TSTP Solution File: KLE007+2 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : KLE007+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n027.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 0.45s 0.99s
% Output   : Refutation 0.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : KLE007+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.33  % Computer : n027.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 : Thu Jun 16 13:45:05 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.45/0.98  ============================== Prover9 ===============================
% 0.45/0.98  Prover9 (32) version 2009-11A, November 2009.
% 0.45/0.98  Process 11321 was started by sandbox2 on n027.cluster.edu,
% 0.45/0.98  Thu Jun 16 13:45:06 2022
% 0.45/0.98  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_11152_n027.cluster.edu".
% 0.45/0.98  ============================== end of head ===========================
% 0.45/0.98  
% 0.45/0.98  ============================== INPUT =================================
% 0.45/0.98  
% 0.45/0.98  % Reading from file /tmp/Prover9_11152_n027.cluster.edu
% 0.45/0.98  
% 0.45/0.98  set(prolog_style_variables).
% 0.45/0.98  set(auto2).
% 0.45/0.98      % set(auto2) -> set(auto).
% 0.45/0.98      % set(auto) -> set(auto_inference).
% 0.45/0.98      % set(auto) -> set(auto_setup).
% 0.45/0.98      % set(auto_setup) -> set(predicate_elim).
% 0.45/0.98      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/0.98      % set(auto) -> set(auto_limits).
% 0.45/0.98      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/0.98      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/0.98      % set(auto) -> set(auto_denials).
% 0.45/0.98      % set(auto) -> set(auto_process).
% 0.45/0.98      % set(auto2) -> assign(new_constants, 1).
% 0.45/0.98      % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/0.98      % set(auto2) -> assign(max_weight, "200.000").
% 0.45/0.98      % set(auto2) -> assign(max_hours, 1).
% 0.45/0.98      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/0.98      % set(auto2) -> assign(max_seconds, 0).
% 0.45/0.98      % set(auto2) -> assign(max_minutes, 5).
% 0.45/0.98      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/0.98      % set(auto2) -> set(sort_initial_sos).
% 0.45/0.98      % set(auto2) -> assign(sos_limit, -1).
% 0.45/0.98      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/0.98      % set(auto2) -> assign(max_megs, 400).
% 0.45/0.98      % set(auto2) -> assign(stats, some).
% 0.45/0.98      % set(auto2) -> clear(echo_input).
% 0.45/0.98      % set(auto2) -> set(quiet).
% 0.45/0.98      % set(auto2) -> clear(print_initial_clauses).
% 0.45/0.98      % set(auto2) -> clear(print_given).
% 0.45/0.98  assign(lrs_ticks,-1).
% 0.45/0.98  assign(sos_limit,10000).
% 0.45/0.98  assign(order,kbo).
% 0.45/0.98  set(lex_order_vars).
% 0.45/0.98  clear(print_given).
% 0.45/0.98  
% 0.45/0.98  % formulas(sos).  % not echoed (17 formulas)
% 0.45/0.98  
% 0.45/0.98  ============================== end of input ==========================
% 0.45/0.98  
% 0.45/0.98  % From the command line: assign(max_seconds, 300).
% 0.45/0.98  
% 0.45/0.98  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/0.98  
% 0.45/0.98  % Formulas that are not ordinary clauses:
% 0.45/0.98  1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.98  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].
% 0.45/0.98  3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.98  4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.98  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].
% 0.45/0.98  6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.98  7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.98  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].
% 0.45/0.98  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].
% 0.45/0.98  10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.98  11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.98  12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.98  13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.98  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].
% 0.45/0.99  15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.99  16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.99  17 -(all X0 all X1 (test(X1) & test(X0) -> leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) & leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.45/0.99  
% 0.45/0.99  ============================== end of process non-clausal formulas ===
% 0.45/0.99  
% 0.45/0.99  ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/0.99  
% 0.45/0.99  ============================== PREDICATE ELIMINATION =================
% 0.45/0.99  18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom).  [clausify(13)].
% 0.45/0.99  19 test(c2) # label(goals) # label(negated_conjecture).  [clausify(17)].
% 0.45/0.99  20 test(c1) # label(goals) # label(negated_conjecture).  [clausify(17)].
% 0.45/0.99  21 test(A) | c(A) = zero # label(test_4) # label(axiom).  [clausify(16)].
% 0.45/0.99  22 test(A) | -complement(B,A) # label(test_1) # label(axiom).  [clausify(13)].
% 0.45/0.99  Derived: complement(f1(c2),c2).  [resolve(18,a,19,a)].
% 0.45/0.99  Derived: complement(f1(c1),c1).  [resolve(18,a,20,a)].
% 0.45/0.99  Derived: complement(f1(A),A) | c(A) = zero.  [resolve(18,a,21,a)].
% 0.45/0.99  Derived: complement(f1(A),A) | -complement(B,A).  [resolve(18,a,22,a)].
% 0.45/0.99  23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom).  [clausify(15)].
% 0.45/0.99  Derived: c(c2) != A | complement(c2,A).  [resolve(23,a,19,a)].
% 0.45/0.99  Derived: c(c1) != A | complement(c1,A).  [resolve(23,a,20,a)].
% 0.45/0.99  Derived: c(A) != B | complement(A,B) | c(A) = zero.  [resolve(23,a,21,a)].
% 0.45/0.99  Derived: c(A) != B | complement(A,B) | -complement(C,A).  [resolve(23,a,22,a)].
% 0.45/0.99  24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom).  [clausify(15)].
% 0.45/0.99  Derived: c(c2) = A | -complement(c2,A).  [resolve(24,a,19,a)].
% 0.45/0.99  Derived: c(c1) = A | -complement(c1,A).  [resolve(24,a,20,a)].
% 0.45/0.99  Derived: c(A) = B | -complement(A,B) | c(A) = zero.  [resolve(24,a,21,a)].
% 0.45/0.99  Derived: c(A) = B | -complement(A,B) | -complement(C,A).  [resolve(24,a,22,a)].
% 0.45/0.99  
% 0.45/0.99  ============================== end predicate elimination =============
% 0.45/0.99  
% 0.45/0.99  Auto_denials:  (non-Horn, no changes).
% 0.45/0.99  
% 0.45/0.99  Term ordering decisions:
% 0.45/0.99  Function symbol KB weights:  zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 0.45/0.99  
% 0.45/0.99  ============================== end of process initial clauses ========
% 0.45/0.99  
% 0.45/0.99  ============================== CLAUSES FOR SEARCH ====================
% 0.45/0.99  
% 0.45/0.99  ============================== end of clauses for search =============
% 0.45/0.99  
% 0.45/0.99  ============================== SEARCH ================================
% 0.45/0.99  
% 0.45/0.99  % Starting search at 0.01 seconds.
% 0.45/0.99  
% 0.45/0.99  ============================== PROOF =================================
% 0.45/0.99  % SZS status Theorem
% 0.45/0.99  % SZS output start Refutation
% 0.45/0.99  
% 0.45/0.99  % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.45/0.99  % Length of proof is 32.
% 0.45/0.99  % Level of proof is 6.
% 0.45/0.99  % Maximum clause weight is 22.000.
% 0.45/0.99  % Given clauses 38.
% 0.45/0.99  
% 0.45/0.99  1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.99  4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.99  6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.99  7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.99  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].
% 0.45/0.99  12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.99  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].
% 0.45/0.99  15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause).  [assumption].
% 0.45/0.99  17 -(all X0 all X1 (test(X1) & test(X0) -> leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) & leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.45/0.99  19 test(c2) # label(goals) # label(negated_conjecture).  [clausify(17)].
% 0.45/0.99  20 test(c1) # label(goals) # label(negated_conjecture).  [clausify(17)].
% 0.45/0.99  23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom).  [clausify(15)].
% 0.45/0.99  26 addition(A,A) = A # label(additive_idempotence) # label(axiom).  [clausify(4)].
% 0.45/0.99  27 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(6)].
% 0.45/0.99  28 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [clausify(7)].
% 0.45/0.99  31 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(1)].
% 0.45/0.99  35 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom).  [clausify(8)].
% 0.45/0.99  36 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)).  [copy(35),flip(a)].
% 0.45/0.99  39 -leq(one,addition(multiplication(addition(c1,c(c1)),c2),multiplication(addition(c1,c(c1)),c(c2)))) | -leq(addition(multiplication(addition(c1,c(c1)),c2),multiplication(addition(c1,c(c1)),c(c2))),one) # label(goals) # label(negated_conjecture).  [clausify(17)].
% 0.45/0.99  40 -leq(one,multiplication(addition(c1,c(c1)),addition(c2,c(c2)))) | -leq(multiplication(addition(c1,c(c1)),addition(c2,c(c2))),one).  [copy(39),rewrite([36(15),36(25)])].
% 0.45/0.99  42 leq(A,B) | addition(A,B) != B # label(order) # label(axiom).  [clausify(12)].
% 0.45/0.99  45 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom).  [clausify(14)].
% 0.45/0.99  46 -complement(A,B) | addition(A,B) = one.  [copy(45),rewrite([31(2)])].
% 0.45/0.99  53 c(c2) != A | complement(c2,A).  [resolve(23,a,19,a)].
% 0.45/0.99  54 c(c1) != A | complement(c1,A).  [resolve(23,a,20,a)].
% 0.45/0.99  70 leq(A,A).  [resolve(42,b,26,a)].
% 0.45/0.99  89 complement(c2,c(c2)).  [resolve(53,a,28,a(flip)),rewrite([28(5)])].
% 0.45/0.99  91 complement(c1,c(c1)).  [resolve(54,a,28,a(flip)),rewrite([28(5)])].
% 0.45/0.99  112 addition(c2,c(c2)) = one.  [resolve(89,a,46,a)].
% 0.45/0.99  115 -leq(one,addition(c1,c(c1))) | -leq(addition(c1,c(c1)),one).  [back_rewrite(40),rewrite([112(9),27(7),112(14),27(12)])].
% 0.45/0.99  119 addition(c1,c(c1)) = one.  [resolve(91,a,46,a)].
% 0.45/0.99  122 $F.  [back_rewrite(115),rewrite([119(5),119(7)]),merge(b),unit_del(a,70)].
% 0.45/0.99  
% 0.45/0.99  % SZS output end Refutation
% 0.45/0.99  ============================== end of proof ==========================
% 0.45/0.99  
% 0.45/0.99  ============================== STATISTICS ============================
% 0.45/0.99  
% 0.45/0.99  Given=38. Generated=278. Kept=91. proofs=1.
% 0.45/0.99  Usable=37. Sos=49. Demods=31. Limbo=3, Disabled=39. Hints=0.
% 0.45/0.99  Megabytes=0.13.
% 0.45/0.99  User_CPU=0.02, System_CPU=0.01, Wall_clock=0.
% 0.45/0.99  
% 0.45/0.99  ============================== end of statistics =====================
% 0.45/0.99  
% 0.45/0.99  ============================== end of search =========================
% 0.45/0.99  
% 0.45/0.99  THEOREM PROVED
% 0.45/0.99  % SZS status Theorem
% 0.45/0.99  
% 0.45/0.99  Exiting with 1 proof.
% 0.45/0.99  
% 0.45/0.99  Process 11321 exit (max_proofs) Thu Jun 16 13:45:06 2022
% 0.45/0.99  Prover9 interrupted
%------------------------------------------------------------------------------