TSTP Solution File: SEU114+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU114+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 13:29:04 EDT 2022
% Result : Theorem 1.52s 1.78s
% Output : Refutation 1.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU114+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.32 % Computer : n021.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Mon Jun 20 07:19:33 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.68/0.98 ============================== Prover9 ===============================
% 0.68/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.68/0.98 Process 15580 was started by sandbox on n021.cluster.edu,
% 0.68/0.98 Mon Jun 20 07:19:34 2022
% 0.68/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15240_n021.cluster.edu".
% 0.68/0.98 ============================== end of head ===========================
% 0.68/0.98
% 0.68/0.98 ============================== INPUT =================================
% 0.68/0.98
% 0.68/0.98 % Reading from file /tmp/Prover9_15240_n021.cluster.edu
% 0.68/0.98
% 0.68/0.98 set(prolog_style_variables).
% 0.68/0.98 set(auto2).
% 0.68/0.98 % set(auto2) -> set(auto).
% 0.68/0.98 % set(auto) -> set(auto_inference).
% 0.68/0.98 % set(auto) -> set(auto_setup).
% 0.68/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.68/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.68/0.98 % set(auto) -> set(auto_limits).
% 0.68/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.68/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.68/0.98 % set(auto) -> set(auto_denials).
% 0.68/0.98 % set(auto) -> set(auto_process).
% 0.68/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.68/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.68/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.68/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.68/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.68/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.68/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.68/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.68/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.68/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.68/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.68/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.68/0.98 % set(auto2) -> assign(stats, some).
% 0.68/0.98 % set(auto2) -> clear(echo_input).
% 0.68/0.98 % set(auto2) -> set(quiet).
% 0.68/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.68/0.98 % set(auto2) -> clear(print_given).
% 0.68/0.98 assign(lrs_ticks,-1).
% 0.68/0.98 assign(sos_limit,10000).
% 0.68/0.98 assign(order,kbo).
% 0.68/0.98 set(lex_order_vars).
% 0.68/0.98 clear(print_given).
% 0.68/0.98
% 0.68/0.98 % formulas(sos). % not echoed (36 formulas)
% 0.68/0.98
% 0.68/0.98 ============================== end of input ==========================
% 0.68/0.98
% 0.68/0.98 % From the command line: assign(max_seconds, 300).
% 0.68/0.98
% 0.68/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.68/0.98
% 0.68/0.98 % Formulas that are not ordinary clauses:
% 0.68/0.98 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.98 2 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.98 3 (all A (preboolean(A) -> cup_closed(A) & diff_closed(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.98 4 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.98 5 (all A (cup_closed(A) & diff_closed(A) -> preboolean(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.98 6 (all A all B (element(B,finite_subsets(A)) -> finite(B))) # label(cc3_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.98 7 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.98 8 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.98 9 (all A all B (preboolean(B) -> (B = finite_subsets(A) <-> (all C (in(C,B) <-> subset(C,A) & finite(C)))))) # label(d5_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.98 10 (all A preboolean(finite_subsets(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.98 11 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.98 12 (all A (-empty(powerset(A)) & cup_closed(powerset(A)) & diff_closed(powerset(A)) & preboolean(powerset(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.98 13 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.98 14 (all A (-empty(finite_subsets(A)) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))) # label(fc2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.98 15 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 16 (exists A (-empty(A) & cup_closed(A) & cap_closed(A) & diff_closed(A) & preboolean(A))) # label(rc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 17 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 18 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 19 (all A exists B (element(B,powerset(A)) & empty(B) & relation(B) & function(B) & one_to_one(B) & epsilon_transitive(B) & epsilon_connected(B) & ordinal(B) & natural(B) & finite(B))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 20 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 21 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 22 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 23 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 24 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 25 (all A all B (subset(A,B) & finite(B) -> finite(A))) # label(t13_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 26 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 27 (all A subset(finite_subsets(A),powerset(A))) # label(t26_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 28 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 29 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 30 (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].
% 0.68/0.99 31 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 32 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 33 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 34 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 35 -(all A (finite(A) -> finite_subsets(A) = powerset(A))) # label(t27_finsub_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.68/0.99
% 0.68/0.99 ============================== end of process non-clausal formulas ===
% 0.68/0.99
% 0.68/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.68/0.99
% 0.68/0.99 ============================== PREDICATE ELIMINATION =================
% 0.68/0.99 36 -cup_closed(A) | -diff_closed(A) | preboolean(A) # label(cc2_finsub_1) # label(axiom). [clausify(5)].
% 0.68/0.99 37 cup_closed(c2) # label(rc1_finsub_1) # label(axiom). [clausify(16)].
% 0.68/0.99 38 cup_closed(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(12)].
% 0.68/0.99 39 cup_closed(finite_subsets(A)) # label(fc2_finsub_1) # label(axiom). [clausify(14)].
% 0.68/0.99 40 -preboolean(A) | cup_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(3)].
% 0.68/0.99 Derived: -diff_closed(c2) | preboolean(c2). [resolve(36,a,37,a)].
% 0.68/0.99 Derived: -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(36,a,38,a)].
% 0.68/0.99 Derived: -diff_closed(finite_subsets(A)) | preboolean(finite_subsets(A)). [resolve(36,a,39,a)].
% 0.68/0.99 41 -preboolean(A) | diff_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(3)].
% 0.68/0.99 42 preboolean(c2) # label(rc1_finsub_1) # label(axiom). [clausify(16)].
% 0.68/0.99 43 preboolean(finite_subsets(A)) # label(dt_k5_finsub_1) # label(axiom). [clausify(10)].
% 0.68/0.99 44 preboolean(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(12)].
% 0.68/0.99 45 preboolean(finite_subsets(A)) # label(fc2_finsub_1) # label(axiom). [clausify(14)].
% 0.98/1.26 Derived: diff_closed(c2). [resolve(41,a,42,a)].
% 0.98/1.26 Derived: diff_closed(finite_subsets(A)). [resolve(41,a,43,a)].
% 0.98/1.26 Derived: diff_closed(powerset(A)). [resolve(41,a,44,a)].
% 0.98/1.26 46 -preboolean(A) | finite_subsets(B) != A | -in(C,A) | finite(C) # label(d5_finsub_1) # label(axiom). [clausify(9)].
% 0.98/1.26 Derived: finite_subsets(A) != c2 | -in(B,c2) | finite(B). [resolve(46,a,42,a)].
% 0.98/1.26 Derived: finite_subsets(A) != finite_subsets(B) | -in(C,finite_subsets(B)) | finite(C). [resolve(46,a,43,a)].
% 0.98/1.26 Derived: finite_subsets(A) != powerset(B) | -in(C,powerset(B)) | finite(C). [resolve(46,a,44,a)].
% 0.98/1.26 47 -preboolean(A) | finite_subsets(B) != A | -in(C,A) | subset(C,B) # label(d5_finsub_1) # label(axiom). [clausify(9)].
% 0.98/1.26 Derived: finite_subsets(A) != c2 | -in(B,c2) | subset(B,A). [resolve(47,a,42,a)].
% 0.98/1.26 Derived: finite_subsets(A) != finite_subsets(B) | -in(C,finite_subsets(B)) | subset(C,A). [resolve(47,a,43,a)].
% 0.98/1.26 Derived: finite_subsets(A) != powerset(B) | -in(C,powerset(B)) | subset(C,A). [resolve(47,a,44,a)].
% 0.98/1.26 48 -preboolean(A) | finite_subsets(B) != A | in(C,A) | -subset(C,B) | -finite(C) # label(d5_finsub_1) # label(axiom). [clausify(9)].
% 0.98/1.26 Derived: finite_subsets(A) != c2 | in(B,c2) | -subset(B,A) | -finite(B). [resolve(48,a,42,a)].
% 0.98/1.26 Derived: finite_subsets(A) != finite_subsets(B) | in(C,finite_subsets(B)) | -subset(C,A) | -finite(C). [resolve(48,a,43,a)].
% 0.98/1.26 Derived: finite_subsets(A) != powerset(B) | in(C,powerset(B)) | -subset(C,A) | -finite(C). [resolve(48,a,44,a)].
% 0.98/1.26 49 -preboolean(A) | finite_subsets(B) = A | in(f2(B,A),A) | finite(f2(B,A)) # label(d5_finsub_1) # label(axiom). [clausify(9)].
% 0.98/1.26 Derived: finite_subsets(A) = c2 | in(f2(A,c2),c2) | finite(f2(A,c2)). [resolve(49,a,42,a)].
% 0.98/1.26 Derived: finite_subsets(A) = finite_subsets(B) | in(f2(A,finite_subsets(B)),finite_subsets(B)) | finite(f2(A,finite_subsets(B))). [resolve(49,a,43,a)].
% 0.98/1.26 Derived: finite_subsets(A) = powerset(B) | in(f2(A,powerset(B)),powerset(B)) | finite(f2(A,powerset(B))). [resolve(49,a,44,a)].
% 0.98/1.26 50 -preboolean(A) | finite_subsets(B) = A | in(f2(B,A),A) | subset(f2(B,A),B) # label(d5_finsub_1) # label(axiom). [clausify(9)].
% 0.98/1.26 Derived: finite_subsets(A) = c2 | in(f2(A,c2),c2) | subset(f2(A,c2),A). [resolve(50,a,42,a)].
% 0.98/1.26 Derived: finite_subsets(A) = finite_subsets(B) | in(f2(A,finite_subsets(B)),finite_subsets(B)) | subset(f2(A,finite_subsets(B)),A). [resolve(50,a,43,a)].
% 0.98/1.26 Derived: finite_subsets(A) = powerset(B) | in(f2(A,powerset(B)),powerset(B)) | subset(f2(A,powerset(B)),A). [resolve(50,a,44,a)].
% 0.98/1.26 51 -preboolean(A) | finite_subsets(B) = A | -in(f2(B,A),A) | -subset(f2(B,A),B) | -finite(f2(B,A)) # label(d5_finsub_1) # label(axiom). [clausify(9)].
% 0.98/1.26 Derived: finite_subsets(A) = c2 | -in(f2(A,c2),c2) | -subset(f2(A,c2),A) | -finite(f2(A,c2)). [resolve(51,a,42,a)].
% 0.98/1.26 Derived: finite_subsets(A) = finite_subsets(B) | -in(f2(A,finite_subsets(B)),finite_subsets(B)) | -subset(f2(A,finite_subsets(B)),A) | -finite(f2(A,finite_subsets(B))). [resolve(51,a,43,a)].
% 0.98/1.26 Derived: finite_subsets(A) = powerset(B) | -in(f2(A,powerset(B)),powerset(B)) | -subset(f2(A,powerset(B)),A) | -finite(f2(A,powerset(B))). [resolve(51,a,44,a)].
% 0.98/1.26 52 -diff_closed(c2) | preboolean(c2). [resolve(36,a,37,a)].
% 0.98/1.26 53 -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(36,a,38,a)].
% 0.98/1.26 54 -diff_closed(finite_subsets(A)) | preboolean(finite_subsets(A)). [resolve(36,a,39,a)].
% 0.98/1.26
% 0.98/1.26 ============================== end predicate elimination =============
% 0.98/1.26
% 0.98/1.26 Auto_denials: (non-Horn, no changes).
% 0.98/1.26
% 0.98/1.26 Term ordering decisions:
% 0.98/1.26 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. f1=1. f2=1. finite_subsets=1. powerset=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1.
% 0.98/1.26
% 0.98/1.26 ============================== end of process initial clauses ========
% 0.98/1.26
% 0.98/1.26 ============================== CLAUSES FOR SEARCH ====================
% 0.98/1.26
% 0.98/1.26 ============================== end of clauses for search =============
% 0.98/1.26
% 0.98/1.26 ============================== SEARCH ================================
% 0.98/1.26
% 0.98/1.26 % Starting search at 0.02 seconds.
% 0.98/1.26
% 0.98/1.26 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 373 (0.00 of 0.24 sec).
% 0.98/1.26
% 0.98/1.26 Low Water (keep): wt=26.000, iters=3341
% 1.52/1.78
% 1.52/1.78 Low Water (keep): wt=24.000, iters=3335
% 1.52/1.78
% 1.52/1.78 Low Water (keep): wt=22.000, iters=3350
% 1.52/1.78
% 1.52/1.78 Low Water (keep): wt=21.000, iters=3372
% 1.52/1.78
% 1.52/1.78 Low Water (keep): wt=20.000, iters=3425
% 1.52/1.78
% 1.52/1.78 Low Water (keep): wt=19.000, iters=3337
% 1.52/1.78
% 1.52/1.78 Low Water (keep): wt=17.000, iters=3335
% 1.52/1.78
% 1.52/1.78 Low Water (keep): wt=15.000, iters=3391
% 1.52/1.78
% 1.52/1.78 Low Water (keep): wt=12.000, iters=3362
% 1.52/1.78
% 1.52/1.78 Low Water (keep): wt=11.000, iters=3474
% 1.52/1.78
% 1.52/1.78 Low Water (keep): wt=10.000, iters=3345
% 1.52/1.78
% 1.52/1.78 Low Water (keep): wt=9.000, iters=3477
% 1.52/1.78
% 1.52/1.78 Low Water (keep): wt=8.000, iters=3334
% 1.52/1.78
% 1.52/1.78 ============================== PROOF =================================
% 1.52/1.78 % SZS status Theorem
% 1.52/1.78 % SZS output start Refutation
% 1.52/1.78
% 1.52/1.78 % Proof 1 at 0.78 (+ 0.03) seconds.
% 1.52/1.78 % Length of proof is 34.
% 1.52/1.78 % Level of proof is 9.
% 1.52/1.78 % Maximum clause weight is 14.000.
% 1.52/1.78 % Given clauses 2155.
% 1.52/1.78
% 1.52/1.78 4 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.78 7 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.78 8 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.78 9 (all A all B (preboolean(B) -> (B = finite_subsets(A) <-> (all C (in(C,B) <-> subset(C,A) & finite(C)))))) # label(d5_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.78 10 (all A preboolean(finite_subsets(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.78 26 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.78 27 (all A subset(finite_subsets(A),powerset(A))) # label(t26_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.78 29 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.78 35 -(all A (finite(A) -> finite_subsets(A) = powerset(A))) # label(t27_finsub_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.52/1.78 43 preboolean(finite_subsets(A)) # label(dt_k5_finsub_1) # label(axiom). [clausify(10)].
% 1.52/1.78 48 -preboolean(A) | finite_subsets(B) != A | in(C,A) | -subset(C,B) | -finite(C) # label(d5_finsub_1) # label(axiom). [clausify(9)].
% 1.52/1.78 58 finite(c5) # label(t27_finsub_1) # label(negated_conjecture). [clausify(35)].
% 1.52/1.78 68 subset(finite_subsets(A),powerset(A)) # label(t26_finsub_1) # label(axiom). [clausify(27)].
% 1.52/1.78 72 subset(A,B) | in(f1(A,B),A) # label(d3_tarski) # label(axiom). [clausify(8)].
% 1.52/1.78 79 finite_subsets(c5) != powerset(c5) # label(t27_finsub_1) # label(negated_conjecture). [clausify(35)].
% 1.52/1.78 80 powerset(c5) != finite_subsets(c5). [copy(79),flip(a)].
% 1.52/1.78 91 -in(A,B) | element(A,B) # label(t1_subset) # label(axiom). [clausify(26)].
% 1.52/1.78 93 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(29)].
% 1.52/1.78 96 -finite(A) | -element(B,powerset(A)) | finite(B) # label(cc2_finset_1) # label(axiom). [clausify(4)].
% 1.52/1.78 97 subset(A,B) | -in(f1(A,B),B) # label(d3_tarski) # label(axiom). [clausify(8)].
% 1.52/1.78 99 A = B | -subset(B,A) | -subset(A,B) # label(d10_xboole_0) # label(axiom). [clausify(7)].
% 1.52/1.78 110 finite_subsets(A) != finite_subsets(B) | in(C,finite_subsets(B)) | -subset(C,A) | -finite(C). [resolve(48,a,43,a)].
% 1.52/1.78 121 powerset(c5) = c_0. [new_symbol(80)].
% 1.52/1.78 123 finite_subsets(c5) != c_0. [back_rewrite(80),rewrite([121(2)]),flip(a)].
% 1.52/1.78 243 subset(finite_subsets(c5),c_0). [para(121(a,1),68(a,2))].
% 1.52/1.78 249 -element(A,c_0) | subset(A,c5). [para(121(a,1),93(a,2))].
% 1.52/1.78 250 -element(A,c_0) | finite(A). [para(121(a,1),96(b,2)),unit_del(a,58)].
% 1.52/1.78 392 -subset(c_0,finite_subsets(c5)). [resolve(243,a,99,c),unit_del(a,123)].
% 1.52/1.78 1020 in(f1(c_0,finite_subsets(c5)),c_0). [resolve(392,a,72,a)].
% 1.52/1.78 1023 -in(f1(c_0,finite_subsets(c5)),finite_subsets(c5)). [ur(97,a,392,a)].
% 1.52/1.78 8020 element(f1(c_0,finite_subsets(c5)),c_0). [resolve(1020,a,91,a)].
% 1.52/1.78 9769 finite(f1(c_0,finite_subsets(c5))). [resolve(8020,a,250,a)].
% 1.52/1.78 9770 subset(f1(c_0,finite_subsets(c5)),c5). [resolve(8020,a,249,a)].
% 1.52/1.78 11543 $F. [ur(110,b,1023,a,c,9770,a,d,9769,a),xx(a)].
% 1.52/1.78
% 1.52/1.78 % SZS output end Refutation
% 1.52/1.78 ============================== end of proof ==========================
% 1.52/1.78
% 1.52/1.78 ============================== STATISTICS ============================
% 1.52/1.78
% 1.52/1.78 Given=2155. Generated=35293. Kept=11486. proofs=1.
% 1.52/1.78 Usable=2144. Sos=9295. Demods=6. Limbo=2, Disabled=143. Hints=0.
% 1.52/1.78 Megabytes=7.83.
% 1.52/1.78 User_CPU=0.78, System_CPU=0.03, Wall_clock=0.
% 1.52/1.78
% 1.52/1.78 ============================== end of statistics =====================
% 1.52/1.78
% 1.52/1.78 ============================== end of search =========================
% 1.52/1.78
% 1.52/1.78 THEOREM PROVED
% 1.52/1.78 % SZS status Theorem
% 1.52/1.78
% 1.52/1.78 Exiting with 1 proof.
% 1.52/1.78
% 1.52/1.78 Process 15580 exit (max_proofs) Mon Jun 20 07:19:34 2022
% 1.52/1.78 Prover9 interrupted
%------------------------------------------------------------------------------