TSTP Solution File: SEU230+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU230+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 : n017.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 14:33:38 EDT 2024
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU230+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 : n017.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 13:44:12 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48 % SZS output start Proof for theBenchmark
% 0.19/0.48
% 0.19/0.48 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 0.19/0.48 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.19/0.48
% 0.19/0.48 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(cc1_funct_1-1, axiom, ( ~empty(_u2) | function(_u2) )).
% 0.19/0.48
% 0.19/0.48 % Formula: cc1_relat_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(cc1_relat_1-1, axiom, ( ~empty(_u3) | relation(_u3) )).
% 0.19/0.48
% 0.19/0.48 % Formula: cc2_funct_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(cc2_funct_1-1, axiom, ( ~relation(_u4) | ~empty(_u4) | ~function(_u4) | one_to_one(_u4) )).
% 0.19/0.48
% 0.19/0.48 % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u6, _u5) = set_union2(_u5, _u6)) )).
% 0.19/0.48
% 0.19/0.48 % Formula: d1_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(d1_ordinal1-1, axiom, ( ( succ(_u7) = set_union2(_u7, singleton(_u7))) )).
% 0.19/0.48
% 0.19/0.48 % Formula: d1_tarski ( axiom ) converted to clauses:
% 0.19/0.48 cnf(d1_tarski-1, axiom, ( ( _u16 != singleton(_u18)) | ~in(_u12, _u16) | ( _u12 = _u18) )).
% 0.19/0.48 cnf(d1_tarski-2, axiom, ( ( _u16 != singleton(_u18)) | ( _u13 != _u18) | in(_u13, _u16) )).
% 0.19/0.48 cnf(d1_tarski-3, axiom, ( ( _u17 = singleton(_u19)) | in(skolem1(_u19, _u17), _u17) | ( skolem2(_u19, _u17) = _u19) )).
% 0.19/0.48 cnf(d1_tarski-4, axiom, ( ( _u17 = singleton(_u19)) | in(skolem1(_u19, _u17), _u17) | ~in(skolem2(_u19, _u17), _u17) )).
% 0.19/0.48 cnf(d1_tarski-5, axiom, ( ( _u17 = singleton(_u19)) | ( skolem1(_u19, _u17) != _u19) | ( skolem2(_u19, _u17) = _u19) )).
% 0.19/0.48 cnf(d1_tarski-6, axiom, ( ( _u17 = singleton(_u19)) | ( skolem1(_u19, _u17) != _u19) | ~in(skolem2(_u19, _u17), _u17) )).
% 0.19/0.48
% 0.19/0.48 % Formula: d2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(d2_xboole_0-1, axiom, ( ( _u29 != set_union2(_u33, _u31)) | ~in(_u25, _u29) | in(_u25, _u33) | in(_u25, _u31) )).
% 0.19/0.48 cnf(d2_xboole_0-2, axiom, ( ( _u29 != set_union2(_u33, _u31)) | in(_u26, _u29) | ~in(_u26, _u33) )).
% 0.19/0.48 cnf(d2_xboole_0-3, axiom, ( ( _u29 != set_union2(_u33, _u31)) | in(_u26, _u29) | ~in(_u26, _u31) )).
% 0.19/0.48 cnf(d2_xboole_0-4, axiom, ( ( _u30 = set_union2(_u34, _u32)) | in(skolem3(_u34, _u32, _u30), _u30) | in(skolem4(_u34, _u32, _u30), _u34) | in(skolem4(_u34, _u32, _u30), _u32) )).
% 0.19/0.48 cnf(d2_xboole_0-5, axiom, ( ( _u30 = set_union2(_u34, _u32)) | in(skolem3(_u34, _u32, _u30), _u30) | ~in(skolem4(_u34, _u32, _u30), _u30) )).
% 0.19/0.48 cnf(d2_xboole_0-6, axiom, ( ( _u30 = set_union2(_u34, _u32)) | in(skolem4(_u34, _u32, _u30), _u34) | in(skolem4(_u34, _u32, _u30), _u32) | ~in(skolem3(_u34, _u32, _u30), _u34) )).
% 0.19/0.48 cnf(d2_xboole_0-7, axiom, ( ( _u30 = set_union2(_u34, _u32)) | in(skolem4(_u34, _u32, _u30), _u34) | in(skolem4(_u34, _u32, _u30), _u32) | ~in(skolem3(_u34, _u32, _u30), _u32) )).
% 0.19/0.48 cnf(d2_xboole_0-8, axiom, ( ( _u30 = set_union2(_u34, _u32)) | ~in(skolem4(_u34, _u32, _u30), _u30) | ~in(skolem3(_u34, _u32, _u30), _u34) )).
% 0.19/0.48 cnf(d2_xboole_0-9, axiom, ( ( _u30 = set_union2(_u34, _u32)) | ~in(skolem4(_u34, _u32, _u30), _u30) | ~in(skolem3(_u34, _u32, _u30), _u32) )).
% 0.19/0.48
% 0.19/0.48 % Formula: dt_k1_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(dt_k1_ordinal1, axiom, $true).
% 0.19/0.48
% 0.19/0.48 % Formula: dt_k1_tarski ( axiom ) converted to clauses:
% 0.19/0.48 cnf(dt_k1_tarski, axiom, $true).
% 0.19/0.48
% 0.19/0.48 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(dt_k1_xboole_0, axiom, $true).
% 0.19/0.48
% 0.19/0.48 % Formula: dt_k2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(dt_k2_xboole_0, axiom, $true).
% 0.19/0.48
% 0.19/0.48 % Formula: dt_m1_subset_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(dt_m1_subset_1, axiom, $true).
% 0.19/0.48
% 0.19/0.48 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(existence_m1_subset_1-1, axiom, ( element(skolem5(_u36), _u36) )).
% 0.19/0.48
% 0.19/0.48 % Formula: fc12_relat_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(fc12_relat_1-1, axiom, ( empty(empty_set) )).
% 0.19/0.48 cnf(fc12_relat_1-2, axiom, ( relation(empty_set) )).
% 0.19/0.48 cnf(fc12_relat_1-3, axiom, ( relation_empty_yielding(empty_set) )).
% 0.19/0.48
% 0.19/0.48 % Formula: fc1_ordinal1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(fc1_ordinal1-1, axiom, ( ~empty(succ(_u37)) )).
% 0.19/0.48
% 0.19/0.48 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 0.19/0.48
% 0.19/0.48 % Formula: fc2_relat_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(fc2_relat_1-1, axiom, ( ~relation(_u39) | ~relation(_u38) | relation(set_union2(_u39, _u38)) )).
% 0.19/0.48
% 0.19/0.48 % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(fc2_xboole_0-1, axiom, ( empty(_u41) | ~empty(set_union2(_u41, _u40)) )).
% 0.19/0.48
% 0.19/0.48 % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(fc3_xboole_0-1, axiom, ( empty(_u43) | ~empty(set_union2(_u42, _u43)) )).
% 0.19/0.48
% 0.19/0.48 % Formula: fc4_relat_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(fc4_relat_1-1, axiom, ( empty(empty_set) )).
% 0.19/0.48 cnf(fc4_relat_1-2, axiom, ( relation(empty_set) )).
% 0.19/0.48
% 0.19/0.48 % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u45, _u45) = _u45) )).
% 0.19/0.48
% 0.19/0.48 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(rc1_funct_1-1, axiom, ( relation(skolem6) )).
% 0.19/0.48 cnf(rc1_funct_1-2, axiom, ( function(skolem6) )).
% 0.19/0.48
% 0.19/0.48 % Formula: rc1_relat_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(rc1_relat_1-1, axiom, ( empty(skolem7) )).
% 0.19/0.48 cnf(rc1_relat_1-2, axiom, ( relation(skolem7) )).
% 0.19/0.48
% 0.19/0.48 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(rc1_xboole_0-1, axiom, ( empty(skolem8) )).
% 0.19/0.48
% 0.19/0.48 % Formula: rc2_funct_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(rc2_funct_1-1, axiom, ( relation(skolem9) )).
% 0.19/0.48 cnf(rc2_funct_1-2, axiom, ( empty(skolem9) )).
% 0.19/0.48 cnf(rc2_funct_1-3, axiom, ( function(skolem9) )).
% 0.19/0.48
% 0.19/0.48 % Formula: rc2_relat_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(rc2_relat_1-1, axiom, ( ~empty(skolem10) )).
% 0.19/0.48 cnf(rc2_relat_1-2, axiom, ( relation(skolem10) )).
% 0.19/0.48
% 0.19/0.48 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem11) )).
% 0.19/0.48
% 0.19/0.48 % Formula: rc3_funct_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(rc3_funct_1-1, axiom, ( relation(skolem12) )).
% 0.19/0.48 cnf(rc3_funct_1-2, axiom, ( function(skolem12) )).
% 0.19/0.48 cnf(rc3_funct_1-3, axiom, ( one_to_one(skolem12) )).
% 0.19/0.48
% 0.19/0.48 % Formula: rc3_relat_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(rc3_relat_1-1, axiom, ( relation(skolem13) )).
% 0.19/0.48 cnf(rc3_relat_1-2, axiom, ( relation_empty_yielding(skolem13) )).
% 0.19/0.48
% 0.19/0.48 % Formula: rc4_funct_1 ( axiom ) converted to clauses:
% 0.19/0.48 cnf(rc4_funct_1-1, axiom, ( relation(skolem14) )).
% 0.19/0.48 cnf(rc4_funct_1-2, axiom, ( relation_empty_yielding(skolem14) )).
% 0.19/0.48 cnf(rc4_funct_1-3, axiom, ( function(skolem14) )).
% 0.19/0.48
% 0.19/0.48 % Formula: t10_ordinal1 ( conjecture ) (definitionally) converted to clauses:
% 0.19/0.48 cnf(t10_ordinal1-1, negated_conjecture, ( ~in(skolem15, succ(skolem15)) )).
% 0.19/0.48
% 0.19/0.48 % Formula: t1_boole ( axiom ) converted to clauses:
% 0.19/0.48 cnf(t1_boole-1, axiom, ( ( set_union2(_u56, empty_set) = _u56) )).
% 0.19/0.48
% 0.19/0.48 % Formula: t1_subset ( axiom ) converted to clauses:
% 0.19/0.48 cnf(t1_subset-1, axiom, ( ~in(_u58, _u57) | element(_u58, _u57) )).
% 0.19/0.48
% 0.19/0.48 % Formula: t2_subset ( axiom ) converted to clauses:
% 0.19/0.48 cnf(t2_subset-1, axiom, ( ~element(_u60, _u59) | empty(_u59) | in(_u60, _u59) )).
% 0.19/0.48
% 0.19/0.48 % Formula: t6_boole ( axiom ) converted to clauses:
% 0.19/0.48 cnf(t6_boole-1, axiom, ( ~empty(_u61) | ( _u61 = empty_set) )).
% 0.19/0.48
% 0.19/0.48 % Formula: t7_boole ( axiom ) converted to clauses:
% 0.19/0.48 cnf(t7_boole-1, axiom, ( ~in(_u63, _u62) | ~empty(_u62) )).
% 0.19/0.48
% 0.19/0.48 % Formula: t8_boole ( axiom ) converted to clauses:
% 0.19/0.48 cnf(t8_boole-1, axiom, ( ~empty(_u65) | ( _u65 = _u64) | ~empty(_u64) )).
% 0.19/0.48
% 0.19/0.48 % Problem matrix:
% 0.19/0.48 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.19/0.48 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.19/0.48 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.19/0.48 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 0.19/0.48 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( succ(__eqx_0) = succ(__eqy_0)) )).
% 0.19/0.48 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 0.19/0.48 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 0.19/0.48 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 0.19/0.48 cnf(matrix-8, 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)) )).
% 0.19/0.48 cnf(matrix-9, 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)) )).
% 0.19/0.48 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( skolem5(__eqx_0) = skolem5(__eqy_0)) )).
% 0.19/0.48 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 0.19/0.48 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 0.19/0.48 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 0.19/0.48 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 0.19/0.48 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 0.19/0.48 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 0.19/0.48 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~relation_empty_yielding(__eqx_0) | relation_empty_yielding(__eqy_0) )).
% 0.19/0.48 cnf(matrix-18, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.19/0.48 cnf(matrix-19, plain, ( ~empty(_u2) | function(_u2) )).
% 0.19/0.48 cnf(matrix-20, plain, ( ~empty(_u3) | relation(_u3) )).
% 0.19/0.48 cnf(matrix-21, plain, ( ~relation(_u4) | ~empty(_u4) | ~function(_u4) | one_to_one(_u4) )).
% 0.19/0.48 cnf(matrix-22, plain, ( ( set_union2(_u6, _u5) = set_union2(_u5, _u6)) )).
% 0.19/0.48 cnf(matrix-23, plain, ( ( succ(_u7) = set_union2(_u7, singleton(_u7))) )).
% 0.19/0.48 cnf(matrix-24, plain, ( ( _u16 != singleton(_u18)) | ~in(_u12, _u16) | ( _u12 = _u18) )).
% 0.19/0.48 cnf(matrix-25, plain, ( ( _u16 != singleton(_u18)) | ( _u13 != _u18) | in(_u13, _u16) )).
% 0.19/0.48 cnf(matrix-26, plain, ( ( _u17 = singleton(_u19)) | in(skolem1(_u19, _u17), _u17) | ( skolem2(_u19, _u17) = _u19) )).
% 0.19/0.48 cnf(matrix-27, plain, ( ( _u17 = singleton(_u19)) | in(skolem1(_u19, _u17), _u17) | ~in(skolem2(_u19, _u17), _u17) )).
% 0.19/0.48 cnf(matrix-28, plain, ( ( _u17 = singleton(_u19)) | ( skolem1(_u19, _u17) != _u19) | ( skolem2(_u19, _u17) = _u19) )).
% 0.19/0.48 cnf(matrix-29, plain, ( ( _u17 = singleton(_u19)) | ( skolem1(_u19, _u17) != _u19) | ~in(skolem2(_u19, _u17), _u17) )).
% 0.19/0.48 cnf(matrix-30, plain, ( ( _u29 != set_union2(_u33, _u31)) | ~in(_u25, _u29) | in(_u25, _u33) | in(_u25, _u31) )).
% 0.19/0.48 cnf(matrix-31, plain, ( ( _u29 != set_union2(_u33, _u31)) | in(_u26, _u29) | ~in(_u26, _u33) )).
% 0.19/0.48 cnf(matrix-32, plain, ( ( _u29 != set_union2(_u33, _u31)) | in(_u26, _u29) | ~in(_u26, _u31) )).
% 0.19/0.48 cnf(matrix-33, plain, ( ( _u30 = set_union2(_u34, _u32)) | in(skolem3(_u34, _u32, _u30), _u30) | in(skolem4(_u34, _u32, _u30), _u34) | in(skolem4(_u34, _u32, _u30), _u32) )).
% 0.19/0.48 cnf(matrix-34, plain, ( ( _u30 = set_union2(_u34, _u32)) | in(skolem3(_u34, _u32, _u30), _u30) | ~in(skolem4(_u34, _u32, _u30), _u30) )).
% 0.19/0.48 cnf(matrix-35, plain, ( ( _u30 = set_union2(_u34, _u32)) | in(skolem4(_u34, _u32, _u30), _u34) | in(skolem4(_u34, _u32, _u30), _u32) | ~in(skolem3(_u34, _u32, _u30), _u34) )).
% 0.19/0.48 cnf(matrix-36, plain, ( ( _u30 = set_union2(_u34, _u32)) | in(skolem4(_u34, _u32, _u30), _u34) | in(skolem4(_u34, _u32, _u30), _u32) | ~in(skolem3(_u34, _u32, _u30), _u32) )).
% 0.19/0.48 cnf(matrix-37, plain, ( ( _u30 = set_union2(_u34, _u32)) | ~in(skolem4(_u34, _u32, _u30), _u30) | ~in(skolem3(_u34, _u32, _u30), _u34) )).
% 0.19/0.48 cnf(matrix-38, plain, ( ( _u30 = set_union2(_u34, _u32)) | ~in(skolem4(_u34, _u32, _u30), _u30) | ~in(skolem3(_u34, _u32, _u30), _u32) )).
% 0.19/0.48 cnf(matrix-39, plain, ( element(skolem5(_u36), _u36) )).
% 0.19/0.48 cnf(matrix-40, plain, ( empty(empty_set) )).
% 0.19/0.48 cnf(matrix-41, plain, ( relation(empty_set) )).
% 0.19/0.48 cnf(matrix-42, plain, ( relation_empty_yielding(empty_set) )).
% 0.19/0.48 cnf(matrix-43, plain, ( ~empty(succ(_u37)) )).
% 0.19/0.48 cnf(matrix-44, plain, ( empty(empty_set) )).
% 0.19/0.48 cnf(matrix-45, plain, ( ~relation(_u39) | ~relation(_u38) | relation(set_union2(_u39, _u38)) )).
% 0.19/0.48 cnf(matrix-46, plain, ( empty(_u41) | ~empty(set_union2(_u41, _u40)) )).
% 0.19/0.48 cnf(matrix-47, plain, ( empty(_u43) | ~empty(set_union2(_u42, _u43)) )).
% 0.19/0.48 cnf(matrix-48, plain, ( empty(empty_set) )).
% 0.19/0.48 cnf(matrix-49, plain, ( relation(empty_set) )).
% 0.19/0.48 cnf(matrix-50, plain, ( ( set_union2(_u45, _u45) = _u45) )).
% 0.19/0.48 cnf(matrix-51, plain, ( relation(skolem6) )).
% 0.19/0.48 cnf(matrix-52, plain, ( function(skolem6) )).
% 0.19/0.48 cnf(matrix-53, plain, ( empty(skolem7) )).
% 0.19/0.48 cnf(matrix-54, plain, ( relation(skolem7) )).
% 0.19/0.48 cnf(matrix-55, plain, ( empty(skolem8) )).
% 0.19/0.48 cnf(matrix-56, plain, ( relation(skolem9) )).
% 0.19/0.48 cnf(matrix-57, plain, ( empty(skolem9) )).
% 0.19/0.48 cnf(matrix-58, plain, ( function(skolem9) )).
% 0.19/0.48 cnf(matrix-59, plain, ( ~empty(skolem10) )).
% 0.19/0.48 cnf(matrix-60, plain, ( relation(skolem10) )).
% 0.19/0.48 cnf(matrix-61, plain, ( ~empty(skolem11) )).
% 0.19/0.48 cnf(matrix-62, plain, ( relation(skolem12) )).
% 0.19/0.48 cnf(matrix-63, plain, ( function(skolem12) )).
% 0.19/0.48 cnf(matrix-64, plain, ( one_to_one(skolem12) )).
% 0.19/0.48 cnf(matrix-65, plain, ( relation(skolem13) )).
% 0.19/0.48 cnf(matrix-66, plain, ( relation_empty_yielding(skolem13) )).
% 0.19/0.48 cnf(matrix-67, plain, ( relation(skolem14) )).
% 0.19/0.48 cnf(matrix-68, plain, ( relation_empty_yielding(skolem14) )).
% 0.19/0.48 cnf(matrix-69, plain, ( function(skolem14) )).
% 0.19/0.48 cnf(matrix-70, plain, ( ~in(skolem15, succ(skolem15)) )).
% 0.19/0.48 cnf(matrix-71, plain, ( ( set_union2(_u56, empty_set) = _u56) )).
% 0.19/0.48 cnf(matrix-72, plain, ( ~in(_u58, _u57) | element(_u58, _u57) )).
% 0.19/0.48 cnf(matrix-73, plain, ( ~element(_u60, _u59) | empty(_u59) | in(_u60, _u59) )).
% 0.19/0.48 cnf(matrix-74, plain, ( ~empty(_u61) | ( _u61 = empty_set) )).
% 0.19/0.48 cnf(matrix-75, plain, ( ~in(_u63, _u62) | ~empty(_u62) )).
% 0.19/0.48 cnf(matrix-76, plain, ( ~empty(_u65) | ( _u65 = _u64) | ~empty(_u64) )).
% 0.19/0.48
% 0.19/0.48 % Proof stack:
% 0.19/0.48 cnf(proof-stack, plain,
% 0.19/0.48 proof_stack(
% 0.19/0.48 start(70),
% 0.19/0.48 left_branch(0, 32, 1, 2),
% 0.19/0.48 left_branch(0, 23, 0, 3),
% 0.19/0.48 right_branch(3),
% 0.19/0.48 left_branch(0, 25, 2, 4),
% 0.19/0.48 left_branch(0, 0, 0, 5),
% 0.19/0.48 right_branch(5),
% 0.19/0.48 left_branch(0, 0, 0, 6),
% 0.19/0.48 right_branch(6),
% 0.19/0.48 right_branch(4),
% 0.19/0.48 right_branch(2)
% 0.19/0.48 )).
% 0.19/0.48 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------