TSTP Solution File: SEU212+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU212+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 : n002.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 14:33:34 EDT 2024
% Result : Theorem 3.54s 3.75s
% Output : Proof 3.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU212+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n002.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 15:00:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 3.54/3.75 % SZS status Theorem for theBenchmark
% 3.54/3.75 % SZS output start Proof for theBenchmark
% 3.54/3.75
% 3.54/3.75 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 3.54/3.75 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 3.54/3.75
% 3.54/3.75 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(cc1_funct_1-1, axiom, ( ~empty(_u2) | function(_u2) )).
% 3.54/3.75
% 3.54/3.75 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(cc1_relat_1-1, axiom, ( ~empty(_u3) | relation(_u3) )).
% 3.54/3.75
% 3.54/3.75 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 3.54/3.75 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u5, _u4) = unordered_pair(_u4, _u5)) )).
% 3.54/3.75
% 3.54/3.75 % Formula: d4_funct_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(d4_funct_1-1, axiom, ( ~relation(_u8) | ~function(_u8) | ~in(_u15, relation_dom(_u8)) | ( _u11 != apply(_u8, _u15)) | in(ordered_pair(_u15, _u11), _u8) )).
% 3.54/3.75 cnf(d4_funct_1-2, axiom, ( ~relation(_u8) | ~function(_u8) | ~in(_u15, relation_dom(_u8)) | ~in(ordered_pair(_u15, _u12), _u8) | ( _u12 = apply(_u8, _u15)) )).
% 3.54/3.75 cnf(d4_funct_1-3, axiom, ( ~relation(_u8) | ~function(_u8) | in(_u16, relation_dom(_u8)) | ( _u13 != apply(_u8, _u16)) | ( _u13 = empty_set) )).
% 3.54/3.75 cnf(d4_funct_1-4, axiom, ( ~relation(_u8) | ~function(_u8) | in(_u16, relation_dom(_u8)) | ( _u14 != empty_set) | ( _u14 = apply(_u8, _u16)) )).
% 3.54/3.75
% 3.54/3.75 % Formula: d4_relat_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(d4_relat_1-1, axiom, ( ~relation(_u24) | ( _u29 != relation_dom(_u24)) | ~in(_u25, _u29) | in(ordered_pair(_u25, skolem1(_u24, _u29, _u25)), _u24) )).
% 3.54/3.75 cnf(d4_relat_1-2, axiom, ( ~relation(_u24) | ( _u29 != relation_dom(_u24)) | ~in(ordered_pair(_u26, _u18), _u24) | in(_u26, _u29) )).
% 3.54/3.75 cnf(d4_relat_1-3, axiom, ( ~relation(_u24) | ( _u30 = relation_dom(_u24)) | in(skolem2(_u24, _u30), _u30) | in(ordered_pair(skolem3(_u24, _u30), skolem4(_u24, _u30)), _u24) )).
% 3.54/3.75 cnf(d4_relat_1-4, axiom, ( ~relation(_u24) | ( _u30 = relation_dom(_u24)) | in(skolem2(_u24, _u30), _u30) | ~in(skolem3(_u24, _u30), _u30) )).
% 3.54/3.75 cnf(d4_relat_1-5, axiom, ( ~relation(_u24) | ( _u30 = relation_dom(_u24)) | ~in(ordered_pair(skolem2(_u24, _u30), _u20), _u24) | in(ordered_pair(skolem3(_u24, _u30), skolem4(_u24, _u30)), _u24) )).
% 3.54/3.75 cnf(d4_relat_1-6, axiom, ( ~relation(_u24) | ( _u30 = relation_dom(_u24)) | ~in(ordered_pair(skolem2(_u24, _u30), _u20), _u24) | ~in(skolem3(_u24, _u30), _u30) )).
% 3.54/3.75
% 3.54/3.75 % Formula: d5_tarski ( axiom ) converted to clauses:
% 3.54/3.75 cnf(d5_tarski-1, axiom, ( ( ordered_pair(_u32, _u31) = unordered_pair(unordered_pair(_u32, _u31), singleton(_u32))) )).
% 3.54/3.75
% 3.54/3.75 % Formula: dt_k1_funct_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(dt_k1_funct_1, axiom, $true).
% 3.54/3.75
% 3.54/3.75 % Formula: dt_k1_relat_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(dt_k1_relat_1, axiom, $true).
% 3.54/3.75
% 3.54/3.75 % Formula: dt_k1_tarski ( axiom ) converted to clauses:
% 3.54/3.75 cnf(dt_k1_tarski, axiom, $true).
% 3.54/3.75
% 3.54/3.75 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(dt_k1_xboole_0, axiom, $true).
% 3.54/3.75
% 3.54/3.75 % Formula: dt_k2_tarski ( axiom ) converted to clauses:
% 3.54/3.75 cnf(dt_k2_tarski, axiom, $true).
% 3.54/3.75
% 3.54/3.75 % Formula: dt_k4_tarski ( axiom ) converted to clauses:
% 3.54/3.75 cnf(dt_k4_tarski, axiom, $true).
% 3.54/3.75
% 3.54/3.75 % Formula: dt_m1_subset_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(dt_m1_subset_1, axiom, $true).
% 3.54/3.75
% 3.54/3.75 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(existence_m1_subset_1-1, axiom, ( element(skolem5(_u34), _u34) )).
% 3.54/3.75
% 3.54/3.75 % Formula: fc12_relat_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(fc12_relat_1-1, axiom, ( empty(empty_set) )).
% 3.54/3.75 cnf(fc12_relat_1-2, axiom, ( relation(empty_set) )).
% 3.54/3.75 cnf(fc12_relat_1-3, axiom, ( relation_empty_yielding(empty_set) )).
% 3.54/3.75
% 3.54/3.75 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 3.54/3.75
% 3.54/3.75 % Formula: fc1_zfmisc_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(fc1_zfmisc_1-1, axiom, ( ~empty(ordered_pair(_u36, _u35)) )).
% 3.54/3.75
% 3.54/3.75 % Formula: fc2_subset_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(fc2_subset_1-1, axiom, ( ~empty(singleton(_u37)) )).
% 3.54/3.75
% 3.54/3.75 % Formula: fc3_subset_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(fc3_subset_1-1, axiom, ( ~empty(unordered_pair(_u39, _u38)) )).
% 3.54/3.75
% 3.54/3.75 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 3.54/3.75 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 3.54/3.75
% 3.54/3.75 % Formula: fc5_relat_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(fc5_relat_1-1, axiom, ( empty(_u40) | ~relation(_u40) | ~empty(relation_dom(_u40)) )).
% 3.54/3.75
% 3.54/3.75 % Formula: fc7_relat_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(fc7_relat_1-1, axiom, ( ~empty(_u41) | empty(relation_dom(_u41)) )).
% 3.54/3.75 cnf(fc7_relat_1-2, axiom, ( ~empty(_u41) | relation(relation_dom(_u41)) )).
% 3.54/3.75
% 3.54/3.75 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(rc1_funct_1-1, axiom, ( relation(skolem6) )).
% 3.54/3.75 cnf(rc1_funct_1-2, axiom, ( function(skolem6) )).
% 3.54/3.75
% 3.54/3.75 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(rc1_relat_1-1, axiom, ( empty(skolem7) )).
% 3.54/3.75 cnf(rc1_relat_1-2, axiom, ( relation(skolem7) )).
% 3.54/3.75
% 3.54/3.75 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(rc1_xboole_0-1, axiom, ( empty(skolem8) )).
% 3.54/3.75
% 3.54/3.75 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem9) )).
% 3.54/3.75 cnf(rc2_relat_1-2, axiom, ( relation(skolem9) )).
% 3.54/3.75
% 3.54/3.75 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem10) )).
% 3.54/3.75
% 3.54/3.75 % Formula: rc3_relat_1 ( axiom ) converted to clauses:
% 3.54/3.75 cnf(rc3_relat_1-1, axiom, ( relation(skolem11) )).
% 3.54/3.75 cnf(rc3_relat_1-2, axiom, ( relation_empty_yielding(skolem11) )).
% 3.54/3.75
% 3.54/3.75 % Formula: t1_subset ( axiom ) converted to clauses:
% 3.54/3.75 cnf(t1_subset-1, axiom, ( ~in(_u49, _u48) | element(_u49, _u48) )).
% 3.54/3.75
% 3.54/3.75 % Formula: t2_subset ( axiom ) converted to clauses:
% 3.54/3.75 cnf(t2_subset-1, axiom, ( ~element(_u51, _u50) | empty(_u50) | in(_u51, _u50) )).
% 3.54/3.75
% 3.54/3.75 % Formula: t6_boole ( axiom ) converted to clauses:
% 3.54/3.75 cnf(t6_boole-1, axiom, ( ~empty(_u52) | ( _u52 = empty_set) )).
% 3.54/3.75
% 3.54/3.75 % Formula: t7_boole ( axiom ) converted to clauses:
% 3.54/3.75 cnf(t7_boole-1, axiom, ( ~in(_u54, _u53) | ~empty(_u53) )).
% 3.54/3.75
% 3.54/3.75 % Formula: t8_boole ( axiom ) converted to clauses:
% 3.54/3.75 cnf(t8_boole-1, axiom, ( ~empty(_u56) | ( _u56 = _u55) | ~empty(_u55) )).
% 3.54/3.75
% 3.54/3.75 % Formula: t8_funct_1 ( conjecture ) (definitionally) converted to clauses:
% 3.54/3.75 cnf(t8_funct_1-1, negated_conjecture, ( relation(skolem14) )).
% 3.54/3.75 cnf(t8_funct_1-2, negated_conjecture, ( function(skolem14) )).
% 3.54/3.75 cnf(t8_funct_1-3, negated_conjecture, ( ~_def0 | ~_def1 )).
% 3.54/3.75 cnf(t8_funct_1-4, negated_conjecture, ( _def0 | in(ordered_pair(skolem12, skolem13), skolem14) )).
% 3.54/3.75 cnf(t8_funct_1-5, negated_conjecture, ( _def0 | ~in(skolem12, relation_dom(skolem14)) | ( skolem13 != apply(skolem14, skolem12)) )).
% 3.54/3.75 cnf(t8_funct_1-6, negated_conjecture, ( _def1 | in(skolem12, relation_dom(skolem14)) )).
% 3.54/3.75 cnf(t8_funct_1-7, negated_conjecture, ( _def1 | ( skolem13 = apply(skolem14, skolem12)) )).
% 3.54/3.75 cnf(t8_funct_1-8, negated_conjecture, ( _def1 | ~in(ordered_pair(skolem12, skolem13), skolem14) )).
% 3.54/3.75
% 3.54/3.75 % Problem matrix:
% 3.54/3.75 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 3.54/3.75 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 3.54/3.75 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 3.54/3.75 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 3.54/3.75 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( relation_dom(__eqx_0) = relation_dom(__eqy_0)) )).
% 3.54/3.75 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( apply(__eqx_0, __eqx_1) = apply(__eqy_0, __eqy_1)) )).
% 3.54/3.75 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 3.54/3.75 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 3.54/3.75 cnf(matrix-8, 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)) )).
% 3.54/3.75 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 3.54/3.75 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 3.54/3.75 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 3.54/3.75 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( skolem5(__eqx_0) = skolem5(__eqy_0)) )).
% 3.54/3.75 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 3.54/3.75 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 3.54/3.75 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 3.54/3.75 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 3.54/3.75 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 3.54/3.75 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~relation_empty_yielding(__eqx_0) | relation_empty_yielding(__eqy_0) )).
% 3.54/3.75 cnf(matrix-19, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 3.54/3.75 cnf(matrix-20, plain, ( ~empty(_u2) | function(_u2) )).
% 3.54/3.75 cnf(matrix-21, plain, ( ~empty(_u3) | relation(_u3) )).
% 3.54/3.75 cnf(matrix-22, plain, ( ( unordered_pair(_u5, _u4) = unordered_pair(_u4, _u5)) )).
% 3.54/3.75 cnf(matrix-23, plain, ( ~relation(_u8) | ~function(_u8) | ~in(_u15, relation_dom(_u8)) | ( _u11 != apply(_u8, _u15)) | in(ordered_pair(_u15, _u11), _u8) )).
% 3.54/3.75 cnf(matrix-24, plain, ( ~relation(_u8) | ~function(_u8) | ~in(_u15, relation_dom(_u8)) | ~in(ordered_pair(_u15, _u12), _u8) | ( _u12 = apply(_u8, _u15)) )).
% 3.54/3.75 cnf(matrix-25, plain, ( ~relation(_u8) | ~function(_u8) | in(_u16, relation_dom(_u8)) | ( _u13 != apply(_u8, _u16)) | ( _u13 = empty_set) )).
% 3.54/3.75 cnf(matrix-26, plain, ( ~relation(_u8) | ~function(_u8) | in(_u16, relation_dom(_u8)) | ( _u14 != empty_set) | ( _u14 = apply(_u8, _u16)) )).
% 3.54/3.75 cnf(matrix-27, plain, ( ~relation(_u24) | ( _u29 != relation_dom(_u24)) | ~in(_u25, _u29) | in(ordered_pair(_u25, skolem1(_u24, _u29, _u25)), _u24) )).
% 3.54/3.75 cnf(matrix-28, plain, ( ~relation(_u24) | ( _u29 != relation_dom(_u24)) | ~in(ordered_pair(_u26, _u18), _u24) | in(_u26, _u29) )).
% 3.54/3.75 cnf(matrix-29, plain, ( ~relation(_u24) | ( _u30 = relation_dom(_u24)) | in(skolem2(_u24, _u30), _u30) | in(ordered_pair(skolem3(_u24, _u30), skolem4(_u24, _u30)), _u24) )).
% 3.54/3.75 cnf(matrix-30, plain, ( ~relation(_u24) | ( _u30 = relation_dom(_u24)) | in(skolem2(_u24, _u30), _u30) | ~in(skolem3(_u24, _u30), _u30) )).
% 3.54/3.75 cnf(matrix-31, plain, ( ~relation(_u24) | ( _u30 = relation_dom(_u24)) | ~in(ordered_pair(skolem2(_u24, _u30), _u20), _u24) | in(ordered_pair(skolem3(_u24, _u30), skolem4(_u24, _u30)), _u24) )).
% 3.54/3.75 cnf(matrix-32, plain, ( ~relation(_u24) | ( _u30 = relation_dom(_u24)) | ~in(ordered_pair(skolem2(_u24, _u30), _u20), _u24) | ~in(skolem3(_u24, _u30), _u30) )).
% 3.54/3.75 cnf(matrix-33, plain, ( ( ordered_pair(_u32, _u31) = unordered_pair(unordered_pair(_u32, _u31), singleton(_u32))) )).
% 3.54/3.75 cnf(matrix-34, plain, ( element(skolem5(_u34), _u34) )).
% 3.54/3.75 cnf(matrix-35, plain, ( empty(empty_set) )).
% 3.54/3.75 cnf(matrix-36, plain, ( relation(empty_set) )).
% 3.54/3.75 cnf(matrix-37, plain, ( relation_empty_yielding(empty_set) )).
% 3.54/3.75 cnf(matrix-38, plain, ( empty(empty_set) )).
% 3.54/3.75 cnf(matrix-39, plain, ( ~empty(ordered_pair(_u36, _u35)) )).
% 3.54/3.75 cnf(matrix-40, plain, ( ~empty(singleton(_u37)) )).
% 3.54/3.75 cnf(matrix-41, plain, ( ~empty(unordered_pair(_u39, _u38)) )).
% 3.54/3.75 cnf(matrix-42, plain, ( empty(empty_set) )).
% 3.54/3.75 cnf(matrix-43, plain, ( relation(empty_set) )).
% 3.54/3.75 cnf(matrix-44, plain, ( empty(_u40) | ~relation(_u40) | ~empty(relation_dom(_u40)) )).
% 3.54/3.75 cnf(matrix-45, plain, ( ~empty(_u41) | empty(relation_dom(_u41)) )).
% 3.54/3.75 cnf(matrix-46, plain, ( ~empty(_u41) | relation(relation_dom(_u41)) )).
% 3.54/3.75 cnf(matrix-47, plain, ( relation(skolem6) )).
% 3.54/3.75 cnf(matrix-48, plain, ( function(skolem6) )).
% 3.54/3.75 cnf(matrix-49, plain, ( empty(skolem7) )).
% 3.54/3.75 cnf(matrix-50, plain, ( relation(skolem7) )).
% 3.54/3.75 cnf(matrix-51, plain, ( empty(skolem8) )).
% 3.54/3.75 cnf(matrix-52, plain, ( ~empty(skolem9) )).
% 3.54/3.75 cnf(matrix-53, plain, ( relation(skolem9) )).
% 3.54/3.75 cnf(matrix-54, plain, ( ~empty(skolem10) )).
% 3.54/3.75 cnf(matrix-55, plain, ( relation(skolem11) )).
% 3.54/3.75 cnf(matrix-56, plain, ( relation_empty_yielding(skolem11) )).
% 3.54/3.75 cnf(matrix-57, plain, ( ~in(_u49, _u48) | element(_u49, _u48) )).
% 3.54/3.75 cnf(matrix-58, plain, ( ~element(_u51, _u50) | empty(_u50) | in(_u51, _u50) )).
% 3.54/3.75 cnf(matrix-59, plain, ( ~empty(_u52) | ( _u52 = empty_set) )).
% 3.54/3.75 cnf(matrix-60, plain, ( ~in(_u54, _u53) | ~empty(_u53) )).
% 3.54/3.75 cnf(matrix-61, plain, ( ~empty(_u56) | ( _u56 = _u55) | ~empty(_u55) )).
% 3.54/3.75 cnf(matrix-62, plain, ( relation(skolem14) )).
% 3.54/3.75 cnf(matrix-63, plain, ( function(skolem14) )).
% 3.54/3.75 cnf(matrix-64, plain, ( ~_def0 | ~_def1 )).
% 3.54/3.75 cnf(matrix-65, plain, ( _def0 | in(ordered_pair(skolem12, skolem13), skolem14) )).
% 3.54/3.75 cnf(matrix-66, plain, ( _def0 | ~in(skolem12, relation_dom(skolem14)) | ( skolem13 != apply(skolem14, skolem12)) )).
% 3.54/3.75 cnf(matrix-67, plain, ( _def1 | in(skolem12, relation_dom(skolem14)) )).
% 3.54/3.75 cnf(matrix-68, plain, ( _def1 | ( skolem13 = apply(skolem14, skolem12)) )).
% 3.54/3.75 cnf(matrix-69, plain, ( _def1 | ~in(ordered_pair(skolem12, skolem13), skolem14) )).
% 3.54/3.75
% 3.54/3.75 % Proof stack:
% 3.54/3.75 cnf(proof-stack, plain,
% 3.54/3.75 proof_stack(
% 3.54/3.75 start(64),
% 3.54/3.75 left_branch(0, 66, 0, 2),
% 3.54/3.75 left_branch(0, 24, 4, 3),
% 3.54/3.75 left_branch(0, 62, 0, 4),
% 3.54/3.75 right_branch(4),
% 3.54/3.75 left_branch(0, 65, 1, 5),
% 3.54/3.75 reduction(0, 0),
% 3.54/3.75 right_branch(5),
% 3.54/3.75 left_branch(0, 28, 3, 6),
% 3.54/3.75 left_branch(0, 62, 0, 7),
% 3.54/3.75 right_branch(7),
% 3.54/3.75 left_branch(0, 65, 1, 8),
% 3.54/3.75 reduction(0, 0),
% 3.54/3.75 right_branch(8),
% 3.54/3.75 left_branch(0, 4, 1, 9),
% 3.54/3.75 left_branch(0, 0, 0, 10),
% 3.54/3.75 right_branch(10),
% 3.54/3.75 right_branch(9),
% 3.54/3.75 right_branch(6),
% 3.54/3.75 left_branch(0, 63, 0, 7),
% 3.54/3.75 right_branch(7),
% 3.54/3.75 right_branch(3),
% 3.54/3.75 left_branch(0, 28, 3, 4),
% 3.54/3.75 left_branch(0, 62, 0, 5),
% 3.54/3.75 right_branch(5),
% 3.54/3.75 left_branch(0, 65, 1, 6),
% 3.54/3.75 reduction(0, 0),
% 3.54/3.75 right_branch(6),
% 3.54/3.75 left_branch(0, 4, 1, 7),
% 3.54/3.75 left_branch(0, 0, 0, 8),
% 3.54/3.75 right_branch(8),
% 3.54/3.75 right_branch(7),
% 3.54/3.75 right_branch(4),
% 3.54/3.75 right_branch(2),
% 3.54/3.75 left_branch(0, 69, 0, 3),
% 3.54/3.75 left_branch(0, 23, 4, 4),
% 3.54/3.75 left_branch(0, 62, 0, 5),
% 3.54/3.75 right_branch(5),
% 3.54/3.75 left_branch(0, 68, 1, 6),
% 3.54/3.75 reduction(0, 0),
% 3.54/3.75 right_branch(6),
% 3.54/3.75 left_branch(0, 67, 1, 7),
% 3.54/3.75 reduction(0, 0),
% 3.54/3.75 right_branch(7),
% 3.54/3.75 left_branch(0, 63, 0, 8),
% 3.54/3.75 right_branch(8),
% 3.54/3.75 right_branch(4),
% 3.54/3.75 right_branch(3)
% 3.54/3.75 )).
% 3.54/3.75 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------