TSTP Solution File: SEU243+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU243+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 55.83s 56.17s
% Output : Refutation 55.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU243+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n019.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 20:21:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.76/1.08 ============================== Prover9 ===============================
% 0.76/1.08 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.08 Process 7156 was started by sandbox2 on n019.cluster.edu,
% 0.76/1.08 Sun Jun 19 20:21:25 2022
% 0.76/1.08 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7003_n019.cluster.edu".
% 0.76/1.08 ============================== end of head ===========================
% 0.76/1.08
% 0.76/1.08 ============================== INPUT =================================
% 0.76/1.08
% 0.76/1.08 % Reading from file /tmp/Prover9_7003_n019.cluster.edu
% 0.76/1.08
% 0.76/1.08 set(prolog_style_variables).
% 0.76/1.08 set(auto2).
% 0.76/1.08 % set(auto2) -> set(auto).
% 0.76/1.08 % set(auto) -> set(auto_inference).
% 0.76/1.08 % set(auto) -> set(auto_setup).
% 0.76/1.08 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.08 % set(auto) -> set(auto_limits).
% 0.76/1.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.08 % set(auto) -> set(auto_denials).
% 0.76/1.08 % set(auto) -> set(auto_process).
% 0.76/1.08 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.08 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.08 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.08 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.08 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.08 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.08 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.08 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.08 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.08 % set(auto2) -> assign(stats, some).
% 0.76/1.08 % set(auto2) -> clear(echo_input).
% 0.76/1.08 % set(auto2) -> set(quiet).
% 0.76/1.08 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.08 % set(auto2) -> clear(print_given).
% 0.76/1.08 assign(lrs_ticks,-1).
% 0.76/1.08 assign(sos_limit,10000).
% 0.76/1.08 assign(order,kbo).
% 0.76/1.08 set(lex_order_vars).
% 0.76/1.08 clear(print_given).
% 0.76/1.08
% 0.76/1.08 % formulas(sos). % not echoed (37 formulas)
% 0.76/1.08
% 0.76/1.08 ============================== end of input ==========================
% 0.76/1.08
% 0.76/1.08 % From the command line: assign(max_seconds, 300).
% 0.76/1.08
% 0.76/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.08
% 0.76/1.08 % Formulas that are not ordinary clauses:
% 0.76/1.08 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 2 (all A (empty(A) -> function(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 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].
% 0.76/1.08 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 5 (all A (relation(A) -> (well_founded_relation(A) <-> (all B -(subset(B,relation_field(A)) & B != empty_set & (all C -(in(C,B) & disjoint(fiber(A,C),B)))))))) # label(d2_wellord1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 6 (all A (relation(A) -> (all B (is_well_founded_in(A,B) <-> (all C -(subset(C,B) & C != empty_set & (all D -(in(D,C) & disjoint(fiber(A,D),C))))))))) # label(d3_wellord1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 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].
% 0.76/1.08 8 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 9 $T # label(dt_k1_wellord1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 10 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 11 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 12 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 13 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 14 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 15 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 16 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 17 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 18 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 19 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 20 (exists A (relation(A) & function(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 21 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 22 (exists A (relation(A) & empty(A) & function(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 23 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 24 (exists A (relation(A) & function(A) & one_to_one(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 25 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 26 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 27 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 28 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 29 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 30 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 31 (all A all B all C (in(A,B) & element(B,powerset(C)) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 32 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 33 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 34 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 35 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.09 36 -(all A (relation(A) -> (well_founded_relation(A) <-> is_well_founded_in(A,relation_field(A))))) # label(t5_wellord1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.09
% 0.76/1.09 ============================== end of process non-clausal formulas ===
% 0.76/1.09
% 0.76/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.76/1.09
% 0.76/1.09 ============================== PREDICATE ELIMINATION =================
% 0.76/1.09 37 -relation(A) | -empty(A) | -function(A) | one_to_one(A) # label(cc2_funct_1) # label(axiom). [clausify(3)].
% 0.76/1.09 38 relation(c1) # label(rc1_funct_1) # label(axiom). [clausify(20)].
% 0.76/1.09 39 relation(c3) # label(rc2_funct_1) # label(axiom). [clausify(22)].
% 0.76/1.09 40 relation(c5) # label(rc3_funct_1) # label(axiom). [clausify(24)].
% 0.76/1.09 41 relation(c6) # label(t5_wellord1) # label(negated_conjecture). [clausify(36)].
% 0.76/1.09 Derived: -empty(c1) | -function(c1) | one_to_one(c1). [resolve(37,a,38,a)].
% 0.76/1.09 Derived: -empty(c3) | -function(c3) | one_to_one(c3). [resolve(37,a,39,a)].
% 0.76/1.09 Derived: -empty(c5) | -function(c5) | one_to_one(c5). [resolve(37,a,40,a)].
% 0.76/1.09 Derived: -empty(c6) | -function(c6) | one_to_one(c6). [resolve(37,a,41,a)].
% 0.76/1.09 42 -relation(A) | well_founded_relation(A) | empty_set != f2(A) # label(d2_wellord1) # label(axiom). [clausify(5)].
% 0.76/1.09 Derived: well_founded_relation(c1) | empty_set != f2(c1). [resolve(42,a,38,a)].
% 0.76/1.09 Derived: well_founded_relation(c3) | empty_set != f2(c3). [resolve(42,a,39,a)].
% 0.76/1.09 Derived: well_founded_relation(c5) | empty_set != f2(c5). [resolve(42,a,40,a)].
% 0.76/1.09 Derived: well_founded_relation(c6) | empty_set != f2(c6). [resolve(42,a,41,a)].
% 0.76/1.09 43 -relation(A) | well_founded_relation(A) | subset(f2(A),relation_field(A)) # label(d2_wellord1) # label(axiom). [clausify(5)].
% 0.76/1.09 Derived: well_founded_relation(c1) | subset(f2(c1),relation_field(c1)). [resolve(43,a,38,a)].
% 0.76/1.09 Derived: well_founded_relation(c3) | subset(f2(c3),relation_field(c3)). [resolve(43,a,39,a)].
% 0.76/1.09 Derived: well_founded_relation(c5) | subset(f2(c5),relation_field(c5)). [resolve(43,a,40,a)].
% 0.76/1.09 Derived: well_founded_relation(c6) | subset(f2(c6),relation_field(c6)). [resolve(43,a,41,a)].
% 0.76/1.09 44 -relation(A) | is_well_founded_in(A,B) | subset(f4(A,B),B) # label(d3_wellord1) # label(axiom). [clausify(6)].
% 0.76/1.09 Derived: is_well_founded_in(c1,A) | subset(f4(c1,A),A). [resolve(44,a,38,a)].
% 0.76/1.09 Derived: is_well_founded_in(c3,A) | subset(f4(c3,A),A). [resolve(44,a,39,a)].
% 0.76/1.09 Derived: is_well_founded_in(c5,A) | subset(f4(c5,A),A). [resolve(44,a,40,a)].
% 0.76/1.09 Derived: is_well_founded_in(c6,A) | subset(f4(c6,A),A). [resolve(44,a,41,a)].
% 0.76/1.09 45 -relation(A) | is_well_founded_in(A,B) | f4(A,B) != empty_set # label(d3_wellord1) # label(axiom). [clausify(6)].
% 0.76/1.09 Derived: is_well_founded_in(c1,A) | f4(c1,A) != empty_set. [resolve(45,a,38,a)].
% 0.76/1.09 Derived: is_well_founded_in(c3,A) | f4(c3,A) != empty_set. [resolve(45,a,39,a)].
% 0.76/1.09 Derived: is_well_founded_in(c5,A) | f4(c5,A) != empty_set. [resolve(45,a,40,a)].
% 0.76/1.09 Derived: is_well_founded_in(c6,A) | f4(c6,A) != empty_set. [resolve(45,a,41,a)].
% 0.76/1.09 46 -relation(A) | relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) # label(d6_relat_1) # label(axiom). [clausify(7)].
% 0.76/1.09 Derived: relation_field(c1) = set_union2(relation_dom(c1),relation_rng(c1)). [resolve(46,a,38,a)].
% 0.76/1.09 Derived: relation_field(c3) = set_union2(relation_dom(c3),relation_rng(c3)). [resolve(46,a,39,a)].
% 0.76/1.09 Derived: relation_field(c5) = set_union2(relation_dom(c5),relation_rng(c5)). [resolve(46,a,40,a)].
% 0.76/1.09 Derived: relation_field(c6) = set_union2(relation_dom(c6),relation_rng(c6)). [resolve(46,a,41,a)].
% 0.76/1.09 47 -relation(A) | well_founded_relation(A) | -in(B,f2(A)) | -disjoint(fiber(A,B),f2(A)) # label(d2_wellord1) # label(axiom). [clausify(5)].
% 0.76/1.09 Derived: well_founded_relation(c1) | -in(A,f2(c1)) | -disjoint(fiber(c1,A),f2(c1)). [resolve(47,a,38,a)].
% 0.76/1.09 Derived: well_founded_relation(c3) | -in(A,f2(c3)) | -disjoint(fiber(c3,A),f2(c3)). [resolve(47,a,39,a)].
% 0.76/1.09 Derived: well_founded_relation(c5) | -in(A,f2(c5)) | -disjoint(fiber(c5,A),f2(c5)). [resolve(47,a,40,a)].
% 0.76/1.09 Derived: well_founded_relation(c6) | -in(A,f2(c6)) | -disjoint(fiber(c6,A),f2(c6)). [resolve(47,a,41,a)].
% 0.76/1.09 48 -relation(A) | -well_founded_relation(A) | -subset(B,relation_field(A)) | empty_set = B | in(f1(A,B),B) # label(d2_wellord1) # label(axiom). [clausify(5)].
% 0.76/1.09 Derived: -well_founded_relation(c1) | -subset(A,relation_field(c1)) | empty_set = A | in(f1(c1,A),A). [resolve(48,a,38,a)].
% 0.76/1.09 Derived: -well_founded_relation(c3) | -subset(A,relation_field(c3)) | empty_set = A | in(f1(c3,A),A). [resolve(48,a,39,a)].
% 0.76/1.09 Derived: -well_founded_relation(c5) | -subset(A,relation_field(c5)) | empty_set = A | in(f1(c5,A),A). [resolve(48,a,40,a)].
% 0.76/1.09 Derived: -well_founded_relation(c6) | -subset(A,relation_field(c6)) | empty_set = A | in(f1(c6,A),A). [resolve(48,a,41,a)].
% 0.76/1.09 49 -relation(A) | -is_well_founded_in(A,B) | -subset(C,B) | C = empty_set | in(f3(A,B,C),C) # label(d3_wellord1) # label(axiom). [clausify(6)].
% 0.76/1.09 Derived: -is_well_founded_in(c1,A) | -subset(B,A) | B = empty_set | in(f3(c1,A,B),B). [resolve(49,a,38,a)].
% 0.76/1.09 Derived: -is_well_founded_in(c3,A) | -subset(B,A) | B = empty_set | in(f3(c3,A,B),B). [resolve(49,a,39,a)].
% 0.76/1.09 Derived: -is_well_founded_in(c5,A) | -subset(B,A) | B = empty_set | in(f3(c5,A,B),B). [resolve(49,a,40,a)].
% 0.76/1.09 Derived: -is_well_founded_in(c6,A) | -subset(B,A) | B = empty_set | in(f3(c6,A,B),B). [resolve(49,a,41,a)].
% 0.76/1.09 50 -relation(A) | is_well_founded_in(A,B) | -in(C,f4(A,B)) | -disjoint(fiber(A,C),f4(A,B)) # label(d3_wellord1) # label(axiom). [clausify(6)].
% 0.76/1.09 Derived: is_well_founded_in(c1,A) | -in(B,f4(c1,A)) | -disjoint(fiber(c1,B),f4(c1,A)). [resolve(50,a,38,a)].
% 0.76/1.09 Derived: is_well_founded_in(c3,A) | -in(B,f4(c3,A)) | -disjoint(fiber(c3,B),f4(c3,A)). [resolve(50,a,39,a)].
% 0.76/1.09 Derived: is_well_founded_in(c5,A) | -in(B,f4(c5,A)) | -disjoint(fiber(c5,B),f4(c5,A)). [resolve(50,a,40,a)].
% 0.76/1.09 Derived: is_well_founded_in(c6,A) | -in(B,f4(c6,A)) | -disjoint(fiber(c6,B),f4(c6,A)). [resolve(50,a,41,a)].
% 0.76/1.09 51 -relation(A) | -well_founded_relation(A) | -subset(B,relation_field(A)) | empty_set = B | disjoint(fiber(A,f1(A,B)),B) # label(d2_wellord1) # label(axiom). [clausify(5)].
% 55.83/56.17 Derived: -well_founded_relation(c1) | -subset(A,relation_field(c1)) | empty_set = A | disjoint(fiber(c1,f1(c1,A)),A). [resolve(51,a,38,a)].
% 55.83/56.17 Derived: -well_founded_relation(c3) | -subset(A,relation_field(c3)) | empty_set = A | disjoint(fiber(c3,f1(c3,A)),A). [resolve(51,a,39,a)].
% 55.83/56.17 Derived: -well_founded_relation(c5) | -subset(A,relation_field(c5)) | empty_set = A | disjoint(fiber(c5,f1(c5,A)),A). [resolve(51,a,40,a)].
% 55.83/56.17 Derived: -well_founded_relation(c6) | -subset(A,relation_field(c6)) | empty_set = A | disjoint(fiber(c6,f1(c6,A)),A). [resolve(51,a,41,a)].
% 55.83/56.17 52 -relation(A) | -is_well_founded_in(A,B) | -subset(C,B) | C = empty_set | disjoint(fiber(A,f3(A,B,C)),C) # label(d3_wellord1) # label(axiom). [clausify(6)].
% 55.83/56.17 Derived: -is_well_founded_in(c1,A) | -subset(B,A) | B = empty_set | disjoint(fiber(c1,f3(c1,A,B)),B). [resolve(52,a,38,a)].
% 55.83/56.17 Derived: -is_well_founded_in(c3,A) | -subset(B,A) | B = empty_set | disjoint(fiber(c3,f3(c3,A,B)),B). [resolve(52,a,39,a)].
% 55.83/56.17 Derived: -is_well_founded_in(c5,A) | -subset(B,A) | B = empty_set | disjoint(fiber(c5,f3(c5,A,B)),B). [resolve(52,a,40,a)].
% 55.83/56.17 Derived: -is_well_founded_in(c6,A) | -subset(B,A) | B = empty_set | disjoint(fiber(c6,f3(c6,A,B)),B). [resolve(52,a,41,a)].
% 55.83/56.17
% 55.83/56.17 ============================== end predicate elimination =============
% 55.83/56.17
% 55.83/56.17 Auto_denials: (non-Horn, no changes).
% 55.83/56.17
% 55.83/56.17 Term ordering decisions:
% 55.83/56.17 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. fiber=1. set_union2=1. f1=1. f4=1. relation_field=1. relation_dom=1. relation_rng=1. powerset=1. f2=1. f5=1. f3=1.
% 55.83/56.17
% 55.83/56.17 ============================== end of process initial clauses ========
% 55.83/56.17
% 55.83/56.17 ============================== CLAUSES FOR SEARCH ====================
% 55.83/56.17
% 55.83/56.17 ============================== end of clauses for search =============
% 55.83/56.17
% 55.83/56.17 ============================== SEARCH ================================
% 55.83/56.17
% 55.83/56.17 % Starting search at 0.01 seconds.
% 55.83/56.17
% 55.83/56.17 Low Water (keep): wt=117.000, iters=3467
% 55.83/56.17
% 55.83/56.17 Low Water (keep): wt=94.000, iters=3412
% 55.83/56.17
% 55.83/56.17 Low Water (keep): wt=85.000, iters=3339
% 55.83/56.17
% 55.83/56.17 Low Water (keep): wt=51.000, iters=3880
% 55.83/56.17
% 55.83/56.17 ============================== PROOF =================================
% 55.83/56.17 % SZS status Theorem
% 55.83/56.17 % SZS output start Refutation
% 55.83/56.17
% 55.83/56.17 % Proof 1 at 54.99 (+ 0.06) seconds.
% 55.83/56.17 % Length of proof is 57.
% 55.83/56.17 % Level of proof is 23.
% 55.83/56.17 % Maximum clause weight is 25.000.
% 55.83/56.17 % Given clauses 1460.
% 55.83/56.17
% 55.83/56.17 5 (all A (relation(A) -> (well_founded_relation(A) <-> (all B -(subset(B,relation_field(A)) & B != empty_set & (all C -(in(C,B) & disjoint(fiber(A,C),B)))))))) # label(d2_wellord1) # label(axiom) # label(non_clause). [assumption].
% 55.83/56.17 6 (all A (relation(A) -> (all B (is_well_founded_in(A,B) <-> (all C -(subset(C,B) & C != empty_set & (all D -(in(D,C) & disjoint(fiber(A,D),C))))))))) # label(d3_wellord1) # label(axiom) # label(non_clause). [assumption].
% 55.83/56.17 36 -(all A (relation(A) -> (well_founded_relation(A) <-> is_well_founded_in(A,relation_field(A))))) # label(t5_wellord1) # label(negated_conjecture) # label(non_clause). [assumption].
% 55.83/56.17 41 relation(c6) # label(t5_wellord1) # label(negated_conjecture). [clausify(36)].
% 55.83/56.17 42 -relation(A) | well_founded_relation(A) | empty_set != f2(A) # label(d2_wellord1) # label(axiom). [clausify(5)].
% 55.83/56.17 43 -relation(A) | well_founded_relation(A) | subset(f2(A),relation_field(A)) # label(d2_wellord1) # label(axiom). [clausify(5)].
% 55.83/56.17 44 -relation(A) | is_well_founded_in(A,B) | subset(f4(A,B),B) # label(d3_wellord1) # label(axiom). [clausify(6)].
% 55.83/56.17 45 -relation(A) | is_well_founded_in(A,B) | f4(A,B) != empty_set # label(d3_wellord1) # label(axiom). [clausify(6)].
% 55.83/56.17 47 -relation(A) | well_founded_relation(A) | -in(B,f2(A)) | -disjoint(fiber(A,B),f2(A)) # label(d2_wellord1) # label(axiom). [clausify(5)].
% 55.83/56.17 48 -relation(A) | -well_founded_relation(A) | -subset(B,relation_field(A)) | empty_set = B | in(f1(A,B),B) # label(d2_wellord1) # label(axiom). [clausify(5)].
% 55.83/56.17 49 -relation(A) | -is_well_founded_in(A,B) | -subset(C,B) | C = empty_set | in(f3(A,B,C),C) # label(d3_wellord1) # label(axiom). [clausify(6)].
% 55.83/56.17 50 -relation(A) | is_well_founded_in(A,B) | -in(C,f4(A,B)) | -disjoint(fiber(A,C),f4(A,B)) # label(d3_wellord1) # label(axiom). [clausify(6)].
% 55.83/56.17 51 -relation(A) | -well_founded_relation(A) | -subset(B,relation_field(A)) | empty_set = B | disjoint(fiber(A,f1(A,B)),B) # label(d2_wellord1) # label(axiom). [clausify(5)].
% 55.83/56.17 52 -relation(A) | -is_well_founded_in(A,B) | -subset(C,B) | C = empty_set | disjoint(fiber(A,f3(A,B,C)),C) # label(d3_wellord1) # label(axiom). [clausify(6)].
% 55.83/56.17 60 well_founded_relation(c6) | is_well_founded_in(c6,relation_field(c6)) # label(t5_wellord1) # label(negated_conjecture). [clausify(36)].
% 55.83/56.17 65 -well_founded_relation(c6) | -is_well_founded_in(c6,relation_field(c6)) # label(t5_wellord1) # label(negated_conjecture). [clausify(36)].
% 55.83/56.17 83 well_founded_relation(c6) | empty_set != f2(c6). [resolve(42,a,41,a)].
% 55.83/56.17 84 well_founded_relation(c6) | f2(c6) != empty_set. [copy(83),flip(b)].
% 55.83/56.17 88 well_founded_relation(c6) | subset(f2(c6),relation_field(c6)). [resolve(43,a,41,a)].
% 55.83/56.17 92 is_well_founded_in(c6,A) | subset(f4(c6,A),A). [resolve(44,a,41,a)].
% 55.83/56.17 96 is_well_founded_in(c6,A) | f4(c6,A) != empty_set. [resolve(45,a,41,a)].
% 55.83/56.17 108 well_founded_relation(c6) | -in(A,f2(c6)) | -disjoint(fiber(c6,A),f2(c6)). [resolve(47,a,41,a)].
% 55.83/56.17 112 -well_founded_relation(c6) | -subset(A,relation_field(c6)) | empty_set = A | in(f1(c6,A),A). [resolve(48,a,41,a)].
% 55.83/56.17 119 -is_well_founded_in(c6,A) | -subset(B,A) | B = empty_set | in(f3(c6,A,B),B). [resolve(49,a,41,a)].
% 55.83/56.17 120 -is_well_founded_in(c6,A) | -subset(B,A) | empty_set = B | in(f3(c6,A,B),B). [copy(119),flip(c)].
% 55.83/56.17 124 is_well_founded_in(c6,A) | -in(B,f4(c6,A)) | -disjoint(fiber(c6,B),f4(c6,A)). [resolve(50,a,41,a)].
% 55.83/56.17 128 -well_founded_relation(c6) | -subset(A,relation_field(c6)) | empty_set = A | disjoint(fiber(c6,f1(c6,A)),A). [resolve(51,a,41,a)].
% 55.83/56.17 135 -is_well_founded_in(c6,A) | -subset(B,A) | B = empty_set | disjoint(fiber(c6,f3(c6,A,B)),B). [resolve(52,a,41,a)].
% 55.83/56.17 136 -is_well_founded_in(c6,A) | -subset(B,A) | empty_set = B | disjoint(fiber(c6,f3(c6,A,B)),B). [copy(135),flip(c)].
% 55.83/56.17 166 subset(f4(c6,relation_field(c6)),relation_field(c6)) | -well_founded_relation(c6). [resolve(92,a,65,b)].
% 55.83/56.17 176 -subset(A,relation_field(c6)) | empty_set = A | in(f3(c6,relation_field(c6),A),A) | well_founded_relation(c6). [resolve(120,a,60,b)].
% 55.83/56.17 183 -subset(A,relation_field(c6)) | empty_set = A | disjoint(fiber(c6,f3(c6,relation_field(c6),A)),A) | well_founded_relation(c6). [resolve(136,a,60,b)].
% 55.83/56.17 356 f2(c6) = empty_set | in(f3(c6,relation_field(c6),f2(c6)),f2(c6)) | well_founded_relation(c6). [resolve(176,a,88,b),flip(a),merge(d)].
% 55.83/56.17 501 f2(c6) = empty_set | disjoint(fiber(c6,f3(c6,relation_field(c6),f2(c6))),f2(c6)) | well_founded_relation(c6). [resolve(183,a,88,b),flip(a),merge(d)].
% 55.83/56.17 697 f2(c6) = empty_set | well_founded_relation(c6) | -in(f3(c6,relation_field(c6),f2(c6)),f2(c6)). [resolve(501,b,108,c),merge(c)].
% 55.83/56.17 699 f2(c6) = empty_set | well_founded_relation(c6). [resolve(697,c,356,b),merge(c),merge(d)].
% 55.83/56.17 711 f2(c6) = empty_set | subset(f4(c6,relation_field(c6)),relation_field(c6)). [resolve(699,b,166,b)].
% 55.83/56.17 718 f2(c6) = empty_set | -well_founded_relation(c6) | f4(c6,relation_field(c6)) = empty_set | disjoint(fiber(c6,f1(c6,f4(c6,relation_field(c6)))),f4(c6,relation_field(c6))). [resolve(711,b,128,b),flip(c)].
% 55.83/56.17 719 f2(c6) = empty_set | -well_founded_relation(c6) | f4(c6,relation_field(c6)) = empty_set | in(f1(c6,f4(c6,relation_field(c6))),f4(c6,relation_field(c6))). [resolve(711,b,112,b),flip(c)].
% 55.83/56.17 2923 f2(c6) = empty_set | f4(c6,relation_field(c6)) = empty_set | disjoint(fiber(c6,f1(c6,f4(c6,relation_field(c6)))),f4(c6,relation_field(c6))). [resolve(718,b,699,b),merge(d)].
% 55.83/56.17 2926 f2(c6) = empty_set | f4(c6,relation_field(c6)) = empty_set | in(f1(c6,f4(c6,relation_field(c6))),f4(c6,relation_field(c6))). [resolve(719,b,699,b),merge(d)].
% 55.83/56.17 4222 f2(c6) = empty_set | f4(c6,relation_field(c6)) = empty_set | is_well_founded_in(c6,relation_field(c6)) | -in(f1(c6,f4(c6,relation_field(c6))),f4(c6,relation_field(c6))). [resolve(2923,c,124,c)].
% 55.83/56.17 8965 f2(c6) = empty_set | f4(c6,relation_field(c6)) = empty_set | is_well_founded_in(c6,relation_field(c6)). [resolve(4222,d,2926,c),merge(d),merge(e)].
% 55.83/56.17 8973 f2(c6) = empty_set | f4(c6,relation_field(c6)) = empty_set | -well_founded_relation(c6). [resolve(8965,c,65,b)].
% 55.83/56.17 8974 f2(c6) = empty_set | f4(c6,relation_field(c6)) = empty_set. [resolve(8973,c,699,b),merge(c)].
% 55.83/56.17 8975 f2(c6) = empty_set | is_well_founded_in(c6,relation_field(c6)). [resolve(8974,b,96,b)].
% 55.83/56.17 8984 f2(c6) = empty_set | -well_founded_relation(c6). [resolve(8975,b,65,b)].
% 55.83/56.17 8990 f2(c6) = empty_set. [resolve(8984,b,699,b),merge(b)].
% 55.83/56.17 8994 well_founded_relation(c6). [back_rewrite(84),rewrite([8990(4)]),xx(b)].
% 55.83/56.17 9022 subset(f4(c6,relation_field(c6)),relation_field(c6)). [back_unit_del(166),unit_del(b,8994)].
% 55.83/56.17 9023 -subset(A,relation_field(c6)) | empty_set = A | disjoint(fiber(c6,f1(c6,A)),A). [back_unit_del(128),unit_del(a,8994)].
% 55.83/56.17 9024 -subset(A,relation_field(c6)) | empty_set = A | in(f1(c6,A),A). [back_unit_del(112),unit_del(a,8994)].
% 55.83/56.17 9025 -is_well_founded_in(c6,relation_field(c6)). [back_unit_del(65),unit_del(a,8994)].
% 55.83/56.17 9033 f4(c6,relation_field(c6)) != empty_set. [ur(96,a,9025,a)].
% 55.83/56.17 9100 in(f1(c6,f4(c6,relation_field(c6))),f4(c6,relation_field(c6))). [resolve(9024,a,9022,a),flip(a),unit_del(a,9033)].
% 55.83/56.17 9104 -disjoint(fiber(c6,f1(c6,f4(c6,relation_field(c6)))),f4(c6,relation_field(c6))). [ur(124,a,9025,a,b,9100,a)].
% 55.83/56.17 9120 $F. [resolve(9023,a,9022,a),flip(a),unit_del(a,9033),unit_del(b,9104)].
% 55.83/56.17
% 55.83/56.17 % SZS output end Refutation
% 55.83/56.17 ============================== end of proof ==========================
% 55.83/56.17
% 55.83/56.17 ============================== STATISTICS ============================
% 55.83/56.17
% 55.83/56.17 Given=1460. Generated=48044. Kept=9050. proofs=1.
% 55.83/56.17 Usable=1259. Sos=5542. Demods=11. Limbo=0, Disabled=2342. Hints=0.
% 55.83/56.17 Megabytes=17.78.
% 55.83/56.17 User_CPU=54.99, System_CPU=0.06, Wall_clock=55.
% 55.83/56.17
% 55.83/56.17 ============================== end of statistics =====================
% 55.83/56.17
% 55.83/56.17 ============================== end of search =========================
% 55.83/56.17
% 55.83/56.17 THEOREM PROVED
% 55.83/56.17 % SZS status Theorem
% 55.83/56.17
% 55.83/56.17 Exiting with 1 proof.
% 55.83/56.17
% 55.83/56.17 Process 7156 exit (max_proofs) Sun Jun 19 20:22:20 2022
% 55.83/56.17 Prover9 interrupted
%------------------------------------------------------------------------------