TSTP Solution File: SEU030+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU030+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 : n025.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 14:33:00 EDT 2024
% Result : Theorem 0.51s 0.73s
% Output : Proof 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU030+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n025.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 14:23:08 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.51/0.73 % SZS status Theorem for theBenchmark
% 0.51/0.73 % SZS output start Proof for theBenchmark
% 0.51/0.73
% 0.51/0.73 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 0.51/0.73 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.51/0.73
% 0.51/0.73 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(cc1_funct_1-1, axiom, ( ~empty(_u2) | function(_u2) )).
% 0.51/0.73
% 0.51/0.73 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(cc1_relat_1-1, axiom, ( ~empty(_u3) | relation(_u3) )).
% 0.51/0.73
% 0.51/0.73 % Formula: cc2_funct_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(cc2_funct_1-1, axiom, ( ~relation(_u4) | ~empty(_u4) | ~function(_u4) | one_to_one(_u4) )).
% 0.51/0.73
% 0.51/0.73 % Formula: dt_k2_funct_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(dt_k2_funct_1-1, axiom, ( ~relation(_u5) | ~function(_u5) | relation(function_inverse(_u5)) )).
% 0.51/0.73 cnf(dt_k2_funct_1-2, axiom, ( ~relation(_u5) | ~function(_u5) | function(function_inverse(_u5)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: dt_k5_relat_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(dt_k5_relat_1-1, axiom, ( ~relation(_u7) | ~relation(_u6) | relation(relation_composition(_u7, _u6)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: dt_k6_relat_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(dt_k6_relat_1-1, axiom, ( relation(identity_relation(_u8)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(existence_m1_subset_1-1, axiom, ( element(skolem1(_u10), _u10) )).
% 0.51/0.73
% 0.51/0.73 % Formula: fc10_relat_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(fc10_relat_1-1, axiom, ( ~empty(_u12) | ~relation(_u11) | empty(relation_composition(_u11, _u12)) )).
% 0.51/0.73 cnf(fc10_relat_1-2, axiom, ( ~empty(_u12) | ~relation(_u11) | relation(relation_composition(_u11, _u12)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: fc12_relat_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(fc12_relat_1-1, axiom, ( empty(empty_set) )).
% 0.51/0.73 cnf(fc12_relat_1-2, axiom, ( relation(empty_set) )).
% 0.51/0.73 cnf(fc12_relat_1-3, axiom, ( relation_empty_yielding(empty_set) )).
% 0.51/0.73
% 0.51/0.73 % Formula: fc1_funct_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(fc1_funct_1-1, axiom, ( ~relation(_u14) | ~function(_u14) | ~relation(_u13) | ~function(_u13) | relation(relation_composition(_u14, _u13)) )).
% 0.51/0.73 cnf(fc1_funct_1-2, axiom, ( ~relation(_u14) | ~function(_u14) | ~relation(_u13) | ~function(_u13) | function(relation_composition(_u14, _u13)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: fc1_subset_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(fc1_subset_1-1, axiom, ( ~empty(powerset(_u15)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 0.51/0.73
% 0.51/0.73 % Formula: fc2_funct_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(fc2_funct_1-1, axiom, ( relation(identity_relation(_u17)) )).
% 0.51/0.73 cnf(fc2_funct_1-2, axiom, ( function(identity_relation(_u18)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 0.51/0.73 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 0.51/0.73
% 0.51/0.73 % Formula: fc5_relat_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(fc5_relat_1-1, axiom, ( empty(_u19) | ~relation(_u19) | ~empty(relation_dom(_u19)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: fc6_relat_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(fc6_relat_1-1, axiom, ( empty(_u20) | ~relation(_u20) | ~empty(relation_rng(_u20)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: fc7_relat_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(fc7_relat_1-1, axiom, ( ~empty(_u21) | empty(relation_dom(_u21)) )).
% 0.51/0.73 cnf(fc7_relat_1-2, axiom, ( ~empty(_u21) | relation(relation_dom(_u21)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: fc8_relat_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(fc8_relat_1-1, axiom, ( ~empty(_u22) | empty(relation_rng(_u22)) )).
% 0.51/0.73 cnf(fc8_relat_1-2, axiom, ( ~empty(_u22) | relation(relation_rng(_u22)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: fc9_relat_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(fc9_relat_1-1, axiom, ( ~empty(_u24) | ~relation(_u23) | empty(relation_composition(_u24, _u23)) )).
% 0.51/0.73 cnf(fc9_relat_1-2, axiom, ( ~empty(_u24) | ~relation(_u23) | relation(relation_composition(_u24, _u23)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: l72_funct_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(l72_funct_1-1, axiom, ( ~relation(_u27) | ~function(_u27) | ~relation(_u26) | ~function(_u26) | ~relation(_u25) | ~function(_u25) | ( relation_rng(_u27) != _u28) | ( relation_composition(_u27, _u26) != identity_relation(relation_dom(_u25))) | ( relation_composition(_u26, _u25) != identity_relation(_u28)) | ( _u25 = _u27) )).
% 0.51/0.73
% 0.51/0.73 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(rc1_funct_1-1, axiom, ( relation(skolem2) )).
% 0.51/0.73 cnf(rc1_funct_1-2, axiom, ( function(skolem2) )).
% 0.51/0.73
% 0.51/0.73 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(rc1_relat_1-1, axiom, ( empty(skolem3) )).
% 0.51/0.73 cnf(rc1_relat_1-2, axiom, ( relation(skolem3) )).
% 0.51/0.73
% 0.51/0.73 % Formula: rc1_subset_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(rc1_subset_1-1, axiom, ( empty(_u32) | element(skolem4(_u32), powerset(_u32)) )).
% 0.51/0.73 cnf(rc1_subset_1-2, axiom, ( empty(_u32) | ~empty(skolem4(_u32)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(rc1_xboole_0-1, axiom, ( empty(skolem5) )).
% 0.51/0.73
% 0.51/0.73 % Formula: rc2_funct_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(rc2_funct_1-1, axiom, ( relation(skolem6) )).
% 0.51/0.73 cnf(rc2_funct_1-2, axiom, ( empty(skolem6) )).
% 0.51/0.73 cnf(rc2_funct_1-3, axiom, ( function(skolem6) )).
% 0.51/0.73
% 0.51/0.73 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem7) )).
% 0.51/0.73 cnf(rc2_relat_1-2, axiom, ( relation(skolem7) )).
% 0.51/0.73
% 0.51/0.73 % Formula: rc2_subset_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(rc2_subset_1-1, axiom, ( element(skolem8(_u37), powerset(_u37)) )).
% 0.51/0.73 cnf(rc2_subset_1-2, axiom, ( empty(skolem8(_u37)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem9) )).
% 0.51/0.73
% 0.51/0.73 % Formula: rc3_funct_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(rc3_funct_1-1, axiom, ( relation(skolem10) )).
% 0.51/0.73 cnf(rc3_funct_1-2, axiom, ( function(skolem10) )).
% 0.51/0.73 cnf(rc3_funct_1-3, axiom, ( one_to_one(skolem10) )).
% 0.51/0.73
% 0.51/0.73 % Formula: rc3_relat_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(rc3_relat_1-1, axiom, ( relation(skolem11) )).
% 0.51/0.73 cnf(rc3_relat_1-2, axiom, ( relation_empty_yielding(skolem11) )).
% 0.51/0.73
% 0.51/0.73 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 0.51/0.73 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u42, _u42) )).
% 0.51/0.73
% 0.51/0.73 % Formula: t1_subset ( axiom ) converted to clauses:
% 0.51/0.73 cnf(t1_subset-1, axiom, ( ~in(_u44, _u43) | element(_u44, _u43) )).
% 0.51/0.73
% 0.51/0.73 % Formula: t2_subset ( axiom ) converted to clauses:
% 0.51/0.73 cnf(t2_subset-1, axiom, ( ~element(_u46, _u45) | empty(_u45) | in(_u46, _u45) )).
% 0.51/0.73
% 0.51/0.73 % Formula: t3_subset ( axiom ) converted to clauses:
% 0.51/0.73 cnf(t3_subset-1, axiom, ( ~element(_u51, powerset(_u49)) | subset(_u51, _u49) )).
% 0.51/0.73 cnf(t3_subset-2, axiom, ( ~subset(_u52, _u50) | element(_u52, powerset(_u50)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: t4_subset ( axiom ) converted to clauses:
% 0.51/0.73 cnf(t4_subset-1, axiom, ( ~in(_u55, _u54) | ~element(_u54, powerset(_u53)) | element(_u55, _u53) )).
% 0.51/0.73
% 0.51/0.73 % Formula: t55_funct_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(t55_funct_1-1, axiom, ( ~relation(_u56) | ~function(_u56) | ~one_to_one(_u56) | ( relation_rng(_u56) = relation_dom(function_inverse(_u56))) )).
% 0.51/0.73 cnf(t55_funct_1-2, axiom, ( ~relation(_u56) | ~function(_u56) | ~one_to_one(_u56) | ( relation_dom(_u56) = relation_rng(function_inverse(_u56))) )).
% 0.51/0.73
% 0.51/0.73 % Formula: t5_subset ( axiom ) converted to clauses:
% 0.51/0.73 cnf(t5_subset-1, axiom, ( ~in(_u59, _u58) | ~element(_u58, powerset(_u57)) | ~empty(_u57) )).
% 0.51/0.73
% 0.51/0.73 % Formula: t61_funct_1 ( axiom ) converted to clauses:
% 0.51/0.73 cnf(t61_funct_1-1, axiom, ( ~relation(_u60) | ~function(_u60) | ~one_to_one(_u60) | ( relation_composition(_u60, function_inverse(_u60)) = identity_relation(relation_dom(_u60))) )).
% 0.51/0.73 cnf(t61_funct_1-2, axiom, ( ~relation(_u60) | ~function(_u60) | ~one_to_one(_u60) | ( relation_composition(function_inverse(_u60), _u60) = identity_relation(relation_rng(_u60))) )).
% 0.51/0.73
% 0.51/0.73 % Formula: t63_funct_1 ( conjecture ) (definitionally) converted to clauses:
% 0.51/0.73 cnf(t63_funct_1-1, negated_conjecture, ( relation(skolem12) )).
% 0.51/0.73 cnf(t63_funct_1-2, negated_conjecture, ( function(skolem12) )).
% 0.51/0.73 cnf(t63_funct_1-3, negated_conjecture, ( relation(skolem13) )).
% 0.51/0.73 cnf(t63_funct_1-4, negated_conjecture, ( function(skolem13) )).
% 0.51/0.73 cnf(t63_funct_1-5, negated_conjecture, ( one_to_one(skolem12) )).
% 0.51/0.73 cnf(t63_funct_1-6, negated_conjecture, ( ( relation_rng(skolem12) = relation_dom(skolem13)) )).
% 0.51/0.73 cnf(t63_funct_1-7, negated_conjecture, ( ( relation_composition(skolem12, skolem13) = identity_relation(relation_dom(skolem12))) )).
% 0.51/0.73 cnf(t63_funct_1-8, negated_conjecture, ( ( skolem13 != function_inverse(skolem12)) )).
% 0.51/0.73
% 0.51/0.73 % Formula: t6_boole ( axiom ) converted to clauses:
% 0.51/0.73 cnf(t6_boole-1, axiom, ( ~empty(_u63) | ( _u63 = empty_set) )).
% 0.51/0.73
% 0.51/0.73 % Formula: t7_boole ( axiom ) converted to clauses:
% 0.51/0.73 cnf(t7_boole-1, axiom, ( ~in(_u65, _u64) | ~empty(_u64) )).
% 0.51/0.73
% 0.51/0.73 % Formula: t8_boole ( axiom ) converted to clauses:
% 0.51/0.73 cnf(t8_boole-1, axiom, ( ~empty(_u67) | ( _u67 = _u66) | ~empty(_u66) )).
% 0.51/0.73
% 0.51/0.73 % Problem matrix:
% 0.51/0.73 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.51/0.73 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.51/0.73 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.51/0.73 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( function_inverse(__eqx_0) = function_inverse(__eqy_0)) )).
% 0.51/0.73 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( relation_composition(__eqx_0, __eqx_1) = relation_composition(__eqy_0, __eqy_1)) )).
% 0.51/0.73 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( identity_relation(__eqx_0) = identity_relation(__eqy_0)) )).
% 0.51/0.73 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 0.51/0.73 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( relation_dom(__eqx_0) = relation_dom(__eqy_0)) )).
% 0.51/0.73 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( relation_rng(__eqx_0) = relation_rng(__eqy_0)) )).
% 0.51/0.73 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 0.51/0.73 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( skolem4(__eqx_0) = skolem4(__eqy_0)) )).
% 0.51/0.73 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( skolem8(__eqx_0) = skolem8(__eqy_0)) )).
% 0.51/0.73 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 0.51/0.73 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 0.51/0.73 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 0.51/0.73 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 0.51/0.73 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 0.51/0.73 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 0.51/0.73 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~relation_empty_yielding(__eqx_0) | relation_empty_yielding(__eqy_0) )).
% 0.51/0.73 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 0.51/0.73 cnf(matrix-20, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.51/0.73 cnf(matrix-21, plain, ( ~empty(_u2) | function(_u2) )).
% 0.51/0.73 cnf(matrix-22, plain, ( ~empty(_u3) | relation(_u3) )).
% 0.51/0.73 cnf(matrix-23, plain, ( ~relation(_u4) | ~empty(_u4) | ~function(_u4) | one_to_one(_u4) )).
% 0.51/0.73 cnf(matrix-24, plain, ( ~relation(_u5) | ~function(_u5) | relation(function_inverse(_u5)) )).
% 0.51/0.73 cnf(matrix-25, plain, ( ~relation(_u5) | ~function(_u5) | function(function_inverse(_u5)) )).
% 0.51/0.73 cnf(matrix-26, plain, ( ~relation(_u7) | ~relation(_u6) | relation(relation_composition(_u7, _u6)) )).
% 0.51/0.73 cnf(matrix-27, plain, ( relation(identity_relation(_u8)) )).
% 0.51/0.73 cnf(matrix-28, plain, ( element(skolem1(_u10), _u10) )).
% 0.51/0.73 cnf(matrix-29, plain, ( ~empty(_u12) | ~relation(_u11) | empty(relation_composition(_u11, _u12)) )).
% 0.51/0.73 cnf(matrix-30, plain, ( ~empty(_u12) | ~relation(_u11) | relation(relation_composition(_u11, _u12)) )).
% 0.51/0.73 cnf(matrix-31, plain, ( empty(empty_set) )).
% 0.51/0.73 cnf(matrix-32, plain, ( relation(empty_set) )).
% 0.51/0.73 cnf(matrix-33, plain, ( relation_empty_yielding(empty_set) )).
% 0.51/0.73 cnf(matrix-34, plain, ( ~relation(_u14) | ~function(_u14) | ~relation(_u13) | ~function(_u13) | relation(relation_composition(_u14, _u13)) )).
% 0.51/0.73 cnf(matrix-35, plain, ( ~relation(_u14) | ~function(_u14) | ~relation(_u13) | ~function(_u13) | function(relation_composition(_u14, _u13)) )).
% 0.51/0.73 cnf(matrix-36, plain, ( ~empty(powerset(_u15)) )).
% 0.51/0.73 cnf(matrix-37, plain, ( empty(empty_set) )).
% 0.51/0.73 cnf(matrix-38, plain, ( relation(identity_relation(_u17)) )).
% 0.51/0.73 cnf(matrix-39, plain, ( function(identity_relation(_u18)) )).
% 0.51/0.73 cnf(matrix-40, plain, ( empty(empty_set) )).
% 0.51/0.73 cnf(matrix-41, plain, ( relation(empty_set) )).
% 0.51/0.73 cnf(matrix-42, plain, ( empty(_u19) | ~relation(_u19) | ~empty(relation_dom(_u19)) )).
% 0.51/0.73 cnf(matrix-43, plain, ( empty(_u20) | ~relation(_u20) | ~empty(relation_rng(_u20)) )).
% 0.51/0.73 cnf(matrix-44, plain, ( ~empty(_u21) | empty(relation_dom(_u21)) )).
% 0.51/0.73 cnf(matrix-45, plain, ( ~empty(_u21) | relation(relation_dom(_u21)) )).
% 0.51/0.73 cnf(matrix-46, plain, ( ~empty(_u22) | empty(relation_rng(_u22)) )).
% 0.51/0.73 cnf(matrix-47, plain, ( ~empty(_u22) | relation(relation_rng(_u22)) )).
% 0.51/0.73 cnf(matrix-48, plain, ( ~empty(_u24) | ~relation(_u23) | empty(relation_composition(_u24, _u23)) )).
% 0.51/0.73 cnf(matrix-49, plain, ( ~empty(_u24) | ~relation(_u23) | relation(relation_composition(_u24, _u23)) )).
% 0.51/0.73 cnf(matrix-50, plain, ( ~relation(_u27) | ~function(_u27) | ~relation(_u26) | ~function(_u26) | ~relation(_u25) | ~function(_u25) | ( relation_rng(_u27) != _u28) | ( relation_composition(_u27, _u26) != identity_relation(relation_dom(_u25))) | ( relation_composition(_u26, _u25) != identity_relation(_u28)) | ( _u25 = _u27) )).
% 0.51/0.73 cnf(matrix-51, plain, ( relation(skolem2) )).
% 0.51/0.73 cnf(matrix-52, plain, ( function(skolem2) )).
% 0.51/0.73 cnf(matrix-53, plain, ( empty(skolem3) )).
% 0.51/0.73 cnf(matrix-54, plain, ( relation(skolem3) )).
% 0.51/0.73 cnf(matrix-55, plain, ( empty(_u32) | element(skolem4(_u32), powerset(_u32)) )).
% 0.51/0.73 cnf(matrix-56, plain, ( empty(_u32) | ~empty(skolem4(_u32)) )).
% 0.51/0.73 cnf(matrix-57, plain, ( empty(skolem5) )).
% 0.51/0.73 cnf(matrix-58, plain, ( relation(skolem6) )).
% 0.51/0.73 cnf(matrix-59, plain, ( empty(skolem6) )).
% 0.51/0.73 cnf(matrix-60, plain, ( function(skolem6) )).
% 0.51/0.73 cnf(matrix-61, plain, ( ~empty(skolem7) )).
% 0.51/0.73 cnf(matrix-62, plain, ( relation(skolem7) )).
% 0.51/0.73 cnf(matrix-63, plain, ( element(skolem8(_u37), powerset(_u37)) )).
% 0.51/0.73 cnf(matrix-64, plain, ( empty(skolem8(_u37)) )).
% 0.51/0.73 cnf(matrix-65, plain, ( ~empty(skolem9) )).
% 0.51/0.73 cnf(matrix-66, plain, ( relation(skolem10) )).
% 0.51/0.73 cnf(matrix-67, plain, ( function(skolem10) )).
% 0.51/0.73 cnf(matrix-68, plain, ( one_to_one(skolem10) )).
% 0.51/0.73 cnf(matrix-69, plain, ( relation(skolem11) )).
% 0.51/0.73 cnf(matrix-70, plain, ( relation_empty_yielding(skolem11) )).
% 0.51/0.73 cnf(matrix-71, plain, ( subset(_u42, _u42) )).
% 0.51/0.73 cnf(matrix-72, plain, ( ~in(_u44, _u43) | element(_u44, _u43) )).
% 0.51/0.73 cnf(matrix-73, plain, ( ~element(_u46, _u45) | empty(_u45) | in(_u46, _u45) )).
% 0.51/0.73 cnf(matrix-74, plain, ( ~element(_u51, powerset(_u49)) | subset(_u51, _u49) )).
% 0.51/0.73 cnf(matrix-75, plain, ( ~subset(_u52, _u50) | element(_u52, powerset(_u50)) )).
% 0.51/0.73 cnf(matrix-76, plain, ( ~in(_u55, _u54) | ~element(_u54, powerset(_u53)) | element(_u55, _u53) )).
% 0.51/0.73 cnf(matrix-77, plain, ( ~relation(_u56) | ~function(_u56) | ~one_to_one(_u56) | ( relation_rng(_u56) = relation_dom(function_inverse(_u56))) )).
% 0.51/0.73 cnf(matrix-78, plain, ( ~relation(_u56) | ~function(_u56) | ~one_to_one(_u56) | ( relation_dom(_u56) = relation_rng(function_inverse(_u56))) )).
% 0.51/0.73 cnf(matrix-79, plain, ( ~in(_u59, _u58) | ~element(_u58, powerset(_u57)) | ~empty(_u57) )).
% 0.51/0.73 cnf(matrix-80, plain, ( ~relation(_u60) | ~function(_u60) | ~one_to_one(_u60) | ( relation_composition(_u60, function_inverse(_u60)) = identity_relation(relation_dom(_u60))) )).
% 0.51/0.73 cnf(matrix-81, plain, ( ~relation(_u60) | ~function(_u60) | ~one_to_one(_u60) | ( relation_composition(function_inverse(_u60), _u60) = identity_relation(relation_rng(_u60))) )).
% 0.51/0.73 cnf(matrix-82, plain, ( relation(skolem12) )).
% 0.51/0.73 cnf(matrix-83, plain, ( function(skolem12) )).
% 0.51/0.73 cnf(matrix-84, plain, ( relation(skolem13) )).
% 0.51/0.73 cnf(matrix-85, plain, ( function(skolem13) )).
% 0.51/0.73 cnf(matrix-86, plain, ( one_to_one(skolem12) )).
% 0.51/0.73 cnf(matrix-87, plain, ( ( relation_rng(skolem12) = relation_dom(skolem13)) )).
% 0.51/0.73 cnf(matrix-88, plain, ( ( relation_composition(skolem12, skolem13) = identity_relation(relation_dom(skolem12))) )).
% 0.51/0.73 cnf(matrix-89, plain, ( ( skolem13 != function_inverse(skolem12)) )).
% 0.51/0.73 cnf(matrix-90, plain, ( ~empty(_u63) | ( _u63 = empty_set) )).
% 0.51/0.73 cnf(matrix-91, plain, ( ~in(_u65, _u64) | ~empty(_u64) )).
% 0.51/0.73 cnf(matrix-92, plain, ( ~empty(_u67) | ( _u67 = _u66) | ~empty(_u66) )).
% 0.51/0.73
% 0.51/0.73 % Proof stack:
% 0.51/0.73 cnf(proof-stack, plain,
% 0.51/0.73 proof_stack(
% 0.51/0.73 start(89),
% 0.51/0.73 left_branch(0, 50, 9, 2),
% 0.51/0.73 left_branch(0, 24, 2, 3),
% 0.51/0.73 left_branch(0, 82, 0, 4),
% 0.51/0.73 right_branch(4),
% 0.51/0.73 left_branch(0, 83, 0, 5),
% 0.51/0.73 right_branch(5),
% 0.51/0.73 right_branch(3),
% 0.51/0.73 left_branch(0, 88, 0, 4),
% 0.51/0.73 right_branch(4),
% 0.51/0.73 left_branch(0, 2, 2, 5),
% 0.51/0.73 left_branch(0, 81, 3, 6),
% 0.51/0.73 left_branch(0, 82, 0, 7),
% 0.51/0.73 right_branch(7),
% 0.51/0.73 left_branch(0, 86, 0, 8),
% 0.51/0.73 right_branch(8),
% 0.51/0.73 left_branch(0, 83, 0, 9),
% 0.51/0.73 right_branch(9),
% 0.51/0.73 right_branch(6),
% 0.51/0.73 left_branch(0, 5, 1, 7),
% 0.51/0.73 left_branch(0, 87, 0, 8),
% 0.51/0.73 right_branch(8),
% 0.51/0.73 right_branch(7),
% 0.51/0.73 right_branch(5),
% 0.51/0.73 left_branch(0, 1, 1, 6),
% 0.51/0.73 left_branch(0, 78, 3, 7),
% 0.51/0.73 left_branch(0, 82, 0, 8),
% 0.51/0.73 right_branch(8),
% 0.51/0.73 left_branch(0, 86, 0, 9),
% 0.51/0.73 right_branch(9),
% 0.51/0.73 left_branch(0, 83, 0, 10),
% 0.51/0.73 right_branch(10),
% 0.51/0.73 right_branch(7),
% 0.51/0.73 right_branch(6),
% 0.51/0.73 left_branch(0, 85, 0, 7),
% 0.51/0.73 right_branch(7),
% 0.51/0.73 left_branch(0, 84, 0, 8),
% 0.51/0.73 right_branch(8),
% 0.51/0.73 left_branch(0, 83, 0, 9),
% 0.51/0.73 right_branch(9),
% 0.51/0.73 left_branch(0, 82, 0, 10),
% 0.51/0.73 right_branch(10),
% 0.51/0.73 left_branch(0, 25, 2, 11),
% 0.51/0.73 lemmata(0, 7),
% 0.51/0.73 lemmata(0, 6),
% 0.51/0.73 right_branch(11),
% 0.51/0.73 right_branch(2)
% 0.51/0.73 )).
% 0.51/0.73 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------