TSTP Solution File: SET660+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET660+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 04:31:13 EDT 2022
% Result : Theorem 1.94s 2.23s
% Output : Refutation 1.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SET660+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n028.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jul 10 05:50:57 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.46/1.05 ============================== Prover9 ===============================
% 0.46/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.05 Process 8212 was started by sandbox2 on n028.cluster.edu,
% 0.46/1.05 Sun Jul 10 05:50:57 2022
% 0.46/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_8019_n028.cluster.edu".
% 0.46/1.05 ============================== end of head ===========================
% 0.46/1.05
% 0.46/1.05 ============================== INPUT =================================
% 0.46/1.05
% 0.46/1.05 % Reading from file /tmp/Prover9_8019_n028.cluster.edu
% 0.46/1.05
% 0.46/1.05 set(prolog_style_variables).
% 0.46/1.05 set(auto2).
% 0.46/1.05 % set(auto2) -> set(auto).
% 0.46/1.05 % set(auto) -> set(auto_inference).
% 0.46/1.05 % set(auto) -> set(auto_setup).
% 0.46/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.05 % set(auto) -> set(auto_limits).
% 0.46/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.05 % set(auto) -> set(auto_denials).
% 0.46/1.05 % set(auto) -> set(auto_process).
% 0.46/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.05 % set(auto2) -> assign(stats, some).
% 0.46/1.05 % set(auto2) -> clear(echo_input).
% 0.46/1.05 % set(auto2) -> set(quiet).
% 0.46/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.05 % set(auto2) -> clear(print_given).
% 0.46/1.05 assign(lrs_ticks,-1).
% 0.46/1.05 assign(sos_limit,10000).
% 0.46/1.05 assign(order,kbo).
% 0.46/1.05 set(lex_order_vars).
% 0.46/1.05 clear(print_given).
% 0.46/1.05
% 0.46/1.05 % formulas(sos). % not echoed (35 formulas)
% 0.46/1.05
% 0.46/1.05 ============================== end of input ==========================
% 0.46/1.05
% 0.46/1.05 % From the command line: assign(max_seconds, 300).
% 0.46/1.05
% 0.46/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.05
% 0.46/1.05 % Formulas that are not ordinary clauses:
% 0.46/1.05 1 (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,set_type) -> (member(C,range_of(B)) <-> (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B)))))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 2 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,binary_relation_type) -> (member(ordered_pair(B,C),D) -> member(B,domain_of(D)) & member(C,range_of(D))))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 4 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ((all D (ilf_type(D,set_type) -> (member(D,B) <-> member(D,C)))) -> B = C))))) # label(p4) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 5 (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(p5) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 6 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p6) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 7 (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(p7) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 8 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (exists D ilf_type(D,relation_type(C,B))))))) # label(p8) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 9 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (B = C <-> subset(B,C) & subset(C,B)))))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 10 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p10) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 11 (all B (ilf_type(B,set_type) -> ilf_type(singleton(B),set_type))) # label(p11) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 12 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p12) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 13 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(unordered_pair(B,C),set_type))))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 14 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> unordered_pair(B,C) = unordered_pair(C,B))))) # label(p14) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 15 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 16 (exists B ilf_type(B,binary_relation_type)) # label(p16) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 17 (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(p17) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 18 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p18) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 19 (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(p19) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 20 (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(p20) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 21 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p21) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 22 (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(p22) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 23 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p23) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 24 (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(p24) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 25 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p25) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 26 (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(p26) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 27 (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(p27) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 28 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p28) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 29 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p29) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 30 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> domain(B,C,D) = domain_of(D))))))) # label(p30) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 31 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ilf_type(domain(B,C,D),subset_type(B)))))))) # label(p31) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 32 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> range(B,C,D) = range_of(D))))))) # label(p32) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 33 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ilf_type(range(B,C,D),subset_type(C)))))))) # label(p33) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 34 (all B ilf_type(B,set_type)) # label(p34) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 35 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ((all E (ilf_type(E,set_type) -> (member(E,C) -> (exists F (ilf_type(F,set_type) & member(ordered_pair(F,E),D)))))) <-> range(B,C,D) = C))))))) # label(prove_relset_1_23) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.05
% 0.46/1.05 ============================== end of process non-clausal formulas ===
% 0.46/1.05
% 0.46/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.05
% 0.46/1.05 ============================== PREDICATE ELIMINATION =================
% 0.46/1.05 36 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p15) # label(axiom). [clausify(15)].
% 0.46/1.05 37 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p29) # label(axiom). [clausify(29)].
% 0.46/1.05 38 -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type) | relation_like(A) # label(p15) # label(axiom). [clausify(15)].
% 0.46/1.05 Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -empty(A) | -ilf_type(A,set_type). [resolve(36,c,37,c)].
% 0.46/1.05 39 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f11(A),set_type) # label(p26) # label(axiom). [clausify(26)].
% 0.46/1.05 Derived: -ilf_type(A,set_type) | ilf_type(f11(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(39,b,36,c)].
% 0.46/1.05 40 -ilf_type(A,set_type) | relation_like(A) | member(f11(A),A) # label(p26) # label(axiom). [clausify(26)].
% 0.46/1.05 Derived: -ilf_type(A,set_type) | member(f11(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(40,b,36,c)].
% 0.46/1.05 41 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p27) # label(axiom). [clausify(27)].
% 0.46/1.05 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(41,d,36,c)].
% 0.46/1.05 42 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) # label(p26) # label(axiom). [clausify(26)].
% 0.46/1.05 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(42,b,37,c)].
% 0.46/1.05 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(A,binary_relation_type). [resolve(42,b,38,c)].
% 0.46/1.05 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(42,b,39,b)].
% 0.46/1.05 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(42,b,40,b)].
% 0.46/1.05 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(42,b,41,d)].
% 0.46/1.05 43 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) # label(p26) # label(axiom). [clausify(26)].
% 0.46/1.05 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(43,b,37,c)].
% 0.46/1.05 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(A,binary_relation_type). [resolve(43,b,38,c)].
% 0.46/1.05 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(43,b,39,b)].
% 0.46/1.05 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(43,b,40,b)].
% 1.63/1.91 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(43,b,41,d)].
% 1.63/1.91 44 -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(p26) # label(axiom). [clausify(26)].
% 1.63/1.91 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(A,binary_relation_type). [resolve(44,b,36,c)].
% 1.63/1.91 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(44,b,42,b)].
% 1.63/1.91 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(44,b,43,b)].
% 1.63/1.91 45 -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(p26) # label(axiom). [clausify(26)].
% 1.63/1.91 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(45,b,37,c)].
% 1.63/1.91 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(A,binary_relation_type). [resolve(45,b,38,c)].
% 1.63/1.91 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(45,b,39,b)].
% 1.63/1.91 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(45,b,40,b)].
% 1.63/1.91 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(45,b,41,d)].
% 1.63/1.91 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(45,b,44,b)].
% 1.63/1.91
% 1.63/1.91 ============================== end predicate elimination =============
% 1.63/1.91
% 1.63/1.91 Auto_denials: (non-Horn, no changes).
% 1.63/1.91
% 1.63/1.91 Term ordering decisions:
% 1.63/1.91 Function symbol KB weights: set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. c4=1. c5=1. ordered_pair=1. relation_type=1. cross_product=1. unordered_pair=1. f1=1. f2=1. f3=1. f5=1. f6=1. f7=1. f9=1. f10=1. subset_type=1. power_set=1. range_of=1. member_type=1. domain_of=1. singleton=1. f4=1. f8=1. f11=1. f12=1. f13=1. range=1. domain=1.
% 1.63/1.91
% 1.63/1.91 ============================== end of process initial clauses ========
% 1.63/1.91
% 1.63/1.91 ============================== CLAUSES FOR SEARCH ====================
% 1.63/1.91
% 1.63/1.91 ============================== end of clauses for search =============
% 1.63/1.91
% 1.63/1.91 ============================== SEARCH ================================
% 1.63/1.91
% 1.63/1.91 % Starting search at 0.03 seconds.
% 1.63/1.91
% 1.63/1.91 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 170 (0.00 of 0.45 sec).
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=60.000, iters=3441
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=57.000, iters=3413
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=36.000, iters=3366
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=35.000, iters=3352
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=34.000, iters=3335
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=33.000, iters=3333
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=32.000, iters=3427
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=31.000, iters=3350
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=30.000, iters=3460
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=29.000, iters=3383
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=28.000, iters=3341
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=27.000, iters=3381
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=26.000, iters=3360
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=25.000, iters=3348
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=24.000, iters=3336
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=23.000, iters=3480
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=22.000, iters=3336
% 1.63/1.91
% 1.63/1.91 Low Water (keep): wt=21.000, iters=3343
% 1.63/1.91
% 1.63/1.91 Low Water (displace): id=4031, wt=86.000
% 1.94/2.23
% 1.94/2.23 Low Water (displace): id=3388, wt=79.000
% 1.94/2.23
% 1.94/2.23 Low Water (displace): id=4134, wt=73.000
% 1.94/2.23
% 1.94/2.23 Low Water (displace): id=2664, wt=72.000
% 1.94/2.23
% 1.94/2.23 Low Water (displace): id=3393, wt=71.000
% 1.94/2.23
% 1.94/2.23 Low Water (displace): id=5595, wt=68.000
% 1.94/2.23
% 1.94/2.23 Low Water (displace): id=3384, wt=67.000
% 1.94/2.23
% 1.94/2.23 Low Water (displace): id=2666, wt=65.000
% 1.94/2.23
% 1.94/2.23 Low Water (displace): id=11348, wt=20.000
% 1.94/2.23
% 1.94/2.23 Low Water (displace): id=11354, wt=19.000
% 1.94/2.23
% 1.94/2.23 Low Water (displace): id=11448, wt=15.000
% 1.94/2.23
% 1.94/2.23 Low Water (displace): id=11457, wt=14.000
% 1.94/2.23
% 1.94/2.23 Low Water (keep): wt=20.000, iters=3352
% 1.94/2.23
% 1.94/2.23 Low Water (keep): wt=18.000, iters=3920
% 1.94/2.23
% 1.94/2.23 ============================== PROOF =================================
% 1.94/2.23 % SZS status Theorem
% 1.94/2.23 % SZS output start Refutation
% 1.94/2.23
% 1.94/2.23 % Proof 1 at 1.17 (+ 0.03) seconds.
% 1.94/2.23 % Length of proof is 66.
% 1.94/2.23 % Level of proof is 13.
% 1.94/2.23 % Maximum clause weight is 22.000.
% 1.94/2.23 % Given clauses 1219.
% 1.94/2.23
% 1.94/2.23 1 (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,set_type) -> (member(C,range_of(B)) <-> (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B)))))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.23 7 (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(p7) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.23 15 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.23 17 (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(p17) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.23 19 (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(p19) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.23 22 (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(p22) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.23 23 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p23) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.23 24 (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(p24) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.23 27 (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(p27) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.23 32 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> range(B,C,D) = range_of(D))))))) # label(p32) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.23 33 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ilf_type(range(B,C,D),subset_type(C)))))))) # label(p33) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.23 34 (all B ilf_type(B,set_type)) # label(p34) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.23 35 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ((all E (ilf_type(E,set_type) -> (member(E,C) -> (exists F (ilf_type(F,set_type) & member(ordered_pair(F,E),D)))))) <-> range(B,C,D) = C))))))) # label(prove_relset_1_23) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.94/2.23 36 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p15) # label(axiom). [clausify(15)].
% 1.94/2.23 41 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p27) # label(axiom). [clausify(27)].
% 1.94/2.23 47 ilf_type(A,set_type) # label(p34) # label(axiom). [clausify(34)].
% 1.94/2.23 48 ilf_type(c4,relation_type(c2,c3)) # label(prove_relset_1_23) # label(negated_conjecture). [clausify(35)].
% 1.94/2.23 49 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p23) # label(axiom). [clausify(23)].
% 1.94/2.23 50 -empty(power_set(A)). [copy(49),unit_del(a,47)].
% 1.94/2.23 53 -ilf_type(A,set_type) | -member(ordered_pair(A,c5),c4) | range(c2,c3,c4) != c3 # label(prove_relset_1_23) # label(negated_conjecture). [clausify(35)].
% 1.94/2.23 54 -member(ordered_pair(A,c5),c4) | range(c2,c3,c4) != c3. [copy(53),unit_del(a,47)].
% 1.94/2.23 64 member(c5,c3) | range(c2,c3,c4) != c3 # label(prove_relset_1_23) # label(negated_conjecture). [clausify(35)].
% 1.94/2.23 88 -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(p17) # label(axiom). [clausify(17)].
% 1.94/2.23 89 -ilf_type(A,subset_type(B)) | ilf_type(A,member_type(power_set(B))). [copy(88),unit_del(a,47),unit_del(b,47)].
% 1.94/2.23 97 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | -ilf_type(A,member_type(B)) | member(A,B) # label(p24) # label(axiom). [clausify(24)].
% 1.94/2.23 98 empty(A) | -ilf_type(B,member_type(A)) | member(B,A). [copy(97),unit_del(a,47),unit_del(c,47)].
% 1.94/2.23 102 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | -member(B,range_of(A)) | member(ordered_pair(f1(A,B),B),A) # label(p1) # label(axiom). [clausify(1)].
% 1.94/2.23 103 -ilf_type(A,binary_relation_type) | -member(B,range_of(A)) | member(ordered_pair(f1(A,B),B),A). [copy(102),unit_del(b,47)].
% 1.94/2.23 106 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))) # label(p7) # label(axiom). [clausify(7)].
% 1.94/2.23 107 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [copy(106),unit_del(a,47),unit_del(b,47)].
% 1.94/2.23 108 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(B,range_of(A)) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A) # label(p1) # label(axiom). [clausify(1)].
% 1.94/2.23 109 -ilf_type(A,binary_relation_type) | member(B,range_of(A)) | -member(ordered_pair(C,B),A). [copy(108),unit_del(b,47),unit_del(d,47)].
% 1.94/2.23 123 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C) # label(p32) # label(axiom). [clausify(32)].
% 1.94/2.23 124 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [copy(123),unit_del(a,47),unit_del(b,47)].
% 1.94/2.23 125 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(range(A,B,C),subset_type(B)) # label(p33) # label(axiom). [clausify(33)].
% 1.94/2.23 126 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [copy(125),unit_del(a,47),unit_del(b,47)].
% 1.94/2.23 127 -ilf_type(A,set_type) | -member(A,c3) | member(ordered_pair(f13(A),A),c4) | range(c2,c3,c4) = c3 # label(prove_relset_1_23) # label(negated_conjecture). [clausify(35)].
% 1.94/2.23 128 -member(A,c3) | member(ordered_pair(f13(A),A),c4) | range(c2,c3,c4) = c3. [copy(127),unit_del(a,47)].
% 1.94/2.23 133 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f5(A,B),A) | member(f5(A,B),B) # label(p19) # label(axiom). [clausify(19)].
% 1.94/2.23 134 A = B | member(f5(B,A),B) | member(f5(B,A),A). [copy(133),unit_del(a,47),unit_del(b,47)].
% 1.94/2.23 135 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f5(A,B),A) | -member(f5(A,B),B) # label(p19) # label(axiom). [clausify(19)].
% 1.94/2.23 136 A = B | -member(f5(B,A),B) | -member(f5(B,A),A). [copy(135),unit_del(a,47),unit_del(b,47)].
% 1.94/2.23 137 -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(p22) # label(axiom). [clausify(22)].
% 1.94/2.23 138 -member(A,power_set(B)) | -member(C,A) | member(C,B). [copy(137),unit_del(a,47),unit_del(b,47),unit_del(d,47)].
% 1.94/2.23 148 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(41,d,36,c)].
% 1.94/2.23 149 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(148),unit_del(a,47),unit_del(b,47),unit_del(d,47)].
% 1.94/2.23 188 ilf_type(c4,subset_type(cross_product(c2,c3))). [resolve(107,a,48,a)].
% 1.94/2.23 199 range(c2,c3,c4) = range_of(c4). [resolve(124,a,48,a)].
% 1.94/2.23 200 -member(A,c3) | member(ordered_pair(f13(A),A),c4) | range_of(c4) = c3. [back_rewrite(128),rewrite([199(10)])].
% 1.94/2.23 201 member(c5,c3) | range_of(c4) != c3. [back_rewrite(64),rewrite([199(7)])].
% 1.94/2.23 202 -member(ordered_pair(A,c5),c4) | range_of(c4) != c3. [back_rewrite(54),rewrite([199(8)])].
% 1.94/2.23 204 ilf_type(range_of(c4),subset_type(c3)). [resolve(126,a,48,a),rewrite([199(4)])].
% 1.94/2.23 293 ilf_type(range_of(c4),member_type(power_set(c3))). [resolve(204,a,89,a)].
% 1.94/2.23 317 ilf_type(c4,binary_relation_type). [resolve(188,a,149,a)].
% 1.94/2.23 344 member(range_of(c4),power_set(c3)). [resolve(293,a,98,b),unit_del(a,50)].
% 1.94/2.23 351 -member(A,range_of(c4)) | member(A,c3). [resolve(344,a,138,a)].
% 1.94/2.23 430 member(f5(range_of(c4),A),c3) | range_of(c4) = A | member(f5(range_of(c4),A),A). [resolve(351,a,134,b),flip(b)].
% 1.94/2.23 436 member(f5(range_of(c4),c3),c3) | range_of(c4) = c3. [factor(430,a,c)].
% 1.94/2.23 615 member(ordered_pair(f13(f5(A,c3)),f5(A,c3)),c4) | range_of(c4) = c3 | c3 = A | member(f5(A,c3),A). [resolve(200,a,134,c)].
% 1.94/2.23 1137 range_of(c4) = c3 | -member(f5(range_of(c4),c3),range_of(c4)). [resolve(436,a,136,c),flip(b),merge(b)].
% 1.94/2.23 13055 range_of(c4) = c3 | c3 = A | member(f5(A,c3),A) | member(f5(A,c3),range_of(c4)). [resolve(615,a,109,c),unit_del(d,317)].
% 1.94/2.23 13057 range_of(c4) = c3 | member(f5(range_of(c4),c3),range_of(c4)). [factor(13055,c,d),flip(b),merge(b)].
% 1.94/2.23 13059 range_of(c4) = c3. [resolve(13057,b,1137,b),merge(b)].
% 1.94/2.23 13261 -member(ordered_pair(A,c5),c4). [back_rewrite(202),rewrite([13059(6)]),xx(b)].
% 1.94/2.23 13262 member(c5,c3). [back_rewrite(201),rewrite([13059(5)]),xx(b)].
% 1.94/2.23 13737 $F. [ur(103,a,317,a,c,13261,a),rewrite([13059(3)]),unit_del(a,13262)].
% 1.94/2.23
% 1.94/2.23 % SZS output end Refutation
% 1.94/2.23 ============================== end of proof ==========================
% 1.94/2.23
% 1.94/2.23 ============================== STATISTICS ============================
% 1.94/2.23
% 1.94/2.23 Given=1219. Generated=28852. Kept=13615. proofs=1.
% 1.94/2.23 Usable=1004. Sos=8948. Demods=64. Limbo=44, Disabled=3714. Hints=0.
% 1.94/2.23 Megabytes=19.99.
% 1.94/2.23 User_CPU=1.18, System_CPU=0.03, Wall_clock=2.
% 1.94/2.23
% 1.94/2.23 ============================== end of statistics =====================
% 1.94/2.23
% 1.94/2.23 ============================== end of search =========================
% 1.94/2.23
% 1.94/2.23 THEOREM PROVED
% 1.94/2.24 % SZS status Theorem
% 1.94/2.24
% 1.94/2.24 Exiting with 1 proof.
% 1.94/2.24
% 1.94/2.24 Process 8212 exit (max_proofs) Sun Jul 10 05:50:59 2022
% 1.94/2.24 Prover9 interrupted
%------------------------------------------------------------------------------