TSTP Solution File: SET676+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET676+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 0.45s 1.02s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET676+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 10 12:22:07 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.45/1.01 ============================== Prover9 ===============================
% 0.45/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.01 Process 22541 was started by sandbox on n005.cluster.edu,
% 0.45/1.01 Sun Jul 10 12:22:07 2022
% 0.45/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22387_n005.cluster.edu".
% 0.45/1.01 ============================== end of head ===========================
% 0.45/1.01
% 0.45/1.01 ============================== INPUT =================================
% 0.45/1.01
% 0.45/1.01 % Reading from file /tmp/Prover9_22387_n005.cluster.edu
% 0.45/1.01
% 0.45/1.01 set(prolog_style_variables).
% 0.45/1.01 set(auto2).
% 0.45/1.01 % set(auto2) -> set(auto).
% 0.45/1.01 % set(auto) -> set(auto_inference).
% 0.45/1.01 % set(auto) -> set(auto_setup).
% 0.45/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.01 % set(auto) -> set(auto_limits).
% 0.45/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.01 % set(auto) -> set(auto_denials).
% 0.45/1.01 % set(auto) -> set(auto_process).
% 0.45/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.01 % set(auto2) -> assign(stats, some).
% 0.45/1.01 % set(auto2) -> clear(echo_input).
% 0.45/1.01 % set(auto2) -> set(quiet).
% 0.45/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.01 % set(auto2) -> clear(print_given).
% 0.45/1.01 assign(lrs_ticks,-1).
% 0.45/1.01 assign(sos_limit,10000).
% 0.45/1.01 assign(order,kbo).
% 0.45/1.01 set(lex_order_vars).
% 0.45/1.01 clear(print_given).
% 0.45/1.01
% 0.45/1.01 % formulas(sos). % not echoed (20 formulas)
% 0.45/1.01
% 0.45/1.01 ============================== end of input ==========================
% 0.45/1.01
% 0.45/1.01 % From the command line: assign(max_seconds, 300).
% 0.45/1.01
% 0.45/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.01
% 0.45/1.01 % Formulas that are not ordinary clauses:
% 0.45/1.01 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),relation_type(B,C)))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 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].
% 0.45/1.01 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].
% 0.45/1.01 4 (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(p4) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 5 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,identity_relation_of_type(B))))) # label(p5) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 6 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p6) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 7 (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(p7) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 8 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (exists D ilf_type(D,relation_type(C,B))))))) # label(p8) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 9 (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(p9) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 10 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p10) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 11 (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(p11) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 12 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p12) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 13 (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(p13) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 14 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p14) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 15 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 16 (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(p16) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 17 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 18 (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(p18) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 19 (all B ilf_type(B,set_type)) # label(p19) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 20 -(all B (ilf_type(B,set_type) -> ilf_type(cross_product(B,B),identity_relation_of_type(B)))) # label(prove_relset_1_41) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.01
% 0.45/1.01 ============================== end of process non-clausal formulas ===
% 0.45/1.01
% 0.45/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.01
% 0.45/1.01 ============================== PREDICATE ELIMINATION =================
% 0.45/1.01 21 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) # label(p16) # label(axiom). [clausify(16)].
% 0.45/1.01 22 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p17) # label(axiom). [clausify(17)].
% 0.45/1.01 23 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f11(A),set_type) # label(p16) # label(axiom). [clausify(16)].
% 0.45/1.01 24 -ilf_type(A,set_type) | relation_like(A) | member(f11(A),A) # label(p16) # label(axiom). [clausify(16)].
% 0.45/1.01 25 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p18) # label(axiom). [clausify(18)].
% 0.45/1.01 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(21,b,22,c)].
% 0.45/1.01 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(21,b,23,b)].
% 0.45/1.01 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(21,b,24,b)].
% 0.45/1.01 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(21,b,25,d)].
% 0.45/1.01 26 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) # label(p16) # label(axiom). [clausify(16)].
% 0.45/1.01 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(26,b,22,c)].
% 0.45/1.01 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(26,b,23,b)].
% 0.45/1.01 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(26,b,24,b)].
% 0.45/1.02 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(26,b,25,d)].
% 0.45/1.02 27 -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(p16) # label(axiom). [clausify(16)].
% 0.45/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f11(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f9(A,D),set_type). [resolve(27,b,21,b)].
% 0.45/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f11(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f10(A,D),set_type). [resolve(27,b,26,b)].
% 0.45/1.02 28 -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(p16) # label(axiom). [clausify(16)].
% 0.45/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -empty(A) | -ilf_type(A,set_type). [resolve(28,b,22,c)].
% 0.45/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -ilf_type(A,set_type) | ilf_type(f11(A),set_type). [resolve(28,b,23,b)].
% 0.45/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -ilf_type(A,set_type) | member(f11(A),A). [resolve(28,b,24,b)].
% 0.45/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(28,b,25,d)].
% 0.45/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f11(A). [resolve(28,b,27,b)].
% 0.45/1.02
% 0.45/1.02 ============================== end predicate elimination =============
% 0.45/1.02
% 0.45/1.02 Auto_denials: (non-Horn, no changes).
% 0.45/1.02
% 0.45/1.02 Term ordering decisions:
% 0.45/1.02 Function symbol KB weights: set_type=1. c1=1. cross_product=1. ordered_pair=1. relation_type=1. f4=1. f6=1. f9=1. f10=1. subset_type=1. power_set=1. member_type=1. identity_relation_of_type=1. f3=1. f5=1. f7=1. f8=1. f11=1. f1=1. f2=1.
% 0.45/1.02
% 0.45/1.02 ============================== end of process initial clauses ========
% 0.45/1.02
% 0.45/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.45/1.02
% 0.45/1.02 ============================== end of clauses for search =============
% 0.45/1.02
% 0.45/1.02 ============================== SEARCH ================================
% 0.45/1.02
% 0.45/1.02 % Starting search at 0.02 seconds.
% 0.45/1.02
% 0.45/1.02 ============================== PROOF =================================
% 0.45/1.02 % SZS status Theorem
% 0.45/1.02 % SZS output start Refutation
% 0.45/1.02
% 0.45/1.02 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.45/1.02 % Length of proof is 12.
% 0.45/1.02 % Level of proof is 4.
% 0.45/1.02 % Maximum clause weight is 9.000.
% 0.45/1.02 % Given clauses 12.
% 0.45/1.02
% 0.45/1.02 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),relation_type(B,C)))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 4 (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(p4) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 19 (all B ilf_type(B,set_type)) # label(p19) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 20 -(all B (ilf_type(B,set_type) -> ilf_type(cross_product(B,B),identity_relation_of_type(B)))) # label(prove_relset_1_41) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.02 29 ilf_type(A,set_type) # label(p19) # label(axiom). [clausify(19)].
% 0.45/1.02 32 -ilf_type(cross_product(c1,c1),identity_relation_of_type(c1)) # label(prove_relset_1_41) # label(negated_conjecture). [clausify(20)].
% 0.45/1.02 47 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),relation_type(A,B)) # label(p1) # label(axiom). [clausify(1)].
% 0.45/1.02 48 ilf_type(cross_product(A,B),relation_type(A,B)). [copy(47),unit_del(a,29),unit_del(b,29)].
% 0.45/1.02 53 -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(p4) # label(axiom). [clausify(4)].
% 0.45/1.02 54 ilf_type(A,identity_relation_of_type(B)) | -ilf_type(A,relation_type(B,B)). [copy(53),unit_del(a,29),unit_del(b,29)].
% 0.45/1.02 106 ilf_type(cross_product(A,A),identity_relation_of_type(A)). [resolve(54,b,48,a)].
% 0.45/1.02 107 $F. [resolve(106,a,32,a)].
% 0.45/1.02
% 0.45/1.02 % SZS output end Refutation
% 0.45/1.02 ============================== end of proof ==========================
% 0.45/1.02
% 0.45/1.02 ============================== STATISTICS ============================
% 0.45/1.02
% 0.45/1.02 Given=12. Generated=54. Kept=33. proofs=1.
% 0.45/1.02 Usable=12. Sos=19. Demods=0. Limbo=1, Disabled=56. Hints=0.
% 0.45/1.02 Megabytes=0.12.
% 0.45/1.02 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.45/1.02
% 0.45/1.02 ============================== end of statistics =====================
% 0.45/1.02
% 0.45/1.02 ============================== end of search =========================
% 0.45/1.02
% 0.45/1.02 THEOREM PROVED
% 0.45/1.02 % SZS status Theorem
% 0.45/1.02
% 0.45/1.02 Exiting with 1 proof.
% 0.45/1.02
% 0.45/1.02 Process 22541 exit (max_proofs) Sun Jul 10 12:22:07 2022
% 0.45/1.02 Prover9 interrupted
%------------------------------------------------------------------------------