TSTP Solution File: KLE011+2 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : KLE011+2 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Jul 17 02:21:42 EDT 2022

% Result   : Theorem 89.68s 89.94s
% Output   : Refutation 89.68s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : KLE011+2 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14  % Command  : tptp2X_and_run_prover9 %d %s
% 0.14/0.36  % Computer : n017.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Thu Jun 16 09:31:55 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.50/1.05  ============================== Prover9 ===============================
% 0.50/1.05  Prover9 (32) version 2009-11A, November 2009.
% 0.50/1.05  Process 11611 was started by sandbox on n017.cluster.edu,
% 0.50/1.05  Thu Jun 16 09:31:56 2022
% 0.50/1.05  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11458_n017.cluster.edu".
% 0.50/1.05  ============================== end of head ===========================
% 0.50/1.05  
% 0.50/1.05  ============================== INPUT =================================
% 0.50/1.05  
% 0.50/1.05  % Reading from file /tmp/Prover9_11458_n017.cluster.edu
% 0.50/1.05  
% 0.50/1.05  set(prolog_style_variables).
% 0.50/1.05  set(auto2).
% 0.50/1.05      % set(auto2) -> set(auto).
% 0.50/1.05      % set(auto) -> set(auto_inference).
% 0.50/1.05      % set(auto) -> set(auto_setup).
% 0.50/1.05      % set(auto_setup) -> set(predicate_elim).
% 0.50/1.05      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.50/1.05      % set(auto) -> set(auto_limits).
% 0.50/1.05      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.50/1.05      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.50/1.05      % set(auto) -> set(auto_denials).
% 0.50/1.05      % set(auto) -> set(auto_process).
% 0.50/1.05      % set(auto2) -> assign(new_constants, 1).
% 0.50/1.05      % set(auto2) -> assign(fold_denial_max, 3).
% 0.50/1.05      % set(auto2) -> assign(max_weight, "200.000").
% 0.50/1.05      % set(auto2) -> assign(max_hours, 1).
% 0.50/1.05      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.50/1.05      % set(auto2) -> assign(max_seconds, 0).
% 0.50/1.05      % set(auto2) -> assign(max_minutes, 5).
% 0.50/1.05      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.50/1.05      % set(auto2) -> set(sort_initial_sos).
% 0.50/1.05      % set(auto2) -> assign(sos_limit, -1).
% 0.50/1.05      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.50/1.05      % set(auto2) -> assign(max_megs, 400).
% 0.50/1.05      % set(auto2) -> assign(stats, some).
% 0.50/1.05      % set(auto2) -> clear(echo_input).
% 0.50/1.05      % set(auto2) -> set(quiet).
% 0.50/1.05      % set(auto2) -> clear(print_initial_clauses).
% 0.50/1.05      % set(auto2) -> clear(print_given).
% 0.50/1.05  assign(lrs_ticks,-1).
% 0.50/1.05  assign(sos_limit,10000).
% 0.50/1.05  assign(order,kbo).
% 0.50/1.05  set(lex_order_vars).
% 0.50/1.05  clear(print_given).
% 0.50/1.05  
% 0.50/1.05  % formulas(sos).  % not echoed (17 formulas)
% 0.50/1.05  
% 0.50/1.05  ============================== end of input ==========================
% 0.50/1.05  
% 0.50/1.05  % From the command line: assign(max_seconds, 300).
% 0.50/1.05  
% 0.50/1.05  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.50/1.05  
% 0.50/1.05  % Formulas that are not ordinary clauses:
% 0.50/1.05  1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 0.50/1.05  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].
% 0.50/1.05  3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.50/1.05  4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 0.50/1.05  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].
% 0.50/1.05  6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.50/1.05  7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.50/1.05  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].
% 0.50/1.05  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].
% 0.50/1.05  10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 0.50/1.05  11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 0.50/1.05  12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause).  [assumption].
% 0.50/1.05  13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause).  [assumption].
% 0.50/1.05  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].
% 2.68/2.94  15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause).  [assumption].
% 2.68/2.94  16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause).  [assumption].
% 2.68/2.94  17 -(all X0 all X1 (test(X1) & test(X0) -> leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1)))) & leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 2.68/2.94  
% 2.68/2.94  ============================== end of process non-clausal formulas ===
% 2.68/2.94  
% 2.68/2.94  ============================== PROCESS INITIAL CLAUSES ===============
% 2.68/2.94  
% 2.68/2.94  ============================== PREDICATE ELIMINATION =================
% 2.68/2.94  18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom).  [clausify(13)].
% 2.68/2.94  19 test(c2) # label(goals) # label(negated_conjecture).  [clausify(17)].
% 2.68/2.94  20 test(c1) # label(goals) # label(negated_conjecture).  [clausify(17)].
% 2.68/2.94  21 test(A) | c(A) = zero # label(test_4) # label(axiom).  [clausify(16)].
% 2.68/2.94  22 test(A) | -complement(B,A) # label(test_1) # label(axiom).  [clausify(13)].
% 2.68/2.94  Derived: complement(f1(c2),c2).  [resolve(18,a,19,a)].
% 2.68/2.94  Derived: complement(f1(c1),c1).  [resolve(18,a,20,a)].
% 2.68/2.94  Derived: complement(f1(A),A) | c(A) = zero.  [resolve(18,a,21,a)].
% 2.68/2.94  Derived: complement(f1(A),A) | -complement(B,A).  [resolve(18,a,22,a)].
% 2.68/2.94  23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom).  [clausify(15)].
% 2.68/2.94  Derived: c(c2) != A | complement(c2,A).  [resolve(23,a,19,a)].
% 2.68/2.94  Derived: c(c1) != A | complement(c1,A).  [resolve(23,a,20,a)].
% 2.68/2.94  Derived: c(A) != B | complement(A,B) | c(A) = zero.  [resolve(23,a,21,a)].
% 2.68/2.94  Derived: c(A) != B | complement(A,B) | -complement(C,A).  [resolve(23,a,22,a)].
% 2.68/2.94  24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom).  [clausify(15)].
% 2.68/2.94  Derived: c(c2) = A | -complement(c2,A).  [resolve(24,a,19,a)].
% 2.68/2.94  Derived: c(c1) = A | -complement(c1,A).  [resolve(24,a,20,a)].
% 2.68/2.94  Derived: c(A) = B | -complement(A,B) | c(A) = zero.  [resolve(24,a,21,a)].
% 2.68/2.94  Derived: c(A) = B | -complement(A,B) | -complement(C,A).  [resolve(24,a,22,a)].
% 2.68/2.94  
% 2.68/2.94  ============================== end predicate elimination =============
% 2.68/2.94  
% 2.68/2.94  Auto_denials:  (non-Horn, no changes).
% 2.68/2.94  
% 2.68/2.94  Term ordering decisions:
% 2.68/2.94  Function symbol KB weights:  zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 2.68/2.94  
% 2.68/2.94  ============================== end of process initial clauses ========
% 2.68/2.94  
% 2.68/2.94  ============================== CLAUSES FOR SEARCH ====================
% 2.68/2.94  
% 2.68/2.94  ============================== end of clauses for search =============
% 2.68/2.94  
% 2.68/2.94  ============================== SEARCH ================================
% 2.68/2.94  
% 2.68/2.94  % Starting search at 0.01 seconds.
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=62.000, iters=3362
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=54.000, iters=3433
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=48.000, iters=3359
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=46.000, iters=3358
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=45.000, iters=3395
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=42.000, iters=3341
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=38.000, iters=3353
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=37.000, iters=3342
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=36.000, iters=3355
% 2.68/2.94  
% 2.68/2.94  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 39 (0.00 of 1.21 sec).
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=34.000, iters=3371
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=33.000, iters=3371
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=32.000, iters=3426
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=31.000, iters=3369
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=30.000, iters=3348
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=29.000, iters=3392
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=28.000, iters=3342
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=27.000, iters=3412
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=26.000, iters=3346
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=25.000, iters=3356
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=24.000, iters=3351
% 2.68/2.94  
% 2.68/2.94  Low Water (keep): wt=23.000, iters=3336
% 2.68/2.94  
% 2.68/2.94  Low Water (displace): id=5868, wt=107.000
% 2.68/2.94  
% 2.68/2.94  Low Water (displace): id=5157, wt=88.000
% 2.68/2.94  
% 2.68/2.94  Low Water (displace): id=4716, wt=85.000
% 2.68/2.94  
% 2.68/2.94  Low Water (displace): id=5801, wt=82.000
% 2.68/2.94  
% 2.68/2.94  Low Water (displace): id=5840, wt=81.000
% 2.68/2.94  
% 2.68/2.94  Low Water (displace): id=5152, wt=80.000
% 2.68/2.94  
% 2.68/2.94  Low Water (displace): id=5841, wt=79.000
% 2.68/2.94  
% 2.68/2.94  Low Water (displace): id=5687, wt=74.000
% 89.68/89.94  
% 89.68/89.94  Low Water (keep): wt=22.000, iters=3408
% 89.68/89.94  
% 89.68/89.94  Low Water (displace): id=5156, wt=72.000
% 89.68/89.94  
% 89.68/89.94  Low Water (displace): id=5753, wt=68.000
% 89.68/89.94  
% 89.68/89.94  Low Water (displace): id=5730, wt=67.000
% 89.68/89.94  
% 89.68/89.94  Low Water (displace): id=4859, wt=66.000
% 89.68/89.94  
% 89.68/89.94  Low Water (displace): id=6539, wt=64.000
% 89.68/89.94  
% 89.68/89.94  Low Water (displace): id=11647, wt=18.000
% 89.68/89.94  
% 89.68/89.94  Low Water (displace): id=11648, wt=17.000
% 89.68/89.94  
% 89.68/89.94  Low Water (displace): id=11710, wt=16.000
% 89.68/89.94  
% 89.68/89.94  Low Water (displace): id=11713, wt=15.000
% 89.68/89.94  
% 89.68/89.94  Low Water (displace): id=11740, wt=13.000
% 89.68/89.94  
% 89.68/89.94  Low Water (keep): wt=21.000, iters=3340
% 89.68/89.94  
% 89.68/89.94  Low Water (displace): id=12126, wt=12.000
% 89.68/89.94  
% 89.68/89.94  Low Water (keep): wt=20.000, iters=3345
% 89.68/89.94  
% 89.68/89.94  Low Water (keep): wt=19.000, iters=3333
% 89.68/89.94  
% 89.68/89.94  Low Water (keep): wt=18.000, iters=3343
% 89.68/89.94  
% 89.68/89.94  Low Water (keep): wt=17.000, iters=3336
% 89.68/89.94  
% 89.68/89.94  Low Water (displace): id=18173, wt=11.000
% 89.68/89.94  
% 89.68/89.94  Low Water (keep): wt=16.000, iters=3333
% 89.68/89.94  
% 89.68/89.94  Low Water (keep): wt=15.000, iters=3341
% 89.68/89.94  
% 89.68/89.94  Low Water (keep): wt=14.000, iters=3335
% 89.68/89.94  
% 89.68/89.94  ============================== PROOF =================================
% 89.68/89.94  % SZS status Theorem
% 89.68/89.94  % SZS output start Refutation
% 89.68/89.94  
% 89.68/89.94  % Proof 1 at 86.53 (+ 2.37) seconds.
% 89.68/89.94  % Length of proof is 171.
% 89.68/89.94  % Level of proof is 18.
% 89.68/89.94  % Maximum clause weight is 42.000.
% 89.68/89.94  % Given clauses 8848.
% 89.68/89.94  
% 89.68/89.94  1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 89.68/89.94  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].
% 89.68/89.94  3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
% 89.68/89.94  4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 89.68/89.94  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].
% 89.68/89.94  6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
% 89.68/89.94  7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
% 89.68/89.94  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].
% 89.68/89.94  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].
% 89.68/89.94  10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 89.68/89.94  11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 89.68/89.94  12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause).  [assumption].
% 89.68/89.94  13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause).  [assumption].
% 89.68/89.94  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].
% 89.68/89.94  15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause).  [assumption].
% 89.68/89.94  17 -(all X0 all X1 (test(X1) & test(X0) -> leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1)))) & leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 89.68/89.94  18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom).  [clausify(13)].
% 89.68/89.94  19 test(c2) # label(goals) # label(negated_conjecture).  [clausify(17)].
% 89.68/89.94  20 test(c1) # label(goals) # label(negated_conjecture).  [clausify(17)].
% 89.68/89.94  22 test(A) | -complement(B,A) # label(test_1) # label(axiom).  [clausify(13)].
% 89.68/89.94  23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom).  [clausify(15)].
% 89.68/89.94  25 addition(A,zero) = A # label(additive_identity) # label(axiom).  [clausify(3)].
% 89.68/89.94  26 addition(A,A) = A # label(additive_idempotence) # label(axiom).  [clausify(4)].
% 89.68/89.94  27 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(6)].
% 89.68/89.94  28 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [clausify(7)].
% 89.68/89.94  29 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom).  [clausify(10)].
% 89.68/89.94  30 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom).  [clausify(11)].
% 89.68/89.94  31 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(1)].
% 89.68/89.94  32 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom).  [clausify(2)].
% 89.68/89.94  33 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(32),rewrite([31(2)]),flip(a)].
% 89.68/89.94  34 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom).  [clausify(5)].
% 89.68/89.94  35 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom).  [clausify(8)].
% 89.68/89.94  36 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)).  [copy(35),flip(a)].
% 89.68/89.94  37 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom).  [clausify(9)].
% 89.68/89.94  38 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B).  [copy(37),flip(a)].
% 89.68/89.94  39 -leq(one,addition(addition(multiplication(addition(c2,c(c2)),c1),multiplication(addition(c1,c(c1)),c2)),multiplication(c(c1),c(c2)))) | -leq(addition(addition(multiplication(addition(c2,c(c2)),c1),multiplication(addition(c1,c(c1)),c2)),multiplication(c(c1),c(c2))),one) # label(goals) # label(negated_conjecture).  [clausify(17)].
% 89.68/89.94  40 -leq(one,addition(multiplication(c(c1),c(c2)),addition(multiplication(addition(c1,c(c1)),c2),multiplication(addition(c2,c(c2)),c1)))) | -leq(addition(multiplication(c(c1),c(c2)),addition(multiplication(addition(c1,c(c1)),c2),multiplication(addition(c2,c(c2)),c1))),one).  [copy(39),rewrite([31(14),31(20),31(34),31(40)])].
% 89.68/89.94  41 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom).  [clausify(12)].
% 89.68/89.94  42 leq(A,B) | addition(A,B) != B # label(order) # label(axiom).  [clausify(12)].
% 89.68/89.94  43 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom).  [clausify(14)].
% 89.68/89.94  44 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom).  [clausify(14)].
% 89.68/89.94  45 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom).  [clausify(14)].
% 89.68/89.94  46 -complement(A,B) | addition(A,B) = one.  [copy(45),rewrite([31(2)])].
% 89.68/89.94  49 complement(f1(c2),c2).  [resolve(18,a,19,a)].
% 89.68/89.94  50 complement(f1(c1),c1).  [resolve(18,a,20,a)].
% 89.68/89.94  52 complement(f1(A),A) | -complement(B,A).  [resolve(18,a,22,a)].
% 89.68/89.94  53 c(c2) != A | complement(c2,A).  [resolve(23,a,19,a)].
% 89.68/89.94  54 c(c1) != A | complement(c1,A).  [resolve(23,a,20,a)].
% 89.68/89.94  64 addition(A,addition(A,B)) = addition(A,B).  [para(33(a,1),26(a,1)),rewrite([31(1),31(2),33(2,R),26(1),31(3)])].
% 89.68/89.94  65 addition(zero,multiplication(A,B)) = multiplication(A,B).  [para(25(a,1),36(a,2,2)),rewrite([29(3),31(3)])].
% 89.68/89.94  66 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)).  [para(27(a,1),36(a,1,1)),rewrite([31(4)]),flip(a)].
% 89.68/89.94  67 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)).  [para(28(a,1),38(a,1,1)),rewrite([31(4)]),flip(a)].
% 89.68/89.94  68 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C).  [para(34(a,1),38(a,1,1)),rewrite([31(6)])].
% 89.68/89.94  72 leq(multiplication(A,B),multiplication(A,C)) | multiplication(A,addition(B,C)) != multiplication(A,C).  [para(36(a,1),42(b,1))].
% 89.68/89.94  73 leq(multiplication(A,B),multiplication(C,B)) | multiplication(addition(A,C),B) != multiplication(C,B).  [para(38(a,1),42(b,1))].
% 89.68/89.94  80 addition(c2,f1(c2)) = one.  [resolve(49,a,46,a),rewrite([31(4)])].
% 89.68/89.94  83 addition(c1,f1(c1)) = one.  [resolve(50,a,46,a),rewrite([31(4)])].
% 89.68/89.94  89 complement(c2,c(c2)).  [resolve(53,a,28,a(flip)),rewrite([28(5)])].
% 89.68/89.94  91 complement(c1,c(c1)).  [resolve(54,a,28,a(flip)),rewrite([28(5)])].
% 89.68/89.94  102 leq(A,addition(A,B)).  [resolve(64,a,42,b)].
% 89.68/89.94  111 complement(f1(c(c2)),c(c2)).  [resolve(89,a,52,b)].
% 89.68/89.94  112 addition(c2,c(c2)) = one.  [resolve(89,a,46,a)].
% 89.68/89.94  113 multiplication(c2,c(c2)) = zero.  [resolve(89,a,44,a)].
% 89.68/89.94  114 multiplication(c(c2),c2) = zero.  [resolve(89,a,43,a)].
% 89.68/89.94  115 -leq(one,addition(c1,addition(multiplication(c(c1),c(c2)),multiplication(addition(c1,c(c1)),c2)))) | -leq(addition(c1,addition(multiplication(c(c1),c(c2)),multiplication(addition(c1,c(c1)),c2))),one).  [back_rewrite(40),rewrite([112(16),28(15),31(14),33(15,R),31(14),112(31),28(30),31(29),33(30,R),31(29)])].
% 89.68/89.94  118 complement(f1(c(c1)),c(c1)).  [resolve(91,a,52,b)].
% 89.68/89.94  119 addition(c1,c(c1)) = one.  [resolve(91,a,46,a)].
% 89.68/89.94  120 multiplication(c1,c(c1)) = zero.  [resolve(91,a,44,a)].
% 89.68/89.94  121 multiplication(c(c1),c1) = zero.  [resolve(91,a,43,a)].
% 89.68/89.94  122 -leq(one,addition(c1,addition(c2,multiplication(c(c1),c(c2))))) | -leq(addition(c1,addition(c2,multiplication(c(c1),c(c2)))),one).  [back_rewrite(115),rewrite([119(11),28(10),31(9),119(21),28(20),31(19)])].
% 89.68/89.94  128 leq(multiplication(A,B),multiplication(A,addition(B,C))).  [para(36(a,1),102(a,2))].
% 89.68/89.94  133 addition(A,multiplication(B,addition(C,one))) = addition(B,addition(A,multiplication(B,C))).  [para(66(a,2),33(a,2,2)),rewrite([31(2)]),flip(a)].
% 89.68/89.94  142 leq(A,multiplication(A,B)) | multiplication(A,addition(B,one)) != multiplication(A,B).  [para(66(a,2),42(b,1))].
% 89.68/89.94  176 leq(multiplication(A,multiplication(B,C)),multiplication(D,C)) | multiplication(addition(D,multiplication(A,B)),C) != multiplication(D,C).  [para(68(a,1),42(b,1))].
% 89.68/89.94  181 addition(A,addition(multiplication(A,B),multiplication(C,multiplication(D,addition(B,one))))) = multiplication(addition(A,multiplication(C,D)),addition(B,one)).  [para(66(a,1),68(a,1,2)),rewrite([33(7,R)])].
% 89.68/89.94  189 addition(one,c2) = one.  [para(80(a,1),64(a,1,2)),rewrite([31(3),80(7)])].
% 89.68/89.94  211 addition(A,multiplication(A,c2)) = A.  [para(189(a,1),36(a,2,2)),rewrite([27(2),27(5)])].
% 89.68/89.94  212 addition(A,multiplication(c2,A)) = A.  [para(189(a,1),38(a,2,1)),rewrite([28(2),28(5)])].
% 89.68/89.94  228 addition(one,c1) = one.  [para(83(a,1),64(a,1,2)),rewrite([31(3),83(7)])].
% 89.68/89.94  247 addition(A,multiplication(c1,A)) = A.  [para(228(a,1),38(a,2,1)),rewrite([28(2),28(5)])].
% 89.68/89.94  275 addition(c(c2),f1(c(c2))) = one.  [resolve(111,a,46,a),rewrite([31(6)])].
% 89.68/89.94  281 multiplication(c2,addition(A,c(c2))) = multiplication(c2,A).  [para(113(a,1),36(a,1,1)),rewrite([65(4),31(6)]),flip(a)].
% 89.68/89.94  282 multiplication(addition(A,c2),c(c2)) = multiplication(A,c(c2)).  [para(113(a,1),38(a,1,1)),rewrite([65(5),31(5)]),flip(a)].
% 89.68/89.94  284 multiplication(addition(A,multiplication(B,c2)),c(c2)) = multiplication(A,c(c2)).  [para(113(a,1),68(a,1,1,2)),rewrite([29(2),65(5)]),flip(a)].
% 89.68/89.94  285 multiplication(addition(c2,multiplication(A,B)),c(c2)) = multiplication(A,multiplication(B,c(c2))).  [para(113(a,1),68(a,1,2)),rewrite([31(6),65(6)]),flip(a)].
% 89.68/89.94  294 multiplication(c(c2),multiplication(c2,A)) = zero.  [para(114(a,1),34(a,1,1)),rewrite([30(2)]),flip(a)].
% 89.68/89.94  295 multiplication(c(c2),addition(A,c2)) = multiplication(c(c2),A).  [para(114(a,1),36(a,1,1)),rewrite([65(5),31(7)]),flip(a)].
% 89.68/89.94  301 addition(c(c1),f1(c(c1))) = one.  [resolve(118,a,46,a),rewrite([31(6)])].
% 89.68/89.94  306 multiplication(c1,addition(A,c(c1))) = multiplication(c1,A).  [para(120(a,1),36(a,1,1)),rewrite([65(4),31(6)]),flip(a)].
% 89.68/89.94  309 multiplication(addition(A,multiplication(B,c1)),c(c1)) = multiplication(A,c(c1)).  [para(120(a,1),68(a,1,1,2)),rewrite([29(2),65(5)]),flip(a)].
% 89.68/89.94  314 multiplication(c(c1),multiplication(c1,A)) = zero.  [para(121(a,1),34(a,1,1)),rewrite([30(2)]),flip(a)].
% 89.68/89.94  317 multiplication(addition(A,multiplication(B,c(c1))),c1) = multiplication(A,c1).  [para(121(a,1),68(a,1,1,2)),rewrite([29(2),65(4)]),flip(a)].
% 89.68/89.94  422 addition(A,addition(B,multiplication(c1,A))) = addition(A,B).  [para(247(a,1),33(a,2,2)),rewrite([31(3),31(5)])].
% 89.68/89.94  431 addition(one,c(c2)) = one.  [para(275(a,1),64(a,1,2)),rewrite([31(4),275(10)])].
% 89.68/89.94  454 addition(A,multiplication(A,c(c2))) = A.  [para(431(a,1),36(a,2,2)),rewrite([27(2),27(6)])].
% 89.68/89.94  455 addition(A,multiplication(c(c2),A)) = A.  [para(431(a,1),38(a,2,1)),rewrite([28(2),28(6)])].
% 89.68/89.94  479 multiplication(c(c2),addition(A,multiplication(c2,B))) = multiplication(c(c2),A).  [para(294(a,1),36(a,1,1)),rewrite([65(5),31(8)]),flip(a)].
% 89.68/89.94  485 addition(one,c(c1)) = one.  [para(301(a,1),64(a,1,2)),rewrite([31(4),301(10)])].
% 89.68/89.94  494 leq(addition(A,multiplication(B,A)),multiplication(addition(B,one),addition(A,C))).  [para(67(a,1),128(a,1))].
% 89.68/89.94  516 addition(A,multiplication(A,c(c1))) = A.  [para(485(a,1),36(a,2,2)),rewrite([27(2),27(6)])].
% 89.68/89.94  517 addition(A,multiplication(c(c1),A)) = A.  [para(485(a,1),38(a,2,1)),rewrite([28(2),28(6)])].
% 89.68/89.94  548 multiplication(c(c1),addition(A,multiplication(c1,B))) = multiplication(c(c1),A).  [para(314(a,1),36(a,1,1)),rewrite([65(5),31(8)]),flip(a)].
% 89.68/89.94  555 addition(multiplication(A,B),multiplication(C,addition(B,one))) = addition(C,multiplication(addition(A,C),B)).  [para(38(a,1),133(a,2,2))].
% 89.68/89.94  565 leq(multiplication(A,B),multiplication(A,addition(C,multiplication(B,D)))) | multiplication(A,addition(C,multiplication(B,addition(D,one)))) != multiplication(A,addition(C,multiplication(B,D))).  [para(133(a,2),72(b,1,2))].
% 89.68/89.94  566 leq(multiplication(A,B),multiplication(addition(C,multiplication(A,D)),B)) | multiplication(addition(C,multiplication(A,addition(D,one))),B) != multiplication(addition(C,multiplication(A,D)),B).  [para(133(a,2),73(b,1,1))].
% 89.68/89.94  573 addition(A,addition(B,multiplication(A,c(c2)))) = addition(A,B).  [para(454(a,1),33(a,2,2)),rewrite([31(4),31(6)])].
% 89.68/89.94  658 addition(A,addition(B,multiplication(c(c2),A))) = addition(A,B).  [para(455(a,1),33(a,2,2)),rewrite([31(4),31(6)])].
% 89.68/89.94  718 addition(A,addition(B,multiplication(A,c(c1)))) = addition(A,B).  [para(516(a,1),33(a,2,2)),rewrite([31(4),31(6)])].
% 89.68/89.94  724 addition(A,addition(B,multiplication(c(c1),A))) = addition(A,B).  [para(517(a,1),33(a,2,2)),rewrite([31(4),31(6)])].
% 89.68/89.94  1153 leq(one,A) | addition(A,one) != A.  [para(28(a,1),142(b,1)),rewrite([28(3),28(6)])].
% 89.68/89.94  1261 multiplication(c2,c2) = c2.  [para(112(a,1),281(a,1,2)),rewrite([27(3)]),flip(a)].
% 89.68/89.94  1279 multiplication(addition(A,multiplication(B,c2)),c2) = multiplication(addition(B,A),c2).  [para(1261(a,1),68(a,1,1,2)),rewrite([38(5)]),flip(a)].
% 89.68/89.94  1338 multiplication(c1,c1) = c1.  [para(119(a,1),306(a,1,2)),rewrite([27(3)]),flip(a)].
% 89.68/89.94  1378 multiplication(c1,multiplication(c1,A)) = multiplication(c1,A).  [para(1338(a,1),34(a,1,1)),flip(a)].
% 89.68/89.94  1381 multiplication(addition(A,multiplication(B,c1)),c1) = multiplication(addition(B,A),c1).  [para(1338(a,1),68(a,1,1,2)),rewrite([38(5)]),flip(a)].
% 89.68/89.94  1393 multiplication(c1,addition(A,multiplication(c1,B))) = multiplication(c1,addition(B,A)).  [para(1378(a,1),36(a,1,1)),rewrite([36(5),31(7)]),flip(a)].
% 89.68/89.94  2852 leq(multiplication(A,multiplication(c2,B)),multiplication(A,B)).  [para(211(a,1),176(b,1,1)),xx(b)].
% 89.68/89.94  2854 leq(multiplication(A,multiplication(c(c2),B)),multiplication(A,B)).  [para(454(a,1),176(b,1,1)),xx(b)].
% 89.68/89.94  2921 leq(multiplication(c(c1),multiplication(c2,c1)),zero).  [para(121(a,1),2852(a,2))].
% 89.68/89.94  3083 multiplication(c(c1),multiplication(c2,c1)) = zero.  [resolve(2921,a,41,a),rewrite([31(8),65(8)])].
% 89.68/89.94  3105 multiplication(addition(A,multiplication(c(c1),c2)),c1) = multiplication(A,c1).  [para(3083(a,1),68(a,1,1)),rewrite([65(4)]),flip(a)].
% 89.68/89.94  4304 leq(multiplication(c(c1),multiplication(c(c2),c1)),zero).  [para(121(a,1),2854(a,2))].
% 89.68/89.94  4399 multiplication(c(c1),multiplication(c(c2),c1)) = zero.  [resolve(4304,a,41,a),rewrite([31(9),65(9)])].
% 89.68/89.94  4424 multiplication(addition(A,multiplication(c(c1),c(c2))),c1) = multiplication(A,c1).  [para(4399(a,1),68(a,1,1)),rewrite([65(4)]),flip(a)].
% 89.68/89.94  14832 leq(addition(A,multiplication(c2,B)),addition(A,addition(C,multiplication(c2,B)))).  [para(479(a,1),494(a,1,2)),rewrite([31(7),33(7,R),658(7),31(7),431(7),31(8),33(8,R),31(7),28(9)])].
% 89.68/89.94  16349 leq(multiplication(A,B),addition(C,multiplication(addition(A,C),B))).  [para(555(a,1),102(a,2))].
% 89.68/89.94  16439 leq(multiplication(A,B),multiplication(addition(A,C),addition(B,one))).  [para(64(a,1),16349(a,2,2,1)),rewrite([66(5,R)])].
% 89.68/89.94  16533 leq(multiplication(A,c(c2)),addition(A,addition(B,c2))).  [para(282(a,1),16439(a,1)),rewrite([31(6),33(6,R),31(5),31(10),431(10),27(8)])].
% 89.68/89.94  16544 leq(multiplication(A,c1),addition(A,addition(B,multiplication(C,c(c1))))).  [para(317(a,1),16439(a,1)),rewrite([31(7),33(7,R),31(6),31(10),228(10),27(9)])].
% 89.68/89.94  16631 leq(multiplication(A,c(c2)),addition(A,one)).  [para(189(a,1),16533(a,2,2))].
% 89.68/89.94  16636 leq(multiplication(A,multiplication(B,c(c2))),addition(one,multiplication(A,B))).  [para(34(a,1),16631(a,1)),rewrite([31(7)])].
% 89.68/89.94  16865 leq(multiplication(A,c2),multiplication(A,addition(B,one))).  [para(212(a,1),565(b,1,2)),rewrite([31(7),33(7),31(6),212(6),31(4),31(14),33(14),31(13),212(13),31(11)]),xx(b)].
% 89.68/89.94  16866 leq(multiplication(A,c1),multiplication(A,addition(B,one))).  [para(247(a,1),565(b,1,2)),rewrite([31(7),33(7),31(6),247(6),31(4),31(14),33(14),31(13),247(13),31(11)]),xx(b)].
% 89.68/89.94  16877 leq(multiplication(A,c2),addition(A,multiplication(A,B))).  [para(66(a,1),16865(a,2))].
% 89.68/89.94  16890 leq(multiplication(A,c1),addition(A,multiplication(A,B))).  [para(66(a,1),16866(a,2))].
% 89.68/89.94  16930 leq(multiplication(c2,A),multiplication(addition(B,one),A)).  [para(212(a,1),566(b,1,1)),rewrite([31(7),33(7),31(6),212(6),31(4),31(14),33(14),31(13),212(13),31(11)]),xx(b)].
% 89.68/89.94  16931 leq(multiplication(c1,A),multiplication(addition(B,one),A)).  [para(247(a,1),566(b,1,1)),rewrite([31(7),33(7),31(6),247(6),31(4),31(14),33(14),31(13),247(13),31(11)]),xx(b)].
% 89.68/89.94  16954 leq(multiplication(addition(A,B),c2),addition(A,multiplication(B,c2))).  [para(284(a,1),16877(a,2,2)),rewrite([1279(5),31(1),31(10),33(10,R),573(10)])].
% 89.68/89.94  16988 leq(multiplication(addition(A,B),c1),addition(A,multiplication(B,c1))).  [para(309(a,1),16890(a,2,2)),rewrite([1381(5),31(1),31(10),33(10,R),718(10)])].
% 89.68/89.94  17000 leq(multiplication(c2,A),addition(A,multiplication(B,A))).  [para(67(a,1),16930(a,2))].
% 89.68/89.94  17015 leq(multiplication(c1,A),addition(A,multiplication(B,A))).  [para(67(a,1),16931(a,2))].
% 89.68/89.94  17063 leq(multiplication(c2,A),addition(A,multiplication(B,multiplication(C,A)))).  [para(34(a,1),17000(a,2,2))].
% 89.68/89.94  17115 leq(multiplication(c1,addition(A,B)),addition(A,multiplication(c1,B))).  [para(548(a,1),17015(a,2,2)),rewrite([1393(5),31(2),31(10),33(10,R),724(10)])].
% 89.68/89.94  17891 leq(c2,addition(c1,multiplication(c(c1),c2))).  [para(119(a,1),16954(a,1,1)),rewrite([28(3)])].
% 89.68/89.94  17941 addition(c1,multiplication(c(c1),c2)) = addition(c1,c2).  [resolve(17891,a,41,a),rewrite([724(8),31(3)]),flip(a)].
% 89.68/89.94  17950 multiplication(addition(c1,c2),c1) = c1.  [para(17941(a,1),3105(a,1,1)),rewrite([1338(8)])].
% 89.68/89.94  17963 addition(addition(c1,c2),multiplication(A,B)) = addition(c1,addition(c2,multiplication(A,B))).  [para(17950(a,1),181(a,1,2,1)),rewrite([31(7),228(7),27(6),33(7,R),33(6),31(5),33(6,R),31(5),64(7),31(13),228(13),27(12)]),flip(a)].
% 89.68/89.94  18043 leq(c1,addition(c2,multiplication(c(c2),c1))).  [para(112(a,1),16988(a,1,1)),rewrite([28(3)])].
% 89.68/89.94  18094 addition(c2,multiplication(c(c2),c1)) = addition(c1,c2).  [resolve(18043,a,41,a),rewrite([658(8)]),flip(a)].
% 89.68/89.94  18100 multiplication(c(c2),multiplication(c1,c(c2))) = multiplication(c1,c(c2)).  [para(18094(a,1),285(a,1,1)),rewrite([282(6)]),flip(a)].
% 89.68/89.94  18116 leq(c2,addition(one,multiplication(A,B))).  [para(27(a,1),17063(a,1)),rewrite([27(4)])].
% 89.68/89.94  18147 addition(one,addition(c2,multiplication(A,B))) = addition(one,multiplication(A,B)).  [resolve(18116,a,41,a),rewrite([33(5,R),31(4)])].
% 89.68/89.94  18510 leq(c1,addition(c2,multiplication(c1,c(c2)))).  [para(112(a,1),17115(a,1,2)),rewrite([27(3)])].
% 89.68/89.94  18560 addition(c2,multiplication(c1,c(c2))) = addition(c1,c2).  [resolve(18510,a,41,a),rewrite([573(8)]),flip(a)].
% 89.68/89.94  22490 leq(multiplication(A,c1),addition(A,B)).  [para(30(a,1),16544(a,2,2,2)),rewrite([25(4)])].
% 89.68/89.94  22496 leq(multiplication(A,multiplication(B,c1)),addition(C,multiplication(A,B))).  [para(34(a,1),22490(a,1)),rewrite([31(5)])].
% 89.68/89.94  22541 leq(multiplication(c(c2),multiplication(A,c1)),A).  [para(455(a,1),22496(a,2))].
% 89.68/89.94  22598 addition(A,multiplication(c(c2),multiplication(A,c1))) = A.  [resolve(22541,a,41,a),rewrite([31(6)])].
% 89.68/89.94  23132 leq(multiplication(c(c1),c(c2)),one).  [para(516(a,1),16636(a,2)),rewrite([28(7)])].
% 89.68/89.94  23169 addition(one,multiplication(c(c1),c(c2))) = one.  [resolve(23132,a,41,a),rewrite([31(7)])].
% 89.68/89.94  23672 multiplication(c(c2),c1) = multiplication(c1,c(c2)).  [para(18100(a,1),295(a,2)),rewrite([31(8),18560(8),295(6)])].
% 89.68/89.94  27997 multiplication(addition(c1,addition(c2,multiplication(c(c1),c(c2)))),c1) = c1.  [para(17950(a,1),4424(a,2)),rewrite([17963(9)])].
% 89.68/89.94  28915 leq(addition(A,multiplication(c2,B)),addition(A,B)).  [para(67(a,2),14832(a,2,2)),rewrite([31(6),189(6),28(5)])].
% 89.68/89.94  28933 leq(addition(A,multiplication(c2,B)),addition(B,A)).  [para(31(a,1),28915(a,1)),rewrite([31(3),31(4)])].
% 89.68/89.94  28979 leq(addition(A,multiplication(addition(c1,c2),B)),addition(A,B)).  [para(422(a,1),28933(a,2)),rewrite([31(6),33(6),31(5),33(6,R),31(5),38(5),31(6)])].
% 89.68/89.94  29132 leq(addition(A,multiplication(addition(c1,c2),B)),addition(B,A)).  [para(31(a,1),28979(a,1)),rewrite([31(5),31(6)])].
% 89.68/89.94  29504 leq(addition(c1,addition(c2,multiplication(c(c1),c(c2)))),one).  [para(23169(a,1),29132(a,2)),rewrite([27(10),31(9),17963(9)])].
% 89.68/89.94  29510 -leq(one,addition(c1,addition(c2,multiplication(c(c1),c(c2))))).  [back_unit_del(122),unit_del(b,29504)].
% 89.68/89.94  29511 addition(one,addition(c1,addition(c2,multiplication(c(c1),c(c2))))) != addition(c1,addition(c2,multiplication(c(c1),c(c2)))).  [ur(1153,a,29510,a),rewrite([31(11)])].
% 89.68/89.94  29512 addition(c1,addition(c2,multiplication(c(c1),c(c2)))) != one.  [para(33(a,1),29511(a,1)),rewrite([228(10),31(9),18147(9),23169(7)]),flip(a)].
% 89.68/89.94  33744 $F.  [para(27997(a,1),22598(a,1,2,2)),rewrite([23672(13),31(14),33(14,R),31(13),33(13,R),31(12),38(12),119(6),28(6),112(5),31(3),228(3)]),flip(a),unit_del(a,29512)].
% 89.68/89.94  
% 89.68/89.94  % SZS output end Refutation
% 89.68/89.94  ============================== end of proof ==========================
% 89.68/89.94  
% 89.68/89.94  ============================== STATISTICS ============================
% 89.68/89.94  
% 89.68/89.94  Given=8848. Generated=4434767. Kept=33713. proofs=1.
% 89.68/89.94  Usable=8334. Sos=9714. Demods=783. Limbo=0, Disabled=15702. Hints=0.
% 89.68/89.94  Megabytes=22.71.
% 89.68/89.94  User_CPU=86.53, System_CPU=2.37, Wall_clock=89.
% 89.68/89.94  
% 89.68/89.94  ============================== end of statistics =====================
% 89.68/89.94  
% 89.68/89.94  ============================== end of search =========================
% 89.68/89.94  
% 89.68/89.94  THEOREM PROVED
% 89.68/89.94  % SZS status Theorem
% 89.68/89.94  
% 89.68/89.94  Exiting with 1 proof.
% 89.68/89.94  
% 89.68/89.94  Process 11611 exit (max_proofs) Thu Jun 16 09:33:25 2022
% 89.68/89.94  Prover9 interrupted
%------------------------------------------------------------------------------