TSTP Solution File: GRP567-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : GRP567-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n010.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 : Sat Jul 16 11:19:39 EDT 2022

% Result   : Unsatisfiable 0.72s 1.04s
% Output   : Refutation 0.72s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP567-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun 13 17:11:24 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.72/1.04  ============================== Prover9 ===============================
% 0.72/1.04  Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.04  Process 31183 was started by sandbox on n010.cluster.edu,
% 0.72/1.04  Mon Jun 13 17:11:25 2022
% 0.72/1.04  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30815_n010.cluster.edu".
% 0.72/1.04  ============================== end of head ===========================
% 0.72/1.04  
% 0.72/1.04  ============================== INPUT =================================
% 0.72/1.04  
% 0.72/1.04  % Reading from file /tmp/Prover9_30815_n010.cluster.edu
% 0.72/1.04  
% 0.72/1.04  set(prolog_style_variables).
% 0.72/1.04  set(auto2).
% 0.72/1.04      % set(auto2) -> set(auto).
% 0.72/1.04      % set(auto) -> set(auto_inference).
% 0.72/1.04      % set(auto) -> set(auto_setup).
% 0.72/1.04      % set(auto_setup) -> set(predicate_elim).
% 0.72/1.04      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.04      % set(auto) -> set(auto_limits).
% 0.72/1.04      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.04      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.04      % set(auto) -> set(auto_denials).
% 0.72/1.04      % set(auto) -> set(auto_process).
% 0.72/1.04      % set(auto2) -> assign(new_constants, 1).
% 0.72/1.04      % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.04      % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.04      % set(auto2) -> assign(max_hours, 1).
% 0.72/1.04      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.04      % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.04      % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.04      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.04      % set(auto2) -> set(sort_initial_sos).
% 0.72/1.04      % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.04      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.04      % set(auto2) -> assign(max_megs, 400).
% 0.72/1.04      % set(auto2) -> assign(stats, some).
% 0.72/1.04      % set(auto2) -> clear(echo_input).
% 0.72/1.04      % set(auto2) -> set(quiet).
% 0.72/1.04      % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.04      % set(auto2) -> clear(print_given).
% 0.72/1.04  assign(lrs_ticks,-1).
% 0.72/1.04  assign(sos_limit,10000).
% 0.72/1.04  assign(order,kbo).
% 0.72/1.04  set(lex_order_vars).
% 0.72/1.04  clear(print_given).
% 0.72/1.04  
% 0.72/1.04  % formulas(sos).  % not echoed (5 formulas)
% 0.72/1.04  
% 0.72/1.04  ============================== end of input ==========================
% 0.72/1.04  
% 0.72/1.04  % From the command line: assign(max_seconds, 300).
% 0.72/1.04  
% 0.72/1.04  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.04  
% 0.72/1.04  % Formulas that are not ordinary clauses:
% 0.72/1.04  
% 0.72/1.04  ============================== end of process non-clausal formulas ===
% 0.72/1.04  
% 0.72/1.04  ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/1.04  
% 0.72/1.04  ============================== PREDICATE ELIMINATION =================
% 0.72/1.04  
% 0.72/1.04  ============================== end predicate elimination =============
% 0.72/1.04  
% 0.72/1.04  Auto_denials:
% 0.72/1.04    % copying label prove_these_axioms_3 to answer in negative clause
% 0.72/1.04  
% 0.72/1.04  Term ordering decisions:
% 0.72/1.04  
% 0.72/1.04  % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.72/1.04  Function symbol KB weights:  identity=1. a3=1. b3=1. c3=1. double_divide=1. multiply=1. inverse=0.
% 0.72/1.04  
% 0.72/1.04  ============================== end of process initial clauses ========
% 0.72/1.04  
% 0.72/1.04  ============================== CLAUSES FOR SEARCH ====================
% 0.72/1.04  
% 0.72/1.04  ============================== end of clauses for search =============
% 0.72/1.04  
% 0.72/1.04  ============================== SEARCH ================================
% 0.72/1.04  
% 0.72/1.04  % Starting search at 0.01 seconds.
% 0.72/1.04  
% 0.72/1.04  ============================== PROOF =================================
% 0.72/1.04  % SZS status Unsatisfiable
% 0.72/1.04  % SZS output start Refutation
% 0.72/1.04  
% 0.72/1.04  % Proof 1 at 0.07 (+ 0.00) seconds: prove_these_axioms_3.
% 0.72/1.04  % Length of proof is 63.
% 0.72/1.04  % Level of proof is 25.
% 0.72/1.04  % Maximum clause weight is 23.000.
% 0.72/1.04  % Given clauses 56.
% 0.72/1.04  
% 0.72/1.04  1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom).  [assumption].
% 0.72/1.04  2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom).  [assumption].
% 0.72/1.04  3 double_divide(A,double_divide(A,identity)) = identity.  [copy(2),rewrite([1(2)]),flip(a)].
% 0.72/1.04  4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom).  [assumption].
% 0.72/1.04  5 double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B # label(single_axiom) # label(axiom).  [assumption].
% 0.72/1.04  6 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms_3) # label(negated_conjecture) # answer(prove_these_axioms_3).  [assumption].
% 0.72/1.04  7 double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) # answer(prove_these_axioms_3).  [copy(6),rewrite([4(3),4(7),4(13),4(16)]),flip(a)].
% 0.72/1.04  8 double_divide(double_divide(A,double_divide(double_divide(B,identity),double_divide(identity,double_divide(A,identity)))),double_divide(identity,identity)) = B.  [para(3(a,1),5(a,1,1,2,1,2))].
% 0.72/1.04  9 double_divide(double_divide(A,identity),double_divide(identity,identity)) = A.  [para(3(a,1),5(a,1,1,2,1)),rewrite([3(5)])].
% 0.72/1.04  10 double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,double_divide(identity,identity))),identity)),double_divide(identity,identity)) = B.  [para(3(a,1),5(a,1,1,2,2))].
% 0.72/1.04  12 double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,double_divide(B,C)),double_divide(identity,C))).  [para(5(a,1),5(a,1,1,2,1))].
% 0.72/1.04  13 double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),double_divide(identity,identity)) = A.  [para(3(a,1),8(a,1,1,2,2))].
% 0.72/1.04  15 double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,identity),double_divide(identity,double_divide(B,identity)))).  [para(8(a,1),5(a,1,1,2,1))].
% 0.72/1.04  16 double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(B,A),identity)),double_divide(identity,identity)) = B.  [para(9(a,1),5(a,1,1,2,1,2)),rewrite([3(8)])].
% 0.72/1.04  17 double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(A,identity).  [para(9(a,1),5(a,1,1,2,1))].
% 0.72/1.04  18 double_divide(A,double_divide(double_divide(B,identity),double_divide(identity,double_divide(A,identity)))) = double_divide(B,identity).  [back_rewrite(15),rewrite([17(10)]),flip(a)].
% 0.72/1.04  19 double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))) = double_divide(B,identity).  [back_rewrite(12),rewrite([17(10)]),flip(a)].
% 0.72/1.04  20 double_divide(double_divide(double_divide(double_divide(identity,identity),identity),double_divide(A,identity)),double_divide(identity,identity)) = double_divide(A,identity).  [para(9(a,1),16(a,1,1,2,1))].
% 0.72/1.04  21 double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(A,identity).  [para(13(a,1),16(a,1,1,2,1)),rewrite([20(12)]),flip(a)].
% 0.72/1.04  22 double_divide(double_divide(A,identity),double_divide(double_divide(B,A),identity)) = double_divide(B,identity).  [para(16(a,1),16(a,1,1,2,1)),rewrite([20(12)]),flip(a)].
% 0.72/1.04  24 double_divide(identity,identity) = identity.  [para(22(a,1),3(a,1))].
% 0.72/1.04  26 double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(A,identity)).  [para(9(a,1),22(a,1,2,1)),rewrite([24(3),24(3)]),flip(a)].
% 0.72/1.04  28 double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,identity)),identity)),identity) = double_divide(identity,double_divide(B,identity)).  [para(10(a,1),22(a,1,2,1)),rewrite([24(3),24(3),24(7)]),flip(a)].
% 0.72/1.04  29 double_divide(double_divide(identity,double_divide(double_divide(A,B),identity)),double_divide(identity,double_divide(A,identity))) = double_divide(identity,double_divide(B,identity)).  [para(22(a,1),22(a,1,2,1)),rewrite([26(5),26(9),26(14)])].
% 0.72/1.04  32 double_divide(identity,double_divide(A,identity)) = A.  [back_rewrite(10),rewrite([24(3),24(9),28(8)])].
% 0.72/1.04  33 double_divide(identity,A) = double_divide(A,identity).  [back_rewrite(21),rewrite([26(5),32(5)])].
% 0.72/1.04  35 double_divide(double_divide(identity,double_divide(identity,double_divide(A,B))),A) = B.  [back_rewrite(29),rewrite([33(4,R),32(9),32(10)])].
% 0.72/1.04  36 double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,double_divide(A,identity))))) = B.  [back_rewrite(28),rewrite([33(5,R),33(8,R),32(12)])].
% 0.72/1.04  37 double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(B,identity).  [back_rewrite(18),rewrite([32(6)])].
% 0.72/1.04  39 double_divide(double_divide(A,identity),double_divide(identity,double_divide(B,A))) = double_divide(B,identity).  [back_rewrite(22),rewrite([33(5,R)])].
% 0.72/1.04  40 double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))) = double_divide(B,identity).  [back_rewrite(19),rewrite([33(4)])].
% 0.72/1.04  41 double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) # answer(prove_these_axioms_3).  [back_rewrite(7),rewrite([33(5,R),33(9,R),33(15,R),33(18,R)])].
% 0.72/1.04  42 multiply(A,B) = double_divide(identity,double_divide(B,A)).  [back_rewrite(4),rewrite([33(4,R)])].
% 0.72/1.04  44 double_divide(A,double_divide(B,A)) = B.  [para(35(a,1),37(a,1,2,1)),rewrite([33(6),32(7),33(4),33(6,R),32(6)])].
% 0.72/1.04  47 double_divide(double_divide(A,B),A) = B.  [para(44(a,1),44(a,1,2))].
% 0.72/1.04  49 double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(double_divide(A,identity),B).  [para(47(a,1),36(a,1,2,2,2)),rewrite([33(3)])].
% 0.72/1.04  52 double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(A,B)).  [para(39(a,1),47(a,1,1))].
% 0.72/1.04  57 double_divide(double_divide(A,double_divide(B,C)),double_divide(C,identity)) = double_divide(double_divide(A,identity),B).  [para(40(a,1),47(a,1,1)),flip(a)].
% 0.72/1.04  59 double_divide(identity,double_divide(double_divide(A,B),C)) = double_divide(A,double_divide(C,double_divide(B,identity))).  [para(47(a,1),40(a,1,2,1)),rewrite([33(8,R)]),flip(a)].
% 0.72/1.04  61 double_divide(A,double_divide(A,B)) = B.  [para(47(a,1),40(a,1,2)),rewrite([33(6,R),44(6)])].
% 0.72/1.04  65 double_divide(double_divide(A,identity),B) = double_divide(B,double_divide(A,identity)).  [para(40(a,1),39(a,1,2)),rewrite([33(4,R),44(4),33(5),33(8,R),49(8)]),flip(a)].
% 0.72/1.04  69 double_divide(double_divide(A,double_divide(B,C)),double_divide(C,double_divide(A,identity))) = double_divide(B,identity).  [para(40(a,1),40(a,1,2,1)),rewrite([33(8,R),44(8),65(5)])].
% 0.72/1.04  72 double_divide(double_divide(A,identity),double_divide(B,double_divide(C,A))) = double_divide(C,double_divide(B,identity)).  [back_rewrite(57),rewrite([65(5,R),65(8)])].
% 0.72/1.04  74 double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(A,identity)).  [back_rewrite(49),rewrite([65(8)])].
% 0.72/1.04  77 double_divide(A,B) = double_divide(B,A).  [para(44(a,1),61(a,1,2))].
% 0.72/1.04  78 double_divide(double_divide(A,identity),double_divide(B,double_divide(A,C))) = double_divide(C,double_divide(B,identity)).  [back_rewrite(72),rewrite([77(3)])].
% 0.72/1.04  80 double_divide(identity,double_divide(A,double_divide(B,C))) = double_divide(B,double_divide(A,double_divide(C,identity))).  [back_rewrite(59),rewrite([77(3)])].
% 0.72/1.04  83 multiply(A,B) = double_divide(identity,double_divide(A,B)).  [back_rewrite(42),rewrite([77(3)])].
% 0.72/1.04  84 double_divide(identity,double_divide(c3,double_divide(identity,double_divide(a3,b3)))) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) # answer(prove_these_axioms_3).  [back_rewrite(41),rewrite([77(5),77(8),77(15)]),flip(a)].
% 0.72/1.04  85 double_divide(identity,double_divide(A,identity)) = A.  [para(61(a,1),83(a,2)),rewrite([83(2),77(3)])].
% 0.72/1.04  91 double_divide(double_divide(A,B),double_divide(identity,double_divide(A,B))) = identity.  [para(85(a,1),69(a,1,1,2)),rewrite([52(6),77(3),24(8)])].
% 0.72/1.04  93 double_divide(double_divide(identity,double_divide(A,B)),double_divide(A,double_divide(identity,double_divide(C,B)))) = C.  [para(52(a,1),69(a,1,1,2)),rewrite([52(9),77(6),77(8),77(12),85(12)])].
% 0.72/1.04  97 double_divide(A,double_divide(identity,double_divide(B,double_divide(A,B)))) = identity.  [para(61(a,1),91(a,1,1)),rewrite([77(2)])].
% 0.72/1.04  98 double_divide(identity,double_divide(A,double_divide(B,A))) = double_divide(B,identity).  [para(97(a,1),61(a,1,2)),flip(a)].
% 0.72/1.04  103 double_divide(A,double_divide(B,A)) = B.  [para(98(a,1),61(a,1,2)),rewrite([85(4)]),flip(a)].
% 0.72/1.04  105 double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,identity)) = double_divide(B,double_divide(A,C)).  [para(69(a,1),103(a,1,2)),rewrite([77(7)])].
% 0.72/1.04  112 double_divide(identity,double_divide(A,double_divide(B,double_divide(C,identity)))) = double_divide(B,double_divide(A,C)).  [para(74(a,1),78(a,1,2,2)),rewrite([24(3),105(12),77(7)])].
% 0.72/1.04  116 double_divide(double_divide(A,double_divide(B,C)),double_divide(D,identity)) = double_divide(B,double_divide(D,double_divide(C,double_divide(A,identity)))).  [para(78(a,1),78(a,1,2,2)),rewrite([77(4),103(4)]),flip(a)].
% 0.72/1.04  122 double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(B,identity),double_divide(A,C)).  [para(52(a,1),80(a,1,2,2)),rewrite([77(12),103(12)])].
% 0.72/1.04  124 double_divide(double_divide(identity,b3),double_divide(a3,c3)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)) # answer(prove_these_axioms_3).  [para(80(a,1),84(a,1)),rewrite([77(7),122(9),77(3),77(6),122(16),77(10)]),flip(a)].
% 0.72/1.04  158 double_divide(double_divide(A,B),double_divide(C,D)) = double_divide(double_divide(C,A),double_divide(D,B)).  [para(93(a,1),78(a,1,2,2)),rewrite([77(5),61(5),77(5),116(10),112(10),77(5)]),flip(a)].
% 0.72/1.04  255 double_divide(double_divide(A,B),double_divide(C,D)) = double_divide(double_divide(A,C),double_divide(B,D)).  [para(158(a,1),77(a,1))].
% 0.72/1.04  256 $F # answer(prove_these_axioms_3).  [resolve(255,a,124,a)].
% 0.72/1.04  
% 0.72/1.04  % SZS output end Refutation
% 0.72/1.04  ============================== end of proof ==========================
% 0.72/1.04  
% 0.72/1.04  ============================== STATISTICS ============================
% 0.72/1.04  
% 0.72/1.04  Given=56. Generated=1549. Kept=253. proofs=1.
% 0.72/1.04  Usable=13. Sos=58. Demods=31. Limbo=0, Disabled=186. Hints=0.
% 0.72/1.04  Megabytes=0.21.
% 0.72/1.04  User_CPU=0.07, System_CPU=0.00, Wall_clock=0.
% 0.72/1.04  
% 0.72/1.04  ============================== end of statistics =====================
% 0.72/1.04  
% 0.72/1.04  ============================== end of search =========================
% 0.72/1.04  
% 0.72/1.04  THEOREM PROVED
% 0.72/1.04  % SZS status Unsatisfiable
% 0.72/1.04  
% 0.72/1.04  Exiting with 1 proof.
% 0.72/1.04  
% 0.72/1.04  Process 31183 exit (max_proofs) Mon Jun 13 17:11:25 2022
% 0.72/1.04  Prover9 interrupted
%------------------------------------------------------------------------------