TSTP Solution File: SEU240+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU240+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 : n019.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 14:33:42 EDT 2024
% Result : Theorem 9.65s 9.88s
% Output : Proof 9.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU240+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Mar 20 14:53:48 EDT 2024
% 0.12/0.34 % CPUTime :
% 9.65/9.88 % SZS status Theorem for theBenchmark
% 9.65/9.88 % SZS output start Proof for theBenchmark
% 9.65/9.88
% 9.65/9.88 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 9.65/9.88 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 9.65/9.88
% 9.65/9.88 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(cc1_funct_1-1, axiom, ( ~empty(_u2) | function(_u2) )).
% 9.65/9.88
% 9.65/9.88 % Formula: cc2_funct_1 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(cc2_funct_1-1, axiom, ( ~relation(_u3) | ~empty(_u3) | ~function(_u3) | one_to_one(_u3) )).
% 9.65/9.88
% 9.65/9.88 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 9.65/9.88 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u5, _u4) = unordered_pair(_u4, _u5)) )).
% 9.65/9.88
% 9.65/9.88 % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u7, _u6) = set_union2(_u6, _u7)) )).
% 9.65/9.88
% 9.65/9.88 % Formula: d16_relat_2 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(d16_relat_2-1, axiom, ( ~relation(_u8) | ~transitive(_u8) | is_transitive_in(_u8, relation_field(_u8)) )).
% 9.65/9.88 cnf(d16_relat_2-2, axiom, ( ~relation(_u8) | ~is_transitive_in(_u8, relation_field(_u8)) | transitive(_u8) )).
% 9.65/9.88
% 9.65/9.88 % Formula: d5_tarski ( axiom ) converted to clauses:
% 9.65/9.88 cnf(d5_tarski-1, axiom, ( ( ordered_pair(_u10, _u9) = unordered_pair(unordered_pair(_u10, _u9), singleton(_u10))) )).
% 9.65/9.88
% 9.65/9.88 % Formula: d6_relat_1 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(d6_relat_1-1, axiom, ( ~relation(_u11) | ( relation_field(_u11) = set_union2(relation_dom(_u11), relation_rng(_u11))) )).
% 9.65/9.88
% 9.65/9.88 % Formula: d8_relat_2 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(d8_relat_2-1, axiom, ( ~relation(_u19) | ~is_transitive_in(_u19, _u20) | ~in(_u14, _u20) | ~in(_u13, _u20) | ~in(_u12, _u20) | ~in(ordered_pair(_u14, _u13), _u19) | ~in(ordered_pair(_u13, _u12), _u19) | in(ordered_pair(_u14, _u12), _u19) )).
% 9.65/9.88 cnf(d8_relat_2-2, axiom, ( ~relation(_u19) | is_transitive_in(_u19, _u21) | in(skolem1(_u19, _u21), _u21) )).
% 9.65/9.88 cnf(d8_relat_2-3, axiom, ( ~relation(_u19) | is_transitive_in(_u19, _u21) | in(skolem2(_u19, _u21), _u21) )).
% 9.65/9.88 cnf(d8_relat_2-4, axiom, ( ~relation(_u19) | is_transitive_in(_u19, _u21) | in(skolem3(_u19, _u21), _u21) )).
% 9.65/9.88 cnf(d8_relat_2-5, axiom, ( ~relation(_u19) | is_transitive_in(_u19, _u21) | in(ordered_pair(skolem1(_u19, _u21), skolem2(_u19, _u21)), _u19) )).
% 9.65/9.88 cnf(d8_relat_2-6, axiom, ( ~relation(_u19) | is_transitive_in(_u19, _u21) | in(ordered_pair(skolem2(_u19, _u21), skolem3(_u19, _u21)), _u19) )).
% 9.65/9.88 cnf(d8_relat_2-7, axiom, ( ~relation(_u19) | is_transitive_in(_u19, _u21) | ~in(ordered_pair(skolem1(_u19, _u21), skolem3(_u19, _u21)), _u19) )).
% 9.65/9.88
% 9.65/9.88 % Formula: dt_k1_relat_1 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(dt_k1_relat_1, axiom, $true).
% 9.65/9.88
% 9.65/9.88 % Formula: dt_k1_tarski ( axiom ) converted to clauses:
% 9.65/9.88 cnf(dt_k1_tarski, axiom, $true).
% 9.65/9.88
% 9.65/9.88 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(dt_k1_xboole_0, axiom, $true).
% 9.65/9.88
% 9.65/9.88 % Formula: dt_k2_relat_1 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(dt_k2_relat_1, axiom, $true).
% 9.65/9.88
% 9.65/9.88 % Formula: dt_k2_tarski ( axiom ) converted to clauses:
% 9.65/9.88 cnf(dt_k2_tarski, axiom, $true).
% 9.65/9.88
% 9.65/9.88 % Formula: dt_k2_xboole_0 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(dt_k2_xboole_0, axiom, $true).
% 9.65/9.88
% 9.65/9.88 % Formula: dt_k3_relat_1 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(dt_k3_relat_1, axiom, $true).
% 9.65/9.88
% 9.65/9.88 % Formula: dt_k4_tarski ( axiom ) converted to clauses:
% 9.65/9.88 cnf(dt_k4_tarski, axiom, $true).
% 9.65/9.88
% 9.65/9.88 % Formula: dt_m1_subset_1 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(dt_m1_subset_1, axiom, $true).
% 9.65/9.88
% 9.65/9.88 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(existence_m1_subset_1-1, axiom, ( element(skolem4(_u23), _u23) )).
% 9.65/9.88
% 9.65/9.88 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 9.65/9.88
% 9.65/9.88 % Formula: fc1_zfmisc_1 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(fc1_zfmisc_1-1, axiom, ( ~empty(ordered_pair(_u25, _u24)) )).
% 9.65/9.88
% 9.65/9.88 % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(fc2_xboole_0-1, axiom, ( empty(_u27) | ~empty(set_union2(_u27, _u26)) )).
% 9.65/9.88
% 9.65/9.88 % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(fc3_xboole_0-1, axiom, ( empty(_u29) | ~empty(set_union2(_u28, _u29)) )).
% 9.65/9.88
% 9.65/9.88 % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u31, _u31) = _u31) )).
% 9.65/9.88
% 9.65/9.88 % Formula: l2_wellord1 ( conjecture ) (definitionally) converted to clauses:
% 9.65/9.88 cnf(l2_wellord1-1, negated_conjecture, ( relation(skolem5) )).
% 9.65/9.88 cnf(l2_wellord1-2, negated_conjecture, ( ~_def0 | ~_def1(_u35, _u36, _u37) )).
% 9.65/9.88 cnf(l2_wellord1-3, negated_conjecture, ( _def0 | transitive(skolem5) )).
% 9.65/9.88 cnf(l2_wellord1-4, negated_conjecture, ( _def0 | in(ordered_pair(skolem6, skolem7), skolem5) )).
% 9.65/9.88 cnf(l2_wellord1-5, negated_conjecture, ( _def0 | in(ordered_pair(skolem7, skolem8), skolem5) )).
% 9.65/9.88 cnf(l2_wellord1-6, negated_conjecture, ( _def0 | ~in(ordered_pair(skolem6, skolem8), skolem5) )).
% 9.65/9.88 cnf(l2_wellord1-7, negated_conjecture, ( _def1(_u35, _u36, _u37) | ~in(ordered_pair(_u37, _u36), skolem5) | ~in(ordered_pair(_u36, _u35), skolem5) | in(ordered_pair(_u37, _u35), skolem5) )).
% 9.65/9.88 cnf(l2_wellord1-8, negated_conjecture, ( _def1(_u35, _u36, _u37) | ~transitive(skolem5) )).
% 9.65/9.88
% 9.65/9.88 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(rc1_funct_1-1, axiom, ( relation(skolem9) )).
% 9.65/9.88 cnf(rc1_funct_1-2, axiom, ( function(skolem9) )).
% 9.65/9.88
% 9.65/9.88 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(rc1_xboole_0-1, axiom, ( empty(skolem10) )).
% 9.65/9.88
% 9.65/9.88 % Formula: rc2_funct_1 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(rc2_funct_1-1, axiom, ( relation(skolem11) )).
% 9.65/9.88 cnf(rc2_funct_1-2, axiom, ( empty(skolem11) )).
% 9.65/9.88 cnf(rc2_funct_1-3, axiom, ( function(skolem11) )).
% 9.65/9.88
% 9.65/9.88 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem12) )).
% 9.65/9.88
% 9.65/9.88 % Formula: rc3_funct_1 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(rc3_funct_1-1, axiom, ( relation(skolem13) )).
% 9.65/9.88 cnf(rc3_funct_1-2, axiom, ( function(skolem13) )).
% 9.65/9.88 cnf(rc3_funct_1-3, axiom, ( one_to_one(skolem13) )).
% 9.65/9.88
% 9.65/9.88 % Formula: t1_boole ( axiom ) converted to clauses:
% 9.65/9.88 cnf(t1_boole-1, axiom, ( ( set_union2(_u44, empty_set) = _u44) )).
% 9.65/9.88
% 9.65/9.88 % Formula: t1_subset ( axiom ) converted to clauses:
% 9.65/9.88 cnf(t1_subset-1, axiom, ( ~in(_u46, _u45) | element(_u46, _u45) )).
% 9.65/9.88
% 9.65/9.88 % Formula: t2_subset ( axiom ) converted to clauses:
% 9.65/9.88 cnf(t2_subset-1, axiom, ( ~element(_u48, _u47) | empty(_u47) | in(_u48, _u47) )).
% 9.65/9.88
% 9.65/9.88 % Formula: t30_relat_1 ( axiom ) converted to clauses:
% 9.65/9.88 cnf(t30_relat_1-1, axiom, ( ~relation(_u49) | ~in(ordered_pair(_u51, _u50), _u49) | in(_u51, relation_field(_u49)) )).
% 9.65/9.88 cnf(t30_relat_1-2, axiom, ( ~relation(_u49) | ~in(ordered_pair(_u51, _u50), _u49) | in(_u50, relation_field(_u49)) )).
% 9.65/9.88
% 9.65/9.88 % Formula: t6_boole ( axiom ) converted to clauses:
% 9.65/9.88 cnf(t6_boole-1, axiom, ( ~empty(_u52) | ( _u52 = empty_set) )).
% 9.65/9.88
% 9.65/9.88 % Formula: t7_boole ( axiom ) converted to clauses:
% 9.65/9.88 cnf(t7_boole-1, axiom, ( ~in(_u54, _u53) | ~empty(_u53) )).
% 9.65/9.88
% 9.65/9.88 % Formula: t8_boole ( axiom ) converted to clauses:
% 9.65/9.88 cnf(t8_boole-1, axiom, ( ~empty(_u56) | ( _u56 = _u55) | ~empty(_u55) )).
% 9.65/9.88
% 9.65/9.88 % Problem matrix:
% 9.65/9.88 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 9.65/9.88 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 9.65/9.88 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 9.65/9.88 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 9.65/9.88 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 9.65/9.88 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( relation_field(__eqx_0) = relation_field(__eqy_0)) )).
% 9.65/9.88 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 9.65/9.88 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 9.65/9.88 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( relation_dom(__eqx_0) = relation_dom(__eqy_0)) )).
% 9.65/9.88 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( relation_rng(__eqx_0) = relation_rng(__eqy_0)) )).
% 9.65/9.88 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 9.65/9.88 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 9.65/9.88 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 9.65/9.88 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( skolem4(__eqx_0) = skolem4(__eqy_0)) )).
% 9.65/9.88 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 9.65/9.88 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 9.65/9.88 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 9.65/9.88 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 9.65/9.88 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 9.65/9.88 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~transitive(__eqx_0) | transitive(__eqy_0) )).
% 9.65/9.88 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~is_transitive_in(__eqx_0, __eqx_1) | is_transitive_in(__eqy_0, __eqy_1) )).
% 9.65/9.88 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 9.65/9.88 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~_def1(__eqx_0, __eqx_1, __eqx_2) | _def1(__eqy_0, __eqy_1, __eqy_2) )).
% 9.65/9.88 cnf(matrix-23, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 9.65/9.88 cnf(matrix-24, plain, ( ~empty(_u2) | function(_u2) )).
% 9.65/9.88 cnf(matrix-25, plain, ( ~relation(_u3) | ~empty(_u3) | ~function(_u3) | one_to_one(_u3) )).
% 9.65/9.88 cnf(matrix-26, plain, ( ( unordered_pair(_u5, _u4) = unordered_pair(_u4, _u5)) )).
% 9.65/9.88 cnf(matrix-27, plain, ( ( set_union2(_u7, _u6) = set_union2(_u6, _u7)) )).
% 9.65/9.88 cnf(matrix-28, plain, ( ~relation(_u8) | ~transitive(_u8) | is_transitive_in(_u8, relation_field(_u8)) )).
% 9.65/9.88 cnf(matrix-29, plain, ( ~relation(_u8) | ~is_transitive_in(_u8, relation_field(_u8)) | transitive(_u8) )).
% 9.65/9.88 cnf(matrix-30, plain, ( ( ordered_pair(_u10, _u9) = unordered_pair(unordered_pair(_u10, _u9), singleton(_u10))) )).
% 9.65/9.88 cnf(matrix-31, plain, ( ~relation(_u11) | ( relation_field(_u11) = set_union2(relation_dom(_u11), relation_rng(_u11))) )).
% 9.65/9.88 cnf(matrix-32, plain, ( ~relation(_u19) | ~is_transitive_in(_u19, _u20) | ~in(_u14, _u20) | ~in(_u13, _u20) | ~in(_u12, _u20) | ~in(ordered_pair(_u14, _u13), _u19) | ~in(ordered_pair(_u13, _u12), _u19) | in(ordered_pair(_u14, _u12), _u19) )).
% 9.65/9.88 cnf(matrix-33, plain, ( ~relation(_u19) | is_transitive_in(_u19, _u21) | in(skolem1(_u19, _u21), _u21) )).
% 9.65/9.88 cnf(matrix-34, plain, ( ~relation(_u19) | is_transitive_in(_u19, _u21) | in(skolem2(_u19, _u21), _u21) )).
% 9.65/9.88 cnf(matrix-35, plain, ( ~relation(_u19) | is_transitive_in(_u19, _u21) | in(skolem3(_u19, _u21), _u21) )).
% 9.65/9.88 cnf(matrix-36, plain, ( ~relation(_u19) | is_transitive_in(_u19, _u21) | in(ordered_pair(skolem1(_u19, _u21), skolem2(_u19, _u21)), _u19) )).
% 9.65/9.88 cnf(matrix-37, plain, ( ~relation(_u19) | is_transitive_in(_u19, _u21) | in(ordered_pair(skolem2(_u19, _u21), skolem3(_u19, _u21)), _u19) )).
% 9.65/9.88 cnf(matrix-38, plain, ( ~relation(_u19) | is_transitive_in(_u19, _u21) | ~in(ordered_pair(skolem1(_u19, _u21), skolem3(_u19, _u21)), _u19) )).
% 9.65/9.88 cnf(matrix-39, plain, ( element(skolem4(_u23), _u23) )).
% 9.65/9.88 cnf(matrix-40, plain, ( empty(empty_set) )).
% 9.65/9.88 cnf(matrix-41, plain, ( ~empty(ordered_pair(_u25, _u24)) )).
% 9.65/9.88 cnf(matrix-42, plain, ( empty(_u27) | ~empty(set_union2(_u27, _u26)) )).
% 9.65/9.88 cnf(matrix-43, plain, ( empty(_u29) | ~empty(set_union2(_u28, _u29)) )).
% 9.65/9.88 cnf(matrix-44, plain, ( ( set_union2(_u31, _u31) = _u31) )).
% 9.65/9.88 cnf(matrix-45, plain, ( relation(skolem5) )).
% 9.65/9.88 cnf(matrix-46, plain, ( ~_def0 | ~_def1(_u35, _u36, _u37) )).
% 9.65/9.88 cnf(matrix-47, plain, ( _def0 | transitive(skolem5) )).
% 9.65/9.88 cnf(matrix-48, plain, ( _def0 | in(ordered_pair(skolem6, skolem7), skolem5) )).
% 9.65/9.88 cnf(matrix-49, plain, ( _def0 | in(ordered_pair(skolem7, skolem8), skolem5) )).
% 9.65/9.88 cnf(matrix-50, plain, ( _def0 | ~in(ordered_pair(skolem6, skolem8), skolem5) )).
% 9.65/9.88 cnf(matrix-51, plain, ( _def1(_u35, _u36, _u37) | ~in(ordered_pair(_u37, _u36), skolem5) | ~in(ordered_pair(_u36, _u35), skolem5) | in(ordered_pair(_u37, _u35), skolem5) )).
% 9.65/9.88 cnf(matrix-52, plain, ( _def1(_u35, _u36, _u37) | ~transitive(skolem5) )).
% 9.65/9.88 cnf(matrix-53, plain, ( relation(skolem9) )).
% 9.65/9.88 cnf(matrix-54, plain, ( function(skolem9) )).
% 9.65/9.88 cnf(matrix-55, plain, ( empty(skolem10) )).
% 9.65/9.88 cnf(matrix-56, plain, ( relation(skolem11) )).
% 9.65/9.88 cnf(matrix-57, plain, ( empty(skolem11) )).
% 9.65/9.88 cnf(matrix-58, plain, ( function(skolem11) )).
% 9.65/9.88 cnf(matrix-59, plain, ( ~empty(skolem12) )).
% 9.65/9.88 cnf(matrix-60, plain, ( relation(skolem13) )).
% 9.65/9.88 cnf(matrix-61, plain, ( function(skolem13) )).
% 9.65/9.88 cnf(matrix-62, plain, ( one_to_one(skolem13) )).
% 9.65/9.88 cnf(matrix-63, plain, ( ( set_union2(_u44, empty_set) = _u44) )).
% 9.65/9.88 cnf(matrix-64, plain, ( ~in(_u46, _u45) | element(_u46, _u45) )).
% 9.65/9.88 cnf(matrix-65, plain, ( ~element(_u48, _u47) | empty(_u47) | in(_u48, _u47) )).
% 9.65/9.88 cnf(matrix-66, plain, ( ~relation(_u49) | ~in(ordered_pair(_u51, _u50), _u49) | in(_u51, relation_field(_u49)) )).
% 9.65/9.88 cnf(matrix-67, plain, ( ~relation(_u49) | ~in(ordered_pair(_u51, _u50), _u49) | in(_u50, relation_field(_u49)) )).
% 9.65/9.88 cnf(matrix-68, plain, ( ~empty(_u52) | ( _u52 = empty_set) )).
% 9.65/9.88 cnf(matrix-69, plain, ( ~in(_u54, _u53) | ~empty(_u53) )).
% 9.65/9.88 cnf(matrix-70, plain, ( ~empty(_u56) | ( _u56 = _u55) | ~empty(_u55) )).
% 9.65/9.88
% 9.65/9.88 % Proof stack:
% 9.65/9.88 cnf(proof-stack, plain,
% 9.65/9.88 proof_stack(
% 9.65/9.88 start(46),
% 9.65/9.88 left_branch(0, 47, 0, 2),
% 9.65/9.88 left_branch(0, 28, 1, 3),
% 9.65/9.88 left_branch(0, 45, 0, 4),
% 9.65/9.88 right_branch(4),
% 9.65/9.88 left_branch(0, 32, 1, 5),
% 9.65/9.88 lemmata(0, 0),
% 9.65/9.88 left_branch(0, 49, 1, 7),
% 9.65/9.88 reduction(0, 0),
% 9.65/9.88 right_branch(7),
% 9.65/9.88 left_branch(0, 48, 1, 8),
% 9.65/9.88 reduction(0, 0),
% 9.65/9.88 right_branch(8),
% 9.65/9.88 left_branch(0, 67, 2, 9),
% 9.65/9.88 lemmata(0, 0),
% 9.65/9.88 left_branch(0, 49, 1, 11),
% 9.65/9.88 reduction(0, 0),
% 9.65/9.88 right_branch(11),
% 9.65/9.88 right_branch(9),
% 9.65/9.88 left_branch(0, 67, 2, 10),
% 9.65/9.88 lemmata(0, 0),
% 9.65/9.88 left_branch(0, 48, 1, 12),
% 9.65/9.88 reduction(0, 0),
% 9.65/9.88 right_branch(12),
% 9.65/9.88 right_branch(10),
% 9.65/9.88 left_branch(0, 66, 2, 11),
% 9.65/9.88 lemmata(0, 0),
% 9.65/9.88 left_branch(0, 48, 1, 13),
% 9.65/9.88 reduction(0, 0),
% 9.65/9.88 right_branch(13),
% 9.65/9.88 right_branch(11),
% 9.65/9.88 left_branch(0, 50, 1, 12),
% 9.65/9.88 reduction(0, 0),
% 9.65/9.88 right_branch(12),
% 9.65/9.88 right_branch(5),
% 9.65/9.88 right_branch(3),
% 9.65/9.88 right_branch(2),
% 9.65/9.88 left_branch(0, 52, 0, 3),
% 9.65/9.88 left_branch(0, 29, 2, 4),
% 9.65/9.88 left_branch(0, 45, 0, 5),
% 9.65/9.88 right_branch(5),
% 9.65/9.88 left_branch(0, 38, 1, 6),
% 9.65/9.88 lemmata(0, 1),
% 9.65/9.88 left_branch(0, 51, 3, 8),
% 9.65/9.88 reduction(0, 0),
% 9.65/9.88 left_branch(0, 37, 2, 10),
% 9.65/9.88 lemmata(0, 1),
% 9.65/9.88 reduction(0, 2),
% 9.65/9.88 right_branch(10),
% 9.65/9.88 left_branch(0, 36, 2, 11),
% 9.65/9.88 lemmata(0, 1),
% 9.65/9.88 reduction(0, 2),
% 9.65/9.88 right_branch(11),
% 9.65/9.88 right_branch(8),
% 9.65/9.88 right_branch(6),
% 9.65/9.88 right_branch(4),
% 9.65/9.88 right_branch(3)
% 9.65/9.88 )).
% 9.65/9.88 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------