TSTP Solution File: SEU114+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU114+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 : n016.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 14:33:05 EDT 2024
% Result : Theorem 71.72s 71.93s
% Output : Proof 71.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU114+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n016.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 15:39:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 71.72/71.93 % SZS status Theorem for theBenchmark
% 71.72/71.93 % SZS output start Proof for theBenchmark
% 71.72/71.93
% 71.72/71.93 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 71.72/71.93 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 71.72/71.93
% 71.72/71.93 % Formula: cc1_finset_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(cc1_finset_1-1, axiom, ( ~empty(_u2) | finite(_u2) )).
% 71.72/71.93
% 71.72/71.93 % Formula: cc1_finsub_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(cc1_finsub_1-1, axiom, ( ~preboolean(_u3) | cup_closed(_u3) )).
% 71.72/71.93 cnf(cc1_finsub_1-2, axiom, ( ~preboolean(_u3) | diff_closed(_u3) )).
% 71.72/71.93
% 71.72/71.93 % Formula: cc2_finset_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(cc2_finset_1-1, axiom, ( ~finite(_u5) | ~element(_u4, powerset(_u5)) | finite(_u4) )).
% 71.72/71.93
% 71.72/71.93 % Formula: cc2_finsub_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(cc2_finsub_1-1, axiom, ( ~cup_closed(_u6) | ~diff_closed(_u6) | preboolean(_u6) )).
% 71.72/71.93
% 71.72/71.93 % Formula: cc3_finsub_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(cc3_finsub_1-1, axiom, ( ~element(_u7, finite_subsets(_u8)) | finite(_u7) )).
% 71.72/71.93
% 71.72/71.93 % Formula: d10_xboole_0 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(d10_xboole_0-1, axiom, ( ( _u13 != _u11) | subset(_u13, _u11) )).
% 71.72/71.93 cnf(d10_xboole_0-2, axiom, ( ( _u13 != _u11) | subset(_u11, _u13) )).
% 71.72/71.93 cnf(d10_xboole_0-3, axiom, ( ~subset(_u14, _u12) | ~subset(_u12, _u14) | ( _u14 = _u12) )).
% 71.72/71.93
% 71.72/71.93 % Formula: d3_tarski ( axiom ) converted to clauses:
% 71.72/71.93 cnf(d3_tarski-1, axiom, ( ~subset(_u21, _u19) | ~in(_u15, _u21) | in(_u15, _u19) )).
% 71.72/71.93 cnf(d3_tarski-2, axiom, ( subset(_u22, _u20) | in(skolem1(_u22, _u20), _u22) )).
% 71.72/71.93 cnf(d3_tarski-3, axiom, ( subset(_u22, _u20) | ~in(skolem1(_u22, _u20), _u20) )).
% 71.72/71.93
% 71.72/71.93 % Formula: d5_finsub_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(d5_finsub_1-1, axiom, ( ~preboolean(_u25) | ( _u25 != finite_subsets(_u26)) | ~in(_u27, _u25) | subset(_u27, _u26) )).
% 71.72/71.93 cnf(d5_finsub_1-2, axiom, ( ~preboolean(_u25) | ( _u25 != finite_subsets(_u26)) | ~in(_u27, _u25) | finite(_u27) )).
% 71.72/71.93 cnf(d5_finsub_1-3, axiom, ( ~preboolean(_u25) | ( _u25 != finite_subsets(_u26)) | ~subset(_u28, _u26) | ~finite(_u28) | in(_u28, _u25) )).
% 71.72/71.93 cnf(d5_finsub_1-4, axiom, ( ~preboolean(_u25) | ( _u25 = finite_subsets(_u26)) | in(skolem2(_u26, _u25), _u25) | subset(skolem3(_u26, _u25), _u26) )).
% 71.72/71.93 cnf(d5_finsub_1-5, axiom, ( ~preboolean(_u25) | ( _u25 = finite_subsets(_u26)) | in(skolem2(_u26, _u25), _u25) | finite(skolem3(_u26, _u25)) )).
% 71.72/71.93 cnf(d5_finsub_1-6, axiom, ( ~preboolean(_u25) | ( _u25 = finite_subsets(_u26)) | in(skolem2(_u26, _u25), _u25) | ~in(skolem3(_u26, _u25), _u25) )).
% 71.72/71.93 cnf(d5_finsub_1-7, axiom, ( ~preboolean(_u25) | ( _u25 = finite_subsets(_u26)) | ~subset(skolem2(_u26, _u25), _u26) | ~finite(skolem2(_u26, _u25)) | subset(skolem3(_u26, _u25), _u26) )).
% 71.72/71.93 cnf(d5_finsub_1-8, axiom, ( ~preboolean(_u25) | ( _u25 = finite_subsets(_u26)) | ~subset(skolem2(_u26, _u25), _u26) | ~finite(skolem2(_u26, _u25)) | finite(skolem3(_u26, _u25)) )).
% 71.72/71.93 cnf(d5_finsub_1-9, axiom, ( ~preboolean(_u25) | ( _u25 = finite_subsets(_u26)) | ~subset(skolem2(_u26, _u25), _u26) | ~finite(skolem2(_u26, _u25)) | ~in(skolem3(_u26, _u25), _u25) )).
% 71.72/71.93
% 71.72/71.93 % Formula: dt_k5_finsub_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(dt_k5_finsub_1-1, axiom, ( preboolean(finite_subsets(_u31)) )).
% 71.72/71.93
% 71.72/71.93 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(existence_m1_subset_1-1, axiom, ( element(skolem4(_u33), _u33) )).
% 71.72/71.93
% 71.72/71.93 % Formula: fc1_finsub_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(fc1_finsub_1-1, axiom, ( ~empty(powerset(_u35)) )).
% 71.72/71.93 cnf(fc1_finsub_1-2, axiom, ( cup_closed(powerset(_u36)) )).
% 71.72/71.93 cnf(fc1_finsub_1-3, axiom, ( diff_closed(powerset(_u37)) )).
% 71.72/71.93 cnf(fc1_finsub_1-4, axiom, ( preboolean(powerset(_u38)) )).
% 71.72/71.93
% 71.72/71.93 % Formula: fc1_subset_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(fc1_subset_1-1, axiom, ( ~empty(powerset(_u39)) )).
% 71.72/71.93
% 71.72/71.93 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 71.72/71.93
% 71.72/71.93 % Formula: fc2_finsub_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(fc2_finsub_1-1, axiom, ( ~empty(finite_subsets(_u41)) )).
% 71.72/71.93 cnf(fc2_finsub_1-2, axiom, ( cup_closed(finite_subsets(_u42)) )).
% 71.72/71.93 cnf(fc2_finsub_1-3, axiom, ( diff_closed(finite_subsets(_u43)) )).
% 71.72/71.93 cnf(fc2_finsub_1-4, axiom, ( preboolean(finite_subsets(_u44)) )).
% 71.72/71.93
% 71.72/71.93 % Formula: rc1_finset_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(rc1_finset_1-1, axiom, ( ~empty(skolem5) )).
% 71.72/71.93 cnf(rc1_finset_1-2, axiom, ( finite(skolem5) )).
% 71.72/71.93
% 71.72/71.93 % Formula: rc1_finsub_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(rc1_finsub_1-1, axiom, ( ~empty(skolem6) )).
% 71.72/71.93 cnf(rc1_finsub_1-2, axiom, ( cup_closed(skolem6) )).
% 71.72/71.93 cnf(rc1_finsub_1-3, axiom, ( cap_closed(skolem6) )).
% 71.72/71.93 cnf(rc1_finsub_1-4, axiom, ( diff_closed(skolem6) )).
% 71.72/71.93 cnf(rc1_finsub_1-5, axiom, ( preboolean(skolem6) )).
% 71.72/71.93
% 71.72/71.93 % Formula: rc1_subset_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(rc1_subset_1-1, axiom, ( empty(_u48) | element(skolem7(_u48), powerset(_u48)) )).
% 71.72/71.93 cnf(rc1_subset_1-2, axiom, ( empty(_u48) | ~empty(skolem7(_u48)) )).
% 71.72/71.93
% 71.72/71.93 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(rc1_xboole_0-1, axiom, ( empty(skolem8) )).
% 71.72/71.93
% 71.72/71.93 % Formula: rc2_finset_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(rc2_finset_1-1, axiom, ( element(skolem9(_u51), powerset(_u51)) )).
% 71.72/71.93 cnf(rc2_finset_1-2, axiom, ( empty(skolem9(_u51)) )).
% 71.72/71.93 cnf(rc2_finset_1-3, axiom, ( relation(skolem9(_u51)) )).
% 71.72/71.93 cnf(rc2_finset_1-4, axiom, ( function(skolem9(_u51)) )).
% 71.72/71.93 cnf(rc2_finset_1-5, axiom, ( one_to_one(skolem9(_u51)) )).
% 71.72/71.93 cnf(rc2_finset_1-6, axiom, ( epsilon_transitive(skolem9(_u51)) )).
% 71.72/71.93 cnf(rc2_finset_1-7, axiom, ( epsilon_connected(skolem9(_u51)) )).
% 71.72/71.93 cnf(rc2_finset_1-8, axiom, ( ordinal(skolem9(_u51)) )).
% 71.72/71.93 cnf(rc2_finset_1-9, axiom, ( natural(skolem9(_u51)) )).
% 71.72/71.93 cnf(rc2_finset_1-10, axiom, ( finite(skolem9(_u51)) )).
% 71.72/71.93
% 71.72/71.93 % Formula: rc2_subset_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(rc2_subset_1-1, axiom, ( element(skolem10(_u53), powerset(_u53)) )).
% 71.72/71.93 cnf(rc2_subset_1-2, axiom, ( empty(skolem10(_u53)) )).
% 71.72/71.93
% 71.72/71.93 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem11) )).
% 71.72/71.93
% 71.72/71.93 % Formula: rc3_finset_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(rc3_finset_1-1, axiom, ( empty(_u56) | element(skolem12(_u56), powerset(_u56)) )).
% 71.72/71.93 cnf(rc3_finset_1-2, axiom, ( empty(_u56) | ~empty(skolem12(_u56)) )).
% 71.72/71.93 cnf(rc3_finset_1-3, axiom, ( empty(_u56) | finite(skolem12(_u56)) )).
% 71.72/71.93
% 71.72/71.93 % Formula: rc4_finset_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(rc4_finset_1-1, axiom, ( empty(_u58) | element(skolem13(_u58), powerset(_u58)) )).
% 71.72/71.93 cnf(rc4_finset_1-2, axiom, ( empty(_u58) | ~empty(skolem13(_u58)) )).
% 71.72/71.93 cnf(rc4_finset_1-3, axiom, ( empty(_u58) | finite(skolem13(_u58)) )).
% 71.72/71.93
% 71.72/71.93 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 71.72/71.93 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u60, _u60) )).
% 71.72/71.93
% 71.72/71.93 % Formula: t13_finset_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(t13_finset_1-1, axiom, ( finite(_u62) | ~subset(_u62, _u61) | ~finite(_u61) )).
% 71.72/71.93
% 71.72/71.93 % Formula: t1_subset ( axiom ) converted to clauses:
% 71.72/71.93 cnf(t1_subset-1, axiom, ( ~in(_u64, _u63) | element(_u64, _u63) )).
% 71.72/71.93
% 71.72/71.93 % Formula: t26_finsub_1 ( axiom ) converted to clauses:
% 71.72/71.93 cnf(t26_finsub_1-1, axiom, ( subset(finite_subsets(_u65), powerset(_u65)) )).
% 71.72/71.93
% 71.72/71.93 % Formula: t27_finsub_1 ( conjecture ) (definitionally) converted to clauses:
% 71.72/71.93 cnf(t27_finsub_1-1, negated_conjecture, ( finite(skolem14) )).
% 71.72/71.93 cnf(t27_finsub_1-2, negated_conjecture, ( ( finite_subsets(skolem14) != powerset(skolem14)) )).
% 71.72/71.93
% 71.72/71.93 % Formula: t2_subset ( axiom ) converted to clauses:
% 71.72/71.93 cnf(t2_subset-1, axiom, ( ~element(_u68, _u67) | empty(_u67) | in(_u68, _u67) )).
% 71.72/71.93
% 71.72/71.93 % Formula: t3_subset ( axiom ) converted to clauses:
% 71.72/71.93 cnf(t3_subset-1, axiom, ( ~element(_u73, powerset(_u71)) | subset(_u73, _u71) )).
% 71.72/71.93 cnf(t3_subset-2, axiom, ( ~subset(_u74, _u72) | element(_u74, powerset(_u72)) )).
% 71.72/71.93
% 71.72/71.93 % Formula: t4_subset ( axiom ) converted to clauses:
% 71.72/71.93 cnf(t4_subset-1, axiom, ( ~in(_u77, _u76) | ~element(_u76, powerset(_u75)) | element(_u77, _u75) )).
% 71.72/71.93
% 71.72/71.93 % Formula: t5_subset ( axiom ) converted to clauses:
% 71.72/71.93 cnf(t5_subset-1, axiom, ( ~in(_u80, _u79) | ~element(_u79, powerset(_u78)) | ~empty(_u78) )).
% 71.72/71.93
% 71.72/71.93 % Formula: t6_boole ( axiom ) converted to clauses:
% 71.72/71.93 cnf(t6_boole-1, axiom, ( ~empty(_u81) | ( _u81 = empty_set) )).
% 71.72/71.93
% 71.72/71.93 % Formula: t7_boole ( axiom ) converted to clauses:
% 71.72/71.93 cnf(t7_boole-1, axiom, ( ~in(_u83, _u82) | ~empty(_u82) )).
% 71.72/71.93
% 71.72/71.93 % Formula: t8_boole ( axiom ) converted to clauses:
% 71.72/71.93 cnf(t8_boole-1, axiom, ( ~empty(_u85) | ( _u85 = _u84) | ~empty(_u84) )).
% 71.72/71.93
% 71.72/71.93 % Problem matrix:
% 71.72/71.93 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 71.72/71.93 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 71.72/71.93 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 71.72/71.93 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 71.72/71.93 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( finite_subsets(__eqx_0) = finite_subsets(__eqy_0)) )).
% 71.72/71.93 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 71.72/71.93 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 71.72/71.93 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 71.72/71.93 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( skolem4(__eqx_0) = skolem4(__eqy_0)) )).
% 71.72/71.93 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( skolem7(__eqx_0) = skolem7(__eqy_0)) )).
% 71.72/71.93 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( skolem9(__eqx_0) = skolem9(__eqy_0)) )).
% 71.72/71.93 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( skolem10(__eqx_0) = skolem10(__eqy_0)) )).
% 71.72/71.93 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( skolem12(__eqx_0) = skolem12(__eqy_0)) )).
% 71.72/71.93 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( skolem13(__eqx_0) = skolem13(__eqy_0)) )).
% 71.72/71.93 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 71.72/71.93 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 71.72/71.93 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~finite(__eqx_0) | finite(__eqy_0) )).
% 71.72/71.93 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~preboolean(__eqx_0) | preboolean(__eqy_0) )).
% 71.72/71.93 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~cup_closed(__eqx_0) | cup_closed(__eqy_0) )).
% 71.72/71.93 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~diff_closed(__eqx_0) | diff_closed(__eqy_0) )).
% 71.72/71.93 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 71.72/71.93 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 71.72/71.93 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ~cap_closed(__eqx_0) | cap_closed(__eqy_0) )).
% 71.72/71.93 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 71.72/71.93 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 71.72/71.93 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 71.72/71.93 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ~epsilon_transitive(__eqx_0) | epsilon_transitive(__eqy_0) )).
% 71.72/71.93 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ~epsilon_connected(__eqx_0) | epsilon_connected(__eqy_0) )).
% 71.72/71.93 cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ~ordinal(__eqx_0) | ordinal(__eqy_0) )).
% 71.72/71.93 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ~natural(__eqx_0) | natural(__eqy_0) )).
% 71.72/71.93 cnf(matrix-30, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 71.72/71.93 cnf(matrix-31, plain, ( ~empty(_u2) | finite(_u2) )).
% 71.72/71.93 cnf(matrix-32, plain, ( ~preboolean(_u3) | cup_closed(_u3) )).
% 71.72/71.93 cnf(matrix-33, plain, ( ~preboolean(_u3) | diff_closed(_u3) )).
% 71.72/71.93 cnf(matrix-34, plain, ( ~finite(_u5) | ~element(_u4, powerset(_u5)) | finite(_u4) )).
% 71.72/71.93 cnf(matrix-35, plain, ( ~cup_closed(_u6) | ~diff_closed(_u6) | preboolean(_u6) )).
% 71.72/71.93 cnf(matrix-36, plain, ( ~element(_u7, finite_subsets(_u8)) | finite(_u7) )).
% 71.72/71.93 cnf(matrix-37, plain, ( ( _u13 != _u11) | subset(_u13, _u11) )).
% 71.72/71.93 cnf(matrix-38, plain, ( ( _u13 != _u11) | subset(_u11, _u13) )).
% 71.72/71.93 cnf(matrix-39, plain, ( ~subset(_u14, _u12) | ~subset(_u12, _u14) | ( _u14 = _u12) )).
% 71.72/71.93 cnf(matrix-40, plain, ( ~subset(_u21, _u19) | ~in(_u15, _u21) | in(_u15, _u19) )).
% 71.72/71.93 cnf(matrix-41, plain, ( subset(_u22, _u20) | in(skolem1(_u22, _u20), _u22) )).
% 71.72/71.93 cnf(matrix-42, plain, ( subset(_u22, _u20) | ~in(skolem1(_u22, _u20), _u20) )).
% 71.72/71.93 cnf(matrix-43, plain, ( ~preboolean(_u25) | ( _u25 != finite_subsets(_u26)) | ~in(_u27, _u25) | subset(_u27, _u26) )).
% 71.72/71.93 cnf(matrix-44, plain, ( ~preboolean(_u25) | ( _u25 != finite_subsets(_u26)) | ~in(_u27, _u25) | finite(_u27) )).
% 71.72/71.93 cnf(matrix-45, plain, ( ~preboolean(_u25) | ( _u25 != finite_subsets(_u26)) | ~subset(_u28, _u26) | ~finite(_u28) | in(_u28, _u25) )).
% 71.72/71.93 cnf(matrix-46, plain, ( ~preboolean(_u25) | ( _u25 = finite_subsets(_u26)) | in(skolem2(_u26, _u25), _u25) | subset(skolem3(_u26, _u25), _u26) )).
% 71.72/71.93 cnf(matrix-47, plain, ( ~preboolean(_u25) | ( _u25 = finite_subsets(_u26)) | in(skolem2(_u26, _u25), _u25) | finite(skolem3(_u26, _u25)) )).
% 71.72/71.93 cnf(matrix-48, plain, ( ~preboolean(_u25) | ( _u25 = finite_subsets(_u26)) | in(skolem2(_u26, _u25), _u25) | ~in(skolem3(_u26, _u25), _u25) )).
% 71.72/71.93 cnf(matrix-49, plain, ( ~preboolean(_u25) | ( _u25 = finite_subsets(_u26)) | ~subset(skolem2(_u26, _u25), _u26) | ~finite(skolem2(_u26, _u25)) | subset(skolem3(_u26, _u25), _u26) )).
% 71.72/71.93 cnf(matrix-50, plain, ( ~preboolean(_u25) | ( _u25 = finite_subsets(_u26)) | ~subset(skolem2(_u26, _u25), _u26) | ~finite(skolem2(_u26, _u25)) | finite(skolem3(_u26, _u25)) )).
% 71.72/71.93 cnf(matrix-51, plain, ( ~preboolean(_u25) | ( _u25 = finite_subsets(_u26)) | ~subset(skolem2(_u26, _u25), _u26) | ~finite(skolem2(_u26, _u25)) | ~in(skolem3(_u26, _u25), _u25) )).
% 71.72/71.93 cnf(matrix-52, plain, ( preboolean(finite_subsets(_u31)) )).
% 71.72/71.93 cnf(matrix-53, plain, ( element(skolem4(_u33), _u33) )).
% 71.72/71.93 cnf(matrix-54, plain, ( ~empty(powerset(_u35)) )).
% 71.72/71.93 cnf(matrix-55, plain, ( cup_closed(powerset(_u36)) )).
% 71.72/71.93 cnf(matrix-56, plain, ( diff_closed(powerset(_u37)) )).
% 71.72/71.93 cnf(matrix-57, plain, ( preboolean(powerset(_u38)) )).
% 71.72/71.93 cnf(matrix-58, plain, ( ~empty(powerset(_u39)) )).
% 71.72/71.93 cnf(matrix-59, plain, ( empty(empty_set) )).
% 71.72/71.93 cnf(matrix-60, plain, ( ~empty(finite_subsets(_u41)) )).
% 71.72/71.93 cnf(matrix-61, plain, ( cup_closed(finite_subsets(_u42)) )).
% 71.72/71.93 cnf(matrix-62, plain, ( diff_closed(finite_subsets(_u43)) )).
% 71.72/71.93 cnf(matrix-63, plain, ( preboolean(finite_subsets(_u44)) )).
% 71.72/71.93 cnf(matrix-64, plain, ( ~empty(skolem5) )).
% 71.72/71.93 cnf(matrix-65, plain, ( finite(skolem5) )).
% 71.72/71.93 cnf(matrix-66, plain, ( ~empty(skolem6) )).
% 71.72/71.93 cnf(matrix-67, plain, ( cup_closed(skolem6) )).
% 71.72/71.93 cnf(matrix-68, plain, ( cap_closed(skolem6) )).
% 71.72/71.93 cnf(matrix-69, plain, ( diff_closed(skolem6) )).
% 71.72/71.93 cnf(matrix-70, plain, ( preboolean(skolem6) )).
% 71.72/71.93 cnf(matrix-71, plain, ( empty(_u48) | element(skolem7(_u48), powerset(_u48)) )).
% 71.72/71.93 cnf(matrix-72, plain, ( empty(_u48) | ~empty(skolem7(_u48)) )).
% 71.72/71.93 cnf(matrix-73, plain, ( empty(skolem8) )).
% 71.72/71.93 cnf(matrix-74, plain, ( element(skolem9(_u51), powerset(_u51)) )).
% 71.72/71.93 cnf(matrix-75, plain, ( empty(skolem9(_u51)) )).
% 71.72/71.93 cnf(matrix-76, plain, ( relation(skolem9(_u51)) )).
% 71.72/71.93 cnf(matrix-77, plain, ( function(skolem9(_u51)) )).
% 71.72/71.93 cnf(matrix-78, plain, ( one_to_one(skolem9(_u51)) )).
% 71.72/71.93 cnf(matrix-79, plain, ( epsilon_transitive(skolem9(_u51)) )).
% 71.72/71.93 cnf(matrix-80, plain, ( epsilon_connected(skolem9(_u51)) )).
% 71.72/71.93 cnf(matrix-81, plain, ( ordinal(skolem9(_u51)) )).
% 71.72/71.93 cnf(matrix-82, plain, ( natural(skolem9(_u51)) )).
% 71.72/71.93 cnf(matrix-83, plain, ( finite(skolem9(_u51)) )).
% 71.72/71.93 cnf(matrix-84, plain, ( element(skolem10(_u53), powerset(_u53)) )).
% 71.72/71.93 cnf(matrix-85, plain, ( empty(skolem10(_u53)) )).
% 71.72/71.93 cnf(matrix-86, plain, ( ~empty(skolem11) )).
% 71.72/71.93 cnf(matrix-87, plain, ( empty(_u56) | element(skolem12(_u56), powerset(_u56)) )).
% 71.72/71.93 cnf(matrix-88, plain, ( empty(_u56) | ~empty(skolem12(_u56)) )).
% 71.72/71.93 cnf(matrix-89, plain, ( empty(_u56) | finite(skolem12(_u56)) )).
% 71.72/71.93 cnf(matrix-90, plain, ( empty(_u58) | element(skolem13(_u58), powerset(_u58)) )).
% 71.72/71.93 cnf(matrix-91, plain, ( empty(_u58) | ~empty(skolem13(_u58)) )).
% 71.72/71.93 cnf(matrix-92, plain, ( empty(_u58) | finite(skolem13(_u58)) )).
% 71.72/71.93 cnf(matrix-93, plain, ( subset(_u60, _u60) )).
% 71.72/71.93 cnf(matrix-94, plain, ( finite(_u62) | ~subset(_u62, _u61) | ~finite(_u61) )).
% 71.72/71.93 cnf(matrix-95, plain, ( ~in(_u64, _u63) | element(_u64, _u63) )).
% 71.72/71.93 cnf(matrix-96, plain, ( subset(finite_subsets(_u65), powerset(_u65)) )).
% 71.72/71.93 cnf(matrix-97, plain, ( finite(skolem14) )).
% 71.72/71.93 cnf(matrix-98, plain, ( ( finite_subsets(skolem14) != powerset(skolem14)) )).
% 71.72/71.93 cnf(matrix-99, plain, ( ~element(_u68, _u67) | empty(_u67) | in(_u68, _u67) )).
% 71.72/71.93 cnf(matrix-100, plain, ( ~element(_u73, powerset(_u71)) | subset(_u73, _u71) )).
% 71.72/71.93 cnf(matrix-101, plain, ( ~subset(_u74, _u72) | element(_u74, powerset(_u72)) )).
% 71.72/71.93 cnf(matrix-102, plain, ( ~in(_u77, _u76) | ~element(_u76, powerset(_u75)) | element(_u77, _u75) )).
% 71.72/71.93 cnf(matrix-103, plain, ( ~in(_u80, _u79) | ~element(_u79, powerset(_u78)) | ~empty(_u78) )).
% 71.72/71.93 cnf(matrix-104, plain, ( ~empty(_u81) | ( _u81 = empty_set) )).
% 71.72/71.93 cnf(matrix-105, plain, ( ~in(_u83, _u82) | ~empty(_u82) )).
% 71.72/71.93 cnf(matrix-106, plain, ( ~empty(_u85) | ( _u85 = _u84) | ~empty(_u84) )).
% 71.72/71.93
% 71.72/71.93 % Proof stack:
% 71.72/71.93 cnf(proof-stack, plain,
% 71.72/71.93 proof_stack(
% 71.72/71.93 start(98),
% 71.72/71.93 left_branch(0, 39, 2, 2),
% 71.72/71.93 left_branch(0, 100, 1, 3),
% 71.72/71.93 left_branch(0, 102, 2, 4),
% 71.72/71.93 left_branch(0, 99, 2, 5),
% 71.72/71.93 left_branch(0, 101, 1, 6),
% 71.72/71.93 left_branch(0, 96, 0, 7),
% 71.72/71.93 right_branch(7),
% 71.72/71.93 right_branch(6),
% 71.72/71.93 left_branch(0, 103, 2, 7),
% 71.72/71.93 left_branch(0, 99, 2, 8),
% 71.72/71.93 left_branch(0, 84, 0, 9),
% 71.72/71.93 right_branch(9),
% 71.72/71.93 left_branch(0, 58, 0, 10),
% 71.72/71.93 right_branch(10),
% 71.72/71.93 right_branch(8),
% 71.72/71.93 left_branch(0, 101, 1, 9),
% 71.72/71.93 left_branch(0, 93, 0, 10),
% 71.72/71.93 right_branch(10),
% 71.72/71.93 right_branch(9),
% 71.72/71.93 right_branch(7),
% 71.72/71.93 right_branch(5),
% 71.72/71.93 left_branch(0, 102, 2, 6),
% 71.72/71.93 left_branch(0, 99, 2, 7),
% 71.72/71.93 left_branch(0, 101, 1, 8),
% 71.72/71.93 left_branch(0, 93, 0, 9),
% 71.72/71.93 right_branch(9),
% 71.72/71.93 right_branch(8),
% 71.72/71.93 left_branch(0, 58, 0, 9),
% 71.72/71.93 right_branch(9),
% 71.72/71.93 right_branch(7),
% 71.72/71.93 left_branch(0, 101, 1, 8),
% 71.72/71.93 left_branch(0, 93, 0, 9),
% 71.72/71.93 right_branch(9),
% 71.72/71.93 right_branch(8),
% 71.72/71.93 right_branch(6),
% 71.72/71.93 right_branch(4),
% 71.72/71.93 right_branch(3),
% 71.72/71.93 left_branch(0, 42, 0, 4),
% 71.72/71.93 left_branch(0, 45, 4, 5),
% 71.72/71.93 left_branch(0, 63, 0, 6),
% 71.72/71.93 right_branch(6),
% 71.72/71.93 left_branch(0, 34, 2, 7),
% 71.72/71.93 left_branch(0, 97, 0, 8),
% 71.72/71.93 right_branch(8),
% 71.72/71.93 left_branch(0, 102, 2, 9),
% 71.72/71.93 left_branch(0, 41, 1, 10),
% 71.72/71.93 reduction(0, 1),
% 71.72/71.93 right_branch(10),
% 71.72/71.93 left_branch(0, 101, 1, 11),
% 71.72/71.93 left_branch(0, 93, 0, 12),
% 71.72/71.93 right_branch(12),
% 71.72/71.93 right_branch(11),
% 71.72/71.93 right_branch(9),
% 71.72/71.93 right_branch(7),
% 71.72/71.93 left_branch(0, 100, 1, 8),
% 71.72/71.93 left_branch(0, 102, 2, 9),
% 71.72/71.93 left_branch(0, 41, 1, 10),
% 71.72/71.93 reduction(0, 1),
% 71.72/71.93 right_branch(10),
% 71.72/71.93 left_branch(0, 101, 1, 11),
% 71.72/71.93 left_branch(0, 93, 0, 12),
% 71.72/71.93 right_branch(12),
% 71.72/71.93 right_branch(11),
% 71.72/71.93 right_branch(9),
% 71.72/71.93 right_branch(8),
% 71.72/71.93 left_branch(0, 39, 2, 9),
% 71.72/71.93 left_branch(0, 93, 0, 10),
% 71.72/71.93 right_branch(10),
% 71.72/71.93 lemmata(0, 4),
% 71.72/71.93 right_branch(9),
% 71.72/71.93 right_branch(5),
% 71.72/71.93 right_branch(4),
% 71.72/71.93 right_branch(2)
% 71.72/71.93 )).
% 71.72/71.93 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------