TSTP Solution File: SEU239+1 by ConnectPP---0.3.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU239+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 14:33:42 EDT 2024
% Result : Theorem 0.62s 0.76s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU239+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Mar 20 15:25:39 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.62/0.76 % SZS status Theorem for theBenchmark
% 0.62/0.76 % SZS output start Proof for theBenchmark
% 0.62/0.76
% 0.62/0.76 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 0.62/0.76 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.62/0.76
% 0.62/0.76 % Formula: cc1_funct_1 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(cc1_funct_1-1, axiom, ( ~empty(_u2) | function(_u2) )).
% 0.62/0.76
% 0.62/0.76 % Formula: cc2_funct_1 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(cc2_funct_1-1, axiom, ( ~relation(_u3) | ~empty(_u3) | ~function(_u3) | one_to_one(_u3) )).
% 0.62/0.76
% 0.62/0.76 % Formula: commutativity_k2_tarski ( axiom ) converted to clauses:
% 0.62/0.76 cnf(commutativity_k2_tarski-1, axiom, ( ( unordered_pair(_u5, _u4) = unordered_pair(_u4, _u5)) )).
% 0.62/0.76
% 0.62/0.76 % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u7, _u6) = set_union2(_u6, _u7)) )).
% 0.62/0.76
% 0.62/0.76 % Formula: d1_relat_2 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(d1_relat_2-1, axiom, ( ~relation(_u11) | ~is_reflexive_in(_u11, _u12) | ~in(_u8, _u12) | in(ordered_pair(_u8, _u8), _u11) )).
% 0.62/0.76 cnf(d1_relat_2-2, axiom, ( ~relation(_u11) | is_reflexive_in(_u11, _u13) | in(skolem1(_u11, _u13), _u13) )).
% 0.62/0.76 cnf(d1_relat_2-3, axiom, ( ~relation(_u11) | is_reflexive_in(_u11, _u13) | ~in(ordered_pair(skolem1(_u11, _u13), skolem1(_u11, _u13)), _u11) )).
% 0.62/0.76
% 0.62/0.76 % Formula: d5_tarski ( axiom ) converted to clauses:
% 0.62/0.76 cnf(d5_tarski-1, axiom, ( ( ordered_pair(_u15, _u14) = unordered_pair(unordered_pair(_u15, _u14), singleton(_u15))) )).
% 0.62/0.76
% 0.62/0.76 % Formula: d6_relat_1 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(d6_relat_1-1, axiom, ( ~relation(_u16) | ( relation_field(_u16) = set_union2(relation_dom(_u16), relation_rng(_u16))) )).
% 0.62/0.76
% 0.62/0.76 % Formula: d9_relat_2 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(d9_relat_2-1, axiom, ( ~relation(_u17) | ~reflexive(_u17) | is_reflexive_in(_u17, relation_field(_u17)) )).
% 0.62/0.76 cnf(d9_relat_2-2, axiom, ( ~relation(_u17) | ~is_reflexive_in(_u17, relation_field(_u17)) | reflexive(_u17) )).
% 0.62/0.76
% 0.62/0.76 % Formula: dt_k1_relat_1 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(dt_k1_relat_1, axiom, $true).
% 0.62/0.76
% 0.62/0.76 % Formula: dt_k1_tarski ( axiom ) converted to clauses:
% 0.62/0.76 cnf(dt_k1_tarski, axiom, $true).
% 0.62/0.76
% 0.62/0.76 % Formula: dt_k1_xboole_0 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(dt_k1_xboole_0, axiom, $true).
% 0.62/0.76
% 0.62/0.76 % Formula: dt_k2_relat_1 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(dt_k2_relat_1, axiom, $true).
% 0.62/0.76
% 0.62/0.76 % Formula: dt_k2_tarski ( axiom ) converted to clauses:
% 0.62/0.76 cnf(dt_k2_tarski, axiom, $true).
% 0.62/0.76
% 0.62/0.76 % Formula: dt_k2_xboole_0 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(dt_k2_xboole_0, axiom, $true).
% 0.62/0.76
% 0.62/0.76 % Formula: dt_k3_relat_1 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(dt_k3_relat_1, axiom, $true).
% 0.62/0.76
% 0.62/0.76 % Formula: dt_k4_tarski ( axiom ) converted to clauses:
% 0.62/0.76 cnf(dt_k4_tarski, axiom, $true).
% 0.62/0.76
% 0.62/0.76 % Formula: dt_m1_subset_1 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(dt_m1_subset_1, axiom, $true).
% 0.62/0.76
% 0.62/0.76 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(existence_m1_subset_1-1, axiom, ( element(skolem2(_u19), _u19) )).
% 0.62/0.76
% 0.62/0.76 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 0.62/0.76
% 0.62/0.76 % Formula: fc1_zfmisc_1 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(fc1_zfmisc_1-1, axiom, ( ~empty(ordered_pair(_u21, _u20)) )).
% 0.62/0.76
% 0.62/0.76 % Formula: fc2_xboole_0 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(fc2_xboole_0-1, axiom, ( empty(_u23) | ~empty(set_union2(_u23, _u22)) )).
% 0.62/0.76
% 0.62/0.76 % Formula: fc3_xboole_0 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(fc3_xboole_0-1, axiom, ( empty(_u25) | ~empty(set_union2(_u24, _u25)) )).
% 0.62/0.76
% 0.62/0.76 % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u27, _u27) = _u27) )).
% 0.62/0.76
% 0.62/0.76 % Formula: l1_wellord1 ( conjecture ) (definitionally) converted to clauses:
% 0.62/0.76 cnf(l1_wellord1-1, negated_conjecture, ( relation(skolem3) )).
% 0.62/0.76 cnf(l1_wellord1-2, negated_conjecture, ( ~_def0 | ~_def1(_u29) )).
% 0.62/0.76 cnf(l1_wellord1-3, negated_conjecture, ( _def0 | reflexive(skolem3) )).
% 0.62/0.76 cnf(l1_wellord1-4, negated_conjecture, ( _def0 | in(skolem4, relation_field(skolem3)) )).
% 0.62/0.76 cnf(l1_wellord1-5, negated_conjecture, ( _def0 | ~in(ordered_pair(skolem4, skolem4), skolem3) )).
% 0.62/0.76 cnf(l1_wellord1-6, negated_conjecture, ( _def1(_u29) | ~in(_u29, relation_field(skolem3)) | in(ordered_pair(_u29, _u29), skolem3) )).
% 0.62/0.76 cnf(l1_wellord1-7, negated_conjecture, ( _def1(_u29) | ~reflexive(skolem3) )).
% 0.62/0.76
% 0.62/0.76 % Formula: rc1_funct_1 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(rc1_funct_1-1, axiom, ( relation(skolem5) )).
% 0.62/0.76 cnf(rc1_funct_1-2, axiom, ( function(skolem5) )).
% 0.62/0.76
% 0.62/0.76 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(rc1_xboole_0-1, axiom, ( empty(skolem6) )).
% 0.62/0.76
% 0.62/0.76 % Formula: rc2_funct_1 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(rc2_funct_1-1, axiom, ( relation(skolem7) )).
% 0.62/0.76 cnf(rc2_funct_1-2, axiom, ( empty(skolem7) )).
% 0.62/0.76 cnf(rc2_funct_1-3, axiom, ( function(skolem7) )).
% 0.62/0.76
% 0.62/0.76 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem8) )).
% 0.62/0.76
% 0.62/0.76 % Formula: rc3_funct_1 ( axiom ) converted to clauses:
% 0.62/0.76 cnf(rc3_funct_1-1, axiom, ( relation(skolem9) )).
% 0.62/0.76 cnf(rc3_funct_1-2, axiom, ( function(skolem9) )).
% 0.62/0.76 cnf(rc3_funct_1-3, axiom, ( one_to_one(skolem9) )).
% 0.62/0.76
% 0.62/0.76 % Formula: t1_boole ( axiom ) converted to clauses:
% 0.62/0.76 cnf(t1_boole-1, axiom, ( ( set_union2(_u36, empty_set) = _u36) )).
% 0.62/0.76
% 0.62/0.76 % Formula: t1_subset ( axiom ) converted to clauses:
% 0.62/0.76 cnf(t1_subset-1, axiom, ( ~in(_u38, _u37) | element(_u38, _u37) )).
% 0.62/0.76
% 0.62/0.76 % Formula: t2_subset ( axiom ) converted to clauses:
% 0.62/0.76 cnf(t2_subset-1, axiom, ( ~element(_u40, _u39) | empty(_u39) | in(_u40, _u39) )).
% 0.62/0.76
% 0.62/0.76 % Formula: t6_boole ( axiom ) converted to clauses:
% 0.62/0.76 cnf(t6_boole-1, axiom, ( ~empty(_u41) | ( _u41 = empty_set) )).
% 0.62/0.76
% 0.62/0.76 % Formula: t7_boole ( axiom ) converted to clauses:
% 0.62/0.76 cnf(t7_boole-1, axiom, ( ~in(_u43, _u42) | ~empty(_u42) )).
% 0.62/0.76
% 0.62/0.76 % Formula: t8_boole ( axiom ) converted to clauses:
% 0.62/0.76 cnf(t8_boole-1, axiom, ( ~empty(_u45) | ( _u45 = _u44) | ~empty(_u44) )).
% 0.62/0.76
% 0.62/0.76 % Problem matrix:
% 0.62/0.76 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.62/0.76 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.62/0.76 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.62/0.76 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 0.62/0.76 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 0.62/0.76 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 0.62/0.76 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 0.62/0.76 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( relation_field(__eqx_0) = relation_field(__eqy_0)) )).
% 0.62/0.76 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( relation_dom(__eqx_0) = relation_dom(__eqy_0)) )).
% 0.62/0.76 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( relation_rng(__eqx_0) = relation_rng(__eqy_0)) )).
% 0.62/0.76 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 0.62/0.76 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( skolem2(__eqx_0) = skolem2(__eqy_0)) )).
% 0.62/0.76 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 0.62/0.76 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 0.62/0.76 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 0.62/0.76 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 0.62/0.76 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 0.62/0.76 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~is_reflexive_in(__eqx_0, __eqx_1) | is_reflexive_in(__eqy_0, __eqy_1) )).
% 0.62/0.76 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~reflexive(__eqx_0) | reflexive(__eqy_0) )).
% 0.62/0.76 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 0.62/0.76 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ~_def1(__eqx_0) | _def1(__eqy_0) )).
% 0.62/0.76 cnf(matrix-21, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 0.62/0.76 cnf(matrix-22, plain, ( ~empty(_u2) | function(_u2) )).
% 0.62/0.76 cnf(matrix-23, plain, ( ~relation(_u3) | ~empty(_u3) | ~function(_u3) | one_to_one(_u3) )).
% 0.62/0.76 cnf(matrix-24, plain, ( ( unordered_pair(_u5, _u4) = unordered_pair(_u4, _u5)) )).
% 0.62/0.76 cnf(matrix-25, plain, ( ( set_union2(_u7, _u6) = set_union2(_u6, _u7)) )).
% 0.62/0.76 cnf(matrix-26, plain, ( ~relation(_u11) | ~is_reflexive_in(_u11, _u12) | ~in(_u8, _u12) | in(ordered_pair(_u8, _u8), _u11) )).
% 0.62/0.76 cnf(matrix-27, plain, ( ~relation(_u11) | is_reflexive_in(_u11, _u13) | in(skolem1(_u11, _u13), _u13) )).
% 0.62/0.76 cnf(matrix-28, plain, ( ~relation(_u11) | is_reflexive_in(_u11, _u13) | ~in(ordered_pair(skolem1(_u11, _u13), skolem1(_u11, _u13)), _u11) )).
% 0.62/0.76 cnf(matrix-29, plain, ( ( ordered_pair(_u15, _u14) = unordered_pair(unordered_pair(_u15, _u14), singleton(_u15))) )).
% 0.62/0.76 cnf(matrix-30, plain, ( ~relation(_u16) | ( relation_field(_u16) = set_union2(relation_dom(_u16), relation_rng(_u16))) )).
% 0.62/0.76 cnf(matrix-31, plain, ( ~relation(_u17) | ~reflexive(_u17) | is_reflexive_in(_u17, relation_field(_u17)) )).
% 0.62/0.76 cnf(matrix-32, plain, ( ~relation(_u17) | ~is_reflexive_in(_u17, relation_field(_u17)) | reflexive(_u17) )).
% 0.62/0.76 cnf(matrix-33, plain, ( element(skolem2(_u19), _u19) )).
% 0.62/0.76 cnf(matrix-34, plain, ( empty(empty_set) )).
% 0.62/0.76 cnf(matrix-35, plain, ( ~empty(ordered_pair(_u21, _u20)) )).
% 0.62/0.76 cnf(matrix-36, plain, ( empty(_u23) | ~empty(set_union2(_u23, _u22)) )).
% 0.62/0.76 cnf(matrix-37, plain, ( empty(_u25) | ~empty(set_union2(_u24, _u25)) )).
% 0.62/0.76 cnf(matrix-38, plain, ( ( set_union2(_u27, _u27) = _u27) )).
% 0.62/0.76 cnf(matrix-39, plain, ( relation(skolem3) )).
% 0.62/0.76 cnf(matrix-40, plain, ( ~_def0 | ~_def1(_u29) )).
% 0.62/0.76 cnf(matrix-41, plain, ( _def0 | reflexive(skolem3) )).
% 0.62/0.76 cnf(matrix-42, plain, ( _def0 | in(skolem4, relation_field(skolem3)) )).
% 0.62/0.76 cnf(matrix-43, plain, ( _def0 | ~in(ordered_pair(skolem4, skolem4), skolem3) )).
% 0.62/0.76 cnf(matrix-44, plain, ( _def1(_u29) | ~in(_u29, relation_field(skolem3)) | in(ordered_pair(_u29, _u29), skolem3) )).
% 0.62/0.76 cnf(matrix-45, plain, ( _def1(_u29) | ~reflexive(skolem3) )).
% 0.62/0.76 cnf(matrix-46, plain, ( relation(skolem5) )).
% 0.62/0.76 cnf(matrix-47, plain, ( function(skolem5) )).
% 0.62/0.76 cnf(matrix-48, plain, ( empty(skolem6) )).
% 0.62/0.76 cnf(matrix-49, plain, ( relation(skolem7) )).
% 0.62/0.76 cnf(matrix-50, plain, ( empty(skolem7) )).
% 0.62/0.76 cnf(matrix-51, plain, ( function(skolem7) )).
% 0.62/0.76 cnf(matrix-52, plain, ( ~empty(skolem8) )).
% 0.62/0.76 cnf(matrix-53, plain, ( relation(skolem9) )).
% 0.62/0.76 cnf(matrix-54, plain, ( function(skolem9) )).
% 0.62/0.76 cnf(matrix-55, plain, ( one_to_one(skolem9) )).
% 0.62/0.76 cnf(matrix-56, plain, ( ( set_union2(_u36, empty_set) = _u36) )).
% 0.62/0.76 cnf(matrix-57, plain, ( ~in(_u38, _u37) | element(_u38, _u37) )).
% 0.62/0.76 cnf(matrix-58, plain, ( ~element(_u40, _u39) | empty(_u39) | in(_u40, _u39) )).
% 0.62/0.76 cnf(matrix-59, plain, ( ~empty(_u41) | ( _u41 = empty_set) )).
% 0.62/0.76 cnf(matrix-60, plain, ( ~in(_u43, _u42) | ~empty(_u42) )).
% 0.62/0.76 cnf(matrix-61, plain, ( ~empty(_u45) | ( _u45 = _u44) | ~empty(_u44) )).
% 0.62/0.76
% 0.62/0.76 % Proof stack:
% 0.62/0.76 cnf(proof-stack, plain,
% 0.62/0.76 proof_stack(
% 0.62/0.76 start(40),
% 0.62/0.76 left_branch(0, 43, 0, 2),
% 0.62/0.76 left_branch(0, 26, 3, 3),
% 0.62/0.76 left_branch(0, 39, 0, 4),
% 0.62/0.76 right_branch(4),
% 0.62/0.76 left_branch(0, 42, 1, 5),
% 0.62/0.76 reduction(0, 0),
% 0.62/0.76 right_branch(5),
% 0.62/0.76 left_branch(0, 31, 2, 6),
% 0.62/0.76 lemmata(0, 0),
% 0.62/0.76 left_branch(0, 41, 1, 8),
% 0.62/0.76 reduction(0, 0),
% 0.62/0.76 right_branch(8),
% 0.62/0.76 right_branch(6),
% 0.62/0.76 right_branch(3),
% 0.62/0.76 right_branch(2),
% 0.62/0.76 left_branch(0, 44, 0, 3),
% 0.62/0.76 left_branch(0, 28, 2, 4),
% 0.62/0.76 left_branch(0, 39, 0, 5),
% 0.62/0.76 right_branch(5),
% 0.62/0.76 left_branch(0, 32, 1, 6),
% 0.62/0.76 lemmata(0, 1),
% 0.62/0.76 left_branch(0, 45, 1, 8),
% 0.62/0.76 reduction(0, 0),
% 0.62/0.76 right_branch(8),
% 0.62/0.76 right_branch(6),
% 0.62/0.76 right_branch(4),
% 0.62/0.76 left_branch(0, 27, 2, 5),
% 0.62/0.76 left_branch(0, 39, 0, 6),
% 0.62/0.76 right_branch(6),
% 0.62/0.76 left_branch(0, 32, 1, 7),
% 0.62/0.76 lemmata(0, 2),
% 0.62/0.76 left_branch(0, 45, 1, 9),
% 0.62/0.76 reduction(0, 0),
% 0.62/0.76 right_branch(9),
% 0.62/0.76 right_branch(7),
% 0.62/0.76 right_branch(5),
% 0.62/0.76 right_branch(3)
% 0.62/0.76 )).
% 0.62/0.76 % SZS output end Proof for theBenchmark
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