TSTP Solution File: SEU242+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU242+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 13:30:17 EDT 2022
% Result : Theorem 6.77s 7.10s
% Output : Refutation 6.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU242+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n022.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 : 600
% 0.12/0.33 % DateTime : Sun Jun 19 21:47:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/0.99 ============================== Prover9 ===============================
% 0.42/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.99 Process 32341 was started by sandbox on n022.cluster.edu,
% 0.42/0.99 Sun Jun 19 21:47:47 2022
% 0.42/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32188_n022.cluster.edu".
% 0.42/0.99 ============================== end of head ===========================
% 0.42/0.99
% 0.42/0.99 ============================== INPUT =================================
% 0.42/0.99
% 0.42/0.99 % Reading from file /tmp/Prover9_32188_n022.cluster.edu
% 0.42/0.99
% 0.42/0.99 set(prolog_style_variables).
% 0.42/0.99 set(auto2).
% 0.42/0.99 % set(auto2) -> set(auto).
% 0.42/0.99 % set(auto) -> set(auto_inference).
% 0.42/0.99 % set(auto) -> set(auto_setup).
% 0.42/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.99 % set(auto) -> set(auto_limits).
% 0.42/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.99 % set(auto) -> set(auto_denials).
% 0.42/0.99 % set(auto) -> set(auto_process).
% 0.42/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.99 % set(auto2) -> assign(stats, some).
% 0.42/0.99 % set(auto2) -> clear(echo_input).
% 0.42/0.99 % set(auto2) -> set(quiet).
% 0.42/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.99 % set(auto2) -> clear(print_given).
% 0.42/0.99 assign(lrs_ticks,-1).
% 0.42/0.99 assign(sos_limit,10000).
% 0.42/0.99 assign(order,kbo).
% 0.42/0.99 set(lex_order_vars).
% 0.42/0.99 clear(print_given).
% 0.42/0.99
% 0.42/0.99 % formulas(sos). % not echoed (36 formulas)
% 0.42/0.99
% 0.42/0.99 ============================== end of input ==========================
% 0.42/0.99
% 0.42/0.99 % From the command line: assign(max_seconds, 300).
% 0.42/0.99
% 0.42/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.99
% 0.42/0.99 % Formulas that are not ordinary clauses:
% 0.42/0.99 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 2 (all A (empty(A) -> function(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 3 (all A (relation(A) & empty(A) & function(A) -> relation(A) & function(A) & one_to_one(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 4 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 5 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 6 (all A (relation(A) -> (connected(A) <-> is_connected_in(A,relation_field(A))))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 7 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 8 (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].
% 0.42/0.99 9 (all A (relation(A) -> (all B (is_connected_in(A,B) <-> (all C all D -(in(C,B) & in(D,B) & C != D & -in(ordered_pair(C,D),A) & -in(ordered_pair(D,C),A))))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 10 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 11 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 12 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 13 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 14 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 15 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 16 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 17 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 18 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 19 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 20 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 21 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 22 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 23 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 24 (exists A (relation(A) & function(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 25 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 26 (exists A (relation(A) & empty(A) & function(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 27 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 28 (exists A (relation(A) & function(A) & one_to_one(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 29 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 30 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 31 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 32 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 33 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 34 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 35 -(all A (relation(A) -> (connected(A) <-> (all B all C -(in(B,relation_field(A)) & in(C,relation_field(A)) & B != C & -in(ordered_pair(B,C),A) & -in(ordered_pair(C,B),A)))))) # label(l4_wellord1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.99
% 0.42/0.99 ============================== end of process non-clausal formulas ===
% 0.42/0.99
% 0.42/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/0.99
% 0.42/0.99 ============================== PREDICATE ELIMINATION =================
% 0.42/0.99 36 -relation(A) | -empty(A) | -function(A) | one_to_one(A) # label(cc2_funct_1) # label(axiom). [clausify(3)].
% 0.42/0.99 37 relation(c1) # label(rc1_funct_1) # label(axiom). [clausify(24)].
% 0.42/0.99 38 relation(c3) # label(rc2_funct_1) # label(axiom). [clausify(26)].
% 0.42/0.99 39 relation(c5) # label(rc3_funct_1) # label(axiom). [clausify(28)].
% 0.42/0.99 40 relation(c6) # label(l4_wellord1) # label(negated_conjecture). [clausify(35)].
% 0.42/0.99 Derived: -empty(c1) | -function(c1) | one_to_one(c1). [resolve(36,a,37,a)].
% 0.42/0.99 Derived: -empty(c3) | -function(c3) | one_to_one(c3). [resolve(36,a,38,a)].
% 0.42/0.99 Derived: -empty(c5) | -function(c5) | one_to_one(c5). [resolve(36,a,39,a)].
% 0.42/0.99 Derived: -empty(c6) | -function(c6) | one_to_one(c6). [resolve(36,a,40,a)].
% 0.42/0.99 41 -relation(A) | -connected(A) | is_connected_in(A,relation_field(A)) # label(d14_relat_2) # label(axiom). [clausify(6)].
% 0.42/0.99 Derived: -connected(c1) | is_connected_in(c1,relation_field(c1)). [resolve(41,a,37,a)].
% 0.42/0.99 Derived: -connected(c3) | is_connected_in(c3,relation_field(c3)). [resolve(41,a,38,a)].
% 0.42/0.99 Derived: -connected(c5) | is_connected_in(c5,relation_field(c5)). [resolve(41,a,39,a)].
% 0.42/0.99 Derived: -connected(c6) | is_connected_in(c6,relation_field(c6)). [resolve(41,a,40,a)].
% 0.42/0.99 42 -relation(A) | connected(A) | -is_connected_in(A,relation_field(A)) # label(d14_relat_2) # label(axiom). [clausify(6)].
% 0.42/0.99 Derived: connected(c1) | -is_connected_in(c1,relation_field(c1)). [resolve(42,a,37,a)].
% 0.42/0.99 Derived: connected(c3) | -is_connected_in(c3,relation_field(c3)). [resolve(42,a,38,a)].
% 0.42/0.99 Derived: connected(c5) | -is_connected_in(c5,relation_field(c5)). [resolve(42,a,39,a)].
% 0.42/0.99 Derived: connected(c6) | -is_connected_in(c6,relation_field(c6)). [resolve(42,a,40,a)].
% 0.42/0.99 43 -relation(A) | relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) # label(d6_relat_1) # label(axiom). [clausify(8)].
% 0.42/0.99 Derived: relation_field(c1) = set_union2(relation_dom(c1),relation_rng(c1)). [resolve(43,a,37,a)].
% 0.42/0.99 Derived: relation_field(c3) = set_union2(relation_dom(c3),relation_rng(c3)). [resolve(43,a,38,a)].
% 0.42/0.99 Derived: relation_field(c5) = set_union2(relation_dom(c5),relation_rng(c5)). [resolve(43,a,39,a)].
% 0.42/0.99 Derived: relation_field(c6) = set_union2(relation_dom(c6),relation_rng(c6)). [resolve(43,a,40,a)].
% 0.42/0.99 44 -relation(A) | is_connected_in(A,B) | in(f1(A,B),B) # label(d6_relat_2) # label(axiom). [clausify(9)].
% 0.42/0.99 Derived: is_connected_in(c1,A) | in(f1(c1,A),A). [resolve(44,a,37,a)].
% 0.42/0.99 Derived: is_connected_in(c3,A) | in(f1(c3,A),A). [resolve(44,a,38,a)].
% 0.42/0.99 Derived: is_connected_in(c5,A) | in(f1(c5,A),A). [resolve(44,a,39,a)].
% 0.42/0.99 Derived: is_connected_in(c6,A) | in(f1(c6,A),A). [resolve(44,a,40,a)].
% 0.42/0.99 45 -relation(A) | is_connected_in(A,B) | in(f2(A,B),B) # label(d6_relat_2) # label(axiom). [clausify(9)].
% 0.42/0.99 Derived: is_connected_in(c1,A) | in(f2(c1,A),A). [resolve(45,a,37,a)].
% 0.42/0.99 Derived: is_connected_in(c3,A) | in(f2(c3,A),A). [resolve(45,a,38,a)].
% 0.42/0.99 Derived: is_connected_in(c5,A) | in(f2(c5,A),A). [resolve(45,a,39,a)].
% 0.42/0.99 Derived: is_connected_in(c6,A) | in(f2(c6,A),A). [resolve(45,a,40,a)].
% 0.42/0.99 46 -relation(A) | is_connected_in(A,B) | f2(A,B) != f1(A,B) # label(d6_relat_2) # label(axiom). [clausify(9)].
% 0.42/0.99 Derived: is_connected_in(c1,A) | f2(c1,A) != f1(c1,A). [resolve(46,a,37,a)].
% 0.42/0.99 Derived: is_connected_in(c3,A) | f2(c3,A) != f1(c3,A). [resolve(46,a,38,a)].
% 0.42/0.99 Derived: is_connected_in(c5,A) | f2(c5,A) != f1(c5,A). [resolve(46,a,39,a)].
% 0.42/0.99 Derived: is_connected_in(c6,A) | f2(c6,A) != f1(c6,A). [resolve(46,a,40,a)].
% 0.42/0.99 47 -relation(A) | is_connected_in(A,B) | -in(ordered_pair(f1(A,B),f2(A,B)),A) # label(d6_relat_2) # label(axiom). [clausify(9)].
% 0.42/0.99 Derived: is_connected_in(c1,A) | -in(ordered_pair(f1(c1,A),f2(c1,A)),c1). [resolve(47,a,37,a)].
% 0.42/0.99 Derived: is_connected_in(c3,A) | -in(ordered_pair(f1(c3,A),f2(c3,A)),c3). [resolve(47,a,38,a)].
% 0.42/0.99 Derived: is_connected_in(c5,A) | -in(ordered_pair(f1(c5,A),f2(c5,A)),c5). [resolve(47,a,39,a)].
% 0.42/0.99 Derived: is_connected_in(c6,A) | -in(ordered_pair(f1(c6,A),f2(c6,A)),c6). [resolve(47,a,40,a)].
% 0.42/0.99 48 -relation(A) | is_connected_in(A,B) | -in(ordered_pair(f2(A,B),f1(A,B)),A) # label(d6_relat_2) # label(axiom). [clausify(9)].
% 0.42/0.99 Derived: is_connected_in(c1,A) | -in(ordered_pair(f2(c1,A),f1(c1,A)),c1). [resolve(48,a,37,a)].
% 0.42/0.99 Derived: is_connected_in(c3,A) | -in(ordered_pair(f2(c3,A),f1(c3,A)),c3). [resolve(48,a,38,a)].
% 0.42/0.99 Derived: is_connected_in(c5,A) | -in(ordered_pair(f2(c5,A),f1(c5,A)),c5). [resolve(48,a,39,a)].
% 0.42/0.99 Derived: is_connected_in(c6,A) | -in(ordered_pair(f2(c6,A),f1(c6,A)),c6). [resolve(48,a,40,a)].
% 0.42/0.99 49 -relation(A) | -is_connected_in(A,B) | -in(C,B) | -in(D,B) | D = C | in(ordered_pair(C,D),A) | in(ordered_pair(D,C),A) # label(d6_relat_2) # label(axiom). [clausify(9)].
% 0.42/0.99 Derived: -is_connected_in(c1,A) | -in(B,A) | -in(C,A) | C = B | in(ordered_pair(B,C),c1) | in(ordered_pair(C,B),c1). [resolve(49,a,37,a)].
% 0.42/0.99 Derived: -is_connected_in(c3,A) | -in(B,A) | -in(C,A) | C = B | in(ordered_pair(B,C),c3) | in(ordered_pair(C,B),c3). [resolve(49,a,38,a)].
% 0.42/0.99 Derived: -is_connected_in(c5,A) | -in(B,A) | -in(C,A) | C = B | in(ordered_pair(B,C),c5) | in(ordered_pair(C,B),c5). [resolve(49,a,39,a)].
% 0.42/0.99 Derived: -is_connected_in(c6,A) | -in(B,A) | -in(C,A) | C = B | in(ordered_pair(B,C),c6) | in(ordered_pair(C,B),c6). [resolve(49,a,40,a)].
% 0.42/0.99 50 -element(A,B) | empty(B) | in(A,B) # label(t2_subset) # label(axiom). [clausify(31)].
% 0.42/0.99 51 element(f3(A),A) # label(existence_m1_subset_1) # label(axiom). [clausify(19)].
% 0.42/0.99 52 -in(A,B) | element(A,B) # label(t1_subset) # label(axiom). [clausify(30)].
% 0.42/0.99 Derived: empty(A) | in(f3(A),A). [resolve(50,a,51,a)].
% 0.42/0.99
% 0.42/0.99 ============================== end predicate elimination =============
% 0.42/0.99
% 0.42/0.99 Auto_denials: (non-Horn, no changes).
% 0.42/0.99
% 0.42/0.99 Term ordering decisions:
% 0.42/0.99 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. ordered_pair=1. set_union2=1. unordered_pair=1. f1=1. f2=1. relation_field=1. relation_dom=1. relation_rng=1. singleton=1. f3=1.
% 6.77/7.10
% 6.77/7.10 ============================== end of process initial clauses ========
% 6.77/7.10
% 6.77/7.10 ============================== CLAUSES FOR SEARCH ====================
% 6.77/7.10
% 6.77/7.10 ============================== end of clauses for search =============
% 6.77/7.10
% 6.77/7.10 ============================== SEARCH ================================
% 6.77/7.10
% 6.77/7.10 % Starting search at 0.02 seconds.
% 6.77/7.10
% 6.77/7.10 ============================== PROOF =================================
% 6.77/7.10 % SZS status Theorem
% 6.77/7.10 % SZS output start Refutation
% 6.77/7.10
% 6.77/7.10 % Proof 1 at 6.11 (+ 0.01) seconds.
% 6.77/7.10 % Length of proof is 72.
% 6.77/7.10 % Level of proof is 29.
% 6.77/7.10 % Maximum clause weight is 45.000.
% 6.77/7.10 % Given clauses 450.
% 6.77/7.10
% 6.77/7.10 4 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 6.77/7.10 6 (all A (relation(A) -> (connected(A) <-> is_connected_in(A,relation_field(A))))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption].
% 6.77/7.10 7 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 6.77/7.10 9 (all A (relation(A) -> (all B (is_connected_in(A,B) <-> (all C all D -(in(C,B) & in(D,B) & C != D & -in(ordered_pair(C,D),A) & -in(ordered_pair(D,C),A))))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption].
% 6.77/7.10 35 -(all A (relation(A) -> (connected(A) <-> (all B all C -(in(B,relation_field(A)) & in(C,relation_field(A)) & B != C & -in(ordered_pair(B,C),A) & -in(ordered_pair(C,B),A)))))) # label(l4_wellord1) # label(negated_conjecture) # label(non_clause). [assumption].
% 6.77/7.10 40 relation(c6) # label(l4_wellord1) # label(negated_conjecture). [clausify(35)].
% 6.77/7.10 41 -relation(A) | -connected(A) | is_connected_in(A,relation_field(A)) # label(d14_relat_2) # label(axiom). [clausify(6)].
% 6.77/7.10 42 -relation(A) | connected(A) | -is_connected_in(A,relation_field(A)) # label(d14_relat_2) # label(axiom). [clausify(6)].
% 6.77/7.10 44 -relation(A) | is_connected_in(A,B) | in(f1(A,B),B) # label(d6_relat_2) # label(axiom). [clausify(9)].
% 6.77/7.10 45 -relation(A) | is_connected_in(A,B) | in(f2(A,B),B) # label(d6_relat_2) # label(axiom). [clausify(9)].
% 6.77/7.10 46 -relation(A) | is_connected_in(A,B) | f2(A,B) != f1(A,B) # label(d6_relat_2) # label(axiom). [clausify(9)].
% 6.77/7.10 47 -relation(A) | is_connected_in(A,B) | -in(ordered_pair(f1(A,B),f2(A,B)),A) # label(d6_relat_2) # label(axiom). [clausify(9)].
% 6.77/7.10 48 -relation(A) | is_connected_in(A,B) | -in(ordered_pair(f2(A,B),f1(A,B)),A) # label(d6_relat_2) # label(axiom). [clausify(9)].
% 6.77/7.10 49 -relation(A) | -is_connected_in(A,B) | -in(C,B) | -in(D,B) | D = C | in(ordered_pair(C,D),A) | in(ordered_pair(D,C),A) # label(d6_relat_2) # label(axiom). [clausify(9)].
% 6.77/7.10 58 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(4)].
% 6.77/7.10 60 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(7)].
% 6.77/7.10 61 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(60),rewrite([58(4)])].
% 6.77/7.10 66 -connected(c6) | c8 != c7 # label(l4_wellord1) # label(negated_conjecture). [clausify(35)].
% 6.77/7.10 68 -connected(c6) | -in(ordered_pair(c7,c8),c6) # label(l4_wellord1) # label(negated_conjecture). [clausify(35)].
% 6.77/7.10 69 -connected(c6) | -in(unordered_pair(singleton(c7),unordered_pair(c7,c8)),c6). [copy(68),rewrite([61(5)])].
% 6.77/7.10 70 -connected(c6) | -in(ordered_pair(c8,c7),c6) # label(l4_wellord1) # label(negated_conjecture). [clausify(35)].
% 6.77/7.10 71 -connected(c6) | -in(unordered_pair(singleton(c8),unordered_pair(c7,c8)),c6). [copy(70),rewrite([61(5),58(7)])].
% 6.77/7.10 75 -connected(c6) | in(c7,relation_field(c6)) # label(l4_wellord1) # label(negated_conjecture). [clausify(35)].
% 6.77/7.10 76 -connected(c6) | in(c8,relation_field(c6)) # label(l4_wellord1) # label(negated_conjecture). [clausify(35)].
% 6.77/7.10 78 connected(c6) | -in(A,relation_field(c6)) | -in(B,relation_field(c6)) | B = A | in(ordered_pair(A,B),c6) | in(ordered_pair(B,A),c6) # label(l4_wellord1) # label(negated_conjecture). [clausify(35)].
% 6.77/7.10 79 connected(c6) | -in(A,relation_field(c6)) | -in(B,relation_field(c6)) | B = A | in(unordered_pair(singleton(A),unordered_pair(A,B)),c6) | in(unordered_pair(singleton(B),unordered_pair(A,B)),c6). [copy(78),rewrite([61(10),61(15),58(16)])].
% 6.77/7.10 83 -connected(c6) | is_connected_in(c6,relation_field(c6)). [resolve(41,a,40,a)].
% 6.77/7.10 87 connected(c6) | -is_connected_in(c6,relation_field(c6)). [resolve(42,a,40,a)].
% 6.77/7.10 99 is_connected_in(c6,A) | in(f1(c6,A),A). [resolve(44,a,40,a)].
% 6.77/7.10 103 is_connected_in(c6,A) | in(f2(c6,A),A). [resolve(45,a,40,a)].
% 6.77/7.10 107 is_connected_in(c6,A) | f2(c6,A) != f1(c6,A). [resolve(46,a,40,a)].
% 6.77/7.10 114 is_connected_in(c6,A) | -in(ordered_pair(f1(c6,A),f2(c6,A)),c6). [resolve(47,a,40,a)].
% 6.77/7.10 115 is_connected_in(c6,A) | -in(unordered_pair(singleton(f1(c6,A)),unordered_pair(f1(c6,A),f2(c6,A))),c6). [copy(114),rewrite([61(7)])].
% 6.77/7.10 122 is_connected_in(c6,A) | -in(ordered_pair(f2(c6,A),f1(c6,A)),c6). [resolve(48,a,40,a)].
% 6.77/7.10 123 is_connected_in(c6,A) | -in(unordered_pair(singleton(f2(c6,A)),unordered_pair(f1(c6,A),f2(c6,A))),c6). [copy(122),rewrite([61(7),58(10)])].
% 6.77/7.10 130 -is_connected_in(c6,A) | -in(B,A) | -in(C,A) | C = B | in(ordered_pair(B,C),c6) | in(ordered_pair(C,B),c6). [resolve(49,a,40,a)].
% 6.77/7.10 131 -is_connected_in(c6,A) | -in(B,A) | -in(C,A) | C = B | in(unordered_pair(singleton(B),unordered_pair(B,C)),c6) | in(unordered_pair(singleton(C),unordered_pair(B,C)),c6). [copy(130),rewrite([61(6),61(11),58(12)])].
% 6.77/7.10 154 in(f1(c6,relation_field(c6)),relation_field(c6)) | connected(c6). [resolve(99,a,87,b)].
% 6.77/7.10 157 in(f2(c6,relation_field(c6)),relation_field(c6)) | connected(c6). [resolve(103,a,87,b)].
% 6.77/7.10 199 connected(c6) | -in(A,relation_field(c6)) | f1(c6,relation_field(c6)) = A | in(unordered_pair(singleton(A),unordered_pair(A,f1(c6,relation_field(c6)))),c6) | in(unordered_pair(singleton(f1(c6,relation_field(c6))),unordered_pair(A,f1(c6,relation_field(c6)))),c6). [resolve(154,a,79,c),merge(b)].
% 6.77/7.10 358 connected(c6) | f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | in(unordered_pair(singleton(f2(c6,relation_field(c6))),unordered_pair(f1(c6,relation_field(c6)),f2(c6,relation_field(c6)))),c6) | in(unordered_pair(singleton(f1(c6,relation_field(c6))),unordered_pair(f1(c6,relation_field(c6)),f2(c6,relation_field(c6)))),c6). [resolve(199,b,157,a),rewrite([58(25),58(42)]),flip(b),merge(e)].
% 6.77/7.10 873 connected(c6) | f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | in(unordered_pair(singleton(f1(c6,relation_field(c6))),unordered_pair(f1(c6,relation_field(c6)),f2(c6,relation_field(c6)))),c6) | is_connected_in(c6,relation_field(c6)). [resolve(358,c,123,b)].
% 6.77/7.10 883 connected(c6) | f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | in(unordered_pair(singleton(f1(c6,relation_field(c6))),unordered_pair(f1(c6,relation_field(c6)),f2(c6,relation_field(c6)))),c6). [resolve(873,d,87,b),merge(d)].
% 6.77/7.10 900 connected(c6) | f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | is_connected_in(c6,relation_field(c6)). [resolve(883,c,115,b)].
% 6.77/7.10 903 connected(c6) | f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)). [resolve(900,c,87,b),merge(c)].
% 6.77/7.10 911 f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | is_connected_in(c6,relation_field(c6)). [resolve(903,a,83,a)].
% 6.77/7.10 912 f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | in(c8,relation_field(c6)). [resolve(903,a,76,a)].
% 6.77/7.10 913 f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | in(c7,relation_field(c6)). [resolve(903,a,75,a)].
% 6.77/7.10 914 f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | c8 != c7. [resolve(903,a,66,a)].
% 6.77/7.10 915 f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | -in(A,relation_field(c6)) | -in(B,relation_field(c6)) | B = A | in(unordered_pair(singleton(A),unordered_pair(A,B)),c6) | in(unordered_pair(singleton(B),unordered_pair(A,B)),c6). [resolve(911,b,131,a)].
% 6.77/7.10 1072 f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | -in(A,relation_field(c6)) | c7 = A | in(unordered_pair(singleton(c7),unordered_pair(A,c7)),c6) | in(unordered_pair(singleton(A),unordered_pair(A,c7)),c6). [resolve(915,b,913,b),rewrite([58(18),58(24)]),flip(c),merge(f)].
% 6.77/7.10 1081 f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | c8 = c7 | in(unordered_pair(singleton(c7),unordered_pair(c7,c8)),c6) | in(unordered_pair(singleton(c8),unordered_pair(c7,c8)),c6). [resolve(1072,b,912,b),rewrite([58(17),58(25)]),flip(b),merge(e)].
% 6.77/7.10 1099 f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | c8 = c7 | in(unordered_pair(singleton(c7),unordered_pair(c7,c8)),c6) | -connected(c6). [resolve(1081,d,71,b)].
% 6.77/7.10 1102 f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | c8 = c7 | in(unordered_pair(singleton(c7),unordered_pair(c7,c8)),c6). [resolve(1099,d,903,a),merge(d)].
% 6.77/7.10 1122 f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | c8 = c7 | -connected(c6). [resolve(1102,c,69,b)].
% 6.77/7.10 1125 f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)) | c8 = c7. [resolve(1122,c,903,a),merge(c)].
% 6.77/7.10 1126 c8 = c7 | is_connected_in(c6,relation_field(c6)). [resolve(1125,a,107,b)].
% 6.77/7.10 1131 c8 = c7 | -in(A,relation_field(c6)) | -in(B,relation_field(c6)) | B = A | in(unordered_pair(singleton(A),unordered_pair(A,B)),c6) | in(unordered_pair(singleton(B),unordered_pair(A,B)),c6). [resolve(1126,b,131,a)].
% 6.77/7.10 1132 c8 = c7 | connected(c6). [resolve(1126,b,87,b)].
% 6.77/7.10 1133 c8 = c7 | -in(c7,relation_field(c6)) | -in(c8,relation_field(c6)) | in(unordered_pair(singleton(c7),unordered_pair(c7,c8)),c6) | in(unordered_pair(singleton(c8),unordered_pair(c7,c8)),c6). [factor(1131,a,d)].
% 6.77/7.10 1137 c8 = c7 | in(c8,relation_field(c6)). [resolve(1132,b,76,a)].
% 6.77/7.10 1138 c8 = c7 | in(c7,relation_field(c6)). [resolve(1132,b,75,a)].
% 6.77/7.10 1220 c8 = c7 | -in(c7,relation_field(c6)) | in(unordered_pair(singleton(c7),unordered_pair(c7,c8)),c6) | in(unordered_pair(singleton(c8),unordered_pair(c7,c8)),c6). [resolve(1133,c,1137,b),merge(e)].
% 6.77/7.10 1221 c8 = c7 | in(unordered_pair(singleton(c7),unordered_pair(c7,c8)),c6) | in(unordered_pair(singleton(c8),unordered_pair(c7,c8)),c6). [resolve(1220,b,1138,b),merge(d)].
% 6.77/7.10 1238 c8 = c7 | in(unordered_pair(singleton(c7),unordered_pair(c7,c8)),c6) | -connected(c6). [resolve(1221,c,71,b)].
% 6.77/7.10 1241 c8 = c7 | in(unordered_pair(singleton(c7),unordered_pair(c7,c8)),c6). [resolve(1238,c,1132,b),merge(c)].
% 6.77/7.10 1261 c8 = c7 | -connected(c6). [resolve(1241,b,69,b)].
% 6.77/7.10 1264 c8 = c7. [resolve(1261,b,1132,b),merge(b)].
% 6.77/7.10 1265 f2(c6,relation_field(c6)) = f1(c6,relation_field(c6)). [back_rewrite(914),rewrite([1264(10)]),xx(b)].
% 6.77/7.10 1267 -connected(c6). [back_rewrite(66),rewrite([1264(3)]),xx(b)].
% 6.77/7.10 1336 -is_connected_in(c6,relation_field(c6)). [back_unit_del(87),unit_del(a,1267)].
% 6.77/7.10 1398 $F. [ur(107,a,1336,a),rewrite([1265(4)]),xx(a)].
% 6.77/7.10
% 6.77/7.10 % SZS output end Refutation
% 6.77/7.10 ============================== end of proof ==========================
% 6.77/7.10
% 6.77/7.10 ============================== STATISTICS ============================
% 6.77/7.10
% 6.77/7.10 Given=450. Generated=13836. Kept=1323. proofs=1.
% 6.77/7.10 Usable=340. Sos=339. Demods=13. Limbo=1, Disabled=728. Hints=0.
% 6.77/7.10 Megabytes=3.01.
% 6.77/7.10 User_CPU=6.11, System_CPU=0.01, Wall_clock=6.
% 6.77/7.10
% 6.77/7.10 ============================== end of statistics =====================
% 6.77/7.10
% 6.77/7.10 ============================== end of search =========================
% 6.77/7.10
% 6.77/7.10 THEOREM PROVED
% 6.77/7.10 % SZS status Theorem
% 6.77/7.10
% 6.77/7.10 Exiting with 1 proof.
% 6.77/7.10
% 6.77/7.10 Process 32341 exit (max_proofs) Sun Jun 19 21:47:53 2022
% 6.77/7.10 Prover9 interrupted
%------------------------------------------------------------------------------