TSTP Solution File: SET677+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET677+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 04:31:20 EDT 2022
% Result : Theorem 0.74s 1.08s
% Output : Refutation 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET677+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n005.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 01:30:37 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.42/1.00 ============================== Prover9 ===============================
% 0.42/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.00 Process 22370 was started by sandbox on n005.cluster.edu,
% 0.42/1.00 Sun Jul 10 01:30:37 2022
% 0.42/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22217_n005.cluster.edu".
% 0.42/1.00 ============================== end of head ===========================
% 0.42/1.00
% 0.42/1.00 ============================== INPUT =================================
% 0.42/1.00
% 0.42/1.00 % Reading from file /tmp/Prover9_22217_n005.cluster.edu
% 0.42/1.00
% 0.42/1.00 set(prolog_style_variables).
% 0.42/1.00 set(auto2).
% 0.42/1.00 % set(auto2) -> set(auto).
% 0.42/1.00 % set(auto) -> set(auto_inference).
% 0.42/1.00 % set(auto) -> set(auto_setup).
% 0.42/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.00 % set(auto) -> set(auto_limits).
% 0.42/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.00 % set(auto) -> set(auto_denials).
% 0.42/1.00 % set(auto) -> set(auto_process).
% 0.42/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.00 % set(auto2) -> assign(stats, some).
% 0.42/1.00 % set(auto2) -> clear(echo_input).
% 0.42/1.00 % set(auto2) -> set(quiet).
% 0.42/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.00 % set(auto2) -> clear(print_given).
% 0.42/1.00 assign(lrs_ticks,-1).
% 0.42/1.00 assign(sos_limit,10000).
% 0.42/1.00 assign(order,kbo).
% 0.42/1.00 set(lex_order_vars).
% 0.42/1.00 clear(print_given).
% 0.42/1.00
% 0.42/1.00 % formulas(sos). % not echoed (35 formulas)
% 0.42/1.00
% 0.42/1.00 ============================== end of input ==========================
% 0.42/1.00
% 0.42/1.00 % From the command line: assign(max_seconds, 300).
% 0.42/1.00
% 0.42/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.00
% 0.42/1.00 % Formulas that are not ordinary clauses:
% 0.42/1.00 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(C,B)) -> (subset(identity_relation_of(C),D) -> C = domain(C,B,D) & subset(C,range(C,B,D))))))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 2 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> (subset(identity_relation_of(C),D) -> subset(C,domain(B,C,D)) & C = range(B,C,D)))))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (member(ordered_pair(C,D),identity_relation_of(B)) <-> member(C,B) & C = D))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 4 (all B (ilf_type(B,set_type) -> ilf_type(identity_relation_of(B),binary_relation_type))) # label(p4) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (ilf_type(C,identity_relation_of_type(B)) <-> ilf_type(C,relation_type(B,B))))))) # label(p5) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 6 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,identity_relation_of_type(B))))) # label(p6) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 7 (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,binary_relation_type) -> (subset(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(p7) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 8 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (B = C <-> subset(B,C) & subset(C,B)))))) # label(p8) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 9 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 10 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))) # label(p10) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 11 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p11) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 12 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p12) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 13 (exists B ilf_type(B,binary_relation_type)) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 14 (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(p14) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 15 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (exists D ilf_type(D,relation_type(C,B))))))) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 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].
% 0.42/1.00 17 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 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(p18) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 19 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p19) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 20 (all B (ilf_type(B,binary_relation_type) -> subset(B,B))) # label(p20) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 21 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p21) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 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].
% 0.42/1.00 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].
% 0.42/1.00 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].
% 0.42/1.00 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].
% 0.42/1.00 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].
% 0.42/1.00 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(p27) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 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].
% 0.42/1.00 29 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p29) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 30 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> domain(B,C,D) = domain_of(D))))))) # label(p30) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 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(domain(B,C,D),subset_type(B)))))))) # label(p31) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 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].
% 0.42/1.00 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].
% 0.42/1.00 34 (all B ilf_type(B,set_type)) # label(p34) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 35 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,identity_relation_of_type(B)) -> (subset(identity_relation_of(B),C) -> B = domain(B,B,C) & B = range(B,B,C)))))) # label(prove_relset_1_44) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/1.00
% 0.42/1.00 ============================== end of process non-clausal formulas ===
% 0.42/1.00
% 0.42/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/1.00
% 0.42/1.00 ============================== PREDICATE ELIMINATION =================
% 0.42/1.00 36 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p12) # label(axiom). [clausify(12)].
% 0.42/1.00 37 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p29) # label(axiom). [clausify(29)].
% 0.42/1.00 38 -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type) | relation_like(A) # label(p12) # label(axiom). [clausify(12)].
% 0.42/1.00 Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -empty(A) | -ilf_type(A,set_type). [resolve(36,c,37,c)].
% 0.42/1.00 39 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f11(A),set_type) # label(p26) # label(axiom). [clausify(26)].
% 0.42/1.00 Derived: -ilf_type(A,set_type) | ilf_type(f11(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(39,b,36,c)].
% 0.42/1.00 40 -ilf_type(A,set_type) | relation_like(A) | member(f11(A),A) # label(p26) # label(axiom). [clausify(26)].
% 0.42/1.00 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)].
% 0.42/1.00 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)].
% 0.42/1.00 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(41,d,36,c)].
% 0.42/1.00 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)].
% 0.42/1.00 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(42,b,37,c)].
% 0.42/1.00 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(42,b,38,c)].
% 0.42/1.00 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(42,b,39,b)].
% 0.42/1.00 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(42,b,40,b)].
% 0.42/1.00 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(42,b,41,d)].
% 0.42/1.00 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)].
% 0.42/1.00 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(43,b,37,c)].
% 0.42/1.00 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(43,b,38,c)].
% 0.42/1.00 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(43,b,39,b)].
% 0.42/1.00 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(43,b,40,b)].
% 0.42/1.00 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(43,b,41,d)].
% 0.74/1.08 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)].
% 0.74/1.08 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)].
% 0.74/1.08 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)].
% 0.74/1.08 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)].
% 0.74/1.08 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)].
% 0.74/1.08 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)].
% 0.74/1.08 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)].
% 0.74/1.08 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)].
% 0.74/1.08 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)].
% 0.74/1.08 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)].
% 0.74/1.08 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)].
% 0.74/1.08
% 0.74/1.08 ============================== end predicate elimination =============
% 0.74/1.08
% 0.74/1.08 Auto_denials: (non-Horn, no changes).
% 0.74/1.08
% 0.74/1.08 Term ordering decisions:
% 0.74/1.08 Function symbol KB weights: set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. ordered_pair=1. relation_type=1. cross_product=1. f2=1. f3=1. f4=1. f6=1. f7=1. f9=1. f10=1. subset_type=1. identity_relation_of=1. power_set=1. member_type=1. identity_relation_of_type=1. domain_of=1. range_of=1. f1=1. f5=1. f8=1. f11=1. f12=1. domain=1. range=1.
% 0.74/1.08
% 0.74/1.08 ============================== end of process initial clauses ========
% 0.74/1.08
% 0.74/1.08 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.08
% 0.74/1.08 ============================== end of clauses for search =============
% 0.74/1.08
% 0.74/1.08 ============================== SEARCH ================================
% 0.74/1.08
% 0.74/1.08 % Starting search at 0.02 seconds.
% 0.74/1.08
% 0.74/1.08 ============================== PROOF =================================
% 0.74/1.08 % SZS status Theorem
% 0.74/1.08 % SZS output start Refutation
% 0.74/1.08
% 0.74/1.08 % Proof 1 at 0.09 (+ 0.00) seconds.
% 0.74/1.08 % Length of proof is 62.
% 0.74/1.08 % Level of proof is 10.
% 0.74/1.08 % Maximum clause weight is 15.000.
% 0.74/1.08 % Given clauses 199.
% 0.74/1.08
% 0.74/1.08 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(C,B)) -> (subset(identity_relation_of(C),D) -> C = domain(C,B,D) & subset(C,range(C,B,D))))))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.08 5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (ilf_type(C,identity_relation_of_type(B)) <-> ilf_type(C,relation_type(B,B))))))) # label(p5) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.08 8 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (B = C <-> subset(B,C) & subset(C,B)))))) # label(p8) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.08 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].
% 0.74/1.08 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(p18) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.08 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].
% 0.74/1.08 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].
% 0.74/1.08 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].
% 0.74/1.08 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].
% 0.74/1.08 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].
% 0.74/1.08 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].
% 0.74/1.08 34 (all B ilf_type(B,set_type)) # label(p34) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.08 35 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,identity_relation_of_type(B)) -> (subset(identity_relation_of(B),C) -> B = domain(B,B,C) & B = range(B,B,C)))))) # label(prove_relset_1_44) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.08 47 ilf_type(A,set_type) # label(p34) # label(axiom). [clausify(34)].
% 0.74/1.08 48 ilf_type(c3,identity_relation_of_type(c2)) # label(prove_relset_1_44) # label(negated_conjecture). [clausify(35)].
% 0.74/1.08 49 subset(identity_relation_of(c2),c3) # label(prove_relset_1_44) # label(negated_conjecture). [clausify(35)].
% 0.74/1.08 50 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p23) # label(axiom). [clausify(23)].
% 0.74/1.08 51 -empty(power_set(A)). [copy(50),unit_del(a,47)].
% 0.74/1.08 54 domain(c2,c2,c3) != c2 | range(c2,c2,c3) != c2 # label(prove_relset_1_44) # label(negated_conjecture). [clausify(35)].
% 0.74/1.08 78 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f6(A,B),A) # label(p18) # label(axiom). [clausify(18)].
% 0.74/1.08 79 subset(A,B) | member(f6(A,B),A). [copy(78),unit_del(a,47),unit_del(b,47)].
% 0.74/1.08 80 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f6(A,B),B) # label(p18) # label(axiom). [clausify(18)].
% 0.74/1.08 81 subset(A,B) | -member(f6(A,B),B). [copy(80),unit_del(a,47),unit_del(b,47)].
% 0.74/1.08 82 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(B,identity_relation_of_type(A)) | ilf_type(B,relation_type(A,A)) # label(p5) # label(axiom). [clausify(5)].
% 0.74/1.08 83 -ilf_type(A,identity_relation_of_type(B)) | ilf_type(A,relation_type(B,B)). [copy(82),unit_del(a,47),unit_del(b,47)].
% 0.74/1.08 86 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -subset(A,B) | -subset(B,A) # label(p8) # label(axiom). [clausify(8)].
% 0.74/1.08 87 A = B | -subset(B,A) | -subset(A,B). [copy(86),unit_del(a,47),unit_del(b,47)].
% 0.74/1.08 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(p16) # label(axiom). [clausify(16)].
% 0.74/1.08 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)].
% 0.74/1.08 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)].
% 0.74/1.08 98 empty(A) | -ilf_type(B,member_type(A)) | member(B,A). [copy(97),unit_del(a,47),unit_del(c,47)].
% 0.74/1.08 113 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain_of(C) = domain(A,B,C) # label(p30) # label(axiom). [clausify(30)].
% 0.83/1.08 114 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [copy(113),flip(d),unit_del(a,47),unit_del(b,47)].
% 0.83/1.08 117 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range_of(C) = range(A,B,C) # label(p32) # label(axiom). [clausify(32)].
% 0.83/1.08 118 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [copy(117),flip(d),unit_del(a,47),unit_del(b,47)].
% 0.83/1.08 119 -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)].
% 0.83/1.08 120 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [copy(119),unit_del(a,47),unit_del(b,47)].
% 0.83/1.08 121 -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)].
% 0.83/1.08 122 -member(A,power_set(B)) | -member(C,A) | member(C,B). [copy(121),unit_del(a,47),unit_del(b,47),unit_del(d,47)].
% 0.83/1.08 123 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(B,A)) | -subset(identity_relation_of(B),C) | domain(B,A,C) = B # label(p1) # label(axiom). [clausify(1)].
% 0.83/1.08 124 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(B),A) | domain(B,C,A) = B. [copy(123),unit_del(a,47),unit_del(b,47)].
% 0.83/1.08 125 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(B,A)) | -subset(identity_relation_of(B),C) | subset(B,range(B,A,C)) # label(p1) # label(axiom). [clausify(1)].
% 0.83/1.08 126 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(B),A) | subset(B,range(B,C,A)). [copy(125),unit_del(a,47),unit_del(b,47)].
% 0.83/1.08 167 ilf_type(c3,relation_type(c2,c2)). [resolve(83,a,48,a)].
% 0.83/1.08 171 A = B | -subset(B,A) | member(f6(A,B),A). [resolve(87,c,79,a)].
% 0.83/1.08 198 -ilf_type(c3,relation_type(c2,A)) | domain(c2,A,c3) = c2. [resolve(124,b,49,a)].
% 0.83/1.08 201 -ilf_type(c3,relation_type(c2,A)) | subset(c2,range(c2,A,c3)). [resolve(126,b,49,a)].
% 0.83/1.08 237 ilf_type(range(c2,c2,c3),subset_type(c2)). [resolve(167,a,120,a)].
% 0.83/1.08 238 range(c2,c2,c3) = range_of(c3). [resolve(167,a,118,a)].
% 0.83/1.08 240 domain(c2,c2,c3) = domain_of(c3). [resolve(167,a,114,a)].
% 0.83/1.08 242 ilf_type(range_of(c3),subset_type(c2)). [back_rewrite(237),rewrite([238(4)])].
% 0.83/1.08 243 domain_of(c3) != c2 | range_of(c3) != c2. [back_rewrite(54),rewrite([240(4),238(8)])].
% 0.83/1.08 248 ilf_type(range_of(c3),member_type(power_set(c2))). [resolve(242,a,89,a)].
% 0.83/1.08 284 member(range_of(c3),power_set(c2)). [resolve(248,a,98,b),unit_del(a,51)].
% 0.83/1.08 291 -member(A,range_of(c3)) | member(A,c2). [resolve(284,a,122,a)].
% 0.83/1.08 661 domain_of(c3) = c2. [resolve(198,a,167,a),rewrite([240(4)])].
% 0.83/1.08 665 range_of(c3) != c2. [back_rewrite(243),rewrite([661(2)]),xx(a)].
% 0.83/1.08 814 subset(c2,range_of(c3)). [resolve(201,a,167,a),rewrite([238(5)])].
% 0.83/1.08 866 member(f6(range_of(c3),c2),range_of(c3)). [resolve(814,a,171,b),unit_del(a,665)].
% 0.83/1.08 868 -subset(range_of(c3),c2). [resolve(814,a,87,c),flip(a),unit_del(a,665)].
% 0.83/1.08 869 member(f6(range_of(c3),c2),c2). [resolve(866,a,291,a)].
% 0.83/1.08 907 $F. [ur(81,a,868,a),unit_del(a,869)].
% 0.83/1.08
% 0.83/1.08 % SZS output end Refutation
% 0.83/1.08 ============================== end of proof ==========================
% 0.83/1.08
% 0.83/1.08 ============================== STATISTICS ============================
% 0.83/1.08
% 0.83/1.08 Given=199. Generated=1151. Kept=794. proofs=1.
% 0.83/1.08 Usable=186. Sos=522. Demods=13. Limbo=0, Disabled=176. Hints=0.
% 0.83/1.08 Megabytes=1.23.
% 0.83/1.08 User_CPU=0.09, System_CPU=0.00, Wall_clock=0.
% 0.83/1.08
% 0.83/1.08 ============================== end of statistics =====================
% 0.83/1.08
% 0.83/1.08 ============================== end of search =========================
% 0.83/1.08
% 0.83/1.08 THEOREM PROVED
% 0.83/1.08 % SZS status Theorem
% 0.83/1.08
% 0.83/1.08 Exiting with 1 proof.
% 0.83/1.08
% 0.83/1.08 Process 22370 exit (max_proofs) Sun Jul 10 01:30:37 2022
% 0.83/1.08 Prover9 interrupted
%------------------------------------------------------------------------------