TSTP Solution File: SEU046+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU046+1 : 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 : n009.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 14:33:01 EDT 2024
% Result : Theorem 23.57s 23.79s
% Output : Proof 23.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU046+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Mar 20 14:29:29 EDT 2024
% 0.11/0.33 % CPUTime :
% 23.57/23.79 % SZS status Theorem for theBenchmark
% 23.57/23.79 % SZS output start Proof for theBenchmark
% 23.57/23.79
% 23.57/23.79 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 23.57/23.79 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 23.57/23.79
% 23.57/23.79 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(cc1_funct_1-1, axiom, ( ~empty(_u2) | function(_u2) )).
% 23.57/23.79
% 23.57/23.79 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(cc1_relat_1-1, axiom, ( ~empty(_u3) | relation(_u3) )).
% 23.57/23.79
% 23.57/23.79 % Formula: cc2_funct_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(cc2_funct_1-1, axiom, ( ~relation(_u4) | ~empty(_u4) | ~function(_u4) | one_to_one(_u4) )).
% 23.57/23.79
% 23.57/23.79 % Formula: d3_tarski ( axiom ) converted to clauses:
% 23.57/23.79 cnf(d3_tarski-1, axiom, ( ~subset(_u11, _u9) | ~in(_u5, _u11) | in(_u5, _u9) )).
% 23.57/23.79 cnf(d3_tarski-2, axiom, ( subset(_u12, _u10) | in(skolem1(_u12, _u10), _u12) )).
% 23.57/23.79 cnf(d3_tarski-3, axiom, ( subset(_u12, _u10) | ~in(skolem1(_u12, _u10), _u10) )).
% 23.57/23.79
% 23.57/23.79 % Formula: dt_k8_relat_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(dt_k8_relat_1-1, axiom, ( ~relation(_u13) | relation(relation_rng_restriction(_u14, _u13)) )).
% 23.57/23.79
% 23.57/23.79 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(existence_m1_subset_1-1, axiom, ( element(skolem2(_u16), _u16) )).
% 23.57/23.79
% 23.57/23.79 % Formula: fc12_relat_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(fc12_relat_1-1, axiom, ( empty(empty_set) )).
% 23.57/23.79 cnf(fc12_relat_1-2, axiom, ( relation(empty_set) )).
% 23.57/23.79 cnf(fc12_relat_1-3, axiom, ( relation_empty_yielding(empty_set) )).
% 23.57/23.79
% 23.57/23.79 % Formula: fc1_subset_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(fc1_subset_1-1, axiom, ( ~empty(powerset(_u17)) )).
% 23.57/23.79
% 23.57/23.79 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 23.57/23.79
% 23.57/23.79 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 23.57/23.79 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 23.57/23.79
% 23.57/23.79 % Formula: fc5_funct_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(fc5_funct_1-1, axiom, ( ~relation(_u18) | ~function(_u18) | relation(relation_rng_restriction(_u19, _u18)) )).
% 23.57/23.79 cnf(fc5_funct_1-2, axiom, ( ~relation(_u18) | ~function(_u18) | function(relation_rng_restriction(_u19, _u18)) )).
% 23.57/23.79
% 23.57/23.79 % Formula: fc5_relat_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(fc5_relat_1-1, axiom, ( empty(_u20) | ~relation(_u20) | ~empty(relation_dom(_u20)) )).
% 23.57/23.79
% 23.57/23.79 % Formula: fc6_relat_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(fc6_relat_1-1, axiom, ( empty(_u21) | ~relation(_u21) | ~empty(relation_rng(_u21)) )).
% 23.57/23.79
% 23.57/23.79 % Formula: fc7_relat_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(fc7_relat_1-1, axiom, ( ~empty(_u22) | empty(relation_dom(_u22)) )).
% 23.57/23.79 cnf(fc7_relat_1-2, axiom, ( ~empty(_u22) | relation(relation_dom(_u22)) )).
% 23.57/23.79
% 23.57/23.79 % Formula: fc8_relat_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(fc8_relat_1-1, axiom, ( ~empty(_u23) | empty(relation_rng(_u23)) )).
% 23.57/23.79 cnf(fc8_relat_1-2, axiom, ( ~empty(_u23) | relation(relation_rng(_u23)) )).
% 23.57/23.79
% 23.57/23.79 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(rc1_funct_1-1, axiom, ( relation(skolem3) )).
% 23.57/23.79 cnf(rc1_funct_1-2, axiom, ( function(skolem3) )).
% 23.57/23.79
% 23.57/23.79 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(rc1_relat_1-1, axiom, ( empty(skolem4) )).
% 23.57/23.79 cnf(rc1_relat_1-2, axiom, ( relation(skolem4) )).
% 23.57/23.79
% 23.57/23.79 % Formula: rc1_subset_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(rc1_subset_1-1, axiom, ( empty(_u27) | element(skolem5(_u27), powerset(_u27)) )).
% 23.57/23.79 cnf(rc1_subset_1-2, axiom, ( empty(_u27) | ~empty(skolem5(_u27)) )).
% 23.57/23.79
% 23.57/23.79 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(rc1_xboole_0-1, axiom, ( empty(skolem6) )).
% 23.57/23.79
% 23.57/23.79 % Formula: rc2_funct_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(rc2_funct_1-1, axiom, ( relation(skolem7) )).
% 23.57/23.79 cnf(rc2_funct_1-2, axiom, ( empty(skolem7) )).
% 23.57/23.79 cnf(rc2_funct_1-3, axiom, ( function(skolem7) )).
% 23.57/23.79
% 23.57/23.79 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem8) )).
% 23.57/23.79 cnf(rc2_relat_1-2, axiom, ( relation(skolem8) )).
% 23.57/23.79
% 23.57/23.79 % Formula: rc2_subset_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(rc2_subset_1-1, axiom, ( element(skolem9(_u32), powerset(_u32)) )).
% 23.57/23.79 cnf(rc2_subset_1-2, axiom, ( empty(skolem9(_u32)) )).
% 23.57/23.79
% 23.57/23.79 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem10) )).
% 23.57/23.79
% 23.57/23.79 % Formula: rc3_funct_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(rc3_funct_1-1, axiom, ( relation(skolem11) )).
% 23.57/23.79 cnf(rc3_funct_1-2, axiom, ( function(skolem11) )).
% 23.57/23.79 cnf(rc3_funct_1-3, axiom, ( one_to_one(skolem11) )).
% 23.57/23.79
% 23.57/23.79 % Formula: rc3_relat_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(rc3_relat_1-1, axiom, ( relation(skolem12) )).
% 23.57/23.79 cnf(rc3_relat_1-2, axiom, ( relation_empty_yielding(skolem12) )).
% 23.57/23.79
% 23.57/23.79 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 23.57/23.79 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u37, _u37) )).
% 23.57/23.79
% 23.57/23.79 % Formula: t118_relat_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(t118_relat_1-1, axiom, ( ~relation(_u38) | subset(relation_rng(relation_rng_restriction(_u39, _u38)), relation_rng(_u38)) )).
% 23.57/23.79
% 23.57/23.79 % Formula: t1_subset ( axiom ) converted to clauses:
% 23.57/23.79 cnf(t1_subset-1, axiom, ( ~in(_u41, _u40) | element(_u41, _u40) )).
% 23.57/23.79
% 23.57/23.79 % Formula: t2_subset ( axiom ) converted to clauses:
% 23.57/23.79 cnf(t2_subset-1, axiom, ( ~element(_u43, _u42) | empty(_u42) | in(_u43, _u42) )).
% 23.57/23.79
% 23.57/23.79 % Formula: t3_subset ( axiom ) converted to clauses:
% 23.57/23.79 cnf(t3_subset-1, axiom, ( ~element(_u48, powerset(_u46)) | subset(_u48, _u46) )).
% 23.57/23.79 cnf(t3_subset-2, axiom, ( ~subset(_u49, _u47) | element(_u49, powerset(_u47)) )).
% 23.57/23.79
% 23.57/23.79 % Formula: t4_subset ( axiom ) converted to clauses:
% 23.57/23.79 cnf(t4_subset-1, axiom, ( ~in(_u52, _u51) | ~element(_u51, powerset(_u50)) | element(_u52, _u50) )).
% 23.57/23.79
% 23.57/23.79 % Formula: t5_subset ( axiom ) converted to clauses:
% 23.57/23.79 cnf(t5_subset-1, axiom, ( ~in(_u55, _u54) | ~element(_u54, powerset(_u53)) | ~empty(_u53) )).
% 23.57/23.79
% 23.57/23.79 % Formula: t6_boole ( axiom ) converted to clauses:
% 23.57/23.79 cnf(t6_boole-1, axiom, ( ~empty(_u56) | ( _u56 = empty_set) )).
% 23.57/23.79
% 23.57/23.79 % Formula: t7_boole ( axiom ) converted to clauses:
% 23.57/23.79 cnf(t7_boole-1, axiom, ( ~in(_u58, _u57) | ~empty(_u57) )).
% 23.57/23.79
% 23.57/23.79 % Formula: t85_funct_1 ( axiom ) converted to clauses:
% 23.57/23.79 cnf(t85_funct_1-1, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 != relation_rng_restriction(_u65, _u63)) | ~in(_u66, relation_dom(_u64)) | in(_u66, relation_dom(_u63)) )).
% 23.57/23.79 cnf(t85_funct_1-2, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 != relation_rng_restriction(_u65, _u63)) | ~in(_u66, relation_dom(_u64)) | in(apply(_u63, _u66), _u65) )).
% 23.57/23.79 cnf(t85_funct_1-3, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 != relation_rng_restriction(_u65, _u63)) | ~in(_u67, relation_dom(_u63)) | ~in(apply(_u63, _u67), _u65) | in(_u67, relation_dom(_u64)) )).
% 23.57/23.79 cnf(t85_funct_1-4, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 != relation_rng_restriction(_u65, _u63)) | ~in(_u60, relation_dom(_u64)) | ( apply(_u64, _u60) = apply(_u63, _u60)) )).
% 23.57/23.79 cnf(t85_funct_1-5, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | in(skolem15(_u65, _u64, _u63), relation_dom(_u64)) | in(skolem13(_u65, _u64, _u63), relation_dom(_u64)) | in(skolem14(_u65, _u64, _u63), relation_dom(_u63)) )).
% 23.57/23.79 cnf(t85_funct_1-6, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | in(skolem15(_u65, _u64, _u63), relation_dom(_u64)) | in(skolem13(_u65, _u64, _u63), relation_dom(_u64)) | in(apply(_u63, skolem14(_u65, _u64, _u63)), _u65) )).
% 23.57/23.79 cnf(t85_funct_1-7, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | in(skolem15(_u65, _u64, _u63), relation_dom(_u64)) | in(skolem13(_u65, _u64, _u63), relation_dom(_u64)) | ~in(skolem14(_u65, _u64, _u63), relation_dom(_u64)) )).
% 23.57/23.79 cnf(t85_funct_1-8, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | in(skolem15(_u65, _u64, _u63), relation_dom(_u64)) | ~in(skolem13(_u65, _u64, _u63), relation_dom(_u63)) | ~in(apply(_u63, skolem13(_u65, _u64, _u63)), _u65) | in(skolem14(_u65, _u64, _u63), relation_dom(_u63)) )).
% 23.57/23.79 cnf(t85_funct_1-9, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | in(skolem15(_u65, _u64, _u63), relation_dom(_u64)) | ~in(skolem13(_u65, _u64, _u63), relation_dom(_u63)) | ~in(apply(_u63, skolem13(_u65, _u64, _u63)), _u65) | in(apply(_u63, skolem14(_u65, _u64, _u63)), _u65) )).
% 23.57/23.79 cnf(t85_funct_1-10, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | in(skolem15(_u65, _u64, _u63), relation_dom(_u64)) | ~in(skolem13(_u65, _u64, _u63), relation_dom(_u63)) | ~in(apply(_u63, skolem13(_u65, _u64, _u63)), _u65) | ~in(skolem14(_u65, _u64, _u63), relation_dom(_u64)) )).
% 23.57/23.79 cnf(t85_funct_1-11, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | ( apply(_u64, skolem15(_u65, _u64, _u63)) != apply(_u63, skolem15(_u65, _u64, _u63))) | in(skolem13(_u65, _u64, _u63), relation_dom(_u64)) | in(skolem14(_u65, _u64, _u63), relation_dom(_u63)) )).
% 23.57/23.79 cnf(t85_funct_1-12, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | ( apply(_u64, skolem15(_u65, _u64, _u63)) != apply(_u63, skolem15(_u65, _u64, _u63))) | in(skolem13(_u65, _u64, _u63), relation_dom(_u64)) | in(apply(_u63, skolem14(_u65, _u64, _u63)), _u65) )).
% 23.57/23.79 cnf(t85_funct_1-13, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | ( apply(_u64, skolem15(_u65, _u64, _u63)) != apply(_u63, skolem15(_u65, _u64, _u63))) | in(skolem13(_u65, _u64, _u63), relation_dom(_u64)) | ~in(skolem14(_u65, _u64, _u63), relation_dom(_u64)) )).
% 23.57/23.79 cnf(t85_funct_1-14, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | ( apply(_u64, skolem15(_u65, _u64, _u63)) != apply(_u63, skolem15(_u65, _u64, _u63))) | ~in(skolem13(_u65, _u64, _u63), relation_dom(_u63)) | ~in(apply(_u63, skolem13(_u65, _u64, _u63)), _u65) | in(skolem14(_u65, _u64, _u63), relation_dom(_u63)) )).
% 23.57/23.79 cnf(t85_funct_1-15, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | ( apply(_u64, skolem15(_u65, _u64, _u63)) != apply(_u63, skolem15(_u65, _u64, _u63))) | ~in(skolem13(_u65, _u64, _u63), relation_dom(_u63)) | ~in(apply(_u63, skolem13(_u65, _u64, _u63)), _u65) | in(apply(_u63, skolem14(_u65, _u64, _u63)), _u65) )).
% 23.57/23.79 cnf(t85_funct_1-16, axiom, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | ( apply(_u64, skolem15(_u65, _u64, _u63)) != apply(_u63, skolem15(_u65, _u64, _u63))) | ~in(skolem13(_u65, _u64, _u63), relation_dom(_u63)) | ~in(apply(_u63, skolem13(_u65, _u64, _u63)), _u65) | ~in(skolem14(_u65, _u64, _u63), relation_dom(_u64)) )).
% 23.57/23.79
% 23.57/23.79 % Formula: t89_funct_1 ( conjecture ) (definitionally) converted to clauses:
% 23.57/23.79 cnf(t89_funct_1-1, negated_conjecture, ( relation(skolem17) )).
% 23.57/23.79 cnf(t89_funct_1-2, negated_conjecture, ( function(skolem17) )).
% 23.57/23.79 cnf(t89_funct_1-3, negated_conjecture, ( ~subset(relation_dom(relation_rng_restriction(skolem16, skolem17)), relation_dom(skolem17)) | ~subset(relation_rng(relation_rng_restriction(skolem16, skolem17)), relation_rng(skolem17)) )).
% 23.57/23.79
% 23.57/23.79 % Formula: t8_boole ( axiom ) converted to clauses:
% 23.57/23.79 cnf(t8_boole-1, axiom, ( ~empty(_u73) | ( _u73 = _u72) | ~empty(_u72) )).
% 23.57/23.79
% 23.57/23.79 % Problem matrix:
% 23.57/23.79 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 23.57/23.79 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 23.57/23.79 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 23.57/23.79 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( relation_rng_restriction(__eqx_0, __eqx_1) = relation_rng_restriction(__eqy_0, __eqy_1)) )).
% 23.57/23.79 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 23.57/23.79 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( relation_dom(__eqx_0) = relation_dom(__eqy_0)) )).
% 23.57/23.79 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( relation_rng(__eqx_0) = relation_rng(__eqy_0)) )).
% 23.57/23.79 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( apply(__eqx_0, __eqx_1) = apply(__eqy_0, __eqy_1)) )).
% 23.57/23.79 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 23.57/23.79 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( skolem2(__eqx_0) = skolem2(__eqy_0)) )).
% 23.57/23.79 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( skolem5(__eqx_0) = skolem5(__eqy_0)) )).
% 23.57/23.79 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( skolem9(__eqx_0) = skolem9(__eqy_0)) )).
% 23.57/23.79 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem13(__eqx_0, __eqx_1, __eqx_2) = skolem13(__eqy_0, __eqy_1, __eqy_2)) )).
% 23.57/23.79 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem14(__eqx_0, __eqx_1, __eqx_2) = skolem14(__eqy_0, __eqy_1, __eqy_2)) )).
% 23.57/23.79 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem15(__eqx_0, __eqx_1, __eqx_2) = skolem15(__eqy_0, __eqy_1, __eqy_2)) )).
% 23.57/23.79 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 23.57/23.79 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 23.57/23.79 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 23.57/23.79 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 23.57/23.79 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 23.57/23.79 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 23.57/23.79 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 23.57/23.79 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ~relation_empty_yielding(__eqx_0) | relation_empty_yielding(__eqy_0) )).
% 23.57/23.79 cnf(matrix-23, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 23.57/23.79 cnf(matrix-24, plain, ( ~empty(_u2) | function(_u2) )).
% 23.57/23.79 cnf(matrix-25, plain, ( ~empty(_u3) | relation(_u3) )).
% 23.57/23.79 cnf(matrix-26, plain, ( ~relation(_u4) | ~empty(_u4) | ~function(_u4) | one_to_one(_u4) )).
% 23.57/23.79 cnf(matrix-27, plain, ( ~subset(_u11, _u9) | ~in(_u5, _u11) | in(_u5, _u9) )).
% 23.57/23.79 cnf(matrix-28, plain, ( subset(_u12, _u10) | in(skolem1(_u12, _u10), _u12) )).
% 23.57/23.79 cnf(matrix-29, plain, ( subset(_u12, _u10) | ~in(skolem1(_u12, _u10), _u10) )).
% 23.57/23.79 cnf(matrix-30, plain, ( ~relation(_u13) | relation(relation_rng_restriction(_u14, _u13)) )).
% 23.57/23.79 cnf(matrix-31, plain, ( element(skolem2(_u16), _u16) )).
% 23.57/23.79 cnf(matrix-32, plain, ( empty(empty_set) )).
% 23.57/23.79 cnf(matrix-33, plain, ( relation(empty_set) )).
% 23.57/23.79 cnf(matrix-34, plain, ( relation_empty_yielding(empty_set) )).
% 23.57/23.79 cnf(matrix-35, plain, ( ~empty(powerset(_u17)) )).
% 23.57/23.79 cnf(matrix-36, plain, ( empty(empty_set) )).
% 23.57/23.79 cnf(matrix-37, plain, ( empty(empty_set) )).
% 23.57/23.79 cnf(matrix-38, plain, ( relation(empty_set) )).
% 23.57/23.79 cnf(matrix-39, plain, ( ~relation(_u18) | ~function(_u18) | relation(relation_rng_restriction(_u19, _u18)) )).
% 23.57/23.79 cnf(matrix-40, plain, ( ~relation(_u18) | ~function(_u18) | function(relation_rng_restriction(_u19, _u18)) )).
% 23.57/23.79 cnf(matrix-41, plain, ( empty(_u20) | ~relation(_u20) | ~empty(relation_dom(_u20)) )).
% 23.57/23.79 cnf(matrix-42, plain, ( empty(_u21) | ~relation(_u21) | ~empty(relation_rng(_u21)) )).
% 23.57/23.79 cnf(matrix-43, plain, ( ~empty(_u22) | empty(relation_dom(_u22)) )).
% 23.57/23.79 cnf(matrix-44, plain, ( ~empty(_u22) | relation(relation_dom(_u22)) )).
% 23.57/23.79 cnf(matrix-45, plain, ( ~empty(_u23) | empty(relation_rng(_u23)) )).
% 23.57/23.79 cnf(matrix-46, plain, ( ~empty(_u23) | relation(relation_rng(_u23)) )).
% 23.57/23.79 cnf(matrix-47, plain, ( relation(skolem3) )).
% 23.57/23.79 cnf(matrix-48, plain, ( function(skolem3) )).
% 23.57/23.79 cnf(matrix-49, plain, ( empty(skolem4) )).
% 23.57/23.79 cnf(matrix-50, plain, ( relation(skolem4) )).
% 23.57/23.79 cnf(matrix-51, plain, ( empty(_u27) | element(skolem5(_u27), powerset(_u27)) )).
% 23.57/23.79 cnf(matrix-52, plain, ( empty(_u27) | ~empty(skolem5(_u27)) )).
% 23.57/23.79 cnf(matrix-53, plain, ( empty(skolem6) )).
% 23.57/23.79 cnf(matrix-54, plain, ( relation(skolem7) )).
% 23.57/23.79 cnf(matrix-55, plain, ( empty(skolem7) )).
% 23.57/23.79 cnf(matrix-56, plain, ( function(skolem7) )).
% 23.57/23.79 cnf(matrix-57, plain, ( ~empty(skolem8) )).
% 23.57/23.79 cnf(matrix-58, plain, ( relation(skolem8) )).
% 23.57/23.79 cnf(matrix-59, plain, ( element(skolem9(_u32), powerset(_u32)) )).
% 23.57/23.79 cnf(matrix-60, plain, ( empty(skolem9(_u32)) )).
% 23.57/23.79 cnf(matrix-61, plain, ( ~empty(skolem10) )).
% 23.57/23.79 cnf(matrix-62, plain, ( relation(skolem11) )).
% 23.57/23.79 cnf(matrix-63, plain, ( function(skolem11) )).
% 23.57/23.79 cnf(matrix-64, plain, ( one_to_one(skolem11) )).
% 23.57/23.79 cnf(matrix-65, plain, ( relation(skolem12) )).
% 23.57/23.79 cnf(matrix-66, plain, ( relation_empty_yielding(skolem12) )).
% 23.57/23.79 cnf(matrix-67, plain, ( subset(_u37, _u37) )).
% 23.57/23.79 cnf(matrix-68, plain, ( ~relation(_u38) | subset(relation_rng(relation_rng_restriction(_u39, _u38)), relation_rng(_u38)) )).
% 23.57/23.79 cnf(matrix-69, plain, ( ~in(_u41, _u40) | element(_u41, _u40) )).
% 23.57/23.79 cnf(matrix-70, plain, ( ~element(_u43, _u42) | empty(_u42) | in(_u43, _u42) )).
% 23.57/23.79 cnf(matrix-71, plain, ( ~element(_u48, powerset(_u46)) | subset(_u48, _u46) )).
% 23.57/23.79 cnf(matrix-72, plain, ( ~subset(_u49, _u47) | element(_u49, powerset(_u47)) )).
% 23.57/23.79 cnf(matrix-73, plain, ( ~in(_u52, _u51) | ~element(_u51, powerset(_u50)) | element(_u52, _u50) )).
% 23.57/23.79 cnf(matrix-74, plain, ( ~in(_u55, _u54) | ~element(_u54, powerset(_u53)) | ~empty(_u53) )).
% 23.57/23.79 cnf(matrix-75, plain, ( ~empty(_u56) | ( _u56 = empty_set) )).
% 23.57/23.79 cnf(matrix-76, plain, ( ~in(_u58, _u57) | ~empty(_u57) )).
% 23.57/23.79 cnf(matrix-77, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 != relation_rng_restriction(_u65, _u63)) | ~in(_u66, relation_dom(_u64)) | in(_u66, relation_dom(_u63)) )).
% 23.57/23.79 cnf(matrix-78, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 != relation_rng_restriction(_u65, _u63)) | ~in(_u66, relation_dom(_u64)) | in(apply(_u63, _u66), _u65) )).
% 23.57/23.79 cnf(matrix-79, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 != relation_rng_restriction(_u65, _u63)) | ~in(_u67, relation_dom(_u63)) | ~in(apply(_u63, _u67), _u65) | in(_u67, relation_dom(_u64)) )).
% 23.57/23.79 cnf(matrix-80, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 != relation_rng_restriction(_u65, _u63)) | ~in(_u60, relation_dom(_u64)) | ( apply(_u64, _u60) = apply(_u63, _u60)) )).
% 23.57/23.79 cnf(matrix-81, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | in(skolem15(_u65, _u64, _u63), relation_dom(_u64)) | in(skolem13(_u65, _u64, _u63), relation_dom(_u64)) | in(skolem14(_u65, _u64, _u63), relation_dom(_u63)) )).
% 23.57/23.79 cnf(matrix-82, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | in(skolem15(_u65, _u64, _u63), relation_dom(_u64)) | in(skolem13(_u65, _u64, _u63), relation_dom(_u64)) | in(apply(_u63, skolem14(_u65, _u64, _u63)), _u65) )).
% 23.57/23.79 cnf(matrix-83, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | in(skolem15(_u65, _u64, _u63), relation_dom(_u64)) | in(skolem13(_u65, _u64, _u63), relation_dom(_u64)) | ~in(skolem14(_u65, _u64, _u63), relation_dom(_u64)) )).
% 23.57/23.79 cnf(matrix-84, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | in(skolem15(_u65, _u64, _u63), relation_dom(_u64)) | ~in(skolem13(_u65, _u64, _u63), relation_dom(_u63)) | ~in(apply(_u63, skolem13(_u65, _u64, _u63)), _u65) | in(skolem14(_u65, _u64, _u63), relation_dom(_u63)) )).
% 23.57/23.79 cnf(matrix-85, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | in(skolem15(_u65, _u64, _u63), relation_dom(_u64)) | ~in(skolem13(_u65, _u64, _u63), relation_dom(_u63)) | ~in(apply(_u63, skolem13(_u65, _u64, _u63)), _u65) | in(apply(_u63, skolem14(_u65, _u64, _u63)), _u65) )).
% 23.57/23.79 cnf(matrix-86, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | in(skolem15(_u65, _u64, _u63), relation_dom(_u64)) | ~in(skolem13(_u65, _u64, _u63), relation_dom(_u63)) | ~in(apply(_u63, skolem13(_u65, _u64, _u63)), _u65) | ~in(skolem14(_u65, _u64, _u63), relation_dom(_u64)) )).
% 23.57/23.79 cnf(matrix-87, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | ( apply(_u64, skolem15(_u65, _u64, _u63)) != apply(_u63, skolem15(_u65, _u64, _u63))) | in(skolem13(_u65, _u64, _u63), relation_dom(_u64)) | in(skolem14(_u65, _u64, _u63), relation_dom(_u63)) )).
% 23.57/23.79 cnf(matrix-88, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | ( apply(_u64, skolem15(_u65, _u64, _u63)) != apply(_u63, skolem15(_u65, _u64, _u63))) | in(skolem13(_u65, _u64, _u63), relation_dom(_u64)) | in(apply(_u63, skolem14(_u65, _u64, _u63)), _u65) )).
% 23.57/23.79 cnf(matrix-89, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | ( apply(_u64, skolem15(_u65, _u64, _u63)) != apply(_u63, skolem15(_u65, _u64, _u63))) | in(skolem13(_u65, _u64, _u63), relation_dom(_u64)) | ~in(skolem14(_u65, _u64, _u63), relation_dom(_u64)) )).
% 23.57/23.79 cnf(matrix-90, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | ( apply(_u64, skolem15(_u65, _u64, _u63)) != apply(_u63, skolem15(_u65, _u64, _u63))) | ~in(skolem13(_u65, _u64, _u63), relation_dom(_u63)) | ~in(apply(_u63, skolem13(_u65, _u64, _u63)), _u65) | in(skolem14(_u65, _u64, _u63), relation_dom(_u63)) )).
% 23.57/23.79 cnf(matrix-91, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | ( apply(_u64, skolem15(_u65, _u64, _u63)) != apply(_u63, skolem15(_u65, _u64, _u63))) | ~in(skolem13(_u65, _u64, _u63), relation_dom(_u63)) | ~in(apply(_u63, skolem13(_u65, _u64, _u63)), _u65) | in(apply(_u63, skolem14(_u65, _u64, _u63)), _u65) )).
% 23.57/23.79 cnf(matrix-92, plain, ( ~relation(_u64) | ~function(_u64) | ~relation(_u63) | ~function(_u63) | ( _u64 = relation_rng_restriction(_u65, _u63)) | ( apply(_u64, skolem15(_u65, _u64, _u63)) != apply(_u63, skolem15(_u65, _u64, _u63))) | ~in(skolem13(_u65, _u64, _u63), relation_dom(_u63)) | ~in(apply(_u63, skolem13(_u65, _u64, _u63)), _u65) | ~in(skolem14(_u65, _u64, _u63), relation_dom(_u64)) )).
% 23.57/23.79 cnf(matrix-93, plain, ( relation(skolem17) )).
% 23.57/23.79 cnf(matrix-94, plain, ( function(skolem17) )).
% 23.57/23.79 cnf(matrix-95, plain, ( ~subset(relation_dom(relation_rng_restriction(skolem16, skolem17)), relation_dom(skolem17)) | ~subset(relation_rng(relation_rng_restriction(skolem16, skolem17)), relation_rng(skolem17)) )).
% 23.57/23.79 cnf(matrix-96, plain, ( ~empty(_u73) | ( _u73 = _u72) | ~empty(_u72) )).
% 23.57/23.79
% 23.57/23.79 % Proof stack:
% 23.57/23.79 cnf(proof-stack, plain,
% 23.57/23.79 proof_stack(
% 23.57/23.79 start(95),
% 23.57/23.79 left_branch(0, 28, 0, 2),
% 23.57/23.79 left_branch(0, 77, 5, 3),
% 23.57/23.79 left_branch(0, 39, 2, 4),
% 23.57/23.79 left_branch(0, 93, 0, 5),
% 23.57/23.79 right_branch(5),
% 23.57/23.79 left_branch(0, 94, 0, 6),
% 23.57/23.79 right_branch(6),
% 23.57/23.79 right_branch(4),
% 23.57/23.79 left_branch(0, 29, 1, 5),
% 23.57/23.79 reduction(0, 0),
% 23.57/23.79 right_branch(5),
% 23.57/23.79 left_branch(0, 3, 2, 6),
% 23.57/23.79 left_branch(0, 0, 0, 7),
% 23.57/23.79 right_branch(7),
% 23.57/23.79 left_branch(0, 0, 0, 8),
% 23.57/23.79 right_branch(8),
% 23.57/23.79 right_branch(6),
% 23.57/23.79 left_branch(0, 94, 0, 7),
% 23.57/23.79 right_branch(7),
% 23.57/23.79 left_branch(0, 93, 0, 8),
% 23.57/23.79 right_branch(8),
% 23.57/23.79 left_branch(0, 40, 2, 9),
% 23.57/23.79 lemmata(0, 4),
% 23.57/23.79 lemmata(0, 3),
% 23.57/23.79 right_branch(9),
% 23.57/23.79 right_branch(3),
% 23.57/23.79 right_branch(2),
% 23.57/23.79 left_branch(0, 68, 1, 3),
% 23.57/23.79 left_branch(0, 93, 0, 4),
% 23.57/23.79 right_branch(4),
% 23.57/23.79 right_branch(3)
% 23.57/23.79 )).
% 23.57/23.79 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------