TSTP Solution File: SET997+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET997+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 : n021.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 14:32:56 EDT 2024
% Result : Theorem 189.72s 189.91s
% Output : Proof 189.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET997+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n021.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 21:23:18 EDT 2024
% 0.13/0.34 % CPUTime :
% 189.72/189.91 % SZS status Theorem for theBenchmark
% 189.72/189.91 % SZS output start Proof for theBenchmark
% 189.72/189.91
% 189.72/189.91 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 189.72/189.91 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 189.72/189.91
% 189.72/189.91 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(cc1_funct_1-1, axiom, ( ~empty(_u2) | function(_u2) )).
% 189.72/189.91
% 189.72/189.91 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(cc1_relat_1-1, axiom, ( ~empty(_u3) | relation(_u3) )).
% 189.72/189.91
% 189.72/189.91 % Formula: d3_tarski ( axiom ) converted to clauses:
% 189.72/189.91 cnf(d3_tarski-1, axiom, ( ~subset(_u10, _u8) | ~in(_u4, _u10) | in(_u4, _u8) )).
% 189.72/189.91 cnf(d3_tarski-2, axiom, ( subset(_u11, _u9) | in(skolem1(_u11, _u9), _u11) )).
% 189.72/189.91 cnf(d3_tarski-3, axiom, ( subset(_u11, _u9) | ~in(skolem1(_u11, _u9), _u9) )).
% 189.72/189.91
% 189.72/189.91 % Formula: d5_funct_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(d5_funct_1-1, axiom, ( ~relation(_u19) | ~function(_u19) | ( _u24 != relation_rng(_u19)) | ~in(_u20, _u24) | in(skolem2(_u19, _u24, _u20), relation_dom(_u19)) )).
% 189.72/189.91 cnf(d5_funct_1-2, axiom, ( ~relation(_u19) | ~function(_u19) | ( _u24 != relation_rng(_u19)) | ~in(_u20, _u24) | ( _u20 = apply(_u19, skolem2(_u19, _u24, _u20))) )).
% 189.72/189.91 cnf(d5_funct_1-3, axiom, ( ~relation(_u19) | ~function(_u19) | ( _u24 != relation_rng(_u19)) | ~in(_u13, relation_dom(_u19)) | ( _u21 != apply(_u19, _u13)) | in(_u21, _u24) )).
% 189.72/189.91 cnf(d5_funct_1-4, axiom, ( ~relation(_u19) | ~function(_u19) | ( _u25 = relation_rng(_u19)) | in(skolem3(_u19, _u25), _u25) | in(skolem5(_u19, _u25), relation_dom(_u19)) )).
% 189.72/189.91 cnf(d5_funct_1-5, axiom, ( ~relation(_u19) | ~function(_u19) | ( _u25 = relation_rng(_u19)) | in(skolem3(_u19, _u25), _u25) | ( skolem4(_u19, _u25) = apply(_u19, skolem5(_u19, _u25))) )).
% 189.72/189.91 cnf(d5_funct_1-6, axiom, ( ~relation(_u19) | ~function(_u19) | ( _u25 = relation_rng(_u19)) | in(skolem3(_u19, _u25), _u25) | ~in(skolem4(_u19, _u25), _u25) )).
% 189.72/189.91 cnf(d5_funct_1-7, axiom, ( ~relation(_u19) | ~function(_u19) | ( _u25 = relation_rng(_u19)) | ~in(_u15, relation_dom(_u19)) | ( skolem3(_u19, _u25) != apply(_u19, _u15)) | in(skolem5(_u19, _u25), relation_dom(_u19)) )).
% 189.72/189.91 cnf(d5_funct_1-8, axiom, ( ~relation(_u19) | ~function(_u19) | ( _u25 = relation_rng(_u19)) | ~in(_u15, relation_dom(_u19)) | ( skolem3(_u19, _u25) != apply(_u19, _u15)) | ( skolem4(_u19, _u25) = apply(_u19, skolem5(_u19, _u25))) )).
% 189.72/189.91 cnf(d5_funct_1-9, axiom, ( ~relation(_u19) | ~function(_u19) | ( _u25 = relation_rng(_u19)) | ~in(_u15, relation_dom(_u19)) | ( skolem3(_u19, _u25) != apply(_u19, _u15)) | ~in(skolem4(_u19, _u25), _u25) )).
% 189.72/189.91
% 189.72/189.91 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(existence_m1_subset_1-1, axiom, ( element(skolem6(_u27), _u27) )).
% 189.72/189.91
% 189.72/189.91 % Formula: fc12_relat_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(fc12_relat_1-1, axiom, ( empty(empty_set) )).
% 189.72/189.91 cnf(fc12_relat_1-2, axiom, ( relation(empty_set) )).
% 189.72/189.91 cnf(fc12_relat_1-3, axiom, ( relation_empty_yielding(empty_set) )).
% 189.72/189.91
% 189.72/189.91 % Formula: fc1_subset_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(fc1_subset_1-1, axiom, ( ~empty(powerset(_u28)) )).
% 189.72/189.91
% 189.72/189.91 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 189.72/189.91
% 189.72/189.91 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 189.72/189.91 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 189.72/189.91
% 189.72/189.91 % Formula: fc5_relat_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(fc5_relat_1-1, axiom, ( empty(_u29) | ~relation(_u29) | ~empty(relation_dom(_u29)) )).
% 189.72/189.91
% 189.72/189.91 % Formula: fc6_relat_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(fc6_relat_1-1, axiom, ( empty(_u30) | ~relation(_u30) | ~empty(relation_rng(_u30)) )).
% 189.72/189.91
% 189.72/189.91 % Formula: fc7_relat_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(fc7_relat_1-1, axiom, ( ~empty(_u31) | empty(relation_dom(_u31)) )).
% 189.72/189.91 cnf(fc7_relat_1-2, axiom, ( ~empty(_u31) | relation(relation_dom(_u31)) )).
% 189.72/189.91
% 189.72/189.91 % Formula: fc8_relat_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(fc8_relat_1-1, axiom, ( ~empty(_u32) | empty(relation_rng(_u32)) )).
% 189.72/189.91 cnf(fc8_relat_1-2, axiom, ( ~empty(_u32) | relation(relation_rng(_u32)) )).
% 189.72/189.91
% 189.72/189.91 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(rc1_funct_1-1, axiom, ( relation(skolem7) )).
% 189.72/189.91 cnf(rc1_funct_1-2, axiom, ( function(skolem7) )).
% 189.72/189.91
% 189.72/189.91 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(rc1_relat_1-1, axiom, ( empty(skolem8) )).
% 189.72/189.91 cnf(rc1_relat_1-2, axiom, ( relation(skolem8) )).
% 189.72/189.91
% 189.72/189.91 % Formula: rc1_subset_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(rc1_subset_1-1, axiom, ( empty(_u36) | element(skolem9(_u36), powerset(_u36)) )).
% 189.72/189.91 cnf(rc1_subset_1-2, axiom, ( empty(_u36) | ~empty(skolem9(_u36)) )).
% 189.72/189.91
% 189.72/189.91 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(rc1_xboole_0-1, axiom, ( empty(skolem10) )).
% 189.72/189.91
% 189.72/189.91 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem11) )).
% 189.72/189.91 cnf(rc2_relat_1-2, axiom, ( relation(skolem11) )).
% 189.72/189.91
% 189.72/189.91 % Formula: rc2_subset_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(rc2_subset_1-1, axiom, ( element(skolem12(_u40), powerset(_u40)) )).
% 189.72/189.91 cnf(rc2_subset_1-2, axiom, ( empty(skolem12(_u40)) )).
% 189.72/189.91
% 189.72/189.91 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem13) )).
% 189.72/189.91
% 189.72/189.91 % Formula: rc3_relat_1 ( axiom ) converted to clauses:
% 189.72/189.91 cnf(rc3_relat_1-1, axiom, ( relation(skolem14) )).
% 189.72/189.91 cnf(rc3_relat_1-2, axiom, ( relation_empty_yielding(skolem14) )).
% 189.72/189.91
% 189.72/189.91 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 189.72/189.91 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u44, _u44) )).
% 189.72/189.91
% 189.72/189.91 % Formula: t19_funct_1 ( conjecture ) (definitionally) converted to clauses:
% 189.72/189.91 cnf(t19_funct_1-1, negated_conjecture, ( relation(skolem16) )).
% 189.72/189.91 cnf(t19_funct_1-2, negated_conjecture, ( function(skolem16) )).
% 189.72/189.91 cnf(t19_funct_1-3, negated_conjecture, ( ~in(_u46, skolem15) | ~_def0(_u46) )).
% 189.72/189.91 cnf(t19_funct_1-4, negated_conjecture, ( ~subset(skolem15, relation_rng(skolem16)) )).
% 189.72/189.91 cnf(t19_funct_1-5, negated_conjecture, ( _def0(_u46) | in(skolem17(_u46), relation_dom(skolem16)) )).
% 189.72/189.91 cnf(t19_funct_1-6, negated_conjecture, ( _def0(_u46) | ( _u46 = apply(skolem16, skolem17(_u46))) )).
% 189.72/189.91
% 189.72/189.91 % Formula: t1_subset ( axiom ) converted to clauses:
% 189.72/189.91 cnf(t1_subset-1, axiom, ( ~in(_u50, _u49) | element(_u50, _u49) )).
% 189.72/189.91
% 189.72/189.91 % Formula: t2_subset ( axiom ) converted to clauses:
% 189.72/189.91 cnf(t2_subset-1, axiom, ( ~element(_u52, _u51) | empty(_u51) | in(_u52, _u51) )).
% 189.72/189.91
% 189.72/189.91 % Formula: t3_subset ( axiom ) converted to clauses:
% 189.72/189.91 cnf(t3_subset-1, axiom, ( ~element(_u57, powerset(_u55)) | subset(_u57, _u55) )).
% 189.72/189.91 cnf(t3_subset-2, axiom, ( ~subset(_u58, _u56) | element(_u58, powerset(_u56)) )).
% 189.72/189.91
% 189.72/189.91 % Formula: t4_subset ( axiom ) converted to clauses:
% 189.72/189.91 cnf(t4_subset-1, axiom, ( ~in(_u61, _u60) | ~element(_u60, powerset(_u59)) | element(_u61, _u59) )).
% 189.72/189.91
% 189.72/189.91 % Formula: t5_subset ( axiom ) converted to clauses:
% 189.72/189.91 cnf(t5_subset-1, axiom, ( ~in(_u64, _u63) | ~element(_u63, powerset(_u62)) | ~empty(_u62) )).
% 189.72/189.91
% 189.72/189.91 % Formula: t6_boole ( axiom ) converted to clauses:
% 189.72/189.91 cnf(t6_boole-1, axiom, ( ~empty(_u65) | ( _u65 = empty_set) )).
% 189.72/189.91
% 189.72/189.91 % Formula: t7_boole ( axiom ) converted to clauses:
% 189.72/189.91 cnf(t7_boole-1, axiom, ( ~in(_u67, _u66) | ~empty(_u66) )).
% 189.72/189.91
% 189.72/189.91 % Formula: t8_boole ( axiom ) converted to clauses:
% 189.72/189.91 cnf(t8_boole-1, axiom, ( ~empty(_u69) | ( _u69 = _u68) | ~empty(_u68) )).
% 189.72/189.91
% 189.72/189.91 % Problem matrix:
% 189.72/189.91 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 189.72/189.91 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 189.72/189.91 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 189.72/189.91 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( relation_rng(__eqx_0) = relation_rng(__eqy_0)) )).
% 189.72/189.91 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( relation_dom(__eqx_0) = relation_dom(__eqy_0)) )).
% 189.72/189.91 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( apply(__eqx_0, __eqx_1) = apply(__eqy_0, __eqy_1)) )).
% 189.72/189.91 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 189.72/189.91 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 189.72/189.91 cnf(matrix-8, 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)) )).
% 189.72/189.91 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 189.72/189.91 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 189.72/189.91 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem5(__eqx_0, __eqx_1) = skolem5(__eqy_0, __eqy_1)) )).
% 189.72/189.91 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( skolem6(__eqx_0) = skolem6(__eqy_0)) )).
% 189.72/189.91 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( skolem9(__eqx_0) = skolem9(__eqy_0)) )).
% 189.72/189.91 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( skolem12(__eqx_0) = skolem12(__eqy_0)) )).
% 189.72/189.91 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( skolem17(__eqx_0) = skolem17(__eqy_0)) )).
% 189.72/189.91 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 189.72/189.91 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 189.72/189.91 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 189.72/189.91 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 189.72/189.91 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 189.72/189.91 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 189.72/189.91 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ~relation_empty_yielding(__eqx_0) | relation_empty_yielding(__eqy_0) )).
% 189.72/189.91 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ~_def0(__eqx_0) | _def0(__eqy_0) )).
% 189.72/189.91 cnf(matrix-24, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 189.72/189.91 cnf(matrix-25, plain, ( ~empty(_u2) | function(_u2) )).
% 189.72/189.91 cnf(matrix-26, plain, ( ~empty(_u3) | relation(_u3) )).
% 189.72/189.91 cnf(matrix-27, plain, ( ~subset(_u10, _u8) | ~in(_u4, _u10) | in(_u4, _u8) )).
% 189.72/189.91 cnf(matrix-28, plain, ( subset(_u11, _u9) | in(skolem1(_u11, _u9), _u11) )).
% 189.72/189.91 cnf(matrix-29, plain, ( subset(_u11, _u9) | ~in(skolem1(_u11, _u9), _u9) )).
% 189.72/189.91 cnf(matrix-30, plain, ( ~relation(_u19) | ~function(_u19) | ( _u24 != relation_rng(_u19)) | ~in(_u20, _u24) | in(skolem2(_u19, _u24, _u20), relation_dom(_u19)) )).
% 189.72/189.91 cnf(matrix-31, plain, ( ~relation(_u19) | ~function(_u19) | ( _u24 != relation_rng(_u19)) | ~in(_u20, _u24) | ( _u20 = apply(_u19, skolem2(_u19, _u24, _u20))) )).
% 189.72/189.91 cnf(matrix-32, plain, ( ~relation(_u19) | ~function(_u19) | ( _u24 != relation_rng(_u19)) | ~in(_u13, relation_dom(_u19)) | ( _u21 != apply(_u19, _u13)) | in(_u21, _u24) )).
% 189.72/189.91 cnf(matrix-33, plain, ( ~relation(_u19) | ~function(_u19) | ( _u25 = relation_rng(_u19)) | in(skolem3(_u19, _u25), _u25) | in(skolem5(_u19, _u25), relation_dom(_u19)) )).
% 189.72/189.91 cnf(matrix-34, plain, ( ~relation(_u19) | ~function(_u19) | ( _u25 = relation_rng(_u19)) | in(skolem3(_u19, _u25), _u25) | ( skolem4(_u19, _u25) = apply(_u19, skolem5(_u19, _u25))) )).
% 189.72/189.91 cnf(matrix-35, plain, ( ~relation(_u19) | ~function(_u19) | ( _u25 = relation_rng(_u19)) | in(skolem3(_u19, _u25), _u25) | ~in(skolem4(_u19, _u25), _u25) )).
% 189.72/189.91 cnf(matrix-36, plain, ( ~relation(_u19) | ~function(_u19) | ( _u25 = relation_rng(_u19)) | ~in(_u15, relation_dom(_u19)) | ( skolem3(_u19, _u25) != apply(_u19, _u15)) | in(skolem5(_u19, _u25), relation_dom(_u19)) )).
% 189.72/189.91 cnf(matrix-37, plain, ( ~relation(_u19) | ~function(_u19) | ( _u25 = relation_rng(_u19)) | ~in(_u15, relation_dom(_u19)) | ( skolem3(_u19, _u25) != apply(_u19, _u15)) | ( skolem4(_u19, _u25) = apply(_u19, skolem5(_u19, _u25))) )).
% 189.72/189.91 cnf(matrix-38, plain, ( ~relation(_u19) | ~function(_u19) | ( _u25 = relation_rng(_u19)) | ~in(_u15, relation_dom(_u19)) | ( skolem3(_u19, _u25) != apply(_u19, _u15)) | ~in(skolem4(_u19, _u25), _u25) )).
% 189.72/189.91 cnf(matrix-39, plain, ( element(skolem6(_u27), _u27) )).
% 189.72/189.91 cnf(matrix-40, plain, ( empty(empty_set) )).
% 189.72/189.91 cnf(matrix-41, plain, ( relation(empty_set) )).
% 189.72/189.91 cnf(matrix-42, plain, ( relation_empty_yielding(empty_set) )).
% 189.72/189.91 cnf(matrix-43, plain, ( ~empty(powerset(_u28)) )).
% 189.72/189.91 cnf(matrix-44, plain, ( empty(empty_set) )).
% 189.72/189.91 cnf(matrix-45, plain, ( empty(empty_set) )).
% 189.72/189.91 cnf(matrix-46, plain, ( relation(empty_set) )).
% 189.72/189.91 cnf(matrix-47, plain, ( empty(_u29) | ~relation(_u29) | ~empty(relation_dom(_u29)) )).
% 189.72/189.91 cnf(matrix-48, plain, ( empty(_u30) | ~relation(_u30) | ~empty(relation_rng(_u30)) )).
% 189.72/189.91 cnf(matrix-49, plain, ( ~empty(_u31) | empty(relation_dom(_u31)) )).
% 189.72/189.91 cnf(matrix-50, plain, ( ~empty(_u31) | relation(relation_dom(_u31)) )).
% 189.72/189.91 cnf(matrix-51, plain, ( ~empty(_u32) | empty(relation_rng(_u32)) )).
% 189.72/189.91 cnf(matrix-52, plain, ( ~empty(_u32) | relation(relation_rng(_u32)) )).
% 189.72/189.91 cnf(matrix-53, plain, ( relation(skolem7) )).
% 189.72/189.91 cnf(matrix-54, plain, ( function(skolem7) )).
% 189.72/189.91 cnf(matrix-55, plain, ( empty(skolem8) )).
% 189.72/189.91 cnf(matrix-56, plain, ( relation(skolem8) )).
% 189.72/189.91 cnf(matrix-57, plain, ( empty(_u36) | element(skolem9(_u36), powerset(_u36)) )).
% 189.72/189.91 cnf(matrix-58, plain, ( empty(_u36) | ~empty(skolem9(_u36)) )).
% 189.72/189.91 cnf(matrix-59, plain, ( empty(skolem10) )).
% 189.72/189.91 cnf(matrix-60, plain, ( ~empty(skolem11) )).
% 189.72/189.91 cnf(matrix-61, plain, ( relation(skolem11) )).
% 189.72/189.91 cnf(matrix-62, plain, ( element(skolem12(_u40), powerset(_u40)) )).
% 189.72/189.91 cnf(matrix-63, plain, ( empty(skolem12(_u40)) )).
% 189.72/189.91 cnf(matrix-64, plain, ( ~empty(skolem13) )).
% 189.72/189.91 cnf(matrix-65, plain, ( relation(skolem14) )).
% 189.72/189.91 cnf(matrix-66, plain, ( relation_empty_yielding(skolem14) )).
% 189.72/189.91 cnf(matrix-67, plain, ( subset(_u44, _u44) )).
% 189.72/189.91 cnf(matrix-68, plain, ( relation(skolem16) )).
% 189.72/189.91 cnf(matrix-69, plain, ( function(skolem16) )).
% 189.72/189.91 cnf(matrix-70, plain, ( ~in(_u46, skolem15) | ~_def0(_u46) )).
% 189.72/189.91 cnf(matrix-71, plain, ( ~subset(skolem15, relation_rng(skolem16)) )).
% 189.72/189.91 cnf(matrix-72, plain, ( _def0(_u46) | in(skolem17(_u46), relation_dom(skolem16)) )).
% 189.72/189.91 cnf(matrix-73, plain, ( _def0(_u46) | ( _u46 = apply(skolem16, skolem17(_u46))) )).
% 189.72/189.91 cnf(matrix-74, plain, ( ~in(_u50, _u49) | element(_u50, _u49) )).
% 189.72/189.91 cnf(matrix-75, plain, ( ~element(_u52, _u51) | empty(_u51) | in(_u52, _u51) )).
% 189.72/189.91 cnf(matrix-76, plain, ( ~element(_u57, powerset(_u55)) | subset(_u57, _u55) )).
% 189.72/189.91 cnf(matrix-77, plain, ( ~subset(_u58, _u56) | element(_u58, powerset(_u56)) )).
% 189.72/189.91 cnf(matrix-78, plain, ( ~in(_u61, _u60) | ~element(_u60, powerset(_u59)) | element(_u61, _u59) )).
% 189.72/189.91 cnf(matrix-79, plain, ( ~in(_u64, _u63) | ~element(_u63, powerset(_u62)) | ~empty(_u62) )).
% 189.72/189.91 cnf(matrix-80, plain, ( ~empty(_u65) | ( _u65 = empty_set) )).
% 189.72/189.91 cnf(matrix-81, plain, ( ~in(_u67, _u66) | ~empty(_u66) )).
% 189.72/189.91 cnf(matrix-82, plain, ( ~empty(_u69) | ( _u69 = _u68) | ~empty(_u68) )).
% 189.72/189.91
% 189.72/189.91 % Proof stack:
% 189.72/189.91 cnf(proof-stack, plain,
% 189.72/189.91 proof_stack(
% 189.72/189.91 start(69),
% 189.72/189.91 left_branch(0, 32, 1, 2),
% 189.72/189.91 left_branch(0, 68, 0, 3),
% 189.72/189.91 right_branch(3),
% 189.72/189.91 left_branch(0, 73, 1, 4),
% 189.72/189.91 left_branch(0, 70, 1, 5),
% 189.72/189.91 left_branch(0, 28, 1, 6),
% 189.72/189.91 left_branch(0, 71, 0, 7),
% 189.72/189.91 right_branch(7),
% 189.72/189.91 right_branch(6),
% 189.72/189.91 right_branch(5),
% 189.72/189.91 right_branch(4),
% 189.72/189.91 left_branch(0, 72, 1, 5),
% 189.72/189.91 left_branch(0, 70, 1, 6),
% 189.72/189.91 left_branch(0, 28, 1, 7),
% 189.72/189.91 left_branch(0, 71, 0, 8),
% 189.72/189.91 right_branch(8),
% 189.72/189.91 right_branch(7),
% 189.72/189.91 right_branch(6),
% 189.72/189.91 right_branch(5),
% 189.72/189.91 left_branch(0, 3, 1, 6),
% 189.72/189.91 left_branch(0, 1, 1, 7),
% 189.72/189.91 left_branch(0, 0, 0, 8),
% 189.72/189.91 right_branch(8),
% 189.72/189.91 right_branch(7),
% 189.72/189.91 right_branch(6),
% 189.72/189.91 left_branch(0, 29, 1, 7),
% 189.72/189.91 left_branch(0, 71, 0, 8),
% 189.72/189.91 right_branch(8),
% 189.72/189.91 right_branch(7),
% 189.72/189.91 right_branch(2)
% 189.72/189.91 )).
% 189.72/189.91 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------