TSTP Solution File: SEU204+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU204+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 : 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 14:33:32 EDT 2024
% Result : Timeout 298.61s 298.79s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU204+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12 % 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 14:54:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 298.61/298.79 % SZS status Theorem for theBenchmark
% 298.61/298.79 % SZS output start Proof for theBenchmark
% 298.61/298.79
% 298.61/298.79 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 298.61/298.79 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 298.61/298.79
% 298.61/298.79 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 298.61/298.79 cnf(cc1_relat_1-1, axiom, ( ~empty(_u2) | relation(_u2) )).
% 298.61/298.79
% 298.61/298.79 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 298.61/298.79 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u4, _u3) = unordered_pair(_u3, _u4)) )).
% 298.61/298.79
% 298.61/298.79 % Formula: d13_relat_1 ( axiom ) converted to clauses:
% 298.61/298.79 cnf(d13_relat_1-1, axiom, ( ~relation(_u13) | ( _u18 != relation_image(_u13, _u20)) | ~in(_u14, _u18) | in(ordered_pair(skolem1(_u13, _u20, _u18, _u14), _u14), _u13) )).
% 298.61/298.79 cnf(d13_relat_1-2, axiom, ( ~relation(_u13) | ( _u18 != relation_image(_u13, _u20)) | ~in(_u14, _u18) | in(skolem1(_u13, _u20, _u18, _u14), _u20) )).
% 298.61/298.79 cnf(d13_relat_1-3, axiom, ( ~relation(_u13) | ( _u18 != relation_image(_u13, _u20)) | ~in(ordered_pair(_u6, _u15), _u13) | ~in(_u6, _u20) | in(_u15, _u18) )).
% 298.61/298.79 cnf(d13_relat_1-4, axiom, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | in(skolem2(_u13, _u21, _u19), _u19) | in(ordered_pair(skolem4(_u13, _u21, _u19), skolem3(_u13, _u21, _u19)), _u13) )).
% 298.61/298.79 cnf(d13_relat_1-5, axiom, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | in(skolem2(_u13, _u21, _u19), _u19) | in(skolem4(_u13, _u21, _u19), _u21) )).
% 298.61/298.79 cnf(d13_relat_1-6, axiom, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | in(skolem2(_u13, _u21, _u19), _u19) | ~in(skolem3(_u13, _u21, _u19), _u19) )).
% 298.61/298.79 cnf(d13_relat_1-7, axiom, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | ~in(ordered_pair(_u8, skolem2(_u13, _u21, _u19)), _u13) | ~in(_u8, _u21) | in(ordered_pair(skolem4(_u13, _u21, _u19), skolem3(_u13, _u21, _u19)), _u13) )).
% 298.61/298.79 cnf(d13_relat_1-8, axiom, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | ~in(ordered_pair(_u8, skolem2(_u13, _u21, _u19)), _u13) | ~in(_u8, _u21) | in(skolem4(_u13, _u21, _u19), _u21) )).
% 298.61/298.79 cnf(d13_relat_1-9, axiom, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | ~in(ordered_pair(_u8, skolem2(_u13, _u21, _u19)), _u13) | ~in(_u8, _u21) | ~in(skolem3(_u13, _u21, _u19), _u19) )).
% 298.61/298.79
% 298.61/298.79 % Formula: d3_tarski ( axiom ) converted to clauses:
% 298.61/298.79 cnf(d3_tarski-1, axiom, ( ~subset(_u28, _u26) | ~in(_u22, _u28) | in(_u22, _u26) )).
% 298.61/298.79 cnf(d3_tarski-2, axiom, ( subset(_u29, _u27) | in(skolem5(_u29, _u27), _u29) )).
% 298.61/298.79 cnf(d3_tarski-3, axiom, ( subset(_u29, _u27) | ~in(skolem5(_u29, _u27), _u27) )).
% 298.61/298.79
% 298.61/298.79 % Formula: d5_relat_1 ( axiom ) converted to clauses:
% 298.61/298.79 cnf(d5_relat_1-1, axiom, ( ~relation(_u37) | ( _u42 != relation_rng(_u37)) | ~in(_u38, _u42) | in(ordered_pair(skolem6(_u37, _u42, _u38), _u38), _u37) )).
% 298.61/298.79 cnf(d5_relat_1-2, axiom, ( ~relation(_u37) | ( _u42 != relation_rng(_u37)) | ~in(ordered_pair(_u31, _u39), _u37) | in(_u39, _u42) )).
% 298.61/298.79 cnf(d5_relat_1-3, axiom, ( ~relation(_u37) | ( _u43 = relation_rng(_u37)) | in(skolem7(_u37, _u43), _u43) | in(ordered_pair(skolem9(_u37, _u43), skolem8(_u37, _u43)), _u37) )).
% 298.61/298.79 cnf(d5_relat_1-4, axiom, ( ~relation(_u37) | ( _u43 = relation_rng(_u37)) | in(skolem7(_u37, _u43), _u43) | ~in(skolem8(_u37, _u43), _u43) )).
% 298.61/298.80 cnf(d5_relat_1-5, axiom, ( ~relation(_u37) | ( _u43 = relation_rng(_u37)) | ~in(ordered_pair(_u33, skolem7(_u37, _u43)), _u37) | in(ordered_pair(skolem9(_u37, _u43), skolem8(_u37, _u43)), _u37) )).
% 298.61/298.80 cnf(d5_relat_1-6, axiom, ( ~relation(_u37) | ( _u43 = relation_rng(_u37)) | ~in(ordered_pair(_u33, skolem7(_u37, _u43)), _u37) | ~in(skolem8(_u37, _u43), _u43) )).
% 298.61/298.80
% 298.61/298.80 % Formula: d5_tarski ( axiom ) converted to clauses:
% 298.61/298.80 cnf(d5_tarski-1, axiom, ( ( ordered_pair(_u45, _u44) = unordered_pair(unordered_pair(_u45, _u44), singleton(_u45))) )).
% 298.61/298.80
% 298.61/298.80 % Formula: dt_k1_tarski ( axiom ) converted to clauses:
% 298.61/298.80 cnf(dt_k1_tarski, axiom, $true).
% 298.61/298.80
% 298.61/298.80 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(dt_k1_xboole_0, axiom, $true).
% 298.61/298.80
% 298.61/298.80 % Formula: dt_k1_zfmisc_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(dt_k1_zfmisc_1, axiom, $true).
% 298.61/298.80
% 298.61/298.80 % Formula: dt_k2_relat_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(dt_k2_relat_1, axiom, $true).
% 298.61/298.80
% 298.61/298.80 % Formula: dt_k2_tarski ( axiom ) converted to clauses:
% 298.61/298.80 cnf(dt_k2_tarski, axiom, $true).
% 298.61/298.80
% 298.61/298.80 % Formula: dt_k4_tarski ( axiom ) converted to clauses:
% 298.61/298.80 cnf(dt_k4_tarski, axiom, $true).
% 298.61/298.80
% 298.61/298.80 % Formula: dt_k9_relat_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(dt_k9_relat_1, axiom, $true).
% 298.61/298.80
% 298.61/298.80 % Formula: dt_m1_subset_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(dt_m1_subset_1, axiom, $true).
% 298.61/298.80
% 298.61/298.80 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(existence_m1_subset_1-1, axiom, ( element(skolem10(_u47), _u47) )).
% 298.61/298.80
% 298.61/298.80 % Formula: fc1_subset_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(fc1_subset_1-1, axiom, ( ~empty(powerset(_u48)) )).
% 298.61/298.80
% 298.61/298.80 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 298.61/298.80
% 298.61/298.80 % Formula: fc1_zfmisc_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(fc1_zfmisc_1-1, axiom, ( ~empty(ordered_pair(_u50, _u49)) )).
% 298.61/298.80
% 298.61/298.80 % Formula: fc2_subset_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(fc2_subset_1-1, axiom, ( ~empty(singleton(_u51)) )).
% 298.61/298.80
% 298.61/298.80 % Formula: fc3_subset_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(fc3_subset_1-1, axiom, ( ~empty(unordered_pair(_u53, _u52)) )).
% 298.61/298.80
% 298.61/298.80 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 298.61/298.80 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 298.61/298.80
% 298.61/298.80 % Formula: fc6_relat_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(fc6_relat_1-1, axiom, ( empty(_u54) | ~relation(_u54) | ~empty(relation_rng(_u54)) )).
% 298.61/298.80
% 298.61/298.80 % Formula: fc8_relat_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(fc8_relat_1-1, axiom, ( ~empty(_u55) | empty(relation_rng(_u55)) )).
% 298.61/298.80 cnf(fc8_relat_1-2, axiom, ( ~empty(_u55) | relation(relation_rng(_u55)) )).
% 298.61/298.80
% 298.61/298.80 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(rc1_relat_1-1, axiom, ( empty(skolem11) )).
% 298.61/298.80 cnf(rc1_relat_1-2, axiom, ( relation(skolem11) )).
% 298.61/298.80
% 298.61/298.80 % Formula: rc1_subset_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(rc1_subset_1-1, axiom, ( empty(_u58) | element(skolem12(_u58), powerset(_u58)) )).
% 298.61/298.80 cnf(rc1_subset_1-2, axiom, ( empty(_u58) | ~empty(skolem12(_u58)) )).
% 298.61/298.80
% 298.61/298.80 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(rc1_xboole_0-1, axiom, ( empty(skolem13) )).
% 298.61/298.80
% 298.61/298.80 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem14) )).
% 298.61/298.80 cnf(rc2_relat_1-2, axiom, ( relation(skolem14) )).
% 298.61/298.80
% 298.61/298.80 % Formula: rc2_subset_1 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(rc2_subset_1-1, axiom, ( element(skolem15(_u62), powerset(_u62)) )).
% 298.61/298.80 cnf(rc2_subset_1-2, axiom, ( empty(skolem15(_u62)) )).
% 298.61/298.80
% 298.61/298.80 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 298.61/298.80 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem16) )).
% 298.61/298.80
% 298.61/298.80 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 298.61/298.80 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u65, _u65) )).
% 298.61/298.80
% 298.61/298.80 % Formula: t144_relat_1 ( conjecture ) (definitionally) converted to clauses:
% 298.61/298.80 cnf(t144_relat_1-1, negated_conjecture, ( relation(skolem18) )).
% 298.61/298.80 cnf(t144_relat_1-2, negated_conjecture, ( ~subset(relation_image(skolem18, skolem17), relation_rng(skolem18)) )).
% 298.61/298.80
% 298.61/298.80 % Formula: t1_subset ( axiom ) converted to clauses:
% 298.61/298.80 cnf(t1_subset-1, axiom, ( ~in(_u69, _u68) | element(_u69, _u68) )).
% 298.61/298.80
% 298.61/298.80 % Formula: t2_subset ( axiom ) converted to clauses:
% 298.61/298.80 cnf(t2_subset-1, axiom, ( ~element(_u71, _u70) | empty(_u70) | in(_u71, _u70) )).
% 298.61/298.80
% 298.61/298.80 % Formula: t3_subset ( axiom ) converted to clauses:
% 298.61/298.80 cnf(t3_subset-1, axiom, ( ~element(_u76, powerset(_u74)) | subset(_u76, _u74) )).
% 298.61/298.80 cnf(t3_subset-2, axiom, ( ~subset(_u77, _u75) | element(_u77, powerset(_u75)) )).
% 298.61/298.80
% 298.61/298.80 % Formula: t4_subset ( axiom ) converted to clauses:
% 298.61/298.80 cnf(t4_subset-1, axiom, ( ~in(_u80, _u79) | ~element(_u79, powerset(_u78)) | element(_u80, _u78) )).
% 298.61/298.80
% 298.61/298.80 % Formula: t5_subset ( axiom ) converted to clauses:
% 298.61/298.80 cnf(t5_subset-1, axiom, ( ~in(_u83, _u82) | ~element(_u82, powerset(_u81)) | ~empty(_u81) )).
% 298.61/298.80
% 298.61/298.80 % Formula: t6_boole ( axiom ) converted to clauses:
% 298.61/298.80 cnf(t6_boole-1, axiom, ( ~empty(_u84) | ( _u84 = empty_set) )).
% 298.61/298.80
% 298.61/298.80 % Formula: t7_boole ( axiom ) converted to clauses:
% 298.61/298.80 cnf(t7_boole-1, axiom, ( ~in(_u86, _u85) | ~empty(_u85) )).
% 298.61/298.80
% 298.61/298.80 % Formula: t8_boole ( axiom ) converted to clauses:
% 298.61/298.80 cnf(t8_boole-1, axiom, ( ~empty(_u88) | ( _u88 = _u87) | ~empty(_u87) )).
% 298.61/298.80
% 298.61/298.80 % Problem matrix:
% 298.61/298.80 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 298.61/298.80 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 298.61/298.80 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 298.61/298.80 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 298.61/298.80 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( relation_image(__eqx_0, __eqx_1) = relation_image(__eqy_0, __eqy_1)) )).
% 298.61/298.80 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 298.61/298.80 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( relation_rng(__eqx_0) = relation_rng(__eqy_0)) )).
% 298.61/298.80 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 298.61/298.80 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 298.61/298.80 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( skolem1(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = skolem1(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 298.61/298.80 cnf(matrix-10, 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)) )).
% 298.61/298.80 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem3(__eqx_0, __eqx_1, __eqx_2) = skolem3(__eqy_0, __eqy_1, __eqy_2)) )).
% 298.61/298.80 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem4(__eqx_0, __eqx_1, __eqx_2) = skolem4(__eqy_0, __eqy_1, __eqy_2)) )).
% 298.61/298.80 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem5(__eqx_0, __eqx_1) = skolem5(__eqy_0, __eqy_1)) )).
% 298.61/298.80 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem6(__eqx_0, __eqx_1, __eqx_2) = skolem6(__eqy_0, __eqy_1, __eqy_2)) )).
% 298.61/298.80 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem7(__eqx_0, __eqx_1) = skolem7(__eqy_0, __eqy_1)) )).
% 298.61/298.80 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem8(__eqx_0, __eqx_1) = skolem8(__eqy_0, __eqy_1)) )).
% 298.61/298.80 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem9(__eqx_0, __eqx_1) = skolem9(__eqy_0, __eqy_1)) )).
% 298.61/298.80 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( skolem10(__eqx_0) = skolem10(__eqy_0)) )).
% 298.61/298.80 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( skolem12(__eqx_0) = skolem12(__eqy_0)) )).
% 298.61/298.80 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( skolem15(__eqx_0) = skolem15(__eqy_0)) )).
% 298.61/298.80 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 298.61/298.80 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 298.61/298.80 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 298.61/298.80 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 298.61/298.80 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 298.61/298.80 cnf(matrix-26, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 298.61/298.80 cnf(matrix-27, plain, ( ~empty(_u2) | relation(_u2) )).
% 298.61/298.80 cnf(matrix-28, plain, ( ( unordered_pair(_u4, _u3) = unordered_pair(_u3, _u4)) )).
% 298.61/298.80 cnf(matrix-29, plain, ( ~relation(_u13) | ( _u18 != relation_image(_u13, _u20)) | ~in(_u14, _u18) | in(ordered_pair(skolem1(_u13, _u20, _u18, _u14), _u14), _u13) )).
% 298.61/298.80 cnf(matrix-30, plain, ( ~relation(_u13) | ( _u18 != relation_image(_u13, _u20)) | ~in(_u14, _u18) | in(skolem1(_u13, _u20, _u18, _u14), _u20) )).
% 298.61/298.80 cnf(matrix-31, plain, ( ~relation(_u13) | ( _u18 != relation_image(_u13, _u20)) | ~in(ordered_pair(_u6, _u15), _u13) | ~in(_u6, _u20) | in(_u15, _u18) )).
% 298.61/298.80 cnf(matrix-32, plain, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | in(skolem2(_u13, _u21, _u19), _u19) | in(ordered_pair(skolem4(_u13, _u21, _u19), skolem3(_u13, _u21, _u19)), _u13) )).
% 298.61/298.80 cnf(matrix-33, plain, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | in(skolem2(_u13, _u21, _u19), _u19) | in(skolem4(_u13, _u21, _u19), _u21) )).
% 298.61/298.80 cnf(matrix-34, plain, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | in(skolem2(_u13, _u21, _u19), _u19) | ~in(skolem3(_u13, _u21, _u19), _u19) )).
% 298.61/298.80 cnf(matrix-35, plain, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | ~in(ordered_pair(_u8, skolem2(_u13, _u21, _u19)), _u13) | ~in(_u8, _u21) | in(ordered_pair(skolem4(_u13, _u21, _u19), skolem3(_u13, _u21, _u19)), _u13) )).
% 298.61/298.80 cnf(matrix-36, plain, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | ~in(ordered_pair(_u8, skolem2(_u13, _u21, _u19)), _u13) | ~in(_u8, _u21) | in(skolem4(_u13, _u21, _u19), _u21) )).
% 298.61/298.80 cnf(matrix-37, plain, ( ~relation(_u13) | ( _u19 = relation_image(_u13, _u21)) | ~in(ordered_pair(_u8, skolem2(_u13, _u21, _u19)), _u13) | ~in(_u8, _u21) | ~in(skolem3(_u13, _u21, _u19), _u19) )).
% 298.61/298.80 cnf(matrix-38, plain, ( ~subset(_u28, _u26) | ~in(_u22, _u28) | in(_u22, _u26) )).
% 298.61/298.80 cnf(matrix-39, plain, ( subset(_u29, _u27) | in(skolem5(_u29, _u27), _u29) )).
% 298.61/298.80 cnf(matrix-40, plain, ( subset(_u29, _u27) | ~in(skolem5(_u29, _u27), _u27) )).
% 298.61/298.80 cnf(matrix-41, plain, ( ~relation(_u37) | ( _u42 != relation_rng(_u37)) | ~in(_u38, _u42) | in(ordered_pair(skolem6(_u37, _u42, _u38), _u38), _u37) )).
% 298.61/298.80 cnf(matrix-42, plain, ( ~relation(_u37) | ( _u42 != relation_rng(_u37)) | ~in(ordered_pair(_u31, _u39), _u37) | in(_u39, _u42) )).
% 298.61/298.80 cnf(matrix-43, plain, ( ~relation(_u37) | ( _u43 = relation_rng(_u37)) | in(skolem7(_u37, _u43), _u43) | in(ordered_pair(skolem9(_u37, _u43), skolem8(_u37, _u43)), _u37) )).
% 298.61/298.80 cnf(matrix-44, plain, ( ~relation(_u37) | ( _u43 = relation_rng(_u37)) | in(skolem7(_u37, _u43), _u43) | ~in(skolem8(_u37, _u43), _u43) )).
% 298.61/298.80 cnf(matrix-45, plain, ( ~relation(_u37) | ( _u43 = relation_rng(_u37)) | ~in(ordered_pair(_u33, skolem7(_u37, _u43)), _u37) | in(ordered_pair(skolem9(_u37, _u43), skolem8(_u37, _u43)), _u37) )).
% 298.61/298.80 cnf(matrix-46, plain, ( ~relation(_u37) | ( _u43 = relation_rng(_u37)) | ~in(ordered_pair(_u33, skolem7(_u37, _u43)), _u37) | ~in(skolem8(_u37, _u43), _u43) )).
% 298.61/298.80 cnf(matrix-47, plain, ( ( ordered_pair(_u45, _u44) = unordered_pair(unordered_pair(_u45, _u44), singleton(_u45))) )).
% 298.61/298.80 cnf(matrix-48, plain, ( element(skolem10(_u47), _u47) )).
% 298.61/298.80 cnf(matrix-49, plain, ( ~empty(powerset(_u48)) )).
% 298.61/298.80 cnf(matrix-50, plain, ( empty(empty_set) )).
% 298.61/298.80 cnf(matrix-51, plain, ( ~empty(ordered_pair(_u50, _u49)) )).
% 298.61/298.80 cnf(matrix-52, plain, ( ~empty(singleton(_u51)) )).
% 298.61/298.80 cnf(matrix-53, plain, ( ~empty(unordered_pair(_u53, _u52)) )).
% 298.61/298.80 cnf(matrix-54, plain, ( empty(empty_set) )).
% 298.61/298.80 cnf(matrix-55, plain, ( relation(empty_set) )).
% 298.61/298.80 cnf(matrix-56, plain, ( empty(_u54) | ~relation(_u54) | ~empty(relation_rng(_u54)) )).
% 298.61/298.80 cnf(matrix-57, plain, ( ~empty(_u55) | empty(relation_rng(_u55)) )).
% 298.61/298.80 cnf(matrix-58, plain, ( ~empty(_u55) | relation(relation_rng(_u55)) )).
% 298.61/298.80 cnf(matrix-59, plain, ( empty(skolem11) )).
% 298.61/298.80 cnf(matrix-60, plain, ( relation(skolem11) )).
% 298.61/298.80 cnf(matrix-61, plain, ( empty(_u58) | element(skolem12(_u58), powerset(_u58)) )).
% 298.61/298.80 cnf(matrix-62, plain, ( empty(_u58) | ~empty(skolem12(_u58)) )).
% 298.61/298.80 cnf(matrix-63, plain, ( empty(skolem13) )).
% 298.61/298.80 cnf(matrix-64, plain, ( ~empty(skolem14) )).
% 298.61/298.80 cnf(matrix-65, plain, ( relation(skolem14) )).
% 298.61/298.80 cnf(matrix-66, plain, ( element(skolem15(_u62), powerset(_u62)) )).
% 298.61/298.80 cnf(matrix-67, plain, ( empty(skolem15(_u62)) )).
% 298.61/298.80 cnf(matrix-68, plain, ( ~empty(skolem16) )).
% 298.61/298.80 cnf(matrix-69, plain, ( subset(_u65, _u65) )).
% 298.61/298.80 cnf(matrix-70, plain, ( relation(skolem18) )).
% 298.61/298.80 cnf(matrix-71, plain, ( ~subset(relation_image(skolem18, skolem17), relation_rng(skolem18)) )).
% 298.61/298.80 cnf(matrix-72, plain, ( ~in(_u69, _u68) | element(_u69, _u68) )).
% 298.61/298.80 cnf(matrix-73, plain, ( ~element(_u71, _u70) | empty(_u70) | in(_u71, _u70) )).
% 298.61/298.80 cnf(matrix-74, plain, ( ~element(_u76, powerset(_u74)) | subset(_u76, _u74) )).
% 298.61/298.80 cnf(matrix-75, plain, ( ~subset(_u77, _u75) | element(_u77, powerset(_u75)) )).
% 298.61/298.80 cnf(matrix-76, plain, ( ~in(_u80, _u79) | ~element(_u79, powerset(_u78)) | element(_u80, _u78) )).
% 298.61/298.80 cnf(matrix-77, plain, ( ~in(_u83, _u82) | ~element(_u82, powerset(_u81)) | ~empty(_u81) )).
% 298.61/298.80 cnf(matrix-78, plain, ( ~empty(_u84) | ( _u84 = empty_set) )).
% 298.61/298.80 cnf(matrix-79, plain, ( ~in(_u86, _u85) | ~empty(_u85) )).
% 298.61/298.80 cnf(matrix-80, plain, ( ~empty(_u88) | ( _u88 = _u87) | ~empty(_u87) )).
% 298.61/298.80
% 298.61/298.80 % Proof stack:
% 298.61/298.80 cnf(proof-stack, plain,
% 298.61/298.80 proof_stack(
% 298.61/298.80 start(71),
% 298.61/298.80 left_branch(0, 40, 0, 2),
% 298.61/298.80 left_branch(0, 42, 3, 3),
% 298.61/298.80 left_branch(0, 70, 0, 4),
% 298.61/298.80 right_branch(4),
% 298.61/298.80 left_branch(0, 29, 3, 5),
% 298.61/298.80 lemmata(0, 0),
% 298.61/298.80 left_branch(0, 39, 1, 7),
% 298.61/298.80 reduction(0, 0),
% 298.61/298.80 right_branch(7),
% 298.61/298.80 left_branch(0, 4, 2, 8),
% 298.61/298.80 left_branch(0, 0, 0, 9),
% 298.61/298.80 right_branch(9),
% 298.61/298.80 left_branch(0, 0, 0, 10),
% 298.61/298.80 right_branch(10),
% 298.61/298.80 right_branch(8),
% 298.61/298.80 right_branch(5),
% 298.61/298.80 left_branch(0, 6, 1, 6),
% 298.61/298.80 left_branch(0, 0, 0, 7),
% 298.61/298.80 right_branch(7),
% 298.61/298.80 right_branch(6),
% 298.61/298.80 right_branch(3),
% 298.61/298.80 right_branch(2)
% 298.61/298.80 )).
% 298.61/298.80 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------