TSTP Solution File: SET657+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET657+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 04:31:12 EDT 2022
% Result : Theorem 1.65s 1.93s
% Output : Refutation 1.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET657+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 08:49:14 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.44/1.03 ============================== Prover9 ===============================
% 0.44/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.03 Process 21265 was started by sandbox on n013.cluster.edu,
% 0.44/1.03 Sun Jul 10 08:49:15 2022
% 0.44/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21111_n013.cluster.edu".
% 0.44/1.03 ============================== end of head ===========================
% 0.44/1.03
% 0.44/1.03 ============================== INPUT =================================
% 0.44/1.03
% 0.44/1.03 % Reading from file /tmp/Prover9_21111_n013.cluster.edu
% 0.44/1.03
% 0.44/1.03 set(prolog_style_variables).
% 0.44/1.03 set(auto2).
% 0.44/1.03 % set(auto2) -> set(auto).
% 0.44/1.03 % set(auto) -> set(auto_inference).
% 0.44/1.03 % set(auto) -> set(auto_setup).
% 0.44/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.03 % set(auto) -> set(auto_limits).
% 0.44/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.03 % set(auto) -> set(auto_denials).
% 0.44/1.03 % set(auto) -> set(auto_process).
% 0.44/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.03 % set(auto2) -> assign(stats, some).
% 0.44/1.03 % set(auto2) -> clear(echo_input).
% 0.44/1.03 % set(auto2) -> set(quiet).
% 0.44/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.03 % set(auto2) -> clear(print_given).
% 0.44/1.03 assign(lrs_ticks,-1).
% 0.44/1.03 assign(sos_limit,10000).
% 0.44/1.03 assign(order,kbo).
% 0.44/1.03 set(lex_order_vars).
% 0.44/1.03 clear(print_given).
% 0.44/1.03
% 0.44/1.03 % formulas(sos). % not echoed (38 formulas)
% 0.44/1.03
% 0.44/1.03 ============================== end of input ==========================
% 0.44/1.03
% 0.44/1.03 % From the command line: assign(max_seconds, 300).
% 0.44/1.03
% 0.44/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.03
% 0.44/1.03 % Formulas that are not ordinary clauses:
% 0.44/1.03 1 (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) -> (subset(B,C) & subset(D,E) -> subset(union(B,D),union(C,E))))))))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 2 (all B (ilf_type(B,binary_relation_type) -> field_of(B) = union(domain_of(B),range_of(B)))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (member(D,union(B,C)) <-> member(D,B) | member(D,C)))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 4 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(union(B,C),set_type))))) # label(p4) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 5 (all B (ilf_type(B,binary_relation_type) -> field_of(B) = union(domain_of(B),range_of(B)))) # label(p5) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 6 (all B (ilf_type(B,binary_relation_type) -> ilf_type(field_of(B),set_type))) # label(p6) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 9 (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(p9) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 10 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> union(B,C) = union(C,B))))) # label(p10) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 11 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p11) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 13 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 14 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p14) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 15 (exists B ilf_type(B,binary_relation_type)) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 16 (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(p16) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 17 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 18 (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,binary_relation_type) -> (B = C -> C = B))))) # label(p18) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 19 (all B (ilf_type(B,binary_relation_type) -> B = B)) # label(p19) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 20 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p20) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 21 (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(p21) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 22 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p22) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 23 (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(p23) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 24 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p24) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 25 (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(p25) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 28 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p28) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 29 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p29) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 30 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p30) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 31 (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,relation_type(B,C)) -> union4(B,C,D,E) = union(D,E))))))))) # label(p31) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 32 (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,relation_type(B,C)) -> ilf_type(union4(B,C,D,E),relation_type(B,C)))))))))) # label(p32) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 33 (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(p33) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 34 (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(p34) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 35 (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(p35) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 36 (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(p36) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 37 (all B ilf_type(B,set_type)) # label(p37) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 38 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> subset(field_of(D),union(B,C)))))))) # label(prove_relset_1_19) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.03
% 0.44/1.03 ============================== end of process non-clausal formulas ===
% 0.44/1.03
% 0.44/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.03
% 0.44/1.03 ============================== PREDICATE ELIMINATION =================
% 0.44/1.03 39 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p14) # label(axiom). [clausify(14)].
% 0.44/1.03 40 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p30) # label(axiom). [clausify(30)].
% 0.44/1.03 41 -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type) | relation_like(A) # label(p14) # label(axiom). [clausify(14)].
% 0.44/1.03 Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -empty(A) | -ilf_type(A,set_type). [resolve(39,c,40,c)].
% 0.44/1.03 42 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f9(A),set_type) # label(p26) # label(axiom). [clausify(26)].
% 0.44/1.03 Derived: -ilf_type(A,set_type) | ilf_type(f9(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(42,b,39,c)].
% 0.44/1.03 43 -ilf_type(A,set_type) | relation_like(A) | member(f9(A),A) # label(p26) # label(axiom). [clausify(26)].
% 0.44/1.03 Derived: -ilf_type(A,set_type) | member(f9(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(43,b,39,c)].
% 0.44/1.03 44 -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)].
% 0.44/1.03 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(44,d,39,c)].
% 0.44/1.03 45 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) # label(p26) # label(axiom). [clausify(26)].
% 0.44/1.03 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) | -empty(A) | -ilf_type(A,set_type). [resolve(45,b,40,c)].
% 0.44/1.03 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(45,b,41,c)].
% 0.44/1.03 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f9(A),set_type). [resolve(45,b,42,b)].
% 0.44/1.03 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) | -ilf_type(A,set_type) | member(f9(A),A). [resolve(45,b,43,b)].
% 0.44/1.03 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(45,b,44,d)].
% 0.44/1.03 46 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) # label(p26) # label(axiom). [clausify(26)].
% 0.44/1.03 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) | -empty(A) | -ilf_type(A,set_type). [resolve(46,b,40,c)].
% 0.44/1.03 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(46,b,41,c)].
% 0.44/1.03 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f9(A),set_type). [resolve(46,b,42,b)].
% 1.65/1.93 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) | -ilf_type(A,set_type) | member(f9(A),A). [resolve(46,b,43,b)].
% 1.65/1.93 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(46,b,44,d)].
% 1.65/1.93 47 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f9(A) # label(p26) # label(axiom). [clausify(26)].
% 1.65/1.93 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f9(A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(47,b,39,c)].
% 1.65/1.93 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f9(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f7(A,D),set_type). [resolve(47,b,45,b)].
% 1.65/1.93 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f9(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f8(A,D),set_type). [resolve(47,b,46,b)].
% 1.65/1.93 48 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B # label(p26) # label(axiom). [clausify(26)].
% 1.65/1.93 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -empty(A) | -ilf_type(A,set_type). [resolve(48,b,40,c)].
% 1.65/1.93 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(48,b,41,c)].
% 1.65/1.93 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -ilf_type(A,set_type) | ilf_type(f9(A),set_type). [resolve(48,b,42,b)].
% 1.65/1.93 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -ilf_type(A,set_type) | member(f9(A),A). [resolve(48,b,43,b)].
% 1.65/1.93 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(48,b,44,d)].
% 1.65/1.93 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f9(A). [resolve(48,b,47,b)].
% 1.65/1.93
% 1.65/1.93 ============================== end predicate elimination =============
% 1.65/1.93
% 1.65/1.93 Auto_denials: (non-Horn, no changes).
% 1.65/1.93
% 1.65/1.93 Term ordering decisions:
% 1.65/1.93 Function symbol KB weights: set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. c4=1. relation_type=1. ordered_pair=1. union=1. cross_product=1. f1=1. f2=1. f4=1. f6=1. f7=1. f8=1. subset_type=1. power_set=1. member_type=1. domain_of=1. range_of=1. field_of=1. f3=1. f5=1. f9=1. f10=1. domain=1. range=1. union4=1.
% 1.65/1.93
% 1.65/1.93 ============================== end of process initial clauses ========
% 1.65/1.93
% 1.65/1.93 ============================== CLAUSES FOR SEARCH ====================
% 1.65/1.93
% 1.65/1.93 ============================== end of clauses for search =============
% 1.65/1.93
% 1.65/1.93 ============================== SEARCH ================================
% 1.65/1.93
% 1.65/1.93 % Starting search at 0.03 seconds.
% 1.65/1.93
% 1.65/1.93 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 757 (0.00 of 0.41 sec).
% 1.65/1.93
% 1.65/1.93 Low Water (keep): wt=14.000, iters=3357
% 1.65/1.93
% 1.65/1.93 Low Water (keep): wt=13.000, iters=3342
% 1.65/1.93
% 1.65/1.93 Low Water (keep): wt=12.000, iters=3343
% 1.65/1.93
% 1.65/1.93 Low Water (keep): wt=11.000, iters=3346
% 1.65/1.93
% 1.65/1.93 Low Water (displace): id=4216, wt=50.000
% 1.65/1.93
% 1.65/1.93 Low Water (displace): id=4215, wt=48.000
% 1.65/1.93
% 1.65/1.93 Low Water (displace): id=5249, wt=47.000
% 1.65/1.93
% 1.65/1.93 Low Water (displace): id=4223, wt=46.000
% 1.65/1.93
% 1.65/1.93 Low Water (displace): id=4224, wt=44.000
% 1.65/1.93
% 1.65/1.93 ============================== PROOF =================================
% 1.65/1.93 % SZS status Theorem
% 1.65/1.93 % SZS output start Refutation
% 1.65/1.93
% 1.65/1.93 % Proof 1 at 0.89 (+ 0.03) seconds.
% 1.65/1.93 % Length of proof is 71.
% 1.65/1.93 % Level of proof is 8.
% 1.65/1.93 % Maximum clause weight is 12.000.
% 1.65/1.93 % Given clauses 1404.
% 1.65/1.93
% 1.65/1.93 2 (all B (ilf_type(B,binary_relation_type) -> field_of(B) = union(domain_of(B),range_of(B)))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.93 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (member(D,union(B,C)) <-> member(D,B) | member(D,C)))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.93 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].
% 1.65/1.93 9 (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(p9) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.93 14 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p14) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.93 16 (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(p16) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.93 21 (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(p21) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.93 22 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p22) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.93 23 (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(p23) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.93 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].
% 1.65/1.93 33 (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(p33) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.93 34 (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(p34) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.93 35 (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(p35) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.93 36 (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(p36) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.93 37 (all B ilf_type(B,set_type)) # label(p37) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.93 38 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> subset(field_of(D),union(B,C)))))))) # label(prove_relset_1_19) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.65/1.93 39 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p14) # label(axiom). [clausify(14)].
% 1.65/1.93 44 -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)].
% 1.65/1.93 50 ilf_type(A,set_type) # label(p37) # label(axiom). [clausify(37)].
% 1.65/1.93 51 ilf_type(c4,relation_type(c2,c3)) # label(prove_relset_1_19) # label(negated_conjecture). [clausify(38)].
% 1.65/1.93 52 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p22) # label(axiom). [clausify(22)].
% 1.65/1.93 53 -empty(power_set(A)). [copy(52),unit_del(a,50)].
% 1.65/1.93 54 -subset(field_of(c4),union(c2,c3)) # label(prove_relset_1_19) # label(negated_conjecture). [clausify(38)].
% 1.65/1.93 67 -ilf_type(A,binary_relation_type) | field_of(A) = union(domain_of(A),range_of(A)) # label(p2) # label(axiom). [clausify(2)].
% 1.65/1.93 68 -ilf_type(A,binary_relation_type) | union(domain_of(A),range_of(A)) = field_of(A). [copy(67),flip(b)].
% 1.65/1.93 78 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f2(A,B),A) # label(p9) # label(axiom). [clausify(9)].
% 1.65/1.93 79 subset(A,B) | member(f2(A,B),A). [copy(78),unit_del(a,50),unit_del(b,50)].
% 1.65/1.93 80 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f2(A,B),B) # label(p9) # label(axiom). [clausify(9)].
% 1.65/1.93 81 subset(A,B) | -member(f2(A,B),B). [copy(80),unit_del(a,50),unit_del(b,50)].
% 1.65/1.93 83 -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(p16) # label(axiom). [clausify(16)].
% 1.65/1.93 84 -ilf_type(A,subset_type(B)) | ilf_type(A,member_type(power_set(B))). [copy(83),unit_del(a,50),unit_del(b,50)].
% 1.65/1.93 92 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | -ilf_type(A,member_type(B)) | member(A,B) # label(p23) # label(axiom). [clausify(23)].
% 1.65/1.93 93 empty(A) | -ilf_type(B,member_type(A)) | member(B,A). [copy(92),unit_del(a,50),unit_del(c,50)].
% 1.65/1.93 96 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,union(A,B)) | -member(C,A) # label(p3) # label(axiom). [clausify(3)].
% 1.65/1.93 97 member(A,union(B,C)) | -member(A,B). [copy(96),unit_del(a,50),unit_del(b,50),unit_del(c,50)].
% 1.65/1.93 98 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,union(A,B)) | -member(C,B) # label(p3) # label(axiom). [clausify(3)].
% 1.65/1.93 99 member(A,union(B,C)) | -member(A,C). [copy(98),unit_del(a,50),unit_del(b,50),unit_del(c,50)].
% 1.65/1.93 102 -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)].
% 1.65/1.93 103 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [copy(102),unit_del(a,50),unit_del(b,50)].
% 1.65/1.93 110 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain(A,B,C) = domain_of(C) # label(p33) # label(axiom). [clausify(33)].
% 1.65/1.93 111 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [copy(110),unit_del(a,50),unit_del(b,50)].
% 1.65/1.93 112 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(domain(A,B,C),subset_type(A)) # label(p34) # label(axiom). [clausify(34)].
% 1.65/1.93 113 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [copy(112),unit_del(a,50),unit_del(b,50)].
% 1.65/1.93 114 -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(p35) # label(axiom). [clausify(35)].
% 1.65/1.93 115 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [copy(114),unit_del(a,50),unit_del(b,50)].
% 1.65/1.93 116 -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(p36) # label(axiom). [clausify(36)].
% 1.65/1.93 117 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [copy(116),unit_del(a,50),unit_del(b,50)].
% 1.65/1.93 118 -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(p21) # label(axiom). [clausify(21)].
% 1.65/1.93 119 -member(A,power_set(B)) | -member(C,A) | member(C,B). [copy(118),unit_del(a,50),unit_del(b,50),unit_del(d,50)].
% 1.65/1.93 124 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,union(A,B)) | member(C,A) | member(C,B) # label(p3) # label(axiom). [clausify(3)].
% 1.65/1.93 125 -member(A,union(B,C)) | member(A,B) | member(A,C). [copy(124),unit_del(a,50),unit_del(b,50),unit_del(c,50)].
% 1.65/1.93 137 -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(44,d,39,c)].
% 1.65/1.93 138 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(137),unit_del(a,50),unit_del(b,50),unit_del(d,50)].
% 1.65/1.93 169 member(f2(field_of(c4),union(c2,c3)),field_of(c4)). [resolve(79,a,54,a)].
% 1.65/1.93 170 -member(f2(field_of(c4),union(c2,c3)),union(c2,c3)). [ur(81,a,54,a)].
% 1.65/1.93 182 ilf_type(c4,subset_type(cross_product(c2,c3))). [resolve(103,a,51,a)].
% 1.65/1.93 189 domain(c2,c3,c4) = domain_of(c4). [resolve(111,a,51,a)].
% 1.65/1.93 191 ilf_type(domain_of(c4),subset_type(c2)). [resolve(113,a,51,a),rewrite([189(4)])].
% 1.65/1.93 193 range(c2,c3,c4) = range_of(c4). [resolve(115,a,51,a)].
% 1.65/1.93 195 ilf_type(range_of(c4),subset_type(c3)). [resolve(117,a,51,a),rewrite([193(4)])].
% 1.65/1.93 278 -member(f2(field_of(c4),union(c2,c3)),c3). [ur(99,a,170,a)].
% 1.65/1.93 279 -member(f2(field_of(c4),union(c2,c3)),c2). [ur(97,a,170,a)].
% 1.65/1.93 308 ilf_type(domain_of(c4),member_type(power_set(c2))). [resolve(191,a,84,a)].
% 1.65/1.93 309 ilf_type(range_of(c4),member_type(power_set(c3))). [resolve(195,a,84,a)].
% 1.65/1.93 381 ilf_type(c4,binary_relation_type). [resolve(182,a,138,a)].
% 1.65/1.93 383 union(domain_of(c4),range_of(c4)) = field_of(c4). [resolve(381,a,68,a)].
% 1.65/1.93 447 member(domain_of(c4),power_set(c2)). [resolve(308,a,93,b),unit_del(a,53)].
% 1.65/1.93 457 -member(f2(field_of(c4),union(c2,c3)),domain_of(c4)). [ur(119,a,447,a,c,279,a)].
% 1.65/1.93 471 member(range_of(c4),power_set(c3)). [resolve(309,a,93,b),unit_del(a,53)].
% 1.65/1.93 481 -member(f2(field_of(c4),union(c2,c3)),range_of(c4)). [ur(119,a,471,a,c,278,a)].
% 1.65/1.93 11712 $F. [ur(125,b,457,a,c,481,a),rewrite([383(11)]),unit_del(a,169)].
% 1.65/1.93
% 1.65/1.93 % SZS output end Refutation
% 1.65/1.93 ============================== end of proof ==========================
% 1.65/1.93
% 1.65/1.93 ============================== STATISTICS ============================
% 1.65/1.93
% 1.65/1.93 Given=1404. Generated=37025. Kept=11596. proofs=1.
% 1.65/1.93 Usable=1395. Sos=9994. Demods=116. Limbo=2, Disabled=292. Hints=0.
% 1.65/1.93 Megabytes=11.95.
% 1.65/1.93 User_CPU=0.89, System_CPU=0.03, Wall_clock=1.
% 1.65/1.93
% 1.65/1.93 ============================== end of statistics =====================
% 1.65/1.93
% 1.65/1.93 ============================== end of search =========================
% 1.65/1.93
% 1.65/1.93 THEOREM PROVED
% 1.65/1.93 % SZS status Theorem
% 1.65/1.93
% 1.65/1.93 Exiting with 1 proof.
% 1.65/1.93
% 1.65/1.93 Process 21265 exit (max_proofs) Sun Jul 10 08:49:16 2022
% 1.65/1.93 Prover9 interrupted
%------------------------------------------------------------------------------