4) | in(ordered_pair(_u32, _u33), skolem4) )).
% 0.90/1.06 cnf(matrix-52, plain, ( _def1(_u32, _u33) | ~connected(skolem4) )).
% 0.90/1.06 cnf(matrix-53, plain, ( relation(skolem7) )).
% 0.90/1.06 cnf(matrix-54, plain, ( function(skolem7) )).
% 0.90/1.06 cnf(matrix-55, plain, ( empty(skolem8) )).
% 0.90/1.06 cnf(matrix-56, plain, ( relation(skolem9) )).
% 0.90/1.06 cnf(matrix-57, plain, ( empty(skolem9) )).
% 0.90/1.06 cnf(matrix-58, plain, ( function(skolem9) )).
% 0.90/1.06 cnf(matrix-59, plain, ( ~empty(skolem10) )).
% 0.90/1.06 cnf(matrix-60, plain, ( relation(skolem11) )).
% 0.90/1.06 cnf(matrix-61, plain, ( function(skolem11) )).
% 0.90/1.06 cnf(matrix-62, plain, ( one_to_one(skolem11) )).
% 0.90/1.06 cnf(matrix-63, plain, ( ( set_union2(_u40, empty_set) = _u40) )).
% 0.90/1.06 cnf(matrix-64, plain, ( ~in(_u42, _u41) | element(_u42, _u41) )).
% 0.90/1.06 cnf(matrix-65, plain, ( ~element(_u44, _u43) | empty(_u43) | in(_u44, _u43) )).
% 0.90/1.06 cnf(matrix-66, plain, ( ~empty(_u45) | ( _u45 = empty_set) )).
% 0.90/1.06 cnf(matrix-67, plain, ( ~in(_u47, _u46) | ~empty(_u46) )).
% 0.90/1.06 cnf(matrix-68, plain, ( ~empty(_u49) | ( _u49 = _u48) | ~empty(_u48) )).
% 0.90/1.06
% 0.90/1.06 % Proof stack:
% 0.90/1.06 cnf(proof-stack, plain,
% 0.90/1.06 proof_stack(
% 0.90/1.06 start(44),
% 0.90/1.06 left_branch(0, 50, 0, 2),
% 0.90/1.06 left_branch(0, 31, 6, 3),
% 0.90/1.06 left_branch(0, 43, 0, 4),
% 0.90/1.06 right_branch(4),
% 0.90/1.06 left_branch(0, 49, 1, 5),
% 0.90/1.06 reduction(0, 0),
% 0.90/1.06 right_branch(5),
% 0.90/1.06 left_branch(0, 48, 1, 6),
% 0.90/1.06 reduction(0, 0),
% 0.90/1.06 right_branch(6),
% 0.90/1.06 left_branch(0, 47, 1, 7),
% 0.90/1.06 reduction(0, 0),
% 0.90/1.06 right_branch(7),
% 0.90/1.06 left_branch(0, 46, 1, 8),
% 0.90/1.06 reduction(0, 0),
% 0.90/1.06 right_branch(8),
% 0.90/1.06 left_branch(0, 27, 2, 9),
% 0.90/1.06 lemmata(0, 0),
% 0.90/1.06 left_branch(0, 45, 1, 11),
% 0.90/1.06 reduction(0, 0),
% 0.90/1.06 right_branch(11),
% 0.90/1.06 right_branch(9),
% 0.90/1.06 right_branch(3),
% 0.90/1.06 right_branch(2),
% 0.90/1.06 left_branch(0, 51, 0, 3),
% 0.90/1.06 left_branch(0, 36, 2, 4),
% 0.90/1.06 left_branch(0, 43, 0, 5),
% 0.90/1.06 right_branch(5),
% 0.90/1.06 left_branch(0, 28, 1, 6),
% 0.90/1.06 lemmata(0, 1),
% 0.90/1.06 left_branch(0, 52, 1, 8),
% 0.90/1.06 reduction(0, 0),
% 0.90/1.06 right_branch(8),
% 0.90/1.06 right_branch(6),
% 0.90/1.06 right_branch(4),
% 0.90/1.06 left_branch(0, 35, 2, 5),
% 0.90/1.06 left_branch(0, 43, 0, 6),
% 0.90/1.06 right_branch(6),
% 0.90/1.06 left_branch(0, 28, 1, 7),
% 0.90/1.06 lemmata(0, 2),
% 0.90/1.06 left_branch(0, 52, 1, 9),
% 0.90/1.06 reduction(0, 0),
% 0.90/1.06 right_branch(9),
% 0.90/1.06 right_branch(7),
% 0.90/1.06 right_branch(5),
% 0.90/1.06 left_branch(0, 34, 2, 6),
% 0.90/1.06 left_branch(0, 43, 0, 7),
% 0.90/1.06 right_branch(7),
% 0.90/1.06 left_branch(0, 28, 1, 8),
% 0.90/1.06 lemmata(0, 3),
% 0.90/1.06 left_branch(0, 52, 1, 10),
% 0.90/1.06 reduction(0, 0),
% 0.90/1.06 right_branch(10),
% 0.90/1.06 right_branch(8),
% 0.90/1.06 right_branch(6),
% 0.90/1.06 left_branch(0, 33, 2, 7),
% 0.90/1.06 left_branch(0, 43, 0, 8),
% 0.90/1.06 right_branch(8),
% 0.90/1.06 left_branch(0, 28, 1, 9),
% 0.90/1.06 lemmata(0, 4),
% 0.90/1.06 left_branch(0, 52, 1, 11),
% 0.90/1.06 reduction(0, 0),
% 0.90/1.06 right_branch(11),
% 0.90/1.06 right_branch(9),
% 0.90/1.06 right_branch(7),
% 0.90/1.06 left_branch(0, 32, 2, 8),
% 0.90/1.06 left_branch(0, 43, 0, 9),
% 0.90/1.06 right_branch(9),
% 0.90/1.06 left_branch(0, 28, 1, 10),
% 0.90/1.06 lemmata(0, 5),
% 0.90/1.06 left_branch(0, 52, 1, 12),
% 0.90/1.06 reduction(0, 0),
% 0.90/1.06 right_branch(12),
% 0.90/1.06 right_branch(10),
% 0.90/1.06 right_branch(8),
% 0.90/1.06 right_branch(3)
% 0.90/1.06 )).
% 0.90/1.06 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------