TSTP Solution File: SET656+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET656+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 04:31:12 EDT 2022
% Result : Theorem 0.82s 1.14s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SET656+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.35 % Computer : n016.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 600
% 0.12/0.35 % DateTime : Sun Jul 10 20:54:12 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.39/1.08 ============================== Prover9 ===============================
% 0.39/1.08 Prover9 (32) version 2009-11A, November 2009.
% 0.39/1.08 Process 19407 was started by sandbox2 on n016.cluster.edu,
% 0.39/1.08 Sun Jul 10 20:54:12 2022
% 0.39/1.08 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19254_n016.cluster.edu".
% 0.39/1.08 ============================== end of head ===========================
% 0.39/1.08
% 0.39/1.08 ============================== INPUT =================================
% 0.39/1.08
% 0.39/1.08 % Reading from file /tmp/Prover9_19254_n016.cluster.edu
% 0.39/1.08
% 0.39/1.08 set(prolog_style_variables).
% 0.39/1.08 set(auto2).
% 0.39/1.08 % set(auto2) -> set(auto).
% 0.39/1.08 % set(auto) -> set(auto_inference).
% 0.39/1.08 % set(auto) -> set(auto_setup).
% 0.39/1.08 % set(auto_setup) -> set(predicate_elim).
% 0.39/1.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.39/1.08 % set(auto) -> set(auto_limits).
% 0.39/1.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.39/1.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.39/1.08 % set(auto) -> set(auto_denials).
% 0.39/1.08 % set(auto) -> set(auto_process).
% 0.39/1.08 % set(auto2) -> assign(new_constants, 1).
% 0.39/1.08 % set(auto2) -> assign(fold_denial_max, 3).
% 0.39/1.08 % set(auto2) -> assign(max_weight, "200.000").
% 0.39/1.08 % set(auto2) -> assign(max_hours, 1).
% 0.39/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.39/1.08 % set(auto2) -> assign(max_seconds, 0).
% 0.39/1.08 % set(auto2) -> assign(max_minutes, 5).
% 0.39/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.39/1.08 % set(auto2) -> set(sort_initial_sos).
% 0.39/1.08 % set(auto2) -> assign(sos_limit, -1).
% 0.39/1.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.39/1.08 % set(auto2) -> assign(max_megs, 400).
% 0.39/1.08 % set(auto2) -> assign(stats, some).
% 0.39/1.08 % set(auto2) -> clear(echo_input).
% 0.39/1.08 % set(auto2) -> set(quiet).
% 0.39/1.08 % set(auto2) -> clear(print_initial_clauses).
% 0.39/1.08 % set(auto2) -> clear(print_given).
% 0.39/1.08 assign(lrs_ticks,-1).
% 0.39/1.08 assign(sos_limit,10000).
% 0.39/1.08 assign(order,kbo).
% 0.39/1.08 set(lex_order_vars).
% 0.39/1.08 clear(print_given).
% 0.39/1.08
% 0.39/1.08 % formulas(sos). % not echoed (31 formulas)
% 0.39/1.08
% 0.39/1.08 ============================== end of input ==========================
% 0.39/1.08
% 0.39/1.08 % From the command line: assign(max_seconds, 300).
% 0.39/1.08
% 0.39/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.39/1.08
% 0.39/1.08 % Formulas that are not ordinary clauses:
% 0.39/1.08 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (subset(B,C) -> intersection(B,C) = B))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 2 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (member(D,cross_product(B,C)) <-> (exists E (ilf_type(E,set_type) & (exists F (ilf_type(F,set_type) & member(E,B) & member(F,C) & D = ordered_pair(E,F)))))))))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 4 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (member(D,intersection(B,C)) <-> member(D,B) & member(D,C)))))))) # label(p4) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(intersection(B,C),set_type))))) # label(p5) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 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].
% 0.39/1.08 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].
% 0.39/1.08 8 (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].
% 0.39/1.08 9 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> intersection(B,C) = intersection(C,B))))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 10 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p10) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 11 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p11) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 12 (exists B ilf_type(B,binary_relation_type)) # label(p12) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 13 (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(p13) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 14 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p14) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 15 (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,binary_relation_type) -> (B = C -> C = B))))) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 16 (all B (ilf_type(B,binary_relation_type) -> B = B)) # label(p16) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 17 (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(p17) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 18 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p18) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 19 (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(p19) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 20 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p20) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 21 (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(p21) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 22 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p22) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 23 (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(p23) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 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].
% 0.39/1.08 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].
% 0.39/1.08 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].
% 0.39/1.08 27 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p27) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 28 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> (all E (ilf_type(E,relation_type(B,C)) -> intersection4(B,C,D,E) = intersection(D,E))))))))) # label(p28) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 29 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> (all E (ilf_type(E,relation_type(B,C)) -> ilf_type(intersection4(B,C,D,E),relation_type(B,C)))))))))) # label(p29) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 30 (all B ilf_type(B,set_type)) # label(p30) # label(axiom) # label(non_clause). [assumption].
% 0.39/1.08 31 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> intersection(D,cross_product(B,C)) = D)))))) # label(prove_relset_1_18) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.39/1.08
% 0.39/1.08 ============================== end of process non-clausal formulas ===
% 0.39/1.09
% 0.39/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.39/1.09
% 0.39/1.09 ============================== PREDICATE ELIMINATION =================
% 0.39/1.09 32 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -subset(A,B) | intersection(A,B) = A # label(p1) # label(axiom). [clausify(1)].
% 0.39/1.09 33 -ilf_type(A,set_type) | subset(A,A) # label(p18) # label(axiom). [clausify(18)].
% 0.39/1.09 Derived: -ilf_type(A,set_type) | -ilf_type(A,set_type) | intersection(A,A) = A | -ilf_type(A,set_type). [resolve(32,c,33,b)].
% 0.39/1.09 34 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f7(A,B),set_type) # label(p17) # label(axiom). [clausify(17)].
% 0.39/1.09 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f7(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | intersection(A,B) = A. [resolve(34,c,32,c)].
% 0.39/1.09 35 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f7(A,B),A) # label(p17) # label(axiom). [clausify(17)].
% 0.39/1.09 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f7(A,B),A) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | intersection(A,B) = A. [resolve(35,c,32,c)].
% 0.39/1.09 36 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f7(A,B),B) # label(p17) # label(axiom). [clausify(17)].
% 0.39/1.09 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f7(A,B),B) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | intersection(A,B) = A. [resolve(36,c,32,c)].
% 0.39/1.09 37 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -subset(A,B) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) # label(p17) # label(axiom). [clausify(17)].
% 0.39/1.09 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f7(A,B),set_type). [resolve(37,c,34,c)].
% 0.39/1.09 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f7(A,B),A). [resolve(37,c,35,c)].
% 0.39/1.09 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f7(A,B),B). [resolve(37,c,36,c)].
% 0.39/1.09 38 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p11) # label(axiom). [clausify(11)].
% 0.39/1.09 39 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p27) # label(axiom). [clausify(27)].
% 0.39/1.09 40 -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type) | relation_like(A) # label(p11) # label(axiom). [clausify(11)].
% 0.39/1.09 Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -empty(A) | -ilf_type(A,set_type). [resolve(38,c,39,c)].
% 0.39/1.09 41 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f13(A),set_type) # label(p24) # label(axiom). [clausify(24)].
% 0.39/1.09 Derived: -ilf_type(A,set_type) | ilf_type(f13(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(41,b,38,c)].
% 0.39/1.09 42 -ilf_type(A,set_type) | relation_like(A) | member(f13(A),A) # label(p24) # label(axiom). [clausify(24)].
% 0.39/1.09 Derived: -ilf_type(A,set_type) | member(f13(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(42,b,38,c)].
% 0.39/1.09 43 -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)].
% 0.39/1.09 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(43,d,38,c)].
% 0.39/1.09 44 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f11(A,B),set_type) # label(p24) # label(axiom). [clausify(24)].
% 0.39/1.09 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f11(A,B),set_type) | -empty(A) | -ilf_type(A,set_type). [resolve(44,b,39,c)].
% 0.39/1.09 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f11(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(44,b,40,c)].
% 0.39/1.09 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f11(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f13(A),set_type). [resolve(44,b,41,b)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f11(A,B),set_type) | -ilf_type(A,set_type) | member(f13(A),A). [resolve(44,b,42,b)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f11(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(44,b,43,d)].
% 0.82/1.10 45 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f12(A,B),set_type) # label(p24) # label(axiom). [clausify(24)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f12(A,B),set_type) | -empty(A) | -ilf_type(A,set_type). [resolve(45,b,39,c)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f12(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(45,b,40,c)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f12(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f13(A),set_type). [resolve(45,b,41,b)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f12(A,B),set_type) | -ilf_type(A,set_type) | member(f13(A),A). [resolve(45,b,42,b)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f12(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(45,b,43,d)].
% 0.82/1.10 46 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f13(A) # label(p24) # label(axiom). [clausify(24)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f13(A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(46,b,38,c)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f13(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f11(A,D),set_type). [resolve(46,b,44,b)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f13(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f12(A,D),set_type). [resolve(46,b,45,b)].
% 0.82/1.10 47 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f11(A,B),f12(A,B)) = B # label(p24) # label(axiom). [clausify(24)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f11(A,B),f12(A,B)) = B | -empty(A) | -ilf_type(A,set_type). [resolve(47,b,39,c)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f11(A,B),f12(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(47,b,40,c)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f11(A,B),f12(A,B)) = B | -ilf_type(A,set_type) | ilf_type(f13(A),set_type). [resolve(47,b,41,b)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f11(A,B),f12(A,B)) = B | -ilf_type(A,set_type) | member(f13(A),A). [resolve(47,b,42,b)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f11(A,B),f12(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(47,b,43,d)].
% 0.82/1.10 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f11(A,B),f12(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f13(A). [resolve(47,b,46,b)].
% 0.82/1.10
% 0.82/1.10 ============================== end predicate elimination =============
% 0.82/1.10
% 0.82/1.10 Auto_denials: (non-Horn, no changes).
% 0.82/1.10
% 0.82/1.10 Term ordering decisions:
% 0.82/1.10 Function symbol KB weights: set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. c4=1. ordered_pair=1. cross_product=1. intersection=1. relation_type=1. f3=1. f4=1. f5=1. f7=1. f8=1. f10=1. f11=1. f12=1. subset_type=1. power_set=1. member_type=1. f6=1. f9=1. f13=1. f14=1. f1=1. f2=1. intersection4=1.
% 0.82/1.14
% 0.82/1.14 ============================== end of process initial clauses ========
% 0.82/1.14
% 0.82/1.14 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.14
% 0.82/1.14 ============================== end of clauses for search =============
% 0.82/1.14
% 0.82/1.14 ============================== SEARCH ================================
% 0.82/1.14
% 0.82/1.14 % Starting search at 0.02 seconds.
% 0.82/1.14
% 0.82/1.14 ============================== PROOF =================================
% 0.82/1.14 % SZS status Theorem
% 0.82/1.14 % SZS output start Refutation
% 0.82/1.14
% 0.82/1.14 % Proof 1 at 0.06 (+ 0.00) seconds.
% 0.82/1.14 % Length of proof is 35.
% 0.82/1.14 % Level of proof is 7.
% 0.82/1.14 % Maximum clause weight is 11.000.
% 0.82/1.14 % Given clauses 117.
% 0.82/1.14
% 0.82/1.14 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (subset(B,C) -> intersection(B,C) = B))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 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].
% 0.82/1.14 13 (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(p13) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 17 (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(p17) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 19 (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(p19) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 20 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p20) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 21 (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(p21) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 30 (all B ilf_type(B,set_type)) # label(p30) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 31 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> intersection(D,cross_product(B,C)) = D)))))) # label(prove_relset_1_18) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.14 32 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -subset(A,B) | intersection(A,B) = A # label(p1) # label(axiom). [clausify(1)].
% 0.82/1.14 35 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f7(A,B),A) # label(p17) # label(axiom). [clausify(17)].
% 0.82/1.14 36 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f7(A,B),B) # label(p17) # label(axiom). [clausify(17)].
% 0.82/1.14 49 ilf_type(A,set_type) # label(p30) # label(axiom). [clausify(30)].
% 0.82/1.14 50 ilf_type(c4,relation_type(c2,c3)) # label(prove_relset_1_18) # label(negated_conjecture). [clausify(31)].
% 0.82/1.14 51 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p20) # label(axiom). [clausify(20)].
% 0.82/1.14 52 -empty(power_set(A)). [copy(51),unit_del(a,49)].
% 0.82/1.14 53 intersection(c4,cross_product(c2,c3)) != c4 # label(prove_relset_1_18) # label(negated_conjecture). [clausify(31)].
% 0.82/1.14 72 -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(p13) # label(axiom). [clausify(13)].
% 0.82/1.14 73 -ilf_type(A,subset_type(B)) | ilf_type(A,member_type(power_set(B))). [copy(72),unit_del(a,49),unit_del(b,49)].
% 0.82/1.14 81 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | -ilf_type(A,member_type(B)) | member(A,B) # label(p21) # label(axiom). [clausify(21)].
% 0.82/1.14 82 empty(A) | -ilf_type(B,member_type(A)) | member(B,A). [copy(81),unit_del(a,49),unit_del(c,49)].
% 0.82/1.14 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)].
% 0.82/1.14 92 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [copy(91),unit_del(a,49),unit_del(b,49)].
% 0.82/1.14 97 -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(p19) # label(axiom). [clausify(19)].
% 0.82/1.14 98 -member(A,power_set(B)) | -member(C,A) | member(C,B). [copy(97),unit_del(a,49),unit_del(b,49),unit_del(d,49)].
% 0.82/1.14 126 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f7(A,B),A) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | intersection(A,B) = A. [resolve(35,c,32,c)].
% 0.82/1.14 127 member(f7(A,B),A) | intersection(A,B) = A. [copy(126),merge(d),merge(e),unit_del(a,49),unit_del(b,49)].
% 0.82/1.14 128 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f7(A,B),B) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | intersection(A,B) = A. [resolve(36,c,32,c)].
% 0.82/1.14 129 -member(f7(A,B),B) | intersection(A,B) = A. [copy(128),merge(d),merge(e),unit_del(a,49),unit_del(b,49)].
% 0.82/1.14 183 ilf_type(c4,subset_type(cross_product(c2,c3))). [resolve(92,a,50,a)].
% 0.82/1.14 273 -member(f7(c4,cross_product(c2,c3)),cross_product(c2,c3)). [ur(129,b,53,a)].
% 0.82/1.14 426 ilf_type(c4,member_type(power_set(cross_product(c2,c3)))). [resolve(183,a,73,a)].
% 0.82/1.14 633 member(c4,power_set(cross_product(c2,c3))). [resolve(426,a,82,b),unit_del(a,52)].
% 0.82/1.14 680 -member(f7(c4,cross_product(c2,c3)),c4). [ur(98,a,633,a,c,273,a)].
% 0.82/1.14 690 $F. [resolve(680,a,127,a),unit_del(a,53)].
% 0.82/1.14
% 0.82/1.14 % SZS output end Refutation
% 0.82/1.14 ============================== end of proof ==========================
% 0.82/1.14
% 0.82/1.14 ============================== STATISTICS ============================
% 0.82/1.14
% 0.82/1.14 Given=117. Generated=1020. Kept=572. proofs=1.
% 0.82/1.14 Usable=117. Sos=450. Demods=6. Limbo=0, Disabled=102. Hints=0.
% 0.82/1.14 Megabytes=0.97.
% 0.82/1.14 User_CPU=0.06, System_CPU=0.00, Wall_clock=0.
% 0.82/1.14
% 0.82/1.14 ============================== end of statistics =====================
% 0.82/1.14
% 0.82/1.14 ============================== end of search =========================
% 0.82/1.14
% 0.82/1.14 THEOREM PROVED
% 0.82/1.14 % SZS status Theorem
% 0.82/1.14
% 0.82/1.14 Exiting with 1 proof.
% 0.82/1.14
% 0.82/1.14 Process 19407 exit (max_proofs) Sun Jul 10 20:54:12 2022
% 0.82/1.14 Prover9 interrupted
%------------------------------------------------------------------------------