TSTP Solution File: SEU180+1 by ConnectPP---0.2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : SEU180+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 : 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 : Wed Mar 6 09:20:28 EST 2024
% Result : Theorem 0.18s 0.51s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU180+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.12 % 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 : Sun Mar 3 10:21:33 EST 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.51 % SZS status Theorem for theBenchmark
% 0.18/0.51 % SZS output start Proof for theBenchmark
% 0.18/0.51
% 0.18/0.51 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 0.18/0.51 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.18/0.51
% 0.18/0.51 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 0.18/0.51 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u3, _u2) = unordered_pair(_u2, _u3)) )).
% 0.18/0.51
% 0.18/0.51 % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u5, _u4) = set_union2(_u4, _u5)) )).
% 0.18/0.51
% 0.18/0.51 % Formula: d2_xboole_0 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(d2_xboole_0-1, axiom, ( ( _u15 != set_union2(_u19, _u17)) | ~in(_u11, _u15) | in(_u11, _u19) | in(_u11, _u17) )).
% 0.18/0.51 cnf(d2_xboole_0-2, axiom, ( ( _u15 != set_union2(_u19, _u17)) | in(_u12, _u15) | ~in(_u12, _u19) )).
% 0.18/0.51 cnf(d2_xboole_0-3, axiom, ( ( _u15 != set_union2(_u19, _u17)) | in(_u12, _u15) | ~in(_u12, _u17) )).
% 0.18/0.51 cnf(d2_xboole_0-4, axiom, ( ( _u16 = set_union2(_u20, _u18)) | in(skolem1(_u20, _u18, _u16), _u16) | in(skolem2(_u20, _u18, _u16), _u20) | in(skolem2(_u20, _u18, _u16), _u18) )).
% 0.18/0.51 cnf(d2_xboole_0-5, axiom, ( ( _u16 = set_union2(_u20, _u18)) | in(skolem1(_u20, _u18, _u16), _u16) | ~in(skolem2(_u20, _u18, _u16), _u16) )).
% 0.18/0.51 cnf(d2_xboole_0-6, axiom, ( ( _u16 = set_union2(_u20, _u18)) | in(skolem2(_u20, _u18, _u16), _u20) | in(skolem2(_u20, _u18, _u16), _u18) | ~in(skolem1(_u20, _u18, _u16), _u20) )).
% 0.18/0.51 cnf(d2_xboole_0-7, axiom, ( ( _u16 = set_union2(_u20, _u18)) | in(skolem2(_u20, _u18, _u16), _u20) | in(skolem2(_u20, _u18, _u16), _u18) | ~in(skolem1(_u20, _u18, _u16), _u18) )).
% 0.18/0.51 cnf(d2_xboole_0-8, axiom, ( ( _u16 = set_union2(_u20, _u18)) | ~in(skolem2(_u20, _u18, _u16), _u16) | ~in(skolem1(_u20, _u18, _u16), _u20) )).
% 0.18/0.51 cnf(d2_xboole_0-9, axiom, ( ( _u16 = set_union2(_u20, _u18)) | ~in(skolem2(_u20, _u18, _u16), _u16) | ~in(skolem1(_u20, _u18, _u16), _u18) )).
% 0.18/0.51
% 0.18/0.51 % Formula: d4_relat_1 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(d4_relat_1-1, axiom, ( ~relation(_u28) | ( _u33 != relation_dom(_u28)) | ~in(_u29, _u33) | in(ordered_pair(_u29, skolem3(_u28, _u33, _u29)), _u28) )).
% 0.18/0.51 cnf(d4_relat_1-2, axiom, ( ~relation(_u28) | ( _u33 != relation_dom(_u28)) | ~in(ordered_pair(_u30, _u22), _u28) | in(_u30, _u33) )).
% 0.18/0.51 cnf(d4_relat_1-3, axiom, ( ~relation(_u28) | ( _u34 = relation_dom(_u28)) | in(skolem4(_u28, _u34), _u34) | in(ordered_pair(skolem5(_u28, _u34), skolem6(_u28, _u34)), _u28) )).
% 0.18/0.51 cnf(d4_relat_1-4, axiom, ( ~relation(_u28) | ( _u34 = relation_dom(_u28)) | in(skolem4(_u28, _u34), _u34) | ~in(skolem5(_u28, _u34), _u34) )).
% 0.18/0.51 cnf(d4_relat_1-5, axiom, ( ~relation(_u28) | ( _u34 = relation_dom(_u28)) | ~in(ordered_pair(skolem4(_u28, _u34), _u24), _u28) | in(ordered_pair(skolem5(_u28, _u34), skolem6(_u28, _u34)), _u28) )).
% 0.18/0.51 cnf(d4_relat_1-6, axiom, ( ~relation(_u28) | ( _u34 = relation_dom(_u28)) | ~in(ordered_pair(skolem4(_u28, _u34), _u24), _u28) | ~in(skolem5(_u28, _u34), _u34) )).
% 0.18/0.51
% 0.18/0.51 % Formula: d5_relat_1 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(d5_relat_1-1, axiom, ( ~relation(_u42) | ( _u47 != relation_rng(_u42)) | ~in(_u43, _u47) | in(ordered_pair(skolem7(_u42, _u47, _u43), _u43), _u42) )).
% 0.18/0.51 cnf(d5_relat_1-2, axiom, ( ~relation(_u42) | ( _u47 != relation_rng(_u42)) | ~in(ordered_pair(_u36, _u44), _u42) | in(_u44, _u47) )).
% 0.18/0.51 cnf(d5_relat_1-3, axiom, ( ~relation(_u42) | ( _u48 = relation_rng(_u42)) | in(skolem8(_u42, _u48), _u48) | in(ordered_pair(skolem10(_u42, _u48), skolem9(_u42, _u48)), _u42) )).
% 0.18/0.51 cnf(d5_relat_1-4, axiom, ( ~relation(_u42) | ( _u48 = relation_rng(_u42)) | in(skolem8(_u42, _u48), _u48) | ~in(skolem9(_u42, _u48), _u48) )).
% 0.18/0.51 cnf(d5_relat_1-5, axiom, ( ~relation(_u42) | ( _u48 = relation_rng(_u42)) | ~in(ordered_pair(_u38, skolem8(_u42, _u48)), _u42) | in(ordered_pair(skolem10(_u42, _u48), skolem9(_u42, _u48)), _u42) )).
% 0.18/0.51 cnf(d5_relat_1-6, axiom, ( ~relation(_u42) | ( _u48 = relation_rng(_u42)) | ~in(ordered_pair(_u38, skolem8(_u42, _u48)), _u42) | ~in(skolem9(_u42, _u48), _u48) )).
% 0.18/0.51
% 0.18/0.51 % Formula: d5_tarski ( axiom ) converted to clauses:
% 0.18/0.51 cnf(d5_tarski-1, axiom, ( ( ordered_pair(_u50, _u49) = unordered_pair(unordered_pair(_u50, _u49), singleton(_u50))) )).
% 0.18/0.51
% 0.18/0.51 % Formula: d6_relat_1 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(d6_relat_1-1, axiom, ( ~relation(_u51) | ( relation_field(_u51) = set_union2(relation_dom(_u51), relation_rng(_u51))) )).
% 0.18/0.51
% 0.18/0.51 % Formula: dt_k1_relat_1 ( axiom ) converted to clauses:
% 0.18/0.51
% 0.18/0.51 % Formula: dt_k1_tarski ( axiom ) converted to clauses:
% 0.18/0.51
% 0.18/0.51 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 0.18/0.51
% 0.18/0.51 % Formula: dt_k2_relat_1 ( axiom ) converted to clauses:
% 0.18/0.51
% 0.18/0.51 % Formula: dt_k2_tarski ( axiom ) converted to clauses:
% 0.18/0.51
% 0.18/0.51 % Formula: dt_k2_xboole_0 ( axiom ) converted to clauses:
% 0.18/0.51
% 0.18/0.51 % Formula: dt_k3_relat_1 ( axiom ) converted to clauses:
% 0.18/0.51
% 0.18/0.51 % Formula: dt_k4_tarski ( axiom ) converted to clauses:
% 0.18/0.51
% 0.18/0.51 % Formula: dt_m1_subset_1 ( axiom ) converted to clauses:
% 0.18/0.51
% 0.18/0.51 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(existence_m1_subset_1-1, axiom, ( element(skolem11(_u53), _u53) )).
% 0.18/0.51
% 0.18/0.51 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 0.18/0.51
% 0.18/0.51 % Formula: fc1_zfmisc_1 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(fc1_zfmisc_1-1, axiom, ( ~empty(ordered_pair(_u55, _u54)) )).
% 0.18/0.51
% 0.18/0.51 % Formula: fc2_relat_1 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(fc2_relat_1-1, axiom, ( ~relation(_u57) | ~relation(_u56) | relation(set_union2(_u57, _u56)) )).
% 0.18/0.51
% 0.18/0.51 % Formula: fc2_subset_1 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(fc2_subset_1-1, axiom, ( ~empty(singleton(_u58)) )).
% 0.18/0.51
% 0.18/0.51 % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(fc2_xboole_0-1, axiom, ( empty(_u60) | ~empty(set_union2(_u60, _u59)) )).
% 0.18/0.51
% 0.18/0.51 % Formula: fc3_subset_1 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(fc3_subset_1-1, axiom, ( ~empty(unordered_pair(_u62, _u61)) )).
% 0.18/0.51
% 0.18/0.51 % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(fc3_xboole_0-1, axiom, ( empty(_u64) | ~empty(set_union2(_u63, _u64)) )).
% 0.18/0.51
% 0.18/0.51 % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u66, _u66) = _u66) )).
% 0.18/0.51
% 0.18/0.51 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(rc1_relat_1-1, axiom, ( empty(skolem12) )).
% 0.18/0.51 cnf(rc1_relat_1-2, axiom, ( relation(skolem12) )).
% 0.18/0.51
% 0.18/0.51 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(rc1_xboole_0-1, axiom, ( empty(skolem13) )).
% 0.18/0.51
% 0.18/0.51 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 0.18/0.51 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem14) )).
% 0.18/0.51
% 0.18/0.51 % Formula: t1_boole ( axiom ) converted to clauses:
% 0.18/0.51 cnf(t1_boole-1, axiom, ( ( set_union2(_u70, empty_set) = _u70) )).
% 0.18/0.51
% 0.18/0.51 % Formula: t1_subset ( axiom ) converted to clauses:
% 0.18/0.51 cnf(t1_subset-1, axiom, ( ~in(_u72, _u71) | element(_u72, _u71) )).
% 0.18/0.51
% 0.18/0.51 % Formula: t2_subset ( axiom ) converted to clauses:
% 0.18/0.51 cnf(t2_subset-1, axiom, ( ~element(_u74, _u73) | empty(_u73) | in(_u74, _u73) )).
% 0.18/0.51
% 0.18/0.51 % Formula: t30_relat_1 ( conjecture ) converted to clauses:
% 0.18/0.51 cnf(t30_relat_1-1, negated_conjecture, ( relation(skolem17) )).
% 0.18/0.51 cnf(t30_relat_1-2, negated_conjecture, ( in(ordered_pair(skolem15, skolem16), skolem17) )).
% 0.18/0.51 cnf(t30_relat_1-3, negated_conjecture, ( ~in(skolem15, relation_field(skolem17)) | ~in(skolem16, relation_field(skolem17)) )).
% 0.18/0.51
% 0.18/0.51 % Formula: t6_boole ( axiom ) converted to clauses:
% 0.18/0.51 cnf(t6_boole-1, axiom, ( ~empty(_u78) | ( _u78 = empty_set) )).
% 0.18/0.51
% 0.18/0.51 % Formula: t7_boole ( axiom ) converted to clauses:
% 0.18/0.51 cnf(t7_boole-1, axiom, ( ~in(_u80, _u79) | ~empty(_u79) )).
% 0.18/0.51
% 0.18/0.51 % Formula: t8_boole ( axiom ) converted to clauses:
% 0.18/0.51 cnf(t8_boole-1, axiom, ( ~empty(_u82) | ( _u82 = _u81) | ~empty(_u81) )).
% 0.18/0.51
% 0.18/0.51 % Problem matrix:
% 0.18/0.51 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.18/0.51 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.18/0.51 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.18/0.51 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 0.18/0.51 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 0.18/0.51 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( relation_dom(__eqx_0) = relation_dom(__eqy_0)) )).
% 0.18/0.51 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 0.18/0.51 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( relation_rng(__eqx_0) = relation_rng(__eqy_0)) )).
% 0.18/0.51 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 0.18/0.51 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( relation_field(__eqx_0) = relation_field(__eqy_0)) )).
% 0.18/0.51 cnf(matrix-10, 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)) )).
% 0.18/0.51 cnf(matrix-11, 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)) )).
% 0.18/0.51 cnf(matrix-12, 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)) )).
% 0.18/0.51 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 0.18/0.51 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem5(__eqx_0, __eqx_1) = skolem5(__eqy_0, __eqy_1)) )).
% 0.18/0.51 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem6(__eqx_0, __eqx_1) = skolem6(__eqy_0, __eqy_1)) )).
% 0.18/0.51 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem7(__eqx_0, __eqx_1, __eqx_2) = skolem7(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.18/0.51 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem8(__eqx_0, __eqx_1) = skolem8(__eqy_0, __eqy_1)) )).
% 0.18/0.51 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem9(__eqx_0, __eqx_1) = skolem9(__eqy_0, __eqy_1)) )).
% 0.18/0.51 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem10(__eqx_0, __eqx_1) = skolem10(__eqy_0, __eqy_1)) )).
% 0.18/0.51 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( skolem11(__eqx_0) = skolem11(__eqy_0)) )).
% 0.18/0.51 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 0.18/0.51 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 0.18/0.51 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 0.18/0.51 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 0.18/0.51 cnf(matrix-25, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.18/0.51 cnf(matrix-26, plain, ( ( unordered_pair(_u3, _u2) = unordered_pair(_u2, _u3)) )).
% 0.18/0.51 cnf(matrix-27, plain, ( ( set_union2(_u5, _u4) = set_union2(_u4, _u5)) )).
% 0.18/0.51 cnf(matrix-28, plain, ( ( _u15 != set_union2(_u19, _u17)) | ~in(_u11, _u15) | in(_u11, _u19) | in(_u11, _u17) )).
% 0.18/0.51 cnf(matrix-29, plain, ( ( _u15 != set_union2(_u19, _u17)) | in(_u12, _u15) | ~in(_u12, _u19) )).
% 0.18/0.51 cnf(matrix-30, plain, ( ( _u15 != set_union2(_u19, _u17)) | in(_u12, _u15) | ~in(_u12, _u17) )).
% 0.18/0.51 cnf(matrix-31, plain, ( ( _u16 = set_union2(_u20, _u18)) | in(skolem1(_u20, _u18, _u16), _u16) | in(skolem2(_u20, _u18, _u16), _u20) | in(skolem2(_u20, _u18, _u16), _u18) )).
% 0.18/0.51 cnf(matrix-32, plain, ( ( _u16 = set_union2(_u20, _u18)) | in(skolem1(_u20, _u18, _u16), _u16) | ~in(skolem2(_u20, _u18, _u16), _u16) )).
% 0.18/0.51 cnf(matrix-33, plain, ( ( _u16 = set_union2(_u20, _u18)) | in(skolem2(_u20, _u18, _u16), _u20) | in(skolem2(_u20, _u18, _u16), _u18) | ~in(skolem1(_u20, _u18, _u16), _u20) )).
% 0.18/0.51 cnf(matrix-34, plain, ( ( _u16 = set_union2(_u20, _u18)) | in(skolem2(_u20, _u18, _u16), _u20) | in(skolem2(_u20, _u18, _u16), _u18) | ~in(skolem1(_u20, _u18, _u16), _u18) )).
% 0.18/0.51 cnf(matrix-35, plain, ( ( _u16 = set_union2(_u20, _u18)) | ~in(skolem2(_u20, _u18, _u16), _u16) | ~in(skolem1(_u20, _u18, _u16), _u20) )).
% 0.18/0.51 cnf(matrix-36, plain, ( ( _u16 = set_union2(_u20, _u18)) | ~in(skolem2(_u20, _u18, _u16), _u16) | ~in(skolem1(_u20, _u18, _u16), _u18) )).
% 0.18/0.51 cnf(matrix-37, plain, ( ~relation(_u28) | ( _u33 != relation_dom(_u28)) | ~in(_u29, _u33) | in(ordered_pair(_u29, skolem3(_u28, _u33, _u29)), _u28) )).
% 0.18/0.51 cnf(matrix-38, plain, ( ~relation(_u28) | ( _u33 != relation_dom(_u28)) | ~in(ordered_pair(_u30, _u22), _u28) | in(_u30, _u33) )).
% 0.18/0.51 cnf(matrix-39, plain, ( ~relation(_u28) | ( _u34 = relation_dom(_u28)) | in(skolem4(_u28, _u34), _u34) | in(ordered_pair(skolem5(_u28, _u34), skolem6(_u28, _u34)), _u28) )).
% 0.18/0.51 cnf(matrix-40, plain, ( ~relation(_u28) | ( _u34 = relation_dom(_u28)) | in(skolem4(_u28, _u34), _u34) | ~in(skolem5(_u28, _u34), _u34) )).
% 0.18/0.51 cnf(matrix-41, plain, ( ~relation(_u28) | ( _u34 = relation_dom(_u28)) | ~in(ordered_pair(skolem4(_u28, _u34), _u24), _u28) | in(ordered_pair(skolem5(_u28, _u34), skolem6(_u28, _u34)), _u28) )).
% 0.18/0.51 cnf(matrix-42, plain, ( ~relation(_u28) | ( _u34 = relation_dom(_u28)) | ~in(ordered_pair(skolem4(_u28, _u34), _u24), _u28) | ~in(skolem5(_u28, _u34), _u34) )).
% 0.18/0.51 cnf(matrix-43, plain, ( ~relation(_u42) | ( _u47 != relation_rng(_u42)) | ~in(_u43, _u47) | in(ordered_pair(skolem7(_u42, _u47, _u43), _u43), _u42) )).
% 0.18/0.51 cnf(matrix-44, plain, ( ~relation(_u42) | ( _u47 != relation_rng(_u42)) | ~in(ordered_pair(_u36, _u44), _u42) | in(_u44, _u47) )).
% 0.18/0.51 cnf(matrix-45, plain, ( ~relation(_u42) | ( _u48 = relation_rng(_u42)) | in(skolem8(_u42, _u48), _u48) | in(ordered_pair(skolem10(_u42, _u48), skolem9(_u42, _u48)), _u42) )).
% 0.18/0.51 cnf(matrix-46, plain, ( ~relation(_u42) | ( _u48 = relation_rng(_u42)) | in(skolem8(_u42, _u48), _u48) | ~in(skolem9(_u42, _u48), _u48) )).
% 0.18/0.51 cnf(matrix-47, plain, ( ~relation(_u42) | ( _u48 = relation_rng(_u42)) | ~in(ordered_pair(_u38, skolem8(_u42, _u48)), _u42) | in(ordered_pair(skolem10(_u42, _u48), skolem9(_u42, _u48)), _u42) )).
% 0.18/0.51 cnf(matrix-48, plain, ( ~relation(_u42) | ( _u48 = relation_rng(_u42)) | ~in(ordered_pair(_u38, skolem8(_u42, _u48)), _u42) | ~in(skolem9(_u42, _u48), _u48) )).
% 0.18/0.51 cnf(matrix-49, plain, ( ( ordered_pair(_u50, _u49) = unordered_pair(unordered_pair(_u50, _u49), singleton(_u50))) )).
% 0.18/0.51 cnf(matrix-50, plain, ( ~relation(_u51) | ( relation_field(_u51) = set_union2(relation_dom(_u51), relation_rng(_u51))) )).
% 0.18/0.51 cnf(matrix-51, plain, ( element(skolem11(_u53), _u53) )).
% 0.18/0.51 cnf(matrix-52, plain, ( empty(empty_set) )).
% 0.18/0.51 cnf(matrix-53, plain, ( ~empty(ordered_pair(_u55, _u54)) )).
% 0.18/0.51 cnf(matrix-54, plain, ( ~relation(_u57) | ~relation(_u56) | relation(set_union2(_u57, _u56)) )).
% 0.18/0.51 cnf(matrix-55, plain, ( ~empty(singleton(_u58)) )).
% 0.18/0.51 cnf(matrix-56, plain, ( empty(_u60) | ~empty(set_union2(_u60, _u59)) )).
% 0.18/0.51 cnf(matrix-57, plain, ( ~empty(unordered_pair(_u62, _u61)) )).
% 0.18/0.51 cnf(matrix-58, plain, ( empty(_u64) | ~empty(set_union2(_u63, _u64)) )).
% 0.18/0.51 cnf(matrix-59, plain, ( ( set_union2(_u66, _u66) = _u66) )).
% 0.18/0.51 cnf(matrix-60, plain, ( empty(skolem12) )).
% 0.18/0.51 cnf(matrix-61, plain, ( relation(skolem12) )).
% 0.18/0.51 cnf(matrix-62, plain, ( empty(skolem13) )).
% 0.18/0.51 cnf(matrix-63, plain, ( ~empty(skolem14) )).
% 0.18/0.51 cnf(matrix-64, plain, ( ( set_union2(_u70, empty_set) = _u70) )).
% 0.18/0.51 cnf(matrix-65, plain, ( ~in(_u72, _u71) | element(_u72, _u71) )).
% 0.18/0.51 cnf(matrix-66, plain, ( ~element(_u74, _u73) | empty(_u73) | in(_u74, _u73) )).
% 0.18/0.51 cnf(matrix-67, plain, ( relation(skolem17) )).
% 0.18/0.51 cnf(matrix-68, plain, ( in(ordered_pair(skolem15, skolem16), skolem17) )).
% 0.18/0.51 cnf(matrix-69, plain, ( ~in(skolem15, relation_field(skolem17)) | ~in(skolem16, relation_field(skolem17)) )).
% 0.18/0.51 cnf(matrix-70, plain, ( ~empty(_u78) | ( _u78 = empty_set) )).
% 0.18/0.51 cnf(matrix-71, plain, ( ~in(_u80, _u79) | ~empty(_u79) )).
% 0.18/0.51 cnf(matrix-72, plain, ( ~empty(_u82) | ( _u82 = _u81) | ~empty(_u81) )).
% 0.18/0.51
% 0.18/0.51 % Proof stack:
% 0.18/0.51 cnf(proof-stack, plain,
% 0.18/0.51 proof_stack(
% 0.18/0.51 start(69),
% 0.18/0.51 left_branch(0, 29, 1, 2),
% 0.18/0.51 left_branch(0, 50, 1, 3),
% 0.18/0.51 left_branch(0, 67, 0, 4),
% 0.18/0.51 right_branch(4),
% 0.18/0.51 right_branch(3),
% 0.18/0.51 left_branch(0, 38, 3, 4),
% 0.18/0.51 left_branch(0, 67, 0, 5),
% 0.18/0.51 right_branch(5),
% 0.18/0.51 left_branch(0, 68, 0, 6),
% 0.18/0.51 right_branch(6),
% 0.18/0.51 left_branch(0, 0, 0, 7),
% 0.18/0.51 right_branch(7),
% 0.18/0.51 right_branch(4),
% 0.18/0.51 right_branch(2),
% 0.18/0.51 left_branch(0, 30, 1, 3),
% 0.18/0.51 left_branch(0, 50, 1, 4),
% 0.18/0.51 left_branch(0, 67, 0, 5),
% 0.18/0.51 right_branch(5),
% 0.18/0.51 right_branch(4),
% 0.18/0.51 left_branch(0, 44, 3, 5),
% 0.18/0.51 left_branch(0, 67, 0, 6),
% 0.18/0.51 right_branch(6),
% 0.18/0.51 left_branch(0, 68, 0, 7),
% 0.18/0.51 right_branch(7),
% 0.18/0.51 left_branch(0, 0, 0, 8),
% 0.18/0.51 right_branch(8),
% 0.18/0.51 right_branch(5),
% 0.18/0.51 right_branch(3)
% 0.18/0.51 )).
% 0.18/0.51 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------