TSTP Solution File: SEU238+3 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU238+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n003.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 275.66s 275.82s
% Output : Proof 275.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU238+3 : TPTP v8.1.2. Released v3.2.0.
% 0.04/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n003.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 14:33:34 EDT 2024
% 0.13/0.34 % CPUTime :
% 275.66/275.82 % SZS status Theorem for theBenchmark
% 275.66/275.82 % SZS output start Proof for theBenchmark
% 275.66/275.82
% 275.66/275.82 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 275.66/275.82 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 275.66/275.82
% 275.66/275.82 % Formula: antisymmetry_r2_xboole_0 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(antisymmetry_r2_xboole_0-1, axiom, ( ~proper_subset(_u3, _u2) | ~proper_subset(_u2, _u3) )).
% 275.66/275.82
% 275.66/275.82 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(cc1_funct_1-1, axiom, ( ~empty(_u4) | function(_u4) )).
% 275.66/275.82
% 275.66/275.82 % Formula: cc1_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(cc1_ordinal1-1, axiom, ( ~ordinal(_u5) | epsilon_transitive(_u5) )).
% 275.66/275.82 cnf(cc1_ordinal1-2, axiom, ( ~ordinal(_u5) | epsilon_connected(_u5) )).
% 275.66/275.82
% 275.66/275.82 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(cc1_relat_1-1, axiom, ( ~empty(_u6) | relation(_u6) )).
% 275.66/275.82
% 275.66/275.82 % Formula: cc2_funct_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(cc2_funct_1-1, axiom, ( ~relation(_u7) | ~empty(_u7) | ~function(_u7) | one_to_one(_u7) )).
% 275.66/275.82
% 275.66/275.82 % Formula: cc2_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(cc2_ordinal1-1, axiom, ( ~epsilon_transitive(_u8) | ~epsilon_connected(_u8) | ordinal(_u8) )).
% 275.66/275.82
% 275.66/275.82 % Formula: cc3_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(cc3_ordinal1-1, axiom, ( ~empty(_u9) | epsilon_transitive(_u9) )).
% 275.66/275.82 cnf(cc3_ordinal1-2, axiom, ( ~empty(_u9) | epsilon_connected(_u9) )).
% 275.66/275.82 cnf(cc3_ordinal1-3, axiom, ( ~empty(_u9) | ordinal(_u9) )).
% 275.66/275.82
% 275.66/275.82 % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u11, _u10) = set_union2(_u10, _u11)) )).
% 275.66/275.82
% 275.66/275.82 % Formula: connectedness_r1_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(connectedness_r1_ordinal1-1, axiom, ( ~ordinal(_u13) | ~ordinal(_u12) | ordinal_subset(_u13, _u12) | ordinal_subset(_u12, _u13) )).
% 275.66/275.82
% 275.66/275.82 % Formula: d1_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(d1_ordinal1-1, axiom, ( ( succ(_u14) = set_union2(_u14, singleton(_u14))) )).
% 275.66/275.82
% 275.66/275.82 % Formula: d8_xboole_0 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(d8_xboole_0-1, axiom, ( ~proper_subset(_u19, _u17) | subset(_u19, _u17) )).
% 275.66/275.82 cnf(d8_xboole_0-2, axiom, ( ~proper_subset(_u19, _u17) | ( _u19 != _u17) )).
% 275.66/275.82 cnf(d8_xboole_0-3, axiom, ( ~subset(_u20, _u18) | ( _u20 = _u18) | proper_subset(_u20, _u18) )).
% 275.66/275.82
% 275.66/275.82 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(existence_m1_subset_1-1, axiom, ( element(skolem1(_u22), _u22) )).
% 275.66/275.82
% 275.66/275.82 % Formula: fc12_relat_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(fc12_relat_1-1, axiom, ( empty(empty_set) )).
% 275.66/275.82 cnf(fc12_relat_1-2, axiom, ( relation(empty_set) )).
% 275.66/275.82 cnf(fc12_relat_1-3, axiom, ( relation_empty_yielding(empty_set) )).
% 275.66/275.82
% 275.66/275.82 % Formula: fc1_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(fc1_ordinal1-1, axiom, ( ~empty(succ(_u23)) )).
% 275.66/275.82
% 275.66/275.82 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 275.66/275.82
% 275.66/275.82 % Formula: fc2_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(fc2_ordinal1-1, axiom, ( relation(empty_set) )).
% 275.66/275.82 cnf(fc2_ordinal1-2, axiom, ( relation_empty_yielding(empty_set) )).
% 275.66/275.82 cnf(fc2_ordinal1-3, axiom, ( function(empty_set) )).
% 275.66/275.82 cnf(fc2_ordinal1-4, axiom, ( one_to_one(empty_set) )).
% 275.66/275.82 cnf(fc2_ordinal1-5, axiom, ( empty(empty_set) )).
% 275.66/275.82 cnf(fc2_ordinal1-6, axiom, ( epsilon_transitive(empty_set) )).
% 275.66/275.82 cnf(fc2_ordinal1-7, axiom, ( epsilon_connected(empty_set) )).
% 275.66/275.82 cnf(fc2_ordinal1-8, axiom, ( ordinal(empty_set) )).
% 275.66/275.82
% 275.66/275.82 % Formula: fc2_relat_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(fc2_relat_1-1, axiom, ( ~relation(_u25) | ~relation(_u24) | relation(set_union2(_u25, _u24)) )).
% 275.66/275.82
% 275.66/275.82 % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(fc2_xboole_0-1, axiom, ( empty(_u27) | ~empty(set_union2(_u27, _u26)) )).
% 275.66/275.82
% 275.66/275.82 % Formula: fc3_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(fc3_ordinal1-1, axiom, ( ~ordinal(_u28) | ~empty(succ(_u28)) )).
% 275.66/275.82 cnf(fc3_ordinal1-2, axiom, ( ~ordinal(_u28) | epsilon_transitive(succ(_u28)) )).
% 275.66/275.82 cnf(fc3_ordinal1-3, axiom, ( ~ordinal(_u28) | epsilon_connected(succ(_u28)) )).
% 275.66/275.82 cnf(fc3_ordinal1-4, axiom, ( ~ordinal(_u28) | ordinal(succ(_u28)) )).
% 275.66/275.82
% 275.66/275.82 % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(fc3_xboole_0-1, axiom, ( empty(_u30) | ~empty(set_union2(_u29, _u30)) )).
% 275.66/275.82
% 275.66/275.82 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 275.66/275.82 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 275.66/275.82
% 275.66/275.82 % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u32, _u32) = _u32) )).
% 275.66/275.82
% 275.66/275.82 % Formula: irreflexivity_r2_xboole_0 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(irreflexivity_r2_xboole_0-1, axiom, ( ~proper_subset(_u34, _u34) )).
% 275.66/275.82
% 275.66/275.82 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(rc1_funct_1-1, axiom, ( relation(skolem2) )).
% 275.66/275.82 cnf(rc1_funct_1-2, axiom, ( function(skolem2) )).
% 275.66/275.82
% 275.66/275.82 % Formula: rc1_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(rc1_ordinal1-1, axiom, ( epsilon_transitive(skolem3) )).
% 275.66/275.82 cnf(rc1_ordinal1-2, axiom, ( epsilon_connected(skolem3) )).
% 275.66/275.82 cnf(rc1_ordinal1-3, axiom, ( ordinal(skolem3) )).
% 275.66/275.82
% 275.66/275.82 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(rc1_relat_1-1, axiom, ( empty(skolem4) )).
% 275.66/275.82 cnf(rc1_relat_1-2, axiom, ( relation(skolem4) )).
% 275.66/275.82
% 275.66/275.82 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(rc1_xboole_0-1, axiom, ( empty(skolem5) )).
% 275.66/275.82
% 275.66/275.82 % Formula: rc2_funct_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(rc2_funct_1-1, axiom, ( relation(skolem6) )).
% 275.66/275.82 cnf(rc2_funct_1-2, axiom, ( empty(skolem6) )).
% 275.66/275.82 cnf(rc2_funct_1-3, axiom, ( function(skolem6) )).
% 275.66/275.82
% 275.66/275.82 % Formula: rc2_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(rc2_ordinal1-1, axiom, ( relation(skolem7) )).
% 275.66/275.82 cnf(rc2_ordinal1-2, axiom, ( function(skolem7) )).
% 275.66/275.82 cnf(rc2_ordinal1-3, axiom, ( one_to_one(skolem7) )).
% 275.66/275.82 cnf(rc2_ordinal1-4, axiom, ( empty(skolem7) )).
% 275.66/275.82 cnf(rc2_ordinal1-5, axiom, ( epsilon_transitive(skolem7) )).
% 275.66/275.82 cnf(rc2_ordinal1-6, axiom, ( epsilon_connected(skolem7) )).
% 275.66/275.82 cnf(rc2_ordinal1-7, axiom, ( ordinal(skolem7) )).
% 275.66/275.82
% 275.66/275.82 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem8) )).
% 275.66/275.82 cnf(rc2_relat_1-2, axiom, ( relation(skolem8) )).
% 275.66/275.82
% 275.66/275.82 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem9) )).
% 275.66/275.82
% 275.66/275.82 % Formula: rc3_funct_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(rc3_funct_1-1, axiom, ( relation(skolem10) )).
% 275.66/275.82 cnf(rc3_funct_1-2, axiom, ( function(skolem10) )).
% 275.66/275.82 cnf(rc3_funct_1-3, axiom, ( one_to_one(skolem10) )).
% 275.66/275.82
% 275.66/275.82 % Formula: rc3_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(rc3_ordinal1-1, axiom, ( ~empty(skolem11) )).
% 275.66/275.82 cnf(rc3_ordinal1-2, axiom, ( epsilon_transitive(skolem11) )).
% 275.66/275.82 cnf(rc3_ordinal1-3, axiom, ( epsilon_connected(skolem11) )).
% 275.66/275.82 cnf(rc3_ordinal1-4, axiom, ( ordinal(skolem11) )).
% 275.66/275.82
% 275.66/275.82 % Formula: rc3_relat_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(rc3_relat_1-1, axiom, ( relation(skolem12) )).
% 275.66/275.82 cnf(rc3_relat_1-2, axiom, ( relation_empty_yielding(skolem12) )).
% 275.66/275.82
% 275.66/275.82 % Formula: rc4_funct_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(rc4_funct_1-1, axiom, ( relation(skolem13) )).
% 275.66/275.82 cnf(rc4_funct_1-2, axiom, ( relation_empty_yielding(skolem13) )).
% 275.66/275.82 cnf(rc4_funct_1-3, axiom, ( function(skolem13) )).
% 275.66/275.82
% 275.66/275.82 % Formula: rc5_funct_1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(rc5_funct_1-1, axiom, ( relation(skolem14) )).
% 275.66/275.82 cnf(rc5_funct_1-2, axiom, ( relation_non_empty(skolem14) )).
% 275.66/275.82 cnf(rc5_funct_1-3, axiom, ( function(skolem14) )).
% 275.66/275.82
% 275.66/275.82 % Formula: redefinition_r1_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(redefinition_r1_ordinal1-1, axiom, ( ~ordinal(_u49) | ~ordinal(_u48) | ~ordinal_subset(_u49, _u48) | subset(_u49, _u48) )).
% 275.66/275.82 cnf(redefinition_r1_ordinal1-2, axiom, ( ~ordinal(_u49) | ~ordinal(_u48) | ~subset(_u49, _u48) | ordinal_subset(_u49, _u48) )).
% 275.66/275.82
% 275.66/275.82 % Formula: reflexivity_r1_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(reflexivity_r1_ordinal1-1, axiom, ( ordinal_subset(_u51, _u51) | ~ordinal(_u51) | ~ordinal(_u50) )).
% 275.66/275.82
% 275.66/275.82 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 275.66/275.82 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u53, _u53) )).
% 275.66/275.82
% 275.66/275.82 % Formula: t10_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(t10_ordinal1-1, axiom, ( in(_u54, succ(_u54)) )).
% 275.66/275.82
% 275.66/275.82 % Formula: t1_boole ( axiom ) converted to clauses:
% 275.66/275.82 cnf(t1_boole-1, axiom, ( ( set_union2(_u55, empty_set) = _u55) )).
% 275.66/275.82
% 275.66/275.82 % Formula: t1_subset ( axiom ) converted to clauses:
% 275.66/275.82 cnf(t1_subset-1, axiom, ( ~in(_u57, _u56) | element(_u57, _u56) )).
% 275.66/275.82
% 275.66/275.82 % Formula: t21_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(t21_ordinal1-1, axiom, ( ~epsilon_transitive(_u59) | ~ordinal(_u58) | ~proper_subset(_u59, _u58) | in(_u59, _u58) )).
% 275.66/275.82
% 275.66/275.82 % Formula: t2_subset ( axiom ) converted to clauses:
% 275.66/275.82 cnf(t2_subset-1, axiom, ( ~element(_u61, _u60) | empty(_u60) | in(_u61, _u60) )).
% 275.66/275.82
% 275.66/275.82 % Formula: t33_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(t33_ordinal1-1, axiom, ( ~ordinal(_u63) | ~ordinal(_u62) | ~in(_u63, _u62) | ordinal_subset(succ(_u63), _u62) )).
% 275.66/275.82 cnf(t33_ordinal1-2, axiom, ( ~ordinal(_u63) | ~ordinal(_u62) | ~ordinal_subset(succ(_u63), _u62) | in(_u63, _u62) )).
% 275.66/275.82
% 275.66/275.82 % Formula: t3_subset ( axiom ) converted to clauses:
% 275.66/275.82 cnf(t3_subset-1, axiom, ( ~element(_u68, powerset(_u66)) | subset(_u68, _u66) )).
% 275.66/275.82 cnf(t3_subset-2, axiom, ( ~subset(_u69, _u67) | element(_u69, powerset(_u67)) )).
% 275.66/275.82
% 275.66/275.82 % Formula: t41_ordinal1 ( axiom ) converted to clauses:
% 275.66/275.82 cnf(t41_ordinal1-1, axiom, ( ~ordinal(_u72) | ~being_limit_ordinal(_u72) | ~ordinal(_u70) | ~in(_u70, _u72) | in(succ(_u70), _u72) )).
% 275.66/275.82 cnf(t41_ordinal1-2, axiom, ( ~ordinal(_u72) | being_limit_ordinal(_u72) | ordinal(skolem15(_u72)) )).
% 275.66/275.82 cnf(t41_ordinal1-3, axiom, ( ~ordinal(_u72) | being_limit_ordinal(_u72) | in(skolem15(_u72), _u72) )).
% 275.66/275.82 cnf(t41_ordinal1-4, axiom, ( ~ordinal(_u72) | being_limit_ordinal(_u72) | ~in(succ(skolem15(_u72)), _u72) )).
% 275.66/275.82
% 275.66/275.82 % Formula: t42_ordinal1 ( conjecture ) (definitionally) converted to clauses:
% 275.66/275.82 cnf(t42_ordinal1-1, negated_conjecture, ( ordinal(skolem16) )).
% 275.66/275.82 cnf(t42_ordinal1-2, negated_conjecture, ( ~_def0(_u73) | ~_def1 )).
% 275.66/275.82 cnf(t42_ordinal1-3, negated_conjecture, ( _def0(_u73) | ~being_limit_ordinal(skolem16) )).
% 275.66/275.82 cnf(t42_ordinal1-4, negated_conjecture, ( _def0(_u73) | ~ordinal(_u73) | ( skolem16 != succ(_u73)) )).
% 275.66/275.82 cnf(t42_ordinal1-5, negated_conjecture, ( _def1 | ordinal(skolem17) )).
% 275.66/275.82 cnf(t42_ordinal1-6, negated_conjecture, ( _def1 | ( skolem16 = succ(skolem17)) )).
% 275.66/275.82 cnf(t42_ordinal1-7, negated_conjecture, ( _def1 | being_limit_ordinal(skolem16) )).
% 275.66/275.82
% 275.66/275.82 % Formula: t4_subset ( axiom ) converted to clauses:
% 275.66/275.82 cnf(t4_subset-1, axiom, ( ~in(_u78, _u77) | ~element(_u77, powerset(_u76)) | element(_u78, _u76) )).
% 275.66/275.82
% 275.66/275.82 % Formula: t5_subset ( axiom ) converted to clauses:
% 275.66/275.82 cnf(t5_subset-1, axiom, ( ~in(_u81, _u80) | ~element(_u80, powerset(_u79)) | ~empty(_u79) )).
% 275.66/275.82
% 275.66/275.82 % Formula: t6_boole ( axiom ) converted to clauses:
% 275.66/275.82 cnf(t6_boole-1, axiom, ( ~empty(_u82) | ( _u82 = empty_set) )).
% 275.66/275.82
% 275.66/275.82 % Formula: t7_boole ( axiom ) converted to clauses:
% 275.66/275.82 cnf(t7_boole-1, axiom, ( ~in(_u84, _u83) | ~empty(_u83) )).
% 275.66/275.82
% 275.66/275.82 % Formula: t8_boole ( axiom ) converted to clauses:
% 275.66/275.82 cnf(t8_boole-1, axiom, ( ~empty(_u86) | ( _u86 = _u85) | ~empty(_u85) )).
% 275.66/275.82
% 275.66/275.82 % Problem matrix:
% 275.66/275.82 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 275.66/275.82 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 275.66/275.82 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 275.66/275.82 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 275.66/275.82 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( succ(__eqx_0) = succ(__eqy_0)) )).
% 275.66/275.82 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 275.66/275.82 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 275.66/275.82 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 275.66/275.82 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( skolem15(__eqx_0) = skolem15(__eqy_0)) )).
% 275.66/275.82 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 275.66/275.82 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~proper_subset(__eqx_0, __eqx_1) | proper_subset(__eqy_0, __eqy_1) )).
% 275.66/275.82 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 275.66/275.82 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 275.66/275.82 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ~ordinal(__eqx_0) | ordinal(__eqy_0) )).
% 275.66/275.82 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~epsilon_transitive(__eqx_0) | epsilon_transitive(__eqy_0) )).
% 275.66/275.82 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~epsilon_connected(__eqx_0) | epsilon_connected(__eqy_0) )).
% 275.66/275.82 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 275.66/275.82 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 275.66/275.82 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~ordinal_subset(__eqx_0, __eqx_1) | ordinal_subset(__eqy_0, __eqy_1) )).
% 275.66/275.82 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 275.66/275.82 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 275.66/275.82 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ~relation_empty_yielding(__eqx_0) | relation_empty_yielding(__eqy_0) )).
% 275.66/275.82 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ~relation_non_empty(__eqx_0) | relation_non_empty(__eqy_0) )).
% 275.66/275.82 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ~being_limit_ordinal(__eqx_0) | being_limit_ordinal(__eqy_0) )).
% 275.66/275.82 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ~_def0(__eqx_0) | _def0(__eqy_0) )).
% 275.66/275.82 cnf(matrix-25, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 275.66/275.82 cnf(matrix-26, plain, ( ~proper_subset(_u3, _u2) | ~proper_subset(_u2, _u3) )).
% 275.66/275.82 cnf(matrix-27, plain, ( ~empty(_u4) | function(_u4) )).
% 275.66/275.82 cnf(matrix-28, plain, ( ~ordinal(_u5) | epsilon_transitive(_u5) )).
% 275.66/275.82 cnf(matrix-29, plain, ( ~ordinal(_u5) | epsilon_connected(_u5) )).
% 275.66/275.82 cnf(matrix-30, plain, ( ~empty(_u6) | relation(_u6) )).
% 275.66/275.82 cnf(matrix-31, plain, ( ~relation(_u7) | ~empty(_u7) | ~function(_u7) | one_to_one(_u7) )).
% 275.66/275.82 cnf(matrix-32, plain, ( ~epsilon_transitive(_u8) | ~epsilon_connected(_u8) | ordinal(_u8) )).
% 275.66/275.82 cnf(matrix-33, plain, ( ~empty(_u9) | epsilon_transitive(_u9) )).
% 275.66/275.82 cnf(matrix-34, plain, ( ~empty(_u9) | epsilon_connected(_u9) )).
% 275.66/275.82 cnf(matrix-35, plain, ( ~empty(_u9) | ordinal(_u9) )).
% 275.66/275.82 cnf(matrix-36, plain, ( ( set_union2(_u11, _u10) = set_union2(_u10, _u11)) )).
% 275.66/275.82 cnf(matrix-37, plain, ( ~ordinal(_u13) | ~ordinal(_u12) | ordinal_subset(_u13, _u12) | ordinal_subset(_u12, _u13) )).
% 275.66/275.82 cnf(matrix-38, plain, ( ( succ(_u14) = set_union2(_u14, singleton(_u14))) )).
% 275.66/275.82 cnf(matrix-39, plain, ( ~proper_subset(_u19, _u17) | subset(_u19, _u17) )).
% 275.66/275.82 cnf(matrix-40, plain, ( ~proper_subset(_u19, _u17) | ( _u19 != _u17) )).
% 275.66/275.82 cnf(matrix-41, plain, ( ~subset(_u20, _u18) | ( _u20 = _u18) | proper_subset(_u20, _u18) )).
% 275.66/275.82 cnf(matrix-42, plain, ( element(skolem1(_u22), _u22) )).
% 275.66/275.82 cnf(matrix-43, plain, ( empty(empty_set) )).
% 275.66/275.82 cnf(matrix-44, plain, ( relation(empty_set) )).
% 275.66/275.82 cnf(matrix-45, plain, ( relation_empty_yielding(empty_set) )).
% 275.66/275.82 cnf(matrix-46, plain, ( ~empty(succ(_u23)) )).
% 275.66/275.82 cnf(matrix-47, plain, ( empty(empty_set) )).
% 275.66/275.82 cnf(matrix-48, plain, ( relation(empty_set) )).
% 275.66/275.82 cnf(matrix-49, plain, ( relation_empty_yielding(empty_set) )).
% 275.66/275.82 cnf(matrix-50, plain, ( function(empty_set) )).
% 275.66/275.82 cnf(matrix-51, plain, ( one_to_one(empty_set) )).
% 275.66/275.82 cnf(matrix-52, plain, ( empty(empty_set) )).
% 275.66/275.82 cnf(matrix-53, plain, ( epsilon_transitive(empty_set) )).
% 275.66/275.82 cnf(matrix-54, plain, ( epsilon_connected(empty_set) )).
% 275.66/275.82 cnf(matrix-55, plain, ( ordinal(empty_set) )).
% 275.66/275.82 cnf(matrix-56, plain, ( ~relation(_u25) | ~relation(_u24) | relation(set_union2(_u25, _u24)) )).
% 275.66/275.82 cnf(matrix-57, plain, ( empty(_u27) | ~empty(set_union2(_u27, _u26)) )).
% 275.66/275.82 cnf(matrix-58, plain, ( ~ordinal(_u28) | ~empty(succ(_u28)) )).
% 275.66/275.82 cnf(matrix-59, plain, ( ~ordinal(_u28) | epsilon_transitive(succ(_u28)) )).
% 275.66/275.82 cnf(matrix-60, plain, ( ~ordinal(_u28) | epsilon_connected(succ(_u28)) )).
% 275.66/275.82 cnf(matrix-61, plain, ( ~ordinal(_u28) | ordinal(succ(_u28)) )).
% 275.66/275.82 cnf(matrix-62, plain, ( empty(_u30) | ~empty(set_union2(_u29, _u30)) )).
% 275.66/275.82 cnf(matrix-63, plain, ( empty(empty_set) )).
% 275.66/275.82 cnf(matrix-64, plain, ( relation(empty_set) )).
% 275.66/275.82 cnf(matrix-65, plain, ( ( set_union2(_u32, _u32) = _u32) )).
% 275.66/275.82 cnf(matrix-66, plain, ( ~proper_subset(_u34, _u34) )).
% 275.66/275.82 cnf(matrix-67, plain, ( relation(skolem2) )).
% 275.66/275.82 cnf(matrix-68, plain, ( function(skolem2) )).
% 275.66/275.82 cnf(matrix-69, plain, ( epsilon_transitive(skolem3) )).
% 275.66/275.82 cnf(matrix-70, plain, ( epsilon_connected(skolem3) )).
% 275.66/275.82 cnf(matrix-71, plain, ( ordinal(skolem3) )).
% 275.66/275.82 cnf(matrix-72, plain, ( empty(skolem4) )).
% 275.66/275.82 cnf(matrix-73, plain, ( relation(skolem4) )).
% 275.66/275.82 cnf(matrix-74, plain, ( empty(skolem5) )).
% 275.66/275.82 cnf(matrix-75, plain, ( relation(skolem6) )).
% 275.66/275.82 cnf(matrix-76, plain, ( empty(skolem6) )).
% 275.66/275.82 cnf(matrix-77, plain, ( function(skolem6) )).
% 275.66/275.82 cnf(matrix-78, plain, ( relation(skolem7) )).
% 275.66/275.82 cnf(matrix-79, plain, ( function(skolem7) )).
% 275.66/275.82 cnf(matrix-80, plain, ( one_to_one(skolem7) )).
% 275.66/275.82 cnf(matrix-81, plain, ( empty(skolem7) )).
% 275.66/275.82 cnf(matrix-82, plain, ( epsilon_transitive(skolem7) )).
% 275.66/275.82 cnf(matrix-83, plain, ( epsilon_connected(skolem7) )).
% 275.66/275.82 cnf(matrix-84, plain, ( ordinal(skolem7) )).
% 275.66/275.82 cnf(matrix-85, plain, ( ~empty(skolem8) )).
% 275.66/275.82 cnf(matrix-86, plain, ( relation(skolem8) )).
% 275.66/275.82 cnf(matrix-87, plain, ( ~empty(skolem9) )).
% 275.66/275.82 cnf(matrix-88, plain, ( relation(skolem10) )).
% 275.66/275.82 cnf(matrix-89, plain, ( function(skolem10) )).
% 275.66/275.82 cnf(matrix-90, plain, ( one_to_one(skolem10) )).
% 275.66/275.82 cnf(matrix-91, plain, ( ~empty(skolem11) )).
% 275.66/275.82 cnf(matrix-92, plain, ( epsilon_transitive(skolem11) )).
% 275.66/275.82 cnf(matrix-93, plain, ( epsilon_connected(skolem11) )).
% 275.66/275.82 cnf(matrix-94, plain, ( ordinal(skolem11) )).
% 275.66/275.82 cnf(matrix-95, plain, ( relation(skolem12) )).
% 275.66/275.82 cnf(matrix-96, plain, ( relation_empty_yielding(skolem12) )).
% 275.66/275.82 cnf(matrix-97, plain, ( relation(skolem13) )).
% 275.66/275.82 cnf(matrix-98, plain, ( relation_empty_yielding(skolem13) )).
% 275.66/275.82 cnf(matrix-99, plain, ( function(skolem13) )).
% 275.66/275.82 cnf(matrix-100, plain, ( relation(skolem14) )).
% 275.66/275.82 cnf(matrix-101, plain, ( relation_non_empty(skolem14) )).
% 275.66/275.82 cnf(matrix-102, plain, ( function(skolem14) )).
% 275.66/275.82 cnf(matrix-103, plain, ( ~ordinal(_u49) | ~ordinal(_u48) | ~ordinal_subset(_u49, _u48) | subset(_u49, _u48) )).
% 275.66/275.82 cnf(matrix-104, plain, ( ~ordinal(_u49) | ~ordinal(_u48) | ~subset(_u49, _u48) | ordinal_subset(_u49, _u48) )).
% 275.66/275.82 cnf(matrix-105, plain, ( ordinal_subset(_u51, _u51) | ~ordinal(_u51) | ~ordinal(_u50) )).
% 275.66/275.82 cnf(matrix-106, plain, ( subset(_u53, _u53) )).
% 275.66/275.82 cnf(matrix-107, plain, ( in(_u54, succ(_u54)) )).
% 275.66/275.82 cnf(matrix-108, plain, ( ( set_union2(_u55, empty_set) = _u55) )).
% 275.66/275.82 cnf(matrix-109, plain, ( ~in(_u57, _u56) | element(_u57, _u56) )).
% 275.66/275.82 cnf(matrix-110, plain, ( ~epsilon_transitive(_u59) | ~ordinal(_u58) | ~proper_subset(_u59, _u58) | in(_u59, _u58) )).
% 275.66/275.82 cnf(matrix-111, plain, ( ~element(_u61, _u60) | empty(_u60) | in(_u61, _u60) )).
% 275.66/275.82 cnf(matrix-112, plain, ( ~ordinal(_u63) | ~ordinal(_u62) | ~in(_u63, _u62) | ordinal_subset(succ(_u63), _u62) )).
% 275.66/275.82 cnf(matrix-113, plain, ( ~ordinal(_u63) | ~ordinal(_u62) | ~ordinal_subset(succ(_u63), _u62) | in(_u63, _u62) )).
% 275.66/275.82 cnf(matrix-114, plain, ( ~element(_u68, powerset(_u66)) | subset(_u68, _u66) )).
% 275.66/275.82 cnf(matrix-115, plain, ( ~subset(_u69, _u67) | element(_u69, powerset(_u67)) )).
% 275.66/275.82 cnf(matrix-116, plain, ( ~ordinal(_u72) | ~being_limit_ordinal(_u72) | ~ordinal(_u70) | ~in(_u70, _u72) | in(succ(_u70), _u72) )).
% 275.66/275.82 cnf(matrix-117, plain, ( ~ordinal(_u72) | being_limit_ordinal(_u72) | ordinal(skolem15(_u72)) )).
% 275.66/275.82 cnf(matrix-118, plain, ( ~ordinal(_u72) | being_limit_ordinal(_u72) | in(skolem15(_u72), _u72) )).
% 275.66/275.82 cnf(matrix-119, plain, ( ~ordinal(_u72) | being_limit_ordinal(_u72) | ~in(succ(skolem15(_u72)), _u72) )).
% 275.66/275.82 cnf(matrix-120, plain, ( ordinal(skolem16) )).
% 275.66/275.82 cnf(matrix-121, plain, ( ~_def0(_u73) | ~_def1 )).
% 275.66/275.82 cnf(matrix-122, plain, ( _def0(_u73) | ~being_limit_ordinal(skolem16) )).
% 275.66/275.82 cnf(matrix-123, plain, ( _def0(_u73) | ~ordinal(_u73) | ( skolem16 != succ(_u73)) )).
% 275.66/275.82 cnf(matrix-124, plain, ( _def1 | ordinal(skolem17) )).
% 275.66/275.82 cnf(matrix-125, plain, ( _def1 | ( skolem16 = succ(skolem17)) )).
% 275.66/275.82 cnf(matrix-126, plain, ( _def1 | being_limit_ordinal(skolem16) )).
% 275.66/275.82 cnf(matrix-127, plain, ( ~in(_u78, _u77) | ~element(_u77, powerset(_u76)) | element(_u78, _u76) )).
% 275.66/275.82 cnf(matrix-128, plain, ( ~in(_u81, _u80) | ~element(_u80, powerset(_u79)) | ~empty(_u79) )).
% 275.66/275.82 cnf(matrix-129, plain, ( ~empty(_u82) | ( _u82 = empty_set) )).
% 275.66/275.82 cnf(matrix-130, plain, ( ~in(_u84, _u83) | ~empty(_u83) )).
% 275.66/275.82 cnf(matrix-131, plain, ( ~empty(_u86) | ( _u86 = _u85) | ~empty(_u85) )).
% 275.66/275.82
% 275.66/275.82 % Proof stack:
% 275.66/275.82 cnf(proof-stack, plain,
% 275.66/275.82 proof_stack(
% 275.66/275.82 start(121),
% 275.66/275.82 left_branch(0, 122, 0, 2),
% 275.66/275.82 left_branch(0, 119, 1, 3),
% 275.66/275.82 left_branch(0, 120, 0, 4),
% 275.66/275.82 right_branch(4),
% 275.66/275.82 left_branch(0, 110, 3, 5),
% 275.66/275.82 left_branch(0, 59, 1, 6),
% 275.66/275.82 left_branch(0, 117, 2, 7),
% 275.66/275.82 lemmata(0, 0),
% 275.66/275.82 reduction(0, 1),
% 275.66/275.82 right_branch(7),
% 275.66/275.82 right_branch(6),
% 275.66/275.82 left_branch(0, 41, 2, 7),
% 275.66/275.82 left_branch(0, 103, 3, 8),
% 275.66/275.82 left_branch(0, 61, 1, 9),
% 275.66/275.82 left_branch(0, 117, 2, 10),
% 275.66/275.82 lemmata(0, 0),
% 275.66/275.82 reduction(0, 1),
% 275.66/275.82 right_branch(10),
% 275.66/275.82 right_branch(9),
% 275.66/275.82 left_branch(0, 112, 3, 10),
% 275.66/275.82 left_branch(0, 117, 2, 11),
% 275.66/275.82 lemmata(0, 0),
% 275.66/275.82 reduction(0, 1),
% 275.66/275.82 right_branch(11),
% 275.66/275.82 left_branch(0, 118, 2, 12),
% 275.66/275.82 lemmata(0, 0),
% 275.66/275.82 reduction(0, 1),
% 275.66/275.82 right_branch(12),
% 275.66/275.82 lemmata(0, 0),
% 275.66/275.82 right_branch(10),
% 275.66/275.82 lemmata(0, 0),
% 275.66/275.82 right_branch(8),
% 275.66/275.82 left_branch(0, 1, 0, 9),
% 275.66/275.82 left_branch(0, 123, 2, 10),
% 275.66/275.82 reduction(0, 0),
% 275.66/275.82 left_branch(0, 117, 2, 12),
% 275.66/275.82 lemmata(0, 0),
% 275.66/275.82 reduction(0, 1),
% 275.66/275.82 right_branch(12),
% 275.66/275.82 right_branch(10),
% 275.66/275.82 right_branch(9),
% 275.66/275.82 right_branch(7),
% 275.66/275.82 lemmata(0, 0),
% 275.66/275.82 right_branch(5),
% 275.66/275.82 right_branch(3),
% 275.66/275.82 right_branch(2),
% 275.66/275.82 left_branch(0, 125, 0, 3),
% 275.66/275.82 left_branch(0, 19, 1, 4),
% 275.66/275.82 reduction(0, 1),
% 275.66/275.82 left_branch(0, 106, 0, 6),
% 275.66/275.82 right_branch(6),
% 275.66/275.82 left_branch(0, 115, 0, 7),
% 275.66/275.82 left_branch(0, 127, 1, 8),
% 275.66/275.82 left_branch(0, 116, 4, 9),
% 275.66/275.82 left_branch(0, 61, 1, 10),
% 275.66/275.82 left_branch(0, 124, 1, 11),
% 275.66/275.82 reduction(0, 0),
% 275.66/275.82 right_branch(11),
% 275.66/275.82 right_branch(10),
% 275.66/275.82 left_branch(0, 113, 3, 11),
% 275.66/275.82 left_branch(0, 124, 1, 12),
% 275.66/275.82 reduction(0, 0),
% 275.66/275.82 right_branch(12),
% 275.66/275.82 left_branch(0, 105, 0, 13),
% 275.66/275.82 left_branch(0, 120, 0, 14),
% 275.66/275.82 right_branch(14),
% 275.66/275.82 lemmata(0, 3),
% 275.66/275.82 right_branch(13),
% 275.66/275.82 lemmata(0, 3),
% 275.66/275.82 right_branch(11),
% 275.66/275.82 left_branch(0, 124, 1, 12),
% 275.66/275.82 reduction(0, 0),
% 275.66/275.82 right_branch(12),
% 275.66/275.82 left_branch(0, 23, 2, 13),
% 275.66/275.82 reduction(0, 1),
% 275.66/275.82 left_branch(0, 126, 1, 15),
% 275.66/275.82 reduction(0, 0),
% 275.66/275.82 right_branch(15),
% 275.66/275.82 right_branch(13),
% 275.66/275.82 right_branch(9),
% 275.66/275.82 left_branch(0, 111, 0, 10),
% 275.66/275.82 left_branch(0, 25, 1, 11),
% 275.66/275.82 lemmata(0, 3),
% 275.66/275.82 right_branch(11),
% 275.66/275.82 left_branch(0, 131, 2, 12),
% 275.66/275.82 reduction(0, 5),
% 275.66/275.82 left_branch(0, 9, 1, 14),
% 275.66/275.82 reduction(0, 6),
% 275.66/275.82 lemmata(0, 3),
% 275.66/275.82 lemmata(0, 4),
% 275.66/275.82 right_branch(14),
% 275.66/275.82 right_branch(12),
% 275.66/275.82 right_branch(10),
% 275.66/275.82 right_branch(8),
% 275.66/275.82 right_branch(7),
% 275.66/275.82 right_branch(4),
% 275.66/275.82 right_branch(3)
% 275.66/275.82 )).
% 275.66/275.82 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------