TSTP Solution File: SEU244+1 by ConnectPP---0.3.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SEU244+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 14:33:43 EDT 2024
% Result : Theorem 0.12s 0.35s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU244+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % 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 15:42:09 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % SZS status Theorem for theBenchmark
% 0.12/0.35 % SZS output start Proof for theBenchmark
% 0.12/0.35
% 0.12/0.35 % Formula: commutativity_k2_xboole_0 ( axiom ) converted to clauses:
% 0.12/0.35 cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u1, _u0) = set_union2(_u0, _u1)) )).
% 0.12/0.35
% 0.12/0.35 % Formula: d12_relat_2 ( axiom ) converted to clauses:
% 0.12/0.35 cnf(d12_relat_2-1, axiom, ( ~relation(_u2) | ~antisymmetric(_u2) | is_antisymmetric_in(_u2, relation_field(_u2)) )).
% 0.12/0.35 cnf(d12_relat_2-2, axiom, ( ~relation(_u2) | ~is_antisymmetric_in(_u2, relation_field(_u2)) | antisymmetric(_u2) )).
% 0.12/0.35
% 0.12/0.35 % Formula: d14_relat_2 ( axiom ) converted to clauses:
% 0.12/0.35 cnf(d14_relat_2-1, axiom, ( ~relation(_u3) | ~connected(_u3) | is_connected_in(_u3, relation_field(_u3)) )).
% 0.12/0.35 cnf(d14_relat_2-2, axiom, ( ~relation(_u3) | ~is_connected_in(_u3, relation_field(_u3)) | connected(_u3) )).
% 0.12/0.35
% 0.12/0.35 % Formula: d16_relat_2 ( axiom ) converted to clauses:
% 0.12/0.35 cnf(d16_relat_2-1, axiom, ( ~relation(_u4) | ~transitive(_u4) | is_transitive_in(_u4, relation_field(_u4)) )).
% 0.12/0.35 cnf(d16_relat_2-2, axiom, ( ~relation(_u4) | ~is_transitive_in(_u4, relation_field(_u4)) | transitive(_u4) )).
% 0.12/0.35
% 0.12/0.35 % Formula: d4_wellord1 ( axiom ) converted to clauses:
% 0.12/0.35 cnf(d4_wellord1-1, axiom, ( ~relation(_u5) | ~well_ordering(_u5) | reflexive(_u5) )).
% 0.12/0.35 cnf(d4_wellord1-2, axiom, ( ~relation(_u5) | ~well_ordering(_u5) | transitive(_u5) )).
% 0.12/0.35 cnf(d4_wellord1-3, axiom, ( ~relation(_u5) | ~well_ordering(_u5) | antisymmetric(_u5) )).
% 0.12/0.35 cnf(d4_wellord1-4, axiom, ( ~relation(_u5) | ~well_ordering(_u5) | connected(_u5) )).
% 0.12/0.35 cnf(d4_wellord1-5, axiom, ( ~relation(_u5) | ~well_ordering(_u5) | well_founded_relation(_u5) )).
% 0.12/0.35 cnf(d4_wellord1-6, axiom, ( ~relation(_u5) | ~reflexive(_u5) | ~transitive(_u5) | ~antisymmetric(_u5) | ~connected(_u5) | ~well_founded_relation(_u5) | well_ordering(_u5) )).
% 0.12/0.35
% 0.12/0.35 % Formula: d5_wellord1 ( axiom ) converted to clauses:
% 0.12/0.35 cnf(d5_wellord1-1, axiom, ( ~relation(_u7) | ~well_orders(_u7, _u8) | is_reflexive_in(_u7, _u8) )).
% 0.12/0.35 cnf(d5_wellord1-2, axiom, ( ~relation(_u7) | ~well_orders(_u7, _u8) | is_transitive_in(_u7, _u8) )).
% 0.12/0.35 cnf(d5_wellord1-3, axiom, ( ~relation(_u7) | ~well_orders(_u7, _u8) | is_antisymmetric_in(_u7, _u8) )).
% 0.12/0.35 cnf(d5_wellord1-4, axiom, ( ~relation(_u7) | ~well_orders(_u7, _u8) | is_connected_in(_u7, _u8) )).
% 0.12/0.35 cnf(d5_wellord1-5, axiom, ( ~relation(_u7) | ~well_orders(_u7, _u8) | is_well_founded_in(_u7, _u8) )).
% 0.12/0.35 cnf(d5_wellord1-6, axiom, ( ~relation(_u7) | ~is_reflexive_in(_u7, _u9) | ~is_transitive_in(_u7, _u9) | ~is_antisymmetric_in(_u7, _u9) | ~is_connected_in(_u7, _u9) | ~is_well_founded_in(_u7, _u9) | well_orders(_u7, _u9) )).
% 0.12/0.35
% 0.12/0.35 % Formula: d6_relat_1 ( axiom ) converted to clauses:
% 0.12/0.35 cnf(d6_relat_1-1, axiom, ( ~relation(_u10) | ( relation_field(_u10) = set_union2(relation_dom(_u10), relation_rng(_u10))) )).
% 0.12/0.35
% 0.12/0.35 % Formula: d9_relat_2 ( axiom ) converted to clauses:
% 0.12/0.35 cnf(d9_relat_2-1, axiom, ( ~relation(_u11) | ~reflexive(_u11) | is_reflexive_in(_u11, relation_field(_u11)) )).
% 0.12/0.35 cnf(d9_relat_2-2, axiom, ( ~relation(_u11) | ~is_reflexive_in(_u11, relation_field(_u11)) | reflexive(_u11) )).
% 0.12/0.35
% 0.12/0.35 % Formula: dt_k1_relat_1 ( axiom ) converted to clauses:
% 0.12/0.35 cnf(dt_k1_relat_1, axiom, $true).
% 0.12/0.35
% 0.12/0.35 % Formula: dt_k2_relat_1 ( axiom ) converted to clauses:
% 0.12/0.35 cnf(dt_k2_relat_1, axiom, $true).
% 0.12/0.35
% 0.12/0.35 % Formula: dt_k2_xboole_0 ( axiom ) converted to clauses:
% 0.12/0.35 cnf(dt_k2_xboole_0, axiom, $true).
% 0.12/0.35
% 0.12/0.35 % Formula: dt_k3_relat_1 ( axiom ) converted to clauses:
% 0.12/0.35 cnf(dt_k3_relat_1, axiom, $true).
% 0.12/0.35
% 0.12/0.35 % Formula: idempotence_k2_xboole_0 ( axiom ) converted to clauses:
% 0.12/0.35 cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u13, _u13) = _u13) )).
% 0.12/0.35
% 0.12/0.35 % Formula: t5_wellord1 ( axiom ) converted to clauses:
% 0.12/0.35 cnf(t5_wellord1-1, axiom, ( ~relation(_u14) | ~well_founded_relation(_u14) | is_well_founded_in(_u14, relation_field(_u14)) )).
% 0.12/0.35 cnf(t5_wellord1-2, axiom, ( ~relation(_u14) | ~is_well_founded_in(_u14, relation_field(_u14)) | well_founded_relation(_u14) )).
% 0.12/0.35
% 0.12/0.35 % Formula: t8_wellord1 ( conjecture ) (definitionally) converted to clauses:
% 0.12/0.35 cnf(t8_wellord1-1, negated_conjecture, ( relation(skolem1) )).
% 0.12/0.35 cnf(t8_wellord1-2, negated_conjecture, ( ~_def0 | ~_def1 )).
% 0.12/0.35 cnf(t8_wellord1-3, negated_conjecture, ( _def0 | well_orders(skolem1, relation_field(skolem1)) )).
% 0.12/0.35 cnf(t8_wellord1-4, negated_conjecture, ( _def0 | ~well_ordering(skolem1) )).
% 0.12/0.35 cnf(t8_wellord1-5, negated_conjecture, ( _def1 | well_ordering(skolem1) )).
% 0.12/0.35 cnf(t8_wellord1-6, negated_conjecture, ( _def1 | ~well_orders(skolem1, relation_field(skolem1)) )).
% 0.12/0.35
% 0.12/0.35 % Problem matrix:
% 0.12/0.35 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.12/0.35 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.12/0.35 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.12/0.35 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
% 0.12/0.35 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( relation_field(__eqx_0) = relation_field(__eqy_0)) )).
% 0.12/0.35 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( relation_dom(__eqx_0) = relation_dom(__eqy_0)) )).
% 0.12/0.35 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( relation_rng(__eqx_0) = relation_rng(__eqy_0)) )).
% 0.12/0.35 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 0.12/0.35 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ~antisymmetric(__eqx_0) | antisymmetric(__eqy_0) )).
% 0.12/0.35 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~is_antisymmetric_in(__eqx_0, __eqx_1) | is_antisymmetric_in(__eqy_0, __eqy_1) )).
% 0.12/0.35 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ~connected(__eqx_0) | connected(__eqy_0) )).
% 0.12/0.35 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~is_connected_in(__eqx_0, __eqx_1) | is_connected_in(__eqy_0, __eqy_1) )).
% 0.12/0.35 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ~transitive(__eqx_0) | transitive(__eqy_0) )).
% 0.12/0.35 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~is_transitive_in(__eqx_0, __eqx_1) | is_transitive_in(__eqy_0, __eqy_1) )).
% 0.12/0.35 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~well_ordering(__eqx_0) | well_ordering(__eqy_0) )).
% 0.12/0.35 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~reflexive(__eqx_0) | reflexive(__eqy_0) )).
% 0.12/0.35 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~well_founded_relation(__eqx_0) | well_founded_relation(__eqy_0) )).
% 0.12/0.35 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~well_orders(__eqx_0, __eqx_1) | well_orders(__eqy_0, __eqy_1) )).
% 0.12/0.35 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~is_reflexive_in(__eqx_0, __eqx_1) | is_reflexive_in(__eqy_0, __eqy_1) )).
% 0.12/0.35 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~is_well_founded_in(__eqx_0, __eqx_1) | is_well_founded_in(__eqy_0, __eqy_1) )).
% 0.12/0.35 cnf(matrix-20, plain, ( ( set_union2(_u1, _u0) = set_union2(_u0, _u1)) )).
% 0.12/0.35 cnf(matrix-21, plain, ( ~relation(_u2) | ~antisymmetric(_u2) | is_antisymmetric_in(_u2, relation_field(_u2)) )).
% 0.12/0.35 cnf(matrix-22, plain, ( ~relation(_u2) | ~is_antisymmetric_in(_u2, relation_field(_u2)) | antisymmetric(_u2) )).
% 0.12/0.35 cnf(matrix-23, plain, ( ~relation(_u3) | ~connected(_u3) | is_connected_in(_u3, relation_field(_u3)) )).
% 0.12/0.35 cnf(matrix-24, plain, ( ~relation(_u3) | ~is_connected_in(_u3, relation_field(_u3)) | connected(_u3) )).
% 0.12/0.35 cnf(matrix-25, plain, ( ~relation(_u4) | ~transitive(_u4) | is_transitive_in(_u4, relation_field(_u4)) )).
% 0.12/0.35 cnf(matrix-26, plain, ( ~relation(_u4) | ~is_transitive_in(_u4, relation_field(_u4)) | transitive(_u4) )).
% 0.12/0.35 cnf(matrix-27, plain, ( ~relation(_u5) | ~well_ordering(_u5) | reflexive(_u5) )).
% 0.12/0.35 cnf(matrix-28, plain, ( ~relation(_u5) | ~well_ordering(_u5) | transitive(_u5) )).
% 0.12/0.35 cnf(matrix-29, plain, ( ~relation(_u5) | ~well_ordering(_u5) | antisymmetric(_u5) )).
% 0.12/0.35 cnf(matrix-30, plain, ( ~relation(_u5) | ~well_ordering(_u5) | connected(_u5) )).
% 0.12/0.35 cnf(matrix-31, plain, ( ~relation(_u5) | ~well_ordering(_u5) | well_founded_relation(_u5) )).
% 0.12/0.35 cnf(matrix-32, plain, ( ~relation(_u5) | ~reflexive(_u5) | ~transitive(_u5) | ~antisymmetric(_u5) | ~connected(_u5) | ~well_founded_relation(_u5) | well_ordering(_u5) )).
% 0.12/0.35 cnf(matrix-33, plain, ( ~relation(_u7) | ~well_orders(_u7, _u8) | is_reflexive_in(_u7, _u8) )).
% 0.12/0.35 cnf(matrix-34, plain, ( ~relation(_u7) | ~well_orders(_u7, _u8) | is_transitive_in(_u7, _u8) )).
% 0.12/0.35 cnf(matrix-35, plain, ( ~relation(_u7) | ~well_orders(_u7, _u8) | is_antisymmetric_in(_u7, _u8) )).
% 0.12/0.35 cnf(matrix-36, plain, ( ~relation(_u7) | ~well_orders(_u7, _u8) | is_connected_in(_u7, _u8) )).
% 0.12/0.35 cnf(matrix-37, plain, ( ~relation(_u7) | ~well_orders(_u7, _u8) | is_well_founded_in(_u7, _u8) )).
% 0.12/0.35 cnf(matrix-38, plain, ( ~relation(_u7) | ~is_reflexive_in(_u7, _u9) | ~is_transitive_in(_u7, _u9) | ~is_antisymmetric_in(_u7, _u9) | ~is_connected_in(_u7, _u9) | ~is_well_founded_in(_u7, _u9) | well_orders(_u7, _u9) )).
% 0.12/0.35 cnf(matrix-39, plain, ( ~relation(_u10) | ( relation_field(_u10) = set_union2(relation_dom(_u10), relation_rng(_u10))) )).
% 0.12/0.35 cnf(matrix-40, plain, ( ~relation(_u11) | ~reflexive(_u11) | is_reflexive_in(_u11, relation_field(_u11)) )).
% 0.12/0.35 cnf(matrix-41, plain, ( ~relation(_u11) | ~is_reflexive_in(_u11, relation_field(_u11)) | reflexive(_u11) )).
% 0.12/0.35 cnf(matrix-42, plain, ( ( set_union2(_u13, _u13) = _u13) )).
% 0.12/0.35 cnf(matrix-43, plain, ( ~relation(_u14) | ~well_founded_relation(_u14) | is_well_founded_in(_u14, relation_field(_u14)) )).
% 0.12/0.35 cnf(matrix-44, plain, ( ~relation(_u14) | ~is_well_founded_in(_u14, relation_field(_u14)) | well_founded_relation(_u14) )).
% 0.12/0.35 cnf(matrix-45, plain, ( relation(skolem1) )).
% 0.12/0.35 cnf(matrix-46, plain, ( ~_def0 | ~_def1 )).
% 0.12/0.35 cnf(matrix-47, plain, ( _def0 | well_orders(skolem1, relation_field(skolem1)) )).
% 0.12/0.35 cnf(matrix-48, plain, ( _def0 | ~well_ordering(skolem1) )).
% 0.12/0.35 cnf(matrix-49, plain, ( _def1 | well_ordering(skolem1) )).
% 0.12/0.35 cnf(matrix-50, plain, ( _def1 | ~well_orders(skolem1, relation_field(skolem1)) )).
% 0.12/0.35
% 0.12/0.35 % Proof stack:
% 0.12/0.35 cnf(proof-stack, plain,
% 0.12/0.35 proof_stack(
% 0.12/0.35 start(46),
% 0.12/0.35 left_branch(0, 48, 0, 2),
% 0.12/0.35 left_branch(0, 32, 6, 3),
% 0.12/0.35 left_branch(0, 45, 0, 4),
% 0.12/0.35 right_branch(4),
% 0.12/0.35 left_branch(0, 44, 2, 5),
% 0.12/0.35 lemmata(0, 0),
% 0.12/0.35 left_branch(0, 37, 2, 7),
% 0.12/0.35 lemmata(0, 0),
% 0.12/0.35 left_branch(0, 47, 1, 9),
% 0.12/0.35 reduction(0, 0),
% 0.12/0.35 right_branch(9),
% 0.12/0.35 right_branch(7),
% 0.12/0.35 right_branch(5),
% 0.12/0.35 left_branch(0, 24, 2, 6),
% 0.12/0.35 lemmata(0, 0),
% 0.12/0.35 left_branch(0, 36, 2, 8),
% 0.12/0.35 lemmata(0, 0),
% 0.12/0.35 left_branch(0, 47, 1, 10),
% 0.12/0.35 reduction(0, 0),
% 0.12/0.35 right_branch(10),
% 0.12/0.35 right_branch(8),
% 0.12/0.35 right_branch(6),
% 0.12/0.35 left_branch(0, 22, 2, 7),
% 0.12/0.35 lemmata(0, 0),
% 0.12/0.35 left_branch(0, 35, 2, 9),
% 0.12/0.35 lemmata(0, 0),
% 0.12/0.35 left_branch(0, 47, 1, 11),
% 0.12/0.35 reduction(0, 0),
% 0.12/0.35 right_branch(11),
% 0.12/0.35 right_branch(9),
% 0.12/0.35 right_branch(7),
% 0.12/0.35 left_branch(0, 26, 2, 8),
% 0.12/0.35 lemmata(0, 0),
% 0.12/0.35 left_branch(0, 34, 2, 10),
% 0.12/0.35 lemmata(0, 0),
% 0.12/0.35 left_branch(0, 47, 1, 12),
% 0.12/0.35 reduction(0, 0),
% 0.12/0.35 right_branch(12),
% 0.12/0.35 right_branch(10),
% 0.12/0.35 right_branch(8),
% 0.12/0.35 left_branch(0, 41, 2, 9),
% 0.12/0.35 lemmata(0, 0),
% 0.12/0.35 left_branch(0, 33, 2, 11),
% 0.12/0.35 lemmata(0, 0),
% 0.12/0.35 left_branch(0, 47, 1, 13),
% 0.12/0.35 reduction(0, 0),
% 0.12/0.35 right_branch(13),
% 0.12/0.35 right_branch(11),
% 0.12/0.35 right_branch(9),
% 0.12/0.35 right_branch(3),
% 0.12/0.35 right_branch(2),
% 0.12/0.35 left_branch(0, 50, 0, 3),
% 0.12/0.35 left_branch(0, 38, 6, 4),
% 0.12/0.35 left_branch(0, 45, 0, 5),
% 0.12/0.35 right_branch(5),
% 0.12/0.35 left_branch(0, 43, 2, 6),
% 0.12/0.35 lemmata(0, 1),
% 0.12/0.35 left_branch(0, 31, 2, 8),
% 0.12/0.35 lemmata(0, 1),
% 0.12/0.35 left_branch(0, 49, 1, 10),
% 0.12/0.35 reduction(0, 0),
% 0.12/0.35 right_branch(10),
% 0.12/0.35 right_branch(8),
% 0.12/0.35 right_branch(6),
% 0.12/0.35 left_branch(0, 23, 2, 7),
% 0.12/0.35 lemmata(0, 1),
% 0.12/0.35 left_branch(0, 30, 2, 9),
% 0.12/0.35 lemmata(0, 1),
% 0.12/0.35 left_branch(0, 49, 1, 11),
% 0.12/0.35 reduction(0, 0),
% 0.12/0.35 right_branch(11),
% 0.12/0.35 right_branch(9),
% 0.12/0.35 right_branch(7),
% 0.12/0.35 left_branch(0, 21, 2, 8),
% 0.12/0.35 lemmata(0, 1),
% 0.12/0.35 left_branch(0, 29, 2, 10),
% 0.12/0.35 lemmata(0, 1),
% 0.12/0.35 left_branch(0, 49, 1, 12),
% 0.12/0.35 reduction(0, 0),
% 0.12/0.35 right_branch(12),
% 0.12/0.35 right_branch(10),
% 0.12/0.35 right_branch(8),
% 0.12/0.35 left_branch(0, 25, 2, 9),
% 0.12/0.35 lemmata(0, 1),
% 0.12/0.35 left_branch(0, 28, 2, 11),
% 0.12/0.35 lemmata(0, 1),
% 0.12/0.35 left_branch(0, 49, 1, 13),
% 0.12/0.35 reduction(0, 0),
% 0.12/0.35 right_branch(13),
% 0.12/0.35 right_branch(11),
% 0.12/0.35 right_branch(9),
% 0.12/0.35 left_branch(0, 40, 2, 10),
% 0.12/0.35 lemmata(0, 1),
% 0.12/0.35 left_branch(0, 27, 2, 12),
% 0.12/0.35 lemmata(0, 1),
% 0.12/0.35 left_branch(0, 49, 1, 14),
% 0.12/0.35 reduction(0, 0),
% 0.12/0.35 right_branch(14),
% 0.12/0.35 right_branch(12),
% 0.12/0.35 right_branch(10),
% 0.12/0.35 right_branch(4),
% 0.12/0.35 right_branch(3)
% 0.12/0.35 )).
% 0.12/0.35 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------