TSTP Solution File: SEU177+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SEU177+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n017.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 13:29:40 EDT 2022

% Result   : Theorem 0.72s 0.98s
% Output   : Refutation 0.72s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU177+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.33  % Computer : n017.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jun 19 06:29:58 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.72/0.98  ============================== Prover9 ===============================
% 0.72/0.98  Prover9 (32) version 2009-11A, November 2009.
% 0.72/0.98  Process 30581 was started by sandbox on n017.cluster.edu,
% 0.72/0.98  Sun Jun 19 06:29:58 2022
% 0.72/0.98  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30428_n017.cluster.edu".
% 0.72/0.98  ============================== end of head ===========================
% 0.72/0.98  
% 0.72/0.98  ============================== INPUT =================================
% 0.72/0.98  
% 0.72/0.98  % Reading from file /tmp/Prover9_30428_n017.cluster.edu
% 0.72/0.98  
% 0.72/0.98  set(prolog_style_variables).
% 0.72/0.98  set(auto2).
% 0.72/0.98      % set(auto2) -> set(auto).
% 0.72/0.98      % set(auto) -> set(auto_inference).
% 0.72/0.98      % set(auto) -> set(auto_setup).
% 0.72/0.98      % set(auto_setup) -> set(predicate_elim).
% 0.72/0.98      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/0.98      % set(auto) -> set(auto_limits).
% 0.72/0.98      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/0.98      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/0.98      % set(auto) -> set(auto_denials).
% 0.72/0.98      % set(auto) -> set(auto_process).
% 0.72/0.98      % set(auto2) -> assign(new_constants, 1).
% 0.72/0.98      % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/0.98      % set(auto2) -> assign(max_weight, "200.000").
% 0.72/0.98      % set(auto2) -> assign(max_hours, 1).
% 0.72/0.98      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/0.98      % set(auto2) -> assign(max_seconds, 0).
% 0.72/0.98      % set(auto2) -> assign(max_minutes, 5).
% 0.72/0.98      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/0.98      % set(auto2) -> set(sort_initial_sos).
% 0.72/0.98      % set(auto2) -> assign(sos_limit, -1).
% 0.72/0.98      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/0.98      % set(auto2) -> assign(max_megs, 400).
% 0.72/0.98      % set(auto2) -> assign(stats, some).
% 0.72/0.98      % set(auto2) -> clear(echo_input).
% 0.72/0.98      % set(auto2) -> set(quiet).
% 0.72/0.98      % set(auto2) -> clear(print_initial_clauses).
% 0.72/0.98      % set(auto2) -> clear(print_given).
% 0.72/0.98  assign(lrs_ticks,-1).
% 0.72/0.98  assign(sos_limit,10000).
% 0.72/0.98  assign(order,kbo).
% 0.72/0.98  set(lex_order_vars).
% 0.72/0.98  clear(print_given).
% 0.72/0.98  
% 0.72/0.98  % formulas(sos).  % not echoed (26 formulas)
% 0.72/0.98  
% 0.72/0.98  ============================== end of input ==========================
% 0.72/0.98  
% 0.72/0.98  % From the command line: assign(max_seconds, 300).
% 0.72/0.98  
% 0.72/0.98  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/0.98  
% 0.72/0.98  % Formulas that are not ordinary clauses:
% 0.72/0.98  1 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  3 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  4 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  5 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  6 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  7 (exists A (empty(A) & relation(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  8 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  9 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  10 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  11 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  12 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  13 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  14 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  15 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  16 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  17 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  18 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  19 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  20 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  21 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  22 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  23 (all A (relation(A) -> (all B (B = relation_dom(A) <-> (all C (in(C,B) <-> (exists D in(ordered_pair(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  24 (all A (relation(A) -> (all B (B = relation_rng(A) <-> (all C (in(C,B) <-> (exists D in(ordered_pair(D,C),A)))))))) # label(d5_relat_1) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  25 -(all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(A,relation_dom(C)) & in(B,relation_rng(C))))) # label(t20_relat_1) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.72/0.98  
% 0.72/0.98  ============================== end of process non-clausal formulas ===
% 0.72/0.98  
% 0.72/0.98  ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/0.98  
% 0.72/0.98  ============================== PREDICATE ELIMINATION =================
% 0.72/0.98  26 -relation(A) | relation_dom(A) != B | in(C,B) | -in(ordered_pair(C,D),A) # label(d4_relat_1) # label(axiom).  [clausify(23)].
% 0.72/0.98  27 relation(c1) # label(rc1_relat_1) # label(axiom).  [clausify(7)].
% 0.72/0.98  28 relation(c6) # label(t20_relat_1) # label(negated_conjecture).  [clausify(25)].
% 0.72/0.98  Derived: relation_dom(c1) != A | in(B,A) | -in(ordered_pair(B,C),c1).  [resolve(26,a,27,a)].
% 0.72/0.98  Derived: relation_dom(c6) != A | in(B,A) | -in(ordered_pair(B,C),c6).  [resolve(26,a,28,a)].
% 0.72/0.98  29 -relation(A) | relation_rng(A) != B | in(C,B) | -in(ordered_pair(D,C),A) # label(d5_relat_1) # label(axiom).  [clausify(24)].
% 0.72/0.98  Derived: relation_rng(c1) != A | in(B,A) | -in(ordered_pair(C,B),c1).  [resolve(29,a,27,a)].
% 0.72/0.98  Derived: relation_rng(c6) != A | in(B,A) | -in(ordered_pair(C,B),c6).  [resolve(29,a,28,a)].
% 0.72/0.98  30 -relation(A) | relation_dom(A) != B | -in(C,B) | in(ordered_pair(C,f2(A,B,C)),A) # label(d4_relat_1) # label(axiom).  [clausify(23)].
% 0.72/0.98  Derived: relation_dom(c1) != A | -in(B,A) | in(ordered_pair(B,f2(c1,A,B)),c1).  [resolve(30,a,27,a)].
% 0.72/0.98  Derived: relation_dom(c6) != A | -in(B,A) | in(ordered_pair(B,f2(c6,A,B)),c6).  [resolve(30,a,28,a)].
% 0.72/0.98  31 -relation(A) | relation_rng(A) != B | -in(C,B) | in(ordered_pair(f5(A,B,C),C),A) # label(d5_relat_1) # label(axiom).  [clausify(24)].
% 0.72/0.98  Derived: relation_rng(c1) != A | -in(B,A) | in(ordered_pair(f5(c1,A,B),B),c1).  [resolve(31,a,27,a)].
% 0.72/0.98  Derived: relation_rng(c6) != A | -in(B,A) | in(ordered_pair(f5(c6,A,B),B),c6).  [resolve(31,a,28,a)].
% 0.72/0.98  32 -relation(A) | relation_dom(A) = B | -in(f3(A,B),B) | -in(ordered_pair(f3(A,B),C),A) # label(d4_relat_1) # label(axiom).  [clausify(23)].
% 0.72/0.98  Derived: relation_dom(c1) = A | -in(f3(c1,A),A) | -in(ordered_pair(f3(c1,A),B),c1).  [resolve(32,a,27,a)].
% 0.72/0.98  Derived: relation_dom(c6) = A | -in(f3(c6,A),A) | -in(ordered_pair(f3(c6,A),B),c6).  [resolve(32,a,28,a)].
% 0.72/0.98  33 -relation(A) | relation_rng(A) = B | -in(f6(A,B),B) | -in(ordered_pair(C,f6(A,B)),A) # label(d5_relat_1) # label(axiom).  [clausify(24)].
% 0.72/0.98  Derived: relation_rng(c1) = A | -in(f6(c1,A),A) | -in(ordered_pair(B,f6(c1,A)),c1).  [resolve(33,a,27,a)].
% 0.72/0.98  Derived: relation_rng(c6) = A | -in(f6(c6,A),A) | -in(ordered_pair(B,f6(c6,A)),c6).  [resolve(33,a,28,a)].
% 0.72/0.98  34 -relation(A) | relation_dom(A) = B | in(f3(A,B),B) | in(ordered_pair(f3(A,B),f4(A,B)),A) # label(d4_relat_1) # label(axiom).  [clausify(23)].
% 0.72/0.98  Derived: relation_dom(c1) = A | in(f3(c1,A),A) | in(ordered_pair(f3(c1,A),f4(c1,A)),c1).  [resolve(34,a,27,a)].
% 0.72/0.98  Derived: relation_dom(c6) = A | in(f3(c6,A),A) | in(ordered_pair(f3(c6,A),f4(c6,A)),c6).  [resolve(34,a,28,a)].
% 0.72/0.98  35 -relation(A) | relation_rng(A) = B | in(f6(A,B),B) | in(ordered_pair(f7(A,B),f6(A,B)),A) # label(d5_relat_1) # label(axiom).  [clausify(24)].
% 0.72/0.98  Derived: relation_rng(c1) = A | in(f6(c1,A),A) | in(ordered_pair(f7(c1,A),f6(c1,A)),c1).  [resolve(35,a,27,a)].
% 0.72/0.98  Derived: relation_rng(c6) = A | in(f6(c6,A),A) | in(ordered_pair(f7(c6,A),f6(c6,A)),c6).  [resolve(35,a,28,a)].
% 0.72/0.98  36 -element(A,B) | empty(B) | in(A,B) # label(t2_subset) # label(axiom).  [clausify(12)].
% 0.72/0.98  37 element(f1(A),A) # label(existence_m1_subset_1) # label(axiom).  [clausify(3)].
% 0.72/0.98  38 -in(A,B) | element(A,B) # label(t1_subset) # label(axiom).  [clausify(20)].
% 0.72/0.98  Derived: empty(A) | in(f1(A),A).  [resolve(36,a,37,a)].
% 0.72/0.98  
% 0.72/0.98  ============================== end predicate elimination =============
% 0.72/0.98  
% 0.72/0.98  Auto_denials:  (non-Horn, no changes).
% 0.72/0.98  
% 0.72/0.98  Term ordering decisions:
% 0.72/0.98  Function symbol KB weights:  empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. ordered_pair=1. unordered_pair=1. f3=1. f4=1. f6=1. f7=1. relation_dom=1. relation_rng=1. singleton=1. f1=1. f2=1. f5=1.
% 0.72/0.98  
% 0.72/0.98  ============================== end of process initial clauses ========
% 0.72/0.98  
% 0.72/0.98  ============================== CLAUSES FOR SEARCH ====================
% 0.72/0.98  
% 0.72/0.98  ============================== end of clauses for search =============
% 0.72/0.98  
% 0.72/0.98  ============================== SEARCH ================================
% 0.72/0.98  
% 0.72/0.98  % Starting search at 0.02 seconds.
% 0.72/0.98  
% 0.72/0.98  ============================== PROOF =================================
% 0.72/0.98  % SZS status Theorem
% 0.72/0.98  % SZS output start Refutation
% 0.72/0.98  
% 0.72/0.98  % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.72/0.98  % Length of proof is 23.
% 0.72/0.98  % Level of proof is 8.
% 0.72/0.98  % Maximum clause weight is 15.000.
% 0.72/0.98  % Given clauses 37.
% 0.72/0.98  
% 0.72/0.98  2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  22 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  23 (all A (relation(A) -> (all B (B = relation_dom(A) <-> (all C (in(C,B) <-> (exists D in(ordered_pair(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  24 (all A (relation(A) -> (all B (B = relation_rng(A) <-> (all C (in(C,B) <-> (exists D in(ordered_pair(D,C),A)))))))) # label(d5_relat_1) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.98  25 -(all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(A,relation_dom(C)) & in(B,relation_rng(C))))) # label(t20_relat_1) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.72/0.98  26 -relation(A) | relation_dom(A) != B | in(C,B) | -in(ordered_pair(C,D),A) # label(d4_relat_1) # label(axiom).  [clausify(23)].
% 0.72/0.98  28 relation(c6) # label(t20_relat_1) # label(negated_conjecture).  [clausify(25)].
% 0.72/0.98  29 -relation(A) | relation_rng(A) != B | in(C,B) | -in(ordered_pair(D,C),A) # label(d5_relat_1) # label(axiom).  [clausify(24)].
% 0.72/0.98  42 in(ordered_pair(c4,c5),c6) # label(t20_relat_1) # label(negated_conjecture).  [clausify(25)].
% 0.72/0.98  43 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom).  [clausify(2)].
% 0.72/0.98  44 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom).  [clausify(22)].
% 0.72/0.98  45 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)).  [copy(44),rewrite([43(4)])].
% 0.72/0.98  52 -in(c4,relation_dom(c6)) | -in(c5,relation_rng(c6)) # label(t20_relat_1) # label(negated_conjecture).  [clausify(25)].
% 0.72/0.98  58 relation_dom(c6) != A | in(B,A) | -in(ordered_pair(B,C),c6).  [resolve(26,a,28,a)].
% 0.72/0.98  59 relation_dom(c6) != A | in(B,A) | -in(unordered_pair(singleton(B),unordered_pair(B,C)),c6).  [copy(58),rewrite([45(5)])].
% 0.72/0.98  62 relation_rng(c6) != A | in(B,A) | -in(ordered_pair(C,B),c6).  [resolve(29,a,28,a)].
% 0.72/0.98  63 relation_rng(c6) != A | in(B,A) | -in(unordered_pair(singleton(C),unordered_pair(B,C)),c6).  [copy(62),rewrite([45(5),43(6)])].
% 0.72/0.98  89 in(unordered_pair(singleton(c4),unordered_pair(c4,c5)),c6).  [back_rewrite(42),rewrite([45(3)])].
% 0.72/0.98  119 relation_dom(c6) != A | in(c4,A).  [resolve(89,a,59,c)].
% 0.72/0.98  132 in(c4,relation_dom(c6)).  [xx_res(119,a)].
% 0.72/0.98  133 -in(c5,relation_rng(c6)).  [back_unit_del(52),unit_del(a,132)].
% 0.72/0.98  137 -in(unordered_pair(singleton(A),unordered_pair(A,c5)),c6).  [ur(63,a,xx,b,133,a),rewrite([43(3)])].
% 0.72/0.98  138 $F.  [resolve(137,a,89,a)].
% 0.72/0.98  
% 0.72/0.98  % SZS output end Refutation
% 0.72/0.98  ============================== end of proof ==========================
% 0.72/0.98  
% 0.72/0.98  ============================== STATISTICS ============================
% 0.72/0.98  
% 0.72/0.98  Given=37. Generated=130. Kept=80. proofs=1.
% 0.72/0.98  Usable=34. Sos=25. Demods=4. Limbo=0, Disabled=65. Hints=0.
% 0.72/0.98  Megabytes=0.18.
% 0.72/0.98  User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.72/0.98  
% 0.72/0.98  ============================== end of statistics =====================
% 0.72/0.98  
% 0.72/0.98  ============================== end of search =========================
% 0.72/0.98  
% 0.72/0.98  THEOREM PROVED
% 0.72/0.98  % SZS status Theorem
% 0.72/0.98  
% 0.72/0.98  Exiting with 1 proof.
% 0.72/0.98  
% 0.72/0.98  Process 30581 exit (max_proofs) Sun Jun 19 06:29:58 2022
% 0.72/0.98  Prover9 interrupted
%------------------------------------------------------------------------------