TSTP Solution File: SET009-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SET009-1 : TPTP v8.1.0. Released v1.0.0.
% 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 04:25:32 EDT 2022

% Result   : Unsatisfiable 0.44s 1.03s
% Output   : Refutation 0.44s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SET009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.34  % Computer : n016.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 08:27:41 EDT 2022
% 0.12/0.35  % CPUTime  : 
% 0.44/1.02  ============================== Prover9 ===============================
% 0.44/1.02  Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.02  Process 7649 was started by sandbox2 on n016.cluster.edu,
% 0.44/1.02  Sun Jul 10 08:27:41 2022
% 0.44/1.02  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7268_n016.cluster.edu".
% 0.44/1.02  ============================== end of head ===========================
% 0.44/1.02  
% 0.44/1.02  ============================== INPUT =================================
% 0.44/1.02  
% 0.44/1.02  % Reading from file /tmp/Prover9_7268_n016.cluster.edu
% 0.44/1.02  
% 0.44/1.02  set(prolog_style_variables).
% 0.44/1.02  set(auto2).
% 0.44/1.02      % set(auto2) -> set(auto).
% 0.44/1.02      % set(auto) -> set(auto_inference).
% 0.44/1.02      % set(auto) -> set(auto_setup).
% 0.44/1.02      % set(auto_setup) -> set(predicate_elim).
% 0.44/1.02      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.02      % set(auto) -> set(auto_limits).
% 0.44/1.02      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.02      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.02      % set(auto) -> set(auto_denials).
% 0.44/1.02      % set(auto) -> set(auto_process).
% 0.44/1.02      % set(auto2) -> assign(new_constants, 1).
% 0.44/1.02      % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.02      % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.02      % set(auto2) -> assign(max_hours, 1).
% 0.44/1.02      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.02      % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.02      % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.02      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.02      % set(auto2) -> set(sort_initial_sos).
% 0.44/1.02      % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.02      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.02      % set(auto2) -> assign(max_megs, 400).
% 0.44/1.02      % set(auto2) -> assign(stats, some).
% 0.44/1.02      % set(auto2) -> clear(echo_input).
% 0.44/1.02      % set(auto2) -> set(quiet).
% 0.44/1.02      % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.02      % set(auto2) -> clear(print_given).
% 0.44/1.02  assign(lrs_ticks,-1).
% 0.44/1.02  assign(sos_limit,10000).
% 0.44/1.02  assign(order,kbo).
% 0.44/1.02  set(lex_order_vars).
% 0.44/1.02  clear(print_given).
% 0.44/1.02  
% 0.44/1.02  % formulas(sos).  % not echoed (16 formulas)
% 0.44/1.02  
% 0.44/1.02  ============================== end of input ==========================
% 0.44/1.02  
% 0.44/1.02  % From the command line: assign(max_seconds, 300).
% 0.44/1.02  
% 0.44/1.02  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.02  
% 0.44/1.02  % Formulas that are not ordinary clauses:
% 0.44/1.02  
% 0.44/1.02  ============================== end of process non-clausal formulas ===
% 0.44/1.02  
% 0.44/1.02  ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.02  
% 0.44/1.02  ============================== PREDICATE ELIMINATION =================
% 0.44/1.02  1 -member(A,B) | -member(A,C) | -difference(D,B,C) # label(not_member_of_difference) # label(axiom).  [assumption].
% 0.44/1.02  2 difference(b,a,bDa) # label(b_minus_a) # label(hypothesis).  [assumption].
% 0.44/1.02  3 difference(b,d,bDd) # label(b_minus_d) # label(hypothesis).  [assumption].
% 0.44/1.02  4 difference(A,B,C) | member(k(A,B,C),A) | member(k(A,B,C),C) # label(difference_axiom2) # label(axiom).  [assumption].
% 0.44/1.02  Derived: -member(A,a) | -member(A,bDa).  [resolve(1,c,2,a)].
% 0.44/1.02  Derived: -member(A,d) | -member(A,bDd).  [resolve(1,c,3,a)].
% 0.44/1.02  Derived: -member(A,B) | -member(A,C) | member(k(D,B,C),D) | member(k(D,B,C),C).  [resolve(1,c,4,a)].
% 0.44/1.02  5 -difference(A,B,C) | -member(D,C) | member(D,A) # label(member_of_difference) # label(axiom).  [assumption].
% 0.44/1.02  Derived: -member(A,bDa) | member(A,b).  [resolve(5,a,2,a)].
% 0.44/1.02  Derived: -member(A,bDd) | member(A,b).  [resolve(5,a,3,a)].
% 0.44/1.02  Derived: -member(A,B) | member(A,C) | member(k(C,D,B),C) | member(k(C,D,B),B).  [resolve(5,a,4,a)].
% 0.44/1.02  6 -member(A,B) | -difference(B,C,D) | member(A,D) | member(A,C) # label(member_of_difference_or_set2) # label(axiom).  [assumption].
% 0.44/1.02  Derived: -member(A,b) | member(A,bDa) | member(A,a).  [resolve(6,b,2,a)].
% 0.44/1.02  Derived: -member(A,b) | member(A,bDd) | member(A,d).  [resolve(6,b,3,a)].
% 0.44/1.02  Derived: -member(A,B) | member(A,C) | member(A,D) | member(k(B,D,C),B) | member(k(B,D,C),C).  [resolve(6,b,4,a)].
% 0.44/1.02  7 -member(k(A,B,C),B) | member(k(A,B,C),C) | difference(A,B,C) # label(difference_axiom1) # label(axiom).  [assumption].
% 0.44/1.02  Derived: -member(k(A,B,C),B) | member(k(A,B,C),C) | -member(D,B) | -member(D,C).  [resolve(7,c,1,c)].
% 0.44/1.02  Derived: -member(k(A,B,C),B) | member(k(A,B,C),C) | -member(D,C) | member(D,A).  [resolve(7,c,5,a)].
% 0.44/1.02  Derived: -member(k(A,B,C),B) | member(k(A,B,C),C) | -member(D,A) | member(D,C) | member(D,B).  [resolve(7,c,6,b)].
% 0.44/1.03  8 -member(k(A,B,C),C) | -member(k(A,B,C),A) | member(k(A,B,C),B) | difference(A,B,C) # label(difference_axiom3) # label(axiom).  [assumption].
% 0.44/1.03  Derived: -member(k(A,B,C),C) | -member(k(A,B,C),A) | member(k(A,B,C),B) | -member(D,B) | -member(D,C).  [resolve(8,d,1,c)].
% 0.44/1.03  Derived: -member(k(A,B,C),C) | -member(k(A,B,C),A) | member(k(A,B,C),B) | -member(D,C) | member(D,A).  [resolve(8,d,5,a)].
% 0.44/1.03  Derived: -member(k(A,B,C),C) | -member(k(A,B,C),A) | member(k(A,B,C),B) | -member(D,A) | member(D,C) | member(D,B).  [resolve(8,d,6,b)].
% 0.44/1.03  9 -subset(A,B) | -subset(B,A) | equal_sets(B,A) # label(subsets_are_set_equal_sets) # label(axiom).  [assumption].
% 0.44/1.03  10 -equal_sets(A,B) | subset(A,B) # label(set_equal_sets_are_subsets1) # label(axiom).  [assumption].
% 0.44/1.03  11 -equal_sets(A,B) | subset(B,A) # label(set_equal_sets_are_subsets2) # label(axiom).  [assumption].
% 0.44/1.03  12 -subset(bDa,bDd) # label(prove_bDa_is_a_subset_of_bDd) # label(negated_conjecture).  [assumption].
% 0.44/1.03  13 subset(d,a) # label(d_is_a_subset_of_a) # label(hypothesis).  [assumption].
% 0.44/1.03  14 subset(A,B) | member(member_of_1_not_of_2(A,B),A) # label(subsets_axiom1) # label(axiom).  [assumption].
% 0.44/1.03  Derived: member(member_of_1_not_of_2(bDa,bDd),bDa).  [resolve(12,a,14,a)].
% 0.44/1.03  15 -member(member_of_1_not_of_2(A,B),B) | subset(A,B) # label(subsets_axiom2) # label(axiom).  [assumption].
% 0.44/1.03  Derived: -member(member_of_1_not_of_2(bDa,bDd),bDd).  [resolve(15,b,12,a)].
% 0.44/1.03  16 -member(A,B) | -subset(B,C) | member(A,C) # label(membership_in_subsets) # label(axiom).  [assumption].
% 0.44/1.03  Derived: -member(A,d) | member(A,a).  [resolve(16,b,13,a)].
% 0.44/1.03  Derived: -member(A,B) | member(A,C) | member(member_of_1_not_of_2(B,C),B).  [resolve(16,b,14,a)].
% 0.44/1.03  Derived: -member(A,B) | member(A,C) | -member(member_of_1_not_of_2(B,C),C).  [resolve(16,b,15,b)].
% 0.44/1.03  
% 0.44/1.03  ============================== end predicate elimination =============
% 0.44/1.03  
% 0.44/1.03  Auto_denials:  (non-Horn, no changes).
% 0.44/1.03  
% 0.44/1.03  Term ordering decisions:
% 0.44/1.03  Function symbol KB weights:  b=1. bDa=1. bDd=1. a=1. d=1. member_of_1_not_of_2=1. k=1.
% 0.44/1.03  
% 0.44/1.03  ============================== end of process initial clauses ========
% 0.44/1.03  
% 0.44/1.03  ============================== CLAUSES FOR SEARCH ====================
% 0.44/1.03  
% 0.44/1.03  ============================== end of clauses for search =============
% 0.44/1.03  
% 0.44/1.03  ============================== SEARCH ================================
% 0.44/1.03  
% 0.44/1.03  % Starting search at 0.01 seconds.
% 0.44/1.03  
% 0.44/1.03  ============================== PROOF =================================
% 0.44/1.03  % SZS status Unsatisfiable
% 0.44/1.03  % SZS output start Refutation
% 0.44/1.03  
% 0.44/1.03  % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.44/1.03  % Length of proof is 20.
% 0.44/1.03  % Level of proof is 4.
% 0.44/1.03  % Maximum clause weight is 9.000.
% 0.44/1.03  % Given clauses 29.
% 0.44/1.03  
% 0.44/1.03  1 -member(A,B) | -member(A,C) | -difference(D,B,C) # label(not_member_of_difference) # label(axiom).  [assumption].
% 0.44/1.03  2 difference(b,a,bDa) # label(b_minus_a) # label(hypothesis).  [assumption].
% 0.44/1.03  3 difference(b,d,bDd) # label(b_minus_d) # label(hypothesis).  [assumption].
% 0.44/1.03  5 -difference(A,B,C) | -member(D,C) | member(D,A) # label(member_of_difference) # label(axiom).  [assumption].
% 0.44/1.03  6 -member(A,B) | -difference(B,C,D) | member(A,D) | member(A,C) # label(member_of_difference_or_set2) # label(axiom).  [assumption].
% 0.44/1.03  12 -subset(bDa,bDd) # label(prove_bDa_is_a_subset_of_bDd) # label(negated_conjecture).  [assumption].
% 0.44/1.03  13 subset(d,a) # label(d_is_a_subset_of_a) # label(hypothesis).  [assumption].
% 0.44/1.03  14 subset(A,B) | member(member_of_1_not_of_2(A,B),A) # label(subsets_axiom1) # label(axiom).  [assumption].
% 0.44/1.03  15 -member(member_of_1_not_of_2(A,B),B) | subset(A,B) # label(subsets_axiom2) # label(axiom).  [assumption].
% 0.44/1.03  16 -member(A,B) | -subset(B,C) | member(A,C) # label(membership_in_subsets) # label(axiom).  [assumption].
% 0.44/1.03  17 -member(A,a) | -member(A,bDa).  [resolve(1,c,2,a)].
% 0.44/1.03  20 -member(A,bDa) | member(A,b).  [resolve(5,a,2,a)].
% 0.44/1.03  24 -member(A,b) | member(A,bDd) | member(A,d).  [resolve(6,b,3,a)].
% 0.44/1.03  32 member(member_of_1_not_of_2(bDa,bDd),bDa).  [resolve(12,a,14,a)].
% 0.44/1.03  33 -member(member_of_1_not_of_2(bDa,bDd),bDd).  [resolve(15,b,12,a)].
% 0.44/1.03  34 -member(A,d) | member(A,a).  [resolve(16,b,13,a)].
% 0.44/1.03  52 member(member_of_1_not_of_2(bDa,bDd),b).  [resolve(32,a,20,a)].
% 0.44/1.03  55 -member(member_of_1_not_of_2(bDa,bDd),a).  [ur(17,b,32,a)].
% 0.44/1.03  66 -member(member_of_1_not_of_2(bDa,bDd),d).  [ur(34,b,55,a)].
% 0.44/1.03  69 $F.  [ur(24,b,33,a,c,66,a),unit_del(a,52)].
% 0.44/1.03  
% 0.44/1.03  % SZS output end Refutation
% 0.44/1.03  ============================== end of proof ==========================
% 0.44/1.03  
% 0.44/1.03  ============================== STATISTICS ============================
% 0.44/1.03  
% 0.44/1.03  Given=29. Generated=108. Kept=52. proofs=1.
% 0.44/1.03  Usable=29. Sos=22. Demods=0. Limbo=1, Disabled=36. Hints=0.
% 0.44/1.03  Megabytes=0.08.
% 0.44/1.03  User_CPU=0.02, System_CPU=0.00, Wall_clock=1.
% 0.44/1.03  
% 0.44/1.03  ============================== end of statistics =====================
% 0.44/1.03  
% 0.44/1.03  ============================== end of search =========================
% 0.44/1.03  
% 0.44/1.03  THEOREM PROVED
% 0.44/1.03  % SZS status Unsatisfiable
% 0.44/1.03  
% 0.44/1.03  Exiting with 1 proof.
% 0.44/1.03  
% 0.44/1.03  Process 7649 exit (max_proofs) Sun Jul 10 08:27:42 2022
% 0.44/1.03  Prover9 interrupted
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