TSTP Solution File: SEU362+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU362+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 13:31:16 EDT 2022
% Result : Theorem 0.83s 1.10s
% Output : Refutation 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU362+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 00:15:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.00 ============================== Prover9 ===============================
% 0.43/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00 Process 16308 was started by sandbox on n007.cluster.edu,
% 0.43/1.00 Sun Jun 19 00:15:44 2022
% 0.43/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16155_n007.cluster.edu".
% 0.43/1.00 ============================== end of head ===========================
% 0.43/1.00
% 0.43/1.00 ============================== INPUT =================================
% 0.43/1.00
% 0.43/1.00 % Reading from file /tmp/Prover9_16155_n007.cluster.edu
% 0.43/1.00
% 0.43/1.00 set(prolog_style_variables).
% 0.43/1.00 set(auto2).
% 0.43/1.00 % set(auto2) -> set(auto).
% 0.43/1.00 % set(auto) -> set(auto_inference).
% 0.43/1.00 % set(auto) -> set(auto_setup).
% 0.43/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00 % set(auto) -> set(auto_limits).
% 0.43/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00 % set(auto) -> set(auto_denials).
% 0.43/1.00 % set(auto) -> set(auto_process).
% 0.43/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00 % set(auto2) -> assign(stats, some).
% 0.43/1.00 % set(auto2) -> clear(echo_input).
% 0.43/1.00 % set(auto2) -> set(quiet).
% 0.43/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00 % set(auto2) -> clear(print_given).
% 0.43/1.00 assign(lrs_ticks,-1).
% 0.43/1.00 assign(sos_limit,10000).
% 0.43/1.00 assign(order,kbo).
% 0.43/1.00 set(lex_order_vars).
% 0.43/1.00 clear(print_given).
% 0.43/1.00
% 0.43/1.00 % formulas(sos). % not echoed (42 formulas)
% 0.43/1.00
% 0.43/1.00 ============================== end of input ==========================
% 0.43/1.00
% 0.43/1.00 % From the command line: assign(max_seconds, 300).
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00
% 0.43/1.00 % Formulas that are not ordinary clauses:
% 0.43/1.00 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 2 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 3 (all A all B all C (element(C,powerset(cartesian_product2(A,B))) -> relation(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 4 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 5 (all A (rel_str(A) -> (all B (rel_str(B) -> (subrelstr(B,A) <-> subset(the_carrier(B),the_carrier(A)) & subset(the_InternalRel(B),the_InternalRel(A))))))) # label(d13_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 6 (all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (related(A,B,C) <-> in(ordered_pair(B,C),the_InternalRel(A))))))))) # label(d9_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 7 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 8 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 9 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 10 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 11 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 12 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 13 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 14 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 15 (all A (rel_str(A) -> (all B (subrelstr(B,A) -> rel_str(B))))) # label(dt_m1_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 16 (all A all B all C (relation_of2_as_subset(C,A,B) -> element(C,powerset(cartesian_product2(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 17 (all A (rel_str(A) -> relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)))) # label(dt_u1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 18 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 19 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 20 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 21 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 22 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 23 (all A (rel_str(A) -> (exists B subrelstr(B,A)))) # label(existence_m1_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 24 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 25 (all A all B (finite(A) & finite(B) -> finite(cartesian_product2(A,B)))) # label(fc14_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 26 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 27 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 28 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 29 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 30 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 31 (all A all B all C (relation_of2_as_subset(C,A,B) <-> relation_of2(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 32 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 33 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 34 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 35 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 36 (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].
% 0.43/1.00 37 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 38 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 39 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 40 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 41 -(all A (rel_str(A) -> (all B (subrelstr(B,A) -> (all C (element(C,the_carrier(A)) -> (all D (element(D,the_carrier(A)) -> (all E (element(E,the_carrier(B)) -> (all F (element(F,the_carrier(B)) -> (E = C & F = D & related(B,E,F) -> related(A,C,D)))))))))))))) # label(t60_yellow_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.00
% 0.43/1.00 ============================== end of process non-clausal formulas ===
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.00
% 0.43/1.00 ============================== PREDICATE ELIMINATION =================
% 0.43/1.00 42 -rel_str(A) | -subrelstr(B,A) | rel_str(B) # label(dt_m1_yellow_0) # label(axiom). [clausify(15)].
% 0.43/1.00 43 subrelstr(c7,c6) # label(t60_yellow_0) # label(negated_conjecture). [clausify(41)].
% 0.43/1.00 44 -rel_str(A) | subrelstr(f3(A),A) # label(existence_m1_yellow_0) # label(axiom). [clausify(23)].
% 0.43/1.00 Derived: -rel_str(c6) | rel_str(c7). [resolve(42,b,43,a)].
% 0.43/1.00 Derived: -rel_str(A) | rel_str(f3(A)) | -rel_str(A). [resolve(42,b,44,b)].
% 0.43/1.00 45 -rel_str(A) | -rel_str(B) | -subrelstr(B,A) | subset(the_carrier(B),the_carrier(A)) # label(d13_yellow_0) # label(axiom). [clausify(5)].
% 0.83/1.10 Derived: -rel_str(c6) | -rel_str(c7) | subset(the_carrier(c7),the_carrier(c6)). [resolve(45,c,43,a)].
% 0.83/1.10 Derived: -rel_str(A) | -rel_str(f3(A)) | subset(the_carrier(f3(A)),the_carrier(A)) | -rel_str(A). [resolve(45,c,44,b)].
% 0.83/1.10 46 -rel_str(A) | -rel_str(B) | -subrelstr(B,A) | subset(the_InternalRel(B),the_InternalRel(A)) # label(d13_yellow_0) # label(axiom). [clausify(5)].
% 0.83/1.10 Derived: -rel_str(c6) | -rel_str(c7) | subset(the_InternalRel(c7),the_InternalRel(c6)). [resolve(46,c,43,a)].
% 0.83/1.10 Derived: -rel_str(A) | -rel_str(f3(A)) | subset(the_InternalRel(f3(A)),the_InternalRel(A)) | -rel_str(A). [resolve(46,c,44,b)].
% 0.83/1.10 47 -rel_str(A) | -rel_str(B) | subrelstr(B,A) | -subset(the_carrier(B),the_carrier(A)) | -subset(the_InternalRel(B),the_InternalRel(A)) # label(d13_yellow_0) # label(axiom). [clausify(5)].
% 0.83/1.10 48 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(35)].
% 0.83/1.10 49 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(32)].
% 0.83/1.10 50 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(35)].
% 0.83/1.10 Derived: element(A,powerset(A)). [resolve(48,b,49,a)].
% 0.83/1.10 51 -rel_str(c6) | -rel_str(c7) | subset(the_carrier(c7),the_carrier(c6)). [resolve(45,c,43,a)].
% 0.83/1.10 Derived: -rel_str(c6) | -rel_str(c7) | element(the_carrier(c7),powerset(the_carrier(c6))). [resolve(51,c,48,b)].
% 0.83/1.10 52 -rel_str(A) | -rel_str(f3(A)) | subset(the_carrier(f3(A)),the_carrier(A)) | -rel_str(A). [resolve(45,c,44,b)].
% 0.83/1.10 Derived: -rel_str(A) | -rel_str(f3(A)) | -rel_str(A) | element(the_carrier(f3(A)),powerset(the_carrier(A))). [resolve(52,c,48,b)].
% 0.83/1.10 53 -rel_str(c6) | -rel_str(c7) | subset(the_InternalRel(c7),the_InternalRel(c6)). [resolve(46,c,43,a)].
% 0.83/1.10 Derived: -rel_str(c6) | -rel_str(c7) | element(the_InternalRel(c7),powerset(the_InternalRel(c6))). [resolve(53,c,48,b)].
% 0.83/1.10 54 -rel_str(A) | -rel_str(f3(A)) | subset(the_InternalRel(f3(A)),the_InternalRel(A)) | -rel_str(A). [resolve(46,c,44,b)].
% 0.83/1.10 Derived: -rel_str(A) | -rel_str(f3(A)) | -rel_str(A) | element(the_InternalRel(f3(A)),powerset(the_InternalRel(A))). [resolve(54,c,48,b)].
% 0.83/1.10 55 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(31)].
% 0.83/1.10 56 relation_of2(f1(A,B),A,B) # label(existence_m1_relset_1) # label(axiom). [clausify(21)].
% 0.83/1.10 57 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(31)].
% 0.83/1.10 Derived: relation_of2_as_subset(f1(A,B),A,B). [resolve(55,b,56,a)].
% 0.83/1.10 58 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(16)].
% 0.83/1.10 59 relation_of2_as_subset(f4(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(24)].
% 0.83/1.10 60 -rel_str(A) | relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(dt_u1_orders_2) # label(axiom). [clausify(17)].
% 0.83/1.10 Derived: element(f4(A,B),powerset(cartesian_product2(A,B))). [resolve(58,a,59,a)].
% 0.83/1.10 Derived: element(the_InternalRel(A),powerset(cartesian_product2(the_carrier(A),the_carrier(A)))) | -rel_str(A). [resolve(58,a,60,b)].
% 0.83/1.10 61 relation_of2_as_subset(f1(A,B),A,B). [resolve(55,b,56,a)].
% 0.83/1.10 Derived: element(f1(A,B),powerset(cartesian_product2(A,B))). [resolve(61,a,58,a)].
% 0.83/1.10
% 0.83/1.10 ============================== end predicate elimination =============
% 0.83/1.10
% 0.83/1.10 Auto_denials: (non-Horn, no changes).
% 0.83/1.10
% 0.83/1.10 Term ordering decisions:
% 0.83/1.10 Function symbol KB weights: empty_set=1. c1=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. cartesian_product2=1. ordered_pair=1. f1=1. f4=1. the_carrier=1. powerset=1. the_InternalRel=1. f2=1. f3=1. f5=1. f6=1.
% 0.83/1.10
% 0.83/1.10 ============================== end of process initial clauses ========
% 0.83/1.10
% 0.83/1.10 ============================== CLAUSES FOR SEARCH ====================
% 0.83/1.10
% 0.83/1.10 ============================== end of clauses for search =============
% 0.83/1.10
% 0.83/1.10 ============================== SEARCH ================================
% 0.83/1.10
% 0.83/1.10 % Starting search at 0.02 seconds.
% 0.83/1.10
% 0.83/1.10 ============================== PROOF =================================
% 0.83/1.10 % SZS status Theorem
% 0.83/1.10 % SZS output start Refutation
% 0.83/1.10
% 0.83/1.10 % Proof 1 at 0.11 (+ 0.00) seconds.
% 0.83/1.10 % Length of proof is 39.
% 0.83/1.10 % Level of proof is 7.
% 0.83/1.10 % Maximum clause weight is 20.000.
% 0.83/1.10 % Given clauses 288.
% 0.83/1.10
% 0.83/1.10 5 (all A (rel_str(A) -> (all B (rel_str(B) -> (subrelstr(B,A) <-> subset(the_carrier(B),the_carrier(A)) & subset(the_InternalRel(B),the_InternalRel(A))))))) # label(d13_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 6 (all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (related(A,B,C) <-> in(ordered_pair(B,C),the_InternalRel(A))))))))) # label(d9_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 15 (all A (rel_str(A) -> (all B (subrelstr(B,A) -> rel_str(B))))) # label(dt_m1_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 34 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 35 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 36 (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].
% 0.83/1.10 37 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 41 -(all A (rel_str(A) -> (all B (subrelstr(B,A) -> (all C (element(C,the_carrier(A)) -> (all D (element(D,the_carrier(A)) -> (all E (element(E,the_carrier(B)) -> (all F (element(F,the_carrier(B)) -> (E = C & F = D & related(B,E,F) -> related(A,C,D)))))))))))))) # label(t60_yellow_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.83/1.10 42 -rel_str(A) | -subrelstr(B,A) | rel_str(B) # label(dt_m1_yellow_0) # label(axiom). [clausify(15)].
% 0.83/1.10 43 subrelstr(c7,c6) # label(t60_yellow_0) # label(negated_conjecture). [clausify(41)].
% 0.83/1.10 46 -rel_str(A) | -rel_str(B) | -subrelstr(B,A) | subset(the_InternalRel(B),the_InternalRel(A)) # label(d13_yellow_0) # label(axiom). [clausify(5)].
% 0.83/1.10 48 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(35)].
% 0.83/1.10 53 -rel_str(c6) | -rel_str(c7) | subset(the_InternalRel(c7),the_InternalRel(c6)). [resolve(46,c,43,a)].
% 0.83/1.10 66 rel_str(c6) # label(t60_yellow_0) # label(negated_conjecture). [clausify(41)].
% 0.83/1.10 67 c10 = c8 # label(t60_yellow_0) # label(negated_conjecture). [clausify(41)].
% 0.83/1.10 68 c11 = c9 # label(t60_yellow_0) # label(negated_conjecture). [clausify(41)].
% 0.83/1.10 70 element(c8,the_carrier(c6)) # label(t60_yellow_0) # label(negated_conjecture). [clausify(41)].
% 0.83/1.10 71 element(c9,the_carrier(c6)) # label(t60_yellow_0) # label(negated_conjecture). [clausify(41)].
% 0.83/1.10 72 element(c10,the_carrier(c7)) # label(t60_yellow_0) # label(negated_conjecture). [clausify(41)].
% 0.83/1.10 73 element(c8,the_carrier(c7)). [copy(72),rewrite([67(1)])].
% 0.83/1.10 74 element(c11,the_carrier(c7)) # label(t60_yellow_0) # label(negated_conjecture). [clausify(41)].
% 0.83/1.10 75 element(c9,the_carrier(c7)). [copy(74),rewrite([68(1)])].
% 0.83/1.10 76 related(c7,c10,c11) # label(t60_yellow_0) # label(negated_conjecture). [clausify(41)].
% 0.83/1.10 77 related(c7,c8,c9). [copy(76),rewrite([67(2),68(3)])].
% 0.83/1.10 84 -related(c6,c8,c9) # label(t60_yellow_0) # label(negated_conjecture). [clausify(41)].
% 0.83/1.10 87 -in(A,B) | -element(B,powerset(C)) | -empty(C) # label(t5_subset) # label(axiom). [clausify(37)].
% 0.83/1.10 96 -element(A,B) | empty(B) | in(A,B) # label(t2_subset) # label(axiom). [clausify(34)].
% 0.83/1.10 97 -in(A,B) | -element(B,powerset(C)) | element(A,C) # label(t4_subset) # label(axiom). [clausify(36)].
% 0.83/1.10 98 -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -related(A,B,C) | in(ordered_pair(B,C),the_InternalRel(A)) # label(d9_orders_2) # label(axiom). [clausify(6)].
% 0.83/1.10 99 -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | related(A,B,C) | -in(ordered_pair(B,C),the_InternalRel(A)) # label(d9_orders_2) # label(axiom). [clausify(6)].
% 0.83/1.10 100 -rel_str(c6) | rel_str(c7). [resolve(42,b,43,a)].
% 0.83/1.10 101 rel_str(c7). [copy(100),unit_del(a,66)].
% 0.83/1.10 109 -rel_str(c6) | -rel_str(c7) | element(the_InternalRel(c7),powerset(the_InternalRel(c6))). [resolve(53,c,48,b)].
% 0.83/1.10 110 element(the_InternalRel(c7),powerset(the_InternalRel(c6))). [copy(109),unit_del(a,66),unit_del(b,101)].
% 0.83/1.10 145 in(ordered_pair(c8,c9),the_InternalRel(c7)). [resolve(98,d,77,a),unit_del(a,101),unit_del(b,73),unit_del(c,75)].
% 0.83/1.10 146 -in(ordered_pair(c8,c9),the_InternalRel(c6)). [ur(99,a,66,a,b,70,a,c,71,a,d,84,a)].
% 0.83/1.10 345 -empty(the_InternalRel(c6)). [ur(87,a,145,a,b,110,a)].
% 0.83/1.10 741 -element(ordered_pair(c8,c9),the_InternalRel(c6)). [ur(96,b,345,a,c,146,a)].
% 0.83/1.10 1653 $F. [ur(97,b,110,a,c,741,a),unit_del(a,145)].
% 0.83/1.10
% 0.83/1.10 % SZS output end Refutation
% 0.83/1.10 ============================== end of proof ==========================
% 0.83/1.10
% 0.83/1.10 ============================== STATISTICS ============================
% 0.83/1.10
% 0.83/1.10 Given=288. Generated=1715. Kept=1582. proofs=1.
% 0.83/1.10 Usable=284. Sos=1280. Demods=4. Limbo=1, Disabled=85. Hints=0.
% 0.83/1.10 Megabytes=1.17.
% 0.83/1.10 User_CPU=0.11, System_CPU=0.00, Wall_clock=0.
% 0.83/1.10
% 0.83/1.10 ============================== end of statistics =====================
% 0.83/1.10
% 0.83/1.10 ============================== end of search =========================
% 0.83/1.10
% 0.83/1.10 THEOREM PROVED
% 0.83/1.10 % SZS status Theorem
% 0.83/1.10
% 0.83/1.10 Exiting with 1 proof.
% 0.83/1.10
% 0.83/1.10 Process 16308 exit (max_proofs) Sun Jun 19 00:15:44 2022
% 0.83/1.10 Prover9 interrupted
%------------------------------------------------------------------------------