TSTP Solution File: SET685+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET685+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 04:31:24 EDT 2022
% Result : Theorem 1.41s 1.77s
% Output : Refutation 1.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET685+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 00:17:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.73/1.03 ============================== Prover9 ===============================
% 0.73/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.03 Process 25143 was started by sandbox2 on n011.cluster.edu,
% 0.73/1.03 Sun Jul 10 00:17:11 2022
% 0.73/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24989_n011.cluster.edu".
% 0.73/1.03 ============================== end of head ===========================
% 0.73/1.03
% 0.73/1.03 ============================== INPUT =================================
% 0.73/1.03
% 0.73/1.03 % Reading from file /tmp/Prover9_24989_n011.cluster.edu
% 0.73/1.03
% 0.73/1.03 set(prolog_style_variables).
% 0.73/1.03 set(auto2).
% 0.73/1.03 % set(auto2) -> set(auto).
% 0.73/1.03 % set(auto) -> set(auto_inference).
% 0.73/1.03 % set(auto) -> set(auto_setup).
% 0.73/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.03 % set(auto) -> set(auto_limits).
% 0.73/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.03 % set(auto) -> set(auto_denials).
% 0.73/1.03 % set(auto) -> set(auto_process).
% 0.73/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.03 % set(auto2) -> assign(stats, some).
% 0.73/1.03 % set(auto2) -> clear(echo_input).
% 0.73/1.03 % set(auto2) -> set(quiet).
% 0.73/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.03 % set(auto2) -> clear(print_given).
% 0.73/1.03 assign(lrs_ticks,-1).
% 0.73/1.03 assign(sos_limit,10000).
% 0.73/1.03 assign(order,kbo).
% 0.73/1.03 set(lex_order_vars).
% 0.73/1.03 clear(print_given).
% 0.73/1.03
% 0.73/1.03 % formulas(sos). % not echoed (28 formulas)
% 0.73/1.03
% 0.73/1.03 ============================== end of input ==========================
% 0.73/1.03
% 0.73/1.03 % From the command line: assign(max_seconds, 300).
% 0.73/1.03
% 0.73/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.03
% 0.73/1.03 % Formulas that are not ordinary clauses:
% 0.73/1.03 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,binary_relation_type) -> (member(C,image(D,B)) <-> (exists E (ilf_type(E,set_type) & member(ordered_pair(E,C),D) & member(E,B)))))))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 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,set_type) -> (all F (ilf_type(F,relation_type(B,C)) -> (member(ordered_pair(D,E),F) -> member(D,B) & member(E,C)))))))))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,set_type) -> (all F (ilf_type(F,set_type) -> (F = ordered_pair(D,E) <-> F = unordered_pair(unordered_pair(D,E),singleton(D))))))))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 4 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p4) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 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].
% 0.73/1.03 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].
% 0.73/1.03 7 (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(p7) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 8 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p8) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 9 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 10 (all B (ilf_type(B,set_type) -> ilf_type(singleton(B),set_type))) # label(p10) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 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].
% 0.73/1.03 12 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(unordered_pair(B,C),set_type))))) # label(p12) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 13 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> unordered_pair(B,C) = unordered_pair(C,B))))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 14 (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,set_type) -> ilf_type(image(B,C),set_type))))) # label(p14) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 15 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 16 (exists B ilf_type(B,binary_relation_type)) # label(p16) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 17 (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(p17) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 18 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p18) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 19 (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(p19) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 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].
% 0.73/1.03 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].
% 0.73/1.03 22 (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(p22) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 23 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p23) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 24 (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(p24) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 25 (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,set_type) -> image4(B,C,D,E) = image(D,E))))))))) # label(p25) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 26 (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,set_type) -> ilf_type(image4(B,C,D,E),subset_type(C)))))))))) # label(p26) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 27 (all B ilf_type(B,set_type)) # label(p27) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.03 28 -(all B (-empty(B) & ilf_type(B,set_type) -> (all C (-empty(C) & ilf_type(C,set_type) -> (all D (-empty(D) & ilf_type(D,set_type) -> (all E (ilf_type(E,relation_type(D,B)) -> (all F (ilf_type(F,member_type(B)) -> (member(F,image4(D,B,E,C)) <-> (exists G (ilf_type(G,member_type(D)) & member(ordered_pair(G,F),E) & member(G,C)))))))))))))) # label(prove_relset_1_52) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.03
% 0.73/1.03 ============================== end of process non-clausal formulas ===
% 0.73/1.03
% 0.73/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.03
% 0.73/1.03 ============================== PREDICATE ELIMINATION =================
% 0.73/1.03 29 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p15) # label(axiom). [clausify(15)].
% 0.73/1.04 30 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p23) # label(axiom). [clausify(23)].
% 0.73/1.04 31 -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type) | relation_like(A) # label(p15) # label(axiom). [clausify(15)].
% 0.73/1.04 Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -empty(A) | -ilf_type(A,set_type). [resolve(29,c,30,c)].
% 0.73/1.04 32 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f10(A),set_type) # label(p22) # label(axiom). [clausify(22)].
% 0.73/1.04 Derived: -ilf_type(A,set_type) | ilf_type(f10(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(32,b,29,c)].
% 0.73/1.04 33 -ilf_type(A,set_type) | relation_like(A) | member(f10(A),A) # label(p22) # label(axiom). [clausify(22)].
% 0.73/1.04 Derived: -ilf_type(A,set_type) | member(f10(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(33,b,29,c)].
% 0.73/1.04 34 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p24) # label(axiom). [clausify(24)].
% 0.73/1.04 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(34,d,29,c)].
% 0.73/1.04 35 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) # label(p22) # label(axiom). [clausify(22)].
% 0.73/1.04 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(35,b,30,c)].
% 0.73/1.04 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(35,b,31,c)].
% 0.73/1.04 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(35,b,32,b)].
% 0.73/1.04 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(35,b,33,b)].
% 0.73/1.04 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(35,b,34,d)].
% 0.73/1.04 36 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) # label(p22) # label(axiom). [clausify(22)].
% 0.73/1.04 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(36,b,30,c)].
% 0.73/1.04 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(36,b,31,c)].
% 0.73/1.04 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(36,b,32,b)].
% 0.73/1.04 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(36,b,33,b)].
% 0.73/1.04 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(36,b,34,d)].
% 0.73/1.04 37 -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(p22) # label(axiom). [clausify(22)].
% 0.73/1.04 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(37,b,29,c)].
% 0.73/1.04 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(D,set_type) | -member(D,A) | ilf_type(f8(A,D),set_type). [resolve(37,b,35,b)].
% 0.73/1.04 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(D,set_type) | -member(D,A) | ilf_type(f9(A,D),set_type). [resolve(37,b,36,b)].
% 1.41/1.77 38 -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(p22) # label(axiom). [clausify(22)].
% 1.41/1.77 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(38,b,30,c)].
% 1.41/1.77 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(38,b,31,c)].
% 1.41/1.77 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(38,b,32,b)].
% 1.41/1.77 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(38,b,33,b)].
% 1.41/1.77 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(38,b,34,d)].
% 1.41/1.77 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(38,b,37,b)].
% 1.41/1.77
% 1.41/1.77 ============================== end predicate elimination =============
% 1.41/1.77
% 1.41/1.77 Auto_denials: (non-Horn, no changes).
% 1.41/1.77
% 1.41/1.77 Term ordering decisions:
% 1.41/1.77 Function symbol KB weights: set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. ordered_pair=1. relation_type=1. cross_product=1. unordered_pair=1. image=1. f2=1. f6=1. f7=1. f8=1. f9=1. subset_type=1. member_type=1. power_set=1. singleton=1. f3=1. f4=1. f5=1. f10=1. f1=1. image4=1.
% 1.41/1.77
% 1.41/1.77 ============================== end of process initial clauses ========
% 1.41/1.77
% 1.41/1.77 ============================== CLAUSES FOR SEARCH ====================
% 1.41/1.77
% 1.41/1.77 ============================== end of clauses for search =============
% 1.41/1.77
% 1.41/1.77 ============================== SEARCH ================================
% 1.41/1.77
% 1.41/1.77 % Starting search at 0.04 seconds.
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% 1.41/1.77 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 58 (0.00 of 0.40 sec).
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% 1.41/1.77 ============================== PROOF =================================
% 1.41/1.77 % SZS status Theorem
% 1.41/1.77 % SZS output start Refutation
% 1.41/1.77
% 1.41/1.77 % Proof 1 at 0.74 (+ 0.01) seconds.
% 1.41/1.77 % Length of proof is 68.
% 1.41/1.77 % Level of proof is 20.
% 1.41/1.77 % Maximum clause weight is 19.000.
% 1.41/1.77 % Given clauses 856.
% 1.41/1.77
% 1.41/1.77 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,binary_relation_type) -> (member(C,image(D,B)) <-> (exists E (ilf_type(E,set_type) & member(ordered_pair(E,C),D) & member(E,B)))))))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.77 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,set_type) -> (all F (ilf_type(F,relation_type(B,C)) -> (member(ordered_pair(D,E),F) -> member(D,B) & member(E,C)))))))))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.77 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].
% 1.41/1.77 7 (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(p7) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.77 15 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.77 24 (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(p24) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.77 25 (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,set_type) -> image4(B,C,D,E) = image(D,E))))))))) # label(p25) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.77 27 (all B ilf_type(B,set_type)) # label(p27) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.77 28 -(all B (-empty(B) & ilf_type(B,set_type) -> (all C (-empty(C) & ilf_type(C,set_type) -> (all D (-empty(D) & ilf_type(D,set_type) -> (all E (ilf_type(E,relation_type(D,B)) -> (all F (ilf_type(F,member_type(B)) -> (member(F,image4(D,B,E,C)) <-> (exists G (ilf_type(G,member_type(D)) & member(ordered_pair(G,F),E) & member(G,C)))))))))))))) # label(prove_relset_1_52) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.41/1.77 29 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p15) # label(axiom). [clausify(15)].
% 1.41/1.77 34 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p24) # label(axiom). [clausify(24)].
% 1.41/1.77 40 ilf_type(A,set_type) # label(p27) # label(axiom). [clausify(27)].
% 1.41/1.77 42 ilf_type(c5,relation_type(c4,c2)) # label(prove_relset_1_52) # label(negated_conjecture). [clausify(28)].
% 1.41/1.77 43 member(c6,image4(c4,c2,c5,c3)) | member(c7,c3) # label(prove_relset_1_52) # label(negated_conjecture). [clausify(28)].
% 1.41/1.77 45 member(c6,image4(c4,c2,c5,c3)) | member(ordered_pair(c7,c6),c5) # label(prove_relset_1_52) # label(negated_conjecture). [clausify(28)].
% 1.41/1.77 47 -empty(c3) # label(prove_relset_1_52) # label(negated_conjecture). [clausify(28)].
% 1.41/1.77 48 -empty(c4) # label(prove_relset_1_52) # label(negated_conjecture). [clausify(28)].
% 1.41/1.77 53 -member(c6,image4(c4,c2,c5,c3)) | -ilf_type(A,member_type(c4)) | -member(ordered_pair(A,c6),c5) | -member(A,c3) # label(prove_relset_1_52) # label(negated_conjecture). [clausify(28)].
% 1.41/1.77 72 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | -ilf_type(A,member_type(B)) | member(A,B) # label(p7) # label(axiom). [clausify(7)].
% 1.41/1.77 73 empty(A) | -ilf_type(B,member_type(A)) | member(B,A). [copy(72),unit_del(a,40),unit_del(c,40)].
% 1.41/1.77 74 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B) # label(p7) # label(axiom). [clausify(7)].
% 1.41/1.77 75 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [copy(74),unit_del(a,40),unit_del(c,40)].
% 1.41/1.77 87 -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(p5) # label(axiom). [clausify(5)].
% 1.41/1.77 88 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [copy(87),unit_del(a,40),unit_del(b,40)].
% 1.41/1.77 100 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(B,image(C,A)) | member(f1(A,B,C),A) # label(p1) # label(axiom). [clausify(1)].
% 1.41/1.77 101 -ilf_type(A,binary_relation_type) | -member(B,image(A,C)) | member(f1(C,B,A),C). [copy(100),unit_del(a,40),unit_del(b,40)].
% 1.41/1.77 102 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(B,image(C,A)) | member(ordered_pair(f1(A,B,C),B),C) # label(p1) # label(axiom). [clausify(1)].
% 1.41/1.77 103 -ilf_type(A,binary_relation_type) | -member(B,image(A,C)) | member(ordered_pair(f1(C,B,A),B),A). [copy(102),unit_del(a,40),unit_del(b,40)].
% 1.41/1.77 106 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | -ilf_type(D,set_type) | image4(A,B,C,D) = image(C,D) # label(p25) # label(axiom). [clausify(25)].
% 1.41/1.77 107 -ilf_type(A,relation_type(B,C)) | image4(B,C,A,D) = image(A,D). [copy(106),unit_del(a,40),unit_del(b,40),unit_del(d,40)].
% 1.41/1.77 108 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | member(B,image(C,A)) | -ilf_type(D,set_type) | -member(ordered_pair(D,B),C) | -member(D,A) # label(p1) # label(axiom). [clausify(1)].
% 1.41/1.77 109 -ilf_type(A,binary_relation_type) | member(B,image(A,C)) | -member(ordered_pair(D,B),A) | -member(D,C). [copy(108),unit_del(a,40),unit_del(b,40),unit_del(e,40)].
% 1.41/1.77 110 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(E,relation_type(A,B)) | -member(ordered_pair(C,D),E) | member(C,A) # label(p2) # label(axiom). [clausify(2)].
% 1.41/1.77 111 -ilf_type(A,relation_type(B,C)) | -member(ordered_pair(D,E),A) | member(D,B). [copy(110),unit_del(a,40),unit_del(b,40),unit_del(c,40),unit_del(d,40)].
% 1.41/1.77 123 -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(34,d,29,c)].
% 1.41/1.77 124 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(123),unit_del(a,40),unit_del(b,40),unit_del(d,40)].
% 1.41/1.77 155 -ilf_type(A,member_type(c4)) | -member(ordered_pair(A,c6),c5) | -member(A,c3) | member(c7,c3). [resolve(53,a,43,a)].
% 1.41/1.77 169 ilf_type(c5,subset_type(cross_product(c4,c2))). [resolve(88,a,42,a)].
% 1.41/1.77 214 image4(c4,c2,c5,A) = image(c5,A). [resolve(107,a,42,a)].
% 1.41/1.77 229 -member(c6,image(c5,c3)) | -ilf_type(A,member_type(c4)) | -member(ordered_pair(A,c6),c5) | -member(A,c3). [back_rewrite(53),rewrite([214(6)])].
% 1.41/1.77 230 member(c6,image(c5,c3)) | member(ordered_pair(c7,c6),c5). [back_rewrite(45),rewrite([214(6)])].
% 1.41/1.77 232 member(c6,image(c5,c3)) | member(c7,c3). [back_rewrite(43),rewrite([214(6)])].
% 1.41/1.77 309 ilf_type(c5,binary_relation_type). [resolve(169,a,124,a)].
% 1.41/1.77 397 member(c7,c3) | member(ordered_pair(f1(c3,c6,c5),c6),c5). [resolve(232,a,103,b),unit_del(b,309)].
% 1.41/1.77 398 member(c7,c3) | member(f1(c3,c6,c5),c3). [resolve(232,a,101,b),unit_del(b,309)].
% 1.41/1.77 591 member(c7,c3) | ilf_type(f1(c3,c6,c5),member_type(c3)). [resolve(398,b,75,c),unit_del(b,47)].
% 1.41/1.77 623 member(c6,image(c5,c3)) | member(c6,image(c5,A)) | -member(c7,A). [resolve(230,b,109,c),unit_del(b,309)].
% 1.41/1.77 629 member(c6,image(c5,c3)) | -member(c7,c3). [factor(623,a,b)].
% 1.41/1.77 1088 ilf_type(f1(c3,c6,c5),member_type(c3)) | member(c6,image(c5,c3)). [resolve(591,a,629,b)].
% 1.41/1.77 1203 member(c7,c3) | -ilf_type(f1(c3,c6,c5),member_type(c4)) | -member(f1(c3,c6,c5),c3). [resolve(397,b,155,b),merge(d)].
% 1.41/1.77 1209 member(c7,c3) | -ilf_type(c5,relation_type(A,B)) | member(f1(c3,c6,c5),A). [resolve(397,b,111,b)].
% 1.41/1.77 2868 ilf_type(f1(c3,c6,c5),member_type(c3)) | member(f1(c3,c6,c5),c3). [resolve(1088,b,101,b),unit_del(b,309)].
% 1.41/1.77 6970 ilf_type(f1(c3,c6,c5),member_type(c3)). [resolve(2868,b,75,c),merge(c),unit_del(b,47)].
% 1.41/1.77 6971 member(f1(c3,c6,c5),c3). [resolve(6970,a,73,b),unit_del(a,47)].
% 1.41/1.77 6975 member(c7,c3) | -ilf_type(f1(c3,c6,c5),member_type(c4)). [back_unit_del(1203),unit_del(c,6971)].
% 1.41/1.77 9521 member(c7,c3) | member(f1(c3,c6,c5),c4). [resolve(1209,b,42,a)].
% 1.41/1.77 9526 member(c7,c3) | ilf_type(f1(c3,c6,c5),member_type(c4)). [resolve(9521,b,75,c),unit_del(b,48)].
% 1.41/1.77 9537 ilf_type(f1(c3,c6,c5),member_type(c4)) | ilf_type(c7,member_type(c3)). [resolve(9526,a,75,c),unit_del(b,47)].
% 1.41/1.77 9547 ilf_type(c7,member_type(c3)) | member(c7,c3). [resolve(9537,a,6975,b)].
% 1.41/1.77 9560 ilf_type(c7,member_type(c3)). [resolve(9547,b,75,c),merge(c),unit_del(b,47)].
% 1.41/1.77 9561 member(c7,c3). [resolve(9560,a,73,b),unit_del(a,47)].
% 1.41/1.77 9562 member(c6,image(c5,c3)). [back_unit_del(629),unit_del(b,9561)].
% 1.41/1.77 9569 -ilf_type(A,member_type(c4)) | -member(ordered_pair(A,c6),c5) | -member(A,c3). [back_unit_del(229),unit_del(a,9562)].
% 1.41/1.77 9590 member(ordered_pair(f1(c3,c6,c5),c6),c5). [resolve(9562,a,103,b),unit_del(a,309)].
% 1.41/1.77 9604 -ilf_type(f1(c3,c6,c5),member_type(c4)). [resolve(9590,a,9569,b),unit_del(b,6971)].
% 1.41/1.77 9683 -member(f1(c3,c6,c5),c4). [ur(75,a,48,a,b,9604,a)].
% 1.41/1.77 9719 -ilf_type(c5,relation_type(c4,A)). [ur(111,b,9590,a,c,9683,a)].
% 1.41/1.77 9720 $F. [resolve(9719,a,42,a)].
% 1.41/1.77
% 1.41/1.77 % SZS output end Refutation
% 1.41/1.77 ============================== end of proof ==========================
% 1.41/1.77
% 1.41/1.77 ============================== STATISTICS ============================
% 1.41/1.77
% 1.41/1.77 Given=856. Generated=15413. Kept=9619. proofs=1.
% 1.41/1.77 Usable=829. Sos=8463. Demods=22. Limbo=35, Disabled=377. Hints=0.
% 1.41/1.77 Megabytes=15.54.
% 1.41/1.77 User_CPU=0.75, System_CPU=0.01, Wall_clock=1.
% 1.41/1.77
% 1.41/1.77 ============================== end of statistics =====================
% 1.41/1.77
% 1.41/1.77 ============================== end of search =========================
% 1.41/1.77
% 1.41/1.77 THEOREM PROVED
% 1.41/1.77 % SZS status Theorem
% 1.41/1.77
% 1.41/1.77 Exiting with 1 proof.
% 1.41/1.77
% 1.41/1.77 Process 25143 exit (max_proofs) Sun Jul 10 00:17:12 2022
% 1.41/1.77 Prover9 interrupted
%------------------------------------------------------------------------------