TSTP Solution File: SET669+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET669+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 04:31:17 EDT 2022
% Result : Theorem 0.77s 1.13s
% Output : Refutation 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET669+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.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 12:14:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.04 ============================== Prover9 ===============================
% 0.44/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.04 Process 12642 was started by sandbox2 on n026.cluster.edu,
% 0.44/1.04 Sun Jul 10 12:14:42 2022
% 0.44/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12488_n026.cluster.edu".
% 0.44/1.04 ============================== end of head ===========================
% 0.44/1.04
% 0.44/1.04 ============================== INPUT =================================
% 0.44/1.04
% 0.44/1.04 % Reading from file /tmp/Prover9_12488_n026.cluster.edu
% 0.44/1.04
% 0.44/1.04 set(prolog_style_variables).
% 0.44/1.04 set(auto2).
% 0.44/1.04 % set(auto2) -> set(auto).
% 0.44/1.04 % set(auto) -> set(auto_inference).
% 0.44/1.04 % set(auto) -> set(auto_setup).
% 0.44/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.04 % set(auto) -> set(auto_limits).
% 0.44/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.04 % set(auto) -> set(auto_denials).
% 0.44/1.04 % set(auto) -> set(auto_process).
% 0.44/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.04 % set(auto2) -> assign(stats, some).
% 0.44/1.04 % set(auto2) -> clear(echo_input).
% 0.44/1.04 % set(auto2) -> set(quiet).
% 0.44/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.04 % set(auto2) -> clear(print_given).
% 0.44/1.04 assign(lrs_ticks,-1).
% 0.44/1.04 assign(sos_limit,10000).
% 0.44/1.04 assign(order,kbo).
% 0.44/1.04 set(lex_order_vars).
% 0.44/1.04 clear(print_given).
% 0.44/1.04
% 0.44/1.04 % formulas(sos). % not echoed (33 formulas)
% 0.44/1.04
% 0.44/1.04 ============================== end of input ==========================
% 0.44/1.04
% 0.44/1.04 % From the command line: assign(max_seconds, 300).
% 0.44/1.04
% 0.44/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.04
% 0.44/1.04 % Formulas that are not ordinary clauses:
% 0.44/1.04 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (subset(B,C) & subset(C,B) -> B = C))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 2 (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,relation_type(B,C)) -> (subset(identity_relation_of(D),E) -> subset(D,domain(B,C,E)) & subset(D,range(B,C,E))))))))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 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].
% 0.44/1.04 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].
% 0.44/1.04 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(p5) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 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(p6) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 7 (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(p7) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 8 (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(p8) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 9 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (B = C <-> subset(B,C) & subset(C,B)))))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 10 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p10) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 11 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p11) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 12 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))) # label(p12) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 13 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 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].
% 0.44/1.04 15 (exists B ilf_type(B,binary_relation_type)) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 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].
% 0.44/1.04 17 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 18 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p18) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 19 (all B (ilf_type(B,binary_relation_type) -> subset(B,B))) # label(p19) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 20 (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(p20) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 21 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p21) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 22 (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(p22) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 23 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p23) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 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].
% 0.44/1.04 25 (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(p25) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 26 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p26) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 27 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p27) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 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(p28) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 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(p29) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 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(p30) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 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(p31) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 32 (all B ilf_type(B,set_type)) # label(p32) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 33 -(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(prove_relset_1_32) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.04
% 0.44/1.04 ============================== end of process non-clausal formulas ===
% 0.44/1.04
% 0.44/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.04
% 0.44/1.04 ============================== PREDICATE ELIMINATION =================
% 0.44/1.04 34 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p14) # label(axiom). [clausify(14)].
% 0.44/1.04 35 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p27) # label(axiom). [clausify(27)].
% 0.44/1.04 36 -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type) | relation_like(A) # label(p14) # label(axiom). [clausify(14)].
% 0.44/1.04 Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -empty(A) | -ilf_type(A,set_type). [resolve(34,c,35,c)].
% 0.44/1.04 37 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f10(A),set_type) # label(p24) # label(axiom). [clausify(24)].
% 0.44/1.04 Derived: -ilf_type(A,set_type) | ilf_type(f10(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(37,b,34,c)].
% 0.44/1.04 38 -ilf_type(A,set_type) | relation_like(A) | member(f10(A),A) # label(p24) # label(axiom). [clausify(24)].
% 0.44/1.04 Derived: -ilf_type(A,set_type) | member(f10(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(38,b,34,c)].
% 0.44/1.04 39 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p25) # label(axiom). [clausify(25)].
% 0.44/1.04 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)].
% 0.44/1.04 40 -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)].
% 0.44/1.04 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(40,b,35,c)].
% 0.44/1.04 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(40,b,36,c)].
% 0.44/1.04 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(40,b,37,b)].
% 0.44/1.04 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(40,b,38,b)].
% 0.44/1.04 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(40,b,39,d)].
% 0.44/1.04 41 -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)].
% 0.44/1.04 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(41,b,35,c)].
% 0.44/1.04 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(41,b,36,c)].
% 0.44/1.04 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(41,b,37,b)].
% 0.44/1.04 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(41,b,38,b)].
% 0.44/1.04 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(41,b,39,d)].
% 0.44/1.04 42 -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)].
% 0.44/1.04 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(42,b,34,c)].
% 0.77/1.13 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(42,b,40,b)].
% 0.77/1.13 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(42,b,41,b)].
% 0.77/1.13 43 -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)].
% 0.77/1.13 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(43,b,35,c)].
% 0.77/1.13 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(43,b,36,c)].
% 0.77/1.13 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(43,b,37,b)].
% 0.77/1.13 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(43,b,38,b)].
% 0.77/1.13 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(43,b,39,d)].
% 0.77/1.13 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(43,b,42,b)].
% 0.77/1.13
% 0.77/1.13 ============================== end predicate elimination =============
% 0.77/1.13
% 0.77/1.13 Auto_denials: (non-Horn, no changes).
% 0.77/1.13
% 0.77/1.13 Term ordering decisions:
% 0.77/1.13 Function symbol KB weights: set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. c4=1. ordered_pair=1. relation_type=1. cross_product=1. f1=1. f2=1. f3=1. f4=1. f6=1. f8=1. f9=1. subset_type=1. identity_relation_of=1. power_set=1. member_type=1. domain_of=1. range_of=1. f5=1. f7=1. f10=1. f11=1. domain=1. range=1.
% 0.77/1.13
% 0.77/1.13 ============================== end of process initial clauses ========
% 0.77/1.13
% 0.77/1.13 ============================== CLAUSES FOR SEARCH ====================
% 0.77/1.13
% 0.77/1.13 ============================== end of clauses for search =============
% 0.77/1.13
% 0.77/1.13 ============================== SEARCH ================================
% 0.77/1.13
% 0.77/1.13 % Starting search at 0.03 seconds.
% 0.77/1.13
% 0.77/1.13 ============================== PROOF =================================
% 0.77/1.13 % SZS status Theorem
% 0.77/1.13 % SZS output start Refutation
% 0.77/1.13
% 0.77/1.13 % Proof 1 at 0.10 (+ 0.00) seconds.
% 0.77/1.13 % Length of proof is 58.
% 0.77/1.13 % Level of proof is 9.
% 0.77/1.13 % Maximum clause weight is 15.000.
% 0.77/1.13 % Given clauses 211.
% 0.77/1.13
% 0.77/1.13 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (subset(B,C) & subset(C,B) -> B = C))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.13 2 (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,relation_type(B,C)) -> (subset(identity_relation_of(D),E) -> subset(D,domain(B,C,E)) & subset(D,range(B,C,E))))))))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.13 7 (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(p7) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.13 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].
% 0.77/1.13 20 (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(p20) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.13 21 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p21) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.13 22 (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(p22) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.13 28 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> domain(B,C,D) = domain_of(D))))))) # label(p28) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.13 30 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> range(B,C,D) = range_of(D))))))) # label(p30) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.13 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(p31) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.13 32 (all B ilf_type(B,set_type)) # label(p32) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.13 33 -(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(prove_relset_1_32) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.77/1.13 45 ilf_type(A,set_type) # label(p32) # label(axiom). [clausify(32)].
% 0.77/1.13 46 subset(identity_relation_of(c3),c4) # label(prove_relset_1_32) # label(negated_conjecture). [clausify(33)].
% 0.77/1.13 47 ilf_type(c4,relation_type(c2,c3)) # label(prove_relset_1_32) # label(negated_conjecture). [clausify(33)].
% 0.77/1.13 48 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p21) # label(axiom). [clausify(21)].
% 0.77/1.13 49 -empty(power_set(A)). [copy(48),unit_del(a,45)].
% 0.77/1.13 52 -subset(c3,domain(c2,c3,c4)) | range(c2,c3,c4) != c3 # label(prove_relset_1_32) # label(negated_conjecture). [clausify(33)].
% 0.77/1.13 74 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f2(A,B),A) # label(p7) # label(axiom). [clausify(7)].
% 0.77/1.13 75 subset(A,B) | member(f2(A,B),A). [copy(74),unit_del(a,45),unit_del(b,45)].
% 0.77/1.13 76 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f2(A,B),B) # label(p7) # label(axiom). [clausify(7)].
% 0.77/1.13 77 subset(A,B) | -member(f2(A,B),B). [copy(76),unit_del(a,45),unit_del(b,45)].
% 0.77/1.13 78 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -subset(A,B) | -subset(B,A) | B = A # label(p1) # label(axiom). [clausify(1)].
% 0.77/1.13 79 -subset(A,B) | -subset(B,A) | B = A. [copy(78),unit_del(a,45),unit_del(b,45)].
% 0.77/1.13 81 -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)].
% 0.77/1.13 82 -ilf_type(A,subset_type(B)) | ilf_type(A,member_type(power_set(B))). [copy(81),unit_del(a,45),unit_del(b,45)].
% 0.77/1.13 90 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | -ilf_type(A,member_type(B)) | member(A,B) # label(p22) # label(axiom). [clausify(22)].
% 0.77/1.13 91 empty(A) | -ilf_type(B,member_type(A)) | member(B,A). [copy(90),unit_del(a,45),unit_del(c,45)].
% 0.77/1.13 106 -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(p28) # label(axiom). [clausify(28)].
% 0.77/1.13 107 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [copy(106),flip(d),unit_del(a,45),unit_del(b,45)].
% 0.77/1.13 110 -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(p30) # label(axiom). [clausify(30)].
% 0.77/1.13 111 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [copy(110),flip(d),unit_del(a,45),unit_del(b,45)].
% 0.77/1.13 112 -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(p31) # label(axiom). [clausify(31)].
% 0.77/1.13 113 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [copy(112),unit_del(a,45),unit_del(b,45)].
% 0.77/1.13 114 -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(p20) # label(axiom). [clausify(20)].
% 0.77/1.13 115 -member(A,power_set(B)) | -member(C,A) | member(C,B). [copy(114),unit_del(a,45),unit_del(b,45),unit_del(d,45)].
% 0.77/1.13 118 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,relation_type(A,B)) | -subset(identity_relation_of(C),D) | subset(C,domain(A,B,D)) # label(p2) # label(axiom). [clausify(2)].
% 0.77/1.13 119 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,domain(B,C,A)). [copy(118),unit_del(a,45),unit_del(b,45),unit_del(c,45)].
% 0.77/1.13 120 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,relation_type(A,B)) | -subset(identity_relation_of(C),D) | subset(C,range(A,B,D)) # label(p2) # label(axiom). [clausify(2)].
% 0.77/1.13 121 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,range(B,C,A)). [copy(120),unit_del(a,45),unit_del(b,45),unit_del(c,45)].
% 0.77/1.13 158 -subset(A,B) | B = A | member(f2(B,A),B). [resolve(79,b,75,a)].
% 0.77/1.13 176 domain(c2,c3,c4) = domain_of(c4). [resolve(107,a,47,a)].
% 0.77/1.13 178 -subset(c3,domain_of(c4)) | range(c2,c3,c4) != c3. [back_rewrite(52),rewrite([176(5)])].
% 0.77/1.13 182 range(c2,c3,c4) = range_of(c4). [resolve(111,a,47,a)].
% 0.77/1.13 183 -subset(c3,domain_of(c4)) | range_of(c4) != c3. [back_rewrite(178),rewrite([182(8)])].
% 0.77/1.13 186 ilf_type(range_of(c4),subset_type(c3)). [resolve(113,a,47,a),rewrite([182(4)])].
% 0.77/1.13 196 -ilf_type(c4,relation_type(A,B)) | subset(c3,domain(A,B,c4)). [resolve(119,b,46,a)].
% 0.77/1.13 199 -ilf_type(c4,relation_type(A,B)) | subset(c3,range(A,B,c4)). [resolve(121,b,46,a)].
% 0.77/1.13 223 ilf_type(range_of(c4),member_type(power_set(c3))). [resolve(186,a,82,a)].
% 0.77/1.13 274 member(range_of(c4),power_set(c3)). [resolve(223,a,91,b),unit_del(a,49)].
% 0.77/1.13 281 -member(A,range_of(c4)) | member(A,c3). [resolve(274,a,115,a)].
% 0.77/1.13 707 subset(c3,domain_of(c4)). [resolve(196,a,47,a),rewrite([176(5)])].
% 0.77/1.13 708 range_of(c4) != c3. [back_unit_del(183),unit_del(a,707)].
% 0.77/1.13 882 subset(c3,range_of(c4)). [resolve(199,a,47,a),rewrite([182(5)])].
% 0.77/1.13 934 member(f2(range_of(c4),c3),range_of(c4)). [resolve(882,a,158,a),unit_del(a,708)].
% 0.77/1.13 936 -subset(range_of(c4),c3). [resolve(882,a,79,b),flip(b),unit_del(b,708)].
% 0.77/1.13 937 member(f2(range_of(c4),c3),c3). [resolve(934,a,281,a)].
% 0.77/1.13 1043 $F. [ur(77,a,936,a),unit_del(a,937)].
% 0.77/1.13
% 0.77/1.13 % SZS output end Refutation
% 0.77/1.13 ============================== end of proof ==========================
% 0.77/1.13
% 0.77/1.13 ============================== STATISTICS ============================
% 0.77/1.13
% 0.77/1.13 Given=211. Generated=1269. Kept=936. proofs=1.
% 0.77/1.13 Usable=192. Sos=628. Demods=12. Limbo=0, Disabled=203. Hints=0.
% 0.77/1.13 Megabytes=1.44.
% 0.77/1.13 User_CPU=0.11, System_CPU=0.00, Wall_clock=0.
% 0.77/1.13
% 0.77/1.13 ============================== end of statistics =====================
% 0.77/1.13
% 0.77/1.13 ============================== end of search =========================
% 0.77/1.13
% 0.77/1.13 THEOREM PROVED
% 0.77/1.13 % SZS status Theorem
% 0.77/1.13
% 0.77/1.13 Exiting with 1 proof.
% 0.77/1.13
% 0.77/1.13 Process 12642 exit (max_proofs) Sun Jul 10 12:14:42 2022
% 0.77/1.13 Prover9 interrupted
%------------------------------------------------------------------------------