TSTP Solution File: SEU083+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU083+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 : n012.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 14:33:03 EDT 2024
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU083+1 : TPTP v8.1.2. Released v3.2.0.
% 0.04/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n012.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 : Wed Mar 20 14:18:45 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem for theBenchmark
% 0.19/0.38 % SZS output start Proof for theBenchmark
% 0.19/0.38
% 0.19/0.38 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 0.19/0.38 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u1, _u1) )).
% 0.19/0.38
% 0.19/0.38 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 0.19/0.38 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u3, _u2) | ~in(_u2, _u3) )).
% 0.19/0.38
% 0.19/0.38 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 0.19/0.38 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 0.19/0.38
% 0.19/0.38 % Formula: fc12_relat_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(fc12_relat_1-1, axiom, ( empty(empty_set) )).
% 0.19/0.38 cnf(fc12_relat_1-2, axiom, ( relation(empty_set) )).
% 0.19/0.38 cnf(fc12_relat_1-3, axiom, ( relation_empty_yielding(empty_set) )).
% 0.19/0.38
% 0.19/0.38 % Formula: fc2_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(fc2_ordinal1-1, axiom, ( relation(empty_set) )).
% 0.19/0.38 cnf(fc2_ordinal1-2, axiom, ( relation_empty_yielding(empty_set) )).
% 0.19/0.38 cnf(fc2_ordinal1-3, axiom, ( function(empty_set) )).
% 0.19/0.38 cnf(fc2_ordinal1-4, axiom, ( one_to_one(empty_set) )).
% 0.19/0.38 cnf(fc2_ordinal1-5, axiom, ( empty(empty_set) )).
% 0.19/0.38 cnf(fc2_ordinal1-6, axiom, ( epsilon_transitive(empty_set) )).
% 0.19/0.38 cnf(fc2_ordinal1-7, axiom, ( epsilon_connected(empty_set) )).
% 0.19/0.38 cnf(fc2_ordinal1-8, axiom, ( ordinal(empty_set) )).
% 0.19/0.38
% 0.19/0.38 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 0.19/0.38
% 0.19/0.38 % Formula: t1_boole ( axiom ) converted to clauses:
% 0.19/0.38 cnf(t1_boole-1, axiom, ( ( set_union2(_u4, empty_set) = _u4) )).
% 0.19/0.38
% 0.19/0.38 % Formula: t1_subset ( axiom ) converted to clauses:
% 0.19/0.38 cnf(t1_subset-1, axiom, ( ~in(_u6, _u5) | element(_u6, _u5) )).
% 0.19/0.38
% 0.19/0.38 % Formula: t4_subset ( axiom ) converted to clauses:
% 0.19/0.38 cnf(t4_subset-1, axiom, ( ~in(_u9, _u8) | ~element(_u8, powerset(_u7)) | element(_u9, _u7) )).
% 0.19/0.38
% 0.19/0.38 % Formula: t5_subset ( axiom ) converted to clauses:
% 0.19/0.38 cnf(t5_subset-1, axiom, ( ~in(_u12, _u11) | ~element(_u11, powerset(_u10)) | ~empty(_u10) )).
% 0.19/0.38
% 0.19/0.38 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(existence_m1_subset_1-1, axiom, ( element(skolem1(_u14), _u14) )).
% 0.19/0.38
% 0.19/0.38 % Formula: cc1_finset_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(cc1_finset_1-1, axiom, ( ~empty(_u15) | finite(_u15) )).
% 0.19/0.38
% 0.19/0.38 % Formula: cc2_finset_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(cc2_finset_1-1, axiom, ( ~finite(_u17) | ~element(_u16, powerset(_u17)) | finite(_u16) )).
% 0.19/0.38
% 0.19/0.38 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(cc1_funct_1-1, axiom, ( ~empty(_u18) | function(_u18) )).
% 0.19/0.38
% 0.19/0.38 % Formula: cc2_funct_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(cc2_funct_1-1, axiom, ( ~relation(_u19) | ~empty(_u19) | ~function(_u19) | one_to_one(_u19) )).
% 0.19/0.38
% 0.19/0.38 % Formula: fc2_relat_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(fc2_relat_1-1, axiom, ( ~relation(_u21) | ~relation(_u20) | relation(set_union2(_u21, _u20)) )).
% 0.19/0.38
% 0.19/0.38 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(cc1_relat_1-1, axiom, ( ~empty(_u22) | relation(_u22) )).
% 0.19/0.38
% 0.19/0.38 % Formula: fc8_arytm_3 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(fc8_arytm_3-1, axiom, ( ~empty(positive_rationals) )).
% 0.19/0.38
% 0.19/0.38 % Formula: cc1_arytm_3 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(cc1_arytm_3-1, axiom, ( ~ordinal(_u24) | ~element(_u23, _u24) | epsilon_transitive(_u23) )).
% 0.19/0.38 cnf(cc1_arytm_3-2, axiom, ( ~ordinal(_u24) | ~element(_u23, _u24) | epsilon_connected(_u23) )).
% 0.19/0.38 cnf(cc1_arytm_3-3, axiom, ( ~ordinal(_u24) | ~element(_u23, _u24) | ordinal(_u23) )).
% 0.19/0.38
% 0.19/0.38 % Formula: cc2_arytm_3 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(cc2_arytm_3-1, axiom, ( ~empty(_u25) | ~ordinal(_u25) | epsilon_transitive(_u25) )).
% 0.19/0.38 cnf(cc2_arytm_3-2, axiom, ( ~empty(_u25) | ~ordinal(_u25) | epsilon_connected(_u25) )).
% 0.19/0.38 cnf(cc2_arytm_3-3, axiom, ( ~empty(_u25) | ~ordinal(_u25) | natural(_u25) )).
% 0.19/0.38
% 0.19/0.38 % Formula: cc4_arytm_3 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(cc4_arytm_3-1, axiom, ( ~element(_u26, positive_rationals) | ~ordinal(_u26) | epsilon_transitive(_u26) )).
% 0.19/0.38 cnf(cc4_arytm_3-2, axiom, ( ~element(_u26, positive_rationals) | ~ordinal(_u26) | epsilon_connected(_u26) )).
% 0.19/0.38 cnf(cc4_arytm_3-3, axiom, ( ~element(_u26, positive_rationals) | ~ordinal(_u26) | natural(_u26) )).
% 0.19/0.38
% 0.19/0.38 % Formula: cc1_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(cc1_ordinal1-1, axiom, ( ~ordinal(_u27) | epsilon_transitive(_u27) )).
% 0.19/0.38 cnf(cc1_ordinal1-2, axiom, ( ~ordinal(_u27) | epsilon_connected(_u27) )).
% 0.19/0.38
% 0.19/0.38 % Formula: cc2_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(cc2_ordinal1-1, axiom, ( ~epsilon_transitive(_u28) | ~epsilon_connected(_u28) | ordinal(_u28) )).
% 0.19/0.38
% 0.19/0.38 % Formula: cc3_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(cc3_ordinal1-1, axiom, ( ~empty(_u29) | epsilon_transitive(_u29) )).
% 0.19/0.38 cnf(cc3_ordinal1-2, axiom, ( ~empty(_u29) | epsilon_connected(_u29) )).
% 0.19/0.38 cnf(cc3_ordinal1-3, axiom, ( ~empty(_u29) | ordinal(_u29) )).
% 0.19/0.38
% 0.19/0.38 % Formula: fc1_subset_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(fc1_subset_1-1, axiom, ( ~empty(powerset(_u30)) )).
% 0.19/0.38
% 0.19/0.38 % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(fc2_xboole_0-1, axiom, ( empty(_u32) | ~empty(set_union2(_u32, _u31)) )).
% 0.19/0.38
% 0.19/0.38 % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(fc3_xboole_0-1, axiom, ( empty(_u34) | ~empty(set_union2(_u33, _u34)) )).
% 0.19/0.38
% 0.19/0.38 % Formula: t2_subset ( axiom ) converted to clauses:
% 0.19/0.38 cnf(t2_subset-1, axiom, ( ~element(_u36, _u35) | empty(_u35) | in(_u36, _u35) )).
% 0.19/0.38
% 0.19/0.38 % Formula: t3_subset ( axiom ) converted to clauses:
% 0.19/0.38 cnf(t3_subset-1, axiom, ( ~element(_u41, powerset(_u39)) | subset(_u41, _u39) )).
% 0.19/0.38 cnf(t3_subset-2, axiom, ( ~subset(_u42, _u40) | element(_u42, powerset(_u40)) )).
% 0.19/0.38
% 0.19/0.38 % Formula: t6_boole ( axiom ) converted to clauses:
% 0.19/0.38 cnf(t6_boole-1, axiom, ( ~empty(_u43) | ( _u43 = empty_set) )).
% 0.19/0.38
% 0.19/0.38 % Formula: t7_boole ( axiom ) converted to clauses:
% 0.19/0.38 cnf(t7_boole-1, axiom, ( ~in(_u45, _u44) | ~empty(_u44) )).
% 0.19/0.38
% 0.19/0.38 % Formula: t8_boole ( axiom ) converted to clauses:
% 0.19/0.38 cnf(t8_boole-1, axiom, ( ~empty(_u47) | ( _u47 = _u46) | ~empty(_u46) )).
% 0.19/0.38
% 0.19/0.38 % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u49, _u48) = set_union2(_u48, _u49)) )).
% 0.19/0.38
% 0.19/0.38 % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u51, _u51) = _u51) )).
% 0.19/0.38
% 0.19/0.38 % Formula: fc9_finset_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(fc9_finset_1-1, axiom, ( ~finite(_u53) | ~finite(_u52) | finite(set_union2(_u53, _u52)) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc1_finset_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc1_finset_1-1, axiom, ( ~empty(skolem2) )).
% 0.19/0.38 cnf(rc1_finset_1-2, axiom, ( finite(skolem2) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc2_finset_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc2_finset_1-1, axiom, ( element(skolem3(_u56), powerset(_u56)) )).
% 0.19/0.38 cnf(rc2_finset_1-2, axiom, ( empty(skolem3(_u56)) )).
% 0.19/0.38 cnf(rc2_finset_1-3, axiom, ( relation(skolem3(_u56)) )).
% 0.19/0.38 cnf(rc2_finset_1-4, axiom, ( function(skolem3(_u56)) )).
% 0.19/0.38 cnf(rc2_finset_1-5, axiom, ( one_to_one(skolem3(_u56)) )).
% 0.19/0.38 cnf(rc2_finset_1-6, axiom, ( epsilon_transitive(skolem3(_u56)) )).
% 0.19/0.38 cnf(rc2_finset_1-7, axiom, ( epsilon_connected(skolem3(_u56)) )).
% 0.19/0.38 cnf(rc2_finset_1-8, axiom, ( ordinal(skolem3(_u56)) )).
% 0.19/0.38 cnf(rc2_finset_1-9, axiom, ( natural(skolem3(_u56)) )).
% 0.19/0.38 cnf(rc2_finset_1-10, axiom, ( finite(skolem3(_u56)) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc3_finset_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc3_finset_1-1, axiom, ( empty(_u58) | element(skolem4(_u58), powerset(_u58)) )).
% 0.19/0.38 cnf(rc3_finset_1-2, axiom, ( empty(_u58) | ~empty(skolem4(_u58)) )).
% 0.19/0.38 cnf(rc3_finset_1-3, axiom, ( empty(_u58) | finite(skolem4(_u58)) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc1_funct_1-1, axiom, ( relation(skolem5) )).
% 0.19/0.38 cnf(rc1_funct_1-2, axiom, ( function(skolem5) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc2_funct_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc2_funct_1-1, axiom, ( relation(skolem6) )).
% 0.19/0.38 cnf(rc2_funct_1-2, axiom, ( empty(skolem6) )).
% 0.19/0.38 cnf(rc2_funct_1-3, axiom, ( function(skolem6) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc3_funct_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc3_funct_1-1, axiom, ( relation(skolem7) )).
% 0.19/0.38 cnf(rc3_funct_1-2, axiom, ( function(skolem7) )).
% 0.19/0.38 cnf(rc3_funct_1-3, axiom, ( one_to_one(skolem7) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc4_funct_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc4_funct_1-1, axiom, ( relation(skolem8) )).
% 0.19/0.38 cnf(rc4_funct_1-2, axiom, ( relation_empty_yielding(skolem8) )).
% 0.19/0.38 cnf(rc4_funct_1-3, axiom, ( function(skolem8) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc5_funct_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc5_funct_1-1, axiom, ( relation(skolem9) )).
% 0.19/0.38 cnf(rc5_funct_1-2, axiom, ( relation_non_empty(skolem9) )).
% 0.19/0.38 cnf(rc5_funct_1-3, axiom, ( function(skolem9) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc1_ordinal2 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc1_ordinal2-1, axiom, ( epsilon_transitive(skolem10) )).
% 0.19/0.38 cnf(rc1_ordinal2-2, axiom, ( epsilon_connected(skolem10) )).
% 0.19/0.38 cnf(rc1_ordinal2-3, axiom, ( ordinal(skolem10) )).
% 0.19/0.38 cnf(rc1_ordinal2-4, axiom, ( being_limit_ordinal(skolem10) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc2_ordinal2 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc2_ordinal2-1, axiom, ( relation(skolem11) )).
% 0.19/0.38 cnf(rc2_ordinal2-2, axiom, ( function(skolem11) )).
% 0.19/0.38 cnf(rc2_ordinal2-3, axiom, ( transfinite_sequence(skolem11) )).
% 0.19/0.38 cnf(rc2_ordinal2-4, axiom, ( ordinal_yielding(skolem11) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc1_relat_1-1, axiom, ( empty(skolem12) )).
% 0.19/0.38 cnf(rc1_relat_1-2, axiom, ( relation(skolem12) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem13) )).
% 0.19/0.38 cnf(rc2_relat_1-2, axiom, ( relation(skolem13) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc3_relat_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc3_relat_1-1, axiom, ( relation(skolem14) )).
% 0.19/0.38 cnf(rc3_relat_1-2, axiom, ( relation_empty_yielding(skolem14) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc1_arytm_3 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc1_arytm_3-1, axiom, ( ~empty(skolem15) )).
% 0.19/0.38 cnf(rc1_arytm_3-2, axiom, ( epsilon_transitive(skolem15) )).
% 0.19/0.38 cnf(rc1_arytm_3-3, axiom, ( epsilon_connected(skolem15) )).
% 0.19/0.38 cnf(rc1_arytm_3-4, axiom, ( ordinal(skolem15) )).
% 0.19/0.38 cnf(rc1_arytm_3-5, axiom, ( natural(skolem15) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc2_arytm_3 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc2_arytm_3-1, axiom, ( element(skolem16, positive_rationals) )).
% 0.19/0.38 cnf(rc2_arytm_3-2, axiom, ( ~empty(skolem16) )).
% 0.19/0.38 cnf(rc2_arytm_3-3, axiom, ( epsilon_transitive(skolem16) )).
% 0.19/0.38 cnf(rc2_arytm_3-4, axiom, ( epsilon_connected(skolem16) )).
% 0.19/0.38 cnf(rc2_arytm_3-5, axiom, ( ordinal(skolem16) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc3_arytm_3 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc3_arytm_3-1, axiom, ( element(skolem17, positive_rationals) )).
% 0.19/0.38 cnf(rc3_arytm_3-2, axiom, ( empty(skolem17) )).
% 0.19/0.38 cnf(rc3_arytm_3-3, axiom, ( epsilon_transitive(skolem17) )).
% 0.19/0.38 cnf(rc3_arytm_3-4, axiom, ( epsilon_connected(skolem17) )).
% 0.19/0.38 cnf(rc3_arytm_3-5, axiom, ( ordinal(skolem17) )).
% 0.19/0.38 cnf(rc3_arytm_3-6, axiom, ( natural(skolem17) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc1_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc1_ordinal1-1, axiom, ( epsilon_transitive(skolem18) )).
% 0.19/0.38 cnf(rc1_ordinal1-2, axiom, ( epsilon_connected(skolem18) )).
% 0.19/0.38 cnf(rc1_ordinal1-3, axiom, ( ordinal(skolem18) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc2_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc2_ordinal1-1, axiom, ( relation(skolem19) )).
% 0.19/0.38 cnf(rc2_ordinal1-2, axiom, ( function(skolem19) )).
% 0.19/0.38 cnf(rc2_ordinal1-3, axiom, ( one_to_one(skolem19) )).
% 0.19/0.38 cnf(rc2_ordinal1-4, axiom, ( empty(skolem19) )).
% 0.19/0.38 cnf(rc2_ordinal1-5, axiom, ( epsilon_transitive(skolem19) )).
% 0.19/0.38 cnf(rc2_ordinal1-6, axiom, ( epsilon_connected(skolem19) )).
% 0.19/0.38 cnf(rc2_ordinal1-7, axiom, ( ordinal(skolem19) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc3_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc3_ordinal1-1, axiom, ( ~empty(skolem20) )).
% 0.19/0.38 cnf(rc3_ordinal1-2, axiom, ( epsilon_transitive(skolem20) )).
% 0.19/0.38 cnf(rc3_ordinal1-3, axiom, ( epsilon_connected(skolem20) )).
% 0.19/0.38 cnf(rc3_ordinal1-4, axiom, ( ordinal(skolem20) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc4_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc4_ordinal1-1, axiom, ( relation(skolem21) )).
% 0.19/0.38 cnf(rc4_ordinal1-2, axiom, ( function(skolem21) )).
% 0.19/0.38 cnf(rc4_ordinal1-3, axiom, ( transfinite_sequence(skolem21) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc1_subset_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc1_subset_1-1, axiom, ( empty(_u77) | element(skolem22(_u77), powerset(_u77)) )).
% 0.19/0.38 cnf(rc1_subset_1-2, axiom, ( empty(_u77) | ~empty(skolem22(_u77)) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc2_subset_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc2_subset_1-1, axiom, ( element(skolem23(_u79), powerset(_u79)) )).
% 0.19/0.38 cnf(rc2_subset_1-2, axiom, ( empty(skolem23(_u79)) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc1_xboole_0-1, axiom, ( empty(skolem24) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem25) )).
% 0.19/0.38
% 0.19/0.38 % Formula: rc1_funcop_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(rc1_funcop_1-1, axiom, ( relation(skolem26) )).
% 0.19/0.38 cnf(rc1_funcop_1-2, axiom, ( function(skolem26) )).
% 0.19/0.38 cnf(rc1_funcop_1-3, axiom, ( function_yielding(skolem26) )).
% 0.19/0.38
% 0.19/0.38 % Formula: t14_finset_1 ( conjecture ) (definitionally) converted to clauses:
% 0.19/0.38 cnf(t14_finset_1-1, negated_conjecture, ( finite(skolem27) )).
% 0.19/0.38 cnf(t14_finset_1-2, negated_conjecture, ( finite(skolem28) )).
% 0.19/0.38 cnf(t14_finset_1-3, negated_conjecture, ( ~finite(set_union2(skolem27, skolem28)) )).
% 0.19/0.38
% 0.19/0.38 % Formula: l3_finset_1 ( axiom ) converted to clauses:
% 0.19/0.38 cnf(l3_finset_1-1, axiom, ( ~finite(_u86) | ~finite(_u85) | finite(set_union2(_u86, _u85)) )).
% 0.19/0.38
% 0.19/0.38 % Problem matrix:
% 0.19/0.38 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.19/0.38 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.19/0.38 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.19/0.38 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 0.19/0.38 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 0.19/0.38 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 0.19/0.38 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( skolem3(__eqx_0) = skolem3(__eqy_0)) )).
% 0.19/0.38 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( skolem4(__eqx_0) = skolem4(__eqy_0)) )).
% 0.19/0.38 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( skolem22(__eqx_0) = skolem22(__eqy_0)) )).
% 0.19/0.38 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( skolem23(__eqx_0) = skolem23(__eqy_0)) )).
% 0.19/0.38 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 0.19/0.38 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 0.19/0.38 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 0.19/0.38 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 0.19/0.38 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~relation_empty_yielding(__eqx_0) | relation_empty_yielding(__eqy_0) )).
% 0.19/0.38 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 0.19/0.38 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 0.19/0.38 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~epsilon_transitive(__eqx_0) | epsilon_transitive(__eqy_0) )).
% 0.19/0.38 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~epsilon_connected(__eqx_0) | epsilon_connected(__eqy_0) )).
% 0.19/0.38 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~ordinal(__eqx_0) | ordinal(__eqy_0) )).
% 0.19/0.38 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 0.19/0.38 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ~finite(__eqx_0) | finite(__eqy_0) )).
% 0.19/0.38 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ~natural(__eqx_0) | natural(__eqy_0) )).
% 0.19/0.38 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ~relation_non_empty(__eqx_0) | relation_non_empty(__eqy_0) )).
% 0.19/0.38 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ~being_limit_ordinal(__eqx_0) | being_limit_ordinal(__eqy_0) )).
% 0.19/0.38 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ~transfinite_sequence(__eqx_0) | transfinite_sequence(__eqy_0) )).
% 0.19/0.38 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ~ordinal_yielding(__eqx_0) | ordinal_yielding(__eqy_0) )).
% 0.19/0.38 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ~function_yielding(__eqx_0) | function_yielding(__eqy_0) )).
% 0.19/0.38 cnf(matrix-28, plain, ( subset(_u1, _u1) )).
% 0.19/0.38 cnf(matrix-29, plain, ( ~in(_u3, _u2) | ~in(_u2, _u3) )).
% 0.19/0.38 cnf(matrix-30, plain, ( empty(empty_set) )).
% 0.19/0.38 cnf(matrix-31, plain, ( relation(empty_set) )).
% 0.19/0.38 cnf(matrix-32, plain, ( empty(empty_set) )).
% 0.19/0.38 cnf(matrix-33, plain, ( relation(empty_set) )).
% 0.19/0.38 cnf(matrix-34, plain, ( relation_empty_yielding(empty_set) )).
% 0.19/0.38 cnf(matrix-35, plain, ( relation(empty_set) )).
% 0.19/0.38 cnf(matrix-36, plain, ( relation_empty_yielding(empty_set) )).
% 0.19/0.38 cnf(matrix-37, plain, ( function(empty_set) )).
% 0.19/0.38 cnf(matrix-38, plain, ( one_to_one(empty_set) )).
% 0.19/0.38 cnf(matrix-39, plain, ( empty(empty_set) )).
% 0.19/0.38 cnf(matrix-40, plain, ( epsilon_transitive(empty_set) )).
% 0.19/0.38 cnf(matrix-41, plain, ( epsilon_connected(empty_set) )).
% 0.19/0.38 cnf(matrix-42, plain, ( ordinal(empty_set) )).
% 0.19/0.38 cnf(matrix-43, plain, ( empty(empty_set) )).
% 0.19/0.38 cnf(matrix-44, plain, ( ( set_union2(_u4, empty_set) = _u4) )).
% 0.19/0.38 cnf(matrix-45, plain, ( ~in(_u6, _u5) | element(_u6, _u5) )).
% 0.19/0.38 cnf(matrix-46, plain, ( ~in(_u9, _u8) | ~element(_u8, powerset(_u7)) | element(_u9, _u7) )).
% 0.19/0.38 cnf(matrix-47, plain, ( ~in(_u12, _u11) | ~element(_u11, powerset(_u10)) | ~empty(_u10) )).
% 0.19/0.38 cnf(matrix-48, plain, ( element(skolem1(_u14), _u14) )).
% 0.19/0.38 cnf(matrix-49, plain, ( ~empty(_u15) | finite(_u15) )).
% 0.19/0.38 cnf(matrix-50, plain, ( ~finite(_u17) | ~element(_u16, powerset(_u17)) | finite(_u16) )).
% 0.19/0.38 cnf(matrix-51, plain, ( ~empty(_u18) | function(_u18) )).
% 0.19/0.38 cnf(matrix-52, plain, ( ~relation(_u19) | ~empty(_u19) | ~function(_u19) | one_to_one(_u19) )).
% 0.19/0.38 cnf(matrix-53, plain, ( ~relation(_u21) | ~relation(_u20) | relation(set_union2(_u21, _u20)) )).
% 0.19/0.38 cnf(matrix-54, plain, ( ~empty(_u22) | relation(_u22) )).
% 0.19/0.38 cnf(matrix-55, plain, ( ~empty(positive_rationals) )).
% 0.19/0.38 cnf(matrix-56, plain, ( ~ordinal(_u24) | ~element(_u23, _u24) | epsilon_transitive(_u23) )).
% 0.19/0.38 cnf(matrix-57, plain, ( ~ordinal(_u24) | ~element(_u23, _u24) | epsilon_connected(_u23) )).
% 0.19/0.38 cnf(matrix-58, plain, ( ~ordinal(_u24) | ~element(_u23, _u24) | ordinal(_u23) )).
% 0.19/0.38 cnf(matrix-59, plain, ( ~empty(_u25) | ~ordinal(_u25) | epsilon_transitive(_u25) )).
% 0.19/0.38 cnf(matrix-60, plain, ( ~empty(_u25) | ~ordinal(_u25) | epsilon_connected(_u25) )).
% 0.19/0.38 cnf(matrix-61, plain, ( ~empty(_u25) | ~ordinal(_u25) | natural(_u25) )).
% 0.19/0.38 cnf(matrix-62, plain, ( ~element(_u26, positive_rationals) | ~ordinal(_u26) | epsilon_transitive(_u26) )).
% 0.19/0.38 cnf(matrix-63, plain, ( ~element(_u26, positive_rationals) | ~ordinal(_u26) | epsilon_connected(_u26) )).
% 0.19/0.38 cnf(matrix-64, plain, ( ~element(_u26, positive_rationals) | ~ordinal(_u26) | natural(_u26) )).
% 0.19/0.38 cnf(matrix-65, plain, ( ~ordinal(_u27) | epsilon_transitive(_u27) )).
% 0.19/0.38 cnf(matrix-66, plain, ( ~ordinal(_u27) | epsilon_connected(_u27) )).
% 0.19/0.38 cnf(matrix-67, plain, ( ~epsilon_transitive(_u28) | ~epsilon_connected(_u28) | ordinal(_u28) )).
% 0.19/0.38 cnf(matrix-68, plain, ( ~empty(_u29) | epsilon_transitive(_u29) )).
% 0.19/0.38 cnf(matrix-69, plain, ( ~empty(_u29) | epsilon_connected(_u29) )).
% 0.19/0.38 cnf(matrix-70, plain, ( ~empty(_u29) | ordinal(_u29) )).
% 0.19/0.38 cnf(matrix-71, plain, ( ~empty(powerset(_u30)) )).
% 0.19/0.38 cnf(matrix-72, plain, ( empty(_u32) | ~empty(set_union2(_u32, _u31)) )).
% 0.19/0.38 cnf(matrix-73, plain, ( empty(_u34) | ~empty(set_union2(_u33, _u34)) )).
% 0.19/0.38 cnf(matrix-74, plain, ( ~element(_u36, _u35) | empty(_u35) | in(_u36, _u35) )).
% 0.19/0.38 cnf(matrix-75, plain, ( ~element(_u41, powerset(_u39)) | subset(_u41, _u39) )).
% 0.19/0.38 cnf(matrix-76, plain, ( ~subset(_u42, _u40) | element(_u42, powerset(_u40)) )).
% 0.19/0.38 cnf(matrix-77, plain, ( ~empty(_u43) | ( _u43 = empty_set) )).
% 0.19/0.38 cnf(matrix-78, plain, ( ~in(_u45, _u44) | ~empty(_u44) )).
% 0.19/0.38 cnf(matrix-79, plain, ( ~empty(_u47) | ( _u47 = _u46) | ~empty(_u46) )).
% 0.19/0.38 cnf(matrix-80, plain, ( ( set_union2(_u49, _u48) = set_union2(_u48, _u49)) )).
% 0.19/0.38 cnf(matrix-81, plain, ( ( set_union2(_u51, _u51) = _u51) )).
% 0.19/0.38 cnf(matrix-82, plain, ( ~finite(_u53) | ~finite(_u52) | finite(set_union2(_u53, _u52)) )).
% 0.19/0.38 cnf(matrix-83, plain, ( ~empty(skolem2) )).
% 0.19/0.38 cnf(matrix-84, plain, ( finite(skolem2) )).
% 0.19/0.38 cnf(matrix-85, plain, ( element(skolem3(_u56), powerset(_u56)) )).
% 0.19/0.38 cnf(matrix-86, plain, ( empty(skolem3(_u56)) )).
% 0.19/0.38 cnf(matrix-87, plain, ( relation(skolem3(_u56)) )).
% 0.19/0.38 cnf(matrix-88, plain, ( function(skolem3(_u56)) )).
% 0.19/0.38 cnf(matrix-89, plain, ( one_to_one(skolem3(_u56)) )).
% 0.19/0.38 cnf(matrix-90, plain, ( epsilon_transitive(skolem3(_u56)) )).
% 0.19/0.38 cnf(matrix-91, plain, ( epsilon_connected(skolem3(_u56)) )).
% 0.19/0.38 cnf(matrix-92, plain, ( ordinal(skolem3(_u56)) )).
% 0.19/0.38 cnf(matrix-93, plain, ( natural(skolem3(_u56)) )).
% 0.19/0.38 cnf(matrix-94, plain, ( finite(skolem3(_u56)) )).
% 0.19/0.38 cnf(matrix-95, plain, ( empty(_u58) | element(skolem4(_u58), powerset(_u58)) )).
% 0.19/0.38 cnf(matrix-96, plain, ( empty(_u58) | ~empty(skolem4(_u58)) )).
% 0.19/0.38 cnf(matrix-97, plain, ( empty(_u58) | finite(skolem4(_u58)) )).
% 0.19/0.38 cnf(matrix-98, plain, ( relation(skolem5) )).
% 0.19/0.38 cnf(matrix-99, plain, ( function(skolem5) )).
% 0.19/0.38 cnf(matrix-100, plain, ( relation(skolem6) )).
% 0.19/0.38 cnf(matrix-101, plain, ( empty(skolem6) )).
% 0.19/0.38 cnf(matrix-102, plain, ( function(skolem6) )).
% 0.19/0.38 cnf(matrix-103, plain, ( relation(skolem7) )).
% 0.19/0.38 cnf(matrix-104, plain, ( function(skolem7) )).
% 0.19/0.38 cnf(matrix-105, plain, ( one_to_one(skolem7) )).
% 0.19/0.38 cnf(matrix-106, plain, ( relation(skolem8) )).
% 0.19/0.38 cnf(matrix-107, plain, ( relation_empty_yielding(skolem8) )).
% 0.19/0.38 cnf(matrix-108, plain, ( function(skolem8) )).
% 0.19/0.38 cnf(matrix-109, plain, ( relation(skolem9) )).
% 0.19/0.38 cnf(matrix-110, plain, ( relation_non_empty(skolem9) )).
% 0.19/0.38 cnf(matrix-111, plain, ( function(skolem9) )).
% 0.19/0.38 cnf(matrix-112, plain, ( epsilon_transitive(skolem10) )).
% 0.19/0.38 cnf(matrix-113, plain, ( epsilon_connected(skolem10) )).
% 0.19/0.38 cnf(matrix-114, plain, ( ordinal(skolem10) )).
% 0.19/0.38 cnf(matrix-115, plain, ( being_limit_ordinal(skolem10) )).
% 0.19/0.38 cnf(matrix-116, plain, ( relation(skolem11) )).
% 0.19/0.38 cnf(matrix-117, plain, ( function(skolem11) )).
% 0.19/0.38 cnf(matrix-118, plain, ( transfinite_sequence(skolem11) )).
% 0.19/0.38 cnf(matrix-119, plain, ( ordinal_yielding(skolem11) )).
% 0.19/0.38 cnf(matrix-120, plain, ( empty(skolem12) )).
% 0.19/0.38 cnf(matrix-121, plain, ( relation(skolem12) )).
% 0.19/0.38 cnf(matrix-122, plain, ( ~empty(skolem13) )).
% 0.19/0.38 cnf(matrix-123, plain, ( relation(skolem13) )).
% 0.19/0.38 cnf(matrix-124, plain, ( relation(skolem14) )).
% 0.19/0.38 cnf(matrix-125, plain, ( relation_empty_yielding(skolem14) )).
% 0.19/0.38 cnf(matrix-126, plain, ( ~empty(skolem15) )).
% 0.19/0.38 cnf(matrix-127, plain, ( epsilon_transitive(skolem15) )).
% 0.19/0.38 cnf(matrix-128, plain, ( epsilon_connected(skolem15) )).
% 0.19/0.38 cnf(matrix-129, plain, ( ordinal(skolem15) )).
% 0.19/0.38 cnf(matrix-130, plain, ( natural(skolem15) )).
% 0.19/0.38 cnf(matrix-131, plain, ( element(skolem16, positive_rationals) )).
% 0.19/0.38 cnf(matrix-132, plain, ( ~empty(skolem16) )).
% 0.19/0.38 cnf(matrix-133, plain, ( epsilon_transitive(skolem16) )).
% 0.19/0.38 cnf(matrix-134, plain, ( epsilon_connected(skolem16) )).
% 0.19/0.38 cnf(matrix-135, plain, ( ordinal(skolem16) )).
% 0.19/0.38 cnf(matrix-136, plain, ( element(skolem17, positive_rationals) )).
% 0.19/0.38 cnf(matrix-137, plain, ( empty(skolem17) )).
% 0.19/0.38 cnf(matrix-138, plain, ( epsilon_transitive(skolem17) )).
% 0.19/0.38 cnf(matrix-139, plain, ( epsilon_connected(skolem17) )).
% 0.19/0.38 cnf(matrix-140, plain, ( ordinal(skolem17) )).
% 0.19/0.38 cnf(matrix-141, plain, ( natural(skolem17) )).
% 0.19/0.38 cnf(matrix-142, plain, ( epsilon_transitive(skolem18) )).
% 0.19/0.38 cnf(matrix-143, plain, ( epsilon_connected(skolem18) )).
% 0.19/0.38 cnf(matrix-144, plain, ( ordinal(skolem18) )).
% 0.19/0.38 cnf(matrix-145, plain, ( relation(skolem19) )).
% 0.19/0.38 cnf(matrix-146, plain, ( function(skolem19) )).
% 0.19/0.38 cnf(matrix-147, plain, ( one_to_one(skolem19) )).
% 0.19/0.38 cnf(matrix-148, plain, ( empty(skolem19) )).
% 0.19/0.38 cnf(matrix-149, plain, ( epsilon_transitive(skolem19) )).
% 0.19/0.38 cnf(matrix-150, plain, ( epsilon_connected(skolem19) )).
% 0.19/0.38 cnf(matrix-151, plain, ( ordinal(skolem19) )).
% 0.19/0.38 cnf(matrix-152, plain, ( ~empty(skolem20) )).
% 0.19/0.38 cnf(matrix-153, plain, ( epsilon_transitive(skolem20) )).
% 0.19/0.38 cnf(matrix-154, plain, ( epsilon_connected(skolem20) )).
% 0.19/0.38 cnf(matrix-155, plain, ( ordinal(skolem20) )).
% 0.19/0.38 cnf(matrix-156, plain, ( relation(skolem21) )).
% 0.19/0.38 cnf(matrix-157, plain, ( function(skolem21) )).
% 0.19/0.38 cnf(matrix-158, plain, ( transfinite_sequence(skolem21) )).
% 0.19/0.38 cnf(matrix-159, plain, ( empty(_u77) | element(skolem22(_u77), powerset(_u77)) )).
% 0.19/0.38 cnf(matrix-160, plain, ( empty(_u77) | ~empty(skolem22(_u77)) )).
% 0.19/0.38 cnf(matrix-161, plain, ( element(skolem23(_u79), powerset(_u79)) )).
% 0.19/0.38 cnf(matrix-162, plain, ( empty(skolem23(_u79)) )).
% 0.19/0.38 cnf(matrix-163, plain, ( empty(skolem24) )).
% 0.19/0.38 cnf(matrix-164, plain, ( ~empty(skolem25) )).
% 0.19/0.38 cnf(matrix-165, plain, ( relation(skolem26) )).
% 0.19/0.38 cnf(matrix-166, plain, ( function(skolem26) )).
% 0.19/0.38 cnf(matrix-167, plain, ( function_yielding(skolem26) )).
% 0.19/0.38 cnf(matrix-168, plain, ( finite(skolem27) )).
% 0.19/0.38 cnf(matrix-169, plain, ( finite(skolem28) )).
% 0.19/0.38 cnf(matrix-170, plain, ( ~finite(set_union2(skolem27, skolem28)) )).
% 0.19/0.38 cnf(matrix-171, plain, ( ~finite(_u86) | ~finite(_u85) | finite(set_union2(_u86, _u85)) )).
% 0.19/0.38
% 0.19/0.38 % Proof stack:
% 0.19/0.38 cnf(proof-stack, plain,
% 0.19/0.38 proof_stack(
% 0.19/0.38 start(170),
% 0.19/0.38 left_branch(0, 171, 2, 2),
% 0.19/0.38 left_branch(0, 168, 0, 3),
% 0.19/0.38 right_branch(3),
% 0.19/0.38 left_branch(0, 169, 0, 4),
% 0.19/0.38 right_branch(4),
% 0.19/0.38 right_branch(2)
% 0.19/0.38 )).
% 0.19/0.38 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------