TSTP Solution File: NUN073+2 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : NUN073+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n018.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 : Mon Jul 18 16:37:12 EDT 2022

% Result   : Theorem 0.44s 1.02s
% Output   : Refutation 0.44s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : NUN073+2 : TPTP v8.1.0. Released v7.3.0.
% 0.08/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun  2 06:35:45 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.44/1.01  ============================== Prover9 ===============================
% 0.44/1.01  Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.01  Process 28717 was started by sandbox2 on n018.cluster.edu,
% 0.44/1.01  Thu Jun  2 06:35:45 2022
% 0.44/1.01  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28563_n018.cluster.edu".
% 0.44/1.01  ============================== end of head ===========================
% 0.44/1.01  
% 0.44/1.01  ============================== INPUT =================================
% 0.44/1.01  
% 0.44/1.01  % Reading from file /tmp/Prover9_28563_n018.cluster.edu
% 0.44/1.01  
% 0.44/1.01  set(prolog_style_variables).
% 0.44/1.01  set(auto2).
% 0.44/1.01      % set(auto2) -> set(auto).
% 0.44/1.01      % set(auto) -> set(auto_inference).
% 0.44/1.01      % set(auto) -> set(auto_setup).
% 0.44/1.01      % set(auto_setup) -> set(predicate_elim).
% 0.44/1.01      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.01      % set(auto) -> set(auto_limits).
% 0.44/1.01      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.01      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.01      % set(auto) -> set(auto_denials).
% 0.44/1.01      % set(auto) -> set(auto_process).
% 0.44/1.01      % set(auto2) -> assign(new_constants, 1).
% 0.44/1.01      % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.01      % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.01      % set(auto2) -> assign(max_hours, 1).
% 0.44/1.01      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.01      % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.01      % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.01      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.01      % set(auto2) -> set(sort_initial_sos).
% 0.44/1.01      % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.01      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.01      % set(auto2) -> assign(max_megs, 400).
% 0.44/1.01      % set(auto2) -> assign(stats, some).
% 0.44/1.01      % set(auto2) -> clear(echo_input).
% 0.44/1.01      % set(auto2) -> set(quiet).
% 0.44/1.01      % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.01      % set(auto2) -> clear(print_given).
% 0.44/1.01  assign(lrs_ticks,-1).
% 0.44/1.01  assign(sos_limit,10000).
% 0.44/1.01  assign(order,kbo).
% 0.44/1.01  set(lex_order_vars).
% 0.44/1.01  clear(print_given).
% 0.44/1.01  
% 0.44/1.01  % formulas(sos).  % not echoed (12 formulas)
% 0.44/1.01  
% 0.44/1.01  ============================== end of input ==========================
% 0.44/1.01  
% 0.44/1.01  % From the command line: assign(max_seconds, 300).
% 0.44/1.01  
% 0.44/1.01  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.01  
% 0.44/1.01  % Formulas that are not ordinary clauses:
% 0.44/1.01  1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.01  2 (all X11 exists Y21 all X12 (-r2(X11,X12) & X12 != Y21 | r2(X11,X12) & X12 = Y21)) # label(axiom_2) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.01  3 (all X13 all X14 exists Y22 all X15 (-r3(X13,X14,X15) & X15 != Y22 | r3(X13,X14,X15) & X15 = Y22)) # label(axiom_3) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.01  4 (all X16 all X17 exists Y23 all X18 (-r4(X16,X17,X18) & X18 != Y23 | r4(X16,X17,X18) & X18 = Y23)) # label(axiom_4) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.01  5 (all X1 all X8 exists Y4 ((exists Y5 ((exists Y15 (r2(X8,Y15) & r3(X1,Y15,Y5))) & Y5 = Y4)) & (exists Y7 (r2(Y7,Y4) & r3(X1,X8,Y7))))) # label(axiom_1a) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.01  6 (all X2 all X9 exists Y2 ((exists Y3 ((exists Y14 (r2(X9,Y14) & r4(X2,Y14,Y3))) & Y3 = Y2)) & (exists Y6 (r3(Y6,X2,Y2) & r4(X2,X9,Y6))))) # label(axiom_2a) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.01  7 (all X3 all X10 ((all Y12 ((all Y13 (-r2(X3,Y13) | Y13 != Y12)) | -r2(X10,Y12))) | X3 = X10)) # label(axiom_3a) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.01  8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.01  9 (all X5 exists Y8 ((exists Y17 (r1(Y17) & r4(X5,Y17,Y8))) & (exists Y18 (r1(Y18) & Y8 = Y18)))) # label(axiom_5a) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.01  10 (all X6 ((exists Y19 (r1(Y19) & X6 = Y19)) | (exists Y1 exists Y11 (r2(Y1,Y11) & X6 = Y11)))) # label(axiom_6a) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.01  11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.01  12 -(all Y1 ((all Y2 ((all Y4 (-r1(Y4) | -r2(Y4,Y2))) | Y2 != Y1)) | (all Y3 ((all Y5 (-r1(Y5) | -r2(Y5,Y3))) | -r2(Y3,Y1))))) # label(oneuneqtwo) # label(negated_conjecture) # label(non_clause).  [assumption].
% 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  13 -r1(A) | A != B | -r2(C,B) # label(axiom_7a) # label(axiom).  [clausify(11)].
% 0.44/1.02  14 r1(c4) # label(oneuneqtwo) # label(negated_conjecture).  [clausify(12)].
% 0.44/1.02  15 r1(c6) # label(oneuneqtwo) # label(negated_conjecture).  [clausify(12)].
% 0.44/1.02  16 r1(f13(A)) # label(axiom_4a) # label(axiom).  [clausify(8)].
% 0.44/1.02  17 r1(f15(A)) # label(axiom_5a) # label(axiom).  [clausify(9)].
% 0.44/1.02  18 r1(f16(A)) # label(axiom_5a) # label(axiom).  [clausify(9)].
% 0.44/1.02  19 r1(f17(A)) | f19(A) = A # label(axiom_6a) # label(axiom).  [clausify(10)].
% 0.44/1.02  20 r1(f17(A)) | r2(f18(A),f19(A)) # label(axiom_6a) # label(axiom).  [clausify(10)].
% 0.44/1.02  Derived: c4 != A | -r2(B,A).  [resolve(13,a,14,a)].
% 0.44/1.02  Derived: c6 != A | -r2(B,A).  [resolve(13,a,15,a)].
% 0.44/1.02  Derived: f13(A) != B | -r2(C,B).  [resolve(13,a,16,a)].
% 0.44/1.02  Derived: f15(A) != B | -r2(C,B).  [resolve(13,a,17,a)].
% 0.44/1.02  Derived: f16(A) != B | -r2(C,B).  [resolve(13,a,18,a)].
% 0.44/1.02  Derived: f17(A) != B | -r2(C,B) | f19(A) = A.  [resolve(13,a,19,a)].
% 0.44/1.02  Derived: f17(A) != B | -r2(C,B) | r2(f18(A),f19(A)).  [resolve(13,a,20,a)].
% 0.44/1.02  21 -r1(A) | A = c1 # label(axiom_1) # label(axiom).  [clausify(1)].
% 0.44/1.02  Derived: c4 = c1.  [resolve(21,a,14,a)].
% 0.44/1.02  Derived: c6 = c1.  [resolve(21,a,15,a)].
% 0.44/1.02  Derived: f13(A) = c1.  [resolve(21,a,16,a)].
% 0.44/1.02  Derived: f15(A) = c1.  [resolve(21,a,17,a)].
% 0.44/1.02  Derived: f16(A) = c1.  [resolve(21,a,18,a)].
% 0.44/1.02  Derived: f17(A) = c1 | f19(A) = A.  [resolve(21,a,19,a)].
% 0.44/1.02  Derived: f17(A) = c1 | r2(f18(A),f19(A)).  [resolve(21,a,20,a)].
% 0.44/1.02  22 A != c1 | r1(A) # label(axiom_1) # label(axiom).  [clausify(1)].
% 0.44/1.02  Derived: A != c1 | A != B | -r2(C,B).  [resolve(22,b,13,a)].
% 0.44/1.02  23 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom).  [clausify(3)].
% 0.44/1.02  24 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom).  [clausify(5)].
% 0.44/1.02  25 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom).  [clausify(8)].
% 0.44/1.02  26 r3(A,f6(A,B),f5(A,B)) # label(axiom_1a) # label(axiom).  [clausify(5)].
% 0.44/1.02  27 r3(f11(A,B),A,f8(A,B)) # label(axiom_2a) # label(axiom).  [clausify(6)].
% 0.44/1.02  Derived: f7(A,B) = f2(A,B).  [resolve(23,a,24,a)].
% 0.44/1.02  Derived: f12(A) = f2(A,f13(A)).  [resolve(23,a,25,a)].
% 0.44/1.02  Derived: f5(A,B) = f2(A,f6(A,B)).  [resolve(23,a,26,a)].
% 0.44/1.02  Derived: f8(A,B) = f2(f11(A,B),A).  [resolve(23,a,27,a)].
% 0.44/1.02  28 A != f2(B,C) | r3(B,C,A) # label(axiom_3) # label(axiom).  [clausify(3)].
% 0.44/1.02  29 -r4(A,B,C) | C = f3(A,B) # label(axiom_4) # label(axiom).  [clausify(4)].
% 0.44/1.02  30 r4(A,B,f11(A,B)) # label(axiom_2a) # label(axiom).  [clausify(6)].
% 0.44/1.02  31 r4(A,f15(A),f14(A)) # label(axiom_5a) # label(axiom).  [clausify(9)].
% 0.44/1.02  32 r4(A,f10(A,B),f9(A,B)) # label(axiom_2a) # label(axiom).  [clausify(6)].
% 0.44/1.02  Derived: f11(A,B) = f3(A,B).  [resolve(29,a,30,a)].
% 0.44/1.02  Derived: f14(A) = f3(A,f15(A)).  [resolve(29,a,31,a)].
% 0.44/1.02  Derived: f9(A,B) = f3(A,f10(A,B)).  [resolve(29,a,32,a)].
% 0.44/1.02  33 A != f3(B,C) | r4(B,C,A) # label(axiom_4) # label(axiom).  [clausify(4)].
% 0.44/1.02  
% 0.44/1.02  ============================== end predicate elimination =============
% 0.44/1.02  
% 0.44/1.02  Auto_denials:  (non-Horn, no changes).
% 0.44/1.02  
% 0.44/1.02  Term ordering decisions:
% 0.44/1.02  Function symbol KB weights:  c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f1=1. f12=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1.
% 0.44/1.02  
% 0.44/1.02  ============================== end of process initial clauses ========
% 0.44/1.02  
% 0.44/1.02  ============================== CLAUSES FOR SEARCH ====================
% 0.44/1.02  
% 0.44/1.02  ============================== end of clauses for search =============
% 0.44/1.02  
% 0.44/1.02  ============================== SEARCH ================================
% 0.44/1.02  
% 0.44/1.02  % Starting search at 0.02 seconds.
% 0.44/1.02  
% 0.44/1.02  ============================== PROOF =================================
% 0.44/1.02  % SZS status Theorem
% 0.44/1.02  % SZS output start Refutation
% 0.44/1.02  
% 0.44/1.02  % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.44/1.02  % Length of proof is 38.
% 0.44/1.02  % Level of proof is 7.
% 0.44/1.02  % Maximum clause weight is 12.000.
% 0.44/1.02  % Given clauses 33.
% 0.44/1.02  
% 0.44/1.02  1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  2 (all X11 exists Y21 all X12 (-r2(X11,X12) & X12 != Y21 | r2(X11,X12) & X12 = Y21)) # label(axiom_2) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  3 (all X13 all X14 exists Y22 all X15 (-r3(X13,X14,X15) & X15 != Y22 | r3(X13,X14,X15) & X15 = Y22)) # label(axiom_3) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  7 (all X3 all X10 ((all Y12 ((all Y13 (-r2(X3,Y13) | Y13 != Y12)) | -r2(X10,Y12))) | X3 = X10)) # label(axiom_3a) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  12 -(all Y1 ((all Y2 ((all Y4 (-r1(Y4) | -r2(Y4,Y2))) | Y2 != Y1)) | (all Y3 ((all Y5 (-r1(Y5) | -r2(Y5,Y3))) | -r2(Y3,Y1))))) # label(oneuneqtwo) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.44/1.02  13 -r1(A) | A != B | -r2(C,B) # label(axiom_7a) # label(axiom).  [clausify(11)].
% 0.44/1.02  14 r1(c4) # label(oneuneqtwo) # label(negated_conjecture).  [clausify(12)].
% 0.44/1.02  15 r1(c6) # label(oneuneqtwo) # label(negated_conjecture).  [clausify(12)].
% 0.44/1.02  16 r1(f13(A)) # label(axiom_4a) # label(axiom).  [clausify(8)].
% 0.44/1.02  21 -r1(A) | A = c1 # label(axiom_1) # label(axiom).  [clausify(1)].
% 0.44/1.02  22 A != c1 | r1(A) # label(axiom_1) # label(axiom).  [clausify(1)].
% 0.44/1.02  23 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom).  [clausify(3)].
% 0.44/1.02  25 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom).  [clausify(8)].
% 0.44/1.02  34 r2(c4,c3) # label(oneuneqtwo) # label(negated_conjecture).  [clausify(12)].
% 0.44/1.02  35 c2 = c3 # label(oneuneqtwo) # label(negated_conjecture).  [clausify(12)].
% 0.44/1.02  36 c3 = c2.  [copy(35),flip(a)].
% 0.44/1.02  37 r2(c6,c5) # label(oneuneqtwo) # label(negated_conjecture).  [clausify(12)].
% 0.44/1.02  38 r2(c5,c2) # label(oneuneqtwo) # label(negated_conjecture).  [clausify(12)].
% 0.44/1.02  39 f12(A) = A # label(axiom_4a) # label(axiom).  [clausify(8)].
% 0.44/1.02  48 -r2(A,B) | B = f1(A) # label(axiom_2) # label(axiom).  [clausify(2)].
% 0.44/1.02  49 -r2(A,B) | f1(A) = B.  [copy(48),flip(b)].
% 0.44/1.02  52 -r2(A,B) | B != C | -r2(D,C) | D = A # label(axiom_3a) # label(axiom).  [clausify(7)].
% 0.44/1.02  61 c4 = c1.  [resolve(21,a,14,a)].
% 0.44/1.02  62 c6 = c1.  [resolve(21,a,15,a)].
% 0.44/1.02  63 f13(A) = c1.  [resolve(21,a,16,a)].
% 0.44/1.02  69 A != c1 | A != B | -r2(C,B).  [resolve(22,b,13,a)].
% 0.44/1.02  70 c1 != A | A != B | -r2(C,B).  [copy(69),flip(a)].
% 0.44/1.02  72 f12(A) = f2(A,f13(A)).  [resolve(23,a,25,a)].
% 0.44/1.02  73 f2(A,c1) = A.  [copy(72),rewrite([39(1),63(1)]),flip(a)].
% 0.44/1.02  82 r2(c1,c2).  [back_rewrite(34),rewrite([61(1),36(2)])].
% 0.44/1.02  84 r2(c1,c5).  [back_rewrite(37),rewrite([62(1)])].
% 0.44/1.02  116 c2 != c1.  [ur(70,b,39,a,c,38,a),rewrite([39(3)]),flip(a)].
% 0.44/1.02  118 f1(c1) = c2.  [resolve(82,a,49,a)].
% 0.44/1.02  126 c5 = c2.  [resolve(84,a,49,a),rewrite([118(2)]),flip(a)].
% 0.44/1.02  129 r2(c2,c2).  [back_rewrite(38),rewrite([126(1)])].
% 0.44/1.02  146 $F.  [ur(52,a,82,a,b,73,a(flip),d,116,a),rewrite([73(4)]),unit_del(a,129)].
% 0.44/1.02  
% 0.44/1.02  % SZS output end Refutation
% 0.44/1.02  ============================== end of proof ==========================
% 0.44/1.02  
% 0.44/1.02  ============================== STATISTICS ============================
% 0.44/1.02  
% 0.44/1.02  Given=33. Generated=268. Kept=102. proofs=1.
% 0.44/1.02  Usable=29. Sos=47. Demods=24. Limbo=0, Disabled=85. Hints=0.
% 0.44/1.02  Megabytes=0.15.
% 0.44/1.02  User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.44/1.02  
% 0.44/1.02  ============================== end of statistics =====================
% 0.44/1.02  
% 0.44/1.02  ============================== end of search =========================
% 0.44/1.02  
% 0.44/1.02  THEOREM PROVED
% 0.44/1.02  % SZS status Theorem
% 0.44/1.02  
% 0.44/1.02  Exiting with 1 proof.
% 0.44/1.02  
% 0.44/1.02  Process 28717 exit (max_proofs) Thu Jun  2 06:35:45 2022
% 0.44/1.02  Prover9 interrupted
%------------------------------------------------------------------------------