TSTP Solution File: SET646+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET646+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 04:31:07 EDT 2022
% Result : Theorem 1.41s 1.74s
% Output : Refutation 1.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET646+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n028.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 Jul 10 23:35:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.01 ============================== Prover9 ===============================
% 0.44/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.01 Process 29855 was started by sandbox on n028.cluster.edu,
% 0.44/1.01 Sun Jul 10 23:35:58 2022
% 0.44/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29488_n028.cluster.edu".
% 0.44/1.01 ============================== end of head ===========================
% 0.44/1.01
% 0.44/1.01 ============================== INPUT =================================
% 0.44/1.01
% 0.44/1.01 % Reading from file /tmp/Prover9_29488_n028.cluster.edu
% 0.44/1.01
% 0.44/1.01 set(prolog_style_variables).
% 0.44/1.01 set(auto2).
% 0.44/1.01 % set(auto2) -> set(auto).
% 0.44/1.01 % set(auto) -> set(auto_inference).
% 0.44/1.01 % set(auto) -> set(auto_setup).
% 0.44/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.01 % set(auto) -> set(auto_limits).
% 0.44/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.01 % set(auto) -> set(auto_denials).
% 0.44/1.01 % set(auto) -> set(auto_process).
% 0.44/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.01 % set(auto2) -> assign(stats, some).
% 0.44/1.01 % set(auto2) -> clear(echo_input).
% 0.44/1.01 % set(auto2) -> set(quiet).
% 0.44/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.01 % set(auto2) -> clear(print_given).
% 0.44/1.01 assign(lrs_ticks,-1).
% 0.44/1.01 assign(sos_limit,10000).
% 0.44/1.01 assign(order,kbo).
% 0.44/1.01 set(lex_order_vars).
% 0.44/1.01 clear(print_given).
% 0.44/1.01
% 0.44/1.01 % formulas(sos). % not echoed (26 formulas)
% 0.44/1.01
% 0.44/1.01 ============================== end of input ==========================
% 0.44/1.01
% 0.44/1.01 % From the command line: assign(max_seconds, 300).
% 0.44/1.01
% 0.44/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.01
% 0.44/1.01 % Formulas that are not ordinary clauses:
% 0.44/1.01 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (subset(singleton(B),C) <-> member(B,C)))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 2 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,set_type) -> (member(ordered_pair(B,C),cross_product(D,E)) <-> member(B,D) & member(C,E)))))))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> ilf_type(D,relation_type(B,C)))) & (all E (ilf_type(E,relation_type(B,C)) -> ilf_type(E,subset_type(cross_product(B,C))))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 4 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (exists D ilf_type(D,relation_type(C,B))))))) # label(p4) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (D = singleton(C) <-> (all E (ilf_type(E,set_type) -> (member(E,D) <-> E = C)))))))))) # label(p5) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 6 (all B (ilf_type(B,set_type) -> ilf_type(singleton(B),set_type))) # label(p6) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 7 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,set_type) -> (all F (ilf_type(F,set_type) -> (F = ordered_pair(D,E) <-> F = unordered_pair(unordered_pair(D,E),singleton(D))))))))))))) # label(p7) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 8 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p8) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 9 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 10 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(unordered_pair(B,C),set_type))))) # label(p10) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 11 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> unordered_pair(B,C) = unordered_pair(C,B))))) # label(p11) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 12 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (ilf_type(C,subset_type(B)) <-> ilf_type(C,member_type(power_set(B)))))))) # label(p12) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 13 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 14 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (B = C <-> (all D (ilf_type(D,set_type) -> (member(D,B) <-> member(D,C))))))))) # label(p14) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 15 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (subset(B,C) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 16 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p16) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 17 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (member(B,power_set(C)) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 18 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p18) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 19 (all B (ilf_type(B,set_type) -> (all C (-empty(C) & ilf_type(C,set_type) -> (ilf_type(B,member_type(C)) <-> member(B,C)))))) # label(p19) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 20 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p20) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 21 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p21) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 22 (all B (ilf_type(B,set_type) -> (relation_like(B) <-> (all C (ilf_type(C,set_type) -> (member(C,B) -> (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & C = ordered_pair(D,E))))))))))) # label(p22) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 23 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p23) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 24 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> relation_like(D))))))) # label(p24) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 25 (all B ilf_type(B,set_type)) # label(p25) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 26 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,set_type) -> (member(D,B) & member(E,C) -> ilf_type(singleton(ordered_pair(D,E)),relation_type(B,C))))))))))) # label(prove_relset_1_8) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.02
% 0.44/1.02 ============================== end of process non-clausal formulas ===
% 0.44/1.02
% 0.44/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.02
% 0.44/1.02 ============================== PREDICATE ELIMINATION =================
% 0.44/1.02 27 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) # label(p22) # label(axiom). [clausify(22)].
% 0.44/1.02 28 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p23) # label(axiom). [clausify(23)].
% 0.44/1.02 29 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f11(A),set_type) # label(p22) # label(axiom). [clausify(22)].
% 0.44/1.02 30 -ilf_type(A,set_type) | relation_like(A) | member(f11(A),A) # label(p22) # label(axiom). [clausify(22)].
% 0.44/1.02 31 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p24) # label(axiom). [clausify(24)].
% 0.44/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) | -empty(A) | -ilf_type(A,set_type). [resolve(27,b,28,c)].
% 1.03/1.32 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f11(A),set_type). [resolve(27,b,29,b)].
% 1.03/1.32 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) | -ilf_type(A,set_type) | member(f11(A),A). [resolve(27,b,30,b)].
% 1.03/1.32 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(27,b,31,d)].
% 1.03/1.32 32 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) # label(p22) # label(axiom). [clausify(22)].
% 1.03/1.32 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) | -empty(A) | -ilf_type(A,set_type). [resolve(32,b,28,c)].
% 1.03/1.32 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f11(A),set_type). [resolve(32,b,29,b)].
% 1.03/1.32 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) | -ilf_type(A,set_type) | member(f11(A),A). [resolve(32,b,30,b)].
% 1.03/1.32 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(32,b,31,d)].
% 1.03/1.32 33 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f11(A) # label(p22) # label(axiom). [clausify(22)].
% 1.03/1.32 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f11(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f9(A,D),set_type). [resolve(33,b,27,b)].
% 1.03/1.32 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f11(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f10(A,D),set_type). [resolve(33,b,32,b)].
% 1.03/1.32 34 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B # label(p22) # label(axiom). [clausify(22)].
% 1.03/1.32 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -empty(A) | -ilf_type(A,set_type). [resolve(34,b,28,c)].
% 1.03/1.32 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -ilf_type(A,set_type) | ilf_type(f11(A),set_type). [resolve(34,b,29,b)].
% 1.03/1.32 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -ilf_type(A,set_type) | member(f11(A),A). [resolve(34,b,30,b)].
% 1.03/1.32 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(34,b,31,d)].
% 1.03/1.32 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f11(A). [resolve(34,b,33,b)].
% 1.03/1.32
% 1.03/1.32 ============================== end predicate elimination =============
% 1.03/1.32
% 1.03/1.32 Auto_denials: (non-Horn, no changes).
% 1.03/1.32
% 1.03/1.32 Term ordering decisions:
% 1.03/1.32 Function symbol KB weights: set_type=1. c1=1. c2=1. c3=1. c4=1. ordered_pair=1. cross_product=1. unordered_pair=1. relation_type=1. f1=1. f4=1. f5=1. f6=1. f9=1. f10=1. singleton=1. subset_type=1. power_set=1. member_type=1. f3=1. f7=1. f8=1. f11=1. f2=1.
% 1.03/1.32
% 1.03/1.32 ============================== end of process initial clauses ========
% 1.03/1.32
% 1.03/1.32 ============================== CLAUSES FOR SEARCH ====================
% 1.03/1.32
% 1.03/1.32 ============================== end of clauses for search =============
% 1.03/1.32
% 1.03/1.32 ============================== SEARCH ================================
% 1.03/1.32
% 1.03/1.32 % Starting search at 0.03 seconds.
% 1.03/1.32
% 1.03/1.32 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 957 (0.00 of 0.31 sec).
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=51.000, iters=3339
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=43.000, iters=3396
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=37.000, iters=3333
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=36.000, iters=3377
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=32.000, iters=3353
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=28.000, iters=3353
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=27.000, iters=3442
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=26.000, iters=3398
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=24.000, iters=3366
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=23.000, iters=3484
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=22.000, iters=3389
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=21.000, iters=3349
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=20.000, iters=3350
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=19.000, iters=3346
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=18.000, iters=3355
% 1.41/1.74
% 1.41/1.74 Low Water (keep): wt=17.000, iters=3345
% 1.41/1.74
% 1.41/1.74 ============================== PROOF =================================
% 1.41/1.74 % SZS status Theorem
% 1.41/1.74 % SZS output start Refutation
% 1.41/1.74
% 1.41/1.74 % Proof 1 at 0.72 (+ 0.02) seconds.
% 1.41/1.74 % Length of proof is 51.
% 1.41/1.74 % Level of proof is 9.
% 1.41/1.74 % Maximum clause weight is 18.000.
% 1.41/1.74 % Given clauses 1052.
% 1.41/1.74
% 1.41/1.74 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (subset(singleton(B),C) <-> member(B,C)))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.74 2 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,set_type) -> (member(ordered_pair(B,C),cross_product(D,E)) <-> member(B,D) & member(C,E)))))))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.74 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> ilf_type(D,relation_type(B,C)))) & (all E (ilf_type(E,relation_type(B,C)) -> ilf_type(E,subset_type(cross_product(B,C))))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.74 5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (D = singleton(C) <-> (all E (ilf_type(E,set_type) -> (member(E,D) <-> E = C)))))))))) # label(p5) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.74 12 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (ilf_type(C,subset_type(B)) <-> ilf_type(C,member_type(power_set(B)))))))) # label(p12) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.74 16 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p16) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.74 17 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (member(B,power_set(C)) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.74 18 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p18) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.74 19 (all B (ilf_type(B,set_type) -> (all C (-empty(C) & ilf_type(C,set_type) -> (ilf_type(B,member_type(C)) <-> member(B,C)))))) # label(p19) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.74 25 (all B ilf_type(B,set_type)) # label(p25) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.74 26 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,set_type) -> (member(D,B) & member(E,C) -> ilf_type(singleton(ordered_pair(D,E)),relation_type(B,C))))))))))) # label(prove_relset_1_8) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.41/1.74 35 ilf_type(A,set_type) # label(p25) # label(axiom). [clausify(25)].
% 1.41/1.74 36 member(c3,c1) # label(prove_relset_1_8) # label(negated_conjecture). [clausify(26)].
% 1.41/1.74 37 member(c4,c2) # label(prove_relset_1_8) # label(negated_conjecture). [clausify(26)].
% 1.41/1.74 38 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p18) # label(axiom). [clausify(18)].
% 1.41/1.74 39 -empty(power_set(A)). [copy(38),unit_del(a,35)].
% 1.41/1.74 40 -ilf_type(singleton(ordered_pair(c3,c4)),relation_type(c1,c2)) # label(prove_relset_1_8) # label(negated_conjecture). [clausify(26)].
% 1.41/1.74 43 -ilf_type(A,set_type) | subset(A,A) # label(p16) # label(axiom). [clausify(16)].
% 1.41/1.74 44 subset(A,A). [copy(43),unit_del(a,35)].
% 1.41/1.74 57 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -subset(singleton(A),B) | member(A,B) # label(p1) # label(axiom). [clausify(1)].
% 1.41/1.74 58 -subset(singleton(A),B) | member(A,B). [copy(57),unit_del(a,35),unit_del(b,35)].
% 1.41/1.74 73 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,subset_type(A)) | -ilf_type(B,member_type(power_set(A))) # label(p12) # label(axiom). [clausify(12)].
% 1.41/1.74 74 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [copy(73),unit_del(a,35),unit_del(b,35)].
% 1.41/1.74 76 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f6(A,B),A) # label(p17) # label(axiom). [clausify(17)].
% 1.41/1.74 77 member(A,power_set(B)) | member(f6(A,B),A). [copy(76),unit_del(a,35),unit_del(b,35)].
% 1.41/1.74 78 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f6(A,B),B) # label(p17) # label(axiom). [clausify(17)].
% 1.41/1.74 79 member(A,power_set(B)) | -member(f6(A,B),B). [copy(78),unit_del(a,35),unit_del(b,35)].
% 1.41/1.74 82 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B) # label(p19) # label(axiom). [clausify(19)].
% 1.41/1.74 83 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [copy(82),unit_del(a,35),unit_del(c,35)].
% 1.41/1.74 84 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | ilf_type(C,relation_type(A,B)) # label(p3) # label(axiom). [clausify(3)].
% 1.41/1.74 85 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [copy(84),unit_del(a,35),unit_del(b,35)].
% 1.41/1.74 99 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(A,power_set(B)) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) # label(p17) # label(axiom). [clausify(17)].
% 1.41/1.74 100 -member(A,power_set(B)) | -member(C,A) | member(C,B). [copy(99),unit_del(a,35),unit_del(b,35),unit_del(d,35)].
% 1.41/1.74 105 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | singleton(B) != C | -ilf_type(D,set_type) | -member(D,C) | D = B # label(p5) # label(axiom). [clausify(5)].
% 1.41/1.74 106 singleton(A) != B | -member(C,B) | C = A. [copy(105),unit_del(a,35),unit_del(b,35),unit_del(c,35),unit_del(e,35)].
% 1.41/1.74 109 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | member(ordered_pair(A,B),cross_product(C,D)) | -member(A,C) | -member(B,D) # label(p2) # label(axiom). [clausify(2)].
% 1.41/1.74 110 member(ordered_pair(A,B),cross_product(C,D)) | -member(A,C) | -member(B,D). [copy(109),unit_del(a,35),unit_del(b,35),unit_del(c,35),unit_del(d,35)].
% 1.41/1.74 142 member(A,singleton(A)). [resolve(58,a,44,a)].
% 1.41/1.74 158 -ilf_type(singleton(ordered_pair(c3,c4)),subset_type(cross_product(c1,c2))). [ur(85,b,40,a)].
% 1.41/1.74 196 singleton(A) != B | f6(B,C) = A | member(B,power_set(C)). [resolve(106,b,77,b)].
% 1.41/1.74 208 member(ordered_pair(c3,A),cross_product(c1,B)) | -member(A,B). [resolve(110,b,36,a)].
% 1.41/1.74 254 -ilf_type(singleton(ordered_pair(c3,c4)),member_type(power_set(cross_product(c1,c2)))). [ur(74,a,158,a)].
% 1.41/1.74 255 -member(singleton(ordered_pair(c3,c4)),power_set(cross_product(c1,c2))). [ur(83,a,39,a,b,254,a)].
% 1.41/1.74 271 -member(singleton(singleton(ordered_pair(c3,c4))),power_set(power_set(cross_product(c1,c2)))). [ur(100,b,142,a,c,255,a)].
% 1.41/1.74 324 -member(f6(singleton(singleton(ordered_pair(c3,c4))),power_set(cross_product(c1,c2))),power_set(cross_product(c1,c2))). [ur(79,a,271,a)].
% 1.41/1.74 2547 f6(singleton(A),B) = A | member(singleton(A),power_set(B)). [xx_res(196,a)].
% 1.41/1.74 2985 member(ordered_pair(c3,c4),cross_product(c1,c2)). [resolve(208,b,37,a)].
% 1.41/1.74 10503 -member(f6(f6(singleton(singleton(ordered_pair(c3,c4))),power_set(cross_product(c1,c2))),cross_product(c1,c2)),cross_product(c1,c2)). [ur(79,a,324,a)].
% 1.41/1.74 10751 f6(singleton(singleton(ordered_pair(c3,c4))),power_set(cross_product(c1,c2))) = singleton(ordered_pair(c3,c4)). [resolve(2547,b,271,a)].
% 1.41/1.74 10754 f6(singleton(ordered_pair(c3,c4)),cross_product(c1,c2)) = ordered_pair(c3,c4). [resolve(2547,b,255,a)].
% 1.41/1.74 10767 $F. [back_rewrite(10503),rewrite([10751(10),10754(8)]),unit_del(a,2985)].
% 1.41/1.74
% 1.41/1.74 % SZS output end Refutation
% 1.41/1.74 ============================== end of proof ==========================
% 1.41/1.74
% 1.41/1.74 ============================== STATISTICS ============================
% 1.41/1.74
% 1.41/1.74 Given=1052. Generated=22895. Kept=10672. proofs=1.
% 1.41/1.74 Usable=932. Sos=8114. Demods=66. Limbo=16, Disabled=1686. Hints=0.
% 1.41/1.74 Megabytes=10.85.
% 1.41/1.74 User_CPU=0.72, System_CPU=0.02, Wall_clock=1.
% 1.41/1.74
% 1.41/1.74 ============================== end of statistics =====================
% 1.41/1.74
% 1.41/1.74 ============================== end of search =========================
% 1.41/1.74
% 1.41/1.74 THEOREM PROVED
% 1.41/1.74 % SZS status Theorem
% 1.41/1.74
% 1.41/1.74 Exiting with 1 proof.
% 1.41/1.74
% 1.41/1.74 Process 29855 exit (max_proofs) Sun Jul 10 23:35:59 2022
% 1.41/1.74 Prover9 interrupted
%------------------------------------------------------------------------------