TSTP Solution File: KLE005+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : KLE005+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n008.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 : Sun Jul 17 02:21:38 EDT 2022

% Result   : Theorem 0.80s 1.05s
% Output   : Refutation 0.80s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KLE005+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.34  % Computer : n008.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 : Thu Jun 16 08:27:07 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.80/1.04  ============================== Prover9 ===============================
% 0.80/1.04  Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.04  Process 5145 was started by sandbox2 on n008.cluster.edu,
% 0.80/1.04  Thu Jun 16 08:27:08 2022
% 0.80/1.04  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4947_n008.cluster.edu".
% 0.80/1.04  ============================== end of head ===========================
% 0.80/1.04  
% 0.80/1.04  ============================== INPUT =================================
% 0.80/1.04  
% 0.80/1.04  % Reading from file /tmp/Prover9_4947_n008.cluster.edu
% 0.80/1.04  
% 0.80/1.04  set(prolog_style_variables).
% 0.80/1.04  set(auto2).
% 0.80/1.04      % set(auto2) -> set(auto).
% 0.80/1.04      % set(auto) -> set(auto_inference).
% 0.80/1.04      % set(auto) -> set(auto_setup).
% 0.80/1.04      % set(auto_setup) -> set(predicate_elim).
% 0.80/1.04      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.80/1.04      % set(auto) -> set(auto_limits).
% 0.80/1.04      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.80/1.04      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.80/1.04      % set(auto) -> set(auto_denials).
% 0.80/1.04      % set(auto) -> set(auto_process).
% 0.80/1.04      % set(auto2) -> assign(new_constants, 1).
% 0.80/1.04      % set(auto2) -> assign(fold_denial_max, 3).
% 0.80/1.04      % set(auto2) -> assign(max_weight, "200.000").
% 0.80/1.04      % set(auto2) -> assign(max_hours, 1).
% 0.80/1.04      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.80/1.04      % set(auto2) -> assign(max_seconds, 0).
% 0.80/1.04      % set(auto2) -> assign(max_minutes, 5).
% 0.80/1.04      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.80/1.04      % set(auto2) -> set(sort_initial_sos).
% 0.80/1.04      % set(auto2) -> assign(sos_limit, -1).
% 0.80/1.04      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.80/1.04      % set(auto2) -> assign(max_megs, 400).
% 0.80/1.04      % set(auto2) -> assign(stats, some).
% 0.80/1.04      % set(auto2) -> clear(echo_input).
% 0.80/1.04      % set(auto2) -> set(quiet).
% 0.80/1.04      % set(auto2) -> clear(print_initial_clauses).
% 0.80/1.04      % set(auto2) -> clear(print_given).
% 0.80/1.04  assign(lrs_ticks,-1).
% 0.80/1.04  assign(sos_limit,10000).
% 0.80/1.04  assign(order,kbo).
% 0.80/1.04  set(lex_order_vars).
% 0.80/1.04  clear(print_given).
% 0.80/1.04  
% 0.80/1.04  % formulas(sos).  % not echoed (17 formulas)
% 0.80/1.04  
% 0.80/1.04  ============================== end of input ==========================
% 0.80/1.04  
% 0.80/1.04  % From the command line: assign(max_seconds, 300).
% 0.80/1.04  
% 0.80/1.04  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.80/1.04  
% 0.80/1.04  % Formulas that are not ordinary clauses:
% 0.80/1.04  1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.04  2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.04  3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.04  4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.04  5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.04  6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.04  7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.04  8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.04  9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.04  10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.04  11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.04  12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.04  13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.04  14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.05  15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.05  16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.05  
% 0.80/1.05  ============================== end of process non-clausal formulas ===
% 0.80/1.05  
% 0.80/1.05  ============================== PROCESS INITIAL CLAUSES ===============
% 0.80/1.05  
% 0.80/1.05  ============================== PREDICATE ELIMINATION =================
% 0.80/1.05  17 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom).  [clausify(13)].
% 0.80/1.05  18 test(A) | c(A) = zero # label(test_4) # label(axiom).  [clausify(16)].
% 0.80/1.05  19 test(A) | -complement(B,A) # label(test_1) # label(axiom).  [clausify(13)].
% 0.80/1.05  Derived: complement(f1(A),A) | c(A) = zero.  [resolve(17,a,18,a)].
% 0.80/1.05  Derived: complement(f1(A),A) | -complement(B,A).  [resolve(17,a,19,a)].
% 0.80/1.05  20 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom).  [clausify(15)].
% 0.80/1.05  Derived: c(A) != B | complement(A,B) | c(A) = zero.  [resolve(20,a,18,a)].
% 0.80/1.05  Derived: c(A) != B | complement(A,B) | -complement(C,A).  [resolve(20,a,19,a)].
% 0.80/1.05  21 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom).  [clausify(15)].
% 0.80/1.05  Derived: c(A) = B | -complement(A,B) | c(A) = zero.  [resolve(21,a,18,a)].
% 0.80/1.05  Derived: c(A) = B | -complement(A,B) | -complement(C,A).  [resolve(21,a,19,a)].
% 0.80/1.05  22 leq(A,B) | addition(A,B) != B # label(order) # label(axiom).  [clausify(12)].
% 0.80/1.05  23 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom).  [clausify(12)].
% 0.80/1.05  
% 0.80/1.05  ============================== end predicate elimination =============
% 0.80/1.05  
% 0.80/1.05  Auto_denials:  (non-Horn, no changes).
% 0.80/1.05  
% 0.80/1.05  Term ordering decisions:
% 0.80/1.05  Function symbol KB weights:  zero=1. one=1. multiplication=1. addition=1. c=1. f1=1.
% 0.80/1.05  
% 0.80/1.05  ============================== end of process initial clauses ========
% 0.80/1.05  
% 0.80/1.05  ============================== CLAUSES FOR SEARCH ====================
% 0.80/1.05  
% 0.80/1.05  ============================== end of clauses for search =============
% 0.80/1.05  
% 0.80/1.05  ============================== SEARCH ================================
% 0.80/1.05  
% 0.80/1.05  % Starting search at 0.01 seconds.
% 0.80/1.05  
% 0.80/1.05  ============================== PROOF =================================
% 0.80/1.05  % SZS status Theorem
% 0.80/1.05  % SZS output start Refutation
% 0.80/1.05  
% 0.80/1.05  % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.80/1.05  % Length of proof is 19.
% 0.80/1.05  % Level of proof is 4.
% 0.80/1.05  % Maximum clause weight is 18.000.
% 0.80/1.05  % Given clauses 21.
% 0.80/1.05  
% 0.80/1.05  1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.05  3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.05  6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.05  10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.05  14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.05  15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.05  16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause).  [assumption].
% 0.80/1.05  18 test(A) | c(A) = zero # label(test_4) # label(axiom).  [clausify(16)].
% 0.80/1.05  21 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom).  [clausify(15)].
% 0.80/1.05  24 addition(A,zero) = A # label(additive_identity) # label(axiom).  [clausify(3)].
% 0.80/1.05  26 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(6)].
% 0.80/1.05  28 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom).  [clausify(10)].
% 0.80/1.05  30 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(1)].
% 0.80/1.05  38 c(one) != zero # label(goals) # label(negated_conjecture).  [assumption].
% 0.80/1.05  43 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom).  [clausify(14)].
% 0.80/1.05  44 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(A,B) != one.  [copy(43),rewrite([30(8)])].
% 0.80/1.05  49 c(A) = B | -complement(A,B) | c(A) = zero.  [resolve(21,a,18,a)].
% 0.80/1.05  61 complement(one,zero).  [resolve(44,d,24,a),rewrite([26(6),28(9)]),xx(b),xx(c)].
% 0.80/1.05  72 $F.  [ur(49,a,38,a,c,38,a),unit_del(a,61)].
% 0.80/1.05  
% 0.80/1.05  % SZS output end Refutation
% 0.80/1.05  ============================== end of proof ==========================
% 0.80/1.05  
% 0.80/1.05  ============================== STATISTICS ============================
% 0.80/1.05  
% 0.80/1.05  Given=21. Generated=163. Kept=43. proofs=1.
% 0.80/1.05  Usable=21. Sos=21. Demods=17. Limbo=1, Disabled=29. Hints=0.
% 0.80/1.05  Megabytes=0.08.
% 0.80/1.05  User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.80/1.05  
% 0.80/1.05  ============================== end of statistics =====================
% 0.80/1.05  
% 0.80/1.05  ============================== end of search =========================
% 0.80/1.05  
% 0.80/1.05  THEOREM PROVED
% 0.80/1.05  % SZS status Theorem
% 0.80/1.05  
% 0.80/1.05  Exiting with 1 proof.
% 0.80/1.05  
% 0.80/1.05  Process 5145 exit (max_proofs) Thu Jun 16 08:27:08 2022
% 0.80/1.05  Prover9 interrupted
%------------------------------------------------------------------------------