TSTP Solution File: SEU294+1 by ConnectPP---0.2.2
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%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : SEU294+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 : n022.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 09:20:46 EST 2024
% Result : Theorem 0.18s 0.41s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU294+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n022.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 10:50:49 EST 2024
% 0.12/0.34 % CPUTime :
% 0.18/0.41 % SZS status Theorem for theBenchmark
% 0.18/0.41 % SZS output start Proof for theBenchmark
% 0.18/0.41
% 0.18/0.41 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 0.18/0.41 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.18/0.41
% 0.18/0.41 % Formula: cc1_arytm_3 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(cc1_arytm_3-1, axiom, ( ~ordinal(_u3) | ~element(_u2, _u3) | epsilon_transitive(_u2) )).
% 0.18/0.41 cnf(cc1_arytm_3-2, axiom, ( ~ordinal(_u3) | ~element(_u2, _u3) | epsilon_connected(_u2) )).
% 0.18/0.41 cnf(cc1_arytm_3-3, axiom, ( ~ordinal(_u3) | ~element(_u2, _u3) | ordinal(_u2) )).
% 0.18/0.41
% 0.18/0.41 % Formula: cc1_finset_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(cc1_finset_1-1, axiom, ( ~empty(_u4) | finite(_u4) )).
% 0.18/0.41
% 0.18/0.41 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(cc1_funct_1-1, axiom, ( ~empty(_u5) | function(_u5) )).
% 0.18/0.41
% 0.18/0.41 % Formula: cc1_ordinal1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(cc1_ordinal1-1, axiom, ( ~ordinal(_u6) | epsilon_transitive(_u6) )).
% 0.18/0.41 cnf(cc1_ordinal1-2, axiom, ( ~ordinal(_u6) | epsilon_connected(_u6) )).
% 0.18/0.41
% 0.18/0.41 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(cc1_relat_1-1, axiom, ( ~empty(_u7) | relation(_u7) )).
% 0.18/0.41
% 0.18/0.41 % Formula: cc2_arytm_3 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(cc2_arytm_3-1, axiom, ( ~empty(_u8) | ~ordinal(_u8) | epsilon_transitive(_u8) )).
% 0.18/0.41 cnf(cc2_arytm_3-2, axiom, ( ~empty(_u8) | ~ordinal(_u8) | epsilon_connected(_u8) )).
% 0.18/0.41 cnf(cc2_arytm_3-3, axiom, ( ~empty(_u8) | ~ordinal(_u8) | natural(_u8) )).
% 0.18/0.41
% 0.18/0.41 % Formula: cc2_finset_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(cc2_finset_1-1, axiom, ( ~finite(_u10) | ~element(_u9, powerset(_u10)) | finite(_u9) )).
% 0.18/0.41
% 0.18/0.41 % Formula: cc2_funct_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(cc2_funct_1-1, axiom, ( ~relation(_u11) | ~empty(_u11) | ~function(_u11) | one_to_one(_u11) )).
% 0.18/0.41
% 0.18/0.41 % Formula: cc2_ordinal1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(cc2_ordinal1-1, axiom, ( ~epsilon_transitive(_u12) | ~epsilon_connected(_u12) | ordinal(_u12) )).
% 0.18/0.41
% 0.18/0.41 % Formula: cc3_ordinal1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(cc3_ordinal1-1, axiom, ( ~empty(_u13) | epsilon_transitive(_u13) )).
% 0.18/0.41 cnf(cc3_ordinal1-2, axiom, ( ~empty(_u13) | epsilon_connected(_u13) )).
% 0.18/0.41 cnf(cc3_ordinal1-3, axiom, ( ~empty(_u13) | ordinal(_u13) )).
% 0.18/0.41
% 0.18/0.41 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 0.18/0.41
% 0.18/0.41 % Formula: dt_k1_zfmisc_1 ( axiom ) converted to clauses:
% 0.18/0.41
% 0.18/0.41 % Formula: dt_m1_subset_1 ( axiom ) converted to clauses:
% 0.18/0.41
% 0.18/0.41 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(existence_m1_subset_1-1, axiom, ( element(skolem1(_u15), _u15) )).
% 0.18/0.41
% 0.18/0.41 % Formula: fc12_relat_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(fc12_relat_1-1, axiom, ( empty(empty_set) )).
% 0.18/0.41 cnf(fc12_relat_1-2, axiom, ( relation(empty_set) )).
% 0.18/0.41 cnf(fc12_relat_1-3, axiom, ( relation_empty_yielding(empty_set) )).
% 0.18/0.41
% 0.18/0.41 % Formula: fc1_subset_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(fc1_subset_1-1, axiom, ( ~empty(powerset(_u16)) )).
% 0.18/0.41
% 0.18/0.41 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 0.18/0.41
% 0.18/0.41 % Formula: fc2_ordinal1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(fc2_ordinal1-1, axiom, ( relation(empty_set) )).
% 0.18/0.41 cnf(fc2_ordinal1-2, axiom, ( relation_empty_yielding(empty_set) )).
% 0.18/0.41 cnf(fc2_ordinal1-3, axiom, ( function(empty_set) )).
% 0.18/0.41 cnf(fc2_ordinal1-4, axiom, ( one_to_one(empty_set) )).
% 0.18/0.41 cnf(fc2_ordinal1-5, axiom, ( empty(empty_set) )).
% 0.18/0.41 cnf(fc2_ordinal1-6, axiom, ( epsilon_transitive(empty_set) )).
% 0.18/0.41 cnf(fc2_ordinal1-7, axiom, ( epsilon_connected(empty_set) )).
% 0.18/0.41 cnf(fc2_ordinal1-8, axiom, ( ordinal(empty_set) )).
% 0.18/0.41
% 0.18/0.41 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 0.18/0.41 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc1_arytm_3 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc1_arytm_3-1, axiom, ( ~empty(skolem2) )).
% 0.18/0.41 cnf(rc1_arytm_3-2, axiom, ( epsilon_transitive(skolem2) )).
% 0.18/0.41 cnf(rc1_arytm_3-3, axiom, ( epsilon_connected(skolem2) )).
% 0.18/0.41 cnf(rc1_arytm_3-4, axiom, ( ordinal(skolem2) )).
% 0.18/0.41 cnf(rc1_arytm_3-5, axiom, ( natural(skolem2) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc1_finset_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc1_finset_1-1, axiom, ( ~empty(skolem3) )).
% 0.18/0.41 cnf(rc1_finset_1-2, axiom, ( finite(skolem3) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc1_funct_1-1, axiom, ( relation(skolem4) )).
% 0.18/0.41 cnf(rc1_funct_1-2, axiom, ( function(skolem4) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc1_ordinal1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc1_ordinal1-1, axiom, ( epsilon_transitive(skolem5) )).
% 0.18/0.41 cnf(rc1_ordinal1-2, axiom, ( epsilon_connected(skolem5) )).
% 0.18/0.41 cnf(rc1_ordinal1-3, axiom, ( ordinal(skolem5) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc1_relat_1-1, axiom, ( empty(skolem6) )).
% 0.18/0.41 cnf(rc1_relat_1-2, axiom, ( relation(skolem6) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc1_subset_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc1_subset_1-1, axiom, ( empty(_u23) | element(skolem7(_u23), powerset(_u23)) )).
% 0.18/0.41 cnf(rc1_subset_1-2, axiom, ( empty(_u23) | ~empty(skolem7(_u23)) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc1_xboole_0-1, axiom, ( empty(skolem8) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc2_finset_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc2_finset_1-1, axiom, ( element(skolem9(_u26), powerset(_u26)) )).
% 0.18/0.41 cnf(rc2_finset_1-2, axiom, ( empty(skolem9(_u26)) )).
% 0.18/0.41 cnf(rc2_finset_1-3, axiom, ( relation(skolem9(_u26)) )).
% 0.18/0.41 cnf(rc2_finset_1-4, axiom, ( function(skolem9(_u26)) )).
% 0.18/0.41 cnf(rc2_finset_1-5, axiom, ( one_to_one(skolem9(_u26)) )).
% 0.18/0.41 cnf(rc2_finset_1-6, axiom, ( epsilon_transitive(skolem9(_u26)) )).
% 0.18/0.41 cnf(rc2_finset_1-7, axiom, ( epsilon_connected(skolem9(_u26)) )).
% 0.18/0.41 cnf(rc2_finset_1-8, axiom, ( ordinal(skolem9(_u26)) )).
% 0.18/0.41 cnf(rc2_finset_1-9, axiom, ( natural(skolem9(_u26)) )).
% 0.18/0.41 cnf(rc2_finset_1-10, axiom, ( finite(skolem9(_u26)) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc2_funct_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc2_funct_1-1, axiom, ( relation(skolem10) )).
% 0.18/0.41 cnf(rc2_funct_1-2, axiom, ( empty(skolem10) )).
% 0.18/0.41 cnf(rc2_funct_1-3, axiom, ( function(skolem10) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc2_ordinal1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc2_ordinal1-1, axiom, ( relation(skolem11) )).
% 0.18/0.41 cnf(rc2_ordinal1-2, axiom, ( function(skolem11) )).
% 0.18/0.41 cnf(rc2_ordinal1-3, axiom, ( one_to_one(skolem11) )).
% 0.18/0.41 cnf(rc2_ordinal1-4, axiom, ( empty(skolem11) )).
% 0.18/0.41 cnf(rc2_ordinal1-5, axiom, ( epsilon_transitive(skolem11) )).
% 0.18/0.41 cnf(rc2_ordinal1-6, axiom, ( epsilon_connected(skolem11) )).
% 0.18/0.41 cnf(rc2_ordinal1-7, axiom, ( ordinal(skolem11) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem12) )).
% 0.18/0.41 cnf(rc2_relat_1-2, axiom, ( relation(skolem12) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc2_subset_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc2_subset_1-1, axiom, ( element(skolem13(_u31), powerset(_u31)) )).
% 0.18/0.41 cnf(rc2_subset_1-2, axiom, ( empty(skolem13(_u31)) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem14) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc3_finset_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc3_finset_1-1, axiom, ( empty(_u34) | element(skolem15(_u34), powerset(_u34)) )).
% 0.18/0.41 cnf(rc3_finset_1-2, axiom, ( empty(_u34) | ~empty(skolem15(_u34)) )).
% 0.18/0.41 cnf(rc3_finset_1-3, axiom, ( empty(_u34) | finite(skolem15(_u34)) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc3_funct_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc3_funct_1-1, axiom, ( relation(skolem16) )).
% 0.18/0.41 cnf(rc3_funct_1-2, axiom, ( function(skolem16) )).
% 0.18/0.41 cnf(rc3_funct_1-3, axiom, ( one_to_one(skolem16) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc3_ordinal1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc3_ordinal1-1, axiom, ( ~empty(skolem17) )).
% 0.18/0.41 cnf(rc3_ordinal1-2, axiom, ( epsilon_transitive(skolem17) )).
% 0.18/0.41 cnf(rc3_ordinal1-3, axiom, ( epsilon_connected(skolem17) )).
% 0.18/0.41 cnf(rc3_ordinal1-4, axiom, ( ordinal(skolem17) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc3_relat_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc3_relat_1-1, axiom, ( relation(skolem18) )).
% 0.18/0.41 cnf(rc3_relat_1-2, axiom, ( relation_empty_yielding(skolem18) )).
% 0.18/0.41
% 0.18/0.41 % Formula: rc4_funct_1 ( axiom ) converted to clauses:
% 0.18/0.41 cnf(rc4_funct_1-1, axiom, ( relation(skolem19) )).
% 0.18/0.41 cnf(rc4_funct_1-2, axiom, ( relation_empty_yielding(skolem19) )).
% 0.18/0.41 cnf(rc4_funct_1-3, axiom, ( function(skolem19) )).
% 0.18/0.41
% 0.18/0.41 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 0.18/0.41 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u40, _u40) )).
% 0.18/0.41
% 0.18/0.41 % Formula: t13_finset_1 ( conjecture ) converted to clauses:
% 0.18/0.41 cnf(t13_finset_1-1, negated_conjecture, ( ~finite(skolem20) )).
% 0.18/0.41 cnf(t13_finset_1-2, negated_conjecture, ( subset(skolem20, skolem21) )).
% 0.18/0.41 cnf(t13_finset_1-3, negated_conjecture, ( finite(skolem21) )).
% 0.18/0.41
% 0.18/0.41 % Formula: t1_subset ( axiom ) converted to clauses:
% 0.18/0.41 cnf(t1_subset-1, axiom, ( ~in(_u44, _u43) | element(_u44, _u43) )).
% 0.18/0.41
% 0.18/0.41 % Formula: t2_subset ( axiom ) converted to clauses:
% 0.18/0.41 cnf(t2_subset-1, axiom, ( ~element(_u46, _u45) | empty(_u45) | in(_u46, _u45) )).
% 0.18/0.41
% 0.18/0.41 % Formula: t3_subset ( axiom ) converted to clauses:
% 0.18/0.41 cnf(t3_subset-1, axiom, ( ~element(_u51, powerset(_u49)) | subset(_u51, _u49) )).
% 0.18/0.41 cnf(t3_subset-2, axiom, ( ~subset(_u52, _u50) | element(_u52, powerset(_u50)) )).
% 0.18/0.41
% 0.18/0.41 % Formula: t4_subset ( axiom ) converted to clauses:
% 0.18/0.41 cnf(t4_subset-1, axiom, ( ~in(_u55, _u54) | ~element(_u54, powerset(_u53)) | element(_u55, _u53) )).
% 0.18/0.41
% 0.18/0.41 % Formula: t5_subset ( axiom ) converted to clauses:
% 0.18/0.41 cnf(t5_subset-1, axiom, ( ~in(_u58, _u57) | ~element(_u57, powerset(_u56)) | ~empty(_u56) )).
% 0.18/0.41
% 0.18/0.41 % Formula: t6_boole ( axiom ) converted to clauses:
% 0.18/0.41 cnf(t6_boole-1, axiom, ( ~empty(_u59) | ( _u59 = empty_set) )).
% 0.18/0.41
% 0.18/0.41 % Formula: t7_boole ( axiom ) converted to clauses:
% 0.18/0.41 cnf(t7_boole-1, axiom, ( ~in(_u61, _u60) | ~empty(_u60) )).
% 0.18/0.41
% 0.18/0.41 % Formula: t8_boole ( axiom ) converted to clauses:
% 0.18/0.41 cnf(t8_boole-1, axiom, ( ~empty(_u63) | ( _u63 = _u62) | ~empty(_u62) )).
% 0.18/0.41
% 0.18/0.41 % Problem matrix:
% 0.18/0.41 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.18/0.41 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.18/0.41 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.18/0.41 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 0.18/0.41 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 0.18/0.41 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( skolem7(__eqx_0) = skolem7(__eqy_0)) )).
% 0.18/0.41 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( skolem9(__eqx_0) = skolem9(__eqy_0)) )).
% 0.18/0.41 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( skolem13(__eqx_0) = skolem13(__eqy_0)) )).
% 0.18/0.41 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( skolem15(__eqx_0) = skolem15(__eqy_0)) )).
% 0.18/0.41 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 0.18/0.41 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ~ordinal(__eqx_0) | ordinal(__eqy_0) )).
% 0.18/0.41 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 0.18/0.41 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ~epsilon_transitive(__eqx_0) | epsilon_transitive(__eqy_0) )).
% 0.18/0.41 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ~epsilon_connected(__eqx_0) | epsilon_connected(__eqy_0) )).
% 0.18/0.41 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 0.18/0.41 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~finite(__eqx_0) | finite(__eqy_0) )).
% 0.18/0.41 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 0.18/0.41 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 0.18/0.41 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~natural(__eqx_0) | natural(__eqy_0) )).
% 0.18/0.41 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 0.18/0.41 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ~relation_empty_yielding(__eqx_0) | relation_empty_yielding(__eqy_0) )).
% 0.18/0.41 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 0.18/0.41 cnf(matrix-22, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.18/0.41 cnf(matrix-23, plain, ( ~ordinal(_u3) | ~element(_u2, _u3) | epsilon_transitive(_u2) )).
% 0.18/0.41 cnf(matrix-24, plain, ( ~ordinal(_u3) | ~element(_u2, _u3) | epsilon_connected(_u2) )).
% 0.18/0.41 cnf(matrix-25, plain, ( ~ordinal(_u3) | ~element(_u2, _u3) | ordinal(_u2) )).
% 0.18/0.41 cnf(matrix-26, plain, ( ~empty(_u4) | finite(_u4) )).
% 0.18/0.41 cnf(matrix-27, plain, ( ~empty(_u5) | function(_u5) )).
% 0.18/0.41 cnf(matrix-28, plain, ( ~ordinal(_u6) | epsilon_transitive(_u6) )).
% 0.18/0.41 cnf(matrix-29, plain, ( ~ordinal(_u6) | epsilon_connected(_u6) )).
% 0.18/0.41 cnf(matrix-30, plain, ( ~empty(_u7) | relation(_u7) )).
% 0.18/0.41 cnf(matrix-31, plain, ( ~empty(_u8) | ~ordinal(_u8) | epsilon_transitive(_u8) )).
% 0.18/0.41 cnf(matrix-32, plain, ( ~empty(_u8) | ~ordinal(_u8) | epsilon_connected(_u8) )).
% 0.18/0.41 cnf(matrix-33, plain, ( ~empty(_u8) | ~ordinal(_u8) | natural(_u8) )).
% 0.18/0.41 cnf(matrix-34, plain, ( ~finite(_u10) | ~element(_u9, powerset(_u10)) | finite(_u9) )).
% 0.18/0.41 cnf(matrix-35, plain, ( ~relation(_u11) | ~empty(_u11) | ~function(_u11) | one_to_one(_u11) )).
% 0.18/0.41 cnf(matrix-36, plain, ( ~epsilon_transitive(_u12) | ~epsilon_connected(_u12) | ordinal(_u12) )).
% 0.18/0.41 cnf(matrix-37, plain, ( ~empty(_u13) | epsilon_transitive(_u13) )).
% 0.18/0.41 cnf(matrix-38, plain, ( ~empty(_u13) | epsilon_connected(_u13) )).
% 0.18/0.41 cnf(matrix-39, plain, ( ~empty(_u13) | ordinal(_u13) )).
% 0.18/0.41 cnf(matrix-40, plain, ( element(skolem1(_u15), _u15) )).
% 0.18/0.41 cnf(matrix-41, plain, ( empty(empty_set) )).
% 0.18/0.41 cnf(matrix-42, plain, ( relation(empty_set) )).
% 0.18/0.41 cnf(matrix-43, plain, ( relation_empty_yielding(empty_set) )).
% 0.18/0.41 cnf(matrix-44, plain, ( ~empty(powerset(_u16)) )).
% 0.18/0.41 cnf(matrix-45, plain, ( empty(empty_set) )).
% 0.18/0.41 cnf(matrix-46, plain, ( relation(empty_set) )).
% 0.18/0.41 cnf(matrix-47, plain, ( relation_empty_yielding(empty_set) )).
% 0.18/0.41 cnf(matrix-48, plain, ( function(empty_set) )).
% 0.18/0.41 cnf(matrix-49, plain, ( one_to_one(empty_set) )).
% 0.18/0.41 cnf(matrix-50, plain, ( empty(empty_set) )).
% 0.18/0.41 cnf(matrix-51, plain, ( epsilon_transitive(empty_set) )).
% 0.18/0.41 cnf(matrix-52, plain, ( epsilon_connected(empty_set) )).
% 0.18/0.41 cnf(matrix-53, plain, ( ordinal(empty_set) )).
% 0.18/0.41 cnf(matrix-54, plain, ( empty(empty_set) )).
% 0.18/0.41 cnf(matrix-55, plain, ( relation(empty_set) )).
% 0.18/0.41 cnf(matrix-56, plain, ( ~empty(skolem2) )).
% 0.18/0.41 cnf(matrix-57, plain, ( epsilon_transitive(skolem2) )).
% 0.18/0.41 cnf(matrix-58, plain, ( epsilon_connected(skolem2) )).
% 0.18/0.41 cnf(matrix-59, plain, ( ordinal(skolem2) )).
% 0.18/0.41 cnf(matrix-60, plain, ( natural(skolem2) )).
% 0.18/0.41 cnf(matrix-61, plain, ( ~empty(skolem3) )).
% 0.18/0.41 cnf(matrix-62, plain, ( finite(skolem3) )).
% 0.18/0.41 cnf(matrix-63, plain, ( relation(skolem4) )).
% 0.18/0.41 cnf(matrix-64, plain, ( function(skolem4) )).
% 0.18/0.41 cnf(matrix-65, plain, ( epsilon_transitive(skolem5) )).
% 0.18/0.41 cnf(matrix-66, plain, ( epsilon_connected(skolem5) )).
% 0.18/0.41 cnf(matrix-67, plain, ( ordinal(skolem5) )).
% 0.18/0.41 cnf(matrix-68, plain, ( empty(skolem6) )).
% 0.18/0.41 cnf(matrix-69, plain, ( relation(skolem6) )).
% 0.18/0.41 cnf(matrix-70, plain, ( empty(_u23) | element(skolem7(_u23), powerset(_u23)) )).
% 0.18/0.41 cnf(matrix-71, plain, ( empty(_u23) | ~empty(skolem7(_u23)) )).
% 0.18/0.41 cnf(matrix-72, plain, ( empty(skolem8) )).
% 0.18/0.41 cnf(matrix-73, plain, ( element(skolem9(_u26), powerset(_u26)) )).
% 0.18/0.41 cnf(matrix-74, plain, ( empty(skolem9(_u26)) )).
% 0.18/0.41 cnf(matrix-75, plain, ( relation(skolem9(_u26)) )).
% 0.18/0.41 cnf(matrix-76, plain, ( function(skolem9(_u26)) )).
% 0.18/0.41 cnf(matrix-77, plain, ( one_to_one(skolem9(_u26)) )).
% 0.18/0.41 cnf(matrix-78, plain, ( epsilon_transitive(skolem9(_u26)) )).
% 0.18/0.41 cnf(matrix-79, plain, ( epsilon_connected(skolem9(_u26)) )).
% 0.18/0.41 cnf(matrix-80, plain, ( ordinal(skolem9(_u26)) )).
% 0.18/0.41 cnf(matrix-81, plain, ( natural(skolem9(_u26)) )).
% 0.18/0.41 cnf(matrix-82, plain, ( finite(skolem9(_u26)) )).
% 0.18/0.41 cnf(matrix-83, plain, ( relation(skolem10) )).
% 0.18/0.41 cnf(matrix-84, plain, ( empty(skolem10) )).
% 0.18/0.41 cnf(matrix-85, plain, ( function(skolem10) )).
% 0.18/0.41 cnf(matrix-86, plain, ( relation(skolem11) )).
% 0.18/0.41 cnf(matrix-87, plain, ( function(skolem11) )).
% 0.18/0.41 cnf(matrix-88, plain, ( one_to_one(skolem11) )).
% 0.18/0.41 cnf(matrix-89, plain, ( empty(skolem11) )).
% 0.18/0.41 cnf(matrix-90, plain, ( epsilon_transitive(skolem11) )).
% 0.18/0.41 cnf(matrix-91, plain, ( epsilon_connected(skolem11) )).
% 0.18/0.41 cnf(matrix-92, plain, ( ordinal(skolem11) )).
% 0.18/0.41 cnf(matrix-93, plain, ( ~empty(skolem12) )).
% 0.18/0.41 cnf(matrix-94, plain, ( relation(skolem12) )).
% 0.18/0.41 cnf(matrix-95, plain, ( element(skolem13(_u31), powerset(_u31)) )).
% 0.18/0.41 cnf(matrix-96, plain, ( empty(skolem13(_u31)) )).
% 0.18/0.41 cnf(matrix-97, plain, ( ~empty(skolem14) )).
% 0.18/0.41 cnf(matrix-98, plain, ( empty(_u34) | element(skolem15(_u34), powerset(_u34)) )).
% 0.18/0.41 cnf(matrix-99, plain, ( empty(_u34) | ~empty(skolem15(_u34)) )).
% 0.18/0.41 cnf(matrix-100, plain, ( empty(_u34) | finite(skolem15(_u34)) )).
% 0.18/0.41 cnf(matrix-101, plain, ( relation(skolem16) )).
% 0.18/0.41 cnf(matrix-102, plain, ( function(skolem16) )).
% 0.18/0.41 cnf(matrix-103, plain, ( one_to_one(skolem16) )).
% 0.18/0.41 cnf(matrix-104, plain, ( ~empty(skolem17) )).
% 0.18/0.41 cnf(matrix-105, plain, ( epsilon_transitive(skolem17) )).
% 0.18/0.41 cnf(matrix-106, plain, ( epsilon_connected(skolem17) )).
% 0.18/0.41 cnf(matrix-107, plain, ( ordinal(skolem17) )).
% 0.18/0.41 cnf(matrix-108, plain, ( relation(skolem18) )).
% 0.18/0.41 cnf(matrix-109, plain, ( relation_empty_yielding(skolem18) )).
% 0.18/0.41 cnf(matrix-110, plain, ( relation(skolem19) )).
% 0.18/0.41 cnf(matrix-111, plain, ( relation_empty_yielding(skolem19) )).
% 0.18/0.41 cnf(matrix-112, plain, ( function(skolem19) )).
% 0.18/0.41 cnf(matrix-113, plain, ( subset(_u40, _u40) )).
% 0.18/0.41 cnf(matrix-114, plain, ( ~finite(skolem20) )).
% 0.18/0.41 cnf(matrix-115, plain, ( subset(skolem20, skolem21) )).
% 0.18/0.41 cnf(matrix-116, plain, ( finite(skolem21) )).
% 0.18/0.41 cnf(matrix-117, plain, ( ~in(_u44, _u43) | element(_u44, _u43) )).
% 0.18/0.41 cnf(matrix-118, plain, ( ~element(_u46, _u45) | empty(_u45) | in(_u46, _u45) )).
% 0.18/0.41 cnf(matrix-119, plain, ( ~element(_u51, powerset(_u49)) | subset(_u51, _u49) )).
% 0.18/0.41 cnf(matrix-120, plain, ( ~subset(_u52, _u50) | element(_u52, powerset(_u50)) )).
% 0.18/0.41 cnf(matrix-121, plain, ( ~in(_u55, _u54) | ~element(_u54, powerset(_u53)) | element(_u55, _u53) )).
% 0.18/0.41 cnf(matrix-122, plain, ( ~in(_u58, _u57) | ~element(_u57, powerset(_u56)) | ~empty(_u56) )).
% 0.18/0.41 cnf(matrix-123, plain, ( ~empty(_u59) | ( _u59 = empty_set) )).
% 0.18/0.41 cnf(matrix-124, plain, ( ~in(_u61, _u60) | ~empty(_u60) )).
% 0.18/0.41 cnf(matrix-125, plain, ( ~empty(_u63) | ( _u63 = _u62) | ~empty(_u62) )).
% 0.18/0.41
% 0.18/0.41 % Proof stack:
% 0.18/0.41 cnf(proof-stack, plain,
% 0.18/0.41 proof_stack(
% 0.18/0.41 start(114),
% 0.18/0.41 left_branch(0, 34, 2, 2),
% 0.18/0.41 left_branch(0, 116, 0, 3),
% 0.18/0.41 right_branch(3),
% 0.18/0.41 left_branch(0, 120, 1, 4),
% 0.18/0.41 left_branch(0, 115, 0, 5),
% 0.18/0.41 right_branch(5),
% 0.18/0.41 right_branch(4),
% 0.18/0.41 right_branch(2)
% 0.18/0.41 )).
% 0.18/0.41 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------