TSTP Solution File: SEU244+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU244+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 : 600s
% DateTime : Tue Jul 19 13:30:18 EDT 2022
% Result : Theorem 0.48s 1.03s
% Output : Refutation 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU244+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 20 10:14:35 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.48/1.03 ============================== Prover9 ===============================
% 0.48/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.48/1.03 Process 5093 was started by sandbox on n018.cluster.edu,
% 0.48/1.03 Mon Jun 20 10:14:36 2022
% 0.48/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4938_n018.cluster.edu".
% 0.48/1.03 ============================== end of head ===========================
% 0.48/1.03
% 0.48/1.03 ============================== INPUT =================================
% 0.48/1.03
% 0.48/1.03 % Reading from file /tmp/Prover9_4938_n018.cluster.edu
% 0.48/1.03
% 0.48/1.03 set(prolog_style_variables).
% 0.48/1.03 set(auto2).
% 0.48/1.03 % set(auto2) -> set(auto).
% 0.48/1.03 % set(auto) -> set(auto_inference).
% 0.48/1.03 % set(auto) -> set(auto_setup).
% 0.48/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.48/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.48/1.03 % set(auto) -> set(auto_limits).
% 0.48/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.48/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.48/1.03 % set(auto) -> set(auto_denials).
% 0.48/1.03 % set(auto) -> set(auto_process).
% 0.48/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.48/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.48/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.48/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.48/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.48/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.48/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.48/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.48/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.48/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.48/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.48/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.48/1.03 % set(auto2) -> assign(stats, some).
% 0.48/1.03 % set(auto2) -> clear(echo_input).
% 0.48/1.03 % set(auto2) -> set(quiet).
% 0.48/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.48/1.03 % set(auto2) -> clear(print_given).
% 0.48/1.03 assign(lrs_ticks,-1).
% 0.48/1.03 assign(sos_limit,10000).
% 0.48/1.03 assign(order,kbo).
% 0.48/1.03 set(lex_order_vars).
% 0.48/1.03 clear(print_given).
% 0.48/1.03
% 0.48/1.03 % formulas(sos). % not echoed (15 formulas)
% 0.48/1.03
% 0.48/1.03 ============================== end of input ==========================
% 0.48/1.03
% 0.48/1.03 % From the command line: assign(max_seconds, 300).
% 0.48/1.03
% 0.48/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.48/1.03
% 0.48/1.03 % Formulas that are not ordinary clauses:
% 0.48/1.03 1 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 2 (all A (relation(A) -> (antisymmetric(A) <-> is_antisymmetric_in(A,relation_field(A))))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 3 (all A (relation(A) -> (connected(A) <-> is_connected_in(A,relation_field(A))))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 4 (all A (relation(A) -> (transitive(A) <-> is_transitive_in(A,relation_field(A))))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 5 (all A (relation(A) -> (well_ordering(A) <-> reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 6 (all A (relation(A) -> (all B (well_orders(A,B) <-> is_reflexive_in(A,B) & is_transitive_in(A,B) & is_antisymmetric_in(A,B) & is_connected_in(A,B) & is_well_founded_in(A,B))))) # label(d5_wellord1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 7 (all A (relation(A) -> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)))) # label(d6_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 8 (all A (relation(A) -> (reflexive(A) <-> is_reflexive_in(A,relation_field(A))))) # label(d9_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 9 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 10 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 11 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 12 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 13 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 14 (all A (relation(A) -> (well_founded_relation(A) <-> is_well_founded_in(A,relation_field(A))))) # label(t5_wellord1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 15 -(all A (relation(A) -> (well_orders(A,relation_field(A)) <-> well_ordering(A)))) # label(t8_wellord1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.48/1.03
% 0.48/1.03 ============================== end of process non-clausal formulas ===
% 0.48/1.03
% 0.48/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.48/1.03
% 0.48/1.03 ============================== PREDICATE ELIMINATION =================
% 0.48/1.03 16 -relation(A) | -well_ordering(A) | reflexive(A) # label(d4_wellord1) # label(axiom). [clausify(5)].
% 0.48/1.03 17 relation(c1) # label(t8_wellord1) # label(negated_conjecture). [clausify(15)].
% 0.48/1.03 Derived: -well_ordering(c1) | reflexive(c1). [resolve(16,a,17,a)].
% 0.48/1.03 18 -relation(A) | -well_ordering(A) | transitive(A) # label(d4_wellord1) # label(axiom). [clausify(5)].
% 0.48/1.03 Derived: -well_ordering(c1) | transitive(c1). [resolve(18,a,17,a)].
% 0.48/1.03 19 -relation(A) | -well_ordering(A) | antisymmetric(A) # label(d4_wellord1) # label(axiom). [clausify(5)].
% 0.48/1.03 Derived: -well_ordering(c1) | antisymmetric(c1). [resolve(19,a,17,a)].
% 0.48/1.03 20 -relation(A) | -well_ordering(A) | connected(A) # label(d4_wellord1) # label(axiom). [clausify(5)].
% 0.48/1.03 Derived: -well_ordering(c1) | connected(c1). [resolve(20,a,17,a)].
% 0.48/1.03 21 -relation(A) | -well_ordering(A) | well_founded_relation(A) # label(d4_wellord1) # label(axiom). [clausify(5)].
% 0.48/1.03 Derived: -well_ordering(c1) | well_founded_relation(c1). [resolve(21,a,17,a)].
% 0.48/1.03 22 -relation(A) | -antisymmetric(A) | is_antisymmetric_in(A,relation_field(A)) # label(d12_relat_2) # label(axiom). [clausify(2)].
% 0.48/1.03 Derived: -antisymmetric(c1) | is_antisymmetric_in(c1,relation_field(c1)). [resolve(22,a,17,a)].
% 0.48/1.03 23 -relation(A) | antisymmetric(A) | -is_antisymmetric_in(A,relation_field(A)) # label(d12_relat_2) # label(axiom). [clausify(2)].
% 0.48/1.03 Derived: antisymmetric(c1) | -is_antisymmetric_in(c1,relation_field(c1)). [resolve(23,a,17,a)].
% 0.48/1.03 24 -relation(A) | -connected(A) | is_connected_in(A,relation_field(A)) # label(d14_relat_2) # label(axiom). [clausify(3)].
% 0.48/1.03 Derived: -connected(c1) | is_connected_in(c1,relation_field(c1)). [resolve(24,a,17,a)].
% 0.48/1.03 25 -relation(A) | connected(A) | -is_connected_in(A,relation_field(A)) # label(d14_relat_2) # label(axiom). [clausify(3)].
% 0.48/1.03 Derived: connected(c1) | -is_connected_in(c1,relation_field(c1)). [resolve(25,a,17,a)].
% 0.48/1.03 26 -relation(A) | -transitive(A) | is_transitive_in(A,relation_field(A)) # label(d16_relat_2) # label(axiom). [clausify(4)].
% 0.48/1.03 Derived: -transitive(c1) | is_transitive_in(c1,relation_field(c1)). [resolve(26,a,17,a)].
% 0.48/1.03 27 -relation(A) | transitive(A) | -is_transitive_in(A,relation_field(A)) # label(d16_relat_2) # label(axiom). [clausify(4)].
% 0.48/1.03 Derived: transitive(c1) | -is_transitive_in(c1,relation_field(c1)). [resolve(27,a,17,a)].
% 0.48/1.03 28 -relation(A) | -well_orders(A,B) | is_reflexive_in(A,B) # label(d5_wellord1) # label(axiom). [clausify(6)].
% 0.48/1.03 Derived: -well_orders(c1,A) | is_reflexive_in(c1,A). [resolve(28,a,17,a)].
% 0.48/1.03 29 -relation(A) | -well_orders(A,B) | is_transitive_in(A,B) # label(d5_wellord1) # label(axiom). [clausify(6)].
% 0.48/1.03 Derived: -well_orders(c1,A) | is_transitive_in(c1,A). [resolve(29,a,17,a)].
% 0.48/1.03 30 -relation(A) | -well_orders(A,B) | is_antisymmetric_in(A,B) # label(d5_wellord1) # label(axiom). [clausify(6)].
% 0.48/1.03 Derived: -well_orders(c1,A) | is_antisymmetric_in(c1,A). [resolve(30,a,17,a)].
% 0.48/1.03 31 -relation(A) | -well_orders(A,B) | is_connected_in(A,B) # label(d5_wellord1) # label(axiom). [clausify(6)].
% 0.48/1.03 Derived: -well_orders(c1,A) | is_connected_in(c1,A). [resolve(31,a,17,a)].
% 0.48/1.03 32 -relation(A) | -well_orders(A,B) | is_well_founded_in(A,B) # label(d5_wellord1) # label(axiom). [clausify(6)].
% 0.48/1.03 Derived: -well_orders(c1,A) | is_well_founded_in(c1,A). [resolve(32,a,17,a)].
% 0.48/1.03 33 -relation(A) | -reflexive(A) | is_reflexive_in(A,relation_field(A)) # label(d9_relat_2) # label(axiom). [clausify(8)].
% 0.48/1.03 Derived: -reflexive(c1) | is_reflexive_in(c1,relation_field(c1)). [resolve(33,a,17,a)].
% 0.48/1.03 34 -relation(A) | reflexive(A) | -is_reflexive_in(A,relation_field(A)) # label(d9_relat_2) # label(axiom). [clausify(8)].
% 0.48/1.03 Derived: reflexive(c1) | -is_reflexive_in(c1,relation_field(c1)). [resolve(34,a,17,a)].
% 0.48/1.03 35 -relation(A) | -well_founded_relation(A) | is_well_founded_in(A,relation_field(A)) # label(t5_wellord1) # label(axiom). [clausify(14)].
% 0.48/1.03 Derived: -well_founded_relation(c1) | is_well_founded_in(c1,relation_field(c1)). [resolve(35,a,17,a)].
% 0.48/1.03 36 -relation(A) | well_founded_relation(A) | -is_well_founded_in(A,relation_field(A)) # label(t5_wellord1) # label(axiom). [clausify(14)].
% 0.48/1.03 Derived: well_founded_relation(c1) | -is_well_founded_in(c1,relation_field(c1)). [resolve(36,a,17,a)].
% 0.48/1.03 37 -relation(A) | relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) # label(d6_relat_1) # label(axiom). [clausify(7)].
% 0.48/1.03 Derived: relation_field(c1) = set_union2(relation_dom(c1),relation_rng(c1)). [resolve(37,a,17,a)].
% 0.48/1.03 38 -relation(A) | well_ordering(A) | -reflexive(A) | -transitive(A) | -antisymmetric(A) | -connected(A) | -well_founded_relation(A) # label(d4_wellord1) # label(axiom). [clausify(5)].
% 0.48/1.03 Derived: well_ordering(c1) | -reflexive(c1) | -transitive(c1) | -antisymmetric(c1) | -connected(c1) | -well_founded_relation(c1). [resolve(38,a,17,a)].
% 0.48/1.03 39 -relation(A) | well_orders(A,B) | -is_reflexive_in(A,B) | -is_transitive_in(A,B) | -is_antisymmetric_in(A,B) | -is_connected_in(A,B) | -is_well_founded_in(A,B) # label(d5_wellord1) # label(axiom). [clausify(6)].
% 0.48/1.03 Derived: well_orders(c1,A) | -is_reflexive_in(c1,A) | -is_transitive_in(c1,A) | -is_antisymmetric_in(c1,A) | -is_connected_in(c1,A) | -is_well_founded_in(c1,A). [resolve(39,a,17,a)].
% 0.48/1.03
% 0.48/1.03 ============================== end predicate elimination =============
% 0.48/1.03
% 0.48/1.03 Auto_denials: (non-Horn, no changes).
% 0.48/1.03
% 0.48/1.03 Term ordering decisions:
% 0.48/1.03 Function symbol KB weights: c1=1. set_union2=1. relation_field=1. relation_dom=1. relation_rng=1.
% 0.48/1.03
% 0.48/1.03 ============================== end of process initial clauses ========
% 0.48/1.03
% 0.48/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.48/1.03
% 0.48/1.03 ============================== end of clauses for search =============
% 0.48/1.03
% 0.48/1.03 ============================== SEARCH ================================
% 0.48/1.03
% 0.48/1.03 % Starting search at 0.01 seconds.
% 0.48/1.03
% 0.48/1.03 ============================== PROOF =================================
% 0.48/1.03 % SZS status Theorem
% 0.48/1.03 % SZS output start Refutation
% 0.48/1.03
% 0.48/1.03 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.48/1.03 % Length of proof is 82.
% 0.48/1.03 % Level of proof is 12.
% 0.48/1.03 % Maximum clause weight is 18.000.
% 0.48/1.03 % Given clauses 49.
% 0.48/1.03
% 0.48/1.03 2 (all A (relation(A) -> (antisymmetric(A) <-> is_antisymmetric_in(A,relation_field(A))))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 3 (all A (relation(A) -> (connected(A) <-> is_connected_in(A,relation_field(A))))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 4 (all A (relation(A) -> (transitive(A) <-> is_transitive_in(A,relation_field(A))))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 5 (all A (relation(A) -> (well_ordering(A) <-> reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 6 (all A (relation(A) -> (all B (well_orders(A,B) <-> is_reflexive_in(A,B) & is_transitive_in(A,B) & is_antisymmetric_in(A,B) & is_connected_in(A,B) & is_well_founded_in(A,B))))) # label(d5_wellord1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 8 (all A (relation(A) -> (reflexive(A) <-> is_reflexive_in(A,relation_field(A))))) # label(d9_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 14 (all A (relation(A) -> (well_founded_relation(A) <-> is_well_founded_in(A,relation_field(A))))) # label(t5_wellord1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 15 -(all A (relation(A) -> (well_orders(A,relation_field(A)) <-> well_ordering(A)))) # label(t8_wellord1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.48/1.03 16 -relation(A) | -well_ordering(A) | reflexive(A) # label(d4_wellord1) # label(axiom). [clausify(5)].
% 0.48/1.03 17 relation(c1) # label(t8_wellord1) # label(negated_conjecture). [clausify(15)].
% 0.48/1.03 18 -relation(A) | -well_ordering(A) | transitive(A) # label(d4_wellord1) # label(axiom). [clausify(5)].
% 0.48/1.03 19 -relation(A) | -well_ordering(A) | antisymmetric(A) # label(d4_wellord1) # label(axiom). [clausify(5)].
% 0.48/1.03 20 -relation(A) | -well_ordering(A) | connected(A) # label(d4_wellord1) # label(axiom). [clausify(5)].
% 0.48/1.03 21 -relation(A) | -well_ordering(A) | well_founded_relation(A) # label(d4_wellord1) # label(axiom). [clausify(5)].
% 0.48/1.03 22 -relation(A) | -antisymmetric(A) | is_antisymmetric_in(A,relation_field(A)) # label(d12_relat_2) # label(axiom). [clausify(2)].
% 0.48/1.03 23 -relation(A) | antisymmetric(A) | -is_antisymmetric_in(A,relation_field(A)) # label(d12_relat_2) # label(axiom). [clausify(2)].
% 0.48/1.03 24 -relation(A) | -connected(A) | is_connected_in(A,relation_field(A)) # label(d14_relat_2) # label(axiom). [clausify(3)].
% 0.48/1.03 25 -relation(A) | connected(A) | -is_connected_in(A,relation_field(A)) # label(d14_relat_2) # label(axiom). [clausify(3)].
% 0.48/1.03 26 -relation(A) | -transitive(A) | is_transitive_in(A,relation_field(A)) # label(d16_relat_2) # label(axiom). [clausify(4)].
% 0.48/1.03 27 -relation(A) | transitive(A) | -is_transitive_in(A,relation_field(A)) # label(d16_relat_2) # label(axiom). [clausify(4)].
% 0.48/1.03 28 -relation(A) | -well_orders(A,B) | is_reflexive_in(A,B) # label(d5_wellord1) # label(axiom). [clausify(6)].
% 0.48/1.03 29 -relation(A) | -well_orders(A,B) | is_transitive_in(A,B) # label(d5_wellord1) # label(axiom). [clausify(6)].
% 0.48/1.03 30 -relation(A) | -well_orders(A,B) | is_antisymmetric_in(A,B) # label(d5_wellord1) # label(axiom). [clausify(6)].
% 0.48/1.03 31 -relation(A) | -well_orders(A,B) | is_connected_in(A,B) # label(d5_wellord1) # label(axiom). [clausify(6)].
% 0.48/1.03 32 -relation(A) | -well_orders(A,B) | is_well_founded_in(A,B) # label(d5_wellord1) # label(axiom). [clausify(6)].
% 0.48/1.03 33 -relation(A) | -reflexive(A) | is_reflexive_in(A,relation_field(A)) # label(d9_relat_2) # label(axiom). [clausify(8)].
% 0.48/1.03 34 -relation(A) | reflexive(A) | -is_reflexive_in(A,relation_field(A)) # label(d9_relat_2) # label(axiom). [clausify(8)].
% 0.48/1.03 35 -relation(A) | -well_founded_relation(A) | is_well_founded_in(A,relation_field(A)) # label(t5_wellord1) # label(axiom). [clausify(14)].
% 0.48/1.03 36 -relation(A) | well_founded_relation(A) | -is_well_founded_in(A,relation_field(A)) # label(t5_wellord1) # label(axiom). [clausify(14)].
% 0.48/1.03 38 -relation(A) | well_ordering(A) | -reflexive(A) | -transitive(A) | -antisymmetric(A) | -connected(A) | -well_founded_relation(A) # label(d4_wellord1) # label(axiom). [clausify(5)].
% 0.48/1.03 39 -relation(A) | well_orders(A,B) | -is_reflexive_in(A,B) | -is_transitive_in(A,B) | -is_antisymmetric_in(A,B) | -is_connected_in(A,B) | -is_well_founded_in(A,B) # label(d5_wellord1) # label(axiom). [clausify(6)].
% 0.48/1.03 41 well_orders(c1,relation_field(c1)) | well_ordering(c1) # label(t8_wellord1) # label(negated_conjecture). [clausify(15)].
% 0.48/1.03 43 -well_orders(c1,relation_field(c1)) | -well_ordering(c1) # label(t8_wellord1) # label(negated_conjecture). [clausify(15)].
% 0.48/1.03 44 -well_ordering(c1) | reflexive(c1). [resolve(16,a,17,a)].
% 0.48/1.03 45 -well_ordering(c1) | transitive(c1). [resolve(18,a,17,a)].
% 0.48/1.03 46 -well_ordering(c1) | antisymmetric(c1). [resolve(19,a,17,a)].
% 0.48/1.03 47 -well_ordering(c1) | connected(c1). [resolve(20,a,17,a)].
% 0.48/1.03 48 -well_ordering(c1) | well_founded_relation(c1). [resolve(21,a,17,a)].
% 0.48/1.03 49 -antisymmetric(c1) | is_antisymmetric_in(c1,relation_field(c1)). [resolve(22,a,17,a)].
% 0.48/1.03 50 antisymmetric(c1) | -is_antisymmetric_in(c1,relation_field(c1)). [resolve(23,a,17,a)].
% 0.48/1.03 51 -connected(c1) | is_connected_in(c1,relation_field(c1)). [resolve(24,a,17,a)].
% 0.48/1.03 52 connected(c1) | -is_connected_in(c1,relation_field(c1)). [resolve(25,a,17,a)].
% 0.48/1.03 53 -transitive(c1) | is_transitive_in(c1,relation_field(c1)). [resolve(26,a,17,a)].
% 0.48/1.03 54 transitive(c1) | -is_transitive_in(c1,relation_field(c1)). [resolve(27,a,17,a)].
% 0.48/1.03 55 -well_orders(c1,A) | is_reflexive_in(c1,A). [resolve(28,a,17,a)].
% 0.48/1.03 56 -well_orders(c1,A) | is_transitive_in(c1,A). [resolve(29,a,17,a)].
% 0.48/1.03 57 -well_orders(c1,A) | is_antisymmetric_in(c1,A). [resolve(30,a,17,a)].
% 0.48/1.03 58 -well_orders(c1,A) | is_connected_in(c1,A). [resolve(31,a,17,a)].
% 0.48/1.03 59 -well_orders(c1,A) | is_well_founded_in(c1,A). [resolve(32,a,17,a)].
% 0.48/1.03 60 -reflexive(c1) | is_reflexive_in(c1,relation_field(c1)). [resolve(33,a,17,a)].
% 0.48/1.03 61 reflexive(c1) | -is_reflexive_in(c1,relation_field(c1)). [resolve(34,a,17,a)].
% 0.48/1.03 62 -well_founded_relation(c1) | is_well_founded_in(c1,relation_field(c1)). [resolve(35,a,17,a)].
% 0.48/1.03 63 well_founded_relation(c1) | -is_well_founded_in(c1,relation_field(c1)). [resolve(36,a,17,a)].
% 0.48/1.03 66 well_ordering(c1) | -reflexive(c1) | -transitive(c1) | -antisymmetric(c1) | -connected(c1) | -well_founded_relation(c1). [resolve(38,a,17,a)].
% 0.48/1.03 67 well_orders(c1,A) | -is_reflexive_in(c1,A) | -is_transitive_in(c1,A) | -is_antisymmetric_in(c1,A) | -is_connected_in(c1,A) | -is_well_founded_in(c1,A). [resolve(39,a,17,a)].
% 0.48/1.03 68 is_reflexive_in(c1,relation_field(c1)) | well_ordering(c1). [resolve(55,a,41,a)].
% 0.48/1.03 69 is_transitive_in(c1,relation_field(c1)) | well_ordering(c1). [resolve(56,a,41,a)].
% 0.48/1.03 70 is_antisymmetric_in(c1,relation_field(c1)) | well_ordering(c1). [resolve(57,a,41,a)].
% 0.48/1.03 71 is_connected_in(c1,relation_field(c1)) | well_ordering(c1). [resolve(58,a,41,a)].
% 0.48/1.03 72 is_well_founded_in(c1,relation_field(c1)) | well_ordering(c1). [resolve(59,a,41,a)].
% 0.48/1.03 73 well_ordering(c1) | reflexive(c1). [resolve(68,a,61,b)].
% 0.48/1.03 74 well_ordering(c1) | transitive(c1). [resolve(69,a,54,b)].
% 0.48/1.03 75 well_ordering(c1) | antisymmetric(c1). [resolve(70,a,50,b)].
% 0.48/1.03 76 well_ordering(c1) | connected(c1). [resolve(71,a,52,b)].
% 0.48/1.03 77 well_ordering(c1) | well_founded_relation(c1). [resolve(72,a,63,b)].
% 0.48/1.03 78 well_ordering(c1) | -reflexive(c1) | -transitive(c1) | -antisymmetric(c1) | -connected(c1). [resolve(77,b,66,f),merge(b)].
% 0.48/1.03 79 well_ordering(c1) | -reflexive(c1) | -antisymmetric(c1) | -connected(c1). [resolve(78,c,74,b),merge(e)].
% 0.48/1.03 80 well_ordering(c1) | -antisymmetric(c1) | -connected(c1). [resolve(79,b,73,b),merge(d)].
% 0.48/1.03 81 well_ordering(c1) | -antisymmetric(c1). [resolve(80,c,76,b),merge(c)].
% 0.48/1.03 82 well_ordering(c1). [resolve(81,b,75,b),merge(b)].
% 0.48/1.03 83 well_founded_relation(c1). [back_unit_del(48),unit_del(a,82)].
% 0.48/1.03 84 connected(c1). [back_unit_del(47),unit_del(a,82)].
% 0.48/1.03 85 antisymmetric(c1). [back_unit_del(46),unit_del(a,82)].
% 0.48/1.03 86 transitive(c1). [back_unit_del(45),unit_del(a,82)].
% 0.48/1.03 87 reflexive(c1). [back_unit_del(44),unit_del(a,82)].
% 0.48/1.03 88 -well_orders(c1,relation_field(c1)). [back_unit_del(43),unit_del(b,82)].
% 0.48/1.03 89 is_well_founded_in(c1,relation_field(c1)). [back_unit_del(62),unit_del(a,83)].
% 0.48/1.03 90 is_connected_in(c1,relation_field(c1)). [back_unit_del(51),unit_del(a,84)].
% 0.48/1.03 91 is_antisymmetric_in(c1,relation_field(c1)). [back_unit_del(49),unit_del(a,85)].
% 0.48/1.03 92 is_transitive_in(c1,relation_field(c1)). [back_unit_del(53),unit_del(a,86)].
% 0.48/1.03 93 is_reflexive_in(c1,relation_field(c1)). [back_unit_del(60),unit_del(a,87)].
% 0.48/1.03 94 $F. [resolve(89,a,67,f),unit_del(a,88),unit_del(b,93),unit_del(c,92),unit_del(d,91),unit_del(e,90)].
% 0.48/1.03
% 0.48/1.03 % SZS output end Refutation
% 0.48/1.03 ============================== end of proof ==========================
% 0.48/1.03
% 0.48/1.03 ============================== STATISTICS ============================
% 0.48/1.03
% 0.48/1.03 Given=49. Generated=70. Kept=53. proofs=1.
% 0.48/1.03 Usable=17. Sos=4. Demods=3. Limbo=0, Disabled=83. Hints=0.
% 0.48/1.03 Megabytes=0.09.
% 0.48/1.03 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.48/1.03
% 0.48/1.03 ============================== end of statistics =====================
% 0.48/1.03
% 0.48/1.03 ============================== end of search =========================
% 0.48/1.03
% 0.48/1.03 THEOREM PROVED
% 0.48/1.03 % SZS status Theorem
% 0.48/1.03
% 0.48/1.03 Exiting with 1 proof.
% 0.48/1.03
% 0.48/1.03 Process 5093 exit (max_proofs) Mon Jun 20 10:14:36 2022
% 0.48/1.03 Prover9 interrupted
%------------------------------------------------------------------------------