TSTP Solution File: SEU203+1 by ConnectPP---0.2.2
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%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : SEU203+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 : n023.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 : Wed Mar 6 09:20:31 EST 2024
% Result : Theorem 18.41s 18.57s
% Output : Proof 18.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU203+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n023.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 : Sun Mar 3 09:51:20 EST 2024
% 0.12/0.33 % CPUTime :
% 18.41/18.57 % SZS status Theorem for theBenchmark
% 18.41/18.57 % SZS output start Proof for theBenchmark
% 18.41/18.57
% 18.41/18.57 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 18.41/18.57 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 18.41/18.57
% 18.41/18.57 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(cc1_relat_1-1, axiom, ( ~empty(_u2) | relation(_u2) )).
% 18.41/18.57
% 18.41/18.57 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 18.41/18.57 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u4, _u3) = unordered_pair(_u3, _u4)) )).
% 18.41/18.57
% 18.41/18.57 % Formula: d13_relat_1 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(d13_relat_1-1, axiom, ( ~relation(_u13) | ( _u18 != relation_image(_u13, _u20)) | ~in(_u14, _u18) | in(ordered_pair(skolem1(_u13, _u20, _u18, _u14), _u14), _u13) )).
% 18.41/18.57 cnf(d13_relat_1-2, axiom, ( ~relation(_u13) | ( _u18 != relation_image(_u13, _u20)) | ~in(_u14, _u18) | in(skolem1(_u13, _u20, _u18, _u14), _u20) )).
% 18.41/18.57 cnf(d13_relat_1-3, axiom, ( ~relation(_u13) | ( _u18 != relation_image(_u13, _u20)) | ~in(ordered_pair(_u6, _u15), _u13) | ~in(_u6, _u20) | in(_u15, _u18) )).
% 18.41/18.57 cnf(d13_relat_1-4, axiom, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | in(skolem2(_u13, _u21, _u19), _u19) | in(ordered_pair(skolem4(_u13, _u21, _u19), skolem3(_u13, _u21, _u19)), _u13) )).
% 18.41/18.57 cnf(d13_relat_1-5, axiom, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | in(skolem2(_u13, _u21, _u19), _u19) | in(skolem4(_u13, _u21, _u19), _u21) )).
% 18.41/18.57 cnf(d13_relat_1-6, axiom, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | in(skolem2(_u13, _u21, _u19), _u19) | ~in(skolem3(_u13, _u21, _u19), _u19) )).
% 18.41/18.57 cnf(d13_relat_1-7, axiom, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | ~in(ordered_pair(_u8, skolem2(_u13, _u21, _u19)), _u13) | ~in(_u8, _u21) | in(ordered_pair(skolem4(_u13, _u21, _u19), skolem3(_u13, _u21, _u19)), _u13) )).
% 18.41/18.57 cnf(d13_relat_1-8, axiom, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | ~in(ordered_pair(_u8, skolem2(_u13, _u21, _u19)), _u13) | ~in(_u8, _u21) | in(skolem4(_u13, _u21, _u19), _u21) )).
% 18.41/18.57 cnf(d13_relat_1-9, axiom, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | ~in(ordered_pair(_u8, skolem2(_u13, _u21, _u19)), _u13) | ~in(_u8, _u21) | ~in(skolem3(_u13, _u21, _u19), _u19) )).
% 18.41/18.57
% 18.41/18.57 % Formula: d4_relat_1 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(d4_relat_1-1, axiom, ( ~relation(_u29) | ( _u34 != relation_dom(_u29)) | ~in(_u30, _u34) | in(ordered_pair(_u30, skolem5(_u29, _u34, _u30)), _u29) )).
% 18.41/18.57 cnf(d4_relat_1-2, axiom, ( ~relation(_u29) | ( _u34 != relation_dom(_u29)) | ~in(ordered_pair(_u31, _u23), _u29) | in(_u31, _u34) )).
% 18.41/18.57 cnf(d4_relat_1-3, axiom, ( ~relation(_u29) | ( _u35 = relation_dom(_u29)) | in(skolem6(_u29, _u35), _u35) | in(ordered_pair(skolem7(_u29, _u35), skolem8(_u29, _u35)), _u29) )).
% 18.41/18.57 cnf(d4_relat_1-4, axiom, ( ~relation(_u29) | ( _u35 = relation_dom(_u29)) | in(skolem6(_u29, _u35), _u35) | ~in(skolem7(_u29, _u35), _u35) )).
% 18.41/18.57 cnf(d4_relat_1-5, axiom, ( ~relation(_u29) | ( _u35 = relation_dom(_u29)) | ~in(ordered_pair(skolem6(_u29, _u35), _u25), _u29) | in(ordered_pair(skolem7(_u29, _u35), skolem8(_u29, _u35)), _u29) )).
% 18.41/18.57 cnf(d4_relat_1-6, axiom, ( ~relation(_u29) | ( _u35 = relation_dom(_u29)) | ~in(ordered_pair(skolem6(_u29, _u35), _u25), _u29) | ~in(skolem7(_u29, _u35), _u35) )).
% 18.41/18.57
% 18.41/18.57 % Formula: d5_tarski ( axiom ) converted to clauses:
% 18.41/18.57 cnf(d5_tarski-1, axiom, ( ( ordered_pair(_u37, _u36) = unordered_pair(unordered_pair(_u37, _u36), singleton(_u37))) )).
% 18.41/18.57
% 18.41/18.57 % Formula: dt_k1_relat_1 ( axiom ) converted to clauses:
% 18.41/18.57
% 18.41/18.57 % Formula: dt_k1_tarski ( axiom ) converted to clauses:
% 18.41/18.57
% 18.41/18.57 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 18.41/18.57
% 18.41/18.57 % Formula: dt_k2_tarski ( axiom ) converted to clauses:
% 18.41/18.57
% 18.41/18.57 % Formula: dt_k4_tarski ( axiom ) converted to clauses:
% 18.41/18.57
% 18.41/18.57 % Formula: dt_k9_relat_1 ( axiom ) converted to clauses:
% 18.41/18.57
% 18.41/18.57 % Formula: dt_m1_subset_1 ( axiom ) converted to clauses:
% 18.41/18.57
% 18.41/18.57 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(existence_m1_subset_1-1, axiom, ( element(skolem9(_u39), _u39) )).
% 18.41/18.57
% 18.41/18.57 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 18.41/18.57
% 18.41/18.57 % Formula: fc1_zfmisc_1 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(fc1_zfmisc_1-1, axiom, ( ~empty(ordered_pair(_u41, _u40)) )).
% 18.41/18.57
% 18.41/18.57 % Formula: fc2_subset_1 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(fc2_subset_1-1, axiom, ( ~empty(singleton(_u42)) )).
% 18.41/18.57
% 18.41/18.57 % Formula: fc3_subset_1 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(fc3_subset_1-1, axiom, ( ~empty(unordered_pair(_u44, _u43)) )).
% 18.41/18.57
% 18.41/18.57 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 18.41/18.57 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 18.41/18.57
% 18.41/18.57 % Formula: fc5_relat_1 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(fc5_relat_1-1, axiom, ( empty(_u45) | ~relation(_u45) | ~empty(relation_dom(_u45)) )).
% 18.41/18.57
% 18.41/18.57 % Formula: fc7_relat_1 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(fc7_relat_1-1, axiom, ( ~empty(_u46) | empty(relation_dom(_u46)) )).
% 18.41/18.57 cnf(fc7_relat_1-2, axiom, ( ~empty(_u46) | relation(relation_dom(_u46)) )).
% 18.41/18.57
% 18.41/18.57 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(rc1_relat_1-1, axiom, ( empty(skolem10) )).
% 18.41/18.57 cnf(rc1_relat_1-2, axiom, ( relation(skolem10) )).
% 18.41/18.57
% 18.41/18.57 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(rc1_xboole_0-1, axiom, ( empty(skolem11) )).
% 18.41/18.57
% 18.41/18.57 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem12) )).
% 18.41/18.57 cnf(rc2_relat_1-2, axiom, ( relation(skolem12) )).
% 18.41/18.57
% 18.41/18.57 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 18.41/18.57 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem13) )).
% 18.41/18.57
% 18.41/18.57 % Formula: t143_relat_1 ( conjecture ) converted to clauses:
% 18.41/18.57 cnf(t143_relat_1-1, negated_conjecture, ( relation(skolem16) )).
% 18.41/18.57 cnf(t143_relat_1-2, negated_conjecture, ( in(skolem14, relation_image(skolem16, skolem15)) | in(skolem17, relation_dom(skolem16)) )).
% 18.41/18.57 cnf(t143_relat_1-3, negated_conjecture, ( in(skolem14, relation_image(skolem16, skolem15)) | in(ordered_pair(skolem17, skolem14), skolem16) )).
% 18.41/18.57 cnf(t143_relat_1-4, negated_conjecture, ( in(skolem14, relation_image(skolem16, skolem15)) | in(skolem17, skolem15) )).
% 18.41/18.57 cnf(t143_relat_1-5, negated_conjecture, ( ~in(_u51, relation_dom(skolem16)) | ~in(ordered_pair(_u51, skolem14), skolem16) | ~in(_u51, skolem15) | in(skolem17, relation_dom(skolem16)) )).
% 18.41/18.57 cnf(t143_relat_1-6, negated_conjecture, ( ~in(_u51, relation_dom(skolem16)) | ~in(ordered_pair(_u51, skolem14), skolem16) | ~in(_u51, skolem15) | in(ordered_pair(skolem17, skolem14), skolem16) )).
% 18.41/18.57 cnf(t143_relat_1-7, negated_conjecture, ( ~in(_u51, relation_dom(skolem16)) | ~in(ordered_pair(_u51, skolem14), skolem16) | ~in(_u51, skolem15) | in(skolem17, skolem15) )).
% 18.41/18.57 cnf(t143_relat_1-8, negated_conjecture, ( ~in(_u51, relation_dom(skolem16)) | ~in(ordered_pair(_u51, skolem14), skolem16) | ~in(_u51, skolem15) | ~in(skolem14, relation_image(skolem16, skolem15)) )).
% 18.41/18.57
% 18.41/18.57 % Formula: t1_subset ( axiom ) converted to clauses:
% 18.41/18.57 cnf(t1_subset-1, axiom, ( ~in(_u57, _u56) | element(_u57, _u56) )).
% 18.41/18.57
% 18.41/18.57 % Formula: t2_subset ( axiom ) converted to clauses:
% 18.41/18.57 cnf(t2_subset-1, axiom, ( ~element(_u59, _u58) | empty(_u58) | in(_u59, _u58) )).
% 18.41/18.57
% 18.41/18.57 % Formula: t6_boole ( axiom ) converted to clauses:
% 18.41/18.57 cnf(t6_boole-1, axiom, ( ~empty(_u60) | ( _u60 = empty_set) )).
% 18.41/18.57
% 18.41/18.57 % Formula: t7_boole ( axiom ) converted to clauses:
% 18.41/18.57 cnf(t7_boole-1, axiom, ( ~in(_u62, _u61) | ~empty(_u61) )).
% 18.41/18.57
% 18.41/18.57 % Formula: t8_boole ( axiom ) converted to clauses:
% 18.41/18.57 cnf(t8_boole-1, axiom, ( ~empty(_u64) | ( _u64 = _u63) | ~empty(_u63) )).
% 18.41/18.57
% 18.41/18.57 % Problem matrix:
% 18.41/18.57 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 18.41/18.57 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 18.41/18.57 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 18.41/18.57 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 18.41/18.57 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( relation_image(__eqx_0, __eqx_1) = relation_image(__eqy_0, __eqy_1)) )).
% 18.41/18.57 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 18.41/18.57 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( relation_dom(__eqx_0) = relation_dom(__eqy_0)) )).
% 18.41/18.57 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 18.41/18.57 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( skolem1(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = skolem1(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 18.41/18.57 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem2(__eqx_0, __eqx_1, __eqx_2) = skolem2(__eqy_0, __eqy_1, __eqy_2)) )).
% 18.41/18.57 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem3(__eqx_0, __eqx_1, __eqx_2) = skolem3(__eqy_0, __eqy_1, __eqy_2)) )).
% 18.41/18.57 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem4(__eqx_0, __eqx_1, __eqx_2) = skolem4(__eqy_0, __eqy_1, __eqy_2)) )).
% 18.41/18.57 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem5(__eqx_0, __eqx_1, __eqx_2) = skolem5(__eqy_0, __eqy_1, __eqy_2)) )).
% 18.41/18.57 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem6(__eqx_0, __eqx_1) = skolem6(__eqy_0, __eqy_1)) )).
% 18.41/18.57 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem7(__eqx_0, __eqx_1) = skolem7(__eqy_0, __eqy_1)) )).
% 18.41/18.57 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem8(__eqx_0, __eqx_1) = skolem8(__eqy_0, __eqy_1)) )).
% 18.41/18.57 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( skolem9(__eqx_0) = skolem9(__eqy_0)) )).
% 18.41/18.57 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 18.41/18.57 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 18.41/18.57 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 18.41/18.57 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 18.41/18.57 cnf(matrix-21, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 18.41/18.57 cnf(matrix-22, plain, ( ~empty(_u2) | relation(_u2) )).
% 18.41/18.57 cnf(matrix-23, plain, ( ( unordered_pair(_u4, _u3) = unordered_pair(_u3, _u4)) )).
% 18.41/18.57 cnf(matrix-24, plain, ( ~relation(_u13) | ( _u18 != relation_image(_u13, _u20)) | ~in(_u14, _u18) | in(ordered_pair(skolem1(_u13, _u20, _u18, _u14), _u14), _u13) )).
% 18.41/18.57 cnf(matrix-25, plain, ( ~relation(_u13) | ( _u18 != relation_image(_u13, _u20)) | ~in(_u14, _u18) | in(skolem1(_u13, _u20, _u18, _u14), _u20) )).
% 18.41/18.57 cnf(matrix-26, plain, ( ~relation(_u13) | ( _u18 != relation_image(_u13, _u20)) | ~in(ordered_pair(_u6, _u15), _u13) | ~in(_u6, _u20) | in(_u15, _u18) )).
% 18.41/18.57 cnf(matrix-27, plain, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | in(skolem2(_u13, _u21, _u19), _u19) | in(ordered_pair(skolem4(_u13, _u21, _u19), skolem3(_u13, _u21, _u19)), _u13) )).
% 18.41/18.57 cnf(matrix-28, plain, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | in(skolem2(_u13, _u21, _u19), _u19) | in(skolem4(_u13, _u21, _u19), _u21) )).
% 18.41/18.57 cnf(matrix-29, plain, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | in(skolem2(_u13, _u21, _u19), _u19) | ~in(skolem3(_u13, _u21, _u19), _u19) )).
% 18.41/18.57 cnf(matrix-30, plain, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | ~in(ordered_pair(_u8, skolem2(_u13, _u21, _u19)), _u13) | ~in(_u8, _u21) | in(ordered_pair(skolem4(_u13, _u21, _u19), skolem3(_u13, _u21, _u19)), _u13) )).
% 18.41/18.57 cnf(matrix-31, plain, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | ~in(ordered_pair(_u8, skolem2(_u13, _u21, _u19)), _u13) | ~in(_u8, _u21) | in(skolem4(_u13, _u21, _u19), _u21) )).
% 18.41/18.57 cnf(matrix-32, plain, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | ~in(ordered_pair(_u8, skolem2(_u13, _u21, _u19)), _u13) | ~in(_u8, _u21) | ~in(skolem3(_u13, _u21, _u19), _u19) )).
% 18.41/18.57 cnf(matrix-33, plain, ( ~relation(_u29) | ( _u34 != relation_dom(_u29)) | ~in(_u30, _u34) | in(ordered_pair(_u30, skolem5(_u29, _u34, _u30)), _u29) )).
% 18.41/18.57 cnf(matrix-34, plain, ( ~relation(_u29) | ( _u34 != relation_dom(_u29)) | ~in(ordered_pair(_u31, _u23), _u29) | in(_u31, _u34) )).
% 18.41/18.57 cnf(matrix-35, plain, ( ~relation(_u29) | ( _u35 = relation_dom(_u29)) | in(skolem6(_u29, _u35), _u35) | in(ordered_pair(skolem7(_u29, _u35), skolem8(_u29, _u35)), _u29) )).
% 18.41/18.57 cnf(matrix-36, plain, ( ~relation(_u29) | ( _u35 = relation_dom(_u29)) | in(skolem6(_u29, _u35), _u35) | ~in(skolem7(_u29, _u35), _u35) )).
% 18.41/18.57 cnf(matrix-37, plain, ( ~relation(_u29) | ( _u35 = relation_dom(_u29)) | ~in(ordered_pair(skolem6(_u29, _u35), _u25), _u29) | in(ordered_pair(skolem7(_u29, _u35), skolem8(_u29, _u35)), _u29) )).
% 18.41/18.57 cnf(matrix-38, plain, ( ~relation(_u29) | ( _u35 = relation_dom(_u29)) | ~in(ordered_pair(skolem6(_u29, _u35), _u25), _u29) | ~in(skolem7(_u29, _u35), _u35) )).
% 18.41/18.57 cnf(matrix-39, plain, ( ( ordered_pair(_u37, _u36) = unordered_pair(unordered_pair(_u37, _u36), singleton(_u37))) )).
% 18.41/18.57 cnf(matrix-40, plain, ( element(skolem9(_u39), _u39) )).
% 18.41/18.57 cnf(matrix-41, plain, ( empty(empty_set) )).
% 18.41/18.57 cnf(matrix-42, plain, ( ~empty(ordered_pair(_u41, _u40)) )).
% 18.41/18.57 cnf(matrix-43, plain, ( ~empty(singleton(_u42)) )).
% 18.41/18.57 cnf(matrix-44, plain, ( ~empty(unordered_pair(_u44, _u43)) )).
% 18.41/18.57 cnf(matrix-45, plain, ( empty(empty_set) )).
% 18.41/18.57 cnf(matrix-46, plain, ( relation(empty_set) )).
% 18.41/18.57 cnf(matrix-47, plain, ( empty(_u45) | ~relation(_u45) | ~empty(relation_dom(_u45)) )).
% 18.41/18.57 cnf(matrix-48, plain, ( ~empty(_u46) | empty(relation_dom(_u46)) )).
% 18.41/18.57 cnf(matrix-49, plain, ( ~empty(_u46) | relation(relation_dom(_u46)) )).
% 18.41/18.57 cnf(matrix-50, plain, ( empty(skolem10) )).
% 18.41/18.57 cnf(matrix-51, plain, ( relation(skolem10) )).
% 18.41/18.57 cnf(matrix-52, plain, ( empty(skolem11) )).
% 18.41/18.57 cnf(matrix-53, plain, ( ~empty(skolem12) )).
% 18.41/18.57 cnf(matrix-54, plain, ( relation(skolem12) )).
% 18.41/18.57 cnf(matrix-55, plain, ( ~empty(skolem13) )).
% 18.41/18.57 cnf(matrix-56, plain, ( relation(skolem16) )).
% 18.41/18.57 cnf(matrix-57, plain, ( in(skolem14, relation_image(skolem16, skolem15)) | in(skolem17, relation_dom(skolem16)) )).
% 18.41/18.57 cnf(matrix-58, plain, ( in(skolem14, relation_image(skolem16, skolem15)) | in(ordered_pair(skolem17, skolem14), skolem16) )).
% 18.41/18.57 cnf(matrix-59, plain, ( in(skolem14, relation_image(skolem16, skolem15)) | in(skolem17, skolem15) )).
% 18.41/18.57 cnf(matrix-60, plain, ( ~in(_u51, relation_dom(skolem16)) | ~in(ordered_pair(_u51, skolem14), skolem16) | ~in(_u51, skolem15) | in(skolem17, relation_dom(skolem16)) )).
% 18.41/18.57 cnf(matrix-61, plain, ( ~in(_u51, relation_dom(skolem16)) | ~in(ordered_pair(_u51, skolem14), skolem16) | ~in(_u51, skolem15) | in(ordered_pair(skolem17, skolem14), skolem16) )).
% 18.41/18.57 cnf(matrix-62, plain, ( ~in(_u51, relation_dom(skolem16)) | ~in(ordered_pair(_u51, skolem14), skolem16) | ~in(_u51, skolem15) | in(skolem17, skolem15) )).
% 18.41/18.57 cnf(matrix-63, plain, ( ~in(_u51, relation_dom(skolem16)) | ~in(ordered_pair(_u51, skolem14), skolem16) | ~in(_u51, skolem15) | ~in(skolem14, relation_image(skolem16, skolem15)) )).
% 18.41/18.57 cnf(matrix-64, plain, ( ~in(_u57, _u56) | element(_u57, _u56) )).
% 18.41/18.57 cnf(matrix-65, plain, ( ~element(_u59, _u58) | empty(_u58) | in(_u59, _u58) )).
% 18.41/18.57 cnf(matrix-66, plain, ( ~empty(_u60) | ( _u60 = empty_set) )).
% 18.41/18.57 cnf(matrix-67, plain, ( ~in(_u62, _u61) | ~empty(_u61) )).
% 18.41/18.57 cnf(matrix-68, plain, ( ~empty(_u64) | ( _u64 = _u63) | ~empty(_u63) )).
% 18.41/18.57
% 18.41/18.57 % Proof stack:
% 18.41/18.57 cnf(proof-stack, plain,
% 18.41/18.57 proof_stack(
% 18.41/18.57 start(58),
% 18.41/18.57 left_branch(0, 63, 3, 2),
% 18.41/18.57 left_branch(0, 34, 3, 3),
% 18.41/18.57 left_branch(0, 56, 0, 4),
% 18.41/18.57 right_branch(4),
% 18.41/18.57 left_branch(0, 24, 3, 5),
% 18.41/18.57 lemmata(0, 0),
% 18.41/18.57 reduction(0, 0),
% 18.41/18.57 left_branch(0, 0, 0, 8),
% 18.41/18.57 right_branch(8),
% 18.41/18.57 right_branch(5),
% 18.41/18.57 left_branch(0, 6, 1, 6),
% 18.41/18.57 left_branch(0, 0, 0, 7),
% 18.41/18.57 right_branch(7),
% 18.41/18.57 right_branch(6),
% 18.41/18.57 right_branch(3),
% 18.41/18.57 left_branch(0, 25, 3, 4),
% 18.41/18.57 left_branch(0, 56, 0, 5),
% 18.41/18.57 right_branch(5),
% 18.41/18.57 reduction(0, 0),
% 18.41/18.57 left_branch(0, 4, 2, 7),
% 18.41/18.57 left_branch(0, 0, 0, 8),
% 18.41/18.57 right_branch(8),
% 18.41/18.57 left_branch(0, 0, 0, 9),
% 18.41/18.57 right_branch(9),
% 18.41/18.57 right_branch(7),
% 18.41/18.57 right_branch(4),
% 18.41/18.57 left_branch(0, 24, 3, 5),
% 18.41/18.57 left_branch(0, 56, 0, 6),
% 18.41/18.57 right_branch(6),
% 18.41/18.57 reduction(0, 0),
% 18.41/18.57 left_branch(0, 4, 2, 8),
% 18.41/18.57 left_branch(0, 0, 0, 9),
% 18.41/18.57 right_branch(9),
% 18.41/18.57 left_branch(0, 0, 0, 10),
% 18.41/18.57 right_branch(10),
% 18.41/18.57 right_branch(8),
% 18.41/18.57 right_branch(5),
% 18.41/18.57 right_branch(2),
% 18.41/18.57 left_branch(0, 63, 1, 3),
% 18.41/18.57 left_branch(0, 60, 3, 4),
% 18.41/18.57 left_branch(0, 57, 1, 5),
% 18.41/18.57 lemmata(0, 0),
% 18.41/18.57 right_branch(5),
% 18.41/18.57 left_branch(0, 59, 1, 6),
% 18.41/18.57 lemmata(0, 0),
% 18.41/18.57 right_branch(6),
% 18.41/18.57 reduction(0, 0),
% 18.41/18.57 right_branch(4),
% 18.41/18.57 left_branch(0, 59, 1, 5),
% 18.41/18.57 lemmata(0, 0),
% 18.41/18.57 right_branch(5),
% 18.41/18.57 left_branch(0, 59, 0, 6),
% 18.41/18.57 left_branch(0, 26, 3, 7),
% 18.41/18.57 left_branch(0, 56, 0, 8),
% 18.41/18.57 right_branch(8),
% 18.41/18.57 reduction(0, 1),
% 18.41/18.57 reduction(0, 0),
% 18.41/18.57 left_branch(0, 0, 0, 11),
% 18.41/18.57 right_branch(11),
% 18.41/18.57 right_branch(7),
% 18.41/18.57 right_branch(6),
% 18.41/18.57 right_branch(3)
% 18.41/18.57 )).
% 18.41/18.57 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------