TSTP Solution File: SET681+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET681+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 04:31:22 EDT 2022
% Result : Theorem 0.86s 1.20s
% Output : Refutation 0.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET681+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n009.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 18:15:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.82/1.13 ============================== Prover9 ===============================
% 0.82/1.13 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.13 Process 18758 was started by sandbox on n009.cluster.edu,
% 0.82/1.13 Sun Jul 10 18:15:22 2022
% 0.82/1.13 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18565_n009.cluster.edu".
% 0.82/1.13 ============================== end of head ===========================
% 0.82/1.13
% 0.82/1.13 ============================== INPUT =================================
% 0.82/1.13
% 0.82/1.13 % Reading from file /tmp/Prover9_18565_n009.cluster.edu
% 0.82/1.13
% 0.82/1.13 set(prolog_style_variables).
% 0.82/1.13 set(auto2).
% 0.82/1.13 % set(auto2) -> set(auto).
% 0.82/1.13 % set(auto) -> set(auto_inference).
% 0.82/1.13 % set(auto) -> set(auto_setup).
% 0.82/1.13 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.13 % set(auto) -> set(auto_limits).
% 0.82/1.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.13 % set(auto) -> set(auto_denials).
% 0.82/1.13 % set(auto) -> set(auto_process).
% 0.82/1.13 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.13 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.13 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.13 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.13 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.13 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.13 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.13 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.13 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.13 % set(auto2) -> assign(stats, some).
% 0.82/1.13 % set(auto2) -> clear(echo_input).
% 0.82/1.13 % set(auto2) -> set(quiet).
% 0.82/1.13 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.13 % set(auto2) -> clear(print_given).
% 0.82/1.13 assign(lrs_ticks,-1).
% 0.82/1.13 assign(sos_limit,10000).
% 0.82/1.13 assign(order,kbo).
% 0.82/1.13 set(lex_order_vars).
% 0.82/1.13 clear(print_given).
% 0.82/1.13
% 0.82/1.13 % formulas(sos). % not echoed (32 formulas)
% 0.82/1.13
% 0.82/1.13 ============================== end of input ==========================
% 0.82/1.13
% 0.82/1.13 % From the command line: assign(max_seconds, 300).
% 0.82/1.13
% 0.82/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.13
% 0.82/1.13 % Formulas that are not ordinary clauses:
% 0.82/1.13 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,binary_relation_type) -> (member(B,range_of(C)) <-> (exists D (ilf_type(D,set_type) & member(ordered_pair(D,B),C)))))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 2 (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(p2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 3 (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,relation_type(B,C)) -> (member(ordered_pair(D,E),F) -> member(D,B) & member(E,C)))))))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 4 (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(p4) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p5) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 6 (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(p6) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 7 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (exists D ilf_type(D,relation_type(C,B))))))) # label(p7) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 8 (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(p8) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 9 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 10 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p10) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 11 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p11) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 12 (all B (ilf_type(B,set_type) -> ilf_type(singleton(B),set_type))) # label(p12) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 13 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 14 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))) # label(p14) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 15 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(unordered_pair(B,C),set_type))))) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 16 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> unordered_pair(B,C) = unordered_pair(C,B))))) # label(p16) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 17 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 18 (exists B ilf_type(B,binary_relation_type)) # label(p18) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 19 (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(p19) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 20 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p20) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 21 (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(p21) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 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].
% 0.82/1.13 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].
% 0.82/1.13 24 (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(p24) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 25 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p25) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 26 (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(p26) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 27 (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(p27) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 28 (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(p28) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 29 (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(p29) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 30 (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(p30) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 31 (all B ilf_type(B,set_type)) # label(p31) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 32 -(all B (-empty(B) & ilf_type(B,set_type) -> (all C (-empty(C) & ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(C,B)) -> (all E (ilf_type(E,member_type(B)) -> (member(E,range(C,B,D)) <-> (exists F (ilf_type(F,member_type(C)) & member(ordered_pair(F,E),D)))))))))))) # label(prove_relset_1_48) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.13
% 0.82/1.13 ============================== end of process non-clausal formulas ===
% 0.82/1.13
% 0.82/1.13 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.13
% 0.82/1.13 ============================== PREDICATE ELIMINATION =================
% 0.82/1.13 33 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p17) # label(axiom). [clausify(17)].
% 0.82/1.13 34 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p25) # label(axiom). [clausify(25)].
% 0.82/1.13 35 -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type) | relation_like(A) # label(p17) # label(axiom). [clausify(17)].
% 0.82/1.13 Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -empty(A) | -ilf_type(A,set_type). [resolve(33,c,34,c)].
% 0.82/1.13 36 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f10(A),set_type) # label(p24) # label(axiom). [clausify(24)].
% 0.82/1.13 Derived: -ilf_type(A,set_type) | ilf_type(f10(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(36,b,33,c)].
% 0.82/1.13 37 -ilf_type(A,set_type) | relation_like(A) | member(f10(A),A) # label(p24) # label(axiom). [clausify(24)].
% 0.82/1.13 Derived: -ilf_type(A,set_type) | member(f10(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(37,b,33,c)].
% 0.82/1.13 38 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p26) # label(axiom). [clausify(26)].
% 0.82/1.13 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(38,d,33,c)].
% 0.82/1.13 39 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) # label(p24) # label(axiom). [clausify(24)].
% 0.82/1.13 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(39,b,34,c)].
% 0.82/1.13 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(39,b,35,c)].
% 0.82/1.13 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(f10(A),set_type). [resolve(39,b,36,b)].
% 0.82/1.13 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(f10(A),A). [resolve(39,b,37,b)].
% 0.82/1.13 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(39,b,38,d)].
% 0.82/1.13 40 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) # label(p24) # label(axiom). [clausify(24)].
% 0.82/1.13 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(40,b,34,c)].
% 0.82/1.13 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(40,b,35,c)].
% 0.82/1.13 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(f10(A),set_type). [resolve(40,b,36,b)].
% 0.82/1.13 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(f10(A),A). [resolve(40,b,37,b)].
% 0.82/1.13 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(40,b,38,d)].
% 0.82/1.13 41 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f10(A) # label(p24) # label(axiom). [clausify(24)].
% 0.86/1.20 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f10(A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(41,b,33,c)].
% 0.86/1.20 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f10(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f8(A,D),set_type). [resolve(41,b,39,b)].
% 0.86/1.20 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f10(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f9(A,D),set_type). [resolve(41,b,40,b)].
% 0.86/1.20 42 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f8(A,B),f9(A,B)) = B # label(p24) # label(axiom). [clausify(24)].
% 0.86/1.20 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f8(A,B),f9(A,B)) = B | -empty(A) | -ilf_type(A,set_type). [resolve(42,b,34,c)].
% 0.86/1.20 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f8(A,B),f9(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(42,b,35,c)].
% 0.86/1.20 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f8(A,B),f9(A,B)) = B | -ilf_type(A,set_type) | ilf_type(f10(A),set_type). [resolve(42,b,36,b)].
% 0.86/1.20 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f8(A,B),f9(A,B)) = B | -ilf_type(A,set_type) | member(f10(A),A). [resolve(42,b,37,b)].
% 0.86/1.20 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f8(A,B),f9(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(42,b,38,d)].
% 0.86/1.20 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f8(A,B),f9(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f10(A). [resolve(42,b,41,b)].
% 0.86/1.20
% 0.86/1.20 ============================== end predicate elimination =============
% 0.86/1.20
% 0.86/1.20 Auto_denials: (non-Horn, no changes).
% 0.86/1.20
% 0.86/1.20 Term ordering decisions:
% 0.86/1.20 Function symbol KB weights: set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. ordered_pair=1. relation_type=1. cross_product=1. unordered_pair=1. f1=1. f2=1. f6=1. f7=1. f8=1. f9=1. subset_type=1. member_type=1. power_set=1. range_of=1. domain_of=1. singleton=1. f3=1. f4=1. f5=1. f10=1. range=1. domain=1.
% 0.86/1.20
% 0.86/1.20 ============================== end of process initial clauses ========
% 0.86/1.20
% 0.86/1.20 ============================== CLAUSES FOR SEARCH ====================
% 0.86/1.20
% 0.86/1.20 ============================== end of clauses for search =============
% 0.86/1.20
% 0.86/1.20 ============================== SEARCH ================================
% 0.86/1.20
% 0.86/1.20 % Starting search at 0.04 seconds.
% 0.86/1.20
% 0.86/1.20 ============================== PROOF =================================
% 0.86/1.20 % SZS status Theorem
% 0.86/1.20 % SZS output start Refutation
% 0.86/1.20
% 0.86/1.20 % Proof 1 at 0.08 (+ 0.00) seconds.
% 0.86/1.20 % Length of proof is 64.
% 0.86/1.20 % Level of proof is 9.
% 0.86/1.20 % Maximum clause weight is 15.000.
% 0.86/1.20 % Given clauses 155.
% 0.86/1.20
% 0.86/1.20 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,binary_relation_type) -> (member(B,range_of(C)) <-> (exists D (ilf_type(D,set_type) & member(ordered_pair(D,B),C)))))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.20 2 (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(p2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.20 6 (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(p6) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.20 8 (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(p8) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.20 17 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.20 19 (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(p19) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.20 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].
% 0.86/1.20 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].
% 0.86/1.20 26 (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(p26) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.20 27 (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(p27) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.20 28 (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(p28) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.20 29 (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(p29) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.20 31 (all B ilf_type(B,set_type)) # label(p31) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.20 32 -(all B (-empty(B) & ilf_type(B,set_type) -> (all C (-empty(C) & ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(C,B)) -> (all E (ilf_type(E,member_type(B)) -> (member(E,range(C,B,D)) <-> (exists F (ilf_type(F,member_type(C)) & member(ordered_pair(F,E),D)))))))))))) # label(prove_relset_1_48) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.86/1.20 33 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p17) # label(axiom). [clausify(17)].
% 0.86/1.20 38 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p26) # label(axiom). [clausify(26)].
% 0.86/1.20 44 ilf_type(A,set_type) # label(p31) # label(axiom). [clausify(31)].
% 0.86/1.20 46 ilf_type(c4,relation_type(c3,c2)) # label(prove_relset_1_48) # label(negated_conjecture). [clausify(32)].
% 0.86/1.20 48 member(c5,range(c3,c2,c4)) | member(ordered_pair(c6,c5),c4) # label(prove_relset_1_48) # label(negated_conjecture). [clausify(32)].
% 0.86/1.20 50 -empty(c3) # label(prove_relset_1_48) # label(negated_conjecture). [clausify(32)].
% 0.86/1.20 51 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p23) # label(axiom). [clausify(23)].
% 0.86/1.20 52 -empty(power_set(A)). [copy(51),unit_del(a,44)].
% 0.86/1.20 55 -member(c5,range(c3,c2,c4)) | -ilf_type(A,member_type(c3)) | -member(ordered_pair(A,c5),c4) # label(prove_relset_1_48) # label(negated_conjecture). [clausify(32)].
% 0.86/1.20 74 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | -ilf_type(A,member_type(B)) | member(A,B) # label(p8) # label(axiom). [clausify(8)].
% 0.86/1.20 75 empty(A) | -ilf_type(B,member_type(A)) | member(B,A). [copy(74),unit_del(a,44),unit_del(c,44)].
% 0.86/1.20 76 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B) # label(p8) # label(axiom). [clausify(8)].
% 0.86/1.20 77 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [copy(76),unit_del(a,44),unit_del(c,44)].
% 0.86/1.20 78 -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(p19) # label(axiom). [clausify(19)].
% 0.86/1.20 79 -ilf_type(A,subset_type(B)) | ilf_type(A,member_type(power_set(B))). [copy(78),unit_del(a,44),unit_del(b,44)].
% 0.86/1.20 87 -ilf_type(A,set_type) | -ilf_type(B,binary_relation_type) | -member(A,range_of(B)) | member(ordered_pair(f1(A,B),A),B) # label(p1) # label(axiom). [clausify(1)].
% 0.86/1.20 88 -ilf_type(A,binary_relation_type) | -member(B,range_of(A)) | member(ordered_pair(f1(B,A),B),A). [copy(87),unit_del(a,44)].
% 0.86/1.20 91 -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(p6) # label(axiom). [clausify(6)].
% 0.86/1.20 92 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [copy(91),unit_del(a,44),unit_del(b,44)].
% 0.86/1.20 93 -ilf_type(A,set_type) | -ilf_type(B,binary_relation_type) | member(A,range_of(B)) | -ilf_type(C,set_type) | -member(ordered_pair(C,A),B) # label(p1) # label(axiom). [clausify(1)].
% 0.86/1.20 94 -ilf_type(A,binary_relation_type) | member(B,range_of(A)) | -member(ordered_pair(C,B),A). [copy(93),unit_del(a,44),unit_del(d,44)].
% 0.86/1.20 95 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)) # label(p2) # label(axiom). [clausify(2)].
% 0.86/1.20 96 -ilf_type(A,binary_relation_type) | -member(ordered_pair(B,C),A) | member(B,domain_of(A)). [copy(95),unit_del(a,44),unit_del(b,44)].
% 0.86/1.20 102 -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(p27) # label(axiom). [clausify(27)].
% 0.86/1.20 103 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [copy(102),unit_del(a,44),unit_del(b,44)].
% 0.86/1.20 104 -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(p28) # label(axiom). [clausify(28)].
% 0.86/1.20 105 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [copy(104),unit_del(a,44),unit_del(b,44)].
% 0.86/1.20 106 -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(p29) # label(axiom). [clausify(29)].
% 0.86/1.20 107 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [copy(106),unit_del(a,44),unit_del(b,44)].
% 0.86/1.20 114 -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)].
% 0.86/1.20 115 -member(A,power_set(B)) | -member(C,A) | member(C,B). [copy(114),unit_del(a,44),unit_del(b,44),unit_del(d,44)].
% 0.86/1.20 129 -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(38,d,33,c)].
% 0.86/1.20 130 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(129),unit_del(a,44),unit_del(b,44),unit_del(d,44)].
% 0.86/1.20 174 ilf_type(c4,subset_type(cross_product(c3,c2))). [resolve(92,a,46,a)].
% 0.86/1.20 182 domain(c3,c2,c4) = domain_of(c4). [resolve(103,a,46,a)].
% 0.86/1.20 184 ilf_type(domain_of(c4),subset_type(c3)). [resolve(105,a,46,a),rewrite([182(4)])].
% 0.86/1.20 186 range(c3,c2,c4) = range_of(c4). [resolve(107,a,46,a)].
% 0.86/1.20 193 -member(c5,range_of(c4)) | -ilf_type(A,member_type(c3)) | -member(ordered_pair(A,c5),c4). [back_rewrite(55),rewrite([186(5)])].
% 0.86/1.20 194 member(c5,range_of(c4)) | member(ordered_pair(c6,c5),c4). [back_rewrite(48),rewrite([186(5)])].
% 0.86/1.20 264 ilf_type(domain_of(c4),member_type(power_set(c3))). [resolve(184,a,79,a)].
% 0.86/1.20 306 ilf_type(c4,binary_relation_type). [resolve(174,a,130,a)].
% 0.86/1.20 312 member(domain_of(c4),power_set(c3)). [resolve(264,a,75,b),unit_del(a,52)].
% 0.86/1.20 318 -member(A,domain_of(c4)) | member(A,c3). [resolve(312,a,115,a)].
% 0.86/1.20 567 member(c5,range_of(c4)). [resolve(194,b,94,c),merge(c),unit_del(b,306)].
% 0.86/1.20 568 -ilf_type(A,member_type(c3)) | -member(ordered_pair(A,c5),c4). [back_unit_del(193),unit_del(a,567)].
% 0.86/1.20 576 member(ordered_pair(f1(c5,c4),c5),c4). [resolve(567,a,88,b),unit_del(a,306)].
% 0.86/1.20 609 -ilf_type(f1(c5,c4),member_type(c3)). [resolve(576,a,568,b)].
% 0.86/1.20 619 member(f1(c5,c4),domain_of(c4)). [resolve(576,a,96,b),unit_del(a,306)].
% 0.86/1.20 625 member(f1(c5,c4),c3). [resolve(619,a,318,a)].
% 0.86/1.20 657 $F. [resolve(625,a,77,c),unit_del(a,50),unit_del(b,609)].
% 0.86/1.20
% 0.86/1.20 % SZS output end Refutation
% 0.86/1.20 ============================== end of proof ==========================
% 0.86/1.20
% 0.86/1.20 ============================== STATISTICS ============================
% 0.86/1.20
% 0.86/1.20 Given=155. Generated=815. Kept=550. proofs=1.
% 0.86/1.20 Usable=136. Sos=311. Demods=11. Limbo=6, Disabled=184. Hints=0.
% 0.86/1.20 Megabytes=0.92.
% 0.86/1.20 User_CPU=0.09, System_CPU=0.00, Wall_clock=1.
% 0.86/1.20
% 0.86/1.20 ============================== end of statistics =====================
% 0.86/1.20
% 0.86/1.20 ============================== end of search =========================
% 0.86/1.20
% 0.86/1.20 THEOREM PROVED
% 0.86/1.20 % SZS status Theorem
% 0.86/1.20
% 0.86/1.20 Exiting with 1 proof.
% 0.86/1.20
% 0.86/1.20 Process 18758 exit (max_proofs) Sun Jul 10 18:15:23 2022
% 0.86/1.20 Prover9 interrupted
%------------------------------------------------------------------------------