TSTP Solution File: SET664+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET664+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 04:31:15 EDT 2022
% Result : Theorem 0.75s 1.02s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET664+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n010.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 10:58:00 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.71/1.00 ============================== Prover9 ===============================
% 0.71/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.71/1.00 Process 32022 was started by sandbox2 on n010.cluster.edu,
% 0.71/1.00 Sun Jul 10 10:58:01 2022
% 0.71/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31868_n010.cluster.edu".
% 0.71/1.00 ============================== end of head ===========================
% 0.71/1.00
% 0.71/1.00 ============================== INPUT =================================
% 0.71/1.00
% 0.71/1.00 % Reading from file /tmp/Prover9_31868_n010.cluster.edu
% 0.71/1.00
% 0.71/1.00 set(prolog_style_variables).
% 0.71/1.00 set(auto2).
% 0.71/1.00 % set(auto2) -> set(auto).
% 0.71/1.00 % set(auto) -> set(auto_inference).
% 0.71/1.00 % set(auto) -> set(auto_setup).
% 0.71/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.71/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/1.00 % set(auto) -> set(auto_limits).
% 0.71/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/1.00 % set(auto) -> set(auto_denials).
% 0.71/1.00 % set(auto) -> set(auto_process).
% 0.71/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.71/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.71/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.71/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.71/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.71/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.71/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.71/1.00 % set(auto2) -> assign(stats, some).
% 0.71/1.00 % set(auto2) -> clear(echo_input).
% 0.71/1.00 % set(auto2) -> set(quiet).
% 0.71/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.71/1.00 % set(auto2) -> clear(print_given).
% 0.71/1.00 assign(lrs_ticks,-1).
% 0.71/1.00 assign(sos_limit,10000).
% 0.71/1.00 assign(order,kbo).
% 0.71/1.00 set(lex_order_vars).
% 0.71/1.00 clear(print_given).
% 0.71/1.00
% 0.71/1.00 % formulas(sos). % not echoed (35 formulas)
% 0.71/1.00
% 0.71/1.00 ============================== end of input ==========================
% 0.71/1.00
% 0.71/1.00 % From the command line: assign(max_seconds, 300).
% 0.71/1.00
% 0.71/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/1.00
% 0.71/1.00 % Formulas that are not ordinary clauses:
% 0.71/1.00 1 (all B (ilf_type(B,set_type) -> (subset(B,empty_set) -> B = empty_set))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 2 (all B (ilf_type(B,binary_relation_type) -> (domain_of(B) = empty_set | range_of(B) = empty_set -> B = empty_set))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> subset(domain_of(D),B) & subset(range_of(D),C))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 4 (all B (ilf_type(B,set_type) -> -member(B,empty_set))) # label(p4) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 5 (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].
% 0.71/1.00 6 (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].
% 0.71/1.00 7 (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,binary_relation_type) -> (B = C <-> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,set_type) -> (member(ordered_pair(D,E),B) <-> member(ordered_pair(D,E),C))))))))))) # label(p8) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 8 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 9 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p10) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 10 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))) # label(p11) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 11 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p12) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 12 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 13 (exists B ilf_type(B,binary_relation_type)) # label(p14) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 14 (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(p15) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 15 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p16) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 16 (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,binary_relation_type) -> (B = C -> C = B))))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 17 (all B (ilf_type(B,binary_relation_type) -> B = B)) # label(p18) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 18 (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(p19) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 19 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p20) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 20 (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].
% 0.71/1.00 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(p22) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 22 (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].
% 0.71/1.00 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(p24) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 24 (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].
% 0.71/1.00 25 (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].
% 0.71/1.00 26 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p27) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 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(p28) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 28 (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(p29) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 29 (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(p30) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 30 (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(p31) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 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(range(B,C,D),subset_type(C)))))))) # label(p32) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 32 (all B ilf_type(B,set_type)) # label(p33) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 33 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(C,B)) -> (ilf_type(D,relation_type(C,empty_set)) -> D = empty_set))))))) # label(prove_relset_1_27) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.71/1.00
% 0.71/1.00 ============================== end of process non-clausal formulas ===
% 0.71/1.00
% 0.71/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.71/1.00
% 0.71/1.00 ============================== PREDICATE ELIMINATION =================
% 0.71/1.00 34 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p13) # label(axiom). [clausify(12)].
% 0.71/1.00 35 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p27) # label(axiom). [clausify(26)].
% 0.71/1.00 36 -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type) | relation_like(A) # label(p13) # label(axiom). [clausify(12)].
% 0.71/1.00 Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -empty(A) | -ilf_type(A,set_type). [resolve(34,c,35,c)].
% 0.71/1.00 37 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f11(A),set_type) # label(p26) # label(axiom). [clausify(25)].
% 0.71/1.00 Derived: -ilf_type(A,set_type) | ilf_type(f11(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(37,b,34,c)].
% 0.71/1.00 38 -ilf_type(A,set_type) | relation_like(A) | member(f11(A),A) # label(p26) # label(axiom). [clausify(25)].
% 0.71/1.00 Derived: -ilf_type(A,set_type) | member(f11(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(38,b,34,c)].
% 0.71/1.00 39 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p28) # label(axiom). [clausify(27)].
% 0.71/1.00 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(39,d,34,c)].
% 0.71/1.00 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(p26) # label(axiom). [clausify(25)].
% 0.71/1.00 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,35,c)].
% 0.71/1.00 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,36,c)].
% 0.71/1.00 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(40,b,37,b)].
% 0.71/1.00 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(40,b,38,b)].
% 0.71/1.00 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,39,d)].
% 0.71/1.00 41 -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(25)].
% 0.71/1.00 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(41,b,35,c)].
% 0.71/1.00 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(41,b,36,c)].
% 0.71/1.00 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(41,b,37,b)].
% 0.71/1.00 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(41,b,38,b)].
% 0.71/1.00 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(41,b,39,d)].
% 0.71/1.00 42 -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(25)].
% 0.71/1.00 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(42,b,34,c)].
% 0.71/1.00 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(42,b,40,b)].
% 0.75/1.02 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(42,b,41,b)].
% 0.75/1.02 43 -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(25)].
% 0.75/1.02 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(43,b,35,c)].
% 0.75/1.02 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(43,b,36,c)].
% 0.75/1.02 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(43,b,37,b)].
% 0.75/1.02 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(43,b,38,b)].
% 0.75/1.02 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(43,b,39,d)].
% 0.75/1.02 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(43,b,42,b)].
% 0.75/1.02
% 0.75/1.02 ============================== end predicate elimination =============
% 0.75/1.02
% 0.75/1.02 Auto_denials: (non-Horn, no changes).
% 0.75/1.02
% 0.75/1.02 Term ordering decisions:
% 0.75/1.02 Function symbol KB weights: set_type=1. binary_relation_type=1. empty_set=1. c1=1. c2=1. c3=1. c4=1. ordered_pair=1. relation_type=1. cross_product=1. f1=1. f2=1. f3=1. f5=1. f7=1. f9=1. f10=1. subset_type=1. power_set=1. member_type=1. domain_of=1. range_of=1. f4=1. f6=1. f8=1. f11=1. domain=1. range=1.
% 0.75/1.02
% 0.75/1.02 ============================== end of process initial clauses ========
% 0.75/1.02
% 0.75/1.02 ============================== CLAUSES FOR SEARCH ====================
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% 0.75/1.02 ============================== end of clauses for search =============
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% 0.75/1.02 ============================== SEARCH ================================
% 0.75/1.02
% 0.75/1.02 % Starting search at 0.02 seconds.
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% 0.75/1.02 ============================== PROOF =================================
% 0.75/1.02 % SZS status Theorem
% 0.75/1.02 % SZS output start Refutation
% 0.75/1.02
% 0.75/1.02 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.75/1.02 % Length of proof is 29.
% 0.75/1.02 % Level of proof is 7.
% 0.75/1.02 % Maximum clause weight is 11.000.
% 0.75/1.02 % Given clauses 63.
% 0.75/1.02
% 0.75/1.02 1 (all B (ilf_type(B,set_type) -> (subset(B,empty_set) -> B = empty_set))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 2 (all B (ilf_type(B,binary_relation_type) -> (domain_of(B) = empty_set | range_of(B) = empty_set -> B = empty_set))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> subset(domain_of(D),B) & subset(range_of(D),C))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 5 (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].
% 0.75/1.02 12 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 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(p28) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 32 (all B ilf_type(B,set_type)) # label(p33) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 33 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(C,B)) -> (ilf_type(D,relation_type(C,empty_set)) -> D = empty_set))))))) # label(prove_relset_1_27) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.02 34 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p13) # label(axiom). [clausify(12)].
% 0.75/1.02 39 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p28) # label(axiom). [clausify(27)].
% 0.75/1.02 46 ilf_type(A,set_type) # label(p33) # label(axiom). [clausify(32)].
% 0.75/1.02 47 ilf_type(c4,relation_type(c3,c2)) # label(prove_relset_1_27) # label(negated_conjecture). [clausify(33)].
% 0.75/1.02 48 ilf_type(c4,relation_type(c3,empty_set)) # label(prove_relset_1_27) # label(negated_conjecture). [clausify(33)].
% 0.75/1.02 49 c4 != empty_set # label(prove_relset_1_27) # label(negated_conjecture). [clausify(33)].
% 0.75/1.02 61 -ilf_type(A,set_type) | -subset(A,empty_set) | empty_set = A # label(p1) # label(axiom). [clausify(1)].
% 0.75/1.02 62 -subset(A,empty_set) | empty_set = A. [copy(61),unit_del(a,46)].
% 0.75/1.02 67 -ilf_type(A,binary_relation_type) | range_of(A) != empty_set | empty_set = A # label(p2) # label(axiom). [clausify(2)].
% 0.75/1.02 81 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | subset(range_of(C),B) # label(p3) # label(axiom). [clausify(3)].
% 0.75/1.02 82 -ilf_type(A,relation_type(B,C)) | subset(range_of(A),C). [copy(81),unit_del(a,46),unit_del(b,46)].
% 0.75/1.02 98 -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(5)].
% 0.75/1.02 99 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [copy(98),unit_del(a,46),unit_del(b,46)].
% 0.75/1.02 123 -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(39,d,34,c)].
% 0.75/1.02 124 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(123),unit_del(a,46),unit_del(b,46),unit_del(d,46)].
% 0.75/1.02 157 subset(range_of(c4),empty_set). [resolve(82,a,48,a)].
% 0.75/1.02 170 ilf_type(c4,subset_type(cross_product(c3,c2))). [resolve(99,a,47,a)].
% 0.75/1.02 211 range_of(c4) = empty_set. [resolve(157,a,62,a),flip(a)].
% 0.75/1.02 232 -ilf_type(c4,binary_relation_type). [ur(67,b,211,a,c,49,a(flip))].
% 0.75/1.02 234 -ilf_type(c4,subset_type(cross_product(A,B))). [ur(124,b,232,a)].
% 0.75/1.02 235 $F. [resolve(234,a,170,a)].
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% 0.75/1.02 % SZS output end Refutation
% 0.75/1.02 ============================== end of proof ==========================
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% 0.75/1.02 ============================== STATISTICS ============================
% 0.75/1.02
% 0.75/1.02 Given=63. Generated=214. Kept=133. proofs=1.
% 0.75/1.02 Usable=61. Sos=62. Demods=7. Limbo=1, Disabled=94. Hints=0.
% 0.75/1.02 Megabytes=0.30.
% 0.75/1.02 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
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% 0.75/1.02 ============================== end of statistics =====================
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% 0.75/1.02 ============================== end of search =========================
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% 0.75/1.02 THEOREM PROVED
% 0.75/1.02 % SZS status Theorem
% 0.75/1.02
% 0.75/1.02 Exiting with 1 proof.
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% 0.75/1.02 Process 32022 exit (max_proofs) Sun Jul 10 10:58:01 2022
% 0.75/1.02 Prover9 interrupted
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