TSTP Solution File: SEU045+1 by ConnectPP---0.2.2
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%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : SEU045+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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Mar 6 09:20:10 EST 2024
% Result : Theorem 0.90s 1.06s
% Output : Proof 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : SEU045+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Mar 3 10:24:25 EST 2024
% 0.12/0.33 % CPUTime :
% 0.90/1.06 % SZS status Theorem for theBenchmark
% 0.90/1.06 % SZS output start Proof for theBenchmark
% 0.90/1.06
% 0.90/1.06 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 0.90/1.06 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u1, _u1) )).
% 0.90/1.06
% 0.90/1.06 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 0.90/1.06 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 0.90/1.06
% 0.90/1.06 % Formula: fc12_relat_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(fc12_relat_1-1, axiom, ( empty(empty_set) )).
% 0.90/1.06 cnf(fc12_relat_1-2, axiom, ( relation(empty_set) )).
% 0.90/1.06 cnf(fc12_relat_1-3, axiom, ( relation_empty_yielding(empty_set) )).
% 0.90/1.06
% 0.90/1.06 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 0.90/1.06
% 0.90/1.06 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(existence_m1_subset_1-1, axiom, ( element(skolem1(_u3), _u3) )).
% 0.90/1.06
% 0.90/1.06 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(cc1_funct_1-1, axiom, ( ~empty(_u4) | function(_u4) )).
% 0.90/1.06
% 0.90/1.06 % Formula: cc2_funct_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(cc2_funct_1-1, axiom, ( ~relation(_u5) | ~empty(_u5) | ~function(_u5) | one_to_one(_u5) )).
% 0.90/1.06
% 0.90/1.06 % Formula: fc1_subset_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(fc1_subset_1-1, axiom, ( ~empty(powerset(_u6)) )).
% 0.90/1.06
% 0.90/1.06 % Formula: fc5_relat_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(fc5_relat_1-1, axiom, ( empty(_u7) | ~relation(_u7) | ~empty(relation_dom(_u7)) )).
% 0.90/1.06
% 0.90/1.06 % Formula: fc7_relat_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(fc7_relat_1-1, axiom, ( ~empty(_u8) | empty(relation_dom(_u8)) )).
% 0.90/1.06 cnf(fc7_relat_1-2, axiom, ( ~empty(_u8) | relation(relation_dom(_u8)) )).
% 0.90/1.06
% 0.90/1.06 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(cc1_relat_1-1, axiom, ( ~empty(_u9) | relation(_u9) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t2_subset ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t2_subset-1, axiom, ( ~element(_u11, _u10) | empty(_u10) | in(_u11, _u10) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t3_subset ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t3_subset-1, axiom, ( ~element(_u16, powerset(_u14)) | subset(_u16, _u14) )).
% 0.90/1.06 cnf(t3_subset-2, axiom, ( ~subset(_u17, _u15) | element(_u17, powerset(_u15)) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t4_subset ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t4_subset-1, axiom, ( ~in(_u20, _u19) | ~element(_u19, powerset(_u18)) | element(_u20, _u18) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t5_subset ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t5_subset-1, axiom, ( ~in(_u23, _u22) | ~element(_u22, powerset(_u21)) | ~empty(_u21) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t6_boole ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t6_boole-1, axiom, ( ~empty(_u24) | ( _u24 = empty_set) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t8_boole ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t8_boole-1, axiom, ( ~empty(_u26) | ( _u26 = _u25) | ~empty(_u25) )).
% 0.90/1.06
% 0.90/1.06 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 0.90/1.06 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u28, _u27) | ~in(_u27, _u28) )).
% 0.90/1.06
% 0.90/1.06 % Formula: dt_k8_relat_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(dt_k8_relat_1-1, axiom, ( ~relation(_u29) | relation(relation_rng_restriction(_u30, _u29)) )).
% 0.90/1.06
% 0.90/1.06 % Formula: fc5_funct_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(fc5_funct_1-1, axiom, ( ~relation(_u31) | ~function(_u31) | relation(relation_rng_restriction(_u32, _u31)) )).
% 0.90/1.06 cnf(fc5_funct_1-2, axiom, ( ~relation(_u31) | ~function(_u31) | function(relation_rng_restriction(_u32, _u31)) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc1_funct_1-1, axiom, ( relation(skolem2) )).
% 0.90/1.06 cnf(rc1_funct_1-2, axiom, ( function(skolem2) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc2_funct_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc2_funct_1-1, axiom, ( relation(skolem3) )).
% 0.90/1.06 cnf(rc2_funct_1-2, axiom, ( empty(skolem3) )).
% 0.90/1.06 cnf(rc2_funct_1-3, axiom, ( function(skolem3) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc3_funct_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc3_funct_1-1, axiom, ( relation(skolem4) )).
% 0.90/1.06 cnf(rc3_funct_1-2, axiom, ( function(skolem4) )).
% 0.90/1.06 cnf(rc3_funct_1-3, axiom, ( one_to_one(skolem4) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc1_subset_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc1_subset_1-1, axiom, ( empty(_u37) | element(skolem5(_u37), powerset(_u37)) )).
% 0.90/1.06 cnf(rc1_subset_1-2, axiom, ( empty(_u37) | ~empty(skolem5(_u37)) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc2_subset_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc2_subset_1-1, axiom, ( element(skolem6(_u39), powerset(_u39)) )).
% 0.90/1.06 cnf(rc2_subset_1-2, axiom, ( empty(skolem6(_u39)) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc1_relat_1-1, axiom, ( empty(skolem7) )).
% 0.90/1.06 cnf(rc1_relat_1-2, axiom, ( relation(skolem7) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem8) )).
% 0.90/1.06 cnf(rc2_relat_1-2, axiom, ( relation(skolem8) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc3_relat_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc3_relat_1-1, axiom, ( relation(skolem9) )).
% 0.90/1.06 cnf(rc3_relat_1-2, axiom, ( relation_empty_yielding(skolem9) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc1_xboole_0-1, axiom, ( empty(skolem10) )).
% 0.90/1.06
% 0.90/1.06 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem11) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t1_subset ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t1_subset-1, axiom, ( ~in(_u46, _u45) | element(_u46, _u45) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t7_boole ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t7_boole-1, axiom, ( ~in(_u48, _u47) | ~empty(_u47) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t87_funct_1 ( conjecture ) converted to clauses:
% 0.90/1.06 cnf(t87_funct_1-1, negated_conjecture, ( relation(skolem14) )).
% 0.90/1.06 cnf(t87_funct_1-2, negated_conjecture, ( function(skolem14) )).
% 0.90/1.06 cnf(t87_funct_1-3, negated_conjecture, ( in(skolem13, relation_dom(relation_rng_restriction(skolem12, skolem14))) )).
% 0.90/1.06 cnf(t87_funct_1-4, negated_conjecture, ( ( apply(relation_rng_restriction(skolem12, skolem14), skolem13) != apply(skolem14, skolem13)) )).
% 0.90/1.06
% 0.90/1.06 % Formula: t85_funct_1 ( axiom ) converted to clauses:
% 0.90/1.06 cnf(t85_funct_1-1, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 != relation_rng_restriction(_u58, _u56)) | ~in(_u59, relation_dom(_u57)) | in(_u59, relation_dom(_u56)) )).
% 0.90/1.06 cnf(t85_funct_1-2, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 != relation_rng_restriction(_u58, _u56)) | ~in(_u59, relation_dom(_u57)) | in(apply(_u56, _u59), _u58) )).
% 0.90/1.06 cnf(t85_funct_1-3, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 != relation_rng_restriction(_u58, _u56)) | ~in(_u60, relation_dom(_u56)) | ~in(apply(_u56, _u60), _u58) | in(_u60, relation_dom(_u57)) )).
% 0.90/1.06 cnf(t85_funct_1-4, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 != relation_rng_restriction(_u58, _u56)) | ~in(_u53, relation_dom(_u57)) | ( apply(_u57, _u53) = apply(_u56, _u53)) )).
% 0.90/1.06 cnf(t85_funct_1-5, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | in(skolem17(_u58, _u57, _u56), relation_dom(_u57)) | in(skolem15(_u58, _u57, _u56), relation_dom(_u57)) | in(skolem16(_u58, _u57, _u56), relation_dom(_u56)) )).
% 0.90/1.06 cnf(t85_funct_1-6, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | in(skolem17(_u58, _u57, _u56), relation_dom(_u57)) | in(skolem15(_u58, _u57, _u56), relation_dom(_u57)) | in(apply(_u56, skolem16(_u58, _u57, _u56)), _u58) )).
% 0.90/1.06 cnf(t85_funct_1-7, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | in(skolem17(_u58, _u57, _u56), relation_dom(_u57)) | in(skolem15(_u58, _u57, _u56), relation_dom(_u57)) | ~in(skolem16(_u58, _u57, _u56), relation_dom(_u57)) )).
% 0.90/1.06 cnf(t85_funct_1-8, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | in(skolem17(_u58, _u57, _u56), relation_dom(_u57)) | ~in(skolem15(_u58, _u57, _u56), relation_dom(_u56)) | ~in(apply(_u56, skolem15(_u58, _u57, _u56)), _u58) | in(skolem16(_u58, _u57, _u56), relation_dom(_u56)) )).
% 0.90/1.06 cnf(t85_funct_1-9, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | in(skolem17(_u58, _u57, _u56), relation_dom(_u57)) | ~in(skolem15(_u58, _u57, _u56), relation_dom(_u56)) | ~in(apply(_u56, skolem15(_u58, _u57, _u56)), _u58) | in(apply(_u56, skolem16(_u58, _u57, _u56)), _u58) )).
% 0.90/1.06 cnf(t85_funct_1-10, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | in(skolem17(_u58, _u57, _u56), relation_dom(_u57)) | ~in(skolem15(_u58, _u57, _u56), relation_dom(_u56)) | ~in(apply(_u56, skolem15(_u58, _u57, _u56)), _u58) | ~in(skolem16(_u58, _u57, _u56), relation_dom(_u57)) )).
% 0.90/1.06 cnf(t85_funct_1-11, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | ( apply(_u57, skolem17(_u58, _u57, _u56)) != apply(_u56, skolem17(_u58, _u57, _u56))) | in(skolem15(_u58, _u57, _u56), relation_dom(_u57)) | in(skolem16(_u58, _u57, _u56), relation_dom(_u56)) )).
% 0.90/1.06 cnf(t85_funct_1-12, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | ( apply(_u57, skolem17(_u58, _u57, _u56)) != apply(_u56, skolem17(_u58, _u57, _u56))) | in(skolem15(_u58, _u57, _u56), relation_dom(_u57)) | in(apply(_u56, skolem16(_u58, _u57, _u56)), _u58) )).
% 0.90/1.06 cnf(t85_funct_1-13, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | ( apply(_u57, skolem17(_u58, _u57, _u56)) != apply(_u56, skolem17(_u58, _u57, _u56))) | in(skolem15(_u58, _u57, _u56), relation_dom(_u57)) | ~in(skolem16(_u58, _u57, _u56), relation_dom(_u57)) )).
% 0.90/1.06 cnf(t85_funct_1-14, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | ( apply(_u57, skolem17(_u58, _u57, _u56)) != apply(_u56, skolem17(_u58, _u57, _u56))) | ~in(skolem15(_u58, _u57, _u56), relation_dom(_u56)) | ~in(apply(_u56, skolem15(_u58, _u57, _u56)), _u58) | in(skolem16(_u58, _u57, _u56), relation_dom(_u56)) )).
% 0.90/1.06 cnf(t85_funct_1-15, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | ( apply(_u57, skolem17(_u58, _u57, _u56)) != apply(_u56, skolem17(_u58, _u57, _u56))) | ~in(skolem15(_u58, _u57, _u56), relation_dom(_u56)) | ~in(apply(_u56, skolem15(_u58, _u57, _u56)), _u58) | in(apply(_u56, skolem16(_u58, _u57, _u56)), _u58) )).
% 0.90/1.06 cnf(t85_funct_1-16, axiom, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | ( apply(_u57, skolem17(_u58, _u57, _u56)) != apply(_u56, skolem17(_u58, _u57, _u56))) | ~in(skolem15(_u58, _u57, _u56), relation_dom(_u56)) | ~in(apply(_u56, skolem15(_u58, _u57, _u56)), _u58) | ~in(skolem16(_u58, _u57, _u56), relation_dom(_u57)) )).
% 0.90/1.06
% 0.90/1.06 % Problem matrix:
% 0.90/1.06 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.90/1.06 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.90/1.06 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.90/1.06 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 0.90/1.06 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( relation_dom(__eqx_0) = relation_dom(__eqy_0)) )).
% 0.90/1.06 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( relation_rng_restriction(__eqx_0, __eqx_1) = relation_rng_restriction(__eqy_0, __eqy_1)) )).
% 0.90/1.06 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( apply(__eqx_0, __eqx_1) = apply(__eqy_0, __eqy_1)) )).
% 0.90/1.06 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 0.90/1.06 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( skolem5(__eqx_0) = skolem5(__eqy_0)) )).
% 0.90/1.06 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( skolem6(__eqx_0) = skolem6(__eqy_0)) )).
% 0.90/1.06 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem15(__eqx_0, __eqx_1, __eqx_2) = skolem15(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.90/1.06 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem16(__eqx_0, __eqx_1, __eqx_2) = skolem16(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.90/1.06 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem17(__eqx_0, __eqx_1, __eqx_2) = skolem17(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.90/1.06 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 0.90/1.06 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 0.90/1.06 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 0.90/1.06 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~relation_empty_yielding(__eqx_0) | relation_empty_yielding(__eqy_0) )).
% 0.90/1.06 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 0.90/1.06 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 0.90/1.06 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 0.90/1.06 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 0.90/1.06 cnf(matrix-21, plain, ( subset(_u1, _u1) )).
% 0.90/1.06 cnf(matrix-22, plain, ( empty(empty_set) )).
% 0.90/1.06 cnf(matrix-23, plain, ( relation(empty_set) )).
% 0.90/1.06 cnf(matrix-24, plain, ( empty(empty_set) )).
% 0.90/1.06 cnf(matrix-25, plain, ( relation(empty_set) )).
% 0.90/1.06 cnf(matrix-26, plain, ( relation_empty_yielding(empty_set) )).
% 0.90/1.06 cnf(matrix-27, plain, ( empty(empty_set) )).
% 0.90/1.06 cnf(matrix-28, plain, ( element(skolem1(_u3), _u3) )).
% 0.90/1.06 cnf(matrix-29, plain, ( ~empty(_u4) | function(_u4) )).
% 0.90/1.06 cnf(matrix-30, plain, ( ~relation(_u5) | ~empty(_u5) | ~function(_u5) | one_to_one(_u5) )).
% 0.90/1.06 cnf(matrix-31, plain, ( ~empty(powerset(_u6)) )).
% 0.90/1.06 cnf(matrix-32, plain, ( empty(_u7) | ~relation(_u7) | ~empty(relation_dom(_u7)) )).
% 0.90/1.06 cnf(matrix-33, plain, ( ~empty(_u8) | empty(relation_dom(_u8)) )).
% 0.90/1.06 cnf(matrix-34, plain, ( ~empty(_u8) | relation(relation_dom(_u8)) )).
% 0.90/1.06 cnf(matrix-35, plain, ( ~empty(_u9) | relation(_u9) )).
% 0.90/1.06 cnf(matrix-36, plain, ( ~element(_u11, _u10) | empty(_u10) | in(_u11, _u10) )).
% 0.90/1.06 cnf(matrix-37, plain, ( ~element(_u16, powerset(_u14)) | subset(_u16, _u14) )).
% 0.90/1.06 cnf(matrix-38, plain, ( ~subset(_u17, _u15) | element(_u17, powerset(_u15)) )).
% 0.90/1.06 cnf(matrix-39, plain, ( ~in(_u20, _u19) | ~element(_u19, powerset(_u18)) | element(_u20, _u18) )).
% 0.90/1.06 cnf(matrix-40, plain, ( ~in(_u23, _u22) | ~element(_u22, powerset(_u21)) | ~empty(_u21) )).
% 0.90/1.06 cnf(matrix-41, plain, ( ~empty(_u24) | ( _u24 = empty_set) )).
% 0.90/1.06 cnf(matrix-42, plain, ( ~empty(_u26) | ( _u26 = _u25) | ~empty(_u25) )).
% 0.90/1.06 cnf(matrix-43, plain, ( ~in(_u28, _u27) | ~in(_u27, _u28) )).
% 0.90/1.06 cnf(matrix-44, plain, ( ~relation(_u29) | relation(relation_rng_restriction(_u30, _u29)) )).
% 0.90/1.06 cnf(matrix-45, plain, ( ~relation(_u31) | ~function(_u31) | relation(relation_rng_restriction(_u32, _u31)) )).
% 0.90/1.06 cnf(matrix-46, plain, ( ~relation(_u31) | ~function(_u31) | function(relation_rng_restriction(_u32, _u31)) )).
% 0.90/1.06 cnf(matrix-47, plain, ( relation(skolem2) )).
% 0.90/1.06 cnf(matrix-48, plain, ( function(skolem2) )).
% 0.90/1.06 cnf(matrix-49, plain, ( relation(skolem3) )).
% 0.90/1.06 cnf(matrix-50, plain, ( empty(skolem3) )).
% 0.90/1.06 cnf(matrix-51, plain, ( function(skolem3) )).
% 0.90/1.06 cnf(matrix-52, plain, ( relation(skolem4) )).
% 0.90/1.06 cnf(matrix-53, plain, ( function(skolem4) )).
% 0.90/1.06 cnf(matrix-54, plain, ( one_to_one(skolem4) )).
% 0.90/1.06 cnf(matrix-55, plain, ( empty(_u37) | element(skolem5(_u37), powerset(_u37)) )).
% 0.90/1.06 cnf(matrix-56, plain, ( empty(_u37) | ~empty(skolem5(_u37)) )).
% 0.90/1.06 cnf(matrix-57, plain, ( element(skolem6(_u39), powerset(_u39)) )).
% 0.90/1.06 cnf(matrix-58, plain, ( empty(skolem6(_u39)) )).
% 0.90/1.06 cnf(matrix-59, plain, ( empty(skolem7) )).
% 0.90/1.06 cnf(matrix-60, plain, ( relation(skolem7) )).
% 0.90/1.06 cnf(matrix-61, plain, ( ~empty(skolem8) )).
% 0.90/1.06 cnf(matrix-62, plain, ( relation(skolem8) )).
% 0.90/1.06 cnf(matrix-63, plain, ( relation(skolem9) )).
% 0.90/1.06 cnf(matrix-64, plain, ( relation_empty_yielding(skolem9) )).
% 0.90/1.06 cnf(matrix-65, plain, ( empty(skolem10) )).
% 0.90/1.06 cnf(matrix-66, plain, ( ~empty(skolem11) )).
% 0.90/1.06 cnf(matrix-67, plain, ( ~in(_u46, _u45) | element(_u46, _u45) )).
% 0.90/1.06 cnf(matrix-68, plain, ( ~in(_u48, _u47) | ~empty(_u47) )).
% 0.90/1.06 cnf(matrix-69, plain, ( relation(skolem14) )).
% 0.90/1.06 cnf(matrix-70, plain, ( function(skolem14) )).
% 0.90/1.06 cnf(matrix-71, plain, ( in(skolem13, relation_dom(relation_rng_restriction(skolem12, skolem14))) )).
% 0.90/1.06 cnf(matrix-72, plain, ( ( apply(relation_rng_restriction(skolem12, skolem14), skolem13) != apply(skolem14, skolem13)) )).
% 0.90/1.06 cnf(matrix-73, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 != relation_rng_restriction(_u58, _u56)) | ~in(_u59, relation_dom(_u57)) | in(_u59, relation_dom(_u56)) )).
% 0.90/1.06 cnf(matrix-74, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 != relation_rng_restriction(_u58, _u56)) | ~in(_u59, relation_dom(_u57)) | in(apply(_u56, _u59), _u58) )).
% 0.90/1.06 cnf(matrix-75, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 != relation_rng_restriction(_u58, _u56)) | ~in(_u60, relation_dom(_u56)) | ~in(apply(_u56, _u60), _u58) | in(_u60, relation_dom(_u57)) )).
% 0.90/1.06 cnf(matrix-76, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 != relation_rng_restriction(_u58, _u56)) | ~in(_u53, relation_dom(_u57)) | ( apply(_u57, _u53) = apply(_u56, _u53)) )).
% 0.90/1.06 cnf(matrix-77, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | in(skolem17(_u58, _u57, _u56), relation_dom(_u57)) | in(skolem15(_u58, _u57, _u56), relation_dom(_u57)) | in(skolem16(_u58, _u57, _u56), relation_dom(_u56)) )).
% 0.90/1.06 cnf(matrix-78, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | in(skolem17(_u58, _u57, _u56), relation_dom(_u57)) | in(skolem15(_u58, _u57, _u56), relation_dom(_u57)) | in(apply(_u56, skolem16(_u58, _u57, _u56)), _u58) )).
% 0.90/1.06 cnf(matrix-79, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | in(skolem17(_u58, _u57, _u56), relation_dom(_u57)) | in(skolem15(_u58, _u57, _u56), relation_dom(_u57)) | ~in(skolem16(_u58, _u57, _u56), relation_dom(_u57)) )).
% 0.90/1.06 cnf(matrix-80, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | in(skolem17(_u58, _u57, _u56), relation_dom(_u57)) | ~in(skolem15(_u58, _u57, _u56), relation_dom(_u56)) | ~in(apply(_u56, skolem15(_u58, _u57, _u56)), _u58) | in(skolem16(_u58, _u57, _u56), relation_dom(_u56)) )).
% 0.90/1.06 cnf(matrix-81, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | in(skolem17(_u58, _u57, _u56), relation_dom(_u57)) | ~in(skolem15(_u58, _u57, _u56), relation_dom(_u56)) | ~in(apply(_u56, skolem15(_u58, _u57, _u56)), _u58) | in(apply(_u56, skolem16(_u58, _u57, _u56)), _u58) )).
% 0.90/1.06 cnf(matrix-82, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | in(skolem17(_u58, _u57, _u56), relation_dom(_u57)) | ~in(skolem15(_u58, _u57, _u56), relation_dom(_u56)) | ~in(apply(_u56, skolem15(_u58, _u57, _u56)), _u58) | ~in(skolem16(_u58, _u57, _u56), relation_dom(_u57)) )).
% 0.90/1.06 cnf(matrix-83, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | ( apply(_u57, skolem17(_u58, _u57, _u56)) != apply(_u56, skolem17(_u58, _u57, _u56))) | in(skolem15(_u58, _u57, _u56), relation_dom(_u57)) | in(skolem16(_u58, _u57, _u56), relation_dom(_u56)) )).
% 0.90/1.06 cnf(matrix-84, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | ( apply(_u57, skolem17(_u58, _u57, _u56)) != apply(_u56, skolem17(_u58, _u57, _u56))) | in(skolem15(_u58, _u57, _u56), relation_dom(_u57)) | in(apply(_u56, skolem16(_u58, _u57, _u56)), _u58) )).
% 0.90/1.06 cnf(matrix-85, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | ( apply(_u57, skolem17(_u58, _u57, _u56)) != apply(_u56, skolem17(_u58, _u57, _u56))) | in(skolem15(_u58, _u57, _u56), relation_dom(_u57)) | ~in(skolem16(_u58, _u57, _u56), relation_dom(_u57)) )).
% 0.90/1.06 cnf(matrix-86, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | ( apply(_u57, skolem17(_u58, _u57, _u56)) != apply(_u56, skolem17(_u58, _u57, _u56))) | ~in(skolem15(_u58, _u57, _u56), relation_dom(_u56)) | ~in(apply(_u56, skolem15(_u58, _u57, _u56)), _u58) | in(skolem16(_u58, _u57, _u56), relation_dom(_u56)) )).
% 0.90/1.06 cnf(matrix-87, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | ( apply(_u57, skolem17(_u58, _u57, _u56)) != apply(_u56, skolem17(_u58, _u57, _u56))) | ~in(skolem15(_u58, _u57, _u56), relation_dom(_u56)) | ~in(apply(_u56, skolem15(_u58, _u57, _u56)), _u58) | in(apply(_u56, skolem16(_u58, _u57, _u56)), _u58) )).
% 0.90/1.06 cnf(matrix-88, plain, ( ~relation(_u57) | ~function(_u57) | ~relation(_u56) | ~function(_u56) | ( _u57 = relation_rng_restriction(_u58, _u56)) | ( apply(_u57, skolem17(_u58, _u57, _u56)) != apply(_u56, skolem17(_u58, _u57, _u56))) | ~in(skolem15(_u58, _u57, _u56), relation_dom(_u56)) | ~in(apply(_u56, skolem15(_u58, _u57, _u56)), _u58) | ~in(skolem16(_u58, _u57, _u56), relation_dom(_u57)) )).
% 0.90/1.06
% 0.90/1.06 % Proof stack:
% 0.90/1.06 cnf(proof-stack, plain,
% 0.90/1.06 proof_stack(
% 0.90/1.06 start(72),
% 0.90/1.06 left_branch(0, 76, 6, 2),
% 0.90/1.06 left_branch(0, 45, 2, 3),
% 0.90/1.06 left_branch(0, 69, 0, 4),
% 0.90/1.06 right_branch(4),
% 0.90/1.06 left_branch(0, 70, 0, 5),
% 0.90/1.06 right_branch(5),
% 0.90/1.06 right_branch(3),
% 0.90/1.06 left_branch(0, 71, 0, 4),
% 0.90/1.06 right_branch(4),
% 0.90/1.06 left_branch(0, 5, 2, 5),
% 0.90/1.06 left_branch(0, 0, 0, 6),
% 0.90/1.06 right_branch(6),
% 0.90/1.06 left_branch(0, 0, 0, 7),
% 0.90/1.06 right_branch(7),
% 0.90/1.06 right_branch(5),
% 0.90/1.06 left_branch(0, 70, 0, 6),
% 0.90/1.06 right_branch(6),
% 0.90/1.06 left_branch(0, 69, 0, 7),
% 0.90/1.06 right_branch(7),
% 0.90/1.06 left_branch(0, 46, 2, 8),
% 0.90/1.06 lemmata(0, 4),
% 0.90/1.06 lemmata(0, 3),
% 0.90/1.06 right_branch(8),
% 0.90/1.06 right_branch(2)
% 0.90/1.06 )).
% 0.90/1.06 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------